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lfunc_lfunctions • Show schema
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{'Lhash': '1831647946587170033587910821938', 'a10': [-2.3762054627007037, -2.424040752200193], 'a2': [-0.7590232529144263, 1.3146668381739883], 'a3': [-0.6533670416447436, 0.17506917116982076], 'a4': [-0.15223259692959445, -0.26367459245021146], 'a5': [-0.6002307151757857, 2.1540016454403106], 'a6': [0.26576314357269976, -0.9918415545925375], 'a7': [2.2472340663978145, -1.2974411931668757], 'a8': [-2.5739006879732593, 0.0], 'a9': [-2.2018369349398, 1.271231147099154], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.6002307151757857, -2.1540016454403106]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 13], 'central_character': '845.488', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '199889750832792732791503067251', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7590232529144263, -1.3146668381739883], [-1.0, 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'5.64480190238016333313411333534640', '6.94327404235107507219611567012227', '8.158956564397710710435695953830714', '8.729880505299240421603550608813538', '9.574112849781042418993059247092873', '10.26403538614610844380889081909873'], 'prelabel': '2-845-65.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.13750228596516137, 'root_number': '0.6494371264437886 + 0.7604152936365987*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.137502285965', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44491545719096243363895554817', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32442177048564593445211173068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.85234629273812067005297877453', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '65.33', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/o/g/488/1'], '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': '2-845-65.33-c1-0-42', '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': '2-845-65.33-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': 0.13750228596516137, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44491545719096243363895554817', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1831647946587170033587910821938', 'Lhash_array': ['1831647946587170033587910821938'], 'factors': ['2-845-65.33-c1-0-42'], 'label': '2-845-65.33-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/o/g/488/1'}