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lfunc_lfunctions • Show schema
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{'Lhash': '1546973062004599417922268718022', 'a10': [-0.6742473159730185, 2.1319921568578017], 'a2': [0.5, 0.8660254037844386], 'a3': [-0.25881904510252074, 0.9659258262890683], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.5092357105215246, 1.649911382495008], 'a6': [-0.9659258262890683, 0.25881904510252074], 'a7': [2.7027983916931118, 1.5604613790093056], 'a8': [-1.0, 0.0], 'a9': [-0.8660254037844386, -0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [5, [[1.0, 0], [-1.5092357105215246, -1.649911382495008]]], [13, [[1.0, 0], [1.787712154289294, 3.131147593679725]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.193', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '2932689552783770367008755993063', 'degree': 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'2.24175510572259094348932754426889', '4.15673646950413166579085175415560', '5.00484358810339014797609090813797', '6.03198052846844560027686997911714', '7.24255518133317387604698095866890', '8.319231820985756571327621421436191', '9.298896005982436314961246159366143', '10.17758550548853571329451263482162', '11.35088591041436467794699001276180'], 'prelabel': '2-390-65.63-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.6537179589203879, 'root_number': '-0.4643665291373657 - 0.8856431147007897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32685897946', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22034657004546872034158055556', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24175510572259094348932754427', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15673646950413166579085175416', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.63', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bn/b/193/2'], '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': '2-390-65.63-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': '2-390-65.63-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.32685897946019393, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22034657004546872034158055556', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1546973062004599417922268718022', 'Lhash_array': ['1546973062004599417922268718022'], 'label': '2-390-65.63-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bn/b/193/2'}