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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '1076094449241794909', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 91.02945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [19, [1, -1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '11400.1', 'coefficient_field': '1.1.1.1', 'conductor': 11400, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 4, 7], [1, 4, 11], [1, 2, 13], [1, -6, 17], [1, -1], [1, 4, 23], [1, -6, 29], [1, -8, 31], [1, 10, 37], [1, -2, 41], [1, 0, 43], [1, -4, 47], [1, 2, 53], [1, 12, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, -8, 79], [1, 0, 83], [1, -2, 89], [1, -18, 97]], 'gamma_factors': [[], [0]], 'index': 13, 'label': '2-11400-1.1-c1-0-13', 'leading_term': '2.92153325762', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/11400/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.6752969419131626, 1.006083065065689, 0.6453072279392206, -0.5579279228320959, -2.278237264943603, -3.677253384920779, -3.818687195049308, -2.370090942527407, -0.05263739718925508, 1.689453803985446, 1.759070213649348, 0.4135976305996941, -0.7913905097093789, -0.322709237242185, 1.808658763659947, 3.853044732446984, 3.892184893338405, 1.783871701245022, -0.5591196687967428, -1.053098542287232, 0.3878857374461935, 1.821635112244159, 1.55323487141705, 0.1412162552043664, -0.336003386323422, 1.001841061407683, 2.521258064733524, 2.058581830562602, -0.1130588407323546, -1.295907317243643, 0.2228121125486999, 2.582815431541735, 2.286411758140254, -1.342785722018108, -4.879197222023771, -4.714701762133772, -1.392746163595256, 1.260857206710735, 1.051730463137857, -0.2379373205401431, -0.1012345007669158, 0.7326139972970905, -0.4816341389034577, -3.870478809703825, -5.960233184596904, -4.231227268435571, -0.7033672167633979, 0.8697274765957156, 0.1664784554952978, 0.1187350763078627, 1.804563162736256, 2.563126879723059, 0.5102665175825376, -1.782319657677586, -0.9127323458880623, 1.591562777812055, 0.8273392040647234, -4.087907278672115, -7.940568145138366, -6.399406468158513, -1.890741197479842, 0.3330577456553938, -0.3827556425030511, -0.4914007481258366, 1.119191609170237, 1.589934349649255, -0.2125398335947297, -1.122572198398803, 0.9092947845256375, 2.753910985940936, 0.967651181677459, -2.256135603355842, -2.4057845119605, 0.01444375946910105, 0.5947727957527889, -1.296851298639651, -1.67751724936766, 0.4664354854860683, 0.7612353331779418, -2.839112673217625, -5.491458074397481, -2.817001183212764, 1.760241382863298, 2.397134900328385, 0.0893771795225767, 0.2445588403642599, 3.180776218753012, 4.045123429731227, 1.588883412431008, -0.09412806846677331, 0.7105657089548021, 0.8294009370537406, -0.9094718151575197, -1.158297965391038, 0.9179198044305491, 0.903914459296342, -2.832406131040784, -4.963946488702017, -1.883794257727319, 1.653227051330028, 0.3992018883193736, -2.629505358135262, -2.082062559780179, 0.2394384952715205, -0.3303837004475764, -1.945283582428825, 0.06040922721947042, 3.408311509510886, 2.138993654948643, -2.499987567693039, -3.844856593564397, -1.185783929128652, 0.02243432620285834, -1.477613176681253, -1.605143106727745, 0.1859198212287754, 0.3074968205242581, -0.842858534963507, 0.3588866942954531, 2.159042523818414], 'positive_zeros': ['0.9032030126911798', '2.255779237560669', '3.066735105885855', '3.549034555925662', '4.677312664455673', '5.196724598123839', '6.028958502859256', '6.345316735899821', '7.237215747963065', '7.727535585087895', '8.421743605633587', '9.353274329805021', '9.939898910230539', '10.27631316119146', '10.69966815276558', '11.81565798307224', '12.30394185028904', '12.46569084741741', '13.29380798663411', '13.83516789509485', '14.30430282881790', '15.41310250708560', '15.66156535838854', '16.09058896603410', '16.72459004527026', '17.16558339967452', '17.81902540964816', '18.49832782934785', '18.84350675007897', '19.44846239814561', '19.82337202323454'], 'prelabel': '2-11400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.540935923915415, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1076094449241794909, 'z1': {'__RealLiteral__': 0, 'data': '0.9032030126911798', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.255779237560669', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.066735105885855', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 91.02945830425968, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 11400, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -4, 0, 1, 0, -4, 0, -2, 0, 0, 0, 6, 0, 1, 0, 4, 0, -4, 0, 0, 0, -1, 0, 6, 0, 8, 0, 4, 0, 0, 0, -10, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 9, 0, -6, 0, -2, 0, 0, 0, -1, 0, -12, 0, -2, 0, -4, 0, 0, 0, -4, 0, 4, 0, 0, 0, 14, 0, 0, 0, 16, 0, 8, 0, 1, 0, 0, 0, 0, 0, -6, 0, 2, 0, 8, 0, -8, 0, 0, 0, 18, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -2, 41], 'euler43': [1, 0, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -2, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 4, 7], [1, 4, 11], [1, 2, 13], [1, -6, 17], [1, -1, 0], [1, 4, 23], [1, -6, 29], [1, -8, 31], [1, 10, 37], [1, -2, 41], [1, 0, 43], [1, -4, 47], [1, 2, 53], [1, 12, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, -8, 79], [1, 0, 83], [1, -2, 89], [1, -18, 97]], 'index': 13, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/11400/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-11400-1.1-c1-0-13', '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': '2-11400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.540935923915415, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1076094449241794909, 'z1': {'__RealLiteral__': 0, 'data': '0.9032030126911798', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1076094449241794909', 'Lhash_array': ['1076094449241794909'], 'label': '2-11400-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/11400/a'}