# Trace form for 538.6.a.b, downloaded from the LMFDB on 27 December 2024. [0, 27, -108, 33, 432, 139, -132, -25, -1728, 2346, -556, 1241, 528, -202, 100, 1786, 6912, 1550, -9384, -66, 2224, -1217, -4964, 10568, -2112, 15880, 808, 8256, -400, -2122, -7144, -1621, -27648, 18369, -6200, 23123, 37536, 8542, 264, 589, -8896, 10859, 4868, 23759, 19856, 28006, -42272, 38457, 8448, 57376, -63520, 58237, -3232, 73586, -33024, 25923, 1600, 52534, 8488, 68927, 28576, -76016, 6484, -20738, 110592, 74867, -73476, 94787, 24800, -90601, -92492, 15523, -150144, -96279, -34168, -123786, -1056, -199866, -2356, -246217, 35584, -54473, -43436, -56658, -19472, -120541, -95036, -352954, -79424, -83070, -112024, -132348, 169088, 40727, -153828, -72090, -33792, -36273, -229504, 335378, 254080, 91188, -232948, 207271, 12928, 10034, -294344, 550870, 132096, -35465, -103692, 208737, -6400, 561857, -210136, 412181, -33952, 147455, -275708, 635166, -114304, 520460, 304064, 713322, -25936, 652134, 82952, 525361, -442368, 337857, -299468, 428807, 293904, 308672, -379148, 2362981, -99200, 1578451, 362404, 1579227, 369968, 2051838, -62092, 1875850, 600576, 1340961, 385116, 3976828, 136672, 2367083, 495144, 1171478, 4224, 3263611, 799464, 4112317, 9424, 2416775, 984868, 3677734, -142336, 1546026, 217892, 2448197, 173744, 4341518, 226632, 3063852, 77888, 1755507, 482164, 4189114, 380144, 3447420, 1411816, 2381874, 317696, 4208876, 332280, 2646640, 448096, 445585, 529392, 3611281, -676352, 3507121, -162908, 2435052, 615312, 2583672, 288360, 3291274, 135168, 2156874, 145092, 3669726, 918016, 4653868, -1341512, 1120231, -1016320, 2476073, -364752, 5224879, 931792, 1350960, -829084, 6347955, -51712, 4056014, -40136, 2817332, 1177376, 4090796, -2203480, 3643863, -528384, 2512866, 141860, 3228345, 414768, 3259554, -834948, 2234644, 25600, 3966789, -2247428, 7386071, 840544, -820735, -1648724, 1954969, 135808, 1481653, -589820, 3653217, 1102832, 3254386, -2540664, 2226441, 457216, -748254, -2081840, 3783666, -1216256, 8032210, -2853288, -1385230, 103744, -2811470, -2608536, 2910929, -331808, 549580, -2101444, 6876552, 1769472, 4469490, -1351428, 687818, 1197872, 15563, -1715228, 3873953, -1175616, -357222, -1234688, 9252956, 1516592, 1953747, -9451924, -3395066, 396800, 1732963, -6313804, 425550, -1449616, -2558363, -6316908, -7003464, -1479872, 7955636, -8207352, -2165759, 248368, -2477826, -7503400, 4100725, -2402304, -5837053, -5363844, -953138, -1540464, 2515328, -15907312, -3475027, -546688, 4431798, -9468332, -5982616, -1980576, -1722071, -4685912, -10561193, -16896, -1925659, -13054444, 4028429, -3197856, -7534670, -16449268, 2497887, -37696, -5556468, -9667100, -9941336, -3939472, 1674635, -14710936, -9086052, 569344, -6885609, -6184104, 8404416, -871568, -4306765, -9792788, -2042321, -694976, 1220805, -17366072, -1966963, -906528, -590181, -12255408, 1574797, -311552, -6467617, -7022028, -9699523, -1928656, 1620473, -16756456, -8027564, -1520576, -7848498, -13789680, 5746053, -5647264, -11388679, -9527496, 3297860, -1270784, 8848652, -16835504, -9594202, -1329120, -4178865, -10586560, -7397111, -1792384, -5956777, -1782340, -2567096, -2117568, 1139031, -14445124, -5838449, 2705408, -25334921, -14028484, -2432142, 651632, -15022751, -9740208, -12573249, -2461248, 5016899, -10334688, -6892329, -1153440, -3815045, -13165096, 1105050, -540672, -23560115, -8627496, -4020016, -580368, -212938, -14678904, -19901076, -3672064, 873148, -18615472, 3902225, 5366048, -12554333, -4480924, -27934154, 4065280, -3253393, -9904292, 3869924, 1459008, -5547382, -20899516, 6698496, -3727168, -25675818, -5403840, -5208376, 3316336, 13428913, -25391820, -10997350, 206848, 3797744, -16224056, 10712642, 160544, -1276516, -11269328, -876378, -4709504, 3070419, -16363184, -13711694, 8813920, -21913313, -14575452, -78478, 2113536, -14724552, -10051464, -7001671, -567440, 8328988, -12913380, -15022083, -1659072, 5028110, -13038216, 7248742, 3339792, -16719273, -8938576, -4429941, -102400, 9387274, -15867156, -9394754, 8989712, 4672767, -29544284, 6341033, -3362176, 5023888, 3282940, -6075154, 6594896, -1515533, -7819876, -8943140, -543232, -4847810, -5926612, 15117686, 2359280, -36043395, -14612868, 7664632, -4411328, 12532640, -13017544, -10071430, 10162656, 9208748, -8905764, 9350453, -1828864, -27813244, 2993016, 8990317, 8327360, 4997222, -15134664, 13778856, 4865024, -5229110, -32128840, 16644007, 11413152, -9910423, 5540920, 23045466, -414976, 22918938, 11245880, -27201540, 10434144, -6347568, -11643716, 9535387, 1327232, -22856646, -2198320, 5335084, 8405776, 825072, -27506208, -17971323, -7077888, 4746768, -17877960, 29653565, 5405712, -30354705, -2751272, 85371, -4791488, 18602664, -62252, 565865, 6860912, -17119424, -15495812, 5023892, 4702464, -8273805, 1428888, -6702608, 4938752, 32769080, -37011824, 8997561, -6066368, -15246903, -7814988, 16244078, 37807696, -17416539, 13580264, 40565156, -1587200, 17191151, -6931852, 23857051, 25255216, -7715163, -1702200, 31374010, 5798464, 25360595, 10233452, 39271308, 25267632, 30223236, 28013856, 701684, 5919488, 43607301, -31822544, 33466392, 32829408, 24845530, 8663036, 27818621, -993472, -8824051, 9911304, 28990848, 30013600, -17594878, -16402900, 50558925, 9609216, 27712044, 23348212, 29574593, 21455376, 35202976, 3812552, 61179320, 6161856, 29233764, -10061312, 34220679, 63629248, -45513350, 13900108, 72766894, 2186752, 52310777, -17727192, 31662139, 37873328, 19745065, 23930464, 41714290, 7922304, 9281593, 6888284, 101566344, 18743648, 52593992, 42244772, -19176313, 67584, 56077016, 7702636, 42280601, 52217776, -4774169, -16113716, -11042188, 12791424, 35526552, 30138680, 26620538, 65797072, 38719654, -9991548, 21321113, 150784, -80024375, 22225872, 68706972, 38668400, 4159292, 39765344, 29080039, 15757888, -12939966, -6698540, 54993692, 58843744, -42119982, 36344208, 27485569, -2277376, 15934999, 27542436, -8780638, 24736416, -2612616, -33617664, 13018225, 3486272, -89994993, 17227060, 51439159, 39171152, 20484012, 8169284, -15035212, 2779904, -26676438, -4883220, 27648337, 69464288, -9798919, 7867852, 53663429, 3626112, -25231596, 2360724, -30992423, 49021632, -60073772, -6299188, 20413092, 1246208, -18082196, 25870468, 53562769, 28088112, -37514416, 38798092, -125752468, 7714624, -29497719, -6481892, 118549136, 67025824, -78297325, 32110256, 7171489, 6082304, 9688814, 31393992, -38402954, 55158720, -43413851, -22984212, 22190035, 22589056, -37242908, 45554716, -20919655, 38109984, 36709762, -13191440, -7806004, 5083136, -38262947, -35394608, 17478604, 67342016, -99577391, 38376808, -4045924, 5316480, -24194712, 16715460, -35043719, 42346240, -27479125, 29588444, 27573320, 7169536, -74443933, 23827108, 25644103, 7129360, -32839032, 10268384, -41188930, 8470272, -29617116, -4556124, 52702440, 57780496, -127039595, 23353796, 46468122, -10821632, 261044, 101339684, -42059139, 56113936, 4565740, 9728568, 52939179, -2606528, -71378350, 60091004, -49959352, 38960832, -19210826, 50292996, -33383745, 9844992, 65421076, -20067596, 56632489, 41338752, -102137367, 27569316, 20177981, 4613760, -34042250, 15260180, 5204319, 52660384, -63362304, -4420200, 39635399, 2162688, -114696142, 94240460, 18730881, 34509984, 21326194, 16080064, -39674872, 2321472, -17862161, 851752, -12280996, 58715616, -125692471, 79604304, -71943973, 14688256, 59673438, -3492592, -14228311, 74461888, -74192473, -15608900, 81348475, -21464192, -118642294, 50217332, 100159150, 17923696, -52043422, 111736616, -60773539, -16261120, -40400921, 13013572, 113241338, 39617168, -133178243, -15479696, 2387913, -5836032, 8154000, 22189528, -20484989, 83598064, -33366215, -26793984, 44333519, 14908672, -98081072, 102703272, -13131605, 21615360, 5909314, 20833504, -45403590, -13265344, -30058418, -53715652, 84175755, 101567280, -125390752, 43989400, -30897799, -827392, -37464632, -15190976, -161861043, 64896224, -36945970, -42850568, 73055292, -642176, -91492881, 5106064, 114949261, 45077312, 40831576, 3505512, -106242884, 18838016, -101822757, -12281676, 93715328, 65452736, -32729562, 54846776, 2613554, -35255680, -17223612, 87653252, 10464480, 58301808, -84616546, 313912, 150549387, -8454144, 12045631, 58898208, -10364064, 40205856, -26201791, 28006684, -115832180, 2269760, 24926227, -33315952, 29166558, 51653520, -92876813, 60088332, 3175044, 6636288, -21296307, -20112440, -47633120, 52152864, -179340677, -28994968, 42248298, -13359168, -108134575, 66877092, 40964415, 35754304, 48677752, 17719764, -7616487, 409600, -168000977, -37549096, 50513524, 63468624, -52394378, 37579016, 172105033, -35958848, -4289130, -18691068, -37338533, 118177136, -57930040, -25364132, 33674720, 13448704, -199791046, -20095552, 11526944, -13131760, 9778437, 24300616, -130032403, -26379584, -108400213, 6062132, -32696150, 31279504, -100768629, 35772560, -82423686, 2172928, -46646124, 19391240, -63755920, 23706448, 864416, -60470744, 126698487, -9437120, -112094035, 144173580, -74078958, 58451472, -26333662, -30658528, -57109076, 17645312, -142368367, -50130560, 109620151, 52070176, -153381090, 40285720, -51166583, -40650624, 38874054, -36834992, 54747008, 35623056, -119355476, -37401812, 169236667, 7315456, -41231416, 111252976, 106344013, -11972064, -109806471, -35961268, -54165822, -33309440, -178018552, -19988888, -38805093, 60538656, -51763147, -55115424, -7218422, -19460096, 160155850, 20916440, -17360660, 128515360, -72343536, -66576028, 90343517, -45652608, -128684281, 39641692, -66008330, -22163680, -56569212, -92181864, 13820383, 1659904, -122364709, -91675752, 67806758, -44983520, -56376982, 108806160, -540162, -41736576, -256680916, 25390272, 12723793, 46574864, 25735112, -38141548, 139959476, -5308928, -127207129, 91426584, -87587460, 8793280, 95312341, -21340336, 99818687, -33623104, -147043173, -3300288, 193771517, 110024832, -54220351, 71885292, 59932895, 28311552, 64624587, -18987072, 127796419, 71511840, -119091763, -118614260, 30173518, -21622848, 6480034, 121418820, 56028652, 11005088, -176014096, -341484, 32418949, 19165952, -216184523, -74410656, 150488319, 249008, 120979374, -2263460, 53717969, -27443648, -69673405, 68477696, -66442655, 61983248, -83207804, -20095568, 49450943, -18809856, -156655944, 33095220, 44994523, -5715552, -51053551, 26810432, 110908289, -19755008, -191135654, -131076320, 201324479, 148047296, -228479903, -35990244, 41233241, 24265472, 56575565, 60987612, 3855394, 31259952, -261182936, -64976312, 123988364, -151230784, -171980277, 69666156, 160717717, -54321056, 30696959, -162260624, 9263947, 6348800, 28765370, -68764604, 59236184, 27727408, -21054559, -95428204, -106823566, -101020864, -14034647, 30860652, -25831772, 6808800, -370887333, -125496040, 150086372, -23193856, -126455221, -101442380, -257829130, -40933808, -119411189, -157085232, -155914377, -101070528, -284922524, -120892944, -1391049, -112055424, -100370948, -2806736, -183828100, -23677952, -313572544, -174429204, 19917127, 127290176, -243281389, -133865568, 77112768, -131317632, -228790721, -99382120, 103658956, -34652144, -49016463, -111274484, 38926386, 3973888, -446563595, 35296204, 77858046, -39645216, -410750673, -115963392, 15016167, -120054400, -91874551, 70379512, -46243480, 65611600, -523603457, -202235700, 86602740, -38436864, 52149470, -110848176, -380871128, -93392848, -153598607, -118298372, 135926422, -85821504, -663715344, -140811904, 21064786, -15250208, -252227065, -244717280, -62536980, -24647424, -105351199, -116935056, 68468502, 40245248, -66103189, -136882716, 50614409, -254516992, -234590996, 182053400, -114242057, -55600432, -141751203, -291067576, 21820345, -8747008, -371735641, -209243108, 67293604, 70908768, -174814560, -126648556, -156201760, -151493312, -30154446, -78980260, -10900056, -95721856, -443912924, -166857160, 189073158, -31689216, -265497799, -37126372, -28148666, -27553136, -96909819, -406265376, -33943384, -74974592, -180181333, -210375968, -131440950, -168979088, -241903714, 76705252, 197737079, -270336, 11629140, -224308064, 136881900, -30810544, -552306225, -169122404, 330721767, -208871104, -156320388, 19096676, 88368477, 64454864, 35211057, 44168752, 21310592, -51165696, -189813126, -142106208, 242417606, -120554720, -11857284, -106482152, 52531292, -263188288, 127185876, -154878616, 372272925, 39966192, -461862506, -85284452, 189671885, -603136, -120927288, 320097500, -134165942, -88903488, 472214066, -274827888, 221417631, -154673600, -202352458, -16637168, 188104042, -159061376, -316062212, -116320156, 56381713, -63031552, 103295581, 51759864, 313298591, 26794160, 278087521, -219974768, 401434430, -235374976, 158851546, 168479928, 132729080, -145376832, 311738549, -109942276, 365971459, 9109504, -421515429, -63739996, 315851475, -110169744, -63904627, 35122552, 204885495, -98945664, 200451768, 10450464, -22363383, 134470656, -149345227, -52072900, 497175805, -13945088, -76682705, 359979972, 294212908, -68908240, -48523491, -205756636, 474390035, -156684608, -375506901, -81936048, 377411437, -32677136, 23212874, 60140848, 7135750, -11119616, 468481375, 106705752, 170299672, 19532880, -651793620, -110593348, 287124813, -277857152, -53840369, 39195676, 744894160, -31471408, 224029086, -214653716, 67734406, -14504448, 110899528, 100926384, 653628354, -9442896, 303205710, 123969692, 111466631, -196086528, 17494474, 240295088, 245929889, 25196752, 95096007, -81652368, 593604127, -4984832, 10058179, 72328784, 145058713, -103481872, 276454258, -214251076, 258750874, -112352448, -311509310, 150057664, 722625553, -155192368, 51844723, 503009872, 159088199, -30858496, 18722293, 117990876, 379419241, 25927568, -237009924, -474196544, 631965577, -268103296, 241072073, 313189300, 35541095, -128441024, 403216191, -28685956, -137665672, -24329216, 365185394, -38755256, 412705478, -125575968, -3356146, 153611816, 683858992, -220634880, 13678214, 173655404, 99878206, 91936848, -236650120, -88760140, 800055746, -90356224, 331488807, 148971632, 457020926, -182218864, 666205275, 83678620, 395984746, -152439936, -29739078, -146839048, 349906280, 52765760, 342328485, 31224016, 172154147, -20332544, 47142684, 153051788, 64702096, 141578432, 365537969, -69914416, 411834383, -269368064, 216592090, 398309564, 154024979, -153507232, -113537894, 16183696, 528921844, -21265920, 90265996, 96778848, 137260079, -66861840, -160015360, 140174876, 468458798, -169384960, 303445197, 109916500, 580968666, -118353776, -360900757, -110293280, 762267124, -28678144, 37325532, 297775732, -48269561, -95308432, -18540158, -102576412, 400431820, -28517440, -98129269, 131356128, 427727508, -41073536, 142423741, 164755720, -141805608, -33881088, 410851009, 118468464, 404369903, 18224496, -77417004, -210809760, 431359882, -231121984, -207944238, 508158380, 322877272, -93415184, 39547217, -185872488, -94190964, 43286528, 54057250, -1044176, 999421845, -405358736, -198737921, 168236556, 168271620, -224455744, 360612759, -18262960, 851585071, -38914272, -9806131, -211756716, 178198212, 10426112, 274382105, 285513400, -289566994, -240364016, 454611143, 199837408, 584680415, -155843328, 50460845, 76843304, 332028414, -201171984, -256614026, 133534980, 1099367657, -39379968, 712015177, -261684304, 203991159, 80270384, -127214780, -226529956, 204558770, -165355008, 141941631, 408549468, 219364651, -110277264, 77217048, -80711924, 367601586, -18455040, -555808159, 136169000, 1199242880, -61040720, 213266071, -20817276, -261818506, -210641536, 199438017, 253449216, 282578910, 17680800, 69481333, -158541596, 954095729, -8650752, -505743390, 458784568, 423116324, -376961840, 29270738, -74923524, 602735551, -138039936, 216753083, -85304776, 325176622, -64320256, 354264902, 158699488, 138323466, -9285888, 687577315, 71448644, -207744136, -3407008, 355247201, 49123984, 574036621, -234862464, 422645125, 502769884, 484771213, -318417216, 576884643, 287775892, 272336956, -58753024, -37994088, -238693752, 296469424, 13970368, 717945808, 56913244, -315341189, -297847552, 564175518, 296769892, 303827476, 62435600, -249248235, -325393900, 830559872, 85856768, 135652533, 474569176, 291179382, -200869328, 417812429, -400636600, 200719854, -71694784, 294038631, 208173688, 139131531, -446946464, -170611951, 243094156, -103260940, 65044480, 307994715, 161603684, 460753318, -52054288, 8507170, -452965352, 572573821, -158468672, 140763929, 532712972, -120086069, 61918784, 315100868, -9551652, 793685364, 23344128, 393442932, -32616000, 824754376, -88758112, -202253778, 81939956, 599897110, -334392256, -143313438, 133464860, 241849741, 107175936, 4464685, -177334076, 236412252, -59634688, 976929882, 392324288, 316906382, -410813088, 389741570, 52526420, 156601863, -86461440, -628468433, -23637256, 1113892988, -83334016, -234175745, 181614360, 274568100, 53061376, -80326886, 120233672, 278128277, 214862608, -844768274, -336703020, 212793113, -406269120, 149232785, 501563008, 702517642, -175957600, 534584794, 123591196, -125113754, 3309568, -138940156, 149858528, -227857122, 60763904, 286000423, 647444172, -206833884, -259584896, 797783649, 147783880, 312126754, 171402272, -308634233, -292221168, 65876388, 2568704, -109266814, 365971524, 985250453, -20424256, 396653953, -459797044, -435979090, -180309248, 201137261, -163326304, 363887860, -14022048, 236118155, 424971536, -123760037, -75352064, 32729953, 407291028, 309736341, 49126704, -964394924, -374861312, 487583402, -261810944, -209957383, 130918248, 1030104, -219387104, 177773277, -10454216, -472330367, 141022720, -421759480, 68894448, 209504291, -350613008, 338374989, -41857920, 397408310, -233207232, -339029060, 338466184, 314311347, -1255648, -879084122, -602197548, -200497615, 33816576, 285368000, -48182524, -1034376439, -235592832, 444695627, 41456256, 130212329, -160823424, 258034459, 104807164, -81924887, -112026736, -698222805, 463328720, 198732254, -9079040, -50219464, -99704908, 493963174, 133263808, -259135032, -116666232, -1164357183, -206614080, -612328638, 371507252, 71324649, -240353328, -742241665, -12700176, -105865382, -26545152, -1482258764, 85185228, 742995935, 80449760, 124026736, 190532480, -715179190, -208611456, -499342031, 717362708, -774963890, 115979872, 86378347, -168993192, 140643337, 53436672, 27812958, 432538300, -1260036270, -267508368, -512716945, -163857660, 604277487, -143017216, -1417786916, -194711008, 109377245, -70879056, -406258672, 30465948, -1488281817, -1638400, 382339179, 672003908, 203354034, 150196384, -319157108, -202054096, 209873774, -253874496, -692036460, 209577512, -268757832, -150316064, 206964551, -688420132, -185266117, 143835392, -954111530, 17156520, -510095723, 74764272, 785692720, 149354132, 407891594, -472708544, -78423955, 231720160, -26599612, 101456528, -1865237578, -134698880, -386407417, -53794816, -891330756, 799164184, 305657090, 80382208, -268035891, -46107776, -153374242, 52527040, -543210056, -39113748, -322809838, -97202464, -95378326, 520129612, -1082800319, 105518336, -862435895, 433600852, 347825030, -24248528, -1252567410, 130784600, 34766252, -125118016, -241981522, 403074516, -1745925772, -143090240, 541314836, 329694744, -886024338, -8691712, -285252912, 186584496, -833681295, -77564960, -815899920, 255023680, -59650996, -94825792, -950170828, -3457664, 346992297, 241882976, -703233574, -506793948, -485420272, 37748480, -23180195, 448376140, -1046779296, -576694320, -491800811, 296315832, -187982230, -233805888, -818161782, 105334648, -1809025, 122634112, 294566147, 228436304, -1755677953, -70581248, 214479103, 569473468, -698582878, 200522240, -614033965, -438480604, -341429098, -208280704, 62149070, 613524360, 679269153, -161142880, -1742276153, 204666332, 917319602, 162602496, -1137192147, -155496216, 72724193, 147339968, -1073541468, -218988032, -2227262780, -142492224, -13836014, 477421904, -77992644, 149607248, -502031726, -676946668, -771474352, -29261824, -809328941, 164925664, -1385753987, -445011904, -183579089, -425376052, 347944314, 47888256, -842557639, 439225884, -399002163, 143845072, -507932699, 216663288, -1950084074, 133237760, -141315551, 712074208, 348143975, 79955552, -748208201, 155220372, 77702433, -242154624, 576048108, 207052588, -1310983582, 220461696, -727356636, 28873688, -590260993, 77840384, 70045017, -640623400, 7684823, -83665760, -607628566, 69442640, -1203181305, -514061440, -1144911290, 289374144, 35748130, 266304112, -1014586494, -361374068, 104132692, 182610432, -63407232, 514737124, -826146130, -158566768, -559151103, 264033320, -716487119, 88654720, -717616194, 226276848, -352663330, 368727456, -865703912, -55281532, -1124106896, -6639616, 7631075, 489458836, 282457695, 366703008, -787374253, -271227032, -1597258228, 179934080, -266687005, 225507928, -2086008946, -435224640, -11703720, 2160648, -873281407, 166946304, -2758121392, 1026723664, -258553168, -101561088, -612527725, -50895172, -734181929, -186299456, -852051115, -102940448, 313442641, 152566192, -350821759, -559837904, -1080344101, 21235712, 138011537, 508828516, -634397385, -365706336, -1141895907, 350349840, -911519431, -35173120, -566547921, -381249364, -215637407, 85361344, 356162383, -399274748, -2529391958, 134492416, -179617942, 588172692, 881674159, 13201152, -1373599074, -775086068, -292278505, -440099328, -1374651252, 216881404, 135932823, -287541168, -1823497453, -239731580, -1022528793, -113246208, -596285178, -258498348, -272177538, 75948288, 1053926473, -511185676, -1132713257, -286047360, 532440598, 476367052, -361643767, 474457040, -2786706048, -120694072, -115783500, 86491392, 540855983, -25920136, -593962526, -485675280, -868387603, -224114608, -962065598, -44020352, -330495502, 704056384, -1268933322, 1365936, -922279672, -129675796, -2462521018, -76663808, -262405072, 864738092, 1108757802, 297642624, -905004541, -601953276, -455097582, -996032, -588615131, -483917496, -2146095720, 9053840, -1024663296, -214871876, 719958855, 109774592, -1021221646, 278693620, 191425124, -273910784, -814450722, 265770620, -669037639, -247932992, -746060173, 332831216, 427234511, 80382272, -1236426662, -197803772, -1818617810, 75239424, -508594046, 626623776, -457652515, -132380880, -252056365, -179978092, -216750507, 22862208, -1344681017, 204214204, 1134973146, -107241728, -25377756, -443633156, -961818261, 79020032, -1237512789, 764542616, -1821580930, 524305280, -348393335, -805297916, -1711724429, -592189184, 300446239, 913919612, 307478035, 143960976, -596505096, -164932964, -433761266, -97061888, -1462142738, -226302260, 164379152, -243950448, -562846620, -15421576, -1121061055, -125039808, -414731379, 1044731744, 1016417775, 259905248, -261575150, -495953456, -889234033, 604923136, 345738000, 687921108, -669348200, -278664624, 304366191, -642870868, -145061343, 217284224, 339455843, -122787836, -1084903059, 649042496, -3361954, -37055788, -363901109, -25395200, 375529007, -115061480, 1698882700, 275058416, -1071831709, -236944736, -48175291, -110909632, -1194047796, 84218236, -1445135011, 381712816, -885779795, 427294264, -384519680, 404083456, -124088175, 56138588, 125538859, -123442608, 1302244648, 103327088, -557396229, -27235200, -1934925663, 1483549332, 891000228, 501984160, 1447449790, -600345488, 215810444, 92775424, 126275644, 505820884, 432174839, 405769520, -599137255, 1031316520, 14769726, 163735232, 808680104, 477644756, 350136341, 628340928, -33113438, 623657508, -24567882, 404282112, 284833020, 1139690096, 1529126876, 483571776, 246358873, 5564196, -1042333508, 448221696, 1865930642, 401483792, 1229364497, 11226944, 692048696, 735312400, 993952459, 94711808, -1238856030, 1254290176, 328355752, 697716816, 1309429482, -79668508, 181605273, -509160704, 1155887194, 973125556, 210685324, 535462272, 565578620, -308451072, -196790918, 525270528, 1077935542, 915162884, 1723309320, 397528480, -1675580582, -414635824, 1365228244, 138608576, -465175758, 196065852, 1587744976, 445097936, -38844202, -155705544, 264932732, -15895552, 151947555, 1786254380, 1746492993, -141184816, 1763764177, -311432184, -1838969250, 158580864, 143441333, 1643002692, -1296617740, 463853568, -1103497318, -60064668, 1184093405, 480217600, -539051819, 367498204, 137609173, -281518048, 1916198494, 184973920, 705811249, -262446400, -17547892, 2094413828, 1244483952, 808942800, 211873198, -346410960, 1119992068, 153747456, 2737386720, -208597880, 454170164, 443392704, 1000463143, 1523484512, -1035694857, 373571392, -585688817, 614394428, 322218887, 473193488, 846200841, -543705688, 963836436, 343286016, -594675902, 2654861376, 1752909671, 563247616, -590891170, -84259144, -522091286, 61000832, 1124259323, 1008908260, 378087699, 978869120, 1615344804, 250147920, 1022515880, 98589696, 978073796, 421404796, 239820748, 467740224, 541723278, -273874008, 1474295070, -160980992, 462960151, 264412756, 1445248600, 547530864, 403263299, -202457636, -809035942, 1018067968, 1120271070, 938363984, 1223680712, -728213600, 631911306, 456968228, 2382699857, 222401728, 9926245, 567004812, 121332183, 1164270304, 1001243799, -87281380, -364239089, 34988032, 319326843, 1486942564, 631988420, 836972432, 1179765071, -269174416, 483924290, -283635072, 846050776, 699258240, 1871841497, 506594224, -1212253206, 624807040, 1268978793, 605973248, 3261497046, 120617784, 49535627, 315921040, 1025456011, 43600224, -2192537731, 382887424, 120878325, 1775651696, 461696769, 667428640, 1154470368, -756292632, 795137351, 126756864, 468002239, 1061991196, 1880373501, 148505488, 252140035, 112594664, 2570783250, 110212544, 1711741797, 387639276, -1648882590, 1625061504, 1274316094, 135773536, -597830964, 299898368, 2227542425, 720725332, 2075374036, 841503872, 169758906, 525763800, -189756430, 675916352, 912937243, 967614856, 2584483454, -306821008, 826127003, -790948316, -305071246, 1081344, 1411114630, -46516560, 2187452556, 897232256, 1409686818, -547527600, -1731095291, 123242176, -1406760956, 2209224900, 2810343197, 676489616, 1449508603, -1322887068, -119977454, 835484416, 2869522509, 625281552, -2294843046, -76386704, -207329996, -353473908, 122069706, -257819456, -115596690, -140844228, 1069692124, -176675008, -257173376, -85242368, 1540600808, 204662784, -465999929, 759252504, -883162718, 568424832, 2193089755, -969670424, -1924035744, 482218880, 1317131747, 47429136, 2526024097, 425928608, 433829848, -210125168, -27517476, 1052753152, -593089487, -508743504, 1559898292, 619514464, 1523160526, -1489091700, 699547334, -159864768, 1405989888, 1847450024, 1300885872, 341137808, -699977781, -758687540, -3138118083, 2412544, 1013610773, 483709152, 3965721178, -1280390000, 733434932, 536663768, 1077716631, 355613952, 1160033995, -1888856264, 691688004, 1099311552, 1174898478, -885670524, -2725804991, 618694400, 67135681, 809409832, 2082797714, 66548672, 1253673222, -752416168, 69551261, 636245504, -1848077500, 1264248848, 457826784, 465280624, -1103866083, -225526852, 249812685, 252126208, 3765752039, -413182324, -1960086930, -207039456, -680109449, -1253194364, -2302936684, -107176640, 228977019, -1112350084, 1155422522, 879899072, -2873486098, -1605737720, 1346618926, 941499904, -290743443, -635406184, -542746124, -673919712, 697455132, -530916320, -1646475974, 581507328, 1971762851, -1246954196, -1850394597, 439769104, 2391280258, -1463885836, 93072787, -36438016, -747596041, 1686061716, -1193590103, 254959984, 1341415380, -1263405900, 238866922, 440678976, 1144738265, 255618508, 132711016, -140490208, 723748110, -819541980, 490114691, 395782656, 1334579440, -801807072, 1816140480, -41801856, -1926512306, 89453532, -690985881, -537882624, -1114836519, 597380908, 1476114935, 208291600, 934291416, -1988703220, -2032933290, 55780352, 339620250, 306730820, 2170751046, -1439919888, 2249328734, -1176851632, 1050824473, 275632960, 1795782655, 194093964, 41293302, 823026544, 1546428559, -1897560140, -2446545280, 626738432, 911975917, 1502027604, 436523278, 327744192, 1804526147, -1509645748, -1794004315, 130708544, 550797656, -92851496, 544998722, -240563392, -1460356334, -28543000, -1647519316, 44478464, -539664251, -1873925500, 698658764, -426823008, 2063919313, -681198688, -3025162369, -78131520, 1057690091, 2607174480, -564290233, 442373392, 2337850828, -1148499252, -2621036113, 1111428608, 1274692014, 215361476, 488594593, -156782704, 1634935390, -2979576640, -280897502, 125885632, 1657853451, -896116344, -530846290, 858614864, 1427816299, -270937624, -990975163, 58017792, 822121116, -443598112, 2729459632, -403705536, -1804520525, -2614513416, 486665363, 37771584, 1916592900, -1212822840, 784821225, -495878768, 1263781602, -445866524, -2335544263, 784346112, 2972270752, -69977896, -1564461315, -961180352, 493664483, -983719556, 2252709092, -100787008, -2154610350, -380384028, 2942438624, 326609472, 2389793006, -2374416508, -1960001083, 19939328, 1360630352, -40232716, -2496538837, -289315136, -344453650, -580234852, 710458300, 413927488, 3402519626, -1105817032, 1439032920, 857004304, -404628272, -1035003496, -1667275542, 449409792, -1400746530, 1246037240, -391495562, -600230656, 2630512644, -2890502212, -1528238025, 620769472, 954776555, -207378892, 1274055882, -2012039488, -39329496, -636352796, 1206121447, 123433984, 48796369, -74889172, -1354866796, -471963504, 469787946, -1517676964, -1803729847, -103710272, -857807397, 948039696, -1403881655, 1896786176, -739578123, -2527862308, -967341114, 1072413184, 1200389392, -964288292, 1480276916, -1252757200, -1562798743, -142164380, -1264599229, 513764096, 702580170, -1612864764, -1527155925, 114743824, 3871134593, 550662688, -3744236756, 97316864, 16220222, -1460741576, -677400084, 155021024, 2098559686, -1650821912, -1519254342, 502303872, -861120185, 13424584, 1755570270, -614447264, 1588056239, -2735435968, -599027791, 882539520, 559609946, -54712856, -1713010569, -694621616, 2067247779, -399512824, -1972376640, -367747392, 1683816368, 946600480, -263139033, 355040560, 67996849, -3200222984, -201576692, 361424896, 3432809484, -1325955228, -730719398, -595886528, 1194678350, -1828083704, -1460515260, 728875456, 2575779102, -2664821100, 2837329961, -334714480, 831161685, -1583938984, 2736875389, 609759744, -1985911425, 118956312, -1032550259, 587356192, 3409276186, -1399625120, -3140276423, -211063040, 3724094933, -1369313940, -2236653495, -124896064, 1515170983, -688616588, -3406976171, 81330176, -3297084657, -188570736, 423753746, -612207152, -1762095534, -258808384, -2279691029, -566313728, 2543947020, -1462151876, -2295866490, 279657664, 1007920028, -1647337532, -2227337742, 1077472256, 973260440, -866368360, -230666200, -1593238256, 125805380, -616099916, 1723721325, 614028928, 2904010071, 454151576, 2502961552, -64734784, -2028247685, -2115687376, 270451793, 85063680, 1694734444, -361063984, 611297820, -387115392, 874932662, -549040316, -1137687818, 267447360, -924834445, 640061440, 672993864, -560699504, -1043544638, -1873835192, -1203471172, 677539840, 3197235362, -1213780788, 1812063047, -439666000, 2846856866, -2323874664, -5392935347, 473415104, -3781444522, 1443603028, -932940854, 441173120, 1328086080, -3049068496, 275057192, 114712576, 999514299, -149302128, 525014404, -1191102928, -1935275791, 193078244, -3171364955, 381233728, 1339731160, 74160632, -667326830, 410305648, 3437075219, -1601727280, -1199345866, 114069760, -246232032, 392517076, 1949086879, -525424512, -1427340893, -1710910032, 871052412, 164294144, 837612898, -569694964, 2809361326, -659022880, -444817031, 567222432, -2442946532, 135524352, 830690466, -1643404036, -706656596, -473873856, 3179483658, -1617479612, -3878038802, -72897984, 1680828653, 309668016, 1854487117, 843239040, -6516018, -1725439528, -2102015793, 924487936, 609192454, 831776952, -2431546830, -2032633520, -373379592, -1291509088, 471702585, 373660736, 1562795302, -158188868, 1539575788, 743489952, -3306881458, 376763856, 156705766, -173146112, 347063816, -216229000, 3366183186, 4176704, 4613300740, -3997687380, -2685946939, 1621434944, 4124371131, 794951684, -859343599, -672946224, 238927476, -673086480, 89800001, 897822976, -1795840118, -1442451036, -1336152576, 73051840, -619165742, -3406340284, -2058653427, 155657088, 531580341, 39224524, 89756920, 847026864, 2345270256, -712792848, 1308308553, -41704448, 1453509456, -1097528420, 1546647476, -1142053600, -509583510, 1158267976, -404043830, 961456064, -2584131301, -1818444572, 976080529, -799349632, -957424808, -2338721660, -864965447, 623373312, -797055321, -201843380, 705138570, -307373216, 2371659768, -1328113656, -4109695724, 804687936]