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lfunc_lfunctions • Show schema
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{'Lhash': '1626926919201164058586892358624', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8223733742970273, 1.8007465064456785], 'a4': [0.0, 0.0], 'a5': [0.6548607339452851, -0.7557495743542583], 'a6': [0.0, 0.0], 'a7': [0.9096319953545183, -0.5845849869981136], 'a8': [0.0, 0.0], 'a9': [-1.9115292797783527, -2.2060223871643743], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9182796232447245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.6548607339452851, 0.7557495743542583]]], [23, [[1.0, 0], [-0.9898214418809327, 0.14231483827328514]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1199', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '1363138470459113638405633732474', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.8223733742970273, -1.8007465064456785], [-0.6548607339452851, -0.7557495743542583]], [[1.0, 0], 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['1.28341904220946221199591964011377', '2.15322099495091424901022504415413', '2.93152000439744461002475282390692', '4.95312728390143487465532094050028', '5.44947851288468000673011513075358', '6.50780388156842258647322958562315', '6.64838445398247445233824243028953', '7.80543764084296498491718221891600', '8.160986520672252969594802446944504', '9.236853943375714677388401141860442'], 'prelabel': '2-1840-460.279-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9582690766401285, 'root_angle': -0.21556644518540904, 'root_number': '0.77931652786956142820918015719380 - 0.62663047275833233751399722004542*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10778322259270451', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28341904220946221199591964011', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15322099495091424901022504415', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93152000439744461002475282391', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9182796232447245, 'bad_primes': [2, 5, 23], 'central_character': '460.279', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/1/bq/a/1199/1'], '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': '2-1840-460.279-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1840-460.279-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9582690766401285, 'root_angle': -0.10778322259270452, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28341904220946221199591964011', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1626926919201164058586892358624', 'Lhash_array': ['1626926919201164058586892358624'], 'label': '2-1840-460.279-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/1/bq/a/1199/1'}