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lfunc_lfunctions • Show schema
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{'Lhash': '1265197727538988863411458442132,1830209885788809573412768752640', 'a10': -2, 'a2': 2, 'a3': -1, 'a4': 3, 'a5': -1, 'a6': -2, 'a7': 0, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.14677389390195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, 1, 1]], [5, [1, 1, 1]], [31, [1, -4, 31]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.1', 'coefficient_field': '1.1.1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 1, 1], [1, 1, 1], [1, 0, -7, 0, 49], [1, -1, -10, -11, 121], [1, -6, 23, -78, 169], [1, -1, -16, -17, 289], [1, 4, -3, 76, 361], [1, -14, 95, -322, 529], [1, -12, 94, -348, 841], [1, -4, 31], [1, 7, 12, 259, 1369], [1, -2, -37, -82, 1681], [1, -7, 6, -301, 1849], [1, -6, 103, -282, 2209], [1, -4, -37, -212, 2809], [1, 12, 85, 708, 3481], [1, 28, 318, 1708, 3721], [1, 5, -42, 335, 4489], [1, 6, -35, 426, 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1.2818508206758663, 0.4615105396672705], 'positive_zeros': ['0.998065024629973811541892675766274', '1.44378102724780495009563903982675', '2.68314329674674070251577371413170', '3.00785757185597485027405220046088', '3.46724156998708297664841128707685', '4.21290607583222055117696661273154', '4.59919520368904898218184099729587', '4.75764642334540718625258009648018', '5.65169968243665552542141871900027', '5.80717677167120521784200319954860', '6.47854961586060048717879920478124', '6.52919672020546172684816452614821', '7.20575726398531714710647108545364', '7.48284618114923384848553218494342', '8.151449732357854426048694566240275', '8.681136048549815276933184667396563', '8.938021436634257134779824726231020', '9.265983887851629742557743782328496', '10.38358508955195293006385249304299', '10.45078034470625065355973118829835'], 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1840509271140137679, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.998065024629973811541892675766', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.44378102724780495009563903983', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.68314329674674070251577371413', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.14677389390195, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, 2, -1, 3, -1, -2, 0, 4, 0, -2, 1, -3, 6, 0, 1, 5, 1, 0, -4, -3, 0, 2, 14, -4, 0, 12, 1, 0, 12, 2, 4, 6, -1, 2, 0, 0, -7, -8, -6, -4, 2, 0, 7, 3, 0, 28, 6, -5, 7, 0, -1, 18, 4, 2, -1, 0, 4, 24, -12, 3, -28, 8, 0, 7, -6, -2, -5, 3, -14, 0, -6, 0, -2, -14, 0, -12, 0, -12, -3, -5, -1, 4, -16, 0, -1, 14, -12, 4, 8, 0, 0, 42, -4, 12, 4, -6, -12, 14, 0, 0], 'euler11': [1, -1, -10, -11, 121], 'euler13': [1, -6, 23, -78, 169], 'euler17': [1, -1, -16, -17, 289], 'euler19': [1, 4, -3, 76, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -14, 95, -322, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 1, 1, 0, 0], 'euler31': [1, -4, 31, 0, 0], 'euler37': [1, 7, 12, 259, 1369], 'euler41': [1, -2, -37, -82, 1681], 'euler43': [1, -7, 6, -301, 1849], 'euler47': [1, -6, 103, -282, 2209], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, -4, -37, -212, 2809], 'euler59': [1, 12, 85, 708, 3481], 'euler61': [1, 28, 318, 1708, 3721], 'euler67': [1, 5, -42, 335, 4489], 'euler7': [1, 0, -7, 0, 49], 'euler71': [1, 6, -35, 426, 5041], 'euler73': [1, 2, -69, 146, 5329], 'euler79': [1, 3, -70, 237, 6241], 'euler83': [1, 16, 173, 1328, 6889], 'euler89': [1, -8, 194, -712, 7921], 'euler97': [1, 12, 230, 1164, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 1, 1, 0, 0], [1, 1, 1, 0, 0], [1, 0, -7, 0, 49], [1, -1, -10, -11, 121], [1, -6, 23, -78, 169], [1, -1, -16, -17, 289], [1, 4, -3, 76, 361], [1, -14, 95, -322, 529], [1, -12, 94, -348, 841], [1, -4, 31, 0, 0], [1, 7, 12, 259, 1369], [1, -2, -37, -82, 1681], [1, -7, 6, -301, 1849], [1, -6, 103, -282, 2209], [1, -4, -37, -212, 2809], [1, 12, 85, 708, 3481], [1, 28, 318, 1708, 3721], [1, 5, -42, 335, 4489], [1, 6, -35, 426, 5041], [1, 2, -69, 146, 5329], [1, 3, -70, 237, 6241], [1, 16, 173, 1328, 6889], [1, -8, 194, -712, 7921], [1, 12, 230, 1164, 9409]], 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/i/e'], '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': '4-930e2-1.1-c1e2-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1840509271140137679, 'z1': {'__RealLiteral__': 0, 'data': '0.998065024629973811541892675766', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1265197727538988863411458442132,1830209885788809573412768752640', 'Lhash_array': ['1265197727538988863411458442132', '1830209885788809573412768752640'], 'label': '4-930e2-1.1-c1e2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/i/e'}