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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '658498164139086886', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 115.94278373489918, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [11, [1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '14520.1', 'coefficient_field': '1.1.1.1', 'conductor': 14520, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, 4, 7], [1], [1, 2, 13], [1, 1, 17], [1, 0, 19], [1, 1, 23], [1, -6, 29], [1, -1, 31], [1, -4, 37], [1, 2, 41], [1, -2, 43], [1, -9, 47], [1, -9, 53], [1, 6, 59], [1, 1, 61], [1, -4, 67], [1, 0, 71], [1, 4, 73], [1, -11, 79], [1, 8, 83], [1, 16, 89], [1, -16, 97]], 'gamma_factors': [[], [0]], 'index': 28, 'label': '2-14520-1.1-c1-0-28', 'leading_term': '4.48930799091', '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/14520/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.055953514323888, 1.693215703691296, 1.477998693664615, 0.2029714517632026, -1.775700272249704, -3.512531453352875, -3.981363105759274, -2.861832394512275, -0.9446480179738158, 0.3673813382234348, 0.2252201702991291, -0.8510003133980917, -1.431702974653712, -0.6660368785989269, 0.6743504674936069, 0.8971577010510031, -0.6402884882697016, -2.423802973191853, -2.10660997974622, 0.8204585780498055, 4.009344061383111, 4.448217982010095, 1.746756382840608, -1.28669641591349, -1.734275899616277, 0.1549599873197995, 1.496232621365929, 0.5304989810738302, -1.154765205781317, -0.891962803770693, 1.282290913860311, 2.516722475397022, 1.028417390486797, -1.344101509935556, -1.630537643861786, 0.1203170506586055, 1.004231557283403, -0.3854423980581636, -1.845571944335246, -1.054614443015339, 0.4873154994515678, -0.5828038991935668, -4.045088731363582, -5.499044544459835, -2.313408877621305, 2.266902487467298, 3.252578206316696, 0.6132604207139997, -1.216074823082481, -0.1103132457132182, 1.064732131052286, -0.3249912917584477, -2.238189555921544, -1.515985697214209, 0.5630462366290344, 0.1857814426018659, -2.534479831399027, -3.364163395837765, -0.7094740869533767, 1.749107017207457, 1.022794874838001, -0.5666160509206238, 0.1668088955388805, 1.611846057062738, 0.5261369895348549, -1.521817730986971, -0.3746982273483154, 2.911628754158232, 2.624409937667201, -2.281236075440997, -5.503366389415646, -2.737073800064615, 1.79438401256193, 2.221693275037899, -0.2513462008764421, -0.7452133845799117, 0.869998884305918, 1.126388957194975, 0.06864119289683836, 0.4872939852408678, 1.357006306744074, -0.8918167835028936, -4.788026642736174, -4.820642617278389, -0.8280421113989884, 1.053038197524722, -1.42217927119111, -3.104722293720431, -0.9559668099078783, 0.7607958601492667, -1.060078801130471, -2.352419063189668, 0.214458217696427, 2.436475613820361, 0.2315070681465248, -2.361152107372484, -0.2435770826024488, 3.401393951434989, 2.845374757895374, -0.142833724159335, -0.3888674694500075, 1.039404149084778, -0.03938314293046477, -2.178727095417947, -1.497059819374731, 0.19674900546596, -0.7089774601363916, -1.622474718222583, 1.224589339550573, 4.039694086558219, 1.552232237744829, -2.510932548495935, -1.421716411897914, 2.409928638645133, 2.195991066726422, -0.698050297512213, -0.4366058942605992, 1.370261280151309, -0.6440755360031004, -4.059849695917694], 'positive_zeros': ['1.028429802759306', '2.400814799071766', '2.810997302640359', '3.618393721916394', '4.168720849202068', '4.942288334938795', '5.878293297397137', '6.482080328672738', '7.069967507902970', '7.613670495150595', '8.349211894375810', '8.983896701475094', '9.450710354551090', '10.14663897222992', '10.43931662579830', '11.36633380221514', '12.05350883421954', '12.51492882266002', '12.96409080894604', '13.66907185614693', '14.02118269431416', '14.80341821704175', '15.38375326183576', '15.72554237574642', '16.30465939752909', '16.77951971846361', '17.39636637430543', '18.13649537949153', '18.72168734968759', '19.12156260342140', '19.78475707441745', '19.86192545907518'], 'prelabel': '2-14520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.767673088225663, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 658498164139086886, 'z1': {'__RealLiteral__': 0, 'data': '1.028429802759306', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.400814799071766', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.810997302640359', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 115.94278373489918, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 14520, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, -4, 0, 1, 0, 0, 0, -2, 0, -1, 0, -1, 0, 0, 0, -4, 0, -1, 0, 1, 0, 1, 0, 6, 0, 1, 0, 0, 0, 4, 0, 4, 0, -2, 0, -2, 0, 2, 0, -1, 0, 9, 0, 9, 0, -1, 0, 9, 0, 0, 0, 0, 0, -6, 0, -1, 0, -4, 0, 2, 0, 4, 0, -1, 0, 0, 0, -4, 0, 1, 0, 0, 0, 11, 0, 1, 0, -8, 0, 1, 0, 6, 0, -16, 0, 8, 0, 1, 0, 0, 0, 16, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, 1, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -1, 31], 'euler37': [1, -4, 37], 'euler41': [1, 2, 41], 'euler43': [1, -2, 43], 'euler47': [1, -9, 47], 'euler5': [1, 1, 0], 'euler53': [1, -9, 53], 'euler59': [1, 6, 59], 'euler61': [1, 1, 61], 'euler67': [1, -4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 4, 73], 'euler79': [1, -11, 79], 'euler83': [1, 8, 83], 'euler89': [1, 16, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 4, 7], [1, 0, 0], [1, 2, 13], [1, 1, 17], [1, 0, 19], [1, 1, 23], [1, -6, 29], [1, -1, 31], [1, -4, 37], [1, 2, 41], [1, -2, 43], [1, -9, 47], [1, -9, 53], [1, 6, 59], [1, 1, 61], [1, -4, 67], [1, 0, 71], [1, 4, 73], [1, -11, 79], [1, 8, 83], [1, 16, 89], [1, -16, 97]], 'index': 28, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/14520/y'], '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': '2-14520-1.1-c1-0-28', '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': '2-14520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.767673088225663, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 658498164139086886, 'z1': {'__RealLiteral__': 0, 'data': '1.028429802759306', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '658498164139086886', 'Lhash_array': ['658498164139086886'], 'label': '2-14520-1.1-c1-0-28', 'type': 'ECQ', 'url': 'EllipticCurve/Q/14520/y'}