# Stored data for newform 354.4.a.g, downloaded from the LMFDB on 25 April 2024.
{"label": "354.4.a.g", "space_label": "354.4.a", "level": 354, "weight": 4, "hecke_orbit": 7, "hecke_orbit_code": 27021597831332194, "dim": 3, "is_polredabs": true, "nf_label": "3.3.47277.1", "trace_hash": 328434225627523951, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [-200, 9, 18, 1]]], "qexp_display": "q+2q^{2}-3q^{3}+4q^{4}+(-6+\\beta _{1}+\\beta _{2})q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5664, "fricke_eigenval": -1, "atkin_lehner_string": "-++", "analytic_conductor": 20.886676142032176, "hecke_ring_index": 1, "level_radical": 354, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [354, 1, [119, 61], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 3, 59], "conrey_indexes": [1], "field_disc": 47277, "field_disc_factorization": [[3, 3], [17, 1], [103, 1]], "field_poly": [-25, -48, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.986", "prec": 17}, {"__RealLiteral__": 0, "data": "0.406", "prec": 17}, {"__RealLiteral__": 0, "data": "24.636", "prec": 20}, {"__RealLiteral__": 0, "data": "13.309", "prec": 20}, {"__RealLiteral__": 0, "data": "312.382", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, 1], [59, 1]], "trace_display": [6, -9, -18, 6], "traces": [0, 3, 6, -9, 12, -18, -18, 6, 24, 27, -36, -9, -36, -45, 12, 54, 48, -96, 54, -171, -72, -18, -18, -177, -72, -69, -90, -81, 24, -351, 108, -267, 96, 27, -192, -489, 108, -222, -342, 135, -144, -780, -36, 21, -36, -162, -354, -717, -144, 99, -138, 288, -180, -234, -162, 114, 48, 513, -702, -177, 216, 615, -534, 54, 192, 606, 54, -144, -384, 531, -978, 981, 216, -63, -444, 207, -684, -792, 270, 555, -288, 243, -1560, 66, -72, -807, 42, 1053, -72, -1389, -324, -222, -708, 801, -1434, 1587, -288, 960, 198, -81, -276, -1053, 576, 990, -360, 1467, -468, 1935, -324, 471, 228, 666, 96, 2388, 1026, 3495, -1404, -405, -354, 2415, 432, 1146, 1230, 2340, -1068, -246, 108, 2652, 384, -63, 1212, -1314, 108, -750, -288, 486, -768, 2361, 1062, -954, -1956, 2151, 1962, -4857, 432, 4173, -126, -297, -888, -2226, 414, 4005, -1368, -864, -1584, -813, 540, 2298, 1110, 702, -576, -6000, 486, 3225, -3120, -342, 132, 3405, -144, -252, -1614, -1539, 84, -6912, 2106, 5883, -144, 531, -2778, -441, -648, 489, -444, -1845, -1416, -1569, 1602, 4326, -2868, -162, 3174, 1188, -576, -1683, 1920, -1818, 396, -1782, -162, 1131, -552, 432, -2106, -5829, 1152, 6087, 1980, -1593, -720, -6321, 2934, 3810, -936, -2943, 3870, 4404, -648, 6981, 942, 189, 456, -5364, 1332, 3081, 192, -621, 4776, 834, 2052, 1548, 6990, 2376, -2808, -6822, -810, 8181, -708, -1665, 4830, 6174, 864, -3981, 2292, -729, 2460, -2073, 4680, 10521, -2136, -198, -492, -10476, 216, 1905, 5304, 2421, 768, -1665, -126, 3885, 2424, -3159, -2628, 1086, 216, -378, -1500, 4167, -576, -14475, 972, -1311, -1536, 666, 4722, 4419, 2124, -4452, -1908, -2403, -3912, -3069, 4302, -5334, 3924, -4761, -9714, -3426, 864, 1893, 8346, -2880, -252, -9045, -594, 1062, -1776, 243, -4452, 6147, 828, -11118, 8010, 3159, -2736, -12081, -1728, -1854, -3168, -2970, -1626, 4968, 1080, -8463, 4596, -4401, 2220, -8046, 1404, 4863, -1152, -5805, -12000, -4575, 972, -8997, 6450, -1413, -6240, -11025, -684, -21000, 264, -1998, 6810, -3420, -288, -1659, -504, -7164, -3228, -15849, -3078, -2217, 168, -10485, -13824, -7461, 4212, 2349, 11766, 1215, -288, -5613, 1062, -8106, -5556, -7245, -882, 8229, -1296, 390, 978, -3438, -888, 3207, -3690, -15174, -2832, -7020, -3138, 3609, 3204, 3789, 8652, 738, -5736, 5589, -324, -15594, 6348, -7956, 2376, 3345, -1152, -6963, -3366, 189, 3840, 12306, -3636, -10773, 792, 3942, -3564, -20100, -324, -13830, 2262, 2250, -1104, -333, 864, 15825, -4212, -1458, -11658, 18252, 2304, 5046, 12174, -7083, 3960, -354, -3186, 26091, -1440, 2862, -12642, 13431, 5868, 22293, 7620, -6453, -1872, 26991, -5886, 18597, 7740, 14571, 8808, 7851, -1296, 24684, 13962, -12519, 1884, 16107, 378, -29142, 912, 891, -10728, 5508, 2664, -2787, 6162, 6678, 384, -7431, -1242, -8058, 9552, -12015, 1668, 23163, 4104, 9957, 3096, 2592, 13980, 18987, 4752, -2427, -5616, 2439, -13644, 27735, -1620, 11901, 16362, -6894, -1416, 7677, -3330, -11316, 9660, -2106, 12348, 33387, 1728, -20058, -7962, 18000, 4584, -15036, -1458, 2760, 4920, -9675, -4146, 11505, 9360, -420, 21042, 1026, -4272, 9588, -396, 2616, -984, -10215, -20952, 7995, 432, 4374, 3810, 756, 10608, 1869, 4842, -1425, 1536, 4617, -3330, 894, -252, 9057, 7770, 20736, 4848, -16737, -6318, 16428, -5256, -17649, 2172, 11484, 432, 3918, -756, -1593, -3000, 24912, 8334, 7719, -1152, 1323, -28950, 29181, 1944, -52125, -2622, -1467, -3072, 20967, 1332, 32337, 9444, 5535, 8838, 21486, 4248, 33588, -8904, 4707, -3816, -6996, -4806, 1005, -7824, -12978, -6138, 2742, 8604, 10482, -10668, 486, 7848, 33651, -9522, -12750, -19428, -3564, -6852, -31050, 1728, -9873, 3786, 5049, 16692, -62616, -5760, 162, -504, 5454, -18090, 8103, -1188, 30264, 2124, 5346, -3552, -12669, 486, -18546, -8904, -3393, 12294, -1557, 1656, -7983, -22236, -1296, 16020, 9540, 6318, 26457, -5472, 17487, -24162, 11607, -3456, -12561, -3708, -18261, -6336, -19188, -5940, -42078, -3252, 4779, 9936, 34047, 2160, 11199, -16926, 18963, 9192, 43524, -8802, -30489, 4440, -11430, -16092, 7644, 2808, -33921, 9726, 8829, -2304, 36306, -11610, 8973, -24000, -13212, -9150, -3648, 1944, 531, -17994, -20943, 12900, -16695, -2826, 4134, -12480, -567, -22050, -23307, -1368, 26757, -42000, 16092, 528, 51486, -3996, 46506, 13620, -9243, -6840, 10257, -576, 1398, -3318, 1863, -1008, -8922, -14328, 28077, -6456, -2502, -31698, 35043, -6156, -31590, -4434, -4644, 336, 486, -20970, -66819, -27648, -7128, -14922, 18174, 8424, 5661, 4698, 20466, 23532, -35796, 2430, -20955, -576, -24543, -11226, 909, 2124, -44520, -16212, 4995, -11112, -15912, -14490, 20322, -1764, -18522, 16458, -2901, -2592, -32598, 780, 11943, 1956, -19122, -6876, 80253, -1776, 2187, 6414, -26742, -7380, 12156, -30348, 6219, -5664, -19968, -14040, 19878, -6276, -31563, 7218, -5187, 6408, 24135, 7578, 594, 17304, -36930, 1476, -4296, -11472, 31428, 11178, -62139, -648, 34887, -31188, -5715, 12696, -39576, -15912, -59622, 4752, -7263, 6690, 2655, -2304, 26553, -13926, 4995, -6732, -16404, 378, 25716, 7680, -11655, 24612, 63330, -7272, -23991, -21546, 9477, 1584, -30528, 7884, -29052, -7128, -3258, -40200, -42117, -648, -38109, -27660, 1134, 4524, -41973, 4500, 864, -2208, -12501, -666, -40341, 1728, 73110, 31650, 43425, -8424, -31215, -2916, -68577, -23316, 3933, 36504, -18639, 4608, 2883, 10092, -1998, 24348, 10728, -14166, 9024, 7920, -13257, -708, -87054, -6372, -5895, 52182, 13356, -2880, 33348, 5724, -24285, -25284, 7209, 26862, -15204, 11736, -8532, 44586, 9207, 15240, -13656, -12906, -16164, -3744, 16002, 53982, -20241, -11772, -37545, 37194, 14283, 15480, -55080, 29142, -17268, 17616, 10278, 15702, 31539, -2592, 47271, 49368, -5679, 27924, 40371, -25038, 13992, 3768, 8640, 32214, 8457, 756, 56148, -58284, 27135, 1824, -28116, 1782, 63072, -21456, -3186, 11016, 5286, 5328, -36969, -5574, -729, 12324, 43980, 13356, -2328, 768, -18441, -14862, -3921, -2484, 19935, -16116, 33354, 19104, 10353, -24030, -18864, 3336, -9477, 46326, -5256, 8208, 25020, 19914, 36243, 6192, 8976, 5184, -28872, 27960, 5562, 37974, 1893, 9504, 66207, -4854, 8910, -11232, -35592, 4878, -50982, -27288, -14904, 55470, -44805, -3240, -41778, 23802, 25389, 32724, -57024, -13788, 61956, -2832, 13203, 15354, -2559, -6660, 47133, -22632, 24138, 19320, 5457, -4212, -62592, 24696, -14589, 66774, 23574, 3456, 13590, -40116, 17415, -15924, 49968, 36000, 18459, 9168, 13725, -30072, -68661, -2916, -4923, 5520, 26991, 9840, -131742, -19350, -90255, -8292, 4239, 23010, 63384, 18720, -10626, -840, 33075, 42084, 55221, 2052, -115209, -8544, 63000, 19176, 52857, -792, -67173, 5232, 5994, -1968, -996, -20430, 5664, -41904, 10260, 15990, 8289, 864, 65436, 8748, 4977, 7620, -35085, 1512, 89859, 21216, 21492, 3738, 81522, 9684, 47559, -2850, 47547, 3072, -13563, 9234, -83901, -6660, 6651, 1788, -13698, -504, -6090, 18114, 31455, 15540, 51744, 41472, -39621, 9696, 22383, -33474, -29511, -12636, 25785, 32856, -7047, -10512, 19689, -35298, -59424, 4344, -3645, 22968, -107403, 864, 86205, 7836, 16839, -1512, -33921, -3186, -102357, -6000, 24318, 49824, -45168, 16668, -42822, 15438, 21735, -2304, 7230, 2646, -60693, -57900, -24687, 58362, 26766, 3888, 90684, -104250, -1170, -5244, 28251, -2934, -98904, -6144, 10314, 41934, 14730, 2664, 32145, 64674, -9621, 18888, -129228, 11070, 5169, 17676, 45522, 42972, 20187, 8496, 79629, 67176, 21060, -17808, -74925, 9414, 14031, -7632, -10827, -13992, 46020, -9612, -58176, 2010, -11367, -15648, 10089, -25956, -70689, -12276, -2214, 5484, -20274, 17208, 48870, 20964, -16767, -21336, 150642, 972, -76461, 15696, 46782, 67302, 17817, -19044, -16905, -25500, 23868, -38856, 22611, -7128, -2562, -13704, -10035, -62100, 10569, 3456, 134742, -19746, 20889, 7572, 93015, 10098, -78966, 33384, -567, -125232, -8487, -11520, -61854, 324, -36918, -1008, -19629, 10908, -83097, -36180, 32319, 16206, -34788, -2376, -27327, 60528, -11826, 4248, 50799, 10692, 35472, -7104, 60300, -25338, -16782, 972, 99183, -37092, 41490, -17808, -52635, -6786, -89094, 24588, -6750, -3114, 54825, 3312, 27939, -15966, 999, -44472, -9996, -2592, -33714, 32040, -47475, 19080, -42930, 12636, -64776, 52914, 4374, -10944, 84201, 34974, -8091, -48324, -54756, 23214, 136611, -6912, 49386, -25122, -15138, -7416, 58530, -36522, -29808, -12672, 21249, -38376, -100689, -11880, 100713, -84156, 1062, -6504, -53958, 9558, -78600, 19872, -78273, 68094, 48813, 4320, -155187, 22398, -8586, -33852, 30714, 37926, 123240, 18384, -40293, 87048, 330, -17604, 9336, -60978, -66879, 8880, 40245, -22860, -12309, -32184, 19359, 15288, 86085, 5616, 22335, -67842, -80973, 19452, -8946, 17658, -47724, -4608, -55791, 72612, -31938, -23220, -27252, 17946, -43713, -48000, -27363, -26424, -56685, -18300, -23553, -7296, -52632, 3888, -53103, 1062, -74052, -35988, -36432, -41886, 27840, 25800, 37557, -33390, -35100, -5652, 101043, 8268, -48321, -24960, 1035, -1134, -87789, -44100, 87426, -46614, 123549, -2736, 60573, 53514, -2673, -84000, 31572, 32184, -98199, 1056, -16524, 102972, -139299, -7992, -77019, 93012, 8361, 27240, 170499, -18486, -154794, -13680, -20034, 20514, 140604, -1152, 172806, 2796, 22293, -6636, -34191, 3726, -65931, -2016, 24174, -17844, -40758, -28656, 10443, 56154, 36045, -12912, 16572, -5004, 127965, -63396, -69489, 70086, -75555, -12312, -26091, -63180, -29871, -8868, 126654, -9288, -90618, 672, -7776, 972, 32952, -41940, 42609, -133638, -56961, -55296, 79170, -14256, 68514, -29844, 7281, 36348, 31155, 16848, -111033, 11322, -7317, 9396, -93780, 40932, -119628, 47064, -83205, -71592, -137562, 4860, 32382, -41910, -35703, -1152, 83358, -49086, -172077, -22452, 20682, 1818, 118467, 4248, -15717, -89040, -23031, -32424, -8319, 9990, 22083, -22224, 33948, -31824, 94389, -28980, -14478, 40644, 6318, -3528, 85107, -37044, 173721, 32916, -100161, -5802, -33702, -5184, -21390, -65196, 60174, 1560, -645, 23886, 53478, 3912, -54000, -38244, -191361, -13752, 271068, 160506, 45108, -3552, -1407, 4374, -34281, 12828, -8280, -53484, 21582, -14760, 56265, 24312, 29025, -60696, 85236, 12438, 94485, -11328, -34515, -39936, 4071, -28080, 221499, 39756, 1260, -12552, -73854, -63126, -6636, 14436, -3078, -10374, 146142, 12816, 4812, 48270, -28764, 15156, 178797, 1188, -167565, 34608, -7848, -73860, 16914, 2952, -143937, -8592, 30645, -22944, 69267, 62856, 155733, 22356, -23985, -124278, -92730, -1296, 42456, 69774, -13122, -62376, -2133, -11430, -84291, 25392, -2268, -79152, -240396, -31824, 123822, -119244, -5607, 9504, -197118, -14526, -71613, 13380, 4275, 5310, 108900, -4608, 8775, 53106, -13851, -27852, -46533, 9990, 249531, -13464, -2682, -32808, -152625, 756, -5088, 51432, -27171, 15360, 80514, -23310, -28827, 49224, -62208, 126660, -19140, -14544, -107355, -47982, 50211, -43092, -101523, 18954, -110946, 3168, -49284, -61056, -159, 15768, 163482, -58104, 52947, -14256, 47646, -6516, -83937, -80400, -34452, -84234, -74619, -1296, 118158, -76218, -11754, -55320, 108723, 2268, -44844, 9048, 4779, -83946, 18639, 9000, 153075, 1728, -74736, -4416, 58617, -25002, -110556, -1332, -23157, -80682, 6807, 3456, -184935, 146220, -3969, 63300, -79794, 86850, 143919, -16848, -87543, -62430, 52644, -5832, 37302, -137154, 156375, -46632, 97242, 7866, -249414, 73008, 4401, -37278, 210216, 9216, -87705, 5766, -62901, 20184, -158484, -3996, 13128, 48696, -97011, 21456, 42561, -28332, 178593, 18048, -16605, 15840, -471, -26514, 93156, -1416, -64458, -174108, 119430, -12744, 214158, -11790, -100764, 104364, 48387, 26712, -101496, -5760, -14121, 66696, 129078, 11448, 95874, -48570, 20988, -50568, 179505, 14418, 47172, 53724, -3015, -30408, 33306, 23472, 29037, -17064, 38934, 89172, -39675, 18414, 42495, 30480, -8226, -27312, 172860, -25812, -65676, -32328, -31446, -7488, 25674, 32004, 106191, 107964, -1458, -40482, 37542, -23544, -10911, -75090, -100953, 74388, 115443, 28566, 20709, 30960, 38250, -110160, 67848, 58284, 57303, -34536, 10692, 35232, -157794, 20556, 120486, 31404, 93150, 63078, 289842, -5184, 85890, 94542, 29619, 98736, 11514, -11358, -8079, 55848, -15147, 80742, 16998, -50076, 197646, 27984, 187848, 7536, -179196, 17280, -117411, 64428, -486, 16914, 53184, 1512, 116595, 112296, -16362, -116568, -147483, 54270, -87417, 3648, -24309, -56232, 13200, 3564, 121341, 126144, -90792, -42912, -150399, -6372, -98100, 22032, -16038, 10572, -10311, 10656, 52155, -73938, 38007, -11148, -233079, -1458, 239499, 24648, 55638, 87960, 166737, 26712, -39780, -4656, 10179, 1536, 164367, -36882, 32868, -29724, 4671, -7842, 111483, -4968, 90636, 39870, 23949, -32232, -84297, 66708, 239190, 38208, 3888, 20706, 9678, -48060, 122826, -37728, -28620, 6672, -232923, -18954, -220887, 92652, -79371, -10512, 220023, 16416, -81516, 50040, -52461, 39828, 15753, 72486, 106410, 12384, -34821, 17952, 115398, 10368, 270687, -57744, 37683, 55920, 226398, 11124, -26721, 75948, 54783, 3786, -29646, 19008, -126774, 132414, 57564, -9708, -138363, 17820, 4851, -22464, 126234, -71184, -14028, 9756, 72303, -101964, -14337, -54576, -221469, -29808, 126588, 110940, -102141, -89610, 51027, -6480, 99570, -83556, -33597, 47604, -158811, 50778, 137778, 65448, -56889, -114048, -251076, -27576, -169671, 123912, -130572, -5664, 101802, 26406, 1845, 30708, 91467, -5118, 35004, -13320, 166566, 94266, 34290, -45264, -299595, 48276, 149202, 38640, -22932, 10914, -199932, -8424, 323724, -125184, 101763, 49392, -103941, -29178, -59376, 133548, -26487, 47148, 38754, 6912, -318795, 27180, -108918, -80232, 183387, 34830, 201807, -31848, -26919, 99936, 75639, 72000, 280746, 36918, 39636, 18336, 48498, 27450, -189729, -60144, 10944, -137322, -39813, -5832, -177000, -9846, -1593, 11040, -118029, 53982, -181974, 19680, 62829, -263484, 166035, -38700, -245436, -180510, 50085, -16584, 43425, 8478, -196695, 46020, -12402, 126768, -84417, 37440, -161913, -21252, 1701, -1680, -68598, 66150, 280821, 84168, 69921, 110442, 23448, 4104, -259821, -230418, -80271, -17088, 65472, 126000, 57996, 38352, -48276, 105714, -134337, -1584, -113385, -134346, -154458, 10464, -11199, 11988, -136596, -3936, -139518, -1992, 25113, -40860, -34779, 11328, 27729, -83808, -99843, 20520, -54984, 31980, -30771, 16578, 471, 1728, 137808, 130872, -4194, 17496, 90891, 9954, 17400, 15240, -5589, -70170, -137136, 3024, -34050, 179718, 26766, 42432, -17883, 42984, -122115, 7476, -84231, 163044, -177, 19368, -364686, 95118, 7506, -5700, 211044, 95094, -66084, 6144, -105129, -27126, 6078, 18468, -64104, -167802, 94770, -13320, -285048, 13302, -150687, 3576, 13932, -27396, 253137, -1008, 28851, -12180, -1458, 36228, -94119, 62910, -26847, 31080, 200457, 103488, -373605, 82944, 124761, -79242, 21384, 19392, -244563, 44766, 91548, -66948, -54522, -59022, 7230, -25272, -181716, 51570, -16983, 65712, 280320, -14094, -172224, -21024, -61398, 39378, -273231, -70596, -350196, -118848, 107388, 8688, -106452, -7290, 4263, 45936, 62865, -214806, -255525, 1728, -307608, 172410, 73629, 15672, 11037, 33678, -220995, -3024, -2727, -67842, -212091, -6372, -80025, -204714, 133560, -12000, 250533, 48636, -110106, 99648, -14985, -90336, -284463, 33336, -159180, -85644, 47736, 30876, -243483, 43470, 283104, -4608, -60966, 14460, 42741, 5292, -283758, -121386, 55566, -115800, -223218, -49374, -305997, 116724, 8703, 53532, -330741, 7776, -34224, 181368, 97794, -208500, -218475, -2340, 96942, -10488, -35829, 56502, -339687, -5868, 48177, -197808, 57366, -12288, -106203, 20628, -126117, 83868, -240759, 29460, 13098, 5328, -373635, 64290, -6561, 129348, -170607, -19242, 354522, 37776, 80226, -258456, 281973, 22140, 87093, 10338, -36468, 35352, 3441, 91044, -73776, 85944, -18657, 40374, -185280, 16992, -57666, 159258, 59904, 134352, -106173, 42120, 254679, -35616, -59634, -149850, -163239, 18828, 95640, 28062, 94689, -15264, 104340, -21654, 47070, -27984, 15561, 92040, -175557, -19224, -34011, -116352, -72405, 4020, -195300, -22734, -154962, -31296, -1782, 20178, -109098, -51912, 112584, -141378, 110790, -24552, -13188, -4428, 180015, 10968, 12888, -40548, 31101, 34416, 130518, 97740, -94284, 41928, -299733, -33534, 100437, -42672, 186417, 301284, -214251, 1944, 193863, -152922, -104661, 31392, 10248, 93564, -324021, 134604, 17145, 35634, -42408, -38088, -187947, -33810, 118728, -51000, -66369, 47736, 481626, -77712, 178866, 45222, -210555, -14256, 62118, -5124, 21789, -27408, 169248, -20070, 191310, -124200, -7965, 21138, -18969, 6912, -259503, 269484, -79659, -39492, 45195, 41778, 87372, 15144, -14985, 186030, -5361, 20196, -57054, -157932, 49212, 66768, -200688, -1134, 39672, -250464, -77148, -16974, 159903, -23040, 193236, -123708, 34965, 648, 121059, -73836, -234792, -2016, -189990, -39258, 436005, 21816, -33009, -166194, 71973, -72360, -20745, 64638, 19710, 32412, -28431, -69576, -28692, -4752, 152109, -54654, 91584, 121056, -126468, -23652, 207726, 8496, 87156, 101598, -234717, 21384, 72708, 70944, 9774, -14208, 44508, 120600, 348999, -50676, 126351, -33564, 143205, 1944, 217608, 198366, 114327, -74184, 127923, 82980, 84369, -35616, -3402, -105270, 235263, -13572, -3027, -178188, 125919, 49176, -39780, -13500, -134055, -6228, -2592, 109650, 348090, 6624, -196773, 55878, 37503, -31932, 208443, 1998, 279531, -88944, 121023, -19992, -156435, -5184, 43401, -67428, -219330, 64080, -3129, -94950, 46020, 38160, -130275, -85860, 165231, 25272, 74772, -129552, 93645, 105828, 175623, 8748, 297258, -21888, 205731, 168402, 139467, 69948, 315123, -16182, -11799, -96648, -95052, -109512, 355848, 46428, 55917, 273222, -32949, -13824, 7905, 98772, -8649, -50244, -262215, -30276, 113745, -14832, 5994, 117060, 117861, -73044, 119925, -59616, -32184, -25344, 168930, 42498, 268953, -76752, -27072, -201378, -155040, -23760, 146589, 201426, 39771, -168312, -183009, 2124, 4179, -13008, 261162, -107916, 217884, 19116, -163173, -157200, 17685, 39744, 97542, -156546, 21015, 136188, -40068, 97626, -107400, 8640, 427284, -310374, -100044, 44796, -250647, -17172, 146469, -67704, 72855, 61428, 270705, 75852, 322125, 246480, -21627, 36768, -279627, -80586, -263961, 174096, 45612, 660, 330390, -35208, 68106, 18672, 25596, -121956, 64251, -133758, 127719, 17760, -27621, 80490, -18081, -45720, -1272, -24618, 40968, -64368, -1239, 38718, -29571, 30576, 48492, 172170, -97158, 11232, 305097, 44670, -48006, -135684, 576219, -161946, 328434, 38904, 60723, -17892, 140721, 35316, 74877, -95448, 112635, -9216, -107502, -111582, 79734, 145224, -42849, -63876, 200982, -46440, 18993, -54504, 165240, 35892, -382659, -87426, 28332, -96000, 51804, -54726, 612357, -52848, -10491, -113370, -30834, -36600, 33495, -47106, 269535, -14592, -94617, -105264, -287397, 7776, -51477, -106206, -141813, 2124, 5589, -148104, 154101, -71976, 17037, -72864, -415077, -83772, 370599, 55680, -121113, 51600, 547416, 75114, 535722, -66780, -41976, -70200, -279912, -11304, -507090, 202086, -25920, 16536, -234324, -96642, -169365, -49920, -25371, 2070, -113928, -2268, -418878, -175578, -168444, -88200, 97905, 174852, 105228, -93228, -81405, 247098, 248703, -5472, 369813, 121146, 84348, 107028, -375369, -5346, -13908, -168000, -189216, 63144, 218163, 64368, 36093, -196398, 9558, 2112, 178848, -33048, -400644, 205944, -15858, -278598, 97056, -15984, -289749, -154038, 110907, 186024, 307473, 16722, -93909, 54480, 2187, 340998, -355962, -36972, 147117, -309588, -131940, -27360, 73536, -40068, -218895, 41028, 6984, 281208, 245730, -2304, -320436, 345612, 55323, 5592, 262998, 44586, -115731, -13272, 11763, -68382, -416478, 7452, -186816, -131862, -59805, -4032, 195354, 48348, -79155, -35688, -100062, -81516, 60381, -57312, -89640, 20886, -31059, 112308, 125787, 72090, 230193, -25824, 56592, 33144, 319536, -10008, -311490, 255930, 28431, -126792, -21390, -138978, 95007, 140172, 15768, -151110, 43557, -24624, -178635, -52182, -75060, -126360, 116670, -59742, -36978, -17736, -108729, 253308, 47589, -18576, -343578, -181236, -26928, 1344, 317496, -15552, -404070, 1944, 86616, 65904, 543801, -83880, -43236, 85218, -16686, -267276, -492105, -113922, 8163, -110592, -5679, 158340, 43932, -28512, 42303, 137028, -198621, -59688, 406434, 14562, 1731, 72696, -26730, 62310, 115002, 33696, -193752, -222066, 106776, 22644, 230853, -14634, 39606, 18792, 152946, -187560, -215268, 81864, 230400, -239256, 44712, 94128, -92175, -166410, 329595, -143184, 134415, -275124, -20550, 9720, -412341, 64764, 125334, -83820, -233829, -71406, -149814, -2304, -76167, 166716, 147042, -98172, -220647, -344154, 171072, -44904, -498510, 41364, -243153, 3636, -185868, 236934, 153045, 8496, -103134, -31434, -39609, -178080, 68349, -46062, 164778, -64848, 7677, -16638, 66759, 19980, 103131, 44166, -141399, -44448, 204861, 67896, 35622, -63648, -72414, 188778, 118506, -57960, -155193, -28956, -16371, 81288, 425040, 12636, -455424, -7056, 187776, 170214, -294897, -74088, -435192, 347442, 43767, 65832, 105096, -200322, 16545, -11604, -70722, -67404, 371316, -10368, -122898, -42780, -40770, -130392, 150618, 120348, 429669, 3120, -52245, -1290, -5841, 47772, -334152, 106956, -149904, 7824, -315756, -108000, 335769, -76488, -55377, -382722, 253530, -27504, 451833, 542136, -41175, 321012, 510639, 90216, -227538, -7104, 205983, -2814, -44694, 8748, 131604, -68562, 14769, 25656, 121365, -16560, 375438, -106968, -80973, 43164, 42879, -29520, 110070, 112530, 395226, 48624, 145785, 58050, -252288, -121392, 270765, 170472, 197382, 24876, 291549, 188970, -12717, -22656, 23952, -69030, -35556, -79872, -190152, 8142, -585210, -56160, -441903, 442998, 31878, 79512, 106176, 2520, 273225, -25104, -99225, -147708, -161889, -126252, 49539, -13272, -165663, 28872, 49278, -6156, -161073, -20748, 345627, 292284, 113583, 25632, -294456, 9624, -189000, 96540, -474339, -57528, -593403, 30312, -158571, 357594, 50226, 2376, 169011, -335130, 201519, 69216, 124431, -15696, 430770, -147720, -17982, 33828, 90036, 5904], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "354.4.a.g", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0], [1, 0, 0], [2, 0, 0], [-3, 0, 0], [4, 0, 0], [-6, 1, 1], [-6, 0, 0], [2, -3, -2], [8, 0, 0], [9, 0, 0], [-12, 2, 2], [-3, 6, -2], [-12, 0, 0], [-15, -4, 4], [4, -6, -4], [18, -3, -3], [16, 0, 0], [-32, -2, -9], [18, 0, 0], [-57, -5, 6], [-24, 4, 4], [-6, 9, 6], [-6, 12, -4], [-59, 13, 12], [-24, 0, 0], [-23, -9, -17], [-30, -8, 8], [-27, 0, 0], [8, -12, -8], [-117, 14, 9], [36, -6, -6], [-89, -30, -5], [32, 0, 0], [9, -18, 6], [-64, -4, -18], [-163, 8, 23], [36, 0, 0], [-74, 6, -23], [-114, -10, 12], [45, 12, -12], [-48, 8, 8], [-260, -5, 12], [-12, 18, 12], [7, 30, 20], [-12, 24, -8], [-54, 9, 9], [-118, 26, 24], [-239, 26, 17], [-48, 0, 0], [33, 26, -21], [-46, -18, -34], [96, 6, 27], [-60, -16, 16], [-78, -9, -9], [-54, 0, 0], [38, 3, 27], [16, -24, -16], [171, 15, -18], [-234, 28, 18], [-59, 0, 0], [72, -12, -12], [205, -26, -49], [-178, -60, -10], [18, -27, -18], [64, 0, 0], [202, -27, -67], [18, -36, 12], [-48, -43, -13], [-128, -8, -36], [177, -39, -36], [-326, 16, 46], [327, -34, -2], [72, 0, 0], [-21, -32, 33], [-148, 12, -46], [69, 27, 51], [-228, -20, 24], [-264, -67, -56], [90, 24, -24], [185, -32, -106], [-96, 16, 16], [81, 0, 0], [-520, -10, 24], [22, 153, 126], [-24, 36, 24], [-269, -5, 74], [14, 60, 40], [351, -42, -27], [-24, 48, -16], [-463, -158, -15], [-108, 18, 18], [-74, 101, 114], [-236, 52, 48], [267, 90, 15], [-478, 52, 34], [529, -75, -134], [-96, 0, 0], [320, -91, -29], [66, 52, -42], [-27, 54, -18], [-92, -36, -68]]}