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lfunc_lfunctions • Show schema
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{'Lhash': '2923628621593195822414166001436', 'a10': [0.0, 0.0], 'a2': [0.28790208998275774, 0.28790208998275774], 'a3': [0.0, 0.0], 'a4': [0.0, -7.83422477316712], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-15.055689894034646, 15.055689894034646], 'a8': [4.558706405451572, -4.558706405451572], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.143', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '111650356290071881115042425624', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.28790208998275774, -0.28790208998275774], [0, 8.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [15.055689894034646, -15.055689894034646], [0, -343.0]], [[1.0, 0], [0, 27.999235898287978], [-1331.0, 0]], [[1.0, 0], [2.4986201357696967, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/f/c/143/4'], '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': '2-15e2-15.8-c3-0-17', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-15.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.4901474575797399, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30633632096006743832357387893', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2923628621593195822414166001436', 'Lhash_array': ['2923628621593195822414166001436'], 'label': '2-15e2-15.8-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/f/c/143/4'}