Table lfunc_lfunctions
L-functions
{'Lhash': '1228958178442653792812630076464', 'a10': [32561.327712389302, 56397.873959758756], 'a2': [16.0, -27.712812921102035], 'a3': [121.5, 210.4441731196186], 'a4': [-512.0, -886.8100134752651], 'a5': [-1017.5414910121657, 1762.433561242461], 'a6': [7776.0, 0], 'a7': [42078.187963490076, -14378.902625346582], 'a8': [-32768.0, 0], 'a9': [-29524.5, 51137.93406806732], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.27041358350274, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-16.0, 27.712812921102035]]], [3, [[1.0, 0], [-121.5, -210.4441731196186]]], [7, [[1.0, 0], [-42078.187963490076, 14378.902625346582]]]], 'bad_primes': [2, 3, 7], 'central_character': '42.37', 'coefficient_field': 'CDF', 'conductor': 42, 'conductor_radical': 42, 'conjugate': '1471351378773723741455759538838', 'degree': 2, 'euler_factors': [[[1.0, 0], [-16.0, 27.712812921102035]], [[1.0, 0], [-121.5, -210.4441731196186]], [[1.0, 0], [1017.5414910121657, -1762.433561242461], [-24414062.5, -42286396.66916204]], [[1.0, 0], [-42078.187963490076, 14378.902625346582]], [[1.0, 0], [-39381.169757186544, -68210.186880942], [-142655835305.5, 247087154745.30405]], [[1.0, 0], [788558.2307081192, 0], [1792160394037.0, 0]], [[1.0, 0], [-5116289.493934968, -8861673.349726222], [-17135948153816.5, 29680332838276.28]], [[1.0, 0], [-10330182.936873574, 17892401.698146112], [-58245129449109.5, -100883523499283.9]], [[1.0, 0], [3676573.5034287055, -6368012.105700025], [-476404878956963.5, -825157455327161.9]], [[1.0, 0], [-99302386.82807064, 0], [12200509765705828, 0]], [[1.0, 0], [-100916759.62751122, -174792955.01006508], [-12704238448202416, 22004386463756576]], [[1.0, 0], [-195399424.81764844, 338441731.5539021], [-88958810889730200, -154081180241924220]], [[1.0, 0], [-780703972.2562355, 0], [550329031716248450, 0]], [[1.0, 0], [-21760747.057918176, 0], [929293739471222700, 0]], [[1.0, 0], [-1515564770.6808271, 2625035184.980667], [-1236079607542006300, -2140952682462552600]], [[1.0, 0], [-1985192377.1211417, -3438454059.9722524], [-4634517964686095000, 8027220583427022000]], [[1.0, 0], [1377664846.818461, 2386185510.491169], [-15077944222368922000, 26115765466832577000]], [[1.0, 0], [5258788481.257104, -9108488835.795277], [-21756958805717918000, -37684158069686520000]], [[1.0, 0], [-1145269559.5575817, -1983665065.5157616], [-61065066452484006000, 105767797663272090000]], [[1.0, 0], [-4543662241.503275, 0], [231122292121701580000, 0]], [[1.0, 0], [6982033096.446683, 12093236063.173107], [-156863342784179860000, 271695279547292350000]], [[1.0, 0], [13908955810.79625, -24091018144.529472], [-373996905263760500000, -647781641790357200000]], [[1.0, 0], [61738302664.275085, 0], [1287831418538085800000, 0]], [[1.0, 0], [12075861686.797274, -20916005986.70728], [-1387586536883495000000, -2403370381780759600000]], [[1.0, 0], [103349769679.6987, 0], [7153014030880804000000, 0]], [[1.0, 0], [-24838227375.530094, -43021071784.366295], [-5578341733326583000000, 9661971304103478000000]], [[1.0, 0], [-32246061488.6705, 55851816842.36742], [-6921169353622228000000, -11987816968262345000000]], [[1.0, 0], [38664150703.45798, -66968273449.88916], [-10524259761499174000000, -18228552618969286000000]], [[1.0, 0], [-16809046852.317728, -29114123175.020016], [-12902132026527038000000, 22347148195906435000000]], [[1.0, 0], [-122841505226.45778, 0], [38358611506121120000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23062819, 'index': 8, 'label': '2-42-7.2-c11-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/42/12/e/d/37/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [2.8773021379826464, 2.776747615249667, 2.5743648424405983, 2.2769911532912173, 1.895618264900662, 1.4449820845090617, 0.9429916692100099, 0.41001651943196826, -0.13194301100501196, -0.6601723052886114, -1.1522117718222884, -1.5868409858676262, -1.9450373866111474, -2.210868079013803, -2.3722736403966374, -2.4217048605948137, -2.3565771809281335, -2.179513305029938, -1.8983520130441252, -1.5259104976164866, -1.0794983187040739, -0.5801929859518695, -0.051899742135579165, 0.4797692535733432, 0.9887491438941811, 1.4498521701171692, 1.8401067495722645, 2.1400339634549295, 2.3347875870749184, 2.4150859100696125, 2.3778701662492727, 2.2266355181009483, 1.9713960257469068, 1.6282643616148937, 1.2186493696756302, 0.7680987579608829, 0.3048388286259478, -0.14191344051783064, -0.5437701883443483, -0.8750127887834444, -1.1143312636786777, -1.2463400894575307, -1.2627541527692665, -1.163124163172655, -0.955055017937035, -0.6538624786408771, -0.2816614027715474, 0.13407963704569853, 0.5624400764712154, 0.9712881055205078, 1.3297088418959684, 1.6104431135097297, 1.7921467419164028, 1.8612810534434026, 1.8134615462826296, 1.6541232857271828, 1.3984074608377395, 1.070231050832217, 0.7005668958921811, 0.32502976459319016, -0.019070358462691676, -0.2959895053944766, -0.4748645182168869, -0.532797086816839, -0.457422451838071, -0.24870302996792307, 0.08026292925389261, 0.5035550669160362, 0.9839140141852657, 1.4753392881262195, 1.9266430955567102, 2.285703542977422, 2.5040794549798178, 2.5415929337204695, 2.370462210967322, 1.9785810110263211, 1.3715931195311604, 0.5735000642299454, -0.3743400692486771, -1.4158229702667748, -2.4841667949919093, -3.5071420537877493, -4.41303855133135, -5.136851515402523, -5.626120133508053, -5.845855456771501, -5.782054080436011, -5.443406728517116, -4.860968752341054, -4.085749253547094, -3.18437949438703, -2.2332192304700595, -1.3114306697574394, -0.49367451379465477, 0.15685471953761554, 0.5943461608382853, 0.7946190160427196, 0.7572279215395424, 0.5051675822817628, 0.08216394025457019, -0.45220277990545554, -1.0290564757241554, -1.5777814539045516, -2.0337647154973926, -2.3454702691467606, -2.4800443543510715, -2.426796456593918, -2.198127433399535, -1.827760160418923, -1.3664390967068567, -0.875567537192219, -0.4195087619557176, -0.05745705099585235, 0.16413841553318056, 0.21765320703547675, 0.0980834806734094, -0.17597051582045597, -0.5643278521417421, -1.0100810013380304, -1.4467414811700605, -1.8068289795267933, -2.0308423843651013, -2.0754645108719223, -1.919909368012425, -1.569520717455398, -1.0560541553342109, -0.43448570526674135, 0.22336153035684664, 0.837651672314499, 1.3307572846391982, 1.6375669206616656, 1.7145142139277931, 1.546078027194186, 1.1477890764197383, 0.5652057752881554, -0.13115989176234527, -0.8544423191771321, -1.5125274269755256, -2.0202621461864143, -2.3111604063094777, -2.3470002528046954, -2.1239279396895596, -1.6741045583511478, -1.062500427274455, -0.3790904961465254, 0.2726554370860137, 0.7895497180743183, 1.082924898776895, 1.0913934040377502, 0.7903195194002188, 0.19658115978673799, -0.632201150857361, -1.6040527629728314, -2.603957790171832, -3.508693748239569, -4.203246714294225, -4.596581069627719, -4.634557066510973, -4.308121058625526, -3.6555012931403694, -2.7579495257491144, -1.7294665236731854, -0.7018117421923395, 0.19320136755934056, 0.8416893374625288, 1.1634319298264928, 1.1230923280868506, 0.735263699271311, 0.06253860860405006, -0.7932089143422376, -1.7051521994928582, -2.5394414025045515, -3.1741700402117496, -3.516631242768869, -3.516337948833485, -3.1718836038432348, -2.5306198714090775, -1.6811947337454336, -0.740068595794899, 0.16595692154686953, 0.918547016136132, 1.425114146261387, 1.6319344469069723, 1.531105154358205, 1.1603086659340254, 0.5954815279192763, -0.062386316584320055, -0.7041559396105915, -1.2303815384367058, -1.5671680143102906, -1.6774419195575727, -1.5657857421251908, -1.2760529705650454, -0.8821928525565317, -0.4738697853657553, -0.139367758919185, 0.051232822885616, 0.0596236468805032, -0.11288201478293342, -0.424728047988319, -0.8009919042133307, -1.146709277054769, -1.3644253645479427, -1.3729327892384584, -1.1238452963961048, -0.612923439425423, 0.11611328326202142, 0.9763073241792344, 1.8502647053971515, 2.609136158300125, 3.134704445778079, 3.340824318744778, 3.1904109070748743, 2.7047844473611966, 1.9633731144490614, 1.0933659356316239, 0.2506328459073943, -0.40520592370402014, -0.7375517003008162, -0.6569536574691455, -0.1383816931445454, 0.7715480183617184, 1.958989905872034, 3.258596776579312, 4.4782951733992595, 5.4292421161575435, 5.956110220698126, 5.96266591533937, 5.428281294749875, 4.412459250363106, 3.046423056900683, 1.5129955775044244, 0.017996088807722018, -1.2421378037314246, -2.1111074767652416, -2.4967310879660185, -2.384118166044676, -1.8358636119923992, -0.9793247220935204, 0.016711757540020963, 0.9718185651458116, 1.7249018579663462, 2.1609087208327136, 2.2286128246716728, 1.9464582341502945, 1.3956244053774105, 0.7018105607198317, 0.009296915577506108, -0.5477580590422169, -0.871344876422027, -0.918051445547835, -0.7064876149010996, -0.31235261970185507, 0.14781749913655853, 0.5410052312119283, 0.7453800288674107, 0.6758323404842365], 'positive_zeros': ['0.969477061125037627392974048891966', '2.76213845762736753039474071512870', '4.58428872110303287702798195760384', '5.83555044013265365341735711571065', '7.49250789051589596135050414749572', '8.222950499768543344888403220359275', '9.702525059474743708850485176825117', '11.71611436672429472415618496578759', '12.39559986060462363481336347716357', '14.02533233074674697531412087260397'], 'prelabel': '2-42-7.2-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.680705377283946, 'root_angle': 0.02084059052242498, 'root_number': '0.9914389085753506 + 0.1305714002487443*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.02084059052242498', 'prec': 54}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.969477061125037627392974048891966', 'prec': 110}, 'z2': {'__RealLiteral__': 0, 'data': '2.76213845762736753039474071512870', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '4.58428872110303287702798195760384', 'prec': 110}}