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{'Lhash': '1082418643751456434219097540572,1620543022759494411509569633250,1815733214518355381027034494055,1884362834709810762498247974568', 'a10': 0, 'a2': 0, 'a3': -4, 'a4': 0, 'a5': 8, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1698.762334266752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 4, 10, 12, 9]], [67, [1, -32, 390, -2144, 4489]]], 'bad_primes': [2, 3, 67], 'central_character': '804.1', 'coefficient_field': '1.1.1.1', 'conductor': 417853645056, 'conductor_radical': 402, 'degree': 8, 'euler_factors': [[1], [1, 4, 10, 12, 9], [1, -8, 44, -152, 406, -760, 1100, -1000, 625], [1, -6, 21, -54, 116, -378, 1029, -2058, 2401], [1, -2, -13, 10, 124, 110, -1573, -2662, 14641], [1, -18, 161, -954, 4044, -12402, 27209, -39546, 28561], [1, -6, 31, -114, 276, -1938, 8959, -29478, 83521], [1, 6, -11, 54, 1164, 1026, -3971, 41154, 130321], [1, -18, 163, -990, 4980, -22770, 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'10.44485507188771630860668889399915', '10.59983209227105559332709323987133'], 'prelabel': '8-804e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.533766430141292, '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': 1233879138074391247, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.853877751137873816432974287272', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.27838303588364949801333731156', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.43236094724480744087534942019', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 1698.762334266752, 'bad_primes': [2, 3, 67], 'central_character': '1.1', 'conductor': 417853645056, 'conductor_radical': 402, 'degree': 8, 'dirichlet_coefficients': [1, 0, -4, 0, 8, 0, 6, 0, 6, 0, 2, 0, 18, 0, -32, 0, 6, 0, -6, 0, -24, 0, 18, 0, 20, 0, 4, 0, -6, 0, -6, 0, -8, 0, 48, 0, -10, 0, -72, 0, 2, 0, 0, 0, 48, 0, 6, 0, 15, 0, -24, 0, -24, 0, 16, 0, 24, 0, 0, 0, 18, 0, 36, 0, 144, 0, 32, 0, -72, 0, -30, 0, 2, 0, -80, 0, 12, 0, -18, 0, -37, 0, 6, 0, 48, 0, 24, 0, 0, 0, 108, 0, 24, 0, -48, 0, 18, 0, 12, 0], 'euler11': [1, -2, -13, 10, 124, 110, -1573, -2662, 14641], 'euler13': [1, -18, 161, -954, 4044, -12402, 27209, -39546, 28561], 'euler17': [1, -6, 31, -114, 276, -1938, 8959, -29478, 83521], 'euler19': [1, 6, -11, 54, 1164, 1026, -3971, 41154, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -18, 163, -990, 4980, -22770, 86227, -219006, 279841], 'euler29': [1, 6, 23, 66, -372, 1914, 19343, 146334, 707281], 'euler3': [1, 4, 10, 12, 9, 0, 0, 0, 0], 'euler31': [1, 6, 77, 390, 3636, 12090, 73997, 178746, 923521], 'euler37': [1, 10, 25, 10, 556, 370, 34225, 506530, 1874161], 'euler41': [1, -2, -73, 10, 4084, 410, -122713, -137842, 2825761], 'euler43': [1, 0, -12, 0, -2410, 0, -22188, 0, 3418801], 'euler47': [1, -6, 107, -570, 7380, -26790, 236363, -622938, 4879681], 'euler5': [1, -8, 44, -152, 406, -760, 1100, -1000, 625], 'euler53': [1, 24, 428, 4680, 41046, 248040, 1202252, 3573048, 7890481], 'euler59': [1, 0, -196, 0, 16182, 0, -682276, 0, 12117361], 'euler61': [1, -18, 225, -2106, 16556, -128466, 837225, -4085658, 13845841], 'euler67': [1, -32, 390, -2144, 4489, 0, 0, 0, 0], 'euler7': [1, -6, 21, -54, 116, -378, 1029, -2058, 2401], 'euler71': [1, 30, 499, 5970, 55860, 423870, 2515459, 10737330, 25411681], 'euler73': [1, -2, -119, 46, 9508, 3358, -634151, -778034, 28398241], 'euler79': [1, 18, 261, 2754, 25700, 217566, 1628901, 8874702, 38950081], 'euler83': [1, -6, 83, -426, -852, -35358, 571787, -3430722, 47458321], 'euler89': [1, 0, -76, 0, 3462, 0, -601996, 0, 62742241], 'euler97': [1, -18, 257, -2682, 23268, -260154, 2418113, -16428114, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 10, 12, 9, 0, 0, 0, 0], [1, -8, 44, -152, 406, -760, 1100, -1000, 625], [1, -6, 21, -54, 116, -378, 1029, -2058, 2401], [1, -2, -13, 10, 124, 110, -1573, -2662, 14641], [1, -18, 161, -954, 4044, -12402, 27209, -39546, 28561], [1, -6, 31, -114, 276, -1938, 8959, -29478, 83521], [1, 6, -11, 54, 1164, 1026, -3971, 41154, 130321], [1, -18, 163, -990, 4980, -22770, 86227, -219006, 279841], [1, 6, 23, 66, -372, 1914, 19343, 146334, 707281], [1, 6, 77, 390, 3636, 12090, 73997, 178746, 923521], [1, 10, 25, 10, 556, 370, 34225, 506530, 1874161], [1, -2, -73, 10, 4084, 410, -122713, -137842, 2825761], [1, 0, -12, 0, -2410, 0, -22188, 0, 3418801], [1, -6, 107, -570, 7380, -26790, 236363, -622938, 4879681], [1, 24, 428, 4680, 41046, 248040, 1202252, 3573048, 7890481], [1, 0, -196, 0, 16182, 0, -682276, 0, 12117361], [1, -18, 225, -2106, 16556, -128466, 837225, -4085658, 13845841], [1, -32, 390, -2144, 4489, 0, 0, 0, 0], [1, 30, 499, 5970, 55860, 423870, 2515459, 10737330, 25411681], [1, -2, -119, 46, 9508, 3358, -634151, -778034, 28398241], [1, 18, 261, 2754, 25700, 217566, 1628901, 8874702, 38950081], [1, -6, 83, -426, -852, -35358, 571787, -3430722, 47458321], [1, 0, -76, 0, 3462, 0, -601996, 0, 62742241], [1, -18, 257, -2682, 23268, -260154, 2418113, -16428114, 88529281]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/804/2/o/b'], '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': '8-804e4-1.1-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': '8-804e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.533766430141292, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1233879138074391247, 'z1': {'__RealLiteral__': 0, 'data': '0.853877751137873816432974287272', 'prec': 107}}
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{'Lhash': '1082418643751456434219097540572,1620543022759494411509569633250,1815733214518355381027034494055,1884362834709810762498247974568', 'Lhash_array': ['1082418643751456434219097540572', '1620543022759494411509569633250', '1815733214518355381027034494055', '1884362834709810762498247974568'], 'label': '8-804e4-1.1-c1e4-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/804/2/o/b'}