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lfunc_lfunctions • Show schema
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{'Lhash': '412045125853538847498258553993', 'a10': [1.3019377358048383, 2.2550223067051656], 'a2': [-1.5605238552448022, 0.9009688679024191], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.6234898018587335, -1.0799160148203788], 'a5': [0.0, -1.445041867912629], 'a6': [1.5605238552448022, 0.9009688679024191], 'a7': [-2.983493774713331, -1.7225209339563143], 'a8': [0.0, -1.3568958678922094], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5, 0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.361', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '1435692397893734695627757802544', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5605238552448022, -0.9009688679024191], [1.0, -1.7320508075688772]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 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'9.869340557792317176827965824936097', '10.43979743715989082986777808361106'], 'prelabel': '2-507-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.5666299940653012, 'root_number': '-0.2077989966862352 - 0.9781715478259394*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.283314997033', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32504629097272838986612676365', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63226929964739974845627542132', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19717104586340876490429707256', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '13.10', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/j/h/361/1'], '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': '2-507-13.10-c1-0-1', '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': '2-507-13.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.2833149970326506, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.32504629097272838986612676365', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '412045125853538847498258553993', 'Lhash_array': ['412045125853538847498258553993'], 'label': '2-507-13.10-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/j/h/361/1'}