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{'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 3, 0, 4, 0, 0, 0, 3, 0, 0, 0, 0, -5, 0, 0, 3, -3, 0, -6, 0, 0, 0, -6, 0, 7, -15, 0, 0, 3, 0, 0, 6, 0, -9, 0, 0, 15, -18, 0, 0, 9, 0, -8, 0, 0, -18, 0, 0, -7, 21, 0, -20, 6, 0, 0, 0, 0, 9, -12, 0, -1, 0, 0, 5, 0, 0, 6, -12, 0, 0, -6, 0, 0, 45, 0, -24, 0, 0, 8, 0, 0, 27, 0, 0, 0, -24, 0, 0, 12, 0, 0, -24, 0, 0, 0, 0, 12, -21, 0, 28], 'euler11': [1, 0, 11, 0, 121], 'euler13': [1, 5, 13, 0, 0], 'euler17': [1, 3, -8, 51, 289], 'euler19': [1, 6, 31, 114, 361], 'euler2': [1, -3, 5, -6, 4], 'euler23': [1, 6, 13, 138, 529], 'euler29': [1, -3, -20, -87, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -50, 0, 961], 'euler37': [1, -15, 112, -555, 1369], 'euler41': [1, -9, 68, -369, 1681], 'euler43': [1, 8, 21, 344, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, -7, 0, 25], 'euler53': [1, -6, 115, -318, 2809], 'euler59': [1, 12, 107, 708, 3481], 'euler61': [1, 1, -60, 61, 3721], 'euler67': [1, -6, 79, -402, 4489], 'euler7': [1, 0, 7, 0, 49], 'euler71': [1, 6, 83, 426, 5041], 'euler73': [1, 0, -143, 0, 5329], 'euler79': [1, -8, 174, -632, 6241], 'euler83': [1, 0, 26, 0, 6889], 'euler89': [1, -12, 137, -1068, 7921], 'euler97': [1, -12, 145, -1164, 9409], 'euler_factors': [[1, -3, 5, -6, 4], [1, 0, 0, 0, 0], [1, 0, -7, 0, 25], [1, 0, 7, 0, 49], [1, 0, 11, 0, 121], [1, 5, 13, 0, 0], [1, 3, -8, 51, 289], [1, 6, 31, 114, 361], [1, 6, 13, 138, 529], [1, -3, -20, -87, 841], [1, 0, -50, 0, 961], [1, -15, 112, -555, 1369], [1, -9, 68, -369, 1681], [1, 8, 21, 344, 1849], [1, 0, -82, 0, 2209], [1, -6, 115, -318, 2809], [1, 12, 107, 708, 3481], [1, 1, -60, 61, 3721], [1, -6, 79, -402, 4489], [1, 6, 83, 426, 5041], [1, 0, -143, 0, 5329], [1, -8, 174, -632, 6241], [1, 0, 26, 0, 6889], [1, -12, 137, -1068, 7921], [1, -12, 145, -1164, 9409]], 'id': 9604484, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/2/q/c'], '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': '4-117e2-1.1-c1e2-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-117e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1260473896178419383, 'z1': {'__RealLiteral__': 0, 'data': '2.30048864547383042155892541730', 'prec': 103}}