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lfunc_lfunctions • Show schema
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{'Lhash': '1923760152277351272826346247912', 'a10': [2.1850523408050186, -0.46444721263054817], 'a2': [-0.5717451700569816, 1.759650697343838], 'a3': [0.48844233958681604, 0.10382162427663495], 'a4': [-1.1514440484292732, -0.8365730698025313], 'a5': [-0.6036807319935772, -1.0456056993632463], 'a6': [-0.4619543420678447, 0.8001283912385598], 'a7': [3.4103038108216004, -1.518365082194792], 'a8': [-0.8632876172881394, 0.6272151678602492], 'a9': [-2.512839383494199, -1.1187881751046347], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.673623634245049, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[31, [[1.0, 0], [0, 0]]]], 'bad_primes': [31], 'central_character': '961.846', 'coefficient_field': 'CDF', 'conductor': 961, 'conductor_radical': 31, 'conjugate': '875184922819824250495846411235', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5717451700569816, -1.759650697343838], [-1.618033988749895, -1.1755705045849463]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '-0.0254981070524', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51757917515362284051865268184', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29636137579082978488743231732', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39134098169328783398272537836', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.673623634245049, 'bad_primes': [31], 'central_character': '31.9', 'conductor': 961, 'conductor_radical': 31, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/961/2/g/l/846/1'], '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': '2-31e2-31.9-c1-0-36', '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': '2-31e2-31.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77013061682027, 'root_angle': -0.025498107052436575, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51757917515362284051865268184', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1923760152277351272826346247912', 'Lhash_array': ['1923760152277351272826346247912'], 'label': '2-31e2-31.9-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/961/2/g/l/846/1'}