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lfunc_lfunctions • Show schema
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{'Lhash': '2275865427076174853293007312719', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -2.449489742783178], 'a4': [0.0, 0.0], 'a5': [2.224744871391589, -0.22474487139158905], 'a6': [0.0, 0.0], 'a7': [0.0, 1.0], 'a8': [0.0, 0.0], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.471622513191703, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.224744871391589, 0.22474487139158905]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '560.449', 'coefficient_field': 'CDF', 'conductor': 560, 'conductor_radical': 70, 'conjugate': '1546655333576839914963692035957', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.449489742783178], [-3.0, 0]], [[1.0, 0], [-2.224744871391589, 0.22474487139158905]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [0, 4.449489742783178], [-13.0, 0]], [[1.0, 0], 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'7.19258741600170091374277019536078', '8.914828962261676706959211472869474', '9.353093546516759192468927062866628', '9.853759264125817213968967314347207', '10.94804752328113704417831773015747'], 'prelabel': '2-560-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.114621127576215, 'root_angle': 0.4679528915755125, 'root_number': '0.10050896200520829 + 0.9949361530051241*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.233976445788', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79534126096451592561920406277', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.48738172840794368963940001970', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29419513522135571983399784796', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.471622513191703, 'bad_primes': [2, 5, 7], 'central_character': '5.4', 'conductor': 560, 'conductor_radical': 70, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/560/2/g/e/449/2'], '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': '2-560-5.4-c1-0-12', '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': '2-560-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.114621127576215, 'root_angle': 0.23397644578775625, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79534126096451592561920406277', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2275865427076174853293007312719', 'Lhash_array': ['2275865427076174853293007312719'], 'label': '2-560-5.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/560/2/g/e/449/2'}