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lfunc_lfunctions • Show schema
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{'Lhash': '962847621853444514658263046515', 'a10': [0.0, 0.0], 'a2': [8.36252341815129, 0.0], 'a3': [-9.0, 0.0], 'a4': [37.93179791912876, 0.0], 'a5': [0.0, 0.0], 'a6': [-75.26271076336162, 0.0], 'a7': [-15.441855973118246, 0.0], 'a8': [49.604799010455395, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-8.36252341815129, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [15.441855973118246, 0], [16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [-624.6729281339625, 0], [371293.0, 0]], [[1.0, 0], [-1254.3520543320221, 0], [1419857.0, 0]], [[1.0, 0], [440.2389608152234, 0], 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['0.75955284656520670844282224018551', '2.15634080463039490484642105593329', '3.44965101974111980330366583631228', '3.99207671484462203538640404724547', '5.34500810197405329966102069561841', '5.52858544417441578111448505962508', '6.60503692101893645253158161233917', '7.35780623072521411782596052685584', '8.615459619425008304995493106160293', '9.569941112119286135522374947483093'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75955284656520670844282224019', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15634080463039490484642105593', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44965101974111980330366583631', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 55, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/s/1/8'], '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': '2-825-1.1-c5-0-55', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75955284656520670844282224019', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '962847621853444514658263046515', 'Lhash_array': ['962847621853444514658263046515'], 'label': '2-825-1.1-c5-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/s/1/8'}