Boost C++ Libraries

...one of the most highly regarded and expertly designed C++ library projects in the world. Herb Sutter and Andrei Alexandrescu, C++ Coding Standards

Click here to view the latest version of this page.

libs/math/tools/lanczos_generator.cpp

//  (C) Copyright John Maddock 2006.
//  Use, modification and distribution are subject to the
//  Boost Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#include <boost/math/bindings/rr.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/math/tools/precision.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/math/tools/polynomial.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/operation.hpp>
#include <boost/cstdint.hpp>
#include <boost/bind.hpp>
#include <boost/math/special_functions/log1p.hpp>
#include <boost/lexical_cast.hpp>
#include <boost/array.hpp>
#include <boost/test/included/test_exec_monitor.hpp>

//
// this is a sort of recursive include, since this file
// is used to create the contents of gamma.hpp.
// However, we will be using the "generic" version of gamma
// which doesn't use a lanczos approximation.
//
#include <boost/math/special_functions/gamma.hpp>

#include <iostream>
#include <iomanip>
#include <vector>

using boost::numeric::ublas::matrix;
using boost::numeric::ublas::vector;

struct lanczos_spot_data
{
   int N;
   double g;
   double err;
};

lanczos_spot_data sweet_spots[] = {
// a few selected spots from Pugh's thesis:
3, 2.03209, 6.4e-7,
4, 3.655180, 8.5e-8,
9, 8.406094, 6.9e-15,
10, 9.656578, 2.1e-16,
11, 10.900511, 6.1e-18,
12, 12.066012, 1.1e-19,
13, 13.144565, 5.2e-21,
14, 13.726821, 4.0e-22,
15, 14.977863, 1.2e-23,
20, 20.298892, 7.8e-31,
21, 21.508926, 2.1e-32,
22, 22.618910, 1.8e-34,
23, 23.118012, 5.2e-35,

// some more we've found, these are all the points where the first
// negleted term from the Lanczos series changes sign, there is one 
// point just above that point, and one just below:

3, 0.58613894134759903, 0.00036580426080686315,
3, 0.58613894879817963, 0.00036580416320668711,
3, 1.249951496720314, 4.2305536798953929e-005,
3, 1.2499515041708946, 4.2305534015367749e-005,
3, 1.8384982049465179, 1.164778449938813e-005,
3, 1.8384982123970985, 1.1647786529958048e-005,
3, 2.3276706635951996, 5.3732582230468998e-006,
3, 2.3276706710457802, 5.3732600294516588e-006,
3, 2.6038404405117035, 7.4060771171390379e-007,
3, 2.6038404479622841, 7.406058543248471e-007,
4, 0.62704569846391678, 0.00012800533557793425,
4, 0.62704570591449738, 0.00012800531551557324,
4, 1.3344274088740349, 9.0166140418663663e-006,
4, 1.3344274163246155, 9.0166116338646694e-006,
4, 1.9880444705486298, 1.4955557778725745e-006,
4, 1.9880444779992104, 1.4955557079994109e-006,
4, 2.5835030898451805, 4.5877676859600527e-007,
4, 2.5835030972957611, 4.5877667876325684e-007,
4, 3.1086832508444786, 2.1441725587707906e-007,
4, 3.1086832582950592, 2.1441723688775765e-007,
4, 3.5476611852645874, 1.0813760990515544e-007,
4, 3.547661192715168, 1.0813766234070327e-007,
4, 3.6492579728364944, 1.047642251124206e-007,
4, 3.649257980287075, 1.0476415796074403e-007,
5, 0.65435918420553207, 5.5274429026631278e-005,
5, 0.65435919165611267, 5.527441185903385e-005,
5, 1.389187254011631, 2.6307833416554052e-006,
5, 1.3891872614622116, 2.6307826816540255e-006,
5, 2.0801975876092911, 2.9014694764756466e-007,
5, 2.0801975950598717, 2.9014696142909125e-007,
5, 2.7272208333015442, 5.9176544536206063e-008,
5, 2.7272208407521248, 5.9176528019009275e-008,
5, 3.3269794136285782, 1.9379184595472579e-008,
5, 3.3269794210791588, 1.9379189057179851e-008,
5, 3.8722873777151108, 9.0123694745032944e-009,
5, 3.8722873851656914, 9.0123661007867372e-009,
5, 4.3516943231225014, 4.9816097608842378e-009,
5, 4.351694330573082, 4.9816087871575021e-009,
6, 0.67425807565450668, 2.7371903086326379e-005,
6, 0.67425808310508728, 2.7371893712684938e-005,
6, 1.4284561350941658, 9.4138428977455083e-007,
6, 1.4284561425447464, 9.4138417896969612e-007,
6, 2.1447814926505089, 7.4109049995920916e-008,
6, 2.1447815001010895, 7.4109044064461768e-008,
6, 2.8244904428720474, 1.0708333024058614e-008,
6, 2.824490450322628, 1.0708333661155651e-008,
6, 3.4669468700885773, 2.4940116660002578e-009,
6, 3.4669468775391579, 2.4940118560592828e-009,
6, 4.0696377158164978, 8.5267622527507512e-010,
6, 4.0696377232670784, 8.5267624048985822e-010,
6, 4.6278460025787354, 3.9323405231792876e-010,
6, 4.6278460100293159, 3.9323393550021793e-010,
6, 5.1345816180109978, 2.1943462473419721e-010,
6, 5.1345816254615784, 2.1943458105218707e-010,
6, 5.5917193591594696, 1.242916896389048e-010,
6, 5.5917193666100502, 1.2429175679293363e-010,
7, 0.68959406018257141, 1.4934177419305624e-005,
7, 0.68959406763315201, 1.4934171696393048e-005,
7, 1.4584139510989189, 3.8891482410396904e-007,
7, 1.4584139585494995, 3.8891475436265016e-007,
7, 2.1934122517704964, 2.2977989848570384e-008,
7, 2.193412259221077, 2.2977982819591052e-008,
7, 2.8964230641722679, 2.4742239281355561e-009,
7, 2.8964230716228485, 2.4742234478616864e-009,
7, 3.5678729563951492, 4.2816138965285379e-010,
7, 3.5678729638457298, 4.2816128067858218e-010,
7, 4.2069913893938065, 1.0931003472338519e-010,
7, 4.2069913968443871, 1.0931004659777642e-010,
7, 4.8118086308240891, 3.8518213120095777e-011,
7, 4.8118086382746696, 3.8518212172324096e-011,
7, 5.3790060579776764, 1.7613602961109952e-011,
7, 5.379006065428257, 1.7613603275796266e-011,
7, 5.9039439857006073, 9.7098281187573355e-012,
7, 5.9039439931511879, 9.7098271522398387e-012,
7, 6.3838147521018982, 5.7878801570305524e-012,
7, 6.3838147595524788, 5.7878771973838702e-012,
7, 6.7833591029047966, 2.829092368392454e-012,
7, 6.7833591103553772, 2.8290901754246269e-012,
8, 0.70188850909471512, 8.7610752024780369e-006,
8, 0.70188851654529572, 8.7610704217796693e-006,
8, 1.4822541922330856, 1.7881701068328982e-007,
8, 1.4822541996836662, 1.7881694190606741e-007,
8, 2.231784276664257, 8.2272386690167009e-009,
8, 2.2317842841148376, 8.2272367814664617e-009,
8, 2.9525627419352531, 6.8591536474980462e-010,
8, 2.9525627493858337, 6.8591515664364383e-010,
8, 3.6455128863453865, 9.1549235855884194e-011,
8, 3.6455128937959671, 9.1549217088498416e-011,
8, 4.3106606528162956, 1.8015466799942756e-011,
8, 4.3106606602668762, 1.8015467001952356e-011,
8, 4.9472371935844421, 4.918149362493385e-012,
8, 4.9472372010350227, 4.9181495178774722e-012,
8, 5.553666315972805, 1.7720036810370511e-012,
8, 5.5536663234233856, 1.7720035779693502e-012,
8, 6.1274929493665695, 8.0403304333886761e-013,
8, 6.1274929568171501, 8.0403274526493467e-013,
8, 6.6654317826032639, 4.3551924163930176e-013,
8, 6.6654317900538445, 4.3551918580885179e-013,
8, 7.1646013185381889, 2.6142608803934048e-013,
8, 7.1646013259887695, 2.6142610866873453e-013,
8, 7.6312204822897911, 1.5767278184484503e-013,
8, 7.6312204897403717, 1.576728292094547e-013,
8, 7.8779716044664383, 6.0579161144149095e-014,
8, 7.8779716119170189, 6.0579145495868576e-014,
9, 0.7120363786816597, 5.4383680639900953e-006,
9, 0.7120363861322403, 5.4383647430909934e-006,
9, 1.5018193200230598, 8.9331552269793478e-008,
9, 1.5018193274736404, 8.9331529217486569e-008,
9, 2.2630845010280609, 3.2922940247769628e-009,
9, 2.2630845084786415, 3.2922936681951672e-009,
9, 2.9980199560523033, 2.1887825488935961e-010,
9, 2.9980199635028839, 2.1887818854849753e-010,
9, 3.7078000977635384, 2.3213138957857667e-011,
9, 3.707800105214119, 2.3213132917173771e-011,
9, 4.3928612694144249, 3.6226509291513855e-012,
9, 4.3928612768650055, 3.6226507116549233e-012,
9, 5.0530400574207306, 7.8472620106742312e-013,
9, 5.0530400648713112, 7.8472599177745781e-013,
9, 5.6876183524727821, 2.2542091218064693e-013,
9, 5.6876183599233627, 2.2542085472082343e-013,
9, 6.2953110262751579, 8.261026286619692e-014,
9, 6.2953110337257385, 8.2610267677539022e-014,
9, 6.8742315545678139, 3.7226229880661886e-014,
9, 6.8742315620183945, 3.722621661830273e-014,
9, 7.4219388365745544, 1.9804198141916339e-014,
9, 7.421938844025135, 1.9804197841080089e-014,
9, 7.936030775308609, 1.1800366216622659e-014,
9, 7.9360307827591896, 1.1800362381207757e-014,
9, 8.4175376817584038, 7.341772297716249e-015,
9, 8.4175376892089844, 7.3417744970482286e-015,
10, 0.72060277312994003, 3.5324438420494327e-006,
10, 0.72060278058052063, 3.5324425213780505e-006,
10, 1.5182576552033424, 4.7690979892410133e-008,
10, 1.518257662653923, 4.7690968887170632e-008,
10, 2.2892609387636185, 1.4396365431590603e-009,
10, 2.2892609462141991, 1.4396363283470758e-009,
10, 3.0358340814709663, 7.8118059457005561e-011,
10, 3.0358340889215469, 7.8118048721726738e-011,
10, 3.7592824399471283, 6.7417155809106958e-012,
10, 3.7592824473977089, 6.7417147580480395e-012,
10, 4.4602697342634201, 8.5434024476488055e-013,
10, 4.4602697417140007, 8.5434000006256964e-013,
10, 5.1389683187007904, 1.5015237157428729e-013,
10, 5.138968326151371, 1.5015232503714518e-013,
10, 5.795127771794796, 3.5035278065891386e-014,
10, 5.7951277792453766, 3.5035266685032581e-014,
10, 6.4280949085950851, 1.0474518584578706e-014,
10, 6.4280949160456657, 1.047451900091486e-014,
10, 7.0368044599890709, 3.8902615249132166e-015,
10, 7.0368044674396515, 3.8902605386615012e-015,
10, 7.6197631657123566, 1.742442940023884e-015,
10, 7.6197631731629372, 1.7424426824540998e-015,
10, 8.1750892177224159, 9.1144555287546294e-016,
10, 8.1750892251729965, 9.1144560389833963e-016,
10, 8.7008367404341698, 5.3541847847332351e-016,
10, 8.7008367478847504, 5.3541844723127514e-016,
10, 9.1965094059705734, 3.3560389199894529e-016,
10, 9.196509413421154, 3.3560370421140035e-016,
10, 9.6678015515208244, 2.1059571242602905e-016,
10, 9.667801558971405, 2.1059579862533338e-016,
11, 0.72796426713466644, 2.3816013324880167e-006,
11, 0.72796427458524704, 2.3816003939892356e-006,
11, 1.5323273167014122, 2.6884539057733283e-008,
11, 1.5323273241519928, 2.6884532967611841e-008,
11, 2.3115825653076172, 6.7682186491374862e-010,
11, 2.3115825727581978, 6.768217495558193e-010,
11, 3.0679489448666573, 3.0544688315708309e-011,
11, 3.0679489523172379, 3.054468452617125e-011,
11, 3.8027990683913231, 2.186949692679853e-012,
11, 3.8027990758419037, 2.1869496552307528e-012,
11, 4.5169280469417572, 2.2947351040888336e-013,
11, 4.5169280543923378, 2.2947348773371414e-013,
11, 5.2107065990567207, 3.3353640359739479e-014,
11, 5.2107066065073013, 3.335363154144172e-014,
11, 5.8841593414545059, 6.4351159890193404e-015,
11, 5.8841593489050865, 6.435115249418266e-015,
11, 6.5370001494884491, 1.5930548620019077e-015,
11, 6.5370001569390297, 1.59305482454352e-015,
11, 7.1686412021517754, 4.9183710858836462e-016,
11, 7.168641209602356, 4.9183713116224844e-016,
11, 7.7781866490840912, 1.8464804238726119e-016,
11, 7.7781866565346718, 1.8464801709489452e-016,
11, 8.3644260391592979, 8.2263320775918765e-017,
11, 8.3644260466098785, 8.2263297787354186e-017,
11, 8.9258662387728691, 4.2375346461043962e-017,
11, 8.9258662462234497, 4.2375329267920249e-017,
11, 9.4609249979257584, 2.4482616150935944e-017,
11, 9.460925005376339, 2.4482619419420328e-017,
11, 9.968697115778923, 1.5254006021629585e-017,
11, 9.9686971232295036, 1.5254009931381535e-017,
11, 10.451380550861359, 9.7234265908062383e-018,
11, 10.451380558311939, 9.7234241296957717e-018,
11, 10.909898526966572, 6.3147967493977272e-018,
11, 10.909898534417152, 6.3147961332742783e-018,
12, 0.73438271880149841, 1.6566052109275983e-006,
12, 0.73438272625207901, 1.6566045155548952e-006,
12, 1.5445517003536224, 1.5860666784152459e-008,
12, 1.544551707804203, 1.5860658867525684e-008,
12, 2.33091701567173, 3.380059232629492e-010,
12, 2.3309170231223106, 3.3800585031437757e-010,
12, 3.095676377415657, 1.2884951580384992e-011,
12, 3.0956763848662376, 1.2884947453406877e-011,
12, 3.8402339816093445, 7.7768150022424858e-013,
12, 3.8402339890599251, 7.776814490345326e-013,
12, 4.5654622465372086, 6.8670097741098332e-014,
12, 4.5654622539877892, 6.8670083429297199e-014,
12, 5.2718541026115417, 8.38897478481124e-015,
12, 5.2718541100621223, 8.3889742372884196e-015,
12, 5.9596048966050148, 1.3595098759195538e-015,
12, 5.9596049040555954, 1.3595098086325987e-015,
12, 6.6286550611257553, 2.827608125932321e-016,
12, 6.6286550685763359, 2.8276074709416868e-016,
12, 7.2787091657519341, 7.3455425966950088e-017,
12, 7.2787091732025146, 7.3455407058460195e-017,
12, 7.9092400223016739, 2.3285371485286439e-017,
12, 7.9092400297522545, 2.3285373002934362e-017,
12, 8.5194846615195274, 8.8196897130872609e-018,
12, 8.519484668970108, 8.8196870510698361e-018,
12, 9.1084426045417786, 3.9108299199270105e-018,
12, 9.1084426119923592, 3.9108294386613317e-018,
12, 9.6749012768268585, 1.9869557945423399e-018,
12, 9.6749012842774391, 1.9869552330025425e-018,
12, 10.217559166252613, 1.1287442348688164e-018,
12, 10.217559173703194, 1.1287443889939456e-018,
12, 10.735452570021152, 6.9443548691210419e-019,
12, 10.735452577471733, 6.944357314519752e-019,
12, 11.229217991232872, 4.4666546191302752e-019,
12, 11.229217998683453, 4.4666540313320006e-019,
12, 11.70328252017498, 2.9048073087968165e-019,
12, 11.703282527625561, 2.9048072811110897e-019,
12, 12.068153090775013, 1.1197702118472231e-019,
12, 12.068153098225594, 1.1197723483874788e-019,
13, 0.74004656821489334, 1.1833107184182451e-006,
13, 0.74004657566547394, 1.1833097788321784e-006,
13, 1.5553053691983223, 9.7255030271643972e-009,
13, 1.5553053766489029, 9.7254989421162363e-009,
13, 2.3478806391358376, 1.7766237223855854e-010,
13, 2.3478806465864182, 1.7766232949140296e-010,
13, 3.1199393272399902, 5.7956070959333847e-012,
13, 3.1199393346905708, 5.7956067491263655e-012,
13, 3.8728964179754257, 2.9884476000191141e-013,
13, 3.8728964254260063, 2.9884474795319482e-013,
13, 4.6076695621013641, 2.2511499024927438e-014,
13, 4.6076695695519447, 2.2511492228003123e-014,
13, 5.3248289301991463, 2.3433299337790734e-015,
13, 5.3248289376497269, 2.3433296697120652e-015,
13, 6.024680033326149, 3.2334220967999432e-016,
13, 6.0246800407767296, 3.2334220842696106e-016,
13, 6.7073097303509712, 5.7246438539858037e-017,
13, 6.7073097378015518, 5.7246428548181273e-017,
13, 7.3726105690002441, 1.2665024613881524e-017,
13, 7.3726105764508247, 1.2665026479377931e-017,
13, 8.0202914103865623, 3.4243381685006812e-018,
13, 8.0202914178371429, 3.4243378550191225e-018,
13, 8.6498793810606003, 1.1097375058286432e-018,
13, 8.6498793885111809, 1.1097372565619852e-018,
13, 9.2607174664735794, 4.2345371873704953e-019,
13, 9.26071747392416, 4.234535720073341e-019,
13, 9.8519651964306831, 1.8698553775808502e-019,
13, 9.8519652038812637, 1.8698556036241362e-019,
13, 10.4226189032197, 9.3834845010114218e-020,
13, 10.42261891067028, 9.3834849389696859e-020,
13, 10.971594020724297, 5.2445253216776838e-020,
13, 10.971594028174877, 5.244524330346984e-020,
13, 11.497980736196041, 3.1824489086388546e-020,
13, 11.497980743646622, 3.1824504032698097e-020,
13, 12.001743614673615, 2.0418153275918044e-020,
13, 12.001743622124195, 2.0418144824511038e-020,
13, 12.485165499150753, 1.322118298528861e-020,
13, 12.485165506601334, 1.3221186083014843e-020,
13, 12.954543322324753, 8.948147552026443e-021,
13, 12.954543329775333, 8.9481497369716256e-021,
13, 13.141756847500801, 6.2261736884111559e-021,
13, 13.141756854951382, 6.22616137965588e-021,
14, 0.74509535729885101, 8.6479103419423106e-007,
14, 0.74509536474943161, 8.6479038219181041e-007,
14, 1.5648643523454666, 6.1650149037400714e-009,
14, 1.5648643597960472, 6.1650125500027851e-009,
14, 2.3629250749945641, 9.7577785849465913e-011,
14, 2.3629250824451447, 9.7577755012051767e-011,
14, 3.1414090842008591, 2.7542691144474049e-012,
14, 3.1414090916514397, 2.754268644924632e-012,
14, 3.9017298147082329, 1.2272153763375018e-013,
14, 3.9017298221588135, 1.2272152123703597e-013,
14, 4.6448303312063217, 7.978322520490151e-015,
14, 4.6448303386569023, 7.9783225037342658e-015,
14, 5.3713301867246628, 7.1601479759177548e-016,
14, 5.3713301941752434, 7.1601474269921559e-016,
14, 6.0816079154610634, 8.5112993423908193e-017,
14, 6.081607922911644, 8.5112990415141843e-017,
14, 6.775848351418972, 1.2975876577628266e-017,
14, 6.7758483588695526, 1.2975877961248016e-017,
14, 7.454069696366787, 2.472008704163831e-018,
14, 7.4540697038173676, 2.4720086738065271e-018,
14, 8.1161380037665367, 5.7588911760227473e-019,
14, 8.1161380112171173, 5.7588919455128341e-019,
14, 8.7617733329534531, 1.6104402650810633e-019,
14, 8.7617733404040337, 1.6104400596562633e-019,
14, 9.3905506879091263, 5.3175849261375426e-020,
14, 9.3905506953597069, 5.3175840555484183e-020,
14, 10.001898743212223, 2.0418615673652841e-020,
14, 10.001898750662804, 2.0418619107744165e-020,
14, 10.595101684331894, 8.9828277730487657e-021,
14, 10.595101691782475, 8.9828244400191064e-021,
14, 11.169315472245216, 4.4582227129137701e-021,
14, 11.169315479695797, 4.4582210840169188e-021,
14, 11.723624959588051, 2.4539473008929182e-021,
14, 11.723624967038631, 2.4539478386423601e-021,
14, 12.25720601528883, 1.4682386166943286e-021,
14, 12.25720602273941, 1.4682385418038961e-021,
14, 12.76973832398653, 9.3346251997410079e-022,
14, 12.769738331437111, 9.3346223359077701e-022,
14, 13.262287445366383, 6.0874087090840453e-022,
14, 13.262287452816963, 6.0874060113413987e-022,
14, 13.73819725215435, 4.0622784880680064e-022,
14, 13.738197259604931, 4.0622806176204874e-022,
15, 0.74963488429784775, 6.4472609076683897e-007,
15, 0.74963489174842834, 6.4472546314886359e-007,
15, 1.5734371542930603, 4.0226647054678587e-009,
15, 1.5734371617436409, 4.0226622606167611e-009,
15, 2.3763899058103561, 5.5678382926067953e-011,
15, 2.3763899132609367, 5.5678366001298979e-011,
15, 3.1605874672532082, 1.3728924222156093e-012,
15, 3.1605874747037888, 1.3728922232543816e-012,
15, 3.9274342954158783, 5.3378856950128611e-014,
15, 3.9274343028664589, 5.3378843159211659e-014,
15, 4.6778862848877907, 3.0250264329161316e-015,
15, 4.6778862923383713, 3.0250255465237931e-015,
15, 5.4125945195555687, 2.3643655178483816e-016,
15, 5.4125945270061493, 2.364365094900239e-016,
15, 6.1319867372512817, 2.4459487536429736e-017,
15, 6.1319867447018623, 2.4459487650611821e-017,
15, 6.8363150134682655, 3.2436206211824709e-018,
15, 6.8363150209188461, 3.2436197176022979e-018,
15, 7.5256842151284218, 5.3739371041542508e-019,
15, 7.5256842225790024, 5.3739376909794387e-019,
15, 8.2000685408711433, 1.088934674475772e-019,
15, 8.2000685483217239, 1.0889347191934601e-019,
15, 8.8593204915523529, 2.6504714435038781e-020,
15, 8.8593204990029335, 2.6504716387206021e-020,
15, 9.5031745359301567, 7.6282884779808578e-021,
15, 9.5031745433807373, 7.6282871890206407e-021,
15, 10.131247609853745, 2.5596033506939261e-021,
15, 10.131247617304325, 2.5596033059431966e-021,
15, 10.743038579821587, 9.8815320291260219e-022,
15, 10.743038587272167, 9.881528789722149e-022,
15, 11.337930642068386, 4.3327572929097578e-022,
15, 11.337930649518967, 4.3327579478065768e-022,
15, 11.91520432382822, 2.1290839700926256e-022,
15, 11.915204331278801, 2.1290844593454176e-022,
15, 12.47407853603363, 1.1555853827459651e-022,
15, 12.474078543484211, 1.1555851200022939e-022,
15, 13.013818167150021, 6.8144327801967497e-023,
15, 13.013818174600601, 6.814431722582805e-023,
15, 13.533991023898125, 4.2798966509192708e-023,
15, 13.533991031348705, 4.279897117134478e-023,
15, 14.035010702908039, 2.7914921195937233e-023,
15, 14.03501071035862, 2.7914916878659476e-023,
15, 14.518910378217697, 1.833772281462441e-023,
15, 14.518910385668278, 1.8337712497676989e-023,
15, 14.989013738930225, 1.2608384937256306e-023,
15, 14.989013746380806, 1.2608378195451462e-023,
16, 0.75374705344438553, 4.8915337496543224e-007,
16, 0.75374706089496613, 4.8915306793373716e-007,
16, 1.5811846181750298, 2.6923132475156358e-009,
16, 1.5811846256256104, 2.692312137537266e-009,
16, 2.3885360583662987, 3.2852614483624288e-011,
16, 2.3885360658168793, 3.2852599884042077e-011,
16, 3.1778582483530045, 7.1354837117579206e-013,
16, 3.1778582558035851, 7.1354819499657137e-013,
16, 3.9505422189831734, 2.4415794649042575e-014,
16, 3.950542226433754, 2.4415790464100997e-014,
16, 4.7075485289096832, 1.2166614671909252e-015,
16, 4.7075485363602638, 1.2166612061656969e-015,
16, 5.4495479688048363, 8.3551487091643194e-017,
16, 5.4495479762554169, 8.3551474485434551e-017,
16, 6.1770017296075821, 7.5892566535084655e-018,
16, 6.1770017370581627, 7.5892568568026215e-018,
16, 6.890208899974823, 8.8323530753260686e-019,
16, 6.8902089074254036, 8.8323505679897636e-019,
16, 7.5893355086445808, 1.2838109403040181e-019,
16, 7.5893355160951614, 1.2838108671707829e-019,
16, 8.2744322568178177, 2.2821684437156804e-020,
16, 8.2744322642683983, 2.282168749495082e-020,
16, 8.9454451054334641, 4.8744259157716707e-021,
16, 8.9454451128840446, 4.8744247029595045e-021,
16, 9.6022209450602531, 1.2319495868217162e-021,
16, 9.6022209525108337, 1.2319494772820823e-021,
16, 10.244509845972061, 3.6348978875812834e-022,
16, 10.244509853422642, 3.6348985260615e-022,
16, 10.871965378522873, 1.2367742746291744e-022,
16, 10.871965385973454, 1.2367739126564003e-022,
16, 11.484144628047943, 4.7970119302772392e-023,
16, 11.484144635498524, 4.7970127598781626e-023,
16, 12.080510623753071, 2.0970543482083159e-023,
16, 12.080510631203651, 2.0970540591110336e-023,
16, 12.660443000495434, 1.0212748080573996e-023,
16, 12.660443007946014, 1.0212749016622482e-023,
16, 13.223268158733845, 5.4721418402402487e-024,
16, 13.223268166184425, 5.4721424729500052e-024,
16, 13.768333427608013, 3.1810966077030606e-024,
16, 13.768333435058594, 3.181096582631882e-024,
16, 14.295174412429333, 1.9706877841945116e-024,
16, 14.295174419879913, 1.9706884118909232e-024,
16, 14.803859077394009, 1.2794879837821395e-024,
16, 14.803859084844589, 1.2794882377473996e-024,
16, 15.295545108616352, 8.4344716828413924e-025,
16, 15.295545116066933, 8.4344683346343458e-025,
16, 15.772794611752033, 5.7392825698566701e-025,
16, 15.772794619202614, 5.7392822347696177e-025,
16, 16.216887570917606, 3.6997343524479107e-025,
16, 16.216887578368187, 3.6997346587299121e-025,
17, 0.75749634951353073, 3.7692745372019008e-007,
17, 0.75749635696411133, 3.7692700070692814e-007,
17, 1.5882330387830734, 1.8429395479824224e-009,
17, 1.588233046233654, 1.8429387676315583e-009,
17, 2.3995678052306175, 1.9967644390215291e-011,
17, 2.3995678126811981, 1.9967637238366132e-011,
17, 3.1935207024216652, 3.8482056723979746e-013,
17, 3.1935207098722458, 3.8482046172543379e-013,
17, 3.9714667573571205, 1.1675233373393322e-014,
17, 3.9714667648077011, 1.167523092849099e-014,
17, 4.7343658432364464, 5.1547822958137584e-016,
17, 4.734365850687027, 5.1547809052809859e-016,
17, 5.4829004630446434, 3.1343625323079668e-017,
17, 5.482900470495224, 3.1343618068151562e-017,
17, 6.2175545245409012, 2.5193828294777807e-018,
17, 6.2175545319914818, 2.5193819999045696e-018,
17, 6.9386604055762291, 2.5933718219907985e-019,
17, 6.9386604130268097, 2.5933719595613529e-019,
17, 7.6464280635118484, 3.3330158772752984e-020,
17, 7.646428070962429, 3.3330160862180195e-020,
17, 8.3409634903073311, 5.2379397998875143e-021,
17, 8.3409634977579117, 5.2379386588488221e-021,
17, 9.0222802385687828, 9.8908851451647746e-022,
17, 9.0222802460193634, 9.8908823476058462e-022,
17, 9.6903063133358955, 2.2108045577850313e-022,
17, 9.6903063207864761, 2.2108041448570457e-022,
17, 10.344887860119343, 5.7731399489054422e-023,
17, 10.344887867569923, 5.773138110616153e-023,
17, 10.98579066246748, 1.7407181648032493e-023,
17, 10.98579066991806, 1.7407180865759728e-023,
17, 11.6127003505826, 5.9955236166794974e-024,
17, 11.61270035803318, 5.9955216352412096e-024,
17, 12.225222736597061, 2.3349804655788398e-024,
17, 12.225222744047642, 2.3349807732238287e-024,
17, 12.82288621366024, 1.0179952851287067e-024,
17, 12.822886221110821, 1.0179953150198629e-024,
17, 13.405150465667248, 4.9176017252558557e-025,
17, 13.405150473117828, 4.9176033251919074e-025,
17, 13.971429191529751, 2.6038182860572718e-025,
17, 13.971429198980331, 2.603818076773733e-025,
17, 14.521142840385437, 1.4930454888989484e-025,
17, 14.521142847836018, 1.4930452390494677e-025,
17, 15.053831778466702, 9.123082958623521e-026,
17, 15.053831785917282, 9.1230791767726492e-026,
17, 15.569381833076477, 5.8751079623571136e-026,
17, 15.569381840527058, 5.8751075038868982e-026,
17, 16.068407364189625, 3.8749149875575966e-026,
17, 16.068407371640205, 3.8749167349006019e-026,
17, 16.552637793123722, 2.5963438998656586e-026,
17, 16.552637800574303, 2.5963440101195602e-026,
17, 17.024716928601265, 1.7949322494851864e-026,
17, 17.024716936051846, 1.7949319523018589e-026,
17, 17.346179291605949, 2.8309800520891487e-027,
17, 17.34617929905653, 2.8309773118757838e-027,
18, 0.76093439012765884, 2.9450240370798458e-007,
18, 0.76093439757823944, 2.9450203771031953e-007,
18, 1.5946831777691841, 1.2871185298229725e-009,
18, 1.5946831852197647, 1.2871177488403049e-009,
18, 2.4096476435661316, 1.2461251822064865e-011,
18, 2.4096476510167122, 1.2461248257070009e-011,
18, 3.207812137901783, 2.1447968570473172e-013,
18, 3.2078121453523636, 2.1447959182366632e-013,
18, 3.9905342757701874, 5.8079896477904645e-015,
18, 3.990534283220768, 5.8079874820498712e-015,
18, 4.7587697133421898, 2.2873919040338732e-016,
18, 4.7587697207927704, 2.2873918091132165e-016,
18, 5.5132071524858475, 1.2399411155563791e-017,
18, 5.5132071599364281, 1.2399410449684862e-017,
18, 6.2543457671999931, 8.8806343367361896e-019,
18, 6.2543457746505737, 8.8806339445463331e-019,
18, 6.9825416058301926, 8.1418645242373546e-020,
18, 6.9825416132807732, 8.1418638978404545e-020,
18, 7.6980366632342339, 9.3166546160183016e-021,
18, 7.6980366706848145, 9.316653065404742e-021,
18, 8.4009775668382645, 1.3033282065831878e-021,
18, 8.4009775742888451, 1.303327910841165e-021,
18, 9.0914276838302612, 2.1906432409842348e-022,
18, 9.0914276912808418, 2.1906432254533542e-022,
18, 9.7693748101592064, 4.3589910796802725e-023,
18, 9.769374817609787, 4.3589901608432619e-023,
18, 10.434735849499702, 1.0137066700093108e-023,
18, 10.434735856950283, 1.0137066734442173e-023,
18, 11.087359227240086, 2.7240107890987674e-024,
18, 11.087359234690666, 2.7240105244068185e-024,
18, 11.727025918662548, 8.371655684372496e-025,
18, 11.727025926113129, 8.3716527086860413e-025,
18, 12.353449679911137, 2.9146730821631173e-025,
18, 12.353449687361717, 2.9146728028573778e-025,
18, 12.966277495026588, 1.1392339405640447e-025,
18, 12.966277502477169, 1.1392339608927589e-025,
18, 13.565091922879219, 4.9545881072919797e-026,
18, 13.5650919303298, 4.9545866952502942e-026,
18, 14.149418227374554, 2.3758167105055241e-026,
18, 14.149418234825134, 2.3758158313872783e-026,
18, 14.718741856515408, 1.2442765527084641e-026,
18, 14.718741863965988, 1.244276230271342e-026,
18, 15.272546909749508, 7.0424811711899878e-027,
18, 15.272546917200089, 7.0424832994636221e-027,
18, 15.810395196080208, 4.2497327978932225e-027,
18, 15.810395203530788, 4.2497340544704781e-027,
18, 16.332078844308853, 2.7060819868792312e-027,
18, 16.332078851759434, 2.7060823827611486e-027,
18, 16.83788288384676, 1.778958105553305e-027,
18, 16.83788289129734, 1.7789585636337179e-027,
18, 17.328916251659393, 1.1828714637450282e-027,
18, 17.328916259109974, 1.182871994927067e-027,
18, 17.807191208004951, 8.1726141746863567e-028,
18, 17.807191215455532, 8.1726174566351736e-028,
18, 18.284037873148918, 5.6912247207101229e-028,
18, 18.284037880599499, 5.691222218060101e-028,
18, 18.392694972455502, 5.2831137523744097e-028,
18, 18.392694979906082, 5.2831145046877764e-028,
19, 0.764103002846241, 2.3298449147644669e-007,
19, 0.76410301029682159, 2.3298424269489823e-007,
19, 1.6006165370345116, 9.1529116957755399e-010,
19, 1.6006165444850922, 9.1529068365546486e-010,
19, 2.4189066812396049, 7.9633891310433137e-012,
19, 2.4189066886901855, 7.9633842469171524e-012,
19, 3.220923513174057, 1.2312031507978179e-013,
19, 3.2209235206246376, 1.2312028082814339e-013,
19, 4.0080065280199051, 2.9933906948263948e-015,
19, 4.0080065354704857, 2.9933899839494794e-015,
19, 4.7811048328876495, 1.0579214187674311e-016,
19, 4.7811048403382301, 1.0579211525173792e-016,
19, 5.5409095361828804, 5.1437209226821869e-018,
19, 5.540909543633461, 5.1437201098803477e-018,
19, 6.2879297584295273, 3.30285370901757e-019,
19, 6.2879297658801079, 3.3028526990782213e-019,
19, 7.022538423538208, 2.7137393350465049e-020,
19, 7.0225384309887886, 2.7137390145037245e-020,
19, 7.7450010478496552, 2.7820488626315749e-021,
19, 7.7450010553002357, 2.7820487012081861e-021,
19, 8.4554945304989815, 3.4859333557441231e-022,
19, 8.4554945379495621, 3.4859329845518359e-022,
19, 9.1541195586323738, 5.2474008771752571e-023,
19, 9.1541195660829544, 5.2474000384032056e-023,
19, 9.8409088104963303, 9.3512638696111626e-024,
19, 9.8409088179469109, 9.3512648493398201e-024,
19, 10.515832215547562, 1.9479937239944536e-024,
19, 10.515832222998142, 1.9479938575974556e-024,
19, 11.178800173103809, 4.69085412141189e-025,
19, 11.17880018055439, 4.6908548720156987e-025,
19, 11.829665213823318, 1.2928024618486752e-025,
19, 11.829665221273899, 1.2928026753018633e-025,
19, 12.468222707509995, 4.0409290148689646e-026,
19, 12.468222714960575, 4.04092946286875e-026,
19, 13.094211108982563, 1.4204369152574e-026,
19, 13.094211116433144, 1.4204368039399753e-026,
19, 13.707312539219856, 5.5697729454842655e-027,
19, 13.707312546670437, 5.5697729267586886e-027,
19, 14.307154916226864, 2.4168995964876991e-027,
19, 14.307154923677444, 2.4168993118015141e-027,
19, 14.893317893147469, 1.151182873307859e-027,
19, 14.893317900598049, 1.151183249370605e-027,
19, 15.465346492826939, 5.9684896488404262e-028,
19, 15.465346500277519, 5.9684880973262032e-028,
19, 16.022779874503613, 3.3368863785415361e-028,
19, 16.022779881954193, 3.3368858888570371e-028,
19, 16.565208047628403, 1.988896282534073e-028,
19, 16.565208055078983, 1.9888966397094828e-028,
19, 17.092378154397011, 1.2511355195873936e-028,
19, 17.092378161847591, 1.2511357084655119e-028,
19, 17.604376800358295, 8.1764674788794317e-029,
19, 17.604376807808876, 8.1764689419338323e-029,
19, 18.101884864270687, 5.4403818799662857e-029,
19, 18.101884871721268, 5.4403811124044756e-029,
19, 18.586358889937401, 3.703368785213425e-029,
19, 18.586358897387981, 3.7033672461047739e-029,
19, 19.059829846024513, 2.5704197367132541e-029,
19, 19.059829853475094, 2.5704186883245258e-029,
20, 0.76703650504350662, 1.8640212188134082e-007,
20, 0.76703651249408722, 1.8640189110524636e-007,
20, 1.6060998290777206, 6.6157054588464647e-010,
20, 1.6060998365283012, 6.6157015121944875e-010,
20, 2.4274520501494408, 5.1991605763036711e-012,
20, 2.4274520576000214, 5.1991575903475782e-012,
20, 3.2330104410648346, 7.2582820146985349e-014,
20, 3.2330104485154152, 7.2582783832962019e-014,
20, 4.0240962356328964, 1.5927986670250318e-015,
20, 4.024096243083477, 1.5927979999140583e-015,
20, 4.8016504645347595, 5.0788048744312721e-017,
20, 4.8016504719853401, 5.0788029685345059e-017,
20, 5.5663639381527901, 2.2269814628583385e-018,
20, 5.5663639456033707, 2.2269809381302064e-018,
20, 6.3187519386410713, 1.2891132499721331e-019,
20, 6.3187519460916519, 1.2891130172541847e-019,
20, 7.0591993033885956, 9.5451218618123886e-021,
20, 7.0591993108391762, 9.5451218640099815e-021,
20, 7.7879889234900475, 8.8158015376044649e-022,
20, 7.7879889309406281, 8.8158004848661898e-022,
20, 8.5053204819560051, 9.9494735027566205e-023,
20, 8.5053204894065857, 9.9494722416437504e-023,
20, 9.2113229855895042, 1.3487881180413846e-023,
20, 9.2113229930400848, 1.3487880891331086e-023,
20, 9.9060632660984993, 2.1645350197982161e-024,
20, 9.9060632735490799, 2.1645348970951956e-024,
20, 10.589551687240601, 4.0607366596729865e-025,
20, 10.589551694691181, 4.0607361603086007e-025,
20, 11.26174583286047, 8.808202739315011e-026,
20, 11.26174584031105, 8.8082017838145519e-026,
20, 11.922552742063999, 2.1876047727436381e-026,
20, 11.92255274951458, 2.1876050426774313e-026,
20, 12.571830086410046, 6.1662495078304429e-027,
20, 12.571830093860626, 6.1662499348774014e-027,
20, 13.209386698901653, 1.9567173794914837e-027,
20, 13.209386706352234, 1.9567170332738984e-027,
20, 13.834982834756374, 6.9373607598036741e-028,
20, 13.834982842206955, 6.9373595897190232e-028,
20, 14.448330782353878, 2.7280690089401278e-028,
20, 14.448330789804459, 2.7280680945996177e-028,
20, 15.049096845090389, 1.1813689543546431e-028,
20, 15.04909685254097, 1.181369139348639e-028,
20, 15.636906251311302, 5.5924252241628636e-029,
20, 15.636906258761883, 5.5924267990651051e-029,
20, 16.211354024708271, 2.8725730797162321e-029,
20, 16.211354032158852, 2.8725722552333354e-029,
20, 16.772026851773262, 1.5875830143022102e-029,
20, 16.772026859223843, 1.5875829520216891e-029,
20, 17.318544775247574, 9.3495852893429768e-030,
20, 17.318544782698154, 9.3495854282408101e-030,
20, 17.850637152791023, 5.8080378869545303e-030,
20, 17.850637160241604, 5.8080398155538604e-030,
20, 18.36827152967453, 3.766778846313291e-030,
20, 18.368271537125111, 3.766779811191838e-030,
20, 18.871843047440052, 2.5002689211421573e-030,
20, 18.871843054890633, 2.5002682344308047e-030,
20, 19.362363085150719, 1.674243648785181e-030,
20, 19.362363092601299, 1.6742442653555633e-030,
20, 19.841450870037079, 1.1710157057806629e-030,
20, 19.841450877487659, 1.1710152732309025e-030,
20, 20.30974967777729, 8.0586953650643033e-031,
20, 20.309749685227871, 8.0586997818188476e-031,
21, 0.76976337283849716, 1.5066428073454916e-007,
21, 0.76976338028907776, 1.5066414246643623e-007,
21, 1.6111882776021957, 4.8530823596591033e-010,
21, 1.6111882850527763, 4.8530796828419519e-010,
21, 2.4353722333908081, 3.4610451821120009e-012,
21, 2.4353722408413887, 3.4610441424017983e-012,
21, 3.2442012280225754, 4.3835042623395894e-014,
21, 3.244201235473156, 4.3835023934688873e-014,
21, 4.0389783605933189, 8.7240487039547189e-016,
21, 4.0389783680438995, 8.7240461492198342e-016,
21, 4.820635624229908, 2.5219465898201733e-017,
21, 4.8206356316804886, 2.5219460854936753e-017,
21, 5.5898616313934326, 1.0022039268504888e-018,
21, 5.5898616388440132, 1.0022036172718784e-018,
21, 6.3471750691533089, 5.2559389652856588e-020,
21, 6.3471750766038895, 5.2559375594443955e-020,
21, 7.0929690599441528, 3.5247425965088507e-021,
21, 7.0929690673947334, 3.5247425089738368e-021,
21, 7.827539324760437, 2.9476660458905233e-022,
21, 7.8275393322110176, 2.9476655571904849e-022,
21, 8.551102802157402, 3.0115631228572582e-023,
21, 8.5511028096079826, 3.011562652643058e-023,
21, 9.2638102099299431, 3.6952283110718485e-024,
21, 9.2638102173805237, 3.6952283319575928e-024,
21, 9.9657547101378441, 5.3669656457006436e-025,
21, 9.9657547175884247, 5.3669649762144234e-025,
21, 10.656977899372578, 9.1124256917763825e-026,
21, 10.656977906823158, 9.1124268540483906e-026,
21, 11.337473809719086, 1.7890692227696762e-026,
21, 11.337473817169666, 1.7890693666894125e-026,
21, 12.007191583514214, 4.0227743879756425e-027,
21, 12.007191590964794, 4.0227743211391833e-027,
21, 12.666037052869797, 1.0270242765644747e-027,
21, 12.666037060320377, 1.0270242120978496e-027,
21, 13.313873596489429, 2.9538104523737974e-028,
21, 13.31387360394001, 2.9538105861327128e-028,
21, 13.950522527098656, 9.5012147708737886e-029,
21, 13.950522534549236, 9.5012121359051193e-029,
21, 14.575763396918774, 3.3946835963332503e-029,
21, 14.575763404369354, 3.3946830842745097e-029,
21, 15.189334601163864, 1.338384258083857e-029,
21, 15.189334608614445, 1.3383838228935191e-029,
21, 15.790935188531876, 5.7848622633191873e-030,
21, 15.790935195982456, 5.7848637716726903e-030,
21, 16.380228973925114, 2.7230499400143476e-030,
21, 16.380228981375694, 2.7230500761171659e-030,
21, 16.956853300333023, 1.3866916070525852e-030,
21, 16.956853307783604, 1.3866911116291402e-030,
21, 17.520435951650143, 7.5812793671458848e-031,
21, 17.520435959100723, 7.5812815048755598e-031,
21, 18.070626437664032, 4.4134618820380508e-031,
21, 18.070626445114613, 4.4134600003014153e-031,
21, 18.607151560485363, 2.7073121862111579e-031,
21, 18.607151567935944, 2.7073119631598685e-031,
21, 19.129908226430416, 1.7405231919358924e-031,
21, 19.129908233880997, 1.7405224578827498e-031,
21, 19.639103204011917, 1.149909852362787e-031,
21, 19.639103211462498, 1.1499093604025187e-031,
21, 20.135416276752949, 7.7057380617546439e-032,
21, 20.135416284203529, 7.7057377584979628e-032,
21, 20.62007824331522, 5.313635434227207e-032,
21, 20.6200782507658, 5.313638182607342e-032,
21, 21.09471806883812, 3.6998772136443968e-032,
21, 21.0947180762887, 3.6998750382256628e-032,
21, 21.513655178248882, 2.1423087294246753e-032,
21, 21.513655185699463, 2.1423066695903474e-032,
22, 0.77230742573738098, 1.229185164418409e-007,
22, 0.77230743318796158, 1.2291832454378835e-007,
22, 1.6159280240535736, 3.6084429032500014e-010,
22, 1.6159280315041542, 3.6084396590066408e-010,
22, 2.4427410438656807, 2.3451786403587014e-012,
22, 2.4427410513162613, 2.3451775949384816e-012,
22, 3.2546027079224586, 2.7062134880156874e-014,
22, 3.2546027153730392, 2.7062125966134374e-014,
22, 4.0527982860803604, 4.9058357404375516e-016,
22, 4.052798293530941, 4.9058348176902023e-016,
22, 4.8382501602172852, 1.2913921603181287e-017,
22, 4.8382501676678658, 1.2913917228554348e-017,
22, 5.6116434335708618, 4.6717185843067393e-019,
22, 5.6116434410214424, 4.6717179776425538e-019,
22, 6.3734981417655945, 2.2296903198511069e-020,
22, 6.3734981492161751, 2.2296900974904039e-020,
22, 7.1242129951715469, 1.3604387314615133e-021,
22, 7.1242130026221275, 1.3604385613902272e-021,
22, 7.8640931621193886, 1.0348631251961015e-022,
22, 7.8640931695699692, 1.03486285303848e-022,
22, 8.5933686941862106, 9.6152630844306075e-024,
22, 8.5933687016367912, 9.6152607923175558e-024,
22, 9.3122070804238319, 1.0727676244494742e-024,
22, 9.3122070878744125, 1.0727675822781486e-024,
22, 10.020721986889839, 1.4165824772693852e-025,
22, 10.02072199434042, 1.416582491355437e-025,
22, 10.718979395925999, 2.1866391305081649e-026,
22, 10.718979403376579, 2.1866388838497643e-026,
22, 11.407001882791519, 3.9031522459423558e-027,
22, 11.4070018902421, 3.9031521089045438e-027,
22, 12.084771521389484, 7.9802702761510913e-028,
22, 12.084771528840065, 7.980269670975788e-028,
22, 12.752231821417809, 1.8530613678900598e-028,
22, 12.752231828868389, 1.8530616824287783e-028,
22, 13.409288860857487, 4.8494798585916549e-029,
22, 13.409288868308067, 4.8494785536449382e-029,
22, 14.05581197142601, 1.4202884091535673e-029,
22, 14.055811978876591, 1.4202885442138583e-029,
22, 14.691633984446526, 4.6247809754088509e-030,
22, 14.691633991897106, 4.6247795457938258e-030,
22, 15.316551595926285, 1.6639745508668973e-030,
22, 15.316551603376865, 1.6639743599938902e-030,
22, 15.93032594025135, 6.5756901693418488e-031,
22, 15.930325947701931, 6.575690654043178e-031,
22, 16.532684214413166, 2.8372660249774888e-031,
22, 16.532684221863747, 2.8372664253810075e-031,
22, 17.123323194682598, 1.3286347918438753e-031,
22, 17.123323202133179, 1.328634334065038e-031,
22, 17.701916337013245, 6.7120509402607989e-032,
22, 17.701916344463825, 6.7120512896479518e-032,
22, 18.268127046525478, 3.6325184300463703e-032,
22, 18.268127053976059, 3.6325181235491734e-032,
22, 18.821632660925388, 2.0914308743910646e-032,
22, 18.821632668375969, 2.0914299057002497e-032,
22, 19.362165823578835, 1.2686800121696762e-032,
22, 19.362165831029415, 1.2686799446403407e-032,
22, 19.88958266377449, 8.0696445865656865e-033,
22, 19.889582671225071, 8.0696450863153928e-033,
22, 20.403966307640076, 5.2979414488418604e-033,
22, 20.403966315090656, 5.2979393097828398e-033,
22, 20.905758522450924, 3.5438052686101887e-033,
22, 20.905758529901505, 3.5438058521502753e-033,
22, 21.39586365967989, 2.4059587559014193e-033,
22, 21.39586366713047, 2.4059592126750793e-033,
22, 21.87561222910881, 1.686377885007472e-033,
22, 21.875612236559391, 1.6863776494421034e-033,
22, 22.346770018339157, 1.1684307972912237e-033,
22, 22.346770025789738, 1.1684310754271521e-033,
22, 22.618329457938671, 3.0366386951575348e-034,
22, 22.618329465389252, 3.0366315962617322e-034,
23, 0.77468881756067276, 1.0114160950347676e-007,
23, 0.77468882501125336, 1.0114149032370741e-007,
23, 1.6203579902648926, 2.7163743073571882e-010,
23, 1.6203579977154732, 2.7163720774540249e-010,
23, 2.4496206343173981, 1.6150650901954226e-012,
23, 2.4496206417679787, 1.6150639831714421e-012,
23, 3.2643046677112579, 1.7046911971326696e-014,
23, 3.2643046751618385, 1.7046904575466703e-014,
23, 4.0656779706478119, 2.8259863440888197e-016,
23, 4.0656779780983925, 2.8259849772579011e-016,
23, 4.8546530231833458, 6.8011510032153151e-018,
23, 4.8546530306339264, 6.8011494716482078e-018,
23, 5.6319104433059692, 2.2488464281640756e-019,
23, 5.6319104507565498, 2.2488459534517975e-019,
23, 6.3979701548814774, 9.8079791952490223e-021,
23, 6.397970162332058, 9.8079765385497614e-021,
23, 7.1532344222068787, 5.4671937485617472e-022,
23, 7.1532344296574593, 5.4671917378843881e-022,
23, 7.8980152830481529, 3.7986233108918277e-023,
23, 7.8980152904987335, 3.7986220021765903e-023,
23, 8.6325527653098106, 3.2231569433958688e-024,
23, 8.6325527727603912, 3.2231565617086114e-024,
23, 9.3570273742079735, 3.2834969778924849e-025,
23, 9.3570273816585541, 3.2834965760335941e-025,
23, 10.071568876504898, 3.9585335209485738e-026,
23, 10.071568883955479, 3.958533284993818e-026,
23, 10.776262499392033, 5.5783111048939248e-027,
23, 10.776262506842613, 5.5783106522452834e-027,
23, 11.471153371036053, 9.0901545746996052e-028,
23, 11.471153378486633, 9.0901530603778864e-028,
23, 12.156249642372131, 1.6968039360579984e-028,
23, 12.156249649822712, 1.6968035736701341e-028,
23, 12.831524632871151, 3.5977409707902412e-029,
23, 12.831524640321732, 3.5977400460720119e-029,
23, 13.496918246150017, 8.5996241514863787e-030,
23, 13.496918253600597, 8.5996216693376864e-030,
23, 14.152337834239006, 2.301386888748009e-030,
23, 14.152337841689587, 2.3013866363420915e-030,
23, 14.797658666968346, 6.8517867573579195e-031,
23, 14.797658674418926, 6.8517865061112645e-031,
23, 15.432724215090275, 2.2560267724720382e-031,
23, 15.432724222540855, 2.2560264136538832e-031,
23, 16.057346440851688, 8.1688281380273512e-032,
23, 16.057346448302269, 8.1688278348171516e-032,
23, 16.671306401491165, 3.2350057586674508e-032,
23, 16.671306408941746, 3.2350061703509374e-032,
23, 17.274355687201023, 1.3935974246555884e-032,
23, 17.274355694651604, 1.3935975649494885e-032,
23, 17.86621943116188, 6.494692001260146e-033,
23, 17.866219438612461, 6.4946923994178033e-033,
23, 18.446602113544941, 3.2567180669074382e-033,
23, 18.446602120995522, 3.2567169178931394e-033,
23, 19.015198193490505, 1.7458070339763389e-033,
23, 19.015198200941086, 1.7458065238164995e-033,
23, 19.571710675954819, 9.946196118534568e-034,
23, 19.571710683405399, 9.9461948954570997e-034,
23, 20.11588254570961, 5.9690525712299976e-034,
23, 20.115882553160191, 5.9690500193873946e-034,
23, 20.647547744214535, 3.7545858767414626e-034,
23, 20.647547751665115, 3.7545848159991635e-034,
23, 21.166708528995514, 2.4468390226112094e-034,
23, 21.166708536446095, 2.4468378891837283e-034,
23, 21.673638753592968, 1.6305350714270763e-034,
23, 21.673638761043549, 1.6305353199615473e-034,
23, 22.168985672295094, 1.0990783133763909e-034,
23, 22.168985679745674, 1.0990780643508099e-034,
23, 22.653797566890717, 7.660709966183589e-035,
23, 22.653797574341297, 7.6607108605632843e-035,
23, 23.129408702254295, 5.3481086344930933e-035,
23, 23.129408709704876, 5.3481086507387228e-035,
24, 0.77692466974258423, 8.3878559509491768e-008,
24, 0.77692467719316483, 8.3878444500950374e-008,
24, 1.6245112344622612, 2.0682132657809845e-010,
24, 1.6245112419128418, 2.068211277333234e-010,
24, 2.4560637548565865, 1.1289636914686017e-012,
24, 2.4560637623071671, 1.1289631400035527e-012,
24, 3.2733832001686096, 1.0938619422732816e-014,
24, 3.2733832076191902, 1.0938612911479053e-014,
24, 4.077720619738102, 1.6643113288659459e-016,
24, 4.0777206271886826, 1.6643108721731801e-016,
24, 4.8699784204363823, 3.6754217074679444e-018,
24, 4.8699784278869629, 3.6754201672840378e-018,
24, 5.6508321389555931, 1.1149437498689269e-019,
24, 5.6508321464061737, 1.1149432883776919e-019,
24, 6.4208004623651505, 4.4601526574819404e-021,
24, 6.420800469815731, 4.4601509330870358e-021,
24, 7.1802876740694046, 2.279941873373783e-022,
24, 7.1802876815199852, 2.2799412884161901e-022,
24, 7.9296107068657875, 1.4524227687620892e-023,
24, 7.9296107143163681, 1.4524227325357687e-023,
24, 8.6690171509981155, 1.1297516597255878e-024,
24, 8.6690171584486961, 1.1297516022917642e-024,
24, 9.398697666823864, 1.05489876857462e-025,
24, 9.3986976742744446, 1.0548984739860872e-025,
24, 10.118794731795788, 1.1655531704609301e-026,
24, 10.118794739246368, 1.1655532065990126e-026,
24, 10.82940886169672, 1.5051895754488702e-027,
24, 10.829408869147301, 1.5051892821133279e-027,
24, 11.53060320019722, 2.2476895295962268e-028,
24, 11.5306032076478, 2.2476889060302806e-028,
24, 12.22240673750639, 3.844876383499449e-029,
24, 12.22240674495697, 3.8448759550255258e-029,
24, 12.904816634953022, 7.4714391018572407e-030,
24, 12.904816642403603, 7.4714395302486889e-030,
24, 13.577799834311008, 1.6370125904554994e-030,
24, 13.577799841761589, 1.6370124695278897e-030,
24, 14.241294123232365, 4.0168128083279772e-031,
24, 14.241294130682945, 4.016811469349949e-031,
24, 14.895208783447742, 1.0969746370532075e-031,
24, 14.895208790898323, 1.0969744744608578e-031,
24, 15.539424940943718, 3.315109989109058e-032,
24, 15.539424948394299, 3.3151090923815311e-032,
24, 16.173795841634274, 1.1026485108254938e-032,
24, 16.173795849084854, 1.1026484499551487e-032,
24, 16.798147104680538, 4.0158085477948419e-033,
24, 16.798147112131119, 4.0158088226660865e-033,
24, 17.412277333438396, 1.5934132234896702e-033,
24, 17.412277340888977, 1.5934135053593853e-033,
24, 18.015959389507771, 6.8540171917222488e-034,
24, 18.015959396958351, 6.8540185876176649e-034,
24, 18.608942970633507, 3.1800628171362954e-034,
24, 18.608942978084087, 3.1800629680378069e-034,
24, 19.190959438681602, 1.5836246914151322e-034,
24, 19.190959446132183, 1.5836252472988316e-034,
24, 19.76173035800457, 8.4137600917291117e-035,
24, 19.761730365455151, 8.4137587940032584e-035,
24, 20.320982187986374, 4.745679482731015e-035,
24, 20.320982195436954, 4.7456809155199022e-035,
24, 20.868470467627048, 2.8185196647984626e-035,
24, 20.868470475077629, 2.8185199366681781e-035,
24, 21.404018573462963, 1.7531167534135375e-035,
24, 21.404018580913544, 1.7531173016947469e-035,
24, 21.927576221525669, 1.1332672002404092e-035,
24, 21.92757622897625, 1.1332675797508253e-035,
24, 22.439299717545509, 7.5125238131908317e-036,
24, 22.43929972499609, 7.5125236509015167e-036,
24, 22.939641229808331, 5.0568780187314363e-036,
24, 22.939641237258911, 5.0568784513528091e-036,
24, 23.429403953254223, 3.4736003627413405e-036,
24, 23.429403960704803, 3.4735987495009831e-036,
24, 23.90970042347908, 2.4387081321665308e-036,
24, 23.909700430929661, 2.4387083910949941e-036,
24, 24.38177253305912, 1.694733860647387e-036,
24, 24.381772540509701, 1.694733324885658e-036,
25, 0.77902968227863312, 7.0067469371321597e-008,
25, 0.77902968972921371, 7.0067352105092841e-008,
25, 1.6284160688519478, 1.5913112796142118e-010,
25, 1.6284160763025284, 1.5913095865429296e-010,
25, 2.4621154814958572, 8.0010005048491295e-013,
25, 2.4621154889464378, 8.0009951288958997e-013,
25, 3.2819032743573189, 7.1398107739385184e-015,
25, 3.2819032818078995, 7.1398064213538464e-015,
25, 4.0890141874551773, 1.0003569839311091e-016,
25, 4.0890141949057579, 1.0003565214949822e-016,
25, 4.8843406066298485, 2.0339987591563894e-018,
25, 4.8843406140804291, 2.0339981157202125e-018,
25, 5.6685525178909302, 5.6799254581074817e-020,
25, 5.6685525253415108, 5.6799245689717146e-020,
25, 6.4421665593981743, 2.0912595308116639e-021,
25, 6.4421665668487549, 2.0912591224302577e-021,
25, 7.2055878639221191, 9.8372734035261097e-023,
25, 7.2055878713726997, 9.8372708440629524e-023,
25, 7.9591367468237877, 5.7658750176114061e-024,
25, 7.9591367542743683, 5.7658733776591436e-024,
25, 8.7030665054917336, 4.1258272741964985e-025,
25, 8.7030665129423141, 4.1258258782473198e-025,
25, 9.4375757128000259, 3.5435416447318224e-026,
25, 9.4375757202506065, 3.5435412590635847e-026,
25, 10.162816897034645, 3.6008987404838187e-027,
25, 10.162816904485226, 3.6008987502968748e-027,
25, 10.878902837634087, 4.2764878951239796e-028,
25, 10.878902845084667, 4.2764868457382694e-028,
25, 11.58591116219759, 5.8725831294026438e-029,
25, 11.58591116964817, 5.872583554303668e-029,
25, 12.283887647092342, 9.2378193889837239e-030,
25, 12.283887654542923, 9.2378197873933138e-030,
25, 12.97284871339798, 1.6508371998843517e-030,
25, 12.97284872084856, 1.650837412798272e-030,
25, 13.652783133089542, 3.3266754235730111e-031,
25, 13.652783140540123, 3.3266744536286711e-031,
25, 14.323653288185596, 7.5089192296338788e-032,
25, 14.323653295636177, 7.5089195273493671e-032,
25, 14.985395908355713, 1.8869158708375887e-032,
25, 14.985395915806293, 1.8869156141367114e-032,
25, 15.637922637164593, 5.2491829350088782e-033,
25, 15.637922644615173, 5.2491824971659126e-033,
25, 16.281120285391808, 1.6081191935598747e-033,
25, 16.281120292842388, 1.608118845571321e-033,
25, 16.914851076900959, 5.3986271338461797e-034,
25, 16.91485108435154, 5.3986283194236148e-034,
25, 17.538952887058258, 1.9766512695275074e-034,
25, 17.538952894508839, 1.9766507896017455e-034,
25, 18.153239868581295, 7.8569686415203062e-035,
25, 18.153239876031876, 7.8569708046899769e-035,
25, 18.757503516972065, 3.3749866196468743e-035,
25, 18.757503524422646, 3.374985983250723e-035,
25, 19.351514972746372, 1.5594420539380395e-035,
25, 19.351514980196953, 1.5594416192490925e-035,
25, 19.935029000043869, 7.7158386293794966e-036,
25, 19.93502900749445, 7.7158392148375424e-036,
25, 20.507790975272655, 4.0656659632469917e-036,
25, 20.507790982723236, 4.0656647261416748e-036,
25, 21.069548606872559, 2.2711959500700407e-036,
25, 21.069548614323139, 2.2711951777269612e-036,
25, 21.62007087469101, 1.3353866143298436e-036,
25, 21.62007088214159, 1.3353860101843685e-036,
25, 22.159177884459496, 8.2143426189718226e-037,
25, 22.159177891910076, 8.2143413202705087e-037,
25, 22.68678567558527, 5.2648015059720179e-037,
25, 22.686785683035851, 5.2648001075197064e-037,
25, 23.202968575060368, 3.468211073462519e-037,
25, 23.202968582510948, 3.4682107310949544e-037,
25, 23.70803364366293, 2.3273599976356348e-037,
25, 23.70803365111351, 2.3273591213713725e-037,
25, 24.202582977712154, 1.5765602064246655e-037,
25, 24.202582985162735, 1.576559556129669e-037,
25, 24.687517486512661, 1.1088611117377277e-037,
25, 24.687517493963242, 1.1088604968432837e-037,
25, 25.16395078599453, 7.7583898454128553e-038,
25, 25.16395079344511, 7.7583939097854651e-038,
25, 25.627866134047508, 5.3068781900534944e-038,
25, 25.627866141498089, 5.3068810921059701e-038,
26, 0.78101654350757599, 5.8923908707209337e-008,
26, 0.78101655095815659, 5.8923821371534893e-008,
26, 1.6320968940854073, 1.236317730309333e-010,
26, 1.6320969015359879, 1.2363168158688363e-010,
26, 2.4678146317601204, 5.7429811601560071e-013,
26, 2.467814639210701, 5.7429765734855436e-013,
26, 3.2899207398295403, 4.734388742385331e-015,
26, 3.2899207472801208, 4.7343867559584461e-015,
26, 4.0996342152357101, 6.1272431600609502e-017,
26, 4.0996342226862907, 6.1272407979893011e-017,
26, 4.8978375121951103, 1.1506240642534423e-018,
26, 4.8978375196456909, 1.1506236852699587e-018,
26, 5.6851947978138924, 2.9671094902332928e-020,
26, 5.685194805264473, 2.9671085633439803e-020,
26, 6.4622200652956963, 1.0086511721536377e-021,
26, 6.4622200727462769, 1.0086507678940824e-021,
26, 7.2293184027075768, 4.3801061282054169e-023,
26, 7.2293184101581573, 4.3801050332411078e-023,
26, 7.9868123158812523, 2.3696799980087546e-024,
26, 7.9868123233318329, 2.3696791495984219e-024,
26, 8.7349593564867973, 1.5649197470426281e-025,
26, 8.7349593639373779, 1.5649197320553895e-025,
26, 9.4739642217755318, 1.2402917131745359e-026,
26, 9.4739642292261124, 1.2402913154591754e-026,
26, 10.2039874792099, 1.1629424955001513e-027,
26, 10.20398748666048, 1.1629425103997286e-027,
26, 10.925151742994785, 1.2742687180623173e-028,
26, 10.925151750445366, 1.2742686869329822e-028,
26, 11.637546353042126, 1.6143813265406585e-029,
26, 11.637546360492706, 1.6143813107433007e-029,
26, 12.341230750083923, 2.3428227604690718e-030,
26, 12.341230757534504, 2.3428227187060725e-030,
26, 13.036237008869648, 3.8625446674283068e-031,
26, 13.036237016320229, 3.8625439691448719e-031,
26, 13.722571700811386, 7.1813310277242243e-032,
26, 13.722571708261967, 7.1813308590609393e-032,
26, 14.400217205286026, 1.4957140381405686e-032,
26, 14.400217212736607, 1.4957142743655298e-032,
26, 15.069132648408413, 3.4688292162948178e-033,
26, 15.069132655858994, 3.4688284579266739e-033,
26, 15.729254551231861, 8.9084835395664626e-034,
26, 15.729254558682442, 8.908484325639754e-034,
26, 16.3804971575737, 2.5204945088761422e-034,
26, 16.380497165024281, 2.5204938761288704e-034,
26, 17.022752746939659, 7.8188945402045879e-035,
26, 17.02275275439024, 7.8188922746258055e-035,
26, 17.65589178353548, 2.6473364587263948e-035,
26, 17.655891790986061, 2.6473357716097579e-035,
26, 18.279763206839561, 9.7405122544829131e-036,
26, 18.279763214290142, 9.7405091647747447e-036,
26, 18.894194960594177, 3.878059833810667e-036,
26, 18.894194968044758, 3.8780594112881572e-036,
26, 19.498995013535023, 1.6636902562494894e-036,
26, 19.498995020985603, 1.6636907531659472e-036,
26, 20.093953281641006, 7.6577266090817481e-037,
26, 20.093953289091587, 7.657728188363079e-037,
26, 20.678845040500164, 3.7661248096741531e-037,
26, 20.678845047950745, 3.7661237372250638e-037,
26, 21.253436677157879, 1.9691052657118544e-037,
26, 21.253436684608459, 1.9691047946430182e-037,
26, 21.817495100200176, 1.0899858439496351e-037,
26, 21.817495107650757, 1.0899854262898754e-037,
26, 22.370802812278271, 6.3470096664624425e-038,
26, 22.370802819728851, 6.3470080713999366e-038,
26, 22.913181200623512, 3.86373588174236e-038,
26, 22.913181208074093, 3.8637351113998463e-038,
26, 23.444525294005871, 2.4535347310547519e-038,
26, 23.444525301456451, 2.4535359123032401e-038,
26, 23.964852377772331, 1.6049618186436992e-038,
26, 23.964852385222912, 1.604961872563914e-038,
26, 24.474362745881081, 1.0722943070757005e-038,
26, 24.474362753331661, 1.0722942325976742e-038,
26, 24.973499171435833, 7.2558350814098704e-039,
26, 24.973499178886414, 7.2558340329470219e-039,
26, 25.462974481284618, 5.0337622643621282e-039,
26, 25.462974488735199, 5.0337617320777135e-039,
26, 25.943732649087906, 3.5390684241286765e-039,
26, 25.943732656538486, 3.5390691209096449e-039,
26, 26.416851162910461, 2.4665037699450018e-039,
26, 26.416851170361042, 2.4665034955684909e-039,
26, 26.801410645246506, 1.1171525523613971e-039,
26, 26.801410652697086, 1.1171551092920132e-039,
27, 0.7828962579369545, 4.9861854667393399e-008,
27, 0.7828962653875351, 4.9861772593924402e-008,
27, 1.6355748474597931, 9.6921316479103525e-011,
27, 1.6355748549103737, 9.6921206864357132e-011,
27, 2.4731948226690292, 4.171211347524171e-013,
27, 2.4731948301196098, 4.1712091406116398e-013,
27, 3.2974838986992836, 3.1856718158208548e-015,
27, 3.2974839061498642, 3.1856696336218403e-015,
27, 4.1096459552645683, 3.8192029014720663e-017,
27, 4.1096459627151489, 3.8192010297992792e-017,
27, 4.9105536565184593, 6.6429667302540135e-019,
27, 4.9105536639690399, 6.6429652717397208e-019,
27, 5.7008651793003082, 1.5864616200237458e-020,
27, 5.7008651867508888, 1.5864611294551399e-020,
27, 6.4810914397239685, 4.993999498145391e-022,
27, 6.4810914471745491, 4.9939979049271363e-022,
27, 7.2516367882490158, 2.0079266330070849e-023,
27, 7.2516367956995964, 2.0079265308291086e-023,
27, 8.0128250047564507, 1.0056680741144098e-024,
27, 8.0128250122070312, 1.0056677361707529e-024,
27, 8.7649167329072952, 6.1476317533215932e-026,
27, 8.7649167403578758, 6.1476309156933445e-026,
27, 9.5081214383244514, 4.5096613837282808e-027,
27, 9.508121445775032, 4.5096604070043352e-027,
27, 10.242606043815613, 3.9132924912256924e-028,
27, 10.242606051266193, 3.9132926019691446e-028,
27, 10.96850112080574, 3.9680374563073656e-029,
27, 10.968501128256321, 3.968037549032286e-029,
27, 11.685905538499355, 4.6518641224931443e-030,
27, 11.685905545949936, 4.6518631300160416e-030,
27, 12.394889906048775, 6.2467209675851883e-031,
27, 12.394889913499355, 6.2467197889832523e-031,
27, 13.095499135553837, 9.5296302920980662e-032,
27, 13.095499143004417, 9.5296301328881049e-032,
27, 13.787754379212856, 1.6394978658915808e-032,
27, 13.787754386663437, 1.6394979205807897e-032,
27, 14.471654459834099, 3.1600211613408551e-033,
27, 14.471654467284679, 3.1600209693232782e-033,
27, 15.147176899015903, 6.7828954814670378e-034,
27, 15.147176906466484, 6.7828945671314482e-034,
27, 15.81427863240242, 1.6125447486417395e-034,
27, 15.814278639853001, 1.6125444345876133e-034,
27, 16.472896493971348, 4.2246556605945897e-035,
27, 16.472896501421928, 4.224654227049247e-035,
27, 17.122947536408901, 1.2139966311739369e-035,
27, 17.122947543859482, 1.2139966298630524e-035,
27, 17.764329209923744, 3.8095779223206078e-036,
27, 17.764329217374325, 3.8095779252456187e-036,
27, 18.396919578313828, 1.3000203710965374e-036,
27, 18.396919585764408, 1.3000203411711264e-036,
27, 19.020577564835548, 4.8049120367747199e-037,
27, 19.020577572286129, 4.8049124355340798e-037,
27, 19.635143436491489, 1.9158924823061778e-037,
27, 19.63514344394207, 1.9158920386648308e-037,
27, 20.240439757704735, 8.2093208358169539e-038,
27, 20.240439765155315, 8.2093222197429644e-038,
27, 20.836273021996021, 3.7650963780981519e-038,
27, 20.836273029446602, 3.7650975525688663e-038,
27, 21.422436565160751, 1.8412740319560743e-038,
27, 21.422436572611332, 1.8412734834107893e-038,
27, 21.998715363442898, 9.5568938496580513e-039,
27, 21.998715370893478, 9.5568962750049465e-039,
27, 22.564893670380116, 5.2444711828702124e-039,
27, 22.564893677830696, 5.2444725699857754e-039,
27, 23.120767138898373, 3.0256331670909385e-039,
27, 23.120767146348953, 3.0256324528122128e-039,
27, 23.666161254048347, 1.8245360187243205e-039,
27, 23.666161261498928, 1.8245363450061449e-039,
27, 24.200958535075188, 1.1470036575842657e-039,
27, 24.200958542525768, 1.1470033205632092e-039,
27, 24.725136809051037, 7.4468116835290912e-040,
27, 24.725136816501617, 7.4468134793516934e-040,
27, 25.238818168640137, 4.9485796130614579e-040,
27, 25.238818176090717, 4.9485778772589032e-040,
27, 25.742321841418743, 3.3399923581817735e-040,
27, 25.742321848869324, 3.3399911124650134e-040,
27, 26.236201457679272, 2.2838209417828281e-040,
27, 26.236201465129852, 2.2838217806321604e-040,
27, 26.721238203346729, 1.6104454076256336e-040,
27, 26.72123821079731, 1.6104457017695957e-040,
27, 27.198375716805458, 1.12895575803922e-040,
27, 27.198375724256039, 1.1289556733584685e-040,
27, 27.669778347015381, 7.8496301393215855e-041,
27, 27.669778354465961, 7.8496341262896801e-041,
27, 27.884223878383636, 4.4309665223873591e-041,
27, 27.884223885834217, 4.4309591849200503e-041,
28, 0.78467844426631927, 4.2438470083140721e-008,
28, 0.78467845171689987, 4.2438393278981791e-008,
28, 1.6388683915138245, 7.6621569710548971e-011,
28, 1.6388683989644051, 7.66215089154498e-011,
28, 2.4782853201031685, 3.0631204478184193e-013,
28, 2.4782853275537491, 3.063118924040777e-013,
28, 3.304634802043438, 2.1729815422346648e-015,
28, 3.3046348094940186, 2.1729799923068305e-015,
28, 4.1191061362624168, 2.4196250779813722e-017,
28, 4.1191061437129974, 2.4196239816772689e-017,
28, 4.9225624054670334, 3.9085656395735408e-019,
28, 4.922562412917614, 3.9085649025210167e-019,
28, 5.7156557217240334, 8.6680273869165024e-021,
28, 5.715655729174614, 8.6680236478512346e-021,
28, 6.498893603682518, 2.5335387999951474e-022,
28, 6.4988936111330986, 2.5335376908522942e-022,
28, 7.2726791352033615, 9.4573144592121954e-024,
28, 7.2726791426539421, 9.4573116298964195e-024,
28, 8.0373366698622704, 4.3971230185116881e-025,
28, 8.037336677312851, 4.3971227534536684e-025,
28, 8.793128989636898, 2.4950063652246191e-026,
28, 8.7931289970874786, 2.495005720678091e-026,
28, 9.5402692407369614, 1.6986980617997022e-027,
28, 9.540269248187542, 1.6986976051079919e-027,
28, 10.278929390013218, 1.368000853859253e-028,
28, 10.278929397463799, 1.3680004892213298e-028,
28, 11.009246453642845, 1.2872419602896367e-029,
28, 11.009246461093426, 1.2872420187471339e-029,
28, 11.731327079236507, 1.4003201763391476e-030,
28, 11.731327086687088, 1.4003202386076777e-030,
28, 12.445251040160656, 1.7448255734165301e-031,
28, 12.445251047611237, 1.7448253583893487e-031,
28, 13.151073843240738, 2.4698393595556993e-032,
28, 13.151073850691319, 2.4698391161370222e-032,
28, 13.848828695714474, 3.9427669364651789e-033,
28, 13.848828703165054, 3.9427660690914164e-033,
28, 14.538528017699718, 7.0517495293252521e-034,
28, 14.538528025150299, 7.0517474992045073e-034,
28, 15.22016453742981, 1.4046733706426603e-034,
28, 15.22016454488039, 1.4046729721237711e-034,
28, 15.893712103366852, 3.0994444806456431e-035,
28, 15.893712110817432, 3.0994449626913169e-035,
28, 16.55912622064352, 7.5380952232932651e-036,
28, 16.559126228094101, 7.5380932219859205e-036,
28, 17.216344498097897, 2.0114378107354203e-036,
28, 17.216344505548477, 2.0114379656122684e-036,
28, 17.865286819636822, 5.8633939940250315e-037,
28, 17.865286827087402, 5.8633946299343831e-037,
28, 18.505855575203896, 1.8596224339761576e-037,
28, 18.505855582654476, 1.8596221870214534e-037,
28, 19.137935824692249, 6.3922092248869744e-038,
28, 19.13793583214283, 6.3922102380482483e-038,
28, 19.761395521461964, 2.3724862433709197e-038,
28, 19.761395528912544, 2.3724866454052567e-038,
28, 20.376085996627808, 9.4731318337289952e-039,
28, 20.376086004078388, 9.4731287775953353e-039,
28, 20.981842800974846, 4.0545371346860406e-039,
28, 20.981842808425426, 4.0545370535552068e-039,
28, 21.578487128019333, 1.8533283507255836e-039,
28, 21.578487135469913, 1.853328817895879e-039,
28, 22.165828302502632, 9.0155863853882353e-040,
28, 22.165828309953213, 9.0155831427237625e-040,
28, 22.743667811155319, 4.6472893319487125e-040,
28, 22.7436678186059, 4.6472889307429114e-040,
28, 23.311805583536625, 2.5293602604427438e-040,
28, 23.311805590987206, 2.5293596848335514e-040,
28, 23.870049826800823, 1.4463087106544672e-040,
28, 23.870049834251404, 1.4463085194116285e-040,
28, 24.418231755495071, 8.641896329274563e-041,
28, 24.418231762945652, 8.6418996111656845e-041,
28, 24.956227175891399, 5.3786841208254478e-041,
28, 24.95622718334198, 5.378682136136815e-041,
28, 25.483986794948578, 3.4648144680023666e-041,
28, 25.483986802399158, 3.4648129601794969e-041,
28, 26.001575656235218, 2.2884086968613662e-041,
28, 26.001575663685799, 2.2884098625776109e-041,
28, 26.509218297898769, 1.5387898607295863e-041,
28, 26.50921830534935, 1.538789924506611e-041,
28, 27.00733794271946, 1.0458893902132325e-041,
28, 27.00733795017004, 1.0458899705307257e-041,
28, 27.4965685531497, 7.317848728543107e-042,
28, 27.496568560600281, 7.3178520005717001e-042,
28, 27.977721095085144, 5.1513043977723732e-042,
28, 27.977721102535725, 5.1513042258958866e-042,
28, 28.451707921922207, 3.5986164377315787e-042,
28, 28.451707929372787, 3.5986160057693314e-042,
29, 0.78637154400348663, 3.6315909083995129e-008,
29, 0.78637155145406723, 3.6315849334616369e-008,
29, 1.6419936791062355, 6.1049645545974547e-011,
29, 1.6419936865568161, 6.1049599294982487e-011,
29, 2.4831117615103722, 2.2726035573991162e-013,
29, 2.4831117689609528, 2.2726023881733654e-013,
29, 3.3114102259278297, 1.5011780867764562e-015,
29, 3.3114102333784103, 1.5011775587872939e-015,
29, 4.128064326941967, 1.5563805350068021e-017,
29, 4.1280643343925476, 1.5563800665439041e-017,
29, 4.9339278042316437, 2.3406905946198134e-019,
29, 4.9339278116822243, 2.3406896430597371e-019,
29, 5.7296467050909996, 4.8324621843737061e-021,
29, 5.7296467125415802, 4.8324604821555049e-021,
29, 6.5157249048352242, 1.314795562058049e-022,
29, 6.5157249122858047, 1.3147952115386097e-022,
29, 7.2925638258457184, 4.5681547645026199e-024,
29, 7.292563833296299, 4.5681541042570898e-024,
29, 8.0604878067970276, 1.9767148584973311e-025,
29, 8.0604878142476082, 1.9767144437084469e-025,
29, 8.8197610825300217, 1.0437840229618024e-026,
29, 8.8197610899806023, 1.0437836457111727e-026,
29, 9.5705995559692383, 6.6127541570083993e-028,
29, 9.5705995634198189, 6.6127525803998794e-028,
29, 10.313179194927216, 4.9550353823480331e-029,
29, 10.313179202377796, 4.9550344472793234e-029,
29, 11.047642216086388, 4.3379652668743748e-030,
29, 11.047642223536968, 4.3379651694905502e-030,
29, 11.77410165220499, 4.3903098563318958e-031,
29, 11.774101659655571, 4.3903087396488023e-031,
29, 12.492644853889942, 5.0891392311082294e-032,
29, 12.492644861340523, 5.089138080132273e-032,
29, 13.203336097300053, 6.7015567871931459e-033,
29, 13.203336104750633, 6.7015574012559967e-033,
29, 13.906218603253365, 9.9522699683293545e-034,
29, 13.906218610703945, 9.9522699561603004e-034,
29, 14.60131610929966, 1.6559310130268636e-034,
29, 14.60131611675024, 1.6559308877250499e-034,
29, 15.28863400965929, 3.0688012602367554e-035,
29, 15.288634017109871, 3.0688008505595191e-035,
29, 15.968160234391689, 6.3003656761785947e-036,
29, 15.96816024184227, 6.300365157267352e-036,
29, 16.639865875244141, 1.425912288294408e-036,
29, 16.639865882694721, 1.425911844482608e-036,
29, 17.303705655038357, 3.5413918087008817e-037,
29, 17.303705662488937, 3.5413910585270221e-037,
29, 17.959618203341961, 9.6110663827236623e-038,
29, 17.959618210792542, 9.6110639887579061e-038,
29, 18.607526287436485, 2.8389759994471709e-038,
29, 18.607526294887066, 2.8389752688919641e-038,
29, 19.247336961328983, 9.0931089735817269e-039,
29, 19.247336968779564, 9.0931107476948825e-039,
29, 19.878941707313061, 3.1467556490433912e-039,
29, 19.878941714763641, 3.1467564127571162e-039,
29, 20.502216704189777, 1.1724748656710215e-039,
29, 20.502216711640358, 1.1724746734027557e-039,
29, 21.117023251950741, 4.6876364663697041e-040,
29, 21.117023259401321, 4.6876364357803892e-040,
29, 21.723208487033844, 2.0042123089344851e-040,
29, 21.723208494484425, 2.0042116411036911e-040,
29, 22.320606715977192, 9.132472556056144e-041,
29, 22.320606723427773, 9.1324737655785673e-041,
29, 22.909041479229927, 4.4204627633406315e-041,
29, 22.909041486680508, 4.420462690830891e-041,
29, 23.488328985869884, 2.2638612067742748e-041,
29, 23.488328993320465, 2.2638616763927321e-041,
29, 24.05828333646059, 1.2225551251648693e-041,
29, 24.058283343911171, 1.2225553197479533e-041,
29, 24.618724562227726, 6.9314021088591364e-042,
29, 24.618724569678307, 6.9314047935940562e-042,
29, 25.169490531086922, 4.1049308418651103e-042,
29, 25.169490538537502, 4.1049319553758314e-042,
29, 25.710454262793064, 2.5298050928083053e-042,
29, 25.710454270243645, 2.5298056900518227e-042,
29, 26.241548083722591, 1.6166462380689568e-042,
29, 26.241548091173172, 1.6166465098434285e-042,
29, 26.762795478105545, 1.0606841937797943e-042,
29, 26.762795485556126, 1.0606843404549322e-042,
29, 27.274348974227905, 7.0992566551399511e-043,
29, 27.274348981678486, 7.0992546682756672e-043,
29, 27.776527158915997, 4.8148903392572901e-043,
29, 27.776527166366577, 4.814888042092614e-043,
29, 28.269836388528347, 3.3234515341900158e-043,
29, 28.269836395978928, 3.3234500791670542e-043,
29, 28.754959724843502, 2.3456576866672306e-043,
29, 28.754959732294083, 2.345656656614369e-043,
29, 29.232707068324089, 1.6470684285437321e-043,
29, 29.23270707577467, 1.6470683545256373e-043,
29, 29.70374021679163, 1.14547675702381e-043,
29, 29.70374022424221, 1.1454765601759464e-043,
30, 0.7879829928278923, 3.1234103821482427e-008,
30, 0.7879830002784729, 3.1234044655401994e-008,
30, 1.6449649482965469, 4.9000015491257048e-011,
30, 1.6449649557471275, 4.8999963821072772e-011,
30, 2.4876966997981071, 1.7023669931328061e-013,
30, 2.4876967072486877, 1.7023657129354393e-013,
30, 3.3178424835205078, 1.0494761982366968e-015,
30, 3.3178424909710884, 1.0494757357860962e-015,
30, 4.1365640535950661, 1.0154249700920638e-017,
30, 4.1365640610456467, 1.0154243875133412e-017,
30, 4.9447060599923134, 1.4250864555511693e-019,
30, 4.944706067442894, 1.4250858796996163e-019,
30, 5.7429084852337837, 2.7453691120619369e-021,
30, 5.7429084926843643, 2.7453685866311988e-021,
30, 6.5316714197397232, 6.9693659068680088e-023,
30, 6.5316714271903038, 6.9693629187270163e-023,
30, 7.3113943338394165, 2.2591471868696091e-024,
30, 7.3113943412899971, 2.2591466479292196e-024,
30, 8.0824010968208313, 9.1197383000971079e-026,
30, 8.0824011042714119, 9.1197355380522927e-026,
30, 8.8449568077921867, 4.4921066968594634e-027,
30, 8.8449568152427673, 4.4921064406150814e-027,
30, 9.5992793887853622, 2.6545531428409782e-028,
30, 9.5992793962359428, 2.6545522470546947e-028,
30, 10.34554798156023, 1.855221838168487e-029,
30, 10.345547989010811, 1.8552214020399549e-029,
30, 11.083908997476101, 1.5147783374462689e-030,
30, 11.083909004926682, 1.5147781122476647e-030,
30, 11.81448071449995, 1.4297164287403578e-031,
30, 11.814480721950531, 1.429716050915216e-031,
30, 12.537356749176979, 1.5455160104219774e-032,
30, 12.53735675662756, 1.5455160199328339e-032,
30, 13.252608671784401, 1.8978775176433715e-033,
30, 13.252608679234982, 1.8978774707164247e-033,
30, 13.960288092494011, 2.6282911950633352e-034,
30, 13.960288099944592, 2.6282913708927645e-034,
30, 14.660428203642368, 4.0780899601901608e-035,
30, 14.660428211092949, 4.0780894770882105e-035,
30, 15.353045016527176, 7.0479243716573658e-036,
30, 15.353045023977757, 7.0479222548237397e-036,
30, 16.038138270378113, 1.3494709199819255e-036,
30, 16.038138277828693, 1.3494705517069979e-036,
30, 16.715692117810249, 2.8486491673345358e-037,
30, 16.71569212526083, 2.8486483929154767e-037,
30, 17.385675646364689, 6.5998055420207975e-038,
30, 17.385675653815269, 6.5998062646129257e-038,
30, 18.048043206334114, 1.6711936241018928e-038,
30, 18.048043213784695, 1.6711932368686648e-038,
30, 18.702734716236591, 4.6071433653083805e-039,
30, 18.702734723687172, 4.6071443081395363e-039,
30, 19.349675759673119, 1.3776916161772679e-039,
30, 19.349675767123699, 1.3776916401455473e-039,
30, 19.988777793943882, 4.4532108875418354e-040,
30, 19.988777801394463, 4.4532114573536834e-040,
30, 20.619938254356384, 1.5507563718868067e-040,
30, 20.619938261806965, 1.5507566883583332e-040,
30, 21.243040800094604, 5.7990312184030671e-041,
30, 21.243040807545185, 5.7990304989845352e-041,
30, 21.857955724000931, 2.3212797494554108e-041,
30, 21.857955731451511, 2.3212803480860163e-041,
30, 22.464540585875511, 9.914865440882635e-042,
30, 22.464540593326092, 9.9148662773812494e-042,
30, 23.062641389667988, 4.5045190716090583e-042,
30, 23.062641397118568, 4.5045174791143897e-042,
30, 23.652094401419163, 2.1701628812569051e-042,
30, 23.652094408869743, 2.1701625772121853e-042,
30, 24.232729002833366, 1.1046043114766288e-042,
30, 24.232729010283947, 1.1046045034064885e-042,
30, 24.804372116923332, 5.9211173400922859e-043,
30, 24.804372124373913, 5.9211190991234153e-043,
30, 25.366854824125767, 3.3298155214419811e-043,
30, 25.366854831576347, 3.3298157358067105e-043,
30, 25.92002210021019, 1.9551128692966943e-043,
30, 25.92002210766077, 1.9551123692323681e-043,
30, 26.463746801018715, 1.1933006750773454e-043,
30, 26.463746808469296, 1.1933004727347112e-043,
30, 26.997949115931988, 7.5643757950805542e-044,
30, 26.997949123382568, 7.5643761045987683e-044,
30, 27.522622361779213, 4.9284040353068413e-044,
30, 27.522622369229794, 4.9284056246758231e-044,
30, 28.037864476442337, 3.2810162604333193e-044,
30, 28.037864483892918, 3.281017845647255e-044,
30, 28.543911211192608, 2.2181628671749676e-044,
30, 28.543911218643188, 2.218162484652318e-044,
30, 29.041161552071571, 1.5134037301717584e-044,
30, 29.041161559522152, 1.5134029110911047e-044,
30, 29.530181311070919, 1.0667420585863651e-044,
30, 29.5301813185215, 1.0667417522137867e-044,
30, 30.011674650013447, 7.5174774420740806e-045,
30, 30.011674657464027, 7.5174742900736671e-045,
30, 30.486428417265415, 5.2621270182135051e-045,
30, 30.486428424715996, 5.262130311093599e-045,
30, 30.939444169402122, 3.5015139512069607e-045,
30, 30.939444176852703, 3.5015112710245708e-045,
31, 0.78951938450336456, 2.6990963852982276e-008,
31, 0.78951939195394516, 2.6990901272098622e-008,
31, 1.6477948054671288, 3.9599591893838782e-011,
31, 1.6477948129177094, 3.9599558875077027e-011,
31, 2.4920600801706314, 1.2867416450803074e-013,
31, 2.492060087621212, 1.286740858923318e-013,
31, 3.3239601328969002, 7.4191337236762968e-016,
31, 3.3239601403474808, 7.4191298658981141e-016,
31, 4.144643746316433, 6.7136115607620136e-018,
31, 4.1446437537670135, 6.7136080734499562e-018,
31, 4.9549467116594315, 8.8116416572145598e-020,
31, 4.9549467191100121, 8.8116378746161626e-020,
31, 5.7555030211806297, 1.5874468287337354e-021,
31, 5.7555030286312103, 1.5874462991137669e-021,
31, 6.5468088984489441, 3.7683180579985163e-023,
31, 6.5468089058995247, 3.7683164558120959e-023,
31, 7.3292616009712219, 1.1421590109206418e-024,
31, 7.3292616084218025, 1.1421585299332504e-024,
31, 8.103184200823307, 4.3108518074612864e-026,
31, 8.1031842082738876, 4.3108510892707748e-026,
31, 8.8688421621918678, 1.9851855023091017e-027,
31, 8.8688421696424484, 1.9851853532161421e-027,
31, 9.6264548823237419, 1.0966928714056398e-028,
31, 9.6264548897743225, 1.0966926721759533e-028,
31, 10.376203939318657, 7.164836764783927e-030,
31, 10.376203946769238, 7.1648343154883914e-030,
31, 11.118239149451256, 5.4683058705610656e-031,
31, 11.118239156901836, 5.4683043353071719e-031,
31, 11.8526830971241, 4.8242112495562322e-032,
31, 11.85268310457468, 4.8242113495352988e-032,
31, 12.579634577035904, 4.8742340289959263e-033,
31, 12.579634584486485, 4.8742330295078644e-033,
31, 13.299171291291714, 5.5942948410353604e-034,
31, 13.299171298742294, 5.5942937409224875e-034,
31, 14.011351861059666, 7.2408340380396581e-035,
31, 14.011351868510246, 7.2408326912367206e-035,
31, 14.716217450797558, 1.0500501579246543e-035,
31, 14.716217458248138, 1.0500500363643936e-035,
31, 15.413793005049229, 1.6961373883454169e-036,
31, 15.413793012499809, 1.6961372726275582e-036,
31, 16.104088209569454, 3.0354866582877075e-037,
31, 16.104088217020035, 3.0354856266520219e-037,
31, 16.787098243832588, 5.9896173771901093e-038,
31, 16.787098251283169, 5.98961535516797e-038,
31, 17.462804310023785, 1.2972746518568634e-038,
31, 17.462804317474365, 1.2972745309510283e-038,
31, 18.13117404282093, 3.0713680138571644e-039,
31, 18.131174050271511, 3.0713676965074795e-039,
31, 18.79216181486845, 7.9182263243406493e-040,
31, 18.792161822319031, 7.9182241350107358e-040,
31, 19.445708937942982, 2.214898087434925e-040,
31, 19.445708945393562, 2.2148980677402555e-040,
31, 20.091743782162666, 6.6993154618323218e-041,
31, 20.091743789613247, 6.6993135377084829e-041,
31, 20.730181947350502, 2.1839810764001286e-041,
31, 20.730181954801083, 2.1839807962981238e-041,
31, 21.360926359891891, 7.6498865481473596e-042,
31, 21.360926367342472, 7.6498850691523407e-042,
31, 21.983867526054382, 2.8703402503431693e-042,
31, 21.983867533504963, 2.8703404559755345e-042,
31, 22.598883867263794, 1.1502498454193117e-042,
31, 22.598883874714375, 1.1502498916466649e-042,
31, 23.205842353403568, 4.9084725935443196e-043,
31, 23.205842360854149, 4.9084710329663892e-043,
31, 23.80459950864315, 2.2238235774505732e-043,
31, 23.804599516093731, 2.2238237880748328e-043,
31, 24.395002961158752, 1.0666581061637025e-043,
31, 24.395002968609333, 1.0666576688114463e-043,
31, 24.976893968880177, 5.3977921159553397e-044,
31, 24.976893976330757, 5.3977934865920802e-044,
31, 25.550111055374146, 2.8731051700509201e-044,
31, 25.550111062824726, 2.8731044277207976e-044,
31, 26.114495605230331, 1.6031969299858829e-044,
31, 26.114495612680912, 1.6031970042652873e-044,
31, 26.669899813830853, 9.3355015180719599e-045,
31, 26.669899821281433, 9.3355052705843679e-045,
31, 27.216198123991489, 5.6495965443312072e-045,
31, 27.21619813144207, 5.6495939839503296e-045,
31, 27.753303058445454, 3.5492321895997083e-045,
31, 27.753303065896034, 3.5492321163912673e-045,
31, 28.281186141073704, 2.2957811874765475e-045,
31, 28.281186148524284, 2.2957814583395176e-045,
31, 28.799904033541679, 1.5194259395681735e-045,
31, 28.79990404099226, 1.5194267112625272e-045,
31, 29.309627436101437, 1.0230813499247931e-045,
31, 29.309627443552017, 1.0230809924412674e-045,
31, 29.810666806995869, 6.9676223029316235e-046,
31, 29.810666814446449, 6.9676192007503771e-046,
31, 30.303484387695789, 4.8488184998921204e-046,
31, 30.30348439514637, 4.8488172078839344e-046,
31, 30.788682028651237, 3.4250229581297795e-046,
31, 30.788682036101818, 3.4250250734052242e-046,
31, 31.266962468624115, 2.4084133971405881e-046,
31, 31.266962476074696, 2.4084125559476293e-046,
31, 31.73910990357399, 1.6796117435938392e-046,
31, 31.73910991102457, 1.679611553823398e-046,
32, 0.79098659008741379, 2.3428195699417537e-008,
32, 0.79098659753799438, 2.3428153358786678e-008,
32, 1.6504944264888763, 3.2209746415594332e-011,
32, 1.6504944339394569, 3.220970087503767e-011,
32, 2.496219590306282, 9.8084828719793923e-014,
32, 2.4962195977568626, 9.8084762239900993e-014,
32, 3.3297884985804558, 5.3000509925270763e-016,
32, 3.3297885060310364, 5.3000487530063089e-016,
32, 4.152337446808815, 4.4945824866210701e-018,
32, 4.1523374542593956, 4.4945810140566077e-018,
32, 4.9646936282515526, 5.5281595989002857e-020,
32, 4.9646936357021332, 5.5281565203257855e-020,
32, 5.7674851417541504, 9.332409158236809e-022,
32, 5.767485149204731, 9.3324053526450437e-022,
32, 6.5612042769789696, 2.0758269859270062e-023,
32, 6.5612042844295502, 2.0758259829402165e-023,
32, 7.3462459221482277, 5.895162008888518e-025,
32, 7.3462459295988083, 5.8951601605246428e-025,
32, 8.1229320466518402, 2.0846533511721846e-026,
32, 8.1229320541024208, 2.0846528892286505e-026,
32, 8.8915281295776367, 8.9939213820927554e-028,
32, 8.8915281370282173, 8.9939197373278422e-028,
32, 9.6522545516490936, 4.6546437360965095e-029,
32, 9.6522545590996742, 4.6546426636937451e-029,
32, 10.405294768512249, 2.8486464379340495e-030,
32, 10.40529477596283, 2.8486455621645871e-030,
32, 11.150801315903664, 2.0365499436102757e-031,
32, 11.150801323354244, 2.0365494007674272e-031,
32, 11.888900309801102, 1.682907109838634e-032,
32, 11.888900317251682, 1.6829069079598241e-032,
32, 12.619694881141186, 1.5926342764153439e-033,
32, 12.619694888591766, 1.592634174405931e-033,
32, 13.34326783567667, 1.7120603159420472e-034,
32, 13.343267843127251, 1.7120602511528744e-034,
32, 14.059683710336685, 2.075481423520178e-035,
32, 14.059683717787266, 2.075480991830116e-035,
32, 14.768990404903889, 2.8189962905017707e-036,
32, 14.768990412354469, 2.818995942400197e-036,
32, 15.471220426261425, 4.2648503825577588e-037,
32, 15.471220433712006, 4.2648499164953187e-037,
32, 16.166391901671886, 7.1489312549880753e-038,
32, 16.166391909122467, 7.1489309687917951e-038,
32, 16.854509338736534, 1.3213054825449378e-038,
32, 16.854509346187115, 1.3213054922746664e-038,
32, 17.535564221441746, 2.6807748064712788e-039,
32, 17.535564228892326, 2.6807748199492672e-039,
32, 18.209535457193851, 5.9460888344062753e-040,
32, 18.209535464644432, 5.94608895781776e-040,
32, 18.87638970464468, 1.4363587657615266e-040,
32, 18.876389712095261, 1.4363589517907267e-040,
32, 19.536081604659557, 3.765393350640845e-041,
32, 19.536081612110138, 3.7653931802714443e-041,
32, 20.188553966581821, 1.0676300156436359e-041,
32, 20.188553974032402, 1.067629917232314e-041,
32, 20.833737879991531, 3.263757534857454e-042,
32, 20.833737887442112, 3.2637579615392064e-042,
32, 21.471552819013596, 1.0724762195516768e-042,
32, 21.471552826464176, 1.072475891341324e-042,
32, 22.101906821131706, 3.777144305210756e-043,
32, 22.101906828582287, 3.7771444342513115e-043,
32, 22.724696628749371, 1.4217203788681964e-043,
32, 22.724696636199951, 1.4217200228446998e-043,
32, 23.339808091521263, 5.703322551588163e-044,
32, 23.339808098971844, 5.7033226900296373e-044,
32, 23.947116665542126, 2.4316437058578012e-044,
32, 23.947116672992706, 2.431643496160822e-044,
32, 24.546488344669342, 1.0987930055297978e-044,
32, 24.546488352119923, 1.098793076553521e-044,
32, 25.137781016528606, 5.2484169483265025e-045,
32, 25.137781023979187, 5.2484155226682376e-045,
32, 25.720846608281136, 2.6413713577457922e-045,
32, 25.720846615731716, 2.6413705700550837e-045,
32, 26.295534215867519, 1.3965382507957447e-045,
32, 26.2955342233181, 1.3965377603185929e-045,
32, 26.861694745719433, 7.7349160811880277e-046,
32, 26.861694753170013, 7.7349151441627e-046,
32, 27.419187560677528, 4.4682520650157615e-046,
32, 27.419187568128109, 4.4682538523866773e-046,
32, 27.967889867722988, 2.6819888403852565e-046,
32, 27.967889875173569, 2.6819897728379184e-046,
32, 28.507709659636021, 1.6698136917664954e-046,
32, 28.507709667086601, 1.6698129992594366e-046,
32, 29.038602896034718, 1.0721878956432574e-046,
32, 29.038602903485298, 1.0721875356655942e-046,
32, 29.560595072805882, 7.051821086699878e-047,
32, 29.560595080256462, 7.0518182781581043e-047,
32, 30.073806069791317, 4.7259218308968253e-047,
32, 30.073806077241898, 4.7259227603342754e-047,
32, 30.578474305570126, 3.209662989709749e-047,
32, 30.578474313020706, 3.2096634823719178e-047,
32, 31.074972994625568, 2.2043194970557608e-047,
32, 31.074973002076149, 2.2043198986132966e-047,
32, 31.563809163868427, 1.5587084684342884e-047,
32, 31.563809171319008, 1.5587077448629143e-047,
32, 32.045599952340126, 1.0995759280252866e-047,
32, 32.045599959790707, 1.0995758350300892e-047,
32, 32.521030142903328, 7.709762090925553e-048,
32, 32.521030150353909, 7.7097590622875819e-048,
33, 0.79238983243703842, 2.042106061094407e-008,
33, 0.79238983988761902, 2.0421020445651014e-008,
33, 1.6530738100409508, 2.6358450934546795e-011,
33, 1.6530738174915314, 2.635841919126038e-011,
33, 2.5001910030841827, 7.5364817160196323e-014,
33, 2.5001910105347633, 7.5364760748258798e-014,
33, 3.3353501185774803, 3.8237192966188636e-016,
33, 3.3353501260280609, 3.8237162369967308e-016,
33, 4.1596754416823387, 3.0445800511517908e-018,
33, 4.1596754491329193, 3.0445787674974564e-018,
33, 4.9739858210086823, 3.515919024039416e-020,
33, 4.9739858284592628, 3.5159171374646909e-020,
33, 5.7789035513997078, 5.5725899313574696e-022,
33, 5.7789035588502884, 5.5725880635319834e-022,
33, 6.5749169737100601, 1.1637027161635936e-023,
33, 6.5749169811606407, 1.1637021424764075e-023,
33, 7.3624184802174568, 3.1025238187243698e-025,
33, 7.3624184876680374, 3.1025225685285597e-025,
33, 8.1417287290096283, 1.0299156448677693e-026,
33, 8.1417287364602089, 1.0299152761838333e-026,
33, 8.9131129011511803, 4.1710447383740305e-028,
33, 8.9131129086017609, 4.1710436855039434e-028,
33, 9.6767919734120369, 2.0262351044072931e-029,
33, 9.6767919808626175, 2.0262350205955798e-029,
33, 10.432950802147388, 1.1639387550487137e-030,
33, 10.432950809597969, 1.1639386971982789e-030,
33, 11.181744091212749, 7.8101004107994773e-032,
33, 11.18174409866333, 7.8100993240538107e-032,
33, 11.923300854861736, 6.057244317232184e-033,
33, 11.923300862312317, 6.0572438899922103e-033,
33, 12.6577278226614, 5.37984912688152e-034,
33, 12.65772783011198, 5.3798488576528694e-034,
33, 13.385112091898918, 5.4275123456899329e-035,
33, 13.385112099349499, 5.4275107204683884e-035,
33, 14.105523213744164, 6.1747593213329447e-036,
33, 14.105523221194744, 6.174759584448652e-036,
33, 14.819014765322208, 7.8706673148814995e-037,
33, 14.819014772772789, 7.8706658404194138e-037,
33, 15.525625705718994, 1.1174748948810545e-037,
33, 15.525625713169575, 1.1174747454074421e-037,
33, 16.225381337106228, 1.7579206924880998e-038,
33, 16.225381344556808, 1.7579206925033476e-038,
33, 16.918294116854668, 3.0493015445964011e-039,
33, 16.918294124305248, 3.0493005632386758e-039,
33, 17.604364313185215, 5.8065726456748308e-040,
33, 17.604364320635796, 5.8065735081689733e-040,
33, 18.283580414950848, 1.2088940527454202e-040,
33, 18.283580422401428, 1.2088939296397679e-040,
33, 18.955919578671455, 2.7413543307825419e-041,
33, 18.955919586122036, 2.7413546854069123e-041,
33, 19.621347822248936, 6.7471885014535665e-042,
33, 19.621347829699516, 6.7471864084760131e-042,
33, 20.279820293188095, 1.7965045060899062e-042,
33, 20.279820300638676, 1.796504759041087e-042,
33, 20.931281328201294, 5.158585136120737e-043,
33, 20.931281335651875, 5.1585840276484414e-043,
33, 21.575664646923542, 1.5927422905564557e-043,
33, 21.575664654374123, 1.5927419041709561e-043,
33, 22.212893404066563, 5.2728323500442264e-044,
33, 22.212893411517143, 5.272833301596633e-044,
33, 22.842880316078663, 1.8665508074309968e-044,
33, 22.842880323529243, 1.8665503929597308e-044,
33, 23.465527907013893, 7.0465510247547303e-045,
33, 23.465527914464474, 7.0465525196870561e-045,
33, 24.080728746950626, 2.8295466700413958e-045,
33, 24.080728754401207, 2.8295463117518774e-045,
33, 24.688366025686264, 1.2053907748860486e-045,
33, 24.688366033136845, 1.2053907797297697e-045,
33, 25.288314290344715, 5.4333713658348499e-046,
33, 25.288314297795296, 5.4333707575577163e-046,
33, 25.880440697073936, 2.585041776791976e-046,
33, 25.880440704524517, 2.5850416224891656e-046,
33, 26.464606821537018, 1.294202982713015e-046,
33, 26.464606828987598, 1.2942028212485916e-046,
33, 27.040671370923519, 6.7991411240400703e-047,
33, 27.0406713783741, 6.7991425220113025e-047,
33, 27.608494073152542, 3.7390875624622383e-047,
33, 27.608494080603123, 3.7390890064190258e-047,
33, 28.167941257357597, 2.1434291178003268e-047,
33, 28.167941264808178, 2.1434297287968616e-047,
33, 28.718893639743328, 1.2763496554107086e-047,
33, 28.718893647193909, 1.276349581640255e-047,
33, 29.261256985366344, 7.8765374703932726e-048,
33, 29.261256992816925, 7.8765383060880799e-048,
33, 29.794976234436035, 5.0202153746787421e-048,
33, 29.794976241886616, 5.0202165028924652e-048,
33, 30.320053435862064, 3.2803380052293672e-048,
33, 30.320053443312645, 3.2803376399507223e-048,
33, 30.836568854749203, 2.186926240398172e-048,
33, 30.836568862199783, 2.1869261872266441e-048,
33, 31.34470284730196, 1.4800222204585884e-048,
33, 31.344702854752541, 1.4800222979922586e-048,
33, 31.844753533601761, 1.0115642031264472e-048,
33, 31.844753541052341, 1.0115637741760139e-048,
33, 32.337142929434776, 7.0902267468841998e-049,
33, 32.337142936885357, 7.0902246585797814e-049,
33, 32.822405032813549, 5.0119448719507044e-049,
33, 32.82240504026413, 5.0119465060716533e-049,
33, 33.301155410706997, 3.528710823086788e-049,
33, 33.301155418157578, 3.5287089306302669e-049,
33, 33.774044148623943, 2.4656993779862083e-049,
33, 33.774044156074524, 2.4656989685917994e-049,
34, 0.79373380541801453, 1.7870320447571981e-008,
34, 0.79373381286859512, 1.7870276506455547e-008,
34, 1.6555418819189072, 2.1693956252335518e-011,
34, 1.6555418893694878, 2.169393482031388e-011,
34, 2.5039884224534035, 5.8343794749490693e-014,
34, 2.5039884299039841, 5.8343740733510059e-014,
34, 3.3406651616096497, 2.7843628540545165e-016,
34, 3.3406651690602303, 2.7843608026959051e-016,
34, 4.1666847914457321, 2.0853448751062561e-018,
34, 4.1666847988963127, 2.0853434333931684e-018,
34, 4.9828581064939499, 2.2651177977520453e-020,
34, 4.9828581139445305, 2.2651171559715021e-020,
34, 5.7898016795516014, 3.3767540686259957e-022,
34, 5.789801687002182, 3.3767524749671601e-022,
34, 6.5879999399185181, 6.6322446953759727e-024,
34, 6.5879999473690987, 6.6322430150818036e-024,
34, 7.3778426647186279, 1.6630098401402096e-025,
34, 7.3778426721692085, 1.6630090886507645e-025,
34, 8.1596490517258644, 5.1918949421969129e-027,
34, 8.159649059176445, 5.1918938102481311e-027,
34, 8.9336837232112885, 1.9774101387184887e-028,
34, 8.933683730661869, 1.9774100074245055e-028,
34, 9.7001679241657257, 9.0334282304926846e-030,
34, 9.7001679316163063, 9.0334252197952801e-030,
34, 10.45928755402565, 4.8796281980007448e-031,
34, 10.459287561476231, 4.8796275501777707e-031,
34, 11.211199007928371, 3.0788693773199207e-032,
34, 11.211199015378952, 3.0788688420038392e-032,
34, 11.956033661961555, 2.2452940986090922e-033,
34, 11.956033669412136, 2.2452936227253024e-033,
34, 12.693901240825653, 1.8750759204376034e-034,
34, 12.693901248276234, 1.8750752842804171e-034,
34, 13.424892462790012, 1.7786452616498199e-035,
34, 13.424892470240593, 1.7786446652143788e-035,
34, 14.149081096053123, 1.9025691211750822e-036,
34, 14.149081103503704, 1.9025689251028157e-036,
34, 14.866525582969189, 2.2801269981849123e-037,
34, 14.866525590419769, 2.2801266851530347e-037,
34, 15.577270358800888, 3.0437692249582344e-038,
34, 15.577270366251469, 3.0437684609885821e-038,
34, 16.281346872448921, 4.5019816965721435e-039,
34, 16.281346879899502, 4.5019810695604887e-039,
34, 16.978774391114712, 7.3425208917329903e-040,
34, 16.978774398565292, 7.3425186631243907e-040,
34, 17.669560678303242, 1.3146865852739081e-040,
34, 17.669560685753822, 1.3146863252096356e-040,
34, 18.35370247066021, 2.573793005179037e-041,
34, 18.35370247811079, 2.5737926524360587e-041,
34, 19.031185887753963, 5.4887057171033031e-042,
34, 19.031185895204544, 5.488704513022213e-042,
34, 19.701986730098724, 1.2705620774407438e-042,
34, 19.701986737549305, 1.2705617046116079e-042,
34, 20.366070702672005, 3.1822514918640349e-043,
34, 20.366070710122585, 3.1822520959707345e-043,
34, 21.023393549025059, 8.5971363864955409e-044,
34, 21.023393556475639, 8.5971368255369006e-044,
34, 21.673901222646236, 2.498003731865251e-044,
34, 21.673901230096817, 2.4980037715197431e-044,
34, 22.317529946565628, 7.7848759226391922e-045,
34, 22.317529954016209, 7.7848753371433522e-045,
34, 22.954206325113773, 2.5952409109277662e-045,
34, 22.954206332564354, 2.5952404568207584e-045,
34, 23.583847463130951, 9.2311729606610371e-046,
34, 23.583847470581532, 9.2311703994594061e-046,
34, 24.206361152231693, 3.4946377430994947e-046,
34, 24.206361159682274, 3.4946373106458168e-046,
34, 24.821646146476269, 1.404567831635744e-046,
34, 24.821646153926849, 1.4045672999262031e-046,
34, 25.429592646658421, 5.9787752597865641e-047,
34, 25.429592654109001, 5.978774144262924e-047,
34, 26.030082978308201, 2.6886705972105962e-047,
34, 26.030082985758781, 2.6886710855104201e-047,
34, 26.622992672026157, 1.2744191540785126e-047,
34, 26.622992679476738, 1.2744190635266817e-047,
34, 27.208192080259323, 6.3488544121732746e-048,
34, 27.208192087709904, 6.3488565442893872e-048,
34, 27.785548649728298, 3.3151982200499414e-048,
34, 27.785548657178879, 3.3151988733358574e-048,
34, 28.354930281639099, 1.8107632911932828e-048,
34, 28.35493028908968, 1.810762622330984e-048,
34, 28.916210018098354, 1.030369686149161e-048,
34, 28.916210025548935, 1.0303698430412018e-048,
34, 29.469272509217262, 6.0883468905536887e-049,
34, 29.469272516667843, 6.0883480072652297e-049,
34, 30.014022909104824, 3.7247230632777596e-049,
34, 30.014022916555405, 3.7247243481664488e-049,
34, 30.5503985658288, 2.3565034476155617e-049,
34, 30.550398573279381, 2.3565045469963732e-049,
34, 31.078383937478065, 1.5295192725419689e-049,
34, 31.078383944928646, 1.5295187474814393e-049,
34, 31.598028488457203, 1.0139825532853324e-049,
34, 31.598028495907784, 1.0139828355540632e-049,
34, 32.109466001391411, 6.8337062479563186e-050,
34, 32.109466008841991, 6.8337052044204809e-050,
34, 32.612932130694389, 4.6594878059160857e-050,
34, 32.61293213814497, 4.6594858546745958e-050,
34, 33.108774498105049, 3.2254931820997371e-050,
34, 33.10877450555563, 3.2254943146700602e-050,
34, 33.597449377179146, 2.2823015656071796e-050,
34, 33.597449384629726, 2.2823005358520434e-050,
34, 34.079502046108246, 1.6115058560593531e-050,
34, 34.079502053558826, 1.6115055152975725e-050,
34, 34.555533915758133, 1.1315645762275127e-050,
34, 34.555533923208714, 1.1315650253690704e-050,
35, 0.79502273350954056, 1.5696564658820398e-008,
35, 0.79502274096012115, 1.569652771494294e-008,
35, 1.6579066589474678, 1.7951755140845492e-011,
35, 1.6579066663980484, 1.795172599177779e-011,
35, 2.507624514400959, 4.5488206656301077e-014,
35, 2.5076245218515396, 4.5488171430200434e-014,
35, 3.3457516953349113, 2.0453895657036801e-016,
35, 3.3457517027854919, 2.0453878756521357e-016,
35, 4.1733897626399994, 1.4433530097271576e-018,
35, 4.17338977009058, 1.4433524229991216e-018,
35, 4.991341657936573, 1.4771508022017578e-020,
35, 4.9913416653871536, 1.4771500867280908e-020,
35, 5.8002184182405472, 2.0747399443706034e-022,
35, 5.8002184256911278, 2.0747394467376026e-022,
35, 6.6005005240440369, 3.8392364113459108e-024,
35, 6.6005005314946175, 3.8392354381122762e-024,
35, 7.3925751224160194, 9.0695765619146772e-026,
35, 7.3925751298666, 9.069572293654555e-026,
35, 8.1767597943544388, 2.6675509270034494e-027,
35, 8.1767598018050194, 2.6675506136249358e-027,
35, 8.9533184096217155, 9.5711573941640687e-029,
35, 8.9533184170722961, 9.5711567380562427e-029,
35, 9.7224722355604172, 4.1189536616823487e-030,
35, 9.7224722430109978, 4.1189526875111826e-030,
35, 10.484407857060432, 2.0959152421505451e-031,
35, 10.484407864511013, 2.0959146742138462e-031,
35, 11.239283010363579, 1.2457104495496718e-032,
35, 11.239283017814159, 1.245710395515959e-032,
35, 11.987230971455574, 8.5570757828342368e-034,
35, 11.987230978906155, 8.5570743326376781e-034,
35, 12.728363960981369, 6.731095753214648e-035,
35, 12.72836396843195, 6.731094549427605e-035,
35, 13.462775729596615, 6.013970900796823e-036,
35, 13.462775737047195, 6.0139693771309301e-036,
35, 14.190543636679649, 6.0591243108769631e-037,
35, 14.19054364413023, 6.0591231024049275e-037,
35, 14.911730267107487, 6.839443929807019e-038,
35, 14.911730274558067, 6.8394415403820541e-038,
35, 15.626384757459164, 8.5993135893576983e-039,
35, 15.626384764909744, 8.5993113703963994e-039,
35, 16.334543816745281, 1.1979757172554445e-039,
35, 16.334543824195862, 1.1979757632006563e-039,
35, 17.036232560873032, 1.8402986282934665e-040,
35, 17.036232568323612, 1.840298447545906e-040,
35, 17.731465205550194, 3.1036764541195221e-041,
35, 17.731465213000774, 3.1036753988139571e-041,
35, 18.420245580375195, 5.7234487752041445e-042,
35, 18.420245587825775, 5.7234471494298037e-042,
35, 19.102567538619041, 1.149770724442714e-042,
35, 19.102567546069622, 1.1497708502322311e-042,
35, 19.778415270149708, 2.507447858257058e-043,
35, 19.778415277600288, 2.507447274767876e-043,
35, 20.447763599455357, 5.9171812907016089e-044,
35, 20.447763606905937, 5.9171816490569785e-044,
35, 21.110578097403049, 1.5064097471606263e-044,
35, 21.11057810485363, 1.5064094343379064e-044,
35, 21.766815282404423, 4.1254753413104886e-045,
35, 21.766815289855003, 4.1254740159034148e-045,
35, 22.416422687470913, 1.2120731601684306e-045,
35, 22.416422694921494, 1.2120728149051467e-045,
35, 23.059338957071304, 3.8105029138120807e-046,
35, 23.059338964521885, 3.8105021101908041e-046,
35, 23.695493943989277, 1.278651848624312e-046,
35, 23.695493951439857, 1.2786521162296595e-046,
35, 24.324808806180954, 4.5686807873754579e-047,
35, 24.324808813631535, 4.5686813030043594e-047,
35, 24.947196207940578, 1.7340976532386943e-047,
35, 24.947196215391159, 1.7340973755762597e-047,
35, 25.562560573220253, 6.9757455173091851e-048,
35, 25.562560580670834, 6.9757442629046094e-048,
35, 26.170798495411873, 2.9671302137983893e-048,
35, 26.170798502862453, 2.9671302835781711e-048,
35, 26.771799370646477, 1.3313735478811511e-048,
35, 26.771799378097057, 1.3313732423828031e-048,
35, 27.365446366369724, 6.2883216285973802e-049,
35, 27.365446373820305, 6.2883196145848755e-049,
35, 27.951617792248726, 3.1179757440882583e-049,
35, 27.951617799699306, 3.1179754652665415e-049,
35, 28.530189104378223, 1.6188565517709766e-049,
35, 28.530189111828804, 1.6188569145137587e-049,
35, 29.101035751402378, 8.7839901000343891e-050,
35, 29.101035758852959, 8.7839933208888784e-050,
35, 29.664037145674229, 4.9628865328970608e-050,
35, 29.664037153124809, 4.9628851842787253e-050,
35, 30.219082154333591, 2.910666302031331e-050,
35, 30.219082161784172, 2.9106651919731774e-050,
35, 30.766076467931271, 1.7662748357670119e-050,
35, 30.766076475381851, 1.7662748729607436e-050,
35, 31.304952368140221, 1.1088754025811909e-050,
35, 31.304952375590801, 1.1088750925555595e-050,
35, 31.835681214928627, 7.148526917550325e-051,
35, 31.835681222379208, 7.1485250674653274e-051,
35, 32.358288533985615, 4.7111519826619542e-051,
35, 32.358288541436195, 4.7111536596976385e-051,
35, 32.872870914638042, 3.1602889534590541e-051,
35, 32.872870922088623, 3.1602885134279907e-051,
35, 33.379612505435944, 2.148091569354062e-051,
35, 33.379612512886524, 2.1480920659934694e-051,
35, 33.878796987235546, 1.4727237873765687e-051,
35, 33.878796994686127, 1.4727234796573971e-051,
35, 34.370810106396675, 1.0388313927106246e-051,
35, 34.370810113847256, 1.0388309311598943e-051,
35, 34.856128677725792, 7.3481861602270532e-052,
35, 34.856128685176373, 7.3481880076428873e-052,
35, 35.335296384990215, 5.1792611113515678e-052,
35, 35.335296392440796, 5.1792623965812728e-052,
35, 35.808892630040646, 3.6254223058064593e-052,
35, 35.808892637491226, 3.6254226968771535e-052,
36, 0.79626041650772095, 1.3835929450802035e-08,
36, 0.79626042395830154, 1.3835896181998894e-08,
36, 1.6601753905415535, 1.4931244784143379e-11,
36, 1.6601753979921341, 1.493122352780069e-11,
36, 2.5111106708645821, 3.5703899506473421e-14,
36, 2.5111106783151627, 3.5703866047036898e-14,
36, 3.3506259918212891, 1.5150630070913857e-16,
36, 3.3506259992718697, 1.5150618212430521e-16,
36, 4.1798121482133865, 1.0089426735600951e-18,
36, 4.1798121556639671, 1.0089419359975001e-18,
36, 4.9994645193219185, 9.7443777441926607e-21,
36, 4.9994645267724991, 9.7443743955897572e-21,
36, 5.8101886734366417, 1.2915850916227745e-22,
36, 5.8101886808872223, 1.2915844512005848e-22,
36, 6.6124612390995026, 2.2554128885556015e-24,
36, 6.6124612465500832, 2.2554125155276728e-24,
36, 7.4066666588187218, 5.0278360283194926e-26,
36, 7.4066666662693024, 5.0278338546774676e-26,
36, 8.1931207999587059, 1.3954345955970732e-27,
36, 8.1931208074092865, 1.3954341072244855e-27,
36, 8.972086638212204, 4.724464485871543e-29,
36, 8.9720866456627846, 4.7244634031993712e-29,
36, 9.7437852323055267, 1.9184692326394543e-30,
36, 9.7437852397561073, 1.9184685785039855e-30,
36, 10.508403599262238, 9.2110610577508696e-32,
36, 10.508403606712818, 9.2110601266004317e-32,
36, 11.266100466251373, 5.1654694352379121e-33,
36, 11.266100473701954, 5.1654692852681363e-33,
36, 12.017010666429996, 3.3478329826958101e-34,
36, 12.017010673880577, 3.3478329207700918e-34,
36, 12.761248469352722, 2.4846199342754033e-35,
36, 12.761248476803303, 2.4846197946102983e-35,
36, 13.498910188674927, 2.0944139010211171e-36,
36, 13.498910196125507, 2.0944138836963017e-36,
36, 14.230076223611832, 1.9908156870458648e-37,
36, 14.230076231062412, 1.9908153770563911e-37,
36, 14.954812712967396, 2.1201017545655606e-38,
36, 14.954812720417976, 2.1201018528061542e-38,
36, 15.673172801733017, 2.5148501205885068e-39,
36, 15.673172809183598, 2.5148494485055796e-39,
36, 16.385197751224041, 3.3052861787263118e-40,
36, 16.385197758674622, 3.3052861741406174e-40,
36, 17.090917713940144, 4.7903393120159658e-41,
36, 17.090917721390724, 4.790337928020491e-41,
36, 17.790352486073971, 7.6221913499235464e-42,
36, 17.790352493524551, 7.6221887512160983e-42,
36, 18.483512006700039, 1.3261747318690734e-42,
36, 18.48351201415062, 1.3261743247879955e-42,
36, 19.170396812260151, 2.5137057203282608e-43,
36, 19.170396819710732, 2.5137052677277973e-43,
36, 19.850998379290104, 5.1727759046768898e-44,
36, 19.850998386740685, 5.1727766444918836e-44,
36, 20.525299377739429, 1.1519505703963367e-44,
36, 20.52529938519001, 1.1519504260767373e-44,
36, 21.193273916840553, 2.7678273069030527e-45,
36, 21.193273924291134, 2.767827798374501e-45,
36, 21.854887641966343, 7.1550244945029494e-46,
36, 21.854887649416924, 7.1550255906707147e-46,
36, 22.510097898542881, 1.984671431191121e-46,
36, 22.510097905993462, 1.9846717706719504e-46,
36, 23.158853799104691, 5.8920553246780296e-47,
36, 23.158853806555271, 5.8920563816719921e-47,
36, 23.801096305251122, 1.8676209958225792e-47,
36, 23.801096312701702, 1.8676207067911573e-47,
36, 24.436758331954479, 6.3057370674808548e-48,
36, 24.43675833940506, 6.305738069895672e-48,
36, 25.06576481461525, 2.2626653116936076e-48,
36, 25.06576482206583, 2.2626651438466747e-48,
36, 25.688032925128937, 8.609447490993131e-49,
36, 25.688032932579517, 8.6094493022667365e-49,
36, 26.303472265601158, 3.4661501360200687e-49,
36, 26.303472273051739, 3.4661492034038488e-49,
36, 26.9119853079319, 1.4732834984629157e-49,
36, 26.911985315382481, 1.4732837705852057e-49,
36, 27.513467893004417, 6.5968583742268946e-50,
36, 27.513467900454998, 6.5968571516253582e-50,
36, 28.107810139656067, 3.1053437896353887e-50,
36, 28.107810147106647, 3.1053426179920777e-50,
36, 28.694897629320621, 1.5328565224865415e-50,
36, 28.694897636771202, 1.5328568405292139e-50,
36, 29.274613127112389, 7.9154003962363097e-51,
36, 29.274613134562969, 7.9153981703693011e-51,
36, 29.846839085221291, 4.2678541181450703e-51,
36, 29.846839092671871, 4.2678539866995966e-51,
36, 30.411460973322392, 2.3948652243180979e-51,
36, 30.411460980772972, 2.394865944405174e-51,
36, 30.96837193518877, 1.3944290618424927e-51,
36, 30.968371942639351, 1.3944293152714109e-51,
36, 31.5174790173769, 8.3994203358922169e-52,
36, 31.51747902482748, 8.3994196694359044e-52,
36, 32.058711349964142, 5.2303978505284272e-52,
36, 32.058711357414722, 5.2303986168397962e-52,
36, 32.592030584812164, 3.3488642311760486e-52,
36, 32.592030592262745, 3.3488629175690189e-52,
36, 33.117443718016148, 2.1935874637218713e-52,
36, 33.117443725466728, 2.1935864157428464e-52,
36, 33.635017700493336, 1.4640573341386401e-52,
36, 33.635017707943916, 1.4640577637638097e-52,
36, 34.144894443452358, 9.9145231314678597e-53,
36, 34.144894450902939, 9.9145189377303778e-53,
36, 34.647303439676762, 6.7831948011401348e-53,
36, 34.647303447127342, 6.7831938694253262e-53,
36, 35.142567783594131, 4.728695673093241e-53,
36, 35.142567791044712, 4.728693640419844e-53,
36, 35.631099842488766, 3.3479489237088613e-53,
36, 35.631099849939346, 3.3479487366331723e-53,
36, 36.1133848503232, 2.3658904809482673e-53,
36, 36.113384857773781, 2.3658904632138702e-53,
36, 36.589955143630505, 1.6633995727057523e-53,
36, 36.589955151081085, 1.6634000834145591e-53,
37, 0.79745029658079147, 1.2236661930214837e-08,
37, 0.79745030403137207, 1.2236628758929966e-08,
37, 1.6623546034097672, 1.2479305303495537e-11,
37, 1.6623546108603477, 1.2479287682904157e-11,
37, 2.5144571959972382, 2.8202775702029049e-14,
37, 2.5144572034478188, 2.8202750550262852e-14,
37, 3.3553027361631393, 1.1310984736219153e-16,
37, 3.3553027436137199, 1.1310978210383242e-16,
37, 4.1859716475009918, 7.1192220955675187e-19,
37, 4.1859716549515724, 7.1192189237113434e-19,
37, 5.0072519481182098, 6.4985394002265385e-21,
37, 5.0072519555687904, 6.4985349578088278e-21,
37, 5.8197439312934875, 8.1409638138242418e-23,
37, 5.8197439387440681, 8.1409615658792421e-23,
37, 6.623920351266861, 1.3435858973256726e-24,
37, 6.6239203587174416, 1.3435851897008275e-24,
37, 7.4201629906892776, 2.8307382521732816e-26,
37, 7.4201629981398582, 2.8307372642654064e-26,
37, 8.2087858989834785, 7.4250550358011096e-28,
37, 8.2087859064340591, 7.425054233214666e-28,
37, 8.9900510162115097, 2.3757781581308228e-29,
37, 8.9900510236620903, 2.3757776969798374e-29,
37, 9.7641790360212326, 9.117207529070504e-31,
37, 9.7641790434718132, 9.1172056695682319e-31,
37, 10.531357169151306, 4.1367659138735107e-32,
37, 10.531357176601887, 4.1367656716179671e-32,
37, 11.291744880378246, 2.1922792746035818e-33,
37, 11.291744887828827, 2.1922790321494946e-33,
37, 12.045478232204914, 1.3426890905806162e-34,
37, 12.045478239655495, 1.3426888392460162e-34,
37, 12.792673192918301, 9.4164802467780859e-36,
37, 12.792673200368881, 9.4164787873069284e-36,
37, 13.533428221940994, 7.5006766342224927e-37,
37, 13.533428229391575, 7.5006765352776218e-37,
37, 14.267826303839684, 6.7370840809894097e-38,
37, 14.267826311290264, 6.7370818558224836e-38,
37, 14.995936617255211, 6.7794683533193956e-39,
37, 14.995936624705791, 6.7794685669393241e-39,
37, 15.717815771698952, 7.5988197334410899e-40,
37, 15.717815779149532, 7.5988200044185489e-40,
37, 16.433508925139904, 9.4370881848402715e-41,
37, 16.433508932590485, 9.4370869322809968e-41,
37, 17.143050618469715, 1.2923864433326415e-41,
37, 17.143050625920296, 1.2923862031149783e-41,
37, 17.846465460956097, 1.9431631602162195e-42,
37, 17.846465468406677, 1.9431627337446246e-42,
37, 18.543768703937531, 3.1948008999823789e-43,
37, 18.543768711388111, 3.1948010113204146e-43,
37, 19.234966672956944, 5.7225142187488541e-44,
37, 19.234966680407524, 5.7225139397996951e-44,
37, 19.920057162642479, 1.1128777706945255e-44,
37, 19.92005717009306, 1.1128779257270233e-44,
37, 20.599029682576656, 2.3422790968973117e-45,
37, 20.599029690027237, 2.3422787459449697e-45,
37, 21.271865725517273, 5.3194139126989398e-46,
37, 21.271865732967854, 5.3194138487209108e-46,
37, 21.938538894057274, 1.299888245542366e-46,
37, 21.938538901507854, 1.2998883349852924e-46,
37, 22.599015057086945, 3.4089243411358843e-47,
37, 22.599015064537525, 3.408924229182079e-47,
37, 23.253252446651459, 9.5699439516338502e-48,
37, 23.253252454102039, 9.5699415030365759e-48,
37, 23.901201739907265, 2.8690919156987703e-48,
37, 23.901201747357845, 2.8690914333854321e-48,
37, 24.54280611872673, 9.1649001925442593e-49,
37, 24.542806126177311, 9.1649005780835866e-49,
37, 25.17800135165453, 3.1124278518690985e-49,
37, 25.17800135910511, 3.1124268541854008e-49,
37, 25.806715928018093, 1.1213100444461474e-49,
37, 25.806715935468674, 1.1213100629654459e-49,
37, 26.428871154785156, 4.2765508470155986e-50,
37, 26.428871162235737, 4.2765493833034662e-50,
37, 27.044381447136402, 1.7230608895836024e-50,
37, 27.044381454586983, 1.723060324124993e-50,
37, 27.653154633939266, 7.3189360531595413e-51,
37, 27.653154641389847, 7.3189369856880685e-51,
37, 28.255092471837997, 3.270635849960595e-51,
37, 28.255092479288578, 3.2706356611225313e-51,
37, 28.850091427564621, 1.5346672258666679e-51,
37, 28.850091435015202, 1.5346672310873133e-51,
37, 29.438043721020222, 7.543141992030555e-52,
37, 29.438043728470802, 7.543143707916083e-52,
37, 30.018838845193386, 3.874949153397152e-52,
37, 30.018838852643967, 3.874947763251735e-52,
37, 30.592365711927414, 2.0766876525058779e-52,
37, 30.592365719377995, 2.0766871501237398e-52,
37, 31.158515512943268, 1.1576724655066195e-52,
37, 31.158515520393848, 1.1576721953298155e-52,
37, 31.717185698449612, 6.6936395490480338e-53,
37, 31.717185705900192, 6.6936420210855687e-53,
37, 32.26828520745039, 4.0030047819768722e-53,
37, 32.26828521490097, 4.0030029042549631e-53,
37, 32.811741434037685, 2.4728033585097465e-53,
37, 32.811741441488266, 2.472804014857275e-53,
37, 33.347508952021599, 1.5724714477623819e-53,
37, 33.347508959472179, 1.572471299321689e-53,
37, 33.875580437481403, 1.0235954646285162e-53,
37, 33.875580444931984, 1.0235955617103327e-53,
37, 34.395999230444431, 6.7952496882961977e-54,
37, 34.395999237895012, 6.7952461226991219e-54,
37, 34.908872827887535, 4.5825066833067962e-54,
37, 34.908872835338116, 4.5825058071678801e-54,
37, 35.414385139942169, 3.126558694401219e-54,
37, 35.41438514739275, 3.1265575278948968e-54,
37, 35.91280460357666, 2.1535066491957579e-54,
37, 35.912804611027241, 2.153507153607943e-54,
37, 36.404484450817108, 1.5247311886236291e-54,
37, 36.404484458267689, 1.5247312487526864e-54,
37, 36.889852896332741, 1.079237350892692e-54,
37, 36.889852903783321, 1.0792377265221853e-54,
37, 37.369393646717072, 7.6138428826956967e-55,
37, 37.369393654167652, 7.6138390265469377e-55,
37, 37.843620575964451, 5.3377879130874528e-55,
37, 37.843620583415031, 5.3377878086121768e-55,
38, 0.79859550297260284, 1.0856580287562025e-08,
38, 0.79859551042318344, 1.0856554375618626e-08,
38, 1.6644502282142639, 1.0478085209213337e-11,
38, 1.6644502356648445, 1.0478073726155761e-11,
38, 2.5176734104752541, 2.2412324303407208e-14,
38, 2.5176734179258347, 2.2412296392981232e-14,
38, 3.3597952127456665, 8.5076785133405888e-17,
38, 3.3597952201962471, 8.5076706729828499e-17,
38, 4.1918860524892807, 5.0683042781997589e-19,
38, 4.1918860599398613, 5.0683022594556336e-19,
38, 5.0147268176078796, 4.378910643033748e-21,
38, 5.0147268250584602, 4.3789086546405285e-21,
38, 5.828912615776062, 5.1921247627005068e-23,
38, 5.8289126232266426, 5.1921222391432412e-23,
38, 6.6349124535918236, 8.1105425045874404e-25,
38, 6.6349124610424042, 8.110539774075029e-25,
38, 7.4331053867936134, 1.617316665311046e-26,
38, 7.433105394244194, 1.617316440770334e-26,
38, 8.2238036170601845, 4.0151378429904181e-28,
38, 8.2238036245107651, 4.015136984178548e-28,
38, 9.0072679594159126, 1.2159212965962104e-29,
38, 9.0072679668664932, 1.2159208207433248e-29,
38, 9.7837185859680176, 4.4162423160286735e-31,
38, 9.7837185934185982, 4.4162416946544442e-31,
38, 10.553342707455158, 1.8964272424010951e-32,
38, 10.553342714905739, 1.8964267905280257e-32,
38, 11.316300310194492, 9.5114672897534994e-34,
38, 11.316300317645073, 9.5114641548621261e-34,
38, 12.072728417813778, 5.5130997617066586e-35,
38, 12.072728425264359, 5.5130983436961545e-35,
38, 12.822744384407997, 3.6590686844435314e-36,
38, 12.822744391858578, 3.6590683149523385e-36,
38, 13.566448464989662, 2.758274929688359e-37,
38, 13.566448472440243, 2.7582745019573862e-37,
38, 14.303925864398479, 2.3445435874808282e-38,
38, 14.30392587184906, 2.3445436870215827e-38,
38, 15.035248324275017, 2.2326837025369582e-39,
38, 15.035248331725597, 2.2326833393720502e-39,
38, 15.760475471615791, 2.3682080599328576e-40,
38, 15.760475479066372, 2.3682075080605805e-40,
38, 16.479655846953392, 2.7832534710135998e-41,
38, 16.479655854403973, 2.7832532879192518e-41,
38, 17.192827761173248, 3.6070297549176349e-42,
38, 17.192827768623829, 3.6070286895740662e-42,
38, 17.900020033121109, 5.1323150247195217e-43,
38, 17.90002004057169, 5.1323140369858444e-43,
38, 18.601252518594265, 7.9855046226895403e-44,
38, 18.601252526044846, 7.9855030321548096e-44,
38, 19.296536602079868, 1.3536668948114345e-44,
38, 19.296536609530449, 1.3536664254310531e-44,
38, 19.985875576734543, 2.4914698664149824e-45,
38, 19.985875584185123, 2.4914700473896849e-45,
38, 20.669264905154705, 4.9631023266169206e-46,
38, 20.669264912605286, 4.9631015730240982e-46,
38, 21.346692517399788, 1.0668796068050406e-46,
38, 21.346692524850368, 1.0668792858037233e-46,
38, 22.018138960003853, 2.4679368474617229e-47,
38, 22.018138967454433, 2.46793637331118e-47,
38, 22.683577544987202, 6.1273384648171703e-48,
38, 22.683577552437782, 6.1273388538819925e-48,
38, 23.342974461615086, 1.6287464319431956e-48,
38, 23.342974469065666, 1.6287465589289163e-48,
38, 23.996288873255253, 4.6244141135970417e-49,
38, 23.996288880705833, 4.6244139707011605e-49,
38, 24.643472984433174, 1.3992813641664737e-49,
38, 24.643472991883755, 1.3992815290961278e-49,
38, 25.284472092986107, 4.5025702693911814e-50,
38, 25.284472100436687, 4.5025703981392466e-50,
38, 25.919224686920643, 1.5375035399490303e-50,
38, 25.919224694371223, 1.5375036072619918e-50,
38, 26.547662526369095, 5.5601877247885129e-51,
38, 26.547662533819675, 5.5601876296393229e-51,
38, 27.169710800051689, 2.1252757522561053e-51,
38, 27.16971080750227, 2.1252762417162567e-51,
38, 27.785288318991661, 8.5691767255137375e-52,
38, 27.785288326442242, 8.5691769176802675e-52,
38, 28.394307859241962, 3.6375520068298642e-52,
38, 28.394307866692543, 3.6375509456924231e-52,
38, 28.996676616370678, 1.6224427641883163e-52,
38, 28.996676623821259, 1.622442697148659e-52,
38, 29.592296853661537, 7.5897562486105309e-53,
38, 29.592296861112118, 7.5897537052591606e-53,
38, 30.181066893041134, 3.7153358213302024e-53,
38, 30.181066900491714, 3.7153352370458552e-53,
38, 30.762882404029369, 1.8991275765178409e-53,
38, 30.76288241147995, 1.8991268090216899e-53,
38, 31.337638281285763, 1.011897730905427e-53,
38, 31.337638288736343, 1.011898019843859e-53,
38, 31.905231095850468, 5.6053554722310255e-54,
38, 31.905231103301048, 5.6053535423071908e-54,
38, 32.465562544763088, 3.2191655316314136e-54,
38, 32.465562552213669, 3.2191654248135054e-54,
38, 33.018543861806393, 1.911716584704686e-54,
38, 33.018543869256973, 1.9117164960140519e-54,
38, 33.564101710915565, 1.1716842069253844e-54,
38, 33.564101718366146, 1.171683748939402e-54,
38, 34.102185644209385, 7.400328173238866e-55,
38, 34.102185651659966, 7.4003274298963434e-55,
38, 34.63277729600668, 4.7868574640208661e-55,
38, 34.63277730345726, 4.7868570950777136e-55,
38, 35.15590126812458, 3.1601245063659552e-55,
38, 35.155901275575161, 3.1601256141113849e-55,
38, 35.671637006103992, 2.1213819000229862e-55,
38, 35.671637013554573, 2.1213818245865819e-55,
38, 36.180130407214165, 1.4425889599279148e-55,
38, 36.180130414664745, 1.4425882771152319e-55,
38, 36.681602776050568, 9.8990384739542851e-56,
38, 36.681602783501148, 9.8990409760224132e-56,
38, 37.176354207098484, 6.9441499664883014e-56,
38, 37.176354214549065, 6.9441458354194441e-56,
38, 37.664758898317814, 4.9192031215738617e-56,
38, 37.664758905768394, 4.9192014222924419e-56,
38, 38.147251442074776, 3.4788201160648105e-56,
38, 38.147251449525356, 3.4788200837872443e-56,
38, 38.624306313693523, 2.4486355090333834e-56,
38, 38.624306321144104, 2.4486357196694196e-56,
39, 0.79969886690378189, 9.6612143778886286e-09,
39, 0.79969887435436249, 9.6611833659543116e-09,
39, 1.6664676442742348, 8.8363260213997706e-12,
39, 1.6664676517248154, 8.8363150690020779e-12,
39, 2.5207678005099297, 1.7913041342876869e-14,
39, 2.5207678079605103, 1.7913024593913769e-14,
39, 3.3641155064105988, 6.4446628031215182e-17,
39, 3.3641155138611794, 6.4446578879089881e-17,
39, 4.1975715160369873, 3.6388503086830051e-19,
39, 4.1975715234875679, 3.6388472458720568e-19,
39, 5.0219098404049873, 2.9797587595903091e-21,
39, 5.0219098478555679, 2.9797574573664833e-21,
39, 5.8377205207943916, 3.3486821124159864e-23,
39, 5.8377205282449722, 3.3486810759664543e-23,
39, 6.6454688534140587, 4.9578250919485837e-25,
39, 6.6454688608646393, 4.9578240233007194e-25,
39, 7.4455311968922615, 9.3701457525565861e-27,
39, 7.4455312043428421, 9.3701426658016626e-27,
39, 8.2382178753614426, 2.2047425437621379e-28,
39, 8.2382178828120232, 2.2047414756897301e-28,
39, 9.0237884894013405, 6.3279677678366445e-30,
39, 9.0237884968519211, 6.3279653079178988e-30,
39, 9.8024625554680824, 2.1782510395644173e-31,
39, 9.802462562918663, 2.1782507909039509e-31,
39, 10.574427150189877, 8.8650607816370113e-33,
39, 10.574427157640457, 8.8650590820738999e-33,
39, 11.339842580258846, 4.21383409134695e-34,
39, 11.339842587709427, 4.2138338754137614e-34,
39, 12.098846592009068, 2.3147510097171507e-35,
39, 12.098846599459648, 2.3147505763690007e-35,
39, 12.851557679474354, 1.4559671379309136e-36,
39, 12.851557686924934, 1.4559669477038534e-36,
39, 13.598077602684498, 1.0401252086311623e-37,
39, 13.598077610135078, 1.0401250446118563e-37,
39, 14.338493429124355, 8.3785468663638118e-39,
39, 14.338493436574936, 8.3785458033752376e-39,
39, 15.072879135608673, 7.5612898818531167e-40,
39, 15.072879143059254, 7.5612886562067478e-40,
39, 15.801296919584274, 7.6005354226141264e-41,
39, 15.801296927034855, 7.6005337498656611e-41,
39, 16.523798257112503, 8.4650896576241533e-42,
39, 16.523798264563084, 8.4650886253305973e-42,
39, 17.240424759685993, 1.0396412702585144e-42,
39, 17.240424767136574, 1.0396412770497945e-42,
39, 17.951208882033825, 1.4018620637042408e-43,
39, 17.951208889484406, 1.4018616305158902e-43,
39, 18.656174533069134, 2.067083503736078e-44,
39, 18.656174540519714, 2.0670834410366982e-44,
39, 19.355337493121624, 3.3207815601122839e-45,
39, 19.355337500572205, 3.3207812480398958e-45,
39, 20.048705853521824, 5.7925577857641326e-46,
39, 20.048705860972404, 5.7925562215888879e-46,
39, 20.73628031462431, 1.0936340009548834e-46,
39, 20.73628032207489, 1.0936338912944408e-46,
39, 21.418054424226284, 2.2282416173411488e-47,
39, 21.418054431676865, 2.2282419515714618e-47,
39, 22.094014786183834, 4.8858532361936634e-48,
39, 22.094014793634415, 4.8858528829628252e-48,
39, 22.764141239225864, 1.1499462002800235e-48,
39, 22.764141246676445, 1.1499460310878093e-48,
39, 23.428406953811646, 2.8980663905193471e-49,
39, 23.428406961262226, 2.898066276934411e-49,
39, 24.086778528988361, 7.8023090836169274e-50,
39, 24.086778536438942, 7.8023071601284799e-50,
39, 24.739216089248657, 2.2390305872090235e-50,
39, 24.739216096699238, 2.2390301640135304e-50,
39, 25.385673321783543, 6.8343680810092181e-51,
39, 25.385673329234123, 6.8343669565535207e-51,
39, 26.026097558438778, 2.2143788932280574e-51,
39, 26.026097565889359, 2.214379341700106e-51,
39, 26.660429820418358, 7.6008658486826571e-52,
39, 26.660429827868938, 7.600864771708126e-52,
39, 27.288604959845543, 2.7586423498874149e-52,
39, 27.288604967296124, 2.758642998550457e-52,
39, 27.910551734268665, 1.0566445834836509e-52,
39, 27.910551741719246, 1.0566448391841193e-52,
39, 28.526193052530289, 4.2633663243585857e-53,
39, 28.526193059980869, 4.2633674856406724e-53,
39, 29.135446235537529, 1.8086671216346443e-53,
39, 29.13544624298811, 1.8086664439032788e-53,
39, 29.738223470747471, 8.0525691421281269e-54,
39, 29.738223478198051, 8.0525661133114887e-54,
39, 30.334432370960712, 3.7560490711121251e-54,
39, 30.334432378411293, 3.7560482528346272e-54,
39, 30.923976838588715, 1.8315301227125887e-54,
39, 30.923976846039295, 1.8315294529778216e-54,
39, 31.506758250296116, 9.3176473955502718e-55,
39, 31.506758257746696, 9.3176498591590885e-55,
39, 32.082677021622658, 4.9370713759437589e-55,
39, 32.082677029073238, 4.9370727760416717e-55,
39, 32.651634819805622, 2.7182652304916268e-55,
39, 32.651634827256203, 2.7182656586123935e-55,
39, 33.213537447154522, 1.5509397574117082e-55,
39, 33.213537454605103, 1.5509397191650001e-55,
39, 33.76829868555069, 9.1478312540410161e-56,
39, 33.76829869300127, 9.1478350368113743e-56,
39, 34.315845258533955, 5.5636458609342363e-56,
39, 34.315845265984535, 5.5636451195134233e-56,
39, 34.856123223900795, 3.4904081103721966e-56,
39, 34.856123231351376, 3.4904077582346387e-56,
39, 35.389105789363384, 2.2434410644709078e-56,
39, 35.389105796813965, 2.2434413425309701e-56,
39, 35.914802670478821, 1.4725708246351153e-56,
39, 35.914802677929401, 1.4725709043207682e-56,
39, 36.433270551264286, 9.8372978663326332e-57,
39, 36.433270558714867, 9.8372937681131233e-57,
39, 36.944623731076717, 6.6643897045912897e-57,
39, 36.944623738527298, 6.6643904738423579e-57,
39, 37.449043244123459, 4.5619506187543033e-57,
39, 37.449043251574039, 4.5619516037469389e-57,
39, 37.946782201528549, 3.1638952883437559e-57,
39, 37.94678220897913, 3.1638958376894018e-57,
39, 38.438164800405502, 2.2414198125250737e-57,
39, 38.438164807856083, 2.241419676994563e-57,
39, 38.92357762157917, 1.5874855857137775e-57,
39, 38.923577629029751, 1.5874850938683276e-57,
39, 39.403453819453716, 1.1208658754145761e-57,
39, 39.403453826904297, 1.1208655216309198e-57,
39, 39.878253020346165, 7.8686506952910403e-58,
39, 39.878253027796745, 7.8686503959234645e-58,
40, 0.80076299607753754, 8.6220839569040916e-09,
40, 0.80076300352811813, 8.6220617969632951e-09,
40, 1.6684117615222931, 7.482856429765271e-12,
40, 1.6684117689728737, 7.4828434084303384e-12,
40, 2.5237480700016022, 1.4395249763313945e-14,
40, 2.5237480774521828, 1.4395234884855117e-14,
40, 3.3682745918631554, 4.914945972398221e-17,
40, 3.368274599313736, 4.9149416138302671e-17,
40, 4.2030427530407906, 2.6336469660088453e-19,
40, 4.2030427604913712, 2.6336449591696725e-19,
40, 5.0288198664784431, 2.04669313220365e-21,
40, 5.0288198739290237, 2.0466922069270797e-21,
40, 5.8461910635232925, 2.182856581073528e-23,
40, 5.8461910709738731, 2.1828557610574724e-23,
40, 6.6556179970502853, 3.0670597274357603e-25,
40, 6.6556180045008659, 3.0670587692154617e-25,
40, 7.4574743509292603, 5.5011817992950591e-27,
40, 7.4574743583798409, 5.5011804116695148e-27,
40, 8.2520685344934464, 1.2284121858449798e-28,
40, 8.2520685419440269, 1.2284119905636949e-28,
40, 9.039658859372139, 3.3459882136107596e-30,
40, 9.0396588668227196, 3.3459876354353264e-30,
40, 9.8204641044139862, 1.093046091664667e-31,
40, 9.8204641118645668, 1.093045912726458e-31,
40, 10.594671085476875, 4.221612631880723e-33,
40, 10.594671092927456, 4.2216116455431198e-33,
40, 11.362440258264542, 1.9043015174724808e-34,
40, 11.362440265715122, 1.9043013466761215e-34,
40, 12.123909913003445, 9.927033740522332e-36,
40, 12.123909920454025, 9.9270318491872625e-36,
40, 12.87919944524765, 5.9254204573291864e-37,
40, 12.879199452698231, 5.9254185761345363e-37,
40, 13.628411874175072, 4.0169933059966589e-38,
40, 13.628411881625652, 4.0169919637532185e-38,
40, 14.371635846793652, 3.0706343996807527e-39,
40, 14.371635854244232, 3.0706334592178465e-39,
40, 15.10894725471735, 2.6296368343236479e-40,
40, 15.108947262167931, 2.629636883937738e-40,
40, 15.840410508215427, 2.5083165315198936e-41,
40, 15.840410515666008, 2.508316135677605e-41,
40, 16.566079638898373, 2.6509819483710857e-42,
40, 16.566079646348953, 2.6509813339366169e-42,
40, 17.285999126732349, 3.0895557761508032e-43,
40, 17.28599913418293, 3.0895547199180405e-43,
40, 18.000204637646675, 3.9532735587946378e-44,
40, 18.000204645097256, 3.9532738604335661e-44,
40, 18.708723567426205, 5.5316336293557132e-45,
40, 18.708723574876785, 5.5316323436324288e-45,
40, 19.411575593054295, 8.4330816952067172e-46,
40, 19.411575600504875, 8.4330793832693508e-46,
40, 20.10877301543951, 1.3959734563971271e-46,
40, 20.108773022890091, 1.3959734325249744e-46,
40, 20.800321087241173, 2.5012329433504756e-47,
40, 20.800321094691753, 2.5012321368344211e-47,
40, 21.486218318343163, 4.8365841541015896e-48,
40, 21.486218325793743, 4.8365827723172397e-48,
40, 22.166456647217274, 1.0065510121004077e-48,
40, 22.166456654667854, 1.0065511177259529e-48,
40, 22.841021612286568, 2.2486596435899771e-49,
40, 22.841021619737148, 2.2486595284896741e-49,
40, 23.509892523288727, 5.3795421688687128e-50,
40, 23.509892530739307, 5.3795422441328151e-50,
40, 24.17304252833128, 1.3749934138013411e-50,
40, 24.17304253578186, 1.3749936145620943e-50,
40, 24.830438703298569, 3.7466207092405214e-51,
40, 24.830438710749149, 3.7466195892844483e-51,
40, 25.482042148709297, 1.0860643386448439e-51,
40, 25.482042156159878, 1.0860642115645083e-51,
40, 26.12780799716711, 3.3425556909891041e-52,
40, 26.127808004617691, 3.3425556313746612e-52,
40, 26.767685502767563, 1.0901108511699288e-52,
40, 26.767685510218143, 1.0901105953917385e-52,
40, 27.401618115603924, 3.7602645981940591e-53,
40, 27.401618123054504, 3.7602652607389148e-53,
40, 28.029543526470661, 1.369396504373224e-53,
40, 28.029543533921242, 1.3693960150232702e-53,
40, 28.651393860578537, 5.2556184134729698e-54,
40, 28.651393868029118, 5.2556168198097212e-54,
40, 29.267095804214478, 2.1219341342039526e-54,
40, 29.267095811665058, 2.121934465865967e-54,
40, 29.876570880413055, 8.9967556766314939e-55,
40, 29.876570887863636, 8.9967531699707271e-55,
40, 30.479735873639584, 3.9986560136554673e-55,
40, 30.479735881090164, 3.9986558489137015e-55,
40, 31.076503314077854, 1.8599753253287926e-55,
40, 31.076503321528435, 1.8599757156271693e-55,
40, 31.66678225249052, 9.0360299626257797e-56,
40, 31.666782259941101, 9.036026700725493e-56,
40, 32.250479318201542, 4.5760898608462063e-56,
40, 32.250479325652122, 4.5760887986740979e-56,
40, 32.827500082552433, 2.4117678880943317e-56,
40, 32.827500090003014, 2.4117684357547485e-56,
40, 33.397750958800316, 1.3201202030406543e-56,
40, 33.397750966250896, 1.3201196555992101e-56,
40, 33.961141757667065, 7.4847204235456685e-57,
40, 33.961141765117645, 7.4847221559011106e-57,
40, 34.517588913440704, 4.3855925974584337e-57,
40, 34.517588920891285, 4.385593435217874e-57,
40, 35.067019812762737, 2.6491586845734461e-57,
40, 35.067019820213318, 2.6491580564154119e-57,
40, 35.609378203749657, 1.6497934498550021e-57,
40, 35.609378211200237, 1.649793368648089e-57,
40, 36.144630901515484, 1.0536773043718698e-57,
40, 36.144630908966064, 1.0536776720991313e-57,
40, 36.672775842249393, 6.8759153785157124e-58,
40, 36.672775849699974, 6.8759166513298611e-58,
40, 37.193851247429848, 4.5699678490685328e-58,
40, 37.193851254880428, 4.5699698575441556e-58,
40, 37.707945220172405, 3.0831903169784489e-58,
40, 37.707945227622986, 3.0831907114952658e-58,
40, 38.215204663574696, 2.1042675579982823e-58,
40, 38.215204671025276, 2.1042678320825935e-58,
40, 38.715841598808765, 1.44772765360699e-58,
40, 38.715841606259346, 1.4477275844728336e-58,
40, 39.210134834051132, 1.0212982981853514e-58,
40, 39.210134841501713, 1.0212978783646425e-58,
40, 39.698425233364105, 7.2384658423559274e-59,
40, 39.698425240814686, 7.2384626057588699e-59,
40, 40.181104280054569, 5.1224147534757263e-59,
40, 40.18110428750515, 5.1224148163640331e-59,
40, 40.658597514033318, 3.6091357864666219e-59,
40, 40.658597521483898, 3.6091362660315758e-59,
41, 0.80179024487733841, 7.715754717994936e-09,
41, 0.80179025232791901, 7.7157302111467959e-09,
41, 1.6702870726585388, 6.3618331174118259e-12,
41, 1.6702870801091194, 6.3618226594372705e-12,
41, 2.5266212671995163, 1.162850848252617e-14,
41, 2.5266212746500969, 1.1628493459927956e-14,
41, 3.3722824975848198, 3.7724846530163349e-17,
41, 3.3722825050354004, 3.7724808311832636e-17,
41, 4.2083131596446037, 1.920778816112959e-19,
41, 4.2083131670951843, 1.9207773576706867e-19,
41, 5.0354740768671036, 1.4183648576268382e-21,
41, 5.0354740843176842, 1.4183641694691616e-21,
41, 5.8543455973267555, 1.4374026410740077e-23,
41, 5.8543456047773361, 1.4374021204448828e-23,
41, 6.6653857976198196, 1.9190885863488743e-25,
41, 6.6653858050704002, 1.919087824425809e-25,
41, 7.4689657092094421, 3.270760808097721e-27,
41, 7.4689657166600227, 3.2707591863959973e-27,
41, 8.2653918191790581, 6.9399488701523391e-29,
41, 8.2653918266296387, 6.9399461386502186e-29,
41, 9.0549211129546165, 1.7961988013370199e-30,
41, 9.0549211204051971, 1.7961986170950286e-30,
41, 9.8377715349197388, 5.5755077823717882e-32,
41, 9.8377715423703194, 5.5755069110678978e-32,
41, 10.614129528403282, 2.0461508033605068e-33,
41, 10.614129535853863, 2.0461500591140822e-33,
41, 11.384155571460724, 8.7701108074102184e-35,
41, 11.384155578911304, 8.7701090331652339e-35,
41, 12.147988334298134, 4.3440568875966986e-36,
41, 12.147988341748714, 4.3440564786178534e-36,
41, 12.905747920274734, 2.4637601753857343e-37,
41, 12.905747927725315, 2.4637596423878285e-37,
41, 13.657538384199142, 1.5870121728469763e-38,
41, 13.657538391649723, 1.5870116574060113e-38,
41, 14.403449714183807, 1.1526673651546713e-39,
41, 14.403449721634388, 1.1526669722593979e-39,
41, 15.14355943351984, 9.3791993648929087e-41,
41, 15.143559440970421, 9.3791977758924899e-41,
41, 15.877933889627457, 8.5004955033105688e-42,
41, 15.877933897078037, 8.5004957216667634e-42,
41, 16.606629312038422, 8.53610276763418e-43,
41, 16.606629319489002, 8.5361021103963203e-43,
41, 17.32969269156456, 9.4523530357048223e-44,
41, 17.329692699015141, 9.4523506752230666e-44,
41, 18.047162488102913, 1.1491939884925788e-44,
41, 18.047162495553493, 1.1491939201245561e-44,
41, 18.759069196879864, 1.5278674206431506e-45,
41, 18.759069204330444, 1.5278669100935831e-45,
41, 19.465435892343521, 2.2131950384106822e-46,
41, 19.465435899794102, 2.2131952234933592e-46,
41, 20.166278555989265, 3.4811292143934784e-47,
41, 20.166278563439846, 3.4811282177669865e-47,
41, 20.861606501042843, 5.9267645821030561e-48,
41, 20.861606508493423, 5.9267646789506383e-48,
41, 21.55142255872488, 1.089026097386482e-48,
41, 21.551422566175461, 1.089026021431083e-48,
41, 22.235723368823528, 2.1537298245085798e-49,
41, 22.235723376274109, 2.1537300799057606e-49,
41, 22.914499513804913, 4.5725708362403891e-50,
41, 22.914499521255493, 4.5725705992050573e-50,
41, 23.587735697627068, 1.0396699443959863e-50,
41, 23.587735705077648, 1.0396697016213483e-50,
41, 24.255410842597485, 2.525830841332298e-51,
41, 24.255410850048065, 2.5258301837673761e-51,
41, 24.917498178780079, 6.5425362831654044e-52,
41, 24.917498186230659, 6.5425348121202585e-52,
41, 25.573965318500996, 1.8031239693612795e-52,
41, 25.573965325951576, 1.8031234753289202e-52,
41, 26.224774323403835, 5.2769875821328614e-53,
41, 26.224774330854416, 5.276987836076435e-53,
41, 26.869881734251976, 1.6368353014029421e-53,
41, 26.869881741702557, 1.6368354177457138e-53,
41, 27.50923865288496, 5.3714024253680684e-54,
41, 27.509238660335541, 5.371403525428115e-54,
41, 28.142790779471397, 1.8614995765867043e-54,
41, 28.142790786921978, 1.8614993186913763e-54,
41, 28.770478524267673, 6.8010686240834692e-55,
41, 28.770478531718254, 6.8010665157488161e-55,
41, 29.392237104475498, 2.6151090463060908e-55,
41, 29.392237111926079, 2.6151083985090659e-55,
41, 30.00799672305584, 1.0564964051943473e-55,
41, 30.00799673050642, 1.0564965558976623e-55,
41, 30.617682799696922, 4.4769434240746522e-56,
41, 30.617682807147503, 4.476941847194843e-56,
41, 31.221216365695, 1.9865352596664337e-56,
41, 31.22121637314558, 1.9865355524875975e-56,
41, 31.818514481186867, 9.2159451402794094e-57,
41, 31.818514488637447, 9.2159466688116338e-57,
41, 32.409490957856178, 4.4613696997625097e-57,
41, 32.409490965306759, 4.4613679528438168e-57,
41, 32.994057275354862, 2.2495337343609451e-57,
41, 32.994057282805443, 2.2495336072907286e-57,
41, 33.572123780846596, 1.179515303712195e-57,
41, 33.572123788297176, 1.1795156958792046e-57,
41, 34.14360136538744, 6.4199511051895594e-58,
41, 34.14360137283802, 6.4199510962157903e-58,
41, 34.708403661847115, 3.6178146943975811e-58,
41, 34.708403669297695, 3.6178147081673786e-58,
41, 35.266449868679047, 2.1062679049212825e-58,
41, 35.266449876129627, 2.1062685252617971e-58,
41, 35.817668430507183, 1.2639711870312449e-58,
41, 35.817668437957764, 1.2639716152935793e-58,
41, 36.362001702189445, 7.8141248205685345e-59,
41, 36.362001709640026, 7.8141256095820112e-59,
41, 36.899411715567112, 4.9591961766203501e-59,
41, 36.899411723017693, 4.9591939834951158e-59,
41, 37.429887130856514, 3.2171228324064162e-59,
41, 37.429887138307095, 3.2171241631281812e-59,
41, 37.953451178967953, 2.1269491341026847e-59,
41, 37.953451186418533, 2.1269492501039519e-59,
41, 38.470170341432095, 1.4286189358117899e-59,
41, 38.470170348882675, 1.4286192796461194e-59,
41, 38.980162680149078, 9.7171129843050171e-60,
41, 38.980162687599659, 9.7171121503283134e-60,
41, 39.4836046397686, 6.6707774251818163e-60,
41, 39.483604647219181, 6.6707772095156799e-60,
41, 39.980734407901764, 4.6551475379699454e-60,
41, 39.980734415352345, 4.6551461775452092e-60,
41, 40.471850238740444, 3.2996303654595619e-60,
41, 40.471850246191025, 3.299629164010922e-60,
41, 40.957302808761597, 2.3382554940028968e-60,
41, 40.957302816212177, 2.3382555227359038e-60,
41, 41.437482245266438, 1.6521789716672249e-60,
41, 41.437482252717018, 1.6521799531621949e-60,
41, 41.912801884114742, 1.161253768520295e-60,
41, 41.912801891565323, 1.161254060902467e-60,
42, 0.80278279632329941, 6.9226590222761392e-09,
42, 0.80278280377388, 6.9226375602766169e-09,
42, 1.6720976755023003, 5.4292207524054341e-12,
42, 1.6720976829528809, 5.4292105857191855e-12,
42, 2.529393844306469, 9.4401492831892214e-15,
42, 2.5293938517570496, 9.440137562058038e-15,
42, 3.3761483952403069, 2.9133785168914818e-17,
42, 3.3761484026908875, 2.913375858396887e-17,
42, 4.2133949920535088, 1.4111373398855075e-19,
42, 4.2133949995040894, 1.4111362180318768e-19,
42, 5.0418881699442863, 9.9130527366678168e-22,
42, 5.0418881773948669, 9.9130466763312262e-22,
42, 5.8622036203742027, 9.5571596865742465e-24,
42, 5.8622036278247833, 9.557157157815258e-24,
42, 6.6747959107160568, 1.2138894993380412e-25,
42, 6.6747959181666374, 1.2138890999121016e-25,
42, 7.4800334572792053, 1.9681951625914627e-27,
42, 7.4800334647297859, 1.9681946847574354e-27,
42, 8.2782208025455475, 3.9729393004208446e-29,
42, 8.2782208099961281, 3.9729377246408213e-29,
42, 9.0696135759353638, 9.7824189185222744e-31,
42, 9.0696135833859444, 9.782415933019014e-31,
42, 9.854428842663765, 2.8887602415935609e-32,
42, 9.8544288501143456, 2.8887597673727744e-32,
42, 10.63285256922245, 1.0085526144203417e-33,
42, 10.632852576673031, 1.0085524424097982e-33,
42, 11.405045129358768, 4.1124264530225136e-35,
42, 11.405045136809349, 4.1124259662087623e-35,
42, 12.171145439147949, 1.9378425726639904e-36,
42, 12.17114544659853, 1.9378423676609656e-36,
42, 12.931274153292179, 1.045559969037066e-37,
42, 12.93127416074276, 1.0455596177818872e-37,
42, 13.685536183416843, 6.4070132508159121e-39,
42, 13.685536190867424, 6.407013282659424e-39,
42, 14.43402262032032, 4.4269253093815454e-40,
42, 14.434022627770901, 4.4269241541282206e-40,
42, 15.176812402904034, 3.4267679212328663e-41,
42, 15.176812410354614, 3.4267674343162701e-41,
42, 15.913973532617092, 2.9544897572847338e-42,
42, 15.913973540067673, 2.9544887105567143e-42,
42, 16.645564183592796, 2.8223839882129309e-43,
42, 16.645564191043377, 2.8223832928604173e-43,
42, 17.371633522212505, 2.9731354185298358e-44,
42, 17.371633529663086, 2.9731344508034859e-44,
42, 18.092222459614277, 3.4386472737376164e-45,
42, 18.092222467064857, 3.438646475084569e-45,
42, 18.807364217936993, 4.3491258313818515e-46,
42, 18.807364225387573, 4.3491245093441195e-46,
42, 19.517084851861, 5.9932507487453098e-47,
42, 19.517084859311581, 5.9932510605416288e-47,
42, 20.221403621137142, 8.9680022145373332e-48,
42, 20.221403628587723, 8.9680030564321489e-48,
42, 20.920333370566368, 1.4525643162552315e-48,
42, 20.920333378016949, 1.4525644551988813e-48,
42, 21.613880790770054, 2.5392779271460697e-49,
42, 21.613880798220634, 2.5392781202855432e-49,
42, 22.302046649158001, 4.7778624747879543e-50,
42, 22.302046656608582, 4.7778609688180624e-50,
42, 22.984826005995274, 9.6514724249543887e-51,
42, 22.984826013445854, 9.6514719380202041e-51,
42, 23.662208318710327, 2.0880714410437191e-51,
42, 23.662208326160908, 2.0880713844950678e-51,
42, 24.334177613258362, 4.8272884627393777e-52,
42, 24.334177620708942, 4.827289071207131e-52,
42, 25.000712551176548, 1.1899655825914922e-52,
42, 25.000712558627129, 1.1899654828045305e-52,
42, 25.661786533892155, 3.1214193463127235e-53,
42, 25.661786541342735, 3.1214189097750331e-53,
42, 26.317367739975452, 8.6958244653446017e-54,
42, 26.317367747426033, 8.6958215737634595e-54,
42, 26.967419199645519, 2.568029364046961e-54,
42, 26.9674192070961, 2.568029072939054e-54,
42, 27.611898817121983, 8.0249111457810081e-55,
42, 27.611898824572563, 8.0249107539069643e-55,
42, 28.250759445130825, 2.6489724041957653e-55,
42, 28.250759452581406, 2.6489725573532699e-55,
42, 28.883948929607868, 9.2210130457023447e-56,
42, 28.883948937058449, 9.221012553865369e-56,
42, 29.51141019910574, 3.3793032788582558e-56,
42, 29.51141020655632, 3.3793020931771187e-56,
42, 30.133081384003162, 1.3017207647702263e-56,
42, 30.133081391453743, 1.3017209766503453e-56,
42, 30.748895935714245, 5.2620269591213157e-57,
42, 30.748895943164825, 5.2620264324839771e-57,
42, 31.358782909810543, 2.2286239885660763e-57,
42, 31.358782917261124, 2.2286233962325355e-57,
42, 31.962667249143124, 9.8734765335665241e-58,
42, 31.962667256593704, 9.8734771638543485e-58,
42, 32.560470215976238, 4.5689315053016582e-58,
42, 32.560470223426819, 4.5689315012563647e-58,
42, 33.152110017836094, 2.204279572077455e-58,
42, 33.152110025286674, 2.2042786952183643e-58,
42, 33.737502619624138, 1.1068187252756619e-58,
42, 33.737502627074718, 1.1068183477512304e-58,
42, 34.316562816500664, 5.7749063078169861e-59,
42, 34.316562823951244, 5.7749039481390523e-59,
42, 34.88920570909977, 3.1261765683062832e-59,
42, 34.88920571655035, 3.1261767380643983e-59,
42, 35.455348581075668, 1.7513391881906954e-59,
42, 35.455348588526249, 1.7513391738815631e-59,
42, 36.014913402497768, 1.0132955667514977e-59,
42, 36.014913409948349, 1.0132953554711642e-59,
42, 36.567829996347427, 6.0419225386156667e-60,
42, 36.567830003798008, 6.0419249645517703e-60,
42, 37.114040024578571, 3.7084880489823353e-60,
42, 37.114040032029152, 3.70848786570471e-60,
42, 37.653502009809017, 2.338854994512836e-60,
42, 37.653502017259598, 2.3388544174312297e-60,
42, 38.18619729578495, 1.5082771906917482e-60,
42, 38.186197303235531, 1.5082768335011839e-60,
42, 38.712137028574944, 9.9179507405724581e-61,
42, 38.712137036025524, 9.9179533842514018e-61,
42, 39.231369808316231, 6.6305438401582333e-61,
42, 39.231369815766811, 6.6305466146285408e-61,
42, 39.743989452719688, 4.4929623334862857e-61,
42, 39.743989460170269, 4.4929644560224335e-61,
42, 40.250141784548759, 3.0762046694284016e-61,
42, 40.25014179199934, 3.0762050675393587e-61,
42, 40.750029072165489, 2.1232133872540221e-61,
42, 40.75002907961607, 2.1232143184545875e-61,
42, 41.243910521268845, 1.5040992206787617e-61,
42, 41.243910528719425, 1.5040994366927394e-61,
42, 41.732097789645195, 1.066568753779962e-61,
42, 41.732097797095776, 1.0665688191693734e-61,
42, 42.21494534611702, 7.5520351086269267e-62,
42, 42.2149453535676, 7.5520324461586611e-62,
42, 42.692836992442608, 5.3257794840175116e-62,
42, 42.692836999893188, 5.3257796543161497e-62,
43, 0.80374263972043991, 6.2265229208281086e-09,
43, 0.80374264717102051, 6.2265021676836063e-09,
43, 1.6738473474979401, 4.6500497846984813e-12,
43, 1.6738473549485207, 4.6500437983955095e-12,
43, 2.5320717096328735, 7.6999297251521244e-15,
43, 2.5320717170834541, 7.6999200444794929e-15,
43, 3.3798806890845299, 2.2631148188373452e-17,
43, 3.3798806965351105, 2.2631134624768674e-17,
43, 4.2182994857430458, 1.0439730347593901e-19,
43, 4.2182994931936264, 1.0439725582552017e-19,
43, 5.0480765253305435, 6.9846384600905826e-22,
43, 5.0480765327811241, 6.9846329992999297e-22,
43, 5.8697829768061638, 6.4133648817528039e-24,
43, 5.8697829842567444, 6.4133622301576819e-24,
43, 6.6838699728250504, 7.7581908507981851e-26,
43, 6.683869980275631, 7.7581869040059224e-26,
43, 7.4907033443450928, 1.1980536998817066e-27,
43, 7.4907033517956734, 1.1980533287085893e-27,
43, 8.2905857041478157, 2.3032904037204204e-29,
43, 8.2905857115983963, 2.3032899434237301e-29,
43, 9.0837712809443474, 5.4014825819620076e-31,
43, 9.083771288394928, 5.4014818234672467e-31,
43, 9.8704762011766434, 1.5191783549612291e-32,
43, 9.870476208627224, 1.519177820284746e-32,
43, 10.650885902345181, 5.0515644746481509e-34,
43, 10.650885909795761, 5.0515633182229788e-34,
43, 11.425160549581051, 1.9618008332053675e-35,
43, 11.425160557031631, 1.9618004402996259e-35,
43, 12.193439178168774, 8.8044787784929281e-37,
43, 12.193439185619354, 8.8044753063642099e-37,
43, 12.955842867493629, 4.524398586238088e-38,
43, 12.95584287494421, 4.5243971572220065e-38,
43, 13.712477192282677, 2.6405415266954578e-39,
43, 13.712477199733257, 2.6405409196625623e-39,
43, 14.463434211909771, 1.7376536138713058e-40,
43, 14.463434219360352, 1.7376535898353172e-40,
43, 15.20879402756691, 1.2810567130050931e-41,
43, 15.20879403501749, 1.2810562769780531e-41,
43, 15.948626108467579, 1.0519315407923782e-42,
43, 15.948626115918159, 1.0519312156263242e-42,
43, 16.682990290224552, 9.5706606808167989e-44,
43, 16.682990297675133, 9.5706595162643238e-44,
43, 17.411937654018402, 9.6019964557800178e-45,
43, 17.411937661468983, 9.6019932159219121e-45,
43, 18.13551127165556, 1.0576852894588731e-45,
43, 18.13551127910614, 1.0576850398218628e-45,
43, 18.853746756911278, 1.2740748320858259e-46,
43, 18.853746764361858, 1.2740744275602638e-46,
43, 19.566672801971436, 1.6721803291553602e-47,
43, 19.566672809422016, 1.6721802496179909e-47,
43, 20.274311557412148, 2.3831385055210507e-48,
43, 20.274311564862728, 2.383138722927918e-48,
43, 20.976678997278214, 3.6764564183028991e-49,
43, 20.976679004728794, 3.6764551742830879e-49,
43, 21.673785232007504, 6.1214527112754142e-50,
43, 21.673785239458084, 6.1214517381911048e-50,
43, 22.365634694695473, 1.0970868259989562e-50,
43, 22.365634702146053, 1.0970869292873099e-50,
43, 23.052226364612579, 2.1109654457950782e-51,
43, 23.05222637206316, 2.1109648351815291e-51,
43, 23.73355396091938, 4.3504475736244337e-52,
43, 23.733553968369961, 4.3504474174699854e-52,
43, 24.409606009721756, 9.5811885685959652e-53,
43, 24.409606017172337, 9.5811865620694161e-53,
43, 25.080366007983685, 2.2501451275878645e-53,
43, 25.080366015434265, 2.250144411912722e-53,
43, 25.745812483131886, 5.6237768952562137e-54,
43, 25.745812490582466, 5.6237769737644979e-54,
43, 26.405919045209885, 1.4929156510239942e-54,
43, 26.405919052660465, 1.4929154295863137e-54,
43, 27.060654483735561, 4.2017660690891096e-55,
43, 27.060654491186142, 4.2017661352698133e-55,
43, 27.70998277515173, 1.2515559328727676e-55,
43, 27.70998278260231, 1.2515561411826354e-55,
43, 28.353863142430782, 3.9386790330335798e-56,
43, 28.353863149881363, 3.938678699998805e-56,
43, 28.992250114679337, 1.30742297126559e-56,
43, 28.992250122129917, 1.3074227853186405e-56,
43, 29.625093564391136, 4.5703490079865401e-57,
43, 29.625093571841717, 4.5703489945165746e-57,
43, 30.252338789403439, 1.679839691186224e-57,
43, 30.252338796854019, 1.6798400103101351e-57,
43, 30.873926617205143, 6.4818615616990382e-58,
43, 30.873926624655724, 6.4818617121955273e-58,
43, 31.489793568849564, 2.6216783109665946e-58,
43, 31.489793576300144, 2.621678842878726e-58,
43, 32.099872037768364, 1.1097966007180264e-58,
43, 32.099872045218945, 1.1097965164251156e-58,
43, 32.704090610146523, 4.9093647055745871e-59,
43, 32.704090617597103, 4.9093629238590932e-59,
43, 33.302374452352524, 2.2663027175130519e-59,
43, 33.302374459803104, 2.2663030381968129e-59,
43, 33.894645825028419, 1.089821777981862e-59,
43, 33.894645832479, 1.0898215996640809e-59,
43, 34.480824865400791, 5.4503470421960063e-60,
43, 34.480824872851372, 5.4503475216165703e-60,
43, 35.060830503702164, 2.8302994788743613e-60,
43, 35.060830511152744, 2.8302993299817642e-60,
43, 35.634581781923771, 1.5241498107793508e-60,
43, 35.634581789374352, 1.524150366688098e-60,
43, 36.201999485492706, 8.4901039478581528e-61,
43, 36.201999492943287, 8.4901057099943408e-61,
43, 36.763008333742619, 4.8826921073920482e-61,
43, 36.763008341193199, 4.88269148765274e-61,
43, 37.317539721727371, 2.89325097146544e-61,
43, 37.317539729177952, 2.8932501406101497e-61,
43, 37.865535192191601, 1.763384563649848e-61,
43, 37.865535199642181, 1.763384206032246e-61,
43, 38.406950734555721, 1.1052474884369675e-61,
43, 38.406950742006302, 1.1052472149923624e-61,
43, 38.941761992871761, 7.0853082671685455e-62,
43, 38.941762000322342, 7.0853089890115881e-62,
43, 39.46997033059597, 4.6335481062213602e-62,
43, 39.469970338046551, 4.6335497917407068e-62,
43, 39.991609625518322, 3.0826746406189898e-62,
43, 39.991609632968903, 3.0826749253707252e-62,
43, 40.506753340363503, 2.0804026345727385e-62,
43, 40.506753347814083, 2.0804017787903443e-62,
43, 41.015521101653576, 1.4200099809529536e-62,
43, 41.015521109104156, 1.420009712483586e-62,
43, 41.518083661794662, 9.7731968830010019e-63,
43, 41.518083669245243, 9.7731991835116888e-63,
43, 42.014664947986603, 6.8583190565524262e-63,
43, 42.014664955437183, 6.8583151787402871e-63,
43, 42.505540028214455, 4.8636242162072754e-63,
43, 42.505540035665035, 4.8636220226399413e-63,
43, 42.991028398275375, 3.448316649423409e-63,
43, 42.991028405725956, 3.4483150726159365e-63,
43, 43.471483275294304, 2.4381653298784023e-63,
43, 43.471483282744884, 2.4381645543034918e-63,
43, 43.947278343141079, 1.7155393308219594e-63,
43, 43.94727835059166, 1.7155397584796518e-63,
44, 0.80467161536216736, 5.6136778930781251e-09,
44, 0.80467162281274796, 5.6136608371297985e-09,
44, 1.6755395382642746, 3.996456677211653e-12,
44, 1.6755395457148552, 3.996449766244987e-12,
44, 2.5346603021025658, 6.3089402910587147e-15,
44, 2.5346603095531464, 6.308934747725832e-15,
44, 3.3834870904684067, 1.7678471267789971e-17,
44, 3.3834870979189873, 1.7678457325653622e-17,
44, 4.2230369374155998, 7.7750648421336081e-20,
44, 4.2230369448661804, 7.775059336381719e-20,
44, 5.0540523454546928, 4.9595393901990306e-22,
44, 5.0540523529052734, 4.9595359464101014e-22,
44, 5.8771000504493713, 4.3418177822464477e-24,
44, 5.8771000578999519, 4.3418159986033655e-24,
44, 6.692627839744091, 5.0077047309676213e-26,
44, 6.6926278471946716, 5.0077018300841822e-26,
44, 7.5009989961981773, 7.3731092712775596e-28,
44, 7.5009990036487579, 7.3731071442298436e-28,
44, 8.3025142028927803, 1.35151930219129e-29,
44, 8.3025142103433609, 1.3515188596538854e-29,
44, 9.0974262878298759, 3.0219530142929182e-31,
44, 9.0974262952804565, 3.0219525157972958e-31,
44, 9.885950393974781, 8.1037515418772692e-33,
44, 9.8859504014253616, 8.1037496721190902e-33,
44, 10.668271347880363, 2.5692524853802503e-34,
44, 10.668271355330944, 2.5692522872428457e-34,
44, 11.444549031555653, 9.5134883272533602e-36,
44, 11.444549039006233, 9.5134851368063353e-36,
44, 12.214922517538071, 4.0709150121215076e-37,
44, 12.214922524988651, 4.0709145082759209e-37,
44, 12.9795131534338, 1.9945846540912174e-38,
44, 12.97951316088438, 1.9945845789467207e-38,
44, 13.738427057862282, 1.1099089234391263e-39,
44, 13.738427065312862, 1.1099085251966313e-39,
44, 14.491757087409496, 6.9640101710065686e-41,
44, 14.491757094860077, 6.9640078677027602e-41,
44, 15.239584363996983, 4.8951439415325917e-42,
44, 15.239584371447563, 4.8951421880711173e-42,
44, 15.981979586184025, 3.8325250997128576e-43,
44, 15.981979593634605, 3.8325246691666718e-43,
44, 16.719004042446613, 3.3246034933715899e-44,
44, 16.719004049897194, 3.3246028367467908e-44,
44, 17.450710512697697, 3.1802402277522236e-45,
44, 17.450710520148277, 3.1802402020461697e-45,
44, 18.177143938839436, 3.3400774233097505e-46,
44, 18.177143946290016, 3.3400767496533442e-46,
44, 18.898342065513134, 3.8361752046986516e-47,
44, 18.898342072963715, 3.8361742569729389e-47,
44, 19.614335909485817, 4.800572916017465e-48,
44, 19.614335916936398, 4.8005724839761991e-48,
44, 20.325150176882744, 6.5233421352255798e-49,
44, 20.325150184333324, 6.5233403168874937e-49,
44, 21.030803643167019, 9.5954871171553862e-50,
44, 21.030803650617599, 9.5954850050970341e-50,
44, 21.731309413909912, 1.5234114031559522e-50,
44, 21.731309421360493, 1.5234111451311826e-50,
44, 22.42667518556118, 2.6033920081158185e-51,
44, 22.426675193011761, 2.6033911145943002e-51,
44, 23.116903461515903, 4.7767105988238726e-52,
44, 23.116903468966484, 4.7767099043402472e-52,
44, 23.801991693675518, 9.387467949055562e-53,
44, 23.801991701126099, 9.3874684263904844e-53,
44, 24.481932438910007, 1.971615201422645e-53,
44, 24.481932446360588, 1.9716152109831415e-53,
44, 25.156713478267193, 4.4159911548218363e-54,
44, 25.156713485717773, 4.4159913675159231e-54,
44, 25.826317891478539, 1.0526730104836363e-54,
44, 25.826317898929119, 1.0526729250930486e-54,
44, 26.490724146366119, 2.6655572078148186e-55,
44, 26.4907241538167, 2.6655568543053462e-55,
44, 27.149906150996685, 7.1568186823845456e-56,
44, 27.149906158447266, 7.1568199199919761e-56,
44, 27.803833283483982, 2.0339107389822583e-56,
44, 27.803833290934563, 2.0339100579837449e-56,
44, 28.452470488846302, 6.1079388232656124e-57,
44, 28.452470496296883, 6.1079379800803341e-57,
44, 29.095778256654739, 1.9351084823971883e-57,
44, 29.09577826410532, 1.9351087848232976e-57,
44, 29.733712695538998, 6.4577619511222403e-58,
44, 29.733712702989578, 6.4577623280174925e-58,
44, 30.366225592792034, 2.2665241394008965e-58,
44, 30.366225600242615, 2.2665233610200225e-58,
44, 30.993264488875866, 8.3538981878075504e-59,
44, 30.993264496326447, 8.3538973902278832e-59,
44, 31.614772744476795, 3.228699802800217e-59,
44, 31.614772751927376, 3.2286992972912687e-59,
44, 32.230689719319344, 1.3065931274581666e-59,
44, 32.230689726769924, 1.3065932206329812e-59,
44, 32.840950936079025, 5.5283283462661653e-60,
44, 32.840950943529606, 5.5283297905073914e-60,
44, 33.445488356053829, 2.4420363935005462e-60,
44, 33.44548836350441, 2.4420365090235068e-60,
44, 34.044230751693249, 1.1247018428087803e-60,
44, 34.044230759143829, 1.1247019447882527e-60,
44, 34.637104175984859, 5.3916101329900339e-61,
44, 34.63710418343544, 5.3916117966603539e-61,
44, 35.224032618105412, 2.6860578423081937e-61,
44, 35.224032625555992, 2.6860582812593381e-61,
44, 35.80493887513876, 1.3884862436203571e-61,
44, 35.80493888258934, 1.3884857125492079e-61,
44, 36.379745692014694, 7.4395293787923654e-62,
44, 36.379745699465275, 7.439531573426712e-62,
44, 36.948377177119255, 4.1213785665077009e-62,
44, 36.948377184569836, 4.1213775271898848e-62,
44, 37.510760769248009, 2.3563995586116442e-62,
44, 37.510760776698589, 2.3563998572726389e-62,
44, 38.066829569637775, 1.387825922758731e-62,
44, 38.066829577088356, 1.3878263222132413e-62,
44, 38.616525396704674, 8.4026868409755843e-63,
44, 38.616525404155254, 8.4026849826191917e-63,
44, 39.15980252623558, 5.2330380914494507e-63,
44, 39.159802533686161, 5.2330384337581212e-63,
44, 39.696632169187069, 3.334915925394798e-63,
44, 39.69663217663765, 3.3349150946973438e-63,
44, 40.227007821202278, 2.1688592245996604e-63,
44, 40.227007828652859, 2.1688582534753389e-63,
44, 40.750951237976551, 1.4357225842013951e-63,
44, 40.750951245427132, 1.4357220404846224e-63,
44, 41.268518827855587, 9.6476907882532163e-64,
44, 41.268518835306168, 9.6476938144334747e-64,
44, 41.779807850718498, 6.5625953469000859e-64,
44, 41.779807858169079, 6.5625937860509035e-64,
44, 42.284961640834808, 4.5058398148726142e-64,
44, 42.284961648285389, 4.5058416997625145e-64,
44, 42.784172587096691, 3.129001741872849e-64,
44, 42.784172594547272, 3.1290032694075403e-64,
44, 43.277681954205036, 2.2178639138343572e-64,
44, 43.277681961655617, 2.217862574017806e-64,
44, 43.765775695443153, 1.5734475453107395e-64,
44, 43.765775702893734, 1.5734473760285837e-64,
44, 44.248776264488697, 1.1146763587781778e-64,
44, 44.248776271939278, 1.1146759216720561e-64,
44, 44.72703155875206, 7.8671948445613079e-65,
44, 44.727031566202641, 7.8671929349871774e-65,
45, 0.80557141453027725, 5.0726413534345763e-09,
45, 0.80557142198085785, 5.0726286490438008e-09,
45, 1.6771774515509605, 3.4460674497709128e-12,
45, 1.6771774590015411, 3.4460610672915812e-12,
45, 2.5371646136045456, 5.1916332019115706e-15,
45, 2.5371646210551262, 5.1916266282356591e-15,
45, 3.3869747146964073, 1.388371209350898e-17,
45, 3.3869747221469879, 1.3883700616973645e-17,
45, 4.2276168465614319, 5.8275697184933708e-20,
45, 4.2276168540120125, 5.8275654750778e-20,
45, 5.0598277673125267, 3.5477579887516431e-22,
45, 5.0598277747631073, 3.5477564975097925e-22,
45, 5.8841698914766312, 2.9642841271070067e-24,
45, 5.8841698989272118, 2.9642822863171458e-24,
45, 6.7010877579450607, 3.2630738774830459e-26,
45, 6.7010877653956413, 3.263073017156076e-26,
45, 7.5109421014785767, 4.5854715121871508e-28,
45, 7.5109421089291573, 4.5854688992980262e-28,
45, 8.3140317350625992, 8.0223903144934105e-30,
45, 8.3140317425131798, 8.0223889424453224e-30,
45, 9.1106080338358879, 1.7120675939027816e-31,
45, 9.1106080412864685, 1.7120672151200833e-31,
45, 9.9008851423859596, 4.3820095981211352e-33,
45, 9.9008851498365402, 4.3820077220180574e-33,
45, 10.68504723161459, 1.3260186203855025e-34,
45, 10.68504723906517, 1.3260184368382346e-34,
45, 11.463253825902939, 4.6864022295376335e-36,
45, 11.463253833353519, 4.6864003438291794e-36,
45, 12.235643930733204, 1.9140332469174886e-37,
45, 12.235643938183784, 1.9140329245548746e-37,
45, 13.002339072525501, 8.9509286929604941e-39,
45, 13.002339079976082, 8.9509255547380081e-39,
45, 13.763445809483528, 4.7540198232627669e-40,
45, 13.763445816934109, 4.754018125249747e-40,
45, 14.519057631492615, 2.8470235348619623e-41,
45, 14.519057638943195, 2.8470231939414067e-41,
45, 15.269256517291069, 1.9100959307121379e-42,
45, 15.26925652474165, 1.9100954215055896e-42,
45, 16.014114238321781, 1.4273575426163056e-43,
45, 16.014114245772362, 1.4273572183784119e-43,
45, 16.753693364560604, 1.1818045387769778e-44,
45, 16.753693372011185, 1.1818045406989631e-44,
45, 17.488048121333122, 1.0790078448072891e-45,
45, 17.488048128783703, 1.0790075019516635e-45,
45, 18.217225149273872, 1.0816351664675249e-46,
45, 18.217225156724453, 1.0816350186856221e-46,
45, 18.941264040768147, 1.1857252783860139e-47,
45, 18.941264048218727, 1.1857253231470769e-47,
45, 19.660197868943214, 1.4162599457171879e-48,
45, 19.660197876393795, 1.4162594722619744e-48,
45, 20.374053634703159, 1.8369095424586302e-49,
45, 20.37405364215374, 1.8369090653707792e-49,
45, 21.082852572202682, 2.5790366146060495e-50,
45, 21.082852579653263, 2.5790364403184686e-50,
45, 21.786610469222069, 3.9082959513144336e-51,
45, 21.786610476672649, 3.9082953206667202e-51,
45, 22.485337935388088, 6.3752648464290151e-52,
45, 22.485337942838669, 6.3752654487505152e-52,
45, 23.17904057353735, 1.1165741627665863e-52,
45, 23.17904058098793, 1.1165741068514325e-52,
45, 23.867719195783138, 2.0946976196525122e-53,
45, 23.867719203233719, 2.0946972972903319e-53,
45, 24.551369942724705, 4.199784043907654e-54,
45, 24.551369950175285, 4.1997830354107881e-54,
45, 25.229984417557716, 8.9802156001108849e-55,
45, 25.229984425008297, 8.9802170199891646e-55,
45, 25.903549753129482, 2.0437739932039704e-55,
45, 25.903549760580063, 2.0437737107632989e-55,
45, 26.572048746049404, 4.9412956452360819e-56,
45, 26.572048753499985, 4.9412949268715549e-56,
45, 27.235459871590137, 1.266852119595342e-56,
45, 27.235459879040718, 1.266851943610651e-56,
45, 27.893757358193398, 3.4382556738087285e-57,
45, 27.893757365643978, 3.4382553299106011e-57,
45, 28.546911224722862, 9.8618508840267625e-58,
45, 28.546911232173443, 9.8618491033618367e-58,
45, 29.194887325167656, 2.9846563929548203e-58,
45, 29.194887332618237, 2.9846556456038703e-58,
45, 29.837647385895252, 9.5164851985855428e-59,
45, 29.837647393345833, 9.5164859067162488e-59,
45, 30.475149028003216, 3.1919471145235652e-59,
45, 30.475149035453796, 3.1919465385262668e-59,
45, 31.10734585672617, 1.1245990945651224e-59,
45, 31.10734586417675, 1.1245987676615756e-59,
45, 31.734187498688698, 4.156056326015243e-60,
45, 31.734187506139278, 4.1560548844122152e-60,
45, 32.355619706213474, 1.6087715958830335e-60,
45, 32.355619713664055, 1.6087709778691514e-60,
45, 32.971584491431713, 6.5137250453975497e-61,
45, 32.971584498882294, 6.513725581556009e-61,
45, 33.582020282745361, 2.7547442749945884e-61,
45, 33.582020290195942, 2.754744536546609e-61,
45, 34.186862200498581, 1.2151842423090292e-61,
45, 34.186862207949162, 1.2151844807083802e-61,
45, 34.786042362451553, 5.5842073878826692e-62,
45, 34.786042369902134, 5.584208841716622e-62,
45, 35.379490330815315, 2.668953446148253e-62,
45, 35.379490338265896, 2.6689534358362321e-62,
45, 35.967133708298206, 1.3247417718966731e-62,
45, 35.967133715748787, 1.3247418233453314e-62,
45, 36.54889889061451, 6.81830654860711e-63,
45, 36.54889889806509, 6.818308174202415e-63,
45, 37.124712072312832, 3.6352982698527776e-63,
45, 37.124712079763412, 3.6352977649621008e-63,
45, 37.69450056552887, 2.0032179772713561e-63,
45, 37.69450057297945, 2.0032182198683058e-63,
45, 38.258194424211979, 1.1388655591516622e-63,
45, 38.25819443166256, 1.1388660071209926e-63,
45, 38.815728560090065, 6.6679019732380082e-64,
45, 38.815728567540646, 6.6678989599996421e-64,
45, 39.367045409977436, 4.0127865735433081e-64,
45, 39.367045417428017, 4.0127869714530915e-64,
45, 39.912098117172718, 2.4823303830602347e-64,
45, 39.912098124623299, 2.4823303478495604e-64,
45, 40.450854524970055, 1.5726807857647126e-64,
45, 40.450854532420635, 1.572680157861683e-64,
45, 40.983301803469658, 1.0171102749116892e-64,
45, 40.983301810920238, 1.0171100325088395e-64,
45, 41.509451732039452, 6.6986541124123709e-65,
45, 41.509451739490032, 6.698656106772216e-65,
45, 42.029346436262131, 4.4811565030652948e-65,
45, 42.029346443712711, 4.4811552128179833e-65,
45, 42.543064199388027, 3.0368532731017174e-65,
45, 42.543064206838608, 3.0368549286644374e-65,
45, 43.050724543631077, 2.0792657453220576e-65,
45, 43.050724551081657, 2.0792648606503151e-65,
45, 43.552491940557957, 1.4343039408147246e-65,
45, 43.552491948008537, 1.4343037745621818e-65,
45, 44.048576854169369, 1.0116281113567898e-65,
45, 44.048576861619949, 1.0116281946112367e-65,
45, 44.539233565330505, 7.1772181026542797e-66,
45, 44.539233572781086, 7.1772152894419919e-66,
45, 45.024754360318184, 5.0910329745997959e-66,
45, 45.024754367768764, 5.0910353852429258e-66,
45, 45.505460530519485, 3.6018564323451954e-66,
45, 45.505460537970066, 3.6018566644727318e-66,
46, 0.80644359439611435, 4.5937276590999757e-09,
46, 0.80644360184669495, 4.5937132947588083e-09,
46, 1.6787640303373337, 2.98087274959071e-12,
46, 1.6787640377879143, 2.9808661935097509e-12,
46, 2.5395892709493637, 4.2899194266498207e-15,
46, 2.5395892783999443, 4.2899128733913176e-15,
46, 3.3903501108288765, 1.0959512621942293e-17,
46, 3.3903501182794571, 1.0959500272092307e-17,
46, 4.2320479527115822, 4.3946338657974935e-20,
46, 4.2320479601621628, 4.3946295614372081e-20,
46, 5.0654139667749405, 2.5559124327100822e-22,
46, 5.0654139742255211, 2.5559109015816517e-22,
46, 5.8910063803195953, 2.0402090976949595e-24,
46, 5.8910063877701759, 2.0402082133441809e-24,
46, 6.7092665061354637, 2.145610870292747e-26,
46, 6.7092665135860443, 2.1456095483082796e-26,
46, 7.5205526426434517, 2.8805916737655836e-28,
46, 7.5205526500940323, 2.8805901581525201e-28,
46, 8.3251616805791855, 4.8148199932649022e-30,
46, 8.3251616880297661, 4.8148180062818176e-30,
46, 9.1233435869216919, 9.8170133416748883e-32,
46, 9.1233435943722725, 9.8170091250383215e-32,
46, 9.9153114706277847, 2.4005845709495377e-33,
46, 9.9153114780783653, 2.4005840292112442e-33,
46, 10.701248779892921, 6.9403518737356291e-35,
46, 10.701248787343502, 6.9403506658677479e-35,
46, 11.481314651668072, 2.3434809696862083e-36,
46, 11.481314659118652, 2.3434804155032999e-36,
46, 12.255647927522659, 9.1445672766592834e-38,
46, 12.25564793497324, 9.144564597736229e-38,
46, 13.024370245635509, 4.0857760701521376e-39,
46, 13.02437025308609, 4.0857744961794638e-39,
46, 13.787588477134705, 2.0732944897302441e-40,
46, 13.787588484585285, 2.0732942157647581e-40,
46, 14.545396625995636, 1.1862751290774051e-41,
46, 14.545396633446217, 1.1862750069296983e-41,
46, 15.297877408564091, 7.6040389545684135e-43,
46, 15.297877416014671, 7.6040366169514959e-43,
46, 16.045103512704372, 5.4289663713334323e-44,
46, 16.045103520154953, 5.4289651014099083e-44,
46, 16.787138611078262, 4.2946308014331587e-45,
46, 16.787138618528843, 4.2946309393062078e-45,
46, 17.524038217961788, 3.7462898475103639e-46,
46, 17.524038225412369, 3.7462891712075553e-46,
46, 18.255850434303284, 3.5880254135208017e-47,
46, 18.255850441753864, 3.5880241641149892e-47,
46, 18.982616521418095, 3.7580124520341846e-48,
46, 18.982616528868675, 3.7580126105590187e-48,
46, 19.704371377825737, 4.2886328507162675e-49,
46, 19.704371385276318, 4.2886330882959628e-49,
46, 20.421144008636475, 5.3145793544475191e-50,
46, 20.421144016087055, 5.3145791023640892e-50,
46, 21.132957860827446, 7.129322161861212e-51,
46, 21.132957868278027, 7.1293220408739578e-51,
46, 21.839831113815308, 1.0322705745422839e-51,
46, 21.839831121265888, 1.0322702541941654e-51,
46, 22.541776970028877, 1.6088924619052019e-52,
46, 22.541776977479458, 1.6088926207793541e-52,
46, 23.238803811371326, 2.6924552321776528e-53,
46, 23.238803818821907, 2.6924555089976417e-53,
46, 23.93091543763876, 4.8264330441793963e-54,
46, 23.93091544508934, 4.8264333299674338e-54,
46, 24.618111185729504, 9.2467851317038458e-55,
46, 24.618111193180084, 9.246783397684182e-55,
46, 25.300386071205139, 1.8894165539320044e-55,
46, 25.30038607865572, 1.8894160802674772e-55,
46, 25.977730877697468, 4.1093484735817205e-56,
46, 25.977730885148048, 4.1093479284602969e-56,
46, 26.650132246315479, 9.4952675622529843e-57,
46, 26.65013225376606, 9.4952681597268829e-57,
46, 27.317572742700577, 2.3267585353541947e-57,
46, 27.317572750151157, 2.3267584721107382e-57,
46, 27.980030924081802, 6.0361758747634122e-58,
46, 27.980030931532383, 6.0361744186632288e-58,
46, 28.637481383979321, 1.6551114270590451e-58,
46, 28.637481391429901, 1.6551115121338961e-58,
46, 29.289894767105579, 4.7892134847685121e-59,
46, 29.28989477455616, 4.7892139632868144e-59,
46, 29.937237836420536, 1.4602051759997881e-59,
46, 29.937237843871117, 1.4602053759582893e-59,
46, 30.579473488032818, 4.68423576142464e-60,
46, 30.579473495483398, 4.6842348560181774e-60,
46, 31.216560810804367, 1.5787698767498073e-60,
46, 31.216560818254948, 1.5787694868993428e-60,
46, 31.848455116152763, 5.5827601398471846e-61,
46, 31.848455123603344, 5.5827605505046904e-61,
46, 32.475107997655869, 2.0684054277531821e-61,
46, 32.475108005106449, 2.0684050017914515e-61,
46, 33.096467457711697, 8.0184979475855917e-62,
46, 33.096467465162277, 8.0184996083569093e-62,
46, 33.712477974593639, 3.2481838404050001e-62,
46, 33.71247798204422, 3.2481845661858734e-62,
46, 34.323080711066723, 1.3730902387821525e-62,
46, 34.323080718517303, 1.3730905116669834e-62,
46, 34.928213715553284, 6.0490505093449614e-63,
46, 34.928213723003864, 6.0490502061549865e-63,
46, 35.527812235057354, 2.7738302273726239e-63,
46, 35.527812242507935, 2.7738300120352881e-63,
46, 36.121809102594852, 1.3219315330205259e-63,
46, 36.121809110045433, 1.3219315495101077e-63,
46, 36.710135266184807, 6.5381416094508987e-64,
46, 36.710135273635387, 6.5381395439195238e-64,
46, 37.29272049665451, 3.3511256183575924e-64,
46, 37.292720504105091, 3.3511253777416731e-64,
46, 37.869494251906872, 1.7782224670780664e-64,
46, 37.869494259357452, 1.7782230075236345e-64,
46, 38.440386839210987, 9.7485951877403594e-65,
46, 38.440386846661568, 9.7485987533710605e-65,
46, 39.005330882966518, 5.5118745257229395e-65,
46, 39.005330890417099, 5.5118758087036987e-65,
46, 39.564263164997101, 3.2086062422653907e-65,
46, 39.564263172447681, 3.2086059318791368e-65,
46, 40.117126934230328, 1.9195876578735422e-65,
46, 40.117126941680908, 1.9195871483787689e-65,
46, 40.663874745368958, 1.1796387047474248e-65,
46, 40.663874752819538, 1.1796390835335743e-65,
46, 41.204471878707409, 7.4302744969961591e-66,
46, 41.20447188615799, 7.4302749906208339e-66,
46, 41.738900445401669, 4.7787386204187361e-66,
46, 41.738900452852249, 4.7787368414768313e-66,
46, 42.267164044082165, 3.1309961982361379e-66,
46, 42.267164051532745, 3.1309970241249755e-66,
46, 42.789292871952057, 2.0848199024819712e-66,
46, 42.789292879402637, 2.0848208718454793e-66,
46, 43.305349059402943, 1.4072806979517762e-66,
46, 43.305349066853523, 1.4072808312475605e-66,
46, 43.815431639552116, 9.6052084550853495e-67,
46, 43.815431647002697, 9.6052117675199433e-67,
46, 44.319680452346802, 6.6113571969505894e-67,
46, 44.319680459797382, 6.6113606493408914e-67,
46, 44.818278186023235, 4.6166478078491933e-67,
46, 44.818278193473816, 4.6166471165314981e-67,
46, 45.311449721455574, 3.2739994282155191e-67,
46, 45.311449728906155, 3.2740001617951049e-67,
46, 45.799458242952824, 2.3237282013187023e-67,
46, 45.799458250403404, 2.3237271415390931e-67,
46, 46.282598368823528, 1.6469678742677118e-67,
46, 46.282598376274109, 1.6469671711065112e-67,
46, 46.761186890304089, 1.1632539359263231e-67,
46, 46.761186897754669, 1.1632546267503127e-67,
47, 0.80728960782289505, 4.168696487285219e-09,
47, 0.80728961527347565, 4.1686802748840336e-09,
47, 1.6803020089864731, 2.5862826437989554e-12,
47, 1.6803020164370537, 2.5862783742309297e-12,
47, 2.5419385433197021, 3.5589110032244365e-15,
47, 2.5419385507702827, 3.5589055350312847e-15,
47, 3.3936193436384201, 8.6937819098974955e-18,
47, 3.3936193510890007, 8.693773453710869e-18,
47, 4.236338347196579, 3.3334879834427222e-20,
47, 4.2363383546471596, 3.3334862351113778e-20,
47, 5.0708212777972221, 1.8539122147624523e-22,
47, 5.0708212852478027, 1.8539106465989753e-22,
47, 5.8976223096251488, 1.4151117759288016e-24,
47, 5.8976223170757294, 1.4151112842385029e-24,
47, 6.7171796038746834, 1.4231354913857727e-26,
47, 6.717179611325264, 1.4231349092066792e-26,
47, 7.5298490300774574, 1.8270991916084673e-28,
47, 7.529849037528038, 1.8270981509844472e-28,
47, 8.3359256163239479, 2.9204552900337321e-30,
47, 8.3359256237745285, 2.9204539068875798e-30,
47, 9.135657899081707, 5.6943540186214883e-32,
47, 9.1356579065322876, 5.694351434585495e-32,
47, 9.9292579293251038, 1.3316209970119361e-33,
47, 9.9292579367756844, 1.3316206287916541e-33,
47, 10.716908417642117, 3.681688466369277e-35,
47, 10.716908425092697, 3.6816872878015352e-35,
47, 11.498768046498299, 1.1888624622058115e-36,
47, 11.498768053948879, 1.1888620779052879e-36,
47, 12.274975448846817, 4.4364967703657409e-38,
47, 12.274975456297398, 4.4364963392181388e-38,
47, 13.045652270317078, 1.8956597245535588e-39,
47, 13.045652277767658, 1.895659468029324e-39,
47, 13.810905605554581, 9.1993530960854184e-41,
47, 13.810905613005161, 9.1993516327132913e-41,
47, 14.570829890668392, 5.0337694936051544e-42,
47, 14.570829898118973, 5.0337685733871596e-42,
47, 15.325508452951908, 3.0857782210815548e-43,
47, 15.325508460402489, 3.0857781885111563e-43,
47, 16.075014747679234, 2.1069353065285192e-44,
47, 16.075014755129814, 2.1069351219798955e-44,
47, 16.819413416087627, 1.5939494446404127e-45,
47, 16.819413423538208, 1.5939494724979777e-45,
47, 17.558761104941368, 1.3297370293876914e-46,
47, 17.558761112391949, 1.3297368751262161e-46,
47, 18.293107204139233, 1.2179710847308252e-47,
47, 18.293107211589813, 1.2179707147570524e-47,
47, 19.022494435310364, 1.2199964409560206e-48,
47, 19.022494442760944, 1.2199963161526724e-48,
47, 19.746959328651428, 1.3314974725625693e-49,
47, 19.746959336102009, 1.3314971821520744e-49,
47, 20.466532692313194, 1.5780264769522475e-50,
47, 20.466532699763775, 1.5780266017287087e-50,
47, 21.181239917874336, 2.0245178949773632e-51,
47, 21.181239925324917, 2.0245176315944763e-51,
47, 21.891101337969303, 2.8034948326469036e-52,
47, 21.891101345419884, 2.8034939685782499e-52,
47, 22.596132457256317, 4.1790008688926555e-53,
47, 22.596132464706898, 4.1790007819449501e-53,
47, 23.29634415358305, 6.688690844654884e-54,
47, 23.29634416103363, 6.6886903967838107e-54,
47, 23.99174290150404, 1.1467692853330373e-54,
47, 23.99174290895462, 1.146769186365129e-54,
47, 24.682330906391144, 2.1014056175149362e-55,
47, 24.682330913841724, 2.101405889230169e-55,
47, 25.368106223642826, 4.1070651602071193e-56,
47, 25.368106231093407, 4.1070645819933285e-56,
47, 26.04906290769577, 8.5443697879268007e-57,
47, 26.049062915146351, 8.5443710805019463e-57,
47, 26.725191041827202, 1.8886008815516421e-57,
47, 26.725191049277782, 1.8886004404999289e-57,
47, 27.396476879715919, 4.4272816933018068e-58,
47, 27.3964768871665, 4.4272808898189293e-58,
47, 28.062902852892876, 1.0988364859194886e-58,
47, 28.062902860343456, 1.0988366253920036e-58,
47, 28.724447630345821, 2.8828564728611722e-59,
47, 28.724447637796402, 2.8828560006070042e-59,
47, 29.381086193025112, 7.9823493818795601e-60,
47, 29.381086200475693, 7.9823486515529818e-60,
47, 30.032789826393127, 2.3291962093493194e-60,
47, 30.032789833843708, 2.3291961095189567e-60,
47, 30.679526172578335, 7.1518997842789854e-61,
47, 30.679526180028915, 7.1518973239508013e-61,
47, 31.321259275078773, 2.307641249370635e-61,
47, 31.321259282529354, 2.3076405172220076e-61,
47, 31.957949593663216, 7.8136659014415755e-62,
47, 31.957949601113796, 7.8136652248427256e-62,
47, 32.58955405652523, 2.7726990903841993e-62,
47, 32.589554063975811, 2.7726984868935579e-62,
47, 33.216026142239571, 1.0297785058851998e-62,
47, 33.216026149690151, 1.0297785317772547e-62,
47, 33.837315931916237, 3.9977694884441333e-63,
47, 33.837315939366817, 3.9977697411365166e-63,
47, 34.453370243310928, 1.6201996067502547e-63,
47, 34.453370250761509, 1.6201992966533348e-63,
47, 35.064132787287235, 6.8460691000177028e-64,
47, 35.064132794737816, 6.8460695120204543e-64,
47, 35.669544346630573, 3.0121713471962354e-64,
47, 35.669544354081154, 3.0121713531964038e-64,
47, 36.269543081521988, 1.3784224526611186e-64,
47, 36.269543088972569, 1.3784225213845312e-64,
47, 36.864064872264862, 6.551031389687536e-65,
47, 36.864064879715443, 6.5510309622836689e-65,
47, 37.453043811023235, 3.2290009692268078e-65,
47, 37.453043818473816, 3.2290017963920392e-65,
47, 38.036412797868252, 1.6483961550238261e-65,
47, 38.036412805318832, 1.6483964581988733e-65,
47, 38.614104360342026, 8.7068430193326876e-66,
47, 38.614104367792606, 8.7068402136754839e-66,
47, 39.186051674187183, 4.7496069713042888e-66,
47, 39.186051681637764, 4.7496053262899038e-66,
47, 39.752189837396145, 2.6711638237868345e-66,
47, 39.752189844846725, 2.6711631630388347e-66,
47, 40.312457516789436, 1.5462743542785204e-66,
47, 40.312457524240017, 1.5462749942360846e-66,
47, 40.86679895222187, 9.197576438140017e-67,
47, 40.866798959672451, 9.1975795377859577e-67,
47, 41.415166474878788, 5.6155851602094119e-67,
47, 41.415166482329369, 5.6155838713502694e-67,
47, 41.957523517310619, 3.5168645107743576e-67,
47, 41.9575235247612, 3.5168655127769924e-67,
47, 42.493848152458668, 2.2493284118817205e-67,
47, 42.493848159909248, 2.2493291438227212e-67,
47, 43.024137258529663, 1.4660650820917181e-67,
47, 43.024137265980244, 1.4660656316867027e-67,
47, 43.548411078751087, 9.7156719582995046e-68,
47, 43.548411086201668, 9.7156694474500461e-68,
47, 44.066718079149723, 6.5310259797325952e-68,
47, 44.066718086600304, 6.5310260879476081e-68,
47, 44.579139620065689, 4.442438020547419e-68,
47, 44.57913962751627, 4.4424398622724323e-68,
47, 45.085793986916542, 3.0499884991862987e-68,
47, 45.085793994367123, 3.0499874345652321e-68,
47, 45.586839035153389, 2.1083600642969428e-68,
47, 45.58683904260397, 2.1083609447567937e-68,
47, 46.082472607493401, 1.4938147144274907e-68,
47, 46.082472614943981, 1.4938153354270103e-68,
47, 46.572930358350277, 1.0602813294127947e-68,
47, 46.572930365800858, 1.0602819311490823e-68,
47, 47.058480642735958, 7.5239566886279539e-69,
47, 47.058480650186539, 7.5239599111949498e-69,
47, 47.539416998624802, 5.3260856872391961e-69,
47, 47.539417006075382, 5.3260856592438819e-69,
48, 0.8081108033657074, 3.790537216779154e-09,
48, 0.80811081081628799, 3.7905242694972794e-09,
48, 1.6817938983440399, 2.2504531682948115e-12,
48, 1.6817939057946205, 2.2504483820670804e-12,
48, 2.5442163795232773, 2.9637275510465843e-15,
48, 2.5442163869738579, 2.9637227676420457e-15,
48, 3.3967880085110664, 6.9290264628280876e-18,
48, 3.396788015961647, 6.9290183337540871e-18,
48, 4.2404954805970192, 2.5428118362391363e-20,
48, 4.2404954880475998, 2.5428091511397717e-20,
48, 5.0760592594742775, 1.3535154982948461e-22,
48, 5.0760592669248581, 1.3535145215948875e-22,
48, 5.9040295109152794, 9.8885231815640295e-25,
48, 5.90402951836586, 9.8885168237279911e-25,
48, 6.7248413637280464, 9.518302995514812e-27,
48, 6.724841371178627, 9.5183002220780383e-27,
48, 7.5388482883572578, 1.1696457368664985e-28,
48, 7.5388482958078384, 1.169645374012626e-28,
48, 8.346343457698822, 1.7894833131442889e-30,
48, 8.3463434651494026, 1.7894824081088118e-30,
48, 9.1475740000605583, 3.3397293242857729e-32,
48, 9.1475740075111389, 3.339728176140613e-32,
48, 9.9427508860826492, 7.4755270996096026e-34,
48, 9.9427508935332298, 7.4755256245678417e-34,
48, 10.732056066393852, 1.9783655047619916e-35,
48, 10.732056073844433, 1.9783652198251722e-35,
48, 11.51564771682024, 6.1149507579983915e-37,
48, 11.515647724270821, 6.1149494622707338e-37,
48, 12.293664202094078, 2.1842708433101863e-38,
48, 12.293664209544659, 2.1842700354917262e-38,
48, 13.066227130591869, 8.9337538377953074e-40,
48, 13.06622713804245, 8.9337502859897068e-40,
48, 13.833443738520145, 4.149924620485562e-41,
48, 13.833443745970726, 4.1499237221656357e-41,
48, 14.595408782362938, 2.1736394745132589e-42,
48, 14.595408789813519, 2.173638813907354e-42,
48, 15.352206096053123, 1.2754745467294774e-43,
48, 15.352206103503704, 1.2754741693102798e-43,
48, 16.103909812867641, 8.3362836739294546e-45,
48, 16.103909820318222, 8.3362820544674689e-45,
48, 16.850585393607616, 6.0368656344880979e-46,
48, 16.850585401058197, 6.0368647910276049e-46,
48, 17.592290475964546, 4.8208082646747087e-47,
48, 17.592290483415127, 4.8208065336171195e-47,
48, 18.32907559722662, 4.2267802866741478e-48,
48, 18.3290756046772, 4.2267788247523572e-48,
48, 19.060984767973423, 4.0527677000262975e-49,
48, 19.060984775424004, 4.0527678696098182e-49,
48, 19.788055963814259, 4.2340523931993972e-50,
48, 19.788055971264839, 4.2340524276091812e-50,
48, 20.510321587324142, 4.8034783455880191e-51,
48, 20.510321594774723, 4.8034780348731884e-51,
48, 21.227808803319931, 5.899186088148869e-52,
48, 21.227808810770512, 5.8991860762611689e-52,
48, 21.940539844334126, 7.8199420923371399e-53,
48, 21.940539851784706, 7.8199427514005375e-53,
48, 22.648532271385193, 1.1158743726808565e-53,
48, 22.648532278835773, 1.1158741101131104e-53,
48, 23.351799219846725, 1.7097382876171394e-54,
48, 23.351799227297306, 1.7097378990809491e-54,
48, 24.050349555909634, 2.8062000362026087e-55,
48, 24.050349563360214, 2.8062001977088843e-55,
48, 24.744188040494919, 4.9228561141945363e-56,
48, 24.744188047945499, 4.9228560221850344e-56,
48, 25.433315485715866, 9.2112000380037501e-57,
48, 25.433315493166447, 9.2111973817050768e-57,
48, 26.117728859186172, 1.8346687861945116e-57,
48, 26.117728866636753, 1.8346682350681618e-57,
48, 26.797421365976334, 3.8826606576023508e-58,
48, 26.797421373426914, 3.8826600315338496e-58,
48, 27.47238253057003, 8.7148703279250707e-59,
48, 27.472382538020611, 8.7148674108098657e-59,
48, 28.142598286271095, 2.0711829791398647e-59,
48, 28.142598293721676, 2.0711832322860257e-59,
48, 28.808050975203514, 5.203584010105859e-60,
48, 28.808050982654095, 5.2035828616190226e-60,
48, 29.468719460070133, 1.3798854862844653e-60,
48, 29.468719467520714, 1.3798850951568444e-60,
48, 30.124579109251499, 3.8565307240880389e-61,
48, 30.12457911670208, 3.8565299743759719e-61,
48, 30.775601848959923, 1.134342736876812e-61,
48, 30.775601856410503, 1.1343429076941469e-61,
48, 31.42175617814064, 3.5066060548219019e-62,
48, 31.421756185591221, 3.5066056252289294e-62,
48, 32.063007235527039, 1.1377415805787006e-62,
48, 32.063007242977619, 1.1377415420726448e-62,
48, 32.699316792190075, 3.8694437991207317e-63,
48, 32.699316799640656, 3.8694430678757391e-63,
48, 33.330643333494663, 1.3776788233453704e-63,
48, 33.330643340945244, 1.3776791661638305e-63,
48, 33.956942074000835, 5.1285952783952753e-64,
48, 33.956942081451416, 5.1285947602355625e-64,
48, 34.578165091574192, 1.9937127927134763e-64,
48, 34.578165099024773, 1.9937126593845751e-64,
48, 35.194261386990547, 8.0836531292607215e-65,
48, 35.194261394441128, 8.0836543290621667e-65,
48, 35.805177040398121, 3.4143034915050112e-65,
48, 35.805177047848701, 3.4143040521491458e-65,
48, 36.410855405032635, 1.5004193222265229e-65,
48, 36.410855412483215, 1.5004189889736636e-65,
48, 37.011237367987633, 6.8526723104762059e-66,
48, 37.011237375438213, 6.8526715926507402e-66,
};

//
// A bunch of helper functions used for calculating the coefficients:
//
boost::math::ntl::RR factorial(unsigned n)
{
   static boost::array<boost::array<boost::math::ntl::RR, 1>, 201> result; 
   static bool init = false;
   if(!init)
   {
      unsigned k = 1;
      boost::math::ntl::RR fact = 1;
      do{
         result[k-1][0] = fact;
         fact *= k++;
      }
      while(k < result.size());
      init = true;
   }
   //static const int array_size = result.size();
   if(n < result.size())
      return result[n][0];

   unsigned i = (unsigned)result.size()-1;
   boost::math::ntl::RR r = result[i][0];
   while(i < n)
      r *= ++i;
   return r;
}

template <class T>
T binomial(int n, int k, T)
{
   T result;
   if(k < 0) 
   {
      result = 0;
   }
   else if(k > n)
   {
      result = 1;
   }
   else
   {
      result = factorial(n);
      result /= factorial(k);
      result /= factorial(n-k);
   }
   return result;
}
//
// Functions for creating the matrices that generate the coefficents.
// See http://my.fit.edu/~gabdo/gamma.txt and http://www.rskey.org/gamma.htm
//
template <class T>
matrix<T> make_B(unsigned n, T)
{
   matrix<T> result(n, n);
   for(unsigned i = 0; i < n; ++i)
   {
      for(unsigned j = 0; j < n; ++j)
      {
         if(i == 0)
            result(i, j) = 1;
         else if(j >= i)
         {
            T r = binomial(i+j-1, j-i, T());
            if((j-i) %2)
               r = -r;
            result(i, j) = r;
         }
         else
            result(i, j) = 0;
      }
   }
   return result;
}

template <class T>
matrix<T> make_C(unsigned n, T)
{
   matrix<T> result(n, n);
   for(unsigned i = 0; i < n; ++i)
   {
      for(unsigned j = 0; j < n; ++j)
      {
         if((i==0) && (j == 0))
            result(i, j) = 0.5;
         else if(j > i)
            result(i, j) = 0;
         else
         {
            T r = 0;
            for(unsigned k = 0; k <= i; ++k)
            {
               r += binomial(2*i, 2*k, T()) * binomial(k, k+j-i, T());
            }
            if((i-j)%2)
               r = -r;
            result(i, j) = r;
         }
      }
   }
   return result;
}

template <class T>
matrix<T> make_D(unsigned n, T)
{
   matrix<T> result(n, n);
   for(unsigned i = 0; i < n; ++i)
   {
      for(unsigned j = 0; j < n; ++j)
      {
         if(i != j)
            result(i, j) = 0;
         else if(i == 0)
            result(i, j) = 1;
         else if(i == 1)
            result(i, j) = -1;
         else
         {
            T r = result(i-1, i-1) * (2 * (2*i - 1));
            r /= (i-1);
            result(i, j) = r;
         }
      }
   }
   return result;
}

template <class T>
matrix<T> make_F(unsigned n, T g)
{
   using namespace std;
   matrix<T> result(n, 1);
   for(unsigned i = 0; i < n; ++i)
   {
      T r = factorial(2 * i); 
      r /= factorial(i);
      r *= exp(double(i) + g + 0.5);
      r /= ldexp(1.0, (2*i)-1);
      r /= pow(g + i + 0.5, (long)i);
      r /= sqrt(g + i + 0.5);
      result(i, 0) = r;
   }
   return result;
}

template <class T>
struct lanczos_info
{
   int n;                   // number of coefficients
   T r;                     // the arbitrary parameter
   std::vector<T> c;        // the coefficients
   T err;                   // error found
};
//
// Create the coefficients, caching previous matrix values as appropriate:
//
template <class T>
lanczos_info<T> generate_lanczos(unsigned n, T g)
{
   static unsigned last_n = 0;
   static matrix<T> last_prefix;

   matrix<T> B, C, D;
   matrix<T> F, P, E, T1, T2;

   if(n == last_n)
   {
      F = make_F(n, g);
      P = prod(last_prefix, F);
   }
   else
   {
      B = make_B(n, g);
      C = make_C(n, g);
      D = make_D(n, g);
      F = make_F(n, g);

      T1 = prod(D, B);
      T2 = prod(T1, C);
      P = prod(T2, F);

      last_n = n;
      last_prefix = T2;
   }

   lanczos_info<T> result;
   result.n = n;
   result.r = g;
   for(unsigned i = 0; i < n; ++i)
      result.c.push_back(P(i, 0));

   return result;
}
//
// Returns the factorials and half factorials:
//
template <class T>
std::vector<std::vector<T> > const & get_test_data()
{
   // returns factorials and half factorials in the range [0, 100]:
   static std::vector<std::vector<T> > data;
   if(data.empty())
   {
      T fact = 1;
      int k = 1;
      std::vector<T> item;
      do
      {
         data.push_back(item);
         data.back().push_back(k-1);
         data.back().push_back(fact);
         data.back().push_back(log(fact));
         fact = fact * T(k++);
      }while(k < 100);

      fact = 0.5;
      T srpi = sqrt(boost::math::constants::pi<T>());
      T mul = 1.5;
      do{
         data.push_back(item);
         data.back().push_back(mul-1);
         data.back().push_back(fact*srpi);
         data.back().push_back(log(fact*srpi));
         fact *= mul;
         mul += 1;
      }while(mul < 100);
   }

   return data;
}

struct sort_on_0
{
   template<class T>
   bool operator ()(const T& a, const T& b)
   {
      return ((a[0]) < (b[0]));
   }
};
//
// Get test data for points near 0, 1, 2 etc.
template <class T>
std::vector<std::vector<T> > const & get_test_data_near_x(T x)
{
   // 
   // this *must* be called with a *very* high precision
   // type T in order to stand any chance of long double
   // precision results:
   //
   using namespace std;
   using namespace boost::math;
   static std::vector<std::vector<T> > data;
   static T last_x(-10000);
   if(last_x != x)
      data.clear();
   if(!data.size())
   {
      last_x = x;
      std::vector<T> item;
      for(int i = -4; i > -20; --i)
      {
         double val = ldexp(2.0, i);
         data.push_back(item);
         data.back().push_back(val+x);
         data.back().push_back(tgamma(T(val)+x));
         data.back().push_back(lgamma(T(val)+x));
         data.push_back(item);
         data.back().push_back(-val+x);
         data.back().push_back(tgamma(T(-val)+x));
         data.back().push_back(lgamma(T(-val)+x));
      }
      T v = x-0.5;
      T interval = T(1)/8;
      while(v <= x+0.5)
      {
         if((floor(v) != v) || (v > 0))
         {
            data.push_back(item);
            data.back().push_back(v);
            data.back().push_back(tgamma(v));
            data.back().push_back(lgamma(v));
         }
         v += interval;
      }
      //
      // sort data:
      //
      std::sort(data.begin(), data.end(), sort_on_0());
   }
   return data;
}

template <class T>
std::vector<std::vector<T> > const & get_test_data_near_1()
{
   return get_test_data_near_x(T(1));
}

template <class T>
std::vector<std::vector<T> > const & get_test_data_near_2()
{
   return get_test_data_near_x(T(2));
}

//
// Converts Lanczos approximation into rational form via 
// polynomial arithmetic:
//
template <class T>
struct lanczos_rational
{
   std::vector<T> num, denom;
   int N;
   T g;

   T gamma(T z)
   {
      using namespace std;
      BOOST_ASSERT(num.size() == denom.size());
      BOOST_ASSERT(num.size() == N);
      T zgh = z + g - T(0.5);
      T prefix = pow(zgh, T(z - 0.5)) / exp(zgh);
      T s1, s2;
      if(z < 1)
      {
         s1 = num[N-1];
         s2 = denom[N-1];
         for(unsigned i = N-2; i >= 0; --i)
         {
            s1 *= z;
            s2 *= z;
            s1 += num[i];
            s2 += num[i];
         }
         s1 /= s2;
         return prefix * s1;
      }
      else
      {
         z = 1/z;
         s1 = num[0];
         s2 = denom[0];
         for(int i = 1; i < N; ++i)
         {
            s1 *= z;
            s2 *= z;
            s1 += num[i];
            s2 += denom[i];
         }
         s1 /= s2;
         return prefix * s1;
      }
   }
   T factorial(T z)
   {
      return this->gamma(z+1);
   }
   template <class U>
   lanczos_rational(const lanczos_info<U>& info)
   {
      U l_denom_coef[2] = { 0, 1 };
      boost::math::tools::polynomial<U> l_denom(l_denom_coef, 1), l_num(info.c[1]);
      for(unsigned i = 2; i < info.c.size(); ++i)
      {
         l_denom_coef[0] = i - 1;
         boost::math::tools::polynomial<U> bot(l_denom_coef, 1), top(info.c[i]);
         l_num *= bot;
         top *= l_denom;
         l_denom *= bot;
         l_num += top;
      }
      l_num += l_denom * info.c[0];
      for(unsigned i = 0; i < info.c.size(); ++i)
      {
         num.push_back(boost::math::tools::real_cast<T>(l_num[i]));
         denom.push_back(boost::math::tools::real_cast<T>(l_denom[i]));
      }
      //std::cout << l_num << std::endl;
      //std::cout << l_denom << std::endl;
      BOOST_ASSERT(num.size() == l_num.degree()+1);
      BOOST_ASSERT(denom.size() == l_denom.degree()+1);
      g = boost::math::tools::real_cast<T>(info.r);
      N = info.n;
      /*
      for(unsigned i = 0; i < num.size(); ++i)
         std::cout << num[i] << " ";
      std::cout << std::endl;
      for(unsigned i = 0; i < denom.size(); ++i)
         std::cout << denom[i] << " ";
      std::cout << std::endl;
      */
   }
};
//
// Code to test an approximation against the factorials and
// half factorials, returns the max error found:
//
template <class T, class R>
T get_max_error(const lanczos_info<T>& dat, R)
{
   T max_error = 0;
   std::vector<std::vector<T> > const & tests = get_test_data<T>();
   lanczos_rational<R> rational(dat);

   for(unsigned i = 0; i < tests.size(); ++i)
   {
      R input = boost::math::tools::real_cast<R>(tests[i][0]);
      if(std::numeric_limits<R>::is_specialized && (boost::math::tools::real_cast<R>(tests[i][1]) > (std::numeric_limits<R>::max)()))
         continue;

      R gamr = rational.factorial(input);
      if(std::numeric_limits<R>::is_specialized && (gamr > (std::numeric_limits<R>::max)()))
         continue;
      T gam = gamr;
      T exp = tests[i][1];
      T err = boost::math::tools::relative_error(gam, exp);
      if(err > max_error)
         max_error = err;
   }

   return max_error;
}
//
// This is what prints the "best" approximation out as code:
//
template <class T>
void print_code(const lanczos_info<T>& l, const char* name)
{
   using namespace std;
   lanczos_info<T> l2(l);
   T factor = exp(l.r);
   for(unsigned k = 0; k < l2.c.size(); ++k)
      l2.c[k] /= factor;

   lanczos_rational<T> rat(l);
   T max_term = 0;
   for(unsigned i = 0; i < rat.denom.size(); ++i)
   {
      if(rat.denom[i] > max_term)
         max_term = rat.denom[i];
   }
   const char* denom_type;
   const char* cast_type;
   const char* suffix_type;
   if(max_term < (std::numeric_limits<boost::uint16_t>::max)())
   {
      denom_type = "boost::uint16_t";
      cast_type = "static_cast<boost::uint16_t>";
      suffix_type = "u";
   }
   else if(max_term < (std::numeric_limits<boost::uint32_t>::max)())
   {
      denom_type = "boost::uint32_t";
      cast_type = "static_cast<boost::uint32_t>";
      suffix_type = "u";
   }
#ifdef BOOST_HAS_LONG_LONG
   else if(max_term < (std::numeric_limits<boost::uint64_t>::max)())
   {
      denom_type = "boost::uint64_t";
      cast_type = "";
      suffix_type = "uLL";
   }
#endif
   else
   {
      denom_type = "T";
      cast_type = "static_cast<T>";
      suffix_type = "L";
   }
   
   std::cout <<
      "//\n"
      "// Lanczos Coefficients for N=" << l.n << " G=" << l.r << "\n"
      "// Max experimental error (with ";
   if(std::strlen(name) == 0)
      std::cout << "arbitary";
   else
      std::cout << name;
   std::cout << " precision arithmetic) " << l.err <<
      "\n// Generated with compiler: " << BOOST_COMPILER << " on " << BOOST_PLATFORM << " at " << __DATE__ << "\n"
      "//\n"
      "struct lanczos" << l.n << name << "\n"
      "{\n"
      "   template <class T>\n"
      "   static T lanczos_sum(const T& z)\n"
      "   {\n"
      "      static const T num[" << rat.num.size() << "] = {\n";

   for(unsigned i = 0; i < rat.num.size(); ++i)
   {
      std::cout << "         static_cast<T>(" << rat.num[i] << "L)";
      if(i != rat.num.size() - 1)
         std::cout << ",";
      std::cout << "\n";
   }
   std::cout << 
      "      };\n"
      "      static const " << denom_type << " denom[" << rat.denom.size() << "] = {\n";
   for(unsigned i = 0; i < rat.denom.size(); ++i)
   {
      std::cout << "         " << cast_type << "(" << rat.denom[i] << suffix_type << ")";
      if(i != rat.denom.size() - 1)
         std::cout << ",";
      std::cout << "\n";
   }
   std::cout << 
      "      };\n"
      "      return boost::math::tools::evaluate_rational(num, denom, z);\n"
      "   }\n\n"
      "   template <class T>\n"
      "   static T lanczos_sum_expG_scaled(const T& z)\n"
      "   {\n"
      "      static const T num[" << rat.num.size() << "] = {\n";

   for(unsigned i = 0; i < rat.num.size(); ++i)
   {
      std::cout << "         static_cast<T>(" << (rat.num[i]/factor) << "L)";
      if(i != rat.num.size() - 1)
         std::cout << ",";
      std::cout << "\n";
   }
   std::cout << 
      "      };\n"
      "      static const " << denom_type << " denom[" << rat.denom.size() << "] = {\n";
   for(unsigned i = 0; i < rat.denom.size(); ++i)
   {
      std::cout << "         " << cast_type << "(" << rat.denom[i] << suffix_type << ")";
      if(i != rat.denom.size() - 1)
         std::cout << ",";
      std::cout << "\n";
   }
   std::cout << 
      "      };\n"
      "      return boost::math::tools::evaluate_rational(num, denom, z);\n"
      "   }\n\n";

   std::cout <<
      "\n   template<class T>\n"
      "   static T lanczos_sum_near_1(const T& dz)\n"
      "   {\n"
      "      static const T d[" << l2.n-1 << "] = {\n";

   factor = sqrt((l.r + 0.5)/boost::math::constants::e<T>()) / exp(l.r);

   for(int i = 1; i < l.n; ++i)
   {
      std::cout << "         static_cast<T>(" << l.c[i]*factor << "L)";
      if(i != l.n - 1)
         std::cout << ",";
      std::cout << "\n";
   }
   std::cout << 
      "      };\n"
      "      T result = 0;\n"
      "      for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)\n"
      "      {\n"
      "         result += (-d[k-1]*dz)/(k*dz + k*k);\n"
      "      }\n"
      "      return result;\n"
      "   }\n";

   std::cout <<
      "\n   template<class T>\n"
      "   static T lanczos_sum_near_2(const T& dz)\n"
      "   {\n"
      "      static const T d[" << l2.n-1 << "] = {\n";

   factor = pow(boost::math::constants::e<T>()/(l.r+1.5), T(1.5)) * exp(l.r);
      //pow((l.r + 1.5)/boost::math::constants::e<T>(), 1.5) / exp(l.r);

   for(int i = 1; i < l.n; ++i)
   {
      std::cout << "         static_cast<T>(" << l.c[i]/factor << "L),\n";
   }
   std::cout << 
      "      };\n"
      "      T result = 0;\n"
      "      T z = dz + 2;\n"
      "      for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)\n"
      "      {\n"
      "         result += (-d[k-1]*dz)/(z + k*z + k*k - 1);\n"
      "      }\n"
      "      return result;\n"
      "   }\n\n"
      "   static double g(){ return " << l.r << "; }\n"
      "};\n\n";
}
//
// Print out the test values:
//
void print_test_values(const std::vector<std::vector<boost::math::ntl::RR> >& v, const char* name, int offset = 1)
{
   std::cout << "#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))\n";
   std::cout << 
      "   static const boost::array<boost::array<T, 3>, " << v.size() << "> " << name << " = {\n";
   for(unsigned i = 0; i < v.size(); ++i)
   {
      std::cout << "      SC_(" << (v[i][0] + offset) << "), SC_(" << v[i][1] << "), SC_(" << v[i][2] << "),\n";
   }
   std::cout << "   };\n#undef SC_\n\n";
}
//
// Get the error for a specific approximation, and print out it's code:
//
void calculate_lanczos_spot(int n, boost::math::ntl::RR r, const char* suffix = "")
{
   lanczos_info<boost::math::ntl::RR> info = generate_lanczos(n, r);
   // note error is calculated at high precision:
   info.err = get_max_error(info, r);
   print_code(info, suffix);
}
//
// Scan the sweet-spots for the best approximation:
//
template <class T>
void find_best_lanczos(const char* name, T eps, int max_scan = 100)
{
   using namespace std;

   lanczos_info<boost::math::ntl::RR> best;
   best.err = 100; // best case had better be better than this!
   for(int i = 0; i < sizeof(sweet_spots)/sizeof(sweet_spots[0]); ++i)
   {
      if((sweet_spots[i].err < eps*10) && (sweet_spots[i].N < max_scan))
      {
         lanczos_info<boost::math::ntl::RR> info = generate_lanczos(sweet_spots[i].N, boost::math::ntl::RR(sweet_spots[i].g));
         boost::math::ntl::RR err = get_max_error(info, eps);
         if(err/eps < 1000)
         {
            std::cout << sweet_spots[i].N << " " << sweet_spots[i].g << " " << err/eps << std::endl;
         }
         if(err < best.err)
         {
            best = info;
            best.err = err;
         }
      }
   }
   std::cout << std::endl;

   print_code(best, name);
}
int test_main(int argc, char*argv [])
{
   bool test_double(false), test_long(false), test_float(false), test_quad(false), spots(false), test_data(false);

   if(argc < 2)
   {
      std::cout << 
         "Useage:\n"
         "  -float        test type float for the best approximation\n"
         "  -double       test type double for the best approximation\n"
         "  -long-double  test type long double for the best approximation\n"
         "  -spots        print out the best cases found in previous runs\n"
         "  -data         print out the test data\n" << std::flush;
      return 0;
   }

   for(int i = 1; i < argc; ++i)
   {
      if(std::strcmp(argv[i], "-float") == 0)
         test_float = true;
      else if(std::strcmp(argv[i], "-double") == 0)
         test_double = true;
      else if(std::strcmp(argv[i], "-long-double") == 0)
         test_long = true;
      else if(std::strcmp(argv[i], "-quad-float") == 0)
         test_quad = true;
      else if(std::strcmp(argv[i], "-spots") == 0)
         spots = true;
      else if(std::strcmp(argv[i], "-data") == 0)
         test_data = true;
   }

   boost::math::ntl::RR::SetPrecision(1000);
   boost::math::ntl::RR::SetOutputPrecision(40);

   if(spots)
   {
      // these are optimal N and R from Pugh:
      calculate_lanczos_spot(61, 63.192152);
      calculate_lanczos_spot(31, 32.080670);
      calculate_lanczos_spot(6, 5.581);
      calculate_lanczos_spot(11, 10.900511);
      calculate_lanczos_spot(13, 13.144565);
      calculate_lanczos_spot(22, 22.61891);
      // these are the best cases we've already determined
      // from previous runs:
      calculate_lanczos_spot(6, 1.428456135094165802001953125);
      calculate_lanczos_spot(13, 6.024680040776729583740234375);
      calculate_lanczos_spot(17, 12.2252227365970611572265625);
      boost::math::ntl::RR::SetOutputPrecision(90);
      calculate_lanczos_spot(24, 20.3209821879863739013671875);
   }
   if(test_float)
   {
      find_best_lanczos("float", std::numeric_limits<float>::epsilon());
   }
   if(test_double)
   {
      find_best_lanczos("double", std::numeric_limits<double>::epsilon());
   }

   if(test_long)
   {
      find_best_lanczos("long_double", std::numeric_limits<long double>::epsilon());
   }
   if(test_quad)
   {
      //find_best_lanczos("quad_float", pow(NTL::quad_float(2), NTL::quad_float(-105)));
   }
   if(test_data)
   {
      std::cout << "Test Data follows:\n\n";

      boost::math::ntl::RR::SetPrecision(1000);
      
      std::vector<std::vector<boost::math::ntl::RR> > const & tests = get_test_data<boost::math::ntl::RR>();
      print_test_values(tests, "factorials");
      print_test_values(get_test_data_near_1<boost::math::ntl::RR>(), "near_1", 0);
      print_test_values(get_test_data_near_2<boost::math::ntl::RR>(), "near_2", 0);
      print_test_values(get_test_data_near_x<boost::math::ntl::RR>(boost::math::ntl::RR(0)), "near_0", 0);
      print_test_values(get_test_data_near_x<boost::math::ntl::RR>(boost::math::ntl::RR(-10)), "near_m10", 0);
      print_test_values(get_test_data_near_x<boost::math::ntl::RR>(boost::math::ntl::RR(-55)), "near_m55", 0);
   }
   return 0;
}