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lfunc_lfunctions • Show schema
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{'Lhash': '518802074501762485590458220395', 'a10': [0, 0], 'a2': [0, -5.0], 'a3': [0, -3.0], 'a4': [-17.0, 0], 'a5': [0, 0], 'a6': [-15.0, 0], 'a7': [0, -7.0], 'a8': [0, 45.0], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.976002753013837, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 3.0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 7.0]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.274', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '1501920463879001840616501717510', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 5.0], [-8.0, 0]], [[1.0, 0], [0, 3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 7.0]], [[1.0, 0], [-12.0, 0], [1331.0, 0]], [[1.0, 0], [0, -30.0], [-2197.0, 0]], [[1.0, 0], [0, -134.0], [-4913.0, 0]], [[1.0, 0], [-92.0, 0], [6859.0, 0]], [[1.0, 0], [0, -112.0], [-12167.0, 0]], [[1.0, 0], [-58.0, 0], [24389.0, 0]], [[1.0, 0], [224.0, 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'rational': False, 'root_analytic_conductor': 5.56560892922004, 'root_angle': 0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40926267412199916161492296753', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.97792479975793590736842334955', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38375148537717703945141083609', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.976002753013837, 'bad_primes': [3, 5, 7], 'central_character': '5.4', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/4/d/a/274/1'], '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': '2-525-5.4-c3-0-13', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-525-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.56560892922004, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40926267412199916161492296753', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '518802074501762485590458220395', 'Lhash_array': ['518802074501762485590458220395'], 'label': '2-525-5.4-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/4/d/a/274/1'}