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{
"T79": {
"Title": "$q$-expansion of the $j$-invariant",
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"996": "68603310598009460696686147970119592530563211144023381691126041766537775366897823763775924279564430034513077356101096625038125193950495808266887989470441366474674036539392",
"997": "83648963114621835084474532918652506034173569710437166836571284023692788601965267688842693595085993276126908844337208463634074108490838531214903625829781781378387999887960",
"998": "101984233704022721170905645300649068716876180242786248591356026817937200235953713342050543802855474158659927163145603626783475044333100400202559020578246073266286400512000",
"999": "124326172486926561311901304467462079393970726043624778226103669025852549029027496925893551345963917434438054541183469641943111910654710432133934288005991064371257377400680",
"1000": "151547649950021145575386179998434381092503661719041689592736495704314872732562895885396019044494578625118883814756094442320471364161137721233364134605718648336103833600000"
}
},
"T83": {
"Title": "Rational singular moduli",
"Numbers": {
"-163": "-262537412640768000",
"-67": "-147197952000",
"-43": "-884736000",
"-28": "16581375",
"-27": "-12288000",
"-19": "-884736",
"-16": "287496",
"-12": "54000",
"-11": "-32768",
"-8": "8000",
"-7": "-3375",
"-4": "1728",
"-3": "0"
}
},
"T129": {
"Title": "Hilbert class polynomials $H_\\Delta$",
"Numbers": {
"-3": {
"number": "x",
"comment": "$h(\\Delta)=1$; maximal order of $\\mathbb{Q}(\\sqrt{-3})$. The value is $x$ because $j(\\zeta_3)=0$."
},
"-4": {
"number": "x - 1728",
"comment": "$h(\\Delta)=1$; maximal order of $\\mathbb{Q}(i)$"
},
"-7": {
"number": "x + 3375",
"comment": "$h(\\Delta)=1$; maximal order of $\\mathbb{Q}(\\sqrt{-7})$"
},
"-8": {
"number": "x - 8000",
"comment": "$h(\\Delta)=1$; maximal order of $\\mathbb{Q}(\\sqrt{-2})$"
},
"-11": {
"number": "x + 32768",
"comment": "$h(\\Delta)=1$; maximal order of $\\mathbb{Q}(\\sqrt{-11})$"
},
"-12": {
"number": "x - 54000",
"comment": "$h(\\Delta)=1$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-3})$"
},
"-15": {
"number": "x^2 + 191025*x - 121287375",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-15})$"
},
"-16": {
"number": "x - 287496",
"comment": "$h(\\Delta)=1$; order of conductor $2$ in $\\mathbb{Q}(i)$"
},
"-19": {
"number": "x + 884736",
"comment": "$h(\\Delta)=1$; maximal order of $\\mathbb{Q}(\\sqrt{-19})$"
},
"-20": {
"number": "x^2 - 1264000*x - 681472000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-5})$"
},
"-23": {
"number": "x^3 + 3491750*x^2 - 5151296875*x + 12771880859375",
"comment": "$h(\\Delta)=3$; maximal order of $\\mathbb{Q}(\\sqrt{-23})$"
},
"-24": {
"number": "x^2 - 4834944*x + 14670139392",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-6})$"
},
"-27": {
"number": "x + 12288000",
"comment": "$h(\\Delta)=1$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-3})$"
},
"-28": {
"number": "x - 16581375",
"comment": "$h(\\Delta)=1$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-7})$"
},
"-31": {
"number": "x^3 + 39491307*x^2 - 58682638134*x + 1566028350940383",
"comment": "$h(\\Delta)=3$; maximal order of $\\mathbb{Q}(\\sqrt{-31})$"
},
"-32": {
"number": "x^2 - 52250000*x + 12167000000",
"comment": "$h(\\Delta)=2$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-2})$"
},
"-35": {
"number": "x^2 + 117964800*x - 134217728000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-35})$"
},
"-36": {
"number": "x^2 - 153542016*x - 1790957481984",
"comment": "$h(\\Delta)=2$; order of conductor $3$ in $\\mathbb{Q}(i)$"
},
"-39": {
"number": "x^4 + 331531596*x^3 - 429878960946*x^2 + 109873509788637459*x + 20919104368024767633",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-39})$"
},
"-40": {
"number": "x^2 - 425692800*x + 9103145472000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-10})$"
},
"-43": {
"number": "x + 884736000",
"comment": "$h(\\Delta)=1$; maximal order of $\\mathbb{Q}(\\sqrt{-43})$"
},
"-44": {
"number": "x^3 - 1122662608*x^2 + 270413882112*x - 653249011576832",
"comment": "$h(\\Delta)=3$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-11})$"
},
"-47": {
"number": "x^5 + 2257834125*x^4 - 9987963828125*x^3 + 5115161850595703125*x^2 - 14982472850828613281250*x + 16042929600623870849609375",
"comment": "$h(\\Delta)=5$; maximal order of $\\mathbb{Q}(\\sqrt{-47})$"
},
"-48": {
"number": "x^2 - 2835810000*x + 6549518250000",
"comment": "$h(\\Delta)=2$; order of conductor $4$ in $\\mathbb{Q}(\\sqrt{-3})$"
},
"-51": {
"number": "x^2 + 5541101568*x + 6262062317568",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-51})$"
},
"-52": {
"number": "x^2 - 6896880000*x - 567663552000000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-13})$"
},
"-55": {
"number": "x^4 + 13136684625*x^3 - 20948398473375*x^2 + 172576736359017890625*x - 18577989025032784359375",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-55})$"
},
"-56": {
"number": "x^4 - 16220384512*x^3 + 2059647197077504*x^2 + 2257767342088912896*x + 10064086044321563803648",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-14})$"
},
"-59": {
"number": "x^3 + 30197678080*x^2 - 140811576541184*x + 374643194001883136",
"comment": "$h(\\Delta)=3$; maximal order of $\\mathbb{Q}(\\sqrt{-59})$"
},
"-60": {
"number": "x^2 - 37018076625*x + 153173312762625",
"comment": "$h(\\Delta)=2$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-15})$"
},
"-63": {
"number": "x^4 + 67515199875*x^3 - 193068841781250*x^2 + 4558451243295023437500*x - 6256903954262253662109375",
"comment": "$h(\\Delta)=4$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-7})$"
},
"-64": {
"number": "x^2 - 82226316240*x - 7367066619912",
"comment": "$h(\\Delta)=2$; order of conductor $4$ in $\\mathbb{Q}(i)$"
},
"-67": {
"number": "x + 147197952000",
"comment": "$h(\\Delta)=1$; maximal order of $\\mathbb{Q}(\\sqrt{-67})$"
},
"-68": {
"number": "x^4 - 178211040000*x^3 - 75843692160000000*x^2 - 318507038720000000000*x - 2089297506304000000000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-17})$"
},
"-71": {
"number": "x^7 + 313645809715*x^6 - 3091990138604570*x^5 + 98394038810047812049302*x^4 - 823534263439730779968091389*x^3 + 5138800366453976780323726329446*x^2 - 425319473946139603274605151187659*x + 737707086760731113357714241006081263",
"comment": "$h(\\Delta)=7$; maximal order of $\\mathbb{Q}(\\sqrt{-71})$"
},
"-72": {
"number": "x^2 - 377674768000*x + 232381513792000000",
"comment": "$h(\\Delta)=2$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-2})$"
},
"-75": {
"number": "x^2 + 654403829760*x + 5209253090426880",
"comment": "$h(\\Delta)=2$; order of conductor $5$ in $\\mathbb{Q}(\\sqrt{-3})$"
},
"-76": {
"number": "x^3 - 784074438864*x^2 + 1128678666363648*x - 827237892283232256",
"comment": "$h(\\Delta)=3$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-19})$"
},
"-79": {
"number": "x^5 + 1339190283240*x^4 - 6366718450945836*x^3 + 1793441424178093483069839*x^2 - 5859423003994491322155950334*x + 5458041030919737322344464663391",
"comment": "$h(\\Delta)=5$; maximal order of $\\mathbb{Q}(\\sqrt{-79})$"
},
"-80": {
"number": "x^4 - 1597177172000*x^3 - 13028555239824000*x^2 - 171263969177632000000*x + 422286883970526784000000",
"comment": "$h(\\Delta)=4$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-5})$"
},
"-83": {
"number": "x^3 + 2691907584000*x^2 - 41490055168000000*x + 549755813888000000000",
"comment": "$h(\\Delta)=3$; maximal order of $\\mathbb{Q}(\\sqrt{-83})$"
},
"-84": {
"number": "x^4 - 3196800946944*x^3 - 5663679223085309952*x^2 + 88821246589810089394176*x - 5133201653210986057826304",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-21})$"
},
"-87": {
"number": "x^6 + 5321761711875*x^5 + 85585228375218750*x^4 + 28321090578679361484375000*x^3 + 497577733884372638735595703125*x^2 + 432181202257616392838287353515625*x + 549806430204864490157810211181640625",
"comment": "$h(\\Delta)=6$; maximal order of $\\mathbb{Q}(\\sqrt{-87})$"
},
"-88": {
"number": "x^2 - 6294842640000*x + 15798135578688000000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-22})$"
},
"-91": {
"number": "x^2 + 10359073013760*x - 3845689020776448",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-91})$"
},
"-92": {
"number": "x^3 - 12207823849750*x^2 - 263033266852296875*x - 6267542200571287109375",
"comment": "$h(\\Delta)=3$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-23})$"
},
"-95": {
"number": "x^8 + 19874477919500*x^7 - 688170786018119250*x^6 + 395013575867144519258203125*x^5 - 13089776536501963407329479984375*x^4 + 352163322858664726762725228294921875*x^3 - 1437415939871573574572839010971248046875*x^2 + 2110631639116675267953915424764056884765625*x + 107789694576540010002976771996177148681640625",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-95})$"
},
"-96": {
"number": "x^4 - 23340144296736*x^3 + 670421055192156288*x^2 + 447805364111967209472*x - 984163224549635621646336",
"comment": "$h(\\Delta)=4$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-6})$"
},
"-99": {
"number": "x^2 + 37616060956672*x - 56171326053810176",
"comment": "$h(\\Delta)=2$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-11})$"
},
"-100": {
"number": "x^2 - 44031499226496*x - 292143758886942437376",
"comment": "$h(\\Delta)=2$; order of conductor $5$ in $\\mathbb{Q}(i)$"
},
"-103": {
"number": "x^5 + 70292286280125*x^4 + 85475283659296875*x^3 + 4941005649165514137656250000*x^2 + 13355527720114165506172119140625*x + 28826612937014029067466156005859375",
"comment": "$h(\\Delta)=5$; maximal order of $\\mathbb{Q}(\\sqrt{-103})$"
},
"-104": {
"number": "x^6 - 82028232174464*x^5 + 739545196164376195072*x^4 + 31013571054009020830449664*x^3 + 1378339984770204584193868955648*x^2 - 25735039642229334200564710375424*x + 65437179730333545242323676123103232",
"comment": "$h(\\Delta)=6$; maximal order of $\\mathbb{Q}(\\sqrt{-26})$"
},
"-107": {
"number": "x^3 + 129783279616000*x^2 - 6764523159552000000*x + 337618789203968000000000",
"comment": "$h(\\Delta)=3$; maximal order of $\\mathbb{Q}(\\sqrt{-107})$"
},
"-108": {
"number": "x^3 - 151013228706000*x^2 + 224179462188000000*x - 1879994705688000000000",
"comment": "$h(\\Delta)=3$; order of conductor $6$ in $\\mathbb{Q}(\\sqrt{-3})$"
},
"-111": {
"number": "x^8 + 236917342626795*x^7 + 12257744369763349962*x^6 + 56129700127461627298044206619*x^5 + 2987537813865962860773420720531252*x^4 - 25675269514993965918445147228203062874*x^3 + 88953282358528708595648019437144660946708*x^2 - 64773995403104720702864091375403035855442761*x + 27524793815819191410861831167197250556510894417",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-111})$"
},
"-112": {
"number": "x^2 - 274917323970000*x + 1337635747140890625",
"comment": "$h(\\Delta)=2$; order of conductor $4$ in $\\mathbb{Q}(\\sqrt{-7})$"
},
"-115": {
"number": "x^2 + 427864611225600*x + 130231327260672000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-115})$"
},
"-116": {
"number": "x^6 - 495202728828032*x^5 - 11056847669496432594944*x^4 - 835102260960042427461140480*x^3 - 66527716583835083670963399688192*x^2 + 143376986667050616958401264069115904*x - 100730316193548175256338136121783353344",
"comment": "$h(\\Delta)=6$; maximal order of $\\mathbb{Q}(\\sqrt{-29})$"
},
"-119": {
"number": "x^10 + 764872171216961*x^9 - 70241355662808988599*x^8 + 585035810262130969538043606647*x^7 - 52855712468679496581065487695942573*x^6 + 4794937071328670764609540039796857947016*x^5 + 12480611255809545689627144542329203076373873*x^4 + 29494022920507896313766601313371285654722780443*x^3 - 292223928830848711011022637790896567674102040378617*x^2 + 346485626218561739292181172729923937711295004460654234*x - 11669920442373800031513478208679663025064587635901689887",
"comment": "$h(\\Delta)=10$; maximal order of $\\mathbb{Q}(\\sqrt{-119})$"
},
"-120": {
"number": "x^4 - 883067971104000*x^3 + 26329406807264910336000*x^2 - 2588458316335175909376000000*x + 4934510722321469030006784000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-30})$"
},
"-123": {
"number": "x^2 + 1354146840576000*x + 148809594175488000000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-123})$"
},
"-124": {
"number": "x^3 - 1559739536377947*x^2 - 874125972104525910*x - 599530686551745232383",
"comment": "$h(\\Delta)=3$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-31})$"
},
"-127": {
"number": "x^5 + 2375421230598750*x^4 - 30614197896114609375*x^3 + 5642626198092219066070054687500*x^2 - 64331030949386896516600669921875000*x + 319730671478833667491273673675537109375",
"comment": "$h(\\Delta)=5$; maximal order of $\\mathbb{Q}(\\sqrt{-127})$"
},
"-128": {
"number": "x^4 - 2729960418308000*x^3 - 395258439243352250000*x^2 - 55499520947716391500000000*x - 345363656226658026765625000000",
"comment": "$h(\\Delta)=4$; order of conductor $4$ in $\\mathbb{Q}(\\sqrt{-2})$"
},
"-131": {
"number": "x^5 + 4130485792112640*x^4 - 671177121829224448000*x^3 + 107205484283838454093053952*x^2 - 60354680538951673475558801408*x + 144530638394690224075155326369792",
"comment": "$h(\\Delta)=5$; maximal order of $\\mathbb{Q}(\\sqrt{-131})$"
},
"-132": {
"number": "x^4 - 4736863498464000*x^3 - 325211610485778048000000*x^2 + 54984539729717250048000000000*x + 1656636925108948992000000000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-33})$"
},
"-135": {
"number": "x^6 + 7122306993287625*x^5 + 77686119211324699125*x^4 + 50727257383070661992492657625000*x^3 + 628735820731639650833126829398718750*x^2 + 4321223868213674595045534006061857421875*x + 3284527439242119311242957750346113869140625",
"comment": "$h(\\Delta)=6$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-15})$"
},
"-136": {
"number": "x^4 - 8151279336430848*x^3 + 735960027609078992953344*x^2 - 1834607111282472051029311488*x + 2422829169428572504087521656832",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-34})$"
},
"-139": {
"number": "x^3 + 12183160834031616*x^2 - 53041786755137667072*x + 67408489017571610198016",
"comment": "$h(\\Delta)=3$; maximal order of $\\mathbb{Q}(\\sqrt{-139})$"
},
"-140": {
"number": "x^6 - 13916138006442400*x^5 - 3270237719203124384000*x^4 - 790870172407252503705600000*x^3 + 2848295663082788926282752000000*x^2 - 96864973869318094511286681600000000*x + 242830180406000275493501698048000000000",
"comment": "$h(\\Delta)=6$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-35})$"
},
"-143": {
"number": "x^10 + 20680840776413625*x^9 - 6152626465680933171875*x^8 + 427698864960728554347643841796875*x^7 - 126605537475340807363556327903076171875*x^6 + 34756686762001825564530452864079986572265625*x^5 - 669600645730781825539256319987784782409667968750*x^4 + 6039839065591831041160239782335598758220672607421875*x^3 - 7983490577513055781678247666123524158120155334472656250*x^2 + 172938678455959890794097467818753125064074993133544921875*x - 146892619386926916220452018018596212706528604030609130859375",
"comment": "$h(\\Delta)=10$; maximal order of $\\mathbb{Q}(\\sqrt{-143})$"
},
"-144": {
"number": "x^4 - 23578503968570400*x^3 + 269499185406087942528*x^2 + 490453856866850787293184*x + 571751321233328637579104256",
"comment": "$h(\\Delta)=4$; order of conductor $6$ in $\\mathbb{Q}(i)$"
},
"-147": {
"number": "x^2 + 34848505552896000*x + 11356800389480448000000",
"comment": "$h(\\Delta)=2$; order of conductor $7$ in $\\mathbb{Q}(\\sqrt{-3})$"
},
"-148": {
"number": "x^2 - 39660183801072000*x - 7898242515936467904000000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-37})$"
},
"-151": {
"number": "x^7 + 58309232586862950*x^6 + 1107018219296858557941*x^5 + 3399966616467533664248409155353722*x^4 + 69605133153244389737334180535377491802*x^3 + 779394774943277357155375818745718823538863*x^2 + 271248134304567044479896903675912851345002767*x + 3269200340379000902458720113257045278788199227087",
"comment": "$h(\\Delta)=7$; maximal order of $\\mathbb{Q}(\\sqrt{-151})$"
},
"-152": {
"number": "x^6 - 66246265919280000*x^5 + 17024071380555203520000000*x^4 + 6854544294799483688960000000000*x^3 + 2783058624787093614292992000000000000*x^2 - 1380504171426125758791680000000000000000*x + 472390748138731280269312000000000000000000",
"comment": "$h(\\Delta)=6$; maximal order of $\\mathbb{Q}(\\sqrt{-38})$"
},
"-155": {
"number": "x^4 + 96905542950912000*x^3 - 44477871096357453824000*x^2 + 20396251654725321097216000000*x + 37425860028464856284790784000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-155})$"
},
"-156": {
"number": "x^4 - 109914552886955148*x^3 + 53074935443801207676942*x^2 - 164993592496972989327022035*x + 421266000645144840703921125633",
"comment": "$h(\\Delta)=4$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-39})$"
},
"-159": {
"number": "x^10 + 160004137022342145*x^9 + 80544826577049275346921*x^8 + 25601320617862402763638637112400617*x^7 + 12925574698393828230218975528896357700901*x^6 - 500195761724247829095994019904150074287948239*x^5 + 9137627363862789620098285544333489602867649370969*x^4 - 52482545550359592109373005225946991054504656459581968*x^3 + 131220647466890593981458207559990681761779941677658891350*x^2 - 125380849804846892558943693244057944355284981734410556485821*x + 49213884163212475944268367742683491152148907598858879501540753",
"comment": "$h(\\Delta)=10$; maximal order of $\\mathbb{Q}(\\sqrt{-159})$"
},
"-160": {
"number": "x^4 - 181195519824640800*x^3 - 2940735389875294896000*x^2 + 13208221536779701382400000*x - 293835053960432980416000000",
"comment": "$h(\\Delta)=4$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-10})$"
},
"-163": {
"number": "x + 262537412640768000",
"comment": "$h(\\Delta)=1$; maximal order of $\\mathbb{Q}(\\sqrt{-163})$; $H_\\Delta(0)=640320^3$, the integer that HREF{Ramanujan_constant}[Ramanujan's constant $e^{\\pi\\sqrt{163}}$] exceeds by $744$ to within $10^{-12}$; the root $j\\bigl(\\tfrac{1+\\sqrt{-163}}{2}\\bigr)=-640320^3$"
},
"-164": {
"number": "x^8 - 296853791160440320*x^7 - 161936389233870440957755392*x^6 - 107971538556531472065498397540352*x^5 - 72018009354152588972347870534871023616*x^4 - 82923859178811827895415538602091992842240*x^3 + 58876580988711431943771690012552346623541248*x^2 + 716292304882512928715138362472485709784740265984*x - 852636173252919999445568788749874942641540406706176",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-41})$"
},
"-167": {
"number": "x^11 + 428181809075068500*x^10 - 310443848294435505968750*x^9 + 183339895556073570958521545578125000*x^8 - 132653775309940634844454306979619384765625*x^7 + 99968421621214354876138160879405119659423828125*x^6 + 3228424186003694107655062744056610278450012207031250*x^5 + 54948342744318167377884939629764355959051132202148437500*x^4 - 191958603447999118217843290597001892823611319065093994140625*x^3 + 123751654413478180006143858091723929541723527014255523681640625*x^2 + 41726839319627438364938202440270256635260256938636302947998046875*x + 30337588564062373576333030147629108993519083014689385890960693359375",
"comment": "$h(\\Delta)=11$; maximal order of $\\mathbb{Q}(\\sqrt{-167})$"
},
"-168": {
"number": "x^4 - 483435712076832000*x^3 + 336511679671210230144000000*x^2 - 264691184105480095991808000000000*x + 496644064976895846912000000000000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-42})$"
},
"-171": {
"number": "x^4 + 694282057876537344*x^3 + 472103267541360574464*x^2 + 8391550371275812148084736*x - 1311901521779155773721411584",
"comment": "$h(\\Delta)=4$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-19})$"
},
"-172": {
"number": "x^3 - 782759106183330000*x^2 + 1164707517403692000000*x - 692660810326239000000000000",
"comment": "$h(\\Delta)=3$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-43})$"
},
"-175": {
"number": "x^6 + 1119444674983992405*x^5 - 54813228576976021387185*x^4 + 1253156381651642217978286627708618800*x^3 - 59496933313401566319649813402788210673425*x^2 + 1368302291061523680379707879639549158890532250*x + 27017288450887144631231387755756779460197062625",
"comment": "$h(\\Delta)=6$; order of conductor $5$ in $\\mathbb{Q}(\\sqrt{-7})$"
},
"-176": {
"number": "x^6 - 1260369120052221040*x^5 - 1311227225704547834164432*x^4 - 1417657940638726253547455241728*x^3 + 56139914410303801525997336800408320*x^2 - 233832181396031563359165936367916838912*x + 984315149136933710414929915123613725364224",
"comment": "$h(\\Delta)=6$; order of conductor $4$ in $\\mathbb{Q}(\\sqrt{-11})$"
},
"-179": {
"number": "x^5 + 1795194552944492544*x^4 - 2200273236852299356176384*x^3 + 2672564790656716736213209317376*x^2 - 23408814596997033103434472837087232*x + 69366107283027836458026686806432415744",
"comment": "$h(\\Delta)=5$; maximal order of $\\mathbb{Q}(\\sqrt{-179})$"
},
"-180": {
"number": "x^4 - 2018504138609120000*x^3 - 2867757758882006477169664000*x^2 + 16660473763558887652278272000000*x - 6776421923145961044033929216000000",
"comment": "$h(\\Delta)=4$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-5})$"
},
"-183": {
"number": "x^8 + 2863790268422945625*x^7 + 4218620940804013154578125*x^6 + 8201294924243209292049624110812500000*x^5 + 12093440927683360441327407340610611816406250*x^4 + 655855629401644394905657823337825299835205078125*x^3 + 18238748993199475597203528068101439981700897216796875*x^2 - 26922618461790759850037872887492462842807292938232421875*x + 30451733341148937584624248315225887141980230808258056640625",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-183})$"
},
"-184": {
"number": "x^4 - 3215890895076912384*x^3 + 5767007465145198439020847104*x^2 + 38705419208160503264676104110080*x + 114574710497270997578522590458150912",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-46})$"
},
"-187": {
"number": "x^2 + 4545336381788160000*x - 3845689020776448000000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-187})$"
},
"-188": {
"number": "x^5 - 5097838276115828125*x^4 - 8766069746614632866828125*x^3 - 15093437571402131169817626953125*x^2 + 51644103814690479844366699218750*x - 124343484762728525316005706787109375",
"comment": "$h(\\Delta)=5$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-47})$"
},
"-191": {
"number": "x^13 + 7178874489555770070*x^12 - 14412129900790076822258611*x^11 + 51536266750679803854633551771840260203*x^10 - 103386239396269087020741974285554789917453508*x^9 + 199518440359885837424153227327826660336955370546108*x^8 - 14768638405830894134972427622171024141266129942650181658*x^7 + 541808230910284083390456000848314355028531599104942728173485*x^6 - 832818220571586800392164744000358270319532131590078379471735694*x^5 + 15253788701960481284921391493158919700255797559466559311296323232498*x^4 - 49375911707911743432917242207615322174325427611237741682026488846612521*x^3 + 14061234326903814621176226216076159779271092623995827091347309743554898127*x^2 + 42312753036411362230230450305478672870803475782951657706005442304434341869586*x + 58256749348304523248144969888837463340160093969294532742146556156000521034802783",
"comment": "$h(\\Delta)=13$; maximal order of $\\mathbb{Q}(\\sqrt{-191})$"
},
"-192": {
"number": "x^4 - 8041801037378436000*x^3 + 15705521635909735050750000*x^2 + 826335556188178615474500000000*x - 1080060886113159937649308593750000",
"comment": "$h(\\Delta)=4$; order of conductor $8$ in $\\mathbb{Q}(\\sqrt{-3})$"
},
"-195": {
"number": "x^4 + 11284411506057216000*x^3 + 25349140792043819237376000*x^2 + 104773100319600336175104000000*x - 233490285492432753672585216000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-195})$"
},
"-196": {
"number": "x^4 - 12626092121367165696*x^3 - 44864481851299856707307347968*x^2 + 250850701957837760512539510177792*x - 2108010653658430719613224868701536256",
"comment": "$h(\\Delta)=4$; order of conductor $7$ in $\\mathbb{Q}(i)$"
},
"-199": {
"number": "x^9 + 17656190279770938660*x^8 + 1331303100189256816837434*x^7 + 311741055246397228842310784103371345424*x^6 + 23969299805117437326359388515188205981243787*x^5 + 934682848803434155897358662478037099871861466271*x^4 - 15361831050875895680622837467024669907518877308748738*x^3 + 81311504213341585710631261056689664491326495914681965478*x^2 - 26264856563493863087105499097317110823999604480371275106459*x + 6073712999849700354466000422348421795990254023608138785279471",
"comment": "$h(\\Delta)=9$; maximal order of $\\mathbb{Q}(\\sqrt{-199})$"
},
"-200": {
"number": "x^6 - 19733105507276110720*x^5 + 87605036675549431339528253440*x^4 + 236628493411489493484987107953868800*x^3 + 640004261883602853633325553571308188467200*x^2 + 181651879545544879923314552485535205556224000*x + 1139359927820736630329093876556526883461660672000",
"comment": "$h(\\Delta)=6$; order of conductor $5$ in $\\mathbb{Q}(\\sqrt{-2})$"
},
"-203": {
"number": "x^4 + 27502410406723584000*x^3 - 83053272156952592384000000*x^2 + 250634002097696556449792000000000*x + 31913605837856413057024000000000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-203})$"
},
"-204": {
"number": "x^6 - 30703802307926880672*x^5 + 95864841637996112067555072*x^4 + 775121756231241041610849730560*x^3 + 534484930703209896960446929872814080*x^2 + 6020337293681148983229932704488367325184*x + 28508041377034538166862450172153093456658432",
"comment": "$h(\\Delta)=6$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-51})$"
},
"-207": {
"number": "x^6 + 42653766018394018375*x^5 - 5002547112103664005187500*x^4 + 1819343755841562591564610147379736328125*x^3 - 210672109851582446065248197114115955810546875*x^2 + 12041028291910181818274355885092809398864746093750*x - 183426864580818496179793649372867188930511474609375",
"comment": "$h(\\Delta)=6$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-23})$"
},
"-208": {
"number": "x^4 - 47568078792050004000*x^3 + 4032372412181255526000000*x^2 - 3908668494888708948000000000*x + 1463592841477827633000000000000",
"comment": "$h(\\Delta)=4$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-13})$"
},
"-211": {
"number": "x^3 + 65873587288630099968*x^2 + 277390576406111100862464*x + 5310823021408898698117644288",
"comment": "$h(\\Delta)=3$; maximal order of $\\mathbb{Q}(\\sqrt{-211})$"
},
"-212": {
"number": "x^6 - 73387074029381328000*x^5 - 628986407384453487358016000000*x^4 - 2630171369254890916959016960000000000*x^3 - 11008353578715780277672803110912000000000000*x^2 + 39924086528997881772669622484992000000000000000*x - 67450134022842979455115194007552000000000000000000",
"comment": "$h(\\Delta)=6$; maximal order of $\\mathbb{Q}(\\sqrt{-53})$"
},
"-215": {
"number": "x^14 + 101317491792065048950*x^13 - 457954683668826252585187875*x^12 + 10265236278641511113286053799784137196875*x^11 - 46383555189709675449178936346465988262753187500*x^10 + 216305211312669600602461131862011535495470855064453125*x^9 + 31819020878597171136619913529470148872599322438628242187500*x^8 + 2351448778987099675298661052102610490451869537464225291259765625*x^7 + 8679229611593057808179529156250134166357416938123512070321044921875*x^6 - 88614138697852334973112488420763471147133937041181135996684478759765625*x^5 + 110436829236444604799740867885896850392925278958337508378426724884033203125*x^4 + 166187807838211557025418209756031643199878197730031147253756032087707519531250*x^3 + 62715092921872557538045374958431963236662840144482321841785231404293060302734375*x^2 - 612704211737656962652403751307765352670981237392918094651369297974039745330810546875*x + 449653813406963835882488544526476585426974512124916562811345749830665350437164306640625",
"comment": "$h(\\Delta)=14$; maximal order of $\\mathbb{Q}(\\sqrt{-215})$"
},
"-216": {
"number": "x^6 - 112760061542456628096*x^5 + 1197383573848845385478924955648*x^4 - 9056150910670523557375044574248960*x^3 + 129141069874109492050243812631108386816*x^2 + 34441927383131420224661352250608420126720*x + 9316863967448371969962043382716305179148288",
"comment": "$h(\\Delta)=6$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-6})$"
},
"-219": {
"number": "x^4 + 155212323706544357376*x^3 + 831039118453558669939310592*x^2 - 15979705448736682450562851012608*x + 110979720274963942538198675506593792",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-219})$"
},
"-220": {
"number": "x^4 - 172572544407169076625*x^3 + 2531540097646020954716625*x^2 - 6015443509589489085440390625*x + 4189527305843979870968496890625",
"comment": "$h(\\Delta)=4$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-55})$"
},
"-223": {
"number": "x^7 + 236855705574161972250*x^6 - 43072684586065004589140625*x^5 + 56100625266918564788759127557586158203125*x^4 - 10118589468858067354789356763548186038818359375*x^3 + 904981240117595334764254951261845701135925292968750*x^2 - 3017942224498278012503966427816688964673110961914062500*x + 2606386098587221959562486420442180281995713710784912109375",
"comment": "$h(\\Delta)=7$; maximal order of $\\mathbb{Q}(\\sqrt{-223})$"
},
"-224": {
"number": "x^8 - 263096730270583432768*x^7 - 1723077455096553031935888128*x^6 - 11042808304392149169199170364149760*x^5 - 1547817012108377539813804203697900199936*x^4 - 23454276662221670119469240221271015345094656*x^3 - 134143607306227801938718107847574206949591351296*x^2 + 333907584600306671024017785849535798840531183730688*x + 4573574179879344596745560367912999678227803908603904",
"comment": "$h(\\Delta)=8$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-14})$"
},
"-227": {
"number": "x^5 + 360082897644683264000*x^4 - 2562327002832961536000000000*x^3 + 18227340807938993794580480000000000*x^2 - 2111118203460821622718464000000000000*x + 5085472193216544027705344000000000000000",
"comment": "$h(\\Delta)=5$; maximal order of $\\mathbb{Q}(\\sqrt{-227})$"
},
"-228": {
"number": "x^4 - 399605224650084576000*x^3 - 7985216535621460489954944000000*x^2 + 58827548670433207062445836288000000000*x + 120020259495560805847424176128000000000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-57})$"
},
"-231": {
"number": "x^12 + 545412728031003167382*x^11 + 4575214689490213216643494701*x^10 + 297475044886884495086385167578291254071163*x^9 + 2495822670620928334448459105500627052803887158892*x^8 + 542945869903650549618648833813237732507684112466148436*x^7 + 59883227623310630463788192163427650885804413659842024636798*x^6 + 424012974154213345546525745525460576866398466044926984841121493*x^5 + 10526543646171305092444013519332915620006154949645088229399234651338*x^4 - 11279114369323207645565898199805585890834325844520121148272433760751685*x^3 + 87871631779286293777040608764652776494101765559955668704283513742443115297*x^2 + 5622739472203769328992152587174484508607105253856090982259484423919689974446*x - 10274960660991508138072982056831840368163135985652317753453065819164012139188831",
"comment": "$h(\\Delta)=12$; maximal order of $\\mathbb{Q}(\\sqrt{-231})$"
},
"-232": {
"number": "x^2 - 604729957849891344000*x + 14871070713157137145512000000000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-58})$"
},
"-235": {
"number": "x^2 + 823177419449425920000*x + 11946621170462723407872000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-235})$"
},
"-236": {
"number": "x^9 - 911900087980611037808*x^8 - 8829246291887799055677742080*x^7 - 85653894916610237425482419166691328*x^6 + 890259336020656022114227027503791079424*x^5 - 2609998050684441805972918666809036652763152384*x^4 + 31142196350994346572482398388463886712080993091584*x^3 - 674608806297136836505485361662125850918390913495465984*x^2 + 618701375850809570249968077855481255020992055993767559168*x - 528051042407719084320821843257565323032509500612428437651456",
"comment": "$h(\\Delta)=9$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-59})$"
},
"-239": {
"number": "x^15 + 1238073883315407514496*x^14 - 13666850068795802991492370368*x^13 + 1532827087345492867204119093852378082438678*x^12 - 16918290867054590371279243347863233076912830800656*x^11 + 181721330191211254702985841157524557972842205740584445069*x^10 - 53402042304078887007585772925287830545907353075301922255822235*x^9 + 7812948654819296135589446079820190138351182297783287462126807084194*x^8 - 213242735312342090716157115838233952503532476492926509784331970735677434*x^7 + 2345429910309004121222696836646913020268276389308953560399316037687685228093*x^6 - 3810541708818932268937818042616997315880367489562442234228253037628692447242929*x^5 - 17149947441960712280092489124465992101403607262591607787910136971714285286547327394*x^4 + 6777279017108616482947859571620293678609069493537534791893310613536520130766425993446*x^3 + 208933803735777172616099243225384508569454797521044528682952239050793396911848873404608651*x^2 - 323628361549512079174002784188728374161166898133764200695741531312961505222798905042238214*x + 843729436361519079684848812880135988137701277041482416947907638671428789917777110886130507231",
"comment": "$h(\\Delta)=15$; maximal order of $\\mathbb{Q}(\\sqrt{-239})$"
},
"-240": {
"number": "x^4 - 1370337635584848362400*x^3 + 15510636623637225985530243375*x^2 - 3213137488352330508627918491550000*x + 51848746810441819437662737568196890625",
"comment": "$h(\\Delta)=4$; order of conductor $4$ in $\\mathbb{Q}(\\sqrt{-15})$"
},
"-243": {
"number": "x^3 + 1855762905734664192000*x^2 - 3750657365033091072000000*x + 3338586724673519616000000000",
"comment": "$h(\\Delta)=3$; order of conductor $9$ in $\\mathbb{Q}(\\sqrt{-3})$"
},
"-244": {
"number": "x^6 - 2052295773725248986240*x^5 - 92973717558373200586964869091328*x^4 - 2691275293785918359227938328726732800*x^3 - 31292753080096691789898512325924416913408*x^2 - 24417475317780070950649666808040757791817728*x - 9815190670232173018201554731440614047465078784",
"comment": "$h(\\Delta)=6$; maximal order of $\\mathbb{Q}(\\sqrt{-61})$"
},
"-247": {
"number": "x^6 + 2772410642909877080250*x^5 + 888629892547516768433109375*x^4 + 7686260773063033411724550958439950781250000*x^3 + 2475076441475565987510057965501956793452880859375*x^2 + 400348022833121004028281794619328068026346954345703125*x - 407336295332190846580777495118233696120388820648193359375",
"comment": "$h(\\Delta)=6$; maximal order of $\\mathbb{Q}(\\sqrt{-247})$"
},
"-248": {
"number": "x^8 - 3063517083860376640000*x^7 + 169518269276842782112073472000000*x^6 + 2461626754066908714341150658560000000000*x^5 + 35762831246449484056560587036188672000000000000*x^4 - 27750969592459084458872706174812160000000000000000*x^3 + 271994089256402280576009987295281152000000000000000000*x^2 - 1093432823745012115729536788054671360000000000000000000000*x + 1323449723347621474969758725859966976000000000000000000000000",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-62})$"
},
"-251": {
"number": "x^7 + 4128446190315309498368*x^6 - 66204185373144403998280777728*x^5 + 1062008880270126105976008028408774656*x^4 + 7966552994949346594041401247164174172160*x^3 + 416131608793437401577832999781610387970981888*x^2 - 1791911545705841840084320427251134859220759871488*x + 1937587239465703269672056660685864050152464252403712",
"comment": "$h(\\Delta)=7$; maximal order of $\\mathbb{Q}(\\sqrt{-251})$"
},
"-252": {
"number": "x^4 - 4558302700896532039875*x^3 + 10887176246183122533468750*x^2 - 2443574658947106282398437500*x + 398963060554172791168212890625",
"comment": "$h(\\Delta)=4$; order of conductor $6$ in $\\mathbb{Q}(\\sqrt{-7})$"
},
"-255": {
"number": "x^12 + 6128344649561048076375*x^11 + 109818071224486731519520855500*x^10 + 37556608101691968890237510940495083062359375*x^9 + 673058835898027399768590893111635020590531709609375*x^8 - 257071952051162192994763669120415771028223618153289062500*x^7 + 48780025238715852051357522255186510362783551525181839218750000*x^6 + 1050548488006167152734252478408891496811178954807077033503662109375*x^5 - 2325968187865245555746840267996850910210272748417670038737172851562500*x^4 + 23418529525567894791342125100999050122359225461527148497750530120849609375*x^3 - 30631401929712387173525528417517956965633001886992450471268726906005859375000*x^2 + 8285413263557506490462798160453959059451866515780958833500086781616210937500000*x - 30414382619613446559856313259492414970013542565259802806559309274202724456787109375",
"comment": "$h(\\Delta)=12$; maximal order of $\\mathbb{Q}(\\sqrt{-255})$"
},
"-256": {
"number": "x^4 - 6761166974781862161312*x^3 - 1826592673506207200904172752*x^2 + 26925623396663008311375890966784*x - 1064410681181869521037208505239142408",
"comment": "$h(\\Delta)=4$; order of conductor $8$ in $\\mathbb{Q}(i)$"
},
"-259": {
"number": "x^4 + 9068999694311625523200*x^3 - 368189472100537894019530752*x^2 + 5493320206929896679139197321216*x + 4384296738486457527093398159228928",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-259})$"
},
"-260": {
"number": "x^8 - 9997874035270492198400*x^7 - 999896161895842101863690217472000*x^6 - 21507054600723946274941348498171494400000*x^5 - 463238908732347767153420578775505775886336000000*x^4 + 14865557804649865113150034077076664167379763200000000*x^3 - 85980083235988029405783249092189509918128078848000000000*x^2 + 305486088367929951707960768526477860306636557516800000000000*x - 3302947505675715028946774256661472679426359558144000000000000",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-65})$"
},
"-263": {
"number": "x^13 + 13380310119466658931625*x^12 - 311327635162565982167010546875*x^11 + 179032706285420766577202734457392432796875000*x^10 - 4165394082070752123229551692087292204450178222656250*x^9 + 98905316949525970240143951409615108996096316126037597656250*x^8 + 47530953928226416306068505409986490840011703185605743408203125000*x^7 + 11458136561160708300394038317028343694717312841071722625732421875000000*x^6 - 43719503450979282495514171655395663354927991909842598140180110931396484375*x^5 - 217712350218237684687170899414325350050388748483588898629844188690185546875000*x^4 + 596774975718198603949702355142508889167524972921148663966583088040351867675781250*x^3 + 6162774782812542130030147316585405729653544328652457605331892962567508220672607421875*x^2 - 4487212542386417035130564561724254020346483123482676773093024865374900400638580322265625*x + 1288185729855109347493715381276499192204085431957219681118500147931626997888088226318359375",
"comment": "$h(\\Delta)=13$; maximal order of $\\mathbb{Q}(\\sqrt{-263})$"
},
"-264": {
"number": "x^8 - 14739806897587232709120*x^7 + 1789885567319176457551625511223296*x^6 - 43813781353344480858785503406172212822016*x^5 - 1576759051947634872250887243973927048713338880*x^4 - 19114071480061200751208790258848908645703796916224*x^3 + 189771022593359719599623857042603680684355481140985856*x^2 - 171749422417263603359883069647289043394815149890303164416*x + 327886345447155202813840576100201205111813144244435638288384",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-66})$"
},
"-267": {
"number": "x^2 + 19683091854079488000000*x + 531429662672621376897024000000",
"comment": "$h(\\Delta)=2$; maximal order of $\\mathbb{Q}(\\sqrt{-267})$"
},
"-268": {
"number": "x^3 - 21667237292024856738000*x^2 + 32240842762858236972000000*x - 3189376432736929569384216000000000",
"comment": "$h(\\Delta)=3$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-67})$"
},
"-271": {
"number": "x^11 + 28871507301417512542197*x^10 - 16464632106657057718070503233*x^9 + 833563933860509791181111419288850809747772703*x^8 - 474119236512804370442479006085162435392319850885990*x^7 + 135135894145413545460315236328333854986568618194277465631*x^6 + 1774664025734848444303272990784027252090100477956938931603749*x^5 + 131114086157450672131023977149470819445696255045995630161701416198*x^4 - 270811671641227589728387064696795035502951934500561387965958352794385*x^3 + 402828435183506117139311560601486140106573513556923825752918282230153207*x^2 + 77658572899931472455557097251364224126893796442704184730369602375352670242*x + 16274637962340468994088643348402984244223247201766753166531174639738274287967",
"comment": "$h(\\Delta)=11$; maximal order of $\\mathbb{Q}(\\sqrt{-271})$"
},
"-272": {
"number": "x^8 - 31759326199909682088000*x^7 - 992292506997017283600644000000*x^6 - 31424909544599612739578321240000000000*x^5 + 13460227027917301519133262366182000000000000*x^4 + 3861901192470234862993839021544000000000000000*x^3 - 7711135475352672738710945448900000000000000000000*x^2 - 7751659760972060765625755308904000000000000000000000*x + 9265833623430102037137881938273000000000000000000000000",
"comment": "$h(\\Delta)=8$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-17})$"
},
"-275": {
"number": "x^4 + 42230108051959368384512*x^3 - 1470671864720383632491493195776*x^2 + 51213041627075282291106746090041376768*x - 3984711300201636241319486354007863066624",
"comment": "$h(\\Delta)=4$; order of conductor $5$ in $\\mathbb{Q}(\\sqrt{-11})$"
},
"-276": {
"number": "x^8 - 46421840776490384352768*x^7 - 10000254249186327541943559851360256*x^6 + 359684269203806519420937768802377441214464*x^5 - 7594738933192260668250057199680097904322674688*x^4 + 407334970460053160180107543216439671099066662518784*x^3 + 767440733750724125562378402812781678248671343699558400*x^2 - 6523546308273811582074020329970859860219102556953002377216*x + 11579958468886822266431515535986431304105856851373387044356096",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-69})$"
},
"-279": {
"number": "x^12 + 61599632504312736062442*x^11 + 39085157358431990256370399479*x^10 + 3794514724678786084595916293218126177015471815*x^9 + 2413273773047259527195253084202133346123169130971473*x^8 + 767669753103635395090961318968027363505110782876830273133*x^7 - 58283377462504689708116605269364153282329645388892963462482473*x^6 + 1657978149641301982239247099561052459846466574320400009376232822498*x^5 - 10013227239675271500918792405158329997586590051360922807501315554033466*x^4 + 24732016651714724865787524804888521394564660407243437120880676248642113002*x^3 - 26776389980763040000394320636711170871388575884924609791873059552120526971044*x^2 + 10814510784493696645623229836489660032236288090281566851237671363163259870593752*x + 108587827741394171370512478914675458441925050289489507636190825980073172090094721",
"comment": "$h(\\Delta)=12$; order of conductor $3$ in $\\mathbb{Q}(\\sqrt{-31})$"
},
"-280": {
"number": "x^4 - 67667966893419063840000*x^3 + 17602516524144666384420962098176000*x^2 - 708555761206745670461365038563328000000*x + 1775168961518724506399346503073398784000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-70})$"
},
"-283": {
"number": "x^3 + 89611323386832801792000*x^2 + 90839236535446929408000000*x + 201371843156955365376000000000",
"comment": "$h(\\Delta)=3$; maximal order of $\\mathbb{Q}(\\sqrt{-283})$"
},
"-284": {
"number": "x^7 - 98373700603090523199715*x^6 - 4546951697981923176956448676986*x^5 - 209903939873446020495519316596118272758*x^4 - 12543980353722772760179537174109237891242365*x^3 - 282310474518147042483634599702449209357160103606*x^2 + 904330206367752622526324160408849797910089300094965*x - 709822597815616788561460999971455889888479357689323263",
"comment": "$h(\\Delta)=7$; order of conductor $2$ in $\\mathbb{Q}(\\sqrt{-71})$"
},
"-287": {
"number": "x^14 + 130017330972527578537125*x^13 - 6698357657618306959300749765625*x^12 + 16904506692603022625452451650285182736386718750*x^11 - 870877447830448509906310286855016521261913044677734375*x^10 + 44124406751543298486951757064546752620852454933728424072265625*x^9 - 37440626797808974887161698082710365926423579373005642490386962890625*x^8 + 15857859011592456271411600608807407083008200255495359166626930236816406250*x^7 - 77741168106987348796498736408928032449881769854967153651849091053009033203125*x^6 - 689666073544550013966593282843777525224970203263486012610490672290325164794921875*x^5 + 2796907818941754701021666870337999145633786876397964262080491920933127403259277343750*x^4 + 38922739785997546759451891252935269190758546113162117006238185894908383488655090332031250*x^3 - 88571091393369945585027038239709934745086635483510805720054231573652941733598709106445312500*x^2 - 62484801377078374907978416472072998345681955148585098464247473540905048139393329620361328125000*x + 162270825957231643818056928693921849618705394682014151595002795007445683950209058821201324462890625",
"comment": "$h(\\Delta)=14$; maximal order of $\\mathbb{Q}(\\sqrt{-287})$"
},
"-288": {
"number": "x^4 - 142637765058468510772000*x^3 - 87330008255955399131086000000*x^2 + 136478143044657426076564000000000*x + 40994594700208456153393000000000000",
"comment": "$h(\\Delta)=4$; order of conductor $6$ in $\\mathbb{Q}(\\sqrt{-2})$"
},
"-291": {
"number": "x^4 + 188155567079341753466880*x^3 + 10786588141336392324590050738176*x^2 + 285389231946718842181542553187254272*x + 21782000952710117887925312635418808680448",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-291})$"
},
"-292": {
"number": "x^4 - 206287709860428304608000*x^3 - 93693622511929038759497066112000000*x^2 + 45521551386379385369629968384000000000*x - 380259461042512404779990642688000000000000",
"comment": "$h(\\Delta)=4$; maximal order of $\\mathbb{Q}(\\sqrt{-73})$"
},
"-295": {
"number": "x^8 + 271602295664902418108250*x^7 + 289315392383740839332561391375*x^6 + 73767807010599056699488845989197941140892890625*x^5 + 78688417471647009524122019473588050719938852358765625*x^4 + 41940062336716757201181279559382045880935056981401849609375*x^3 + 1811885751513084753220927364888013159601085995323528927843750000*x^2 - 1122282566856104887683461567415963897525574528336611314070556640625*x + 822204343689207610829131926678660596532719371553249925736718994140625",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-295})$"
},
"-296": {
"number": "x^10 - 297590021529144696899712*x^9 + 162320889747737857249685120747130880*x^8 + 10832757073596276258900582218946579850592256*x^7 + 723330380126653611855128035587837975712897397948416*x^6 - 18343602778583830315600785964203789047910620519106347008*x^5 + 1679209288192190324963522812029010220997720672517680940449792*x^4 + 10593212648456356679691765850382563233587415411210119731327533056*x^3 + 109273800094565901214220123670634449029720795923690895083186480480256*x^2 - 74426868895161208470636584499354600919093741197724233674495663013888*x + 233323899475941320904470255549714742154931061785021169977723889513398272",
"comment": "$h(\\Delta)=10$; maximal order of $\\mathbb{Q}(\\sqrt{-74})$"
},
"-299": {
"number": "x^8 + 391086320728105978429440*x^7 - 28635280874816126174326167699456*x^6 + 2094055410006322146651491130721133658112*x^5 - 186547260770756829961971675685151791296544768*x^4 + 6417141278133218665289808655954275181523718111232*x^3 - 19207839443594488822936988943836177115227877227364352*x^2 + 45797528808215150136248975363201860724351225694802411520*x - 18273883965326272223717626628647422907813731016193733558272",
"comment": "$h(\\Delta)=8$; maximal order of $\\mathbb{Q}(\\sqrt{-299})$"
},
"-300": {
"number": "x^6 - 428244362959801779810720*x^5 + 32278855882815402576742692253440*x^4 - 233405320133674124312518469774131200*x^3 + 21122955530832902270001123584504233628467200*x^2 + 62082816308629282586712746552975312469884928000*x + 66661978554978958501295319312489107870472732672000",
"comment": "$h(\\Delta)=6$; order of conductor $10$ in $\\mathbb{Q}(\\sqrt{-3})$"
}
}
},
"T635": {
"Title": "Hecke-type Faber polynomials of monstrous McKay\u2013Thompson series",
"Numbers": {
"1A": {
"2": "X^2 - 393768",
"3": "X^3 - 590652*X - 64481280",
"4": "X^4 - 787536*X^2 - 85975040*X + 74069419032",
"5": "X^5 - 984420*X^3 - 107468800*X^2 + 189495047430*X + 21057657937920",
"6": "X^6 - 1181304*X^4 - 128962560*X^3 + 343683985284*X^2 + 50659854188544*X - 12858803885140128",
"7": "X^7 - 1378188*X^5 - 150456320*X^4 + 536636232594*X^3 + 88725605326848*X^2 - 47809252624358008*X - 5674272666930008064",
"8": "X^8 - 1575072*X^6 - 171950080*X^5 + 768351789360*X^4 + 135254911352832*X^3 - 112484887649791744*X^2 - 19635086241677574144*X + 2016502627602420645912",
"9": "X^9 - 1771956*X^7 - 193443840*X^6 + 1038830655582*X^5 + 190247772266496*X^4 - 214517584380376440*X^3 - 44381974047141482496*X^2 + 10178665610374591079949*X + 1373880968445473485012992",
"10": "X^10 - 1968840*X^8 - 214937600*X^7 + 1348072831260*X^6 + 253704188067840*X^5 - 361539218235047200*X^4 - 82414443894080716800*X^3 + 30123485467790332998150*X^2 + 6219725247967316587315200*X - 264392503356231456801328368",
"11": "X^11 - 2165724*X^9 - 236431360*X^8 + 1696078316394*X^7 + 325624158756864*X^6 - 561181664632739128*X^5 - 136232003593254260736*X^4 + 68990553191904045616035*X^3 + 17291944447558405263671296*X^2 - 1806143936956943373926224308*X - 308680121292331493369701251072",
"12": "X^12 - 2362608*X^10 - 257925120*X^9 + 2082847110984*X^8 + 406007684333568*X^7 - 821076798992387328*X^6 - 208334160955421097984*X^5 + 135422053934751747165060*X^4 + 38001100973841504887898112*X^3 - 6687730416418166046559185216*X^2 - 1734101440714844019622157451264*X + 20900994943861369711633444933728",
"13": "X^13 - 2559492*X^11 - 279418880*X^10 + 2508379215030*X^9 + 494854764797952*X^8 - 1148856496732926904*X^7 - 301220423791340212224*X^6 + 239562767008351074892617*X^5 + 72413908027857343157616640*X^4 - 18316979239508771782084104708*X^3 - 5745469926475188586673002027008*X^2 + 234432371170332764328351072091406*X + 65230639299981778514596025509453824",
"14": "X^14 - 2756376*X^12 - 300912640*X^11 + 2972674628532*X^10 + 592165400150016*X^9 - 1552152633273292960*X^8 - 417390299911770587136*X^7 + 393060065884701285062034*X^6 + 125253229605064610094252032*X^5 - 41742905634772883940485875824*X^4 - 14634618532549137014877869875200*X^3 + 1154370493764070152996575608379144*X^2 + 439893250924568205954493672948629504*X + 2719676780106679295201358858717703872",
"15": "X^15 - 2953260*X^13 - 322406400*X^12 + 3475733351490*X^11 + 697939590389760*X^10 - 2038597084032420600*X^9 - 559343297127471206400*X^8 + 609063918195783252952575*X^7 + 201898080495339958043033600*X^6 - 83951549510123698012683934452*X^5 - 31677489189941040228665316096000*X^4 + 3886014987027330446640994321129590*X^3 + 1699288783999389436750655401346457600*X^2 - 4732125471145437147519752624386752360*X - 13020431181324119642565741945090630021120",
"16": "X^16 - 3150144*X^14 - 343900160*X^13 + 4017555383904*X^12 + 812177335517184*X^11 - 2615821724429244928*X^10 - 729578923249201053696*X^9 + 902226885733559472859440*X^8 + 308383626282978001672994816*X^7 - 154161812201437302698865802752*X^6 - 61295614797944060874236638789632*X^5 + 10433910539256301107480913877620992*X^4 + 4940099018195170071992141764928471040*X^3 - 103097182627097875055677073555793825792*X^2 - 103133971177736825790439338439656064679936*X - 1949245618099114279933367278713609675079656",
"17": "X^17 - 3347028*X^15 - 365393920*X^14 + 4598140725774*X^13 + 934878635532288*X^12 - 3291458429882701048*X^11 - 930596686087719112704*X^10 + 1288704124449974058093765*X^9 + 451401183346691317976973312*X^8 - 264121293221146500986820632580*X^7 - 109217601215400405937265701853184*X^6 + 24067814229927577236064263062799310*X^5 + 12008819642642698763394868993363353600*X^4 - 538599007006170499989591020405998102584*X^3 - 457413185937416433380772012103443736940544*X^2 - 10639462391700261502948080127518848143403502*X + 2448360409675245677860106703465418348428705792",
"18": "X^18 - 3543912*X^16 - 386887680*X^15 + 5217489377100*X^14 + 1066043490435072*X^13 - 4073139075811724064*X^12 - 1164896093453784367104*X^11 + 1786153384456952740982622*X^10 + 638298218859610446271610880*X^9 - 428402127006834631230272748912*X^8 - 182640609251961559360598757777408*X^7 + 49746908379294784527488216860491144*X^6 + 25768345199288533394205985502068998144*X^5 - 1877432916708819238388046518628668237760*X^4 - 1500558122886515340000182633119133719756800*X^3 - 27744628889562451933005227469536926545888243*X^2 + 22471139557701479015361955942257405537846558720*X + 659956389972972741907558573811866188194490278904",
"19": "X^19 - 3740796*X^17 - 408381440*X^16 + 5875601337882*X^15 + 1205671900225536*X^14 - 4968495537635249080*X^13 - 1434976653158155800576*X^12 + 2413735010026402872869019*X^11 + 877078350789283888197353472*X^10 - 664696819669829388227215193268*X^9 - 290391836659348514661954270443520*X^8 + 94602258920395348096806441898107478*X^7 + 50402705890691441826552102696348770304*X^6 - 5228582669342872078825016501434126475976*X^5 - 4060967262671950082417487685654288811765760*X^4 - 30940858283878242049757379386294831844325275*X^3 + 113254298951731344549995705180609569889278279680*X^2 + 4966546426300752385957503058224443935345813239764*X - 428969687314085837556810166370806784513928652032000",
"20": "X^20 - 3937680*X^18 - 429875200*X^17 + 6572476608120*X^16 + 1353763864903680*X^15 - 5985159690772211200*X^14 - 1743337873011592396800*X^13 + 3192111939590213424111900*X^12 + 1176401347897678107718451200*X^11 - 994114085743796644298243267136*X^10 - 443090000122612007551622737920000*X^9 + 168477519293467407173622963254838240*X^8 + 91759956252259578215231380069357977600*X^7 - 12546431271571442512849725967700049423360*X^6 - 9597015236441734633482106793660552674017280*X^5 + 72217861082859314962678931858332308589330950*X^4 + 415923251530204164973260847091175433664829849600*X^3 + 20314892597552926968269250778460173854877344941600*X^2 - 4535408474949149437067296323630459859968219836006400*X - 180612166589483962719321564578448241282015029854349168"
},
"2A": {
"2": "X^2 - 8744",
"3": "X^3 - 13116*X - 288768",
"4": "X^4 - 17488*X^2 - 385024*X + 33268760",
"5": "X^5 - 21860*X^3 - 481280*X^2 + 89371910*X + 2050662400",
"6": "X^6 - 26232*X^4 - 577536*X^3 + 164589444*X^2 + 4985782272*X - 107259357344",
"7": "X^7 - 30604*X^5 - 673792*X^4 + 258921362*X^3 + 8762564608*X^2 - 444743039608*X - 11719211700224",
"8": "X^8 - 34976*X^6 - 770048*X^5 + 372367664*X^4 + 13381009408*X^3 - 1096391274240*X^2 - 41502310531072*X + 234018624159768",
"9": "X^9 - 39348*X^7 - 866304*X^6 + 504928350*X^5 + 18841116672*X^4 - 2145772148088*X^3 - 94871508111360*X^2 + 1592795656578573*X + 58687165263298560",
"10": "X^10 - 43720*X^8 - 962560*X^7 + 656603420*X^6 + 25142886400*X^5 - 3676453748000*X^4 - 177346426880000*X^3 + 5345126136492550*X^2 + 275840211478118400*X + 213644656132535056",
"11": "X^11 - 48092*X^9 - 1058816*X^8 + 827392874*X^7 + 32286318592*X^6 - 5772004160824*X^5 - 294446689275904*X^4 + 13125180226030499*X^3 + 783569541396381696*X^2 - 2263527674236166580*X - 263592855549972461568",
"12": "X^12 - 52464*X^10 - 1155072*X^9 + 1017296712*X^8 + 40271413248*X^7 - 8515991473408*X^6 - 451691917737984*X^5 + 26932487763020676*X^4 + 1746161357781204992*X^3 - 15246692238252255552*X^2 - 1567069922180230250496*X - 6740820777199941676960",
"13": "X^13 - 56836*X^11 - 1251328*X^10 + 1226314934*X^9 + 49098170368*X^8 - 11991983772600*X^7 - 654601734705152*X^6 + 49131938260990793*X^5 + 3360077582466269184*X^4 - 53060694476028731908*X^3 - 5378687508080176928768*X^2 - 24896242946524361638642*X + 1057501151296489775669248",
"14": "X^14 - 61208*X^12 - 1347584*X^11 + 1454447540*X^10 + 58766589952*X^9 - 16283549145248*X^8 - 908695762616320*X^7 + 82453780909168018*X^6 + 5853955856355819520*X^5 - 138137402906356123760*X^4 - 14034521464279993327616*X^3 - 39196471180286526155000*X^2 + 7770794602184447261016064*X + 53938317320618104429620928",
"15": "X^15 - 65580*X^13 - 1443840*X^12 + 1701694530*X^11 + 69276672000*X^10 - 21474255678200*X^9 - 1219493623910400*X^8 + 129993624572478975*X^7 + 9488609539424665600*X^6 - 302613061628860508916*X^5 - 30914307491036912793600*X^4 + 10481880004761202696310*X^3 + 31732701273338284946350080*X^2 + 313380494698654141315391640*X - 3654422759553446952764960768",
"16": "X^16 - 69952*X^14 - 1540096*X^13 + 1968055904*X^12 + 80628416512*X^11 - 27647671458304*X^10 - 1592514941026304*X^9 + 195212437791549744*X^8 + 14557027710718181376*X^7 - 589925642826161536512*X^6 - 60617281442555855372288*X^5 + 261009538397232798324992*X^4 + 95907466104812724998373376*X^3 + 1012646560231337290893176832*X^2 - 33285658990304843601205526528*X - 326472028389489168611182116840",
"17": "X^17 - 74324*X^15 - 1636352*X^14 + 2253531662*X^13 + 92821823488*X^12 - 34887364572408*X^11 - 2033279336402944*X^10 + 281936548782705861*X^9 + 21384375168352305152*X^8 - 1056412199266030448644*X^7 - 109138019631710061991936*X^6 + 964881951387078673793998*X^5 + 239930181681739100604014592*X^4 + 2363944535537890445550385096*X^3 - 161475835721750980142840729600*X^2 - 2396873713058933694027784432110*X + 9565459627376975622637107724288",
"18": "X^18 - 78696*X^16 - 1732608*X^15 + 2558121804*X^14 + 105856892928*X^13 - 43276903107360*X^12 - 2547306432479232*X^11 + 394357645437972318*X^10 + 30327992429513539584*X^9 - 1772906216803548102000*X^8 - 184042279134761728647168*X^7 + 2536080288400990656560520*X^6 + 526328740434733502046142464*X^5 + 4331970869406638765914953792*X^4 - 563956918438900616087130243072*X^3 - 9771692563155990130499934634995*X^2 + 115673153580431309341328373448704*X + 1701512642998472590782767090058232",
"19": "X^19 - 83068*X^17 - 1828864*X^16 + 2881826330*X^15 + 119733624832*X^14 - 52899855150008*X^13 - 3140115851694080*X^12 + 537032775325073563*X^11 + 41777395730458951680*X^10 - 2826334966883262989492*X^9 - 294642838096082640582656*X^8 + 5602916068477241833792086*X^7 + 1047668315414991257960538112*X^6 + 6257445382572798782188010808*X^5 - 1598504726279691866357740875776*X^4 - 29198204211252267201824145274779*X^3 + 685648066343126356020669033005056*X^2 + 14915390025479728906664789710358484*X - 6516101044995270732825771088087040",
"20": "X^20 - 87440*X^18 - 1925120*X^17 + 3224645240*X^16 + 134452019200*X^15 - 63839788787200*X^14 - 3817227216486400*X^13 + 714884345687433500*X^12 + 56154277026516172800*X^11 - 4321316859041349261888*X^10 - 452175336032874806476800*X^9 + 11067859412979961268257760*X^8 + 1934618369644067751774126080*X^7 + 6299048314517247261032944640*X^6 - 3914542371073783223833630081024*X^5 - 71216433228460730766007402937850*X^4 + 2805749757838212179994547784253440*X^3 + 71590327784579963457092015428453920*X^2 - 244168301981607069652752766335139840*X - 7920275773961092952870043713428137840"
},
"2B": {
"2": "X^2 - 552",
"3": "X^3 - 828*X + 6144",
"4": "X^4 - 1104*X^2 + 8192*X + 107544",
"5": "X^5 - 1380*X^3 + 10240*X^2 + 324870*X - 2580480",
"6": "X^6 - 1656*X^4 + 12288*X^3 + 618372*X^2 - 6488064*X - 12019872",
"7": "X^7 - 1932*X^5 + 14336*X^4 + 988050*X^3 - 11526144*X^2 - 75815544*X + 840806400",
"8": "X^8 - 2208*X^6 + 16384*X^5 + 1433904*X^4 - 17694720*X^3 - 213331712*X^2 + 3164995584*X - 2783526888",
"9": "X^9 - 2484*X^7 + 18432*X^6 + 1955934*X^5 - 24993792*X^4 - 445592952*X^3 + 7444279296*X^2 + 1767958029*X - 223908151296",
"10": "X^10 - 2760*X^8 + 20480*X^7 + 2554140*X^6 - 33423360*X^5 - 793623840*X^4 + 14146682880*X^3 + 30819561990*X^2 - 1166080737280*X + 2482913768208",
"11": "X^11 - 3036*X^9 + 22528*X^8 + 3228522*X^7 - 42983424*X^6 - 1278448952*X^5 + 23740231680*X^4 + 107352345507*X^3 - 3500652412928*X^2 + 8954045378124*X + 46615300098048",
"12": "X^12 - 3312*X^10 + 24576*X^9 + 3979080*X^8 - 53673984*X^7 - 1921092864*X^6 + 36692951040*X^5 + 260150152068*X^4 - 8074034151424*X^3 + 17411497907904*X^2 + 334267329576960*X - 1070875637673888",
"13": "X^13 - 3588*X^11 + 26624*X^10 + 4805814*X^9 - 65495040*X^8 - 2742580152*X^7 + 53472866304*X^6 + 523799608137*X^5 - 15904870252544*X^4 + 20704765242876*X^3 + 1272165214414848*X^2 - 5785154015101682*X - 5566199400652800",
"14": "X^14 - 3864*X^12 + 28672*X^11 + 5708724*X^10 - 78446592*X^9 - 3763935392*X^8 + 74548002816*X^7 + 938690123154*X^6 - 28184038342656*X^5 + 4933033670544*X^4 + 3543916130033664*X^3 - 17708319131756792*X^2 - 66951974741213184*X + 353246966446763712",
"15": "X^15 - 4140*X^13 + 30720*X^12 + 6687810*X^11 - 92528640*X^10 - 5006183160*X^9 + 100386385920*X^8 + 1551013889535*X^7 - 46274649374720*X^6 - 52156386220788*X^5 + 8166946170193920*X^4 - 40396324400570250*X^3 - 343157851636899840*X^2 + 2478633229267222680*X - 1019138268253188096",
"16": "X^16 - 4416*X^14 + 32768*X^13 + 7743072*X^12 - 107741184*X^11 - 6490348032*X^10 + 131456040960*X^9 + 2412765882672*X^8 - 71712047628288*X^7 - 182769627643392*X^6 + 16551920844668928*X^5 - 75950245382235904*X^4 - 1185992159822610432*X^3 + 9603649191850881024*X^2 + 2516673818431324160*X - 95193214316845989864",
"17": "X^17 - 4692*X^15 + 34816*X^14 + 8874510*X^13 - 124084224*X^12 - 8237454584*X^11 + 168224993280*X^10 + 3581743860933*X^9 - 106203810709504*X^8 - 430667835711492*X^7 + 30562165576919040*X^6 - 123128898719988786*X^5 - 3243815105868521472*X^4 + 27371851123822942152*X^3 + 48214794131373830144*X^2 - 837528114522914105838*X + 1007789957595884077056",
"18": "X^18 - 4968*X^16 + 36864*X^15 + 10082124*X^14 - 141557760*X^13 - 10268527392*X^12 + 211161268224*X^11 + 5121548365662*X^10 - 151629749551104*X^9 - 852768735542640*X^8 + 52573086201765888*X^7 - 175019428278403704*X^6 - 7584962917318262784*X^5 + 64191059494053779520*X^4 + 255658743623318077440*X^3 - 3935394824216519787507*X^2 + 5801216589926238781440*X + 20175374090332584338424",
"19": "X^19 - 5244*X^17 + 38912*X^16 + 11365914*X^15 - 160161792*X^14 - 12604591032*X^13 + 260732891136*X^12 + 7101582721179*X^11 - 210041908412416*X^10 - 1520748200359092*X^9 + 85531589463066624*X^8 - 216265858486214058*X^7 - 15840852055656800256*X^6 + 131200274081213930808*X^5 + 907200143845060431872*X^4 - 13301118595476006533019*X^3 + 14919088078341980602368*X^2 + 226677773832509124851668*X - 444031482904230742099968",
"20": "X^20 - 5520*X^18 + 40960*X^17 + 12725880*X^16 - 179896320*X^15 - 15266670080*X^14 + 317407887360*X^13 + 9597053034780*X^12 - 283664564879360*X^11 - 2522641819589184*X^10 + 133015503511388160*X^9 - 219855614883150880*X^8 - 30368763498108026880*X^7 + 241733304803745960960*X^6 + 2565936725960089403392*X^5 - 36419999165190869270010*X^4 + 11090853791265152040960*X^3 + 1291132320003274816439840*X^2 - 3658584617224256599572480*X - 2554391997476628780164976"
},
"3A": {
"2": "X^2 - 1566",
"3": "X^3 - 2349*X - 26016",
"4": "X^4 - 3132*X^2 - 34688*X + 964710",
"5": "X^5 - 3915*X^3 - 43360*X^2 + 2738610*X + 32093280",
"6": "X^6 - 4698*X^4 - 52032*X^3 + 5125599*X^2 + 79252992*X - 437842386",
"7": "X^7 - 5481*X^5 - 60704*X^4 + 8125677*X^3 + 139993056*X^2 - 2129554252*X - 31262747040",
"8": "X^8 - 6264*X^6 - 69376*X^5 + 11738844*X^4 + 214313472*X^3 - 5563892560*X^2 - 113934076416*X + 13637817990",
"9": "X^9 - 7047*X^7 - 78048*X^6 + 15965100*X^5 + 302214240*X^4 - 11220905997*X^3 - 264007081728*X^2 + 831733996221*X + 25875161029920",
"10": "X^10 - 7830*X^8 - 86720*X^7 + 20804445*X^6 + 403695360*X^5 - 19580643250*X^4 - 497431886400*X^3 + 3660734461950*X^2 + 127432205452800*X + 275674130014284",
"11": "X^11 - 8613*X^9 - 95392*X^8 + 26256879*X^7 + 518756832*X^6 - 31123153006*X^5 - 830158613856*X^4 + 10083149239977*X^3 + 371442496165312*X^2 + 717762053993688*X - 18234280002213792",
"12": "X^12 - 9396*X^10 - 104064*X^9 + 32322402*X^8 + 647398656*X^7 - 46328483952*X^6 - 1278137387520*X^5 + 22057366477023*X^4 + 841330049090560*X^3 + 444027556577340*X^2 - 117144304421337216*X - 429009093512051766",
"13": "X^13 - 10179*X^11 - 112736*X^10 + 39001014*X^9 + 789620832*X^8 - 65676684775*X^7 - 1857318330816*X^6 + 41917652441730*X^5 + 1637170809006304*X^4 - 2497169521454166*X^3 - 420684312850940736*X^2 - 2105075617569040090*X + 10247000208712023744",
"14": "X^14 - 10962*X^12 - 121408*X^11 + 46292715*X^10 + 945423360*X^9 - 89647804162*X^8 - 2583651567168*X^7 + 72374151524661*X^6 + 2875692649544960*X^5 - 11421188445346722*X^4 - 1130632108232155200*X^3 - 5806549397932712128*X^2 + 87319034849900754432*X + 466617283283435949072",
"15": "X^15 - 11745*X^13 - 130080*X^12 + 54197505*X^11 + 1114806240*X^10 - 118721890800*X^9 - 3473087220000*X^8 + 116512886238300*X^7 + 4690275373193600*X^6 - 31301420155836849*X^5 - 2542887140869411200*X^4 - 11603781118360245615*X^3 + 387719615176972633440*X^2 + 3035921352810766307910*X - 3257835634385044155936",
"16": "X^16 - 12528*X^14 - 138752*X^13 + 62715384*X^12 + 1297769472*X^11 - 153378993376*X^10 - 4541575412736*X^9 + 177795757217052*X^8 + 7230950711293952*X^7 - 69063599838615840*X^6 - 5063768583796933632*X^5 - 17960305839970289712*X^4 + 1236859001489686468608*X^3 + 11059249546416436974144*X^2 - 46207420274825339942912*X - 420068756947874925617658",
"17": "X^17 - 13311*X^15 - 147424*X^14 + 71846352*X^13 + 1494313056*X^12 - 194099160577*X^11 - 5805066268800*X^10 + 260060543217243*X^9 + 10664402324042400*X^8 - 133880119493793903*X^7 - 9226313408145236256*X^6 - 20603579751556989338*X^5 + 3213349492152798492768*X^4 + 29786790863890374188346*X^3 - 272769244823637576654528*X^2 - 3375475886670895686708054*X - 1976945837316976216828224",
"18": "X^18 - 14094*X^16 - 156096*X^15 + 81590409*X^14 + 1704436992*X^13 - 241362441090*X^12 - 7279509911616*X^11 + 367520901117120*X^10 + 15173965800489984*X^9 - 237464340505364304*X^8 - 15706574458507616256*X^7 - 11165270178013585533*X^6 + 7248614384310047649792*X^5 + 66007973312340964795890*X^4 - 1067291431964305556898240*X^3 - 14864828825419028429536863*X^2 + 3145706727222003484322304*X + 323725581647422475796288018",
"19": "X^19 - 14877*X^17 - 164768*X^16 + 91947555*X^15 + 1928141280*X^14 - 295648883602*X^13 - 8980856464608*X^12 + 504766365916851*X^11 + 20959628658542400*X^10 - 394364906210667510*X^9 - 25339918528306648800*X^8 + 24408901153134408148*X^7 + 14741810606212499169216*X^6 + 126968213366591025459222*X^5 - 3260113832241049547478912*X^4 - 47737266506622054989374725*X^3 + 98350782099600469499315136*X^2 + 3141018636810902707074625208*X + 5216059939872005050687234848",
"20": "X^20 - 15660*X^18 - 173440*X^17 + 102917790*X^16 + 2165425920*X^15 - 357438536800*X^14 - 10925056051200*X^13 + 676762350738525*X^12 + 28238030344960000*X^11 - 622260054469855332*X^10 - 39137324435160681600*X^9 + 107679761587086453210*X^8 + 27690065021161246429440*X^7 + 218381587745475854414160*X^6 - 8419744207979802705207808*X^5 - 125161270334260160688014850*X^4 + 601154139668915750004126720*X^3 + 16291758526697587024301778680*X^2 + 33783639854788694856608997120*X - 208537195951289923939556173980"
},
"3B": {
"2": "X^2 - 108",
"3": "X^3 - 162*X + 228",
"4": "X^4 - 216*X^2 + 304*X + 6804",
"5": "X^5 - 270*X^3 + 380*X^2 + 15795*X - 26460",
"6": "X^6 - 324*X^4 + 456*X^3 + 27702*X^2 - 56376*X - 368028",
"7": "X^7 - 378*X^5 + 532*X^4 + 42525*X^3 - 94500*X^2 - 1235836*X + 2150064",
"8": "X^8 - 432*X^6 + 608*X^5 + 60264*X^4 - 140832*X^3 - 2753968*X^2 + 6664032*X + 19000116",
"9": "X^9 - 486*X^7 + 684*X^6 + 80919*X^5 - 195372*X^4 - 5079888*X^3 + 14224248*X^2 + 84691575*X - 158481672",
"10": "X^10 - 540*X^8 + 760*X^7 + 104490*X^6 - 258120*X^5 - 8371060*X^4 + 25495560*X^3 + 232193115*X^2 - 644766840*X - 909008568",
"11": "X^11 - 594*X^9 + 836*X^8 + 130977*X^7 - 329076*X^6 - 12784948*X^5 + 41142816*X^4 + 505210068*X^3 - 1678143632*X^2 - 5184518724*X + 10940073408",
"12": "X^12 - 648*X^10 + 912*X^9 + 160380*X^8 - 408240*X^7 - 18479016*X^6 + 61830864*X^5 + 955950822*X^4 - 3525861872*X^3 - 17156805048*X^2 + 55244025648*X + 38438031252",
"13": "X^13 - 702*X^11 + 988*X^10 + 192699*X^9 - 495612*X^8 - 25610728*X^7 + 88224552*X^6 + 1645126821*X^5 - 6503040440*X^4 - 43504162182*X^3 + 170181539892*X^2 + 279999706649*X - 718619517252",
"14": "X^14 - 756*X^12 + 1064*X^11 + 227934*X^10 - 591192*X^9 - 34337548*X^8 + 120988728*X^7 + 2641952565*X^6 - 10972667272*X^5 - 93711873024*X^4 + 411124817376*X^3 + 1114034881652*X^2 - 4346617554720*X - 1240052515488",
"15": "X^15 - 810*X^13 + 1140*X^12 + 266085*X^11 - 694980*X^10 - 44816940*X^9 + 160788240*X^8 + 4024145610*X^7 - 17345599360*X^6 - 180531373752*X^5 + 854778941640*X^4 + 3279822180600*X^3 - 15510842224920*X^2 - 12504295399680*X + 45270116562888",
"16": "X^16 - 864*X^14 + 1216*X^13 + 307152*X^12 - 806976*X^11 - 57206368*X^10 + 208287936*X^9 + 5877926568*X^8 - 26080562752*X^7 - 320439418848*X^6 + 1602413039808*X^5 + 8016575338128*X^4 - 42452195038272*X^3 - 61508686453344*X^2 + 320109222564544*X + 6763963225716",
"17": "X^17 - 918*X^15 + 1292*X^14 + 351135*X^13 - 927180*X^12 - 71663296*X^11 + 264152664*X^10 + 8298019107*X^9 - 37684152552*X^8 - 534097246122*X^7 + 2783091443868*X^6 + 17238243670639*X^5 - 98412669984780*X^4 - 212922963176076*X^3 + 1302246359519928*X^2 + 344052646922412*X - 2744442325476792",
"18": "X^18 - 972*X^16 + 1368*X^15 + 398034*X^14 - 1055592*X^13 - 88345188*X^12 + 329047272*X^11 + 11387649951*X^10 - 52710832920*X^9 - 846809741736*X^8 + 4556904851952*X^7 + 33733107459072*X^6 - 203231773347984*X^5 - 594359306622360*X^4 + 3991741493218416*X^3 + 2523937160990439*X^2 - 22299277458590352*X + 3721986387280116",
"19": "X^19 - 1026*X^17 + 1444*X^16 + 447849*X^15 - 1192212*X^14 - 107409508*X^13 + 403636608*X^12 + 15258548880*X^11 - 71762937072*X^10 - 1288984605228*X^9 + 7118201489616*X^8 + 61388168242966*X^7 - 385152322769856*X^6 - 1431666234083664*X^5 + 10227516717525240*X^4 + 11027669062945986*X^3 - 102179104316608392*X^2 + 12200918744412164*X + 160159339045660608",
"20": "X^20 - 1080*X^18 + 1520*X^17 + 500580*X^16 - 1337040*X^15 - 129013720*X^14 + 488585520*X^13 + 20030948730*X^12 - 95490667280*X^11 - 1896591514536*X^10 + 10698818271120*X^9 + 105438334025820*X^8 - 682835625566640*X^7 - 3094866651283560*X^6 + 23104709619272144*X^5 + 36416504124392715*X^4 - 347636578284756720*X^3 - 19413579400705840*X^2 + 1477170907746423840*X - 465851382290697096"
},
"5A": {
"2": "X^2 - 268",
"3": "X^3 - 402*X - 2280",
"4": "X^4 - 536*X^2 - 3040*X + 22532",
"5": "X^5 - 670*X^3 - 3800*X^2 + 73055*X + 447920",
"6": "X^6 - 804*X^4 - 4560*X^3 + 141534*X^2 + 1148544*X - 626128",
"7": "X^7 - 938*X^5 - 5320*X^4 + 227969*X^3 + 2052848*X^2 - 6799758*X - 67033064",
"8": "X^8 - 1072*X^6 - 6080*X^5 + 332360*X^4 + 3160832*X^3 - 21123744*X^2 - 261478144*X - 295854588",
"9": "X^9 - 1206*X^7 - 6840*X^6 + 454707*X^5 + 4472496*X^4 - 46004190*X^3 - 624959496*X^2 - 449179551*X + 7797154992",
"10": "X^10 - 1340*X^8 - 7600*X^7 + 595010*X^6 + 5987840*X^5 - 83847200*X^4 - 1198416800*X^3 + 415163775*X^2 + 43430515200*X + 86631459132",
"11": "X^11 - 1474*X^9 - 8360*X^8 + 753269*X^7 + 7706864*X^6 - 137058878*X^5 - 2022789736*X^4 + 3496881410*X^3 + 134837625296*X^2 + 351807252192*X - 607405541072",
"12": "X^12 - 1608*X^10 - 9120*X^9 + 929484*X^8 + 9629568*X^7 - 208045328*X^6 - 3139017984*X^5 + 10318097310*X^4 + 317276794112*X^3 + 811670660784*X^2 - 5180025267264*X - 15754493708272",
"13": "X^13 - 1742*X^11 - 9880*X^10 + 1123655*X^9 + 11755952*X^8 - 299212654*X^7 - 4588041224*X^6 + 22723353367*X^5 + 633320886640*X^4 + 1360783739042*X^3 - 21309758972008*X^2 - 91079481288094*X - 4343746596176",
"14": "X^14 - 1876*X^12 - 10640*X^11 + 1335782*X^10 + 14086016*X^9 - 412966960*X^8 - 6410799136*X^7 + 42879609409*X^6 + 1132857324032*X^5 + 1728906505676*X^4 - 62058420981200*X^3 - 295491686088606*X^2 + 293299210085504*X + 2206490649103872",
"15": "X^15 - 2010*X^13 - 11400*X^12 + 1565865*X^11 + 16619760*X^10 - 551714350*X^9 - 8648231400*X^8 + 73276243200*X^7 + 1873088083600*X^6 + 1437792940548*X^5 - 147182971296000*X^4 - 714591936209785*X^3 + 2102088598077600*X^2 + 16687466635183890*X + 13272593196883880",
"16": "X^16 - 2144*X^14 - 12160*X^13 + 1813904*X^12 + 19357184*X^11 - 717860928*X^10 - 11341277696*X^9 + 116725050440*X^8 + 2918529698816*X^7 - 242013018752*X^6 - 304360703749632*X^5 - 1434619347375008*X^4 + 8330843213015040*X^3 + 68170780162142208*X^2 + 54631743158488064*X - 236381981043036156",
"17": "X^17 - 2278*X^15 - 12920*X^14 + 2079899*X^13 + 22298288*X^12 - 913812798*X^11 - 14530877704*X^10 + 176360244765*X^9 + 4341013259312*X^8 - 4334381480330*X^7 - 570414434164184*X^6 - 2521216064402940*X^5 + 24582020995115600*X^4 + 202660539378806916*X^3 + 53709529325591456*X^2 - 2345713545049042502*X - 3235867746801442208",
"18": "X^18 - 2412*X^16 - 13680*X^15 + 2363850*X^14 + 25443072*X^13 - 1141976064*X^12 - 18257971104*X^11 + 255638457747*X^10 + 6219684410880*X^9 - 12200800601412*X^8 - 992537688507408*X^7 - 3992402666220606*X^6 + 60342709607622144*X^5 + 493059877540248240*X^4 - 341112898553680800*X^3 - 11875530143618239743*X^2 - 22952599560310625280*X + 14917967214550554404",
"19": "X^19 - 2546*X^17 - 14440*X^16 + 2665757*X^15 + 28791536*X^14 - 1404756830*X^13 - 22563497576*X^12 + 358338738894*X^11 + 8641003355472*X^10 - 25583580591768*X^9 - 1629519891049520*X^8 - 5785764234417647*X^7 + 130372627270858304*X^6 + 1043023858472783774*X^5 - 2099077406773522760*X^4 - 42302405604779147900*X^3 - 84663969004786682320*X^2 + 232344477408487992764*X + 543892089932412316000",
"20": "X^20 - 2680*X^18 - 15200*X^17 + 2985620*X^16 + 32343680*X^15 - 1704561200*X^14 - 27488396800*X^13 + 488562555650*X^12 + 11698744851200*X^11 - 46649057717136*X^10 - 2552971552520000*X^9 - 7719847085341760*X^8 + 256289133851897600*X^7 + 1988266746701356640*X^6 - 7314524734144737280*X^5 - 120593845075361703425*X^4 - 209896479183034150400*X^3 + 1542758972489584216600*X^2 + 5015109427757732293600*X + 1007068731932510988332"
},
"5B": {
"2": "X^2 - 18",
"3": "X^3 - 27*X - 30",
"4": "X^4 - 36*X^2 - 40*X + 282",
"5": "X^5 - 45*X^3 - 50*X^2 + 555*X + 420",
"6": "X^6 - 54*X^4 - 60*X^3 + 909*X^2 + 1044*X - 2628",
"7": "X^7 - 63*X^5 - 70*X^4 + 1344*X^3 + 1848*X^2 - 8008*X - 8064",
"8": "X^8 - 72*X^6 - 80*X^5 + 1860*X^4 + 2832*X^3 - 16744*X^2 - 24144*X + 27162",
"9": "X^9 - 81*X^7 - 90*X^6 + 2457*X^5 + 3996*X^4 - 29565*X^3 - 51246*X^2 + 104949*X + 112992",
"10": "X^10 - 90*X^8 - 100*X^7 + 3135*X^6 + 5340*X^5 - 47200*X^4 - 91800*X^3 + 263775*X^2 + 440200*X - 234618",
"11": "X^11 - 99*X^9 - 110*X^8 + 3894*X^7 + 6864*X^6 - 70378*X^5 - 148236*X^4 + 541035*X^3 + 1121296*X^2 - 1164933*X - 1532322",
"12": "X^12 - 108*X^10 - 120*X^9 + 4734*X^8 + 8568*X^7 - 99828*X^6 - 222984*X^5 + 980685*X^4 + 2323112*X^3 - 3510216*X^2 - 7251264*X + 1708728",
"13": "X^13 - 117*X^11 - 130*X^10 + 5655*X^9 + 10452*X^8 - 136279*X^7 - 318474*X^6 + 1633242*X^5 + 4241640*X^4 - 8323458*X^3 - 21464508*X^2 + 10741406*X + 19453824",
"14": "X^14 - 126*X^12 - 140*X^11 + 6657*X^10 + 12516*X^9 - 180460*X^8 - 437136*X^7 + 2555784*X^6 + 7102032*X^5 - 17050824*X^4 - 50425200*X^3 + 38679144*X^2 + 109179504*X - 6046128",
"15": "X^15 - 135*X^13 - 150*X^12 + 7740*X^11 + 14760*X^10 - 233100*X^9 - 581400*X^8 + 3811950*X^7 + 11158600*X^6 - 31590702*X^5 - 102658500*X^4 + 106035840*X^3 + 369957600*X^2 - 62127360*X - 236646120",
"16": "X^16 - 144*X^14 - 160*X^13 + 8904*X^12 + 17184*X^11 - 294928*X^10 - 753696*X^9 + 5471940*X^8 + 16694816*X^7 - 54352752*X^6 - 189289632*X^5 + 245695992*X^4 + 974171040*X^3 - 294675792*X^2 - 1536779936*X - 99998406",
"17": "X^17 - 153*X^15 - 170*X^14 + 10149*X^13 + 19788*X^12 - 366673*X^11 - 956454*X^10 + 7612515*X^9 + 24023312*X^8 - 88316955*X^7 - 324371934*X^6 + 506889935*X^5 + 2191016100*X^4 - 983611959*X^3 - 5874371794*X^2 - 350416002*X + 2747430792",
"18": "X^18 - 162*X^16 - 180*X^15 + 11475*X^14 + 22572*X^13 - 449064*X^12 - 1192104*X^11 + 10316997*X^10 + 33485880*X^9 - 137092662*X^8 - 525214908*X^7 + 959700519*X^6 + 4415260644*X^5 - 2662750260*X^4 - 17160706800*X^3 - 332275743*X^2 + 20340108720*X + 3199647654",
"19": "X^19 - 171*X^17 - 190*X^16 + 12882*X^15 + 25536*X^14 - 542830*X^13 - 1463076*X^12 + 13675269*X^11 + 45453472*X^10 - 204977643*X^9 - 812712270*X^8 + 1700101228*X^7 + 8199545304*X^6 - 6254488476*X^5 - 42305115760*X^4 + 1776621600*X^3 + 86820304680*X^2 + 20343202264*X - 30429507000",
"20": "X^20 - 180*X^18 - 200*X^17 + 14370*X^16 + 28680*X^15 - 648700*X^14 - 1771800*X^13 + 17783775*X^12 + 60326200*X^11 - 297017136*X^10 - 1211670000*X^9 + 2855525740*X^8 + 14290227600*X^7 - 13243548360*X^6 - 92583767280*X^5 + 10890346575*X^4 + 279223599600*X^3 + 74525879100*X^2 - 253861631400*X - 60342942918"
},
"7A": {
"2": "X^2 - 102",
"3": "X^3 - 153*X - 612",
"4": "X^4 - 204*X^2 - 816*X + 2478",
"5": "X^5 - 255*X^3 - 1020*X^2 + 9600*X + 42240",
"6": "X^6 - 306*X^4 - 1224*X^3 + 19323*X^2 + 113112*X + 37122",
"7": "X^7 - 357*X^5 - 1428*X^4 + 31647*X^3 + 204792*X^2 - 186956*X - 2129988",
"8": "X^8 - 408*X^6 - 1632*X^5 + 46572*X^4 + 317280*X^3 - 830560*X^2 - 9014496*X - 10701810",
"9": "X^9 - 459*X^7 - 1836*X^6 + 64098*X^5 + 450576*X^4 - 2026341*X^3 - 22319496*X^2 - 28425870*X + 71302284",
"10": "X^10 - 510*X^8 - 2040*X^7 + 84225*X^6 + 604680*X^5 - 3906950*X^4 - 43636800*X^3 - 37989300*X^2 + 479394400*X + 868859448",
"11": "X^11 - 561*X^9 - 2244*X^8 + 106953*X^7 + 779592*X^6 - 6605038*X^5 - 74558220*X^4 - 17247186*X^3 + 1617562364*X^2 + 4028572251*X - 302240796",
"12": "X^12 - 612*X^10 - 2448*X^9 + 132282*X^8 + 975312*X^7 - 10253256*X^6 - 116675568*X^5 + 62710587*X^4 + 3987819984*X^3 + 10603236132*X^2 - 13115444544*X - 48141654882",
"13": "X^13 - 663*X^11 - 2652*X^10 + 160212*X^9 + 1191840*X^8 - 14984255*X^7 - 171580656*X^6 + 237559335*X^5 + 8200424284*X^4 + 21003754317*X^3 - 72286807944*X^2 - 315044744625*X - 180225789276",
"14": "X^14 - 714*X^12 - 2856*X^11 + 190743*X^10 + 1429176*X^9 - 20930686*X^8 - 240865296*X^7 + 549739575*X^6 + 14973875504*X^5 + 34581679146*X^4 - 240437794632*X^3 - 1114987573952*X^2 - 559055270760*X + 1863267140388",
"15": "X^15 - 765*X^13 - 3060*X^12 + 223875*X^11 + 1687320*X^10 - 28225200*X^9 - 326121300*X^8 + 1048457025*X^7 + 25134917100*X^6 + 49284186822*X^5 - 615867150600*X^4 - 2896895906535*X^3 + 55384706160*X^2 + 17179809440625*X + 17336946733068",
"16": "X^16 - 816*X^14 - 3264*X^13 + 259608*X^12 + 1966272*X^11 - 37000448*X^10 - 428940480*X^9 + 1789682604*X^8 + 39618535744*X^7 + 61309052160*X^6 - 1339451409216*X^5 - 6217010149440*X^4 + 5589475392192*X^3 + 78885747867360*X^2 + 109307989667520*X - 29813688561714",
"17": "X^17 - 867*X^15 - 3468*X^14 + 297942*X^13 + 2266032*X^12 - 47389081*X^11 - 550914648*X^10 + 2836152432*X^9 + 59467961324*X^8 + 64759623336*X^7 - 2601545396244*X^6 - 11693950888085*X^5 + 24652797708972*X^4 + 254235144582246*X^3 + 355239589058264*X^2 - 577012686527130*X - 1057699051732800",
"18": "X^18 - 918*X^16 - 3672*X^15 + 338877*X^14 + 2586600*X^13 - 59523750*X^12 - 693635616*X^11 + 4257367830*X^10 + 85834666944*X^9 + 51299796636*X^8 - 4648882734864*X^7 - 19946188133397*X^6 + 72909145773936*X^5 + 658026148176450*X^4 + 764836393233240*X^3 - 3782760467157666*X^2 - 9133229346096456*X - 2708588894485728",
"19": "X^19 - 969*X^17 - 3876*X^16 + 382413*X^15 + 2927976*X^14 - 73537106*X^13 - 858695196*X^12 + 6129595320*X^11 + 119978368924*X^10 + 9808991205*X^9 - 7791476350692*X^8 - 31511914281168*X^7 + 175869851332416*X^6 + 1465178168502975*X^5 + 1086959072460288*X^4 - 15599777819977887*X^3 - 41000090227192452*X^2 - 4542355910399712*X + 46044646873946808",
"20": "X^20 - 1020*X^18 - 4080*X^17 + 428550*X^16 + 3290160*X^15 - 89561800*X^14 - 1047685200*X^13 + 8535866625*X^12 + 163267026800*X^11 - 73962876204*X^10 - 12409518976800*X^9 - 46751320783610*X^8 + 372109419096960*X^7 + 2921762648334000*X^6 + 493687988473664*X^5 - 49025686386830100*X^4 - 129141055144249920*X^3 + 68313385071947920*X^2 + 528348194646192000*X + 334212288470817288"
},
"7B": {
"2": "X^2 - 4",
"3": "X^3 - 6*X - 24",
"4": "X^4 - 8*X^2 - 32*X + 28",
"5": "X^5 - 10*X^3 - 40*X^2 + 45*X + 100",
"6": "X^6 - 12*X^4 - 48*X^3 + 66*X^2 + 216*X + 176",
"7": "X^7 - 14*X^5 - 56*X^4 + 91*X^3 + 364*X^2 + 322*X - 644",
"8": "X^8 - 16*X^6 - 64*X^5 + 120*X^4 + 544*X^3 + 480*X^2 - 1632*X - 1092",
"9": "X^9 - 18*X^7 - 72*X^6 + 153*X^5 + 756*X^4 + 642*X^3 - 3132*X^2 - 3420*X + 228",
"10": "X^10 - 20*X^8 - 80*X^7 + 190*X^6 + 1000*X^5 + 800*X^4 - 5240*X^3 - 7195*X^2 + 1920*X + 8696",
"11": "X^11 - 22*X^9 - 88*X^8 + 231*X^7 + 1276*X^6 + 946*X^5 - 8052*X^4 - 12661*X^3 + 6116*X^2 + 31812*X + 6688",
"12": "X^12 - 24*X^10 - 96*X^9 + 276*X^8 + 1584*X^7 + 1072*X^6 - 11664*X^5 - 20046*X^4 + 14176*X^3 + 76152*X^2 + 24816*X - 25808",
"13": "X^13 - 26*X^11 - 104*X^10 + 325*X^9 + 1924*X^8 + 1170*X^7 - 16172*X^6 - 29562*X^5 + 27716*X^4 + 150150*X^3 + 59072*X^2 - 126919*X - 92716",
"14": "X^14 - 28*X^12 - 112*X^11 + 378*X^10 + 2296*X^9 + 1232*X^8 - 21672*X^7 - 41405*X^6 + 48608*X^5 + 263424*X^4 + 112504*X^3 - 375046*X^2 - 418656*X + 36844",
"15": "X^15 - 30*X^13 - 120*X^12 + 435*X^11 + 2700*X^10 + 1250*X^9 - 28260*X^8 - 55755*X^7 + 78980*X^6 + 426744*X^5 + 186240*X^4 - 871620*X^3 - 1177680*X^2 + 241380*X + 465616",
"16": "X^16 - 32*X^14 - 128*X^13 + 496*X^12 + 3136*X^11 + 1216*X^10 - 36032*X^9 - 72776*X^8 + 121216*X^7 + 652000*X^6 + 278848*X^5 - 1751840*X^4 - 2638784*X^3 + 885472*X^2 + 2606464*X + 642172",
"17": "X^17 - 34*X^15 - 136*X^14 + 561*X^13 + 3604*X^12 + 1122*X^11 - 45084*X^10 - 92616*X^9 + 177956*X^8 + 952170*X^7 + 385696*X^6 - 3188945*X^5 - 5143860*X^4 + 2466326*X^3 + 8668164*X^2 + 3250485*X - 1782348",
"18": "X^18 - 36*X^16 - 144*X^15 + 630*X^14 + 4104*X^13 + 960*X^12 - 55512*X^11 - 115407*X^10 + 252096*X^9 + 1341288*X^8 + 498312*X^7 - 5398422*X^6 - 9110448*X^5 + 5795892*X^4 + 22310280*X^3 + 9916164*X^2 - 11524680*X - 5438596",
"19": "X^19 - 38*X^17 - 152*X^16 + 703*X^15 + 4636*X^14 + 722*X^13 - 67412*X^12 - 141265*X^11 + 346788*X^10 + 1834412*X^9 + 603744*X^8 - 8642150*X^7 - 15032952*X^6 + 12104368*X^5 + 49020152*X^4 + 23461105*X^3 - 43380952*X^2 - 34504798*X + 203528",
"20": "X^20 - 40*X^18 - 160*X^17 + 780*X^16 + 5200*X^15 + 400*X^14 - 80880*X^13 - 170290*X^12 + 465440*X^11 + 2447592*X^10 + 683920*X^9 - 13232480*X^8 - 23482320*X^7 + 23157080*X^6 + 96562688*X^5 + 47223285*X^4 - 124604720*X^3 - 127697960*X^2 + 8256720*X + 31008488"
},
"13A": {
"2": "X^2 - 24",
"3": "X^3 - 36*X - 84",
"4": "X^4 - 48*X^2 - 112*X + 24",
"5": "X^5 - 60*X^3 - 140*X^2 + 390*X + 1020",
"6": "X^6 - 72*X^4 - 168*X^3 + 900*X^2 + 3240*X + 2100",
"7": "X^7 - 84*X^5 - 196*X^4 + 1554*X^3 + 6132*X^2 + 2674*X - 7476",
"8": "X^8 - 96*X^6 - 224*X^5 + 2352*X^4 + 9696*X^3 - 1296*X^2 - 45600*X - 44808",
"9": "X^9 - 108*X^7 - 252*X^6 + 3294*X^5 + 13932*X^4 - 11538*X^3 - 129276*X^2 - 170127*X - 19524",
"10": "X^10 - 120*X^8 - 280*X^7 + 4380*X^6 + 18840*X^5 - 29780*X^4 - 270600*X^3 - 355650*X^2 + 231800*X + 503076",
"11": "X^11 - 132*X^9 - 308*X^8 + 5610*X^7 + 24420*X^6 - 57750*X^5 - 481668*X^4 - 554433*X^3 + 1353044*X^2 + 3196974*X + 1492920",
"12": "X^12 - 144*X^10 - 336*X^9 + 6984*X^8 + 30672*X^7 - 97176*X^6 - 774576*X^5 - 698796*X^4 + 4148240*X^3 + 10231992*X^2 + 5254992*X - 2482812",
"13": "X^13 - 156*X^11 - 364*X^10 + 8502*X^9 + 37596*X^8 - 149786*X^7 - 1161420*X^6 - 700323*X^5 + 9614956*X^4 + 23669490*X^3 + 5859360*X^2 - 32384001*X - 24577488",
"14": "X^14 - 168*X^12 - 392*X^11 + 10164*X^10 + 45192*X^9 - 217308*X^8 - 1654296*X^7 - 449862*X^6 + 18944296*X^5 + 45211404*X^4 - 12018216*X^3 - 155500758*X^2 - 162369480*X - 30593580",
"15": "X^15 - 180*X^13 - 420*X^12 + 11970*X^11 + 53460*X^10 - 301470*X^9 - 2265300*X^8 + 182475*X^7 + 33520900*X^6 + 75951414*X^5 - 76541400*X^4 - 485866515*X^3 - 533513160*X^2 + 27337860*X + 226688196",
"16": "X^16 - 192*X^14 - 448*X^13 + 13920*X^12 + 62400*X^11 - 404000*X^10 - 3006528*X^9 + 1347312*X^8 + 54922944*X^7 + 116126112*X^6 - 231616320*X^5 - 1188294224*X^4 - 1187188800*X^3 + 1018632096*X^2 + 2359194304*X + 941335992",
"17": "X^17 - 204*X^15 - 476*X^14 + 16014*X^13 + 72012*X^12 - 526626*X^11 - 3890076*X^10 + 3216009*X^9 + 84922140*X^8 + 164866170*X^7 - 539794608*X^6 - 2477864869*X^5 - 1953110688*X^4 + 5338627776*X^3 + 11289280236*X^2 + 5858642034*X - 449825100",
"18": "X^18 - 216*X^16 - 504*X^15 + 18252*X^14 + 82296*X^13 - 671076*X^12 - 4928040*X^11 + 5980662*X^10 + 125483736*X^9 + 219947508*X^8 - 1085176440*X^7 - 4616429994*X^6 - 2251096920*X^5 + 17894651004*X^4 + 36214683768*X^3 + 15250017609*X^2 - 17261297640*X - 12719333508",
"19": "X^19 - 228*X^17 - 532*X^16 + 20634*X^15 + 93252*X^14 - 839078*X^13 - 6132516*X^12 + 9854103*X^11 + 178766516*X^10 + 277542462*X^9 - 1976313576*X^8 - 7906128247*X^7 - 858835416*X^6 + 47159268972*X^5 + 90262240788*X^4 + 10869810225*X^3 - 132177306612*X^2 - 126045733734*X - 26122558728",
"20": "X^20 - 240*X^18 - 560*X^17 + 23160*X^16 + 104880*X^15 - 1032360*X^14 - 7515600*X^13 + 15069900*X^12 + 247122800*X^11 + 331970952*X^10 - 3349112400*X^9 - 12679915940*X^8 + 4362153840*X^7 + 106279281960*X^6 + 188036291568*X^5 - 75529872210*X^4 - 583804000080*X^3 - 593833297720*X^2 - 93980231280*X + 91698544884"
},
"13B": {
"2": "X^2 + 2",
"3": "X^3 + 3*X - 6",
"4": "X^4 + 4*X^2 - 8*X - 2",
"5": "X^5 + 5*X^3 - 10*X^2 - 20",
"6": "X^6 + 6*X^4 - 12*X^3 + 3*X^2 - 36*X + 20",
"7": "X^7 + 7*X^5 - 14*X^4 + 7*X^3 - 56*X^2 + 35*X - 14",
"8": "X^8 + 8*X^6 - 16*X^5 + 12*X^4 - 80*X^3 + 56*X^2 - 48*X + 94",
"9": "X^9 + 9*X^7 - 18*X^6 + 18*X^5 - 108*X^4 + 84*X^3 - 108*X^2 + 225*X - 24",
"10": "X^10 + 10*X^8 - 20*X^7 + 25*X^6 - 140*X^5 + 120*X^4 - 200*X^3 + 420*X^2 - 120*X + 132",
"11": "X^11 + 11*X^9 - 22*X^8 + 33*X^7 - 176*X^6 + 165*X^5 - 330*X^4 + 693*X^3 - 308*X^2 + 495*X - 286",
"12": "X^12 + 12*X^10 - 24*X^9 + 42*X^8 - 216*X^7 + 220*X^6 - 504*X^5 + 1059*X^4 - 632*X^3 + 1200*X^2 - 960*X + 136",
"13": "X^13 + 13*X^11 - 26*X^10 + 52*X^9 - 260*X^8 + 286*X^7 - 728*X^6 + 1534*X^5 - 1144*X^4 + 2392*X^3 - 2236*X^2 + 793*X - 832",
"14": "X^14 + 14*X^12 - 28*X^11 + 63*X^10 - 308*X^9 + 364*X^8 - 1008*X^7 + 2135*X^6 - 1904*X^5 + 4242*X^4 - 4396*X^3 + 2499*X^2 - 3276*X + 828",
"15": "X^15 + 15*X^13 - 30*X^12 + 75*X^11 - 360*X^10 + 455*X^9 - 1350*X^8 + 2880*X^7 - 2980*X^6 + 6948*X^5 - 7800*X^4 + 6015*X^3 - 8760*X^2 + 3735*X - 1046",
"16": "X^16 + 16*X^14 - 32*X^13 + 88*X^12 - 416*X^11 + 560*X^10 - 1760*X^9 + 3788*X^8 - 4448*X^7 + 10736*X^6 - 12896*X^5 + 12376*X^4 - 19232*X^3 + 10960*X^2 - 6176*X + 3262",
"17": "X^17 + 17*X^15 - 34*X^14 + 102*X^13 - 476*X^12 + 680*X^11 - 2244*X^10 + 4879*X^9 - 6392*X^8 + 15861*X^7 - 20230*X^6 + 22933*X^5 - 37332*X^4 + 26027*X^3 - 20774*X^2 + 16014*X - 2584",
"18": "X^18 + 18*X^16 - 36*X^15 + 117*X^14 - 540*X^13 + 816*X^12 - 2808*X^11 + 6174*X^10 - 8904*X^9 + 22608*X^8 - 30456*X^7 + 39396*X^6 - 66528*X^5 + 54180*X^4 - 53856*X^3 + 49473*X^2 - 16200*X + 6554",
"19": "X^19 + 19*X^17 - 38*X^16 + 133*X^15 - 608*X^14 + 969*X^13 - 3458*X^12 + 7695*X^11 - 12084*X^10 + 31293*X^9 - 44346*X^8 + 63878*X^7 - 111264*X^6 + 102866*X^5 - 119244*X^4 + 122474*X^3 - 59280*X^2 + 39938*X - 11628",
"20": "X^20 + 20*X^18 - 40*X^17 + 150*X^16 - 680*X^15 + 1140*X^14 - 4200*X^13 + 9465*X^12 - 16040*X^11 + 42264*X^10 - 62800*X^9 + 98940*X^8 - 177120*X^7 + 182280*X^6 - 237008*X^5 + 264420*X^4 - 166480*X^3 + 144040*X^2 - 68640*X + 11828"
}
}
},
"T643": {
"Title": "Zagier traces of singular moduli",
"Numbers": {
"1": {
"3": "-248",
"4": "492",
"7": "-4119",
"8": "7256",
"11": "-33512",
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