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lfunc_lfunctions • Show schema
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{'Lhash': '1984683151646637901390342766980', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.4270509831248424, 1.7633557568774194], 'a4': [1.618033988749895, -1.1755705045849463], 'a5': [-0.30901699437494745, 0.9510565162951535], 'a6': [0.0, 0.0], 'a7': [0.8090169943749475, -0.5877852522924731], 'a8': [0.0, 0.0], 'a9': [1.8541019662496845, 5.706339097770922], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '847.148', 'coefficient_field': 'CDF', 'conductor': 847, 'conductor_radical': 77, 'conjugate': '2240147705387449154628297916719', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.618033988749895, 1.1755705045849463]], [[1.0, 0], [-2.4270509831248424, -1.7633557568774194], [0.9270509831248422, 2.853169548885461]], [[1.0, 0], 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'2.37437655398428988609208952775018', '3.34293613773245273288453843195197', '4.42618131772671582762030967787715', '6.08442812907609159812148395059223', '6.95619799680519449721577433087690', '7.70674897683723552635041874944157', '8.173538262825589658740771463949882', '9.040310955317030568855175922687021', '9.753671676855240177644420885806371'], 'prelabel': '2-847-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': -0.2151349484086869, 'root_number': '0.7801652637548132 - 0.6255734658938011*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.107567474204', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56563894758485742161374946476', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37437655398428988609208952775', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34293613773245273288453843195', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.763329051202452, 'bad_primes': [7, 11], 'central_character': '11.5', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/2/f/i/148/1'], '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': '2-847-11.5-c1-0-31', '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': '2-847-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': -0.10756747420434346, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56563894758485742161374946476', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1984683151646637901390342766980', 'Lhash_array': ['1984683151646637901390342766980'], 'label': '2-847-11.5-c1-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/f/i/148/1'}