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lfunc_lfunctions • Show schema
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{'Lhash': '624011664930152308339936948782', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 8.369636098671585], 'a6': [0, 0], 'a7': [0, 2.4390964670987256], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.084589681459306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1728.1567', 'coefficient_field': 'CDF', 'conductor': 1728, 'conductor_radical': 6, 'conjugate': '2062634126783179628141144055052', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -8.369636098671585], [-25.0, 0]], [[1.0, 0], [0, -2.4390964670987256], [-49.0, 0]], [[1.0, 0], [-2.412946285525965, 0], [121.0, 0]], [[1.0, 0], [0, -20.884269290438013], [-169.0, 0]], [[1.0, 0], [13.17934556246557, 0], [289.0, 0]], [[1.0, 0], [-32.79764891672925, 0], [361.0, 0]], [[1.0, 0], [0, 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'2.65085370093428803966547081304', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.084589681459306, 'bad_primes': [2, 3], 'central_character': '8.3', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/3/b/i/1567/12'], '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': '2-12e3-8.3-c2-0-18', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-12e3-8.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.861821163616792, 'root_angle': -0.45833333333333337, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49225840686527065640907329717', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '624011664930152308339936948782', 'Lhash_array': ['624011664930152308339936948782'], 'label': '2-12e3-8.3-c2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/3/b/i/1567/12'}