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lfunc_lfunctions • Show schema
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{'Lhash': '1332311227477614166801922617349', 'a10': [8.47213595499958, 0.0], 'a2': [-2.618033988749895, 0.0], 'a3': [-0.38196601125010515, 0.0], 'a4': [4.854101966249685, 0.0], 'a5': [-3.23606797749979, 0.0], 'a6': [1.0, 0.0], 'a7': [0.2360679774997897, 0.0], 'a8': [-7.47213595499958, 0.0], 'a9': [-2.8541019662496847, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.76433933373475, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [0, 0]]]], 'bad_primes': [43], 'central_character': '1849.1', 'coefficient_field': 'CDF', 'conductor': 1849, 'conductor_radical': 43, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.618033988749895, 0], [2.0, 0]], [[1.0, 0], [0.38196601125010515, 0], [3.0, 0]], [[1.0, 0], [3.23606797749979, 0], [5.0, 0]], [[1.0, 0], [-0.2360679774997897, 0], [7.0, 0]], [[1.0, 0], [1.381966011250105, 0], [11.0, 0]], [[1.0, 0], [-3.618033988749895, 0], [13.0, 0]], [[1.0, 0], [5.0901699437494745, 0], 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'6.84501209372292946358705588150837', '7.56596489010481016075079183952723', '8.249104312004390166682832740262280', '8.727670441824332670059547046330482'], 'prelabel': '2-43e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8424392426861806, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05100824094410808861932932596', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60813248420782571482756066315', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44041233431509068387055370179', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.76433933373475, 'bad_primes': [43], 'central_character': '1.1', 'conductor': 1849, 'conductor_radical': 43, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1849/2/a/e/1/1'], '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': '2-43e2-1.1-c1-0-47', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-43e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8424392426861806, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05100824094410808861932932596', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1332311227477614166801922617349', 'Lhash_array': ['1332311227477614166801922617349'], 'label': '2-43e2-1.1-c1-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1849/2/a/e/1/1'}