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{'Lhash': '561598031389294321174539211905,1535622409420535379766781909121,1650854641908520723848235662663,2437928556914689813228333165891', 'a10': 3, 'a2': 3, 'a3': -4, 'a4': 7, 'a5': 1, 'a6': -12, 'a7': -1, 'a8': 15, 'a9': 10, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2234.1947855779968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 4, 6, 4, 1]], [7, [1, 1, 1, 1, 1]], [41, [1, -11, 111, -451, 1681]]], 'bad_primes': [3, 7, 41], 'central_character': '861.1', 'coefficient_field': '1.1.1.1', 'conductor': 549556825041, 'conductor_radical': 861, 'degree': 8, 'euler_factors': [[1, -3, 2, 0, 1, 0, 8, -24, 16], [1, 4, 6, 4, 1], [1, -1, -4, 9, 11, 45, -100, -125, 625], [1, 1, 1, 1, 1], [1, -1, -10, 21, 89, 231, -1210, -1331, 14641], [1, 6, 23, 60, 61, 780, 3887, 13182, 28561], [1, -2, 7, -70, 441, -1190, 2023, -9826, 83521], [1, 12, 35, -198, -1781, -3762, 12635, 82308, 130321], [1, 17, 161, 1121, 6044, 25783, 85169, 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{'algebraic': True, 'analytic_conductor': 2234.1947855779968, 'bad_primes': [3, 7, 41], 'central_character': '1.1', 'conductor': 549556825041, 'conductor_radical': 861, 'degree': 8, 'dirichlet_coefficients': [1, 3, -4, 7, 1, -12, -1, 15, 10, 3, 1, -28, -6, -3, -4, 30, 2, 30, -12, 7, 4, 3, -17, -60, 5, -18, -20, -7, 12, -12, 20, 57, -4, 6, -1, 70, 3, -36, 24, 15, 11, 12, 8, 7, 10, -51, 7, -120, 0, 15, -8, -42, -19, -60, 1, -15, 48, 36, -3, -28, -11, 60, -10, 96, -6, -12, -8, 14, 68, -3, -13, 150, -2, 9, -20, -84, -1, 72, 60, 30, 35, 33, -34, 28, 2, 24, -48, 15, -6, 30, 6, -119, -80, 21, -12, -228, 12, 0, 10, 35], 'euler11': [1, -1, -10, 21, 89, 231, -1210, -1331, 14641], 'euler13': [1, 6, 23, 60, 61, 780, 3887, 13182, 28561], 'euler17': [1, -2, 7, -70, 441, -1190, 2023, -9826, 83521], 'euler19': [1, 12, 35, -198, -1781, -3762, 12635, 82308, 130321], 'euler2': [1, -3, 2, 0, 1, 0, 8, -24, 16], 'euler23': [1, 17, 161, 1121, 6044, 25783, 85169, 206839, 279841], 'euler29': [1, -12, 65, -432, 3049, -12528, 54665, -292668, 707281], 'euler3': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler31': [1, -20, 159, -670, 2591, -20770, 152799, -595820, 923521], 'euler37': [1, -3, 42, -175, 891, -6475, 57498, -151959, 1874161], 'euler41': [1, -11, 111, -451, 1681, 0, 0, 0, 0], 'euler43': [1, -8, 21, 176, -2311, 7568, 38829, -636056, 3418801], 'euler47': [1, -7, -28, 185, 941, 8695, -61852, -726761, 4879681], 'euler5': [1, -1, -4, 9, 11, 45, -100, -125, 625], 'euler53': [1, 19, 98, -105, -2869, -5565, 275282, 2828663, 7890481], 'euler59': [1, 3, -50, -327, 1969, -19293, -174050, 616137, 12117361], 'euler61': [1, 11, 35, 589, 8344, 35929, 130235, 2496791, 13845841], 'euler67': [1, 8, -33, 10, 4811, 670, -148137, 2406104, 20151121], 'euler7': [1, 1, 1, 1, 1, 0, 0, 0, 0], 'euler71': [1, 13, 68, 981, 13325, 69651, 342788, 4652843, 25411681], 'euler73': [1, 2, 271, 416, 29029, 30368, 1444159, 778034, 28398241], 'euler79': [1, -60, 1666, -27720, 301371, -2189880, 10397506, -29582340, 38950081], 'euler83': [1, 34, 743, 10540, 113281, 874820, 5118527, 19440758, 47458321], 'euler89': [1, 6, -13, 768, 12565, 68352, -102973, 4229814, 62742241], 'euler97': [1, -12, 117, -1780, 26181, -172660, 1100853, -10952076, 88529281], 'euler_factors': [[1, -3, 2, 0, 1, 0, 8, -24, 16], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, -1, -4, 9, 11, 45, -100, -125, 625], [1, 1, 1, 1, 1, 0, 0, 0, 0], [1, -1, -10, 21, 89, 231, -1210, -1331, 14641], [1, 6, 23, 60, 61, 780, 3887, 13182, 28561], [1, -2, 7, -70, 441, -1190, 2023, -9826, 83521], [1, 12, 35, -198, -1781, -3762, 12635, 82308, 130321], [1, 17, 161, 1121, 6044, 25783, 85169, 206839, 279841], [1, -12, 65, -432, 3049, -12528, 54665, -292668, 707281], [1, -20, 159, -670, 2591, -20770, 152799, -595820, 923521], [1, -3, 42, -175, 891, -6475, 57498, -151959, 1874161], [1, -11, 111, -451, 1681, 0, 0, 0, 0], [1, -8, 21, 176, -2311, 7568, 38829, -636056, 3418801], [1, -7, -28, 185, 941, 8695, -61852, -726761, 4879681], [1, 19, 98, -105, -2869, -5565, 275282, 2828663, 7890481], [1, 3, -50, -327, 1969, -19293, -174050, 616137, 12117361], [1, 11, 35, 589, 8344, 35929, 130235, 2496791, 13845841], [1, 8, -33, 10, 4811, 670, -148137, 2406104, 20151121], [1, 13, 68, 981, 13325, 69651, 342788, 4652843, 25411681], [1, 2, 271, 416, 29029, 30368, 1444159, 778034, 28398241], [1, -60, 1666, -27720, 301371, -2189880, 10397506, -29582340, 38950081], [1, 34, 743, 10540, 113281, 874820, 5118527, 19440758, 47458321], [1, 6, -13, 768, 12565, 68352, -102973, 4229814, 62742241], [1, -12, 117, -1780, 26181, -172660, 1100853, -10952076, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/861/2/n/a'], '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': '8-861e4-1.1-c1e4-0-0', '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': 0, 'prelabel': '8-861e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.622044929827146, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1119766178900367736, 'z1': {'__RealLiteral__': 0, 'data': '0.44302273141209692034612821299', 'prec': 103}}
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{'Lhash': '561598031389294321174539211905,1535622409420535379766781909121,1650854641908520723848235662663,2437928556914689813228333165891', 'Lhash_array': ['561598031389294321174539211905', '1535622409420535379766781909121', '1650854641908520723848235662663', '2437928556914689813228333165891'], 'label': '8-861e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/861/2/n/a'}