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lfunc_lfunctions • Show schema
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{'Lhash': '646388888030308781201530856614', 'a10': [0.05080493543267335, 0.0], 'a2': [-0.4259834557676498, 0.0], 'a3': [-1.3720546666784519, 0.0], 'a4': [-1.8185380954122508, 0.0], 'a5': [-0.11926504361799584, 0.0], 'a6': [0.5844725884138178, 0.0], 'a7': [-3.280173698555509, 0.0], 'a8': [1.6266340538641302, 0.0], 'a9': [-1.1174659916458825, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.4259834557676498, 0], [2.0, 0]], [[1.0, 0], [1.3720546666784519, 0], [3.0, 0]], [[1.0, 0], [0.11926504361799584, 0], [5.0, 0]], [[1.0, 0], [3.280173698555509, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'3.46520608857083429664680969706438', '4.33209164865023032238149313957069', '5.16467853933406600594679054964549', '5.79991369079355510936634132299825', '6.28698976777962491923458231385538', '7.13629058311567530115280262898174', '7.80601113092381438169887504129063'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50991092333639262770974482686', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29584275218500611756979290573', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95330179640996663809943546021', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 107, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/35'], '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': '2-8041-1.1-c1-0-107', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50991092333639262770974482686', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '646388888030308781201530856614', 'Lhash_array': ['646388888030308781201530856614'], 'label': '2-8041-1.1-c1-0-107', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/35'}