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lfunc_lfunctions • Show schema
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{'Lhash': '1286418102636378833386778312728', 'a10': [-0.49409589449919905, -4.446975920642324e-61], 'a2': [-0.24704794724959953, 0.42789959654190224], 'a3': [0.6749277348684924, 1.5951402924837947], 'a4': [0.8779346235195182, 1.5206273736596598], 'a5': [0.5, 0.8660254037844386], 'a6': [-0.8492993990226307, -0.10527482938807936], 'a7': [2.142692716129489, -3.7112526493440323], 'a8': [-1.8557595752377858, 0.0], 'a9': [-2.088945105410572, 2.153208848807104], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.6749277348684924, -1.5951402924837947]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.196', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '2706515495437474528964510640823', 'degree': 2, 'euler_factors': 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'5.60368913535721248415210153509386', '6.71240945706453184568488134644971', '7.962167416693124519131813617888330', '8.722306935737297664629677258585952', '9.215038063083320428599662474152029', '10.62029970197243545353925578134786'], 'prelabel': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.6992661035590367, 'root_number': '-0.5859184191196427 - 0.810370042718966*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.34963305178', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01480494893843027980633457920', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21421014198268510835319625559', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.03519936334191694044787628538', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '9.7', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/i/e/196/5'], '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': '2-585-9.7-c1-0-19', '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': '2-585-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.34963305177951837, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01480494893843027980633457920', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1286418102636378833386778312728', 'Lhash_array': ['1286418102636378833386778312728'], 'label': '2-585-9.7-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/i/e/196/5'}