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lfunc_lfunctions • Show schema
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{'Lhash': '454898939196183094748570493817,2552590313151359496020691307503', 'a10': 1, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.614594053632576, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1]], [5, [1, -1, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '3240.1', 'coefficient_field': '1.1.1.1', 'conductor': 10497600, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, -1, 1], [1], [1, -1, 1], [1, 1, 0, 1, 1], [1, 2, 3, 2, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 4, 6, 4, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, -2, 3, -2, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -4, 6, -4, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, 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'5.06483125179744344767590084823864', '5.13607577752474990027587761519196', '5.57494243814410927230452997667143', '5.83561951833600399530233948507838', '6.36825306964191468156133545407974', '6.58574643577698575444650269879977', '7.05741951983430526880300858984021', '7.38832894674501836911077391259336', '7.932854904842347185063128532296745', '8.401562012503533660608637083480425', '8.592146186600905207199010545851786', '9.300241446207699138752368806779440'], 'prelabel': '4-3240e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2716016046431082, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 81712141510765158, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35885198895837900450068662967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01363870509096744759729799137', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.15989324418934498254941759176', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.614594053632576, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 10497600, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, 1, 0, -1, -1, 0, 1, -2, 0, -1, -1, 0, -1, 0, 0, -2, 0, 0, -2, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -4, -2, 0, -1, 1, 0, 0, 0, 0, -1, -1, 0, 1, 0, 0, 0, 2, 0, -2, 1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 2, 4, 0, 1, 0, 0, -1, -2, 0, 0, 1, 0, 0], 'euler11': [1, 2, 3, 2, 1], 'euler13': [1, 1, 0, 1, 1], 'euler17': [1, 0, -2, 0, 1], 'euler19': [1, 2, 3, 2, 1], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, 1, 0, 1, 1], 'euler29': [1, 0, 1, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 1, 0, 1], 'euler37': [1, 4, 6, 4, 1], 'euler41': [1, -1, 0, -1, 1], 'euler43': [1, 0, 1, 0, 1], 'euler47': [1, 1, 0, 1, 1], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, -2, 3, -2, 1], 'euler59': [1, -1, 0, -1, 1], 'euler61': [1, 0, 1, 0, 1], 'euler67': [1, 0, 1, 0, 1], 'euler7': [1, 1, 0, 1, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 0, 1, 0, 1], 'euler83': [1, 0, 1, 0, 1], 'euler89': [1, -4, 6, -4, 1], 'euler97': [1, 0, 1, 0, 1], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 0, 0, 0], [1, -1, 1, 0, 0], [1, 1, 0, 1, 1], [1, 2, 3, 2, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 4, 6, 4, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, -2, 3, -2, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -4, 6, -4, 1], [1, 0, 1, 0, 1]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3240/1/z/h'], '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': '4-3240e2-1.1-c0e2-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-3240e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2716016046431082, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 81712141510765158, 'z1': {'__RealLiteral__': 0, 'data': '0.35885198895837900450068662967', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '454898939196183094748570493817,2552590313151359496020691307503', 'Lhash_array': ['454898939196183094748570493817', '2552590313151359496020691307503'], 'label': '4-3240e2-1.1-c0e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3240/1/z/h'}