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{'Lhash': '1343732877530133714462143786263,1457303604592262246103183977163,1549170400173951425561430075044,1989229905558270400833398985260', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 3, 'a5': -3, 'a6': 0, '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, 0, -3, 0, 5, 0, -12, 0, 16], [1, 1, 0, -5, -11, -15, 0, 27, 81], [1, 3, 12, 27, 71, 135, 300, 375, 625], [1], [1, -9, 54, -243, 905, -2673, 6534, -11979, 14641], [1, -14, 75, -182, 169], [1, -12, 122, -720, 3651, -12240, 35258, -58956, 83521], [1, -9, 56, -261, 993, -4959, 20216, -61731, 130321], [1, -12, 104, -684, 3870, -15732, 55016, -146004, 279841], [1, -9, 8, -135, 2139, -3915, 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'10.79526417684735664833950029497428', '10.93255889481806058243812868331416'], 'prelabel': '8-637e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, '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': 949287619917119317, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06001833414365627601565033938', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.14960984070049545214224612595', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.22207996422282042602728488688', 'prec': 103}}
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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, 0, -1, 3, -3, 0, 0, 0, 1, 0, 9, -3, 14, 0, 3, 4, 12, 0, 9, -9, 0, 0, 12, 0, -3, 0, 4, 0, 9, 0, -30, 0, -9, 0, 0, 3, 0, 0, -14, 0, 18, 0, -5, 27, -3, 0, -24, -4, 0, 0, -12, 42, 6, 0, -27, 0, -9, 0, 0, 9, 2, 0, 0, 9, -42, 0, -12, 36, -12, 0, 6, 0, 12, 0, 3, 27, 0, 0, 12, -12, 2, 0, 0, 0, -36, 0, -9, 0, 0, 0, 0, 36, 30, 0, -27, 0, -39, 0, 9, -9], 'euler11': [1, -9, 54, -243, 905, -2673, 6534, -11979, 14641], 'euler13': [1, -14, 75, -182, 169, 0, 0, 0, 0], 'euler17': [1, -12, 122, -720, 3651, -12240, 35258, -58956, 83521], 'euler19': [1, -9, 56, -261, 993, -4959, 20216, -61731, 130321], 'euler2': [1, 0, -3, 0, 5, 0, -12, 0, 16], 'euler23': [1, -12, 104, -684, 3870, -15732, 55016, -146004, 279841], 'euler29': [1, -9, 8, -135, 2139, -3915, 6728, -219501, 707281], 'euler3': [1, 1, 0, -5, -11, -15, 0, 27, 81], 'euler31': [1, 30, 437, 4110, 27108, 127410, 419957, 893730, 923521], 'euler37': [1, 0, -52, 0, 3414, 0, -71188, 0, 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, 0, -6, 0, 5627, 0, -20886, 0, 12117361], 'euler61': [1, -2, 70, 376, 391, 22936, 260470, -453962, 13845841], 'euler67': [1, 12, 131, 996, 5616, 66732, 588059, 3609156, 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, 0, -87, 0, 1853, 0, -689127, 0, 62742241], 'euler97': [1, 39, 812, 11895, 132795, 1153815, 7640108, 35594247, 88529281], 'euler_factors': [[1, 0, -3, 0, 5, 0, -12, 0, 16], [1, 1, 0, -5, -11, -15, 0, 27, 81], [1, 3, 12, 27, 71, 135, 300, 375, 625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -9, 54, -243, 905, -2673, 6534, -11979, 14641], [1, -14, 75, -182, 169, 0, 0, 0, 0], [1, -12, 122, -720, 3651, -12240, 35258, -58956, 83521], [1, -9, 56, -261, 993, -4959, 20216, -61731, 130321], [1, -12, 104, -684, 3870, -15732, 55016, -146004, 279841], [1, -9, 8, -135, 2139, -3915, 6728, -219501, 707281], [1, 30, 437, 4110, 27108, 127410, 419957, 893730, 923521], [1, 0, -52, 0, 3414, 0, -71188, 0, 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, 0, -6, 0, 5627, 0, -20886, 0, 12117361], [1, -2, 70, 376, 391, 22936, 260470, -453962, 13845841], [1, 12, 131, 996, 5616, 66732, 588059, 3609156, 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, 0, -87, 0, 1853, 0, -689127, 0, 62742241], [1, 39, 812, 11895, 132795, 1153815, 7640108, 35594247, 88529281]], 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/k/d'], '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-c1e4-0-27', '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': 949287619917119317, 'z1': {'__RealLiteral__': 0, 'data': '1.06001833414365627601565033938', 'prec': 103}}
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{'Lhash': '1343732877530133714462143786263,1457303604592262246103183977163,1549170400173951425561430075044,1989229905558270400833398985260', 'Lhash_array': ['1343732877530133714462143786263', '1457303604592262246103183977163', '1549170400173951425561430075044', '1989229905558270400833398985260'], 'label': '8-637e4-1.1-c1e4-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/k/d'}