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lfunc_lfunctions • Show schema
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{'Lhash': '1479954026487357632515556911535', 'a10': [10.0, 0.0], 'a2': [2.0, 0.0], 'a3': [0.0, 0.0], 'a4': [4.0, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [17.167759120351846, 0.0], 'a8': [8.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.79154710464992, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '810.1', 'coefficient_field': 'CDF', 'conductor': 810, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-17.167759120351846, 0], [343.0, 0]], [[1.0, 0], [-47.59708049452575, 0], [1331.0, 0]], [[1.0, 0], [12.51318338676054, 0], [2197.0, 0]], [[1.0, 0], [123.48209001639464, 0], [4913.0, 0]], [[1.0, 0], [-65.95241078663945, 0], [6859.0, 0]], [[1.0, 0], [-181.8915291488014, 0], [12167.0, 0]], 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'4.67238184083870327413801107069136', '5.11605839421456370660276338239066', '6.55080477288104078978003305036540', '6.85288790106442133106756688155531', '8.195902054235912042670536165511141', '9.000283204818785577195294664917928', '9.854236795401271995640674465468576'], 'prelabel': '2-810-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.913143069881451, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16747787302029822436520771987', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20379222792637822805658460049', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45486600850490984795400454158', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.79154710464992, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 810, 'conductor_radical': 30, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/810/4/a/v/1/3'], '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': '2-810-1.1-c3-0-24', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-810-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.913143069881451, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16747787302029822436520771987', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1479954026487357632515556911535', 'Lhash_array': ['1479954026487357632515556911535'], 'label': '2-810-1.1-c3-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/810/4/a/v/1/3'}