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lfunc_lfunctions • Show schema
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{'Lhash': '2878535314603913491263082599009', 'a10': [-0.573877878961702, 2.514323270336916], 'a2': [0.3118986720730601, -0.647664266122208], 'a3': [1.162411883697396, 2.4137731481275972], 'a4': [2.1717709874642543, 2.72331468076674], 'a5': [-3.4976871643381884, 0.7983242707183795], 'a6': [1.925869337494714, -1.2775341602707222e-61], 'a7': [0.0, -9.275382392507124], 'a8': [5.24448590947444, -1.1970196853686315], 'a9': [1.1363087934677185, -1.4248861583458798], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1716651367492767, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-42.39335871882661, -7.197439582024141]]]], 'bad_primes': [43], 'central_character': '43.22', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '4171309824737436043410976114274', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3118986720730601, 0.647664266122208], [-2.493959207434934, -3.127325929872119]], [[1.0, 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0, 'data': '-0.0572392714691', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27076397398909320008153392811', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.16298958393678408042868388055', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.71786936564995857216307261637', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1716651367492767, 'bad_primes': [43], 'central_character': '43.22', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/3/f/a/22/5'], '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': '2-43-43.22-c2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-43-43.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0824348187070096, 'root_angle': -0.05723927146912877, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27076397398909320008153392811', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2878535314603913491263082599009', 'Lhash_array': ['2878535314603913491263082599009'], 'label': '2-43-43.22-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/3/f/a/22/5'}