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lfunc_lfunctions • Show schema
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{'Lhash': '5450122558043496245889212543677', 'a10': [0.0, 19.11010273249461], 'a2': [0.0, -3.0454748755547754], 'a3': [0.0, -1.7320508075688772], 'a4': [-5.274917217635375, 0.0], 'a5': [-6.274917217635375, 0.0], 'a6': [-5.274917217635375, 0.0], 'a7': [12.274917217635375, 0.0], 'a8': [0.0, 3.882728354720734], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5531375068536926, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.7320508075688772]]], [19, [[1.0, 0], [-7.54983443527075, -17.435595774162696]]]], 'bad_primes': [3, 19], 'central_character': '57.37', 'coefficient_field': 'CDF', 'conductor': 57, 'conductor_radical': 57, 'conjugate': '1621916259303053866494996062935', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 3.0454748755547754], [-4.0, 0]], [[1.0, 0], [0, 1.7320508075688772]], [[1.0, 0], [6.274917217635375, 0], [25.0, 0]], [[1.0, 0], [-12.274917217635375, 0], [49.0, 0]], [[1.0, 0], 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['4.29938861470364890416464825219569', '5.24489624718865330608606822678280', '7.19656061476251659370600715078642', '8.031676185563881664076279202166845', '8.999869473752230897751361533189167', '11.09344555195370457874892071452468', '11.80692615019403898550036843073676', '13.96540824083863286578772865298245', '14.72300263131676798033107809626228', '15.40734100412113252571816446618231'], 'prelabel': '2-57-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.246249375868928, 'root_angle': 0.869926530853497, 'root_number': '-0.917662935482247 + 0.39735970711951324*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.434963265427', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.29938861470364890416464825220', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.24489624718865330608606822678', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.19656061476251659370600715079', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5531375068536926, 'bad_primes': [3, 19], 'central_character': '19.18', 'conductor': 57, 'conductor_radical': 57, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/57/3/c/b/37/1'], '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': '2-57-19.18-c2-0-5', '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': '2-57-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.246249375868928, 'root_angle': 0.4349632654267485, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '4.29938861470364890416464825220', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5450122558043496245889212543677', 'Lhash_array': ['5450122558043496245889212543677'], 'label': '2-57-19.18-c2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/57/3/c/b/37/1'}