From 0693f6a9a5ec844b7cfe2a3fbd5384578c381d2e Mon Sep 17 00:00:00 2001
From: "Joachim Wuttke (l)" <j.wuttke@fz-juelich.de>
Date: Tue, 9 Aug 2016 19:10:43 +0200
Subject: [PATCH] PyPersistTest now compares dat and ref YAML tree entry by
 entry, allowing for a tolerance for floating-point numbers. Still to do: -
 allow for "VARIABILITY" anywhere in the tree - generate YAML output from Fit
 tests.

---
 .../PyCore/persistence/PyPersistenceTest.cpp  |    90 +-
 .../PyCore/persistence/PyPersistenceTest.h    |    17 +-
 .../TestMachinery/IReferencedTest.cpp         |     2 +-
 .../TestMachinery/IReferencedTest.h           |     3 +-
 .../PyPersist/SpecularSimulation.ref.yaml     | 12166 +++++++++++++++-
 5 files changed, 12248 insertions(+), 30 deletions(-)

diff --git a/Tests/Functional/PyCore/persistence/PyPersistenceTest.cpp b/Tests/Functional/PyCore/persistence/PyPersistenceTest.cpp
index 97225746ab9..42648aa466e 100644
--- a/Tests/Functional/PyCore/persistence/PyPersistenceTest.cpp
+++ b/Tests/Functional/PyCore/persistence/PyPersistenceTest.cpp
@@ -21,12 +21,15 @@
 #include "IntensityDataIOFactory.h"
 #include "PythonFormatting.h"
 #include "SimulationFactory.h"
+#include "Numeric.h"
 #include "Utils.h"
+#include <yaml-cpp/yaml.h>
 #include <cstdio>
 #include <cstdlib>
 #include <fstream>
 #include <sstream>
 #include <map>
+#include <string>
 
 PyPersistenceTest::PyPersistenceTest(
     const std::string& directory, const std::string& name)
@@ -103,7 +106,8 @@ void PyPersistenceTest::runTest()
 }
 
 //! Returns true if test output and reference file agree.
-bool PyPersistenceTest::compareFilePair(const std::string& dat_fpath, const std::string& ref_fpath)
+bool PyPersistenceTest::compareFilePair(
+    const std::string& dat_fpath, const std::string& ref_fpath) const
 {
     std::cout << "Comparing dat='" << dat_fpath << "' with ref='" << ref_fpath << "':\n";
     const std::string extension = Utils::String::split(FileSystem::filename(dat_fpath), ".")[2];
@@ -117,7 +121,7 @@ bool PyPersistenceTest::compareFilePair(const std::string& dat_fpath, const std:
 
 //! Returns true if intensity maps from test output and reference file agree reasonably.
 bool PyPersistenceTest::compareIntensityPair(
-    const std::string& dat_fpath, const std::string& ref_fpath)
+    const std::string& dat_fpath, const std::string& ref_fpath) const
 {
     const OutputData<double>* dat = IntensityDataIOFactory::readOutputData( dat_fpath );
     const OutputData<double>* ref = IntensityDataIOFactory::readOutputData( ref_fpath );
@@ -125,34 +129,76 @@ bool PyPersistenceTest::compareIntensityPair(
 }
 
 //! Returns true if YAML files from test output and reference agree.
-bool PyPersistenceTest::compareYamlPair(const std::string& dat_fpath, const std::string& ref_fpath)
+bool PyPersistenceTest::compareYamlPair(
+    const std::string& dat_fpath, const std::string& ref_fpath) const
 {
     std::fstream fdat(dat_fpath);
     std::fstream fref(ref_fpath);
-    const YAML::Node& dat = YAML::Load(fdat);
-    const YAML::Node& ref = YAML::Load(fref);
     return compareYamlNode( YAML::Load(fdat), YAML::Load(fref) );
 }
 
-    for (size_t i = 1; ; ++i) {
-        std::string datline;
-        std::string refline;
-        std::getline(fdat, datline);
-        std::getline(fref, refline);
-        if (datline!=refline) {
-            std::cerr << "Line " << i << " of " << dat_fpath << " and " << ref_fpath
-                      << " differs:\n";
-            std::cerr << "dat: '" << datline << "'\n";
-            std::cerr << "ref: '" << refline << "'\n";
-            return false;
+//! Returns true if all entries of the two YAML files agree.
+//! Floating-point entries must agree within a certain tolerance.
+//! The investigation is performed recursively, iterating over all lists and maps.
+bool PyPersistenceTest::compareYamlNode(const YAML::Node& dat, const YAML::Node& ref) const
+{
+//    std::cout << "DEBUG: " << dat.as<std::string>() << " vs " << ref.as<std::string>() << "\n";
+    if (dat.Type() != ref.Type()) {
+        std::cerr << "YAML node type differs: " << dat.Type() << " vs " << ref.Type() << "\n";
+        return false;
+    }
+    if      (dat.Type()==YAML::NodeType::Undefined)
+        throw std::runtime_error("Invalid node type 'Undefined' in YAML tree");
+    else if (dat.Type()==YAML::NodeType::Null)
+        throw std::runtime_error("Invalid node type 'Null' in YAML tree");
+    else if (dat.Type()==YAML::NodeType::Sequence) {
+        auto it_dat=dat.begin();
+        auto it_ref=ref.begin();
+        for (size_t idx=0; ; ++it_dat, ++it_ref, ++idx) {
+            if (it_dat==dat.end() || it_ref==ref.end()) {
+                if (!(it_dat==dat.end() && it_ref==ref.end())) {
+                    std::cerr << "lists have different length\n";
+                    return false;
+                }
+                return true; // regular exit
+            }
+            // now recurse into the node
+            if (!compareYamlNode(*it_dat, *it_ref)) {
+                std::cerr << "at list position " << idx << "\n";
+                return false;
+            }
         }
-        if (fdat.eof() && fref.eof())
-            break;
-        if (fdat.eof() || fref.eof()) {
-            std::cerr << "File length of " << dat_fpath << " and " << ref_fpath << " differs.\n";
+    } else if (dat.Type()==YAML::NodeType::Map) {
+        auto it_dat=dat.begin();
+        auto it_ref=ref.begin();
+        for ( ; ; ++it_dat, ++it_ref) {
+            if (it_dat==dat.end() || it_ref==ref.end()) {
+                if (!(it_dat==dat.end() && it_ref==ref.end())) {
+                    std::cerr << "maps have different length\n";
+                    return false;
+                }
+                return true; // regular exit
+            }
+            // now recurse into the node
+            if (!compareYamlNode(it_dat->second, it_ref->second)) {
+                std::cerr << "at map entry [" << it_dat->first << "]\n";
+                return false;
+            }
+        }
+    } else if (dat.Type()==YAML::NodeType::Scalar) {
+        if (dat.as<std::string>() == ref.as<std::string>())
+            return true;
+        try {
+            if (!Numeric::areAlmostEqual( dat.as<double>(), ref.as<double>(), 1e-10 )) {
+                std::cerr << "numbers differ: " << dat << " vs " << ref << "\n";
+                return false;
+            }
+            return true;
+        } catch(...) {
+            std::cerr << "scalar entries differ: '" << dat << "' vs '" << ref << "'\n";
             return false;
         }
-    }
-    std::cout << "Files fully agree.\n";
+    } else
+        throw std::runtime_error("Bug in PyPersistenceTest::compareYamlNode: unexpected node type");
     return true;
 }
diff --git a/Tests/Functional/PyCore/persistence/PyPersistenceTest.h b/Tests/Functional/PyCore/persistence/PyPersistenceTest.h
index 3de5048452b..611414b5d3b 100644
--- a/Tests/Functional/PyCore/persistence/PyPersistenceTest.h
+++ b/Tests/Functional/PyCore/persistence/PyPersistenceTest.h
@@ -19,6 +19,10 @@
 #include "IReferencedTest.h"
 #include "OutputData.h"
 
+namespace YAML {
+    class Node;
+}
+
 //! @class PyPersistenceTest
 //! @ingroup standard_samples
 //! @brief A functional test that runs a Python script and compares its output with a reference.
@@ -32,12 +36,17 @@ public:
 
     void runTest() final;
 
-    bool compareFilePair(const std::string& dat_fname, const std::string& ref_fname);
-    bool compareIntensityPair(const std::string& dat_fname, const std::string& ref_fname);
-    bool compareYamlPair(const std::string& dat_fname, const std::string& ref_fname);
-
 private:
     std::string m_directory;
+
+    bool compareFilePair(
+        const std::string& dat_fname, const std::string& ref_fname) const;
+    bool compareIntensityPair(
+        const std::string& dat_fname, const std::string& ref_fname) const;
+    bool compareYamlPair(
+        const std::string& dat_fname, const std::string& ref_fname) const;
+    bool compareYamlNode(
+        const YAML::Node& dat, const YAML::Node& ref) const;
 };
 
 #endif // PYPERSISTENCETEST_H
diff --git a/Tests/Functional/TestMachinery/IReferencedTest.cpp b/Tests/Functional/TestMachinery/IReferencedTest.cpp
index cc981fa4c70..6f4185a9d61 100644
--- a/Tests/Functional/TestMachinery/IReferencedTest.cpp
+++ b/Tests/Functional/TestMachinery/IReferencedTest.cpp
@@ -18,7 +18,7 @@
 #include <iostream>
 
 IFunctionalTest::ETestResult IReferencedTest::compareIntensityMaps(
-    const OutputData<double>& dat, const OutputData<double>& ref)
+    const OutputData<double>& dat, const OutputData<double>& ref) const
 {
     if( dat.getVariability() != ref.getVariability() ) {
         std::cerr << "Failed: reproducibility threshold has changed from "
diff --git a/Tests/Functional/TestMachinery/IReferencedTest.h b/Tests/Functional/TestMachinery/IReferencedTest.h
index 56263f95eff..4b5c3043943 100644
--- a/Tests/Functional/TestMachinery/IReferencedTest.h
+++ b/Tests/Functional/TestMachinery/IReferencedTest.h
@@ -37,7 +37,8 @@ public:
 protected:
     double m_threshold;
 
-    ETestResult compareIntensityMaps(const OutputData<double>& dat, const OutputData<double>& ref);
+    ETestResult compareIntensityMaps(
+        const OutputData<double>& dat, const OutputData<double>& ref) const;
 };
 
 #endif // IREFERENCEDTEST_H
diff --git a/Tests/ReferenceData/PyPersist/SpecularSimulation.ref.yaml b/Tests/ReferenceData/PyPersist/SpecularSimulation.ref.yaml
index e659d069cd2..9fcb5c7ecfb 100644
--- a/Tests/ReferenceData/PyPersist/SpecularSimulation.ref.yaml
+++ b/Tests/ReferenceData/PyPersist/SpecularSimulation.ref.yaml
@@ -1,2 +1,12164 @@
-Simulation passed
-...
+coeff_R: [[1.0, 1.0, 0.9999999999999999, 1.0, 1.0, 0.9999999999999999, 1.0,
+        0.9999999999999999, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        0.9999999999999999, 0.9999999999999999, 1.0, 0.9999999999999999,
+        1.0, 1.0, 0.9999999999999999, 1.0, 0.9999999999999999, 0.9999999999999999,
+        1.0, 1.0, 0.9999999999999999, 1.0, 0.9999999999999999, 1.0, 0.9999999999999999,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9999999999999999, 1.0, 0.9999999999999999,
+        0.9999999999999999, 1.0, 0.9999999999999999, 0.9999999999999999,
+        1.0, 1.0, 0.9999999999999999, 1.0, 0.9999999999999999, 0.9999999999999999,
+        1.0, 1.0, 1.0, 0.9999999999999999, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        0.9999999999999999, 0.9999999999999999, 1.0, 0.9999999999999999,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9999999999999999, 1.0, 1.0,
+        1.0, 1.0, 1.0, 0.9999999999999999, 1.0, 0.9999999999999999, 1.0,
+        0.9999999999999999, 1.0, 1.0, 0.9999999999999999, 0.9999999999999999,
+        1.0, 1.0, 1.0, 0.9999999999999999, 0.9999999999999999, 0.9999999999999999,
+        1.0, 1.0, 1.0, 0.9999999999999999, 1.0, 1.0, 1.0, 0.9999999999999999,
+        0.9999999999999999, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9999999999999999,
+        1.0, 1.0, 1.0, 0.9999999999999999, 1.0, 1.0, 0.9999999999999999,
+        1.0, 1.0, 0.9999999999999999, 1.0, 1.0, 0.9999999999999999, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9999999999999999,
+        0.9999999999999999, 1.0, 1.0, 0.9999999999999999, 1.0, 0.9999999999999999,
+        0.9999999999999999, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9999999999999999,
+        0.9999999999999999, 1.0, 0.9999999999999999, 0.9999999999999999,
+        1.0, 1.0, 1.0, 1.0, 0.8512380424211637, 0.7380144834849892, 0.6096006719018573,
+        0.44535820574272966, 0.278678082522423, 0.24319785606410124, 0.3495332651997906,
+        0.4555075404876353, 0.5252190557523305, 0.5604339846160725, 0.5661851897442107,
+        0.5444907415464123, 0.49380175810734894, 0.4099350612954126, 0.28870102685194754,
+        0.13127101231194904, 0.04977318726616108, 0.23117955239001256, 0.39071750593944715,
+        0.5176659335143483, 0.6127536356281731, 0.6820419983789654, 0.7321928152572491,
+        0.7686058423887675, 0.7951662695544666, 0.814521755553523, 0.8284230362878786,
+        0.8379949548882419, 0.8439237662538082, 0.846576434909264, 0.8460694702662732,
+        0.842300345355182, 0.8349499960052401, 0.8234618842008273, 0.8070025082641089,
+        0.7844117735231672, 0.7541627151095999, 0.714373795262797, 0.6629566456589497,
+        0.5980258352596574, 0.5186918180667348, 0.4262042430022863, 0.3251060071060279,
+        0.2241158953917732, 0.13870740671222498, 0.10150342026149665, 0.1288526840168076,
+        0.17405533476382523, 0.21194590814923553, 0.23719787072452808, 0.249385199162751,
+        0.24937770611929821, 0.23847584057529847, 0.21825612369831654, 0.19067135293704573,
+        0.15830167724174887, 0.12485122611555217, 0.09621876182183191, 0.08143751743583329,
+        0.08641926473576086, 0.10426760682471944, 0.12481505965914319, 0.14238599935416224,
+        0.15443615491494778, 0.1599322809760354, 0.1586540981298069, 0.1509235776128152,
+        0.1375234169574915, 0.11973343208260233, 0.09950641917041311, 0.0799069736275803,
+        0.0658121829936284, 0.06284774105734547, 0.07136391786196256, 0.08551878525318625,
+        0.09993812788798868, 0.11162224776897346, 0.11906181273994405, 0.12158129199115025,
+        0.1190475283763105, 0.11175346883757366, 0.10039397326078715, 0.08612466271058776,
+        0.0707618587575364, 0.0572376135109461, 0.04991445598656294, 0.05207203282692674,
+        0.06152523229474857, 0.07347475503442157, 0.08455974871371683, 0.09296288293349356,
+        0.09775553669218293, 0.09854675795335026, 0.09533393676062403, 0.08844676430829206,
+        0.07854884792965282, 0.06671013706230092, 0.054616563302764064,
+        0.044969791171141346, 0.041339198457340326, 0.0452473981966463,
+        0.053966646618038114, 0.06389796601966939, 0.07274760561690373,
+        0.0792671255717047, 0.08281152778823253, 0.08312178820002608, 0.08023224475650716,
+        0.0744367228296489, 0.06629487145153666, 0.05669301619037358, 0.04700755607699403,
+        0.039381329216328954, 0.03652506712091183, 0.039605375269215565,
+        0.04668707137104594, 0.05502420308090559, 0.06275131084049244, 0.06880366277364239,
+        0.07259862851170407, 0.07386082324194011, 0.0725424880549816, 0.06878993832127094,
+        0.0629382295556319, 0.055537372271979635, 0.04743389063189791, 0.039943407080098046,
+        0.03501197082944881, 0.034611978974972576, 0.03890894969331585,
+        0.046072110723112444, 0.054131401852422455, 0.061766394461159925,
+        0.06816454494387826, 0.07281552758927805, 0.07539778605954192, 0.07572427773614009,
+        0.0737190074156648, 0.06941381598189002, 0.06296847659675062, 0.054736435286498485,
+        0.04544827844793469, 0.03671339686639326, 0.03197649083845292, 0.03544927636283824,
+        0.04677311101812649, 0.06250577365610317, 0.08029122448289706, 0.09885668678880567,
+        0.1174022167211642, 0.13533575482943155, 0.1521792049173181, 0.16753602055244543,
+        0.18108020147724252, 0.19255217845542288, 0.2017562047657836, 0.20855741226260363,
+        0.212878141061441, 0.21469371179649205, 0.21402794861635463, 0.21094870517117412,
+        0.20556352267572328, 0.19801543557643647, 0.18847887808191663, 0.17715564806983417,
+        0.16427094664705824, 0.150069613441753, 0.1348128032036034, 0.11877551234343736,
+        0.1022456635807115, 0.08552623163686461, 0.06894425328773757, 0.05287861668430692,
+        0.03785028585262572, 0.024865075360551245, 0.016717967535676198,
+        0.017901280355780782, 0.025124426578179027, 0.03312163401525281,
+        0.040097274927417645, 0.0454665195621427, 0.04899543877324104, 0.050598738408651645,
+        0.05028406812354004, 0.04813400480070082, 0.0442995179305718, 0.0389981257948587,
+        0.0325175915668394, 0.02523719327465842, 0.017723551504549743, 0.011210620510263307,
+        0.009236582549925031, 0.01351846400883872, 0.019658823652123382,
+        0.025492572447603744, 0.030325039462184077, 0.03383325780659255,
+        0.035843946153093664, 0.03628248945429607, 0.03515748013948715,
+        0.03255378825484689, 0.028628017265256607, 0.02360695808487788,
+        0.017799108455891683, 0.011676005241715276, 0.006471664005543431,
+        0.006573730155190034, 0.011520698742477598, 0.01695780557905323,
+        0.02177988388067562, 0.025605556848133103, 0.028226237176309694,
+        0.029525643845011895, 0.02946267836023251, 0.028065654852898348,
+        0.025428257416951556, 0.021705639986842214, 0.01711317526222134,
+        0.01194270396065161, 0.006707200337275171, 0.0037334096059025647,
+        0.007126400791023603, 0.012016307534989322, 0.01654451989293229,
+        0.020300185868369944, 0.023072094204245972, 0.024732022120852886,
+        0.02521681052526023, 0.024524055260005798, 0.02270936760550567,
+        0.01988298931876939, 0.016206371087911516, 0.0118938425144683, 0.007252229517203274,
+        0.003181326053649061, 0.00436334389652836, 0.008641743653057981,
+        0.01280392064888501, 0.01637165673858551, 0.019135558783377003,
+        0.02096416066760661, 0.02178254151994198, 0.02156866082971733, 0.020351641505209732,
+        0.018209295235313727, 0.015264829661275478, 0.011684910981124199,
+        0.0076913036221880875, 0.0037070806817968887, 0.0026055235749358682,
+        0.006118616472328664, 0.009894901120328429, 0.013236329946098824,
+        0.015927602919365163, 0.017835932827123615, 0.018879115125068055,
+        0.019021203282842333, 0.018271354576537863, 0.016682181136692047,
+        0.014347147257518253, 0.011398094994760776, 0.00800862810387121,
+        0.004446384149246607, 0.0019296996881781638, 0.0041746680754064305,
+        0.007534036770454582, 0.010630943705877607, 0.013216522868620682,
+        0.015154125796691485, 0.01635599772328101, 0.01677564875578629,
+        0.01640657196339064, 0.015281194334412728, 0.013469098378544484,
+        0.011075146364834925, 0.008241149108922385, 0.005172643330227893,
+        0.0024301180240996526, 0.002847367346794632, 0.0056351184896834775,
+        0.00844633718672175, 0.010891300429196827, 0.012815396962599658,
+        0.014123776586045309, 0.014761577590699631, 0.014710824680283502,
+        0.013989814206486017, 0.012652938586881057, 0.010791991816231071,
+        0.008544504284089757, 0.006133047068972155, 0.004053526130287933,
+        0.00357396443151331, 0.005157036727278475, 0.007389337785342093,
+        0.009537350534091956, 0.011333684192368045, 0.01264301503135725,
+        0.013387692624263169, 0.013529976973060692, 0.01306653473050041,
+        0.012025653561771522, 0.010464856210913398, 0.008468895497856847,
+        0.006151057159386147, 0.003678129529281687, 0.0015983105946367254,
+        0.0024742713131756136, 0.004770618021313968, 0.006976415430195392,
+        0.008860616495600012, 0.010315500978592027, 0.011272227762166982,
+        0.01169105525534243, 0.011559688301936166, 0.010892394795368913,
+        0.009728506532429881, 0.008130006871231985, 0.006178212041378903,
+        0.003969712964339108, 0.0016124095386583356, 0.000793307942681379,
+        0.0031119191622758858, 0.005253517233279311, 0.007118153928483956,
+        0.00862348590474117, 0.009705405323370503, 0.010320541905563425,
+        0.010447887687079207, 0.010089389398683441, 0.009269496536481112,
+        0.008033725807200378, 0.0064464057077946646, 0.004588098042313065,
+        0.0025557033696150403, 0.0005611479246564308, 0.0017726243898592159,
+        0.003754484721022888, 0.005551431556783395, 0.007069766817997569,
+        0.008241461418599312, 0.009017229463715118, 0.00936728030923601,
+        0.009282087126516991, 0.008772428322940215, 0.007868606414774661,
+        0.0066189440595696095, 0.005087952496404205, 0.00335601937873685,
+        0.0015393621031649996, 0.0007337994057096207, 0.002406887211999343,
+        0.0041092299519153615, 0.005617809655484389, 0.006854559509686607,
+        0.007764159800587457, 0.008309026516603335, 0.008469447886611721,
+        0.008243856880001838, 0.007648555310990446, 0.006716824547609136,
+        0.005497651025680592, 0.004055050404499144, 0.00247391013695987,
+        0.000959653353027473, 0.001247219533076415, 0.0027712487480048803,
+        0.004241123375537217, 0.005519796656225713, 0.006541162353700764,
+        0.007259642129181372, 0.0076460583438594035, 0.007687396669097025,
+        0.0073867839155690364, 0.006763087792928948, 0.005850144819074636,
+        0.004696094582821575, 0.0033650047410850375, 0.0019557317116305206,
+        0.000859863158536264, 0.0015650514798312481, 0.0029145716677390827,
+        0.0042042103847823795, 0.0053178729433470745, 0.006196337346913398,
+        0.006800026753803868, 0.007104507646590361, 0.007099853722348986,
+        0.006790449042188413, 0.006194628306213976, 0.00534423180563639,
+        0.004284868569228388, 0.0030804936225012785, 0.0018457027630530809,
+        0.0010345037221814787, 0.0016706573970579272, 0.0028629423753228716,
+        0.00403833042867456, 0.005071417888678988, 0.005902250575040581,
+        0.006491997194246712, 0.006816072039110747, 0.006862759138994187,
+        0.006632835982136612, 0.006139330607258089, 0.00540743418560877,
+        0.004475366687775655, 0.003399486182281335, 0.00228032277121464,
+        0.0014154177539316955, 0.0015891795078764473, 0.0026003175299509893,
+        0.0037620497900103336, 0.004865742869394189, 0.005830372219072139,
+        0.0066070392369155405, 0.007161640631942347, 0.0074708112954126205,
+        0.007520751900852698, 0.007306792473083042, 0.006833239985373897,
+        0.0061136912096533625, 0.005172840709143199, 0.004053763047989396,
+        0.0028497421208324466, 0.0018716846050801565, 0.002017580466222357,
+        0.003316272524239777, 0.005004704088866154, 0.006819936273982337,
+        0.008671324472394585, 0.010507576959164162, 0.012290104060239983,
+        0.013986271980522668, 0.015567319827496352, 0.017007661733560085,
+        0.018284687306147455, 0.019378775408319657, 0.02027341413977035,
+        0.02095537692675877, 0.021414922708770504, 0.021645993340145463,
+        0.02164638290085459, 0.021417855296845714, 0.02096618968285327,
+        0.02030113816756461, 0.01943628676046804, 0.018388818188322453,
+        0.01717918366840915, 0.015830699883758126, 0.014369097889641925,
+        0.012822064741268107, 0.011218842535213915, 0.009590000229795332,
+        0.007967619548817978, 0.0063864899184324, 0.004888022445569928,
+        0.0035324998775386335, 0.002438459402138869, 0.0018676585942912001,
+        0.0020410190328086645, 0.0026433013618563654, 0.003314019145051176,
+        0.003908115893882533, 0.004373148834409943, 0.004688923124874814,
+        0.004849256610765542, 0.004856016018116426, 0.00471689968591878,
+        0.004444569718847526, 0.004056445762504782, 0.0035751247337282538,
+        0.00302995992857134, 0.0024614694844126493, 0.0019327751825043828,
+        0.0015519149135802494, 0.0014607590624898198, 0.0016813680976488024,
+        0.0020687477727328535, 0.002488692835770858, 0.0028678540205876626,
+        0.0031673993282034557, 0.0033657221390915194, 0.003451508429801917,
+        0.003421064529211275, 0.0032772666779494848, 0.0030292348192851896,
+        0.0026926030743167555, 0.0022909021587639465, 0.0018598187749341668,
+        0.0014588861703870221, 0.001193261334175928, 0.0011876517252339485,
+        0.001429640117562081, 0.001783334970250467, 0.002145312693123904,
+        0.0024607877660044928, 0.002699844428098373, 0.0028454983352202,
+        0.002889219258176057, 0.002829249815736804, 0.0026699768186815727,
+        0.0024218587334484706, 0.002102067918940354, 0.0017368690231782122,
+        0.0013688327403292995, 0.0010749849352673828, 0.0009769275518474382,
+        0.001129291220180349, 0.001427732448918055, 0.001759055831224831,
+        0.002061631930419559, 0.002302986081411676, 0.0024647450364412124,
+        0.00253701191106847, 0.00251633257717284, 0.002404936480683203,
+        0.0022105416993801904, 0.0019467097123680112, 0.0016343987338323228,
+        0.001306802263581108, 0.0010223564159683321, 0.0008811458463752984,
+        0.0009628677917400877, 0.0012057969635417005, 0.0015012115174914606,
+        0.0017837248519200466, 0.0020191914271510294, 0.0021884585732653812,
+        0.0022808034555446715, 0.00229154540853943, 0.002221148275529697,
+        0.002074926683687909, 0.0018631983021541293, 0.0016022282387644516,
+        0.001317167561338401, 0.0010498979854635774, 0.0008726531307590274,
+        0.0008697237066951445, 0.0010377238918539563, 0.00128927018708927,
+        0.0015531690299672141, 0.001790094161848027, 0.0019780687495885006,
+        0.0021042595928115484, 0.0021617203485282525, 0.0021481136838770397,
+        0.0020652067885040333, 0.0019187674335182743, 0.0017188969187726048,
+        0.0014812473682224282, 0.0012303348446353547, 0.001007138771869222,
+        0.0008776527654294651, 0.0009055136258364392, 0.0010777333862054875,
+        0.0013243909396233634, 0.00158859436069589, 0.001836758427161404,
+        0.002048673221248927, 0.0022112256478879267, 0.0023156344866775785,
+        0.002356266886920613, 0.0023301325787620547, 0.0022367317254219986,
+        0.002078220505400587, 0.0018601209528511093, 0.0015933551147524255,
+        0.0013000585252152248, 0.0010304045747451538, 0.0008960423646684284,
+        0.0010264033438741559, 0.0013902658721523698, 0.0018786386191975962,
+        0.0024272562926222147, 0.0030037012009364325, 0.003587998179702698,
+        0.004165106564778171, 0.004722286147606579, 0.00524817281745161,
+        0.005732495160281057, 0.006166050211937646, 0.006540785012978279,
+        0.006849913572131272, 0.007088032439206837, 0.007251213702126433,
+        0.007337062901217274, 0.007344735220402901, 0.007274907921863718,
+        0.00712971088382018, 0.006912620394877392, 0.006628324004964835,
+        0.006282566140552627, 0.005881985309603858, 0.00543395412762075,
+        0.0049464334103694815, 0.004427852029054125, 0.003887027068328457,
+        0.0033331490145604033, 0.0027758882011426145, 0.0022257768816517426,
+        0.0016953579611688574, 0.001202937974885857, 0.0007869687094589379,
+        0.0005556831960190223, 0.0006411443224791862, 0.000898781536473974,
+        0.0011729290458253325, 0.0014128715395596643, 0.0016012429792281017,
+        0.0017307098263576834, 0.0017983219896557034, 0.001803898993702363,
+        0.0017494900345598591, 0.0016391671367450688, 0.0014789476446499593,
+        0.0012768366781380548, 0.0010431790539411686, 0.0007921004855179096,
+        0.0005474792129499463, 0.00036864652992458195, 0.0003770827773565333,
+        0.0005481845269158786, 0.0007562676072969364, 0.0009503929601842425,
+        0.0011113968340937853, 0.0012294834037598706, 0.0012991129948798298,
+        0.0013176770490477428, 0.0012850782733488657, 0.0012035499261159102,
+        0.00107754828875372, 0.0009137328446304294, 0.0007212771993546079,
+        0.0005136473048801488, 0.0003185361848632477, 0.0002293067256522533,
+        0.000343054564651589, 0.0005280807891657444, 0.0007094392414059846,
+        0.0008654922297899064, 0.000986069520247131, 0.0010651472465381116,
+        0.0010993895878405138, 0.0010877754731868866, 0.001031457457208564,
+        0.0009336612029798795, 0.0007996081361319954, 0.0006365869925895855,
+        0.00045479880708083637, 0.0002730002875889197, 0.00016316514523326365,
+        0.0002582159868621553, 0.00042815395721936184, 0.0005938149508108865,
+        0.0007365575185858496, 0.0008476456203051829, 0.000921703008514687,
+        0.000955630234792434, 0.0009483662088186573, 0.0009008003954419399,
+        0.000815692096094587, 0.0006975850162576519, 0.0005528092803644162,
+        0.0003900376639288853, 0.00022468153575277983, 0.00012378567300840455,
+        0.00022244648219210393, 0.0003792198111404539, 0.0005282837082971324,
+        0.0006554631644750458, 0.0007536055731712135, 0.0008181497359984413,
+        0.0008464619129824265, 0.0008377055264448905, 0.0007927872067800328,
+        0.0007142882742251432, 0.0006063811221845996, 0.00047481521074172476,
+        0.00032740643980945093, 0.0001784380154255685, 0.0001015920669099622,
+        0.00020959925470404636, 0.0003526662219251608, 0.0004852472839973529,
+        0.0005968060356398461, 0.0006814879892914861, 0.0007354851739293707,
+        0.0007566567565238779, 0.0007444610369697507, 0.0006999173928076552,
+        0.000625544018408209, 0.0005252811053029195, 0.000404491173707067,
+        0.0002705216806464315, 0.0001381719789086465, 9.524246146693212e-05,
+        0.00020725531112600104, 0.00033605068448416814, 0.00045289656932886253,
+        0.000549683629231744, 0.0006215571984077357, 0.0006653612737559513,
+        0.0006794148575928808, 0.0006634727143923211, 0.0006186931479364385,
+        0.0005475815901074356, 0.00045393113495169714, 0.0003428802370779365,
+        0.00022175813577860184, 0.00010841183115405822, 0.00010223818630557895,
+        0.00020970090358003239, 0.0003239880495184304, 0.00042601630107518804,
+        0.0005091382912287615, 0.0005692521952532898, 0.000603757733434551,
+        0.0006113970592620301, 0.0005922266320789254, 0.0005475964952939353,
+        0.00048012804714279734, 0.00039375459564886336, 0.00029410978083828793,
+        0.00019081176760006471, 0.00011283465432709564, 0.00013629075855303924,
+        0.00022753065169552395, 0.0003246345532406885, 0.00041118989467130455,
+        0.000480595082414415, 0.0005289688928298892, 0.0005539750062106665,
+        0.0005545627003761921, 0.000530880314751761, 0.00048420549764848853,
+        0.0004168514185966668, 0.000332038774977273, 0.00023373408759842052,
+        0.00012645955903157327, 1.5086076321585695e-05, 9.541352572869702e-05,
+        0.00020013597702951612, 0.0002945225749724177, 0.00037452651382981775,
+        0.0004367939923957067, 0.0004788044943335028, 0.0004989723998789397,
+        0.0004967060404500398, 0.00047242265069786973, 0.00042752043806899885,
+        0.0003643133670707414, 0.00028594567506857115, 0.00019635727197728778,
+        0.00010088664344476092, 3.0605194971107045e-05, 0.00010810098421267863,
+        0.00019942498515422948, 0.00028210364639991446, 0.00035159492916613644,
+        0.0004047721760591929, 0.0004394179670102062, 0.0004542123474866591,
+        0.00044875487081818703, 0.0004235641015319423, 0.0003800455092561595,
+        0.0003204331782484428, 0.0002477327750749712, 0.00016580110261314217,
+        8.083971359205166e-05, 4.0230899759763704e-05, 0.00011394180229501742,
+        0.0001950212507586619, 0.0002680753002711289, 0.0003288952244593009,
+        0.00037468210554616907, 0.00040351120099501887, 0.0004142907364558918,
+        0.00040676871864878285, 0.00038152556361979, 0.00033994239343805257,
+        0.0002841528636268523, 0.0002170187219394038, 0.0001423420661251041,
+        6.747988023299205e-05, 4.7528459519836654e-05, 0.00011526431373357823,
+        0.00018772989242765598, 0.0002528028651519225, 0.0003066177069383455,
+        0.0003466571658414918, 0.0003712285641860512, 0.000379406128730928,
+        0.00037102827727794087, 0.0003466871730204039, 0.0003077007010090291,
+        0.00025607809238247496, 0.00019453456967064278, 0.00012685568920182437,
+        6.160869876592327e-05, 5.2189147681192014e-05, 0.00011261566323615575,
+        0.0001777483934001646, 0.00023643749770337917, 0.0002849790737373726,
+        0.0003210396483612365, 0.00034307514426868996, 0.00035024859727313123,
+        0.00034241810744343846, 0.0003201254878449355, 0.00028457475217438273,
+        0.00023761464858476774, 0.00018179404943382258, 0.00012085081892301337,
+        6.373860426309206e-05, 5.44130375116663e-05, 0.00010590629768902283,
+        0.00016484997501973266, 0.00021892879429971567, 0.00026425465433453193,
+        0.0002985242475061405, 0.0003202270101318062, 0.00032851092467283587,
+        0.0003231559683098573, 0.00030456223933960936, 0.0002737365699610367,
+        0.00023229144099989782, 0.0001825255771301215, 0.0001279112523009828,
+        7.613494664076473e-05, 5.687588388308856e-05, 9.467831250162099e-05,
+        0.0001480756802432581, 0.00019979273144520504, 0.00024486804441814947,
+        0.00028071352082861215, 0.00030565256028950127, 0.0003186432456178748,
+        0.0003192145908543466, 0.0003074480048533686, 0.00028396904443123584,
+        0.00024995345594443604, 0.00020719232018611493], [0.0005129200273857926,
+        0.0015392625630668382, 0.002567113997513955, 0.0035974844661026857,
+        0.004631390330907904, 0.0056698569747731225, 0.006713921163892017,
+        0.007764633894429467, 0.00882306305807979, 0.00989029627523969,
+        0.01096744381981159, 0.012055641695414706, 0.013156054757742031,
+        0.014269880092100888, 0.015398350471858481, 0.016542738071850572,
+        0.017704358362734703, 0.018884574246773006, 0.02008480048489239,
+        0.021306508366374724, 0.022551230783348683, 0.02382056759394345,
+        0.025116191434782557, 0.026439853971797204, 0.027793392645243033,
+        0.029178737953831625, 0.030597921384435848, 0.03205308398377418,
+        0.03354648572187908, 0.035080515653595754, 0.036657703079592034,
+        0.03828072969170181, 0.03995244293692198, 0.04167587065747811, 0.04345423722735272,
+        0.04529098130807122, 0.04718977548625794, 0.0491545479680108, 0.05118950666626005,
+        0.053299165915619756, 0.05548837624835974, 0.05776235756461484,
+        0.06012673624957487, 0.0625875867186077, 0.06515147811641644, 0.06782552680102558,
+        0.07061745568289456, 0.07353566121165137, 0.07658928950415016, 0.07978832282714018,
+        0.08314367831773609, 0.08666732095515689, 0.09037239320910309, 0.09427336441825357,
+        0.09838620344900838, 0.10272857897504745, 0.10732009282894017, 0.11218255282977896,
+        0.11734029333081568, 0.12282055345650232, 0.12865392562650843, 0.1348748902302087,
+        0.1415224565011455, 0.14864093522465793, 0.15628087629859244, 0.16450021407648877,
+        0.17336567666911717, 0.18295453370330242, 0.19335678230932984, 0.20467790631588198,
+        0.2170423939547914, 0.23059827178686165, 0.24552301884314534, 0.26203138327518216,
+        0.28038586571726887, 0.3009110092813334, 0.3240132369034074, 0.3502089610593416,
+        0.38016535823570957, 0.4147611243188479, 0.45517986685144135, 0.5030590207389084,
+        0.5607378974506354, 0.6316933722704606, 0.721357301203807, 0.8387851206774961,
+        1.0004669115491984, 1.2405255284338998, 1.645573015718536, 2.542144856686667,
+        10.61122968183272, 3.704729008968028, 2.5901924071674727, 2.1266741246516916,
+        1.8595787972031323, 1.6820749907293902, 1.5541602851522576, 1.4570458007770535,
+        1.380598193134844, 1.3188133999063683, 1.2678824545656882, 1.2252604232600388,
+        1.1891767324729123, 1.158359391011678, 1.1318710270747467, 1.1090071126269592,
+        1.0892306672661864, 1.0721294643725916, 1.0573879286165508, 1.044769456882473,
+        1.034107317841022, 1.0253046905320158, 1.018348491401052, 1.0133524985722127,
+        1.010685457452452, 1.0114587163032651, 1.0210995218638894, 1.281752405784205,
+        1.029059914525033, 1.1693442562044634, 1.0628629347630054, 1.0157126713011764,
+        1.0650427506557765, 1.248628034813529, 1.2606038958482955, 1.0182940176324384,
+        1.018857697576411, 1.0657736590839588, 1.1803674513096178, 1.3816824464045172,
+        1.1476756178580496, 1.0198645258176506, 1.0145654072804962, 1.0480117242864613,
+        1.117447611473516, 1.2430547067356879, 1.3155883793162284, 1.1291162682369988,
+        1.0253872483920965, 1.0111354499660097, 1.0327308633359344, 1.078847291773838,
+        1.1547109314923611, 1.251446275571533, 1.244592582299329, 1.1034596377432757,
+        1.0246691752455541, 1.0105041512910131, 1.0270153029417168, 1.0629249852242018,
+        1.118385355223555, 1.1910066081001631, 1.2301219539034938, 1.146972310326015,
+        1.0466686661602604, 1.0113187536060058, 1.0185498395479007, 0.8859094250783301,
+        0.7956801025403285, 0.6963974650773427, 0.5599092718839944, 0.40030148400835985,
+        0.2982039022186691, 0.32873572686299307, 0.41550283125032395, 0.490349532546923,
+        0.5390626670702324, 0.5613029111101449, 0.5570370205074013, 0.52361478316988,
+        0.45576730566111806, 0.3478267202225476, 0.19964361483831675, 0.04367298169807864,
+        0.17945642099064063, 0.3501750216742802, 0.49313240979322864, 0.6055183557511244,
+        0.6918246038195043, 0.7580342720726285, 0.8093081389676046, 0.8494767004829669,
+        0.8811892709063547, 0.9061968334587455, 0.9255991706423411, 0.9400231852393394,
+        0.9497390802048894, 0.954727813748409, 0.9547111704781, 0.9491526038112595,
+        0.9372350998379629, 0.91782314391471, 0.8894217572250134, 0.8501605606207562,
+        0.7978602207994662, 0.7302838529946347, 0.6457180346099567, 0.5440002587410053,
+        0.4279122275935043, 0.304600612930271, 0.18761754735785574, 0.1085076227561041,
+        0.12229055032180783, 0.18074837607266625, 0.23133109564696147, 0.2639798135848285,
+        0.27826494779065203, 0.27605410898507754, 0.2599214193928498, 0.23278883942697062,
+        0.1980147394283903, 0.15979824890494781, 0.12407447546496439, 0.09979577285683838,
+        0.09597788430027221, 0.10998790510336225, 0.1301178246419511, 0.14803489746802884,
+        0.1599782443450321, 0.16468482252860978, 0.16222796619994334, 0.1534934532843854,
+        0.1399507359179339, 0.12359536218109445, 0.10700458234661246, 0.09334686809984463,
+        0.08579002918275054, 0.0857159935813847, 0.0913820801345959, 0.09936552352956887,
+        0.10670680126754928, 0.1116022390806957, 0.11324562322942411, 0.11155510180727682,
+        0.1069706081699577, 0.10031987076886388, 0.09272101778015104, 0.08547130506165058,
+        0.07984197697636103, 0.07672245758677608, 0.07624771653395844, 0.07774805885831072,
+        0.08012627128932748, 0.0823312266648723, 0.08363193348687885, 0.0836843589265618,
+        0.0824918835651679, 0.08032646459702752, 0.07763313102415108, 0.07491922697358891,
+        0.07262968949258586, 0.07102832978376274, 0.07012880119621454, 0.06971464533364498,
+        0.06944213683458914, 0.06897408727130282, 0.0680907999252888, 0.06675287241748634,
+        0.06511322325904026, 0.06348043700095259, 0.0622330900974642, 0.06169302678787748,
+        0.06199444383681138, 0.06301237666192962, 0.06439228419846177, 0.06565747505766349,
+        0.0663334297747024, 0.06604682366736073, 0.06459209107851875, 0.061976074019627396,
+        0.0584518000150211, 0.054542515057642016, 0.05103091370519279, 0.04883764496323106,
+        0.048700191084943716, 0.05076558377943472, 0.05448233757776302,
+        0.05890672338015797, 0.06307199612621493, 0.06617930184233237, 0.06764977930836981,
+        0.06712979555442743, 0.0644956123475108, 0.059875469009111275, 0.05370567982155863,
+        0.04685094917900525, 0.04080498947304951, 0.03772251195757704, 0.03938114796133801,
+        0.04543899206327606, 0.05391422440353622, 0.06286095415759542, 0.07088421688340212,
+        0.0770168530989866, 0.0805774975735482, 0.08110093407869434, 0.07831606106493061,
+        0.0721549920487368, 0.06280248271995938, 0.05085597422926005, 0.03791384149928911,
+        0.02878068007563221, 0.0327103397907861, 0.04906729150032319, 0.07058294716693404,
+        0.09383167987717589, 0.11725996994871109, 0.13988876733248698, 0.1609808998983486,
+        0.1799538550633134, 0.19635477098349002, 0.20985089291352033, 0.22022220409506166,
+        0.22735264955800658, 0.23121957373641308, 0.2318820190451039, 0.22946870748248752,
+        0.2241663623959727, 0.2162087653914723, 0.205866708986052, 0.19343885556997137,
+        0.17924345838279615, 0.16361092074874592, 0.14687723122619464, 0.12937838032427912,
+        0.11144592851242975, 0.09340400366915547, 0.07556836805703845, 0.058249588358580774,
+        0.04176830562718501, 0.026523472396473093, 0.013444554139760694,
+        0.00829874386320909, 0.015841491151679366, 0.02469754217328767,
+        0.032209087369112516, 0.037960023022339244, 0.041835692427464384,
+        0.04382364928028082, 0.04397606559962929, 0.04239886466517583, 0.03924654847092276,
+        0.034717745270130926, 0.029049925858601285, 0.022512823660977607,
+        0.01540105783804255, 0.00803170749379951, 0.0011007501965822272,
+        0.006477060962855483, 0.01287206596114127, 0.018443080979996345,
+        0.02297346548170452, 0.02630992059238216, 0.028355752315345, 0.029071808907155307,
+        0.028476249428920044, 0.02664241710275739, 0.02369495560791208,
+        0.019804736734699936, 0.015184438499804718, 0.010093736161872438,
+        0.004937641037822903, 0.0025130741416872857, 0.006718886966476412,
+        0.01133993713487086, 0.015407830640934614, 0.01868428120146978,
+        0.021028026014492184, 0.022355667227919502, 0.02263615658494476,
+        0.021888930829041357, 0.020181813281818027, 0.017628571289992314,
+        0.014388207095549168, 0.010674848191502695, 0.006827253964508817,
+        0.0038298560988043566, 0.004578004001539325, 0.007831376226094937,
+        0.011214078921489758, 0.014157654592792989, 0.016446898203042817,
+        0.01796391936716565, 0.01864781191723621, 0.0184853478495172, 0.01750757898926497,
+        0.015787840129929592, 0.013441510252697068, 0.010632756308427097,
+        0.007611727926875726, 0.004905798173414624, 0.003992522392969689,
+        0.0057617491335695955, 0.008420946621434494, 0.010986304574371263,
+        0.013129982940116866, 0.014696623905789854, 0.015601824769087613,
+        0.01580897825865064, 0.01532242360043051, 0.014184695636821102,
+        0.012475717642296612, 0.01031613480111629, 0.007885756558883952,
+        0.005505096326226721, 0.003951130410945962, 0.004428558857362373,
+        0.006353872940691178, 0.008544305124542793, 0.010520990765756822,
+        0.012082689092334868, 0.013123342863320762, 0.013587908912248137,
+        0.013460104959570755, 0.012758175021143724, 0.011533270049297866,
+        0.009870344652450513, 0.007896335150142977, 0.0058157548679082785,
+        0.004055149557961356, 0.003553997910067176, 0.004717315549328895,
+        0.0065389537260466535, 0.008350184563286442, 0.009886385633042971,
+        0.011018560684236785, 0.011676003998583137, 0.011825829805260988,
+        0.0114665457508049, 0.01062553417422481, 0.009358294254315214, 0.007750796671609397,
+        0.0059327964092779255, 0.004137231096882809, 0.002938654802179629,
+        0.0032767918744353117, 0.004739880481900965, 0.0064162089166589255,
+        0.007938523686673622, 0.00915212053589783, 0.009973223294519742,
+        0.010355328962245522, 0.010279908164555306, 0.009752901688902684,
+        0.008802505054820838, 0.0074770749323755156, 0.005843276326522655,
+        0.003986940363243826, 0.0020393552653426316, 0.0008532023586530062,
+        0.0024338946732497964, 0.004311922600458942, 0.006030043785279074,
+        0.007489769533259885, 0.008629969013228178, 0.009411152294941135,
+        0.009814408634539208, 0.009842103223644011, 0.009518902350951684,
+        0.008893347825387178, 0.008040988854651479, 0.007070781520946249,
+        0.006135466000945101, 0.00543519201632378, 0.005168591522318921,
+        0.005398080840660845, 0.005983521660314216, 0.006703579168585137,
+        0.007375008120962117, 0.007876305434474965, 0.008134839331387015,
+        0.008114063110824464, 0.007806196748969096, 0.007228948902911627,
+        0.006425586352487513, 0.005470039838814904, 0.00448283667698128,
+        0.0036656259961386694, 0.003311290091065867, 0.0035946863302401544,
+        0.004329691769455909, 0.0052146124608069685, 0.006047436558415198,
+        0.006713356177902545, 0.00714657688669763, 0.007311747701437448,
+        0.0071964546655681715, 0.006808304300244873, 0.006174307373936649,
+        0.005342796196014513, 0.004391169230892131, 0.0034495803282511652,
+        0.0027556163298476832, 0.0026427672833070365, 0.003165323616235958,
+        0.0039997591281947025, 0.004869562771706881, 0.005628044988016179,
+        0.0061958271824115955, 0.006527964393276568, 0.006602032094758179,
+        0.006413821159248711, 0.005975799905097936, 0.005317131529231876,
+        0.0044861619153596525, 0.003560018831178654, 0.0026770025254649623,
+        0.0021173803290820636, 0.002232988857528437, 0.0029096071763863034,
+        0.0037671036344819903, 0.004588016527735487, 0.005268172079793783,
+        0.0057505063703236405, 0.006002599285027712, 0.006009561093987261,
+        0.005771579613654364, 0.005303056672880755, 0.0046328012777315545,
+        0.003806538537309124, 0.00289748069304105, 0.0020486752220220954,
+        0.001600514842986247, 0.0019222806304836889, 0.002704650214312042,
+        0.0035649491404719214, 0.004343477871678066, 0.004965820389181446,
+        0.0053894016392628296, 0.005589632242267339, 0.005555955588765883,
+        0.00529050927615021, 0.0048075634710583685, 0.004133515241315356,
+        0.0033085525639295543, 0.00239550977988479, 0.0015270753193026548,
+        0.0011292773949434542, 0.0016445455054792646, 0.002515113751514194,
+        0.0033869204386062874, 0.00414952830371922, 0.004748949965899236,
+        0.005151657846568389, 0.005337299664497731, 0.005296912016099717,
+        0.0050323181867514295, 0.004555700592774552, 0.0038891813112014568,
+        0.0030648305080554833, 0.002127556704157122, 0.001160605325503685,
+        0.0006252769015291274, 0.0013497046879096012, 0.0023247344589007166,
+        0.0032476165367107705, 0.00404965800472161, 0.004689963996634481,
+        0.0051390991359567305, 0.005376968171078971, 0.00539264005054105,
+        0.005184367822390726, 0.004759421238662103, 0.004133634549747414,
+        0.003330657650409676, 0.00238093467916083, 0.0013204557616986396,
+        0.00018945728126065376, 0.0009698936784230431, 0.0021133147994707503,
+        0.003197938360412125, 0.0041826747164018085, 0.00502981442454003,
+        0.005706168929314292, 0.0061839975890059734, 0.00644169556227346,
+        0.006464239272244576, 0.00624340862939885, 0.005777842200981026,
+        0.005073071167000803, 0.004141993643565196, 0.0030078594629853283,
+        0.0017256517468608936, 0.0007391498950611178, 0.0018009498187544941,
+        0.0035106036784292617, 0.005357122180366962, 0.0072694730173178896,
+        0.009206200032871058, 0.011131073757079644, 0.013009610770415276,
+        0.014808456105903376, 0.016495426426460666, 0.018039777884014105,
+        0.01941258944609389, 0.02058722854172137, 0.021539882015099727,
+        0.022250134200897786, 0.022701567832820988, 0.022882357038218136,
+        0.022785816912314887, 0.022410872092923254, 0.02176240778924937,
+        0.020851470937243623, 0.019695296475490096, 0.018317144139804013,
+        0.016745945086695375, 0.015015776827187074, 0.013165214726624148,
+        0.011236664522474947, 0.009275912204757503, 0.0073325065474407055,
+        0.005462910045866534, 0.0037440119689866186, 0.002333502346706541,
+        0.0016833780463147033, 0.002147405258865009, 0.0030183536272908257,
+        0.0038398353874947496, 0.004489650841733873, 0.0049326995164183434,
+        0.005162200548492447, 0.00518554839375047, 0.005019765707910676,
+        0.004689605727802688, 0.004226765187425303, 0.0036701605324852876,
+        0.003068162757332194, 0.002484898403079645, 0.002012130599149096,
+        0.001768400970244191, 0.0018196437146412484, 0.002085484620340179,
+        0.0024282584071687523, 0.002752819861919524, 0.0030085530649237844,
+        0.0031710041796191267, 0.0032311600975760335, 0.0031904789356753125,
+        0.003058568807201323, 0.002852121506441064, 0.002594625521435151,
+        0.0023166800196345962, 0.002056294325953896, 0.0018565582215045399,
+        0.0017549976302645178, 0.0017639320732270678, 0.001860603716995103,
+        0.0020024217312823328, 0.0021486246072280704, 0.0022699057807953845,
+        0.0023487432536241446, 0.002377195862478968, 0.0023548795430706677,
+        0.0022875208484791046, 0.00218588912076596, 0.0020648051151038126,
+        0.0019418243845070989, 0.0018350478564242124, 0.001759643061079033,
+        0.0017236746380351747, 0.001725482718421298, 0.0017548392664947165,
+        0.001797299337322081, 0.0018388818713064648, 0.001869047727928651,
+        0.0018818407431277428, 0.0018758696289633279, 0.0018536837042317509,
+        0.0018207749712247133, 0.0017842457839565482, 0.0017511725816448007,
+        0.0017268663583098782, 0.0017134837130395502, 0.0017095288842787352,
+        0.0017104916719325022, 0.0017103442490727352, 0.0017033056144191408,
+        0.0016853681371668291, 0.0016553555344028315, 0.0016154705307331407,
+        0.0015712985821818783, 0.0015311156581241214, 0.0015042593272240315,
+        0.0014985445488595148, 0.0015174319855315234, 0.0015583686114152594,
+        0.0016133099859011021, 0.0016709693916824027, 0.001719442781829889,
+        0.0017482536786923636, 0.0017496539202801926, 0.00171942883968995,
+        0.0016575031714004818, 0.0015685693452629679, 0.001462847736606747,
+        0.001356788787762597, 0.0012726302337796793, 0.001234188494829374,
+        0.0012570835638323243, 0.0013393114485630013, 0.0014624564218441946,
+        0.0016014962399130645, 0.0017328687817436588, 0.001837543986477252,
+        0.0019014206063493733, 0.001915085393292695, 0.0018736951355731509,
+        0.001777195764610596, 0.0016310692585315939, 0.0014480818569487166,
+        0.0012520332573992912, 0.0010842125134270292, 0.001005159393542264,
+        0.001063871346217876, 0.0012479040357383897, 0.001501673884199932,
+        0.0017735450742218202, 0.002027263446605912, 0.0022374116321233926,
+        0.0023853401222528226, 0.0024572530238822824, 0.002443528272644923,
+        0.002338670904297306, 0.002141748782049228, 0.001857691838444208,
+        0.0015012852121891259, 0.0011119963226966486, 0.0008145315891178211,
+        0.0008906048013496141, 0.0013593935467374008, 0.001996491661457524,
+        0.002698065865868339, 0.0034208014674950243, 0.004138116683897563,
+        0.004829324628608301, 0.005476853010700203, 0.006065544119546549,
+        0.0065825618428387595, 0.007017468483705831, 0.007362318641725711,
+        0.007611710795668794, 0.007762773647581166, 0.007815081208344014,
+        0.007770499870512368, 0.007632976424154192, 0.007408279636368968,
+        0.00710371019595875, 0.006727794740512211, 0.0062899794420887235,
+        0.005800337337756968, 0.005269301436374191, 0.004707432926502944,
+        0.004125231129354755, 0.0035329903234701354, 0.002940710958210731,
+        0.0023580873341541315, 0.0017946520374708785, 0.0012604147365973344,
+        0.00076888431840864, 0.00036065872069963455, 0.0003005748914249548,
+        0.0005910272159008567, 0.0008862386808619615, 0.0011342245110531007,
+        0.0013254322087283478, 0.0014569636247498549, 0.0015285396335689852,
+        0.0015416720560694239, 0.0014994090464591494, 0.001406202149213106,
+        0.0012677827928437395, 0.00109101457007093, 0.0008837140692578863,
+        0.0006544528354892145, 0.00041242090623079975, 0.00016830739870160073,
+        8.627059416876409e-05, 0.0003079245506404104, 0.0005134813628456213,
+        0.0006911726228053858, 0.0008348938558529426, 0.0009402362047942818,
+        0.0010043925467221623, 0.0010261970247326172, 0.0010061345571240484,
+        0.0009462973909956929, 0.0008502880867404271, 0.0007230803721771156,
+        0.0005708747306596768, 0.0004010996426222425, 0.00022363198321820096,
+        7.632357910713945e-05, 0.00017229384262660547, 0.00033484271241497306,
+        0.0004846296002093073, 0.0006117315652013918, 0.0007106877441048663,
+        0.0007778653369960659, 0.0008111868467307145, 0.0008100969482110502,
+        0.000775539400942282, 0.0007099081369757032, 0.0006169868504320104,
+        0.0005019532686020648, 0.0003717555528819809, 0.00023755426172913352,
+        0.00013288804743852336, 0.00015915568502154545, 0.00027401386657204744,
+        0.0003947180416637307, 0.0005017412116267879, 0.0005876612164997403,
+        0.0006482392376221097, 0.0006810315479886792, 0.0006850880561671778,
+        0.0006608598448404559, 0.000610148872429342, 0.0005360852020135503,
+        0.0004432157144592263, 0.00033805614449351697, 0.00023173823649364088,
+        0.00015288645389181235, 0.000162957144191822, 0.00024647596756116147,
+        0.00034402522343735594, 0.0004337271418233017, 0.0005071459376148966,
+        0.0005597812604831953, 0.0005890842935956708, 0.0005939647988181095,
+        0.0005746385230925361, 0.0005325668307388332, 0.0004704510685615418,
+        0.00039236239132811173, 0.0003043559162249689, 0.00021700647212253473,
+        0.00015500680597287125, 0.00016154331329719238, 0.00022716719912057234,
+        0.00030813288431721686, 0.00038429893635799807, 0.00044731828852113037,
+        0.0004927864131124257, 0.0005182271082050489, 0.0005225419615541943,
+        0.0005058336965431294, 0.0004693417960190226, 0.00041544492096885,
+        0.00034780559814696205, 0.00027198741874048587, 0.00019781185977364818,
+        0.00014706561178996237, 0.00015348138843801286, 0.00020886036371017193,
+        0.00027836541820463876, 0.0003443817334740516, 0.0003992225808777302,
+        0.0004387999923648766, 0.00046081057082435846, 0.0004642105718495209,
+        0.00044904242335318863, 0.0004163715573071228, 0.0003682886810828174,
+        0.0003080452324756526, 0.00024062592328511162, 0.0001749271985039236,
+        0.00013077563125817512, 0.0001380304436155139, 0.0001881818241730449,
+        0.00025043189196022754, 0.00030939795465941987, 0.00035830000873537655,
+        0.00039348473640195226, 0.00041285827701878746, 0.00041542827784478615,
+        0.0004011456239984407, 0.00037083282832262076, 0.0003261489885802899,
+        0.0002696207740726302, 0.00020492653684895393, 0.00013837949022177802,
+        8.716865460733348e-05, 9.387401912970442e-05, 0.00014866211448720678,
+        0.0002116494031288415, 0.00026974686405796663, 0.0003180316277800213,
+        0.00035382370700259857, 0.000375585308049433, 0.0003826777470499097,
+        0.0003753108277910794, 0.00035455500947617456, 0.0003224111305072072,
+        0.00028200310156146395, 0.00023805704819879867, 0.00019789811355663838,
+        0.0001723234264400121, 0.00017159889374033347, 0.00019476187645576403,
+        0.00023053325909642796, 0.000268241232823549, 0.00030112850346311517,
+        0.0003252036834097577, 0.0003381726905412212, 0.00033892065967065473,
+        0.0003272874993749875, 0.00030398226331873076, 0.0002705951876182042,
+        0.00022976648534126355, 0.0001857506619360284, 0.00014597392578240902,
+        0.00012340675971150728, 0.00013047562090635144, 0.0001615001565188455,
+        0.0002013939816124351, 0.00024024735766232946, 0.000272801159430349,
+        0.0002960912955994682, 0.00030843058352735296, 0.0003090383459045285,
+        0.00029790390569192084, 0.0002757426124357573, 0.0002440190374883457,
+        0.00020509994826413202, 0.0001627830618390963, 0.00012394307901374534,
+        0.00010183198650137741, 0.00011023265610514071, 0.00014200554705931612,
+        0.00018115566505318948, 0.0002185177716751217, 0.00024952610727109193,
+        0.0002716273753974912, 0.0002833565438087013, 0.0002840311048215787,
+        0.0002736439778670947, 0.0002528284004963904, 0.00022287301293587712,
+        0.00018584117686664718, 0.000145022658731968, 0.0001065427092788515,
+        8.367998366007455e-05, 9.25047583660862e-05, 0.00012479416617785906,
+        0.00016336343833513463, 0.00019965231228038754, 0.00022965128004568265,
+        0.00025111552612667196, 0.0002627305587517022, 0.00026386139712795937,
+        0.00025446899897863895, 0.00023508049243253803, 0.000206792090246416,
+        0.0001713434222793713, 0.0001314460950667444, 9.217014273752204e-05,
+        6.632630403502364e-05, 7.46115931455047e-05, 0.00010806523961867325,
+        0.00014690606910749328, 0.00018303037335068163, 0.00021293311430836865,
+        0.000234625072282844, 0.00024689537326121584, 0.0002491170351921451,
+        0.00024118718683751556, 0.0002235028809149876, 0.0001969511107552417,
+        0.00016293112767841098, 0.00012351400119027224, 8.229345080757452e-05,
+        4.965945585123303e-05, 5.475699715209221e-05, 9.06516199763071e-05,
+        0.00013112301878270448, 0.00016845174394269002, 0.0001996535409499285,
+        0.00022295440640252956, 0.00023719417188470559, 0.00024170056854136532,
+        0.0002362580816572781, 0.00022109378147335603, 0.00019686111969636805,
+        0.00016462199643274976, 0.00012585132848997975, 8.260575413742433e-05,
+        3.93266424756985e-05, 2.9883712482384555e-05, 7.0726516475764e-05,
+        0.00011508908014040632, 0.00015597422260857634, 0.00019103939108139082,
+        0.0002186706905236737, 0.00023766581778656188, 0.00024720176606882763,
+        0.0002468409520658899, 0.00023653616970153012, 0.00021662508356037517,
+        0.0001878120356889861], [1.578840721876905e-05, 4.738344941336167e-05,
+        7.903322340384214e-05, 0.00011077435875269489, 0.00014264369508812402,
+        0.00017467837529683465, 0.00020691592523173547, 0.00023939434809134975,
+        0.0002721522129004224, 0.0003052287477663109, 0.0003386639354850884,
+        0.0003724986132560657, 0.00040677457312392716, 0.00044153466951383797,
+        0.0004768229282974298, 0.0005126846626382592, 0.0005491665931184656,
+        0.0005863169738060188, 0.0006241857255702486, 0.000662824574808252,
+        0.0007022872023422388, 0.0007426293984164367, 0.000783909228394818,
+        0.000826187208271151, 0.0008695264911269136, 0.0009139930652233751,
+        0.0009596559662731772, 0.001006587502773941, 0.0010548634980462812,
+        0.0011045635478183467, 0.0011557712982782193, 0.0012085747422591402,
+        0.0012630665389928508, 0.0013193443567838545, 0.0013775112428317526,
+        0.0014376760207596693, 0.0014999537203820763, 0.0015644660406962598,
+        0.0016313418515357528, 0.0017007177350156512, 0.0017727385732699147,
+        0.0018475581842897395, 0.0019253400132260676, 0.002006257882160601,
+        0.0020904968070082136, 0.0021782538841803294, 0.002269739260576303,
+        0.002365177187089287, 0.0024648071736493465, 0.0025688852483011855,
+        0.0026776853370134327, 0.0027915007756152024, 0.0029106459669574307,
+        0.003035458202233062, 0.0031662996633483134, 0.0033035596261579226,
+        0.0034476568915925584, 0.0035990424663822425, 0.0037582025281253546,
+        0.003925661706019305, 0.004101986716806221, 0.004287790401262734,
+        0.004483736211255625, 0.004690543205251731, 0.0049089916189608025,
+        0.005139929088759458, 0.005384277614280023, 0.005643041362587884,
+        0.005917315433376771, 0.0062082957195631035, 0.006517290022958449,
+        0.0068457306105564825, 0.007195188430255898, 0.007567389235743976,
+        0.007964231924386033, 0.008387809436312848, 0.00884043263895192,
+        0.009324657686555746, 0.009843317447780244, 0.010399557714399934,
+        0.010996879032776624, 0.011639185187784744, 0.0123308395812252,
+        0.013076731010371304, 0.013882350696259515, 0.014753882824643069,
+        0.015698311403293943, 0.01672354690823197, 0.017838577055536223,
+        0.0190536471710573, 0.020380477039927056, 0.02183252305167492, 0.02342529693029685,
+        0.025176755678120555, 0.027107781825065375, 0.029242779192065863,
+        0.031610417674036904, 0.03424457228334057, 0.03718551802615803,
+        0.04048146578753372, 0.04419055863366759, 0.048383498793366446,
+        0.05314705244709161, 0.05858879870953109, 0.06484367837285213, 0.0720832081243216,
+        0.08052875099136647, 0.09047115957296475, 0.10230081949303611, 0.1165554672579866,
+        0.13400017324869173, 0.15576993287642807, 0.18364640631670995, 0.22066276066388674,
+        0.2726827726896654, 0.3539376549208351, 0.522381457173901, 1.7281607524167497,
+        0.5407292922398463, 1.5215746949318132, 1.0328265564373431, 0.0834421126792304,
+        0.7504953775130799, 2.244445353054232, 3.5606481024004055, 1.7050025175836008,
+        0.9538582790591001, 0.16463085453658088, 2.4184426076846695, 5.062812130340401,
+        4.264866778996454, 2.5921601298102765, 1.7386487828864208, 1.2699821546863785,
+        1.1292790075634074, 1.5790581010043936, 2.4490023956909686, 2.3116039932024712,
+        1.8041123461553272, 1.4542969258680971, 1.2338406551175862, 1.124287219752225,
+        1.1837142664289895, 1.5214712978097436, 1.9005349019999354, 1.8024252873895261,
+        1.5397659978324367, 1.3369758161522858, 1.20207379783807, 1.1272145631153152,
+        1.130371226298617, 1.2649512720216125, 1.5254054060100477, 1.6258546630586057,
+        1.4871376905470008, 1.3243688902425879, 1.2020114567127391, 0.9326322815448951,
+        0.7681566303555731, 0.6286945213298659, 0.5088473732688211, 0.4535411152473711,
+        0.4869213378176831, 0.5525898276396899, 0.6015759816720033, 0.6231657776536412,
+        0.6202610377070438, 0.595969689588699, 0.5504967834892276, 0.4811782515369562,
+        0.38379768932270947, 0.2567661515595476, 0.1213503012029641, 0.15047573029691952,
+        0.3115189441830448, 0.46338754024454315, 0.5850651328271871, 0.6765895109823913,
+        0.7441168247383326, 0.7943024801653243, 0.8324189789450389, 0.8621706209414345,
+        0.8860122623479522, 0.9055060087818422, 0.9215944077684229, 0.934783525273287,
+        0.9452550427781923, 0.9529259722468736, 0.9574688785261142, 0.9583003338302911,
+        0.954542041802423, 0.9449585958810812, 0.9278803644915773, 0.9011340232055908,
+        0.8620337433062594, 0.8075381280155487, 0.7347377045537243, 0.6418356453824282,
+        0.5295788917279236, 0.4026303416765225, 0.2701498879978848, 0.14700403582867183,
+        0.0771776254404663, 0.12655261962961428, 0.1979949906182014, 0.2541790294208978,
+        0.29117834309226825, 0.3094843983365214, 0.31059552917239364, 0.2963566159515564,
+        0.26888754965215766, 0.23071751375097907, 0.18503918710033, 0.13625956225526364,
+        0.09194563284216915, 0.06893080722601573, 0.08294262665390616, 0.114683709588906,
+        0.1460271785570087, 0.17075813832829448, 0.18673910717451178, 0.1933410817700955,
+        0.1907222825889701, 0.17957945902999659, 0.16107130173943576, 0.1368519878981071,
+        0.10926723856525714, 0.08200045488576488, 0.06186110882325214, 0.058879769204088564,
+        0.07306844223863843, 0.09343207984128776, 0.11272808350245456, 0.12781193113810096,
+        0.13729770339183014, 0.14064740270870804, 0.1378527511817025, 0.12931494462022897,
+        0.11581219265540635, 0.09854147511018098, 0.07929945696185095, 0.061029348226481483,
+        0.04895002836059605, 0.04916290859805764, 0.06027976476379656, 0.07533817297023157,
+        0.08970380423099106, 0.10113627187577633, 0.10853497509801827, 0.11139669936766015,
+        0.10961465026138194, 0.10340236839497714, 0.0932747802195469, 0.08007966657635686,
+        0.06512863665935421, 0.050594994015890765, 0.04039556263465541,
+        0.03960853591233414, 0.04811826900185583, 0.060570562796192474,
+        0.0729797301936018, 0.08333815951219495, 0.090606739806542, 0.09424387844786634,
+        0.09403368138559769, 0.0900226211013696, 0.08250093253034013, 0.07201656792144313,
+        0.0594483019566399, 0.04625021349407469, 0.03518020931884799, 0.03116219007416972,
+        0.036913070884189804, 0.048132216117821675, 0.060336718738477124,
+        0.07128034715270859, 0.07981613174631876, 0.08529252165497662, 0.08735103555242864,
+        0.08585779301515242, 0.0808809617637642, 0.07269018421589285, 0.06178242762910856,
+        0.048981633037480626, 0.03581611744302373, 0.025915832392836027,
+        0.026182554735758604, 0.03659954514816618, 0.050407737062594014,
+        0.06406503861045922, 0.07603584693110745, 0.08544510992707581, 0.09171096388348561,
+        0.09444363860298244, 0.09341468870672147, 0.08854805301088851, 0.07992139773570395,
+        0.0677820691842501, 0.05261253254831664, 0.035446875950937595, 0.02014496304719724,
+        0.022708960720069404, 0.042416783452751836, 0.06598045887014056,
+        0.09025006986754289, 0.11407312914246771, 0.13669358498388814, 0.15752143818344555,
+        0.17608872462223865, 0.19204001728599804, 0.20512807236505382, 0.21520764905533005,
+        0.2222263126869462, 0.22621285751316786, 0.2272645070494782, 0.22553401827140124,
+        0.2212175404300671, 0.21454373200955307, 0.2057643247685333, 0.1951460974870604,
+        0.18296410119265197, 0.16949595116664784, 0.15501703903051886, 0.1397965829223809,
+        0.1240944877826341, 0.10815900512646535, 0.09222515284859974, 0.07651379107431756,
+        0.06123117630128006, 0.04656877362056885, 0.03270316691398747, 0.019796424446951105,
+        0.008003657093920516, 0.002717293967524679, 0.011898335210603574,
+        0.019735314987323442, 0.026107081923070843, 0.03097794776117001,
+        0.03434361373813832, 0.03623024374156574, 0.03669500180364845, 0.03582629895047087,
+        0.03374347382423484, 0.03059593994481333, 0.026562275615918594,
+        0.021851047413501825, 0.01671004703424959, 0.011474291686492458,
+        0.006839710440926372, 0.005184194757377274, 0.008063031118616955,
+        0.012117198714245301, 0.01591266234010508, 0.019065136959449173,
+        0.02141187485299932, 0.02287354920387801, 0.02342428373081741, 0.02308261040464215,
+        0.021907815026013747, 0.01999858401487453, 0.017494753884355667,
+        0.014587084302768977, 0.011550188186746977, 0.00883843119908733,
+        0.007252793202396913, 0.007582659689581323, 0.009415690613704526,
+        0.011754170832424624, 0.013994325971503314, 0.015843985158072966,
+        0.017154616229710543, 0.01785343505737058, 0.017918759577666442,
+        0.017370472810713872, 0.01626649236722157, 0.014703185803388592,
+        0.012821390652063495, 0.010823532051872429, 0.009008990591144185,
+        0.007802929038926092, 0.007613823452569273, 0.008436631664716615,
+        0.009836988797737466, 0.011369475282738786, 0.012745749474445857,
+        0.01379912887259217, 0.014438258072083153, 0.01462243231936129,
+        0.014350216991751945, 0.013654587201281508, 0.0126019413781739,
+        0.011294970554727052, 0.009880987729358193, 0.008565776726332578,
+        0.007616159044479161, 0.007288259583462133, 0.007649008773511902,
+        0.00850409044460806, 0.009563107127481716, 0.01058919677103244,
+        0.011425992465550087, 0.011979643270086935, 0.01220153333833068,
+        0.012078231477225547, 0.011626496051972832, 0.010891497474592119,
+        0.00994772907406754, 0.008902807549390294, 0.00790293046641815,
+        0.007130115614641575, 0.006762337454545751, 0.0068789704886702534,
+        0.0073963222342507, 0.008129606852732946, 0.008895697624515956,
+        0.009558116410307967, 0.0100280592792617, 0.010255009209768691,
+        0.010219093484191106, 0.009926566651032673, 0.009407681147267446,
+        0.008716414882974416, 0.007931763272306835, 0.0071592900661598255,
+        0.006527131870807627, 0.006162175105977201, 0.006136738626038332,
+        0.006421561265524862, 0.006903750063507162, 0.0074491249700526325,
+        0.007945590179404891, 0.008314737892138137, 0.00850928856663963,
+        0.008508258644537693, 0.008313298414771282, 0.007946461557543603,
+        0.0074490097368405395, 0.006880613710193538, 0.0063174050887856315,
+        0.005845054669791768, 0.005540861637530943, 0.005444541449966859,
+        0.005536074357264735, 0.005744231102179515, 0.005978649849584664,
+        0.006157900208258139, 0.006222258448927986, 0.006136664868426537,
+        0.005890930426268104, 0.0055011238888024, 0.005014403855730541,
+        0.004518528362832215, 0.004150298144694434, 0.004072257796655886,
+        0.004380625916995214, 0.005028279695952269, 0.005879991885501403,
+        0.006801256884540748, 0.007688262980163052, 0.00846502708723451,
+        0.009076434216694016, 0.009483900076911904, 0.009663303472610667,
+        0.009604154188105384, 0.009309374211065449, 0.008795479268357203,
+        0.008093302854756639, 0.0072498208445332495, 0.006332191597815925,
+        0.005435365117858885, 0.004691037411813451, 0.00425701632068089,
+        0.004241394122446701, 0.004601419079191237, 0.0051761898376348784,
+        0.005802716496215382, 0.006365570231138921, 0.006792406824196639,
+        0.007041184568162806, 0.007091765022898342, 0.006941548404574836,
+        0.00660355148699916, 0.006106178036196794, 0.005494783533099579,
+        0.004835722677522873, 0.00422272201856558, 0.0037779203247094092,
+        0.003620390087391168, 0.0037874359128158815, 0.00419733991058805,
+        0.004717272906923863, 0.005233191841043197, 0.0056663536664210154,
+        0.005966817480009707, 0.006105843890057866, 0.006071285553961041,
+        0.005865298761907587, 0.005503601862391222, 0.0050161456849129385,
+        0.0044497365986937475, 0.003873501009798115, 0.0033856193163087256,
+        0.003106217979756021, 0.003122602883852812, 0.003413089318919045,
+        0.003865721940816023, 0.004361582855048724, 0.004813296113239847,
+        0.005163751899866292, 0.005377750767375918, 0.0054363254065917695,
+        0.005333798810918751, 0.005076540880805815, 0.004682956650695862,
+        0.0041849585601820005, 0.003632005171878456, 0.0030992520173867776,
+        0.0026964848783848695, 0.0025491035779487393, 0.0027100648001897004,
+        0.003100493411538587, 0.0035896623693847944, 0.004073458410466817,
+        0.004484053583829813, 0.004778978585154354, 0.004932834514199629,
+        0.004933076154488378, 0.004778114550100671, 0.004476693929393491,
+        0.004048335213715578, 0.0035254974307060774, 0.002959502782700893,
+        0.002434109257872921, 0.002083298680718098, 0.002053988522881172,
+        0.002355046294885024, 0.002842959654312923, 0.003376635959161791,
+        0.0038677908517171923, 0.004263713927628455, 0.004531947140691583,
+        0.004653213867798028, 0.004618479318431906, 0.004427765009803846,
+        0.00408982128268215, 0.003622606364656755, 0.003055461873264091,
+        0.002436209527519371, 0.00185338568801668, 0.0014882442670010772,
+        0.001569010220952738, 0.0020353066407732003, 0.0026472019119316787,
+        0.0032602252279783223, 0.0038029699636595244, 0.004234256347281532,
+        0.0045276198442851445, 0.004666266260566988, 0.0046413423912511085,
+        0.004451282337585467, 0.0041015277436224195, 0.0036044956897353726,
+        0.0029801637546883583, 0.0022590964941489934, 0.0014978008338531938,
+        0.0008798379764738969, 0.000994855246786722, 0.0017209460190932356,
+        0.0025542573762223643, 0.0033603136305704936, 0.004087053862625078,
+        0.004700583466543839, 0.005174742806991246, 0.005488897562293065,
+        0.005627439133654356, 0.005579669797793984, 0.00533972150107022,
+        0.004906403107231527, 0.004282949425682113, 0.0034766759976577587,
+        0.00249855759792675, 0.0013627551126888006, 8.611801261502513e-05,
+        0.0013123108507601623, 0.002811764196032466, 0.0043901744035204455,
+        0.006024540440351871, 0.007691233283928182, 0.009366243296245715,
+        0.011025380400268925, 0.01264444385467162, 0.014199382269891004,
+        0.015666465777326243, 0.017022490803821885, 0.018245033886675862,
+        0.01931276486608722, 0.020205822329524933, 0.020906246169006094,
+        0.021398454379857546, 0.021669744500672473, 0.021710794933839143,
+        0.021516138155850118, 0.021084576696623055, 0.02041951374741906,
+        0.019529173233393097, 0.018426688995181587, 0.01713004922842997,
+        0.01566189059916525, 0.014049147112373274, 0.012322574103287225,
+        0.010516194668378335, 0.00866677758450889, 0.006813638645927445,
+        0.004999753020358229, 0.003278740473375297, 0.001760778409563802,
+        0.0010230730237102614, 0.0018137417630030173, 0.0028936027226349244,
+        0.003851032249536634, 0.004617817624380041, 0.0051729222315239015,
+        0.005510297957747482, 0.005632833039311805, 0.005550521191945374,
+        0.0052795831007980305, 0.00484186642928253, 0.004264462000902809,
+        0.0035798552722306988, 0.002827790376758971, 0.0020633329046654976,
+        0.001390624990776882, 0.0010681027855184728, 0.0013328082254097475,
+        0.0018851561297006845, 0.002460965763933361, 0.002967293491755842,
+        0.003365834708621798, 0.0036374956392098115, 0.003773409079063285,
+        0.003772157473433055, 0.003638681248388263, 0.003383752863524773,
+        0.0030238139876298227, 0.0025814740204660376, 0.002087861951027097,
+        0.0015907959792509998, 0.0011802707905785579, 0.0010236461531384076,
+        0.001214525293639225, 0.0015946774328204224, 0.0020083909734039227,
+        0.002383131178513824, 0.002684141151991885, 0.002892625723508448,
+        0.0029987125769531282, 0.0029990454941916916, 0.002895852155573297,
+        0.0026965741022976887, 0.002413898756514762, 0.002066522411949097,
+        0.0016818747544951559, 0.0013044979791556864, 0.0010172648086366563,
+        0.0009480586225809848, 0.0011323616582931176, 0.001447850787750134,
+        0.0017862802665128382, 0.0020926354867824275, 0.0023382091191323055,
+        0.0025066077353356722, 0.0025887842030970875, 0.0025812494562230375,
+        0.002485387713358983, 0.0023072364005026313, 0.0020576564748915655,
+        0.0017532798216641267, 0.0014195872776929061, 0.0011000710764743856,
+        0.000877212012909894, 0.0008640180318434598, 0.0010631597554378765,
+        0.0013596858692533603, 0.0016675324021089817, 0.001942936590760504,
+        0.0021619638833025516, 0.0023102968472179116, 0.002379659088143125,
+        0.002366543325591444, 0.002271750968750237, 0.0021002918386998264,
+        0.0018616352041752457, 0.0015707513001654138, 0.001251507144572387,
+        0.0009475050952949894, 0.0007492743614339624, 0.000778954207269373,
+        0.0010129557290394838, 0.0013249718359597748, 0.0016385705181224666,
+        0.0019167158013035411, 0.002138348831030089, 0.002290048812096467,
+        0.0023633846598047955, 0.0023540503088764065, 0.0022615955860820986,
+        0.002089410655399234, 0.0018449731318049543, 0.0015407685889491248,
+        0.0011975198471438303, 0.0008566354024751278, 0.000626492983670051,
+        0.0006935422122744158, 0.0010052913230563865, 0.0013891070661361507,
+        0.0017688228136872478, 0.0021105823866106013, 0.0023936350648610704,
+        0.002602989247142131, 0.002727475528470079, 0.0027592326459223754,
+        0.0026936109142769154, 0.002529211451131354, 0.002268023659457374,
+        0.0019158427455696781, 0.001483835312473361, 0.0009961229576128453,
+        0.0005469994324099848, 0.0005963318501620992, 0.0011597776796369243,
+        0.001838877139113868, 0.0025485870930990226, 0.00326011859027778,
+        0.0039543499663002675, 0.004615456944578863, 0.005229699145133062,
+        0.005785229576962005, 0.006272146123064038, 0.006682581130182527,
+        0.007010763558405038, 0.0072530306812302915, 0.007407782659917738,
+        0.007475381093474753, 0.007457997099117079, 0.007359417338596442,
+        0.007184818274453674, 0.006940520031714068, 0.00663373162164856,
+        0.006272298980447609, 0.005864466310699895, 0.005418659630761797,
+        0.004943299322738962, 0.004446645948692677, 0.003936680858651893,
+        0.0034210203607944966, 0.0029068597170422935, 0.0024009412318878862,
+        0.0019095395180764292, 0.0014384571578631958, 0.0009930274553476726,
+        0.0005781435403394743, 0.00019869684569083984, 0.00014630888712765383,
+        0.0004452144601739267, 0.0007009230498188498, 0.0009107244539750812,
+        0.00107347309670297, 0.0011889124177956738, 0.001257670190040435,
+        0.001281277588448863, 0.001262174176589011, 0.0012036916753163092,
+        0.001110016994854087, 0.0009861430567979642, 0.0008378339648597852,
+        0.000671687541603901, 0.0004956095825942757, 0.0003213117509667557,
+        0.0001806562364867308, 0.0001812567345461673, 0.0003068951111904612,
+        0.0004472743387715977, 0.0005741511442360223, 0.0006789079299404299,
+        0.0007573154072166086, 0.0008071155556539427, 0.0008274694189461929,
+        0.0008187848329972885, 0.0007826410027252663, 0.0007217526370902236,
+        0.0006399938012133739, 0.0005425867007352417, 0.0004367768145880899,
+        0.0003339699468656364, 0.0002554566191305462, 0.0002351727803980248,
+        0.0002822712950467073, 0.0003627772292455168, 0.0004481364303674617,
+        0.0005246321410925902, 0.0005854703663844515, 0.0006270042607003785,
+        0.0006474342827559273, 0.0006463402230201128, 0.0006244980408006948,
+        0.0005838187943098651, 0.0005273881105207117, 0.0004596781860578477,
+        0.00038713414741890073, 0.00031948234089737646, 0.0002714105966808211,
+        0.0002593275947863607, 0.0002864066563262142, 0.0003377826213999726,
+        0.0003964802422801384, 0.00045140048629762583, 0.0004961031023665685,
+        0.0005269038726021107, 0.0005418789722951335, 0.0005404184998659088,
+        0.0005230332134913696, 0.0004912909361138843, 0.00044785842494161036,
+        0.00039669217324196844, 0.0003434722766566882, 0.00029627061372553486,
+        0.00026553347724640665, 0.00026034005469234204, 0.00028093154812534687,
+        0.0003181521792387381, 0.0003610980087050868, 0.000401645099549027,
+        0.00043458228127823414, 0.00045676818772268134, 0.00046652822577699564,
+        0.00046333441235460227, 0.0004476547904542213, 0.0004209067541205096,
+        0.00038550111133442086, 0.0003450002397696667, 0.0003044060490139787,
+        0.0002703868246311895, 0.00025051141009378594, 0.0002499829638998838,
+        0.000267632535348351, 0.00029676779882118777, 0.00032970803478762217,
+        0.0003604384318380113, 0.0003848992552632904, 0.000400579834193747,
+        0.000406157174289402, 0.00040128126822470294, 0.0003864693215423935,
+        0.00036307747376548415, 0.0003333439733218139, 0.0003005095436980573,
+        0.0002689730290737181, 0.0002442048466108998, 0.0002316532355504757,
+        0.00023413088185774818, 0.00024974656842122206, 0.0002732235094102916,
+        0.000298855118980426, 0.0003221191076372372, 0.0003399059526608312,
+        0.0003502996080147123, 0.0003523536533243683, 0.0003459485445791223,
+        0.00033171944478159156, 0.00031103888409894415, 0.0002860467918556271,
+        0.00025970929776765234, 0.00023580958824252567, 0.0002185671356651618,
+        0.0002114228975114245, 0.00021524139494904875, 0.00022764868614487285,
+        0.00024442244258628695, 0.00026133435272075994, 0.0002750654677273008,
+        0.00028335767598648877, 0.0002849135551523091, 0.00027929264585557637,
+        0.0002668716491611806, 0.00024888665772725697, 0.00022757312170371217,
+        0.00020638584859267314, 0.00019006665245956212, 0.00018378435373335206,
+        0.00019063998982597546, 0.0002094695436432814, 0.00023592652962719493,
+        0.0002651480011028811, 0.0002931480986282681, 0.0003169949652048469,
+        0.0003346347781593452, 0.00034472593335533377, 0.0003465399134266816,
+        0.0003399125539804856, 0.00032522909376009464, 0.00030343953393504187,
+        0.0002761163256622607, 0.0002455825107612485, 0.00021513682945382395,
+        0.00018928182917415235, 0.00017335556548236808, 0.0001713648852401041,
+        0.00018285884762254468, 0.00020313874749196528, 0.00022659618510395693,
+        0.00024881255504701, 0.0002667987466495965, 0.00027867724580776847,
+        0.0002834030527667121, 0.0002806018489389875, 0.0002704927798708346,
+        0.0002538702294082785, 0.00023214240583699068, 0.0002074451205628145,
+        0.000182844095452244, 0.0001625008794272806, 0.00015117233614530463,
+        0.00015204352409691784, 0.00016418199408315404, 0.00018326978528666985,
+        0.000204516578347798, 0.00022421284747764665, 0.00023983740264695635,
+        0.0002497918942954388, 0.00025318446241612573, 0.0002497076960979931,
+        0.00023958392727722625, 0.0002235607136544658, 0.0002029613424688813,
+        0.00017981716791642082, 0.00015710663754464832, 0.00013896569315729535,
+        0.00013010440158709718, 0.00013329303865669383, 0.0001468738121587718,
+        0.00016623496420595105, 0.00018684963407829597, 0.00020542355085869328,
+        0.00021977663311576425, 0.00022854199747005934, 0.00023096791676233006,
+        0.000226816174511308, 0.00021632109649356095, 0.0002001941971576086,
+        0.000179685211699168, 0.00015674108875854672, 0.00013432466065290847,
+        0.00011679500751614925, 0.00010934626075384826, 0.00011473678810480568,
+        0.0001303745217934004, 0.00015096817487033376, 0.00017201789822801798,
+        0.00019051019830769263, 0.0002045198002805293, 0.00021285096128304424,
+        0.00021484693244422395, 0.0002103022737508212, 0.00019943042600390965,
+        0.0001828712392757746, 0.00016175350281920825, 0.0001378726191006871,
+        0.00011412057122188632, 9.526785264128003e-05, 8.788789150861065e-05,
+        9.557176284018009e-05, 0.00011425629587944093, 0.00013732566251610604,
+        0.00016011256536512864, 0.0001798143498587204, 0.00019470127578937276,
+        0.00020369035248726447, 0.00020616332355215223, 0.000201892216703809,
+        0.00019101185408785054, 0.00017402099744641067, 0.00015182349981209654,
+        0.00012587049820252956, 9.860932793486303e-05, 7.484507843591551e-05,
+        6.404623785986706e-05, 7.396121737439585e-05, 9.765316106436946e-05,
+        0.0001254359304845669, 0.00015226070351266266, 0.00017553258572325467,
+        0.00019367313470355124, 0.00020563831896627251, 0.00021076096004516345,
+        0.00020869643449883995, 0.0001994022304032647, 0.0001831295003523657,
+        0.00016042412851292163, 0.0001321549932976047, 9.965257278637645e-05],
+    [4.236088680652613e-05, 0.0001271474661700779, 0.0002121286891668419,
+        0.00029743501978222965, 0.0003831979702880339, 0.00046955055048063173,
+        0.0005566276859864667, 0.0006445666830168735, 0.0007335076859022077,
+        0.0008235941579334138, 0.0009149733808895809, 0.0010077969800957494,
+        0.0011022214679491957, 0.0011984088257127878, 0.0012965271109254912,
+        0.0013967511077002046, 0.0014992630161594959, 0.0016042531890241112,
+        0.0017119209228692376, 0.0018224753030720044, 0.0019361361206651168,
+        0.002053134854788436, 0.002173715739736032, 0.0022981369207235322,
+        0.00242667170907216, 0.0025596099471418884, 0.002697259499998163,
+        0.002839947881159114, 0.002988024035399959, 0.003141860288820513,
+        0.0033018544968010898, 0.0034684324004641354, 0.00364205022872818,
+        0.003823197567211438, 0.0040124005339394605, 0.004210225294229386,
+        0.004417281964568775, 0.004634228949319681, 0.004861777775153189,
+        0.005100698481439503, 0.0053518256517668065, 0.0056160651664918715,
+        0.005894401787815107, 0.006187907688750694, 0.0064977520751459145,
+        0.006825212049564592, 0.007171684931373494, 0.007538702229043348,
+        0.007927945564384841, 0.008341264835771644, 0.008780699016460733,
+        0.009248500032385087, 0.009747160253317752, 0.010279444258258368,
+        0.010848425656158095, 0.011457529914560352, 0.012110584380989846,
+        0.01281187691217792, 0.013566224905523457, 0.014379056924044124,
+        0.015256509672518589, 0.016205543796554443, 0.0172340828952671,
+        0.018351181356571915, 0.019567228235566336, 0.02089419655496508,
+        0.0223459502975059, 0.02393862534107584, 0.025691106076810803, 0.027625627097921945,
+        0.029768540246262954, 0.032151302973909585, 0.03481176693944106,
+        0.03779587992177758, 0.04115996622719014, 0.044973831578743434,
+        0.04932506744611303, 0.054325140748539634, 0.06011821157497519,
+        0.0668942459679872, 0.07490912913269455, 0.0845166612867195, 0.0962217196605616,
+        0.11077338688941689, 0.12933918541678222, 0.15385970318774297, 0.18785608930341868,
+        0.23858401063034004, 0.3243712230642978, 0.5139303048952604, 2.201666986012245,
+        0.7894831402796035, 0.5673542186158469, 0.4791957834302699, 0.43141071504746153,
+        0.4021457140652118, 0.3832822804689348, 0.37105041721584103, 0.3634531056340355,
+        0.359341634986298, 0.35802277770620544, 0.35907173553676813, 0.3622359710135397,
+        0.3673837201085132, 0.37447683867512527, 0.3835586390866685, 0.3947527307064376,
+        0.4082721126858556, 0.4244405995806774, 0.4437325064104483, 0.46684366306325226,
+        0.4948227841278032, 0.5293333564947057, 0.5732407438339806, 0.632188289114297,
+        0.7203038759391458, 0.8981030447267384, 2.0308640854959044, 0.9017335617927681,
+        1.8226501395665269, 0.9327400222706231, 0.6058337504042653, 1.0399148537681562,
+        1.9815772165018042, 2.1075801642600376, 0.7094154466796062, 0.5695883740429609,
+        0.8630032871469261, 1.4558760746812194, 2.3914829567721303, 1.709025132248349,
+        0.9091982017885964, 0.6184253642429873, 0.6617516599474684, 0.9692168213948155,
+        1.5541496355746378, 2.112310646015454, 1.6843377056080144, 1.1272115815522479,
+        0.8066641955002926, 0.6721530077861599, 0.7288150181282717, 1.0055347568589186,
+        1.493508438839173, 1.8352369677148783, 1.5951937877824485, 1.228605375682295,
+        0.9647417026230847, 0.8011594439623211, 0.7394100579889984, 0.8210621235431707,
+        1.096600164384563, 1.4848176468841519, 1.5993542478283733, 1.3907141442283275,
+        1.1495611517166622, 0.9575329996921388, 0.6640482841924216, 0.5041772282195045,
+        0.41181388711240713, 0.4114215067235712, 0.4917353034966177, 0.5798544090927241,
+        0.6286760210244802, 0.635147857618657, 0.6118812979236782, 0.5690485442230973,
+        0.5110824282797013, 0.43805772390496167, 0.34741771062664056, 0.23618872596684634,
+        0.10899582493182157, 0.0936681090190486, 0.2436330369156975, 0.39254231164733755,
+        0.5141022406517028, 0.6031500660810103, 0.6643905561954483, 0.7054369961762019,
+        0.7330021517353555, 0.7519168206178649, 0.765355892754512, 0.7753106662958056,
+        0.782986439610218, 0.7890751487050115, 0.7939264427482283, 0.7976477351031462,
+        0.8001556926169654, 0.8011930518611963, 0.8003183833542392, 0.7968724952271963,
+        0.7899237452317837, 0.7781970276638261, 0.7600011119361245, 0.7331922997058555,
+        0.6952547660356073, 0.6436320854244633, 0.5764598219521508, 0.4937106128989253,
+        0.398395442542113, 0.2971700163023278, 0.2004153237048271, 0.12512078334999688,
+        0.10270359256036955, 0.13395612299608758, 0.1761766405788112, 0.21109736981789662,
+        0.23472694360740803, 0.24666965251391185, 0.2475717395782102, 0.23851985959424643,
+        0.22095609961242552, 0.19675874994358478, 0.16838798128279825, 0.1391022079072386,
+        0.11328379029071903, 0.09643658107703, 0.09276465358205949, 0.10057862653694775,
+        0.11374286268196757, 0.12702943838073227, 0.13752431805655135, 0.14388012934572306,
+        0.1456470084093693, 0.1429324321540292, 0.13625296729383637, 0.12647926930756834,
+        0.1148208051462467, 0.10281073738629455, 0.09222483734660096, 0.08479568306162855,
+        0.081605771808499, 0.0824800734124946, 0.086093784187314, 0.09075303334796775,
+        0.09504589620597487, 0.0980467444992946, 0.09927614560984849, 0.0986098998667154,
+        0.09620318542661767, 0.09243317021487031, 0.08784543941640847, 0.08308607435706325,
+        0.07880363756431269, 0.07551942791484709, 0.07349784435035224, 0.07268270286390317,
+        0.0727482648674111, 0.07323828767963939, 0.07371382080951817, 0.07385229097382968,
+        0.07348969084535413, 0.07262223747573193, 0.07138244331472883, 0.06999571987739742,
+        0.06871935994367714, 0.0677700954241638, 0.06725729836045762, 0.06714629239316598,
+        0.06726804280262706, 0.06736947873425837, 0.06718131637095179, 0.06648067671990165,
+        0.06513792783195624, 0.06314795197327543, 0.06064929622858008, 0.057930663093603035,
+        0.055414286494452444, 0.05359371952373458, 0.05290637087032798,
+        0.05356759658994206, 0.055463616503884275, 0.058186996294508304,
+        0.06117857250621207, 0.063871327280751, 0.06577922949641253, 0.06653662803276313,
+        0.06591276918125714, 0.06382020163053591, 0.06032835295960594, 0.05569098450681458,
+        0.050396674931652015, 0.04524345336894082, 0.041379385307963236,
+        0.04008268740604333, 0.04206392830044909, 0.0468974067729911, 0.05340830686404446,
+        0.06038041876928741, 0.06684793923868206, 0.07209605856802628, 0.07560378537830693,
+        0.07700234106485253, 0.07605448470109112, 0.0726500406819268, 0.06681793586605027,
+        0.058767720397116974, 0.04900875245224834, 0.03871263814439888,
+        0.030761009076253072, 0.030604193113612198, 0.040354155828732245,
+        0.05591431275051839, 0.07393270741973773, 0.09277201172497603, 0.11150344718106257,
+        0.1294838205673915, 0.14622038216702873, 0.16132686018078274, 0.17450772928975286,
+        0.1855503997251346, 0.19431852033480634, 0.20074438701672312, 0.20482030067591964,
+        0.20658939253424533, 0.20613656654358095, 0.20358008744074002, 0.19906412845169758,
+        0.1927523799000443, 0.18482266134189196, 0.17546239583911608, 0.16486479271767354,
+        0.15322562545470014, 0.1407405567620523, 0.12760302436688264, 0.11400273770153221,
+        0.10012484303861506, 0.08614981565594468, 0.07225420408745498, 0.058612682917164205,
+        0.04540313751768277, 0.032821703134458195, 0.021142340682300562,
+        0.011085827029986528, 0.00695970814146974, 0.012719626190579989,
+        0.019987338122292985, 0.026462194955894573, 0.03175721764498758,
+        0.03574600576119806, 0.03838016848428004, 0.03965544765497485, 0.03960317106111074,
+        0.038287552946501144, 0.035804174680015545, 0.0322781193156621,
+        0.027861146124422653, 0.022727680463200433, 0.017069647693788687,
+        0.011090404690231792, 0.004998571937801156, 0.0010188681566114654,
+        0.006721067577725202, 0.011964642927625536, 0.016579737684147926,
+        0.02043140004642875, 0.02341421153293709, 0.025454833100393804,
+        0.02651382256564053, 0.02658650248370804, 0.02570280767078783, 0.023926103223190963,
+        0.021351120749603974, 0.01810158402668962, 0.014329461728676142,
+        0.010223918332793465, 0.006080989671388923, 0.0030078908382484074,
+        0.0045992231036665705, 0.008249436180646467, 0.011828482719905583,
+        0.014964983352962433, 0.017504532663044477, 0.01935346404790186,
+        0.02045603925867391, 0.020789536738545725, 0.020362631153821087,
+        0.019214184325667277, 0.017411961909008275, 0.015051926375461237,
+        0.012260760194511413, 0.009211587914497344, 0.006199971233875146,
+        0.004026069784801854, 0.0044199937853427115, 0.00678511207117196,
+        0.009492327896671315, 0.011994532479921865, 0.014087322801906405,
+        0.015662087243597616, 0.016655662632156305, 0.017037621476642128,
+        0.01680617069234147, 0.01598626710481609, 0.014628472570561312,
+        0.012808860032477496, 0.010632322074702598, 0.008247688819721839,
+        0.005907807845684885, 0.0041933799840260565, 0.004183626549424174,
+        0.005789484784854301, 0.007886683514393771, 0.009920877862988977,
+        0.011670193152011557, 0.013021214455696872, 0.013908741862097772,
+        0.014298948829820503, 0.014183785634430545, 0.01357863610515341,
+        0.012521153083206957, 0.011071223923841772, 0.009313801710448802,
+        0.0073708292130048704, 0.005444823964992576, 0.00396561413497735,
+        0.003729536216900322, 0.004870338728073551, 0.006557942554834484,
+        0.008265603953645928, 0.009770859369877039, 0.01096184988686748,
+        0.011774308792140094, 0.01217299335621779, 0.012145453481920813,
+        0.011699500341626092, 0.010861972811146441, 0.009678427198809535,
+        0.008214787256099573, 0.006565058709744109, 0.004880337793035887,
+        0.0034747953560495476, 0.0030213051338530868, 0.0038622857766499653,
+        0.005302036000646073, 0.006808193424749102, 0.008162398223714106,
+        0.009258821398189815, 0.010036259976144084, 0.010458976007188913,
+        0.010510496999315104, 0.010191084473548028, 0.009516237856229947,
+        0.008515445318322228, 0.007231091448921665, 0.00571813737623333,
+        0.0040477640962868905, 0.0023374125034640227, 0.0011106702567781025,
+        0.0020063657655102264, 0.003631853314931177, 0.005218014791522377,
+        0.006635452984643405, 0.007822980313059714, 0.008740734521579517,
+        0.009363765459641037, 0.00968107215729114, 0.0096957156941086, 0.0094252485879177,
+        0.008902509054079128, 0.008177246240181868, 0.007319468637257718,
+        0.006425581622695944, 0.005626093440633973, 0.005081533980301432,
+        0.0049307140928423485, 0.005192168325103894, 0.005742304133712396,
+        0.006410361066379223, 0.007055611243829304, 0.007581640028273173,
+        0.007927205922467026, 0.008056834297564715, 0.00795503833234915,
+        0.007623254181647712, 0.007078569847408504, 0.006354142910967742,
+        0.005502359842369659, 0.004603787402433977, 0.0037871866123066165,
+        0.0032527900838930307, 0.003209491183235686, 0.0036579795917247213,
+        0.004383306911019031, 0.005177538739738464, 0.005910920464660228,
+        0.006506884698051838, 0.006919270064336478, 0.00712147333015642,
+        0.007101755630435007, 0.006861208488055128, 0.006412984332043871,
+        0.005782525134859727, 0.005009488006436882, 0.004153831217085075,
+        0.0033126603827599026, 0.00265769788392611, 0.0024443282976133202,
+        0.0027828567430683536, 0.003463801616450331, 0.004244331453073341,
+        0.004983634579718878, 0.00560487688504915, 0.006062820875636316,
+        0.006330508448227194, 0.006394148374756047, 0.00625106037841917,
+        0.005908823451175928, 0.005385103585400178, 0.00470841058891835,
+        0.003921184754926153, 0.0030898280553974104, 0.0023356683614659587,
+        0.0019000885660259068, 0.0020475130945724535, 0.002652054935927125,
+        0.0034129954125011537, 0.004160618039174682, 0.004812378613320629,
+        0.0053219241246424895, 0.005660926206839106, 0.005813021773988015,
+        0.005771625867869575, 0.005539038002204197, 0.005126048784032016,
+        0.004551951394516129, 0.0038454811581753053, 0.0030487557641549028,
+        0.0022323889712534363, 0.001555053934573985, 0.0013820244483824635,
+        0.0018647927245654325, 0.0026169751541348036, 0.003391667562237052,
+        0.004092750609174704, 0.004671855888343551, 0.005099143880474207,
+        0.0053555938548580165, 0.005430690919060571, 0.0053216091034761544,
+        0.005032811913134024, 0.004575766362235034, 0.003968792576287113,
+        0.003237479031333521, 0.002417526355828413, 0.0015702015819180062,
+        0.0008904577577575504, 0.001019515770582433, 0.0017764673342482138,
+        0.002615367215249726, 0.0034030157238597192, 0.004089746218596072,
+        0.004644900923657058, 0.005046756183329725, 0.005280424719444133,
+        0.005337373229930642, 0.0052152723637186715, 0.004917838435462897,
+        0.004454564479974493, 0.003840318853266278, 0.0030948381983601997,
+        0.002242247281248946, 0.0013114560516539577, 0.0003571846713378623,
+        0.0007170968213386986, 0.001703278603247245, 0.002657839781066764,
+        0.003543942261497262, 0.0043332035945943415, 0.0050008935956908,
+        0.005525942800042434, 0.005891272284284542, 0.006084070268212456,
+        0.006095951356194948, 0.005922992216644992, 0.0055656631550920314,
+        0.005028707598037331, 0.004321104605871627, 0.003456559060979605,
+        0.002456591360085812, 0.001372722191556064, 0.0006413677713367585,
+        0.0015593392572019003, 0.002933902576986537, 0.004405473923167134,
+        0.005922596193037228, 0.007457813849367832, 0.008988532247137592,
+        0.010493952515558501, 0.011954315721124936, 0.013350673629037633,
+        0.014664824544692322, 0.015879326538540052, 0.016977568517581303,
+        0.017943897361999573, 0.018763801624799414, 0.019424149134237914,
+        0.01991347088898928, 0.020222278581711557, 0.020343398834714088,
+        0.020272304293963046, 0.020007420349237998, 0.019550386491236697,
+        0.018906253122753344, 0.018083597893379016, 0.017094550226623602,
+        0.015954718678089484, 0.014683023452890248, 0.013301446911110624,
+        0.011834731142760875, 0.010310081400511685, 0.008756998539459349,
+        0.007207525986147207, 0.00569766778637332, 0.00427230409280773,
+        0.003001831982154118, 0.002038676357309148, 0.0017022353964486095,
+        0.0020780316586231154, 0.002731433643868508, 0.003377845716144721,
+        0.003919614566600406, 0.0043227721776774395, 0.004576473562647728,
+        0.004681123625285748, 0.004644255955600472, 0.004478797840256475,
+        0.0042022400545720425, 0.003836323433733138, 0.0034072829133076437,
+        0.002946990333276577, 0.0024955693522248517, 0.002105383310015479,
+        0.0018408984064368357, 0.0017561656543653111, 0.00184856641623937,
+        0.0020546908911115453, 0.0023010321678995243, 0.00253505257814571,
+        0.002725449263618512, 0.0028553545078543042, 0.0029174006407798685,
+        0.002910952006219544, 0.0028406007228070056, 0.0027153332325496374,
+        0.0025480740733209288, 0.002355443033704044, 0.0021575085075907687,
+        0.0019770058047753284, 0.0018369214768144595, 0.0017552906365924917,
+        0.0017383960865582325, 0.0017775492325323604, 0.0018532819741638419,
+        0.0019433617152246553, 0.00202872580432431, 0.0020957487768912967,
+        0.0021363021408369663, 0.0021470603353105234, 0.0021287093207105843,
+        0.002085218774922929, 0.0020231423003220232, 0.0019508420476646794,
+        0.0018775151687272433, 0.0018119381304522193, 0.0017609960230550942,
+        0.0017283327444193293, 0.0017136670446241562, 0.001713173771830175,
+        0.001720811677241066, 0.0017300231886905467, 0.0017352144049048366,
+        0.0017327249716308374, 0.0017212783286428017, 0.0017020085476570639,
+        0.0016781369511280676, 0.0016543162396180588, 0.0016356485976472411,
+        0.0016264673405769622, 0.0016291401642538142, 0.001643284804618793,
+        0.0016657092135188695, 0.001691081449961658, 0.0017130293360505646,
+        0.001725294263712695, 0.0017227000647223145, 0.0017018773205570758,
+        0.0016617919734117177, 0.0016041531835717258, 0.0015337408032314167,
+        0.0014585918728617546, 0.0013897756131747122, 0.001340179080675768,
+        0.0013216726911377623, 0.0013410306744744997, 0.0013968969096301476,
+        0.0014801991432456655, 0.001577463766654298, 0.0016743866950337644,
+        0.0017580606269461025, 0.0018179355114893978, 0.0018461263141572764,
+        0.0018375171103106823, 0.0017898845259953064, 0.0017041613895696452,
+        0.0015849695244155228, 0.001441635014845225, 0.001289974421205289,
+        0.0011547175077199566, 0.0010697769623244163, 0.0010680766871520699,
+        0.001159510351034018, 0.0013233167818094652, 0.001526062360088045,
+        0.0017377917826394773, 0.0019356543828186307, 0.00210252090228562,
+        0.0022253698627578066, 0.0022943426141048807, 0.002302322014953355,
+        0.002244837399272037, 0.0021202182372376172, 0.0019300864927852231,
+        0.0016806227526215726, 0.0013860942018223527, 0.0010798852567416957,
+        0.000848015259633559, 0.0008571298902619882, 0.001160520833194306,
+        0.0016295581664854872, 0.0021715099209752616, 0.0027439628747816676,
+        0.0033233419701526115, 0.0038930361126363064, 0.004439662795609926,
+        0.004951851893111713, 0.005419859493104124, 0.005835472353607961,
+        0.006192008899023738, 0.006484338948468298, 0.006708888639326746,
+        0.006863616109747556, 0.006947952889512407, 0.006962711195414183,
+        0.006909960599438134, 0.006792879709972893, 0.006615589942367955,
+        0.00638297929560064, 0.006100524348566911, 0.005774118461234213,
+        0.00540991343048577, 0.005014180654489092, 0.0045931962875606315,
+        0.004153153077579581, 0.0037000998239986507, 0.003239908121171678,
+        0.0027782661370683824, 0.00232070277708733, 0.0018726592687831173,
+        0.0014396737896527926, 0.0010279468940622791, 0.0006466962460489867,
+        0.0003242589095582372, 0.00023871279349740613, 0.000456430868096298,
+        0.0007017345346162422, 0.0009191530325328788, 0.0010985987469391836,
+        0.0012365137964513784, 0.0013314550610923023, 0.0013832282044116495,
+        0.0013926562806050387, 0.001361497606535073, 0.001292394974757557,
+        0.0011888197096973354, 0.001054997764882868, 0.0008958137954950919,
+        0.0007166931978673059, 0.0005234644492533562, 0.00032220589762169344,
+        0.00011908747566911634, 7.989402009213566e-05, 0.00026877942098183226,
+        0.00044227014263683575, 0.0005955330588746847, 0.0007244633230625482,
+        0.0008257855732733759, 0.0008971426086617934, 0.0009371563479961868,
+        0.0009454587327978956, 0.0009226921655068479, 0.0008704810385266824,
+        0.0007913790146371822, 0.0006888034332150343, 0.0005669879164783292,
+        0.0004310614917686239, 0.000287787823150808, 0.00015139966885466594,
+        0.0001024142277396559, 0.00020871143413856246, 0.000338205365604867,
+        0.00045899955186100955, 0.0005634380456111334, 0.00064738211193243,
+        0.0007081118941991338, 0.0007439626587868596, 0.0007542414889899917,
+        0.0007391965480972489, 0.0006999896099563615, 0.0006386658170719737,
+        0.0005581395104918386, 0.00046226316947189835, 0.000356217048753114,
+        0.000248265465278335, 0.00015847818327403599, 0.00014275543355348486,
+        0.00021469030135229218, 0.0003112700401961987, 0.0004052880607988523,
+        0.00048765929492069137, 0.0005538572548960047, 0.0006011455211992777,
+        0.0006279213106964787, 0.000633523911692787, 0.0006181639561044091,
+        0.0005828873768285741, 0.0005295589993797661, 0.0004608916062712462,
+        0.00038062100095008776, 0.0002941760491553974, 0.0002111932691305567,
+        0.00015410525851650603, 0.0001600728430770672, 0.00022072276440506097,
+        0.00029780817353087776, 0.000372895396158503, 0.00043833391576796906,
+        0.0004900915741853944, 0.0005257617476033316, 0.0005439890745415895,
+        0.0005442790243882854, 0.0005269233352243419, 0.0004929671759064915,
+        0.00044420845332926256, 0.00038326686902935726, 0.00031385832673282914,
+        0.00024172914538075343, 0.00017775406894911347, 0.00014472555262243553,
+        0.00016465320263676082, 0.000219988199457526, 0.0002847475974876962,
+        0.00034642374928795563, 0.00039916235824751043, 0.0004396965480308942,
+        0.00046607191866818035, 0.00047723651388134917, 0.0004728931423806082,
+        0.00045343862511007727, 0.0004199399817358474, 0.00037414825554525584,
+        0.0003186009378660477, 0.00025698672100620457, 0.00019535170847971407,
+        0.00014580262718683464, 0.00013081680218513507, 0.00016031687404037174,
+        0.00021271511478557686, 0.000269293189038694, 0.0003214204662583781,
+        0.0003647673394327096, 0.0003968045411405588, 0.00041600971444534637,
+        0.0004215991140382659, 0.00041342349442241767, 0.00039191837323456245,
+        0.00035807648129584246, 0.0003134448204991845, 0.00026019021931188765,
+        0.0002014025577368453, 0.0001423578709283028, 9.601773812465252e-05,
+        9.232695707490661e-05, 0.00013363644432684682, 0.0001885894506397593,
+        0.0002427354838459446, 0.00029074294652016674, 0.00032988542947604146,
+        0.0003585146129444642, 0.0003756744433516975, 0.0003809915311566289,
+        0.00037464573633782866, 0.0003573726980020762, 0.00033049595069584316,
+        0.0002960159430954756, 0.0002568251296133064, 0.00021717947927435167,
+        0.00018349687525035224, 0.00016449520502646807, 0.00016699649310601336,
+        0.00018879471075804562, 0.00022100500506791, 0.00025549040132028287,
+        0.00028693377904104815, 0.0003120618222228413, 0.0003288680262388441,
+        0.000336203319356272, 0.0003335836472358389, 0.000321101623254337,
+        0.00029939334388228616, 0.0002696535439480632, 0.00023373436099362638,
+        0.0001944425743559079, 0.00015632244757922553, 0.00012724571865126895,
+        0.00011832787619388876, 0.0001339333434250008, 0.00016499344068830098,
+        0.00020087984638792201, 0.000235210877930783, 0.00026442566522287764,
+        0.00028640118110923827, 0.0002998514239748358, 0.0003040893648088131,
+        0.0002989299899845473, 0.0002846505695764236, 0.0002619825551984788,
+        0.00023214227488243307, 0.00019695023097616738, 0.00015919417662664152,
+        0.00012366991932522713, 9.943085818464881e-05, 9.848463424724751e-05,
+        0.00012075590167405927, 0.0001539121993107862, 0.00018870285744661836,
+        0.00022038506277482575, 0.0002463531670634725, 0.0002650274224853618,
+        0.0002754541610686618, 0.00027715890607164003, 0.0002700883957356019,
+        0.00025458709929413234, 0.00023139491516383946, 0.00020167894731642293,
+        0.00016715746392528566, 0.00013051275837648571, 9.67548267999345e-05,
+        7.662046324250986e-05, 8.317968641942224e-05, 0.00011061970043106747,
+        0.00014482776778540447, 0.0001784105234629397, 0.00020791762980860304,
+        0.00023141028480950233, 0.00024767514344123756, 0.00025597633496034206,
+        0.0002559699305683321, 0.0002476704739813919, 0.0002314358070844118,
+        0.00020796351135199712, 0.00017831169755653124, 0.0001439985483695453,
+        0.00010739376499869555, 7.336819181048615e-05, 5.523835423506359e-05,
+        6.914037433414583e-05, 0.00010129363833271749, 0.00013666863776486696,
+        0.00016980455784821891, 0.00019825312576517593, 0.00022054702855216655,
+        0.0002357153683181075, 0.0002431510838184027, 0.00024256960487115884,
+        0.0002339923944554399, 0.0002177359990065608, 0.0001944023258140841,
+        0.0001648757577849448, 0.00013035446028194082, 9.254187835409896e-05,
+        5.4839381568488145e-05, 3.2363290821119446e-05, 5.41580759327863e-05,
+        9.169422650356472e-05, 0.00012940538721393995, 0.00016385698072068878,
+        0.00019337233627312076, 0.00021678917630294983, 0.0002332549259319234,
+        0.00024218594375383155, 0.00024326058766945279, 0.0002364172574593762,
+        0.0002218492132569446, 0.00019999362550918734, 0.00017151434395070995,
+        0.0001372790029982819, 9.833290242771808e-05, 5.5883573246580663e-05,
+        1.1717673614169894e-05], [1.303928283826924e-06, 3.914007704639663e-06,
+        6.530763377677412e-06, 9.158670147828548e-06, 1.1802238750504755e-05,
+        1.4466031090841244e-05, 1.715467457004267e-05, 1.9872877843336646e-05,
+        2.26254463539105e-05, 2.541729858214717e-05, 2.8253482865024185e-05,
+        3.1139194993834306e-05, 3.4079796365184284e-05, 3.7080833292808674e-05,
+        4.014805707782315e-05, 4.328744536307512e-05, 4.650522464038324e-05,
+        4.9807894142384576e-05, 5.320225133248313e-05, 5.6695418934227646e-05,
+        6.0294874040296244e-05, 6.400847906189377e-05, 6.784451506952355e-05,
+        7.181171759808983e-05, 7.59193151854245e-05, 8.017707088860734e-05,
+        8.459532721974044e-05, 8.918505461599882e-05, 9.39579040368051e-05,
+        9.892626384508248e-05, 0.00010410332175498771, 0.00010950313194638162,
+        0.00011514068825530068, 0.00012103200378526667, 0.00012719419782535326,
+        0.00013364559063838897, 0.00014040580715754934, 0.0001474958903241348,
+        0.00015493842535312788, 0.000162757675834648, 0.00017097973326589945,
+        0.00017963268120158767, 0.0001887467759601194, 0.00019835464547392974,
+        0.00020849150868920718, 0.00021919541739694464, 0.00023050752389490036,
+        0.0002424723765123003, 0.0002551382474743862, 0.0002685574960036443,
+        0.0002827869716715388, 0.0002978884627925494, 0.0003139291953347247,
+        0.000330982389147515, 0.0003491278786944469, 0.00036845280659856107,
+        0.00038905240017714134, 0.00041103084140861504, 0.0004345022437715847,
+        0.0004595917502959535, 0.0004864367699371783, 0.0005151883721240321,
+        0.0005460128622390362, 0.0005790935645709726, 0.0006146328436958786,
+        0.0006528544005978362, 0.0006940058855266281, 0.0007383618772861561,
+        0.0007862272875725981, 0.0008379412587774913, 0.0008938816367156932,
+        0.0009544701147682266, 0.0010201781645550678, 0.001091533889187399,
+        0.0011691299637898328, 0.0012536328591108438, 0.0013457935865103315,
+        0.001446460249679783, 0.0015565927513001717, 0.001677280079823237,
+        0.0018097606935486984, 0.0019554466406820816, 0.0021159522029047424,
+        0.00229312803813698, 0.002489102041005734, 0.002706328446105975,
+        0.002947647098404871, 0.0032163553283293404, 0.0035162955407687397,
+        0.003851962516653663, 0.004228635587252984, 0.004652542417226189,
+        0.005131063236209225, 0.005672987234245254, 0.0062888367821635465,
+        0.006991280639763491, 0.0077956650191492016, 0.008720702410417459,
+        0.009789373959317303, 0.01103012456757379, 0.01247846474628363,
+        0.014179146308464206, 0.016189161350911866, 0.018581945011257154,
+        0.021453376234467324, 0.02493053050194517, 0.02918476465387159,
+        0.03445184895171824, 0.041064018427904435, 0.04950315399151081,
+        0.06049365581444694, 0.0751755588599354, 0.09545624814646479, 0.12481572639954466,
+        0.17050813381820737, 0.251624967977341, 0.4525644663056859, 2.9268183470752502,
+        0.26742841214894314, 1.4405068668756176, 1.7319109302554219, 0.6022189923032285,
+        0.11918908612018428, 0.9075457111596222, 2.7568803779814557, 2.143635341000016,
+        2.307928166384319, 3.8296188274486513, 6.511405047916822, 3.7557713811330458,
+        1.7301317564091783, 1.4174047667823366, 1.518019997988656, 1.7011193040077466,
+        2.0066551951261142, 2.496087200881536, 2.690280099676185, 1.7934007461360537,
+        1.1486968295003923, 0.9786854251602503, 1.0634018829389313, 1.2996158217999134,
+        1.6848867625810486, 2.190755304960999, 2.343817962170848, 1.8034227489485344,
+        1.2720000745536761, 0.9784650564676621, 0.8863338463972367, 0.9666416197038336,
+        1.2109428796002661, 1.6172289854590276, 2.0319933092111655, 1.9917007597871146,
+        1.5826567499747455, 1.2133691408473815, 0.9682055743696157, 0.6662809479363695,
+        0.5671800744041452, 0.5835094312510376, 0.6676093339391966, 0.7563615928454934,
+        0.797147155793382, 0.7787435401510093, 0.7205910833971251, 0.6433344782887578,
+        0.5576357875888097, 0.46635550050846836, 0.36853721889744806, 0.2631458615775169,
+        0.15925870242095075, 0.13065755894575753, 0.23995771534172497, 0.38357791078561515,
+        0.5133263938683388, 0.611907488758752, 0.6779689877242601, 0.7186049992547229,
+        0.7423605649708297, 0.755991302066854, 0.764005277781508, 0.7691755528583387,
+        0.7731304270964855, 0.7767858863219678, 0.7806195863913737, 0.7848323450818908,
+        0.789436550342085, 0.7942967595446756, 0.7991365983018694, 0.8035185462639083,
+        0.8067983574061749, 0.8080533868438585, 0.8059851924195838, 0.7988051367442173,
+        0.7841344832512249, 0.7589966591224875, 0.7200476312924776, 0.6642349114444555,
+        0.589967192047481, 0.498477197047994, 0.3945594008367929, 0.2860117156428788,
+        0.182591140637376, 0.09955874844638445, 0.07995722829689189, 0.12617660766064612,
+        0.1789116135752899, 0.22239149804057026, 0.2539654439876384, 0.27325834033379626,
+        0.2804918736645541, 0.27620300216655513, 0.26127535921789813, 0.23703685754305645,
+        0.2053355371030997, 0.16859025622541032, 0.12995175656308833, 0.09406247548310022,
+        0.06948175069420752, 0.06807218509792895, 0.08675381570222766, 0.11151476615417799,
+        0.1347958781144704, 0.1535858863718187, 0.16655142456899916, 0.1730963939629722,
+        0.17308284646182528, 0.1667514423728098, 0.15469991843572317, 0.13787500264442906,
+        0.1175828185157224, 0.09558162304949043, 0.07443301939100941, 0.058371690561665884,
+        0.05335376119382439, 0.06104779663877278, 0.07564320055841926, 0.09151948838587436,
+        0.10571490404888002, 0.11673239417322578, 0.12377998997040181, 0.12648532631819376,
+        0.12479223393731527, 0.11891717850519382, 0.10932461658821883, 0.0967169883275456,
+        0.08206272101868756, 0.06672794939524894, 0.052850124892974436,
+        0.04392867102302375, 0.04371419699109654, 0.05159409034936942, 0.06326154471764708,
+        0.07533067502664595, 0.08595209496930413, 0.09411457458408193, 0.09925445640654583,
+        0.10109882317177402, 0.09959974215683963, 0.0949009470038938, 0.08731936581004383,
+        0.07734355609715989, 0.0656685356260266, 0.0533211957647377, 0.04200566012767092,
+        0.03471005881188232, 0.03486498209787287, 0.04202788499361823, 0.052448512561397716,
+        0.06327518387047368, 0.07297833128226111, 0.08070822368764619, 0.08596486366848514,
+        0.08846933852690339, 0.08811089392189993, 0.08492182459858279, 0.0790653296174319,
+        0.07083538029369991, 0.06067901143514954, 0.049276916866748455,
+        0.03780149746136979, 0.028678612411055904, 0.026353693387319292,
+        0.032660430166665914, 0.04351092586203189, 0.05537737438247732,
+        0.06657671612756375, 0.07621957139015496, 0.08374831944671855, 0.08878734690113764,
+        0.09109106821349805, 0.09052311369807996, 0.08704667323773731, 0.08072061124775223,
+        0.07170255044729973, 0.060268752431288916, 0.04689045270874706,
+        0.03256282763589225, 0.02062260837415154, 0.0216448680905585, 0.03623702651342847,
+        0.05492539282287931, 0.07459510725817327, 0.09417281129401107, 0.11303621385840446,
+        0.1307244602134592, 0.14687350265711518, 0.16120005880889413, 0.1734968704408812,
+        0.18362919232160646, 0.1915296166608907, 0.19719078673688645, 0.20065652001306877,
+        0.20201219547572022, 0.2013752572484048, 0.19888650171891664, 0.19470255661527286,
+        0.18898970543192042, 0.1819190082422687, 0.1736625429972446, 0.16439054158932426,
+        0.15426920907203912, 0.14345906980916998, 0.13211375491069619, 0.12037920552326699,
+        0.10839329795851026, 0.09628589083280224, 0.08417925582836931, 0.07218879718837043,
+        0.06042391224500668, 0.048988815681131545, 0.03798315832586126,
+        0.027502327465718783, 0.017637478054925465, 0.008476409164889377,
+        0.00039275291245185746, 0.007461181616409788, 0.014075295571100429,
+        0.019725750326075903, 0.02437061973602896, 0.02798412318207086,
+        0.030556760820269237, 0.03209667387269532, 0.032630934553850376,
+        0.03220651085022658, 0.030890776733450653, 0.028771550831853822,
+        0.025956885559075927, 0.022575384215469455, 0.018779298438884623,
+        0.014757390198015894, 0.010782852420146543, 0.007397339048185482,
+        0.005889553851843274, 0.0072747909369596814, 0.010106437795743313,
+        0.013121144400589617, 0.01585332096837559, 0.018108947701059547,
+        0.019789573967542096, 0.02084504941876239, 0.02125876728514987,
+        0.021042147529772244, 0.02023215176935826, 0.018890173846188858,
+        0.01710241216676003, 0.014983290548174964, 0.012685942490304166,
+        0.010428281115771107, 0.008543735986614643, 0.007504937373034185,
+        0.007669980557144144, 0.008843553094854541, 0.010498423777532743,
+        0.0122197166839264, 0.013765303275613256, 0.014998493300748508,
+        0.015842610094525176, 0.016259727444303734, 0.016241024878011642,
+        0.01580223262788995, 0.014981590191142006, 0.013839672110201894,
+        0.012461596189233091, 0.01096308279731642, 0.00950189871076409,
+        0.008290158096312181, 0.007576208736918487, 0.007534471216968543,
+        0.008118059782664167, 0.00909263211012225, 0.010203422934030799,
+        0.011261038189041147, 0.012142221762317551, 0.012771439186634016,
+        0.013106933882292112, 0.013132690092542717, 0.012854124335779734,
+        0.01229598850386745, 0.011501876400515604, 0.010535360920897333,
+        0.009483068535808669, 0.008459196684262546, 0.007606550167801105,
+        0.007078020856081788, 0.006978670214278632, 0.007297296869559587,
+        0.0079107250322881, 0.008658625709191296, 0.009402793983716632,
+        0.010043333819247793, 0.01051444485737631, 0.010777115050494022,
+        0.010813671806184083, 0.010624441190641305, 0.010225950112084123,
+        0.009650281809562152, 0.008945445838016984, 0.008176622353778052,
+        0.007427356445133984, 0.006797104716768339, 0.006386826210248607,
+        0.006265547473855778, 0.0064336333891584375, 0.006820687051059294,
+        0.007322668745188926, 0.007840131090930954, 0.008295358241833948,
+        0.008634366277882891, 0.00882389187556746, 0.008848105226535782,
+        0.008706222982367519, 0.008411016542002193, 0.007987998053043496,
+        0.007475048703248116, 0.006922067586901144, 0.0063895439534673165,
+        0.005943583983192382, 0.005643909830769482, 0.005524767327661947,
+        0.005578925951147255, 0.00575944658308335, 0.005998793813334205,
+        0.006229646615699604, 0.006396870796296128, 0.0064614229853855966,
+        0.006400560577644937, 0.006207369154946551, 0.005891036883839026,
+        0.005478656414325997, 0.005019103878910924, 0.0045882873760709824,
+        0.004289353536277008, 0.004230119980965287, 0.0044685453871009945,
+        0.004974567267486215, 0.0056587115046330275, 0.006423567998594428,
+        0.007188345036496613, 0.007891396058666525, 0.008486651053117245,
+        0.008940345066837704, 0.009229029318347286, 0.009338526340147342,
+        0.009263431137683131, 0.009006921538125788, 0.008580799646744991,
+        0.008005833487560496, 0.007312636580932132, 0.006543536974062704,
+        0.005756040497058659, 0.005027828498866591, 0.004458900657070389,
+        0.004154689305851637, 0.00417279737343901, 0.0044737900980606595,
+        0.0049483153925840755, 0.005482449997008497, 0.005989541350738078,
+        0.0064110923816404885, 0.006709829704115098, 0.006864025746780565,
+        0.00686407536953778, 0.006710648562662341, 0.006413851776787372,
+        0.005993175892794173, 0.005478321069967213, 0.004911227813131889,
+        0.0043494995273194205, 0.0038694488647638306, 0.0035601277693502035,
+        0.003492271560937562, 0.0036709873036436004, 0.004029435958945272,
+        0.004474576360552899, 0.0049258833704349395, 0.00532511208374459,
+        0.0056330134915670545, 0.0058246564082645716, 0.005886219051377723,
+        0.005813159429442866, 0.005609311515540137, 0.005286660153053644,
+        0.004865818198345313, 0.004377511563091002, 0.00386559403912564,
+        0.0033915548573898256, 0.0030362844210832214, 0.0028835991039865704,
+        0.0029725310189658996, 0.0032628964588861985, 0.003667831600434089,
+        0.004104032513473097, 0.004510007692781693, 0.004844014280145878,
+        0.0050787039882492415, 0.00519735609674593, 0.005191762369588804,
+        0.005061156526801586, 0.004811802269659826, 0.0044571474444683665,
+        0.0040187591355817795, 0.003528668466444835, 0.0030342359408216764,
+        0.0026058324989769615, 0.0023386381826164156, 0.002317270303327166,
+        0.0025426145417102295, 0.0029290919982982735, 0.0033785145405949685,
+        0.0038189165937795523, 0.004203194375835861, 0.0045006886284961155,
+        0.004691653131717028, 0.004764408162159213, 0.004713963701708097,
+        0.004541393198391905, 0.004253664228370291, 0.003863942458781186,
+        0.0033927570049548817, 0.002871160941582949, 0.0023486904832976233,
+        0.001910595987828269, 0.001691592541727934, 0.0017984683535820735,
+        0.0021710647880338633, 0.0026663293054250436, 0.003181564269009294,
+        0.003657745372866286, 0.00405916432256138, 0.004362525487730219,
+        0.004552387811468303, 0.004619285610940685, 0.004558919995926553,
+        0.004371788860672774, 0.004063031248911777, 0.003642483308483173,
+        0.003125206597946005, 0.0025334504399351235, 0.0019037424480143784,
+        0.001315633124715977, 0.0009947913684019098, 0.001236025091040321,
+        0.0018258000529450587, 0.002501172889814588, 0.0031652939946085665,
+        0.0037750616347840926, 0.004303660900394214, 0.004731385764560913,
+        0.005043050099634622, 0.005227161933826951, 0.005275623097037714,
+        0.005183575364236418, 0.0049492616986890735, 0.004573855719342547,
+        0.004061246952859572, 0.003417788700217292, 0.0026520412270463877,
+        0.0017746592446296198, 0.0008000174210764633, 0.00029883001083930497,
+        0.0014216825835169824, 0.0026212176866436737, 0.003868071924435691,
+        0.005147003229400656, 0.006443613948997239, 0.007743875393476912,
+        0.00903407816651949, 0.010300815066463943, 0.011530954195570473,
+        0.012711604907064652, 0.013830088799087235, 0.014873929787108752,
+        0.01583087612167935, 0.016688964342900667, 0.017436631211316916,
+        0.01806287515247335, 0.01855746416975897, 0.01891118294277139, 0.019116108264604127,
+        0.01916589930801206, 0.01905608756097236, 0.01878435065679205, 0.018350754695416995,
+        0.017757950914962607, 0.017011314617920114, 0.0161190169860382,
+        0.015092023788406695, 0.013944019065473262, 0.012691257011776667,
+        0.01135235250586136, 0.009948032857508492, 0.00850089838362107,
+        0.007035302428479609, 0.005577651782494924, 0.004158128424492699,
+        0.00281813612567935, 0.0016494325059745625, 0.001033633493098724,
+        0.0015060879969919863, 0.002346824370326825, 0.0031535644039926754,
+        0.0038440014737320806, 0.004392427785784198, 0.004788587644475687,
+        0.005029560995102944, 0.005117474629733489, 0.005058622838926407,
+        0.004863002247428995, 0.0045439982323536325, 0.004118186478438867,
+        0.0036053572683977585, 0.0030291211048301477, 0.002419182003576564,
+        0.001818890573946574, 0.0013100561834593248, 0.0010641259905476306,
+        0.0012243822643128886, 0.0016308791861217294, 0.002093531166017538,
+        0.0025284494069824364, 0.002899062944470115, 0.003186494431174713,
+        0.0033803844272333504, 0.003475835921380031, 0.003472233039477465,
+        0.003372701354058191, 0.003183831178346052, 0.002915582657059496,
+        0.002581472902281628, 0.002199419031151783, 0.0017942969847273272,
+        0.0014051114433535116, 0.0011020038898911912, 0.0009949838443940745,
+        0.0011341780731278324, 0.0014243094715075527, 0.0017588284885119835,
+        0.0020797947607504572, 0.0023574058301839085, 0.0025747620775832375,
+        0.0027218589058283175, 0.0027932973475130554, 0.0027873470719668985,
+        0.002705529285146757, 0.0025524387088147783, 0.0023357544620511714,
+        0.002066561358636292, 0.0017603906266795528, 0.001440090470822843,
+        0.001143189091967839, 0.0009356106646400126, 0.0009023932518794546,
+        0.0010552302530257112, 0.0013115243673629585, 0.0015956380494602945,
+        0.0018653935607094174, 0.002097499554326321, 0.0022779241400390495,
+        0.0023979412443870607, 0.002452564219608404, 0.0024398975615440147,
+        0.0023608605430560283, 0.0022190974767610505, 0.002021061808111708,
+        0.0017764230929001206, 0.0014992687474058271, 0.0012114324941795377,
+        0.0009512718500546916, 0.0007891931109422979, 0.0008063267776515057,
+        0.0009892849003400495, 0.0012507608255667834, 0.0015274576814468383,
+        0.001785911962058575, 0.0020070649658363144, 0.0021787904411454603,
+        0.002293072292101524, 0.002344934838415584, 0.002332024262311431,
+        0.0022544495251387744, 0.0021147552906043417, 0.0019180321072621213,
+        0.001672317351090073, 0.001389797096839887, 0.001090490485534009,
+        0.0008140952176465471, 0.0006497895804311562, 0.0007113366235492977,
+        0.0009571315830235206, 0.0012717500733912684, 0.0015939314445383521,
+        0.0018946999989102405, 0.002156929012691297, 0.0023686435157213147,
+        0.0025208995428075906, 0.002607076144674396, 0.0026226398355057657,
+        0.002565078110726436, 0.0024339023997733533, 0.002230709820464565,
+        0.001959381141912414, 0.0016267154086170956, 0.0012447085510126324,
+        0.0008408255051831858, 0.000520241562302689, 0.0006095025642993673,
+        0.001053147005161889, 0.001594588229182483, 0.002164605745335808,
+        0.0027391642257526246, 0.0033037648448791365, 0.0038471076072479323,
+        0.004359608673740935, 0.004833013743309111, 0.005260315958042489,
+        0.00563576075599468, 0.005954865277015058, 0.0062144250109811856,
+        0.006412497004313178, 0.006548356147099843, 0.006622424727854051,
+        0.006636177599629126, 0.006592026711989141, 0.0064931897309722965,
+        0.006343548110086758, 0.006147500332773038, 0.005909816127442804,
+        0.005635497256115609, 0.005329649991919019, 0.004997373630007801,
+        0.004643668341739171, 0.004273364420454869, 0.0038910735493244324,
+        0.003501161239219606, 0.003107738155718791, 0.002714666805597603,
+        0.0023255791095268957, 0.001943899847755464, 0.0015728709016423032,
+        0.001215571665727932, 0.0008749321132719808, 0.0005537379161723546,
+        0.0002546477505221869, 2.1938978401072233e-05, 0.0002683084787686192,
+        0.00048758595858497096, 0.0006766193618761849, 0.0008341096342357361,
+        0.0009592014247646064, 0.001051511665402141, 0.0011111668036305746,
+        0.001138831757097178, 0.00113572711365011, 0.0011036336712800636,
+        0.0010448855080217212, 0.0009623560457978835, 0.000859448297559415,
+        0.0007401172400026451, 0.0006090016870842769, 0.0004719161007501211,
+        0.0003376793267856627, 0.0002255893364725071, 0.00018518489694625357,
+        0.00024581864759725736, 0.00034840061060516936, 0.00045414463330101836,
+        0.0005499455355613751, 0.0006302030985044642, 0.000691914047700495,
+        0.0007334105693438054, 0.0007539697535230836, 0.0007536683016845892,
+        0.0007333177986633725, 0.0006944346333137407, 0.0006392410989089123,
+        0.0005707245344185808, 0.0004928302092466889, 0.0004109721073127532,
+        0.0003332580737150976, 0.00027274726339805597, 0.0002473822141270379,
+        0.0002663958555384372, 0.0003171355382102056, 0.000380522352984877,
+        0.000443876026834627, 0.0005001127067803097, 0.0005451874113675017,
+        0.0005767543597214391, 0.0005935821251734913, 0.0005952962460449546,
+        0.0005822617031582671, 0.0005555339250466486, 0.0005168599084762962,
+        0.00046874374467464165, 0.0004146238487569296, 0.00035924294810243517,
+        0.0003092417072894346, 0.00027345369060519234, 0.0002607374839229037,
+        0.0002738509106914639, 0.00030646304632915333, 0.0003486335112515317,
+        0.0003921460787525146, 0.000431485223477867, 0.0004631518874762034,
+        0.00048500542343580844, 0.000495876749960967, 0.0004953652231621199,
+        0.0004837369527952166, 0.00046188278445923113, 0.00043132362444106055,
+        0.0003942715722423494, 0.0003537689416570887, 0.00031391160016133935,
+        0.0002800219082357152, 0.00025818338533254906, 0.0002531293252134962,
+        0.0002651608164394017, 0.0002897669575808527, 0.00032062614408483495,
+        0.0003522122327336665, 0.0003805085469570284, 0.0004028153720077187,
+        0.00041743545842519837, 0.0004234490427135255, 0.0004205807358277552,
+        0.00040912894971371276, 0.00038993861152661894, 0.0003644116660726538,
+        0.000334559550533219, 0.0003030992450806182, 0.00027355003287192107,
+        0.00025013402944605643, 0.00023702272543240112, 0.00023664627924268512,
+        0.0002481763946595781, 0.00026799476812833765, 0.0002916173709350081,
+        0.00031512499510388554, 0.0003355887565698721, 0.0003510005589352506,
+        0.00036010650460787313, 0.0003622735500386127, 0.0003574049313655698,
+        0.00034589423842744637, 0.0003286093849937172, 0.0003069030705183107,
+        0.00028264665503385377, 0.0002582674397145225, 0.00023670972868250747,
+        0.00022112192685660518, 0.00021403124237356916, 0.0002162050378083314,
+        0.00022615875463255982, 0.00024090369586495867, 0.0002571643049465514,
+        0.0002721450082702545, 0.0002837576582651687, 0.0002905948151375861,
+        0.00029184854328048244, 0.00028724789545054024, 0.0002770321577397501,
+        0.0002619641919371416, 0.00024338980423811138, 0.00022334484848637835,
+        0.00020466624568367823, 0.00019090593762459852, 0.00018560351350205723,
+        0.00019073875605811263, 0.00020553812406031433, 0.00022706807551317273,
+        0.00025181012355006746, 0.00027667772125427817, 0.0002992761977838038,
+        0.0003178409629296779, 0.0003311258926279309, 0.00033831970266527304,
+        0.0003389953945677054, 0.0003330836503810762, 0.00032086336024528554,
+        0.00030296801677671704, 0.00028041296947316414, 0.00025465510276079825,
+        0.00022769912378654014, 0.00020224060036935074, 0.0001817120350464627,
+        0.00016979211780962028, 0.00016887657625454304, 0.00017840003095462737,
+        0.00019514535556687475, 0.00021516987559974746, 0.0002351523133522385,
+        0.0002526856089321139, 0.0002661369589721526, 0.00027446750700481614,
+        0.00027710769482028796, 0.00027388526711503525, 0.000264989839139693,
+        0.0002509649103993278, 0.00023272756832684417, 0.0002116246311149575,
+        0.00018953622195727864, 0.00016900688124237638, 0.00015324025250919348,
+        0.00014548937052229557, 0.00014750075858743292, 0.0001582242862741854,
+        0.0001745450860251498, 0.00019303964806269476, 0.00021094144111658312,
+        0.00022626644032485913, 0.00023766667575824289, 0.0002442838515647397,
+        0.0002456545820244116, 0.00024165801260429462, 0.0002324925996959792,
+        0.0002186765430179447, 0.00020107570505043125, 0.00018097285291427675,
+        0.00016019774333224314, 0.00014130477205293854, 0.00012759434900657177,
+        0.00012234291800493574, 0.0001268874243649054, 0.00013946807967760182,
+        0.00015661360913463593, 0.0001750280620632558, 0.0001922554593905404,
+        0.00020660177170034232, 0.00021693444360294364, 0.00022253944894314373,
+        0.00022304025676769598, 0.0002183567005247993, 0.00020868911229714716,
+        0.00019452368163827858, 0.0001766660970198939, 0.00015632547296471017,
+        0.0001352902577000425, 0.00011622826999324404, 0.00010289926785470974,
+        9.922454173162039e-05, 0.00010639889070891383, 0.00012160093187306842,
+        0.00014063702775027245, 0.00016016060710331148, 0.000177926054082166,
+        0.00019245478863099072, 0.0002027693412665211, 0.00020824955737348152,
+        0.00020856196833026603, 0.0002036267434017951, 0.00019360531326069092,
+        0.0001789045775913197, 0.0001602055862529788, 0.00013854467613115643,
+        0.00011552077434287504, 9.379397213515086e-05, 7.797406894419768e-05,
+        7.421433363267355e-05, 8.452663914142843e-05, 0.00010390584622476855,
+        0.0001266180248690312, 0.0001491129946428851, 0.00016932698342759413,
+        0.00018595598479596737, 0.0001981226369261954, 0.00020523934029613986,
+        0.0002069514157986549, 0.000203112501651567, 0.00019377349162683413,
+        0.00017917885920004775, 0.00015977214250912917, 0.00013622416139426617,
+        0.00010953233985101211, 8.138119493575417e-05, 5.563858096289142e-05,
+        4.3489489171694935e-05, 5.6971832041496025e-05, 8.441801057375248e-05],
+    [3.498488331955166e-06, 1.0502742378961582e-05, 1.7528859571962977e-05,
+        2.4591514383575978e-05, 3.1705529860637614e-05, 3.8885940234054423e-05,
+        4.614805167402944e-05, 5.350750782383187e-05, 6.0980355885012475e-05,
+        6.858311602658334e-05, 7.633285398957181e-05, 8.424725773630213e-05,
+        9.234471783367607e-05, 0.00010064441356737842, 0.00010916640405327243,
+        0.00011793172619842537, 0.0001269624996043327, 0.00013628203955584598,
+        0.0001459149792581652, 0.00015588740178325744, 0.00016622698396187162,
+        0.00017696315233978375, 0.00018812725366604025, 0.00019975274114699068,
+        0.00021187537839570218, 0.00022453346309473862, 0.00023776807316169523,
+        0.0002516233374542974, 0.0002661467347175748, 0.00028138942346064117,
+        0.00029740660767463756, 0.00031425794161904844, 0.0003320079798254489,
+        0.0003507266772675975, 0.00037048994694178545, 0.0003913802818180498,
+        0.000413487450479326, 0.00043690927579456045, 0.00046175250894834284,
+        0.0004881338113198261, 0.0005161808606312545, 0.0005460335984209354,
+        0.0005778456407808697, 0.0006117858759541538, 0.0006480402786045856,
+        0.0006868139728303201, 0.0007283335863281198, 0.0007728499392234798,
+        0.0008206411272224101, 0.0008720160619395039, 0.0009273185499808172,
+        0.0009869320051243324, 0.0010512849071511315, 0.0011208571467741255,
+        0.0011961874235566473, 0.0012778819005656843, 0.0013666243681213547,
+        0.0014631882219854936, 0.0015684506401256182, 0.0016834094311269031,
+        0.0018092031491007629, 0.0019471352250504024, 0.0020987030651106312,
+        0.002265633330904459, 0.002449924967730662, 0.0026539020154376616,
+        0.00288027886656969, 0.003132241500774932, 0.0034135494166118692,
+        0.003728664643342818, 0.004082916577938204, 0.004482714787540195,
+        0.004935826885625925, 0.005451745974875533, 0.00604218338713235,
+        0.006721739864899374, 0.0075088360642787825, 0.00842702856152563,
+        0.009506913990657829, 0.010788957501685263, 0.012327824748129466,
+        0.014199260405999236, 0.016511492047420962, 0.019425157491937167,
+        0.023190483906360526, 0.028222732713651846, 0.03527344071162321,
+        0.04588565799248751, 0.06393924143608866, 0.10389823286295218, 0.45681204371908657,
+        0.16824000548556978, 0.12427293373827315, 0.10797545152769425, 0.10008460267590576,
+        0.09614385579618968, 0.094523909749073, 0.09449147861590926, 0.09568182883767275,
+        0.09791105448475117, 0.10109794399240787, 0.1052286590194282, 0.11034095701273643,
+        0.11651893085398646, 0.12389477175359266, 0.13265670469999152, 0.143064018738161,
+        0.15547200040209203, 0.17037248212490405, 0.18846118081099977, 0.21075456342839938,
+        0.23880607679207988, 0.2751430155922147, 0.3242647547310634, 0.39537939760774315,
+        0.5125125020590762, 0.782577731957257, 3.755752653720154, 0.6130238071265707,
+        2.0038324235182907, 1.7966683773617411, 0.48927642346172495, 0.5681455484193784,
+        1.6454693423378737, 2.6391577981983634, 1.290482360614598, 0.8266623692872099,
+        0.6486650029294035, 0.8067018461439635, 1.6226534240803259, 1.6444468508405699,
+        1.2430590781299267, 1.0534849646569406, 0.9805165736689616, 0.9964704994790581,
+        1.130939019440316, 1.2953379332275632, 1.1366672611523716, 0.9949313965565334,
+        0.9665725311465813, 1.0088697216944789, 1.1129665716883446, 1.2901188997862794,
+        1.5095481495872904, 1.4827100472993031, 1.1041193077846867, 0.8362982225595078,
+        0.7639941078454111, 0.8164733741323419, 0.9545515691326314, 1.1768801938217415,
+        1.4842418183349981, 1.736100714345457, 1.5799212067107058, 1.172230881216961,
+        0.8597183389944385, 0.7059881248858813, 0.5563643154614943, 0.5653608817165098,
+        0.6467168384221978, 0.7416485038529753, 0.8007326267767204, 0.7933332646568411,
+        0.7274415189006577, 0.631637218546573, 0.5273856711537349, 0.4232652044633994,
+        0.3202474060055104, 0.21713024441508416, 0.11950625669378401, 0.09669283721016048,
+        0.200937707138145, 0.33382804651302267, 0.4605579950742418, 0.5620484997267284,
+        0.6300227956543251, 0.6678393877222281, 0.6844589245326627, 0.6885272785856933,
+        0.6861709013688205, 0.6811325506313011, 0.675516716135285, 0.6704348030704964,
+        0.6664276611580146, 0.6637139715753089, 0.662327767939965, 0.6621892355552359,
+        0.6631346146512631, 0.6649187956509249, 0.6671965979424261, 0.669483968384555,
+        0.6710976302832897, 0.6710716974817819, 0.6680552056645954, 0.6602112568563625,
+        0.6451747827931628, 0.6201837652411639, 0.5825465310006706, 0.5305436987753314,
+        0.4645609925631559, 0.3878185060011925, 0.3060670059691407, 0.22650349300503808,
+        0.15740339715754134, 0.11055212205047689, 0.10067191073538513, 0.12157021565563646,
+        0.1513437084338067, 0.178751481566001, 0.20006905974723435, 0.21408646268689688,
+        0.22049795828756102, 0.21947504821910382, 0.2115853577692373, 0.1977942391487312,
+        0.17945702709355482, 0.15828509867826968, 0.1363152576882854, 0.11591794393434025,
+        0.09977321681306375, 0.09042178209026541, 0.088941419294394, 0.09387409256763231,
+        0.10224279630578675, 0.11130165729899812, 0.11918533788350667, 0.12479963417201408,
+        0.1276011324952819, 0.1274478865571452, 0.12450994494576485, 0.11920697667727556,
+        0.11215480039131828, 0.10411490757326744, 0.09594296218722093, 0.08852290267542674,
+        0.08266021287238909, 0.07891766903068019, 0.07744234497831325, 0.07790934177865692,
+        0.07965645683684461, 0.08192092527427065, 0.08403340852523905, 0.08551307260744807,
+        0.08608771815388579, 0.08567623981936347, 0.0843558212222299, 0.08232327303597797,
+        0.07985343720623576, 0.07725478455424002, 0.07482189130101718, 0.0727870587594345,
+        0.07127890571435573, 0.07030054995859866, 0.0697376279059852, 0.06939527142928843,
+        0.069051036208076, 0.06850700727769339, 0.06762951513676231, 0.06637261347193317,
+        0.0647863499586177, 0.06301178762034125, 0.06126297390026182, 0.05979378630978834,
+        0.05884816521298209, 0.058599377943484514, 0.05909629021431842,
+        0.06024051996868177, 0.06180591672941805, 0.06348882969500735, 0.06496566330029432,
+        0.06594020442438503, 0.06617548602258806, 0.06551286439136908, 0.06388338436750834,
+        0.06131638892872107, 0.05794978591436748, 0.0540454930826795, 0.05001001987036529,
+        0.04640738190812511, 0.04392076353879791, 0.043190550205142765,
+        0.04453385452805024, 0.04776164975567529, 0.052292314072375085,
+        0.05741755634556283, 0.062485580827895425, 0.06696188786228896,
+        0.0704298565449703, 0.072576707234572, 0.0731811137555526, 0.07210582219086083,
+        0.06929586540619201, 0.06478432551940239, 0.05871197193411753, 0.05137794541144721,
+        0.04336690319824409, 0.035857579782274225, 0.031152251526147208,
+        0.03224292069547668, 0.0397120156683988, 0.05134853929128415, 0.06508282310536594,
+        0.07969679350721692, 0.09445448288872285, 0.10884958399530566, 0.12249965780468904,
+        0.1351050750269973, 0.14643298903330762, 0.1563102300607293, 0.16461858082003644,
+        0.17128987811534072, 0.17630019263007662, 0.17966319144979911, 0.18142314551863367,
+        0.18164811522110436, 0.1804237556122176, 0.17784801692890004, 0.17402683962328339,
+        0.16907079734786554, 0.16309254715962768, 0.15620490859297595, 0.14851940526835064,
+        0.14014514923403373, 0.13118801007453332, 0.12175006750900258, 0.11192938141700548,
+        0.10182011794045179, 0.0915130466078792, 0.08109638480457972, 0.07065693834598076,
+        0.06028151083500266, 0.05005871151869984, 0.04008181588679641, 0.03045514987165136,
+        0.021314324506453604, 0.01291906043766218, 0.006367289068095806,
+        0.006830349642827573, 0.012413356702724955, 0.01818073367291126,
+        0.023324928459293622, 0.027652567304236226, 0.03107982029365587,
+        0.03356284391709996, 0.035083104933253534, 0.03564381219327205,
+        0.035269066745541415, 0.03400343964234027, 0.03191118836037414,
+        0.02907484077998666, 0.025593133965802022, 0.021578476673886085,
+        0.017154322213972978, 0.012453502122583875, 0.007622864490003552,
+        0.0029073082759739784, 0.002476599127724973, 0.0068078016376719895,
+        0.01096523941134143, 0.014698407735970554, 0.017902152630521993,
+        0.020500230809710217, 0.02243767463768893, 0.02368023439556658,
+        0.024214528312007506, 0.024047879557392474, 0.0232076526024482,
+        0.021740157404809043, 0.01970935728818416, 0.017195869263948952,
+        0.01429744084292555, 0.011134657022640734, 0.007877685541882803,
+        0.0048847092323837625, 0.00341872114688989, 0.0049815448888178675,
+        0.007728394912698923, 0.010519056439684007, 0.01305063833019174,
+        0.015194751415432382, 0.016876438716199683, 0.018049077654518353,
+        0.01868746495026856, 0.01878531986453632, 0.018354003954803896,
+        0.01742161260498167, 0.016032320434389322, 0.014246306585150366,
+        0.012141360131551815, 0.009819578488628333, 0.007431078496401192,
+        0.005260834940446219, 0.003990682937757309, 0.004494446060225251,
+        0.006236200529301106, 0.008295578717166529, 0.010279548848857201,
+        0.0120230322631375, 0.01343788596379184, 0.014470887291106087, 0.015090957090216895,
+        0.015284636328454195, 0.015054188325502798, 0.014416626218316768,
+        0.013403183911142447, 0.012059336346975905, 0.01044616745174196,
+        0.008645549737943846, 0.006776848211957886, 0.005050068410371246,
+        0.0039034976197366462, 0.0039560869919490135, 0.005101211381093512,
+        0.006672581653451571, 0.008274740502531594, 0.009729962094300609,
+        0.010945556730401087, 0.011866255610511465, 0.012458606946743202,
+        0.012705362394413968, 0.012603170301330631, 0.012161441116845771,
+        0.011401705467576906, 0.01035740569366267, 0.009074598346537777,
+        0.0076151192786178155, 0.006066962691293137, 0.004577258189785261,
+        0.0034471561975004702, 0.0031998046608974983, 0.003973080548809974,
+        0.005241893364344691, 0.006603449906549398, 0.007874901514218944,
+        0.008964510910284757, 0.009818272281923755, 0.010402493316242566,
+        0.010697662101004833, 0.010695957200013052, 0.010399987866569317,
+        0.009821941867876383, 0.008982873463395505, 0.007912131687594345,
+        0.006647227667023952, 0.005235279039574038, 0.003740956176103168,
+        0.002290772643750264, 0.001384074893057096, 0.002032422493193975,
+        0.003378697597175329, 0.004770690046210792, 0.006062242870829273,
+        0.007193700020845074, 0.008128785061443837, 0.008843397513520987,
+        0.009322988010265671, 0.00956190577869571, 0.009563302507325839,
+        0.009339256822896998, 0.008911116918598602, 0.008310248658767927,
+        0.0075795768623848105, 0.00677652243159938, 0.005977806368651971,
+        0.005284394071235061, 0.0048162897941557495, 0.004674882660349632,
+        0.004877241035880484, 0.005338535078568958, 0.005931792074512171,
+        0.00654500504015878, 0.007096960362488623, 0.0075327891101483295,
+        0.007817003307071323, 0.007928615068475588, 0.007858257210575904,
+        0.007606589912298491, 0.007183535673872913, 0.006608233686089792,
+        0.005910005601192681, 0.00513126206150241, 0.0043344108506794855,
+        0.00361568800608403, 0.003120167240159181, 0.003006310675205631,
+        0.0033072673923959664, 0.0038857407080502026, 0.004575519478165767,
+        0.005261744842937647, 0.005874059458979005, 0.006368556375776104,
+        0.006717354521409261, 0.006903641997376536, 0.006919358992729686,
+        0.0067640826556207055, 0.0064445032113589155, 0.005974312101690754,
+        0.005374639395838824, 0.004675628446983156, 0.003920732777544668,
+        0.0031776359944859067, 0.0025621080170626885, 0.0022567972168525937,
+        0.0024010272643892427, 0.0029015263010643386, 0.003560226977166756,
+        0.004240652327217376, 0.004866847225415755, 0.005394304882024618,
+        0.005795022467579513, 0.0060512938853752056, 0.006153115402815945,
+        0.006097031477132752, 0.0058855796874129045, 0.005527034722400648,
+        0.005035424013280493, 0.004431050406570194, 0.0037422932838752166,
+        0.0030110080463310453, 0.0023086430946045624, 0.001778889918500387,
+        0.0016606885704813122, 0.002024805839857093, 0.00264324876200559,
+        0.0033238657148024382, 0.003973699585972722, 0.004544635095650402,
+        0.005007535415090946, 0.005343333350653351, 0.00553985733727741,
+        0.005590596465467805, 0.005494156067153045, 0.005253967486225202,
+        0.004878109991697416, 0.004379256202976857, 0.003774935526989704,
+        0.0030887837375710584, 0.002355212182612464, 0.0016381906487468738,
+        0.0011124566438685778, 0.0011573367902204068, 0.0017180921532885998,
+        0.002423956319002632, 0.0031261984771725386, 0.0037691722058389803,
+        0.0043227242355941215, 0.00476666369487665, 0.005086695551186569,
+        0.005273184831666719, 0.005320732454834207, 0.005227985691135224,
+        0.004997491048350699, 0.004635522253521494, 0.004151868765256751,
+        0.00355961147599036, 0.002874998286667245, 0.0021178833836335608,
+        0.001315523064260487, 0.0005467252306472222, 0.0005971176679615806,
+        0.0013865348301652335, 0.002206212337626171, 0.0029878068136187114,
+        0.0037051737716239973, 0.004338858574983267, 0.004872714418260347,
+        0.005293399248964721, 0.005590356990807635, 0.005755873704414918,
+        0.005785108243153396, 0.005676069435724315, 0.00542953618745672,
+        0.005048930891221759, 0.004540174255275344, 0.00391159202344479,
+        0.003174089465060806, 0.0023424849760258727, 0.0014436890645830585,
+        0.0006125971604544632, 0.0008970720216645551, 0.0019313022686738078,
+        0.0030668574183374893, 0.00423972175717353, 0.0054284667609391275,
+        0.006618350723272978, 0.007796858536122425, 0.00895267563806582,
+        0.010075332737520395, 0.011155022830063241, 0.01218247207890345,
+        0.013148836214488088, 0.014045620195778315, 0.014864626621424015,
+        0.015597939559697863, 0.0162379488329788, 0.01677741687240709, 0.0172095868723598,
+        0.017528327647794675, 0.01772830770232004, 0.017805188787676122,
+        0.017755827804827866, 0.017578475293836687, 0.01727295894648298,
+        0.016840841472279967, 0.01628554365820955, 0.015612425499253232,
+        0.01482882079179457, 0.013944023607676258, 0.012969228775800699,
+        0.01191743337402487, 0.01080331340040835, 0.009643101854415125,
+        0.00845451764854781, 0.007256844797535041, 0.006071380543047068,
+        0.004922781950866639, 0.003842715726150001, 0.002879715079255839,
+        0.0021240832558249247, 0.0017370648799439575, 0.0018256363405412266,
+        0.002224302295436796, 0.0027115719631884147, 0.0031742029083514393,
+        0.003564758651201535, 0.003863201496402177, 0.004061923333910031,
+        0.004160121844798571, 0.004161464204929422, 0.004072989388809308,
+        0.0039045395254932967, 0.003668474450146794, 0.0033796103612376252,
+        0.003055419657570658, 0.002716578970735114, 0.002387885191539816,
+        0.002099052740947049, 0.00188327800907042, 0.0017692177827582335,
+        0.0017658692703179677, 0.0018542337696557402, 0.0019982449388931474,
+        0.0021620902562912345, 0.0023186530212287826, 0.0024500010352087286,
+        0.002545405466910303, 0.0025994521886191033, 0.0026107316555910734,
+        0.0025809941690591474, 0.0025145990216771724, 0.0024181325143026364,
+        0.0023001050440414118, 0.002170637989143659, 0.002041012631770982,
+        0.001922890168687864, 0.0018269977136744278, 0.0017612751220948525,
+        0.001728999779041109, 0.001727902118565442, 0.001750993125475315,
+        0.0017887201597319117, 0.0018313053540225377, 0.0018703996015693113,
+        0.0018998893631428466, 0.0019160988087435847, 0.0019176672326398556,
+        0.0019052754487803463, 0.0018812921760557272, 0.001849349141128041,
+        0.0018138277062423411, 0.001779245787968321, 0.0017495728916875558,
+        0.0017275666820775247, 0.0017142841652058947, 0.0017089204522762731,
+        0.0017090389992694282, 0.001711121340598467, 0.0017112697591971828,
+        0.0017058937452595674, 0.0016922754189363756, 0.0016689817668334964,
+        0.0016361340174599413, 0.001595549381593908, 0.0015507448238489066,
+        0.0015067460569833033, 0.0014695966529249043, 0.0014454627301636468,
+        0.0014393613617611632, 0.001453827693170427, 0.0014880769669321514,
+        0.0015380806190468123, 0.0015974669435569573, 0.0016587507217937908,
+        0.0017144207363465238, 0.001757692036430592, 0.001782955808714386,
+        0.001786039042202932, 0.0017643777543220902, 0.0017171795162136216,
+        0.0016456343962440664, 0.0015532330143224408, 0.0014462539616673959,
+        0.001334442839022609, 0.0012316751908989607, 0.0011556887060794124,
+        0.0011249020951604749, 0.001151259375225333, 0.0012336627489133588,
+        0.0013590557105324832, 0.0015094197952541196, 0.0016674694355648667,
+        0.0018187231888049332, 0.0019515602544567512, 0.002056758313051026,
+        0.0021270847010083993, 0.0021570499488231917, 0.0021428038666500547,
+        0.002082148129725699, 0.0019746731842758777, 0.0018220948057557226,
+        0.0016290156745601973, 0.0014047276502518768, 0.001167732812028404,
+        0.0009568367897475003, 0.0008480108192176658, 0.0009255793428517358,
+        0.001181651674365735, 0.0015446593650491436, 0.0019619888017225655,
+        0.0024048407124754516, 0.0028559495802943477, 0.0033032202999984726,
+        0.00373716522457266, 0.004149883767767425, 0.004534652491194649,
+        0.004885765032434378, 0.00519847498733855, 0.005468977515203551,
+        0.005694399733774255, 0.005872785407513172, 0.006003067014418456,
+        0.006085022368154533, 0.006119215406844887, 0.006106922343937037,
+        0.006050045479886597, 0.005951017762557131, 0.005812701734314027,
+        0.005638286838624675, 0.005431189180674551, 0.0051949577364282466,
+        0.004933190672077655, 0.004649464871940238, 0.004347280990438007,
+        0.004030025384680783, 0.0037009492162504913, 0.003363163941491998,
+        0.0030196514894405427, 0.0026732868814746914, 0.0023268712624640413,
+        0.001983175146261996, 0.0016449974874064909, 0.0013152639185466815,
+        0.0009972494507988683, 0.0006952849669742199, 0.00041803836418409236,
+        0.00020455774054319874, 0.00023290688748366182, 0.0004230203811373782,
+        0.0006178487677104227, 0.0007929277514128337, 0.0009423132060909221,
+        0.0010634107017378832, 0.0011548366023115023, 0.0012159460042329335,
+        0.0012467032929581107, 0.0012476416479261449, 0.0012198445524085754,
+        0.0011649274594540998, 0.001085011564639044, 0.0009826868662856543,
+        0.0008609643052585089, 0.0007232189677763812, 0.0005731305165075319,
+        0.0004146430504050583, 0.00025207234976437414, 9.224465651195319e-05,
+        8.271746182736558e-05, 0.000231535332767949, 0.00037368271305538467,
+        0.0005025884997290614, 0.0006150608028724627, 0.0007086481235514956,
+        0.0007814766376163488, 0.0008322464978624113, 0.0008602447301974424,
+        0.000865352093801056, 0.0008480389883827807, 0.0008093501659654584,
+        0.0007508807332742193, 0.0006747498758577223, 0.0005835881346334908,
+        0.00048058275422993606, 0.0003697336684542541, 0.0002569962475215773,
+        0.00015638633954086215, 0.00011906165155656997, 0.00018475012281895687,
+        0.0002831806093474772, 0.0003817159982438041, 0.0004715090335807961,
+        0.0005485411694466947, 0.0006103353668953881, 0.0006552538911710521,
+        0.0006823057909888208, 0.0006910828832688267, 0.000681731314815115,
+        0.000654932200303282, 0.0006118856828955813, 0.0005543043052063807,
+        0.00048443767026191856, 0.0004051914725166616, 0.0003205390422799981,
+        0.00023693885208626877, 0.0001683388813047708, 0.00014549148447375488,
+        0.00018493124251935618, 0.0002547064970587628, 0.0003299404584954575,
+        0.00040071407251707236, 0.00046240337563064195, 0.0005123270876957454,
+        0.0005487860391011944, 0.0005707542610779317, 0.0005777653752186949,
+        0.0005698637157444483, 0.0005475789463585666, 0.0005119130484964423,
+        0.00046434447768464797, 0.0004068738375490454, 0.0003421811371869298,
+        0.0002741013459992835, 0.00020905502237875763, 0.0001598892203138485,
+        0.00014815920215718997, 0.0001802732368018499, 0.00023522530481274542,
+        0.00029549158102618023, 0.0003527595709461772, 0.0004028317575399873,
+        0.00044323975919888405, 0.0004724278345650686, 0.0004894611917336906,
+        0.0004939112217542194, 0.00048580469269437907, 0.00046559853188763963,
+        0.0004341694768867844, 0.00039282365376479446, 0.00034335134074594425,
+        0.00028819932458366897, 0.00023096958832889724, 0.00017783683865248273,
+        0.00014077680065570087, 0.00013681157228383886, 0.0001671449605777157,
+        0.00021444874395898174, 0.00026546169557376545, 0.00031362116167611947,
+        0.0003554568566969613, 0.0003888771413345287, 0.0004125496196152468,
+        0.00042566951492504064, 0.0004278645816473948, 0.00041915044421006914,
+        0.0003999056873063587, 0.0003708572397011386, 0.00033307867481594287,
+        0.00028801961236519434, 0.00023762369806139998, 0.0001847256619307971,
+        0.0001344298545639426, 9.860148734699529e-05, 9.815035842453684e-05,
+        0.00013218129453799617, 0.00017909827487444215, 0.0002271705669099831,
+        0.00027159125388939514, 0.0003099044671235412, 0.00034061024984316025,
+        0.0003627511713161265, 0.0003757761924584309, 0.0003794924181841756,
+        0.00037404861214374887, 0.0003599338160451071, 0.00033799004474159127,
+        0.0003094491846634609, 0.00027601943388714324, 0.00024007220398636835,
+        0.00020500791730204755, 0.00017578674744123175, 0.00015886782382425088,
+        0.00015934273919130293, 0.00017619706585623906, 0.00020320659349268565,
+        0.000233956916006387, 0.00026393249860073067, 0.00029023025573918964,
+        0.0003109808430157522, 0.00032498816475066245, 0.00033154317627271627,
+        0.0003303305945900347, 0.0003213820067720892, 0.00030505452678683905,
+        0.00028202995281004125, 0.0002533432578315156, 0.00022047101876158354,
+        0.00018555712107045839, 0.00015194552412565825, 0.00012518572856236136,
+        0.00011327015001912979, 0.00012124129263255203, 0.00014457070897226168,
+        0.00017490648074541454, 0.0002063275086664262, 0.0002353945241276297,
+        0.000260040332870866, 0.00027894802020631064, 0.0002912767019470879,
+        0.00029654236446192115, 0.0002945639967232323, 0.0002854382568770261,
+        0.00026952908408786613, 0.00024747085750820665, 0.00022019523028009373,
+        0.00018901327840676447, 0.00015583951246290892, 0.00012378581598440213,
+        9.851605026673065e-05, 8.902083283606658e-05, 0.00010024438172071339,
+        0.00012539358941971072, 0.00015561956092929253, 0.00018576531253652886,
+        0.0002130735660507106, 0.0002359069500646627, 0.0002532098679633684,
+        0.0002643001081885902, 0.0002687847248145435, 0.00026652352408841433,
+        0.00025761174319752195, 0.00024237198693841526, 0.00022135468474145776,
+        0.00019535533501843663, 0.00016547551020190836, 0.00013331027715808008,
+        0.00010153337215937029, 7.56789440855896e-05, 6.664030747535449e-05,
+        8.066260493566197e-05, 0.00010780471668914581, 0.00013843441942637297,
+        0.00016810764802811947, 0.00019463760186773078, 0.0002167177329184395,
+        0.00023347862327370147, 0.0002443389061264237, 0.0002489504156212019,
+        0.00024717564879584764, 0.00023907650937878894, 0.00022490703789710507,
+        0.00020510884217261023, 0.00018031303718622234, 0.0001513629155632328,
+        0.00011940633605587048, 8.625996710881915e-05, 5.6094735423811545e-05,
+        4.234988863181212e-05, 5.9074268109663835e-05, 8.958638693708419e-05,
+        0.00012205974403211698, 0.00015286354186267205, 0.0001803637804025232,
+        0.0002035289256850713, 0.00022161783866040573, 0.0002340951153056061,
+        0.00024060545825431372, 0.00024096499893620015, 0.00023515670597813233,
+        0.00022332539129539595, 0.00020577074896830443, 0.00018293822297533901,
+        0.0001554087385902854, 0.00012389126052815195, 8.923508047893327e-05,
+        5.257509867224112e-05, 1.7740963774594948e-05, 3.023795587723546e-05,
+        6.761777304727203e-05, 0.00010491334186251066, 0.00014026110038918877,
+        0.00017266645956234286], [1.0768844163980119e-07, 3.2330816987035756e-07,
+        5.39657481478087e-07, 7.572261290538512e-07, 9.765089122085764e-07,
+        1.1980077967039427e-06, 1.4222339787258343e-06, 1.64971009936074e-06,
+        1.8809724795476272e-06, 2.1165734615162776e-06, 2.357083853232912e-06,
+        2.6030955025259923e-06, 2.8552239914430123e-06, 3.1141115129261054e-06,
+        3.380429906924908e-06, 3.6548839132785425e-06, 3.938214643704599e-06,
+        4.231203307649348e-06, 4.534675227086948e-06, 4.84950415282574e-06,
+        5.176616950174102e-06, 5.516998654447828e-06, 5.871697969985558e-06,
+        6.241833246461147e-06, 6.62859898696583e-06, 7.033272943603452e-06,
+        7.457223879101889e-06, 7.901920046632021e-06, 8.368938490468198e-06,
+        8.859975234268984e-06, 9.37685649104398e-06, 9.921550969741795e-06,
+        1.0496183441353366e-05, 1.1103049681423386e-05, 1.1744632970963715e-05,
+        1.2423622317666455e-05, 1.3142932622308635e-05, 1.3905726999882361e-05,
+        1.471544154176349e-05, 1.557581278638946e-05, 1.6490908263903764e-05,
+        1.7465160464256587e-05, 1.850340469247599e-05, 1.961092127334917e-05,
+        2.0793482702186306e-05, 2.2057406327499634e-05, 2.3409613383814785e-05,
+        2.485769509889226e-05, 2.6409986963775363e-05, 2.8075652155907068e-05,
+        2.986477546176122e-05, 3.1788469141781915e-05, 3.3858992403160944e-05,
+        3.608988647750102e-05, 3.849612754365102e-05, 4.109430010447039e-05,
+        4.3902793938889405e-05, 4.694202809973505e-05, 5.023470620054336e-05,
+        5.380610779991284e-05, 5.7684421594397954e-05, 6.190112713848727e-05,
+        6.649143296654698e-05, 7.14947804237114e-05, 7.695542422406944e-05,
+        8.292310283265402e-05, 8.945381416959379e-05, 9.661071517985726e-05,
+        0.00010446516747045242, 0.00011309795552235981, 0.0001226007094423703,
+        0.0001330775707970761, 0.00014464714823258392, 0.00015744481935902753,
+        0.0001716254480285745, 0.00018736660118090715, 0.000204872368972221,
+        0.00022437791543854108, 0.00024615491740764096, 0.00027051808772970835,
+        0.00029783302681552057, 0.0003285257088681821, 0.0003630939884785868,
+        0.00040212161547841327, 0.00044629537934464585, 0.0004964261777511675,
+        0.0005534750326056868, 0.0006185853786448319, 0.0006931233522115926,
+        0.0007787283501192914, 0.0008773768586048505, 0.0009914635555202608,
+        0.0011239050667649977, 0.0012782736794612836, 0.0014589710161642345,
+        0.0016714555247583998, 0.001922543176883972, 0.002220808873700503,
+        0.0025771280476654425, 0.0030054160219118078, 0.0035236503650087118,
+        0.004155304716895035, 0.004931391542285115, 0.005893424035544292,
+        0.007097796672585169, 0.00862241160762393, 0.010576965569207933,
+        0.013119408881726182, 0.016483236936879357, 0.021024730908333084,
+        0.02730917319908862, 0.0362790924363136, 0.04961273888878418, 0.07058602245821438,
+        0.10654837977679482, 0.17843370769676323, 0.3864989054206368, 3.83812047032701,
+        0.06033330674174497, 0.9156453683688066, 1.718386224575511, 0.9784904089596019,
+        0.9155807531786659, 1.0782220705063885, 0.29057001123649345, 0.6282621266254749,
+        1.3355694602536206, 3.2695517152308615, 7.241691824742018, 7.099692602008909,
+        4.370030801892724, 2.2015654021024464, 1.3291006238898584, 1.0021072382360496,
+        1.1109998701012866, 1.7383448333746234, 2.57596292851463, 2.3237986622793785,
+        1.7943486802359807, 1.4798246431532767, 1.3193810953324017, 1.2702769321341998,
+        1.337047346944417, 1.5322055349670798, 1.6493729003298794, 1.4621157582597344,
+        1.278508190383073, 1.2037347492439952, 1.2127256000307243, 1.2925812374304304,
+        1.4486933768085446, 1.6762488500213568, 1.829673127123755, 1.6007437747663116,
+        1.2042391507508667, 0.966911267560818, 0.9151199994754029, 0.8205466336296457,
+        0.8310779953320871, 0.8876222146390284, 0.935649802001309, 0.9316232925817937,
+        0.8569347154789668, 0.7331541968381181, 0.5949992584895796, 0.46324213251621826,
+        0.34443617722873554, 0.24088630775021735, 0.16480573809327523, 0.15900904053564807,
+        0.23631430093007755, 0.3506095177302816, 0.472401893332748, 0.5807318656070651,
+        0.6594899117183386, 0.7038353073720803, 0.7200920603817088, 0.7186903115219853,
+        0.708480454669858, 0.6951792655162542, 0.6819622699650096, 0.6704133100818033,
+        0.6612301051206235, 0.6546482201808549, 0.6506731128362743, 0.6491994327057732,
+        0.6500665796740496, 0.6530770294913795, 0.6579902467106759, 0.6644968429091136,
+        0.6721724156174795, 0.680407044227532, 0.6883051417998511, 0.6945540375423519,
+        0.69727485459642, 0.6939067029821948, 0.6812424678196192, 0.6558070260271389,
+        0.6147410665873124, 0.557060862997897, 0.4846490104357933, 0.4021553248886261,
+        0.3157093975234605, 0.23142133380396063, 0.1550881554627305, 0.0953806734869988,
+        0.07400587267046783, 0.0992296536652617, 0.13846743115205865, 0.17560513971139252,
+        0.20643905434513402, 0.22953661546656465, 0.24427617571561402, 0.2504721545421456,
+        0.24833693603170096, 0.2384875838178437, 0.22191159554123185, 0.19988432532212666,
+        0.1738752203530921, 0.14550534200263618, 0.11664765194763042, 0.08984899114092096,
+        0.06936054906675991, 0.06160715679196092, 0.06909260279870466, 0.08550044037490681,
+        0.1041174189192547, 0.12139751001333247, 0.1356083555883264, 0.14587146663281716,
+        0.15178807458607582, 0.15328455911678054, 0.15052708497193573, 0.14386063432465612,
+        0.13376532892980997, 0.1208353180814558, 0.1057908101720915, 0.08954370009671951,
+        0.0733637091286765, 0.05922546882436921, 0.05019361301092289, 0.04933407134968932,
+        0.05622483630416839, 0.06724626992289962, 0.07921806400734886, 0.09030154206431056,
+        0.09949955232330639, 0.10626613729367392, 0.11031667061101977, 0.11153744217254837,
+        0.10994118213332857, 0.10564683341898776, 0.09887470805591583, 0.0899538619754514,
+        0.07934398566499341, 0.06768483613524522, 0.05590918013088069, 0.045483208776137804,
+        0.03869114390120307, 0.03792224296626551, 0.04313260457215513, 0.05177891053889005,
+        0.061467571114915937, 0.0707583884462059, 0.07882803675729069, 0.08517865459391069,
+        0.0894993833474336, 0.09160728390014894, 0.0914231186791221, 0.0889619143086159,
+        0.0843295464544095, 0.07772254122183724, 0.06943329097810298, 0.05987036417551094,
+        0.04962022781194937, 0.039618076281780226, 0.031550060752921195,
+        0.028169056442633962, 0.03128418669267546, 0.03906722260158146,
+        0.04873116349388687, 0.05858626713746748, 0.06772091026829036, 0.0755856928059677,
+        0.08181352998399831, 0.08615060005387785, 0.0884290383298846, 0.08855491567097215,
+        0.08650165242240153, 0.0823055620142938, 0.07606337908717312, 0.06793423299129778,
+        0.058153463262641605, 0.0470814875428488, 0.03537598132957688, 0.02468150053340272,
+        0.01986429902429378, 0.026196558608877672, 0.03911848337038026,
+        0.054185881449441475, 0.06982399521112735, 0.08534168923895938,
+        0.10031295143184901, 0.11442137479508932, 0.12741640343299274, 0.13910063576966467,
+        0.1493263389281923, 0.15799398421655897, 0.1650501331235481, 0.17048377689981045,
+        0.17432109750102753, 0.17661907374685273, 0.17745855543093383, 0.17693744020454397,
+        0.17516447345196987, 0.17225401046360245, 0.16832188666582165, 0.16348237483536346,
+        0.15784609041561998, 0.15151864433968057, 0.14459983291190526, 0.1371831848495588,
+        0.1293557407956797, 0.12119800357986868, 0.11278405167448277, 0.10418184133039768,
+        0.09545372821710674, 0.08665721860141014, 0.07784592183324716, 0.06907063444854747,
+        0.060380455966408134, 0.051823829949785426, 0.04344942931435454,
+        0.035306874640555645, 0.02744744007108662, 0.019925441784750683,
+        0.012803801828480347, 0.006194789225469461, 0.0017103522628719905,
+        0.00624636087233695, 0.011293469270634408, 0.015797219413692856,
+        0.01967235909489643, 0.022880310774796592, 0.02539819827624269,
+        0.02721525981231322, 0.02833280077096217, 0.028764683969657798,
+        0.02853767354887929, 0.02769144810144344, 0.026278309565922836,
+        0.02436278771899305, 0.022021567542377055, 0.01934459459211506,
+        0.01643924560074878, 0.013442284417176232, 0.010552291994382073,
+        0.008111973189796631, 0.006728552688560339, 0.006975953208470337,
+        0.008533568646851366, 0.010628202772623831, 0.012775055942353022,
+        0.014738219693656693, 0.016395844140448305, 0.017680135010384693,
+        0.01855424146202287, 0.0190027544528497, 0.01902732850756026, 0.01864442900666342,
+        0.017884160118294475, 0.01678991469681202, 0.01541903090698288,
+        0.013845086740786527, 0.012163095506795596, 0.01049948506650021,
+        0.009027020616550143, 0.007970781400970762, 0.007553394337345045,
+        0.007845944147914072, 0.008690051641278, 0.009827180966228206, 0.011037942660035572,
+        0.01217353008549617, 0.013139255428476994, 0.013876280520629173,
+        0.014350206151552188, 0.014544782791040442, 0.014458525671321021,
+        0.014102920917315544, 0.01350159280358922, 0.012690227549085041,
+        0.011717339892641026, 0.010646162351974015, 0.009557836480293553,
+        0.008554855310822148, 0.007759373622704029, 0.007293208229644223,
+        0.0072297398711804566, 0.007547462872365874, 0.008140498983988421,
+        0.008875357834456057, 0.00963495620659274, 0.01033173780621768,
+        0.01090502062288115, 0.011315229844936832, 0.011539238442316904,
+        0.011567284648567665, 0.011401065999789033, 0.011052627846106527,
+        0.010543840638662027, 0.009906411105002774, 0.009182441910570308,
+        0.008425436281002148, 0.007701043744386318, 0.007085245230611058,
+        0.006655227064785135, 0.006468796598555526, 0.006539332321996509,
+        0.0068273945544307536, 0.007259021174036886, 0.007753338146893796,
+        0.00824029822045525, 0.008666288139573947, 0.008993505547625744,
+        0.009197652139924501, 0.009265772954506242, 0.009194663419278996,
+        0.008989809484410057, 0.008664747114684943, 0.008240744777686795,
+        0.00774671103332787, 0.007219128576395252, 0.006701505308688461,
+        0.00624221219795614, 0.00588890520796771, 0.0056783483925667575,
+        0.005624304039871306, 0.005711171548947165, 0.005899200934916282,
+        0.006137562955079454, 0.006376571533807086, 0.006574562276371643,
+        0.006700207830829726, 0.006732571665187142, 0.006660528139283951,
+        0.006482330634347276, 0.006205667601250869, 0.005848412275124431,
+        0.005440228168678756, 0.005024899187220355, 0.004661959383114665,
+        0.004422910006876865, 0.004374325165743119, 0.004549012360336256,
+        0.004928747847452217, 0.005457790136564483, 0.006069980221804997,
+        0.006705907921917119, 0.0073177005523186785, 0.007868226409776542,
+        0.008329192263085773, 0.008679597284592146, 0.008904729980799378,
+        0.00899557271902291, 0.00894846438099764, 0.008764924872015597,
+        0.008451602755175099, 0.008020361545751963, 0.007488577985043984,
+        0.00687979463244516, 0.00622494056093156, 0.0055643190948805165,
+        0.004950088095511303, 0.004446989526931893, 0.004124606649443166,
+        0.004032981484476913, 0.004171887218933232, 0.004487831222996542,
+        0.00490433129265546, 0.005351035961669274, 0.005774188378887207,
+        0.006135809176000067, 0.006410209163715277, 0.006581043131646749,
+        0.00663936918611964, 0.006582483277886407, 0.006413274775807571,
+        0.006139957297289621, 0.0057761406965244335, 0.005341311746580859,
+        0.004861874368295997, 0.004372873534030671, 0.00392000990980369,
+        0.0035595732741652004, 0.0033499931096220687, 0.003329313901933048,
+        0.0034914376238872973, 0.003788896910858121, 0.004159343179080202,
+        0.0045470131259123065, 0.004909357876660353, 0.005215936997765979,
+        0.005445762645135214, 0.005585166869694762, 0.0056264256892890035,
+        0.0055669478594110875, 0.005408844322929071, 0.005158785303942406,
+        0.004828149585881454, 0.004433575992262649, 0.0039981477896219265,
+        0.0035535097318879893, 0.0031428205890123924, 0.002822158182674845,
+        0.0026521324606044983, 0.002670629523848783, 0.0028648160318117746,
+        0.003180047374306399, 0.0035532666233042062, 0.003933009528436619,
+        0.004282155691633228, 0.004574830660506803, 0.004793281598001094,
+        0.004925831249250095, 0.0049656900748958725, 0.004910298685699522,
+        0.004760991992565772, 0.004522894963041697, 0.00420506293278461,
+        0.0038210009278478205, 0.0033898928715414725, 0.0029392076275530756,
+        0.0025096767647383076, 0.0021621982036499326, 0.0019759712572689552,
+        0.0020101334958451205, 0.002247625175582803, 0.0026123012350714493,
+        0.0030286934017593613, 0.003443995298291315, 0.0038237427711875272,
+        0.0041449055303182025, 0.004391665919902395, 0.004553244304166047,
+        0.004622811563833736, 0.004596937510872971, 0.0044753061381246715,
+        0.0042605809720105935, 0.003958396425393443, 0.003577541017346201,
+        0.0031305593059770243, 0.0026354122450442954, 0.002120071015393762,
+        0.0016356183445399763, 0.001288383460394798, 0.0012459536178725686,
+        0.0015420594309596366, 0.00202020345578713, 0.0025555509868573365,
+        0.0030871368553243824, 0.003582592478652093, 0.004021358865038037,
+        0.004388701532092437, 0.0046735043589195705, 0.004867391835439534,
+        0.004964346750924478, 0.004960516292366397, 0.004854083403302618,
+        0.004645151396992751, 0.004335620939862468, 0.0039290554167822735,
+        0.003430546119598895, 0.002846620467100943, 0.002185356040324183,
+        0.0014575665620991643, 0.0006882071950832209, 0.0003428060694460888,
+        0.001143491103005672, 0.0020597346437105273, 0.0030103235657752267,
+        0.003980453312692021, 0.004960272920591679, 0.005941325241314908,
+        0.006915926296888614, 0.007876977253977393, 0.008817860707601146,
+        0.009732348891885914, 0.010614508806715967, 0.011458605385754108,
+        0.01225900924652313, 0.013010117211772603, 0.013706293631838045,
+        0.014341839288457961, 0.014910992703651336, 0.015407966311562743,
+        0.01582701745276686, 0.016162551754384004, 0.016409254361742974,
+        0.016562242818894915, 0.016617234228120233, 0.016570718665529956,
+        0.0164201306610567, 0.01616401081262814, 0.01580215022649649, 0.015335711392880215,
+        0.014767320259891312, 0.01410112562169467, 0.013342823472927812,
+        0.012499645737894928, 0.011580314884484636, 0.010594968695605127,
+        0.009555063660966426, 0.008473272934474614, 0.007363410404668279,
+        0.006240449722535116, 0.005120808655088387, 0.004023387593936436,
+        0.002973036477634505, 0.002013543572414986, 0.0012653830166084966,
+        0.0010747206449962048, 0.0015242192906009915, 0.002161446957487386,
+        0.0027845291924961696, 0.003337008846578254, 0.003797989206700508,
+        0.004157962094824734, 0.004412730560336069, 0.004561474594439068,
+        0.004605994588323143, 0.00455034763884917, 0.004400632031046595,
+        0.004164841308385928, 0.0038527773984699818, 0.003476062078530322,
+        0.003048362790332647, 0.0025861273476573054, 0.002110607780962198,
+        0.001653322201152341, 0.0012699814938569114, 0.0010604195493223963,
+        0.0011155296872454854, 0.001377879593555283, 0.0017240220183002701,
+        0.0020790674057693257, 0.002406670671353196, 0.0026876926332853567,
+        0.002911002664788497, 0.0030699737858603665, 0.003161064074445525,
+        0.003183183377365415, 0.0031373777469195503, 0.003026657742203283,
+        0.002855913515608363, 0.002631922932287808, 0.00236352280416637,
+        0.002062128235730364, 0.001743047664522075, 0.001428638075981357,
+        0.0011551403684754798, 0.0009811075037721075, 0.0009684722315100446,
+        0.001113924572579819, 0.0013500953734826551, 0.0016161282822002448,
+        0.0018762495957387322, 0.002110158626141206, 0.002305508815089225,
+        0.0024544148190527083, 0.0025519282213389036, 0.002595349416107216,
+        0.002583898526503303, 0.0025185509205678976, 0.002401963563459936,
+        0.002238480999193126, 0.002034263274333717, 0.001797662900831272,
+        0.001540163631263476, 0.001278623912699258, 0.001040306218456202,
+        0.0008708143355577594, 0.0008279248765975505, 0.0009287751825596117,
+        0.0011251447122977213, 0.0013606485949367948, 0.0015996671161608753,
+        0.0018216981384487421, 0.0020141011502357517, 0.0021684983009794337,
+        0.0022792040469063204, 0.002342534679140934, 0.0023564938489244245,
+        0.002320625669662647, 0.002235951754598985, 0.0021049684143480797,
+        0.0019317236967153237, 0.0017220554944277072, 0.0014842102547756664,
+        0.0012304351665005766, 0.0009811663063597595, 0.0007752785292391632,
+        0.0006816085741588176, 0.0007543993842770181, 0.0009535852578239712,
+        0.001207928712781915, 0.0014743210399302163, 0.0017300741582253938,
+        0.001961623183113199, 0.0021596795763129746, 0.0023173734655473803,
+        0.0024295199396930202, 0.002492318020003287, 0.0025032251672407226,
+        0.002460906828893079, 0.0023652229721401294, 0.002217245666753823,
+        0.002019331992353042, 0.0017753352061519309, 0.001491208187510118,
+        0.0011768813508976942, 0.0008531418478316874, 0.0005815206912625053,
+        0.0005387880671367926, 0.0008010843663657965, 0.0011955422937137098,
+        0.0016329954644688028, 0.002084038159579181, 0.002534696058562427,
+        0.0029757543753627593, 0.0034000102436591677, 0.0038014329839729517,
+        0.004174881788263865, 0.004516010547902576, 0.004821238630488252,
+        0.005087742047903925, 0.005313446058879583, 0.005497010856839312,
+        0.005637806740309165, 0.005735877547120679, 0.00579189247743803,
+        0.0058070872757962815, 0.005783196324176273, 0.005722377621321065,
+        0.005627132935820388, 0.005500225639762103, 0.0053445988601243735,
+        0.005163296620667759, 0.004959390577827488, 0.0047359147686454935,
+        0.00449581047556577, 0.004241882869765609, 0.00397677052494093,
+        0.003702928219348198, 0.0034226226997277056, 0.0031379403201053477,
+        0.0028508047552441985, 0.0025630023947763665, 0.0022762126164408703,
+        0.0019920399809928383, 0.001712045546172866, 0.0014377750740885208,
+        0.00117078323879857, 0.0009126563509187151, 0.0006650479631920315,
+        0.0004298034637872772, 0.00020984815500895066, 4.688179600252464e-05,
+        0.00019987496238549611, 0.00037064792983529843, 0.0005240415189368834,
+        0.0006577101345242089, 0.0007705223268301688, 0.0008617632427551041,
+        0.0009310407852961217, 0.0009782790753069138, 0.0010037266780544276,
+        0.0010079646299098123, 0.0009919104470866287, 0.0009568177772465102,
+        0.0009042734914083901, 0.0008361967384880784, 0.0007548496918896197,
+        0.0006628816323644601, 0.0005634585396565251, 0.00046061626178484164,
+        0.00036023203648739735, 0.0002726914174438752, 0.00021816004940259758,
+        0.0002206646468730698, 0.0002732581950801676, 0.000347418675005911,
+        0.0004250020165926069, 0.000497551679947525, 0.0005607882048410339,
+        0.0006122726664398763, 0.0006505569265851722, 0.0006748544225459809,
+        0.0006848994526937162, 0.0006808805779189726, 0.0006634067684660981,
+        0.0006334924695731541, 0.0005925612018967063, 0.0005424781628315336,
+        0.00048563711734538365, 0.00042515152258554246, 0.00036523222348423394,
+        0.00031180492788520096, 0.0002729613603179007, 0.0002572823121318408,
+        0.00026810417530344436, 0.0002998747112870779, 0.0003430190550714074,
+        0.0003894755618556335, 0.0004338482763733729, 0.0004727045916414965,
+        0.0005038647638837359, 0.0005259784280005144, 0.0005382988936365831,
+        0.0005405642805036682, 0.0005329345276231198, 0.000515960101459825,
+        0.000490573560158356, 0.0004581050345859687, 0.0004203308411844737,
+        0.000379571048545027, 0.00033884758727976863, 0.0003020601265191702,
+        0.00027393540113210675, 0.0002591431981525316, 0.000260204961855652,
+        0.00027573320315346243, 0.0003012716449950617, 0.00033169756354032947,
+        0.0003627402314277158, 0.0003912807611133589, 0.0004151625131685548,
+        0.00043295391502047527, 0.00044377734417227365, 0.0004472024807073372,
+        0.0004431835753608277, 0.00043202510670713005, 0.0004143678683805237,
+        0.00039119365732892026, 0.0003638511100738644, 0.00033410636563884096,
+        0.00030421313133484497, 0.00027695782080475157, 0.0002555368607995551,
+        0.00024300309082681495, 0.00024117998787757125, 0.00024968763143340996,
+        0.00026609623221837697, 0.000287077616140879, 0.0003094676710831988,
+        0.00033072390972251276, 0.0003489690649903174, 0.00036289518986283765,
+        0.00037165934484586105, 0.00037480566141463565, 0.00037221428254080406,
+        0.00036407087982408054, 0.00035085181998062345, 0.0003333227884506042,
+        0.00031255048655735434, 0.00028992577282331344, 0.00026718738247620143,
+        0.00024640837208224695, 0.000229855890642534, 0.00021959808506942974,
+        0.00021685412308497095, 0.0002214395050579087, 0.00023180793721639385,
+        0.00024567699010915293, 0.0002607137553457817, 0.0002749245096596905,
+        0.0002867691135535614, 0.0002951438532789371, 0.00029933036154200006,
+        0.00029895024061063745, 0.00029393596992617025, 0.00028451950050799573,
+        0.000271239167601305, 0.00025496704420998066, 0.0002369581432659679,
+        0.00021891151361480297, 0.00020299283244485763, 0.00019168114583121497,
+        0.00018724004390426125, 0.00019085048831436911, 0.00020202210944851568,
+        0.00021889037073891777, 0.00023906284241386787, 0.0002602828479134979,
+        0.0002806901846833371, 0.00029884140702745844, 0.0003136543762598018,
+        0.0003243497580946065, 0.0003304080215095812, 0.0003315417627180467,
+        0.0003276794890289484, 0.0003189579028083365, 0.00030572169150986294,
+        0.0002885320316228614, 0.0002681873669233699, 0.0002457620527245715,
+        0.0002226673295949075, 0.0002007244013639755, 0.00018218485808226594,
+        0.00016951484397846443, 0.000164700496391905, 0.00016825287666544065,
+        0.00017883204445621909, 0.00019397318185062577, 0.0002111062393482227,
+        0.00022809935019299778, 0.00024335493008901713, 0.0002557334368683157,
+        0.0002644579650023715, 0.00026904272108705713, 0.00026924719764661155,
+        0.00026504946304071206, 0.0002566332628455314, 0.00024438678193761316,
+        0.00022891419121495602, 0.00021106418069546313, 0.00019198116785854982,
+        0.0001731780783948059, 0.0001565934647738359, 0.0001444942491657233,
+        0.00013896558302845612, 0.00014096231684976722, 0.00014968595693994462,
+        0.00016305397839071428, 0.00017870060957441222, 0.0001946011187780754,
+        0.0002092172230623441, 0.0002214367845372099, 0.0002304826948815,
+        0.00023584318361378326, 0.0002372273132860915, 0.0002345390673982772,
+        0.00022786436622945303, 0.00021746845636162485, 0.00020380451506496608,
+        0.00018753815545405716, 0.00016959699152104533, 0.00015125674796317108,
+        0.00013425957998267012, 0.00012087296711038626, 0.00011357551621441248,
+        0.00011400717093073609, 0.00012181818638819122, 0.000134901538603363,
+        0.00015069218816726832, 0.00016703293494802103, 0.00018233743563744623,
+        0.0001954819908385197, 0.00020567996792048297, 0.00021239627575428773,
+        0.00021529694938943612, 0.00021422112387284927, 0.00020916657247745332,
+        0.00020028450432980514, 0.000187883181268956, 0.0001724441257130802,
+        0.00015466113474109787, 0.00013552370132590035, 0.00011648280450986162,
+        9.972676469429014e-05, 8.837384742793616e-05, 8.565386572066802e-05,
+        9.245513366440112e-05, 0.00010636239069347107, 0.00012393286676755516,
+        0.00014247422115981734, 0.00016019636355455518, 0.00017591084356383967,
+        0.00018879983390281024, 0.00019829048555451147, 0.00020399168461105935,
+        0.00020566240730935867, 0.0002031956401137847, 0.0001966102834008738,
+        0.00018604806969477395, 0.0001717757507254272, 0.00015419676286713155,
+        0.00013388483677058302, 0.00011167453972373742, 8.89129507530958e-05,
+        6.817940147227566e-05, 5.489705775389507e-05, 5.6401992439084266e-05,
+        7.197959424127976e-05, 9.428814094921823e-05, 0.00011849780758075818,
+        0.0001422868212601313, 0.0001643770550358099, 0.0001839270730019996,
+        0.0002003179768091592], [2.8893211477671124e-07, 8.67556395746682e-07,
+        1.4484646989542026e-06, 2.0331922586667678e-06, 2.623293184429422e-06,
+        3.2203483657694705e-06, 3.8259733156009014e-06, 4.4418265308362035e-06,
+        5.06961804945362e-06, 5.711118466063834e-06, 6.368168429696078e-06,
+        7.042688732221256e-06, 7.736691000627787e-06, 8.452289206312264e-06,
+        9.191711976940875e-06, 9.957315922262068e-06, 1.0751600040846616e-05,
+        1.1577221371646052e-05, 1.243701206491837e-05, 1.3333997993702733e-05,
+        1.4271419195241461e-05, 1.5252752254922209e-05, 1.628173496881645e-05,
+        1.7362393526654914e-05, 1.8499072537292853e-05, 1.9696468247285658e-05,
+        2.095966539929295e-05, 2.2294178133226252e-05, 2.3705995521333335e-05,
+        2.5201632267753664e-05, 2.678818535893382e-05, 2.8473397335760925e-05,
+        3.0265727199009437e-05, 3.217442990708208e-05, 3.420964572800546e-05,
+        3.638250076686579e-05, 3.870522033125105e-05, 4.119125691952578e-05,
+        4.385543506528857e-05, 4.671411545314084e-05, 4.9785381329466205e-05,
+        5.308925052783312e-05, 5.6647917225410914e-05, 6.048602804748206e-05,
+        6.463099820325083e-05, 6.911337403869824e-05, 7.396725010227308e-05,
+        7.923074959197122e-05, 8.494657969326829e-05, 9.116267463652456e-05,
+        9.793294264232789e-05, 0.0001053181358412809, 0.00011338686625447539,
+        0.00012221679615271734, 0.00013189603704967618, 0.0001425247993215722,
+        0.00015421734449702783, 0.00016710430389184775, 0.00018133544354770906,
+        0.00019708297475818057, 0.00021454553531423046, 0.000233952999802432,
+        0.0002555723203998544, 0.0002797146565319004, 0.0003067441272343495,
+        0.00033708862118826287, 0.0003712532355422762, 0.00040983710131231945,
+        0.0004535546108769953, 0.0005032624227228568, 0.0005599941295250356,
+        0.0006250052099844555, 0.0006998319587547554, 0.0007863696846374929,
+        0.0008869778921196732, 0.0010046239162997245, 0.0011430824519849132,
+        0.0013072181571719946, 0.0015033949157666016, 0.0017400839532678493,
+        0.002028794951736136, 0.00238555325083242, 0.0028333454297201155,
+        0.0034063844592691376, 0.004158048020048591, 0.005176941235244225,
+        0.006623238162507438, 0.008824956894849632, 0.012603542809109436,
+        0.02100448775033147, 0.09478147451316653, 0.03585218987874316, 0.02722067018678057,
+        0.024329717706053626, 0.02321900534284155, 0.022985800146819717,
+        0.0233111990232833, 0.02406314378647531, 0.025188978280579248, 0.026678162716958644,
+        0.028547888402929322, 0.03083804602531118, 0.03361103753069684,
+        0.036954988718420005, 0.04099029027268119, 0.045880339902374945,
+        0.051848435887060194, 0.05920447828062404, 0.06838828822931609,
+        0.0800427384377256, 0.09514387810929724, 0.11524882669493912, 0.14301262282114685,
+        0.18340842337281377, 0.24718435649704046, 0.36403655645543376, 0.6735796582771852,
+        5.269066256399402, 0.2917032720367451, 1.6305462590075612, 2.173022765531736,
+        0.9366745872567773, 0.6614907894277463, 0.8746907714928809, 1.617398204074107,
+        1.118755678685662, 1.0160411048498337, 1.095139890038023, 1.3840297886827873,
+        1.8545128199504124, 1.2045050452431936, 0.7227333887696132, 0.6653589297037489,
+        0.7999285637719911, 1.0949535134851909, 1.626009698330484, 2.1183781603689154,
+        1.6791158246817148, 1.153698156431429, 0.8628697976399349, 0.726414593106758,
+        0.7196552474255182, 0.8769568937996945, 1.2358605559095355, 1.5527146740391942,
+        1.4468483535775432, 1.2317466290611154, 1.0907655057809544, 1.0223152906487774,
+        1.0127126493467258, 1.0602755023759223, 1.163063640406, 1.246599639003135,
+        1.1423886342947438, 0.9654200783976045, 0.883403312920063, 0.9003681230101627,
+        0.8348317646674184, 0.8277716017912375, 0.8453486851630955, 0.8446963228186273,
+        0.7938107539456918, 0.6858587421848816, 0.5466551631365825, 0.4071502224841709,
+        0.28341926066137413, 0.1824415351906105, 0.12290881601540835, 0.14460842546669536,
+        0.22427051263753345, 0.32461278672944655, 0.4318865386596221, 0.5341977536057032,
+        0.6167498913989383, 0.6680132809083422, 0.6870597888627581, 0.6823383815300129,
+        0.664550840058777, 0.6418283672632248, 0.6189384774432922, 0.5982255636024006,
+        0.5806435950916676, 0.5664423405438284, 0.5555491709388509, 0.5477632329447761,
+        0.5428470565782112, 0.540564016963012, 0.540686386978573, 0.5429853724725128,
+        0.5472069951808962, 0.5530330197354983, 0.5600229349053665, 0.5675313610621174,
+        0.5745971802254416, 0.579811388226969, 0.5811993473353503, 0.5762079700205701,
+        0.5619541678013668, 0.5358867051982581, 0.49679855034125897, 0.445704976530716,
+        0.3859025300599879, 0.32203517174879653, 0.25883401948819235, 0.20042351713485634,
+        0.15064070709924693, 0.11429877700138018, 0.0975600218107416, 0.1018140059069697,
+        0.1187757642079524, 0.1393929903985303, 0.15872490180602467, 0.17445883734413473,
+        0.18551278222353126, 0.1914679960795863, 0.19236199061592751, 0.18858574810175172,
+        0.18079410500714177, 0.16981436427552665, 0.15656790440490195, 0.1420227547663317,
+        0.12718470504928334, 0.11311732996168966, 0.10095364874053418, 0.09181763625350357,
+        0.08655513465029598, 0.08532861770910367, 0.08743645871165834, 0.09162082449281973,
+        0.09657738312849498, 0.10127309008223169, 0.10502143926439002, 0.10743843692298993,
+        0.10837019150217737, 0.10782742770880903, 0.1059358478161452, 0.10290229619188232,
+        0.09899338104032447, 0.09452131675580284, 0.08983039378463367, 0.08527698235516402,
+        0.08119751067267152, 0.07786423613993589, 0.07543833408452696, 0.0739391139825158,
+        0.07324704179109758, 0.0731423762253487, 0.07336236456026657, 0.07365453651022659,
+        0.07381291330021836, 0.07369609480794674, 0.07323245406927043, 0.07241786323976092,
+        0.07130888706259414, 0.07001185547956652, 0.06866686645654035, 0.06742600869031425,
+        0.06642699125651103, 0.06576635068765573, 0.06547883357237493, 0.065529208078292,
+        0.06581882371132089, 0.06620385513187807, 0.06651888988409667, 0.06659994486593947,
+        0.06630372060251224, 0.06552258751526456, 0.0641962157644353, 0.06232099144105373,
+        0.05995796577036228, 0.05723937495446414, 0.05437248633475957, 0.05163685403754021,
+        0.04936649099053179, 0.047904790190581, 0.04752730277287973, 0.0483551559891798,
+        0.05030967659462158, 0.05314029458949702, 0.0565009708704157, 0.06002487378664037,
+        0.06337071245579076, 0.06624301433486743, 0.06839806402181625, 0.06964440054604704,
+        0.06984217090055263, 0.06890290941741013, 0.06679043515427302, 0.06352389691967217,
+        0.059185302118689574, 0.05393654694371908, 0.048056262525198304,
+        0.042015834592794496, 0.036616575926903754, 0.03312794239448337,
+        0.033026697883546646, 0.03695558353738873, 0.044198347809887434,
+        0.053559155357414234, 0.06408494264854904, 0.07513314530279946,
+        0.08626073638897336, 0.09714030138092908, 0.10751621163928085, 0.11718426271416578,
+        0.12598282829858823, 0.1337890421367852, 0.14051663009641538, 0.14611368641031486,
+        0.15055965270292263, 0.15386135385360653, 0.1560483043958736, 0.1571676781351564,
+        0.15727937039533985, 0.15645151816584157, 0.15475672283865954, 0.1522690836929848,
+        0.1490620283084178, 0.1452068369399312, 0.1407717087760969, 0.13582120773868822,
+        0.13041594724012845, 0.12461241648708157, 0.11846290310364922, 0.11201551484576233,
+        0.10531433593290243, 0.09839976378451078, 0.09130905874016143, 0.08407710796987271,
+        0.07673736631207773, 0.06932290394155109, 0.061867475934987176,
+        0.054406540844628266, 0.046978202847245173, 0.03962415464014461,
+        0.032390932443928294, 0.025332474872596197, 0.01851760214987322,
+        0.012060080694839851, 0.006310961393960677, 0.0037913089320622934,
+        0.0074540851013438015, 0.01218428018534951, 0.01665071485964694,
+        0.020637874230841336, 0.024062746042958674, 0.02687709180864374,
+        0.02905020694217182, 0.03056493417117472, 0.03141666996934306, 0.03161300170829089,
+        0.031173304995627982, 0.0301281284894975, 0.02851837696298595, 0.02639437460709651,
+        0.023814915022728103, 0.020846428416206975, 0.017562503682378838,
+        0.01404445734745259, 0.010385664151466573, 0.006714217031421235,
+        0.0033668393744188396, 0.0025721600668742743, 0.005346827050044731,
+        0.008538574207826565, 0.01156196646003094, 0.014284140999776746,
+        0.01663613777779736, 0.018571391966202777, 0.02005759284779058,
+        0.02107443547826614, 0.021612811102874104, 0.02167440148135127,
+        0.021271374939423108, 0.02042608135928504, 0.01917072517981771,
+        0.01754707998107422, 0.015606475018383113, 0.013410693243454768,
+        0.01103559555966241, 0.008583276425080449, 0.006224349227758392,
+        0.004351531929845736, 0.0038478207232209064, 0.005053818685095378,
+        0.007007461272938442, 0.009081079668828608, 0.011041213770119771,
+        0.012781894999253241, 0.014242265512286321, 0.015383341549284238,
+        0.016180467192055382, 0.016620482311659596, 0.016700458403520125,
+        0.016426971500897895, 0.015815563660874034, 0.014890320832247495,
+        0.013683663798695312, 0.012236653022511465, 0.010600539299041593,
+        0.008841455555540615, 0.007053630022304882, 0.005396777459404297,
+        0.004187264487359421, 0.003922865683895803, 0.004718702747617495,
+        0.006080573583459562, 0.007595365060586813, 0.009063689623816212,
+        0.010385831808312746, 0.011504127401128035, 0.012382106740744449,
+        0.012996666987498608, 0.013334832481322861, 0.013392252979626325,
+        0.013172412846375563, 0.01268616402491997, 0.011951458460588137,
+        0.010993314250073691, 0.009844240656533304, 0.008545739334498679,
+        0.007152510971833784, 0.005743856660129358, 0.004454302775448017,
+        0.0035398816994767685, 0.003368870891439605, 0.004005242236614263,
+        0.005084815485847609, 0.006294528602555255, 0.0074747714393545665,
+        0.008542861633189291, 0.009450009274981226, 0.010164787097898758,
+        0.010666734110433665, 0.010943675256595486, 0.010990463807554956,
+        0.010808281952607824, 0.01040415583311893, 0.009790554894784658,
+        0.00898505549058324, 0.008010143386700055, 0.006893396790633467,
+        0.005668760843025063, 0.004381319964770164, 0.003105577378956457,
+        0.0020269749065445204, 0.0016909853768919568, 0.0024086963714449656,
+        0.0035348704481242325, 0.0047121338768943664, 0.005828469884145415,
+        0.0068342053943430195, 0.007699740919049784, 0.00840522418578779,
+        0.008937482138609827, 0.009288980294127185, 0.00945744553062772,
+        0.00944573838289288, 0.00926185045568934, 0.00891901776540724, 0.008436012838087014,
+        0.007837754122014004, 0.007156469432580522, 0.006433742788530036,
+        0.00572364669132462, 0.005095979871624895, 0.004634471028318298,
+        0.0044182157235437, 0.004482349673014914, 0.004791601785920972,
+        0.005262689871425441, 0.005806926898762275, 0.006352783622952908,
+        0.006848490580477287, 0.007257976087473922, 0.007556728088286234,
+        0.0077289542823247796, 0.007765835750548636, 0.007664484824480769,
+        0.007427337094666675, 0.007061844184797538, 0.006580454038648, 0.006000998825192494,
+        0.005347817034740697, 0.0046543112339366, 0.0039682337076057655,
+        0.00336095973142137, 0.0029355942808429658, 0.0028034965083509012,
+        0.0030001062669615056, 0.0034433894642466826, 0.004012670370187034,
+        0.004614774650726725, 0.005189581033028574, 0.005698610819604671,
+        0.006116430599253975, 0.006426029672393219, 0.006616489901628541,
+        0.006681796759530185, 0.0066202079980593066, 0.006433907454923337,
+        0.006128832248323835, 0.00571466049882122, 0.0052050430237604445,
+        0.004618321450638862, 0.003979323375283329, 0.0033236449609047444,
+        0.002707475930077638, 0.002225853709997594, 0.0020167398182939058,
+        0.0021652191426509856, 0.0025900682764882017, 0.0031469499424589395,
+        0.00373543679712624, 0.004298191723903072, 0.004801051917904457,
+        0.005221934014423973, 0.005545895646815722, 0.0057629561977581055,
+        0.005867091552368356, 0.005855737343260606, 0.005729518973638687,
+        0.005492091034579961, 0.005150050848324179, 0.004712952213818407,
+        0.004193531879506571, 0.0036084558439427998, 0.0029804404274041125,
+        0.0023443413841826256, 0.0017652784469436094, 0.0013830563349788328,
+        0.0013981863933216821, 0.001790991282959718, 0.002353083046594389,
+        0.0029533794006974656, 0.0035322143353680416, 0.004058270654746078,
+        0.0045119032831207155, 0.004879473520928647, 0.005151281163074204,
+        0.005320739110148285, 0.005384009185325466, 0.005339813564566797,
+        0.005189308656073796, 0.004935975900621348, 0.004585515848436839,
+        0.0041457548242609665, 0.0036266074646987157, 0.003040226293997288,
+        0.00240177688022818, 0.0017326774713422477, 0.0010771654243715064,
+        0.0006215456289296601, 0.0008605573429414002, 0.0014820558204644678,
+        0.0021549560967359235, 0.0028103201931478335, 0.0034226186176585173,
+        0.003975927236697503, 0.004458104799404213, 0.004859384617563905,
+        0.005171972311474412, 0.00538992471344151, 0.00550910819128324,
+        0.005527168976765166, 0.005443490349231581, 0.005259127439283314,
+        0.0049767179121210404, 0.004600371972000836, 0.004135551565673719,
+        0.0035889624350766963, 0.002968524522883174, 0.0022836538161773927,
+        0.0015470311722649256, 0.0007886028390981337, 0.0003674444235947478,
+        0.0010568979792783208, 0.0019227600456500184, 0.0028189631586417073,
+        0.0037256932891351338, 0.004632691835970455, 0.005532109456545005,
+        0.006417292943963185, 0.007282446172566192, 0.00812247976897604,
+        0.008932903494641339, 0.009709723598392497, 0.01044933679110045,
+        0.01114842240998002, 0.011803838112811648, 0.012412525724540241,
+        0.012971433814576761, 0.013477462678611357, 0.01392743591018049,
+        0.014318100898943429, 0.014646158599473576, 0.014908320979545262,
+        0.015101392844555299, 0.015222373368708363, 0.015268571710106128,
+        0.01523773056422941, 0.01512815139333514, 0.014938815306574236,
+        0.014669494093481296, 0.014320846667681159, 0.013894497103646578,
+        0.013393091508464879, 0.012820332148525133, 0.01218098855857082,
+        0.01148088686108906, 0.010726880357496926, 0.009926806908885543,
+        0.00908944229664996, 0.008224464858380305, 0.007342457807923372,
+        0.006454997420709235, 0.00557492053315429, 0.004716963398548225,
+        0.0038991836871045877, 0.003146044101154098, 0.002494718934368359,
+        0.00200470558260291, 0.0017542069317087407, 0.0017784946255798224,
+        0.002006218152551866, 0.00232595515128713, 0.0026603593964497274,
+        0.0029680980411632084, 0.0032282198706754376, 0.0034303515685249948,
+        0.0035699913009585673, 0.003646284637954149, 0.0036609164927668488,
+        0.003617517786908465, 0.0035213260843089704, 0.003378986988698624,
+        0.003198450055069171, 0.002988944789282247, 0.0027610340005967313,
+        0.002526729517319331, 0.002299594110889672, 0.0020945947607660014,
+        0.0019271925150580347, 0.001810972540380839, 0.0017537772557323164,
+        0.001754259478342997, 0.001801881970337422, 0.001880795177964702,
+        0.001974602913258943, 0.002069366287999798, 0.0021545867372193264,
+        0.0022230684905310935, 0.0022704192266817156, 0.002294540328399679,
+        0.002295208303263269, 0.0022737489461262393, 0.002232777332157694,
+        0.00217597228702773, 0.0021078539878744192, 0.002033532105523973,
+        0.001958390856886306, 0.0018876836206774075, 0.0018260348620638,
+        0.0017768991908661425, 0.0017420944147551617, 0.0017215634261705946,
+        0.0017134772034713903, 0.0017146691179542085, 0.0017212653671081425,
+        0.0017293315424926532, 0.001735401547992932, 0.0017368367370636548,
+        0.0017320250996746265, 0.0017204549983205304, 0.001702695065338442,
+        0.0016802968030552492, 0.0016556201106679, 0.0016315714994985157,
+        0.0016112468018399696, 0.0015974911241616954, 0.0015924286179043808,
+        0.0015970572654506144, 0.001611017474627441, 0.0016326033423978259,
+        0.0016590052210525524, 0.0016866999573611438, 0.0017118816306481853,
+        0.0017308508292435654, 0.0017403251078706074, 0.0017376700980358513,
+        0.0017210703219034914, 0.0016896646430068032, 0.0016436702477303944,
+        0.0015845152776006524, 0.0015149932054312994, 0.00143943474993648,
+        0.001363849051311655, 0.001295890695848854, 0.0012443632609973384,
+        0.0012179014151361257, 0.0012228166364814026, 0.0012609802746670561,
+        0.001329150894040121, 0.0014202007886951783, 0.0015252052057856077,
+        0.0016351486321604086, 0.0017418294452633996, 0.0018381671191476097,
+        0.0019182214205229321, 0.0019771213312803006, 0.0020109923378010385,
+        0.0020169122723587944, 0.0019929040612684627, 0.001937971538859671,
+        0.0018521943232595035, 0.001736921209359674, 0.001595150890424949,
+        0.001432294510078982, 0.00125773312912615, 0.0010879184461281247,
+        0.0009514115927484964, 0.0008907497947681613, 0.0009434653666869227,
+        0.0011088395570451517, 0.0013550239680231255, 0.0016500745368387203,
+        0.001972256889323836, 0.0023074985878207585, 0.002646064989309458,
+        0.002980634101807582, 0.003305332688016438, 0.0036152665973155063,
+        0.003906292368372841, 0.004174906432720847, 0.004418191353327842,
+        0.004633788495847122, 0.004819881093054851, 0.004975179047390823,
+        0.005098900758560475, 0.005190749498583486, 0.005250883211572071,
+        0.005279877498077217, 0.005278682161966966, 0.005248572158176653,
+        0.005191094138691392, 0.00510801007785551, 0.0050012396776856006,
+        0.0048728034078271585, 0.0047247681156539195, 0.004559197137803708,
+        0.004378106740477344, 0.004183430502119156, 0.003976992921367117,
+        0.003760493092185335, 0.0035354987541221165, 0.0033034504339811777,
+        0.0030656747940403955, 0.0028234057529394037, 0.0025778115140028773,
+        0.0023300253971187683, 0.002081178405174488, 0.0018324318984763216,
+        0.0015850098933887515, 0.0013402331679562532, 0.0010995642140609735,
+        0.0008646930543031177, 0.0006377741020925729, 0.0004223363190117257,
+        0.000228718038058723, 0.00012724871345691047, 0.00023610096291907246,
+        0.0003940347225118196, 0.000546036292470807, 0.0006837876819693154,
+        0.0008044048902184739, 0.0009062912637558168, 0.0009884103219611696,
+        0.0010501062235689458, 0.001091053676446671, 0.0011112444243714045,
+        0.0011109833694339449, 0.0010908849804828343, 0.0010518664065178888,
+        0.000995136009224136, 0.0009221772179652895, 0.0008347285838609302,
+        0.0007347623608783449, 0.0006244673402151013, 0.0005062521390404085,
+        0.0003828260797088896, 0.00025763202699269165, 0.0001377994698132916,
+        7.162313839445493e-05, 0.00015189424666117658, 0.00026241930989381396,
+        0.00036975248762475903, 0.00046852015798766575, 0.0005562222810716258,
+        0.0006311467051088187, 0.0006920221658217357, 0.0007379368777065777,
+        0.0007683168072918383, 0.0007829187118687086, 0.0007818253036592014,
+        0.0007654386385169824, 0.0007344710038376966, 0.000689934459225043,
+        0.0006331324257612824, 0.0005656611385285784, 0.000489439794433839,
+        0.00040682009520517427, 0.0003209321953620081, 0.0002368339239865266,
+        0.00016565836526767665, 0.00013478819893943442, 0.0001667429388336684,
+        0.00023325649605031277, 0.00030786029093651785, 0.0003804517294370829,
+        0.00044670460849814946, 0.0005042145866149765, 0.000551424082932573,
+        0.0005872823066285288, 0.0006111218755944632, 0.0006226080127142285,
+        0.0006217141019167812, 0.0006087071881805379, 0.0005841378155773151,
+        0.0005488337925370467, 0.0005039018286605499, 0.00045074792807777125,
+        0.0003911432190316932, 0.00032740396635983946, 0.00026287610922630687,
+        0.0002032526702987379, 0.00015961837575489705, 0.00014911690305620208,
+        0.00017656153643561941, 0.0002256254753857957, 0.0002814620211890381,
+        0.00033657530708868763, 0.0003871594041505672, 0.0004309922678443445,
+        0.0004666383142223907, 0.0004931447488802441, 0.0005099168463229652,
+        0.0005166619561811088, 0.0005133615335116073, 0.0005002554060507277,
+        0.0004778326511300202, 0.0004468288928858488, 0.00040823486253632003,
+        0.000363329455511259, 0.00031376958303342556, 0.00026181798267056576,
+        0.0002109161690144547, 0.00016703914398698118, 0.00014062267767121084,
+        0.00014268053225257953, 0.0001708330147305801, 0.00021242688886162183,
+        0.00025788557800371045, 0.00030207982749290923, 0.0003421737966808309,
+        0.00037642198188976393, 0.00040367100306911775, 0.00042315358682298436,
+        0.0004343980665758425, 0.00043718517245215784, 0.0004315249547495759,
+        0.0004176427292315545, 0.000395969986266631, 0.00036714032388197816,
+        0.0003319947191769586, 0.0002916083165566753, 0.00024737063671449185,
+        0.00020120838377050122, 0.00015621769696941325, 0.00011842692218764719,
+        9.965979133581804e-05, 0.00011038943946683589, 0.0001425952599277111,
+        0.00018292350291390956, 0.00022423664493543497, 0.00026316027030937603,
+        0.0002978393224422886, 0.000327103410156341, 0.00035016918515516095,
+        0.00036652630842617213, 0.0003758904477692868, 0.0003781828552368661,
+        0.0003735216052805128, 0.00036221932519316265, 0.0003447869970482811,
+        0.0003219470655167611, 0.00029466378448820527, 0.00026420651362375953,
+        0.00023227414824899563, 0.00020121950064428467, 0.00017436587935357078,
+        0.00015608983434799227, 0.0001506013561701685, 0.0001590211686080024,
+        0.00017821252037626426, 0.00020336632977882514, 0.00023043496622827302,
+        0.000256613677786046, 0.0002800306678764011, 0.00029942329170880603,
+        0.00031393747398374854, 0.0003230174624801517, 0.00032634635847145346,
+        0.0003238135320487963, 0.0003154966129724759, 0.0003016526035450164,
+        0.0002827171694023105, 0.00025931548191589535, 0.00023229456538513476,
+        0.00020280019736111394, 0.00017244879841751275, 0.00014368953379926495,
+        0.00012041425786649438, 0.00010811535417423175, 0.00011101107478220614,
+        0.00012738125999660758, 0.00015150539716452877, 0.00017844068651075854,
+        0.0002050793033832771, 0.0002295232852803799, 0.0002505487013882914,
+        0.00026732931001381964, 0.0002793058430048086, 0.0002861235839487717,
+        0.0002876013343935786, 0.00028371514535855704, 0.0002745895349752414,
+        0.00026049359571106786, 0.00024184254624477937, 0.0002192089466891785,
+        0.00019335469477620707, 0.00016531124642826166, 0.00013657709769725922,
+        0.00010959731385779768, 8.873850565283479e-05, 8.063240700838305e-05,
+        8.900749202725313e-05, 0.00010926188543812382, 0.00013469402060032544,
+        0.0001611132580508171, 0.00018623674267374336, 0.00020871287909629072,
+        0.00022765677435880184, 0.00024245713196659313, 0.0002526942613501686,
+        0.0002581033166327315, 0.0002585565809081617, 0.00025405400451081867,
+        0.0002447175149953781, 0.000230787618814137, 0.00021262287296075323,
+        0.00019070544977612062, 0.00016566169515392452, 0.00013832229826486435,
+        0.0001098972715673488, 8.251975166926982e-05, 6.0930154036231864e-05,
+        5.469344180372411e-05, 6.825823806677495e-05, 9.240373086449352e-05,
+        0.0001194898775116491, 0.00014622693385243378, 0.00017103885706081298,
+        0.00019298219198228135, 0.00021140559634693636, 0.00022583416783384118,
+        0.00023592615507460644, 0.00024145533539215267, 0.00024230296616204467,
+        0.00023845314146219603, 0.0002299890232374369, 0.0002170889514875467,
+        0.00020002227038098532, 0.00017914548239530512, 0.00015490078424886978,
+        0.00012782320901547564, 9.857847520264402e-05, 6.813485347931022e-05,
+        3.8812211309183584e-05, 2.3609384203268257e-05, 4.335524870635986e-05,
+        7.341150373956386e-05, 0.00010412229340645288, 0.00013360423669056876,
+        0.00016098637746664464, 0.00018565273806092194, 0.00020710663058305952,
+        0.0002249377166893763, 0.0002388134214224764, 0.00024847705423850083,
+        0.00025374750553677224], [8.893741018310515e-09, 2.6706174487340215e-08,
+        4.459359196976309e-08, 6.26064047800346e-08, 8.079565883903322e-08,
+        9.92132998989498e-08, 1.179124373349683e-07, 1.3694762446521178e-07,
+        1.5637514564230232e-07, 1.762533183263118e-07, 1.9664281100182194e-07,
+        2.176069804184508e-07, 2.392122286751204e-07, 2.615283868719717e-07,
+        2.846291249780527e-07, 3.0859239457299644e-07, 3.335009066146446e-07,
+        3.594426493816247e-07, 3.8651145205570444e-07, 4.1480759769233647e-07,
+        4.444384945710783e-07, 4.7551940929166953e-07, 5.081742719421233e-07,
+        5.425365606023464e-07, 5.787502748500087e-07, 6.169710086806727e-07,
+        6.57367136113502e-07, 7.001211211024764e-07, 7.454309690621986e-07,
+        7.935118349839934e-07, 8.445978108222654e-07, 8.989439105114371e-07,
+        9.56828281156324e-07, 1.0185546663078882e-06, 1.0844551558236127e-06,
+        1.154893257268225e-06, 1.2302673330354251e-06, 1.3110144490815375e-06,
+        1.39761469290341e-06, 1.4905960208160651e-06, 1.590539710020782e-06,
+        1.6980864951825186e-06, 1.8139434884196497e-06, 1.938891989496905e-06,
+        2.0737963171914905e-06, 2.219613802483941e-06, 2.3774061233175698e-06,
+        2.548352164959574e-06, 2.7337626495805313e-06, 2.9350967882364046e-06,
+        3.1539812746901784e-06, 3.3922319813971587e-06, 3.6518787790027545e-06,
+        3.935193982094072e-06, 4.244725002742049e-06, 4.583331897116452e-06,
+        4.954230624842676e-06, 5.361042968322357e-06, 5.807854258990412e-06,
+        6.299280251827775e-06, 6.840544753771455e-06, 7.437569922545112e-06,
+        8.097081522463253e-06, 8.826731879692465e-06, 9.635243833934106e-06,
+        1.0532579663839842e-05, 1.153013978134431e-05, 1.2640997015534293e-05,
+        1.3880173566290937e-05, 1.5264969242829305e-05, 1.6815351537883795e-05,
+        1.8554420482742025e-05, 2.0508964234296416e-05, 2.2710125068165535e-05,
+        2.5194200232915345e-05, 2.8003608054462713e-05, 3.1188057350018845e-05,
+        3.480596783170353e-05, 3.892620165977989e-05, 4.363018235989161e-05,
+        4.9014497950161765e-05, 5.5194112205425805e-05, 6.23063432848626e-05,
+        7.051581539404735e-05, 8.00206508157243e-05, 9.106025166125267e-05,
+        0.0001039251309769507, 0.00011896940171491346, 0.00013662673492569066,
+        0.00015743087743596743, 0.000182042204514585, 0.0002112823227549863,
+        0.0002461794987524905, 0.00028802877387052784, 0.0003384721884697776,
+        0.00039960682042890504, 0.00047413171099444705, 0.000565549802441998,
+        0.0006784486892099646, 0.0008188958611992065, 0.0009950028134464235,
+        0.0012177424249490672, 0.0015021533052460227, 0.0018691477651409552,
+        0.00234828354242104, 0.002982115493410429, 0.0038332171132481343,
+        0.004995874906358055, 0.006616306621030697, 0.00892921670668867,
+        0.012327614804185082, 0.017505685513734624, 0.025778613784674005,
+        0.03989182880528764, 0.06646862471736263, 0.12589319672239685, 0.3236371391111799,
+        4.3725953408151, 0.3758083636943211, 0.10869037332708001, 0.9978172914328253,
+        0.8520628962775884, 1.1489554857600726, 2.293093201406455, 3.101540463809851,
+        1.4597961733424352, 0.9830646742619275, 0.8976723290344779, 1.5091634753043164,
+        2.7629958439565336, 2.8721022198733106, 2.16203079552537, 1.8592209872420584,
+        1.8076573294449196, 1.9670339834562982, 2.3655371209612066, 2.567830260687796,
+        1.7777518509916226, 1.1671331704362307, 0.9527386401237379, 0.970413132256576,
+        1.1544973396283171, 1.5195805379712202, 2.0707690906872047, 2.3781211988475044,
+        1.996265583337108, 1.536653834741414, 1.244431436524108, 1.0856322128541829,
+        1.029575752797154, 1.0794120430972458, 1.2598893076212883, 1.5124372227252012,
+        1.5507591681964823, 1.3797416818022066, 1.2370641885611409, 1.1792575285985107,
+        1.0115338060398253, 0.9401296653928954, 0.899137442318691, 0.842838356372075,
+        0.7441647984960497, 0.6048009863964509, 0.45517577243551494, 0.3265039824233933,
+        0.2384522380011577, 0.20652472806913108, 0.2317017795932892, 0.2929485336201389,
+        0.37289118236117974, 0.4631254399038593, 0.5562413417698588, 0.640849548544282,
+        0.7026251940459295, 0.731902495980618, 0.7303416738075665, 0.7082387603340035,
+        0.6768404479222674, 0.6439444035513571, 0.6136765681391118, 0.587753767401012,
+        0.5666260700214119, 0.5501730983940247, 0.5380643238392799, 0.5299278870682161,
+        0.5254214353690091, 0.5242546368882296, 0.5261872086920094, 0.5310125281535727,
+        0.5385293549043716, 0.5484994052462773, 0.5605848659793474, 0.5742572814127125,
+        0.5886694990024839, 0.6024910459355219, 0.6137352821679559, 0.6196665914850573,
+        0.6169597279514493, 0.6023121187821292, 0.5735182449140575, 0.5305515939839669,
+        0.4758775225644805, 0.41364281578453416, 0.3482929681703934, 0.28351763939358454,
+        0.22196419010636814, 0.1656570027172437, 0.11714229637491154, 0.08216984567186386,
+        0.07212485271039992, 0.08835534012744872, 0.11547620705727521, 0.1434164721715541,
+        0.16830203917700856, 0.1885071662871312, 0.20330742110553124, 0.21248887346187376,
+        0.21619200004828568, 0.21480115948500025, 0.20884496342705752, 0.19891495098501974,
+        0.18561445104983942, 0.16954278430568082, 0.15131390731335198, 0.13160830759504416,
+        0.11126572339244213, 0.09144933572160832, 0.07394246032352772, 0.06151512632986251,
+        0.05735570560076884, 0.062094382452133924, 0.0726021417298097, 0.08528406866470865,
+        0.0978861103821662, 0.10919851885595969, 0.1185700116352367, 0.1256390443670756,
+        0.13020607920783092, 0.13217621801058824, 0.13153738921653552, 0.12835638775403355,
+        0.12278216119671602, 0.11504972976886566, 0.10548212770664289, 0.09449285767629761,
+        0.08259798042464576, 0.07045593827999776, 0.05896370190727414, 0.049423192745236925,
+        0.04360204842457349, 0.04300949292451095, 0.047413896925014416,
+        0.05497384388431691, 0.06380975470840122, 0.07265397963395491, 0.08072882263707203,
+        0.08755189979788713, 0.09282201670227279, 0.09636108403357252, 0.09808263155496512,
+        0.09797187136450383, 0.09607141556457217, 0.09247116887984116, 0.08730272524595244,
+        0.08073928044459243, 0.07300278466275983, 0.06438210096599355, 0.055271400606132726,
+        0.0462499788543317, 0.038237643302215796, 0.03268418695823404, 0.03126987302872225,
+        0.03444149508329333, 0.04080900567436315, 0.048651061076785615,
+        0.056806939609382975, 0.06458996297296532, 0.07157751586563582,
+        0.0774896760461325, 0.08213071091909294, 0.08536163717527585, 0.08708767742054381,
+        0.08725304242110199, 0.08583925535731639, 0.08286498630460684, 0.07838642956262551,
+        0.0724982640305246, 0.06533666605216112, 0.05708865265327855, 0.04801925486483908,
+        0.038550412865810305, 0.029500181899988213, 0.02275694187235274,
+        0.0217944249771202, 0.02778224156754064, 0.03770401906532639, 0.04919069280510975,
+        0.06119081257887225, 0.07319134995753104, 0.08488012673115963, 0.09603232211695875,
+        0.10647070100984425, 0.11605138021316463, 0.12465929221382299, 0.132207375083526,
+        0.13863683658319773, 0.14391714430298921, 0.1480450474422579, 0.15104236635062,
+        0.15295261189358358, 0.15383673142765886, 0.15376841065253913, 0.15282938837973495,
+        0.1511051809519976, 0.1486814958453359, 0.1456414754933485, 0.14206378307380227,
+        0.13802144187600104, 0.13358127781951804, 0.12880379079673746, 0.12374328917879199,
+        0.11844815445863527, 0.11296114943219535, 0.10731973322603316, 0.10155638968084392,
+        0.09569900419883717, 0.08977133333922847, 0.08379360123104307, 0.07778323187137866,
+        0.07175569533679212, 0.06572541838672691, 0.059706694586120046,
+        0.05371453061021064, 0.04776538470174121, 0.041877788435591326,
+        0.036072895333349016, 0.03037508684999493, 0.024812961752009893,
+        0.01942163121293393, 0.01424957343044152, 0.009385436266218147,
+        0.005116475782768611, 0.0032078517534077085, 0.005711140846225617,
+        0.009207961551083815, 0.012574808896369971, 0.015619893090653243,
+        0.018277562465237967, 0.020514242238137404, 0.0223108192033702,
+        0.023658022546705366, 0.024554877095460982, 0.02500798795284565,
+        0.02503105467753568, 0.024644469623375905, 0.02387500430163264,
+        0.022755641867950493, 0.0213256470322915, 0.019631023743992712,
+        0.017725652185446472, 0.015673715968782316, 0.013554703173942384,
+        0.011473505703414657, 0.0095793257768491, 0.008091163916956079,
+        0.007286798495196143, 0.0073498863758182246, 0.008169177739236207,
+        0.0094360001486323, 0.010873200602089584, 0.012301266470025494,
+        0.01361212605869571, 0.014739785890015603, 0.015643309238084248,
+        0.016298101288908132, 0.016691478080180913, 0.01682033810061903,
+        0.01668987158808944, 0.01631280457523194, 0.01570896492577046, 0.014905128066462927,
+        0.013935222543901974, 0.012841081743414844, 0.011674013882160337,
+        0.010497429385650911, 0.009390224062687155, 0.008448525882936746,
+        0.007778527308038949, 0.0074694252976303666, 0.007550324901204694,
+        0.007968711367406383, 0.008618169436447701, 0.00938469627487296,
+        0.01017354422945039, 0.010914515140012569, 0.011558249993194046,
+        0.012071275508849596, 0.012432142365368297, 0.0126288179419821,
+        0.012657009277014958, 0.012519110213748793, 0.012223571563022142,
+        0.011784583353233685, 0.01122202334251584, 0.010561669890459183,
+        0.00983569138165109, 0.009083364186404467, 0.008351720261962632,
+        0.007695178432598297, 0.007172083775362614, 0.006835396490535851,
+        0.006717497249264724, 0.006816669673846946, 0.007096616461891812,
+        0.007500247252632256, 0.00796669987217339, 0.008442201856941021,
+        0.008883893104936546, 0.009259720073744078, 0.009547019522339967,
+        0.009731021172562491, 0.009803643321275715, 0.00976261225616689,
+        0.00961084465608298, 0.009356031531053015, 0.009010383503498776,
+        0.008590513136825354, 0.008117424918512802, 0.0076165365562039814,
+        0.007117531427596368, 0.0066536029641734076, 0.0062593339797120595,
+        0.005966368348719741, 0.005796889342009531, 0.005757076888419249,
+        0.005834448559790527, 0.006001295566558486, 0.006222119658990415,
+        0.006460897554305694, 0.006685699273717457, 0.0068706521074869175,
+        0.006996288664547294, 0.007049215500033484, 0.007021640583489787,
+        0.006911002752359907, 0.00671980114190777, 0.0064556735964467725,
+        0.006131766749709113, 0.005767428226570504, 0.00538915474259166,
+        0.005031386949678393, 0.004735920704440783, 0.004547547903916229,
+        0.004503834996782561, 0.004621829187647732, 0.004891126167613295,
+        0.005279553327372119, 0.005745762717734383, 0.006249376589005931,
+        0.006755598042032832, 0.0072360838409741375, 0.0076683337093730874,
+        0.00803480313923894, 0.008322157467847903, 0.00852073787351774,
+        0.008624202479971399, 0.00862929071986535, 0.008535671768376276,
+        0.00834585578826079, 0.008065164106869197, 0.007701771233469512,
+        0.00726684954745776, 0.006774867815106872, 0.006244113947987086,
+        0.005697509517908019, 0.005163684807843066, 0.004677893179730485,
+        0.004281332471904983, 0.004015932670937388, 0.003912200893741447,
+        0.003974777207883011, 0.0041784408384525655, 0.004479484030160998,
+        0.00483140893481141, 0.00519425839527865, 0.005537030623903957,
+        0.005836817015594862, 0.00607721166570173, 0.00624694271796681,
+        0.006338899162498473, 0.006349489982322022, 0.006278241494981908,
+        0.0061275637323165945, 0.005902650291761317, 0.005611508217995655,
+        0.005265145505829888, 0.004877973321750103, 0.0044684945948044305,
+        0.004060293195453887, 0.0036830385327922847, 0.0033723412175727476,
+        0.00316577119797026, 0.0030923196599553114, 0.003158831991673328,
+        0.0033454251087573733, 0.003615357042317124, 0.003929157076502026,
+        0.004252889170581553, 0.004560162238325092, 0.0048313119290998695,
+        0.00505202250722703, 0.005212178683662981, 0.005305066431727234,
+        0.0053268543418201085, 0.0052762708147136295, 0.005154418196988964,
+        0.004964695258119085, 0.004712828541756829, 0.004407045171187529,
+        0.0040584616304545065, 0.0036818192914761317, 0.0032967478735426003,
+        0.002929649592481645, 0.0026155692811587355, 0.00239699146338551,
+        0.002313176992267217, 0.002379385979538301, 0.002575361291927564,
+        0.0028588160444722424, 0.003186339734990494, 0.0035232682378622737,
+        0.003844261360945485, 0.004131107671561836, 0.00437066900792272,
+        0.004553501568028373, 0.004673018861908233, 0.004724997792424261,
+        0.004707287615229786, 0.00461963935406715, 0.004463614077687904,
+        0.004242558379881116, 0.003961664092776579, 0.0036281696281632043,
+        0.0032518357404025303, 0.0028459888636303923, 0.002429770846938546,
+        0.002032848421000404, 0.0017037723830845136, 0.0015152155668279592,
+        0.0015333837905658842, 0.001750706175350401, 0.0020951710229717797,
+        0.0024976780132227746, 0.002913707021428256, 0.003316067339883404,
+        0.0036870613732267058, 0.004014255906579226, 0.0042884486902825284,
+        0.004502688562964038, 0.004651785307288457, 0.004732049795973344,
+        0.0047411433649908186, 0.00467797803655852, 0.004542638812020342,
+        0.004336314383360794, 0.004061231810488433, 0.0037205989636857058,
+        0.0033185714938629147, 0.00286029252865021, 0.0023521527878015143,
+        0.0018028178002762118, 0.0012277451770235002, 0.0006788532944635071,
+        0.0004943883931070399, 0.0009822386546921786, 0.001642825813221277,
+        0.0023436713963429024, 0.0030598063923334535, 0.0037808999787109538,
+        0.004500349245441693, 0.005213092845839099, 0.005914980353417473,
+        0.006602530203380441, 0.007272801827494176, 0.007923301141985611,
+        0.008551892713251527, 0.00915671035824934, 0.009736065316526862,
+        0.010288354479435454, 0.010811972718867587, 0.011305233927543405,
+        0.011766305283824798, 0.012193158653745697, 0.01258354207703621,
+        0.01293497308275212, 0.01324475427827501, 0.01351001038410639, 0.013727744751356087,
+        0.01389491247906756, 0.014008506585349207, 0.014065653289689823,
+        0.014063712315148084, 0.014000378181984383, 0.01387377869708291,
+        0.013682567201789987, 0.013426005588338969, 0.01310403560227459,
+        0.012717336496579279, 0.012267367679542658, 0.011756395602134054,
+        0.011187504771400854, 0.010564593481843628, 0.009892355692738943,
+        0.009176251581485027, 0.008422470956470725, 0.007637896533145291,
+        0.00683007945124899, 0.006007250649712396, 0.005178417359987098,
+        0.004353657956024675, 0.0035449049276841146, 0.002768051829130624,
+        0.002049116130654241, 0.0014439133324608844, 0.0010887051392034965,
+        0.0011531922501180686, 0.0015238807438927545, 0.001987423702123627,
+        0.0024483921891936197, 0.0028710722527459285, 0.003239754034312919,
+        0.0035464299068528157, 0.0037868196185902917, 0.003958895836288649,
+        0.004062259394500073, 0.004097838720618675, 0.004067724867576619,
+        0.003975068550249087, 0.0038240105551039377, 0.0036196382903019818,
+        0.0033679760572363376, 0.003076034223254657, 0.0027519737282882192,
+        0.002405508899379073, 0.002048823413642134, 0.0016986161982211036,
+        0.001380487813423554, 0.0011363128473724996, 0.001024169852431633,
+        0.0010780053145037897, 0.0012618297432602143, 0.001510845627306931,
+        0.0017785448586901211, 0.0020384652300672176, 0.0022754174519756315,
+        0.0024800762580171644, 0.002646429569426662, 0.0027705992475030917,
+        0.0028502722833577483, 0.002884409045158697, 0.0028730830325158015,
+        0.0028173875443218686, 0.0027193819791638115, 0.0025820708106572532,
+        0.0024094240720053373, 0.0022064680800982905, 0.001979510341645692,
+        0.0017366341282171475, 0.0014887443037725112, 0.0012516881720159288,
+        0.001049934686973571, 0.0009193279332799447, 0.0008958178431358464,
+        0.0009834297252858857, 0.0011481434948010186, 0.0013502035323734907,
+        0.001561883868576214, 0.0017661036620918538, 0.0019520886512053466,
+        0.0021126567748356354, 0.0022428379895660417, 0.0023391920823508383,
+        0.002399464064674535, 0.0024224035159314938, 0.0024076662653186843,
+        0.002355760628147975, 0.0022680228880697026, 0.002146621077512877,
+        0.001994600188842008, 0.001816003752736942, 0.0016161506263175896,
+        0.0014022441655101216, 0.0011847129520376977, 0.0009800944654406014,
+        0.000816190541190867, 0.0007342534999964871, 0.000766316874688021,
+        0.0008982136061958188, 0.0010875952726419327, 0.0013001525450242171,
+        0.0015151878316181611, 0.0017202078028733677, 0.0019069940470294252,
+        0.0020696823500197777, 0.002203876079313414, 0.0023062296739526735,
+        0.0023742465319185283, 0.0024061777324829933, 0.0024009699338959265,
+        0.0023582388199613565, 0.0022782586482513294, 0.0021619677867947525,
+        0.002011000173606775, 0.0018277703811680045, 0.0016156816381041148,
+        0.001379640902739438, 0.0011274241394256318, 0.0008736875389888523,
+        0.0006526256743676439, 0.0005460731269175786, 0.0006411504435498891,
+        0.0008862932630529122, 0.0011964587435845137, 0.0015321992485143984,
+        0.001876467538473768, 0.0022200421105362696, 0.002556768060582492,
+        0.002881951089359531, 0.003191755750058049, 0.003482960182880188,
+        0.0037528505716037893, 0.003999173937346037, 0.004220115477780509,
+        0.004414285207379505, 0.004580706572101582, 0.004718803379199984,
+        0.004828383217959059, 0.004909616540473659, 0.0049630111526059685,
+        0.004989382235787743, 0.004989818276461393, 0.004965643470828917,
+        0.004918377324170983, 0.004849692289388226, 0.004761370394894589,
+        0.004655259899147969, 0.0045332330757570346, 0.00439714627389391,
+        0.004248803405533841, 0.004089923974437073, 0.003922116670212144,
+        0.003746859396927128, 0.003565486382754957, 0.0033791827286032174,
+        0.0031889864088468956, 0.002995797357787153, 0.0028003928903737054,
+        0.0026034483522026433, 0.0024055616082524155, 0.00220727979967841,
+        0.0020091267484766396, 0.0018116294946045129, 0.0016153427318424173,
+        0.001420870418708474, 0.001228884736946411, 0.0010401443347097178,
+        0.000855518006467528, 0.000676032424524731, 0.0005030087848875468,
+        0.00033858157030793826, 0.00018862980205493646, 9.277549063319994e-05,
+        0.00016023497350972697, 0.00027954941090620753, 0.00039628556441057266,
+        0.0005033063419599679, 0.0005984831476531242, 0.0006807402669685352,
+        0.0007494134289948477, 0.0008040939466348918, 0.0008445832680702199,
+        0.000870879140334019, 0.0008831715369235168, 0.000881841204208625,
+        0.0008674584466970033, 0.0008407817640136457, 0.000802757206342675,
+        0.0007545206628636986, 0.0006974074319790294, 0.0006329774676849083,
+        0.0005630730076773463, 0.0004899430095359821, 0.0004165060530140538,
+        0.0003468890338127139, 0.00028739396505602835, 0.0002473660645688256,
+        0.00023658850976056924, 0.0002565286445823424, 0.0002977816873280726,
+        0.0003490858847865038, 0.00040269597771723574, 0.0004540044680157341,
+        0.0005002423783726645, 0.0005396730432566896, 0.0005711859917524566,
+        0.0005940967232699688, 0.0006080447761071341, 0.0006129392320586128,
+        0.000608928167616676, 0.000596381358996288, 0.000575881928493735,
+        0.0005482263717487003, 0.0005144353632248188, 0.00047578091719397423,
+        0.00043383931045188245, 0.00039058240171627417, 0.0003485149748296675,
+        0.00031082507940535635, 0.0002813748375143553, 0.0002641060289185773,
+        0.0002615160382317484, 0.000273088610418314, 0.00029549002788364616,
+        0.00032435630536069965, 0.00035577788520758946, 0.00038677440482570214,
+        0.00041521256889273184, 0.00043960147095968273, 0.00045892217571353417,
+        0.00047251315444755065, 0.0004799983606680745, 0.00048124294989729954,
+        0.0004763263402321561, 0.00046552669535731433, 0.00044931407777611696,
+        0.00042835179397903914, 0.0004035071723067247, 0.00037587409855518067,
+        0.0003468089662975361, 0.00031797566981024434, 0.0002913754946850879,
+        0.0002692928136188185, 0.00025402901279077806, 0.0002473285855464691,
+        0.00024968678510394317, 0.00026007278051635313, 0.00027636064185377246,
+        0.0002960824830717557, 0.0003169792662062505, 0.0003372170682443112,
+        0.0003553980385362168, 0.00037049946703278326, 0.0003818064588973642,
+        0.00038885838038218046, 0.0003914109150428129, 0.0003894106408719555,
+        0.00038297887562734805, 0.0003724026085410706, 0.00035813148709735066,
+        0.00034078069597019933, 0.0003211398426291283, 0.0003001868993996139,
+        0.00027910208643384536, 0.00025926618847605987, 0.00024220870245692647,
+        0.0002294516713146996, 0.00022221274923836547, 0.00022103795678472745,
+        0.00022557882507046067, 0.0002346976373838474, 0.0002468288194530752,
+        0.00026035358564992423, 0.0002738314976120527, 0.0002860878281801283,
+        0.0002962186374523421, 0.0003035651827369831, 0.00030768403928821235,
+        0.0003083226365395129, 0.00030540245336022065, 0.0002990097604104833,
+        0.0002893936316396198, 0.000276971518485766, 0.000262343189341046,
+        0.0002463133009527087, 0.00022991913483142416, 0.00021444869933477648,
+        0.00020141012563473348, 0.0001923824939140057, 0.0001886898420500139,
+        0.00019097505698170277, 0.0001989440565449569, 0.00021149868535420466,
+        0.00022713868547325928, 0.00024433839938122, 0.0002617512042323858,
+        0.00027827013493277345, 0.0002930186621307521, 0.0003053209978610769,
+        0.0003146730447326018, 0.0003207199215775994, 0.0003232402014239982,
+        0.00032213550900829713, 0.00031742420293947026, 0.00030923840839024006,
+        0.00029782431867934233, 0.00028354637865339355, 0.0002668966870998555,
+        0.00024851156642907154, 0.0002291970970263044, 0.00020996244168747846,
+        0.00019204886758678196, 0.00017691504158035917, 0.00016609653891007725,
+        0.00016085557847700616, 0.00016169882728996624, 0.00016810773412463412,
+        0.0001787531560674852, 0.00019199646616111917, 0.00020629415496007126,
+        0.0002203712125947746, 0.0002332400745008602, 0.0002441620620719783,
+        0.00025260167775483725, 0.00025818993847594407, 0.00026069864520192267,
+        0.00026002351555084655, 0.0002561738798078993, 0.00024926744087550154,
+        0.00023952957850501108, 0.00022729767358505652, 0.0002130319431440918,
+        0.0001973351616926205, 0.00018098352455057413, 0.00016496674942299367,
+        0.00015051948807458292, 0.00013908637267777394, 0.00013211106877966848,
+        0.00013058434736628563, 0.0001345680614388699, 0.0001431385040157456,
+        0.0001548211641442057, 0.00016809586241278755, 0.000181666133708444,
+        0.00019451693127724054, 0.00020588185576547263, 0.0002151937810184018,
+        0.00022204413192637528, 0.00022615452377721139, 0.00022735837849117976,
+        0.00022558958136740696, 0.00022087611461603517, 0.0002133376673822466,
+        0.00020318727727925692, 0.00019073824009666458, 0.00017641908111472193,
+        0.00016080151130437926, 0.00014464847740358296, 0.00012898769194741216,
+        0.00011519459302866609, 0.00010498902864674481, 0.0001001086040240721,
+        0.00010151805658010461, 0.00010874842208072688, 0.00012020698719219032,
+        0.00013404990664453252, 0.00014872367005410068, 0.0001630657989226192,
+        0.00017623140971295803, 0.00018760439326940143, 0.0001967336404194769,
+        0.00020329332444256212, 0.00020705929160243382, 0.00020789519262597467,
+        0.0002057443896566113, 0.00020062546368943845, 0.00019263039962859132,
+        0.00018192556873150673, 0.00016875686664541051, 0.000153462435553987,
+        0.00013650059433182224, 0.00011850974944612033, 0.00010043632777235315,
+        8.379493724029804e-05, 7.106937704740386e-05, 6.5646476296651e-05,
+        6.966624383480316e-05, 8.158963981850832e-05, 9.805137028528685e-05,
+        0.00011638632923770846, 0.0001349468691746035, 0.00015270991181388823,
+        0.00016898868643402907, 0.00018328674026842184, 0.00019522827530013792,
+        0.00020452439130471268, 0.0002109560783730498, 0.00021436513399099197,
+        0.00021464883469416346, 0.00021175632324399262, 0.00020568569689141458],
+    [2.3862239638435658e-08, 7.166262606888521e-08, 1.196911855847912e-07,
+        1.681015124251765e-07, 2.1704942834029127e-07, 2.666939139056085e-07,
+        3.171980458697401e-07, 3.687299919669122e-07, 4.2146404025294803e-07,
+        4.755816886592167e-07, 5.312728010214457e-07, 5.887368433312538e-07,
+        6.481842063456095e-07, 7.098376382247856e-07, 7.739337921753112e-07,
+        8.407249140827189e-07, 9.104806836558643e-07, 9.8349023191179e-07,
+        1.0600643600090176e-06, 1.1405379810191713e-06, 1.2252728226915431e-06,
+        1.3146604153135927e-06, 1.4091254107477468e-06, 1.5091292727385778e-06,
+        1.6151743885087626e-06, 1.7278086574250246e-06, 1.8476306251260981e-06,
+        1.9752952316151565e-06, 2.111520264392762e-06, 2.2570936076731957e-06,
+        2.412881409852837e-06, 2.579837288007295e-06, 2.759012730259689e-06,
+        2.9515688624322826e-06, 3.1587897876794975e-06, 3.382097728338753e-06,
+        3.6230702507585294e-06, 3.883459886559608e-06, 4.16521653374563e-06,
+        4.470513068280426e-06, 4.801774694040263e-06, 5.161712630442587e-06,
+        5.553362869798434e-06, 5.9801308476887465e-06, 6.445843054322861e-06,
+        6.954806774458981e-06, 7.511879433297447e-06, 8.122549232837686e-06,
+        8.79302920882096e-06, 9.530367168299552e-06, 1.0342574571437583e-05,
+        1.1238778030887361e-05, 1.2229397903147906e-05, 1.3326359478523875e-05,
+        1.454334349869713e-05, 1.589608430397278e-05, 1.7402725941987408e-05,
+        1.9084249011889873e-05, 2.096498432658518e-05, 2.3073233535561665e-05,
+        2.5442022222471796e-05, 2.8110017945294563e-05, 3.112265476832337e-05,
+        3.4533517853226605e-05, 3.840605766957403e-05, 4.281572487577901e-05,
+        4.785264597408176e-05, 5.362499972683663e-05, 6.0263309522631e-05,
+        6.792594410458695e-05, 7.680622886869423e-05, 8.714172796452615e-05,
+        9.922648867531412e-05, 0.00011342738342539632, 0.0001302062070734875,
+        0.00015014999594610006, 0.00017401331994211782, 0.0002027783931916897,
+        0.00023774237107928692, 0.00028064733461260366, 0.00033387958078997474,
+        0.00040078596733188985, 0.00048619751074442175, 0.0005973416227550013,
+        0.0007455369811438177, 0.0009496146554595498, 0.0012436349550740172,
+        0.0016972594011459546, 0.002484378736514361, 0.004246352369516762,
+        0.019665698548888867, 0.007640153844371613, 0.005962399592829648,
+        0.005482127274870969, 0.005386664877002816, 0.005495379918547228,
+        0.005748937059459517, 0.006127906006401491, 0.0066311926583155845,
+        0.007269091202463504, 0.008061310885796164, 0.009037320434994766,
+        0.010238282290569155, 0.011720594805966768, 0.013561538737048882,
+        0.01586806355735571, 0.018790598219036583, 0.02254531207249972,
+        0.027451272082155156, 0.03399526748409558, 0.0429513267449354, 0.055617073287874186,
+        0.07432601248455228, 0.10370600521875536, 0.15438924479022112, 0.25769345742073296,
+        0.5702284482610187, 6.313847138107146, 0.4071254696256903, 0.8917112725721819,
+        1.7737183155179557, 1.0669113406400528, 1.0894218941230518, 1.631411793730598,
+        1.6346168013263542, 0.6533254754488088, 0.5646757017480043, 0.7696042314141937,
+        1.2922284446021706, 2.306395352441572, 1.9220859568134687, 1.2504775596891307,
+        0.9594248432254071, 0.8482254350937367, 0.8648961854379278, 1.0467572606856712,
+        1.2960262646673149, 1.1445634479916298, 0.964796577033112, 0.9146630195983295,
+        0.9583314967930036, 1.0905472188595915, 1.3358427317355968, 1.6838328216401937,
+        1.792068829649226, 1.40251000122698, 1.018705292225905, 0.7976144462956901,
+        0.7033417298909306, 0.7169421352635927, 0.8488809640569369, 1.1218007219447874,
+        1.4598163578930123, 1.5348057655461422, 1.3435098605835685, 1.157010174748327,
+        1.042157022988131, 0.8366903179308738, 0.7384087104269685, 0.6658135457708906,
+        0.5839488984994189, 0.4783485176069125, 0.35965765771498936, 0.2591637887657863,
+        0.20762952980789393, 0.21302349629132908, 0.2537086450421141, 0.30961209813449486,
+        0.3734277947787624, 0.4432455558374277, 0.5171411085962351, 0.5899454580670053,
+        0.6516784653534023, 0.6901148054424697, 0.6982920805623739, 0.6798699497203008,
+        0.6455573316945653, 0.6058295576849679, 0.567364923447234, 0.5333142882101783,
+        0.5046889082897807, 0.48146779803219986, 0.46322667218845515, 0.4494417333510582,
+        0.43961956621701687, 0.43334332132541786, 0.4302806062684947, 0.43017387800347595,
+        0.43282166283497286, 0.43805241062052536, 0.44568878043466936, 0.4554970581382083,
+        0.4671139316506125, 0.4799423434890259, 0.4930139028822303, 0.5048362792042536,
+        0.5132915576486957, 0.5157225942925646, 0.5093795625124357, 0.4922626241377801,
+        0.46402742934386654, 0.4263272307367781, 0.38225454862699365, 0.3352661471068681,
+        0.2883002194605424, 0.24345282741365834, 0.20212712504583663, 0.16542244749742485,
+        0.13460360011808184, 0.11150152985448045, 0.09832823867296304, 0.09603170438312415,
+        0.10248814883224446, 0.11370365199755156, 0.12621803077421753, 0.13784896148361533,
+        0.1474166695622077, 0.1543850862761013, 0.15861525816327562, 0.16020325284422016,
+        0.15937125479013295, 0.1563978424341304, 0.1515801839701349, 0.14522145704012793,
+        0.13763600868236997, 0.12916424721006062, 0.12018907461300284, 0.11114565338875919,
+        0.10251634263656756, 0.09480283246329077, 0.08846946691466762, 0.0838606261876009,
+        0.08111570860646784, 0.08012616887876889, 0.08056837464531, 0.08199729632172362,
+        0.08394876504617493, 0.0860095969140437, 0.08784922278318094, 0.08922642136407723,
+        0.08998549004493658, 0.09004957241269018, 0.08941318439005154, 0.08813331612133682,
+        0.08631816080347195, 0.08411330071308075, 0.08168602903556224, 0.07920885633425738,
+        0.07684316693893138, 0.07472387077305578, 0.07294615017062277, 0.07155601015717869,
+        0.070546723624764, 0.06986267798038372, 0.0694104228702872, 0.06907467299876095,
+        0.0687357876311025, 0.06828540425234243, 0.06763812620746687, 0.06673869075353461,
+        0.06556524497189299, 0.06412995069703294, 0.06247811496427698, 0.06068651720627927,
+        0.05886073842502521, 0.05713029733458714, 0.05563962582167375, 0.05453303411236194,
+        0.053933663962425354, 0.05392014321481672, 0.05450833315936695,
+        0.05564561745818162, 0.057220034597621136, 0.05907966486488689,
+        0.061054377814896095, 0.06297375584929986, 0.06467889673605638,
+        0.06602881370756124, 0.06690336510491227, 0.06720459503373487, 0.06685781829013723,
+        0.06581321241866613, 0.06404829384678179, 0.06157153493341928, 0.058427575744064805,
+        0.05470505369456176, 0.05054903831661324, 0.046181143976011314,
+        0.04192992422536517, 0.03826573207570462, 0.03580326612095817, 0.035184543250106635,
+        0.036802270990134806, 0.04058254469946012, 0.04608941646827893,
+        0.052795423100027945, 0.060245102980589556, 0.06808669986171724,
+        0.07605198230398748, 0.08393086746994519, 0.09155331800253036, 0.098778682755807,
+        0.10549025124210325, 0.11159298186621867, 0.1170128986003514, 0.1216970839626383,
+        0.12561352403656645, 0.12875033835830255, 0.13111418072983394, 0.13272782211788656,
+        0.13362710263465252, 0.13385754651665666, 0.1334709651025365, 0.13252233763988908,
+        0.1310671798915877, 0.12915951169950476, 0.1268504395459153, 0.12418729412919546,
+        0.12121321355054641, 0.11796704104797745, 0.11448340931177006, 0.1107929059190352,
+        0.10692224950968353, 0.10289444652596477, 0.09872893562802276, 0.09444175425460213,
+        0.09004577404540887, 0.08555104736710628, 0.08096528825598459, 0.07629448392965275,
+        0.07154360544158969, 0.0667173659947612, 0.061820967952013466, 0.0568607860596333,
+        0.05184495187982856, 0.04678382738659311, 0.04169037792875082, 0.0365804720840326,
+        0.0314731499311465, 0.026390925453093832, 0.021360272243098007,
+        0.01641277565245852, 0.011589005661168267, 0.006957697724122302,
+        0.002814697258399236, 0.0028205504356493, 0.006526899832734892,
+        0.01025220434806786, 0.013716320195537129, 0.016854273990067534,
+        0.01962973326532548, 0.022016867354096074, 0.023996829059299646,
+        0.02555679964943085, 0.02668962650651032, 0.027393623493058062,
+        0.027672439863805465, 0.027534980261705585, 0.02699536311046105,
+        0.026072890648495953, 0.024791992884456365, 0.02318211175726541,
+        0.021277518701355896, 0.019117118463218022, 0.01674441099159031,
+        0.014208053875113865, 0.01156423334423846, 0.008884751103207826,
+        0.006286604797930064, 0.004061678749994472, 0.0031411892821630286,
+        0.004320691830089747, 0.0064094104240050515, 0.00863558937503297,
+        0.010774519316356427, 0.012737941758700291, 0.014477307315744198,
+        0.015960734358046683, 0.01716616777130603, 0.01807894911136321,
+        0.01869078546746617, 0.01899919236298752, 0.019007098007123507,
+        0.018722508099793183, 0.01815821231413828, 0.01733154780717666,
+        0.01626425530247577, 0.014982493164168498, 0.013517146334822119,
+        0.01190474641576111, 0.010189779142777716, 0.008430396328124472,
+        0.006713034856172449, 0.005190153886543397, 0.004155921471839772,
+        0.004011463486809436, 0.0047845011721206615, 0.006057165001694139,
+        0.007490877810671678, 0.008916520827735459, 0.01024852310870665,
+        0.011437501639540317, 0.01245172482964633, 0.013269776017049291,
+        0.013877437325769936, 0.014266257566231363, 0.014432826963471902,
+        0.01437835314630487, 0.01410836402044927, 0.013632470079192978,
+        0.01296417858129788, 0.01212079760793525, 0.011123522278587282,
+        0.009997892169147683, 0.008775022725938914, 0.007494530164338044,
+        0.006211349556349113, 0.005011501744661805, 0.004044014159218873,
+        0.0035443858818609572, 0.0036990703379085102, 0.0043989030983924236,
+        0.005378387952034133, 0.006446295313438399, 0.007497776751855075,
+        0.0084739835559876, 0.009338659413851183, 0.010067741354271558,
+        0.010644766429354198, 0.011058733174839373, 0.011303036933213518,
+        0.01137489631548343, 0.011275010262655408, 0.01100732248196305,
+        0.010578834700767537, 0.00999944706791937, 0.009281833720569566,
+        0.008441398822804543, 0.0074964267047968654, 0.0064686999062625854,
+        0.0053853011270442895, 0.004283707367282802, 0.0032271387188366535,
+        0.002352643388197527, 0.001963281760030029, 0.0023057476995682036,
+        0.0031105689708057394, 0.004064470832319193, 0.005030109678937642,
+        0.005947951865216119, 0.006786134721470993, 0.007524497786218358,
+        0.008149186249991117, 0.008650605612944775, 0.009022563635031637,
+        0.009261877950287403, 0.009368183698003976, 0.009343838090246068,
+        0.009193884554073859, 0.008926070948881924, 0.008550937952003339,
+        0.008082016130557548, 0.0075362002574141515, 0.006934409959098763,
+        0.0063026856312688164, 0.005673842632401552, 0.005089481203421548,
+        0.004600931644525049, 0.004265004934653536, 0.004128788035579158,
+        0.004206612452967168, 0.004469791498142856, 0.00486206982803965,
+        0.0053235332768626865, 0.005804007791591716, 0.00626555658755777,
+        0.006680527874188886, 0.007029026541212952, 0.007296962151886705,
+        0.007474742444471307, 0.007556436158427923, 0.007539238124246282,
+        0.007423124292561362, 0.007210632772419416, 0.006906743681451032,
+        0.006518861670432028, 0.00605693976899476, 0.0055338354761213, 0.004966082325285277,
+        0.004375425715226934, 0.0037917173098726362, 0.0032577947744903395,
+        0.002835011146785203, 0.0025991638461103734, 0.0026060767728923167,
+        0.0028436081296793797, 0.0032408691671043893, 0.003720331842672947,
+        0.004224310523599342, 0.004714426986576526, 0.005165127213628056,
+        0.005558836137286227, 0.005883163813120385, 0.006129388525845778,
+        0.006291632081565532, 0.006366399122948465, 0.006352308384935292,
+        0.006249927464363782, 0.006061667994167408, 0.005791725587952464,
+        0.005446070618671261, 0.005032521518148721, 0.004560975450859813,
+        0.004043960064184379, 0.0034978708019957555, 0.002945721768812942,
+        0.002423181249562077, 0.0019901916454486746, 0.0017405506542988564,
+        0.0017611819161150052, 0.0020347751091035, 0.002459696341382104,
+        0.0029470785352386517, 0.003443686348734978, 0.003918618137880264,
+        0.004352492148080788, 0.00473212188047335, 0.0050480725922580315,
+        0.005293513765355605, 0.0054636539517902965, 0.0055554454210247125,
+        0.005567417266169566, 0.005499570397205764, 0.005353302418632217,
+        0.005131348060971062, 0.004837732036467914, 0.004477741930012447,
+        0.004057945401736489, 0.0035863116392431805, 0.0030725888193282825,
+        0.002529362012241891, 0.001975150921321169, 0.001444578407972916,
+        0.001024176017285144, 0.000914620545705684, 0.0012045256128462444,
+        0.0016871149134133066, 0.0022212008977955636, 0.0027542558653980277,
+        0.0032627769353155197, 0.003732962301684031, 0.004155127522443925,
+        0.004521858416063889, 0.004827317728559443, 0.005066958343908672,
+        0.005237392965918255, 0.005336325579031194, 0.005362505243162396,
+        0.005315684675574002, 0.005196575567024777, 0.0050067970083412855,
+        0.004748815612835724, 0.004425877138860484, 0.004041930275150958,
+        0.0036015442281297884, 0.003109823629238026, 0.002572329509817029,
+        0.0019950344538650763, 0.0013844399399006433, 0.000748872092470156,
+        0.0001451953254639409, 0.0006141466465435857, 0.001295593142971487,
+        0.001986102937015026, 0.0026769481072093223, 0.0033626871265843837,
+        0.0040387833330340055, 0.004701319914792496, 0.005346942543181295,
+        0.005972838075621026, 0.006576712478332505, 0.007156758522548583,
+        0.007711610912507458, 0.008240289097706051, 0.008742129374616046,
+        0.009216708813385835, 0.009663764255248624, 0.010083110134359433,
+        0.010474559161393605, 0.01083784991732017, 0.011172585128740269,
+        0.011478183837340948, 0.011753849875244539, 0.011998558088586549,
+        0.012211058702968958, 0.012389899193510422, 0.01253346209938831,
+        0.012640016474348356, 0.012707780132740293, 0.012734989545711041,
+        0.012719974151548841, 0.012661231936098354, 0.012557503373259043,
+        0.012407841150611706, 0.012211673504474588, 0.011968859423490017,
+        0.011679734430761047, 0.011345146112156776, 0.01096647901842708,
+        0.010545669037947162, 0.010085207829163476, 0.009588138443408748,
+        0.009058043909616379, 0.008499031378339794, 0.007915715585783014,
+        0.007313207171931681, 0.0066971142630527815, 0.006073570600957174,
+        0.005449312019567984, 0.004831838179210501, 0.004229723075524727,
+        0.0036531819506667473, 0.0031150602279576053, 0.0026324119483119197,
+        0.002228427879724601, 0.0019325864608239623, 0.0017729475880984447,
+        0.0017569643302831296, 0.0018587648094222343, 0.0020335753979949527,
+        0.0022403172629623107, 0.0024502478685227273, 0.0026453827685152293,
+        0.002814954289328788, 0.0029527581047875495, 0.003055534507681752,
+        0.003122027283906325, 0.0031524320335440848, 0.003148062272354171,
+        0.0031111388366074424, 0.0030446515712503706, 0.002952265663140533,
+        0.0028382571627450816, 0.0027074677245116953, 0.0025652690437212512,
+        0.0024175226377462287, 0.0022705091805821894, 0.0021307829779125495,
+        0.0020048864485369675, 0.0018988561372126592, 0.001817504141093933,
+        0.001763597771083446, 0.0017372353554902227, 0.0017357581235961236,
+        0.0017543155518202878, 0.0017868536429575526, 0.001827127564656906,
+        0.001869450791531323, 0.0019091090250941138, 0.0019425096759171498,
+        0.001967172803599787, 0.0019816465324445027, 0.0019853955483663636,
+        0.0019786848915750803, 0.001962465352876374, 0.0019382583132086034,
+        0.0019080337372570906, 0.0018740735604976103, 0.0018388136265978098,
+        0.0018046613262389679, 0.0017737939536235634, 0.0017479540763119202,
+        0.0017282697744768834, 0.0017151335801219528, 0.0017081685386667038,
+        0.001706292108436441, 0.0017078651700156754, 0.0017108949121235225,
+        0.0017132543430152366, 0.0017128875731249333, 0.0017079829087989359,
+        0.0016971085202115374, 0.0016793141363885392, 0.0016542061580592468,
+        0.001622003698631719, 0.0015835804132045186, 0.0015404918942601153,
+        0.0014949804355233911, 0.001449937498475786, 0.0014087904529734494,
+        0.001375270703115167, 0.0013530305297051353, 0.001345125057656639,
+        0.0013534628466035181, 0.0013784031329456166, 0.0014186591344007376,
+        0.00147153600340403, 0.0015333826748542849, 0.0016000812085864749,
+        0.0016674471220729013, 0.0017314987313088448, 0.001788611995040473,
+        0.0018355976793742932, 0.0018697347847623324, 0.001888784030705571,
+        0.0018909960566083851, 0.0018751233007551313, 0.0018404422345897808,
+        0.0017867933366003566, 0.001714649989624951, 0.0016252354246033395,
+        0.001520721182926823, 0.001404564374759541, 0.0012820733042751113,
+        0.001161302970690357, 0.001054231735165784, 0.0009774415418155164,
+        0.0009498985308321974, 0.000985499258966855, 0.001085152022702926,
+        0.0012379075600520853, 0.001428940156047854, 0.0016451830346408897,
+        0.00187666512420078, 0.002115976402227156, 0.002357481807498773,
+        0.002596734878887537, 0.0028301074755121077, 0.003054569057046807,
+        0.003267557776678794, 0.0034669055860293624, 0.0036507944459736753,
+        0.003817730006628257, 0.003966524597425024, 0.004096284584556995,
+        0.004206399065325951, 0.004296528033949043, 0.004366588887758329,
+        0.004416740623375636, 0.004447365403430969, 0.0044590474147363345,
+        0.004452549123941058, 0.004428785188318198, 0.004388794410080334,
+        0.004333710240114104, 0.0042647304444064305, 0.004183086643950954,
+        0.0040900145230876464, 0.0039867255660060216, 0.0038743812181224286,
+        0.0037540703670429537, 0.0036267909874361935, 0.003493436685210115,
+        0.003354788705737781, 0.0032115137395450264, 0.003064167578070278,
+        0.0029132043602886283, 0.002758990835296951, 0.0026018247753751837,
+        0.0024419564406164083, 0.002279611842323567, 0.0021150164958106195,
+        0.0019484183983965056, 0.0017801091105619133, 0.0016104420505455358,
+        0.0014398474323612024, 0.0012688437130823856, 0.0010980460861922145,
+        0.0009281738486613482, 0.0007600616967416783, 0.0005946902509821783,
+        0.0004332928807164881, 0.00027783449875455477, 0.0001346082490635081,
+        7.453107739260777e-05, 0.0001831415269008535, 0.00030868231317243705,
+        0.0004282086857947778, 0.0005384820847751585, 0.0006380906651334011,
+        0.0007260860978578091, 0.0008017464398161321, 0.0008645196305742768,
+        0.0009140101658392221, 0.0009499779492466497, 0.0009723402111179475,
+        0.0009811733010070868, 0.000976713115047514, 0.0009593536899915289,
+        0.0009296438728652541, 0.0008882822305197527, 0.0008361106297182643,
+        0.0007741073235530515, 0.0007033811601151011, 0.0006251702651224356,
+        0.0005408528903739541, 0.0004519903652631586, 0.0003604619877917419,
+        0.0002689076193909643, 0.00018245458976744294, 0.00011682629514674912,
+        0.00011440788080811837, 0.00017405085615192293, 0.0002510696328189288,
+        0.00032915093791842284, 0.0004033304279065223, 0.00047135076579796176,
+        0.0005318355741364523, 0.0005838191199702674, 0.0006265964727008919,
+        0.0006596680532184253, 0.0006827165609625877, 0.0006955959497751796,
+        0.0006983248814292725, 0.0006910816417162708, 0.0006741994050542039,
+        0.0006481617338288834, 0.0006135989883159395, 0.0005712873410592677,
+        0.0005221539192697029, 0.0004672954816166115, 0.00040802713436847055,
+        0.00034600068723513816, 0.0002834947941617448, 0.00022414887304062847,
+        0.00017473977680730106, 0.00014762004192871348, 0.00015461935684411696,
+        0.00019011722664667504, 0.00023917840579727793, 0.00029211105520027345,
+        0.00034409660374467096, 0.0003925644576252007, 0.00043595248794232714,
+        0.0004732159612932666, 0.0005036259520162869, 0.0005266804239946383,
+        0.0005420619266474483, 0.000549615737472245, 0.0005493373784358143,
+        0.0005413646310389221, 0.000525972009720943, 0.0005035672129895695,
+        0.0004746902893870468, 0.00044001776575965, 0.0004003766198056549,
+        0.00035677842020753444, 0.0003104961546100286, 0.0002632345357969515,
+        0.00021750649143869013, 0.00017741182666617707, 0.00014970161508693058,
+        0.0001425328729186258, 0.00015802044562893562, 0.00018910946572424332,
+        0.00022745180577325884, 0.0002676796087897703, 0.0003067371754096656,
+        0.0003427934634360182, 0.00037465793429267684, 0.0004015103585146871,
+        0.0004227752099677984, 0.00043806060931888126, 0.00044712685205934626,
+        0.0004498689601757305, 0.0004463060840685485, 0.000436574409060321,
+        0.0004209221503296211, 0.00039970641110032495, 0.00037339275493366637,
+        0.00034255986767056505, 0.00030791460090540785, 0.0002703291779798713,
+        0.00023092805492419432, 0.00019129162794419126, 0.00015393828818015943,
+        0.0001233575945444845, 0.0001070172173841939, 0.00011143683880708753,
+        0.00013360416252484227, 0.00016501783791969494, 0.00019956772150104806,
+        0.0002339656683234538, 0.00026638659022162404, 0.0002957042713650688,
+        0.00032116110218063996, 0.0003422258538267491, 0.00035852935830131793,
+        0.000369833770050732, 0.0003760170885658932, 0.0003770650111183581,
+        0.0003730666223528645, 0.0003642125403320792, 0.0003507953650565882,
+        0.0003332132762379871, 0.00031197882755115166, 0.0002877368190227585,
+        0.0002612981503392527, 0.00023370119608268032, 0.00020631689512296548,
+        0.00018100611724361173, 0.0001602685627265992, 0.00014709008313291768,
+        0.00014394228427491308, 0.00015116737863257452, 0.00016662145268253397,
+        0.00018714012802192723, 0.00020991630816452974, 0.00023288654998838987,
+        0.00025461085922402787, 0.0002740809494852788, 0.0002905806011337314,
+        0.00030360017087837634, 0.0003127866716078618, 0.0003179146490071118,
+        0.0003188688511460368, 0.00031563364640440933, 0.000308286531800894,
+        0.00029699455256640433, 0.0002820135404460018, 0.00026369118545159894,
+        0.00024247655841964913, 0.00021894158886843855, 0.000193825686680447,
+        0.00016812577259943566, 0.00014327163789904242, 0.00012142710335464521,
+        0.00010578174789893322, 9.997261034556272e-05, 0.00010558242240087156,
+        0.00012040942818842222, 0.00014060005326169643, 0.00016300428344869367,
+        0.0001855641711220581, 0.00020696681603560156, 0.00022633706903170322,
+        0.00024306292467843592, 0.0002567050272586674, 0.00026694993571564597,
+        0.0002735853492580297, 0.0002764864288425403, 0.0002756078320158484,
+        0.0002709787939457077, 0.00026270000850873694, 0.00025094192463032334,
+        0.00023594478540303233, 0.00021802164533518177, 0.00019756722403655377,
+        0.00017507892531318432, 0.00015120450124436348, 0.00012685089407709884,
+        0.0001034360653722139, 8.343383152381904e-05, 7.107252115439423e-05,
+        7.094550805146767e-05, 8.282198012777927e-05, 0.0001018597769227678,
+        0.00012381592163608916, 0.0001462659584050435, 0.0001678552135967093,
+        0.00018774829226187803, 0.00020537643847569212, 0.00022032730303738287,
+        0.00023229515336698945, 0.0002410572034776676, 0.0002464617003617292,
+        0.0002484214635310603, 0.0002469099650073882, 0.0002419585584522463,
+        0.00023365421193026012, 0.00022213752660957728, 0.00020760116205414316,
+        0.00019028922150461327, 0.00017049897861153398, 0.00014858832236148257,
+        0.00012499789676208455, 0.00010031511194735552, 7.54770740439736e-05,
+        5.2523656507718826e-05, 3.743038663158883e-05, 4.1075303887575235e-05,
+        5.9914076160573436e-05, 8.362281961014647e-05, 0.00010816523062846991,
+        0.00013207813507227887, 0.00015462120883330858, 0.00017530873062845368,
+        0.000193774694454395, 0.00020972708155094795, 0.00022293047088728417,
+        0.0002331988917532811, 0.00024039263787726704, 0.0002444165801947094,
+        0.00024521891799487777, 0.00024278988222685915, 0.00023716016369155102,
+        0.00022839896780955327, 0.0002166116705343707, 0.00020193710094862588,
+        0.00018454452756186087], [7.345136404075258e-10, 2.2060059788008042e-09,
+        3.6849085076438406e-09, 5.17621060471466e-09, 6.684975841430256e-09,
+        8.216372968231164e-09, 9.775707152168043e-09, 1.1368453071484697e-08,
+        1.300028918011284e-08, 1.4677133954934822e-08, 1.6405184340183188e-08,
+        1.8190956835604997e-08, 2.0041331439301217e-08, 2.1963599201182258e-08,
+        2.3965513562990548e-08, 2.6055346283133156e-08, 2.8241948388153684e-08,
+        3.0534816882076907e-08, 3.294416801282466e-08, 3.548101778539788e-08,
+        3.8157270926179185e-08, 4.098581905970981e-08, 4.3980649545152674e-08,
+        4.715696622367078e-08, 5.053132362993199e-08, 5.412177638863349e-08,
+        5.794804589828798e-08, 6.203170638209503e-08, 6.63963930716473e-08,
+        7.106803524535966e-08, 7.607511778408859e-08, 8.144897472743252e-08,
+        8.722411957363166e-08, 9.343861713189603e-08, 1.0013450295167723e-07,
+        1.0735825683236522e-07, 1.1516133834734017e-07, 1.2360079307930527e-07,
+        1.3273994015517644e-07, 1.4264915272724408e-07, 1.5340674560511723e-07,
+        1.6509998580509753e-07, 1.7782624513620677e-07, 1.9169431634228835e-07,
+        2.068259187768906e-07, 2.2335742281273436e-07, 2.4144182910439447e-07,
+        2.612510423568703e-07, 2.829784896380033e-07, 3.068421387362793e-07,
+        3.3308798490024093e-07, 3.619940853518879e-07, 3.938752356454267e-07,
+        4.290884007039421e-07, 4.680390337973124e-07, 5.111884425506648e-07,
+        5.590623937021056e-07, 6.12261183690168e-07, 6.714714511078182e-07,
+        7.374800609077347e-07, 8.111904599204442e-07, 8.936419876249965e-07,
+        9.86032728946668e-07, 1.0897466235001486e-06, 1.2063857034516087e-06,
+        1.3378085283327966e-06, 1.486176126987037e-06, 1.6540070616841371e-06,
+        1.8442436108379312e-06, 2.0603315427469487e-06, 2.30631655795059e-06,
+        2.586961241915645e-06, 2.9078873434702914e-06, 3.275749429556033e-06,
+        3.698447565210298e-06, 4.1853887073569045e-06, 4.7478091615265955e-06,
+        5.399173880286322e-06, 6.155672886469769e-06, 7.036841015313622e-06,
+        8.066334943189194e-06, 9.272911830336268e-06, 1.069166771130927e-05,
+        1.2365612308564858e-05, 1.4347682044165459e-05, 1.6703327157235526e-05,
+        1.9513855675508633e-05, 2.2880781657266448e-05, 2.6931515183922568e-05,
+        3.182685815174488e-05, 3.7770949024424116e-05, 4.5024556236046224e-05,
+        5.392299034450833e-05, 6.490044625783963e-05, 7.852338646832594e-05,
+        9.553677289322509e-05, 0.00011692876860145463, 0.00014402232208725815,
+        0.00017860640689886287, 0.0002231266216502959, 0.00028096608103229286,
+        0.00035686608652748365, 0.000457567447692103, 0.0005928077589348299,
+        0.0007769070579761011, 0.0010313532406269741, 0.0013891405816052465,
+        0.0019022964033350404, 0.002655458425094267, 0.003791534418658206,
+        0.005563025720788434, 0.008442222460832576, 0.01338049133716538,
+        0.02249877487624705, 0.04128605245798222, 0.08792274024294651, 0.2634580890945831,
+        4.477768134293034, 0.6147513926910632, 0.7317501265953654, 0.13331182071990746,
+        0.28788852193431436, 0.675804449645004, 1.868471024561326, 3.388327194665842,
+        2.217194130994581, 2.310753856187241, 4.07453278635917, 7.761162713971286,
+        5.942430368496039, 3.1127852830043463, 1.4605980680983255, 0.9701672809918545,
+        0.9548154232754253, 1.256570628015828, 1.9343668154443803, 2.6979679425075567,
+        2.335651035882205, 1.7803371561423924, 1.4880187540952898, 1.3753280840118767,
+        1.3947515325501056, 1.5454612585152887, 1.7993667123704902, 1.8250193642201744,
+        1.4254474614605153, 1.0949019961671675, 0.9534021181211368, 0.9482422038909971,
+        1.0531167346389931, 1.2777480432977584, 1.641891913345645, 2.0187957402567918,
+        1.9849726459982042, 1.6239456250510007, 1.3115081660879937, 1.112309906570387,
+        0.8233723283164813, 0.6895455858486914, 0.5995710522167755, 0.5218221048549431,
+        0.44996404106522525, 0.39476495265332123, 0.36872609362793196, 0.37009463333064824,
+        0.3892526780763166, 0.4192964470996836, 0.4574722402975289, 0.5030776454050735,
+        0.555496530980094, 0.6123961031527145, 0.6678194486713916, 0.7113431552836983,
+        0.7312407146510537, 0.7220209331598765, 0.6889026694189537, 0.6433075559700947,
+        0.5955091967839203, 0.5515494798865419, 0.5139094380355292, 0.4830607863409606,
+        0.45859501227263144, 0.4398253942984636, 0.4260577906612822, 0.4166942166172203,
+        0.4112608600379457, 0.4094043855026514, 0.41087547711066613, 0.415506484872527,
+        0.42318387643417466, 0.43381230555640976, 0.44726378003191675, 0.46330221353044926,
+        0.48147176034490113, 0.5009410868135231, 0.5203149296162802, 0.5374734652364964,
+        0.5495822150574408, 0.5534757462003018, 0.5465089015830497, 0.527585738371153,
+        0.4977003928204118, 0.459530514247898, 0.4163729348662099, 0.3711488094502392,
+        0.3259261005477205, 0.2819244384425042, 0.2397644521031215, 0.19977830294971002,
+        0.16231989614049336, 0.12811845058296065, 0.09882274321452252, 0.07785067536200979,
+        0.07011604345716609, 0.07669023509354857, 0.09186952244590946, 0.10975428099535377,
+        0.12717741216473935, 0.14270841228104003, 0.155740923969518, 0.16605529495229782,
+        0.17361029743469278, 0.17843807186116145, 0.18059394751193097, 0.18014039738239263,
+        0.1771530232089468, 0.1717387630876474, 0.16405707073456777, 0.1543359256527228,
+        0.14287755898025414, 0.13005387205373747, 0.11629749425827947, 0.10209966158889491,
+        0.08802992770004142, 0.07479472495692115, 0.06334227543410739, 0.05494795992304371,
+        0.05098326921919014, 0.052040142516117514, 0.05724624654232217,
+        0.064933486424941, 0.07362125146771666, 0.08230170424170027, 0.09034099336860227,
+        0.09734796589932221, 0.10308751346760725, 0.10742805327701102, 0.11030768561967953,
+        0.11171093917899133, 0.11165301640265808, 0.11017049106349563, 0.10731775493363716,
+        0.10316816924218201, 0.09781846937067795, 0.09139488325947771, 0.08405993151845198,
+        0.07602019916875549, 0.0675376843432339, 0.05895073204618535, 0.050714216560691916,
+        0.04346536615524596, 0.03807836276761331, 0.035527278557242525,
+        0.036333029589520165, 0.04006515680454698, 0.04569467875279033,
+        0.052244350968303474, 0.059019151029617786, 0.06555983259824763,
+        0.07155913961009126, 0.07680569962565913, 0.08115278963643022, 0.08450108841325428,
+        0.08678815750549394, 0.08798095796648162, 0.08806990419406396, 0.08706411036224494,
+        0.08498797036716964, 0.08187930602533308, 0.07778923795836476, 0.0727838653198965,
+        0.06694797366933623, 0.060391598333650424, 0.05326191440525328,
+        0.04576698660474603, 0.038227803176253954, 0.031196259945310424,
+        0.025686711453057065, 0.02330497734138619, 0.025233236113296125,
+        0.03075095104056873, 0.03829660118778019, 0.046785695603566886,
+        0.05563042180829718, 0.06450179476495267, 0.07319397880949711, 0.08156269932466123,
+        0.08949736076668108, 0.09690805462627039, 0.10371958407531635, 0.10986908925861213,
+        0.11530563611658012, 0.11999084807741135, 0.12389995382163703, 0.12702276156188774,
+        0.12936417096357944, 0.13094394972612988, 0.13179564569979715, 0.131964663150942,
+        0.1315056755096378, 0.13047964790524635, 0.1289507834199039, 0.1269836861873946,
+        0.1246409663276923, 0.12198141865588881, 0.11905881190438154, 0.11592124509925941,
+        0.11261097208592816, 0.10916456629889694, 0.10561329318020948, 0.10198357217116331,
+        0.09829743807890527, 0.09457294671299935, 0.09082450609417396, 0.08706314629319335,
+        0.08329676321101939, 0.07953038096517343, 0.07576647334778572, 0.07200536924170681,
+        0.06824574499636706, 0.06448518467162152, 0.06072077290346432, 0.05694967883990751,
+        0.053169694313832484, 0.04937970309441347, 0.04558007671461089,
+        0.04177301146339394, 0.03796283736619872, 0.03415634362882513, 0.0303631819009016,
+        0.026596445661345537, 0.02287362217275454, 0.01921838244976197,
+        0.015664443352837416, 0.01226512796199896, 0.009120526165075386,
+        0.006463472050118534, 0.004883873153942442, 0.0051560632974818835,
+        0.006837925023313982, 0.00899255918800828, 0.011191508964918098,
+        0.013274883623638857, 0.015172571768896656, 0.01684805800518084,
+        0.018280169498062982, 0.01945628527417986, 0.020369499618342675,
+        0.021017352707417048, 0.021401258762058836, 0.02152626424392426,
+        0.021400954716551512, 0.0210374110414011, 0.02045116462567978, 0.019661141928157835,
+        0.018689627928058457, 0.017562318907309922, 0.016308579043991682,
+        0.014962068113536913, 0.013561974091786926, 0.012155149603645119,
+        0.010799404548538437, 0.00956762000709617, 0.008550071582247253,
+        0.007847073672990207, 0.0075405191321994, 0.007650099931568992,
+        0.008114955944132893, 0.008825577398696233, 0.009670151676184015,
+        0.010558604534176293, 0.011425489401633664, 0.012225024850292553,
+        0.012925600614801991, 0.013505692462872925, 0.013951163940264797,
+        0.014253553960494186, 0.014409003899156088, 0.014417588902461266,
+        0.014282903471436426, 0.01401180818473961, 0.013614283373013117,
+        0.013103365291752198, 0.012495165154727537, 0.011808991393929515,
+        0.011067605921064693, 0.010297632566918336, 0.009530069453550475,
+        0.008800676712322923, 0.008149636357485768, 0.007619329483053118,
+        0.0072488197442033666, 0.007064903951193259, 0.00707309306603357,
+        0.0072545665022907165, 0.007571933507567087, 0.007979798898306953,
+        0.008433910700173634, 0.008896092098478104, 0.00933566756698321,
+        0.009729068287691923, 0.010058830384074676, 0.010312568296037909,
+        0.010482122753697554, 0.010562913962083734, 0.010553473451348007,
+        0.010455116684983501, 0.010271722526861744, 0.01000959349700218,
+        0.009677378549654723, 0.009286046129512, 0.008848897060073671, 0.00838159956884485,
+        0.007902203925807576, 0.007431039706638149, 0.006990305543597177,
+        0.006603047170991934, 0.00629117805614516, 0.006072428863375013,
+        0.0059567854872350934, 0.005943811851383046, 0.006022362788453524,
+        0.006173020760606141, 0.00637204258117237, 0.006595113739022907,
+        0.006819908409783868, 0.007027370996555769, 0.007202101666396527,
+        0.007332266871160656, 0.007409325070295178, 0.0074277253367438095,
+        0.007384651165587029, 0.007279838324361864, 0.007115477797043683,
+        0.006896210185177853, 0.006629218361873971, 0.006324424285748302,
+        0.005994784226480605, 0.0056566357871545994, 0.005329947284283269,
+        0.005038117818029758, 0.004806699810223628, 0.004660321888913638,
+        0.004617761797510564, 0.0046868198001689294, 0.004861960435951255,
+        0.005126368334844603, 0.005456900060698879, 0.005828981671346529,
+        0.006219734660339237, 0.006609312821688646, 0.0069811390946437546,
+        0.007321662930668169, 0.0076199907686579985, 0.007867539432593565,
+        0.00805775635911844, 0.00818590704752394, 0.008248917165390293,
+        0.008245256276717133, 0.008174853769812647, 0.008039041869010706,
+        0.00784052456810201, 0.007583374915622293, 0.007273066728329956,
+        0.006916550975976138, 0.00652239181892536, 0.006100981234651454,
+        0.005664849226861162, 0.005229064671017838, 0.004811647552078153,
+        0.004433729372527203, 0.004118858781795163, 0.003890503617389715,
+        0.0037671304185128815, 0.0037561519387962323, 0.003850481271187251,
+        0.004030645951316729, 0.004270916148934338, 0.0045452818090802784,
+        0.004830878924585512, 0.0051090608579037345, 0.005365215055515442,
+        0.005588164366948398, 0.005769553064755834, 0.005903347347819809,
+        0.005985464204685741, 0.006013506614987897, 0.005986579066229132,
+        0.00590516335587633, 0.005771042514606217, 0.005587268167722417,
+        0.005358173697158442, 0.005089442810996933, 0.004788251044332812,
+        0.004463505360742612, 0.004126208852619598, 0.0037899553415393374,
+        0.003471465326481967, 0.0031908188660525754, 0.002970550146647127,
+        0.0028323429666781844, 0.002790931325099475, 0.002847964302063012,
+        0.002990827506034121, 0.0031976920777172795, 0.003444444284095424,
+        0.0037092699708344244, 0.003974279638983788, 0.004225440299887396,
+        0.004451943141968755, 0.004645544817625664, 0.004800045705370957,
+        0.004910916240244479, 0.00497503994389144, 0.004990539238340772,
+        0.0049566583016391365, 0.004873686445621877, 0.004742913513886475,
+        0.004566615867064183, 0.0043480788051664995, 0.004091670577186248,
+        0.0038029971630553386, 0.003489189813524121, 0.0031594135286049456,
+        0.0028257321958504588, 0.002504481071716145, 0.0022180680734999693,
+        0.0019960093060159357, 0.0018713159383056959, 0.001867611200141697,
+        0.0019836849863320125, 0.0021940203768391195, 0.0024647202135414724,
+        0.0027661418218135696, 0.003076159057653935, 0.0033789234090305614,
+        0.003662964666480001, 0.0039197644450062324, 0.004142851500101491,
+        0.004327256428952047, 0.004469185065346386, 0.004565819620071531,
+        0.004615193372091902, 0.004616107376650123, 0.004568071028567734,
+        0.004471256291453541, 0.004326460425400992, 0.004135075652975558,
+        0.0038990675757183757, 0.0036209687031503943, 0.0033039018337403885,
+        0.0029516666698416088, 0.0025689701199917456, 0.002162014285108524,
+        0.0017400877182586153, 0.0013204156134758531, 0.000945058592667934,
+        0.0007319531402882535, 0.0008460097421802134, 0.0012091800494640915,
+        0.0016698899486163254, 0.002166499288671254, 0.002676309813561964,
+        0.003188736027201431, 0.0036976263901092776, 0.0041988454710492965,
+        0.004689386019279753, 0.005166994492968612, 0.005629990198260598,
+        0.006077162835463533, 0.006507702130576761, 0.006921139342765578,
+        0.00731729145344868, 0.007696204005977061, 0.008058091269978605,
+        0.008403273989481883, 0.008732115983845812, 0.00904496152245316,
+        0.00934207577769129, 0.009623590796821251, 0.00988945933982763,
+        0.010139418626483538, 0.010372965556273572, 0.010589344363247715,
+        0.010787547006404951, 0.010966325940765529, 0.011124218325749651,
+        0.01125958024936177, 0.011370629206370083, 0.011455492871552108,
+        0.011512262145487505, 0.011539046498068951, 0.011534029765465347,
+        0.011495524743075044, 0.011422025134748218, 0.011312253649606615,
+        0.011165205269563811, 0.010980184936803966, 0.010756839127428355,
+        0.010495180985103944, 0.010195608888065026, 0.009858918515783728,
+        0.009486308672970086, 0.009079381326185479, 0.008640136527223445,
+        0.008170963165819415, 0.007674626864349893, 0.007154256890393894,
+        0.006613334904105511, 0.0060556900242963235, 0.00548550781874493,
+        0.004907366969269539, 0.004326330097053627, 0.003748143181396535,
+        0.0031796631517175314, 0.002629794589165643, 0.0021116329918500197,
+        0.0016475341744826347, 0.0012801519250043218, 0.0010832005352348893,
+        0.001116120242433583, 0.0013316447241079942, 0.0016327687588067528,
+        0.001956936198940139, 0.002273644974642943, 0.002567727236151319,
+        0.00283092343600436, 0.003058376293329132, 0.00324713312891983,
+        0.0033954595727076833, 0.003502500435158053, 0.0035680991892226045,
+        0.00359269438225962, 0.0035772554753963075, 0.0035232402551315404,
+        0.0034325654884503755, 0.0033075877589324367, 0.003151095102215421,
+        0.002966313711987115, 0.002756939034878721, 0.002527209082725222,
+        0.00228205352111394, 0.002027382174367346, 0.0017706329437659522,
+        0.001521790241408245, 0.0012951421566919459, 0.0011115592799723077,
+        0.0009983079372946505, 0.0009784836449312382, 0.0010516758052687154,
+        0.0011926751558282674, 0.0013711832273586918, 0.0015643320319378973,
+        0.0017572553608380822, 0.0019404165150555047, 0.0021074829519974313,
+        0.0022540844931258517, 0.0023771362316092636, 0.00247446902902971,
+        0.0025446225752740657, 0.0025867252178464065, 0.0026004212807659213,
+        0.0025858253908315624, 0.0025434932768319722, 0.0024744041829490157,
+        0.002379953836930953, 0.0022619602892918725, 0.0021226891394700415,
+        0.0019649113474676967, 0.0017920188905466343, 0.0016082464124028033,
+        0.0014190901036074156, 0.0012320871791744392, 0.0010581819816485529,
+        0.0009136284647402553, 0.0008205090675959219, 0.0007998488725953804,
+        0.0008560428251618962, 0.0009721893784548749, 0.0011243734322099327,
+        0.0012933467498820665, 0.0014661697168449417, 0.0016343242782859125,
+        0.0017919777093202665, 0.0019349294250422216, 0.002060031063363695,
+        0.002164871066912556, 0.0022476003645484745, 0.002306833487498003,
+        0.0023415907393985404, 0.002351263271393355, 0.0023355914583459494,
+        0.0022946517218838678, 0.002228849923316148, 0.002138921825963313,
+        0.0020259438366431034, 0.0018913615095111865, 0.0017370515020848083,
+        0.0015654503033839778, 0.0013798240246424198, 0.0011848550520470636,
+        0.0009879823093715367, 0.0008025560730073951, 0.0006545307232358604,
+        0.0005881781057018802, 0.0006398260121554611, 0.000791623440245015,
+        0.0010004528107965215, 0.0012370177238383371, 0.00148589103392851,
+        0.0017385684463807182, 0.0019897459072906335, 0.002235704948878503,
+        0.002473605793134771, 0.0027011611484832176, 0.002916477271165205,
+        0.003117972758375803, 0.0033043351957373714, 0.0034744967729933005,
+        0.0036276194043798845, 0.0037630843737721156, 0.003880483775680179,
+        0.0039796122125617785, 0.004060457866768705, 0.004123192448138705,
+        0.004168159750943729, 0.004195862703029342, 0.004206948891571615,
+        0.004202194622866035, 0.0041824876303284434, 0.004148808592223085,
+        0.004102211663024321, 0.0040438042629527965, 0.003974726411179041,
+        0.0038961299300892707, 0.0038091578913618395, 0.0037149247175372164,
+        0.0036144973926602346, 0.003508878267559227, 0.0033989899636964324,
+        0.003285662876106359, 0.0031696257444759294, 0.0030514996941852094,
+        0.0029317960438499007, 0.00281091803233365, 0.002689166443394066,
+        0.002566748911684033, 0.0024437924975101366, 0.0023203589382962916,
+        0.002196461843610035, 0.002072085012246992, 0.0019472010265034693,
+        0.0018217893231765407, 0.0016958530501193416, 0.0015694341866470426,
+        0.0014426266318008055, 0.001315587255759341, 0.0011885453069223194,
+        0.0010618111766699588, 0.0009357866215035563, 0.0008109808255677214,
+        0.0006880420798952115, 0.000567829154607075, 0.00045158933643203253,
+        0.0003414580509128056, 0.0002420802970232397, 0.0001663360645729246,
+        0.00014506140399294726, 0.00018864095657667132, 0.00026044227474994084,
+        0.00033775970420569536, 0.0004129397520499172, 0.0004830225584477576,
+        0.0005465604122024927, 0.0006027117333416912, 0.0006509403887729793,
+        0.000690900843729596, 0.0007223893369486897, 0.0007453213094356945,
+        0.0007597201285335042, 0.0007657109238545668, 0.000763516832364796,
+        0.0007534564961523231, 0.000735942450010028, 0.0007114805483818005,
+        0.000680671039747997, 0.0006442124571200213, 0.0006029103217249725,
+        0.0005576939828590693, 0.0005096470616174601, 0.00046006023541631007,
+        0.0004105190581280902, 0.000363039913332914, 0.00032024591916526813,
+        0.0002854790087532086, 0.00026250793508431465, 0.00025433556222036034,
+        0.00026143155548252777, 0.00028120630168969785, 0.00030949286333913453,
+        0.00034229414435823065, 0.0003765143069967038, 0.0004099468134048776,
+        0.0004410514925647865, 0.00046875191745501945, 0.0004922961512860936,
+        0.0005111689040736525, 0.0005250372731948858, 0.0005337170155096878,
+        0.0005371512072254147, 0.0005353965070613196, 0.0005286143275307475,
+        0.0005170655153200658, 0.0005011079940375084, 0.00048119744999905516,
+        0.0004578916679063086, 0.0004318595833867506, 0.0004038964014268365,
+        0.0003749457877018121, 0.00034612796817374024, 0.00031876592061371513,
+        0.0002943864856719729, 0.00027464767172152713, 0.0002611254645346274,
+        0.00025494055865515577, 0.0002563633393523832, 0.00026467110683195253,
+        0.0002783908497701974, 0.0002957436915515996, 0.0003150146082058009,
+        0.00033473736100857226, 0.00035373717135980587, 0.00037110605706171826,
+        0.0003861596342691948, 0.0003983965039592707, 0.00040746619792370286,
+        0.00041314564421426984, 0.00041532244065770247, 0.00041398318192864206,
+        0.0004092055070577207, 0.0004011530062009511, 0.0003900725311155229,
+        0.0003762937707686064, 0.00036023116631147265, 0.00034238828567977053,
+        0.00032336448464517737, 0.00030386267253304267, 0.00028469460497826464,
+        0.00026677549431576147, 0.00025109281796386614, 0.0002386286523791776,
+        0.00023022175604794627, 0.00022638907610208556, 0.00022717783997752816,
+        0.00023213598819617535, 0.00024042620898390946, 0.00025101774317865086,
+        0.0002628630280998642, 0.0002750096913100283, 0.0002866493840928625,
+        0.0002971264704969778, 0.00030592803441700724, 0.00031266826915102693,
+        0.00031707338683444926, 0.00031896924853147096, 0.0003182721340034975,
+        0.00031498245325964824, 0.00030918112192901556, 0.00030102845753337545,
+        0.00029076564876024584, 0.00027871900528691004, 0.0002653071761017938,
+        0.0002510510501626277, 0.00023658455751179107, 0.00022266111779375937,
+        0.00021014408290479859, 0.00019996126116669002, 0.0001930012290815239,
+        0.00018994932673664766, 0.00019111231783993822, 0.0001963250291424948,
+        0.00020500172259794807, 0.0002162979984871521, 0.00022928884078852953,
+        0.00024309440689482893, 0.0002569416851442326, 0.00027018150490447644,
+        0.0002822833341261941, 0.00029282244536561985, 0.0003014665207949835,
+        0.00030796429990613577, 0.0003121367891117453, 0.00031387077611613593,
+        0.0003131142138298878, 0.0003098730979816312, 0.00030420960256618255,
+        0.00029624140055389006, 0.0002861422691010666, 0.0002741442580473857,
+        0.00026054187962269536, 0.0002456989109064173, 0.00023005834234567318,
+        0.00021415537234556963, 0.00019863128451104206, 0.0001842410308025887,
+        0.00017183790882201365, 0.00016230743883380232, 0.00015642470385634756,
+        0.00015465236345212264, 0.0001569748965728555, 0.00016288772014293364,
+        0.00017155502818275343, 0.00018202603254780254, 0.0001933977502067418,
+        0.0002048929145405034, 0.00021587725187663124, 0.00022584829229976632,
+        0.00023441607768378758, 0.0002412847968137453, 0.00024623810086954934,
+        0.0002491282380708252, 0.0002498683494372467, 0.00024842720265319524,
+        0.0002448258178242879, 0.00023913567394119332, 0.0002314784275410425,
+        0.0002220273262873936, 0.00021101077555802609, 0.0001987188182137587,
+        0.00018551355376642445, 0.0001718444885208272, 0.0001582686783751885,
+        0.0001454713640188369, 0.00013427215237888848, 0.00012558281986327957,
+        0.0001202693718470677, 0.00011891020592603878, 0.00012156302044091734,
+        0.0001277265500313873, 0.00013653670956615828, 0.000147032745138784,
+        0.0001583362068811727, 0.0001697178550650274, 0.00018059836001803767,
+        0.00019052550810362307, 0.00019914917592698107, 0.00020620102934595718,
+        0.0002114797857418055, 0.00021484102077072727, 0.00021619027519980633,
+        0.00021547846846435326, 0.00021269894959437095, 0.00020788580826212172,
+        0.0002011133288349408, 0.00019249673527381406, 0.0001821947038967068,
+        0.00017041460406865225, 0.0001574222024313319, 0.0001435588249805237,
+        0.00012927082824509823, 0.0001151579788274491, 0.00010204441202201662,
+        9.10511197501686e-05, 8.356646443813687e-05, 8.089828355944285e-05,
+        8.358273736651385e-05, 9.099345801003983e-05, 0.00010177771354000974,
+        0.00011454317854892105, 0.00012818264321100888, 0.00014189013971386506,
+        0.00015508415216869488, 0.00016733560551584627, 0.00017831902583452644,
+        0.0001877824627700699, 0.00019552944402639554, 0.00020140811030337362,
+        0.0002053045376314338, 0.00020713848361523973, 0.00020686052983175904,
+        0.0002044500240663283, 0.0001999134847530225, 0.00019328329671713932,
+        0.00018461665407865202, 0.00017399483586754184, 0.0001615230885289822,
+        0.0001473317479559879, 0.00013158003790662652, 0.00011446602018866133,
+        9.625199243211972e-05], [1.9707275566951233e-09, 5.919536759397741e-09,
+        9.890458440659044e-09, 1.3898399603534291e-08, 1.7958516656105468e-08,
+        2.2086319752161617e-08, 2.6297778894873193e-08, 3.0609436465532265e-08,
+        3.5038524699025104e-08, 3.960309069932662e-08, 4.432213001968179e-08,
+        4.9215730511938205e-08, 5.4305227565300556e-08, 5.961337341697604e-08,
+        6.516452171549246e-08, 7.098483032393159e-08, 7.710248448959343e-08,
+        8.354794344068433e-08, 9.035421382616206e-08, 9.75571532929598e-08,
+        1.0519580916556354e-07, 1.1331279620193691e-07, 1.219547196439491e-07,
+        1.3117264958929798e-07, 1.4102265399271292e-07, 1.5156639858334006e-07,
+        1.628718236824443e-07, 1.750139085310224e-07, 1.88075536569507e-07,
+        2.021484759578252e-07, 2.1733449358132445e-07, 2.3374662163538677e-07,
+        2.515106013160478e-07, 2.707665303310129e-07, 2.9167074701880215e-07,
+        3.1439798819074596e-07, 3.3914386567332634e-07, 3.661277130626382e-07,
+        3.9559586517797645e-07, 4.2782544216545293e-07, 4.6312872580930475e-07,
+        5.018582297301565e-07, 5.444125871618182e-07, 5.912434015395511e-07,
+        6.428632367166172e-07, 6.998549551837274e-07, 7.628826618284653e-07,
+        8.327045548895352e-07, 9.101880615793074e-07, 9.963277051492473e-07,
+        1.092266258402013e-06, 1.1993198579432604e-06, 1.3190079074296481e-06,
+        1.4530887954112593e-06, 1.6036026938225657e-06, 1.7729230117177587e-06,
+        1.963818476724291e-06, 2.1795283084994287e-06, 2.423853604273655e-06,
+        2.7012688806032946e-06, 3.017058802638585e-06, 3.37748655104776e-06,
+        3.7900021426704266e-06, 4.263501501854617e-06, 4.808650398780097e-06,
+        5.438291852826243e-06, 6.1679616915825386e-06, 7.016545349000742e-06,
+        8.007120650572039e-06, 9.168047717750706e-06, 1.0534390480912527e-05,
+        1.2149788004976028e-05, 1.4068943275619613e-05, 1.6360970768934093e-05,
+        1.9113956145886345e-05, 2.2441255061533086e-05, 2.6490333986942044e-05,
+        3.1455405638533555e-05, 3.7595867490712566e-05, 4.52638666965462e-05,
+        5.4946694904186574e-05, 6.733423209596724e-05, 8.343071232721042e-05,
+        0.00010474948811475369, 0.00013367460244695375, 0.00017418935269225395,
+        0.0002335153834038003, 0.0003264253546692037, 0.0004897145438825511,
+        0.0008584598830882011, 0.00408033042104024, 0.0016281280599403048,
+        0.0013060006518568622, 0.0012352680783726635, 0.001249672969228262,
+        0.0013138201107128252, 0.0014177857234605334, 0.001560529365244749,
+        0.0017457131323468376, 0.001980635109579534, 0.0022763419995156984,
+        0.002648455366537384, 0.0031186911854362677, 0.003717287758917499,
+        0.004486798739828817, 0.005488077759582035, 0.006809940690847638,
+        0.008585256228918712, 0.011018783407491399, 0.014437618150288652,
+        0.019387974428662642, 0.026834650921826443, 0.03861218712542913,
+        0.058582350628526896, 0.09619680204237482, 0.18117874727718503,
+        0.4717091712309205, 6.765692770159037, 0.7452647885683332, 0.7378022226123298,
+        0.9094563926437228, 0.7448845713964546, 1.0054529705656348, 1.9856261048260957,
+        2.64347147141612, 1.2300275614390774, 0.8335246838357708, 0.7346133601016925,
+        0.8591431729118385, 1.3041303068077954, 1.1486292043676796, 0.8915231551133082,
+        0.8511667610443825, 0.944300791172329, 1.1881906038525016, 1.6661194951135063,
+        2.111470165423827, 1.673610695288305, 1.1783391064174453, 0.9187222125282914,
+        0.8036507554041247, 0.7909986390997508, 0.887310314965107, 1.1072868992634959,
+        1.2682609359324688, 1.1412907139537851, 0.9878945977238816, 0.9234232240323745,
+        0.9384286781141297, 1.0283336520820203, 1.207029268585827, 1.486328617266613,
+        1.7444605352650833, 1.6354170501364287, 1.2763192458039143, 0.9856208965552121,
+        0.8047912633606292, 0.5582283748932053, 0.4562941206300746, 0.4094810154292067,
+        0.39837871896408966, 0.4110781392248153, 0.43077285926148645, 0.4463338417344302,
+        0.45765120153433897, 0.4690488951969538, 0.4841893377277139, 0.5052114793741473,
+        0.5330302067463305, 0.567261121814008, 0.6054378031661084, 0.641763036155744,
+        0.6667778098421592, 0.6705692541714317, 0.6494276932448745, 0.609126649552781,
+        0.5602606394871708, 0.5117265788129578, 0.4683680266599284, 0.4318647882324478,
+        0.4022207950848226, 0.3787746774533994, 0.36071020154235167, 0.3472703927876407,
+        0.3378290735957925, 0.33190158501246714, 0.3291322545114102, 0.3292741474272721,
+        0.33216637514227965, 0.33770920554898776, 0.34583413012109976, 0.35646337100487896,
+        0.36945061794652073, 0.3844928860416345, 0.4010055794460525, 0.41796691716065937,
+        0.433775984143277, 0.44623524171699525, 0.4528231352978341, 0.4513476163087754,
+        0.4407732172713633, 0.4216992480942443, 0.3960978375426305, 0.36650382612331006,
+        0.33522056664381883, 0.3039120570681847, 0.2735729551215745, 0.24469496677915079,
+        0.2174779065311355, 0.19201582544367932, 0.16844263872164852, 0.14703978184882416,
+        0.12830240768102397, 0.11293636853253919, 0.10172231556408166, 0.0951916840129224,
+        0.09323453705175039, 0.09499572834009463, 0.09921777614619016, 0.1046968306258083,
+        0.11051705477676411, 0.11606312979562729, 0.12094379050883916, 0.12491218373625944,
+        0.1278107874740455, 0.12954213117314975, 0.13005857649853558, 0.12936288638046342,
+        0.1275117819924035, 0.12461637864515197, 0.12083623248292684, 0.11636707891707054,
+        0.11142499385455872, 0.10623066368827384, 0.10099660633829773, 0.09591830481334844,
+        0.09116834629717352, 0.08689160883554382, 0.08319969201477018, 0.08016412894929814,
+        0.07780992827582191, 0.0761125683906835, 0.07500141961182129, 0.07437033290934297,
+        0.07409307148534403, 0.07403941657559633, 0.07408818117926588, 0.07413533084988934,
+        0.07409749540830805, 0.07391238462434369, 0.0735378486058505, 0.07295088725240445,
+        0.0721472161727081, 0.07114132054080394, 0.06996642994777408, 0.06867360702736537,
+        0.06732919039388278, 0.06601014240919038, 0.06479733959965202, 0.0637673855874112,
+        0.06298399628104903, 0.06249028885651722, 0.062303295948610504,
+        0.06241166506944436, 0.06277685027631265, 0.06333737164214069, 0.06401517850089158,
+        0.06472296109194065, 0.06537137276413711, 0.06587539506500088, 0.06615936538805478,
+        0.06616044314114744, 0.06583052622741238, 0.06513685517542894, 0.06406173809205952,
+        0.06260195908772077, 0.060768471095389395, 0.058586925457903956,
+        0.056099483138358094, 0.05336821139597738, 0.050480176139120106,
+        0.047553962690105145, 0.044746455869670645, 0.042256701128126524,
+        0.04032023086800468, 0.03918433199135882, 0.03905935146835388, 0.04006023110051368,
+        0.04217292197281401, 0.04526983515292856, 0.04915970948322677, 0.05363743985436474,
+        0.0585140924202527, 0.0636277338013338, 0.06884328425000345, 0.07404817859317211,
+        0.0791474318778561, 0.08405954581757044, 0.08871364328373868, 0.09304779731874552,
+        0.09700837204112199, 0.10055013844313367, 0.10363689944851348, 0.10624233972995623,
+        0.10835081287004295, 0.1099578042086921, 0.11106986962276234, 0.11170394540170708,
+        0.11188603677122425, 0.11164939941630328, 0.11103240667084179, 0.11007633031246745,
+        0.10882325287087567, 0.10731428326928773, 0.10558818133391898, 0.10368042683861096,
+        0.10162270824014692, 0.09944276247314571, 0.0971644724038029, 0.09480812157826098,
+        0.09239071372713617, 0.08992628340383216, 0.08742615008786855, 0.08489909689621301,
+        0.08235148210280333, 0.0797873127015052, 0.07720832072359002, 0.0746140832929368,
+        0.07200221713166963, 0.06936866071889312, 0.06670803732238838, 0.06401407509483735,
+        0.06128005052156139, 0.05849922084118139, 0.05566521891233021, 0.052772397451413315,
+        0.04981612432358042, 0.04679304219187239, 0.04370131115665223, 0.04054085053729603,
+        0.03731358640929595, 0.03402369727411614, 0.030677835148358583,
+        0.027285287552513318, 0.02385804139748086, 0.02041071510451245,
+        0.016960341484997317, 0.013526010222027379, 0.0101284192885915,
+        0.006789487186711215, 0.0035329234515080674, 0.00043677227280685874,
+        0.002680520262146998, 0.005568023367200847, 0.00829729551514966,
+        0.010847609083930164, 0.013202047237271686, 0.015345544939036239,
+        0.01726475495293964, 0.018948163751467757, 0.020386293331603706,
+        0.021571934450108566, 0.022500367076092317, 0.02316952732708808,
+        0.02358009030831159, 0.023735455319629537, 0.023641639926490158,
+        0.023307107264323754, 0.022742562341498258, 0.021960755960721962,
+        0.020976330001999183, 0.019805728776024382, 0.018467193897968963,
+        0.016980862968446777, 0.015369018051859078, 0.013656602923657573,
+        0.011872306812993097, 0.010050957626531087, 0.008239156836210125,
+        0.00650944498495021, 0.004996862765941499, 0.003973814062711653,
+        0.0038229243030432204, 0.004571094605001332, 0.005814434507264892,
+        0.0072316692500046355, 0.008667711196547492, 0.010047417824095366,
+        0.011329099713083301, 0.01248647880323538, 0.013501562473655413,
+        0.014361612367031627, 0.015057749331977883, 0.015584251204562864,
+        0.01593815259298707, 0.01611897667344054, 0.01612852636307302, 0.01597070837674294,
+        0.0156513856646488, 0.015178263155516918, 0.014560814984666789,
+        0.01381026339472359, 0.012939625294271007, 0.011963858481159575,
+        0.01090017621062204, 0.009768676535099398, 0.008593596221835042,
+        0.007405845604303416, 0.006248190667380419, 0.005185567225339602,
+        0.004322225270571052, 0.0038103138973371595, 0.0037852118348207448,
+        0.00422737541613685, 0.0049758679183702125, 0.005871898077949004,
+        0.00681295589774571, 0.007738649703669654, 0.00861207571017773,
+        0.009409128985846149, 0.010113166679687842, 0.010712354754819435,
+        0.011198298158296822, 0.011565291579639723, 0.011809877855943651,
+        0.011930563914161895, 0.011927621743593601, 0.011802939742488978,
+        0.011559908237231555, 0.011203331787718795, 0.010739365403553011,
+        0.010175475552750415, 0.00952043291169218, 0.00878435596778396,
+        0.007978849480561151, 0.007117334221566813, 0.006215781295351352,
+        0.005294343542818253, 0.0043810801315579346, 0.003520709768025274,
+        0.0027942453952104662, 0.002346410550889138, 0.002337852941699593,
+        0.0027515497396474273, 0.0034089167629326495, 0.004164132822533376,
+        0.0049391460784530454, 0.00569293784493457, 0.006401643598124402,
+        0.007049834326809944, 0.007626778904989758, 0.008124756162994263,
+        0.008538240461150978, 0.008863480711214917, 0.0090982667350714,
+        0.009241790343865568, 0.009294558452594125, 0.009258338696991556,
+        0.009136129321686648, 0.008932151224837818, 0.008651864385738995,
+        0.00830201552515638, 0.007890730233242556, 0.007427672110450087,
+        0.006924304328457322, 0.006394304066926077, 0.005854189163183738,
+        0.005324189306681476, 0.004829247175357845, 0.004399588211184131,
+        0.0040693734138307555, 0.003871090938780786, 0.003825053936879097,
+        0.003929571630485191, 0.00416081131152629, 0.004482862148926549,
+        0.0048590193560409, 0.005257926622897145, 0.0056549564294575165,
+        0.006031406016789421, 0.006373214601264799, 0.006669849048301218,
+        0.006913484464399666, 0.007098437440228776, 0.0072207812863542215,
+        0.00727808456235364, 0.007269231868301822, 0.007194300232157426,
+        0.007054474648617488, 0.006851993650986248, 0.0065901217710509835,
+        0.006273151882186135, 0.005906448413269564, 0.005496554629348636,
+        0.005051407474978847, 0.004580738460446601, 0.004096798234001916,
+        0.0036156298117031075, 0.0031591766218155804, 0.0027582129073959,
+        0.002454252836415061, 0.0022937203173753057, 0.0023064681654528167,
+        0.0024826649429763024, 0.002779382103943845, 0.0031476518635210264,
+        0.003548526920620617, 0.003954744549085523, 0.004347612821840195,
+        0.0047140272087963795, 0.005044507961472607, 0.005332032514325806,
+        0.005571354920698274, 0.005758604871507559, 0.005891045441300977,
+        0.0059669217719078215, 0.00598536272997964, 0.0059463140458713955,
+        0.00585049069674305, 0.005699341823713983, 0.005495025276573643,
+        0.005240392248942859, 0.004938986512121803, 0.004595068949864406,
+        0.004213689214626076, 0.0038008484859314373, 0.00336384506380572,
+        0.0029120039558689593, 0.0024582521880806532, 0.0020226047939021254,
+        0.0016396304967957452, 0.0013700825408638777, 0.001294061472220314,
+        0.0014400466985224152, 0.0017446302360858462, 0.0021287848194506045,
+        0.002542695716164587, 0.002959016445719557, 0.0033618460942565214,
+        0.003740937872656895, 0.004089063541116417, 0.004400799027361636,
+        0.004671937153518906, 0.004899187830635496, 0.005080016430369509,
+        0.00521255135694564, 0.0052955271960404724, 0.0053282461624789175,
+        0.005310548492368179, 0.005242786462141501, 0.005125798901113763,
+        0.004960884351114276, 0.00474977187514281, 0.004494589148151545,
+        0.004197827992486435, 0.003862308035977956, 0.0034911398274895056,
+        0.003087689942346417, 0.002655553563103305, 0.0021985489573033016,
+        0.0017207810675356461, 0.0012269776569692665, 0.0007244519227110386,
+        0.0002507233937010996, 0.00038496008511933606, 0.000891183650845331,
+        0.0014140112628805764, 0.001936081497327353, 0.002452160928773611,
+        0.002958798996653978, 0.003453215831854716, 0.003933072160079246,
+        0.004396407659208997, 0.004841621816934763, 0.00526746535402304,
+        0.005673032032789369, 0.006057747054796198, 0.006421350483136078,
+        0.00676387504236517, 0.00708561811027927, 0.007387108017547318,
+        0.007669065037297344, 0.007932357719872265, 0.00817795551882122,
+        0.008406878951594799, 0.008620148818673106, 0.00881873623415249,
+        0.009003515361888245, 0.00917522077802557, 0.009334411269105244,
+        0.009481441623545988, 0.009616443596856889, 0.009739316758206022,
+        0.00984972940368419, 0.009947129199431212, 0.010030762744664523,
+        0.010099702860464847, 0.010152882139095033, 0.01018913113997605,
+        0.010207219584934285, 0.010205898969341013, 0.01018394514257241,
+        0.010140199594670033, 0.010073608392958459, 0.00998325792433935,
+        0.009868406803565639, 0.009728513498289607, 0.009563259396123982,
+        0.009372567197160831, 0.009156614660048456, 0.00891584386357522,
+        0.008650966271290299, 0.008362964008305381, 0.00805308788197329,
+        0.007722852809163421, 0.00737403146444566, 0.007008647154460891,
+        0.0066289671788690345, 0.00623749830185083, 0.005836986485265438,
+        0.00543042381111705, 0.00502106665991038, 0.0046124708384191904,
+        0.004208551553478496, 0.0038136787016146995, 0.00343281975062618,
+        0.003071739626228636, 0.0027372487053413967, 0.0024374312775040314,
+        0.002181645703276759, 0.001979848907880117, 0.0018406570087589613,
+        0.0017681306029114674, 0.0017589114577424342, 0.0018022444978683624,
+        0.001883246719036327, 0.0019869001585755886, 0.0021005025338717365,
+        0.002214352532276991, 0.0023214703593297005, 0.002417035620699375,
+        0.0024978576371897233, 0.002561964890544181, 0.002608309740842145,
+        0.0026365614393653466, 0.0026469610959996425, 0.002640218525584175,
+        0.0026174369220779976, 0.002580055764896834, 0.0025298052926178583,
+        0.002468667607088122, 0.002398840283777845, 0.0023226984744581305,
+        0.0022427510833477014, 0.0021615859425757134, 0.0020817984816352705,
+        0.0020058989879002493, 0.0019361963137520587, 0.0018746618382115767,
+        0.0018227866234803098, 0.0017814547099848554, 0.0017508614259990234,
+        0.001730501974793866, 0.0017192407059160259, 0.00171545050309566,
+        0.0017171943375925063, 0.0017224149057737663, 0.0017291040366300091,
+        0.00173543582655541, 0.0017398596596870013, 0.0017411574743875526,
+        0.001738473189391919, 0.0017313223423396102, 0.0017195883194238016,
+        0.0017035092443090257, 0.0016836572675531197, 0.0016609098933542234,
+        0.001636411194226904, 0.0016115194555008819, 0.0015877373296654714,
+        0.001566621581399652, 0.001549672649036189, 0.0015382097816262162,
+        0.001533244504231938, 0.0015353710814259766, 0.0015446940306059038,
+        0.0015608072705288643, 0.0015828282031567914, 0.001609477411978587,
+        0.0016391860266203654, 0.0016702109390026882, 0.0017007420324645476,
+        0.0017289922485530357, 0.001753267620401414, 0.0017720187368726894,
+        0.0017838772836550581, 0.001787681915782807, 0.0017824974850315057,
+        0.0017676311529788286, 0.001742648526622787, 0.001707392855767918,
+        0.0016620106392215422, 0.0016069877707618357, 0.0015432016405735182,
+        0.001471996250202473, 0.0013952887017585228, 0.0013157141433411351,
+        0.0012368064781395477, 0.001163181075050889, 0.001100614043471254,
+        0.001055798018716738, 0.0010354891896667362, 0.0010449959869241081,
+        0.0010866167657606035, 0.001159070102108422, 0.0012583098748665425,
+        0.0013790062226143103, 0.0015157668742873903, 0.0016637641733407767,
+        0.0018189083840391548, 0.0019777999482478875, 0.0021376133129468945,
+        0.002295981199826547, 0.0024509011950905038, 0.0026006667615062753,
+        0.0027438184444449148, 0.0028791100685344605, 0.003005485459991998,
+        0.00312206228886284, 0.0032281205587654537, 0.003323093988181928,
+        0.003406563046116813, 0.0034782487729287997, 0.003538006775526108,
+        0.0035858209695055427, 0.0036217967718797373, 0.0036461535437100198,
+        0.0036592161541209485, 0.0036614055930374078, 0.003653228605766027,
+        0.003635266362172881, 0.0036081622097394427, 0.003572608595866403,
+        0.0035293332824094265, 0.0034790850158027443, 0.0034226188601899654,
+        0.0033606814482741686, 0.0032939964535909404, 0.0032232506354643643,
+        0.003149080849618947, 0.003072062446541819, 0.002992699490074668,
+        0.0029114172123561074, 0.002828557073423166, 0.00274437471087466,
+        0.002659040948843453, 0.002572645891849487, 0.002485205969506603,
+        0.002396673636312887, 0.0023069492846202002, 0.0022158948119096944,
+        0.002123348208853231, 0.002029138507563866, 0.001933100449735604,
+        0.0018350882965764482, 0.0017349882957866253, 0.0016327294328676333,
+        0.0015282922132281314, 0.0014217153354380329, 0.0013131002190095106,
+        0.0012026134347398656, 0.0010904871524491596, 0.0009770177685195446,
+        0.0008625629067337827, 0.000747537003478727, 0.0006324056950844777,
+        0.0005176792250934831, 0.00040390508821961464, 0.0002916601427958753,
+        0.00018154257740269435, 7.416638063418198e-05, 2.9907272808441304e-05,
+        0.0001299599143557052, 0.00022547826860962192, 0.0003158708933359386,
+        0.00040059197566305377, 0.0004791330080453438, 0.0005510287451418769,
+        0.000615863136656547, 0.0006732746839794042, 0.0007229611093386564,
+        0.000764683290029302, 0.0007982684318855312, 0.0008236124700049006,
+        0.0008406816979638606, 0.0008495136407683968, 0.0008502172029305845,
+        0.0008429721427954135, 0.000828027949983681, 0.0008057022390400711,
+        0.000776378827372027, 0.0007405057551092007, 0.0006985936596347194,
+        0.000651215201603822, 0.0005990067880940201, 0.0005426749593417447,
+        0.00048301223661097864, 0.0004209328657449797, 0.00035755295997019873,
+        0.00029437738648290635, 0.0002337630129778953, 0.0001801089246032531,
+        0.0001424037636687881, 0.00013421068080890424, 0.00015848892919501797,
+        0.0002018401135557906, 0.0002524383413403253, 0.00030445010237528495,
+        0.00035506817896185976, 0.0004027504118827003, 0.00044652712219278286,
+        0.0004857273914645531, 0.000519862356906738, 0.0005485713395887498,
+        0.0005715951203884478, 0.0005887617382518123, 0.0005999783505612883,
+        0.0006052261188332678, 0.000604556631202303, 0.0005980891308695126,
+        0.0005860082300363638, 0.0005685620510243583, 0.0005460609551884908,
+        0.0005188772728028779, 0.00048744682320524187, 0.00045227366312103784,
+        0.00041394071434067733, 0.00037313131052597127, 0.00033067157535572166,
+        0.00028761361557938064, 0.000245399420567387, 0.00020617556861689644,
+        0.00017331228253653555, 0.00015177425369230124, 0.00014664489638497433,
+        0.00015883090897918806, 0.0001837982546255844, 0.00021579443612125098,
+        0.00025066428076214227, 0.000285853108689244, 0.00031978646968503996,
+        0.0003514381154649938, 0.0003800983707686022, 0.00040525536193491307,
+        0.00042653311212250783, 0.0004436581089478115, 0.00045644045591341977,
+        0.00046476270685679897, 0.0004685728521392173, 0.000467879600347563,
+        0.0004627489713402584, 0.0004533017021386858, 0.00043971127052857894,
+        0.0004222025739293539, 0.0004010515415190255, 0.00037658628929054236,
+        0.00034919098182508405, 0.00031931459341668397, 0.0002874887952657147,
+        0.00025436338103265385, 0.00022077639121693228, 0.00018789357003967967,
+        0.00015747819163625644, 0.00013233300112553138, 0.00011656877256786234,
+        0.00011417254219130126, 0.00012540020015940444, 0.00014629966988897555,
+        0.00017234906121798513, 0.00020041637598616652, 0.00022860069596331308,
+        0.0002557285437241846, 0.00028102932076415083, 0.00030396561563181816,
+        0.00032414707479325866, 0.0003412857657394466, 0.00035517221362152407,
+        0.0003656620251837833, 0.0003726681128215543, 0.0003761559811763016,
+        0.0003761407604745586, 0.0003726853162368266, 0.0003658991373978149,
+        0.0003559379556003831, 0.00034300426233048047, 0.0003273491298973624,
+        0.0003092760702932658, 0.0002891481656818724, 0.00026740048871026637,
+        0.0002445610185801504, 0.0002212847941193487, 0.000198406945046596,
+        0.0001770160973144923, 0.00015852661304592095, 0.00014465969613536628,
+        0.00013714139193559056, 0.00013701111464584645, 0.000143981330658446,
+        0.00015657184908209718, 0.0001728716200596779, 0.00019115705940269924,
+        0.0002100936291938272, 0.00022870212398232927, 0.00024626840928261486,
+        0.0002622655077634973, 0.0002762996560947109, 0.00028807561185561673,
+        0.00029737479889222585, 0.00030404149253978116, 0.0003079739406407553,
+        0.00030911851429453024, 0.0003074657467180108, 0.00030304759799374087,
+        0.0002959355959079039, 0.00028623973003446575, 0.00027410817795232205,
+        0.00025972817565620565, 0.00024332868294633199, 0.00022518606148006076,
+        0.00020563500423165105, 0.0001850888498202871, 0.00016407688196812012,
+        0.00014331189780921252, 0.00012380674101392905, 0.00010704263155775939,
+        9.507132838285063e-05, 9.010572731109006e-05, 9.320859744687205e-05,
+        0.0001033128424135689, 0.00011810634242042807, 0.00013541820923768184,
+        0.00015369680282245908, 0.00017191099789019623, 0.00018936589552338327,
+        0.00020557309100161758, 0.00022017484497432197, 0.0002329016474029829,
+        0.0002435483888139384, 0.00025196069261746904, 0.00025802683505875924,
+        0.00026167278078541984, 0.00026285897816716753, 0.00026157815999160503,
+        0.0002578537310197397, 0.00025173852382295316, 0.00024331383860524728,
+        0.00023268879511181007, 0.0002200001523836511, 0.00020541294404778456,
+        0.00018912262303612934, 0.0001713601061253256, 0.00015240262248328006,
+        0.00013259678837085632, 0.00011240900859208924, 9.254044706822019e-05,
+        7.419606837490118e-05, 5.964894357206003e-05, 5.26935112431047e-05,
+        5.629717142909271e-05, 6.855375679821167e-05, 8.536766845248913e-05,
+        0.00010399248572507849, 0.00012299141898487235, 0.00014157724410536563,
+        0.00015926325910801606, 0.0001757129784018748, 0.00019067461130125085,
+        0.0002039508654450999, 0.00021538419213341548, 0.0002248491778061628,
+        0.00023224840329011796, 0.0002375100358799848, 0.00024058628881702248,
+        0.00024145229521971447, 0.00024010515023423806, 0.00023656298410375734,
+        0.00023086398909338084, 0.0002230653581591444, 0.00021324211457520988,
+        0.00020148582564685034, 0.00018790320367975024, 0.00017261460613753285,
+        0.0001557524575186661, 0.00013745963403729878, 0.00011788789659549832,
+        9.719658995595794e-05, 7.555231721831521e-05, 5.3132723952820894e-05,
+        3.0156934632032552e-05, 7.546975693288699e-06], [6.066179403231812e-11,
+        1.8222236815328162e-10, 3.04495557690103e-10, 4.2796190282022285e-10,
+        5.531101851866682e-10, 6.804408738680588e-10, 8.104696340657412e-10,
+        9.437310447369566e-10, 1.0807824822426475e-09, 1.2222082527296635e-09,
+        1.3686240077692904e-09, 1.5206814989589273e-09, 1.6790737092344498e-09,
+        1.8445404473316325e-09, 2.0178744454137227e-09, 2.199928056239549e-09,
+        2.3916206196919153e-09, 2.5939465977546615e-09, 2.807984588352865e-09,
+        3.03490732468493e-09, 3.275992819157597e-09, 3.5326367797699868e-09,
+        3.806366497133616e-09, 4.098856393902339e-09, 4.4119454680239074e-09,
+        4.7476568910598174e-09, 5.108220075041947e-09, 5.4960955388617516e-09,
+        5.914002992158563e-09, 6.3649530773725035e-09, 6.852283331319092e-09,
+        7.3796989471947135e-09, 7.951319082055869e-09, 8.571729512109041e-09,
+        9.246042616377487e-09, 9.979965786688167e-09, 1.077987958691173e-08,
+        1.1652927158610877e-08, 1.2607116677477062e-08, 1.3651438910056412e-08,
+        1.4796002346814253e-08, 1.605218874388167e-08, 1.7432832488854518e-08,
+        1.8952427736481093e-08, 2.0627368067619902e-08, 2.247622416841647e-08,
+        2.4520066259023468e-08, 2.678283896227253e-08, 2.9291798151178755e-08,
+        3.207802076589053e-08, 3.5177001060580546e-08, 3.8629349245784924e-08,
+        4.2481611691990556e-08, 4.678723589352131e-08, 5.1607708056812486e-08,
+        5.701389701900586e-08, 6.308764554508865e-08, 6.992365855506851e-08,
+        7.7631749063876e-08, 8.63395157723203e-08, 9.619554304610267e-08,
+        1.0737323479047541e-07, 1.200754195224075e-07, 1.3453989633546484e-07,
+        1.5104613211474251e-07, 1.6992337165356197e-07, 1.9156048684216372e-07,
+        2.1641797334743701e-07, 2.450426078612745e-07, 2.7808541222033074e-07,
+        3.1632374228456033e-07, 3.6068854014183374e-07, 4.1229807398691705e-07,
+        4.724998600049414e-07, 5.429229457308462e-07, 6.255433674134661e-07,
+        7.227664314964102e-07, 8.375305745785618e-07, 9.734390299873548e-07,
+        1.1349275010948286e-06, 1.3274786903519485e-06, 1.5578981265501914e-06,
+        1.834670623860776e-06, 2.1684234114538802e-06, 2.572531235213612e-06,
+        3.0639116059395006e-06, 3.6640764118690065e-06, 4.400531585823e-06,
+        5.308652793753808e-06, 6.434217251655152e-06, 7.836847345663996e-06,
+        9.594732491529088e-06, 1.1811159579550333e-05, 1.462362779660492e-05,
+        1.8216695531646312e-05, 2.2840278105678594e-05, 2.883600378389899e-05,
+        3.667564028843455e-05, 4.7017859882012396e-05, 6.079329958980894e-05,
+        7.933402081088909e-05, 0.00010457393963707642, 0.00013936504188262607,
+        0.0001879868315596151, 0.00025698656113567065, 0.00035660216608165133,
+        0.0005032457498755569, 0.0007239912775137014, 0.0010650196468181617,
+        0.0016082948377852924, 0.0025064703773269264, 0.0040614384247388115,
+        0.006918271252623656, 0.012607491540525444, 0.02535665601161708,
+        0.060127886179144274, 0.20546291485330967, 4.14331296986724, 0.7285025012397838,
+        1.346751871589265, 1.2095886814145331, 0.4241884280704502, 0.21291817665927873,
+        0.10794774321455015, 0.9175292838171111, 0.9535343853822373, 1.3091661040325646,
+        2.7561350354396468, 5.642132520995871, 6.056596244320961, 4.267088135892595,
+        2.5841672596049197, 1.9481450549468282, 1.7513991730456564, 1.8335359042728778,
+        2.1941810770966446, 2.4406970829134185, 1.7623425915913502, 1.1914187730505177,
+        0.953769754791881, 0.9146253217781629, 1.0268333004992256, 1.3111738863087283,
+        1.7868975272975554, 2.1055928843135847, 1.8515311655901825, 1.5182592526362049,
+        1.3265821361251833, 1.256722670297466, 1.287146105445405, 1.4196675032261208,
+        1.6543658586017322, 1.8541477737079513, 1.6802205728874686, 1.2900927752793954,
+        1.0069134378439446, 0.8685048378109562, 0.6651253669224161, 0.6046190696569512,
+        0.6109249746427016, 0.6443822457592233, 0.6742176443765708, 0.6790671741770683,
+        0.6603553816285599, 0.6331987264450536, 0.609950818786874, 0.5962174646737178,
+        0.5934734267247302, 0.6012981748860481, 0.6180041864449093, 0.6400818459381009,
+        0.6611105356205782, 0.6716438319899497, 0.6625015851192291, 0.6310028211099752,
+        0.5834675197520287, 0.5302318319667838, 0.4794742427082273, 0.43530386087319745,
+        0.3988482139311229, 0.369751840048982, 0.347136611984061, 0.3300621633625531,
+        0.31770498223338756, 0.30940847115984754, 0.3046814525068199, 0.3031791987593728,
+        0.3046802927736658, 0.3090632989507869, 0.3162827670859519, 0.3263412502561876,
+        0.33925129494179984, 0.35497823995771227, 0.3733517932688181, 0.3939348830476496,
+        0.4158502445622666, 0.4376024665721278, 0.45700465938784834, 0.47138999606275206,
+        0.4782377169543561, 0.4760499172802532, 0.4649544578718948, 0.44657191435617083,
+        0.4232595359978245, 0.39728344983092906, 0.3703352419395816, 0.34343115613412534,
+        0.31703079663304656, 0.29122126129409615, 0.2658890255167284, 0.24085810336811075,
+        0.2159959059765737, 0.19129121999520915, 0.16690602036326077, 0.1432040711877101,
+        0.12076885849278983, 0.10043764831370701, 0.08337490915722229, 0.0711096392635381,
+        0.06516130995460387, 0.06591787724445425, 0.07196314103780155, 0.0811102193277752,
+        0.09158397116884168, 0.1022486958041453, 0.1124103982875529, 0.12162874279410552,
+        0.1296131201576697, 0.13617610878473826, 0.14121437382286472, 0.14469779064313465,
+        0.1466570326684095, 0.14716694681851697, 0.14632757763027116, 0.14424655783961943,
+        0.1410262560289705, 0.13675756981114462, 0.1315205354773508, 0.12539053558571445,
+        0.11844798974605157, 0.1107890432782696, 0.10253500492132106, 0.09383923950554805,
+        0.08489186791205657, 0.07592463710420966, 0.06721997445520818, 0.059128017577232864,
+        0.05208933853051803, 0.0466401722934119, 0.04333756853294962, 0.04254452183343881,
+        0.04418792283617262, 0.047765440753457636, 0.05260783907292574,
+        0.05811255308126036, 0.06382209353099866, 0.06941182183378782, 0.0746568841991357,
+        0.07940392667996332, 0.08355074669872908, 0.08703158318800241, 0.08980595675777436,
+        0.0918500761494399, 0.09315056503377038, 0.09370051222290487, 0.09349776570474007,
+        0.09254515453180244, 0.09085207051342455, 0.0884366732056177, 0.08532796592527142,
+        0.08156716108037017, 0.0772080950806758, 0.0723169021547689, 0.0669716282392024,
+        0.061262914789349754, 0.05529736723165398, 0.04920595889099711,
+        0.04316114647281968, 0.037408242872533394, 0.032315670272675436,
+        0.028427480450934694, 0.026419481483626116, 0.026787661779053187,
+        0.029444002780465738, 0.03380117987091581, 0.03920738558964958,
+        0.04517553779110113, 0.051385820883892964, 0.05763152914715878,
+        0.06377554265816307, 0.06972362279003441, 0.0754087541271596, 0.08078170164591611,
+        0.08580502683113356, 0.09044914468494944, 0.0946897130220143, 0.09850599447532514,
+        0.10187999402713535, 0.10479624242334246, 0.10724211376063228, 0.109208555684036,
+        0.11069108566881003, 0.11169087784551615, 0.11221574431333442, 0.11228081557381697,
+        0.1119087562253073, 0.11112941591684071, 0.10997890305422617, 0.10849816207208268,
+        0.1067312129113615, 0.10472325624469463, 0.10251885218551793, 0.10016034740258381,
+        0.09768666812324127, 0.0951325302629775, 0.09252805691619613, 0.08989874685956059,
+        0.08726570918179147, 0.08464606806540317, 0.08205344509974044, 0.07949844051605781,
+        0.07698905573820912, 0.07453102419408143, 0.0721280422911575, 0.06978191450095432,
+        0.06749264273673286, 0.0652584983095508, 0.06307611382542169, 0.06094062323202552,
+        0.0588458635739401, 0.05678463559869472, 0.05474900636628936, 0.05273062864560624,
+        0.050721050791675944, 0.048711996521867494, 0.04669560444207148,
+        0.04466462914493748, 0.04261261587596089, 0.04053406666537817, 0.03842461612976932,
+        0.03628123015474064, 0.0341024319182404, 0.03188855000035987, 0.029641976076509095,
+        0.02736741896195874, 0.0250721517016393, 0.022766273921214688, 0.02046305934640011,
+        0.01817954091144782, 0.01593762993262603, 0.013766327423859206,
+        0.011706058844380996, 0.009816871925469078, 0.008192265743598607,
+        0.0069740086846133325, 0.0063351523506812255, 0.006374636634277234,
+        0.007002699504391839, 0.00800800959919054, 0.0091988746386887, 0.010448875463888146,
+        0.011681863983849737, 0.012851677673876063, 0.013929339241863934,
+        0.014896104164113645, 0.015739743370064486, 0.016452484126753826,
+        0.017029798596398686, 0.01746964151460482, 0.017771944852563133,
+        0.017938277846998318, 0.01797162715334546, 0.01787627053291109,
+        0.01765772279275969, 0.01732273308899815, 0.016879313271817284,
+        0.016336780474430396, 0.015705804549636493, 0.014998461602818135,
+        0.014228306937811939, 0.013410491514530243, 0.012561951883973433,
+        0.011701698908157303, 0.010851204977449217, 0.010034822968850337,
+        0.009280030653561986, 0.00861705380400894, 0.00807713429960278,
+        0.007688680046993935, 0.0074713675293971125, 0.0074301801886671,
+        0.007552836844858068, 0.007812641583547785, 0.00817509753543012,
+        0.008604620052286457, 0.00906892989924224, 0.009540900352956988,
+        0.00999873833421131, 0.010425403456715537, 0.010807823485923665,
+        0.011136163536905289, 0.011403234077565813, 0.011604044150984599,
+        0.011735476949683328, 0.011796057723410613, 0.011785785894583683,
+        0.011706008682131237, 0.01155932024383517, 0.011349477195912838,
+        0.011081327504002803, 0.010760754411655749, 0.010394639668225913,
+        0.009990850408770525, 0.009558251272860821, 0.009106737199597073,
+        0.008647271767818623, 0.00819189925585771, 0.007753674104017942,
+        0.0073464203397823205, 0.006984206157217786, 0.0066804236071028615,
+        0.006446446901657965, 0.00629003813962309, 0.00621392206314147,
+        0.006215077588255259, 0.00628510307806473, 0.006411555258810243,
+        0.006579761260260139, 0.006774532815331422, 0.006981431817062294,
+        0.007187515935249465, 0.0073816664469395854, 0.007554648519641371,
+        0.007699030679527404, 0.007809046778343855, 0.007880446507386984,
+        0.007910356173460188, 0.007897158299606976, 0.007840392852547078,
+        0.007740681224257002, 0.007599674248627821, 0.007420026163428753,
+        0.007205396791036876, 0.006960483848904473, 0.006691085670651698,
+        0.006404190646799354, 0.006108081253297008, 0.005812424058428668,
+        0.005528288145624854, 0.005267991315259192, 0.005044627398735584,
+        0.00487111933640162, 0.004758745447958084, 0.004715355011827389,
+        0.004743829119393301, 0.004841455978663011, 0.005000538472489289,
+        0.005209937325880774, 0.005456880305324758, 0.005728464468439099,
+        0.006012620321645988, 0.0062985862219549354, 0.006577051508545416,
+        0.006840119364422743, 0.007081192238973378, 0.007294837053546585,
+        0.007476656903319876, 0.007623179133320258, 0.007731761762725021,
+        0.007800517202429126, 0.00782825145100625, 0.007814417028088768,
+        0.0077590781478407925, 0.00766288683449055, 0.007527068862900761,
+        0.007353418698379672, 0.007144303149902579, 0.006902674329868357,
+        0.006632093731192409, 0.006336770658470039, 0.006021619554603945,
+        0.0056923412520592746, 0.005355531435021677, 0.005018812837302739,
+        0.00469097083926575, 0.004382037447685036, 0.004103209173058407,
+        0.003866408283610893, 0.0036832598022785014, 0.003563385979374125,
+        0.0035123308932242503, 0.0035299537762400216, 0.003610206800633075,
+        0.0037424937739477956, 0.003913872408149755, 0.004111099222525765,
+        0.004321961194457416, 0.004535879401240926, 0.004744024153727168,
+        0.004939186223224799, 0.0051155644846837016, 0.005268551407105402,
+        0.005394548597645838, 0.005490819800048519, 0.005555378327984904,
+        0.005586902641740907, 0.005584673653677163, 0.0055485284491982485,
+        0.005478826611049633, 0.005376426910761891, 0.005242673683169532,
+        0.0050793937290324, 0.004888906160191598, 0.004674049324891136,
+        0.004438230963371761, 0.004185510105496268, 0.003920721631652337,
+        0.003649655462720563, 0.0033792977412242247, 0.0031181203976050897,
+        0.0028763460227926867, 0.002665985126248917, 0.0025002414350790265,
+        0.002391768274888905, 0.0023496797237910583, 0.0023764460094756637,
+        0.002466754581374643, 0.002609305617382675, 0.0027901754666226825,
+        0.002995684040880523, 0.0032138875942972207, 0.003434963099601197,
+        0.0036510382966042387, 0.003855851820961271, 0.004044420985435853,
+        0.004212773353136714, 0.004357746295454964, 0.00447684223789107,
+        0.004568125092275321, 0.0046301457194794105, 0.00466188741891277,
+        0.004662725197130375, 0.004632394683642644, 0.00457096810155076,
+        0.00447883581333488, 0.004356692814475148, 0.00420553031910981,
+        0.004026633482941444, 0.003821587634862452, 0.003592297618800778,
+        0.0033410288654050907, 0.003070486406728673, 0.002783963005859981,
+        0.002485618238974168, 0.002181015097772138, 0.001878176888167799,
+        0.001589683762391799, 0.0013365609937221524, 0.0011532785193464521,
+        0.0010843930878552867, 0.0011553529017695207, 0.0013456367129018624,
+        0.0016126677080109998, 0.001922339851107008, 0.002253799607409751,
+        0.0025947968178864273, 0.0029378048661265533, 0.003277889664482827,
+        0.0036116242978976375, 0.003936530734881218, 0.004250782211676032,
+        0.004553037294620743, 0.004842342388420917, 0.005118070635800479,
+        0.005379880309267511, 0.005627683427746247, 0.005861619324012601,
+        0.0060820300564681865, 0.006289435790436655, 0.006484509018405152,
+        0.006668046979845999, 0.00684094201022851, 0.007004149860784017,
+        0.00715865631627978, 0.007305442704564594, 0.007445451131584499,
+        0.007579550471326449, 0.00770850426942469, 0.007832941765831204,
+        0.00795333319099083, 0.008069970341106888, 0.00818295320155215,
+        0.008292183084839718, 0.008397362412697172, 0.008498000934824659,
+        0.00859342787318171, 0.008682809236974795, 0.008765169385393937,
+        0.00883941582795223, 0.008904366239669486, 0.008958776717357815,
+        0.009001370396422894, 0.009030865666149393, 0.009046003350527933,
+        0.009045572348401839, 0.009028433344053158, 0.008993540303533998,
+        0.008939959562583985, 0.0088668863902467, 0.008773658980040308,
+        0.008659769879958954, 0.008524874924634829, 0.008368799778640943,
+        0.00819154423954668, 0.007993284483211606, 0.0077743734630496344,
+        0.007535339701948323, 0.007276884741784647, 0.006999879548400503,
+        0.006705360214570879, 0.0063945233720569105, 0.006068721834017751,
+        0.005729461165528523, 0.005378398174631858, 0.00501734280202725,
+        0.004648265716917503, 0.004273315356888612, 0.0038948506953823923,
+        0.0035155006566147755, 0.003138269791825776, 0.0027667265031484827,
+        0.0024053424025145304, 0.002060112235574113, 0.0017396824777516902,
+        0.001457278474947547, 0.0012331874246189012, 0.001094505569411186,
+        0.0010634750709092756, 0.0011365970152441903, 0.0012843471972253137,
+        0.001473377100842174, 0.0016796204686206704, 0.0018881876668293274,
+        0.0020900605830497894, 0.0022796113758637646, 0.002453179760584155,
+        0.002608302427703923, 0.0027432927679681336, 0.002857004977347444,
+        0.002948696795381685, 0.0030179464911855042, 0.0030646006016017244,
+        0.0030887396373195214, 0.003090654629823373, 0.003070830491405405,
+        0.0030299339384706058, 0.0029688048166100147, 0.002888450407190428,
+        0.002790042896090112, 0.0026749207985199705, 0.002544595910507225,
+        0.002400768493460639, 0.002245355195290067, 0.0020805371585228783,
+        0.0019088406479260754, 0.001733270448316601, 0.001557528095019376,
+        0.0013863601330533516, 0.0012260774169275113, 0.0010851916256143558,
+        0.0009747366876465594, 0.0009070171182979532, 0.0008912878471657756,
+        0.0009281512516348804, 0.0010086922723886204, 0.001119627656239498,
+        0.0012485620517295947, 0.0013859708593954969, 0.0015250360794499828,
+        0.001660919969507604, 0.0017901258029977467, 0.001910058771110143,
+        0.0020187471750368574, 0.0021146690285024448, 0.0021966438226383896,
+        0.0022637639476939487, 0.0023153503305223845, 0.002350923036217821,
+        0.002370181275107707, 0.0023729894628986194, 0.002359367328190396,
+        0.002329482921358209, 0.0022836479772863345, 0.0022223155687205033,
+        0.0021460804735469255, 0.002055683289521545, 0.0019520202377137559,
+        0.0018361620961686287, 0.0017093883520736721, 0.001573247542328202,
+        0.0014296640453271784, 0.001281129578240556, 0.0011310519892217014,
+        0.0009843929901341504, 0.0008487868018945639, 0.0007361611470920914,
+        0.0006635411518625813, 0.0006484475154203963, 0.0006968700593387089,
+        0.000798058005946252, 0.0009346393048326699, 0.0010922383000761201,
+        0.001261278333050508, 0.0014356383902737985, 0.001611278206555442,
+        0.001785376972427608, 0.00195585019284292, 0.002121082760380331,
+        0.0022797790696537003, 0.0024308766047167465, 0.0025734946536061327,
+        0.0027069029467593902, 0.0028305018531140018, 0.0029438093931889197,
+        0.003046452303193066, 0.0031381594908590858, 0.0032187568623206924,
+        0.0032881628781387864, 0.003346384427508295, 0.003393512753519075,
+        0.0034297192546031223, 0.0034552510473126446, 0.0034704262159090185,
+        0.0034756287015018173, 0.00347130280286759, 0.0034579472749784773,
+        0.003436109021889685, 0.0034063763892244877, 0.003369372069067009,
+        0.0033257456374326654, 0.0032761657525676086, 0.003221312051819704,
+        0.0031618667965781157, 0.0030985063298784228, 0.0030318924297696643,
+        0.0029626636645538537, 0.002891426882589044, 0.0028187489989367097,
+        0.0027451492713824683, 0.0026710922865624217, 0.002596981898263277,
+        0.0025231563704937792, 0.0024498849717094736, 0.0023773662403963405,
+        0.0023057280929818344, 0.0022350298736777082, 0.002165266355721339,
+        0.0020963736021729447, 0.002028236490959521, 0.0019606976154627896,
+        0.0018935671976607386, 0.0018266336050293413, 0.0017596740486495374,
+        0.001692465058372082, 0.00162479237784726, 0.0015564599906046717,
+        0.0014872980700153858, 0.00141716973379123, 0.0013459765704469033,
+        0.0012736629894543842, 0.0012002195274047646, 0.0011256853263965005,
+        0.00105015009867145, 0.0009737560256427417, 0.0008967002496771246,
+        0.000819238977140123, 0.0007416948659877173, 0.0006644706129820862,
+        0.0005880740966192195, 0.0005131653846553437, 0.00044064615086810116,
+        0.000371832804121446, 0.00030879086654875124, 0.0002549284061589356,
+        0.00021568237049735366, 0.00019776034173661126, 0.00020435040157569341,
+        0.00023091961802601898, 0.00026933292945816175, 0.00031313899330560343,
+        0.00035841647090775785, 0.000402898292637011, 0.00044522844942724806,
+        0.00048454970336428665, 0.0005202925650210587, 0.000552066474363534,
+        0.0005796017588397572, 0.0006027173931208048, 0.0006213023312925503,
+        0.0006353042385115635, 0.0006447223951368665, 0.0006496030326420841,
+        0.000650036142380144, 0.0006461532294885456, 0.0006381257366042902,
+        0.0006261640227760735, 0.0006105168989559143, 0.0005914718201368275,
+        0.0005693559336249967, 0.0005445382959900132, 0.0005174337063407004,
+        0.0004885087588599317, 0.00045829086438805937, 0.0004273810318081756,
+        0.0003964708742615746, 0.00036636300915304505, 0.00033799055253157717,
+        0.0003124239587170398, 0.0002908411177068806, 0.00027442502014548474,
+        0.00026416353101800825, 0.00026058671807167345, 0.00026356900481570503,
+        0.0002723356788106594, 0.0002856792993941051, 0.00030224668533442185,
+        0.0003207572202433715, 0.0003401099654701663, 0.0003594078479361686,
+        0.00037794060180252324, 0.0003951547230318837, 0.00041062392044535854,
+        0.0004240246599512196, 0.000435117373260702, 0.00044373249688530093,
+        0.0004497602358998095, 0.000453143077037767, 0.000453870301727667,
+        0.0004519739635314743, 0.000447525968253826, 0.0004406360291944721,
+        0.0004314503727769839, 0.0004201511490022985, 0.0004069565614050988,
+        0.00039212177122554685, 0.000375940639837125, 0.0003587483259257354,
+        0.00034092459664910034, 0.00032289735258239015, 0.0003051451641079998,
+        0.00028819641597328794, 0.0002726209310098396, 0.00025900817517420736,
+        0.00024792591104691827, 0.0002398572952011305, 0.00023512506664858933,
+        0.0002338253589221979, 0.00023579947039670474, 0.00024065917717918062,
+        0.0002478556206425661, 0.00025676355541018656, 0.0002667540729919512,
+        0.00027724299755953343, 0.00028771551925663174, 0.00029773391326565196,
+        0.00030693564654382064, 0.00031502718453112004, 0.00032177662343133473,
+        0.0003270066949711006, 0.00033058875967140704, 0.00033243793128012473,
+        0.00033250927122665863, 0.00033079492975091653, 0.00032732211572009145,
+        0.0003221518111797322, 0.0003153781901598123, 0.0003071287439281877,
+        0.0002975651486328044, 0.00028688492370513837, 0.00027532389703108885,
+        0.0002631593708772779, 0.00025071359263693183, 0.0002383565575246101,
+        0.00022650617182974741, 0.00021562235579290393, 0.00020619015371181712,
+        0.00019868664094961245, 0.00019352970565701452, 0.0001910154261441014,
+        0.00019126211231946692, 0.00019418399401038462, 0.00019950759267819198,
+        0.00020682353681875963, 0.00021565188417148565, 0.0002254996548939109,
+        0.00023590006439863108, 0.0002464334044904417, 0.00025673459426535177,
+        0.00026649295895156676, 0.0002754483645925802, 0.0002833861859998972,
+        0.0002901323658089539, 0.00029554908794691287, 0.00029953120481594926,
+        0.00030200338377324925, 0.00030291787710432384, 0.00030225281308340267,
+        0.00030001092334043473, 0.0002962186489583912, 0.00029092559825796545,
+        0.00028420436111682945, 0.0002761507177995585, 0.000266884314643566,
+        0.00025654991325167503, 0.00024531934834517137, 0.00023339433690038573,
+        0.00022101023237297267, 0.0002084406394626225, 0.00019600236033195196,
+        0.00018405921526856475, 0.00017302162902955485, 0.00016333653262191484,
+        0.000155460168945152, 0.00014980788973359717, 0.00014668428929732108,
+        0.00014621375690530234, 0.00014830340985859085, 0.00015266012290589615,
+        0.0001588534651284439, 0.00016639348392077195, 0.00017479450072495494,
+        0.00018361350466931128, 0.00019246625209381072, 0.00020102932753308288,
+        0.00020903543111017799, 0.00021626643973213713, 0.0002225465200029521,
+        0.00022773619175445097, 0.00023172754734720815, 0.00023444053945192834,
+        0.00023582015929159478, 0.00023583432596627072, 0.00023447234037438954,
+        0.00023174380011698855, 0.00022767791604687236, 0.00022232321542040644,
+        0.00021574766315266713, 0.00020803928554952208, 0.0001993074451779356,
+        0.00018968499622531028, 0.00017933164811276145, 0.00016843896929831907,
+        0.00015723752159663826, 0.00014600647604577082, 0.0001350853455198353,
+        0.00012488538469088785, 0.00011589354406806681, 0.00010865420475015498,
+        0.00010370803430056548, 0.0001014787193082684, 0.00010214167824553956,
+        0.00010555445816959901, 0.00011130380096085221, 0.0001188337774822564,
+        0.00012757148947817602, 0.00013700176947861024, 0.00014669287225289271,
+        0.00015629441499519025, 0.00016552503421444638, 0.00017415878522280257,
+        0.00018201360878629679, 0.00018894250360541314, 0.0001948270743019578,
+        0.00019957290518175252, 0.00020310625581479363, 0.00020537168591567526,
+        0.00020633032472114552, 0.0002059585862530886, 0.00020424719663549243,
+        0.00020120044811943488, 0.00019683563244869736, 0.00019118263937224018,
+        0.00018428374042502192, 0.00017619362133997494, 0.00016697979068556676,
+        0.00015672359958695384, 0.00014552230060876567, 0.00013349294212970138,
+        0.00012077962999287643, 0.00010756721729962118, 9.410775204922721e-05,
+        8.077294465437754e-05, 6.815881643781233e-05, 5.727786050930257e-05,
+        4.978302703547136e-05, 4.769200788663416e-05, 5.1887786522127016e-05,
+        6.116938971296158e-05, 7.361795163938461e-05, 8.781135539337047e-05],
+    [1.6275786364139332e-10, 4.889705799562936e-10, 8.172796414689116e-10,
+        1.1491003910920353e-09, 1.4858750217874465e-09, 1.829083830577762e-09,
+        2.1802567562578433e-09, 2.5409856311573333e-09, 2.9129370714829207e-09,
+        3.297866273055835e-09, 3.697631854584416e-09, 4.114211954077917e-09,
+        4.549721742161079e-09, 5.006432657849814e-09, 5.486793555727104e-09,
+        5.993454120216552e-09, 6.529290844300517e-09, 7.097435967674187e-09,
+        7.70130982135685e-09, 8.344657038522631e-09, 9.031587266881606e-09,
+        9.766620962847417e-09, 1.0554741085556088e-08, 1.1401451537669988e-08,
+        1.2312843367708482e-08, 1.329566989963675e-08, 1.435743218461152e-08,
+        1.5506476313146406e-08, 1.6752104490883175e-08, 1.8104701980414345e-08,
+        1.957588252803881e-08, 2.1178655143581557e-08, 2.292761582282129e-08,
+        2.4839168253818203e-08, 2.693177842538345e-08, 2.922626882330316e-08,
+        3.174615908885604e-08, 3.4518061159945974e-08, 3.757213861499391e-08,
+        4.094264161862985e-08, 4.4668531336241204e-08, 4.8794210198963024e-08,
+        5.337037797956442e-08, 5.845503747307131e-08, 6.411467884717508e-08,
+        7.042567745846809e-08, 7.747594814893814e-08, 8.536690742422362e-08,
+        9.421580770365952e-08, 1.0415852105088602e-07, 1.1535286881328324e-07,
+        1.2798261574004056e-07, 1.4226227557913138e-07, 1.5844291162075162e-07,
+        1.7681916102379312e-07, 1.977377701346221e-07, 2.2160800354360983e-07,
+        2.489143849016357e-07, 2.8023235386894005e-07, 3.1624758525932053e-07,
+        3.5777993026029537e-07, 4.0581322110571605e-07, 4.6153255378860994e-07,
+        5.263711629078362e-07, 6.020696757498664e-07, 6.907514473358161e-07,
+        7.950189301853966e-07, 9.180777667700112e-07, 1.0638977167967722e-06,
+        1.2374229558008573e-06, 1.444849185334334e-06, 1.693992105586063e-06,
+        1.9947822692230643e-06, 2.3599369889022214e-06, 2.8058838333483387e-06,
+        3.354047328127036e-06, 4.032669484084842e-06, 4.879431061707085e-06,
+        5.945302383135623e-06, 7.300334091920681e-06, 9.042607641534885e-06,
+        1.1312530478093384e-05, 1.4316592788168261e-05, 1.836883451150253e-05,
+        2.3967858836778346e-05, 3.1951886216554324e-05, 4.3846895324384706e-05,
+        6.277986833501997e-05, 9.653151614439818e-05, 0.00017355013411949927,
+        0.0008466076450236779, 0.00034695722360906194, 0.0002860663361182442,
+        0.00027833928859468597, 0.0002899173083658355, 0.0003141055492913641,
+        0.00034965145647559493, 0.00039740530826741396, 0.00045957471013654573,
+        0.0005396732762300129, 0.0006427933552329807, 0.0007761530342167542,
+        0.0009499891351958538, 0.0011789685700452717, 0.0014844342685344449,
+        0.0018980532555680444, 0.002467908914231844, 0.003269023127194559,
+        0.004422272066755606, 0.006130063135479443, 0.008747676557002416,
+        0.012936718552423308, 0.020027700062287032, 0.03299210563587636,
+        0.059566012767388286, 0.12564590902226955, 0.37728778596201756,
+        6.574866807025479, 0.9761342643947251, 1.480388426362263, 1.0904885267705688,
+        0.41473697166223994, 0.5253718149881265, 1.264727569510353, 2.0910248664464324,
+        1.2051040928177996, 1.0130829935487762, 1.0998362887329687, 1.4989454310561727,
+        2.287666517911476, 1.7078779865707032, 1.037491162184348, 0.7751049391185283,
+        0.699335011160667, 0.7631057932996348, 1.0096054200866649, 1.3175941674242784,
+        1.1527885399503501, 0.9355158563828274, 0.858633767608559, 0.8872083796681232,
+        1.0161273220698595, 1.2768566299585296, 1.6800199240393947, 1.895302639784797,
+        1.5913428314970066, 1.2461381635541118, 1.041415577214365, 0.9460769010802722,
+        0.9328277358523778, 0.9965220115027684, 1.135872141562941, 1.2649112989937608,
+        1.1658586513590148, 0.9384268368131852, 0.7921967082385472, 0.7570129603147003,
+        0.6611848181612965, 0.6456525575243296, 0.6782705053264245, 0.7225032405182167,
+        0.748156149603584, 0.7372593664752276, 0.697785958545636, 0.6502083020654829,
+        0.6089238675269748, 0.5794662229412273, 0.5625346380514605, 0.5569003671605335,
+        0.5602998064008095, 0.5690759076290021, 0.5773440208023906, 0.5770381406549331,
+        0.5607916593805408, 0.5270015468250092, 0.48145835222349537, 0.4328592370554144,
+        0.387742831415073, 0.3491435641728209, 0.3176554082085259, 0.29272452706000923,
+        0.2734405191212498, 0.2588991896585774, 0.24833363603157516, 0.2411430759414183,
+        0.23688298378211345, 0.23524358218972868, 0.23602684910872254, 0.23912487305871893,
+        0.24449898226344877, 0.25215691560581965, 0.26212319730926514, 0.2743953981438364,
+        0.28887656027077, 0.3052740677372129, 0.3229638254910004, 0.3408467084712876,
+        0.3572796945802416, 0.37022205225996996, 0.37770427832795717, 0.3785057646960773,
+        0.3726418657984181, 0.3612924658010195, 0.34623957302931163, 0.3292302200795348,
+        0.311591605112089, 0.2941380021385797, 0.27724927781383724, 0.26100317336593154,
+        0.24530066237608866, 0.22996725606102913, 0.21483139433248352, 0.1997832142220768,
+        0.18481313415152664, 0.17002684254224498, 0.15563511854701093, 0.14192296704496218,
+        0.12920848429589302, 0.11780286475939315, 0.10797796604802534, 0.09994064065256691,
+        0.09380938101636538, 0.08959228407790759, 0.08717358317042904, 0.08632026265778545,
+        0.08671326078206612, 0.08799439438789809, 0.08981323359879058, 0.09186216523731003,
+        0.09389594707538015, 0.09573739598422039, 0.0972726778516075, 0.09843992407374134,
+        0.09921477624171736, 0.09959605435472356, 0.09959395470029962, 0.09922215273860986,
+        0.09849417709112279, 0.0974236034207366, 0.09602702169961891, 0.09432833866908051,
+        0.0923628185529751, 0.09017942107737731, 0.08784050971631853, 0.08541877391929815,
+        0.08299198329742782, 0.08063668717793505, 0.0784220474690283, 0.07640471773822918,
+        0.07462526684694294, 0.0731062933647682, 0.07185217602105386, 0.07085032262128493,
+        0.07007372371504828, 0.06948451755110838, 0.06903812829988061, 0.0686874155039148,
+        0.06838625459459315, 0.06809210255690731, 0.06776736316257517, 0.06737966599692433,
+        0.06690141311699672, 0.06630906203488857, 0.06558259396310129, 0.06470549414097491,
+        0.063665394708487, 0.0624553443852875, 0.06107550829045886, 0.059534993922895206,
+        0.057853466635499236, 0.05606226544284133, 0.054204836411429445,
+        0.052336414929110286, 0.050522943402153984, 0.04883915904638372,
+        0.04736563944472158, 0.04618445916787535, 0.04537318982041002, 0.04499746817156817,
+        0.045103242983173183, 0.04571064360040636, 0.0468114676265078, 0.04837120749120026,
+        0.050334875223767, 0.052634701747361075, 0.05519767600056441, 0.057951584746526265,
+        0.060829075925313274, 0.0637698713008426, 0.0667215251669653, 0.06963917469649239,
+        0.07248467591035354, 0.07522543989941448, 0.07783320649190004, 0.08028292563287581,
+        0.08255186156510948, 0.08461899058645297, 0.0864647277370663, 0.08807098785628062,
+        0.08942155826734209, 0.09050273085815344, 0.09130411000217764, 0.09181948273210405,
+        0.09204761563871236, 0.09199283755732743, 0.09166528523034397, 0.09108073236630058,
+        0.09025998494485994, 0.08922789442689129, 0.08801209986314358, 0.08664164631327406,
+        0.08514563386442481, 0.08355203070365183, 0.08188674360905532, 0.08017299122160383,
+        0.07843097992070584, 0.07667784606801022, 0.0749278048524571, 0.07319243493188217,
+        0.07148102771977279, 0.06980093813469057, 0.06815788761227398, 0.06655618798274385,
+        0.06499887430988832, 0.06348775347932556, 0.06202339072355073, 0.06060506601916514,
+        0.05923073492343003, 0.057897023747817335, 0.056599278484014415,
+        0.05533167326970027, 0.05408737087338345, 0.052858717821022146,
+        0.051637452542688096, 0.05041490680310936, 0.04918218766627434,
+        0.047930337056105735, 0.046650475754414125, 0.0453339458226243,
+        0.04397246802362968, 0.04255832811428582, 0.04108459823024689, 0.03954538852407206,
+        0.03793611204829724, 0.03625373553231097, 0.03449698299316957, 0.03266646036446973,
+        0.030764678228054176, 0.02879596527983007, 0.02676628427739954,
+        0.02468298080251576, 0.02255450930067884, 0.020390188558834742,
+        0.018200041676505987, 0.015994781123586925, 0.013786026664530614,
+        0.011586942408335821, 0.009413805026828478, 0.007290163040493268,
+        0.005260018751249839, 0.0034411847351043805, 0.002271411566342872,
+        0.002637058697026016, 0.0040518592712980705, 0.005711391858108343,
+        0.007384833292595893, 0.00900398185469206, 0.010540215675791062,
+        0.011977775241201782, 0.013306310016813474, 0.014518273637177278,
+        0.015607850672938843, 0.016570470800276356, 0.017402591581386222,
+        0.01810162163757909, 0.01866591922585291, 0.019094823979195097,
+        0.019388690386720264, 0.01954890049664995, 0.01957784322985584,
+        0.019478858307486194, 0.01925615245826977, 0.018914702437912826,
+        0.01846016225311878, 0.017898790682999394, 0.01723741066423274,
+        0.016483406116470544, 0.015644756530017442, 0.014730107393520226,
+        0.0137488775038648, 0.012711414717905184, 0.011629233078798267,
+        0.010515402681921714, 0.00938523219705411, 0.008257508935671858,
+        0.00715678695664031, 0.006117563440812571, 0.005191348880194269,
+        0.004455529282377608, 0.0040118718866483764, 0.003944746089405758,
+        0.004248786294858988, 0.004827156258750399, 0.005566075703757837,
+        0.006380767576480878, 0.007217013182517679, 0.008040776562838178,
+        0.00882995564682186, 0.00956951957128149, 0.010248822923985115,
+        0.010860112125690623, 0.011397665701830071, 0.011857277475774863,
+        0.012235933420355918, 0.01253160471751973, 0.012743115184675724,
+        0.01287005836907471, 0.012912747560807054, 0.012872185748996678,
+        0.012750044904253938, 0.01254864633910494, 0.012270936827062196,
+        0.011920458608439464, 0.011501315004462895, 0.01101813665693482,
+        0.010476056144542329, 0.0098807010485992, 0.009238218221446423,
+        0.008555346699876084, 0.007839566482289251, 0.0070993708551412805,
+        0.0063447518287316484, 0.005588071948406017, 0.004845656475361368,
+        0.004140707868033773, 0.003508346640522682, 0.003002323749882304,
+        0.002695240686666409, 0.002649845541683809, 0.0028653517697152567,
+        0.003274125415156393, 0.003796116608190459, 0.0043722642299512966,
+        0.004965194092864318, 0.005551585567308165, 0.006116290171434459,
+        0.006648932057392015, 0.007142063485928976, 0.007590162041198732,
+        0.007989071923745525, 0.008335681527881538, 0.00862772875888504,
+        0.008863676554179668, 0.009042627908065651, 0.009164264274558923,
+        0.009228799270003203, 0.00923694393764854, 0.009189881962678711,
+        0.009089254051847616, 0.00893715086034663, 0.008736113864250578,
+        0.008489143828604962, 0.008199717287042699, 0.007871812894451415,
+        0.007509951708322449, 0.007119258384103538, 0.006705553835089797,
+        0.006275493768010986, 0.005836770571183435, 0.00539839511735346,
+        0.004971061758147063, 0.004567554948333515, 0.004203044209990827,
+        0.003894898170721453, 0.003661378662754144, 0.0035185971509176304,
+        0.00347607558805996, 0.0035330665844346943, 0.0036783480289858225,
+        0.003893788207781704, 0.004159130181117661, 0.004455475116070994,
+        0.004766825745272662, 0.0050802944319499185, 0.005385717593064843,
+        0.005675128141804097, 0.005942277221683735, 0.006182257534532363,
+        0.006391224769016612, 0.0065661975045830994, 0.006704915017882118,
+        0.006805735970376165, 0.006867565103337109, 0.006889798673142207,
+        0.006872282259950698, 0.006815276860741992, 0.006719430949820023,
+        0.006585757542068204, 0.006415616305991385, 0.006210701541702096,
+        0.005973037510146583, 0.005704983388596146, 0.0054092513510607095,
+        0.005088943395935224, 0.0047476162789077785, 0.004389390401312882,
+        0.004019129557585303, 0.0036427367079592335, 0.003267638765662351,
+        0.002903566049700941, 0.002563729119953923, 0.002266290197867783,
+        0.0020351627492550058, 0.0018972407380976138, 0.0018726088118089018,
+        0.0019620564296166706, 0.0021457323348882144, 0.002394987273478684,
+        0.0026836725143472855, 0.0029920136830921657, 0.0033060042038294594,
+        0.0036157650893527404, 0.00391417005802113, 0.004195920774413119,
+        0.004456966158141536, 0.0046941431870506966, 0.0049049528852057045,
+        0.0050874179139455, 0.005239989797545255, 0.005361486850450788,
+        0.005451051492230634, 0.005508120042096424, 0.005532400622990812,
+        0.005523856279030636, 0.005482691294384145, 0.005409339278047785,
+        0.0053044520114187655, 0.005168888430207093, 0.005003703467198328,
+        0.004810136832937273, 0.0045896021644765, 0.00434367736016615, 0.004074097421718136,
+        0.0037827519350777886, 0.0034716908641104455, 0.0031431455598624376,
+        0.002799579126912472, 0.002443797637068681, 0.002079198935891863,
+        0.0017103669938788285, 0.001344652030812914, 0.0009970053544244783,
+        0.0007065882804212646, 0.0005772268539254167, 0.0007059941285828457,
+        0.0009955339328996482, 0.0013420508006123481, 0.001706660869337904,
+        0.0020748434019462465, 0.0024398032310869074, 0.002797624811423928,
+        0.003145684232918642, 0.003482047457010413, 0.003805213843592127,
+        0.0041139966596486, 0.004407463495514983, 0.004684904773764708,
+        0.004945815942016112, 0.005189886277442093, 0.005416990591458317,
+        0.005627181778870663, 0.005820683037118811, 0.005997879075334417,
+        0.006159305924052005, 0.006305639127743337, 0.006437680200890436,
+        0.006556341286299095, 0.006662627991062879, 0.006757620412303061,
+        0.006842452415446053, 0.00691828930119678, 0.006986304098930156,
+        0.007047652850340792, 0.007103449388480628, 0.007154740258706721,
+        0.007202480550821426, 0.007247511495727233, 0.007290540706751076,
+        0.00733212590399119, 0.007372662844538129, 0.0074123779983096705,
+        0.0074513262740778866, 0.007489393835930971, 0.007526305784927146,
+        0.007561638240711583, 0.007594834166280051, 0.007625222150396958,
+        0.007652037301371811, 0.007674443409351666, 0.007691555590552128,
+        0.007702462720944307, 0.007706249082529057, 0.007702014767458246,
+        0.007688894502680288, 0.007666074662962933, 0.007632808329504591,
+        0.007588428324547258, 0.007532358211158134, 0.0074641212942203935,
+        0.007383347696434788, 0.007289779614182983, 0.007183274883669993,
+        0.0070638090088881705, 0.0069314758199226926, 0.006786486943002874,
+        0.006629170272955641, 0.0064599676453470254, 0.006279431909497379,
+        0.006088223608007346, 0.005887107473495867, 0.005676948961599556,
+        0.005458711053170201, 0.005233451577641308, 0.005002321338634588,
+        0.004766563356797819, 0.0045275135868801854, 0.004286603502914271,
+        0.00404536496621717, 0.003805437754902375, 0.0035685799788599776,
+        0.003336681205118189, 0.0031117772709771774, 0.00289606413749522,
+        0.0026919052949001916, 0.0025018227429362025, 0.002328455470418434,
+        0.0021744632005872774, 0.0020423516242206955, 0.0019342070341342892,
+        0.0018513619767445487, 0.0017940659976400275, 0.0017612778465169686,
+        0.0017506825984428172, 0.001758953584417426, 0.0017821737698655163,
+        0.0018162791569730993, 0.001857413231088963, 0.0019021478790388934,
+        0.00194758227858986, 0.001991356358956726, 0.0020316160879275294,
+        0.002066957950818866, 0.0020963690837547473, 0.0021191713582030844,
+        0.0021349726721965273, 0.002143625995176634, 0.0021451954458412284,
+        0.002139928198625379, 0.002128230908067367, 0.0021106493860488756,
+        0.0020878503512223572, 0.002060604143345656, 0.0020297673453970335,
+        0.0019962642940524427, 0.001961066514100515, 0.0019251692302697922,
+        0.0018895643495235532, 0.001855209728513629, 0.0018229951845874213,
+        0.001793706560722969, 0.0017679901107625366, 0.0017463203209794908,
+        0.0017289747409640374, 0.0017160191922408596, 0.0017073057376117318,
+        0.0017024841617715289, 0.0017010258189083653, 0.001702257048000845,
+        0.0017053983577413124, 0.0017096054125311858, 0.0017140084055245828,
+        0.0017177473988549427, 0.0017200023210948306, 0.0017200172888343567,
+        0.001717119635407935, 0.0017107344655733537, 0.0017003957578514695,
+        0.0016857550790245358, 0.0016665889276416834, 0.0016428056373363042,
+        0.00161445267633764, 0.0015817250841802587, 0.001544975673285961,
+        0.0015047274447395809, 0.0014616883360328687, 0.0014167677859826676,
+        0.0013710934513375636, 0.001326024470160479, 0.0012831547306697126,
+        0.001244295839552389, 0.0012114260406384005, 0.0011865910520962829,
+        0.0011717500817716173, 0.001168578476035776, 0.0011782640887440204,
+        0.001201353281803963, 0.0012376965105960198, 0.001286508991451478,
+        0.0013465187677282233, 0.0014161498058070329, 0.0014936916644393337,
+        0.001577428556500932, 0.00166572233432783, 0.0017570569544132048,
+        0.0018500561418657577, 0.0019434849205782103, 0.0020362427856470675,
+        0.002127353446991252, 0.0022159539293235674, 0.002301284414970148,
+        0.0023826793887731664, 0.0024595601963137083, 0.0025314289074539515,
+        0.002597863287018325, 0.0026585126523995203, 0.002713094408379046,
+        0.002761391073644374, 0.0028032476412763376, 0.0028385691422847447,
+        0.0028673183046973565, 0.0028895132206954756, 0.0029052249504792262,
+        0.0029145750047691724, 0.002917732658202102, 0.0029149120542753776,
+        0.0029063690691057526, 0.0028923979066708162, 0.0028733274027494173,
+        0.002849517018856262, 0.002821352511469824, 0.002789241266409199,
+        0.002753607293809573, 0.0027148858865447467, 0.0026735179551136967,
+        0.00262994406536378, 0.002584598223107768, 0.0025379014716605496,
+        0.002490255394615664, 0.0024420356457303697, 0.002393585658998789,
+        0.002345210721520096, 0.0022971726164851183, 0.0022496850583764304,
+        0.0022029101435522397, 0.0021569560225257046, 0.0021118759638327727,
+        0.002067668923455154, 0.002024281661979209, 0.0019816123694366425,
+        0.0019395156741735323, 0.0018978088348824817, 0.0018562788535447642,
+        0.0018146902068178926, 0.0017727928778078813, 0.0017303303788578995,
+        0.0016870474855791237, 0.0016426974471867018, 0.001597048492384157,
+        0.001549889506335654, 0.0015010348085935234, 0.00145032800912545,
+        0.0013976449588214005, 0.001342895840566119, 0.0012860264680609663,
+        0.001227018873380185, 0.0011658912723478752, 0.0011026975015815629,
+        0.0010375260249020607, 0.0009704986122570869, 0.0009017688066418498,
+        0.0008315203194184401, 0.0007599655472353845, 0.0006873445124086107,
+        0.0006139247594201786, 0.0005400032552117089, 0.0004659125704487688,
+        0.00039203683909330353, 0.0003188524807101763, 0.00024704128088083924,
+        0.00017786098739001015, 0.00011471347574088878, 7.147430089115468e-05,
+        8.262033485272803e-05, 0.00013231421475833004, 0.00019030379473209045,
+        0.00024880658074117034, 0.00030567825984859325, 0.00036002688296588953,
+        0.0004113475769582989, 0.00045929358030035345, 0.0005035999836567557,
+        0.0005440540151333936, 0.000580482158490862, 0.0006127441494169268,
+        0.0006407300311078367, 0.0006643586426485531, 0.0006835767879300686,
+        0.0006983587143970248, 0.0007087057103775701, 0.0007146457206046404,
+        0.0007162329287736175, 0.0007135472852457612, 0.0007066939774957982,
+        0.0006958028561776564, 0.000681027844290205, 0.0006625463737211048,
+        0.0006405589158387497, 0.0006152887055937575, 0.0005869818094715197,
+        0.0005559077699516115, 0.0005223611963501836, 0.0004866649076266613,
+        0.00044917564863561257, 0.0004102941552609058, 0.0003704827433784432,
+        0.0003302962323639601, 0.0002904369356950194, 0.0002518529898156334,
+        0.00021591003228635034, 0.0001846576193291167, 0.00016108000535812524,
+        0.0001487506725118771, 0.00014999727670059738, 0.00016379190175489695,
+        0.00018651629784165042, 0.00021442813492608396, 0.0002448161602813203,
+        0.0002759305049076127, 0.0003066488156306861, 0.0003362240705409679,
+        0.00036413484120035753, 0.00039000123823336577, 0.00041353764279925513,
+        0.00043452552157812954, 0.00045279732018320163, 0.00046822660501767656,
+        0.0004807218175495786, 0.0004902221659096148, 0.000496694806553013,
+        0.000500132818012306, 0.0005005536692893756, 0.0004979980050204615,
+        0.0004925286442938895, 0.0004842297401985697, 0.0004732060849160136,
+        0.00045958257842719003, 0.0004435039145610983, 0.00042513458341764186,
+        0.0004046593545041442, 0.00038228450652518376, 0.0003582402358781999,
+        0.00033278495649564086, 0.0003062126887888951, 0.00027886558512124995,
+        0.000251155121538059, 0.00022359796202148973, 0.00019687604043498367,
+        0.00017193265601162644, 0.00015010427173228034, 0.00013321718813710202,
+        0.00012338785661095708, 0.00012216722510111942, 0.00012943638154842035,
+        0.00014341327527452274, 0.00016179149290153057, 0.00018262810421814637,
+        0.00020454035847701748, 0.0002265896016469798, 0.00024813246529923846,
+        0.00026871388500806175, 0.00028800056670135165, 0.00030574119357002996,
+        0.0003217426315876907, 0.00033585547931585787, 0.00034796509633409147,
+        0.0003579858905958157, 0.0003658575794704546, 0.00037154266867302736,
+        0.0003750246976416118, 0.0003763069791564571, 0.0003754116697766401,
+        0.0003723790770641439, 0.0003672671566874107, 0.00036015118841718926,
+        0.0003511236516742424, 0.0003402943545901637, 0.00032779091109624966,
+        0.00031375971537455385, 0.0002983676414277582, 0.00028180481046027336,
+        0.00026428893717510434, 0.0002460720051559595, 0.00022745033109199263,
+        0.00020877938323934206, 0.00019049470297290624, 0.00017313895957561028,
+        0.00015739010493659493, 0.00014407239845300589, 0.0001341087136020166,
+        0.00012835838286610099, 0.000127340866900984, 0.00013099523536788977,
+        0.00013868527242394464, 0.00014945196012654404, 0.00016230083020393879,
+        0.00017636799903345077, 0.00019096479150847216, 0.00020556088297968744,
+        0.00021975057057036903, 0.00023322138905759745, 0.00024573004860269044,
+        0.0002570853338558242, 0.00026713631012980965, 0.00027576425476717726,
+        0.00028287711514742307, 0.0002884056583323525, 0.000292300750441321,
+        0.00029453139289808034, 0.00029508326975014076, 0.0002939576452674096,
+        0.00029117050876641755, 0.0002867519042997745, 0.00028074541360082156,
+        0.0002732077867513678, 0.00026420874104762305, 0.00025383097935445677,
+        0.000242170521487127, 0.00022933750608162033, 0.00021545772337272772,
+        0.000200675312019125, 0.00018515735049319241, 0.00016910159365566034,
+        0.00015274951196642825, 0.0001364083086595016, 0.00012048777735646132,
+        0.00010555935888591087, 9.243786046707068e-05, 8.224475300962007e-05,
+        7.629737748409314e-05, 7.559999031916625e-05, 8.015796718113755e-05,
+        8.894091773521042e-05, 0.00010055916327426786, 0.00011382064253994813,
+        0.00012786757262060896, 0.00014211249318413246, 0.00015614887670486788,
+        0.0001696856237845396, 0.00018250600117543378, 0.00019444299511867628,
+        0.00020536455531346845, 0.00021516463648983014, 0.00022375764459033447,
+        0.00023107490768014844, 0.00023706236940087712, 0.00024167903059791322,
+        0.0002448958529052835, 0.00024669494808802393, 0.0002470689427218388,
+        0.00024602044807024595, 0.00024356159036264307, 0.0002397135731581275,
+        0.0002345062546807145, 0.00022797773120588098, 0.00022017392430581973,
+        0.00021114817634170394, 0.0002009608665277798, 0.00018967907140543126,
+        0.00017737631270086976, 0.00016413247054927835, 0.00015003400886103867,
+        0.00013517480451458297, 0.00011965820027124925, 0.00010360171101533664,
+        8.714802565905721e-05, 7.049281348566993e-05, 5.3964793460535164e-05,
+        3.830230005688099e-05, 2.5779419036652536e-05, 2.2859743487358094e-05,
+        3.2342158656039556e-05, 4.719531283998282e-05, 6.361846562644961e-05,
+        8.046944625196266e-05, 9.731970178402454e-05, 0.00011395481077541682,
+        0.00013024148687849058, 0.00014608443725202045, 0.0001614099296809204,
+        0.0001761587518242938], [5.0099153202833574e-12, 1.5052077223486743e-11,
+        2.516140929757935e-11, 3.5383275196507497e-11, 4.57639199369345e-11,
+        5.63508392469406e-11, 6.719315863701961e-11, 7.834203575886735e-11,
+        8.985108404308649e-11, 1.0177682617963448e-10, 1.1417918218665813e-10,
+        1.2712199880334264e-10, 1.4067362567360001e-10, 1.5490754822335597e-10,
+        1.6990308355165257e-10, 1.8574615087969352e-10, 2.0253012633256115e-10,
+        2.2035679491402416e-10, 2.393374142107336e-10, 2.5959390479852223e-10,
+        2.8126018787246565e-10, 3.044836889212879e-10, 3.294270337652503e-10,
+        3.5626996419638545e-10, 3.8521150572928326e-10, 4.164724246862391e-10,
+        4.502980189978506e-10, 4.869612914722858e-10, 5.267665656224163e-10,
+        5.700536101001466e-10, 6.172023537181654e-10, 6.686382802470593e-10,
+        7.248386142217907e-10, 7.863394220795399e-10, 8.537437792153641e-10,
+        9.277311757086268e-10, 1.0090683684152029e-09, 1.0986219196591809e-09,
+        1.1973727118112237e-09, 1.3064327736627387e-09, 1.4270648242943842e-09,
+        1.560705008395908e-09, 1.7089893956741011e-09, 1.873784918640902e-09,
+        2.057225564338375e-09, 2.2617547825407714e-09, 2.4901752884180474e-09,
+        2.745707642455107e-09, 3.032059316473098e-09, 3.353506266077836e-09,
+        3.7149894911735296e-09, 4.122229577492e-09, 4.581862858341541e-09,
+        5.101603649268835e-09, 5.690437984010252e-09, 6.3588555050702444e-09,
+        7.1191277074396816e-09, 7.985642595526001e-09, 8.975308233048236e-09,
+        1.0108040609392336e-08, 1.1407355008975278e-08, 1.2901084804297165e-08,
+        1.4622257571288193e-08, 1.661016603346903e-08, 1.8911681038067995e-08,
+        2.1582866181560714e-08, 2.469096959586282e-08, 2.8316888944875115e-08,
+        3.255823224714924e-08, 3.7533131571381455e-08, 4.338501165625298e-08,
+        5.028857441154991e-08, 5.845733781513201e-08, 6.815317003693955e-08,
+        7.969839587585512e-08, 9.349123398548902e-08, 1.1002556729401736e-07,
+        1.2991637724403731e-07, 1.539326182771518e-07, 1.8303991708235984e-07,
+        2.1845631469226434e-07, 2.6172542189092653e-07, 3.1481295947559554e-07,
+        3.802348954904714e-07, 4.6122855112651845e-07, 5.619825334012154e-07,
+        6.879477774003113e-07, 8.46261254239858e-07, 1.046327406945505e-06,
+        1.3006222346721338e-06, 1.6258144142162843e-06, 2.044342066839251e-06,
+        2.586650833121841e-06, 3.2944018352749348e-06, 4.2251180424624194e-06,
+        5.458989505518589e-06, 7.108960522009178e-06, 9.33587537842929e-06,
+        1.2371538106260162e-05, 1.6554355465790433e-05, 2.2385342932218707e-05,
+        3.061772578119956e-05, 4.2403156319532616e-05, 5.953561730616815e-05,
+        8.486836016304975e-05, 0.00012304653474597078, 0.0001818354119391809,
+        0.0002746163103770003, 0.00042527645351301196, 0.0006782721421583939,
+        0.0011206023888681474, 0.0019334275864396656, 0.0035251598907212996,
+        0.006919926398992373, 0.01511028281734006, 0.03929184006606896,
+        0.14917087861025627, 3.4020667065570143, 0.6938966832882522, 1.546844135745234,
+        1.788170272810942, 0.9183387978285272, 0.9707112932496729, 1.7297549578251992,
+        2.2999983600254033, 1.1793086166551399, 1.0120820701256765, 1.6029889264868336,
+        3.518040762225469, 2.6372224092729284, 1.7294043235006935, 1.1830563492223711,
+        1.0746554881721861, 1.1746441623709247, 1.4876190112568974, 2.135096239577242,
+        2.811203154591255, 2.347152452986082, 1.7622024291744605, 1.4785090011810065,
+        1.3950061808908851, 1.4650413922511625, 1.6991823407284543, 2.0794408350532883,
+        2.2006366785617253, 1.7500338203595176, 1.312703205758498, 1.0654223689658902,
+        0.9561008966699943, 0.9504726775406669, 1.0473568822213393, 1.2588159418354845,
+        1.5017699134179756, 1.4883341371816927, 1.2726596483476331, 1.111953593176493,
+        1.0625068155282207, 0.9304124591835677, 0.8923784255172349, 0.9061685453841711,
+        0.9276465960298705, 0.9221724449883483, 0.8735371223244226, 0.7966342333014694,
+        0.7172582288599736, 0.6508905060049308, 0.601842074209236, 0.5691431322534114,
+        0.5501582655902894, 0.541630467252825, 0.5393656423116714, 0.5374920791627242,
+        0.5285797196983516, 0.5062751450322538, 0.46964431989711897, 0.424208292850354,
+        0.3776874645585186, 0.3355958417400051, 0.3002655775679808, 0.2719201107647648,
+        0.24985072629686286, 0.23310507751958431, 0.22078807442672155, 0.21216167111796475,
+        0.20665981860369143, 0.20387351712704557, 0.20352834386635701, 0.2054623567080364,
+        0.2096062596987061, 0.21596497830259292, 0.2245979402998077, 0.2355933242361701,
+        0.24902890146670895, 0.26490917609175446, 0.28306739308072393, 0.30302755518073804,
+        0.32384719690114505, 0.34401658923664385, 0.361554932357024, 0.3744297119478295,
+        0.38122187447523226, 0.38166284294688274, 0.3766532387955669, 0.36777409806415134,
+        0.35667073148575634, 0.3446446691128471, 0.3325214476390742, 0.32069431401724147,
+        0.30923265660955934, 0.2979939828032567, 0.28672059250796333, 0.2751212404287298,
+        0.2629405706303648, 0.250014050422115, 0.23630101729022757, 0.22188867524209974,
+        0.20696684955506967, 0.191783135394533, 0.17659425109818339, 0.1616282485574266,
+        0.1470655467136095, 0.13303930955497845, 0.11965102805754621, 0.10699585717592701,
+        0.09519286753902437, 0.08441590503202716, 0.0749190427197737, 0.06704393535227238,
+        0.06118398077286543, 0.057676401760764204, 0.056639254611657426,
+        0.05786564263202126, 0.060886350756652184, 0.06514694707684963,
+        0.0701529096264373, 0.07552279858703316, 0.08097971250385111, 0.0863229038064212,
+        0.09140159730180211, 0.09609767522398631, 0.10031707209099916, 0.10398736988852364,
+        0.10705848857691085, 0.10950359768287825, 0.11131820041355926, 0.11251655183827479,
+        0.1131257980171055, 0.11317907418658318, 0.1127090760681473, 0.11174337774891951,
+        0.11030223237600247, 0.10839898452381354, 0.10604268764825674, 0.10324211896215506,
+        0.10001015255002484, 0.09636743216793826, 0.09234451305840972, 0.08798209572826982,
+        0.08332954286202704, 0.07844237875837633, 0.07337976163263825, 0.0682029329973353,
+        0.06297544438788491, 0.05776567004070221, 0.052651849528394835,
+        0.04772967313204722, 0.04312199322704548, 0.03898891735483244, 0.03553296050061201,
+        0.03298728467910906, 0.03157088948518803, 0.03141151573079156, 0.032481510517787235,
+        0.034605888650926224, 0.03753627367852538, 0.041027027358680856,
+        0.04487410324233115, 0.04892152710187348, 0.053053393511889986,
+        0.057183057120602836, 0.06124408185426303, 0.06518391537731454,
+        0.06895997750509761, 0.07253753166737939, 0.07588870244718729, 0.07899208875044342,
+        0.0818325428771172, 0.08440082496881138, 0.08669298589033078, 0.08870946012988715,
+        0.09045394563275175, 0.09193219968794739, 0.09315089086620303, 0.0941166272520576,
+        0.09483524543070715, 0.09531140576805511, 0.09554850549860153, 0.09554889460995132,
+        0.09531435888041354, 0.09484681635464488, 0.09414915530739772, 0.0932261231749448,
+        0.09208516024893001, 0.09073706503962747, 0.08919638672142094, 0.08748146795772006,
+        0.08561410746394202, 0.08361886823409259, 0.08152211221700442, 0.07935088234967616,
+        0.07713176927947443, 0.07488989060704024, 0.07264808000470982, 0.07042634150287186,
+        0.06824158088278542, 0.06610758955213675, 0.06403523092562674, 0.0620327660338261,
+        0.06010625236242406, 0.05825995527056723, 0.0564967222360604, 0.05481828454945126,
+        0.05322546718418051, 0.05171830389269432, 0.05029606936282449, 0.048957251833638006,
+        0.047699496305706766, 0.04651954946393039, 0.04541323266876796,
+        0.04437546012216569, 0.04340030767708946, 0.0424811264424655, 0.04161068677844737,
+        0.04078133420112202, 0.03998513960248511, 0.03921403134824817, 0.03845990457646813,
+        0.037714711236015275, 0.03697054104986571, 0.03621970708686058,
+        0.03545484920578361, 0.03466906429908359, 0.033856064845969605,
+        0.03301035823293423, 0.032127430603580434, 0.03120391276338675,
+        0.0302377038398762, 0.029228032033993673, 0.028175440782304783,
+        0.027081701329123166, 0.025949666335351812, 0.024783090545398206,
+        0.023586451100107774, 0.022364800581833696, 0.02112368072788877,
+        0.019869115880312167, 0.018607695306183485, 0.01734674541080132,
+        0.016094588726937278, 0.014860887430007259, 0.013657073708022447,
+        0.012496872133122373, 0.011396906505051863, 0.010377326592122676,
+        0.009462238643068263, 0.008679423463341268, 0.008058425628744339,
+        0.007626008030956735, 0.007399081892994756, 0.0073778523588583726,
+        0.0075436887732896075, 0.007863709607398793, 0.00829905922597002,
+        0.008812145713032966, 0.00937056790810383, 0.009948179440472871,
+        0.010524616726047362, 0.011084307052627279, 0.011615463442342626,
+        0.012109240450283547, 0.012559072339337621, 0.012960164502236918,
+        0.01330910267548531, 0.013603552485834154, 0.013842031378914071,
+        0.014023741564960642, 0.014148455555980299, 0.014216445983737351,
+        0.014228450023842723, 0.014185657261551098, 0.014089709291884987,
+        0.013942700370070582, 0.013747171097855856, 0.013506091024964011,
+        0.013222830371152775, 0.01290112491014028, 0.012545040601502968,
+        0.012158945337737377, 0.011747494144635124, 0.011315631659055829,
+        0.010868612262704046, 0.010412034440598064, 0.009951882156747721,
+        0.009494562371111065, 0.009046924034470412, 0.008616239606196318,
+        0.008210125334139175, 0.007836372409760043, 0.0075026611794169066,
+        0.007216141124524851, 0.006982887453207062, 0.0068072926710462025,
+        0.0066915059803006076, 0.006635065087512568, 0.006634841621309624,
+        0.006685337165202279, 0.00677925894606003, 0.006908229655925043,
+        0.007063477685620443, 0.007236400512532901, 0.007418958060213824,
+        0.007603903446363598, 0.007784884692059342, 0.007956457000893946,
+        0.008114040303045678, 0.008253848297628673, 0.008372807150985742,
+        0.008468475625375333, 0.00853897370287092, 0.00858292330627209,
+        0.008599402129229319, 0.008587909668693064, 0.008548343260136504,
+        0.008480981267309581, 0.008386470579223097, 0.00826581614749976,
+        0.00812037129444081, 0.007951828696614776, 0.007762213024510784,
+        0.007553876944003305, 0.007329502366341304, 0.007092108362768289,
+        0.006845065991191113, 0.0065921183947665555, 0.006337401878003754,
+        0.006085460153096564, 0.005841239529590885, 0.005610047757619905,
+        0.005397454625396701, 0.005209110898541889, 0.0050504682915060335,
+        0.004926402062079959, 0.0048407712485536705, 0.004795991590228152,
+        0.004792722607985212, 0.004829759922149431, 0.004904170206432651,
+        0.005011632049432803, 0.0051468902655041615, 0.005304218996540661,
+        0.005477815653560542, 0.005662089702721692, 0.005851845671475558,
+        0.00604237945591826, 0.006229512740092402, 0.006409587898198291,
+        0.006579440322367984, 0.006736359728125198, 0.006878047814814309,
+        0.00700257681109768, 0.007108351606700631, 0.007194076979780828,
+        0.0072587305842414206, 0.007301541696693941, 0.0073219751797942625,
+        0.007319719708575447, 0.0072946790691067, 0.007246965308284232,
+        0.00717689269536676, 0.007084971816289597, 0.006971903592693962,
+        0.006838573510095073, 0.006686046764807207, 0.006515565329730894,
+        0.006328548061752392, 0.006126594935203225, 0.0059114963257630845,
+        0.005685248036925065, 0.005450072493850284, 0.005208446208308059,
+        0.004963133129204311, 0.004717222572557309, 0.004474168607156355,
+        0.004237824380268235, 0.004012459106513114, 0.003802736888282477,
+        0.003613626248496139, 0.0034502018451550375, 0.0033173053733914605,
+        0.0032190648429099326, 0.003158336186051434, 0.003136207092702021,
+        0.0031517356810185203, 0.0032020367038345958, 0.0032826926385851997,
+        0.0033883438055286423, 0.0035132780313876957, 0.003651894560731448,
+        0.0037990000477142478, 0.003949955405629334, 0.00410071712289126,
+        0.00424781612534224, 0.0043883063173161645, 0.004519703064168621,
+        0.004639922784857116, 0.004747228937713122, 0.004840186264138554,
+        0.004917623330512778, 0.004978602518168013, 0.005022396241305404,
+        0.005048468092067222, 0.005056457699381361, 0.00504616827873531,
+        0.005017556102869655, 0.004970721403193954, 0.004905900487612707,
+        0.0048234591046018675, 0.004723887278352075, 0.004607795982289803,
+        0.004475916122276092, 0.0043291003995662505, 0.004168328764966593,
+        0.003994718425333247, 0.003809539799240242, 0.003614240532551245,
+        0.0034104807908872836, 0.003200184662547704, 0.002985614725225775,
+        0.0027694795407879227, 0.0025550862494509814, 0.0023465497232420178,
+        0.002149058074917788, 0.0019691535532468485, 0.001814886894059858,
+        0.0016955246784878578, 0.0016203446652114594, 0.0015963391208378718,
+        0.001625696459910611, 0.001704844934960745, 0.0018259003819209717,
+        0.001979309500554781, 0.0021559718277181163, 0.0023482255776487468,
+        0.002550003342634915, 0.0027566191710399245, 0.0029644710840618033,
+        0.0031707750247110503, 0.003373359002769275, 0.0035705132881019923,
+        0.003760884221087845, 0.003943399654175743, 0.004117216669712277,
+        0.004281684814802979, 0.004436320103297756, 0.004580786458013051,
+        0.0047148822396341555, 0.004838530170487983, 0.004951769421879149,
+        0.005054748961640224, 0.005147721504113341, 0.005231037589377032,
+        0.005305139460012441, 0.005370554505795165, 0.005427888116705962,
+        0.005477815826381814, 0.005521074648683097, 0.005558453519117531,
+        0.005590782759216411, 0.0056189224966841774, 0.005643750005305726,
+        0.00566614598163185, 0.0056869798522371446, 0.005707094302657162,
+        0.005727289329183806, 0.005748306225833026, 0.005770812016548493,
+        0.0057953849120241, 0.005822501397571383, 0.005852525534382166,
+        0.005885700978088982, 0.005922146090335404, 0.005961852353324722,
+        0.006004686111438567, 0.006050393479125649, 0.006098608090017453,
+        0.0061488612350039185, 0.0062005938566021546, 0.0062531698357122705,
+        0.0063058900208822835, 0.006358006499849194, 0.006408736686686775,
+        0.006457276883181558, 0.0065028150587621535, 0.006544542672318821,
+        0.0065816654260540276, 0.006613412894815826, 0.00663904701462913,
+        0.006657869443207152, 0.0066692278262405185, 0.006672521018285523,
+        0.006667203318551149, 0.0066527877909888416, 0.006628848745416972,
+        0.006595023462108784, 0.0065510132459560486, 0.006496583897814825,
+        0.006431565689958835, 0.006355852929338163, 0.006269403187540518,
+        0.006172236270036743, 0.006064432990176052, 0.005946133806493346,
+        0.005817537374685886, 0.005678899060731848, 0.0055305294570552836,
+        0.005372792943297598, 0.0052061063351455, 0.005030937673914274,
+        0.0048478052248119964, 0.0046572767790782, 0.00445996939576939,
+        0.004256549780599356, 0.004047735587251105, 0.0038342980554342135,
+        0.0036170665871022955, 0.0033969361378389912, 0.003174878714726388,
+        0.0029519608997480395, 0.0027293702809048103, 0.002508455144553434,
+        0.0022907839868721233, 0.0020782345172760384, 0.0018731255793500636,
+        0.001678407751296408, 0.0014979216538460152, 0.0013366951528687974,
+        0.0012011340076305734, 0.0010987172847754915, 0.0010365833313467714,
+        0.0010188526444541144, 0.0010441768234115123, 0.0011058567534941806,
+        0.001194545330394628, 0.0013011126167021341, 0.0014180808944638298,
+        0.001539826448568293, 0.0016622584461973256, 0.001782415106681815,
+        0.0018981317158791424, 0.0020078023693430986, 0.002110217642950583,
+        0.0022044558231372772, 0.002289810004135321, 0.00236573878422113,
+        0.0024318324608772275, 0.0024877894649556675, 0.002533399624956407,
+        0.002568532042112917, 0.0025931261219663765, 0.0026071848035201855,
+        0.002610769351537173, 0.0026039952926643706, 0.0025870292212044526,
+        0.0025600863010392066, 0.0025234283638015196, 0.0024773625625408597,
+        0.002422240594637451, 0.0023584585664532497, 0.00228645764379058,
+        0.0022067257272532495, 0.002119800524807592, 0.002026274585716358,
+        0.0019268031452609113, 0.0018221160593068911, 0.0017130357650626522,
+        0.0016005042113590425, 0.0014856232272606738, 0.0013697150135546388,
+        0.0012544123258481181, 0.001141790537461277, 0.0010345521641439118,
+        0.0009362563621424106, 0.0008515223048694609, 0.0007859855782165761,
+        0.000745591516901608, 0.000734927675148327, 0.0007552428523301253,
+        0.0008037904855906385, 0.0008751741775168805, 0.0009633907670489112,
+        0.0010631566307995207, 0.0011703134138924016, 0.001281735904475933,
+        0.0013950976854164132, 0.0015086500900885395, 0.0016210541223375926,
+        0.001731262532602596, 0.0018384395598415443, 0.0019419067174948823,
+        0.0020411060300042087, 0.0021355748564274857, 0.002224928418758262,
+        0.002308847486923582, 0.002387069544007624, 0.002459382320813351,
+        0.0025256189566644684, 0.0025856542841081777, 0.0026394018944170556,
+        0.0026868117468978273, 0.002727868156824337, 0.0027625880453125244,
+        0.0027910193679268934, 0.0028132396617775116, 0.002829354666935669,
+        0.002839496989400357, 0.0028438247808775124, 0.0028425204164236407,
+        0.002835789155160367, 0.002823857772173925, 0.002806973151670441,
+        0.0027854008327009073, 0.002759423499433346, 0.0027293394081071448,
+        0.002695460742749709, 0.0026581118912983115, 0.002617627633176165,
+        0.0025743512287864957, 0.002528632400520391, 0.0024808251943240146,
+        0.0024312857103540183, 0.0023803696913588263, 0.002328429958383227,
+        0.0022758136856384998, 0.0022228595108192465, 0.0021698944837668806,
+        0.0021172308665520843, 0.0020651628114329488, 0.002013962960299076,
+        0.00196387902936871, 0.001915130465314666, 0.0018679052812902296,
+        0.0018223572015467898, 0.0017786032575775128, 0.0017367219842340537,
+        0.0016967523574800492, 0.0016586935947353082, 0.0016225059035438296,
+        0.0015881122167214269, 0.0015554008957475388, 0.0015242293255620517,
+        0.001494428268817216, 0.0014658068033675167, 0.0014381576375907992,
+        0.0014112625869679278, 0.0013848980021187814, 0.0013588399607707712,
+        0.0013328690696270127, 0.0013067747622438415, 0.0012803590203477328,
+        0.001253439485292421, 0.0012258519599098552, 0.001197452328047298,
+        0.0011681179387254604, 0.001137748514907654, 0.0011062666543902636,
+        0.0010736179936193938, 0.0010397711059055255, 0.0010047172049665798,
+        0.0009684697240489955, 0.0009310638418626634, 0.000892556029679551,
+        0.0008530237014423654, 0.0008125650618720991, 0.0007712992690392573,
+        0.0007293670615236666, 0.000686932050627713, 0.0006441829529677159,
+        0.000601337146702023, 0.0005586460858425782, 0.0005164033067760241,
+        0.0004749559918060124, 0.00043472123051016505, 0.00039620796924985993,
+        0.00036004445549232925, 0.00032700719266822885, 0.00029803829643375003,
+        0.0002742214593954372, 0.0002566689578865595, 0.0002462839021252174,
+        0.00024344827405587145, 0.0002478141914968882, 0.0002583687891867052,
+        0.0002737336543404303, 0.00029249224794946005, 0.00031339424670158975,
+        0.00033542523086156194, 0.0003577967371241469, 0.00037990685506629013,
+        0.0004012979851239207, 0.000421621445051875, 0.0004406105768497868,
+        0.00045806117852578487, 0.0004738175119358637, 0.0004877623340359333,
+        0.0004998097641983623, 0.0005099001342803572, 0.0005179962251850784,
+        0.0005240804781125986, 0.0005281528972483774, 0.0005302294491660387,
+        0.0005303408253344379, 0.000528531476568861, 0.00052485885833387,
+        0.000519392847548357, 0.0005122153078259762, 0.0005034197927231574,
+        0.0004931113868013204, 0.000481406692814184, 0.00046843398044549604,
+        0.00045433351746925783, 0.00043925810718177126, 0.00042337385447526816,
+        0.00040686117351671955, 0.0003899160264143549, 0.0003727513348066823,
+        0.0003555984201361045, 0.0003387081841405462, 0.00032235151810631704,
+        0.0003068181190883827, 0.00029241252538150325, 0.0002794458841106699,
+        0.00026822199718692816, 0.0002590169598968213, 0.0002520535517557741,
+        0.0002474742914547989, 0.00024531958545761937, 0.0002455178128484422,
+        0.00024789128809541984, 0.0002521768188696246, 0.00025805493143617083,
+        0.0002651802600399927, 0.0002732072440319022, 0.00028180839800283445,
+        0.00029068515411605553, 0.0002995727850409916, 0.0003082413106651617,
+        0.0003164940495514031, 0.00032416501792740404, 0.0003311159412239782,
+        0.0003372333117875397, 0.0003424257069854671, 0.00034662145030087604,
+        0.00034976662609770027, 0.0003518234238482007, 0.0003527687741882606,
+        0.0003525932372698513, 0.0003513001078076081, 0.00034890470759922306,
+        0.0003454338435351287, 0.0003409254162378666, 0.00033542817112715116,
+        0.00032900158956239233, 0.0003217159224952803, 0.00031365237220053194,
+        0.00030490342816067134, 0.00029557335934206813, 0.0002857788539927916,
+        0.00027564977530527684, 0.00026532996010981627, 0.00025497791962867235,
+        0.0002447671967270497, 0.00023488598740528346, 0.00022553545362079567,
+        0.0002169259802533161, 0.00020927055588970773, 0.00020277464541393998,
+        0.00019762255600301536, 0.00019396144888812107, 0.00019188556771633245,
+        0.00019142426778264232, 0.00019253721771741186, 0.000195118394394367,
+        0.00019900788174210228, 0.00020400834311661736, 0.00020990235497382107,
+        0.00021646756153113986, 0.00022348807639063255, 0.0002307619080902711,
+        0.00023810501551938012, 0.00024535290250670045, 0.0002523606235549844,
+        0.00025900188620206553, 0.0002651677247371702, 0.00027076504274466904,
+        0.0002757151934752168, 0.00027995268260606383, 0.0002834240266934651,
+        0.00028608677189196805, 0.0002879086630415469, 0.0002888669472861642,
+        0.00028894779528006306, 0.000288145824562113, 0.00028646371246444176,
+        0.0002839118893620131, 0.000280508306732651, 0.0002762782783281273,
+        0.00027125439668618825, 0.00026547653131880216, 0.00025899191921672495,
+        0.0002518553628141457, 0.00024412955507669258, 0.00023588555544384312,
+        0.00022720344286866293, 0.00021817317092498779, 0.00020889564085247486,
+        0.00019948398415319175, 0.00019006499503243187, 0.00018078055649840241,
+        0.00017178873892537678, 0.0001632639951776415, 0.00015539553656778512,
+        0.0001483826284692412, 0.0001424254180558002, 0.0001377104004604681,
+        0.0001343911619557827, 0.00013256755576493157, 0.00013226886152392246,
+        0.00013344680293098422, 0.00013598137544273755, 0.0001396975698931993,
+        0.00014438736586795374, 0.00014983087931846444, 0.0001558127117715296,
+        0.00016213234588037596, 0.00016860936294488862, 0.00017508500594114865,
+        0.00018142156152902117, 0.00018750066062672672, 0.00019322119651475714,
+        0.0001984972496161215, 0.00020325620504039828, 0.00020743713023890314,
+        0.00021098941757081462, 0.00021387166765228787, 0.0002160507790750139,
+        0.00021750120926648065, 0.00021820437477967035, 0.00021814816448456113,
+        0.00021732654461249022, 0.00021573923987169665, 0.00021339147975081154,
+        0.00021029380377641577, 0.0002064619240524239, 0.00020191664832398717,
+        0.00019668387238044608, 0.00019079465762270457, 0.00018428541881100133,
+        0.00017719825974628895, 0.00016958151275912135, 0.00016149056407273682,
+        0.00015298908531407115, 0.000144150846731224, 0.0001350623657334932,
+        0.0001258267478628536, 0.00011656919430802016, 0.00010744472121184507,
+        9.864847245583972e-05, 9.042811815411823e-05, 8.309518405130434e-05,
+        7.702635309578704e-05, 7.26374330511461e-05, 7.031115811678901e-05,
+        7.028563004365141e-05, 7.256222774421781e-05, 7.690557642152448e-05,
+        8.293588440974885e-05, 9.024117243593212e-05, 9.845012051800701e-05,
+        0.00010725843501526985, 0.00011642760479687172, 0.00012577348865334414,
+        0.00013515378641768352, 0.00014445758893116416, 0.00015359752572273976,
+        0.00016250412842128175, 0.00017112186123272407, 0.00017940634072095794,
+        0.0001873223845249558, 0.00019484263251769285, 0.00020194656207444365],
+    [1.3441819809312725e-11, 4.039042614540808e-11, 6.753449212597703e-11,
+        9.500617897639287e-11, 1.2294045210504612e-10, 1.5147625952828523e-10,
+        1.8075774832006321e-10, 2.1093555943915277e-10, 2.421681997428723e-10,
+        2.7462351892208977e-10, 3.084803093979317e-10, 3.439300533147187e-10,
+        3.811788381360788e-10, 4.2044947548916155e-10, 4.6198384931997407e-10,
+        5.060455351888019e-10, 5.529227294087188e-10, 6.029315372697535e-10,
+        6.564196767029625e-10, 7.137706577950608e-10, 7.754085175606457e-10,
+        8.418031886502603e-10, 9.134766066822813e-10, 9.910096693490943e-10,
+        1.0750501823618191e-09, 1.1663219491006609e-09, 1.2656351914603455e-09,
+        1.373898513979798e-09, 1.4921326707826142e-09, 1.6214864296974793e-09,
+        1.7632548959616546e-09, 1.918900704768105e-09, 2.0900785886388334e-09,
+        2.2786639027288896e-09, 2.4867858165748265e-09, 2.7168660046789623e-09,
+        2.971663844571339e-09, 3.2543293165624174e-09, 3.5684650569154647e-09,
+        3.918199292141972e-09, 4.308271763552442e-09, 4.744135168994273e-09,
+        5.2320752154679616e-09, 5.779353018633508e-09, 6.394374439749455e-09,
+        7.0868919303174684e-09, 7.868245798027618e-09, 8.751653290424077e-09,
+        9.752556010557507e-09, 1.088903854171e-08, 1.2182334415445585e-08,
+        1.3657439490227012e-08, 1.5343857865819604e-08, 1.72765119753988e-08,
+        1.949685674080858e-08, 2.2054248346127444e-08, 2.500763207667026e-08,
+        2.842763148483883e-08, 3.239914478765455e-08, 3.702458512385963e-08,
+        4.242794215445242e-08, 4.8759896788955545e-08, 5.620429346661689e-08,
+        6.498637244651188e-08, 7.53832977362249e-08, 8.773769872404443e-08,
+        1.0247519536980699e-07, 1.2012722808527923e-07, 1.4136100804870624e-07,
+        1.6701910735980375e-07, 1.9817222243077726e-07, 2.361901233000053e-07,
+        2.8283799129959203e-07, 3.4040863884652367e-07, 4.1190614378271284e-07,
+        5.013042912701251e-07, 6.139157622935112e-07, 7.569285310592044e-07,
+        9.402004996009327e-07, 1.1774635730376733e-06, 1.4881972575686436e-06,
+        1.9006380635031795e-06, 2.456803254676168e-06, 3.2212876864599296e-06,
+        4.297630432448579e-06, 5.861275941870886e-06, 8.23349456560339e-06,
+        1.2074801712505138e-05, 1.9029137174066963e-05, 3.508760516684625e-05,
+        0.0001756668754742054, 7.394068330665075e-05, 6.266310199234124e-05,
+        6.272074964862269e-05, 6.72631161357249e-05, 7.510034305863155e-05,
+        8.623588045859682e-05, 0.00010121017900505334, 0.0001209952639008808,
+        0.0001470569106157113, 0.00018152258722923102, 0.00022746897396548987,
+        0.0002893847580014453, 0.00037391557223087857, 0.0004910841458207808,
+        0.0006563391627646923, 0.0008941007147913138, 0.0012441156897746318,
+        0.0017733313222106735, 0.0025991955711073263, 0.003938181882236926,
+        0.006214570231049418, 0.010328399160389785, 0.018404034887080038,
+        0.03629254417845405, 0.08469537560393524, 0.286367912733622, 5.762179266763,
+        1.0250643434382423, 1.965502365855392, 1.9229284040371977, 0.8218645852296415,
+        0.7154529963482354, 1.065547145956658, 1.2678945774393504, 0.644687080410972,
+        0.5599679830797905, 0.6790233748900277, 1.0646100973568449, 1.8888937715691523,
+        1.6457080059867586, 1.166531464776255, 1.010078793172014, 1.0354157796726142,
+        1.2323064819822234, 1.6715778809207267, 2.0917304354614528, 1.6678260252314847,
+        1.2008676267278584, 0.9701847060477871, 0.885380018008818, 0.9043393203617651,
+        1.0277567049322074, 1.2451907165429306, 1.3227837181868605, 1.074493572505189,
+        0.8396367324907568, 0.7235492584178573, 0.6993465051061978, 0.7533728265044609,
+        0.8962177425196003, 1.148416108825137, 1.4346762546152607, 1.4602115084177174,
+        1.2595795599481594, 1.0934187911962714, 1.0225704941415332, 0.8854460516940771,
+        0.8434307718142883, 0.8445913479302449, 0.8500927219824341, 0.829803081677749,
+        0.7714966937393363, 0.690593166054311, 0.6105040121699212, 0.5442210645944512,
+        0.49458977194188825, 0.4599817776544668, 0.4375619855740402, 0.4242094550114217,
+        0.4162952200688553, 0.4091485574525899, 0.39719984374488876, 0.3759572387733794,
+        0.345077886637417, 0.3088547250348043, 0.2729297933398417, 0.24113569623480563,
+        0.2149270520550764, 0.19425010919672425, 0.17842346449398408, 0.16663465061828067,
+        0.15814865726472507, 0.1523717432419555, 0.14885594655792034, 0.14728342244917525,
+        0.1474462073608827, 0.14922691132297644, 0.15258171452925956, 0.15752509541964574,
+        0.16411430750469688, 0.1724300549246524, 0.1825478111246113, 0.1944919922094484,
+        0.20816421393804158, 0.2232414452824817, 0.2390584315670936, 0.25452922296030506,
+        0.2682114893984519, 0.27860922699615764, 0.28466178951601734, 0.2861467469143682,
+        0.28370571087474145, 0.27849349770188936, 0.27172632739799757, 0.26437764634476685,
+        0.2570751522514377, 0.2501277707934336, 0.24360129227475022, 0.2373974853525533,
+        0.23132280892777382, 0.2251473667318102, 0.2186568507473921, 0.21169628275597094,
+        0.2041998080192359, 0.19619990050360875, 0.18781380062574696, 0.1792124872012529,
+        0.17058309613438835, 0.16209604456458862, 0.15388385844177072, 0.14603317720897235,
+        0.13858751597930213, 0.13155691575012998, 0.12493083997680902, 0.1186914659304542,
+        0.11282519486886701, 0.10733067442374758, 0.10222215450604, 0.09752784202794462,
+        0.0932840362004173, 0.08952683052048571, 0.08628360337017399, 0.08356621279336249,
+        0.08136699415414192, 0.07965777071727402, 0.07839147213877584, 0.07750571104224101,
+        0.07692768124860369, 0.07657982509891857, 0.07638573051042394, 0.0762756350456064,
+        0.07619082616159575, 0.07608627759522271, 0.07593113940440246, 0.07570715627887702,
+        0.07540555835001977, 0.07502326851366006, 0.07455931148802487, 0.07401212797879214,
+        0.07337819902389135, 0.07265207230424726, 0.07182760989008646, 0.07090006385739987,
+        0.06986844376908145, 0.06873759223714711, 0.06751946029707878, 0.0662332767086248,
+        0.06490458857641236, 0.06356342595744736, 0.06224201884355326, 0.060972523699616095,
+        0.059785115239601, 0.05870662996797374, 0.05775978170282088, 0.05696285350733937,
+        0.05632971984055222, 0.05587005634767949, 0.05558962964093618, 0.055490602342857964,
+        0.05557182295243961, 0.05582908871096199, 0.056255374758611316,
+        0.05684102255356261, 0.05757388357963695, 0.058439425657549775,
+        0.059420827539141303, 0.060499106856311304, 0.061653338918930885,
+        0.06286102245383497, 0.06409862955438643, 0.0653423419620219, 0.06656893046271467,
+        0.06775668954099746, 0.06888630841293021, 0.0699415533499926, 0.07090965941435322,
+        0.07178137777120175, 0.07255068491682568, 0.07321421620489484, 0.07377052444261929,
+        0.0742192785992076, 0.07456050953484789, 0.07479398645032011, 0.07491877864649414,
+        0.07493302963899366, 0.0748339486809174, 0.07461800871035235, 0.07428132755452244,
+        0.0738201979394911, 0.07323171929044703, 0.07251447032051334, 0.07166914846220154,
+        0.07069909485989202, 0.06961062715330632, 0.06841312010951467, 0.0671188060409656,
+        0.06574230776086823, 0.06429995784000696, 0.06280898941855384, 0.0612866987045412,
+        0.059749675235153656, 0.05821317596738276, 0.05669068976339505,
+        0.05519370725082819, 0.053731683397150135, 0.052312159919847966,
+        0.05094100276954329, 0.04962270556464772, 0.04836071144306353, 0.047157711743454775,
+        0.04601588898332813, 0.04493708275624258, 0.0439228695322253, 0.04297455972807129,
+        0.04209312648733586, 0.04127908887425597, 0.04053237643400408, 0.03985220166209129,
+        0.03923696214483109, 0.038684186074570456, 0.03819052535648019,
+        0.03775179165157555, 0.037363024292872755, 0.03701857621269405,
+        0.03671220509086751, 0.036437161204653665, 0.03618626956306047,
+        0.035952010166060026, 0.0357266050024422, 0.035502122442027016,
+        0.03527060830168037, 0.035024248092005744, 0.0347555575195883, 0.03445758968101288,
+        0.034124139503085654, 0.033749921031279106, 0.03333069292087421,
+        0.03286331278045259, 0.032345711252207206, 0.03177678986593694,
+        0.0311562597872823, 0.030484448527765027, 0.02976210623963952, 0.028990241521597685,
+        0.02817000938365096, 0.027302662920722524, 0.02638956775071465,
+        0.025432266765338628, 0.024432574327677144, 0.023392675162950176,
+        0.022315204473798273, 0.021203291972430902, 0.020060562318096196,
+        0.018891095849726078, 0.017699364247923958, 0.016490163931859023,
+        0.015268574754111978, 0.014039973633664642, 0.012810134793585918,
+        0.01158545513236611, 0.010373363124618357, 0.009183016450082248,
+        0.008026491763763731, 0.00692085877168215, 0.005891836779395463,
+        0.00497993971688675, 0.00424855973818278, 0.0037848908195258868,
+        0.003668025671399649, 0.003903681962571989, 0.004410895589752745,
+        0.005085700835122453, 0.005848648648232988, 0.0066494092249310376,
+        0.007457355440755448, 0.00825340667364066, 0.009025106381902615,
+        0.009763895928090382, 0.010463621695763228, 0.011119708404333207,
+        0.0117286923777206, 0.012287949307801875, 0.012795525043341612,
+        0.013250018409127937, 0.01365048876709213, 0.013996375750913932,
+        0.014287427755820696, 0.014523640862486243, 0.014705211778038978,
+        0.014832507834328683, 0.014906054926762936, 0.014926541408744557,
+        0.014894833259877985, 0.014811994044585431, 0.014679302734012582,
+        0.014498263492255256, 0.014270603786990613, 0.0139982601435597,
+        0.01368335383286986, 0.013328161109481994, 0.012935083821891988,
+        0.012506626138675354, 0.01204538192564636, 0.011554035390753477,
+        0.011035375566094026, 0.010492323621382825, 0.009927971432460566,
+        0.009345630651392982, 0.008748893984288216, 0.00814171465948, 0.007528516365260619,
+        0.006914354686622781, 0.006305162921473294, 0.005708130402571237,
+        0.005132277170112601, 0.0045892892973608415, 0.004094609100490455,
+        0.003668485970011394, 0.0033359360555733275, 0.003123424607289275,
+        0.0030504686229022005, 0.0031195258336271445, 0.0033132874467851994,
+        0.003602670040567334, 0.003957534292908345, 0.0043527385367545185,
+        0.004769352228763216, 0.005193673239483289, 0.005615836393640819,
+        0.006028654219743872, 0.006426787926535736, 0.00680618679510653,
+        0.007163716223497072, 0.007496912212681137, 0.007803819653755562,
+        0.008082886128550076, 0.008332892262160154, 0.008552905567597364,
+        0.008742248598578764, 0.008900475010405954, 0.009027349335248255,
+        0.009122828118639324, 0.009187041570393623, 0.009220275999209935,
+        0.009222957964750454, 0.009195641279518574, 0.009138997778342211,
+        0.009053812267448658, 0.00894098143236123, 0.008801515900495348,
+        0.008636544271527278, 0.008447317844793462, 0.008235215016086449,
+        0.008001744843417806, 0.007748549991108641, 0.007477410026362583,
+        0.007190246737820517, 0.006889133680253639, 0.0065763124942833096,
+        0.006254218721914717, 0.005925519891301877, 0.0055931685975223145,
+        0.005260473046932301, 0.004931186636626144, 0.004609615582595231,
+        0.004300737354268303, 0.004010309320383348, 0.0037449222872692283,
+        0.0035119159014756576, 0.0033190334282800194, 0.0031736927798573325,
+        0.0030818600888769658, 0.0030467678702268504, 0.0030679895831822665,
+        0.003141367090047019, 0.0032598625522151335, 0.0034149056355709676,
+        0.003597666499304077, 0.0037999185708136474, 0.004014456762776378,
+        0.004235197114118946, 0.004457103540619473, 0.004676045846235728,
+        0.00488864670217734, 0.005092143229329693, 0.005284271228160726,
+        0.00546317203401533, 0.005627319047073705, 0.005775460432227367,
+        0.005906574828649434, 0.0060198374591655685, 0.006114594507843006,
+        0.006190343974447666, 0.006246721442458754, 0.006283489369210586,
+        0.0063005286811252115, 0.006297831666257353, 0.006275495414643097,
+        0.006233715347182525, 0.006172778665760672, 0.006093057811366527,
+        0.005995004198809174, 0.0058791425856667, 0.005746066428313409,
+        0.005596434497895376, 0.005430968909874223, 0.005250454607160858,
+        0.005055740276003266, 0.004847740708290806, 0.004627440788949747,
+        0.0043959016135937225, 0.004154269770138045, 0.003903791611139641,
+        0.003645835540186159, 0.00338192719721389, 0.003113805453661744,
+        0.0028435122299923384, 0.0025735378827825067, 0.0023070586331049555,
+        0.002048325418177911, 0.0018032901807679758, 0.001580546862341332,
+        0.0013924575658585193, 0.001255510790472258, 0.0011873674568998154,
+        0.0011986661617917676, 0.0012853799816600362, 0.001431415203628029,
+        0.001618021155990053, 0.0018298911689248222, 0.002056226486041757,
+        0.0022897399122246633, 0.0025254888932153517, 0.0027600298590394214,
+        0.002990880179861308, 0.0032161882078338847, 0.0034345312765398646,
+        0.003644790529289383, 0.003846072021281236, 0.004037656055406837,
+        0.004218963992952847, 0.004389536005386961, 0.0045490157240981625,
+        0.0046971392565383135, 0.004833726986239744, 0.004958677185693848,
+        0.0050719608694083495, 0.005173617567157691, 0.00526375184562394,
+        0.005342530477415594, 0.00541018017344406, 0.005466985777265969,
+        0.005513288787125713, 0.005549486038827965, 0.005576028361625535,
+        0.0055934190161810796, 0.005602211740509334, 0.005603008262022663,
+        0.005596455175850541, 0.005583240132435597, 0.00556408731410916,
+        0.00553975220519295, 0.005511015671327282, 0.005478677362696756,
+        0.005443548447635395, 0.005406443674434757, 0.005368172758219531,
+        0.005329531103193433, 0.0052912899027995, 0.005254185713413962,
+        0.005218909667581983, 0.00518609657426077, 0.005156314235709746,
+        0.005130053381247361, 0.005107718663885368, 0.005089621175972526,
+        0.005075972907255449, 0.005066883491238684, 0.00506235946919284,
+        0.005062306156590996, 0.005066532040676976, 0.005074755488192035,
+        0.005086613416191202, 0.005101671488913167, 0.005119435357004484,
+        0.005139362452061879, 0.005160873883934489, 0.0051833660510456885,
+        0.005206221653377939, 0.005228819882594952, 0.005250545644696659,
+        0.005270797740658599, 0.005288995986475652, 0.005304587294791968,
+        0.005317050767238773, 0.005325901862308237, 0.005330695711046049,
+        0.005331029655311821, 0.005326545083018985, 0.005316928633554652,
+        0.005301912845293714, 0.0052812763160478525, 0.005254843446262675,
+        0.005222483833290403, 0.005184111382772803, 0.00513968319993085,
+        0.005089198318920707, 0.0050326963230087705, 0.004970255902036255,
+        0.004901993386881054, 0.004828061293916789, 0.004748646905308847,
+        0.004663970904812235, 0.004574286081946573, 0.004479876112012151,
+        0.0043810544135784455, 0.004278163081115637, 0.00417157188639109,
+        0.004061677340110707, 0.003948901803389068, 0.003833692637940643,
+        0.0037165213820438458, 0.003597882936484731, 0.003478294738147155,
+        0.0033582958865580417, 0.0032384461690659477, 0.0031193248998918266,
+        0.0030015294465604862, 0.002885673262261983, 0.0027723831759935273,
+        0.002662295617797942, 0.0025560513819429666, 0.002454288473042777,
+        0.0023576325617818334, 0.0022666846321654603, 0.002182005571767052,
+        0.002104097776881518, 0.002033384335083181, 0.0019701869798150837,
+        0.0019147046921589, 0.001866995381845631, 0.0018269633000312553,
+        0.0017943545343995196, 0.0017687620552248773, 0.001749640455170937,
+        0.0017363290729753911, 0.0017280809979465972, 0.0017240948190812724,
+        0.001723546010116221, 0.0017256154171789895, 0.0017295131935088622,
+        0.0017344974429528092, 0.001739887597823152, 0.0017450730770630731,
+        0.0017495180450699374, 0.0017527631696112231, 0.001754425225496731,
+        0.0017541952697715025, 0.001751835968820317, 0.0017471785155213097,
+        0.0017401194492808175, 0.0017306175879413818, 0.0017186911972161907,
+        0.0017044154568730155, 0.0016879202287506806, 0.0016693880850938148,
+        0.0016490525122291716, 0.0016271961603130517, 0.0016041489617282171,
+        0.001580285887192839, 0.0015560240502637461, 0.0015318188127067668,
+        0.0015081584946715102, 0.0014855572721164745, 0.0014645458731363517,
+        0.0014456597935826872, 0.0014294249665995243, 0.0014163411525164953,
+        0.0014068637461073833, 0.0014013851657331002, 0.0014002173868905843,
+        0.0014035773813292323, 0.0014115771131067328, 0.0014242192884954216,
+        0.0014413993277155035, 0.0014629131889373425, 0.0014884699335981383,
+        0.001517707444255271, 0.001550209565268316, 0.001585523101243997,
+        0.0016231734749943612, 0.0016626782904113591, 0.0017035584621918408,
+        0.001745346901692805, 0.0017875949655131002, 0.0018298769892877357,
+        0.0018717932674215394, 0.0019129718261460334, 0.0019530692956373872,
+        0.0019917711342294195, 0.002028791403973418, 0.0020638722490844284,
+        0.0020967831885320126, 0.0021273203022175065, 0.0021553053658576794,
+        0.002180584971605678, 0.002203029658263934, 0.002222533065391638,
+        0.002239011118956315, 0.0022524012513273775, 0.0022626616551596635,
+        0.0022697705684072513, 0.0022737255862318416, 0.0022745429946957997,
+        0.0022722571206162173, 0.0022669196917246698, 0.0022585992012025134,
+        0.0022473802706042666, 0.0022333630050924824, 0.002216662334737133,
+        0.0021974073353397796, 0.0021757405217730495, 0.002151817106322538,
+        0.0021258042137530966, 0.0020978800439417937, 0.002068232971941023,
+        0.0020370605740145076, 0.0020045685668701077, 0.001970969645731368,
+        0.0019364822054108058, 0.001901328927265889, 0.0018657352141368475,
+        0.00182992745575389, 0.0017941311087740321, 0.0017585685797122633,
+        0.001723456905724332, 0.0016890052382951368, 0.0016554121485053267,
+        0.0016228627898542574, 0.0015915259746339865, 0.0015615512418012802,
+        0.0015330660156400663, 0.0015061729730759656, 0.0014809477498219962,
+        0.0014574371188331523, 0.0014356577661402677, 0.0014155957680794403,
+        0.0013972068403471393, 0.0013804173863871815, 0.0013651263238276497,
+        0.00135120761938401, 0.0013385134197911343, 0.001326877634232584,
+        0.0013161198052896936, 0.001306049101802668, 0.0012964682768696408,
+        0.0012871774550185493, 0.0012779776401801502, 0.0012686738669887706,
+        0.0012590779481821003, 0.0012490107981817458, 0.001238304335390612,
+        0.0012268029828668347, 0.0012143647987742355, 0.0012008622750222266,
+        0.0011861828456807412, 0.0011702291470626748, 0.0011529190695776029,
+        0.0011341856386077114, 0.0011139767579582396, 0.0010922548456652186,
+        0.0010689963881421844, 0.0010441914350601473, 0.0010178430542754052,
+        0.0009899667632578598, 0.0009605899514204742, 0.000929751306239223,
+        0.0008975002554088929, 0.0008638964378323618, 0.0008290092179935622,
+        0.0007929172621246058, 0.0007557082007927142, 0.0007174784127538815,
+        0.0006783329807234929, 0.000638385894705592, 0.0005977606184660051,
+        0.0005565912000565671, 0.0005150242167479934, 0.00047322203335111763,
+        0.00043136818728003806, 0.0003896763232858031, 0.0003484052429629768,
+        0.0003078848190444373, 0.0002685617227180705, 0.00023108165116396978,
+        0.00019643648013955043, 0.0001662077892802851, 0.00014285337119967402,
+        0.00012958300367696144, 0.00012885217715689765, 0.0001401166082637045,
+        0.00016013986055215962, 0.0001854125727494346, 0.0002134221678509727,
+        0.00024260683179224828, 0.0002720131902719537, 0.00030104002760699924,
+        0.00032928909152853526, 0.0003564828608571537, 0.00038241896806462123,
+        0.00040694427243451837, 0.0004299396318771022, 0.00045131066288246286,
+        0.00047098195637309626, 0.0004888933484657374, 0.0005049974470895086,
+        0.0005192579450988738, 0.000531648436486011, 0.0005421515603489089,
+        0.0005507583615964108, 0.0005574677968022885, 0.0005622863382281235,
+        0.0005652276448046147, 0.0005663122791903232, 0.0005655674569710237,
+        0.0005630268189344818, 0.0005587302209524353, 0.0005527235388217244,
+        0.0005450584878780675, 0.0005357924594814902, 0.0005249883788593955,
+        0.0005127145914549649, 0.0004990447881417429, 0.00048405798378095154,
+        0.00046783856908001314, 0.00045047646341634767, 0.00043206740712187436,
+        0.00041271344759227297, 0.0003925236967180547, 0.00037161547161880434,
+        0.0003501159819455755, 0.0003281648037993285, 0.00030591749442320453,
+        0.00028355086826735356, 0.0002612706862723649, 0.00023932279552113043,
+        0.0002180089960112012, 0.00019770873780182717, 0.0001789061116948821,
+        0.0001622160469441759, 0.00014839029152634327, 0.00013826252978999532,
+        0.00013258481473759823, 0.00013176961647753474, 0.00013568654684045488,
+        0.0001436924473964607, 0.00015487354918594602, 0.00016830453489289946,
+        0.00018319341961895173, 0.00019891744215520303, 0.00021500437638531192,
+        0.00023109912309507506, 0.00024693285039698287, 0.00026229920294439313,
+        0.0002770372384463755, 0.00029101953857889844, 0.0003041439934073255,
+        0.00031632811029301474, 0.00032750503876610655, 0.000337620761537408,
+        0.0003466320822169636, 0.00035450516167210156, 0.0003612144356723143,
+        0.0003667418000809485, 0.00037107598563316705, 0.0003742120685019946,
+        0.00037615107931940046, 0.00037689968470943985, 0.0003764699234882501,
+        0.00037487898538611996, 0.0003721490245535039, 0.0003683070033981053,
+        0.0003633845651456234, 0.00035741793602436225, 0.0003504478605397863,
+        0.0003425195760815344, 0.0003336828364243335, 0.0003239919978490315,
+        0.00031350618698152945, 0.00030228957662428583, 0.0002904118055752764,
+        0.00027794859148161643, 0.0002649826036351065, 0.00025160468636733,
+        0.00023791555454623998, 0.0002240281204238252, 0.0002100706508415641,
+        0.00019619098039334656, 0.0001825619784579796, 0.00016938829240025204,
+        0.0001569138741410947, 0.00014542861280334563, 0.0001352701483643282,
+        0.00012681368108363977, 0.00012044019269166817, 0.00011647721565910441,
+        0.00011512205092440646, 0.00011637977104356147, 0.00012005326580098942,
+        0.00012579339868271818, 0.00013317916227667065, 0.00014178879280854123,
+        0.00015124249955066405, 0.00016121863707969979, 0.00017145351547559758,
+        0.0001817339804302904, 0.00019188820679972362, 0.00020177718610697522,
+        0.000211287715117602, 0.00022032693205630054, 0.000228818173779235,
+        0.00023669787273927117, 0.00024391324053862337, 0.0002504205347536491,
+        0.00025618375430243746, 0.00026117364860938404, 0.0002653669565606399,
+        0.00026874581406291916, 0.00027129728563270265, 0.0002730129875458004,
+        0.0002738887787973264, 0.00027392450253225196, 0.00027312376527120904,
+        0.0002714937447686053, 0.0002690450199878777, 0.0002657914187515719,
+        0.00026174988031356865, 0.00025694033156441225, 0.00025138557695861675,
+        0.00024511120366677594, 0.00023814550513196993, 0.00023051942826672435,
+        0.0002222665523755636, 0.00021342311191291174, 0.00020402808116213114,
+        0.00019412334805893582, 0.0001837540186439159, 0.00017296891654472506,
+        0.00016182137945909027, 0.0001503705177897529, 0.00013868320926327748,
+        0.00012683729433036307, 0.00011492677872836784, 0.0001030704638442352,
+        9.14265079692526e-05, 8.021715914789345e-05, 6.976981088783923e-05,
+        6.05783556108545e-05, 5.336479223650344e-05, 4.903841557609909e-05,
+        4.8362522014174815e-05, 5.142268510577597e-05, 5.7538754234165856e-05,
+        6.575831143261966e-05, 7.527945714021568e-05, 8.554704645996909e-05,
+        9.61986213682218e-05, 0.00010699615106853205, 0.00011777808355678105,
+        0.00012843011798108626, 0.00013886799177913742, 0.00014902730309053017,
+        0.00015885738017788908, 0.00016831750097227063, 0.00017737450472510232,
+        0.00018600124765671508, 0.00019417558237882384, 0.00020187966953503895,
+        0.00020909950429777788, 0.00021582458411747332, 0.00022204767053293217,
+        0.00022776461411121843, 0.00023297422185248774, 0.00023767815292562928,
+        0.00024188083285757526, 0.00024558937910658407, 0.00024881353274898134,
+        0.0002515655922248794, 0.0002538603458365052], [4.137222898224676e-13,
+        1.2432388187618115e-12, 2.07898944271864e-12, 2.9251907508015513e-12,
+        3.786150850960949e-12, 4.6663078323911355e-12, 5.570269507804012e-12,
+        6.502855712991689e-12, 7.469143162954926e-12, 8.474513758340451e-12,
+        9.52470694056703e-12, 1.0625876886308152e-11, 1.1784655254744082e-11,
+        1.3008220613706514e-11, 1.4304375410111301e-11, 1.568163184626208e-11,
+        1.7149307933492845e-11, 1.871763533024495e-11, 2.0397880802075205e-11,
+        2.2202483275680273e-11, 2.4145209063060507e-11, 2.6241327816997375e-11,
+        2.8507812604092787e-11, 3.096356775528117e-11, 3.362968884921302e-11,
+        3.652975987449858e-11, 3.9690193583869296e-11, 4.314062182406387e-11,
+        4.6914344113911866e-11, 5.104884382123113e-11, 5.558638340989375e-11,
+        6.057469165345839e-11, 6.606775870102759e-11, 7.212675720675034e-11,
+        7.882111155386634e-11, 8.622974090573294e-11, 9.44425071053445e-11,
+        1.0356190390810759e-10, 1.1370503164248409e-10, 1.2500590937223608e-10,
+        1.376181877116156e-10, 1.5171833729328015e-10, 1.6750940400835234e-10,
+        1.852254399782766e-10, 2.0513674295347012e-10, 2.275560633225768e-10,
+        2.5284597443048555e-10, 2.8142764058926937e-10, 3.137912732488328e-10,
+        3.5050862553564483e-10, 3.9224795826808716e-10, 4.3979200745391894e-10,
+        4.940596058374347e-10, 5.561317660996092e-10, 6.27283223985174e-10,
+        7.0902068084668e-10, 8.031292917421146e-10, 9.11729324787e-10, 1.0373454098038763e-09,
+        1.1829914092202995e-09, 1.3522747359542436e-09, 1.5495249548225785e-09,
+        1.779952801559241e-09, 2.0498474278875195e-09, 2.366821847194864e-09,
+        2.7401193698258563e-09, 3.180997479992788e-09, 3.7032104083459536e-09,
+        4.323617965195853e-09, 5.0629565181087684e-09, 5.94681903929802e-09,
+        7.0069058461780964e-09, 8.282627332402004e-09, 9.823166407470142e-09,
+        1.1690144121289015e-08, 1.3961080449129632e-08, 1.6733908540787315e-08,
+        2.0132891707546815e-08, 2.4316418193350224e-08, 2.948732358378396e-08,
+        3.5906635036310414e-08, 4.391197572013062e-08, 5.394235566642038e-08,
+        6.657177166954955e-08, 8.255504095418891e-08, 1.0289074602501792e-07,
+        1.2890829224024015e-07, 1.6238921183308547e-07, 2.0573750965357266e-07,
+        2.6222085169850365e-07, 3.363150303327476e-07, 4.342004594751842e-07,
+        5.644847800950306e-07, 7.392654497897969e-07, 9.757095227141657e-07,
+        1.2984300346358867e-06, 1.7431057968372588e-06, 2.3620699884790782e-06,
+        3.233064554257598e-06, 4.473170898540886e-06, 6.261359141041971e-06,
+        8.875674588940127e-06, 1.2755829970815945e-05, 1.8610967221739356e-05,
+        2.7609902753679745e-05, 4.172657552964845e-05, 6.438759229047833e-05,
+        0.0001017310150329374, 0.0001651586013504714, 0.00027677324787342514,
+        0.00048167171034258453, 0.0008778382380436006, 0.0016958928150932302,
+        0.0035396735735044845, 0.008250479546054049, 0.02300317431883278,
+        0.09411536036253261, 2.326805015471173, 0.5179812897811523, 1.2703821727725775,
+        1.630994412809117, 0.9406930966070653, 1.131586120884883, 2.330734408517299,
+        3.645676035087794, 2.237166469264984, 2.313135291443106, 4.193603587509305,
+        8.194759701810701, 7.074723869242503, 4.368327670664488, 2.4365575833859263,
+        1.7523480791775332, 1.5458216750164204, 1.6267112104464012, 1.9972726052983099,
+        2.3134786656564046, 1.747197682108454, 1.2208317559572963, 0.9816135924535945,
+        0.9139414401405913, 0.9738133174148625, 1.174535778409244, 1.5255874571714843,
+        1.7404315590129382, 1.5077812381457396, 1.2387345186052612, 1.1011624210285231,
+        1.076017085061618, 1.1508676009759575, 1.3402281322076186, 1.6648045280503243,
+        2.0039731097451923, 1.9587875455070118, 1.6199247188096824, 1.3463572740835723,
+        1.200108496979906, 0.9803182392808056, 0.9046750124986305, 0.8792946260709047,
+        0.8602887848268288, 0.8174355055560107, 0.7407782654613566, 0.6471163174218348,
+        0.5588962982197356, 0.48721205416124874, 0.43335333335411996, 0.39471363230571715,
+        0.3679197434099974, 0.34965226533115085, 0.3364534013041599, 0.3243185650764465,
+        0.3088687249037634, 0.2869051136392592, 0.2586007221471419, 0.22753529055013053,
+        0.1979984605888318, 0.17267938686464102, 0.15240917379975757, 0.13691546048967385,
+        0.12550827677219872, 0.11744533598219725, 0.11207689309898043, 0.10888601353093905,
+        0.10748797174589948, 0.10761606115766978, 0.10910421804095327, 0.11187029663856285,
+        0.1159012485279182, 0.12124003682854084, 0.1279728389804433, 0.13621357335146114,
+        0.14608082186591897, 0.15765991380319583, 0.1709414146198607, 0.18573017668331337,
+        0.20153408913050447, 0.21747708920755657, 0.2323280408932105, 0.24474030899845847,
+        0.25367676700446545, 0.25879393030099385, 0.26051579438275313, 0.2597656621194646,
+        0.2575790645254045, 0.2548221219631438, 0.2520785247096618, 0.24965347759704623,
+        0.24762640589060672, 0.2459121507996459, 0.2443175069829836, 0.2425935415582431,
+        0.24048646746978816, 0.23778581898662307, 0.2343631329725097, 0.23019193937002483,
+        0.22534338206031518, 0.21995980825378086, 0.21421616932504434, 0.20828156231840525,
+        0.20229024607874224, 0.19632602916483122, 0.19041939023192014, 0.18455446013255616,
+        0.17868259696683061, 0.17273957130243334, 0.16666352179299507, 0.16041071471145182,
+        0.15396619688877838, 0.14734724865129753, 0.1405992740762651, 0.13378586375756538,
+        0.1269762857809379, 0.12023393354632193, 0.11360833861664694, 0.10713187498243845,
+        0.10082093358559809, 0.09468049843971016, 0.08871070545952722, 0.08291393671519193,
+        0.07730114939588983, 0.07189641945481527, 0.06673910564859617, 0.06188356577084041,
+        0.05739681883578157, 0.053354717063384106, 0.04983694117556448,
+        0.046920612850514035, 0.04467203224188738, 0.04313665704726949,
+        0.04232913819712333, 0.04222697459001499, 0.04277118032326875, 0.04387451315954933,
+        0.045434290008929144, 0.04734540676949193, 0.049510376904675496,
+        0.05184530964678789, 0.0542822236855845, 0.056768641669129524, 0.05926543040338365,
+        0.06174371442684648, 0.06418154524700606, 0.06656086938394411, 0.06886519070771249,
+        0.0710781612425668, 0.0731831645629329, 0.0751637869081908, 0.07700491921471948,
+        0.07869412357406919, 0.08022285949738907, 0.08158721829112954, 0.0827879518625032,
+        0.08382976896923545, 0.08472005246562206, 0.08546727536680292, 0.08607943589090847,
+        0.08656279627665522, 0.08692112184705647, 0.0871555057298017, 0.08726475535950268,
+        0.08724622498626891, 0.08709691307426087, 0.08681461101219583, 0.08639889420201743,
+        0.08585178826060529, 0.08517801426876534, 0.08438480229776477, 0.08348134197731714,
+        0.08247799488891651, 0.08138541638896449, 0.08021372502395645, 0.07897182537415465,
+        0.07766694807089894, 0.07630443056505977, 0.07488773120736232, 0.07341864943857507,
+        0.07189771442460265, 0.07032469947063225, 0.06869921607698606, 0.06702133715609497,
+        0.06529219360743167, 0.06351448441761544, 0.06169284137753552, 0.05983399919055984,
+        0.057946741791391795, 0.056041624593260786, 0.05413050483666246,
+        0.05222594094997226, 0.05034053976902626, 0.04848633362029462, 0.046674257745103635,
+        0.044913776414501505, 0.043212679397566664, 0.04157704511283431,
+        0.0400113469388025, 0.03851866657119731, 0.0371009727564162, 0.03575942385864162,
+        0.03449465687410433, 0.033307032293471255, 0.03219681268272522,
+        0.031164262346594418, 0.03020966545624693, 0.029333269827954183,
+        0.028535172278502312, 0.02781516807644546, 0.02717259048537067,
+        0.02660616607610822, 0.026113907325689977, 0.02569305662217888,
+        0.025340086524798227, 0.025050751768468382, 0.024820180931144294,
+        0.024642991342281356, 0.024513410373250496, 0.024425389423225963,
+        0.0243727025847022, 0.02434902856903029, 0.02434802036081336, 0.024363370935544738,
+        0.024388884423401144, 0.024418560155776845, 0.024446692518757647,
+        0.02446798343920814, 0.024477658052601586, 0.024471569250613247,
+        0.024446274835228776, 0.02439907279445184, 0.024327985728074587,
+        0.024231693633251155, 0.024109423267285997, 0.023960810035277218,
+        0.023785753048082114, 0.023584284710482833, 0.023356472949568236,
+        0.023102367803539168, 0.022821995911852487, 0.022515397991559254,
+        0.022182697121257044, 0.021824180803253462, 0.021440378175642375,
+        0.021032115697417086, 0.02060053976539864, 0.02014710198056385,
+        0.019673510614793083, 0.019181658536857316, 0.018673542046976382,
+        0.01815118601379251, 0.017616588479123837, 0.017071693255160027,
+        0.016518393169119322, 0.01595856078823971, 0.015394098776278132,
+        0.014826999269324388, 0.014259401143288287, 0.013693635698977072,
+        0.013132254593383914, 0.012578037958303609, 0.0120339845668404,
+        0.011503288669512644, 0.010989309044820145, 0.010495534654137422,
+        0.010025548321101361, 0.009582985792058907, 0.009171483439990868,
+        0.00879460504369686, 0.00845573787744538, 0.008157951984954738,
+        0.007903824548849647, 0.007695242914104001, 0.0075332122789715655,
+        0.007417702639864889, 0.007347569297875646, 0.0073205696926331,
+        0.00733347909697495, 0.007382285962528415, 0.007462432641181816,
+        0.0075690635263201515, 0.0076972495300682234, 0.007842170386712729,
+        0.007999248992281511, 0.008164241183019921, 0.008333288949018662,
+        0.008502945884199455, 0.008670182279198326, 0.008832375171339795,
+        0.008987286896172477, 0.009133034692462412, 0.009268053705545991,
+        0.009391056034516284, 0.009500988898331796, 0.009596995201825088,
+        0.009678379542399768, 0.009744581949839962, 0.009795160486996085,
+        0.009829782466446725, 0.009848222720725927, 0.009850366361106878,
+        0.009836212970216732, 0.00980587928966074, 0.009759598151724024,
+        0.00969771250719134, 0.00962066467510357, 0.009528982109684631,
+        0.009423261802776682, 0.009304155763769575, 0.009172359807915179,
+        0.009028607217123856, 0.008873667887464468, 0.008708352554717023,
+        0.00853352081132975, 0.008350091057127817, 0.008159050361510716,
+        0.007961462457344994, 0.0077584726567640995, 0.007551309226856293,
+        0.007341281507369148, 0.007129775614499751, 0.006918248828658664,
+        0.006708223646433879, 0.006501282012982379, 0.006299059530683839,
+        0.006103238607617306, 0.005915538733915983, 0.00573770152618573,
+        0.005571468021073751, 0.005418546064443187, 0.005280566619534426,
+        0.005159029419145785, 0.0050552404902407646, 0.004970246377798115,
+        0.004904771885318994, 0.004859169209082931, 0.0048333859298474325,
+        0.004826957237532338, 0.00483902432901155, 0.004868376964311156,
+        0.00491351472694537, 0.00497271944192234, 0.005044130782736779,
+        0.005125818120523857, 0.005215843561582185, 0.005312313254844448,
+        0.005413415959935667, 0.005517449318339861, 0.005622835229058909,
+        0.005728126269931199, 0.0058320053303484495, 0.005933280615867116,
+        0.006030878010959735, 0.006123832481022949, 0.006211279793088044,
+        0.006292449375765313, 0.006366658671258959, 0.006433308910541046,
+        0.0064918819194109, 0.006541937377246364, 0.006583109919542068,
+        0.0066151055901768, 0.006637697373757126, 0.006650719817105801,
+        0.006654063018367474, 0.006647666463829324, 0.006631513285440867,
+        0.006605625479963129, 0.006570060484836931, 0.0065249092804504725,
+        0.006470295932994488, 0.006406378260135033, 0.006333349140107834,
+        0.00625143792452139, 0.006160911464822282, 0.006062074409810962,
+        0.005955268641609201, 0.005840871948628106, 0.005719296236796386,
+        0.005590985718878393, 0.005456415572084393, 0.005316091513719341,
+        0.005170550630384113, 0.005020363636777336, 0.004866138573781081,
+        0.004708525816396501, 0.004548224174856264, 0.0043859878498242934,
+        0.004222634030305363, 0.004059050981591346, 0.0038962065074780597,
+        0.00373515663753257, 0.0035770542160946874, 0.0034231566943400734,
+        0.003274831792667349, 0.003133558786796412, 0.0030009220268442825,
+        0.0028785921180414166, 0.002768289404143687, 0.002671724727915508,
+        0.0025905148406954568, 0.0025260750461529925, 0.0024794994505967886,
+        0.0024514474693203216, 0.0024420600917404067, 0.00245092686501918,
+        0.0024771136138144493, 0.0025192453462091783, 0.0025756254242922955,
+        0.0026443663804333628, 0.0027235106107806363, 0.0028111272853366823,
+        0.0029053807037605754, 0.0030045719505325448, 0.0031071591640447985,
+        0.003211762601811175, 0.003317160016806557, 0.0034222765758457814,
+        0.00352617222939773, 0.003628028351406944, 0.0037271346835403224,
+        0.0038228771112972853, 0.00391472650819026, 0.004002228736541448,
+        0.004084995831003263, 0.0041626983678826925, 0.004235059008981876,
+        0.004301847187953479, 0.0043628748731440225, 0.004417993299040297,
+        0.004467090514952689, 0.0045100895657160375, 0.0045469471032667155,
+        0.004577652234341935, 0.004602225439921613, 0.004620717450979945,
+        0.004633208024988451, 0.004639804628221266, 0.004640641079831498,
+        0.004635876246899399, 0.004625692890590412, 0.0046102967517261915,
+        0.004589915933254496, 0.004564800594001461, 0.0045352229211362465,
+        0.004501477306409549, 0.004463880620094182, 0.004422772460756922,
+        0.004378515259626794, 0.004331494132479804, 0.004282116395870622,
+        0.0042308106909993695, 0.004178025682795529, 0.004124228317747562,
+        0.004069901630212487, 0.004015542082383806, 0.003961656410945182,
+        0.003908757938554, 0.003857362296114345, 0.0038079824997499074,
+        0.0037611233394113557, 0.003717275067883457, 0.0036769064314637655,
+        0.003640457153387013, 0.0036083300627053677, 0.0035808831450749702,
+        0.0035584218656521567, 0.0035411921646546405, 0.0035293745415227278,
+        0.0035230796160682426, 0.003522345482285909, 0.003527137058711018,
+        0.003537347500532382, 0.003552801591118818, 0.003573260893372734,
+        0.003598430331874537, 0.003627965806790516, 0.00366148241488933,
+        0.0036985628691100533, 0.003738765757645297, 0.003781633355051487,
+        0.0038266987789275196, 0.0038734923655236765, 0.003921547208279152,
+        0.003970403859376611, 0.004019614234930743, 0.004068744789380515,
+        0.004117379036828333, 0.0041651194995359145, 0.004211589159643472,
+        0.0042564324830024316, 0.004299316075574081, 0.004339929025095254,
+        0.004377982974445159, 0.004413211968476175, 0.004445372112875902,
+        0.004474241081339871, 0.004499617505476011, 0.0045213202799778964,
+        0.004539187813469953, 0.004553077252666556, 0.004562863704463, 0.004568439477040471,
+        0.004569713357291499, 0.0045666099378451185, 0.0045590690027075345,
+        0.004547044976146564, 0.004530506434859172, 0.0045094356789222865,
+        0.0044838283527979875, 0.0044536931040112665, 0.004419051264649318,
+        0.004379936539765399, 0.004336394687740581, 0.004288483180312568,
+        0.00423627083466831, 0.0041798374158849875, 0.004119273214423475,
+        0.004054678609693595, 0.003986163635609714, 0.003913847567278932,
+        0.0038378585487011813, 0.0037583332797775783, 0.003675416777516735,
+        0.003589262221479013, 0.003500030889031948, 0.003407892182341442,
+        0.0033130237475169, 0.003215611688305666, 0.0031158508816867404,
+        0.0030139454121065313, 0.002910109152879596, 0.0028045665393986695,
+        0.002697553596505763, 0.0025893193036806003, 0.002480127405458826,
+        0.002370258803034888, 0.0022600146971793935, 0.0021497206954045503,
+        0.002039732149344429, 0.0019304410525210459, 0.0018222849008076062,
+        0.0017157579850366352, 0.0016114256149107812, 0.0015099416965637699,
+        0.0014120697624374209, 0.0013187067286721708, 0.0012309069143785275,
+        0.001149900635270702, 0.0010770965258443406, 0.00101405015281242,
+        0.0009623766627645281, 0.0009235898466727468, 0.0008988741381158788,
+        0.0008888403139486072, 0.0008933550712787872, 0.0009115263137456347,
+        0.0009418567885894051, 0.0009824975849335226, 0.0010315033804487782,
+        0.0010870218410780107, 0.0011473995196641478, 0.001211219929680047,
+        0.0012772993153864166, 0.0013446617117453675, 0.0014125071955687102,
+        0.0014801807072647142, 0.001547144619370546, 0.0016129559352284373,
+        0.0016772479225633274, 0.0017397155738337487, 0.0018001041986250325,
+        0.0018582005060474877, 0.0019138256344853957, 0.0019668296901743324,
+        0.0020170874489573104, 0.002064494951886724, 0.002108966787193911,
+        0.002150433899358816, 0.0021888418040049203, 0.0022241491170178814,
+        0.0022563263292013085, 0.0022853547752839866, 0.0023112257592996974,
+        0.0023339398078277705, 0.0023535060291664804, 0.002369941560909267,
+        0.0023832710911433313, 0.0023935264401641326, 0.00240074619087056,
+        0.0024049753570473155, 0.002406265079930215, 0.002404672344961526,
+        0.0024002597122673307, 0.002393095056313497, 0.0023832513119327443,
+        0.0023708062256425928, 0.002355842112406201, 0.0023384456189381097,
+        0.0023187074950594203, 0.0022967223746777794, 0.0022725885676949304,
+        0.0022464078636768585, 0.0022182853475906966, 0.002188329227377714,
+        0.002156650672740798, 0.0021233636641721215, 0.0020885848510624042,
+        0.002052433417585466, 0.002015030954985349, 0.0019765013386871485,
+        0.0019369706085587029, 0.0018965668503238236, 0.0018554200758427635,
+        0.0018136620993888428, 0.0017714264066416392, 0.0017288480122877787,
+        0.0016860633012352353, 0.001643209847468222, 0.0016004262030529855,
+        0.001557851648299139, 0.0015156258920581102, 0.001473888708988166,
+        0.0014327794983344003, 0.0013924367465057354, 0.0013529973741040035,
+        0.0013145959469873674, 0.001277363731659909, 0.001241427577809431,
+        0.0012069086162776012, 0.0011739207694905233, 0.001142569084104427,
+        0.0011129479120182656, 0.0010851389858726147, 0.0010592094568731571,
+        0.0010352099844462511, 0.001013172985450288, 0.0009931111621149708,
+        0.0009750164289196067, 0.0009588593468929401, 0.0009445891481789559,
+        0.0009321343961867179, 0.0009214042805147088, 0.0009122904976189375,
+        0.0009046696239379196, 0.0008984058542681438, 0.000893353958530299,
+        0.0008893623063213431, 0.0008862758194741585, 0.0008839387351436839,
+        0.0008821970909648826, 0.0008809008752840852, 0.0008799058151810937,
+        0.0008790748004429692, 0.0008782789612163012, 0.0008773984305653881,
+        0.0008763228309732728, 0.0008749515270032368, 0.0008731936860367931,
+        0.0008709681863523221, 0.0008682034077671121, 0.0008648369354318876,
+        0.0008608152026269036, 0.0008560930939266846, 0.0008506335260222894,
+        0.0008444070199070322, 0.00083739127507178, 0.0008295707536870713,
+        0.000820936280581921, 0.0008114846630037949, 0.0008012183326861432,
+        0.000790145011685103, 0.0007782774026426661, 0.000765632903734195,
+        0.0007522333483676125, 0.0007381047698313604, 0.0007232771913763636,
+        0.0007077844426645403, 0.0006916640040478994, 0.0006749568807241782,
+        0.0006577075093614114, 0.000639963700328339, 0.0006217766191813056,
+        0.0006032008114975677, 0.0005842942755826245, 0.0005651185879148326,
+        0.0005457390863739219, 0.0005262251161601344, 0.0005066503426045087,
+        0.00048709313318285897, 0.00046763700749920045, 0.0004483711474586747,
+        0.00042939094911723346, 0.00041079858062451345, 0.0003927034850620707,
+        0.0003752227305764549, 0.00035848106133230876, 0.0003426104429427143,
+        0.0003277488320184477, 0.00031403784850906474, 0.0003016190226224775,
+        0.0002906283706987878, 0.0002811892750523827, 0.0002734040258792191,
+        0.00026734488589823593, 0.0002630460167900093, 0.0002604978349131425,
+        0.0002596451373694113, 0.0002603896239351342, 0.0002625964531081302,
+        0.00026610359297862303, 0.00027073228725507133, 0.0002762970468266529,
+        0.0002826140475722257, 0.00028950740865474426, 0.00029681332968745875,
+        0.0003043823823954725, 0.0003120803859264976, 0.0003197882986200744,
+        0.00032740149369678837, 0.000334828697986275, 0.00034199078825411587,
+        0.0003488195705924937, 0.00035525661715917454, 0.000361252199236114,
+        0.00036676433275057834, 0.00037175793847585916, 0.00037620411126895904,
+        0.00038007948878369957, 0.00038336570855021794, 0.0003860489421898729,
+        0.00038811949618632513, 0.0003895714696297079, 0.00039040246053105587,
+        0.00039061331349069846, 0.0003902079026221736, 0.0003891929447216966,
+        0.0003875778385974083, 0.0003853745273547783, 0.00038259738115066857,
+        0.0003792630985862129, 0.0003753906254275248, 0.0003710010897808069,
+        0.00036611775320290565, 0.00036076597750807284, 0.00035497320723002553,
+        0.0003487689678665109, 0.00034218488008703086, 0.00033525469011302787,
+        0.0003280143162868324, 0.00032050191156997516, 0.0003127579410588731,
+        0.0003048252726216188, 0.00029674927717857974, 0.00028857793285662624,
+        0.00028036192397772167, 0.00027215472139861346, 0.00026401262490307925,
+        0.00025599474104906483, 0.0002481628613327667, 0.00024058119625525434,
+        0.00023331591228703904, 0.00022643441309490666, 0.00022000430726551112,
+        0.00021409201660092645, 0.00020876100673785253, 0.00020406966842362968,
+        0.00020006894246180957, 0.00019679985604363414, 0.000194291206684283,
+        0.00019255766999643097, 0.0001915985978278329, 0.00019139770355633046,
+        0.00019192371061280047, 0.00019313189655891622, 0.0001949663363990947,
+        0.00019736256756206638, 0.0002002503800110124, 0.0002035564720132284,
+        0.00020720678457557859, 0.00021112841079906159, 0.00021525105071319993,
+        0.0002195080368211713, 0.00022383698825008072, 0.00022818016522302043,
+        0.00023248459600113305, 0.00023670204095782387, 0.000240788847365232,
+        0.00024470573672675, 0.00024841755571547425, 0.00025189301272765324,
+        0.0002551044149065874, 0.00025802741508410514, 0.00026064077419361403,
+        0.0002629261419601102, 0.0002648678568624013, 0.00026645276518358677,
+        0.0002676700582906999, 0.00026851112690052257, 0.0002689694309554707,
+        0.00026904038371240296, 0.00026872124873084737, 0.00026801104856265083,
+        0.0002669104841043525, 0.00026542186373566633, 0.0002635490415388521,
+        0.000261297364081479, 0.00025867362543888694, 0.0002556860303332802,
+        0.00025234416549055084, 0.0002486589795577192, 0.00024464277218050627,
+        0.0002403091931227546, 0.0002356732526246966, 0.00023075134453355738,
+        0.00022556128411044455, 0.00022012236282488624, 0.00021445542288983527,
+        0.00020858295473742176, 0.00020252922108668044, 0.00019632041162161108,
+        0.00018998483250269092, 0.00018355313475311037, 0.00017705858474201965,
+        0.00017053737801211424, 0.00016402899388170763, 0.00015757658152472422,
+        0.00015122735723705597, 0.00014503297552444921, 0.00013904981181516314,
+        0.00013333906091021782, 0.0001279665141653337, 0.00012300183624725143,
+        0.00011851713432225135, 0.00011458462494446515, 0.00011127329162210513,
+        0.00010864461805556408, 0.00010674777330715678, 0.00010561494456706509,
+        0.00010525772025714155, 0.0001056653688708518, 0.00010680548139105331,
+        0.00010862686399677251, 0.00011106402774157457, 0.00011404234395479194,
+        0.00011748298317382433, 0.0001213070324964583, 0.00012543852676739426,
+        0.0001298064051625505, 0.0001343455663495341, 0.00013899725315873177,
+        0.0001437089880063593, 0.00014843423887502205, 0.00015313194694552203,
+        0.0001577660035324327, 0.0001623047303506902, 0.00016672039332811482,
+        0.00017098876446987703, 0.00017508873655755537, 0.0001790019898281617,
+        0.00018271270681612133, 0.00018620733024234264, 0.0001894743584874491,
+        0.00019250417337300803, 0.00019528889545274684, 0.0001978222625577274,
+        0.00020009952792824877, 0.00020211737480991735, 0.00020387384487785236,
+        0.00020536827829073607, 0.00020660126353629218, 0.0002075745955459018,
+        0.00020829124080939314, 0.00020875530843231637, 0.00020897202623426932,
+        0.000208947721116803, 0.00020868980300846833, 0.00020820675173341272,
+        0.00020750810617869108, 0.000206604455083897, 0.00020550742873300226,
+        0.00020422969072371452], [1.1103921431213198e-12, 3.337155288652005e-12,
+        5.581911892425125e-12, 7.856846559814039e-12, 1.0174429886687166e-11,
+        1.2547539013307954e-11, 1.498958282418928e-11, 1.7514635626595485e-11,
+        2.0137579740582482e-11, 2.287425989405802e-11, 2.574165158644202e-11,
+        2.8758046184738042e-11, 3.194325539942301e-11, 3.531883903078548e-11,
+        3.8908359302022415e-11, 4.273766662199053e-11, 4.6835221573345977e-11,
+        5.123245908431945e-11, 5.5964201668630357e-11, 6.106912932920094e-11,
+        6.659031582136009e-11, 7.257584141486796e-11, 7.907949520579783e-11,
+        8.616158151399102e-11, 9.388984772753525e-11, 1.0234055395532762e-10,
+        1.1159970887325608e-10, 1.2176449987625002e-10, 1.3294495179947635e-10,
+        1.4526585384061776e-10, 1.5886900326052575e-10, 1.7391582196045863e-10,
+        1.9059041497900874e-10, 2.091031519035375e-10, 2.2969486983003844e-10,
+        2.526418153112416e-10, 2.7826146826243636e-10, 3.0691941924176444e-10,
+        3.390375095890057e-10, 3.75103486908278e-10, 4.156824858721892e-10,
+        4.614307103514259e-10, 5.131117802344691e-10, 5.716163091326165e-10,
+        6.379854137952258e-10, 7.134390160705173e-10, 7.994100125385158e-10,
+        8.975856359556811e-10, 1.0099576758750297e-09, 1.1388836285479005e-09,
+        1.2871613895998567e-09, 1.458120776599211e-09, 1.6557360395616332e-09,
+        1.8847646471557993e-09, 2.150919086170974e-09, 2.4610803032539987e-09,
+        2.823563900130101e-09, 3.248453423025512e-09, 3.74801939349327e-09,
+        4.337248401272825e-09, 5.034514183120078e-09, 5.862432819130135e-09,
+        6.848957971117851e-09, 8.028790873058646e-09, 9.445205546373264e-09,
+        1.1152425329360774e-08, 1.3218736425436417e-08, 1.5730593989840392e-08,
+        1.879807542387871e-08, 2.2562177790758173e-08, 2.7204662837408657e-08,
+        3.2961456748620245e-08, 4.014106438343886e-08, 4.915014257521737e-08,
+        6.05294315843542e-08, 7.500489777052978e-08, 9.356159234363161e-08,
+        1.1755208584204608e-07, 1.488586943433798e-07, 1.9014154759352105e-07,
+        2.4522780103558756e-07, 3.1974134664235044e-07, 4.2216041517869657e-07,
+        5.656782017662478e-07, 7.716755076714297e-07, 1.0767247011059519e-06,
+        1.5482930527238283e-06, 2.325751927664138e-06, 3.756490093738075e-06,
+        7.103379199783676e-06, 3.6490625467899354e-05, 1.577373534734989e-05,
+        1.3740759412477129e-05, 1.4148468060535896e-05, 1.5622325379296654e-05,
+        1.797520908651408e-05, 2.129119941048292e-05, 2.5802380572840035e-05,
+        3.1886029078065354e-05, 4.0107004313862006e-05, 5.1299338065978394e-05,
+        6.670145761081087e-05, 8.817683864502246e-05, 0.00011857862734907131,
+        0.00016236549149206193, 0.00022667017234724422, 0.00032321240216927517,
+        0.0004718493185582651, 0.0007074479862134149, 0.001093865324845975,
+        0.0017541353187502052, 0.0029406319044267223, 0.00521416720746766,
+        0.009961899801114452, 0.02118569464680592, 0.05368502192584466,
+        0.19871144490761977, 4.42006145271334, 0.8794735023946815, 1.9125758699636368,
+        2.156085524600325, 1.0786564785862638, 1.1079496493150103, 1.907986526778067,
+        2.4213176061378534, 1.1495422579580867, 0.8403242357670178, 0.8284114968235069,
+        1.0649128543149557, 1.5895067201710782, 1.2033459475319883, 0.7680321479985491,
+        0.6214310019266012, 0.6173642325177098, 0.7362523086264113, 1.0294985510018233,
+        1.358239098785856, 1.161325973372013, 0.9076594665803251, 0.8025885626190751,
+        0.8055680483104791, 0.9064757160407924, 1.132779513577784, 1.4999275596381583,
+        1.7222482105991461, 1.4875568442987708, 1.2103669714980134, 1.0608254491383724,
+        1.019067434966981, 1.0695823884683933, 1.2209541997367668, 1.4856946983666948,
+        1.7510714662951974, 1.6750759952378216, 1.3546496444103582, 1.0990112511512968,
+        0.9506875698157763, 0.7372840583238076, 0.6653409490216531, 0.6337170510870789,
+        0.6078568712537994, 0.5661907781710599, 0.5027780907279822, 0.430105309756238,
+        0.3634622421470427, 0.30968339640559195, 0.26887629244244665, 0.2386955536434493,
+        0.21648105261549117, 0.19980097489898344, 0.18636485360500898, 0.17384947554846286,
+        0.16007035333351766, 0.14380254809550982, 0.12568911741126246, 0.10788407721254745,
+        0.09250822879233025, 0.08060457438526135, 0.07219384724339613, 0.06675855111526649,
+        0.06363313923860686, 0.06221000657744917, 0.06201729644647238, 0.062727488636481,
+        0.06413652055485705, 0.06613595939724076, 0.06868821356679218, 0.07180757685028355,
+        0.07554668334335726, 0.07998675376065331, 0.08522945673893914, 0.09138757538328712,
+        0.09857064501762287, 0.10686034959798968, 0.11626952268962881, 0.12668062415557554,
+        0.13776983315659216, 0.14894724228356626, 0.15937613012761648, 0.1681369260057531,
+        0.17451935986376188, 0.17828784004152398, 0.1797343757521157, 0.1794959754116561,
+        0.17828909433228202, 0.17671555755802715, 0.17518400078906823, 0.1739117200681984,
+        0.17296013758712775, 0.1722761615879366, 0.17173039796589198, 0.17115261778448382,
+        0.17036658241105299, 0.1692235632944025, 0.16762994304918277, 0.1655623860460099,
+        0.16306626070235755, 0.1602384601917948, 0.15720109812104607, 0.15407454014528996,
+        0.1509563925369932, 0.14790941629890297, 0.1449581992829254, 0.14209283866786718,
+        0.13927758264397255, 0.13646255406784238, 0.13359671677919213, 0.13064002031025676,
+        0.1275724906758888, 0.12439839826715693, 0.1211447445349335, 0.11785485949120296,
+        0.11457920706786029, 0.11136597354803555, 0.10825358226897085, 0.10526632356789986,
+        0.10241332179585448, 0.09969039031233871, 0.09708398257842511, 0.09457630859783042,
+        0.09215063272633281, 0.0897957802259116, 0.08750902000995914, 0.08529682348849109,
+        0.08317349391614544, 0.08115817077342691, 0.07927105273523387, 0.0775297407918,
+        0.07594640798726118, 0.07452618198422789, 0.07326681797256891, 0.07215951793605259,
+        0.07119062233907293, 0.07034382884470781, 0.06960255176760155, 0.06895202544754676,
+        0.06838079728629876, 0.06788137155385353, 0.06744994372546728, 0.06708536197449609,
+        0.066787607249787, 0.06655615289931448, 0.06638854299622143, 0.06627944180337138,
+        0.06622029259597155, 0.06619961060365553, 0.0662038343992314, 0.06621857531541198,
+        0.06623003934226261, 0.06622636167508422, 0.0661986057000314, 0.06614124380436048,
+        0.06605204781869335, 0.06593144442655309, 0.0657814994713812, 0.06560475617515356,
+        0.0654031560333813, 0.06517722703922703, 0.0649256522134618, 0.06464525275723551,
+        0.06433134894111334, 0.06397840572995751, 0.06358083285103484, 0.06313379314214469,
+        0.06263388065208171, 0.06207956080002531, 0.06147131400460623, 0.06081148146925784,
+        0.060103864288970354, 0.059353163243837125, 0.058564360479087994,
+        0.0577421367106854, 0.0568903951235988, 0.05601193459894164, 0.05510828808028842,
+        0.05417972147228833, 0.05322537569222378, 0.052243527879513786,
+        0.05123194456641567, 0.050188297038866715, 0.0491106054584057, 0.04799767349523912,
+        0.04684947089906362, 0.04566742037353367, 0.04445455031177497, 0.04321548793977789,
+        0.04195628750777524, 0.040684111844298904, 0.03940680763352529,
+        0.03813242984326295, 0.036868775471278856, 0.035622980728058966,
+        0.034401221444025146, 0.03320853801727805, 0.03204878787032161,
+        0.030924713293627976, 0.02983810222247503, 0.028790013943438095,
+        0.027781040119266655, 0.026811572732110687, 0.025882053608208968,
+        0.024993184457920994, 0.024146081434737954, 0.023342363844466182,
+        0.02258417247793606, 0.021874118773222706, 0.02121517124606885,
+        0.020610490102391004, 0.02006322451835703, 0.019576289741274035,
+        0.019152142809935328, 0.01879257608144109, 0.018498546422282085,
+        0.01827005448670108, 0.018106082941437788, 0.01800459548686866,
+        0.01796259141071781, 0.01797620480974222, 0.018040834808776492,
+        0.018151293483447392, 0.018301961103089664, 0.018486942334679787,
+        0.018700220558594337, 0.018935809190324615, 0.019187898382080137,
+        0.01945099309150973, 0.019720035343020064, 0.01999050103921273,
+        0.020258461213906436, 0.02052059990142573, 0.020774185698783774,
+        0.021017000650012947, 0.021247236770608725, 0.02146337577565545,
+        0.02166407018502294, 0.021848043399817076, 0.022014022728939785,
+        0.022160713370308283, 0.022286814077108367, 0.022391067881615184,
+        0.02247233507392864, 0.02252967177665279, 0.02256239672875537, 0.022570131549715534,
+        0.022552805347468462, 0.022510621913905706, 0.022443995328001943,
+        0.022353465926056512, 0.0222396120586554, 0.022102973271439733,
+        0.02194399769831278, 0.021763021318462077, 0.021560280432028782,
+        0.021335952477262263, 0.02109021527211608, 0.020823311781198044,
+        0.020535607088848728, 0.020227626429293735, 0.019900067408531973,
+        0.019553785031850693, 0.01918975364443346, 0.01880901424485421,
+        0.01841261799161865, 0.018001576739997385, 0.01757682930913752,
+        0.017139228505679335, 0.01668954958297283, 0.01622851669088328,
+        0.015756840731903966, 0.015275260403288532, 0.014784578289671209,
+        0.014285685560107982, 0.01377957169292122, 0.013267319075272966,
+        0.012750085553776967, 0.012229080405952794, 0.01170554032768614,
+        0.011180711777722818, 0.010655844601735708, 0.010132199719405412,
+        0.009611071361652969, 0.009093822425691601, 0.008581930390014356,
+        0.008077041103068503, 0.007581028625277514, 0.007096060887647877,
+        0.006624672714451361, 0.0061698488875015405, 0.0057351191320043704,
+        0.0053246622337150456, 0.004943405177091686, 0.004597081938206798,
+        0.004292184036001261, 0.0040356987233008635, 0.003834519446267461,
+        0.0036944817595834256, 0.003619170431323896, 0.0036088958377874154,
+        0.0036603275524112093, 0.0037670123492174515, 0.003920540689382498,
+        0.004111851022259853, 0.004332250739266347, 0.004574004112020127,
+        0.004830548761382915, 0.005096476417911353, 0.005367398593961118,
+        0.005639775612583286, 0.005910750623150089, 0.006178006553632829,
+        0.0064396510399517305, 0.006694128093677357, 0.00694015254319439,
+        0.00717666232668965, 0.007402783669536431, 0.007617804659835189,
+        0.00782115356947953, 0.008012379327046905, 0.008191132698342225,
+        0.008357147809306699, 0.008510224507453337, 0.008650212583182887,
+        0.008776999010771136, 0.008890499138707183, 0.008990652247138242,
+        0.00907742123204101, 0.009150795525860032, 0.009210795868242213,
+        0.00925747930791549, 0.0092909428964382, 0.00931132491000991, 0.009318803026203566,
+        0.009313589562499034, 0.009295924511681587, 0.009266067558828923,
+        0.00922429045214343, 0.009170870999487485, 0.009106089609227718,
+        0.009030228770991236, 0.008943575292804056, 0.008846424593228252,
+        0.008739085990830729, 0.00862188780234592, 0.008495181171566913,
+        0.008359341871152708, 0.008214769774778278, 0.008061886190390343,
+        0.007901129675536965, 0.007732951238768226, 0.0075578099218269355,
+        0.007376169648701285, 0.0071884979575902634, 0.006995266866333592,
+        0.006796955741674356, 0.006594055726355372, 0.006387075085938777,
+        0.006176544800725873, 0.005963023847734061, 0.005747103861767373,
+        0.005529413179447065, 0.005310620592197186, 0.005091439400946486,
+        0.0048726325290841185, 0.00465501948516693, 0.004439485866143607,
+        0.004226995863688333, 0.004018607888304508, 0.0038154929449776883,
+        0.003618954734161389, 0.0034304495141250736, 0.003251602408982491,
+        0.0030842149594164994, 0.0029302563233066857, 0.002791828100940096,
+        0.0026710915205507444, 0.0025701479288003644, 0.0024908719185397056,
+        0.0024347122397590007, 0.0024024954105319007, 0.0023942808265216375,
+        0.002409312158678535, 0.0024460839368862946, 0.0025025054642176477,
+        0.002576116364538636, 0.0026643022252595687, 0.0027644726661869615,
+        0.002874185529157205, 0.0029912185454033014, 0.003113599319156774,
+        0.0032396068319360287, 0.0033677560051014535, 0.003496773809818532,
+        0.00362557248699751, 0.003753223193602869, 0.0038789318677051243,
+        0.004002018145246684, 0.0041218975806120274, 0.0042380670741154315,
+        0.004350093197491175, 0.004457602981607812, 0.004560276665946121,
+        0.0046578418985666606, 0.004750068913349461, 0.0048367662940307235,
+        0.004917777047687851, 0.004992974838397229, 0.005062260355086517,
+        0.0051255578862812986, 0.0051828122350388375, 0.00523398612229897,
+        0.005279058197448384, 0.005318021711346079, 0.005350883823968839,
+        0.0053776654352773595, 0.005398401361526104, 0.005413140642954218,
+        0.005421946770615991, 0.0054248976585877795, 0.005422085255643618,
+        0.005413614773865239, 0.00539960359483182, 0.005380179981380389,
+        0.005355481762676434, 0.005325655166423981, 0.005290853945146449,
+        0.005251238890012646, 0.005206977757614519, 0.005158245565015611,
+        0.005105225150127465, 0.005048107857759281, 0.0049870942018269936,
+        0.004922394372461284, 0.004854228497033434, 0.0047828266186578285,
+        0.004708428413472686, 0.004631282717907955, 0.0045516469711464206,
+        0.004469786690431465, 0.0043859750872709555, 0.0043004929034875135,
+        0.004213628504308444, 0.0041256782182930146, 0.0040369468694207815,
+        0.003947748411509437, 0.0038584065531208434, 0.0037692552536123746,
+        0.0036806389770864395, 0.0035929126051624616, 0.003506440929187503,
+        0.0034215976598315095, 0.003338763906034487, 0.0032583260812815654,
+        0.00318067319636836, 0.0031061934955797336, 0.0030352703940373905,
+        0.002968277684470474, 0.0029055740074001705, 0.0028474966258700465,
+        0.002794354614696701, 0.0027464216612882834, 0.002703928771994638,
+        0.002667057268811395, 0.0026359325283833493, 0.0026106189398507626,
+        0.002591116526062206, 0.0025773595786447853, 0.002569217508646391,
+        0.002566497930019102, 0.002568951800455255, 0.00257628027348814,
+        0.0025881427921351104, 0.0026041658928187966, 0.0026239521908113907,
+        0.002647089075917584, 0.002673156742499025, 0.00270173529192308,
+        0.0027324107601958557, 0.002764780025445958, 0.002798454631217312,
+        0.0028330636189644893, 0.0028682554976924204, 0.002903699493635063,
+        0.002939086222202172, 0.0029741279133127167, 0.0030085583033781804,
+        0.0030421322865403604, 0.00307462539698782, 0.0031058331751134616,
+        0.0031355704545460526, 0.003163670594859868, 0.003189984676301337,
+        0.0032143806677395015, 0.003236742576517953, 0.0032569695882283863,
+        0.003274975204803525, 0.0032906863900847103, 0.0033040427326873865,
+        0.0033149956362687467, 0.003323507546957399, 0.003329551226953323,
+        0.003333109082019107, 0.0033341725489688893, 0.0033327415473474965,
+        0.0033288239973049607, 0.003322435403304845, 0.0033135985007059564,
+        0.0033023429596152265, 0.003288705137872283, 0.0032727278728054104,
+        0.003254460299874329, 0.0032339576856742517, 0.003211281263409656,
+        0.003186498060698903, 0.003159680712623444, 0.0031309072567896517,
+        0.0031002609113938697, 0.003067829841392252, 0.003033706921059424,
+        0.002997989503177113, 0.0029607792052872787, 0.0029221817218850112,
+        0.0028823066683205598, 0.0028412674577969156, 0.0027991812081448702,
+        0.0027561686704089465, 0.0027123541674402996, 0.0026678655284072127,
+        0.002622834004192916, 0.0025773941496315404, 0.0025316836602960065,
+        0.0024858431546263856, 0.002440015894840084, 0.002394347442593657,
+        0.002348985246578273, 0.002304078159382717, 0.002259775879687052,
+        0.002216228313768935, 0.0021735848477577166, 0.0021319935198946473,
+        0.002091600081089993, 0.002052546932942116, 0.002014971935576941,
+        0.001979007083787708, 0.001944777058470426, 0.0019123976713436076,
+        0.00188197423325707, 0.0018535998892397708, 0.0018273539754337597,
+        0.0018033004627113775, 0.0017814865578844332, 0.0017619415345844483,
+        0.0017446758615369676, 0.001729680685706588, 0.0017169277121280642,
+        0.0017063695022841738, 0.001697940190420387, 0.0016915565942606959,
+        0.0016871196755271298, 0.001684516288422825, 0.0016836211423619262,
+        0.0016842988995218844, 0.0016864063281800627, 0.0016897944387104082,
+        0.00169431053913961, 0.0016998001599015133, 0.0017061088111977513,
+        0.0017130835497995297, 0.0017205743441468726, 0.0017284352364723703,
+        0.001736525308204398, 0.00174470946006988, 0.001752859021492336,
+        0.0017608522054678242, 0.0017685744256823416, 0.001775918492461954,
+        0.0017827847038053523, 0.001789080847216714, 0.0017947221275163646,
+        0.001799631035229506, 0.0018037371694164129, 0.001806977027815453,
+        0.0018092937758863983, 0.0018106370047061397, 0.0018109624857648042,
+        0.0018102319286297283, 0.001808412745386567, 0.0018054778238562163,
+        0.0018014053100235414, 0.0017961783990013236, 0.0017897851332229866,
+        0.0017822182064207246, 0.0017734747722112426, 0.0017635562566512574,
+        0.0017524681747507834, 0.0017402199516391075, 0.0017268247495264004,
+        0.0017122993019597714, 0.0016966637569002495, 0.0016799415300406497,
+        0.00166215916945994, 0.0016433462323206347, 0.00162353517391508,
+        0.001602761248990924, 0.0015810624250445957, 0.0015584793070743173,
+        0.0015350550732313145, 0.001510835420803399, 0.0014858685220377546,
+        0.0014602049893259106, 0.0014338978493822023, 0.0014070025260549109,
+        0.0013795768314680474, 0.001351680965103836, 0.0013233775205221468,
+        0.0012947314992511436, 0.0012658103312486956, 0.0012366839011493077,
+        0.0012074245789748719, 0.0011781072534065033, 0.0011488093646716843,
+        0.00111961093275131, 0.0010905945748214893, 0.001061845503525718,
+        0.0010334514950457408, 0.0010055028126608055, 0.0009780920681347499,
+        0.000951313999599427, 0.0009252651411972658, 0.0009000433568405961,
+        0.0008757472088444267, 0.0008524751323985889, 0.000830324390207313,
+        0.0008093897887912224, 0.000789762150274064, 0.0007715265513244614,
+        0.0007547603644249965, 0.0007395311644537711, 0.0007258945932621198,
+        0.0007138923020875586, 0.0007035501115109821, 0.0006948765352195661,
+        0.0006878618034421373, 0.0006824774924136559, 0.0006786768200410019,
+        0.0006763956107240685, 0.0006755538728775657, 0.0006760578803912157,
+        0.0006778026121982699, 0.0006806743866294623, 0.0006845535299469457,
+        0.0006893169379378239, 0.0006948404201926248, 0.0007010007522518592,
+        0.0007076773957488058, 0.0007147538768072097, 0.0007221188362857497,
+        0.0007296667813653587, 0.0007372985771165047, 0.0007449217203275334,
+        0.0007524504374489968, 0.0007598056455536835, 0.0007669148106888298,
+        0.0007737117329216369, 0.000780136282258811, 0.0007861341048182262,
+        0.0007916563143216001, 0.0007966591802442584, 0.0008011038207875649,
+        0.000804955906234809, 0.0008081853761416466, 0.0008107661721827805,
+        0.0008126759872724616, 0.0008138960307559716, 0.0008144108089696451,
+        0.0008142079202475296, 0.0008132778634289492, 0.0008116138590129089,
+        0.0008092116822805712, 0.0008060695078474351, 0.0008021877652369038,
+        0.0007975690050834827, 0.0007922177755375132, 0.0007861405083344336,
+        0.000779345413850304, 0.0007718423843202303, 0.0007636429043080192,
+        0.0007547599674819034, 0.0007452079988211536, 0.0007350027815281601,
+        0.0007241613881393536, 0.000712702115620111, 0.0007006444244996013,
+        0.0006880088823483135, 0.0006748171121453054, 0.0006610917462012969,
+        0.0006468563864069625, 0.0006321355716037251, 0.0006169547529172346,
+        0.0006013402779322166, 0.0005853193847263471, 0.0005689202069901387,
+        0.0005521717918568831, 0.0005351041326095086, 0.0005177482191626564,
+        0.0005001361102205307, 0.00048230103220327594, 0.0004642775115853122,
+        0.0004461015491721612, 0.00042781084727950007, 0.0004094451037712761,
+        0.0003910463908506431, 0.00037265964142864654, 0.0003543332722377195,
+        0.0003361199806181457, 0.0003180777612186983, 0.0003002711989478251,
+        0.00028277310374521034, 0.00026566655658644757, 0.0002490474257426606,
+        0.00023302736977663866, 0.00021773723701245463, 0.0002033305479109753,
+        0.000189986334746581, 0.00017790994783580094, 0.00016732955727479168,
+        0.00015848532757656728, 0.0001516085160478358, 0.00014689037722805958,
+        0.00014444630715236518, 0.00014428676569294886, 0.00014630768020700463,
+        0.0001503056603662818, 0.00015601163576598316, 0.00016312948482811947,
+        0.0001713679608513, 0.0001804608721016354, 0.0001901762827509793,
+        0.00020031808011401135, 0.00021072332106568175, 0.00022125781346505696,
+        0.0002318113694250425, 0.00024229343096975148, 0.00025262933044342575,
+        0.00026275722216200984, 0.00027262562221839625, 0.00028219146038847604,
+        0.000291418546622521, 0.0003002763658148836, 0.0003087391293616422,
+        0.00031678502636004244, 0.00032439562965983247, 0.00033155542209325274,
+        0.0003382514161750161, 0.0003444728467601858, 0.0003502109209195621,
+        0.00035545861289108094, 0.00036021049474713835, 0.0003644625954875513,
+        0.00036821228284457597, 0.0003714581633113665, 0.0003741999967946778,
+        0.0003764386230559358, 0.00037817589763541176, 0.00037941463544839926,
+        0.00038015856061239165, 0.00038041226138275984, 0.00038018114934476805,
+        0.0003794714222234867, 0.0003782900298243158, 0.0003766446427936811,
+        0.00037454362391362754, 0.00037199600177585966, 0.0003690114466726663,
+        0.0003656002486098512, 0.0003617732973582496, 0.0003575420645157381,
+        0.00035291858759424927, 0.0003479154562193248, 0.0003425458006251324,
+        0.0003368232827164872, 0.00033076209008831513, 0.00032437693354077715,
+        0.0003176830487244827, 0.00031069620274450874, 0.0003034327067088109,
+        0.0002959094353842446, 0.00028814385543135247, 0.0002801540639303862,
+        0.00027195883936640563, 0.0002635777077201127, 0.0002550310269660095,
+        0.00024634009409655206, 0.00023752727981213344, 0.00022861619726416475,
+        0.00021963191275116984, 0.00021060120803337412, 0.0002015529059312796,
+        0.00019251827292605453, 0.0001835315142961119, 0.00017463037820276145,
+        0.00016585688377143243, 0.00015725818228583429, 0.00014888754613841596,
+        0.00014080545075874297, 0.00013308066113147868, 0.00012579114513609448,
+        0.00011902450105595716, 0.00011287740995425062, 0.00010745344530758845,
+        0.00010285850076423325, 9.919332266044392e-05, 9.654336160109371e-05,
+        9.4967393400872e-05, 9.448764073651012e-05, 9.508454539305313e-05,
+        9.6698194115775e-05, 9.923604430395083e-05, 0.00010258441480496156,
+        0.00010662045201532408, 0.00011122204382317858, 0.00011627457711798444,
+        0.0001216746345022094, 0.00012733134200952926, 0.0001331661992696381,
+        0.0001391120822283006, 0.00014511189511393568, 0.0001511171592058077,
+        0.00015708669023310482, 0.00016298543063846235, 0.0001687834541796511,
+        0.00017445513538501075, 0.0001799784654365308, 0.0001853344928232448,
+        0.00019050686766942804, 0.00019548147090734557, 0.00020024611225987965,
+        0.0002047902837089865, 0.0002091049576107157, 0.0002131824206987991,
+        0.00021701613696168816, 0.00022060063378263702, 0.00022393140688018134,
+        0.00022700484047857638, 0.00022981813987938104, 0.00023236927415252673,
+        0.00023465692713596877, 0.00023668045527850415, 0.00023843985114110056,
+        0.00023993571159829923, 0.00024116920995648507, 0.00024214207134921542,
+        0.00024285655089409313, 0.00024331541418500983, 0.0002435219197896552,
+        0.0002434798034850172, 0.00024319326402651116, 0.00024266695030167087,
+        0.00024190594976112578, 0.00024091577804420975, 0.00023970236976067735,
+        0.00023827207039410568, 0.0002366316293143523, 0.0002347881938933224,
+        0.00023274930473544681, 0.00023052289202334016, 0.00022811727300214586,
+        0.00022554115061565677, 0.00022280361332227915, 0.00021991413610595128,
+        0.00021688258269952766, 0.0002137192090261928, 0.00021043466783347744,
+        0.0002070400144699172, 0.00020354671369152816, 0.00019996664732492835,
+        0.00019631212250634, 0.0001925958801078356, 0.00018883110278662468,
+        0.00018503142191915738, 0.0001812109224387842], [3.374327462006686e-14,
+        1.0141694935976288e-13, 1.6965381408435747e-13, 2.388353558286598e-13,
+        3.093521842373039e-13, 3.816078775234035e-13, 4.560229795549833e-13,
+        5.330392677592272e-13, 6.131243083126326e-13, 6.967763902401513e-13,
+        7.845299081753303e-13, 8.769612822284214e-13, 9.746955002607617e-13,
+        1.0784134064107396e-12, 1.1888598426771681e-12, 1.3068527977658835e-12,
+        1.4332937166371816e-12, 1.5691791606017089e-12, 1.7156140370925539e-12,
+        1.8738266408714593e-12, 2.045185814034115e-12, 2.231220546547316e-12,
+        2.4336424297595107e-12, 2.6543714217886035e-12, 2.895565471496146e-12,
+        3.1596546406843316e-12, 3.4493804885384314e-12, 3.7678415966541e-12,
+        4.1185463019487635e-12, 4.505473867758742e-12, 4.933145596307431e-12,
+        5.406707611029668e-12, 5.932027428713679e-12, 6.5158067963224035e-12,
+        7.1657137936273104e-12, 7.890537755797179e-12, 8.700371321400984e-12,
+        9.606824736356152e-12, 1.0623278648493507e-11, 1.1765182854298824e-11,
+        1.3050410099809812e-11, 1.4499675888052157e-11, 1.613703769021208e-11,
+        1.7990489783487316e-11, 2.0092673624474065e-11, 2.248172795828058e-11,
+        2.520230860556275e-11, 2.83068143469484e-11, 3.1856864289304545e-11,
+        3.5925082271770194e-11, 4.059725756993567e-11, 4.5974967708629645e-11,
+        5.217877023950778e-11, 5.935209715054972e-11, 6.7666019148529e-11,
+        7.732508990841251e-11, 8.857453534152358e-11, 1.0170912228174612e-10,
+        1.170841312843611e-10, 1.3512897314547036e-10, 1.5636413804488113e-10,
+        1.8142235953960807e-10, 2.1107512687058606e-10, 2.462660073037644e-10,
+        2.881526704698312e-10, 3.381600730127381e-10, 3.980480092875475e-10,
+        4.699972264384627e-10, 5.567196246869845e-10, 6.615998319855188e-10,
+        7.888778213072527e-10, 9.43885451435033e-10, 1.133354173692524e-09,
+        1.3658170921365087e-09, 1.6521367248778128e-09, 2.0062010528771276e-09,
+        2.445846036622729e-09, 2.9940845049255936e-09, 3.6807518077562537e-09,
+        4.544721658510474e-09, 5.63690669865327e-09, 7.024345750933946e-09,
+        8.795805638699e-09, 1.1069508124332106e-08, 1.4003859639423207e-08,
+        1.781245512877124e-08, 2.278521246086684e-08, 2.931837117230826e-08,
+        3.7957417049295985e-08, 4.9459023357685315e-08, 6.488123244695497e-08,
+        8.571599242890761e-08, 1.1408588612736982e-07, 1.5303923407500773e-07,
+        2.069977439200334e-07, 2.8244370570291963e-07, 3.889884407511889e-07,
+        5.410563635144125e-07, 7.605786296024916e-07, 1.0813704942008561e-06,
+        1.5563682274353882e-06, 2.269819992341055e-06, 3.358247896524456e-06,
+        5.047316997343874e-06, 7.718331472441427e-06, 1.2031583112346027e-05,
+        1.9162533489032885e-05, 3.127071738465789e-05, 5.247047369392347e-05,
+        9.094184158275795e-05, 0.00016379921906362502, 0.00030916269895662346,
+        0.0006189638946784566, 0.0013396547505221414, 0.003239802874096477,
+        0.009376745389051434, 0.03983998994131115, 1.0230972533264857, 0.23658086086814883,
+        0.60253882850002, 0.8027324092451283, 0.47976681524870923, 0.5966161017760422,
+        1.2653082100400403, 2.0243261282756633, 1.2557610643247081, 1.2825110537623947,
+        2.1575943048038995, 3.5151328373777533, 3.913363851855454, 2.8767267190055925,
+        1.846208493721509, 1.500041231927762, 1.4775342175275623, 1.7203057077897757,
+        2.316269832097474, 2.9125175755167794, 2.358294608424995, 1.7401091214357478,
+        1.4517255152884199, 1.3762152268889782, 1.465693601932451, 1.7382361449264294,
+        2.1908771695604488, 2.402085418204379, 1.9873524762282866, 1.5536952003493214,
+        1.3123222350366366, 1.2184431182748283, 1.2394837326917099, 1.3751104211859109,
+        1.6306082368530836, 1.8779347238889164, 1.7602797078850734, 1.3991423196141968,
+        1.119680497068247, 0.9607458670670642, 0.7114528031279506, 0.6189970569470606,
+        0.5735108697756778, 0.5373195242822607, 0.4900949652542053, 0.42689676857856335,
+        0.3586290151999086, 0.2978080993950775, 0.24938365316146527, 0.21271192409686576,
+        0.18529931502969058, 0.164557448181518, 0.14820101910082384, 0.13415714677979249,
+        0.12045316169231038, 0.10541590277522164, 0.08833017783744262, 0.06999096532955341,
+        0.05217957162843289, 0.036407067366544886, 0.023265912072724274,
+        0.012642433904697492, 0.00426505099857664, 0.003599342384943757,
+        0.009185229257394279, 0.014133023672193469, 0.01850037965452101,
+        0.022461429508791545, 0.026172536125300773, 0.029772712138953217,
+        0.033390230809624846, 0.037148203109539014, 0.04116849479646549,
+        0.04557375740587194, 0.05048674796680825, 0.056025101051708034,
+        0.06228842845894224, 0.06933352155336309, 0.07713411200685741, 0.08552769626146633,
+        0.09416787201206898, 0.10252404688109053, 0.1099771373275853, 0.11601040885601598,
+        0.12039964544860836, 0.1232733334470385, 0.12501192880295653, 0.1260775271313735,
+        0.12687879569857477, 0.127708162971456, 0.12873345333093622, 0.13001460993686273,
+        0.13152685039976347, 0.13318374942578978, 0.13486042921915256, 0.13641848518011046,
+        0.13773227851640626, 0.13871293091829145, 0.13932427155753827, 0.13958607475442578,
+        0.13956403207769985, 0.1393505473562325, 0.13904282836585563, 0.13872401671506396,
+        0.13845054404583762, 0.1382464002838508, 0.13810356912363428, 0.13798746234786174,
+        0.13784616281754922, 0.13762211596196916, 0.1372644298696195, 0.1367394388306606,
+        0.13603717813152985, 0.135172265700957, 0.13417922409407373, 0.13310384592870997,
+        0.13199310186211607, 0.13088604027279227, 0.1298073897484571, 0.1287646405850158,
+        0.12774861549746422, 0.12673703682904933, 0.12570026407253998, 0.12460810222229521,
+        0.12343636905067491, 0.12217187915629751, 0.12081479454062939, 0.11937792054945764,
+        0.11788331405963569, 0.1163572255048206, 0.11482468620058292, 0.11330493530761761,
+        0.11180849160777853, 0.11033620844906411, 0.10888024449714631, 0.10742658348195809,
+        0.10595852887970929, 0.10446046912355204, 0.1029211723169877, 0.10133596545062187,
+        0.0997074001074892, 0.0980443630398309, 0.09635995413946734, 0.0946687102300913,
+        0.09298383045965777, 0.0913149635598846, 0.08966691371154412, 0.08803938968819676,
+        0.08642771848140256, 0.08482429353085168, 0.08322043132414154, 0.08160826715081686,
+        0.07998233505223329, 0.07834055336263165, 0.0766844694261433, 0.07501877933205926,
+        0.07335028969665523, 0.07168658818837544, 0.0700347155500078, 0.06840008860270846,
+        0.06678583572170159, 0.06519260453750829, 0.06361881074391891, 0.06206122994744303,
+        0.060515794664009526, 0.058978444387754646, 0.057445885410055436,
+        0.05591614613440955, 0.05438885858594148, 0.05286525022129083, 0.05134788170415208,
+        0.04984020538352191, 0.04834603857498024, 0.04686904388844983, 0.04541229024843746,
+        0.04397794077960632, 0.04256708570731138, 0.04117971578662783, 0.03981481715746474,
+        0.03847056157029865, 0.037144564340242284, 0.03583418342424333,
+        0.034536834324683525, 0.03325029590720182, 0.03197298178791558,
+        0.03070415196709477, 0.02944404162511326, 0.02819389013612324, 0.026955863799142346,
+        0.025732879508525645, 0.024528350868815572, 0.023345889786958902,
+        0.022189002399556016, 0.021060817055672358, 0.01996387459291298,
+        0.018899999633732973, 0.017870259020029092, 0.0168750024037174,
+        0.015913972029644702, 0.0149864643732577, 0.014091525135426625,
+        0.013228160349056639, 0.012395549154252082, 0.011593247446966036,
+        0.010821375570519303, 0.010080786977410197, 0.009373217675234451,
+        0.008701417105523756, 0.008069258086334392, 0.007481813907051385,
+        0.006945371560154026, 0.006467320040621079, 0.006055817655990823,
+        0.005719125730849507, 0.005464545437431608, 0.005297058834626118,
+        0.005218028855115823, 0.005224481314992621, 0.005309348553364141,
+        0.005462606893914385, 0.005672824029796785, 0.005928561492131805,
+        0.006219314232087057, 0.006535956231675749, 0.006870823441094638,
+        0.007217595516208601, 0.007571100814975453, 0.007927118843320629,
+        0.008282214291856726, 0.008633611084085483, 0.008979100700555461,
+        0.00931697284705998, 0.009645955626903475, 0.00996515487340378,
+        0.010273986726874521, 0.010572102585211886, 0.0108593100715169,
+        0.011135496785733875, 0.011400564853486088, 0.011654383602232275,
+        0.0118967653410487, 0.01212746573375979, 0.012346206291966038, 0.012552712821133677,
+        0.012746760950091737, 0.012928218750352424, 0.01309707722000325,
+        0.01325346199562846, 0.013397623560450003, 0.013529907615550538,
+        0.013650711231050586, 0.013760433083796635, 0.013859427030406992,
+        0.013947967377334966, 0.014026231774392944, 0.014094304212112552,
+        0.014152196812947626, 0.014199885652681257, 0.014237353344772004,
+        0.014264630018484386, 0.014281824835125363, 0.014289142220070574,
+        0.014286880128236, 0.014275411249323586, 0.01425515134276346, 0.014226521206962937,
+        0.014189909714710824, 0.014145644789857198, 0.014093977369047828,
+        0.014035080718139855, 0.013969064499760443, 0.013896000267701878,
+        0.01381595307175503, 0.013729012929728529, 0.01363532020566314,
+        0.013535080343125477, 0.013428565641879239, 0.013316104364023168,
+        0.013198059878368968, 0.013074804318748098, 0.012946692026678112,
+        0.012814037780517826, 0.012677103610690015, 0.01253609616322383,
+        0.012391174488913517, 0.012242466202342707, 0.012090088511772908,
+        0.011934169906396955, 0.011774868395405156, 0.011612383072067136,
+        0.01144695722368548, 0.011278872922059426, 0.011108438656466577,
+        0.010935972798392576, 0.010761786293958134, 0.01058616789535576,
+        0.010409374535127679, 0.010231628301845628, 0.010053120144528001,
+        0.009874019174410435, 0.009694485472104327, 0.009514683799521155,
+        0.009334795621878696, 0.009155027337131146, 0.008975613463528499,
+        0.00879681457097066, 0.008618910745054765, 0.008442192153221782,
+        0.008266948703236639, 0.008093460793331772, 0.007921992783952028,
+        0.007752790174672375, 0.007586080696672084, 0.00742207877915565,
+        0.007260992259221551, 0.007103029864808246, 0.0069484079565834776,
+        0.006797355247570782, 0.00665011466746773, 0.006506942102009997,
+        0.00636810230327319, 0.0062338627265994696, 0.006104486330198558,
+        0.005980224436470966, 0.005861310612918558, 0.005747956231859088,
+        0.005640347985270248, 0.005538647242813983, 0.0054429908169505254,
+        0.005353492490313544, 0.005270244592993807, 0.005193318988486877,
+        0.005122767013853268, 0.005058618179491587, 0.005000877715823858,
+        0.0049495233082543656, 0.004904501545672921, 0.004865724695382932,
+        0.00483306840056998, 0.004806370783630473, 0.004785433253588883,
+        0.004770023088886968, 0.004759877633800456, 0.004754709740679196,
+        0.004754213940208204, 0.004758072748434186, 0.004765962532267785,
+        0.004777558451788543, 0.0047925381623165906, 0.004810584164949469,
+        0.004831384906993872, 0.004854634918119858, 0.004880034393484906,
+        0.00490728868181235, 0.0049361080984766156, 0.004966208370238008,
+        0.004997311851630589, 0.0050291494644827475, 0.005061463136698322,
+        0.005094008386901985, 0.00512655664202813, 0.005158896896786027,
+        0.005190836423011812, 0.005222200394121473, 0.005252830474805853,
+        0.005282582603081112, 0.005311324326750721, 0.005338932124147453,
+        0.005365289127720927, 0.005390283581931309, 0.0054138082217802495,
+        0.005435760582754985, 0.005456044080200223, 0.005474569557854332,
+        0.005491256926416488, 0.005506036507205899, 0.005518849762480424,
+        0.005529649219266298, 0.005538397551918748, 0.005545065949774133,
+        0.005549632029126754, 0.0055520776292581515, 0.005552386846786418,
+        0.005550544610621335, 0.005546535993326708, 0.005540346315287449,
+        0.005531961952720044, 0.005521371636204486, 0.005508567945520813,
+        0.005493548682413945, 0.005476317838592166, 0.005456885962716766,
+        0.005435269850040158, 0.005411491607716248, 0.0053855772634233065,
+        0.005357555163804231, 0.005327454439285899, 0.005295303789644167,
+        0.005261130776553286, 0.0052249617100928675, 0.005186822105285791,
+        0.005146737583058418, 0.00510473501569683, 0.005060843682248386,
+        0.005015096208893904, 0.004967529119842848, 0.004918182903776335,
+        0.004867101594316995, 0.004814331952079253, 0.004759922404305212,
+        0.004703921934824937, 0.004646379116745394, 0.004587341444987108,
+        0.004526855064324655, 0.004464964912853341, 0.004401715226091408,
+        0.004337150286244707, 0.004271315264273999, 0.004204256995661113,
+        0.004136024552358767, 0.004066669519083786, 0.003996245940915271,
+        0.003924809971301136, 0.003852419301826409, 0.0037791324903040007,
+        0.0037050083156339323, 0.0036301052762371016, 0.0035544813177970764,
+        0.0034781938314486075, 0.0034012999159939547, 0.003323856853940824,
+        0.0032459227204987427, 0.003167557030569241, 0.00308882133247192,
+        0.003009779678003565, 0.002930498929865144, 0.0028510489045975077,
+        0.0027715023846521555, 0.002691935060764043, 0.0026124254820267282,
+        0.002533055093750004, 0.0024539084336639805, 0.0023750735378964423,
+        0.0022966425844329315, 0.002218712777595829, 0.002141387457422175,
+        0.0020647774056213315, 0.0019890023161192763, 0.001914192402538518,
+        0.0018404901254592974, 0.0017680520334962717, 0.0016970507211465588,
+        0.0016276769049144385, 0.001560141603891155, 0.0014946783733928103,
+        0.0014315454767366198, 0.001371027784326754, 0.0013134380593471185,
+        0.0012591171287728957, 0.0012084322609866836, 0.001161772912654733,
+        0.0011195429298540825, 0.0010821483867935263, 0.0010499806335975868,
+        0.0010233948881414815, 0.0010026858275237844, 0.0009880629020730673,
+        0.0009796290842923106, 0.0009773669591587333, 0.0009811351218153616,
+        0.0009906758900999062, 0.0010056329842945703, 0.0010255759181006807,
+        0.001050026998044528, 0.0010784871422410366, 0.0011104578370676244,
+        0.0011454579075000362, 0.0011830349439834475, 0.0012227719969129943,
+        0.001264290513312798, 0.0013072505519650475, 0.001351349199583472,
+        0.0013963179238832735, 0.0014419194048184742, 0.0014879442156332265,
+        0.0015342075913376124, 0.0015805464238474944, 0.0016268165538949615,
+        0.001672890383658728, 0.001718654804568547, 0.0017640094168837428,
+        0.001808865008325764, 0.0018531422552040535, 0.0018967706095727064,
+        0.0019396873386703887, 0.0019818366871115463, 0.002023169137324687,
+        0.0020636407489237054, 0.0021032125626094054, 0.0021418500584829935,
+        0.002179522662357763, 0.002216203296309517, 0.002251867971830469,
+        0.0022864954252915424, 0.0023200667961264265, 0.0023525653485445414,
+        0.0023839762371335683, 0.002414286316275581, 0.00244348399195285,
+        0.0024715591132895075, 0.002498502899222497, 0.002524307894088582,
+        0.0025489679441729925, 0.0025724781862045305, 0.0025948350382800894,
+        0.002616036184288012, 0.0026360805443987677, 0.002654968226641935,
+        0.0026727004578547577, 0.002689279495689814, 0.002704708526795509,
+        0.00271899155886191, 0.002732133315811096, 0.0027441391455472566,
+        0.002755014948306796, 0.0027647671310561056, 0.0027734025897290207,
+        0.0027809287171616766, 0.0027873534308857323, 0.0027926852120490338,
+        0.0027969331452898567, 0.0028001069494529764, 0.0028022169908017685,
+        0.0028032742734042915, 0.002803290405286336, 0.002802277543008616,
+        0.0028002483209320084, 0.0027972157739226157, 0.0027931932632827864,
+        0.0027881944150518726, 0.002782233077675569, 0.00277532330276632,
+        0.0027674793488403266, 0.0027587157041854137, 0.0027490471219784795,
+        0.002738488659022641, 0.0027270557091332967, 0.00271476402346806,
+        0.002701629712525437, 0.0026876692278542426, 0.0026728993250161944,
+        0.0026573370124659632, 0.002640999493272291, 0.0026239041075650092,
+        0.002606068283217034, 0.0025875095006454916, 0.0025682452750380317,
+        0.0025482931562823717, 0.0025276707439525516, 0.002506395712303725,
+        0.002484485838844042, 0.0024619590297594975, 0.0024388333363225515,
+        0.002415126958318206, 0.002390858232793008, 0.002366045609151639,
+        0.002340707613758702, 0.0023148628089139822, 0.0022885297517155757,
+        0.0022617269581661817, 0.002234472876639646, 0.002206785873172038,
+        0.0021786842289466574, 0.0021501861483282265, 0.0021213097742433656,
+        0.002092073206748632, 0.002062494520303375, 0.002032591776002026,
+        0.002002383025929009, 0.001971886308447875, 0.001941119634801713,
+        0.001910100968798048, 0.0018788482023985808, 0.0018473791305645216,
+        0.0018157114285738633, 0.001783862634472124, 0.0017518501384026282,
+        0.0017196911793460356, 0.0016874028486995216, 0.0016550020992684112,
+        0.001622505757525543, 0.0015899305368582454, 0.0015572930497104829,
+        0.001524609816875377, 0.0014918972730927535, 0.0014591717686854074,
+        0.001426449567734801, 0.0013937468439336259, 0.001361079675504571,
+        0.0013284640407610594, 0.0012959158157429247, 0.0012634507751860301,
+        0.0012310845976811625, 0.0011988328755655215, 0.001166711129743918,
+        0.0011347348294082087, 0.0011029194165274251, 0.0010712803349023615,
+        0.0010398330636727526, 0.0010085931552853663, 0.0009775762781378422,
+        0.0009467982642524214, 0.0009162751626403455, 0.0008860232992125086,
+        0.0008560593444379894, 0.0008264003901822021, 0.0007970640376760267,
+        0.000768068498928349, 0.0007394327144223647, 0.0007111764905969129,
+        0.0006833206611345162, 0.0006558872768347052, 0.0006288998294678091,
+        0.0006023835156542966, 0.0005763655473860883, 0.0005508755161336329,
+        0.0005259458176151421, 0.0005016121436163485, 0.0004779140457441194,
+        0.0004548955725520091, 0.00043260597533907786, 0.00041110046734766216,
+        0.0003904410041675968, 0.00037069702705362444, 0.00035194607309137237,
+        0.00033427410441304675, 0.00031777534410381273, 0.00030255133612707883,
+        0.00028870888944950503, 0.0002763565576498819, 0.00026559939640110377,
+        0.00025653198699028, 0.00024923013860751823, 0.00024374222670761533,
+        0.00024008161343478892, 0.00023822176901687288, 0.00023809536329159677,
+        0.00023959774162510855, 0.0002425941412889676, 0.00024692917857195785,
+        0.0002524368487137548, 0.00025894954146637365, 0.0002663051559054596,
+        0.0002743520132153368, 0.00028295172405197407, 0.0002919804108198332,
+        0.00030132875099781354, 0.0003109012645653115, 0.0003206151787997486,
+        0.00033039910756418715, 0.0003401916996452831, 0.00034994034809875395,
+        0.0003596000088629284, 0.0003691321486496153, 0.00037850382492162865,
+        0.0003876868912134297, 0.0003966573164027309, 0.0004053946047890314,
+        0.0004138813038489617, 0.00042210258734271287, 0.0004300459026708047,
+        0.00043770067268824274, 0.0004450580434267762, 0.00045211067034654854,
+        0.0004588525367461553, 0.00046527879891988767, 0.00047138565345365306,
+        0.0004771702228428536, 0.0004826304562968797, 0.00048776504322309007,
+        0.000492573337430407, 0.0004970552905453362, 0.0005012113935058216,
+        0.0005050426252369313, 0.0005085504077852698, 0.0005117365672609546,
+        0.0005146032999446287, 0.0005171531428999719, 0.0005193889484031175,
+        0.0005213138614712652, 0.0005229312998258289, 0.0005242449356622972,
+        0.000525258678731519, 0.0005259766603768684, 0.0005264032183225392,
+        0.0005265428821753265, 0.0005264003597037077, 0.0005259805240573435,
+        0.0005252884020958495, 0.0005243291639769815, 0.0005231081140746538,
+        0.0005216306832075037, 0.0005199024220375773, 0.0005179289954249986,
+        0.0005157161774512959, 0.0005132698468218011, 0.0005105959823767739,
+        0.0005077006585205235, 0.0005045900404661723, 0.0005012703793121977,
+        0.0004977480070511115, 0.0004940293316919409, 0.0004901208327116648,
+        0.0004860290570403412, 0.0004817606157407624, 0.0004773221814810895,
+        0.0004727204867919436, 0.000467962323039787, 0.00046305453995907546,
+        0.00045800404557142784, 0.00045281780629750765, 0.0004475028471082216,
+        0.0004420662516270294, 0.0004365151621498167, 0.0004308567796399872,
+        0.00042509836380961996, 0.0004192472334410126, 0.00041331076711873893,
+        0.00040729640450213537, 0.0004012116482652038, 0.0003950640667194305,
+        0.0003888612971200028, 0.000382611049550001, 0.0003763211112679119,
+        0.00036999935135592735, 0.00036365372551653587, 0.0003572922808675061,
+        0.0003509231606385455, 0.0003445546086748647, 0.0003381949737071878,
+        0.00033185271333725585, 0.0003255363976932462, 0.00031925471267012565,
+        0.00031301646260846195, 0.0003068305721988465, 0.0003007060873097658,
+        0.0002946521743342271, 0.00028867811758006396, 0.00028279331412156734,
+        0.0002770072655042183, 0.00027132956558871443, 0.00026576988384216705,
+        0.0002603379433316004, 0.0002550434926950821, 0.00024989627138459047,
+        0.00024490596752817706, 0.000240082167843883, 0.00023543429916539815,
+        0.0002309715613307267, 0.00022670285142085606, 0.00022263667968296116,
+        0.0002187810778585948, 0.00021514350111381174, 0.00021173072529776036,
+        0.00020854874181256048, 0.00020560265289814274, 0.00020289657062746977,
+        0.00020043352323905657, 0.00019821537261513852, 0.00019624274666536103,
+        0.00019451499006411805, 0.00019303013622611287, 0.00019178490261502335,
+        0.00019077471045593765, 0.00018999372885055278, 0.0001894349421164113,
+        0.00018909023813874168, 0.00018895051458930054, 0.00018900579919613997,
+        0.00018924537983221472, 0.00018965794005915867, 0.00019023169590847572,
+        0.000190954530045891, 0.0001918141199994935, 0.0001927980577901846,
+        0.00019389395898191883, 0.0001950895598577291, 0.00019637280205796366,
+        0.00019773190454623463, 0.00019915542322742035, 0.00020063229886208201,
+        0.0002021518941694916, 0.0002037040211547449, 0.00020527895975859935,
+        0.000206867468960374, 0.00020846079142031973, 0.0002100506526990712,
+        0.00021162925601031951, 0.00021318927338614466, 0.00021472383402945243,
+        0.00021622651055172587, 0.00021769130368882412, 0.00021911262601105589,
+        0.0002204852850474145, 0.0002218044661728565, 0.00022306571552576984,
+        0.00022426492316029493, 0.0002253983065759775, 0.00022646239472750985,
+        0.00022745401257126272, 0.0002283702661858891, 0.00022920852848652337,
+        0.00022996642554365033, 0.00023064182351256033, 0.00023123281618199246,
+        0.0002317377131493418, 0.00023215502862897696, 0.00023248347089248995,
+        0.00023272193233846505, 0.00023286948017878518, 0.00023292534770869998,
+        0.00023288892613316703, 0.00023275975689935382, 0.00023253752449066607,
+        0.00023222204962631708, 0.00023181328283000926, 0.0002313112983189123,
+        0.0002307162881900628, 0.00023002855688389405, 0.0002292485159166134,
+        0.00022837667887820818, 0.00022741365669996552, 0.00022636015319587455,
+        0.00022521696087220942, 0.00022398495700531073, 0.00022266509997166827,
+        0.0002212584258120114, 0.00021976604500282401, 0.00021818913941426662,
+        0.00021652895942523686, 0.00021478682117490814, 0.00021296410393810913,
+        0.00021106224761636817, 0.00020908275034315762, 0.0002070271662213662,
+        0.00020489710318841284, 0.00020269422104505168, 0.00020042022964316848,
+        0.00019807688725801922, 0.00019566599914624396, 0.000193189416292869,
+        0.00019064903435215107, 0.00018804679277328293, 0.00018538467411136363,
+        0.00018266470352588793, 0.00017988894846870877, 0.00017705951857646714,
+        0.0001741785657869937, 0.00017124828470677393, 0.00016827091326669752,
+        0.0001652487337111652, 0.0001621840739642208, 0.00015907930943078073,
+        0.00015593686528853114, 0.00015275921933643747, 0.0001495489054595272,
+        0.00014630851780189665, 0.00014304071572309148, 0.00013974822964750092,
+        0.0001364338679299136, 0.00013310052488219094, 0.00012975119013490554,
+        0.0001263889595411179, 0.0001230170478669947, 0.00011963880354970792,
+        0.00011625772585675828, 0.00011287748482065228, 0.00010950194438867431,
+        0.00010613518927242935, 0.0001027815560540292, 9.944566914966247e-05,
+        9.613248228885154e-05, 9.284732619620992e-05], [9.489071882990918e-14,
+        2.852368545907373e-13, 4.772829823503451e-13, 6.721820568992349e-13,
+        8.711167679015274e-13, 1.0753121175723575e-12, 1.2860485571966076e-12,
+        1.5046760641181082e-12, 1.732629254527475e-12, 1.9714438457501e-12,
+        2.2227747279361617e-12, 2.488415967793271e-12, 2.77032306951918e-12,
+        3.070637942726709e-12, 3.3917169953725847e-12, 3.736162926675599e-12,
+        4.106860817784475e-12, 4.5070192531455335e-12, 4.940217326957038e-12,
+        5.410458498151699e-12, 5.922232502497708e-12, 6.480586635477849e-12,
+        7.091208064347772e-12, 7.760519058723576e-12, 8.495787403333154e-12,
+        9.305254671995857e-12, 1.0198285584174185e-11, 1.118554221511579e-11,
+        1.2279187656116629e-11, 1.3493124526401509e-11, 1.4843274956364505e-11,
+        1.6347909823466027e-11, 1.8028036816887566e-11, 1.990785873146473e-11,
+        2.201531593653955e-11, 2.4382729822927514e-11, 2.7047567810154163e-11,
+        3.005335487550631e-11, 3.345076231326556e-11, 3.729891116718882e-11,
+        4.166693662753679e-11, 4.663587019134274e-11, 5.230091011938795e-11,
+        5.877416734170367e-11, 6.618799558035935e-11, 7.469904083865149e-11,
+        8.44931803363666e-11, 9.579156305725844e-11, 1.0885802100751116e-10,
+        1.240081895175754e-10, 1.4162076744297536e-10, 1.6215146518416183e-10,
+        1.8615034091317295e-10, 2.14283424777241e-10, 2.4735979007131683e-10,
+        2.8636557161078636e-10, 3.325068833449443e-10, 3.872641828654102e-10,
+        4.5246143019307545e-10, 5.303544552114862e-10, 6.237443907438723e-10,
+        7.361239850780383e-10, 8.71867278938924e-10, 1.0364768056209557e-09,
+        1.2369075607034502e-09, 1.4819940890553448e-09, 1.7830170247431323e-09,
+        2.154459601741655e-09, 2.6150249763792276e-09, 3.1890146161129388e-09,
+        3.908211077055887e-09, 4.814472304814778e-09, 5.96334042510563e-09,
+        7.429114006812285e-09, 9.312059031358516e-09, 1.1748790724471104e-08,
+        1.4927433467037835e-08, 1.9110114346286094e-08, 2.4666953135813743e-08,
+        3.2128522142353134e-08, 4.2268848573131044e-08, 5.6240696935604896e-08,
+        7.580417316666186e-08, 1.0373079853382843e-07, 1.4455998501153774e-07,
+        2.0612671430078944e-07, 3.029845965973817e-07, 4.6532320489958665e-07,
+        7.684447398262621e-07, 1.4851504480784554e-06, 7.775837631884214e-06,
+        3.4407148128431454e-06, 3.0788829762166794e-06, 3.258818290733597e-06,
+        3.7014917168285965e-06, 4.384403432797052e-06, 5.350336838297002e-06,
+        6.685580238402496e-06, 8.526052456023382e-06, 1.1077024914207207e-05,
+        1.4647909600949463e-05, 1.970996252775813e-05, 2.6992227757710012e-05,
+        3.764391464692145e-05, 5.3515778788747716e-05, 7.766138144884732e-05,
+        0.00011525871552788061, 0.00017536727476370214, 0.00027442166635680085,
+        0.00044353031746830585, 0.0007446564097185973, 0.0013092090476287278,
+        0.0024390391545493764, 0.004905497122939002, 0.011004932055370268,
+        0.029482000992857936, 0.11563853895319001, 2.732521321110213, 0.5791026043870786,
+        1.3450828889750528, 1.6242100185566206, 0.8729354000297638, 0.9660804995654968,
+        1.7975150996519422, 2.4706419575272673, 1.2726452388315594, 1.0099844052562945,
+        1.0795995800138873, 1.4988689589718374, 2.3978640145625287, 1.9221807082842568,
+        1.277459777164595, 1.0546005396709395, 1.046017793676741, 1.2204352720098466,
+        1.642001616311435, 2.059575405212211, 1.6617657403926298, 1.2210516614564035,
+        1.0140929381360055, 0.9568791053522144, 1.0143877332332754, 1.1976516878254435,
+        1.5032210554543757, 1.6418998533929692, 1.3539582069953617, 1.0556953020332662,
+        0.889986852684063, 0.8254942997815451, 0.8398327319036847, 0.9330692820476477,
+        1.1098606760056078, 1.2848443222187325, 1.2139383087371574, 0.9763217804712756,
+        0.7954107468917664, 0.7044117062572836, 0.5257096085812741, 0.45049174587457963,
+        0.4149010825504915, 0.3885865243002343, 0.35602060826269605, 0.3129737516675373,
+        0.2666786844220206, 0.22585318201863372, 0.194089732371335, 0.17110528200338365,
+        0.15533104582599216, 0.14513583391215867, 0.1390730095758196, 0.13572272782070113,
+        0.13343455911601104, 0.13028017862127633, 0.12460284309885439, 0.11599626873491073,
+        0.10556243676274117, 0.09495591728567516, 0.08536988322152625, 0.07729765935703524,
+        0.0707676147982843, 0.06560724672988831, 0.06159816084486689, 0.058542982566228995,
+        0.05628617531033701, 0.05471533736984248, 0.05375580173672149, 0.05336395387857723,
+        0.053521265661793466, 0.054229514929995476, 0.055506906807488224,
+        0.05738431308207587, 0.05990033750849637, 0.06309325626924144, 0.06698709432939569,
+        0.07156862334195241, 0.07675331885234189, 0.082344189270765, 0.08800092787387025,
+        0.09325430512512659, 0.09760068451793284, 0.10066447774469459, 0.10234051147516388,
+        0.10281529672749917, 0.10245933688023784, 0.10167815291162044, 0.10080673301508937,
+        0.10006915546520193, 0.09958203717008432, 0.09937531466086504, 0.09941520405337449,
+        0.09962478264212384, 0.09990289742901737, 0.10014301342103385, 0.10025197921125224,
+        0.10016627057548225, 0.09986189257206227, 0.09935505401815621, 0.09869369511962969,
+        0.09794310674736555, 0.09717031242860465, 0.0964311318447118, 0.09576192565565667,
+        0.09517626005979235, 0.094665787635435, 0.09420441733227647, 0.09375489182923745,
+        0.09327682182227455, 0.09273494083654009, 0.09210603929247546, 0.09138306317403402,
+        0.09057544947004241, 0.0897057960638887, 0.08880398614843735, 0.08790044664590757,
+        0.08702015196426266, 0.08617847293066713, 0.08537934561048785, 0.08461573430060708,
+        0.08387204296354746, 0.08312792245028913, 0.08236275184128215, 0.08155994007481844,
+        0.08071017776922708, 0.07981296051451457, 0.07887611428689632, 0.07791356555552136,
+        0.07694202340638805, 0.07597742853231086, 0.07503194733290042, 0.07411203670180849,
+        0.07321780267185185, 0.07234361362649075, 0.07147973474707306, 0.07061461465736758,
+        0.06973736735194168, 0.06883996374050101, 0.0679187042511058, 0.06697470095348451,
+        0.06601332939426598, 0.06504285111603879, 0.06407258098416886, 0.06311103094708612,
+        0.062164405284116764, 0.06123569280167018, 0.06032445046941161,
+        0.05942723828435298, 0.0585385626918849, 0.05765211759974334, 0.05676207760471471,
+        0.0558642011413787, 0.05495654664147234, 0.05403968997287195, 0.0531164403571933,
+        0.05219115715322823, 0.05126884302203328, 0.05035421327348537, 0.04945091760932715,
+        0.04856103438976653, 0.047684889532804905, 0.04682118916291646,
+        0.0459674066105124, 0.045120333159924815, 0.04427668769988146, 0.043433682037426674,
+        0.04258945508876084, 0.04174331819423423, 0.04089579077923707, 0.040048443358940915,
+        0.039203595515606815, 0.03836393396762369, 0.037532118132301784,
+        0.03671043003532313, 0.035900507276440737, 0.03510317801424507,
+        0.03431840018813599, 0.03354529578026752, 0.03278226492929623, 0.03202716267036699,
+        0.031277520982957725, 0.030530798821002854, 0.029784641802577918,
+        0.029037131196544736, 0.02828699973936103, 0.027533791248277564,
+        0.026777943710238877, 0.02602078243353553, 0.02526442064329606,
+        0.024511577690956743, 0.023765337014066037, 0.023028874209691103,
+        0.02230518824903562, 0.021596865700402756, 0.020905900202815728,
+        0.020233579583925913, 0.019580443246982004, 0.018946304440453015,
+        0.01833032655356229, 0.017731139628373745, 0.017146982360969783,
+        0.01657585536129158, 0.016015672844215272, 0.015464401923574182,
+        0.014920181102263898, 0.014381412299953596, 0.013846823636827259,
+        0.013315502954198984, 0.012786904369578897, 0.01226083177828824,
+        0.01173740399920731, 0.011217006339944904, 0.01070023297078197,
+        0.010187824011330891, 0.00968060090837666, 0.009179403642767134,
+        0.008685033448318738, 0.008198204846136039, 0.0077195106417965505,
+        0.007249402910244726, 0.006788191890130496, 0.006336063236861347,
+        0.00589311251503525, 0.005459394468509546, 0.005034983893153066,
+        0.004620045262778811, 0.004214910133631307, 0.003820165389229055,
+        0.003436762555112583, 0.003066170239108208, 0.0027106108440361847,
+        0.0023734524075375053, 0.0020598659559433754, 0.0017778765047241443,
+        0.0015397685767875738, 0.0013629393881898144, 0.0012671889747198101,
+        0.0012651529725602822, 0.0013519936588118392, 0.001507930264683938,
+        0.001710327629416419, 0.001941403995108344, 0.002189216683563157,
+        0.002446146143528105, 0.0027073445966763025, 0.002969680984930304,
+        0.0032310988887073546, 0.003490233537051907, 0.0037461777857680668,
+        0.003998331555761964, 0.004246298645903427, 0.0044898122548870335,
+        0.00472868033979676, 0.004962747031903871, 0.005191868495760961,
+        0.005415901985217179, 0.005634706208398191, 0.005848150090458456,
+        0.006056126112144976, 0.006258563982701229, 0.0064554406907912166,
+        0.00664678398555477, 0.006832667902458896, 0.007013200747105008,
+        0.00718850760815369, 0.007358710649412663, 0.007523910908480969,
+        0.007684175040008322, 0.007839529470512968, 0.00798996298591189,
+        0.008135437136643005, 0.008275902331018697, 0.008411316385509232,
+        0.008541661832313337, 0.008666958553636452, 0.008787269266943929,
+        0.00890269683555828, 0.00901337401613658, 0.00911944773805, 0.009221061040448966,
+        0.009318336178939825, 0.009411362107042721, 0.009500188625435873,
+        0.009584828170508986, 0.009665264740459298, 0.009741468109730186,
+        0.00981341050729086, 0.00988108251360996, 0.00994450514125539, 0.010003735861782857,
+        0.010058867561940283, 0.010110020805335424, 0.010157331056809231,
+        0.010200933445137377, 0.01024094802736232, 0.010277468324348716,
+        0.010310555186364494, 0.010340236976278176, 0.01036651584003011,
+        0.010389378697944242, 0.010408810742590292, 0.01042480881966114,
+        0.010437392165521787, 0.010446608551521729, 0.010452534819595205,
+        0.010455271895445211, 0.010454935413754217, 0.010451643881077171,
+        0.010445506693387074, 0.010436614260400535, 0.010425032002834251,
+        0.01041079919404836, 0.010393932675678256, 0.01037443456748265,
+        0.010352302379462249, 0.010327539543834858, 0.01030016437789437,
+        0.01027021585663091, 0.010237755235721862, 0.010202863385463194,
+        0.010165634510567192, 0.010126167583253028, 0.010084557188887804,
+        0.010040885517960488, 0.00999521694597598, 0.009947596096158437,
+        0.009898049593119372, 0.00984659102165664, 0.009793228030911273,
+        0.009737970170548428, 0.009680835968234715, 0.009621857961423456,
+        0.009561084832938683, 0.009498580377853184, 0.009434419633931466,
+        0.009368683022724852, 0.009301449679766118, 0.009232791247181623,
+        0.009162767254441201, 0.009091422865031125, 0.009018789292383741,
+        0.008944886682666593, 0.008869728817729588, 0.008793328687095531,
+        0.008715703862471204, 0.008636880694676155, 0.008556896616896209,
+        0.008475800222449129, 0.008393649213229631, 0.00831050670403294,
+        0.008226436646235917, 0.00814149925681268, 0.008055747290057057,
+        0.007969223789521607, 0.007881961651969544, 0.007793984985632042,
+        0.007705311918029099, 0.007615958262230797, 0.007525941324858833,
+        0.007435283151456312, 0.0073440126457249314, 0.007252166236137423,
+        0.007159787048259842, 0.007066922817979711, 0.006973622998639856,
+        0.006879935637022717, 0.0067859046018698636, 0.006691567649757736,
+        0.006596955631825227, 0.00650209291870035, 0.00640699889481607,
+        0.006311690187529474, 0.006216183182517594, 0.00612049635140261,
+        0.006024651979418384, 0.005928677015591495, 0.005832602943795798,
+        0.005736464758842139, 0.005640299289192227, 0.005544143212292984,
+        0.005448031142422768, 0.00535199413314583, 0.0052560588393207016,
+        0.0051602474477497945, 0.0050645783393563895, 0.004969067315853253,
+        0.0048737291322692175, 0.004778579039233065, 0.004683634055449411,
+        0.004588913759505077, 0.0044944404902821904, 0.004400238960837017,
+        0.004306335396123787, 0.004212756383970466, 0.004119527667144108,
+        0.004026673098900057, 0.003934213938925603, 0.0038421685921788355,
+        0.0037505528058195845, 0.0036593802557601577, 0.0035686633892453344,
+        0.0034784143537093144, 0.0033886458392572002, 0.003299371690479746,
+        0.003210607196385528, 0.0031223690317471985, 0.003034674888512628,
+        0.0029475428889916854, 0.0028609909044585544, 0.0027750359101748334,
+        0.0026896934906078833, 0.0026049775721095235, 0.0025209004132995825,
+        0.0024374728342195537, 0.0023547046243247737, 0.002272605042602259,
+        0.0021911833138306973, 0.002110449034819441, 0.0020304124282526444,
+        0.001951084415696252, 0.001872476516687193, 0.0017946006129921938,
+        0.0017174686383814107, 0.0016410922636095476, 0.0015654826420158962,
+        0.0014906502657639487, 0.0014166049607428133, 0.0013433560234220436,
+        0.0012709124823556664, 0.0011992834526869615, 0.0011284785486859942,
+        0.0010585083270485544, 0.0009893847522934648, 0.000921121705658742,
+        0.0008537355988969927, 0.0007872462087514146, 0.0007216779257720739,
+        0.0006570617348139134, 0.0005934384642232198, 0.0005308642639733747,
+        0.00046942014502049, 0.0004092293196987788, 0.0003504905340311024,
+        0.00029354674081445606, 0.000239038622654129, 0.00018827870996971247,
+        0.0001442127704680826, 0.00011352435850588552, 0.00010689641789946926,
+        0.00012698364146781406, 0.00016338901303675554, 0.00020702277937636521,
+        0.00025364280924311636, 0.0003014159787826786, 0.00034948637798516675,
+        0.0003974147058939869, 0.00044495623807321624, 0.000491965279253236,
+        0.0005383503274759845, 0.0005840513649433603, 0.0006290275916899806,
+        0.0006732504403051693, 0.0007166994262118483, 0.0007593596006999508,
+        0.0008012199493122598, 0.0008422723664929743, 0.0008825109892866391,
+        0.0009219317570636883, 0.000960532113281841, 0.0009983107948828116,
+        0.0010352676740716057, 0.0010714036294862893, 0.0011067204320294405,
+        0.0011412206362174254, 0.001174907471640717, 0.0012077847318579934,
+        0.0012398566601569782, 0.001271127833260588, 0.00130160304564719,
+        0.0013312871984103307, 0.0013601851975827207, 0.0013883018673059128,
+        0.0014156418831058363, 0.0014422097297629613, 0.0014680096866261892,
+        0.001493045841296251, 0.0015173221301271978, 0.001540842401659421,
+        0.0015636104970202784, 0.0015856303397862488, 0.0016069060271474448,
+        0.0016274419143406768, 0.0016472426852622976, 0.0016663134038167647,
+        0.0016846595425902592, 0.0017022869876413597, 0.0017192020203009703,
+        0.001735411278673071, 0.001750921702867079, 0.0017657404689285386,
+        0.0017798749167815056, 0.0017933324775547016, 0.0018061206053416616,
+        0.0018182467178724905, 0.0018297181498666973, 0.0018405421218315985,
+        0.0018507257260584153, 0.0018602759302139386, 0.0018691995976286649,
+        0.0018775035218498266, 0.0018851944717111736, 0.0018922792419742683,
+        0.0018987647038739993, 0.0019046578496884246, 0.0019099658259749733,
+        0.0019146959512967498, 0.0019188557160676415, 0.001922452764399178,
+        0.001925494860172264, 0.0019279898417420233, 0.0019299455712920768,
+        0.0019313698856692583, 0.0019322705553672232, 0.0019326552571539291,
+        0.0019325315638551038, 0.0019319069522232444, 0.0019307888271100295,
+        0.0019291845576801096, 0.0019271015195919663, 0.00192454713621263,
+        0.0019215289121708222, 0.0019180544538442922, 0.0019141314735424124,
+        0.0019097677767907044, 0.0019049712348437474, 0.0018997497468916727,
+        0.0018941111979923163, 0.0018880634193294667, 0.0018816141568649802,
+        0.001874771052942026, 0.0018675416431629373, 0.0018599333683117815,
+        0.0018519535986389823, 0.0018436096658534433, 0.0018349088970786344,
+        0.0018258586448484735, 0.0018164663081127964, 0.0018067393408377653,
+        0.0017966852469958748, 0.0017863115630346138, 0.0017756258309484926,
+        0.0017646355665496927, 0.0017533482281446462, 0.0017417711905615355,
+        0.0017299117284054635, 0.0017177770107198681, 0.0017053741072504615,
+        0.0016927100045813317, 0.001679791628838643, 0.001666625870730513,
+        0.0016532196084839757, 0.0016395797247856154, 0.0016257131150567128,
+        0.001611626685885323, 0.0015973273442233872, 0.0015828219793757546,
+        0.00156811744096067, 0.001553220516489751, 0.0015381379121431227,
+        0.001522876239536223, 0.0015074420102068665, 0.0014918416381660285,
+        0.001476081449511918, 0.0014601676970406258, 0.001444106577091446,
+        0.0014279042456263394, 0.0014115668309434102, 0.001395100441026978,
+        0.0013785111646021407, 0.0013618050660141347, 0.0013449881750200836,
+        0.001328066473328553, 0.00131104588013031, 0.001293932238834678,
+        0.0012767313068963125, 0.0012594487500231972, 0.0012420901412428485,
+        0.0012246609645443296, 0.0012071666221726161, 0.0011896124441313034,
+        0.0011720036982852992, 0.0011543455995195798, 0.0011366433166320692,
+        0.0011189019761903563, 0.0011011266630057645, 0.001083322417411356,
+        0.0010654942299807499, 0.0010476470345535827, 0.00102978570058442,
+        0.0010119150257624182, 0.0009940397297413207, 0.000976164449535707,
+        0.0009582937369005839, 0.0009404320577395112, 0.0009225837933766297,
+        0.0009047532433981659, 0.0008869446296576673, 0.0008691621010233726,
+        0.0008514097384604202, 0.0008336915600851889, 0.000816011525840935,
+        0.0007983735415257488, 0.0007807814619191032, 0.0007632390928298453,
+        0.0007457501918732743, 0.0007283184679425868, 0.000710947579350004,
+        0.0006936411307323615, 0.0006764026689602087, 0.0006592356783304757,
+        0.0006421435754568671, 0.0006251297042993256, 0.0006081973317764407,
+        0.0005913496443710393, 0.0005745897460200568, 0.000557920657508488,
+        0.0005413453173629461, 0.0005248665841735999, 0.0005084872400946559,
+        0.0004922099952110648, 0.00047603749239546144, 0.0004599723123117696,
+        0.0004440169782170358, 0.0004281739603471014, 0.0004124456797141852,
+        0.00039683451128018436, 0.0003813427865394455, 0.00036597279563548013,
+        0.0003507267891786617, 0.00033560698000873243, 0.00032061554513952587,
+        0.0003057546282159622, 0.0002910263428338941, 0.0002764327771630188,
+        0.0002619760004735035, 0.0002476580723086678, 0.00023348105537162315,
+        0.00021944703360821487, 0.00020555813759912407, 0.00019181658046446838,
+        0.0001782247090978039, 0.00016478507847734482, 0.0001515005616519067,
+        0.00013837451689352237, 0.00012541104994446623, 0.00011261544130427701,
+        9.999487423120942e-05, 8.755974257814682e-05, 7.53261552203315e-05,
+        6.332112379895218e-05, 5.159442529678254e-05, 4.024940173959684e-05,
+        2.9537108052650193e-05, 2.0202037159386934e-05, 1.4696835429229488e-05,
+        1.688462426362078e-05, 2.4587079580830902e-05, 3.411046054236332e-05,
+        4.417491070068933e-05, 5.438450496914129e-05, 6.458989299983539e-05,
+        7.472394479397553e-05, 8.475232343572477e-05, 9.465570023778436e-05,
+        0.00010442237451655631, 0.00011404485407200621, 0.00012351812756165713,
+        0.00013283872883088795, 0.00014200420037175287, 0.00015101277052317723,
+        0.0001598631511157015, 0.00016855440602506073, 0.00017708586310408845,
+        0.00018545705361980373, 0.000193667669702684, 0.00020171753395224239,
+        0.00020960657746090883, 0.00021733482377742295, 0.00022490237707633828,
+        0.00023230941331657084, 0.0002395561734527793, 0.0002466429580276379,
+        0.0002535701226371948, 0.0002603380739283195, 0.0002669472659387006,
+        0.0002733981966768811, 0.00027969140496393515, 0.0002858274675872454,
+        0.0002918069968603909, 0.0002976306386551343, 0.00030329907095248064,
+        0.00030881300287973585, 0.000314173174169006, 0.0003193803548970512,
+        0.0003244353453479858, 0.0003293389758337941, 0.0003340921063212942,
+        0.0003386956257667894, 0.00034315045112380836, 0.0003474575260568353,
+        0.0003516178194403193, 0.0003556323237944331, 0.000359502053794333,
+        0.0003632280450003993, 0.00036681135291215743, 0.000370253052389578,
+        0.00037355423743057364, 0.00037671602122413506, 0.00037973953635107155,
+        0.0003826259349921867, 0.00038537638899311007, 0.00038799208967318596,
+        0.0003904742473073536, 0.0003928240902835683, 0.0003950428639821951,
+        0.00039713182948356837, 0.0003990922622456039, 0.00040092545087755594,
+        0.0004026326961449684, 0.00040421531027101925, 0.00040567461656783674,
+        0.000407011949360976, 0.00040822865412023433, 0.00040932608768195686,
+        0.00041030561843304357, 0.00041116862632641196, 0.000411916502655718,
+        0.00041255064953343244, 0.00041307247909942285, 0.0004134834125114308,
+        0.0004137848788234105, 0.0004139783138739179, 0.00041406515929094196,
+        0.0004140468617132573, 0.00041392487227742035, 0.000413700646373905,
+        0.00041337564363463957, 0.0004129513280590658, 0.00041242916819498064,
+        0.0004118106372421228, 0.0004110972130068138, 0.0004102903776352654,
+        0.00040939161711303396, 0.00040840242055004686, 0.0004073242793177853,
+        0.0004061586861216182, 0.0004049071341120669, 0.00040357111611786947,
+        0.00040215212406452923, 0.0004006516486178639, 0.00039907117902911713,
+        0.00039741220315416405, 0.00039567620755543424, 0.0003938646776239785,
+        0.0003919790976189398, 0.0003900209505731823, 0.0003879917180202175,
+        0.0003858928795398789, 0.0003837259121524141, 0.0003814922896210004,
+        0.0003791934817198103, 0.00037683095356463294, 0.0003744061650460124,
+        0.00037192057042606844, 0.0003693756180998413, 0.0003667727505128373,
+        0.00036411340418983633, 0.0003613990098189012, 0.00035863099232410453,
+        0.00035581077086657383, 0.0003529397587328592, 0.00035001936308794396,
+        0.00034705098459666083, 0.00034403601694685064, 0.00034097584631164065,
+        0.0003378718508120777, 0.0003347254000381892, 0.00033153785465349546,
+        0.00032831056613377225, 0.0003250448766193345, 0.00032174211887927304,
+        0.00031840361634863406, 0.0003150306831897098, 0.0003116246243382941,
+        0.00030818673548609673, 0.00030471830298131657, 0.00030122060362898777,
+        0.0002976949044048979, 0.0002941424621063797, 0.0002905645229745576,
+        0.0002869623223270508, 0.00028333708423962834, 0.0002796900213004284,
+        0.0002760223344513072, 0.0002723352129182948, 0.00026862983421093416,
+        0.00026490736416144594, 0.00026116895698187736, 0.00025741575529463195,
+        0.0002536488901218849, 0.00024986948081147793, 0.00024607863489962533,
+        0.00024227744791835995, 0.0002384670031659487, 0.00023464837146924914,
+        0.00023082261095746576, 0.00022699076687842626, 0.00022315387146512705,
+        0.00021931294386659278, 0.00021546899013237677, 0.000211623003239239,
+        0.00020777596314711157, 0.00020392883685373944, 0.0002000825784316391,
+        0.00019623812903788595, 0.00019239641688032925, 0.00018855835714557615,
+        0.00018472485189556723, 0.0001808967899468938, 0.00017707504674783939,
+        0.00017326048427071265, 0.0001694539509365469, 0.0001656562815712773,
+        0.00016186829740652455, 0.00015809080611231527, 0.00015432460185679878,
+        0.00015057046538031433, 0.00014682916406811997, 0.000143101452013936,
+        0.00013938807006380358, 0.0001356897458392213, 0.0001320071937397405,
+        0.00012834111493080687, 0.0001246921973325796, 0.00012106111560700555,
+        0.00011744853117085447, 0.00011385509222510326, 0.00011028143381975052,
+        0.00010672817794585831, 0.0001031959336564765, 9.968529721526467e-05,
+        9.619685226165339e-05, 9.273116999269106e-05, 8.928880935934829e-05,
+        8.587031727817836e-05, 8.247622886268775e-05, 7.910706768913124e-05,
+        7.576334610688354e-05, 7.244556561770467e-05, 6.91542173494051e-05,
+        6.588978265325001e-05, 6.265273386965956e-05, 5.944353531425965e-05,
+        5.626264455834227e-05, 5.3110514103319375e-05, 4.998759360533561e-05,
+        4.6894332867380986e-05, 4.3831185940405415e-05, 4.079861685981928e-05,
+        3.779710785331137e-05, 3.482717138485236e-05, 3.188936833335006e-05,
+        2.898433631268958e-05, 2.6112835432167856e-05, 2.3275825456360376e-05,
+        2.0474602673595234e-05, 1.771105809934922e-05, 1.4988203256531128e-05,
+        1.2311350467482747e-05, 9.69112614540596e-06, 7.152651025575855e-06,
+        4.771495603167542e-06], [2.3604627120241137e-15, 7.0956675355536e-15,
+        1.1873860791694601e-14, 1.6724201464974138e-14, 2.1676606088557072e-14,
+        2.676206912295567e-14, 3.201299758921665e-14, 3.7463569559879544e-14,
+        4.3150118987323815e-14, 4.911155478989606e-14, 5.5389820781143566e-14,
+        6.203040459467409e-14, 6.908290381988281e-14, 7.660166067582715e-14,
+        8.464647575084581e-14, 9.328341524927293e-14, 1.0258572673819287e-13,
+        1.1263488174114362e-13, 1.2352176652456406e-13, 1.353480450897917e-13,
+        1.4822772444372012e-13, 1.6228895472766204e-13, 1.7767610526829656e-13,
+        1.9455216317948202e-13, 2.1310151023230284e-13, 2.335331437300831e-13,
+        2.560844202016326e-13, 2.8102541380100586e-13, 3.086640010916282e-13,
+        3.393518028403077e-13, 3.7349114240626217e-13, 4.1154320727619915e-13,
+        4.5403764252797343e-13, 5.015838470141248e-13, 5.548843020049294e-13,
+        6.147503271881643e-13, 6.82120745147301e-13, 7.580840338915366e-13,
+        8.43904676123186e-13, 9.410545628159912e-13, 1.0512505040732703e-12,
+        1.1764991283388432e-12, 1.3191507483444153e-12, 1.4819641258071867e-12,
+        1.668184524508337e-12, 1.8816379893591095e-12, 2.126845512194313e-12,
+        2.409161593994993e-12, 2.734942861495845e-12, 3.111753752831199e-12,
+        3.5486180900804893e-12, 4.056327585654278e-12, 4.647821184053498e-12,
+        5.3386528065501214e-12, 6.147569724201026e-12, 7.097229785703607e-12,
+        8.215093494443797e-12, 9.534536883073316e-12, 1.1096244180525592e-11,
+        1.294995612510612e-11, 1.515667189386744e-11, 1.779143160942366e-11,
+        2.0946844527817063e-11, 2.4737578445522878e-11, 2.930609278821053e-11,
+        3.4829987038196586e-11, 4.153145541329714e-11, 4.9689499076255693e-11,
+        5.965576362767691e-11, 7.187516301174945e-11, 8.691285089000579e-11,
+        1.0548964800307447e-10, 1.285287875416324e-10, 1.572178822874599e-10,
+        1.9309146705528834e-10, 2.38141496150582e-10, 2.9496602729129747e-10,
+        3.6697035627337363e-10, 4.5864061057985507e-10, 5.759180414265923e-10,
+        7.267141246500448e-10, 9.216238299931588e-10, 1.174919655155389e-09,
+        1.5059462262666823e-09, 1.941090557580508e-09, 2.516585898259056e-09,
+        3.282532287158811e-09, 4.308707845354858e-09, 5.693038745501491e-09,
+        7.574052852601819e-09, 1.0149360188059123e-08, 1.37033446125088e-08,
+        1.8649085888358538e-08, 2.5592518203373175e-08, 3.5431758465782695e-08,
+        4.9512781517998804e-08, 6.987662099025053e-08, 9.965744480289222e-08,
+        1.4373330734846073e-07, 2.098073630302302e-07, 3.1023611488059556e-07,
+        4.6518047406652635e-07, 7.081513954367566e-07, 1.0959967118942404e-06,
+        1.7273495858964818e-06, 2.777690291825928e-06, 4.5681500116196975e-06,
+        7.7055421358975e-06, 1.3379600006362918e-05, 2.4025784778214914e-05,
+        4.4892933790283104e-05, 8.802841290747501e-05, 0.00018337800554163192,
+        0.00041368274567928906, 0.0010447577414995249, 0.0031644804093431673,
+        0.014105135964659494, 0.381058353085119, 0.0929984134536913, 0.25093564634050236,
+        0.35582048471182687, 0.22763941333166532, 0.3052303151987785, 0.7047756540407525,
+        1.2445183445637835, 0.8703188357508196, 1.0409048879038163, 2.258796733866531,
+        5.644588871056084, 4.917127956107993, 3.1082663012014504, 1.7948533785655705,
+        1.3478528813652457, 1.2492357300658417, 1.386363904285158, 1.7967193521557017,
+        2.1915468592811687, 1.7323421120336575, 1.2545621081726568, 1.0320182133175249,
+        0.9686007088157045, 1.025051174560949, 1.2120136466773628, 1.5277918419112781,
+        1.680195626738042, 1.3982999594694665, 1.1026740630216718, 0.9420507181294637,
+        0.8871681499958766, 0.9180529282826418, 1.0392731490670641, 1.2617555530822964,
+        1.4935335087285062, 1.4455954416426526, 1.193759877155633, 1.0019018125155945,
+        0.9211985429093559, 0.7493083637963425, 0.6706632692235069, 0.6409799214180811,
+        0.621560532268594, 0.588907341220294, 0.5349011539712474, 0.47050898413694964,
+        0.41093059279091826, 0.36369305682211056, 0.32965194282159777, 0.30703937801729786,
+        0.2935845319086605, 0.2870053350292447, 0.28473765467565276, 0.28344666344794617,
+        0.27899695398396024, 0.2677707384523695, 0.24896299450387638, 0.22521916615118143,
+        0.20046673044119606, 0.17757964638179324, 0.15781040395128665, 0.14131755219632725,
+        0.12777093194809938, 0.11671087216752253, 0.10770536309268663, 0.10040030592822932,
+        0.09452399408579581, 0.08987570524467829, 0.0863111196996326, 0.08372924667785264,
+        0.08206198377652461, 0.08126586126189138, 0.08131475924109198, 0.08219187255006265,
+        0.08387867653786113, 0.08633813754691443, 0.0894894540222667, 0.09317375009080232,
+        0.09711717575141382, 0.1009119092453534, 0.10405054582194716, 0.10604181778091118,
+        0.10658013308757897, 0.10566886407270547, 0.10360388614373356, 0.10083305887693132,
+        0.09779587815577388, 0.09482570678184712, 0.09212468285845428, 0.08978108125466844,
+        0.08779957110559987, 0.08612949392916007, 0.08468764309786335, 0.08337694486872695,
+        0.08210297068394884, 0.08078861465675223, 0.07938530552464712, 0.07787824902239435,
+        0.07628420282810343, 0.07464266678693222, 0.07300356485578138, 0.07141514989731336,
+        0.06991488207757185, 0.06852436892267744, 0.06724812138146406, 0.06607527735671936,
+        0.06498339951440509, 0.06394359006808298, 0.06292620249971122, 0.06190631137840043,
+        0.06086797354931133, 0.059806405236770124, 0.058727636014398205,
+        0.0576458742109355, 0.05657943303814493, 0.055546345621903054, 0.05456067156928013,
+        0.05363011647922852, 0.05275516941804903, 0.05192965565181823, 0.051142424406822845,
+        0.050379791328205574, 0.049628280433091636, 0.04887715733327429,
+        0.048120259258623864, 0.0473567584191285, 0.04659074447745379, 0.04582980819498229,
+        0.04508304193031135, 0.04435896211683508, 0.04366379626773817, 0.04300041925483401,
+        0.04236804544137753, 0.041762634933984556, 0.041177867231500506,
+        0.040606465373691614, 0.040041610419278686, 0.03947817493936552,
+        0.03891353966865022, 0.03834784711417249, 0.037783675629949345,
+        0.03722525077587213, 0.03667740547485471, 0.036144530576520145,
+        0.035629724535671065, 0.035134278277670794, 0.03465754765435051,
+        0.034197191734863, 0.03374969884540757, 0.033311084326227605, 0.03287762398923506,
+        0.03244648736973246, 0.0320161582331079, 0.031586575761967293, 0.031158990125357798,
+        0.03073558568238071, 0.030318967882196648, 0.029911626013687794,
+        0.029515473154725236, 0.02913153500686687, 0.028759822010536288,
+        0.02839938368288363, 0.028048515902570428, 0.02770507264057507,
+        0.027366823423679545, 0.027031796336435928, 0.026698553494818908,
+        0.026366360890857695, 0.026035235078675143, 0.025705871423732346,
+        0.025379477836659378, 0.025057550141779888, 0.024741628719462005,
+        0.024433071679047017, 0.024132870341519, 0.023841521701191807, 0.02355896265909715,
+        0.02328456378541851, 0.023017176438335587, 0.022755225490661165,
+        0.022496839481869448, 0.022240009503151113, 0.021982766728839778,
+        0.02172336606740748, 0.02146046049495886, 0.021193248408828757,
+        0.02092157621280922, 0.020645981377487254, 0.02036766765330625,
+        0.020088413028872914, 0.019810420567706818, 0.0195361301869682,
+        0.019268013986650713, 0.01900837813106457, 0.018759190967758462,
+        0.01852195133999513, 0.018297604502057384, 0.018086507027016335,
+        0.017888437396009843, 0.017702645786236117, 0.01752793474288309,
+        0.017362761576990998, 0.017205353167123395, 0.01705382418993067,
+        0.016906290622911477, 0.016760971669609676, 0.016616275000921995,
+        0.016470862222747205, 0.016323693475120957, 0.01617405171382314,
+        0.01602154826987429, 0.01586611167118891, 0.01570796159666942, 0.015547569547010304,
+        0.015385607715242557, 0.015222887883889974, 0.015060293011661471,
+        0.014898705335950007, 0.014738935986500468, 0.014581661911457721,
+        0.014427376067405082, 0.014276356150443472, 0.014128655636583946,
+        0.013984118666352486, 0.013842417576048623, 0.013703108953704777,
+        0.013565701390034296, 0.01342972606814661, 0.01329480047567521,
+        0.013160676176129567, 0.01302726384310361, 0.012894632358500125,
+        0.012762983068875031, 0.012632604422038481, 0.01250381532780633,
+        0.012376907110766814, 0.01225209364515484, 0.01212947737415569,
+        0.012009035875369172, 0.011890630038062077, 0.011774031348995526,
+        0.011658962771276154, 0.011545145668480205, 0.011432344479198362,
+        0.011320401520215061, 0.011209256298250639, 0.01109894668695262,
+        0.01098959270903645, 0.010881366779184805, 0.010774456504415794,
+        0.010669027115423167, 0.010565190221041012, 0.010462984024754408,
+        0.010362367800654759, 0.010263230766017001, 0.010165412970360476,
+        0.01006873384663929, 0.009973022932155804, 0.009878147133268615,
+        0.009784029782771868, 0.009690658450001603, 0.009598080676246982,
+        0.009506389080639218, 0.009415699167520147, 0.009326124316402427,
+        0.009237752676264928, 0.009150630041692276, 0.009064751450777167,
+        0.008980062510749736, 0.008896469658773085, 0.008813857011872633,
+        0.008732106400295899, 0.008651116773098577, 0.008570819462518506,
+        0.00849118672085321, 0.0084122323133944, 0.00833400448628546, 0.008256573027982215,
+        0.00818001314174387, 0.008104389275602909, 0.008029741874092843,
+        0.007956079301896945, 0.007883376115082096, 0.0078115776382056586,
+        0.007740609668856816, 0.007670391265858017, 0.007600848122109757,
+        0.007531924039574013, 0.007463588494067459, 0.007395839098329579,
+        0.007328698777999213, 0.007262208466238586, 0.007196416910855631,
+        0.007131369631782913, 0.007067099105555332, 0.007003617906831602,
+        0.006940915896045072, 0.006878961744036248, 0.006817708280680554,
+        0.006757100487496227, 0.006697084533980688, 0.006637616146650901,
+        0.0065786668069884625, 0.006520226748246806, 0.006462304364516466,
+        0.006404922329472015, 0.006348111315887291, 0.006291902601882159,
+        0.006236320983348845, 0.006181379275768631, 0.006127075324899656,
+        0.006073391937384318, 0.006020299587779427, 0.005967761261640323,
+        0.005915738437853981, 0.005864197056004896, 0.005813112374259808,
+        0.005762471881012927, 0.0057122758235780315, 0.005662535379266556,
+        0.0056132689280727985, 0.005564497212635223, 0.00551623833372067,
+        0.005468503508330036, 0.005421294327254314, 0.005374601935209296,
+        0.00532840818381944, 0.005282688445776943, 0.005237415491623704,
+        0.005192563666563576, 0.005148112586689511, 0.005104049699620989,
+        0.005060371294547389, 0.005017081851749437, 0.004974191932614468,
+        0.004931715069333797, 0.004889664273605114, 0.004848048821633662,
+        0.004806871888027251, 0.00476612941730566, 0.004725810376847416,
+        0.004685898277548983, 0.0046463736242970295, 0.004607216806199191,
+        0.004568410880195838, 0.004529943746955102, 0.004491809352454319,
+        0.004454007743661513, 0.004416544024083636, 0.004379426453391746,
+        0.004342664078832169, 0.004306264351718965, 0.004270231161630272,
+        0.0042345636230485244, 0.004199255796036368, 0.004164297344689548,
+        0.0041296749677589475, 0.004095374304742091, 0.004061381949289877,
+        0.004027687200145043, 0.003994283245108474, 0.0039611675908568,
+        0.003928341697367309, 0.003895809922000816, 0.0038635779982559427,
+        0.003831651347264228, 0.0038000335352928565, 0.0037687251483014385,
+        0.003737723265846224, 0.0037070215995738086, 0.0036766112389261816,
+        0.0036464818404032305, 0.003616623024964538, 0.0035870257220422764,
+        0.003557683220575892, 0.0035285917518480454, 0.0034997505213297847,
+        0.003471161210289859, 0.0034428270622150294, 0.0034147517383025443,
+        0.0033869381586530793, 0.0033593875375644952, 0.003332098776302548,
+        0.00330506830462276, 0.003278290377729604, 0.0032517577537725926,
+        0.0032254626125759016, 0.00319939754017449, 0.0031735563999539455,
+        0.0031479349402652396, 0.003122531042248415, 0.0030973445806588306,
+        0.0030723769407508244, 0.0030476302936493353, 0.003023106770643215,
+        0.002998807687987108, 0.0029747329574178107, 0.0029508807780016908,
+        0.002927247650478878, 0.002903828696245956, 0.002880618210155674,
+        0.002857610338418839, 0.002834799755953791, 0.0028121822235046712,
+        0.0027897549318467115, 0.002767516582180298, 0.002745467200849353,
+        0.0027236077334131985, 0.002701939499735814, 0.002680463612236398,
+        0.0026591804609561163, 0.0026380893523028715, 0.0026171883573463217,
+        0.002596474386201071, 0.0025759434649376416, 0.0025555911574122367,
+        0.002535413051907437, 0.002515405225143463, 0.002495564604220309,
+        0.002475889168575132, 0.002456377964366861, 0.0024370309375549458,
+        0.0024178486227677794, 0.0023988317481362727, 0.0023799808277138183,
+        0.0023612958116817164, 0.002342775851265076, 0.0023244192128558097,
+        0.002306223348939306, 0.0022881851064097125, 0.0022703010307102314,
+        0.002252567710168047, 0.0022349821008209258, 0.002217541778352825,
+        0.0022002450785164208, 0.002183091107915227, 0.002166079629483786,
+        0.0021492108474114226, 0.0021324851315465752, 0.002115902729082359,
+        0.0020994635108733967, 0.002083166791550468, 0.0020670112486404863,
+        0.0020509949486678773, 0.002035115470803967, 0.0020193701038262947,
+        0.0020037560820563654, 0.001988270821863818, 0.0019729121225939192,
+        0.0019576783032784714, 0.0019425682580954515, 0.0019275814266338715,
+        0.0019127176879664477, 0.0018979771978796078, 0.0018833601954235148,
+        0.0018688668072341554, 0.0018544968760835453, 0.0018402498346275255,
+        0.0018261246373435039, 0.0018121197548735856, 0.0017982332266095673,
+        0.0017844627605290001, 0.001770805864884542, 0.0017572599944958465,
+        0.0017438226949909503, 0.00173049173092103, 0.0017172651875256805,
+        0.0017041415402112047, 0.001691119689857981, 0.0016781989655059342,
+        0.0016653790982548344, 0.0016526601715603957, 0.0016400425535265722,
+        0.0016275268165994404, 0.0016151136496151456, 0.0016028037666431416,
+        0.001590597816741143, 0.0015784962986096624, 0.0015664994841408854,
+        0.0015546073548684705, 0.0015428195551216934, 0.0015311353651706898,
+        0.0015195536966899187, 0.0015080731114335065, 0.0014966918623581249,
+        0.0014854079545348336, 0.001474219221481434, 0.0014631234111568447,
+        0.0014521182749830286, 0.0014412016531334683, 0.001430371549779061,
+        0.0014196261931376359, 0.0014089640767416193, 0.0013983839801567756,
+        0.001387884969227563, 0.0013774663775774692, 0.0013671277723981226,
+        0.0013568689084533922, 0.0013466896746654653, 0.0013365900376684293,
+        0.0013265699864449937, 0.0013166294816456784, 0.0013067684125333942,
+        0.0012969865638143754, 0.0012872835938145682, 0.0012776590247822674,
+        0.0012681122452555993, 0.001258642523708036, 0.0012492490318510927,
+        0.0012399308752885777, 0.0012306871285375802, 0.0012215168710372158,
+        0.0012124192205810475, 0.001203393360823855, 0.0011944385600670174,
+        0.0011855541794687106, 0.0011767396700359486, 0.0011679945590775146,
+        0.0011593184281375101, 0.0011507108854849693, 0.001142171536965984,
+        0.0011336999591976607, 0.0011252956787284325, 0.0011169581599179965,
+        0.001108686802992048, 0.001100480952253458, 0.0010923399129489579,
+        0.0010842629740145187, 0.00107624943313691, 0.0010682986202651312,
+        0.001060409916072321, 0.0010525827626792703, 0.0010448166652636457,
+        0.001037111184596575, 0.0010294659219824947, 0.0010218804992119127,
+        0.0010143545368580887, 0.001006887634387237, 0.0009994793551685978,
+        0.0009921292185791533, 0.0009848367001824934, 0.000977601239646104,
+        0.000970422254820789, 0.0009632991594629224, 0.000956231381600731,
+        0.0009492183795320201, 0.0009422596529617019, 0.0009353547476521992,
+        0.0009285032530875404, 0.0009217047938204172, 0.0009149590161526308,
+        0.0009082655725221474, 0.0009016241062227182, 0.0008950342389344789,
+        0.000888495562972744, 0.0008820076393139365, 0.0008755700014605271,
+        0.0008691821642512157, 0.0008628436359515834, 0.0008565539314998199,
+        0.0008503125846858432, 0.000844119157310532, 0.0008379732439780952,
+        0.0008318744719122223, 0.0008258224960751774, 0.0008198169905806607,
+        0.0008138576379703883, 0.000807944118188307, 0.0008020760990569552,
+        0.0007962532297012219, 0.0007904751378451315, 0.0007847414312134437,
+        0.0007790517026005755, 0.0007734055376105428, 0.0007678025236840675,
+        0.0007622422589017862, 0.0007567243591819635, 0.0007512484628009056,
+        0.0007458142316705869, 0.0007404213493465307, 0.0007350695162451768,
+        0.0007297584429689391, 0.0007244878428749277, 0.0007192574250627734,
+        0.0007140668888205044, 0.0007089159202831994, 0.0007038041916591991,
+        0.0006987313629761962, 0.0006936970859305277, 0.0006887010091316666,
+        0.0006837427838955537, 0.0006788220697238197, 0.0006739385387136883,
+        0.000669091878376689, 0.0006642817925876597, 0.0006595080006794293,
+        0.000654770234936965, 0.0006500682369303879, 0.0006454017532196839,
+        0.0006407705309775854, 0.0006361743140359343, 0.0006316128397305138,
+        0.0006270858367971663, 0.0006225930244213695, 0.0006181341124243502,
+        0.000613708802472977, 0.0006093167901365739, 0.0006049577675756201,
+        0.0006006314266515666, 0.0005963374622429926, 0.0005920755755605151,
+        0.0005878454772679385, 0.0005836468902201228, 0.0005794795516460832,
+        0.0005753432145912397, 0.0005712376485004036, 0.000567162638825417,
+        0.0005631179856267937, 0.0005591035012135014, 0.0005551190069423731,
+        0.0005511643293900046, 0.0005472392961863104, 0.0005433437318375651,
+        0.0005394774538816892, 0.0005356402696951532, 0.0005318319742148636,
+        0.0005280523487334153, 0.0005243011608384852, 0.0005205781654461679,
+        0.000516883106777619, 0.0005132157210612566, 0.000509575739694329,
+        0.0005059628925813984, 0.0005023769113986126, 0.0004988175325645182,
+        0.0004952844997644033, 0.0004917775659301991, 0.0004882964946372034,
+        0.0004848410609170965, 0.00048141105151319443, 0.00047800626462372425,
+        0.0004746265091713488, 0.0004712716036552349, 0.00046794137461822016,
+        0.0004646356548106408, 0.0004613542811148103, 0.0004580970923495317,
+        0.00045486392708979703, 0.0004516546216615455, 0.0004484690084852357,
+        0.0004453069149251133, 0.0004421681627740842, 0.0004390525684415859,
+        0.0004359599438325827, 0.0004328900978426527, 0.0004298428382853711,
+        0.00042681797403392536, 0.00042381531710429656, 0.00042083468442594726,
+        0.00041787589907014603, 0.00041493879077856167, 0.0004120231957512715,
+        0.00040912895572453774, 0.00040625591650019584, 0.00040340392614649775,
+        0.0004005728331425308, 0.00039776248474312435, 0.0003949727257951734,
+        0.00039220339816899456, 0.0003894543408724351, 0.000386725390796102,
+        0.00038401638395920286, 0.00038132715703822193, 0.00037865754892498117,
+        0.0003760074020703857, 0.00037337656340101185, 0.000370764884683176,
+        0.0003681722222893265, 0.0003655984364295816, 0.0003630433899889805,
+        0.00036050694717460765, 0.00035798897219739805, 0.00035548932819980345,
+        0.0003530078765962171, 0.0003505444769162067, 0.00034809898715164734,
+        0.00034567126453414213, 0.00034326116658844663, 0.0003408685522828185,
+        0.0003384932830696893, 0.00033613522365505595, 0.0003337942423673481,
+        0.00033147021108893983, 0.0003291630047707941, 0.00032687250062922376,
+        0.00032459857716974006, 0.0003223411132120052, 0.0003200999870753752,
+        0.00031787507605444845, 0.00031566625626266103, 0.0003134734028528073,
+        0.00031129639056010706, 0.0003091350944605162, 0.00030698939080603643,
+        0.00030485915778862477, 0.00030274427610798936, 0.0003006446292464691,
+        0.00029856010341957294, 0.0002964905872221995, 0.00029443597103878737,
+        0.0002923961463308527, 0.0002903710049226473, 0.00028836043841352487,
+        0.00028636433780131703, 0.00028438259338239114, 0.0002824150949234256,
+        0.00028046173207106503, 0.0002785223949085778, 0.0002765969745685377,
+        0.0002746853637806707, 0.00027278745726739845, 0.0002709031519270272,
+        0.00026903234677220724, 0.000267174942651341, 0.00026533084180178836,
+        0.00026349994732235857, 0.00026168216265940993, 0.0002598773911837932,
+        0.0002580855359448483, 0.00025630649961410804, 0.0002545401846394366,
+        0.00025278649355825515, 0.0002510453294174471, 0.0002493165962158775,
+        0.0002476001992966673, 0.0002458960456125673, 0.0002442040438358157,
+        0.0002425241042855098, 0.0002408561387020056, 0.00023920005990415852,
+        0.00023755578139872228, 0.00023592321700904875, 0.00023430228058381934,
+        0.00023269288583259128, 0.0002310949463155658, 0.00022950837557178118,
+        0.00022793308737035042, 0.0002263689960188762, 0.00022481601669055825,
+        0.00022327406569375532, 0.00022174306064992843, 0.00022022292054883142,
+        0.00021871356567268924, 0.00021721491741158688, 0.00021572689800051755,
+        0.00021424943023168355, 0.00021278243718596742, 0.00021132584203679421,
+        0.00020987956794726097, 0.0002084435380812595, 0.00020701767571962144,
+        0.00020560190445187613, 0.00020419614841080884, 0.00020280033250577332,
+        0.00020141438261120587, 0.00020003822567884745, 0.0001986717897592745,
+        0.00019731500392639465, 0.00019596779812695818, 0.0001946301029796955,
+        0.00019330184956005268, 0.00019198296921180038, 0.00019067339340915932,
+        0.00018937305370160578, 0.00018808188173462316, 0.00018679980934817114,
+        0.000185526768728251, 0.00018426269258206774, 0.00018300751430718137,
+        0.00018176116812153938, 0.00018052358913260162, 0.00017929471334099652,
+        0.00017807447757135626, 0.00017686281935121436, 0.00017565967675727066,
+        0.00017446498825496434, 0.00017327869256594585, 0.00017210072857250081,
+        0.0001709310352875751, 0.00016976955187932512, 0.00016861621775086472,
+        0.00016747097265940443, 0.00016633375684312296, 0.00016520451114365828,
+        0.00016408317709537372, 0.00016296969696863675, 0.00016186401376069257,
+        0.00016076607113897618, 0.00015967581334345679, 0.0001585931850721952,
+        0.00015751813136350218, 0.00015645059750063085, 0.00015539052894887815,
+        0.00015433787133802503, 0.00015329257048931987, 0.00015225457247835245,
+        0.00015122382372352385, 0.00015020027108175025, 0.00014918386193583848,
+        0.00014817454425277498, 0.0001471722666111263, 0.00014617697818905824,
+        0.00014518862871424354, 0.000144207168390144, 0.00014323254780825525,
+        0.00014226471786420245, 0.00014130362968711602, 0.00014034923459793784,
+        0.00013940148410209661, 0.00013846032991047887, 0.00013752572399076653,
+        0.00013659761863303867, 0.00013567596652079138, 0.0001347607207908138,
+        0.00013385183507653474, 0.00013294926352240338, 0.00013205296077112966,
+        0.00013116288192412966, 0.00013027898248487446, 0.00012940121829368114,
+        0.00012852954546385958, 0.0001276639203330937, 0.00012680429943351292,
+        0.00012595063948704147, 0.00012510289742440628, 0.00012426103042324332,
+        0.0001234249959560323, 0.00012259475184343217, 0.00012177025629735669,
+        0.00012095146795087655, 0.00012013834586687405, 0.00011933084952881597,
+        0.00011852893880756313, 0.00011773257392222254, 0.00011694171538591552,
+        0.00011615632396465431, 0.00011537636063644215, 0.00011460178657145079,
+        0.00011383256312772944, 0.00011306865186504666, 0.0001123100145720285,
+        0.00011155661330413542, 0.00011080841041873048, 0.00011006536860977231,
+        0.00010932745092914944, 0.00010859462079336442, 0.00010786684197742535,
+        0.00010714407859082393, 0.00010642629504659976, 0.00010571345602593167,
+        0.0001050055264417717, 0.00010430247140912294, 0.00010360425622990286,
+        0.00010291084638608345, 0.00010222220754775353, 0.00010153830559245576,
+        0.00010085910663105874, 0.00010018457703471867, 9.951468346071814e-05,
+        9.8849392869687e-05, 9.818867253307092e-05, 9.753249003241536e-05,
+        9.688081324224775e-05, 9.623361031127504e-05, 9.559084963409192e-05,
+        9.495249982426385e-05, 9.431852969219226e-05, 9.368890822559167e-05,
+        9.306360458307702e-05, 9.244258809579855e-05, 9.182582827493399e-05,
+        9.121329482965357e-05], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        0.0, 0.0, 0.0, 0.0]]
+coeff_T: [[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+        1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], [0.010405701588193256,
+        0.031217458622475387, 0.052030282300007044, 0.07284488729284219,
+        0.09366199165923768, 0.11448232348001261, 0.13530661795199833, 0.15613562312768578,
+        0.1769701006550951, 0.1978108282598657, 0.21865860215350527, 0.239514240229231,
+        0.2603785837064265, 0.2812525009254954, 0.3021368895909426, 0.3230326804028972,
+        0.3439408402623957, 0.364862375760732, 0.3857983373704186, 0.40674982298375406,
+        0.4277179831038003, 0.448704025069048, 0.4697092184557, 0.4907349007351052,
+        0.5117824833621327, 0.5328534582101059, 0.5539494051126325, 0.5750719994713749,
+        0.5962230211269365, 0.6174043634081521, 0.6386180439591509, 0.65986621569872,
+        0.6811511795892895, 0.7024753982332104, 0.7238415112733477, 0.7452523520473575,
+        0.766710966406405, 0.7882206332163809, 0.809784887584458, 0.8314075462770933,
+        0.8530927365312952, 0.8748449278390161, 0.8966689679635017, 0.9185701230181873,
+        0.9405541230165837, 0.9626272125465405, 0.9847962090756154, 1.0070685678374995,
+        1.0294524567351395, 1.051956840780757, 1.0745915790479181, 1.0973675357834407,
+        1.1202967078627388, 1.1433923720909103, 1.166669255603407, 1.1901437335798832,
+        1.2138340602285362, 1.2377606387244824, 1.2619463389893995, 1.286416872853609,
+        1.3112012392852694, 1.3363322556352497, 1.3618471948372457, 1.3877885541648267,
+        1.4142049885597927, 1.44115245152897, 1.4686955995943163, 1.496909534836941,
+        1.5258819853838104, 1.555716058594904, 1.5865337522778187, 1.6184804816041274,
+        1.6517309857684475, 1.6864971363579606, 1.723038411835424, 1.76167617772883,
+        1.8028135134538859, 1.846963310358761, 1.8947890333564306, 1.9471654623432884,
+        2.0052720688685612, 2.070741914624462, 2.1459096815630576, 2.2342473377862917,
+        2.341181530593291, 2.4757621593130326, 2.6544734090493263, 2.911431845669583,
+        3.3332427926214367, 4.246434535359267, 12.33198797799215, 3.7047290089680276,
+        2.5901924071674722, 2.1266741246516916, 1.8595787972031326, 1.6820749907293904,
+        1.5541602851522576, 1.4570458007770533, 1.380598193134844, 1.3188133999063683,
+        1.2678824545656882, 1.2252604232600388, 1.1891767324729121, 1.158359391011678,
+        1.1318710270747467, 1.1090071126269592, 1.0892306672661864, 1.0721294643725914,
+        1.0573879286165508, 1.0447694568824728, 1.034107317841022, 1.025304690532016,
+        1.018348491401052, 1.0133524985722124, 1.0106854574524518, 1.0114587163032653,
+        1.0210995218638894, 1.281752405784205, 1.029059914525033, 1.1693442562044634,
+        1.0628629347630054, 1.0157126713011764, 1.0650427506557762, 1.2486280348135295,
+        1.2606038958482955, 1.0182940176324384, 1.0188576975764108, 1.0657736590839586,
+        1.1803674513096176, 1.3816824464045172, 1.1476756178580496, 1.0198645258176506,
+        1.0145654072804962, 1.0480117242864615, 1.1174476114735161, 1.2430547067356879,
+        1.3155883793162282, 1.1291162682369988, 1.0253872483920965, 1.0111354499660097,
+        1.0327308633359344, 1.078847291773838, 1.1547109314923614, 1.2514462755715328,
+        1.2445925822993291, 1.1034596377432755, 1.0246691752455541, 1.010504151291013,
+        1.0270153029417168, 1.0629249852242015, 1.1183853552235548, 1.191006608100163,
+        1.230121953903494, 1.1469723103260148, 1.0466686661602602, 1.0113187536060058,
+        1.0185498395479007, 1.059006842492749, 1.0899613736063312, 1.117346351241253,
+        1.1334223623968573, 1.1288827522697948, 1.1055494026872759, 1.0782227451629802,
+        1.0592969855865202, 1.051539850959424, 1.0526667078703404, 1.0596402544584982,
+        1.0698948214444752, 1.0811285705425582, 1.090767216085298, 1.0956942085814387,
+        1.0930260228284718, 1.0823754465668394, 1.067569294527044, 1.0544971702555512,
+        1.0469618815746162, 1.0454178071096434, 1.0484853893817572, 1.0544986187644243,
+        1.0621375677517755, 1.0704961381196123, 1.078975476497045, 1.0871689544277774,
+        1.0947787721611761, 1.1015628916094793, 1.107303159391586, 1.1117869245622154,
+        1.1147974538690013, 1.1161112748895632, 1.11550325724361, 1.1127632190761765,
+        1.107731488233205, 1.10036470664352, 1.090844108377679, 1.0797270846995537,
+        1.068100791088984, 1.0576106421377411, 1.050157183893458, 1.047162022520985,
+        1.0487358740048018, 1.053453001514237, 1.059041613801824, 1.0634348119687,
+        1.0654310815888854, 1.0647724196293349, 1.0618980129874867, 1.0576431601746994,
+        1.0529928237887773, 1.0488908075517966, 1.0460802033245953, 1.0449704591320863,
+        1.0455557830797932, 1.0474228581483835, 1.0498674919026483, 1.052095320475364,
+        1.0534399818615563, 1.0535242603209813, 1.0523203689085976, 1.0501106800767313,
+        1.0473816072904314, 1.044690891740227, 1.0425402963033517, 1.0412743070249761,
+        1.0410177731273513, 1.0416609951179947, 1.0428954728662563, 1.044294284447198,
+        1.0454190170918856, 1.0459256657042948, 1.0456410169038655, 1.0445907102986085,
+        1.0429762184832572, 1.0411128728198937, 1.039349086491563, 1.0379872154187428,
+        1.0372219054469785, 1.0371057485960116, 1.03754643545231, 1.0383343928693123,
+        1.039194622753038, 1.039851345096965, 1.0400905350796983, 1.0398054365428926,
+        1.0390145497142762, 1.0378493034591483, 1.0365168007304022, 1.0352487301788948,
+        1.0342493124078929, 1.0336534346837394, 1.0335024355866766, 1.0337407768799747,
+        1.0342328591886303, 1.0347957253560638, 1.0352405049784545, 1.035413628237045,
+        1.0352287481228717, 1.0346824070258047, 1.0338504906983814, 1.0328673096136052,
+        1.0318932156198737, 1.0310788169941705, 1.0305337560206578, 1.0303061329155807,
+        1.0303758523350888, 1.0306622069758296, 1.0310433774744285, 1.0313834682247933,
+        1.0315614041540004, 1.0314957088850405, 1.0311600613630825, 1.0305865595419696,
+        1.0298564167402346, 1.0290806677055413, 1.0283755836611521, 1.0278383516492084,
+        1.0275280675734446, 1.0274555392595364, 1.0275833210554317, 1.0278353166565697,
+        1.028113557925156, 1.028318600813872, 1.028369475253657, 1.028219327037513,
+        1.0278637828584793, 1.0273405425345867, 1.0267205037525202, 1.0260924777975466,
+        1.025544846477137, 1.0251480247763716, 1.0249412260910433, 1.0249259194814684,
+        1.025066850029444, 1.02529995611181, 1.0255452901970294, 1.0257223210282607,
+        1.0257648029010262, 1.0256326726435252, 1.0253190599343214, 1.0248513529866337,
+        1.0242862431570319, 1.023699671537429, 1.023173487432206, 1.0227812423457414,
+        1.0225757227911578, 1.0225804729583896, 1.0227867079291795, 1.0231558625920434,
+        1.0236268660368188, 1.0241263838599448, 1.0245799238158844, 1.02492186791376,
+        1.0251030339440999, 1.025095064587609, 1.02489159294604, 1.0245066150620976,
+        1.0239707746709208, 1.023326358346689, 1.0226217644558833, 1.021906101285261,
+        1.0212244281588494, 1.0206140012575355, 1.0201017346645487, 1.01970294409935,
+        1.0194213136148502, 1.019249923346768, 1.0191731069429275, 1.0191688732852615,
+        1.0192116243150124, 1.019274919370764, 1.019334065137976, 1.0193683409956829,
+        1.0193627001526906, 1.0193088210229058, 1.0192054267310708, 1.0190578476296723,
+        1.0188768716183283, 1.0186770037802042, 1.0184743303128918, 1.0182842404063064,
+        1.0181192928879848, 1.0179875135743663, 1.0178913688768616, 1.0178275801104455,
+        1.0177878261768085, 1.01776024320873, 1.0177314906847554, 1.017689042931833,
+        1.0176233107476458, 1.017529218398587, 1.017406957562585, 1.0172617934412895,
+        1.0171029760102193, 1.0169419730549216, 1.0167903589175813, 1.0166577444354123,
+        1.01655011485032, 1.0164688612724377, 1.016410663622559, 1.0163682300463488,
+        1.0163317440769504, 1.0162907424106593, 1.0162360674601332, 1.0161615273233446,
+        1.0160649562456838, 1.0159484898525504, 1.0158180256603866, 1.0156819968739115,
+        1.0155497135962204, 1.0154295969155545, 1.015327638021018, 1.015246360032874,
+        1.0151844582925176, 1.0151371653441932, 1.0150972525599804, 1.0150564643951137,
+        1.0150071042609794, 1.0149434677375253, 1.0148628545201308, 1.0147659783139051,
+        1.014656715542796, 1.0145412634182047, 1.014426888745126, 1.014320519504479,
+        1.0142274503865967, 1.0141504008694917, 1.0140890894700092, 1.0140403862164862,
+        1.0139989961703382, 1.013958529318288, 1.0139127435508026, 1.0138567201346054,
+        1.0137877501630936, 1.013705772018573, 1.0136132911614988, 1.0135148155341038,
+        1.0134159316099207, 1.0133222097772312, 1.013238152350964, 1.0131663806748057,
+        1.013107205139215, 1.0130586450967491, 1.0130168795286392, 1.0129770295941685,
+        1.012934115015503, 1.012883998063757, 1.0128241366056252, 1.0127540093472274,
+        1.0126751434108507, 1.0125907528879876, 1.0125050710878407, 1.0124225143808807,
+        1.012346841951275, 1.0122804698812466, 1.0122240626895564, 1.0121764688278378,
+        1.0121350000291731, 1.0120959902327247, 1.0120555195973866, 1.0120101616894819,
+        1.0119576119279183, 1.0118970823064477, 1.011829395589384, 1.0117567717144933,
+        1.0116823580356233, 1.0116096017926428, 1.011541589244373, 1.0114804772355979,
+        1.011427120592204, 1.0113809580179527, 1.0113401684618293, 1.0113020589145187,
+        1.0112636025825794, 1.0112220208143148, 1.0111752973437766, 1.011122529824837,
+        1.0110640576541152, 1.0110013497456665, 1.010936682251987, 1.0108726751634736,
+        1.010811781001463, 1.0107558244061186, 1.010705678091151, 1.0106611317601257,
+        1.0106209722029562, 1.0105832523757623, 1.010545692317457, 1.0105061315501431,
+        1.0104629451548468, 1.0104153450546665, 1.0103635120489503, 1.0103085379125731,
+        1.0102521936713247, 1.0101965728120186, 1.0101436805395205, 1.0100950483463809,
+        1.0100514461083596, 1.0100127435757589, 1.0099779437760297, 1.0099453782018328,
+        1.0099130238107803, 1.0098788801888623, 1.0098413355041884, 1.009799453634957,
+        1.009753131119184, 1.0097030980338897, 1.0096507665618628, 1.009597959136256,
+        1.009546569402766, 1.0094982200198905, 1.0094539798998494, 1.0094141906055767,
+        1.0093784300724977, 1.0093456158707848, 1.009314224724616, 1.009282584554074,
+        1.0092491834503914, 1.0092129386498239, 1.0091733777014147, 1.0091307016712698,
+        1.0090857228877932, 1.0090396930447783, 1.0089940570768945, 1.0089501805876138,
+        1.008909101722467, 1.0088713520347024, 1.0088368766350904, 1.0088050646719322,
+        1.0087748806396108, 1.008745068930576, 1.0087143916122217, 1.0086818546968452,
+        1.008646881798769, 1.008609405122993, 1.0085698599445934, 1.0085290869590005,
+        1.0084881636653849, 1.0084481982281592, 1.0084101249387631, 1.0083745386823282,
+        1.0083415973140373, 1.0083110073937698, 1.0082820929587366, 1.0082539318779784,
+        1.0082255325447815, 1.008196017241137, 1.0081647784389702, 1.0081315803968898,
+        1.008096589358193, 1.0080603292927317, 1.0080235738524617, 1.007987196496741,
+        1.007952007599135, 1.007918608682187, 1.0078872897127427, 1.0078579866176038,
+        1.007830304621483, 1.0078036008653775, 1.0077771092459857, 1.0077500833614499,
+        1.0077219310058754, 1.0076923161091453, 1.0076612107616285, 1.0076288896263605,
+        1.00759586976518, 1.0075628086958366, 1.0075303806016007, 1.0074991538405131,
+        1.0074694918138651, 1.007441494223361, 1.0074149878421532, 1.0073895666840098,
+        1.0073646725873548, 1.0073397003077658, 1.0073141073965304, 1.007287509001263,
+        1.007259741148251, 1.0072308823128022, 1.0072012309277896, 1.0071712444518055,
+        1.0071414522763298, 1.0071123589508804, 1.007084355292379, 1.0070576528569253,
+        1.0070322524987743, 1.0070079512837438, 1.0069843850814366, 1.0069610979781083,
+        1.0069376252857096, 1.0069135750617237, 1.006888693919658, 1.0068629062349377,
+        1.0068363209464968, 1.0068092060490894, 1.0067819364935298, 1.0067549255861505,
+        1.0067285523965412, 1.0067030978164142, 1.0066786998545127, 1.0066553349736487,
+        1.0066328275205416, 1.0066108844363937, 1.0065891483027334, 1.006567259034751,
+        1.0065449135683335, 1.0065219137579575, 1.0064981951563647, 1.0064738328761433,
+        1.0064490246813667, 1.006424055138228, 1.0063992474746775, 1.0063749113548357,
+        1.0063512949048172, 1.0063285481242963, 1.006306702589928, 1.006285669551234,
+        1.0062652556355078, 1.0062451928754748, 1.0062251779975258, 1.006204915047432,
+        1.0061841555029067, 1.0061627308957186, 1.006140574400942, 1.0061177295573822,
+        1.0060943459782636, 1.0060706633668766, 1.006046986225324, 1.0060236522869384,
+        1.0060009979464701, 1.0059793238938222, 1.0059588638828372, 1.005939759179242,
+        1.0059220407880731, 1.005905621072898, 1.005890295822479, 1.005875757154413,
+        1.0058616168389123, 1.0058474386849332, 1.0058327776133245, 1.0058172220617463,
+        1.0058004355805388, 1.0057821930593824, 1.0057624071222526, 1.0057411409336925,
+        1.0057186049733524, 1.0056951371510272, 1.0056711677401593, 1.0056471727137106,
+        1.0056236208456135, 1.0056009210860495, 1.0055793769974526, 1.005559154342196,
+        1.0055402662873574, 1.0055225783377373, 1.0055058323576913, 1.0054896863085911,
+        1.0054737640396496, 1.0054577079953644, 1.005441227291396, 1.0054241343436368,
+        1.0054063650104594, 1.005387979753308, 1.0053691462363903, 1.005350106610578,
+        1.0053311350106238, 1.0053124921777015, 1.0052943843865167, 1.0052769329771671,
+        1.0052601589228032, 1.0052439843232612, 1.0052282499275507, 1.0052127452157678,
+        1.0051972456327642, 1.005181550568926, 1.0051655157721977, 1.0051490750096375,
+        1.0051322477614246, 1.0051151321745313, 1.0050978850040333, 1.0050806924040143,
+        1.0050637368467736, 1.00504716592876, 1.0050310683090782, 1.005015460637307,
+        1.0050002873232313, 1.0049854327421859, 1.0049707433500774, 1.0049560555613386,
+        1.0049412243854576, 1.0049261478487086, 1.0049107831162323, 1.0048951517967495,
+        1.004879333866887, 1.0048634516439823, 1.004847646918783, 1.0048320554497974,
+        1.0048167833475017, 1.0048018894053692, 1.0047873762716293, 1.0047731917239697,
+        1.004759239507216, 1.0047453975405134, 1.0047315400798442, 1.0047175598340647,
+        1.0047033861621957, 1.0046889962827001, 1.0046744177417375, 1.0046597219713995,
+        1.0046450103354831, 1.0046303953356026, 1.0046159804195656, 1.0046018419772276,
+        1.0045880166198005, 1.004574495821226, 1.0045612286483363, 1.004548131866739,
+        1.004535105436288, 1.0045220505218047, 1.004508886785804, 1.0044955659479673,
+        1.0044820793363338, 1.004468458272866, 1.004454767424789, 1.0044410924821465,
+        1.0044275244780707, 1.0044141435917402, 1.0044010052859171, 1.0043881311437604,
+        1.0043755058829849, 1.004363080905348, 1.0043507835881802, 1.0043385305437196,
+        1.0043262424274968, 1.004313857671509, 1.0043013427750629, 1.0042886974478022,
+        1.004275953839573, 1.0042631701391602, 1.0042504197938527, 1.00423777832851,
+        1.004225310107359, 1.004213057331462, 1.0042010331201765, 1.004189219773916,
+        1.0041775723960105, 1.0041660271262636, 1.0041545124667177, 1.0041429616887037,
+        1.0041313241754, 1.0041195737883857, 1.004107712899317, 1.004095771495971,
+        1.0040838016187599, 1.0040718681643934, 1.004060037678154, 1.0040483670531961,
+        1.0040368940238404, 1.0040256309957885, 1.004014563166944, 1.0040036511638006,
+        1.0039928376750156, 1.0039820569282016, 1.0039712454280074, 1.003960352214797,
+        1.0039493470288163, 1.0039382251428886, 1.003927008186194, 1.0039157409255786,
+        1.0039044845933, 1.0038933078543892, 1.0038822768199542, 1.0038714455964286,
+        1.0038608487149134, 1.0038504964455726, 1.0038403735333976, 1.0038304413733574,
+        1.0038206431567318, 1.003810911136624, 1.0038011749284255, 1.0037913697018082,
+        1.003781443227811, 1.0037713609862555, 1.0037611088661988, 1.0037506933488893,
+        1.003740139394034, 1.00372948651213, 1.003718783669916, 1.0037080837333645,
+        1.0036974381109263, 1.0036868921407482, 1.003676481599047, 1.0036662305244275,
+        1.0036561503825878, 1.0036462404577338, 1.0036364892615925, 1.0036268766990954,
+        1.003617376715109, 1.0036079601582646, 1.0035985976242945, 1.0035892620730702,
+        1.0035799310452282, 1.0035705883351977, 1.0035612250102968, 1.0035518397048562,
+        1.0035424381679208, 1.0035330321039582, 1.0035236374150702, 1.003514272023044,
+        1.0035049535092861, 1.003495696848536, 1.0034865125175654, 1.0034774052267623,
+        1.0034683734504337, 1.0034594098279324, 1.003450502385985, 1.0034416364111682,
+        1.0034327967002126, 1.0034239698527112, 1.003415146258213, 1.0034063214722522,
+        1.0033974967684425, 1.0033886787828847, 1.0033798783121073, 1.0033711084626418,
+        1.0033623824561555, 1.00335371145019, 1.0033451027312252, 1.003336558573717,
+        1.0033280759464218, 1.0033196471045605, 1.0033112609574546, 1.0033029049717288,
+        1.0032945672820623, 1.0032862386499586, 1.0032779139410684, 1.0032695928778625,
+        1.0032612799515102, 1.0032529835224548, 1.0032447142779257, 1.0032364833225722,
+        1.0032283002371645, 1.0032201714402154, 1.0032120991293048, 1.003204080973658,
+        1.0031961105962397, 1.0031881787458672, 1.0031802749418426, 1.0031723892955413,
+        1.0031645141883905, 1.0031566455170744, 1.0031487832982195, 1.0031409315409736,
+        1.003133097425817, 1.0031252899485843, 1.003117518278922, 1.003109790127089,
+        1.003102110405131, 1.0030944804104727, 1.0030868976631397, 1.0030793564100107,
+        1.0030718486918737, 1.0030643657724372, 1.0030568996693134, 1.0030494445150646,
+        1.003041997512676, 1.0030345593268735, 1.0030271338559258, 1.0030197274392603,
+        1.0030123476544541, 1.0030050019260108, 1.002997696196226, 1.00299043389136,
+        1.0029832153584788, 1.0029760378607668, 1.002968896118175, 1.0029617832840816,
+        1.0029546921741943, 1.0029476165238225, 1.0029405520502193, 1.0029334971368482,
+        1.0029264530280102, 1.0029194235118863, 1.0029124141613015, 1.0029054312781684,
+        1.0028984807364103, 1.0028915669311587, 1.0028846920178596, 1.0028778555686961,
+        1.0028710546964152, 1.002864284611323, 1.0028575395012302, 1.0028508135696024,
+        1.002844102043404, 1.002837401972426, 1.0028307126836362, 1.002824035818992,
+        1.0028173749610991, 1.0028107349242736, 1.0028041208460021, 1.0027975372457245,
+        1.002790987219219, 1.002784471908246, 1.0027779903323777, 1.0027715396031218,
+        1.002765115471824, 1.0027587131046818, 1.0027523279405999, 1.0027459564767331,
+        1.0027395968436341, 1.0027332490731786, 1.002726915019855, 1.0027205979589588,
+        1.002714301942289, 1.002708031033127, 1.0027017885605911, 1.0026955765263073,
+        1.002689395265556, 1.0026832434168675, 1.002677118197416, 1.0026710159268648,
+        1.0026649326992978, 1.0026588650788706, 1.0026528106936643, 1.0026467686235827,
+        1.0026407395175285, 1.0026347254251924, 1.0026287293801883, 1.002622754814946,
+        1.0026168049159716, 1.0026108820362392, 1.00260498726862, 1.00259912025311,
+        1.0025932792472916, 1.002587461441899, 1.0025816634601126, 1.0025758819479529,
+        1.0025701141490446, 1.0025643583622477, 1.0025586142037632, 1.0025528826317796,
+        1.0025471657347227, 1.002541466325996, 1.0025357874211938, 1.002530131692727,
+        1.00252450099839, 1.0025188960649345, 1.0025133163783342, 1.0025077602946155,
+        1.0025022253459268, 1.002496708682748, 1.0024912075707555, 1.0024857198534045,
+        1.0024802442997747, 1.002474780779632, 1.0024693302397545, 1.0024638944912905,
+        1.0024584758510071, 1.0024530767038147, 1.0024476990659663, 1.002442344225949,
+        1.0024370125242061, 1.0024317033065777, 1.0024264150547104, 1.0024211456653578,
+        1.0024158928250042, 1.002410654410974, 1.0024054288474524, 1.00240021535488,
+        1.0023950140517541, 1.0023898258950923, 1.0023846524746887, 1.0023794957016596,
+        1.0023743574492563, 1.0023692392106798, 1.0023641418337685, 1.0023590653771346,
+        1.0023540091096321, 1.0023489716491236, 1.0023439512120766, 1.0023389459268224,
+        1.0023339541534393, 1.002328974753737, 1.002324007265237, 1.0023190519513046,
+        1.0023141097221846, 1.002309181944591, 1.0023042701765674, 1.0022993758764058,
+        1.0022945001375492, 1.0022896434952882, 1.0022848058371003, 1.002279986429342,
+        1.0022751840521889, 1.0022703972159808, 1.0022656244186283, 1.0022608643977673,
+        1.0022561163336448, 1.0022513799686805, 1.0022466556252572, 1.0022419441216668,
+        1.00223724660395, 1.0022325643255245, 1.0022278984146376, 1.002223249670587,
+        1.0022186184233568, 1.0022140044791958, 1.0022094071589878, 1.0022048254199016,
+        1.00220025803662, 1.0021957038088312, 1.002191161758181, 1.0021866312808674,
+        1.0021821122308445, 1.002177604921432, 1.002173110047609, 1.0021686285449458,
+        1.002164161411498, 1.0021597095245196, 1.0021552734836827, 1.0021508535068488,
+        1.002146449394552, 1.0021420605669982, 1.0021376861648554, 1.002133325194508,
+        1.0021289766915364, 1.0021246398740293, 1.0021203142600692, 1.0021159997307576,
+        1.0021116965300374, 1.0021074052035783, 1.002103126489156, 1.0020988611786288,
+        1.0020946099755925, 1.002090373372548, 1.0020861515672244, 1.0020819444303906,
+        1.0020777515284713, 1.0020735721951342, 1.002069405638235, 1.002065251063372],
+    [0.004516222979432857, 0.01354940391320797, 0.02258479187183469, 0.03162385942175675,
+        0.0406680800870291, 0.04971893101137473, 0.058777891459474325, 0.06784644505477049,
+        0.07692607981981735, 0.08601828894347388, 0.09512457148042773, 0.10424643335372223,
+        0.11338538763185795, 0.12254295569137671, 0.13172066763889315, 0.14092006327143816,
+        0.1501426927716658, 0.15939011743898987, 0.16866391063137337, 0.17796565830726727,
+        0.1872969601748406, 0.19665943027413027, 0.2060546979259844, 0.21548440862154095,
+        0.22495022490969827, 0.23445382722119126, 0.24399691494623194, 0.25358120726851746,
+        0.2632084442629107, 0.2728803877288395, 0.28259882244468904, 0.29236555704685474,
+        0.30218242524449945, 0.31205128685976674, 0.3219740290720429, 0.33195256753207203,
+        0.34198884767523824, 0.3520848459040866, 0.36224257100415996, 0.3724640654020906,
+        0.38275140666636404, 0.3931067088628626, 0.40353212413878187, 0.41402984419637284,
+        0.42460210202493875, 0.4352511733688806, 0.44597937871646226, 0.4567890848090633,
+        0.4676827067421226, 0.4786627097298631, 0.4897316111436353, 0.5008919826309075,
+        0.5121464521802126, 0.5234977063968954, 0.534948492828811, 0.5465016222706526,
+        0.5581599713578375, 0.5699264850272773, 0.5818041792404458, 0.5937961437200199,
+        0.6059055447594376, 0.6181356281690047, 0.6304897223001301, 0.6429712411358054,
+        0.6555836874517933, 0.6683306561036566, 0.681215837321093, 0.6942430200418102,
+        0.7074160953462774, 0.720739059845325, 0.7342160190358954, 0.7478511905957873,
+        0.7616489076477808, 0.7756136217401765, 0.7897499056694942, 0.8040624558670817,
+        0.818556094466186, 0.8332357706575794, 0.8481065612272254, 0.8631736702007363,
+        0.8784424270531688, 0.8939182832775204, 0.9096068068649863, 0.9255136740190777,
+        0.9416446574841966, 0.9580056104851917, 0.9746024452099964, 0.9914411042810979,
+        1.008527523251874, 1.025867581935946, 1.0434670410405553, 1.0613314602726671,
+        1.0794660923862236, 1.0978757460939816, 1.1165646082812386, 1.1355360130933188,
+        1.1547921403330135, 1.1743336202447807, 1.1941590119139875, 1.2142641102990652,
+        1.234641017728519, 1.255276887777639, 1.2761522063875257, 1.2972384093628353,
+        1.3184945288986378, 1.3398623895280375, 1.361259580450768, 1.3825689157958163,
+        1.4036221443429542, 1.424173820619501, 1.443857390716018, 1.462106776727851,
+        1.4780044415739515, 1.4899509116858898, 1.4948079222520136, 1.4849090973527366,
+        1.4286986966863968, 1.971730082839934, 1.4528645548114194, 0.8016719105625986,
+        2.195891505455267, 1.7770330506788583, 1.3822700382344235, 0.12079407408645067,
+        3.4834600571182386, 3.1458798788869453, 2.8136867485360164, 2.290093394677793,
+        2.4184426076846695, 5.062812130340401, 4.264866778996453, 2.5921601298102765,
+        1.7386487828864208, 1.2699821546863785, 1.1292790075634076, 1.5790581010043936,
+        2.449002395690969, 2.3116039932024712, 1.8041123461553272, 1.4542969258680971,
+        1.2338406551175858, 1.124287219752225, 1.1837142664289895, 1.5214712978097436,
+        1.9005349019999354, 1.802425287389526, 1.5397659978324367, 1.3369758161522862,
+        1.20207379783807, 1.1272145631153154, 1.130371226298617, 1.2649512720216125,
+        1.5254054060100475, 1.6258546630586057, 1.4871376905470008, 1.3243688902425879,
+        1.2020114567127391, 1.158999365138489, 1.1676697257311508, 1.2042505766797733,
+        1.2608850969523977, 1.3117265632905268, 1.3291289835345097, 1.3108406830813453,
+        1.2749107689753978, 1.237846809826947, 1.2077603427448849, 1.1874014617468287,
+        1.1773681837042564, 1.1774711284910075, 1.18666725612106, 1.2020046623512328,
+        1.217536158628653, 1.2255300364278487, 1.2211564781496345, 1.2060519337365168,
+        1.1859857992274836, 1.166246848263695, 1.1496919600621494, 1.1372074643992094,
+        1.1286706473817383, 1.123593669206943, 1.1214272042272373, 1.121670331130462,
+        1.123893749026739, 1.1277304677232163, 1.1328570502375443, 1.1389737484700537,
+        1.1457855499036453, 1.1529837166179266, 1.160226804882487, 1.1671207542716635,
+        1.1731997124728266, 1.1779139429241692, 1.1806401276208311, 1.180742931267227,
+        1.1777274045898138, 1.1715031387804462, 1.1626892715850374, 1.152730931056277,
+        1.1435528588602717, 1.1367913098044702, 1.1331170696684676, 1.132141214720984,
+        1.1328408539720496, 1.1340826705206357, 1.1349559228046415, 1.1348910491729522,
+        1.1336545026219336, 1.1312971461242696, 1.1280890837783606, 1.124444243787302,
+        1.1208301789742166, 1.1176671364842106, 1.1152358489618417, 1.113622332202177,
+        1.1127196020877768, 1.1122830707077642, 1.112014164417068, 1.111640200724198,
+        1.1109685722997826, 1.1099091690827945, 1.1084704249037285, 1.1067383221294416,
+        1.104846671448089, 1.1029447199078006, 1.1011667916580694, 1.099608366347618,
+        1.0983125893192345, 1.0972694582269222, 1.096426721648557, 1.0957081689738635,
+        1.0950332874348379, 1.0943330424590347, 1.0935590769939827, 1.092686378761951,
+        1.0917112289212718, 1.0906467140637235, 1.0895176276733947, 1.088355771464121,
+        1.0871959257204376, 1.0860723140536812, 1.0850152907123212, 1.0840481520296836,
+        1.0831842625251582, 1.0824249206740715, 1.081758460836038, 1.0811609885574902,
+        1.080598939633475, 1.0800334025305207, 1.0794258660454084, 1.0787447335167717,
+        1.0779715921501762, 1.077105934149827, 1.076166972549542, 1.0751915600700734,
+        1.074228052483873, 1.0733270689565397, 1.0725310936498416, 1.0718653232450597,
+        1.0713319025999009, 1.070908837415057, 1.0705537767285138, 1.0702118651822317,
+        1.069826160679886, 1.069348715453396, 1.0687502820125625, 1.0680267263046934,
+        1.0672006711460564, 1.0663177101726176, 1.0654376631141955, 1.0646225405614782,
+        1.063923777892787, 1.0633715534565318, 1.0629685151844381, 1.0626891741918125,
+        1.062484940680441, 1.0622936377033854, 1.0620515553983232, 1.061705758916348,
+        1.0612243933723924, 1.0606030795283892, 1.059866130607387, 1.0590622110449592,
+        1.0582551127217579, 1.057511357436312, 1.0568870870893425, 1.0564169338268448,
+        1.056107161208592, 1.055934423774452, 1.0558502700628776, 1.0557903448101793,
+        1.0556864018996557, 1.0554788535078325, 1.0551276424520462, 1.054619633300732,
+        1.0539713484272126, 1.0532266218228343, 1.052449526951436, 1.05171368479237,
+        1.0510896886877679, 1.0506327829577236, 1.0503729853487664, 1.050309471798359,
+        1.0504102631909942, 1.0506172114505803, 1.0508552252579049, 1.0510438799751576,
+        1.0511092231712698, 1.0509937676540262, 1.0506632501503508, 1.0501095160119542,
+        1.0493496457607547, 1.0484220067755337, 1.0473802258977158, 1.0462861527203149,
+        1.0452027839298137, 1.0441879226197, 1.0432891153297696, 1.0425401827516796,
+        1.0419594563259622, 1.0415496593458644, 1.0412992311416491, 1.0411847907300051,
+        1.0411743766585462, 1.04123108453238, 1.041316748471636, 1.041395366093457,
+        1.0414360328925494, 1.0414152165358526, 1.0413182562405707, 1.041140017280905,
+        1.0408846728974552, 1.0405646347301218, 1.040198714214442, 1.0398096699031767,
+        1.0394213705976998, 1.039055867774604, 1.0387307085603927, 1.0384568207610017,
+        1.0382372575399677, 1.0380670003479566, 1.0379338898511088, 1.0378205979028923,
+        1.0377073888441144, 1.0375752728654564, 1.0374090593077592, 1.0371998020529682,
+        1.0369462083057481, 1.0366547506614672, 1.0363384513011615, 1.036014549551722,
+        1.0357014680912526, 1.0354156167377475, 1.0351685942558673, 1.0349652691771667,
+        1.034803060111865, 1.0346725253713862, 1.034559146009425, 1.0344459807233954,
+        1.0343167180785175, 1.0341585785381628, 1.0339645429073965, 1.0337345059083627,
+        1.0334751543053797, 1.0331986099154722, 1.0329201096469398, 1.0326551696941701,
+        1.0324167654601246, 1.0322130403730558, 1.0320459450000725, 1.031911028705006,
+        1.031798394359327, 1.0316946191284029, 1.0315852752253607, 1.031457581666565,
+        1.031302699779599, 1.0311172563610598, 1.0309038274085685, 1.030670314405303,
+        1.0304283547720754, 1.0301910861269505, 1.0299706956891779, 1.0297762122921497,
+        1.0296119384279383, 1.029476789577349, 1.0293646350936085, 1.0292655513787496,
+        1.029167735820289, 1.0290597161041972, 1.028932443224215, 1.028780885856447,
+        1.0286048435631736, 1.0284088477689068, 1.0282011930894135, 1.0279923030962104,
+        1.0277927526131452, 1.0276113218144802, 1.0274534385274663, 1.0273202814734426,
+        1.027208687394454, 1.0271118545095415, 1.0270206907475388, 1.0269255425145798,
+        1.0268179773355701, 1.026692291892518, 1.0265464755222635, 1.02638246675294,
+        1.026205676046539, 1.0260238850850465, 1.0258457452274468, 1.0256791644616117,
+        1.025529882516936, 1.0254004885184453, 1.0252900457215068, 1.025194371814761,
+        1.0251069027680804, 1.0250199646124438, 1.0249262086026338, 1.0248199423786784,
+        1.0246981162911775, 1.0245607943226804, 1.0244110391744368, 1.024254251572107,
+        1.0240971034191249, 1.0239462745424266, 1.0238072313538797, 1.0236832692863411,
+        1.0235749844917394, 1.023480256114879, 1.0233947247998134, 1.0233126634208578,
+        1.0232280680656927, 1.023135762538679, 1.023032313557344, 1.022916594841294,
+        1.0227899080668037, 1.0226556534776075, 1.0225186264405701, 1.0223840827212576,
+        1.0222567528525226, 1.0221399888336682, 1.0220351954892408, 1.0219416412527538,
+        1.0218566704531216, 1.0217762650054287, 1.0216958410680956, 1.021611126546177,
+        1.0215189548655492, 1.0214178304463633, 1.0213081674239688, 1.0211921662657142,
+        1.0210733608329128, 1.020955928324516, 1.020843895508108, 1.0207403897691634,
+        1.0206470709813946, 1.0205638433695257, 1.0204888929631315, 1.0204190361149177,
+        1.0203503087962407, 1.0202786847747412, 1.0202007903701598, 1.020114487426996,
+        1.0200192231703429, 1.0199160902774045, 1.0198075942070484, 1.0196971775034989,
+        1.0195885928291033, 1.0194852405983459, 1.0193895895855973, 1.019302780164298,
+        1.0192244740857312, 1.0191529689150132, 1.0190855478500362, 1.0190189950401527,
+        1.0189501796166986, 1.0188766027758198, 1.018796812454401, 1.0187106170228477,
+        1.018619067641118, 1.0185242212229135, 1.0184287345462757, 1.018335368119652,
+        1.0182464913439973, 1.018163676635775, 1.0180874509122775, 1.018017242261455,
+        1.0179515235865575, 1.017888120081172, 1.0178246196485845, 1.0177588094532617,
+        1.0176890600818858, 1.0176145911101644, 1.0175355755286326, 1.0174530708296008,
+        1.017368795891819, 1.0172847994534502, 1.0172030833538854, 1.0171252491482574,
+        1.0170522297255638, 1.016984149981897, 1.016920335984292, 1.0168594650373937,
+        1.0167998244780918, 1.0167396290952502, 1.016677338700424, 1.0166119196825543,
+        1.0165430065514027, 1.0164709389711988, 1.0163966728395317, 1.0163215863174757,
+        1.0162472194079413, 1.0161749957700708, 1.0161059765052276, 1.0160406878878994,
+        1.015979050215247, 1.01592041602713, 1.015863706397207, 1.0158076172597428,
+        1.0157508566247646, 1.0156923697619726, 1.0156315133651266, 1.0155681503335001,
+        1.0155026519702461, 1.0154358112216586, 1.0153686860171198, 1.0153024031557032,
+        1.015237958707988, 1.015176049875331, 1.0151169661737889, 1.015060556213958,
+        1.0150062724656668, 1.0149532827434669, 1.0149006260802425, 1.0148473839731182,
+        1.0147928366476497, 1.0147365779839193, 1.014678571138903, 1.0146191380149885,
+        1.014558887492374, 1.0144985976798475, 1.0144390746170522, 1.0143810128014623,
+        1.014324881333232, 1.014270853886807, 1.0142187923073793, 1.0141682839841841,
+        1.014118723986453, 1.014069425797857, 1.0140197404626363, 1.0139691635811028,
+        1.0139174127307686, 1.013864463815883, 1.0138105423954669, 1.0137560738280285,
+        1.0137016027603685, 1.0136476970092128, 1.0135948526094347, 1.013543415620685,
+        1.013493532585439, 1.0134451361009416, 1.0133979658249828, 1.0133516194450476,
+        1.0133056236309916, 1.013259512412761, 1.0132129000605166, 1.013165537290605,
+        1.0131173430341867, 1.0130684083995594, 1.0130189740443138, 1.012969386192638,
+        1.0129200393933528, 1.0128713154671405, 1.012823527871176, 1.0127768791126124,
+        1.0127314362652993, 1.012687126595314, 1.0126437522996603, 1.0126010208540699,
+        1.0125585857571824, 1.0125160916859983, 1.0124732182115286, 1.0124297170978198,
+        1.012385439570255, 1.0123403515105105, 1.0122945360627253, 1.0122481844316638,
+        1.0122015766168568, 1.0121550544409206, 1.0121089895429463, 1.0120637491013686,
+        1.0120196620088657, 1.0119769881022078, 1.0119358928702267, 1.011896429800644,
+        1.0118585321321505, 1.011822015200596, 1.0117865897790987, 1.011751885828589,
+        1.0117174849713186, 1.0116829589027745, 1.011647910031414, 1.0116120100521733,
+        1.0115750320641146, 1.0115368723189226, 1.0114975587342754, 1.01145724482726,
+        1.0114161895313383, 1.011374725205627, 1.0113332177511978, 1.0112920238603824,
+        1.0112514508525745, 1.0112117242063572, 1.0111729668163494, 1.011135192336549,
+        1.0110983129689666, 1.011062160021924, 1.0110265138080792, 1.0109911382433516,
+        1.0109558150214273, 1.0109203725336289, 1.0108847057141832, 1.0108487845382534,
+        1.010812650724108, 1.010776403996566, 1.0107401807722962, 1.01070412910556,
+        1.010668384054107, 1.0106330472713911, 1.010598173694549, 1.010563766861542,
+        1.01052978289496, 1.0104961417889682, 1.010462743554195, 1.0104294861719825,
+        1.0103962822539083, 1.0103630717670682, 1.010329829056876, 1.0102965635007655,
+        1.0102633142546795, 1.010230140514826, 1.0101971093573396, 1.0101642834522633,
+        1.0101317107658787, 1.0100994178310136, 1.0100674073999913, 1.0100356604521368,
+        1.0100041417635712, 1.0099728076908903, 1.0099416145559768, 1.0099105260696788,
+        1.009879518562506, 1.0098485833161492, 1.009817725896995, 1.0097869629613616,
+        1.0097563174285449, 1.0097258131330789, 1.0096954700488427, 1.0096653009483192,
+        1.009635309982803, 1.0096054932303913, 1.0095758408506577, 1.0095463401875597,
+        1.009516979027525, 1.0094877482634326, 1.0094586434157005, 1.0094296647663747,
+        1.0094008161996735, 1.0093721031386733, 1.0093435301605989, 1.0093150989251478,
+        1.0092868069553484, 1.0092586475940752, 1.0092306111721863, 1.0092026871310993,
+        1.0091748666080391, 1.0091471448678835, 1.0091195229787344, 1.0090920082772457,
+        1.0090646134237773, 1.0090373541531705, 1.0090102461204407, 1.0089833014590113,
+        1.00895652576482, 1.0089299161693133, 1.008903460974503, 1.0088771410283714,
+        1.0088509326760293, 1.0088248117981753, 1.0087987582089029, 1.0087727595795322,
+        1.0087468141085831, 1.008720931364444, 1.008695131051735, 1.0086694398353466,
+        1.0086438867269634, 1.00861849782671, 1.0085932913611801, 1.0085682739373953,
+        1.0085434387401053, 1.0085187660687966, 1.0084942261986838, 1.0084697841303327,
+        1.008445405441321, 1.0084210622353154, 1.0083967381406953, 1.0083724314527918,
+        1.0083481558189336, 1.0083239382820557, 1.0082998149546376, 1.0082758250112938,
+        1.0082520039916423, 1.0082283775420524, 1.0082049566699547, 1.0081817353457365,
+        1.0081586909044697, 1.0081357872370897, 1.0081129802961626, 1.0080902250527548,
+        1.0080674827932348, 1.0080447275786564, 1.0080219508150379, 1.00799916317864,
+        1.0079763935567254, 1.0079536851328592, 1.0079310891906594, 1.0079086575604939,
+        1.0078864348360774, 1.007864451513707, 1.007842719055997, 1.0078212275830116,
+        1.0077999464970375, 1.0077788279173774, 1.0077578124047126, 1.00773683614945,
+        1.007715838626242, 1.0076947696958647, 1.007673595260328, 1.007652300819471,
+        1.0076308925939177, 1.007609396218458, 1.0075878533210167, 1.0075663165435176,
+        1.0075448437046493, 1.0075234918412281, 1.0075023118014899, 1.0074813439219656,
+        1.0074606151297336, 1.007440137607184, 1.0074199089672036, 1.0073999137358949,
+        1.0073801258401145, 1.0073605117506377, 1.007341033931748, 1.0073216542819257,
+        1.007302337303313, 1.0072830527964503, 1.007263777932037, 1.0072444985994184,
+        1.0072252099730128, 1.007205916277601, 1.0071866297767649, 1.0071673690595109,
+        1.0071481567586313, 1.0071290168958795, 1.0071099721047827, 1.0070910410203278,
+        1.007072236133832, 1.0070535623826387, 1.0070350166741187, 1.0070165884364566,
+        1.0069982611562693, 1.0069800147237784, 1.006961828281808, 1.006943683187112,
+        1.0069255656589813, 1.0069074687204986, 1.0068893931313672, 1.0068713471567898,
+        1.006853345192787, 1.006835405447523, 1.006817547030955, 1.0067997869052177,
+        1.0067821371774555, 1.0067646031680735, 1.0067471825671062, 1.0067298658177248,
+        1.006712637666936, 1.006695479632177, 1.0066783729807862, 1.0066613017334742,
+        1.0066442551978063, 1.0066272296151697, 1.0066102286520708, 1.0065932626594902,
+        1.0065763468299513, 1.0065594985660806, 1.006542734505462, 1.0065260677022847,
+        1.0065095054372477, 1.006493048018402, 1.0064766887659495, 1.0064604151724614,
+        1.0064442110311622, 1.0064280591626364, 1.006411944272225, 1.00639585545261,
+        1.0063797879113918, 1.0063637436397066, 1.0063477309214484, 1.0063317627814088,
+        1.0063158546504019, 1.0063000216557256, 1.0062842760040085, 1.0062686249016188,
+        1.006253069359796, 1.0062376040755199, 1.0062222183921858, 1.0062068981591883,
+        1.0061916281580938, 1.0061763946710471, 1.0061611877491838, 1.0061460027972946,
+        1.006130841214571, 1.006115709997589, 1.0061006203915743, 1.006085585838087,
+        1.0060706195839904, 1.006055732368409, 1.006040930583658, 1.0060262152174193,
+        1.006011581743441, 1.0059970209616436, 1.005982520625034, 1.0059680675583644,
+        1.005953649894417, 1.0059392590406835, 1.0059248910432586, 1.005910547125225,
+        1.005896233323555, 1.0058819593055213, 1.005867736585505, 1.0058535764619492,
+        1.0058394880358887, 1.005825476650838, 1.0058115430139705, 1.0057976831353597,
+        1.0057838890779784, 1.0057701503712584, 1.0057564558297492, 1.005742795454069,
+        1.0057291620843336, 1.0057155525263586, 1.005701967968308, 1.0056884136322086,
+        1.0056748977382235, 1.0056614299765594, 1.0056480197624753, 1.0056346745808995,
+        1.0056213987044633, 1.005608192497457, 1.005595052411799, 1.0055819716588432,
+        1.0055689414243005, 1.0055559524027704, 1.0055429963784992, 1.0055300675776806,
+        1.0055171635639522, 1.0055042855335345, 1.0054914379740778, 1.005478627762495,
+        1.0054658628725, 1.0054531509260205, 1.0054404978439209, 1.0054279068278758,
+        1.0054153778419326, 1.0054029076713487, 1.00539049053402, 1.0053781191244007,
+        1.0053657858975333, 1.0053534843637604, 1.0053412101683241, 1.00532896177292,
+        1.005316740629741, 1.0053045508294134, 1.0052923982960056, 1.005280289679282,
+        1.0052682311434398, 1.00525622726491, 1.0052442802280634, 1.0052323894516972,
+        1.0052205517015989, 1.0052087616592305, 1.0051970128384193, 1.005185298684488,
+        1.00517361366264, 1.0051619541488483, 1.005150318974939, 1.0051387095425657,
+        1.0051271294968664, 1.005115584026415, 1.0051040789183694, 1.0050926195364114,
+        1.0050812098978656, 1.0050698520047257, 1.0050585455357346, 1.005047287941974,
+        1.0050360749182656, 1.0050249011592507, 1.0050137612629613, 1.00500265062347,
+        1.0049915661607196, 1.0049805067679363, 1.0049694734089027, 1.0049584688592146,
+        1.0049474971467234, 1.0049365627960614, 1.00492567001243, 1.004914821946006,
+        1.0049040201601187, 1.0048932643876294, 1.0048825526079928, 1.004871881421587,
+        1.0048612466478122, 1.0048506440375196, 1.0048400699743114, 1.0048295220451917,
+        1.0048189993872805, 1.004808502758623, 1.0047980343300154, 1.0047875972425706,
+        1.0047771950143156, 1.0047668309021647, 1.0047565073297167, 1.0047462254763762,
+        1.0047359850925501, 1.004725784564866, 1.0047156212118669, 1.0047054917519407,
+        1.0046953928578224, 1.004685321700185, 1.0046752763880278, 1.0046652562343843,
+        1.0046552618081017, 1.0046452947703244, 1.0046353575309919, 1.0046254527901346,
+        1.0046155830460164, 1.004605750154959, 1.0045959550157912, 1.0045861974281185,
+        1.0045764761422156, 1.0045667890851904, 1.0045571337186494, 1.0045475074624228,
+        1.004537908110123, 1.0045283341664333, 1.004518785051925, 1.0045092611456643,
+        1.0044997636644837, 1.0044902944054608, 1.0044808554002649, 1.0044714485430797,
+        1.0044620752558486, 1.0044527362458289, 1.0044434313927009, 1.0044341597791657,
+        1.0044249198542619, 1.0044157096967063, 1.004406527330095, 1.0043973710350267,
+        1.0043882396060024, 1.0043791325123597, 1.0043700499402684, 1.0043609927136943,
+        1.0043519621125314, 1.0043429596225082, 1.0043339866613386, 1.0043250443276033,
+        1.0043161332130301, 1.0043072533065005, 1.0042984040016372, 1.0042895842021389,
+        1.0042807925031685, 1.0042720274155388, 1.0042632875939936, 1.0042545720320148,
+        1.0042458801929095, 1.0042372120588186, 1.0042285680935819, 1.0042199491296093,
+        1.0042113562007347, 1.0042027903506086, 1.0041942524485914, 1.0041857430421823,
+        1.004177262267602, 1.0041688098296644, 1.0041603850504486, 1.004151986975446],
+    [0.0008593829906906719, 0.0025786508808534206, 0.004299425577504465,
+        0.006022714120695904, 0.007749527146833857, 0.009480880778741808,
+        0.011217797738574562, 0.012961309196095705, 0.014712456224205047,
+        0.016472291425551556, 0.01824188058402285, 0.02002230441908, 0.021814660248851588,
+        0.023620063881930244, 0.02543965142768177, 0.027274581282519163,
+        0.029126036142468805, 0.030995225109143723, 0.032883385934023755,
+        0.03479178728724434, 0.036721731266071964, 0.03867455591559291,
+        0.0406516379645959, 0.04265439570392167, 0.04468429203392491, 0.046742837684124065,
+        0.04883159469186691, 0.05095218005354518, 0.053106269680706024,
+        0.05529560257013358, 0.057521985368438035, 0.05978729718407699,
+        0.062093494841814215, 0.06444261850278074, 0.066836797781657, 0.06927825833207481,
+        0.07176932903464156, 0.0743124497712732, 0.07691017994725052, 0.07956520774577679,
+        0.08228036030949973, 0.08505861485696366, 0.08790311095390216, 0.0908171639918977,
+        0.0938042801377076, 0.09686817279850568, 0.10001278104405133, 0.10324228995921689,
+        0.10656115353669886, 0.10997412019505742, 0.11348626151929866, 0.11710300466634659,
+        0.12083016898242871, 0.12467400762405145, 0.12864125498346418, 0.13273918091897524,
+        0.13697565314584878, 0.14135920916454, 0.14589913973682017, 0.15060558613558,
+        0.15548965406503137, 0.16056354788116828, 0.16584072963941296, 0.1713361087479801,
+        0.17706626964488795, 0.18304974712017594, 0.18930736176422489, 0.19586263209009952,
+        0.20274228542175415, 0.20997689725565089, 0.2176016998161855, 0.2256576162440178,
+        0.23419259992057434, 0.2432633925657119, 0.2529378670992304, 0.2632982020255234,
+        0.27444526339022995, 0.28650478128578283, 0.29963626492931716, 0.3140462250223512,
+        0.33000841050398294, 0.3478959442044444, 0.36823464355629454, 0.39179632970611133,
+        0.4197732684959484, 0.45413303312730774, 0.49842627280068613, 0.559940985086855,
+        0.657040454045498, 0.8584764120479909, 2.5586978717017055, 0.7894831402796035,
+        0.567354218615847, 0.47919578343026986, 0.4314107150474616, 0.40214571406521177,
+        0.38328228046893487, 0.37105041721584103, 0.36345310563403543, 0.359341634986298,
+        0.35802277770620544, 0.35907173553676813, 0.3622359710135397, 0.3673837201085132,
+        0.37447683867512527, 0.38355863908666854, 0.3947527307064376, 0.4082721126858555,
+        0.4244405995806775, 0.44373250641044837, 0.4668436630632522, 0.49482278412780323,
+        0.5293333564947057, 0.5732407438339806, 0.6321882891142969, 0.7203038759391458,
+        0.8981030447267385, 2.0308640854959044, 0.9017335617927682, 1.8226501395665267,
+        0.9327400222706231, 0.6058337504042653, 1.0399148537681562, 1.9815772165018044,
+        2.107580164260038, 0.7094154466796063, 0.5695883740429609, 0.863003287146926,
+        1.4558760746812194, 2.3914829567721303, 1.709025132248349, 0.9091982017885963,
+        0.6184253642429874, 0.6617516599474683, 0.9692168213948154, 1.5541496355746378,
+        2.112310646015454, 1.6843377056080144, 1.1272115815522479, 0.8066641955002924,
+        0.6721530077861599, 0.7288150181282717, 1.0055347568589188, 1.4935084388391728,
+        1.8352369677148785, 1.5951937877824485, 1.2286053756822952, 0.9647417026230847,
+        0.8011594439623211, 0.7394100579889983, 0.8210621235431708, 1.0966001643845629,
+        1.4848176468841519, 1.5993542478283733, 1.3907141442283275, 1.1495611517166622,
+        0.9575329996921388, 0.881827708082902, 0.8995018887308217, 0.9659627927019875,
+        1.067902390218461, 1.1644477656717118, 1.2122479326557019, 1.204047610969693,
+        1.1631338280409622, 1.113414620361861, 1.0683327592618952, 1.0339157409307707,
+        1.0130544191753663, 1.0076535171111198, 1.0187415752047808, 1.044721236153788,
+        1.0787131353060098, 1.108596560826855, 1.123204815701765, 1.119661935637487,
+        1.1030592051632186, 1.0805835106238146, 1.057516753943456, 1.036650150141338,
+        1.0190855970714765, 1.0050477399803612, 0.9943843205690635, 0.986818827908353,
+        0.9820622819275666, 0.9798553015003696, 0.979978507746643, 0.9822495099057202,
+        0.9865141917214383, 0.992634488292974, 1.000471717842361, 1.0098624567258152,
+        1.0205824815579259, 1.0322941436120943, 1.0444763689026584, 1.0563499709775803,
+        1.0668410289692705, 1.074667350940666, 1.0786433171572687, 1.0781862996027494,
+        1.0737581701375616, 1.066843767464985, 1.0593721591074963, 1.052982265652563,
+        1.048605529591839, 1.0464669953269727, 1.0463068901435526, 1.0476163043939584,
+        1.0498002953718404, 1.052270425623891, 1.054497832229916, 1.0560536814298656,
+        1.0566486765945697, 1.0561675812730338, 1.0546845123181956, 1.0524449825239153,
+        1.0498119647178488, 1.0471887686423595, 1.0449407544316889, 1.043335415123547,
+        1.0425098543842362, 1.0424642713977033, 1.0430750464625502, 1.0441213626663652,
+        1.0453218181427777, 1.0463789285256735, 1.0470281962690073, 1.0470850673502483,
+        1.0464799493776995, 1.0452714535163934, 1.0436326473720938, 1.0418129363118829,
+        1.0400854693971766, 1.038693223665078, 1.0378053409192176, 1.037490773591395,
+        1.0377115486048052, 1.0383346006317518, 1.039159168166275, 1.039955301348744,
+        1.0405073957633155, 1.0406550247176027, 1.0403227372136539, 1.0395320717868115,
+        1.0383930461110535, 1.0370776431327782, 1.0357822853466172, 1.0346883117458976,
+        1.0339287131934347, 1.0335667660299013, 1.033589073786041, 1.0339128129649462,
+        1.0344049244102875, 1.03490942340611, 1.0352777857082838, 1.0353966907688863,
+        1.0352077036708056, 1.034715072672412, 1.0339805268264248, 1.0331070142870542,
+        1.0322157224166706, 1.0314217500950724, 1.0308133641006723, 1.0304383133177424,
+        1.0302988375463615, 1.030355287262778, 1.0305368911662818, 1.0307572065033284,
+        1.030931170875469, 1.0309905177915237, 1.0308947311097005, 1.0306357181445975,
+        1.0302358038261075, 1.029740123921384, 1.0292056057500416, 1.0286891851563507,
+        1.0282376804091797, 1.0278810126842792, 1.0276295164854534, 1.0274751813766554,
+        1.027395970940314, 1.0273619421473559, 1.0273417463016623, 1.027308213844745,
+        1.027242073659728, 1.0271333666863083, 1.026980677725713, 1.0267887963580455,
+        1.0265657077322505, 1.0263198418054813, 1.0260582902589015, 1.0257863194792853,
+        1.0255080864408535, 1.0252281155844085, 1.024952895279183, 1.0246919317046297,
+        1.0244577445705259, 1.0242645625683209, 1.0241258180423487, 1.024050880221835,
+        1.0240417301944524, 1.0240904002347033, 1.0241779285970367, 1.024275312513942,
+        1.0243465246539314, 1.0243531901939344, 1.0242601276789822, 1.0240407472809552,
+        1.0236813305692682, 1.0231834672959508, 1.022564313398791, 1.0218547477094468,
+        1.0210958426825714, 1.0203342686344523, 1.0196173120932635, 1.018988134187999,
+        1.0184817679609501, 1.0181221954625521, 1.0179206859396712, 1.0178754315341312,
+        1.0179723936226126, 1.01818717437794, 1.0184876572513546, 1.0188371201864905,
+        1.0191975182389663, 1.019532655418079, 1.019811011024974, 1.0200080415174673,
+        1.0201078328310262, 1.0201040223928433, 1.01999994444078, 1.0198079832914233,
+        1.0195481567255191, 1.019246003344696, 1.0189299145800352, 1.0186281266472563,
+        1.0183656562630685, 1.018161510091406, 1.0180265075834731, 1.0179620213161709,
+        1.017959855867959, 1.0180033598938452, 1.0180697069235807, 1.0181331059108751,
+        1.0181685375265923, 1.0181554876640004, 1.0180810980808528, 1.0179422006733743,
+        1.0177458539000164, 1.0175082394206565, 1.0172520610852247, 1.0170028585856927,
+        1.0167848467776512, 1.016616978292146, 1.0165098876136351, 1.0164642220200473,
+        1.0164706306208906, 1.0165114084669167, 1.0165635210431088, 1.0166025054018457,
+        1.01660659295076, 1.0165603529678096, 1.0164572296080434, 1.016300533068009,
+        1.0161027185328035, 1.0158830943049963, 1.0156643822286642, 1.0154687529919397,
+        1.015314038995481, 1.0152107780675135, 1.0151605785490079, 1.015156055342927,
+        1.0151823119502714, 1.015219680921461, 1.0152472257105953, 1.0152463835697305,
+        1.0152041128019664, 1.0151150030719356, 1.014981999568797, 1.0148156461470876,
+        1.0146320207114858, 1.014449766163713, 1.0142867690418662, 1.014157080849139,
+        1.014068611770249, 1.014021971166061, 1.014010616204309, 1.0140222381632562,
+        1.0140411043894937, 1.014050916745357, 1.0140376698016271, 1.0139920065131787,
+        1.013910672594489, 1.0137968438586284, 1.013659310291575, 1.0135107062830924,
+        1.0133651395026748, 1.0132356627470986, 1.013132040644039, 1.0130591901268082,
+        1.0130165379922413, 1.0129983677225964, 1.0129950519867128, 1.0129949166439538,
+        1.0129863812929, 1.0129599864397396, 1.0129099528870094, 1.0128350170117417,
+        1.0127384265974353, 1.012627138163917, 1.0125103984045913, 1.0123979936253178,
+        1.0122984955251157, 1.0122178147023306, 1.0121583019300342, 1.012118527558027,
+        1.0120937427041476, 1.0120769049512404, 1.0120600566929838, 1.0120357915279243,
+        1.011998541071348, 1.0119454601248292, 1.0118767722457513, 1.0117955432275547,
+        1.0117069560796321, 1.0116172478105345, 1.0115325205622443, 1.0114576498950472,
+        1.0113954821570268, 1.0113464491758926, 1.0113086454540101, 1.0112783265345238,
+        1.0112507127907375, 1.0112209333029343, 1.0111849276230245, 1.0111401408568936,
+        1.0110858949455204, 1.0110233860917268, 1.010955331297402, 1.010885351689781,
+        1.0108172248115088, 1.0107541550425225, 1.0106981992646262, 1.0106499477901705,
+        1.0106085068139645, 1.0105717690633764, 1.0105369052030309, 1.0105009696700868,
+        1.010461497608656, 1.0104169768324662, 1.0103671080330707, 1.0103128113514614,
+        1.0102559886612814, 1.01019909824473, 1.0101446329158694, 1.0100946079501376,
+        1.0100501593123274, 1.0100113277049856, 1.0099770654440792, 1.0099454589150632,
+        1.0099141178916877, 1.0098806520185073, 1.0098431398237173, 1.0098004991960572,
+        1.0097526892532966, 1.009700707558402, 1.0096463868599805, 1.009592034029186,
+        1.009539983248366, 1.0094921503835748, 1.0094496734311305, 1.0094127058688542,
+        1.0093803995356925, 1.0093510772819347, 1.009322559975649, 1.0092925840901625,
+        1.0092592301300705, 1.0092212813293742, 1.0091784463005846, 1.009131405748614,
+        1.0090816768470687, 1.0090313229976757, 1.0089825650338347, 1.0089373673009057,
+        1.0088970754663922, 1.0088621720941957, 1.0088321933044986, 1.0088058196692362,
+        1.0087811225039378, 1.0087559187204775, 1.0087281683686227, 1.0086963421953457,
+        1.0086596930273148, 1.0086183831626958, 1.0085734467200893, 1.008526596024162,
+        1.008479909056018, 1.0084354557233992, 1.008394930618054, 1.0083593575037209,
+        1.0083289167704788, 1.0083029242956705, 1.008279962828599, 1.0082581400894686,
+        1.0082354259614625, 1.0082100081730252, 1.0081806038097696, 1.0081466730038093,
+        1.0081084994071865, 1.0080671261429588, 1.0080241614477194, 1.0079814906252558,
+        1.0079409463518976, 1.0079039952995916, 1.007871494723506, 1.0078435591696417,
+        1.0078195574208113, 1.0077982368756224, 1.0077779507711184, 1.007756946716698,
+        1.0077336656683464, 1.0077070001232469, 1.007676468759188, 1.0076422802705434,
+        1.0076052788722396, 1.0075667843206062, 1.0075283568021909, 1.0074915287628585,
+        1.0074575498978489, 1.007427187685112, 1.0074006149879389, 1.0073774004946219,
+        1.0073565999532925, 1.0073369293720658, 1.0073169883644122, 1.007295494658993,
+        1.0072714904370736, 1.0072444874025022, 1.0072145290137513, 1.007182162956069,
+        1.0071483321035535, 1.007114205343299, 1.0070809786027148, 1.0070496799411686,
+        1.0070210103263624, 1.0069952443804215, 1.0069722044259835, 1.006951308577427,
+        1.0069316815558749, 1.0069123073054618, 1.0068921967925473, 1.006870543302999,
+        1.0068468410391247, 1.00682095003552, 1.0067930999686951, 1.006763835629688,
+        1.0067339159610684, 1.0067041852131897, 1.0066754380362861, 1.0066482999007604,
+        1.0066231404546393, 1.0066000311290337, 1.0065787506734238, 1.0065588346475483,
+        1.0065396584227324, 1.0065205388778886, 1.0065008382320915, 1.006480054396055,
+        1.0064578854784332, 1.0064342609421588, 1.0064093374724168, 1.0063834629631974,
+        1.0063571163530798, 1.0063308337863057, 1.0063051324961183, 1.0062804429724421,
+        1.0062570577193144, 1.006235101742482, 1.0062145264187925, 1.0061951251400767,
+        1.0061765665329168, 1.0061584394008727, 1.0061403029005573, 1.006121735761367,
+        1.0061023793777988, 1.0060819710614768, 1.0060603653471363, 1.0060375427561132,
+        1.0060136066622798, 1.0059887697997656, 1.0059633325019357, 1.00593765502852,
+        1.005912126411432, 1.0058871322135086, 1.0058630235043786, 1.0058400892305646,
+        1.0058185339722843, 1.005798462794575, 1.0057798744707032, 1.0057626637574753,
+        1.0057466326481175, 1.0057315096766166, 1.005716975495353, 1.0057026922174865,
+        1.0056883335303533, 1.0056736124445327, 1.0056583037966258, 1.0056422592607543,
+        1.0056254135679812, 1.0056077817522806, 1.0055894483703771, 1.0055705506092274,
+        1.005551257853085, 1.0055317505377692, 1.0055122009475532, 1.005492758057735,
+        1.0054735377045014, 1.0054546184259225, 1.0054360424298503, 1.0054178204536273,
+        1.0053999388903443, 1.0053823675081466, 1.0053650663571143, 1.0053479909585574,
+        1.0053310954796246, 1.005314334175124, 1.005297661805112, 1.0052810339277027,
+        1.005264407892229, 1.0052477450486565, 1.0052310142263015, 1.0052141960335437,
+        1.0051972871135675, 1.0051803032651412, 1.0051632803670267, 1.0051462723399913,
+        1.0051293458938926, 1.0051125724413592, 1.005096018186977, 1.005079733888746,
+        1.0050637460264293, 1.0050480510335487, 1.0050326138497971, 1.0050173713852562,
+        1.00500224066711, 1.004987130608546, 1.004971955651069, 1.0049566491178479,
+        1.0049411740636884, 1.0049255297398179, 1.004909752463496, 1.0048939105849408,
+        1.0048780942252968, 1.004862401349693, 1.0048469223823788, 1.0048317258509534,
+        1.0048168474103087, 1.0048022840626392, 1.0047879945452536, 1.004773905844913,
+        1.0047599247871108, 1.0047459528124512, 1.0047319015314775, 1.0047177065311523,
+        1.0047033372090661, 1.0046888010817694, 1.0046741419356786, 1.0046594322055231,
+        1.0046447609046096, 1.004630219137122, 1.0046158855809424, 1.0046018142864657,
+        1.00458802670772, 1.004574509146594, 1.0045612158786268, 1.0045480772958664,
+        1.0045350116042076, 1.004521938078432, 1.0045087896887253, 1.0044955230885086,
+        1.0044821244540683, 1.0044686103970688, 1.0044550240024184, 1.0044414268338946,
+        1.0044278883691335, 1.0044144746780639, 1.0044012381976868, 1.0043882101886243,
+        1.0043753969440066, 1.0043627801561814, 1.0043503211497062, 1.0043379680775455,
+        1.004325664748725, 1.0043133595710891, 1.0043010131694947, 1.0042886035492384,
+        1.0042761281510546, 1.0042636026971101, 1.0042510572589374, 1.0042385304001546,
+        1.0042260624951878, 1.004213689370238, 1.0042014372617452, 1.0041893197811593,
+        1.004177337177694, 1.004165477778745, 1.0041537211337332, 1.0041420421481748,
+        1.004130415403288, 1.004118818915766, 1.0041072367783443, 1.0040956603895195,
+        1.0040840882733437, 1.0040725247511033, 1.0040609779093577, 1.004049457385241,
+        1.0040379724545936, 1.004026530777642, 1.004015137964691, 1.0040037979141772,
+        1.0039925136922987, 1.0039812886038926, 1.00397012707038, 1.0039590349862373,
+        1.0039480193560208, 1.003937087190355, 1.0039262438238552, 1.0039154909722134,
+        1.0039048249378193, 1.0038942353842526, 1.003883705026502, 1.0038732104390313,
+        1.0038627239942024, 1.0038522167438382, 1.003841661882849, 1.0038310383170228,
+        1.0038203338175709, 1.0038095472892568, 1.003798689798646, 1.0037877841832457,
+        1.003776863261701, 1.0037659668573469, 1.003755138002766, 1.0037444187896007,
+        1.0037338463547012, 1.003723449451873, 1.003713245959687, 1.0037032415399698,
+        1.0036934295120663, 1.0036837918676262, 1.0036743012377747, 1.0036649235502462,
+        1.0036556210813423, 1.0036463556121538, 1.0036370914306707, 1.0036277979691848,
+        1.0036184519185418, 1.0036090387090366, 1.0035995532885014, 1.0035900001623648,
+        1.0035803926925082, 1.0035707516873058, 1.0035611033588527, 1.0035514767762537,
+        1.0035419010025994, 1.0035324021597813, 1.0035230007080387, 1.0035137092435438,
+        1.0035045310965538, 1.003495459949182, 1.0034864805867822, 1.0034775707602746,
+        1.003468703985431, 1.0034598529619592, 1.0034509931842581, 1.0034421062586534,
+        1.0034331824534137, 1.0034242220922807, 1.0034152355520083, 1.0034062418203344,
+        1.0033972657843, 1.003388334616746, 1.0033794737784283, 1.003370703227896,
+        1.0033620344159841, 1.0033534685350076, 1.0033449963087437, 1.0033365993750951,
+        1.003328253065339, 1.0033199301619982, 1.0033116050579434, 1.0033032576697256,
+        1.0032948764910326, 1.0032864603040268, 1.0032780182768872, 1.003269568431871,
+        1.003261134728275, 1.0032527432265, 1.0032444179464883, 1.0032361770818494,
+        1.003228030171882, 1.0032199766769803, 1.0032120061743153, 1.0032041001276994,
+        1.003196234931528, 1.003188385725082, 1.0031805303536283, 1.0031726528356066,
+        1.0031647457829402, 1.0031568113986447, 1.0031488609125165, 1.003140912572051,
+        1.003132988539403, 1.0031251112179695, 1.0031172996162656, 1.0031095663397303,
+        1.0031019156872438, 1.003094343138943, 1.0030868362881307, 1.0030793770322166,
+        1.003071944635097, 1.0030645191391174, 1.003057084559558, 1.0030496313440804,
+        1.0030421577134703, 1.003034669694121, 1.003027179873374, 1.0030197051186975,
+        1.0030122636660959, 1.0030048720758236, 1.0029975425609734, 1.002990281117707,
+        1.0029830867401095, 1.0029759518140071, 1.0029688635854919, 1.00296180642477,
+        1.0029547644829477, 1.0029477242874911, 1.0029406768478244, 1.0029336189391225,
+        1.0029265533812173, 1.002919488303993, 1.0029124355604706, 1.0029054085854512,
+        1.0028984200793005, 1.0028914799112527, 1.0028845935844308, 1.0028777614968107,
+        1.002870979088987, 1.0028642378163277, 1.002857526746503, 1.0028508344858054,
+        1.0028441510944568, 1.0028374696673719, 1.0028307873275397, 1.0028241054900993,
+        1.0028174293857188, 1.00281076695886, 1.0028041273583177, 1.0027975192975382,
+        1.0027909495720222, 1.0027844219809958, 1.002777936819485, 1.002771491000693,
+        1.0027650787566154, 1.002758692766888, 1.0027523254983095, 1.0027459705109227,
+        1.0027396235038049, 1.002733282929997, 1.0027269500937508, 1.0027206287385941,
+        1.0027143242244019, 1.0027080424599704, 1.0027017887934764, 1.002695567061499,
+        1.0026893789598854, 1.0026832238347456, 1.0026770989119393, 1.0026709999034775,
+        1.0026649218636128, 1.0026588601272974, 1.002652811155386, 1.0026467731348263,
+        1.0026407462325744, 1.0026347324691558, 1.0026287352488064, 1.0026227586450411,
+        1.002616806582367, 1.0026108820696338, 1.0026049866264373, 1.0025991200043618,
+        1.0025932802476927, 1.0025874640744057, 1.002581667499529, 1.0025758865800158,
+        1.002570118140418, 1.0025643603450332, 1.0025586130130562, 1.0025528776223878,
+        1.0025471570058857, 1.0025414548002145, 1.0025357747518053, 1.0025301200090673,
+        1.0025244925306727, 1.0025188927168511, 1.0025133193287012, 1.0025077697074272,
+        1.0025022402508799, 1.0024967270587368, 1.0024912266281425, 1.0024857364737731,
+        1.002480255561187, 1.002474784476892, 1.0024693253065227, 1.0024638812449032,
+        1.0024584560094605, 1.0024530531627438, 1.0024476754650617, 1.0024423243718052,
+        1.002436999763421, 1.0024316999541796, 1.0024264219763601, 1.0024211620881212,
+        1.0024159164145892, 1.0024106816092193, 1.00240545542002, 1.002400237062917,
+        1.0023950273390083, 1.0023898284775263, 1.002384643733969, 1.0023794768148397,
+        1.0023743312294833, 1.0023692096809207, 1.0023641135995351, 1.0023590428977145,
+        1.0023539959848027, 1.0023489700367523, 1.0023439614716059, 1.002338966547617,
+        1.002333981981234, 1.0023290054803713, 1.0023240361043402, 1.0023190743925001,
+        1.0023141222436154, 1.0023091825701493, 1.0023042587890743, 1.0022993542370555,
+        1.0022944716088515, 1.0022896125119856, 1.0022847772094492, 1.0022799645894416,
+        1.0022751723625236, 1.0022703974488385, 1.0022656364873608, 1.0022608863805176,
+        1.0022561447837322, 1.002251410460744, 1.0022466834496315, 1.0022419650170387,
+        1.0022372574134806, 1.002232563474896, 1.0022278861395209, 1.0022232279611003,
+        1.0022185906976522, 1.0022139750403622, 1.0022093805224046, 1.0022048056169952,
+        1.002200248002985, 1.0021957049498433, 1.0021911737561882, 1.002186652169581,
+        1.002182138720877, 1.0021776329225163, 1.0021731353038723, 1.0021686472839049,
+        1.0021641709074354, 1.0021597084921134, 1.0021552622455778, 1.0021508339145937,
+        1.0021464245203606, 1.002142034218177, 1.0021376622983353, 1.002133307322034,
+        1.0021289673651068, 1.0021246403266664, 1.0021203242515837, 1.00211601761605,
+        1.002111719533716, 1.0021074298544388, 1.0021031491457733, 1.0020988785660125,
+        1.002094619653856, 1.002090374071189, 1.0020861433405912, 1.0020819286175406,
+        1.0020777305296358, 1.0020735491030173, 1.002069383781738, 1.0020652335315512],
+    [0.0003729844814207124, 0.0011192193047603698, 0.0018662522581848044,
+        0.0026146167805112595, 0.003364848270477302, 0.004117485067008013,
+        0.0048730690920542235, 0.005632146813105256, 0.006395270035216434,
+        0.007162996767511551, 0.00793589210057287, 0.00871452912868112,
+        0.009499489831936863, 0.010291366057852832, 0.01109076046652801,
+        0.011898287551713956, 0.012714574671792038, 0.013540263119467537,
+        0.014376009249381509, 0.015222485612509178, 0.0160803821915141,
+        0.016950407635178008, 0.01783329058035361, 0.0187297810275984, 0.019640651780278937,
+        0.020566699946049, 0.021508748536877193, 0.0224676481254831, 0.023444278613806293,
+        0.02443955106786768, 0.025454409695384386, 0.02648983389313172,
+        0.02754684044520045, 0.0286264858285183, 0.029729868675501953, 0.030858132368592677,
+        0.03201246781433417, 0.03319411637285994, 0.03440437299785852, 0.03564458955689713,
+        0.03691617839524412, 0.038220616114731217, 0.03955944763227161,
+        0.04093429049746849, 0.042346839539296334, 0.04379887179909808,
+        0.04529225188183761, 0.04682893762172542, 0.04841098624181379, 0.05004056091660027,
+        0.051719937863049036, 0.05345151397930381, 0.05523781505949799,
+        0.057081504679926856, 0.05898539379390667, 0.06095245108999981,
+        0.06298581424071545, 0.06508880205497881, 0.0672649276945054, 0.06951791301650435,
+        0.07185170416867814, 0.07427048857949606, 0.07677871348033323, 0.07938110612200941,
+        0.08208269587236096, 0.08488883841722861, 0.08780524227817164, 0.09083799792241994,
+        0.09399360978664549, 0.09727903153096111, 0.10070170492440104, 0.10426960281154224,
+        0.1079912766943181, 0.11187590946768547, 0.11593337403840771, 0.12017429855864065,
+        0.1246101392456622, 0.12925326176910856, 0.13411703244768003, 0.1392159207358812,
+        0.1445656145974464, 0.15018315078576425, 0.15608706236803607, 0.1622975462209878,
+        0.16883665382996346, 0.1757285093020924, 0.18299955937490767, 0.19067886112891258,
+        0.1987984143434055, 0.20739354713778824, 0.21650336522101635, 0.22617127787344282,
+        0.23644561680932052, 0.2473803683223042, 0.2590360444949693, 0.27148072669013995,
+        0.28479132380382527, 0.29905510142909036, 0.3143715554983706, 0.3308547295009379,
+        0.34863610977892384, 0.36786828504439684, 0.38872963198313953, 0.41143040431097866,
+        0.43622078042844803, 0.46340171170865635, 0.49333988841524035, 0.5264889639366823,
+        0.5634206770260783, 0.6048724085967322, 0.6518237236983494, 0.7056281202394288,
+        0.7682610737808423, 0.8428491893382639, 0.9350284726935845, 1.057659431787342,
+        1.2606640597978176, 0.9370989666660237, 1.3996016836122358, 2.214026136988973,
+        0.17879251572048932, 1.325279462435783, 1.9808815216581572, 3.002581752242233,
+        1.4781582946016236, 1.0992788783714627, 2.5156201080254004, 5.02872439033541,
+        6.511405047916822, 3.7557713811330453, 1.7301317564091783, 1.4174047667823368,
+        1.518019997988656, 1.7011193040077468, 2.0066551951261142, 2.4960872008815356,
+        2.690280099676185, 1.7934007461360537, 1.1486968295003923, 0.9786854251602504,
+        1.0634018829389313, 1.2996158217999136, 1.6848867625810486, 2.190755304960999,
+        2.343817962170848, 1.803422748948534, 1.2720000745536761, 0.9784650564676622,
+        0.8863338463972367, 0.9666416197038336, 1.2109428796002661, 1.6172289854590278,
+        2.0319933092111655, 1.9917007597871148, 1.5826567499747455, 1.2133691408473812,
+        0.9682055743696157, 0.9578135817552239, 1.0464612828150521, 1.1812899333534872,
+        1.3328945199065139, 1.4446487091171747, 1.4713718271187592, 1.4210521736154633,
+        1.335198605674919, 1.2481219448095409, 1.176825799432361, 1.1279316527629495,
+        1.1040692066531612, 1.1064137983336513, 1.134126026822963, 1.1815065592018796,
+        1.2350093550731456, 1.2753089580259014, 1.28751041866999, 1.2705369058845735,
+        1.23446468342963, 1.1911135502828816, 1.1485560337209055, 1.1107867643653444,
+        1.0792034739710628, 1.053923899046944, 1.0345587961311697, 1.0205878271796625,
+        1.0115175951653967, 1.0069347439609035, 1.0065128252492954, 1.0100003135368072,
+        1.0172006565901477, 1.0279464845783093, 1.042064930180835, 1.0593273257647717,
+        1.0793737651698476, 1.1016026396325567, 1.1250225882948288, 1.148090575737718,
+        1.1686192435343905, 1.183923403802198, 1.1914083378034412, 1.1896036833131203,
+        1.1791561812630758, 1.1629647445137914, 1.1451364252108496, 1.129442388493985,
+        1.1182663110704634, 1.1124104732060982, 1.1114627680203648, 1.114295777197372,
+        1.1194647807380735, 1.1254670628555237, 1.1309112068477403, 1.13465077651266,
+        1.1359073917670692, 1.1343719105763796, 1.1302476198640334, 1.1242001232381786,
+        1.1172076318160222, 1.1103463538157947, 1.1045719889017653, 1.100554140624075,
+        1.0985926902307241, 1.0986141874126922, 1.1002279866313875, 1.1028189135379396,
+        1.105658889618244, 1.1080256992433966, 1.1093180992691756, 1.109153068008928,
+        1.1074275650516825, 1.1043291869231193, 1.1002900880694702, 1.0958935553589881,
+        1.0917557209174011, 1.0884099284439772, 1.0862170222164578, 1.085315006768841,
+        1.085611311720336, 1.0868135611733396, 1.0884906237453185, 1.0901533446317468,
+        1.0913423216139597, 1.0917083070961715, 1.0910706564902686, 1.089442380156375,
+        1.0870171886103521, 1.08412270727115, 1.0811516476784524, 1.0784865121642333,
+        1.0764327025962492, 1.0751709883034857, 1.0747352044827279, 1.0750163256711307,
+        1.0757902174205922, 1.0767632752753789, 1.0776276611719622, 1.078116223129767,
+        1.0780471021153404, 1.0773500512296064, 1.0760704845277094, 1.07435220846798,
+        1.0724041570950105, 1.0704590206507407, 1.0687320357042642, 1.0673868453703732,
+        1.0665130830528515, 1.0661179067601254, 1.0661314780130267, 1.0664244207457805,
+        1.0668336413700912, 1.0671917005268403, 1.0673544882986457, 1.0672225115467595,
+        1.0667526368137557, 1.0659592742368411, 1.0649061340198016, 1.0636912659918845,
+        1.0624288026184563, 1.0612307051514198, 1.0601911362300016, 1.0593751802032167,
+        1.058812748470235, 1.0584977525878767, 1.0583920179215645, 1.0584329313598908,
+        1.05854347572616, 1.0586431383292831, 1.0586582299373275, 1.058530412616453,
+        1.0582226500176835, 1.057722256128454, 1.057041118160309, 1.056213434632197,
+        1.0552914296918934, 1.054339521411319, 1.0534274030709885, 1.0526225039257784,
+        1.0519823610900891, 1.051547548024856, 1.0513359216612492, 1.0513390005509737,
+        1.0515212010321575, 1.0518223930423107, 1.0521637965919852, 1.052456689837473,
+        1.0526128592931592, 1.0525553337957765, 1.052227824218151, 1.051601489684112,
+        1.0506781258546327, 1.0494895005101688, 1.0480931891785978, 1.046565750338148,
+        1.0449943464112808, 1.0434679556689248, 1.0420691798863304, 1.04086740776269,
+        1.0399138160892125, 1.039238429600976, 1.038849241409924, 1.0387332247154444,
+        1.0388589396380488, 1.039180352147457, 1.0396414339073414, 1.0401811035042472,
+        1.0407381005011256, 1.0412554480284137, 1.0416842441944967, 1.0419866099946675,
+        1.0421376953623913, 1.0421266965810274, 1.0419568694123276, 1.0416445446884495,
+        1.0412171828019345, 1.0407105534185117, 1.0401652004296842, 1.0396224416687796,
+        1.0391202409537483, 1.0386893554161203, 1.0383501848257684, 1.0381107191093786,
+        1.0379658910277407, 1.037898496552887, 1.0378816571023006, 1.0378825847754973,
+        1.0378672023514954, 1.037805000313621, 1.0376734229993525, 1.0374610980258188,
+        1.0371693715364083, 1.0368118721559678, 1.0364121543767837, 1.035999802260836,
+        1.0356056386523877, 1.035256831313709, 1.0349726917808628, 1.0347618321308063,
+        1.034621109672019, 1.0345364931412695, 1.0344856732789376, 1.0344419611123692,
+        1.034378810189242, 1.0342741985189914, 1.034114133505203, 1.0338947000564247,
+        1.0336223344264726, 1.0333123261169483, 1.032985864704336, 1.032666195874061,
+        1.0323745858411952, 1.0321267966074266, 1.0319306545587628, 1.0317850816044116,
+        1.0316806933780553, 1.0316017985223978, 1.0315293998542576, 1.031444638688349,
+        1.0313320635545713, 1.0311821545265842, 1.0309926858085496, 1.0307687336079938,
+        1.0305213896696883, 1.0302654731797212, 1.0300167009102137, 1.0297888491405138,
+        1.029591413526789, 1.0294281569881176, 1.02929675769746, 1.029189564009902,
+        1.0290952667184263, 1.029001144047687, 1.0288954464626345, 1.0287694807794963,
+        1.0286190262989539, 1.028444854714034, 1.0282523023318746, 1.0280500222329116,
+        1.0278481904143022, 1.0276565270942684, 1.0274825091734017, 1.0273300943704269,
+        1.0271991666588072, 1.0270857697436984, 1.0269830474824246, 1.0268826835616136,
+        1.0267765489863432, 1.0266582388274264, 1.0265242128829948, 1.0263743408942587,
+        1.0262117739722876, 1.0260421954047674, 1.0258726199424621, 1.0257099890935768,
+        1.0255598376308521, 1.0254252809660087, 1.025306502061699, 1.0252008156781012,
+        1.0251032767818382, 1.025007699308373, 1.0249078789637864, 1.0247987818080797,
+        1.024677473988108, 1.0245436237289995, 1.024399493068495, 1.0242494364498673,
+        1.0240990164787929, 1.0239539160649906, 1.0238188585228618, 1.0236967384611737,
+        1.0235881199942416, 1.0234911852390283, 1.0234021298154927, 1.023315919239945,
+        1.023227255542389, 1.02313156838861, 1.0230258452282985, 1.0229091498124843,
+        1.0227827406488508, 1.0226497782404536, 1.022514687194777, 1.0223823017793874,
+        1.0222569598783204, 1.0221417147177951, 1.0220378066523061, 1.0219444850051165,
+        1.021859202948968, 1.0217781393142376, 1.0216969425085631, 1.021611553702809,
+        1.021518955479478, 1.021417709688755, 1.0213081905108883, 1.0211924773150955,
+        1.0210739355118652, 1.0209565701891856, 1.020844276572397, 1.020740126588987,
+        1.0206458201620283, 1.0205613962539444, 1.0204852490741005, 1.02041443870315,
+        1.0203452328739482, 1.0202737769907262, 1.0201967693636622, 1.020112021179527,
+        1.0200188048978658, 1.019917935613832, 1.0198115795448914, 1.019702832827366,
+        1.019595153298879, 1.0194917510603179, 1.0193950468418496, 1.0193062908282902,
+        1.0192254024239693, 1.0191510498615852, 1.0190809453294145, 1.019012294102357,
+        1.0189423113610303, 1.0188687119307862, 1.0187900870114102, 1.018706105905652,
+        1.0186175149105114, 1.0185259432999014, 1.0184335606557735, 1.0183426545723413,
+        1.01825520888192, 1.0181725586542365, 1.018095180729594, 1.0180226512587358,
+        1.0179537699952481, 1.0178868208079792, 1.0178199144292872, 1.0177513467854176,
+        1.017679906254546, 1.0176050754018549, 1.0175270944649986, 1.017446880755593,
+        1.0173658250322286, 1.017285507813113, 1.0172073916804738, 1.0171325478391833,
+        1.0170614665801767, 1.0169939838917073, 1.016929333790623, 1.0168663123410586,
+        1.0168035191163853, 1.0167396286089663, 1.0166736399977756, 1.0166050592261773,
+        1.016533981221816, 1.0164610595149886, 1.016387371733162, 1.0163142084974333,
+        1.0162428266757555, 1.0161742134667167, 1.0161089046385916, 1.016046889280385,
+        1.0159876168652866, 1.0159301034355366, 1.0158731157735246, 1.0158153987180822,
+        1.0157559036687356, 1.0156939769151707, 1.0156294744531893, 1.015562783791829,
+        1.0154947502992315, 1.0154265227398742, 1.015359346756332, 1.015294343707183,
+        1.015232314100058, 1.0151735997271498, 1.0151180276232383, 1.0150649442117634,
+        1.015013332156233, 1.0149619882672725, 1.0149097307319268, 1.0148555995646926,
+        1.014799016132736, 1.0147398753806225, 1.0146785564767482, 1.0146158518227064,
+        1.0145528282006957, 1.0144906449258484, 1.0144303604169758, 1.0143727596472938,
+        1.0143182305085365, 1.0142667081639394, 1.014217694646541, 1.0141703483506908,
+        1.0141236267845337, 1.0140764578087762, 1.0140279108010146, 1.0139773402078696,
+        1.0139244794166127, 1.0138694717130303, 1.0138128356997105, 1.013755373114902,
+        1.0136980357986975, 1.013641774261275, 1.013587392161268, 1.013535428916476,
+        1.013486087202582, 1.013439214312997, 1.0133943376199779, 1.0133507461194096,
+        1.0133076035146877, 1.0132640743982555, 1.013219444248099, 1.0131732160866203,
+        1.0131251712089473, 1.01307538749287, 1.0130242153998101, 1.0129722178212124,
+        1.0129200845550794, 1.0128685348509194, 1.0128182219403206, 1.0127696519331737,
+        1.0127231263548129, 1.0126787135627433, 1.0126362500084554, 1.0125953684402205,
+        1.0125555471676062, 1.012516172711804, 1.0124766076119773, 1.0124362557136204,
+        1.0123946186533235, 1.012351339123851, 1.0123062285005662, 1.0122592782405553,
+        1.01221065593245, 1.0121606878959453, 1.012109830824977, 1.012058635230421,
+        1.0120077034933572, 1.011957645306378, 1.0119090332378573, 1.0118623611265107,
+        1.0118180079695123, 1.0117762098370011, 1.0117370420456426, 1.0117004132875334,
+        1.0116660726130513, 1.0116336291396515, 1.011602583194631, 1.0115723664365333,
+        1.0115423874999174, 1.0115120790274592, 1.0114809417124118, 1.0114485812330956,
+        1.0114147347054052, 1.0113792844214113, 1.0113422580334044, 1.0113038157980339,
+        1.011264226823618, 1.0112238372993338, 1.0111830343120345, 1.0111422090254452,
+        1.0111017227269967, 1.0110618786190129, 1.011022901364949, 1.010984925435714,
+        1.0109479923668927, 1.0109120562381118, 1.0108769960833999, 1.0108426335569096,
+        1.0108087539935655, 1.0107751289789013, 1.0107415386258158, 1.010707791906196,
+        1.010673743575853, 1.0106393064583326, 1.010604458129863, 1.0105692413964307,
+        1.0105337583914957, 1.0104981586495794, 1.0104626220995794, 1.0104273385159814,
+        1.010392485485703, 1.0103582073003756, 1.0103245972827202, 1.0102916858403426,
+        1.0102594359931754, 1.0102277472774805, 1.0101964678800075, 1.0101654137370124,
+        1.0101343923072985, 1.010103227961037, 1.0100717855550252, 1.010039988875103,
+        1.0100078312321896, 1.0099753765343373, 1.0099427504863299, 1.0099101229979346,
+        1.0098776841954638, 1.009845617421041, 1.0098140731070508, 1.0097831473388297,
+        1.0097528682655228, 1.009723192377595, 1.0096940112090946, 1.0096651674659776,
+        1.0096364781687257, 1.0096077613480372, 1.00957886231062, 1.0095496755792186,
+        1.0095201592927312, 1.0094903400203554, 1.0094603074136546, 1.0094301996616772,
+        1.009400182086592, 1.0093704222104334, 1.0093410650895072, 1.0093122125893186,
+        1.0092839095908293, 1.0092561389965498, 1.0092288260267552, 1.009201850881798,
+        1.0091750676153057, 1.0091483261995449, 1.009121494389473, 1.0090944761469562,
+        1.009067224028295, 1.00903974394861, 1.0090120919458165, 1.0089843637799476,
+        1.0089566792343725, 1.0089291636842448, 1.0089019297739426, 1.0088750618787703,
+        1.0088486054667047, 1.008822562630776, 1.0087968940777372, 1.0087715268923312,
+        1.0087463665943048, 1.008721311477847, 1.008696267031413, 1.0086711583838714,
+        1.0086459391628984, 1.0086205957937984, 1.0085951469979464, 1.0085696389525485,
+        1.008544137144684, 1.0085187163197042, 1.0084934500529419, 1.008468401370193,
+        1.0084436155476537, 1.0084191158019102, 1.0083949021127239, 1.0083709529804283,
+        1.0083472295669744, 1.0083236814434726, 1.008300253080199, 1.0082768902569355,
+        1.0082535457118158, 1.0082301835460001, 1.0082067821174032, 1.0081833353537932,
+        1.0081598525701307, 1.0081363569770854, 1.0081128831208854, 1.0080894735116757,
+        1.008066174696184, 1.0080430330267798, 1.0080200903838232, 1.0079973801240236,
+        1.0079749235480642, 1.007952727193572, 1.0079307812491385, 1.00790905933801,
+        1.0078875198287371, 1.0078661086963843, 1.0078447637933672, 1.0078234202145273,
+        1.0078020162825385, 1.0077804995645903, 1.007758832281696, 1.007736995501968,
+        1.007714991620265, 1.0076928448073252, 1.0076705993391548, 1.007648315960947,
+        1.007626066665498, 1.007603928442652, 1.007581976660309, 1.007560278756816,
+        1.0075388888599512, 1.007517843812669, 1.0074971609028869, 1.0074768373924248,
+        1.0074568517472124, 1.007437166311581, 1.0074177310602055, 1.0073984880088724,
+        1.0073793758663727, 1.0073603345534752, 1.0073413092851884, 1.0073222539923883,
+        1.0073031339342613, 1.0072839274146888, 1.0072646265612346, 1.0072452371583298,
+        1.0072257775542188, 1.007206276693294, 1.0071867713688794, 1.0071673028488457,
+        1.0071479130944496, 1.0071286408617668, 1.0071095180309206, 1.0070905665353194,
+        1.0070717962470062, 1.0070532041072497, 1.0070347746731354, 1.007016482091637,
+        1.006998293331122, 1.006980172322697, 1.0069620845186622, 1.0069440012890483,
+        1.0069259035688578, 1.0069077842460332, 1.0068896489374128, 1.006871515017869,
+        1.0068534090154844, 1.0068353627260378, 1.0068174085952437, 1.0067995750346048,
+        1.0067818823557495, 1.0067643399225235, 1.0067469449412374, 1.006729683063365,
+        1.006712530699467, 1.0066954586815413, 1.0066784367047108, 1.0066614378617045,
+        1.0066444425737764, 1.0066274413216543, 1.0066104357736163, 1.0065934381638015,
+        1.0065764690508816, 1.0065595538406542, 1.0065427186451381, 1.0065259861455562,
+        1.0065093721128748, 1.0064928831208844, 1.0064765157840854, 1.0064602576000652,
+        1.0064440892158872, 1.0064279877126898, 1.0064119303487515, 1.0063958981422119,
+        1.0063798787184297, 1.0063638679837914, 1.0063478703930644, 1.0063318978153415,
+        1.006315967233919, 1.006300097700174, 1.0062843070708336, 1.0062686090760915,
+        1.0062530111921246, 1.006237513640982, 1.0062221096409043, 1.0062067868162168,
+        1.0061915294843293, 1.0061763214000028, 1.0061611484752355, 1.0061460010151808,
+        1.0061308751099103, 1.0061157729791075, 1.0061007022532804, 1.0060856743577926,
+        1.0060707023138502, 1.0060557983590996, 1.0060409718065995, 1.006026227504019,
+        1.006011565137426, 1.0059969794681234, 1.0059824614251502, 1.0059679998293196,
+        1.005953583422092, 1.005939202830509, 1.0059248521234294, 1.005910529698091,
+        1.0058962383628829, 1.0058819846287816, 1.0058677773616345, 1.005853626056016,
+        1.0058395390505819, 1.0058255220056067, 1.0058115769073805, 1.0057977017626816,
+        1.005783891019093, 1.005770136616455, 1.005756429464739, 1.0057427610727612,
+        1.0057291250321534, 1.0057155180940482, 1.0057019406548322, 1.0056883965769636,
+        1.0056748923910843, 1.005661436034855, 1.0056480353630974, 1.0056346966995144,
+        1.0056214236872574, 1.0056082166372295, 1.0055950724806686, 1.0055819853232713,
+        1.005568947491626, 1.0055559508777476, 1.0055429883385798, 1.0055300549023256,
+        1.0055171485723342, 1.005504270594206, 1.0054914251488707, 1.005478618536037,
+        1.0054658580007338, 1.0054531504153184, 1.0054405010505456, 1.0054279126491446,
+        1.0054153849581733, 1.0054029147931576, 1.005390496612636, 1.0053781234930728,
+        1.0053657883264997, 1.0053534850280146, 1.005341209542882, 1.0053289604821782,
+        1.0053167392839109, 1.0053045498811413, 1.0052923979444428, 1.0052802898383146,
+        1.0052682314776669, 1.0052562272836447, 1.0052442794165348, 1.005232387411663,
+        1.0052205482719414, 1.0052087569909236, 1.0051970074068646, 1.0051852932339722,
+        1.0051736090904884, 1.0051619513484589, 1.005150318665201, 1.0051387121147253,
+        1.0051271349079953, 1.005115591761542, 1.0051040880321835, 1.0050926287720605,
+        1.005081217867013, 1.0050698574019172, 1.0050585473532108, 1.0050472856495476,
+        1.0050360685771733, 1.0050248914484168, 1.0050137494094036, 1.0050026382436539,
+        1.0049915550340607, 1.004980498575104, 1.0049694694741984, 1.0049584699369052,
+        1.0049475032856416, 1.004936573305701, 1.0049256835388711, 1.0049148366494527,
+        1.0049040339701867, 1.004893275300186, 1.0048825589802532, 1.0048718822214893,
+        1.004861241619635, 1.0048506337574479, 1.0048400557855228, 1.0048295058797356,
+        1.0048189834988448, 1.004808489403807, 1.0047980254438305, 1.0047875941553726,
+        1.004777198251877, 1.0047668400989718, 1.0047565212693925, 1.004746242254792,
+        1.004736002381343, 1.0047257999383516, 1.0047156324908817, 1.00470549731539,
+        1.0046953918770545, 1.0046853142621612, 1.0046752634890754, 1.0046652396447893,
+        1.0046552438262986, 1.0046452779012693, 1.0046353441342135, 1.0046254447473388,
+        1.0046155814953959, 1.0046057553298828, 1.0045959662107316, 1.0045862130966052,
+        1.0045764941129138, 1.0045668068655134, 1.0045571488430332, 1.0045475178362213,
+        1.0045379123008658, 1.0045283316017952, 1.004518776097049, 1.0045092470495582,
+        1.004499746383607, 1.0044902763297785, 1.0044808390204991, 1.004471436105838,
+        1.0044620684546377, 1.0044527359905777, 1.0044434376891345, 1.0044341717338274,
+        1.004424935803409, 1.0044157274401544, 1.0044065444367802, 1.0043973851775116,
+        1.004388248877656, 1.0043791356838778, 1.0043700466210879, 1.0043609833973426,
+        1.0043519481011534, 1.0043429428423798, 1.0043339693959108, 1.0043250289054242,
+        1.004316121693473, 1.0043072472058028, 1.0042984040956038, 1.0042895904308633,
+        1.004280803988921, 1.0042720425895686, 1.0042633044134461, 1.0042545882565097,
+        1.00424589368299, 1.004237221056377, 1.0042285714476376, 1.0042199464388544,
+        1.0042113478558878, 1.0042027774731503, 1.0041942367360597, 1.004185726542072,
+        1.0041772471105357, 1.0041687979568774, 1.0041603779703285, 1.0041519855791263],
+    [7.09744670677872e-05, 0.00021300389777849425, 0.0003552750336797058,
+        0.0004979496396749049, 0.0006411904117735231, 0.0007851613909321921,
+        0.0009300283164879005, 0.0010759590458060326, 0.0012231239477622905,
+        0.0013716963181198674, 0.0015218528059926838, 0.0016737738594023873,
+        0.0018276441748733586, 0.001983653179796104, 0.002141995522751791,
+        0.0023028715955578376, 0.0024664880760458777, 0.002633058499286045,
+        0.002802803863428113, 0.0029759532622813303, 0.0031527445663895575,
+        0.003333425134838397, 0.0035182525789845326, 0.003707495574782499,
+        0.0039014347295670297, 0.004100363507264426, 0.004304589224472457,
+        0.0045144341136333, 0.004730236471025892, 0.004952351886073164,
+        0.005181154575924329, 0.005417038817167124, 0.005660420501650166,
+        0.005911738816675629, 0.006171458072151321, 0.0064400696815522535,
+        0.006718094322068663, 0.007006084284388452, 0.007304626043544835,
+        0.007614343064332419, 0.007935898880335555, 0.008270000466547384,
+        0.008617401952610628, 0.008978908706970797, 0.009355381850788377,
+        0.009747743237486641, 0.010156980987522594, 0.010584155614062367,
+        0.01103040686219221, 0.011496961323718, 0.011985140964009306, 0.012496372687110912,
+        0.013032199089628218, 0.013594290600887597, 0.014184459223759736,
+        0.014804674136325899, 0.015457079488442896, 0.016144014755725432,
+        0.016868038139395875, 0.017631953571105537, 0.018438842030413228,
+        0.019292098053812906, 0.020195472525549953, 0.021153123127295285,
+        0.022169674198282318, 0.023250288257298097, 0.024400752087791452,
+        0.02562758119744392, 0.026938147701964586, 0.02834083837955096,
+        0.029845252075419975, 0.03146244909822004, 0.03320527030740534,
+        0.03508875104903793, 0.03713066648616254, 0.03935226238868119, 0.041779253392123024,
+        0.044443216191268585, 0.047383581855418605, 0.05065056532591917,
+        0.05430961349041195, 0.05844841751602815, 0.06318847148137087, 0.06870517931255382,
+        0.07526524305834521, 0.08330235236922322, 0.09358871276359827, 0.10769062214067467,
+        0.12951416536731641, 0.17355306997154912, 0.5308904622978109, 0.16824000548556975,
+        0.12427293373827317, 0.10797545152769426, 0.10008460267590577, 0.09614385579618968,
+        0.094523909749073, 0.09449147861590926, 0.09568182883767273, 0.09791105448475117,
+        0.10109794399240787, 0.10522865901942821, 0.11034095701273643, 0.11651893085398646,
+        0.12389477175359266, 0.13265670469999155, 0.143064018738161, 0.155472000402092,
+        0.17037248212490405, 0.18846118081099977, 0.21075456342839938, 0.23880607679207988,
+        0.27514301559221477, 0.3242647547310634, 0.3953793976077431, 0.5125125020590762,
+        0.7825777319572571, 3.755752653720154, 0.6130238071265707, 2.0038324235182907,
+        1.7966683773617411, 0.489276423461725, 0.5681455484193783, 1.645469342337874,
+        2.6391577981983634, 1.290482360614598, 0.8266623692872099, 0.6486650029294035,
+        0.8067018461439633, 1.6226534240803259, 1.6444468508405699, 1.2430590781299267,
+        1.0534849646569406, 0.9805165736689616, 0.9964704994790582, 1.1309390194403162,
+        1.2953379332275634, 1.1366672611523716, 0.9949313965565333, 0.9665725311465813,
+        1.0088697216944789, 1.1129665716883443, 1.2901188997862794, 1.5095481495872907,
+        1.4827100472993031, 1.1041193077846867, 0.8362982225595079, 0.7639941078454111,
+        0.8164733741323419, 0.9545515691326313, 1.1768801938217415, 1.484241818334998,
+        1.7361007143454568, 1.579921206710706, 1.172230881216961, 0.8597183389944386,
+        0.7059881248858814, 0.8038664282844395, 0.9351694482554926, 1.0870768640555255,
+        1.2333654616969643, 1.3248802700084557, 1.3276639572176514, 1.258438823896954,
+        1.161220511681095, 1.0693124146969666, 0.9983346493732207, 0.9541147268024985,
+        0.9388984129168063, 0.9533877963758052, 0.9956901061799435, 1.0582713893742315,
+        1.1252952849244586, 1.175475624939612, 1.193062491082201, 1.1773998723103694,
+        1.1397188493988264, 1.093037022082418, 1.0463126409700028, 1.004082608765184,
+        0.9680382743259438, 0.9384424067803919, 0.914973427422746, 0.8971451733456922,
+        0.884490232475867, 0.8766272226938088, 0.8732757582890902, 0.8742496693916285,
+        0.8794412708799955, 0.8887997597433626, 0.9023007638679906, 0.9198992812232972,
+        0.9414537752641925, 0.9666060555403354, 0.9946048665314177, 1.0240832836450913,
+        1.052860590188974, 1.0779445484966463, 1.095991721076949, 1.1043476281606295,
+        1.1022929660235683, 1.0916347073751764, 1.076065980044646, 1.0597166853884734,
+        1.0458733601599681, 1.036431279552166, 1.0319764174400483, 1.032137636780714,
+        1.035947312778748, 1.0421175130823999, 1.0492411392346954, 1.0559579204279967,
+        1.0611134326076888, 1.0639096818405083, 1.0640171790528699, 1.0616082369077542,
+        1.0572886642532933, 1.0519414839691061, 1.046528590093062, 1.0419050073942255,
+        1.0386849459529572, 1.0371737535967278, 1.0373603068306139, 1.0389561869078479,
+        1.0414682339089179, 1.0442936060957988, 1.0468266269575026, 1.0485634792360075,
+        1.0491869235343725, 1.0486132353270503, 1.0469904956987592, 1.0446498894486818,
+        1.0420243447827908, 1.0395559269252035, 1.0376127008073286, 1.0364294928714557,
+        1.0360791921885648, 1.0364749425710647, 1.037399503551397, 1.0385553076427505,
+        1.0396262730808503, 1.040340171766957, 1.0405193834803887, 1.040109614510392,
+        1.0391810969647164, 1.0379036609125947, 1.0365033953758254, 1.0352121347124978,
+        1.03422098166693, 1.0336463843505825, 1.0335135066803203, 1.0337580241779878,
+        1.0342445192471423, 1.0347972739561795, 1.0352373623844133, 1.0354187570377027,
+        1.0352562069129208, 1.0347393337214743, 1.0339305726658812, 1.032948393932425,
+        1.0319404713055658, 1.031053174802809, 1.0304037112281133, 1.0300598402325016,
+        1.0300300567975327, 1.0302650398681081, 1.03066931776118, 1.0311205782805517,
+        1.0314929102065211, 1.0316796504271144, 1.031611637092588, 1.031267649890205,
+        1.0306755165173038, 1.029904360549064, 1.0290502086924445, 1.0282182211534743,
+        1.027504997489467, 1.026983877762038, 1.0266952079909257, 1.026642475082734,
+        1.026794243739258, 1.0270910376046256, 1.0274557259603865, 1.0278056230705588,
+        1.0280644103575143, 1.0281721775596167, 1.0280923305258214, 1.0278147448724722,
+        1.0273552140102635, 1.0267517938205282, 1.0260589763467771, 1.025340703293165,
+        1.024663107396337, 1.0240876427288836, 1.0236650342786917, 1.0234303135241654,
+        1.0233991359570793, 1.0235655812362474, 1.023901669479929, 1.024358828629974,
+        1.024871465614523, 1.025362601143415, 1.0257512358999552, 1.0259607789466891,
+        1.0259275746109175, 1.0256084075754721, 1.0249859172994946, 1.0240711265375537,
+        1.0229027318185806, 1.0215433115228651, 1.0200730594145462, 1.0185819534984066,
+        1.0171613802080954, 1.0158961668943853, 1.014857785000441, 1.014099238308944,
+        1.0136519011929221, 1.013524355191587, 1.0137031012197815, 1.0141548978900166,
+        1.01483038745038, 1.0156686152142131, 1.0166020256379573, 1.0175615299034866,
+        1.0184812851964147, 1.0193028979085603, 1.0199788480315073, 1.0204750127867914,
+        1.0207722293554389, 1.0208668732208614, 1.0207704454534794, 1.0205081739933228,
+        1.020116658660989, 1.0196406405822118, 1.0191290564584203, 1.0186306365062179,
+        1.018189402096178, 1.017840491700921, 1.0176067711521386, 1.01749665306138,
+        1.0175034560695433, 1.0176064812612762, 1.0177737824422752, 1.0179663791760991,
+        1.0181434359343877, 1.0182677454488245, 1.018310751134078, 1.0182563578785182,
+        1.0181029290797934, 1.017863137449781, 1.0175616829297922, 1.0172312455556582,
+        1.01690733238476, 1.0166228492349487, 1.0164032526402322, 1.0162630195871414,
+        1.0162039417146351, 1.0162154501769611, 1.0162768549976275, 1.0163610849815958,
+        1.0164392837634708, 1.016485490439407, 1.0164806336120438, 1.0164152004329101,
+        1.0162901871599928, 1.0161162498945808, 1.0159112924029672, 1.015696989923518,
+        1.0154949057936598, 1.015322888852059, 1.0151923483021124, 1.0151068153449019,
+        1.0150619566127201, 1.015046946866944, 1.0150468794224172, 1.0150457281832634,
+        1.0150293010501956, 1.0149876526986994, 1.014916549373385, 1.0148177746018714,
+        1.0146982927926245, 1.0145685013452193, 1.0144399595620999, 1.0143230568418267,
+        1.0142250650096114, 1.0141489204487888, 1.0140929251230657, 1.0140513734182923,
+        1.014015937425829, 1.0139775070961716, 1.0139281067248398, 1.0138625079917452,
+        1.0137792314789145, 1.0136807583885359, 1.0135729353766736, 1.0134637149308174,
+        1.0133614995701736, 1.0132734266704548, 1.0132039312819452, 1.01315386040013,
+        1.013120299125716, 1.0130971300829272, 1.0130762084655065, 1.0130489210499347,
+        1.0130078285065889, 1.0129480784794578, 1.0128683241032896, 1.012770979677937,
+        1.012661773053478, 1.0125486876089058, 1.0124404994351808, 1.0123451862490804,
+        1.0122685016820714, 1.0122129709815997, 1.012177481170306, 1.0121575272125962,
+        1.0121460565514417, 1.0121347486172827, 1.0121154917448438, 1.0120817898561396,
+        1.0120298500238791, 1.0119591655617082, 1.0118725051855677, 1.0117753285095439,
+        1.0116747507350297, 1.0115782558957782, 1.0114923952941788, 1.0114217008106483,
+        1.0113679950857808, 1.0113302027600544, 1.0113046741917582, 1.0112859422348084,
+        1.0112677594908932, 1.0112442201429364, 1.0112107637491257, 1.0111648883466,
+        1.0111064603098012, 1.0110375865540926, 1.0109620956617296, 1.0108847430985777,
+        1.0108102996955086, 1.0107426951250431, 1.0106843686540639, 1.0106359333582802,
+        1.0105961970578705, 1.0105625156742855, 1.010531394872245, 1.0104992141858815,
+        1.0104629311866415, 1.0104206337783928, 1.0103718434913584, 1.0103175242918205,
+        1.0102598095092477, 1.0102015126795556, 1.0101455264704893, 1.0100942307585954,
+        1.0100490241621265, 1.0100100652688633, 1.0099762666172378, 1.0099455348287036,
+        1.0099152035659449, 1.0098825707405825, 1.0098454338195029, 1.0098025200098204,
+        1.009753730514214, 1.0097001552688074, 1.0096438591975812, 1.009587484370992,
+        1.0095337463427834, 1.009484921231241, 1.009442419861417, 1.0094065271346975,
+        1.0093763526552983, 1.0093499988190597, 1.009324912507555, 1.0092983534885511,
+        1.009267892425348, 1.0092318474508453, 1.0091895809864786, 1.009141605252674,
+        1.0090894805494235, 1.0090355281526058, 1.008982412595641, 1.0089326703007555,
+        1.0088882692752028, 1.0088502769586194, 1.0088186921741398, 1.008792466704025,
+        1.0087697079595048, 1.0087480226474241, 1.0087249377252012, 1.0086983232076843,
+        1.0086667432873202, 1.008629677043321, 1.008587574744619, 1.0085417456857761,
+        1.0084941031144805, 1.0084468158350588, 1.0084019304354348, 1.0083610306280149,
+        1.0083249909709455, 1.008293863378662, 1.0082669100642063, 1.0082427704633588,
+        1.00821972688564, 1.0081960179761382, 1.0081701430187948, 1.0081411043579107,
+        1.0081085486005683, 1.0080727870373496, 1.0080346980784851, 1.0079955353248649,
+        1.0079566805071027, 1.0079193883702098, 1.0078845696205214, 1.007852648882435,
+        1.007823519268081, 1.0077965966732416, 1.0077709587212622, 1.0077455386218839,
+        1.007719335571758, 1.007691602010147, 1.0076619740093982, 1.0076305229650644,
+        1.0075977221681072, 1.0075643378430323, 1.0075312678737753, 1.0074993603115314,
+        1.00746924642738, 1.0074412192846343, 1.0074151794842785, 1.007390656759475,
+        1.0073669019204707, 1.0073430308613747, 1.0073181931866875, 1.0072917340379086,
+        1.0072633194770801, 1.007233002855653, 1.007201220571707, 1.0071687184445313,
+        1.0071364222843213, 1.0071052759305308, 1.007076075434783, 1.007049328342982,
+        1.0070251622795543, 1.0070032982153505, 1.0069830925364567, 1.00696364030933,
+        1.006943921955449, 1.0069229685787262, 1.0069000185123107, 1.0068746395971657,
+        1.0068467978160516, 1.0068168620442828, 1.0067855452345431, 1.0067537925401397,
+        1.0067226350442837, 1.0066930326528574, 1.0066657306719646, 1.0066411516492388,
+        1.0066193378602069, 1.006599951504559, 1.0065823306515223, 1.0065655906789277,
+        1.0065487546282266, 1.0065308924075986, 1.0065112484841938, 1.0064893404609994,
+        1.0064650161185076, 1.006438463165443, 1.0064101729772408, 1.006380865924964,
+        1.0063513906318222, 1.006322612082414, 1.0062953037768732, 1.006270057264147,
+        1.006247218900846, 1.0062268592478554, 1.0062087758765244, 1.006192526186095,
+        1.0061774836489872, 1.006162908996056, 1.0061480272914542, 1.006132102478849,
+        1.0061145025072828, 1.00609475018624, 1.0060725570932159, 1.006047839842903,
+        1.0060207196099835, 1.005991506885043, 1.0059606740553264, 1.0059288186407802,
+        1.005896620023572, 1.0058647924241382, 1.005834036798882, 1.0058049943049827,
+        1.0057782039758483, 1.0057540672088838, 1.0057328214954782, 1.0057145254395745,
+        1.0056990564690187, 1.0056861217502364, 1.0056752817377637, 1.005665984642939,
+        1.005657609039246, 1.0056495109876777, 1.0056410715921884, 1.0056317408612994,
+        1.0056210741720175, 1.0056087584531799, 1.0055946263160822, 1.0055786576108798,
+        1.0055609691151257, 1.0055417941178586, 1.005521454437363, 1.0055003278435262,
+        1.0054788139423265, 1.0054573013647123, 1.0054361386637654, 1.0054156107552583,
+        1.0053959221257434, 1.0053771874468989, 1.0053594297137998, 1.0053425855787874,
+        1.0053265171694759, 1.0053110293388778, 1.0052958909803134, 1.005280858748956,
+        1.0052657012858615, 1.0052502218806614, 1.005234277489243, 1.005217792195186,
+        1.005200763602867, 1.00518326127853, 1.0051654171735616, 1.0051474088892995,
+        1.005129437557589, 1.0051117028801866, 1.005094378362204, 1.0050775898876978,
+        1.0050614004677456, 1.005045803256086, 1.0050307238559675, 1.0050160316758616,
+        1.0050015588129309, 1.0049871238460257, 1.004972557180011, 1.0049577243262477,
+        1.004942543784197, 1.0049269969756915, 1.0049111288645791, 1.0048950392916443,
+        1.004878866452007, 1.0048627651200728, 1.0048468829991875, 1.0048313388170482,
+        1.0048162054658112, 1.0048015006511961, 1.0047871863036073, 1.0047731766127095,
+        1.0047593531988992, 1.0047455848460014, 1.0047317485602978, 1.0047177485909178,
+        1.0047035304575629, 1.0046890879071722, 1.0046744619102512, 1.004659732110846,
+        1.0046450023470745, 1.0046303827685192, 1.0046159715517775, 1.00460183919,
+        1.0045880178238866, 1.0045744971868609, 1.004561227613111, 1.0045481293942542,
+        1.0045351067596826, 1.0045220640576806, 1.0045089214334375, 1.0044956274684695,
+        1.0044821668217645, 1.0044685617879525, 1.0044548677093748, 1.0044411631748833,
+        1.004427536747704, 1.0044140724629562, 1.0044008364538213, 1.004387866799712,
+        1.0043751680990307, 1.004362711461981, 1.004350439734686, 1.0043382769498104,
+        1.0043261403781925, 1.0043139532201704, 1.0043016559636349, 1.0042892147331461,
+        1.0042766254971935, 1.0042639136895757, 1.0042511295190957, 1.0042383398753805,
+        1.0042256181943687, 1.0042130338661905, 1.0042006427338686, 1.004188479967634,
+        1.0041765561651137, 1.0041648570025472, 1.0041533462342074, 1.0041419713861568,
+        1.0041306711767555, 1.0041193835526538, 1.004108053257791, 1.0040966380298506,
+        1.004085112798628, 1.0040734715888506, 1.0040617271509462, 1.004049908611215,
+        1.0040380576178367, 1.004026223549562, 1.0040144583562582, 1.0040028115343664,
+        1.0039913256334934, 1.0039800325709323, 1.0039689509221716, 1.0039580842716005,
+        1.0039474206521428, 1.0039369330696057, 1.0039265810850284, 1.0039163134021112,
+        1.0039060713656862, 1.003895793215993, 1.0038854188653228, 1.0038748948794665,
+        1.0038641792728362, 1.003853245682171, 1.0038420864853184, 1.0038307144889582,
+        1.0038191629227289, 1.0038074836374427, 1.0037957435930882, 1.003784019912827,
+        1.003772393945114, 1.003760944892848, 1.0037497436187928, 1.0037388472130577,
+        1.0037282948152981, 1.0037181050360817, 1.0037082751407889, 1.0036987819717773,
+        1.003689584415561, 1.0036806270919327, 1.003671844863657, 1.003663167741589,
+        1.0036545257846692, 1.0036458536544017, 1.003637094562477, 1.0036282034316983,
+        1.0036191491615534, 1.0036099159433647, 1.0036005036058995, 1.003590926996122,
+        1.003581214421018, 1.003571405205113, 1.0035615464621315, 1.0035516892403635,
+        1.0035418842753139, 1.0035321776590391, 1.0035226067973688, 1.0035131970566062,
+        1.0035039594849864, 1.003494889922445, 1.003485969684858, 1.0034771678367909,
+        1.0034684448701143, 1.003459757412499, 1.0034510634302365, 1.0034423272925062,
+        1.003433524049781, 1.0034246423565367, 1.0034156856323098, 1.003406671285797,
+        1.0033976280922319, 1.0033885920756664, 1.0033796014650127, 1.003370691430651,
+        1.003361889344133, 1.0033532112288277, 1.0033446598941755, 1.0033362249960527,
+        1.0033278849787313, 1.0033196105744475, 1.0033113693081053, 1.0033031303128723,
+        1.0032948687291021, 1.0032865690387005, 1.0032782268659557, 1.0032698490245329,
+        1.0032614518681362, 1.0032530582646277, 1.003244693718332, 1.0032363822812327,
+        1.0032281429040932, 1.003219986784033, 1.0032119160839592, 1.003203924163228,
+        1.0031959972084348, 1.003188116929689, 1.0031802638274794, 1.0031724204626788,
+        1.003164574186808, 1.003156718904, 1.0031488556180386, 1.003140991734417,
+        1.0031331393005967, 1.0031253125415165, 1.003117525153282, 1.0031097878401711,
+        1.0031021065174173, 1.0030944814684206, 1.0030869075655315, 1.0030793754711578,
+        1.0030718735645545, 1.0030643902188578, 1.0030569160022615, 1.0030494454038283,
+        1.0030419777813835, 1.003034517377276, 1.0030270724199817, 1.0030196534944034,
+        1.0030122714922325, 1.0030049355238355, 1.0029976511736203, 1.0029904194129986,
+        1.0029832363623183, 1.0029760939381869, 1.0029689812635876, 1.0029618865832162,
+        1.002954799339129, 1.002947712036625, 1.0029406215708268, 1.0029335297825788,
+        1.0029264431497555, 1.0029193716723916, 1.0029123271501659, 1.0029053211544692,
+        1.002898363047076, 1.0028914583854416, 1.0028846079840412, 1.002877807785006,
+        1.0028710495506603, 1.0028643222498894, 1.0028576138940979, 1.0028509135060601,
+        1.002844212888145, 1.0028375078967027, 1.0028307990189131, 1.0028240911705897,
+        1.0028173927667559, 1.0028107142381537, 1.0028040662557869, 1.0027974579677887,
+        1.0027908955423273, 1.0027843812501818, 1.0027779132226513, 1.0027714859023968,
+        1.0027650910874482, 1.0027587193719303, 1.002752361726962, 1.0027460109508037,
+        1.0027396627495904, 1.0027333162818726, 1.0027269740979545, 1.0027206415109733,
+        1.0027143255323578, 1.0027080335734084, 1.002701772146506, 1.002695545789535,
+        1.0026893563888524, 1.0026832029993347, 1.0026770821690718, 1.0026709886876328,
+        1.0026649166058694, 1.0026588603337925, 1.0026528156173633, 1.002646780224807,
+        1.0026407542316937, 1.0026347398703028, 1.0026287409883772, 1.0026227622311084,
+        1.0026168081062217, 1.002610882107764, 1.0026049860578925, 1.0025991197814093,
+        1.00259328116387, 1.0025874665727899, 1.002581671555737, 1.0025758916806677,
+        1.0025701233608693, 1.0025643645129168, 1.0025586149293073, 1.0025528763013385,
+        1.0025471518922437, 1.0025414459238704, 1.0025357627909224, 1.002530106246311,
+        1.002524478704468, 1.0025188807866134, 1.0025133111873692, 1.0025077668841365,
+        1.0025022436496878, 1.0024967367754407, 1.0024912418768348, 1.0024857556393887,
+        1.0024802763760503, 1.0024748043008809, 1.0024693414745973, 1.002463891434776,
+        1.0024584585777974, 1.0024530474011928, 1.0024476617373697, 1.0024423041089408,
+        1.0024369753128854, 1.0024316742998831, 1.0024263983637365, 1.0024211436029964,
+        1.002415905571702, 1.0024106800061097, 1.002405463504203, 1.0024002540458226,
+        1.0023950512709674, 1.0023898564767193, 1.0023846723415888, 1.00237950243155,
+        1.002374350576904, 1.0023692202279484, 1.0023641138973254, 1.0023590327786656,
+        1.0023539765983562, 1.0023489437159914, 1.0023439314466833, 1.002338936542077,
+        1.0023339557426683, 1.0023289863055347, 1.002324026419724, 1.002319075444302,
+        1.002314133936975, 1.0023092034783332, 1.0023042863314338, 1.0022993850029593,
+        1.0022945017861675, 1.0022896383654503, 1.0022847955481384, 1.0022799731642036,
+        1.0022751701434867, 1.0022703847486178, 1.0022656149153883, 1.0022608586354083,
+        1.0022561143110058, 1.002251381019952, 1.0022466586459537, 1.00224194785629,
+        1.0022372499358898, 1.002232566512482, 1.0022278992258629, 1.0022232494028538,
+        1.002218617796835, 1.0022140044377936, 1.0022094086180355, 1.002204829013997,
+        1.0022002639203922, 1.0021957115533684, 1.0021911703678572, 1.0021866393325212,
+        1.0021821181139132, 1.0021776071378312, 1.002173107517558, 1.002168620861741,
+        1.0021641489952589, 1.0021596936409156, 1.0021552561160716, 1.0021508370952412,
+        1.0021464364782413, 1.002142053385453, 1.002137686280611, 1.0021333332005395,
+        1.0021289920541223, 1.0021246609420542, 1.0021203384462696, 1.0021160238435574,
+        1.0021117172106484, 1.0021074194057251, 1.0021031319309006, 1.0020988566985745,
+        1.0020945957388385, 1.0020903508931736, 1.002086123540543, 1.002081914395731,
+        1.0020777234077523, 1.0020735497703581, 1.0020693920397503, 1.0020652483391714],
+    [3.0803931518489375e-05, 9.245069821316637e-05, 0.00015421428326392397,
+        0.0002161728844591258, 0.00027840517327360273, 0.00034099050265492024,
+        0.0004040090888987897, 0.00046754222271725777, 0.0005316724694555524,
+        0.000596483879435196, 0.000662062203821785, 0.0007284951196070836,
+        0.0007958724572170268, 0.0008642864433877719, 0.0009338319485527795,
+        0.0010046067492219522, 0.0010767118006230626, 0.0011502515230568781,
+        0.0012253341047569648, 0.001302071817827712, 0.0013805813569199529,
+        0.0014609841928159815, 0.0015434069503116354, 0.00162798180892015,
+        0.0017148469289551844, 0.001804146904677101, 0.00189603324994729,
+        0.0019906649145178808, 0.0020882088386676638, 0.0021888405442770003,
+        0.0022927447727327044, 0.0024001161654389172, 0.0025111599984656754,
+        0.002626092970603979, 0.0027451440540405317, 0.002868555409457971,
+        0.002996583375540237, 0.0031294995356747875, 0.0032675918738501427,
+        0.0034111660229774413, 0.0035605466200086776, 0.003716078772645075,
+        0.0038781296540154136, 0.004047090232791046, 0.004223377158084784,
+        0.0044074348060355786, 0.004599737517980672, 0.004800792032270425,
+        0.005011140149334929, 0.005231361637218757, 0.005462077414833462,
+        0.005703953039282318, 0.005957702527388886, 0.0062240925541977386,
+        0.006503947067172407, 0.006798152361273108, 0.0071076626758362176,
+        0.007433506363104793, 0.00777679270653218, 0.008138719460005356,
+        0.008520581197178136, 0.008923778572958894, 0.0093498286097183,
+        0.009800376138165057, 0.010277206542253892, 0.010782259981664962,
+        0.011317647284665814, 0.011885667739312123, 0.01248882904819909,
+        0.013129869744582134, 0.01381178442278762, 0.014537852191978557,
+        0.015311668834509493, 0.016137183216483664, 0.017018738615150963,
+        0.017961119722332265, 0.0189696062466548, 0.020050034175523836,
+        0.021208865978519918, 0.022453271288767774, 0.023791219868608948,
+        0.02523158906342205, 0.026784288392310958, 0.028460404474593606,
+        0.030272370208792684, 0.03223416297727848, 0.03436153776956783,
+        0.03667230249421674, 0.03918664452308226, 0.041927519839513996,
+        0.044921119027565085, 0.04819742827711259, 0.05179090858190951,
+        0.05574132304907215, 0.06009475121191451, 0.06490484151338756, 0.07023436970010427,
+        0.07615719429584829, 0.08276073279160903, 0.09014912907635733, 0.0984473504885147,
+        0.10780655357644363, 0.11841120976325194, 0.13048871816901353, 0.144322607505048,
+        0.16027104427007016, 0.17879340867011015, 0.2004895475033537, 0.2261597439334436,
+        0.2569001944694861, 0.2942630361838355, 0.340542844776551, 0.39933648523274695,
+        0.47677882527387794, 0.5848109050034741, 0.7528163454446831, 1.1030794102695611,
+        3.7539234967968125, 1.0613149398087423, 2.9442796331778873, 1.9118721336697297,
+        0.19266425231029458, 1.361391993222126, 3.737612950661533, 5.236779893936161,
+        1.9493570879194289, 0.31823193292579616, 2.219378285813057, 7.241691824742019,
+        7.0996926020089095, 4.370030801892724, 2.2015654021024464, 1.3291006238898584,
+        1.0021072382360496, 1.1109998701012866, 1.7383448333746236, 2.5759629285146306,
+        2.323798662279378, 1.7943486802359807, 1.4798246431532764, 1.3193810953324014,
+        1.2702769321341998, 1.3370473469444168, 1.5322055349670798, 1.6493729003298796,
+        1.4621157582597344, 1.2785081903830726, 1.2037347492439954, 1.212725600030724,
+        1.29258123743043, 1.4486933768085446, 1.6762488500213564, 1.8296731271237545,
+        1.6007437747663116, 1.2042391507508667, 0.9669112675608179, 0.9151199994754028,
+        1.0708750318187121, 1.209991162759065, 1.3575109009522057, 1.4853774370237238,
+        1.5436479497939577, 1.504602463191635, 1.396589723272963, 1.2718207124936889,
+        1.1655566959604566, 1.0920611570758152, 1.05487846395288, 1.0537125142445374,
+        1.0863653269732934, 1.1474854941324995, 1.2254849593734154, 1.3003199417030147,
+        1.3477872326557767, 1.3524444665863966, 1.317276506402226, 1.2580912851394899,
+        1.19116502156048, 1.126954439550285, 1.0703263980170776, 1.022765179016689,
+        0.984163888893624, 0.9538377730347086, 0.9310034865585954, 0.9149734457564301,
+        0.9052158152255007, 0.9013570648663182, 0.9031627193205892, 0.9105103172333194,
+        0.9233569056453842, 0.9416960685468131, 0.9654935799665163, 0.9945851209250084,
+        1.0285154545376805, 1.066302564567107, 1.106138578109582, 1.1451173062136244,
+        1.1792156138194234, 1.2038683975601636, 1.215316507112151, 1.2122775434440018,
+        1.196834658937199, 1.1737420207993117, 1.148600887286089, 1.1261344147494352,
+        1.1093394419440339, 1.0994621359615322, 1.0963775010668972, 1.0990342024081667,
+        1.1058223881364113, 1.1148549456054244, 1.1242025369455502, 1.1321182090925266,
+        1.1372552307515686, 1.1388451313539107, 1.13678475105442, 1.131596301597786,
+        1.1242664362363142, 1.1160126151794636, 1.1080421465865335, 1.1013565949293536,
+        1.0966268421496306, 1.0941401096647305, 1.093808197689327, 1.0952241738235078,
+        1.0977563089707734, 1.1006677112322574, 1.1032460469802932, 1.1049223380752373,
+        1.1053560157314408, 1.1044691839432954, 1.1024259585460667, 1.099567498196614,
+        1.0963233100617216, 1.0931212003904056, 1.0903132598198775, 1.088127622046833,
+        1.0866489655003015, 1.0858261513062422, 1.0855024270446554, 1.085461181164838,
+        1.0854779318829584, 1.0853678215335434, 1.085018647376945, 1.084403060769963,
+        1.083569211951396, 1.0826147772912482, 1.0816529155070937, 1.0807793462738648,
+        1.0800479280837678, 1.079459073918427, 1.0789621882679388, 1.0784705729647541,
+        1.0778850298923768, 1.0771207367582094, 1.0761311604396118, 1.0749232268797766,
+        1.0735599112850158, 1.0721495155296081, 1.0708242501033414, 1.0697132447933742,
+        1.0689160606892303, 1.0684821336213728, 1.068399867693477, 1.068596996167941,
+        1.0689518259165356, 1.0693132848015712, 1.069526342129776, 1.069458441697517,
+        1.0690222630876218, 1.0681906380696877, 1.06700087403682, 1.0655478460677443,
+        1.0639674858653596, 1.0624140961289026, 1.0610358076061968, 1.0599523765807997,
+        1.0592386200454058, 1.0589154844693398, 1.0589493877313056, 1.0592592739307214,
+        1.0597298618614392, 1.0602288753530973, 1.0606256471749955, 1.0608084384192518,
+        1.0606981505724518, 1.060256800734451, 1.0594900586888736, 1.0584441089977803,
+        1.0571978923920595, 1.055852253116637, 1.0545176363608444, 1.053301810284613,
+        1.0522987578624645, 1.0515795252168374, 1.0511855163195178, 1.0511245234819584,
+        1.0513696627240063, 1.0518612950101138, 1.0525119018392695, 1.0532137031186113,
+        1.053848543031998, 1.0542992521371581, 1.0544613869680723, 1.0542540423302518,
+        1.0536284131871931, 1.052573001636367, 1.051114804954471, 1.0493163996339352,
+        1.0472694255034958, 1.045085443482139, 1.0428854014790572, 1.0407889718398338,
+        1.0389048585568852, 1.037322888109972, 1.0361083746874302, 1.0352989504831187,
+        1.0349038079367903, 1.0349051208094486, 1.0352612872458868, 1.0359115589566568,
+        1.0367815785531052, 1.0377893399255935, 1.0388511153781639, 1.0398869568488638,
+        1.0408254690722758, 1.041607654570635, 1.042189724489785, 1.0425448389406569,
+        1.0426637785494504, 1.0425545612179772, 1.0422410213158302, 1.0417603835113474,
+        1.0411599064319619, 1.0404927470381764, 1.0398132958357587, 1.039172335693135,
+        1.0386124582937033, 1.038164209750386, 1.0378434154763523, 1.0376500480580673,
+        1.0375688534531673, 1.0375717514408753, 1.0376217955071876, 1.0376782443760943,
+        1.0377021002944007, 1.0376613504710726, 1.0375351449723929, 1.0373162758254275,
+        1.0370115778002005, 1.0366402089095867, 1.0362301220306318, 1.0358133362824837,
+        1.035420800098714, 1.035077677734802, 1.0347997894086258, 1.034591719962476,
+        1.0344468241356544, 1.0343490453680613, 1.034276175687787, 1.0342039589351282,
+        1.0341103138591128, 1.033978951041501, 1.0338017827220476, 1.033579757571891,
+        1.0333220494972915, 1.0330438313835215, 1.0327631110961177, 1.0324972521386606,
+        1.032259823679815, 1.0320583292218712, 1.0318931762809562, 1.0317580099867385,
+        1.0316412846719991, 1.0315287306615148, 1.0314062237020536, 1.0312625066469012,
+        1.0310912572976374, 1.0308921346194178, 1.0306706409587452, 1.0304368690066592,
+        1.0302034122770716, 1.029982865783703, 1.0297854035037122, 1.029616884893058,
+        1.0294778266101368, 1.0293634038092838, 1.0292644511662226, 1.029169251722154,
+        1.0290657626873092, 1.028943855028586, 1.0287971503746454, 1.0286241229609934,
+        1.0284282796633268, 1.0282174088343803, 1.0280020632502076, 1.0277935798923366,
+        1.027602014426448, 1.0274343699052446, 1.0272934312231472, 1.0271773955254864,
+        1.0270803385314315, 1.0269934051340583, 1.0269064860050996, 1.026810061619894,
+        1.0266968744184999, 1.0265631315789976, 1.026409036471196, 1.0262385773035958,
+        1.0260586410135826, 1.0258776420065017, 1.0257039364049783, 1.0255443196625138,
+        1.0254028765918357, 1.0252803765283602, 1.0251742988932793, 1.0250794565189285,
+        1.0249890770001584, 1.0248961245297736, 1.0247946091231952, 1.0246806421781,
+        1.0245530535931902, 1.0244134745446314, 1.024265893691381, 1.024115792731963,
+        1.0239690413055291, 1.0238307682229408, 1.0237044208183717, 1.0235911800063988,
+        1.023489825565804, 1.0233970589264356, 1.0233082056658733, 1.0232181522544161,
+        1.0231223330051222, 1.0230175799394081, 1.0229026800996126, 1.0227785449146396,
+        1.0226479724424318, 1.0225150606672335, 1.0223843937137165, 1.0222601612524698,
+        1.0221453783126042, 1.022041348267558, 1.0219474618200257, 1.021861359586878,
+        1.021779417794547, 1.0216974580403395, 1.0216115433654898, 1.021518710555248,
+        1.0214175042910918, 1.021308219007719, 1.021192810985852, 1.0210745052937413,
+        1.0209571778571653, 1.0208446319720739, 1.0207399043168377, 1.0206447259803488,
+        1.0205592319693457, 1.020481964796303, 1.0204101632791998, 1.0203402765692091,
+        1.0202686046766136, 1.0201919469623923, 1.0201081422559102, 1.020016407474591,
+        1.0199174210522952, 1.0198131454140411, 1.0197064300549725, 1.019600474782218,
+        1.0194982547332487, 1.0194020115232643, 1.0193128986467794, 1.0192308378371517,
+        1.0191546027776632, 1.0190821049412193, 1.0190108209012891, 1.0189382773240923,
+        1.018862502763006, 1.0187823650889378, 1.0186977375892026, 1.0186094705301296,
+        1.0185191817422672, 1.0184289126363029, 1.0183407190615692, 1.0182562757229872,
+        1.018176567331237, 1.0181017209047347, 1.0180310056233959, 1.0179629947974596,
+        1.0178958547618733, 1.0178277031552452, 1.0177569679178076, 1.0176826801461358,
+        1.0176046479881864, 1.017523482136245, 1.0174404716179424, 1.0173573361684969,
+        1.0172759034314482, 1.0171977717272682, 1.0171240201837677, 1.0170550178373021,
+        1.0169903641092222, 1.0169289685848426, 1.0168692528138275, 1.0168094354248212,
+        1.0167478479114969, 1.0166832242790498, 1.016614913828281, 1.0165429813346285,
+        1.016468179825664, 1.0163918041392415, 1.0163154542713901, 1.0162407525377402,
+        1.0161690652969941, 1.0161012775251788, 1.0160376576627144, 1.015977833112151,
+        1.0159208767620314, 1.015865485557671, 1.0158102167902183, 1.015753738973428,
+        1.015695053238979, 1.0156336480013288, 1.0155695627497618, 1.0155033536802243,
+        1.0154359713605596, 1.0153685756103394, 1.015302322719615, 1.0152381634827714,
+        1.0151766869746104, 1.0151180354667304, 1.0150619022987462, 1.0150076094287404,
+        1.0149542474889248, 1.01490085084716, 1.0148465750922355, 1.0147908452131689,
+        1.014733449161426, 1.0146745621331772, 1.014614699752346, 1.0145546110232273,
+        1.0144951322228497, 1.0144370290957159, 1.0143808558715468, 1.0143268557458405,
+        1.0142749194149259, 1.0142246075976753, 1.0141752321406763, 1.0141259802665654,
+        1.014076059459673, 1.0140248374939196, 1.0139719535676557, 1.0139173820180793,
+        1.0138614385709912, 1.0138047289981509, 1.0137480496791824, 1.0136922572940479,
+        1.013638129491267, 1.0135862392510817, 1.013536862809855, 1.0134899350643023,
+        1.0134450584350128, 1.013401562604543, 1.0133586047476324, 1.0133152940313532,
+        1.0132708210954073, 1.013224573256464, 1.0131762191346807, 1.0131257516476384,
+        1.013073484906708, 1.0130200073905022, 1.0129660998054335, 1.0129126304317624,
+        1.0128604429771015, 1.0128102518829643, 1.0127625578832937, 1.0127175929169048,
+        1.0126752989465204, 1.0126353405780655, 1.0125971472730473, 1.0125599779017962,
+        1.0125229986672728, 1.0124853650728707, 1.0124462994394445, 1.012405157173999,
+        1.0123614771591176, 1.0123150138777894, 1.012265750892879, 1.0122138968564773,
+        1.0121598662537057, 1.0121042476251922, 1.0120477621822679, 1.011991215687028,
+        1.0119354463647496, 1.0118812715536072, 1.0118294358153337, 1.0117805633011872,
+        1.0117351172095042, 1.0116933690776468, 1.0116553803238404, 1.0116209978314126,
+        1.011589864446171, 1.0115614440988643, 1.0115350599883657, 1.0115099430258292,
+        1.011485286713232, 1.011460303959819, 1.0114342811276524, 1.0114066248792994,
+        1.0113768981422306, 1.0113448426078568, 1.011310386504356, 1.0112736377565699,
+        1.011234863914586, 1.0111944612654256, 1.0111529162562913, 1.0111107627216518,
+        1.0110685384368099, 1.0110267442714354, 1.0109858087604, 1.0109460603218177,
+        1.0109077086972789, 1.0108708365106365, 1.010835401164485, 1.010801246626269,
+        1.0107681240059727, 1.0107357192061188, 1.0107036853616664, 1.010671677328384,
+        1.0106393851859916, 1.0106065636627493, 1.0105730546176062, 1.0105388002627345,
+        1.0105038456610385, 1.0104683301277284, 1.010432468392054, 1.010396523587425,
+        1.0103607751699182, 1.0103254855603596, 1.0102908695418755, 1.0102570701607783,
+        1.0102241440853597, 1.0101920581636772, 1.010160697445594, 1.010129883400448,
+        1.0100993996910916, 1.0100690218611867, 1.0100385468077626, 1.0100078180215415,
+        1.00997674326807, 1.0099453025495495, 1.0099135456505415, 1.0098815801057823,
+        1.0098495517991768, 1.0098176214021075, 1.0097859403397993, 1.0097546298745181,
+        1.0097237662452094, 1.0096933737231442, 1.009663426117141, 1.0096338559093896,
+        1.009604569041873, 1.0095754625845448, 1.0095464422137097, 1.0095174366434818,
+        1.0094884068287635, 1.009459348764134, 1.0094302898578942, 1.0094012799636143,
+        1.009372379018174, 1.0093436437271341, 1.0093151157855622, 1.009286813733818,
+        1.009258729806225, 1.009230832176731, 1.0092030720125884, 1.0091753938886394,
+        1.009147747536934, 1.0091200987020656, 1.0090924370676844, 1.009064779770826,
+        1.0090371698234772, 1.0090096696711932, 1.0089823509765439, 1.0089552823745183,
+        1.008928517298517, 1.008902083965382, 1.0088759792443833, 1.008850167486444,
+        1.0088245845696073, 1.0087991465644213, 1.008773761679394, 1.0087483436307734,
+        1.008722824370559, 1.008697164228105, 1.0086713579445532, 1.008645435729751,
+        1.008619459238233, 1.0085935131203712, 1.0085676934397674, 1.0085420946661445,
+        1.0085167971005757, 1.0084918564583298, 1.0084672969587365, 1.0084431087214079,
+        1.0084192496362723, 1.0083956512591847, 1.0083722277734304, 1.0083488867158594,
+        1.0083255400289746, 1.0083021140675656, 1.0082785574313695, 1.0082548458606462,
+        1.00823098385572, 1.0082070030989891, 1.008182958113408, 1.0081589198467424,
+        1.0081349680082612, 1.0081111830069558, 1.008087638266641, 1.0080643935533127,
+        1.0080414897762802, 1.0080189455465134, 1.007996755614868, 1.0079748911805084,
+        1.0079533019575124, 1.007931919809225, 1.0079106636959787, 1.0078894456233833,
+        1.00786817722104, 1.0078467765264272, 1.0078251745037377, 1.0078033208042898,
+        1.0077811882874854, 1.0077587758793551, 1.0077361094545045, 1.0077132405828322,
+        1.007690243171865, 1.0076672082384912, 1.0076442372347187, 1.0076214345050543,
+        1.007598899546053, 1.0075767197575007, 1.0075549643160828, 1.0075336796739554,
+        1.0075128870046244, 1.0074925817116531, 1.007472734910268, 1.0074532966137855,
+        1.007434200226282, 1.0074153678712303, 1.0073967160742456, 1.0073781613581174,
+        1.0073596253849568, 1.007341039374709, 1.0073223476232984, 1.0073035100235037,
+        1.0072845035495388, 1.0072653227024153, 1.0072459789339212, 1.00722649908309,
+        1.0072069228819516, 1.007187299626132, 1.007167684163842, 1.007148132430369,
+        1.0071286968335516, 1.007109421862716, 1.007090340331279, 1.0070714706550328,
+        1.0070528155043272, 1.007034362047147, 1.0070160838314213, 1.0069979441581187,
+        1.0069799005992417, 1.0069619101474658, 1.0069439343758038, 1.0069259439581675,
+        1.0069079219653476, 1.0068898655017402, 1.0068717854680322, 1.0068537044932813,
+        1.0068356533383833, 1.0068176662921398, 1.006799776225876, 1.0067820100193017,
+        1.0067643850097145, 1.0067469069573978, 1.0067295697859382, 1.0067123570837837,
+        1.00669524508556, 1.0066782066307083, 1.0066612154578818, 1.0066442501576585,
+        1.0066272971782861, 1.0066103524464178, 1.0065934213986591, 1.0065765174812897,
+        1.0065596594215236, 1.0065428677640775, 1.006526161271381, 1.0065095537889963,
+        1.0064930520812048, 1.0064766549636897, 1.0064603538321801, 1.006444134447484,
+        1.0064279796285993, 1.0064118723614888, 1.0063957987742542, 1.0063797504678014,
+        1.0063637258157445, 1.0063477300351429, 1.0063317740470978, 1.0063158723552303,
+        1.0063000403351021, 1.0062842914209962, 1.0062686346839131, 1.0062530732163866,
+        1.006237603591348, 1.0062222164705819, 1.0062068982374954, 1.0061916333536587,
+        1.006176407018804, 1.0061612076690782, 1.0061460288847317, 1.0061308703881178,
+        1.0061157379754362, 1.0061006424120653, 1.0060855974988128, 1.0060706176547367,
+        1.006055715438128, 1.0060408994292838, 1.0060261728278734, 1.00601153298796,
+        1.0059969719486224, 1.0059824778468989, 1.0059680369519535, 1.005953635959928,
+        1.0059392641536153, 1.0059249150645468, 1.0059105873698038, 1.0058962848938031,
+        1.0058820157418924, 1.0058677907401206, 1.0058536214689933, 1.0058395182397415,
+        1.005825488360592, 1.0058115349797823, 1.0057976566836035, 1.005783847892018,
+        1.005770099955314, 1.005756402737439, 1.0057427463944353, 1.0057291230324026,
+        1.0057155279609165, 1.005701960337834, 1.0056884231144294, 1.0056749223152102,
+        1.0056614658021903, 1.005648061759001, 1.0056347171719187, 1.0056214365766303,
+        1.005608221284274, 1.0055950692091253, 1.0055819753101423, 1.0055689325495978,
+        1.0055559331831225, 1.0055429701419283, 1.0055300382581642, 1.0055171351188583,
+        1.0055042614054077, 1.005491420670571, 1.0054786186059281, 1.0054658619419654,
+        1.0054531571846865, 1.0054405094169683, 1.0054279213762227, 1.005415392966328,
+        1.0054029212815956, 1.0053905011284219, 1.0053781259428474, 1.0053657889346275,
+        1.0053534842521648, 1.0053412079632542, 1.0053289586832423, 1.0053167377473629,
+        1.0053045489059789, 1.0052923976051473, 1.005280289985828, 1.0052682317811525,
+        1.0052562273048513, 1.0052442787037787, 1.0052323855976961, 1.0052205451595422,
+        1.0052087526120324, 1.0051970020450982, 1.0051852874058473, 1.005173603486835,
+        1.0051619467435016, 1.00515031580572, 1.0051387116049557, 1.0051271371069963,
+        1.005115596708498, 1.0051040954116774, 1.0050926379261977, 1.0050812278550476,
+        1.0050698671016047, 1.0050585555922709, 1.0050472913512303, 1.0050360709014805,
+        1.0050248899105003, 1.0050137439590028, 1.0050026292939038, 1.0049915434341075,
+        1.004980485527875, 1.0049694564076141, 1.0049584583428444, 1.0049474945453578,
+        1.0049365685225395, 1.0049256833987616, 1.0049148413267641, 1.0049040430914218,
+        1.0048932879712995, 1.0048825738758504, 1.0048718977267357, 1.0048612560092498,
+        1.0048506453914814, 1.0048400632993038, 1.0048295083456869, 1.0048189805408627,
+        1.0048084812501548, 1.0047980129115317, 1.00478757856694, 1.004777181293111,
+        1.00476682363346, 1.0047565071305113, 1.0047462320387794, 1.0047359972650922,
+        1.004725800542904, 1.0047156388065162, 1.0047055086972492, 1.0046954071122598,
+        1.0046853317012212, 1.0046752812270712, 1.004665255732108, 1.0046552564852984,
+        1.0046452857245356, 1.0046353462421016, 1.0046254408870847, 1.004615572070633,
+        1.0046057413572282, 1.0045959492082963, 1.0045861949168953, 1.0045764767387833,
+        1.004566792191913, 1.0045571384688052, 1.0045475128889878, 1.0045379133142824,
+        1.0045283384585233, 1.0045187880434634, 1.0045092627802084, 1.00449976418576,
+        1.0044902942718046, 1.0044808551631321, 1.004471448713014, 1.0044620761808214,
+        1.0044527380243005, 1.004443433837442, 1.0044341624389566, 1.004424922090507,
+        1.0044157108023966, 1.004406526670987, 1.0043973681885854, 1.004388234473333,
+        1.0043791253820455, 1.0043700414902723, 1.004360983947083, 1.004351954233379,
+        1.0043429538681532, 1.0043339841148304, 1.004325045738296, 1.0043161388533364,
+        1.0043072628885537, 1.0042984166697277, 1.0042895986062532, 1.0042808069473852,
+        1.0042720400639984, 1.0042632967083267, 1.0042545762087494, 1.0042458785683226,
+        1.004237204452145, 1.004228555067036, 1.0042199319542897, 1.0042113367297674,
+        1.0042027708131611, 1.0041942351890087, 1.0041857302360258, 1.0041772556498088,
+        1.004168810468957, 1.0041603931986618, 1.004152002011346], [5.86161819598961e-06,
+        1.7594727850020368e-05, 2.9357491432466834e-05, 4.116978469894854e-05,
+        5.30516425532194e-05, 6.502332686145079e-05, 7.710538999067635e-05,
+        8.931874479165691e-05, 0.00010168473358842194, 0.00011422520040077544,
+        0.00012696256575302363, 0.00013991990501098817, 0.0001531210292456591,
+        0.00016659057136274066, 0.00018035407570467726, 0.00019443809350158715,
+        0.00020887028360189481, 0.00022367951954693866, 0.00023889600397626381,
+        0.00025455139013596655, 0.0002706789129542617, 0.0002873135286627125,
+        0.00030449206549343913, 0.00032225338585134474, 0.00034063856125359735,
+        0.0003596910612343132, 0.0003794569583149522, 0.0003999851497015203,
+        0.0004213275985368744, 0.00044353959561947823, 0.0004666800453370819,
+        0.0004908117765609682, 0.0005160018829206777, 0.0005423220944239146,
+        0.0005698491848868082, 0.0005986654182968462, 0.0006288590394711166,
+        0.0006605248131508864, 0.0006937646183200871, 0.0007286881030537449,
+        0.0007654134085219835, 0.0008040679692668982, 0.0008447894005912993,
+        0.0008877264827968937, 0.0009330402562183076, 0.0009809052393463995,
+        0.0010315107899604963, 0.0010850626241140154, 0.0011417845200370781,
+        0.0012019202285467184, 0.0012657356230097254, 0.0013335211233913736,
+        0.0014055944350818959, 0.0014823036530489271, 0.0015640307885395376,
+        0.0016511957868459769, 0.0017442611210449546, 0.0018437370580484294,
+        0.0019501877199918074, 0.0020642380851249044, 0.0021865821071306766,
+        0.0023179921733754087, 0.0024593301743006733, 0.002611560524563372,
+        0.002775765565308981, 0.00295316389425312, 0.003145132322912102,
+        0.003353232370171985, 0.0035792424856183175, 0.0038251975838940397,
+        0.004093438020924795, 0.004386670920904231, 0.004708047891188524,
+        0.005061264817512631, 0.005450691940744948, 0.0058815462589373625,
+        0.0063601243921711705, 0.006894123918493623, 0.007493097772997388,
+        0.008169115128372354, 0.008937754383224542, 0.009819653166547287,
+        0.010843039887840635, 0.012048100777090799, 0.01349503943633683,
+        0.015280284419159905, 0.017573004544230306, 0.020711593553987488,
+        0.025529507244473386, 0.03508619185786479, 0.11015160723442291,
+        0.03585218987874316, 0.02722067018678057, 0.024329717706053626,
+        0.02321900534284155, 0.022985800146819713, 0.0233111990232833, 0.02406314378647531,
+        0.025188978280579245, 0.026678162716958647, 0.028547888402929322,
+        0.030838046025311185, 0.03361103753069684, 0.036954988718420005,
+        0.04099029027268118, 0.04588033990237494, 0.0518484358870602, 0.05920447828062404,
+        0.06838828822931609, 0.08004273843772561, 0.09514387810929723, 0.11524882669493912,
+        0.14301262282114682, 0.1834084233728138, 0.24718435649704046, 0.36403655645543376,
+        0.6735796582771854, 5.269066256399403, 0.2917032720367451, 1.6305462590075612,
+        2.173022765531736, 0.9366745872567774, 0.6614907894277462, 0.874690771492881,
+        1.617398204074107, 1.118755678685662, 1.0160411048498337, 1.095139890038023,
+        1.384029788682787, 1.8545128199504126, 1.2045050452431936, 0.7227333887696132,
+        0.6653589297037489, 0.7999285637719911, 1.0949535134851909, 1.626009698330484,
+        2.118378160368915, 1.6791158246817144, 1.153698156431429, 0.8628697976399348,
+        0.726414593106758, 0.7196552474255183, 0.8769568937996945, 1.2358605559095355,
+        1.5527146740391942, 1.4468483535775432, 1.2317466290611154, 1.0907655057809544,
+        1.0223152906487774, 1.0127126493467258, 1.0602755023759223, 1.163063640406,
+        1.2465996390031349, 1.142388634294744, 0.9654200783976045, 0.8834033129200631,
+        0.9003681230101627, 1.0166631980658887, 1.1136044158978735, 1.2157745838653504,
+        1.29794442740162, 1.3207083339453713, 1.266379140982344, 1.1633266856109403,
+        1.0560486752818554, 0.9724298799402565, 0.922390130363728, 0.9071290359714309,
+        0.9248222983113569, 0.9720924892869274, 1.0427956386968322, 1.125205916129808,
+        1.2000898106358115, 1.2449938580334319, 1.246491610502104, 1.2088808418303767,
+        1.148274912549596, 1.0806820676282258, 1.0161909182436033, 0.9593936721696773,
+        0.9116086737070127, 0.8726387004863764, 0.8417544017599924, 0.8181555572333267,
+        0.8011562236212463, 0.7902405597153008, 0.7850639609390722, 0.7854341069412734,
+        0.7912856998810597, 0.8026513615442366, 0.8196239414942632, 0.8422994395363874,
+        0.870683543882127, 0.904539345918523, 0.9431549092094076, 0.9850323613121272,
+        1.027571478983138, 1.066956641837919, 1.098588092583953, 1.118291360797319,
+        1.1239659761097236, 1.1166512816944565, 1.1001458143851832, 1.0794529510351119,
+        1.0591500838045307, 1.0424718635332024, 1.0311451009638994, 1.0256320690347454,
+        1.0254759063431444, 1.0296062182058179, 1.036583021532274, 1.0448068599310443,
+        1.0527242307447675, 1.0590327850732244, 1.0628593461987026, 1.0638657619882574,
+        1.0622474906922685, 1.0586243642680035, 1.0538605403327845, 1.0488683703542963,
+        1.044442808938975, 1.0411506943196547, 1.0392783993088528, 1.0388301151351433,
+        1.0395664969837368, 1.0410743404293914, 1.0428576179027989, 1.0444369082359541,
+        1.0454399132462768, 1.045664469055258, 1.04510048969934, 1.0439081353162696,
+        1.0423616641403644, 1.040776427297563, 1.0394376204202418, 1.0385450335706197,
+        1.0381815720587773, 1.0383076033968672, 1.03877916024223, 1.0393851430363192,
+        1.0398961070230952, 1.0401149431592505, 1.0399187184974108, 1.0392823760795054,
+        1.0382793105883046, 1.0370598988934228, 1.0358146429463857, 1.0347316700266933,
+        1.0339582815240287, 1.0335738380169248, 1.0335779249566746, 1.0338945606209315,
+        1.0343905960441075, 1.034904352496062, 1.0352788767706913, 1.0353932080968336,
+        1.0351852348992856, 1.034661433803406, 1.0338918309750176, 1.032992057584479,
+        1.0320972473805992, 1.0313339007589097, 1.0307955479462119, 1.0305265307706952,
+        1.0305161733166108, 1.0307035772825643, 1.0309915284826032, 1.0312666142803852,
+        1.0314216879067806, 1.0313764207876217, 1.031092045003984, 1.0305775749694752,
+        1.0298866197996475, 1.0291059010191559, 1.028338223242678, 1.0276835004676095,
+        1.0272214102393, 1.0269985134627864, 1.0270215654624892, 1.0272575616092932,
+        1.027640005460158, 1.0280800467501423, 1.0284805445751368, 1.0287507996917176,
+        1.0288197114142332, 1.0286454723238645, 1.0282205777877222, 1.0275717723411912,
+        1.0267553957982996, 1.0258492436464774, 1.0249424005495076, 1.024124526234588,
+        1.0234758449434174, 1.0230587363266197, 1.022911467184421, 1.0230443202130866,
+        1.023438195791247, 1.0240456680565926, 1.0247944213116167, 1.025592923863066,
+        1.0263380720145787, 1.0269243421998495, 1.0272537452875659, 1.0272456407132535,
+        1.0268453183605362, 1.0260302688290153, 1.0248132791685098, 1.0232418947953212,
+        1.0213943019699536, 1.0193721936505442, 1.017291570990465, 1.0152726290883918,
+        1.0134298644086361, 1.0118633625805333, 1.0106519497576893, 1.0098485910339852,
+        1.0094781491023888, 1.0095374019523364, 1.0099970635605133, 1.0108054471395749,
+        1.0118933453164638, 1.013179668905981, 1.0145773849342978, 1.0159993270489664,
+        1.0173635166070458, 1.0185977226625749, 1.0196430883044916, 1.0204567400094726,
+        1.021013359696864, 1.0213057295892471, 1.0213442645717619, 1.0211555430818755,
+        1.0207798572657847, 1.020267842929471, 1.0196763245852138, 1.0190636113663656,
+        1.018484585280536, 1.0179860089702164, 1.0176025230002221, 1.0173537871104332,
+        1.0172431394948072, 1.0172580054298603, 1.0173720920494158, 1.0175491786377848,
+        1.0177480797020895, 1.0179281584772524, 1.018054643361661, 1.0181029864291222,
+        1.0180616216414273, 1.017932722415727, 1.0177308838478512, 1.0174800004046767,
+        1.017208904804489, 1.0169465205683488, 1.0167173289196514, 1.016537860936081,
+        1.0164147240132024, 1.0163443985927307, 1.016314742740016, 1.0163078637375886,
+        1.016303798683807, 1.0162843245952204, 1.0162362152927853, 1.0161533814978656,
+        1.016037552645483, 1.0158974416037487, 1.0157466197712168, 1.015600562217189,
+        1.0154734568307158, 1.0153753875971163, 1.015310405278715, 1.0152758145333833,
+        1.015262772641902, 1.015258053576249, 1.015246622535925, 1.0152145247274251,
+        1.0151515423415285, 1.015053125035795, 1.0149212431141752, 1.0147640216063405,
+        1.0145942459164228, 1.01442703889487, 1.0142771544505098, 1.0141563888882483,
+        1.0140715724818832, 1.014023483345025, 1.0140068498260237, 1.0140114097394193,
+        1.0140238091719105, 1.014029981263964, 1.0140175698064706, 1.0139779663511401,
+        1.0139076116983936, 1.0138083572316106, 1.0136868601909252, 1.0135531643229336,
+        1.0134187591223396, 1.0132944915209208, 1.013188711575097, 1.01310597160323,
+        1.0130464820782024, 1.0130063813081647, 1.0129787267162391, 1.0129549893814656,
+        1.012926751622176, 1.0128872830960596, 1.0128327072781964, 1.0127625592002993,
+        1.012679658826878, 1.0125893575827858, 1.0124983321221581, 1.0124131775439993,
+        1.012339078813465, 1.0122788119064725, 1.0122322532392214, 1.0121964731172284,
+        1.0121663763127895, 1.0121357511202198, 1.0120985153141242, 1.012049915863312,
+        1.0119874540222737, 1.0119113649561966, 1.0118245696524075, 1.0117321188640338,
+        1.0116402442084238, 1.0115552021766288, 1.011482130176817, 1.0114241251456748,
+        1.011381708203342, 1.0113527636155917, 1.0113329516820535, 1.0113165094029655,
+        1.0112972850412525, 1.0112698145970835, 1.0112302459352918, 1.011176949524214,
+        1.0111107165744948, 1.011034523599119, 1.0109529219154962, 1.0108711764137017,
+        1.010794318259429, 1.010726284734047, 1.010669296092108, 1.0106235699428048,
+        1.0105874083779516, 1.01055762426499, 1.0105302132121954, 1.0105011370726824,
+        1.0104670701562688, 1.0104259724360558, 1.0103773917194503, 1.010322451233219,
+        1.0102635395776156, 1.0102037749222188, 1.0101463545228175, 1.0100939174459294,
+        1.0100480406617833, 1.0100089589519317, 1.0099755538061077, 1.0099456045716517,
+        1.0099162462667277, 1.0098845414649498, 1.0098480549095359, 1.0098053219781877,
+        1.0097561248133717, 1.0097015281326085, 1.0096436728911886, 1.0095853712037461,
+        1.009529581788816, 1.009478865298181, 1.0094349200564539, 1.0093982814408553,
+        1.0093682361991065, 1.00934296272306, 1.0093198671820376, 1.0092960508630322,
+        1.0092688220711603, 1.0092361601375432, 1.0091970501080743, 1.0091516321257457,
+        1.0091011443598963, 1.009047675946058, 1.0089937798195106, 1.0089420186034692,
+        1.008894525998779, 1.0088526602931849, 1.0088168073289656, 1.0087863615325485,
+        1.0087598809085265, 1.0087353811868471, 1.0087107109619697, 1.008683937570995,
+        1.0086536744027148, 1.0086192937054808, 1.0085809919289246, 1.0085397026852967,
+        1.008496880247501, 1.008454199038237, 1.0084132279043512, 1.0083751400632688,
+        1.0083405105474945, 1.0083092348651306, 1.0082805790757654, 1.0082533469979578,
+        1.008226129258462, 1.0081975850305025, 1.008166702861289, 1.0081329924766793,
+        1.0080965735787037, 1.008058147588394, 1.0080188602136526, 1.0079800825707703,
+        1.007943152801786, 1.0079091263067255, 1.0078785799978174, 1.0078515051652528,
+        1.007827306822476, 1.0078049079388685, 1.0077829383040051, 1.0077599731794553,
+        1.0077347788459405, 1.0077065218916257, 1.007674906450369, 1.0076402170767955,
+        1.0076032619804474, 1.0075652288136452, 1.0075274800166805, 1.0074913243509114,
+        1.007457804189427, 1.007427534119645, 1.0074006164040832, 1.0073766448059962,
+        1.0073547927916344, 1.0073339678913409, 1.0073130034353206, 1.0072908536569638,
+        1.0072667589768445, 1.0072403547755755, 1.0072117077925453, 1.0071812774029492,
+        1.0071498120577171, 1.0071182018618126, 1.0070873148629134, 1.0070578461654827,
+        1.0070302054373226, 1.0070044605796808, 1.0069803448203785, 1.006957323184598,
+        1.0069347041693768, 1.006911775176813, 1.0068879369706067, 1.0068628135116002,
+        1.0068363186361744, 1.0068086691330147, 1.0067803433464575, 1.006751993797174,
+        1.00672432988384, 1.0066979913107388, 1.0066734338395118, 1.0066508462930925,
+        1.0066301120541483, 1.0066108206718682, 1.0065923269520345, 1.0065738474146861,
+        1.0065545784242393, 1.006533817421063, 1.0065110688268777, 1.0064861191747805,
+        1.0064590712048889, 1.006430333131999, 1.0064005659573136, 1.0063705975308062,
+        1.0063413162531936, 1.0063135593400065, 1.006288010335843, 1.0062651183052413,
+        1.0062450473632965, 1.0062276606414085, 1.0062125381493425, 1.0061990239535252,
+        1.0061862951299834, 1.0061734433287435, 1.0061595595285246, 1.0061438134826406,
+        1.0061255211288394, 1.0061041954559802, 1.0060795785957286, 1.006051654917467,
+        1.0060206464444363, 1.0059869929045204, 1.0059513192232086, 1.0059143933857182,
+        1.0058770775052512, 1.0058402747906738, 1.0058048750200925, 1.0057717011398046,
+        1.00574145969379, 1.0057146978656168, 1.0056917698729786, 1.005672815191129,
+        1.0056577505266826, 1.00564627660622, 1.0056378997384339, 1.0056319668662665,
+        1.0056277115988645, 1.0056243076664113, 1.0056209255217214, 1.0056167875238333,
+        1.0056112173231297, 1.005603679698239, 1.0055938080843363, 1.005581418247439,
+        1.0055665078453762, 1.0055492428238175, 1.0055299326021043, 1.005508996729022,
+        1.00548692610181, 1.0054642419561106, 1.005441455697372, 1.005419032319092,
+        1.0053973597049015, 1.0053767255921577, 1.0053573034170011, 1.0053391476796634,
+        1.0053221988651913, 1.0053062973303002, 1.005291204931611, 1.0052766325540734,
+        1.0052622711516435, 1.0052478235044535, 1.0052330337032815, 1.0052177114598777,
+        1.0052017487505482, 1.0051851270289447, 1.0051679142400975, 1.0051502520291453,
+        1.0051323347227372, 1.0051143827055713, 1.0050966135613506, 1.005079214670285,
+        1.0050623207843328, 1.0050459994383578, 1.0050302459782805, 1.0050149886420632,
+        1.0050001027094526, 1.0049854314534281, 1.004970810676552, 1.0049560931472155,
+        1.0049411693393882, 1.004925981512656, 1.004910529248766, 1.0048948659154626,
+        1.0048790869433273, 1.0048633120517008, 1.004847664448566, 1.0048322504191862,
+        1.0048171425544403, 1.0048023691881172, 1.004787911532888, 1.0047737087107191,
+        1.0047596695805463, 1.0047456891859181, 1.0047316669507742, 1.004717523548159,
+        1.0047032136766538, 1.004688732739031, 1.0046741164896427, 1.0046594339152788,
+        1.0046447747354148, 1.0046302337667614, 1.0046158948572737, 1.0046018170899744,
+        1.0045880255008166, 1.0045745077362038, 1.0045612170420146, 1.0045480809063052,
+        1.004535013752331, 1.004521931448026, 1.0045087651594455, 1.0044954722571289,
+        1.0044820425431769, 1.0044684988976726, 1.0044548923991221, 1.0044412928908675,
+        1.004427776692632, 1.0044144135784017, 1.0044012551990114, 1.0043883268228178,
+        1.0043756236640133, 1.0043631122754222, 1.004350736638511, 1.0043384278282317,
+        1.0043261155844165, 1.0043137398656512, 1.0043012605261514, 1.00428866361734,
+        1.0042759634028908, 1.0042631998848404, 1.0042504323498265, 1.004237730045506,
+        1.0042251614979538, 1.004212784128678, 1.004200635715554, 1.0041887288982143,
+        1.0041770494221436, 1.0041655582349316, 1.0041541969862118, 1.0041428960231993,
+        1.0041315836775953, 1.0041201955377663, 1.004108682490603, 1.004097016569577,
+        1.004085194006467, 1.0040732352908392, 1.0040611824305468, 1.0040490939256876,
+        1.0040370381828305, 1.0040250861915376, 1.0040133042678518, 1.0040017475612166,
+        1.0039904548546517, 1.0039794449970358, 1.0039687151215135, 1.0039582406469019,
+        1.0039479769398882, 1.0039378624347541, 1.0039278229562283, 1.0039177769578866,
+        1.0039076413618713, 1.0038973376583704, 1.0038867978943538, 1.0038759701564128,
+        1.003864823142676, 1.0038533494365922, 1.0038415671513192, 1.0038295197130263,
+        1.0038172736920028, 1.0038049147608445, 1.0037925420405442, 1.0037802612645206,
+        1.0037681773234428, 1.0037563868296715, 1.0037449713462896, 1.003733991859289,
+        1.0037234849403869, 1.0037134608700673, 1.0037039037898376, 1.0036947737565471,
+        1.0036860104047043, 1.0036775378040068, 1.003669270038911, 1.003661117035153,
+        1.0036529902056472, 1.0036448075695743, 1.003636498094878, 1.0036280051077744,
+        1.0036192886899817, 1.0036103270379109, 1.0036011167891081, 1.003591672336726,
+        1.0035820241642366, 1.003572216251951, 1.0035623026436173, 1.0035523433189455,
+        1.0035423995926804, 1.0035325293418755, 1.003522782433749, 1.00351319676848,
+        1.0035037953475248, 1.0034945847179626, 1.0034855550250068, 1.0034766817374428,
+        1.0034679289135757, 1.0034592536756335, 1.0034506113892203, 1.003441960930663,
+        1.0034332693912413, 1.0034245156240895, 1.0034156921839463, 1.0034068054241694,
+        1.003397873769737, 1.0033889244415413, 1.0033799891269688, 1.0033710992393794,
+        1.0033622814609786, 1.0033535542100465, 1.0033449255224782, 1.0033363926122576,
+        1.0033279431114994, 1.003319557730172, 1.0033112138600746, 1.0033028895115066,
+        1.003294566935496, 1.0032862353541365, 1.0032778923838575, 1.0032695439633186,
+        1.0032612028507697, 1.0032528859927907, 1.0032446112480635, 1.0032363940467965,
+        1.0032282445637788, 1.0032201658827875, 1.0032121534508902, 1.0032041958944518,
+        1.0031962770338854, 1.003188378730991, 1.003180484065515, 1.0031725802883376,
+        1.0031646610446465, 1.0031567274921613, 1.0031487881331245, 1.003140857400457,
+        1.0031329532498252, 1.0031250941747083, 1.0031172961533226, 1.0031095700402695,
+        1.0031019198327187, 1.00309434208666, 1.0030868265607107, 1.003079357957664,
+        1.0030719184527723, 1.0030644905729496, 1.0030570599424822, 1.0030496174451666,
+        1.0030421604621387, 1.0030346930087337, 1.0030272247832763, 1.0030197693227758,
+        1.003012341604415, 1.003004955513852, 1.0029976216095673, 1.0029903455473357,
+        1.0029831274038266, 1.002975961976419, 1.0029688399665826, 1.002961749805987,
+        1.002954679782827, 1.002947620086754, 1.0029405644191545, 1.002933510904428,
+        1.0029264621697889, 1.0029194246120408, 1.0029124070124635, 1.0029054187709407,
+        1.0028984680892714, 1.0028915604324946, 1.0028846975378607, 1.0028778771357998,
+        1.0028710934157437, 1.0028643381356668, 1.002857602161625, 1.002850877151426,
+        1.0028441570768818, 1.0028374393138804, 1.0028307251114592, 1.0028240193646216,
+        1.0028173297401508, 1.0028106653179503, 1.0028040349928915, 1.0027974459199762,
+        1.0027909022731631, 1.0027844045287966, 1.0027779493895899, 1.002771530351939,
+        1.002765138808117, 1.0027587654849, 1.00275240196657, 1.0027460420414798,
+        1.0027396826477974, 1.0027333242683416, 1.0027269707226154, 1.0027206284086851,
+        1.0027143051401701, 1.002708008788494, 1.0027017459673948, 1.0026955209818194,
+        1.0026893352105666, 1.002683187011706, 1.0026770721465856, 1.002670984628818,
+        1.0026649178343827, 1.0026588656695634, 1.002652823590768, 1.0026467893037174,
+        1.0026407630318854, 1.0026347473238906, 1.0026287464519459, 1.0026227655240298,
+        1.00261680947919, 1.0026108821505932, 1.00260498556307, 1.0025991195849329,
+        1.002593281986979, 1.0025874688872032, 1.0025816754911343, 1.0025758969870082,
+        1.002570129430479, 1.0025643704591853, 1.0025586197112257, 1.0025528788770002,
+        1.002547151380511, 1.0025414417521539, 1.0025357548085698, 1.0025300947872355,
+        1.0025244645888527, 1.002518865259062, 1.0025132957967977, 1.0025077533180908,
+        1.0025022335416958, 1.0024967315078106, 1.002491242402469, 1.0024857623445618,
+        1.0024802890018896, 1.0024748219348938, 1.0024693626158043, 1.0024639141276392,
+        1.0024584806021895, 1.0024530664989943, 1.0024476758517191, 1.002442311610189,
+        1.0024369751861903, 1.00243166627306, 1.0024263829600564, 1.0024211221114683,
+        1.0024158799361405, 1.0024106526430168, 1.0024054370672772, 1.0024002311608255,
+        1.0023950342681849, 1.0023898471488384, 1.0023846717525102, 1.0023795107966094,
+        1.0023743672277516, 1.0023692436666707, 1.0023641419352052, 1.0023590627462127,
+        1.0023540056058233, 1.0023489689382992, 1.0023439504040614, 1.002338947348045,
+        1.0023339572942278, 1.0023289783962315, 1.0023240097640458, 1.0023190516107898,
+        1.002314105196657, 1.0023091725835687, 1.0023042562472213, 1.0022993586174744,
+        1.0022944816292532, 1.0022896263629035, 1.0022847928359198, 1.0022799799806121,
+        1.002275185809502, 1.0022704077378033, 1.002265643005894, 1.0022608891285685,
+        1.0022561442946125, 1.0022514076501006, 1.0022466794198155, 1.0022419608493591,
+        1.0022372539810331, 1.0022325613041108, 1.0022278853400404, 1.0022232282324919,
+        1.0022185914093822, 1.002213975370236, 1.0022093796298674, 1.0022048028225494,
+        1.0022002429441825, 1.0021956976879096, 1.0021911648147872, 1.0021866424973802,
+        1.0021821295810174, 1.0021776257231314, 1.0021731313928997, 1.002168647737276,
+        1.0021641763415319, 1.002159718928804, 1.0021552770516096, 1.0021508518273987,
+        1.0021464437608698, 1.0021420526794076, 1.0021376777880844, 1.002133317830195,
+        1.0021289713221535, 1.0021246368200978, 1.0021203131717007, 1.0021159997107014,
+        1.0021116963625747, 1.0021074036455802, 1.0021031225692754, 1.0020988544494989,
+        1.0020946006721017, 1.0020903624452622, 1.002086140581093, 1.0020819353415344,
+        1.002077746372444, 1.0020735727352594, 1.002069413030148, 1.002065265590588],
+    [2.5440259427991582e-06, 7.636690650124145e-06, 1.274321038771961e-05,
+        1.787287388488377e-05, 2.3035047727281348e-05, 2.8239209373829382e-05,
+        3.349497838620301e-05, 3.881215054883702e-05, 4.420073166893235e-05,
+        4.9670972914548056e-05, 5.523340743225542e-05, 6.0898888678298226e-05,
+        6.667863004886451e-05, 7.258424703044086e-05, 7.862780111153871e-05,
+        8.482184652168004e-05, 9.11794795757459e-05, 9.771439111788083e-05,
+        0.00010444092252828428, 0.0001113741252209142, 0.00011852982475010885,
+        0.00012592468910472594, 0.00013357630233954437, 0.00014150324375227131,
+        0.00014972517320936194, 0.00015826292318137607, 0.00016713859845179184,
+        0.00017637568381702944, 0.00018599916106276749, 0.00019603563563693754,
+        0.00020651347471029063, 0.0002174629569532637, 0.00022891643600429047,
+        0.00024090851848064868, 0.0002534762584956776, 0.00026665937001118183,
+        0.00028050045934113754, 0.0002950452795241826, 0.00031034300943999407,
+        0.00032644655979954145, 0.00034341290957918966, 0.0003613034756700554,
+        0.0003801845200963962, 0.00040012759848288056, 0.00042121005518913114,
+        0.00044351556950044226, 0.000467134760477724, 0.0004921658552941128,
+        0.0005187154310561635, 0.0005468992369005471, 0.0005768431076741221,
+        0.0006086839801569572, 0.0006425710243358482, 0.0006786669051638112,
+        0.000717149191211302, 0.0007582119291452921, 0.0008020674071213063,
+        0.0008489481309495412, 0.0008991090434980384, 0.0009528300199826652,
+        0.0010104186779936204, 0.0010722135472955997, 0.001138587651035559,
+        0.0012099525585078997, 0.0012867629795734754, 0.0013695219828642852,
+        0.0014587869327244009, 0.0015551762570765438, 0.0016593771783971764,
+        0.0017721545619500574, 0.001894361064539537, 0.0020269488005797472,
+        0.0021709827837416147, 0.0023276564490187367, 0.0024983096235496353,
+        0.002684449383512691, 0.0028877743282471093, 0.0031102029065811425,
+        0.003353906568651929, 0.003621348685563135, 0.003915330380683084,
+        0.004239044681996679, 0.0045961407293875645, 0.004990800179757581,
+        0.005427828479564589, 0.00591276433723581, 0.006452011589036777,
+        0.007052998755303553, 0.007724373023867622, 0.008476237299054295,
+        0.00932044142837129, 0.010270942067437236, 0.011344250097090119,
+        0.012559990575726373, 0.01394160850993905, 0.015517265264452716,
+        0.017320986532430863, 0.01939414579341658, 0.021787400169160438,
+        0.024563244008886077, 0.027799417514119164, 0.031593516974679645,
+        0.03606932238406765, 0.04138562682011527, 0.04774878934191352, 0.055430968241450614,
+        0.06479727000920234, 0.07634736639212442, 0.09078153732200082, 0.10910997058943225,
+        0.132843319671478, 0.16434773904773298, 0.20756700456383081, 0.26968091151534457,
+        0.3656632216737774, 0.535099295006721, 0.9546384860701584, 6.202187245858004,
+        0.506895207785075, 2.7674547285015105, 3.21588117768692, 1.0389321153935769,
+        0.0952566213835383, 1.80036226546925, 4.73345659307324, 3.221079114254368,
+        2.8313010834505685, 3.038513205287193, 1.5091634753043164, 2.7629958439565336,
+        2.8721022198733097, 2.1620307955253706, 1.8592209872420586, 1.8076573294449199,
+        1.9670339834562984, 2.3655371209612066, 2.567830260687796, 1.7777518509916228,
+        1.1671331704362304, 0.9527386401237378, 0.9704131322565759, 1.1544973396283171,
+        1.51958053797122, 2.0707690906872047, 2.3781211988475044, 1.9962655833371084,
+        1.536653834741414, 1.2444314365241083, 1.0856322128541829, 1.0295757527971543,
+        1.0794120430972458, 1.2598893076212885, 1.5124372227252012, 1.5507591681964823,
+        1.3797416818022068, 1.2370641885611406, 1.1792575285985107, 1.2233875904933802,
+        1.2873351418265528, 1.3650680534181336, 1.4287344306784449, 1.438300483537016,
+        1.37669012446354, 1.2728443591510208, 1.1705164064049425, 1.095805004536776,
+        1.0566994624366246, 1.0528191084496674, 1.081188223538004, 1.1375208053308046,
+        1.214645497051127, 1.2993424421688584, 1.3705314829786208, 1.4046220445680526,
+        1.3891941387597917, 1.3316276562597147, 1.2513445760295623, 1.1663924453875834,
+        1.08754133210559, 1.0192758789314553, 0.9625126310066241, 0.9166185995796133,
+        0.8804951354473589, 0.8530629615608226, 0.8334413429653778, 0.8209893138489076,
+        0.8152919260449694, 0.8161288315654366, 0.8234392376356576, 0.8372847705891698,
+        0.8578037810332887, 0.8851437731166595, 0.919351412569111, 0.9601929536360405,
+        1.0068785412265024, 1.0576894809519706, 1.1095895771102444, 1.1580612740277971,
+        1.1975693834291972, 1.2229474987196374, 1.2313477059308462, 1.2235782410533265,
+        1.2037849836061187, 1.1777249917581476, 1.150872988633208, 1.1272997056095788,
+        1.1094063104979341, 1.0981436237028173, 1.0933685710275574, 1.0941699974817238,
+        1.099131990577564, 1.1065618105787407, 1.114714794836221, 1.1220243919193373,
+        1.1273118251630725, 1.1299279402117501, 1.129786243012026, 1.1272800260019238,
+        1.1231166916678645, 1.1181242385395453, 1.1130798858190087, 1.1085893352150573,
+        1.1050232800807538, 1.1025047982257572, 1.1009373051150178, 1.1000630208232964,
+        1.0995417020880889, 1.099036838408478, 1.0982931566023972, 1.09718873203339,
+        1.0957500951521437, 1.0941288356479524, 1.092549153195507, 1.0912426900933387,
+        1.0903875971596504, 1.090064529329517, 1.0902363027407862, 1.0907527323177055,
+        1.091378371441817, 1.091837876117271, 1.0918708436925766, 1.0912854572095725,
+        1.0899993193222317, 1.088057849382409, 1.0856258087822086, 1.0829544288473112,
+        1.080332649851774, 1.0780339771233036, 1.0762698915693014, 1.075157692889031,
+        1.0747067717370993, 1.0748238125023537, 1.0753346885361785, 1.0760186453671412,
+        1.0766486029573403, 1.0770302596634964, 1.0770327025772914, 1.0766048892803683,
+        1.0757755516603433, 1.0746379300539035, 1.073324038717038, 1.0719749092732387,
+        1.070713185051589, 1.0696229679598812, 1.0687396840423058, 1.0680505650484828,
+        1.0675044807205023, 1.0670284109483215, 1.0665468730595438, 1.0660002317752253,
+        1.0653581665015954, 1.0646256979523783, 1.063840893624198, 1.0630652498394806,
+        1.0623692721408973, 1.0618165667581425, 1.061449715060785, 1.061280499788968,
+        1.0612859901108884, 1.0614108589847668, 1.0615752880573355, 1.0616870033028882,
+        1.0616554242581093, 1.061405645476186, 1.0608900486328974, 1.060095784859912,
+        1.0590471127249936, 1.0578024821779684, 1.0564471166424116, 1.055082474016841,
+        1.0538142517092106, 1.052740540739302, 1.051941422638535, 1.0514708775281043,
+        1.0513514591927644, 1.0515718740557058, 1.0520874002420588, 1.052822978262493,
+        1.0536787470134155, 1.054537732695592, 1.0552752821045084, 1.055769651913728,
+        1.0559129451244464, 1.055621383229747, 1.0548437969350501, 1.0535672824559588,
+        1.0518192395561232, 1.0496654563326515, 1.0472044482952785, 1.0445587742647449,
+        1.0418644245201205, 1.0392595380950544, 1.0368736504320615, 1.0348184493414778,
+        1.033180704738486, 1.0320177127164596, 1.031355311132854, 1.0311883063814236,
+        1.0314829996669934, 1.0321814035386827, 1.0332066820915582, 1.0344693232359563,
+        1.0358735577605225, 1.0373235796945983, 1.0387291952175437, 1.0400106251434067,
+        1.0411022928219387, 1.0419555249163128, 1.0425401598097257, 1.0428450903030415,
+        1.042877770534883, 1.042662709864125, 1.0422389814935165, 1.04165680881,
+        1.0409733636538694, 1.040248009247909, 1.0395373258473248, 1.0388903436745613,
+        1.0383444519333418, 1.037922438511868, 1.0376310356772536, 1.0374612049803844,
+        1.0373902004494735, 1.0373852220945572, 1.0374082402466736, 1.0374213726386878,
+        1.0373920723246766, 1.037297372646186, 1.0371265551587028, 1.0368818490296916,
+        1.036577095639919, 1.0362346560346987, 1.035881131040177, 1.0355426469418811,
+        1.0352405034734522, 1.03498788639297, 1.0347881403385921, 1.0346348201547517,
+        1.0345134369962405, 1.0344045351880407, 1.0342875191432563, 1.0341445317332343,
+        1.0339636891475823, 1.0337411060424577, 1.033481377911969, 1.033196480944262,
+        1.032903344225902, 1.0326205859022335, 1.0323650393841104, 1.0321487079591931,
+        1.0319766823382541, 1.0318463625925678, 1.0317480825985423, 1.0316669845142625,
+        1.031585774132947, 1.0314878402313667, 1.0313601671037413, 1.0311955194496856,
+        1.0309935242508914, 1.0307604876370537, 1.0305080236724973, 1.0302507886960954,
+        1.0300037674737816, 1.0297796196442623, 1.0295865605413548, 1.029427132257933,
+        1.029298045405138, 1.029191073229431, 1.0290947925434406, 1.0289968216486032,
+        1.0288861278847679, 1.0287549793746702, 1.028600195803639, 1.0284234957645773,
+        1.028230914839972, 1.028031443896635, 1.0278351768067189, 1.0276513354882608,
+        1.0274865460757108, 1.0273436764404869, 1.027221428064737, 1.0271147285103583,
+        1.0270158217927094, 1.0269158290732228, 1.0268064725350832, 1.0266816343634615,
+        1.0265384632824979, 1.026377834575027, 1.0262040971518709, 1.0260241775913548,
+        1.0258462294313844, 1.0256780942113273, 1.0255258657576853, 1.0253928190266854,
+        1.0252788879754788, 1.0251807697758486, 1.0250926157679858, 1.0250071639734541,
+        1.024917092073684, 1.0248163363029106, 1.0247011358631255, 1.0245706206978031,
+        1.0244268509327092, 1.024274321050903, 1.024119040496266, 1.023967376315358,
+        1.0238248797169789, 1.0236953120704382, 1.0235800402222766, 1.0234778964138802,
+        1.0233855093644781, 1.0232980267317753, 1.0232100804999975, 1.0231168076258375,
+        1.0230147347845275, 1.0229023680393055, 1.022780388864451, 1.022651435004975,
+        1.0225195230449449, 1.0223892343488714, 1.0222648255052507, 1.0221494322242561,
+        1.022044511818643, 1.0219496197816706, 1.0218625507643184, 1.0217798058881649,
+        1.0216972892580376, 1.0216110971356536, 1.0215182501143412, 1.0214172335429605,
+        1.0213082509485147, 1.021193151313117, 1.021075052784989, 1.0209577409604622,
+        1.020844959049994, 1.0207397233499784, 1.0206437884402486, 1.0205573551188472,
+        1.02047906690006, 1.0204062870675656, 1.020335597689235, 1.0202634236249413,
+        1.0201866649292084, 1.0201032232013056, 1.0200123303974005, 1.0199146276133129,
+        1.0198119887065438, 1.0197071303069636, 1.0196030871303003, 1.0195026530009481,
+        1.0194078902988855, 1.0193197940612444, 1.0192381654869211, 1.019161709420904,
+        1.0190883291012023, 1.0190155564929817, 1.018941033986332, 1.0188629567813643,
+        1.018780395621324, 1.0186934442803515, 1.0186031703866134, 1.0185113851564664,
+        1.0184202804915534, 1.018332004716343, 1.0182482571754419, 1.018169975862263,
+        1.0180971728945876, 1.0180289439985792, 1.0179636457136967, 1.0178992037439907,
+        1.0178334931225947, 1.0177647194902883, 1.0176917325417216, 1.017614216886701,
+        1.01753272928258, 1.0174485798257835, 1.017363582869237, 1.017279726038778,
+        1.0171988188392433, 1.0171221839444573, 1.0170504445035926, 1.0169834418531727,
+        1.0169202936263717, 1.0168595769362239, 1.0167995996011896, 1.0167387080136008,
+        1.016675575538877, 1.0166094208138494, 1.0165401196777835, 1.016468194851482,
+        1.0163946899983078, 1.0163209553146806, 1.0162483866737022, 1.0161781671156347,
+        1.0161110572399075, 1.016047270558361, 1.0159864533113687, 1.015927768801947,
+        1.015870067524957, 1.0158121095667743, 1.0157527974206337, 1.0156913767790428,
+        1.0156275698914685, 1.0155616192225507, 1.0154942358725438, 1.0154264644191822,
+        1.0153594904177665, 1.015294426243381, 1.0152321137760563, 1.0151729783556023,
+        1.0151169584342583, 1.015063521396607, 1.0150117606744087, 1.01496055527588,
+        1.0149087625623043, 1.0148554102035001, 1.0147998544027903, 1.014741878304432,
+        1.0146817156084826, 1.014619997743222, 1.0145576360889927, 1.0144956614384613,
+        1.0144350493617311, 1.0143765614725249, 1.0143206287491944, 1.0142672949246512,
+        1.014216227091088, 1.0141667890257984, 1.0141181623359363, 1.014069493049094,
+        1.0140200378823643, 1.0139692855120688, 1.013917033369177, 1.0138634087532379,
+        1.013808832864583, 1.013753935981496, 1.0136994398479104, 1.013646028159453,
+        1.0135942271843517, 1.0135443160218216, 1.013496280386836, 1.0134498161911552,
+        1.0134043809066142, 1.013359283118434, 1.0133137949802553, 1.0132672692749431,
+        1.0132192427943367, 1.0131695106027025, 1.0131181608278748, 1.013065565998696,
+        1.0130123335461125, 1.0129592238766485, 1.012907048590002, 1.0128565634479394,
+        1.0128083704882112, 1.0127628414523715, 1.0127200709820459, 1.0126798635282435,
+        1.0126417533463652, 1.0126050529708222, 1.0125689226603465, 1.0125324517338554,
+        1.0124947424971569, 1.0124549884066083, 1.0124125398951518, 1.0123669534976485,
+        1.0123180221647325, 1.0122657866309708, 1.0122105292033186, 1.0121527522915732,
+        1.0120931444622117, 1.012032536892122, 1.0119718529981663, 1.0119120538794137,
+        1.0118540821413866, 1.0117988067162411, 1.0117469714178522, 1.0116991500894295,
+        1.0116557111981193, 1.0116167944966779, 1.0115823018333685, 1.0115519033332958,
+        1.0115250590497957, 1.011501054905753, 1.011479050466972, 1.011458134981118,
+        1.011437387329486, 1.0114159351839282, 1.011393008786046, 1.0113679853494382,
+        1.0113404210451082, 1.0113100687352843, 1.0112768809188672, 1.0112409985929247,
+        1.0112027277940359, 1.011162506377839, 1.0111208640887541, 1.0110783791721516,
+        1.011035634729338, 1.0109931777686736, 1.0109514835228106, 1.0109109271296095,
+        1.0108717642412341, 1.010834121545235, 1.0107979975530605, 1.0107632733389542,
+        1.0107297322081794, 1.0106970865733436, 1.010665009677828, 1.0106331693025534,
+        1.010601260309072, 1.0105690328822714, 1.0105363136854597, 1.0105030178326366,
+        1.0104691505676089, 1.0104347987156153, 1.0104001131964755, 1.010365284992155,
+        1.0103305177833128, 1.0102960008763424, 1.0102618859580756, 1.0102282706348698,
+        1.0101951907081541, 1.010162621850888, 1.0101304899685304, 1.010098688263684,
+        1.0100670980714588, 1.01003561004191, 1.0100041422944792, 1.0099726527479784,
+        1.0099411438445909, 1.0099096591708312, 1.0098782728228384, 1.0098470735474774,
+        1.0098161465221194, 1.0097855559809996, 1.0097553317029055, 1.0097254616814118,
+        1.009695892225651, 1.009666535469702, 1.009637283015689, 1.009608023408524,
+        1.00957866050778, 1.009549129685167, 1.009519409151735, 1.0094895245382385,
+        1.0094595459729707, 1.0094295781337397, 1.0093997448884604, 1.0093701709957474,
+        1.0093409637766462, 1.0093121976269184, 1.0092839037332237, 1.0092560664793448,
+        1.0092286269327981, 1.009201492672321, 1.0091745522378377, 1.0091476918118119,
+        1.009120811474304, 1.0090938385436392, 1.0090667360780283, 1.0090395054641637,
+        1.0090121830078003, 1.0089848314011505, 1.0089575277174285, 1.00893035005481,
+        1.0089033650566486, 1.0088766182711622, 1.008850128742568, 1.0088238884546643,
+        1.0087978664137152, 1.0087720164005203, 1.0087462868627306, 1.008720631140149,
+        1.0086950162504875, 1.008669428789178, 1.0086438770465873, 1.008618389117798,
+        1.0085930074573632, 1.0085677809033728, 1.0085427555738125, 1.0085179661721904,
+        1.0084934291202972, 1.0084691385966449, 1.0084450660658846, 1.0084211633243905,
+        1.0083973685519523, 1.0083736144304045, 1.008349837126096, 1.0083259848626251,
+        1.0083020249289454, 1.0082779482431699, 1.0082537709694226, 1.0082295330999784,
+        1.0082052943039828, 1.008181127654954, 1.0081571120482133, 1.0081333241934016,
+        1.0081098310248047, 1.0080866832371191, 1.00806391046113, 1.008041518378642,
+        1.0080194878711, 1.007997776124558, 1.0079763194860378, 1.0079550377832573,
+        1.0079338397727495, 1.0079126293578724, 1.0078913122056712, 1.007869802381436,
+        1.0078480286097036, 1.007825939764868, 1.0078035092024902, 1.0077807375757681,
+        1.0077576538496864, 1.0077343143332405, 1.0077107996947496, 1.0076872100954675,
+        1.0076636587542562, 1.007640264417911, 1.0076171433347019, 1.0075944013931735,
+        1.0075721270822569, 1.0075503858505757, 1.0075292163010958, 1.0075086284707606,
+        1.0074886042378626, 1.0074690997003017, 1.007450049200187, 1.0074313705533442,
+        1.0074129709858162, 1.0073947532830583, 1.0073766217113633, 1.0073584873590113,
+        1.0073402726470784, 1.0073219148582393, 1.0073033686125838, 1.0072846072749684,
+        1.0072656233097486, 1.0072464276131148, 1.0072270478623564, 1.0072075259377244,
+        1.0071879145059919, 1.0071682729092934, 1.0071486625751354, 1.007129142242874,
+        1.0071097633721287, 1.0070905661411527, 1.0070715764408844, 1.0070528042127604,
+        1.0070342433628525, 1.0070158733206955, 1.0069976621170817, 1.0069795706581364,
+        1.0069615577037379, 1.006943584945824, 1.0069256215485234, 1.0069076475681324,
+        1.0068896558135185, 1.0068716519191507, 1.0068536526537475, 1.0068356827401481,
+        1.0068177706774235, 1.0067999441996038, 1.0067822260534482, 1.0067646307209166,
+        1.0067471625588522, 1.0067298156020819, 1.0067125750126034, 1.0066954198989204,
+        1.0066783270173199, 1.0066612747352295, 1.0066442466065415, 1.0066272339842532,
+        1.0066102372637493, 1.0065932655820873, 1.006576335055901, 1.0065594658802965,
+        1.0065426787938037, 1.0065259915105498, 1.0065094157155385, 1.006492955114484,
+        1.0064766048451188, 1.006460352324141, 1.0064441793630547, 1.0064280651772406,
+        1.006411989770606, 1.0063959371254727, 1.0063798976714726, 1.0063638696387525,
+        1.0063478590959647, 1.006331878698122, 1.0063159453848176, 1.0063000774394764,
+        1.0062842914171306, 1.0062685994572262, 1.0062530074193121, 1.0062375141288376,
+        1.0062221118247556, 1.0062067876947438, 1.0061915262028054, 1.0061763117882632,
+        1.0061611314645564, 1.0061459768777619, 1.0061308454907045, 1.006115740718788,
+        1.006100671029376, 1.0060856481948623, 1.0060706850302037, 1.0060557930250222,
+        1.0060409802867312, 1.0060262501449333, 1.0060116006423403, 1.0059970249765295,
+        1.0059825127891895, 1.0059680520541359, 1.0059536312172268, 1.00593924120603,
+        1.0059248769593803, 1.0059105382195435, 1.0058962294646265, 1.0058819590120402,
+        1.0058677374677147, 1.0058535758057634, 1.005839483420996, 1.0058254664933726,
+        1.0058115269412857, 1.0057976621316191, 1.0057838653792581, 1.005770127130932,
+        1.0057564366124299, 1.0057427836434938, 1.0057291603033558, 1.005715562164068,
+        1.0057019888911563, 1.0056884441260776, 1.00567493469168, 1.0056614692779045,
+        1.0056480568504715, 1.0056347050662306, 1.0056214189692718, 1.0056082001848885,
+        1.0055950467353554, 1.0055819534893828, 1.0055689131462775, 1.005555917565451,
+        1.0055429591972982, 1.0055300323611214, 1.0055171341502405, 1.0055042648164634,
+        1.0054914275819948, 1.0054786279291177, 1.0054658725085945, 1.0054531678709437,
+        1.0054405192503788, 1.0054279296156667, 1.0054153991493164, 1.0054029252367032,
+        1.0053905029545747, 1.0053781259605477, 1.0053657876168582, 1.005353482144387,
+        1.005341205602495, 1.0053289565257637, 1.0053167361128765, 1.0053045479440779,
+        1.0052923972868066, 1.0052802901198017, 1.0052682320522357, 1.0052562273285086,
+        1.0052442780899005, 1.0052323840153254, 1.0052205423944474, 1.0052087486099246,
+        1.005196996935012, 1.005185281500509, 1.005173597259487, 1.0051619407833408,
+        1.005150310756557, 1.0051387080936627, 1.0051271356695564, 1.0051155977218849,
+        1.0051040990393476, 1.00509264408367, 1.0050812362000752, 1.0050698770509443,
+        1.0050585663643308, 1.0050473020311823, 1.0050360805230194, 1.0050248975466023,
+        1.0050137488129236, 1.005002630781413, 1.0049915412485964, 1.0049804796814539,
+        1.0049694472434885, 1.004958446516931, 1.0049474809780163, 1.0049365543241566,
+        1.0049256697754967, 1.0049148294747576, 1.0049040340890094, 1.004893282679143,
+        1.0048825728543263, 1.0048719011784915, 1.0048612637526455, 1.0048506568678834,
+        1.004840077614163, 1.0048295243402463, 1.0048189968885362, 1.0048084965693154,
+        1.0047980258848732, 1.0047875880569017, 1.0047771864430837, 1.0047668239456857,
+        1.0047565025135763, 1.0047462228202444, 1.0047359841678642, 1.0047257846271294,
+        1.0047156213818296, 1.004705491212834, 1.0046953910341507, 1.0046853183874234,
+        1.0046752718113, 1.0046652510262155, 1.0046552569088556, 1.004645291267688,
+        1.0046353564649435, 1.0046254549556437, 1.004615588826394, 1.0046057594142543,
+        1.0045959670696367, 1.0045862111003376, 1.0045764899012453, 1.0045668012419093,
+        1.0045571426574953, 1.004547511872174, 1.004537907180239, 1.0045283277194612,
+        1.0045187735915406, 1.0045092458119815, 1.004499746101612, 1.0044902765589534,
+        1.0044808392721194, 1.004471435938055, 1.0044620675539586, 1.004452734232063,
+        1.0044434351667295, 1.0044341687563623, 1.004424932856451, 1.0044157251185293,
+        1.0044065433565807, 1.0043973858792756, 1.0043882517338198, 1.0043791408233238,
+        1.0043700538817315, 1.0043609923143766, 1.0043519579342914, 1.0043429526406114,
+        1.0043339780935974, 1.0043250354394866, 1.0043161251285513, 1.0043072468528387,
+        1.0042983996096204, 1.0042895818756472, 1.0042807918597598, 1.004272027789673,
+        1.004263288184779, 1.0042545720708154, 1.0042458791033386, 1.0042372095829768,
+        1.0042285643636675, 1.0042199446723648, 1.0042113518724187, 1.0042027872107542,
+        1.0041942515902051, 1.0041857454029097, 1.0041772684497752, 1.0041688199565582,
+        1.0041603986816368, 1.0041520030964974], [4.84097581778825e-07,
+        1.4533745689396469e-06, 2.4259016860283226e-06, 3.4038606258744636e-06,
+        4.389455497018074e-06, 5.384922240141361e-06, 6.392537797199066e-06,
+        7.414629954786751e-06, 8.453587278595165e-06, 9.51186952552366e-06,
+        1.059201851789891e-05, 1.1696669599843156e-05, 1.2828563633768997e-05,
+        1.3990559816417693e-05, 1.518564921251605e-05, 1.6416969264573422e-05,
+        1.7687819290769096e-05, 1.900167712882794e-05, 2.0362217085723386e-05,
+        2.1773329252651425e-05, 2.323914049339077e-05, 2.4764037113022472e-05,
+        2.635268954317712e-05, 2.8010079202521723e-05, 2.9741527785548554e-05,
+        3.155272924038449e-05, 3.344978480061199e-05, 3.543924132120916e-05,
+        3.7528133398022694e-05, 3.97240295940042e-05, 4.203508340165082e-05,
+        4.4470089312912785e-05, 4.7038544768903286e-05, 4.975071856536054e-05,
+        5.261772659227817e-05, 5.5651615710182884e-05, 5.8865456864078706e-05,
+        6.227344848822474e-05, 6.589103162346934e-05, 6.973501811592413e-05,
+        7.38237337419917e-05, 7.8177178080733e-05, 8.28172035233002e-05,
+        8.776771587477805e-05, 9.305489969397803e-05, 9.870747157937723e-05,
+        0.00010475696578659547, 0.00011123805631551952, 0.00011818892144993189,
+        0.0001256516565650914, 0.00013367274295454615, 0.00014230358129166642,
+        0.00015160109988696346, 0.00016162845008618236, 0.0001724558031371864,
+        0.00018416126565114983, 0.00019683193456207227, 0.00021056511596762137,
+        0.00022546973819829734, 0.0002416679952620327, 0.00025929726516127653,
+        0.0002785123577977898, 0.00029948815996155576, 0.0003224227615195205,
+        0.00034754116838406335, 0.0003750997359611881, 0.00040539149338740586,
+        0.0004387525783946233, 0.000475570069354056, 0.0005162915916573733,
+        0.000561437202436303, 0.000611614236016589, 0.0006675360489670436,
+        0.0007300459773399141, 0.0008001483798932636, 0.0008790494954238883,
+        0.0009682121866815462, 0.0010694308080733486, 0.001184936048291684,
+        0.0013175458468094193, 0.001470889742825263, 0.0016497553298688186,
+        0.0018606481731026862, 0.002112748031672203, 0.0024196572286116613,
+        0.0028028871378125092, 0.0032996552654219334, 0.003983356204200878,
+        0.005032312403598572, 0.007093166725926962, 0.022854764729182714,
+        0.007640153844371612, 0.005962399592829649, 0.005482127274870969,
+        0.005386664877002816, 0.005495379918547228, 0.005748937059459517,
+        0.006127906006401491, 0.006631192658315584, 0.0072690912024635035,
+        0.008061310885796164, 0.009037320434994764, 0.010238282290569157,
+        0.011720594805966766, 0.013561538737048883, 0.01586806355735571,
+        0.018790598219036586, 0.02254531207249972, 0.027451272082155156,
+        0.03399526748409557, 0.04295132674493541, 0.05561707328787418, 0.0743260124845523,
+        0.10370600521875534, 0.15438924479022115, 0.25769345742073296, 0.5702284482610188,
+        6.313847138107146, 0.4071254696256903, 0.8917112725721819, 1.773718315517956,
+        1.066911340640053, 1.0894218941230518, 1.6314117937305979, 1.6346168013263545,
+        0.6533254754488088, 0.5646757017480043, 0.7696042314141937, 1.2922284446021706,
+        2.306395352441572, 1.9220859568134683, 1.2504775596891307, 0.9594248432254071,
+        0.8482254350937367, 0.8648961854379278, 1.0467572606856714, 1.2960262646673149,
+        1.1445634479916298, 0.9647965770331122, 0.9146630195983296, 0.9583314967930036,
+        1.0905472188595913, 1.3358427317355963, 1.6838328216401932, 1.7920688296492258,
+        1.40251000122698, 1.018705292225905, 0.7976144462956901, 0.7033417298909306,
+        0.7169421352635927, 0.8488809640569368, 1.1218007219447876, 1.4598163578930123,
+        1.5348057655461422, 1.3435098605835685, 1.1570101747483272, 1.0421570229881312,
+        1.0181898993425103, 1.0488834034389296, 1.0985449999877095, 1.1454886184062651,
+        1.158858185702488, 1.1236848068906085, 1.0590859169482378, 0.996281848948328,
+        0.9542915718264329, 0.9390882362157527, 0.9505977920021657, 0.9868297749111917,
+        1.0445731988036946, 1.1178032961916957, 1.1948213317948502, 1.2567947866855127,
+        1.2829215574972872, 1.2629772053993416, 1.2048090657050465, 1.1268069383822552,
+        1.0455980897243236, 0.9708775853089234, 0.9065183447391048, 0.8531514772777338,
+        0.8100386148866918, 0.7760621737646685, 0.7501609868411809, 0.7314862256268272,
+        0.7194328665837202, 0.7136227059594874, 0.7138729106775531, 0.7201628537604364,
+        0.7326005917717819, 0.751382973960796, 0.7767369105404057, 0.8088222381588015,
+        0.8475695616676064, 0.8924251482803979, 0.9419956158549271, 0.9936577594211156,
+        1.0433473933051138, 1.085904588379828, 1.1162836821954158, 1.1313567273550433,
+        1.13125780875575, 1.119255422596642, 1.1002849691102217, 1.0792341406494865,
+        1.0598699178666837, 1.0445340509036243, 1.0342957842478229, 1.0292486929096474,
+        1.028792434636255, 1.0318635555524098, 1.0371354146650111, 1.0432143790807118,
+        1.0488393432595935, 1.0530626702963708, 1.0553717640145792, 1.055716259967486,
+        1.0544352948763522, 1.0521140243711276, 1.049417186757394, 1.0469429378558794,
+        1.045121573885965, 1.0441650315466082, 1.0440620865171408, 1.0446107859915437,
+        1.0454795042101506, 1.046286983515557, 1.0466884336996647, 1.0464510677691607,
+        1.0455020650174387, 1.0439375658396257, 1.0419919850454245, 1.0399781629071565,
+        1.0382156212228986, 1.0369643559793091, 1.0363768327716263, 1.036474548242093,
+        1.037150249743627, 1.0381933106969587, 1.0393331180071996, 1.0402928136350906,
+        1.040843400678239, 1.0408471642630395, 1.0402809218622429, 1.0392342176351292,
+        1.0378839781587044, 1.0364529775546294, 1.035162612995725, 1.034190315893932,
+        1.033639293625431, 1.0335247231646263, 1.0337771678375156, 1.0342612815350198,
+        1.0348057089211373, 1.0352383781443406, 1.0354203336201093, 1.0352713713837793,
+        1.03478240894723, 1.03401258280108, 1.0330726819687535, 1.0320995360368426,
+        1.0312274956944516, 1.0305629656070987, 1.0301665017275121, 1.03004495889204,
+        1.0301541397921368, 1.0304106415841086, 1.0307102053537431, 1.0309488990336462,
+        1.031043037676736, 1.0309440419388105, 1.0306455285412355, 1.0301816428702284,
+        1.0296175561247383, 1.0290346298881634, 1.0285136005664979, 1.0281191391206919,
+        1.027888460551701, 1.0278256006143864, 1.0279018415042458, 1.0280617506821121,
+        1.0282334920909186, 1.0283415179628232, 1.0283194866472547, 1.028121314667864,
+        1.0277286712921894, 1.0271539081046561, 1.0264382510133052, 1.0256458822939845,
+        1.0248551297400321, 1.0241482545085467, 1.023601286122212, 1.0232750763974194,
+        1.0232083596589174, 1.0234132320038074, 1.0238731733215187, 1.0245435558740272,
+        1.0253544923656452, 1.0262158285863543, 1.0270240289876291, 1.0276705982856487,
+        1.0280515153080605, 1.028076948560795, 1.027680331718436, 1.0268257762882391,
+        1.0255128569512129, 1.0237780554324851, 1.0216925670464887, 1.0193566790523974,
+        1.0168914076390139, 1.0144284236737038, 1.0120994421649914, 1.0100261925070624,
+        1.0083118734570027, 1.00703470231038, 1.0062438635897455, 1.0059578985620998,
+        1.0061653749162636, 1.0068275354031642, 1.0078825332095545, 1.0092508076943978,
+        1.010841130045606, 1.0125568542642824, 1.0143019472908903, 1.015986442865817,
+        1.0175310590871822, 1.0188708237248287, 1.0199576440854572, 1.020761822609601,
+        1.021272548432299, 1.0214973956121107, 1.0214608487424044, 1.0212018788620605,
+        1.0207706249518145, 1.0202243049075461, 1.0196225762562396, 1.0190226708875212,
+        1.0184747143683144, 1.0180176857189855, 1.0176764617797223, 1.0174603147327823,
+        1.0173630941955079, 1.01736513703271, 1.0174367273686913, 1.0175427039712774,
+        1.0176476185686887, 1.017720727521836, 1.0177400867345792, 1.0176951349485717,
+        1.0175873853210167, 1.017429160427785, 1.0172406395377833, 1.0170457706967615,
+        1.0168677779730213, 1.016725036613965, 1.0166279964407055, 1.0165776318319906,
+        1.0165656251089934, 1.0165761944674816, 1.0165892029240535, 1.0165839726357944,
+        1.016543114243619, 1.0164556862290066, 1.0163191282212394, 1.0161396441610648,
+        1.0159310023734571, 1.015712011539389, 1.0155031657744227, 1.0153230847016363,
+        1.015185385996772, 1.0150965246254204, 1.015054941542844, 1.0150516235024363,
+        1.0150719271871695, 1.0150983056026666, 1.0151134269991013, 1.0151031210323591,
+        1.0150586335890563, 1.0149778127363698, 1.0148650568318376, 1.0147300905531065,
+        1.0145858485254713, 1.0144458980077447, 1.0143218955085611, 1.0142215407429591,
+        1.0141473772638172, 1.0140966184179343, 1.0140619832049818, 1.0140333436198123,
+        1.0139998440643354, 1.0139520779001232, 1.0138839086943288, 1.013793602990593,
+        1.0136840817429933, 1.0135622708123688, 1.013437702423995, 1.0133206556357377,
+        1.01322019972933, 1.0131425086513675, 1.0130897505198468, 1.0130597394727472,
+        1.01304639149366, 1.013040878259086, 1.013033249347947, 1.0130142143836929,
+        1.0129767560053107, 1.0129172849011585, 1.012836141133765, 1.0127373730970226,
+        1.0126278614713449, 1.0125159739624743, 1.012410015375219, 1.012316763611071,
+        1.0122403534365245, 1.0121816946980033, 1.012138506190306, 1.0121059309399423,
+        1.0120775941033837, 1.0120468891278576, 1.0120082439368332, 1.0119581318212107,
+        1.0118956480105938, 1.0118225609858236, 1.0117428498641146, 1.011661835593225,
+        1.0115850859699465, 1.0115173099167931, 1.0114614500781258, 1.0114181378887355,
+        1.0113856019561758, 1.0113600334781698, 1.0113363277277692, 1.0113090535002076,
+        1.0112734644233772, 1.0112263633874736, 1.0111666637582815, 1.0110955516914497,
+        1.0110162306633774, 1.0109333072847444, 1.0108519417601813, 1.0107769253879402,
+        1.0107118550218879, 1.0106585504700056, 1.010616811205027, 1.010584543636245,
+        1.0105582218780285, 1.0105335857963667, 1.0105064404199116, 1.0104734071535435,
+        1.0104324914110125, 1.0103833699448277, 1.0103273564392201, 1.0102670650012349,
+        1.0102058463753603, 1.010147110882028, 1.0100936685721404, 1.010047208814787,
+        1.0100080111067549, 1.009974932820258, 1.0099456668842557, 1.0099172127955502,
+        1.0098864667302603, 1.009850817331032, 1.0098086359754916, 1.0097595730236169,
+        1.0097046099690197, 1.0096458640069874, 1.0095861873512457, 1.0095286401658963,
+        1.0094759367744583, 1.0094299666212738, 1.0093914747073012, 1.009359954679671,
+        1.0093337676813767, 1.0093104589658846, 1.0092872095432814, 1.0092613377729713,
+        1.0092307595086396, 1.0091943258242486, 1.0091519821416148, 1.009104726791317,
+        1.0090543840984392, 1.0090032400848998, 1.0089536119076954, 1.0089074313759017,
+        1.0088659171859042, 1.008829391531817, 1.0087972684515818, 1.008768209110286,
+        1.008740409109673, 1.0087119601742405, 1.0086812170438286, 1.0086471018295855,
+        1.0086092918153904, 1.0085682598372834, 1.0085251644240052, 1.0084816145297595,
+        1.0084393558802898, 1.008399938815913, 1.0083644290461122, 1.008333213072532,
+        1.0083059313466216, 1.008281548186416, 1.0082585425690205, 1.0082351826140217,
+        1.0082098325669142, 1.008181236665409, 1.0081487299438419, 1.0081123404934866,
+        1.0080727680902486, 1.0080312465681205, 1.0079893177402877, 1.0079485594429545,
+        1.0079103169515242, 1.0078754847035767, 1.0078443747132222, 1.0078166914620743,
+        1.0077916135640002, 1.0077679636647998, 1.0077444331481638, 1.0077198197641979,
+        1.0076932355540251, 1.0076642492902688, 1.0076329406199955, 1.007599859668102,
+        1.0075659029525403, 1.0075321310075807, 1.0074995626074033, 1.00746898343008,
+        1.0074408031288478, 1.007414985028676, 1.0073910589787916, 1.0073682128125023,
+        1.0073454440829492, 1.0073217436216322, 1.0072962776532635, 1.0072685363654523,
+        1.0072384235810676, 1.0072062731554583, 1.0071727908633494, 1.0071389334820722,
+        1.007105747271668, 1.0070741943648769, 1.0070449967780228, 1.007018523829521,
+        1.0069947405789816, 1.0069732240373803, 1.0069532422942074, 1.0069338813497757,
+        1.0069141970251827, 1.0068933659793629, 1.006870810994078, 1.006846280923464,
+        1.0068198739987724, 1.006792003010659, 1.006763310547164, 1.0067345503414313,
+        1.006706455652966, 1.0066796168118295, 1.0066543875838525, 1.0066308344629467,
+        1.0066087354309152, 1.0065876264780644, 1.0065668866133481, 1.006545846382929,
+        1.0065239018662404, 1.0065006160597758, 1.0064757923232954, 1.0064495095444548,
+        1.006422114955174, 1.0063941770447222, 1.0063664067390028, 1.0063395591374962,
+        1.0063143301230395, 1.0062912619626585, 1.0062706698335036, 1.0062525975522423,
+        1.0062368063446248, 1.0062227959901386, 1.0062098537627329, 1.00619712373907,
+        1.0061836875131356, 1.0061686471585032, 1.0061512022313293, 1.0061307143781988,
+        1.0061067553051373, 1.0060791360894938, 1.0060479177617643, 1.0060134045527802,
+        1.0059761221270198, 1.0059367835557613, 1.0058962458571736, 1.0058554598137557,
+        1.0058154156286088, 1.00577708691115, 1.0057413755304891, 1.0057090600092864,
+        1.0056807502649912, 1.0056568515230084, 1.0056375400168358, 1.005622752578747,
+        1.0056121913946319, 1.0056053440980384, 1.0056015181215547, 1.0055998869610467,
+        1.0055995449062638, 1.005599566001986, 1.0055990626356326, 1.005597239249345,
+        1.0055934372274806, 1.005587167933397, 1.0055781320354644, 1.0055662245215626,
+        1.005551526007353, 1.0055342819741986, 1.0055148723467209, 1.0054937743030377,
+        1.0054715214109835, 1.0054486621418877, 1.0054257205861423, 1.00540316183923,
+        1.0053813640884244, 1.0053605989356103, 1.0053410209510025, 1.0053226668640687,
+        1.0053054641625205, 1.0052892481986877, 1.0052737862278782, 1.0052588061807983,
+        1.0052440274766408, 1.0052291908972066, 1.0052140845390052, 1.0051985631861922,
+        1.0051825591070054, 1.0051660832224798, 1.0051492167296918, 1.0051320944417141,
+        1.0051148821693838, 1.0050977512559727, 1.0050808537550815, 1.0050643016397032,
+        1.0050481528426294, 1.005032405927239, 1.0050170039134383, 1.0050018464244803,
+        1.004986808084076, 1.0049717601729862, 1.004956592097048, 1.0049412292996154,
+        1.004925644859843, 1.004909863058538, 1.0048939544981057, 1.0048780237219195,
+        1.0048621914712779, 1.0048465745523727, 1.0048312666284607, 1.0048163230520257,
+        1.0048017521466224, 1.0047875142593374, 1.0047735286159312, 1.0047596867359376,
+        1.0047458701140368, 1.0047319692165904, 1.00471790068054, 1.004703619954416,
+        1.0046891274207252, 1.004674467144886, 1.004659718619441, 1.004644983008556,
+        1.0046303662607339, 1.0046159619109873, 1.0046018363720424, 1.004588019033224,
+        1.0045744986367275, 1.004561226334266, 1.004548124724721, 1.0045351012184116,
+        1.004522063419174, 1.004508933960441, 1.0044956624052783, 1.0044822323806555,
+        1.0044686629572692, 1.0044550042601195, 1.0044413282360585, 1.004427716259054,
+        1.0044142457045415, 1.0044009777085585, 1.004387948045898, 1.0043751624755284,
+        1.0043625971195576, 1.004350203600703, 1.0043379179028806, 1.0043256713608488,
+        1.0043134019099533, 1.0043010637678333, 1.0042886340547934, 1.0042761154198478,
+        1.0042635344234452, 1.0042509361184395, 1.0042383758565485, 1.004225909739896,
+        1.0042135852840706, 1.0042014337513485, 1.0041894652823722, 1.0041776674674443,
+        1.004166007441155, 1.004154437047709, 1.0041429001905648, 1.0041313412078545,
+        1.0041197130335755, 1.0041079840101945, 1.0040961424792578, 1.0040841986394817,
+        1.0040721835633557, 1.0040601456409906, 1.0040481450220693, 1.0040362468200812,
+        1.0040245139146655, 1.00401300014642, 1.004001744567381, 1.0039907672236623,
+        1.0039800667400365, 1.0039696197809287, 1.0039593823007222, 1.003949292378791,
+        1.0039392743610334, 1.0039292439910423, 1.0039191141972819, 1.0039088011950845,
+        1.0038982305551392, 1.0038873428810342, 1.003876098731809, 1.0038644824305782,
+        1.003852504429174, 1.0038402019611385, 1.0038276378166509, 1.003814897210557,
+        1.0038020828778884, 1.0037893087022824, 1.0037766923389604, 1.0037643474125646,
+        1.0037523759317648, 1.0037408615553323, 1.0037298642665051, 1.0037194168725458,
+        1.0037095235627567, 1.0037001605551916, 1.0036912786668788, 1.0036828074790882,
+        1.0036746606563285, 1.0036667419248932, 1.003658951223149, 1.003651190591589,
+        1.0036433694596556, 1.0036354090889825, 1.0036272460305111, 1.0036188345324568,
+        1.0036101478898698, 1.0036011787559365, 1.0035919384473617, 1.0035824552831638,
+        1.0035727720105643, 1.0035629424033417, 1.0035530271711846, 1.0035430893899733,
+        1.0035331897420496, 1.00352338192597, 1.0035137086386687, 1.0035041985321431,
+        1.0034948644910067, 1.0034857034640186, 1.0034766979208574, 1.0034678188135764,
+        1.003459029727196, 1.003450291735995, 1.0034415683702456, 1.0034328300643753,
+        1.0034240575125932, 1.0034152434988315, 1.003406392976975, 1.0033975214253836,
+        1.0033886517492936, 1.0033798102172928, 1.0033710220590126, 1.0033623073974143,
+        1.0033536781313013, 1.003345136230314, 1.0033366736789942, 1.0033282740442566,
+        1.0033199153838175, 1.0033115740030292, 1.0033032284381578, 1.003294863016132,
+        1.0032864704182303, 1.003278052844854, 1.0032696216119135, 1.0032611952675758,
+        1.0032527965585156, 1.00324444875784, 1.003236171963022, 1.0032279799667019,
+        1.0032198781983608, 1.003211863049657, 1.003203922662481, 1.003196039016641,
+        1.0031881909436, 1.0031803575488842, 1.0031725214711429, 1.0031646714478444,
+        1.0031568037872294, 1.0031489225395736, 1.0031410383842108, 1.0031331664635232,
+        1.0031253235652882, 1.0031175251524267, 1.0031097827496274, 1.0031021021197823,
+        1.003094482514997, 1.0030869170940995, 1.003079394395313, 1.0030719005740532,
+        1.0030644219919242, 1.0030569476936113, 1.0030494713403957, 1.0030419922747678,
+        1.0030345155500329, 1.0030270509431323, 1.0030196111455012, 1.0030122094654679,
+        1.0030048574531434, 1.0029975628632517, 1.0029903283036277, 1.002983150790808,
+        1.00297602227234, 1.0029689310071428, 1.0029618635496371, 1.0029548069851855,
+        1.0029477510293545, 1.0029406896362396, 1.0029336218542924, 1.0029265518038377,
+        1.0029194878046281, 1.0029124408267838, 1.002905422549739, 1.0028984433728567,
+        1.0028915107193654, 1.002884627914333, 1.0028777938094982, 1.0028710031932517,
+        1.0028642478866818, 1.0028575183106823, 1.0028508052338867, 1.0028441013889293,
+        1.0028374026773885, 1.0028307087645993, 1.0028240229787624, 1.002817351553843,
+        1.0028107023702864, 1.002804083431878, 1.0027975013572166, 1.0027909601543135,
+        1.0027844604899299, 1.0027779995726203, 1.0027715716572168, 1.002765169068728,
+        1.0027587835544707, 1.0027524077198626, 1.0027460362941503, 1.0027396670078164,
+        1.0027333009362966, 1.0027269422611356, 1.0027205975023552, 1.0027142743666222,
+        1.0027079804189551, 1.0027017218111969, 1.0026955022846002, 1.002689322610593,
+        1.0026831805533927, 1.002677071345347, 1.0026709885772709, 1.0026649253369182,
+        1.0026588753906502, 1.002652834202081, 1.002646799616293, 1.0026407721017783,
+        1.0026347545230185, 1.002628751499624, 1.002622768478702, 1.002616810693753,
+        1.0026108821980801, 1.002604985142042, 1.0025991194155308, 1.002593282709074,
+        1.0025874709714675, 1.0025816791722184, 1.0025759022255363, 1.0025701359075299,
+        1.0025643776035862, 1.0025586267566797, 1.0025528849431145, 1.0025471555694303,
+        1.0025414432509663, 1.002535752987069, 1.002530089281006, 1.002524455359009,
+        1.0025188526221103, 1.0025132804208658, 1.0025077361848973, 1.0025022158768162,
+        1.002496714684789, 1.0024912278288187, 1.0024857513394878, 1.0024802826765082,
+        1.0024748210856902, 1.0024693676411103, 1.0024639249750853, 1.0024584967525236,
+        1.0024530869886417, 1.0024476993331657, 1.002442336446056, 1.002436999569947,
+        1.002431688366979, 1.0024264010394337, 1.0024211347034504, 1.0024158859417764,
+        1.0024106514323734, 1.0024054285395219, 1.0024002157639105, 1.0023950129759722,
+        1.0023898213968798, 1.0023846433370065, 1.0023794817440506, 1.0023743396450886,
+        1.0023692195834966, 1.0023641231501055, 1.0023590506891835, 1.0023540012274659,
+        1.0023489726344437, 1.0023439619817767, 1.0023389660357875, 1.002333981795511,
+        1.0023290069828403, 1.0023240404018106, 1.0023190821084498, 1.0023141333666004,
+        1.002309196402371, 1.0023042740039445, 1.0022993690386766, 1.002294483971453,
+        1.002289620465744, 1.0022847791322715, 1.0022799594630978, 1.0022751599561945,
+        1.0022703784028621, 1.0022656122834712, 1.00226085920022, 1.0022561172715687,
+        1.0022513854220048, 1.0022466635209377, 1.0022419523518535, 1.0022372534227084,
+        1.0022325686555407, 1.002227900012882, 1.0022232491278507, 1.0022186170021352,
+        1.0022140038226857, 1.0022094089260662, 1.0022048309132863, 1.002200267892038,
+        1.002195717801975, 1.0021911787656008, 1.0021866494042533, 1.002182129066072,
+        1.0021776179288917, 1.0021731169629666, 1.0021686277622563, 1.0021641522748375,
+        1.0021596924789586, 1.0021552500592024, 1.0021508261356988, 1.002146421089317,
+        1.0021420345087242, 1.0021376652646914, 1.0021333116960132, 1.0021289718739093,
+        1.0021246439000564, 1.0021203261894955, 1.0021160176937711, 1.0021117180308412,
+        1.0021074275044581, 1.0021031470141015, 1.0020988778739182, 1.0020946215730089,
+        1.0020903795174272, 1.002086152795606, 1.0020819420035578, 1.0020777471553732,
+        1.0020735676901038, 1.0020694025706658, 1.002065250456288], [2.101052586014986e-07,
+        6.308123704076828e-07, 1.0530114821320923e-06, 1.4777043925014383e-06,
+        1.9059036064558405e-06, 2.338636823753357e-06, 2.776951330848025e-06,
+        3.221918699600618e-06, 3.674639542780128e-06, 4.136248497803331e-06,
+        4.607919435616484e-06, 5.090870950860993e-06, 5.586372118894519e-06,
+        6.095748645929209e-06, 6.620389372217081e-06, 7.161753246152804e-06,
+        7.72137677964783e-06, 8.30088205939796e-06, 8.90198539011723e-06,
+        9.526506601930722e-06, 1.017637916437968e-05, 1.0853661117002122e-05,
+        1.1560546972463927e-05, 1.2299380670411619e-05, 1.3072669702497245e-05,
+        1.3883100532989201e-05, 1.4733555486542832e-05, 1.562713122386947e-05,
+        1.6567159029039085e-05, 1.7557227062545427e-05, 1.860120487204718e-05,
+        1.9703270336586837e-05, 2.0867939400485188e-05, 2.2100098864051404e-05,
+        2.34050426338813e-05, 2.478851179946098e-05, 2.6256739035802628e-05,
+        2.7816497806486234e-05, 2.9475157004470658e-05, 3.1240741637057545e-05,
+        3.312200037008566e-05, 3.512848072333315e-05, 3.727061295417369e-05,
+        3.9559803675848736e-05, 4.2008540547409556e-05, 4.4630509365652404e-05,
+        4.7440725387813814e-05, 5.0455680539610034e-05, 5.369350894156026e-05,
+        5.71741730096387e-05, 6.0919673157213454e-05, 6.495428436174878e-05,
+        6.930482336398962e-05, 7.400095100671505e-05, 7.907551478250094e-05,
+        8.45649374928499e-05, 9.050965906879186e-05, 9.695463941746049e-05,
+        0.0001039499318813384, 0.00011155133819770684, 0.00011982115787774822,
+        0.0001288290472027631, 0.00013865300565415946, 0.00014938051082917587,
+        0.00016110982675980335, 0.0001739515152419903, 0.00018803018521032903,
+        0.000203486522054299, 0.0002204796470146283, 0.00023918986650412928,
+        0.00025982188347065864, 0.0002826085577073708, 0.00030781532034132976,
+        0.0003357453696786724, 0.0003667458039144615, 0.00040121487991316327,
+        0.00043961063093493125, 0.00048246112875037614, 0.0005303767434900719,
+        0.0005840648399563894, 0.0006443474556400236, 0.0007121826441171018,
+        0.000788690343108149, 0.0008751838524626835, 0.0009732083016571975,
+        0.0010845878679587185, 0.001211484008961446, 0.0013564676346063066,
+        0.0015226090241065291, 0.0017135904762442971, 0.0019338482700194063,
+        0.002188752689771927, 0.0024848378507929757, 0.002830097208318767,
+        0.003234366446565525, 0.0037098237054790425, 0.004271648948029146,
+        0.004938901556172177, 0.005735700728589714, 0.00669283154947435,
+        0.00784995805700844, 0.009258715687330023, 0.010987100279525538,
+        0.01312580686819585, 0.015797566557447597, 0.019171212039678937,
+        0.023483422593432873, 0.02907337365255981, 0.03643996415365704,
+        0.04634051173258075, 0.05997029271083, 0.07931200665563787, 0.10787915541483929,
+        0.15250275306407154, 0.22846927034460443, 0.3793111342261624, 0.8141108199949787,
+        8.041519305814752, 0.15075191873170707, 1.738027923751271, 3.196689307746941,
+        1.7367776590919988, 1.493329200206657, 1.4240937910282268, 0.377817251485686,
+        1.5566636749142009, 2.4903733491670663, 4.944142696520038, 7.761162713971286,
+        5.942430368496038, 3.1127852830043463, 1.4605980680983255, 0.9701672809918545,
+        0.9548154232754253, 1.2565706280158282, 1.93436681544438, 2.6979679425075567,
+        2.335651035882205, 1.7803371561423924, 1.4880187540952898, 1.3753280840118767,
+        1.3947515325501059, 1.545461258515289, 1.7993667123704902, 1.8250193642201744,
+        1.425447461460515, 1.0949019961671675, 0.9534021181211367, 0.9482422038909971,
+        1.053116734638993, 1.2777480432977584, 1.641891913345645, 2.0187957402567918,
+        1.9849726459982044, 1.6239456250510007, 1.3115081660879933, 1.112309906570387,
+        1.073041726518166, 1.1175245386984793, 1.1893057205528386, 1.2661768784610314,
+        1.3104940564054057, 1.2982029246202986, 1.2445508068907507, 1.1834161756309363,
+        1.138176957045638, 1.1179314832136362, 1.1242878684273414, 1.1559568541573637,
+        1.2097446609134677, 1.2790259956611776, 1.3508771845549699, 1.404876324284503,
+        1.4191525314573628, 1.3840134823992722, 1.3093586759739528, 1.2157737116286795,
+        1.121155452275839, 1.0355136807092424, 0.9625109337511375, 0.9023989123738781,
+        0.8540690482324694, 0.8161051542661526, 0.7872283282386839, 0.7664430682272413,
+        0.7530546219949926, 0.7466391037469909, 0.747001973767268, 0.7541375948678515,
+        0.7681904153533126, 0.7894104418182307, 0.8180886235919382, 0.854449843817362,
+        0.8984730297377246, 0.9496056596334315, 1.0063615987905452, 1.0658705694700037,
+        1.1236134653858507, 1.1737665616838597, 1.2105161654785237, 1.230072717506922,
+        1.232229676850317, 1.2203139764955424, 1.1996226846070757, 1.1755329952300582,
+        1.1522865735554282, 1.1326171057398435, 1.1178927019940141, 1.1084287613115111,
+        1.1037906222167857, 1.1030407082069724, 1.1049480624949797, 1.108188394178059,
+        1.1115437099911574, 1.114081860353896, 1.1152772084773481, 1.115038759752745,
+        1.1136405929665727, 1.1115832204215048, 1.1094326610748704, 1.1076795725620199,
+        1.106642726940087, 1.1064229929370752, 1.1069033857759794, 1.1077873288384246,
+        1.1086666686668731, 1.1091091814486629, 1.108751192647933, 1.1073767764493536,
+        1.1049649015223206, 1.101692592482127, 1.0978943233223055, 1.0939902287848733,
+        1.0904027633160471, 1.087481055651381, 1.0854464861522983, 1.0843658536878282,
+        1.084152753875643, 1.0845941054037256, 1.0853962390323428, 1.086242576355748,
+        1.086852602093146, 1.0870306556505787, 1.086694483017181, 1.0858780424186347,
+        1.084709594325924, 1.0833722267659114, 1.082057449120169, 1.0809225510875953,
+        1.0800598696477233, 1.0794824527694395, 1.0791270781629356, 1.0788726708942844,
+        1.0785698370211425, 1.0780754325089479, 1.0772850641837275, 1.0761566697950546,
+        1.0747201959785455, 1.0730716508429305, 1.0713535410214299, 1.0697267139621223,
+        1.068340044617747, 1.0673040780822483, 1.0666731536844298, 1.0664384171764962,
+        1.0665320466812924, 1.0668412410671293, 1.0672291048477798, 1.0675585527451756,
+        1.0677148904278067, 1.0676230057232314, 1.0672562237097198, 1.0666356755268336,
+        1.0658210613209642, 1.0648953909234382, 1.0639472266419123, 1.063053993736415,
+        1.0622692283794903, 1.061615525351388, 1.061083749492399, 1.060638003356318,
+        1.0602250047052242, 1.0597859649920922, 1.0592688034746103, 1.0586386099117715,
+        1.057884684487803, 1.0570231763392328, 1.0560951749327956, 1.0551608967210553,
+        1.054291181004789, 1.053557764796605, 1.0530237485671823, 1.0527353796526993,
+        1.0527158938480063, 1.0529617843626318, 1.0534415844199982, 1.0540970768437656,
+        1.0548467592961763, 1.05559135050009, 1.0562210686620572, 1.056624309252863,
+        1.056697183420471, 1.056353174110978, 1.0555319815873112, 1.0542065394697022,
+        1.052387255212135, 1.050122795793889, 1.0474971724884414, 1.044623392623947,
+        1.0416344244021716, 1.0386725555543346, 1.035878355769414, 1.0333803760307831,
+        1.0312864868086202, 1.0296774484926872, 1.02860299468197, 1.028080441602732,
+        1.0280956355487538, 1.0286059125599805, 1.0295446571100468, 1.0308269958119307,
+        1.0323561409486928, 1.0340299070318903, 1.035746964638545, 1.0374124696352691,
+        1.0389428048588447, 1.0402692792378616, 1.0413407255936566, 1.0421250053882047,
+        1.0426094591293527, 1.042800341722149, 1.0427212712056826, 1.0424107202374386,
+        1.0419186109087186, 1.041302141431721, 1.040621069534832, 1.039932781681289,
+        1.0392875637330767, 1.0387245337007645, 1.0382686843195357, 1.0379294054551875,
+        1.0377007160574852, 1.0375632433252986, 1.0374877621813001, 1.0374398795784252,
+        1.0373852527322176, 1.0372946096133278, 1.037147830459088, 1.0369364697364445,
+        1.0366643397996915, 1.0363461001495684, 1.0360041362133114, 1.0356642992393088,
+        1.0353512577242616, 1.0350842512604932, 1.034873940993135, 1.0347208431191721,
+        1.0346155538991337, 1.0345406726404553, 1.0344740487555926, 1.0343927624145197,
+        1.0342771308495589, 1.0341140371380115, 1.033899009078784, 1.03363671183797,
+        1.033339814869913, 1.0330264917845606, 1.0327170516238076, 1.032430336597092,
+        1.032180534592551, 1.0319749509532634, 1.0318130902243279, 1.0316871541365074,
+        1.0315838102339987, 1.031486867513628, 1.031380346202821, 1.0312513731110382,
+        1.0310923819083597, 1.0309022408893016, 1.030686141911386, 1.030454321229441,
+        1.030219898366191, 1.029996271285694, 1.0297945686328962, 1.0296216263038431,
+        1.0294788386830167, 1.0293620609317928, 1.0292625413962329, 1.0291686774263538,
+        1.0290682450102073, 1.0289506764473506, 1.0288089635376938, 1.0286408452249411,
+        1.028449082254775, 1.0282407985825333, 1.0280260446107958, 1.0278158766167076,
+        1.0276203245317812, 1.0274466250052001, 1.0272980318345675, 1.0271733974050266,
+        1.0270675709070145, 1.0269725092112176, 1.0268788705776186, 1.0267777811699093,
+        1.0266624429145716, 1.0265292914885125, 1.0263785066559439, 1.0262138050595504,
+        1.026041582444521, 1.025869591401925, 1.025705419818177, 1.025555061133954,
+        1.0254218381932918, 1.025305866349527, 1.0252041348986243, 1.0251111693834745,
+        1.0250201319602814, 1.0249241411787058, 1.0248175589963096, 1.024697006787293,
+        1.0245619299748991, 1.0244146209056055, 1.024259713771937, 1.024103263412486,
+        1.0239515931521717, 1.023810132614185, 1.0236824596958851, 1.0235697150192682,
+        1.0234704824700607, 1.0233811407506552, 1.0232966046581176, 1.0232113063638664,
+        1.0231202280509843, 1.0230197941277523, 1.022908463598351, 1.0227869241637593,
+        1.0226578670372104, 1.022525400148243, 1.0223942224189695, 1.0222687213783745,
+        1.0221521642173093, 1.0220461284822084, 1.0219502688290156, 1.0218624508271326,
+        1.0217792141796378, 1.021696468379031, 1.0216102841422274, 1.0215176305951577,
+        1.021416922871248, 1.0213082841297358, 1.0211934820135513, 1.0210755612725426,
+        1.0209582498914591, 1.0208452553607643, 1.0207395840118492, 1.0206430075450625,
+        1.0205557696942582, 1.0204765790064911, 1.02040288008284, 1.0203313452102067,
+        1.0202584900641931, 1.0201812976064426, 1.0200977364645445, 1.0200070829977357,
+        1.0199099951411055, 1.0198083333281105, 1.0197047702843836, 1.0196022686459016,
+        1.0195035266432668, 1.0194104942159774, 1.0193240452810948, 1.0192438602838592,
+        1.0191685329180735, 1.019095873592361, 1.0190233472933512, 1.0189485610316942,
+        1.0188697097324526, 1.018785899934062, 1.0186972955967335, 1.0186050646958105,
+        1.0185111424639244, 1.0184178601918346, 1.0183275114563588, 1.0182419366721915,
+        1.0181622008527182, 1.0180884200941795, 1.0180197635812303, 1.0179546253581853,
+        1.0178909296831573, 1.0178265108563234, 1.0177594968633148, 1.0176886277381059,
+        1.0176134535628125, 1.0175343805723145, 1.0174525623408945, 1.01736966112943,
+        1.0172875270514743, 1.0172078558590563, 1.0171318878251798, 1.017060200551199,
+        1.0169926297282672, 1.016928327649689, 1.0168659441319823, 1.0168038929705605,
+        1.0167406528540688, 1.0166750470939403, 1.0166064521203302, 1.016534899135253,
+        1.0164610537240706, 1.0163860807252445, 1.016311422105831, 1.0162385303597397,
+        1.016168606577906, 1.0161023899421338, 1.0160400347321812, 1.0159810942123502,
+        1.0159246111639815, 1.0158692959193856, 1.015813757846109, 1.0157567478295186,
+        1.0156973686859385, 1.015635217474874, 1.01557043687659, 1.0155036696163022,
+        1.015435927233502, 1.015368399214471, 1.0153022381063148, 1.0152383592011776,
+        1.0151772894483864, 1.0151190903779987, 1.0150633659590371, 1.0150093510418137,
+        1.0149560620599252, 1.0149024813801872, 1.0148477417521655, 1.0147912784005215,
+        1.0147329230301259, 1.014672925008721, 1.0146118981864034, 1.0145507048201203,
+        1.0144902986330087, 1.014431555406484, 1.0143751207367615, 1.0143213006775007,
+        1.0142700128125672, 1.0142208044268892, 1.0141729328254967, 1.0141254924909218,
+        1.0140775663701467, 1.0140283752785164, 1.0139774006007447, 1.0139244607812543,
+        1.013869730472037, 1.013813701113063, 1.0137570914322762, 1.0137007242560774,
+        1.0136453908847616, 1.0135917254521702, 1.0135401091461287, 1.0134906185209644,
+        1.0134430244634418, 1.0133968400235345, 1.013351407667004, 1.0133060107292973,
+        1.013259990761243, 1.013212852389775, 1.013164340101624, 1.013114476383785,
+        1.0130635569923112, 1.0130121057010921, 1.0129607966736571, 1.0129103567817497,
+        1.0128614622628003, 1.0128146439399124, 1.0127702130559126, 1.0127282161150164,
+        1.012688422671314, 1.0126503454822815, 1.0126132885099026, 1.0125764153818395,
+        1.0125388293746533, 1.0124996557695771, 1.0124581183728567, 1.0124136037563314,
+        1.0123657089603904, 1.0123142706217696, 1.0122593754293971, 1.01220135327513,
+        1.012140755387885, 1.0120783201705712, 1.012014929533332, 1.011951558404363,
+        1.0118892199590288, 1.011828909049327, 1.0117715463785075, 1.0117179261167495,
+        1.011668669804056, 1.011624189417948, 1.0115846622838407, 1.0115500199988814,
+        1.0115199527084051, 1.011493928967982, 1.0114712301539939, 1.0114509971058976,
+        1.0114322855614493, 1.0114141261360465, 1.0113955842090965, 1.0113758151644319,
+        1.011354110970108, 1.0113299349951452, 1.0113029431205218, 1.0112729904590947,
+        1.0112401242075966, 1.0112045641907952, 1.011166673442079, 1.0111269216610668,
+        1.011085844605032, 1.011044002447349, 1.0110019399283436, 1.0109601507883756,
+        1.0109190485541804, 1.010878945272567, 1.01084003926028, 1.0108024123616621,
+        1.010766036577255, 1.0107307892564612, 1.010696475369203, 1.0106628547402556,
+        1.01062967162163, 1.0105966836757765, 1.0105636874206378, 1.01053053749404,
+        1.0104971577356905, 1.010463543013259, 1.0104297518365366, 1.0103958909701445,
+        1.0103620943072098, 1.01032849904431, 1.0102952225716437, 1.0102623433871738,
+        1.0102298887556247, 1.0101978308348358, 1.0101660917236983, 1.0101345565361963,
+        1.0101030923825838, 1.0100715702348415, 1.0100398862154847, 1.0100079789512348,
+        1.0099758402636039, 1.0099435175303455, 1.0099111073754508, 1.009878741719176,
+        1.009846568421625, 1.0098147295904036, 1.0097833409612265, 1.0097524755488407,
+        1.0097221540435208, 1.009692343318254, 1.0096629630989988, 1.0096338995513263,
+        1.009605023463005, 1.009576210025296, 1.0095473570391882, 1.0095183987159229,
+        1.0094893130367664, 1.0094601217441261, 1.0094308832653318, 1.0094016800155736,
+        1.0093726024004988, 1.0093437323043493, 1.0093151288400803, 1.0092868186686672,
+        1.0092587923567398, 1.0092310071847956, 1.0092033957249287, 1.009175878560111,
+        1.009148378870097, 1.0091208363605713, 1.0090932181913579, 1.0090655251238347,
+        1.009037791950573, 1.009010082243575, 1.0089824783949028, 1.0089550686714406,
+        1.008927933446544, 1.0089011328435642, 1.0088746977308554, 1.0088486254072861,
+        1.0088228805210429, 1.008797400910526, 1.0087721072857394, 1.0087469151032955,
+        1.008721746710524, 1.008696541876422, 1.0086712651670344, 1.0086459091915039,
+        1.0086204934395782, 1.0085950591338184, 1.0085696611176167, 1.0085443582040532,
+        1.00851920356762, 1.0084942366612932, 1.0084694778171575, 1.008444926205408,
+        1.0084205612707615, 1.0083963472287407, 1.0083722397686672, 1.0083481938349734,
+        1.0083241712729045, 1.0083001472254367, 1.0082761144239154, 1.0082520848719398,
+        1.0082280888176554, 1.0082041712812488, 1.0081803867006733, 1.0081567924464303,
+        1.0081334420230041, 1.0081103787291539, 1.0080876304152933, 1.0080652057880664,
+        1.0080430925055464, 1.0080212571126705, 1.0079996467078436, 1.0079781921181359,
+        1.007956812291751, 1.0079354195831423, 1.0079139255948915, 1.0078922472381293,
+        1.0078703126708828, 1.0078480667685275, 1.0078254757769773, 1.0078025308062937,
+        1.0077792498523446, 1.0077556780965757, 1.0077318863343883, 1.0077079675187424,
+        1.0076840315666358, 1.0076601987445777, 1.0076365921024708, 1.0076133295407956,
+        1.007590516154413, 1.0075682374859174, 1.0075465542407382, 1.007525498873699,
+        1.0075050742711649, 1.0074852545485193, 1.0074659877866767, 1.0074472003682264,
+        1.0074288024618145, 1.0074106941520076, 1.0073927717202726, 1.0073749336408158,
+        1.0073570859463712, 1.0073391467239616, 1.0073210496003853, 1.0073027461582214,
+        1.007284207277934, 1.007265423431445, 1.0072464039647386, 1.007227175413533,
+        1.0072077789095972, 1.0071882667660133, 1.007168698381711, 1.0071491356759699,
+        1.007129638341673, 1.007110259275633, 1.007091040587004, 1.0070720105832873,
+        1.0070531820772455, 1.0070345522444055, 1.0070161040988648, 1.0069978094633425,
+        1.0069796331147416, 1.0069615376192327, 1.0069434882599637, 1.0069254574279514,
+        1.0069074279032255, 1.0068893945956472, 1.00687136452553, 1.006853355073575,
+        1.0068353907802314, 1.006817499187755, 1.0067997063590657, 1.0067820327530748,
+        1.0067644900770185, 1.0067470795811344, 1.0067297920331582, 1.0067126093455045,
+        1.0066955075690276, 1.0066784607551695, 1.0066614450575513, 1.0066444424152206,
+        1.0066274432371078, 1.0066104476774824, 1.0065934653266457, 1.0065765134008127,
+        1.006559613757247, 1.0065427892454706, 1.0065260600031516, 1.0065094403011852,
+        1.006492936438665, 1.0064765460039784, 1.0064602585849525, 1.0064440577690343,
+        1.006427924064065, 1.006411838226359, 1.0063957844280822, 1.006379752737859,
+        1.0063637405180055, 1.0063477525350355, 1.0063317998031067, 1.0063158973942459,
+        1.006300061618618, 1.006284307074641, 1.0062686440779598, 1.0062530769003248,
+        1.00623760309983, 1.0062222140298458, 1.0062068964096798, 1.0061916346606703,
+        1.0061764135873739, 1.0061612209345119, 1.0061460493832468, 1.0061308976574181,
+        1.0061157705713863, 1.0061006780372344, 1.006085633227374, 1.0060706502288614,
+        1.0060557416043583, 1.006040916280035, 1.0060261781133242, 1.0060115253671424,
+        1.0059969511549387, 1.0059824447519943, 1.0059679935219086, 1.0059535851081205,
+        1.005939209504377, 1.0059248606499471, 1.0059105372878887, 1.0058962429597673,
+        1.0058819851638994, 1.0058677738487234, 1.0058536195237728, 1.0058395313293766,
+        1.0058255154038707, 1.0058115738258733, 1.0057977043010802, 1.0057839006284908,
+        1.0057701538436936, 1.005756453821352, 1.0057427910443546, 1.0057291582256744,
+        1.0057155515028295, 1.0057019710067499, 1.005688420721186, 1.0056749076748506,
+        1.005661440623786, 1.0056480284662876, 1.0056346786730088, 1.0056213960047824,
+        1.0056081817333098, 1.0055950334865027, 1.005581945728113, 1.0055689107705381,
+        1.0055559201295512, 1.005542965975428, 1.005530042425064, 1.0055171464546175,
+        1.005504278284774, 1.0054914411871203, 1.0054786407627931, 1.0054658838355615,
+        1.005453177164906, 1.0054405262104624, 1.0054279341636463, 1.0054154014093166,
+        1.0054029255003376, 1.0053905016354225, 1.0053781235424653, 1.0053657846008464,
+        1.005353478998566, 1.0053412027192354, 1.00532895418922, 1.0053167344791452,
+        1.0053045470350452, 1.0052923969975711, 1.0052802902384008, 1.005268232289431,
+        1.0052562273545944, 1.0052442775749904, 1.0052323826693743, 1.005220540003351,
+        1.0052087450644516, 1.0051969922499593, 1.005185275822333, 1.0051735908616417,
+        1.0051619340495845, 1.0051503041534944, 1.0051387021346814, 1.0051271308730396,
+        1.0051155945670682, 1.005104097923413, 1.0050926452836177, 1.0050812398425728,
+        1.00506988309278, 1.005058574585307, 1.005047312040363, 1.0050360917782197,
+        1.0050249093860324, 1.005013760496937, 1.0050026415415383, 1.0049915503404458,
+        1.0049804864377399, 1.0049694511233311, 1.0049584471478312, 1.0049474781873302,
+        1.0049365481576207, 1.0049256605012162, 1.0049148175720808, 1.0049040202227484,
+        1.0048932676606404, 1.0048825575917815, 1.0048718866197428, 1.0048612508241557,
+        1.0048506464139713, 1.0048400703405653, 1.004829520765829, 1.0048189973084793,
+        1.0048085010323402, 1.0047980341861784, 1.0047875997474451, 1.004777200854756,
+        1.0047668402308834, 1.0047565196967216, 1.0047462398580007, 1.0047360000142154,
+        1.0047257982991558, 1.0047156320219572, 1.0047054981435448, 1.0046953938016239,
+        1.00468531679128, 1.004675265918517, 1.0046652411682924, 1.004655243662374,
+        1.0046452754194868, 1.0046353389640863, 1.0046254368552157, 1.0046155712187828,
+        1.0046057433639846, 1.0045959535479667, 1.0045862009256976, 1.0045764836892146,
+        1.0045667993678138, 1.0045571452338928, 1.0045475187425648, 1.0045379179293021,
+        1.0045283416990944, 1.0045187899610055, 1.0045092635895874, 1.0044997642246816,
+        1.004490293948334, 1.0044808548972506, 1.0044714488786177, 1.004462077054375,
+        1.004452739745603, 1.0044434363866506, 1.0044341656323346, 1.0044249255954447,
+        1.0044157141702845, 1.0044065293847404, 1.0043973697200896, 1.0043882343450736,
+        1.0043791232266817, 1.004370037102037, 1.0043609773195699, 1.0043519455795074,
+        1.0043429436197004, 1.0043339729008127, 1.0043250343434156, 1.004316128159595,
+        1.0043072538047144, 1.0042984100545307, 1.0042895951919353, 1.0042808072701879,
+        1.0042720444078685, 1.0042633050669838, 1.0042545882698362, 1.0042458937215584,
+        1.0042372218214304, 1.0042285735645087, 1.0042199503525073, 1.0042113537467274,
+        1.0042027852038036, 1.0041942458363267, 1.0041857362349051, 1.0041772563773215,
+        1.0041688056358504, 1.0041603828782493, 1.0041519866437296], [3.9980507233411785e-08,
+        1.2005287354526802e-07, 2.0045987252748267e-07, 2.8142646956038477e-07,
+        3.6318045272560437e-07, 4.459536128345956e-07, 5.299829168050148e-07,
+        6.155117550598931e-07, 7.027912190450364e-07, 7.920814457160457e-07,
+        8.836530328304635e-07, 9.777885406458399e-07, 1.0747840823467674e-06,
+        1.1749510333974134e-06, 1.2786178582589057e-06, 1.3861320844105949e-06,
+        1.497862433410992e-06, 1.614201132226515e-06, 1.7355664295151335e-06,
+        1.862405333915513e-06, 1.9951966149774165e-06, 2.1344540822361966e-06,
+        2.2807301892561866e-06, 2.434619995876125e-06, 2.5967655328403204e-06,
+        2.7678606165577636e-06, 2.9486561748068458e-06, 3.1399661371477546e-06,
+        3.342673969691857e-06, 3.557739923949767e-06, 3.7862091045924668e-06,
+        4.029220442424638e-06, 4.288016705397901e-06, 4.563955669931491e-06,
+        4.858522614709427e-06, 5.1733443030212025e-06, 5.5102046632589785e-06,
+        5.871062387691679e-06, 6.258070725676767e-06, 6.673599762732746e-06,
+        7.120261551406139e-06, 7.600938485666982e-06, 8.118815404941692e-06,
+        8.677415959976836e-06, 9.28064389440463e-06, 9.932829956283945e-06,
+        1.0638785350284261e-05, 1.1403862687700963e-05, 1.2234025692666023e-05,
+        1.3135929009863531e-05, 1.4117009811815001e-05, 1.5185593158951677e-05,
+        1.6351013431499927e-05, 1.7623754636205694e-05, 1.9015612898524677e-05,
+        2.0539885116672793e-05, 2.221158861878279e-05, 2.404771757998181e-05,
+        2.6067543305554493e-05, 2.829296695812929e-05, 3.074893529210593e-05,
+        3.346393242435453e-05, 3.64705637737287e-05, 3.980625230599276e-05,
+        4.351407238467098e-05, 4.764375326602526e-05, 5.225289306043275e-05,
+        5.740843574908899e-05, 6.318847963279585e-05, 6.968450696308435e-05,
+        7.700415414758098e-05, 8.527468336579852e-05, 9.46473755434505e-05,
+        0.00010530315019809191, 0.00011745984494519793, 0.0001313817798796313,
+        0.00014739253219822601, 0.00016589232628231402, 0.00018738223936804735,
+        0.00021249878772397173, 0.0002420649021874314, 0.0002771679009892037,
+        0.0003192842296571714, 0.00037049028317976616, 0.0004338439448543182,
+        0.0005141380989128867, 0.0006195710577637337, 0.0007660987987678909,
+        0.0009919568191798097, 0.0014339833864953494, 0.0047420125806389435,
+        0.0016281280599403044, 0.001306000651856862, 0.0012352680783726633,
+        0.001249672969228262, 0.001313820110712825, 0.0014177857234605334,
+        0.001560529365244749, 0.0017457131323468378, 0.001980635109579534,
+        0.0022763419995156984, 0.002648455366537384, 0.0031186911854362677,
+        0.0037172877589174993, 0.0044867987398288164, 0.005488077759582035,
+        0.006809940690847638, 0.008585256228918712, 0.0110187834074914,
+        0.01443761815028865, 0.019387974428662642, 0.026834650921826443,
+        0.038612187125429125, 0.058582350628526896, 0.09619680204237482,
+        0.18117874727718503, 0.4717091712309206, 6.765692770159037, 0.7452647885683333,
+        0.7378022226123298, 0.9094563926437228, 0.7448845713964546, 1.0054529705656345,
+        1.9856261048260957, 2.64347147141612, 1.2300275614390777, 0.8335246838357708,
+        0.7346133601016925, 0.8591431729118385, 1.3041303068077954, 1.1486292043676796,
+        0.8915231551133082, 0.8511667610443825, 0.944300791172329, 1.1881906038525016,
+        1.6661194951135063, 2.1114701654238264, 1.673610695288305, 1.1783391064174453,
+        0.9187222125282913, 0.8036507554041246, 0.7909986390997507, 0.887310314965107,
+        1.1072868992634959, 1.2682609359324688, 1.1412907139537851, 0.9878945977238817,
+        0.9234232240323746, 0.9384286781141296, 1.02833365208202, 1.2070292685858273,
+        1.486328617266613, 1.7444605352650833, 1.6354170501364287, 1.2763192458039145,
+        0.9856208965552121, 0.8047912633606293, 0.8051576873754318, 0.8735635608796805,
+        0.9649705390647556, 1.0629456536263169, 1.1327489690224695, 1.148424647401852,
+        1.119692372193393, 1.0765278088193895, 1.041777452324759, 1.0256500151605858,
+        1.031026260450995, 1.0575943872969353, 1.1029287035937723, 1.1612941988486298,
+        1.221237964523692, 1.2646900653252662, 1.2725142052803968, 1.2366308747300305,
+        1.166352010101487, 1.0802044214130757, 0.9940372245212981, 0.916552746815106,
+        0.8507987862323583, 0.7968300427500933, 0.7535393641645416, 0.7195869629296213,
+        0.6937869703358612, 0.6752297521936774, 0.6632916986645561, 0.657604750051215,
+        0.6580170449514582, 0.6645558252639929, 0.6773929584269681, 0.696806379211216,
+        0.7231243275477973, 0.756631843698893, 0.7974109907747108, 0.8450830796998515,
+        0.8984388767912337, 0.9550126303478064, 1.0108065491492164, 1.060551756502229,
+        1.0988546031028654, 1.122019437626544, 1.1295218360201909, 1.1240585651877348,
+        1.1102020889986752, 1.0927040505568935, 1.0753685424329844, 1.0606781654167259,
+        1.0498946661183832, 1.0433270736066589, 1.0406014412952354, 1.040887543059406,
+        1.043095622439183, 1.046065929034324, 1.0487564401847327, 1.0504082186287962,
+        1.0506515506115002, 1.0495226657839165, 1.0473887647952718, 1.0448106466052127,
+        1.042388016039624, 1.0406268964760852, 1.0398506956201845, 1.040159344232871,
+        1.0414314296022706, 1.0433616921847346, 1.0455262573054023, 1.0474665968605295,
+        1.048779327287742, 1.049194687021678, 1.048625878347134, 1.0471772485475728,
+        1.0451105153666855, 1.0427801064445483, 1.040555826046691, 1.0387512344495429,
+        1.0375710597833485, 1.0370842595312273, 1.0372237663435893, 1.0378102202154569,
+        1.038594369081273, 1.039310413024172, 1.0397303411513776, 1.0397082834888973,
+        1.039205399041528, 1.038290285739656, 1.0371161651273904, 1.0358818590615004,
+        1.0347867604983059, 1.0339899303230038, 1.0335809465465333, 1.0335666537506807,
+        1.0338746549284656, 1.0343716832308123, 1.0348928200202554, 1.0352758058119247,
+        1.035393655150659, 1.0351789332210537, 1.0346347550385149, 1.033830644009596,
+        1.0328849852966546, 1.031938774698757, 1.0311268270689191, 1.0305523819377007,
+        1.0302695685341832, 1.0302761589698077, 1.0305170078673485, 1.0308968257816584,
+        1.0312995381087708, 1.0316104927187117, 1.0317373364245064, 1.0316256689584018,
+        1.0312666847117542, 1.0306957568219768, 1.0299828712080006, 1.029217439973731,
+        1.028490903171299, 1.0278805434594769, 1.0274372540113232, 1.0271789313573139,
+        1.027090017555315, 1.0271266930287077, 1.0272264184181368, 1.0273199788450997,
+        1.0273439256133499, 1.0272513699598058, 1.0270194695184178, 1.0266526085278616,
+        1.0261810791474117, 1.0256558451394826, 1.0251405409396028, 1.0247021276373198,
+        1.0244015891345828, 1.024285787189239, 1.0243812243741597, 1.0246901028683832,
+        1.025188788028884, 1.0258286121096025, 1.0265388660734704, 1.027231781699479,
+        1.0278092518505535, 1.0281709355888147, 1.0282232346631544, 1.027888430707465,
+        1.0271130927752867, 1.0258747755260813, 1.0241860955088318, 1.022095526505352,
+        1.01968466858582, 1.0170622379995478, 1.0143554843130285, 1.0117000640158638,
+        1.0092295262061486, 1.0070654950847582, 1.0053094148442214, 1.0040364286469026,
+        1.0032916647012473, 1.0030889464531778, 1.003411750312674, 1.0042161010481105,
+        1.005435009283291, 1.0069840047424576, 1.008767296573754, 1.0106840987155952,
+        1.0126346971173759, 1.0145259069937158, 1.0162756646346125, 1.0178166037176004,
+        1.0190985602229023, 1.0200900155705748, 1.0207785171099768, 1.0211701151160606,
+        1.0212878440471727, 1.02116927583276, 1.0208632026928115, 1.0204255729278946,
+        1.019914897155269, 1.0193874447007467, 1.018892635004935, 1.0184690735937254,
+        1.0181416701405122, 1.0179202004855572, 1.0177995373366213, 1.0177615863092693,
+        1.0177787439114234, 1.0178184700740334, 1.0178483764121453, 1.0178411133322511,
+        1.0177783301903416, 1.0176531015702601, 1.0174704503566625, 1.0172459150121143,
+        1.017002442007476, 1.0167661663706877, 1.0165618184624514, 1.016408534511334,
+        1.0163167533607824, 1.0162866778937811, 1.0163085066871682, 1.0163643447563997,
+        1.0164314265037986, 1.0164860704724847, 1.0165076690150983, 1.0164820194099613,
+        1.0164034303201674, 1.0162752687118133, 1.016108903921154, 1.0159212991324504,
+        1.0157317372932377, 1.0155583041214413, 1.0154147652607348, 1.0153083736761224,
+        1.015238953579405, 1.0151993671606643, 1.0151772227876144, 1.0151574688129839,
+        1.015125370245974, 1.0150693107229598, 1.0149829093790907, 1.0148660831540899,
+        1.0147248927917993, 1.014570243921054, 1.0144157263745024, 1.0142750243204819,
+        1.0141593909758075, 1.0140756484016444, 1.0140250575315328, 1.0140032320971823,
+        1.0140010755838171, 1.0140065370736264, 1.014006840671293, 1.0139907676444735,
+        1.013950573073866, 1.013883198619354, 1.0137905842763466, 1.0136790566244933,
+        1.013557944206506, 1.0134377085194821, 1.0133279564966815, 1.0132357057759245,
+        1.0131642107462697, 1.0131125410573587, 1.0130759587758478, 1.013046992728108,
+        1.0130169846743313, 1.0129778028753158, 1.0129233974705807, 1.012850911760167,
+        1.0127611556021738, 1.0126583732032932, 1.0125493724727785, 1.0124422004411806,
+        1.0123446270857543, 1.012262725268863, 1.0121998053647228, 1.0121558878549402,
+        1.012127791792024, 1.01210980182417, 1.0120947722597886, 1.012075451530612,
+        1.012045777044253, 1.0120019039399095, 1.0119427882339518, 1.0118702336488559,
+        1.0117884143916724, 1.0117029831697668, 1.011619946479322, 1.0115445249034354,
+        1.0114802098730022, 1.011428183350867, 1.0113871933675893, 1.0113538909018556,
+        1.0113235485335177, 1.011291013743269, 1.011251711300607, 1.0112025060813792,
+        1.0111422696143262, 1.0110720538864344, 1.0109948523727739, 1.0109150059364291,
+        1.0108373753869226, 1.0107664414867548, 1.010705500813887, 1.0106561021288094,
+        1.0106178185571808, 1.0105883860774896, 1.0105641708149922, 1.010540868815866,
+        1.0105143025946144, 1.0104811653869985, 1.0104395784665754, 1.0103893657363356,
+        1.010332005216719, 1.0102702781631479, 1.0102076916970124, 1.010147789893312,
+        1.0100934845820557, 1.0100465286240885, 1.0100072237489166, 1.0099744087208715,
+        1.0099457206410665, 1.0099180723792516, 1.0098882513238654, 1.0098535253062435,
+        1.0098121436991052, 1.0097636443530251, 1.009708915493457, 1.0096500083782767,
+        1.0095897424747344, 1.0095311816265964, 1.0094770806771471, 1.0094294040321379,
+        1.0093890010896691, 1.0093554920965926, 1.0093273780634964, 1.0093023473777567,
+        1.0092777170835379, 1.009250924468099, 1.0092199782587739, 1.0091837890847397,
+        1.0091423235323544, 1.0090965601811928, 1.009048262890886, 1.008999619422625,
+        1.0089528163252726, 1.0089096300757687, 1.008871108624275, 1.0088373984101924,
+        1.0088077435547997, 1.0087806517526396, 1.008754191286239, 1.0087263609043624,
+        1.0086954628750757, 1.0086604110769286, 1.0086209198685288, 1.0085775427960597,
+        1.008531558422499, 1.0084847283758744, 1.008438975049145, 1.0083960393622464,
+        1.0083571806072102, 1.00832297078021, 1.0082932171161678, 1.0082670224658457,
+        1.0082429681802516, 1.0082193827691273, 1.0081946454723245, 1.0081674693153329,
+        1.0081371137392572, 1.0081034912019864, 1.008067152392327, 1.0080291570351863,
+        1.007990857585739, 1.0079536378136227, 1.0079186549193284, 1.0078866315130453,
+        1.0078577332737888, 1.0078315515745693, 1.0078071909635677, 1.007783442667079,
+        1.0077590105162026, 1.0077327473783082, 1.0077038595669718, 1.0076720436796862,
+        1.0076375333945657, 1.0076010504221729, 1.007563670967687, 1.007526633637443,
+        1.0074911242210776, 1.0074580756981775, 1.0074280178874049, 1.0074010013270125,
+        1.0073766061913307, 1.0073540318604948, 1.0073322488644858, 1.007310184687251,
+        1.0072869099951967, 1.0072617929220353, 1.0072345957102131, 1.0072054989234795,
+        1.0071750515524016, 1.0071440582676643, 1.0071134255874767, 1.0070839950796833,
+        1.0070563929793277, 1.0070309217556215, 1.007007511075974, 1.006985734844237,
+        1.0069648894775611, 1.0069441183154315, 1.0069225597171942, 1.0068994931273327,
+        1.006874458570029, 1.0068473303032304, 1.006818333670013, 1.0067880040103825,
+        1.00675709612705, 1.006726460632566, 1.006696908319507, 1.0066690848365056,
+        1.0066433754124227, 1.0066198537495514, 1.0065982815752628, 1.00657815703545,
+        1.0065588024990688, 1.0065394765950155, 1.0065194922272174, 1.006498322242741,
+        1.0064756771933923, 1.0064515446267386, 1.0064261856454935, 1.0064000910211721,
+        1.0063739049147113, 1.0063483284249863, 1.0063240172568293, 1.006301487647955,
+        1.0062810425496953, 1.0062627264334114, 1.0062463126768297, 1.0062313229974709,
+        1.0062170744916563, 1.0062027469842338, 1.006187461849693, 1.0061703632491381,
+        1.0061506936555793, 1.0061278572839982, 1.0061014672064332, 1.0060713741299714,
+        1.0060376767356534, 1.0060007149234917, 1.0059610482183827, 1.0059194220151595,
+        1.0058767244114974, 1.0058339362644158, 1.0057920769668407, 1.0057521483845517,
+        1.0057150794599707, 1.0056816741446744, 1.0056525654781647, 1.0056281786687638,
+        1.0056087058414118, 1.0055940946203952, 1.005584051895236, 1.0055780630241415,
+        1.005575425471611, 1.0055752946075565, 1.005576738281384, 1.0055787959786624,
+        1.0055805379797456, 1.0055811200195175, 1.0055798294772793, 1.0055761200263023,
+        1.0055696328184096, 1.005560203521443, 1.0055478557213382, 1.0055327822242517,
+        1.0055153165672521, 1.0054958975339734, 1.0054750296822552, 1.0054532428643763,
+        1.0054310535124742, 1.0054089301283302, 1.0053872650020685, 1.0053663537135014,
+        1.00534638345215, 1.0053274306240272, 1.0053094675949457, 1.0052923777613478,
+        1.0052759774727293, 1.0052600427096763, 1.0052443379231404, 1.005228644146252,
+        1.005212783473826, 1.0051966373140242, 1.005180156456927, 1.0051633619296048,
+        1.0051463367188826, 1.0051292096017632, 1.0051121333669903, 1.0050952604807564,
+        1.0050787196159372, 1.0050625963533346, 1.0050469207716681, 1.0050316636426302,
+        1.0050167416781524, 1.0050020309270882, 1.0049873861946526, 1.0049726634526508,
+        1.0049577417679088, 1.004942541374531, 1.0049270351409398, 1.004911251738571,
+        1.0048952701373663, 1.0048792064227388, 1.0048631951288778, 1.0048473681213326,
+        1.0048318344047094, 1.0048166640275256, 1.0048018785446342, 1.0047874493997206,
+        1.004773304290347, 1.0047593402908694, 1.0047454414447305, 1.0047314978676882,
+        1.0047174232303413, 1.004703167831014, 1.0046887252619698, 1.0046741317726984,
+        1.0046594586552966, 1.0046447991137046, 1.00463025194462, 1.004615904816711,
+        1.004601819920538, 1.0045880242894283, 1.0045745062522857, 1.0045612184223485,
+        1.0045480865329388, 1.0045350224845917, 1.0045219393204465, 1.004508765596823,
+        1.0044954567926168, 1.0044820019621996, 1.0044684246760345, 1.0044547782635915,
+        1.0044411363088002, 1.004427580096115, 1.0044141851482118, 1.0044010090725555,
+        1.0043880826445861, 1.0043754054617897, 1.0043629467144997, 1.00435065077285,
+        1.0043384465255423, 1.004326258845797, 1.0043140202852967, 1.0043016811398897,
+        1.0042892163695012, 1.0042766284202786, 1.0042639456873512, 1.0042512170541695,
+        1.004238503537372, 1.0042258684655707, 1.004213367773793, 1.0042010418930658,
+        1.0041889103884958, 1.0041769700148488, 1.0041651963022742, 1.0041535482479333,
+        1.004141975253382, 1.0041304251717855, 1.0041188522427593, 1.004107223792503,
+        1.0040955248315133, 1.004083760038484, 1.0040719530141864, 1.004060143060922,
+        1.0040483800402489, 1.0040367180510628, 1.0040252087390926, 1.0040138950061646,
+        1.0040028057566084, 1.0039919521330172, 1.00398132548969, 1.0039708971606274,
+        1.0039606199220799, 1.0039504309373768, 1.0039402559035782, 1.0039300140862317,
+        1.003919623916767, 1.003909008823889, 1.0038981029667593, 1.0038868565311807,
+        1.0038752402448707, 1.0038632487733252, 1.0038509026858948, 1.0038382487422999,
+        1.0038253583484116, 1.0038123241644124, 1.0037992550078603, 1.0037862693612563,
+        1.0037734879459401, 1.0037610259390675, 1.003748985468724, 1.0037374490123279,
+        1.0037264742436065, 1.0037160907323672, 1.0037062987172465, 1.0036970699690437,
+        1.00368835056794, 1.0036800652563669, 1.0036721229186203, 1.0036644226879246,
+        1.0036568601906346, 1.003649333495632, 1.0036417484282865, 1.0036340230130023,
+        1.0036260909076693, 1.003617903773905, 1.003609432581125, 1.0036006678717693,
+        1.0035916190265228, 1.003582312574235, 1.0035727896041258, 1.0035631023677984,
+        1.0035533102099516, 1.0035434750362489, 1.003533656604307, 1.0035239079928133,
+        1.0035142716462062, 1.003504776390945, 1.0034954357635246, 1.0034862478774962,
+        1.0034771968957026, 1.0034682559833112, 1.003459391423705, 1.0034505674131355,
+        1.003441750939975, 1.003432916122454, 1.0034240474354184, 1.0034151413988643,
+        1.0034062065111387, 1.0033972614584088, 1.0033883318817078, 1.0033794461952459,
+        1.0033706310898356, 1.0033619074004057, 1.0033532869573192, 1.0033447708860697,
+        1.0033363495923977, 1.0033280044056017, 1.0033197105942155, 1.003311441256343,
+        1.0033031714561549, 1.003294881948921, 1.003286561913751, 1.0032782102826805,
+        1.003269835488384, 1.003261453711707, 1.0032530859517312, 1.0032447544255592,
+        1.0032364789028752, 1.003228273576742, 1.003220144969161, 1.003212091186587,
+        1.0032041026085707, 1.0031961638520506, 1.0031882566444696, 1.003180363095881,
+        1.0031724688059227, 1.003164565283491, 1.0031566512860868, 1.0031487328783868,
+        1.003140822231792, 1.0031329354000103, 1.0031250894743042, 1.0031172996179634,
+        1.0031095764883307, 1.0031019244765755, 1.003094341045834, 1.0030868172543845,
+        1.0030793393464181, 1.0030718911138157, 1.0030644566083227, 1.0030570227344102,
+        1.0030495812857225, 1.0030421300946435, 1.003034673125054, 1.0030272195239875,
+        1.003019781825853, 1.0030123736429977, 1.0030050072551477, 1.0029976915159873,
+        1.0029904304284023, 1.0029832226144018, 1.002976061744396, 1.002968937822438,
+        1.002961839078301, 1.0029547541187172, 1.0029476739544707, 1.0029405935519051,
+        1.0029335126496697, 1.0029264357161736, 1.0029193710763136, 1.0029123293799647,
+        1.0029053216950359, 1.0028983575661052, 1.0028914433769944, 1.0028845812942921,
+        1.0028777689606956, 1.0028709999725784, 1.002864265039016, 1.0028575536040452,
+        1.0028508556392772, 1.0028441632924434, 1.0028374721110984, 1.002830781642354,
+        1.0028240953235532, 1.0028174197045943, 1.0028107631577683, 1.0028041343157736,
+        1.002797540519037, 1.0027909865436826, 1.0027844738245775, 1.0027780002950657,
+        1.002771560853456, 1.0027651483561304, 1.0027587549474473, 1.0027523734826607,
+        1.002745998790313, 1.0027396285554582, 1.002733263677426, 1.002726908051898,
+        1.0027205678293791, 1.0027142502927235, 1.0027079625594466, 1.0027017103400842,
+        1.0026954969681172, 1.0026893228639688, 1.0026831855155327, 1.0026770799652858,
+        1.0026709997058725, 1.0026649378173544, 1.0026588881416534, 1.0026528462887896,
+        1.0026468103046429, 1.0026407808937157, 1.0026347611712623, 1.0026287560021712,
+        1.0026227710546534, 1.002616811743259, 1.00261088225018, 1.0026049847948706,
+        1.0025991192737196, 1.0025932833231836, 1.0025874727839976, 1.002581682474112,
+        1.0025759071262443, 1.0025701423206526, 1.0025643852489496, 1.0025586351785174,
+        1.0025528935428754, 1.0025471636507184, 1.0025414500732797, 1.0025357578244056,
+        1.0025300914810924, 1.0025244543988587, 1.0025188481558864, 1.002513272316543,
+        1.0025077245469658, 1.0025022010532072, 1.0024966972572544, 1.0024912085870816,
+        1.002485731240572, 1.002480262791627, 1.0024748025379064, 1.002469351537612,
+        1.0024639123382997, 1.002458488454404, 1.0024530836923204, 1.0024477014457271,
+        1.0024423440855534, 1.0024370125489246, 1.0024317061937817, 1.0024264229375137,
+        1.0024211596477965, 1.0024159127105594, 1.0024106786709759, 1.0024054548333658,
+        1.0024002397159548, 1.002395033284453, 1.002389836928815, 1.0023846531932292,
+        1.0023794853119847, 1.0023743366361844, 1.0023692100530999, 1.0023641074985388,
+        1.0023590296438745, 1.0023539758070332, 1.002348944096663, 1.002343931758256,
+        1.0023389356569243, 1.0023339528098358, 1.00232898087516, 1.0023240185146192,
+        1.0023190655708758, 1.0023141230347328, 1.0023091928141674, 1.0023042773511013,
+        1.0022993791569157, 1.002294500349653, 1.002289642273336, 1.0022848052633149,
+        1.00227998859459, 1.0022751906173994, 1.0022704090518983, 1.0022656413870432,
+        1.0022608853122557, 1.0022561391066367, 1.0022514019197044, 1.0022466738979972,
+        1.002241956139359, 1.002237250486709, 1.0022325592001895, 1.0022278845661892,
+        1.00222322851106, 1.0022185922845537, 1.0022139762645428, 1.0022093799125553,
+        1.00220480188333, 1.0022002402655374, 1.0021956929092952, 1.0021911577828568,
+        1.0021866332975704, 1.0021821185474753, 1.0021776134258047, 1.0021731186025515,
+        1.0021686353710433, 1.00216416539329, 1.0021597103898598, 1.0021552718280926,
+        1.0021508506610082, 1.0021464471594297, 1.0021420608629328, 1.0021376906549084,
+        1.0021333349461599, 1.002128991934126, 1.00212465989324, 1.0021203374481387,
+        1.0021160237856412, 1.00211171877265, 1.0021074229632996, 1.002103137497062,
+        1.002098863906824, 1.002094603869772, 1.0020903589418542, 1.002086130317813,
+        1.0020819186532886, 1.0020777239745688, 1.0020735456869638, 1.0020693826772569,
+        1.0020652334914615], [1.7352110664150693e-08, 5.2106896153002676e-08,
+        8.701364473810568e-08, 1.2217454706379348e-07, 1.5769312050491136e-07,
+        1.936747633761096e-07, 2.3022730765696743e-07, 2.67461605709118e-07,
+        3.0549213235824414e-07, 3.4443761882777795e-07, 3.844217206974098e-07,
+        4.25573727218144e-07, 4.680293135570627e-07, 5.119313497690867e-07,
+        5.574307664726784e-07, 6.04687491041024e-07, 6.538714593519299e-07,
+        7.051637141221073e-07, 7.587576015923984e-07, 8.148600750522205e-07,
+        8.736931242011399e-07, 9.35495338363837e-07, 1.000523625533694e-06,
+        1.0690551033590322e-06, 1.1413891831740744e-06, 1.2178498699125795e-06,
+        1.2987883067409155e-06, 1.3845855902701701e-06, 1.475655893951828e-06,
+        1.5724499330079146e-06, 1.6754588201845268e-06, 1.7852183534789131e-06,
+        1.9023137980880335e-06, 2.027385220242497e-06, 2.1611334487168467e-06,
+        2.3043267416494994e-06, 2.4578082560326924e-06, 2.6225044218992086e-06,
+        2.7994343484620894e-06, 2.989720395964518e-06, 3.194600080265569e-06,
+        3.415439487895264e-06, 3.653748420931396e-06, 3.911197509961657e-06,
+        4.1896375861875215e-06, 4.4911216272584694e-06, 4.817929676192717e-06,
+        5.172597146443668e-06, 5.5579470549631175e-06, 5.9771267515254925e-06,
+        6.433649857512585e-06, 6.931444221267066e-06, 7.474906834366248e-06,
+        8.068966834912387e-06, 8.719157902593047e-06, 9.431701583666276e-06,
+        1.021360338499325e-05, 1.1072763766567555e-05, 1.2018106608567615e-05,
+        1.305972816964261e-05, 1.420907014758656e-05, 1.5479121154128093e-05,
+        1.688465175032281e-05, 1.8442489216646554e-05, 2.0171839481743936e-05,
+        2.2094665166943873e-05, 2.4236130548295545e-05, 2.6625126547770764e-05,
+        2.9294891702829266e-05, 3.2283748522541356e-05, 3.563597899572864e-05,
+        3.940286840640623e-05, 4.3643953373937286e-05, 4.84285184097728e-05,
+        5.383739602326484e-05, 5.996513874026494e-05, 6.692264860751864e-05,
+        7.484037133513363e-05, 8.387219018638815e-05, 9.420019065684928e-05,
+        0.000106040513119597, 0.0001196505710910489, 0.0001353379915107646,
+        0.00015347173689116587, 0.00017449600635779494, 0.00019894769476739533,
+        0.00022747843363370856, 0.00026088256713989623, 0.00030013286470929185,
+        0.000346426386653726, 0.00040124376718530863, 0.0004664263642514175,
+        0.0005442773914404085, 0.0006376955179290669, 0.000750352830042913,
+        0.0008869340087004201, 0.0010534608804944811, 0.0012577374227543553,
+        0.00150996685390804, 0.0018236179689147176, 0.0022166579389524496,
+        0.0027133329351507834, 0.0033467828951688717, 0.004162952818404681,
+        0.005226566511182101, 0.006630468780681944, 0.008510638005250886,
+        0.011071085598217869, 0.01462672334132331, 0.01968054624087819,
+        0.02707045299153589, 0.03826856078174097, 0.05604905060466489, 0.0861736152652099,
+        0.14248065836148485, 0.2674219611596907, 0.6803315399888152, 9.091333774678793,
+        0.7776989566571803, 0.17314668322995902, 1.862193177501464, 1.542354600328908,
+        1.9731107101682763, 3.630365223123942, 4.285308053000669, 1.5267105590562262,
+        0.36089064786044334, 1.3951104622003239, 5.642132520995871, 6.056596244320961,
+        4.267088135892596, 2.584167259604919, 1.9481450549468282, 1.7513991730456564,
+        1.833535904272878, 2.1941810770966446, 2.4406970829134185, 1.7623425915913504,
+        1.1914187730505177, 0.9537697547918811, 0.914625321778163, 1.0268333004992254,
+        1.3111738863087286, 1.7868975272975554, 2.1055928843135847, 1.851531165590182,
+        1.5182592526362049, 1.3265821361251833, 1.256722670297466, 1.287146105445405,
+        1.4196675032261203, 1.654365858601732, 1.854147773707951, 1.6802205728874686,
+        1.2900927752793956, 1.0069134378439446, 0.8685048378109561, 0.9570100885233461,
+        1.0672170346385366, 1.1950698619434599, 1.3214136585807557, 1.4033874965991533,
+        1.4108946426626432, 1.3597856481284487, 1.290133494757981, 1.2312469855796038,
+        1.1955904632405605, 1.1861505253037867, 1.2019603265034866, 1.239691462881453,
+        1.292510456406432, 1.347573186152028, 1.3851981226583847, 1.3849871028511238,
+        1.3387843933175536, 1.2570869504617757, 1.1599167650956725, 1.0640741957844102,
+        0.9785556731550843, 0.9063135687192041, 0.8471673370549754, 0.799767704553737,
+        0.7625760795052194, 0.7342612992213449, 0.7138168593531695, 0.7005616005823726,
+        0.6941005884853302, 0.6942790303083648, 0.7011404964629326, 0.7148892989284331,
+        0.7358494009090841, 0.7644053559740417, 0.8009027065635225, 0.8454763690923068,
+        0.8977714789587027, 0.9565393182933806, 1.019165474189051, 1.0813509454340713,
+        1.1373658461916338, 1.1812657284849295, 1.2088654609859466, 1.2193715362398743,
+        1.21549347279085, 1.2020302822091795, 1.1840441392227683, 1.1656263191950988,
+        1.1494716517718044, 1.136972131009794, 1.1285002311044643, 1.1237005663880806,
+        1.121738424295096, 1.121516169136053, 1.121879280575179, 1.121815840191393,
+        1.120626791316194, 1.1180287830714548, 1.1141602913193955, 1.109492069198782,
+        1.1046755839535236, 1.100377930701897, 1.0971439472694091, 1.0953064792020797,
+        1.0949477437255655, 1.0959053587511285, 1.097814646905175, 1.10017938820176,
+        1.1024620286887539, 1.104180259585007, 1.1049921627215429, 1.104751074274318,
+        1.1035171087531108, 1.1015240003030762, 1.0991125465647715, 1.0966497517674183,
+        1.094453226487016, 1.0927352082424864, 1.0915734786284788, 1.0909104231091171,
+        1.0905773624360098, 1.0903383829056241, 1.0899453147471156, 1.0891932414604792,
+        1.0879650172105801, 1.0862550499651318, 1.084167444199279, 1.0818901947774255,
+        1.079653054253752, 1.0776798396918372, 1.0761456839986963, 1.0751469996228389,
+        1.074688264137089, 1.0746863369490904, 1.074990281904053, 1.075412490681466,
+        1.0757651613242383, 1.0758951143346318, 1.0757100484205822, 1.0751910579966888,
+        1.0743893905871318, 1.0734091509632786, 1.0723807630601176, 1.0714315652863533,
+        1.0706597237488535, 1.0701161411351783, 1.0697969278470438, 1.0696468740306981,
+        1.0695725160366023, 1.0694619211372198, 1.0692072844199767, 1.0687259885248748,
+        1.067976108637844, 1.0669635240847475, 1.0657396326968527, 1.064390693994061,
+        1.0630214905512352, 1.06173687506699, 1.0606247501714048, 1.0597432910944402,
+        1.059114101287828, 1.0587218050271174, 1.0585195344241694, 1.058438953565876,
+        1.0584029125378083, 1.0583385638764924, 1.058188834326707, 1.0579205356844865,
+        1.057528069555802, 1.057032503738164, 1.0564765918619017, 1.0559168991833903,
+        1.0554144808312447, 1.0550255284034387, 1.054793136866283, 1.0547409691289755,
+        1.0548692267643773, 1.0551530481420894, 1.0555432745449234, 1.0559694319422381,
+        1.0563447262258696, 1.0565727919687835, 1.0565558304056466, 1.056203609241631,
+        1.0554425976934532, 1.0542243304289782, 1.0525320078039422, 1.0503844134047935,
+        1.0478364926638661, 1.044976360145465, 1.0419190041791364, 1.038797421645783,
+        1.0357522384927715, 1.0329209933292933, 1.0304281829412425, 1.028376940871384,
+        1.0268429187326287, 1.0258706357496157, 1.0254723029061417, 1.0256289332888673,
+        1.0262934169413036, 1.0273951533563952, 1.02884578453058, 1.0305455497575362,
+        1.0323897907059225, 1.0342751753452577, 1.0361052824417487, 1.0377952870533376,
+        1.0392755955141122, 1.0404943750120328, 1.041418990231904, 1.0420363900630607,
+        1.0423524876421477, 1.0423905654124546, 1.0421887367187037, 1.0417965254107635,
+        1.0412706916444647, 1.040670527323955, 1.0400529481835612, 1.0394677956248257,
+        1.038953806317785, 1.0385356946914206, 1.0382227157254282, 1.0380089351145556,
+        1.0378752416821846, 1.037792912211356, 1.03772831029919, 1.0376481057563347,
+        1.0375242811087262, 1.0373381834323958, 1.0370830019764592, 1.0367642954122098,
+        1.0363985164719265, 1.0360098224398484, 1.0356257476318504, 1.0352724922237342,
+        1.0349706212961234, 1.0347318702471144, 1.0345575441418418, 1.034438720106541,
+        1.0343581596576104, 1.0342935574423764, 1.0342215361718696, 1.0341216797271744,
+        1.0339799005597665, 1.0337905674416163, 1.0335570547756707, 1.033290670781776,
+        1.0330082196755532, 1.032728692834846, 1.0324697210177156, 1.0322444336853267,
+        1.0320592684265855, 1.0319130803523193, 1.0317976573465608, 1.0316994954864809,
+        1.0316024710951015, 1.0314908968678278, 1.0313523941460112, 1.0311800617816613,
+        1.0309735657642318, 1.0307389853949709, 1.0304874891493734, 1.0302331288677886,
+        1.029990192859709, 1.0297706206160777, 1.029581947829159, 1.0294261329934147,
+        1.0292994424857642, 1.0291933733883831, 1.029096407304299, 1.0289962453233603,
+        1.0288820978958135, 1.0287466063555923, 1.0285870539976794, 1.0284056679434233,
+        1.0282089899811946, 1.0280064698175841, 1.0278085735040514, 1.0276247777935725,
+        1.0274618262306472, 1.0273225582488295, 1.027205504411427, 1.0271052933212732,
+        1.0270137660462022, 1.0269215683841106, 1.0268199112536138, 1.0267021682374233,
+        1.0265650197297376, 1.0264089467459285, 1.0262380054708542, 1.0260589505655058,
+        1.0258798943487066, 1.025708767979254, 1.0255518765252678, 1.0254128102933378,
+        1.025291898476627, 1.0251862843992672, 1.0250905849451923, 1.0249979912674538,
+        1.0249015919105315, 1.0247956658315878, 1.0246767066376055, 1.0245439971286578,
+        1.024399643153804, 1.024248079938006, 1.0240951620676715, 1.0239470217096096,
+        1.0238089154975991, 1.0236842738979266, 1.0235741211105287, 1.023476958990467,
+        1.0233891199002003, 1.0233055072903738, 1.0232205744607534, 1.023129353109296,
+        1.0230283402054627, 1.0229160841376856, 1.0227933721099445, 1.0226629981836113,
+        1.0225291700342523, 1.0223966774611053, 1.0222699852062487, 1.0221524203999897,
+        1.022045600960328, 1.0219492014140568, 1.0218610870969538, 1.0217777789966416,
+        1.0216951520939286, 1.0216092303325552, 1.0215169279351848, 1.0214166014522246,
+        1.0213083162622683, 1.0211937872644377, 1.0210760152340121, 1.0209586959668349,
+        1.0208455186890224, 1.0207394865514885, 1.0206423832975688, 1.0205544790675838,
+        1.0204745213948918, 1.0204000038647962, 1.0203276545333992, 1.0202540479867768,
+        1.020176225386791, 1.0200922090250921, 1.0200013208189247, 1.019904253054582,
+        1.0198028868608469, 1.0196999003463842, 1.0195982454460955, 1.0195005937578094,
+        1.0194088537207586, 1.0193238447991888, 1.0192451826940052, 1.019171389328302,
+        1.019100200010402, 1.0190290052302042, 1.0189553420656043, 1.0188773438478418,
+        1.018794067245379, 1.0187056408827388, 1.0186132140169142, 1.0185187210230526,
+        1.0184245105339271, 1.0183329110853714, 1.0182458141961415, 1.0181643498431003,
+        1.0180887099602842, 1.018018146906158, 1.0179511413148328, 1.0178857033379025,
+        1.0178197483677607, 1.0177514767842581, 1.0176796888213993, 1.0176039796448886,
+        1.0175247832529692, 1.0174432622849905, 1.0173610688803503, 1.0172800242644748,
+        1.017201777835789, 1.0171275081619102, 1.0170577186077812, 1.0169921614890534,
+        1.016929900387848, 1.016869495112053, 1.016809272237596, 1.0167476299690845,
+        1.0166833214928788, 1.016615666606178, 1.0165446558690459, 1.0164709319680525,
+        1.0163956555164384, 1.0163202830042157, 1.0162462994227828, 1.0161749547604508,
+        1.0161070512035517, 1.0160428172459022, 1.0159818882102776, 1.015923393103552,
+        1.0158661288276343, 1.0158087878663522, 1.0157501971651248, 1.0156895252947422,
+        1.0156264220096625, 1.0155610674847402, 1.0154941252991523, 1.0154266105192826,
+        1.015359698915587, 1.015294512912828, 1.0152319228098357, 1.0151723978444989,
+        1.0151159317808052, 1.0150620538155113, 1.0150099203147778, 1.0149584689097437,
+        1.0149066061910952, 1.0148533953105525, 1.0147982108993694, 1.014740835457279,
+        1.0146814823821664, 1.0146207440315846, 1.0145594762453232, 1.0144986413501702,
+        1.0144391380655582, 1.0143816479898122, 1.014326524460339, 1.014273741422739,
+        1.0142229090823391, 1.0141733515034654, 1.014124230966529, 1.0140746964938923,
+        1.0140240306465715, 1.013971769876762, 1.0139177790189469, 1.0138622688601038,
+        1.0138057556151976, 1.013748970823067, 1.0136927380582084, 1.013637837694783,
+        1.0135848821033642, 1.0135342211005838, 1.0134858918125145, 1.0134396194325745,
+        1.0133948669987152, 1.013350924658103, 1.0133070231117154, 1.0132624528475374,
+        1.0132166707123962, 1.0131693781687308, 1.0131205606224643, 1.0130704835616073,
+        1.0130196478420008, 1.0129687122646822, 1.0129183957858208, 1.012869373782582,
+        1.0128221826413326, 1.0127771447711444, 1.0127343224930043, 1.0126935048029244,
+        1.0126542264851877, 1.0126158151124838, 1.0125774585931886, 1.0125382843671535,
+        1.0124974411298875, 1.0124541748954659, 1.0124078929606766, 1.0123582115080039,
+        1.0123049847947396, 1.0122483158068685, 1.012188549712392, 1.0121262523648817,
+        1.0120621765358873, 1.0119972186282782, 1.0119323685122932, 1.0118686549897364,
+        1.011807089339378, 1.0117486094673562, 1.0116940273466395, 1.01164398258976,
+        1.0115989050405063, 1.011558989080277, 1.011524181846535, 1.0114941867367022,
+        1.0114684824704796, 1.0114463567173162, 1.0114269520175176, 1.0114093206027284,
+        1.011392483908212, 1.0113754921755786, 1.0113574796212081, 1.0113377111747222,
+        1.0113156176936355, 1.0112908177089366, 1.0112631250023787, 1.0112325425139153,
+        1.0111992441047, 1.0111635464768325, 1.0111258740407651, 1.0110867197330615,
+        1.0110466047615676, 1.0110060400476408, 1.010965491802357, 1.010925353259981,
+        1.0108859241222603, 1.0108473987508406, 1.0108098635783047, 1.0107733035912094,
+        1.0107376170803364, 1.010702637187028, 1.0106681581546135, 1.010633963696021,
+        1.010599854595094, 1.0105656726445833, 1.0105313183353581, 1.0104967603548984,
+        1.0104620358816014, 1.0104272417767197, 1.0103925179376043, 1.0103580251210582,
+        1.0103239203148398, 1.010290333098907, 1.0102573463216822, 1.0102249838171182,
+        1.0101932068783417, 1.010161919924146, 1.0101309844345476, 1.0101002389990625,
+        1.0100695224099432, 1.0100386962889376, 1.0100076638350626, 1.009976381910053,
+        1.009944864741063, 1.0099131788470155, 1.0098814301740435, 1.0098497456344435,
+        1.0098182520890122, 1.0097870561604967, 1.009756228064486, 1.0097257919322975,
+        1.009695724000367, 1.0096659587374073, 1.0096364016900035, 1.0096069467607933,
+        1.0095774949622678, 1.009547971516597, 1.0095183385171012, 1.0094886011627355,
+        1.0094588066823384, 1.0094290362911018, 1.009399391661754, 1.0093699782604841,
+        1.0093408883555308, 1.0093121864887409, 1.0092838997226663, 1.00925601412926,
+        1.0092284779212664, 1.0092012105266965, 1.009174115953446, 1.0091470981389115,
+        1.0091200757271155, 1.00909299389265, 1.00906583139422, 1.0090386018841278,
+        1.0090113494755772, 1.0089841395105843, 1.0089570462239232, 1.008930139445143,
+        1.0089034725591748, 1.0088770736573058, 1.008850941216422, 1.008825044854731,
+        1.0087993308642738, 1.0087737314555496, 1.008748176088885, 1.0087226029930663,
+        1.008696969016449, 1.0086712562968525, 1.00864547480521, 1.0086196605114053,
+        1.008593869620944, 1.0085681699258322, 1.008542630713019, 1.0085173128262117,
+        1.0084922603724442, 1.0084674952354133, 1.0084430150692147, 1.0084187948855592,
+        1.0083947918066452, 1.0083709521165005, 1.0083472194653391, 1.0083235429937314,
+        1.0082998842427648, 1.0082762219715633, 1.008252554360958, 1.0082288984789225,
+        1.0082052872569578, 1.0081817645253892, 1.0081583788463897, 1.0081351769536657,
+        1.0081121975659233, 1.0080894662108237, 1.0080669915114897, 1.0080447631841225,
+        1.0080227518043083, 1.0080009102432697, 1.007979176563599, 1.0079574780965044,
+        1.007935736389906, 1.0079138727054668, 1.0078918137397674, 1.0078694972413682,
+        1.0078468771888016, 1.0078239281891246, 1.007800648761613, 1.007777063198869,
+        1.0077532217577247, 1.0077291990305288, 1.007705090481408, 1.0076810072912545,
+        1.0076570698220964, 1.007633400163546, 1.007610114338672, 1.0075873148045893,
+        1.0075650838726005, 1.0075434785922728, 1.0075225275019757, 1.0075022294636837,
+        1.0074825545965822, 1.0074634471292254, 1.007444829828216, 1.0074266095507287,
+        1.007408683418142, 1.0073909451176157, 1.0073732908975848, 1.0073556249153337,
+        1.0073378637003645, 1.0073199395973444, 1.0073018031336538, 1.0072834243111743,
+        1.0072647928515066, 1.0072459174354627, 1.0072268239835345, 1.007207553036857,
+        1.0071881563280742, 1.0071686926827679, 1.0071492234616766, 1.0071298078313107,
+        1.0071104982195123, 1.0070913363547132, 1.007072350285826, 1.007053552723347,
+        1.0070349409286181, 1.0070164982163927, 1.0069981969443893, 1.0069800026692526,
+        1.0069618789816361, 1.0069437924227826, 1.0069257168530743, 1.0069076367001462,
+        1.0068895486571117, 1.0068714616126706, 1.006853394844715, 1.0068353747599341,
+        1.00681743067534, 1.0067995902784772, 1.006781875448632, 1.006764299062001,
+        1.0067468632482814, 1.0067295593378798, 1.0067123694738267, 1.0066952696029805,
+        1.006678233348444, 1.006661236133804, 1.0066442589003977, 1.0066272908356906,
+        1.0066103307006362, 1.0065933865780328, 1.0065764741233751, 1.006559613641705,
+        1.0065428264987337, 1.0065261314724103, 1.0065095416472474, 1.0064930623502226,
+        1.0064766904430058, 1.006460415052394, 1.0064442195794012, 1.0064280846175104,
+        1.0064119912672267, 1.0063959242798386, 1.006379874505601, 1.0063638402513848,
+        1.006347827346329, 1.0063318479372225, 1.0063159182495889, 1.0063000557198445,
+        1.006284276000318, 1.0062685903479494, 1.006253003829224, 1.0062375146239988,
+        1.0062221145163865, 1.006206790456153, 1.0061915268943895, 1.0061763084727644,
+        1.0061611225963267, 1.0061459614524204, 1.0061308231450812, 1.0061157117751087,
+        1.0061006364819964, 1.0060856096421475, 1.0060706445581151, 1.0060557530522967,
+        1.006040943384073, 1.0060262188421845, 1.006011577238102, 1.0059970113641752,
+        1.0059825103117048, 1.0059680613978772, 1.0059536523517043, 1.005939273373436,
+        1.0059249187139907, 1.0059105875136705, 1.0058962837746168, 1.0058820154952097,
+        1.0058677931391724, 1.0058536277229677, 1.0058395288636302, 1.0058255031267225,
+        1.0058115529526979, 1.0057976763316634, 1.0057838672617925, 1.005770116889138,
+        1.005756415110906, 1.005742752349367, 1.0057291211820194, 1.005715517547286,
+        1.0057019413268753, 1.005688396220161, 1.0056748889519882, 1.005661427970607,
+        1.00564802187734, 1.0056346778699368, 1.0056214004716175, 1.0056081907605225,
+        1.0055950462210854, 1.0055819612268244, 1.0055689280534739, 1.0055559382313435,
+        1.0055429839916743, 1.0055300595519636, 1.0055171620202636, 1.0055042917710708,
+        1.005491452241833, 1.0054786492017858, 1.005465889635778, 1.005453180449114,
+        1.005440527225146, 1.005427933251722, 1.0054153989795347, 1.0054029219953007,
+        1.005390497500127, 1.0053781191951388, 1.0053657804076317, 1.0053534752533202,
+        1.0053411996293484, 1.0053289518679862, 1.0053167329448163, 1.0053045462163102,
+        1.0052923967448462, 1.0052802903400007, 1.00526823249144, 1.0052562273830832,
+        1.0052442771591241, 1.005232381563945, 1.0052205380093362, 1.0052087420463534,
+        1.0051969881488745, 1.0051852706639857, 1.0051735847589036, 1.0051619271993306,
+        1.0051502968279793, 1.0051386946679202, 1.005127123642969, 1.0051155879745004,
+        1.005104092368963, 1.0050926411439156, 1.0050812374470983, 1.005069882702637,
+        1.0050585763751507, 1.0050473160845286, 1.0050360980418824, 1.0050249177219615,
+        1.0050137706481237, 1.0050026531496559, 1.0049915629598125, 1.0049804995541491,
+        1.004969464176875, 1.0049584595586176, 1.0049474893828494, 1.004936557600412,
+        1.0049256677154672, 1.004914822167832, 1.00490402191648, 1.0048932662911891,
+        1.0048825531307564, 1.0048718791758653, 1.0048612406412443, 1.0048506338625909,
+        1.0048400559036665, 1.0048295050189864, 1.0048189808956076, 1.0048084846379675,
+        1.004798018505534, 1.0047875854557315, 1.004777188577001, 1.004766830513758,
+        1.004756512983623, 1.0047462364685429, 1.0047360001290815, 1.0047258019510104,
+        1.0047156390928569, 1.0047055083689727, 1.0046954067809906, 1.0046853320044287,
+        1.004675282747517, 1.0046652589235487, 1.0046552616119087, 1.0046452928201015,
+        1.0046353550930314, 1.0046254510409884, 1.0046155828696997, 1.0046057519933025,
+        1.00459595879446, 1.0045862025688277, 1.0045764816582532, 1.0045667937445562,
+        1.0045571362488797, 1.004547506765015, 1.004537903451227, 1.0045283253143085,
+        1.0045187723399767, 1.0045092454512254, 1.004499746306286, 1.0044902769749993,
+        1.0044808395520237, 1.0044714357746591, 1.0044620667102775, 1.0044527325648644,
+        1.0044434326421203, 1.004434165456213, 1.0044249289751899, 1.0044157209505125,
+        1.0044065392749555, 1.0043973823078405, 1.0043882491139053, 1.0043791395780717,
+        1.0043700543803393, 1.0043609948388958, 1.004351962651408, 1.0043429595805013,
+        1.0043339871375003, 1.0043250463170443, 1.0043161374253304, 1.0043072600277638,
+        1.0042984130214239, 1.0042895948168031, 1.0042808035959154, 1.0042720376022043,
+        1.0042632954138946, 1.0042545761565789, 1.0042458796221072, 1.0042372062770093,
+        1.004228557162095, 1.0042199337022037, 1.0042113374589168, 1.0042027698669833,
+        1.0041942319964485, 1.004185724376949, 1.0041772469097192, 1.0041687988782153,
+        1.0041603790527314, 1.0041519858701355], [3.30189825142678e-09,
+        9.916708848419717e-09, 1.656462861997893e-08, 2.3267949684811865e-08,
+        3.004929457527346e-08, 3.6931754248458736e-08, 4.393902719767739e-08,
+        5.109556686787474e-08, 5.84267342774399e-08, 6.595895949052615e-08,
+        7.37199128942228e-08, 8.173868827882062e-08, 9.004599866138154e-08,
+        9.867438824126956e-08, 1.0765846127281408e-07, 1.170351314360654e-07,
+        1.2684389368843447e-07, 1.371271218821452e-07, 1.4793039574083895e-07,
+        1.5930286030287625e-07, 1.7129762325350472e-07, 1.839721935902694e-07,
+        1.9738896815233365e-07, 2.116157716795826e-07, 2.2672645743926952e-07,
+        2.4280157623240946e-07, 2.599291233294422e-07, 2.782053728216927e-07,
+        2.977358119934853e-07, 3.18636188182864e-07, 3.410336848833377e-07,
+        3.650682431326798e-07, 3.908940499886861e-07, 4.1868121633600273e-07,
+        4.486176718942497e-07, 4.809113076770055e-07, 5.157924028468245e-07,
+        5.535163767002537e-07, 5.943669154489161e-07, 6.38659528796409e-07,
+        6.86745603506462e-07, 7.390170291060053e-07, 7.959114870782084e-07,
+        8.579185071876743e-07, 9.255864164902352e-07, 9.995303235310853e-07,
+        1.0804413144032508e-06, 1.1690970572974684e-06, 1.2663740639684385e-06,
+        1.3732618878745304e-06, 1.4908796050855533e-06, 1.620494985099831e-06,
+        1.7635468394687282e-06, 1.9216711398005573e-06, 2.0967316140068824e-06,
+        2.2908556792958303e-06, 2.5064767615439454e-06, 2.746384268763788e-06,
+        3.013782785464591e-06, 3.3123624028369685e-06, 3.646382556061626e-06,
+        4.020772313622534e-06, 4.4412507909293e-06, 4.914472298567016e-06,
+        5.448202048334774e-06, 6.051529823752517e-06, 6.735131093984671e-06,
+        7.511587815779918e-06, 8.395784876950764e-06, 9.405403154124043e-06,
+        1.0561537083065931e-05, 1.1889474290863505e-05, 1.3419688531374646e-05,
+        1.5189116886455191e-05, 1.7242821305865198e-05, 1.9636178295741113e-05,
+        2.2437808226122468e-05, 2.5733563099768493e-05, 2.9632068032761543e-05,
+        3.427261222479679e-05, 3.983671934541288e-05, 4.656572531164024e-05,
+        5.4788666896975636e-05, 6.496897463439754e-05, 7.778812937362036e-05,
+        9.430920567152456e-05, 0.00011633592229167848, 0.00014733998972716242,
+        0.0001955321781011425, 0.00028990018844439437, 0.0009838963576450214,
+        0.00034695722360906194, 0.00028606633611824415, 0.00027833928859468597,
+        0.00028991730836583547, 0.0003141055492913641, 0.00034965145647559493,
+        0.00039740530826741396, 0.0004595747101365457, 0.000539673276230013,
+        0.0006427933552329807, 0.0007761530342167543, 0.0009499891351958539,
+        0.0011789685700452715, 0.001484434268534445, 0.0018980532555680442,
+        0.002467908914231844, 0.003269023127194559, 0.004422272066755606,
+        0.006130063135479443, 0.008747676557002414, 0.01293671855242331,
+        0.020027700062287036, 0.03299210563587636, 0.05956601276738829,
+        0.12564590902226958, 0.3772877859620176, 6.57486680702548, 0.976134264394725,
+        1.4803884263622633, 1.090488526770569, 0.41473697166223994, 0.5253718149881265,
+        1.264727569510353, 2.091024866446433, 1.2051040928177996, 1.0130829935487762,
+        1.099836288732969, 1.498945431056173, 2.2876665179114766, 1.7078779865707032,
+        1.037491162184348, 0.7751049391185284, 0.6993350111606669, 0.7631057932996348,
+        1.009605420086665, 1.3175941674242786, 1.15278853995035, 0.9355158563828274,
+        0.858633767608559, 0.8872083796681233, 1.0161273220698595, 1.2768566299585296,
+        1.680019924039395, 1.895302639784797, 1.5913428314970066, 1.2461381635541118,
+        1.041415577214365, 0.9460769010802722, 0.9328277358523778, 0.9965220115027684,
+        1.1358721415629411, 1.2649112989937608, 1.1658586513590148, 0.9384268368131853,
+        0.7921967082385472, 0.7570129603147003, 0.8796734318886932, 0.9857870943631396,
+        1.106139375332853, 1.2219487679108858, 1.293782290210602, 1.2949383336434235,
+        1.2415322605611596, 1.1714257710032374, 1.1117920986096235, 1.0739179402354162,
+        1.0602932282419972, 1.069823679716186, 1.0993645518853774, 1.142758360906036,
+        1.1886498600405428, 1.2197628168644188, 1.2182432282722324, 1.176958037458496,
+        1.1050537910880835, 1.019959179078251, 0.9362640736374372, 0.8617433247204768,
+        0.7989094677768702, 0.7475588256270902, 0.7064849853768115, 0.6743310300790113,
+        0.6499332498692416, 0.6324213139635887, 0.6212171628255625, 0.615999601697609,
+        0.6166633123373596, 0.6232821584423011, 0.6360766187667756, 0.6553785124953881,
+        0.6815799504026835, 0.71504602811332, 0.7559624169663148, 0.8040846928532752,
+        0.8583715419705443, 0.91655005230488, 0.9748090936240144, 1.0280007803200284,
+        1.0707134490049077, 1.099051046701744, 1.1121381579412235, 1.1122708334351583,
+        1.1036781531703508, 1.0908812270893924, 1.077564054708282, 1.066167516443788,
+        1.0579557387835639, 1.053260366290575, 1.0517384167971857, 1.0525962633493309,
+        1.0547892244882278, 1.0572160388277319, 1.058910450437876, 1.0592068369606038,
+        1.057841913625224, 1.0549631631814302, 1.0510441801515968, 1.046739048235866,
+        1.0427226816329462, 1.039556852667022, 1.0376025342348094, 1.0369815997878682,
+        1.037581612462576, 1.0390953811220442, 1.0410874989940182, 1.0430791205184036,
+        1.0446385680717107, 1.045461091638386, 1.045420221628532, 1.0445785962697285,
+        1.043157066855586, 1.0414726303617678, 1.039862993397089, 1.0386159957470449,
+        1.037917308225718, 1.0378232651058448, 1.0382601276668624, 1.0390472669401447,
+        1.0399390197572291, 1.0406774645192693, 1.0410460842320015, 1.040913267182954,
+        1.040256156015064, 1.039159901630678, 1.0377937049593866, 1.036370803651517,
+        1.0351027050257329, 1.034157830350979, 1.0336321700272049, 1.0335360384124679,
+        1.0337977100726723, 1.0342820343038996, 1.0348199786419279, 1.035243348666971,
+        1.0354178963023788, 1.0352681608907865, 1.0347890689653625, 1.0340423780990429,
+        1.033139646367627, 1.0322163873573684, 1.0314035565077797, 1.0308023103094768,
+        1.030466517913998, 1.03039547348724, 1.0305372207449501, 1.030801141040541,
+        1.031077054988517, 1.0312571007327294, 1.0312562180656708, 1.0310273695842918,
+        1.0305687434859112, 1.0299219316409773, 1.0291620246053343, 1.0283821740554737,
+        1.0276760367083106, 1.0271215160884846, 1.0267685276878118, 1.0266324450151636,
+        1.0266937424089864, 1.026903334441668, 1.0271923134593488, 1.0274842418915997,
+        1.0277078925298804, 1.0278083809227678, 1.0277550108523654, 1.0275448077016243,
+        1.0272015194509052, 1.0267706432338175, 1.0263116157501941, 1.02588858459405,
+        1.0255611484007947, 1.0253761951762748, 1.0253616007898971, 1.0255221876089586,
+        1.0258380613893356, 1.0262652673737547, 1.0267386159383491, 1.0271764803239964,
+        1.0274873141244538, 1.0275775361676083, 1.0273602729634417, 1.0267642555446432,
+        1.0257419919959851, 1.0242762511026684, 1.0223839611631182, 1.0201168801527682,
+        1.0175588026315299, 1.0148195543465515, 1.0120264768711422, 1.0093144203242406,
+        1.0068153837905947, 1.004648870431662, 1.0029138063461516, 1.0016825817263877,
+        1.0009974785986655, 1.0008694978587942, 1.0012794083557608, 1.0021807099710196,
+        1.0035041182273086, 1.0051631274517738, 1.0070601867980193, 1.0090930293269111,
+        1.011160732432663, 1.0131691587285634, 1.015035522657824, 1.0166919336954838,
+        1.018087861622128, 1.0191915354602166, 1.0199903177129774, 1.0204900958997927,
+        1.0207137219986164, 1.0206985301069855, 1.020492991783039, 1.0201526337350852,
+        1.0197354358313309, 1.0192970290259888, 1.0188860975387988, 1.018540434108484,
+        1.0182840850461685, 1.0181259460978862, 1.0180600328262477, 1.0180674608054665,
+        1.018119950319427, 1.0181844455817266, 1.0182282464700116, 1.0182239323640419,
+        1.018153348901328, 1.0180100480224554, 1.0177998104670436, 1.0175391980665982,
+        1.0172524181189964, 1.0169670651878233, 1.0167094813113997, 1.0165005149717357,
+        1.0163523636368241, 1.0162669801029143, 1.0162362494717012, 1.0162438467246324,
+        1.016268409266104, 1.0162874456870814, 1.0162812859248627, 1.0162363816277025,
+        1.0161473927209559, 1.0160177267810224, 1.0158584884477653, 1.0156860886030643,
+        1.0155189988583178, 1.015374271895782, 1.015264462390667, 1.0151954824101137,
+        1.0151657357177122, 1.0151666357477926, 1.0151843646123444, 1.0152025159921618,
+        1.0152051177245693, 1.0151794748739356, 1.0151183211317514, 1.015020907440719,
+        1.0148928648497089, 1.0147449123466883, 1.0145906929029067, 1.0144441710505328,
+        1.0143170870043272, 1.0142169293304513, 1.0141457728492955, 1.0141001568697967,
+        1.014071984174245, 1.014050237804599, 1.0140231715340087, 1.013980554420611,
+        1.013915552592543, 1.0138259112496733, 1.0137142410290791, 1.0135873872463432,
+        1.01345503326722, 1.0133278266528691, 1.013215393682351, 1.0131246129313005,
+        1.0130584550660084, 1.0130155796118787, 1.0129907339455535, 1.0129758521358019,
+        1.0129616273717663, 1.0129392526067615, 1.0129020028518916, 1.012846372183418,
+        1.012772570651605, 1.0126843124275944, 1.0125879615909408, 1.0124912195363833,
+        1.0124016160994853, 1.0123250921365372, 1.0122649323888195, 1.0122212323275368,
+        1.0121909773927895, 1.0121686978873232, 1.0121475586029571, 1.012120667168106,
+        1.0120823517727668, 1.0120291724859785, 1.0119604873733585, 1.0118784834140824,
+        1.0117876851270349, 1.0116940507263172, 1.0116038382251524, 1.011522459441643,
+        1.0114535334132135, 1.0113983055923796, 1.0113555255534297, 1.011321788423245,
+        1.011292260126354, 1.011261638935821, 1.0112251673516213, 1.0111795051957275,
+        1.0111233067487562, 1.011057404978036, 1.0109845823616979, 1.0109089855401059,
+        1.0108353052414698, 1.01076788202124, 1.0107099060730929, 1.0106628557082318,
+        1.010626269850376, 1.0105978851469657, 1.0105741003698294, 1.0105506720004913,
+        1.0105235055543293, 1.0104893938685948, 1.0104465680271655, 1.010394965458134,
+        1.0103361751447213, 1.0102730809794591, 1.0102092794035162, 1.0101483864801521,
+        1.0100933658045306, 1.0100460000920999, 1.0100065985527291, 1.0099739857794905,
+        1.0099457648711638, 1.0099187976497532, 1.009889806990415, 1.0098559869176502,
+        1.0098155082426923, 1.0097678301675739, 1.0097137667390756, 1.009655303724856,
+        1.0095952074670624, 1.0095365040149922, 1.0094819278748233, 1.00943344177796,
+        1.0093919123581037, 1.0093569953037258, 1.0093272436663412, 1.0093004120504423,
+        1.0092738947749627, 1.009245213796976, 1.0092124658781014, 1.0091746488410394,
+        1.0091318114460306, 1.0090850054722968, 1.009036055458524, 1.0089871943465132,
+        1.0089406360872384, 1.0088981652928262, 1.008860818141582, 1.0088287096220396,
+        1.0088010338062303, 1.0087762316252105, 1.008752290490698, 1.008727117392904,
+        1.0086989156494248, 1.0086664970105175, 1.008629474688005, 1.008588306187673,
+        1.0085441830519672, 1.0084987924454252, 1.008453997870819, 1.0084114993082551,
+        1.0083725347099257, 1.0083376751977189, 1.0083067476542253, 1.0082788943526106,
+        1.008252754325319, 1.0082267298017906, 1.0081992869442566, 1.008169235567509,
+        1.0081359380682717, 1.0080994121114681, 1.0080603118740739, 1.0080197949839553,
+        1.0079793026034616, 1.0079402947960157, 1.0079039899349247, 1.0078711545778483,
+        1.007841979692144, 1.00781606255777, 1.007792494252257, 1.0077700338721534,
+        1.0077473358561917, 1.0077231884300561, 1.0076967205625063, 1.0076675417780765,
+        1.0076357922374415, 1.0076020971506576, 1.0075674367430347, 1.0075329575740894,
+        1.0074997605152287, 1.0074687036224663, 1.0074402542263434, 1.0074144147513835,
+        1.0073907330136571, 1.0073683925789778, 1.0073463648894954, 1.0073235946525987,
+        1.0072991850856872, 1.0072725506982456, 1.0072435119794985, 1.0072123172901144,
+        1.0071795903759013, 1.0071462148621941, 1.0071131776019377, 1.0070813991027194,
+        1.0070515805118114, 1.0070240927815477, 1.0069989255385479, 1.0069757023954413,
+        1.0069537579155659, 1.006932261154129, 1.0069103633456122, 1.0068873440136135,
+        1.006862730945396, 1.0068363747267355, 1.0068084668263826, 1.0067795000331825,
+        1.0067501796705163, 1.0067213018411942, 1.0066936197682972, 1.0066677204400585,
+        1.0066439312309017, 1.0066222705562753, 1.006602448996323, 1.0065839190275132,
+        1.0065659638983104, 1.006547810448374, 1.0065287476070917, 1.0065082322476757,
+        1.0064859668498443, 1.0064619384298148, 1.0064364145083897, 1.0064098984422871,
+        1.0063830522160473, 1.0063565989632406, 1.0063312195572447, 1.006307457458227,
+        1.0062856438550762, 1.0062658515128522, 1.0062478813122715, 1.00623128097336,
+        1.0062153915388097, 1.0061994143312796, 1.0061824895464762, 1.0061637774202596,
+        1.0061425338292536, 1.0061181739226026, 1.0060903195416235, 1.0060588283782823,
+        1.006023804741516, 1.0059855932470025, 1.0059447576563567, 1.0059020475173723,
+        1.005858355330707, 1.0058146668597956, 1.0057720070665686, 1.005731384104978,
+        1.0056937338762475, 1.0056598678108857, 1.005630426703541, 1.0056058434699509,
+        1.0055863175082416, 1.0055718028532856, 1.0055620114952113, 1.0055564321404562,
+        1.0055543634359256, 1.00555495940651, 1.0055572837401068, 1.005560368745431,
+        1.0055632744156773, 1.005565143106371, 1.0055652458606197, 1.0055630173102903,
+        1.0055580772223844, 1.0055502379974834, 1.0055394986167319, 1.0055260265538428,
+        1.005510129938933, 1.0054922227469958, 1.0054727859936239, 1.0054523278943293,
+        1.0054313457369328, 1.005410291885128, 1.0053895459195399, 1.0053693944552726,
+        1.0053500196612692, 1.0053314969432239, 1.005313801638012, 1.0052968239133777,
+        1.0052803904040837, 1.0052642904997344, 1.0052483047046754, 1.0052322321990468,
+        1.0052159147162154, 1.0051992541626171, 1.0051822220470141, 1.0051648597108,
+        1.0051472694615762, 1.005129597869168, 1.005112013524266, 1.0050946823262938,
+        1.005077743729982, 1.0050612912654224, 1.0050453600507239, 1.0050299230121127,
+        1.0050148962534724, 1.0050001526640153, 1.0049855416259939, 1.0049709117766361,
+        1.0049561333360613, 1.0049411166099644, 1.0049258239006944, 1.004910273116439,
+        1.0048945326873433, 1.0048787087683395, 1.0048629269106513, 1.0048473112243932,
+        1.0048319644003283, 1.0048169517579588, 1.004802291778515, 1.0047879544864111,
+        1.0047738677455231, 1.0047599302519725, 1.0047460289434684, 1.0047320578770442,
+        1.0047179354550928, 1.0047036172230688, 1.0046891022543711, 1.0046744322383985,
+        1.0046596836082955, 1.0046449541804066, 1.0046303466419386, 1.0046159516802324,
+        1.004601833530723, 1.004588020246279, 1.004574500149144, 1.0045612248675184,
+        1.0045481182638862, 1.004535089613739, 1.004522048744363, 1.0045089205922746,
+        1.004495656813829, 1.0044822426442506, 1.004468698039895, 1.004455073109401,
+        1.0044414387758394, 1.0044278743609332, 1.0044144542267948, 1.0044012356883902,
+        1.0043882501221995, 1.0043754986048044, 1.0043629526284632, 1.0043505595959563,
+        1.0043382520347022, 1.0043259589111644, 1.0043136171530034, 1.0043011815301208,
+        1.0042886313848538, 1.0042759732672204, 1.0042632392212403, 1.0042504811654063,
+        1.0042377624025247, 1.0042251476925468, 1.0042126934741185, 1.004200439716931,
+        1.0041884045594163, 1.0041765824004785, 1.0041649455562227, 1.0041534490544062,
+        1.0041420377022785, 1.0041306542867068, 1.0041192476784395, 1.00410777971173,
+        1.004096229964868, 1.0040845979235524, 1.0040729024044357, 1.0040611784885152,
+        1.0040494725118594, 1.004037835851453, 1.0040263183139422, 1.0040149618935175,
+        1.0040037955353511, 1.0039928313570272, 1.0039820625776732, 1.0039714632140488,
+        1.0039609894469586, 1.0039505824497856, 1.003940172403393, 1.0039296833887605,
+        1.003919038837132, 1.0039081672143138, 1.0038970076119245, 1.0038855149114634,
+        1.0038736641813664, 1.0038614539719448, 1.0038489082004358, 1.0038360763781438,
+        1.0038230320293642, 1.0038098692851878, 1.003796697793849, 1.003783636255599,
+        1.0037708050416227, 1.0037583184709191, 1.0037462773769519, 1.003734762585701,
+        1.0037238298468056, 1.0037135066184504, 1.0037037909227935, 1.0036946522865045,
+        1.0036860345870546, 1.0036778604644325, 1.0036700368478075, 1.0036624610969254,
+        1.003655027267594, 1.0036476320695942, 1.003640180177224, 1.0036325886578181,
+        1.0036247903833027, 1.0036167363707222, 1.0036083970520293, 1.0035997625028243,
+        1.0035908416712092, 1.0035816606536838, 1.003572260077655, 1.0035626916797695,
+        1.0035530142202707, 1.003543288942731, 1.0035335748655563, 1.0035239242602392,
+        1.0035143787133365, 1.0035049661672968, 1.003495699279044, 1.0034865753220203,
+        1.003477577696113, 1.0034686789191314, 1.00345984477992, 1.0034510391670775,
+        1.003442228977323, 1.0034333884757929, 1.0034245025374895, 1.0034155683416621,
+        1.0034065953013998, 1.0033976032598562, 1.0033886192346135, 1.0033796732045046,
+        1.0033707935737295, 1.0033620029935733, 1.003353315163033, 1.003344733074761,
+        1.0033362489452995, 1.0033278458044106, 1.0033195004596447, 1.0033111873403469,
+        1.0033028825942945, 1.0032945677808336, 1.0032862325808451, 1.0032778761130121,
+        1.0032695066791266, 1.003261140019703, 1.0032527964022802, 1.0032444970489216,
+        1.0032362605069325, 1.003228099562921, 1.003220019197156, 1.0032120158916555,
+        1.0032040783732998, 1.0031961896325714, 1.0031883298492186, 1.003180479713191,
+        1.0031726235751186, 1.0031647519027371, 1.0031568626490956, 1.0031489613312552,
+        1.003141059840728, 1.0031331742205456, 1.0031253218127527, 1.0031175182764078,
+        1.0031097749852025, 1.0031020972359785, 1.0030944835500304, 1.003086926155338,
+        1.0030794125338238, 1.0030719277386817, 1.0030644570627467, 1.0030569885897374,
+        1.003049515192666, 1.0030420356501923, 1.0030345547119999, 1.0030270821296974,
+        1.0030196308474002, 1.003012214686034, 1.0030048459338203, 1.0029975332609358,
+        1.00299028030929, 1.0029830851826897, 1.0029759409011072, 1.0029688367145777,
+        1.0029617600264162, 1.0029546985768465, 1.0029476425025148, 1.0029405859192522,
+        1.0029335277678373, 1.0029264717972375, 1.0029194257131073, 1.0029123996633909,
+        1.002905404343415, 1.0028984490612591, 1.0028915401017637, 1.002884679666359,
+        1.002877865557973, 1.0028710916459547, 1.0028643490089182, 1.0028576275380667,
+        1.0028509177089553, 1.0028442122081653, 1.0028375071349853, 1.002830802579836,
+        1.0028241024951143, 1.0028174138998647, 1.00281074557471, 1.0028041064881434,
+        1.0027975042356025, 1.0027909437628109, 1.002784426587803, 1.002777950643102,
+        1.002771510747826, 1.0027650996091992, 1.0027587091631616, 1.0027523320097254,
+        1.002745962688961, 1.0027395985783265, 1.002733240264464, 1.0027268913386471,
+        1.0027205576674438, 1.002714246280811, 1.0027079640829932, 1.0027017166172296,
+        1.0026955070996355, 1.002689335884726, 1.0026832004451005, 1.002677095855507,
+        1.0026710156834104, 1.0026649531195988, 1.0026589021447154, 1.0026528585267451,
+        1.002646820479615, 1.0026407888768254, 1.00263476699488, 1.0026287598443049,
+        1.0026227732166022, 1.0026168126219606, 1.002610882306842, 1.0026049845216072,
+        1.0025991191599317, 1.0025932838233793, 1.0025874742886296, 1.0025816852848035,
+        1.0025759114365391, 1.0025701482031308, 1.0025643926492211, 1.0025586439162748,
+        1.0025529033198455, 1.0025471740650322, 1.002541460639484, 1.0025357679980849,
+        1.0025301006868728, 1.0025244620604195, 1.0025188537265246, 1.0025132753088224,
+        1.002507724560049, 1.0025021977965578, 1.0024966905695902, 1.0024911984496738,
+        1.00248571778423, 1.00248024629701, 1.0024747834290764, 1.0024693303690662,
+        1.0024638897759763, 1.0024584652514448, 1.002453060660572, 1.0024476794241712,
+        1.0024423239069709, 1.0024369950061767, 1.0024316920071212, 1.002426412724276,
+        1.0024211538957464, 1.002415911756005, 1.0024106826825707, 1.0024054638022935,
+        1.0024002534529295, 1.0023950514236954, 1.0023898589388858, 1.0023846783943244,
+        1.002379512899057, 1.0023743657070041, 1.002369239640194, 1.0023641366037974,
+        1.0023590572744967, 1.0023540010114618, 1.0023489659991396, 1.0023439495907014,
+        1.0023389487869498, 1.0023339607638484, 1.002328983355704, 1.0023240154113422,
+        1.002319056964726, 1.002314109195263, 1.0023091741900823, 1.002304254554421,
+        1.0022993529413857, 1.0022944715842044, 1.0022896119116085, 1.0022847743103638,
+        1.0022799580720032, 1.0022751615280883, 1.0022703823458279, 1.0022656179291063,
+        1.0022608658534178, 1.0022561242593324, 1.0022513921382983, 1.0022466694649377,
+        1.0022419571574326, 1.0022372568775686, 1.002232570709126, 1.0022279007728703,
+        1.0022232488457652, 1.0022186160492452, 1.002214002657957, 1.002209408058362,
+        1.0022048308603368, 1.0022002691388543, 1.0021957207613619, 1.0021911837432778,
+        1.0021866565707602, 1.0021821384372205, 1.0021776293559796, 1.0021731301333792,
+        1.0021686422104619, 1.0021641674031716, 1.0021597075870103, 1.0021552643801481,
+        1.00215083887751, 1.0021464314785298, 1.0021420418342981, 1.002137668919533,
+        1.0021333112138406, 1.0021289669594444, 1.0021246344508916, 1.0021203123084519,
+        1.0021159996910818, 1.0021116964160504, 1.002107402968452, 1.002103120402215,
+        1.0020988501514918, 1.0020945937851362, 1.0020903527448985, 1.002086128109205,
+        1.0020819204188733, 1.002077729590247, 1.002073554926593, 1.0020693952231567,
+        1.0020652489470165], [1.4330709589268089e-09, 4.3041778400931925e-09,
+        7.190210645400453e-09, 1.0101221883023028e-08, 1.3047417594219004e-08,
+        1.603922147185998e-08, 1.908733962579327e-08, 2.220282917666544e-08,
+        2.5397169387545218e-08, 2.8682336975748818e-08, 3.207088608327126e-08,
+        3.557603384419081e-08, 3.921175203154743e-08, 4.299286634301484e-08,
+        4.693516375573956e-08, 5.1055509612710245e-08, 5.5371975415023754e-08,
+        5.990397887676282e-08, 6.467243794976875e-08, 6.969994032644085e-08,
+        7.501093096683753e-08, 8.063191934308172e-08, 8.659170947848259e-08,
+        9.292165550214131e-08, 9.965594607343224e-08, 1.0683192140402e-07,
+        1.1449042741134807e-07, 1.226762115445855e-07, 1.314383662542682e-07,
+        1.4083082605794968e-07, 1.5091292611864482e-07, 1.6175002998453665e-07,
+        1.7341423677355708e-07, 1.8598517834148543e-07, 1.9955091956154635e-07,
+        2.1420897597228469e-07, 2.300674661295368e-07, 2.4724641776006063e-07,
+        2.658792509020013e-07, 2.861144636592932e-07, 3.081175517408322e-07,
+        3.320731965345156e-07, 3.5818776377038154e-07, 3.8669216027365933e-07,
+        4.178451060668569e-07, 4.5193688643082186e-07, 4.892936636154714e-07,
+        5.302824361777258e-07, 5.753167565284303e-07, 6.248633299657799e-07,
+        6.794496466728149e-07, 7.396728230398986e-07, 8.062098614544255e-07,
+        8.798295794629957e-07, 9.614065050371972e-07, 1.051937092433354e-06,
+        1.1525586859701902e-06, 1.2645717386029406e-06, 1.3894659014453372e-06,
+        1.5289507214359037e-06, 1.6849918404543671e-06, 1.859853778483192e-06,
+        2.056150614303286e-06, 2.276906163785919e-06, 2.5256256101420846e-06,
+        2.8063809811101167e-06, 3.123913411681964e-06, 3.4837558159867103e-06,
+        3.892380449158475e-06, 4.3573769102614065e-06, 4.88766749758388e-06,
+        5.493768545348042e-06, 6.1881085593737265e-06, 6.9854167456490645e-06,
+        7.903199116499202e-06, 8.962323941576261e-06, 1.0187744284542578e-05,
+        1.1609393065811812e-05, 1.3263296196943715e-05, 1.5192962586387644e-05,
+        1.7451127237101243e-05, 2.0101946853692057e-05, 2.3223778267740463e-05,
+        2.6912711438663544e-05, 3.1287084838473764e-05, 3.649328716948111e-05,
+        4.2713253726005994e-05, 5.01742096050174e-05, 5.916141208830178e-05,
+        7.003492531584729e-05, 8.32518570839622e-05, 9.939605477277896e-05,
+        0.00011921807481200194, 0.00014368943202016203, 0.00017407689232786175,
+        0.00021204519609979613, 0.00025980056613345915, 0.0003202934441553893,
+        0.000397508386177544, 0.0004968840873653894, 0.0006259307905560595,
+        0.0007951523549730646, 0.0010194477255520004, 0.0013202831805578209,
+        0.0017291341412250338, 0.002293076175788518, 0.003084130136624212,
+        0.004215407223531101, 0.005870106737502305, 0.008356072899294808,
+        0.012214418583592491, 0.018451680235576313, 0.029083630023400364,
+        0.04857736165547919, 0.08842531447452792, 0.18648245534033595, 0.5521917132045137,
+        9.248559707889626, 1.246270386049037, 1.4450778657086452, 0.23851774063212103,
+        0.5555476825662461, 1.2395697037204134, 3.2410337009515993, 5.46084228584212,
+        3.218429415221865, 2.8483710858837354, 3.693087631235531, 3.518040762225469,
+        2.6372224092729284, 1.7294043235006937, 1.1830563492223714, 1.0746554881721861,
+        1.1746441623709247, 1.4876190112568974, 2.135096239577242, 2.811203154591254,
+        2.347152452986082, 1.7622024291744607, 1.4785090011810063, 1.3950061808908854,
+        1.4650413922511625, 1.6991823407284543, 2.0794408350532883, 2.2006366785617253,
+        1.7500338203595174, 1.3127032057584975, 1.0654223689658902, 0.9561008966699942,
+        0.9504726775406668, 1.047356882221339, 1.2588159418354847, 1.5017699134179754,
+        1.4883341371816927, 1.2726596483476331, 1.111953593176493, 1.0625068155282207,
+        1.1572138523262663, 1.2528875583860084, 1.369709488514641, 1.4803492106796565,
+        1.537962630208528, 1.5141197342773631, 1.4309346178208573, 1.3334028551012442,
+        1.2520333817304703, 1.1984052623792574, 1.1741662000931894, 1.1772099424335454,
+        1.2034406141286058, 1.2457101615250308, 1.2914271512129785, 1.3217658347992496,
+        1.3174199965295386, 1.270726122637577, 1.1915477036773285, 1.0985940684364721,
+        1.0074636041598692, 0.9264130672897058, 0.8580588171721183, 0.8021230947830138,
+        0.7572730888079892, 0.7220308990334429, 0.6951372342853372, 0.6756546361097949,
+        0.6629631812511325, 0.6567204786911158, 0.6568166191147243, 0.6633344986707882,
+        0.6765151829930202, 0.6967208651866276, 0.7243813371055073, 0.7599019596652035,
+        0.8035020850838414, 0.8549480015623455, 0.9131603039650177, 0.9757455364846471,
+        1.0386597239514828, 1.0964098270295017, 1.1431863437623153, 1.1747605273419082,
+        1.1901053823856695, 1.1915811218715306, 1.183632523945538, 1.1710424393747678,
+        1.15772037752031, 1.146259408843986, 1.1379990965383748, 1.1332818645363167,
+        1.1317271768397212, 1.1324721474500286, 1.1343879332794449, 1.1362915704254997,
+        1.137154424464545, 1.1362812900788655, 1.1334186458653663, 1.1287606966797188,
+        1.1228544193971794, 1.1164394719409538, 1.110274418687799, 1.10499228482359,
+        1.1010072877147064, 1.0984753353287156, 1.0973007996976922, 1.0971799693742992,
+        1.0976723707934024, 1.09829041541338, 1.0985942717890564, 1.09827465898813,
+        1.097205543212458, 1.0954545010436463, 1.0932498665034474, 1.090915866365814,
+        1.0887943069238701, 1.087171663652211, 1.0862253557847097, 1.085996197130374,
+        1.0863883024579366, 1.0871938415171103, 1.0881372276261045, 1.088930710367554,
+        1.0893309245152751, 1.0891848308617829, 1.0884550713018186, 1.0872194986687387,
+        1.0856462789635268, 1.0839520474974196, 1.082353934960006, 1.0810261621929405,
+        1.080069214644313, 1.0794959060612892, 1.079235141267311, 1.079151342704743,
+        1.079075240893603, 1.0788399529617085, 1.0783152226548105, 1.0774328825289865,
+        1.0761984064318502, 1.074686648166611, 1.0730236180453177, 1.071359227302613,
+        1.0698374312446846, 1.0685699388271999, 1.0676180966933748, 1.0669854254388387,
+        1.0666211720330503, 1.0664334333344134, 1.0663089785434796, 1.0661359027680297,
+        1.0658248156850296, 1.0653245927497434, 1.0646298676544175, 1.0637792434941926,
+        1.0628451994535566, 1.061918319122027, 1.0610893506336563, 1.0604326095644054,
+        1.059993525578721, 1.0597820367769213, 1.0597723623101156, 1.0599086378905231,
+        1.0601150750025583, 1.0603087403876426, 1.0604127781146437, 1.0603679476918222,
+        1.0601407410449486, 1.0597270185087486, 1.0591509385477014, 1.0584597629588384,
+        1.0577157210026986, 1.0569864043845838, 1.0563351337162883, 1.0558124675947764,
+        1.0554496429744729, 1.0552543587098506, 1.055209020678289, 1.055271382343169,
+        1.0553774202978898, 1.0554462351100318, 1.0553867122232843, 1.0551055765062893,
+        1.0545163146062455, 1.053548243589288, 1.0521548272800147, 1.050320256545609,
+        1.048063382358087, 1.0454383500106263, 1.042531701806043, 1.0394562111397212,
+        1.036342170298048, 1.0333271742175743, 1.0305455638263026, 1.0281186159856046,
+        1.0261463428597528, 1.0247014661834388, 1.0238258315617101, 1.02352927175553,
+        1.0237907348975506, 1.0245613609692583, 1.0257691044653292, 1.0273244501739838,
+        1.029126746199197, 1.031070684649396, 1.0330524995411632, 1.034975524012828,
+        1.03675484735478, 1.0383209204178703, 1.0396220547769706, 1.040625828699806,
+        1.0413194437908793, 1.0417090766428805, 1.0418182582709046, 1.0416853138064974,
+        1.0413599246100036, 1.040898941329861, 1.0403616713533277, 1.0398049673802743,
+        1.0392785298239149, 1.0388208806176835, 1.0384564532058769, 1.0381941659048886,
+        1.0380277055716236, 1.0379375563118345, 1.0378945831061426, 1.0378647513876558,
+        1.0378143681605612, 1.0377151099388655, 1.0375480942421844, 1.037306373615833,
+        1.0369954747927237, 1.0366319300298368, 1.0362400889538868, 1.0358477874954048,
+        1.0354816291186402, 1.0351626732240902, 1.034903227802315, 1.034705234582868,
+        1.0345604561511412, 1.0344523720398282, 1.0343594102860936, 1.034258924324808,
+        1.0341312075112747, 1.0339628419921267, 1.0337488088248248, 1.033493021513657,
+        1.033207241164595, 1.0329086290214295, 1.0326164316737476, 1.0323484309362854,
+        1.0321178041076158, 1.0319309371142094, 1.0317865399143675, 1.0316761696587367,
+        1.0315860156695136, 1.031499582564514, 1.0314007588609033, 1.031276702961756,
+        1.0311200266614533, 1.0309298998696002, 1.0307119117382022, 1.0304767606834921,
+        1.030238061345776, 1.030009708616317, 1.0298033011574559, 1.0296260930339534,
+        1.0294798247893573, 1.0293606110007627, 1.0292598637197872, 1.0291660451626992,
+        1.0290668998800594, 1.028951740219523, 1.028813361906499, 1.0286492477984444,
+        1.028461861292493, 1.0282580079118901, 1.0280474189069493, 1.0278408500505232,
+        1.0276480667615442, 1.0274760916647447, 1.0273280260745639, 1.0272026386684032,
+        1.0270947669433155, 1.02699642733858, 1.026898404374972, 1.026792009125291,
+        1.0266706760686335, 1.0265311077855614, 1.0263737705183873, 1.0262026715834205,
+        1.0260244865055927, 1.0258472227922586, 1.025678686241065, 1.0255250414323835,
+        1.0253897285593419, 1.0252729224663661, 1.0251716130211377, 1.0250802692871015,
+        1.0249919444938012, 1.0248996028518835, 1.0247974156212234, 1.024681787680848,
+        1.0245519336384727, 1.0244099124586368, 1.024260133773297, 1.024108447104613,
+        1.023960998651315, 1.0238230761763094, 1.0236981559263942, 1.0235873197652576,
+        1.0234891361253617, 1.0234000098015281, 1.0233149194865445, 1.023228393594525,
+        1.023135536067289, 1.0230329107808473, 1.0229191255749426, 1.0227950179421097,
+        1.0226634218179038, 1.022528573567454, 1.0223952802094585, 1.0222680124164294,
+        1.0221500925707148, 1.0220431241527266, 1.0219467588677738, 1.0218588324020492,
+        1.0217758310014697, 1.02169359165793, 1.0216080989611833, 1.0215162282630414,
+        1.021416299471507, 1.0213083451293448, 1.0211940524607324, 1.0210764008115212,
+        1.020959071575715, 1.0208457470660013, 1.0207394311430849, 1.0206419156999877,
+        1.020553485983839, 1.020472910837359, 1.020397710366538, 1.0203246431733528,
+        1.0202503170814554, 1.0201718077538005, 1.02008717178007, 1.0199957637254207,
+        1.0198983055031574, 1.0197967036062738, 1.0196936561775376, 1.019592128999898,
+        1.0194948007154792, 1.019403579641574, 1.019319277854737, 1.0192414965654246,
+        1.0191687365210393, 1.0190987058259415, 1.0190287626119874, 1.0189564075068451,
+        1.018879734512228, 1.0187977594085504, 1.0187105697545165, 1.0186192749538532,
+        1.018525772090799, 1.0184323763317125, 1.0183413877030025, 1.0182546751383554,
+        1.0181733527276824, 1.0180976037747496, 1.0180266795926682, 1.0179590674440637,
+        1.017892791629827, 1.0178257888212339, 1.0177562871884778, 1.0176831204413292,
+        1.017605921899507, 1.0175251672390493, 1.0174420630385537, 1.0173583063107443,
+        1.0172757627400553, 1.0171961244430978, 1.017120609700527, 1.0170497574195334,
+        1.0169833502526855, 1.0169204760383528, 1.0168597120677059, 1.016799395136987,
+        1.0167379261345406, 1.0166740533447773, 1.0166070842538206, 1.0165369900973826,
+        1.0164643878254571, 1.016390406687442, 1.0163164671237739, 1.0162440144568583,
+        1.0161742565431882, 1.0161079521856633, 1.016045286473361, 1.0159858525177798,
+        1.0159287394740142, 1.0158727078374798, 1.0158164181069818, 1.015758670504281,
+        1.0156986128184045, 1.0156358804666232, 1.0155706460431544, 1.0155035724179187,
+        1.015435680737405, 1.0153681593695567, 1.015302149404851, 1.0152385452674833,
+        1.0151778450338689, 1.0151200751595906, 1.0150648004385538, 1.015011214732165,
+        1.0149582940258324, 1.0149049830815924, 1.0148503820235062, 1.0147939002938768,
+        1.01473535216006, 1.0146749789658454, 1.0146133965385855, 1.0145514791968326,
+        1.014490202390189, 1.0144304723954245, 1.0143729727489692, 1.0143180532049516,
+        1.014265678845654, 1.0142154461063815, 1.0141666608657307, 1.0141184633945166,
+        1.0140699775553967, 1.0140204583345143, 1.0139694129680452, 1.013916676223476,
+        1.01386242875312, 1.0138071573237675, 1.0137515654168985, 1.0136964505766703,
+        1.013642569726739, 1.0135905148245459, 1.0135406186649465, 1.0134929049892318,
+        1.01344708937891, 1.0134026290606617, 1.0133588120951962, 1.0133148706495085,
+        1.0132700999706918, 1.0132239646229713, 1.0131761763477105, 1.013126732947548,
+        1.0130759139502856, 1.0130242354054428, 1.0129723719743062, 1.0129210586700295,
+        1.0128709866854193, 1.0128227075872847, 1.012776557990609, 1.0127326131708159,
+        1.0126906736177061, 1.0126502840101193, 1.0126107801484399, 1.0125713565032346,
+        1.0125311454772303, 1.0124892992544057, 1.0124450660386781, 1.0123978542353957,
+        1.0123472803027929, 1.0122931982094958, 1.0122357103650783, 1.0121751613467405,
+        1.012112116661656, 1.0120473292131975, 1.0119816962137975, 1.011916209178351,
+        1.0118518994974015, 1.0117897820388242, 1.0117307992994011, 1.0116757687899776,
+        1.0116253364999865, 1.0115799393305147, 1.0115397791968608, 1.0115048110048466,
+        1.0114747458824045, 1.0114490699487264, 1.011427077637782, 1.0114079173153214,
+        1.011390645805834, 1.0113742876324743, 1.0113578943786103, 1.0113405996553797,
+        1.0113216656875141, 1.0113005184299948, 1.0112767692750195, 1.0112502226528954,
+        1.0112208700262244, 1.0111888718017203, 1.0111545294578885, 1.0111182506747183,
+        1.0110805104616927, 1.0110418112533868, 1.0110026447333256, 1.0109634578131486,
+        1.0109246247798909, 1.0108864271540965, 1.0108490422852259, 1.0108125411442388,
+        1.0107768951566534, 1.0107419912619988, 1.0107076537202802, 1.0106736705674442,
+        1.0106398221253907, 1.0106059086800812, 1.0105717744284968, 1.0105373251085574,
+        1.01050253737148, 1.0104674588862976, 1.0104321992832621, 1.0103969132062427,
+        1.0103617777907339, 1.0103269676543836, 1.0102926308513733, 1.0102588691261862,
+        1.010225725203079, 1.010193178837552, 1.0101611520763287, 1.0101295228117848,
+        1.0100981444834742, 1.0100668688670078, 1.0100355684457447, 1.0100041549583458,
+        1.009972591342974, 1.0099408953602476, 1.0099091345023057, 1.0098774131726935,
+        1.0098458543292392, 1.0098145786260089, 1.0097836844369699, 1.009753231941409,
+        1.0097232337384157, 1.0096936533569347, 1.0096644117241154, 1.00963540036376,
+        1.0096064990300766, 1.0095775948109138, 1.0095485995623998, 1.0095194628826265,
+        1.0094901786285349, 1.0094607840864465, 1.0094313521334748, 1.0094019778682681,
+        1.0093727620583517, 1.0093437942105397, 1.0093151380545693, 1.0092868217536368,
+        1.0092588343102096, 1.0092311285715887, 1.0092036301399867, 1.009176250539379,
+        1.0091489023398736, 1.0091215136885217, 1.009094039872658, 1.009066470105504,
+        1.009038828567297, 1.0090111697105881, 1.0089835687788717, 1.0089561092398185,
+        1.0089288692803449, 1.0089019095884304, 1.0088752643570091, 1.0088489368504419,
+        1.0088229000834539, 1.0087971023135411, 1.0087714762819417, 1.008745950576657,
+        1.0087204612160643, 1.0086949615955674, 1.008669429280164, 1.008643868693894,
+        1.0086183094501326, 1.0085928007666187, 1.0085674030036282, 1.0085421777636652,
+        1.0085171781435818, 1.0084924406258327, 1.0084679797665275, 1.0084437863500113,
+        1.0084198291196365, 1.0083960596540746, 1.0083724195197787, 1.0083488485525736,
+        1.0083252930342843, 1.0083017126303564, 1.008278085210233, 1.0082544090303207,
+        1.0082307021567243, 1.0082069993790093, 1.0081833471654387, 1.0081597974013252,
+        1.0081364007224831, 1.0081132002141187, 1.008090226115122, 1.0080674919830523,
+        1.0080449925715036, 1.0080227034803255, 1.0080005824826432, 1.007978572320537,
+        1.0079566046934056, 1.0079346051299367, 1.007912498422929, 1.0078902143029358,
+        1.007867693022767, 1.0078448905178083, 1.0078217828013083, 1.0077983692583614,
+        1.0077746745297194, 1.0077507487363888, 1.007726665893972, 1.007702520499568,
+        1.0076784224330841, 1.0076544904817117, 1.0076308449483418, 1.0076075999194432,
+        1.0075848558259783, 1.0075626929206405, 1.007541166214436, 1.0075203022740211,
+        1.0075000980966933, 1.0074805220769658, 1.0074615168840884, 1.0074430039083715,
+        1.0074248888237636, 1.0074070677642843, 1.007389433621707, 1.007371882031161,
+        1.0073543167036965, 1.0073366538704616, 1.0073188257033134, 1.0073007826579536,
+        1.007282494740268, 1.0072639517260964, 1.0072451623762233, 1.0072261526941584,
+        1.007206963286966, 1.0071876459191598, 1.0071682594007973, 1.0071488650202924,
+        1.0071295218097172, 1.0071102819991273, 1.0070911870585235, 1.0070722647240913,
+        1.0070535273488932, 1.007034971804465, 1.0070165809978653, 1.0069983268772302,
+        1.0069801746045717, 1.0069620874078624, 1.006944031514101, 1.0069259805332047,
+        1.0069079187197503, 1.0068898426825974, 1.0068717613237552, 1.0068536940377997,
+        1.006835667454117, 1.006817711217812, 1.006799853446046, 1.0067821165422493,
+        1.0067645139913763, 1.0067470486039896, 1.0067297124487466, 1.0067124884478336,
+        1.0066953533504384, 1.0066782815867104, 1.006661249373369, 1.006644238412714,
+        1.006627238603644, 1.006610249353043, 1.0065932793100039, 1.0065763446047475,
+        1.0065594659160664, 1.0065426648757785, 1.0065259604165222, 1.0065093656652473,
+        1.0064928858811968, 1.0064765177530144, 1.0064602501366637, 1.0064440660743583,
+        1.0064279457246668, 1.0064118696905786, 1.0063958221780211, 1.0063797934596075,
+        1.0063637812482134, 1.0063477907784752, 1.0063318336175102, 1.0063159254404315,
+        1.0063000831756452, 1.0062843220214308, 1.0062686528443296, 1.0062530803917134,
+        1.006237602601046, 1.006222211093929, 1.006206892738392, 1.0061916319832334,
+        1.0061764135438498, 1.0061612249696874, 1.0061460586561093, 1.0061309129703044,
+        1.0061157923217199, 1.006100706193532, 1.0060856673298884, 1.0060706894140068,
+        1.0060557846508664, 1.0060409616738002, 1.006026224127045, 1.006011570150262,
+        1.0059969928290202, 1.0059824815065461, 1.0059680237058084, 1.0059536073121458,
+        1.0059392226309338, 1.005924863966809, 1.0059105304636644, 1.0058962260797466,
+        1.0058819587259336, 1.005867738739774, 1.0058535769786796, 1.0058394828742065,
+        1.0058254627868888, 1.0058115189396837, 1.0057976490997997, 1.0057838470439535,
+        1.0057701037046023, 1.0057564087790527, 1.0057427525084666, 1.0057291273122677,
+        1.0057155289971451, 1.0057019573417252, 1.0056884159722577, 1.0056749115707213,
+        1.0056614525721113, 1.0056480475925629, 1.0056347038703812, 1.0056214259920773,
+        1.0056082151182664, 1.0055950688310875, 1.0055819816127811, 1.0055689458545032,
+        1.0055559532044038, 1.005542996009877, 1.0055300685990824, 1.0055171681818502,
+        1.0055042952226776, 1.0054914532349197, 1.0054786480479225, 1.0054658866898054,
+        1.0054531760918965, 1.005440521846564, 1.005427927234487, 1.0054153926843699,
+        1.005402915747945, 1.005390491580551, 1.0053781138292428, 1.005365775761624,
+        1.0053534714308447, 1.0053411966713441, 1.0053289497551627, 1.0053167316025358,
+        1.0053045455215839, 1.005292396535103, 1.0052802904232094, 1.0052682326571558,
+        1.0052562274139487, 1.0052442768423637, 1.0052323807024073, 1.0052205364316538,
+        1.0052087396158476, 1.005196984770882, 1.0051852662913414, 1.005173579395401,
+        1.0051619209010452, 1.0051502897024285, 1.0051386868711079, 1.0051271153744394,
+        1.0051155794705966, 1.0051040838945466, 1.0050926329828598, 1.0050812298918999,
+        1.0050698760435304, 1.00505857088911, 1.0050473120245642, 1.0050360956269995,
+        1.00502491712815, 1.005013772000697, 1.0050026565172077, 1.004991568350018,
+        1.0049805069115572, 1.0049694733827903, 1.0049584704330823, 1.0049475016886786,
+        1.0049365710491653, 1.0049256819751728, 1.0049148368722272, 1.0049040366754791,
+        1.0048932807022581, 1.0048825667908305, 1.0048718916934452, 1.0048612516482902,
+        1.004850643025842, 1.0048400629350351, 1.0048295096847015, 1.0048189830238254,
+        1.0048084841246068, 1.0047980153181548, 1.0047875796353394, 1.0047771802377101,
+        1.0047668198403186, 1.0047565002268872, 1.0047462219389953, 1.004735984188624,
+        1.00472578500324, 1.0047156215721174, 1.0047054907285018, 1.0046953894805055,
+        1.0046853154975006, 1.0046752674691095, 1.0046652452780624, 1.0046552499620833,
+        1.004645283477077, 1.0046353483078478, 1.0046254469977667, 1.004615581680674,
+        1.0046057536958413, 1.004595963350145, 1.0045862098646063, 1.0045764915096167,
+        1.0045668059006412, 1.0045571503993387, 1.004547522548448, 1.0045379204649385,
+        1.004528343125098, 1.0045187904956703, 1.004509263492617, 1.0044997637791628,
+        1.0044902934419284, 1.004480854603575, 1.0044714490397781, 1.0044620778655322,
+        1.0044527413423392, 1.004443438835758, 1.004434168926465, 1.0044249296518717,
+        1.0044157188338187, 1.0044065344346376, 1.0043973748805997, 1.0043882392991024,
+        1.0043791276318983, 1.004370040608635, 1.0043609795888202, 1.0043519463022184,
+        1.0043429425336874, 1.0043339698065585, 1.0043250291171537, 1.0043161207632119,
+        1.0043072442919703, 1.004298398573314, 1.0042895819824, 1.004280792658843,
+        1.0042720287978537, 1.0042632889249237, 1.0042545721098266, 1.004245878086952,
+        1.0042372072651624, 1.0042285606287862, 1.0042199395486706, 1.0042113455360868,
+        1.004202779980203, 1.0041942439110971, 1.0041857378247419, 1.0041772615955191,
+        1.0041688144871357, 1.0041603952573384, 1.004152002337553], [2.72696195515166e-10,
+        8.191483708477731e-10, 1.3687872877675697e-09, 1.9237617951066966e-09,
+        2.4862574807358686e-09, 3.058512034314709e-09, 3.6428308875997026e-09,
+        4.2416037882803945e-09, 4.857322113077646e-09, 5.492597290552986e-09,
+        6.150180487414036e-09, 6.832983807260785e-09, 7.544103170051879e-09,
+        8.28684325923805e-09, 9.064744715063148e-09, 9.881614005650024e-09,
+        1.0741556288357569e-08, 1.1649011705462497e-08, 1.260879560926841e-08,
+        1.3626143195170926e-08, 1.470675925711213e-08, 1.5856873640391862e-08,
+        1.708330328319704e-08, 1.839352171073809e-08, 1.9795737025316233e-08,
+        2.1298979571637526e-08, 2.2913200693625085e-08, 2.4649384081416636e-08,
+        2.6519671601773568e-08, 2.853750561330516e-08, 3.0717790316587084e-08,
+        3.3077074787603974e-08, 3.5633761091339454e-08, 3.8408341146471606e-08,
+        4.1423666832291894e-08, 4.4705258383218946e-08, 4.828165715997423e-08,
+        5.2184829713580725e-08, 5.645063149361945e-08, 6.11193397270846e-08,
+        6.623626700261207e-08, 7.185246881809165e-08, 7.802556112403398e-08,
+        8.48206664830583e-08, 9.231151135593067e-08, 1.005817007110641e-07,
+        1.0972620213460336e-07, 1.1985307652654728e-07, 1.310855015318286e-07,
+        1.4356414138946248e-07, 1.5744992929701428e-07, 1.729273413911522e-07,
+        1.9020825813493475e-07, 2.0953653009251156e-07, 2.3119339012548876e-07,
+        2.5550388576565716e-07, 2.828445458592076e-07, 3.1365254369603246e-07,
+        3.4843668272740473e-07, 3.877906083553866e-07, 4.324087497433127e-07,
+        4.831056232813642e-07, 5.408392927489354e-07, 6.067399928667803e-07,
+        6.821451982109875e-07, 7.686427805177166e-07, 8.681243728662625e-07,
+        9.828516947331274e-07, 1.115539446725385e-06, 1.2694595438882872e-06,
+        1.448573056235284e-06, 1.6576984544742837e-06, 1.902727915954319e-06,
+        2.190907983444615e-06, 2.5312075360890967e-06, 2.9348060058268824e-06,
+        3.4157501037114394e-06, 3.991851495993878e-06, 4.6859372890733644e-06,
+        5.527631819576375e-06, 6.555965758894731e-06, 7.8233264002978e-06,
+        9.401691039945454e-06, 1.1392987089376118e-05, 1.3947490095273496e-05,
+        1.7299439768175e-05, 2.1844451213210617e-05, 2.8337552990157022e-05,
+        3.854351921113726e-05, 5.8608863826910805e-05, 0.00020415139839115995,
+        7.394068330665075e-05, 6.266310199234124e-05, 6.27207496486227e-05,
+        6.72631161357249e-05, 7.510034305863153e-05, 8.623588045859682e-05,
+        0.00010121017900505335, 0.00012099526390088082, 0.0001470569106157113,
+        0.00018152258722923102, 0.00022746897396548987, 0.0002893847580014453,
+        0.0003739155722308785, 0.0004910841458207808, 0.0006563391627646922,
+        0.0008941007147913138, 0.0012441156897746316, 0.0017733313222106732,
+        0.0025991955711073267, 0.003938181882236926, 0.006214570231049419,
+        0.010328399160389787, 0.018404034887080038, 0.03629254417845406,
+        0.08469537560393524, 0.28636791273362205, 5.762179266763, 1.0250643434382425,
+        1.9655023658553923, 1.9229284040371974, 0.8218645852296415, 0.7154529963482354,
+        1.0655471459566581, 1.2678945774393506, 0.644687080410972, 0.5599679830797905,
+        0.6790233748900277, 1.0646100973568446, 1.888893771569152, 1.6457080059867584,
+        1.166531464776255, 1.010078793172014, 1.0354157796726142, 1.2323064819822234,
+        1.6715778809207265, 2.0917304354614523, 1.6678260252314847, 1.2008676267278584,
+        0.9701847060477871, 0.885380018008818, 0.9043393203617649, 1.0277567049322074,
+        1.2451907165429308, 1.3227837181868607, 1.074493572505189, 0.8396367324907569,
+        0.7235492584178573, 0.6993465051061978, 0.753372826504461, 0.8962177425196003,
+        1.1484161088251368, 1.434676254615261, 1.4602115084177176, 1.2595795599481594,
+        1.0934187911962714, 1.0225704941415332, 1.0586192391339178, 1.1252930450413619,
+        1.2152481163386426, 1.301462828822672, 1.3426496730848365, 1.3147323160759683,
+        1.2375039519417979, 1.1498620133612654, 1.077715157745821, 1.030600641053185,
+        1.0096334714253048, 1.012840154198796, 1.036638898850723, 1.0748725473418024,
+        1.1166758318704968, 1.1456945620476182, 1.144977346232874, 1.1075099726089823,
+        1.0415051499866463, 0.9630370086213261, 0.885659266461451, 0.8166357615253486,
+        0.7583432496319434, 0.7106275267061388, 0.6723975192192873, 0.6424208476662228,
+        0.6196456912135543, 0.6032949760329503, 0.5928656018963038, 0.5880955282904862,
+        0.5889258343337365, 0.595467147478208, 0.6079702857055437, 0.6267945360966173,
+        0.6523609292903825, 0.6850705738422186, 0.7251597367651358, 0.7724585922964182,
+        0.8260343905558168, 0.8837626680323661, 0.9420133301570089, 0.9958205859512744,
+        1.0398989707563608, 1.0703639211775116, 1.0862178800649744, 1.0895426065321645,
+        1.0843349353941467, 1.0749253512703305, 1.0648711206102943, 1.0565432517047944,
+        1.0511741458478108, 1.0490835678292734, 1.0499232583654003, 1.0528932503758253,
+        1.0569385586929387, 1.0609445030012004, 1.0639317476343728, 1.0652265289009166,
+        1.0645664023698846, 1.0621107149447333, 1.0583553995635677, 1.0539846834005704,
+        1.049707805678999, 1.0461216756008096, 1.0436208640735254, 1.0423581728550044,
+        1.042249294074769, 1.0430128178029108, 1.0442373557055316, 1.0454666722640902,
+        1.046290205748721, 1.0464222883709497, 1.0457526815090143, 1.0443565991579877,
+        1.0424633066239652, 1.0403940029390581, 1.0384867765805619, 1.0370267114767473,
+        1.036194355966737, 1.0360392448671802, 1.0364796790222734, 1.0373262421121863,
+        1.0383238635075802, 1.039204758220341, 1.0397422910247256, 1.0397947604228572,
+        1.0393296092281372, 1.0384230699240338, 1.0372365584925762, 1.035976913629033,
+        1.03485075409009, 1.0340231274556457, 1.0335880840794942, 1.0335553070154455,
+        1.0338536133141103, 1.034349439894853, 1.0348762633745983, 1.0352691882861225,
+        1.0353979010074599, 1.0351913259993986, 1.034649015065634, 1.03383737158819,
+        1.0328724134693816, 1.0318937541476647, 1.0310359576397639, 1.030403208086825,
+        1.030051763899789, 1.0299826324716956, 1.0301448672575317, 1.0304481353593256,
+        1.030781809505362, 1.0310368563896692, 1.0311263601740277, 1.0310008180072299,
+        1.0306554506264622, 1.0301285124374924, 1.029491528340408, 1.0288339926971435,
+        1.0282459331773102, 1.0278017509659703, 1.0275480645819588, 1.027497221025835,
+        1.0276269976592247, 1.0278860003228973, 1.0282034608878259, 1.0285015878083748,
+        1.0287083559891852, 1.028768671545654, 1.0286522248949315, 1.0283570029217457,
+        1.0279082406903124, 1.027353376011858, 1.0267541537085034, 1.026177306134039,
+        1.0256852061832198, 1.0253276278381507, 1.0251353787430908, 1.0251162044002489,
+        1.025253079623779, 1.025504824622991, 1.0258088923090158, 1.0260861262350618,
+        1.026247234942706, 1.0262006301175923, 1.0258611204086505, 1.0251587613127302,
+        1.024046987502589, 1.0225090688222598, 1.0205619993564068, 1.0182571794436803,
+        1.0156776570154484, 1.0129321770575281, 1.0101467365277563, 1.0074546558712627,
+        1.004986299290659, 1.0028595040588286, 1.0011715629634512, 0.9999933156440154,
+        0.9993656124513467, 0.9992981645845072, 0.9997706053992694, 1.000735457458321,
+        1.0021226154451222, 1.0038449041565272, 1.0058042474700633, 1.0078979894235376,
+        1.0100249460385378, 1.0120908369018637, 1.0140128414166534, 1.0157231301848764,
+        1.0171713167220833, 1.0183258410608143, 1.0191743271401925, 1.0197229565009285,
+        1.0199948896025304, 1.0200277658406083, 1.019870342424717, 1.0195783973160084,
+        1.019210114504908, 1.0188212713167846, 1.0184606320200207, 1.018165996439201,
+        1.0179613402380385, 1.0178554079650612, 1.0178419828423322, 1.017901869018709,
+        1.0180064014629715, 1.0181220739042773, 1.0182156829329383, 1.0182592675619342,
+        1.0182341143092282, 1.0181332170129755, 1.0179618191509654, 1.0177359846418434,
+        1.0174794783203658, 1.0172195207964265, 1.0169821585648828, 1.0167880300328547,
+        1.0166492128397286, 1.0165676332717297, 1.0165352449872536, 1.0165358870799128,
+        1.016548455590422, 1.0165508092368383, 1.0165237140181709, 1.0164541351461274,
+        1.0163373122790291, 1.016177285043669, 1.0159858268122643, 1.015780037409208,
+        1.015579081249082, 1.015400692233266, 1.015258080618212, 1.015157775918169,
+        1.0150987501889508, 1.015072926259031, 1.0150669281035882, 1.0150647161915551,
+        1.0150506037899023, 1.0150120953476895, 1.014942035212988, 1.014839695927228,
+        1.0147106432819368, 1.014565448822987, 1.0144175327337395, 1.0142805699425932,
+        1.0141659539195462, 1.014080779659893, 1.0140266921594605, 1.0139997752504026,
+        1.0139914611205616, 1.0139902575426618, 1.0139839486669724, 1.013961849673841,
+        1.0139166982311376, 1.0138458454448873, 1.013751550106289, 1.0136403544250239,
+        1.0135216922684482, 1.0134060184450928, 1.0133028246696854, 1.0132189130340556,
+        1.0131572343511788, 1.0131164823470873, 1.0130914891302027, 1.0130743196879164,
+        1.0130558392244509, 1.0130274480211565, 1.0129826573198841, 1.012918219404542,
+        1.01283461724014, 1.0127358452326898, 1.0126285477704475, 1.012520699779244,
+        1.0124200916076675, 1.0123329061319126, 1.0122626469959308, 1.012209601708901,
+        1.012170917999843, 1.012141256661081, 1.0121138799330445, 1.0120819594060193,
+        1.0120398540921114, 1.0119841228770872, 1.0119140925360088, 1.0118318912564879,
+        1.011741960485656, 1.0116501547928147, 1.0115626120159187, 1.0114846114884364,
+        1.0114196317067674, 1.0113687736860844, 1.0113306426358246, 1.0113016930937715,
+        1.0112769575514517, 1.0112510110138277, 1.011218985468698, 1.0111774451092395,
+        1.0111249650918863, 1.0110623168458959, 1.0109922394219353, 1.010918854115428,
+        1.0108468438394866, 1.0107805578364526, 1.0107232100511148, 1.010676315836337,
+        1.0106394624144834, 1.0106104437684842, 1.0105857227044215, 1.010561124045106,
+        1.0105326235705734, 1.0104970839912193, 1.0104528036866607, 1.0103997828048163,
+        1.010339666715382, 1.0102753878931003, 1.0102105824066105, 1.0101488961822722,
+        1.010093312451864, 1.0100456232206962, 1.0100061368476718, 1.0099736674431992,
+        1.0099457987756932, 1.0099193655153964, 1.0098910567963009, 1.0098580277091451,
+        1.0098184064551226, 1.0097716075366785, 1.0097183998172155, 1.00966072497062,
+        1.0096013078272925, 1.0095431368747827, 1.009488914214539, 1.0094405763473728,
+        1.009398970656165, 1.009363741137403, 1.0093334370523996, 1.009305817219502,
+        1.009278288037611, 1.0092483910378063, 1.0092142494560377, 1.0091748936939275,
+        1.0091304102240897, 1.0090818925578142, 1.0090312097664025, 1.0089806408396396,
+        1.0089324459799383, 1.0088884549529353, 1.0088497467358903, 1.0088164755806426,
+        1.0087878702089927, 1.0087624006386007, 1.0087380770059717, 1.0087128220368278,
+        1.0086848473556163, 1.0086529653518055, 1.00861678217666, 1.0085767407498734,
+        1.0085340108751615, 1.008490251382731, 1.008447291566549, 1.008406792184679,
+        1.0083699479292727, 1.0083372836864901, 1.0083085782500376, 1.0082829251072039,
+        1.008258914970866, 1.0082349033609486, 1.0082093124373852, 1.0081809117435405,
+        1.0081490280597247, 1.0081136488903837, 1.008075404365606, 1.0080354346792333,
+        1.007995170503903, 1.007956068517575, 1.0079193508023667, 1.0078857945450572,
+        1.0078556079337142, 1.0078284115887457, 1.007803325446353, 1.0077791422639464,
+        1.0077545541297972, 1.0077283900159297, 1.0076998217853592, 1.0076685030222745,
+        1.0076346181209603, 1.0075988357237493, 1.0075621777519421, 1.0075258298523115,
+        1.007490928583982, 1.0074583635976666, 1.007428629141503, 1.0074017494145622,
+        1.007377288522464, 1.0073544406210184, 1.0073321819568566, 1.0073094562979887,
+        1.0072853603444964, 1.00725929679481, 1.0072310694269153, 1.0072009054811355,
+        1.0071694037478887, 1.007137419702449, 1.007105909541705, 1.0070757613296801,
+        1.0070476427127397, 1.0070218908096613, 1.0069984617843413, 1.0069769468255432,
+        1.0069566497314963, 1.0069367110115486, 1.0069162560647895, 1.0068945417034134,
+        1.0068710764563247, 1.0068456953437404, 1.0068185781095365, 1.0067902097142931,
+        1.0067612915162079, 1.0067326193979755, 1.0067049499123042, 1.006678876663046,
+        1.0066547366042098, 1.0066325603253587, 1.0066120727696501, 1.0065927425348264,
+        1.0065738703043055, 1.0065547012185658, 1.0065345429329917, 1.0065128710483007,
+        1.0064894063758043, 1.00646415350469, 1.0064373964494617, 1.0064096537087763,
+        1.0063816008375288, 1.006353972803781, 1.0063274604719061, 1.0063026153980104,
+        1.0062797749742158, 1.0062590163288114, 1.0062401429641186, 1.0062227036185538,
+        1.0062060389221372, 1.0061893485528786, 1.0061717700487827, 1.006152460206496,
+        1.0061306709188589, 1.006105813041987, 1.0060775040419254, 1.0060455973656044,
+        1.0060101933995271, 1.0059716333269868, 1.0059304781058593, 1.0058874752156304,
+        1.0058435158971157, 1.005799585500768, 1.005756709426286, 1.0057158970866533,
+        1.0056780864025576, 1.0056440914950868, 1.0056145564063452, 1.0055899177213776,
+        1.0055703787782768, 1.0055558976600973, 1.0055461903447995, 1.0055407492968091,
+        1.005538876525866, 1.0055397288683614, 1.005542372129911, 1.0055458399186274,
+        1.0055491926057725, 1.005551571925094, 1.00555224724628, 1.0055506504525,
+        1.0055463974919026, 1.005539295909716, 1.0055293388564008, 1.005516687086555,
+        1.0055016412329378, 1.0054846071253956, 1.0054660571338065, 1.0054464904875366,
+        1.005426395316787, 1.0054062148297025, 1.0053863196273332, 1.0053669876912497,
+        1.0053483930651803, 1.0053306036886718, 1.0053135882273614, 1.0052972310906405,
+        1.0052813541654029, 1.0052657431791014, 1.0052501761110881, 1.0052344507804465,
+        1.0052184087252962, 1.0052019527999219, 1.0051850565576868, 1.005167764412827,
+        1.0051501826853768, 1.0051324627908573, 1.005114778877755, 1.0050973029825325,
+        1.0050801811349972, 1.0050635137322361, 1.0050473429037028, 1.0050316485856747,
+        1.0050163537503134, 1.005001337881022, 1.0049864565587623, 1.004971564115905,
+        1.0049565358714119, 1.0049412865577794, 1.0049257821745228, 1.0049100435586689,
+        1.0048941412813093, 1.004878182849787, 1.0048622943967946, 1.0048465998777072,
+        1.0048312011427278, 1.0048161620492104, 1.0048014990706353, 1.0047871797635224,
+        1.004773129156187, 1.0047592428385155, 1.0047454044702664, 1.004731504757238,
+        1.004717458772796, 1.004703218845889, 1.0046887810289904, 1.004674184260174,
+        1.004659502554301, 1.004644831694143, 1.0046302727570662, 1.0046159152701655,
+        1.0046018227707554, 1.0045880230750903, 1.0045745047170296, 1.0045612199594889,
+        1.0045480936868536, 1.0045350365383103, 1.004521959993261, 1.0045087908690706,
+        1.0044954828674297, 1.0044820233664182, 1.0044684344949226, 1.0044547684968712,
+        1.00444109832914, 1.0044275051858091, 1.004414065085666, 1.0044008367374404,
+        1.004387852609281, 1.0043751145370219, 1.0043625944188697, 1.0043502396991046,
+        1.004337982580869, 1.004325751348866, 1.0043134819090167, 1.0043011276955667,
+        1.0042886664350672, 1.004276102822112, 1.0042634668516952, 1.0042508082499977,
+        1.0042381880374742, 1.004225668656488, 1.004213304247832, 1.00420113255688,
+        1.004189169622619, 1.0041774079170718, 1.0041658180450006, 1.004154353575686,
+        1.0041429581416856, 1.0041315736628669, 1.0041201484671625, 1.004108644179046,
+        1.004097040501251, 1.0040853373718135, 1.0040735543741137, 1.0040617276500912,
+        1.0040499048647562, 1.0040381389605704, 1.0040264815103417, 1.0040149764358353,
+        1.0040036547295152, 1.0039925306328863, 1.003981599522185, 1.0039708375616685,
+        1.0039602030288353, 1.0039496391042604, 1.0039390778510948, 1.0039284450762833,
+        1.0039176657538627, 1.0039066696874301, 1.0038953970848898, 1.003883803711519,
+        1.0038718652815743, 1.0038595807532178, 1.0038469742187806, 1.0038340951419897,
+        1.0038210167914094, 1.0038078328526439, 1.0037946523603594, 1.0037815932574232,
+        1.0037687750399775, 1.0037563110616328, 1.003744301127857, 1.003732825001497,
+        1.0037219373604305, 1.0037116646073982, 1.0037020037482551, 1.003692923352732,
+        1.0036843664179746, 1.0036762547942177, 1.0036684947219412, 1.0036609829801777,
+        1.0036536131553384, 1.0036462815989755, 1.0036388927348792, 1.0036313634811078,
+        1.0036236266523408, 1.0036156332888924, 1.0036073539131103, 1.003598778743327,
+        1.0035899169070186, 1.003580794700612, 1.0035714529560023, 1.003561943603469,
+        1.003552325571646, 1.00354266023429, 1.003533006690603, 1.0035234172343765,
+        1.0035139334091616, 1.0035045830447382, 1.0034953786138836, 1.003486317135148,
+        1.0034773816860056, 1.0034685443999207, 1.003459770627215, 1.0034510237734757,
+        1.0034422702192305, 1.003433483692853, 1.0034246485255445, 1.0034157613597894,
+        1.0034068310931659, 1.0033978770885454, 1.0033889259317939, 1.003380007230948,
+        1.0033711490913613, 1.0033623739468422, 1.0033536953678488, 1.003345116312944,
+        1.0033366290623562, 1.0033282168083546, 1.0033198566185735, 1.003311523276494,
+        1.003303193372387, 1.003294848988718, 1.0032864804005317, 1.0032780873805303,
+        1.0032696789318485, 1.0032612715300997, 1.0032528861973946, 1.003244544915176,
+        1.0032362669802333, 1.0032280659043584, 1.0032199473549193, 1.0032119084500923,
+        1.0032039384903206, 1.0031960209668573, 1.0031881364788902, 1.0031802660477596,
+        1.003172394262682, 1.003164511734432, 1.0031566164628656, 1.0031487139169601,
+        1.00314081584856, 1.003132938074603, 1.00312509763147, 1.0031173098013593,
+        1.003109585519569, 1.0031019295937322, 1.003094340016635, 1.0030868084604767,
+        1.0030793218364056, 1.0030718646240868, 1.0030644215520217, 1.0030569801601685,
+        1.0030495328089548, 1.0030420778052245, 1.0030346194760202, 1.003027167206563,
+        1.0030197336364528, 1.0030123323480629, 1.003004975459546, 1.0029976715404314,
+        1.0029904242007945, 1.0029832315793368, 1.0029760867941788, 1.0029689792520313,
+        1.0029618965655724, 1.0029548267303066, 1.002947760176555, 1.002940691344143,
+        1.0029336195197414, 1.002926548811543, 1.0029194872892546, 1.0029124454614429,
+        1.002905434372803, 1.002898463662298, 1.002891539920674, 1.002884665624654,
+        1.0028778388171653, 1.002871053568607, 1.0028643011171041, 1.0028575714703274,
+        1.0028508551768214, 1.0028441449532868, 1.0028374368878457, 1.0028307310209508,
+        1.0028240312195138, 1.002817344385552, 1.0028106791556488, 1.002804044332209,
+        1.0027974473277772, 1.0027908928937719, 1.0027843823479103, 1.002777913421659,
+        1.0027714807373593, 1.002765076814397, 1.0027586934140038, 1.002752322978255,
+        1.0027459599090838, 1.0027396014679721, 1.0027332481494173, 1.002726903477339,
+        1.0027205732760052, 1.0027142645577172, 1.0027079842326612, 1.0027017378719973,
+        1.0026955287396084, 1.0026893572550606, 1.002683220970387, 1.0026771150509952,
+        1.0026710331629214, 1.0026649686000697, 1.0026589154474066, 1.0026528695752293,
+        1.0026468292947657, 1.0026407955690724, 1.0026347717540853, 1.0026287629276511,
+        1.002622774934935, 1.0026168133250446, 1.0026108823680129, 1.0026049843222928,
+        1.0025991190745138, 1.0025932842048324, 1.0025874754553425, 1.0025816875089426,
+        1.0025759149342568, 1.0025701531268656, 1.0025643990822626, 1.0025586518697072,
+        1.002552912731906, 1.0025471848028538, 1.0025414725031256, 1.0025357807266913,
+        1.002530113966748, 1.0025244755347469, 1.0025188670064304, 1.002513287985439,
+        1.0025077362172274, 1.0025022080238442, 1.0024966989751047, 1.0024912046725205,
+        1.0024857215060845, 1.0024802472525784, 1.002474781415123, 1.0024693252517776,
+        1.0024638814964606, 1.0024584538292207, 1.002453046194962, 1.0024476620935596,
+        1.0024423039659582, 1.002436972780701, 1.0024316678876823, 1.0024263871574386,
+        1.0024211273741435, 1.002415884807104, 1.0024106558564816, 1.002405437658936,
+        1.0024002285488762, 1.0023950282990284, 1.002389838104378, 1.0023846603192734,
+        1.0023794980000595, 1.0023743543379462, 1.0023692320836841, 1.0023641330642583,
+        1.0023590578730597, 1.0023540057827869, 1.0023489748902195, 1.0023439624616732,
+        1.002338965413878, 1.002333980843407, 1.0023290065116313, 1.0023240412025132,
+        1.0023190848946368, 1.002314138722707, 1.0023092047407576, 1.002304285533198,
+        1.0022993837449572, 1.0022945016138236, 1.0022896405856303, 1.0022848010763103,
+        1.0022799824178927, 1.0022751829927836, 1.0022704005281875, 1.0022656324957582,
+        1.002260876544994, 1.002256130895063, 1.0022513946188778, 1.0022466677736401,
+        1.0022419513594718, 1.0022372471177494, 1.0022325572078743, 1.002227883820746,
+        1.0022232287966149, 1.0022185933121668, 1.002213977688266, 1.0022093813477828,
+        1.0022048029266402, 1.002200240515171, 1.0021956919854151, 1.0021911553467582,
+        1.002186629069065, 1.0021821123197665, 1.00217760507728, 1.0021731081050482,
+        1.0021686227942903, 1.0021641509053894, 1.002159694253818, 1.0021552543945798,
+        1.0021508323576376, 1.0021464284770185, 1.0021420423392617, 1.0021376728566427,
+        1.0021333184495809, 1.0021289773054196, 1.0021246476690469, 1.002120328117065,
+        1.002116017771369, 1.0021117164192213, 1.0021074245230452, 1.0021031431215508,
+        1.0020988736410756, 1.0020946176498542, 1.0020903765958695, 1.0020861515701527,
+        1.002081943131906, 1.0020777512209533, 1.0020735751683758, 1.0020694138007533,
+        1.0020652656191689], [1.1835403379745314e-10, 3.555373187140863e-10,
+        5.941496557999488e-10, 8.351549640571563e-10, 1.0795340881946528e-09,
+        1.3282918774450536e-09, 1.5824644040581848e-09, 1.8431266124274074e-09,
+        2.1114003208268495e-09, 2.3884627436182535e-09, 2.675555608280313e-09,
+        2.9739949837870196e-09, 3.2851819024854505e-09, 3.6106139541388902e-09,
+        3.9518979409167125e-09, 4.3107637941219666e-09, 4.689079902911046e-09,
+        5.088870064627245e-09, 5.512332290898418e-09, 5.961859698554379e-09,
+        6.44006382098526e-09, 6.949800616973548e-09, 7.49419959700268e-09,
+        8.076696478808458e-09, 8.701069867553336e-09, 9.371482521090996e-09,
+        1.009252787152983e-08, 1.0869282516950241e-08, 1.1707365579724517e-08,
+        1.2613005883687069e-08, 1.359311815618895e-08, 1.4655389514343985e-08,
+        1.58083778406285e-08, 1.70616237874708e-08, 1.8425778531603454e-08,
+        1.9912749661831513e-08, 2.153586806883265e-08, 2.331007909390415e-08,
+        2.5252161858060937e-08, 2.738098123977489e-08, 2.9717777894699538e-08,
+        3.228650250474628e-08, 3.511420171352082e-08, 3.823146438444515e-08,
+        4.167293858319187e-08, 4.547793134413181e-08, 4.969110596979556e-08,
+        5.436329377868231e-08, 5.955244124939384e-08, 6.532471677583582e-08,
+        7.175580667404212e-08, 7.893243565599573e-08, 8.695415408635549e-08,
+        9.593544327540622e-08, 1.0600820044371926e-07, 1.1732467798360091e-07,
+        1.3006096795850082e-07, 1.444211417613296e-07, 1.606421798331929e-07,
+        1.7899985572295546e-07, 1.9981577623815885e-07, 2.234658258158518e-07,
+        2.5039032088635e-07, 2.811062524207453e-07, 3.162220858067405e-07,
+        3.564557019838802e-07, 4.026562082509758e-07, 4.5583053137458073e-07,
+        5.171759401361209e-07, 5.88119943126571e-07, 6.703693923030219e-07,
+        7.659711177603822e-07, 8.773870602106759e-07, 1.0075876977970794e-06,
+        1.160168652264552e-06, 1.3394967800346295e-06, 1.5508939328151033e-06,
+        1.8008690498160917e-06, 2.0974125491956944e-06, 2.4503714083486315e-06,
+        2.8719292607637398e-06, 3.3772238893109066e-06, 3.985145450235829e-06,
+        4.719373771140952e-06, 5.609733785647903e-06, 6.693976940438192e-06,
+        8.020136705018219e-06, 9.649663144393877e-06, 1.1661622360481309e-05,
+        1.4158362667271698e-05, 1.7273217349174793e-05, 2.118105971151687e-05,
+        2.611288939013673e-05, 3.2376171906734795e-05, 4.038347473817091e-05,
+        5.06932016164986e-05, 6.40681810801985e-05, 8.156094721130574e-05,
+        0.00010463948727792045, 0.00013537528160356013, 0.00017672884111544432,
+        0.00023299066077073037, 0.0003104749667545564, 0.0004186339898508787,
+        0.0005718896064753661, 0.0007927239927382913, 0.0011170526544350273,
+        0.0016038924897671196, 0.0023534728657599786, 0.003542825861318381,
+        0.005499902567771971, 0.008869461979449008, 0.015020395455293857,
+        0.027178266565380825, 0.05418816420118147, 0.12712520819255782,
+        0.4286291537569104, 8.49776063936103, 1.4610433126933227, 2.618100503530531,
+        2.2410885612430644, 0.7166715628649272, 0.2562183598399911, 0.5344596612803187,
+        2.1920788009435213, 1.9764261082635415, 2.464647802972177, 4.7068596840575365,
+        8.194759701810701, 7.074723869242503, 4.368327670664487, 2.436557583385926,
+        1.7523480791775332, 1.5458216750164206, 1.6267112104464012, 1.99727260529831,
+        2.313478665656405, 1.747197682108454, 1.2208317559572963, 0.9816135924535945,
+        0.9139414401405913, 0.9738133174148624, 1.1745357784092438, 1.5255874571714843,
+        1.7404315590129382, 1.5077812381457396, 1.2387345186052612, 1.1011624210285234,
+        1.0760170850616182, 1.1508676009759577, 1.3402281322076186, 1.6648045280503245,
+        2.0039731097451923, 1.958787545507012, 1.6199247188096828, 1.346357274083572,
+        1.2001084969799058, 1.197706310444427, 1.261675417002817, 1.352080504156667,
+        1.4390977630907837, 1.4775411464205512, 1.4416115649609835, 1.353405817589055,
+        1.2553361618660266, 1.175289208612121, 1.1232793072690999, 1.1002459779422185,
+        1.103863247398859, 1.130116124709725, 1.1722113297821242, 1.2182236590136666,
+        1.2502272958105844, 1.249638135225881, 1.2087404291397414, 1.136488259007296,
+        1.0504591837452348, 0.9654928872661669, 0.8895562435457426, 0.8252697924979392,
+        0.7724819747356806, 0.7300123018219299, 0.6965216976639728, 0.6708646389108317,
+        0.6521921271691313, 0.6399507678938758, 0.6338467723114429, 0.633804586912462,
+        0.6399304434329366, 0.6524807027775047, 0.6718279368381469, 0.6984112289241113,
+        0.7326494394008112, 0.7747873111873346, 0.8246392566341783, 0.8812103835461106,
+        0.942241123126477, 1.0038739426935772, 1.0608340389902875, 1.1075085671108718,
+        1.1397736973364783, 1.1565719146934528, 1.160114816226524, 1.1546455576284647,
+        1.1447590832135837, 1.1342269783511871, 1.125559284019806, 1.1200553377201807,
+        1.1180437314646525, 1.1191419815740833, 1.1224863076226552, 1.126940953484582,
+        1.1313065589718483, 1.1345286489912711, 1.135879869311709, 1.135073377163573,
+        1.1322742924718, 1.1280086849776731, 1.123004956439269, 1.1180191426190274,
+        1.1136880255026913, 1.110433023392973, 1.1084183497157574, 1.10755644565828,
+        1.1075512058702737, 1.1079700122632292, 1.1083346530372906, 1.1082175247371098,
+        1.1073253076023655, 1.105551739368711, 1.1029871778785976, 1.099884309986258,
+        1.096591654596612, 1.0934738757064193, 1.0908380494475323, 1.0888797312285938,
+        1.0876556840257399, 1.0870843098769554, 1.0869709224751776, 1.0870522452320222,
+        1.0870519972506378, 1.0867371278922027, 1.0859632516921613, 1.0846994883605634,
+        1.0830276503186136, 1.0811172898546626, 1.079184097270979, 1.077442379712226,
+        1.07606218128047, 1.0751389199228436, 1.0746797591266268, 1.0746074947084188,
+        1.074779950838324, 1.0750206571442147, 1.0751548205732784, 1.0750435456150698,
+        1.0746094102900692, 1.0738482653383048, 1.072825306768182, 1.0716572011491128,
+        1.0704851216855313, 1.0694450782971558, 1.0686416978199975, 1.0681300843460406,
+        1.0679082803927258, 1.0679207404753832, 1.0680714100700366, 1.0682435569233808,
+        1.0683224838373142, 1.0682168047098948, 1.0678742781996668, 1.0672893450090475,
+        1.0665013245829316, 1.0655842438012995, 1.0646309369612832, 1.0637349520500345,
+        1.062973801920381, 1.0623963837259898, 1.062016282518805, 1.0618114898953213,
+        1.061730013063927, 1.0617000203438436, 1.0616426040396034, 1.0614849707714284,
+        1.0611719268112876, 1.0606739226952449, 1.0599906050519867, 1.0591496618655427,
+        1.0582015547421166, 1.0572113307095314, 1.0562489899517646, 1.055379849658957,
+        1.0546560706990353, 1.0541101290435866, 1.0537506364999705, 1.0535606226206142,
+        1.0534982067259682, 1.053499496607819, 1.0534835032191017, 1.0533588068908208,
+        1.053031610999291, 1.0524146608037055, 1.0514363102741118, 1.050048842803927,
+        1.0482350658917166, 1.0460122710026274, 1.0434329072648345, 1.0405817342716168,
+        1.037569712840893, 1.034525350753974, 1.0315845402545707, 1.0288800463333878,
+        1.026531729816276, 1.0246383669605992, 1.023271631639137, 1.02247250714163,
+        1.0222501391612182, 1.0225829487037872, 1.0234216908062999, 1.0246940590441314,
+        1.0263103841928414, 1.0281699519867957, 1.0301674706735826, 1.0321992577684242,
+        1.0341687876894552, 1.0359913402454168, 1.037597598014142, 1.038936137580193,
+        1.0399748274496838, 1.0407011764727214, 1.0411216772367613, 1.0412601774522472,
+        1.0411553120981196, 1.0408570587482144, 1.040422544784037, 1.039911329996282,
+        1.0393804912432878, 1.0388799217140663, 1.0384483021768751, 1.0381101888137705,
+        1.037874584730778, 1.0377352221054914, 1.0376725898643604, 1.0376575170380218,
+        1.037655893150207, 1.0376339115181712, 1.037563100906885, 1.0374244022396657,
+        1.0372106690706486, 1.0369272139756445, 1.036590347317012, 1.0362241961411918,
+        1.0358563793312157, 1.0355132939683551, 1.0352158077590665, 1.0349760547850513,
+        1.0347958231200542, 1.0346667441030037, 1.034572190511255, 1.0344905102144542,
+        1.034399005099568, 1.0342779473390749, 1.034113929426183, 1.0339019745982545,
+        1.033646069636752, 1.033358078220327, 1.0330552907311112, 1.0327571060693388,
+        1.0324814777987346, 1.0322417706332856, 1.0320445699889613, 1.0318887940725794,
+        1.0317662139846016, 1.031663235794495, 1.0315635807817074, 1.031451351070729,
+        1.0313139125276536, 1.0311440751079284, 1.0309411944883393, 1.0307110303471536,
+        1.030464433962149, 1.030215153302872, 1.029977195804606, 1.029762251227776,
+        1.029577643133513, 1.0294251601886049, 1.029300944215597, 1.0291964143112422,
+        1.0291000203606737, 1.0289994761900092, 1.0288840462152975, 1.0287464624634113,
+        1.0285841300523575, 1.0283994226043847, 1.0281990460667279, 1.0279926246880173,
+        1.0277908022233517, 1.0276032293973865, 1.0274368136516454, 1.027294542616062,
+        1.0271750745570043, 1.027073141409896, 1.0269806603056555, 1.0268883239661224,
+        1.0267873602931505, 1.0266711301945857, 1.0265362730778769, 1.0263832030003905,
+        1.0262158864307596, 1.026040969472382, 1.0258664414663583, 1.0257001008899889,
+        1.0255481152386325, 1.0254139370892381, 1.0252977622606816, 1.0251966092317681,
+        1.0251049823082492, 1.0250159755491433, 1.0249225985050683, 1.0248190711814238,
+        1.02470184948343, 1.0245702001965484, 1.0244262345048158, 1.0242744132399655,
+        1.0241206351211898, 1.0239710926634022, 1.0238311163106981, 1.0237042207357203,
+        1.0235915214872615, 1.0234916155865348, 1.0234009310866419, 1.0233144644871943,
+        1.023226756543339, 1.023132918160316, 1.023029514987919, 1.0229151517346817,
+        1.022790658232798, 1.0226588566862624, 1.0225239681842022, 1.0223907815040916,
+        1.0222637467255646, 1.022146163916445, 1.0220396131512774, 1.0219437222552517,
+        1.0218563031532506, 1.0217738190090175, 1.021692084931438, 1.0216070652989302,
+        1.0215156173412818, 1.0214160452892158, 1.0213083687394768, 1.0211942649138566,
+        1.0210767062347361, 1.0209593703095214, 1.020845938784248, 1.0207394178856695,
+        1.020641604753982, 1.020552792555208, 1.0204717604620128, 1.0203960410158195,
+        1.0203224070154733, 1.0202474818672251, 1.020168357802747, 1.0200831085518913,
+        1.019991105971606, 1.0198930890040232, 1.0197909805088883, 1.0196874939592486,
+        1.0195856090897786, 1.019488016811755, 1.0193966357669977, 1.0193122861944555,
+        1.0192345751336633, 1.0191620067044738, 1.019092289853187, 1.0190227810002304,
+        1.0189509765378266, 1.0188749637900503, 1.0187937495505819, 1.0187074102635671,
+        1.0186170423148406, 1.0185245281286024, 1.018432166859418, 1.018342241482069,
+        1.0182566031649403, 1.0181763478529695, 1.0181016406616048, 1.018031715006144,
+        1.0179650408687224, 1.017899626202147, 1.0178333925601177, 1.0177645545011873,
+        1.0176919338761377, 1.0176151541106382, 1.0175346831245444, 1.0174517220081882,
+        1.0173679646392677, 1.017285275960926, 1.0172053497391829, 1.0171294082505389,
+        1.017057996661689, 1.0169909060297904, 1.0169272345909937, 1.016865571844543,
+        1.0168042683934448, 1.016741740293985, 1.016676752099765, 1.0166086283895308,
+        1.0165373580247963, 1.016463575818033, 1.016388428821485, 1.0163133549289156,
+        1.0162398162886195, 1.0161690366941827, 1.0161017897555855, 1.0160382740205849,
+        1.0159780945175114, 1.0159203506097612, 1.0158638111544087, 1.0158071430575941,
+        1.0157491509187062, 1.0156889848331823, 1.0156262804469012, 1.0155612085333716,
+        1.015494428155144, 1.015426954759503, 1.0153599692474162, 1.0152946036243105,
+        1.015231741782667, 1.0151718700097487, 1.0151150019178996, 1.0150606886178157,
+        1.0150081096694938, 1.0149562263651357, 1.014903968609739, 1.0148504217326773,
+        1.014794980664753, 1.014737445656674, 1.014678044729145, 1.0146173812621344,
+        1.0145563181649955, 1.0144958206567125, 1.014436786078673, 1.0143798904191887,
+        1.0143254773386878, 1.01427350732267, 1.0142235737249141, 1.0141749808525926,
+        1.0141268688872571, 1.014078363034578, 1.01402872098516, 1.0139774539506383,
+        1.013924401836595, 1.0138697514719972, 1.0138139967016864, 1.0137578488393528,
+        1.0137021138614213, 1.01364755756616, 1.0135947810697647, 1.0135441264541658,
+        1.013495626725125, 1.013449006562216, 1.01340373198896, 1.013359099437543,
+        1.0133143489090874, 1.0132687828490143, 1.013221872300416, 1.0131733346962795,
+        1.0131231726926075, 1.0130716697986502, 1.0130193451573997, 1.012966875636997,
+        1.0129149975890341, 1.0128644027104041, 1.0128156422862595, 1.0127690519257835,
+        1.0127247052472594, 1.0126824005141697, 1.0126416796994513, 1.012601875513096,
+        1.0125621790494752, 1.012521719149707, 1.012479644351006, 1.012435199223685,
+        1.012387788647286, 1.0123370257513447, 1.0122827614553087, 1.0122250954732108,
+        1.0121643701049086, 1.0121011490523883, 1.0120361839285148, 1.0119703712003718,
+        1.011904702200755, 1.0118402087069382, 1.011777906535536, 1.0117187396752085,
+        1.0116635276414354, 1.0116129188998662, 1.0115673532483163, 1.0115270358594108,
+        1.0114919251892902, 1.0114617361352007, 1.0114359587256436, 1.0114138913613517,
+        1.0113946863477663, 1.0113774043370545, 1.0113610734842813, 1.0113447487279812,
+        1.0113275666810368, 1.011308792145577, 1.0112878531657679, 1.0112643626791433,
+        1.0112381260710654, 1.0112091351324666, 1.0111775499457756, 1.0111436709976274,
+        1.0111079043046554, 1.0110707225486373, 1.011032625190043, 1.0109941003202698,
+        1.0109555906790764, 1.0109174658493576, 1.0108800021711744, 1.010843371400628,
+        1.0108076385724507, 1.0107727689085562, 1.0107386429573375, 1.010705078483121,
+        1.010671857006535, 1.0106387524000473, 1.0106055586509377, 1.0105721138911434,
+        1.0105383181068206, 1.0105041425858707, 1.0104696300919982, 1.0104348858709802,
+        1.0104000607583505, 1.0103653287043393, 1.0103308618023854, 1.0102968062721056,
+        1.010263262731991, 1.0102302734980113, 1.010197818634438, 1.0101658212035391,
+        1.0101341608003414, 1.0101026932254844, 1.0100712732369075, 1.0100397768764178,
+        1.0100081199649171, 1.0099762699878707, 1.009944249654056, 1.0099121317359463,
+        1.0098800261775065, 1.0098480616626728, 1.0098163646817149, 1.0097850394792158,
+        1.0097541520647724, 1.009723720754738, 1.0096937146124658, 1.0096640598506557,
+        1.0096346529684153, 1.0096053783289805, 1.0095761272129316, 1.0095468152093898,
+        1.0095173951533205, 1.0094878636134668, 1.0094582600416098, 1.0094286589205252,
+        1.0093991563890867, 1.0093698536916722, 1.0093408402580992, 1.0093121792039104,
+        1.0092838975642429, 1.0092559827291674, 1.0092283854843738, 1.0092010289613615,
+        1.009173821848707, 1.009146673564446, 1.009119508837749, 1.0090922793252084,
+        1.0090649704506818, 1.0090376025011698, 1.0090102259865796, 1.0089829122117935,
+        1.0089557407615788, 1.0089287860449108, 1.008902105123018, 1.0088757287559262,
+        1.0088496570075551, 1.0088238599588557, 1.008798283229674, 1.0087728572442027,
+        1.0087475086133286, 1.0087221717323345, 1.008696798736359, 1.008671366296572,
+        1.0086458783081282, 1.0086203642140792, 1.008594873409391, 1.0085694667638003,
+        1.0085442067022665, 1.0085191474343544, 1.008494326819713, 1.0084697610277953,
+        1.0084454426620484, 1.008421342458748, 1.0083974141303258, 1.0083736014843059,
+        1.0083498466713174, 1.008326098328554, 1.0083023184851003, 1.0082784873513029,
+        1.0082546054724035, 1.008230693123974, 1.0082067872007139, 1.008182936149314,
+        1.0081591936872456, 1.008135612119605, 1.0081122360244688, 1.0080890969467702,
+        1.008066209555991, 1.008043569519321, 1.0080211531506653, 1.0079989187393215,
+        1.0079768093500194, 1.0079547568181593, 1.0079326866309364, 1.007910523373364,
+        1.0078881964148811, 1.0078656455083181, 1.0078428259658705, 1.0078197130709519,
+        1.007796305389347, 1.0077726266705107, 1.0077487260896811, 1.007724676679504,
+        1.0077005719337149, 1.0076765207245046, 1.0076526408421067, 1.0076290516171853,
+        1.0076058662014031, 1.0075831841395917, 1.0075610848567218, 1.0075396226026228,
+        1.007518823255808, 1.007498683203312, 1.0074791703104682, 1.0074602268000417,
+        1.0074417736986363, 1.007423716397914, 1.0074059508283382, 1.0073883697529529,
+        1.007370868748014, 1.007353351529657, 1.0073357343914064, 1.0073179496175186,
+        1.0072999478184024, 1.0072816991889666, 1.0072631937202827, 1.0072444404064986,
+        1.0072254654947295, 1.0072063098383166, 1.0071870254435944, 1.00716767135141,
+        1.0071483090640039, 1.0071289978051188, 1.0071097899699084, 1.0070907271633247,
+        1.0070718372236394, 1.0070531325712941, 1.0070346101095213, 1.007016252741264,
+        1.0069980323754142, 1.006979914101059, 1.0069618610417144, 1.0069438392911736,
+        1.0069258223007378, 1.0069077941447564, 1.0068897512344321, 1.0068717022611413,
+        1.0068536664004908, 1.0068356700592842, 1.006817742661148, 1.0067999121074813,
+        1.006782200596101, 1.0067646214206605, 1.0067471772185626, 1.0067298599068821,
+        1.0067126522807772, 1.0066955309894483, 1.006678470392058, 1.0066614466647401,
+        1.0066444415004578, 1.006627444820296, 1.0066104560845708, 1.0065934840262274,
+        1.0065765448884358, 1.006559659490223, 1.0065428496286886, 1.0065261344241778,
+        1.0065095272108207, 1.0064930334712938, 1.006476650130504, 1.0064603662899299,
+        1.0064441652429028, 1.0064280274010458, 1.0064119336187098, 1.0063958683479763,
+        1.0063798220990423, 1.006363792810654, 1.0063477859287138, 1.0063318132144146,
+        1.0063158905174978, 1.0063000349196625, 1.006284261749632, 1.0062685819804325,
+        1.0062530004412507, 1.0062375151263856, 1.0062221176893833, 1.0062067950057938,
+        1.0061915315083405, 1.00617631187392, 1.0061611235925234, 1.0061459589808526,
+        1.0061308163102147, 1.00611569987913, 1.0061006190471409, 1.0060855864244953,
+        1.0060706155527568, 1.0060557184900327, 1.0060409037200813, 1.0060261747373167,
+        1.0060115295336933, 1.0059969610514123, 1.0059824584967398, 1.005968009263963,
+        1.0059536011196744, 1.0059392242618659, 1.0059248729003285, 1.0059105460975672,
+        1.005896247744551, 1.0058819856993886, 1.0058677702614955, 1.005853612264671,
+        1.0058395211310258, 1.0058255032252335, 1.005811560787196, 1.0057976916129108,
+        1.0057838895186046, 1.0057701454857182, 1.0057564492686568, 1.00574279117237,
+        1.0057291636852754, 1.0057155626867647, 1.0057019880303868, 1.005688443418072,
+        1.0056749356068395, 1.0056614731047646, 1.0056480645978816, 1.0056347173901088,
+        1.0056214361283187, 1.0056082220274083, 1.0055950727170442, 1.0055819827197305,
+        1.0055689444592655, 1.0055559496086321, 1.00554299053221, 1.0055300615674163,
+        1.0055171599258674, 1.0055042860667693, 1.005491443491619, 1.0054786380119498,
+        1.0054658766328202, 1.005453166258021, 1.0054405124487389, 1.0054279184516874,
+        1.0054153846597036, 1.0054029085876348, 1.0053904853537785, 1.0053781085688214,
+        1.0053657714654576, 1.0053534680641028, 1.0053411941692836, 1.0053289480265128,
+        1.0053167305333526, 1.0053045449794717, 1.0052923963737117, 1.0052802904868878,
+        1.0052682327856715, 1.0052562274471601, 1.0052442766247554, 1.0052323800873868,
+        1.0052205352855335, 1.0052087378214285, 1.0051969822305762, 1.0051852629297768,
+        1.0051735751614643, 1.0051619157693314, 1.00515028367408, 1.0051386799740338,
+        1.005127107662924, 1.0051155710243143, 1.005104074817012, 1.0050926233993545,
+        1.0050812199469268, 1.00506986589785, 1.0050585607164284, 1.0050473020079418,
+        1.0050360859550542, 1.0050249079911375, 1.0050137635865433, 1.005002649007574,
+        1.0049915619164802, 1.0049805017119642, 1.004969469557881, 1.0049584681034203,
+        1.0049475009519624, 1.0049365719779633, 1.0049256846151262, 1.0049148412407494,
+        1.0049040427609772, 1.0048932884638844, 1.0048825761587719, 1.0048719025697392,
+        1.0048612639081538, 1.0048506565194817, 1.0048400774899104, 1.0048295251081976,
+        1.004818999106283, 1.0048085006426573, 1.0047980320382988, 1.0047875963177095,
+        1.004777196639945, 1.0047668357214847, 1.0047565153513827, 1.0047462360803627,
+        1.0047359971332173, 1.0047257965536727, 1.0047156315504477, 1.0047054989790911,
+        1.0046953958725138, 1.004685319926972, 1.0046752698606267, 1.0046652455859326,
+        1.0046552481710518, 1.004645279602553, 1.0046353423956433, 1.0046254391233655,
+        1.004615571948033, 1.0046057422357586, 1.0045959503182225, 1.00458619543884,
+        1.0045764758876614, 1.004566789296795, 1.004557133041299, 1.004547504673888,
+        1.0045379023179717, 1.004528324952672, 1.0045187725439615, 1.004509246003476,
+        1.0044997469866608, 1.0044902775690694, 1.0044808398592078, 1.004471435615762,
+        1.0044620659341958, 1.0044527310542606, 1.0044434303179004, 1.0044341622806876,
+        1.004424924953834, 1.0044157161322833, 1.0044065337511807, 1.0043973762097185,
+        1.0043882426087134, 1.0043791328642127, 1.0043700476813824, 1.0043609883968032,
+        1.0043519567191568, 1.0043429544143239, 1.0043339829889881, 1.0043250434253255,
+        1.004316136009575, 1.0043072602802037, 1.0042984151011123, 1.0042895988442548,
+        1.0042808096487892, 1.0042720457121312, 1.004263305564522, 1.0042545882828688,
+        1.0042458936108944, 1.004237221968773, 1.0042285743538837, 1.0042199521516033,
+        1.0042113568889326, 1.004202789971686, 1.004194252447216, 1.0041857448291036,
+        1.0041772670093936, 1.0041688182692312, 1.0041603973833193, 1.0041520027993123],
+    [2.252139948862946e-11, 6.766412724153118e-11, 1.1310742833044891e-10,
+        1.5905428847550227e-10, 2.0571162559391553e-10, 2.5329193769943615e-10,
+        3.0201499398716164e-10, 3.521096299210442e-10, 4.03815637133482e-10,
+        4.573857864585597e-10, 5.13088005250314e-10, 5.712077390695795e-10,
+        6.320505221163008e-10, 6.95944800697459e-10, 7.632450379242024e-10,
+        8.343351512831544e-10, 9.096323267788699e-10, 9.895912671995519e-10,
+        1.0747089395858893e-09, 1.165529888964201e-09, 1.2626522103276774e-09,
+        1.3667342632752908e-09, 1.4785022474219404e-09, 1.5987587609255233e-09,
+        1.7283924882552151e-09, 1.8683891846737992e-09, 2.0198441572652824e-09,
+        2.1839764623193165e-09, 2.3621450901786226e-09, 2.5558674360391705e-09,
+        2.766840427429501e-09, 2.996964712562516e-09, 3.248372413996298e-09,
+        3.5234590126613677e-09, 3.824920047508788e-09, 4.155793418693543e-09,
+        4.5195082430596045e-09, 4.919941362154273e-09, 5.361482830095631e-09,
+        5.8491119271602025e-09, 6.388485570137508e-09, 6.986041312814746e-09,
+        7.64911759352904e-09, 8.386094370488887e-09, 9.206557955523311e-09,
+        1.012149456444471e-08, 1.1143518131808836e-08, 1.2287138941009384e-08,
+        1.3569081194277287e-08, 1.5008659193232024e-08, 1.6628224067553462e-08,
+        1.8453695547999992e-08, 2.05151965342802e-08, 2.284781233574936e-08,
+        2.5492501485947373e-08, 2.849719140297058e-08, 3.191810029164674e-08,
+        3.5821336663554356e-08, 4.028484094251961e-08, 4.540074991303908e-08,
+        5.127828592498587e-08, 5.8047299961519644e-08, 6.586263283911525e-08,
+        7.490950470105435e-08, 8.541020315388952e-08, 9.76324199303334e-08,
+        1.1189969157607926e-07, 1.286045415866749e-07, 1.482251134815356e-07,
+        1.7134634645545744e-07, 1.9868710796015195e-07, 2.3113520471145303e-07,
+        2.6979291307054875e-07, 3.160367049825527e-07, 3.715963649010188e-07,
+        4.3866096278719116e-07, 5.200226244715665e-07, 6.192744991619529e-07,
+        7.410881724301216e-07, 8.916106325804197e-07, 1.0790469120936694e-06,
+        1.3145423781281602e-06, 1.613571934370811e-06, 1.9982384439748117e-06,
+        2.501326794041925e-06, 3.1740848036498736e-06, 4.102971536094566e-06,
+        5.452081569558435e-06, 7.601188363529591e-06, 1.1855862207566827e-05,
+        4.239699647194868e-05, 1.577373534734989e-05, 1.374075941247713e-05,
+        1.4148468060535896e-05, 1.5622325379296654e-05, 1.797520908651408e-05,
+        2.1291199410482918e-05, 2.580238057284003e-05, 3.1886029078065354e-05,
+        4.0107004313862006e-05, 5.1299338065978394e-05, 6.670145761081087e-05,
+        8.817683864502248e-05, 0.00011857862734907132, 0.00016236549149206193,
+        0.00022667017234724422, 0.0003232124021692752, 0.0004718493185582651,
+        0.0007074479862134149, 0.0010938653248459753, 0.001754135318750205,
+        0.0029406319044267223, 0.005214167207467661, 0.009961899801114452,
+        0.021185694646805916, 0.05368502192584466, 0.19871144490761977,
+        4.42006145271334, 0.8794735023946814, 1.9125758699636366, 2.1560855246003245,
+        1.0786564785862636, 1.1079496493150105, 1.9079865267780665, 2.421317606137854,
+        1.1495422579580867, 0.8403242357670178, 0.8284114968235068, 1.0649128543149557,
+        1.589506720171078, 1.2033459475319883, 0.7680321479985491, 0.6214310019266012,
+        0.6173642325177098, 0.7362523086264113, 1.0294985510018233, 1.358239098785856,
+        1.161325973372013, 0.9076594665803251, 0.8025885626190749, 0.8055680483104792,
+        0.9064757160407924, 1.132779513577784, 1.4999275596381585, 1.722248210599146,
+        1.4875568442987708, 1.2103669714980139, 1.0608254491383724, 1.019067434966981,
+        1.0695823884683933, 1.2209541997367668, 1.4856946983666948, 1.7510714662951972,
+        1.6750759952378216, 1.354649644410358, 1.0990112511512968, 0.9506875698157763,
+        0.9382152022123006, 0.9987930460411946, 1.0793936909693764, 1.157859160161574,
+        1.1977925477973554, 1.17732736441477, 1.1133228137207822, 1.039986683742733,
+        0.9804066503732443, 0.9432990509203871, 0.9299204687376772, 0.9387484928773284,
+        0.9667403862774823, 1.0083556621728738, 1.0534638159740497, 1.0864947453397262,
+        1.0910125805136865, 1.0598572289784247, 1.0004902350290006, 0.9281742187090081,
+        0.8560040944307569, 0.7911461817368539, 0.7360761397344748, 0.6908007856392521,
+        0.6543862788781114, 0.6257313263534777, 0.6038860590637702, 0.5881498351184223,
+        0.5780754107457935, 0.5734405261342755, 0.5742136321751701, 0.5805232514562416,
+        0.592631076970386, 0.6109025657572916, 0.6357628073092423, 0.6676182740588444,
+        0.7067168054517209, 0.7529133673634671, 0.8053223280311771, 0.8618979328391283,
+        0.91912418629726, 0.972173846188766, 1.0158921172542905, 1.0464719758862604,
+        1.0629091570354652, 1.0672012963321225, 1.0632226620247416, 1.0551854410293318,
+        1.0465578588430118, 1.0396564061988482, 1.0356874381558667, 1.0349637442372692,
+        1.0371404718052306, 1.041424641701097, 1.0467669266269928, 1.052053797327931,
+        1.0563011227229144, 1.0588247230235395, 1.0593479729391944, 1.0580150057888473,
+        1.0553082015890607, 1.051901756537496, 1.0484990765665543, 1.0456950562763034,
+        1.0438850580948589, 1.0432243001731023, 1.0436315172120665, 1.0448283439642163,
+        1.0464062402474859, 1.0479117906350384, 1.0489376224924478, 1.0492020668607591,
+        1.0485999963780757, 1.0472128933141682, 1.045277216904692, 1.0431218604905732,
+        1.0410926247343997, 1.0394819145385175, 1.0384769529359703, 1.0381332200070152,
+        1.0383742888296967, 1.0390154782800838, 1.0398060656031585, 1.040482334686202,
+        1.0408214743125328, 1.0406853176607924, 1.0400444524525105, 1.0389777496700412,
+        1.0376486657077035, 1.0362654424152196, 1.0350354839954032, 1.034124070926576,
+        1.0336250211098401, 1.0335474053876905, 1.0338191167613915, 1.0343054012124746,
+        1.0348383041314815, 1.035251277706266, 1.0354121588224723, 1.0352478627570765,
+        1.0347558253214897, 1.034000290223689, 1.033095135589103, 1.0321779088032212,
+        1.0313812189431226, 1.030807426182296, 1.030511102471311, 1.0304917068867963,
+        1.0306968852681249, 1.0310350479093116, 1.0313944809468676, 1.0316652608387822,
+        1.031759804740466, 1.0316281862289094, 1.0312654531650556, 1.0307099291112376,
+        1.0300334268575497, 1.0293259144369227, 1.0286780432464255, 1.0281649562995252,
+        1.0278341082199212, 1.0276987619586315, 1.0277376838854444, 1.0279005388682487,
+        1.028117683793236, 1.0283125088840595, 1.0284142105887746, 1.0283689314018523,
+        1.0281475821911006, 1.0277493216273061, 1.0272004776881711, 1.0265494785072604,
+        1.0258589419068378, 1.0251963507866668, 1.024624709451828, 1.0241943135379301,
+        1.0239363950749707, 1.0238590393922542, 1.0239454871066034, 1.0241547568934257,
+        1.024424434754292, 1.024675429086142, 1.0248184379505403, 1.0247617772497175,
+        1.0244200635584915, 1.02372305433573, 1.02262377435824, 1.0211049718097103,
+        1.0191830149316166, 1.0169085895131724, 1.0143639627309455, 1.0116570600891108,
+        1.0089130499560643, 1.00626444377377, 1.0038408413823277, 1.0017593798221962,
+        1.0001167287762345, 0.9989831884554304, 0.998399154367559, 0.9983739640088397,
+        0.9988869518419584, 0.9998904085432901, 1.0013140558324658, 1.0030705969786604,
+        1.0050618794180004, 1.0071852108356343, 1.0093394072867927, 1.0114302221129279,
+        1.0133749001887213, 1.0151057075523098, 1.0165723812523189, 1.0177435107004968,
+        1.0186068922913019, 1.0191688998085424, 1.0194529020528857, 1.0194967589613106,
+        1.0193494565967782, 1.0190670063975906, 1.0187078270854308, 1.0183279289409097,
+        1.0179763046402854, 1.0176909751936722, 1.0174961274468546, 1.0174007040522688,
+        1.017398669776664, 1.0174709898794712, 1.0175891359044587, 1.017719709610088,
+        1.0178295835777273, 1.0178908382533363, 1.0178847658670953, 1.0178043306594053,
+        1.017654713168001, 1.017451884293388, 1.0172194898818414, 1.0169846099905626,
+        1.0167731331871217, 1.0166055261760065, 1.0164936839643253, 1.0164393414315653,
+        1.016434253767703, 1.01646205615863, 1.0165014371833785, 1.0165300469501461,
+        1.0165284447180765, 1.0164833943608422, 1.016389943382073, 1.016251952109003,
+        1.0160810306700792, 1.0158941341590848, 1.0157103023670746, 1.0155471654594292,
+        1.015417851002524, 1.0153288266721685, 1.015279023258908, 1.0152603427324725,
+        1.0152594086378777, 1.015260201599141, 1.0152470757540486, 1.0152075970268506,
+        1.0151346912865291, 1.0150277314999907, 1.014892401038843, 1.0147394039148465,
+        1.0145823050568972, 1.0144349337002319, 1.0143088445654302, 1.0142112984783487,
+        1.0141441088008438, 1.0141035285173943, 1.014081158208845, 1.0140656718169636,
+        1.0140450159414334, 1.0140086628989926, 1.0139495004875554, 1.0138650212053415,
+        1.0137576148356244, 1.0136339427094356, 1.0135035447706604, 1.0133769680434515,
+        1.013263782145371, 1.01317085262565, 1.0131011794168667, 1.0130534912863187,
+        1.013022641642763, 1.0130007034064326, 1.0129785367528266, 1.0129475244412705,
+        1.0129011482776678, 1.0128361199354765, 1.0127528715253438, 1.0126553374784444,
+        1.0125500943733465, 1.0124450428826424, 1.012347894085697, 1.0122647479705644,
+        1.0121990229898756, 1.012150920365765, 1.0121175015413144, 1.0120933420268643,
+        1.012071620719367, 1.0120454286941107, 1.0120090481348833, 1.011958965609282,
+        1.011894440854945, 1.0118175409921577, 1.0117326529481534, 1.01164558375993,
+        1.011562431010264, 1.0114884411941272, 1.0114270673890071, 1.0113793924986363,
+        1.011344010725233, 1.0113173724299251, 1.011294512427827, 1.011270014166536,
+        1.011239023762824, 1.0111981247373263, 1.0111459162268441, 1.0110831976925434,
+        1.0110127396196242, 1.0109386974585612, 1.0108657903012437, 1.0107984049006193,
+        1.0107397933744924, 1.0106915092774138, 1.0106531774719958, 1.010622628476642,
+        1.0105963600315673, 1.0105702298414974, 1.010540244110792, 1.0105032931585356,
+        1.0104576998507055, 1.0104034854493469, 1.0103423128783477, 1.0102771284851553,
+        1.0102115784755263, 1.0101493151889807, 1.0100933246194155, 1.0100453980112143,
+        1.010005839615562, 1.0099734563065255, 1.0099458217422939, 1.00991975789612,
+        1.009891938934137, 1.009859503049365, 1.0098205599770382, 1.0097745045618784,
+        1.0097220852021245, 1.0096652226834606, 1.0096066209017152, 1.0095492477254258,
+        1.0094957852942428, 1.0094481511218794, 1.0094071748697993, 1.0093724843418632,
+        1.009342614369713, 1.0093153113088118, 1.0092879712334157, 1.0092581276245862,
+        1.0092238980413, 1.0091843096392301, 1.0091394480922098, 1.0090904085344565,
+        1.0090390640168314, 1.0089876997641376, 1.0089385843365357, 1.0088935578206424,
+        1.0088537112960962, 1.0088192126979196, 1.008789305795174, 1.008762476785928,
+        1.0087367528767999, 1.008710074499421, 1.008680671358455, 1.0086473740327382,
+        1.0086098067081193, 1.0085684299267796, 1.0085244304575114, 1.0084794832095028,
+        1.0084354324610605, 1.0083939526736234, 1.0083562507984745, 1.008322862396326,
+        1.008293575233029, 1.0082674899699693, 1.008243202622874, 1.0082190720933768,
+        1.008193521976775, 1.0081653213063972, 1.0081337944352706, 1.0080989245788854,
+        1.008061335798708, 1.0080221605465844, 1.0079828202071583, 1.0079447607691214,
+        1.0079091923822618, 1.0078768792262063, 1.0078480155824996, 1.0078222074462633,
+        1.0077985595939651, 1.0077758492756927, 1.0077527529129915, 1.00772808383964,
+        1.007700998494296, 1.0076711354308558, 1.00763866457923, 1.0076042408436756,
+        1.00756887327984, 1.0075337356709646, 1.0074999538267273, 1.0074684078562053,
+        1.0074395837493777, 1.007413498788831, 1.0073897115467867, 1.0073674120539131,
+        1.0073455738491246, 1.0073231394032727, 1.0072992055067276, 1.007273176296178,
+        1.007244858280148, 1.007214482650569, 1.007182653285062, 1.0071502317838177,
+        1.0071181813983376, 1.0070873980612605, 1.0070585579806608, 1.0070320074061758,
+        1.0070077120765561, 1.006985273074474, 1.0069640042874914, 1.0069430563882873,
+        1.006921564894944, 1.0068987965800154, 1.0068742696650375, 1.006847828492558,
+        1.0068196616638525, 1.0067902624466922, 1.0067603398815523, 1.0067306968453016,
+        1.0067020961455935, 1.006675136863083, 1.0066501606235465, 1.0066272018679294,
+        1.0066059885659648, 1.0065859915229902, 1.0065665128264794, 1.0065467982419054,
+        1.006526155303579, 1.0065040587860945, 1.0064802280180778, 1.00645466550477,
+        1.006427652636781, 1.00639970481527, 1.0063714940942634, 1.0063437516104725,
+        1.006317164140679, 1.0062922789714706, 1.0062694291167094, 1.0062486872886518,
+        1.0062298526036295, 1.0062124695079884, 1.0061958744928758, 1.0061792633047848,
+        1.0061617698061567, 1.0061425474167174, 1.006120844987512, 1.00609607069804,
+        1.0060678397263672, 1.006036003636852, 1.0060006613488994, 1.0059621529976188,
+        1.005921038908589, 1.0058780663356592, 1.005834126685583, 1.0057902058458068,
+        1.0057473300986288, 1.0057065100553946, 1.0056686851172825, 1.0056346711311852,
+        1.005605114070963, 1.0055804526180843, 1.005560892329178, 1.0055463935847218,
+        1.0055366746957175, 1.0055312304525343, 1.0055293651421624, 1.005530237789672,
+        1.0055329162631306, 1.0055364360719818, 1.005539859296025, 1.0055423291567178,
+        1.005543116266605, 1.0055416534871071, 1.005537557464763, 1.0055306361526675,
+        1.0055208828126072, 1.0055084580125244, 1.005493661903555, 1.0054768995462278,
+        1.0054586422646845, 1.0054393879811152, 1.005419623275451, 1.005399789583814,
+        1.0053802555374376, 1.005361296976449, 1.0053430856594898, 1.005325687126754,
+        1.0053090675606273, 1.0052931088343127, 1.005277630276712, 1.0052624150664133,
+        1.0052472386733533, 1.0052318964759952, 1.005216227668618, 1.0052001328847326,
+        1.0051835836042393, 1.0051666223371352, 1.0051493536877507, 1.0051319275609345,
+        1.0051145168130493, 1.0050972924174073, 1.0050803995769118, 1.0050639381021143,
+        1.0050479497773064, 1.0050324144329568, 1.0050172551698318, 1.0050023518266453,
+        1.004987560556072, 1.004972736465886, 1.0049577558392329, 1.0049425345447136,
+        1.0049270398713017, 1.0049112940788443, 1.0048953692734939, 1.004879374587948,
+        1.0048634378480907, 1.0048476847476664, 1.0048322188978822, 1.0048171059175863,
+        1.0048023640207817, 1.0047879624630043, 1.0047738279107221, 1.0047598575131125,
+        1.0047459363939393, 1.004731956613007, 1.0047178344748442, 1.0047035234058348,
+        1.0046890204133532, 1.00467436524113, 1.0046596325558896, 1.0046449186360658,
+        1.004630324898185, 1.0046159410537534, 1.0046018306734708, 1.0045880214615124,
+        1.0045745017014924, 1.0045612232767722, 1.0045481105731489, 1.0045350736236924,
+        1.0045220232067162, 1.0045088853569313, 1.0044956129258753, 1.0044821923884921,
+        1.0044686449323044, 1.004455021836455, 1.0044413950842566, 1.0044278449017447,
+        1.0044144463589588, 1.0044012572482572, 1.0043883091660426, 1.0043756031322955,
+        1.0043631102954491, 1.004350777425082, 1.0043385361324282, 1.0043263141994674,
+        1.004314047123591, 1.0043016880283022, 1.0042892144293911, 1.0042766309114481,
+        1.0042639674596303, 1.004251273888537, 1.0042386114021253, 1.0042260427169996,
+        1.0042136223335085, 1.0042013884355003, 1.0041893575720946, 1.0041775227891119,
+        1.0041658553201667, 1.0041543094093561, 1.0041428294005736, 1.004131357951886,
+        1.0041198441465369, 1.004108250371725, 1.0040965570907898, 1.004084764991023,
+        1.0040728943848796, 1.0040609821148805, 1.0040490765104175, 1.0040372311351244,
+        1.004025498133521, 1.004013921944197, 1.00400253401699, 1.003991348987664,
+        1.0039803625608528, 1.003969551161521, 1.0039588732592837, 1.0039482721582274,
+        1.0039376799772795, 1.0039270225131227, 1.0039162246659816, 1.003905216105304,
+        1.0038939368483897, 1.0038823424179297, 1.0038704082386052, 1.0038581329374385,
+        1.003845540239834, 1.0038326792128447, 1.0038196227048242, 1.003806463963929,
+        1.0037933115764353, 1.0037802830320848, 1.0037674973751987, 1.0037550675146634,
+        1.0037430928237998, 1.0037316526509814, 1.0037208012819476, 1.0037105647538167,
+        1.0037009397369845, 1.003691894498991, 1.0036833717705687, 1.0036752931732504,
+        1.0036675647578468, 1.003660083153485, 1.0036527418365766, 1.0036454370881545,
+        1.0036380732999934, 1.0036305673951595, 1.0036228522283905, 1.0036148789127162,
+        1.003606618073066, 1.0035980600570935, 1.0035892141449287, 1.003580106805347,
+        1.0035707790584834, 1.0035612830348353, 1.003551677871264, 1.0035420251538028,
+        1.0035323841940829, 1.00352280749469, 1.0035133368007159, 1.0035040001328173,
+        1.0034948101408279, 1.0034857640036676, 1.0034768449399505, 1.0034680252028578,
+        1.0034592702391865, 1.0034505435263246, 1.0034418114908974, 1.003433047881045,
+        1.003424237021185, 1.0034153755206434, 1.0034064722180271, 1.003397546392357,
+        1.0033886245220434, 1.003379736085668, 1.0033709090390175, 1.003362165648372,
+        1.0033535193010716, 1.0033449727595338, 1.0033365180975184, 1.003328138293318,
+        1.0033198101959622, 1.0033115083686128, 1.0033032091824012, 1.0032948945046805,
+        1.003286554402171, 1.0032781884486675, 1.0032698054602995, 1.0032614217398632,
+        1.0032530581529195, 1.003244736542468, 1.0032364760865464, 1.0032282901991973,
+        1.0032201844720698, 1.0032121559703921, 1.0032041939648695, 1.00319628194038,
+        1.0031884005129563, 1.0031805307435804, 1.003172657283209, 1.0031647708255036,
+        1.0031568694731579, 1.0031489588165228, 1.0031410507457366, 1.0031331612311658,
+        1.0031253074758208, 1.0031175049396714, 1.0031097647447915, 1.0031020918923828,
+        1.0030944845733516, 1.0030869346603264, 1.0030794292649687, 1.0030719530653707,
+        1.0030644909842727, 1.003057030749689, 1.0030495649020372, 1.003042091918354,
+        1.0030346162844948, 1.003027147531715, 1.0030196984316504, 1.0030122826836978,
+        1.0030049125072036, 1.0029975965564593, 1.002990338509476, 1.0029831365558801,
+        1.0029759838477268, 1.0029688698088919, 1.0029617820528631, 1.0029547085601864,
+        1.0029476397312216, 1.0029405699617386, 1.0029334984813145, 1.002926429329179,
+        1.0029193704954824, 1.0029123323999993, 1.0029053259908183, 1.0028983608039483,
+        1.0028914433223237, 1.0028845759114917, 1.002877756501323, 1.0028709790487278,
+        1.0028642346793089, 1.0028575132905178, 1.002850805324238, 1.002844103395229,
+        1.0028374034954517, 1.0028307055759202, 1.002824013421653, 1.0028173338610118,
+        1.002810675465725, 1.002804046982564, 1.0027974557779498, 1.002790906566844,
+        1.0027844006401916, 1.002777935712263, 1.0027715063975544, 1.0027651052166113,
+        1.0027587239403806, 1.002752355028666, 1.0027459929085079, 1.0027396348731716,
+        1.0027332814548466, 1.0027269362202398, 1.0027206050406448, 1.0027142949787542,
+        1.0027080129976205, 1.0027017647228615, 1.002695553473534, 1.0026893797242469,
+        1.0026832410811328, 1.0026771327619866, 1.0026710484828094, 1.0026649815843967,
+        1.002658926194948, 1.0026528782238355, 1.002646836016772, 1.0026408005663676,
+        1.002634775252917, 1.0026287651732648, 1.0026227761861164, 1.0026168138486615,
+        1.0026108824336333, 1.0026049841969553, 1.0025991190177257, 1.00259328446386,
+        1.002587476260858, 1.0025816890710784, 1.0025759174391171, 1.002570156733531,
+        1.0025644039203205, 1.002558658037332, 1.0025529202944967, 1.0025471937922419,
+        1.0025414829173473, 1.00253579253031, 1.0025301270917155, 1.002524489881773,
+        1.0025188824468296, 1.0025133043634176, 1.002507753352567, 1.002502225714932,
+        1.0024967170022625, 1.002491222801573, 1.0024857394921147, 1.0024802648438114,
+        1.0024747983568723, 1.0024693412904069, 1.0024638963832952, 1.0024584673243593,
+        1.002453058070929, 1.002447672138755, 1.0024423119878576, 1.0024369786087617,
+        1.0024316713759236, 1.0024263881866609, 1.002421125853765, 1.0024158806765897,
+        1.0024106490863547, 1.0024054282513613, 1.0024002165378185, 1.0023950137499784,
+        1.00238982111367, 1.0023846410129915, 1.0023794765325733, 1.0023743308900808,
+        1.0023692068605659, 1.002364106292862, 1.0023590297994984, 1.002353976669378,
+        1.002348945012371, 1.0023439321046326, 1.0023389348693825, 1.0023339504062896,
+        1.0023289764764098, 1.0023240118600245, 1.0023190565287419, 1.0023141116071153,
+        1.002309179136004, 1.0023042616838123, 1.0022993618768543, 1.0022944819319417,
+        1.0022896232718457, 1.0022847862876454, 1.0022799702850387, 1.0022751736189441,
+        1.002270393988259, 1.0022656288358411, 1.002260875782242, 1.0022561330178665,
+        1.0022513995873636, 1.0022466755204846, 1.0022419617910072, 1.002237260115344,
+        1.0022325726295658, 1.0022279015031008, 1.00222324855679, 1.0022186149501404,
+        1.0022140009892118, 1.0022094060845528, 1.002204828862325, 1.0022002674057093,
+        1.002195719582214, 1.0021911833992985, 1.0021866573274594, 1.0021821405372415,
+        1.002177633012556, 1.0021731355245915, 1.0021686494744138, 1.0021641766341838,
+        1.002159718832891, 1.0021552776405966, 1.0021508541036401, 1.0021464485735248,
+        1.0021420606551326, 1.002137689279715, 1.002133332887067, 1.002128989684077,
+        1.0021246579351226, 1.0021203362360236, 1.0021160237274125, 1.0021117202146197,
+        1.0021074261772849, 1.0021031426703244, 1.0020988711351257, 1.0020946131536963,
+        1.0020903701864061, 1.0020861433352102, 1.0020819331687048, 1.0020777396345422,
+        1.0020735620700418, 1.0020693993064378, 1.0020652498479026], [9.774530641004083e-12,
+        2.9368222061725554e-11, 4.9096163758086745e-11, 6.904904711181973e-11,
+        8.931936301279692e-11, 1.1000215627591023e-10, 1.3119580088849651e-10,
+        1.5300282316562298e-10, 1.7553076952682206e-10, 1.988931363159373e-10,
+        2.2321037170516432e-10, 2.4861096370725494e-10, 2.7523262593626195e-10,
+        3.0322360158301987e-10, 3.3274409919204177e-10, 3.6396788425428993e-10,
+        3.9708404736045895e-10, 4.32298975960264e-10, 4.698385603556244e-10,
+        5.099506657279046e-10, 5.52907913333004e-10, 5.990108110636921e-10,
+        6.485912889155913e-10, 7.020166973109067e-10, 7.596943373622055e-10,
+        8.220766023195781e-10, 8.896668246176248e-10, 9.63025932727325e-10,
+        1.0427800458982002e-09, 1.1296291482672275e-09, 1.2243570174267762e-09,
+        1.327842599030579e-09, 1.4410730656432692e-09, 1.5651588271872124e-09,
+        1.7013508165231033e-09, 1.8510604223308527e-09, 2.015882516649276e-09,
+        2.1976220957542043e-09, 2.3983251589326002e-09, 2.6203145520721617e-09,
+        2.8662316540103487e-09, 3.139084933551507e-09, 3.4423066193428386e-09,
+        3.779818948139592e-09, 4.156111764732682e-09, 4.57633357059206e-09,
+        5.046398587550498e-09, 5.573112856756676e-09, 6.1643231038530745e-09,
+        6.829092791904331e-09, 7.577910794411624e-09, 8.422939249621131e-09,
+        9.37830858271069e-09, 1.046046947626496e-08, 1.1688613726995114e-08,
+        1.3085178635578322e-08, 1.4676452993952528e-08, 1.649330686339008e-08,
+        1.857207269600224e-08, 2.095561188945479e-08, 2.369460921992209e-08,
+        2.684914812009298e-08, 3.0490633067086866e-08, 3.470414227956547e-08,
+        3.959131552225205e-08, 4.527390948599798e-08, 5.189818866382708e-08,
+        5.964036547692421e-08, 6.87133627235644e-08, 7.937524835159423e-08,
+        9.19397931448598e-08, 1.0678973363458234e-07, 1.2439349603771504e-07,
+        1.45326365991892e-07, 1.7029739382345902e-07, 2.001837312043508e-07,
+        2.360746412313877e-07, 2.793281590061237e-07, 3.316443781248052e-07,
+        3.9516070021722504e-07, 4.7257625114169857e-07, 5.673152471876581e-07,
+        6.837426778913546e-07, 8.274506846821495e-07, 1.0056410798377558e-06,
+        1.2276394769022027e-06, 1.5055908525090641e-06, 1.8554070545330779e-06,
+        2.2980668852677646e-06, 2.8614136200454616e-06, 3.5826603838528093e-06,
+        4.511912060994407e-06, 5.717161191637943e-06, 7.291443295122834e-06,
+        9.363190739214808e-06, 1.211138036582088e-05, 1.578795680521327e-05,
+        2.0751449663799937e-05, 2.7518067533339763e-05, 3.684051700771914e-05,
+        4.983157545034751e-05, 6.816129449905648e-05, 9.43779122252421e-05,
+        0.00013244150277702025, 0.00018863308586960936, 0.00027314603538080944,
+        0.00040295923089941123, 0.0006072115853470528, 0.0009376793583353302,
+        0.0014902226347742362, 0.0024513455662060063, 0.004206901277269746,
+        0.007620563495440471, 0.014841225832420321, 0.032095856568055275,
+        0.0824806004825358, 0.3086196179750599, 6.912650136074149, 1.3782799989183279,
+        2.9845345309207905, 3.3215449539109, 1.6207011724645837, 1.594450385865707,
+        2.554237109988354, 2.860704493023282, 1.0671655915195735, 0.4034799796754325,
+        0.5277542367527591, 3.5151328373777537, 3.913363851855454, 2.8767267190055925,
+        1.846208493721509, 1.5000412319277618, 1.4775342175275623, 1.7203057077897754,
+        2.3162698320974746, 2.912517575516779, 2.358294608424995, 1.7401091214357478,
+        1.4517255152884203, 1.3762152268889785, 1.465693601932451, 1.7382361449264294,
+        2.1908771695604488, 2.402085418204379, 1.9873524762282864, 1.5536952003493214,
+        1.3123222350366366, 1.2184431182748283, 1.2394837326917099, 1.3751104211859106,
+        1.6306082368530836, 1.8779347238889166, 1.7602797078850738, 1.3991423196141968,
+        1.1196804970682468, 0.9607458670670642, 0.9897684814593772, 1.0754279781272926,
+        1.1763831722845364, 1.2726420744298026, 1.3248094612394892, 1.3083318832284647,
+        1.2415967740589366, 1.1628385404647164, 1.0982355597157838, 1.0579261095477377,
+        1.0435890937531533, 1.0536737090385664, 1.0848360662976888, 1.1308742858746648,
+        1.180421668679915, 1.216051361795251, 1.219460185940999, 1.1828262031125563,
+        1.1146999426352497, 1.0322725322672255, 0.9502103174446104, 0.8764939162982949,
+        0.8138443203392849, 0.7622263633716782, 0.7205615326284716, 0.6875907123486338,
+        0.6622276525830542, 0.6436656138764346, 0.6313800522316968, 0.6250955245107865,
+        0.6247465075010795, 0.6304425921653867, 0.6424381417153306, 0.6610996116800978,
+        0.6868573497039819, 0.7201211054296038, 0.7611298033031902, 0.8097012248730526,
+        0.8648616726238683, 0.9244010665597354, 0.9845477116972225, 1.0401460089256922,
+        1.0857128433016188, 1.1172245047371492, 1.1336579599337686, 1.137186977785346,
+        1.1319700291429184, 1.1225069830365353, 1.1124903385539062, 1.1043774237609725,
+        1.0994404952909809, 1.098001251078586, 1.0996841825664039, 1.103640511078256,
+        1.1087522814425872, 1.1138360707193244, 1.1178476372995294, 1.1200617289305257,
+        1.1201850272341727, 1.1183692171279942, 1.115123040380659, 1.1111571176189932,
+        1.1072120402979575, 1.1039130524199114, 1.1016742453468797, 1.100656059358122,
+        1.1007695160064483, 1.101718086867548, 1.1030685169944585, 1.1043408986489167,
+        1.105104523765802, 1.1050617273274843, 1.1041012410870958, 1.1023085321762462,
+        1.0999322261808118, 1.0973180548871082, 1.0948292547313394, 1.0927725980539373,
+        1.0913440286529772, 1.0906009164719312, 1.0904621078961814, 1.0907329982849239,
+        1.0911500443799087, 1.0914365561809427, 1.0913592567131072, 1.0907740571995739,
+        1.0896511455126587, 1.0880742550289948, 1.0862156067390392, 1.084294055606698,
+        1.082527249657365, 1.081088449611097, 1.080075953230722, 1.0794993782447808,
+        1.0792835855057914, 1.0792882097458447, 1.0793385243861835, 1.0792616008655438,
+        1.0789206667487443, 1.078240736179327, 1.0772203704321182, 1.0759276351864369,
+        1.0744820700502884, 1.0730275715030893, 1.0717026089124424, 1.070613950095578,
+        1.0698185281469403, 1.0693159565707457, 1.0690520817311786, 1.0689321410672232,
+        1.0688406533416066, 1.0686641573274656, 1.0683124780231363, 1.0677345218525462,
+        1.0669257610689347, 1.0659263800169467, 1.0648110703175167, 1.0636731225199643,
+        1.0626063497064349, 1.061688375375105, 1.060968098628735, 1.0604590414524717,
+        1.0601390998237799, 1.0599561686104577, 1.0598382852244865, 1.0597063760057897,
+        1.0594874214633063, 1.0591259154281774, 1.0585918895761746, 1.0578844565285315,
+        1.0570306600693113, 1.0560802252068593, 1.0550973972035074, 1.0541513411499959,
+        1.053306537286061, 1.0526143346613788, 1.0521064423884372, 1.0517907618877917,
+        1.051649672142122, 1.0516406979558086, 1.051699399388187, 1.0517442735289027,
+        1.0516834061113791, 1.0514225108430424, 1.0508738360492753, 1.0499652231288523,
+        1.0486484240124778, 1.046905698402145, 1.0447537819012633, 1.042244572719807,
+        1.0394623004910748, 1.0365174338459378, 1.0335380415039803, 1.0306596417631513,
+        1.0280146981904972, 1.0257228451165252, 1.0238827049737727, 1.0225658644523743,
+        1.0218132776992057, 1.021634109383158, 1.0220068374922464, 1.022882302635227,
+        1.0241883044276139, 1.0258352936452448, 1.0277226851592027, 1.0297453222289887,
+        1.0317996613007268, 1.0337893186582663, 1.035629718544517, 1.037251690463282,
+        1.0386039603633683, 1.0396545483400903, 1.0403911165919162, 1.0408203120869721,
+        1.0409661370187016, 1.0408673799184336, 1.040574169960826, 1.0401437832711429,
+        1.039635924806646, 1.0391078125020226, 1.0386094761948859, 1.0381797286323524,
+        1.037843253045945, 1.037609174261005, 1.037471340196766, 1.037410348589585,
+        1.0373971290966426, 1.037397662224534, 1.037378221123972, 1.0373104019059458,
+        1.0371751994038418, 1.0369655072680994, 1.0366866646454287, 1.0363549958803298,
+        1.0359946308651615, 1.0356331819407398, 1.0352970320407366, 1.035007028689959,
+        1.0347752809324178, 1.0346035476479525, 1.0344834270692256, 1.0343982548601203,
+        1.0343263375173197, 1.0342449310885757, 1.034134257459027, 1.0339808547466476,
+        1.0337796884594177, 1.03353468534547, 1.0332576479854214, 1.0329658058635833,
+        1.032678498314576, 1.0324136215502033, 1.0321844857234141, 1.0319976247681295,
+        1.0318519085592959, 1.031739062975184, 1.0316454519298122, 1.0315547576548687,
+        1.0314510465043554, 1.0313216521454422, 1.031159356278214, 1.0309634906433638,
+        1.0307397956024278, 1.0304991078972632, 1.0302551657338983, 1.0300219713848324,
+        1.029811213753409, 1.0296302194915363, 1.0294807839483573, 1.0293590589177373,
+        1.0292564765358847, 1.0291615026560168, 1.0290618699165255, 1.028946864317531,
+        1.0288092421342518, 1.028646435216205, 1.0284608461257254, 1.0282592115937201,
+        1.028051188064994, 1.0278474524446037, 1.0276576891170748, 1.0274888393010508,
+        1.0273439242018085, 1.0272216352189172, 1.0271167368056888, 1.0270211778665819,
+        1.0269256820400716, 1.0268215071668598, 1.0267020429705995, 1.0265639563778102,
+        1.026407687473777, 1.026237227065247, 1.0260592437212, 1.0258817472274535,
+        1.0257125543835002, 1.025557848833169, 1.0254210971227857, 1.0253025068910595,
+        1.0251991063378805, 1.0251054074506265, 1.0250145099893826, 1.0249194272803783,
+        1.0248143812324564, 1.0246958278394922, 1.0245630322297206, 1.0244181022709622,
+        1.0242654939280715, 1.024111099631937, 1.0239611043336265, 1.0238208297935467,
+        1.02369378103872, 1.0235810631639382, 1.0234812620729772, 1.0233907941730727,
+        1.0233046439159086, 1.0232173397273914, 1.0231239800207856, 1.0230211179102406,
+        1.0229073456454945, 1.0227834807977492, 1.022652333626452, 1.0225181137052528,
+        1.0223855988280774, 1.0222592287131527, 1.0221422937651063, 1.022036365155509,
+        1.0219410626160457, 1.021854190826067, 1.021772206581537, 1.0216909195238464,
+        1.0216062894801057, 1.0215151700539906, 1.0214158627765637, 1.0213083854638434,
+        1.0211944144587868, 1.0210769221801603, 1.020959587071312, 1.0208460924103875,
+        1.020739446802938, 1.0206414504606582, 1.0205524002565431, 1.0204710796459333,
+        1.0203950259665118, 1.0203210172623192, 1.020245682566311, 1.0201661200481877,
+        1.020080409614669, 1.0199879294646503, 1.01988942497372, 1.019786825454847,
+        1.0196828507856983, 1.0195804869930525, 1.0194824311088344, 1.019390607669943,
+        1.0193058425349437, 1.019227748041039, 1.0191548332400167, 1.019084811602995,
+        1.0190150436293808, 1.0189430293092843, 1.0188668590530032, 1.0187855422042031,
+        1.0186991572032957, 1.0186088018688846, 1.0185163594923274, 1.0184241295345844,
+        1.01833439472671, 1.018249005458279, 1.0181690563784842, 1.0180947108104288,
+        1.0180251999025831, 1.0179589909198268, 1.017894088673799, 1.0178284111828244,
+        1.0177601691093576, 1.017688180084889, 1.0176120630339285, 1.0175322811376852,
+        1.017450030556661, 1.0173670000944546, 1.0172850495221328, 1.0172058673804034,
+        1.017130670709917, 1.0170599994715852, 1.0169936395857029, 1.0169306842580568,
+        1.0168697181008057, 1.016809087009321, 1.016747202547139, 1.0166828250241562,
+        1.0166152750565185, 1.0165445378532583, 1.0164712449095732, 1.0163965403162103,
+        1.0163218593770256, 1.0162486620332594, 1.016178170261552, 1.0161111562490186,
+        1.0160478175160825, 1.015987758458772, 1.0159300782010492, 1.0158735457495527,
+        1.0158168285430564, 1.0157587320881485, 1.0156984077504256, 1.0156354927937843,
+        1.0155701599389082, 1.015503070502604, 1.0154352424685624, 1.0153678595292859,
+        1.015302056708574, 1.0152387211153429, 1.0151783424226546, 1.0151209377697406,
+        1.0150660619074707, 1.0150128981218416, 1.0149604114895079, 1.0149075357308706,
+        1.0148533599939042, 1.0147972830033014, 1.014739108751156, 1.0146790689198393,
+        1.0146177704451735, 1.0145560796621125, 1.0144949650626445, 1.0144353270885764,
+        1.0143778446385057, 1.0143228640777975, 1.0142703483784448, 1.0142198931510344,
+        1.0141708047202662, 1.0141222250378457, 1.0140732808256714, 1.0140232310317467,
+        1.0139715878632647, 1.0139181919586389, 1.0138632306184026, 1.0138071979016088,
+        1.0137508050851431, 1.0136948578662028, 1.0136401215319826, 1.0135871964679444,
+        1.0135364238190503, 1.0134878354621923, 1.0134411547711437, 1.0133958463021497,
+        1.0133512048745306, 1.0133064687472744, 1.0132609385112195, 1.0132140832597936,
+        1.0131656183991602, 1.0131155444997662, 1.013064142945366, 1.013011930732479,
+        1.0129595825806683, 1.0129078327093566, 1.0128573707175523, 1.012808745843827,
+        1.0127622917180379, 1.0127180800611753, 1.012675907334979, 1.012635313818417,
+        1.0125956306462323, 1.0125560474659399, 1.0125156918086207, 1.0124737110454607,
+        1.0124293487307163, 1.0123820088825715, 1.0123313039273778, 1.012277084241789,
+        1.0122194491583776, 1.012158740756542, 1.0120955226772315, 1.0120305466288793,
+        1.0119647093267576, 1.011899002499357, 1.011834458461, 1.0117720936995713,
+        1.0117128530012232, 1.0116575567963293, 1.0116068545733183, 1.0115611872504953,
+        1.0115207612079578, 1.0114855361850712, 1.0114552284264078, 1.0114293293598862,
+        1.0114071388254642, 1.0113878105951424, 1.0113704068024045, 1.0113539570858316,
+        1.011337517857237, 1.011320227180354, 1.0113013512739153, 1.0112803195531048,
+        1.011256746270155, 1.0112304380587525, 1.0112013878824966, 1.0111697569123734,
+        1.011135846631869, 1.0111000639560614, 1.0110628823609609, 1.011024801992143,
+        1.010986311512955, 1.0109478541187742, 1.0109097997294603, 1.0108724249018708,
+        1.0108359014880286, 1.0108002944977885, 1.0107655690082307, 1.010731605304568,
+        1.0106982207719635, 1.0106651964390174, 1.0106323055771693, 1.0105993414682697,
+        1.0105661414397387, 1.010532604580125, 1.0104987011932558, 1.0104644729794907,
+        1.010430024049673, 1.0103955040408958, 1.0103610856498348, 1.0103269396698613,
+        1.0102932109827483, 1.0102599988401482, 1.0102273441709761, 1.0101952256409505,
+        1.0101635649109117, 1.0101322401800732, 1.0101011058672167, 1.0100700153705144,
+        1.010038843402008, 1.0100075044904604, 1.0099759648741122, 1.0099442460663224,
+        1.0099124197023888, 1.0098805946532752, 1.0098488985994731, 1.0098174571021667,
+        1.0097863735554249, 1.0097557132005122, 1.0097254936706557, 1.009695683433725,
+        1.009666208196449, 1.0096369640427816, 1.0096078350123727, 1.0095787121539708,
+        1.0095495109162547, 1.0095201840842074, 1.009490728265571, 1.009461183038081,
+        1.0094316230948808, 1.0094021448665964, 1.0093728499672612, 1.0093438282703706,
+        1.0093151434049359, 1.0092868229848149, 1.0092588550392443, 1.0092311910485057,
+        1.0092037548888977, 1.0091764560386298, 1.0091492047446928, 1.0091219265989222,
+        1.009094574148592, 1.0090671337305273, 1.009039626561245, 1.0090121040910234,
+        1.0089846385703543, 1.0089573105293625, 1.0089301953168062, 1.0089033509229914,
+        1.0088768090214206, 1.0088505705692365, 1.0088246065159832, 1.0087988633213705,
+        1.0087732722169196, 1.00874776058481, 1.0087222635523947, 1.008696733944797,
+        1.0086711490785618, 1.008645513447432, 1.0086198570444345, 1.0085942297644388,
+        1.0085686929259106, 1.008543309350623, 1.0085181335926485, 1.0084932038037833,
+        1.008468536393544, 1.0084441241539388, 1.0084199379591736, 1.0083959316101272,
+        1.008372048954695, 1.0083482321374464, 1.008324429744957, 1.008300603713216,
+        1.0082767341192687, 1.0082528213372945, 1.0082288854366368, 1.0082049630733283,
+        1.0081811024257876, 1.0081573569165239, 1.0081337785319586, 1.0081104115107868,
+        1.008087287040881, 1.0080644194199875, 1.0080418039318766, 1.008019416498275,
+        1.0079972150104164, 1.0079751421318635, 1.007953129296434, 1.007931101591908,
+        1.0079089832085033, 1.0078867031278134, 1.0078642007239538, 1.0078414309415649,
+        1.0078183687095403, 1.007795012253887, 1.0077713850005596, 1.0077475358189394,
+        1.007723537454641, 1.0076994831342, 1.007675481483269, 1.0076516500668438,
+        1.007628108012127, 1.0076049682893853, 1.007582330284246, 1.0075602732846285,
+        1.007538851425266, 1.0075180904911867, 1.007497986797065, 1.0074785081563877,
+        1.0074595967598468, 1.0074411736209095, 1.0074231441360928, 1.0074054042576799,
+        1.0073878467863964, 1.0073703673508732, 1.007352869733089, 1.0073352703046223,
+        1.0073175014386897, 1.007299513844252, 1.0072812778230342, 1.007262783479855,
+        1.007244039928224, 1.0072250735389283, 1.0072059252920171, 1.0071866473223319,
+        1.0071672987998295, 1.0071479413553226, 1.0071286343395014, 1.007109430271817,
+        1.007090370877921, 1.0070714841123019, 1.0070527825063296, 1.0070342630681541,
+        1.0070159087989774, 1.006997691698736, 1.0069795769398635, 1.0069615277211368,
+        1.0069435102032127, 1.0069254978956355, 1.0069074749222342, 1.006889437734862,
+        1.006871395056732, 1.0068533660865622, 1.0068353772456984, 1.0068174579639644,
+        1.0067996361408973, 1.0067819339647324, 1.0067643647122124, 1.0067469309969421,
+        1.006729624705785, 1.0067124285977895, 1.0066953192806896, 1.0066782710673934,
+        1.0066612600835767, 1.0066442679681429, 1.0066272845851247, 1.0066103093354022,
+        1.0065933508907154, 1.0065764254318617, 1.0065595537149183, 1.0065427574740353,
+        1.0065260557671625, 1.0065094618671198, 1.006492981196861, 1.0064766106236323,
+        1.0064603391937497, 1.0064441501482861, 1.0064280238498762, 1.0064119411074788,
+        1.0063958863316667, 1.0063798499952599, 1.0063638300039595, 1.0063478317751198,
+        1.0063318670459986, 1.0063159516470979, 1.0063001026456049, 1.0062843353604596,
+        1.0062686607595903, 1.006253083671695, 1.0062376020950776, 1.0062222076916423,
+        1.006206887349471, 1.0061916255177914, 1.0061764068937507, 1.0061612189910805,
+        1.0061460541534462, 1.0061309106820524, 1.006115792907945, 1.006100710225511,
+        1.006085675281833, 1.0060707016569765, 1.0060558014488836, 1.0060409831821486,
+        1.0060262503926964, 1.0060116011143443, 1.0059970283311888, 1.0059825212911238,
+        1.0059680674294986, 1.005953654553126, 1.0059392728991112, 1.0059249167150017,
+        1.0059105850994794, 1.0058962819778992, 1.0058820152407764, 1.005867795217791,
+        1.0058536327707197, 1.0058395373472433, 1.0058255153351012, 1.0058115689946825,
+        1.0057976961398398, 1.0057838906019998, 1.0057701433751323, 1.005756444223523,
+        1.0057427834593835, 1.0057291535758301, 1.0057155504544624, 1.005701973948639,
+        1.005688427757803, 1.0056749186343144, 1.0056614550795473, 1.0056480457709414,
+        1.0056346980020798, 1.0056214164079242, 1.0056082021900556, 1.0055950529635962,
+        1.0055819632354543, 1.0055689254129643, 1.0055559311519593, 1.005542972799163,
+        1.0055300446740085, 1.0055171439699766, 1.0055042711281532, 1.0054914296320956,
+        1.0054786252757333, 1.0054658650470016, 1.005453155833189, 1.0054405031797256,
+        1.0054279103184318, 1.0054153776282193, 1.0054029026110682, 1.0053904803735485,
+        1.0053781045158243, 1.0053657682613286, 1.0053534656225152, 1.0053411923972777,
+        1.0053289468258413, 1.0053167298018257, 1.0053045446122957, 1.005292396264804,
+        1.0052802905301634, 1.0052682328762825, 1.0052562274826866, 1.0052442765063307,
+        1.0052323797207585, 1.0052205345820397, 1.0052087366988982, 1.0051969806141337,
+        1.005185260752555, 1.0051735723652195, 1.0051619123049556, 1.0051502795020133,
+        1.0051386750645706, 1.0051271019964159, 1.0051155645912702, 1.0051040676180953,
+        1.005092615445286, 1.0050812112582863, 1.0050698565047904, 1.0050585506583005,
+        1.0050472913328408, 1.0050360747192877, 1.005024896258625, 1.0050137514281552,
+        1.005002636500411, 1.0049915491431118, 1.0049804887596212, 1.0049694565176175,
+        1.0049584550692527, 1.0049474880199931, 1.0049365592454926, 1.0049256721797664,
+        1.0049148291995467, 1.004904031209545, 1.0048932774955626, 1.0048825658638114,
+        1.0048718930345228, 1.004861255214458, 1.004850648743785, 1.004840070702752,
+        1.0048295193735932, 1.0048189944812018, 1.0048084971765596, 1.0047980297727404,
+        1.0047875952860152, 1.0047771968669532, 1.0047668372233578, 1.0047565181354945,
+        1.0047462401452543, 1.0047360024686216, 1.00472580314061, 1.0047156393613883,
+        1.0047055079781795, 1.0046954060158606, 1.0046853311629969, 1.0046752821304619,
+        1.0046652588238771, 1.0046552623050675, 1.0046452945548068, 1.0046353580830856,
+        1.0046254554583376, 1.0046155888389043, 1.0046057595875855, 1.0045959680334178,
+        1.0045862134178594, 1.0045764940296895, 1.0045668075004355, 1.0045571512052545,
+        1.0045475226976317, 1.0045379201024043, 1.0045283424007567, 1.004518789561333,
+        1.0045092624990242, 1.0044997628730763, 1.0044902927633577, 1.0044808542831594,
+        1.0044714491963849, 1.004462078604098, 1.0044527427519885, 1.0044434409882277,
+        1.0044341718748553, 1.004424933429738, 1.0044157234546114, 1.0044065398915,
+        1.0043973811465101, 1.0043882463273561, 1.0043791353569205, 1.0043700489470928,
+        1.0043609884410187, 1.0043519555537461, 1.0043429520572764, 1.004333979464135,
+        1.0043250387620233, 1.004316130242354, 1.0043072534483912, 1.0042984072484276,
+        1.0042895900183817, 1.0042807999009307, 1.0042720350965488, 1.0042632941380643,
+        1.0042545761044925, 1.0042458807411827, 1.0042372084694509, 1.0042285602873418,
+        1.004219937580425, 1.004211341875435, 1.004202774577473, 1.0041942367327474,
+        1.0041857288532878, 1.0041772508292, 1.0041688019393276, 1.0041603809557398,
+        1.004151986323151], [1.860561262000302e-12, 5.590965144381883e-12,
+        9.34929463369726e-12, 1.3154437226175725e-11, 1.702568931308895e-11,
+        2.0982928027455134e-11, 2.5046788793157408e-11, 2.923885430425005e-11,
+        3.3581854914317976e-11, 3.8099884436610834e-11, 4.2818634026429384e-11,
+        4.776564768034582e-11, 5.297060253854495e-11, 5.846561902961817e-11,
+        6.428560472448649e-11, 7.04686379940848e-11, 7.705639715973789e-11,
+        8.409464233222935e-11, 9.163375817022624e-11, 9.972936639463722e-11,
+        1.0844301960925005e-10, 1.1784298791613632e-10, 1.2800515352408085e-10,
+        1.3901402978733642e-10, 1.509639242483601e-10, 1.63960268378703e-10,
+        1.7812114108065555e-10, 1.935790165123481e-10, 2.1048277353189044e-10,
+        2.2900000896947084e-10, 2.4931970654748365e-10, 2.7165531979872763e-10,
+        2.962483409156056e-10, 3.2337243813545756e-10, 3.5333826170938615e-10,
+        3.8649903552240276e-10, 4.232570757011358e-10, 4.6407140277893975e-10,
+        5.094666490756048e-10, 5.600435000132424e-10, 6.164909594518053e-10,
+        6.796007845091172e-10, 7.502845105848845e-10, 8.295935712716726e-10,
+        9.187431295298995e-10, 1.0191403623211478e-09, 1.1324181140042024e-09,
+        1.2604750198716513e-09, 1.4055234695482989e-09, 1.5701470706166886e-09,
+        1.7573696752330557e-09, 1.970738508541497e-09, 2.214424543675805e-09,
+        2.4933440401904073e-09, 2.8133061228300535e-09, 3.181192503383437e-09,
+        3.605177022134952e-09, 4.094994662291286e-09, 4.662272280618745e-09,
+        5.3209365882551336e-09, 6.087719214750639e-09, 6.9827842815298505e-09,
+        8.030511227582495e-09, 9.260475276627495e-09, 1.0708680719807698e-08,
+        1.2419119251414948e-08, 1.4445748493756375e-08, 1.6855016888245378e-08,
+        1.972910351438395e-08, 2.3170099760937402e-08, 2.7305441100640806e-08,
+        3.2295011723255995e-08, 3.8340508150708054e-08, 4.5697884220410605e-08,
+        5.4694047634142974e-08, 6.574949919124998e-08, 7.940940404298696e-08,
+        9.638683700821566e-08, 1.1762396974391741e-07, 1.443803566014069e-07,
+        1.783633788389051e-07, 2.219266971474567e-07, 2.78383451682192e-07,
+        3.525243036666565e-07, 4.51528410520993e-07, 5.867019250527802e-07,
+        7.771907035807035e-07, 1.0592984663135622e-06, 1.5165223475406203e-06,
+        2.4327248207525564e-06, 8.983344043039741e-06, 3.4407148128431454e-06,
+        3.0788829762166794e-06, 3.2588182907335967e-06, 3.701491716828597e-06,
+        4.384403432797052e-06, 5.350336838297003e-06, 6.685580238402497e-06,
+        8.52605245602338e-06, 1.1077024914207207e-05, 1.4647909600949463e-05,
+        1.9709962527758127e-05, 2.6992227757710016e-05, 3.764391464692145e-05,
+        5.3515778788747716e-05, 7.766138144884731e-05, 0.00011525871552788063,
+        0.0001753672747637021, 0.00027442166635680085, 0.0004435303174683058,
+        0.0007446564097185972, 0.0013092090476287275, 0.0024390391545493764,
+        0.004905497122939002, 0.011004932055370268, 0.02948200099285794,
+        0.11563853895319001, 2.732521321110213, 0.5791026043870786, 1.3450828889750528,
+        1.6242100185566206, 0.8729354000297639, 0.9660804995654967, 1.7975150996519422,
+        2.470641957527267, 1.2726452388315592, 1.0099844052562945, 1.0795995800138871,
+        1.4988689589718376, 2.3978640145625287, 1.922180708284257, 1.277459777164595,
+        1.0546005396709393, 1.046017793676741, 1.2204352720098466, 1.642001616311435,
+        2.0595754052122115, 1.6617657403926298, 1.2210516614564035, 1.0140929381360055,
+        0.9568791053522144, 1.0143877332332754, 1.1976516878254437, 1.5032210554543755,
+        1.6418998533929694, 1.3539582069953617, 1.055695302033266, 0.889986852684063,
+        0.8254942997815451, 0.8398327319036846, 0.9330692820476476, 1.1098606760056078,
+        1.2848443222187322, 1.2139383087371576, 0.9763217804712756, 0.7954107468917665,
+        0.7044117062572833, 0.782962691038673, 0.870546830145479, 0.9672829718172239,
+        1.0593145640966821, 1.113950476359102, 1.1096244786938543, 1.060949871952351,
+        1.00023855190829, 0.9502442940101028, 0.9202150055064109, 0.9120878491930178,
+        0.924904912422527, 0.9560375760825652, 1.000234943212829, 1.0475529356479392,
+        1.0825069231077051, 1.0886483116730994, 1.0587514939505986, 1.000242552747917,
+        0.9284213666807476, 0.8564659533406149, 0.7916282318355482, 0.7364505649693227,
+        0.6909854266581344, 0.6543283965143536, 0.6253965370301493, 0.6032509991968498,
+        0.5871971589035828, 0.5767901712094978, 0.5718073783222042, 0.5722145516855826,
+        0.5781356107408433, 0.5898260161414104, 0.6076436817253424, 0.6320053074594587,
+        0.6633089376638734, 0.7017953972479273, 0.7473165358100832, 0.7989913287664381,
+        0.8547912524184059, 0.9112344112023989, 0.9635442915524818, 1.006624389547119,
+        1.0367159333335476, 1.052835648376407, 1.0569697944156797, 1.052958470011013,
+        1.0449726123597496, 1.0364443839609532, 1.0296649186474982, 1.025826381657114,
+        1.025236653585608, 1.0275527554349104, 1.0319879127553895, 1.0375010212141247,
+        1.0429865978078257, 1.0474664227684858, 1.050258671966199, 1.0510849735797796,
+        1.0500840794212034, 1.047730634119699, 1.044690371505133, 1.0416589745484877,
+        1.0392253275694212, 1.037780885104897, 1.0374789546835539, 1.0382379208381407,
+        1.0397800226820921, 1.0416976388127566, 1.043538022166426, 1.0448938176797684,
+        1.0454825484922194, 1.0451975196812018, 1.0441181479323578, 1.0424786914473518,
+        1.0406060585528356, 1.038844532031916, 1.0374855755269465, 1.0367160228810668,
+        1.0365913981206616, 1.0370355887206488, 1.0378643379667611, 1.0388273328171669,
+        1.039661181622674, 1.0401432992952186, 1.0401356808643676, 1.0396090725104836,
+        1.038642563938241, 1.0373999366007616, 1.036089881384877, 1.0349203650855159,
+        1.0340573148061731, 1.0335952430459716, 1.0335439319138284, 1.0338319827636788,
+        1.0343253408612716, 1.0348567462428777, 1.0352603504360989, 1.0354047022454007,
+        1.0352174430006165, 1.0346967420459643, 1.0339075707875536, 1.0329645133633205,
+        1.0320057880521853, 1.031164632600948, 1.030543994459109, 1.0301989992150888,
+        1.030129637538598, 1.0302840761204861, 1.0305712423943463, 1.0308799359162006,
+        1.031100735022664, 1.0311465330720602, 1.0309678371530693, 1.030560070472412,
+        1.029961863946267, 1.0292452681284134, 1.028500426214555, 1.0278181159226978,
+        1.0272735749524962, 1.0269143377890495, 1.026753745406227, 1.0267706471889426,
+        1.0269147957934726, 1.0271166339774096, 1.0272996245959942, 1.0273930102155384,
+        1.0273429406735644, 1.0271202867776232, 1.0267241164808563, 1.0261806190431562,
+        1.0255380437713721, 1.0248588010709763, 1.0242101509160462, 1.0236548717906366,
+        1.0232430411436073, 1.0230056878865879, 1.0229507132416311, 1.0230611932900935,
+        1.023295999378356, 1.0235925827520769, 1.0238717234828063, 1.024043990891198,
+        1.0240175650011165, 1.0237069135980053, 1.0230416283852815, 1.0219745497122825,
+        1.020488223685328, 1.0185988025938766, 1.016356748545842, 1.013844105063282,
+        1.0111685823756928, 1.0084551498273295, 1.0058361425308835, 1.0034410110610932,
+        1.0013867722754282, 0.9997700045128431, 0.9986609433488269, 0.9980999428922507,
+        0.9980963182669526, 0.9986293962075101, 0.9996514702189195, 1.0010922719491204,
+        1.002864519065662, 1.0048700761375822, 1.007006269832265, 1.0091719368729724,
+        1.0112728533297644, 1.0132262895717419, 1.0149645407291983, 1.0164373773226982,
+        1.0176134272146464, 1.018480530562337, 1.0190451102617448, 1.0193305893312337,
+        1.0193748865588297, 1.0192270508696464, 1.0189431598939478, 1.018581701224391,
+        1.0181987561451067, 1.01784339007152, 1.017553698248494, 1.0173539431346228,
+        1.0172531443062476, 1.0172453446511327, 1.0173115884821993, 1.0174234268284372,
+        1.0175475405856749, 1.0176508800847983, 1.0177056009195438, 1.0176930666229616,
+        1.0176063077975848, 1.0174505656242285, 1.0172418655897302, 1.017003902216711,
+        1.0167637989103175, 1.0165474831385133, 1.016375457044547, 1.0162596484909794,
+        1.0162018232122878, 1.0161937654152922, 1.0162191371693028, 1.0162566511095843,
+        1.0162839776255843, 1.0162816914820136, 1.0162365664450175, 1.0161436538084534,
+        1.0160068115600147, 1.0158376418103254, 1.0156530868069846, 1.015472169756974,
+        1.0153125016369853, 1.015187189202676, 1.0151026783800026, 1.0150578775768193,
+        1.015044665682958, 1.0150496421131012, 1.015056761804461, 1.0150503511516509,
+        1.0150179459329824, 1.0149524393810572, 1.0148531695499923, 1.0147257831131848,
+        1.0145809462843214, 1.014432185856907, 1.0142932933090512, 1.0141757865483445,
+        1.0140868908865424, 1.0140283856025594, 1.0139964909744346, 1.0139827760808966,
+        1.0139758843607394, 1.0139637327511606, 1.0139357646923874, 1.0138848399665013,
+        1.0138084241109055, 1.013708881278515, 1.013592848801723, 1.0134698445273413,
+        1.0133503954771135, 1.0132440534532616, 1.013157668369121, 1.0130942266153735,
+        1.0130524453840477, 1.0130271683452672, 1.0130104604174683, 1.012993175460649,
+        1.012966691605635, 1.0129244877550043, 1.0128632744550876, 1.0127834845013652,
+        1.0126890548182852, 1.0125865662294036, 1.0124839252931812, 1.012388850462386,
+        1.0123074504105016, 1.0122431534135616, 1.012196171503396, 1.012163577803255,
+        1.0121399602975658, 1.0121185111073148, 1.0120923352559936, 1.012055729574098,
+        1.0120051959317837, 1.0119400099534268, 1.0118622551252239, 1.0117763350851312,
+        1.0116880737728102, 1.0116035857090138, 1.0115281342166118, 1.01146518896865,
+        1.0114158491393346, 1.011378724813154, 1.011350281806219, 1.01132556993695,
+        1.0112991871842965, 1.0112662936989776, 1.0112234865015937, 1.0111693776455706,
+        1.0111047788658147, 1.011032472214399, 1.0109566239405792, 1.0108819631152663,
+        1.0108128856134382, 1.0107526517971457, 1.0107028225821966, 1.0106630293165961,
+        1.0106311081433006, 1.0106035615846487, 1.0105762513033871, 1.0105451866542212,
+        1.0105072603134295, 1.0104607967250898, 1.0104058179661237, 1.0103439870320021,
+        1.0102782496240832, 1.01021225061621, 1.010149640367657, 1.0100934022854384,
+        1.0100453244644532, 1.0100057074884656, 1.0099733540902913, 1.0099458333561582,
+        1.0099199622990798, 1.009892409779178, 1.0098603083811402, 1.0098217619745253,
+        1.009776159327591, 1.0097242425988815, 1.0096679262186206, 1.0096099076574616,
+        1.0095531483324722, 1.0095003239455516, 1.0094533456228154, 1.009413036721614,
+        1.0093790188563545, 1.0093498208140175, 1.009323183080244, 1.0092964960647404,
+        1.0092672878199487, 1.009233670742217, 1.0091946671187633, 1.0091503580739878,
+        1.009101834531946, 1.0090509656875142, 1.0090000332731857, 1.0089513027252484,
+        1.0089066113761493, 1.0088670479203323, 1.0088327782753184, 1.0088030445595506,
+        1.0087763316874307, 1.0087506659495125, 1.0087239872292915, 1.0086945250499852,
+        1.0086611101715435, 1.0086233673154708, 1.0085817579017369, 1.0085374699024332,
+        1.0084921797355013, 1.0084477334711968, 1.0084058076230349, 1.0083676114319031,
+        1.0083336829644065, 1.0083038126890627, 1.0082771041487055, 1.0082521564022047,
+        1.0082273315389432, 1.0082010564686221, 1.0081721036461682, 1.0081398009321736,
+        1.0081041351128892, 1.008065733860031, 1.008025733251408, 1.0079855582904207,
+        1.0079466585560286, 1.0079102477406248, 1.007877093501802, 1.0078473935193948,
+        1.0078207570935138, 1.0077962921994712, 1.007772779167458, 1.0077488973676865,
+        1.0077234629383531, 1.007695634965638, 1.0076650544820924, 1.0076318937167486,
+        1.0075968096846815, 1.0075608133575618, 1.0075250802357936, 1.0074907376455202,
+        1.0074586670115682, 1.007429355440143, 1.0074028211323391, 1.0073786233830915,
+        1.0073559527517415, 1.0073337831134068, 1.0073110570843151, 1.0072868714115126,
+        1.007260630002799, 1.0072321389568477, 1.0072016288811485, 1.0071697029025335,
+        1.0071372217139727, 1.0071051475145387, 1.0070743750512134, 1.0070455792253652,
+        1.0070191048707355, 1.0069949162121852, 1.0069726127308734, 1.0069515066348482,
+        1.006930746848356, 1.0069094670810375, 1.0068869322460658, 1.0068626586641998,
+        1.0068364887459886, 1.0068086091403088, 1.006779511153452, 1.0067499018668582,
+        1.006720582212208, 1.0066923130767118, 1.0066656916554333, 1.0066410577325147,
+        1.006618443959229, 1.0065975765745674, 1.0065779247180806, 1.006558788881708,
+        1.0065394133103907, 1.0065191040972932, 1.0064973346593853, 1.006473823055115,
+        1.0064485706106885, 1.006421857632209, 1.0063941985338136, 1.0063662644824003,
+        1.0063387858291992, 1.0063124486681831, 1.0062877997060706, 1.0062651714793134,
+        1.0062446363240387, 1.0062259930799264, 1.006208786013799, 1.0061923515316031,
+        1.0061758853857625, 1.0061585215322615, 1.006139413568177, 1.006117810601659,
+        1.006093121144773, 1.006064960779097, 1.0060331815387313, 1.0059978828741352,
+        1.0059594055077017, 1.0059183104032974, 1.005875345498719, 1.00583140292491,
+        1.005787469328296, 1.0057445717794866, 1.005703721702057, 1.00566585932799,
+        1.0056318013483128, 1.0056021945892368, 1.0055774785878213, 1.005557859754703,
+        1.0055432993181257, 1.0055335164261192, 1.0055280066910153, 1.0055260752025474,
+        1.0055268817653442, 1.0055294950000695, 1.0055329511382498, 1.0055363129479373,
+        1.0055387243019642, 1.0055394564246138, 1.0055379427469728, 1.0055338004410812,
+        1.005526837939623, 1.0055170489366825, 1.0055045943841925, 1.0054897747683014,
+        1.0054729954352455, 1.005454727945559, 1.00543547040879, 1.005415709543745,
+        1.0053958868777344, 1.0053763710865022, 1.0053574380092156, 1.005339259359467,
+        1.0053219005898475, 1.0053053277542752, 1.0052894225584343, 1.0052740041266124,
+        1.005258855397765, 1.0052437515693833, 1.0052284877170037, 1.005212902703949,
+        1.0051968968073117, 1.005180441127781, 1.0051635777761017, 1.0051464109401256,
+        1.0051290900938445, 1.0051117876512428, 1.0050946741345563, 1.0050778942896998,
+        1.0050615474670261, 1.0050456749900374, 1.0050302562303373, 1.0050152138341684,
+        1.0050004271923687, 1.004985752018591, 1.0049710429925436, 1.0049561759822632,
+        1.0049410664560934, 1.0049256813193843, 1.0049100424666508, 1.0048942216585317,
+        1.004878327703407, 1.004862488125264, 1.0048468283394298, 1.0048314517030656,
+        1.0048164236060684, 1.0048017620591447, 1.0047874361405875, 1.0047733723659282,
+        1.0047594677598164, 1.0047456073478664, 1.0047316831179478, 1.004717611328578,
+        1.0047033453856387, 1.004688882300971, 1.0046742618470899, 1.0046595587430516,
+        1.0046448693422965, 1.0046302951580548, 1.0046159260191712, 1.0046018256331744,
+        1.0045880218593441, 1.0045745031533955, 1.0045612215864657, 1.0045481017464282,
+        1.0045350538813278, 1.0045219889959143, 1.004508833361346, 1.004495540074147,
+        1.0044820958613154, 1.0044685221680225, 1.0044548705351937, 1.0044412132106206,
+        1.0044276306860982, 1.0044141982973314, 1.0044009741009157, 1.0043879899547732,
+        1.0043752471364524, 1.0043627170468228, 1.0043503467016437, 1.0043380679510179,
+        1.0043258088074827, 1.0043135049897527, 1.004301109832566, 1.00428860105208,
+        1.0042759834216899, 1.004263287103178, 1.004250562075062, 1.0042378696920615,
+        1.0042252728080316, 1.0042128260467789, 1.004200567701619, 1.0041885144170315,
+        1.0041766593200423, 1.0041649737113434, 1.004153411888075, 1.004141918233307,
+        1.00413043543064, 1.0041189125755006, 1.0041073120542743, 1.0040956143169044,
+        1.004083820025169, 1.0040719494544137, 1.0040600393990253, 1.0040481381298487,
+        1.0040362991422056, 1.0040245745032241, 1.0040130085657293, 1.0040016326861554,
+        1.0039904613999657, 1.0039794903053627, 1.003968695715509, 1.003958035983621,
+        1.0039474542935576, 1.003936882640957, 1.0039262466969066, 1.0039154712344813,
+        1.0039044857951558, 1.0038932302681538, 1.0038816600486797, 1.0038697504351959,
+        1.0038574999304217, 1.0038449321379934, 1.0038320960063207, 1.0038190642687954,
+        1.0038059300628117, 1.003792801868569, 1.0037797970748579, 1.003767034630576,
+        1.0037546273550721, 1.0037426745383313, 1.003731255451863, 1.0037204243112434,
+        1.0037102070903094, 1.0037006004031996, 1.0036915724683164, 1.0036830659744316,
+        1.0036750025083123, 1.0036672880931712, 1.0036598193376507, 1.003652489704691,
+        1.0036451954687382, 1.0036378410216993, 1.0036303432933023, 1.0036226351512452,
+        1.0036146677275715, 1.0036064116719965, 1.003597857362435, 1.0035890141144277,
+        1.0035799084369739, 1.003570581394887, 1.0035610851674264, 1.0035514789439177,
+        1.0035418243661682, 1.0035321808044952, 1.0035226008226794, 1.003513126229112,
+        1.0035037851094495, 1.0034945901798191, 1.003485538686335, 1.003476613915309,
+        1.0034677881877425, 1.003459027017995, 1.0034502939504013, 1.0034415554775618,
+        1.0034327854122873, 1.0034239681420412, 1.0034151003372682, 1.003406190895482,
+        1.0033972591521385, 1.0033883316393672, 1.0033794378865335, 1.0033706058970713,
+        1.0033618579815982, 1.0033532075683267, 1.0033446574569493, 1.0033361997547958,
+        1.003327817469933, 1.0033194874773075, 1.0033111843620959, 1.0033028845135183,
+        1.003294569813094, 1.0032862303378052, 1.0032778656678472, 1.0032694846219494,
+        1.0032611035017893, 1.0032527431681888, 1.0032444254559016, 1.0032361695313463,
+        1.0032279887937188, 1.0032198888167478, 1.0032118666448429, 1.0032039115251659,
+        1.0031960069165213, 1.0031881334065331, 1.0031802720256426, 1.0031724073923465,
+        1.0031645301661418, 1.0031566384140707, 1.003148737689569, 1.0031408398448165,
+        1.0031329608114037, 1.0031251177529645, 1.0031173260897137, 1.0031095969038015,
+        1.0031019351565507, 1.0030943389992328, 1.0030868002652842, 1.003079306027806,
+        1.0030718409271384, 1.0030643898492568, 1.0030569404865526, 1.003049485345119,
+        1.0030420228691093, 1.0030345575130621, 1.003027098778609, 1.0030196594095548,
+        1.0030122530793588, 1.003004891983404, 1.0029975847540613, 1.0029903350495244,
+        1.0029831410417487, 1.0029759958672972, 1.0029688889367565, 1.0029618078525337,
+        1.0029547405863015, 1.0029476775317423, 1.0029406130801155, 1.0029335464586253,
+        1.0029264817062165, 1.002919426814791, 1.0029123922078456, 1.0029053888390917,
+        1.002898426251981, 1.0028915109386216, 1.0028846452753772, 1.0028778272044712,
+        1.002871050696605, 1.002864306892499, 1.0028575857059352, 1.0028508775962295,
+        1.0028441751965516, 1.0028374745181345, 1.0028307755320063, 1.002824082043817,
+        1.002817400903057, 1.002810740702962, 1.0028041102120675, 1.002797516818701,
+        1.0027909652597586, 1.002784456848033, 1.0027779893194553, 1.0027715573098828,
+        1.0027651533608324, 1.0027587692637343, 1.0027523974982981, 1.002746032510812,
+        1.0027396716130517, 1.002733315354908, 1.0027269673199184, 1.0027206333952723,
+        1.0027143206585751, 1.0027080360867626, 1.0027017853182665, 1.0026955716838573,
+        1.0026893956687313, 1.002683254888464, 1.0026771445691376, 1.0026710584338758,
+        1.0026649898294355, 1.0026589328888234, 1.0026528835250736, 1.0026468400864383,
+        1.0026408035669645, 1.0026347773473119, 1.00262876652365, 1.0026227769530083,
+        1.0026168141899436, 1.0026108825036408, 1.0026049841456137, 1.002599118989741,
+        1.002593284597962, 1.0025874766891043, 1.0025816899182176, 1.0025759188220134,
+        1.0025701587606506, 1.0025644066912849, 1.002558661642531, 1.0025529248147718,
+        1.0025471992986288, 1.0025414894708846, 1.0025358001819111, 1.0025301358821033,
+        1.0025244998414728, 1.0025188935962235, 1.0025133167128528, 1.002507766902523,
+        1.0025022404562365, 1.002496732916357, 1.002491239860828, 1.002485757660186,
+        1.0024802840760378, 1.002474818600712, 1.0024693624859056, 1.0024639184635853,
+        1.0024584902161873, 1.0024530816952053, 1.0024476964111229, 1.0024423368192785,
+        1.0024370039061135, 1.0024316970426068, 1.0024264141232118, 1.002421151958468,
+        1.0024159068460914, 1.00241067521627, 1.0024054542368748, 1.00240024227427,
+        1.0023950391334417, 1.0023898460415082, 1.0023846653843973, 1.0023795002490852,
+        1.002374353856078, 1.0023692289837332, 1.002364127484631, 1.002359049975457,
+        1.002353995749651, 1.0023489629219642, 1.0023439487737487, 1.0023389502336997,
+        1.0023339644072087, 1.0023289890612608, 1.0023240229822425, 1.0023190661480064,
+        1.0023141196894525, 1.002309185653857, 1.0023042666160735, 1.0022993652088645,
+        1.0022944836554593, 1.00228962338498, 1.0022847847947611, 1.0022799671966287,
+        1.0022751689514775, 1.0022703877639985, 1.0022656210826368, 1.0022608665333017,
+        1.0022561223115045, 1.0022513874667272, 1.002246662033267, 1.0022419469891402,
+        1.0022372440546767, 1.0022325553695348, 1.0022278831063847, 1.0022232290889612,
+        1.002218594479308, 1.0022139795856595, 1.0022093838203765, 1.002204805811068,
+        1.0022002436420023, 1.0021956951814137, 1.0021911584371384, 1.0021866318796984,
+        1.0021821146793273, 1.0021776068192967, 1.0021731090698374, 1.0021686228307545,
+        1.0021641498726557, 1.0021596920227018, 1.0021552508488656, 1.0021508273951552,
+        1.0021464220105183, 1.0021420342970717, 1.0021376631831163, 1.0021333071053278,
+        1.0021289642673263, 1.002124632930091, 1.0021203116859358, 1.0021159996719,
+        1.0021116966896502, 1.002107403215114, 1.002103120299469, 1.002098849380351,
+        1.0020945920360278, 1.0020903497231541, 1.0020861235400165, 1.0020819140516033,
+        1.002077721202038, 1.002073544325203, 1.0020693822490032, 1.002065233474402],
+    [8.06564244779419e-13, 2.4238188913528835e-12, 4.053489027171017e-12,
+        5.703974484447685e-12, 7.383860870648792e-12, 9.101997682599901e-12,
+        1.0867579107706212e-11, 1.2690230065959475e-11, 1.458009755807974e-11,
+        1.654794913758527e-11, 1.860527975700619e-11, 2.0764428624776746e-11,
+        2.3038707570177476e-11, 2.5442543237155977e-11, 2.799163493433789e-11,
+        3.070313096229277e-11, 3.359582608681211e-11, 3.669038351454225e-11,
+        4.000958521451811e-11, 4.357861473260523e-11, 4.742537788335678e-11,
+        5.15808667275077e-11, 5.607957393656814e-11, 6.095996526219728e-11,
+        6.62650192921049e-11, 7.204284514609263e-11, 7.834739080761802e-11,
+        8.523925646052575e-11, 9.278663033266711e-11, 1.0106636689600027e-10,
+        1.1016523174251128e-10, 1.2018134058285404e-10, 1.3122582612963802e-10,
+        1.434247716851843e-10, 1.5692145839042063e-10, 1.718789810944923e-10,
+        1.8848329912336988e-10, 2.0694680004433386e-10, 2.275124708520878e-10,
+        2.5045878829579134e-10, 2.7610546389360354e-10, 3.0482020489527337e-10,
+        3.3702668722721765e-10, 3.732139752102099e-10, 4.1394767418356073e-10,
+        4.598831598500282e-10, 5.117813072013626e-10, 5.705272264670116e-10,
+        6.371526350919086e-10, 7.128626255161208e-10, 7.990677689277961e-10,
+        8.974227069901457e-10, 1.0098726514632126e-09, 1.138709550643181e-09,
+        1.2866400992792108e-09, 1.4568682973461221e-09, 1.6531959354886787e-09,
+        1.880145218915559e-09, 2.1431088228650643e-09, 2.448534025712595e-09,
+        2.804149308423645e-09, 3.21924403786332e-09, 3.705014712091144e-09,
+        4.274994939536148e-09, 4.945591105829142e-09, 5.736751899184321e-09,
+        6.6728079622420675e-09, 7.783528558512883e-09, 9.105456106478524e-09,
+        1.0683597852122542e-08, 1.2573578406609377e-08, 1.4844389443385352e-08,
+        1.7581916456637323e-08, 2.089348106423366e-08, 2.4913716636779156e-08,
+        2.981220261055259e-08, 3.5803429973801924e-08, 4.3159872222717046e-08,
+        5.222921507774258e-08, 6.345718596983899e-08, 7.74179661232832e-08,
+        9.485493112514578e-08, 1.1673554689129263e-07, 1.4432579055046485e-07,
+        1.7929168405979103e-07, 2.238387419984248e-07, 2.809048301311559e-07,
+        3.5442884827489113e-07, 4.4972793444809405e-07, 5.740313237919751e-07,
+        7.37242392870762e-07, 9.530362768813506e-07, 1.240456004798027e-06,
+        1.6262572309858223e-06, 2.1483900434142826e-06, 2.8612292046892064e-06,
+        3.843528333275691e-06, 5.210678047650061e-06, 7.133868659957014e-06,
+        9.870513137808483e-06, 1.3813365327003911e-05, 1.957129047687464e-05,
+        2.810478856422634e-05, 4.0958505853238085e-05, 6.0670149691576056e-05,
+        9.150990116188751e-05, 0.00014086016107635964, 0.00022188450660039083,
+        0.0003589104342139791, 0.0005988319700055329, 0.0010367324872368985,
+        0.0018777981957881816, 0.003601393704104081, 0.007452697724296055,
+        0.01719698560451111, 0.047381757556403434, 0.19116831416779587,
+        4.648854588836236, 1.0148348973000396, 2.4314883638592506, 3.0353241977899357,
+        1.6920964131268008, 1.9522090180271434, 3.8167304606320553, 5.585308033029022,
+        3.1379948212739825, 2.8648934740380265, 4.233599946564369, 5.644588871056083,
+        4.917127956107992, 3.108266301201451, 1.7948533785655705, 1.347852881365246,
+        1.2492357300658417, 1.3863639042851583, 1.7967193521557017, 2.1915468592811687,
+        1.7323421120336573, 1.2545621081726568, 1.0320182133175246, 0.9686007088157046,
+        1.025051174560949, 1.2120136466773626, 1.5277918419112784, 1.6801956267380422,
+        1.3982999594694665, 1.1026740630216718, 0.9420507181294638, 0.8871681499958766,
+        0.9180529282826418, 1.0392731490670641, 1.2617555530822964, 1.4935335087285062,
+        1.4455954416426529, 1.193759877155633, 1.0019018125155945, 0.9211985429093559,
+        1.0173198021600358, 1.105973417544652, 1.210709672028973, 1.3104362150475293,
+        1.3644555288338645, 1.3474459952699753, 1.2784077921242056, 1.196815674703627,
+        1.1296910098521158, 1.08748870983375, 1.0719214244072672, 1.0813607209174485,
+        1.1123299020582742, 1.1584274005783142, 1.2079852493913885, 1.2431845005060584,
+        1.2453843154423414, 1.2067152374003738, 1.136026816240504, 1.050927217428943,
+        0.9663813302846318, 0.8904975450657662, 0.8260115239191601, 0.7728528222139679,
+        0.7298945002871887, 0.6958316539141566, 0.6695397084779836, 0.6501812763601246,
+        0.6372075102367346, 0.6303234167941966, 0.6294472796593191, 0.6346747530848248,
+        0.6462476778863331, 0.6645207440478618, 0.6899127561042774, 0.7228217117070043,
+        0.7634742976364943, 0.8116756117631811, 0.8664394896613682, 0.9255452937889714,
+        0.985215622042453, 1.0402975803975587, 1.0853212770850826, 1.1162846876093901,
+        1.1321882371458638, 1.1352231819908842, 1.129555430378369, 1.1196831774669482,
+        1.1092918638683604, 1.100830176010428, 1.0955627518451085, 1.0938060674815406,
+        1.0951823038814819, 1.098843238808627, 1.1036738654016462, 1.1084952355025064,
+        1.112267935314588, 1.1142706251822927, 1.1142119476407437, 1.1122430998460966,
+        1.1088700572398391, 1.1047991154361592, 1.1007659686307734, 1.0973913455214623,
+        1.095085923044525, 1.094008228323555, 1.0940689529651006, 1.0949726231181927,
+        1.0962879965098709, 1.097537553156101, 1.098292709676563, 1.0982570998069072,
+        1.0973195718857023, 1.0955644636102706, 1.0932382562031628, 1.090683965236095,
+        1.0882620615404845, 1.0862769731524977, 1.084923047887166, 1.08425695028658,
+        1.084197670691088, 1.0845514024782872, 1.0850557526397637, 1.0854351861108156,
+        1.085457261488426, 1.0849781726625451, 1.0839677425574632, 1.082508750086184,
+        1.0807720573316861, 1.0789750116506551, 1.07733386431958, 1.0760207965564477,
+        1.0751334624165212, 1.0746812922957558, 1.0745893485313858, 1.0747177236872572,
+        1.074892238976511, 1.0749404374467977, 1.0747258086242255, 1.0741733430095308,
+        1.0732812856916896, 1.0721171508646348, 1.0707997933288553, 1.0694724103882038,
+        1.0682728660381586, 1.0673074931058066, 1.0666329946434365, 1.0662489514412443,
+        1.0661013323574904, 1.066095588399889, 1.0661164713036404, 1.066050707071779,
+        1.0658082150753765, 1.0653378812576457, 1.0646350471169554, 1.0637396829249117,
+        1.0627262237751511, 1.0616877057113936, 1.0607177279677407, 1.05989376705466,
+        1.0592646528543674, 1.0588439121390785, 1.058609504438852, 1.0585094247842621,
+        1.0584718231836794, 1.0584177291926034, 1.05827420099972, 1.05798577594019,
+        1.0575224941932917, 1.0568834477601157, 1.0560956411219176, 1.055208753704953,
+        1.0542869907946457, 1.0533994925786745, 1.0526107354457377, 1.0519720878855687,
+        1.051515300643157, 1.0512483353241546, 1.0511536444126646, 1.051188833607283,
+        1.0512895454158089, 1.051374355777156, 1.0513514216414799, 1.0511265176764526,
+        1.0506119418518944, 1.049735574417033, 1.04844919732658, 1.0467350945951432,
+        1.0446100242439156, 1.042125908977283, 1.0393670085604376, 1.0364438300552965,
+        1.0334844903485862, 1.0306245657402524, 1.0279965864953595, 1.025720260233534,
+        1.0238942865688865, 1.0225903303706814, 1.02184942223063, 1.0216807992387733,
+        1.0220630061146394, 1.0229469435481366, 1.0242604643239213, 1.025914065835665,
+        1.027807203876829, 1.0298347581282281, 1.0318932183234932, 1.033886232284377,
+        1.0357292553118753, 1.037353148545984, 1.038706670935162, 1.0397578774237266,
+        1.0404944670950702, 1.0409231257452296, 1.0410678959998814, 1.0409676078873613,
+        1.0406724324589625, 1.0402396873308541, 1.0397291177932824, 1.0391979802533662,
+        1.0386963405988503, 1.0382630448407422, 1.0379228065556738, 1.0376847780982619,
+        1.037542832412132, 1.037477590215846, 1.0374600026436698, 1.0374560706988878,
+        1.0374320874789953, 1.037359668765666, 1.0372198288725594, 1.0370054806431797,
+        1.0367219818916584, 1.0363856747906561, 1.0360207059092312, 1.0356547028722367,
+        1.0353140623824046, 1.0350196442327277, 1.0347835683712592, 1.034607603437766,
+        1.0344833565302114, 1.0343941715065614, 1.0343183625388708, 1.0342331928882138,
+        1.0341188911512569, 1.033962001542189, 1.0337574949021184, 1.0335093024133113,
+        1.0332292301087924, 1.0329345099406353, 1.0326444828095966, 1.0323770457460506,
+        1.032145509167629, 1.0319564069125222, 1.031808608553984, 1.031693839549042,
+        1.0315984632761395, 1.0315061612463199, 1.0314009987832433, 1.0312703080692414,
+        1.031106868737799, 1.0309100098046187, 1.030685468243054, 1.0304440768154624,
+        1.0301995692934403, 1.0299659432353139, 1.0297548827313543, 1.029573709674945,
+        1.0294242148112258, 1.029302545517081, 1.0292001296640294, 1.0291054289047243,
+        1.029006171623378, 1.0288916393937102, 1.0287545838002383, 1.0285924316924755,
+        1.0284075803352186, 1.0282067609302532, 1.0279996242681506, 1.0277968416004633,
+        1.0276080917803943, 1.0274403107132521, 1.027296514564453, 1.0271753899766995,
+        1.0270716968967404, 1.0269773799095048, 1.0268831584437519, 1.0267802861670272,
+        1.0266621486126835, 1.0265254084759223, 1.0263705015790126, 1.0262014144727893,
+        1.0260248115363215, 1.0258486984978636, 1.0256808882925101, 1.0255275609374794,
+        1.0253921796123031, 1.0252749488468251, 1.0251728939676585, 1.0250805242887309,
+        1.0249909370561303, 1.0248971432052043, 1.024793362351489, 1.0246760482821273,
+        1.024544464009035, 1.02440071539, 1.0242492565090449, 1.0240959780695664,
+        1.0239470634684342, 1.023807833097081, 1.0236817908009461, 1.0235700406735058,
+        1.0234711677833344, 1.0233815878507464, 1.0232962847708145, 1.023209786528063,
+        1.0231171911993042, 1.023015051662209, 1.022901960029699, 1.02277873383852,
+        1.022648183419696, 1.022514518527201, 1.0223825172443632, 1.0222566196852207,
+        1.0221401167510804, 1.0220345802034414, 1.02193963044858, 1.0218530729166935,
+        1.0217713652234948, 1.0216903178931818, 1.0216058916943809, 1.0215149412277449,
+        1.021415769074009, 1.0213083941486603, 1.0211944939404065, 1.0210770420557465,
+        1.0209597181627381, 1.0208462067958401, 1.0207395178432055, 1.0206414528205654,
+        1.0205523099222251, 1.0204708739386863, 1.0203946835537594, 1.0203205181659107,
+        1.0202450081679932, 1.020165253091804, 1.020079334204513, 1.019986631059487,
+        1.019887890376275, 1.0197850427969528, 1.0196808095097165, 1.0195781778304709,
+        1.0194798460570782, 1.0193877399682922, 1.0193026866401307, 1.01922429960263,
+        1.0191510890751765, 1.0190807696698605, 1.01901070299806, 1.0189383901295863,
+        1.0188619225183115, 1.0187803105114284, 1.018693633509417, 1.01860299024512,
+        1.0185102648773137, 1.018417757688006, 1.0183277521846086, 1.0182420994907928,
+        1.018161894950146, 1.0180873025425123, 1.0180175540364576, 1.0179511172800002,
+        1.0178859976293375, 1.017820113606139, 1.0177516763319072, 1.017679503849995,
+        1.0176032154475625, 1.017523274618563, 1.0174408777872326, 1.0173577139742846,
+        1.0172756431248235, 1.0171963539146254, 1.0171210634844492, 1.0170503118636367,
+        1.0169838850113346, 1.0169208761433048, 1.0168598698522109, 1.016799211982902,
+        1.016737314015396, 1.0166729361413123, 1.0166053988227484, 1.0165346870790952,
+        1.0164614321818248, 1.01638677796664, 1.0163121594547224, 1.0162390362811318,
+        1.0161686300968271, 1.016101712747135, 1.0160384813969952, 1.0159785400745507,
+        1.0159209875237027, 1.0158645923582987, 1.0158080216106484, 1.0157500803663289,
+        1.0156899195549907, 1.0156271759900362, 1.0155620219283985, 1.0154951182120169,
+        1.0154274823413678, 1.0153602975204659, 1.0152946982823599, 1.0152315712455673,
+        1.0151714055950871, 1.015114217985662, 1.0150595626877794, 1.0150066225111556,
+        1.0149543620599448, 1.014901714585489, 1.0148477687700155, 1.0147919228760536,
+        1.0147339804378719, 1.0146741726855546, 1.0146131061097203, 1.0145516466089044,
+        1.014490762249136, 1.0144313530581694, 1.0143740975335747, 1.0143193416534244,
+        1.0142670480164875, 1.0142168118742223, 1.0141679392061498, 1.0141195716325435,
+        1.014070835557501, 1.0140209896248848, 1.013969545751636, 1.0139163443002108,
+        1.0138615723100035, 1.0138057235943214, 1.013749509200212, 1.013693734611356,
+        1.013639164917982, 1.0135864003251915, 1.0135357818140813, 1.0134873411139285,
+        1.0134408014668443, 1.0133956273130384, 1.0133511133711472, 1.0133064978146022,
+        1.013261081163658, 1.0132143324560337, 1.0131659670569768, 1.0131159855107137,
+        1.013064669189326, 1.0130125350919772, 1.0129602579548742, 1.012908572027673,
+        1.0128581669527235, 1.0128095920245197, 1.0127631809408764, 1.0127190055022441,
+        1.0126768622608238, 1.0126362915965876, 1.0125966247554123, 1.0125570515057047,
+        1.0125166995088433, 1.0124747162753696, 1.0124303455075985, 1.0123829913800868,
+        1.0123322664834509, 1.0122780213660356, 1.0122203555390188, 1.0121596112667761,
+        1.0120963523810256, 1.0120313307861715, 1.0119654433980498, 1.0118996821497117,
+        1.0118350795634443, 1.01177265233794, 1.011713345472463, 1.0116579796123044,
+        1.0116072044621591, 1.0115614611575277, 1.011520956296254, 1.0114856498356606,
+        1.0114552582381666, 1.0114292731491346, 1.011406994625262, 1.0113875766542957,
+        1.011370081584156, 1.0113535392662238, 1.0113370063231244, 1.0113196210270397,
+        1.0113006498024004, 1.0112795222669415, 1.0112558528719051, 1.0112294484460633,
+        1.011200302143819, 1.0111685753223516, 1.011134569646443, 1.0110986922073226,
+        1.0110614166518015, 1.0110232432907418, 1.0109846609471378, 1.0109461129702753,
+        1.010907969428111, 1.010870507019727, 1.0108338977334506, 1.0107982067094627,
+        1.0107633991491363, 1.010729355455872, 1.0106958931268348, 1.0106627932963503,
+        1.0106298293352076, 1.0105967946181347, 1.0105635265588737, 1.0105299243256716,
+        1.0104959582953967, 1.0104616702347924, 1.0104271643144673, 1.0103925902247441,
+        1.0103581207091077, 1.0103239266014594, 1.010290152817978, 1.0102568986387623,
+        1.010224205015357, 1.010192050630428, 1.0101603571561912, 1.010129002797746,
+        1.0100978419743416, 1.0100667280792595, 1.010035535814354, 1.0100041796929895,
+        1.0099726259329023, 1.0099408960219824, 1.0099090615652713, 1.0098772313989006,
+        1.009845533164189, 1.0098140923790508, 1.0097830123904432, 1.0097523583889068,
+        1.0097221479535534, 1.009692349494928, 1.0096628886593944, 1.0096336614676342,
+        1.009604551893246, 1.00957545091627, 1.0095462739141485, 1.0095169735982465,
+        1.0094875465004771, 1.0094580321207294, 1.0094285050724943, 1.0093990617051756,
+        1.009369803550244, 1.0093408203975256, 1.0093121757914734, 1.009283897260692,
+        1.0092559727486425, 1.0092283536494613, 1.0092009637530548, 1.009173712451113,
+        1.009146509904087, 1.0091192816173655, 1.009091980051986, 1.0090645914588792,
+        1.0090371369691529, 1.0090096679483127, 1.008982256562876, 1.0089549832599445,
+        1.0089279233063593, 1.00890113461175, 1.0088746487703089, 1.0088484666613353,
+        1.0088225591580877, 1.0087968726456145, 1.0087713382824668, 1.0087458833795961,
+        1.0087204429949272, 1.0086949698860053, 1.0086694413037094, 1.0086438616780893,
+        1.008618260940517, 1.0085926889263097, 1.0085672068965443, 1.0085418776178254,
+        1.0085167555913244, 1.00849187891824, 1.008467263959823, 1.0084429034621605,
+        1.0084187682558905, 1.0083948121006747, 1.0083709788055368, 1.0083472104785114,
+        1.0083234556719642, 1.008299676289989, 1.008275852380035, 1.0082519842889792,
+        1.0082280920611348, 1.0082042123297674, 1.0081803932527682, 1.0081566882343376,
+        1.008133149244779, 1.0081098205088295, 1.008086733202524, 1.008063901613851,
+        1.0080413210188588, 1.008018967333537, 1.0079967984453178, 1.0079747570158415,
+        1.0079527744788317, 1.0079307759237408, 1.0079086855441757, 1.0078864323267709,
+        1.0078639556522822, 1.0078412104735286, 1.0078181717290617, 1.0077948376559696,
+        1.0077712316926482, 1.007747402722222, 1.00772342350529, 1.0076993872845506,
+        1.0076754027029355, 1.0076515873437755, 1.007628060353596, 1.0076049347229126,
+        1.00758230985846, 1.007560265070065, 1.007538854515095, 1.007518104001882,
+        1.0074980098690078, 1.0074785399544077, 1.0074596364737045, 1.007441220465719,
+        1.0074231973526855, 1.0074054631129128, 1.0073879105734067, 1.00737043538928,
+        1.0073529413691387, 1.0073353449112916, 1.007317578415729, 1.0072995926181911,
+        1.0072813578471334, 1.0072628642340162, 1.007244120918852, 1.007225154298755,
+        1.0072060053798815, 1.0071867263229197, 1.0071673763233773, 1.0071480170372837,
+        1.0071287078401763, 1.0071095012759543, 1.0070904390942836, 1.0070715492732072,
+        1.007052844367161, 1.007034321406848, 1.0070159634154887, 1.0069977424144798,
+        1.0069796235971387, 1.0069615701825327, 1.0069435483509976, 1.0069255316311305,
+        1.006907504165176, 1.0068894624227527, 1.0068714151441769, 1.0068533815446021,
+        1.006835388061133, 1.0068174641386693, 1.0067996376911406, 1.0067819309204826,
+        1.006764357116453, 1.0067469189049811, 1.0067296081845694, 1.0067124077252194,
+        1.0066952941449414, 1.006678241766245, 1.0066612267237394, 1.0066442306645997,
+        1.0066272434604808, 1.0066102645192392, 1.0065933025189604, 1.0065763736461648,
+        1.0065594986620447, 1.0065426993052664, 1.0065259946377163, 1.006509397935582,
+        1.006492914624633, 1.0064765415743933, 1.0064602678329362, 1.00644407664259,
+        1.0064279483667549, 1.0064118638146862, 1.006395807396801, 1.0063797695853278,
+        1.0063637482849603, 1.0063477489116466, 1.0063317832008594, 1.006315866980954,
+        1.0063000173166314, 1.0062842495240218, 1.006268574567941, 1.0062529972736909,
+        1.0062375156359151, 1.006222121312609, 1.0062068011877208, 1.0061915397061327,
+        1.0061763215604551, 1.006161134259711, 1.006145970142697, 1.0061308275056136,
+        1.006115710674378, 1.0061006290381458, 1.0060855952386776, 1.0060706228506464,
+        1.0060557239665433, 1.0060409071054728, 1.0060261757978424, 1.0060115280719406,
+        1.0059969569063367, 1.0059824515434121, 1.005967999413032, 1.0059535883165638,
+        1.0059392084857197, 1.005924854162716, 1.0059105244409783, 1.0058962232406865,
+        1.0058819584472778, 1.0058677403854528, 1.0058535799121227, 1.0058394864702225,
+        1.0058254664428712, 1.0058115220859731, 1.0057976512090367, 1.0057838476392889,
+        1.0057701023666545, 1.0057564051515273, 1.00574274630239, 1.0057291183087933,
+        1.0057155170489387, 1.0057019423729574, 1.0056883979772386, 1.005674890611262,
+        1.0056614287736991, 1.0056480211394623, 1.0056346749997869, 1.0056213949874637,
+        1.0056081823020808, 1.005595034556944, 1.0055819462573206, 1.005568909809079,
+        1.0055559168667585, 1.0055429597759584, 1.0055300328551553, 1.0055171332970376,
+        1.0055042615420626, 1.0054914210733161, 1.0054786176844106, 1.0054658583631157,
+        1.0054531499967017, 1.005440498130723, 1.0054279059972617, 1.0054153739756246,
+        1.0054028995683164, 1.005390477882555, 1.0053781025192705, 1.0053657667027747,
+        1.0053534644465094, 1.0053411915494574, 1.0053289462530304, 1.0053167294521266,
+        1.0053045444351736, 1.0052923962111686, 1.0052802905524436, 1.0052682329284932,
+        1.0052562275204937, 1.0052442764871083, 1.0052323796036395, 1.0052205343279643,
+        1.005208736270654, 1.0051969799763907, 1.005185259871896, 1.0051735712101637,
+        1.0051619108459806, 1.0051502777115686, 1.0051386729170861, 1.005127099468309,
+        1.0051155616609433, 1.0051040642659324, 1.0050926116536432, 1.0050812070114792,
+        1.0050698517890762, 1.0050585454618552, 1.005047285645736, 1.0050360685334603,
+        1.0050248895678449, 1.0050137442279892, 1.005002628788183, 1.0049915409178625,
+        1.0049804800220612, 1.0049694472700816, 1.0049584453156473, 1.004947477765746,
+        1.0049365484974981, 1.0049256609463275, 1.0049148174903189, 1.0049040190354745,
+        1.004893264868828, 1.0048825527977567, 1.0048718795435985, 1.0048612413141549,
+        1.004850634450569, 1.0048400560339985, 1.0048295043475204, 1.0048189791168056,
+        1.0048084814935476, 1.0047980137914627, 1.0047875790274006, 1.004777180352444,
+        1.0047668204748412, 1.004756501175242, 1.004746222995854, 1.004735985152918,
+        1.00472578568164, 1.004715621782321, 1.0047054903022554, 1.0046953882663356,
+        1.0046853133630813, 1.0046752643032668, 1.0046652409923602, 1.0046552444919814,
+        1.0046452767826457, 1.0046353403740385, 1.0046254378342407, 1.004615571321195,
+        1.0046057421972598, 1.004595950790989, 1.0045861963433178, 1.0045764771424677,
+        1.0045667908193712, 1.0045571347485573, 1.0045475064828546, 1.0045379041464138,
+        1.004528326719705, 1.0045187741706365, 1.0045092474133388, 1.0044997481062796,
+        1.0044902783285299, 1.004480840192568, 1.0044714354614719, 1.0044620652354679,
+        1.0044527297593993, 1.0044434283805839, 1.004434159660202, 1.0044249216152585,
+        1.0044157120466266, 1.0044065288954678, 1.0043973705670277, 1.0043882361681657,
+        1.0043791256209147, 1.0043700396363229, 1.0043609795567021, 1.0043519470962805,
+        1.0043429440262497, 1.004333971858342, 1.0043250315794774, 1.0043161234803084,
+        1.0043072471033527, 1.0042984013161789, 1.0042895844940014, 1.004280794778814,
+        1.0042720303704298, 1.0042632898010404, 1.004254572149048, 1.0042458771592135,
+        1.004237205252291, 1.0042285574257905, 1.0042199350647727, 1.0042113396954917,
+        1.0042027727225944, 1.0041942351918653, 1.0041857276149375, 1.0041772498815515,
+        1.0041688012702126, 1.004160380552681, 1.0041519861733927], [1.167970921382559e-13,
+        3.5102383601331975e-13, 5.871542429223121e-13, 8.264773008472775e-13,
+        1.0703120789518248e-12, 1.3200203975184062e-12, 1.5770199756862047e-12,
+        1.8427984561664425e-12, 2.1189283476729903e-12, 2.407083183717392e-12,
+        2.70905511837165e-12, 3.026774241184049e-12, 3.3623298791488603e-12,
+        3.717994282036797e-12, 4.096249023751104e-12, 4.499814609244754e-12,
+        4.931683766676078e-12, 5.395159020864565e-12, 5.893895234132205e-12,
+        6.431947866102846e-12, 7.013827913591316e-12, 7.644564523788678e-12,
+        8.329776562530056e-12, 9.075754553037403e-12, 9.8895546697588e-12,
+        1.0779106752274603e-11, 1.1753338683457753e-11, 1.2822319812527402e-11,
+        1.399742668087117e-11, 1.52915347851281e-11, 1.6719240941664334e-11,
+        1.8297121467062605e-11, 2.0044032572274115e-11, 2.1981460398927636e-11,
+        2.4133929693085324e-11, 2.6529481722742057e-11, 2.920023426052937e-11,
+        3.2183038844885226e-11, 3.5520253764200336e-11, 3.926065474073991e-11,
+        4.346051005632508e-11, 4.818485215533133e-11, 5.350898480199303e-11,
+        5.95202729033738e-11, 6.632027263391793e-11, 7.402727159443106e-11,
+        8.277932504011773e-11, 9.273789225980155e-11, 1.0409220246323143e-10,
+        1.1706450766922195e-10, 1.319164182492654e-10, 1.4895656238951802e-10,
+        1.68549868552845e-10, 1.9112884342605023e-10, 2.1720730913618935e-10,
+        2.4739717956849833e-10, 2.8242900383543443e-10, 3.2317719059186774e-10,
+        3.7069106795227355e-10, 4.262332382813046e-10, 4.913270809947099e-10,
+        5.678157635497804e-10, 6.579357758176476e-10, 7.644088539198416e-10,
+        8.905572681288269e-10, 1.0404488997051712e-09, 1.2190804330783195e-09,
+        1.4326094992171442e-09, 1.688649927417857e-09, 1.996648673060338e-09,
+        2.36836888245495e-09, 2.8185114573683053e-09, 3.365518132077784e-09,
+        4.032613482881055e-09, 4.849162918897301e-09, 5.852450521582491e-09,
+        7.090017522768565e-09, 8.62275321793634e-09, 1.0529001106133432e-08,
+        1.2910042399576497e-08, 1.5897458875740975e-08, 1.966307533577762e-08,
+        2.443246484948679e-08, 3.0503406553897425e-08, 3.82712745798905e-08,
+        4.826419577906423e-08, 6.11920779723549e-08, 7.801548594412745e-08,
+        1.0004315054571659e-07, 1.290711414143622e-07, 1.6758321398186932e-07,
+        2.1904184225012798e-07, 2.883150533790008e-07, 3.823088240921848e-07,
+        5.109142142807453e-07, 6.884423210679879e-07, 9.358252639779532e-07,
+        1.2840370975540945e-06, 1.7794871077289083e-06, 2.4926547298993587e-06,
+        3.5321477565151617e-06, 5.068011921821935e-06, 7.371162557809278e-06,
+        1.0881582342528037e-05, 1.632921037885996e-05, 2.49542306752802e-05,
+        3.892122711364742e-05, 6.212615237155852e-05, 0.00010183520355758966,
+        0.00017217968336903145, 0.00030205860966374626, 0.0005543456285328763,
+        0.0010770605595605142, 0.0022574306991721754, 0.005273883053374681,
+        0.014704497134078098, 0.05999527478632855, 1.4740080690114064, 0.3246691154115971,
+        0.783493288143344, 0.9826595465353132, 0.5484184709815931, 0.6301236790473702,
+        1.2170228181246951, 1.7361908570639608, 0.9281537607932921, 0.7644171446179899,
+        0.8479573295895876, 1.22173310674817, 2.028417788946721, 1.6876351250632744,
+        1.164196983953763, 0.9977398537693069, 1.02750801582723, 1.244960941492091,
+        1.7397967357120594, 2.267183539345813, 1.9009635602121306, 1.451960425295003,
+        1.2538561994400503, 1.2306073100591786, 1.3574155662225307, 1.6682094954551325,
+        2.1803685560875468, 2.481005495654012, 2.132352234057897, 1.733707404287133,
+        1.5248552266098687, 1.4764079889435486, 1.5688816979841043, 1.8217886903186251,
+        2.2664947477546806, 2.746675833771576, 2.7194800453871384, 2.2954337164041902,
+        1.9677446179457152, 1.8467246338048073, 1.7854302693843311, 1.7955235707581079,
+        1.8713515883430303, 1.9524876365138624, 1.974056166797651, 1.9022647100490826,
+        1.767400632713955, 1.6247179661631528, 1.509129732469678, 1.4320645257947606,
+        1.3934651086591188, 1.3893898113003582, 1.4140181373645502, 1.4582893346578616,
+        1.5070428196596422, 1.5380945456373774, 1.528954155817484, 1.4708582618470214,
+        1.3754234792790945, 1.2644109253610496, 1.1558453947264398, 1.0591848120194158,
+        0.9773529261422903, 0.9099444155906804, 0.8553557110612467, 0.811831469538337,
+        0.7778773406402539, 0.7523724349520153, 0.734559141722879, 0.7239933311849812,
+        0.7204901328956377, 0.7240770969469056, 0.7349543365726705, 0.753453481354641,
+        0.7799803194389109, 0.8149178592802674, 0.8584573357387459, 0.9103198870336856,
+        0.9693485088245299, 1.033023140172021, 1.09711601619496, 1.1559096275160403,
+        1.2033828861945286, 1.2351852432085924, 1.2503111248349863, 1.2512733475640079,
+        1.2427325623242236, 1.2296763293412352, 1.2161638492737954, 1.204872449423348,
+        1.1971684463287824, 1.1933760331782508, 1.1930623047658122, 1.1952864328475954,
+        1.1988242069622455, 1.2023895830735787, 1.2048549988981943, 1.2054429883916977,
+        1.2038444624298936, 1.2002291245013712, 1.1951479005335515, 1.189364497920152,
+        1.183670579237874, 1.178730772138535, 1.1749815535070895, 1.172587501021994,
+        1.17144740956491, 1.1712402208240902, 1.1715012847365867, 1.1717184958715459,
+        1.1714339561611025, 1.1703323591515826, 1.1682966868246845, 1.16541821943867,
+        1.161960193427164, 1.158287435991341, 1.154782092680923, 1.151765695120348,
+        1.1494422079475342, 1.1478693001249025, 1.1469589229857802, 1.1465041389877224,
+        1.1462262270432442, 1.1458334263258299, 1.145080262979467, 1.143815366394609,
+        1.1420074624944294, 1.1397442638547404, 1.137205924110991, 1.134621023866494,
+        1.132216442225206, 1.1301722513413288, 1.1285899043427432, 1.1274781061597394,
+        1.1267571221313744, 1.126279346232357, 1.1258616263125392, 1.1253230214319103,
+        1.1245205881700517, 1.1233759926677513, 1.1218876237392048, 1.1201262358854276,
+        1.118216054464998, 1.1163064761973656, 1.114541060324783, 1.1130302333407949,
+        1.1118325077295255, 1.1109467964161188, 1.1103162000943443, 1.1098417554367368,
+        1.1094031408295377, 1.1088822970454835, 1.1081854770300135, 1.1072595839246246,
+        1.106099866864247, 1.104747928302196, 1.103281085023932, 1.1017958415996094,
+        1.100389147658983, 1.099141098716698, 1.0981019879431186, 1.097285463707557,
+        1.0966683207570966, 1.0961963646401192, 1.0957949376883767, 1.0953821182777426,
+        1.0948823325340726, 1.0942381831138965, 1.0934187133785238, 1.0924230325633713,
+        1.0912790917392494, 1.0900382305105087, 1.08876672837843, 1.0875358835673514,
+        1.086412101639337, 1.0854481923376331, 1.0846766757343744, 1.0841055099918706,
+        1.0837163521482613, 1.0834652757359888, 1.0832857747043538, 1.0830938351241541,
+        1.0827948013661715, 1.0822916614563605, 1.0814942141275727, 1.080328380317449,
+        1.078744740741333, 1.0767252938447913, 1.0742875024026375, 1.0714849622804465,
+        1.0684044552935823, 1.0651596550940308, 1.0618822251116682, 1.058711375092703,
+        1.055783067208823, 1.0532199845690777, 1.0511231457399792, 1.0495657446654152,
+        1.04858948796537, 1.048203439213339, 1.048385181937354, 1.0490839769717872,
+        1.0502255019841735, 1.051717708491642, 1.053457308174678, 1.0553364067607174,
+        1.0572488440047607, 1.0590958729082007, 1.0607909124922699, 1.0622632194945845,
+        1.0634604238530891, 1.064349942420024, 1.064919317120719, 1.065175524393641,
+        1.0651432910007708, 1.0648624509885867, 1.0643844088394563, 1.0637678415025675,
+        1.0630738686798777, 1.06236102583747, 1.0616804616890554, 1.0610718271249657,
+        1.0605603088832576, 1.0601551815175723, 1.0598501076685456, 1.059625220294084,
+        1.0594507910946278, 1.0592920561432073, 1.0591145708076564, 1.0588893439533782,
+        1.0585969933974242, 1.0582302899138996, 1.057794706090603, 1.057306917442157,
+        1.0567915511973607, 1.056276771789172, 1.0557894736903937, 1.0553508920577936,
+        1.0549733413295255, 1.0546585785242109, 1.0543980035080418, 1.0541746001074193,
+        1.0539662361900688, 1.0537497204363937, 1.0535048942303402, 1.053218042210725,
+        1.052884038242188, 1.0525068836988585, 1.052098596751374, 1.051676714406018,
+        1.0512609127108055, 1.0508693892791905, 1.0505156656581327, 1.0502063614254962,
+        1.0499402948428056, 1.049709016399647, 1.049498625672046, 1.0492925005632852,
+        1.0490744168029966, 1.0488314797019966, 1.0485563397496627, 1.048248310094671,
+        1.047913219288961, 1.047562074026069, 1.047208825590763, 1.0468676880035581,
+        1.0465505187272244, 1.046264737994683, 1.0460121432573404, 1.045788797906708,
+        1.0455859725619219, 1.0453919283041295, 1.0451941860681948, 1.0449818490917069,
+        1.0447475487062794, 1.0444886665340123, 1.044207631987728, 1.0439112738138159,
+        1.0436093823554944, 1.043312780519607, 1.0430312803354513, 1.0427719067948813,
+        1.0425377048510571, 1.0423273253083254, 1.0421354354013528, 1.0419538479626056,
+        1.041773135808844, 1.0415844169426398, 1.0413809747952765, 1.0411594189241584,
+        1.0409201866488893, 1.0406673159967823, 1.0404075591722817, 1.0401490264299893,
+        1.0398996301901648, 1.0396656251853804, 1.0394505103488467, 1.039254480674649,
+        1.0390745089765159, 1.0389050191964047, 1.038739006057256, 1.0385693789822625,
+        1.0383902742535718, 1.038198093559535, 1.0379920857667877, 1.0377743799697638,
+        1.0375494834511512, 1.0373233574994305, 1.0371022583178338, 1.0368915664885028,
+        1.036694821634697, 1.0365131324754004, 1.036345056865633, 1.0361869566813058,
+        1.0360337452210286, 1.0358798756477072, 1.0357203797482726, 1.0355517632722744,
+        1.0353725970048577, 1.0351837045552774, 1.034987926219929, 1.034789517875748,
+        1.034593309544797, 1.034403788173008, 1.0342242769194465, 1.0340563588887406,
+        1.0338996427218792, 1.0337519011434668, 1.0336095440625275, 1.0334683277523276,
+        1.033324161500773, 1.0331738596219748, 1.033015701625537, 1.032849703182236,
+        1.0326775572262035, 1.0325022669842008, 1.0323275489998396, 1.0321571239883713,
+        1.031994029844811, 1.0318400822567872, 1.0316955768680582, 1.0315592794900554,
+        1.031428696686507, 1.0313005681522476, 1.031171483714417, 1.0310385080902014,
+        1.0308996987872827, 1.030754425736499, 1.030603440561818, 1.030448691076979,
+        1.0302929235244518, 1.0301391525372634, 1.029990100214249, 1.0298477077375594,
+        1.029712806051954, 1.0295850001219866, 1.0294627805719543, 1.0293438347452089,
+        1.0292254939273024, 1.0291052307921578, 1.0289811147646641, 1.0288521436339373,
+        1.0287183949757885, 1.028580975700278, 1.0284417856362977, 1.02830314447277,
+        1.028167354591569, 1.0280362814709985, 1.0279110272932388, 1.0277917538551924,
+        1.027677681915217, 1.0275672612719202, 1.0274584751861926, 1.0273492196475027,
+        1.0272376863565724, 1.0271226798968718, 1.0270038137213726, 1.0268815533431657,
+        1.026757103867313, 1.0266321673192715, 1.026508617957528, 1.0263881569578794,
+        1.0262720094846356, 1.0261607173692573, 1.026054061599836, 1.025951124339322,
+        1.0258504748058606, 1.0257504416181191, 1.0256494198876056, 1.0255461567486668,
+        1.0254399646862855, 1.0253308266176384, 1.0252193773044147, 1.0251067683990323,
+        1.0249944450824253, 1.0248838771744637, 1.0247762943102015, 1.0246724723772664,
+        1.0245726076745993, 1.024476298404481, 1.0243826333608754, 1.0242903686231144,
+        1.024198158046883, 1.0241047948844582, 1.0240094212506252, 1.0239116692430603,
+        1.0238117108206004, 1.0237102104748197, 1.0236081921594402, 1.023506846745336,
+        1.0234073159077017, 1.023310491307115, 1.0232168639278796, 1.0231264484542366,
+        1.0230387935726029, 1.0229530736803045, 1.0228682433934606, 1.0227832258832161,
+        1.0226971011067496, 1.0226092611176507, 1.022519506441755, 1.0224280686089335,
+        1.0223355572528758, 1.0222428433234962, 1.022150900621039, 1.0220606342963212,
+        1.0219727262206864, 1.0218875232027955, 1.0218049858007212, 1.0217247045291034,
+        1.0216459785633039, 1.021567941610392, 1.0214897121655375, 1.021410542042975,
+        1.0213299382674466, 1.0212477387530225, 1.0211641306187662, 1.0210796099506574,
+        1.0209948915790967, 1.0209107853782564, 1.020828060467815, 1.0207473198483916,
+        1.0206689054220766, 1.020592847649534, 1.020518866361721, 1.0204464208317126,
+        1.0203747995060646, 1.0203032339839655, 1.020231018733209, 1.0201576179790026,
+        1.0200827440222346, 1.0200063963226187, 1.0199288570810903, 1.0198506456981575,
+        1.0197724403305701, 1.0196949789904615, 1.0196189547230077, 1.019544919235612,
+        1.0194732071686918, 1.0194038895164286, 1.0193367602203265, 1.0192713554035873,
+        1.019207000746765, 1.019142879608753, 1.019078112927406, 1.019011841711049,
+        1.0189433038685618, 1.0188718988893453, 1.018797236073528, 1.018719164236553,
+        1.0186377827560376, 1.0185534352940806, 1.0184666884504177, 1.0183782980329272,
+        1.018289165706688, 1.0182002886730566, 1.0181127048944183, 1.0180274363292192,
+        1.0179454327148327, 1.0178675185988042, 1.017794346481881, 1.017726358979491,
+        1.0176637627187275, 1.0176065161878234, 1.0175543329271706, 1.0175067003450906,
+        1.0174629131684794, 1.017422119253545, 1.0173833743529175, 1.0173457016178,
+        1.017308151217906, 1.0172698555387327, 1.0172300759474202, 1.0171882380244868,
+        1.0171439533126452, 1.0170970268853023, 1.0170474512399241, 1.0169953880519182,
+        1.0169411401025206, 1.016885116184308, 1.0168277919985458, 1.0167696700307898,
+        1.0167112411806924, 1.016652950585858, 1.0165951696625886, 1.0165381759130723,
+        1.016482141529311, 1.016427131253918, 1.016373109337966, 1.0163199547748993,
+        1.0162674833207515, 1.016215474189008, 1.0161636988096243, 1.0161119487484673,
+        1.0160600598710217, 1.01600793014966, 1.015955529163048, 1.0159028982718268,
+        1.0158501415779042, 1.0157974089444204, 1.015744873405422, 1.0156927060685108,
+        1.0156410519798158, 1.0155900103038853, 1.0155396215684716, 1.0154898637085905,
+        1.0154406573577626, 1.0153918794667083, 1.0153433830903897, 1.015295020267561,
+        1.0152466644704388, 1.0151982292008475, 1.015149679940561, 1.0151010377309013,
+        1.015052373988849, 1.0150037975514288, 1.0149554361535318, 1.0149074153922812,
+        1.0148598385789074, 1.0148127706750143, 1.0147662287934307, 1.014720180637112,
+        1.0146745509391826, 1.0146292346697552, 1.0145841147034473, 1.0145390809674089,
+        1.0144940479168338, 1.0144489675326678, 1.0144038358368463, 1.0143586920321408,
+        1.0143136106064548, 1.0142686878879141, 1.014224025409786, 1.0141797129052719,
+        1.014135813735378, 1.0140923550738652, 1.0140493243236903, 1.0140066721700887,
+        1.013964321570539, 1.0139221810248522, 1.013880159814254, 1.013838182645575,
+        1.0137962013148738, 1.0137542015714358, 1.0137122042106161, 1.0136702604040875,
+        1.0136284422208512, 1.013586830047873, 1.013545499067053, 1.013504507023111,
+        1.0134638852258198, 1.0134236341324276, 1.0133837240618153, 1.0133441007392219,
+        1.013304694601194, 1.013265432226446, 1.0132262479823924, 1.0131870940215357,
+        1.0131479471040847, 1.0131088112939886, 1.0130697162718378, 1.0130307117111519,
+        1.0129918587616757, 1.012953220085015, 1.0129148500409755, 1.012876786518194,
+        1.0128390455720824, 1.0128016195428997, 1.012764478764277, 1.0127275764298769,
+        1.0126908557452714, 1.0126542582134013, 1.0126177318146428, 1.0125812379430625,
+        1.0125447562174563, 1.0125082866453528, 1.0124718490171951, 1.0124354797835784,
+        1.0123992269687054, 1.0123631438651712, 1.012327282325645, 1.0122916864251124,
+        1.0122563871362737, 1.0122213984751505, 1.0121867153694544, 1.012152313310151,
+        1.012118149689528, 1.012084166616409, 1.0120502949311314, 1.0120164591095868,
+        1.011982582733986, 1.0119485942046518, 1.0119144323632894, 1.0118800516910225,
+        1.0118454267387733, 1.0118105554520787, 1.011775461080082, 1.0117401924184781,
+        1.0117048222346323, 1.0116694438575036, 1.0116341660746928, 1.0115991066464718,
+        1.0115643848993057, 1.0115301139765247, 1.011496393382079, 1.011463302442943,
+        1.0114308952351618, 1.0113991973763305, 1.0113682049021013, 1.0113378852405723,
+        1.0113081801031123, 1.0112790099481297, 1.0112502795634912, 1.0112218842633283,
+        1.0111937162048728, 1.0111656703904925, 1.0111376500128781, 1.0111095709073878,
+        1.0110813649760746, 1.0110529825295718, 1.0110243935477596, 1.0109955878897936,
+        1.0109665744956888, 1.010937379627441, 1.0109080442103515, 1.0108786203651259,
+        1.0108491672725464, 1.010819746582154, 1.0107904176538947, 1.0107612329905828,
+        1.0107322342613334, 1.0107034493139602, 1.0106748905177254, 1.0106465546636003,
+        1.010618424486673, 1.0105904716831968, 1.0105626610996852, 1.010534955604269,
+        1.0105073210397508, 1.010479730625914, 1.010452168236037, 1.0104246301161104,
+        1.0103971248273746, 1.010369671443604, 1.0103422962863917, 1.0103150286960265,
+        1.010287896476848, 1.0102609217018585, 1.0102341175017595, 1.0102074863076829,
+        1.0101810197878527, 1.0101547004524458, 1.0101285046406498, 1.0101024063905282,
+        1.0100763815606408, 1.010050411542928, 1.0100244859835148, 1.0099986040984723,
+        1.0099727744065192, 1.009947012960913, 1.0099213404055543, 1.009895778365608,
+        1.009870345781055, 1.0098450557875887, 1.0098199136453112, 1.0097949160309079,
+        1.0097700517752133, 1.0097453038858506, 1.0097206524838491, 1.0096960781393902,
+        1.0096715650373447, 1.00964710344575, 1.0096226910906327, 1.0095983332347351,
+        1.0095740414816308, 1.0095498315416547, 1.009525720366043, 1.0095017231524155,
+        1.0094778507338005, 1.009454107784916, 1.009430492129075, 1.0094069952340259,
+        1.0093836037797292, 1.0093603020008728, 1.009337074382188, 1.009313908235162,
+        1.0092907957175703, 1.0092677349644157, 1.0092447301602314, 1.0092217905693572,
+        1.0091989287195022, 1.0091761580747625, 1.0091534906130484, 1.009130934728513,
+        1.0091084938120334, 1.009086165736407, 1.009063943310331, 1.0090418155961123,
+        1.0090197698393013, 1.0089977936593826, 1.0089758771148065, 1.008954014287803,
+        1.008932204127458, 1.0089104504249975, 1.008888760949529, 1.0088671459173486,
+        1.0088456160791217, 1.0088241807678973, 1.0088028462484444, 1.0087816146468083,
+        1.0087604836303279, 1.0087394468732744, 1.008718495205316, 1.0086976182240859,
+        1.0086768060780233, 1.0086560511040747, 1.008635349038701, 1.0086146996027143,
+        1.008594106375102, 1.008573575997431, 1.0085531168660895, 1.008532737554761,
+        1.0085124452500307, 1.008492244473024, 1.0084721363025282, 1.0084521182215886,
+        1.008432184597227, 1.0084123276920294, 1.0083925390160817, 1.0083728107734398,
+        1.0083531371475103, 1.0083335152048414, 1.008313945269616, 1.0082944307178339,
+        1.0082749772430615, 1.008255591736891, 1.0082362809906509, 1.0082170504507666,
+        1.0081979032443662, 1.0081788396385636, 1.0081598570164558, 1.008140950360042,
+        1.0081221131417195, 1.0081033384570721, 1.0080846201937919, 1.0080659540307557,
+        1.0080473380966324, 1.008028773181424, 1.0080102624757195, 1.007991810895854,
+        1.007973424124046, 1.0079551075393542, 1.007936865229571, 1.0079186992551115,
+        1.007900609287269, 1.0078825926743888, 1.0078646449133006, 1.0078467604328434,
+        1.0078289335443176, 1.0078111593881895, 1.0077934347116144, 1.0077757583452667,
+        1.0077581313040398, 1.0077405565039186, 1.0077230381546678, 1.0077055809429816,
+        1.0076881891543965, 1.007670865888896, 1.0076536125047084, 1.007636428381305,
+        1.0076193110344591, 1.007602256553732, 1.0075852602774775, 1.00756831758107,
+        1.0075514246377237, 1.0075345790199453, 1.007517780040797, 1.0075010287825896,
+        1.007484327816276, 1.007467680668918, 1.0074510911388155, 1.007434562581889,
+        1.0074180972945146, 1.0074016960977754, 1.0073853581902465, 1.0073690812876994,
+        1.0073528620177206, 1.0073366964936563, 1.0073205809630879, 1.0073045124159858,
+        1.0072884890477216, 1.0072725105002907, 1.0072565778456635, 1.0072406933210978,
+        1.007224859869104, 1.0072090805671463, 1.0071933580491768, 1.0071776940197088,
+        1.0071620889422512, 1.007146541951602, 1.0071310509991593, 1.0071156131999048,
+        1.0071002253154722, 1.0070848842860158, 1.0070695877173883, 1.0070543342405927,
+        1.0070391236846041, 1.0070239570376993, 1.0070088362096148, 1.0069937636408732,
+        1.0069787418308964, 1.0069637728683707, 1.0069488580449082, 1.006933997616292,
+        1.006919190748561, 1.0069044356532473, 1.0068897298835109, 1.0068750707359604,
+        1.0068604556863592, 1.0068458827835476, 1.0068313509350717, 1.0068168600385827,
+        1.0068024109404978, 1.0067880052336278, 1.0067736449326918, 1.0067593320862267,
+        1.0067450683929102, 1.0067308548874114, 1.0067166917474333, 1.006702578251501,
+        1.00668851289061, 1.0066744936107548, 1.00666051814171, 1.0066465843542514,
+        1.0066326905846639, 1.0066188358727866, 1.0066050200758043, 1.0065912438420115,
+        1.0065775084526927, 1.0065638155621832, 1.0065501668822179, 1.0065365638648094,
+        1.0065230074363172, 1.0065094978256302, 1.0064960345122005, 1.0064826162994,
+        1.0064692414975278, 1.0064559081835118, 1.0064426144925822, 1.0064293588934181,
+        1.0064161404024312, 1.006402958704156, 1.006389814160889, 1.0063767077132224,
+        1.0063636406904202, 1.0063506145635253, 1.0063376306819956, 1.0063246900359457,
+        1.0063117930804955, 1.0062989396478488, 1.0062861289579892, 1.006273359723399,
+        1.0062606303288661]]
-- 
GitLab