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lfunc_lfunctions • Show schema
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{'Lhash': '1351428746026600505684985550415', 'a10': [-0.6260636950001419, -1.2680868463172266], 'a2': [-0.7851635756155405, 1.1762304874158889], 'a3': [1.0826861073808183, -1.8752673466325505], 'a4': [-0.7670363190532387, -1.8470666704949386], 'a5': [-0.5, 0.8660254037844386], 'a6': [1.355660929824311, 2.7458800229200317], 'a7': [0.0, 3.948038300320836], 'a8': [2.774825109020728, 0.5480379679804173], 'a9': [-0.8444184142308576, -1.4625755962945877], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7851635756155405, -1.1762304874158889]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [19, [[1.0, 0], [-3.5860581584361833, -2.4779400485712504]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.331', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '2060808525066019583116454823588', 'degree': 2, 'euler_factors': 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'6.64481926928904894184308317179465', '8.145536366698065402172297303397866', '8.432460077283907434250897399911617', '9.667057312413603194916697847193966', '10.19999226992397407121886952925477', '10.95202363532466489682471051131715'], 'prelabel': '2-380-76.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': -0.297313347012729, 'root_number': '0.5945926366719679 - 0.8040271117415613*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.148656673506', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06608930393224093603276272067', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.24647408364644649328634403899', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87065867432408172786189837987', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '76.27', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/n/b/331/6'], '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': '2-380-76.27-c1-0-15', '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': '2-380-76.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': -0.1486566735063645, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06608930393224093603276272067', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1351428746026600505684985550415', 'Lhash_array': ['1351428746026600505684985550415'], 'label': '2-380-76.27-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/n/b/331/6'}