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lfunc_lfunctions • Show schema
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{'Lhash': '2722604361250745591740132454749', 'a10': [-1.706501292676551, -1.4319246052884456], 'a2': [-0.6862416378687336, -0.7273736415730487], 'a3': [1.7297854068840872, -0.08855758652341872], 'a4': [-0.05814482891047583, 0.9983081582712682], 'a5': [2.2126164567181745, -0.25861777316557516], 'a6': [-1.251465224980029, -1.1974284073236634], 'a7': [-2.5886272469481812, -1.3000574664041689], 'a8': [0.766044443118978, -0.6427876096865394], 'a9': [2.9843151077382943, -0.3063712416741692], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6862416378687336, 0.7273736415730487]]], [3, [[1.0, 0], [-1.7297854068840872, 0.08855758652341872]]]], 'bad_primes': [2, 3], 'central_character': '162.103', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2417698905033098200173212843933', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.20647739990229874, 'root_number': '0.7968892712725671 + 0.6041253920591957*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.103238699951', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14775614097493780472675474139', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.71603956015917593546583110871', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.84839820626803782236146836631', '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': '81.22', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/b/103/5'], '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': '2-162-81.22-c1-0-5', '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': '2-162-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.10323869995114937, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14775614097493780472675474139', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2722604361250745591740132454749', 'Lhash_array': ['2722604361250745591740132454749'], 'label': '2-162-81.22-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/b/103/5'}