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lfunc_lfunctions • Show schema
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{'Lhash': '2860897225127538879356492353627', 'a10': [43166922325.924095, 0.0], 'a2': [1937.9551395599815, 0.0], 'a3': [59049.0, 0.0], 'a4': [1658518.1229469478, 0.0], 'a5': [22274469.33354983, 0.0], 'a6': [114434313.03587735, 0.0], 'a7': [47820541.31785039, 0.0], 'a8': [-850052776.4200836, 0.0], 'a9': [3486784401.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.384320328611864, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[3, [[1.0, 0], [-59049.0, 0]]]], 'bad_primes': [3], 'central_character': '3.1', 'coefficient_field': 'CDF', 'conductor': 3, 'conductor_radical': 3, 'conjugate': '2860897225127538879356492353627', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1937.9551395599815, 0], [2097152.0, 0]], [[1.0, 0], [-59049.0, 0]], [[1.0, 0], [-22274469.33354983, 0], [476837158203125.0, 0]], [[1.0, 0], [-47820541.31785039, 0], [558545864083284030, 0]], [[1.0, 0], [-160110646361.6561, 0], [7400249944258161000000, 0]], [[1.0, 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'13.89971987886233398034241738487488', '14.78307903655031106595731429575358', '17.32901364553384648815509377693767', '19.75672159148241859643238816433837', '21.49544547100370862712309988849735'], 'prelabel': '2-3-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955690854496745, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25684997475839112161469020857', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.31001648806194752940832954182', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.34537009998925288438717855760', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.384320328611864, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 3, 'conductor_radical': 3, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3/22/a/c/1/2'], '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': '2-3-1.1-c21-0-2', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-3-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955690854496745, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25684997475839112161469020857', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2860897225127538879356492353627', 'Lhash_array': ['2860897225127538879356492353627'], 'label': '2-3-1.1-c21-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3/22/a/c/1/2'}