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lfunc_lfunctions • Show schema
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{'Lhash': '843837647133455970858737753180', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.29114601204887913, 0.5042796852897191], 'a4': [0, 0], 'a5': [0, -1.688165411011704], 'a6': [0, 0], 'a7': [-0.8660254037844386, 0.5], 'a8': [0, 0], 'a9': [1.330467999336068, 2.304438172694585], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.62621853429843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-1.8012432279477526, -3.1233832351750177]]]], 'bad_primes': [2, 7, 13], 'central_character': '1456.225', 'coefficient_field': 'CDF', 'conductor': 1456, 'conductor_radical': 182, 'conjugate': '1577631761486908012283118016918', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.29114601204887913, -0.5042796852897191], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 1.688165411011704], [-5.0, 0]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], 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'8.527323834645394598509367718827286', '9.552702270136097936375980756012250'], 'prelabel': '2-1456-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': -0.3372590432362068, 'root_number': '0.4892815704428650919618237424418473051027840962854245249 - 0.8721258767087258286526446376141133017801023890964347325*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.16862952161810338', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66567053017726681481662773492', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16299073063294698636216958086', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41910141972432898384396565164', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.62621853429843, 'bad_primes': [2, 7, 13], 'central_character': '13.4', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1456/2/cc/c/225/3'], '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': '2-1456-13.4-c1-0-9', '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': '2-1456-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': -0.1686295216181034, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66567053017726681481662773492', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '843837647133455970858737753180', 'Lhash_array': ['843837647133455970858737753180'], 'label': '2-1456-13.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1456/2/cc/c/225/3'}