# Stored data for newform 150.6.a.a, downloaded from the LMFDB on 23 April 2024.
{"label": "150.6.a.a", "space_label": "150.6.a", "level": 150, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 100663446, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 161608775931610864, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[7, [47, 1]]], "qexp_display": "q-4q^{2}-9q^{3}+2^{4}q^{4}+6^{2}q^{6}-47q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5400, "fricke_eigenval": 1, "atkin_lehner_string": "+++", "analytic_conductor": 24.057572971947096, "hecke_ring_index": 1, "level_radical": 30, "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": [150, 1, [101, 127], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [2, 3, 5], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.005", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.021", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.092", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "5.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, 1], [5, 1]], "trace_display": [-4, -9, 0, -47], "traces": [0, 1, -4, -9, 16, 0, 36, -47, -64, 81, 0, 222, -144, -101, 188, 0, 256, -162, -324, 1685, 0, 423, -888, -306, 576, 0, 404, -729, -752, 7890, 0, -8593, -1024, -1998, 648, 0, 1296, -8642, -6740, 909, 0, -18168, -1692, -14351, 3552, 0, 1224, 1098, -2304, -14598, 0, 1458, -1616, -17916, 2916, 0, 3008, -15165, -31560, 17610, 0, -21853, 34372, -3807, 4096, 0, 7992, -107, -2592, 2754, 0, -40728, -5184, -34706, 34568, 0, 26960, -10434, -3636, -69160, 0, 6561, 72672, 108534, 6768, 0, 57404, -71010, -14208, 35040, 0, 4747, -4896, 77337, -4392, 0, 9216, 823, 58392, 17982, 0, -33828, -5832, 133444, 6464, 0, 71664, -81252, -11664, -217015, 0, 77778, -12032, 138324, 60660, 0, 126240, -8181, -70440, 7614, 0, -111767, 87412, 163512, -137488, 0, 15228, 256048, -16384, 129159, 0, 118452, -31968, -79195, 428, 0, 10368, 13218, -11016, -350740, 0, -9882, 162912, -22422, 20736, 0, 138824, 131382, -138272, 109890, 0, -172603, -107840, -13122, 41736, 0, 14544, 349993, 276640, 161244, 0, 14382, -26244, -192581, -290688, 0, -434136, -580692, -27072, -361092, 0, 136485, -229616, -738126, 284040, 0, 56832, -158490, -140160, 497370, 0, -333163, -18988, 196677, 19584, 0, -309348, -35964, 17568, 34263, 0, -40638, -36864, -494651, -3292, 0, -233568, -552342, -71928, 685625, 0, 963, 135312, -370830, 23328, 0, -533776, -24786, -25856, 374070, 0, 749477, -286656, 366552, 325008, 0, 46656, 403871, 868060, 312354, 0, 16362, -311112, -169271, 48128, 0, -553296, 46488, -242640, -90115, 0, 93906, -504960, -1064136, 32724, 0, 281760, 622440, -30456, 1151580, 0, 856217, 447068, -59049, -349648, 0, -654048, -170185, 549952, -976806, 0, -207708, -60912, -67932, -1024192, 0, 65536, 1453188, -516636, 406174, 0, 639090, -473808, -169296, 127872, 0, 316780, -315360, -1712, -1581090, 0, 822512, -41472, -42723, -52872, 0, 44064, 546823, 1402960, -696033, 0, -1092498, 39528, 2484799, -651648, 0, 89688, 853896, -82944, -1393613, 0, -7407, -555296, 341394, -525528, 0, 553088, -161838, -439560, 30906, 0, 674497, 690412, 304452, 431360, 0, 52488, -2028977, -166944, -1200996, 0, -206598, -58176, 3342229, -1399972, 0, -1106560, 2532888, -644976, 1751580, 0, 731268, -57528, -272970, 104976, 0, 770324, 1953135, 1162752, -51606, 0, 602132, 1736544, -700002, 2322768, 0, 108288, -209777, 1444368, -1244916, 0, -1907646, -545940, 1476035, 918464, 0, 2952504, -4021662, -1136160, 8330, 0, 73629, -227328, -1950006, 633960, 0, 560640, -68526, -1989480, 2270880, 0, 363126, 1332652, 1005903, 75952, 0, -786708, -2861537, -78336, -1471608, 0, 842052, 1237392, -615311, 143856, 0, -70272, -796890, -137052, 5398775, 0, -2304432, 162552, -1086876, 147456, 0, 1978604, -1162431, 13168, -3484320, 0, 49572, 934272, -1066068, 2209368, 0, 287712, -3265907, -2742500, 712755, 0, -4273188, -3852, 867893, -541248, 0, 1483320, -1918524, -93312, -1451875, 0, -118962, 2135104, -827670, 99144, 0, 103424, 3156660, -1496280, 559380, 0, -3914698, -2997908, 88938, 1146624, 0, -1466208, 1027091, -1300032, 201798, 0, -3574998, -186624, -7159691, -1615484, 0, -3472240, -515610, -1249416, 1717895, 0, -1182438, -65448, -3396696, 1244448, 0, 677084, -989010, -192512, -3396060, 0, -4033296, 2213184, 1553427, -185952, 0, 970560, 4528138, 360460, 118098, 0, -1278948, -375624, 7198624, 2019840, 0, 4256544, -4830342, -130896, 5029, 0, -3149937, -1127040, -3185922, -2489760, 0, 121824, -1451196, -4606320, 748650, 0, 872842, -3424868, -129438, -1788272, 0, 236196, 5163943, 1398592, 1733229, 0, 8542872, 2616192, -1278180, 680740, 0, -2199808, 1914216, 3907224, -4205875, 0, 5226228, 830832, 8183424, 243648, 0, 271728, 3249828, 4096768, 3859230, 0, 1631182, -262144, -1228365, -5812752, 0, 2066544, 243756, -1624696, 6643134, 0, 4554102, -2556360, -4822241, 1895232, 0, 677184, 1392066, -511488, -6342707, 0, 1426410, -1267120, 1834968, 1261440, 0, 6848, -4476330, 6324360, -3240756, 0, 362537, -3290048, 2998467, 165888, 0, 170892, -3114392, 211488, -1770093, 0, 13294650, -176256, 3250520, -2187292, 0, -5611840, 7993038, 2784132, 1449451, 0, 323676, 4369992, 12323574, -158112, 0, -9939196, -308367, 2606592, 10136430, 0, 6530837, -358752, 365742, -3415584, 0, 331776, 1244533, 5574452, 4451859, 0, -5101098, 29628, -3977352, 2221184, 0, -1365576, 1334028, 2102112, -14479205, 0, 4971078, -2212352, 11940144, 647352, 0, 1758240, -6170625, -123624, -7164300, 0, 1151627, -2697988, -8667, -2761648, 0, -1217808, 13426768, -1725440, 3337470, 0, -110898, -209952, -12018386, 8115908, 0, 667776, 6985188, 4803984, -8206255, 0, 223074, 826392, -1646880, 232704, 0, -13368916, -3366630, 5599888, 1400004, 0, -10768573, 4426240, -6745293, -10131552, 0, 2579904, 1474398, -7006320, -3298968, 0, 19257132, -2925072, -10099916, 230112, 0, 1091880, -7521132, -419904, 3909420, 0, -3634839, -3081296, 2671974, -7812540, 0, -4651008, -2811186, 206424, 6999480, 0, 408122, -2408528, -147258, -6946176, 0, 2800008, -2414340, -9291072, 1523439, 0, -4851366, -433152, -17493926, 839108, 0, -5777472, 8674398, 4979664, -38681, 0, -418392, 7630584, -11847816, 2183760, 0, -5904140, 811035, -3673856, 1809516, 0, 9477752, -11810016, -845154, 16086648, 0, 4544640, 2943216, -33320, 9577224, 0, -22814658, -294516, -14561770, 909312, 0, 7800024, 1589916, -2535840, 12743645, 0, -5601960, -2242560, 2629458, 274104, 0, 7957920, -10364220, -9083520, 2449290, 0, -6271868, -1452504, -7705953, -5330608, 0, -4023612, 415033, -303808, 531441, 0, 2324862, 3146832, 17287714, 11446148, 0, 313344, -23754, 5886432, 5188340, 0, 1531665, -3368208, -4795716, -4949568, 0, 2461244, 8791254, -575424, 3818844, 0, -18565408, 281088, 1869372, 3187560, 0, 548208, -28206797, -21595100, 611388, 0, 6561612, 9217728, 10199705, -650208, 0, 4347504, -1778610, -589824, 22092995, 0, -13078692, -7914416, 30078744, 4649724, 0, -52672, -3655566, 13937280, -30613080, 0, -9041616, -198288, -5751810, -3737088, 0, 4264272, 3289543, -8837472, 1523664, 0, -6501228, -1150848, 2207153, 13063628, 0, 10970000, -6710532, -2851020, -177876, 0, 2838240, 17092752, -7704732, 15408, 0, -3471572, 14229810, 2164992, 8742540, 0, -24841003, -5933280, -7402608, 7674096, 0, 373248, -24181435, 5807500, 384507, 0, 21221862, 475848, 8706589, -8540416, 0, 3310680, -37118412, -396576, 1017650, 0, -4921407, -413696, 2364876, -12626640, 0, 5985120, 6264297, -2237520, -33619410, 0, 41740951, 15658792, 9832482, 11991632, 0, -355752, 5253049, -4586496, -22363191, 0, 2644452, 5864832, 35257369, -4108364, 0, 5200128, 31494108, -807192, 11934440, 0, -7685064, 14299992, -8704416, 746496, 0, 28638764, 12542517, 6461936, -15353520, 0, 10807, 13888960, 66663, 2062440, 0, 4997664, -11799887, -6871580, -3072546, 0, -27384048, 4729752, 8805769, 261792, 0, 13586784, -250122, -4977792, -12034256, 0, 1456542, -2708336, 1850130, 3956040, 0, 770048, -278154, 13584240, -67798770, 0, 2902392, 16133184, -6070473, -8852736, 0, -6213708, 32495548, 743808, -2740068, 0, 42459522, -3882240, 24094548, -18112552, 0, -1441840, -5567244, -472392, 14162885, 0, 18260793, 5115792, 4113528, 1502496, 0, -28794496, 10808964, -8079360, 43729230, 0, -24597630, -17026176, 1859382, 19321368, 0, 523584, -5735087, -20116, -30080061, 0, -33739458, 12599748, 5559408, 4508160, 0, 12743688, 30734238, 9959040, 3505306, 0, -22795992, -487296, 25184664, 5804784, 0, 18425280, -15764220, -2994600, -621246, 0, 45210498, -3491368, -6581412, 13699472, 0, 517752, -14455592, 7153088, 2456730, 0, -10697418, -944784, 16484780, -20655772, 0, -5594368, 8415678, -6932916, 7778880, 0, -17578215, -34171488, -38940876, -10464768, 0, 5112720, 464454, -2722960, 4391406, 0, 48459227, 8799232, -5419188, -7656864, 0, -15628896, -38473322, 16823500, 6300018, 0, 1053834, -20904912, -2852820, -3323328, 0, -32733696, -30188460, -974592, 38652125, 0, 1887993, -1086912, 12026454, -12999312, 0, -16387072, 11204244, -15436920, 45630270, 0, -19828993, -6524728, 17168814, 1048576, 0, 4913460, 6985160, 23251008, -13284315, 0, -26854998, -8266176, -45461621, -975024, 0, 6498784, 3540186, -26572536, -32929135, 0, 36194958, -18216408, -5164830, 10225440, 0, 19288964, -74970, -7580928, 46887840, 0, -9676963, -2708736, -662661, -5568264, 0, 2045952, 8112341, 25370828, 17550054, 0, -50978298, -5705640, -242231, 5068480, 0, -7339872, 182706, -5045760, 41017055, 0, 616734, -27392, -68185380, 17905320, 0, -25297440, -20437920, 12963024, -10961934, 0, -335988, -1450148, -3268134, 13160192, 0, -11993868, 14782453, -663552, -9053127, 0, 47874792, -683568, -23265221, 12457568, 0, -845952, 48144678, 7080372, -16449671, 0, 25753833, -53178600, -74256846, 705024, 0, -13002080, 13244472, 8749168, 74970750, 0, -7509816, 22447360, -7578468, -31972152, 0, -11136528, -11226557, -5797804, 5537799, 0, 29672850, -1294704, -17339141, -17479968, 0, -49294296, 4466988, 632448, 12340565, 0, 7172010, 39756784, 29624568, 1233468, 0, -10426368, -48588975, -40545720, 17334, 0, 9051307, -26123348, 20739888, 1435008, 0, -1462968, 74260706, 13662336, 9781884, 0, -53998698, -1327104, -67685681, -4978132, 0, -22297808, -3539040, -17807436, -36822305, 0, 10461879, 20404392, -66644496, -118512, 0, 15909408, 31358880, -8884736, 27292524, 0, 6604667, 5462304, -446148, -5336112, 0, -8408448, -18037944, 57916820, 9594612, 0, -19121058, -19884312, 16971324, 8849408, 0, -47760576, -61049622, -2589408, -143345520, 0, 29393163, -7032960, 10964994, 24682500, 0, 494496, -6414795, 28657200, -48177330, 0, 13133942, -4606508, 38458692, 10791952, 0, 34668, 6597936, 11046592, -7811037, 0, 34691922, 4871232, 24489274, -53707072, 0, 6901760, 88035798, -13349880, 5482296, 0, 17266716, 443592, 47851734, 839808, 0, 48073544, 13066875, -32463632, 32695920, 0, -52388788, -2671104, 1070658, -27940752, 0, -19215936, 11480518, 32825020, 7449030, 0, 5622372, -892296, 30707928, -3305568, 0, 6587520, -113229390, -930816, -78928150, 0, -28409940, 53475664, -23376390, 13466520, 0, -22399552, -5034420, -5600016, 36279780, 0, -83123, 43074292, 35232282, -17704960, 0, 26981172, 15658661, 40526208, -800442, 0, 156117624, -10319616, -180295, -5897592, 0, 28025280, -98229042, 13195872, -7189135, 0, -9243819, -77028528, 88001034, 11700288, 0, 40399664, -1816182, -920448, -31850580, 0, 17855627, -4367520, 32174982, 30084528, 0, 1679616, 112462093, -15637680, 64437219, 0, -118001118, 14539356, -34198331, 12325184, 0, -10687896, 21914148, 31250160, 1690308, 0, 4640490, 18604032, 3416628, 11244744, 0, -825696, -15461055, -27997920, 39132150, 0, 74093702, -1632488, 10641942, 9634112, 0, 589032, 73541593, 27784704, 30570264, 0, -60565596, -11200032, 123318143, 9657360, 0, 37164288, 1909986, -6093756, -13477844, 0, 8901090, 19405464, 11203920, 1732608, 0, 69975704, 30564540, -3356432, -68626680, 0, 23248597, 23109888, 36299664, -34697592, 0, -19918656, -5388660, 154724, -13980843, 0, 119133882, 1673568, 8663220, -30522336, 0, 47391264, -46307832, -8735040, 5340207, 0, -40753242, 23616560, 30383634, -3244140, 0, 14695424, -1062882, -7238064, 25960074, 0, -130667023, -37911008, 11510532, 47240064, 0, 3380616, -58479610, -64346592, -64787616, 0, 8206452, -18178560, -32224375, -11772864, 0, 133280, 56842656, -38308896, 40802045, 0, 43473078, 91258632, 6687018, 1178064, 0, 58247080, -45261, -3637248, 53922690, 0, -17582508, -31200096, 28349433, -6359664, 0, 10143360, 21918515, -50974580, 28673298, 0, -115178220, 22407840, 80416744, 8970240, 0, -10517832, -88327032, -1096416, -124315345, 0, 13060764, -31831680, -59593626, 41456880, 0, 36334080, -6737850, -9797160, -25850610, 0, 26296344, 25087472, -7855578, 5810016, 0, 30823812, -55792217, 21322432, 1164942, 0, -30952698, 16094448, -146648561, -1660132, 0, 1215232, -9435114, -2125764, 32079620, 0, -46475487, -9299448, -17581290, -12587328, 0, -69150856, -15599061, -45784592, -13970724, 0, -78495643, -1253376, -76885848, 95016, 0, -23545728, -35225419, -20753360, 11503620, 0, -19306698, -6126660, -9019796, 13472832, 0, 19182864, -106550952, 19798272, 45014210, 0, -17227944, -9844976, 89096124, -35165016, 0, 2301696, 37852875, -15275376, -126952290, 0, -116534600, 74261632, -47036052, -1124352, 0, -7477488, 2934396, -12750240, -73650816, 0, -103593948, -2192832, -5676480, 112827188, 0, 86380400, 157007856, -2445552, 125440614, 0, -29248452, -26246448, -134973726, -36870912, 0, -40798820, -34733070, 2600832, -77864280, 0, -59923573, -17390016, -14680638, 7114440, 0, 2359296, -141357240, -88371980, 11055285, 0, 32742, 52314768, -6385961, 31657664, 0, -120314976, -769014, -18598896, -52383445, 0, -2193804, 210688, -90119526, 14622264, 0, -55749120, -59788206, 122452320, 123277410, 0, 7955737, 36166464, -40986918, 793152, 0, 23007240, -6526757, 14948352, 43400169, 0, 102847662, -17057088, 11288467, -13158172, 0, 35349888, 182879790, -6094656, 172428995, 0, -12528594, 26004912, -13882266, 4603392, 0, -8828612, 57084363, -52254512, -2184936, 0, 124021342, -43880000, -12837690, 26842128, 0, 11404080, -188157302, 711504, -16514712, 0, -104821998, -11352960, 4235405, -68371008, 0, 30818928, -37819812, -61632, -5165635, 0, 40286970, 13886288, 43022454, -56919240, 0, -8659968, 29166804, -34970160, 42338700, 0, 101334497, 99364012, -3262833, 23733120, 0, 29610432, -134042972, -30696384, -26986203, 0, 50014392, -1492992, 12462768, 96725740, 0, -23230000, 33676548, -1538028, 24395580, 0, 28029528, -84887448, 153952188, -1903392, 0, -34826356, 15930837, 34161664, -133326, 0, -25860848, -13242720, -119651850, 148473648, 0, 1586304, 153815938, -4070600, -29254680, 0, -38317866, 19685628, 91852429, 1654784, 0, -9459504, 42839478, 50506560, 111984470, 0, -71937342, -23940480, -54124260, -25057188, 0, 8950080, -13045059, 134477640, 10620036, 0, 214220023, -166963804, -2913084, -62635168, 0, -39329928, -40242199, -47966528, -110912166, 0, 59042400, 1423008, -1548071, -21012196, 0, 18345984, 73918278, 89452764, 126846680, 0, 2775303, -10577808, -11963652, -23459328, 0, -141029476, -91227870, 16433456, -103041150, 0, 138942900, -20800512, -58777533, -125976432, 0, 3228768, 5480136, -47737760, -3291678, 0, 186721992, 30740256, 18382924, -57199968, 0, 34817664, 77698446, -2985984, 7998695, 0, -11200797, -114555056, 157002174, -50170068, 0, -25847744, -40066731, 61414080, -9488916, 0, -129874513, -43228, 45909882, -55555840, 0, -266652, -36221672, -8249760, 35796168, 0, -21617928, -19990656, -90988826, 47199548, 0, 27486320, 9762276, 12290184, 68277275, 0, -12006252, 109536192, 260728968, -18919008, 0, -35223076, 130312845, -1047168, -172420170, 0, 3192804, -54347136, -44739702, 1000488, 0, 19911168, 238312663, 48137024, -107461296, 0, -1335018, -5826168, 95503189, 10833344, 0, -7400520, 120559758, -15824160, -27431065, 0, 55535625, -3080192, -42752982, 1112616, 0, -54336960, 64478700, 271195080, -68299836, 0, 104331047, -11609568, -10364643, -64532736, 0, 24281892, 35424740, 35410944, 78003, 0, 169938912, 24854832, 126155916, -129982192, 0, -2975232, 21162960, 10960272, 13162824, 0, -120840912, -169838088, -96317376, 15528960, 0, -96378192, -30037230, 72450208, -151322730, 0, 23686352, 5767360, 998082, 22268976, 0, 1889568, -128913624, -56651540, 108165474, 0, 7956912, -73043172, 1386755, -20463168, 0, -16454112, 212376498, -6009984, 58942758, 0, -62866692, 115177984, 35156430, -43235856, 0, 32317440, 73856295, -174916920, -80162424, 0, -165563293, 98390520, -2007666, 68104704, 0, -7437528, 136817263, -77285472, 14821920, 0, 88168902, -2094336, -79967921, 22940348, 0, 80464, -197184192, 120320244, -137642080, 0, 30299670, 134957832, 74311230, -50398992, 0, -22237632, -12600036, -18032640, 146217120, 0, 187782829, -50974752, 96917157, -122936952, 0, -39836160, -38658064, -14021224, 60707637, 0, 25635162, 91183968, -163863972, 1949184, 0, -100738656, -121893852, -23219136, -33211404, 0, -13269582, -73701120, -75161196, 63056880, 0, 11978400, 29690712, 2484984, -57000180, 0, -22408488, -180841992, -173314188, 13965472, 0, 26325648, -19948464, -54797888, 90899244, 0, 115636632, -2071008, -217615331, 57822368, 0, -28612352, -11098890, -9826920, -25700681, 0, 67690188, 42789672, -844230, 3779136, 0, -65939120, -35184780, 82623088, -56911920, 0, -60639673, 22377472, 32713551, -33662712, 0, 27731664, 224853140, -31115520, -24047766, 0, 154830072, 70312860, 17432903, 136685952, 0, 155763504, 51347406, 41859072, 110416140, 0, 25300674, -20450880, -38585256, -1857816, 0, 10891840, -62995320, -17565624, -126757410, 0, -116785553, -193836908, -3673098, -35196928, 0, 21676752, -128984972, 30627456, 1325322, 0, -73962186, 62515584, 54859834, 153893288, 0, -67294000, -167410452, -25200072, -37585645, 0, 21729060, -4215336, -87829206, 83619648, 0, 11411280, -13710951, 13293312, 265216464, 0, -230040388, 130934784, 43662294, 120753840, 0, 3898368, -251410277, -154608500, 157445334, 0, -15757398, -7551972, 65499811, 4347648, 0, -48105816, -267129492, 51997248, 93028385, 0, -78069582, 65548288, -136909620, -44816976, 0, 61747680, 348129, -182521080, 332262660, 0, -35349293, 79315972, 3765528, 26098912, 0, -68675256, -10722240, -4194304, 106630344, 0, -16045518, -19653840, -18509366, -27940640, 0, -93004032, 18106254, 53137260, -321343920, 0, -7299315, 107419992, 190115634, 33064704, 0, 181846484, -16285644, 3900096, 68274060, 0, -365670275, -25995136, -85299768, -14160744, 0, 106290144, 919451, 131716540, 7606386, 0, -149510148, -144779832, -124816211, 72865632, 0, 20659320, -216896082, -40901760, -68372935, 0, -26488944, -77155856, -1452582, 299880, 0, 30323712, -86195016, -187551360, 42063630, 0, -9021636, 38707852, 205331922, 10834944, 0, 2650644, 209495898, 22273056, 131055930, 0, -339614988, -8183808, -119212721, -32449364, 0, -101483312, -273830340, -70200216, 19450681, 0, -14309244, 203913192, -109812522, 22822560, 0, 968924, -114692805, -20273920, -177101250, 0, 178940192, 29359488, 50417640, -730824, 0, 20183040, 202295293, -164068220, -23665122, 0, -233230908, -2466936, -294347471, 109568, 0, 272741520, 233075940, -71621280, 95361919, 0, 93277980, 101189760, 251590014, 81751680, 0, -51852096, -22043610, 43847736, -41479776, 0, -265197958, 1343952, 56446812, 5800592, 0, 13072536, -122619924, -52640768, 69353577, 0, 58649892, 47975472, 325497888, -59129812, 0, 2654208, 9710106, 36212508, -122789755, 0, -3735297, -191499168, -152185620, 2734272, 0, 93060884, -4782969, -49830272, 152208750, 0, -157084763, 3383808, -20923758, -192578712, 0, -28321488, 73970885, 65798684, -155589426, 0, 349975704, -103015332, -393121181, 212714400, 0, 297027384, 292369338, -2820096, -228139403, 0, 213786, 52008320, 157569864, -52977888, 0, -34996672, -46695060, -299883000, -119045736, 0, 13176977, 30039264, -13784985, -89789440, 0, 30313872, -19189224, 127888608, 43161444, 0, -251838, 44546112, -82324260, 44906228, 0, 23191216, -274997622, -22151196, -384707725, 0, -79121286, -118691400, 227373294, 5178816, 0, 69356564, -34369596, 69919872, 74550726, 0, 9887957, 197177184, 167088672, -17867952, 0, -2529792, 188853626, -49362260, -16824348, 0, 12829590, -28688040, 298228658, -159027136, 0, -118498272, 467388708, -4933872, -312252565, 0, 253861173, 41705472, 203815884, 194355900, 0, 162182880, -5502492, -69336, 257112516, 0, 262165517, -36205228, -59054508, 104493392, 0, -82959552, 204826408, -5740032, -91797345, 0, -545672400, 5851872, 141917269, -297042824, 0, -54649344, -194901912, -39127536, -188327395, 0, 16007490, 215994792, -16028604, 5308416, 0, 270742724, -198836955, 19912528, 35312010, 0, 423142337, 89191232, 117708228, 14156160, 0, 71229744, -28300204, 147289220, -270708696, 0, 166383894, -41847516, 10351368, -81617568, 0, 266577984, -50234370, 474048, -2141316, 0, 32900094, -63637632, -184632126, -125435520, 0, 35538944, 275517720, -109170096, 105422130, 0, 51796097, -26418668, 81374544, -21849216, 0, 1784592, -269642957, 21344448, 51766290, 0, -489576108, 33633792, 33649463, 72151776, 0, -231667280, 225399108, -38378448, 9859519, 0, -29605887, 76484232, 56819880, 79537248, 0, -67885296, -13712976, -35397632, -40833864, 0, -158696923, 191042304, 58511052, 244198488, 0, 10357632, -281241002, 573382080, -19864377, 0, 353304462, -117572652, 158724259, 28131840, 0, -43859976, 89659362, -98730000, 171982295, 0, 60394788, -1977984, 234242874, 25659180, 0, -114628800, 1600884, 192709320, 97158600, 0, 175974941, -52535768, -25544160, 18426032, 0, -153834768, 856333260, -43167808, 69342588, 0, 234274542, -138672, 431440880, -26391744, 0, -44186368, -133913082, 31244148, -319938480, 0, -128068290, -138767688, -428799306, -19484928, 0, -97957096, -78682860, 214828288, 189018114, 0, 3632364, -27607040, 223569027, -352143192, 0, 53399520, -476749247, -21929184, 66623472, 0, -181251258, -69066864, -391510, -1774368, 0, -191406936, 41504418, -3359232, 594291880, 0, 217632915, -192294176, -37578162, -52267500, 0, 129854528, -3460563, -130783680, -474841920, 0, 24863112, 209555152, -190996758, 10684416, 0, -4282632, -515661572, 111763008, -78359301, 0, 91650282, 76863744, 489474349, -45922072, 0, -131300080, -310803192, -29796120, 924694, 0, 334065708, -22489488, 4104438, 3569184, 0, -122831712, -9158850, 13222272, 199591620, 0, -19671768, -26350080, 44292663, 452917560, 0, 3723264, 10320336, 315712600, -21283884, 0, 397025304, 113639760, -60302396, -213902656, 0, 93505560, 66406590, -53866080, 49959751, 0, -56378673, 89598208, -106731360, 20137680, 0, 22400064, 302574690, -145119120, -20005530, 0, 132142487, 332492, -375668559, -172297168, 0, -140929128, -17066922, 70819840, -88492338, 0, -267062748, -107924688, -17802180, -62634644, 0, -162104832, -252721110, 3201768, 455121755, 0, -47277441, -624470496, -385343646, 41278464, 0, 721180, 201268719, 23590368, -335456100, 0, 232103312, -112101120, -23800068, 392916168, 0, -52783488, 520041643, 28756540, -317316321, 0, 55786542, 36975276, -236238192, 308114112, 0, -352004136, 27961686, -46801152, 134492239, 0, -283446972, -161598656, -932632662, 7264728, 0, 3681792, -107409960, 127402320, 332664240, 0, 276465600, -71422508, 69165576, 17470080, 0, -128699928, -69248125, -120338112, 78339744, 0, -26896098, -6718464, -405422591, -449848372, 0, 62550720, 261537768, -257748876, -42327144, 0, -112882653, 472004472, 22272330, -58157424, 0, 136793324, 138181680, -49300736, 162074820, 0, 28919617, 42751584, -97263, -87656592, 0, -125000640, -9758357, -6761232, -599967, 0, -229136178, -18561960, 313612403, -74416128, 0, -13666512, 351971376, -44978976, 255650760, 0, 106198983, 3302784, -497871606, 61844220, 0, 111991680, 27652914, -156528600, 37453830, 0, -590996900, -296374808, 246456432, 6529952, 0, -42567768, -647177312, -38536448, -79251921, 0, 190080174, -2356128, -253742425, -294166372, 0, -111138816, -461755512, -122281056, 424171700, 0, 2251098, 242262384, -635246166, 44800128, 0, -493272572, 108308304, -38629440, -56698866, 0, 245506727, -148657152, -13108878, -7639944, 0, 24375024, 312394618, 53911376, -16651170, 0, 51083172, -35604360, -586466876, -77621856, 0, -44815680, 392048538, -6930432, 411354845, 0, 2503386, -279902816, 357132144, -122258160, 0, 13425728, 610188930, 274506720, 69109260, 0, 299929252, -92994388, -26121528, -92439552, 0, -145198656, 143987533, 138790368, 54634257, 0, -659003658, 79674624, 725296759, 21554640, 0, -618896, -37781070, 55923372, -282173185, 0, -292459932, -476535528, 163763040, -6694272, 0, -34652880, 24660612, 122089344, -305049180, 0, 101243267, -189565056, -382135698, 185231328, 0, 34940160, -2329884, -21360828, -216850932, 0, -263055588, 163012968, -75697177, -94466240, 0, -121534536, 1943976, 12976560, 706539050, 0, 50105196, -58781696, -676562196, 4251528, 0, 28952256, -127465965, -103840296, -301098720, 0, -46111176, 522668092, -164347137, 151644032, 0, -46042128, -79251617, -188960256, -37021752, 0, 31198122, -13522464, 19335780, 233918440, 0, 257386368, -606343692, 259150464, 153497629, 0, -97280676, -32825808, 34200702, 72714240, 0, 128897500, -393563070, 47091456, 49264620, 0, -180636928, -533120, 221378670, -227370624, 0, 153235584, -130235477, -163208180, -16734438, 0, 200634552, -173892312, 304189579, -365034528, 0, -26748072, 200839836, -4712256, -97212437, 0, 51615783, -232988320, 6493470, 181044, 0, 14548992, 270720549, -215690760, -381440460, 0, -40790971, 70330032, 303655122, 124800384, 0, -113397732, 322607736, 25438656, -50034672, 0, 185164650, -40573440, 309478609, -87674060, 0, 203898320, -270081132, -114693192, 94072104, 0, -276608142, 460712880, 443937354, -89631360, 0, -321666976, -31547754, -35880960, 90170628, 0, 93044597, 42071328, 205163928, 353308128, 0, 4385664, 369198283, 497261380, -226661976, 0, 439198812, -52243056, 68238125, 127326720, 0, 238374504, -23994594, -165827520, -290836055, 0, 141877980, -145336320, 58496904, 26951400, 0, 39188640, 5591214, 103402440, 652291470, 0, 1535557, -105185376, -406894482, -100349888, 0, 31422312, -781317977, -23240064, 59232708, 0, -257070780, -123295248, -37583712, 223168868, 0, -85289728, -90302952, -4659768, 17096371, 0, 130100328, 123810792, 688189044, -64377792, 0, 586594244, -22110570, 6640528, -517947240, 0, 739946304, -4860928, 96276762, 37740456, 0, 8503056, -456777947, -128318480, -148363020, 0, -78350688, 185901948, 597680720, 37197792, 0, 70325160, -340572282, 50349312, -266902920, 0, -75741102, 276603424, -26290860, 62396244, 0, 183138368, -70009920, 55882896, 357955110, 0, 119576412, 313982572, 158203935, 5013504, 0, 307543392, 183990806, -380064, 350467884, 0, -4695288, 94182912, -289958366, 140901676, 0, 83013440, 285126288, -46014480, -351001980, 0, -4180086, 77226792, 755672064, 24506640, 0, 36079184, -39522654, -53891328, -783114660, 0, -254109133, -76731456, -436133043, 426203808, 0, -79193088, 9101615, -180056840, 48772692, 0, 182597664, 68911776, 589738205, 39379904, 0, -356384496, 1052873160, 140660064, 319010094, 0, 346259898, -9206784, 630538608, -151411500, 0, 61101504, -56700162, 507809160, 659932230, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "150.6.a.a", "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], [1], [-4], [-9], [16], [0], [36], [-47], [-64], [81], [0], [222], [-144], [-101], [188], [0], [256], [-162], [-324], [1685], [0], [423], [-888], [-306], [576], [0], [404], [-729], [-752], [7890], [0], [-8593], [-1024], [-1998], [648], [0], [1296], [-8642], [-6740], [909], [0], [-18168], [-1692], [-14351], [3552], [0], [1224], [1098], [-2304], [-14598], [0], [1458], [-1616], [-17916], [2916], [0], [3008], [-15165], [-31560], [17610], [0], [-21853], [34372], [-3807], [4096], [0], [7992], [-107], [-2592], [2754], [0], [-40728], [-5184], [-34706], [34568], [0], [26960], [-10434], [-3636], [-69160], [0], [6561], [72672], [108534], [6768], [0], [57404], [-71010], [-14208], [35040], [0], [4747], [-4896], [77337], [-4392], [0], [9216], [823], [58392], [17982], [0]]}