Table lfunc_lfunctions
L-functions
{'Lhash': '1294063253647901775282645504776', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [0, 3.414213562373095], 'a6': [0, 0], 'a7': [1.4142135623730951, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.265021750468673, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3], 'central_character': '1536.769', 'coefficient_field': 'CDF', 'conductor': 1536, 'conductor_radical': 6, 'conjugate': '1276373925132429441615414881256', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -3.414213562373095], [-5.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [7.0, 0]], [[1.0, 0], [0, 4.82842712474619], [-11.0, 0]], [[1.0, 0], [0, -0.8284271247461901], [-13.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [17.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-19.0, 0]], [[1.0, 0], [1.17157287525381, 0], [23.0, 0]], [[1.0, 0], [0, 7.414213562373095], [-29.0, 0]], [[1.0, 0], [-7.0710678118654755, 0], [31.0, 0]], [[1.0, 0], [0, -11.65685424949238], [-37.0, 0]], [[1.0, 0], [-10.48528137423857, 0], [41.0, 0]], [[1.0, 0], [0, -6.82842712474619], [-43.0, 0]], [[1.0, 0], [-12.48528137423857, 0], [47.0, 0]], [[1.0, 0], [0, -1.7573593128807148], [-53.0, 0]], [[1.0, 0], [0, -1.6568542494923801], [-59.0, 0]], [[1.0, 0], [0, 0.3431457505076198], [-61.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-67.0, 0]], [[1.0, 0], [-8.48528137423857, 0], [71.0, 0]], [[1.0, 0], [-11.313708498984761, 0], [73.0, 0]], [[1.0, 0], [17.414213562373096, 0], [79.0, 0]], [[1.0, 0], [0, -8.82842712474619], [-83.0, 0]], [[1.0, 0], [5.31370849898476, 0], [89.0, 0]], [[1.0, 0], [7.656854249492381, 0], [97.0, 0]], [[1.0, 0], [0, 10.727922061357855], [-101.0, 0]], [[1.0, 0], [-9.414213562373096, 0], [103.0, 0]], [[1.0, 0], [0, 7.31370849898476], [-107.0, 0]], [[1.0, 0], [0, 7.17157287525381], [-109.0, 0]], [[1.0, 0], [-3.65685424949238, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23207462, 'index': 17, 'label': '2-1536-8.5-c1-0-17', 'leading_term': '1.8516507041735267586594370087186902592541949186377394987', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1536/2/d/e/769/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.8516507041735268, 1.8453309841749075, 1.829248240258812, 1.8030754449529731, 1.7662800046066036, 1.7181709054298504, 1.6579590636393755, 1.584826991493098, 1.4980037515820483, 1.3968413996364069, 1.2808895700941771, 1.1499653964752514, 1.0042164707646568, 0.8441749700452137, 0.6708013962980353, 0.4855166005328149, 0.29022092686511275, 0.08729945294795746, -0.12038754540481254, -0.3295295884772198, -0.5364068840139224, -0.7369472440093044, -0.9267987788967423, -1.1014176835954563, -1.2561699419658414, -1.3864452531488443, -1.487780943761465, -1.555993095412489, -1.5873116107933434, -1.578515488055185, -1.5270641968751262, -1.4312207743992773, -1.290162107303079, -1.1040718570173569, -0.8742116345189559, -0.6029663500838375, -0.29386015756752776, 0.04845991873731986, 0.4182747516439742, 0.8088793637346777, 1.2127046410217461, 1.6214732700957117, 2.026387386187751, 2.418344125722405, 2.7881740120164724, 3.1268959178535765, 3.4259812963474725, 3.6776195039365933, 3.8749754059688377, 4.012430100569524, 4.085795557431225, 4.092494272348543, 4.031695701672778, 3.9044022659942277, 3.7134790872731727, 3.463623320939212, 3.161270921194974, 2.814440875842427, 2.43251929445887, 2.025988146773168, 1.6061058333592981, 1.1845490288977731, 0.7730272675828854, 0.38288344103924454, 0.024694658062180175, -0.2921113096427538, -0.5596085675169605, -0.7716796096819827, -0.9242618432506335, -1.0155218618236055, -1.045947508960687, -1.018350627174569, -0.9377767060537369, -0.8113213110674001, -0.6478570558913161, -0.4576788205403549, -0.2520787471014141, -0.04286609013904284, 0.1581499130657011, 0.3396935200127038, 0.4915499754786995, 0.6050638736752417, 0.6735854079079866, 0.6928427136555596, 0.6612207293117482, 0.5799302058545686, 0.45305460288100774, 0.28746747737415596, 0.09261842342298073, -0.11980856160574326, -0.33635447346887737, -0.5423468624409526, -0.7225425997848935, -0.8618262224221056, -0.9459345109064451, -0.9621754095566762, -0.9001082026675032, -0.7521521421827424, -0.5140925414988048, -0.18545669832048753, 0.23026319595360165, 0.7255569185598467, 1.2890224605713985, 1.905673346214063, 2.5574203669658844, 3.22371267018165, 3.8823150923171688, 4.510191332552718, 5.0844564103883645, 5.583357189598575, 5.98723687273718, 6.279438492559516, 6.447103677447944, 6.481826375295306, 6.380126706071786, 6.1437174917359965, 5.77954499437056, 5.299595597307073, 4.720471129434475, 4.062746741785203, 3.350136145892789, 2.60849905643513, 1.864734309186036, 1.145608862769918, 0.4765773307854165, -0.11935147597986745, -0.6226454715718359, -1.0181259410502705, -1.295644686225951, -1.4505254434951464, -1.4837444376020836, -1.4018376088827664, -1.216535694240916, -0.944142267510517, -0.6046833280082412, -0.22086934097834976, 0.18307890746264732, 0.5826812860568692, 0.9544617419486406, 1.2771580782474943, 1.532813781741227, 1.707692886029961, 1.7929674501699737, 1.785138751920476, 1.6861671830683815, 1.5033013888750748, 1.248613597126552, 0.9382644451296138, 0.5915360213825948, 0.22968540504527876, -0.1253180991715932, -0.45210125412679664, -0.731166205589129, -0.9460667442321877, -1.0844121091537442, -1.138637678161054, -1.1064943205063553, -0.9912236742779236, -0.8014043342081705, -0.550472923673766, -0.2559432029933533, 0.061635381177623225, 0.37992206698853703, 0.6761612221385686, 0.9286106877990407, 1.1179370517514269, 1.2284930178613371, 1.249397227546529, 1.1753469501284217, 1.0071085180824397, 0.7516484888165552, 0.4218892754530637, 0.03609522652484675, -0.3830824519651995, -0.8098522963023879, -1.2167523133127525, -1.5762593703905718, -1.8624443995941204, -2.052574629656924, -2.128565002316453, -2.0781878436834065, -1.8959624748238195, -1.5836641285113127, -1.1504133328418866, -0.6123315899368834, 0.008224727936815649, 0.6838143952547912, 1.3833831984961644, 2.0739746803465593, 2.7225805518023094, 3.2980211000132957, 3.7727420236797413, 4.1244171904502895, 4.337256799168176, 4.402936875223673, 4.321088043005015, 4.099307845875031, 3.752689958709135, 3.3028936867127627, 2.776806288754876, 2.204877038549394, 1.619223809959549, 1.0516288576447579, 0.5315492238591316, 0.08426812949081323, -0.2706934178238027, -0.5208004506268359, -0.6612808006956307, -0.695399825148721, -0.6342097013642057, -0.49578352636474393, -0.3039780177894372, -0.08679992101047318, 0.12552180173571945, 0.3026351330001052, 0.41619951301003244, 0.44191523931505955, 0.3613119516730679, 0.1631740610763516, -0.15549708661093264, -0.5890556068215765, -1.1233552042506978, -1.7364650326564484, -2.3999194693285597, -3.080428020531223, -3.7419398813431846, -4.347932440431271, -4.863776045577038, -5.2590199102499, -5.509446811971244, -5.59875720438147, -5.519765845836457, -5.275024693851541, -4.876822706989011, -4.346553956885729, -3.7134874010998726, -3.013011991727957, -2.284466744991016, -1.5686944720238607, -0.9054779946264948, -0.3310273406093883, 0.12431518060376849, 0.43799803485921807, 0.5966811775420632, 0.5970566006657998, 0.44601056469226835, 0.16011343956016544, -0.2355314258632863, -0.7090045870781871, -1.223738862705247, -1.7409933351139995, -2.2224653833705217, -2.6328627709297585, -2.9422597025528705, -3.1280749210600023, -3.1765354766166505, -3.0835250958795104], 'positive_zeros': ['1.02083590968593160180627277631932', '2.15997493957355491526568976978616', '3.75428818299688049187412982155035', '4.52390459294648897482734798405359', '5.18218450219201128083370969165358', '5.82839817279760611905709151322728', '7.31178115425513598536167729455341', '7.942327186063656874885192115820918', '8.768021977938976622211674722813306', '9.422361560508224599468130206694084'], 'prelabel': '2-1536-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5021453068752977, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02083590968593160180627277632', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.15997493957355491526568976979', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.75428818299688049187412982155', 'prec': 100}}