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lfunc_lfunctions • Show schema
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{'Lhash': '2769135368998153135688926976409', 'a10': [-1.8035229544983753, -1.3218566308784971], 'a2': [0.8660254037844386, -0.5], 'a3': [0.9659258262890683, 0.25881904510252074], 'a4': [0.5, -0.8660254037844386], 'a5': [-0.9009683794647106, -2.046522899750876], 'a6': [0.9659258262890683, -0.25881904510252074], 'a7': [0.029886729287170816, -0.051765333597436625], 'a8': [0.0, -1.0], '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], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [5, [[1.0, 0], [0.9009683794647106, 2.046522899750876]]], [13, [[1.0, 0], [-0.9142641778225383, 3.4877099955630597]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.37', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '1725923866164787676156194811899', 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'4.24226469636214063188450779961033', '5.94024946423812547841379928289123', '6.73468701737299888545130329908216', '7.59536036215833313058533896184973', '8.497857946571902508436190222614996', '9.607683607960149567020379399572935', '10.64967039114933407371930072552595', '11.82437315890645650533091117637857'], 'prelabel': '2-390-65.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.34443267306071657, 'root_number': '0.4695042146550021 + 0.8829302307777154*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17221633653', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18446263386740363327990973183', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.54531645266995313837682336631', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24226469636214063188450779961', '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': '65.37', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/c/37/6'], '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': '2-390-65.37-c1-0-11', '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': '2-390-65.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.17221633653035828, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.18446263386740363327990973183', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2769135368998153135688926976409', 'Lhash_array': ['2769135368998153135688926976409'], 'label': '2-390-65.37-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/c/37/6'}