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{'Lhash': '949314722333919582347907683699,1193151020319330065037890174663,1629502370639165897169732526917,2521665027532356418677724119060', 'a10': -9, 'a2': -3, 'a3': 2, 'a4': 3, 'a5': 3, 'a6': -6, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 669.3698663148037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [13, [1, -14, 75, -182, 169]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': '1.1.1.1', 'conductor': 164648481361, 'conductor_radical': 91, 'degree': 8, 'euler_factors': [[1, 3, 6, 9, 11, 18, 24, 24, 16], [1, -2, 3, -8, 25, -24, 27, -54, 81], [1, -3, 12, -27, 71, -135, 300, -375, 625], [1], [1, 0, -27, 0, 377, 0, -3267, 0, 14641], [1, -14, 75, -182, 169], [1, 6, -7, 54, 948, 918, -2023, 29478, 83521], [1, 0, -31, 0, 537, 0, -11191, 0, 130321], [1, 6, 2, -72, -201, -1656, 1058, 73002, 279841], [1, -9, 8, -135, 2139, -3915, 6728, -219501, 707281], [1, -30, 437, 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{'algebraic': True, 'analytic_conductor': 669.3698663148037, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 164648481361, 'conductor_radical': 91, 'degree': 8, 'dirichlet_coefficients': [1, -3, 2, 3, 3, -6, 0, 0, 1, -9, 0, 6, 14, 0, 6, -2, -6, -3, 0, 9, 0, 0, -6, 0, -3, -42, 4, 0, 9, -18, 30, -6, 0, 18, 0, 3, -24, 0, 28, 0, 18, 0, -5, 0, 3, 18, 24, -4, 0, 9, -12, 42, 6, -12, 0, 0, 0, -27, -6, 18, -4, -90, 0, 27, 42, 0, 0, -18, -12, 0, 6, 0, -12, 72, -6, 0, 0, -84, 12, -6, -4, -54, 0, 0, -18, 15, 18, 0, 33, -9, 0, -18, 60, -72, 0, -12, -39, 0, 0, -9], 'euler11': [1, 0, -27, 0, 377, 0, -3267, 0, 14641], 'euler13': [1, -14, 75, -182, 169, 0, 0, 0, 0], 'euler17': [1, 6, -7, 54, 948, 918, -2023, 29478, 83521], 'euler19': [1, 0, -31, 0, 537, 0, -11191, 0, 130321], 'euler2': [1, 3, 6, 9, 11, 18, 24, 24, 16], 'euler23': [1, 6, 2, -72, -201, -1656, 1058, 73002, 279841], 'euler29': [1, -9, 8, -135, 2139, -3915, 6728, -219501, 707281], 'euler3': [1, -2, 3, -8, 25, -24, 27, -54, 81], 'euler31': [1, -30, 437, -4110, 27108, -127410, 419957, -893730, 923521], 'euler37': [1, 24, 314, 2928, 20619, 108336, 429866, 1215672, 1874161], 'euler41': [1, -18, 210, -1836, 13151, -75276, 353010, -1240578, 2825761], 'euler43': [1, 5, -20, -205, -899, -8815, -36980, 397535, 3418801], 'euler47': [1, -24, 327, -3240, 25040, -152280, 722343, -2491752, 4879681], 'euler5': [1, -3, 12, -27, 71, -135, 300, -375, 625], 'euler53': [1, -6, 5, 450, -3756, 23850, 14045, -893262, 7890481], 'euler59': [1, 6, 21, 54, -2692, 3186, 73101, 1232274, 12117361], 'euler61': [1, 4, -128, -20, 12286, -1220, -476288, 907924, 13845841], 'euler67': [1, 0, -118, 0, 9435, 0, -529702, 0, 20151121], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, -6, 150, -828, 14855, -58788, 756150, -2147466, 25411681], 'euler73': [1, 12, 206, 1896, 23139, 138408, 1097774, 4668204, 28398241], 'euler79': [1, -12, -50, -432, 20019, -34128, -312050, -5916468, 38950081], 'euler83': [1, 0, -270, 0, 31667, 0, -1860030, 0, 47458321], 'euler89': [1, -33, 588, -7425, 75011, -660825, 4657548, -23263977, 62742241], 'euler97': [1, 39, 812, 11895, 132795, 1153815, 7640108, 35594247, 88529281], 'euler_factors': [[1, 3, 6, 9, 11, 18, 24, 24, 16], [1, -2, 3, -8, 25, -24, 27, -54, 81], [1, -3, 12, -27, 71, -135, 300, -375, 625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -27, 0, 377, 0, -3267, 0, 14641], [1, -14, 75, -182, 169, 0, 0, 0, 0], [1, 6, -7, 54, 948, 918, -2023, 29478, 83521], [1, 0, -31, 0, 537, 0, -11191, 0, 130321], [1, 6, 2, -72, -201, -1656, 1058, 73002, 279841], [1, -9, 8, -135, 2139, -3915, 6728, -219501, 707281], [1, -30, 437, -4110, 27108, -127410, 419957, -893730, 923521], [1, 24, 314, 2928, 20619, 108336, 429866, 1215672, 1874161], [1, -18, 210, -1836, 13151, -75276, 353010, -1240578, 2825761], [1, 5, -20, -205, -899, -8815, -36980, 397535, 3418801], [1, -24, 327, -3240, 25040, -152280, 722343, -2491752, 4879681], [1, -6, 5, 450, -3756, 23850, 14045, -893262, 7890481], [1, 6, 21, 54, -2692, 3186, 73101, 1232274, 12117361], [1, 4, -128, -20, 12286, -1220, -476288, 907924, 13845841], [1, 0, -118, 0, 9435, 0, -529702, 0, 20151121], [1, -6, 150, -828, 14855, -58788, 756150, -2147466, 25411681], [1, 12, 206, 1896, 23139, 138408, 1097774, 4668204, 28398241], [1, -12, -50, -432, 20019, -34128, -312050, -5916468, 38950081], [1, 0, -270, 0, 31667, 0, -1860030, 0, 47458321], [1, -33, 588, -7425, 75011, -660825, 4657548, -23263977, 62742241], [1, 39, 812, 11895, 132795, 1153815, 7640108, 35594247, 88529281]], 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/u/e'], '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': '8-637e4-1.1-c1e4-0-19', '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': '8-637e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1003383957729687654, 'z1': {'__RealLiteral__': 0, 'data': '0.74887727119996927461514584847', 'prec': 103}}
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{'Lhash': '949314722333919582347907683699,1193151020319330065037890174663,1629502370639165897169732526917,2521665027532356418677724119060', 'Lhash_array': ['949314722333919582347907683699', '1193151020319330065037890174663', '1629502370639165897169732526917', '2521665027532356418677724119060'], 'label': '8-637e4-1.1-c1e4-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/u/e'}