test_spec_functions_data.hpp 164 KB

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  1. // complex(z), n, complex(D1(n,z)), abs_err_real, abs_err_imag
  2. std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
  3. D1_test_16digits
  4. = {
  5. {{0.07425,0.0},0,{13.44325436668153,0.0},1.3e-15,0.0},
  6. {{0.07425,0.0},1,{26.92117459633998,0.0},2.7e-15,0.0},
  7. {{0.07425,0.0},2,{40.39343233283062,0.0},4.0e-15,0.0},
  8. {{0.07425,0.0},3,{53.8638034125887,0.0},5.4e-15,0.0},
  9. {{0.07425,0.0},4,{67.33331707981798,0.0},6.7e-15,0.0},
  10. {{0.07575,0.0},0,{13.17606046765979,0.0},1.3e-15,0.0},
  11. {{0.07575,0.0},1,{26.38748777963147,0.0},2.6e-15,0.0},
  12. {{0.07575,0.0},2,{39.59313798170167,0.0},4.0e-15,0.0},
  13. {{0.07575,0.0},3,{52.79686337350637,0.0},5.3e-15,0.0},
  14. {{0.07575,0.0},4,{65.99971402008605,0.0},6.6e-15,0.0},
  15. {{7.5,0.0},0,{0.3695472563090164,0.0},3.7e-17,0.0},
  16. {{7.5,0.0},1,{-4.366784043615744,0.0},4.4e-16,0.0},
  17. {{7.5,0.0},2,{-0.05084479598595977,0.0},5.1e-18,0.0},
  18. {{7.5,0.0},3,{1.818058207399475,0.0},1.8e-16,0.0},
  19. {{7.5,0.0},4,{-1.311710105034662,0.0},1.3e-16,0.0},
  20. {{7.5,0.0},5,{-0.1612017752951218,0.0},1.6e-17,0.0},
  21. {{7.5,0.0},6,{0.2403642873973738,0.0},2.4e-17,0.0},
  22. {{7.5,0.0},7,{0.509732566745001,0.0},5.1e-17,0.0},
  23. {{7.5,0.0},8,{0.7288779051967778,0.0},7.3e-17,0.0},
  24. {{7.5,0.0},9,{0.9225920223879098,0.0},9.2e-17,0.0},
  25. {{7.5,0.0},10,{1.101289075837662,0.0},1.1e-16,0.0},
  26. {{7.5,0.0},11,{1.270228055670032,0.0},1.3e-16,0.0},
  27. {{7.5,0.0},12,{1.432398653656861,0.0},1.4e-16,0.0},
  28. {{7.5,0.0},13,{1.589646926286713,0.0},1.6e-16,0.0},
  29. {{7.5,0.0},14,{1.743184380873933,0.0},1.7e-16,0.0},
  30. {{7.5,0.0},16,{2.042220854428171,0.0},2.0e-16,0.0},
  31. {{7.5,0.0},17,{2.188751725980377,0.0},2.2e-16,0.0},
  32. {{7.5,0.0},18,{2.33376648704411,0.0},2.3e-16,0.0},
  33. {{7.5,0.0},19,{2.477519013106746,0.0},2.5e-16,0.0},
  34. {{7.5,0.0},21,{2.761992897922038,0.0},2.8e-16,0.0},
  35. {{7.5,0.0},22,{2.90300061550683,0.0},2.9e-16,0.0},
  36. {{7.5,0.0},24,{3.183085123876985,0.0},3.2e-16,0.0},
  37. {{7.5,0.0},26,{3.461101068633011,0.0},3.5e-16,0.0},
  38. {{7.5,0.0},27,{3.599479435575162,0.0},3.6e-16,0.0},
  39. {{7.5,0.0},30,{4.012605389511785,0.0},4.0e-16,0.0},
  40. {{750.0,0.0},0,{-0.8951915139149222,0.0},9.0e-17,0.0},
  41. {{750.0,0.0},1,{1.114084720130935,0.0},1.1e-16,0.0},
  42. {{750.0,0.0},2,{-0.9024181120233614,0.0},9.0e-17,0.0},
  43. {{750.0,0.0},3,{1.099243620946342,0.0},1.1e-16,0.0},
  44. {{750.0,0.0},4,{-0.9194850798920686,0.0},9.2e-17,0.0},
  45. {{750.0,0.0},5,{1.073070000370522,0.0},1.1e-16,0.0},
  46. {{750.0,0.0},6,{-0.9469054237300034,0.0},9.5e-17,0.0},
  47. {{750.0,0.0},7,{1.036430596034115,0.0},1.0e-16,0.0},
  48. {{750.0,0.0},9,{0.990456172692469,0.0},9.9e-17,0.0},
  49. {{750.0,0.0},10,{-1.036746111869826,0.0},1.0e-16,0.0},
  50. {{750.0,0.0},11,{0.9364345757891685,0.0},9.4e-17,0.0},
  51. {{750.0,0.0},13,{0.875701892481254,0.0},8.8e-17,0.0},
  52. {{750.0,0.0},15,{0.8095451807506758,0.0},8.1e-17,0.0},
  53. {{750.0,0.0},18,{-1.422356478541503,0.0},1.4e-16,0.0},
  54. {{750.0,0.0},20,{-1.592210408225887,0.0},1.6e-16,0.0},
  55. {{750.0,0.0},23,{0.5110077375181897,0.0},5.1e-17,0.0},
  56. {{750.0,0.0},27,{0.3496666467211573,0.0},3.5e-17,0.0},
  57. {{750.0,0.0},31,{0.1809968576664919,0.0},1.8e-17,0.0},
  58. {{750.0,0.0},35,{0.0004860079342239934,0.0},4.9e-20,0.0},
  59. {{750.0,0.0},41,{-0.317251336807483,0.0},3.2e-17,0.0},
  60. {{750.0,0.0},47,{-0.7807372174284117,0.0},7.8e-17,0.0},
  61. {{750.0,0.0},54,{0.4580930397540441,0.0},4.6e-17,0.0},
  62. {{750.0,0.0},62,{-0.1958618028998245,0.0},2.0e-17,0.0},
  63. {{750.0,0.0},71,{0.6403656124320398,0.0},6.4e-17,0.0},
  64. {{750.0,0.0},81,{-0.4803642218027248,0.0},4.8e-17,0.0},
  65. {{750.0,0.0},93,{3.417692358670104,0.0},3.4e-16,0.0},
  66. {{750.0,0.0},107,{-0.6675908137518288,0.0},6.7e-17,0.0},
  67. {{750.0,0.0},123,{0.07336983052954298,0.0},7.3e-18,0.0},
  68. {{750.0,0.0},141,{0.01864087618833894,0.0},1.9e-18,0.0},
  69. {{750.0,0.0},162,{0.4662167115741941,0.0},4.7e-17,0.0},
  70. {{750.0,0.0},186,{1.869792416792102,0.0},1.9e-16,0.0},
  71. {{750.0,0.0},214,{-0.1962317049357189,0.0},2.0e-17,0.0},
  72. {{750.0,0.0},246,{-0.9241109217019534,0.0},9.2e-17,0.0},
  73. {{750.0,0.0},282,{-2.278752089160206,0.0},2.3e-16,0.0},
  74. {{750.0,0.0},324,{0.1492340462699953,0.0},1.5e-17,0.0},
  75. {{750.0,0.0},372,{-1.501050800107926,0.0},1.5e-16,0.0},
  76. {{750.0,0.0},427,{1.251448627689853,0.0},1.3e-16,0.0},
  77. {{750.0,0.0},490,{-2.307846776579645,0.0},2.3e-16,0.0},
  78. {{750.0,0.0},562,{-0.6678454189015009,0.0},6.7e-17,0.0},
  79. {{750.0,0.0},645,{4.123866493958505,0.0},4.1e-16,0.0},
  80. {{750.0,0.0},740,{-0.04954886515946186,0.0},5.0e-18,0.0},
  81. {{750.0,0.0},850,{0.5377162125402363,0.0},5.4e-17,0.0},
  82. {{133.0,-0.001},0,{0.5694948983815571,0.001324324427352377},5.7e-17,1.3e-19},
  83. {{133.0,-0.001},1,{-1.786944015800289,0.004193067842684484},1.8e-16,4.2e-19},
  84. {{133.0,-0.001},2,{0.5399040215866582,0.001291157104802603},5.4e-17,1.3e-19},
  85. {{133.0,-0.001},3,{-1.955480625798034,0.004823242927232421},2.0e-16,4.8e-19},
  86. {{133.0,-0.001},4,{0.4735591560334697,0.001223127495142088},4.7e-17,1.2e-19},
  87. {{133.0,-0.001},5,{-2.331337152694187,0.006433469776449445},2.3e-16,6.4e-19},
  88. {{133.0,-0.001},6,{0.3756798707528821,0.00113876079036902},3.8e-17,1.1e-19},
  89. {{133.0,-0.001},7,{-3.148105562806491,0.01090750730183105},3.1e-16,1.1e-18},
  90. {{133.0,-0.001},8,{0.2515418522954845,0.001059202692643652},2.5e-17,1.1e-19},
  91. {{133.0,-0.001},9,{-5.506034746297112,0.03131226964093978},5.5e-16,3.1e-18},
  92. {{133.0,-0.001},10,{0.1039785994199451,0.001004592673307026},1.0e-17,1.0e-19},
  93. {{133.0,-0.001},11,{-46.98874438931292,2.213832762775254},4.7e-15,2.2e-16},
  94. {{133.0,-0.001},13,{5.89811290505382,0.03577867985992821},5.9e-16,3.6e-18},
  95. {{133.0,-0.001},14,{-0.2778831807551624,0.001065347008820747},2.8e-17,1.1e-19},
  96. {{133.0,-0.001},16,{-0.5501021158428141,0.001287235517159257},5.5e-17,1.3e-19},
  97. {{133.0,-0.001},18,{-0.9604617468736273,0.001903153851503216},9.6e-17,1.9e-19},
  98. {{133.0,-0.001},20,{-1.781366135936702,0.004149533558522542},1.8e-16,4.1e-19},
  99. {{133.0,-0.001},22,{-5.364106315522472,0.02974587750840188},5.4e-16,3.0e-18},
  100. {{133.0,-0.001},24,{5.606849372659069,0.03240384877063995},5.6e-16,3.2e-18},
  101. {{133.0,-0.001},27,{-0.9371713952326589,0.001835552825885577},9.4e-17,1.8e-19},
  102. {{133.0,-0.001},30,{0.1444928510146065,0.0009683028517003325},1.4e-17,9.7e-20},
  103. {{133.0,-0.001},34,{-1.077435738938742,0.002093596104973148},1.1e-16,2.1e-19},
  104. {{133.0,-0.001},38,{2.388603684198123,0.006621682434854192},2.4e-16,6.6e-19},
  105. {{133.0,-0.001},42,{-0.04594418870488948,0.0009000132524188679},4.6e-18,9.0e-20},
  106. {{133.0,-0.001},47,{-0.1928537665101976,0.0009096554574653678},1.9e-17,9.1e-20},
  107. {{133.0,-0.001},52,{-0.5759136780922404,0.001175873583204343},5.8e-17,1.2e-19},
  108. {{133.0,-0.001},58,{-0.001534349994635456,0.0008065485786972979},1.5e-19,8.1e-20},
  109. {{133.0,-0.001},65,{3.34959880398593,0.01197741989906779},3.3e-16,1.2e-18},
  110. {{133.0,-0.001},72,{-1.128245159231274,0.001975805382904386},1.1e-16,2.0e-19},
  111. {{133.0,-0.001},80,{0.3810052575576299,0.0007788355962317044},3.8e-17,7.8e-20},
  112. {{133.0,-0.001},89,{-1.389569631366617,0.002478084310925133},1.4e-16,2.5e-19},
  113. {{133.0,-0.001},99,{0.3062835121565152,0.0005341397085202431},3.1e-17,5.3e-20},
  114. {{133.0,-0.001},111,{-1.197963349765192,0.0017323088546027},1.2e-16,1.7e-19},
  115. {{133.0,-0.001},123,{19.56837074945142,0.3832056790545297},2.0e-15,3.8e-17},
  116. {{133.0,-0.001},137,{0.3055541934481533,2.456354568026977e-5},3.1e-17,2.5e-21},
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  432. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},0,{-2.772406603042443e-285,-1.003741873197321},2.8e-301,1.0e-16},
  433. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},1,{0.05631023432676338,-0.9842532929662963},5.6e-18,9.8e-17},
  434. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},2,{0.1932838439806838,-0.9820447865781992},1.9e-17,9.8e-17},
  435. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},3,{0.3699265824204035,-1.027128174680124},3.7e-17,1.0e-16},
  436. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},4,{0.5559869776590445,-1.10966762489327},5.6e-17,1.1e-16},
  437. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},5,{0.7410609869524249,-1.216012185642558},7.4e-17,1.2e-16},
  438. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},6,{0.9226942125877388,-1.337200280531054},9.2e-17,1.3e-16},
  439. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},7,{1.100802842322886,-1.467947433294319},1.1e-16,1.5e-16},
  440. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},8,{1.275880545379177,-1.605113981437066},1.3e-16,1.6e-16},
  441. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},9,{1.448479195149733,-1.746766652042906},1.4e-16,1.7e-16},
  442. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},10,{1.619076470209989,-1.891665842771343},1.6e-16,1.9e-16},
  443. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},11,{1.78805677376105,-2.03898576446601},1.8e-16,2.0e-16},
  444. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},12,{1.955722406219257,-2.188157203986427},2.0e-16,2.2e-16},
  445. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},13,{2.122310073438798,-2.338775902756937},2.1e-16,2.3e-16},
  446. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},14,{2.288005790801036,-2.490547179941639},2.3e-16,2.5e-16},
  447. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},15,{2.452956780753838,-2.643251296520418},2.5e-16,2.6e-16},
  448. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},16,{2.617280562926164,-2.796721106255066},2.6e-16,2.8e-16},
  449. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},17,{2.781071793755662,-2.950827224606459},2.8e-16,3.0e-16},
  450. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},18,{2.94440739842864,-3.105467935915553},2.9e-16,3.1e-16},
  451. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},20,{3.269953015162791,-3.416044503953443},3.3e-16,3.4e-16},
  452. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},21,{3.432258548223354,-3.571861569112058},3.4e-16,3.6e-16},
  453. {{3.1415926535897932384626433832795,3.1415926535897932384626433832795},22,{3.594303449441325,-3.72796937979865},3.6e-16,3.7e-16},
  454. {{6.2831853071795862319959269370884,-1.0},0,{-1.773439590975416e-16,1.313035285499331},1.8e-32,1.3e-16},
  455. {{6.2831853071795862319959269370884,-1.0},1,{-0.06304185943615409,0.7403873087787056},6.3e-18,7.4e-17},
  456. {{6.2831853071795862319959269370884,-1.0},2,{0.2949375696085568,1.070592030672524},2.9e-17,1.1e-16},
  457. {{6.2831853071795862319959269370884,-1.0},3,{-0.2986322034569661,0.9008011017614757},3.0e-17,9.0e-17},
  458. {{6.2831853071795862319959269370884,-1.0},4,{-0.003223801583153805,0.4398947553395593},3.2e-19,4.4e-17},
  459. {{6.2831853071795862319959269370884,-1.0},5,{0.3254847904858648,0.3236711082223025},3.3e-17,3.2e-17},
  460. {{6.2831853071795862319959269370884,-1.0},6,{0.5915216297442743,0.2927648081692745},5.9e-17,2.9e-17},
  461. {{6.2831853071795862319959269370884,-1.0},7,{0.8216613358485906,0.2889872711150469},8.2e-17,2.9e-17},
  462. {{6.2831853071795862319959269370884,-1.0},8,{1.031011238016646,0.2965575908077732},1.0e-16,3.0e-17},
  463. {{6.2831853071795862319959269370884,-1.0},9,{1.227344826394146,0.3098261586314655},1.2e-16,3.1e-17},
  464. {{6.2831853071795862319959269370884,-1.0},10,{1.414970410777237,0.3263361380815797},1.4e-16,3.3e-17},
  465. {{6.2831853071795862319959269370884,-1.0},11,{1.596461936103797,0.3448619156356228},1.6e-16,3.4e-17},
  466. {{6.2831853071795862319959269370884,-1.0},12,{1.773455192293614,0.36472724630896},1.8e-16,3.6e-17},
  467. {{6.2831853071795862319959269370884,-1.0},13,{1.947042664720708,0.3855292662286455},1.9e-16,3.9e-17},
  468. {{6.2831853071795862319959269370884,-1.0},14,{2.117983884070411,0.4070131164963634},2.1e-16,4.1e-17},
  469. {{6.2831853071795862319959269370884,-1.0},15,{2.28682458641427,0.4290096105470636},2.3e-16,4.3e-17},
  470. {{6.2831853071795862319959269370884,-1.0},16,{2.453967796322013,0.4514019204534639},2.5e-16,4.5e-17},
  471. {{6.2831853071795862319959269370884,-1.0},18,{2.784310371123592,0.4970627630731119},2.8e-16,5.0e-17},
  472. {{6.2831853071795862319959269370884,-1.0},19,{2.947928703075273,0.5202242302820364},2.9e-16,5.2e-17},
  473. {{6.2831853071795862319959269370884,-1.0},20,{3.110719695447307,0.5435558939596922},3.1e-16,5.4e-17},
  474. {{6.2831853071795862319959269370884,-1.0},22,{3.434270806979098,0.590625695740279},3.4e-16,5.9e-17},
  475. {{6.2831853071795862319959269370884,-1.0},23,{3.595206946808026,0.6143246109772049},3.6e-16,6.1e-17},
  476. {{6.2831853071795862319959269370884,-1.0},25,{3.915734156142959,0.6619787064788887},3.9e-16,6.6e-17},
  477. {{6.2831853071795862319959269370884,-1.0},26,{4.075427821953628,0.6859125175106776},4.1e-16,6.9e-17},
  478. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},0,{-1.836418620170526e-18,-1.003741873197321},1.8e-34,1.0e-16},
  479. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},1,{0.01415314238170799,-0.9809158089497843},1.4e-18,9.8e-17},
  480. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},2,{0.05114736246509357,-0.9580400080884279},5.1e-18,9.6e-17},
  481. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},3,{0.09211316557854763,-0.9082339053736075},9.2e-18,9.1e-17},
  482. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},4,{0.1846022792219881,-0.8324588456241011},1.8e-17,8.3e-17},
  483. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},5,{0.3278509422643821,-0.7787308740926149},3.3e-17,7.8e-17},
  484. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},6,{0.490657891841003,-0.7594698540777983},4.9e-17,7.6e-17},
  485. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},7,{0.6556002657420997,-0.7661759616695461},6.6e-17,7.7e-17},
  486. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},8,{0.8170144707370777,-0.7897178762870168},8.2e-17,7.9e-17},
  487. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},9,{0.9738269711673275,-0.8240443504069009},9.7e-17,8.2e-17},
  488. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},10,{1.126363788598225,-0.8654702596325609},1.1e-16,8.7e-17},
  489. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},11,{1.275267657078007,-0.9117424236160586},1.3e-16,9.1e-17},
  490. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},12,{1.421169391490898,-0.9614426612842512},1.4e-16,9.6e-17},
  491. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},13,{1.564605168974907,-1.013646817955554},1.6e-16,1.0e-16},
  492. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},14,{1.70600982438213,-1.067731854089558},1.7e-16,1.1e-16},
  493. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},15,{1.845730814291544,-1.123264438028688},1.8e-16,1.1e-16},
  494. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},16,{1.984045299099804,-1.179934666313605},2.0e-16,1.2e-16},
  495. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},17,{2.121175274622946,-1.237515369840869},2.1e-16,1.2e-16},
  496. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},19,{2.392564196036499,-1.354767638565249},2.4e-16,1.4e-16},
  497. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},20,{2.527087793751678,-1.414208223835596},2.5e-16,1.4e-16},
  498. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},22,{2.794289611881632,-1.534314595034528},2.8e-16,1.5e-16},
  499. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},23,{2.927118403808978,-1.594865107779637},2.9e-16,1.6e-16},
  500. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},25,{3.191523552338415,-1.716747727625207},3.2e-16,1.7e-16},
  501. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},27,{3.454552595281413,-1.839467692756036},3.5e-16,1.8e-16},
  502. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},29,{3.716477216297216,-1.962842613985385},3.7e-16,2.0e-16},
  503. {{6.2831853071795862319959269370884,1.0},0,{-1.773439590975416e-16,-1.313035285499331},1.8e-32,1.3e-16},
  504. {{6.2831853071795862319959269370884,1.0},1,{-0.06304185943615409,-0.7403873087787056},6.3e-18,7.4e-17},
  505. {{6.2831853071795862319959269370884,1.0},2,{0.2949375696085568,-1.070592030672524},2.9e-17,1.1e-16},
  506. {{6.2831853071795862319959269370884,1.0},3,{-0.2986322034569661,-0.9008011017614757},3.0e-17,9.0e-17},
  507. {{6.2831853071795862319959269370884,1.0},4,{-0.003223801583153805,-0.4398947553395593},3.2e-19,4.4e-17},
  508. {{6.2831853071795862319959269370884,1.0},5,{0.3254847904858648,-0.3236711082223025},3.3e-17,3.2e-17},
  509. {{6.2831853071795862319959269370884,1.0},6,{0.5915216297442743,-0.2927648081692745},5.9e-17,2.9e-17},
  510. {{6.2831853071795862319959269370884,1.0},7,{0.8216613358485906,-0.2889872711150469},8.2e-17,2.9e-17},
  511. {{6.2831853071795862319959269370884,1.0},8,{1.031011238016646,-0.2965575908077732},1.0e-16,3.0e-17},
  512. {{6.2831853071795862319959269370884,1.0},9,{1.227344826394146,-0.3098261586314655},1.2e-16,3.1e-17},
  513. {{6.2831853071795862319959269370884,1.0},10,{1.414970410777237,-0.3263361380815797},1.4e-16,3.3e-17},
  514. {{6.2831853071795862319959269370884,1.0},11,{1.596461936103797,-0.3448619156356228},1.6e-16,3.4e-17},
  515. {{6.2831853071795862319959269370884,1.0},12,{1.773455192293614,-0.36472724630896},1.8e-16,3.6e-17},
  516. {{6.2831853071795862319959269370884,1.0},13,{1.947042664720708,-0.3855292662286455},1.9e-16,3.9e-17},
  517. {{6.2831853071795862319959269370884,1.0},14,{2.117983884070411,-0.4070131164963634},2.1e-16,4.1e-17},
  518. {{6.2831853071795862319959269370884,1.0},15,{2.28682458641427,-0.4290096105470636},2.3e-16,4.3e-17},
  519. {{6.2831853071795862319959269370884,1.0},16,{2.453967796322013,-0.4514019204534639},2.5e-16,4.5e-17},
  520. {{6.2831853071795862319959269370884,1.0},18,{2.784310371123592,-0.4970627630731119},2.8e-16,5.0e-17},
  521. {{6.2831853071795862319959269370884,1.0},19,{2.947928703075273,-0.5202242302820364},2.9e-16,5.2e-17},
  522. {{6.2831853071795862319959269370884,1.0},20,{3.110719695447307,-0.5435558939596922},3.1e-16,5.4e-17},
  523. {{6.2831853071795862319959269370884,1.0},22,{3.434270806979098,-0.590625695740279},3.4e-16,5.9e-17},
  524. {{6.2831853071795862319959269370884,1.0},23,{3.595206946808026,-0.6143246109772049},3.6e-16,6.1e-17},
  525. {{6.2831853071795862319959269370884,1.0},25,{3.915734156142959,-0.6619787064788887},3.9e-16,6.6e-17},
  526. {{6.2831853071795862319959269370884,1.0},26,{4.075427821953628,-0.6859125175106776},4.1e-16,6.9e-17},
  527. {{3.1415926535897932384626433832795,0.0},0,{-2.704418609247059e+282,0.0},2.7e+266,0.0},
  528. {{3.1415926535897932384626433832795,0.0},1,{-0.3183098861837907,0.0},3.2e-17,0.0},
  529. {{3.1415926535897932384626433832795,0.0},2,{0.4105777788290164,0.0},4.1e-17,0.0},
  530. {{3.1415926535897932384626433832795,0.0},3,{0.8821173642494784,0.0},8.8e-17,0.0},
  531. {{3.1415926535897932384626433832795,0.0},4,{1.283506275095942,0.0},1.3e-16,0.0},
  532. {{3.1415926535897932384626433832795,0.0},5,{1.654748956488027,0.0},1.7e-16,0.0},
  533. {{3.1415926535897932384626433832795,0.0},6,{2.010012841716631,0.0},2.0e-16,0.0},
  534. {{3.1415926535897932384626433832795,0.0},7,{2.355698958080709,0.0},2.4e-16,0.0},
  535. {{3.1415926535897932384626433832795,0.0},8,{2.695156885492767,0.0},2.7e-16,0.0},
  536. {{3.1415926535897932384626433832795,0.0},9,{3.030322020436486,0.0},3.0e-16,0.0},
  537. {{3.1415926535897932384626433832795,0.0},10,{3.362395801011574,0.0},3.4e-16,0.0},
  538. {{3.1415926535897932384626433832795,0.0},11,{3.692165818289568,0.0},3.7e-16,0.0},
  539. {{3.1415926535897932384626433832795,0.0},12,{4.02017100538644,0.0},4.0e-16,0.0},
  540. {{3.1415926535897932384626433832795,0.0},13,{4.346793172787544,0.0},4.3e-16,0.0},
  541. {{3.1415926535897932384626433832795,0.0},14,{4.672310695202237,0.0},4.7e-16,0.0},
  542. {{3.1415926535897932384626433832795,0.0},15,{4.996931497029032,0.0},5.0e-16,0.0},
  543. {{3.1415926535897932384626433832795,0.0},16,{5.320814119475183,0.0},5.3e-16,0.0},
  544. {{3.1415926535897932384626433832795,0.0},17,{5.644081624955091,0.0},5.6e-16,0.0},
  545. {{3.1415926535897932384626433832795,0.0},18,{5.966831036716778,0.0},6.0e-16,0.0},
  546. {{3.1415926535897932384626433832795,0.0},20,{6.611070983143532,0.0},6.6e-16,0.0},
  547. //{{3.141592653589793,0.0},0,{-4193528956200935.0,0.0},0.42,0.0}, // TODO fails for pi truncated to double precision
  548. {{3.141592653589793,0.0},1,{-0.3183098861837905,0.0},3.2e-17,0.0},
  549. {{3.141592653589793,0.0},2,{0.4105777788290165,0.0},4.1e-17,0.0},
  550. {{3.141592653589793,0.0},3,{0.8821173642494785,0.0},8.8e-17,0.0},
  551. {{3.141592653589793,0.0},4,{1.283506275095942,0.0},1.3e-16,0.0},
  552. {{3.141592653589793,0.0},5,{1.654748956488027,0.0},1.7e-16,0.0},
  553. {{3.141592653589793,0.0},6,{2.010012841716632,0.0},2.0e-16,0.0},
  554. {{3.141592653589793,0.0},7,{2.355698958080709,0.0},2.4e-16,0.0},
  555. {{3.141592653589793,0.0},8,{2.695156885492767,0.0},2.7e-16,0.0},
  556. {{3.141592653589793,0.0},9,{3.030322020436486,0.0},3.0e-16,0.0},
  557. {{3.141592653589793,0.0},10,{3.362395801011574,0.0},3.4e-16,0.0},
  558. {{3.141592653589793,0.0},11,{3.692165818289568,0.0},3.7e-16,0.0},
  559. {{3.141592653589793,0.0},12,{4.02017100538644,0.0},4.0e-16,0.0},
  560. {{3.141592653589793,0.0},13,{4.346793172787545,0.0},4.3e-16,0.0},
  561. {{3.141592653589793,0.0},14,{4.672310695202237,0.0},4.7e-16,0.0},
  562. {{3.141592653589793,0.0},15,{4.996931497029033,0.0},5.0e-16,0.0},
  563. {{3.141592653589793,0.0},16,{5.320814119475183,0.0},5.3e-16,0.0},
  564. {{3.141592653589793,0.0},17,{5.644081624955091,0.0},5.6e-16,0.0},
  565. {{3.141592653589793,0.0},18,{5.966831036716779,0.0},6.0e-16,0.0},
  566. {{3.141592653589793,0.0},20,{6.611070983143533,0.0},6.6e-16,0.0},
  567. };
  568. // complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
  569. std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
  570. D2_test_16digits
  571. = {
  572. {{0.07425,0.0},0,{-0.07438674986902373,0.0},7.4e-18,0.0},
  573. {{0.07425,0.0},1,{-13.39417131419206,0.0},1.3e-15,0.0},
  574. {{0.07425,0.0},2,{-26.91123162027382,0.0},2.7e-15,0.0},
  575. {{0.07425,0.0},3,{-40.3891849341013,0.0},4.0e-15,0.0},
  576. {{0.07425,0.0},4,{-53.86144505752241,0.0},5.4e-15,0.0},
  577. {{0.07575,0.0},0,{-0.07589521939842851,0.0},7.6e-18,0.0},
  578. {{0.07575,0.0},1,{-13.12600313416894,0.0},1.3e-15,0.0},
  579. {{0.07575,0.0},2,{-26.37734215323807,0.0},2.6e-15,0.0},
  580. {{0.07575,0.0},3,{-39.58880458732769,0.0},4.0e-15,0.0},
  581. {{0.07575,0.0},4,{-52.79445732439479,0.0},5.3e-15,0.0},
  582. {{7.5,0.0},0,{-2.706013866772691,0.0},2.7e-16,0.0},
  583. {{7.5,0.0},1,{0.2188602976402436,0.0},2.2e-17,0.0},
  584. {{7.5,0.0},2,{20.65104828146692,0.0},2.1e-15,0.0},
  585. {{7.5,0.0},3,{-0.4493801597873413,0.0},4.5e-17,0.0},
  586. {{7.5,0.0},4,{0.4842572533435941,0.0},4.8e-17,0.0},
  587. {{7.5,0.0},5,{4.81550654897139,0.0},4.8e-16,0.0},
  588. {{7.5,0.0},6,{-1.049034583259778,0.0},1.0e-16,0.0},
  589. {{7.5,0.0},7,{-0.4288861055358842,0.0},4.3e-17,0.0},
  590. {{7.5,0.0},8,{-0.3980175767871659,0.0},4.0e-17,0.0},
  591. {{7.5,0.0},9,{-0.5742246552691164,0.0},5.7e-17,0.0},
  592. {{7.5,0.0},10,{-0.809102874298828,0.0},8.1e-17,0.0},
  593. {{7.5,0.0},11,{-1.027254862439886,0.0},1.0e-16,0.0},
  594. {{7.5,0.0},12,{-1.219374574466933,0.0},1.2e-16,0.0},
  595. {{7.5,0.0},13,{-1.39466116147432,0.0},1.4e-16,0.0},
  596. {{7.5,0.0},14,{-1.560043091026306,0.0},1.6e-16,0.0},
  597. {{7.5,0.0},16,{-1.873757439540259,0.0},1.9e-16,0.0},
  598. {{7.5,0.0},17,{-2.025145514642434,0.0},2.0e-16,0.0},
  599. {{7.5,0.0},18,{-2.174018730753354,0.0},2.2e-16,0.0},
  600. {{7.5,0.0},19,{-2.320899679256512,0.0},2.3e-16,0.0},
  601. {{7.5,0.0},21,{-2.610108605596247,0.0},2.6e-16,0.0},
  602. {{7.5,0.0},22,{-2.752939994498599,0.0},2.8e-16,0.0},
  603. {{7.5,0.0},24,{-3.035926615655057,0.0},3.0e-16,0.0},
  604. {{7.5,0.0},26,{-3.316132176384959,0.0},3.3e-16,0.0},
  605. {{7.5,0.0},27,{-3.455410513492717,0.0},3.5e-16,0.0},
  606. {{7.5,0.0},30,{-3.870677968225079,0.0},3.9e-16,0.0},
  607. {{750.0,0.0},0,{1.117079400838733,0.0},1.1e-16,0.0},
  608. {{750.0,0.0},1,{-0.8975946145725433,0.0},9.0e-17,0.0},
  609. {{750.0,0.0},2,{1.108121968632076,0.0},1.1e-16,0.0},
  610. {{750.0,0.0},3,{-0.9096970410967588,0.0},9.1e-17,0.0},
  611. {{750.0,0.0},4,{1.087526562845337,0.0},1.1e-16,0.0},
  612. {{750.0,0.0},5,{-0.9318559567267879,0.0},9.3e-17,0.0},
  613. {{750.0,0.0},6,{1.055992830861736,0.0},1.1e-16,0.0},
  614. {{750.0,0.0},7,{-0.9647538902206642,0.0},9.6e-17,0.0},
  615. {{750.0,0.0},9,{-1.009474246275747,0.0},1.0e-16,0.0},
  616. {{750.0,0.0},10,{0.9643676731279237,0.0},9.6e-17,0.0},
  617. {{750.0,0.0},11,{-1.067629644695052,0.0},1.1e-16,0.0},
  618. {{750.0,0.0},13,{-1.141571574212259,0.0},1.1e-16,0.0},
  619. {{750.0,0.0},15,{-1.234734314089206,0.0},1.2e-16,0.0},
  620. {{750.0,0.0},18,{0.7026309682530627,0.0},7.0e-17,0.0},
  621. {{750.0,0.0},20,{0.6275884453721258,0.0},6.3e-17,0.0},
  622. {{750.0,0.0},23,{-1.95499529719246,0.0},2.0e-16,0.0},
  623. {{750.0,0.0},27,{-2.856016621139734,0.0},2.9e-16,0.0},
  624. {{750.0,0.0},31,{-5.515179542724612,0.0},5.5e-16,0.0},
  625. {{750.0,0.0},35,{-2046.667830368851,0.0},2.0e-13,0.0},
  626. {{750.0,0.0},41,{3.142443680429311,0.0},3.1e-16,0.0},
  627. {{750.0,0.0},47,{1.275705385420439,0.0},1.3e-16,0.0},
  628. {{750.0,0.0},54,{-2.171423411849925,0.0},2.2e-16,0.0},
  629. {{750.0,0.0},62,{5.070303280958446,0.0},5.1e-16,0.0},
  630. {{750.0,0.0},71,{-1.547407386670151,0.0},1.5e-16,0.0},
  631. {{750.0,0.0},81,{2.057198576589978,0.0},2.1e-16,0.0},
  632. {{750.0,0.0},93,{-0.2880574210963995,0.0},2.9e-17,0.0},
  633. {{750.0,0.0},107,{1.467167039386753,0.0},1.5e-16,0.0},
  634. {{750.0,0.0},123,{-13.25668132285312,0.0},1.3e-15,0.0},
  635. {{750.0,0.0},141,{-51.66788150986426,0.0},5.2e-15,0.0},
  636. {{750.0,0.0},162,{-2.044123043949385,0.0},2.0e-16,0.0},
  637. {{750.0,0.0},186,{-0.5017806375070012,0.0},5.0e-17,0.0},
  638. {{750.0,0.0},214,{4.680543422413898,0.0},4.7e-16,0.0},
  639. {{750.0,0.0},246,{0.9652329906986826,0.0},9.7e-17,0.0},
  640. {{750.0,0.0},282,{0.3764839152874788,0.0},3.8e-17,0.0},
  641. {{750.0,0.0},324,{-5.441038845652591,0.0},5.4e-16,0.0},
  642. {{750.0,0.0},372,{0.5017189777039316,0.0},5.0e-17,0.0},
  643. {{750.0,0.0},427,{-0.5396391858059278,0.0},5.4e-17,0.0},
  644. {{750.0,0.0},490,{0.2475300359343486,0.0},2.5e-17,0.0},
  645. {{750.0,0.0},562,{0.6550877387674529,0.0},6.6e-17,0.0},
  646. {{750.0,0.0},645,{-0.0647479220258492,0.0},6.5e-18,0.0},
  647. {{750.0,0.0},740,{0.9500952443721748,0.0},9.5e-17,0.0},
  648. {{750.0,0.0},850,{-0.5317183378262854,0.0},5.3e-17,0.0},
  649. {{133.0,-0.001},0,{-1.755932485461304,0.004083310122507825},1.8e-16,4.1e-19},
  650. {{133.0,-0.001},1,{0.5595479819348692,0.001312980852946314},5.6e-17,1.3e-19},
  651. {{133.0,-0.001},2,{-1.85153917185983,0.004427871815312255},1.9e-16,4.4e-19},
  652. {{133.0,-0.001},3,{0.5110313502646276,0.001260474562555223},5.1e-17,1.3e-19},
  653. {{133.0,-0.001},4,{-2.109252486188721,0.005447837827720917},2.1e-16,5.4e-19},
  654. {{133.0,-0.001},5,{0.4282025099144422,0.001181661243690889},4.3e-17,1.2e-19},
  655. {{133.0,-0.001},6,{-2.655442472579592,0.00804905444898751},2.7e-16,8.0e-19},
  656. {{133.0,-0.001},7,{0.316631280080747,0.001097089303706201},3.2e-17,1.1e-19},
  657. {{133.0,-0.001},8,{-3.959004842334986,0.01666990476526257},4.0e-16,1.7e-18},
  658. {{133.0,-0.001},9,{0.1806704887948465,0.001027553610539269},1.8e-17,1.0e-19},
  659. {{133.0,-0.001},10,{-9.554533249350271,0.09229128245066224},9.6e-16,9.2e-18},
  660. {{133.0,-0.001},11,{0.02104786595968763,0.0009929804198924497},2.1e-18,9.9e-20},
  661. {{133.0,-0.001},13,{-0.1678332578687873,0.00101787881523943},1.7e-17,1.0e-19},
  662. {{133.0,-0.001},14,{3.556396506011055,0.01363625230438085},3.6e-16,1.4e-18},
  663. {{133.0,-0.001},16,{1.790016651664875,0.00418879487195259},1.8e-16,4.2e-19},
  664. {{133.0,-0.001},18,{1.021038366775945,0.002023186744680601},1.0e-16,2.0e-19},
  665. {{133.0,-0.001},20,{0.5479729709732455,0.001276530775240961},5.5e-17,1.3e-19},
  666. {{133.0,-0.001},22,{0.1809795706420653,0.001004147964731335},1.8e-17,1.0e-19},
  667. {{133.0,-0.001},24,{-0.1724263550949475,0.000995811171991787},1.7e-17,1.0e-19},
  668. {{133.0,-0.001},27,{1.021452430742276,0.002000628091838396},1.0e-16,2.0e-19},
  669. {{133.0,-0.001},30,{-6.547396546792233,0.04381769113586676},6.5e-16,4.4e-18},
  670. {{133.0,-0.001},34,{0.8656406474529488,0.001682061020627086},8.7e-17,1.7e-19},
  671. {{133.0,-0.001},38,{-0.3838684285342646,0.001063573921879943},3.8e-17,1.1e-19},
  672. {{133.0,-0.001},42,{19.71892539138212,0.3898854651258534},2.0e-15,3.9e-17},
  673. {{133.0,-0.001},47,{4.536308169130143,0.02145099010357844},4.5e-16,2.1e-18},
  674. {{133.0,-0.001},52,{1.466938589766846,0.002996111386699881},1.5e-16,3.0e-19},
  675. {{133.0,-0.001},58,{485.6616787894604,618.8805818920891},4.9e-14,6.2e-14},
  676. {{133.0,-0.001},65,{-0.2272687651498732,0.0008091273274344002},2.3e-17,8.1e-20},
  677. {{133.0,-0.001},72,{0.622303863806427,0.001090128451858948},6.2e-17,1.1e-19},
  678. {{133.0,-0.001},80,{-1.656082363658833,0.003376287990811771},1.7e-16,3.4e-19},
  679. {{133.0,-0.001},89,{0.3916329094110811,0.0007005525248592523},3.9e-17,7.0e-20},
  680. {{133.0,-0.001},99,{-1.421092555792892,0.002459838815433856},1.4e-16,2.5e-19},
  681. {{133.0,-0.001},111,{0.2415850593901129,0.0003555536690688075},2.4e-17,3.6e-20},
  682. {{133.0,-0.001},123,{-0.02936353008964981,0.0001386314460729032},2.9e-18,1.4e-20},
  683. {{133.0,-0.001},137,{-0.2015744636220535,-2.816755428233205e-5},2.0e-17,2.8e-21},
  684. {{133.0,-0.001},153,{-0.5603119660277999,-1.806474698095854e-5},5.6e-17,1.8e-21},
  685. {{133.0,-0.001},170,{-0.7923542900597165,-1.556887877560696e-5},7.9e-17,1.6e-21},
  686. {{133.0,-0.001},190,{-1.018068108577178,-1.509479127100921e-5},1.0e-16,1.5e-21},
  687. {{13300.0,-0.1},0,{4.614747555432858,6.903177205927318},4.6e-16,6.9e-16},
  688. {{13300.0,-0.1},1,{-0.06700391181106944,0.1001199654937619},6.7e-18,1.0e-17},
  689. {{13300.0,-0.1},2,{4.620439133200172,6.888811904783909},4.6e-16,6.9e-16},
  690. {{13300.0,-0.1},3,{-0.06737777840760444,0.1001250179841278},6.7e-18,1.0e-17},
  691. {{13300.0,-0.1},4,{4.633500440086391,6.855341200224173},4.6e-16,6.9e-16},
  692. {{13300.0,-0.1},5,{-0.06805078507601441,0.1001341840454214},6.8e-18,1.0e-17},
  693. {{13300.0,-0.1},6,{4.653411812962385,6.802886700800537},4.7e-16,6.8e-16},
  694. {{13300.0,-0.1},8,{4.67937396079206,6.731654983192257},4.7e-16,6.7e-16},
  695. {{13300.0,-0.1},10,{4.710331246539195,6.641956515928427},4.7e-16,6.6e-16},
  696. {{13300.0,-0.1},12,{4.745003601522665,6.534228448806732},4.7e-16,6.5e-16},
  697. {{13300.0,-0.1},15,{-0.07590717256243298,0.1002479325549111},7.6e-18,1.0e-17},
  698. {{13300.0,-0.1},18,{4.856045166555225,6.109630111782805},4.9e-16,6.1e-16},
  699. {{13300.0,-0.1},22,{4.919273005297511,5.752106274215477},4.9e-16,5.8e-16},
  700. {{13300.0,-0.1},27,{-0.09525261713282836,0.1005810209670254},9.5e-18,1.0e-17},
  701. {{13300.0,-0.1},32,{4.952248503162073,4.686287618645416},5.0e-16,4.7e-16},
  702. {{13300.0,-0.1},40,{4.797687411598633,3.78137609812792},4.8e-16,3.8e-16},
  703. {{13300.0,-0.1},48,{4.492316448297681,2.947900994893757},4.5e-16,2.9e-16},
  704. {{13300.0,-0.1},59,{-0.2012137580358194,0.1037434227328889},2.0e-17,1.0e-17},
  705. {{13300.0,-0.1},71,{-0.2628537776724217,0.1066253638228959},2.6e-17,1.1e-17},
  706. {{13300.0,-0.1},87,{-0.3668752907013172,0.1132318830176521},3.7e-17,1.1e-17},
  707. {{13300.0,-0.1},105,{-0.521456532121871,0.1271109141308341},5.2e-17,1.3e-17},
  708. {{13300.0,-0.1},128,{1.186380086092666,0.243429422789328},1.2e-16,2.4e-17},
  709. {{13300.0,-0.1},155,{-1.433857954348046,0.3111242864463406},1.4e-16,3.1e-17},
  710. {{13300.0,-0.1},189,{-4.525078832396816,3.018783582231741},4.5e-16,3.0e-16},
  711. {{13300.0,-0.1},229,{1.847521018961361,0.4560381399785403},1.8e-16,4.6e-17},
  712. {{13300.0,-0.1},279,{0.1365813763007464,0.1015023822518041},1.4e-17,1.0e-17},
  713. {{13300.0,-0.1},338,{0.3464203993678584,0.111699197945671},3.5e-17,1.1e-17},
  714. {{13300.0,-0.1},411,{-0.1502261435561727,0.1018452715781982},1.5e-17,1.0e-17},
  715. {{13300.0,-0.1},499,{-0.02327966666385402,0.09958243666762214},2.3e-18,1.0e-17},
  716. {{13300.0,-0.1},606,{0.2404529773197536,0.1052851410218373},2.4e-17,1.1e-17},
  717. {{13300.0,-0.1},736,{-0.04406458473931691,0.09955884001348248},4.4e-18,1.0e-17},
  718. {{13300.0,-0.1},894,{-0.3202522349091168,0.1095537561774465},3.2e-17,1.1e-17},
  719. {{0.0825,-0.055},0,{-0.08243635461047968,0.05531913702894625},8.2e-18,5.5e-18},
  720. {{0.0825,-0.055},1,{-8.308927454476161,-5.648450253463678},8.3e-16,5.6e-16},
  721. {{0.0825,-0.055},2,{-16.7557368852332,-11.20725067418851},1.7e-15,1.1e-15},
  722. {{0.0825,-0.055},3,{-25.15832772040454,-16.79422954904686},2.5e-15,1.7e-15},
  723. {{0.0825,-0.055},4,{-33.55464861977138,-22.38548342593486},3.4e-15,2.2e-15},
  724. {{0.0825,-0.055},5,{-41.94887562222077,-27.97814077051338},4.2e-15,2.8e-15},
  725. {{0.084,-0.056},0,{-0.0839327708281362,0.05633687249618312},8.4e-18,5.6e-18},
  726. {{0.084,-0.056},1,{-8.157567495279937,-5.549497143255095},8.2e-16,5.5e-16},
  727. {{0.084,-0.056},2,{-16.45553767517591,-11.00778969816477},1.6e-15,1.1e-15},
  728. {{0.084,-0.056},3,{-24.70847741417365,-16.49472995881217},2.5e-15,1.6e-15},
  729. {{0.084,-0.056},4,{-32.95503377743467,-21.98602610042692},3.3e-15,2.2e-15},
  730. {{0.084,-0.056},5,{-41.19945822470811,-27.47875147585194},4.1e-15,2.7e-15},
  731. {{150.0,-100.0},0,{0.0,1.0},0.0,1.0e-16},
  732. {{150.0,-100.0},1,{2.843446142415215e-5,0.9999879975137707},2.8e-21,1.0e-16},
  733. {{150.0,-100.0},2,{8.530546307582867e-5,0.9999639945278075},8.5e-21,1.0e-16},
  734. {{150.0,-100.0},3,{0.0001706171621018294,0.9999279950163633},1.7e-20,1.0e-16},
  735. {{150.0,-100.0},4,{0.0002843757930710271,0.9998800049439736},2.8e-20,1.0e-16},
  736. {{150.0,-100.0},5,{0.0004265896665886721,0.9998200322692436},4.3e-20,1.0e-16},
  737. {{150.0,-100.0},6,{0.0005972691674419548,0.9997480869498983},6.0e-20,1.0e-16},
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  1023. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},17,{-1.973144021086521,1.188294020790342},2.0e-16,1.2e-16},
  1024. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},19,{-2.248507874014136,1.302018460544428},2.2e-16,1.3e-16},
  1025. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},20,{-2.384616726791012,1.360171448495848},2.4e-16,1.4e-16},
  1026. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},22,{-2.654392752188639,1.478316329319233},2.7e-16,1.5e-16},
  1027. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},23,{-2.788272523600718,1.53810912969502},2.8e-16,1.5e-16},
  1028. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},25,{-3.05442272767237,1.658785490026429},3.1e-16,1.7e-16},
  1029. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},27,{-3.318830366257712,1.78059624870022},3.3e-16,1.8e-16},
  1030. {{6.2831853071795862319959269370884,3.1415926535897932384626433832795},29,{-3.581862130100558,1.903267755210881},3.6e-16,1.9e-16},
  1031. {{6.2831853071795862319959269370884,1.0},0,{1.028640466363268e-16,-0.7615941559557649},1.0e-32,7.6e-17},
  1032. {{6.2831853071795862319959269370884,1.0},1,{0.118490443174149,-1.274694049282418},1.2e-17,1.3e-16},
  1033. {{6.2831853071795862319959269370884,1.0},2,{-0.1856513350192726,-0.7471769785178116},1.9e-17,7.5e-17},
  1034. {{6.2831853071795862319959269370884,1.0},3,{0.2768024289482062,-0.6931437961850393},2.8e-17,6.9e-17},
  1035. {{6.2831853071795862319959269370884,1.0},4,{0.1086976874372488,-1.161358574339028},1.1e-17,1.2e-16},
  1036. {{6.2831853071795862319959269370884,1.0},5,{-0.3377602226494415,-0.5581206587888317},3.4e-17,5.6e-17},
  1037. {{6.2831853071795862319959269370884,1.0},6,{-0.2178103265918506,-0.08222821063750248},2.2e-17,8.2e-18},
  1038. {{6.2831853071795862319959269370884,1.0},7,{-0.3235985508010899,0.2259866086401661},3.2e-17,2.3e-17},
  1039. {{6.2831853071795862319959269370884,1.0},8,{-0.646555100667698,0.358716765185808},6.5e-17,3.6e-17},
  1040. {{6.2831853071795862319959269370884,1.0},9,{-0.9442688856366345,0.3510704658280867},9.4e-17,3.5e-17},
  1041. {{6.2831853071795862319959269370884,1.0},10,{-1.173414015067102,0.3378028411431261},1.2e-16,3.4e-17},
  1042. {{6.2831853071795862319959269370884,1.0},11,{-1.375210607885232,0.3420479591705745},1.4e-16,3.4e-17},
  1043. {{6.2831853071795862319959269370884,1.0},12,{-1.565394193409859,0.355077628599805},1.6e-16,3.6e-17},
  1044. {{6.2831853071795862319959269370884,1.0},13,{-1.748424803477854,0.3720139875979341},1.7e-16,3.7e-17},
  1045. {{6.2831853071795862319959269370884,1.0},14,{-1.926390248329804,0.3910302018583015},1.9e-16,3.9e-17},
  1046. {{6.2831853071795862319959269370884,1.0},15,{-2.100611141547864,0.4113324738841946},2.1e-16,4.1e-17},
  1047. {{6.2831853071795862319959269370884,1.0},16,{-2.27197885499843,0.4325025916540024},2.3e-16,4.3e-17},
  1048. {{6.2831853071795862319959269370884,1.0},18,{-2.608469851298015,0.4765432487676611},2.6e-16,4.8e-17},
  1049. {{6.2831853071795862319959269370884,1.0},19,{-2.77437412514539,0.4991481353599046},2.8e-16,5.0e-17},
  1050. {{6.2831853071795862319959269370884,1.0},20,{-2.939080962634986,0.5220318339355322},2.9e-16,5.2e-17},
  1051. {{6.2831853071795862319959269370884,1.0},22,{-3.265643862194712,0.56843085660439},3.3e-16,5.7e-17},
  1052. {{6.2831853071795862319959269370884,1.0},23,{-3.427777831706615,0.5918741791259039},3.4e-16,5.9e-17},
  1053. {{6.2831853071795862319959269370884,1.0},25,{-3.750257209199445,0.6391251649246937},3.8e-16,6.4e-17},
  1054. {{6.2831853071795862319959269370884,1.0},26,{-3.910752977720189,0.6628981349489083},3.9e-16,6.6e-17},
  1055. {{3.1415926535897932384626433832795,0.0},0,{3.697652414388656e-283,0.0},3.7e-299,0.0},
  1056. {{3.1415926535897932384626433832795,0.0},1,{2.823282767406003,0.0},2.8e-16,0.0},
  1057. {{3.1415926535897932384626433832795,0.0},2,{-1.093937613419915,0.0},1.1e-16,0.0},
  1058. {{3.1415926535897932384626433832795,0.0},3,{-0.4668550947764989,0.0},4.7e-17,0.0},
  1059. {{3.1415926535897932384626433832795,0.0},4,{-0.6985581582787117,0.0},7.0e-17,0.0},
  1060. {{3.1415926535897932384626433832795,0.0},5,{-1.154888723484527,0.0},1.2e-16,0.0},
  1061. {{3.1415926535897932384626433832795,0.0},6,{-1.583568220165334,0.0},1.6e-16,0.0},
  1062. {{3.1415926535897932384626433832795,0.0},7,{-1.965821646540506,0.0},2.0e-16,0.0},
  1063. {{3.1415926535897932384626433832795,0.0},8,{-2.324862655082562,0.0},2.3e-16,0.0},
  1064. {{3.1415926535897932384626433832795,0.0},9,{-2.672097814251814,0.0},2.7e-16,0.0},
  1065. {{3.1415926535897932384626433832795,0.0},10,{-3.012310405818385,0.0},3.0e-16,0.0},
  1066. {{3.1415926535897932384626433832795,0.0},11,{-3.347886623965971,0.0},3.3e-16,0.0},
  1067. {{3.1415926535897932384626433832795,0.0},12,{-3.680202022452916,0.0},3.7e-16,0.0},
  1068. {{3.1415926535897932384626433832795,0.0},13,{-4.010122340785055,0.0},4.0e-16,0.0},
  1069. {{3.1415926535897932384626433832795,0.0},14,{-4.338225297702631,0.0},4.3e-16,0.0},
  1070. {{3.1415926535897932384626433832795,0.0},15,{-4.66491342262249,0.0},4.7e-16,0.0},
  1071. {{3.1415926535897932384626433832795,0.0},16,{-4.990476814065978,0.0},5.0e-16,0.0},
  1072. {{3.1415926535897932384626433832795,0.0},17,{-5.315130348653373,0.0},5.3e-16,0.0},
  1073. {{3.1415926535897932384626433832795,0.0},18,{-5.639036854808338,0.0},5.6e-16,0.0},
  1074. {{3.1415926535897932384626433832795,0.0},20,{-6.285084985730819,0.0},6.3e-16,0.0},
  1075. {{3.141592653589793,0.0},0,{2.384626433832795e-16,0.0},2.4e-32,0.0},
  1076. {{3.141592653589793,0.0},1,{2.823282767406005,0.0},2.8e-16,0.0},
  1077. {{3.141592653589793,0.0},2,{-1.093937613419914,0.0},1.1e-16,0.0},
  1078. {{3.141592653589793,0.0},3,{-0.4668550947764989,0.0},4.7e-17,0.0},
  1079. {{3.141592653589793,0.0},4,{-0.6985581582787118,0.0},7.0e-17,0.0},
  1080. {{3.141592653589793,0.0},5,{-1.154888723484528,0.0},1.2e-16,0.0},
  1081. {{3.141592653589793,0.0},6,{-1.583568220165334,0.0},1.6e-16,0.0},
  1082. {{3.141592653589793,0.0},7,{-1.965821646540506,0.0},2.0e-16,0.0},
  1083. {{3.141592653589793,0.0},8,{-2.324862655082562,0.0},2.3e-16,0.0},
  1084. {{3.141592653589793,0.0},9,{-2.672097814251814,0.0},2.7e-16,0.0},
  1085. {{3.141592653589793,0.0},10,{-3.012310405818385,0.0},3.0e-16,0.0},
  1086. {{3.141592653589793,0.0},11,{-3.347886623965971,0.0},3.3e-16,0.0},
  1087. {{3.141592653589793,0.0},12,{-3.680202022452917,0.0},3.7e-16,0.0},
  1088. {{3.141592653589793,0.0},13,{-4.010122340785055,0.0},4.0e-16,0.0},
  1089. {{3.141592653589793,0.0},14,{-4.338225297702632,0.0},4.3e-16,0.0},
  1090. {{3.141592653589793,0.0},15,{-4.664913422622491,0.0},4.7e-16,0.0},
  1091. {{3.141592653589793,0.0},16,{-4.990476814065978,0.0},5.0e-16,0.0},
  1092. {{3.141592653589793,0.0},17,{-5.315130348653373,0.0},5.3e-16,0.0},
  1093. {{3.141592653589793,0.0},18,{-5.639036854808339,0.0},5.6e-16,0.0},
  1094. {{3.141592653589793,0.0},20,{-6.285084985730819,0.0},6.3e-16,0.0},
  1095. };
  1096. // complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
  1097. std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
  1098. D3_test_16digits
  1099. = {
  1100. {{13300.0,-0.1},0,{0.0,1.0},0.0,1.0e-16},
  1101. {{13300.0,-0.1},1,{-3.400439576064988e-13,0.9999999943467692},3.4e-29,1.0e-16},
  1102. {{13300.0,-0.1},2,{-1.02013189877118e-12,0.9999999830403075},1.0e-28,1.0e-16},
  1103. {{13300.0,-0.1},3,{-2.040263875397417e-12,0.9999999660806147},2.0e-28,1.0e-16},
  1104. {{13300.0,-0.1},4,{-3.400439965340277e-12,0.9999999434676906},3.4e-28,1.0e-16},
  1105. {{13300.0,-0.1},5,{-5.100660272406543e-12,0.9999999152015347},5.1e-28,1.0e-16},
  1106. {{13300.0,-0.1},6,{-7.140924926354723e-12,0.9999998812821465},7.1e-28,1.0e-16},
  1107. {{13300.0,-0.1},8,{-1.224158792368965e-11,0.9999997964836711},1.2e-27,1.0e-16},
  1108. {{13300.0,-0.1},10,{-1.870243051444869e-11,0.9999996890722586},1.9e-27,1.0e-16},
  1109. {{13300.0,-0.1},12,{-2.652345467096505e-11,0.9999995590479018},2.7e-27,1.0e-16},
  1110. {{13300.0,-0.1},15,{-4.080533667787133e-11,0.999999321612076},4.1e-27,1.0e-16},
  1111. {{13300.0,-0.1},18,{-5.814764248686488e-11,0.999999033297069},5.8e-27,1.0e-16},
  1112. {{13300.0,-0.1},22,{-8.603139703783761e-11,0.9999985697315893},8.6e-27,1.0e-16},
  1113. {{13300.0,-0.1},27,{-1.28537232356385e-10,0.9999978630764811},1.3e-26,1.0e-16},
  1114. {{13300.0,-0.1},32,{-1.795444131588628e-10,0.9999970150896922},1.8e-26,1.0e-16},
  1115. {{13300.0,-0.1},40,{-2.788389500368772e-10,0.999995364340014},2.8e-26,1.0e-16},
  1116. {{13300.0,-0.1},48,{-3.99897670899495e-10,0.9999933517785008},4.0e-26,1.0e-16},
  1117. {{13300.0,-0.1},59,{-6.018913482575541e-10,0.999989993731453},6.0e-26,1.0e-16},
  1118. {{13300.0,-0.1},71,{-8.691806030714543e-10,0.9999855502377231},8.7e-26,1.0e-16},
  1119. {{13300.0,-0.1},87,{-1.301751636840212e-9,0.999978359198404},1.3e-25,1.0e-16},
  1120. {{13300.0,-0.1},105,{-1.892478559255885e-9,0.999968539275809},1.9e-25,1.0e-16},
  1121. {{13300.0,-0.1},128,{-2.807697724335093e-9,0.9999533258374243},2.8e-25,1.0e-16},
  1122. {{13300.0,-0.1},155,{-4.111763702027196e-9,0.9999316501039903},4.1e-25,1.0e-16},
  1123. {{13300.0,-0.1},189,{-6.106883864825003e-9,0.9998984910892781},6.1e-25,1.0e-16},
  1124. {{13300.0,-0.1},229,{-8.95805814929697e-9,0.9998511110833991},9.0e-25,1.0e-16},
  1125. {{13300.0,-0.1},279,{-1.328871882120813e-8,0.9997791604205924},1.3e-24,1.0e-16},
  1126. {{13300.0,-0.1},338,{-1.949566427437159e-8,0.9996760682893887},1.9e-24,1.0e-16},
  1127. {{13300.0,-0.1},411,{-2.882119692710565e-8,0.99952124896133},2.9e-24,1.0e-16},
  1128. {{13300.0,-0.1},499,{-4.248789333886431e-8,0.9992945106023009},4.2e-24,1.0e-16},
  1129. {{13300.0,-0.1},606,{-6.268784827324142e-8,0.9989597110407947},6.3e-24,1.0e-16},
  1130. {{13300.0,-0.1},736,{-9.254452618551611e-8,0.9984655761319616},9.3e-24,1.0e-16},
  1131. {{13300.0,-0.1},894,{-1.367351871332925e-7,0.9977357768741157},1.4e-23,1.0e-16},
  1132. {{13300.0,-0.1},1086,{-2.022251492259403e-7,0.9966576457442607},2.0e-23,1.0e-16},
  1133. {{13300.0,-0.1},1319,{-2.993332266274127e-7,0.9950664665997103},3.0e-23,1.0e-16},
  1134. {{13300.0,-0.1},1601,{-4.432934379930979e-7,0.9927238197940671},4.4e-23,9.9e-17},
  1135. {{13300.0,-0.1},1945,{-6.593672942603503e-7,0.989243494339538},6.6e-23,9.9e-17},
  1136. {{13300.0,-0.1},2362,{-9.83775545482961e-7,0.9840970601559616},9.8e-23,9.8e-17},
  1137. {{13300.0,-0.1},13560,{-0.1978882692837703,-3.967948672613146e-5},2.0e-17,4.0e-21},
  1138. {{15000.0,-10000.0},0,{0.0,1.0},0.0,1.0e-16},
  1139. {{15000.0,-10000.0},1,{2.84026945162933e-9,0.9999999988164005},2.8e-25,1.0e-16},
  1140. {{15000.0,-10000.0},2,{8.520808375061527e-9,0.9999999964492016},8.5e-25,1.0e-16},
  1141. {{15000.0,-10000.0},3,{1.704161681064366e-8,0.9999999928984033},1.7e-24,1.0e-16},
  1142. {{15000.0,-10000.0},4,{2.840269481889634e-8,0.9999999881640057},2.8e-24,1.0e-16},
  1143. {{15000.0,-10000.0},6,{5.96456598963634e-8,0.9999999751444127},6.0e-24,1.0e-16},
  1144. {{15000.0,-10000.0},7,{7.952754718748665e-8,0.9999999668592176},8.0e-24,1.0e-16},
  1145. {{15000.0,-10000.0},9,{1.278121319805862e-7,0.9999999467380309},1.3e-23,1.0e-16},
  1146. {{15000.0,-10000.0},11,{1.874577982316124e-7,0.9999999218824499},1.9e-23,1.0e-16},
  1147. {{15000.0,-10000.0},13,{2.584645476351414e-7,0.9999998922924764},2.6e-23,1.0e-16},
  1148. {{15000.0,-10000.0},16,{3.862767071525949e-7,0.9999998390305346},3.9e-23,1.0e-16},
  1149. {{15000.0,-10000.0},20,{5.964567324115234e-7,0.9999997514442596},6.0e-23,1.0e-16},
  1150. {{15000.0,-10000.0},24,{8.520811370830121e-7,0.9999996449204608},8.5e-23,1.0e-16},
  1151. {{15000.0,-10000.0},30,{1.320726020447437e-6,0.99999944962697},1.3e-22,1.0e-16},
  1152. {{15000.0,-10000.0},36,{1.891620943893063e-6,0.9999992117242355},1.9e-22,1.0e-16},
  1153. {{15000.0,-10000.0},44,{2.811870049126164e-6,0.9999988282397975},2.8e-22,1.0e-16},
  1154. {{15000.0,-10000.0},54,{4.217807545189578e-6,0.9999982423621463},4.2e-22,1.0e-16},
  1155. {{15000.0,-10000.0},67,{6.470151250788692e-6,0.9999973037777175},6.5e-22,1.0e-16},
  1156. {{15000.0,-10000.0},82,{9.665475868536043e-6,0.9999959722496228},9.7e-22,1.0e-16},
  1157. {{15000.0,-10000.0},100,{1.434344645897526e-5,0.9999940229077095},1.4e-21,1.0e-16},
  1158. {{15000.0,-10000.0},122,{2.131073094626111e-5,0.9999911196408604},2.1e-21,1.0e-16},
  1159. {{15000.0,-10000.0},149,{3.174043095735599e-5,0.9999867736922388},3.2e-21,1.0e-16},
  1160. {{15000.0,-10000.0},182,{4.729993952558016e-5,0.999980290442509},4.7e-21,1.0e-16},
  1161. {{15000.0,-10000.0},223,{7.094066703164427e-5,0.9999704404991336},7.1e-21,1.0e-16},
  1162. {{15000.0,-10000.0},272,{0.0001054581586252006,0.9999560599143091},1.1e-20,1.0e-16},
  1163. {{15000.0,-10000.0},333,{0.0001579606214003589,0.999934189160139},1.6e-20,1.0e-16},
  1164. {{15000.0,-10000.0},407,{0.0002358450668200512,0.9999017510880184},2.4e-20,1.0e-16},
  1165. {{15000.0,-10000.0},497,{0.0003515433469161231,0.9998535770854752},3.5e-20,1.0e-16},
  1166. {{15000.0,-10000.0},608,{0.0005259513321601364,0.9997809874552286},5.3e-20,1.0e-16},
  1167. {{15000.0,-10000.0},742,{0.0007831841585954275,0.9996739907967603},7.8e-20,1.0e-16},
  1168. {{15000.0,-10000.0},907,{0.0011701301961291,0.9995131858706238},1.2e-19,1.0e-16},
  1169. {{15000.0,-10000.0},1108,{0.001746289656337749,0.9992740743002811},1.7e-19,1.0e-16},
  1170. {{15000.0,-10000.0},1354,{0.0026083036501201,0.9989170579410502},2.6e-19,1.0e-16},
  1171. {{15000.0,-10000.0},1655,{0.003898434272384769,0.9983843598666412},3.9e-19,1.0e-16},
  1172. {{15000.0,-10000.0},2022,{0.005823086211357998,0.9975932972803287},5.8e-19,1.0e-16},
  1173. {{15000.0,-10000.0},2471,{0.008705827478245269,0.9964165769276073},8.7e-19,1.0e-16},
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  1605. {{6.2831853071795862319959269370884,1.0},26,{-3.910752977720189,0.6628981349489083},3.9e-16,6.6e-17},
  1606. {{3.1415926535897932384626433832795,0.0},0,{0.0,1.0},0.0,1.0e-16},
  1607. {{3.1415926535897932384626433832795,0.0},1,{-0.02928440396155443,0.9080003316496248},2.9e-18,9.1e-17},
  1608. {{3.1415926535897932384626433832795,0.0},2,{-0.111414420013723,0.7161490362627657},1.1e-17,7.2e-17},
  1609. {{3.1415926535897932384626433832795,0.0},3,{-0.3086445141021306,0.4340404684115407},3.1e-17,4.3e-17},
  1610. {{3.1415926535897932384626433832795,0.0},4,{-0.6853420975491589,0.1613084612168837},6.9e-17,1.6e-17},
  1611. {{3.1415926535897932384626433832795,0.0},5,{-1.154547531604494,0.03095979893899376},1.2e-16,3.1e-18},
  1612. {{3.1415926535897932384626433832795,0.0},6,{-1.583565196074497,0.003296559784896674},1.6e-16,3.3e-19},
  1613. {{3.1415926535897932384626433832795,0.0},7,{-1.965821634628246,0.0002268900069871888},2.0e-16,2.3e-20},
  1614. {{3.1415926535897932384626433832795,0.0},8,{-2.324862655057826,1.114344043688996e-5},2.3e-16,1.1e-21},
  1615. {{3.1415926535897932384626433832795,0.0},9,{-2.672097814251784,4.137546472473845e-7},2.7e-16,4.1e-23},
  1616. {{3.1415926535897932384626433832795,0.0},10,{-3.012310405818385,1.206868381771849e-8},3.0e-16,1.2e-24},
  1617. {{3.1415926535897932384626433832795,0.0},11,{-3.347886623965971,2.84447322718975e-10},3.3e-16,2.8e-26},
  1618. {{3.1415926535897932384626433832795,0.0},12,{-3.680202022452916,5.536734412459245e-12},3.7e-16,5.5e-28},
  1619. {{3.1415926535897932384626433832795,0.0},13,{-4.010122340785055,9.05809239443902e-14},4.0e-16,9.1e-30},
  1620. {{3.1415926535897932384626433832795,0.0},14,{-4.338225297702631,1.263667883273076e-15},4.3e-16,1.3e-31},
  1621. {{3.1415926535897932384626433832795,0.0},15,{-4.66491342262249,1.521676227453879e-17},4.7e-16,1.5e-33},
  1622. {{3.1415926535897932384626433832795,0.0},16,{-4.990476814065978,1.598129828453938e-19},5.0e-16,1.6e-35},
  1623. {{3.1415926535897932384626433832795,0.0},17,{-5.315130348653373,1.4770651858539e-21},5.3e-16,1.5e-37},
  1624. {{3.1415926535897932384626433832795,0.0},18,{-5.639036854808338,1.21085227329631e-23},5.6e-16,1.2e-39},
  1625. {{3.1415926535897932384626433832795,0.0},20,{-6.285084985730819,5.832688628117013e-28},6.3e-16,5.8e-44},
  1626. {{3.141592653589793,0.0},0,{0.0,1.0},0.0,1.0e-16},
  1627. {{3.141592653589793,0.0},1,{-0.02928440396155444,0.9080003316496248},2.9e-18,9.1e-17},
  1628. {{3.141592653589793,0.0},2,{-0.111414420013723,0.7161490362627657},1.1e-17,7.2e-17},
  1629. {{3.141592653589793,0.0},3,{-0.3086445141021306,0.4340404684115406},3.1e-17,4.3e-17},
  1630. {{3.141592653589793,0.0},4,{-0.685342097549159,0.1613084612168837},6.9e-17,1.6e-17},
  1631. {{3.141592653589793,0.0},5,{-1.154547531604494,0.03095979893899374},1.2e-16,3.1e-18},
  1632. {{3.141592653589793,0.0},6,{-1.583565196074497,0.003296559784896672},1.6e-16,3.3e-19},
  1633. {{3.141592653589793,0.0},7,{-1.965821634628247,0.0002268900069871886},2.0e-16,2.3e-20},
  1634. {{3.141592653589793,0.0},8,{-2.324862655057826,1.114344043688994e-5},2.3e-16,1.1e-21},
  1635. {{3.141592653589793,0.0},9,{-2.672097814251784,4.13754647247384e-7},2.7e-16,4.1e-23},
  1636. {{3.141592653589793,0.0},10,{-3.012310405818385,1.206868381771847e-8},3.0e-16,1.2e-24},
  1637. {{3.141592653589793,0.0},11,{-3.347886623965971,2.844473227189745e-10},3.3e-16,2.8e-26},
  1638. {{3.141592653589793,0.0},12,{-3.680202022452917,5.536734412459235e-12},3.7e-16,5.5e-28},
  1639. {{3.141592653589793,0.0},13,{-4.010122340785055,9.058092394439002e-14},4.0e-16,9.1e-30},
  1640. {{3.141592653589793,0.0},14,{-4.338225297702632,1.263667883273073e-15},4.3e-16,1.3e-31},
  1641. {{3.141592653589793,0.0},15,{-4.664913422622491,1.521676227453876e-17},4.7e-16,1.5e-33},
  1642. {{3.141592653589793,0.0},16,{-4.990476814065978,1.598129828453934e-19},5.0e-16,1.6e-35},
  1643. {{3.141592653589793,0.0},17,{-5.315130348653373,1.477065185853896e-21},5.3e-16,1.5e-37},
  1644. {{3.141592653589793,0.0},18,{-5.639036854808339,1.210852273296306e-23},5.6e-16,1.2e-39},
  1645. {{3.141592653589793,0.0},20,{-6.285084985730819,5.832688628116996e-28},6.3e-16,5.8e-44},
  1646. };
  1647. // complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
  1648. std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
  1649. psi_test_16digits
  1650. = {
  1651. {{0.055,0.0},0,{0.05497227502706773,0.0},5.5e-18,0.0},
  1652. {{0.055,0.0},1,{0.001008028345451298,0.0},1.0e-19,0.0},
  1653. {{0.055,0.0},2,{1.108927027577585e-5,0.0},1.1e-21,0.0},
  1654. {{0.055,0.0},3,{8.713416468907156e-8,0.0},8.7e-24,0.0},
  1655. {{0.055,0.0},4,{5.325028332528807e-10,0.0},5.3e-26,0.0},
  1656. {{0.055,0.0},5,{2.662570490744701e-12,0.0},2.7e-28,0.0},
  1657. {{0.056,0.0},0,{0.05597073525575547,0.0},5.6e-18,0.0},
  1658. {{0.056,0.0},1,{0.00104500555351332,0.0},1.0e-19,0.0},
  1659. {{0.056,0.0},2,{1.170511102950751e-5,0.0},1.2e-21,0.0},
  1660. {{0.056,0.0},3,{9.364554985109859e-8,0.0},9.4e-24,0.0},
  1661. {{0.056,0.0},4,{5.827018798125993e-10,0.0},5.8e-26,0.0},
  1662. {{0.056,0.0},5,{2.966547354864994e-12,0.0},3.0e-28,0.0},
  1663. {{0.099,0.0},0,{0.09883836273067998,0.0},9.9e-18,0.0},
  1664. {{0.099,0.0},1,{0.003263799133906297,0.0},3.3e-19,0.0},
  1665. {{0.099,0.0},2,{6.464132708660462e-5,0.0},6.5e-21,0.0},
  1666. {{0.099,0.0},3,{9.143553161581762e-7,0.0},9.1e-23,0.0},
  1667. {{0.099,0.0},4,{1.005890437753418e-8,0.0},1.0e-24,0.0},
  1668. {{0.101,0.0},0,{0.100828370729568,0.0},1.0e-17,0.0},
  1669. {{0.101,0.0},1,{0.003396865916775768,0.0},3.4e-19,0.0},
  1670. {{0.101,0.0},2,{6.863669941520236e-5,0.0},6.9e-21,0.0},
  1671. {{0.101,0.0},3,{9.904899174185251e-7,0.0},9.9e-23,0.0},
  1672. {{0.101,0.0},4,{1.111664350730229e-8,0.0},1.1e-24,0.0},
  1673. {{1.0,0.0},0,{0.8414709848078965,0.0},8.4e-17,0.0},
  1674. {{1.0,0.0},1,{0.3011686789397568,0.0},3.0e-17,0.0},
  1675. {{1.0,0.0},2,{0.06203505201137386,0.0},6.2e-18,0.0},
  1676. {{1.0,0.0},3,{0.009006581117112516,0.0},9.0e-19,0.0},
  1677. {{1.0,0.0},4,{0.001011015808413753,0.0},1.0e-19,0.0},
  1678. {{1.0,0.0},5,{9.256115861125816e-5,0.0},9.3e-21,0.0},
  1679. {{1.0,0.0},6,{7.156936310087086e-6,0.0},7.2e-22,0.0},
  1680. {{1.0,0.0},7,{4.790134198739489e-7,0.0},4.8e-23,0.0},
  1681. {{1.0,0.0},8,{2.826498802214729e-8,0.0},2.8e-24,0.0},
  1682. {{1.0,0.0},9,{1.491376502555146e-9,0.0},1.5e-25,0.0},
  1683. {{1.0,0.0},10,{7.116552640047313e-11,0.0},7.1e-27,0.0},
  1684. {{1.0,0.0},11,{3.09955185479008e-12,0.0},3.1e-28,0.0},
  1685. {{1.0,0.0},12,{1.241662596987106e-13,0.0},1.2e-29,0.0},
  1686. {{1.0,0.0},13,{4.604637677683787e-15,0.0},4.6e-31,0.0},
  1687. {{1.0,0.0},14,{1.589575987516976e-16,0.0},1.6e-32,0.0},
  1688. {{1.0,0.0},15,{5.132686115443762e-18,0.0},5.1e-34,0.0},
  1689. {{1.0,0.0},16,{1.556708270590172e-19,0.0},1.6e-35,0.0},
  1690. {{1.0,0.0},17,{4.451177503806802e-21,0.0},4.5e-37,0.0},
  1691. {{1.0,0.0},19,{3.088742363539549e-24,0.0},3.1e-40,0.0},
  1692. {{1.0,0.0},20,{7.537795722236873e-26,0.0},7.5e-42,0.0},
  1693. {{1.0,0.0},22,{3.899361309912283e-29,0.0},3.9e-45,0.0},
  1694. {{1.0,0.0},24,{1.694580173763896e-32,0.0},1.7e-48,0.0},
  1695. {{1.0,0.0},26,{6.273730960048117e-36,0.0},6.3e-52,0.0},
  1696. {{1.0,0.0},28,{2.002424424322351e-39,0.0},2.0e-55,0.0},
  1697. {{1.0,0.0},30,{5.566831266981347e-43,0.0},5.6e-59,0.0},
  1698. {{1.0,0.0},32,{1.360066050758899e-46,0.0},1.4e-62,0.0},
  1699. {{1.0,0.0},35,{4.146142464888971e-52,0.0},4.1e-68,0.0},
  1700. {{1.0,0.0},38,{9.840005687079579e-58,0.0},9.8e-74,0.0},
  1701. {{1.0,0.0},41,{1.853528272155995e-63,0.0},1.9e-79,0.0},
  1702. {{10.0,0.0},0,{-0.5440211108893698,0.0},5.4e-17,0.0},
  1703. {{10.0,0.0},1,{0.7846694179875155,0.0},7.8e-17,0.0},
  1704. {{10.0,0.0},2,{0.7794219362856245,0.0},7.8e-17,0.0},
  1705. {{10.0,0.0},3,{-0.3949584498447032,0.0},3.9e-17,0.0},
  1706. {{10.0,0.0},4,{-1.055892851176917,0.0},1.1e-16,0.0},
  1707. {{10.0,0.0},5,{-0.5553451162145218,0.0},5.6e-17,0.0},
  1708. {{10.0,0.0},6,{0.4450132233409427,0.0},4.5e-17,0.0},
  1709. {{10.0,0.0},7,{1.133862306557747,0.0},1.1e-16,0.0},
  1710. {{10.0,0.0},8,{1.255780236495678,0.0},1.3e-16,0.0},
  1711. {{10.0,0.0},9,{1.000964095484906,0.0},1.0e-16,0.0},
  1712. {{10.0,0.0},10,{0.6460515449256426,0.0},6.5e-17,0.0},
  1713. {{10.0,0.0},11,{0.3557441488589438,0.0},3.6e-17,0.0},
  1714. {{10.0,0.0},12,{0.1721599974499281,0.0},1.7e-17,0.0},
  1715. {{10.0,0.0},13,{0.07465584476587637,0.0},7.5e-18,0.0},
  1716. {{10.0,0.0},14,{0.02941078341793813,0.0},2.9e-18,0.0},
  1717. {{10.0,0.0},16,{0.00355904073510893,0.0},3.6e-19,0.0},
  1718. {{10.0,0.0},17,{0.001109407279715256,0.0},1.1e-19,0.0},
  1719. {{10.0,0.0},18,{0.0003238847438944672,0.0},3.2e-20,0.0},
  1720. {{10.0,0.0},19,{8.896627269427228e-5,0.0},8.9e-21,0.0},
  1721. {{10.0,0.0},21,{5.676977719825934e-6,0.0},5.7e-22,0.0},
  1722. {{10.0,0.0},22,{1.327284582056831e-6,0.0},1.3e-22,0.0},
  1723. {{10.0,0.0},24,{6.298904526324468e-8,0.0},6.3e-24,0.0},
  1724. {{10.0,0.0},26,{2.512408773243373e-9,0.0},2.5e-25,0.0},
  1725. {{10.0,0.0},27,{4.723441380941795e-10,0.0},4.7e-26,0.0},
  1726. {{10.0,0.0},30,{2.512057384998943e-12,0.0},2.5e-28,0.0},
  1727. {{80.0,0.0},0,{-0.9938886539233752,0.0},9.9e-17,0.0},
  1728. {{80.0,0.0},1,{0.09796363566500537,0.0},9.8e-18,0.0},
  1729. {{80.0,0.0},30,{0.9085891506822639,0.0},9.1e-17,0.0},
  1730. {{80.0,0.0},50,{-0.8510856094465454,0.0},8.5e-17,0.0},
  1731. {{80.0,0.0},60,{-0.6405828831301126,0.0},6.4e-17,0.0},
  1732. {{80.0,0.0},70,{-0.9641731454914271,0.0},9.6e-17,0.0},
  1733. {{80.0,0.0},75,{1.681221392899474,0.0},1.7e-16,0.0},
  1734. {{80.0,0.0},80,{1.039376092082608,0.0},1.0e-16,0.0},
  1735. {{80.0,0.0},85,{0.2018445846611147,0.0},2.0e-17,0.0},
  1736. {{80.0,0.0},90,{0.01915014115966514,0.0},1.9e-18,0.0},
  1737. {{80.0,0.0},99,{7.337119877778807e-5,0.0},7.3e-21,0.0},
  1738. {{80.0,0.0},116,{6.387468798952271e-11,0.0},6.4e-27,0.0},
  1739. {{80.0,0.0},130,{4.862998628516291e-17,0.0},4.9e-33,0.0},
  1740. {{100.0,0.0},0,{-0.5063656411097588,0.0},5.1e-17,0.0},
  1741. {{100.0,0.0},1,{-0.8673825286987815,0.0},8.7e-17,0.0},
  1742. {{100.0,0.0},2,{0.4803441652487953,0.0},4.8e-17,0.0},
  1743. {{100.0,0.0},3,{0.8913997369612213,0.0},8.9e-17,0.0},
  1744. {{100.0,0.0},4,{-0.4179461836615099,0.0},4.2e-17,0.0},
  1745. {{100.0,0.0},5,{-0.9290148934907572,0.0},9.3e-17,0.0},
  1746. {{100.0,0.0},6,{0.3157545453775266,0.0},3.2e-17,0.0},
  1747. {{100.0,0.0},7,{0.9700629843898356,0.0},9.7e-17,0.0},
  1748. {{100.0,0.0},8,{-0.1702450977190512,0.0},1.7e-17,0.0},
  1749. {{100.0,0.0},9,{-0.9990046510020743,0.0},1.0e-16,0.0},
  1750. {{100.0,0.0},10,{-0.0195657859713429,0.0},2.0e-18,0.0},
  1751. {{100.0,0.0},12,{0.2483918282394041,0.0},2.5e-17,0.0},
  1752. {{100.0,0.0},14,{-0.5002472555392293,0.0},5.0e-17,0.0},
  1753. {{100.0,0.0},17,{-0.5420601927737344,0.0},5.4e-17,0.0},
  1754. {{100.0,0.0},19,{0.196419721012541,0.0},2.0e-17,0.0},
  1755. {{100.0,0.0},23,{-0.6306580152858614,0.0},6.3e-17,0.0},
  1756. {{100.0,0.0},26,{-0.143891546591607,0.0},1.4e-17,0.0},
  1757. {{100.0,0.0},31,{-0.245348080601665,0.0},2.5e-17,0.0},
  1758. {{100.0,0.0},36,{-0.08022559212383603,0.0},8.0e-18,0.0},
  1759. {{100.0,0.0},42,{-0.7409802829736421,0.0},7.4e-17,0.0},
  1760. {{100.0,0.0},49,{-0.8988354032424621,0.0},9.0e-17,0.0},
  1761. {{100.0,0.0},57,{0.7715080707056898,0.0},7.7e-17,0.0},
  1762. {{100.0,0.0},66,{0.5915705424339723,0.0},5.9e-17,0.0},
  1763. {{100.0,0.0},76,{-0.987829555147092,0.0},9.9e-17,0.0},
  1764. {{100.0,0.0},89,{-1.119551845294465,0.0},1.1e-16,0.0},
  1765. {{100.0,0.0},103,{0.4862349872932045,0.0},4.9e-17,0.0},
  1766. {{100.0,0.0},120,{0.0001044935577431419,0.0},1.0e-20,0.0},
  1767. {{100.0,0.0},140,{2.229243941309043e-11,0.0},2.2e-27,0.0},
  1768. {{100.0,0.0},162,{9.763089067519337e-21,0.0},9.8e-37,0.0},
  1769. {{100.0,0.0},188,{6.861471624173392e-34,0.0},6.9e-50,0.0},
  1770. {{100.0,0.0},219,{5.960550110959533e-52,0.0},6.0e-68,0.0},
  1771. {{100.0,0.0},254,{6.750243200363117e-75,0.0},6.8e-91,0.0},
  1772. {{100.0,0.0},296,{2.077300079982611e-105,0.0},2.1e-121,0.0},
  1773. {{100.0,0.0},343,{8.525637576350521e-143,0.0},8.5e-159,0.0},
  1774. {{100.0,0.0},399,{3.970577452228161e-191,0.0},4.0e-207,0.0},
  1775. {{100.0,0.0},464,{1.275975218077633e-251,0.0},1.3e-267,0.0},
  1776. {{100.0,0.0},539,{2.005718001506372e-326,0.0},2.0e-342,0.0},
  1777. {{100.0,0.0},626,{6.078701921888599e-419,0.0},6.1e-435,0.0},
  1778. {{100.0,0.0},727,{5.501888319350496e-533,0.0},5.5e-549,0.0},
  1779. {{100.0,0.0},844,{9.499262854440157e-673,0.0},9.5e-689,0.0},
  1780. {{100.0,0.0},981,{2.265887828424654e-845,0.0},2.3e-861,0.0},
  1781. {{100.0,0.0},1139,{8.842715022418808e-1055,0.0},8.8e-1071,0.0},
  1782. {{100.0,0.0},1324,{4.668811390736464e-1312,0.0},4.7e-1328,0.0},
  1783. {{100.0,0.0},1537,{3.675773987185818e-1622,0.0},3.7e-1638,0.0},
  1784. {{1000.0,0.0},0,{0.8268795405320026,0.0},8.3e-17,0.0},
  1785. {{1000.0,0.0},1,{-0.561552196750171,0.0},5.6e-17,0.0},
  1786. {{1000.0,0.0},2,{-0.8285641971222531,0.0},8.3e-17,0.0},
  1787. {{1000.0,0.0},3,{0.5574093757645597,0.0},5.6e-17,0.0},
  1788. {{1000.0,0.0},4,{0.832466062752605,0.0},8.3e-17,0.0},
  1789. {{1000.0,0.0},5,{-0.5499171811997863,0.0},5.5e-17,0.0},
  1790. {{1000.0,0.0},6,{-0.8385151517458026,0.0},8.4e-17,0.0},
  1791. {{1000.0,0.0},7,{0.5390164842270908,0.0},5.4e-17,0.0},
  1792. {{1000.0,0.0},9,{-0.5246242774439343,0.0},5.2e-17,0.0},
  1793. {{1000.0,0.0},10,{-0.8565682602806438,0.0},8.6e-17,0.0},
  1794. {{1000.0,0.0},11,{0.5066363439780408,0.0},5.1e-17,0.0},
  1795. {{1000.0,0.0},13,{-0.4849308215732373,0.0},4.8e-17,0.0},
  1796. {{1000.0,0.0},15,{0.4593727147503734,0.0},4.6e-17,0.0},
  1797. {{1000.0,0.0},18,{-0.9105982620053164,0.0},9.1e-17,0.0},
  1798. {{1000.0,0.0},20,{0.9260472258407888,0.0},9.3e-17,0.0},
  1799. {{1000.0,0.0},23,{0.3157941780843729,0.0},3.2e-17,0.0},
  1800. {{1000.0,0.0},27,{0.2175256230184992,0.0},2.2e-17,0.0},
  1801. {{1000.0,0.0},31,{0.1010717270922797,0.0},1.0e-17,0.0},
  1802. {{1000.0,0.0},35,{-0.03281014717791907,0.0},3.3e-18,0.0},
  1803. {{1000.0,0.0},41,{0.2609242061122253,0.0},2.6e-17,0.0},
  1804. {{1000.0,0.0},47,{-0.5066400369537076,0.0},5.1e-17,0.0},
  1805. {{1000.0,0.0},54,{-0.6313512330276828,0.0},6.3e-17,0.0},
  1806. {{1000.0,0.0},62,{-0.2129900416598473,0.0},2.1e-17,0.0},
  1807. {{1000.0,0.0},71,{-0.926462659427137,0.0},9.3e-17,0.0},
  1808. {{1000.0,0.0},81,{0.4047902506937166,0.0},4.0e-17,0.0},
  1809. {{1000.0,0.0},93,{-0.5947534057635428,0.0},5.9e-17,0.0},
  1810. {{1000.0,0.0},107,{0.8923701726937493,0.0},8.9e-17,0.0},
  1811. {{1000.0,0.0},123,{-0.6881373362486023,0.0},6.9e-17,0.0},
  1812. {{1000.0,0.0},141,{-0.005790484710336857,0.0},5.8e-19,0.0},
  1813. {{1000.0,0.0},162,{-1.004341451851323,0.0},1.0e-16,0.0},
  1814. {{1000.0,0.0},186,{0.4243208523362115,0.0},4.2e-17,0.0},
  1815. {{1000.0,0.0},214,{0.8850377283334687,0.0},8.9e-17,0.0},
  1816. {{1000.0,0.0},246,{-0.09666900461099306,0.0},9.7e-18,0.0},
  1817. {{1000.0,0.0},282,{0.3093032076039036,0.0},3.1e-17,0.0},
  1818. {{1000.0,0.0},324,{-0.6574666571444073,0.0},6.6e-17,0.0},
  1819. {{1000.0,0.0},372,{0.909222573405285,0.0},9.1e-17,0.0},
  1820. {{1000.0,0.0},427,{0.9597285605463302,0.0},9.6e-17,0.0},
  1821. {{1000.0,0.0},490,{1.046104365597067,0.0},1.0e-16,0.0},
  1822. {{1000.0,0.0},562,{-0.4772156439441007,0.0},4.8e-17,0.0},
  1823. {{1000.0,0.0},645,{0.7143679947886889,0.0},7.1e-17,0.0},
  1824. {{1000.0,0.0},740,{1.209734186991773,0.0},1.2e-16,0.0},
  1825. {{1000.0,0.0},850,{-1.034435797754064,0.0},1.0e-16,0.0},
  1826. {{10000.0,0.0},0,{-0.3056143888882521,0.0},3.1e-17,0.0},
  1827. {{10000.0,0.0},1,{0.952124806820126,0.0},9.5e-17,0.0},
  1828. {{10000.0,0.0},2,{0.3059000263302982,0.0},3.1e-17,0.0},
  1829. {{10000.0,0.0},3,{-0.9519718568069609,0.0},9.5e-17,0.0},
  1830. {{10000.0,0.0},4,{-0.3065664066300631,0.0},3.1e-17,0.0},
  1831. {{10000.0,0.0},5,{0.9516959470409938,0.0},9.5e-17,0.0},
  1832. {{10000.0,0.0},6,{0.3076132721718081,0.0},3.1e-17,0.0},
  1833. {{10000.0,0.0},8,{-0.3090402162464889,0.0},3.1e-17,0.0},
  1834. {{10000.0,0.0},11,{-0.9501179033904149,0.0},9.5e-17,0.0},
  1835. {{10000.0,0.0},14,{0.315595157092464,0.0},3.2e-17,0.0},
  1836. {{10000.0,0.0},18,{0.3218510506540846,0.0},3.2e-17,0.0},
  1837. {{10000.0,0.0},23,{-0.9433601457445342,0.0},9.4e-17,0.0},
  1838. {{10000.0,0.0},29,{0.9379666478839471,0.0},9.4e-17,0.0},
  1839. {{10000.0,0.0},37,{0.9283397516018927,0.0},9.3e-17,0.0},
  1840. {{10000.0,0.0},48,{-0.4152217424854132,0.0},4.2e-17,0.0},
  1841. {{10000.0,0.0},61,{0.8777422109084248,0.0},8.8e-17,0.0},
  1842. {{10000.0,0.0},78,{0.5799735094103576,0.0},5.8e-17,0.0},
  1843. {{10000.0,0.0},99,{-0.6927046245889522,0.0},6.9e-17,0.0},
  1844. {{10000.0,0.0},126,{0.8960430419640289,0.0},9.0e-17,0.0},
  1845. {{10000.0,0.0},161,{-0.04390438580192674,0.0},4.4e-18,0.0},
  1846. {{10000.0,0.0},205,{-0.7522577756314945,0.0},7.5e-17,0.0},
  1847. {{10000.0,0.0},262,{-0.5766402963422176,0.0},5.8e-17,0.0},
  1848. {{10000.0,0.0},333,{0.9169823827831649,0.0},9.2e-17,0.0},
  1849. {{10000.0,0.0},425,{-0.9986331409734894,0.0},1.0e-16,0.0},
  1850. {{10000.0,0.0},541,{-0.7439210236606826,0.0},7.4e-17,0.0},
  1851. {{10000.0,0.0},690,{-0.8276630796953436,0.0},8.3e-17,0.0},
  1852. {{10000.0,0.0},879,{-0.2559686924018959,0.0},2.6e-17,0.0},
  1853. {{10000.0,0.0},1120,{-0.3161896326121199,0.0},3.2e-17,0.0},
  1854. {{10000.0,0.0},1427,{0.2687936760264434,0.0},2.7e-17,0.0},
  1855. {{10000.0,0.0},1818,{0.3801110903322125,0.0},3.8e-17,0.0},
  1856. {{10000.0,0.0},2316,{0.3363664648717635,0.0},3.4e-17,0.0},
  1857. {{10000.0,0.0},2950,{-0.8588302425401225,0.0},8.6e-17,0.0},
  1858. {{10000.0,0.0},3758,{-0.8541132755119114,0.0},8.5e-17,0.0},
  1859. {{10000.0,0.0},7771,{-1.18058612315672,0.0},1.2e-16,0.0},
  1860. {{10000.0,0.0},9900,{-1.747822111395514,0.0},1.7e-16,0.0},
  1861. {{10000.0,0.0},12612,{7.25197826864343e-541,0.0},7.3e-557,0.0},
  1862. {{10000.0,0.0},16067,{1.369451063257112e-1882,0.0},1.4e-1898,0.0},
  1863. {{10000.0,0.0},20468,{1.387136027206115e-4188,0.0},1.4e-4204,0.0},
  1864. {{10000.0,0.0},26075,{3.402710534773112e-7804,0.0},3.4e-7820,0.0},
  1865. {{10000.0,0.0},33218,{1.467628954663695e-13224,0.0},1.5e-13240,0.0},
  1866. {{10000.0,0.0},42318,{5.445358924275546e-21134,0.0},5.4e-21150,0.0},
  1867. {{10000.0,0.0},53911,{3.266521110728529e-32465,0.0},3.3e-32481,0.0},
  1868. {{10000.0,0.0},68679,{2.775502574785064e-48480,0.0},2.8e-48496,0.0},
  1869. {{10000.0,0.0},87493,{8.914211935647729e-70883,0.0},8.9e-70899,0.0},
  1870. {{10000.0,0.0},111461,{2.619912559375462e-101959,0.0},2.6e-101975,0.0},
  1871. {{10000.0,0.0},141995,{5.82392981843591e-144773,0.0},5.8e-144789,0.0},
  1872. };
  1873. // complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
  1874. std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
  1875. zeta_test_16digits
  1876. = {
  1877. {{0.055,0.0},0,{0.05497227502706773,-0.9984878812375984},5.5e-18,1.0e-16},
  1878. {{0.055,0.0},1,{0.001008028345451298,-18.20929738843795},1.0e-19,1.8e-15},
  1879. {{0.055,0.0},2,{1.108927027577585e-5,-992.2359151244687},1.1e-21,9.9e-14},
  1880. {{0.055,0.0},3,{8.713416468907156e-8,-90185.05571392689},8.7e-24,9.0e-12},
  1881. {{0.055,0.0},4,{5.325028332528807e-10,-11477105.76403921},5.3e-26,1.1e-9},
  1882. {{0.055,0.0},5,{2.662570490744701e-12,-1877981667.241611},2.7e-28,1.9e-7},
  1883. {{0.056,0.0},0,{0.05597073525575547,-0.9984324097278344},5.6e-18,1.0e-16},
  1884. {{0.056,0.0},1,{0.00104500555351332,-17.88512090896708},1.0e-19,1.8e-15},
  1885. {{0.056,0.0},2,{1.170511102950751e-5,-957.1330448563659},1.2e-21,9.6e-14},
  1886. {{0.056,0.0},3,{9.364554985109859e-8,-85440.42245555228},9.4e-24,8.5e-12},
  1887. {{0.056,0.0},4,{5.827018798125993e-10,-10679095.67389918},5.8e-26,1.1e-9},
  1888. {{0.056,0.0},5,{2.966547354864994e-12,-1716197792.88277},3.0e-28,1.7e-7},
  1889. {{0.099,0.0},0,{0.09883836273067998,-0.9951035011759925},9.9e-18,1.0e-16},
  1890. {{0.099,0.0},1,{0.003263799133906297,-10.1503888796599},3.3e-19,1.0e-15},
  1891. {{0.099,0.0},2,{6.464132708660462e-5,-306.5924383066997},6.5e-21,3.1e-14},
  1892. {{0.099,0.0},3,{9.143553161581762e-7,-15474.31619226679},9.1e-23,1.5e-12},
  1893. {{0.099,0.0},4,{1.005890437753418e-8,-1093836.97671187},1.0e-24,1.1e-10},
  1894. {{0.101,0.0},0,{0.100828370729568,-0.9949038343759767},1.0e-17,9.9e-17},
  1895. {{0.101,0.0},1,{0.003396865916775768,-9.951361384353099},3.4e-19,1.0e-15},
  1896. {{0.101,0.0},2,{6.863669941520236e-5,-294.5900877800725},6.9e-21,2.9e-14},
  1897. {{0.101,0.0},3,{9.904899174185251e-7,-14573.71635050042},9.9e-23,1.5e-12},
  1898. {{0.101,0.0},4,{1.111664350730229e-8,-1009764.958956804},1.1e-24,1.0e-10},
  1899. {{1.0,0.0},0,{0.8414709848078965,-0.5403023058681397},8.4e-17,5.4e-17},
  1900. {{1.0,0.0},1,{0.3011686789397568,-1.381773290676036},3.0e-17,1.4e-16},
  1901. {{1.0,0.0},2,{0.06203505201137386,-3.605017566159969},6.2e-18,3.6e-16},
  1902. {{1.0,0.0},3,{0.009006581117112516,-16.64331454012381},9.0e-19,1.7e-15},
  1903. {{1.0,0.0},4,{0.001011015808413753,-112.8981842147067},1.0e-19,1.1e-14},
  1904. {{1.0,0.0},5,{9.256115861125816e-5,-999.4403433922364},9.3e-21,1.0e-13},
  1905. {{1.0,0.0},6,{7.156936310087086e-6,-10880.94559309989},7.2e-22,1.1e-12},
  1906. {{1.0,0.0},7,{4.790134198739489e-7,-140452.8523669064},4.8e-23,1.4e-11},
  1907. {{1.0,0.0},8,{2.826498802214729e-8,-2095911.839910496},2.8e-24,2.1e-10},
  1908. {{1.0,0.0},9,{1.491376502555146e-9,-35490048.42611152},1.5e-25,3.5e-9},
  1909. {{1.0,0.0},10,{7.116552640047313e-11,-672215008.2562084},7.1e-27,6.7e-8},
  1910. {{1.0,0.0},11,{3.09955185479008e-12,-14081025124.95427},3.1e-28,1.4e-6},
  1911. {{1.0,0.0},12,{1.241662596987106e-13,-323191362865.6919},1.2e-29,3.2e-5},
  1912. {{1.0,0.0},13,{4.604637677683787e-15,-8065703046517.343},4.6e-31,0.00081},
  1913. {{1.0,0.0},14,{1.589575987516976e-16,-217450790893102.6},1.6e-32,0.022},
  1914. {{1.0,0.0},15,{5.132686115443762e-18,-6298007232853457.0},5.1e-34,0.63},
  1915. {{1.0,0.0},16,{1.556708270590172e-19,-1.950207734275641e+17},1.6e-35,20.0},
  1916. {{1.0,0.0},17,{4.451177503806802e-21,-6.429387515876761e+18},4.5e-37,6.4e+2},
  1917. {{1.0,0.0},19,{3.088742363539549e-24,-8.312411676927709e+21},3.1e-40,8.3e+5},
  1918. {{1.0,0.0},20,{7.537795722236873e-26,-3.239592218578984e+23},7.5e-42,3.2e+7},
  1919. {{1.0,0.0},22,{3.899361309912283e-29,-5.704587152115091e+26},3.9e-45,5.7e+10},
  1920. {{1.0,0.0},24,{1.694580173763896e-32,-1.205325845219959e+30},1.7e-48,1.2e+14},
  1921. {{1.0,0.0},26,{6.273730960048117e-36,-3.009595435582847e+33},6.3e-52,3.0e+17},
  1922. {{1.0,0.0},28,{2.002424424322351e-39,-8.766714157290797e+36},2.0e-55,8.8e+20},
  1923. {{1.0,0.0},30,{5.566831266981347e-43,-2.946428547496782e+40},5.6e-59,2.9e+24},
  1924. {{1.0,0.0},32,{1.360066050758899e-46,-1.131703135696075e+44},1.4e-62,1.1e+28},
  1925. {{1.0,0.0},35,{4.146142464888971e-52,-3.398364364339443e+49},4.1e-68,3.4e+33},
  1926. {{1.0,0.0},38,{9.840005687079579e-58,-1.320263364413848e+55},9.8e-74,1.3e+39},
  1927. {{1.0,0.0},41,{1.853528272155995e-63,-6.502028762468467e+60},1.9e-79,6.5e+44},
  1928. {{10.0,0.0},0,{-0.5440211108893698,0.8390715290764525},5.4e-17,8.4e-17},
  1929. {{10.0,0.0},1,{0.7846694179875155,0.6279282637970151},7.8e-17,6.3e-17},
  1930. {{10.0,0.0},2,{0.7794219362856245,-0.6506930499373479},7.8e-17,6.5e-17},
  1931. {{10.0,0.0},3,{-0.3949584498447032,-0.953274788765689},3.9e-17,9.5e-17},
  1932. {{10.0,0.0},4,{-1.055892851176917,-0.01659930219863438},1.1e-16,1.7e-18},
  1933. {{10.0,0.0},5,{-0.5553451162145218,0.9383354167869181},5.6e-17,9.4e-17},
  1934. {{10.0,0.0},6,{0.4450132233409427,1.048768260664244},4.5e-17,1.0e-16},
  1935. {{10.0,0.0},7,{1.133862306557747,0.4250633220765995},1.1e-16,4.3e-17},
  1936. {{10.0,0.0},8,{1.255780236495678,-0.4111732775493451},1.3e-16,4.1e-17},
  1937. {{10.0,0.0},9,{1.000964095484906,-1.124057893910486},1.0e-16,1.1e-16},
  1938. {{10.0,0.0},10,{0.6460515449256426,-1.724536720880578},6.5e-17,1.7e-16},
  1939. {{10.0,0.0},11,{0.3557441488589438,-2.497469219938729},3.6e-17,2.5e-16},
  1940. {{10.0,0.0},12,{0.1721599974499281,-4.019642484978498},1.7e-17,4.0e-16},
  1941. {{10.0,0.0},13,{0.07465584476587637,-7.551636992507515},7.5e-18,7.6e-16},
  1942. {{10.0,0.0},14,{0.02941078341793813,-16.36977739479179},2.9e-18,1.6e-15},
  1943. {{10.0,0.0},16,{0.00355904073510893,-107.3844467076131},3.6e-19,1.1e-14},
  1944. {{10.0,0.0},17,{0.001109407279715256,-314.4479566827347},1.1e-19,3.1e-14},
  1945. {{10.0,0.0},18,{0.0003238847438944672,-993.1834016819582},3.2e-20,9.9e-14},
  1946. {{10.0,0.0},19,{8.896627269427228e-5,-3360.330629540511},8.9e-21,3.4e-13},
  1947. {{10.0,0.0},21,{5.676977719825934e-6,-46299.30418991622},5.7e-22,4.6e-12},
  1948. {{10.0,0.0},22,{1.327284582056831e-6,-186974.9019631137},1.3e-22,1.9e-11},
  1949. {{10.0,0.0},24,{6.298904526324468e-8,-3549937.544864135},6.3e-24,3.5e-10},
  1950. {{10.0,0.0},26,{2.512408773243373e-9,-81108054.15260572},2.5e-25,8.1e-9},
  1951. {{10.0,0.0},27,{4.723441380941795e-10,-413273080.7936202},4.7e-26,4.1e-8},
  1952. {{10.0,0.0},30,{2.512057384998943e-12,-69083186460.94516},2.5e-28,6.9e-6},
  1953. {{80.0,0.0},0,{-0.9938886539233752,0.1103872438390476},9.9e-17,1.1e-17},
  1954. {{80.0,0.0},1,{0.09796363566500537,0.9952684944713633},9.8e-18,1.0e-16},
  1955. {{80.0,0.0},30,{0.9085891506822639,-0.5060739517940013},9.1e-17,5.1e-17},
  1956. {{80.0,0.0},50,{-0.8510856094465454,-0.7514741282998871},8.5e-17,7.5e-17},
  1957. {{80.0,0.0},60,{-0.6405828831301126,1.056795272698575},6.4e-17,1.1e-16},
  1958. {{80.0,0.0},70,{-0.9641731454914271,1.082903079393562},9.6e-17,1.1e-16},
  1959. {{80.0,0.0},75,{1.681221392899474,0.2861031097638479},1.7e-16,2.9e-17},
  1960. {{80.0,0.0},80,{1.039376092082608,-2.229727207344475},1.0e-16,2.2e-16},
  1961. {{80.0,0.0},85,{0.2018445846611147,-6.79766591437198},2.0e-17,6.8e-16},
  1962. {{80.0,0.0},90,{0.01915014115966514,-49.68517113491355},1.9e-18,5.0e-15},
  1963. {{80.0,0.0},99,{7.337119877778807e-5,-9222.855138429382},7.3e-21,9.2e-13},
  1964. {{80.0,0.0},116,{6.387468798952271e-11,-7395385511.699251},6.4e-27,7.4e-7},
  1965. {{80.0,0.0},130,{4.862998628516291e-17,-7978214064656749.0},4.9e-33,0.8},
  1966. {{100.0,0.0},0,{-0.5063656411097588,-0.8623188722876839},5.1e-17,8.6e-17},
  1967. {{100.0,0.0},1,{-0.8673825286987815,0.497742452386882},8.7e-17,5.0e-17},
  1968. {{100.0,0.0},2,{0.4803441652487953,0.8772511458592904},4.8e-17,8.8e-17},
  1969. {{100.0,0.0},3,{0.8913997369612213,-0.4538798950939174},8.9e-17,4.5e-17},
  1970. {{100.0,0.0},4,{-0.4179461836615099,-0.9090227385158646},4.2e-17,9.1e-17},
  1971. {{100.0,0.0},5,{-0.9290148934907572,0.3720678486274896},9.3e-17,3.7e-17},
  1972. {{100.0,0.0},6,{0.3157545453775266,0.9499502018648885},3.2e-17,9.5e-17},
  1973. {{100.0,0.0},7,{0.9700629843898356,-0.2485743223850541},9.7e-17,2.5e-17},
  1974. {{100.0,0.0},8,{-0.1702450977190512,-0.9872363502226466},1.7e-17,9.9e-17},
  1975. {{100.0,0.0},9,{-0.9990046510020743,0.0807441428472042},1.0e-16,8.1e-18},
  1976. {{100.0,0.0},10,{-0.0195657859713429,1.002577737363615},2.0e-18,1.0e-16},
  1977. {{100.0,0.0},12,{0.2483918282394041,-0.9727243855038097},2.5e-17,9.7e-17},
  1978. {{100.0,0.0},14,{-0.5002472555392293,0.8720202503425307},5.0e-17,8.7e-17},
  1979. {{100.0,0.0},17,{-0.5420601927737344,-0.8496049309427912},5.4e-17,8.5e-17},
  1980. {{100.0,0.0},19,{0.196419721012541,0.9904419668956676},2.0e-17,9.9e-17},
  1981. {{100.0,0.0},23,{-0.6306580152858614,0.794394952285829},6.3e-17,7.9e-17},
  1982. {{100.0,0.0},26,{-0.143891546591607,-1.008142711740272},1.4e-17,1.0e-16},
  1983. {{100.0,0.0},31,{-0.245348080601665,-0.9967036472620608},2.5e-17,1.0e-16},
  1984. {{100.0,0.0},36,{-0.08022559212383603,-1.033265431104683},8.0e-18,1.0e-16},
  1985. {{100.0,0.0},42,{-0.7409802829736421,-0.7454135574907433},7.4e-17,7.5e-17},
  1986. {{100.0,0.0},49,{-0.8988354032424621,0.5855924676754787},9.0e-17,5.9e-17},
  1987. {{100.0,0.0},57,{0.7715080707056898,0.7917840064320207},7.7e-17,7.9e-17},
  1988. {{100.0,0.0},66,{0.5915705424339723,-0.9943577408622831},5.9e-17,9.9e-17},
  1989. {{100.0,0.0},76,{-0.987829555147092,-0.758958460609405},9.9e-17,7.6e-17},
  1990. {{100.0,0.0},89,{-1.119551845294465,0.9874911064736249},1.1e-16,9.9e-17},
  1991. {{100.0,0.0},103,{0.4862349872932045,-3.932782745345558},4.9e-17,3.9e-16},
  1992. {{100.0,0.0},120,{0.0001044935577431419,-7123.747314608973},1.0e-20,7.1e-13},
  1993. {{100.0,0.0},140,{2.229243941309043e-11,-22728970587.22979},2.2e-27,2.3e-6},
  1994. {{100.0,0.0},162,{9.763089067519337e-21,-3.998455948928182e+19},9.8e-37,4.0e+3},
  1995. {{100.0,0.0},188,{6.861471624173392e-34,-4.560507264377804e+32},6.9e-50,4.6e+16},
  1996. {{100.0,0.0},219,{5.960550110959533e-52,-4.293053043714103e+50},6.0e-68,4.3e+34},
  1997. {{100.0,0.0},254,{6.750243200363117e-75,-3.165039335082101e+73},6.8e-91,3.2e+57},
  1998. {{100.0,0.0},296,{2.077300079982611e-105,-8.62319701238945e+103},2.1e-121,8.6e+87},
  1999. {{100.0,0.0},343,{8.525637576350521e-143,-1.784625319681049e+141},8.5e-159,1.8e+125},
  2000. {{100.0,0.0},399,{3.970577452228161e-191,-3.255744216903431e+189},4.0e-207,3.3e+173},
  2001. {{100.0,0.0},464,{1.275975218077633e-251,-8.638673889350171e+249},1.3e-267,8.6e+233},
  2002. {{100.0,0.0},539,{2.005718001506372e-326,-4.702192956140304e+324},2.0e-342,4.7e+308},
  2003. {{100.0,0.0},626,{6.078701921888599e-419,-1.329971011220177e+417},6.1e-435,1.3e+401},
  2004. {{100.0,0.0},727,{5.501888319350496e-533,-1.261151833780533e+531},5.5e-549,1.3e+515},
  2005. {{100.0,0.0},844,{9.499262854440157e-673,-6.276922570590454e+670},9.5e-689,6.3e+654},
  2006. {{100.0,0.0},981,{2.265887828424654e-845,-2.259993447656205e+843},2.3e-861,2.3e+827},
  2007. {{100.0,0.0},1139,{8.842715022418808e-1055,-4.981370725943817e+1052},8.8e-1071,5.0e+1036},
  2008. {{100.0,0.0},1324,{4.668811390736464e-1312,-8.108733995411389e+1309},4.7e-1328,8.1e+1293},
  2009. {{100.0,0.0},1537,{3.675773987185818e-1622,-8.865977477340542e+1619},3.7e-1638,8.9e+1603},
  2010. {{1000.0,0.0},0,{0.8268795405320026,-0.562379076290703},8.3e-17,5.6e-17},
  2011. {{1000.0,0.0},1,{-0.561552196750171,-0.8274419196082933},5.6e-17,8.3e-17},
  2012. {{1000.0,0.0},2,{-0.8285641971222531,0.5598967505318781},8.3e-17,5.6e-17},
  2013. {{1000.0,0.0},3,{0.5574093757645597,0.8302414033609527},5.6e-17,8.3e-17},
  2014. {{1000.0,0.0},4,{0.832466062752605,-0.5540850607083514},8.3e-17,5.5e-17},
  2015. {{1000.0,0.0},5,{-0.5499171811997863,-0.8352281689073278},5.5e-17,8.4e-17},
  2016. {{1000.0,0.0},6,{-0.8385151517458026,0.5448975508503708},8.4e-17,5.4e-17},
  2017. {{1000.0,0.0},7,{0.5390164842270908,0.8423118370683826},5.4e-17,8.4e-17},
  2018. {{1000.0,0.0},9,{-0.5246242774439343,-0.8513603059143865},5.2e-17,8.5e-17},
  2019. {{1000.0,0.0},10,{-0.8565682602806438,0.5160870274819718},8.6e-17,5.2e-17},
  2020. {{1000.0,0.0},11,{0.5066363439780408,0.8621981334915079},5.1e-17,8.6e-17},
  2021. {{1000.0,0.0},13,{-0.4849308215732373,-0.8746045452517996},4.8e-17,8.7e-17},
  2022. {{1000.0,0.0},15,{0.4593727147503734,0.8883111675348058},4.6e-17,8.9e-17},
  2023. {{1000.0,0.0},18,{-0.9105982620053164,0.4134995149333431},9.1e-17,4.1e-17},
  2024. {{1000.0,0.0},20,{0.9260472258407888,-0.3776858501060111},9.3e-17,3.8e-17},
  2025. {{1000.0,0.0},23,{0.3157941780843729,0.9489732087840213},3.2e-17,9.5e-17},
  2026. {{1000.0,0.0},27,{0.2175256230184992,0.976248337884936},2.2e-17,9.8e-17},
  2027. {{1000.0,0.0},31,{0.1010717270922797,0.9951285718767434},1.0e-17,1.0e-16},
  2028. {{1000.0,0.0},35,{-0.03281014717791907,0.9997770197744073},3.3e-18,1.0e-16},
  2029. {{1000.0,0.0},41,{0.2609242061122253,-0.9658057107645263},2.6e-17,9.7e-17},
  2030. {{1000.0,0.0},47,{-0.5066400369537076,0.8628127163075355},5.1e-17,8.6e-17},
  2031. {{1000.0,0.0},54,{-0.6313512330276828,-0.7764560092822195},6.3e-17,7.8e-17},
  2032. {{1000.0,0.0},62,{-0.2129900416598473,-0.9780562249615457},2.1e-17,9.8e-17},
  2033. {{1000.0,0.0},71,{-0.926462659427137,-0.379779907874921},9.3e-17,3.8e-17},
  2034. {{1000.0,0.0},81,{0.4047902506937166,0.9162327671042002},4.0e-17,9.2e-17},
  2035. {{1000.0,0.0},93,{-0.5947534057635428,0.8066400984512723},5.9e-17,8.1e-17},
  2036. {{1000.0,0.0},107,{0.8923701726937493,0.4577161030388435},8.9e-17,4.6e-17},
  2037. {{1000.0,0.0},123,{-0.6881373362486023,0.7308771114070519},6.9e-17,7.3e-17},
  2038. {{1000.0,0.0},141,{-0.005790484710336857,1.00505240530667},5.8e-19,1.0e-16},
  2039. {{1000.0,0.0},162,{-1.004341451851323,-0.06905501630232919},1.0e-16,6.9e-18},
  2040. {{1000.0,0.0},186,{0.4243208523362115,0.9153196261481822},4.2e-17,9.2e-17},
  2041. {{1000.0,0.0},214,{0.8850377283334687,0.4904474893116481},8.9e-17,4.9e-17},
  2042. {{1000.0,0.0},246,{-0.09666900461099306,1.011184752036795},9.7e-18,1.0e-16},
  2043. {{1000.0,0.0},282,{0.3093032076039036,-0.973033201417064},3.1e-17,9.7e-17},
  2044. {{1000.0,0.0},324,{-0.6574666571444073,0.7905362270426355},6.6e-17,7.9e-17},
  2045. {{1000.0,0.0},372,{0.909222573405285,0.500862067695031},9.1e-17,5.0e-17},
  2046. {{1000.0,0.0},427,{0.9597285605463302,-0.4302284984951585},9.6e-17,4.3e-17},
  2047. {{1000.0,0.0},490,{1.046104365597067,-0.2306282264858935},1.0e-16,2.3e-17},
  2048. {{1000.0,0.0},562,{-0.4772156439441007,0.9908332203529922},4.8e-17,9.9e-17},
  2049. {{1000.0,0.0},645,{0.7143679947886889,0.8938610251077628},7.1e-17,8.9e-17},
  2050. {{1000.0,0.0},740,{1.209734186991773,-0.1565477440422447},1.2e-16,1.6e-17},
  2051. {{1000.0,0.0},850,{-1.034435797754064,-0.9116631948399486},1.0e-16,9.1e-17},
  2052. {{10000.0,0.0},0,{-0.3056143888882521,0.9521553682590149},3.1e-17,9.5e-17},
  2053. {{10000.0,0.0},1,{0.952124806820126,0.305709604425078},9.5e-17,3.1e-17},
  2054. {{10000.0,0.0},2,{0.3059000263302982,-0.9520636553776873},3.1e-17,9.5e-17},
  2055. {{10000.0,0.0},3,{-0.9519718568069609,-0.3061856362527669},9.5e-17,3.1e-17},
  2056. {{10000.0,0.0},4,{-0.3065664066300631,0.9518493254323104},3.1e-17,9.5e-17},
  2057. {{10000.0,0.0},5,{0.9516959470409938,0.307042300645656},9.5e-17,3.1e-17},
  2058. {{10000.0,0.0},6,{0.3076132721718081,-0.9515115789016002},3.1e-17,9.5e-17},
  2059. {{10000.0,0.0},8,{-0.3090402162464889,0.9510491600030528},3.1e-17,9.5e-17},
  2060. {{10000.0,0.0},11,{-0.9501179033904149,-0.3118920160210031},9.5e-17,3.1e-17},
  2061. {{10000.0,0.0},14,{0.315595157092464,-0.9488944866640447},3.2e-17,9.5e-17},
  2062. {{10000.0,0.0},18,{0.3218510506540846,-0.946791218377749},3.2e-17,9.5e-17},
  2063. {{10000.0,0.0},23,{-0.9433601457445342,-0.3317746154126867},9.4e-17,3.3e-17},
  2064. {{10000.0,0.0},29,{0.9379666478839471,0.3467317659022176},9.4e-17,3.5e-17},
  2065. {{10000.0,0.0},37,{0.9283397516018927,0.3717422973913016},9.3e-17,3.7e-17},
  2066. {{10000.0,0.0},48,{-0.4152217424854132,0.9097266978464748},4.2e-17,9.1e-17},
  2067. {{10000.0,0.0},61,{0.8777422109084248,0.4791529210238686},8.8e-17,4.8e-17},
  2068. {{10000.0,0.0},78,{0.5799735094103576,-0.8146542455580336},5.8e-17,8.1e-17},
  2069. {{10000.0,0.0},99,{-0.6927046245889522,-0.7212557152272793},6.9e-17,7.2e-17},
  2070. {{10000.0,0.0},126,{0.8960430419640289,-0.44405730097627},9.0e-17,4.4e-17},
  2071. {{10000.0,0.0},161,{-0.04390438580192674,0.9991010161245437},4.4e-18,1.0e-16},
  2072. {{10000.0,0.0},205,{-0.7522577756314945,0.659029176819063},7.5e-17,6.6e-17},
  2073. {{10000.0,0.0},262,{-0.5766402963422176,0.8172090777658204},5.8e-17,8.2e-17},
  2074. {{10000.0,0.0},333,{0.9169823827831649,-0.3996246788860864},9.2e-17,4.0e-17},
  2075. {{10000.0,0.0},425,{-0.9986331409734894,0.06031857764924985},1.0e-16,6.0e-18},
  2076. {{10000.0,0.0},541,{-0.7439210236606826,0.6693660079881031},7.4e-17,6.7e-17},
  2077. {{10000.0,0.0},690,{-0.8276630796953436,-0.5633527627627941},8.3e-17,5.6e-17},
  2078. {{10000.0,0.0},879,{-0.2559686924018959,-0.9686951076386396},2.6e-17,9.7e-17},
  2079. {{10000.0,0.0},1120,{-0.3161896326121199,0.9520301748728291},3.2e-17,9.5e-17},
  2080. {{10000.0,0.0},1427,{0.2687936760264434,-0.9685541537392371},2.7e-17,9.7e-17},
  2081. {{10000.0,0.0},1818,{0.3801110903322125,0.9340620975427486},3.8e-17,9.3e-17},
  2082. {{10000.0,0.0},2316,{0.3363664648717635,0.9564616952166914},3.4e-17,9.6e-17},
  2083. {{10000.0,0.0},2950,{-0.8588302425401225,-0.555880388869997},8.6e-17,5.6e-17},
  2084. {{10000.0,0.0},3758,{-0.8541132755119114,-0.591279183531158},8.5e-17,5.9e-17},
  2085. {{10000.0,0.0},7771,{-1.18058612315672,-0.4418649322239787},1.2e-16,4.4e-17},
  2086. {{10000.0,0.0},9900,{-1.747822111395514,2.011491146878234},1.7e-16,2.0e-16},
  2087. {{10000.0,0.0},12612,{7.25197826864343e-541,-8.970385150483627e+539},7.3e-557,9.0e+523},
  2088. {{10000.0,0.0},16067,{1.369451063257112e-1882,-2.90314618431218e+1881},1.4e-1898,2.9e+1865},
  2089. {{10000.0,0.0},20468,{1.387136027206115e-4188,-2.018288229524841e+4187},1.4e-4204,2.0e+4171},
  2090. {{10000.0,0.0},26075,{3.402710534773112e-7804,-6.101780411131719e+7802},3.4e-7820,6.1e+7786},
  2091. {{10000.0,0.0},33218,{1.467628954663695e-13224,-1.075478687761038e+13223},1.5e-13240,1.1e+13207},
  2092. {{10000.0,0.0},42318,{5.445358924275546e-21134,-2.233007868840026e+21132},5.4e-21150,2.2e+21116},
  2093. {{10000.0,0.0},53911,{3.266521110728529e-32465,-2.889388190778695e+32463},3.3e-32481,2.9e+32447},
  2094. {{10000.0,0.0},68679,{2.775502574785064e-48480,-2.651272528165235e+48478},2.8e-48496,2.7e+48462},
  2095. {{10000.0,0.0},87493,{8.914211935647729e-70883,-6.453073029871699e+70880},8.9e-70899,6.5e+70864},
  2096. {{10000.0,0.0},111461,{2.619912559375462e-101959,-1.71914792791431e+101957},2.6e-101975,1.7e+101941},
  2097. {{10000.0,0.0},141995,{5.82392981843591e-144773,-6.061204591967546e+144770},5.8e-144789,6.1e+144754},
  2098. };