# Trace form for 462.8.a.a, downloaded from the LMFDB on 26 June 2022. [0, 1, -8, -27, 64, 182, 216, 343, -512, 729, -1456, 1331, -1728, 13758, -2744, -4914, 4096, 14738, -5832, 34516, 11648, -9261, -10648, 49816, 13824, -45001, -110064, -19683, 21952, 141174, 39312, -86112, -32768, -35937, -117904, 62426, 46656, 535038, -276128, -371466, -93184, 708282, 74088, 162292, 85184, 132678, -398528, 397296, -110592, 117649, 360008, -397926, 880512, 224798, 157464, 242242, -175616, -931932, -1129392, 694668, -314496, 50110, 688896, 250047, 262144, 2503956, 287496, -3228404, 943232, -1345032, -499408, -1871496, -373248, -937542, -4280304, 1215027, 2209024, 456533, 2971728, 1266032, 745472, 531441, -5666256, -2545004, -592704, 2682316, -1298336, -3811698, -681472, -9909830, -1061424, 4718994, 3188224, 2325024, -3178368, 6281912, 884736, -14010830, -941192, 970299, -2880064, -7342810, 3183408, -8860296, -7044096, -1685502, -1798384, -15018476, -1259712, 10625094, -1937936, -14446026, 1404928, -7093102, 7455456, 9066512, 9035136, 10029582, -5557344, 5055134, 2515968, 1771561, -400880, -19123614, -5511168, -22408932, -2000376, 36039408, -2097152, -4381884, -20031648, 22563748, -2299968, 11838988, 25827232, -3582306, -7545856, 12446138, 10760256, 1633004, 3995264, -10726992, 14971968, 18311898, 2985984, 25693668, 7500336, -3176523, 34242432, 67513070, -9720216, -62321768, -17672192, 10744002, -3652264, -15672384, -23773824, -80277154, -10128256, -6069546, -5963776, 17086888, -4251528, -11784932, 45330048, -6540534, 20360032, -55180344, 4741632, 126534047, -21458528, 25162164, 10386688, 56395214, 30493584, -15435343, 5451776, -18756036, 79278640, 10331180, 8491392, 66724102, -37751952, -1352970, -25505792, 97376916, -18600192, 19616278, 25426944, -6751269, -50255296, -45386208, -7077888, -29202974, 112086640, -67606812, 7529536, 117637534, -7762392, -62134696, 23040512, 87166908, 58742480, 48422682, -25467264, 128907324, 70882368, 36315864, 56352768, 45940796, 13484016, -184022500, 14387072, 50530392, 120147808, 29537144, 10077696, -29536416, -85000752, 25313634, 15503488, 202765404, 115568208, 88107216, -11239424, -32805729, 56744816, 275878404, -59643648, -82891594, -72532096, -12326391, -72281088, -236402150, -80236656, 72307872, 44458752, -34182864, -40441072, 278052464, -20127744, -148269086, -14172488, -14348907, 3207040, 21412118, 152988912, 474871128, 44089344, 68715108, 179271456, 289063580, 16003008, 66305096, -288315264, -72422532, 16777216, -199415470, 35055072, 183518034, 160253184, 102915846, -180509984, -404762712, 18399744, 40913236, -94711904, 267565410, -206617856, 43535582, 28658448, -264981040, 60366848, -127412838, -99569104, -59896331, -86082048, 649499246, -13064032, -62775648, -31962112, 175805930, 85815936, -121586900, -119775744, -169611624, -146495184, 242940726, -23887872, -193130029, -205549344, 378292410, -60002688, 527431270, 25412184, 126429576, -273939456, -26198073, -540104560, 685368528, 77761728, 55666156, 498574144, 198255870, 141377536, 9120020, -85952016, 123803956, 29218112, 239227992, 125379072, 517448344, 190190592, -98467846, 642217232, 45508554, 81026048, 352105686, 48556368, 187902594, 47710208, 405498852, -136695104, 508696808, 34012224, -619123758, 94279456, -286877538, -362640384, 136272528, 52324272, -536200108, -162880256, 390042702, 441442752, -587569528, -37933056, -728923086, -1012272376, 191513754, 171668224, -114615072, -201297312, 40353607, -83093504, -244795824, -451161712, 808560212, -243948672, -665357874, 123482744, -270798714, -43614208, -66661710, 150048288, -340612272, -634229120, -136488618, -82649440, -400001256, -67931136, 297482517, -533792816, -47832147, 302015616, -170632644, 10823760, -349647904, 204046336, 516337578, -779015328, 77105714, 148801536, 323621038, -156930224, 605041164, -203415552, 1942271892, 54010152, -649660060, 402042368, -973064016, 363089664, 1116974720, 56623104, 83089006, 233623792, 118310868, -896693120, 1187718558, 540854496, 734188208, -60236288, -609221196, -941100272, 230417824, 62099136, 2202426766, 497077568, -319652676, -184324096, 822757426, -697335264, -1184728896, -469939840, 96722262, -387381456, 712135578, 203738112, 901095034, -1031258592, -336045726, -567058944, 238271124, -290526912, -463190728, -450822144, -44091108, -367526368, -1768290060, -107872128, 456925934, 1472180000, 289628784, -115096576, -663224738, -404243136, 17187730, -961182464, -494421246, -236297152, -1566353808, -80621568, -1703070718, 236291328, -693729036, 680006016, 1719449056, -202509072, 1645347688, -124027904, 85766121, -1622123232, 1373059684, -924545664, -1803589060, -704857728, -1822852890, 89915392, 2611572866, 262445832, 942723342, -453958528, 1682687736, -2207027232, 858856908, 477149184, -3130573094, 663132752, -290088054, 580256768, -1695396178, 98611128, -834761472, 578248704, 423154368, 1891217200, -1124594028, 641893248, -1107342572, -578462976, 2167483158, -355670016, 216010652, 273462912, -1553254516, 323528576, 163877742, -2224419712, -3772263888, 161021952, 7361052804, 1186152688, -461345976, 113379904, -2549971060, 114791256, -4403489416, -25656320, 318193164, -171296944, -2615319820, -1223911296, 2080622412, -3798969024, 176594418, -352714752, -641923128, -549720864, 2155412732, -1434171648, 1489869288, -2312508640, -4755267256, -128024064, -1336391420, -530440768, -3416419269, 2306522112, -3042566290, 579380256, -321576906, -134217728, -679378428, 1595323760, -1612573872, -280440576, 528800976, -1468144272, -1522670778, -1282025472, -1813798086, -823326768, 485163836, 1444079872, 416754261, 3238101696, -1269118656, -147197952, -923191591, -327305888, 506412972, 757695232, 9744543756, -2140523280, -2733362632, 1652942848, -278941860, -348284656, 156590819, -229267584, -4459217498, 2119848320, -1801550754, -482934784, 1933767108, 1019302704, -3957797380, 796552832, 36530190, 479170648, 4872761784, 688656384, 434248976, -5195993968, -2629176732, 104512256, 2300184246, 502205184, 2232813336, 255696896, -529639506, -1406447440, 3771331108, -686527488, -1290944564, 972695200, 182284263, 958205952, -3868822454, 1356892992, 2655106084, 1171961472, 1225427616, -1943525808, -2241769816, 191102976, -6505290142, 1545040232, 788480298, 1644394752, -872936372, -3026339280, 299206138, 480021504, 1825383924, -4219450160, 5828314476, -203297472, -2972241792, -1011436608, -3176213418, 2191515648, 9215645826, 209584584, 920034388, 4320836480, 1677636792, -5482948224, 8324571240, -622093824, -1805325302, -445329248, -2353506516, -3988593152, 322424102, -1586046960, 9913273696, -1131020288, -1307412414, -72960160, 5465998368, 687616128, -1211566386, -990431648, -3480497748, -233744896, -957640582, -1913823936, -4812354148, -1003032576, -980528328, -4139586752, -3399071690, -1521524736, -562722499, 787742768, -1240401492, -5137737856, 7885390044, -364068432, -5182799624, -648208384, 4968607500, -2816845488, 6559172256, -388450944, 1618614942, -1503220752, -1364320584, -381681664, -2631064446, -3243990816, -4324693804, 1093560832, -797502888, -4069574464, -4343232328, -272097792, 924603108, 4952990064, 797483232, -754235648, 4591427382, 2295020304, 4106602136, 2901123072, -683468118, -1090180224, 3992437116, -418594176, -4958049642, 4289600864, -5474665908, 1303042048, 2154695816, -3120341616, 7032723984, -3531542016, -2378894832, 4700556224, 66696410, 303464448, 286854626, 5831384688, 885754683, 8098179008, 736156150, -1532110032, -4805714690, -1373345792, -7448716908, 916920576, 238050132, 1610378496, 2265197116, -322828856, 2238073038, 664748032, 3092770884, 1958366592, 2184335028, 3609293696, 332812557, -6468481696, 297206728, 1951589376, 10438660116, 5322862992, 6382858050, -987861952, 13389059286, 2166389712, 18467371608, 348913664, -1952312544, 533293680, -2518583830, -1200386304, 12046826526, 2724898176, 922937328, 5073832960, -4289755392, 1091908944, 3332765436, 661195520, -7507416528, 3200010048, -1406037456, 543449088, -3039081528, -2379860136, 4003265322, 4270342528, -6352971174, 382657176, 2211379848, -2416124928, 387420489, 1365061152, 2391859496, -86590080, -6282789058, 2797183232, -578127186, -1632370688, -4297005724, -4130700624, -20423592676, 6232122624, -12821520456, -616845712, -10457266184, -1190412288, 12287378740, -2588968304, -1855307916, 1255441792, -5151337268, -4840329312, -3969790480, 1627324416, -7804716660, -15538175136, -11342561776, -432081216, -2095207954, 5197280480, -1790237592, -3216338944, 2989629834, 7784512128, 3644407242, -2904717312, 1955408364, -8935797760, 9557242344, -452984832, 22886323090, -664712048, 5384217690, -1868990336, 15012119190, -946486944, 3875126112, 7173544960, -4954986918, -9501748464, 24447061512, -4326835968, -2490961176, -5873505664, -2778727842, 481890304, -14610442028, 4873769568, 12372165556, 7528802176, 10928593224, -1843342592, -2432933986, -496793088, 689413380, -17619414128, -1104657372, -3976620544, 15998765454, 2557221408, 5855348448, 1474592768, -7224266070, -6582059408, -1247868402, 5578682112, 3109813616, 9477831168, -1175460714, 3759518720, 11916555610, -773778096, -20325228484, 3099051648, 7154488080, -5697084624, -2144857624, -1629904896, 5601670672, -7208760272, 3440146626, 8250068736, -8132320658, 2688365808, 12751381496, 4536471552, 1617200937, -1906168992, -3434327260, 2324215296, 31069621102, 3705525824, -17536479642, 3606577152, 1733910962, 352728864, -10042822608, 2940210944, 1694942496, 14146320480, -26926080840, 862977024, 2680221967, -3655407472, -4746760110, -11777440000, 23029196554, -2317030272, 607645423, 920772608, 3282846300, 5305797904, 26653453008, 3233945088, -22886222346, -137501840, 4579513848, 7689459712, -29422112182, 3955369968, -10393199780, 1890377216, -6559399602, 12530830464, 22189991456, 644972544, 10263928948, 13624565744, 5214510783, -1890330624, 1685088592, 5549832288, -44416382232, -5440048128, -10213895070, -13755592448, -7686263676, 1620072576, 35947316934, -13162781504, -14240644290, 992223232, -27629460350, -686128968, -23222515748, 12976985856, -3413598552, -10984477472, 29332325400, 7396365312, 12361516944, 14428712480, 707347971, 5638861824, 13713068736, 14582823120, 1880274760, -719323136, -18504950256, -20892582928, -12156775488, -2099566656, 3313072924, -7541786736, -1502986212, 3631668224, 12143786564, -13461501888, -13888308572, 17656217856, -5352908490, -6870855264, 4831929216, -3817193472, -3387400324, 25044584752, -246240540, -5305062016, 7739365564, 2320704432, 19519170440, -4642054144, -3342706812, 13563169424, -25748041968, -788889024, -24077245038, 6678091776, -6459155784, -4625989632, -39699712830, -3385234944, 4060772884, -15129737600, -13971105288, 8996752224, 3570162596, -5135145984, 3041553082, 8858740576, 2658631842, 4627703808, -7605926370, -17339865264, 35283776112, 2845360128, -1228730958, -1728085216, 22278219036, -2187703296, -12898702836, 12426036128, -9506853522, -2588228608, -49383612150, -1311021936, -8260289856, 17795357696, -5073370038, 30178111104, 4269025334, -1288175616, -20097337567, -58888422432, -10948469004, -9489221504, -5314941268, 3690767808, -459603608, -907039232, -13734813816, 20399768480, 2518529916, -918330048, 560120372, 35227915328, 16716341466, 205250560, 24781064114, -2545545312, -13189983730, 1370375552, 7745693526, 20922558560, 49975370952, 9791290368, 21410031188, -16644979296, -3679358256, 30391752192, 8084738272, -1412755344, 2076348464, 2821718016, 14477402916, 5135385024, -11308514672, 4397766912, -19257960554, -17243301856, -10531152954, 11473373184, 6280981014, -11918954304, 10238016984, 18500069120, 15864377256, 38042138048, 7759127768, 1024192512, -26842334414, 10691131360, 19680923322, 4243526144, 46593031190, 27331354152, 8812928124, -18452176896, -5170871358, 24340530320, -47847426844, -4635042048, 60793014974, 2572615248, 3094606944, 1073741824, -31873398282, 5435027424, 17418068256, -12762590080, -1089547389, 12900590976, 65617213800, 2243524608, 63440894714, -4230407808, 6609487248, 11745154176, 738521180, 12181366224, -66800653776, 10256203776, -21831125724, 14510384688, 23156983010, 6586614144, 8361224872, -3881310688, 17964662598, -11552638976, 30339993658, -3334034088, -73249550572, -25904813568, 7311565278, 10152949248, -33492095000, 1177583616, -21376366424, 7385532728, 1799866170, 2618447104, -38237446530, -4051303776, 4072205688, -6061561856, 9196531344, -77956350048, -18648414730, 17124186240, 27044488814, 21866901056, 3685192686, -13223542784, 75533454612, 2231534880, -7303302292, 2786277248, 10800033912, -1252726552, -35014165032, 1834140672, 19791697536, 35673739984, -8032027959, -16958786560, -5375627712, 14412406032, -55171546496, 3863478272, 1291467969, -15470136864, -13281756204, -8154421632, -68092887330, 31662379040, 4607081388, -6372422656, 8868500874, -292241520, -27535063822, -3833365184, 9440493408, -38982094272, 28729055520, -5509251072, 36903303528, -3473991808, -13941114606, 41567951744, 9240060182, 21033413856, -9773280110, -836098048, -2081854278, -18401473968, 16035513312, -4017641472, 61361235782, -17862506688, -8737768026, -2045575168, 23977160688, 4237116048, 42840113988, 11251579520, -16336111428, -30170648864, 5860802584, 5492219904, -77261893734, 10327556512, -52441341084, -7781561600, -11793053976, -1458274104, 50209869528, -7665647616, 17540821620, 30950579632, -47580218152, -10855143936, -4042231676, -21240848672, 26272728432, -9375691776, -15086270108, -9803420928, -46073192256, 15548206464, -30158317440, 17934158528, -6138531920, -1528823808, 42449232002, 52042321136, -2243403162, -12360321856, -136339441140, -6307842384, 1729596760, -13155158016, -3194393436, 6983490976, -37342938444, 24210714240, -43025191300, -2393649104, -32068401066, -3840172032, -18926857992, -14603071392, -71256527364, 33755601280, -19823081616, -46626515808, -17878717296, 1626379776, -19989591556, 23777934336, 16448972292, 8091492864, -39412855890, 25409707344, 43401178121, -17532125184, -6221281248, -73725166608, -42685863076, -1676676672, 99991003068, -7360275104, -59465522682, -34566691840, -40737895126, -13421094336, 50605548448, 43863585792, 8630622252, -66596569920, 14142000114, 4976750592, 534766290, 14442602416, -22214450502, 3562633984, -26984973652, 18828052128, -27582108048, 31908745216, 31987680192, -2579392816, 19343558402, 12688375680, 38601152966, -79306189568, -2611501074, 9048162304, -8414941038, 10459299312, 11198537168, 583681280, -19227660606, -43727986944, -27004302600, -5500929024, -5294322649, 9692531088, -24329565918, 7923453184, -72700345802, 27843981984, -22596880448, 1869959168, 9073234602, 7661124656, 86426545296, 15310591488, -62670467306, 38498833184, -6433320348, 8024260608, -13817493996, 7844226624, -9440918762, 33116694016, 12506149656, 27192573520, 22911410808, 12172197888, 50349677730, 4501779992, 1190459916, -6301942144, 3543594740, 9923211936, 52609571560, 41101902848, 47743831620, -63083120352, 9532785276, 2912547456, -192760999140, 41462396992, -12337000218, 5185667072, 12067527472, -39748860000, 22886366986, 22534763904, -7819977168, -52473378048, -60991579584, 3107607552, -111431592464, -12948919536, 17907067926, 12025766016, -70620382498, 10914564672, 58891463552, 3053453312, -464068710, 21048515568, -94160933684, 25951926528, -36293615540, 34597550432, 13349373642, -8748486656, 14643706842, 6380023104, -128015783380, 32556595712, 42291552816, 34745858624, 33400282188, 2176782336, 30633962802, -7396824864, 45982909386, -39623920512, 42671547654, -6379865856, 87358673992, 6033885184, 18730683972, -36731419056, 104096139660, -18360162432, 6728383354, -32852817088, -46425124512, -23208984576, -101022379980, 5467744944, -73666813584, 8721441792, -44424387576, -31939496928, -125025823272, 3348753408, -35010922006, 39664397136, -2315685267, -34316806912, -10116134798, 43797327264, -135668853584, -10424336384, -37072611468, -17237566528, 2357947691, 24962732928, -13975288704, -56261791872, 48696904620, 28252336128, -15567469344, 19031158656, -121899952368, -37604449792, 49217028030, -533571280, 18658779616, -2427715584, 7923475924, -2294837008, -70512467382, -46651077504, -64596555936, -7086037464, -10016620082, -64785432064, -25453530234, -5889249200, -48226549280, 12256880256, 34605581088, 38445717520, -45432568872, 10986766336, 53067666706, 59589735264, 56087865504, -7335364608, -23189136516, -1904401056, -8234819864, -12883027968, 191333784311, -18121576928, 84525473538, 2582630848, -52851839450, -17904584304, -29826288492, -5317984256, 7832377458, -24742167072, 40349674162, -15666932736, 65453951182, -17474680224, 45775696806, -28874349568, 118208862772, -2662500456, -32360199672, 51747853568, 22538559744, -2377653824, -206624192808, -15612715008, -21312200728, -83509280928, -11425167936, -42582903936, 47968452048, -51062864400, 127767011080, 7902895616, 30364038756, -107112474288, 2496279760, -17331117696, 31996679260, -147738972864, 29898249444, -2791309312, -14567753534, 15618500352, -37508268952, -4266349440, -58522045266, 20148670640, -22128815800, 9603090432, 146180043252, -96374612208, -5832287604, -21799185408, 16608979926, -7383498624, -102560823344, -40590663680, 41937871932, 34318043136, -28098663244, -8735271552, 21130131294, -26662123488, -4424699034, -5289564160, -23175334790, 60059332224, 44215212132, -25600080384, 101851124976, 11248299648, -120616398864, -4347592704, 30032348588, 24312652224, -198748425708, 19038881088, -35149665278, -32026122576, 140928827896, -34162740224, 12456341352, 50823769392, 149207944068, -3061257408, 144151636886, -17691038784, 68849218620, 19328999424, -34211953152, -3099363912, 129729861508, -10920489216, 118894214232, -19134875968, 15757693028, 692720640, 95992491140, 50262312464, -8591215428, -22377465856, -97586897316, 4625017488, -16207634656, 13058965504, 70613635140, 34376045792, -31260754668, 33045604992, -63119717500, 163388741408, -56176805124, -49856980992, -18971274470, 102572163648, 24318163196, 4934765696, -4768049286, 83658129472, -143637687888, 9523298304, 136388183138, -98299029920, 17331924456, 20711746432, 234096997422, 14842463328, 124737072096, -10043534336, -58196143764, 41210698144, -73314197820, 38722634496, 43698360512, 31758323840, -40226470776, -13018595328, 10131240392, 62437733280, 16565809678, 124305401088, 128392215912, 90740494208, 157240864360, 3456649728, -146051074540, 16761663632, 36082568340, -41578243840, 378957784716, 14321900736, -10130990688, 25730711552, 92243320263, -23917038672, -129543928068, -62276097024, -2255000110, -29155257936, 82149289830, 23237738496, 2173528324, -15643266912, 87210842732, 71486382080, 8682576462, -76457938752, 22532319992, 3623878656, 31735632852, -183090584720, 18343217556, 5317696384, -160826173664, -43073741520, 74655948808, 14951922688, 43539494544, -120096953520, 69548533572, 7571895552, 164407304870, -31001008896, -14277626352, -57388359680, 38906868290, 39639895344, 94175598608, 76013987712, 41112111006, -195576492096, -139674851560, 34614687744, 30220775088, 19927689408, 48972548322, 46988045312, -17921147972, 22229822736, -73233481680, -3855122432, -13099423572, 116883536224, 46067161060, -38990156544, 24373136238, -98977324448, -11252365047, -60230417408, -87843358064, -87428745792, 54035373812, 14746740736, 34266203712, 19463471888, -262578993664, 3974344704, 64083234852, -5515307040, 24926172957, 140955313024, 94626292572, 8837258976, 86832387096, 31812964352, -13673150244, -127990123632, 34198272108, -20457771264, 173680075942, -46842787584, -263102681412, -11796742144, 107463530322, 57794128560, -28431816742, 52656475264, 73800791064, 9982947216, 262724354296, -44629456896, 34518833562, -24878508928, 7531430220, -75822649344, 77817386078, 9403685712, 92582819056, -30076149760, -4227952113, -95332444880, -233270830356, 6190224768, -189875578642, 162601827872, 120398872446, -24792413184, -308302086456, -57235904640, 199676600380, 45576676992, 48641870358, 17158860992, -81085937450, 13039239168, -93230444736, -44813365376, -52211711916, 57670082176, 173194375158, -27521173008, 89859896170, -66000549888, 106860529260, 65058565264, -19357805376, -21506926464, 24801600096, -102011051968, -986315130, -36291772416, -206491612540, -12937607496, 495830175264, 15249351936, -131564568168, 27474618080, -97588419656, -18593722368, 69208486458, -248556968816, -11724722352, -29644206592, -82950273208, 140291837136, 132815668816, -28852617216, 70987771764, -13871287696, -135596674164, -2821830912, 212888387478, 80342580864, -62104974642, -23521687552, 95371995152, -13559539968, 145281408404, -113170563840, -60285960072, 215408646720, -46704592272, -6903816192, 306909117643, -21441775736, 14300266662, 29243259776, -132664001652, 37974080880, -50856296498, 94219520000, -101825939916, -184233572432, -342047692280, 18536242176, 95547824766, -4861163384, 34855503228, -7366180864, 119787184002, -26262770400, 7175415572, -42446383232, -4921675101, -213227624064, 310432044984, -25871560704, -20859943104, 183089778768, 104458206258, 1100014720, 229540226854, -36636110784, 98069060232, -61515677696, -71687864268, 235376897456, 7344356474, -31642959744, -108218333780, 83145598240, -33086545632, -15123017728, 262799960250, 52475196816, -299302900524, -100246643712, 60527785032, -177519931648, -106848891974, -5159780352, 162880796904, -82111431584, 175642833834, -108996525952, 153154414382, -41716086264, 147157958584, 15122644992, -21288968046, -13480708736, 212568457248, -44398658304, 288293787470, 355331057856, 23569282044, 43520385024, -121095133068, 81711160560, -48453743796, 110044739584, -8078565726, 61490109408, -130583042448, -12960580608, 268597940458, -287578535472, -49285365948, 105302252032, 99148807940, 113925154320, 320953593424, -7937785856, -157364490852, 221035682800, 114948502344, 5489031744, -12132431220, 185780125984, 80250528384, -103815886848, 7074229140, 27308788416, 22742647928, 87875819776, 85757762286, -234658603200, 84219191496, -59170922496, 228054742546, -98892135552, -248822437302, -115429699840, 171233966604, -5658783768, 256633199768, -45110894592, -24840928476, -109704549888, -383640292460, -116662584960, -322598063770, -15042198080, -45296193384, 5754585088, -15685744492, 148039602048, -72800228592, 167140663424, -224763423480, 97254203904, -68399506210, 16796533248, -322589484230, -26504583392, 48743783154, 60334293888, 54141818094, 12023889696, 22466869032, -29053345792, 63544675932, -97150292512, 180044020148, 107692015104, 62946685662, 111106468576, -8705450754, -141249742848, 63068650112, 42823267920, -221342299288, 54966842112, -267658389792, -38655433728, -178159622592, 30537547776, 42190327542, 27099202592, 35300135178, -200356678016, -59819250816, 1969924320, 252591280264, 42440496128, -147581955936, -61914924512, -63635918528, -18565635456, -73445037864, -156153363520, 32712292422, 37136433152, -138833610216, 26741654496, -483597808280, -108505355392, 93973439196, 205984335744, -237282518184, 6311112192, -245479917843, 192617960304, 25856295714, -53424734208, 156592635372, 51673246272, 14033239948, 37007917056, 129933561996, 317597702640, 168416816557, 27081879552, 24206281526, -32486183072, 26474264856, 121037900800, 58899028916, 111768842304, -55059753348, -71974017792, 91774935630, -28561300768, -364472710080, 41081167872, -364672376846, -24332424656, 15193507473, -70869924608, -323229331410, -21269054736, 206059426824, -37021630464, 33490840284, 60847410960, 14932704626, 138718922112, 353493484344, -282270208896, -212905531188, -22762881024, -559787269550, 9829847664, -4315072320, 13824681728, 139935589848, -178225752288, -118238130920, 17501626368, -90888496720, 103189622688, -134152402500, -99408289024, 111510431750, 76054828176, 75062029834, 20705828864, -177097650912, 395068897200, -593157491148, 10488175488, -126781919264, 66082318848, -43702603434, -142362861568, -16452415350, 40586960304, 203289399040, -241424888832, 36836655768, -34152202672, -253444429960, 10305404928, -104538137276, 160778700536, 71038740042, 471107379456, -20544441533, 87587752032, 281397605472, 75913772032, 116766732708, 42519530144, -165968716932, -29526142464, 295784308342, 3676828864, 21532577976, 7256313856, 928844817060, 109878510528, 222778241378, -163198147840, 117267272856, -20148239328, -455766706296, 7346640384, 216164777556, -4480962976, -24964283916, -281823322624, -10371728194, -133730731728, 523617599056, -1642004480, -21532047264, -198248512912, 133622253856, 20364362496, -305821976736, 105519869840, -123968539314, -10963004416, 120275472324, -61965548208, -857422884144, -167380468480, -110878257672, -399802967616, 60301433990, -78330322944, 13750800580, -171280249504, 18453639186, 133159834368, -331944523306, 29434866048, -56972706032, -243134017536, -107795802132, -64677906176, -224627489796, 11302042752, -41704306700, -16610787712, 133867340334, -22573744128, 400841671412, -115819223328, 31362704180, -41083080192, 147815979516, 90468117376, 88809779762, -35182135296, -544170803350, 154063684432, -58176787032, 137946414848, 328156902214, 84249223632, -634429719536, -91786985472, -189883547568, -50247848112, 571114327548, 95351634432, 149741851532, -81904135872, 64230160464, -148000552960, 83328669018, -126915018048, -252647721212, -304337104384, -1800803070, -62073022144, -215620659072, -8193540096, 334513986306, 214738675312, -7745074902, -85529050880, 64477962432, -157447386576, -66243599947, -33948209152, -23915376441, -372744249520, 197171007396, -218650833216, 555696888158, -70503424992, -19876216050, 147617415168, -518377717616, 41366970864, 129608675196, -194724242560, 129754296630, 382779414752, 133592069208, 37080336384, -1104453084732, -486344119792, 201115356516, -20580921984, 163999296188, -24756855552, -493668091280, -8589934592, -6427353564, 254987186256, 180908925610, -43480219392, 388511162750, -139344546048, -61160322132, 102100720640, 26109266018, 8716379112, -264206576304, -103204727808, -60427972026, -524937710400, 506391006288, -17948196864, 43365344568, -507527157712, -83504813868, 33843262464, -346725187506, -52875897984, 366735744504, -93961233408, -58977045756, -5908169440, 114527725004, -97450929792, 278004325248, 534405230208, -8985939039, -82049630208, -509313949470, 174649005792, -432482638116, -116083077504, -8024581656, -185255864080, 520561238056, -52692913152, -711468588710, -66889798976, -281843823132, 31050485504, 235081405104, -143717300784, -321828790920, 92421111808, -172337167350, -242719949264, 566987682692, 26672272704, -60409042848, 585996404576, -361504600722, 207238508544, 83160519988, -58492522224, 19093491508, -81223593984, -498619033416, 267936760000, -775534154416, -9420668928, 15001650210, 171010931392, 52712438688, -59084261824, -132356554308, -14398929360, -162137094456, -20947576832, 68001763410, 305899572240, -38869158394, 32410430208, -330262839816, -32577645504, -325264316202, 48492494848, -362644302990, -73572250752, -785209564956, 623650800384, -24919307856, 149187317840, 3128166860, -136993489920, 262541822602, -216355910512, 115823395584, -174935208448, -293332349810, -29481541488, 88649443888, 105788342272, -89984666772, -604267636896, -244825508632, -17852279040, 42464756908, 58426418336, 202700246256, -22290217984, 556060208602, -86400271296, -285076393056, 10021812416, 37963011312, 280113320256, 531148795104, -14673125376, 429558861602, -158333580288, 82055201256, -285389919872, -309958870676, 64256223672, 156575557754, 135670292480, -108088163694, 43005021696, -759171172752, -115299248256, 159220377036, 441372371968, 171530221698, -30907826176, 177484781992, -10331743752, -574493787396, 123761094912, -59707255896, 106254049632, 371673777384, 65235373056, 312939728192, 544743098640, -10460353203, -253299032320, -82701280376, -36856651104, -33774471178, 50979381248, -64580206392, -70948006992, 299453279216, 2337932160, 877561321740, 220280510576, 169635304566, 30666921472, 161158263552, -75523947264, -742851139156, 311856754176, 15609434022, -229832444160, -380607489024, 44074008576, -348779008847, -295226428224, 116019154548, 27791934464, 344067398830, 111528916848, 249896862488, -332543613952, 551437002252, -73920481456, 120772250298, -168267310848, 865368669846, 78186240880, 346181052312, 6688784384, 445952259830, 16654834224, 332544518024, 147211791744, 282346186968, -128284106496, -697963507280, 32141131776, 64450589742, -490889886256, -331759225980, 142900053504, -297274491354, 69902144208, -971529629296, 16364601344, 50093313732, -191817285504, 61027113812, -33896928384, 475306261612, -342720911904, 139086106236, -90012636160, 775885354212, 130688891424, 829985797188, 241365190912, 107184342960, -46886420672, 171575648244, -43937759232, 26810754180, 618095149872, 210727349820, -82620452096, 174483005144, 419530728672, 80733616704, 62252492800, 306249167952, 94344431808, 910558720716, 11666192832, -747795285690, -401678956224, 56570614758, 61325180928, -291535364206, -140326572960, -212359448994, -247604637056, 48336414984, 380641745216, 36482917016, 86841151488, -808899335526, 32337853408, -80720005518, 169926789376, -569764303108, -210181827456, 948726346912, 75005534208, -98398995534, 120690160864, 178730801568, 78427367424, 484861329118, 368585538048, -52796025828, -124385651712, -477239069814, 241266539520, 61147199476, -143473268224, -258045543288, 49108255360, 46741477104, 12230590464, -308562104396, -339593856016, -617930723430, -416338569088, 69028246774, 17947225296, -994542205208, 98882574848, -145373877630, 1090715529120, -151926587904, 50462739072, -183916637044, -13836774080, -405327218130, 105241264128, -244933947500, 25555147488, -365789422960, -55867927808, -104628405024, 298743507552, 142136374440, -193685713920, 183431181844, 344201530400, 133784646786, 19149192832, 1052818306854, 256547208528, -204676113096, 30721376256, -660070660824, 151414863936, -450958663412, 116824571136, -96177501482, 570052218912, 67255951752, -270044810240, -201536348104, 158584652928, -760874183596, 373012126464, 75025651734, 143029738368, 487915838480, -13011038208, 917990195316, 159916732448, 394481934756, -190223474688, -294145042586, -131591778336, -250020618498, -64731942912, -334048470012, 315302847120, 24067212952, -203277658752, 39313938664, -347209424968, -295072017048, 140257001472, -441384505536, 49770249984, -443844184876, 589801332864, 65689217622, 341486904608, -773466696912, 13413413376, 3701419898, -799928024544, -18614161260, 58882200832, -270643469178, 475724181456, -297059967072, 276533534720, 29825749044, 325903161008, -39312969696, 107368754688, 392686596750, -404844387584, -431966667258, -350908686336, 574541962810, -69044978016, -686552027616, 532772559360, -158094408096, -113136000912, -307618759840, -39814004736, 13841287201, -4278130320, 195055183890, -115540819328, 1339711610328, 177715604016, -359288394696, -28501071872, 33692446854, 215879789216, -516373890244, -150624417024, 1243936206528, 220656864384, -83964967632, -255269961728, -951746264238, -255901441536, 492020840376, 20635142528, 31737439278, -154748467216, 955580852632, -101507005440, 630501360830, -308809223728, -321747001470, 634449516544, 277336152716, 20892008592, 269880752724, -72385298432, 548781169068, 67319528304, -801435073712, -83674394496, 906118594814, -89588297344, -193171178160, -4669450240, 1012812456778, 153821284848, -228217750782, 349823895552, 57911155848, 216034420800, -295131480416, 44007432192, -109020547584, 42354581192, -151245108144, -77540248704, 117270704496, 194636527344, -475988207240, -63387625472, -92883958902, 581602766416, -1235730432220, -222751855872, -748160400416, 180775043584, 219572657766, -14959673344, 378673278984, -72585876816, -477640102780, -61288997248, -344287300392, -691412362368, -22864966530, -122484731904, -56360461030, 501363738448, -43664425299, -307990665472, -611335720018, 51466562784, -1727318819352, -64194084864, 92726836020, 110539951968, -624423449664, -62753812992, -116830009296, 75527350096, -838879769754, -264933552128, 778810325968, -100049197248, 89311346208, -217540588160, 473484950334, -183291286464, 392285117224, -97377583104, 367194155724, -402797421840, -46815595974, -36014239936, 35492011020, -9523679328, 919593175752, 50415537152, 271156210416, -28348757920, 529299682704, -79385695488, -401774516292, -420876572480, -45763447392, -328815222784, -137200430808, -381950652960, -865458640592, 504664962816, 727004182680, -76262282208, -110328711614, -23300379648, -928456859446, 1542087993120, -72365993109, -331699175936, 330433792810, 98696001744, 102036503331, -41485336576, 128162522970, -96540219776, -526349640324, 317990880000, 995007625660, -183090935888, -621788306958, -180278111232, 112739059056, 62559817344, 662505398124, 419787024384, -16406426421, 487932636672, 510692368704, -24860860416, -553747064780, 891452739712, -88636850100, 103591356288, -414316727346, -143256543408, 1568416928904, -96206128128, -719643231216, 564963059984, -58526996892, -87316517376, -1255539185098, -471131708416, 617928003342, -24427626496, 1618457192772, 3712549680, -314651261650, -168388124544, -123646873896, 753287469472, -918498216784, -207615412224, -119929231072, 290348924320, 794397028914, -276780403456, 219155384448, -106794989136, 398722180296, 69987893248, 280616394060, -117149654736, 699191176340, -51040184832, -1399010340420, 1024126267040, 177103789254, -260452765696, 96241777632, -338332422528, -854849147568, -277966868992, -599129769312, -267202257504, 230090193664, -17414258688, -895583452414, -245071702416, -277126081596, 59174598912, 26447259902, -367863275088, -353349969232, 316991364096, -140791791141, -341372381232, 429590899208, 51038926848, -330111251652, -698869391936, -45497391984, -48271081472, 1155861830290, -149845471776, 111002016034, 293851352448, 1199242320264, -832769117280, 88299818152, 146881299456, -1117247740006, -53827066832, 275775166890, 262822536704, 1737186238382, 371400996096, 8132452120, 185671876608, 207529119252, 808179039840, -1001321476848, -43741959552, 370087829584, 589334508672, -970577557218, -69771534336, 57324142266, 355395100608, -230979595392, 255515975424, 384497395830, 1000206586176, 666199258956, -26790027264, 56364766064, 280087376048, 745995429450, -317315177088, -168020869562, 18525482136, -1275506946520, 274534455296, 627007925196, 80929078384, -197346153466, -350378618112, -222833400580, 1085350828672, 92167160904, 83394691072, 1844658919490, 296580891744, 126209319284, 137900532224, -791972785800, -18863581528, -1692959745528, -199701863424, 1773506963592, 111802309632, -333760957488, 450094334976, -1183124695652, -389575236960, 1609056372736, -226018689024, -19098395217, 124539754752, 675846438476, -152249269248, -1196398816586, 975199618944, -370252855872, 300835598336, 383122328960, -393736224240, -127127210220, 4268570240, -50767418520, -149270236928, 672429890496, 19421724672, 27571903042, -63387807392, 499633656912, 18358696064, 1371726642582, 564099739056, 28499529058, 373208620032, 328232938176, 516772447488, 527651553556, 56688299712, -501620596596, 80132960656, -89452968948, 518283456512, -811577584636, 203628241872, 1616618604900, 47113993600, 40580627724, 385812394240, -410206132360, -98055042048, -824571571798, -276844648704, -327882237228, -307565740160, 632053471368, 363460550976, -167865399984, -87894130688, 374984331444, -424541333648, 407387465394, -476717882112, -478139855094, -448702924032, 144528529230, 58682916864, 1508682993946, 185513092128, -42542388060, 15235208448, -130462088832, 65878558912, -720319123160, 103064223744, 251826555344, -1530670274488, 91459808748, 144972615424, -1223350937922, -676203788304, -2531781555000, -20661046784, 6648494580, 422814715600, -2286620441928, 143236674432, -1326080998466, 238610307936, -208962870228, 42543874048, 1147269038082, -62659019664, 886842644688, 197937336576, -527017601880, -322797393296, 853355280960, 125335461888, 384743624980, -523631609456, 90253083924, 139797441792, 79033313632, -366205574448, -108598431056, 230994796544, 695197133136, -945670902176, -173686327816, 21300003648, 275988817728, 258881597376, 650085616026, -413982828544, -145106922902, -180308477952, 755432380738, 19021230592, 174397206168, 1652993542464, 88252082776, 124901720064, 418633532772, 170497605824, 1071892246410, 668074247424, 594519027766, 91401343488, 1365445908488, 340663231488, -109640867868, -383747616384, 406372027152, 408502915200, 703070171366, -1022136088640, 377219842776, -63223164928, -57381804462, -242912310048, -81994650428, 856899794304, -96394390092, -19970238080, 282205797118, 138648941568, -1124176999033, -255973434080, -82121933214, 1181911782912, -1977964914420, -239185995552, 686382261656, 22330474496, -71783059734, 116542028272, -389233030412, -124948002816, -406362011328, 300066151616, 205360011990, 34130795520, 319196683102, 468176362128, -265421990570, -161189365120, -952661955024, 177030526400, 2330281124120, -76824723456, 1439189048210, -1169440346016, 33175735866, 770996897664, 1067263080862, 46658300832, -813247909872, 174393483264, -601511913972, -132871839408, -1246347138156, 59067988992, -704125686628, 820486586752, 348264976572, 324725309440, 244262503254, -335502975456, 784016319276, -274544345088, 256685045094, 224789305952, 483229307288, 69882172416, 867461574106, -169041050352, 1333357528050, 213296987904, -222578288386, 35397592272, 309075596662, 42316513280, 223027826112, 185402678320, 19908502560, -480474657792, -2151098144288, -353721697056, 136980991026, 204800643072, 1864858784686, -814808999808, -1116323356512, -89986397184, -115263684018, 964931190912, -860370862960, 34780741632, -523944141968, -240258788704, 542628114309, -194501217792, -1183962805844, 1589987405664, 1152102984088, -152311048704, 295608663108, 281197322224, 81726995532, 256208980608, -538739169672, -1127430623168, 143503414236, 273301921792, -87416488750, -99650730816, 1212179077728, -406590155136, 12409297416, -1193663552544, 2317100741064, 24490059264, -158874419704, -1153213095088, 370839973032, 141528310272, -771576762810, -550793748960, -1325546929872, -154631995392, -68000307732, 273695625216, 54455517116, 24794911296, -1775811009162, -1037838892064, -15123250044, 87363913728, 1795339148928, -951153713856, 677375229216, 153079007744, -451341219582, -126061544224, -403716576304, -5541765120, -1036613858940, -767939929120, -669088731078, -402098499712, -606523490580, 68729723424, 1060753234632, 179019726848, 356129560710, 780695178528, -563664123492, -37000139904, 831152663932, 129661077248, -209133725202, -104471724032, -540948006144, -564909081120, 156725595362, -275008366336, -1349335015704, 250086037344, 3795535082232, -264364839936, -1840933906390, 504957740000, -578070842076, -1307109931264, 1794377093838, 449414440992, 57945859642, 398855847936, 99342672912, 151770195760, 180296327388, -820577309184, 1677247540332, -194545305568, -218287933344, -39478125568, 2263752434090, 38144394288, -747162519140, -669265035776, -56061408528, 1149101503104, -227486085134, -76186386432, -1140422550252, -1091105465104, -390889878732, 786392239360, -352689764240, -138655395648, -2770846247464, -165693971456, 305329896144, -1872775979376, -1250843427504, -118739706624, 5895391390, -997896576768, 519964934958, 80348274688, -664044122844, 465569150112, 1515071965680, -329685585152, 284341129758, 586513582560, 1377259792056, -309781075968]