-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '947093713648382713231381362143', 'a10': [-2.2618022452599718, 0.0], 'a2': [-2.2618022452599718, 0.0], 'a3': [-1.0, 0.0], 'a4': [3.115749396663049, 0.0], 'a5': [1.0, 0.0], 'a6': [2.2618022452599718, 0.0], 'a7': [-1.2618022452599718, 0.0], 'a8': [-2.5236044905199435, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.242076912394587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 13], 'central_character': '2535.1', 'coefficient_field': 'CDF', 'conductor': 2535, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2618022452599718, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.2618022452599718, 0], [7.0, 0]], [[1.0, 0], [-4.5236044905199435, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.49330103858607, 0], [17.0, 0]], [[1.0, 0], [-5.115749396663049, 0], [19.0, 0]], [[1.0, 0], [-2.2314987933260984, 0], [23.0, 0]], [[1.0, 0], [1.377551641923021, 0], [29.0, 0]], [[1.0, 0], [-8.87085268050909, 0], [31.0, 0]], [[1.0, 0], [0.23149879332609835, 0], [37.0, 0]], [[1.0, 0], [-1.1460528485969226, 0], [41.0, 0]], [[1.0, 0], [-6.377551641923021, 0], [43.0, 0]], [[1.0, 0], [10.785406735779915, 0], [47.0, 0]], [[1.0, 0], [-4.5236044905199435, 0], [53.0, 0]], [[1.0, 0], [0.8539471514030774, 0], [59.0, 0]], [[1.0, 0], [-4.639353887182993, 0], [61.0, 0]], [[1.0, 0], [-13.132654925769062, 0], [67.0, 0]], [[1.0, 0], [9.609050435249118, 0], [71.0, 0]], [[1.0, 0], [-13.785406735779915, 0], [73.0, 0]], [[1.0, 0], [8.87085268050909, 0], [79.0, 0]], [[1.0, 0], [8.231498793326098, 0], [83.0, 0]], [[1.0, 0], [-6.622448358076979, 0], [89.0, 0]], [[1.0, 0], [-10.669657339116865, 0], [97.0, 0]], [[1.0, 0], [17.047208981039887, 0], [101.0, 0]], [[1.0, 0], [13.94836511348285, 0], [103.0, 0]], [[1.0, 0], [-12.49330103858607, 0], [107.0, 0]], [[1.0, 0], [2.2787077743659854, 0], [109.0, 0]], [[1.0, 0], [1.4763955094800565, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-2535-1.1-c1-0-19', 'leading_term': '0.72428900802618046444196005913010', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2535/2/a/bb/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.7242890080261805, 0.7196875867319501, 0.7058592660924726, 0.6827401564970575, 0.650250635995706, 0.6083331505581394, 0.5570004998528634, 0.49639069161313076, 0.4268241532278097, 0.34885914406572544, 0.2633415151153663, 0.17144540743126047, 0.07470198295964905, -0.024986210408485417, -0.12534714162955915, -0.2237588799562623, -0.317287771407852, -0.4027455882060748, -0.47676545012870164, -0.5358956787532035, -0.5767100519878964, -0.5959321883460031, -0.5905710282643287, -0.5580636210686117, -0.49642070445090636, -0.4043699160971001, -0.28149094407120706, -0.12833654357722504, 0.053466839249239805, 0.26114505680629796, 0.49073478996652753, 0.7370799786997551, 0.9938706625895419, 1.2537276069484398, 1.5083346884739652, 1.7486193722407928, 1.9649797710899153, 2.14755479456497, 2.2865318355182893, 2.3724843873989068, 2.396730021679344, 2.3516973760771007, 2.231289305300649, 2.031228219906606, 1.7493689717101841, 1.3859645109184175, 0.9438699996742779, 0.42867215762829447, -0.15126764803082837, -0.7848656857154485, -1.4584696724342339, -2.15611679380925, -2.8598947125105054, -3.5504001648512182, -4.207285432782059, -4.80987870997855, -5.337860344446038, -5.7719733303677705, -6.094743430576784, -6.291182118161745, -6.349444290367715, -6.261412558868653, -6.023180947533996, -5.635413075536301, -5.103553361457517, -4.437874388426605, -3.653349199429791, -2.7693437679349433, -1.8091319821482656, -0.7992429169900077, 0.23134236346478032, 1.252120061371657, 2.2320880185384615, 3.1408287148943694, 3.949610130924597, 4.632460999832162, 5.167176030605812, 5.536207650505312, 5.72740375619361, 5.734555848201391, 5.55772863056202, 5.203350469079247, 4.684053711370366, 4.0182643937998845, 3.229551844081289, 2.3457596369665037, 1.3979497534890148, 0.41920111205485544, -0.5566886101380747, -1.4965432031765844, -2.3691321587846788, -3.1464201223716897, -3.80468478602348, -4.325451231536578, -4.696198157782011, -4.910801219143279, -4.969690457622473, -4.879712009727995, -4.653698294860737, -4.309765062326016, -3.870367273499362, -3.361158111284061, -2.8097057692247907, -2.244130484783972, -1.6917290666648686, -1.1776555904809864, -0.7237248346708399, -0.3473994174175861, -0.06101268349786307, 0.12873242885183533, 0.22096247236448022, 0.22052025171997058, 0.13754559159549098, -0.013227031337208853, -0.21341559972690666, -0.4421303540559831, -0.6772432326835316, -0.8967162642202213, -1.0799144258171787, -1.208828824030963, -1.2691406024028906, -1.2510645550158415, -1.1499236133285213, -0.9664205388646685, -0.7065904710474464, -0.38143647491506605, -0.006268841583057681, 0.40021348325226197, 0.8170453964177531, 1.2222555616448934, 1.5941885382764585, 1.9128095891939723, 2.1609131027336965, 2.325160841253627, 2.396886086051759, 2.3726136574371286, 2.254262959552217, 2.0490206206203827, 1.7688897956921374, 1.4299435018856992, 1.051328180751415, 0.6540798092326822, 0.25982723522447965, -0.11053486075761848, -0.4381184576193948, -0.7071781615189877, -0.9060369798518342, -1.0277414590001734, -1.07040311018696, -1.0372034843693676, -0.9360624665508215, -0.7789918975400185, -0.5811779968682346, -0.3598547972863425, -0.13304559407682726, 0.08174081901223026, 0.26876837723151165, 0.41519788901867616, 0.5119969136470813, 0.5545692682854826, 0.543057006285469, 0.4822903134656179, 0.38138553982227064, 0.25301683600297137, 0.11241083258468386, -0.023865238331850953, -0.1392351874343481, -0.21846794895643812, -0.2489529949810578, -0.22179942891186868, -0.1326717328210967, 0.01770760114632776, 0.22343548821896542, 0.4737057100350183, 0.7534771857205684, 1.0444943671865954, 1.3265935094003596, 1.5792049717731922, 1.7829439353590442, 1.9211714739197898, 1.9814058209220082, 1.9564703875945348, 1.8452804458377847, 1.653193596828525, 1.39187880387629, 1.078692955945524, 0.7355903214196586, 0.38762627326976984, 0.061149664401141814, -0.21819433332286123, -0.42750947807358064, -0.5485902728942172, -0.5696094495395969, -0.4864119568427161, -0.3032987467614471, -0.03321565827856625, 0.3026976614812428, 0.6761991382629953, 1.0536295140553984, 1.398099475288971, 1.672045738709017, 1.8399899610221186, 1.8713116016085645, 1.7428356862388992, 1.4410400616504864, 0.9637045221658685, 0.32085545385239067, -0.46509729081213674, -1.360082286298799, -2.3199400286844685, -3.2927807185567763, -4.222001080352658, -5.049783427405949, -5.720858938681317, -6.186289474854297, -6.407010692934844, -6.3568851338721455, -6.0250375811720795, -5.417285298555613, -4.556530512850479, -3.482048378946543, -2.2476764153154587, -0.9189861768229989, 0.4304104148925437, 1.7232042244660504, 2.88311512081832, 3.839701055417944, 4.532935606602461, 4.9172465250248445, 4.964735939333873, 4.667350786124005, 4.0378368722117015, 3.109387657356744, 1.9339842591781262, 0.57951056780868, -0.874189308258925, -2.340070623793366, -3.729165736429864, -4.956042402238657, -5.944088791129768, -6.630279112612423, -6.969105219321857, -6.935412886367437, -6.525953175797771, -5.759544563774785, -4.675834488109313, -3.332743207255542, -1.8027617370290585, -0.16835286098972504, 1.4832357077056517, 3.065398309947147, 4.497476387999993, 5.709590436310382, 6.6466831451271595, 7.271515449293405, 7.5664324321088765, 7.53380362180575], 'positive_zeros': ['0.74712520427779293049359071043112', '1.62427717701669106561410556519010', '2.79777535135361529284954269598910', '4.08842349534311842685138679787725', '5.12268696289500800055779870207271', '6.34397721532183717445105786044343', '6.61671312441268628995401131953367', '7.38374377854596774315812180517236', '8.360827733947179507965142659579476', '9.059052696551416850029426786354451'], 'prelabel': '2-2535-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.499119570804336, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74712520427779293049359071043', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62427717701669106561410556519', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79777535135361529284954269599', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 20.242076912394587, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 2535, 'conductor_radical': 195, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2535/2/a/bb/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-2535-1.1-c1-0-19', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2535-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.499119570804336, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74712520427779293049359071043', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '947093713648382713231381362143', 'Lhash_array': ['947093713648382713231381362143'], 'factors': ['2-2535-1.1-c1-0-19'], 'label': '2-2535-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2535/2/a/bb/1/1'}