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{'algebraic': True, 'analytic_conductor': 25.066245894480033, 'bad_primes': [3, 11, 19], 'central_character': '1.1', 'conductor': 393129, 'conductor_radical': 627, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -3, 0, 0, 4, 0, -3, 0, 0, 0, 0, 0, 0, 5, 0, 0, 6, 0, 0, 0, 0, 0, -6, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -12, -3, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -18, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18], 'euler11': [1, 0, 1, 0, 0], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, -6, 19, 0, 0], 'euler2': [1, 0, 3, 0, 4], 'euler23': [1, 0, -30, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, 38, 0, 1369], 'euler41': [1, 0, -18, 0, 1681], 'euler43': [1, -12, 122, -516, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 0, 70, 0, 4489], 'euler7': [1, -4, 18, -28, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, 58, 0, 6241], 'euler83': [1, 0, -22, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, 0, 190, 0, 9409], 'euler_factors': [[1, 0, 3, 0, 4], [1, 0, 3, 0, 0], [1, 0, 6, 0, 25], [1, -4, 18, -28, 49], [1, 0, 1, 0, 0], [1, 0, 22, 0, 169], [1, 0, -30, 0, 289], [1, -6, 19, 0, 0], [1, 0, -30, 0, 529], [1, 0, 22, 0, 841], [1, 0, 46, 0, 961], [1, 0, 38, 0, 1369], [1, 0, -18, 0, 1681], [1, -12, 122, -516, 1849], [1, 0, -30, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 102, 0, 3481], [1, -12, 158, -732, 3721], [1, 0, 70, 0, 4489], [1, 0, 142, 0, 5041], [1, 4, 150, 292, 5329], [1, 0, 58, 0, 6241], [1, 0, -22, 0, 6889], [1, 0, 178, 0, 7921], [1, 0, 190, 0, 9409]], 'id': 9476284, 'index': 2, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF', 'ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-121.1-b', 'EllipticCurve/2.2.57.1/121.1/c', 'EllipticCurve/2.2.57.1/121.1/b', 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-121.1-c', 'EllipticCurve/2.0.3.1/43681.3/b', 'EllipticCurve/2.0.3.1/43681.1/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43681.1/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43681.3/b'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-627e2-1.1-c1e2-0-2', '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': '4-627e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.237547811049919, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1544655982320988492, 'z1': {'__RealLiteral__': 0, 'data': '0.65533493528900419546138704461501', 'prec': 113}}