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lfunc_lfunctions • Show schema
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{'Lhash': '2405510755666412895853501775203', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.1214045738709872, 0], 'a4': [0, 0], 'a5': [2.022926507169695, -0.9527687791852844], 'a6': [0, 0], 'a7': [0, -1.0], 'a8': [0, 0], 'a9': [1.500357366040744, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.943245026383407, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.022926507169695, 0.9527687791852844]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '1120.1009', 'coefficient_field': 'CDF', 'conductor': 1120, 'conductor_radical': 70, 'conjugate': '148075274335630517921856240196', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.1214045738709872, 0], [3.0, 0]], [[1.0, 0], [-2.022926507169695, 0.9527687791852844]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 5.198340483479325], [-11.0, 0]], [[1.0, 0], [6.027258983603086, 0], [13.0, 0]], [[1.0, 0], [0, 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'4.74224833582811275957779313160446', '5.04272569674119299818642554662085', '5.99531967625293970568286480088539', '6.98969001126051096319324599515889', '7.26364280355705571954504796387073', '8.868877923515095394744292613575271', '9.736596991525132520504217764413041', '10.17267723493528080473981689747208'], 'prelabel': '2-1120-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9905258778989703, 'root_angle': -0.9615135289051957, 'root_number': '-0.99269942963429194895994599392843600094202043612923497905 - 0.1206144369623779634795594235765330964477099188670010723*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.48075676445259785', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89761339223388663017382954200', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80277571510824551552089755583', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74224833582811275957779313160', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.943245026383407, 'bad_primes': [2, 5, 7], 'central_character': '40.29', 'conductor': 1120, 'conductor_radical': 70, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1120/2/l/a/1009/8'], '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': '2-1120-40.29-c1-0-33', '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': '2-1120-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9905258778989703, 'root_angle': -0.48075676445259785, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89761339223388663017382954200', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2405510755666412895853501775203', 'Lhash_array': ['2405510755666412895853501775203'], 'label': '2-1120-40.29-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1120/2/l/a/1009/8'}