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lfunc_lfunctions • Show schema
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{'Lhash': '7189764571995482347197712198138', 'a10': [-5.925721866121337, 10.263651343644016], 'a2': [-2.1794791952299817, -2.597402160899668], 'a3': [-2.9995764293505154, -0.050410757629817476], 'a4': [-1.3017757123382154, 7.382736930603614], 'a5': [-1.1954673313999307, -3.284519498716985], 'a6': [6.406577411471406, 7.900975496848707], 'a7': [-1.8871775513116444, -10.702715737144397], 'a8': [10.26751243376312, -5.927951067540967], 'a9': [8.994917511030376, 0.3024218407442043], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7356967137728017, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.9995764293505154, 0.050410757629817476]]]], 'bad_primes': [3], 'central_character': '27.5', 'coefficient_field': 'CDF', 'conductor': 27, 'conductor_radical': 3, 'conjugate': '1008359471598525707428181267579', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1794791952299817, 2.597402160899668], [-0.6945927106677214, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.67172418859031670886391691590', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.57036893846826254802442919311', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.189162651482107326984126588893', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7356967137728017, 'bad_primes': [3], 'central_character': '27.5', 'conductor': 27, 'conductor_radical': 3, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/27/3/f/a/5/1'], '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': '2-3e3-27.5-c2-0-4', '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': '2-3e3-27.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.857727645452099, 'root_angle': 0.4709864618414916, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '5.67172418859031670886391691590', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '7189764571995482347197712198138', 'Lhash_array': ['7189764571995482347197712198138'], 'label': '2-3e3-27.5-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/27/3/f/a/5/1'}