-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4033.1043', 'a10': [0.11609291412523023, -0.993238357741943], 'a2': [-0.6427876096865394, 0.766044443118978], 'a3': [-0.28680323271109026, 0.9579895123154889], 'a4': [-0.17364817766693036, -0.984807753012208], 'a5': [-0.8354878114129364, 0.549508978070806], 'a6': [-0.549508978070806, -0.8354878114129364], 'a7': [-0.05814482891047583, -0.9983081582712682], 'a8': [0.8660254037844386, 0.5], 'a9': [-0.8354878114129364, -0.549508978070806], 'algebraic': True, 'analytic_conductor': 433.4060416967227, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.1043', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.3975', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^39', 'a^32', 'a^78', 'a^44', 'a^71', 'a^80', 'a^9', 'a^64', 'a^83', 'a^25', 'a^2', 'a^89', 'a^11', 'a^76', 'a^48', 'a^39', 'a^103', 'a^45', 'a^14', 'a^4', 'a^64', 'a^3', 'a^41', 'a^88', 'a^20', 'a^96', 'a^50', 'a^2', 'a^7', 'a^22', 'a^87', 'a^57', 'a^78', 'a^16', 'a^34', 0, 'a^84', 'a^13', 'a^53', 'a^39', 'a^43', 'a^78', 'a^103', 'a^0', 'a^42', 'a^55', 'a^80', 'a^52', 'a^19', 'a^71', 'a^59', 'a^83', 'a^27', 'a^69', 'a^89', 'a^77', 'a^41', 'a^49', 'a^46', 'a^38', 'a^61', 'a^36', 'a^18', 'a^25', 'a^96', 'a^97', 'a^9', 'a^35', 'a^55', 'a^42', 'a^73', 'a^88', 0, 'a^12', 'a^15', 'a^105', 'a^52', 'a^61', 'a^92', 'a^20', 'a^78', 'a^26', 'a^82', 'a^83', 'a^9', 'a^34', 'a^34', 'a^104', 'a^39', 'a^61', 'a^81', 'a^54', 'a^94', 'a^89', 'a^11', 'a^104', 'a^91', 'a^89', 'a^58'], 'euler_factors': [[1, 'a^39'], [1, 'a^32'], [1, 'a^44'], [1, 'a^80'], [1, 'a^25'], [1, 'a^89'], [1, 'a^39'], [1, 'a^45'], [1, 'a^3'], [1, 'a^2'], [1, 'a^22'], [0], [1, 'a^39'], [1, 'a^78'], [1, 'a^55'], [1, 'a^83'], [1, 'a^49'], [1, 'a^38'], [1, 'a^97'], [1, 'a^42'], [1, 'a^88'], [1, 'a^61'], [1, 'a^26'], [1, 'a^104'], [1, 'a^104'], [1, 'a^27']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-4033-4033.1043-r1-0-0', 'leading_term': '0.0214654556171638603438182965878+0.614211658670861954119391570410*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/4033/1043', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.614586631348311, 0.7851146565713817, -0.35087312154271455, -2.214523546533492, -2.8983965741094577, -0.644360127513049, 4.0090155924275725, 7.832067205708055, 7.528144874046998, 3.1742687211382163, -1.4492319515817604, -2.602283126588648, -0.46349821195482555, 1.4752039278156284, 0.8866791300796394, -0.6395548069015768, -0.12012621779412799, 2.4569950518698658, 3.972093498684491, 2.50730361215259, 0.04441929126492824, -0.3937999081636228, 0.9704144156763926, 1.2673166154162145, -0.48277615246762184, -1.8601633481693916, -0.9457029723305562, 0.48284961680376404, -0.32948375095741955, -2.6208873685002896, -3.0971058343549167, -1.0400535891951097, 0.6573637997916109, 0.28635525945170387, -0.0738526451792816, 1.194664504633543, 1.380842197853916, -2.3933984199138596, -6.815941692865938, -5.2462788262629285, 2.4553843438762533, 7.923021463546394, 4.776921732103108, -2.7996594525890393, -5.931944669837664, -2.7213547218978356, 0.9729524665947673, 1.093456464363568, -0.08561740931968921, 0.27311386721524616, 0.8540000975251681, -0.14121394705410112, -1.0468941964605791, 0.0006976500605028549, 1.219270208962154, 0.47062997495580816, -0.44106716571473215, 0.8682057340159324, 2.124440372923565, -0.26503639027355486, -4.257424342447924, -4.531388998590877, -1.2285108757437462, 0.21679256742128147, -1.4306444754925294, -1.1139640438398182, 2.7962078568516846, 4.145017514257727, -1.0638373915206696, -6.894522192123552, -5.930728445670426, -0.4402070247131651, 2.0715495863251245, 0.5738499589176997, -0.22874066183928227, 0.2839673091976387, -1.5682961567738425, -4.933544886886844, -4.297042916034872, 0.804648544334686, 4.0815188851777675, 2.4311805807242974, 0.11022551968967478, 0.5967740045642769, 1.48772224652344, 0.4600270821342922, -0.48680494105846006, -0.011969805599415056, -0.22769938679142296, -1.4079249129234555, -0.562807989338849, 1.6951984362172885, 0.4381288132458081, -3.8291236128056534, -3.348369032450803, 3.9054684646759656, 8.579212724021298, 4.232589180398108, -1.6491886633484625, 0.26186614303761996, 6.0774239187540084, 6.117738009110545, 0.905282056884781, -1.5599632897028248, 0.14280222825277364, 0.7768601887029166, -0.7220278162608771, -0.8791776813091974, 0.10710455607089235, -0.7301251618466531, -2.1464758874453898, -1.1176356761028199, 0.46411892208348393, -0.47015820362401806, -1.3548237823814058, 0.9926007608850506, 2.993669163221101, 0.5006747539058146, -2.617738166694443, -1.1111709602717852, 1.835091660423768, 0.8671359254914511, -1.3328770916816368, -0.06681356893933452, 1.5003122881949262, -0.9633758015770268, -3.151323481332819, -0.2649573600467286, 2.16175444203324, -2.2351478807592997, -7.416024819466091, -4.283833954286962, 3.236925449502176, 4.861471525398978, 0.8618835511397349, -0.8576673047916342, 0.7014292490433159, 0.6849840171895091, -0.7798223566949752, -0.32976063274240197, 0.611663946868455, -0.6245934462983985, -1.543407386633122, 0.2280251547822446, 1.517736737486658, 0.17984482987439915, -0.5193478889517096, 0.6201887054321242, 0.07728301129731244, -1.7137007845224839, -0.4155087224475855, 0.6680805823714003, -6.744896660291593, -18.617429171620547, -20.166816933705334, -8.847921315119041, 1.0236002697678814, 0.9985893861464993, -1.3482226171875327, 0.4912800344921319, 2.0444776786641805, 0.1411415379665419, -0.804472353330202, 0.7373425527187455, 0.6215229869666097, -1.050357113440198, -0.10415165922650442, 1.899558888308407, 0.47168565432429366, -1.7382946276409723, 0.2116980742289895, 3.1336426736365333, 1.736043809510031, -1.0709189480656374, -0.5653105364602272, 0.8042008832851214, 0.07250466029455635, -0.009395397457968574, 1.1389915684133882, -0.8899238811572976, -4.907211353039004, -4.059240945691013, 0.19947732779578453, -0.3429589927980131, -3.550021450063389, 0.5474346759973705, 9.53289491809624, 10.691379074686253, 3.4536861799827046, -0.4357824522990442, 1.5552277049851773, 1.1092222692035518, -2.6610948033625172, -2.5430380913535484, 1.3085014785060003, 2.230726867780094, 0.06216549729097664, -0.6260106231144804, -0.028958402130193902, -0.10295737807988192, 0.5500302296344182, 1.4938830677250086, -0.2690755498186903, -2.210113613938099, 0.6003003729056182, 4.143418766107507, 1.3779366038100687, -3.4822196887218695, -2.3911804551574845, 0.7847093347673997, -1.256172399056146, -3.7636434971562904, -0.2090094117197425, 2.9987099463189755, -0.96599940426455, -5.008085458595411, -1.9822056694842745, 1.598475922344854, -0.6108077534900199, -2.995815071992074, -1.0608050019123958, 0.18443464031937934, -1.2733639689646004, -0.3153323755840018, 2.7866762737490784, 2.285791211194173, -0.26074981586063056, 0.9790174426005884, 3.6535766224180515, 2.4111201791275056, -0.0732816014749505, 0.2647149203737199, 0.6280247410571634, -0.8124300791119505, -0.5873916924443223, 0.968866405002448, -0.2184292236243745, -1.8563879361864193, 0.06339669373911007, 1.1127892205246273, -1.1393301963446194, 2.955422440218124, 16.844124889445272, 24.256621729447996, 13.4450938505318, -2.001433489813195, -5.281402209916359, -0.790980678125747, 0.24311442753627238, -0.9416790839560469, 0.05120919220644475, 0.44007247976467256, -0.9502447229138704, -0.6597222716378411, 0.18705309567003833, -1.7694099591889973, -3.2384670173350036, -0.8381189470855539, 1.1036803769499768, -0.16092092682302717, -0.38297219014299266, 0.9223290078634581, -0.81451784643029, -3.196417362705616, -0.5534500180628352, 2.637948508013124, -0.054287683632770235, -2.8524660782719433, 0.43498205362721637, 2.8013507228097803, -1.2352171457869179, -3.7396999817815884, -0.14886319269026843, 1.6467754801669783, -0.951407643279004, -0.3569462044876798, 3.020287474956497, 0.9945349769246372, -3.5305030285285186, -1.2179790467428744, 4.348248466862406, 3.6919597692227946, -0.4820146944314018, -0.8658491095681639, 0.45974836125358054, -0.16201486586289987, 0.003041596082401049, 1.4889209726903634, 0.6746611371012139, -1.1129389737425521, -0.47789236011423386, 0.1647012068273443, -0.6220023974171993, 0.8985975419861275, 2.8294848842820124, -1.040189384101144, -5.533023542871526, -0.9251298126040006, 6.096173352227059, 2.966017032244378, -4.101170212684454, -2.2586653853158265, 2.8376971268164706, -0.02084685596012179, -4.934110895948682, -2.5046319729023683, 1.7326695769340377, 0.8461852702580985, -0.6966291609708196, 0.4379108425705351, 0.39447373343762693, -0.8289061755594994, -0.026126742753574475, 0.36639985355556876, -1.253431506316684, -0.13035068338809344, 3.3259562736406547, 1.8425917144523225, -3.233014668669872, -3.3867078317745323, 0.08449744543948867, -0.033388965997677766, -1.8435366806324274, -0.8195092781827579, 0.036371404043264784, -0.5160529152169149, 0.9675086266628833, 0.15119861901651477, -8.953427867664923, -16.531262538348223, -10.594477168950805, -0.1894332358687014, 0.6362768038447865, -2.4230213868568478, 0.5499970192122281, 3.248920313140781, -0.6929543234650517, -3.4874605336950957, -0.4277068823940736, 1.5367778599555768, 0.03465874101465331, 0.17639756362361517, 1.3486498479695603, 0.028677031509901883, -0.9690657725815582, 0.25071133518235744, 0.053845062020361906, -1.3035822157134525, -0.4375057933785694, 0.1803557230787835, -1.0194332140863667, 1.3008749469618068, 5.912966687869499, 3.4063377357820883, -3.53030004432459, -2.719147731369336, 2.1046944474586198, -2.362826025144519, -11.051924811695837, -9.646287140198542, -1.9833449516820252, 0.0660376615871266, -1.087857766598118, 0.4771427721660959, 0.7109435541227376, -1.756598309651844, -1.2606873097414901, 0.6192234482594667, -1.5886489356964404, -3.2689357378308337, 0.6079787536083285, 3.405680853289406, 0.5451877788053503, -1.62249536083154, -0.26165468300503947, 0.08353569189692965, -0.2498888134214149, 1.2366597899492697, 0.6913339594988817, -2.7439224761291463, -2.7533362025055967, 0.2346401294121252, -0.2521527397022467, -1.7556185821304517, 0.3953226976995094, 0.6804795606801417, -2.280091183561694, 1.7128566491437833, 10.905342846453959, 8.643758837789498, -4.330217898685857, -8.121912677897145, 0.42065409886224053, 5.0347544401599755, 1.5573140569975825, -0.5018254924632022, 0.13267367826825835, -0.7010678289013433, -0.7375300550225568, 1.0824073993947037, 0.914928928366266, -0.30590035372503027, 0.31672423812090594, -0.10817300385386722, -1.8052139656312778, 0.4370314169318119, 4.028133684797993, 1.797953791383346, -2.1079145309821627, -0.9579732010115092, -0.21850861975221186, -3.6967803196216904, -3.490681322596362, 1.2902295683190899, 0.9858314451143718, -2.620118897810732, 0.2149473953742584, 4.72354944344771, 2.054645105238082, -0.5649502720607361, 3.8538694023454756, 6.395947162058382, 2.1584476824196672, -0.12006830752455777, 1.7305939351775825, 0.9464624499920046, -0.865193830996102, 0.7018236589358817, 0.3055401554129891, -4.4617361193389, -5.559743571694854, -1.2674506277227282, 0.8402308765578861, -0.0854597617504307, 0.24906458676062856, 0.37152683342880033, -0.7656326949014268, -0.09304539899984042, 0.7027427838304904, -0.4132383504493484, 1.8416364030786319, 6.181878870387525, 1.5945166498016432, -7.79354354566409, -4.1902956851133, 9.052455904351577, 10.781563123261776, 0.8665956619025624, -3.137918348566153, -0.0942079772265971, -0.13123042434485557, -1.174774996619719, 1.1677514397267506, 1.3247778635335448, -1.8562535933345898, -1.7980019577641289, 0.5920532928063033, 0.32133622668030376, -0.181187597748415, 0.7794205675748299, -0.17309473954603208, -0.6251436230634388, 3.241278128920853, 5.211001573595495, 1.2041696675495215, -1.1696935224537701, 0.6357154382537455, -0.3579012205710336, -2.9576613232067177, -1.1584734486592414, 0.14966569858429582, -3.120510005541752, -3.237716528641852, 0.8779882750417352, -0.2947310288630425, -4.5322182575365195, -2.3992586091671506, 0.25539082307890904, -4.172338635430257, -5.5965148635732, 2.083036736369879, 5.986359097193689, 0.518595776721058, -2.6686190340401206, 0.1384444180047957, 0.9638182237194772, -0.4805056890967442, 0.18352633992621417, 0.6008119976476513, -0.3722995130336248, 0.23462070578131825, 0.42108027300130535, -1.5387143606121678, -0.7721510569778576, 2.3590701645855052, 1.4337199745036733, -1.0169455110368895, 0.27536246304677653, 0.14906906676521406, -2.4957761964765575, 1.9817553602413935, 10.222583480748678, 7.332992926493591, -1.3151490027770059, 1.777743738674127, 10.911659717256022, 9.317340840121068, 1.492425442588436, -0.3757792561391357, 0.6146618733183192, -0.44020859005181495, -0.26655988330376734, 0.2784048115342265, -1.252089990008337, 0.15062724335132505, 4.738974500285626, 4.338787546475276, 0.11937117566633715, 0.21094283245106726, 1.780212640881005, -0.6833966725772236, -2.147335920053059, 0.0012034736570266996, 0.13000811627240097, -1.230648460072552, 0.17283336777076344, 0.8685099089766597, -0.40848731140527883, 1.4711260985199544, 2.953387411530436, -1.6518794627431985, -2.8477777647474634, 5.273585443101838, 7.872218077184501, -1.502894653365444, -5.980223747396561, 0.4890868716593454, 3.105394833330284, -1.1075949077345333, -1.0161204289059327, 2.132671531106588, 0.8215918540760857, -0.8939505378688402, 0.5992169692829753, 0.34355604458649813, -1.4661868762337578, -0.5232031878533743, 0.5012384108509892, -0.39898757049777545, 0.2671663864470197, 1.2757673579674427, -0.03477950137210746, -0.12712272148363876, -0.8107007608003496, -8.94685427012523, -16.51492113349798, -10.53012550325455, 0.2618566939192938, 1.3015120530832789, -1.497588807956978, -0.12416538004047556, -0.962742673090911, -3.9042319138399852, 0.09791635479939287, 5.726734663778528, 2.782842115701229, -1.7077305267064804, -0.15467397209351685, 0.38118283666577424, -2.1079998001737397, -0.21182902950455637, 3.268989775311467, 1.4574819362529539, -0.5818177795428165, 1.1251584441725768, 0.9053132601120308, -0.9690430921772688, 0.8264604193842248, 2.552751434676034, 0.4685158171321965, -0.21266826154584306, 1.3773801783876203, 0.6221267175892996, -0.1850509150096095, 0.9380505379190552, -0.5455627643974896, -2.024969756652033, 1.6820884686505044, 1.794211895784529, -5.8591376070414025, -4.581279419209988, 10.393796042660714, 16.78213037254408, 6.574925927638763, -0.9512113703863807, 1.1253715181867703, 0.6071494112029242, -3.270779063075758, -2.5393208231553563, -0.08950015744437667, -0.14852270844587714, 0.06385395266935637, -0.10472789724973681, -1.9470634499742918, -0.9602214221496608, 1.7563599400449312, 0.1314576611458543, -1.7888137073419628, 1.3155590322786919, 2.7365796566168457, -0.608733185354828, -1.2052701341227596, 0.708931793483014, -0.4976041171012689, -0.3891851216882989, 2.733111729257776, 0.20590626423138642, -5.014184889354841, -1.0142821491705867, 5.879679613025097, 3.2799004044775955, -1.3759796015633292, 0.3512247028354274, 0.5662673031058187, -2.7252464809542545, -1.5284574222535046, -0.10537310255822764, -5.306136485806247, -7.705328954775919, -1.5170078509791245, 2.486846129715694, 0.3620988888987119, 0.05067214780866741, 1.6472983835869301, 0.7177283667489571, 0.0031529561109824083, 0.5727935713771776, -0.25956794114586834, -0.1744055398488836, 1.108786860327382, -1.1630146724330035], 'positive_zeros': ['0.55756507804782770664104775161', '1.6127012663336786772039215645', '3.00922141577054803501128769824', '3.80483811036303674270743073629', '4.53645791880094053190695986726', '5.018982512526015973893163039485', '6.25795712787902395583786466220', '6.66950939971785490385169490389', '7.42894794690053759329057389875', '8.29758887574166764761596411763', '8.69505834515127673350770349813', '9.83453819472097678671350770531', '10.422515137728141168182526369803', '10.66036567112503340098530236966', '11.40263315196663460205199629287', '12.409448314373110511252982098228', '13.31814952536552344062870674902', '14.26355537731452006902308040207', '14.96008189631533789154637502626', '15.21270382095989950516184453987', '15.907081846441509034992791092448', '16.562370082727259001311504371410', '17.293674035502452695786543947349', '17.6655651547772821238886052512', '18.416923825473969431395045746468', '19.53054058847829980569740864133', '19.75526710355348062563328555364', '20.41806138988893230848165859114', '21.20281405282370039526736936611', '22.21609740856575657401013341574', '22.92780315693070315173063358503', '23.24154841838617353598787636851', '23.55329410100430709378302249256', '24.64164967705805004151386748081', '25.67628993486279703260244198198', '25.7513632147796247081873502341', '26.66353146131199954447911568778', '27.19437094646230136662893733228', '27.41798735470874369672283784875', '28.19758457070460157785556746718', '28.78494612514930457993934007118', '29.5374593546277439846802285945', '30.504305577021607533382596542088', '30.92268044249021685115854600879', '31.93659163672624521944293325349', '32.47820018412893617399448633591', '32.983179778974970443859947095489', '33.6912672883639175223761357537', '33.89665411506948876087548608169', '34.86484350212562893233290890739', '35.22510933201672314510491848126', '35.83977614818649426096204210391', '36.60095614738125274004539591772', '37.28528756976576173470983136108', '37.90984012992335680468134446730', '38.445695061184726350466377420963', '38.97804440273239725054189596426', '39.7068440893853866357524124907', '40.201407101493221963229825173916', '41.10681890891988206555433785593', '41.95194791815732489106131812652', '42.37277550223073331037716392520', '42.94549710817945769728460806951', '43.511052985646098652042122130191', '43.95296057308559150889844116441', '44.65712963381828576355954502223', '45.34614446048759317672955185751', '45.7783163894386903983097629769', '46.262497610648210062316116382440', '46.92349412922647908238476346922', '47.25027295057181745362195246004', '48.694640987149721675983130130107', '49.15876858005619003438479413461', '49.63458039583742740934858479724', '50.33170376751634091288731265533', '50.80066604859852096058200706609', '51.35616492637683261111043944107', '51.888483536477731866407790271950', '52.54957360136886609109527577121', '53.10662615812021434535315870933', '53.9151542586205845977897598123', '54.46995486777965029001818833039', '55.02196117997670898126064048466', '55.31519113488870555653604646012', '55.86234464861954975423610218060', '56.8544512102831126526812955892', '57.15521674265160607437042008808', '57.791850878116239093310582173730', '58.95495425213395320753498452084', '59.17736454690832450021220782831', '59.78245723793568582328443461838', '60.516761702352052578935347769596', '61.26011631424684507663113124472', '61.920383755896541288922581990253', '61.99405799225427534338450627164', '62.325679192991880185502267026708', '63.09568173247858118240152335718', '63.70911718220647873610157571620', '64.45027660611740126898640017410', '65.195557230977556826725168954063', '65.51735153298438792547117918210', '66.262326152493108230571206129774', '66.82435710039984899275302717210', '67.62573236059433180544242653035', '68.07436659578870040898258495906', '68.90224710824140402392420863235', '69.12155590163729860488683195009', '69.71946641904842799513269886696', '70.57251878498970818502098986930', '70.82057159609235421878363359628', '71.85696038865829100336748060568', '72.11390814950893176703631270913', '72.64821954651550069320126350969', '73.22654495685329530036640101086', '73.72155016792157907017747124986', '74.36780612214959789865330475642', '74.8427275147719357509090257676', '75.19522785549372413306901797398', '76.50938802283863659662353080431', '77.26845797442106133955246074123', '77.55486960297695005346396825429', '78.11409694134041534748391697493', '78.54487706824118712229174174015', '79.21888630068196920749755738165', '79.44388314430436584546962476906', '80.39760095076341981007021748250', '80.90669220744695768243639183779', '81.33152022111961125027802660374', '81.791244913083117575641376257962', '82.5379500860189704743646458490', '83.12126915712657699071763814320', '83.72135596901836276983850540577', '84.301421027569363925164886771293', '85.0109280640684009426379346715', '85.51650643686495689196429144140', '85.969411481410046969711392748378', '86.62131855506679699444187799687', '87.24970269042237406376988093718', '88.07786792431279361997864719707', '88.60137715899433469600428981792', '89.00985852521549688210501456908', '89.37429965313482395528897595632', '90.09621840943080886813529431814', '90.74548687290692914338797351380', '91.01176131483028869433126169263', '91.45385813738843097938827303136', '92.13393547604722009175316000901', '92.84612890406809163608185250312', '93.549806854595922201332124227540', '94.17456261107330909582218479350', '94.68644414075605979453484982643', '95.46354081980382180456161955303', '96.04852761835267054407958362618', '96.46575615070515183236306835340', '96.96033178216539860528431351022', '97.505854055317911522350726575873', '97.89535318613269910917885285809', '98.44946806981587438222850061874', '99.17217367845756944432830794875', '99.98918774973220315930037601888', '100.30748698007034499019381040865', '101.13119614807063240036008809280', '101.27500168833851749994695984650', '101.7242006690227797981529079185', '102.196635642068239563864858673745', '103.44678730379102167071528903760', '103.80185132413585353570180234780', '104.339725788036667246081371095812', '104.95920810904918336344221249733', '105.66035899522957850764185746191', '106.258006464645065133509706067771', '106.522215965244879577181439629969', '107.19198443956588774274242852804', '107.75156248021603773463058104234', '108.13632909593032588294189580483', '108.84478214770269543877526206899', '109.117890727105663953662020924369', '109.59142511646839764899125385930', '110.45366662634375097902895270747', '111.083114981729485776150042521852', '111.47396587009666951511857757965', '112.66211182114214540809206731615', '112.82983791357272523466241706252', '113.36690942731107625088159200282', '113.8457440953279103721861450694', '114.53333742893451611122365133951', '114.843428252098429109586507818482', '115.58751505219686890146810818693', '116.29530616692321497495152717173', '116.936270306937482654528811502758', '117.22275354791367565169410098222', '117.57728231359669680440776236142', '118.19408825379383836243742477097', '119.02823411752009321351375245378', '119.33902491961024194551032008744', '119.954898464807490023702036031419', '120.38409001551902899113606225355', '120.87129376508323853463144462952', '121.76995499458269665551659204994', '122.48588488345886074237045463633', '123.27315542349089579005127249242', '123.657042030150305703035030087438', '123.8707999317232087642138910928', '124.5043173134750757013831007965', '125.190797642630336318048478575564', '125.52074540891218817187405224362', '125.91808758531068726482973203292', '126.53023153698268321116334188599', '127.30289189075005788937592359182', '127.9614922364621958901150314334', '128.08175453704085102300154264598', '128.97001898383281492325956654228', '129.448923914774856789848578320961', '129.98839814149893111411483614501', '130.774101262593453681946713391732', '131.01444536422149741390828437808', '132.072990826827566867617964262007', '132.22357934015436794274294778772', '132.928612153873906799661287488018', '133.33589202614745996507748978206', '133.77658626459420080009263765919', '134.79506985291497934372504918081', '135.27709025363920531877255892405', '135.53322332609876595102448744951', '136.03858160000607172192995812524', '136.58129194930619114599731564996', '137.0642036175183694374852791145', '137.34462408337621757065603577325', '138.1735650523714331209861753258', '138.8493787460541486906454348600', '139.7179506866723875994405590760', '140.32472873598888748686636576055', '140.60314989414186157592407880377', '141.1186391819465966273513618051', '141.69544854232318595967674693952', '142.40150235411304222447652251186', '142.89754326342750887819053604561', '143.19159418575612830368481337671', '143.71992834448558906272586988219', '144.13971419670880859720820180572', '145.08705124699707440828292528288', '145.52061029600188775061628960167', '145.89951320580009278732677715368', '146.69745749575923511495130666779', '146.90148110175335236737272070795', '147.7337018834952545403712548223', '148.104357387691048111264439978550', '148.94075977948235075581640995933', '149.10728929381302124038019067768', '149.92656862780174955035738208003', '150.65054759431425543916147270501', '151.23579480211154630945311821899', '151.7456825123281551502018377919', '152.143594688935016032196100467966', '152.67705872420689274952223993758', '153.0636302504944163454341745048', '153.51707575418873693041653538218', '154.13561325668995464419806134094', '154.82988231844437576431498936074', '155.27016293402789593345000423399', '155.64227943798280498437735655337', '156.173266102608715889800687557895', '157.11867438273597434728919346395', '157.43451220950044400236596214598', '158.5461025392605079604809547732', '158.83743003683495977201524159058', '159.26674571792729427976850075454', '159.757811479871462642060728908723', '160.07758498869636412265686604717', '160.61329892542355502970150882787', '161.57633879636692906854456707762', '161.84510342216719993208078721534', '162.43653108666613828517923382980', '163.12481260726327144716089735806', '163.46206777458008728807989190345', '164.03653791597706852295497088172', '164.55842060510528214523561376736', '164.83737519911989380295189630182', '165.53436638715867108412840322988', '166.07030592962800303235293142516', '166.83069680407685985591849604877', '167.47900007075904666155434097940', '168.04166450379989761084946276576', '168.52497739187817853377730925052', '169.153797547905829399769713625688', '169.58190379300421823579738002773', '170.05211203590757258056949101255', '170.71623732018044138501674356383', '171.118822989944765917413999537779', '171.50929928693898123460229913067', '172.17983548845743580587376695319', '172.542163382676714567586639147824', '172.71852091967119869751896915746', '174.05088655846087440607540931026', '174.48761780352805624635142868425', '175.02498889599474947671681881656', '175.19624163244031231853846509335', '175.933240568901406519518414955023', '176.711908674090738334687880020020', '177.20602412804506783456709376430', '177.55079971421640253695741384324', '178.14015402605225053976670769740', '178.89642247358741060065665862607', '179.20670890998468123618600924709', '179.80773787645461520471433043086', '180.22539095214045031437126324517', '181.005139682113898658269618946979', '181.2960943531684608630178016858', '182.00024335385597868744775298216', '182.25128092889127825887171551858', '182.75135729762465470270485982867', '183.322582905960321130371159188059', '183.836763679063026451591626544890', '184.48557918695352713558192370251', '185.53242538429272284645070784128', '185.82451216398327547308865887502', '186.29757436109759694382476074377', '187.21748109504506598168328595623', '187.4058506928342480649898146103', '187.781944193776259258839717914542', '188.09996005555891451057979761987', '188.84273994757013318265896904252', '189.38722363989017864670681368048', '189.898357252598880469546759673614', '190.56998539541404092338580612266', '191.10316568534053383750597218298', '191.48479087525390290859324636058', '191.91665845466502892897646063268', '192.510458052513062884805393327146', '193.162470006646308441363342996442', '193.923456525354145759990210461265', '194.33687021792838014645426636684', '194.74365579016600520272515048301', '195.48751180430619810448946592323', '195.607225747826647150229005462209', '196.632297716383817279908548056', '197.241427087282855496428456259685', '197.49016481694222859395254836827', '198.32254694284311759997940025630', '198.43505503118358585655078130585', '198.992665965075880018264559982681', '199.411028193433983495443545749013', '199.8975322565374570509711935108'], 'prelabel': '1-4033-4033.1043-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 433.4060416967227, 'root_angle': 0.9777604773314905, 'root_number': '-0.997560257455448250607982011388+0.0698106921998328486647563997066*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.441003712002128736463918467051+0.327920035591581396292816091230*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.557565078048', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.61270126633', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.00922141577', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 433.4060416967227, 'bad_primes': [37, 109], 'central_character': '4033.1043', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/1043'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-4033-4033.1043-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4033-4033.1043-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 433.4060416967227, 'root_angle': 0.48888023866574526, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.557565078048', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4033.1043', 'Lhash_array': ['dirichlet_L_4033.1043'], 'label': '1-4033-4033.1043-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/1043'}