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{'Lhash': '1593306318092928036233359784108,1943590791790904054565638309770,2069208248803859344623070366432,2191625912437677970328968685402', 'a10': -4, 'a2': -1, 'a3': 1, 'a4': -3, 'a5': 4, 'a6': -1, 'a7': -3, 'a8': 2, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 198980.78210023177, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -4, 6, -4, 1]], [23, [1]]], 'bad_primes': [5, 23], 'central_character': '2645.1', 'coefficient_field': '1.1.1.1', 'conductor': 48944365800625, 'conductor_radical': 115, 'degree': 8, 'euler_factors': [[1, 1, 4, 5, 10, 10, 16, 8, 16], [1, -1, 2, 4, -8, 12, 18, -27, 81], [1, -4, 6, -4, 1], [1, 3, 8, 26, 120, 182, 392, 1029, 2401], [1, 5, 49, 163, 835, 1793, 5929, 6655, 14641], [1, 0, 23, 75, 214, 975, 3887, 0, 28561], [1, -5, 32, -90, 584, -1530, 9248, -24565, 83521], [1, 4, 27, 137, 357, 2603, 9747, 27436, 130321], [1], [1, 5, 53, 262, 2590, 7598, 44573, 121945, 707281], [1, 13, 161, 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{'algebraic': True, 'analytic_conductor': 198980.78210023177, 'bad_primes': [5, 23], 'central_character': '1.1', 'conductor': 48944365800625, 'conductor_radical': 115, 'degree': 8, 'dirichlet_coefficients': [1, -1, 1, -3, 4, -1, -3, 2, -1, -4, -5, -3, 0, 3, 4, 5, 5, 1, -4, -12, -3, 5, 0, 2, 10, 0, -7, 9, -5, -4, -13, 2, -5, -5, -12, 3, -3, 4, 0, 8, -20, 3, -12, 15, -4, 0, -9, 5, 1, -10, 5, 0, -5, 7, -20, -6, -4, 5, -4, -12, -12, 13, 3, -8, 0, 5, -18, -15, 0, 12, 30, -2, 1, 3, 10, 12, 15, 0, -16, 20, -1, 20, -24, 9, 20, 12, -5, -10, 9, 4, 0, 0, -13, 9, -16, 2, -39, -1, 5, -30], 'euler11': [1, 5, 49, 163, 835, 1793, 5929, 6655, 14641], 'euler13': [1, 0, 23, 75, 214, 975, 3887, 0, 28561], 'euler17': [1, -5, 32, -90, 584, -1530, 9248, -24565, 83521], 'euler19': [1, 4, 27, 137, 357, 2603, 9747, 27436, 130321], 'euler2': [1, 1, 4, 5, 10, 10, 16, 8, 16], 'euler23': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler29': [1, 5, 53, 262, 2590, 7598, 44573, 121945, 707281], 'euler3': [1, -1, 2, 4, -8, 12, 18, -27, 81], 'euler31': [1, 13, 161, 1163, 7861, 36053, 154721, 387283, 923521], 'euler37': [1, 3, 110, 238, 5520, 8806, 150590, 151959, 1874161], 'euler41': [1, 20, 287, 2739, 20345, 112299, 482447, 1378420, 2825761], 'euler43': [1, 12, 205, 1529, 13844, 65747, 379045, 954084, 3418801], 'euler47': [1, 9, 111, 524, 5012, 24628, 245199, 934407, 4879681], 'euler5': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler53': [1, 5, 118, 694, 7486, 36782, 331462, 744385, 7890481], 'euler59': [1, 4, 171, 791, 13404, 46669, 595251, 821516, 12117361], 'euler61': [1, 12, 278, 2176, 26415, 132736, 1034438, 2723772, 13845841], 'euler67': [1, 18, 311, 2953, 29748, 197851, 1396079, 5413734, 20151121], 'euler7': [1, 3, 8, 26, 120, 182, 392, 1029, 2401], 'euler71': [1, -30, 585, -7567, 74555, -537257, 2948985, -10737330, 25411681], 'euler73': [1, -1, 134, -420, 8898, -30660, 714086, -389017, 28398241], 'euler79': [1, 16, 278, 2984, 31759, 235736, 1734998, 7888624, 38950081], 'euler83': [1, 24, 449, 5977, 60332, 496091, 3093161, 13722888, 47458321], 'euler89': [1, -9, 266, -2012, 32324, -179068, 2106986, -6344721, 62742241], 'euler97': [1, 39, 898, 13972, 159698, 1355284, 8449282, 35594247, 88529281], 'euler_factors': [[1, 1, 4, 5, 10, 10, 16, 8, 16], [1, -1, 2, 4, -8, 12, 18, -27, 81], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 3, 8, 26, 120, 182, 392, 1029, 2401], [1, 5, 49, 163, 835, 1793, 5929, 6655, 14641], [1, 0, 23, 75, 214, 975, 3887, 0, 28561], [1, -5, 32, -90, 584, -1530, 9248, -24565, 83521], [1, 4, 27, 137, 357, 2603, 9747, 27436, 130321], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 5, 53, 262, 2590, 7598, 44573, 121945, 707281], [1, 13, 161, 1163, 7861, 36053, 154721, 387283, 923521], [1, 3, 110, 238, 5520, 8806, 150590, 151959, 1874161], [1, 20, 287, 2739, 20345, 112299, 482447, 1378420, 2825761], [1, 12, 205, 1529, 13844, 65747, 379045, 954084, 3418801], [1, 9, 111, 524, 5012, 24628, 245199, 934407, 4879681], [1, 5, 118, 694, 7486, 36782, 331462, 744385, 7890481], [1, 4, 171, 791, 13404, 46669, 595251, 821516, 12117361], [1, 12, 278, 2176, 26415, 132736, 1034438, 2723772, 13845841], [1, 18, 311, 2953, 29748, 197851, 1396079, 5413734, 20151121], [1, -30, 585, -7567, 74555, -537257, 2948985, -10737330, 25411681], [1, -1, 134, -420, 8898, -30660, 714086, -389017, 28398241], [1, 16, 278, 2984, 31759, 235736, 1734998, 7888624, 38950081], [1, 24, 449, 5977, 60332, 496091, 3093161, 13722888, 47458321], [1, -9, 266, -2012, 32324, -179068, 2106986, -6344721, 62742241], [1, 39, 898, 13972, 159698, 1355284, 8449282, 35594247, 88529281]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2645/2/a/l'], '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': '8-2645e4-1.1-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': 4, 'prelabel': '8-2645e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.595697045566502, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 240446069453431769, 'z1': {'__RealLiteral__': 0, 'data': '1.25689706438514459069855289791', 'prec': 103}}
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{'Lhash': '1593306318092928036233359784108,1943590791790904054565638309770,2069208248803859344623070366432,2191625912437677970328968685402', 'Lhash_array': ['1593306318092928036233359784108', '1943590791790904054565638309770', '2069208248803859344623070366432', '2191625912437677970328968685402'], 'label': '8-2645e4-1.1-c1e4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2645/2/a/l'}