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lfunc_lfunctions • Show schema
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{'Lhash': '2035009362119840577124742912432', 'a10': [0.0, 0.0], 'a2': [3.1220825543686352, 4.2971779820514495], 'a3': [5.963929276941217, 1.9377980890182767], 'a4': [-6.246203178135205, 19.223836691198464], 'a5': [0.0, 0.0], 'a6': [10.292816269235809, 31.67803118299666], 'a7': [0.0, -9.636018005118958], 'a8': [-61.69632422425634, 20.046350925632268], 'a9': [9.969932138430115, 7.24357969989691], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.37523875071758, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]]], 'bad_primes': [5], 'central_character': '125.74', 'coefficient_field': 'CDF', 'conductor': 125, 'conductor_radical': 5, 'conjugate': '4149709023769680449560096772421', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.1220825543686352, -4.2971779820514495], [-2.4721359549995796, 7.608452130361228]], [[1.0, 0], [-5.963929276941217, -1.9377980890182767], [21.843458848123582, 15.870201811896775]], [[1.0, 0], 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'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70362074289415435153519405033', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82912426266088561053983294640', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.37523875071758, 'bad_primes': [5], 'central_character': '25.14', 'conductor': 125, 'conductor_radical': 5, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/125/4/e/b/74/14'], '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': '2-5e3-25.14-c3-0-10', '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': '2-5e3-25.14-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7157390800144223, 'root_angle': -0.3941592075476776, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60533932753509124927822306906', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2035009362119840577124742912432', 'Lhash_array': ['2035009362119840577124742912432'], 'label': '2-5e3-25.14-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/125/4/e/b/74/14'}