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lfunc_lfunctions • Show schema
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{'Lhash': '2376302831686517699928499163953', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.0], 'a4': [0.0, 0.0], 'a5': [0.0, -2.23606797749979], 'a6': [0.0, 0.0], 'a7': [0.0, 2.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8328192970214605, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 2.23606797749979]]]], 'bad_primes': [2, 3, 5], 'central_character': '480.289', 'coefficient_field': 'CDF', 'conductor': 480, 'conductor_radical': 30, 'conjugate': '1144396350298381638710302721899', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [11.0, 0]], [[1.0, 0], [0, 4.47213595499958], [-13.0, 0]], [[1.0, 0], [0, 4.47213595499958], [-17.0, 0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [0, 4.0], 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'2-480-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9577587433137569, 'root_angle': 0.5, 'root_number': '6.123233995736766e-17 + 1.0*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.87457240288348000810015451236', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.75372778525713033668020913087', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98415373856896940226694788275', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8328192970214605, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 480, 'conductor_radical': 30, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/480/2/f/e/289/1'], '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': '2-480-5.4-c1-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-480-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9577587433137569, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.87457240288348000810015451236', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2376302831686517699928499163953', 'Lhash_array': ['2376302831686517699928499163953'], 'label': '2-480-5.4-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/480/2/f/e/289/1'}