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lfunc_lfunctions • Show schema
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{'Lhash': '4758001847503592087912909786048', 'a10': [-23.861739379323623, 0.0], 'a2': [2.5615528128088303, 0.0], 'a3': [-6.68465843842649, 0.0], 'a4': [-1.4384471871911697, 0.0], 'a5': [-9.31534156157351, 0.0], 'a6': [-17.12310562561766, 0.0], 'a7': [0.12310562561766054, 0.0], 'a8': [-24.177080940897135, 0.0], 'a9': [17.684658438426492, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4811126903386977, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[59, [[1.0, 0], [-59.0, 0]]]], 'bad_primes': [59], 'central_character': '59.1', 'coefficient_field': 'CDF', 'conductor': 59, 'conductor_radical': 59, 'conjugate': '4758001847503592087912909786048', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.5615528128088303, 0], [8.0, 0]], [[1.0, 0], [6.68465843842649, 0], [27.0, 0]], [[1.0, 0], [9.31534156157351, 0], [125.0, 0]], [[1.0, 0], [-0.12310562561766054, 0], [343.0, 0]], [[1.0, 0], [-8.56155281280883, 0], [1331.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4811126903386977, 'bad_primes': [59], 'central_character': '1.1', 'conductor': 59, 'conductor_radical': 59, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/59/4/a/b/1/2'], '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': '2-59-1.1-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': 1, 'prelabel': '2-59-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.865774019097355, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.75340164446493022369092648062', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4758001847503592087912909786048', 'Lhash_array': ['4758001847503592087912909786048'], 'label': '2-59-1.1-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/59/4/a/b/1/2'}