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lfunc_lfunctions • Show schema
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{'Lhash': '1440598678937963334604483858733', 'a10': [0.0, 0.0], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.0, 0.0], 'a6': [0.30901699437494745, -0.9510565162951535], 'a7': [1.618033988749895, -1.1755705045849463], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.797139186744959, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [3, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 11], 'central_character': '726.511', 'coefficient_field': 'CDF', 'conductor': 726, 'conductor_radical': 66, 'conjugate': '1371402620037856977344931312383', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.30901699437494745, 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'positive_zeros': ['1.13643197792719550989874134069017', '2.65106637520017102663001367327418', '3.83518993371636689364007079745602', '4.83519058430739381297876480849093', '5.67652766325058390640449832940083', '6.51595497315274371819400239302803', '8.106281515319968784669713522478107', '8.555134410757491799142193076658191', '9.776817584972162389607369622924539', '10.54840296141053349207030373624172'], 'prelabel': '2-726-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.407724898476767, 'root_angle': -0.15573357186974024, 'root_number': '0.8826849005956153 - 0.4699652819735822*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0778667859349', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13643197792719550989874134069', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65106637520017102663001367327', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83518993371636689364007079746', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.797139186744959, 'bad_primes': [2, 3, 11], 'central_character': '11.5', 'conductor': 726, 'conductor_radical': 66, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/726/2/e/b/511/1'], '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': '2-726-11.5-c1-0-9', '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': '2-726-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.407724898476767, 'root_angle': -0.07786678593487012, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13643197792719550989874134069', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1440598678937963334604483858733', 'Lhash_array': ['1440598678937963334604483858733'], 'label': '2-726-11.5-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/726/2/e/b/511/1'}