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lfunc_lfunctions • Show schema
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{'Lhash': '886854537662185871178644967876', 'a10': [1.795795857266113, 1.3323352577432854], 'a2': [0.5, 0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, 0.8660254037844386], 'a5': [2.0517341081964293, -0.8890372035316649], 'a6': [0, 0], 'a7': [0.9708349950330258, 2.461194712414933], 'a8': [-1.0, 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], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0517341081964293, 0.8890372035316649]]], [7, [[1.0, 0], [-0.9708349950330258, -2.461194712414933]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1890.89', 'coefficient_field': 'CDF', 'conductor': 1890, 'conductor_radical': 210, 'conjugate': '2206112622329580472742870823561', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0517341081964293, 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'2.94633909342826653354997487011571', '3.82411611724576511721409041627444', '4.82942299366562545848330272187126', '5.66624388100748107882898100963425', '6.42532486260136752581099983951816', '7.26996327892094416781145577991293', '8.275016358147726109978328395168808', '9.106953830567870120080570406821809'], 'prelabel': '2-1890-315.299-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': -0.7051036918368331, 'root_number': '-0.60068069674899173100811810432556113793553767736815223403 - 0.79948902466084288009055628110919766416788687503550168605*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.35255184591841654', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69960487337955385312250281207', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93193660672603627770485381003', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94633909342826653354997487012', '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': '315.299', 'conductor': 1890, 'conductor_radical': 210, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1890/2/r/b/89/22'], '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': '2-1890-315.299-c1-0-12', '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': '2-1890-315.299-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': -0.35255184591841654, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69960487337955385312250281207', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '886854537662185871178644967876', 'Lhash_array': ['886854537662185871178644967876'], 'label': '2-1890-315.299-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1890/2/r/b/89/22'}