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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -3, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 6, 'Lhash': '264869700384339372', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.7320508075688774, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'algebraic': True, 'analytic_conductor': 425.6984632558502, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [17, [1, 1]]], 'bad_primes': [2, 7, 17], 'central_character': '53312.1', 'coefficient_field': '1.1.1.1', 'conductor': 53312, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[1], [1, 3, 3], [1, 2, 5], [1], [1, -5, 11], [1, -7, 13], [1, 1], [1, -2, 19], [1, 0, 23], [1, 6, 29], [1, -4, 31], [1, -8, 37], [1, -2, 41], [1, -8, 43], [1, 10, 47], [1, -3, 53], [1, 0, 59], [1, 12, 61], [1, -2, 67], [1, 1, 71], [1, 2, 73], [1, 13, 79], [1, 4, 83], [1, 15, 89], [1, 0, 97]], 'gamma_factors': [[], [0]], 'index': 8, 'label': '2-53312-1.1-c1-0-8', 'leading_term': '1.14631748771', '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': 0, 'origin': 'EllipticCurve/Q/53312/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.146317487712889, 0.7992682929706496, -0.03283357749641599, -0.7431860139085253, -0.6596890243981423, 0.1750215744249303, 0.5092044081962493, -1.34167583146512, -5.619497157159982, -9.96903558747209, -10.84956104916168, -6.864158044148511, -0.654106875674082, 3.253035849389292, 2.859109249876864, 0.4452711059983843, -0.5647576245388221, 0.20438500234307, 0.2300837753115417, -1.766719837505651, -3.669458231800594, -3.013916835815439, -0.7014870801094228, 0.3601992515344277, -0.3488254959685363, -0.5369522481351624, 0.6327452538214147, 0.8674127835413112, -1.008027341802884, -2.02705047414377, 0.5008977407608204, 3.617432353964045, 2.277889584280296, -2.345353344193741, -3.490989779822923, 1.050711411744767, 5.011491686132797, 3.063596292465035, -0.9473819812354667, -0.2907002088626495, 4.042156793005789, 5.513443673557304, 2.564715203435349, -0.1020428815809046, -0.00515802335641367, 0.4329986618436233, -0.0624949208421012, 0.1959705893841726, 0.8430725830639721, -0.4936543342625342, -2.31745682283759, -0.800310078416909, 2.07932584350744, 0.5466626946137458, -3.675716109893613, -2.318450547805307, 4.727845435817623, 7.112597044355685, 0.7466802776901375, -4.996515252954027, -2.740368635099629, 1.863582540421924, 1.643072453808855, -0.70398229204127, -0.4418085180885268, 0.3292077957697174, -0.8881451969982772, -1.275565276668488, 0.3370390584593942, 0.2715860410066656, -1.820217936369944, -1.638696813502316, 0.4835785564619351, 0.07041555519511997, -1.399082256560928, 0.7245946338809026, 3.187217369341985, 0.3862268053001921, -2.932265890568503, 0.2066741197422002, 4.199873352218715, 0.7358221592214147, -4.354417779193197, -1.553641758184074, 4.2463433503688, 3.531218724874627, -0.2919177388078139, 0.5113299329162214, 3.126812677668525, 2.06008662959472, -0.01875438543378268, 0.08264938713985831, 0.03567968344667446, -0.4458317019970077, 1.079793787766929, 2.23584408485886, 0.478587000827129, 0.1015417677496217, 2.420742566434316, 0.4929720964567562, -5.267972910058427, -3.810493838195228, 4.598621724568536, 5.68987780338686, -2.116214822902115, -4.228967557346096, 2.432928334065864, 5.476963418320861, 1.658302887386527, -0.4968076474827402, 0.5707068090399211, 0.3000000813920887, -0.1565544791832262, 0.7756948541339413, -0.005756459633503217, -1.31380632567825, 1.040396457547989, 3.380358240614328, 1.288152627740934, 0.08986785237914964, 2.915775522433446], 'positive_zeros': ['0.4908803065005152', '1.202075266593297', '1.614990594337569', '3.029294025145286', '3.808607094170241', '4.195544060627674', '4.544755224516389', '5.601527727791619', '5.906035185035232', '6.379334569687012', '6.885755664443868', '7.466230780190200', '8.124099181997970', '8.703741667261129', '9.424140621796663', '9.770032551632455', '10.73030889333012', '11.00159868955627', '11.46619402404985', '11.68407657194448', '12.19285541378714', '12.80974630849655', '13.28173239879062', '13.83980860034422', '14.52302527754722', '15.12995498189707', '15.65624377193516', '16.08637543379455', '16.35182096150471', '16.94762369424323', '17.28707965690687', '17.93118505539623', '18.25923262636849', '18.69749837358867', '19.27037838562021', '19.74057862303950'], 'prelabel': '2-53312-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.63246139596171, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 264869700384339372, 'z1': {'__RealLiteral__': 0, 'data': '0.4908803065005152', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.202075266593297', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.614990594337569', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 425.6984632558502, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 53312, 'conductor_radical': 238, 'degree': 2, 'dirichlet_coefficients': [1, 0, -3, 0, -2, 0, 0, 0, 6, 0, 5, 0, 7, 0, 6, 0, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, -9, 0, -6, 0, 4, 0, -15, 0, 0, 0, 8, 0, -21, 0, 2, 0, 8, 0, -12, 0, -10, 0, 0, 0, 3, 0, 3, 0, -10, 0, -6, 0, 0, 0, -12, 0, 0, 0, -14, 0, 2, 0, 0, 0, -1, 0, -2, 0, 3, 0, 0, 0, -13, 0, 9, 0, -4, 0, 2, 0, 18, 0, -15, 0, 0, 0, -12, 0, -4, 0, 0, 0, 30, 0], 'euler11': [1, -5, 11], 'euler13': [1, -7, 13], 'euler17': [1, 1, 0], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 3, 3], 'euler31': [1, -4, 31], 'euler37': [1, -8, 37], 'euler41': [1, -2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 10, 47], 'euler5': [1, 2, 5], 'euler53': [1, -3, 53], 'euler59': [1, 0, 59], 'euler61': [1, 12, 61], 'euler67': [1, -2, 67], 'euler7': [1, 0, 0], 'euler71': [1, 1, 71], 'euler73': [1, 2, 73], 'euler79': [1, 13, 79], 'euler83': [1, 4, 83], 'euler89': [1, 15, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, 0, 0], [1, 3, 3], [1, 2, 5], [1, 0, 0], [1, -5, 11], [1, -7, 13], [1, 1, 0], [1, -2, 19], [1, 0, 23], [1, 6, 29], [1, -4, 31], [1, -8, 37], [1, -2, 41], [1, -8, 43], [1, 10, 47], [1, -3, 53], [1, 0, 59], [1, 12, 61], [1, -2, 67], [1, 1, 71], [1, 2, 73], [1, 13, 79], [1, 4, 83], [1, 15, 89], [1, 0, 97]], 'index': 8, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/53312/c'], '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': '2-53312-1.1-c1-0-8', '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': '2-53312-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.63246139596171, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 264869700384339372, 'z1': {'__RealLiteral__': 0, 'data': '0.4908803065005152', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '264869700384339372', 'Lhash_array': ['264869700384339372'], 'label': '2-53312-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/53312/c'}