# Trace form for 1045.6.a.g, downloaded from the LMFDB on 25 April 2024. [0, 39, 12, 27, 670, -975, 69, -251, 270, 3666, -300, -4719, 872, -717, 2647, -675, 15078, 2155, 3293, 14079, -16750, 6891, -1452, 1296, -3138, 24375, 2585, 3846, -20901, -7635, -1725, 9595, -43, -3267, -28383, 6275, 80573, -28965, 4332, 21358, -6750, 19627, 12478, 3711, -81070, -91650, 37459, 38450, -12259, 78758, 7500, -68114, -50322, 20631, -124732, 117975, 94893, 9747, -148140, 170405, -21800, -22345, 246390, -151688, 340312, 17925, -8349, -16408, -32276, 93536, -66175, 119338, 135668, -141606, 71843, 16875, 241870, 30371, 708290, 14727, -376950, 441659, -219870, 384909, 877024, -53875, 250290, -77038, -32670, 443394, -82325, -207088, -237112, 396718, 409516, -351975, 100332, -152942, 895680, -443586, 418750, 226622, -533254, 10066, 1116296, -172275, 135421, 141770, 697697, 158562, 36300, 627751, -981613, 153741, 24909, -32400, -468, -184486, 93487, 317952, 78450, 570999, 1065909, 248702, 1260042, -609375, 1778101, -576240, 2098706, -592931, -64625, 930456, -105512, -90611, 572980, -96150, -692788, 1092208, 4084839, 491921, 522525, -210381, -475901, 86757, 5820074, 190875, -25985, -284219, -895813, 1546379, 43125, -390159, 97470, 477438, -320287, -239875, 641523, -745011, 2205547, 573144, 1075, 989325, 2047782, 109367, 3737177, 81675, 1383428, 701355, 6454041, 2010584, 709575, 1323426, 547926, 911358, 1946618, -156875, -1824438, 1367924, 1755189, 3516624, -2014325, 611006, 2092440, -291528, 3275971, 724125, 2277470, -260755, 5095166, 3462188, -108300, 3187905, -2334623, -3106848, 3047462, -533950, 1327731, 2385732, -398453, -932214, 168750, 2910047, 806602, 4022406, -693693, -490675, 3593690, 178546, 4017852, -1703559, -311950, 2050645, -1993972, 3495252, 1841960, -92775, -3035708, -2505238, 107749, 2164597, 2026750, -1303967, 653590, 795931, 4328280, 2291250, 958425, 1410274, 314792, 1249992, -936475, -833811, -11258910, 3202604, 6122815, -961250, 8158342, -3761451, -3297850, 2218605, 306475, -1809681, 175692, 4497550, 1291490, -1968950, -7309160, -258837, 13563338, -5876098, -187500, 3600675, -12559610, -156816, 4120983, 1702850, 6358462, 257143, -2499802, 4720399, 1258050, -8876367, 1294587, 3484693, 379698, -515775, 955567, 6964811, 4157998, -14503, 3118300, 2105380, -7860448, 2878713, 7590477, -2949375, 20783657, 2568516, 7848522, 18443757, -2372325, 452530, 25208544, -2209, 20514924, -243675, -312785, -1562593, 15379977, 8710836, 3703500, 5537021, -2955874, 9973653, 15416434, -4260125, 6504915, -465366, 8541519, 7760550, 545000, 7674752, 6638829, 4249306, 5443158, 558625, 13267641, 1893022, 2529021, 1813582, -6159750, 8961344, 39962095, -4192873, 7075926, 3792200, 10310527, 12909632, 29043016, 923835, -8507800, 13145288, 12420791, 777955, 40218038, -448125, -1661378, -249257, 4571736, 8175360, 208725, 9430803, 6913959, 229706, 21761477, 410200, 47911252, -6038891, 11453387, 22762976, 806900, -1160995, 1188773, -637546, 8981769, -2338400, 10710222, 19692018, 9225598, 6597293, 1654375, 3998338, 5203, 4572225, 5731932, -2983450, 22514882, 7411837, 7673990, 9139318, -3391700, 5082519, 15046171, 395307, 10434522, 3540150, 15118651, 10149534, -7988837, 16180329, -1796075, 23777186, 12372717, -3939172, 3434343, -421875, 27425943, 12466104, 43909924, 1731106, -6046750, 34505107, -3351100, 10387135, 40909677, -759275, -3273825, 13953711, 11076676, 22942306, -17707250, 7774882, 8490899, -857497, 38834350, -368175, -9749333, -17047460, 10438227, 2487651, 9423750, -4535103, -27815231, -3643939, 19128436, -11041475, 23419237, 3504765, -17533819, -1424266, 5496750, 25353859, 16258470, -7159134, 3983691, -9622725, 37106397, 7289450, -524172, 13249959, -21925600, -153057, 22883947, -10928610, -5942458, 1346875, 45931441, 12439305, 7110910, -2584318, -6257250, 14496273, 9401207, 11323487, -6394461, 1925950, 9552626, 467856, 35531030, 14454923, 816750, -2432288, -18558699, -8459990, 48513109, -11084850, -29865952, 34594209, -16052054, 5023286, 2058125, -2374867, 5847116, -19535896, 891014, 5177200, -1132818, -5625601, -7938525, -24106326, 5927800, 39877854, -1509838, -32466337, -4894439, -9917950, 41393993, 6866801, -33511152, -14423015, -10237900, 28471259, 12248644, -449031, -21726862, 8799375, 33868754, 29025606, -46867057, 20158217, -2508300, -4078775, 3289354, 11312851, 9809470, 3823550, -66448690, -23189173, 73715829, -2529502, -22392000, 33165510, -66371577, 12333880, 933185, 11089650, -16019533, -15473383, -37266871, 21885047, -10468750, 8831926, -54539321, -6455047, 20498903, -5665550, -4532539, 55864261, -20607798, -18104701, 13331350, -31921586, 30346237, 1388406, 10190796, -251650, -103463288, -4652450, -5879820, 27006371, -27907400, 51302853, -147174423, -17638758, -34879103, 4306875, 33210871, 21814549, 1483339, -9622419, -3385525, 70030022, -7545261, -11747869, -71722211, -3544250, -33376274, 18407547, 22701615, -9529718, -17442425, -15494675, -454770, 21602424, -114643673, -3964050, -51732088, 40642933, 38441657, -34611441, -907500, -2756235, 98938130, -28217387, 7117183, -15693775, -115453535, 40464473, 30552455, 10989998, 24540325, 8241794, -98803949, 7534297, -8463215, -3843525, -31249149, -53230962, -81304067, 39083078, -622725, 21086734, 6088962, -9931580, -75045049, 810000, 141628150, 6377141, -23531159, 9830700, 11700, 4967330, -10618899, -2496351, -34770593, 4612150, -7836769, 93362100, -99700919, 3463795, -2337175, 30816470, -185239593, 24847871, 15092572, -7948800, 71368841, -35930647, -18803742, 27433585, -1961250, -59138994, -34266693, 61178935, 6777237, -14274975, -117640177, -32377760, -15523, -16763351, -26647725, 15331289, -212757968, 18573029, 22274343, -6217550, -11482053, 60662115, -53183107, -54525219, -31501050, 64429293, -123810058, 8489925, 67779301, 15234375, -34561424, -1179387, -41435188, 63356861, -44452525, 18371137, -87673217, -8575871, -70374571, 14406000, -74832355, 35588849, 17924940, -31631690, -52467650, 28276408, -29231772, -62202955, -20168560, 14823275, -10246263, 85748946, -25381052, -20619005, 1615625, 20457386, -74579638, 50493088, -181323353, -23261400, -26095961, -12145485, -72675458, 35007290, 2637800, -8055059, 34203466, -117079830, 32001651, 2265275, -140980327, -7403684, -50554576, -39781645, -14324500, 2703745, 51487940, -25206589, -133541240, 2403750, -150340763, -15406592, -155570278, 37787317, 17319700, 4285487, -29813190, 471442, 29086853, -27305200, -29534647, -105056892, -97988570, 37530903, -102120975, 25065881, 6865511, 18354248, 90039197, -12298025, -76104043, 11879625, -126557014, -2299901, -13063125, 67567321, 9651546, -10456365, -41177752, 5259525, -98874769, 63037925, -22153447, 13284749, 11897525, -80931668, 90476414, 12780761, 20481686, -2168925, 116615009, 106659038, -150345786, 18682898, -145501850, -46734523, 1563852, 18333115, -59479152, -4771875, 1010229, -624248, -30883335, 57324006, 649625, 59864238, -102089487, -74872757, -70422872, 7105475, 88110822, 1985368, -166544068, -1302144, 22395325, 7710238, -42415924, 13721752, -337684897, -38659475, -17812288, 124540836, 3905396, 1015368, -1078125, 24035051, 134475331, -157208810, -19468554, 9753975, 209196700, -6980211, -157196762, -11317856, -2436750, 160958211, -106041068, -70009419, -58403874, -11935950, -92369218, 84397803, -54391653, 15834264, 8007175, 110043326, -245013090, 8171801, 19436838, 5996875, 125006566, -142488291, -18518174, 7085347, -16038075, -14439898, -15001966, -13635353, -47700683, 18625275, -332279462, -91822160, -47672061, 48659768, -55138675, 7401214, -16415828, 26593390, 109873348, -14328600, -115664262, 18260534, 4504558, -46939575, -26875, 40949686, -157602552, 17134326, 49619839, -24733125, -21368470, 159846258, -151199819, -1625658, -51194550, 167185038, 125595671, -5103443, -8693003, -2734175, -128808919, 1339671, -20910127, 52474716, -93429425, 81877805, -106566779, -59645827, 127950393, -2041875, 77858690, 165045134, -289964070, 21301129, -34585700, 70956321, 108411905, 12075617, -360759977, -17533875, -29266270, 10472073, 21768703, -16848962, -161351025, 69168584, 2331675, -145944755, 28884897, -50264600, 249626373, -3674891, -269295694, 126620819, -17739375, 109116012, 191876946, -126978679, -324932102, -33085650, 156562082, 5111826, -85703090, -2194802, -13698150, 72971781, 20315835, -203950934, -248243612, -22783950, 226286484, -113236015, -179605612, -1781967, -48665450, 20562846, 6227150, -176032197, 13522699, 3921875, -143786883, 4014311, -29906506, -74778745, 45610950, 136200959, -21716034, -168941155, -41330811, -34198100, -115669503, 102972987, -213039283, 7347850, -43879725, -53440739, 43001564, 13880450, -262296055, -87915600, -180150381, 47116798, -378024058, 664166, 50358125, -26350259, 26604270, -86478988, 104660006, -15275150, 103804083, -119986521, -217849864, -179318815, -52311000, -3269825, -4425499, -46573989, -106996998, 7288200, -99105535, 54534849, -325503432, -128130571, -81899275, 129660131, 256904362, -111068817, -106119904, -18103125, 35656753, 164475423, -516247752, 60721516, -56936750, 28431638, 241788205, -124752700, -265271882, 6518875, 211081114, 47295463, -183889698, -243392120, -127379150, 73437642, 17756773, -330162435, 264996658, -86554700, -30285090, 248230225, -483043269, -230598281, 2707500, 95578604, -478393691, -107098387, -118799303, -79697625, 141114934, 9321598, -386893318, -107158548, 58365575, 184810900, -5579084, -56162994, -260110090, 77671200, -167973877, -128746681, 3953070, -24589154, -76186550, -90034729, 141429467, -175174490, -39842802, 13348750, 259785752, -445085, -374810464, -53650674, -33193275, 245190448, 188253751, -41423984, -710718326, -59643300, -282614530, 30194458, -18166242, -150304768, 9961325, 61509641, 260674566, -128686971, 212933845, 23305350, -801853016, -99808979, -173218780, 110872888, -4218750, 25057648, -92477457, -138098923, -147815633, -72751175, -58737602, 7447791, -866783506, -26203753, -20165050, 172477600, 28690552, 124965163, -183172584, -100560150, 439364645, 327171950, -392879243, -261360117, 17342325, 61918065, 247800589, -48002878, -76928479, 12266875, -45028252, -93105311, -352035302, 40363828, -89842250, 29222384, -403177118, -140505693, -49551436, -4463650, 515170820, 449875714, -605852878, 59861263, -100446300, -34447190, 195828755, -360399726, -586128214, 42588975, -69221541, 301836, -308385937, 171576905, 7798750, 126201052, 93071373, -206278570, 109721314, -51266125, -12140172, 284641694, -22957787, 217650544, 49849300, 212481725, -349196159, -303329017, 34256373, -87381300, 30573349, 18505982, -140124109, 24558849, -46049000, 300829770, -66822453, 56050525, -125708100, 2319375, 23046188, 438055045, -108377280, -18483881, 75892700, 296405929, 68415797, 3518667, -239025046, 62630950, 173457019, -47045369, -372420153, 53673906, -2693725, 99611691, 397591076, 214828858, -95061517, -54114925, -36027166, 432302921, 253537314, 49324769, -50668750, 113270819, -53478540, -134533248, 738219873, 32599175, -84985774, 335965902, -70109510, 207970823, -16339750, -27421262, 566782077, 129013067, -137489553, -19898275, 823287797, 182836144, -179723394, -36873169, -108207000, 61516205, 64523734, -124540727, -305190454, -57281250, 429546373, 364852701, 397721477, 26633385, -23960625, 92205977, 286099011, -1217986, 410118873, -35256850, 661760941, 263144578, -415674146, -5698224, -7869800, 388302630, 43458219, -106072309, -135071816, -31249800, 521345987, 261340533, -517609755, 492625500, 23411875, 278056608, 1040815116, 640416886, 156325600, 20845275, 615250963, 204891314, -283102769, -8066545, 281472750, 74974088, 51518951, 244720902, 131127320, -80065100, -16385941, -284939, -334495602, 303567045, -153070375, 251142661, 675751356, 232850202, 127809851, 24031250, -279521642, -17154170, 88946790, -39776583, -203958550, 529868702, -166059919, -309285449, -265487166, 94036275, 246173723, 69833977, -84421337, 308370994, 82446250, 754001752, 682278068, -57346408, 8851904, -55465125, 466588670, -54759368, -155028037, -19186002, -7661875, 197908890, 276981002, 407569334, -1696162, 45242025, -154543648, 201650403, 456258143, 277844346, -4392300, 530360875, -72920203, -2882133, -213519120, -112438750, 122852632, 440918966, -706810526, 450892114, -32287250, -75957871, 457898738, -35175884, -90183226, 49223750, 220694715, 7948291, 28811326, 334099650, 182729000, 176806354, 118775173, 584806766, 191815017, 6470925, 147124361, 526762135, -320248343, 215801037, -339083450, 196572241, 713441140, -18602661, -91530880, 146902450, 397580687, 141261450, 500545505, 324221374, 4687500, 701678924, -211039983, -79124707, -3013989, -90016875, 63643322, 337601713, 183930232, 193615600, 313990250, 491532827, 34667347, -206676979, 277220589, 3920400, -129935866, 470152589, 212712979, 6478391, -103024575, 189512674, 1096307859, -5923288, -188642145, -42571250, 56628, 496327858, -652239321, 452050481, -158961550, 999514448, -150669211, 55508872, 275939375, -6428575, 468427848, 22322806, 266765492, 547665884, 62495050, 297932460, -11651636, 195682012, -538065156, -118009975, 1086862109, 21036717, -11311927, 463153057, -31451250, 314132844, 1095243252, -204385618, -249418784, 221909175, 730275751, 423880341, -402554668, -38472192, -32364675, 33766496, -6895163, 144060760, -540335227, -87117325, 845548616, 752930810, 30155501, 28929313, -9492450, 461374296, 344391278, -200452770, 657693962, 12894375, -994872721, 163516261, -520756875, 307931212, -23889175, -69090879, -1299712813, 411686069, 749074678, -174120275, 670787985, 292947497, -1180364094, 360096268, -103949950, 685457189, -128974989, 391140465, 1046395436, 362575, 654278978, 192387648, -979016538, 43081018, -77957500, 435327765, 479087557, -30092942, 72351075, -52634500, 898120212, -504064822, -532472694, -160345755, 196511200, 197699229, -704868867, 367586556, -152465082, -71967825, -433538740, 59230389, 48976148, 683683928, -189761925, 277757297, -67368272, 61916788, -48204739, 73734375, -198726744, 156109848, -316508965, 419894436, -519591425, 39994352, 70714290, 169908676, 791306767, -64212900, -215150221, -51119766, -7325998, 791226918, -196213050, 811768943, -718486972, 188277558, 345591045, -461093925, 268920491, 69725040, -224272981, -14616856, 59308125, 874642053, -54622547, 234877780, -1118395104, -11313250, 25935323, -138690677, -253943426, 488622733, -630213600, 659337083, 968998512, 301399828, -1196614342, 55225, 416687231, -105456651, -77410802, 71744651, -512873100, 346543440, 665698515, -398774450, 507461808, 6091875, -460373149, -143389946, -1193603654, 698671627, 7819625, 384315408, 527383695, 227723305, 199224931, 39064825, 883915235, 390270401, -179319918, 558245540, -384499425, -112585176, -189129742, -374908782, 87315070, -217770900, 197729920, -42894380, -571425493, 1140338819, -92587500, 550232720, 12766952, -146096351, -125883759, -138425525, 1209130565, 300418446, -589883414, 163127865, 73896850, -12121996, 177672852, 10963931, -65430057, -249341325, 172400714, 443262617, -412305203, 146462622, -385410850, 77320513, -579946662, -330701618, -69330580, 106503125, 691028425, 671416633, -766113194, 894497755, -162622875, 268193923, 255692690, -225648730, 371408704, 11634150, 266675079, 108036824, -740835728, 299212954, -213537975, 205613968, 230791145, 342007045, -361659387, -194013750, 83827348, -440796939, -65280610, 122901207, -13625000, 5316447, -607777908, -568801793, 182835108, -191868800, 616807344, -132157168, -538838750, 374995405, -165970725, -165083336, 1525901398, -325446930, -528384568, -106232650, -22208246, 534631309, -494265519, 585822439, -136078950, 1022068589, -301717456, 538662822, 4062732, -13965625, 203725927, -515253548, -942456687, -59522441, -331691025, 561294948, 1154883921, 10284533, 1109906403, -47325550, 1340803359, -341189276, -828960395, 159438899, -63225525, 671646705, -433508811, 596895577, 108282777, -45339550, 627099060, 56314332, -539018521, -239516134, 153993750, 25456101, 561748763, 391739915, -644811421, -224033600, -15931677, 631663466, -79373070, 370226889, -999052375, -55622448, 57584021, -290992571, -210495114, 104821825, 628329969, 485315935, -762318797, 195142661, -176898150, 785233828, -742503890, -10497597, 738663400, -94805000, 1773735525, 138952149, -1318406691, 212690070, -257763175, 633671154, -674830378, -670798567, -704228954, -322740800, 201602682, 231028306, -437962865, -48707471, -726075400, 1102333953, -676387693, -483470140, -10269057, -23095875, 316605664, -268030305, -1342824398, 138819776, 212695000, 528103141, 235863646, 112295684, -516430161, -328632200, 3144185, 308727102, -1964843511, 640847732, -310519775, 1164499902, 136835955, -435938840, 436974349, -19448875, -122200720, 34390499, -535769461, 670141458, -1005450950, 324243987, 35365673, -661104095, 627850569, 11203125, -1091474038, 46233269, 108393373, 1575782896, 41534450, 1258095582, -1358043593, 29047231, 90354690, 6231425, 340179569, -816010751, -2103938701, -187111859, -114293400, 55995941, -151856845, 294919757, 149366590, -204384000, 126830221, 26157844, 374480526, -244760039, -5218125, 188916158, -478413808, -27810718, 199917225, -235770075, -898950012, -116340014, 311994394, -201577159, -172848975, 47209239, -782610151, -901417677, 1296623561, -5742650, 733209883, 946939363, -1570340242, -90806331, -544036925, 1224527595, -11793870, -210811303, -597214368, -10255000, 1054145350, 510037561, -1216632181, 290487132, -1197781300, 210114584, 399580320, -57769998, 639565001, 150972275, 961729236, -211562602, 528526909, -366605014, -286334675, 160065234, -833151640, -337401519, 38754727, -569074400, 112119833, 705621321, -339888222, 913067027, -20172500, 298696007, 790193872, -1701819384, 75829308, 29024875, 329060707, 611374681, -709922093, 325480241, -29719325, -239137540, -152316294, -1007811722, -794076711, 15938650, -77624283, -228846122, -996449546, 575687396, -224544225, 755596065, 666450300, 298997538, 468486458, 58460000, 1039336691, 90146331, -1368627048, -74758768, -267755550, 235777859, 1431995106, 394516063, 972147122, -492300450, -724946212, -1729524726, -266871187, 217483080, -230639950, 237385659, 329397645, 1991915869, 32627916, -164932325, 369838232, -269543753, -85597432, -69350424, -41359375, 210045082, 511129387, -611373045, -35630970, -99958450, 96676053, 554859741, -2215013040, 247993329, -130075, -432933581, 555293109, 1389313717, 1726283490, -114305625, 63464681, 143215198, -1931311459, -303887785, -143298300, -119708325, -1886795837, 276208521, 1213047953, 74586250, 1985518872, -276764683, -696719405, -674672870, -562872050, 219808205, -247781622, -397576662, -711996273, -185295925, 147835276, 1418344331, -2035695424, -239225536, -191849750, -149022005, 460937863, -13233407, -920748164, -228482950, 786701277, -1377884514, -684782178, 636196665, 84792500, -268263313, 519835491, -572600789, -452198417, -127062975, 826690399, -231656877, -176806248, 1443753387, -376154275, 898796377, 916601641, -1256996052, -290562500, -9882675, 1102088938, -623238430, 453384171, 1464042403, -260863050, -12636179, 180091175, -99016149, 36219852, -88503750, -167394788, -68632175, -1287963280, 863281943, -377966275, 1334868063, -967163363, 64242703, -71388647, -253738350, -334343062, -84863955, -240023876, 342981415, 199720925, -625354580, -201994401, -55212062, 1084693374, -404508225, 1278791788, 431271988, -780938961, 619546124, 44901875, 1181012304, -704345452, 232499877, 329310169, -594429650, -664129498, -1682483663, 241554893, -243280664, -309317925, 57915320, 323340480, -1104728626, 720122082, 98479300, -774832129, 261179292, -1215150510, 218398342, -85858575, 815393155, 324939629, -259520514, 1118888946, 10546875, -511335427, 454245819, -212563520, 211753732, -685648575, -160134546, -1094062059, 408498265, 1453123255, -311652600, 633372687, -429965832, 595392321, -920061727, -1097748100, 695272031, -66299046, -488386204, 66814185, -43277650, -468906089, 206522936, -1919200595, 1431995162, 151168750, 170417515, -3119163773, -110274318, 267345211, -862627675, 1664207094, 54963351, -2176413718, -1253770970, 83777500, -86923303, -998719029, -397368293, -235540778, -259678375, 2426532116, 1543351647, -170038305, 81810542, -1022741925, -799364028, 813799349, 871635849, -768681963, 18981875, 639050248, -1708982833, 443616999, -1321460046, 81845625, 719592692, -1783819921, -129358339, -1057248956, -348842775, 220756998, -568481893, -192504694, 49740319, -276916900, 470189943, -1112261609, -114940865, -1172985185, -573557650, -564151711, -165518804, -1824898496, -959970147, 442681250, 141623688, 1620074528, -1521029145, -244761131, -194372050, 8879801, 3633826, -212377869, -118858296, -212272475, 128795535, -1516452164, 906835086, -371864256, 21437425, 1060302190, -1486178754, -3777140690, -425511504, -970858750, 529493014, 2418247640, -574891319, -1311844823, 9204375, 402982856, -537255730, -1971155736, 1323179141, 243733325, -229177255, 1240955993, 504012969, -849595887, 426186500, -431971971, 903952602, -1085914563, -2091473339, -260955675, -73931726, -377142588, -2575858459, 393268471, -62191275, 762210918, -473525672, -1258416199, 1013778306, -235593750, -2148380954, -253185240, -470729353, -68302319, 113377575, 1336504435, 1531798197, -3674124438, 1123447320, 695380775, -887201246, 126860013, 35274888, 48886981, 91098475, -438490007, -524938019, -1472252156, 350284005, -478210900, -55172646, -3359793903, 299309931, -396392491, 276036875, -420431534, 940947053, 2118674296, -80748173, -585480925, 51405364, 581135978, 51178970, -327754443, -87619125, -1207604463, -2782554610, -1445670141, -760701225, 438345475, -2096278222, 962303236, -442625659, -2845558660, 35606650, -275573870, -1216771454, 984453473, -153226326, -137418750, 1372298540, 251868617, -1856058854, 697078472, -633846475, -720554737, 31551355, -1609402945, -164870921, -406461750, -1210153768, 1882872185, -425894873, -5454510055, 178978350, -1129837771, 1909157390, -616515086, 48094610, -99592275, 57240882, 1831756726, 1240953298, -4054007038, 240568125, 984059821, -1682232650, -1753340087, -418924748, -927659925, -649870948, 1816365340, -1426980119, 1176572539, -182236250, -618992050, 447625981, -6505302290, -694968622, 13104300, 447668018, -1954904734, 103126572, -1051838734, -331248975, -254551342, 916632660, -2606552099, 438102940, 548140000, -385736505, -472894164, -2460500882, 983302489, 3826425, 2421224562, -627580400, -437005295, 226618111, -572098675, -1086371269, 282489383, -1495652378, -563890282, 273215250, -88448963, 2419586694, -2857140463, -1615989087, 148561450, -3924766968, -418145726, 375928608, 2789203318, -33671875, 906929605, 456535310, -354362293, -280736124, -1148286025, 734268185, -2814671556, -2339924212, -368742902, -310982625, -2985390345, 524137534, -329813069, 1490692497, -177772750, 746897949, -484194863, -995994751, -650480429, 64607950, 2139509907, 55500501, 868476039, -421717645, 156431250, -1742717641, 23816057, 127097134, -519288773, -362406825, -160655451, -835745011, -4333858732, -295520144, -235030175, 356094651, 915486403, -240252208, -2202722811, -283087175, 8992149, -288673572, -607433997, -3048610295, 159861525, 1819626610, 3432402512, -1991856165, -136617180, -48148750, -4118497085, -686480125, 48212813, -583514867, -238815650, 180373729, 1093892472, 160368801, -2034720381, -11696400, 1471629879, -911454512, 1017887358, 112797894, -888275750, -1767126603, 2714595842, -1346498219, 654401935, -361373075, -1435053638, -1293884499, -1431800345, 888786007, -20418750, -443271572, -145848837, 1309584710, -168948, 60807200, -1649579922, -547005930, 3128432470, -772403653, 463967475, -352115687, -2764995748, 1067357452, -4060374573, 211499750, 1486881408, -2505916559, -2830223191, 1516655840, -1212827725, -1300340013, -97598842, -66599446, -3678960455, 277121250, -2319526912, 1132756724, -2577311397, -2165356470, 746648800, 510604620, 3250966373, -486711126, 903836028, -864855225, -1374910681, -712464994, 912458288, -2374512698, 401301350, -2091151406, 33748807, 1953821188, 83936853, -125582150, -1092297869, 647716761, -4767156811, -1120124997, -51453125, 513365484, 3152369312, -2772017045, -2847042997, 59371675, 732786277, -802432613, 136955892, 803422988, -146177900, 114780672, -1368014061, -243549482, -658074907, 488397400, -434836490, -1076588074, -3480546433, -1784556066, -22275350, 1458157436, -1556679850, -1558821367, -1253570605, -129430000, 905502663, -21604066, -679413649, 437249448, 28320450, 515338891, 811914061, -790990333, -1118400036, 140640025, -1304459945, -193508937, -486160092, -573720025, 198463125, 539464341, 1445977823, -674466879, -2054499816, 602658150, 4709937, -1176680308, 1162915757, 206130639, -148195000, -1259027052, 1651782670, 1496636429, 2524976513, -996946350, 703332113, -1137584067, -428034208, -897892964, 37745950, -1353095211, -1711064149, 627589722, -28404388, 811658425, -2984718388, 249559263, 384793149, -2623973129, 122360975, -248128045, -3596470273, -2043236789, -162508607, 247948750, -195426095, 1637632731, -2292589287, -2566810353, -1034849825, 3019375902, 241270612, 1182873538, -486562070, -171670025, -66704747, 89781422, -3889335804, 1427500546, 837778800, -1467099833, -779012539, -422925492, 894987873, 360575375, 1163179864, -225557471, 1740130703, -4173968951, 255947500, 1173241265, -5069800975, -1713198711, -222877160, -711781475, 454875162, 2448278238, 496290428, 1957919511, -306216100, 628029189, 2093229754, 242915283, 230730839, 11225775, 1816733771, 280423629, -5811758585, -973201703, 543171550, 1287618363, 3839198859, -804305886, 140804011, -219984375, 367320668, -1061429241, 2088055095, 2758040461, -846718850, 1353759896, 2517040758, -2074400752, 6859296153, -725640150, -1022469851, 303133798, -2406806231, -2941862140, 1171676425, 606042160, 2124155768, -203568119, 641894461, -503955425, 2019806089, -100113173, -13037629, 1874213481, 62707500, -84523485, 1891527642, 1864236888, -4266524096, 101969375, 4147958643, -2129170520, 131996113, -261916237, -82233850, 1347058328, 5584946804, -208022640, 1436267476, -282821275, -856094496, -566456035, -866292740, 1868035411, -245236750, -649041189, 2456212428, 27101243, -3136581710, -95588750, 284367786, 1007588737, 1661004760, -1204119134, 1661217250, 157780007, 757632866, -1037239860, 1237718776, 579729325, -4362709019, -2276168192, 1262541882, 3039985854, -1842895725, 311374472, -79084390, -2385365459, 3641101468, 63237550, 1121619715, 2036769897, -8327870371, -2650334279, 559800000, -214048091, 3548327526, -96307651, 473277254, -829137750, 5705480968, -615049623, 1774758015, -756248476, 1659289425, -155741561, 799346725, -963668846, -523721880, -308347000, -1338338561, 871852828, 5580767606, -869656868, -23329625, 1093707123, 1050983418, -2365346734, 1972958805, -277241250, -3369596, 1270933083, 2954648986, 1560205900, 400488325, -2150978780, 3071499079, 4175533112, 1906886102, 386834575, -115969425, -2204633203, -1454319721, 335894616, 931671775, 3057506155, 1632301217, -1028093136, 1351450744, -547126175, 5794758248, -170643154, 5147498817, 201201603, 261718750, -934214955, 1184791559, -2717122650, -46425040, -220798150, 1358885464, 1372179365, -38089832, 667817233, 1363483025, 2628755288, 252993840, 2784437486, -2694785419, 161376175, 6118322847, -1168827696, 796299792, -151249032, -512472575, -4551195788, 3657371053, 2031722578, 716287347, 141638750, 2126946243, -32710571, 680087174, -1603566065, 113313475, 1159503839, 3637006150, -3244012679, 5255866091, -1396606525, 198403401, 1214111996, 7878320031, -3037029932, 515194950, 100891131, 2933322278, -124210307, 2205833869, 452617525, 206845780, -233270542, -1438351981, -228983824, -333283750, 2539540295, 1362328110, -631405640, 1598759956, 798039650, 5436831369, -980238051, -1015632408, -975480677, -758655925, -2994349942, 4729226993, -387515084, 3845139953, -34710150, 1277327986, 1809834332, 2102609464, -3209095626, -254769900, 1922106420, -1945247913, 1617519623, -740860615, 6291250, 3727729581, -2243908424, -2213169186, 2468490281, 2586582200, -581837369, 7089029361, -4065810782, -250096468, 116311250, -1030173276, 725571949, 4997883143, 2305517767, 146995500, -1234591629, -1213826702, -845934718, 3619943889, -675159275, -987159382, -2161741707, -1617473360, 497074193, 697685000, 436772725, 640865265, 394287088, 4975051507, -1282571325, 1691823390, 455135571, -386751497, 749464768, 3679360575, 807021163, 4763234660, -6669675028, -711342208, 440968950, -6514068677, -167983027, 399039850, -938472607, 871977575, 2328036948, 1474626879, -457096898, -1737733740, -107671875, 621778679, -2460306932, 4548132873, -268451205, -830271775, 1363825416, 3179841143, 776666959, -789657592, -545363725, -1151664550, 2430461000, -4424291183, 1861704271, -37083475, 177583481, 7597746816, 2775577824, -990459019, 240560475, -1613448466, -1933273474, 7821205554, -1369667493, 84638125, 218971401, -631078640, -3715534641, 3490317163, -1750750550, 580563546, -426614246, -724672112, 3824174621, 188631525, -411436907, -21258732, 3044169294, -8367876826, 293696725, 7177197919, -250990876, -3384364757, 418938656, 1793055275, -2003096544, 3344894174, -544203550, 1565711085, 88606250, -6711912, -110983051, 3582911119, -75947541, 834406850, 924492886, -1270193294, 1315874725, -156270290, -460188675, -59140204, 927113516, 6327816169, -2514119061, -567540375, 1111377576, -382699573, 163831942, 1401698012, 238242950, -767889845, 671861674, -171800261, 4760018964, 436060625, -3648697948, -2699548691, 3052316916, -2582376132, 387366875, 884408360, -1316531401, 7960102127, -5448991620, 11369250, -1862752494, -6498038639, -6146977, 3814940244, -540060600, 4720850450, 31319277, 5013643589, -163264792, 2866091825, -3779366996, 1942889067, -751064895, -5603142339, 99101250, 1587150922, -893348348, -1641163898, -440104280, 1293302200, 4222687163, 2149221933, -1681993050, -1774291109, -1016073325, 2101046714, -4457043268, 5665286991, 711007858, -961041425, 1669765426, 4675956277, 1424179444, 1040191419, 865286025, -660586825, 3093350115, -5707327394, -537064066, 22687500, -2272701741, -164186615, 2823857044, 6700202332, 68905875, 3718803241, -131656004, 2013485594, 733987384, -2473453250, -435681675, -40329453, 2604664080, 1863129934, 705434675, -3612486693, -3036444789, -2073259477, 1790841407, -177929575, 5442955709, 1519712810, -1343460983, -9380585, 392344375, 6240468498, -790307432, -4242971668, 4552756831, 2886338375, -3293226712, -227028394, 18974736, 1951397711, -1011611825, 3202346395, -3376944708, 2282646682, 346748257, -763811375, 776112833, -5246832694, -102603059, -498638943, -274749950, -155058303, 191924768, 5991003281, 2103703037, -613508125, -1507781656, 6193177114, -4031608323, 5744192647, -206044850, -1095733055, 856964902, 11492866335, 7116716, 2470098725, -1130184775, -323388493, 2916540492, 1187525316, -188357425, -769373902, -3302391207, 605722205, 5620382463, 211580375, 1135970033, 4443067968, -4033509404, -1074542071, 96088125, -2999440745, -31114303, 4426131194, -494778216, 781228725, 558242819, 2957435117, -2384142513, 243494426, 1330774050, -46984980, 1444234661, 302476042, -16596130, 2032601675, -2069394903, 4245980047, 1147023635, -8702638043, -977076950, -1606258223, -6114278591, 6426066928, -571168279, 15568125, -764057329, 4717064716, 4457489790, 749715397, -527168350, -1555432757, -1551774362, -1752814532, 5199531919, -152224050, -2301215680, 10742773374, -1259296351, 4117321359, 248289500, 1813884678, 1812775785, 9332998428, -140847399, 1876126225, 1074040407, -2871439846, 843597982, 750117674, -20250000, 1148485282, -5261599252, 523462782, 987215612, -3540703750, -1230403114, -156645027, 1422546393, -1901692344, -159428525, -1000793045, 22796475, 35186670, -2205684974, 588278975, -7653585, -4802645746, -421647853, 4398396867, -245767500, -2156508011, 3703179975, 4675702319, -6540749986, -292500, -2979082014, -943524156, 3615027994, -45943458, -124183250, 800825927, 172355118, 1102604991, 4798099514, 265472475, 1978760221, 6059367322, -2333384240, 3369889912, 62408775, 1966248541, -2283159827, 5748600655, 748019055, 869264825, -2975111299, -3408346208, 776893233, 3479307821, -115303750, -115623607, -1024857244, 523302573, 2206265174, 195919225, 360218152, 566093994, 3295902879, -1749363191, -2334052500, -124758634, -842742131, 1617217333, 643493782, 2492522975, -1324512775, 283925062, -448968884, -590675816, -86594875, 1725584499, 784151656, -503117758, -3053468729, 58429375, 6142116416, 871013109, -137481997, 221862414, -770411750, -176485258, -2688487336, 3421342641, 1754863, 4630989825, -906589455, 3867094413, 3157222481, 231589803, -621196775, -738945185, 3745354593, 1169837157, 149380507, -377314300, 1543565063, 2217906858, -1531550559, 2645109235, 198720000, -14945257790, -3341506329, 8150822034, -2734079758, -1784221025, -254750980, 402422171, -268948971, 2237523289, 898266175, 2274861627, -3988587924, 1538884288, -2354268361, 470093550, 936166602, 951114208, 1236802980, -5872757225, -685839625, 1068962893, -2286511595, -1695850157, 748730338, 49031250]