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lfunc_lfunctions • Show schema
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{'Lhash': '3591324849739290794279384209530', 'a10': [-1.511034585954068, 2.6171886748662474], 'a2': [-0.6782328502098008, -1.174733755925627], 'a3': [1.1139497191021142, -1.929417510561941], 'a4': [0.0800004017925797, -0.13856476053067232], 'a5': [-1.1139497191021142, -1.929417510561941], 'a6': [-3.022069171908136, 4.450986508811298e-61], 'a7': [2.609267034371289, 0.43786475462550967], 'a8': [-2.9299670029420457, 0.0], 'a9': [-0.9817679533753585, -1.7004719764890337], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.291706538010748, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-2.609267034371289, -0.43786475462550967]]], [41, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 41], 'central_character': '287.165', 'coefficient_field': 'CDF', 'conductor': 287, 'conductor_radical': 287, 'conjugate': '1505463519188383834320421656919', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6782328502098008, 1.174733755925627], [-1.0, 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'8.514020884142501271913062939796469', '9.091816622472562791868659249791708', '10.23507117813507083181903811375955', '11.20657267513683344248015043038944', '11.83905430778535620895465396541375'], 'prelabel': '2-287-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5138383460629963, 'root_angle': 0.9064292090550871, 'root_number': '-0.9571036148729587 + 0.2897458720967655*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.453214604528', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.83305577190805113889428931608', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.88448479431798720993026874451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.10080870315216375890931933431', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.291706538010748, 'bad_primes': [7, 41], 'central_character': '7.4', 'conductor': 287, 'conductor_radical': 287, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/287/2/e/c/165/2'], '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': '2-287-7.4-c1-0-22', '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': '2-287-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5138383460629963, 'root_angle': 0.45321460452754353, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.83305577190805113889428931608', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3591324849739290794279384209530', 'Lhash_array': ['3591324849739290794279384209530'], 'label': '2-287-7.4-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/287/2/e/c/165/2'}