# Trace form for 546.8.a.i, downloaded from the LMFDB on 16 April 2024. [0, 5, -40, 135, 320, -340, -1080, 1715, -2560, 3645, 2720, -1303, 8640, 10985, -13720, -9180, 20480, -4247, -29160, -16984, -21760, 46305, 10424, -78072, -69120, -79555, -87880, 98415, 109760, -213142, 73440, -186027, -163840, -35181, 33976, -116620, 233280, 101025, 135872, 296595, 174080, -23976, -370440, -55528, -83392, -247860, 624576, -985981, 552960, 588245, 636440, -114669, 703040, -1891657, -787320, 1746955, -878080, -458568, 1705136, -2802208, -587520, 1140591, 1488216, 1250235, 1310720, -746980, 281448, 265168, -271808, -2107944, 932960, -4483276, -1866240, -2350578, -808200, -2147985, -1086976, -446929, -2372760, -4079889, -1392640, 2657205, 191808, -8731571, 2963520, -1715895, 444224, -5754834, 667136, -20077879, 1982880, 3767855, -4996608, -5022729, 7887848, -11580740, -4423680, 3780209, -4705960, -949887, -5091520, -13024644, 917352, -13266037, -5624320, -3148740, 15133256, -12682030, 6298560, 23208829, -13975640, 2727675, 7024640, -9506755, 3668544, -20664740, -13641088, 8008065, 22417664, -1456721, 4700160, 14917190, -9124728, -647352, -11905728, 4511550, -10001880, 21521014, -10485760, -1499256, 5975840, -3465729, -2251584, -5825512, -2121344, -6692220, 2174464, 59644667, 16863552, 37915854, -7463680, -26621487, 35866208, -2862691, 14929920, 37357380, 18804624, 15882615, 6465600, 29047308, 17183880, 62740347, 8695808, -3096063, 3575432, -48529065, 18982080, 113984817, 32639112, -51074739, 11141120, -26778696, -21257640, -23097674, -1534464, 47167785, 69852568, -93511436, -23708160, 24134045, 13727160, -12381336, -3553792, -88341648, 46038672, -27287365, -5337088, -75659616, 160623032, 109879117, -15863040, 45849562, -30142840, 30795957, 39972864, 92657185, 40181832, 54821045, -63102784, 33756345, 92645920, 6561007, 35389440, 91505128, -30241672, -20168460, 37647680, -154160592, 7599096, 9685585, 40732160, 7159536, 104197152, -73107706, -7338816, 8918390, 106128296, -56914488, 44994560, -215145033, 25189920, -222294502, -121066048, -121048452, 101456240, -550620340, -50388480, -63807261, -185670632, -63465606, 111805120, -9330659, -21821400, -186054507, -56197120, -57995595, 76054040, -260408958, -29348352, -440956338, 165317920, -12067083, 109128704, -547775563, -64064520, -162377095, -179341312, -110157003, 11653768, -682113292, -37601280, -710420487, -119337520, 71744535, 72997824, -40000660, 5178816, -37313848, 95245824, -235752417, -36092400, -880966207, 80015040, -819745825, -172168112, -46329165, 83886080, -382797582, 11994048, 34651575, -47806720, -155380518, 27725832, -523500925, 18012672, -721267045, 46604096, -542102733, 16970752, -925471064, 53537760, -305080982, -17395712, 101732085, -477157336, -1024055220, -134908416, -1084285127, -303326832, -135613683, 59709440, -1486940406, 212971896, -192306052, -286929664, -312679980, 22901528, -8223768, -119439360, -1157650720, -298859040, 102065643, -150436992, -2792137785, -127060920, -1318911140, -51724800, -25646949, -232378464, -171524184, -137471040, -19046104, -501922776, -351665388, -69566464, -249924925, 24768504, -1647949977, -28603456, -358182999, 388232520, 77600064, -151856640, 158735892, -911878536, -85015980, -261112896, -2257380286, 408597912, -2180248559, -89128960, -342414810, 214229568, -1938486067, 170061120, -174782335, 184781392, 626638383, 12275712, -338191483, -377342280, 524116556, -558820544, 73647225, 748091488, -463969620, 189665280, -581677374, -193072360, -256682385, -109817280, 691999602, 99050688, 201768035, 28430336, -557947980, 706733184, -1450064932, -368309376, -1285293375, 218298920, 216217755, 42696704, -2001462182, 605276928, 1308464720, -1284984256, -39331467, -879032936, -1107953912, 126904320, 1598555827, -366796496, 402764130, 241142720, -2377683860, -246367656, 2288177638, -319782912, -17478504, -741257480, -648838351, -321454656, -1992727580, -438568360, 121811850, 504822272, -468272974, -270050760, -663543110, -741167360, 581067378, -52488056, 1574309815, -283115520, 599205565, -732041024, -40479912, 241933376, -1826954210, 161347680, 346198205, -301181440, -93574683, 1233284736, -961973635, -60792768, -1151260803, -77484680, -157288824, -325857280, -1650728116, -57276288, -408701319, -833577216, -180689940, 584861648, -2368197895, 58710528, 321941996, -71347120, 1610406009, -849026368, -961157344, 455315904, 3251584235, -359956480, 1023728058, 1721160264, -1007612213, -201519360, 636693672, 1778356016, -718780149, 968528384, 1754686970, 968387616, 391222713, -811649920, -77292657, 4404962720, -458443768, 403107840, -1093274302, 510458088, 1008649260, 1485365056, -609068062, 507724848, 6302317173, -894440960, 428830605, 74645272, 1788003691, 174571200, 3318013105, 1488436056, 784277316, 449576960, -4230615737, 463964760, 816531484, -608432320, 1693989369, 2083271664, -256214140, 234786816, 2521625642, 3527650704, -83593701, -1322543360, -4452779467, 96536664, 2708753557, -873029632, -1310284755, 4382204504, 1980928849, 512516160, 90952624, 1299016760, 3077590059, 1434730496, -3853287541, 881256024, -4685259540, -93230144, -1379017953, 5456906336, -3124900838, 300810240, 221951925, 5683363896, -723024792, 954700160, 2932185205, -573956280, -58078678, -583982592, -623637198, 320005280, -966965874, -41430528, -764218041, 298510784, 1273530195, -761966592, -1537763668, 1886019336, 4908230240, 288739200, -2524808772, 7047729656, -3314974524, -640120320, 38222110, 6557966600, 651619215, 1377344896, -2449706238, 370633320, -806248254, -671088640, -334296072, 3062380656, 1855481145, -95952384, -3095190154, -277212600, -2385224496, 382453760, 5947255923, 1243044144, 12376141562, -221806656, -736758855, 4188007400, 1363432548, -144101376, -4025331225, 5770136360, -2042809632, -372832768, -52675272, 4336821864, 8606355990, -135766016, 2966736159, 7403768512, -153296647, -428302080, 9526379075, 2440647856, 1237938174, 139165696, -12082876635, -813856680, 11650191571, 3817258688, 831490839, 8192441760, 5415705946, 1079267328, -1399401927, 8674281016, 2501743995, 2426614656, -1554014042, 1084909464, -121995016, -477675520, 1480168215, 11895523248, 3667301243, -1703775168, 14049183465, 1538448416, 911421315, 2295437312, 3975146851, 2501439840, 793982081, -183212224, 177147189, 65790144, 17677858820, 955514880, 2109229934, 9261205760, 2470638456, 2390872320, -2994928853, -816525144, 10154208248, 1203495936, -544548420, 22337102280, -10758029787, 1016487360, 8673616629, 10551289120, -4162335984, 413798400, 1664665159, 205175592, -588551985, 1859027712, 261510795, 1372193472, -173143222, 1099768320, -4007967312, 152368832, 193307472, 4015382208, -14634689925, 2813323104, 12523677985, 556531712, -1973908062, 1999399400, -2166200257, -198148032, 13564093299, 13183599816, 240796530, 228827648, -2319127985, 2865463992, 2784066315, -3105860160, -1536691176, -620800512, -6886712497, 1214853120, 2320831725, -1269887136, -5808915891, 7295028288, -13743838375, 680127840, 1597040261, 2088903168, -6001951554, 18059042288, -6017211270, -3268783296, 1292374265, 17441988472, -3268308204, 713031680, -10010727987, 2739318480, -11138569951, -1713836544, -14866749180, 15507888536, -12686365546, -1360488960, 2363889540, 1398258680, -1722796047, -1478251136, -1030695449, -5013107064, 7299011785, -98205696, -1713571362, 2705531864, -3280754379, 3018738240, -8322453987, -4192932448, -251927793, 4470564352, -3972193820, -589177800, 7530623074, -5984731904, -5023471689, 3711756960, -43669456919, -1517322240, 6008173502, 4653418992, -1565881065, 1544578880, -3472004550, 2053459080, 1296611687, 878538240, -7031041866, -5535996816, -21349312575, -792405504, -2767218005, -1614144280, -11905821126, -227442688, -4155970429, 4463583840, 19437385023, -5653865472, -325811241, 11600519456, -15544296530, 2946475008, -13613942324, 10282347000, -14789940201, -1746391360, -17278601647, -1729742040, 13957769045, -341573632, -4384181565, 16011697456, -4467452892, -4842215424, 3006366478, -10467717760, -2974239081, 10279874048, -16170726387, 314651736, 3838060135, 7032263488, -18417058884, 8863631296, -5773562656, -1015234560, -4550250691, -12788446616, -19181353149, 2934371968, 8245349230, -3222113040, -24680272147, -1929141760, 1937102445, 19021470880, 9055537561, 1970941248, 31383623211, -18305421104, -1080017820, 2558263296, 2255196938, 139828032, 28672939152, 5930059840, -1007473896, 5190706808, 14901901026, 2571637248, 18890070290, 15941820640, -6365315259, 3508546880, -4349936290, -974494800, 26062824461, -4038578176, -23786087589, 3746183792, 17380206065, 2160406080, 3694610345, 5308344880, -22133137275, 5929338880, -26461212723, -4648539024, 7960628347, 419904448, -1250887455, -12594478520, -6156450976, 2264924160, 7000054074, -4793644520, -10335534714, 5856328192, 400786897, 323839296, -26429369460, -1935467008, 935592525, 14615633680, 10908006766, -1290781440, 41276100692, -2769585640, -4195273986, 2409451520, 32042603025, 748597464, -41608846536, -9866277888, -14134524975, 7695789080, -3260816965, 486342144, 2505878427, 9210086424, -19474210215, 619877440, -14502871240, 1258310592, 20176579204, 2606858240, -14636773791, 13205824928, 17348265743, 458210304, -7088005820, 3269610552, -24987718728, 6668617728, 15679053553, 1445519520, 3899166135, -4678893184, -8237186514, 18945583160, 2356677510, -469684224, 26154033554, -2575535968, 2746766295, 570776960, 28319596648, -12883248072, 47952460308, 6792210944, -27649490940, 7689258752, -40192942961, -3642527232, 28331753247, -26012673880, -29275698429, 2879651840, -499655303, -8189824464, 23350636980, -13769282112, -3661569441, 8060897704, -28135762996, 1612154880, 3228618533, -5093549376, -40147390962, -14226848128, -1641115060, 5750241192, 5116596170, -7748227072, -5192263404, -14037495760, 30752866165, -7747100928, -21452796723, -3129781704, -8442359460, 6493199360, -30846254402, 618341256, 51505286194, -35239701760, -222041736, 3667550144, 43252756850, -3224862720, 23357922450, 8746194416, -31256569440, -4083664704, 34471723024, -8069194080, 582574096, -11882920448, 2755772361, 4872544496, 1547461650, -4061798784, -60898621580, -50418537384, -75387720195, 7155527680, -35954041633, -3430644840, 20074125167, -597162176, -35610600780, -14304029528, 20017175108, -1396569600, 7381707802, -26544104840, -692467623, -11907488448, 14639537507, -6274218528, -13161573265, -3596615680, -4631152968, 33844925896, 21344411607, -3711718080, 69977273122, -6532251872, -514244808, 4867458560, -13815442660, -13551914952, -8650126635, -16666173312, -9494965476, 2049713120, 104247658924, -1878294528, -20635788108, -20173005136, -6747972975, -28221205632, -1188745047, 668749608, 459662742, 10580346880, -44494649379, 35622235736, -9849757372, -772293312, 29957607650, -21670028456, -9670940973, 6984237056, -16753787515, 10482278040, -1998150616, -35057636032, 2095201728, -15847430792, -3817218745, -4100129280, -20826382876, -727620992, 4285869084, -10392134080, -2848254583, -24620720472, 37635041126, -11477843968, -2295431460, 30826300328, 15581447801, -7050048192, -5164219866, 37482076320, -60949267722, 745841152, 86361313231, 11032143624, -18757517575, -43655250688, -58866711093, 24999206704, 20458120781, -2406481920, -35087491874, -1775615400, -9245199870, -45466911168, -82352310870, 5784198336, 28457176299, -7637601280, -52339123809, -23457481640, 43351032018, 4591650240, 13005137922, 464629424, -4719123045, 4671860736, -2364615193, 4989097584, -14867248764, -2560042240, 16919236341, 7735726992, -23365752330, 331444224, -21546230930, 6113744328, -9131170041, -2388086272, 24821290506, -10188241560, -34802058258, 6095732736, 14151147012, 12302109344, 86976239875, -15088154688, 11286376176, -39265841920, 1988475075, -2309913600, -981903013, 20198470176, -11997082660, -56381837248, -12527179740, 26519796192, -118471762183, 5120962560, 18340004350, -305776880, -15705289098, -52463732800, 61255499778, -5212953720, 12813581340, -11018759168, -6930424395, 19597649904, 23507584397, -2965066560, -12063659710, 6449986032, 18683989254, 5368709120, 36572348950, 2674368576, -8963516133, -24499045248, 5447736945, -14843849160, 40061762759, 767619072, -52552772852, 24761521232, -15064595460, 2217700800, 37451229229, 19081795968, -28090884495, -3059630080, -39151753164, -47578047384, 9963226644, -9944353152, 40771157125, -99009132496, -34702921125, 1774453248, -7762261704, 5894070840, 34050690798, -33504059200, 5837879385, -10907460384, 75632600050, 1152811008, 21519939021, 32202649800, -54039478914, -46161090880, -85520891712, 16342477056, -55168884650, 2982662144, 35328547440, 421402176, 15861696840, -34694574912, 34729813557, -68850847920, -1061949609, 1086128128, -4663593665, -23733889272, 22059744620, -59230148096, -29914755624, 1226373176, -19183261487, 3426416640, -46030736301, -76211032600, 43161007329, -19525182848, -16645469295, -9903505392, -227128855371, -1113325568, 10874631510, 96663013080, -36618460422, 6510853440, 199382901882, -93201532568, -64197464220, -30538069504, 102947132983, -6651926712, 39096792231, -65539534080, 61780796226, -43325647568, -22674462238, -8634138624, -3769821315, 11195215416, -471919608, -69394248128, -18158405500, -20013951960, -87897773800, -19412917248, -17518635477, 12432112336, 23706405335, -8679275712, -18891956371, 975960128, -53803644660, 3821404160, 85850082012, -11841345720, 49314433592, -95164185984, 3288919950, -29338409944, -9185092728, 13630201344, -10362031758, -112393467720, -12643370298, -12307587328, -17894190935, -7291370520, 123154095050, -18363498496, -17915663970, -31801174808, -89846684418, -20011518720, -7922502182, -6351856648, 15688819206, 1465697792, -34867693560, -1417177512, -172015640040, -526321152, 42506365005, -141422870560, -60271486556, -7644119040, 263681049998, -16873839472, 16178550255, -74089646080, -44111100163, -19765107648, -80877244061, -19126978560, -1092957624, 23959430824, 47780930989, 6532201152, -37022663455, -81233665984, -49327763670, -9627967488, -32074422548, 4356387360, -31785637875, -178696818240, 9347351535, 86064238296, -60016481980, -8131898880, 74290401898, -69388933032, -2526516441, -84410312960, 52276470160, 33298687872, 8277977435, -3310387200, -25973288145, -13317321272, 19077209529, -1641404736, -147778452802, 4708415880, -31084041681, -14872221696, -120181069279, -2092086360, 222990029600, -10977547776, -4246798248, 1385145776, 177065735, -8798146560, -133057826692, 32063738496, -44569659132, -1218950656, 176513867765, -1546459776, -81568443812, -32123057664, -11034935613, 117077519400, -30301185264, -22506584832, -41740719451, -100189423880, -4878628380, -4452253696, -99188849611, 15791264496, 87020446497, -15995195200, -63941343165, 17329602056, 106017982878, 1585184256, -9359566195, -108512746392, 8692433892, -105468798528, -186174137246, -1926372240, 47593301015, -1830621184, 43480962243, 18553023880, -25442885780, -22923711936, 75100822953, -22272530520, -25951248288, 24846881280, -80966337943, 12293529408, -196671887564, 4966404096, 87792774345, 55093699976, 57068033522, -9718824960, 122641772468, -18566653800, 27640657566, 10159097088, 37688537131, 46471327128, -141210413585, -58360226304, -27205529751, 109950707000, 9250786199, -5441022720, 8305119173, -12776322088, 17190729144, -16711225344, 212328923925, 48015612432, 15726399766, -144472338304, -19407064023, 48137690160, -207096312690, 26150266368, 222237592112, -10338994120, 47376548190, -139535907776, 85510452236, 26146465632, 259052877585, -5704253440, 10563013251, 80085823896, -8453998227, -21914547840, -29522038260, 89108559608, -2086901739, 13710692352, 202172168121, 118933993440, 75054382766, -124063108288, -12377981736, 101490924368, 31781414455, 10883911680, -104826686278, -18911116320, -29518406154, -11186069440, 273883379438, 13782368376, 249252353482, 11826009088, 27233530020, 8245563592, 247344081314, 40104856512, 18803618435, -58392094280, -16444837674, 785645568, -28615142868, 13708570896, -56496829715, -21644254912, 170162563671, 26246035032, -91367428366, -24149905920, 92699952614, 66579631896, 11578426335, 33543459584, 183339324650, 2015422344, 52215191943, -35764514816, 48276099657, 31777550560, 210790596273, 4713422400, 252873459633, -60244984592, 89586353835, 47877855232, 2250425401, 40187773512, -29145483289, -29694055680, 21175487532, 349355655352, 150663288586, 12138577920, 87561182610, -48065388016, -114226624899, -37227351936, 173369017040, 12527048520, 31386258904, -12356631040, 22046350068, 27776036400, 109858759630, -16427672640, 214445460740, -10372893496, 45737712963, -7028305920, 230310952453, 56248334928, 334667967281, 44287974528, -6917781780, 170794500600, 43083097688, 6339244032, -20076317860, 22137744040, 68083892334, 12913154240, -24378461706, 95246569008, 133395328325, 1819541504, -2257029927, 33247763432, -52877083056, -35708670720, 7980230423, -155499080184, -120225045609, 45230923776, 343264939785, 2606489928, 309774951926, -92804155648, 73136346039, 124354372240, -27862419910, -23571800064, 3322155655, 108911538592, -35377688385, -82258776000, -125558249074, 118319521608, 30255307336, 13971130880, 53485078923, 138228813176, 312755917139, 13837936320, 380869718680, -111662152360, 2455720848, 2732589056, 169755164135, 35073452520, -71065267142, -128093579648, 83094931593, 35739623136, 69870443360, 38737723392, 50989797313, -24050931824, -104038763607, 83741742080, -25075943158, 23793912648, -475047527230, -82238992384, -126502007580, 129365811096, -172476414941, -2517213888, 231483028387, -30704481080, -37233484731, -56258107904, 326067441677, 147336471072, 3059007770, -70909050368, -84372322626, 46188501248, -140667546077, 8121876480, 153653324489, 36402005528, 5992701975, 102307572928, 95696513575, 153450825192, 202323021369, -23474975744, -19521669384, -65962793840, -182689335017, 25776904320, -296213272142, 197442177176, 79169000535, 15433134080, 507057715503, -15496819560, 114722362926, -152171767040, -1568124306, -72444300488, -73794746319, -15767529984, 161753007575, -251068985688, -16838204346, 146443368832, -20886340735, 8640142560, -20227002891, -20466106368, -26108078598, -18041575504, 208173416580, -1118624256, -76247014186, -229383513216, -20633887107, -47440478720, 36769192960, 8059791168, 370450453864, -41525654464, 34385315265, -119215208208, 22638374410, -20573097984, 347712943221, -151120562320, -41519619036, -127534565120, 480526061154, 50922522072, -45400433780, -28068375040, 132522216480, 34799490320, 20619642733, 7795958400, -34077302357, -208502595688, -68169836844, 32308625408, -188862776620, 190288700712, -198110363277, -29969470336, -89504312148, -139041648520, -168142769394, -17283248640, -74311175686, -29556882760, 1031996970, -42466759040, 506574686540, 177065098200, -21885890523, -47434711040, 17593718805, 211689701784, -229089408612, 37188312192, 505457034850, -63685026776, -66142068426, -3359235584, 174575554268, 10007099640, -465269077590, 100755828160, -21768702858, 49251607808, 220501602425, -18119393280, -379283299249, -56000432592, -9025993944, 38349156160, -25124635168, 82684277712, 104738234259, -46850625536, 50097990915, -3206295176, -3200416037, -2590714368, -225983623822, 211434955680, -83570134158, 15483736064, 416902696445, -7484740200, -111684382880, -116925069440, -64401061392, -87264054128, 395840078420, 10326251520, -63816695901, -330208805536, 160575909921, 22156685120, -87371479770, 33562191888, -204571460255, -19275612160, 334155822174, -256340824200, 123499779829, -5988779712, 32773066430, 332870772288, -19892489085, 78930223104, 285269898165, 113076199800, -566511127090, -61566312640, 36812678796, 26086535720, -443933815584, -3890737152, -43825743860, -20047027416, -108683943075, -73680691392, -89320272594, 155793681720, -470076924015, -4959019520, -55155860064, 116022969920, 83686969075, -10066484736, 172131412985, -161412633632, -1422232344, -20854865920, 298337680592, 117094190328, -151248023934, -105646599424, 232371611730, -138786125944, -572874921886, -3665682432, -303031179686, 56704046560, 80101876293, -26156884416, 473829595328, 199901749824, 53223212255, -53348941824, -4139009469, -125432428424, 168422088141, -11564156160, -180048008463, -31193329080, 257212235025, 37431145472, 9911875350, 65897492112, -429779790556, -151564665280, 33424330698, -18853420080, -187887018109, 3757473792, -361038130152, -209232268432, -326237669145, 20604287744, 829100195612, -21974130360, 341075265460, -4566215680, 314555172417, -226556773184, 220965590835, 103065984576, -55695343585, -383619682464, 22450252653, -54337687552, 708145737950, 221195927520, 47281667758, -61514070016, 146224060542, 321543543688, -63839855800, 29140217856, 95987186626, -226654025976, -37783852029, 208101391040, -308475596663, 234205587432, -473997074751, -23037214720, 67547087865, 3997242424, 153058872239, 65518595712, 330029991953, -186805095840, -41958379134, 110154256896, -233964859156, 29292555528, -190147472500, -64487181632, -3293865432, 225086103968, 95907114142, -12897239040, -116722752669, -25828948264, 39964541805, 40748395008, 517662236440, 321179127696, -243674227041, 113814785024, 99017133561, 13128920480, 105209779899, -46001929536, -229299625161, -40932769360, 379327953555, 61985816576, 102385695700, 41538107232, 74289370600, 112299966080, 24608375505, -246022929320, -7614206613, 61976807424, -189372345210, 171622373784, 107328964977, 25038253632, 1063379916574, 67538875680, -551097999524, -51945594880, 21437516187, 246770035216, -13720226380, -4946730048, 305574064280, -412042289552, 4782974103, 281917614080, 327827518609, 1776333888, -428887719690, -29340401152, 477302188140, -346022054800, 632045391753, 25798901760, -12798649864, -186863379600, 56949208218, -69969555328, 189812815870, 250052555520, -267137002900, 32669317632, 66707238312, -275773784192, -997304090520, 64553552640, 56587629986, -4660592768, -80863079031, 95063363584, 256653985665, -22046178888, -974656140654, -38980355968, 274163622696, -12379693200, 39303000645, 32494390272, -231128416933, 487188972640, -14702807340, 403348299072, -302171409001, 603101761560, -217603627585, -57244221440, -290466804249, 287632333064, -515177827818, 27445158720, -455740727380, -160593001336, 234187648983, 4777297408, 999937329017, 284884806240, -281172817975, 114432236224, -112383071568, -160137400864, -635569123420, 11172556800, 502932792454, -59053662416, 44945959293, 212352838720, 131039333399, 5539740984, -827433696336, 95259907584, -15890903595, -117116300056, 118057256573, 50193748224, -236032290567, 105292586120, 7060791465, 28772925440, 90228834974, 37049223744, 252212298620, -270759407168, -4674866994, -170755292856, -131299570626, 29693744640, -856995942974, -559818184976, -108215117424, 52258014976, 669799866050, 4113958464, 83301131238, -38939668480, 5219301744, 110523541280, -436076628648, 108415319616, 11885490225, 69201013080, -395136627975, 133329386496, -577812833629, 75959723808, -502031911998, -16397704960, 338139305595, -833981271392, -801067590206, 15026356224, -110402455990, 165086304864, -53295517674, 161384041088, 15573580272, 53983783800, -1404021408633, 225769645056, -58487406939, 9509960376, 560557115450, -5349996864, -330138299641, -3677301936, 366230519073, -84642775040, -179560817275, 355957195032, -2171119096041, -284977885888, 6501506310, 78798058976, 249302120072, 6178346496, 14348020923, -239660861200, -62616455595, 173360227648, 525220327035, 77367527784, -247394596435, -55873896448, 75169790505, 134030300120, -6289332127, -83858224320, -1030793837277, 15985204928, -41490661752, 280461088256, 484308748850, -16761613824, -190707618993, 126779446336, -185941237419, 30537749960, -635617065067, 32801034240, -273214448096, 166611063008, 62662456575, 5820967936, 383122304216, -34286952672, -30647451332, 83137072640, -156840729057, 22786036664, -317436574952, 196965763776, 82074163860, -301080329008, -371083636125, 91822751744, 734090775895, 18363451680, -357817359150, -246610402624, 43120087047, -124651582408, -383671023430, 56400385536, -104642776826, 41313758928, -162052691958, -299856610560, -463422014896, 487594141776, -863685510510, -5966729216, -162464704290, -690890505848, 55569743161, -88257148992, -465338397947, 150060140600, 34894105155, 349242005504, 155909094469, 470933688744, -831269815435, -199993653632, -88244321508, -163664966248, -835935637954, 19251855360, -779206402806, 280699934992, -270289655649, 14204923200, -351250940460, 73961598960, -1608660327990, 363735289344, -300741388677, 658818486960, -183342484491, -46273586688, -531372389975, -227657410392, -401402227860, 61100810240, 63816935676, 418712990472, -371909798561, 187659853120, -342531869742, -346808256144, -319580445264, -36733201920, 37022749840, -104041103376, 63825017580, -3717035392, 164871832202, 37752984360, -33708624298, -37374885888, -46515493269, 18916921544, -84382075265, -39912780672, -621437819327, 118937990112, -27828777123, 20480337920, -1163848992570, -135353890728, 137840542359, -61885815936, 197073318195, 186926018640, -510020559258, -2651553792, -425271362898, 172369847440, -46266426774, -48909954624, -1707108887512, 73049360328, -718732455620, 19104690176, -88580368233, -198570324048, 572399838697, 81505932480, -65960975836, 278416466064, -224706257649, -48765861888, 1079340363805, -113209176096, -1149153505098, -98416874752, -6802050411, -695809919000, -1033392050598, 120705237504, 253216754932, -90291009408, -107249233140, 314126735360, -742294566490, -15907800600, -1820558854573, 18479308800, 203326822998, 7855224104, 183341817541, -161587761408, -1107531665610, 95976661280, -135633735603, 451054697984, -2820752424, 100217437920, -750380471304, -212158369536, -1179075336813, 947774097464, -106618355805, -40967700480, -1312987018952, -146720034800, 162220684554, 2446215040, 1426673392439, 125642312784, -397074196960, 419709862400, -42278788755, -490043998224, 317140749312, 41703629760, 962603883863, -102508650720, -93744122850, 88150073344, 649519043494, 55443395160, 420097907115, -156781199232, 35008515549, -188060675176, -644077175024, 23720532480, 250424642949, 96509277680, -189838130382, -51599888256, -478389075890, -149471914032, 453825154619, -42949672960, -576431439525, -292578791600, -957703260255, -21394948608, -2640340788121, 71708129064, -74714886135, 195992361984, 901980669840, -43581895560, -507211219240, 118750793280, -321457170402, -320494102072, 352200071880, -6140952576, -452386521020, 420422182816, -112211201583, -198092169856, 973983257076, 120516763680, -609809612131, -17741606400, 524809395621, -299609833832, -766518070320, -152654367744, -20481316230, 224727075960, -8796903507, 24477040640, -313951955572, 313214025312, -861950061530, 380624379072, -419696006310, -79705813152, 1063183554998, 79554825216, 612795062606, -326169257000, -367576442748, 792073059968, -58832795112, 277623369000, -1102394277755, -14195625984, -399328385427, 62098093632, -311878158135, -47152566720, -1553266710987, -272405526384, -466522244469, 268032473600, 1997656319030, -46703035080, -6532813672, 87259683072, 376859764215, -605060800400, 323283874410, -9222488064, 756667023914, -172159512168, -118372902255, -257621198400, -1203289931342, 432315831312, -50745589778, 369288727040, -120621228084, 684167133696, 191500279484, -130739816448, -13407643525, 441351077200, 81171894906, -23861297152, 14989478741, -282628379520, -1160258486486, -3371217408, -80304455187, -126893574720, -85724249275, 277556599296, -239641477286, -277838508456, -436609612449, 550806783360, 717661056556, 8495596872, -2879042196645, -8689025024, 103627623645, 37308749320, 1429526793643, 189871114176, -565246842111, -176477956960, -497260589868, 473841184768, 314524891743, 239318044992, -929543770060, -9810985408, -155886191712, 153466091896, -852891547026, -27411333120, 72222325500, 368245890408, -122856768657, 609688260800, 199745188040, -345288058632, 89821559912, 156201462784, -517896535023, 133163754360, -205444624892, 79228043136, -275186137578, 1817030842968, 222624429210, 8906604544, 26616821952, -86997052080, -1692996924492, -773304104640, -666367347969, 292947683376, 355293582020, -52086827520, 211206979470, -1595063215056, 52301766015, 745612260544, 1102788803779, 513579713760, 54446410956, 244304556032, 244499514147, -823577063864, -372889420705, 53215413696, 53022496865, -312774337848, 847357826697, 524316272640, 450013202772, -494246369808, 1648775372394, 346605180544, -29160481140, 181395697904, -1989978102141, 69073108992, 952381296574, 30158570520, 60890317326, -89561723328, 1370999679283, 3775356864, -425322866495, 555153985024, 774169357104, 145267244000, -774281438098, 160111615680, -2522973597501, 703182190400, -27201795192, 155303337984, 475597126050, 140149083816, -912567345619, -99456898688, 402351327702, -189651242680, 910824099215, 69434205696, -747825255737, 151135650968, 510031897830, -7807681024, 2044299767872, 430429157280, 285744615302, -30571233280, -171863511993, -686800656096, 578379603753, 94730765760, 1516483043935, -394515468736, -117448279830, 761313487872, -194086600656, -26311359600, -1363122677110, 234707279552, 703696260447, 73480741824, 408892748820, -109041610752, 236677347305, 82896254064, -642224364903, 899147741760, -664900720981, 101146962384, 426360531369, 98460698624, 469265563755, 143153527480, 125632112255, 58330964160, 235189982113, -985232760400, 99754479315, 146907987968, 1821242085924, 143325311760, -59950340905, 254409398464, -597594706425, 718773475344, 1572986750309, 160092149760, 1764115859982, 63380017456, -714452743521, 50814853184, -716107834800, -125510553648, 1621262863861, -11725582336, 214936965369, 278941548480, 501820911569, 11337420096, -748537199712, 1376125120320, -33773961285, 4210569216, 1635426858700, -340050920040, -1151967789905, 1131382964480, -166224176352, 482171892448, -115999678669, 61152952320, 536237143025, -2109448399984, 189001459998, 134990715776, 1563638725403, -129428402040, -887388607898, 592717168640, -279059437278, 352888801304, 539891673055, 158120861184, 179771978708, 647017952488, 10821246219, 153015828480, 2045127892797, 8743660992, 1689412997950, -191675446592, -713592975420, -382247447912, 241404420049, -52257609216, 98007446867, 296181307640, 25260998175, 649869327872, -893329608716, 394622109360, 475577877495, 77023739904, 294516182682, 256595380384, 1417112719814, -34851098880, 473554865997, 254285103000, 1114454718684, 1429574545920, -159141579660, -74778812280, 1265709059378, -688513906368, -113272397622, 480131855840, -1943275364899, 65055191040, 100731487714, -594323215184, 865150281675, 555111464256, 2253935437454, 20212131528, -199515339282, 675282503680, -1123438856472, -418211761280, -606718759528, -266389502976, 1653447662785, -66223819480, -381632174325, 26483097600, 1708073369665, 207786305160, 2482415890809, 106538570176, -88042058055, -152617676232, 895551700700, 13131237888, -984326913812, 1182227622416, 67658717529, -37667327040, -309023076894, 248672333448, 145146992562, 118977773568, -525803675805, 961448554232, 237355863486, 16736690880, -194464499770, -1783920236800, -391577523480, 87820382208, 1781411584495, 33974385984, 700695239310, -11081166208, 544767638508, -1416525880, 3644214412136, 70385172480, 69206436005, 1064462613536, -395192892357, -256509907968, 203567835445, 356557273056, 2801146412135, 9751605248, 468403175061, -1412110942120, -2355090072803, 12371678208, 1941734195042, 652547550496, -191376157140, 256984461312, 1115304213870, 88279484904, 2046738217504, -936620155200, -674668405656, 242409482112, -630131127242, 180052678656, 2621575039710, 333925755608, 423334445931, 801515391040, -497372271676, 39029027040, 120441835865, 35618029568, 105277485645, 793510796888, 1864881705230, -126330115968, 955444880989, -696163571976, -222404035878, 127961561600, -897751336393, 511530745320, -440855627625, -138636816448, 63630292770, -848143863024, 2904813887604, -12681474048, 3069243666537, 74876529560, 706158905958, 868101971136, 1048021117816, -69539471136, -93873758990, 843750388224, 74162689965, 1489393097968, -1064727581292, 15410977920, -672378604298, -380746408120, 764629109496, 14644969472, 548690538265, -347847697944, -49612190096, -148424191040, 1294716428316, 203543086240, -686501528426, 183389695488, 2655323262315, -600806583624, -746536255380, 178180244160, 1133226084146, 207609986304, 1205725412030, -198775050240, -1085209459947, 647730703544, 14414532379, -98348235264, 448803398960, 1573375100512, 764957337669, -39731232768, 1472471729033, -702342194760, 887590793765, -440749599808, -790443857583, -456544268176, 756666907260, 77750599680, 4866366499006, -981134179744, -13490693181, 148533230400, -1551370158056, -221125260528, 1859299118031, -81272776704, 630467198460, -301508297048, 155408303165, -371770617024, 201036766216, 1129683308680, -98862374907, 466881810432, -380028191816, 217644238008, 743116118260, -879605656000, -759665600892, -74006289592, -3597443411238, 43528181760, 140649296114, -66440953384, 87172700391, 102210576704, 2792162955290, -137525833152, 548304648661, 133689802752, -1083979555974, -1698631391400, -461501114406, -384124899456, 1153601555860, -125811198128, -44310106620, 1155778706432, 1699619109884, 155256512184, -180034510774, -385101521280, 138148096590, 1656770501520, 442993694908, -209202130944, -2275939627640, -1777900736896, -140191111908, 82711952960, -72482972810, -379012385520, 683317304253, 1116287262208, 830327386455, -684083617888, -815545563980, -209171725056, 1906095911497, -2072423020680, -579225511521, 45634027520, -338690820624, -84504106008, -1234326078214, -640686591168, -227943705420, 67631985816, 734080968853, 175316382720, 784844929834, 236176306080, -832848868854, -712868476864, 1799873499987, 16695213912, 2539136795020, -109685538816, 1390642727238, -1617377344968, -165887871624, -951471947520, 1358910648997, -600435062128, -5995126872, 992504866304, -397586281430, 99023853888, 21279230245, -811927394944, 1167824434950, -254251315640, -1179279702879, -87071293440, 577792901713, 838613490224, 630663906150, 151288930560, -222551554393, 236147249232, -512604476141, 89488555520, -843927374880, -2191067035504, -1230978287649, -110258947008, 3297607361215, -1994018827856, 930736521648, -94608072704, 1844117612521, -217868240160, -683505559940, -65964508736, 15729500592, -1978752650512, -10487380110, -320838852096, 2961842792258, -150428947480, 74405853747, 467136754240, -353596595361, 131558701392, 1120078470183, -6285164544, 41781464550, 228921142944, 324457060260, -109668567168, 1323754930952, 451974637720, -1644262782660, 173154039296, 2550151140735, -1361300509368, -113255638020, -209968280256, -2035468445265, 730939426928, -160617630082, 193199247360, 519170459618, -741599620912, -970759124091, -532637055168, -1809088180830, -92627410680, -995361728467, -268347676672, 542001379509, -1466714597200, 779628126256, -16123378752, -227595286730, -417721535544, -961486221060, 286116118528, 2533945205144, -386208797256, 3877425643851, -254220404480, 540463727916, -1686324770184, -3461557166366, -37707379200, 19593702830, -2022987677064, 199306110654, 481959876736, 645115848777, -716690830680, -2020526302951, -383022841856, -18696625821, -18003403208, -1469691918320, -321502188096, 2063727351517, 233163866312, 395267512689, 237552445440, 539988266545, -169403900256, 2714679182324, -2794845242816, -355362478155, -1205306308688, -403060742446, -97108623360, -2597715624338, -700489460880, -125041130136, 384523104128, -1903255084215, 913812999192, 205527508795, 297818815488, 576299113389, -1386952136320, 1490317490632, -100216388160, 564259976065, -251090071232, 1889386374294, 98853048320, -57789199505, -176370800544, 402675756372, -222208291200, -13884609816, -878870077040, 934609338124, 131421381120, -663361000879, -1715563685920, -373016951820, 82983147968, -472673637501, -365901703704, 691574894918, 56226447360, -233553419145, -1842487619624, -626645294030, -449986679424, 728966066210, -2677343738248, -256364067852, -354303796224, 1132299543071, 55342254240, 1266671397326, -1366356004800, 2814686790948, -344664781504, 821770188285, -50713952256, 118745984315, 160610542880, -557166278916, -177101952320, -3648514459820, -544671138672, -488381020894, -103305233920, -182195270325, 195027693648, 2035054233652, -761972552064, 5155404048661, -1067162626600, -32096116269, -14556332032, -2052831141649, 18056239416, -1799380337330, -265982107456, 12410894034, 423016664448, -560196449355, 285669365760, 1728454545993, -63841843384, -1201355533233, 1243992641472, -329956956805, 961800364872, 3425902704565, -361847390208, -265943449044, -2746119518280, -3727914144354, -20851919424, -2199037874944, -2478199615408, 808855406550, 742433245184, 4371141851431, -585090768312, -394882455429, -994834977920, -261115406271, 222899359280, -880141921985, 188574400512, 5122776303960, -26577245240, -452352262905, -871292308736, 209781386643, 283021507080, -1309025498573, 658070208000, -53950066632, 1004465992592, -1209712886980, -946556172864, -4220532437340, -242042458688, 56570446656, -111769047040, -3879374088045, -427880631384, 264585786094, -1105830505408, -103064906115, -2502047337112, -566199743788, -110703490560, 3254383203184, -3046957749440, -562312337652, 893297218880, -1008048276143, -19645766784, 622351286325, -21860712448, 115718465268, -1358041313080, -1993648901997, -280587620160, -140184552417, 568522137136, -76902873741, 1024748637184, -1484175587090, -664759452744, 2171592033042, -285916985088, 1016146110402, -558963546880, -5306995181462, -309901787136, 2148321378192, -407918378504, -61976649420, 192407454592, 2878313881736, 832310108856, -242687032779, -669933936640, 420699090627, 200607545264, -3159037879649, -190351301184, -5485473675125, 3800380217840, -139433936382, 657911939072, -812291877985, 1012016060640, -174093993183, -1034926488768, -1645630228494, 1379811319528, -2710268633865, 20137711104, 882248799422, -1851864227096, 2331755457237, 245635848640, -4047073352142, 297867877848, 110426104628, 450064863232, -506452974525, -2608539533416, 2509353369870, -1178691768576, -1854860765687, -24472062160, -1589401199511, 567272402944, -20499457823, 674978581008, -2557064373500, -369508009984, 552369261087, 1125340368616, -4734856011790, -64975011840, -76188292976, -1229226595912, -947362280598, -291216044224, -1310242937660, -47941615800, 474610692157, -818460583424, -249620396490, -765572108600, -329676968992, -1227606601536, 6664437407946, -1618584170952, -2223512393490, 187799805952, -3266971576022, 156173355072, -408761751879, 527702350720, 768343760073, 1461514680136, 2738543804876, -206215234560, 1115293392605, 2369706177136, -1413156342843, -1579537417408, -3671305374852, -633352004280, 1470969835152, -123465072640, 1170477864486, -4056461724024, 670932295240, 123974556480, 1491511161378, -917778903408, 351138723894, 1217374136320, 699360474194, 12544994448, -6757846385770, 579554403904, -127416322215, 590357970552, -793736988056, 126140239872, 1395376717558, -1294024060600, -63844610211, 2008551885504, -345610989059, 134705634768, -48403591085, -1171546950656, -401415716628, 167090725880, -5432111769968, -69121140480, 508208946510, 161816023128, 456819381207, 163728850944, 2737339976775, 208864628784, 218385929496, 144332604032, -630875312910, -1665387332640, -572118480726, 8948994048, 2044906286651, 609976113488, -581748235110, 1835068105728, -1104043087573, 165071096856, 189877021850, 379523829760, -246541591107, -294153543680, 195092542323, -64478329344, 783504771435, -2963603630912, 670174843662, 332205235712, -2375853610912, -275082522120, 4247214574978, 953721665664, -939655572966, -181106995280, 601857630710, 164584783872, -968781074586, -2781703545768, 382080969324, 1208964498560, -3012604282538, 332156952288, -2614932876219, 1020276520960, 2348358476625, -3844208489232, -1836428655921, -407380176576, 134189390559, 363203470240, 304732156752, 224547000320, 3619523676770, -1060177731840, 555560812570, -278395922560, 53688827025, -164957141864, -2806074272322, -62367667200]