# Trace form for 546.8.a.g, downloaded from the LMFDB on 23 April 2024.
[0, 4, 32, 108, 256, -328, 864, 1372, 2048, 2916, -2624, -7945, 6912, -8788, 10976, -8856, 16384, -27285, 23328, -34802, -20992, 37044, -63560, -22316, 55296, -64650, -70304, 78732, 87808, -158470, -70848, -274647, 131072, -214515, -218280, -112504, 186624, -319169, -278416, -237276, -167936, -711254, 296352, -893034, -508480, -239112, -178528, -563129, 442368, 470596, -517200, -736695, -562432, -2186067, 629856, -1242387, 702464, -939654, -1267760, 53200, -566784, -2419497, -2197176, 1000188, 1048576, 720616, -1716120, -4908916, -1746240, -602532, -900032, -5546448, 1492992, 6114536, -2553352, -1745550, -2227328, -2725135, -1898208, 6523461, -1343488, 2125764, -5690032, 5265065, 2370816, -10347427, -7144272, -4278690, -4067840, -4679151, -1912896, -3014284, -1428224, -7415469, -4505032, 13009536, 3538944, 12566137, 3764768, -5791905, -4137600, -11222518, -5893560, -14529815, -4499456, -3037608, -17488536, -39440250, 5038848, 595991, -9939096, -8617563, 5619712, -14533045, -7517232, -22036566, -10142080, -6406452, 425600, -9358755, -4534272, -42679407, -19355976, -19203858, -17577408, -42510684, 8001504, 25236574, 8388608, -24111918, 5764928, -80004989, -13728960, -11937086, -39271328, -6456024, -13969920, -127684089, -4820256, -39545810, -7200256, -15204483, -44371584, 17455165, 11943936, -864468, 48916288, 12706092, -20426816, -45009694, -13964400, 25272707, -17818624, -19890765, -21801080, 12355957, -15185664, 35964121, 52187688, -59023809, -10747904, -7654388, 17006112, -83572314, -45520256, -33544449, 42120520, 50415872, 18966528, 19307236, -82779416, -25370658, -57154176, -89492026, -34229520, -22174950, -32542720, 1436400, -37433208, 6319559, -15303168, 230594044, -24114272, -65326419, -11425792, 21438533, -59323752, 121761835, -36040256, 27005076, 104076288, -185818907, 28311552, 69777922, 100529096, 19456632, 30118144, -63434210, -46335240, 77236967, -33100800, -132540732, -89780144, -54355210, -47148480, -9834578, -116238520, -16268364, -35995648, -19599029, -24300864, 280668672, -139908288, -149754096, -315522000, 186581844, 40310784, -94203921, 4767928, 165092472, -79512768, 59945145, -68940504, 63159145, 44957696, -47129850, -116264360, -314869394, -60137856, -306912524, -176292528, -73578645, -81136640, -314319745, -51251616, -340669785, 3404800, 176133447, -74870040, -388427368, -36274176, -120842823, -341435256, 57395628, -154847808, -38588872, -153630864, 76459994, -140619264, 142156755, -340085472, 48390041, 64012032, 410786491, 201892592, -279380529, 67108864, 17350108, -192895344, -109474967, 46119424, -115524630, -640039912, -168645259, -109831680, 437959289, -95496688, -126337077, -314170624, -466955230, -51648192, -459937502, -111759360, -81385668, -1021472712, 611226284, -38562048, -393498745, -316366480, -200217663, -57602048, 252680116, -121635864, -104972120, -354972672, 351257472, 139641320, -243960122, 95551488, 685470461, -6915744, 339285699, 391330304, -543253137, 101648736, -1856465588, -163414528, -156381435, -360077552, 49028252, -111715200, -306310662, 202181656, -303007986, -142548992, 646030777, -159126120, -488068181, -174408640, -392305005, 98847656, -1288356640, -121485312, -809500786, 287712968, -82015416, 417501504, 1419177148, -472190472, 829966853, -85983232, -1064886750, -61235104, -1000436113, 136048896, 142036050, -668578512, 16091757, -364162048, -193153247, -268355592, -191558648, 336964160, -232674201, 403326976, 2004390424, 151732224, -1695017944, 154457888, -392392215, -662235328, 310369694, -202965264, 161414428, -457233408, -594987282, -715936208, -1361838132, -273836160, 921975713, -177399600, -172974204, -260341760, 450228312, 11491200, 2401599432, -299465664, -252686385, 50556472, -3139356, -122425344, -2304937250, 1844752352, -1152343989, -192914176, -2081384082, -522611352, 1468208626, -91406336, -518504166, 171508264, -749820981, -474590016, 1507203646, 974094680, -1147788468, -288322048, 348158590, 216040608, -1246649486, 832610304, 681387498, -1486551256, 1270556411, 226492416, -426138741, 558223376, -651021786, 804232768, 1620745932, 155653056, -3702891565, 240945152, -2160134703, -507473680, -363155891, -370681920, 349205273, 617895736, -322301322, -264806400, 5066214766, -1060325856, 603399459, -718241152, -174312648, -434841680, -336736309, -377187840, 1525806074, -78676624, -3447470403, -929908160, 18247600, -130146912, -898145163, -287965184, -1067736870, -156792232, 3435028011, -194406912, -3112986682, 2245349376, -410521041, -1119266304, 5904072068, -1198032768, -829887471, -2524176000, 471289455, 1492654752, 323140900, 322486272, 5342314224, -753631368, -23340636, 38143424, 1374316388, 1320739776, -3763895381, -636102144, 343064484, 479561160, 2909048781, -551524032, 2851983749, 505273160, -1215261738, 359661568, 483283063, -377038800, 2632664256, -930114880, 682363089, -2518955152, 247171288, -481102848, 259020072, -2455300192, -537050655, -1410340224, 1835141459, -588629160, -2414235163, -649093120, 333610839, -2514557960, 691798269, -410012928, -1683758188, -2725358280, 971031267, 27238400, 1316931117, 1409067576, -2344024688, -598960320, -1593642843, -3107418944, 142000558, -290193408, 701214293, -966742584, -206668476, -2731482048, 7509751269, 459165024, 4029614174, -1238782464, -2256452478, -308710976, -6728780942, -1229046912, 3319724473, 611679952, -905700123, -1124954112, -1902431664, 1137254040, 1028624020, -2720683776, 1361228544, 387120328, 543219228, 512096256, 5837496506, 3286291928, 521295372, 1615140736, -7502064066, -2235044232, 2097285848, 536870912, -685007766, 138800864, -2916029897, -1543162752, 3353941546, -875799736, -2416284702, 368955392, 86028577, -924197040, 7465650358, -5120319296, -598723650, -1349162072, 420708536, -878653440, 8275584630, 3503674312, 38782800, -763973504, 1562625038, -1010696616, 1682283214, -2513364992, 170628093, -3735641840, -934721305, -413185536, -1330160887, -3679500016, 6226039188, -894074880, -65481271, -651085344, -6569957415, -8171781696, -1763813313, 4889810272, -4136553206, -308496384, 2237547123, -3147989960, 578840391, -2530931840, 11363220880, -1601741304, 1961995698, -460816384, 3287569545, 2021440928, 2251085119, -973086912, 13697219943, -839776960, 729137052, -2839781376, 10311872913, 2810059776, 19642867899, 1117130560, -5017110489, -1951680976, 2857463116, 764411904, 3947149564, 5483763688, 1884003894, -55325952, 1805917295, 2714285592, -409895420, 3130642432, 525329064, -4346025096, -753414447, 813189888, 6515782921, -14851724704, -1712723670, -1307316224, 23239447247, -1251051480, -3549167461, -2880620416, 2085398109, 392226016, 8177234226, -893721600, 18537603714, -2450485296, -3578599764, 1617453248, 11035332611, -2424063888, 13099509055, -1140391936, -1467590670, 5168246216, 1237194413, -1273008960, 9287787285, -3904545448, -265533606, -1395269120, -2382672217, -3138440040, 15543634033, 790781248, -439245828, -10306853120, -1604948793, -971882496, 13004242512, -6476006288, -529173783, 2301703744, 8572763649, -656123328, 22996996089, 3340012032, 7578054144, 11353417184, 5464811170, -3777523776, -1033899412, 6639734824, -4043360592, -687865856, 21045918855, -8519094000, 18082979075, -489880832, 5037709788, -8003488904, 61094130, 1088391168, 19866398820, 1136288400, -2543505867, -5348628096, 12244993779, 128734056, 22703119077, -2913296384, 4457496744, -1545225976, 2572455127, -2146844736, 3580281921, -1532469184, 1618518915, 2695713280, 4462270848, -1861393608, 32460208, 3226615808, 1705296915, 16035123392, 9332889617, 1213857792, -1521219764, -13560143552, -1272505950, 1235663104, -16615303732, -3139137720, 4310184991, -5297882624, -8501473638, 2482957552, -14369931841, -1623722112, 22070642313, 1291315424, -8286638148, -3657867264, 4802789199, -4759898256, 33397352203, -5727489664, -1986623415, -10894705056, 29324342486, -2190689280, 15563296348, 7375805704, -8486633115, -1419196800, 1819935615, -1383793632, 7780841959, -2082734080, -9198084195, 3601826496, -3849323674, 91929600, -9780620736, 19212795456, 4755603069, -2395725312, 7501321807, -2021491080, 2729524239, 404451776, -10487538936, -25114848, -4766700788, -979402752, -4983726545, -18439498000, -3262756221, 14758018816, -14366088100, -9218751912, 26518727719, -1543313408, 1549681956, -16651072656, 9377713233, -4180890816, 28650156051, 11745669008, -1041899544, -731250688, -7127079218, -4148033328, 16565935864, 1372066112, 2064419838, -5998567848, -26226471838, -3796720128, 3022270794, 12057629168, 3838232385, 7792757440, -13528005750, -9182307744, 1748351323, -2306576384, 1306531107, 2785268720, 4062288701, 1728324864, 8962618391, -9973195888, 11091235257, 6660882432, -167803435, 5451099984, 204424913, -11892410048, -7543274283, 10164451288, -116880400, 1811939328, 33617933324, -3409109928, 468452916, 4465787008, -4671889249, -5208174288, 25817420692, 6433862144, -2955824109, 12965967456, -8080532130, 1245224448, -4251579564, -29623132520, -3119165010, 1927561216, -35031875509, -17281077624, 22543264566, -4059789440, -4553421993, -2905247128, -4984834435, -2965455360, 5315634909, 2793642184, 11824900803, 4943165888, -14545347634, -2578410576, 57549875816, -2118451200, -3411101079, 40529718128, -8375984797, -8482606848, -7558542138, 4827195672, -12607791210, -5745929216, -7767127957, -1394501184, 13593156125, -3478733440, -12418312554, -2693890472, -20805956294, -3017502720, 865939050, 12206448592, -2197413036, -629412992, -16252207734, -27579763224, 42832651804, -7439265280, 16503109668, 145980800, -25023473643, -1041175296, -26123023325, -7185161304, -10624466115, -2303721472, -3210052965, -8541894960, -27229304630, -1254337856, -5405876901, 27480224088, -20995064704, -1555255296, 30108682470, -24903893456, 6822363132, 17962795008, -1583193352, -3284168328, -14639036601, -8954130432, -2834247240, 47232576544, -25809892757, -9584262144, 55959807045, -6639099768, 9483951744, -20193408000, -43435113600, 3770315640, 12485460558, 11941238016, -6586923294, 2585127200, -51106422130, 2579890176, 52216562066, 42738513792, 18507702447, -6029050944, -35204030800, -186725088, 10784888452, 305147392, 9160713873, 10994531104, -14581164612, 10565918208, -12460649422, -30111163048, -14667834699, -5088817152, -34292183243, 2744515872, -11428465729, 3836489280, -50124570876, 23272390248, -48309977484, -4412192256, 8656144882, 22815869992, -4222298745, 4042185280, -25781130853, -9722093904, 71305844055, 2877292544, 1323762804, 3866264504, -69108392365, -3016310400, 11730776782, 21061314048, -8270387874, -7440919040, -18137771860, 5458904712, -48043581945, -20151641216, -8181215622, 1977370304, -80479783664, -3848822784, 8034821156, 2072160576, 17442830979, -19642401536, -27441711227, -4296405240, 18151421878, -11282721792, -13177840887, 14681131672, 12185546256, -4709033280, 55981812312, -19313881304, -10592235135, -5192744960, 18620352601, 2668886712, -4094420498, -20116463680, -34785629280, 5534386152, 7032346869, -3280103424, -57532417758, -13470065504, -21856521222, -21802866240, -44653106835, 7768250136, -8072159142, 217907200, -2214416232, 10535448936, -111714517205, 11272540608, -13433635592, -18752197504, 38317782996, -4791682560, -83256240471, -12749142744, -21059380113, -24859351552, 22409105031, 1136004464, -43795642527, -2321547264, -19622018379, 5609714344, -28751942250, -7733940672, -19270711930, -1653347808, 37805861863, -21851856384, -27011775051, 60078010152, -9372135994, 3673320192, -13564212830, 32236913392, 3834973350, -9910259712, -10951073313, -18051619824, -15816362660, -2469687808, 434477439, -53830247536, 18085666322, -9832375296, -19116412970, 26557795784, -5215137669, 4893439616, -37591207368, -7245600984, -21384284762, -8999632896, -5172083496, -15219453312, -57918591399, 9098032320, -30217160594, 8228992160, -6282203427, -21765470208, 5987121595, 10889828352, 1717947628, 3096962624, 54118541448, 4345753824, 46791530441, 4096770048, -20673310316, 46699972048, -45765484488, 26290335424, 14337404028, 4170362976, -296512524, 12921125888, -10594589805, -60016512528, -57894012441, -17880353856, -72067494144, 16778286784, 8379981738, 4294967296, -2990879284, -5480062128, -14332043817, 1110406912, 4358189556, -23328239176, -145719063383, -12345302016, 62365695698, 26831532368, -16064656614, -7006397888, -157761796201, -19330277616, 8411239399, 2951643136, -36769629564, 688228616, -15438325042, -7393576320, -331857183, 59725202864, 24893344251, -40962554368, 122871402, -4789789200, -64354079386, -10793296576, -4670303508, 3365668288, -20865356678, -7029227520, 8668538501, 66204677040, 12156164424, 28029394496, -57733647990, 310262400, -74130076342, -6111788032, 64843184664, 12501000304, -84630531488, -8085572928, 39985945693, 13458265712, -6822532395, -20106919936, -154138376071, 1365024744, -55748052528, -29885134720, -84762612, -7477770440, -11567347805, -3305484288, -72312727147, -10641287096, -62233305750, -29436000128, 4238093251, 49808313504, -95925584127, -7152599040, -31113287703, -523850168, 12999426038, -5208682752, -66541552364, -52559659320, -56197370214, -65374253568, -84470799561, -14110506504, 12335693503, 39118482176, 39641632902, -33092425648, -93412916430, -2467971072, 22733297119, 17900376984, -13999612482, -25183919680, -203707050222, 4630723128, -29790294624, -20247454720, -20245166487, 90905767040, -133146504095, -12813930432, -2407743425, 15695965584, 40694498442, -3686531072, -48959457012, 26300556360, -16618594314, 16171527424, -30990288636, 18008680952, -2625455084, -7784695296, -43979536328, 109577759544, 9400281930, -6718215680, 46502644461, 5833096416, 17985589558, -22718251008, -33659536122, 82494983304, -45939216666, 22480478208, -28665303702, 157142943192, 18397462446, 8937044480, -104974312156, -40136883912, 163862977080, -15613447808, 34305023097, 22859704928, -78787663912, 6115295232, -15784522948, 31577196512, -11505746007, 43870109504, 10280094747, 15072031152, 70573495807, -442607616, -17577588222, 14447338360, 36669288807, 21714284736, -43288094185, -3279163360, 43760140164, 25045139456, 17292644096, 4202632512, -164408099985, -34768200768, -99978072255, -6027315576, 175755053824, 6505519104, 106927173734, 52126263368, -58323636981, -118813797632, 23605278916, -13701789360, 6622381948, -10458529792, -9805209057, 185915577976, -69698298393, -10008411840, 210893671218, -28393339688, 9428542371, -23044963328, -184090279145, 16683184872, 196281574040, 3137808128, -8702135694, 65417873808, 31938840405, -7149772800, 68818290474, 148300829712, 136787798682, -19603882368, -130659864723, -28628798112, 94741406340, 12939625984, 16291785393, 88282660888, -30695764918, -19392511104, -67409081817, 104796072440, -4706441496, -9123135488, 95663968321, -11740725360, -72991867021, 41345969728, -9091880343, 9897555304, 132366837078, -10184071680, -7606007850, 74302298280, 41196763998, -31236363584, -102285135240, -2124268848, 203676367005, -11162152960, -93081700881, -19061377736, -28581950592, -25107520320, 227408117157, 124349072264, 492685200, 6326249984, 62353513459, -3513966624, -104255064064, -82454824960, -24249919401, -12839590344, 201698347986, -7775059968, -4260466390, 104033940096, -28828895490, -51808050304, 2167608737, -4233390264, 26830719235, 18413629952, 92745756297, 68582109192, 14252789767, -5248986624, -27607802989, 183975968712, -84050640414, 26720096256, 54238524705, 60624433152, 79093757092, 90827337472, -11084068107, 43718489360, -106658414302, -30220190208, 137920760300, -8271195296, 159409945836, 53117878592, -8297208098, -32346884736, 194700415073, -5502926848, -22406961717, 168367350840, -79784093937, -68152752000, 116119035056, 144663832600, 12724815285, -3919046656, 220973176053, 40301678304, 87525326014, -64027911232, 8724804300, 488753040, 7353416819, 8707129344, -43079870080, 158931190560, 144242484048, 9090307200, 159899775824, -20348046936, -16523300410, -42789024768, -630197172, 97959950232, 2265561682, 1029872448, 41764309405, 181624952616, 37106542476, -23306371072, 24655872046, 35659973952, 328445085605, -12361807808, -101625175287, 20579641016, 95384866958, -17174757888, 40019939416, 28642255368, 9262741068, -12259753472, 74984337176, 12948151320, -107412274283, 21565706240, 78544317087, 35698166784, 148180353375, -14891148864, -99758051013, 259681664, 77003561223, 25812926464, -63735885101, 13642375320, 31922003555, 128280987136, -32812066926, 74663116936, 282962629298, 9710862336, -13060964106, -12169758112, 13048642701, -108481148416, 720471720, -10180047600, 23933827246, 9885304832, 71081934912, -132922429856, 6647081646, -25113101760, 586363480548, 34481479928, 18423803403, -42383060992, -31164389581, -68011789104, 40784669041, 19863660416, 6673624776, -114959454728, 182214593304, -12989776896, 4165256493, 176565138504, 6993541944, 10330523392, -21318661576, -66293105184, 94889318787, -29262938112, -14500367685, 38422313592, -21757934030, -38079186048, -226955135667, 267178817624, 49548819393, -45819917312, 242794177987, -15892987320, -42167911712, -87157640448, -65184349401, 234594739888, 86650229250, -17525514240, 26492279681, 124506370784, 9007492653, 59006445632, -76358546934, -67893064920, -120476617816, -11353574400, 18678553263, 14559484920, 538047020431, -11070349056, -148768802904, 62246735672, -45461471076, -16661872640, -138096793661, -73584673560, -152538240314, 28814611968, 26217844209, -30794589392, 79603327480, 735436800, -1309392227, -78244965888, 35557140159, 153702363648, -18643837030, 38044824552, -163771419558, -19165802496, -63288666576, 60010574456, 49914236579, -16171928640, 292465917529, 21836193912, -43028356761, 3235614208, -258913289401, -83900311488, -3373260254, -200918784, 3834015066, -38133606304, -270146216315, -7835222016, -58397383325, -39869812360, 18932785911, -147515984000, -93706543145, -26102049768, 398219367899, 118064150528, -5580048852, -114928704800, -359956427235, -73750015296, -437959201168, 212149821752, 202763284263, -12346507264, 44285857939, 12397455648, -10434715394, -133208581248, 108799582698, 75021705864, -6722466947, -33447126528, 25998932379, 229201248408, -60924216906, 93965352064, 31929099865, -8335196352, -287307418391, -5850005504, -181677085434, -57016633744, 460637554700, -33184266624, 96269354496, 132527486912, 89632560771, 10976528896, -70399899442, 16515358704, -11133440312, -47988542784, -24453903321, -209811774704, 388487822206, -30373761024, -47558556447, 24178166352, -51365654928, 96461033344, -274056955028, 30705859080, 48414335502, 62342059520, 27772848540, -108224046000, 161617583887, -73458461952, -97033952339, 13986810584, 36753170688, -18452611072, 63997572492, 10452248856, 171462346983, 22282149760, 14666919156, 32498309608, 121403846598, 13826598912, 143475743374, 71700947128, 157612405662, -79785567104, -240873807908, 88729882056, -32311944903, 53287059456, 14074975044, -1342427480, 77456177400, 43608799872, -460266941744, 1635399304, -202555729782, -95139280384, -147993095608, -60346194264, 308680246390, 81315610304, 56626717896, -935043200, 122115172287, 14495514624, -374493627389, 268943466592, -18495209682, -27272879424, -207925316080, 3747623328, -229197379755, 35726296064, -78732807219, -37375113992, 20561184735, -41665394304, -415770227752, 206539365536, 90556421742, 51470897152, -68749344863, -23646592872, -292507664348, 103727739648, -65239686954, -64644257040, 420017500896, 9961795584, 21663586735, -34012636512, 2322771579, -236985060160, -194534120614, -24953320080, -86506294383, 15420489728, 201572559666, -280255004072, 79982894629, -138248620992, 93766657179, 180346116528, -16165538550, -32478315520, -101366118395, -36427375944, -338199889466, -23241977024, 11359130472, -39878675480, -120097967324, -23723642880, 105005923116, 42525079272, 223440785010, 22349137472, -108000202142, 94599206424, -202447730391, 39545327104, 1047135600, -116362781072, 255356380623, -20627284608, -167512686133, 460399006528, 42190876026, -16947609600, -103159408426, -27288808632, -105270995732, 324237745024, 45421646778, -67007878376, -565310984418, -67860854784, 2364399052, -60468337104, 4606958511, 38617565376, -310780222182, -100862329680, 210725816265, -45967433728, -25237475235, -62137023656, 85449456783, -11156009472, -438170232041, 108745249000, -35914343949, -27829867520, 93395972748, -99346500432, 38415152032, -21551123776, 168103058076, -166447650352, -107811672535, -24140021760, -752076023496, 6927512400, -1767994317, 97651588736, -385171756206, -17579304288, 142988724596, -5035303936, -177388850205, -130017661872, 518158446167, -220638105792, -116849736255, 342661214432, -47622959451, -59514122240, -872398350190, 132024877344, -55444753078, 1167846400, -111686936562, -200187789144, 250621361476, -8329402368, 267161904460, -208984186600, 60413772321, -57481290432, -165582974265, -84995728920, -120972430829, -18429771776, 15628690557, -25680423720, -671254299019, -68335159680, 130801064861, -217834437040, 306806963760, -10034702848, -133230587224, -43247015208, -295584070872, 219841792704, 52973883846, -167960517632, 21599241358, -12442042368, -273757948848, 240869459760, 88764377715, -199231147648, 230946432506, 54578905056, -41449088289, 143702360064, 60779298213, -12665546816, 6787161101, -26273346624, -510895103753, -117112292808, 369824938461, -71633043456, -705963424754, -22673977920, 742836870404, 377860612352, 19686700404, -206479142056, 175770960833, -76674097152, -78246929274, 447678456360, 278420568651, -53112798144, 532619370172, 75871613952, 250861396860, -161547264000, 530357433273, -347480908800, -13235983096, 30162525120, -646932064492, 99883684464, -135461983203, 95529904128, 134845942921, -52695386352, -280628372926, 20681017600, 77151504132, -408851377040, 216396014825, 20639121408, 26225777942, 417732496528, 106573038228, 341908110336, 220873673300, 148061619576, -20473042400, -48232407552, 50868105138, -281632246400, 262339746256, -1493800704, 629108020100, 86279107616, 48759766965, 2441179136, -569562273587, 73285710984, 662259010602, 87956248832, -11067176340, -116649316896, 1095995165935, 84527345664, -237060153285, -99685195376, 14183884728, -240889304384, 16597784063, -117342677592, -153910722919, -40710537216, -20342190069, -274337465944, 480444308538, 21956126976, 196407358128, -91427725832, 175926138867, 30691914240, 775460997065, -400996567008, 140899766413, 186179121984, -46243539090, -386479819872, -728503197432, -35297538048, -637379692756, 69249159056, 627465075669, 182526959936, 280521943533, -33778389960, 909500747612, 32337482240, -95827521447, -206249046824, -311680060777, -77776751232, -391312050469, 570446752440, 56305748943, 23018340352, 547854449666, 10590102432, -853483754836, 30930116032, 220785324102, -552867138920, 5951087044, -24130483200, -888284785668, 93846214256, 500515300278, 168490512384, 27583931164, -66163102992, 86882144570, -59527352320, -96622193628, -145102174880, 661553562552, 43671237696, -37549913681, -384348655560, 297953980497, -161213129728, -1365916970033, -65449724976, 190292141930, 15818962432, 353686744485, -643838269312, 164332456414, -30790582272, 928409122052, 64278569248, -39624948090, 16577284608, 18948435992, 139542647832, -91841861461, -157139212288, 33404249151, -219533689816, 149639853762, -34371241920, 57875234569, 145211375024, 250770256695, -90261774336, -57845323837, -105422727096, 373857899165, 117449053376, -7169407362, 97484370048, 182732085924, -37672266240, -467614626874, 447854498496, -64332149859, -154511050432, -636066739765, -84737881080, 150220036127, -41541959680, 419678118891, 148962820808, -38348997505, 21351093696, -794927175625, -32755363984, -11859637356, -160931709440, -353243698558, -278285034240, -278255439763, 44275089216, -43333617411, 56258774952, -487655254429, -26240827392, -545475947082, -460259342064, 351114547824, -107760524032, 480208411962, -174852169776, -688590267440, -174422929920, -14287692141, -357224854680, -160165643890, 62146001088, 1899236196, -64577273136, 231464618523, 1743257600, -561204176547, -17715329856, -388074440378, 84283591488, 620918894403, -893716137640, 145711785018, 90180324864, -157758563186, -107469084736, 204607461888, -150017580032, -820365322564, 306542263968, -85720803966, -38333460480, 147549901590, -666049923768, 92910888025, -101993141952, 616008957127, -168475040904, -27915284124, -198874812416, 182344802557, 179272840248, 113226590657, 9088035712, -109170735984, -350365140216, 745230677346, -18572378112, -1019283501818, -156976147032, 568239809085, 44877714752, 209650615412, -230015538000, 299310190734, -61871525376, 488240435025, -154165695440, -450048210267, -13226782464, 911897342019, 302446894904, 136018164276, -174814851072, 98886297718, -216094200408, -134970069535, 480624081216, 1649541510, -74977087952, -475841552468, 29386561536, -1009578691444, -108513702640, 536392768140, 257895307136, -348814229156, 30679786800, 872759915046, -79282077696, -68674658409, -87608586504, 279279637869, -144412958592, -454435531971, -126530901280, 330614832033, -19757502464, 1093232949462, 3475819512, -55524137279, -430641980288, 612984215079, 144685330576, 86669279788, -78659002368, -794303175382, -152931303760, 120352412088, 212462366272, -449238756590, -41721101352, 726954862132, 39147516928, 69456288429, -300729658944, -249742143651, -57964807872, -36005437160, -171074278096, 96667611867, -71997063168, -230854081171, -41376667968, 169364772880, -121755626496, 43700010705, -463348731192, -685980081670, 72784258560, 676528926982, -241737284752, 120481312896, 65831937280, -309808982060, -50257627416, 501476289833, -174123761664, 876425616, 47896972760, 818075005187, 87118626816, -501826125102, 13743581024, 46043016705, 24775700992, -83678321846, 432948331584, 207262428386, 34766030592, 251988019659, 374332243528, -27146037529, 32774160384, 52496912506, -165386482528, -41072933628, 373599776384, 75258297681, -366123875904, 235116368123, 210322683392, -34357660650, 114699232224, -1950089185288, 33362903808, 3506750871, -2372100192, -448613200764, 103369007104, 247677462754, -84756718440, -328604953875, -480132100224, 116374994757, -463152099528, 672864521092, -143042830848, -79013173837, -576539953152, -229539788226, 134226294272, 470252116964, 67039853904, -1142341951225, 34359738368, -387988159707, -23927034272, -186335825991, -43840497024, 65938548557, -114656350536, 595907342451, 8883255296, 74341091266, 34865516448, 1544182438200, -186625913408, -223739229996, -1165752507064, 878754115660, -98762416128, -636767696684, 498925565584, 129675308373, 214652258944, -458947678250, -128517252912, 142261146951, -56051183104, 901728509481, -1262094369608, -603967315096, -154642220928, 751681540530, 67289915192, -53638832205, 23613145088, -20179168690, -294157036512, 4092811400, 5505828928, 791757247122, -123506600336, 47921177954, -59148610560, -384427152884, -2654857464, 420209001396, 477801622912, 16816690436, 199146754008, 668591781633, -327700434944, -229139094105, 982971216, -209767668323, -38318313600, 465560569801, -514832635088, 49138261605, -86346372608, -784173768210, -37362428064, -105064557066, 26925346304, 210082732893, -166922853424, 1294865205018, -56233820160, -2256186901556, 69348308008, -248348273265, 529637416320, -2068147873612, 97249315392, 183608373858, 224235155968, -103931739198, -461869183920, 2221418660, 2482099200, -522184403085, -593040610736, -264076759872, -48894304256, -361726126525, 518745477312, -791274378554, 100008002432, 128401282863, -677044251904, 221588556511, -64684583424, -529588566036, 319887565544, 202535688789, 107666125696, 851096980238, -54580259160, 252701984195, -160855359488, 73697154453, -1233107008568, 1249280632639, 10920197952, -167407386083, -445984420224, -283163551272, -239081077760, -920166283669, -678100896, -1003789080344, -59822163520, -128700921276, -92538782440, -917582498570, -26443874304, 756414390430, -578501817176, -134560616715, -85130296768, -1763588835052, -497866446000, 306934777032, -235488001024, -88094417967, 33904746008, -110763670784, 398466508032, -501089340482, -767404673016, -387884378700, -57220792320, -441906327520, -248906301624, -1130840656576, -4190801344, 716005648413, 103995408304, -873094622204, -41669462016, 50518742574, -532332418912, 41841412812, -420477274560, 647998442831, -449578961712, -277658769598, -522994028544, 253198257291, -675766396488, 823704833873, -112884052032, -42417997492, 98685548024, 773554213377, 312947857408, -1055751360396, 317133063216, 766249675120, -264739405184, -28131287688, -747303331440, -162041965607, -19743768576, -549322749627, 181866376952, -192431138886, 143203015872, -16532198049, -111996899856, 464007513345, -201471357440, 447280268328, -1629656401776, 486777761764, 37045785024, 1047181714857, -238322356992, 55739335626, -161979637760, -684185305912, -161961331896, 205014439097, 727246136320, -708114739626, -1065172032760, 141032877863, -102511443456, 284678630579, -19261947400, 81601311438, 125567724672, -1035418262964, 325555987536, 198484969270, -29492248576, 103632274395, -391675656096, -728958867035, 210404450880, 1723973828737, -132948754512, -365256155250, 129372219392, 196613981122, -247922309088, 1327751501598, 144069447616, 47205485721, -21003640672, 610375686912, -62277562368, -2102125943817, -351836290624, 35276339889, 876622076352, -343149586759, 75202255440, 1316489374067, -53745725440, 109681794927, 372021155688, 2006910212395, 46664771328, -334774419869, 143884716464, 241990696557, -181746008064, -445517534598, -269276288976, 48718365150, 659959866432, 299463351939, -367513733328, -125335054221, 179843825664, -409324047572, -229322429616, -4530692745, 1257143545536, 294064401860, 147179699568, 1152104269975, 71496355840, 5519472651, -839794497248, -2248761237433, -321095071296, 829419807178, 1310903816640, -203668405641, -124907582464, 729024209898, 274440184776, 819513718079, 182877639424, -3155770800, -630301311296, -66251563721, 48922361856, 1195317295253, -126276183584, 907684199748, 252617572096, 940768504713, -92045968056, 637689445874, 350960876032, 12648228732, 82240757976, 657209829143, 120576249216, -65704616264, 564587966456, -126141009723, -3540860928, -697512581485, -140620705776, 1003179778926, 115578706880, 697070358684, 293354310456, -13884071123, 173714277888, 1877256447189, -346304753480, -79807250943, -26233306880, -1409065739442, 350081121312, -339639392937, 200361115648, -218174367510, 138341152768, 133474494750, 33621060096, -602362923363, -1315264799880, -114792648228, -278145606144, 687505915432, -799824578040, 260789435878, -48218524608, -84217455270, 1406040430592, 2325473749697, 52044152832, -506615114668, 855417389872, -945860638743, 417010106944, -506173519692, -466589095848, -581391154792, -950510381056, 608668143282, 188842231328, -783811954620, -109614314880, 541182975879, 52979055584, -122942393811, -83668238336, -2241916882599, -78441672456, 2764755065901, 1487324623808, -134590529745, -557586387144, 516464343912, -80067294720, -644816654114, 1687149369744, 143522142543, -227146717504, 1245828618196, 75428338968, 34953013518, -184359706624, 319272321681, -1472722233160, 106456805042, 133465478976, 113057893876, 1570252592320, -392724386118, 25102465024, -676276243099, -69617085552, 1032540600036, 523342990464, 1553846647032, 255510723240, 1841522598100, -57198182400, 55365148804, 550546323792, -92099729133, 1186406637696, -47100457001, 1094302389456, 1834881979511, -156831058944, -226151589519, -1045278917784, -1456010226159, -229030384896, -9488539218, 757931250720, -204080637726, 103517007872, -2981741886836, 130334283144, 524620079000, 706261287104, -340410362670, -245566119344, 2702405122922, -155140088832, -3574199359136, -539272654536, -209712454839, 838368579520, -467110479276, -37651531968, -267510751495, -72985083904, 367015215375, 765311746568, 163436844390, -93925802880, 2031099404831, -583934936168, -335294438958, 330767757824, -353667708279, -72735042744, 316237669559, 79180442432, -561760819938, 1058934696624, -1800313368352, -81472573440, 1079652058495, -60848062800, 23380354350, 594418386240, 775560293232, 329574111984, 1113717160250, -249890908672, -59330151972, -818281081920, 1815840769340, -16994150784, 1071100396258, 1629410936040, -438809608818, -89297223680, 1704496631823, -744653607048, -651678725976, -152491021888, 1156481598708, -228655604736, 154428311016, -200860162560, -717610880783, 1819264937256, 445583961036, 994792578112, -2256970824162, 3941481600, 1522710822374, 50609999872, -675633788361, 498828107672, 408244138679, -28111732992, 823748605176, -834040512512, -705321629775, -659638599680, 1771768557983, -193999355208, 303765470765, -102716722752, -286860585105, 1613586783888, -1427590457860, -62200479744, 724418417598, -34083731120, -86671430055, 832271520768, 1206786086720, -230631163920, -565632664541, -414464402432, -735191225010, 17340869896, 2418270598383, -33867122112, -153302094634, 214645753880, -145958676327, 147309039616, -1076799108, 741966050376, 621671296232, 548656873536, -566866747008, 114022318136, 1633307194646, -41991892992, 651349151032, -220862423912, 812934426690, 1471807749696, -677858439056, -672405123312, -790593476750, 213760770048, 184203804564, 433908197640, -1294538285262, 484995465216, -653249929400, 632750056736, -42746220504, 726618699776, -1232137992012, -88672544856, 1191555465770, 349747914880, -395253988227, -853267314416, -863500039636, -241761521664, 1452597465300, 1103366082400, -76524675480, -66169562368, 222758754190, 1275279566688, -2265889872661, 424943028736, -696867104439, -66377664784, -713914740126, -258775077888, 988638936487, 1557603320584, 1510914790215, -44023414784, 139364959370, -179255693736, 1042949428710, 1346938806720, 256066697088, -638272751496, 402322672157, -545222016000, 503595558718, 928952280448, -1172748067200, 1157310660800, -2011011983413, 101798522280, 2075642464484, -31352373248, 337107435066, 1767785408424, 1348885914444, 322413426432, 945594900463, 700202608112, -177846928938, -512223289856, 109659649746, 69798434400, -169689616499, 3910024320, -1379873397510, 58827334552, 4045532970299, 69657034752, -65755219467, -344638960640, 1409847175782, 1271449524480, -257188596483, 1153939872384, -35570197763, 72722457600, 499707966069, 1279198206592, 252149711403, -162784375488, -1274737593121, -132186403280, -950508831600, -342312198144, 1858692885719, -5041577376, 516970850578, 783679601856, 291191988204, 18124493456, 479055380430, 8238979584, -1506713671136, 334114475240, 247339274571, 1452999620928, 1899966891127, 296852339808, 1304412754473, -186450968576, -393691444524, 197246976368, -1320862059828, 285279791616, -340466718012, 2627560684840, -336437534394, -98894462464, -2746415782797, -813001402296, -635321068856, 164637128128, -396031536873, 763078935664, 119418396370, -137398063104, 1253969618518, 320159515328, -925888947561, 229138042944, 1034617331540, 74101928544, 1138167448737, -98078027776, -308568574683, 599874697408, 1056712081320, 103585210560, -427600773698, -859298194264, -1353363413652, 172525649920, -623312442194, 628354536696, 11159821039, 285585334272, -1304369392068, 1185442827000, 2195559751638, -119129190912, 21606567866, -798064408104, 233715911814, 2077453312, -1661426961309, 616028489784, 2757855151017, 206503411712, -114002066115, -509887080808, 451778501212, 109139002560, -793701486199, 255376028440, -696090533031, 1026247897088, 435800848973, -262496535408, -1046787668408, 597304935488, 1925257789485, 2263701034384, 2963617574026, 77686898688, 2442621344556, -104487712848, 35741595708, -97358064896, -1464633413011, 104389141608, -146165588163, -867849187328, -1865926593855, 5763773760, 368828243628, -81440380800, 3321084368627, 191470617968, 316730973114, 79082438656, -3015946160533, 568655479296, -3978096677984, -1063379438848, -223300472598, 53176653168, -2756110365324, -200904814080, -138533122169, 4690907844384, -489719840220, 275851839424, 43059066713, 147390427224, -95728581154, -339064487936, -1297176712515, -249315116648, 555915854676, -544094312832, -1359758945432, 326277352328, -220892821794, 158909283328, -1431029538307, 53388998208, 1270020567800, -919675637824, -2172954158928, 1457716746432, -752898691331, -103918215168, -1270091806795, 33322051944, 216940171212, 1412521108032, 1488661465070, 55948335552, -616629072384, 82644187136, 470956436433, -170549292608, -667360546324, -530344841472, 108891992993, 759114550296, -740926203129, -234103504896, -4989162454503, -116002941480, -1579637210544, 307378508736, 490088390706, -174063472240, -723647181997, -304633488384, 337279991779, -1815641085336, -355801703949, 2137430540992, -124562470613, 396390555144, 3112365371477, -366559338496, 329009748912, 1942353423896, 960259692158, -127143898560, 833103099648, -337343293696, 1511508932424, -697261123584, -2750032338477, -521474795208, 119777408639, 1876757919104, -285990348645, 693201834000, -1494545420215, -140204113920, -2381959204040, 211938237448, 502749520227, 996050966272, -2618853641981, 72059941224, 68950196157, 472051565056, -110549353446, -610868375472, -409920311268, -543144519360, 3853428014026, -963812942528, -939211990560, -90828595200, 1321249911343, 149428426104, -3937145659220, 116475879360, 189873365463, 4304376163448, 1737711664738, -88562792448, -803073116263, -1190150423232, -1553375279466, 497973885376, -298374780737, -363691768608, -2639548253391, -133294981120, -590126072994, -1104774349288, 2278172742387, -588677388480, 206966014437, -1220305922512, -1205633884545, 230516895744, -2332748512600, 209742753672, -556116402898, -246356715136, -217948296834, 636826619840, 634677664738, 5883494400, 2003124678934, -10475137816, -59789238264, -625959727104, -3379574427824, 284457121272, 355183181337, 1229618909184, -3016291964535, -149150696240, 1570045673877, 304358596416, 1466743608165, -1310171356464, -362708160984, -153326419968, -115500553987, -506309332608, -170511010055, 480084595648, 1034580140892, 399313892632, -573362303465, -129375429120, 832723508004, 2339727340232, -2247918492717, 174689551296, -1214682621640, -344226854088, 523351483382, 25884913664, -568603263051, -2071306315208, -4113582226166, -671202491904, -13404243201, -26986082032, 605045835837, -1607350272, -131699483565, 30672120528, 2019902233374, -305068850432, -1182482348229, -2161169730520, -1741303959570, -62681776128, 947086835772, -467179066600, -529794496233, -318958498880, 232911882252, 151462287288, -2428437884465, -1180127872000, -776302440750, -749652345160, 6258926800, -208816398144, -2621580265710, 3185754943192, -520309222110, 944513204224, 4102813585148, -44640390816, -138760641565, -919429638400, 1020758270301, -2879651417880, -4918532090328, -590000122368, -308063790909, -3503673609344, -729317926377, 1697198574016, 1686058408224, 1622106274104, 3608329356672, -98772058112, -253047671838, 354286863512, -559561219320, 99179645184, 628733784396, -83477723152, -366233746410, -1065668649984, 402589156590, 870396661584, 5375834292402, 600173646912, 103544280450, -53779735576, 1657922150920, -267577012224, -4965971492394, 207991459032, -295678979451, 1833609987264, 1178214607773, -487393735248, 2156591476821, 751722816512, -427041791820, 255432798920, 1082969583056, -66681570816, -965285741122, -2298459347128, 11730890853, -46800044032, 393132862365, -1453416683472, -1067754431926, -456133069952, 488312990694, 3685100437600, 691768058618, -265474132992, 1171299240683, 770154835968, -516143150190, 1060219895296, -669825328181, 717060486168, 1378593533090, 87812231168, -140808717063, -563199195536, -4298277787851, 132122869632, -1085839769429, -89067522496, -1014962598936, -383908342272, 393848547010, -195631226568, -1514407880184, -1678494197632, -577375688574, 3107902577648, 2025096719324, -242990088192, 674286815228, -380468451576, -139646254392, 193425330816, 1107730786426, -410925239424, 473887261489, 771688266752, -1563801967773, -2192455640224, 2443447418811, 245646872640, -284651402553, 387314684016, -815863336038, 498736476160, -4207814026326, 222182788320, 1047936388356, -865792368000, -169619492529, 1292940671096, -348435039666, -587667695616]