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lfunc_lfunctions • Show schema
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{'Lhash': '2104996123805644506565061042741', 'a10': [-30.45342254553497, 0.0], 'a2': [-4.084806558564545, 0.0], 'a3': [0.0, 0.0], 'a4': [8.685644620891926, 0.0], 'a5': [7.455291238133123, 0.0], 'a6': [0.0, 0.0], 'a7': [34.02371257863265, 0.0], 'a8': [-2.8007256442638413, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.33001421304828, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [59, [[1.0, 0], [59.0, 0]]]], 'bad_primes': [3, 59], 'central_character': '531.1', 'coefficient_field': 'CDF', 'conductor': 531, 'conductor_radical': 177, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.084806558564545, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.455291238133123, 0], [125.0, 0]], [[1.0, 0], [-34.02371257863265, 0], [343.0, 0]], [[1.0, 0], [30.101406945842328, 0], [1331.0, 0]], [[1.0, 0], [5.30716817095149, 0], [2197.0, 0]], [[1.0, 0], [63.25060434248879, 0], [4913.0, 0]], [[1.0, 0], 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'6.60671314280134095457151977687401', '7.73977567604736657454602598700937', '8.255888463660043470429432861740645', '8.977802618602611659320196089004945', '9.994841998406878244326588079640438'], 'prelabel': '2-531-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5973220572920654, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66054914771204176326416849112', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.19286466322148765262118060720', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41326524051808771235073567869', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.33001421304828, 'bad_primes': [3, 59], 'central_character': '1.1', 'conductor': 531, 'conductor_radical': 177, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/531/4/a/e/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': '2-531-1.1-c3-0-56', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-531-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5973220572920654, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66054914771204176326416849112', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2104996123805644506565061042741', 'Lhash_array': ['2104996123805644506565061042741'], 'label': '2-531-1.1-c3-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/531/4/a/e/1/2'}