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lfunc_lfunctions • Show schema
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{'Lhash': '1644487036324362184909432945401', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.2880328179513119, -0.8864738619749495], 'a4': [0.0, 0.0], 'a5': [-2.568530281262384, 1.866146483806693], 'a6': [0.0, 0.0], 'a7': [-0.7800718906750053, -2.4008144157436377], 'a8': [0.0, 0.0], 'a9': [1.724177979377034, 1.2526886278677654], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.56744299561724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-3.315688636495371, -0.07879635661291445]]], [13, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [2, 11, 13], 'central_character': '572.521', 'coefficient_field': 'CDF', 'conductor': 572, 'conductor_radical': 286, 'conjugate': '1244133957478999323424145471268', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.2880328179513119, 0.8864738619749495], [-2.4270509831248424, -1.7633557568774194]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '3.96044163952308804232723937324', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.56744299561724, 'bad_primes': [2, 11, 13], 'central_character': '11.4', 'conductor': 572, 'conductor_radical': 286, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/572/2/n/b/521/4'], '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': '2-572-11.4-c1-0-6', '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': '2-572-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1371576908635546, 'root_angle': 0.09999782111067208, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29727153209905527560966275640', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1644487036324362184909432945401', 'Lhash_array': ['1644487036324362184909432945401'], 'label': '2-572-11.4-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/572/2/n/b/521/4'}