// x, complex(m), n, complex(f(n,z)), abs_err_real, abs_err_imag
std::vector< std::tuple< nmie::FloatType, std::complex<nmie::FloatType>, int, std::complex<nmie::FloatType>, nmie::FloatType, nmie::FloatType > >
D1_test_30digits
= {
{0.055,{1.5,1.0},0,{8.36411257086632417805161802858,-5.61276019081108331390757079001},8.4e-30,5.6e-30},
{0.055,{1.5,1.0},1,{16.7667178551556094176027309859,-11.1998166559046869795781820105},1.7e-29,1.1e-29},
{0.055,{1.5,1.0},2,{25.1630398855185873499464281292,-16.7910760954753548964102344384},2.5e-29,1.7e-29},
{0.055,{1.5,1.0},3,{33.5572671100165012325784588331,-22.383734562458543657022226896},3.4e-29,2.2e-29},
{0.055,{1.5,1.0},4,{41.950542077104701040110101859,-27.9770285802158263291599997509},4.2e-29,2.8e-29},
{0.055,{1.5,1.0},5,{50.3433042696727764406721141662,-33.5706647130503739752197276732},5.0e-29,3.4e-29},
{0.056,{1.5,1.0},0,{8.21376265391609712733518768023,-5.51319460541938323883420760048},8.2e-30,5.5e-30},
{0.056,{1.5,1.0},1,{16.4667176150866353509824561506,-11.0002167597831574900159439215},1.6e-29,1.1e-29},
{0.056,{1.5,1.0},2,{24.7132751738799796648583369427,-16.4915187734177778992311772646},2.5e-29,1.6e-29},
{0.056,{1.5,1.0},3,{32.9576998556341496388761472745,-21.9842453336088048343502057669},3.3e-29,2.2e-29},
{0.056,{1.5,1.0},4,{41.2011549708335168057075901037,-27.477619023587507943936207531},4.1e-29,2.7e-29},
{0.056,{1.5,1.0},5,{49.4440879900606885600071029339,-32.9713410576881911651850209714},4.9e-29,3.3e-29},
{0.099,{0.75,0.0},0,{13.4432543666815307037297423125,0.0},1.3e-29,0.0},
{0.099,{0.75,0.0},1,{26.9211745963399821140396209297,0.0},2.7e-29,0.0},
{0.099,{0.75,0.0},2,{40.3934323328306157741044239646,0.0},4.0e-29,0.0},
{0.099,{0.75,0.0},3,{53.8638034125886963781700192119,0.0},5.4e-29,0.0},
{0.099,{0.75,0.0},4,{67.3333170798179775907657077628,0.0},6.7e-29,0.0},
{0.101,{0.75,0.0},0,{13.1760604676597854251278771639,0.0},1.3e-29,0.0},
{0.101,{0.75,0.0},1,{26.3874877796314674196927795896,0.0},2.6e-29,0.0},
{0.101,{0.75,0.0},2,{39.5931379817016747992033032232,0.0},4.0e-29,0.0},
{0.101,{0.75,0.0},3,{52.7968633735063707213589804011,0.0},5.3e-29,0.0},
{0.101,{0.75,0.0},4,{65.9997140200860522244781602823,0.0},6.6e-29,0.0},
//{1.0,{3.141592653589793,0.0},0,{-4193528956200935.44940210704681,0.0},4.2e-15,0.0}, //TODO it fails
{1.0,{3.141592653589793,0.0},1,{-0.31830988618379045723644142554,0.0},3.2e-31,0.0},
{1.0,{3.141592653589793,0.0},2,{0.410577778829016536772047563585,0.0},4.1e-31,0.0},
{1.0,{3.141592653589793,0.0},3,{0.882117364249478549575956540158,0.0},8.8e-31,0.0},
{1.0,{3.141592653589793,0.0},4,{1.28350627509594182742011853076,0.0},1.3e-30,0.0},
{1.0,{3.141592653589793,0.0},5,{1.65474895648802722294908309803,0.0},1.7e-30,0.0},
{1.0,{3.141592653589793,0.0},6,{2.01001284171663163343136710203,0.0},2.0e-30,0.0},
{1.0,{3.141592653589793,0.0},7,{2.3556989580807089636275015334,0.0},2.4e-30,0.0},
{1.0,{3.141592653589793,0.0},8,{2.69515688549276743436155915861,0.0},2.7e-30,0.0},
{1.0,{3.141592653589793,0.0},9,{3.03032202043648638445429887499,0.0},3.0e-30,0.0},
{1.0,{3.141592653589793,0.0},10,{3.36239580101157416890855524563,0.0},3.4e-30,0.0},
{1.0,{3.141592653589793,0.0},11,{3.69216581828956804940195304251,0.0},3.7e-30,0.0},
{1.0,{3.141592653589793,0.0},12,{4.02017100538644019728337831661,0.0},4.0e-30,0.0},
{1.0,{3.141592653589793,0.0},13,{4.34679317278754460646714985352,0.0},4.3e-30,0.0},
{1.0,{3.141592653589793,0.0},14,{4.67231069520223706243680197115,0.0},4.7e-30,0.0},
{1.0,{3.141592653589793,0.0},15,{4.99693149702903278777277435329,0.0},5.0e-30,0.0},
{1.0,{3.141592653589793,0.0},16,{5.32081411947518340799146068208,0.0},5.3e-30,0.0},
{1.0,{3.141592653589793,0.0},17,{5.64408162495509135334284431755,0.0},5.6e-30,0.0},
{1.0,{3.141592653589793,0.0},18,{5.96683103671677868142566809307,0.0},6.0e-30,0.0},
{1.0,{3.141592653589793,0.0},20,{6.61107098314353294269578290597,0.0},6.6e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},0,{-2.6716342902051994927252215966e-231,1.31303528549933130363616124693},2.7e-261,1.3e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},1,{-0.105454733144282573874737514743,0.683525109490997258708886093775},1.1e-31,6.8e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},2,{0.375625526268801268114481216368,0.512975081648671832008667823661},3.8e-31,5.1e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},3,{0.783851283060567238445438250606,0.520073115070454006654550784711},7.8e-31,5.2e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},4,{1.14604488551154019334529698611,0.572490471112493028076614293934},1.1e-30,5.7e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},5,{1.48404359072601097206901667891,0.641733304379550739427032499845},1.5e-30,6.4e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},6,{1.80811624351877378090791630677,0.718912588148377402368142277488},1.8e-30,7.2e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},7,{2.12347980630751576532252355551,0.800452445291865201629029299576},2.1e-30,8.0e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},8,{2.43303696494205830783858553538,0.884649106040885755899158077052},2.4e-30,8.8e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},9,{2.73852738222687009330211647101,0.970588580896081781642230963596},2.7e-30,9.7e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},10,{3.0410569509060891604618551053,1.05773599713031942130130797795},3.0e-30,1.1e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},11,{3.34136260812952743711100056731,1.14575692325188463896185378694},3.3e-30,1.1e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},12,{3.63995462790817336653762591698,1.234431120418641661728201002},3.6e-30,1.2e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},13,{3.93719773020948102455547825667,1.32360738235542208862536026901},3.9e-30,1.3e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},14,{4.23335964545017964042849360761,1.41317829414564700232361756505},4.2e-30,1.4e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},15,{4.52864142199512016467859555213,1.50306534896781795302640202012},4.5e-30,1.5e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},16,{4.82319701874385130081753994655,1.59320977218167917426149042564},4.8e-30,1.6e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},17,{5.11714636116284552978521815319,1.68356664681612135141981731014},5.1e-30,1.7e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},18,{5.41058427404166609975539845822,1.77410102931703950879786333048},5.4e-30,1.8e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},20,{5.99621535040140812635283510785,1.95559736586759311172186430919},6.0e-30,2.0e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},0,{-2.71018254115422982591015027278e+230,0.0},2.7e+200,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},1,{-0.318309886183790671537767526745,0.0},3.2e-31,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},2,{0.410577778829016403078679407603,0.0},4.1e-31,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},3,{0.882117364249478415493934816912,0.0},8.8e-31,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},4,{1.28350627509594167934323821122,0.0},1.3e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},5,{1.65474895648802705636895284875,0.0},1.7e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},6,{2.0100128417166314463188136696,0.0},2.0e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},7,{2.35569895808070875489368658328,0.0},2.4e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},8,{2.69515688549276720335196669156,0.0},2.7e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},9,{3.03032202043648613074315705525,0.0},3.0e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},10,{3.36239580101157389220238864404,0.0},3.4e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},11,{3.69216581828956774948934910125,0.0},3.7e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},12,{4.02017100538643987400666352476,0.0},4.0e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},13,{4.34679317278754425970539399711,0.0},4.3e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},14,{4.67231069520223669209509601635,0.0},4.7e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},15,{4.99693149702903239377518208757,0.0},5.0e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},16,{5.32081411947518299027622332802,0.0},5.3e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},17,{5.64408162495509091185902151892,0.0},5.6e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},18,{5.96683103671677821613072547396,0.0},6.0e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},20,{6.61107098314353242967621469735,0.0},6.6e-30,0.0},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},0,{-2.6716342902051994927252215966e-231,-1.31303528549933130363616124693},2.7e-261,1.3e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},1,{-0.105454733144282573874737514743,-0.683525109490997258708886093775},1.1e-31,6.8e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},2,{0.375625526268801268114481216368,-0.512975081648671832008667823661},3.8e-31,5.1e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},3,{0.783851283060567238445438250606,-0.520073115070454006654550784711},7.8e-31,5.2e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},4,{1.14604488551154019334529698611,-0.572490471112493028076614293934},1.1e-30,5.7e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},5,{1.48404359072601097206901667891,-0.641733304379550739427032499845},1.5e-30,6.4e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},6,{1.80811624351877378090791630677,-0.718912588148377402368142277488},1.8e-30,7.2e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},7,{2.12347980630751576532252355551,-0.800452445291865201629029299576},2.1e-30,8.0e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},8,{2.43303696494205830783858553538,-0.884649106040885755899158077052},2.4e-30,8.8e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},9,{2.73852738222687009330211647101,-0.970588580896081781642230963596},2.7e-30,9.7e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},10,{3.0410569509060891604618551053,-1.05773599713031942130130797795},3.0e-30,1.1e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},11,{3.34136260812952743711100056731,-1.14575692325188463896185378694},3.3e-30,1.1e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},12,{3.63995462790817336653762591698,-1.234431120418641661728201002},3.6e-30,1.2e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},13,{3.93719773020948102455547825667,-1.32360738235542208862536026901},3.9e-30,1.3e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},14,{4.23335964545017964042849360761,-1.41317829414564700232361756505},4.2e-30,1.4e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},15,{4.52864142199512016467859555213,-1.50306534896781795302640202012},4.5e-30,1.5e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},16,{4.82319701874385130081753994655,-1.59320977218167917426149042564},4.8e-30,1.6e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},17,{5.11714636116284552978521815319,-1.68356664681612135141981731014},5.1e-30,1.7e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},18,{5.41058427404166609975539845822,-1.77410102931703950879786333048},5.4e-30,1.8e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},20,{5.99621535040140812635283510785,-1.95559736586759311172186430919},6.0e-30,2.0e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},0,{-2.76651033493641321335573306744e-233,-1.00374187319732128820155269119},2.8e-263,1.0e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},1,{0.0563102343267633802588595634886,-0.984253292966296255927862927266},5.6e-32,9.8e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},2,{0.19328384398068375259537842403,-0.982044786578199175924654201079},1.9e-31,9.8e-31},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},3,{0.369926582420403451826298840749,-1.02712817468012352294588465251},3.7e-31,1.0e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},4,{0.555986977659044508138804914978,-1.10966762489326965502913096518},5.6e-31,1.1e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},5,{0.741060986952424856196822624575,-1.21601218564255785124341626102},7.4e-31,1.2e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},6,{0.92269421258773880389427021755,-1.33720028053105399840816371903},9.2e-31,1.3e-30},
{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},7,{1.10080284232288554819780150221,-1.46794743329431891873059790007},1.1e-30,1.5e-30},
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{1.0,{10.0,10.0},5,{0.0791726880391281666997225242442,-0.999072454013369868591936075898},7.9e-32,1.0e-30},
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{1.0,{10.0,10.0},10,{0.283708605495395394831233045379,-1.02935684293226886621110157729},2.8e-31,1.0e-30},
{1.0,{10.0,10.0},11,{0.335589054349980438942172973061,-1.04416782513127579191610071709},3.4e-31,1.0e-30},
{1.0,{10.0,10.0},12,{0.389568569853508960416013682004,-1.06231590152049942026035820713},3.9e-31,1.1e-30},
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{1.0,{10.0,10.0},15,{0.558537579168910751003945549541,-1.13501372412398971886485222661},5.6e-31,1.1e-30},
{1.0,{10.0,10.0},16,{0.615883859867129039969678885626,-1.16444864251962661351625236743},6.2e-31,1.2e-30},
{1.0,{10.0,10.0},17,{0.67331775407422752928607355153,-1.19601527952251068728082333999},6.7e-31,1.2e-30},
{1.0,{10.0,10.0},19,{0.787905775653871603577229509263,-1.26453490151046026115345425588},7.9e-31,1.3e-30},
{1.0,{10.0,10.0},20,{0.844896406360398448686602290182,-1.30105034994772515643896646783},8.4e-31,1.3e-30},
{1.0,{10.0,10.0},22,{0.958070279684197652580719975714,-1.37769692003985213599175795023},9.6e-31,1.4e-30},
{1.0,{10.0,10.0},24,{1.07008780519409858444303383507,-1.45823754332105690672232019651},1.1e-30,1.5e-30},
{1.0,{10.0,10.0},26,{1.18096795607221459569055695932,-1.54181321247259830487628575079},1.2e-30,1.5e-30},
{1.0,{10.0,10.0},28,{1.29079198278488953604156797582,-1.62778527931549276633754343216},1.3e-30,1.6e-30},
{1.0,{10.0,10.0},30,{1.39966266535906637974920954207,-1.71567491366464965060235173443},1.4e-30,1.7e-30},
{1.0,{10.0,10.0},32,{1.50768491720806801940831992772,-1.80511892859587168847197684848},1.5e-30,1.8e-30},
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{2.03575204,{1.4558642,0.20503704},2,{0.500494234180556049881381711457,-0.237580915342568651260553744582},5.0e-31,2.4e-31},
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{2.03575204,{1.4558642,0.20503704},4,{1.36767229894254144534894723283,-0.279279471612299024281843701102},1.4e-30,2.8e-31},
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{2.03575204,{1.4558642,0.20503704},6,{2.11157246697626561235756521424,-0.357159041882805288613617798438},2.1e-30,3.6e-31},
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{2.03575204,{1.4558642,0.20503704},8,{2.81827161492519605804661528857,-0.44286127643154932643520008468},2.8e-30,4.4e-31},
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{10000.0,{1.33,0.00001},59,{3.92606850470495042177384952376,-2.02423427621442319010119668067},3.9e-30,2.0e-30},
{10000.0,{1.33,0.00001},71,{3.26674950261361158627164898099,-1.32514114288134543589844823591},3.3e-30,1.3e-30},
{10000.0,{1.33,0.00001},87,{2.48855009697603046790844588412,-0.768062667041327264511146336696},2.5e-30,7.7e-31},
{10000.0,{1.33,0.00001},105,{1.8100333368813792769679687223,-0.441216052123063220096243878027},1.8e-30,4.4e-31},
{10000.0,{1.33,0.00001},128,{-0.808770970217153894870769289707,-0.165949051845660517331247942413},8.1e-31,1.7e-31},
{10000.0,{1.33,0.00001},155,{0.665968633227214892155935348198,-0.144504562300786105627793056587},6.7e-31,1.4e-31},
{10000.0,{1.33,0.00001},189,{0.152898034474756381010533731575,-0.102001780320843156242698091829},1.5e-31,1.0e-31},
{10000.0,{1.33,0.00001},229,{-0.510029144301100752592676986814,-0.125894502891165895124201114656},5.1e-31,1.3e-31},
{10000.0,{1.33,0.00001},279,{-4.71457961257623572108128627635,-3.50370615462883984192187478053},4.7e-30,3.5e-30},
{10000.0,{1.33,0.00001},338,{-2.61311930021103522218149464482,-0.84256965522606706207986467112},2.6e-30,8.4e-31},
{10000.0,{1.33,0.00001},411,{4.55618515192797704776156285915,-3.08884994128511305139516236809},4.6e-30,3.1e-30},
{10000.0,{1.33,0.00001},499,{2.22274252736833028392896550664,-9.50815186162741310877036197813},2.2e-30,9.5e-30},
{10000.0,{1.33,0.00001},606,{-3.48249445021244041282403768507,-1.52485041756523527803619531855},3.5e-30,1.5e-30},
{10000.0,{1.33,0.00001},736,{3.70597965627417429386120961109,-8.37325420258967211904861561724},3.7e-30,8.4e-30},
{10000.0,{1.33,0.00001},894,{2.78276850718847276723353552769,-0.951946068194726261587503188954},2.8e-30,9.5e-31},
{10000.0,{1.33,0.00001},1086,{-0.523575039076550244950056895238,-0.126677108854641468387722798307},5.2e-31,1.3e-31},
{10000.0,{1.33,0.00001},1319,{-2.22013251016694490048230051249,-0.622464557883368332682867911404},2.2e-30,6.2e-31},
{10000.0,{1.33,0.00001},1601,{-0.976665005304722023552798520472,-0.195189326007154844108853551561},9.8e-31,2.0e-31},
{10000.0,{1.33,0.00001},1945,{0.332430666483775745004332398369,-0.108678026511995583941533309484},3.3e-31,1.1e-31},
{10000.0,{1.33,0.00001},2362,{0.0340206645261169246323779852518,-0.0966497693369055501246527469113},3.4e-32,9.7e-32},
{10000.0,{1.33,0.00001},13560,{0.199864912106558956512165001411,-0.0000389421189486975408410344235208},2.0e-31,3.9e-35},
{10000.0,{1.5,1.0},0,{0.0,-1.0},0.0,1.0e-30},
{10000.0,{1.5,1.0},1,{0.00000000284026945162933035614468709793,-0.999999998816400539533034692329},2.8e-39,1.0e-30},
{10000.0,{1.5,1.0},2,{0.00000000852080837506152679970295386634,-0.999999996449201638597141258992},8.5e-39,1.0e-30},
{10000.0,{1.5,1.0},3,{0.0000000170416168106436602994987635092,-0.999999992898403337188395278695},1.7e-38,1.0e-30},
{10000.0,{1.5,1.0},4,{0.0000000284026948188963360744833647582,-0.999999988164005695300913156251},2.8e-38,1.0e-30},
{10000.0,{1.5,1.0},6,{0.0000000596456598963633971958935111152,-0.99999997514441273005643331397},6.0e-38,1.0e-30},
{10000.0,{1.5,1.0},7,{0.0000000795275471874866484320057937066,-0.99999996685921762667791140466},8.0e-38,1.0e-30},
{10000.0,{1.5,1.0},9,{0.00000012781213198058620115349224272,-0.999999946738030878339953598639},1.3e-37,1.0e-30},
{10000.0,{1.5,1.0},11,{0.000000187457798231612368739291488438,-0.99999992188244990778052256969},1.9e-37,1.0e-30},
{10000.0,{1.5,1.0},13,{0.00000025846454763514138192748568863,-0.999999892292476394836637752302},2.6e-37,1.0e-30},
{10000.0,{1.5,1.0},16,{0.000000386276707152594870657282138753,-0.999999839030534570519452320079},3.9e-37,1.0e-30},
{10000.0,{1.5,1.0},20,{0.000000596456732411523409989285638493,-0.999999751444259587701892034404},6.0e-37,1.0e-30},
{10000.0,{1.5,1.0},24,{0.000000852081137083012144645985927711,-0.999999644920460830925841903643},8.5e-37,1.0e-30},
{10000.0,{1.5,1.0},30,{0.0000013207260204474366878422689379,-0.999999449626970013623559270898},1.3e-36,1.0e-30},
{10000.0,{1.5,1.0},36,{0.00000189162094389306320787417911897,-0.99999921172423548807880179364},1.9e-36,1.0e-30},
{10000.0,{1.5,1.0},44,{0.00000281187004912616401820340476569,-0.999998828239797530444817241056},2.8e-36,1.0e-30},
{10000.0,{1.5,1.0},54,{0.00000421780754518957803434632014392,-0.999998242362146329712425322891},4.2e-36,1.0e-30},
{10000.0,{1.5,1.0},67,{0.00000647015125078869249243583311288,-0.999997303777717538661461572449},6.5e-36,1.0e-30},
{10000.0,{1.5,1.0},82,{0.00000966547586853604323006776827044,-0.999995972249622794911049294155},9.7e-36,1.0e-30},
{10000.0,{1.5,1.0},100,{0.0000143434464589752551934717715865,-0.999994022907709537509771024326},1.4e-35,1.0e-30},
{10000.0,{1.5,1.0},122,{0.0000213107309462611141568731550013,-0.999991119640860420373680971931},2.1e-35,1.0e-30},
{10000.0,{1.5,1.0},149,{0.0000317404309573559881483990321585,-0.999986773692238760740945393644},3.2e-35,1.0e-30},
{10000.0,{1.5,1.0},182,{0.0000472999395255801647217189767452,-0.999980290442508962869157699206},4.7e-35,1.0e-30},
{10000.0,{1.5,1.0},223,{0.0000709406670316442739586349415798,-0.999970440499133562516057740445},7.1e-35,1.0e-30},
{10000.0,{1.5,1.0},272,{0.000105458158625200584133316465693,-0.999956059914309053710104893829},1.1e-34,1.0e-30},
{10000.0,{1.5,1.0},333,{0.000157960621400358912517647947444,-0.999934189160139009467144323324},1.6e-34,1.0e-30},
{10000.0,{1.5,1.0},407,{0.000235845066820051150510724269082,-0.999901751088018412863644865252},2.4e-34,1.0e-30},
{10000.0,{1.5,1.0},497,{0.000351543346916123120055966058915,-0.999853577085475238684547205056},3.5e-34,1.0e-30},
{10000.0,{1.5,1.0},608,{0.000525951332160136394786872021363,-0.999780987455228640776595591461},5.3e-34,1.0e-30},
{10000.0,{1.5,1.0},742,{0.000783184158595427543716290968724,-0.999673990796760316318775811573},7.8e-34,1.0e-30},
{10000.0,{1.5,1.0},907,{0.00117013019612910016851373080282,-0.999513185870623794834597760852},1.2e-33,1.0e-30},
{10000.0,{1.5,1.0},1108,{0.00174628965633774934781173112034,-0.999274074300281070513662951137},1.7e-33,1.0e-30},
{10000.0,{1.5,1.0},1354,{0.0026083036501200996263903639749,-0.998917057941050221903840688035},2.6e-33,1.0e-30},
{10000.0,{1.5,1.0},1655,{0.00389843427238476857496694972154,-0.998384359866641199709560633882},3.9e-33,1.0e-30},
{10000.0,{1.5,1.0},2022,{0.00582308621135799815506374570135,-0.997593297280328691913057468711},5.8e-33,1.0e-30},
{10000.0,{1.5,1.0},2471,{0.0087058274782452694117940397738,-0.996416576927607250102158049156},8.7e-33,1.0e-30},
{10000.0,{1.5,1.0},3019,{0.0130172370907979195580895783133,-0.99467488075013653177297817897},1.3e-32,9.9e-31},
{10000.0,{1.5,1.0},3688,{0.0194747160530896448895062672865,-0.992107024240956363865505943671},1.9e-32,9.9e-31},
{10000.0,{1.5,1.0},4506,{0.0291811966176294228657368649807,-0.988339185462439776996122282096},2.9e-32,9.9e-31},
{10000.0,{1.5,1.0},5506,{0.043811343495739899138115132426,-0.982868678723677832823529241772},4.4e-32,9.8e-31},
{10000.0,{1.5,1.0},6727,{0.0659173404600141857758867750086,-0.975077539737756078886962956854},6.6e-32,9.8e-31},
{10000.0,{1.5,1.0},8219,{0.0994940101951035239859034026682,-0.964331273180472734236318449551},9.9e-32,9.6e-31},
{10000.0,{1.5,1.0},10042,{0.150692576262564773782806989573,-0.950442108401446907761076343239},1.5e-31,9.5e-31},
{10000.0,{1.5,1.0},12270,{0.228707328536049721966018105977,-0.934932710366162415964574869548},2.3e-31,9.3e-31},
{10000.0,{1.5,1.0},14991,{0.345508860352487955051706770356,-0.923781757849539657993567234287},3.5e-31,9.2e-31},
{10000.0,{1.5,1.0},18316,{0.51220827843261226096284772895,-0.930205048274121867882725380011},5.1e-31,9.3e-31},
{10000.0,{10.0,10.0},0,{0.0,-1.0},0.0,1.0e-30},
{10000.0,{10.0,10.0},1,{5.0000249999999987499874999375e-11,-0.9999999999999997499974999875},5.0e-41,1.0e-30},
{10000.0,{10.0,10.0},2,{1.5000075000000011250337503375e-10,-0.9999999999999992500000001125},1.5e-40,1.0e-30},
{10000.0,{10.0,10.0},3,{3.00001500000000675012374949375e-10,-0.999999999999998500022500675},3.0e-40,1.0e-30},
{10000.0,{10.0,10.0},4,{5.00002500000002125015623953125e-10,-0.999999999999997500087502125},5.0e-40,1.0e-30},
{10000.0,{10.0,10.0},5,{7.500037500000050624718699375e-10,-0.9999999999999962502250050625},7.5e-40,1.0e-30},
{10000.0,{10.0,10.0},6,{0.00000000105000525000001023728735858062,-0.9999999999999947504725102375},1.1e-39,1.0e-30},
{10000.0,{10.0,10.0},8,{0.00000000180000900000003104818415350875,-0.99999999999999100148503105},1.8e-39,1.0e-30},
{10000.0,{10.0,10.0},11,{0.00000000330001650000010641078047475562,-0.999999999999983505197606425001},3.3e-39,1.0e-30},
{10000.0,{10.0,10.0},14,{0.00000000525002625000027162469415517185,-0.999999999999973763387771687503},5.3e-39,1.0e-30},
{10000.0,{10.0,10.0},18,{0.00000000855004275000072432540033809606,-0.999999999999957285910724612512},8.6e-39,1.0e-30},
{10000.0,{10.0,10.0},23,{0.0000000138000690000018928023078987324,-0.999999999999931094186894050051},1.4e-38,1.0e-30},
{10000.0,{10.0,10.0},29,{0.0000000217501087500047093329066024601,-0.999999999999891484904714312703},2.2e-38,1.0e-30},
{10000.0,{10.0,10.0},37,{0.0000000351501757500123075791051691929,-0.99999999999982486513732886336},3.5e-38,1.0e-30},
{10000.0,{10.0,10.0},48,{0.0000000588002940000344298562215747316,-0.999999999999707724344530304037},5.9e-38,1.0e-30},
{10000.0,{10.0,10.0},61,{0.0000000945504727500889065983393584212,-0.999999999999531712849326129299},9.5e-38,1.0e-30},
{10000.0,{10.0,10.0},78,{0.000000154050770250235378806359645929,-0.999999999999241604384698560118},1.5e-37,1.0e-30},
{10000.0,{10.0,10.0},99,{0.000000247501237500604817546281227691,-0.999999999998793110174877175501},2.5e-37,1.0e-30},
{10000.0,{10.0,10.0},126,{0.000000400052000251568142713038943976,-0.999999999998079741597601251027},4.0e-37,1.0e-30},
{10000.0,{10.0,10.0},161,{0.00000065205326025411273045332145638,-0.999999999996952289948708416763},6.5e-37,1.0e-30},
{10000.0,{10.0,10.0},205,{0.00000105575527876055728164664195298,-0.999999999995278485995311565222},1.1e-36,1.0e-30},
{10000.0,{10.0,10.0},262,{0.00000172265861327711887284941132068,-0.9999999999928704119865349605},1.7e-36,1.0e-30},
{10000.0,{10.0,10.0},333,{0.00000278056390281656592047217690746,-0.999999999989962847922890180822},2.8e-36,1.0e-30},
{10000.0,{10.0,10.0},425,{0.0000045262726314085068078508041287,-0.99999999998761208493008815871},4.5e-36,1.0e-30},
{10000.0,{10.0,10.0},541,{0.00000733058665309041431655930197549,-0.999999999990215719230208763863},7.3e-36,1.0e-30},
{10000.0,{10.0,10.0},690,{0.0000119198095993240296550678599985,-1.00000000001144199686671559473},1.2e-35,1.0e-30},
{10000.0,{10.0,10.0},879,{0.0000193380966901237519273527945894,-1.00000000009029141127516622005},1.9e-35,1.0e-30},
{10000.0,{10.0,10.0},1120,{0.0000313881569343899367400192004138,-1.00000000033567076995371891658},3.1e-35,1.0e-30},
{10000.0,{10.0,10.0},1427,{0.0000509441546793441688609787575865,-1.00000000104294310401823287787},5.1e-35,1.0e-30},
{10000.0,{10.0,10.0},1818,{0.0000826739631535568096835054849937,-1.00000000300415231548423812825},8.3e-35,1.0e-30},
{10000.0,{10.0,10.0},2316,{0.000134154969744218993679465696278,-1.00000000832808636217130874854},1.3e-34,1.0e-30},
{10000.0,{10.0,10.0},2950,{0.000217637333500486996381344698014,-1.00000002259504354343004401177},2.2e-34,1.0e-30},
{10000.0,{10.0,10.0},3758,{0.000353159795013579326689180595842,-1.00000006059572576719974369349},3.5e-34,1.0e-30},
{10000.0,{10.0,10.0},4788,{0.000573246075312842744030989905371,-1.00000016144090335650458476847},5.7e-34,1.0e-30},
{10000.0,{10.0,10.0},6100,{0.000930406757952853086007401881032,-1.00000042818052794775276693523},9.3e-34,1.0e-30},
{10000.0,{10.0,10.0},111461,{0.297683898094015480001780023692,-1.04336653952589758958420139883},3.0e-31,1.0e-30},
{10000.0,{10.0,10.0},141995,{0.458248246056317114621851710924,-1.09999508039847614612758302675},4.6e-31,1.1e-30},
};

// complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
D2_test_16digits
= {
{{0.07425,0.0},0,{-0.07438674986902373,0.0},7.4e-18,0.0},
{{0.07425,0.0},1,{-13.39417131419206,0.0},1.3e-15,0.0},
{{0.07425,0.0},2,{-26.91123162027382,0.0},2.7e-15,0.0},
{{0.07425,0.0},3,{-40.3891849341013,0.0},4.0e-15,0.0},
{{0.07425,0.0},4,{-53.86144505752241,0.0},5.4e-15,0.0},
{{0.07575,0.0},0,{-0.07589521939842851,0.0},7.6e-18,0.0},
{{0.07575,0.0},1,{-13.12600313416894,0.0},1.3e-15,0.0},
{{0.07575,0.0},2,{-26.37734215323807,0.0},2.6e-15,0.0},
{{0.07575,0.0},3,{-39.58880458732769,0.0},4.0e-15,0.0},
{{0.07575,0.0},4,{-52.79445732439479,0.0},5.3e-15,0.0},
{{7.5,0.0},0,{-2.706013866772691,0.0},2.7e-16,0.0},
{{7.5,0.0},1,{0.2188602976402436,0.0},2.2e-17,0.0},
{{7.5,0.0},2,{20.65104828146692,0.0},2.1e-15,0.0},
{{7.5,0.0},3,{-0.4493801597873413,0.0},4.5e-17,0.0},
{{7.5,0.0},4,{0.4842572533435941,0.0},4.8e-17,0.0},
{{7.5,0.0},5,{4.81550654897139,0.0},4.8e-16,0.0},
{{7.5,0.0},6,{-1.049034583259778,0.0},1.0e-16,0.0},
{{7.5,0.0},7,{-0.4288861055358842,0.0},4.3e-17,0.0},
{{7.5,0.0},8,{-0.3980175767871659,0.0},4.0e-17,0.0},
{{7.5,0.0},9,{-0.5742246552691164,0.0},5.7e-17,0.0},
{{7.5,0.0},10,{-0.809102874298828,0.0},8.1e-17,0.0},
{{7.5,0.0},11,{-1.027254862439886,0.0},1.0e-16,0.0},
{{7.5,0.0},12,{-1.219374574466933,0.0},1.2e-16,0.0},
{{7.5,0.0},13,{-1.39466116147432,0.0},1.4e-16,0.0},
{{7.5,0.0},14,{-1.560043091026306,0.0},1.6e-16,0.0},
{{7.5,0.0},16,{-1.873757439540259,0.0},1.9e-16,0.0},
{{7.5,0.0},17,{-2.025145514642434,0.0},2.0e-16,0.0},
{{7.5,0.0},18,{-2.174018730753354,0.0},2.2e-16,0.0},
{{7.5,0.0},19,{-2.320899679256512,0.0},2.3e-16,0.0},
{{7.5,0.0},21,{-2.610108605596247,0.0},2.6e-16,0.0},
{{7.5,0.0},22,{-2.752939994498599,0.0},2.8e-16,0.0},
{{7.5,0.0},24,{-3.035926615655057,0.0},3.0e-16,0.0},
{{7.5,0.0},26,{-3.316132176384959,0.0},3.3e-16,0.0},
{{7.5,0.0},27,{-3.455410513492717,0.0},3.5e-16,0.0},
{{7.5,0.0},30,{-3.870677968225079,0.0},3.9e-16,0.0},
{{750.0,0.0},0,{1.117079400838733,0.0},1.1e-16,0.0},
{{750.0,0.0},1,{-0.8975946145725433,0.0},9.0e-17,0.0},
{{750.0,0.0},2,{1.108121968632076,0.0},1.1e-16,0.0},
{{750.0,0.0},3,{-0.9096970410967588,0.0},9.1e-17,0.0},
{{750.0,0.0},4,{1.087526562845337,0.0},1.1e-16,0.0},
{{750.0,0.0},5,{-0.9318559567267879,0.0},9.3e-17,0.0},
{{750.0,0.0},6,{1.055992830861736,0.0},1.1e-16,0.0},
{{750.0,0.0},7,{-0.9647538902206642,0.0},9.6e-17,0.0},
{{750.0,0.0},9,{-1.009474246275747,0.0},1.0e-16,0.0},
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{{3.141592653589793,0.0},17,{-5.315130348653373,0.0},5.3e-16,0.0},
{{3.141592653589793,0.0},18,{-5.639036854808339,0.0},5.6e-16,0.0},
{{3.141592653589793,0.0},20,{-6.285084985730819,0.0},6.3e-16,0.0},
};

// complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
D3_test_16digits
= {
{{13300.0,-0.1},0,{0.0,1.0},0.0,1.0e-16},
{{13300.0,-0.1},1,{-3.400439576064988e-13,0.9999999943467692},3.4e-29,1.0e-16},
{{13300.0,-0.1},2,{-1.02013189877118e-12,0.9999999830403075},1.0e-28,1.0e-16},
{{13300.0,-0.1},3,{-2.040263875397417e-12,0.9999999660806147},2.0e-28,1.0e-16},
{{13300.0,-0.1},4,{-3.400439965340277e-12,0.9999999434676906},3.4e-28,1.0e-16},
{{13300.0,-0.1},5,{-5.100660272406543e-12,0.9999999152015347},5.1e-28,1.0e-16},
{{13300.0,-0.1},6,{-7.140924926354723e-12,0.9999998812821465},7.1e-28,1.0e-16},
{{13300.0,-0.1},8,{-1.224158792368965e-11,0.9999997964836711},1.2e-27,1.0e-16},
{{13300.0,-0.1},10,{-1.870243051444869e-11,0.9999996890722586},1.9e-27,1.0e-16},
{{13300.0,-0.1},12,{-2.652345467096505e-11,0.9999995590479018},2.7e-27,1.0e-16},
{{13300.0,-0.1},15,{-4.080533667787133e-11,0.999999321612076},4.1e-27,1.0e-16},
{{13300.0,-0.1},18,{-5.814764248686488e-11,0.999999033297069},5.8e-27,1.0e-16},
{{13300.0,-0.1},22,{-8.603139703783761e-11,0.9999985697315893},8.6e-27,1.0e-16},
{{13300.0,-0.1},27,{-1.28537232356385e-10,0.9999978630764811},1.3e-26,1.0e-16},
{{13300.0,-0.1},32,{-1.795444131588628e-10,0.9999970150896922},1.8e-26,1.0e-16},
{{13300.0,-0.1},40,{-2.788389500368772e-10,0.999995364340014},2.8e-26,1.0e-16},
{{13300.0,-0.1},48,{-3.99897670899495e-10,0.9999933517785008},4.0e-26,1.0e-16},
{{13300.0,-0.1},59,{-6.018913482575541e-10,0.999989993731453},6.0e-26,1.0e-16},
{{13300.0,-0.1},71,{-8.691806030714543e-10,0.9999855502377231},8.7e-26,1.0e-16},
{{13300.0,-0.1},87,{-1.301751636840212e-9,0.999978359198404},1.3e-25,1.0e-16},
{{13300.0,-0.1},105,{-1.892478559255885e-9,0.999968539275809},1.9e-25,1.0e-16},
{{13300.0,-0.1},128,{-2.807697724335093e-9,0.9999533258374243},2.8e-25,1.0e-16},
{{13300.0,-0.1},155,{-4.111763702027196e-9,0.9999316501039903},4.1e-25,1.0e-16},
{{13300.0,-0.1},189,{-6.106883864825003e-9,0.9998984910892781},6.1e-25,1.0e-16},
{{13300.0,-0.1},229,{-8.95805814929697e-9,0.9998511110833991},9.0e-25,1.0e-16},
{{13300.0,-0.1},279,{-1.328871882120813e-8,0.9997791604205924},1.3e-24,1.0e-16},
{{13300.0,-0.1},338,{-1.949566427437159e-8,0.9996760682893887},1.9e-24,1.0e-16},
{{13300.0,-0.1},411,{-2.882119692710565e-8,0.99952124896133},2.9e-24,1.0e-16},
{{13300.0,-0.1},499,{-4.248789333886431e-8,0.9992945106023009},4.2e-24,1.0e-16},
{{13300.0,-0.1},606,{-6.268784827324142e-8,0.9989597110407947},6.3e-24,1.0e-16},
{{13300.0,-0.1},736,{-9.254452618551611e-8,0.9984655761319616},9.3e-24,1.0e-16},
{{13300.0,-0.1},894,{-1.367351871332925e-7,0.9977357768741157},1.4e-23,1.0e-16},
{{13300.0,-0.1},1086,{-2.022251492259403e-7,0.9966576457442607},2.0e-23,1.0e-16},
{{13300.0,-0.1},1319,{-2.993332266274127e-7,0.9950664665997103},3.0e-23,1.0e-16},
{{13300.0,-0.1},1601,{-4.432934379930979e-7,0.9927238197940671},4.4e-23,9.9e-17},
{{13300.0,-0.1},1945,{-6.593672942603503e-7,0.989243494339538},6.6e-23,9.9e-17},
{{13300.0,-0.1},2362,{-9.83775545482961e-7,0.9840970601559616},9.8e-23,9.8e-17},
{{13300.0,-0.1},13560,{-0.1978882692837703,-3.967948672613146e-5},2.0e-17,4.0e-21},
{{15000.0,-10000.0},0,{0.0,1.0},0.0,1.0e-16},
{{15000.0,-10000.0},1,{2.84026945162933e-9,0.9999999988164005},2.8e-25,1.0e-16},
{{15000.0,-10000.0},2,{8.520808375061527e-9,0.9999999964492016},8.5e-25,1.0e-16},
{{15000.0,-10000.0},3,{1.704161681064366e-8,0.9999999928984033},1.7e-24,1.0e-16},
{{15000.0,-10000.0},4,{2.840269481889634e-8,0.9999999881640057},2.8e-24,1.0e-16},
{{15000.0,-10000.0},6,{5.96456598963634e-8,0.9999999751444127},6.0e-24,1.0e-16},
{{15000.0,-10000.0},7,{7.952754718748665e-8,0.9999999668592176},8.0e-24,1.0e-16},
{{15000.0,-10000.0},9,{1.278121319805862e-7,0.9999999467380309},1.3e-23,1.0e-16},
{{15000.0,-10000.0},11,{1.874577982316124e-7,0.9999999218824499},1.9e-23,1.0e-16},
{{15000.0,-10000.0},13,{2.584645476351414e-7,0.9999998922924764},2.6e-23,1.0e-16},
{{15000.0,-10000.0},16,{3.862767071525949e-7,0.9999998390305346},3.9e-23,1.0e-16},
{{15000.0,-10000.0},20,{5.964567324115234e-7,0.9999997514442596},6.0e-23,1.0e-16},
{{15000.0,-10000.0},24,{8.520811370830121e-7,0.9999996449204608},8.5e-23,1.0e-16},
{{15000.0,-10000.0},30,{1.320726020447437e-6,0.99999944962697},1.3e-22,1.0e-16},
{{15000.0,-10000.0},36,{1.891620943893063e-6,0.9999992117242355},1.9e-22,1.0e-16},
{{15000.0,-10000.0},44,{2.811870049126164e-6,0.9999988282397975},2.8e-22,1.0e-16},
{{15000.0,-10000.0},54,{4.217807545189578e-6,0.9999982423621463},4.2e-22,1.0e-16},
{{15000.0,-10000.0},67,{6.470151250788692e-6,0.9999973037777175},6.5e-22,1.0e-16},
{{15000.0,-10000.0},82,{9.665475868536043e-6,0.9999959722496228},9.7e-22,1.0e-16},
{{15000.0,-10000.0},100,{1.434344645897526e-5,0.9999940229077095},1.4e-21,1.0e-16},
{{15000.0,-10000.0},122,{2.131073094626111e-5,0.9999911196408604},2.1e-21,1.0e-16},
{{15000.0,-10000.0},149,{3.174043095735599e-5,0.9999867736922388},3.2e-21,1.0e-16},
{{15000.0,-10000.0},182,{4.729993952558016e-5,0.999980290442509},4.7e-21,1.0e-16},
{{15000.0,-10000.0},223,{7.094066703164427e-5,0.9999704404991336},7.1e-21,1.0e-16},
{{15000.0,-10000.0},272,{0.0001054581586252006,0.9999560599143091},1.1e-20,1.0e-16},
{{15000.0,-10000.0},333,{0.0001579606214003589,0.999934189160139},1.6e-20,1.0e-16},
{{15000.0,-10000.0},407,{0.0002358450668200512,0.9999017510880184},2.4e-20,1.0e-16},
{{15000.0,-10000.0},497,{0.0003515433469161231,0.9998535770854752},3.5e-20,1.0e-16},
{{15000.0,-10000.0},608,{0.0005259513321601364,0.9997809874552286},5.3e-20,1.0e-16},
{{15000.0,-10000.0},742,{0.0007831841585954275,0.9996739907967603},7.8e-20,1.0e-16},
{{15000.0,-10000.0},907,{0.0011701301961291,0.9995131858706238},1.2e-19,1.0e-16},
{{15000.0,-10000.0},1108,{0.001746289656337749,0.9992740743002811},1.7e-19,1.0e-16},
{{15000.0,-10000.0},1354,{0.0026083036501201,0.9989170579410502},2.6e-19,1.0e-16},
{{15000.0,-10000.0},1655,{0.003898434272384769,0.9983843598666412},3.9e-19,1.0e-16},
{{15000.0,-10000.0},2022,{0.005823086211357998,0.9975932972803287},5.8e-19,1.0e-16},
{{15000.0,-10000.0},2471,{0.008705827478245269,0.9964165769276073},8.7e-19,1.0e-16},
{{15000.0,-10000.0},3019,{0.01301723709079792,0.9946748807501365},1.3e-18,9.9e-17},
{{15000.0,-10000.0},3688,{0.01947471605308964,0.9921070242409564},1.9e-18,9.9e-17},
{{15000.0,-10000.0},4506,{0.02918119661762942,0.9883391854624398},2.9e-18,9.9e-17},
{{15000.0,-10000.0},5506,{0.0438113434957399,0.9828686787236778},4.4e-18,9.8e-17},
{{15000.0,-10000.0},6727,{0.06591734046001419,0.9750775397377561},6.6e-18,9.8e-17},
{{15000.0,-10000.0},8219,{0.09949401019510352,0.9643312731804727},9.9e-18,9.6e-17},
{{15000.0,-10000.0},10042,{0.1506925762625648,0.9504421084014469},1.5e-17,9.5e-17},
{{15000.0,-10000.0},12270,{0.2287073285360497,0.9349327103661624},2.3e-17,9.3e-17},
{{15000.0,-10000.0},14991,{0.345508860352488,0.9237817578495397},3.5e-17,9.2e-17},
{{15000.0,-10000.0},18316,{0.5122082784326123,0.9302050482741219},5.1e-17,9.3e-17},
{{100000.0,-100000.0},0,{0.0,1.0},0.0,1.0e-16},
{{100000.0,-100000.0},1,{5.000024999999999e-11,0.9999999999999997},5.0e-27,1.0e-16},
{{100000.0,-100000.0},2,{1.500007500000001e-10,0.9999999999999992},1.5e-26,1.0e-16},
{{100000.0,-100000.0},3,{3.000015000000007e-10,0.9999999999999985},3.0e-26,1.0e-16},
{{100000.0,-100000.0},4,{5.000025000000021e-10,0.9999999999999975},5.0e-26,1.0e-16},
{{100000.0,-100000.0},5,{7.500037500000051e-10,0.9999999999999963},7.5e-26,1.0e-16},
{{100000.0,-100000.0},6,{1.05000525000001e-9,0.9999999999999948},1.1e-25,1.0e-16},
{{100000.0,-100000.0},8,{1.800009000000031e-9,0.999999999999991},1.8e-25,1.0e-16},
{{100000.0,-100000.0},11,{3.300016500000106e-9,0.9999999999999835},3.3e-25,1.0e-16},
{{100000.0,-100000.0},14,{5.250026250000272e-9,0.9999999999999738},5.3e-25,1.0e-16},
{{100000.0,-100000.0},18,{8.550042750000724e-9,0.9999999999999573},8.6e-25,1.0e-16},
{{100000.0,-100000.0},23,{1.380006900000189e-8,0.9999999999999311},1.4e-24,1.0e-16},
{{100000.0,-100000.0},29,{2.175010875000471e-8,0.9999999999998915},2.2e-24,1.0e-16},
{{100000.0,-100000.0},37,{3.515017575001231e-8,0.9999999999998249},3.5e-24,1.0e-16},
{{100000.0,-100000.0},48,{5.880029400003443e-8,0.9999999999997077},5.9e-24,1.0e-16},
{{100000.0,-100000.0},61,{9.455047275008891e-8,0.9999999999995317},9.5e-24,1.0e-16},
{{100000.0,-100000.0},78,{1.540507702502354e-7,0.9999999999992416},1.5e-23,1.0e-16},
{{100000.0,-100000.0},99,{2.475012375006048e-7,0.9999999999987931},2.5e-23,1.0e-16},
{{100000.0,-100000.0},126,{4.000520002515681e-7,0.9999999999980797},4.0e-23,1.0e-16},
{{100000.0,-100000.0},161,{6.520532602541127e-7,0.9999999999969523},6.5e-23,1.0e-16},
{{100000.0,-100000.0},205,{1.055755278760557e-6,0.9999999999952785},1.1e-22,1.0e-16},
{{100000.0,-100000.0},262,{1.722658613277119e-6,0.9999999999928704},1.7e-22,1.0e-16},
{{100000.0,-100000.0},333,{2.780563902816566e-6,0.9999999999899628},2.8e-22,1.0e-16},
{{100000.0,-100000.0},425,{4.526272631408507e-6,0.9999999999876121},4.5e-22,1.0e-16},
{{100000.0,-100000.0},541,{7.330586653090414e-6,0.9999999999902157},7.3e-22,1.0e-16},
{{100000.0,-100000.0},690,{1.191980959932403e-5,1.000000000011442},1.2e-21,1.0e-16},
{{100000.0,-100000.0},879,{1.933809669012375e-5,1.000000000090291},1.9e-21,1.0e-16},
{{100000.0,-100000.0},1120,{3.138815693438994e-5,1.000000000335671},3.1e-21,1.0e-16},
{{100000.0,-100000.0},1427,{5.094415467934417e-5,1.000000001042943},5.1e-21,1.0e-16},
{{100000.0,-100000.0},1818,{8.267396315355681e-5,1.000000003004152},8.3e-21,1.0e-16},
{{100000.0,-100000.0},2316,{0.000134154969744219,1.000000008328086},1.3e-20,1.0e-16},
{{100000.0,-100000.0},2950,{0.000217637333500487,1.000000022595044},2.2e-20,1.0e-16},
{{100000.0,-100000.0},3758,{0.0003531597950135793,1.000000060595726},3.5e-20,1.0e-16},
{{100000.0,-100000.0},4788,{0.0005732460753128427,1.000000161440903},5.7e-20,1.0e-16},
{{100000.0,-100000.0},6100,{0.0009304067579528531,1.000000428180528},9.3e-20,1.0e-16},
{{84.0,80.0},0,{0.0,1.0},0.0,1.0e-16},
{{84.0,80.0},1,{-7.380873229998488e-5,0.9999968564160156},7.4e-21,1.0e-16},
{{84.0,80.0},30,{-0.03434386053057851,0.9991195766939804},3.4e-18,1.0e-16},
{{84.0,80.0},50,{-0.09402245799827037,1.000353490231355},9.4e-18,1.0e-16},
{{84.0,80.0},60,{-0.1345473903609001,1.003170792738456},1.3e-17,1.0e-16},
{{84.0,80.0},70,{-0.1817230618520317,1.00843270031902},1.8e-17,1.0e-16},
{{84.0,80.0},75,{-0.2076228712594277,1.012212612957787},2.1e-17,1.0e-16},
{{84.0,80.0},80,{-0.2349404747348349,1.016871463304636},2.3e-17,1.0e-16},
{{84.0,80.0},85,{-0.2635686609374602,1.022481687455244},2.6e-17,1.0e-16},
{{84.0,80.0},90,{-0.2933911867598706,1.029102693099821},2.9e-17,1.0e-16},
{{84.0,80.0},99,{-0.3496890700331609,1.043699563710252},3.5e-17,1.0e-16},
{{84.0,80.0},116,{-0.4629585425983123,1.080906756288357},4.6e-17,1.1e-16},
{{84.0,80.0},130,{-0.5604711899756067,1.120598153464464},5.6e-17,1.1e-16},
{{0.07425,0.0},0,{0.0,1.0},0.0,1.0e-16},
{{0.07425,0.0},1,{-13.39417056853348,0.005482835286388932},1.3e-15,5.5e-19},
{{0.07425,0.0},2,{-26.91123162027365,3.370889322669448e-6},2.7e-15,3.4e-22},
{{0.07425,0.0},3,{-40.3891849341013,7.439046667283003e-10},4.0e-15,7.4e-26},
{{0.07425,0.0},4,{-53.86144505752241,8.372419817902392e-14},5.4e-15,8.4e-30},
{{0.07575,0.0},0,{0.0,1.0},0.0,1.0e-16},
{{0.07575,0.0},1,{-13.12600231038109,0.005705324988632415},1.3e-15,5.7e-19},
{{0.07575,0.0},2,{-26.37734215323787,3.651376172994635e-6},2.6e-15,3.7e-22},
{{0.07575,0.0},3,{-39.58880458732769,8.387157675741533e-10},4.0e-15,8.4e-26},
{{0.07575,0.0},4,{-52.79445732439479,9.824862221764371e-14},5.3e-15,9.8e-30},
{{7.5,0.0},0,{0.0,1.0},0.0,1.0e-16},
{{7.5,0.0},1,{-0.002328966521106259,0.9825327510917031},2.3e-19,9.8e-17},
{{7.5,0.0},2,{-0.007451046400718173,0.9468103012960781},7.5e-19,9.5e-17},
{{7.5,0.0},3,{-0.01650442711542185,0.8911440088718337},1.7e-18,8.9e-17},
{{7.5,0.0},4,{-0.03186665153046955,0.8127470706499601},3.2e-18,8.1e-17},
{{7.5,0.0},5,{-0.05845656171049404,0.7076555523774308},5.8e-18,7.1e-17},
{{7.5,0.0},6,{-0.1064232998486411,0.571739357299301},1.1e-17,5.7e-17},
{{7.5,0.0},7,{-0.1948591940771026,0.4060707249045435},1.9e-17,4.1e-17},
{{7.5,0.0},8,{-0.3483973155893959,0.2312026769682724},3.5e-17,2.3e-17},
{{7.5,0.0},9,{-0.5682560945313477,0.09433036381049633},5.7e-17,9.4e-18},
{{7.5,0.0},10,{-0.808748339097055,0.02602259595616378},8.1e-17,2.6e-18},
{{7.5,0.0},11,{-1.027243869978313,0.005025422555087043},1.0e-16,5.0e-19},
{{7.5,0.0},12,{-1.219374374570939,0.0007280651122391265},1.2e-16,7.3e-20},
{{7.5,0.0},13,{-1.394661159137556,8.350823004188534e-5},1.4e-16,8.4e-21},
{{7.5,0.0},14,{-1.560043091007645,7.851278209385419e-6},1.6e-16,7.9e-22},
{{7.5,0.0},16,{-1.873757439540259,4.174058904183023e-8},1.9e-16,4.2e-24},
{{7.5,0.0},17,{-2.025145514642434,2.434831527630243e-9},2.0e-16,2.4e-25},
{{7.5,0.0},18,{-2.174018730753354,1.243408419440626e-10},2.2e-16,1.2e-26},
{{7.5,0.0},19,{-2.320899679256512,5.611260650480046e-12},2.3e-16,5.6e-28},
{{7.5,0.0},21,{-2.610108605596247,8.133802787253441e-15},2.6e-16,8.1e-31},
{{7.5,0.0},22,{-2.752939994498599,2.646882313155865e-16},2.8e-16,2.6e-32},
{{7.5,0.0},24,{-3.035926615655057,2.10389295861044e-19},3.0e-16,2.1e-35},
{{7.5,0.0},26,{-3.316132176384959,1.175216078553222e-22},3.3e-16,1.2e-38},
{{7.5,0.0},27,{-3.455410513492717,2.456920790399526e-24},3.5e-16,2.5e-40},
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{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},15,{-1.692284051392539,1.079676237510791},1.7e-16,1.1e-16},
{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},16,{-1.833516950412929,1.133178106606117},1.8e-16,1.1e-16},
{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},17,{-1.973144021666479,1.188294020548408},2.0e-16,1.2e-16},
{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},19,{-2.248507874013405,1.302018460543744},2.2e-16,1.3e-16},
{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},20,{-2.384616726790979,1.360171448495856},2.4e-16,1.4e-16},
{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},22,{-2.654392752188639,1.478316329319233},2.7e-16,1.5e-16},
{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},23,{-2.788272523600718,1.53810912969502},2.8e-16,1.5e-16},
{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},25,{-3.05442272767237,1.658785490026429},3.1e-16,1.7e-16},
{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},27,{-3.318830366257712,1.78059624870022},3.3e-16,1.8e-16},
{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},29,{-3.581862130100558,1.903267755210881},3.6e-16,1.9e-16},
{{6.2831853071795862319959269370884,1.0},0,{0.0,1.0},0.0,1.0e-16},
{{6.2831853071795862319959269370884,1.0},1,{-0.0107103550235295,0.97870468885667},1.1e-18,9.8e-17},
{{6.2831853071795862319959269370884,1.0},2,{-0.03362513398684257,0.9355922315987426},3.4e-18,9.4e-17},
{{6.2831853071795862319959269370884,1.0},3,{-0.07215247140260382,0.8699089855443275},7.2e-18,8.7e-17},
{{6.2831853071795862319959269370884,1.0},4,{-0.1324003193922573,0.7816245319680321},1.3e-17,7.8e-17},
{{6.2831853071795862319959269370884,1.0},5,{-0.2237229202421749,0.6738669791565766},2.2e-17,6.7e-17},
{{6.2831853071795862319959269370884,1.0},6,{-0.3566827737268949,0.5572280064731737},3.6e-17,5.6e-17},
{{6.2831853071795862319959269370884,1.0},7,{-0.534881214573448,0.4520353301037817},5.3e-17,4.5e-17},
{{6.2831853071795862319959269370884,1.0},8,{-0.7453172985703958,0.3791789032364014},7.5e-17,3.8e-17},
{{6.2831853071795862319959269370884,1.0},9,{-0.9643357843499773,0.3438258795491612},9.6e-17,3.4e-17},
{{6.2831853071795862319959269370884,1.0},10,{-1.175625522079248,0.3354693797128221},1.2e-16,3.4e-17},
{{6.2831853071795862319959269370884,1.0},11,{-1.375335050387865,0.3416989205502342},1.4e-16,3.4e-17},
{{6.2831853071795862319959269370884,1.0},12,{-1.565392601516738,0.3550436439844526},1.6e-16,3.6e-17},
{{6.2831853071795862319959269370884,1.0},13,{-1.748423760549718,0.3720116512461041},1.7e-16,3.7e-17},
{{6.2831853071795862319959269370884,1.0},14,{-1.926390134893502,0.3910300876389843},1.9e-16,3.9e-17},
{{6.2831853071795862319959269370884,1.0},15,{-2.100611133732458,0.4113324702563825},2.1e-16,4.1e-17},
{{6.2831853071795862319959269370884,1.0},16,{-2.271978854602206,0.4325025916197443},2.3e-16,4.3e-17},
{{6.2831853071795862319959269370884,1.0},18,{-2.608469851297546,0.4765432487679804},2.6e-16,4.8e-17},
{{6.2831853071795862319959269370884,1.0},19,{-2.774374125145379,0.499148135359919},2.8e-16,5.0e-17},
{{6.2831853071795862319959269370884,1.0},20,{-2.939080962634986,0.5220318339355327},2.9e-16,5.2e-17},
{{6.2831853071795862319959269370884,1.0},22,{-3.265643862194712,0.56843085660439},3.3e-16,5.7e-17},
{{6.2831853071795862319959269370884,1.0},23,{-3.427777831706615,0.5918741791259039},3.4e-16,5.9e-17},
{{6.2831853071795862319959269370884,1.0},25,{-3.750257209199445,0.6391251649246937},3.8e-16,6.4e-17},
{{6.2831853071795862319959269370884,1.0},26,{-3.910752977720189,0.6628981349489083},3.9e-16,6.6e-17},
{{3.1415926535897932384626433832795,0.0},0,{0.0,1.0},0.0,1.0e-16},
{{3.1415926535897932384626433832795,0.0},1,{-0.02928440396155443,0.9080003316496248},2.9e-18,9.1e-17},
{{3.1415926535897932384626433832795,0.0},2,{-0.111414420013723,0.7161490362627657},1.1e-17,7.2e-17},
{{3.1415926535897932384626433832795,0.0},3,{-0.3086445141021306,0.4340404684115407},3.1e-17,4.3e-17},
{{3.1415926535897932384626433832795,0.0},4,{-0.6853420975491589,0.1613084612168837},6.9e-17,1.6e-17},
{{3.1415926535897932384626433832795,0.0},5,{-1.154547531604494,0.03095979893899376},1.2e-16,3.1e-18},
{{3.1415926535897932384626433832795,0.0},6,{-1.583565196074497,0.003296559784896674},1.6e-16,3.3e-19},
{{3.1415926535897932384626433832795,0.0},7,{-1.965821634628246,0.0002268900069871888},2.0e-16,2.3e-20},
{{3.1415926535897932384626433832795,0.0},8,{-2.324862655057826,1.114344043688996e-5},2.3e-16,1.1e-21},
{{3.1415926535897932384626433832795,0.0},9,{-2.672097814251784,4.137546472473845e-7},2.7e-16,4.1e-23},
{{3.1415926535897932384626433832795,0.0},10,{-3.012310405818385,1.206868381771849e-8},3.0e-16,1.2e-24},
{{3.1415926535897932384626433832795,0.0},11,{-3.347886623965971,2.84447322718975e-10},3.3e-16,2.8e-26},
{{3.1415926535897932384626433832795,0.0},12,{-3.680202022452916,5.536734412459245e-12},3.7e-16,5.5e-28},
{{3.1415926535897932384626433832795,0.0},13,{-4.010122340785055,9.05809239443902e-14},4.0e-16,9.1e-30},
{{3.1415926535897932384626433832795,0.0},14,{-4.338225297702631,1.263667883273076e-15},4.3e-16,1.3e-31},
{{3.1415926535897932384626433832795,0.0},15,{-4.66491342262249,1.521676227453879e-17},4.7e-16,1.5e-33},
{{3.1415926535897932384626433832795,0.0},16,{-4.990476814065978,1.598129828453938e-19},5.0e-16,1.6e-35},
{{3.1415926535897932384626433832795,0.0},17,{-5.315130348653373,1.4770651858539e-21},5.3e-16,1.5e-37},
{{3.1415926535897932384626433832795,0.0},18,{-5.639036854808338,1.21085227329631e-23},5.6e-16,1.2e-39},
{{3.1415926535897932384626433832795,0.0},20,{-6.285084985730819,5.832688628117013e-28},6.3e-16,5.8e-44},
{{3.141592653589793,0.0},0,{0.0,1.0},0.0,1.0e-16},
{{3.141592653589793,0.0},1,{-0.02928440396155444,0.9080003316496248},2.9e-18,9.1e-17},
{{3.141592653589793,0.0},2,{-0.111414420013723,0.7161490362627657},1.1e-17,7.2e-17},
{{3.141592653589793,0.0},3,{-0.3086445141021306,0.4340404684115406},3.1e-17,4.3e-17},
{{3.141592653589793,0.0},4,{-0.685342097549159,0.1613084612168837},6.9e-17,1.6e-17},
{{3.141592653589793,0.0},5,{-1.154547531604494,0.03095979893899374},1.2e-16,3.1e-18},
{{3.141592653589793,0.0},6,{-1.583565196074497,0.003296559784896672},1.6e-16,3.3e-19},
{{3.141592653589793,0.0},7,{-1.965821634628247,0.0002268900069871886},2.0e-16,2.3e-20},
{{3.141592653589793,0.0},8,{-2.324862655057826,1.114344043688994e-5},2.3e-16,1.1e-21},
{{3.141592653589793,0.0},9,{-2.672097814251784,4.13754647247384e-7},2.7e-16,4.1e-23},
{{3.141592653589793,0.0},10,{-3.012310405818385,1.206868381771847e-8},3.0e-16,1.2e-24},
{{3.141592653589793,0.0},11,{-3.347886623965971,2.844473227189745e-10},3.3e-16,2.8e-26},
{{3.141592653589793,0.0},12,{-3.680202022452917,5.536734412459235e-12},3.7e-16,5.5e-28},
{{3.141592653589793,0.0},13,{-4.010122340785055,9.058092394439002e-14},4.0e-16,9.1e-30},
{{3.141592653589793,0.0},14,{-4.338225297702632,1.263667883273073e-15},4.3e-16,1.3e-31},
{{3.141592653589793,0.0},15,{-4.664913422622491,1.521676227453876e-17},4.7e-16,1.5e-33},
{{3.141592653589793,0.0},16,{-4.990476814065978,1.598129828453934e-19},5.0e-16,1.6e-35},
{{3.141592653589793,0.0},17,{-5.315130348653373,1.477065185853896e-21},5.3e-16,1.5e-37},
{{3.141592653589793,0.0},18,{-5.639036854808339,1.210852273296306e-23},5.6e-16,1.2e-39},
{{3.141592653589793,0.0},20,{-6.285084985730819,5.832688628116996e-28},6.3e-16,5.8e-44},
};

// x, complex(m), n, complex(f(n,z)), abs_err_real, abs_err_imag
std::vector< std::tuple< nmie::FloatType, std::complex<nmie::FloatType>, int, std::complex<nmie::FloatType>, nmie::FloatType, nmie::FloatType > >
an_test_30digits
= {
{100.0,{10.0,10.0},0,{0.679828962402973494402566660504,0.415226053497115475049695981529},6.8e-31,4.2e-31},
{100.0,{10.0,10.0},1,{0.31190848427862392884480891022,-0.411544182145685558882194237961},3.1e-31,4.1e-31},
{100.0,{10.0,10.0},2,{0.70438815403586704544487912367,0.40368838606853976648041733313},7.0e-31,4.0e-31},
{100.0,{10.0,10.0},3,{0.271786765226200517064815984117,-0.390698399100492775796853574116},2.7e-31,3.9e-31},
{100.0,{10.0,10.0},4,{0.758690038301546480739410311883,0.371200152186914976444353907355},7.6e-31,3.7e-31},
{100.0,{10.0,10.0},5,{0.205560122807135500337250162455,-0.343503542058148814527059522736},2.1e-31,3.4e-31},
{100.0,{10.0,10.0},6,{0.833429352082835899591003797477,0.305760816312223565075588260235},8.3e-31,3.1e-31},
{100.0,{10.0,10.0},7,{0.127179302650854455613815261322,-0.256204313876684678415191746175},1.3e-31,2.6e-31},
{100.0,{10.0,10.0},8,{0.908862794970906860364913362218,0.193478822314053281910646966824},9.1e-31,1.9e-31},
{100.0,{10.0,10.0},9,{0.0631253453573123094216345683524,-0.117072919685495698168367821685},6.3e-32,1.2e-31},
{100.0,{10.0,10.0},10,{0.951385978828859119241125239906,0.0278328375104210335077734584032},9.5e-31,2.8e-32},
{100.0,{10.0,10.0},12,{0.916580851669130357604817820322,-0.175750732415289643888454774451},9.2e-31,1.8e-31},
{100.0,{10.0,10.0},14,{0.76635574590482422302341275995,-0.365197200225141544724269361373},7.7e-31,3.7e-31},
{100.0,{10.0,10.0},17,{0.647926380391943217307719536705,0.426881869738574912351528918309},6.5e-31,4.3e-31},
{100.0,{10.0,10.0},19,{0.897772858263070079882919373316,0.213840805949102983601660543366},9.0e-31,2.1e-31},
{100.0,{10.0,10.0},23,{0.646734688251639791789425805676,-0.426665368687914425026177551898},6.5e-31,4.3e-31},
{100.0,{10.0,10.0},26,{0.917541389422035436679093404389,0.16999167039455108885653697522},9.2e-31,1.7e-31},
{100.0,{10.0,10.0},31,{0.874710608275606256890577696798,0.249314249326626560672820647449},8.7e-31,2.5e-31},
{100.0,{10.0,10.0},36,{0.933952125179636651915361473572,0.11586004308049819374986059397},9.3e-31,1.2e-31},
{100.0,{10.0,10.0},42,{0.454296610104593060751628117406,0.445440314478011244574851240308},4.5e-31,4.5e-31},
{100.0,{10.0,10.0},49,{0.366407827716750193813191896865,-0.425226144777264582375107728238},3.7e-31,4.3e-31},
{100.0,{10.0,10.0},57,{0.460026617113670522420364769771,0.440740935073404320746433591059},4.6e-31,4.4e-31},
{100.0,{10.0,10.0},66,{0.754499276857564796661886030636,-0.355764558148565584411383376264},7.5e-31,3.6e-31},
{100.0,{10.0,10.0},76,{0.335490226138710838198779303754,0.395332122126832970606361956864},3.4e-31,4.0e-31},
{100.0,{10.0,10.0},89,{0.504927718220382142362743520035,-0.399954618225341028857538051784},5.0e-31,4.0e-31},
{100.0,{10.0,10.0},103,{0.155247890156101871963549534713,-0.193475207076534876752489443021},1.6e-31,1.9e-31},
{100.0,{10.0,10.0},120,{0.00000000267662196122883033815657363983,-0.0000000176408825619443339894450903787},2.7e-39,1.8e-38},
{100.0,{10.0,10.0},140,{1.12875229120676669224511124715e-22,-1.10142183824566380812854059223e-21},1.1e-52,1.1e-51},
{100.0,{10.0,10.0},162,{2.10081681780835363518344699642e-41,-2.66352219539497430358222180119e-40},2.1e-71,2.7e-70},
{100.0,{10.0,10.0},188,{1.01984812326280191108805960758e-67,-1.61153632927051257702806108056e-66},1.0e-97,1.6e-96},
{100.0,{10.0,10.0},219,{7.61464157272661971649643098205e-104,-1.4678827098307714849815760751e-102},7.6e-134,1.5e-132},
{100.0,{10.0,10.0},254,{9.70920247033645772180595742951e-150,-2.23345866953863686315418137136e-148},9.7e-180,2.2e-178},
{100.0,{10.0,10.0},296,{9.17410098778793332575560576757e-211,-2.50329537330001021720238188425e-209},9.2e-241,2.5e-239},
{100.0,{10.0,10.0},343,{1.54728924444235547832673390408e-285,-4.93445805599162272803774901168e-284},1.5e-315,4.9e-314},
{100.0,{10.0,10.0},399,{3.37317181957757910282198935269e-382,-1.25323308786056013454730417662e-380},3.4e-412,1.3e-410},
{100.0,{10.0,10.0},464,{3.51699765785293987454784526004e-503,-1.51130647609297077462735471327e-501},3.5e-533,1.5e-531},
{100.0,{10.0,10.0},539,{8.82119712438242287441958257536e-653,-4.34856698178728791133377787619e-651},8.8e-683,4.3e-681},
{100.0,{10.0,10.0},626,{8.28112018731353239277625222426e-838,-4.64503396342828376845115709631e-836},8.3e-868,4.6e-866},
{100.0,{10.0,10.0},727,{6.99476097776062140376902112325e-1066,-4.42171962856892626252493359032e-1064},7.0e-1096,4.4e-1094},
{100.0,{10.0,10.0},844,{2.17357239700355847203966561926e-1345,-1.53028532339923376703349340156e-1343},2.2e-1375,1.5e-1373},
{100.0,{10.0,10.0},981,{1.30745043446731375351676810589e-1690,-1.01174034009383554627992640203e-1688},1.3e-1720,1.0e-1718},
{100.0,{10.0,10.0},1139,{2.13810300916710064143281813763e-2109,-1.78817394919795125381215062143e-2107},2.1e-2139,1.8e-2137},
{100.0,{10.0,10.0},1324,{6.51588610784717425941070317004e-2624,-5.79120465820773576402244540831e-2622},6.5e-2654,5.8e-2652},
{100.0,{10.0,10.0},1537,{4.48628014234319302717168249273e-3244,-4.16479512959805049251097333075e-3242},4.5e-3274,4.2e-3272},
};

// x, complex(m), n, complex(f(n,z)), abs_err_real, abs_err_imag
std::vector< std::tuple< nmie::FloatType, std::complex<nmie::FloatType>, int, std::complex<nmie::FloatType>, nmie::FloatType, nmie::FloatType > >
bn_test_30digits
= {
{100.0,{10.0,10.0},0,{0.320171037597026505597433339496,-0.415226053497115475049695981529},3.2e-31,4.2e-31},
{100.0,{10.0,10.0},1,{0.688102688663558269637950176817,0.411549035340502143130949131489},6.9e-31,4.1e-31},
{100.0,{10.0,10.0},2,{0.295577765824838644962123836823,-0.403701596625138688081843237131},3.0e-31,4.0e-31},
{100.0,{10.0,10.0},3,{0.728282875037678869362296916378,0.390720693130263506269626825291},7.3e-31,3.9e-31},
{100.0,{10.0,10.0},4,{0.24119125420829264782986390491,-0.371227927142728379240185173628},2.4e-31,3.7e-31},
{100.0,{10.0,10.0},5,{0.794621289753212100235139895232,0.343527232702889516292009750323},7.9e-31,3.4e-31},
{100.0,{10.0,10.0},6,{0.166314387386566068719161425326,-0.30576333984052832356391572643},1.7e-31,3.1e-31},
{100.0,{10.0,10.0},7,{0.873159717417740513199219644963,0.256159925040697794776071626493},8.7e-31,2.6e-31},
{100.0,{10.0,10.0},8,{0.0907156873785831286863369142185,-0.19335290888519022800477857831},9.1e-32,1.9e-31},
{100.0,{10.0,10.0},9,{0.937365225010850674141316739717,0.116823465327552252176889872593},9.4e-31,1.2e-31},
{100.0,{10.0,10.0},10,{0.0480865745094912581949176840588,-0.0274144079577837282996668447782},4.8e-32,2.7e-32},
{100.0,{10.0,10.0},12,{0.0830121464840077022459981700383,0.176616664886728250759222326918},8.3e-32,1.8e-31},
{100.0,{10.0,10.0},14,{0.233775711304103861981117912554,0.366481692739659771334668324041},2.3e-31,3.7e-31},
{100.0,{10.0,10.0},17,{0.350419877877778844192262138072,-0.427796461057480059924772760242},3.5e-31,4.3e-31},
{100.0,{10.0,10.0},19,{0.0999390308639136635819217917173,-0.213284040180075118803341298841},1.0e-31,2.1e-31},
{100.0,{10.0,10.0},23,{0.354609837857012604962471334256,0.429840913844464502801549295326},3.5e-31,4.3e-31},
{100.0,{10.0,10.0},26,{0.0783018366402718218364640426886,-0.16849822674380600665898841356},7.8e-32,1.7e-31},
{100.0,{10.0,10.0},31,{0.11902497427184810754983602268,-0.248405876458500447346883714383},1.2e-31,2.5e-31},
{100.0,{10.0,10.0},36,{0.0583385326135556985670917972947,-0.111948520179255044347215446356},5.8e-32,1.1e-31},
{100.0,{10.0,10.0},42,{0.538655172522649519977279389364,-0.45516819181088439051089258237},5.4e-31,4.6e-31},
{100.0,{10.0,10.0},49,{0.648077620631044408169541380757,0.433896442439453138458949348299},6.5e-31,4.3e-31},
{100.0,{10.0,10.0},57,{0.525811128847205437888096222567,-0.460076703347602731659377388603},5.3e-31,4.6e-31},
{100.0,{10.0,10.0},66,{0.248667049534323140402225574527,0.390149542561216364452441234431},2.5e-31,3.9e-31},
{100.0,{10.0,10.0},76,{0.649781496533962419404239413327,-0.444315643934545667941241837069},6.5e-31,4.4e-31},
{100.0,{10.0,10.0},89,{0.538312060560845433134797633675,0.476614200565498692626866890834},5.4e-31,4.8e-31},
{100.0,{10.0,10.0},103,{0.0173039291278402253813949756937,0.117940098848570493436362521487},1.7e-32,1.2e-31},
{100.0,{10.0,10.0},120,{9.19216235319901235701738165726e-10,0.000000013681944872947274432834968601},9.2e-40,1.4e-38},
{100.0,{10.0,10.0},140,{8.73180467252494061041580803526e-23,8.8403917299578952247189061153e-22},8.7e-53,8.8e-52},
{100.0,{10.0,10.0},162,{2.73414826602380818509020985972e-41,2.12963402058720924272112483812e-40},2.7e-71,2.1e-70},
{100.0,{10.0,10.0},188,{2.03080368113977014860416145422e-67,1.26522239818490345170866686757e-66},2.0e-97,1.3e-96},
{100.0,{10.0,10.0},219,{2.2036139808853879904497051823e-103,1.11924145049993964499101911009e-102},2.2e-133,1.1e-132},
{100.0,{10.0,10.0},254,{3.88223194450670784061884980786e-149,1.63963865067996789659679399685e-148},3.9e-179,1.6e-178},
{100.0,{10.0,10.0},296,{4.96628178106412153587756817648e-210,1.74859913634476842249836867014e-209},5.0e-240,1.7e-239},
{100.0,{10.0,10.0},343,{1.0938988573382398273775007954e-284,3.2472666700854452431061674146e-284},1.1e-314,3.2e-314},
{100.0,{10.0,10.0},399,{3.06316027652451015800702086373e-381,7.64681972914809364498799216655e-381},3.1e-411,7.6e-411},
{100.0,{10.0,10.0},464,{4.0014535593885155240539166209e-502,8.40049560424774201136260375949e-502},4.0e-532,8.4e-532},
{100.0,{10.0,10.0},539,{1.22254518632653819324508981073e-651,2.15578359013488655725284479002e-651},1.2e-681,2.2e-681},
{100.0,{10.0,10.0},626,{1.35567791144631050248833144862e-836,1.99911730969488683578184205668e-836},1.4e-866,2.0e-866},
{100.0,{10.0,10.0},727,{1.30431560458674867647620310749e-1064,1.59729912349148684724035151749e-1064},1.3e-1094,1.6e-1094},
{100.0,{10.0,10.0},844,{4.41918873229972943145982099725e-1344,4.45319085047179627586948315397e-1344},4.4e-1374,4.5e-1374},
{100.0,{10.0,10.0},981,{2.75349167001965712979314404723e-1689,2.25126126172658200755061854137e-1689},2.8e-1719,2.3e-1719},
{100.0,{10.0,10.0},1139,{4.39719433207010461252662146274e-2108,2.87841737954565469068030273469e-2108},4.4e-2138,2.9e-2138},
{100.0,{10.0,10.0},1324,{1.22886278826232761310170941483e-2622,6.32593986562542026145495765727e-2623},1.2e-2652,6.3e-2653},
{100.0,{10.0,10.0},1537,{7.31652560046970872228490692244e-3243,2.92279258110586610473527638618e-3243},7.3e-3273,2.9e-3273},
};

// complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
psi_mul_zeta_test_16digits
= {
{{0.055,0.0},0,{0.003021951021651575,-0.0548891504185874},3.0e-19,5.5e-18},
{{0.055,0.0},1,{1.016121145233281e-6,-0.01835548791829774},1.0e-22,1.8e-18},
{{0.055,0.0},2,{1.229719152492059e-10,-0.01100317224014702},1.2e-26,1.1e-18},
{{0.055,0.0},3,{7.592362656062244e-15,-0.0078581994970704},7.6e-31,7.9e-19},
{{0.055,0.0},4,{2.835592674223453e-19,-0.006111591336893846},2.8e-35,6.1e-19},
{{0.055,0.0},5,{7.089281618184475e-24,-0.005000258569357047},7.1e-40,5.0e-19},
{{0.056,0.0},0,{0.003132723205069868,-0.05588299607564259},3.1e-19,5.6e-18},
{{0.056,0.0},1,{1.092036606873679e-6,-0.01869005067512779},1.1e-22,1.9e-18},
{{0.056,0.0},2,{1.370096242130984e-10,-0.01120334856005436},1.4e-26,1.1e-18},
{{0.056,0.0},3,{8.769489006914592e-15,-0.008001115340360345},8.8e-31,8.0e-19},
{{0.056,0.0},4,{3.395414807371369e-19,-0.006222729123879648},3.4e-35,6.2e-19},
{{0.056,0.0},5,{8.800403208656495e-24,-0.005091182022901522},8.8e-40,5.1e-19},
{{0.099,0.0},0,{0.00976902194728147,-0.09835440080380238},9.8e-19,9.8e-18},
{{0.099,0.0},1,{1.06523847864875e-5,-0.03312883043424608},1.1e-21,3.3e-18},
{{0.099,0.0},2,{4.178501167517404e-9,-0.01981854208686302},4.2e-25,2.0e-18},
{{0.099,0.0},3,{8.360456441867183e-13,-0.01414902327431168},8.4e-29,1.4e-18},
{{0.099,0.0},4,{1.011815572763764e-16,-0.01100280155335579},1.0e-32,1.1e-18},
{{0.101,0.0},0,{0.0101663603439792,-0.1003145326527297},1.0e-18,1.0e-17},
{{0.101,0.0},1,{1.153869805655288e-5,-0.03380344031202756},1.2e-21,3.4e-18},
{{0.101,0.0},2,{4.71099650661284e-9,-0.02021969130565892},4.7e-25,2.0e-18},
{{0.101,0.0},3,{9.810702765077567e-13,-0.01443511910448818},9.8e-29,1.4e-18},
{{0.101,0.0},4,{1.235797628684462e-16,-0.01122519707488852},1.2e-32,1.1e-18},
{{1.0,0.0},0,{0.7080734182735712,-0.4546487134128408},7.1e-17,4.5e-17},
{{1.0,0.0},1,{0.0907025731743183,-0.4161468365471424},9.1e-18,4.2e-17},
{{1.0,0.0},2,{0.00384834767805386,-0.2236374522186501},3.8e-19,2.2e-17},
{{1.0,0.0},3,{8.111850341912774e-5,-0.1498993624632433},8.1e-21,1.5e-17},
{{1.0,0.0},4,{1.022152964862514e-6,-0.1141418489822765},1.0e-22,1.1e-17},
{{1.0,0.0},5,{8.567568083458491e-9,-0.09250935614721912},8.6e-25,9.3e-18},
{{1.0,0.0},6,{5.122173734664295e-11,-0.07787423460333869},5.1e-27,7.8e-18},
{{1.0,0.0},7,{2.29453856419336e-13,-0.06727880114332268},2.3e-29,6.7e-18},
{{1.0,0.0},8,{7.9890954789213e-16,-0.05924092305054686},8.0e-32,5.9e-18},
{{1.0,0.0},9,{2.224203872373618e-18,-0.05292902429724696},2.2e-34,5.3e-18},
{{1.0,0.0},10,{5.064532147856438e-21,-0.04783853491685147},5.1e-37,4.8e-18},
{{1.0,0.0},11,{9.607221700532625e-24,-0.04364486754339771},9.6e-40,4.4e-18},
{{1.0,0.0},12,{1.541726004756763e-26,-0.0401294626939617},1.5e-42,4.0e-18},
{{1.0,0.0},13,{2.120268814274514e-29,-0.03713964014500267},2.1e-45,3.7e-18},
{{1.0,0.0},14,{2.52675182009057e-32,-0.0345654555670251},2.5e-48,3.5e-18},
{{1.0,0.0},15,{2.634446675966918e-35,-0.03232569427903133},2.6e-51,3.2e-18},
{{1.0,0.0},16,{2.423340639723846e-38,-0.03035904509315811},2.4e-54,3.0e-18},
{{1.0,0.0},17,{1.981298117039575e-41,-0.02861834507392694},2.0e-57,2.9e-18},
{{1.0,0.0},19,{9.540329388323879e-48,-0.02567489808970744},9.5e-64,2.6e-18},
{{1.0,0.0},20,{5.68183643501725e-51,-0.02441938436699653},5.7e-67,2.4e-18},
{{1.0,0.0},22,{1.520501862524084e-57,-0.02224424642998028},1.5e-73,2.2e-18},
{{1.0,0.0},24,{2.871601965313674e-64,-0.02042521280234952},2.9e-80,2.0e-18},
{{1.0,0.0},26,{3.935970015906627e-71,-0.0188813920614356},3.9e-87,1.9e-18},
{{1.0,0.0},28,{4.009703575122698e-78,-0.01755468254961163},4.0e-94,1.8e-18},
{{1.0,0.0},30,{3.098961035504115e-85,-0.01640227056413152},3.1e-101,1.6e-18},
{{1.0,0.0},32,{1.849779662426908e-92,-0.01539191014397623},1.8e-108,1.5e-18},
{{1.0,0.0},35,{1.71904973391556e-103,-0.01409010280215318},1.7e-119,1.4e-18},
{{1.0,0.0},38,{9.682571192175845e-115,-0.01299139901427509},9.7e-131,1.3e-18},
{{1.0,0.0},41,{3.435567055681588e-126,-0.01205169413760676},3.4e-142,1.2e-18},
{{10.0,0.0},0,{0.295958969093304,-0.4564726253638138},3.0e-17,4.6e-17},
{{10.0,0.0},1,{0.6157060955248663,0.4927161052915149},6.2e-17,4.9e-17},
{{10.0,0.0},2,{0.607498554763232,-0.5071644369097663},6.1e-17,5.1e-17},
{{10.0,0.0},3,{0.155992177103731,0.3765039328469335},1.6e-17,3.8e-17},
{{10.0,0.0},4,{1.114909713166518,0.01752708452606332},1.1e-16,1.8e-18},
{{10.0,0.0},5,{0.3084081981033207,-0.5210999910837328},3.1e-17,5.2e-17},
{{10.0,0.0},6,{0.1980367689482958,0.4667157442158694},2.0e-17,4.7e-17},
{{10.0,0.0},7,{1.285643730232455,0.4819632788028717},1.3e-16,4.8e-17},
{{10.0,0.0},8,{1.576984002373142,-0.5163432757216197},1.6e-16,5.2e-17},
{{10.0,0.0},9,{1.001929120449916,-1.125141593050778},1.0e-16,1.1e-16},
{{10.0,0.0},10,{0.4173825987008097,-1.114139612805899},4.2e-17,1.1e-16},
{{10.0,0.0},11,{0.1265538994473744,-0.8884600619485133},1.3e-17,8.9e-17},
{{10.0,0.0},12,{0.02963906472195924,-0.6920216399635206},3.0e-18,6.9e-17},
{{10.0,0.0},13,{0.00557349515770663,-0.5637738390408905},5.6e-19,5.6e-17},
{{10.0,0.0},14,{0.0008649941812568645,-0.481447977558081},8.6e-20,4.8e-17},
{{10.0,0.0},16,{1.266677095416471e-5,-0.3821856201495292},1.3e-21,3.8e-17},
{{10.0,0.0},17,{1.230784512285205e-6,-0.3488508522354134},1.2e-22,3.5e-17},
{{10.0,0.0},18,{1.049013273275846e-7,-0.3216769516939968},1.0e-23,3.2e-17},
{{10.0,0.0},19,{7.914997677111618e-9,-0.2989560911306167},7.9e-25,3.0e-17},
{{10.0,0.0},21,{3.222807603140006e-11,-0.2628401183295979},3.2e-27,2.6e-17},
{{10.0,0.0},22,{1.761684361765775e-12,-0.2481689046072283},1.8e-28,2.5e-17},
{{10.0,0.0},24,{3.967619823175087e-15,-0.2236071766951387},4.0e-31,2.2e-17},
{{10.0,0.0},26,{6.31219784387027e-18,-0.2037765868337052},6.3e-34,2.0e-17},
{{10.0,0.0},27,{2.231089847919333e-19,-0.1952071171449887},2.2e-35,2.0e-17},
{{10.0,0.0},30,{6.310432305527727e-24,-0.1735409287284763},6.3e-40,1.7e-17},
{{80.0,0.0},0,{0.9878146563976187,-0.1097126291895024},9.9e-17,1.1e-17},
{{80.0,0.0},1,{0.009596873912705912,0.09750012018125104},9.6e-19,9.8e-18},
{{80.0,0.0},30,{0.8255342447375176,-0.4598133020429286},8.3e-17,4.6e-17},
{{80.0,0.0},50,{0.7243467146069976,0.6395688164674208},7.2e-17,6.4e-17},
{{80.0,0.0},60,{0.4103464301592875,-0.6769649626635265},4.1e-17,6.8e-17},
{{80.0,0.0},70,{0.9296298544868326,-1.044106068321243},9.3e-17,1.0e-16},
{{80.0,0.0},75,{2.826505371942847,0.4810026687100474},2.8e-16,4.8e-17},
{{80.0,0.0},80,{1.080302660792914,-2.317525151179967},1.1e-16,2.3e-16},
{{80.0,0.0},85,{0.0407412363570179,-1.372072053151429},4.1e-18,1.4e-16},
{{80.0,0.0},90,{0.0003667279064351009,-0.9514780407757143},3.7e-20,9.5e-17},
{{80.0,0.0},99,{5.38333281008969e-9,-0.6766919376604463},5.4e-25,6.8e-17},
{{80.0,0.0},116,{4.079975765758877e-21,-0.4723779421220265},4.1e-37,4.7e-17},
{{80.0,0.0},130,{2.364875566095132e-33,-0.3879804405443515},2.4e-49,3.9e-17},
{{100.0,0.0},0,{0.256406162496497,0.4366486486069973},2.6e-17,4.4e-17},
{{100.0,0.0},1,{0.7523524510918926,-0.4317331069920665},7.5e-17,4.3e-17},
{{100.0,0.0},2,{0.230730517088562,0.4213824693713301},2.3e-17,4.2e-17},
{{100.0,0.0},3,{0.7945934910545345,-0.4045884190987047},7.9e-17,4.0e-17},
{{100.0,0.0},4,{0.1746790124372205,0.3799225844242402},1.7e-17,3.8e-17},
{{100.0,0.0},5,{0.8630686723276429,-0.3456565727640024},8.6e-17,3.5e-17},
{{100.0,0.0},6,{0.09970093292656848,0.2999510941211375},1.0e-17,3.0e-17},
{{100.0,0.0},7,{0.9410221936833145,-0.2411327490155267},9.4e-17,2.4e-17},
{{100.0,0.0},8,{0.0289833932973693,0.1680721489154539},2.9e-18,1.7e-17},
{{100.0,0.0},9,{0.9980102927237763,-0.08066377424553287},1.0e-16,8.1e-18},
{{100.0,0.0},10,{0.0003828199806763987,-0.01961622142888973},3.8e-20,2.0e-18},
{{100.0,0.0},12,{0.06169850033611365,-0.2416167884883422},6.2e-18,2.4e-17},
{{100.0,0.0},14,{0.250247316674531,-0.4362257370084827},2.5e-17,4.4e-17},
{{100.0,0.0},17,{0.2938292525898981,0.4605370126483646},2.9e-17,4.6e-17},
{{100.0,0.0},19,{0.03858070680264446,0.1945423348167594},3.9e-18,1.9e-17},
{{100.0,0.0},23,{0.3977295322443018,-0.5009915439616875},4.0e-17,5.0e-17},
{{100.0,0.0},26,{0.0207047771805246,0.1450632139773643},2.1e-18,1.5e-17},
{{100.0,0.0},31,{0.06019568065492113,0.2445393267844256},6.0e-18,2.4e-17},
{{100.0,0.0},36,{0.006436145631620102,0.08289433103146386},6.4e-19,8.3e-18},
{{100.0,0.0},42,{0.5490517797556987,0.5523367487618802},5.5e-17,5.5e-17},
{{100.0,0.0},49,{0.8079050821220394,-0.5263512418188373},8.1e-17,5.3e-17},
{{100.0,0.0},57,{0.5952247031640156,0.6108677512179897},6.0e-17,6.1e-17},
{{100.0,0.0},66,{0.3499557066756242,-0.58823274813532},3.5e-17,5.9e-17},
{{100.0,0.0},76,{0.9758072300221017,0.7497215985189103},9.8e-17,7.5e-17},
{{100.0,0.0},89,{1.253396334302241,-1.105547490464419},1.3e-16,1.1e-16},
{{100.0,0.0},103,{0.2364244628680228,-1.912256568210032},2.4e-17,1.9e-16},
{{100.0,0.0},120,{1.091890360981933e-8,-0.7443857013666448},1.1e-24,7.4e-17},
{{100.0,0.0},140,{4.969528549863077e-22,-0.5066841997377345},5.0e-38,5.1e-17},
{{100.0,0.0},162,{9.53179081403156e-41,-0.3903728156193839},9.5e-57,3.9e-17},
{{100.0,0.0},188,{4.707979284933665e-67,-0.3129179118636492},4.7e-83,3.1e-17},
{{100.0,0.0},219,{3.55281576252597e-103,-0.2558895779606525},3.6e-119,2.6e-17},
{{100.0,0.0},254,{4.55657832640485e-149,-0.2136478525051976},4.6e-165,2.1e-17},
{{100.0,0.0},296,{4.315175622295763e-210,-0.1791296784354242},4.3e-226,1.8e-17},
{{100.0,0.0},343,{7.268649608327999e-285,-0.1521506868517931},7.3e-301,1.5e-17},
{{100.0,0.0},399,{1.576548530414267e-381,-0.1292718457785899},1.6e-397,1.3e-17},
{{100.0,0.0},464,{1.628112757148264e-502,-0.1102273379986514},1.6e-518,1.1e-17},
{{100.0,0.0},539,{4.022904701566716e-652,-0.09431273058687071},4.0e-668,9.4e-18},
{{100.0,0.0},626,{3.695061705517215e-837,-0.08084497341960217},3.7e-853,8.1e-18},
{{100.0,0.0},727,{3.027077507860543e-1065,-0.06938716543204574},3.0e-1081,6.9e-18},
{{100.0,0.0},844,{9.023599477774656e-1345,-0.05962613741500692},9.0e-1361,6.0e-18},
{{100.0,0.0},981,{5.134247651002995e-1690,-0.05120891645363667},5.1e-1706,5.1e-18},
{{100.0,0.0},1139,{7.819360896771125e-2109,-0.04404884175054067},7.8e-2125,4.4e-18},
{{100.0,0.0},1324,{2.179779980227056e-2623,-0.03785814964222869},2.2e-2639,3.8e-18},
{{100.0,0.0},1537,{1.351131440487193e-3243,-0.03258932938218371},1.4e-3259,3.3e-18},
{{1000.0,0.0},0,{0.6837297745504157,-0.4650197522080685},6.8e-17,4.7e-17},
{{1000.0,0.0},1,{0.3153408696749427,0.4646518276392155},3.2e-17,4.6e-17},
{{1000.0,0.0},2,{0.6865186287528438,-0.463910401575804},6.9e-17,4.6e-17},
{{1000.0,0.0},3,{0.3107052121902361,0.4627843423813207},3.1e-17,4.6e-17},
{{1000.0,0.0},4,{0.6929997456348241,-0.4612570089179194},6.9e-17,4.6e-17},
{{1000.0,0.0},5,{0.3024089061787186,0.4593063203041767},3.0e-17,4.6e-17},
{{1000.0,0.0},6,{0.7031076597072864,-0.4569048525372149},7.0e-17,4.6e-17},
{{1000.0,0.0},7,{0.2905387702685337,0.4540199650394618},2.9e-17,4.5e-17},
{{1000.0,0.0},9,{0.2752306324835701,0.4466442853347819},2.8e-17,4.5e-17},
{{1000.0,0.0},10,{0.7337091845202087,-0.4420637672836413},7.3e-17,4.4e-17},
{{1000.0,0.0},11,{0.2566803850394357,0.4368209101368283},2.6e-17,4.4e-17},
{{1000.0,0.0},13,{0.2351579017116949,0.4241227006806428},2.4e-17,4.2e-17},
{{1000.0,0.0},15,{0.211023291057128,0.4080659125735375},2.1e-17,4.1e-17},
{{1000.0,0.0},18,{0.8291891947671029,-0.3765319396383436},8.3e-17,3.8e-17},
{{1000.0,0.0},20,{0.8575634644874209,-0.3497549337299916},8.6e-17,3.5e-17},
{{1000.0,0.0},23,{0.09972596291198461,0.29968021449204},1.0e-17,3.0e-17},
{{1000.0,0.0},27,{0.04731739666958621,0.212359027919195},4.7e-18,2.1e-17},
{{1000.0,0.0},31,{0.01021549401741627,0.1005793634384563},1.0e-18,1.0e-17},
{{1000.0,0.0},35,{0.00107650575783671,-0.0328028311638996},1.1e-19,3.3e-18},
{{1000.0,0.0},41,{0.06808144133529505,-0.2520020883398875},6.8e-18,2.5e-17},
{{1000.0,0.0},47,{0.2566841270444542,-0.4371354664741786},2.6e-17,4.4e-17},
{{1000.0,0.0},54,{0.3986043794455755,0.4902164588520832},4.0e-17,4.9e-17},
{{1000.0,0.0},62,{0.04536475784626348,0.2083162361002326},4.5e-18,2.1e-17},
{{1000.0,0.0},71,{0.8583330593128032,0.3518519034467923},8.6e-17,3.5e-17},
{{1000.0,0.0},81,{0.1638551470566819,0.3708820914899069},1.6e-17,3.7e-17},
{{1000.0,0.0},93,{0.3537316136673334,-0.4797519457793337},3.5e-17,4.8e-17},
{{1000.0,0.0},107,{0.796324525113472,0.4084521979134828},8.0e-17,4.1e-17},
{{1000.0,0.0},123,{0.473532993539322,-0.5029438285687216},4.7e-17,5.0e-17},
{{1000.0,0.0},141,{3.352971318064491e-5,-0.005819740586015554},3.4e-21,5.8e-19},
{{1000.0,0.0},162,{1.008701751906824,0.06935481533069809},1.0e-16,6.9e-18},
{{1000.0,0.0},186,{0.180048185727329,0.3883892039272592},1.8e-17,3.9e-17},
{{1000.0,0.0},214,{0.7832917805736668,0.4340645318072342},7.8e-17,4.3e-17},
{{1000.0,0.0},246,{0.009344896452480198,-0.09775022345721083},9.3e-19,9.8e-18},
{{1000.0,0.0},282,{0.09566847423406349,-0.3009622903033931},9.6e-18,3.0e-17},
{{1000.0,0.0},324,{0.4322624052566416,-0.5197512105452738},4.3e-17,5.2e-17},
{{1000.0,0.0},372,{0.8266856879897288,0.4553950981107681},8.3e-17,4.6e-17},
{{1000.0,0.0},427,{0.9210789099283309,-0.4129025775667674},9.2e-17,4.1e-17},
{{1000.0,0.0},490,{1.094334343721242,-0.2412611945568023},1.1e-16,2.4e-17},
{{1000.0,0.0},562,{0.2277347708249827,-0.4728411132919602},2.3e-17,4.7e-17},
{{1000.0,0.0},645,{0.5103216319784123,0.6385457081259945},5.1e-17,6.4e-17},
{{1000.0,0.0},740,{1.463456803176647,-0.1893811578643412},1.5e-16,1.9e-17},
{{1000.0,0.0},850,{1.070057419675087,0.943057044237281},1.1e-16,9.4e-17},
{{10000.0,0.0},0,{0.09340015469553981,-0.2909923809971475},9.3e-18,2.9e-17},
{{10000.0,0.0},1,{0.9065416477622623,0.2910736980562846},9.1e-17,2.9e-17},
{{10000.0,0.0},2,{0.09357482610887712,-0.2912362972481545},9.4e-18,2.9e-17},
{{10000.0,0.0},3,{0.9062504161524928,0.2914801086711672},9.1e-17,2.9e-17},
{{10000.0,0.0},4,{0.09398296167406917,-0.2918050273510329},9.4e-18,2.9e-17},
{{10000.0,0.0},5,{0.9057251756142541,0.2922109130946131},9.1e-17,2.9e-17},
{{10000.0,0.0},6,{0.09462592521624692,-0.2926975902952848},9.5e-18,2.9e-17},
{{10000.0,0.0},8,{0.09550585525767662,-0.2939124380683851},9.6e-18,2.9e-17},
{{10000.0,0.0},11,{0.9027240303429979,0.2963341883460851},9.0e-17,3.0e-17},
{{10000.0,0.0},14,{0.09960030318021704,-0.2994665045829122},1.0e-17,3.0e-17},
{{10000.0,0.0},18,{0.1035880988071382,-0.3047257483849394},1.0e-17,3.0e-17},
{{10000.0,0.0},23,{0.8899283645791489,0.3129829495500489},8.9e-17,3.1e-17},
{{10000.0,0.0},29,{0.8797814325426485,0.3252228321781845},8.8e-17,3.3e-17},
{{10000.0,0.0},37,{0.8618146944042639,0.3451031520201578},8.6e-17,3.5e-17},
{{10000.0,0.0},48,{0.1724090954326228,-0.3777383046653143},1.7e-17,3.8e-17},
{{10000.0,0.0},61,{0.7704313888104097,0.4205727442627203},7.7e-17,4.2e-17},
{{10000.0,0.0},78,{0.3363692716177661,-0.4724778817523399},3.4e-17,4.7e-17},
{{10000.0,0.0},99,{0.4798396969269212,0.4996171694491488},4.8e-17,5.0e-17},
{{10000.0,0.0},126,{0.8028931330521504,-0.3978944547731133},8.0e-17,4.0e-17},
{{10000.0,0.0},161,{0.001927595092644426,-0.043864916467029},1.9e-19,4.4e-18},
{{10000.0,0.0},205,{0.5658917609980439,-0.4957598226301632},5.7e-17,5.0e-17},
{{10000.0,0.0},262,{0.3325140313656405,-0.471235684776433},3.3e-17,4.7e-17},
{{10000.0,0.0},333,{0.8408566903346908,-0.3664487902639207},8.4e-17,3.7e-17},
{{10000.0,0.0},425,{0.9972681502505771,-0.06023613065692369},1.0e-16,6.0e-18},
{{10000.0,0.0},541,{0.5534184894443579,-0.4979554458661743},5.5e-17,5.0e-17},
{{10000.0,0.0},690,{0.6850261734907807,0.4662662825831345},6.9e-17,4.7e-17},
{{10000.0,0.0},879,{0.06551997148993641,0.2479556200383764},6.6e-18,2.5e-17},
{{10000.0,0.0},2950,{0.7375893855015257,0.4774068891965172},7.4e-17,4.8e-17},
{{10000.0,0.0},53911,{1.067016016683514e-64929,-0.09438247522268317},1.1e-64945,9.4e-18},
{{10000.0,0.0},68679,{7.70341454263852e-96960,-0.07358613728379516},7.7e-96976,7.4e-18},
{{10000.0,0.0},87493,{7.946317443364444e-141765,-0.05752406062448876},7.9e-141781,5.8e-18},
{{10000.0,0.0},111461,{6.863941818773283e-203918,-0.04504017247767002},6.9e-203934,4.5e-18},
{{10000.0,0.0},141995,{3.391815853006694e-289545,-0.03530003015880046},3.4e-289561,3.5e-18},
};

// complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
psi_test_16digits
= {
{{0.055,0.0},0,{0.05497227502706773,0.0},5.5e-18,0.0},
{{0.055,0.0},1,{0.001008028345451298,0.0},1.0e-19,0.0},
{{0.055,0.0},2,{1.108927027577585e-5,0.0},1.1e-21,0.0},
{{0.055,0.0},3,{8.713416468907156e-8,0.0},8.7e-24,0.0},
{{0.055,0.0},4,{5.325028332528807e-10,0.0},5.3e-26,0.0},
{{0.055,0.0},5,{2.662570490744701e-12,0.0},2.7e-28,0.0},
{{0.056,0.0},0,{0.05597073525575547,0.0},5.6e-18,0.0},
{{0.056,0.0},1,{0.00104500555351332,0.0},1.0e-19,0.0},
{{0.056,0.0},2,{1.170511102950751e-5,0.0},1.2e-21,0.0},
{{0.056,0.0},3,{9.364554985109859e-8,0.0},9.4e-24,0.0},
{{0.056,0.0},4,{5.827018798125993e-10,0.0},5.8e-26,0.0},
{{0.056,0.0},5,{2.966547354864994e-12,0.0},3.0e-28,0.0},
{{0.099,0.0},0,{0.09883836273067998,0.0},9.9e-18,0.0},
{{0.099,0.0},1,{0.003263799133906297,0.0},3.3e-19,0.0},
{{0.099,0.0},2,{6.464132708660462e-5,0.0},6.5e-21,0.0},
{{0.099,0.0},3,{9.143553161581762e-7,0.0},9.1e-23,0.0},
{{0.099,0.0},4,{1.005890437753418e-8,0.0},1.0e-24,0.0},
{{0.101,0.0},0,{0.100828370729568,0.0},1.0e-17,0.0},
{{0.101,0.0},1,{0.003396865916775768,0.0},3.4e-19,0.0},
{{0.101,0.0},2,{6.863669941520236e-5,0.0},6.9e-21,0.0},
{{0.101,0.0},3,{9.904899174185251e-7,0.0},9.9e-23,0.0},
{{0.101,0.0},4,{1.111664350730229e-8,0.0},1.1e-24,0.0},
{{1.0,0.0},0,{0.8414709848078965,0.0},8.4e-17,0.0},
{{1.0,0.0},1,{0.3011686789397568,0.0},3.0e-17,0.0},
{{1.0,0.0},2,{0.06203505201137386,0.0},6.2e-18,0.0},
{{1.0,0.0},3,{0.009006581117112516,0.0},9.0e-19,0.0},
{{1.0,0.0},4,{0.001011015808413753,0.0},1.0e-19,0.0},
{{1.0,0.0},5,{9.256115861125816e-5,0.0},9.3e-21,0.0},
{{1.0,0.0},6,{7.156936310087086e-6,0.0},7.2e-22,0.0},
{{1.0,0.0},7,{4.790134198739489e-7,0.0},4.8e-23,0.0},
{{1.0,0.0},8,{2.826498802214729e-8,0.0},2.8e-24,0.0},
{{1.0,0.0},9,{1.491376502555146e-9,0.0},1.5e-25,0.0},
{{1.0,0.0},10,{7.116552640047313e-11,0.0},7.1e-27,0.0},
{{1.0,0.0},11,{3.09955185479008e-12,0.0},3.1e-28,0.0},
{{1.0,0.0},12,{1.241662596987106e-13,0.0},1.2e-29,0.0},
{{1.0,0.0},13,{4.604637677683787e-15,0.0},4.6e-31,0.0},
{{1.0,0.0},14,{1.589575987516976e-16,0.0},1.6e-32,0.0},
{{1.0,0.0},15,{5.132686115443762e-18,0.0},5.1e-34,0.0},
{{1.0,0.0},16,{1.556708270590172e-19,0.0},1.6e-35,0.0},
{{1.0,0.0},17,{4.451177503806802e-21,0.0},4.5e-37,0.0},
{{1.0,0.0},19,{3.088742363539549e-24,0.0},3.1e-40,0.0},
{{1.0,0.0},20,{7.537795722236873e-26,0.0},7.5e-42,0.0},
{{1.0,0.0},22,{3.899361309912283e-29,0.0},3.9e-45,0.0},
{{1.0,0.0},24,{1.694580173763896e-32,0.0},1.7e-48,0.0},
{{1.0,0.0},26,{6.273730960048117e-36,0.0},6.3e-52,0.0},
{{1.0,0.0},28,{2.002424424322351e-39,0.0},2.0e-55,0.0},
{{1.0,0.0},30,{5.566831266981347e-43,0.0},5.6e-59,0.0},
{{1.0,0.0},32,{1.360066050758899e-46,0.0},1.4e-62,0.0},
{{1.0,0.0},35,{4.146142464888971e-52,0.0},4.1e-68,0.0},
{{1.0,0.0},38,{9.840005687079579e-58,0.0},9.8e-74,0.0},
{{1.0,0.0},41,{1.853528272155995e-63,0.0},1.9e-79,0.0},
{{10.0,0.0},0,{-0.5440211108893698,0.0},5.4e-17,0.0},
{{10.0,0.0},1,{0.7846694179875155,0.0},7.8e-17,0.0},
{{10.0,0.0},2,{0.7794219362856245,0.0},7.8e-17,0.0},
{{10.0,0.0},3,{-0.3949584498447032,0.0},3.9e-17,0.0},
{{10.0,0.0},4,{-1.055892851176917,0.0},1.1e-16,0.0},
{{10.0,0.0},5,{-0.5553451162145218,0.0},5.6e-17,0.0},
{{10.0,0.0},6,{0.4450132233409427,0.0},4.5e-17,0.0},
{{10.0,0.0},7,{1.133862306557747,0.0},1.1e-16,0.0},
{{10.0,0.0},8,{1.255780236495678,0.0},1.3e-16,0.0},
{{10.0,0.0},9,{1.000964095484906,0.0},1.0e-16,0.0},
{{10.0,0.0},10,{0.6460515449256426,0.0},6.5e-17,0.0},
{{10.0,0.0},11,{0.3557441488589438,0.0},3.6e-17,0.0},
{{10.0,0.0},12,{0.1721599974499281,0.0},1.7e-17,0.0},
{{10.0,0.0},13,{0.07465584476587637,0.0},7.5e-18,0.0},
{{10.0,0.0},14,{0.02941078341793813,0.0},2.9e-18,0.0},
{{10.0,0.0},16,{0.00355904073510893,0.0},3.6e-19,0.0},
{{10.0,0.0},17,{0.001109407279715256,0.0},1.1e-19,0.0},
{{10.0,0.0},18,{0.0003238847438944672,0.0},3.2e-20,0.0},
{{10.0,0.0},19,{8.896627269427228e-5,0.0},8.9e-21,0.0},
{{10.0,0.0},21,{5.676977719825934e-6,0.0},5.7e-22,0.0},
{{10.0,0.0},22,{1.327284582056831e-6,0.0},1.3e-22,0.0},
{{10.0,0.0},24,{6.298904526324468e-8,0.0},6.3e-24,0.0},
{{10.0,0.0},26,{2.512408773243373e-9,0.0},2.5e-25,0.0},
{{10.0,0.0},27,{4.723441380941795e-10,0.0},4.7e-26,0.0},
{{10.0,0.0},30,{2.512057384998943e-12,0.0},2.5e-28,0.0},
{{80.0,0.0},0,{-0.9938886539233752,0.0},9.9e-17,0.0},
{{80.0,0.0},1,{0.09796363566500537,0.0},9.8e-18,0.0},
{{80.0,0.0},30,{0.9085891506822639,0.0},9.1e-17,0.0},
{{80.0,0.0},50,{-0.8510856094465454,0.0},8.5e-17,0.0},
{{80.0,0.0},60,{-0.6405828831301126,0.0},6.4e-17,0.0},
{{80.0,0.0},70,{-0.9641731454914271,0.0},9.6e-17,0.0},
{{80.0,0.0},75,{1.681221392899474,0.0},1.7e-16,0.0},
{{80.0,0.0},80,{1.039376092082608,0.0},1.0e-16,0.0},
{{80.0,0.0},85,{0.2018445846611147,0.0},2.0e-17,0.0},
{{80.0,0.0},90,{0.01915014115966514,0.0},1.9e-18,0.0},
{{80.0,0.0},99,{7.337119877778807e-5,0.0},7.3e-21,0.0},
{{80.0,0.0},116,{6.387468798952271e-11,0.0},6.4e-27,0.0},
{{80.0,0.0},130,{4.862998628516291e-17,0.0},4.9e-33,0.0},
{{100.0,0.0},0,{-0.5063656411097588,0.0},5.1e-17,0.0},
{{100.0,0.0},1,{-0.8673825286987815,0.0},8.7e-17,0.0},
{{100.0,0.0},2,{0.4803441652487953,0.0},4.8e-17,0.0},
{{100.0,0.0},3,{0.8913997369612213,0.0},8.9e-17,0.0},
{{100.0,0.0},4,{-0.4179461836615099,0.0},4.2e-17,0.0},
{{100.0,0.0},5,{-0.9290148934907572,0.0},9.3e-17,0.0},
{{100.0,0.0},6,{0.3157545453775266,0.0},3.2e-17,0.0},
{{100.0,0.0},7,{0.9700629843898356,0.0},9.7e-17,0.0},
{{100.0,0.0},8,{-0.1702450977190512,0.0},1.7e-17,0.0},
{{100.0,0.0},9,{-0.9990046510020743,0.0},1.0e-16,0.0},
{{100.0,0.0},10,{-0.0195657859713429,0.0},2.0e-18,0.0},
{{100.0,0.0},12,{0.2483918282394041,0.0},2.5e-17,0.0},
{{100.0,0.0},14,{-0.5002472555392293,0.0},5.0e-17,0.0},
{{100.0,0.0},17,{-0.5420601927737344,0.0},5.4e-17,0.0},
{{100.0,0.0},19,{0.196419721012541,0.0},2.0e-17,0.0},
{{100.0,0.0},23,{-0.6306580152858614,0.0},6.3e-17,0.0},
{{100.0,0.0},26,{-0.143891546591607,0.0},1.4e-17,0.0},
{{100.0,0.0},31,{-0.245348080601665,0.0},2.5e-17,0.0},
{{100.0,0.0},36,{-0.08022559212383603,0.0},8.0e-18,0.0},
{{100.0,0.0},42,{-0.7409802829736421,0.0},7.4e-17,0.0},
{{100.0,0.0},49,{-0.8988354032424621,0.0},9.0e-17,0.0},
{{100.0,0.0},57,{0.7715080707056898,0.0},7.7e-17,0.0},
{{100.0,0.0},66,{0.5915705424339723,0.0},5.9e-17,0.0},
{{100.0,0.0},76,{-0.987829555147092,0.0},9.9e-17,0.0},
{{100.0,0.0},89,{-1.119551845294465,0.0},1.1e-16,0.0},
{{100.0,0.0},103,{0.4862349872932045,0.0},4.9e-17,0.0},
{{100.0,0.0},120,{0.0001044935577431419,0.0},1.0e-20,0.0},
{{100.0,0.0},140,{2.229243941309043e-11,0.0},2.2e-27,0.0},
{{100.0,0.0},162,{9.763089067519337e-21,0.0},9.8e-37,0.0},
{{100.0,0.0},188,{6.861471624173392e-34,0.0},6.9e-50,0.0},
{{100.0,0.0},219,{5.960550110959533e-52,0.0},6.0e-68,0.0},
{{100.0,0.0},254,{6.750243200363117e-75,0.0},6.8e-91,0.0},
{{100.0,0.0},296,{2.077300079982611e-105,0.0},2.1e-121,0.0},
{{100.0,0.0},343,{8.525637576350521e-143,0.0},8.5e-159,0.0},
{{100.0,0.0},399,{3.970577452228161e-191,0.0},4.0e-207,0.0},
{{100.0,0.0},464,{1.275975218077633e-251,0.0},1.3e-267,0.0},
{{100.0,0.0},539,{2.005718001506372e-326,0.0},2.0e-342,0.0},
{{100.0,0.0},626,{6.078701921888599e-419,0.0},6.1e-435,0.0},
{{100.0,0.0},727,{5.501888319350496e-533,0.0},5.5e-549,0.0},
{{100.0,0.0},844,{9.499262854440157e-673,0.0},9.5e-689,0.0},
{{100.0,0.0},981,{2.265887828424654e-845,0.0},2.3e-861,0.0},
{{100.0,0.0},1139,{8.842715022418808e-1055,0.0},8.8e-1071,0.0},
{{100.0,0.0},1324,{4.668811390736464e-1312,0.0},4.7e-1328,0.0},
{{100.0,0.0},1537,{3.675773987185818e-1622,0.0},3.7e-1638,0.0},
{{1000.0,0.0},0,{0.8268795405320026,0.0},8.3e-17,0.0},
{{1000.0,0.0},1,{-0.561552196750171,0.0},5.6e-17,0.0},
{{1000.0,0.0},2,{-0.8285641971222531,0.0},8.3e-17,0.0},
{{1000.0,0.0},3,{0.5574093757645597,0.0},5.6e-17,0.0},
{{1000.0,0.0},4,{0.832466062752605,0.0},8.3e-17,0.0},
{{1000.0,0.0},5,{-0.5499171811997863,0.0},5.5e-17,0.0},
{{1000.0,0.0},6,{-0.8385151517458026,0.0},8.4e-17,0.0},
{{1000.0,0.0},7,{0.5390164842270908,0.0},5.4e-17,0.0},
{{1000.0,0.0},9,{-0.5246242774439343,0.0},5.2e-17,0.0},
{{1000.0,0.0},10,{-0.8565682602806438,0.0},8.6e-17,0.0},
{{1000.0,0.0},11,{0.5066363439780408,0.0},5.1e-17,0.0},
{{1000.0,0.0},13,{-0.4849308215732373,0.0},4.8e-17,0.0},
{{1000.0,0.0},15,{0.4593727147503734,0.0},4.6e-17,0.0},
{{1000.0,0.0},18,{-0.9105982620053164,0.0},9.1e-17,0.0},
{{1000.0,0.0},20,{0.9260472258407888,0.0},9.3e-17,0.0},
{{1000.0,0.0},23,{0.3157941780843729,0.0},3.2e-17,0.0},
{{1000.0,0.0},27,{0.2175256230184992,0.0},2.2e-17,0.0},
{{1000.0,0.0},31,{0.1010717270922797,0.0},1.0e-17,0.0},
{{1000.0,0.0},35,{-0.03281014717791907,0.0},3.3e-18,0.0},
{{1000.0,0.0},41,{0.2609242061122253,0.0},2.6e-17,0.0},
{{1000.0,0.0},47,{-0.5066400369537076,0.0},5.1e-17,0.0},
{{1000.0,0.0},54,{-0.6313512330276828,0.0},6.3e-17,0.0},
{{1000.0,0.0},62,{-0.2129900416598473,0.0},2.1e-17,0.0},
{{1000.0,0.0},71,{-0.926462659427137,0.0},9.3e-17,0.0},
{{1000.0,0.0},81,{0.4047902506937166,0.0},4.0e-17,0.0},
{{1000.0,0.0},93,{-0.5947534057635428,0.0},5.9e-17,0.0},
{{1000.0,0.0},107,{0.8923701726937493,0.0},8.9e-17,0.0},
{{1000.0,0.0},123,{-0.6881373362486023,0.0},6.9e-17,0.0},
{{1000.0,0.0},141,{-0.005790484710336857,0.0},5.8e-19,0.0},
{{1000.0,0.0},162,{-1.004341451851323,0.0},1.0e-16,0.0},
{{1000.0,0.0},186,{0.4243208523362115,0.0},4.2e-17,0.0},
{{1000.0,0.0},214,{0.8850377283334687,0.0},8.9e-17,0.0},
{{1000.0,0.0},246,{-0.09666900461099306,0.0},9.7e-18,0.0},
{{1000.0,0.0},282,{0.3093032076039036,0.0},3.1e-17,0.0},
{{1000.0,0.0},324,{-0.6574666571444073,0.0},6.6e-17,0.0},
{{1000.0,0.0},372,{0.909222573405285,0.0},9.1e-17,0.0},
{{1000.0,0.0},427,{0.9597285605463302,0.0},9.6e-17,0.0},
{{1000.0,0.0},490,{1.046104365597067,0.0},1.0e-16,0.0},
{{1000.0,0.0},562,{-0.4772156439441007,0.0},4.8e-17,0.0},
{{1000.0,0.0},645,{0.7143679947886889,0.0},7.1e-17,0.0},
{{1000.0,0.0},740,{1.209734186991773,0.0},1.2e-16,0.0},
{{1000.0,0.0},850,{-1.034435797754064,0.0},1.0e-16,0.0},
{{10000.0,0.0},0,{-0.3056143888882521,0.0},3.1e-17,0.0},
{{10000.0,0.0},1,{0.952124806820126,0.0},9.5e-17,0.0},
{{10000.0,0.0},2,{0.3059000263302982,0.0},3.1e-17,0.0},
{{10000.0,0.0},3,{-0.9519718568069609,0.0},9.5e-17,0.0},
{{10000.0,0.0},4,{-0.3065664066300631,0.0},3.1e-17,0.0},
{{10000.0,0.0},5,{0.9516959470409938,0.0},9.5e-17,0.0},
{{10000.0,0.0},6,{0.3076132721718081,0.0},3.1e-17,0.0},
{{10000.0,0.0},8,{-0.3090402162464889,0.0},3.1e-17,0.0},
{{10000.0,0.0},11,{-0.9501179033904149,0.0},9.5e-17,0.0},
{{10000.0,0.0},14,{0.315595157092464,0.0},3.2e-17,0.0},
{{10000.0,0.0},18,{0.3218510506540846,0.0},3.2e-17,0.0},
{{10000.0,0.0},23,{-0.9433601457445342,0.0},9.4e-17,0.0},
{{10000.0,0.0},29,{0.9379666478839471,0.0},9.4e-17,0.0},
{{10000.0,0.0},37,{0.9283397516018927,0.0},9.3e-17,0.0},
{{10000.0,0.0},48,{-0.4152217424854132,0.0},4.2e-17,0.0},
{{10000.0,0.0},61,{0.8777422109084248,0.0},8.8e-17,0.0},
{{10000.0,0.0},78,{0.5799735094103576,0.0},5.8e-17,0.0},
{{10000.0,0.0},99,{-0.6927046245889522,0.0},6.9e-17,0.0},
{{10000.0,0.0},126,{0.8960430419640289,0.0},9.0e-17,0.0},
{{10000.0,0.0},161,{-0.04390438580192674,0.0},4.4e-18,0.0},
{{10000.0,0.0},205,{-0.7522577756314945,0.0},7.5e-17,0.0},
{{10000.0,0.0},262,{-0.5766402963422176,0.0},5.8e-17,0.0},
{{10000.0,0.0},333,{0.9169823827831649,0.0},9.2e-17,0.0},
{{10000.0,0.0},425,{-0.9986331409734894,0.0},1.0e-16,0.0},
{{10000.0,0.0},541,{-0.7439210236606826,0.0},7.4e-17,0.0},
{{10000.0,0.0},690,{-0.8276630796953436,0.0},8.3e-17,0.0},
{{10000.0,0.0},879,{-0.2559686924018959,0.0},2.6e-17,0.0},
{{10000.0,0.0},1120,{-0.3161896326121199,0.0},3.2e-17,0.0},
{{10000.0,0.0},1427,{0.2687936760264434,0.0},2.7e-17,0.0},
{{10000.0,0.0},1818,{0.3801110903322125,0.0},3.8e-17,0.0},
{{10000.0,0.0},2316,{0.3363664648717635,0.0},3.4e-17,0.0},
{{10000.0,0.0},2950,{-0.8588302425401225,0.0},8.6e-17,0.0},
{{10000.0,0.0},3758,{-0.8541132755119114,0.0},8.5e-17,0.0},
{{10000.0,0.0},7771,{-1.18058612315672,0.0},1.2e-16,0.0},
{{10000.0,0.0},9900,{-1.747822111395514,0.0},1.7e-16,0.0},
{{10000.0,0.0},12612,{7.25197826864343e-541,0.0},7.3e-557,0.0},
{{10000.0,0.0},16067,{1.369451063257112e-1882,0.0},1.4e-1898,0.0},
{{10000.0,0.0},20468,{1.387136027206115e-4188,0.0},1.4e-4204,0.0},
{{10000.0,0.0},26075,{3.402710534773112e-7804,0.0},3.4e-7820,0.0},
{{10000.0,0.0},33218,{1.467628954663695e-13224,0.0},1.5e-13240,0.0},
{{10000.0,0.0},42318,{5.445358924275546e-21134,0.0},5.4e-21150,0.0},
{{10000.0,0.0},53911,{3.266521110728529e-32465,0.0},3.3e-32481,0.0},
{{10000.0,0.0},68679,{2.775502574785064e-48480,0.0},2.8e-48496,0.0},
{{10000.0,0.0},87493,{8.914211935647729e-70883,0.0},8.9e-70899,0.0},
{{10000.0,0.0},111461,{2.619912559375462e-101959,0.0},2.6e-101975,0.0},
{{10000.0,0.0},141995,{5.82392981843591e-144773,0.0},5.8e-144789,0.0},
};

// complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
xi_test_16digits
= {
{{0.055,0.0},0,{0.9984878812375984,0.0},1.0e-16,0.0},
{{0.055,0.0},1,{18.20929738843795,0.0},1.8e-15,0.0},
{{0.055,0.0},2,{992.2359151244687,0.0},9.9e-14,0.0},
{{0.055,0.0},3,{90185.05571392689,0.0},9.0e-12,0.0},
{{0.055,0.0},4,{11477105.76403921,0.0},1.1e-9,0.0},
{{0.055,0.0},5,{1877981667.241611,0.0},1.9e-7,0.0},
{{0.056,0.0},0,{0.9984324097278344,0.0},1.0e-16,0.0},
{{0.056,0.0},1,{17.88512090896708,0.0},1.8e-15,0.0},
{{0.056,0.0},2,{957.1330448563659,0.0},9.6e-14,0.0},
{{0.056,0.0},3,{85440.42245555228,0.0},8.5e-12,0.0},
{{0.056,0.0},4,{10679095.67389918,0.0},1.1e-9,0.0},
{{0.056,0.0},5,{1716197792.88277,0.0},1.7e-7,0.0},
{{0.099,0.0},0,{0.9951035011759925,0.0},1.0e-16,0.0},
{{0.099,0.0},1,{10.1503888796599,0.0},1.0e-15,0.0},
{{0.099,0.0},2,{306.5924383066997,0.0},3.1e-14,0.0},
{{0.099,0.0},3,{15474.31619226679,0.0},1.5e-12,0.0},
{{0.099,0.0},4,{1093836.97671187,0.0},1.1e-10,0.0},
{{0.101,0.0},0,{0.9949038343759767,0.0},9.9e-17,0.0},
{{0.101,0.0},1,{9.951361384353099,0.0},1.0e-15,0.0},
{{0.101,0.0},2,{294.5900877800725,0.0},2.9e-14,0.0},
{{0.101,0.0},3,{14573.71635050042,0.0},1.5e-12,0.0},
{{0.101,0.0},4,{1009764.958956804,0.0},1.0e-10,0.0},
{{1.0,0.0},0,{0.5403023058681397,0.0},5.4e-17,0.0},
{{1.0,0.0},1,{1.381773290676036,0.0},1.4e-16,0.0},
{{1.0,0.0},2,{3.605017566159969,0.0},3.6e-16,0.0},
{{1.0,0.0},3,{16.64331454012381,0.0},1.7e-15,0.0},
{{1.0,0.0},4,{112.8981842147067,0.0},1.1e-14,0.0},
{{1.0,0.0},5,{999.4403433922364,0.0},1.0e-13,0.0},
{{1.0,0.0},6,{10880.94559309989,0.0},1.1e-12,0.0},
{{1.0,0.0},7,{140452.8523669064,0.0},1.4e-11,0.0},
{{1.0,0.0},8,{2095911.839910496,0.0},2.1e-10,0.0},
{{1.0,0.0},9,{35490048.42611152,0.0},3.5e-9,0.0},
{{1.0,0.0},10,{672215008.2562084,0.0},6.7e-8,0.0},
{{1.0,0.0},11,{14081025124.95427,0.0},1.4e-6,0.0},
{{1.0,0.0},12,{323191362865.6919,0.0},3.2e-5,0.0},
{{1.0,0.0},13,{8065703046517.343,0.0},0.00081,0.0},
{{1.0,0.0},14,{217450790893102.6,0.0},0.022,0.0},
{{1.0,0.0},15,{6298007232853457.0,0.0},0.63,0.0},
{{1.0,0.0},16,{1.950207734275641e+17,0.0},20.0,0.0},
{{1.0,0.0},17,{6.429387515876761e+18,0.0},6.4e+2,0.0},
{{1.0,0.0},19,{8.312411676927709e+21,0.0},8.3e+5,0.0},
{{1.0,0.0},20,{3.239592218578984e+23,0.0},3.2e+7,0.0},
{{1.0,0.0},22,{5.704587152115091e+26,0.0},5.7e+10,0.0},
{{1.0,0.0},24,{1.205325845219959e+30,0.0},1.2e+14,0.0},
{{1.0,0.0},26,{3.009595435582847e+33,0.0},3.0e+17,0.0},
{{1.0,0.0},28,{8.766714157290797e+36,0.0},8.8e+20,0.0},
{{1.0,0.0},30,{2.946428547496782e+40,0.0},2.9e+24,0.0},
{{1.0,0.0},32,{1.131703135696075e+44,0.0},1.1e+28,0.0},
{{1.0,0.0},35,{3.398364364339443e+49,0.0},3.4e+33,0.0},
{{1.0,0.0},38,{1.320263364413848e+55,0.0},1.3e+39,0.0},
{{1.0,0.0},41,{6.502028762468467e+60,0.0},6.5e+44,0.0},
{{10.0,0.0},0,{-0.8390715290764525,0.0},8.4e-17,0.0},
{{10.0,0.0},1,{-0.6279282637970151,0.0},6.3e-17,0.0},
{{10.0,0.0},2,{0.6506930499373479,0.0},6.5e-17,0.0},
{{10.0,0.0},3,{0.953274788765689,0.0},9.5e-17,0.0},
{{10.0,0.0},4,{0.01659930219863438,0.0},1.7e-18,0.0},
{{10.0,0.0},5,{-0.9383354167869181,0.0},9.4e-17,0.0},
{{10.0,0.0},6,{-1.048768260664244,0.0},1.0e-16,0.0},
{{10.0,0.0},7,{-0.4250633220765995,0.0},4.3e-17,0.0},
{{10.0,0.0},8,{0.4111732775493451,0.0},4.1e-17,0.0},
{{10.0,0.0},9,{1.124057893910486,0.0},1.1e-16,0.0},
{{10.0,0.0},10,{1.724536720880578,0.0},1.7e-16,0.0},
{{10.0,0.0},11,{2.497469219938729,0.0},2.5e-16,0.0},
{{10.0,0.0},12,{4.019642484978498,0.0},4.0e-16,0.0},
{{10.0,0.0},13,{7.551636992507515,0.0},7.6e-16,0.0},
{{10.0,0.0},14,{16.36977739479179,0.0},1.6e-15,0.0},
{{10.0,0.0},16,{107.3844467076131,0.0},1.1e-14,0.0},
{{10.0,0.0},17,{314.4479566827347,0.0},3.1e-14,0.0},
{{10.0,0.0},18,{993.1834016819582,0.0},9.9e-14,0.0},
{{10.0,0.0},19,{3360.330629540511,0.0},3.4e-13,0.0},
{{10.0,0.0},21,{46299.30418991622,0.0},4.6e-12,0.0},
{{10.0,0.0},22,{186974.9019631137,0.0},1.9e-11,0.0},
{{10.0,0.0},24,{3549937.544864135,0.0},3.5e-10,0.0},
{{10.0,0.0},26,{81108054.15260572,0.0},8.1e-9,0.0},
{{10.0,0.0},27,{413273080.7936202,0.0},4.1e-8,0.0},
{{10.0,0.0},30,{69083186460.94516,0.0},6.9e-6,0.0},
{{80.0,0.0},0,{-0.1103872438390476,0.0},1.1e-17,0.0},
{{80.0,0.0},1,{-0.9952684944713633,0.0},1.0e-16,0.0},
{{80.0,0.0},30,{0.5060739517940013,0.0},5.1e-17,0.0},
{{80.0,0.0},50,{0.7514741282998871,0.0},7.5e-17,0.0},
{{80.0,0.0},60,{-1.056795272698575,0.0},1.1e-16,0.0},
{{80.0,0.0},70,{-1.082903079393562,0.0},1.1e-16,0.0},
{{80.0,0.0},75,{-0.2861031097638479,0.0},2.9e-17,0.0},
{{80.0,0.0},80,{2.229727207344475,0.0},2.2e-16,0.0},
{{80.0,0.0},85,{6.79766591437198,0.0},6.8e-16,0.0},
{{80.0,0.0},90,{49.68517113491355,0.0},5.0e-15,0.0},
{{80.0,0.0},99,{9222.855138429382,0.0},9.2e-13,0.0},
{{80.0,0.0},116,{7395385511.699251,0.0},7.4e-7,0.0},
{{80.0,0.0},130,{7978214064656749.0,0.0},0.8,0.0},
{{100.0,0.0},0,{0.8623188722876839,0.0},8.6e-17,0.0},
{{100.0,0.0},1,{-0.497742452386882,0.0},5.0e-17,0.0},
{{100.0,0.0},2,{-0.8772511458592904,0.0},8.8e-17,0.0},
{{100.0,0.0},3,{0.4538798950939174,0.0},4.5e-17,0.0},
{{100.0,0.0},4,{0.9090227385158646,0.0},9.1e-17,0.0},
{{100.0,0.0},5,{-0.3720678486274896,0.0},3.7e-17,0.0},
{{100.0,0.0},6,{-0.9499502018648885,0.0},9.5e-17,0.0},
{{100.0,0.0},7,{0.2485743223850541,0.0},2.5e-17,0.0},
{{100.0,0.0},8,{0.9872363502226466,0.0},9.9e-17,0.0},
{{100.0,0.0},9,{-0.0807441428472042,0.0},8.1e-18,0.0},
{{100.0,0.0},10,{-1.002577737363615,0.0},1.0e-16,0.0},
{{100.0,0.0},12,{0.9727243855038097,0.0},9.7e-17,0.0},
{{100.0,0.0},14,{-0.8720202503425307,0.0},8.7e-17,0.0},
{{100.0,0.0},17,{0.8496049309427912,0.0},8.5e-17,0.0},
{{100.0,0.0},19,{-0.9904419668956676,0.0},9.9e-17,0.0},
{{100.0,0.0},23,{-0.794394952285829,0.0},7.9e-17,0.0},
{{100.0,0.0},26,{1.008142711740272,0.0},1.0e-16,0.0},
{{100.0,0.0},31,{0.9967036472620608,0.0},1.0e-16,0.0},
{{100.0,0.0},36,{1.033265431104683,0.0},1.0e-16,0.0},
{{100.0,0.0},42,{0.7454135574907433,0.0},7.5e-17,0.0},
{{100.0,0.0},49,{-0.5855924676754787,0.0},5.9e-17,0.0},
{{100.0,0.0},57,{-0.7917840064320207,0.0},7.9e-17,0.0},
{{100.0,0.0},66,{0.9943577408622831,0.0},9.9e-17,0.0},
{{100.0,0.0},76,{0.758958460609405,0.0},7.6e-17,0.0},
{{100.0,0.0},89,{-0.9874911064736249,0.0},9.9e-17,0.0},
{{100.0,0.0},103,{3.932782745345558,0.0},3.9e-16,0.0},
{{100.0,0.0},120,{7123.747314608973,0.0},7.1e-13,0.0},
{{100.0,0.0},140,{22728970587.22979,0.0},2.3e-6,0.0},
{{100.0,0.0},162,{3.998455948928182e+19,0.0},4.0e+3,0.0},
{{100.0,0.0},188,{4.560507264377804e+32,0.0},4.6e+16,0.0},
{{100.0,0.0},219,{4.293053043714103e+50,0.0},4.3e+34,0.0},
{{100.0,0.0},254,{3.165039335082101e+73,0.0},3.2e+57,0.0},
{{100.0,0.0},296,{8.62319701238945e+103,0.0},8.6e+87,0.0},
{{100.0,0.0},343,{1.784625319681049e+141,0.0},1.8e+125,0.0},
{{100.0,0.0},399,{3.255744216903431e+189,0.0},3.3e+173,0.0},
{{100.0,0.0},464,{8.638673889350171e+249,0.0},8.6e+233,0.0},
{{100.0,0.0},539,{4.702192956140304e+324,0.0},4.7e+308,0.0},
{{100.0,0.0},626,{1.329971011220177e+417,0.0},1.3e+401,0.0},
{{100.0,0.0},727,{1.261151833780533e+531,0.0},1.3e+515,0.0},
{{100.0,0.0},844,{6.276922570590454e+670,0.0},6.3e+654,0.0},
{{100.0,0.0},981,{2.259993447656205e+843,0.0},2.3e+827,0.0},
{{100.0,0.0},1139,{4.981370725943817e+1052,0.0},5.0e+1036,0.0},
{{100.0,0.0},1324,{8.108733995411389e+1309,0.0},8.1e+1293,0.0},
{{100.0,0.0},1537,{8.865977477340542e+1619,0.0},8.9e+1603,0.0},
{{1000.0,0.0},0,{0.562379076290703,0.0},5.6e-17,0.0},
{{1000.0,0.0},1,{0.8274419196082933,0.0},8.3e-17,0.0},
{{1000.0,0.0},2,{-0.5598967505318781,0.0},5.6e-17,0.0},
{{1000.0,0.0},3,{-0.8302414033609527,0.0},8.3e-17,0.0},
{{1000.0,0.0},4,{0.5540850607083514,0.0},5.5e-17,0.0},
{{1000.0,0.0},5,{0.8352281689073278,0.0},8.4e-17,0.0},
{{1000.0,0.0},6,{-0.5448975508503708,0.0},5.4e-17,0.0},
{{1000.0,0.0},7,{-0.8423118370683826,0.0},8.4e-17,0.0},
{{1000.0,0.0},9,{0.8513603059143865,0.0},8.5e-17,0.0},
{{1000.0,0.0},10,{-0.5160870274819718,0.0},5.2e-17,0.0},
{{1000.0,0.0},11,{-0.8621981334915079,0.0},8.6e-17,0.0},
{{1000.0,0.0},13,{0.8746045452517996,0.0},8.7e-17,0.0},
{{1000.0,0.0},15,{-0.8883111675348058,0.0},8.9e-17,0.0},
{{1000.0,0.0},18,{-0.4134995149333431,0.0},4.1e-17,0.0},
{{1000.0,0.0},20,{0.3776858501060111,0.0},3.8e-17,0.0},
{{1000.0,0.0},23,{-0.9489732087840213,0.0},9.5e-17,0.0},
{{1000.0,0.0},27,{-0.976248337884936,0.0},9.8e-17,0.0},
{{1000.0,0.0},31,{-0.9951285718767434,0.0},1.0e-16,0.0},
{{1000.0,0.0},35,{-0.9997770197744073,0.0},1.0e-16,0.0},
{{1000.0,0.0},41,{0.9658057107645263,0.0},9.7e-17,0.0},
{{1000.0,0.0},47,{-0.8628127163075355,0.0},8.6e-17,0.0},
{{1000.0,0.0},54,{0.7764560092822195,0.0},7.8e-17,0.0},
{{1000.0,0.0},62,{0.9780562249615457,0.0},9.8e-17,0.0},
{{1000.0,0.0},71,{0.379779907874921,0.0},3.8e-17,0.0},
{{1000.0,0.0},81,{-0.9162327671042002,0.0},9.2e-17,0.0},
{{1000.0,0.0},93,{-0.8066400984512723,0.0},8.1e-17,0.0},
{{1000.0,0.0},107,{-0.4577161030388435,0.0},4.6e-17,0.0},
{{1000.0,0.0},123,{-0.7308771114070519,0.0},7.3e-17,0.0},
{{1000.0,0.0},141,{-1.00505240530667,0.0},1.0e-16,0.0},
{{1000.0,0.0},162,{0.06905501630232919,0.0},6.9e-18,0.0},
{{1000.0,0.0},186,{-0.9153196261481822,0.0},9.2e-17,0.0},
{{1000.0,0.0},214,{-0.4904474893116481,0.0},4.9e-17,0.0},
{{1000.0,0.0},246,{-1.011184752036795,0.0},1.0e-16,0.0},
{{1000.0,0.0},282,{0.973033201417064,0.0},9.7e-17,0.0},
{{1000.0,0.0},324,{-0.7905362270426355,0.0},7.9e-17,0.0},
{{1000.0,0.0},372,{-0.500862067695031,0.0},5.0e-17,0.0},
{{1000.0,0.0},427,{0.4302284984951585,0.0},4.3e-17,0.0},
{{1000.0,0.0},490,{0.2306282264858935,0.0},2.3e-17,0.0},
{{1000.0,0.0},562,{-0.9908332203529922,0.0},9.9e-17,0.0},
{{1000.0,0.0},645,{-0.8938610251077628,0.0},8.9e-17,0.0},
{{1000.0,0.0},740,{0.1565477440422447,0.0},1.6e-17,0.0},
{{1000.0,0.0},850,{0.9116631948399486,0.0},9.1e-17,0.0},
{{10000.0,0.0},0,{-0.9521553682590149,0.0},9.5e-17,0.0},
{{10000.0,0.0},1,{-0.305709604425078,0.0},3.1e-17,0.0},
{{10000.0,0.0},2,{0.9520636553776873,0.0},9.5e-17,0.0},
{{10000.0,0.0},3,{0.3061856362527669,0.0},3.1e-17,0.0},
{{10000.0,0.0},4,{-0.9518493254323104,0.0},9.5e-17,0.0},
{{10000.0,0.0},5,{-0.307042300645656,0.0},3.1e-17,0.0},
{{10000.0,0.0},6,{0.9515115789016002,0.0},9.5e-17,0.0},
{{10000.0,0.0},8,{-0.9510491600030528,0.0},9.5e-17,0.0},
{{10000.0,0.0},11,{0.3118920160210031,0.0},3.1e-17,0.0},
{{10000.0,0.0},14,{0.9488944866640447,0.0},9.5e-17,0.0},
{{10000.0,0.0},18,{0.946791218377749,0.0},9.5e-17,0.0},
{{10000.0,0.0},23,{0.3317746154126867,0.0},3.3e-17,0.0},
{{10000.0,0.0},29,{-0.3467317659022176,0.0},3.5e-17,0.0},
{{10000.0,0.0},37,{-0.3717422973913016,0.0},3.7e-17,0.0},
{{10000.0,0.0},48,{-0.9097266978464748,0.0},9.1e-17,0.0},
{{10000.0,0.0},61,{-0.4791529210238686,0.0},4.8e-17,0.0},
{{10000.0,0.0},78,{0.8146542455580336,0.0},8.1e-17,0.0},
{{10000.0,0.0},99,{0.7212557152272793,0.0},7.2e-17,0.0},
{{10000.0,0.0},126,{0.44405730097627,0.0},4.4e-17,0.0},
{{10000.0,0.0},161,{-0.9991010161245437,0.0},1.0e-16,0.0},
{{10000.0,0.0},205,{-0.659029176819063,0.0},6.6e-17,0.0},
{{10000.0,0.0},262,{-0.8172090777658204,0.0},8.2e-17,0.0},
{{10000.0,0.0},333,{0.3996246788860864,0.0},4.0e-17,0.0},
{{10000.0,0.0},425,{-0.06031857764924985,0.0},6.0e-18,0.0},
{{10000.0,0.0},541,{-0.6693660079881031,0.0},6.7e-17,0.0},
{{10000.0,0.0},690,{0.5633527627627941,0.0},5.6e-17,0.0},
{{10000.0,0.0},879,{0.9686951076386396,0.0},9.7e-17,0.0},
{{10000.0,0.0},1120,{-0.9520301748728291,0.0},9.5e-17,0.0},
{{10000.0,0.0},1427,{0.9685541537392371,0.0},9.7e-17,0.0},
{{10000.0,0.0},1818,{-0.9340620975427486,0.0},9.3e-17,0.0},
{{10000.0,0.0},2316,{-0.9564616952166914,0.0},9.6e-17,0.0},
{{10000.0,0.0},2950,{0.555880388869997,0.0},5.6e-17,0.0},
{{10000.0,0.0},3758,{0.591279183531158,0.0},5.9e-17,0.0},
{{10000.0,0.0},7771,{0.4418649322239787,0.0},4.4e-17,0.0},
{{10000.0,0.0},9900,{-2.011491146878234,0.0},2.0e-16,0.0},
{{10000.0,0.0},12612,{8.970385150483627e+539,0.0},9.0e+523,0.0},
{{10000.0,0.0},16067,{2.90314618431218e+1881,0.0},2.9e+1865,0.0},
{{10000.0,0.0},20468,{2.018288229524841e+4187,0.0},2.0e+4171,0.0},
{{10000.0,0.0},26075,{6.101780411131719e+7802,0.0},6.1e+7786,0.0},
{{10000.0,0.0},33218,{1.075478687761038e+13223,0.0},1.1e+13207,0.0},
{{10000.0,0.0},42318,{2.233007868840026e+21132,0.0},2.2e+21116,0.0},
{{10000.0,0.0},53911,{2.889388190778695e+32463,0.0},2.9e+32447,0.0},
{{10000.0,0.0},68679,{2.651272528165235e+48478,0.0},2.7e+48462,0.0},
{{10000.0,0.0},87493,{6.453073029871699e+70880,0.0},6.5e+70864,0.0},
{{10000.0,0.0},111461,{1.71914792791431e+101957,0.0},1.7e+101941,0.0},
{{10000.0,0.0},141995,{6.061204591967546e+144770,0.0},6.1e+144754,0.0},
};

// complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
zeta_test_16digits
= {
{{0.055,0.0},0,{0.05497227502706773,-0.9984878812375984},5.5e-18,1.0e-16},
{{0.055,0.0},1,{0.001008028345451298,-18.20929738843795},1.0e-19,1.8e-15},
{{0.055,0.0},2,{1.108927027577585e-5,-992.2359151244687},1.1e-21,9.9e-14},
{{0.055,0.0},3,{8.713416468907156e-8,-90185.05571392689},8.7e-24,9.0e-12},
{{0.055,0.0},4,{5.325028332528807e-10,-11477105.76403921},5.3e-26,1.1e-9},
{{0.055,0.0},5,{2.662570490744701e-12,-1877981667.241611},2.7e-28,1.9e-7},
{{0.056,0.0},0,{0.05597073525575547,-0.9984324097278344},5.6e-18,1.0e-16},
{{0.056,0.0},1,{0.00104500555351332,-17.88512090896708},1.0e-19,1.8e-15},
{{0.056,0.0},2,{1.170511102950751e-5,-957.1330448563659},1.2e-21,9.6e-14},
{{0.056,0.0},3,{9.364554985109859e-8,-85440.42245555228},9.4e-24,8.5e-12},
{{0.056,0.0},4,{5.827018798125993e-10,-10679095.67389918},5.8e-26,1.1e-9},
{{0.056,0.0},5,{2.966547354864994e-12,-1716197792.88277},3.0e-28,1.7e-7},
{{0.099,0.0},0,{0.09883836273067998,-0.9951035011759925},9.9e-18,1.0e-16},
{{0.099,0.0},1,{0.003263799133906297,-10.1503888796599},3.3e-19,1.0e-15},
{{0.099,0.0},2,{6.464132708660462e-5,-306.5924383066997},6.5e-21,3.1e-14},
{{0.099,0.0},3,{9.143553161581762e-7,-15474.31619226679},9.1e-23,1.5e-12},
{{0.099,0.0},4,{1.005890437753418e-8,-1093836.97671187},1.0e-24,1.1e-10},
{{0.101,0.0},0,{0.100828370729568,-0.9949038343759767},1.0e-17,9.9e-17},
{{0.101,0.0},1,{0.003396865916775768,-9.951361384353099},3.4e-19,1.0e-15},
{{0.101,0.0},2,{6.863669941520236e-5,-294.5900877800725},6.9e-21,2.9e-14},
{{0.101,0.0},3,{9.904899174185251e-7,-14573.71635050042},9.9e-23,1.5e-12},
{{0.101,0.0},4,{1.111664350730229e-8,-1009764.958956804},1.1e-24,1.0e-10},
{{1.0,0.0},0,{0.8414709848078965,-0.5403023058681397},8.4e-17,5.4e-17},
{{1.0,0.0},1,{0.3011686789397568,-1.381773290676036},3.0e-17,1.4e-16},
{{1.0,0.0},2,{0.06203505201137386,-3.605017566159969},6.2e-18,3.6e-16},
{{1.0,0.0},3,{0.009006581117112516,-16.64331454012381},9.0e-19,1.7e-15},
{{1.0,0.0},4,{0.001011015808413753,-112.8981842147067},1.0e-19,1.1e-14},
{{1.0,0.0},5,{9.256115861125816e-5,-999.4403433922364},9.3e-21,1.0e-13},
{{1.0,0.0},6,{7.156936310087086e-6,-10880.94559309989},7.2e-22,1.1e-12},
{{1.0,0.0},7,{4.790134198739489e-7,-140452.8523669064},4.8e-23,1.4e-11},
{{1.0,0.0},8,{2.826498802214729e-8,-2095911.839910496},2.8e-24,2.1e-10},
{{1.0,0.0},9,{1.491376502555146e-9,-35490048.42611152},1.5e-25,3.5e-9},
{{1.0,0.0},10,{7.116552640047313e-11,-672215008.2562084},7.1e-27,6.7e-8},
{{1.0,0.0},11,{3.09955185479008e-12,-14081025124.95427},3.1e-28,1.4e-6},
{{1.0,0.0},12,{1.241662596987106e-13,-323191362865.6919},1.2e-29,3.2e-5},
{{1.0,0.0},13,{4.604637677683787e-15,-8065703046517.343},4.6e-31,0.00081},
{{1.0,0.0},14,{1.589575987516976e-16,-217450790893102.6},1.6e-32,0.022},
{{1.0,0.0},15,{5.132686115443762e-18,-6298007232853457.0},5.1e-34,0.63},
{{1.0,0.0},16,{1.556708270590172e-19,-1.950207734275641e+17},1.6e-35,20.0},
{{1.0,0.0},17,{4.451177503806802e-21,-6.429387515876761e+18},4.5e-37,6.4e+2},
{{1.0,0.0},19,{3.088742363539549e-24,-8.312411676927709e+21},3.1e-40,8.3e+5},
{{1.0,0.0},20,{7.537795722236873e-26,-3.239592218578984e+23},7.5e-42,3.2e+7},
{{1.0,0.0},22,{3.899361309912283e-29,-5.704587152115091e+26},3.9e-45,5.7e+10},
{{1.0,0.0},24,{1.694580173763896e-32,-1.205325845219959e+30},1.7e-48,1.2e+14},
{{1.0,0.0},26,{6.273730960048117e-36,-3.009595435582847e+33},6.3e-52,3.0e+17},
{{1.0,0.0},28,{2.002424424322351e-39,-8.766714157290797e+36},2.0e-55,8.8e+20},
{{1.0,0.0},30,{5.566831266981347e-43,-2.946428547496782e+40},5.6e-59,2.9e+24},
{{1.0,0.0},32,{1.360066050758899e-46,-1.131703135696075e+44},1.4e-62,1.1e+28},
{{1.0,0.0},35,{4.146142464888971e-52,-3.398364364339443e+49},4.1e-68,3.4e+33},
{{1.0,0.0},38,{9.840005687079579e-58,-1.320263364413848e+55},9.8e-74,1.3e+39},
{{1.0,0.0},41,{1.853528272155995e-63,-6.502028762468467e+60},1.9e-79,6.5e+44},
{{10.0,0.0},0,{-0.5440211108893698,0.8390715290764525},5.4e-17,8.4e-17},
{{10.0,0.0},1,{0.7846694179875155,0.6279282637970151},7.8e-17,6.3e-17},
{{10.0,0.0},2,{0.7794219362856245,-0.6506930499373479},7.8e-17,6.5e-17},
{{10.0,0.0},3,{-0.3949584498447032,-0.953274788765689},3.9e-17,9.5e-17},
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