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{'Lhash': '657908440657389157263018659589,1045850132871548428225747651735,1458743430804847497907129366835,2239304376353401336657778590752', 'a10': 0, 'a2': 0, 'a3': -4, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 829.0591566244398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 4, 10, 12, 9]], [7, [1, 0, 2, 0, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '672.1', 'coefficient_field': '1.1.1.1', 'conductor': 203928109056, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1], [1, 4, 10, 12, 9], [1, 0, 4, 0, 54, 0, 100, 0, 625], [1, 0, 2, 0, 1], [1, 0, 20, 0, 342, 0, 2420, 0, 14641], [1, 0, -20, 0, 438, 0, -3380, 0, 28561], [1, 0, -52, 0, 1254, 0, -15028, 0, 83521], [1, -8, 100, -488, 3094, -9272, 36100, -54872, 130321], [1, 0, 76, 0, 2502, 0, 40204, 0, 279841], [1, 0, 52, 0, 2358, 0, 43732, 0, 707281], [1, 0, -124, 0, 5766, 0, -119164, 0, 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'10.66528005920400787134996775452096', '10.76527963464080392025405707044426'], 'prelabel': '8-672e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 2051625317497354710, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51899824804953233780099688543', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.825030282542565167897527962824', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.15074566330991639486068196642', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 829.0591566244398, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 203928109056, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, -4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 40, 0, 16, 0, 0, 0, 0, 0, -37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0], 'euler11': [1, 0, 20, 0, 342, 0, 2420, 0, 14641], 'euler13': [1, 0, -20, 0, 438, 0, -3380, 0, 28561], 'euler17': [1, 0, -52, 0, 1254, 0, -15028, 0, 83521], 'euler19': [1, -8, 100, -488, 3094, -9272, 36100, -54872, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 76, 0, 2502, 0, 40204, 0, 279841], 'euler29': [1, 0, 52, 0, 2358, 0, 43732, 0, 707281], 'euler3': [1, 4, 10, 12, 9, 0, 0, 0, 0], 'euler31': [1, 0, -124, 0, 5766, 0, -119164, 0, 923521], 'euler37': [1, 0, -20, 0, 2838, 0, -27380, 0, 1874161], 'euler41': [1, 0, -148, 0, 8838, 0, -248788, 0, 2825761], 'euler43': [1, -40, 772, -9160, 72694, -393880, 1427428, -3180280, 3418801], 'euler47': [1, 0, 188, 0, 13254, 0, 415292, 0, 4879681], 'euler5': [1, 0, 4, 0, 54, 0, 100, 0, 625], 'euler53': [1, 0, 148, 0, 11094, 0, 415732, 0, 7890481], 'euler59': [1, 0, -92, 0, 9078, 0, -320252, 0, 12117361], 'euler61': [1, 0, 44, 0, 7926, 0, 163724, 0, 13845841], 'euler67': [1, 24, 484, 5688, 57174, 381096, 2172676, 7218312, 20151121], 'euler7': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler71': [1, 0, 140, 0, 14982, 0, 705740, 0, 25411681], 'euler73': [1, -40, 892, -12760, 129574, -931480, 4753468, -15560680, 28398241], 'euler79': [1, 0, -188, 0, 21318, 0, -1173308, 0, 38950081], 'euler83': [1, 0, -316, 0, 38742, 0, -2176924, 0, 47458321], 'euler89': [1, 0, -340, 0, 44742, 0, -2693140, 0, 62742241], 'euler97': [1, 8, 412, 2360, 61126, 228920, 3876508, 7301384, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 10, 12, 9, 0, 0, 0, 0], [1, 0, 4, 0, 54, 0, 100, 0, 625], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, 20, 0, 342, 0, 2420, 0, 14641], [1, 0, -20, 0, 438, 0, -3380, 0, 28561], [1, 0, -52, 0, 1254, 0, -15028, 0, 83521], [1, -8, 100, -488, 3094, -9272, 36100, -54872, 130321], [1, 0, 76, 0, 2502, 0, 40204, 0, 279841], [1, 0, 52, 0, 2358, 0, 43732, 0, 707281], [1, 0, -124, 0, 5766, 0, -119164, 0, 923521], [1, 0, -20, 0, 2838, 0, -27380, 0, 1874161], [1, 0, -148, 0, 8838, 0, -248788, 0, 2825761], [1, -40, 772, -9160, 72694, -393880, 1427428, -3180280, 3418801], [1, 0, 188, 0, 13254, 0, 415292, 0, 4879681], [1, 0, 148, 0, 11094, 0, 415732, 0, 7890481], [1, 0, -92, 0, 9078, 0, -320252, 0, 12117361], [1, 0, 44, 0, 7926, 0, 163724, 0, 13845841], [1, 24, 484, 5688, 57174, 381096, 2172676, 7218312, 20151121], [1, 0, 140, 0, 14982, 0, 705740, 0, 25411681], [1, -40, 892, -12760, 129574, -931480, 4753468, -15560680, 28398241], [1, 0, -188, 0, 21318, 0, -1173308, 0, 38950081], [1, 0, -316, 0, 38742, 0, -2176924, 0, 47458321], [1, 0, -340, 0, 44742, 0, -2693140, 0, 62742241], [1, 8, 412, 2360, 61126, 228920, 3876508, 7301384, 88529281]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/672/2/j/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': '8-672e4-1.1-c1e4-0-5', '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': '8-672e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 2051625317497354710, 'z1': {'__RealLiteral__': 0, 'data': '0.51899824804953233780099688543', 'prec': 103}}
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{'Lhash': '657908440657389157263018659589,1045850132871548428225747651735,1458743430804847497907129366835,2239304376353401336657778590752', 'Lhash_array': ['657908440657389157263018659589', '1045850132871548428225747651735', '1458743430804847497907129366835', '2239304376353401336657778590752'], 'label': '8-672e4-1.1-c1e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/672/2/j/a'}