# Trace form for 462.8.a.l, downloaded from the LMFDB on 19 May 2024. [0, 5, -40, 135, 320, 238, -1080, -1715, -2560, 3645, -1904, 6655, 8640, 3856, 13720, 6426, 20480, 13858, -29160, 21774, 15232, -46305, -53240, 91970, -69120, 194809, -30848, 98415, -109760, -247096, -51408, -276472, -163840, 179685, -110864, -81634, 233280, -209584, -174192, 104112, -121856, -329284, 370440, -789694, 425920, 173502, -735760, 422806, 552960, 588245, -1558472, 374166, 246784, 1369080, -787320, 316778, 878080, 587898, 1976768, 4381164, 411264, -100702, 2211776, -1250235, 1310720, 7610078, -1437480, 7576344, 886912, 2483190, 653072, 1983224, -1866240, 6438410, 1676672, 5259843, 1393536, -2282665, -832896, 8444820, 974848, 2657205, 2634272, -1219560, -2963520, -12910306, 6317552, -6671592, -3407360, 8280990, -1388016, -1322608, 5886080, -7464744, -3382448, 7189536, -4423680, 8221796, -4705960, 4851495, 12467776, -27385980, -2993328, 5101842, -1974272, -2204118, -10952640, -23631356, 6298560, 17038772, -2534224, -5658768, -7024640, 937738, -4703184, 599710, -15814144, 2811024, -35049312, -4753294, -3290112, 8857805, 805616, -8890668, -17694208, -47779158, 10001880, -61731266, -10485760, -21321738, -60880624, 11237502, 11499840, -7468482, -60610752, 4684554, -7095296, -28709424, -19865520, -1527554, -5224576, 11415762, -15865792, 5132336, 14929920, 78826846, -51507280, 15882615, -13413376, 5556052, -42078744, 56306778, -11148288, 10102482, 18261320, 51161926, 6663168, 135459260, -67558560, 36965160, -7798784, -31545710, -21257640, 164294120, -21074176, 8553006, 9756480, -93905806, 23708160, 213839589, 103282448, 15873246, -50540416, -51721822, 53372736, -66819487, 27258880, 118291428, -66247920, 52192124, 11104128, 125683870, 10580864, -2718954, -47088640, 94107574, 59717952, 18444998, 27059584, -33756345, -57516288, 209496850, 35389440, 231152404, -65774368, 205472106, 37647680, 89702934, -38811960, 86222756, -99742208, 204561288, 219087840, 84753928, 23946624, 776039716, -40814736, 67046130, 15794176, 28981194, 17632944, 123563180, 87621120, 53547048, 189050848, 472620562, -50388480, 94829896, -136310176, 173837070, 20273792, 90382010, 45270144, 491824514, 56197120, 142015761, -7501904, -189925558, 37625472, 481959190, -4797680, -61631955, 126513152, 543595890, -22488192, 112088960, 280394496, 228010140, 38026352, 160415948, 26320896, 395961906, -70862440, 71744535, -6444928, 28000462, 71125344, 1102374180, 141553664, -32928120, 382233264, 4134516, -80015040, 122412070, 493850128, -348578262, 83886080, 209333388, 170573904, 71887312, 487044992, -180132984, -89900016, -24267252, -91998720, 1572382302, 59747856, 223586730, 484886016, 226098900, -37476432, 864251924, 56762368, -35710416, 229675392, 259290779, 158924160, 688049406, 12220432, -201548088, 41796608, 826803892, -91326096, 1393822410, 126926336, 194117472, -41058688, 112944412, -119439360, 1615839247, -630614768, 221988492, 412058240, -379151754, -127060920, 1863791364, 107307008, 130990365, -44448416, 317454034, 336629952, 270865042, -450454224, -739421460, 89186304, 451531780, -80819856, 178266202, -146090560, 137749734, -409295408, 339765202, -53305344, 2575904108, -1083674080, -59511186, 540468480, -55066404, -295721280, -328884776, 62390272, -638046612, 252365680, 1388662758, 170061120, 377276234, -1314352960, 460046844, 168593408, -145022458, -68424048, 1802162024, -78051840, -152786736, 751246448, 1230107892, -189665280, 2372539008, -1710716712, 25318926, -826259584, -367984232, -126985968, -201768035, 404323328, 16192170, 413774576, -1899932936, -426981888, 178577572, 534555896, 75897648, -218071040, 1659344628, -946331424, 593471620, 529983360, -128338938, -417536992, -816669932, -88833024, -1669918361, -1005470960, 239160735, -84646912, -1376307110, 21751632, 356102618, 376709120, -240048036, -752860592, -469594440, -477743616, -1699529288, -147559984, -1290037266, -216476672, 1174589038, 270050760, 2424793952, 460130304, -1666744182, -1675974800, -822892766, -283115520, -108654854, -1849219232, -575686926, 526194944, -471070950, -1643776848, -3301159544, -301181440, 303412554, -717623472, -1760444580, 310495680, 1769739582, -689782048, -201649014, 797937664, -3084071280, -1636490304, -2039064674, -1752702720, 126482958, -678031424, -278956304, -191572992, -1281840676, -6208317728, -775154448, 326517888, -1502739252, -536369040, 2056925442, -126353408, -41243958, -231849552, 2902809068, -141063552, 653647448, -988505440, 308225574, -700968960, -5954947408, -428376384, 34540786, -1512406784, 138573072, -3780964496, -6973695964, 403107840, 1363487074, -758639168, 2128324842, 1090481408, -356293254, -1390696560, -1151676988, -162190336, 428830605, -723056080, -237949680, -362161152, -2781319920, -3934596112, 150013404, -449576960, 1132822386, -1136126088, -438277004, 60015232, 1520283006, 1519404464, -2610256754, -301003776, -928785128, -3855673520, 272767014, 38381440, -4271255550, 493055640, 3828771548, -1012105216, 1381372002, -4348767120, -385486020, 179905536, -2598685992, -896711680, 3657400020, -2243155968, -1051082714, -1824081120, 951876858, -304210816, 998059320, -1283327584, -10184358506, -210567168, -4012117274, -3167695248, -851734170, 566899520, -7516025678, -573956280, -3442534292, 51559424, 4435941240, -224003696, 1869022008, -569002752, 6341129110, -8818993440, 230931162, -1132429312, -680245832, 263424960, 2135994040, -3057866112, -2535456762, -33076128, 7699514490, 640120320, 2537044830, -979296560, 5773668903, -3950801024, -9441959876, 2788626096, -2208374630, -671088640, 428577642, -1674667104, -12418104864, -1364591232, 562754786, -575098496, -1396489194, -3896359936, -7654041208, 1441063872, -2314892882, 719200128, -1804126149, 194138016, -1528199108, 735989760, -6939318599, -12579058416, 3193868556, -477982848, 10109344372, -1788693840, 9908509556, -3879088128, 1409187348, -1808791200, 782954095, 299811456, 5518544134, -6914015392, 3393464490, -454098944, -15151617434, 285683328, 7759861224, -1837403136, -73411758, -2074326232, 2044867896, -1271393280, -2896573260, -5504395248, 2540904498, -97763456, 986319388, 1612384704, 24968139238, -334372864, 498014946, -6614431136, 8949058072, 730608768, 5708003768, -11150579280, -911421315, -1015410688, -189383694, -1552939776, -2988599068, 328469504, 5656414950, -903555296, 3879576520, 955514880, 14169135928, -12926713976, 6241114908, 5044918144, 418309080, -1775907936, 1822245480, -3296465920, 5547746862, 3033214032, 13417910412, 1016487360, -7801704174, -14910330912, 2421979218, -858456064, -10565920608, -1047922920, 4428234958, 355587328, 2328014412, -2539632272, -6482187624, -2693039616, -85301942, -2166920336, 5523154776, 3603633792, 421631518, 5915371680, 19963560580, -713490432, 2288356056, -3612254240, -22796994748, 646558848, 3677567648, -1426129616, 20953072332, 1168724480, -1410981858, -1101997872, 17975355982, 3274363264, 1810245510, -2718121616, -2840379570, 426442752, 13042329241, -20607232864, 782492238, 8669392640, 3955645066, 476089488, -964777920, -4323747840, 3336205860, 440531232, 10243515794, 2365770240, 453654544, 2631078208, 1445770296, -499122176, -12034951704, 5104372896, -8987274058, -2018925440, 12760755174, -11109302064, -3868488258, -1360488960, 5831329284, -3018209872, 2560407192, 10514823680, -20533204054, -3680374752, -22396662888, -1348747264, 4693600890, 1160179664, 9128116268, 547392384, 15084199954, -14417296192, 2440314270, 624414720, -2466010848, 1222293888, -7779190042, -6009971584, 13279261878, -9840863136, -134034362, 1517322240, 7812961448, -18980312064, 3834425547, 13685733696, -28876256906, -202551408, -2820076028, 6610076672, -5127990066, 2943873856, -3557600370, 1015887744, 44337301650, 1614144280, 13012898130, -3234586624, -4126119186, -129537360, 16887177876, -3310196608, -1664062785, 15199463488, 11214230156, 3415855104, -30856810424, -1428620576, 14677089030, -4276447168, -707338962, -607181184, -6297403044, 1744568320, 3026401920, -13274757024, 9393391140, 7570651392, -47912561796, -4747772960, 6156273780, -4239866880, 6931120112, 1026711504, 10129013818, 3340295936, 4331230596, 6533359456, -3598587166, 710664192, -1749931806, 13359346888, 10690971462, 8043767680, -60846999902, -1913285880, 3052743568, 677175296, 1937102445, 11010456880, -18475878752, -174013056, 153863722, -2848820944, 756012474, -3013672960, 10084113864, 1920384288, 4009887642, 6022884736, 29764102860, 3756755520, -18718806540, 3821948928, -11020625938, 13596234304, -889059240, 1180479872, 8105555108, 10320298128, -21916935388, 1731813376, 111631932, -9396712304, -8899613058, -2160406080, 17286523312, -19398351616, 3305125890, -3681042432, 6895811220, 13333953456, -5844298796, 13407798400, -9411613074, 6583142128, 15151011900, 2264924160, 1454813846, 869238832, 5652001476, 14793753856, 29539251294, 4605495408, -73455218822, -4209559552, 1940957424, 3768567600, 9721212972, 13150214784, 2639671144, 26409276352, -4863590568, 2409451520, 18572170444, -2427300432, 26958567022, 5740987776, -655215804, 14083556640, -321644134, -2483965440, -19916466344, -14157916656, 42454322154, 5518256384, -51355543982, 1613192112, 2855298878, -6383501312, 6036841710, 24672570240, 8569523710, 13091922432, -205700530, 16312517392, 6104670300, 14021621760, -54816257712, -1011863664, -6989554538, 5424251392, 23334801948, 2231650432, 8677328884, 1532583936, 39406322646, 10254725408, -964181232, 49666541824, -17881064532, 6201235584, -19226158604, -2612143104, 7000851033, 12021914016, 34840867204, 4290952320, 49087125620, -16455403536, 18577333962, 1010827264, 1630379842, 329951664, -67160098718, 1854796416, -5441798376, -23222472544, -9908785758, 1128508416, -14749597763, -5229179584, 22323705084, 7908043520, 44043816432, -2465804592, -3038227115, 5607751680, 37633205070, 47639579264, -49611748030, 3427011072, 10078910326, -276326288, 5241171744, 12099254272, 31473164272, -1108584576, 10432221992, 30247715968, 3049499124, 55789567712, -92023186030, -3224862720, 319702564, -10907896592, 43627659669, 6069113344, 11240055420, -17026598736, 18688299396, -8723851264, 5993689284, 2850346032, 16388251194, 11125572480, -45603807226, 9213415904, -10237097358, 1297522688, -24351609936, -3430644840, -23675547172, 5784448640, 50322366828, 1903597440, -65621844226, 2897289216, 21173824238, 22250559360, 3536739855, 31476768896, -54066466410, -1200107232, -30340069736, 3596615680, 8571258918, -9062579088, 68914211210, 9089008704, -46908313008, 3506216032, 7313356134, -480121856, 55536283766, -12162264048, -66021149852, -12155235712, -19964379420, 20882054032, 4358908392, 2408030208, -1623234360, 7430281024, 12191358060, 30845388160, -3854463186, -2182136112, -7614506202, -307051520, 4813187454, 34170044400, -71409025676, -3944445120, 33273332482, -30630172384, 3719242818, 8096841728, -30014736072, -11050976016, 2561689326, 34790136960, 9173660454, 3083888160, -17183617286, -1439244288, 37471851048, 20789487936, 69549410916, 7173693440, 39530477330, -29259200160, -53117205928, 17945247744, -1606802022, 8408661712, 95106679516, 14592648960, -35476465994, -7615014864, -1486792908, 2433686528, 42779055292, -7984474560, 112643941190, 10266620672, -8879888952, 81474868048, 9847332432, 1684537344, -14141369595, 32096938192, -17227258524, 25341561984, -32807004286, 6813873360, 17224522816, -4535196160, 37493894466, 60128205424, -70681954376, 4591650240, 523951022, 27540274336, 10186458318, -412475392, 64198707316, -35487529920, 11021997690, 1792029568, 12421264788, -14952176064, 39440297538, 4552022016, 49136160024, -50729032880, -3915606366, 70551947520, 42920285468, -1847449296, 28896653720, 9059434496, 48658374648, 5441966656, -6042364778, -2107399680, 56737569174, -17087952320, -4125241872, 24462928896, -1760391248, 20283654096, -49541692458, 264609024, 33212913084, -61596115920, -36879409074, -5120962560, 114514616426, -20296358640, 64058553216, 7834372480, -69130858226, -46189351224, -27037608178, 31606408192, 683611002, 75535679008, -34519377000, -22309008768, 49085803384, 17666997040, -9935574264, 5368709120, 118684153048, -3428621136, 27111190932, 13397336832, -5447736945, 99344838912, -113635806616, 10916729856, -168661176904, -4502038288, 437188590, 4600787968, 92026256884, 11171913552, 13579201126, 31170879488, -51298189272, 61232329664, -1905725836, -11528510976, 9569272416, 18519143056, 4821594444, -5753601024, -37501472554, 14433009192, -32446816574, -1553104128, 2049236496, 12225592864, -93361028624, -5887918080, -19313224854, 55514548792, 44802304956, 100632467328, -92421547790, -25550948448, -106287363840, 3823862784, 16023733740, -80874754976, 10943210476, 14309550720, -159609228580, -79268076448, -3465151326, 31032705024, -14356424794, -11273498784, -75573525164, 14470329600, -22050088164, -6263632760, 127342187706, -2398491648, 17631501586, -44148353072, -45087795747, 55312123136, -17548540618, -27147715920, -50374383072, 3632791552, 6457339845, 121212939472, -131133181004, -2285466624, 46098746750, -62078889792, -37160291970, 14699225088, -141171476584, 587294064, -46462526180, 16594609856, 9614770686, -16358943168, -66001602052, 10171146240, -266004136826, 23172586080, -6481296972, 44035161984, 45042321510, -20327235984, -36450739380, 782107648, -12679049880, -7890555104, -57675943316, -12899077632, 14573617514, -199745113904, -45887290776, 2674982912, 3889579446, -3984119568, 125185956642, 52915449088, -34831006182, -71592464576, 10820178530, -5844870144, -54140763512, -45664030144, 31713904026, 89204634240, 6790551702, 7291370520, 56705559220, 8123285504, 65469436704, 1515069552, -254996318490, 12423518208, -56352883160, 23908792544, -45002092914, -2627756032, 192124766702, -45251319600, -78549915778, 7228442368, -22218104682, -31036612160, -91779687394, -7644119040, -90814086202, -113353087424, -2933681058, 103413711808, 183394577004, -49928919264, -36545727900, -40359345152, -15543547002, -3346472640, -87144537052, 14207263488, -109648810668, -14577963840, -12718915650, 26371727360, 32209691458, -44381974896, -202477521128, -24265712256, -89131307688, -107343283296, -215178178270, -8131898880, -31453334836, 62413633392, 8192138958, 119282647296, -133854495154, -19375833744, -73346979027, 6867648512, -47532003660, 84527364864, 75693969548, 8383383360, -19867458244, -35425879664, 47782968714, -2844698624, -61533253764, -18624115296, -351146909708, 20317058176, -5444523378, 51857500992, 22678605532, 21544316928, 17718972508, 682415536, -83269924560, 17335362688, 34010931642, -44185238208, -78289844384, -28829070336, -55054746198, -3373052144, 17740584946, -47322973440, 17510631406, -159708484640, 3415039866, 5707923456, -123512903538, -18306848448, 8361053220, 28898033920, -7531820208, 182375957984, -123801722358, -5172470784, 22919084041, -29420541184, -34609698252, 11409036928, -47639539402, -167624578656, -219468449716, -9349795840, -20929170096, 11287854864, 92810161296, 8815982976, -180262527730, -143802847856, -40573959804, -26194906112, 200661656974, -14481964080, 1248129278, 21744972928, 55536986934, 22723036560, 150478182722, -3411542016, 81815656078, -104338633928, -1113586866, 164857862912, -17901898532, -6259937904, -115323152244, -69355141120, 78375844836, -31645160528, -214207950660, -3808715904, 11587046218, 7718223360, 17648481096, 34589982720, 798214010, -26689646880, -43109567410, -3524249856, 8322090498, -81948126352, -171130442200, -18926161920, -44225915538, -3629236352, -160783580016, -21048625664, 308551065420, -11566162368, -62266150298, 3992977408, 932601222, 96279613632, -252533639448, -40834983168, 206116144914, 71898192464, 3741472944, 16151403520, 221803939050, -102086041392, 1241163526, 88874416512, -188289791028, 30947906064, -32278897882, 10883911680, 93100626070, -46650634272, 36814150998, 24145678976, 40980969806, -20483257536, -365287852388, -84118589440, 57464770734, 164265632432, -59250744812, 29442998016, -6326634314, 179173303104, -9619917858, 10789978112, -99628955274, -37548807120, 143661410724, -9281437312, -31095278676, -73024930144, 50913029340, -4379139072, -173758821286, -120673599632, 11578426335, 115338369536, -115523792214, -19522514160, -70399241192, -4995317760, -6424641360, 19728086784, 11789738455, -9778351104, 111429932288, 62233520336, -75095637840, 48079772672, -71857419550, -106234095024, -376813870692, 78726905088, 4050361908, 1072274896, -316470363672, -12138577920, 368384560572, -62503691584, 30586204422, 151842496512, -152599054284, -30675404376, -79285274572, -109485869568, -11833479108, 231010055248, 173358504064, 1620411264, 140287273386, 22560608224, 41047641162, -52880613376, 49043543802, 41023920528, 149597573032, -23550990848, -70476932358, 28460802960, 279083893050, -8127101952, -109559599443, -354698413200, -25077198456, -12913154240, 289551162100, -104103185040, -63594059298, 25876692992, 7364709378, 33008953488, -30768106362, 1036298880, 283501764780, -135097423008, -115323899850, 26481572864, 230174952828, 13312502280, 35175746184, -121595707904, 103376831796, -89713841248, -361313965156, -27326840832, -29574405308, 246854483392, 37297044054, 11428964608, -82164315046, -117416712240, -258151366540, 34211577344, -10408122540, 5658711696, -31017329212, 4857449472, -81712777438, 50379224352, -70164521784, -13956546560, 406188750936, -24211215360, 270199544580, 106198056192, 98749800540, -75147129120, -250882930344, -60565211136, -92843903330, 383300494368, -28379233278, 37982183680, -29070597304, -49250190240, -374917105000, 33918935040, 25700675166, -55448960896, -344989788726, -8213692032, 431923106798, -81032110544, 26947601640, -26722367488, 50981914028, -34649844768, -266181622588, -52266875648, -274977679662, 28788697328, 292898143524, -5685313536, 14957115162, 13999454448, -108327166398, -106874775104, 535258865078, -85527771696, -275062919860, -64350141440, -22996822590, 486775999216, 434183782168, 15306287040, -135723688046, -24421948544, -202932693306, -5417402368, 390248995930, -15496819560, -331154682746, -88083655040, -92948425884, 147807030016, -9940549542, 1392104448, -143910008208, -1230909776, 119770413480, 22790567552, 320023134620, -6048099792, 64135822988, 24109383680, 50463594216, -80672910912, -74548183128, -15363074304, -42382170740, -32079101136, 171210485970, -48183077888, -91098146640, -238112822880, -106093036950, -30054044160, 6235141374, 149750452320, 339869498676, -30575591424, -279989711412, 88165007504, -18366637464, -108769874432, 269695673832, 7112473920, 275506757150, -9443838976, 57671839080, -64844440864, 594617937018, -82562385024, -20337956724, 175335483104, -68457332574, -13854507008, -162108852766, -893055456, -38212243344, 75173698432, 207886891230, 71196904464, 104683520626, 17283248640, 459781195596, -138292186496, 68500210410, 155186812928, 579838819172, -26441007120, -32526654328, 29448339456, 155889060381, -55166489760, 69212137494, -106671627648, -751195298510, 46754390368, -254932916652, -107262387200, -2033174374, 75292904592, -235730279938, -52665137024, -59626115010, -121208095200, 383149136912, -18119393280, 180277652226, -11638510768, 11571596334, -6953910656, 639199321050, -45216011808, -131162311356, -118350030848, -335288831328, -236314010352, -31001029430, -36843963264, 259855666642, 587641750576, 15194379222, 33676476416, 195815749212, -15527659392, 134325946256, -30148540800, -37705208238, -77769703776, 117995175744, -105201718272, -168695808302, -21117369152, -206659112616, -211274210816, 916981241350, 38908724544, -238887769690, -19275612160, -62502107814, -148577363552, 235408067780, 19418403456, 6831139216, -215668536176, -48711406023, -45927902208, 267102259206, 5241726432, -290164962420, -112668453120, -41261375916, 2573153072, 406563834720, 19871723520, 307755640338, 159331730752, -187361602173, 113263333248, 65144466394, -339634577232, -393440896906, -44146051072, 86234451012, 410844351856, 104918532026, -12905536896, 418498262394, -22842391024, 272952298044, 51068010496, 185393702902, -48294733680, -165312002170, -197380561920, 267529758012, -68556189680, 150548559680, -104735379456, 135727744814, 1645604240, 38048058396, -130500139136, -199984652714, -48837362400, -355490783502, -112172974080, 21139760565, 438530061696, 950895917472, 8094909312, -126810867212, 55916436304, 149000691618, -43394011136, 1289083253682, -186678415584, 64709108366, -17853203456, 91623541230, -69418631072, -186453390270, -12260671488, -260214097768, -315250581168, -409093670718, -82037803264, 880757098162, 7713449856, 7395105212, -397332334592, 209516253048, 143048516256, 292602765972, -49609884672, -38446513280, 153809268832, -1982117466, 20897144832, 707700955048, -56006808264, -380404815394, -96175312128, 55211433192, -278726937632, 82599195244, -34327618560, 7755687382, -392697004960, -78207478020, 131643228288, 74944321518, -148618671696, -219072090400, -8086618112, 68604421446, -13043038736, 754703881580, -2639613312, 72091019370, 537280789744, 26630623476, -14838371328, -55022670164, 43534387008, 330859152156, 185779780352, 674139759426, 79270286064, -335120322226, -9028067328, 1054501132219, 117996782104, 13446403542, 41833436672, 365522625978, -178589640672, -135814933758, -63264348160, 241624567944, -352350531456, 576018875520, 19726436736, 289597946128, 24305816920, 154116101736, -44862013440, 787302705312, -301065640560, -394510783830, -381116634112, -24608375505, 396893984240, 325797413580, -27416088576, 68096523506, -80631282608, -5113359738, 2210610304, 1352477137878, -41929373952, 123701468088, -96794034176, -80692174836, -251785314176, -9604158466, 8868676608, 678539841924, -83457775936, 152723203650, -241981727744, -47017771096, -24395992992, -526578009868, -446316541696, 104748566040, 736185488240, 180296275060, 25798901760, -378114343740, -2557620512, 382566670056, 87263172736, 801493224130, -349021277352, -805660914664, -48552906752, 168510102516, -89920443360, -56411831876, 136212789888, 965554763888, -149506395168, 11294345160, 69790810112, 92535731270, -47949514272, 448433972792, -22802768256, 49200627960, -131106009552, 1229963304300, -89004579840, -66009219348, 364830457808, 149789165274, -73707327232, -1418138988, 81896778864, -583562531714, -10380181504, 362283581124, 194812879488, 362012909528, 27445158720, -109346403606, 189404377376, -210646012698, -46275589120, 717278582936, -402578934624, -41987340010, -15228779520, 65393438886, 524974753808, 725646425380, -23178313728, 641726556158, -169390593904, -285279856416, -178004474880, 1184375091042, -28293918840, -416853739724, -251814151168, 119562343866, 432531731280, 190145465772, 9600857856, -371239181954, 242720557888, 62856389124, -28772925440, 218675473720, -68570071344, -198581182948, 72500632704, -175019065848, -551313689680, -71801352084, -72712069632, -255610495612, 375266504064, -2303152434, -28049728256, -64573273900, -58506849072, 1153456314608, 3840974848, 149125178952, -444290270128, -341101598880, 97298112384, -24657348016, 528169198816, 11384050986, 97241885696, 1030076853744, 159715035360, -407907006886, -167056432256, 539016135660, -34871267136, -782281206942, -19264241664, 694243992340, 12985874880, 61785613512, -59442248192, 265489105686, -97530864480, -214055080952, -246763105280, -615518858196, 30835705488, 1604342924092, 17457088896, -124988627786, 60916049616, 99294326496, 2456412160, 8323667436, -38505499632, 382974477426, -273360355200, 565732952964, 571272205408, -11825110746, 31555560960, 372222213933, -266186659856, -38096510166, 245041379072, 61985900068, -29753942544, -539327129586, -64774733824, 485334611514, 240117888576, 284620492959, 88407808128, -513783015916, -20493514608, 48876628770, -278321095680, 283383497246, -73389283632, 253967261162, -24671105280, -76690248390, 137468938288, -645956650122, 11513954304, 196465232936, -299774808384, 352142889507, -166315903488, -51070630006, -556395287328, -1153653517920, -57389547520, 21127290426, -316243818640, -77551922700, 234073601280, -1814621424154, 424937647424, 106802416782, -143561981952, -575530161102, 12854416176, 956656693760, -67269293696, -26049003840, -760853436128, -632331635444, -116741191680, -296438409932, 283811727952, 90077558220, 60920118912, 429910912476, 11894343264, -68841745082, -19469492224, 276574926438, -342232442336, -245491756028, 63875796480, 320999513712, -901151529520, 12248672688, -82132965376, -514399027488, 71039111616, -1528627743136, -651798944384, 39035797992, -78778659456, -164965338750, -13476298752, -1765480690516, 113130956760, -324943696008, -256775505536, -88936737197, 137818068192, -750425081684, -202732495872, -242656399566, 262456034288, -731333447948, -54510986880, 443118354182, -137796182528, 344540389698, 36281569280, -1398969158986, -299951155728, -236000946258, -481025643392, -104449182966, 565455635008, -522767187168, -36733201920, -1136561675088, -4191608176, 157445890668, -220322194688, -342952721540, -81491666544, -136529733030, 3299803136, 69130994184, -513589658528, -1458576719320, 283900239360, -250317025872, -88175981520, -554396509458, -14336236544, 434106487854, -99370118304, -380280662094, 119617408512, -604709897976, -315522380304, -283593734956, -36416176128, 69467717044, -393089280192, 126727224030, 405832263040, -1253620624204, 31324850928, 703026786000, -564415580160, 246459139236, -343362283744, -907072609604, 14779594368, -478081086630, -231173229760, 407273398758, -72475475968, 204030414618, -389266997184, -964015245642, -43535733248, 65888485290, 48338918224, 167285230970, 16859197440, 209836488130, -453900553392, -66582292896, 136703618560, -184448447776, 33001934976, 90072324766, -195703431168, -210038131134, 14083129984, -649145998722, -162269232768, 447387266874, 396333539664, 358540070706, -2116872192, -38739933316, -265703304672, 411250968904, 492768927360, -3618927774, 295035272592, -2224083935074, 40967700480, -89268928844, -916116931408, 210949959096, 162370869120, -747988227266, -512468425728, -554232861721, -62674979840, 103529489769, 553046865808, 1033322146298, 369514809792, -1096072780414, 216300865424, -779658936462, -252851265536, -1113621579726, -5468888016, 125257180994, -604285432064, -76142052756, 276155016000, -899105632206, 178472070144, 121649740876, -392686427072, -138455731782, -141335976320, 186453271348, 79484594112, 65127817284, -42949672960, -96055209990, -949473224384, 130049051622, 27428969088, -1039344613128, -216889527456, 1197107144550, -107178694656, 24550292338, 43581895560, -747451722100, -794758711296, 351348249510, 909086452928, -1182664593000, -87333838848, -639280437852, 1349289415232, -111405218022, 36016306304, -298702401146, -3497508720, -83906878134, -36806303744, 455953802652, -736210055072, -2377494785394, -89375308416, 416556538014, -108633609008, -44929695195, -249367035904, -1617455798744, 410385514176, -1733211797724, -489858637312, 302784214212, 15245806688, -454609707024, 92228087808, -661900703016, -76554179328, -833133881448, -148153144448, -108886733662, -38572755552, -964086395216, 46028808192, 396281403810, 300011780432, -213561256588, -115464073536, 278840307350, 259574532592, -19098151974, 12424833024, -580170070406, -16393891968, -92906709406, -97804742912, -170029882188, 746888228992, -10143794976, 47103344640, -444585057144, 154505798832, 81712851840, -444116390336, -763486084618, -358418439648, -46156490060, -805059738624, 253621560780, 739372382320, 307663849724, 204407587584, -475248185334, 850298910720, -1293639168492, -30590902272, -710506694394, -128189869920, 90191084830, 646998039808, 166219392060, -87545683808, -154875400540, -114476405760, 726816716848, 1276873828640, 187140243024, 634144611584, -697260067234, 27721210608, 588315198224, -248261640192, 273483373086, 114851398352, 158727667920, 90187990272, -61145307286, 604588201312, 116943226092, -115762636800, -415606528752, 176400705312, -129054211628, 50109062080, -97161853482, -1018737501648, -28842607204, 19187933184, 762151299918, -141052012688, -47248158762, 353186824576, 436071358940, 360702365976, 119394605154, -442496985088, 288656229474, 140388324944, -1598740953194, 217181727360, 1830998609784, 402995064576, -1642868997354, -29062332416, -116539464286, -51658718760, -618913090292, -969703515776, 82424076336, 1049065448032, -290945954892, 18283732992, 24009717510, -368789974000, 52301766015, 496631118336, 114762488236, 297282335760, -883535109044, -117593800704, -498848726304, 1129371812672, -415455126320, -4698352512, 1853426611682, 371700209440, 4154320494, -132756878848, -878201640952, -76918165488, 1578446557134, 130871545344, 20412336798, 528012816416, -446876641536, -81369169920, -306509134253, 2128033094608, 272271074328, -185380688640, -973352629692, 51850375776, -2244327597852, -352281295872, 108266966334, -360338572080, 18887776572, 162617887872, -111141279594, 291605915040, 803630777220, -6256861184, 265756044810, 101432399040, 842187762936, 63124440832, -505407776580, 461407546528, -845290907212, 103192621056, 112807478168, -116588940112, -297556900326, 1597960911232, -1101414799442, 367098326208, -576281006624, -21399863296, -24004599480, -31116635568, 1663052464768, 31872956544, 1772122330176, -1001487653136, 218849987916, -423323592704, -1007925108440, 278648049456, -3088425886, 572739716608, -591757255476, -86561428240, 1032908861996, 46758961152, -338668538248, 433126108096, 3014062164, 365312241152, -476311325994, -253711232208, -1596093034162, -713637073920, -240289552566, -54324413616, -912920388024, -58330964160, 1359843313472, -453644473760, 466736129424, -64986284032, -543498352146, -523755493632, -129405748262, -12120556416, 89238399030, 2039970547920, 111106686204, -99388145664, 184541382876, 450823065280, 186186902940, -191270340352, -2359234880746, 360016743312, 271520095368, 21022048256, -157796067492, -1536998133616, -1203530167476, 362010556800, 450146101162, 628399326224, -254113552998, -57827538944, 854724903960, 177744837456, 38573969214, 248292897280, 409077321300, 734237499152, 49742703094, 61152952320, 2867449744656, 726512689616, 39279973842, 906824699392, 1289311950604, 23469448464, 297142185908, -827309694464, 152604039852, -1467156616032, -3266264003996, 399431354112, -618141574232, 292365823200, 797559784938, 322874761216, 164462592580, 124348376016, -1316623490064, 26771781120, -1983290908194, 697156296416, -130382795648, -113658107904, -753707064852, 877190485344, 52405850448, 116623710720, 52384466676, 101751325200, 812476283160, -210973818880, 262472750244, -257677531664, -1090252572480, 355055799168, 424587578956, 1619820169024, 71271120888, 194125698048, -421927006956, 713050461504, -195732336208, 858746266368, -131316945336, 1721425426160, -970871450628, 65055191040, 1646269362986, 251626678688, 501448601988, -499309067136, 2027067738528, -65537111664, -813780879744, -954261178368, 727881309594, 1070835961232, 1007509055960, 155006669952, 629057968022, 586775832216, -17690826708, -54941188096, -2072509501236, 380256029280, 130892069670, -676218918912, -8684391618, -605551756384, 2121924255144, -67067066880, 626421554416, 158939665952, -537744591288, 283407037312, 1139011319666, -382263749712, -1555219966244, 22757588992, 1146266698158, 492266030112, 126218591576, 148992922368, 328682844636, 2809175277664, -1386599687514, -162536465408, 2908636632366, 43556187024, 610281775010, -414860007936, 77093069706, -181428844256, -3156663746662, -172354535424, 69206436005, -141751780064, 162994726170, -5459324288, 390596989214, 666159396480, 2599137063870, -138682901504, 231377140170, -272087453136, -1121874094906, 353481905664, -1224612676686, 626318755072, -5553914310, 230632562688, -364778082640, 440437969584, 1157576097012, 26984417152, 164826098100, -141924679568, 986798899998, 378583787520, 1632934441066, -140085051248, -1480038958224, 1277667877120, 651676997048, -27320318928, 120298455310, -45663387648, -188717972526, 988103228304, 1338456984680, 146454787584, 3472481750530, -66888425760, 630039652596, -231184271360, -1327253382064, 60254561664, -61252107196, -1459007663872, 234287879868, 990413778864, 106213421768, 41379766272, 218612766936, -183352672328, 1063970711442, 235364329472, 654618428134, 276877586016, -538020034116, -91272295424, -26032893264, 381116315216, -742373213904, 1340996629248, -628964368970, 1755747597728, -482788742364, 74798366720, 1204747990058, 167433360768, 3716976487924, -90302838912, -519106282308, -742481290368, -569155207404, -70527863808, 1928525415912, 1442100221840, 189022977891, 1150422782848, -515308965724, 324591678432, -2604435679620, 209559248896, 940703414508, -1605293255792, -2489793472486, 115855712640, -203560765660, -9985034224, 1325352391740, -173959783424, 1195515863028, -444295895472, 1889918872374, -181784292480, 501588016974, -1203825461776, -2253367910956, 27292336128, -252790917698, -654525248624, 44020255734, 834709071424, -1916801141032, 8908694928, -2293799379208, -1318862903296, -1813322665386, 143215188256, 2067111914432, 50079503232, -8576342758, 922585217952, -146928556152, 554841128960, 280117786676, -627006758688, 898536700314, 253161284224, -267537215466, 1713663605280, 641487681890, 30469727232, 727164965794, -92696369744, -398239139601, -61745786880, -4998984010770, -141187848768, 572781997823, -276719861760, 602740037268, -6385712080, -1853788275822, 213517175040, 4098897779702, 344876539280, 1189183043664, 28193998848, 899821841646, -66576723984, -797447926214, 655585010816, -82032132105, 1369043537600, -1054772233684, 151409295360, -2871137304580, 353807324304, 1016096536890, 29033890816, -802693267640, 1286268640128, 2846767096384, 168389005312, -1339517196810, -2468408523360, 472073338730, 92529298944, 663224980380, 498129202384, 272130578802, -31943819264, 2847955505268, -7460809776, 723526129590, -770236909056, 141511637088, 2020269115584, -4704338107980, 326679865344, -122143197974, -1648929159312, 849775435344, -575185539712, 2807324837808, -29931783552, 427523561118, -129211228160, 281669993784, -1774431512400, -2060255147448, 816688331136, -95288025372, -9929308208, 82336476348, -710995332096, 149190405760, 1506318328224, -1299600622442, -247583248512, -2484626022810, 258231183056, 599901874276, -87071293440, -1734768678902, -744805008560, 8631969228, 373205074176, 161070892920, -294513207984, 2206610383588, -193165431808, 1177946811063, -327847758448, 1984170545766, 163866060288, 3896439146062, 2922302819104, 303481496340, 672948715520, -5641743652196, -459718165872, 582938545784, -1314125059456, 504584083692, 474005958496, -3234410761444, -235543984128, 4712662355448, 50613074512, 161829610668, -1433386424832, -2452488972974, 76959342864, -198111778588, -86319824896, 442482782238, 797031642192, 3113145981332, 300390456960, 213513626788, -1149291285792, -1231302795102, 74251498496, -3010586023804, 248762229408, 649696059788, 584199441152, -276401628666, -407304234720, -402884040034, 35033112576, 2883973478040, 1390070570288, -657493468272, 965388797056, 1303558719554, -92627410680, 1117716936736, -922706956288, -639239773644, 924190337712, 527025296886, 156180113280, -831704325536, 563193929536, 1358703904356, 39962542080, -2508933289220, 51397130880, 440524042802, -157824694272, -1771789794102, -94317907640, -344053825270, 78226808832, 5299767632396, -891439458304, 571693254426, -497868162688, -2999414302904, 600765102720, 492075972112, -384638181376, 95491976085, 574859356400, -4302593584912, 849872760192, -2172855469812, 3014510965536, -1459794593070, -629815240704, 282252218738, -32402895264, 5536159279958, -8578199168, -819181882872, 2531762909376, 3136277731966, 97108623360, 1154455560740, -2947076484576, 231423990786, 500029532672, -2044002369796, -244689635376, 37268614922, -1214739972096, 1860683702670, 1220792434272, -2982037353886, 245403235008, 2337587494190, 634282196576, -1266524451216, 875886956544, 1450797160208, 94667832864, 2547970438, -1848080441984, 197460615618, -1386868032512, -3395761552404, -12963290112, -642493205628, -1122298187088, 1499479661682, -180484865792, 1467260033580, -328381129296, -2491645308740, 423044907008, -1782571046004, -392348350416, 161577335850, -328191364224, -49262535242, -1196780584256, -539038244340, 188407926784, -1107511613540, 563815458864, 1741935299872, -227686423680, 117690526584, -2232671144400, -3098194949136, 65016815616, 1132297723592, 876476795544, -43827327720, 2837587305600, -3852248039168, 200617587648, -1512030570920, 103305233920, 329166667620, -2316409296800, -1431578394540, 832825480320, 748085664480, 508752474384, -104070506022, -207013543936, -343235482800, -58917675024, -2284070254308, -264071627904, -205591667454, 246144850896, -1886406907368, -8290391040, 5503040796, -2268014118240, 129956061258, 1080779384064, 603832490940, 922591198800, 2023158528510, -211852582912, -1928043693252, -1841399622624, 3757005668422, -106500018240, 1879197146382, -281405969472, 898379977014, 972765663232, -637029374370, -827014654368, -607020676626, 717710729984, 100419556086, 2890511721248, 162930465170, 218614726656, -258810978094, 236595242464, -810397873944, -1974835867136, -1543134303216, -298376352432, -5280429101980, -91431716864, 69165611802, 657314520368, 561980833202, 939333697920, 2450793575504, 2065210932320, 247688832258, -273692618752, 252726007950, 83264980320, -2553164448932, -45269693568, -463957666722, 248138633696, 1057836449040, -38859595776, -94154126425, 653702219504, 1011739978296, -403033794816, -1743152860858, 561316174272, 2125006788758, 111652372480, 1877834094732, -3249510007488, -1480964325688, 193689722880, 699399183182, -2161596356640, 1067322887910, -849584449536, 4771534418774, -789998404320, 278622739428, 601177032960, -1434164560056, 2007063442752, -1693933294944, 484521689088, 4098291650148, 742751226640, -43383654594, -3066403954944, 4979488841334, 227033866224, -2302010995760, -303857469440, 2567880346932, 232564778432, -261879736920, 394001521920, 2009716378476, 2999336840000, -957864581838, -271351480320, 95682012272, -205605401328, 512858789306, 443591687168, -40143408516, 2759918309808, 1301017807852, 65709536256, 1992706733594, -3455384854384, 1155034492884, 648256884352, -654018399786, -215580813120, 439671351868, 213778939904, 3041386412130, -407855312224, 4097886163156, 277198758144, -1800917887794, 2129452980704, -239757001704, 418135005184, -5426377540128, 2199821437296, 1125208895970, -230309578624, 265877975664, -2343185148192, 99859684936, 45482508288, 2494488025998, -119656921296, -381816979065, -111995635584, 3016092678890, 866617331184, 1607864047228, 854998200832, -465135980148, -4282070920624, 515439563436, 684222173568, -32299712412, 2200503358880, -885789115722, 514801131520, 5861153293082, 183974580720, -2348047915400, -3894207993728, 465062116032, -3473470257344, -3914319530, -122450296320, -705525426606, 1085789504368, 1012335150582, 195375588352, -3459855116656, 1623461546448, 4845490115984, 43339218944, -1908412768152, -3121991967440, 2092840843962, 123974556480, 3104215476972, 2649237461968, 14146677594, 704669240320, -1227598051472, 743587407072, -5313779739756, -1182456240128, 275034374586, 79524396336, 2023717382078, -11136835584, 5508263228322, 1151280065664, 1733365097532, 9847278208, -995663510324, -958163307840, -455511149124, -182324540416, 297593937630, -2560185076960, 1509078830564, 48384798336, 2439596332552, -513086583904, 335374149276, -192875069440, -3476510163198, -403708753728, -224201074664, 645383287296, 1064888033526, 596385465024, 1729326335200, 122904594432, 883700480614, 339057365920, 1326676320648, 256632809088, -2122082054730, -1369683887760, 300937635900, 385464623104, -105721371882, 728785173120, 4798704395622, 1904902583040, -1164110642712, 848744295600, 1158847707636, 240432353280, 796224873888, -49881130992, 241762455040, -1198003618560, 780209650440, -2718955989408, 2042546960944, 244604731392, 6136683726482, 2239917691296, 1313776115496, -705320060032, 1150319310844, 146933099712, -168925618812, 870158995456, -163143849006, -2157565390656, -1278559369164, -56899791360, -11847489598, -2204054057200, 1531914367698, 75550711808, 865254203108, -461374712640, 3201265066620, 518755526912, -111381530544, -4756943496144, -4491957014944, 660499080192]