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{'Lhash': '1329287770251374880602141654551,1413066271036786538141027038628,1984704323319053765121024517346,2718823978983356453987820691312', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.816197289027485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 3, 2, 1]], [7, [1, -6, 23, -42, 49]]], 'bad_primes': [2, 3, 7], 'central_character': '336.1', 'coefficient_field': '1.1.1.1', 'conductor': 12745506816, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1], [1, 2, 3, 2, 1], [1, -1, 5, 14, -14, 70, 125, -125, 625], [1, -6, 23, -42, 49], [1, 1, -7, -14, -68, -154, -847, 1331, 14641], [1, -10, 61, -310, 1312, -4030, 10309, -21970, 28561], [1, -8, 14, -128, 1123, -2176, 4046, -39304, 83521], [1, 5, -5, -40, 64, -760, -1805, 34295, 130321], [1, -8, 2, -128, 1843, -2944, 1058, -97336, 279841], [1, -6, 101, -450, 4320, -13050, 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'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 868505811949361224, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04862315373971995582105982313', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.11471273770735904449800676994', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.56565564908952444260223596235', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 51.816197289027485, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 12745506816, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, -2, 0, 1, 0, 6, 0, 1, 0, -1, 0, 10, 0, -2, 0, 8, 0, -5, 0, -12, 0, 8, 0, -4, 0, 2, 0, 6, 0, -2, 0, 2, 0, 6, 0, -3, 0, -20, 0, 12, 0, 14, 0, 1, 0, -12, 0, 13, 0, -16, 0, -11, 0, -1, 0, 10, 0, 5, 0, -20, 0, 6, 0, 10, 0, 7, 0, -16, 0, -8, 0, 1, 0, 8, 0, -6, 0, 8, 0, -4, 0, -14, 0, 8, 0, -12, 0, 6, 0, 60, 0, 4, 0, -5, 0, 50, 0, -1, 0], 'euler11': [1, 1, -7, -14, -68, -154, -847, 1331, 14641], 'euler13': [1, -10, 61, -310, 1312, -4030, 10309, -21970, 28561], 'euler17': [1, -8, 14, -128, 1123, -2176, 4046, -39304, 83521], 'euler19': [1, 5, -5, -40, 64, -760, -1805, 34295, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -8, 2, -128, 1843, -2944, 1058, -97336, 279841], 'euler29': [1, -6, 101, -450, 4320, -13050, 84941, -146334, 707281], 'euler3': [1, 2, 3, 2, 1, 0, 0, 0, 0], 'euler31': [1, 2, -59, 2, 2884, 62, -56699, 59582, 923521], 'euler37': [1, 3, -53, -36, 2142, -1332, -72557, 151959, 1874161], 'euler41': [1, -12, 104, -900, 7470, -36900, 174824, -827052, 2825761], 'euler43': [1, -14, 217, -1778, 14968, -76454, 401233, -1113098, 3418801], 'euler47': [1, 12, 14, 432, 7923, 20304, 30926, 1245876, 4879681], 'euler5': [1, -1, 5, 14, -14, 70, 125, -125, 625], 'euler53': [1, 11, -1, 176, 5662, 9328, -2809, 1637647, 7890481], 'euler59': [1, -5, -85, 40, 7144, 2360, -295885, -1026895, 12117361], 'euler61': [1, 20, 178, 2000, 21163, 122000, 662338, 4539620, 13845841], 'euler67': [1, -7, -83, 14, 9652, 938, -372587, -2105341, 20151121], 'euler7': [1, -6, 23, -42, 49, 0, 0, 0, 0], 'euler71': [1, 8, 308, 1736, 33670, 123256, 1552628, 2863288, 25411681], 'euler73': [1, -1, -131, 14, 12022, 1022, -698099, -389017, 28398241], 'euler79': [1, -8, -53, 328, 2392, 25912, -330773, -3944312, 38950081], 'euler83': [1, 14, 377, 3458, 48808, 287014, 2597153, 8005018, 47458321], 'euler89': [1, -6, -94, 288, 5775, 25632, -744574, -4229814, 62742241], 'euler97': [1, -50, 1297, -21650, 252964, -2100050, 12203473, -45633650, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 3, 2, 1, 0, 0, 0, 0], [1, -1, 5, 14, -14, 70, 125, -125, 625], [1, -6, 23, -42, 49, 0, 0, 0, 0], [1, 1, -7, -14, -68, -154, -847, 1331, 14641], [1, -10, 61, -310, 1312, -4030, 10309, -21970, 28561], [1, -8, 14, -128, 1123, -2176, 4046, -39304, 83521], [1, 5, -5, -40, 64, -760, -1805, 34295, 130321], [1, -8, 2, -128, 1843, -2944, 1058, -97336, 279841], [1, -6, 101, -450, 4320, -13050, 84941, -146334, 707281], [1, 2, -59, 2, 2884, 62, -56699, 59582, 923521], [1, 3, -53, -36, 2142, -1332, -72557, 151959, 1874161], [1, -12, 104, -900, 7470, -36900, 174824, -827052, 2825761], [1, -14, 217, -1778, 14968, -76454, 401233, -1113098, 3418801], [1, 12, 14, 432, 7923, 20304, 30926, 1245876, 4879681], [1, 11, -1, 176, 5662, 9328, -2809, 1637647, 7890481], [1, -5, -85, 40, 7144, 2360, -295885, -1026895, 12117361], [1, 20, 178, 2000, 21163, 122000, 662338, 4539620, 13845841], [1, -7, -83, 14, 9652, 938, -372587, -2105341, 20151121], [1, 8, 308, 1736, 33670, 123256, 1552628, 2863288, 25411681], [1, -1, -131, 14, 12022, 1022, -698099, -389017, 28398241], [1, -8, -53, 328, 2392, 25912, -330773, -3944312, 38950081], [1, 14, 377, 3458, 48808, 287014, 2597153, 8005018, 47458321], [1, -6, -94, 288, 5775, 25632, -744574, -4229814, 62742241], [1, -50, 1297, -21650, 252964, -2100050, 12203473, -45633650, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/2/q/g'], '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': '8-336e4-1.1-c1e4-0-4', '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': '8-336e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 868505811949361224, 'z1': {'__RealLiteral__': 0, 'data': '1.04862315373971995582105982313', 'prec': 103}}
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{'Lhash': '1329287770251374880602141654551,1413066271036786538141027038628,1984704323319053765121024517346,2718823978983356453987820691312', 'Lhash_array': ['1329287770251374880602141654551', '1413066271036786538141027038628', '1984704323319053765121024517346', '2718823978983356453987820691312'], 'label': '8-336e4-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/2/q/g'}