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lfunc_lfunctions • Show schema
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{'Lhash': '1494670558325680997719225067433', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.3826834323650898, 0.9238795325112867], 'a8': [0.0, 0.0], 'a9': [0.3826834323650898, -0.9238795325112867], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7886490052766808, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.3826834323650898, -0.9238795325112867]]]], 'bad_primes': [2, 7], 'central_character': '3584.545', 'coefficient_field': 'CDF', 'conductor': 3584, 'conductor_radical': 14, 'conjugate': '1340716397337132998437410281230', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [0, 0], [-0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [-0.3826834323650898, -0.9238795325112867]], [[1.0, 0], [-0.21677275132473922, 0.32442334882145774], 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'2-3584-448.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908664, 'root_angle': 0.03125, 'root_number': '0.99518472667219688624483695310913 + 0.098017140329560601994195563888964*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.015625', 'prec': 27}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17908716964799183519340592230', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14015438198263714535510167101', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32162454629884592162181488922', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7886490052766808, 'bad_primes': [2, 7], 'central_character': '448.13', 'conductor': 3584, 'conductor_radical': 14, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3584/1/bf/b/545/1'], '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': '2-3584-448.13-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': '2-3584-448.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908664, 'root_angle': 0.015625, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17908716964799183519340592230', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1494670558325680997719225067433', 'Lhash_array': ['1494670558325680997719225067433'], 'label': '2-3584-448.13-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3584/1/bf/b/545/1'}