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{'algebraic': True, 'analytic_conductor': 8821024.958919967, 'bad_primes': [3, 5, 7, 13], 'central_character': '1.1', 'conductor': 2169754625390625, 'conductor_radical': 1365, 'degree': 8, 'dirichlet_coefficients': [1, -1, -4, 0, 0, 4, -4, 0, 10, 0, -2, 0, -4, 4, 0, -1, 2, -10, 7, 0, 16, 2, -3, 0, 0, 4, -20, 0, 1, 0, 3, 1, 8, -2, 0, 0, -10, -7, 16, 0, -16, -16, -3, 0, 0, 3, -5, 4, 10, 0, -8, 0, -5, 20, 0, 0, -28, -1, -20, 0, 12, -3, -40, -2, 0, -8, 22, 0, 12, 0, 0, 0, 13, 10, 0, 0, 8, -16, 11, 0, 35, 16, -1, 0, 0, 3, -4, 0, -5, 0, 16, 0, -12, 5, 0, -4, 17, -10, -20, 0], 'euler11': [1, 2, 20, 34, 294, 374, 2420, 2662, 14641], 'euler13': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler17': [1, -2, 40, -62, 878, -1054, 11560, -9826, 83521], 'euler19': [1, -7, 64, -351, 1774, -6669, 23104, -48013, 130321], 'euler2': [1, 1, 1, 1, 2, 2, 4, 8, 16], 'euler23': [1, 3, 40, -49, 494, -1127, 21160, 36501, 279841], 'euler29': [1, -1, 86, -35, 3378, -1015, 72326, -24389, 707281], 'euler3': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler31': [1, -3, -4, -119, 1798, -3689, -3844, -89373, 923521], 'euler37': [1, 10, 64, 270, 1870, 9990, 87616, 506530, 1874161], 'euler41': [1, 16, 164, 1280, 8694, 52480, 275684, 1102736, 2825761], 'euler43': [1, 3, 128, 275, 7246, 11825, 236672, 238521, 3418801], 'euler47': [1, 5, 148, 689, 9638, 32383, 326932, 519115, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 5, 174, 727, 12802, 38531, 488766, 744385, 7890481], 'euler59': [1, 20, 316, 3236, 28790, 190924, 1099996, 4107580, 12117361], 'euler61': [1, -12, 180, -1508, 15014, -91988, 669780, -2723772, 13845841], 'euler67': [1, -22, 228, -1254, 6086, -84018, 1023492, -6616786, 20151121], 'euler7': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler71': [1, 0, 52, 304, 7478, 21584, 262132, 0, 25411681], 'euler73': [1, -13, 126, 261, -3934, 19053, 671454, -5057221, 28398241], 'euler79': [1, -11, 196, -1167, 15030, -92193, 1223236, -5423429, 38950081], 'euler83': [1, 1, 296, 329, 35310, 27307, 2039144, 571787, 47458321], 'euler89': [1, 5, 194, 139, 16986, 12371, 1536674, 3524845, 62742241], 'euler97': [1, -17, 374, -4127, 52210, -400319, 3518966, -15515441, 88529281], 'euler_factors': [[1, 1, 1, 1, 2, 2, 4, 8, 16], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, 2, 20, 34, 294, 374, 2420, 2662, 14641], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, -2, 40, -62, 878, -1054, 11560, -9826, 83521], [1, -7, 64, -351, 1774, -6669, 23104, -48013, 130321], [1, 3, 40, -49, 494, -1127, 21160, 36501, 279841], [1, -1, 86, -35, 3378, -1015, 72326, -24389, 707281], [1, -3, -4, -119, 1798, -3689, -3844, -89373, 923521], [1, 10, 64, 270, 1870, 9990, 87616, 506530, 1874161], [1, 16, 164, 1280, 8694, 52480, 275684, 1102736, 2825761], [1, 3, 128, 275, 7246, 11825, 236672, 238521, 3418801], [1, 5, 148, 689, 9638, 32383, 326932, 519115, 4879681], [1, 5, 174, 727, 12802, 38531, 488766, 744385, 7890481], [1, 20, 316, 3236, 28790, 190924, 1099996, 4107580, 12117361], [1, -12, 180, -1508, 15014, -91988, 669780, -2723772, 13845841], [1, -22, 228, -1254, 6086, -84018, 1023492, -6616786, 20151121], [1, 0, 52, 304, 7478, 21584, 262132, 0, 25411681], [1, -13, 126, 261, -3934, 19053, 671454, -5057221, 28398241], [1, -11, 196, -1167, 15030, -92193, 1223236, -5423429, 38950081], [1, 1, 296, 329, 35310, 27307, 2039144, 571787, 47458321], [1, 5, 194, 139, 16986, 12371, 1536674, 3524845, 62742241], [1, -17, 374, -4127, 52210, -400319, 3518966, -15515441, 88529281]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6825/2/a/bg'], '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': '8-6825e4-1.1-c1e4-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 4, 'prelabel': '8-6825e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.3822692567749035, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1723584420527741462, 'z1': {'__RealLiteral__': 0, 'data': '0.906226939728232026591100592178', 'prec': 107}}
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{'Lhash': '1148779124089484797521787944314,1312077195819664553273263942388,1394667405485202024308816899847,2116564023182864876249687909250', 'Lhash_array': ['1148779124089484797521787944314', '1312077195819664553273263942388', '1394667405485202024308816899847', '2116564023182864876249687909250'], 'label': '8-6825e4-1.1-c1e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6825/2/a/bg'}