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lfunc_lfunctions • Show schema
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{'Lhash': '3469638557866226192583060380290', 'a10': [9.108725129584109, 4.055465714281558], 'a2': [-2.0874781137195, 1.5166416258976276], 'a3': [0.9135454576426009, -0.4067366430758002], 'a4': [1.439329065102627, -4.429799368244203], 'a5': [-1.9321158014834654, -3.3465227342760246], 'a6': [-1.2901324250501691, 2.2345749086789395], 'a7': [-2.0756271032836504, -2.3052174370254876], 'a8': [2.119158817073428, 6.522100203966675], 'a9': [0.6691306063588582, -0.7431448254773942], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9135454576426009, 0.4067366430758002]]], [31, [[1.0, 0], [-3.0381449375249847, 4.665798467421338]]]], 'bad_primes': [3, 31], 'central_character': '93.49', 'coefficient_field': 'CDF', 'conductor': 93, 'conductor_radical': 93, 'conjugate': '1096371935185001477357280308497', 'degree': 2, 'euler_factors': [[[1.0, 0], 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+ 0.744571391643678*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.133673049771', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.73706221354807714501593820411', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.42400127481338135360562000459', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.74256899135794711688566228226', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7426087387979079, 'bad_primes': [3, 31], 'central_character': '31.18', 'conductor': 93, 'conductor_radical': 93, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/93/2/m/b/49/1'], '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': '2-93-31.18-c1-0-2', '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': '2-93-31.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8617474913209251, 'root_angle': 0.1336730497711652, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.73706221354807714501593820411', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3469638557866226192583060380290', 'Lhash_array': ['3469638557866226192583060380290'], 'label': '2-93-31.18-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/93/2/m/b/49/1'}