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lfunc_lfunctions • Show schema
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{'Lhash': '843731803971772961074919560319', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -46.76537180435969], 'a4': [0, 0], 'a5': [-726.0, 0], 'a6': [0, 0], 'a7': [0, 3055.3376245514996], 'a8': [0, 0], 'a9': [-2187.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.21669313173645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 46.76537180435969]]]], 'bad_primes': [2, 3], 'central_character': '192.127', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '170554923437870167113959930512', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 46.76537180435969]], [[1.0, 0], [726.0, 0], [390625.0, 0]], [[1.0, 0], [0, -3055.3376245514996], [-5764801.0, 0]], [[1.0, 0], [0, -13281.365592438151], [-214358881.0, 0]], [[1.0, 0], [39034.0, 0], [815730721.0, 0]], [[1.0, 0], [65814.0, 0], [6975757441.0, 0]], [[1.0, 0], [0, 130257.14893240985], 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{'__RealLiteral__': 0, 'data': '4.06683794083073691805518643085', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.21669313173645, 'bad_primes': [2, 3], 'central_character': '4.3', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/9/g/a/127/1'], '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': '2-192-4.3-c8-0-15', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-192-4.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.844020190599773, 'root_angle': 0.25, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66558703464493010180718701347', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '843731803971772961074919560319', 'Lhash_array': ['843731803971772961074919560319'], 'label': '2-192-4.3-c8-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/9/g/a/127/1'}