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lfunc_lfunctions • Show schema
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{'Lhash': '796166531796106449188580245591', 'a10': [1515768282.471858, -982591482.4109682], 'a2': [-429.6270427901572, 278.50422636539014], 'a3': [0, -11363.985348459404], 'a4': [107014.79179323107, -239305.89435584616], 'a5': [-3528102.590162615, 0], 'a6': [3164917.947900315, 4882275.419569287], 'a7': [0, 38415566.23177818], 'a8': [20671254.43932247, 132616355.51238307], 'a9': [-129140163.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.646336525171634, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '9.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [429.6270427901572, -278.50422636539014]]], [3, [[1.0, 0], [0, 11363.985348459404]]]], 'bad_primes': [2, 3], 'central_character': '12.7', 'coefficient_field': 'CDF', 'conductor': 12, 'conductor_radical': 6, 'conjugate': '451280525130243397542109388247', 'degree': 2, 'euler_factors': [[[1.0, 0], [429.6270427901572, -278.50422636539014]], [[1.0, 0], [0, 11363.985348459404]], [[1.0, 0], [3528102.590162615, 0], 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'3.21617149273350670897417601184245', '4.24235465867724776669794026118723', '7.35613133604403223626615840205683', '8.311268350433390301959059847582851', '10.13608267949179571806935624917934', '11.27784308877552964323246734647933', '12.35660095793707763533337524084860', '14.67479208604173224258633654471891', '16.25252150787800626568958809987550'], 'prelabel': '2-12-4.3-c18-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.964507682053845, 'root_angle': 0.1338535217492071, 'root_number': '0.91287954084719148018848570155049405631364727718707699606 + 0.4082290336350672422975221272425745863115134638832469773*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.06692676087460356', 'prec': 64}, 'spectral_label': 'c18-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62806465097935001158389181037', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21617149273350670897417601184', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24235465867724776669794026119', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.646336525171634, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 12, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/12/19/d/a/7/4'], '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': '2-12-4.3-c18-0-7', 'motivic_weight': 18, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [18], 'order_of_vanishing': 0, 'prelabel': '2-12-4.3-c18-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.964507682053845, 'root_angle': 0.06692676087460354, 'self_dual': False, 'spectral_label': 'c18-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62806465097935001158389181037', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '796166531796106449188580245591', 'Lhash_array': ['796166531796106449188580245591'], 'label': '2-12-4.3-c18-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/12/19/d/a/7/4'}