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lfunc_lfunctions • Show schema
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{'Lhash': '2815463515405560744593063408437', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [1.618033988749895, -1.1755705045849463], 'a5': [0.9270509831248422, -2.853169548885461], 'a6': [0.0, 0.0], 'a7': [-0.8090169943749475, 0.5877852522924731], 'a8': [0.0, 0.0], 'a9': [-0.6180339887498949, -1.902113032590307], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '847.148', 'coefficient_field': 'CDF', 'conductor': 847, 'conductor_radical': 77, 'conjugate': '874466823259211426835421611973', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.618033988749895, 1.1755705045849463]], [[1.0, 0], [0.8090169943749475, 0.5877852522924731], [0.9270509831248422, 2.853169548885461]], [[1.0, 0], 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'4.12688071217290781634657243456070', '5.31633966397534630010666565521128', '6.51887970957155090763272677190641', '6.88708609974219274471799328848661', '7.68206840464541440709195840614958', '8.922111594456197934246078415332121', '9.945824480622569039926007524019017', '10.68645287055453599619263423409496'], 'prelabel': '2-847-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 0.7848650515913131, 'root_number': '-0.7801652637548133 + 0.6255734658938009*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.392432525796', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.22100909737956276562279289811', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87925569857934023940611611846', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12688071217290781634657243456', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.763329051202452, 'bad_primes': [7, 11], 'central_character': '11.5', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/2/f/f/148/1'], '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': '2-847-11.5-c1-0-50', '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': '2-847-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 0.3924325257956566, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.22100909737956276562279289811', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2815463515405560744593063408437', 'Lhash_array': ['2815463515405560744593063408437'], 'label': '2-847-11.5-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/f/f/148/1'}