# Trace form for 115.6.a.e, downloaded from the LMFDB on 24 April 2024.
[0, 12, 8, 22, 294, 300, 454, 16, 675, 1598, 200, 132, 728, -236, 359, 550, 4514, 1666, -3096, 616, 7350, 2732, 305, -6348, 18873, 7500, -4502, 11584, 5407, 23722, 11350, 18446, 35808, 4416, 53123, 400, 68916, 10394, 18681, 27032, 16875, 48232, -18980, 10732, -4765, 39950, -4232, -30448, -2052, 26948, 5000, 1524, -55346, 36494, 55567, 3300, -50981, 37572, -83373, -23870, 18200, 30862, 63582, -49698, 29965, -5900, -235225, -71910, -39371, -11638, 8975, 167158, -296052, 52152, -59356, 13750, -230417, 4808, -469771, -123092, 112850, 159868, -140098, 89322, -488082, 41650, -55318, -334376, -104551, -46184, -77400, -153444, -155526, -16576, -456595, 15400, 330540, -94220, 413841, -740784, 183750, 653626, -829907, -141622, -617811, 68300, -8934, 3042, -260103, -43550, 7625, 722228, -1272855, 127734, -1481630, -158700, 364459, 52396, -880500, 146450, 471825, 1146834, -788773, 1467294, -387748, 187500, 1392346, -223544, 1384466, 358084, -112550, 1162528, -876975, 1324408, 71322, 289600, 1882831, 214296, -240166, -436106, 135175, 1036344, -901578, 879424, 252180, 593050, 1363191, 510372, -367532, 1055898, 283750, 2060932, -824531, -457874, -759180, 461150, 1996865, 518378, 1083132, 1748696, 895200, -8464, -3822404, 284634, 566402, 110400, 1577362, -203284, -3582720, 777758, 1328075, -143016, -1274412, 63288, 1025311, 10000, 1415465, -577048, -2133004, 1152648, 1722900, 1012702, -966151, -490326, -357075, 259850, 2453619, -1147382, -2975441, 1014978, 467025, 255316, 736861, 189168, -1362123, 675800, 1624649, 4248, -1986281, -2148892, 421875, -2487048, -5064968, -120758, -1895, 1205800, 558963, -845342, -4369160, 1647800, -474500, 1282394, 1619396, -1212324, -5143664, 268300, 2648742, -1205842, 1162753, -1245644, -119125, 741068, -5580540, -1151052, -6541535, 998750, 2861462, -501452, -1301784, 333396, -105800, -4114056, -5707012, -253864, -5772312, -761200, -939166, -1842248, -1769806, 1309242, -51300, 2082464, -803653, -3873676, -2154507, 673700, -500136, -3055210, 4846831, -1325312, 125000, 2226880, -8402772, -69828, -6225761, 38100, 3630482, -4023436, -1537374, -3432874, -1383650, 4948918, 749085, -396448, -8003021, 912350, 11443049, -1781736, 3406870, 3905034, 1389175, 1912110, 8324005, -3175120, -3655737, 82500, -385112, -5370148, 11663899, -2998054, -1274525, 1880700, 3102057, -375390, 8773676, 939300, 3678812, 2011210, 3944166, 3461260, -2084325, -7508212, 2374147, 5033494, 6895627, -596750, 12534676, 4706508, -1782269, 124844, 455000, -4213408, 15924072, -7920104, -13015007, 771550, 7558837, 566394, 17105344, 2544522, 1589550, -2907556, 4244560, -1386830, 17506836, -1242450, -1468926, 6705188, 9604284, -3200840, 749125, -8668392, -189911, 1777772, 11574378, -147500, 868788, -9262672, 7889443, 16645496, -5880625, -3471182, 24714668, -6399022, 1958144, -1797750, -22619216, -8090176, 10343720, -7371304, -984275, -4486528, 16954592, -8608162, 538158, -290950, 2448983, -136854, -5139151, 1110658, 224375, -8755912, 10330549, -1857520, -3106478, 4178950, -240062, -10872020, 11882685, 2205320, -7401300, 2757490, 14035431, -7065586, -11511381, 1303800, -9137205, -12647750, -2387906, 9534020, -1483900, -12662730, 8340555, -10137604, 13524069, 343750, -19692094, 16740852, 16461523, -5549416, -5760425, -10784688, -6368500, 2010146, 6943050, 120200, -7082649, -9326276, -6041513, 8482598, -11744275, -881314, 28165976, -3410040, -1188146, -3077300, -37327745, 4593348, 22975432, 6188724, 2821250, -3920192, 21919744, -20625914, 14876494, 3996700, -2406978, 3978728, 4775587, 19429024, -3502450, -26782548, -24587005, 2358534, 1637784, 2233050, -5149122, 23229112, -16693276, -6517420, -12202050, 690882, 5860198, -12813276, 4846298, 1041250, -15483734, -18048360, -5499140, 24479030, -1382950, -5632896, -19857215, -25658082, -17809523, -8359400, -11433309, -325864, -1467201, -5992536, -2613775, -20107854, -15896696, 1434930, 28040482, -1154600, -5355200, -1828776, -35092931, 10736956, -1935000, -33650064, -1088142, -10805196, 568676, -3836100, -76731616, 4799410, -6953876, -10615432, -3888150, 2264828, 9153967, 562512, -19010561, -414400, 3090221, 11991442, 1078968, 25508430, -11414875, -6257668, -30097634, 14082908, -54060352, 385000, -24220320, 40500566, 23617067, -6929536, 8263500, 15704220, -3344268, -1445228, -7287807, -2355500, 22828566, -19686024, -4995989, 48581708, 10346025, 394370, 96867930, -5045246, -25876299, -18519600, 23070938, 15228962, 66910678, 10903750, 4593750, 13162396, -6519085, -3446548, -15011908, 16340650, -161345, 18315172, 37194357, 20591464, -20747675, -40895120, 43454199, 80373288, -16175539, -3540550, 29471144, 24402380, -28563458, 8436196, -15445275, 21073748, -31718226, -15778728, 3586341, 1707500, 38929703, 9219306, -4207005, 3358092, -223350, -9452562, 103128133, -7673916, -40564494, 76050, 16296598, 19215248, 34117703, 13282716, -6502575, 16097492, -1499331, -44079336, 45522531, -1088750, 24082675, -3263846, -13952313, 29167242, 190625, -35218440, -9983817, 19472980, -29038367, 18055700, -21775951, -770746, 83616574, 40831344, -31821375, 40063176, 19406786, -13768034, -30596857, 3193350, -53782972, 7281322, 1617371, 12055680, -37040750, -35077952, -562850, 22281504, -45173338, -3967500, -31327058, 16336668, 15567289, -43028272, 9111475, 30861486, 38468173, -36131744, 5572278, 1309900, 40130700, -33053086, 79351749, 11625394, -22012500, -14258288, 34595298, 23537512, -102674817, 3661250, 18982483, 11760308, 2381558, -2512520, 11795625, 36980604, -64574256, -8853266, 88428468, 28670850, 20678722, -8417096, -61991247, 44753356, -19719325, 18215040, -79141645, 7908956, -75932003, 36682350, 53502436, 16558798, -3336623, 17515244, -9693700, -6127936, -51066419, -45636212, 7572187, 4687500, -3516065, -28772818, 44760272, 47558310, 34808650, 6468484, -11983106, -33953308, 22151027, -5588600, 73924392, -37273804, 2825556, 59337190, 34611650, 42995364, -3464648, -67848126, -2860303, 8952100, 10098168, 4973668, -119471817, 9124832, -2813750, 26776788, -9172254, 9716548, -47835902, 29063200, -61923366, 22242152, -74992052, 62123980, -21924375, 5928746, -57564089, -42294138, 26246932, 33110200, -39419336, -12548938, -53705136, 46994276, 1783050, -50760508, -206289722, 10650260, -40277119, 7240000, 39961392, -10072022, -33001568, 20949896, 47070775, 51028, -50970238, -14034138, -143274496, 5357400, -105136908, -20815316, 6153438, -47419504, -6004150, -47801056, -62163753, -27444232, -58875697, -10902650, 128490644, -26062494, -15640307, 64568700, 3379375, 57642906, -181229510, -33864876, -144670489, 25908600, -9316739, -2278718, 13777914, -22962542, -22539450, -22924080, -80238632, -9757934, -154863567, 21985600, 33886561, -83042572, -44605988, 32130490, 6304500, 65871440, 54959239, -100841068, -6286267, 14826250, 121612406, -52902732, 21138463, 62052770, 34079775, 16733564, 49594981, -17827234, -100149086, 12759300, -18942432, -67316076, 190361621, 27703014, -9188300, -27749450, 54173920, 26955002, 24416318, 26397450, 130574946, 50478926, -5315987, 30805054, 7093750, 34338260, -148195261, -68034724, 37693563, 51523300, 201961685, 47163966, -99998837, -2336064, -20613275, 20458792, 54238857, -140975818, -75747888, -11446850, 145590360, 53300120, 286671396, 21871104, -18979500, -26220872, 91494931, -36176232, 25914540, 11528750, -42207153, -83759948, 72975369, 52449256, 49921625, -35382030, -28102067, -90399288, 156356877, 12959450, 66308177, -135350530, 172063906, 66589382, 27078300, 83185646, 108849573, 7682588, -141768672, 43717400, -91971022, -39407810, 243970439, -29387508, 22380000, 23274484, 9996702, -48915836, -261403118, -211600, 4331306, -741788, -87029108, -79603404, -95560100, -3518278, 22863006, 86340068, 112948328, 7115850, 206394313, -100382032, 72604660, -93252600, 14160050, 10449560, 121265068, -37918732, -178328307, 2760000, 70237974, -80223302, -36456564, 38150714, 39434050, 22678100, -71453591, -25607268, 166699315, -5082100, 195337000, 88267204, 164599242, -19878764, -89568000, 49816922, -94125103, 79587500, 219620992, 19443950, 214857182, 22604278, 62516972, -82018696, 33201875, -5498426, -117427882, 5245824, -174319716, -3575400, -175118268, -35950980, 273283799, 86947446, -31860300, -5699926, 70375480, -19230920, 35666919, 1582200, -86146573, -79278550, 15114813, 108088496, 25632775, -91223800, 88386883, -183579424, -9882249, 250000, 194073307, 132899172, -27500158, 29061680, 35386625, 10921976, 200141031, 11050694, -102552984, -14426200, 35403720, 113058812, -34924482, -365208, -53325100, -118010692, 136283316, 37845052, 39199330, 28816200, -231485417, -14299928, -81204413, -38326430, 43072500, -108409122, -349858417, 13335412, 270170404, 25317550, 335303330, 70053882, -69801318, 97355946, -24153775, -32360844, -211828902, -110242088, -143231592, -12258150, 950754, 11451504, 18659681, -48080760, -8926875, -33698742, 269618833, -50027676, -187026521, 6496250, 24702524, -61587738, -24926375, 22450662, 61340475, -104529000, -189994943, 33762508, -138879370, -28684550, 8143094, -34144960, 103040982, -74277988, -74386025, 46851926, 119543354, -25514728, -291998518, 25374450, 3312888, -89974406, -17319014, 187856640, 11675625, -116822148, -252972, 14082324, -66696178, 6382900, 75179765, -10936628, -34235108, -66003548, 18421525, -110578472, -112264032, 74415798, 144098060, 4729200, 10040420, 83149952, -99476564, -251464602, -34053075, -24382408, -212586338, -22952478, -75160893, 16895000, 63176135, -51483262, -74335665, 114097976, 40616225, -39980460, 34221715, -39760712, 33778789, 106200, 18449474, 74914556, -65497625, -5677228, -49657025, -120176082, 81180108, -172756836, 160837918, -53722300, 82800986, 82234788, 146975915, 43225492, 10546875, -119729414, 384049176, -245023422, -82528137, -62176200, -208534889, -798032, -183402936, 63445748, -126624200, -237960500, 2520685, -58043732, -171245334, -3018950, -183023570, -432664554, 153562749, 97217224, -47375, -23322814, 70818006, -104893930, 146806814, 30145000, -162061581, -32016172, -228779131, -74026318, 13974075, -96657340, 169327670, -65062758, -297851576, -21133550, -230166316, 156787056, -1066355, 20544020, -109229000, 34623942, -4073798, -14890106, 440140716, 41195000, -66731650, -80469740, -90534374, -90949508, -11862500, -59213924, 161121691, -9963116, 25919928, 32059850, -118904641, -35761732, 2238728, -80942708, 40484900, 152282046, -179691284, 2785828, 398542355, -30308100, -200571863, 265434882, 217709832, 75634750, -128591600, -99278586, 110056680, -82966218, 277584297, 6707500, -56869141, -64575576, -167019770, -14108268, 66218550, 16106992, 170566911, -56883036, 219820563, -30146050, -208414188, -37598780, 520214761, -70353990, 29068825, -37949352, 38434213, 202452852, -129930838, -31141100, -188218307, -177577196, 2636077, 134962678, -2978125, -30939632, 308568970, 190162740, 1085508, 18526700, 32540824, 520508314, -463854079, 237996886, -139513500, -62823260, 145490544, 101884272, 360045394, -28776300, -142369804, 117243224, 32493654, 230056612, -163538375, 120045864, 157506624, -88139494, 189614140, 24968750, -321685322, -14255492, -103036148, 16273840, 71536550, -88683900, -127407610, 218046192, 405304678, -12536300, 58283574, -209362296, -3559940, 152551830, -32544600, -134598666, 202841877, 136629892, 28450494, 8334900, -360615384, 21763854, -211992114, -90033744, -2645000, 184449018, 461699146, -314712620, -46048027, -102851400, 68462377, 279820412, 217849831, 76175764, -142675300, -111157252, -266835692, 532269468, -369303229, -6346600, -132600682, 413024838, 43371021, -194319992, -144307800, -204126572, 409180334, -806196, 261587046, -19030000, 239820200, -95713460, -172781745, 291726764, -23479150, 221433818, 23779242, 158856808, 296662780, -46056200, -65510762, 200950356, 353963381, 5551238, -44245150, 52856328, -15884573, 133734770, -209851022, 32731050, 29278034, 313347316, -112366055, 159981020, -1282500, -5636312, -238646636, 40691432, -158971900, 52061600, -225625622, 57234672, 358868307, -279141394, -20091325, 413196468, -263316634, -129271688, -203247464, -96841900, -511115917, 24013320, 73515444, -19305326, -53862675, 164863792, 332789593, 307096036, 47946025, 16842500, 98475890, -62955712, 124601, -14629674, -12503400, -36137108, 348100392, -181003380, -3178061, -76380250, -8888247, -214631416, 77024307, 1748012, 121170775, 13526824, -29394943, 142852856, -352926131, -33132800, -336502192, 360616544, 161262155, -3105124, 3125000, 18855838, -53931251, 349079032, 161472437, 55672000, 429440510, -131741800, -95368326, 6936984, -210069300, -201204592, 239514052, 386568280, 17248764, -1745700, 78791246, 248340210, 140635203, -105283504, -155644025, 291535206, 86761842, -307658248, -329475358, 952500, -340429426, -129996540, -480356101, 6882652, 90762050, -417200378, 104376588, 145640534, -427411982, -100585900, -192421238, 286534134, 26968949, 125282596, -38434350, 269035300, -112473628, 199864236, 101327511, -85821850, -345372682, -497387560, 42045498, -149380780, -34591250, 83481884, -145762709, 57154834, 51515905, 123722950, -219155494, 247853492, -162950468, 77420290, 18727125, -19875588, 238759942, -138694488, -347672494, -9911200, 182106750, 96183264, -173858428, 206634990, -200075525, -5535256, 27834777, 242427638, -83228791, 22808750, 362312381, -67378740, 186721240, -516187876, 286076225, 222262188, -160201150, 22685672, 44104317, -44543400, 27716364, -298188572, 400004976, 251427348, 85171750, 135855936, -463433049, 221932792, -765992220, 97625850, -409052009, 115328860, -754311377, -11881096, 34729375, -223965812, 90204786, -526104548, 454557922, 47802750, -353025694, 12627230, -101506000, -128296204, 208100125, 268132778, -616530986, -19712572, -172753792, -79378000, -467451224, 112676328, 144828048, -154769850, -91393425, 239069496, -227772838, 204632308, -140890816, 2062500, 199691424, -631497458, -482369324, -90333808, -9627800, 249223698, -279497146, -28440932, -52976229, -134253700, -480804651, -302759940, -175948997, -128882432, 291597475, -11687740, -485006907, -322024272, -106653725, -74951350, 331928461, 225981536, -821598039, -109369692, -31863125, -213519320, -207686713, -16325998, -86763914, 47017500, -522337456, 315072852, -455549533, 129225368, 77551425, -73221974, -815964923, -358540162, 665705212, -9384750, -466057270, -264223324, 247670535, -182396272, 219341900, 166619444, 458581012, -532512080, -98809548, 23482500, -33634878, 262325296, -733701415, 155866878, 91970300, 472319216, -228513856, 168739840, -174445905, 50280250, 295342414, -163755864, 180192171, 93236758, 98604150, -366899384, -93301408, 582324756, 967764253, 86531500, 583820370, 127636158, 146985651, 26290242, -52108125, 46160674, -130181428, 57844616, 122208063, -187705300, -3798363, 17296464, -383760741, 7072100, 59353675, -264809428, -361040892, 78092450, 573264239, 125837350, 247557480, 89608904, -313343100, -217226376, 172390675, -163776928, -15851485, -194561916, 904327964, -14918750, 217682851, -246577478, 203816061, -283524172, 313366900, 120447440, -134474945, 35762890, -393135598, 117662700, 211963379, 162657728, 631777673, -286661976, -44556725, 103549096, 16627674, 266525700, 421552180, 3121100, 258748775, -343278396, 128147728, 397766754, 11375000, 664423772, 124466928, 328577988, -550709479, -105335200, 606206626, 77544452, -45913185, 157222980, 398101800, 104983550, 126332113, -317514072, 539485644, -198002600, 216827659, 198178550, 124434025, 426375344, -325375175, 104725380, -75638916, 397687570, -634332957, 19288750, -260414557, 521870776, 306006714, -497184620, 188970925, -156352950, 390043720, 4714740, 980669496, 14159850, 787419313, -194111170, -158640452, -325028156, 427633600, 38040390, -126050855, 105737024, -251297510, 63613050, 477275704, 190966846, 51461528, -236177232, 39738750, -179419652, -59741459, 119576692, -594333372, -72688900, 183030461, -249331588, -961008250, 21596696, 106114000, -154106952, 146423859, 426026940, 20827259, -34670750, 923488715, -109258168, 911739233, -134433912, 437670900, -472730616, -129029303, -589289320, -63590992, -31061250, 567980815, -344074756, 632300315, 203567668, -36723150, 286761814, -171875360, 355510580, -23771993, 167629700, 475553268, 6156502, -414009272, -205033664, 240107100, 367402296, 430264170, 171541588, -210940270, -80021000, 571611479, -122862292, -651292652, -257548388, 18728125, 779066572, -429603606, -240355884, -172936866, -216709800, 596784934, 224049096, 210597158, 64380864, -4747775, 394825140, -437993256, 50660816, 536855183, 44444300, -616317618, -1271378164, 512612443, -335032578, 289359450, 154237842, -428779859, 434229692, 619359496, -3687500, 843587712, 48808252, -14233944, -586875008, 21719700, -51369304, 697085027, -88426582, -402501468, -231566800, 434391776, -162665068, -131474627, -114441620, 197236075, 219625132, -219366392, 211672802, -420443164, 416137400, -14082841, 132573562, -1131868981, -643345754, -147015625, 186803892, 474517992, 525139352, 687247260, -86779550, 156611508, -515210692, -965568070, -570059796, 617866700, 819951382, -1078094025, -191726824, -345589222, -159975550, 17647648, 85190826, 1141483759, -7792018, 48953600, 9674964, 478664228, -125520206, 133341282, -44943750, 1029994920, -158568652, 176406952, -27588408, -565480400, 782901944, -637104301, 902608920, 559451491, -202254400, -792259614, -325789600, 69196956, -1166722576, 258593000, -292601860, -1248188630, -431306306, 113413068, -184282600, 228014888, -455748268, 1359539008, -466954552, -24606875, 611977566, 31399324, 30972496, 14048803, -112163200, 119815445, 960729792, -1472896284, -478638714, 423864800, -394309022, -662033594, -147987544, 1035668767, -215204050, 1279731721, -1064623954, 108801317, -567678984, 13453950, 41903348, 1130954851, 162053230, 330175638, -7273750, 413194347, -355766728, -695065228, -812806056, 61224575, -573265040, -560198007, 753484800, -507839562, -3421350, -939332711, 384094464, -1038032352, -131954536, -128478775, 124941262, -443925616, -417792196, 1594369477, 27766450, 354621733, -283043046, 121890593, -443367508, 5609375, -235308796, 812980556, 384323062, -828493875, -218897800, -1236739442, 284355336, 669453062, -347089560, 258263725, 322963762, -285411422, 27785380, 117525809, -46438000, 796485757, -419219030, -1100584240, -606408204, -77661950, -2543432, 202389286, -690890168, 170562723, 104473750, 879428556, -347087500, -277051586, 268459736, -6001550, 110146670, 270730864, 279454496, -382301960, -271800500, -309509386, 151559686, -111872494, -86227886, 297067125, -990655880, -1226383973, 727713012, 248508859, 55133000, 128080285, -582664032, 385742453, 355914896, -185032500, -942873420, -204995992, -19276128, 152692333, 68937250, -219621348, -116801716, 348675920, -1673713748, 350885775, -142058724, -267591202, 233116176, 726662840, -176639650, 14043108, 65115668, -1650355452, -448028922, -287784525, 300729668, 852453994, -600330716, -1938654404, 32595000, -1114628846, -220330554, -642642506, -359685874, -228430125, 463240536, -813894856, -702444388, 377637056, -316193750, 399091589, -1032830812, -238521490, -89113408, -59697650, 450761246, 379758801, -87717336, 781767163, 238350500, -2037121521, -509497774, 452251537, -514055484, -37097500, -301731476, 1406579860, 757501256, 1612753057, -316568250, -383718490, -272445076, -142971517, -175023664, 208513875, 294593748, -1021392067, -84570172, 120776058, -253440100, -1693295877, -127202910, -642345404, -558063836, 338101725, 103562658, -121164524, -512033122, -665160337, 8593750, 111350424, 1126935000, 584171420, 132383952, -492302350, 101677046, 556860659, -580088306, 1188101128, 418521300, 74111842, 652557856, -1400720682, -806676982, 411538075, 513670412, -952259720, 360523548, 548206256, -138735400, -968351322, -364735350, 690152027, 1167722610, -144010625, -344209880, 1843844400, 456589018, -214811816, -269617200, 644214949, 239458158, 1894526188, -47251338, -159212500, -580833832, 823358554, 637347388, -341282766, 50253650, -998626604, 437007368, -1174567385, 146922336, 173576250, 1040383126, -431868258, 173134712, 815742002, 3005000, -609543182, 499378256, 1329905102, -375682360, -177066225, -967227956, 258195378, 712777340, 60489287, -233156900, -510934763, 502991140, -970659309, -97680484, -151037825, 1025968288, 1197593129, 457147970, 23006562, 212064950, 287820780, 1007374260, -383757523, 669385310, -293606875, -322731688, 1387505967, 839679282, 1335684891, -22032850, 1683804217, 973383804, -1334619964, 620460816, 704149400, 15296066, -645049280, -540374648, -176355787, -85251000, -155406001, 510245020, 981011290, 155065340, -29703650, -560449664, -860887476, -168638480, 1692194112, -76932500, -929330799, -180378768, 29263222, -103434002, -933193625, 593174158, 556742431, 381326930, 1141830719, 114833700, -976552985, 320242458, 844164858, 550165914, 574385800, -39750988, 2490441970, -127948646, 379118548, 154718100, -13293159, 252648478, -2057521372, 139603652, 70531250, 176884904, 1192622321, -174577084, 225203416, -98004800, -189205484, 865747480, -983847467, 531944780, 547993600, -513440316, -918887239, 2107666340, -308088822, -515647850, -1958162988, -116058668, 64162380, 76831648, 371912350, 427596144, -775845982, 1037349468, 55307479, 99917500, 507110180, 546993314, 1218916210, 1301197086, -60174450, -1522555640, 113071105, -342406876, 956070538, 99468200, -759182649, 709260460, -79319240, -68678612, 119389675, 11219092, -221773733, 290088436, -1019223692, 485725600, -552674191, 24431336, -489129916, -957612180, -87561250, -902229722, 4193109205, 390285440, -1054459932, -669563700, -1983665542, -1320407074, -687043731, 1454754070, -614675125, 2147414616, -1103381814, -1018496856, 702121702, 58963350, -90735611, 41353400, 636420258, 719026410, 40944600, -58204800, -578683524, -533792004, 1616944457, 55826250, -2223848751, -430706290, 949943966, -944761468, -128728050, 596467656, -29069933, 517195950, 659675378, 580727800, 296107949, -46582480, -2049074050, 983700104, -417331900, -992449572, -143008916, 81171876, 1773408249, -162935500, -449393585, -87251484, -2191914618, -1128095722, -305051250, 1484598380, -467174749, 414954536, 1146470965, 17272050, -1202726283, 1096314616, 416388298, -1083459412, 146504950, -703514090, -375402595, -1122862042, -849090180, -320331900, 82273254, 1008393536, -1027599395, 1241559316, 121157450, 1286042704, 918777907, -196198192, -405857870, 26031250, -659955807, 1177016246, 3834311873, 272152746, -387093350, -524056904, 718590677, 1651148708, 76146331, -451209000, 1208878210, -523642002, 1523889053, 8768704, -137478500, -72063844, -2142637691, 49255560, -940144810, 611975750, -560361006, 281507032, -191430307, -266289616, -34573750, -835229098, -1245333320, 69333202, -942001538, -140822400, -1095397460, 789992340, 1005726734, -956020336, -496430375, -725236148, 241538755, 561371526, 2185779377, -641452050, 2910874743, 2182169814, -986016495, -675277132, -445238075, -1078832400, -995380290, 1062995794, -1127009293, -208985000, 44474727, 611545048, 2256258926, 519653020, -285832725, 836455738, 510118569, -367190162, 1429231697, -8146600, 352267512, -723991438, -474170904, 395733784, -36680025, -694597614, -78495717, 585343080, -1477907730, -149813400, -420494239, 900331760, -2237153652, 1984268784, -65344375, -387082686, 195086028, -18263590, -806498688, -502696350, -904330457, -1264133382, -174855660, 1021132296, -397417400, -148857036, 1601337104, 964962066, -3088393636, 35873250, -1785717440, -711077412, 887808377, 63635240, 701012050, 630631962, 1089166224, 814919658, -172206805, -28865000, 747525500, 569254640, -933209854, -84075620, -133880000, 49842380, 1001886690, -2275705308, -345445469, -45719400, 588894448, 711933096, 569829684, 585200406, -877323275, -1538936812, -934892308, 264611330, -1566165192, 268423900, -1199266978, 1283116532, 580738494, -1537623700, -48375000, -1420619448, -1133226556, 3137951372, -218921889, -841251600, 265266939, 488117236, 1159318424, 182629064, -27203550, 142457702, -1854927827, -589472732, -1501026824, -270129900, -2045650063, -587362618, 324167370, -88949310, 14216900, -808234880, 1020612820, -832969592, -473088419, -95902500, 602992444, 391874736, -847687290, -475521720, -1918290400, -606333578, -709845085, -93123968, -906162379, 119985250, -2862558924, -699594684, -1082446252, -1151781850, -173846900, -450905016, 704225020, 274900932, 160784826, -265385800, -3245616164, -227329820, 370631622, 1201169376, -97203750, 2221039056, 1642956233, -678691556, 568004524, 56620700, -1696679735, -594442096, -1016678391, 83581344, 228849175, -765195332, -276492042, -19289344, -364362074, 14062800, -974222793, -2778542, -2806231384, -811558660, -475264025, -149688124, -775109106, -345768154, -2142487482, -10360000, 624596612, 251497096, -947022637, -505831784, 77255525, -1457839110, -2186746602, 115093846, -176294939, 299786050, 24038869, -1014507220, -613609096, -1746139366, 26974200, 1435083430, -475107446, -1554500812, 2196235914, 637710750, 439020803, 1481489582, -108621184, 2173420190, -285371875, -191864912, 1760014857, 556453428, -598253364, -156441700, -701727651, 516125222, 242813572, -150717724, -752440850, 1014637816, 676672866, -133213422, -683910946, 352072700, 3018239243, 815623220, 1792132668, 74918038, -1351508800, 447017570, 209484026, -795540784, -928828494, 9625000, -1267155041, -478544828, 1255607105, -60733352, -605508000, 940148370, -3037085760, -408199144, -246373149, 1012514150, -447592053, -357514078, 2775404572, -158385348, 590426675, -893051168, 326822019, -78874408, 799697235, -173238400, 1725795257, 1620305740, 820143162, -503052176, 206587500, -418177804, 2004197372, 727213516, -1197572236, 392605500, 131167240, 601638114, -343333260, 1135364108, -83606700, -1891235216, 1308086668, -444440064, 1337966135, -36130700, 3696122726, -1892794224, -603172800, 735710958, -182195175, 1626398206, 2004642990, -904812200, -1031936112, -58887500, 1141922054, 1333437982, -2378927668, 1242870028, 570714150, -2296847432, -3194638493, -1124359472, 1619832770, -492150600, 1630248454, -444612766, 4726086, 2220001070, -124899725, 1813126122, 1140489900, 1056098846, 1075241585, 1214542700, -1364124893, 460732092, 799429919, -153495828, 258650625, -555420068, -88017754, 1127886748, 669020609, 9859250, 896106987, -3017980156, -1623386973, -97362568, 2421698250, -1609218, -1087655677, -2441394404, 2397211264, -126131150, 768950648, 362547742, 2752630567, 1040003480, -646907475, -1634312104, -1376161625, -377155972, -930305110, -462990000, -1285817457, 805435772, 2663431710, -71058586, 576773450, 1285467588, -311419894, 792073780, 137594487, 380724050, 3356389434, -348828696, 859791758, 560020676, 1672766950, -1599839072, -793347676, -1053381920, -442989246, 272593750, -2243942138, 7424476, -352191630, 731833560, 114843750, 2188676382, 3573556270, 542187638, 1862134939, 329059900, -1848792924, 23037950, -3688849347, 277609224, -162977125, -1528319230, 1394308426, -117652296, 681074726, -86163700, 1809378500, -1881872748, -1619153820, -1067395216, -375297700, 419463788, 1277126402, -3104668250, 1897718306, 408516250, -115784418, -962784056, 1567653130, 143528188, -4033625, 416811838, -756173182, 56621196, 1786582527, 457879300, -800514925, -1598718520, -1385328535, -216876338, 929858925, 2832360766, 969358169, 857348268, -427132568, 514786600, 4757541284, -434271022, -2279101074, 394011122, -518691875, 849281072, 1090902082, -382058612, -505345879, -1022378000, 4017649557, -2149674340, -443604576, 134620356, 1086354975, 14028648, -1681733049, -304669740, 1586698626, 2009332200, -3294317812, 257906926, 492340234, -834446170, -404388475, -758135944, -1310316444, -489263750, 478409053, -88513750, 673340295, -225508828, 1409430520, 1447188402, 736778600, 2444503376, -437221139, 880746872, -2254713668, 610059500, 3669164794, 511262512, 158452265, 1050452964, -714086450, -1259117932, -1883590052, -906704590, 349692181, 210904900, 3747289694, 793954704, 3628392630, -67571286, -386131875, 25935424, -997747483, -1231251842, -1953173235, 526843700, 1091803173, -1408803292, 115499690, -376376904, -792955650, -569089356, -992765550, -499867540, -1343911820, -394468200, 786235270, -766153848, 5154436623, -396150344, 89658525, 1656405798, 783782270, -1302706772, 1971563147, 42687500, -302783392, 213109926, 2587459226, -677560564, 973242575, 137709468, 432907568, -482776276, -4459854803, 230482650, 4147892752, 858519090, 800524042, -264460808, -105175125, -547260992, 1909697578, 221305776, -372035943, 83952300, 135631388, 1152360128, -2248174012, -1830806056, -5583750, -579921604, 86716909, 2361734540, -1468854803, -236314050, 2065921884, 259188820, -2340245747, 700860576, 2578203325, 1878941916, -2431913080, -1609676084, 1513175702, -191847900, 477239214, -2145296412, -192798811, 2196510754, -1014112350, 469889030, 1261657584, -1407292100, -2337204312, 1901250, 1155005368, -203014540, 4124314564, 900206048, 407414950, 1307594006, -2061428788, 164906702, 379178819, 480381200, 2790064940, -2428103312, -4159262624, -927177576, 852942575, -27717484, -2892492493, -2383290112, -42888924, 332067900, -415688601, 81388652, 4833050282, -1278126306, -162564375, 17848180, 915443526, 62179668, -3014901528, 402437300, -1010702646, -217790496, 2732937848, -267165404, -37483275, -852865612, -2819534808, 628552550, 465784500, -1101983400, 4318010504, -626283368, 1806963993, -439346992, 1138063275, -1707528860, 2157972981, -510324348, 1062444952, -27218750, 290255863, 1631380224, -2897806732, -705310940, 602066875, -1464387660, 1688101730, 678438348, 1994480249, -81596150, -5295689596, -77472050, -1573229978, -997943736, -348807825, 1503058898, -4212665246, -25273416, -2587728706, 729181050, -1019436101, -3242508178, -2440523050, -650966982, 4765625, 1548928468, 1015661462, -1238533168, -352912768, -880461000, 328601016, -2108431716, -785202772, -942399700, -249595425, 2312975040, 3180591237, -1738585694, -3447832398, 486824500, 4747473, -991199422, -1025430629, 697023942, -725959175, -736491264, -2303637543, 499762624, -960665944, 451392500, -421172287, -752653614, -1779619466, -549087556, -544398775, 742192802, -1859809034, -606675186, -1856808753, -19268650, 1806196586, -471510352, -1660264839, 1246560382, 2090414350, 313239110, -971251762, -2389897328, -604118398, 1020783600, 2100307961, -1944556442, 2071950636, -3651998560, -795534375, 506892658, -2865930452, -1133142528, 31640669, 1001579400, 417260917, 137606388, -3308947807, -1207105234, 485169650, -706492892, -1385949048, 674162376, -3617066716, -344200850, 93496959, -1928052314, 1911384814, 1609040052, -764921425, 336474192, 2831002156, -725976086, -2833091184, 79833750, 7590906460, -173695384, 4687272946, -776198526, -1344574300, -1357174608, -2506025686, -1945449908, -1370855895, 182033050, -3928929571, -241245312, 1920485940, 54120492, 40434275, -2891326340, -448721103, -1739622280, -4440030728, 301392000, 993888273, 792512876, 3025781510, 1418584, -926018750, -1424903584, 205118692, 1097416280, 466086055, -876948800, -3768135877, -1154496814, -1394557639, 737546500, -14071250, 1177761384, 871895666, -1308528072, -119185653, 557037600, -258916103, 525819276, 921747331, -951264492, -1129333450, -4650777208, 2339252434, -756950370, -5210420786, -99187500, 1092108781, 714496792, 793191720, -1967270340, -783176450, 367399448, -22869854, 253484864, 2925193960, 408416700, 554205864, 594159000, 3672404632, -512169708, 389182225, -3089427984, -5226384926, -1358307300, 1654385219, -1075706800, -1683460317, -1210628966, -736551034, 624942188, 227786875, 2244957444, 1111034066, 714443210, -1289192155, 771537150, 1446480033, 1587030810, 1158796689, 2176557510, 961704325, 345237394, -1028281211, -2523760032, -2142336427, -903293600, 4750309205, -3953767744, -1352723649, 2818308800, 139306950, 118254776, -1605735403, -1537398888, 248103692, 32747500, -2974869569, 2162547044, 7883457891, 2610151594, 1003267500, -2515240140, 63858330, 1491236660, -852296000, -826327150, -107779096, -1534795132, 2732666568, 1998931552, 1983793725, 905735578, -1588476614, 417897114, -732382514, 290634850, 5826940793, 1870920046, -1635528284, 1686822090, -550312500, -1759788548, 3315700543, 1841096572, 2388827312, -356457200, -1363453861, 668771480, -4731926166, 129497948, 864882450, 406149332, 1197769257, 174541448, 968692949, 588437800, -2051841132, -189426436, -3247000458, -894933752, -2566870425, -923524588, -222244637, 922566800, 1153626846, 91531250, 1155513937, -1674609368, 1601968928, 1321104582, 474562075, 946873976, 67089659, -1423467492, 2000813864, 294007700, -1611281072, -640158700, 2218112306, -2929261816, 59538950, 2772420816, 2001268465, -1060020352, -13298161, -62813000, 2707819602, -1619966114, 1935092429, 2896891214, 294890625]