# Trace form for 546.8.a.k, downloaded from the LMFDB on 29 March 2024. [0, 5, -40, 135, 320, 509, -1080, -1715, -2560, 3645, -4072, 958, 8640, 10985, 13720, 13743, 20480, 7864, -29160, 60173, 32576, -46305, -7664, 122869, -69120, 73722, -87880, 98415, -109760, -17317, -109944, -177665, -163840, 25866, -62912, -174587, 233280, -55136, -481384, 296595, -260608, -237570, 370440, -970601, 61312, 371061, -982952, -384035, 552960, 588245, -589776, 212328, 703040, -1977, -787320, 1520014, 878080, 1624671, 138536, 2057936, 879552, -723756, 1421320, -1250235, 1310720, 1118273, -206928, 2695018, 503296, 3317463, 1396696, 7392916, -1866240, 8720441, 441088, 1990494, 3851072, -328594, -2372760, 4646419, 2084864, 2657205, 1900560, 17766733, -2963520, 16495320, 7764808, -467559, -490496, 4692321, -2968488, -3767855, 7863616, -4796955, 3072280, -2355945, -4423680, 15680305, -4705960, 698382, 4718208, 2421846, -1698624, -15280072, -5624320, -4713849, 15816, -15194840, 6298560, 26793918, -12160112, -1488672, -7024640, -8526783, -12997368, -12314529, -1108288, 8008065, -16463488, -2697352, -7036416, 5324999, 5790048, -6414390, -11370560, 25383423, 10001880, 12056660, -10485760, -26206227, -8946184, -48657226, 1655424, -20639339, -21560144, 10018647, -4026368, -2587474, -26539704, -9816886, -11173568, -10368945, -59143328, 2104726, 14929920, -56127631, -69763528, 15882615, -3528704, -27106134, -15923952, 26614822, -30808576, 5732856, 2628752, 12433797, 18982080, -20571374, -37171352, -53379, -16678912, -42144067, -21257640, -101414272, -15204480, 41040378, -142133864, 97344959, 23708160, 24134045, -131962560, 43866117, -62118464, -40134432, 3740472, -25286646, 3923968, 55564272, -37538568, 65865171, 23747904, -163369882, 30142840, -19541412, -62908928, 232578040, 38375640, 116928870, -24578240, -33756345, 18847560, 285029754, 35389440, -98092790, -125442440, 30193371, 37647680, 185838558, -5587056, 147156624, -37745664, 72765486, -19374768, 5939731, 13588992, -153095058, 122240576, 89571501, 44994560, -29531302, 37710792, 96455595, -126528, 199608732, 121558720, 336727305, -50388480, 60939095, -214351344, 235451907, 97280896, 17277208, 11909376, 397166333, 56197120, 53743338, 68214264, 784539152, 103978944, 349895278, 98516232, -8872038, 8866304, 409702019, -64064520, 273512503, 131707904, 125453313, 21578816, 716457272, 56291328, 158943937, -42599992, 71744535, -46320384, 59883341, 51315120, 132200081, 90964480, 479701791, -203067384, 749966568, -80015040, -260496074, -96453280, 445373640, 83886080, 436278242, 209649816, 18911648, 71569472, -12624093, 389257808, 641496969, -13243392, 27245873, 165114712, 126692667, 172481152, 669595124, -80149176, -330221368, 32210944, -101732085, 20699792, 1771310088, 212317632, 626617665, 78535088, -129517785, 89388544, 390914818, 82951560, 667311116, 473146624, -63610515, -16837808, 81486510, -119439360, -556309163, 449021048, 423368235, 558108224, 54619083, -127060920, -40833240, 28229632, 18856314, 216849072, 269943193, 127391616, 332916143, -212918576, 65389842, 246468608, 1648733352, -45862848, -310646495, -21030016, -412561944, -99470376, 3583522826, -151856640, 1458546362, 164570992, -127273923, 297370816, 1436675644, 427032, 1350946164, 133431296, -410260680, 337152536, 1042186788, 170061120, 161967234, 811314176, 723435786, 121635840, 131724005, -328323024, 116447254, 1137070912, -40194144, -778759672, 854629318, -189665280, 773675251, -193072360, -230223141, 1055700480, 2092798622, -350928936, -201768035, 496947712, -332492283, 321075456, 2156727288, -29923776, 245939037, 202293168, 216217755, -31391744, 3690669318, -444514176, 1172502412, 300308544, -72828504, -526921368, 1960749908, -189983232, -199446332, 1306959056, 143774973, -241142720, 3379076347, 156331296, 737787674, 503271424, -173188530, -1860624320, 678111, -307005120, -524242750, -935430960, 685352421, 196625920, -38045449, 270050760, 2911710570, -150780480, 325529820, -2280238032, 2812139564, -283115520, -521364802, 784742320, -707568129, 1003539520, 4440645770, -241546968, -1432957320, -301181440, -1313745102, -1486708464, 2393494649, 44696448, 2262317749, -1177252992, -557262153, 301965312, 1570602332, -582123888, -390330005, 154998144, 270503469, -47517848, 143029830, -108711936, -19918967, 1224760464, -69861798, -977924608, -705872048, -716572008, -456310489, -359956480, -265055922, 236250416, -4239404340, -301686336, 121938720, -771644760, -279961515, 1012224, 1456225156, -1596869856, 248248308, -972469760, 56827602, -2693818440, 3200363302, 403107840, -6598478048, -487512760, -1515446037, 1714810752, -657178997, -1883615256, 2400630738, -778247168, 428830605, -138217664, -590463729, -95275008, -1733650073, -3177330664, -731865618, -449576960, 3630957294, -429946704, -6627403072, -545714112, 718600194, -6276313216, -383567639, -831831552, 7099620276, -2799162224, 154787112, -788129856, -2953589628, 70976304, -2367061828, -70930432, 335712519, -3277616152, 4574237896, 512516160, -924391174, -2188100024, -555427098, -1053663232, -2066603972, -1003626504, -2982540980, -172630528, -1441233, -5731658176, -884322849, -450330624, -121133792, -1271551496, -1137889809, 340799936, -6239347177, -573956280, -6110174594, 370563072, -2738185344, -479066728, 1954874456, -410520960, -3920838510, -1057600648, 1108090206, -727715840, -2535770188, -3837614328, -3040243108, 1624539072, 2628313893, -5999732544, -8207779458, 640120320, -7930870746, 2083968592, 651619215, 771626240, 7411400161, -3562989120, -2991111263, -671088640, 1184385159, -3490225936, -543006316, -1677198528, -10680433898, -151293184, -1083629664, -572555776, 305039428, 100992744, -3114703910, -3114062464, -682739442, -5131975752, 7849995160, 105947136, -9421753520, -217966984, 1500235344, -1320917696, -521941290, -1013541336, 5567618768, -1379849216, 1778359617, -5356760992, 112707742, 641193408, 3799202892, 2641770944, -4410986814, -257687552, -8184689830, 813856680, -2060971187, -165598336, -527618124, -14170480704, 3140759189, -1698541056, -1593721717, -5012941320, 6279607080, -628280704, -4148919296, 1036142280, -2132410397, -715108352, 3157079490, -3127318544, -12316497262, -663612480, 9731882959, -5338488928, -911421315, -3785172992, 5684528015, 508884120, -6979467053, 134702464, 7695803358, -651892080, -3954240476, 955514880, -8474529678, 4450473304, -2648505330, -3592168384, -6093989419, -3386945880, -9105911114, -4464865792, 815221017, -436952664, -790482791, 1016487360, -6312432043, 326665920, 5017641066, -225837056, -3010467877, -150850512, -5657894760, -1734792576, 3973228848, -2159545544, 3052853625, -1019132928, -13238456106, -2663329144, 1964668122, 1703348608, 621887043, -523118736, -5877887786, -1971748864, 160372737, -13189866816, -843724895, 366902784, -9705851388, 2485171960, -4133566566, 168240128, 17305134356, 3300495552, -2187464826, 795763008, 2418430527, -28668182608, -1609466103, 1214853120, 1734328147, -11668370896, -797345154, -1316567936, -4478444478, 1018191384, 10601676408, -2378966528, 2604301065, -11493405152, -6278301852, -3416256, 1292374265, -10807569312, 5389435764, -1067450368, 5725562637, 3282085440, -15731063242, -2697220288, 9091637235, -8337494304, -4636552158, -1360488960, 26987618368, -1295737872, 1645355565, -6490513408, 9645086486, -5787486288, -19954794662, -973086720, 6357201489, -1053792040, 31743630225, 2626584192, 8642772229, -931578032, 466484616, -9096567296, 808089135, 321553152, -6852699199, 6230077376, 10723490991, -6837034544, 14435774980, 1517322240, -4415811277, -6189402008, 1451070126, 1544578880, 8541119386, 1841785128, -5378344615, -8445603840, 21182557104, -16742388976, 18440368300, 2807431488, -7613421130, 1614144280, 9447172506, -3975581696, -4343469, 2659938264, 17563424277, -2568603648, -239545026, -17253818304, 27673652254, 239390208, 11624375252, -1967512296, 11061954513, -1618345344, 35645737789, -1729742040, -26656815412, 251133952, 7384837581, -29525354544, -830693178, 3556113408, 36727530974, -9380019296, 3387239451, -2402468352, 1020664621, 582628032, 3339470758, 4215370944, 19344346344, -15685999264, -14716924198, 1519865856, 5241064696, 1595570656, 4291486299, -10455672448, 23995275776, -1150199784, 4455353450, 1929141760, 1937102445, -27032610776, 22974921882, -1250650368, -17743529747, -5902301392, 1616850207, -4026171392, 41034640188, 1385508240, -15924105014, 14884994560, 3569402187, -5424888, 1176722248, 2456040960, -44441818246, 4193942000, 12951948357, 7483447680, 5211830120, -5482819368, -11996101741, -1573007360, 20249097336, 304363592, -33670538342, -2160406080, -31438324147, -23293684560, -7033393998, 1206243840, -915153865, -2604238560, -9190313874, 18241904256, 12025088280, -22497116512, 4521285392, 2264924160, -12556526265, 4170918416, 11779512534, -6277938560, -5088998240, 5660545032, 19408848100, -8028316160, 510614496, -35525166160, 38107674710, 1932375744, -6994282696, 11463658560, -340850511, 2409451520, 17972342546, 10509960816, -16774568867, 11893667712, 17320418163, -19147957192, 2924686569, -357571584, -1590091932, -18098541992, 735638571, 9418023936, -23631898526, 4458097224, -14143471676, -2415722496, 3420702009, -12564818656, 8077093164, 4656991104, 4223883447, 3122640040, 18079068348, -1239985152, -16530232003, -2164027752, -59874504514, 380142784, -8915976936, -1144238640, -32794197104, 869695488, 18519662717, 159351736, -2746766295, -9798083712, 24968556050, 558894384, -11857762532, 7823396864, 47825372376, 5646976384, 26966884528, 5732576064, -21525301932, 3650483912, 16918676955, 2879651840, 925191736, 2120447376, 4454757241, -1890003328, -3496980195, 33915234720, -5411859472, 2413490688, -15048235230, -975509760, 10554700086, 6173158080, 2456845781, 2239692120, -1826474657, -8097792, 18017400132, -11649801248, -3825764720, 12774958848, 3203959947, -1985986464, -1717483905, 7779758080, 4404226170, -454620816, 11961503518, 21550547520, 2200135770, -25602906416, -35343734264, -3224862720, -13075340724, 52787824384, -15020347401, 3900102080, 1074169018, 12123568296, 5920954546, -13718486016, 11430942345, 5257431976, -8706514089, 15068922048, 24849072196, -19205045904, 1474715241, 6225977344, -40950127794, -3430644840, -17591508800, 1105741312, -1102497480, 4723709832, 27392209016, 762200064, -4135434380, 13869200584, 509120478, 25418645312, -24620538473, 5854924944, 1108712729, 3596615680, 7288466211, -29047658352, -44897714183, 3439573632, -3608898840, 53019224576, 8988735861, 4365712896, 28457317670, -5748801552, 11895727723, 50210505728, 1765525734, 3068541112, -41911753489, 6654652416, -8348022982, -56796962208, 44515800504, 22393297792, 16689428518, -1238296896, -70317225336, 6305038848, -8387455365, 23628717024, 16242236452, -567810432, 49699000956, 18936494624, -11139172488, 567443456, -15813243369, -2685700152, 7079293277, 26220929216, 96755116302, -36593903168, 10568357498, -4100129280, -66879184616, 7395129392, 39380751774, 17504800192, -89097336239, 4443416784, -7224500402, 8429305856, -3436395921, 16532831776, 30890409586, 8029012032, 19158808877, 23860327840, 38790242388, 1381044224, -52308345483, 11529864, -43610098434, 45853265408, 36475546428, 7074582792, 887503582, 3602644992, 49191765470, 969070336, -11077038360, 10172411968, 8544183666, 9103118472, 21020174752, -2726399488, 28139043276, 49914777416, 17587994170, 4591650240, 3367191898, 48881396752, 4373115318, -2964504576, 28773818568, 21905482752, -108287643118, 3832533824, 19532766222, -15638995648, 644235315, 3284167680, 43783867294, 31366708080, 3556548135, 8460805184, -79696751143, -8864721648, 42042414776, 5821726720, 3144075858, 20286161504, 125528057604, 30700914624, 23335234460, 24321944864, -1085241888, -12996312576, -721921018, -21026511144, 1344398912, 47997860352, 23074991586, 65662235664, -84746779391, -5120962560, 3178151110, 63446965968, 20889231777, -16671748736, 16478646132, -5212953720, 19251777433, -6173009920, -6216024807, -59291201288, -62587642770, 28503912960, -5210526798, 23928890104, 56505562794, 5368709120, -163132282044, -9475081272, 10208182543, 27921807488, -5447736945, 4344050528, -41008705375, 13417588224, -81546227748, 85443471184, -8977291641, 1210345472, 149800988272, 8669037312, 5679991032, 4580446208, 58231636776, -2440315424, 9297403962, -807941952, -127256600790, 24917631280, 6640353999, 24912499712, -138530164248, 5461915536, 49740664356, 41055806016, 5837879385, -62799961280, 56029340477, -847577088, -9128883946, 75374028160, 99648071586, 1743735872, 41561797130, -12001882752, -111740381926, 10567341568, 31657565124, 4175530320, -175390650998, 8108330688, -38549727236, -44540950144, -1966369608, 11038793728, -5781641250, -14226876936, -24825995148, 42854087936, 52940247516, -901661936, 39033512401, -5129547264, -8198829609, -30393623136, -5385050964, -21134167552, -4264792371, 35287894512, -5184270250, 2061500416, 3881924271, 65477518640, -61923637430, -6510853440, -26722262814, 16487769496, 91235061369, 1324786688, -8723572517, 4220944992, 7055981282, 113363845632, 19920267198, -25126073512, -98711376018, 13588328448, 36240218040, 12749773736, -4676090310, 40103530560, -58361784278, -50236856640, 172516405332, 5026245632, 18308997, 33191354368, 59673353095, -8289138240, -42416771661, 17059283176, -14154554250, 5720866816, 135622650872, -25256635920, -70392245211, 25018548352, 18504515367, 98531978096, 14455414981, 5308899840, -109970230834, -77855063672, -1027227123, 42707911424, -49799246606, 7291370520, 223294455160, 30281383936, 78616185390, -45476224120, 85469339184, -4071072960, 34785095296, 55835736424, 8789305140, -1077619712, -152461127514, -61566426864, -69339299980, 5215136640, 75927768228, 31633923808, 115499133243, -7644119040, -90456754192, 67796237424, -14076849654, -35603786432, 10309029237, 21188042640, 62946683580, 28737347072, -19104339483, 48751915352, 217219430506, 27095567040, 209774986429, 72847288912, 119897435790, 35718926336, -33389320937, -6521768136, -71949298349, 3495621312, -38689847640, 6323862328, -107062180948, -8131898880, 153637401024, 50499456344, -35471117754, -2613327360, 82292800789, -40141128528, -8277977435, 1806696448, 64624355523, 24083743016, 124443610273, 1206804096, -118618664978, 45263158080, 61082579223, 13878340608, -103624538764, -31785830784, 184212064392, 17276364352, -15046078131, -24422829000, 35385957710, 8153063424, -257745641438, 105907648848, 42406262964, 21306633152, 247729998711, -15717344976, -48278613424, -13626788864, -10538910135, -4975096344, 13766110176, 4184949888, -158845238951, 47023102288, 7303593663, 15773990912, 114646833361, -1282981896, 126492370105, 105518934528, 3861805410, 6749799160, -136670407670, -2935222272, 8673319578, 77646811104, -537812109, -19881375680, -80637665828, 33068532528, -67200896268, -1345921024, -1886268546, -138441074848, -5176011165, -26403964416, 194946132665, 17499718608, -19058545296, -6366104064, -60959796610, -19347444216, -153000002202, 229345460864, -12320383203, 12875728824, -32262278217, -9718824960, -230330797316, -13874625176, -7156509894, 93346967168, -22591753653, 6378761232, -122848544816, 10532543488, -114463917180, 35827555824, -90438058983, -8145531072, 34449630085, -84813411264, 3292345440, 19031732224, -7545252626, -20834408520, 56035869526, 91947241216, -7558960905, 50226414816, -40308964878, 27330048, -181726092546, -10338994120, 39318079212, 86460554496, -183514324972, -43115486112, 22231772819, 8539602944, 6702704316, -45804501096, -363320768949, -26256683520, -270557478646, 125848505936, 1534345254, 21577762304, -45029852898, -72733097880, 249702548594, 66699954432, 86409809154, 37092417264, -79774267720, 10883911680, -253314162407, -215900946944, -178158907296, 10365902976, -161282139740, -13162844520, 167259156788, 51924107264, -40917042999, -77160691888, 141844796480, 46299890304, -40106602410, 159638357296, -17743832919, 7784693760, 5320795662, -50857611912, 19529014043, 8430336320, 64817029926, -253949041800, -105949274859, -21012673536, 153487780219, -69142177832, 11578426335, 7452624256, -161340754552, -3731876928, -375941950089, 72772538368, -15942520683, -6464713080, -10982729844, -2572425216, -130019943851, 54821593592, -46808551971, -49840619008, -97765205622, -85787927928, -33570318184, 54696276352, -19760371686, -115486199840, 167592087476, -12138577920, 200486764896, 35326490216, 98035846938, 49515216064, 54353189260, -11608561008, 33645826970, -12356631040, -178939882944, -68328955088, -195304207584, -14734281024, -140393600392, 43026756920, 19402205238, 67564830720, -241461987676, -169460456832, -108173021733, 133939111808, -10356326253, -147522946400, -228600647220, -22459451904, -129856757423, 60907369040, 191689747452, -12913154240, -149547225192, -75577380048, 333928810442, 31804653568, 4179252024, 34747752, -63742625394, -21279506112, -306245048391, -140507394216, -79746919956, 20548829184, 113307617607, 1916360208, -86212519201, 138030546432, -63910669356, -221389218032, -33383063480, -1915121664, -50474722032, -92995002016, 9064238013, 15740098368, -294500638716, -88495636104, 154757128052, 12946762752, 123504423192, -285165902312, -175746259492, 13837936320, -316648395310, 213254523296, -24958561698, -2009071616, -453122824638, -59078700648, -284831326608, 236202836352, -14996531646, 6645545424, -80393370940, -28448907264, 58866237846, -293820247792, -55798307244, 75040154368, -2037327733, -27097915608, 26528710890, 19219746816, -80528606460, -8165316968, -44303816860, -4661024256, -9620646389, -26715766064, -38913291, -33722967552, -214781321360, -154754770752, 52511604894, 125487994112, -23876716923, 117735393584, -538637224947, -12158926848, -60983081148, -41928517568, -3270612384, -12764565248, -128624082623, -34331890392, 553711473650, 83645379584, -30723024843, -191962206208, 65950364922, 9201598272, -176477342214, -35642827600, -168462373779, -15433134080, -428160020425, -15496819560, -66788844748, 216260886208, -164974714038, -183799375056, 10129236586, 10005202944, -456194049787, 141948237976, -73931004288, 47218411136, -18733342251, -12934801656, 405374557222, 32209371136, 52781610312, -328277121504, 476805889816, -11084065920, -33084269085, 127392840112, -105862639770, -119079956480, -261743295038, -28555217496, -230294668446, 43399104, 29918435562, -9413777984, 182289987717, -19648327680, -330181203742, 355534545968, -68465795076, -33551536000, -70510334736, -103615586856, -27055020213, -59867581440, -82086563916, -41694640960, 82111031017, 43862554944, 366982439281, 95968813928, 70964475111, 12584058880, -115497465615, -161992778688, -130973024292, -2434908736, -221610045366, 269364306736, -60084940766, 17283248640, -332474858016, 251506593176, -214133510142, 186349476480, -355722949468, 56267151984, -20902109585, -9649950720, 17593718805, 7321230920, 35354207096, 20833908480, 192676010140, 73522510992, 200107804347, -145935234048, -87155288872, -96200706240, 601302396534, 179976932096, -80760004101, -36170283136, -336399021493, -18119393280, -551850025151, 100452210120, 31978399293, -33367347328, 247341213454, -94236100272, -111911719324, 50223508480, -14661170532, 40711985920, -5926082344, -45284360256, -304596334670, -155270784800, -288371715246, 64226529280, 179077350541, -4084915968, 429605045678, 284201329280, -29258000928, -304861397680, 259894523684, -15459005952, -136228052219, 55954261568, 8236064556, -91709268480, -159235487974, 2726804088, 144257040685, -19275612160, -84097005570, -143778740368, 35107019527, -84079686528, 11699022803, 134196550936, -18433964934, -95149341696, -443566731233, -138563345304, -306607290896, 153183657536, 211949869320, -23397492552, 488703443643, 2860572672, -67732903504, 12720735456, -254387345040, 144788335936, -269096929136, -5885108568, 105732386062, -75344191488, 40506354288, 189055188208, -62294802684, -35664777792, 21288468232, 113147773408, -14092414830, 19325779968, -20754976234, -27365616072, -120014080354, 100518549248, 150325706736, -64616745312, -103537503430, -37255928832, -40418898634, -33791067576, 48015709659, -24981120320, -370443527822, -144632546784, 252256305344, 9919881216, 3043109034, 132241856024, 286368974268, 17312222016, -458101941361, 478996036112, 102578478084, -3041142272, 55767380331, 71327815488, 567546409604, 9153909120, -119096643978, 262353576832, -140527792517, -6957563904, 123523180556, -148157301736, -220986625410, -1274813888, -151547653436, 21974130360, -62363963312, 78384669696, -55646222049, -199748448400, 535797092201, -4471155072, -93814788529, 94862100256, -14245689348, -62587174912, -264096095656, -382602979008, 26488482020, -45175811072, 84800498103, -215735076224, -298364849134, -45860608512, 445379600033, 172202415456, -43030486359, -29203871296, 287895677984, -135349415640, 14880042015, -23037214720, 169549391160, -7401533888, 206889980145, -16963579008, 3220612945, -35638057928, -112020820992, 15120026624, -245744844296, 27975841560, 613981726832, -271321877760, -57575080719, 43294875776, 35845351027, -19307925504, -903991233, 120385881840, 85241146230, 7804078080, -10697118451, -84437600688, -54517770391, -49385264640, -332545426074, -19654766248, -363837312569, -17917536960, -431927502216, 14611797256, 262760839893, 64782336, -278742178054, -144139201056, 372647417214, 93198409984, -24608375505, 30606117760, -106899925522, -102199670784, -57802763886, -25631679576, 153482256405, 15887891712, -123696716342, 13739871240, 1057983034872, -62238064640, -188445610431, -35233809360, -20539985963, 3636966528, 311132271096, -95692028144, 207786690666, -172404380160, 327959309577, -17601086160, 146200057262, 204823251328, -106764492852, 282749874112, 548297173136, 25798901760, -45344627783, 104602725792, -228812301306, -422302595072, -426978552194, 120162779208, 434698895264, -31200816640, -71509643910, -8593352144, 530001985744, -96988546368, 337618392402, -47367636368, -164537714313, 109747888128, -878433784589, -91447538760, 498170188036, -42059455808, -245859600078, 69652112712, -314636709050, -120551376384, 586705732774, -198792577568, 22010967459, 153640367232, -257238532824, -11797721928, -210286299567, -49807818752, -21343035357, 327601022352, 471458654614, 27445158720, 1281725737574, 140732070400, -170435665161, -8845930496, -409129461194, 8819979840, 89350153382, -37789678656, 135476308782, -219137672128, 175218717504, -6097600512, 107618961132, 33083475040, -81282632679, -110953604672, -5684680378, -4072963824, 1428503649016, -203349162496, -152763158520, 196964307784, 269411812612, -46839399552, 624326201928, -8869701832, 107277178896, -28772925440, -671251041444, -58307729688, 802733554428, 232381266816, 82427047875, 359181713464, -149643437006, -27516589056, -424576142148, 28871190720, -357438314862, -424153796608, 220683505770, -71909886888, -21567698542, -34925703168, 53046039294, -227658541360, 314600678016, 45990412416, -6486695264, -95165821784, 16790950161, -401684045824, -317272589471, -14124205872, 307049468728, -24548328896, -158702970222, 335294027912, -208574333846, -53237219328, 825740526784, 66784183856, 4330063899, 454375697664, -605552114728, -356126404032, 428304349648, -179146382336, -22780572165, -133515428144, -277238734850, 9906375168, 639597992316, 562537802688, -262057987476, -50440310784, -220033460367, 67099642920, 812990045463, -189029736192, -111606297282, -129937891616, 172430662744, 4542483456, -89064374444, -397592007648, 467238627612, -151491956992, 410373857974, 89113379904, -9345334439, -4539547648, -59061550302, 126505946952, 4624083022, 21485601216, 810417030757, -56634346216, 65297624229, -209767433728, -684467240166, -774040930416, 1628670045846, 292751225344, -43455584781, -84546859984, -583987780905, 32801034240, -666566154043, 535033476928, 46826859969, -59161035136, 190065986756, -315046014192, 257469251268, -140038401536, -21528319158, 712778689912, -229671127532, -35547334272, -123312405307, 57796003216, -120918000906, -67434446848, -1197620023144, 27491167368, 972722207154, -132262654208, 286245263016, -247123276688, 1632377289806, -64232096256, 113265929224, -153270471016, 70316128755, -190882622720, -17305245781, -310321939104, 386533275428, -11048353792, -169514150004, 418466763864, -975414070418, -92238912, 1192874864823, 348880787472, 34894105155, -366826123264, -459645972480, -291804371424, 1376565062160, -56596662336, 145514765628, -7100028656, 243009970574, -28821159936, 1387608837556, -393534123760, 154590191199, -7752562688, -607559360184, 88616306880, 265071967294, -81379295744, -424738707534, -68353469328, 377309919215, -72824947776, 445367760945, -168161398016, 245474205345, 21811195904, -59552176398, -225112346208, -214929859095, -399318219328, -125186908266, -140703953360, -742397814062, -36733201920, 1548294711738, -26937535184, 728665695936, -391051174016, -811083370052, -34984922544, 1762360841482, 23716036608, 44424600255, -230190548544, 334869831772, -175243862016, -162151246264, 866301144944, 260417335122, -30660270592, 153337750300, -156262129776, 58472763934, 125111965184, -538779455874, -5153882520, -134083782574, -26273341440, -510513397298, -350270938352, 171644440203, -250933664640, 1454754364044, -28452385080, 75813835908, -67686441472, 857078016075, 637574009144, 529629000842, 70917773184, -228887712788, -336339318208, 233354850183, -46573813760, -985568757733, -25152606864, 2249700374733, -162289292032, 12595084632, -1004224460832, 969583599868, -245607316992, 1696468510442, -186681875680, 21818406645, -194575558912, -1172725039476, 8681935104, 1331587353675, 103970500608, -185022878373, 5775368144, 321325598887, 168212089152, 737779086032, -10755191296, 289534256757, -383982882816, -27949872930, -184599932688, 420160975905, -525297885312, 389765924460, 677974235128, 27317052009, 40967700480, 1037450602454, -25425208880, -119226904479, -507575727744, 795490144087, -167113854216, 190814042909, 133373989888, 39178893402, -131829169056, 507945502632, 41703629760, 410002328154, -154014219464, 230610223422, 49384079360, 370204266648, 49728198456, 1858871031538, 474329610304, -145215304605, 500701142160, 1090036071586, -228031303680, -45195308678, 41684214384, 571929041808, -191431120832, -1433211083709, -452044502352, 820049752415, -42949672960, 497889944100, 1305058256352, -18734345469, 75800650176, -506030067445, -81665460344, -205562370510, -223374459904, -1092726422904, 43581895560, 350810657740, -34752404224, 255073657662, 328069643000, 752287415760, -107340705792, 14005801320, 652369821984, -117273663, -683547769472, 551776104466, 71818333128, 2110708403910, -9682763776, 474212455479, -1198407906176, 299711549284, -69352298496, 3042028721210, -45439928256, -6467715702, -36643569664, -675678076582, -465853094208, 1364472401865, 19522523392, 747188610858, -74379231696, -761815317948, 6463535616, -816808794232, 1018052806320, 313858131804, -199341050240, -92590515199, -53122831992, 1199195611788, -199299997696, 298672771851, 1108241313984, -1089199228393, -43695324288, 485239708044, -397925314848, 962434920303, -328446448128, 420438241068, -46703035080, -114190237049, 502399690240, -719734016124, -448234723816, -170139355550, 6780616704, 1222977243043, 73031071568, 199390614687, -602992225280, 680823537957, -797184572688, -222807155584, -13949886976, -22428715806, -332494377040, -178423714848, 96015062016, -969432456312, 893923055408, 991643336298, -84538732544, 459491267585, -253260520992, 288486529488, -33404242560, 91455465177, 1403125207984, -565515539736, -64866645504, -990079228436, 308397817888, 27557944767, 356327601152, -403350737034, 15730956864, 147399489630, -88310349824, 90165710466, 46253130000, 1375060410527, 113815015488, 106551747785, 198607961184, 522297351288, -342832703488, 1051541002542, -423521980128, 2810489392314, 7213295488, -397356953346, -312268099208, -625541903420, 41036378112, 1435124575944, 65590636872, 141508746792, 243148985088, -1087393170252, 43080407712, -91680905404, 169073340416, 115870130073, 34118338968, 213866874923, -282303156096, 218672179346, 41474162000, 647872445952, -16492003328, -1229148329318, -31055394168, -254431761172, -523820149120, 120294543150, 495389099440, -337720648448, 52086827520, -494809501759, 213778102512, 52301766015, -131902155968, 1466032921166, -729880490952, -500281402166, -10598293504, 620322890814, 69788580136, 1566837871906, -33767559936, 53022496865, -56447850256, -479075303169, -906910765056, -1546244355748, -159362137584, 2063169176223, 201008588096, 43654955589, 789691008144, 730363693390, -108706627584, -377486751330, -289921744320, 1107935285076, -101998189888, 222632175522, 37408722480, -1729648319771, -320828244480, -429950835378, 466894274224, -492779745892, 401894853120, 1116234217474, -1380131242656, 96373859049, -40209965056, -1480031078968, -146471976, -166962728212, -265530834944, 31771500696, -477386824760, 731250768031, 66313105920, -463374534252, 339334173288, -1199929092642, -136474265408, 277279072111, 113236434000, -975088539070, -45766934528, 349702605639, -1084981206976, -1112465091691, 202053087360, -760435834074, 563137961688, 140719413240, -200148386816, -88175347104, -148036122936, -820671447138, -788255824768, -323894747007, -115643319848, -2414965756808, -42471198720, -273719488988, 879761846672, 546725628072, 622840509376, -357470068284, 8217816984, -2234088610065, -341663291392, -909104535234, 398393972848, -1594091230181, -58330964160, -2053958789128, -1786355641280, -848834751969, -242251071488, 1924349390690, -628929483120, -55554761262, 363809792960, -189901637946, -683754713472, -1059555754035, 32568583680, -585654643702, -278280762368, -24709154355, -446685891392, -630139164552, -70314441120, 105485708886, 8620957696, -248138474598, 1219689020112, 302658599473, 492531414912, -2230392399692, 554714399840, 324677383560, -41721093120, -2929217776386, -607422145824, -1813686286553, -253071390464, 122074705584, -923993065944, -45181333715, 61152952320, -2340376733296, 723654033536, -339026209155, -542369899392, 37164870616, 112614797232, 1465997861256, 284830291456, 318046838418, -82472233896, -179207039252, -169504341120, -39941408122, -503573468640, -137402952480, -229898776576, -770637088992, 152834715864, 673694637006, -390015322816, 524038898700, -1737755444048, 144705780687, -216764536320, -1294925863548, -1678199891432, 13786591392, -582778311296, -2853485896872, -959179486320, -2636248074720, -285751410688, 1028907217170, 267114567496, -1104300411560, 52174145088, -240347551136, 575594386792, -188845632792, -27964970496, -293137856074, 309518781120, -1420627587700, -50590898624, -9202963797, 856497447584, 1507759836491, 65055191040, -358923630754, -1229099208192, 485253248742, -403995650752, -1122163394898, 283768942032, -265370611093, 20906618880, -452913359409, -658342406312, 2144529047380, 321129028224, 289178486276, 66223819480, 467651290401, -14453571584, -753251753324, -516994844184, -1459788449025, -192669944128, 78966537363, -995548882184, -2221108143039, -9654432768, 1487026590, 948949319824, -42932482164, -362105264640, 408253334168, -488660633784, -1438026850070, -111026724864, 19862241417, 828996310112, -717829927346, 254286646272, -448895163258, -1473696515136, -638061260202, -138210914816, -755317243174, 120368625048, -1081974893983, 195382632000, -381873735252, -283087661680, -42987432923, -65224507392, 69206436005, 2061965131504, 92358954243, -847261190784, 510973953880, -339250103712, -769452121297, -170453065216, 218081515428, -1981839989688, -974190075663, 125738759808, -1071333583892, 386228907392, 114044853069, 109014310912, -2508758911466, 84311281080, -1442459497824, 39800770752, 488134845396, -110128881408, -1234365430754, -33479599104, -3451814610440, 1270761911608, -446316264081, -376184818304, -739757459784, -58428749304, 256892727390, -126191927296, -1616611621878, -917174666888, -792297470934, 10263855168, -1624544356782, -1011938960840, -240731377272, -844151476224, 1729887716626, -30894443280, -84357089691, -53998393280, -885443321808, 1093363261360, -1248626519519, 23481778176, -1290754993275, -69386556624, 500030893359, -621174488832, -2145324362946, 4302496872, 38552941216, 159051005440, -74162689965, 645101326624, -287609667776, -264548260224, -2004740905720, 537607170144, 674151013350, 10767368192, -89802245162, 15090148368, 81585665482, 1107528598784, -320159588364, 41408089320, -1265899576074, 211231715328, -1233221837609, -1559569061320, 1291285054152, -139997748864, -845569322059, 152468362368, -231608933136, 50928832512, 728105882256, 487678372880, 626210369538, 154779553728, -402168327316, 1224000017616, -581183152164, -1834763686912, -580460013130, 98563065624, 356522230255, -103005830592, 456804277785, 258098225736, -110129791004, 77750599680, -2972709863984, 1842646378528, 24980176872, 110997001408, 858264679520, 57252079152, -2306663187920, -746775737344, 120278445507, 180734029224, 112901203650, -51030089856, -215509859630, 982788358528, -94418465265, -84260347904, -672537218444, 915711337440, -2361006595454, -286620446592, -146120205744, 723504471864, 782676847576, 65164248576, -496389755259, -275597040680, -406302351210, 678507290112, 900322515388, -26338763520, 68410091876, -152253857792, 284976902322, 60362021008, 1128237474388, 166675268160, 90403477692, -448286956208, 66334836087, -735577929728, 289318747656, 60471687240, 971459048318, -401811318528, -49314815739, 322471719024, -888802881016, -218640384, 1099215305031, 1453808740368, 486469803564, 82711952960, 278421188187, -314544633696, -2121848739216, -691684435968, -103295647440, 1468114599776, -1159023187021, 344923888896, -765704128909, -177854182552, 86506918569, -68316823552, 408287311926, -53621634528, -125909442586, 366436008768, -46372065435, 2906566151592, 612763807040, 210053468160, -253061172182, 2164459829168, 118914106590, -1006788047488, 631996416687, -12274762032, -155776348248, -172622098432, 322960594986, 360238823184, 2105381734168, 581864783040, -1561258453889, -1997620388752, 59403665790, -533599635456, 1713317840482, -691278473232, 323303102928, -296739338112, -954280825128, 638194141760, -933981269802, -87071293440, -1276874646766, 2026513299256, -353034199548, 1727207575552, -232592073, 1425271258368, -1187559095777, -82927223808, -405549379827, 1290257117920, -1886722678710, 105302756160, -1773790027516, -1338073254304, 29002563486, -415392858112, -81029758296, 327336343992, 179815263250, 617285535104, 159865772742, -1134758371840, 1936088772750, -370399122432, 267761115286, 320852819280, 308635443315, -1277106858368, 593830921551, 141950663352, 2404992930370, -62277550080, -235075880403, -42566365296, 1218019554656, 406860895296, -2038251054032, -156232112344, 670924949292, -67442690560, 593066124920, -518536239408, -265214672976, 2031592334400, 39817311507, 847594198872, 13049589007, 168101388288, 1179291527422, -1227902241752, -1105653450438, 553137422656, -1990032704330, -92627410680, -3957020108698, -59620994048, -474970737600, 1290726036416, 1588646843778, 29855015424, -998716725510, 3007535600712, -29767431960, -582180306944, 512424608172, 127540165464, -1652326483567, 51717704640, 739589643432, 87861838752, 1708505467965, 20579401728, -336349842426, 1040159550808, -111656728260, -438572748736, -1863603170688, 374468415768, -527336932462, 398724952064, 13746252906, 782121644976, 3062479620264, 686303423424, 709794854058, 268562545472, -664754538771, -437570210816, -964563870452, 158082973488, -39545540864, 923889598720, 29935243683, -1340736699808, -79703952880, 97108623360, 941335987474, -1603894119168, 196788587697, -282611921728, -497057240195, -784286775504, 178828127086, -396121728512, -1212238282941, -434825514080, 3549653782848, 92868488064, 3823054375770, -269166615760, -97440268680, 98853048320, -888508117276, 1431519063552, -2892446346400, 546631640704, 242695868247, 1562433660672, 654838316384, 117874248192, -2999040386511, 1123148803136, 768347577090, -344214055360, -64880270494, -155217641904, 2334618354664, -540518645760, 321184648521, 1931695901408, -1523141499110, 1355683654656, -1563850244636, 865384173864, 47669194818, -1071512894464, -1020670105510, 82850610024, -1791341983955, 1180183571200, -1131617344203, 1828805177760, 1164796777759, 179675615232, 491504360760, 1038854059384, -225396620514, -487258952320, 2270535092452, -1533517979616, 211912942215, 103305233920, 1201926613608, 1196377801536, -2962366126468, 604619040384, 1542097406991, -2671430483536, 450614569986, -254437228544, 2046244387003, -33434016192, -1725619374101, -277982016, -1898565084072, 509941003152, -2169530133233, 170236048896, -316759560920, 2449960387128, -226461294855, 1124059153728, -820968664607, 637975359648, 5412878955900, -164390633472, 438540384204, -906460940856, -704581487020, -15330881664, -2374982236600, 689700153608, 1341873025812, -1104244371456, 943239821261, 511285354848, -775974987907, 1771113744256, -300757657176, 267064507840, 1101194876479, 15320973312, -2397043736956, 403797776256, -426957570963, 743960016128, -1691094776929, -72513904104, 4095506083780, -125920786944, 191140918479, 2356005109728, 739789889085, 707965088832, -5051808254256, -1238057024416, 2612388140154, -103574102016, -1810794043706, -988035385536, -2727282998437, 2281327218496, 285345652446, 1405970075936, -538716599876, -110703490560, 235196822232, 2533187162480, -1805737984632, -1706036186368, -434829168657, 199668493584, -3064051402242, 16072572928, 1063280297898, 3624982597104, 3863842640385, 472629605184, 133883191715, 2278650612864, -2405628078453, -1889622690816, -4055097292168, 119972253168, -519897692344, -53164363392, -195061510854, 643146967520, 6373456085538, 227591258112, 1512372272520, -470929902768, -92782689867, 2350561982336, -1429307206951, 446386457952, -210218815822, -600321234944, 834041058822, 16298621864, 3992197189349, 216783324864, 2213905118961, -212229687120, 517287839679, -153757974528, -49059231690, 644228851680, 4951790420904, 65322535744, 1047336544476, 354430534880, -667737002975, 37288194048, 188390993237, 76965171112, -1412325328041, 213726128512, 723352639512, 311306328, 6832205681, 269783740416, -1177472657718, 1718250570880, -1487007895118, 1238038166016, 5548813379006, -420092839152, 984839753556, -1003903952896, 37958025976, 191013735384, 976080616217, -941883148672, 23962596714, 4309097799576, 4408075922744, 97271414784, -4918904147710, 487864649184, 1328177667690, 335428140544, 425893118634, 26164899072, -3566909291172, 102116521984, -299080035720, 1028992660984, 242114112464, 274655123136, -1973633985658, -4429691789200, 230692958982, -669163036672, 1694570049082, 245784198744, 872574433601, 1535697649664, 567544718304, -527602919376, 2866373351508, -73612786176, 156514497727, 1411818737712, 759754168452, 285142620800, 2347653360479, 1347698990232, -1230853367688, 123465072640, 474875842590, 3425280163400, 904994326370, 123974556480, -799619888066, 534310757984, 90914181246, -1730087089664, 2840675025108, 1319797712304, -526187580704, 1470395000448, 118074113586, -81033892688, 3693439537608, -80041623552, -483689918818, 3649552398296, 776893101336, -1135585903808, 1454115688620, 591448034304, 4480032512291, -377747289088, -2923766364186, 149866738008, -231329096504, 103478413248, 2049269627468, -3242996457776, 527384687994, -257674969088, -3455456342137, -422252882496, -41824980960, 2626216972032, 17394353505, -3814447118528, 1723632516944, 88672527360, -2861534961194, 264674152680, 1182164416938, -1019142720896, 1711111311679, 846901118160, 795013967584, 952639651840, 96026799645, 2093946360304, 639818400579, 228441739968, -6649540020435, 1842357347568, -2151812280861, -347192832, 657298334944, -239347484496, -3430833588797, 75310223872, 1135145198952, -1458319901736, -499485228508, 157186621440, 768719925766, 2641449629936, 84890048166, -2844276367744, -1684052878772, 547726360608, -4814531170122, 268412288000, 3389257555308, 564082677888, 2332052107502, 828924694848, -85149169644, 216440161704, 630051330420, 478940651520, -4679505881030, 656692511328, -1828384891925, 333557127680, -29301530976, -656888248136, 3483489523006, -350900439552]