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lfunc_lfunctions • Show schema
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{'Lhash': '641240871173582206355348703090', 'a10': [0.0, 0.0], 'a2': [2.6457513110645907, 0.0], 'a3': [0.0, 0.0], 'a4': [-25.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-150.80782473068166, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.72926453752447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.6457513110645907, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [799.0168959415064, 0], [161051.0, 0]], [[1.0, 0], [0, 0], [371293.0, 0]], [[1.0, 0], [0, 0], [1419857.0, 0]], [[1.0, 0], [0, 0], [2476099.0, 0]], [[1.0, 0], [1105.924048024999, 0], [6436343.0, 0]], [[1.0, 0], [-5386.749669327506, 0], [20511149.0, 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'8.281773270098613762436877864159427', '9.576159980438837808377951025932858', '10.19291046148522459549216267901509'], 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.50584985409870227403924018514', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36312681513080519248858569483', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44330473172198677993418964807', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 70.72926453752447, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/o/1/2'], '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': '2-21e2-1.1-c5-0-11', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-21e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.50584985409870227403924018514', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '641240871173582206355348703090', 'Lhash_array': ['641240871173582206355348703090'], 'label': '2-21e2-1.1-c5-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/o/1/2'}