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lfunc_lfunctions • Show schema
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{'Lhash': '567172051962440813342051604407', 'a10': [-1.0685316697713623, -1.850751141540409], 'a2': [0.5, 0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-2.1370633395427245, 0], 'a6': [-0.5, 0.8660254037844386], 'a7': [-0.024458669761152657, 0.04236365871186494], 'a8': [-1.0, 0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.096830764957835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '1014.991', 'coefficient_field': 'CDF', 'conductor': 1014, 'conductor_radical': 78, 'conjugate': '2617617715909529504453694133930', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [2.1370633395427245, 0], [5.0, 0]], [[1.0, 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'8.705676288825512239072287658961303', '9.361884223350330692580462276775109'], 'prelabel': '2-1014-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 0.9571820145637041, 'root_number': '-0.99096626719860455186375397613639199912587964733274165501 + 0.1341113614667448233689954170275991839576864280300208693*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4785910072818521', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44741985832714980520524067479', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86821030736969631949843729010', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46427778106207052608353915587', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.096830764957835, 'bad_primes': [2, 3, 13], 'central_character': '13.3', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1014/2/e/n/991/2'], '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': '2-1014-13.3-c1-0-4', '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': '2-1014-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 0.47859100728185205, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44741985832714980520524067479', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '567172051962440813342051604407', 'Lhash_array': ['567172051962440813342051604407'], 'label': '2-1014-13.3-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1014/2/e/n/991/2'}