# Trace form for 177.8.a.b, downloaded from the LMFDB on 09 March 2021. [0, 17, -32, 459, 1166, -1072, -864, -2407, -6645, 12393, -6391, -8888, 31482, -12702, -17555, -28944, 139226, -36167, -23328, -71037, -274883, -64989, -325182, -269995, -179415, 97329, -336906, 334611, -901362, -543825, -172557, -633109, -837062, -239976, -529288, -287621, 850014, -867607, -1727169, -342954, -815662, -1428939, -473985, -477060, -1667926, -781488, 5305549, -1217849, 3759102, 4350738, 4561369, -976509, 4175994, -3487068, -629856, -960484, -5363196, -1917999, -3082906, -3491443, -7421841, 998917, -5742614, -1754703, 17531621, -6075816, -8779914, -356026, -16149231, -7289865, -548798, -12879428, -4844205, -6176157, -5971906, 2627883, -17624580, 239687, -9096462, -18886490, -70463349, 9034497, -19351611, -22824893, -24336774, -7973079, -27502196, -14683275, -62527651, -30609647, -4659039, -36301521, -41388548, -17093943, 1010176, -29303629, -22600674, -26249806, -93110852, -6479352, 3997977, -61425668, -14290776, -85406472, -57685257, -7765767, 21361679, -59216667, 22950378, -48522979, 15689539, -23425389, -40055637, -33403706, -46633563, -62913235, -97541001, -9259758, 6572128, -69428018, -22022874, 45571729, 60977940, -38581353, 41457325, -95570040, -12797595, -34253586, -45538536, -12880620, 96146873, -65588418, -45034002, -23531170, 11472473, -21100176, 102545816, -84882328, 143249823, -36189892, 454622735, -32881923, 125582928, -116365114, 101495754, 3680441, 261265266, 117469926, -73724837, -67860999, 123156963, -34847731, -95411863, -26365743, 341003233, 17147723, 112751838, 44330972, 180075928, -94150836, 147887797, -94181592, -17006112, 64521971, 69445858, -25933068, 247137493, -224801241, -144806292, 89999523, 220185619, -51785973, 279677004, -285540209, -83238462, -26442628, 87091242, -94268961, 615808534, 216452762, -200389707, 167841449, 272309375, 26970759, 1347292265, 438369109, -155050578, 543630601, 5095165, -47376981, 1021523565, -211499676, 473353767, 461742608, -150106805, -164047032, 1774270265, 234983974, -237057678, 555547847, 707906329, -9612702, 47155171, -315327279, -436029237, 889201747, 189750304, -196826355, 932425494, -49115019, -14817546, -78048781, -54865585, -347744556, 486511395, -132813628, -130793535, -196466115, 16637311, -166756239, 2078728407, -552102047, -161241462, 210053408, -1366476700, 70952841, 944692213, -349845337, -475863660, -134784075, -1120513435, 6471549, 185975093, 49083756, -245604474, 785520573, -239471914, -509935230, 1443904732, -1002159252, -1902510423, 922460284, 859383508, 243931419, 1010651223, -1492945209, -522493497, 676067567, -1162366967, -616272111, 169679043, 408131908, -657092898, -795305297, 805131215, -215273133, 4023128498, -251145060, -742559292, 956733884, -1427804971, -396448425, 795006230, -81864441, -1688246577, 1027768150, 2834209421, -826460469, 1611593391, -1372810210, -125794053, 603162604, -2389141384, -980141067, -824587214, -1545967234, -1117490796, 472092820, -332855077, -461536461, 1673711299, -931340030, 27274752, 147561265, -2159374508, -791197983, 1311948960, -402661237, -610218198, -1557647492, 2046820066, -708744762, 687397945, -2624956639, -2513993004, 220166288, 2699942834, -174942504, 2294894450, -707986275, 107945379, -1357720423, -1623614176, -1658493036, -1330606331, -4831240509, -385850952, -1271849904, 3013141440, -2305974744, 2576376228, -1742776251, -1557501939, 558965617, 1395426003, -209675709, -248394540, -943277548, 576765333, 856322081, -7379606524, -1598850009, -521718087, 289419089, 619660206, -1106472576, -237046006, -1310120433, -4351901228, -3644097207, 423617553, 365831026, 56424658, -632485503, 238816242, -197953492, -1081502199, -5464745651, -1841823148, -901900062, 5814795446, -4273499909, -1259106201, -628694702, -4107715095, -1698657345, 2734856635, -2093626221, -2633607027, -2787455560, 1083007159, -250013466, -7831714274, -2312382361, 177447456, 3723247464, -1799115697, -1874556486, 367427634, -2873405450, -594617598, -653298524, -2439393732, 1230436683, -3801561060, -8183669573, 1646404380, -1227470030, -1173001065, -1041696531, -4636037549, -2920175603, 1119347775, 1055856063, 4842065018, -2580391080, 3865218495, -4406966745, -345535065, 460349322, 717580878, -924846822, 835959017, -986301346, -1229540472, -9608426051, 5560737811, -347776740, 4901520047, -4199878044, 2595965571, -617646563, -11169877871, -1770887286, 11129697102, 2988640208, -1215918054, -7489754764, -2920259702, -635341590, 15111887977, -3242800821, 309756771, 7490706521, -490296765, -569704752, 21728936893, -2939246689, 2768737032, 1092693026, 13880271098, -2291822856, -5843868182, 494347253, 3867745221, 1417732727, 4023018054, -977127084, 13476090029, -2629856014, 12274813845, 1040558736, 11784499204, -887811921, 21109733846, -17617268, 3390739056, -2324464691, 1693416230, -3141858078, 12057350629, 2236217581, 2740385358, -1293801473, 24432350273, 99371907, -724842578, -937791561, 7054162182, 301619001, 28018993218, 3171688002, 4917363554, 8773188563, -1990570599, 2965524533, 1556968673, -1832246973, 644357156, -4057923334, 3325238001, 1414243453, 7609002669, -940888737, 12779497738, 8170304823, -2576120301, -14510988177, 12308737699, -711875061, -5674741096, 265071661, 9207087291, 1757911853, -3823621550, 462988521, -4982302226, -482120546, 3044299626, 1974044037, 4891452014, 1196936244, 1364743455, 732891000, 4862050056, -4980925820, -2032513928, -2542072572, -1554743767, 5221675501, 3992970519, -8847179413, 868277605, -2542902984, 5702049014, 6038781262, -459165024, -5556065133, 17012062039, 1742093217, 5377758828, -2173399257, 1875038166, 13778201890, 4687827175, -700192836, 6066718422, -1907439117, 6672712311, 748194022, 1421625855, -6069633507, -7488592005, -8396740447, -3909769884, -1295670210, 7786842947, 2429987121, -8202580383, 619563253, 5945011713, -11923908987, -806752349, -1398221271, -10801346143, 7144012610, 7551279108, -10326934267, 4013457782, -7709585643, 3655746754, -2845425409, -2247438474, -50921882, 2334085216, -713950956, -3871415071, -8306286184, 2351463534, 2296957412, -30540290741, -2545261947, -13012470997, -3566733707, 16626830418, -8630619951, -13021426772, 5844224574, -1037196954, 16048895099, -5410522089, -7732342830, -2655314224, 4531719123, -16532895297, 7084288837, 7352353125, -5661844611, -3169407472, 728210493, -29164563787, 19299528542, 36376891155, 10567064515, -23319417105, 11835965943, -19317948281, 6043281412, -4186365606, 3862290174, 62499248150, 14678026227, -17950003757, 16582156110, 137569455, 1129808430, 4262983878, -1279178487, -6200000535, 1177044587, 27581136255, -7555677640, -5872545512, -5710491252, -53105398556, 9381214628, 12780551709, -695662270, 6954132169, 12467050416, -23288409011, 6587229725, -4052883735, -23167573264, -5214758539, -4429269864, -29060434447, -2645023650, 47905297155, -5724716312, 1312577189, 6344567298, -76402117238, 4257177163, -6400557306, -18730777880, -47745799783, 14999791869, -17574412991, -5237466204, 19113470883, -19525508613, 20957025809, -259542954, -49874305115, -12634693936, 1273189617, -11927618040, -26447620146, -8513836533, -44508365032, 18169473199, -11772789399, -7115127554, 48612032422, 24008447169, -18541514398, 10286059039, 5123258208, 12068998916, -18893506223, -5314311585, -67197678360, -2381983757, 25175488338, 19190114345, -29489313015, -1326105513, -22232347205, -4796145909, -400073742, -18908609962, 31663961681, -2107317087, -66841032293, -15263318120, -1481370795, -11794381591, 44011563310, -9389103012, -20076119283, -10565272668, 13135807665, -19046324949, -58913973403, -3585967956, -20237017930, -6153395946, -3531425445, 1825408552, -9243265873, -5304585105, -26990867937, 6937860021, 449207397, -20587446838, -13420388273, -4502418453, -28603044197, 5998304213, 56125666989, -9552536563, -51946084336, -14906755269, -77581097250, 27186063612, -4353519474, -9765028960, -16716678295, 5671442016, -30405947439, -14710741749, -36894870900, 15390095642, 4626366401, 1915726707, -61810067830, 27222370854, 25506689751, -27975076491, 60655553767, -9445824099, -45192715874, -8698934222, -12848318820, 20724800058, 21177103544, -3639170025, 463911440, 5782195940, -30253862745, -42604143008, -77876319592, 174731823, -88988334788, -38869985466, 5021327511, 17107464196, 24328419394, 1325261412, -187371067367, -30540095603, -6631320798, -13236117627, -59316645657, 21209055471, -50370870945, -32608132034, -6465741678, 41062419928, 5073825865, -13768251210, 30604043583, 21659735322, 38985427764, 68925825076, 92040893852, -27058299804, -23878237743, 3112846163, -51367781421, 60342472318, -48775327566, 24906427668, -85207552959, 15486296780, 23203354716, 19187331164, 81060514126, 6586148313, 46326535044, 2212235223, 27287583021, 50683155360, -12492762641, -40309520643, 145473630538, 64444712494, -14107324419, 71335195863, 117515576278, 18253824309, -34040032602, -30079308181, -31383908109, 88562904019, -2302984749, -16639346997, 35728344197, 59635175894, 4581334161, 19240173732, -46722347784, 11019561516, -949401406, 88652358457, -17741508246, 58356565333, 155019912037, -21473243019, 136073245569, 4122792154, 21738542805, 97531569458, 2480960313, -5812374591, -37908511714, 2608724058, 108624469446, 84672384317, -19389823582, -6780916620, 64442931353, -5889718204, -20049100884, 47783869274, -10272594530, 25831814868, 24250028740, 50467662394, -38550734217, 82294375606, -44769013882, -10704107475, 239253662798, -28987393174, 21465168210, 15334497414, 42659804060, -2210339907, -100007839647, 12304700281, -45582657579, 106853922053, 104706214561, 27749740050, 2928296663, -23173963176, 76523654367, 50746640022, 167312080305, -22314432663, -5894951843, 664144511, 43513021557, 90641045694, -51663143878, -37065875670, -23659004631, 14482905981, -3396439431, 92772932836, -149778577656, 16285390308, 12745942796, -5370970575, -64506817368, 124414232507, 45882917216, -26463808809, 91977384819, -35837004857, -22263854778, 25611175428, -20068909746, -41741115318, 3605428345, -24821939740, -30172251492, 119972601751, 102824691396, 12746506140, -1982819691, 57187635642, -8987087079, 76892489939, 13763626532, -12461484447, -20137369841, 3241204954, 45190205073, 111650652326, -11542376786, -25146180810, -83162084023, 84267747308, 736418304, 63075096782, -13535991339, 3984154155, -96222146691, 14402407153, -58303111716, 22748747617, 86241571263, -21362345541, -38828639767, -15988412238, 35422621920, 69240732152, -22110726195, -10871853399, -76943071234, -29843286513, -16475891346, 160990003987, -44817987762, -42056482284, -126182041568, -35288457958, 55264141782, -22051606042, -5495832527, -19136108574, -44988357108, -1135191611, 18559744515, 80312960574, 9716408294, -70873829253, 205358549385, 78574876580, -67877811108, 66846651468, -44568845149, 5944489776, -43985267904, -30736944508, 72898456518, 80050326431, -55873053468, -4723447608, -15454780477, -46374336962, 61962150150, -35819976574, -255802685387, -19115629425, 32527557880, -23541099649, 2914525233, -6463063357, -7654858223, -36658451421, -21901151408, 84898501485, -43837582752, 38506576382, -35209857533, -44779311972, -28842241586, -26077172629, -35926370937, 104501620877, -5999428236, -130443493743, 39284791148, -27138730696, -10417975704, -21513711120, -358512779817, -34339947408, -111875424327, -118772211204, 81354818880, 34612684672, -59519623065, -62261318088, -44052388167, 94481356388, 69562158156, -9416011840, -12321384972, -47054958777, -32979230055, -152365583793, -42052552353, 132523445874, -104081675188, 15092071659, -70641819847, -192634286690, 37676502081, -132536001168, -28594096654, -5661244143, 973879866, -40889191695, -6706652580, 136370417077, -202993162484, -25468493796, 135145312611, -144611343980, 15572663991, -46437956218, -169954056577, 23120696187, -177742463359, -6835541201, -199249376148, 246818919148, -37622685240, -43168950243, 114781628423, 51943078432, -14086388349, -120982026337, 214658161252, 7814315403, 56242747599, -42894286623, 16730825562, 222149815089, 8445056304, -29874759552, 12101039576, 131613044646, -6400242162, -96000163355, -350288961991, -35373251691, -9483660734, -84773632326, -117501333156, 90364218926, -92659966121, -98390624589, 32468796944, -59574133271, 11437673931, 4685237951, -255046470621, 9877437702, 134692243417, -101113099179, 1523465766, 176197823285, -70715611311, -17077108581, -313216514954, 4959799133, 6448038534, 7427942293, 64521540303, -5344744284, 153636647710, -124769939511, -29200559373, 161745923526, 130778805522, -147548132577, -415798655248, 22159940794, -49729224996, 105308426821, 209379809740, -24351301674, -14097249040, -134892695602, 156999477042, 94649699876, 18890512277, -115384497543, 307586705974, -242526232544, -33995867427, 27191769568, 80552243143, -16974756954, 71117468788, -184158573607, -110908307565, 46365837780, 213330689420, -45863748315, 100497214622, 45466470608, 73841129145, 9704958732, -102470768289, -56527907967, -32116880118, -259457278046, -71107389729, 128801023913, -156196646573, -75261300120, -176432368258, 171618694864, 29241193293, -168967512676, 111679613382, -6750363582, -9733254199, 67080564261, -211456285398, 301423398315, -181639331738, -62434323747, -136616142927, -138395312556, 4791081312, -47558127135, 631802535596, 100527681528, 61905239343, -203190938636, -48576123819, 313353088030, 104042632703, -50613025122, -51069762541, -123438062894, 9920546118, -13833297366, -136312471672, -77581947150, -252847491176, -2985091295, -16054675146, 179451885484, -157273682832, -17639060148, -46034822626, 203041293837, -65863630764, -7441167384, -305596840678, 33221790441, -178383903101, -358114060988, -102642148620, 155067138336, 171450752381, -220959078471, -408795161447, -46498300256, 44452918260, -150139177593, -675154294809, -33141690810, -456050162381, -353515199308, -31671028755, 243368883129, -164272532635, -28125806337, -78964468407, 67252665157, -125173013823, 82557617794, 61457047002, -78844741281, 339031470194, 707830256, 30222389925, 8250193134, -200469502318, 28508113701, 65882384713, 14589508023, 130735755486, 78430112036, 121947804323, -69670559160, 267521358223, -433446922614, 104360899365, 166357930942, 4225004899, -118988102115, 156490264689, -29983971774, -9329446755, -159553961263, -414985869888, 12429431694, 251066395512, -79533120915, 19374683706, 317229341913, 360211967869, -24970864194, -81636137941, -44591179637, 22570893459, -140286613472, 976498215355, -26630136342, 39161712810, -196793529553, -33197592744, 75783038698, 176951563830, -259427503377, -431888187358, 78035533299, 150139920897, -45551537156, 804207612381, -9389971980, -249809032326, -108463003476, 132341041269, 135991561698, -243124894251, -113396707188, 144660061382, 172139611041, 70091070417, -79217715298, -301426824072, -16676457201, -5746210262, -190097193256, -301586702517, 78781199491, 245857240111, -47813956722, 56455195657, -56572980983, 300501821754, 21640565700, 899944784569, 80693285616, -83438557230, -231782736876, -32829787458, -90029306023, -340526242753, -202223378628, 298550301436, 210507124447, -78847011954, -41563010104, 293153401036, -17154222930, -162450210739, -3011921621, 408020975379, 231905712647, 417812315611, -87555622167, 131886014110, 68282076916, 8363432817, -103093681635, -48537608647, 202249076067, -409889362950, -47622464331, -13238012655, 4767696781, 500854661876, -15382028304, 40235163275, 87976914691, 586681296111, 298688008839, -309084249059, -79359660603, -48056381948, 42464858091, 74755899864, 298958596551, 352392958345, 29502711702, -580347906290, 236782423864, 374767319646, -212931348626, 1657785056571, -61879217112, 28263846536, -531834962865, -157784440914, 361718271713, 393628043559, 13347375831, 256087881459, 416339750428, 104429120967, 12520006256, 639625908939, 38278783629, -112620810253, -6535830433, 108621487458, 54661857677, 460783768494, -26382431268, 667612602234, -668183414793, 363854430783, -108200256318, 619787238384, -71006112378, 62107972959, -15877310354, 331419973815, 213039883792, -65134968822, 28095085872, 66848401092, 734780537731, 318181478508, 84279252195, 436312206635, -23970921867, 46433975707, -488724655939, 569962813842, -194542128945, 210223911028, -475666236, -13473701511, 285174851403, 91549954512, -227740235624, -740771362519, -62760546657, 120228031655, -67992052839, 45722238210, -106312682356, 471762115737, -84830168106, -30860811884, 113722665601, 325548466983, -223038359752, 780048249485, 60377874687, -201672626944, -621769773712, 73990404666, 164010764647, 66785553978, -34932639771, 596867318289, -3345679182, 659673457371, -447006297057, -86781866867, 2683041489, -27135679392, -241442473972, -19570749606, -159371249518, 224029904894, -25320372147, -1171780082312, 233364652984, 190462378914, -343799585453, -241982131490, 8143713027, 123890102231, -120571306926, 756512816886, -113655966219, 561099002690, 85635576054, 15937870306, -2485380552, 132768815958, -91211735094, 463967951243, 236876091201, -1003406587075, -308089963608, -53745406173, -569149009787, 237330343729, 80069162391, 221156671505, 245560780839, 42038154171, -245116272258, 474692567021, -49470668271, 258275729960, -659861886867, 17397643212, 306203807998, 101370118428, -109563930018, -900417193930, 207293794447, 89781426027, -531305861856, -90393908146, 38184573231, -974764899624, 11407873882, 205443072063, 55451303105, 734209648690, -25403995899, 549052927949, 406797462407, 345046438926, -679723439821, 764615564843, 220598230221, -314504596832, -184657973657, -69555248127, -91245107864, 949590931417, -391796680779, -561400817400, -21303119920, 332335917873, -504510287164, -88118645264, -19220626647, 175228232895, -479276913356, -153218009592, -243609700860, 282271918527, 7156934847, 634093220934, 265544125800, 248591356857, -84169500772, -168749064659, 47463620031, -190796662245, -339440570551, -103237781850, 481689260931, 648878824964, 12500690067, -203442620904, -809692451162, -134522160102, -289653929942, 387696912193, -13017254742, -483479496777, -127529934594, 82196089902, -315193189206, 405502493330, 53299188999, -1982265828928, 509286472774, 132069204378, -533746184566, 537676762046, 32317278588, 868833120233, -748580255905, 36848073285, -72057641231, 351924468396, 19788057000, 744918143021, 175002609603, 131275351512, -466814834189, -55393376466, -134484997140, -595090349395, -308096479664, -54877876056, 219460579873, 93752212455, -68635959444, 146764006681, -126923956263, -41978081709, -811254822717, -124742178545, 140985238527, -783676459741, -298814341298, 107810204013, 294200181674, 238416727982, -238873844151, 52686854761, -77558784339, 23443495335, -24058633534, -474145614043, -68658380568, -1218606493766, -1267854384885, 153955323378, -129482029433, 575327385887, 163047094074, -1563553628403, -69672623649, -12397455648, -45114646912, -651970965107, -150013758591, -368148994340, -841450455334, 459325675053, 713382858465, 363315788533, 47036516859, -390601838489, -404367700072, 145199488356, -975495121863, -1081689580877, -58681779939, -324698702889, -19989332691, 50626030482, 352639530072, -391997688792, 372011451030, -971841710809, -327703436742, 126571333725, -572198144168, 58862683465, -18905206572, -328462781903, -1349454533560, 163801397394, 361009977228, -425052442317, -51500856159, 224432907830, -148829799931, 180163232397, -25304609971, 1320021118206, 20201238594, -1202720962387, 85359230162, 38383898085, -410491777189, 124177831708, -163880104689, 583588482647, 318219674455, -202191984135, 14438713274, -97559725857, -226711992069, -472386504020, 212101006031, -105563786868, -497673558480, -265508525455, -34983095670, -958159802477, 325445654238, 210244759569, 313244671457, 206887735739, 65609652267, -1113090854893, -931365865136, -221469670341, 808038478176, -986128182271, 16728207831, -1253050246126, 417746039940, 160515316251, -167805969714, -325698430480, -321945542649, 69193417374, -326521518224, -21782313423, 500435880479, -95542381099, -37751974317, -1817647711991, -390691243951, -291636345861, -263039159834, 767210416529, 192888340470, -794692012660, 476683672548, 203884535916, 620414123892, -975376301100, -278827225209, -801252080727, 239103490713, 108363360114, 289342985551, -1093619703060, -208158812361, 111724532493, 512670798999, 98705162358, 594471320018, 201278650466, -76826486043, -98328480595, -134657845925, -60680838798, 206196232842, -2398574548009, -1374890814, 95379523509, 280594373624, 63020300832, -414993038384, 425060431756, -19276675812, 669322668826, 296258491016, -104528206917, -230293332183, 99309312417, -224269726968, -1829808410664, 67405521650, 63489515418, -436636113866, -202299491376, 62017850124, -1219901968715, -503734281968, -824587850007, 567476937929, -1846600819529, -68722072569, 1232213221087, 92947086747, -351336716919, 687335295579, 246461351557, -96301810089, 1660587687753, 672484975387, 448924421286, -214270194787, -1182159224948, -233026738677, 1030700951818, -434067103053, -351578522844, 1052743853180, 1561763875143, 157794063498, 600929078629, -294949404398, -28004317758, 352133830947, -1497957967339, 433320167673, -661248591691, 295098786128, -146084096403, 1133072145550, -1363004327305, -208773256410, 3740722474737, 937418432120, -71693484048, -284313509554, -661415217721, 122356416321, 863391704662, 653499323800, -446388173019, 200613645125, -734760282581, 191275798599, -168208957364, 740070513630, 198513534375, 475046977553, -21306661989, -152869804497, 37654509275, 296274984965, -85574001744, 1379276711513, -1071784319079, 19661683311, -1337504460004, -450631862949, -787443222249, -36575622730, 185120826198, 521087270634, 1129309538151, 1562839207262, 982176061185, 591224580305, -1653677971070, 285310741905, -371110929679, 910076333873, -629624261835, -731279847060, 915604420816, 319571080461, 284369062355, -431708285570, -521584603587, 826686588756, -480230838812, 163168598124, 1878195669767, 1924444777417, -113031871362, -520057762988, -454991441863, 104281834698, 94399988693, 417233352122, 1687479700050, 1953808221852, -1330208057871, 396306708129, 1863884277088, 471579504823, -484650101439, -552380130924, 1280214270294, 447718214970, 158844324272, 439949985408, 3714375285, -678188797224, -1958143378490, 30504827610, 2721707429119, 601320795132, 115100564706, 131238009706, -1471979528301, -34537819149, -926379469538, -633322209806, -167400014445, 1278959879905, -24311044637, 31780203849, -3729178195126, 1357535944185, 744690678885, 111690234675, -540692762835, -204003296280, 1837143843649, 1913280164508, -158558728824, 793236498986, 1128850517474, -154183263804, 643181242810, 403672790528, -1433845761012, -772456861038, 1656774268473, 253292794956, -284585859137, -684911907236, 345074896143, 1180556914050, -585998449810, -18782881290, 617020794709, -145974057334, 187761568563, 470313920533, 3861345897207, 336610361232, -1221537357050, 379897143718, -628787043297, 1482267270180, 433145804781, 177855202575, -61998201299, 1016246955602, -109427860845, -25493648125, -966773065575, -625524478128, 223716886026, 314617629432, -140798480553, 751331491825, 897690023834, -119590286328, -136603662237, 200528216289, -784631730069, -7647679870, 2672312222791, -71415638550, -1214609575048, 935217392655, 1293443023185, -425988975887, -1535045697356, -154567340424, -210002528202, 302998500195, 35439584103, 517439368304, 349938752837, 171303317046, 907033256797, -902957391834, -2062857165426, 997164686008, -649093005252, 114943783401, -1164007861789, 439229596760, -172815047262, -52922575439, 888571630103, -505731002760, -141670973265, 923364989219, -1289136594141, 1074988117752, -689757281667, 404994380463, 668522094394, -804869372867, -474509150757, 1596033660260, -597224955236, -141411587508, -59958028301, -396949689660, 516063713841, 2193539638874, -1061506636351, -527188732551, 4373625561056, -243187747111, 565839696843, 400112100388, 125242424431, -7007659758, 1881827175620, 10884568990, -1346606238105, -1421714806604, 199697684681, -341136736272, 1297020966360, 1876573259877, 34376119659, 1223592151743, 1695654787343, -322045687080, 1414598413493, -903425115900, -714085743942, 1319629021250, 403680885277, -229873586391, -3561073251177, 130027293311, -1201725855864, 747842162992, -457674874726, 490575776373, 2755158388854, 24991623730, -317865313773, -429084933789, -862942369852, -192108443958, 473629879779, 2288253049, 1312524875394, -505792230643, 1208747030884, 648228073563, 891202583730, -737947881738, -500620888746, 512975186441, 2182909761335, 277723594053, 194628572940, -395960915965, 138327971616, 1594410777879, -1788407458535, 325862970732, -770882840507, 1301651387704, -510124668021, 1447770659796, -1485118968597, -143486412795, -1092607642606, -767683203827, -1814337315720, -562914096502, -1305015095141, -64313561439, -1628906410063, 747686061883, 679738185126, 219049229612, -2108495031471, 518133087315, 251327264767, 85326095729, -796211451405, 133695203596, -294629126667, -35804848851, 2212723596481, -811225917973, -600273374535, -77210941475, 714324000769, -129495939543, 171914956498, 1251601042786, -10801991034, 191885597427, -627503641298, -510532468974, 1012343301316, 817397629968, 854926965387, 194960575673, -2163656802170, -56897561349, 559762364396, -309615360448, -1804707871911, -1538714087777, 1353897556752, -412109589240, -674160440633, 1300985957354, -39997011465, 858855046826, 1783581743637, -318448302957, 414050901344, -163657850367, 1188312209370, -73360124662, 1942295177342, -253505781324, 1309813745681, 710069751022, -542055220641, -180661593293, -1584212949055, -285262362036, 1556606051761, 4321074589452, 354666806955, 390665052573, -3667263133365, -514250773623, -1222754687524, 761038503242, -1590677281881, -1291382882864, 456206489249, -96821134812, 1478490083098, 109538221689, -546399484110, -360289576551, -506123362435, -166141690542, -1588751114853, -2174958377337, -95348487015, 2407167495028, -2858831442758, 49286030904, -304654101005, 145569624708, -249568178571, -80478910747, 4418159819629, -143223797835, 2506460013573, -148399339329, -728753434299, 191725532256, -2378698192626, 187322220567, 4367381782687, 114961322087, 12128599719, -1973870884409, -971000648757, -555861064626, 1673045179517, 136327603130, -362350483371, 861152192518, -2371162968274, -121565298231, 2644752223221, -1052547412954, -772282193319, -138146968908, -2609071708567, 161954213751, 1050445366425, 1517853680495, 1515393008703, 363745711538, -1085120865809, -257918487201, 2210285490057, 20350708506, -1402544277072, -987343656894, -296045650298, -402482392263, 2449563184024, -804771973803, -2094689625750, -644885170945, -1018568029796, 734023717524, 558171289151, 856185323672, -117545025798, 279359909712, -3958233022463, -263655781920, -922782744981, 883167956982, -451350313965, -1011934844039, 108704640152, 153128934432, -1401829099338, -478281539617, -820960580853, -1655717596476, -3763155820155, -397190027223, 852043651971, -615296883049, -996161514300, -201971544454, -2255772369832, 415532582334, 1599435323368, -1105108909201, 124911892827, -1024461257338, -1104229488045, 51724621089, 521009135701, 163662241742, -1668871831410, -193767754327, -5093319090475, 735004013058, -490334193335, -605926659951, 688680623277, -699843842177, -1640334386355, -755327065257, 1691243606439, -405171711283, 1637699951709, -1282012183996, 2353866026453, -255037250673, -3470137329404, -1219138183720, -1220203328598, -820994221878, -2945659872874, -234871223994, 558172544647, 1100781793342, -346904608140, -1727010908382, -1443821876994, 559569601566, 1809409186027, -1038737592808, 571781795688, 939463931903, 1097339440662, -98257590675, 596638017704, -1789625558276, 12525608880, 59071313359, -2024978828625, 156119290380, -2001072107813, 203706068239, -816854294115, -2759486220259, -1224162981031, -1150311861216, -580210656601, -1635842693982, -2102660628984, 500591005785, 1246136876447, 4717759221, 630354297381, -1586714952434, -2402685039276, -1709746958463, 1164244089105, -1049489607582, 3135012777896, 465340661505, 135575842797, -1724320718930, -2573838888169, 461901533292, 1550596456677, 139391794872, 656867323638, -340668993912, 1479923709018, 35782058124, -2913660117876, -998254970983, -5059018818909, -982612096224, -3056963380567, -824582581281, 3054954060044, 586169269134, -179045661546, -1089536377567, -567925695195, -357375175929, -3407615641811, -1746891978002, -1601549432739, -427727629192, 738731021073, 572644497717, 1497815729817, -362600243481, -1360013515515, -2838245132065, -6784101923236, -880419564918, -255014302577, -2221703829002, -174575025306, -971781873537, -4383375906351, 1108685338056, -2968489955561, 1262756057288, 136993298355, -363868255928, -2460662974748, -371742782670, 946153876781, 75753331353, 826309176741, 642380640864, -5477664370948, 584812853694, 1344879371370, 737999149381, 1052606549628, -90620282204, -3133007249741, 1860997277052, 2620493393607, -266916847975, 2485104134004, 14964367760, 1912248342749, -730574094708, -2193930672661, -784083398064, -644712419061, -546978718873, 1608215010249, 84046846401, 89109668787, -465804442277, -1386930098367, 848103582486, -3418577712719, 1629246752586, -2258335720204, 161513385011, -1316933844282, -998084267118, -1420814654813, 672473547036, -5127861930993, -728159551863, -2300603929893, -1677621455395, 7779948528478, 418130013060, -1636414305124, 2950617234488, 626490577332, -3165476969564, 556735569378, 518057941428, 2437866815806, 178188258053, 2188633881402, 1885916820261, 890379180314, 177826004451, 728758454900, 2466419294877, 1250816446188, -2814135528694, -1481764520858, 59730351021, 1679607794992, 1930588427545, 736764741567, -1381062966570, -496965585628, 1368445194720, -4825517844353, 127780533085, -337304591307, -2147562213562, 9690920853173, -1088357057361, -1892623312106, -3230776549500, 3927788024526, 352326731880, 1800343072147, 1740007237338, 3543692635898, 931743013983, -380897759313, -1313219684175, -2080981696138, 1926050288301, -1244389306491, 397631261221, 3172920559506, -2100398666285, 3349615302287, 492853256343, 4478545781813, 1195625064382, -919080880254, -84041546250, -942672973554, -812141320887, -2422184446328, 1850617109455, -847365518943, -1779825599281, -238897210668, 2391198408513, 2809037362, 644867500888, -62180588223, -376060950190, 10425733518963, -449262368919, 354724242051, 325467251758, 964665293319, 2442997276004, 1275428030035, 1610149749138, -1169880460597, 2991942899763, 123696022347, -1301937988507, -2123100756767, 519484690764, 9264148310621, 325850563517, -1261503390168, 1489845650112, 4186645911073, 297528160932, 261390200985, -2365904863795, -25633837962, -2601961771749, 6351696637506, 2393613678339, 2473521505428, 4696797856621, -479020722642, -452402795883, -1996321176671, 1575627263991, -1481600497904, 3789799759214, 4185537624999, -3514015562246, 3773961394543, -579777561513, 2002445028693, 1926365064216, 3673977630363, -116110144001, -3609577253311, 111315388158, -677344745451, 3507160593539, 586940655735, -2960589246252, -3225300223676, 2633352375366, -570551419358, -624448551233, 66985928451, -2448660235960, 8010038677189, -156934113957, -8444135323194, -3260255800818, -1023529816278, -2084855998934, 7143056786910, 70435549566, 1111046093235, 147260277839, 2932860675042, 2436948106613, 1016484211201, 2286154376559, 3009002322578, -230925371104, -523525236714, -1174309375686, 4905587086601, -183084748740, 4948328880210, 770155149131, 1739959146531, 836481323616, -4235362706801, -159022391508, 1460676619698, -690599180171, -541325723868, -381360350610, 2675352681783, 1290164470398, 307859542302, 118747661524, -277360052310, 1667841773923, 2498300046870, 697459001436, -2418547089059, 2276985109828, 654750775980, 1136689071856, -141528148353, 1362626884638, -1120980016271, 749144746096, -1040869823859, -3100720271308, -339449000315, 2221948141362, 5531646832003, 796097527447, -1208763374814, -3320519587720, -4827363028748, -289010901825, 607214440652, -1167219326396, 6459848895546, 804006284851, 3607174746845, -782659615698, 1135447472719, 367009272638, 579559541670, -811162276710, 167519845898, 414031430178, -1137665696804, 1609404259575, 1151814709620, -2462762585572, 4778804680932, -59679177489, -8405381709220, 165893628648, -2700211670469, -2329387588735, -203274553335, 332226907587, 4158715287874, 4540608664245, -1230731754633, -178464293795, 2090488806317, 2885055895431, -1174185897521, 356107239825, 2827067793147, -3427000822289, -4353367290834, 749242981350, 415931211063, -2917291722829, 79064009901, 671420659943, -784930155191, -625697005752, 3503397117613, -1615431655018, 2066138667909, -1259545249777, -5547060814591, 1370159280594, 2630906891309, 1140269384776, 4517426168235, 168175880153, 1548536755549, -602489681901, 2132133968762, 52417632477, -159163699761, -3989794291117, 1011217849640, 17931901797, 2568106704128, 2492172934009, 1174851582039, 1296257797201, 1313238633280, 2447308233738, -5849782949608, 2044439871441, -1394904884706, 293474062881, -562873409566, -1000778643090, 991535009990, -1785449839642, -638793125037, 738000568314, 407611243823, 391038461487, 905245953666, 4407254694213, -91703864637, -4283225401521, -4053643338587, 2504869186572, 5547085420474, 3858386807187, -4044021596712, -2304691885370, 2347157215419, 439705538316, -1000950285949, -1797173912843, 344140455492, -6548520743971, 5160457834533, -145016205525, -4761806882673, 3016483569054, -1741684068936, 315610967217, 49546919766, 3359184277689, -5325175454547, -2300737846400, 1238838764832, -4020927612379, 10693799018770, -714522837843, -1580040871678, -2691191816712, 2483389390113, -3011663571775, 5844551881119, -967599131139, 1143075841042, 2102150706664, -601124079006, -5112189127435, 2979359354255, 691501736556, 4953003852461, 1496079744260, -541860563142, -4401476699435, -1819848068129, -1127010113586, 2060570275763, -2256756259978, 97346565315, -2554492390827, -1026940837236, -670192372980, -732604665763, 2336848594740, -814650790284, -1920839732665, -2787487955209, 3239260247277, -14129795990216, 1638182217874, 2776266667692, -2752897588093, 1712516192984, 344155665780, 1223827752502, -1245222368752, -53536131657, -44505609087, 1053188698053, 1544066162334, 1793004594592, -7115732162819, -242651351133, -387222887170, -5609995124313, 2076097228353, -4110689391107, 3499041776497, 371617916364, 710227019100, 6053738146951, -336460080069, 5933548177429, -606117119322, -543708985707, 959179251435, -311128136582, 87512533758, -25915177450, 2344654195155, 1220135536971, -602210457622, -6269581132313, 3014567612802, 5612837712814, -4436114765130, -311644173222, -4288220551024, 10159921630912, -678946881870, 8386462068943, 2270979578883, -2245376268621, -1797483738113, 7430907034177, 2275229177316, -7394629189670, 97978105740, 19883294208, -2902075357534, -3358391431665, 1703027613114, 6293653981905, 377554022414, -365471766153, -932947757223, 6638245028227, 107572162185, 4971298858891, -3196533653299, -2597997960657, -2373260373720, 8809776818779, 388864993131, 6638459379341, 3102591555913, -1574184016332, -4359724155297, -1375560538705, 614216185659, -5401841484470, -4370365960482, 2328522424101, -105430524606, 5198134691661, -576783329607, 983312699452, -1299697837728, -1048373273709, 3751859715477, 2613216786016, -431687130426, -7344864216510, 1096532355183, 956410791840, -3802487149530, -14089371300553, 1869499768104, 4575085949523, 357857717585, -596989607265, -2804272666659, 778462410275, -293540041773, 2778601253297, -1706892271189, -2077462923318, -2781647560985, 173760688192, -805768735851, 7619077261627, -717008899227, -444849066342, -3920358898889, 2130786494857, 4346730107649, 342556973954, -4273501109079, -1210085669574, -4060224978013, 3286123627945, -1135525021668, 1010512297847, 1630587940431, -3406915122336, 2299336973599, -5647190551820, -952788364866, 7220906615050, 1454527943126, 1492131828114, 2220928499308, 4004275490015, -595393363134, -1740112743806, 2367524999768, -148387478229, 2879274056562, -1733650054754, -516674931498, -3890025757848, -3609116726042, -1214685641916, -6782795738371, 1846911288756, -30650173497, -2121238330047, -406460632361, 501113101905, -1165128841782, -3212577066682, 2168449935498, 3518489692359, 2536519892283, 262343023938, 40035751594, 2304684571106, -1913593389831, 1533808043698, -19488837459, 5544680833395, -3258106454711, -748492077959, 2121521667660, 2136276660803, 3627274876869, -1832700899916, -644253824511, -7031031362864, 1804859589636, 6667442866620, -2821868638334, -1203358819023, -456496431545, 7895846277818, 160501223952, -11719529105176, -1888368246308, -1187602233408, -3455426174424, 4341993135177, -829897501716, -3519394032842, 1333695062306, 1968258325986, -3276672669425, 3687499605978, 2161358813637, 3140839205009, -1454682075083, -1508572443636, -1953170185676, -5717333642214, -127533085416, 10779909318286, 1137089255036, -417279072879, -4429031596261, 1021235989588, -1252107097974, 2818395091146, -6857843618335, 1672978054050, -260460138589, -15418282493599, -967139367498, 670526118396, 4018096203386, -6906672505449, 3732519319760, 535294379391, -516121994475, 1130565913216, -4989882393277, 878244062760, 15459522437, 3786681675107, -635609690523, 3545494599243, 1126099387909, 78692181291, -3313893794064, -9294655725683, -174502710639, -5363205560050, -1657950305764, -206681172021, -1324660397060, 5241515005546, -989778188367, 7366102807833, -3936135583555, -591331088016, -853482716772, -1089648348071, 2292259540095, -11595948671995, -1226201252883, -1183614734304, -4902062400851, 7243866858884, 1039677562314, -7582949908857, 5790877523874, -950666153391, -4156508512544, -5338919012947, -1209041423244, 2660728176591, -3085539632194, -778740522822, 105862712633, -629776727874, -704083660983, 4113279740587, -3026275749667, -970012015299, 5011526989051, -11364078112911, 2821543763679, -2233296020221, -9709213219940, -161984562372, -1368721969023, 7437837512421, -3521974331061, 2306706250853, -3920384685275, 1060689360996, -526424303280, 4925302733685, -732745728792, 6887273056519, -3382890165906, -281285344008, -2081415686184, -8198337340345, -580870200240, -383099984474, 4165655195233, -9679845055059, -6265683037080, -2299350726754, -927178580016, -5935492888145, -4662508888909, -3020636456829, -2691450726366, -17072568356635, -3206849702508, -262303500175, 2337853542434, 2196580109760, 250120609771, -10442140889177, 934542486144, -9194232153229, 1866619798877, -1607029822755, 4339641141485, 3677055247493, -1681055588376, 1608065753623, -3444839551870, -1189414480509, 2800881952540, -667578289125, 2550996622476, 4853473684756, -4071543049963, 1878178270212, -10392808583676, 2386729395109, -254232319680, 8261850758497, -3872332177464, -332677394244, -2591523036430, 1654177054891, -1270483886979, -25579777208547, -2792082580010, -890439211485, -3734594535222, -5729199515446, -4113870762411, -1327494697527, 139558022118, -1135418913531, -462681708839, -4891086998484, 3578133038598, -3629853807811, -1766956065177, -2810205230076, -1098489985520, 1692579577794, 407485934793, 7601130061842, -6563967895150, -1907329135869, -5422105620843, 5858609754840, -5201125740630, -1264591786573, 694511348086, 1017265556187, -5790235188110, -6000432353421, -3578472031536, -10493807713431, -2965526544363, -772040609658, -4550377743361, 879124078455, -152853591861, 5527025205438, -8632742416909, 26294756382, -1420965248908, 6798563478306, -1104008175765, -12596493256389, 2606711167203, -181079619660, -4646740163285, -2486599213276, 3682001261079, 8934640695545, -4671263907304, -5480815387068, 1840908394744, -4574759367125, -687649332492, 7227410294445, 2902853409614, 3648923440497, -1442090776828, -17673171549791, -3904506287460, 1453173701659, -4585479531120, 420461927757, -4521438592766, 19563720458618, -1253824817886, 5423136437277, 3613850801811, -4588759527579, 2532068229080, 8989885238811, 624258797049, 1515356269459, -2584043705114, -4799046510693, -392088994233, -209043424920, -184559612427, -1343801709530, -2744601952052, -5379733155996, 1343181751638, -9719118660326, 6664110816996, 16570188655544, 3606206628620, -1015812501480, -1291996715869, -326391387930, -1165561656561, -2899134074425, -893550219702, 3099103967421, -4925410196989, -6216268125438, 1402463117664, -15143391287084, 5519137139082, -380332485423, 2800653930354, 6208610512814, -3266514711099, 12010185460167, -1955496910655, 5795770353804, 4534536647085, 2988136202733, 210986515881, -3025642654327, -2946083749227, 1518554185173, 4193214387857, 6901505785970, -1158145738821, 1449554150707, 10724658297406, 451732290174, -3371121219990, -8860378047472, 5998045007403, 5544080372655, -495573397849, 228016520208, 8597700018015, 640269205721, -806618507904, -4768888964677, 3500277291669, 326728068552, 10910941702916, 2300840503027, 3553552205442, -727356521809, 2113546753390, -172806538374, 6015621308566, -18213935949014, -2592004410585, 1687102208533, 6459041268702, -9457801973757, 1197654793298, 6955465807409, -955077795657, 30061278548147, -15385789283474, -256058839818, -2763009687955, 10500534544945, -2288888072802, -936809403851, 3875792813697, -3172535995212, -2807613754976, -1030835853530, 2439833911002, 9877886948077, 3811847809000, -2501819085267, 12331786032516, 10356469436893, -2656546863903, -721586451149, -3916064674497, 876657517488, 5631667724807, 3404816404678, -1608501598317, -7211527735959, 4363352194653, 308817196137, 3913563049553, -15942445392224, 126501424677, 2811613778913, 16964736652240, -6886254706767, -1113718453569, -13026855855725, 266690817954, 7787397385504, -2003216280060, 3636690572259, 4754719598331, 1729239570707, -2730053677833, 3828010319962, 8358664212486, 41133575682, 7771384816759, -5808046527763, 4757341228695, 1078966020158, -6502746006363, -1909321505397, 6003295335170, 8843073982163, -461081931687, -1756512166599, 9559518327782, -8456845903758]