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'trace_hash': 1467090975463980512, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19556023110908663204122553119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.63712503260384284201440131060', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.13214929686437944892638840308', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 5490.140660461492, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 1350439223056, 'conductor_radical': 154, 'degree': 8, 'dirichlet_coefficients': [1, -2, -2, 1, -4, 4, 0, 2, 5, 8, -2, -2, 4, 0, 8, -4, -4, -10, -4, -4, 0, 4, 4, -4, 12, -8, -10, 0, -12, -16, -8, 2, 4, 8, 0, 5, 16, 8, -8, -8, 16, 0, 0, -2, -20, -8, -4, 8, 0, -24, 8, 4, 4, 20, 8, 0, 8, 24, -14, 8, 18, 16, 0, 3, -16, -8, -14, -4, -8, 0, -16, 10, -16, -32, -24, -4, 0, 16, 18, 16, 17, -32, -8, 0, 16, 0, 24, -4, 8, 40, 0, 4, 16, 8, 16, -4, 4, 0, -10, 12], 'euler11': [1, 2, 3, 2, 1, 0, 0, 0, 0], 'euler13': [1, -4, 42, -128, 803, -1664, 7098, -8788, 28561], 'euler17': [1, 4, 10, -112, -525, -1904, 2890, 19652, 83521], 'euler19': [1, 4, -24, 8, 935, 152, -8664, 27436, 130321], 'euler2': [1, 2, 3, 2, 1, 0, 0, 0, 0], 'euler23': [1, -4, -16, 56, 127, 1288, -8464, -48668, 279841], 'euler29': [1, 12, 106, 768, 4995, 22272, 89146, 292668, 707281], 'euler3': [1, 2, -1, -2, 4, -6, -9, 54, 81], 'euler31': [1, 8, -14, 128, 3139, 3968, -13454, 238328, 923521], 'euler37': [1, -16, 120, -992, 7655, -36704, 164280, -810448, 1874161], 'euler41': [1, -16, 256, -2192, 17826, -89872, 430336, -1102736, 2825761], 'euler43': [1, 0, 108, 0, 6614, 0, 199692, 0, 3418801], 'euler47': [1, 4, -10, -272, -2285, -12784, -22090, 415292, 4879681], 'euler5': [1, 4, 4, 8, 39, 40, 100, 500, 625], 'euler53': [1, -4, 4, 376, -3513, 19928, 11236, -595508, 7890481], 'euler59': [1, 14, 31, 658, 12180, 38822, 107911, 2875306, 12117361], 'euler61': [1, -18, 129, -1314, 14540, -80154, 480009, -4085658, 13845841], 'euler67': [1, 14, 31, 434, 9604, 29078, 139159, 4210682, 20151121], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 16, 280, 2864, 30834, 203344, 1411480, 5726576, 25411681], 'euler73': [1, 16, 48, 992, 19247, 72416, 255792, 6224272, 28398241], 'euler79': [1, -18, 103, -1134, 17004, -89586, 642823, -8874702, 38950081], 'euler83': [1, 8, -44, 424, 17334, 35192, -303116, 4574296, 47458321], 'euler89': [1, -8, -58, 448, 1267, 39872, -459418, -5639752, 62742241], 'euler97': [1, -4, 378, -1136, 54563, -110192, 3556602, -3650692, 88529281], 'euler_factors': [[1, 2, 3, 2, 1, 0, 0, 0, 0], [1, 2, -1, -2, 4, -6, -9, 54, 81], [1, 4, 4, 8, 39, 40, 100, 500, 625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 3, 2, 1, 0, 0, 0, 0], [1, -4, 42, -128, 803, -1664, 7098, -8788, 28561], [1, 4, 10, -112, -525, -1904, 2890, 19652, 83521], [1, 4, -24, 8, 935, 152, -8664, 27436, 130321], [1, -4, -16, 56, 127, 1288, -8464, -48668, 279841], [1, 12, 106, 768, 4995, 22272, 89146, 292668, 707281], [1, 8, -14, 128, 3139, 3968, -13454, 238328, 923521], [1, -16, 120, -992, 7655, -36704, 164280, -810448, 1874161], [1, -16, 256, -2192, 17826, -89872, 430336, -1102736, 2825761], [1, 0, 108, 0, 6614, 0, 199692, 0, 3418801], [1, 4, -10, -272, -2285, -12784, -22090, 415292, 4879681], [1, -4, 4, 376, -3513, 19928, 11236, -595508, 7890481], [1, 14, 31, 658, 12180, 38822, 107911, 2875306, 12117361], [1, -18, 129, -1314, 14540, -80154, 480009, -4085658, 13845841], [1, 14, 31, 434, 9604, 29078, 139159, 4210682, 20151121], [1, 16, 280, 2864, 30834, 203344, 1411480, 5726576, 25411681], [1, 16, 48, 992, 19247, 72416, 255792, 6224272, 28398241], [1, -18, 103, -1134, 17004, -89586, 642823, -8874702, 38950081], [1, 8, -44, 424, 17334, 35192, -303116, 4574296, 47458321], [1, -8, -58, 448, 1267, 39872, -459418, -5639752, 62742241], [1, -4, 378, -1136, 54563, -110192, 3556602, -3650692, 88529281]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/e/m'], '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': '8-1078e4-1.1-c1e4-0-3', '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': '8-1078e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1467090975463980512, 'z1': {'__RealLiteral__': 0, 'data': '0.19556023110908663204122553119', 'prec': 103}}
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{'Lhash': '247902044346204929061622570668,807651930000691605855003598078,1435169735718098483487476299576,1780407596061610685237240390581', 'Lhash_array': ['247902044346204929061622570668', '807651930000691605855003598078', '1435169735718098483487476299576', '1780407596061610685237240390581'], 'label': '8-1078e4-1.1-c1e4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/e/m'}