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lfunc_lfunctions • Show schema
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{'Lhash': '1481957033069480049337985984179', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 1.0], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6422966712586741, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [11, [[1.0, 0], [-0.8660254037844386, 0.5]]], [13, [[1.0, 0], [0.8660254037844386, 0.5]]]], 'bad_primes': [3, 11, 13], 'central_character': '1287.1231', 'coefficient_field': 'CDF', 'conductor': 1287, 'conductor_radical': 429, 'conjugate': '3131362718025492954043967685409', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], 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-0.284080917743263, -0.26440113608314225, -0.10964486346571102, 0.1985199526612902], 'positive_zeros': ['1.16905796660583495902150279350887', '1.71326617048426051152931158464558', '3.47872133900900992813000905752040', '4.52355382343400520020966575399225', '5.37990334083587375773434503035887', '6.31088634539373859357618005381280', '7.16589398490219261997396560825688', '7.896217400761290188464828547642872', '8.977911122570370094087615637512832', '9.562991585285932689141769927221757'], 'prelabel': '2-1287-1287.1231-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8014341340738327, 'root_angle': -0.6924034930518778, 'root_number': '-0.56831241191396273166779576262143 - 0.82281285992899646157881422808101*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3462017465259389', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16905796660583495902150279351', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.71326617048426051152931158465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.47872133900900992813000905752', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6422966712586741, 'bad_primes': [3, 11, 13], 'central_character': '1287.1231', 'conductor': 1287, 'conductor_radical': 429, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1287/1/bg/a/1231/2'], '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': '2-1287-1287.1231-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1287-1287.1231-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8014341340738327, 'root_angle': -0.3462017465259389, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16905796660583495902150279351', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1481957033069480049337985984179', 'Lhash_array': ['1481957033069480049337985984179'], 'label': '2-1287-1287.1231-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1287/1/bg/a/1231/2'}