Sharedwww / Tables / an_s12g0new_1-24.gpOpen in CoCalc
\\ an_s12g0new_1-24.gp
\\ This is a PARI readable nonnormalized basis for S_k(Gamma_0(N)) for N 
\\ in the range:  1 <= N <= 24.
\\ The number of a_n computed is sufficient to satisfy Sturm's bound.
\\ William Stein ([email protected])

E[1,1] = [x, [1,-24]];

E[3,1] = [x, [1,78,-243,4036]];

E[4,1] = [x, [1,0,-516,0,-10530,0]];

E[5,1] = [x, [1,34,-792,-892,3125,-26928]];
E[5,2] = [x^2+20*x-5336, [3,3*x,16*x-170,-60*x+9864,-9375,-490*x+85376]];

E[6,1] = [x, [1,32,243,1024,3630,7776,32936,32768,59049,116160,-758748,248832]];
E[6,2] = [x, [1,-32,-243,1024,5766,7776,72464,-32768,59049,-184512,-408948,-248832]];
E[6,3] = [x, [1,-32,243,1024,-11730,-7776,-50008,-32768,59049,375360,-531420,248832]];

E[7,1] = [x^2+54*x-2640, [1,x,-6*x-102,-54*x+592,10*x-6480,222*x-15840,16807,1460*x-142560]];
E[7,2] = [x^3-77*x^2-2854*x+225104, [21,21*x,-11*x^2+309*x+33758,21*x^2-43008,177*x^2-1551*x-611592,-538*x^2+2364*x+2476144,-352947,1617*x^2-26082*x-4727184]];

E[8,1] = [x, [1,0,-36,0,-3490,0,-55464,0,-175851,0,-597004,0]];
E[8,2] = [x^2-56*x-445680, [1,0,x,0,-12*x+4270,0,42*x+44352,0,56*x+268533,0,-693*x+98944,0]];

E[9,1] = [x, [1,-78,0,4036,5370,0,-27760,-155064,0,-418860,-637836,0]];
E[9,2] = [x, [1,24,0,-1472,-4830,0,-16744,-84480,0,-115920,-534612,0]];
E[9,3] = [x^2-2520, [1,x,0,472,224*x,0,58100,-1576*x,0,564480,-3200*x,0]];

E[10,1] = [x, [1,-32,-12,1024,3125,384,-14176,-32768,-177003,-100000,-756348,-12288,-905482,453632,-37500,1048576,2803794,5664096]];
E[10,2] = [x, [1,-32,738,1024,-3125,-23616,25574,-32768,367497,100000,769152,755712,-918982,-818368,-2306250,1048576,10312794,-11759904]];
E[10,3] = [x, [1,32,-318,1024,-3125,-10176,-70714,32768,-76023,-100000,238272,-325632,-2097478,-2262848,993750,1048576,5955546,-2432736]];
E[10,4] = [x^2-604*x-105696, [1,32,x,1024,3125,32*x,-177*x+60500,32768,604*x-71451,100000,-1254*x+589500,1024*x,1452*x+426758,-5664*x+1936000,3125*x,1048576,-5028*x-1643358,19328*x-2286432]];

E[11,1] = [x^3-4500*x+92224, [17,17*x,-4*x^2-110*x+9773,17*x^2-34816,90*x^2+1540*x-311395,-110*x^2-8227*x+368896,-440*x^2-21110*x+1291202,6868*x-1567808,348*x^2+19668*x-2167122,1540*x^2+93605*x-8300160,2737867,-35*x^2+99176*x-9870464]];
E[11,2] = [x^5-32*x^4-7718*x^3+140876*x^2+11993504*x-87564928, [36792,36792*x,-x^4-146*x^3+15018*x^2+692728*x-25286104,36792*x^2-75350016,17*x^4-1898*x^3-120402*x^2+11421856*x+103045688,-178*x^4+7300*x^3+833604*x^2-13292600*x-87564928,448*x^4-14308*x^3-2742264*x^2+54646760*x+2577197392,36792*x^3-150700032*x,-301*x^4-25550*x^3+2030826*x^2+84313600*x+3456075728,-1354*x^4+10804*x^3+9026964*x^2-100843880*x+1488603776,-5925388392,3652*x^4-241192*x^3-18973536*x^2+628571840*x+36199383808]];

E[12,1] = [x, [1,0,-243,0,9990,0,-86128,0,59049,0,-806004,0,-960250,0,-2427570,0,-4306878,0,401300,0,20929104,0,17751528,0]];
E[12,2] = [x, [1,0,243,0,2862,0,9128,0,59049,0,668196,0,2052950,0,695466,0,1604178,0,-230500,0,2218104,0,-43012728,0]];

E[13,1] = [x^5+41*x^4-5776*x^3-137132*x^2+8660928*x+8321280, [48192,48192*x,2*x^4+312*x^3-16334*x^2-1118052*x+31740576,48192*x^2-98697216,-93*x^4-10743*x^3+337098*x^2+31030416*x-499506624,230*x^4-4782*x^3-843788*x^2+14418720*x-16642560,-510*x^4+37908*x^3+2782662*x^2-165485916*x-1053622176,48192*x^3-197394432*x,4393*x^4+9867*x^3-21277714*x^2+15666768*x+13799973504,-6930*x^4-200070*x^3+18277140*x^2+305959680*x+773879040,6972*x^4+111744*x^3-11868756*x^2+331439208*x-45683537472,-18308*x^4-154284*x^3+79411112*x^2+281114496*x-66918594048,17893352256,58818*x^4-163098*x^3-235423236*x^2+3363451104*x+4243852800]];
E[13,2] = [x^6-55*x^5-12286*x^4+603264*x^3+39388912*x^2-1594524928*x-11319915520, [1004386560,1004386560*x,5015*x^5+156023*x^4-54551082*x^3-1079806128*x^2+130401886736*x+266658911360,1004386560*x^2-2056983674880,-32988*x^5+343092*x^4+245290488*x^3-172277856*x^2-189472046400*x-4746587308800,431848*x^5+7063208*x^4-4105175088*x^3-67133506944*x^2+8263201425280*x+56769376332800,-558237*x^5-12465693*x^4+5166414126*x^3+97210953552*x^2-9169186725552*x-45272293027200,1004386560*x^3-4113967349760*x,-1490932*x^5+14206364*x^4+12622531848*x^3-26516029920*x^2-19663529940928*x+33434714240000,-1471248*x^5-160000080*x^4+19728194976*x^3+1109889382656*x^2-57346775633664*x-373421373173760,-191334*x^5-85096902*x^4+3593804676*x^3+553644479520*x^2-14058557928096*x-96682307001600,20544128*x^5+880974336*x^4-215931242880*x^3-6535378493952*x^2+478298713404416*x+4342365427015680,-372921699022080,-43168728*x^5-1692085656*x^4+433975239120*x^3+12819161342592*x^2-935395105259136*x-6319195680138240]];

E[14,1] = [x, [1,-32,-396,1024,7350,12672,16807,-32768,-20331,-235200,-108780,-405504,-635842,-537824,-2910600,1048576,-9225918,650592,-7555372,7526400,-6655572,3480960,26489400,12976128]];
E[14,2] = [x^2-350*x-122544, [1,-32,x,1024,21*x-3542,-32*x,-16807,-32768,350*x-54603,-672*x+113344,-1386*x+629300,1024*x,2199*x+1252986,537824,3808*x+2573424,1048576,4050*x+3979514,-11200*x+1747296,-41757*x+8178296,21504*x-3627008,-16807*x,44352*x-20137600,94248*x-22489936,-32768*x]];
E[14,3] = [x, [1,32,-90,1024,-7480,-2880,-16807,32768,-169047,-239360,-294536,-92160,-210588,-537824,673200,1048576,-6962906,-5409504,-9346390,-7659520,1512630,-9425152,51172000,-2949120]];
E[14,4] = [x^2+350*x-322344, [1,32,x,1024,3*x+2394,32*x,16807,32768,-350*x+145197,96*x+76608,-714*x+351900,1024*x,1449*x+140714,537824,1344*x+967032,1048576,750*x+2689386,-11200*x+4646304,-7893*x+6884696,3072*x+2451456,16807*x,-22848*x+11260800,1848*x-6727464,32768*x]];

E[15,1] = [x, [1,-56,-243,1088,3125,13608,27984,53760,59049,-175000,-112028,-264384,-1096922,-1567104,-759375,-5238784,-249566,-3306744,-13712420,3400000,-6800112,6273568,41395728,-13063680]];
E[15,2] = [x^2+22*x-1488, [1,x,243,-22*x-560,-3125,243*x,-1276*x-19468,-2124*x-32736,59049,-3125*x,10384*x-66672,-5346*x-136080,-1916*x-1087942,8604*x-1898688,-759375,59048*x-2013632,67540*x-3159354,59049*x,-208364*x-10073116,68750*x+1750000,-310068*x-4730724,-295120*x+15451392,692028*x-11112816,-516132*x-7954848]];
E[15,3] = [x^2+13*x-408, [1,x,-243,-13*x-1640,-3125,-243*x,3584*x+27188,-3519*x-5304,59049,-3125*x,30976*x+349128,3159*x+398520,-71936*x-138838,-19404*x+1462272,759375,67067*x+1922968,-78080*x+3782454,59049*x,131584*x+9669284,40625*x+5125000,-870912*x-6606684,-53560*x+12638208,1571328*x-4706904,855117*x+1288872]];
E[15,4] = [x^3+x^2-5450*x+7248, [1,x,243,x^2-2048,3125,243*x,-12*x^2+460*x+38888,-x^2+1354*x-7248,59049,3125*x,88*x^2+1320*x-139116,243*x^2-497664,-628*x^2-6732*x+2560022,472*x^2-26512*x+86976,759375,-693*x^2-12698*x+4201552,-1484*x^2-117108*x+10408338,59049*x,4556*x^2+74868*x-10615444,3125*x^2-6400000,-2916*x^2+111780*x+9449784,1232*x^2+340484*x-637824,-8996*x^2-41884*x+23294232,-243*x^2+329022*x-1761264]];

E[16,1] = [x, [1,0,-252,0,4830,0,16744,0,-113643,0,-534612,0,-577738,0,-1217160,0,-6905934,0,-10661420,0,-4219488,0,-18643272,0]];
E[16,2] = [x, [1,0,36,0,-3490,0,55464,0,-175851,0,597004,0,1373878,0,-125640,0,10140850,0,7297396,0,1996704,0,32057464,0]];
E[16,3] = [x, [1,0,516,0,-10530,0,-49304,0,89109,0,309420,0,-1723594,0,-5433480,0,-2279502,0,-4550444,0,-25440864,0,7282872,0]];
E[16,4] = [x^2+56*x-445680, [1,0,x,0,12*x+4270,0,42*x-44352,0,-56*x+268533,0,-693*x-98944,0,-948*x+498694,0,3598*x+5348160,0,10824*x+1018514,0,-4587*x+10804864,0,-46704*x+18718560,0,-24738*x-18596032,0]];

E[17,1] = [x^8-55*x^7-12058*x^6+726176*x^5+33040416*x^4-2383120192*x^3+15657421696*x^2+351034071040*x+166084534272, [602357138283368448,602357138283368448*x,-2591759369*x^7+87208475815*x^6+31630798819810*x^5-1201410795172304*x^4-95227849019500576*x^3+4039145429374549056*x^2+2462277442170566272*x-393099324369007875072,602357138283368448*x^2-1233627419204338581504,9075144642*x^7+200107836834*x^6-87910959320292*x^5-422723870740704*x^4+140822418184177728*x^3-3464583784924650624*x^2+360225454617972923136*x-3099166053241511467008,-55338289480*x^7+379364348408*x^6+680662656370640*x^5-9595041295843072*x^4-2137328655694529792*x^3+43042546817162436096*x^2+516696518087123698688*x+430451147745457594368,-283344267846*x^7+10957905599226*x^6+3230082504164940*x^5-154658856096773472*x^4-8314227343635637056*x^3+522843745133932308864*x^2-4068983329833792122112*x-38023832894736824653824,602357138283368448*x^3-2467254838408677163008*x,147851350080*x^7-21625955341632*x^6-1505281338023808*x^5+270266592675568512*x^4-292842092832977664*x^3-866244441060131450880*x^2+22999394566960778692608*x+161480809948550504140800,699240792144*x^7+21517134772944*x^6-7012876106289696*x^5-159024136047673344*x^4+18162576656746160640*x^3+218132088005983970304*x^2-6284851022199614834688*x-1507241171317606170624,1502994966399*x^7-72464177893329*x^6-19846930011006510*x^5+911313489067287984*x^4+64024917162363191520*x^3-2818112687442277778880*x^2+1257740206816548553344*x+65464169084688881617920,2643681614720*x^7-165209396648320*x^6-34189579577385472*x^5+2151560757965972480*x^4+106191386558570435584*x^3-6889018386948272209920*x^2+14813331986734542528512*x+814258250343423045206016,-2455938086964*x^7+357497362461324*x^6+31635908966728488*x^5-4247060058563031744*x^4-73735961846112573312*x^3+12639308993970015479040*x^2-148986505758640934340096*x-913298075898861892349952,-4626029132304*x^7-186482677522128*x^6+51098950950563424*x^5+1047585137211626880*x^4-152399700857326637568*x^3+367457356975403464704*x^2+61439658953092727126016*x+47059100763843734618112,-147229421876*x^7+15679081197388*x^6+10509543561862888*x^5+416486845737609664*x^4-84929645628585965440*x^3-3260033254569145590528*x^2+162472570143045491001856*x+2217655378892155080585216,602357138283368448*x^4-3700882257613015744512*x^2+2526468954530485414920192,-855260999291608674471936,-13494131087232*x^7+277510241240832*x^6+162900490679874432*x^5-5177912205637810944*x^4-513896903270022635520*x^3+20684423630435295356928*x^2+109579948621207874457600*x-24555822619523229941760]];
E[17,2] = [x^6+9*x^5-8410*x^4-88580*x^3+18705368*x^2+99820416*x-12230355456, [437669760,437669760*x,-223*x^5-213873*x^4+2427784*x^3+1334082788*x^2+2112025552*x-1412801748864,437669760*x^2-896347668480,32112*x^5+3443352*x^4-212829096*x^3-24808655712*x^2+115921872672*x+27720793875456,-211866*x^5+552354*x^4+1314329448*x^3+6283322616*x^2-1390541796096*x-2727369266688,417387*x^5+22372317*x^4-2882068416*x^3-158286618132*x^2+2682646705872*x+157749557260416,437669760*x^3-1792695336960*x,-947614*x^5-55692714*x^4+6810459352*x^3+403110009704*x^2-7999471483904*x-414137853942912,3154344*x^5+57232824*x^4-21964174752*x^3-484744904544*x^2+24515360676864*x+392741174403072,-4554297*x^5-179859207*x^4+28151431176*x^3+1440863554812*x^2-22683333873552*x-1681704395750016,2915852*x^5-29451708*x^4-17455869296*x^3-159711849232*x^2+14095754659072*x+302221492632576,-17131818*x^5-637609038*x^4+120212574504*x^3+4595900276088*x^2-133567760861568*x-4364895132136704,18615834*x^5+628156254*x^4-121314477672*x^3-5124730727544*x^2+116085813287424*x+5104791372713472,21910314*x^5+1241635494*x^4-159813014112*x^3-8017954079064*x^2+190174211119584*x+6247665886885632,437669760*x^4-2689043005440*x^2+1835720025047040,621428472424320,-47164188*x^5-1158974388*x^4+319170361584*x^3+9725997108048*x^2-319546630255488*x-11589656055081984]];

E[18,1] = [x, [1,-32,0,1024,5280,0,-49036,-32768,0,-168960,414336,0,-522982,1569152,0,1048576,9499968,0,13053944,5406720,0,-13258752,58755840,0,-20949725,16735424,0,-50212864,-117142944,0,142907156,-33554432,0,-303998976,-258910080,0]];
E[18,2] = [x, [1,-32,0,1024,-3630,0,32936,-32768,0,116160,758748,0,-2482858,-1053952,0,1048576,-8290386,0,-10867300,-3717120,0,-24279936,-20539272,0,-35651225,79451456,0,33726464,-28814550,0,150501392,-33554432,0,265292352,-119557680,0]];
E[18,3] = [x, [1,32,0,1024,11730,0,-50008,32768,0,375360,531420,0,1332566,-1600256,0,1048576,5109678,0,2901404,12011520,0,17005440,-30597000,0,88764775,42642112,0,-51208192,77006634,0,-239418352,33554432,0,163509696,-586593840,0]];
E[18,4] = [x, [1,32,0,1024,-5766,0,72464,32768,0,-184512,408948,0,1367558,2318848,0,1048576,-5422914,0,15166100,-5904384,0,13086336,52194072,0,-15581369,43761856,0,74203136,-118581150,0,-57652408,33554432,0,-173533248,-417827424,0]];
E[18,5] = [x, [1,32,0,1024,-5280,0,-49036,32768,0,-168960,-414336,0,-522982,-1569152,0,1048576,-9499968,0,13053944,-5406720,0,-13258752,-58755840,0,-20949725,-16735424,0,-50212864,117142944,0,142907156,33554432,0,-303998976,258910080,0]];

E[19,1] = [x^7+9*x^6-10458*x^5-57780*x^4+33079800*x^3-56001024*x^2-33006306816*x+384276234240, [5762148641280,5762148641280*x,-717377*x^6+49610991*x^5+5226105474*x^4-418524537708*x^3-5575317505944*x^2+806910167736576*x-10678249598008320,5762148641280*x^2-11800880417341440,-1687875*x^6-133778835*x^5+20752149510*x^4+1420499203740*x^3-90066512297160*x^2-3268202549466240*x+113735272930444800,56067384*x^6-2276223192*x^5-459974580768*x^4+18155370178656*x^3+766736321142528*x^2-34356214962749952*x+275670932090388480,31572873*x^6-4565519559*x^5-164396339586*x^4+35672318722332*x^3-211804553418984*x^2-64591250977998144*x+1200765008196979200,5762148641280*x^3-23601760834682880*x,-156095849*x^6+14114806887*x^5+1079227231218*x^4-102105015909516*x^3-923684983694808*x^2+153559477416886272*x-2313792964924392960,-118587960*x^6+3100352760*x^5+1322973786240*x^4-34231944872160*x^3-3362725277850240*x^2+58024752813388800*x+648610248867840000,497724717*x^6-39966461091*x^5-4265816157594*x^4+291201056460828*x^3+9209526483937464*x^2-473219601378281856*x-1730958365753464320,-1311641552*x^6+24774811536*x^5+10691879615424*x^4-230823274874688*x^3-19798133793575424*x^2+473696187240370176*x+323691989513011200,2852503524*x^6+58063047588*x^5-24627053348568*x^4-480969171419904*x^3+52455356300269728*x^2+693987787428723648*x-25588076692902266880,-4849675416*x^6+165792766248*x^5+37496599324272*x^4-1256228877684384*x^3-62823137759376192*x^2+2242868941497581568*x-12132704740577771520,1031424660*x^6-43239029580*x^5-9162210908520*x^4+376759660476240*x^3+19809095056132320*x^2-670770065998327680*x-10348604264527488000,5762148641280*x^4-35402641252024320*x^2+24168203094715269120,-7366412550*x^6-189105021990*x^5+58322098978380*x^4+1616654509635960*x^3-105473403161427600*x^2-2402440649851921920*x+32872208629079646720,15519669528*x^6-553223157624*x^5-111124234064736*x^4+4239934482055392*x^3+144817950030736896*x^2-7465940449722399744*x+59983925034215669760,14267650488524766720,7624412400*x^6+356759954640*x^5-83584359397440*x^4-2349041647901760*x^3+235839922803901440*x^2+3427738477731164160*x-187359304266547200000]];
E[19,2] = [x^9-87*x^8-11322*x^7+1111298*x^6+23062032*x^5-3703642344*x^4+49908522752*x^3+1569947506944*x^2-33506908250112*x+139839674073088, [327070935857619263084544,327070935857619263084544*x,-22526112771542*x^8+2278536037669798*x^7+253921896486169600*x^6-29342833425467745948*x^5-518203191213814442184*x^4+100381507895835631373472*x^3-1055704997746837070746432*x^2-53238533910587587862250496*x+566454046649070210958469120,327070935857619263084544*x^2-669841276636404250797146112,676038771698390*x^8-42971593707580570*x^7-8640811226829668428*x^6+551391311167446797532*x^5+27781277424784299152928*x^4-1879398206173685314829520*x^3-5351749668166571008336448*x^2+976320776691188039789407744*x-6156099417422016356596932608,318764226545644*x^8-1118752313228924*x^7-4309609354678664432*x^6+1294742359095851160*x^5+16952842789433481999024*x^4+68540014025784614377152*x^3-17873719323765826731662848*x^2-188326347218663718693443584*x+3150044268106058287554461696,-7465577669119091*x^8+519296829750127633*x^7+91899808754435236834*x^6-6638474656464921678006*x^5-267906290837944255251192*x^4+22399010523420235606826856*x^3-43768575781446533742501568*x^2-10884744014836925530857715456*x+88610911048316816839793045504,327070935857619263084544*x^3-1339682553272808501594292224*x,-5870129740408114*x^8+556826161000476890*x^7+69677498821831295432*x^6-7069586100813087016500*x^5-173368973212642763236008*x^4+23240927062906868556794880*x^3-182763030549383479929407168*x^2-9031020371788927683692380160*x+150951878430492070898998214656,15843779430179360*x^8-986700253660496848*x^7-199889223743430612688*x^6+12190449638635334624448*x^5+624407614874220685796640*x^4-39091846086709802005105728*x^3-85024607534183325409212416*x^2+16495869679394350388550787072*x-94537041495073605670751928320,9620004592385950*x^8-900733858309219634*x^7-118035602416602407516*x^6+11657544738277718701260*x^5+340916911243343011481184*x^4-40954792167492376741516368*x^3+68270768420898873878388032*x^2+27672494174947723753311059456*x-113967833364443947890570612736,72747214352360120*x^8-5367002586876629368*x^7-872979349076300575552*x^6+69695614851740534311920*x^5+2310408836818532559119520*x^4-239364099147514155725025792*x^3+1473314385398592379372297216*x^2+122863365409272247767979589632*x-1204673773083598634912768786432,27351391869725747*x^8-3159671765211363601*x^7-334886501950539720178*x^6+41249458977356513789190*x^5+909429051898945543081464*x^4-142397477413092956711807496*x^3+606254347672524954312422656*x^2+76053526218108772136899588864*x-421711303538864540477642989568,-130208427463233284*x^8+7374538384668888532*x^7+1658006876071785912112*x^6-95734899734234366798280*x^5-5250819054350050999562448*x^4+328827377174606747228556864*x^3+835821034693389921227752448*x^2-161537514944941568319549042688*x+1043983948016937693296910123008,-216315657880327374*x^8+15905291930278766130*x^7+2743420726506798619068*x^6-204689083320002693145564*x^5-8867021806213209949866624*x^4+693832739309162665547569776*x^3+2521591139565792229748169984*x^2-341868357220530187643111072256*x+1333712033584647684803496038400,327070935857619263084544*x^4-2009523829909212752391438336*x^2+1371834934551355905632555237376,427860289163069174*x^8-25065602212644651334*x^7-5600614707596522533264*x^6+320038447397597811887724*x^5+19290745586074924338904008*x^4-1067400390201083057955579840*x^3-9624749013969033109832061824*x^2+449071807101638437880149633024*x+926710079551360750908152129536,46124873584970972*x^8+3215889900930628724*x^7-546122660557030744528*x^6-37991853295199145108360*x^5+1500065991557649705215664*x^4+110206473156966731405002560*x^3+184775179602620787716563456*x^2-45738020197616376985467994112*x+820877029665411331181784236032,-809860017206115199704376313856,-992818847673195248*x^8+67499870878185108592*x^7+12279670637983033155712*x^6-870231538616448521608416*x^5-37308209866059577459482432*x^4+2973243292540748015360845824*x^3+2582350982818772666858356736*x^2-1563165928456595111299558899712*x+10392102655278111883388928917504]];

E[20,1] = [x, [1,0,306,0,-3125,0,-32074,0,-83511,0,-5280,0,227834,0,-956250,0,-5097318,0,-16279036,0,-9814644,0,-33055038,0,9765625,0,-79761348,0,-2112786,0,91337396,0,-1615680,0,100231250,0]];
E[20,2] = [x^2-220*x-174816, [1,0,x,0,3125,0,111*x-10540,0,220*x-2331,0,-390*x+192060,0,-3156*x+952070,0,3125*x,0,-5028*x+5081250,0,15180*x+8049884,0,13880*x+19404576,0,6537*x+27244140,0,9765625,0,-131078*x+38459520,0,-336840*x+57973254,0,593250*x-34142104,0,106260*x-68178240,0,346875*x-32937500,0]];

E[21,1] = [x, [1,-62,243,1796,-3310,-15066,-16807,15624,59049,205220,628904,436428,176854,1042034,-804330,-4646896,566958,-3661038,-12916124,-5944760,-4084101,-38992048,-25664100,3796632,-37872025,-10964948,14348907,-30185372,-47411458,49868460,13942680,256109600]];
E[21,2] = [x, [1,8,243,-1984,4390,1944,-16807,-32256,59049,35120,-804836,-482112,358294,-134456,1066770,3805184,-5657862,472392,-14602004,-8709760,-4084101,-6438688,-36724800,-7838208,-29556025,2866352,14348907,33345088,51126982,8534160,-208102080,96501760]];
E[21,3] = [x^3+33*x^2-2910*x-69840, [13,13*x,-3159,13*x^2-26624,-46*x^2+310*x+122790,-3159*x,218491,-429*x^2-15418*x+907920,767637,1828*x^2-11070*x-3212640,-242*x^2-122518*x-2191044,-3159*x^2+6469632,8864*x^2-424224*x-32453050,218491*x,11178*x^2-75330*x-29837970,-27885*x^2-340470*x+24564592,-71698*x^2-293110*x+104327058,767637*x,127180*x^2+2563812*x-249712876,22814*x^2+1471960*x-123806400,-53093313,-114532*x^2-2895264*x-16901280,263846*x^2+7170610*x-610126224,104247*x^2+3746574*x-220624560,-138272*x^2-4790880*x-3322565,-716736*x^2-6658810*x+619061760,-186535791,218491*x^2-447469568,780980*x^2+13104540*x-1934624274,-444204*x^2+2690010*x+780671520,-1739316*x^2-40961052*x+3422043968,1458327*x^2-25004694*x-3806908560]];
E[21,4] = [x^3+68*x^2-1720*x-7232, [4,4*x,-972,4*x^2-8192,37*x^2+2204*x-45064,-972*x,-67228,-272*x^2-9504*x+28928,236196,-312*x^2+18576*x+267584,275*x^2-5500*x+933808,-972*x^2+1990656,6222*x^2+537192*x-5737928,-67228*x,-8991*x^2-535572*x+10950552,800*x^2-438912*x+14810112,3047*x^2+271092*x-5312984,236196*x,9896*x^2+1148256*x+14169680,-35984*x^2-4782848*x+90034688,16336404,-24200*x^2+1406808*x+1988800,134497*x^2+9345900*x-136786240,66096*x^2+2309472*x-7029504,-220678*x^2-17083656*x+438945756,114096*x^2+4963912*x+44997504,-57395628,-67228*x^2+137682944,-403608*x^2-30224800*x+661657368,75816*x^2-4513968*x-65022912,604904*x^2+52642656*x-527367680,63744*x^2+35650304*x-53458944]];
E[21,5] = [x^4-45*x^3-5484*x^2+154872*x+3433536, [12,12*x,2916,12*x^2-24576,-x^3+45*x^2+3732*x-56376,2916*x,201684,12*x^3-49152*x,708588,-1752*x^2+98496*x+3433536,-53*x^3-1071*x^2+321060*x+3619728,2916*x^2-5971968,54*x^3+2562*x^2-274104*x-3380088,201684*x,-243*x^3+10935*x^2+906876*x-13699368,540*x^3-7920*x^2-1858464*x+9129216,-319*x^3-16749*x^2+1381356*x+77567544,708588*x,540*x^3+5268*x^2-3995568*x+60346320,296*x^3+6336*x^2-4209600*x+115458048,49009212,-3456*x^3+30408*x^2+11827944*x+181977408,209*x^3-123453*x^2-573780*x+492671808,2916*x^3-11943936*x,-3510*x^3+127614*x^2+3363768*x+245450388,4992*x^3+22032*x^2-11743176*x-185410944,172186884,201684*x^2-413048832,-1948*x^3-67860*x^2+34019760*x+82711368,-425736*x^2+23934528*x+834349248,22572*x^3-378684*x^2-106561008*x+808433664,-8196*x^3+1102896*x^2+26161632*x-1854109440]];

E[22,1] = [x^2+426*x-145287, [3,96,3*x,3072,-50*x-7215,96*x,-165*x-164631,98304,-1278*x-95580,-1600*x-230880,-483153,3072*x,8839*x-1267569,-5280*x-5268192,14085*x-7264350,3145728,19951*x-73851,-40896*x-3058560,6371*x-28000545,-51200*x-7388160,-94341*x-23972355,-15460896,106463*x+41697420,98304*x,-114500*x-8059800,282848*x-40562208,-82593*x-185676786,-168960*x-168582144,-420342*x-21039102,450720*x-232459200,190135*x-719257500,100663296,-483153*x,638432*x-2363232,1969175*x+795476805,-1308672*x-97873920]];
E[22,2] = [x^3-370*x^2-378387*x+63480996, [27,864,27*x,27648,-x^2+334*x+239346,864*x,x^2-91*x+239580,884736,27*x^2-4782969,-32*x^2+10688*x+7659072,4348377,27648*x,-53*x^2-44425*x+33409566,32*x^2-2912*x+7666560,-36*x^2-139041*x+63480996,28311552,-323*x^2-150913*x+154849410,864*x^2-153055008,755*x^2+81793*x-117231336,-1024*x^2+342016*x+245090304,279*x^2+617967*x-63480996,139148064,-2214*x^2+483273*x+688898844,884736*x,-3667*x^2-605822*x+1504005237,-1696*x^2-1421600*x+1069106112,9990*x^2+650511*x-1713986892,1024*x^2-93184*x+245329920,14920*x^2-4141690*x-1385175510,-1152*x^2-4449312*x+2031391872,-23642*x^2+929861*x+6732930420,905969664,4348377*x,-10336*x^2-4829216*x+4955181120,-14395*x^2+5278945*x+1994483700,27648*x^2-4897760256]];
E[22,3] = [x^3+70*x^2-530187*x+80369604, [105,-3360,105*x,107520,x^2+238*x-546378,-3360*x,-21*x^2-12873*x+6086388,-3440640,105*x^2-18600435,-32*x^2-7616*x+17484096,16910355,107520*x,-823*x^2-307699*x+299867274,672*x^2+411936*x-194764416,168*x^2-16191*x-80369604,110100480,2383*x^2+1275589*x-1405256874,-3360*x^2+595213920,2713*x^2-493661*x-1420679064,1024*x^2+243712*x-559491072,-11403*x^2-5047539*x+1687761684,-541131360,12026*x^2-1613017*x-4706861628,-3440640*x,-5089*x^2-1192282*x-2594583033,26336*x^2+9846368*x-9595752768,-7350*x^2+18468765*x-8438808420,-21504*x^2-13181952*x+6232461312,-47208*x^2-8396094*x+11777523534,-5376*x^2+518112*x+2571827328,96374*x^2+34306307*x-24949655892,-3523215360,16910355*x,-76256*x^2-40818848*x+44968219968,42959*x^2+14040467*x-19117396452,107520*x^2-19046845440]];
E[22,4] = [x^3-106*x^2-210879*x-28406052, [81,-2592,81*x,82944,19*x^2-5488*x-2080098,-2592*x,-47*x^2+26915*x+6189084,-2654208,81*x^2-14348907,-608*x^2+175616*x+66563136,-13045131,82944*x,3349*x^2-1340593*x-450791262,1504*x^2-861280*x-198050688,-3474*x^2+1926603*x+539714988,84934656,-8425*x^2+2241691*x+1195040646,-2592*x^2+459165024,-8821*x^2+1897135*x+1516163688,19456*x^2-5619712*x-2130020352,21933*x^2-3722229*x-1335084444,417444192,-30336*x^2+12825645*x+6151285260,-2654208*x,112991*x^2-34843382*x-10252831617,-107168*x^2+42898976*x+14425320384,8586*x^2-11616615*x+2300890212,-48128*x^2+27560960*x+6337622016,-142528*x^2+26265358*x+22197438198,111168*x^2-61651296*x-17270879616,53968*x^2-41239963*x-6950733516,-2717908992,-13045131*x,269600*x^2-71734112*x-38241300672,-606827*x^2+332766959*x+77661864324,82944*x^2-14693280768]];

E[23,1] = [x^11-32*x^10-16384*x^9+453021*x^8+91689644*x^7-2171413128*x^6-205410732416*x^5+4226023192464*x^4+148783481621696*x^3-3199980978790400*x^2+5191695182200832*x+60024577238663168, 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E[23,2] = [x^8+32*x^7-10240*x^6-243056*x^5+32897712*x^4+475545152*x^3-32355612672*x^2-118888316928*x+6030172585984, [44959706219409408,44959706219409408*x,10909*x^7+11113331544*x^6+616506138272*x^5-56815083407856*x^4-3025600557803280*x^3+43690161214260416*x^2+2546413828219665920*x-11234605015976255488,44959706219409408*x^2-92077478337350467584,-3647286714*x^7-326400117120*x^6+15138309794880*x^5+1774234767981024*x^4+1710001829431584*x^3-2066674932597342336*x^2-11872904298750597120*x+629544118864430456832,11112982456*x^7+616617846432*x^6-56812431909952*x^5-3025959438943488*x^4+43684973492197248*x^3+2546766795598304768*x^2-11233308063326887936*x-65783152740499456,14025425484*x^7+873820655568*x^6-127576545987072*x^5-7019305607393856*x^4+342565459792702272*x^3+14500156554713421312*x^2-219369824497388651520*x-3729767347955097329664,44959706219409408*x^3-184154956674700935168*x,-20711749709*x^7-5527147126536*x^6-17936084078752*x^5+35394826952713200*x^4+480562806383282448*x^3-55580909640415595968*x^2-501031415218721755648*x+21496318164474784182272,-209686942272*x^7-22209906156480*x^6+887739848423040*x^5+121697389728029952*x^4-332225417800631808*x^3-129883100520666236928*x^2+195924340083114762240*x+21993768355986465816576,14143482948*x^7+432358856496*x^6-56960836141440*x^5-1455387668457408*x^4+51892317267489216*x^3+8042852542926985728*x^2-412410159184507825152*x-21513437957626089259008,260980066208*x^7+34224405437376*x^6-1587486946299008*x^5-205549431987054336*x^4+3458471806767568896*x^3+258856597746935062528*x^2-3893917523102384488448*x-44004731081972972257280,53917651239*x^7+32893410177432*x^6+1462722969891936*x^5-181000782724521168*x^4-7958968145926971696*x^3+214550457591192368448*x^2+4810079171979888784896*x-94808094614557168312320,425007040080*x^7+16043810969088*x^6-3610341790954752*x^5-118838948457390336*x^4+7830433461059967744*x^3+234431410022913481728*x^2-2062308117963257536512*x-84575736260378174816256,185281859490*x^7-366872425920*x^6+974882082498240*x^5+49996971512560800*x^4-11468272025963521440*x^3-118174556966126801280*x^2+13232478642445312481280*x-84970612750212758446080,44959706219409408*x^4-276232435012051402752*x^2+188574675634893757612032,344464443714*x^7+93228539721408*x^6+3910649203468608*x^5-342742086230241888*x^4-23790958699259613600*x^3-250212707249808768384*x^2+10813305079225461110784*x+301492762646667325145088,-4864371135848*x^7-230024401098912*x^6+30360711915442496*x^5+1161931983326048256*x^4-45731537476863235200*x^3-1171172766562534468096*x^2+19033933100937780408320*x+124895425302973889478656,6443938652256*x^7+378566116229952*x^6-42146054458075008*x^5-1972256075487629568*x^4+79979504688867538944*x^3+1858191897724794003456*x^2-55942698049286076628992*x-339404007126725898706944,-8030280813504*x^7-590987000580480*x^6+39728461827252480*x^5+2932362414399112704*x^4-33669575432188655616*x^3-2356074884486383804416*x^2+21380148711330912337920*x-24857904506929611276288,741314786044*x^7-304253520972912*x^6-25325178635048320*x^5+1161233890128682944*x^4+94871292581471579712*x^3+959213797144332208640*x^2-32326092667170278437888*x-1733676047439604060463104,-20232597840*x^7+87868429246080*x^6+1982270722951680*x^5-413395911432725760*x^4+1316987794610917632*x^3+45210896914016891904*x^2-19831943074438501515264*x-85287643143361767800832,289376090407352207314944,3113655248832*x^7-177884417821824*x^6-25764800463220992*x^5+1069989681872116224*x^4+45281966781061675008*x^3-665525983148748865536*x^2+10028564654947621404672*x-1573620116838958349942784]];

E[24,1] = [x, [1,0,-243,0,-7130,0,-19536,0,59049,0,-196148,0,361414,0,1732590,0,-130942,0,18516692,0,4747248,0,21560872,0,2008775,0,-14348907,0,191663742,0,207933800,0,47663964,0,139291680,0,-200784930,0,-87823602,0,-1435256598,0,712703116,0,-421019370,0,-496082400,0]];
E[24,2] = [x, [1,0,-243,0,1190,0,18480,0,59049,0,135884,0,-848186,0,-289170,0,-7124606,0,-5046316,0,-4490640,0,-14891224,0,-47412025,0,-14348907,0,-115001346,0,-163990552,0,-33019812,0,21991200,0,-223622178,0,206109198,0,105358314,0,1419475852,0,70268310,0,2469276960,0]];
E[24,3] = [x, [1,0,243,0,1870,0,-72312,0,59049,0,147940,0,-1562858,0,454410,0,-145774,0,1096796,0,-17571816,0,-60014264,0,-45331225,0,14348907,0,-19626954,0,-239950480,0,35949420,0,-135223440,0,488238078,0,-379774494,0,47066010,0,428866948,0,110421630,0,450903216,0]];
E[24,4] = [x^2-1564*x-112229180, [1,0,243,0,x,0,-x+19670,0,59049,0,-66*x+336896,0,142*x-247342,0,243*x,0,-574*x+976758,0,-218*x+9647304,0,-243*x+4779810,0,1022*x+35575780,0,1564*x+63401055,0,14348907,0,5315*x+126557132,0,-16093*x-15124538,0,-16038*x+81865728,0,18106*x-112229180,0,34936*x+137981806,0,34506*x-60104106,0,-87098*x+422456134,0,-5038*x-1016988024,0,59049*x,0,-73094*x-1939233404,0]];