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lfunc_lfunctions • Show schema
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{'Lhash': '244006712256192031830974814152', 'a10': [-7240589332736219.0, 5848817927901667.0], 'a2': [8626.629171793276, 8626.629171793276], 'a3': [98911029.9249818, -98911029.9249818], 'a4': [0, -17031031722.26473], 'a5': [-80667163101.50812, 758662914562.0792], 'a6': [1706537552325.9314, 0], 'a7': [110847966661370.8, 110847966661370.8], 'a8': [295124755751312.3, -295124755751312.3], 'a9': [0, -2889601981974722.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.612827021342156, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '17.0', 'prec': 14}, 'bad_lfactors': [[5, [[1.0, 0], [80667163101.50812, -758662914562.0792]]]], 'bad_primes': [5], 'central_character': '5.2', 'coefficient_field': 'CDF', 'conductor': 5, 'conductor_radical': 5, 'conjugate': '2333239753491084264481678189796', 'degree': 2, 'euler_factors': [[[1.0, 0], [-8626.629171793276, -8626.629171793276], [0, 17179869184.0]], [[1.0, 0], [-98911029.9249818, 98911029.9249818], [0, -16677181699666568]], 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0.9014692530196299386425457225844703344353533163554664836*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3212448024519525', 'prec': 64}, 'spectral_label': 'c34-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19248735591042260209229275586', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42877056733720794014044835067', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84403109956904798396832792088', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.612827021342156, 'bad_primes': [5], 'central_character': '5.2', 'conductor': 5, 'conductor_radical': 5, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5/35/c/a/2/8'], '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': '2-5-5.2-c34-0-1', 'motivic_weight': 34, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [34], 'order_of_vanishing': 0, 'prelabel': '2-5-5.2-c34-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.050853412647026, 'root_angle': -0.3212448024519525, 'self_dual': False, 'spectral_label': 'c34-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19248735591042260209229275586', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '244006712256192031830974814152', 'Lhash_array': ['244006712256192031830974814152'], 'label': '2-5-5.2-c34-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5/35/c/a/2/8'}