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lfunc_lfunctions • Show schema
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{'Lhash': '911129692431787598458766803508', 'a10': [0.8660254037844386, -0.5], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [0.5, 0.8660254037844386], 'a6': [0, 0], 'a7': [1.557786119072034, 2.138528093625728], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [-1.557786119072034, -2.138528093625728]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1890.341', 'coefficient_field': 'CDF', 'conductor': 1890, 'conductor_radical': 210, 'conjugate': '1704248522095398184136981565565', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-1.557786119072034, -2.138528093625728]], [[1.0, 0], [-3.9070096099717837, -2.255713050043664], [5.5, 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'8.249632789969274027121794264485374', '9.149275433866624961534107789405043'], 'prelabel': '2-1890-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': -0.14057614985599304, 'root_number': '0.90405489818364382943217131441958788616484298609669135238 - 0.4274163556418511565649376771924023812340302610307148765*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07028807492799652', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71875459394548203397654172336', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93211667788885855949287438221', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62571325379199063149293074293', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.091725982022, 'bad_primes': [2, 3, 5, 7], 'central_character': '63.5', 'conductor': 1890, 'conductor_radical': 210, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1890/2/bk/b/341/2'], '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': '2-1890-63.5-c1-0-10', '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': '2-1890-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': -0.07028807492799652, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71875459394548203397654172336', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '911129692431787598458766803508', 'Lhash_array': ['911129692431787598458766803508'], 'label': '2-1890-63.5-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1890/2/bk/b/341/2'}