Table lfunc_lfunctions
L-functions
{'Lhash': '2507184243859368868349086087184', 'a10': [0.0, 0.0], 'a2': [2.0, 0.0], 'a3': [5.968681960123665, 0.0], 'a4': [4.0, 0.0], 'a5': [0.0, 0.0], 'a6': [11.93736392024733, 0.0], 'a7': [-15.248418575920573, 0.0], 'a8': [8.0, 0.0], 'a9': [8.625164341105677, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.85219650660174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [23.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.1', 'coefficient_field': 'CDF', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [-5.968681960123665, 0], [27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [15.248418575920573, 0], [343.0, 0]], [[1.0, 0], [-12.026849015008578, 0], [1331.0, 0]], [[1.0, 0], [90.19829808104963, 0], [2197.0, 0]], [[1.0, 0], [83.98311976543928, 0], [4913.0, 0]], [[1.0, 0], [-74.85028737637339, 0], [6859.0, 0]], [[1.0, 0], [23.0, 0]], [[1.0, 0], [-94.53208441818578, 0], [24389.0, 0]], [[1.0, 0], [178.39298771657928, 0], [29791.0, 0]], [[1.0, 0], [296.4866946631733, 0], [50653.0, 0]], [[1.0, 0], [-193.07362135142296, 0], [68921.0, 0]], [[1.0, 0], [15.457638794876095, 0], [79507.0, 0]], [[1.0, 0], [128.89905854249034, 0], [103823.0, 0]], [[1.0, 0], [342.9610057303172, 0], [148877.0, 0]], [[1.0, 0], [-725.0115418267961, 0], [205379.0, 0]], [[1.0, 0], [784.2882495058714, 0], [226981.0, 0]], [[1.0, 0], [-782.8220316273687, 0], [300763.0, 0]], [[1.0, 0], [141.7677024955034, 0], [357911.0, 0]], [[1.0, 0], [404.3400281009071, 0], [389017.0, 0]], [[1.0, 0], [721.0377070706166, 0], [493039.0, 0]], [[1.0, 0], [-985.3908533320164, 0], [571787.0, 0]], [[1.0, 0], [-463.05437297208226, 0], [704969.0, 0]], [[1.0, 0], [-1680.0504304875844, 0], [912673.0, 0]], [[1.0, 0], [1142.692981336391, 0], [1030301.0, 0]], [[1.0, 0], [716.0895503019161, 0], [1092727.0, 0]], [[1.0, 0], [710.3945072088578, 0], [1225043.0, 0]], [[1.0, 0], [827.3486402998429, 0], [1295029.0, 0]], [[1.0, 0], [1425.5061006660926, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 19882264, 'index': 100, 'label': '2-1150-1.1-c3-0-100', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1150/4/a/x/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [8.515321296229523e-60, 0.44694461755963966, 0.8896432750799255, 1.3238748726242655, 1.7454690232446348, 2.1503338253388495, 2.5344863520646617, 2.894086469272506, 3.2254743588162302, 3.5252118516395017, 3.7901273768586434, 4.017364022255251, 4.204429891613727, 4.349249648510456, 4.450215867223849, 4.506238581189938, 4.5167912384554345, 4.4819511510125265, 4.4024324682472695, 4.279609719731109, 4.115530063053884, 3.912912540108627, 3.6751328897853814, 3.406192783700793, 3.1106727392624753, 2.7936684134439034, 2.46071048103198, 2.1176688402625503, 1.770642451821273, 1.4258366872149848, 1.0894306208168953, 0.7674372264529622, 0.4655599134603151, 0.18904923782872507, -0.05743606893799324, -0.26995941610002366, -0.4454236126131693, -0.5816707436108457, -0.6775605691379323, -0.7330237371389816, -0.7490866473123418, -0.7278654984047347, -0.6725278867899499, -0.5872212804886082, -0.4769687457811059, -0.34753342314753677, -0.20525440024007227, -0.05685777255386128, 0.09075222504268782, 0.23071613485416043, 0.35644950082274174, 0.46187298304793695, 0.5416344873027292, 0.5913152316163213, 0.6076117501589949, 0.5884862118104899, 0.5332781146416624, 0.442771404430129, 0.31921233943134775, 0.1662749565765977, -0.011027254684725329, -0.20648294802266276, -0.41287524320300967, -0.6222201841677903, -0.8260447373532738, -1.015695862288628, -1.1826705257394752, -1.318955162273468, -1.4173620819870947, -1.4718497543325066, -1.4778138064333206, -1.4323359996118212, -1.3343794047758997, -1.18491948058897, -0.9870027404983337, -0.7457271256198176, -0.4681410079732249, -0.16306083990076875, 0.15918927002972402, 0.48710946188160736, 0.808417691936026, 1.1104921468766638, 1.3808470565797546, 1.6076243239120194, 1.7800818733245036, 1.8890588197862763, 1.9273975501409555, 1.8903036348593096, 1.7756261602674246, 1.584043564218324, 1.3191433089895401, 0.9873876341530196, 0.5979620647922658, 0.16250814148153456, -0.30525320253117044, -0.7899962729714766, -1.2753472512034043, -1.7445026494383915, -2.18088590144997, -2.5688157844904453, -2.8941587818518615, -3.1449370654810895, -3.311864579219482, -3.3887857582973404, -3.3729946961925488, -3.2654169746980255, -3.0706417593319637, -2.796797929717782, -2.455274716873, -2.060294273239041, -1.6283504981156114, -1.1775349601891325, -0.7267765818252598, -0.29502657627445206, 0.0995763085172509, 0.440523107155199, 0.7136969476027335, 0.9080440849419076, 1.0161204262622998, 1.0344850223540303, 0.9639182215432835, 0.8094496765569102, 0.5801898585607723, 0.2889677951650799, -0.048213001906963295, -0.41287945827684813, -0.7849254497882293, -1.1435434814218435, -1.4682094599258624, -1.7396746944637516, -1.9409175742907432, -2.058007955323246, -2.080840191946184, -2.003695916165775, -1.8256049173031197, -1.5504815243141377, -1.1870243503653295, -0.7483786503207126, -0.25157232582803385, 0.2832517910480445, 0.8337739291263404, 1.3765627379744914, 1.8882175326291282, 2.346531694018539, 2.7316189280617995, 3.026944416063354, 3.2202061941069364, 3.304018306062383, 3.276356156497857, 3.14073567187321, 2.906110853383587, 2.5864884539186987, 2.2002731332829235, 1.7693707899866924, 1.3180910739501153, 0.8719016212982172, 0.4560956586073689, 0.09444074540702531, -0.1921208528153079, -0.38665058881288183, -0.47720590461534773, -0.4575895851701337, -0.3278108474379193, -0.094226948560659, 0.23064973807925912, 0.6286768401053463, 1.076919243278111, 1.5487613402692886, 2.0152415862713795, 2.446543579194911, 2.81356799702228, 3.089503671506872, 3.2513142829869577, 3.281059831043163, 3.166979135826695, 2.9042708761443867, 2.4955255575614124, 1.9507785973660947, 1.2871745041979001, 0.5282528758127277, -0.29711248260084977, -1.1560707442723333, -2.013380102324004, -2.8331417294981596, -3.5805914319940904, -4.223854288416079, -4.735568224503835, -5.094288338094463, -5.285594623022141, -5.302841025028936, -5.147502713349666, -4.829100060135889, -4.364700906699973, -3.7780259742399585, -3.0982044262148505, -2.3582463303018755, -1.5933149371903148, -0.8388933158635947, -0.12894623311076378, 0.5058211928780039, 1.0395117036658923, 1.4523053604163834, 1.7313803919221602, 1.8714354663350476, 1.8747863311594253, 1.7510343660925076, 1.5163294436930088, 1.1922731192155382, 0.8045291535425577, 0.3812254339225545, -0.048756560181543895, -0.4575022610769513, -0.8196918341335234, -1.1140387194378047, -1.3244542465731965, -1.4408708230673914, -1.4596775173360814, -1.3837460536632509, -1.2220508202797715, -0.9889118693993088, -0.7029134634604765, -0.385570994831026, -0.05983477016112936, 0.25147082193526304, 0.5271705283882595, 0.7491244852040688, 0.903387493886621, 0.9810665368378965, 0.9788219205087723, 0.8989812679764669, 0.7492615374817837, 0.5421206235837324, 0.2937851567202392, 0.02302317347277941, -0.2502521210906555, -0.5064494612381063, -0.7277342365569537, -0.8993293518566086, -1.0105895503947218, -1.0557717811112561, -1.0344449744495463, -0.9515075519029929, -0.816808478094412, -0.6443958156795844, -0.4514436274771063, -0.2569318018656902, -0.08017225121881405, 0.060712456443608745, 0.1502466279018454, 0.1768861759623696, 0.13403181584977175, 0.020689454192977054, -0.15827986141241843, -0.3923497603189391, -0.6659563700170207, -0.9595306115468484, -1.250871218783309], 'positive_zeros': ['1.97781963216675973444988455803734', '2.77628966699808700922923028034343', '3.51216909322230850278039185207516', '4.54163034909032702287598342482764', '5.46994235453718755493871845649276', '6.66422259294030883552663782432568', '7.25760443123851139237460294481258', '8.113872677859011630557339241931133', '9.216744744416754607486336350974156'], 'prelabel': '2-1150-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.237244472917006, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97781963216675973444988455804', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.77628966699808700922923028034', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.51216909322230850278039185208', 'prec': 100}}