-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1886248032697649829754210889177', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.0774219157468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '5520.1', 'coefficient_field': 'CDF', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [7.0, 0]], [[1.0, 0], [-6.242640687119285, 0], [11.0, 0]], [[1.0, 0], [2.585786437626905, 0], [13.0, 0]], [[1.0, 0], [1.5857864376269049, 0], [17.0, 0]], [[1.0, 0], [7.0710678118654755, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [7.242640687119285, 0], [29.0, 0]], [[1.0, 0], [0.6568542494923802, 0], [31.0, 0]], [[1.0, 0], [3.0, 0], [37.0, 0]], [[1.0, 0], [4.414213562373095, 0], [41.0, 0]], [[1.0, 0], [2.0, 0], [43.0, 0]], [[1.0, 0], [2.585786437626905, 0], [47.0, 0]], [[1.0, 0], [3.585786437626905, 0], [53.0, 0]], [[1.0, 0], [2.071067811865475, 0], [59.0, 0]], [[1.0, 0], [13.071067811865476, 0], [61.0, 0]], [[1.0, 0], [-0.6568542494923802, 0], [67.0, 0]], [[1.0, 0], [-12.071067811865476, 0], [71.0, 0]], [[1.0, 0], [15.556349186104045, 0], [73.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [79.0, 0]], [[1.0, 0], [1.9289321881345247, 0], [83.0, 0]], [[1.0, 0], [5.17157287525381, 0], [89.0, 0]], [[1.0, 0], [6.82842712474619, 0], [97.0, 0]], [[1.0, 0], [-11.242640687119286, 0], [101.0, 0]], [[1.0, 0], [6.48528137423857, 0], [103.0, 0]], [[1.0, 0], [-5.242640687119285, 0], [107.0, 0]], [[1.0, 0], [-18.384776310850235, 0], [109.0, 0]], [[1.0, 0], [9.242640687119286, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 77, 'label': '2-5520-1.1-c1-0-77', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/5520/2/a/bk/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.0750501979039414e-60, 0.17864464399865687, 0.3564201910977644, 0.5324228983737632, 0.7056822826452829, 0.8751339483498867, 1.0395993681361384, 1.1977741901422807, 1.348226123179277, 1.4894029128388202, 1.6196504104322935, 1.7372402821971635, 1.8404065238102294, 1.92738963804307, 1.9964870957979544, 2.046108522563598, 2.0748339222855385, 2.0814731590397106, 2.065124856962171, 2.025232847234145, 1.961638287262063, 1.8746256036447109, 1.7649604707334166, 1.6339181348622351, 1.4833005347974002, 1.3154408549547132, 1.133194381446216, 0.9399148123074448, 0.7394155006093056, 0.5359154787370772, 0.33397051792002885, 0.13838991099724035, -0.04585988169817383, -0.21376312544191697, -0.36037219454837455, -0.4809319684360598, -0.5710083705297225, -0.6266178404307968, -0.6443542574729682, -0.6215096431845188, -0.5561848741489709, -0.4473866461489786, -0.29510705362258094, -0.10038239064928765, 0.13467185726292505, 0.4068523794053038, 0.7118877182352241, 1.0444875168243204, 1.3984218071371413, 1.766629956205516, 2.1413579853318176, 2.5143220537732653, 2.876894981061148, 3.2203118011930396, 3.5358895283784055, 3.81525559877386, 4.050578865575988, 4.2347965936000005, 4.361830648382875, 4.4267860238124666, 4.426125015772622, 4.357810735463444, 4.221414266014558, 4.01818059329575, 3.7510494721210024, 3.424628600130778, 3.045117833688645, 2.6201846562359252, 2.1587926565848066, 1.670986344384251, 1.1676371705656337, 0.6601570780089531, 0.1601872277592479, -0.32072932365076917, -0.7714813286800497, -1.1817191582704123, -1.542170147257881, -1.8449289579350145, -2.083712854334396, -2.254072552526672, -2.3535504378641505, -2.3817793959695894, -2.340517254570836, -2.2336138297022865, -2.066909752616321, -1.8480685534584331, -1.5863458171228328, -1.2923015232494448, -0.9774638511682867, -0.6539546875318013, -0.33408873907775294, -0.02995945224895157, 0.24697418764266998, 0.4862855120884425, 0.6789483333255429, 0.8176617171491538, 0.8971188372890706, 0.9142090577747014, 0.8681445216144803, 0.7605050513088766, 0.5951980084470049, 0.3783328196173428, 0.11801304534210241, -0.17594796977225882, -0.49237879597649115, -0.8191571170485367, -1.1436581683345954, -1.4532282184626144, -1.7356655317330454, -1.9796905224124022, -2.175386778680006, -2.3145953178967176, -2.39124583347146, -2.4016107753475207, -2.3444708107132297, -2.22118345118656, -2.0356502946617825, -1.7941822800980372, -1.5052664409326402, -1.1792417055426527, -0.8278951644262756, -0.46399373859025156, -0.10076918591252067, 0.24862326838184462, 0.5716508127101874, 0.856930860103915, 1.094718409063847, 1.2773317146779182, 1.3994970917536156, 1.4585965962640812, 1.4548060228541804, 1.3911149823586728, 1.2732256205667933, 1.1093316184692288, 0.9097842671206111, 0.686657419042824, 0.4532277636604812, 0.22339094581197663, 0.011037350915525716, -0.17058624829233596, -0.3095016815506291, -0.395583352062309, -0.4210745752399873, -0.38101189997161183, -0.2735363804054695, -0.10007513194859428, 0.13461827735652826, 0.4225701829771304, 0.7528392344282322, 1.1119077449682804, 1.4841985758026883, 1.852698275002273, 2.199662002371187, 2.507371518429433, 2.7589144141503734, 2.9389509788744466, 3.034434763658064, 3.035254051966685, 2.9347640893926656, 2.7301839722168237, 2.422837408706471, 2.0182229433801333, 1.525906415542579, 0.9592361079153844, 0.3348888965420645, -0.327736610339603, -1.007256810309312, -1.6811403078039602, -2.326611057635794, -2.9215792576164312, -3.4455597600780323, -3.8805375036041028, -4.211741020700677, -4.428288426470096, -4.523675326116481, -4.496080603257129, -4.348473800684573, -4.088516451222583, -3.728258879839811, -3.28364326728079, -2.7738327135568115, -2.220394245185925, -1.6463707766350573, -1.0752826119916554, -0.5301028676818947, -0.03225299874830648, 0.3993357030469605, 0.7490512266048603, 1.005281682981012, 1.1609153913126598, 1.2136357626052614, 1.165995837404573, 1.0252674857544744, 0.8030708111323098, 0.5147997178489856, 0.17886940316682076, -0.1841797593240438, -0.5526803062771349, -0.9048908335430066, -1.2200542194804378, -1.4794102259393518, -1.6671135143826352, -1.7710122443330658, -1.7832487810144124, -1.7006523505362787, -1.5249033650352175, -1.2624601333730228, -0.9242502489932148, -0.5251405411781179, -0.08321051464700725, 0.3811358712485229, 0.8461769285768049, 1.2899490725970422, 1.6913385156588976, 2.031134361350359, 2.292990141072966, 2.464245022057566, 2.536562609229434, 2.5063541569248384, 2.3749636770193074, 2.148604356997405, 1.8380482919462224, 1.4580841522630463, 1.0267694066970467, 0.5645144728624636, 0.09304510396491678, -0.36570404416159547, -0.7907077608671081, -1.162922592384656, -1.4662571267513747, -1.6883891642272661, -1.8213863123428584, -1.8620965305951611, -1.8122870003431204, -1.678522810538241, -1.4717906536178091, -1.2068863008256436, -0.9015973509279329, -0.5757239333929153, -0.24998908050183344, 0.05510314821598596, 0.3204003777271419, 0.5291639861054128, 0.6680022912779646, 0.7276230373327295, 0.7033626596601094, 0.595461522012854, 0.4090678488987646, 0.15396771638714482, -0.15594656513365776, -0.5034428504272188, -0.8689102971848913, -1.231463993809358, -1.5701332801006482, -1.865068577899732, -2.0986996687611663, -2.256780138306897], 'positive_zeros': ['1.48798733054522071923383153399903', '2.03660463170726851993443952445145', '3.39035498720159624891161968549261', '4.27045187131788394301113708874079', '4.80062121280810881805876208081219', '5.73200606517624761887001746110080', '6.47135976633997813671930328080396', '6.81829885701393525496777589447406', '7.71143626023053175143171229733890'], 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48798733054522071923383153400', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03660463170726851993443952445', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39035498720159624891161968549', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 44.0774219157468, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 5520, 'conductor_radical': 690, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5520/2/a/bk/1/2'], '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': '2-5520-1.1-c1-0-77', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.639082912251269, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48798733054522071923383153400', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1886248032697649829754210889177', 'Lhash_array': ['1886248032697649829754210889177'], 'label': '2-5520-1.1-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5520/2/a/bk/1/2'}