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lfunc_lfunctions • Show schema
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{'Lhash': '2157708407894166510493873921778', 'a10': [2.0237502613000644, -3.505238274402503], 'a2': [-0.17364817766693036, -0.984807753012208], 'a3': [0.0, 0.0], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [3.1005652838589883, 2.6016831861271554], 'a6': [0.0, 0.0], 'a7': [0.14436501972824756, 0.052544570050335186], 'a8': [0.5, 0.8660254037844386], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.17364817766693036, 0.984807753012208]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.91', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2637636382087278889614931086921', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.1005652838589883, -2.6016831861271554], [0.8682408883346517, 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103}, 'z3': {'__RealLiteral__': 0, 'data': '5.61606811388652442260099606933', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '27.13', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/e/b/91/2'], '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': '2-162-27.13-c1-0-1', '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': '2-162-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.04823409676849818, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70213180785438036846964555543', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2157708407894166510493873921778', 'Lhash_array': ['2157708407894166510493873921778'], 'label': '2-162-27.13-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/e/b/91/2'}