# Trace form for 471.8.a, downloaded from the LMFDB on 30 April 2024. [0, 182, -28, 0, 11960, 0, 324, 24, -2436, 132678, 6916, 228, 0, -9572, 8356, 34776, 745384, -3748, -20412, -60584, 31980, 37044, -123192, 286676, -71280, 2672882, -23080, 0, -524148, -110712, -157248, 382052, -1635116, -426168, 976612, 569772, 8718840, -993560, 181104, 0, 2886520, -299156, 334368, -932624, 479556, 0, 542176, -1381000, 78192, 23764602, -3826196, 1634364, -4744208, 4682068, 236196, 1692352, 7290852, 2671488, -1109368, -4027812, 1573776, 2566668, 6491376, 17496, 50753124, 3613888, 1045224, 720156, 16750952, -4188240, -2325248, -17032076, -1775844, 11095660, -12019956, -7541856, -25384960, 4237008, -7741548, 7746804, 17231792, 96722262, 21528560, 9571496, -7583544, -14595704, 3791504, -1099116, -29640504, 1012372, 5041764, 28942708, 33762380, -19225296, 34503872, -16391128, 29901204, 15645932, 45517432, 166212, 199524452, -37782408, 42102288, -7278036, -81351820, 4840452, -101292360, -35701156, 0, -21097508, -24394664, 6555600, -25342012, 21659556, -8987760, 1895008, 35662904, -6977988, 835696, -82663996, -43369992, 250158106, -198574428, -54132300, 18105724, 84498096, 6091524, -53461860, -235685324, 33310980, -146496676, 18495800, -148898088, -60455072, 86944500, 25351704, 177041660, 50929408, -37731096, -64552172, 142603904, 86859108, 88945144, 108947320, 543384936, -107292252, 26759272, 69020208, -1095944, 57730972, 49386348, 77826376, -91816012, -2732292, 173920124, 151766780, -28084968, 23219358, 20757156, -44860500, -16653972, -25320472, -14880348, 350791668, -85714488, 68563368, -49354388, -210745824, 143425836, 1033557650, -54786100, -44165736, -292821524, 363360688, 244755648, -122914608, 13270800, 121110336, 395888140, 733131396, 23313420, 260484756, -262872152, 160537032, 303014580, 147227956, -50155416, 463006516, 385675204, 27005076, 1581677432, 105228000, 4692384, -462683596, 86918060, -217866888, 1778003940, -112356292, -89806968, 372363232, 315603040, -186530040, -173480076, -313413504, 240011532, 840199488, 252986432, 208986804, -1018777540, 751541576, 367026768, -673971712, 1915463880, 249025320, -541086364, 553286816, -51963120, 106581784, 132971788, -329762448, 778494208, 428331488, 442950552, 1342433004, 1195758336, 1948530978, 241629644, -201635320, 451526184, 694904300, 696296836, 102052440, -134594964, 62897216, -16825320, 1066454088, -329202268, 128143404, 1014910700, -777527740, -244026216, 1013379292, 964715052, 0, -1346360968, -334221944, -627862752, -859171504, 1533676672, 78881472, 1203573396, -1111367460, -382103892, 153691456, 886246288, 375995304, 4840810808, 1736811332, -519604740, -832365564, -65499704, -80709048, -2251636656, 207489412, 280986624, 162661344, 1038154760, -906042888, 1153432200, -1026249256, -114633792, -424718640, 2642753820, 455658048, -502642196, -23293096, -1369472616, -299718320, -2569244024, 278515908, 1966135064, 1519854852, 2638499832, 1538173696, -4105374380, 1146250764, -2473049544, -50340284, -1191999564, 2924862566, 353381124, -585996120, 3164033680, -1371987752, 1409889996, 161869472, 1993681828, -310676472, 2533756148, 956902576, -535008240, -1921390476, -2032883996, 183282156, -1424306000, 487166684, 711950148, -2007164272, 4736033256, 593814996, -5413014012, -2052153764, -2469638160, -1512783804, 0, 415363788, -2430337448, -1213298992, 455134464, 2249175280, 4199098984, 656517204, 3906694868, -2398337992, 6356034360, -2312681072, -956911000, 396882072, 4186039156, -1628653840, -843280740, -2885223060, -4284266000, -724305240, 8105476416, 1974787720, -1870963704, 2899336332, 7752167256, -334687140, 1052554280, -2542637320, 132024816, 1020306612, 1400303224, -2259611424, 1427775488, 9043864508, -768778776, -126228456, 5217553456, 0, -4502707832, 4894043036, 1551685680, -1747352904, 1417708356, -2424406896, -2061227964, 2371397164, 2104273080, 12119334990, -5262534452, -1530858744, 7289318700, -4964189572, 1701006156, -2262498152, -155786872, -218084724, -7312574120, -3162877872, 791241696, -392505284, 2868849960, 2986082172, -106577592, 7599892236, 243754272, 5027336800, -6092043788, 122578704, 1779370620, -6009603956, 4122780336, -1677438556, -12549770836, -679882896, 1680101056, -1823851688, -5770452096, 2035072980, 2717829816, -1175744808, -5904622516, 8060442756, 349596324, -5736520508, 13193068548, 1239061752, 5097395436, -5993190592, 2129236956, 869395124, 272792004, 0, 5577736688, -1656131600, 5329830672, -2021621988, 2325056440, 2564878284, 16854007080, 5464740532, 395246304, -4888861276, -4990213588, -3732323292, 2760926144, -3178364548, -1184312556, -4332535588, 2874818908, -1006749000, -17350678144, 4808178640, -4012418160, 2424990872, -11222872720, -7437548844, -2159205360, 5594358164, 57001968, -8303308300, -14777115432, -1643497560, -2715574940, -796774716, -12106445220, 8669767480, 2159355812, 17324394858, 3932114972, -11105839732, -1597167504, -5881228504, 10393466780, 445064652, -23035635268, 8738654400, -2789296884, 8497166736, 6405449808, 2506703220, -7591594104, -15346776476, 2952222336, -9468669908, 5959937896, 1191451356, 12491190764, -9788288572, 2769715080, -4726382296, 12256691468, -11263026024, -743501620, 10421899512, -3458527632, -10772198488, 20565831204, 1671793776, -8333616712, -7849662616, 10000553544, 2181958472, -51017195804, 3413227572, 3882178760, 2989180612, -14425107264, -9825000724, -3060418404, -3340806228, 8098855128, -11102281772, 172186884, 4224772736, -45513513900, 3531904884, -24234694504, -12599022756, -4291042068, 8443509080, -777518728, 1233724608, -2888827120, -10783640080, 1545289272, -9234599164, -2726385956, -216051084, -12554605644, -4369013088, 5315031108, 4559107408, -24788913280, 398665584, -20351736768, 5886572456, -16827821064, -16552977404, -29046109148, 1947514752, -24125442976, 4497913196, -8468951544, -7117421632, -985888240, 5038104312, -44107734876, 2958361712, -808729272, -163550232, -10579281692, 13315024188, 10896908128, -17258370356, -19537707600, 19499131378, -4453722984, -2936274948, 15854557776, 625670616, -1736401320, -11798964972, 30766758528, -13834715112, 7613452268, -10216064592, 1147282704, 29175900452, -24855622848, 9032957568, -6577673372, -2387461416, 3154397580, -1707390836, 23160725912, 1871100972, -33780975392, -9444543492, -3920272992, 5935361880, -39905908220, 5288514624, -13128713304, -1472318456, 4732213104, 39246295180, 49990539956, -5747313528, -1373467660, -17850986240, 4057683552, 15286006232, -7140265976, 12754584, 47814190536, -6018847600, -4031025696, -1856658904, 2044371556, 2089520388, -29400989712, 36880845744, 36999027396, 8319043388, -15006991392, 6966739800, -44343438460, 23569567860, -9581782680, 15836068352, -25024576308, 2634524352, -36738086728, -19095075812, 16077450024, -5917150904, -83548038692, -19364793228, -54044205816, -16323392672, 761968296, -27829938976, -14462649864, -19516538088, -5061093356, -24177438924, 13157894448, 23958409712, -1798989068, 524993724, 5318928196, 10259340536, 16261835184, -35771338752, -24050727424, 10415172132, 48777372664, 37753644092, 12211444008, -557802660, -102824877616, -6346392336, -69563802188, -16845435324, 2896799004, 2954216596, -129205365032, -3053226960, -14622309552, 46279302308, -4489615080, 28350796318, -59952254396, 11265067656, 4458116736, 9176282444, -1695105792, 3334434272, 15145730732, 3253512204, 30464311028, 17851404520, -21623588388, -51986340612, -116050255284, -12416383404, -2670380268, 18442564200, -15546606048, 19811733184, 7574358832, 19649848752, -16849800904, -32330382556, -1294590276, -39380744672, 67036605976, 13982667984, 90933561888, -3733466312, -14843069208, 457182056, -43724497712, 8088736140, -16004940360, -27018344752, 56876473296, 47528937744, -36216961708, 24017391216, -6017114508, -35707280864, -8762547924, 29174320532, -69596113612, 4189265892, 27530808308, -129856656, 6937731540, 3385876732, 42438302660, -5498013024, 41620788484, 28352037744, 32403232656, 31004877176, 57362256036, -6849636696, 150644883136, -39354087324, -18505635840, -37937330888, 15170259420, 576683928, -59935626580, 17747406736, -4129940844, 7766841092, 79014081836, 3088778832, -64460471400, -31213413384, 55958932728, 43992632144, -16301284612, -18165260772, -24271536276, 60916025224, -5643588492, -30186869432, -44655871756, 23674743504, -78640375560, 68453173340, -2317219272, 44875144828, -11807912856, 5647420116, 63330076108, -8795815672, -21902114880, 98096414744, 25460137044, -19813753548, 2294463564, 19629096700, 12561976368, 46413335652, -91612074912, 17614512072, 78434690848, -18537907316, 52860345660, -11998295060, -7388675460, 70510528998, -59615176768, 12669414740, 44957330856, 48177098112, -36635426692, 45376813224, 29033189280, -50188307856, 15694320240, -7965165700, 85529541520, -3759469416, -40390346320, 16907898628, -39237048540, 4265263540, -22982129824, 6977620584, 88327737056, -53206338440, -20183002416, -72679836184, 71227930844, 22478973012, -44614235420, 20671252240, -5528403576, 10382376812, 50786089380, 22233832560, 189073910560, 11172613232, 4680968400, 26508650580, 74624009916, -10640268216, 9957882172, 50290994888, -26628819120, -53746844064, -159002979520, 27292958640, 37119801400, -16897635876, 2764006416, 52561444976, -39051641420, 16908324048, 13884940820, -86410729748, 37402748136, -26404201780, 58618065212, -801255564, 158249917564, 0, 50067558216, 64679985576, -71581814648, 47361271644, -100424742656, 45111314924, -21607927416, 27734016336, -126797014392, -57664924056, 80380273456, 10084676980, -187037424, -19662109100, -138174231428, 738019188, 35815428396, 39073879256, 21173462424, 43658830376, 65639535952, 58808082996, -78523309652, 99545249596, 3675445956, 55584128672, -45241282348, -38335040316, -7506021952, -83978872148, -23242319928, 134548789368, -13017659332, 21099234132, 275461283556, 18521048656, 42425596584, -66314385000, 98687854412, -49452165144, 54491916532, 54772823460, 24612775020, -82846945068, 210434076756, -684141336, -91074378036, -52574549972, -58981042620, 101597768280, 14378448960, -14015240784, -110852011136, 103688454040, 157062306528, 123535644910, -79553545376, 7167983976, 92934069428, 57722096824, 25153322688, 91063917152, 368652295960, 3214119312, 47562234492, 178981943300, 46476540396, 96576689064, -14030988872, -11949132312, -327574821652, -145939550504, -63595496304, -41426119256, 261722176608, -56772291852, 70386712184, -55344434532, 21797977716, 1026203048, 188420332992, 16497336960, -164675804856, 41077452408, 5047432164, -2156496244, 455077984, 11405884428, -238418694768, 106213055156, -80789488560, 123095821492, -195014748892, -49844183652, 110717742104, 162789737920, 33182207928, 141679008416, -318532918964, 22614146136, 93302683168, -57710513376, 21714547068, 188032968528, -99256947104, 121168548, 91290370680, 156608864664, -100252260144, 47738591608, -3240935268, 145078231356, 16676442088, -47573529920, 145453325508, -40641880616, -264054119648, -41617884024, -4138607428, 372461656560, -122701409604, -202800849908, -155128375668, -27543375432, 74461095160, -78963240968, 162425662128, 44171551456, 122032378980, -74853064980, 42692569392, 385892287060, 30692567952, 79959601708, 3315582144, -102780963180, -255516845916, 145113833120, -72656053704, -44733110856, -93207250268, -5305688244, -165440713596, 40750394604, -74964684384, 114702187904, -78251303436, 107202366540, -330890886616, 313983762784, -59305476780, -1565825564, -130010867616, -12191737896, 122162459200, 372668028960, 5015381328, 4429791840, 182207781572, 3528689508, 317448431988, -68987556600, -3448081872, 14393948408, -185031172524, -44756212392, -211268948896, 81801928300, -73842130440, -104091893648, -143768458984, -62397085968, 3524992616, 9374005608, -58730342976, 40160536362, 132367217620, -26026142724, 268212100264, -74539059664, 202043034072, 87208215884, -25674256380, -64856685096, 217902775744, 9871957288, 0, 171324120512, -264744416488, 135549710496, -34454893632, 281897081040, 98207960004, -229616985532, -594723308252, -15380083332, 33288148412, -211146111180, -21170764368, 278333496568, -157299452036, -30017757816, 66702870576, -7321769284, -17783710056, -213871420244, 482297259480, 96566341968, -236866543188, 25451694896, 73144312632, 24904202484, 306958362556, 4779032400, 491872664048, 26183898048, 81886671576, -129754661292, -297545813336, -23364095976, 26628161028, -106428752908, -18474326748, 124531255704, 167260737460, 45171086616, 131829798536, -159797540708, 4082708988, -17506138232, 56776754372, 15789816324, -170597711460, -76854050120, -88486642944, 268873185252, 183789395016, 44082771588, 288819755488, 117354429832, -6552077040, 188889515888, 118480701008, 104987850192, -271691818704, 81600052968, -146867243580, -229379761508, 147123352512, 1381460832, -117236403252, 359144306160, 20140713720, 70097945344, 166822654980, 23415285168, -213842002864, 342921391148, 25998257016, 56892988328, 162822200344, -41795397792, -442854927648, -29515067960, 4209103872, -60328436988, -37448826280, -5086953252, 568200516992, 274740191572, -91491931728, -76162616744, -104968478584, -83640078684, 146687162736, -140176201328, 609222384, -250757273136, 399349203920, 149047182216, -189677482372, -101358916512, -194294001564, -2616031584, -439084760800, -60262053084, 173245576316, -112846521328, 199484441712, 237353573504, -310833108744, 87937121016, -613411210160, -277713869804, -31616724168, 184320370480, 29035611140, -266885841168, -72556854172, -108978405212, 27331112340, -158881907552, 220131983492, 182365259274, -518287464064, -17799900656, -366959768904, -50877068468, 604585428320, -118338154416, -22832828628, -410534348760, -144760758012, 31856959176, -35735871304, -60737491116, -83117128632, -214922444892, -237645194112, 66799313744, -167711709800, -39462446700, -55747560644, -60917894436, -18623724336, -476317114512, -774821407424, 73277171208, -405290959344, -295417611788, 13199072796, -239541208204, -363497063888, 139674463560, -298255931592, 149896443848, 107092858320, 612567785480, -348603393084, 61599111984, -101179642068, 485266085240, 227744330832, -169991205192, 234258251268, 96301777068, 178611758428, -508787166952, 4440720996, 263524292620, -1046248038680, 131012595180, -331037293324, 122514410052, 553441754520, 279379116756, -712050984032, -38973695940, -536892050160, -107402885180, -57001075920, -257800461008, -375970730208, -60315578100, 336674344652, -19381410816, -171814601196, 268142636356, -565340324124, -134980069680, 719908595276, 853893596, -28025477604, 101683030888, 633039554656, 24283704420, 192981940672, 378619829652, -1960163280, 29068528056, -1005521215192, 84619211004, 56323020952, 547419643512, -106796076804, -50173448896, -781457195888, -231932443824, 606343951332, 216806308144, 281669964624, -129813891104, -632271694628, 13483438200, -435661094008, 158010199532, -129394323288, -406406467004, -9581950668, 59587658748, -12248881340, 327295933832, -108546706152, -53464181540, -817120294640, 144194014944, -586547447604, 109888404668, 380382203196, 650155444672, 471692198664, -44071747488, -131619327136, -46947980020, -207886224600, -507384617140, -87362182824, -103257105480, -806533930136, -687701120832, 63382540500, 72303031652, -438741296840, 40869357408, 217918499052, -574512575736, 206682691284, -423686007484, 75916906728, 18481392216, -820250347272, 238818620572, -40595568768, 365265370400, -817458387856, -121093318224, -137643505792, 40146761908, 129063370140, -223648935482, -78197972020, 186654646080, -811262628732, 565778414712, -358610803848, 493355928324, 1033053193736, 37127538432, -373174093052, -60271245140, -389938257144, 202869876484, -320484458680, -12725843688, -1910657658940, -267561532112, -27505968984, 228781150260, -651112394232, -54646183008, -98709853020, -180619491080, -747371921688, -70002427108, -191377818048, -47058533388, -259581391252, -157895563360, -362647304496, 349177804004, 0, 201886450380, -515420679516, -331548293792, 103958246016, -351947304128, -124079457912, -12757758120, -298090648072, -168835093932, -54283715136, 325096638236, -342729600560, 63320289732, -320737338296, -592071118616, 319913778096, 718648594840, -568494856492, 4447434816, -36645224424, 105983277896, 64841009976, 265785361660, 805801954316, -346604967216, 879148541776, 739243379672, 137987731872, 212248588416, -336517945948, 79422596280, 62607733180, 147029761000, -267412978152, 348797333436, 73757194800, 242699714964, -212663316640, -717103255008, 396127618344, 692403543012, -319444854136, 587866686696, -937983582224, -256785066476, 84227024124, -403618857672, -559498104924, -78216051708, -308945248376, 196104969044, -45475830432, -598630588056, 218866506392, 42253340904, 243247813152, -41429541360, 19507509288, -226497448512, -105077100816, -138913730244, 78850526464, 103185567432, -234215053200, -206083470396, 166374109972, 50315731632, 164821439532, 597731649592, -171052396272, 104253792952, -1710774345684, -174108450888, 65261784112, 162895084860, -798943176, 896773587328, 117042361296, 357321590568, 1286937736832, -236854121416, -225714940632, 381625550688, 799712435512, 42085878588, 563593420768, 481606098704, -77320630728, -237318748932, 553580980020, 334191763656, 161995293384, -97505414776, 36002647692, 1066153917672, 1839502708048, 145362675600, 347084265960, 342204043812, 29386310220, -90357963420, -947426600472, 56735428104, -276157189640, -249074167648, -39311064720, 330292095112, -717986681628, -97010212248, -786868250112, 861433070324, -66933872748, 827254889046, -1122965339484, 306240819552, 674493071444, -738486669656, 42304510656, -467733926232, -60488674360, -1991840868, -449975929096, 391482221308, -506675401416, 94016348276, 1181711061008, 46241988912, -79899294680, 765880439768, 126787770396, -1008861995480, 783701941524, 99186321420, -369398388640, 1097859741596, -508974940224, -672324728144, 402345222492, 110637982620, 693966258508, -707738617180, 378940773528, -208129197956, 1511084015360, -281989234872, -89573346116, -561023925860, -20473941672, -612219150384, 1895885798324, -22178918232, 314591751184, 495396028844, -220198805964, -224822096928, 884677846228, 16926911982, 969028668328, 404877408748, 272058588648, 247613892724, 212206132228, -14406037488, -1383555558824, -153067726424, 15131966724, 154492923752, 1624924570128, -53098533720, -730879864960, 136088834264, -627930709056, -495150932704, 465413123436, -32703304500, -1173314472784, -110615257576, -24638737248, 999841031880, 1022341782244, 365473815696, -563555977416, -485325607364, -12140745588, 1380179978392, -1142228193744, -323096361624, 631270930088, -696253610680, -126943292988, -882117320464, -918074730656, -18458624088, 368825524896, -637938102864, -743087859984, -366396875500, 855219915576, -615628095012, 2808115092588, -301635908244, -10847773692, -128049110408, -80030938508, -745165438920, -790499276312, 396996800328, 49391252496, -540319302056, 2751967889432, 255727125972, -1035889015580, 797925062600, 322823999016, -94384416760, -1806207868792, 476738567136, 1107515559888, -668859842004, -62485861752, 1227119322116, 147924801784, -438101123904, 138531136928, -392974111500, -701394043320, 386627548084, 182316152720, 49982695272, -961906670256, 1180425435492, 903618538560, -591390303320, 1139737284232, 62117789544, 1242589521056, 1521850289000, -35979348852, -287307253444, 792321052400, -184387857084, 809008626428, 137348071588, -123760817136, 263440136208, 334972398020, -153633705696, -617369919176, -1620999531136, -795617576496, -157835933328, 1391212766156, 193585160520, -2551833184, 1152291780576, 104557434444, 135493577672, 601655155212, 207065131272, -268352458252, 424156156496, -841555172808, -1176948362712, 606631746944, 753463526850, 15205874232, -887241181224, -185949716256, -704160598156, 1853947641404, -217899386820, 607248044996, 354587851032, -39939066900, -25891090176, 78041221864, 71847373464, -620059372880, -420646684080, 1038066253992, 42720836344, -586659942852, -32196821544, 588085702448, -388340431220, -1535872434048, 379935447856, -2468007608136, 116487637488, -455843940500, -255672660732, -213466890996, 207805063396, -281861956788, -93967786584, -64962773744, 525702957188, -738496738296, -338272748208, -349085544980, 264889941552, -560124828696, -1178843605812, 304493029632, 480608406064, 11322938616, -259238904948, -1781100230236, 1594246972416, 178426867392, 247818624360, -400266012592, -562385859840, 77397860000, -205220847604, -818709401124, 776274335116, 156827027864, -89604749232, -1684813667884, -1554843898852, -123775518744, 42451660512, 116217691472, -129037513320, -402752108028, -1627220289716, 9674413200, -2095435726672, -557870297384, 30970952424, 25292936616, 225031469548, -830255037120, -887081264844, 900114660264, 88289434944, 1332105458400, 271170851748, 1217791285488, 1170783325640, 2614628319608, 595292006376, -979898620476, 277841793968, 288602454060, -949438633300, 295986550980, 747895975704, -1156808885584, -156127100580, 194998001184, -1560571268216, 55917228860, 534452787684, -628448372132, -198728535568, 54205164576, -459960352232, 2634270803396, -651420923328, -3645867037292, 218579801976, 16995483180, 962870947048, -659658416720, -421530877224, 2955289195240, -1828041842076, -987331192164, 940959986432, -343948997856, 189893387124, 1853373697384, 2662175815260, 1137652972344, 200357646536, 2060551871832, -84685453884, 61984826280, -1486037865896, -191633798808, 1578056096184, 1079476770600, -124053671880, 1298249709764, -1576763018888, -162567591408, 1609015651444, -1972433828776, 117031496328, 2555640690416, 530358195760, -83990678760, 1981473063192, 2598572291536, 214165352808, -563148274976, -1201639617128, 220897628820, 90097695964, 435238960156, -342061210008, -1213550311416, -1227876273600, 457660947528, -726366685444, -885748996860, 107329179924, 1710605101768, 386812483092, -345838034160, -787592240144, 2718196191652, -498104824788, 1206333518384, 388938870488, -36563298264, -1826479738216, 1336167766688, 402110653752, -2463896920076, -2221785890388, -1750249106568, 337118856690, 404967642068, 337531750164, -1842082479568, 719117532860, 321264913608, -1507356480420, 1009089009956, -47118408912, 2545603741724, -466194394072, 281157223716, 1858014538636, -550931724880, 736751548800, -2124264620696, -2268598218188, -133128274032, -1222497264816, 2648135246800, 19686700404, 1135621410768, 51141602052, -1362769060968, -3719970120, 482514349696, -27369940176, -204595584684, -1402067017368, 1153042847928, 331927113392, -1333698279540, 584255394576, 4307754299012, 217936022620, -422764732944, -357729661336, 2230265389648, 76711212000, 584370084504, 165012496304, 1257890872680, 80344352360, 1853296076056, -466890180624, 122141884744, 0, 3420747936, -705062141360, 2204856077176, -363851137728, -847183667208, -1088453303884, -751832022636, 121378866104, -583994334332, -337296341484, 1016284035316, 198918545456, 375383470392, 742407861916, -3709355956952, 111829149288, -252309576288, -1720493450616, 63363265740, -925064079872, -1866230071384, 733143157560, 1366052037624, -1155166515336, -2474275175424, 159705552060, 3287106885956, -158824961352, 3475739874436, 304651030600, 1126240584696, 974938358640, -1971948580, -441363638664, -15839195924, -1159047134096, 1296164872260, -15106409816, 1262507559532, 56468973312, 4258713380564, 1312216188552, 2611736807652, -1896154695876, 426318466264, -81907736868, -463014247732, -1096292369464, -1019287696752, -1021850202468, 1528069237516, 394383499992, -973808135344, 923988863140, -65469279672, -103206600072, 3968835756260, 4053206952, -826479012592, 87624945244, -159915619332, 548395281900, 3738043192788, 271452796128, -2504847630148, -2722969650968, 1717802954928, -590903700796, 4382178413932, 439542734472, -399956657948, 625345138088, 230074616160, 1553506803644, 2290678018488, -1045870432704, 3549976988488, 2654160616832, 1205055342504, 148746996816, 1860047709364, -135980399160, 115322755768, -317431743884, 1968778254024, 1807015723428, -4030552529260, 206140033512, -1232750765868, -484066234572, -126466975404, -1600993208740, -5940251138572, 808175256948, 3453912554072, 1618731171684, 113396566896, -76537992612, 2050284179900, -228478444416, -2917108172876, 2532811609156, -693456237720, 315295857560, -5322087009364, 31891408668, 2616170372420, -1797229542068, 174968406828, 418257105600, 1529767079932, -34609983696, 8288533231844, -1709240009544, 622114103160, 810212934816, -5344422499196, 612505426752, -1020788337664, 839596964040, -980033074128, -1265922842734, 1914660318400, -487950175440, 181384180468, -489480683244, 184427108928, -278498274928, 3418533536340, 5231966688, -4031711820620, 329277944400, -2110842083124, 1257697572756, 3115213597096, 152351380116, 92922916012, -1446002826996, 722127681144, 2439719584176, 1809296194704, 979908158304, 3016392027644, 1757860982840, -742688826660, -2686754504136, 55132968404, -129148436880, -134184420448, 1543672615480, -1309438559232, 570531177952, 5305322979008, 547873808904, -3250304036512, 3300338062964, 213989603328, 2309830913264, 1649991980500, -1331307673200, -1748745329584, -689223955936, 267562513872, -1829911661544, 843552191336, -725038068816, 868603208312, 2420171117144, 470232163620, -2387043973144, 614280106460, -491325378048, 181213495888, -1931964716840, 1699581220416, 1199619161524, -6280892905980, -366316166988, -822087242684, 2979101450024, 1396373168520, -3128418029460, -921207332272, -197679971664, 2115423951056, -48621254988, -1944070156584, 35741211168, -700132058668, 181539458280, 755506702624, -1492546144848, -1728030102192, 186369745188, -1619444826776, -2883386700756, -1381233502392, -395512552800, -394451959356, 1339684247008, 1399667588024, 465832717956, 2017286541804, -331641728560, -2774378057220, -1628348586940, -949655800196, 403346088864, 784486266564, 2461500385000, 2649706424568, -1938758483140, 3061260118240, -893107494828, 2701915922116, 2877101559092, -37881114480, -3133714042816, -3548869539256, -633550296816, 1326805509696, -61314515528, -154090119852, -1327580153648, -5780246271712, 77698120536, 3078127006692, -899963605668, 789057905544, -3158737317352, -1719351530848, -666846984204, -2641633207288, -487777548600, 96936433452, 17473013164, 4044626122548, 1278367253424, -1205209217480, 926646268860, -329294044440, 2674726506576, 1120562999156, -240396824592, 1936473188360, 896774372372, -1286722606032, -1498357123812, 5610432140, 753126030900, -2488307423788, 2617396053932, 567522277632, 1503575812840, 8351647615704, -1629271666512, -1063122610168, -6245767563244, 984807648612, 1302941575148, 884862276008, 312253654752, 1252971035004, -516255263424, -1701234701928, -1654738461468, -951032869464, -1879310019600, -2799472058600, -1629609414748, 322910952408, -710727383800, 652991144200, 301360655736, 1832585039296, 2148021826304, -324736636248, -3136722389920, -1145589341592, 978633659916, -2534658731684, -3871298675988, 771978841920, -597761549056, 2967737232908, -1837378844208, -1614001009544, -7915867299524, 871707826944, -1850138585668, 3388793707460, -210358416744, 5063368999568, -1337477967712, -719399084904, -3313222914628, -1155640463788, 1420479082962, 2350431681860, -1517994662744, 2847791702520, -1745849223872, -1834702718108, -564175789524, -2041280407460, -4103593405632, 176148010476, -2568967664008, 141985491632, -103724055792, 1629782915820, -1198219229760, -1929773483028, 272068957472, 2912683572144, -146992148280, -8992957936144, -2280110314480, -962291750832, 1252567917724, -9892578759780, -1691232360768, 3900992156828, 5571744661936, 329162588136, -560661832988, -6196506008144, 1200370699728, -3046312399744, 1163269500268, -51380302968, -3541941316312, -1148568881100, 506585234700, -4591340494504, 4384972280004, 871009249680, 4172335378872, 232107165752, 748246751712, -884154290860, 3163993028232, 507600393444, -2163776840432, 1372428040792, 522234092340, -596039717388, -1307510715444, 862391292480, -2636131676636, -3404707581088, 74396228760, -3879246085144, -4108452783212, 1302100059456, -2507030853328, 1726941758768, -2803097822544, 2760572370088, -28188361136, -98119728756, -2251714882004, -5504769892248, -948045853584, 1824402357380, -3739378245064, -3424454452368, 2875760426424, -4725076823220, 45852070464, 4963394665684, -1173084090772, 3936114374760, 1818411499880, 5395289334080, 1134895630284, 2304892762728, 4702031806908, -12265658280, -1108809912164, -9272076293892, -385411328496, -883462002136, 288986494692, -4947738363540, 348820611228, -4302653246212, 777445030152, 2481691231792, -3803827402092, 891355153032, 142311819560, 3873121256200, -1463657044536, -3524230541664, -3544190111228, -239988453372, -1391891158120, -2585158360816, 275432261544, -4644657131648, 1613678518248, -554966234676, -20309673992, -1902843728152, 93416541516, 410878128644, -2723940419784, 3190130200152, 2021184035412, -5515076969256, -2340578642868, -4731798947064, 2974295590936, 739869900300, 4928382865476, 9473897699376, 320113750680, 1062325397648, -100714313984, -2603802659472, -76004983580, -2166967335496, -566817722460, -441400316084, -5633718221588, 4818180565296, 2764345642360, 2019257092120, 2528071714008, -4984524230600, -49310664096, -177895111464, -2393272706496, -618196329972, -2757556666152, 4168928317328, -5302504836364, -640744402752, 200146857532, -9837072886516, 738753503868, -2194728138800, -4146346838132, 39599555184, 2091310591584, 1413383365560, 923822413596, -885076085660, -1720321912040, 703277272908, -1612184101180, -6316748097700, 3614838787728, -7228487722964, -1061943529512, 3832421061168, 1757352809936, -1151690681624, 0, -3812143048900, -1052683144236, 336092705136, -1989520725212, -883397600536, 302145839928, 5230326479996, -742513294500, -981497145672, -1458555816508, 0, -683743525128, -2133295770040, 687950998032, -1793046179088, -3498894873280, -1491048673728, -243647797176, 3502927161744, 4666350125956, -1104114899664, 5360604295882, -10407210879192, -106651309716, -3083220534740, -1928369711344, -457711946208, -2089622163552, -8332422915264, 999308769408, -1125149794532, -4238853221140, -3467836572012, 3062843375724, -3940028355440, -626336026416, 5822568870120, 3323374823936, 998833744584, 1696042514796, 3333295907504, 744688762776, 3674536757888, -803024045612, 1118050293888, 714158495184, -903219669496, 1095442867944, 9501320413116, 5699454667060, 1365916132260, 2218092264392, 4689832245940, 57504593088, -2043988128832, 61933814036, 2782943553528, 73071864064, 1226020583100, -786220788744, -17249980364, 5055403753800, 877405005684, -1068044326448, 3277963471092, 1115682083172, -7789646515948, 5934546663828, 1988016857028, 5365916380896, -109739594364, -810186878340, -7858779120448, 4049051462000, -1688466147912, -1338724513264, -6164739465504, -2311768984068, -4150252718416, -848988338420, -278553737268, -5234461200840, -5676977380912, -1649530301328, -4830210681712, 2398378855916, -1848857935896, -2815594726860, -2179872222876, 112041071424, -3815435064912, -713241748848, -2231165786328, 1023008894172, 303140068648, 1866318140916, 8211569126012, 1298369503816, 646073543952, 1221220478576, 11580146037460, -310406591664, 2000907775360, -2410234016080, 2909264554512, 801807178436, 5343770162684, 274100576616, -3331566531448, 1082420457360, -1312357276728, -6285562332960, 7253436755492, 376044619500, -2157701387256, -425624559936, 3528951079032, -2391582440928, -4432800296944, 3723899379696, 3938496028692, 246162831612, -1112985747288, 687327080608, -4485469580400, 1266135461028, 7828415276484, -5136187149672, 4255418822472, -760340918568, 4450305244816, -2634992083476, -4885129763384, 1300559105936, -378791855460, -584357524236, 3113698855796, -2145486670128, 12716794875104, 2675337634016, -1774108218924, 1793853707008, 3296219898212, -606794496156, 10095266211944, 1734269200936, 2624648388120, 4916295220088, -9152341357460, -400272924456, 10832527258712, -1456083193460, -47749284216, 2512485609172, -3964638650880, -1045534850352, -2845954633896, -3180541815644, -4633367864184, -4106646979032, -5861533722684, -58836895992, -2646091173304, 4811989525744, 5896287130464, -8672646970544, 11984127573452, 313461333000, -516791134832, -598258097976, -1641443122224, -3673970991624, -9316958711604, -706129392420, -3362514146088, 1995091633584, 127523148120, 3585314323816, 4454307408224, 151259781348, -6334188131264, -1502473425684, -360185611032, 4029421303528, -5462080784792, -1768093050384, -420318058056, -12515162733400, 204839248896, 1145510874908, 12130175365204, 2720634413904, 2350496081540, -2772210972416, -4001179902912, 861721621772, -340126151992, 118580119776, 7738522063708, -671641254648, -2739104930736, 1384891068556, 6356612215428, -3684660857604, -1304554372620, 5381967202968, 756814820040, -6360720022540, -6277627859604, -874659703032, 5002592523872, 3202434947732, 3129865012692, 7094596718998, -3356108677168, -660505265352, -3996334995652, 2909773800428, -66361638960, -2154495716080, 16052123806500, 3786140559888, -2372682141568, -2300644240388, 840852073800, 3806851324200, 7991964487520, 2357862420816, -2417954007988, -3365217199328, 1907643761496, 3458754709888, 1626263486444, -748135707624, -9294587503876, -3126805801916, 684459162936, 6123672271916, 3760118180292, -1738510251228, -3430733765908, -4821011523160, -83568034368, -7242638090980, -5561292243580, 358366595004, 8058047243668, -5430839874144, -2741781442464, -4175444535840, -284889567380, -309619888560, 6747737254944, 2177122194464, -2311060934664, 3014917419156, -2957191323928, 567038447136, 602733584768, 897172672812, 1926567534780, -443543498032, 7866629839240, 3907490362560, -530783965520, 9289192850528, -6879935605356, 4789330387624, -12425196082208, 332174716992, 12616883905148, -320194876624, 3991198181112, 1810804355016, 2874436016072, -4236823200168, 3807121075184, -279812881400, -366426160884, -6840249987320, -1411858623388, 3410145137628, 10739395824160, -1783103803328, -1491487818984, 7479715418800, 7250706318020, -16980666984, -8422274608456, 119982540640, 2402615757816, 363417953392, -5195669753220, 2803475513772, -8393105722764, 7343473680528, -998345537064, -10496694144476, -4707910646400, 2890625289192, -883432877032, 6499663907436, -2905568196516, 2644146319960, 11659669266780, -218494655280, -7070803101336, -3365104211972, -3799436959584, 773978252776, -831338474996, -552692974752, 555130544776, -1193212534516, -1872978893496, -8613324498624, -14466775870352, -3190299626664, -8385442584052, -5423723217608, -188602191072, 7597418690060, -3559078273600, 203038096932, 665745432576, 404589328860, 67238605008, -14773089376440, 567836137264, -294267868488, -8595412402880, -3539721100624, 1433312461656, 1860249128668, 14697797306696, 571723585632, -7515423562248, -16473154888824, 86742243576, -2040634389480, 9918454479536, 1107974187108, -12934642343712, 35996451324, -3204282543048, -6437889004248, 7715064461064, 358387165440, 3359385688148, 1929623336804, 1923466377528, -2290283777636, 17761077660516, 3359178191700, 2086666707784, -500375970936, -31968751032, 1079381327384, 11891797629488, 1121328624384, -8605643286920, -1132114371600, 4799196370224, -288020689616, -26344676290924, 1065536213724, 2191900165328, -5853738251744, -2992817923020, 7386212797812, 10535546313728, -488009145168, -11728272589256, -988122287688, -5718923164944, -3704300566616, 940411180808, 835616806956, 9234935441720, -1853763100292, -9678774235896, 9293712514012, 19244744167648, 4890543697512, 12753088563108, -103624579888, -1802853117576, 5082398635836, 4614582281524, 1181494070604, -4571844488140, -9079942665492, -5295225323232, 2431304752280, 6066920343300, -36698067036, -67019201496, -8663711104760, -4186532836440, 2071165344636, -10293149237288, -2516815100052, -1012612884736, 1247490559368, -868967682156, 2153302366580, -16200512625904, -4273425072576, -14339261944736, 5491450441324, 2986415475012, 310837660292, -205517440576, 2132224810614, 5955797050208, -8769015641136, 1288979920512, 13711949572536, -6766603189400, 109864846152, 14312201638960, -2882597728560, 257614839396, 1363354368484, 17887635337192, 461311788600, 8458402948464, 12118385549848, 1278105989760, 5375233334744, 11559992976032, -427191171480, -11386248378344, -5180608333536, -1792783773216, -6625948459320, -20166648229024, 5361811390836, 5587003518348, 2778166535840, 2306580552720, 2774993691140, 4517247864956, 1730847765168, 8638814633292, -1672532414736, -4562274845448, 11590516825832, 3478409352860, -1000179071208, 10266064713632, -10106153647324, 11236819887720, 1273559229528, -19268083000788, 6100661215260, 11976361211332, -929485452980, 1027809807084, 6444790005620, 20944969008, 2418420876876, -21920656532544, -7634404693840, 10976880230820, -4240713192024, 14813181324468, 118002845088, 9145486828064, 5912912239020, -219551087520, -11377589392112, -11012747232392, 2537905050180, -12900779310224, -6487410908872, 1453394052612, -2768510921452, -605181617320, -4618636198920, 20723262889292, 0, -4050324083916, -1290358094144, -20517358621428, -226483148088, -6509969919544, -3906972178988, 5920765711488, 930604458212, 8542274852148, -1600819043616, 464458141340, -10312244048700, 1847108231892, -597354081840, 882094725056, 4640925784752, -10870946741668, -4271937559892, 2398024194624, -8425941737924, -19361185624892, 697581977904, 10555108449024, 2938578875688, -1058679360144, -4436593295480, -9644820298604, -1272847707036, 10098030013616, 12470539081036, -390021006960, 3202418166704, 7557715473324, 350626861512, 14199751301864, -2682204261148, 6714894091968, 10930894973128, 15618935464880, -1400693657004, -62372698296, -4127122841000, 10221953436648, -3478683896144, 22547343139772, -192358898388, 8136512108084, 3347488990648, -1481972433084, 1588680342672, 10217206018768, 1616936223384, 4320037239028, 2705923664228, -2674993713372, -5425824765936, 14297001747392, 133612691724, 37903531697344, -2339755381440, -7042098967992, -7121622516408, 6101370958164, 917936262936, 3282787026672, -4099524059948, -1038319074000, -1750209907612, -7506057521284, -840627430344, -9890261409976, -1916871854744, -4727245559544, 3621882042452, 12968489897636, 355144512636, 5308193222420, -3057590679744, -594544490424, 2136606141412, 11999664152880, -2988618494112, -14615873548468, 2391043386984, 519011657892, 1828955484040, -6906362440344, 6604580153412, 4865465000092, 9956723961432, 4038525455652, 8800130125056, 10086699122324, -1463222754288, -1154504075424, 6038682097544, 2613549836376, 2182580139504, 9286624775592, 4284649338588, -12907952888908, 11694605444152, 3452568243624, 2439428909416, -590832705560, 4236974864136, -20547183334472, -5793385917596, 5990380733268, -434852199988, -16640896110800, 432891132084, 9400688612752, 3604335102020, 11193885146304, 9388728094760, 3425193481004, 1039581549072, -3333935500168, 1153322694076, -3946087214748, -14729996073700, 1353438415268, -673919779896, -11990587524296, 2716117240832, -7668525246120, 14374120950612, 3597256512872, -1496020093956, -1863830067020, 5465299001608, 235851548040, 13133339617460, 6490888427096, 7645205663208, 14741812558072, -15543839293696, -1800366218640, 16903338369498, 3213127562184, 156336861456, -3876155340128, 1432860174968, -3611490353460, -4716717107944, 1390281378172, -1102819393116, 5471311703348, -3436455190620, -4151936311920, -1653890418136, 23924856408096, 2015231310468, -25028560842480, 22353423313056, 0, -6313101224096, 11162409193612, -6780529402848, -10069051687612, -12949212584508, -7453220949612, -4563026591340, 9654681529724, 302800201452, 10833621266528, 6209648418928, -3359621650392, -5586638045156, -3778243443364, -1844627920416, 11071318359080, -19355852224388, -1771715999592, 6394966987708, -13129327336796, -893117104344, 4967313495724, 15869148902120, 7140302732412, -2800702930024, 1970854940132, -884494965168, -2314028818928, -6517142672760, -8597477714040, 7733271240868, 9523347750880, -3932049987972, 31025192717944, 1810844978636, 331793024256, 7636267663052, 8364950217596, -2142764751096, -13927701972824, -16566964384488, -6948197328492, 15085310809104, -217772672612, 1639648779120, 12275184107752, 5418331118944, -8807930809416, -2375534430360, 7308746194976, -6434473386240, 3093476655980, -2270492176292, 3061143159336, -2051935225440, -928651228640, 6293520707472, 18346547434992, 13212202617408, 9425881882584, -2880299385772, -17470957896460, 478601041716, 20345247923624, -4852456245328, -2475911731392, -11225260801452, -3092544260204, 2007896406336, 3868927039608, -4257067368804, 2847980558772, -13910136062016, -2386973277040, 3127398926112, -10138679286148, -1611017309116, 10404796547160, 6868395682224, -15119372128784, -1748388396168, -21019440535168, 11128333619552, -7224465528072, 16467852787792, 8620433435908, 4181514923592, 7277866575024, 3763635830080, 4633549048440, -408252496556, 7135715873964, -3278175080760, -941647688416, 12715703023636, 5880324506472, -3096105615032, 33570731036812, -1685944501488, 35867182053592, -17428067759624, 5325882949944, 12816202304608, -3337191072908, 2872606350168, 21639702627768, 11212638420392, -697588119000, 1005585656128, 18862711016460, -1552968207000, -14576181863700, 505112792888, 12891522995496, 18551173670668, -8508877833444, 289327030488, 9814891365864, 1954425698112, 7235296130304, -1199942148420, -19066750708772, 2490157192644, 83132343040, -4113969787396, 3051622544724, -5355984284800, 10422116818892, -5462685810360, -36197507601988, -14752394619392, 7714355820588, -14306022312360, 16178177852492, -1187288649360, 12206495554116, 18710347987812, -2845056313080, -11734552209184, 6099151084076, 1761577819272, 7388068728568, 8474148273168, -614751659460, -6931371450212, -8384525057116, -3731283773856, -6709548382608, -13317015244468, -12002867705952, -10275605528256, 793386734992, -2103327610740, 27278492231576, -5594261248536, 6260449897440, 1061743843480, -2710815008852, -62548875000, -42074009461384, -9990394852932, -3123229914000, -2915638658044, -41499819585312, 2871179662392, 13562475086396, 20388301028956, -4820580860220, -1911515230088, -41400243950028, -528018519960, -4685896039816, -1094509860092, -10176733236384]