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lfunc_lfunctions • Show schema
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{'Lhash': '2093839634810456003867085621834', 'a10': [-3.1500895785280623, 0.27737275866403394], 'a2': [-1.3276737598821062, -0.4871164001760888], 'a3': [0.39681389370788306, 0.39681389370788306], 'a4': [1.525435225358977, 1.293463325044049], 'a5': [2.023589227491228, -0.9513604145545762], 'a6': [-0.3335448387897624, -0.7201339496754446], 'a7': [0.4771034312147997, -0.4771034312147997], 'a8': [-1.3952131224537094, -2.460361831709509], 'a9': [0.0, -2.685077467520778], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3276737598821062, 0.4871164001760888]]], [5, [[1.0, 0], [-2.023589227491228, 0.9513604145545762]]], [13, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.27', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '1757023094623362758362616496392', 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0.15776829578733145, 'root_number': '0.8796627406325925 + 0.47559800540241565*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0788841478937', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65174822970420910460536596641', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97450702457495152303342134628', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.39230722563172931758504175585', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '20.7', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/o/a/27/5'], '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': '2-260-20.7-c1-0-13', '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': '2-260-20.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.07888414789366573, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65174822970420910460536596641', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2093839634810456003867085621834', 'Lhash_array': ['2093839634810456003867085621834'], 'label': '2-260-20.7-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/o/a/27/5'}