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lfunc_lfunctions • Show schema
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{'Lhash': '1481210906409554535814970800375', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [0, 0.6697801903088662], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [2.8786538988385, 3.835798708313811]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1241', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'conjugate': '550345855925352422655224893237', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -0.6697801903088662], [-7.0, 0]], [[1.0, 0], [-6.531989240772527, 0], [11.0, 0]], [[1.0, 0], [1.677591113168254, 0], [13.0, 0]], [[1.0, 0], [-4.865826414050913, 0], [17.0, 0]], [[1.0, 0], [0, 7.936200466661396], 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'3.11910156043375954844450892258383', '3.85125618872600086975340957686080', '4.11189402493097215334146078794706', '5.32381372400671106134847679925879', '5.87271771687984910334666956297434', '6.68009080574882365521268733203849', '7.32096894016965983264054307546360', '7.888664294518741579201494928433267'], 'prelabel': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.4909846768887564, 'root_number': '0.0283186864704316399797417641516571623199645274276912870 + 0.99959894557596917864536705298161264699183551602236702679*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2454923384443782', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16846937645347658839097133672', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.69524728610587807999222732716', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11910156043375954844450892258', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '69.68', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 83, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/27'], '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': '2-8280-69.68-c1-0-83', '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': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.2454923384443782, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16846937645347658839097133672', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1481210906409554535814970800375', 'Lhash_array': ['1481210906409554535814970800375'], 'label': '2-8280-69.68-c1-0-83', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/27'}