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lfunc_lfunctions • Show schema
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{'Lhash': '1643010054051936460889099148085', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.8691249689690157, 0.13368245616045674], 'a4': [0.5406408174555976, -0.8412535328311812], 'a5': [-0.9898214418809327, 0.14231483827328514], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [2.485935708657399, -0.35742359517194583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.631317240980748, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.9898214418809327, -0.14231483827328514]]], [11, [[1.0, 0], [-0.28173255684142967, -0.9594929736144974]]], [23, [[1.0, 0], [0.28173255684142967, 0.9594929736144974]]]], 'bad_primes': [5, 11, 23], 'central_character': '1265.373', 'coefficient_field': 'CDF', 'conductor': 1265, 'conductor_radical': 1265, 'conjugate': '692744927384361256456618181691', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5406408174555976, 0.8412535328311812]], [[1.0, 0], [1.8691249689690157, 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['1.29610639852663413189511207185947', '3.24710648075900842549481039691157', '4.13116069995146217485599671453333', '5.06450603628314098015937372778882', '6.03617455799143923306594895901998', '6.73865743532793529685918178690632', '7.47717270947728388546919156165437', '8.169976621830366479995686482248325', '9.280288251899863071223172592078462', '10.58044477841868199737043082987090'], 'prelabel': '2-1265-1265.373-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7945547438539071, 'root_angle': 0.4888471322035767, 'root_number': '0.035030598984817896520481999035894 + 0.99938624021684672950404140007358*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.24442356610178836', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29610639852663413189511207186', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.24710648075900842549481039691', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13116069995146217485599671453', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.631317240980748, 'bad_primes': [5, 11, 23], 'central_character': '1265.373', 'conductor': 1265, 'conductor_radical': 1265, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1265/1/bi/a/373/1'], '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': '2-1265-1265.373-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': '2-1265-1265.373-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7945547438539071, 'root_angle': 0.24442356610178834, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29610639852663413189511207186', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1643010054051936460889099148085', 'Lhash_array': ['1643010054051936460889099148085'], 'label': '2-1265-1265.373-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1265/1/bi/a/373/1'}