# Trace form for 294.8.a.c, downloaded from the LMFDB on 14 December 2025.
[0, 1, -8, -27, 64, 122, 216, 0, -512, 729, -976, -1012, -1728, -3126, 0, -3294, 4096, 28294, -5832, 22228, 7808, 0, 8096, -108640, 13824, -63241, 25008, -19683, 0, -41354, 26352, -46656, -32768, 27324, -226352, 0, 46656, -85714, -177824, 84402, -62464, 155694, 0, 926804, -64768, 88938, 869120, 529152, -110592, 0, 505928, -763938, -200064, -294066, 157464, -123464, 0, -600156, 330832, 667292, -210816, -833430, 373248, 0, 262144, -381372, -218592, 1153996, 1810816, 2933280, 0, 3842336, -373248, -1483690, 685712, 1707507, 1422592, 0, -675216, -3763824, 499712, 531441, -1245552, 5393092, 0, 3451868, -7414432, 1116558, 518144, -2502690, -711504, 0, -6952960, 1259712, -4233216, 2711816, 884736, 4597550, 0, -737748, -4047424, -20528470, 6111504, -14233400, 1600512, 0, 2352528, -9320244, -1259712, 4306246, 987712, 2314278, 0, 6935698, 4801248, -13254080, -2646656, -2278854, -5338336, 0, 1686528, -18463027, 6667440, -4203738, -2985984, -17246652, 0, -31450176, -2097152, -25023708, 3050976, 4488020, 1748736, 0, -9231968, -2401326, -14486528, 15625642, -23466240, 54243548, 0, -14287104, -30738688, 3163512, 2985984, -5045188, 11869520, 0, -5485696, -32494962, -13660056, -76333832, -11380736, 20626326, 0, -5692032, 5401728, 29242090, 30110592, 7939782, -3997696, 0, -4251528, -95089780, 9964416, 3333528, -43144736, 22994936, 0, -52976641, -27614944, 16204212, 59315456, -119486062, -8932464, 0, -4145152, -18016884, 20021520, 93825492, 5692032, -148834062, 0, 22502610, 55623680, -10457108, -10077696, -28633528, 33865728, 0, -21694528, -101405976, -7077888, 70589570, -36780400, 10297044, 0, 50230718, 5901984, -208897256, 32379392, -31157892, 164227760, 0, -48892032, 18994668, 113867200, -79198560, -12804096, -22494736, 0, -84493108, -18820224, -103743072, 74561952, 113070088, 10077696, 0, -34449968, 40059630, -7901696, -88447044, -18514224, -150174512, 0, -46102689, -55485584, 302873796, -38409984, 53137346, 106032640, 0, 21173248, -136350742, 18230832, 64556544, 42706688, 101623248, 0, 226801992, -13492224, -405053090, 147704216, -14348907, -53339520, 0, 33629904, -69484728, 23887872, -145613484, 137973216, 30806460, 0, 109943680, 251601408, -93200436, 16777216, 275131590, 200189664, 0, -24407808, -30147066, -35904160, -483995952, -13989888, -35876052, 0, 67572630, 73855744, -247374526, 19210608, 228286608, 115892224, 0, -125005136, 63999892, 187729920, -355115746, -433948384, -34012224, 0, 228167162, 114296832, 213791228, 245909504, -73219032, -25308096, 0, -23887872, 390211763, 40361504, -124133850, -94956160, -378816342, 0, 81409624, 43885568, 19919196, 259959696, 339608640, 109280448, 0, 610670656, 554268690, 91045888, -101678460, -165010608, -633813676, 0, 384301800, 45536256, 390195368, -43213824, 1004441750, -233936720, 0, -240884736, 242974566, -63518256, 41850248, 31981568, 251646588, 0, 628919032, 34012224, 197691366, 760718240, -116268642, -79715328, 0, -26668224, -28351660, 345157888, -62485506, -183959488, 140787512, 0, -1016754606, 423813128, -187263846, 220919552, 47215872, -129633696, 0, -474523648, 357860160, 955888496, -970493652, 71459712, -884144662, 0, 61529058, 33161216, 1090461270, 144135072, 468764992, -160172160, 0, -750603936, 1033729216, -45536256, -399787755, 1190672496, 498501729, 0, -181010180, -180020880, 242183104, -444989440, 113500926, 83656864, 0, 80621568, -1437687362, 229068224, 465659604, -270925824, 129272604, 0, 1201689028, 173556224, 849154752, 811247808, -630858560, 56623104, 0, -564716560, 675640116, 294243200, -1421858066, -82376352, -3073860160, 0, -121176540, -401845744, -459186528, -47215872, -70496934, 1671178048, 0, -259035136, 2023221378, 249263136, 145846656, -1313822080, 64835802, 0, 86742568, 391136256, -1437263930, -151957344, -421892334, -910937600, 0, 633588480, 657957224, 102432768, -1464575796, 179957888, -86209788, 0, -1182543090, 675944864, 385751808, 150561792, -1789340854, 829944576, 0, -596495616, -85414824, -904560704, 604657464, -80621568, -71639378, 0, 136220076, 275599744, -2414849920, -320477040, -194917464, 63213568, 0, 707576352, -2080181332, 148113792, -305328180, 1201396096, 877363974, 0, 1786059490, 368821512, -157562328, 443884672, 2061013464, -2422990368, 0, 307279872, -2243079686, -425098768, -556910802, -848261120, 2602543442, 0, -712556816, -169385984, 153684864, 1090805936, 633468788, -145846656, 0, -516452352, -789536430, -341653504, -937925648, -812985984, -1405720948, 0, -214374114, -1814415936, 220552048, 107937792, 267941964, 3240424720, 0, -1181633728, 560901100, 114791256, 3929324552, 426716160, 2567424060, 0, -3289035972, -269039232, -1170070076, 555877824, -90005256, -191102976, 0, 1164907872, -4306303412, -1103785728, -620863272, -246451680, 2563922328, 0, -2504473340, -879549440, 1430369307, -2012811264, -4203859278, 745603488, 0, -134217728, -437513724, -2201052720, -1736474800, -1601517312, -535501824, 0, 3226123674, 195262464, -4507695714, 241176528, 5463516796, 287233280, 0, 3871967616, -1320084864, 111919104, 8397824153, 287008416, 486455868, 0, -486699444, -540581040, -1137069768, -590845952, -2533288284, 1978996208, 0, -153684864, -6586294122, -1826292864, 4018519674, -927137792, 525362012, 0, -1717485300, 1000041088, -607570470, -511999136, -919216712, -1501839360, 0, 2840925968, 282341916, 3471587072, 4942642582, 272097792, -2897189304, 0, 773105256, -1825337296, 3383078164, -914374656, 846155156, -1710329824, 0, -1967276032, -2246350758, 585752256, -681093804, 202464768, 2737961352, 0, 6870502240, 191102976, 748295774, -3121694104, -1905918390, -322892032, 0, 993070800, 297594792, 759649280, -278020188, 3030530736, 6172941292, 0, -1037069568, -651276992, -1356229386, -351084544, -10042491834, -159353568, 0, -2079677568, 5640225912, -2716869120, -1322442384, -874243584, 448599862, 0, 841263084, -4885365248, -2252489294, -4434149520, -891499728, -728367104, 0, 813427680, -1654129152, 1320084864, 3514170126, 5070509408, -512856036, 0, 3780665834, -3074414400, -2689663108, -364290048, 2138361120, -3121562944, 0, 345710592, 2836611581, -8035534000, 607357872, 1871493760, -2425191916, 0, -6918236248, 1927077888, 2281313916, -1943796528, -3836921472, 508146048, 0, -334801984, 2801062944, -255852544, -5499586990, -2013172704, 1359307300, 0, -3052892376, -5031352256, 7291846488, -272097792, -675299504, -1581530928, 0, -6085745920, -996883962, 930149136, 547538440, 637722624, -1081610010, 0, -13511781244, 213345792, 7799360450, 226813280, 2388070188, -2761263104, 0, 499884048, 4492698560, 1471675904, 4054711824, -1126300096, 843431160, 0, -6852306334, 8134036848, 1244772603, -3390505024, 7657038090, 1498110768, 0, -1767356416, -8177592492, -377726976, -5526750756, 1037069568, 1906328324, 0, -1434708342, 3796189184, 919250316, -2862881280, -1519270556, -7647107968, 0, 7763949216, 6617712856, -571677696, 4405206036, 7073157296, 3681470034, 0, 6819665110, -492232464, -1905250792, -265289728, -1743026688, -8723690160, 0, -1153080576, 12169941998, -3750119936, -2743827696, 1281377280, 5068707840, 0, 385948464, 6004831488, -6123653784, -8269833728, -2000250480, 364290048, 0, 3198302040, 10936433430, -9525379968, 2615268314, -3988013832, -12119316712, 0, 387420489, 1448081440, 26222992376, 1440167040, -13045326150, -1937464832, 0, 3559915520, -1167843952, -908007408, 2275871340, -669254912, 1876087656, 0, 2134110048, -644972544, -3964385364, 11501498896, 3931564068, -1832545792, 0, -3725276832, 20417709984, 2167406592, -831774420, -1034180832, -9312727504, 0, 8047591422, -9613512224, -2968479360, -1388449792, -5617343426, -6793238016, 0, -6489982464, 2516411772, 5046868480, -2085954792, -452984832, 8926527038, 0, -7428552930, 4517732480, 17986566506, -5405120928, 2950572096, -2353945600, 0, 11374864528, 3460766232, 659010816, -3888444032, 24590881280, 813970782, 0, 3567534980, 969412320, 13158819108, 3214765952, 13067890704, 3673492224, 0, 377726976, 2605302180, 563975472, 968653404, -13369424384, -2500988670, 0, 14971826688, 2072281088, -1824461010, -16185771024, 1501494280, -1994105088, 0, -1166773248, 6679112202, 10510576640, 11211856474, -518686416, 23819361596, 0, -6163738416, -693940544, -11600953160, -3129090048, 20600999312, 11498111440, 0, 1215658752, -20292141586, 3375138672, -5559294872, 7287500800, -1727997084, 0, 20219455068, -5068707840, -3747994534, -5263657792, 9588125142, -819462144, 0, 11716606368, 2805382192, -1439663104, 918330048, 689678304, -20322373256, 0, -15539722993, 9460344720, -6160513374, -5407558912, -6463150202, -3086014464, 0, -1204494336, -5772363156, 14314726832, 9311968960, -6639556608, -386409950, 0, 1976913864, 4771964928, 4642442910, 683318592, 27330733564, 7236485632, 0, -4837259712, 18433380664, 644972544, -14577299564, 573115024, -10535717601, 0, 3808989888, -1089760608, -3607391496, -2204797952, 3351613950, 19318799360, 0, 2563816320, -13028744186, 1559339712, 10228041234, -505708544, -34634824314, 0, 34034588396, -5660610816, -2198059848, 16641450656, 4781482248, -1184910336, 0, 2442625440, -537818292, -9611168768, 11761990656, -7018911792, 11446710024, 0, -9169433280, -14288475920, 1929412224, -2950572096, -8320303404, 1260498624, 0, -3551077376, -18157755564, -16488107712, -27863911788, 19383922944, -14965254630, 0, 32105038776, -2458238976, -5457809104, 17944637488, 2745318420, 3400790144, 0, 4455286416, 28245375544, 6786088960, 17112969252, -20820347536, -12011142336, 0, 5420639074, 5700454528, -10376148600, 1355087872, -10297418298, -1229478912, 0, -8726447488, -10535274936, -5067750304, -3493290416, 1166773248, 39664794022, 0, -27119927250, 4131618816, -2862940894, 6316291440, -16914596160, 2733228032, 0, 7503405184, 6842471524, 6503887872, 4638014940, 11245767584, -6560313282, 0, -25028279254, 1714992912, -12371529072, 14515327488, -1129956696, -1764416384, 0, -863502336, -25335831775, -2143535712, -6794457876, -25923397760, 8611927540, 0, -51329233768, 9453069824, -16980813864, -4487208800, -36253196004, -918330048, 0, -31434596416, -5337666882, -3413729280, -35797372926, -20539392480, 2532722280, 0, 3139253334, 26312287776, -48901986216, 2152313856, 6128147596, 9360560608, 0, -4447022592, -100687986560, 720042048, -6898821040, 1528823808, 765494820, 0, -25485465232, -9319262976, 5530307986, 34450427296, 1687108662, 8830285824, 0, 4966906176, 18880359848, 1971613440, -3801262824, -20511378624, -6536499048, 0, 18785719442, 20035786720, 27452374362, 7036395520, -33124282182, -11442954456, 0, 16102490112, 5056123842, 33630874224, -52931812772, -5964827904, 46578828938, 0, -1274828544, 1073741824, -9846244254, 3500109792, 11765713824, 17608421760, 0, 13891798400, -25781468640, 12812138496, 62213991642, 4284014592, -9662224320, 0, -23581068420, -25808989392, 18255483168, -1562099712, 26203328604, 36061565712, 0, -1929412224, -2744357792, -43708134368, 23871905874, -2297866240, 19554281102, 0, 13805737332, -30975740928, -1661284566, 10560678912, -10308159176, -895352832, 0, -67182593224, -29442454290, -2296067328, -37282159858, -3891646944, 9162995560, 0, -12656654784, 3893595552, -4652720600, 4324648320, -42805917926, 9096558144, 0, 4726767616, 3544616756, 20266306272, -58612011764, -15831969664, -27910688832, 0, -16858805592, 1229478912, -57487073280, 52690352976, 10794269385, 14610342912, 0, -32148157392, 57642021024, 7417102336, -13459546683, -4202896096, -77811723308, 0, 32478021262, 13739882400, 4887274860, -8000328704, -6124034914, 4860563760, 0, 4095993088, -6538943808, 7353733696, 7999457608, 12014714880, -10790539368, 0, -3064525002, -22727407744, -23881644294, -2258735328, 20774811640, -27772696576, 0, -39541140656, -18321290464, -2176782336, 35242100790, 23177514432, 38817558774, 0, 14832566576, -6184842048, -22081890860, 14602698368, -12572809308, -27064625312, 0, 7314997248, -34037064774, -6769241248, -3490360308, 13682638592, 14404200800, 0, 36950603112, 15738208256, -32445603756, 17970806064, 32651162824, -4686018048, 0, 5448750432, -22927178304, -1619718144, 6482756212, -21903690816, 3999072384, 0, 17033181120, -54964017920, 64938398880, -1528823808, -64677521842, -5986366192, 0, 24973552832, 7823408940, 15247347120, -18525482040, 2583136256, -18242283132, 0, 61379515020, -7944566400, -16634790524, -2380758336, 38390167782, -6077194240, 0, 2224161504, 9460201708, -24244245888, 82994224320, -49383530336, -33464101632, 0, 9432086928, 8296556544, 3271766580, 5210215936, -54571017374, 10849835088, 0, 2808676352, 12398036256, 80339934672, -512387916, 1274828544, -6438569676, 0, 1903417218, 16637420544, -94215696482, -45121807296, 27669843024, 21734952960, 0, 10579539072, -4357920952, 6993948672, -74077651630, -3588798896, -54626977206, 0, -49416476980, -6730104672, 108715054784, 39082921984, -3937859712, 18019914352, 0, 35473196160, -14980149290, 7131997824, -1750566654, 5826936832, 43861970406, 0, 31947330240, -6507421440, -2342049336, 13233033216, 84259956312, -10560678912, 0, -28113361008, 38806126110, -40564075264, -77209061706, 4102848288, 16304032032, 0, 11391093018, -30245326672, -8477136816, 24595315200, 90327537874, 21517304864, 0, 2914320384, -41979524860, -17106888960, -7018926376, 24972503552, -17764845048, 0, -38327052616, -2765684736, -19759329522, -22692892648, 39543546492, 64284272000, 0, -4858862976, 3758388120, -14971950080, 2327664276, 19401535328, 84581195964, 0, -14371941300, 55345889984, 31928663430, -15416623104, 13413128960, -18250511328, 0, 15550372224, -10415298816, 30695371776, -7264059264, -4065168384, 25651023088, 0, 48312203058, 2678415872, 18578761122, -22408503552, 105523544656, 2046820352, 0, 43996695920, 116002348596, 16105381632, 33566053980, -10874458400, 2306200248, 0, 66783088410, 24423139008, 87063219052, 40250818048, -16325751528, -58334771904, 0, 2176782336, -5560296718, 5402396032, 1934263206, 12652247424, 87649184810, 0, -29713856712, 48685967360, -3677942052, 7975071696, -106280223316, -7441193088, 0, -4380307520, 65200947840, -5101780992, 64171997220, 8652880080, -59047506144, 0, 5262771528, 108094249952, 14946241176, -1706766336, -91568504186, -62394883600, 0, -1814506240, 18597027906, -19104561504, -26852388992, 22090104832, 56164895964, 0, 38405600376, -3999072384, -43240967424, -35941588480, 8243860860, -11773407232, 0, -32437694592, 44493608400, 9010400768, -23688827298, -6747449280, -106493636256, 0, -30179692172, 54818450672, -48223606230, -65072294784, 85407444608, -9958180824, 0, 27124040192, 4254182856, -61256304720, 27850966176, -11984886144, -72494602880, 0, -55647363528, 14138851328, 43944643750, 65420739936, -21882551808, 3021815808, 0, 44214006048, 153274589696, -8296556544, -87584987337, -15250626592, 60563151522, 0, 30332721302, 11477666736, 17453611824, -30369513472, 15036591654, -7354002528, 0, 22903050240, 22952295886, 12154164448, -70268672934, 61176863744, -43324121012, 0, -32979461320, -62111593728, 19239034032, -52941702848, 29135082744, 4573421568, 0, -35241648288, -4149491328, -56585258368, 31827578112, -29451760272, -120434637064, 0, -17103657276, -54557320880, 90543835200, 3937859712, 27836393764, 15242006336, 0, 2122317824, -33763695870, 13944213504, 152592145048, 69789521280, 21317483610, 0, 26082529816, 9224644608, -13461324996, -97359535984, 25323992496, 30000959488, 0, 21950621568, 43808862304, -10251018240, 37954465596, -40549662720, -134753198364, 0, -113599804354, -3087587712, 5788101078, -48038651904, -130317203618, 48989230272, 0, 66158669824, -5954905296, 16002003840, -125352896936, -2914320384, -4541876240, 0, -7234433028, -25586416320, 47605835086, -87491467440, 136834262664, 76203039744, 0, -20922146512, 113264991132, 31904110656, 187869887622, 96954533696, -15144329700, 0, -24688115712, -3099363912, 94872473876, -11584651520, -106091762904, -209783939008, 0, -11521336320, -46215593724, 104362609200, -69320449620, 15499718656, -21680991948, 0, -7815739568, -28479324160, 88803971244, 9342751616, -42200213372, 7264059264, 0, -18206970720, 31591892052, 5354039296, -2067463686, -15008701248, -182372519828, 0, 2430141912, -17072880384, 73379360688, 5159780352, -45342264226, 31715082912, 0, -92011991168, -134295902418, -31452512544, 41432254080, 14660366336, 116270192124, 0, 24439756716, 29802214656, -83662279872, -163341679872, 16763308344, -17339252736, 0, 6654195360, -15813149704, 8273446656, -69225902856, 74501820032, 29033589128, 0, -70811110860, -64380731376, 67620780180, 76908097792, -13345155516, 23747834880, 0, 11107598336, -38619971289, 44938747408, 87522367700, 54345904128, 52706946630, 0, 113504200506, 51919859712, -54894470576, -20131294176, -260556903572, -40374947840, 0, 16687638336, -77325268472, 3623878656, 12160805364, -71412216304, 11812870548, 0, -125370125440, 59428423440, -13373998472, -36141859840, 46884819600, -143892532048, 0, 43240967424, 126615634950, -23604576768, 14458549248, 18831564800, 262842090166, 0, 47603834896, -90998916224, -87105339198, -27686129856, 224757860904, -5272086528, 0, 31107552256, 121707784278, -196727050240, 122541893500, -6511766256, 235729859424, 0, -147514953492, -28540279840, 168551985508, -7755298560, 57715422402, -105270552864, 0, -25718127616, 119877648976, -104543125632, 125565281636, -29387937792, 35642291328, 0, 105715543944, -3021815808, 29642897052, -20842417440, -226741252131, -4511803776, 0, -7749227232, -79440078056, 106955395072, -13134308436, 20007909360, 5105730256, 0, -232373010602, -119774613504, 13140884988, -16578248704, -179585992458, 14595688080, 0, 129486168192, 30700883736, -12011954240, 240873710688, 15952840704, -303405829354, 0, 68398783668, 9334185984, 141210575218, -53432897616, 76728121904, -84084613120, 0, -89694851792, -27582279772, 4149491328, -66027448642, -190554892768, 177829941294, 0, 53913034152, 49309907328, -241619873316, 5551524352, -108500031198, 92807625280, 0, 25032720384, -417431383040, -164807994496, -14184774324, -91984891520, 207509022410, 0, 32884901544, -9725270016, 46372103100, 162337132688, 13719943296, -27001109376, 0, 44474358976, 16404402690, -58300006400, 130083079700, 13823976672, 98313250176, 0, 24818851224, -161755640544, -3458902520, 40549662720, 213398674966, 29983956272, 0, 42109262336, 77249837984, -76705001136, 244075652896, 6555697152, -7623231732, 0, 115227569476, -93732850944, -264531087934, -22443057536, -133451349714, 11517304832, 0, -7346640384, -72979861036, -5517426432, 78224111208, 162578986048, 161188081600, 0, -170513652245, 124317783944, -20873841912, -75682757760, -124044061932, 49284106992, 0, 43260471296, -91343110428, 51705201616, -55629793320, 24688115712, 110171976266, 0, -22846189212, 9635954688, -268157176650, 46178905248, -16047659404, -114517814656, 0, -74495751680, -14029550520, 53116452864, 5760336384, 3091279600, 60651470466, 0, 114771687894, -15815310912, -27595193368, -38175719424, 18389532708, -37139543280, 0, -5466548736, -580832530180, -218645868512, -73924956504, -57891885056, 220270180622, 0, -84074413196, 38698077696, -185503560480, -147467045312, -29592995080, -5159780352, 0, 116618396512, -20203985898, -4584920192, -87232762578, 84285740808, -118400225544, 0, 51459796530, -30471919104, -45355734528, 8718084864, -167971610886, 28859131968, 0, 17638383616, -107865648764, -26812911600, -224702127796, -154550394880, -8035059384, 0, -402719819600, -20510530560, 127499650662, 104229953488, 7506545076, -12474717696, 0, -81824329872, 196551467024, 4045668352, -166669414884, 277078594512, 144297821976, 0, 133036274940, -272276707168, 28000878336, 45284886528, 34465664220, 17584478784, 0, -133131605248, 36618193422, -38251857984, -242993170976, 9479282688, 169263250910, 0, 271147279518, -19541003520, -48845756892, 4302546336, -77229479112, 76889350144, 0, -94095925248, -104868047140, 56151294336, 24353940630, -91573680192, -152286099624, 0, 96230857360, 73355466240, 126114964352, 114307807360, 35705944368, -15435297792, 0, 23604576768, -15951120518, 66562427232, -12112196274, -10083988992, -48774106110, 0, -169565331048, 28408619008, -22714103268, 145262044512, 306136714260, 131904861696, 0, 222911294304, 60817210938, -155071383552, 408901839360, 119722037040, -263706983736, 0, 24070492656, -256840310208, 7821129024, 19665911808, 93830039290, 43662472832, 0, -143557099904, -31133175552, -21962547360, -86193346920, -27206321152, 44661487104, 0, 29546338688, -35642291328, -23270875232, -225963004352, -94882593402, -54288711680, 0, -136903754016, 102194341400, 166562780288, 13847112972, 96089138688, 141820868376, 0, 587147043309, -43365112592, -102077977518, -45603636224, 121840924324, 83009188800, 0, -10840702976, 72620903916, 82379346384, 53612360692, 9835831296, -401337196814, 0, -57735750240, 69811579904, -175397858164, 84282199488, -345133255620, 40542002432, 0, 27946323328, -47076878152, -9334185984, 354670994226, -317318352176, -76588512687, 0, -133229302642, 216959418000, -212890592264, -33052950528, -16398662544, 22903527152, 0, -50530331520, 15771257688, 135316769280, 65480181732, -21865824256, -363574289370, 0, 38884510080, -60027241472, 186792378696, -54739772192, 146606061416, -52031102976, 0, -37104119520, -61595475732, -89966140672, -104708824170, 52482506256, 120919894744, 0, 103596879744, 200226234032, -347814688764, -13719943296, -585905514880, 98972232576, 0, -116122619904, 499027198746, 9039653568, -76964744320, 14115331072, -75628699488, 0, -456306831160, 6908018688, 196238639212, 202686654200, 148488848730, 17148285696, 0, 54355663008, 82385791488, 207387182080, -36701297100, -68895420320, -133409904436, 0, 199313979686, 410633870144, 82428094152, -75624558592, 101579251212, 135846510912, 0, 35897670400, -196879855176, 290025568032, -47722350584, 7346640384, -173466684052, 0, 18233086608, 251476771328, 258083710722, 42701335056, 243136891504, 27309834240, 0, 286378983408, -375010939520, 164315139840, -316380015200, -20261778240, 26915866974, 0, 25205573124, -25114026672, 238619558832, -210498302208, -14783537880, 391215889728, 0, -17218510848, -94951397904, -49025180768, 29203470270, -74884484864, 194256203274, 0, 238027993584, 35576180736, 364818093588, 805503892480, 150548410524, -5760336384, 0, 55190568320, -210582732150, -12230590464, -8600625948, -6123958560, -132811839276, 0, -64477895076, 203883721856, 150620070744, 74554103808, 280300474886, -44242463888, 0, -275603418368, 613361237766, -13496869296, -196210211120, -70642286592, -121302861120, 0, -216837529692, -39735249408, 246833008116, -151042878784, -109477219248, -15772907520, 0, 30410102592, 37765767188, 164091028992, -22772641320, 52291992384, 17793292032, 0, -491744407678, -150285755536, 185012271018, -160286293760, 490420190208, -219618994896, 0, -56291164160, -33608860281, 264994257456, -548172515684, 91543635648, -477200863190, 0, -206740028430, -128819920896, -207170383632, -40448990736, 10582593296, -269046993792, 0, 423454502176, 438454284848, 47718623232, -91410773340, -372630631504, 220794997284, 0, -175346199460, 10198628352, 271892241600, -8589934592, 149222270412, 78769954032, 0, -28000878336, 359364854030, -94125710592, -51470864748, -140867374080, -522392885938, 0, -158895962944, -111134387200, 38737125234, 206251749120, 441012690768, -102497107968, 0, -497711933136, -24819758532, -34272116736, -570095772482, 77297794560, 95719236088, 0, 41020305012, 188648547360, -341064531172, 206471915136, -53840837376, -146043865344, 0, 12496797696, 386824918162, -209626628832, -613347054820, -288492525696, -178678247112, 0, -30444553616, 15435297792, -26535112202, 21954862336, -118940562972, 349665074944, 0, -190975246992, -10517594136, 18382929920, -99399690918, -156434248816, -549122983164, 0, 102622847712, -110445898656, -184130957970, 247805927424, -144270256980, 13290276528, 0, -84485431296, 51441771384, 82465273408, 806621202232, 7162822656, 490854409294, 0, 47061720576, 537460745792, 61356516260, 235539634320, 297250652280, 18368538624, 0, 298257278864, -71436644840, 31133175552, -487976771688, -73303964480, -328588433946, 0, 765357901410, 101253238272, 379931097076, -31148764416, 74083347792, 37221764800, 0, -34597186560, 344777562538, 342447343408, -136855111680, -72772465152, -109227916254, 0, 645155223760, -37814140928, -10420608528, -28356934048, 154166695144, -162130450176, 0, 468896094112, 165338652168, 126655757312, 96553636570, 223285510656, 73768210608, 0, 54006762960, 134870444736, -889851279744, -9835831296, 399987806398, 459896586240, 0, -421522823808, -8740004116, -86354155080, -50833486616, -116882743296, -295283702610, 0, -71882169936, 257185259136, -45784311804, -461136168192, -70612244478, -59336818688, 0, 107676373464, 63605327372, 33623168768, 327221551224, 622493786464, -57196266488, 0, -294611690240, -259824170096, -10460353203, -109919059200, 211404023072, -39098198880, 0, 64002629632, -708020794152, 48992279312, -23779930608, -38884510080, 361756843908, 0, 352223806050, -32767944704, -179268028416, 52311550464, -71907827524, -58829869568, 0, -63995660864, -335467000984, -96117719040, -226621281359, 86324314944, 31531786704, 0, -228759378514, 24516200016, -253782122504, 181819261952, -61448526180, 191053154352, 0, 18069882624, 683186898662, -166198493120, -50654366712, 222181572608, 158272618290, 0, 126984037880, 316329125248, -57620971296, 146570323712, -499477832000, 17414258688, 0, -281936806320, 107038404828, -185420115456, -417243655210, -310540470192, -5844684576, 0, -106152229836, -118660532608, 42746196868, 49478736384, 217899257780, 176655126880, 0, -116821586944, 373513429812, 100582474464, -85631394908, 216517002496, -551278169568, 0, -19222604016, -58519977984, 71436619020, 272296518192, 22457909340, 54153929984, 0, 27922882464, 69223040640, -109461108736, 251443642608, -115233606400, -338431513348, 0, 829996285782, -295604824896, -217284968394, -125905666048, 645861118502, 259564830048, 0, -143766448512, 80148942720, -261209302592, -272541545064, 37488144384, 507983045590, 0, 151668272502, -43590003456, -273655721692, 183417426432, -760688414512, 12957745152, 0, -51862049696, 155649177696, 175229526528, -210651828994, -31992579072, -67943117844, 0, 928441664058, -136265448960, -410396164156, 439712143360, 56320779384, -519507191040, 0, 12230590464, 317510299924, 517420174736, -241016230026, 47890929536, 666936167706, 0, 536169003720, -199788422656, 200570929110, -62587271520, -86931931552, -121978776960, 0, 148203856320, -485637295662, -20665090048, 85507025296, 145938265056, 2230212980800, 0, -79665446592, -491036120160, -293298487992, 63556531200, 442111914748, 133078324192, 0, 19046066688, -304625218602, -307121342256, 77283192136, 48617553920, -93440688264, 0, -803589236364, -17793292032, 1200124775938, -75681613664, 104987988864, 193953967104, 0, -663953794560, -1064735176012, 395068242688, -21977211114, 267712813056, -1113069251664, 0, 465255277812, -75456695424, -96323444460, -66372452352, -145122584454, -26174132640, 0, -41681727488, -355288115916, 436568138992, 1534766947112, -86798680704, -114426929056, 0, -352833049008, -22469410816, 1546316576000, -99184290048, -958171644476, -642719477376, 0, 4099103328, -383358580656, -10198628352, -229384217926, 51508557408, -70343158860, 0, -652924844586, -15227337744, -466128524448, -133099364352, -26153641908, 753725571856, 0, 360974458368, -30290987618, -221358744192, 67526694090, -173879623680, 216512468494, 0, 26907349856, -84636312576, -404239320576, 34863367616, 755603735360, -55951589376, 0, 592621213040, 49260447270, 28710391168, 32688919608, 437015817648, -223025926568, 0, -40540345560, 395331815840, -14741344740, 53840837376, -699074512128, -869720438272, 0, -312663375872, -883418589454, 31502877696, 103893360648, -144159314816, -180336029454, 0, 426635435792, -283785569280, -290753659550, 119841194320, -302720124798, -57055982592, 0, 14004533232, 89508408528, -46615494656, -643122763092, -350895763248, 479377595344, 0, -871385673554, -255578641920, 166420937232, 52059371520, -1087846226450, 18736394688, 0, -105864265728, 313225735320, -674079650496, 1167844698424, 84485431296, 175604972544, 0, -556226981424, 224906888064, 151976606144, -310449008880, -401262388584, 324512602112, 0, 617672493648, -1137225468388, -32822786304, 1012551308160, -130432256256, 547887822822, 0, -142748549272, -91128744144, -764665404748, 241962613376, 150100961544, 67817094528, 0, -196762521600, -349648408102, -722620302992, 46655921268, -172138438912, 301502612418, 0, -98913613144, -23314563072, -545925286836, 335836198880, 316995080976, 136855111680, 0, 56151411008, 101195852418, -199780028416, 99759708560, 142118760384, -155605612032, 0, -258879378834, 306616420928, -525369016264, 22125477888, -306508281552, 158074636176, 0, 181543141184, -129760050420, -316348371936, -210912671592, -514274176000, -75745319184, 0, -467830565440, 38870903808, -220662995820, -30067104960, -24794911296, 119775600640, 0, -18621314208, 312798524016, -155212282624, 548704077912, -676649567712, -53774994152, 0, 829393850026, 114975530400, 419572520811, -442767119872, 1298240971270, -255429307440, 0, 123332984832, 166333861098, -107305031680, -45439427644, 146004090624, -919412454828, 0, 174505055454, -124402977792, 618448894768, 83322390528, 161374008620, -245562974208, 0, 58112474112, -684460549608, 32521347072, -512870831916, -205208184704, 155853805212, 0, -1130564922002, -386497624464, -622537414216, -21427326976, -251423161920, -148630088976, 0, 179268028416, 908565203446, -844188357248, 10433068650, -16374562816, -157021224468, 0, 137986950904, -351973567360, -53376674328, -928018788768, -2159789442608, -128843053056, 0, -268528431840, -125345958570, 86995667200, -251620100352, -18449601984, 900134449400, 0, -737929806228, -534264707280, 564780928260, -195385112064, 103496242260, -696505752416, 0, -322006544384, -65331222528, 130606012224, 653012822256, 466678175232, -497701277928, 0, -846653081416, -17414258688, 552348828350, 44482373744, 393587088228, -43219168256, 0, -15474105648, -753494230720, -101217979392, 284464375227, -701193478480, 347326770376, 0, -549938877108, 237710853696, -102842726976, -389487738880, 496936422118, 29423536416, 0, -63800573568, 97399570392, 850241786528, 666549049112, 59529544704, -445204188122, 0, -90493576650, 35042460160, 86243162370, -521607582720, -772426257720, 40814247936, 0, -513375977760, -329341987904, -69223040640, -229523615904, 472380049152, 351776093022, 0, 571827629242, -42102172224, -161050353408, -864753999616, -276157113318, -119569929408, 0, 13654130688, 1205725584944, 732548033488, 935140256478, 499159068800, 1024534546666, 0, -1160457345896, 14516049920, -918933886692, -148776223248, 409913727080, 152836492032, 0, 214819111936, 59347615896, -176720838656, -1341133994046, -449319167712, 1296625051604, 0, -129100020696, -307244803008, 445853867144, 31992579072, -59377332168, 345927739392, 0, 287532707840, 827375694460, -65950886880, -737540775520, 94187257856, 14521093884, 0, 589421550804, 259501556736, -676892603566, -355948867200, -317573747712, -72083206144, 0, 189510618384, -1618247920748, 53979594240, -309061170648, 851949090048, -404736128816, 0, -410151196510, 241437537376, 247574698560, -438547605376, -475919717958, 385788849840, 0, 520578358272, -52094130048, -683259556864, -366085693780, 79665446592, 127173004660, 0, 224648191908, -216992321536, -803527882884, -34033462848, -765778241804, 490050437760, 0, -222807729408, -256471931120, 95879089152, 1070028498954, 579956823040, 490259400228, 0, 70318544736, 445178908224, 1109331713936, -113110810624, 752325618276, -351557150000, 0, -523365919488, -272331303286, 175060414464, 404061875010, -24174526464, -89094250658, 0, -935843641212, -353712048384, -866836046952, -1226196717568, -209533206600, 66372452352, 0, 700679898696, 147360845808, 122005012736, 757041209822, -484505212176, 264125455608, 0, -74123597340, -242661770416, 179670253224, -91821333888, -1043129624438, -139628894592, 0, 242956107776, 1585922957730, -120292733232, -112144438864, 58832020224, -762625139688, 0, 116765504640, -183224401920, -31176137520, -183618367088, -462050169804, -97233315584, 0, 562149383472, 1343635578064, -489414909952, 324300843072, 346592968096, -2690470235320, 0, 353098896384, 263835690560, -146357254998, 496892749824, 455059578590, -153912272256, 0, 423533622784, 280156012200, -233080661952, 2005823253280, -36587372544, 603002395004, 0, 278030294046, 281933186304, 1916252263002, 33195930624, 964407238264, 452682066944, 0, -254620624896, -353457095088, 235614082176, 1763438121094, 963477096512, 284452423272, 0, 1261909278930, 136829258208, 638952261316, 436458567040, 94318841232, -724350681600, 0, -31502877696, -1088236327481, -222691150112, -1070949438594, -121936050688, -190127082700, 0, 412735536008, -16978542592, 732238035750, 270109566960, -1337377647260, -111553708032, 0, -1220737160384, 77299404138, -558316170240, -438620477218, -170539868880, -278433169080, 0, 456694096320, -208660238528, -722298015336, -73797156864, 2296261508078, 107690599968, 0, 778876287872, 1207284362270, -202591939968, 650618719184, -240007675904, -184746731148, 0, 1122334174124, -175604972544, -274054792476, -350470898432, -125226403380, 82008145920, 0, -303635724768, 305670182172, 324397301760, 177128458614, 1078025586912, -83093444088, 0, 417083647610, 908798434832, 675763539858, 24700701696, -1618197575678, -46304808624, 0, 384309215232, 334031284944, 1042537628944, -441011151360, -391913842176, -1696748417696, 0, 30508830792, -529269358592, -1498921080454, 47639242368, 1873676273280, -128016030720, 0, 1002823175488, -2232127586248, 23314563072, 1069528108784, 36335009920, 684067457925, 0, 91292084428, 57875464224, 1625780346344, 204691330560, 183450362652, -380846680688, 0, 699931739520, 489803903424, -1094674101312, -232522043580, -609624317952, 2419595971494, 0, 469445524512, 167377172096, 1385889311736, -906119929056, 49823510024, -255232885248, 0, -1502959100976, 458481974328, -775636269568, -1011662061898, 121154637600, 598228661184, 0, 978836292108, 197504925696, 36306564624, 24794911296, 1694614482994, -758979791008, 0, 92677212160, 3416747120640, 848734103232, 322612410336, 1678271512064, 144117005814, 0, 799629622616, 92170690560, 848934348380, 369724749792, 966529069002, -834900873600, 0, 554563596960, 753098837624, -123997749248, -68383501560, 173447935584, 1336760316012, 0, -3380738638228, 62525916544, -84759840018, 227834593280, -126522487296, -710431769952, 0, -74742012928, 1320353627832, 337601706976, -946783486296, -58112474112, -2488741856762, 0, -165459985092, 145655765760, 2175677804210, -252735136416, 250343020312, -42832314368, 0, 16539709488, -658679922956, 120069609984, -1225184003748, 1458980158624, 2718575637120, 0, 1725081808218, -19441135296, -54091859028, 136583043072, 186268168080, -587034885504, 0, -41278242816, -166107343596, 362738113808, -20668360140, -253720663296, -231026047296, 0, 649993176520, 736095929344, 688107561264, 1074367219344, 588608023600, 251620100352, 0, -331458032640, -149318315622, -117282930688, -231001630860, -930161536992, -161337970848, 0, -45551933874, -195518053728, 530219308264, -238417717248]