Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 310)

Label	Polynomial	Discriminant	Galois group	Class group
36.0.1102766555593920971763188134004988790509406708671598011853.1	x^36 - x^35 + 3x^34 - 4x^33 + 9x^32 - 14x^31 + 28x^30 - 47x^29 + 89x^28 - 155x^27 + 286x^26 - 507x^25 + 924x^24 + 442x^23 + 899x^22 + 909x^21 + 1331x^20 + 1386x^19 + 2185x^18 + 1918x^17 + 3838x^16 + 2183x^15 + 7411x^14 + 793x^13 + 16212x^12 - 7215x^11 + 3211x^10 - 1429x^9 + 636x^8 - 283x^7 + 126x^6 - 56x^5 + 25x^4 - 11x^3 + 5x^2 - 2x + 1	\( 7^{24}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	$[2, 74]$ (GRH)
36.0.459146050215773460843525344476713987772454059613596693862733.1	x^36 + 3x^34 - x^33 + 9x^32 - 6x^31 + 28x^30 - 27x^29 + 90x^28 - 109x^27 + 297x^26 - 417x^25 + 1000x^24 + 1845x^23 + 3417x^22 + 4535x^21 + 8406x^20 + 10188x^19 + 20683x^18 + 22158x^17 + 51861x^16 + 45791x^15 + 133425x^14 + 85512x^13 + 354484x^12 + 123111x^11 + 42756x^10 + 14849x^9 + 5157x^8 + 1791x^7 + 622x^6 + 216x^5 + 75x^4 + 26x^3 + 9x^2 + 3x + 1	\( 3^{48}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	$[3, 3, 9, 9]$ (GRH)
36.0.113857935275994928933450454958497004305286414921283721923828125.1	x^36 + 15x^34 - 4x^33 + 171x^32 + 132x^31 + 1809x^30 + 1683x^29 + 17889x^28 + 12647x^27 + 85860x^26 + 52491x^25 + 358026x^24 + 22707x^23 + 1329663x^22 + 118787x^21 + 4193811x^20 + 697212x^19 + 3532755x^18 + 635940x^17 + 2414307x^16 + 853087x^15 + 1609083x^14 + 558075x^13 + 908302x^12 + 274491x^11 + 259680x^10 + 62761x^9 + 63297x^8 + 693x^7 + 10925x^6 + 846x^5 + 1881x^4 + 286x^3 + 45x^2 + 6x + 1	\( 3^{48}\cdot 5^{27}\cdot 7^{24} \)	$C_3\times C_{12}$ (as 36T3)	$[14, 518]$ (GRH)
36.36.129739382499069208406967320777552926214641189868504834496493597.1	x^36 - x^35 - 36x^34 + 35x^33 + 594x^32 - 560x^31 - 5952x^30 + 5426x^29 + 40454x^28 - 35554x^27 - 197288x^26 + 166634x^25 + 712180x^24 - 576199x^23 - 1934944x^22 + 1494700x^21 + 3983738x^20 - 2928983x^19 - 6208136x^18 + 4331906x^17 + 7259749x^16 - 4795428x^15 - 6263633x^14 + 3907332x^13 + 3879994x^12 - 2278575x^11 - 1655004x^10 + 908896x^9 + 456052x^8 - 230058x^7 - 73571x^6 + 32327x^5 + 6018x^4 - 1922x^3 - 216x^2 + 24x + 1	\( 7^{30}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.36.334717470607298852954929976123524497086119009458311989825932357.1	x^36 - 36x^34 - x^33 + 594x^32 + 33x^31 - 5952x^30 - 495x^29 + 40455x^28 + 4467x^27 - 197316x^26 - 27054x^25 + 712529x^24 + 116154x^23 - 1937496x^22 - 364067x^21 + 3995883x^20 + 845295x^19 - 6247579x^18 - 1459998x^17 + 7348878x^16 + 1867585x^15 - 6403833x^14 - 1746123x^13 + 4030936x^12 + 1165464x^11 - 1761969x^10 - 534544x^9 + 502173x^8 + 158337x^7 - 83631x^6 - 27162x^5 + 6471x^4 + 2145x^3 - 108x^2 - 36x + 1	\( 3^{54}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.36.83002434816200303192485381664744316138553796477615833282470703125.1	x^36 - 60x^34 - 4x^33 + 1566x^32 + 192x^31 - 23491x^30 - 3897x^29 + 225594x^28 + 44322x^27 - 1463265x^26 - 315834x^25 + 6595406x^24 + 1493037x^23 - 20954832x^22 - 4829603x^21 + 47178711x^20 + 10844637x^19 - 75203780x^18 - 16934940x^17 + 84384807x^16 + 18269987x^15 - 65933622x^14 - 13456680x^13 + 35213992x^12 + 6642171x^11 - 12459300x^10 - 2131789x^9 + 2769012x^8 + 423228x^7 - 351580x^6 - 47619x^5 + 21066x^4 + 2501x^3 - 360x^2 - 24x + 1	\( 3^{54}\cdot 5^{27}\cdot 7^{24} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.36.427234358221042548307849539075210285658672906173431042163517056117.1	x^36 - x^35 - 62x^34 + 61x^33 + 1673x^32 - 1613x^31 - 25920x^30 + 24367x^29 + 256293x^28 - 233479x^27 - 1701570x^26 + 1490905x^25 + 7778369x^24 - 6496035x^23 - 24747903x^22 + 19486869x^21 + 54933520x^20 - 40274564x^19 - 84897695x^18 + 57204830x^17 + 90928152x^16 - 55712580x^15 - 66860091x^14 + 37010766x^13 + 33119347x^12 - 16533426x^11 - 10663861x^10 + 4809468x^9 + 2090230x^8 - 852134x^7 - 220627x^6 + 79647x^5 + 10022x^4 - 2741x^3 - 216x^2 + 24x + 1	\( 3^{18}\cdot 7^{24}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.0.774789154400244180875705134624385939659291459329426288604736328125.1	x^36 + 20x^34 - 8x^33 + 297x^32 + 296x^31 + 4101x^30 + 5256x^29 + 51773x^28 + 53598x^27 + 332705x^26 + 342662x^25 + 1750974x^24 + 1731140x^23 + 8191554x^22 + 7356788x^21 + 32849307x^20 + 24190390x^19 + 78438432x^18 + 37935396x^17 + 151542669x^16 - 46316204x^15 + 205249519x^14 - 67004790x^13 + 240290549x^12 - 33283168x^11 + 136087020x^10 - 14642248x^9 + 73074896x^8 + 3567392x^7 + 38305280x^6 + 2431744x^5 + 14561024x^4 + 1893376x^3 + 246784x^2 + 30720x + 4096	\( 5^{27}\cdot 7^{24}\cdot 13^{24} \)	$C_3\times C_{12}$ (as 36T3)	$[2, 26426]$ (GRH)
36.36.13395272227285527394091512575412214059512641429074108600616455078125.1	x^36 - 3x^35 - 69x^34 + 194x^33 + 2100x^32 - 5496x^31 - 37141x^30 + 90237x^29 + 423339x^28 - 958293x^27 - 3261144x^26 + 6959373x^25 + 17329413x^24 - 35601552x^23 - 63680853x^22 + 129922520x^21 + 159349053x^20 - 337769112x^19 - 259925101x^18 + 616092369x^17 + 246176712x^16 - 763692862x^15 - 79242273x^14 + 608220999x^13 - 78776304x^12 - 281930013x^11 + 88315116x^10 + 63028536x^9 - 29887359x^8 - 4534752x^7 + 3622138x^6 - 118797x^5 - 108390x^4 + 1113x^3 + 1272x^2 + 69x + 1	\( 3^{48}\cdot 5^{27}\cdot 7^{30} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.0.28197918371845586674949922450633451482314152257891038265473838050413.1	x^36 - x^35 + 7x^34 - 6x^33 + 41x^32 - 28x^31 + 232x^30 - 113x^29 + 1309x^28 - 363x^27 + 7426x^26 - 441x^25 + 42456x^24 - 101318x^23 + 352967x^22 - 663683x^21 + 2072259x^20 - 3583588x^19 + 11371361x^18 - 18367076x^17 + 61510126x^16 - 92113055x^15 + 332604279x^14 - 454711727x^13 + 1805546016x^12 - 2205586425x^11 + 2694284257x^10 - 3288980695x^9 + 4015581262x^8 - 4889475633x^7 + 5960098340x^6 - 7187883304x^5 + 8722143913x^4 - 10128755357x^3 + 12146435707x^2 - 11863960458x + 13841287201	\( 13^{33}\cdot 19^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.75781540662375302882102919875947077697351951905720209039476085751808.1	x^36 - 65x^34 + 1859x^32 - 30940x^30 + 334113x^28 - 2472002x^26 + 12905893x^24 - 48291581x^22 + 130412230x^20 - 254526168x^18 + 358202936x^16 - 361633805x^14 + 259562875x^12 - 130409526x^10 + 44665010x^8 - 9967789x^6 + 1337973x^4 - 92274x^2 + 2197	\( 2^{36}\cdot 7^{24}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.0.322589924575014201866984217657349278106004681202180683612823486328125.1	x^36 - 3x^35 + 27x^34 - 91x^33 + 546x^32 - 879x^31 + 6766x^30 - 8742x^29 + 79572x^28 - 109299x^27 + 677004x^26 - 773109x^25 + 4800131x^24 - 1125369x^23 + 20272767x^22 - 7098692x^21 + 86239137x^20 - 79515333x^19 + 179581154x^18 - 149538474x^17 + 288977244x^16 - 145690029x^15 + 279084165x^14 - 159459888x^13 + 279984346x^12 - 206283594x^11 + 180939411x^10 - 94040687x^9 + 79247853x^8 - 16999917x^7 + 2966770x^6 - 471501x^5 + 68880x^4 - 4902x^3 + 336x^2 - 21x + 1	\( 3^{48}\cdot 5^{27}\cdot 13^{24} \)	$C_3\times C_{12}$ (as 36T3)	$[10, 20410]$ (GRH)
36.0.4206720564246829878857376609821276819265009722410575911914825439453125.1	x^36 - 9x^35 + 52x^34 - 208x^33 + 763x^32 - 2473x^31 + 7774x^30 - 21073x^29 + 55175x^28 - 126998x^27 + 301106x^26 - 609219x^25 + 1314509x^24 - 2161107x^23 + 4589322x^22 - 5937815x^21 + 16165015x^20 - 18096988x^19 + 93286907x^18 - 201850025x^17 + 928905669x^16 - 2319599256x^15 + 7079450070x^14 - 15030668107x^13 + 33733591464x^12 - 57654424490x^11 + 98895340726x^10 - 131090685506x^9 + 175257385390x^8 - 177210083687x^7 + 186781470161x^6 - 135288523899x^5 + 123224165522x^4 - 71789180593x^3 + 47347720069x^2 - 20963341532x + 32332243789	\( 5^{18}\cdot 7^{24}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.6992452104054031444913323530856475516697486875506646931171417236328125.1	x^36 + 26x^34 - 14x^33 + 495x^32 + 476x^31 + 8655x^30 + 11760x^29 + 134201x^28 + 164766x^27 + 1245581x^26 + 1641584x^25 + 10003278x^24 + 17605574x^23 + 73281546x^22 + 115896662x^21 + 420977265x^20 + 540199534x^19 + 1258004478x^18 + 1344337974x^17 + 2875411227x^16 + 1250872126x^15 + 4489581151x^14 + 2102836554x^13 + 7030264277x^12 + 4148560640x^11 + 5060682060x^10 + 2659981016x^9 + 2836346576x^8 + 701556128x^7 + 885129728x^6 + 244545280x^5 + 290205440x^4 + 99398656x^3 + 61465600x^2 + 14751744x + 9834496	\( 5^{27}\cdot 7^{24}\cdot 19^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.9765153453691149470292712667475504049384715601795025169849395751953125.1	x^36 + 30x^34 - 4x^33 + 261x^32 - 153x^31 - 151x^30 - 2232x^29 - 12486x^28 - 17223x^27 - 40545x^26 - 69369x^25 + 219791x^24 + 80127x^23 + 2244003x^22 + 3598192x^21 + 11476701x^20 + 27824757x^19 + 55944685x^18 + 122149350x^17 + 246367347x^16 + 364897592x^15 + 821493693x^14 + 857521695x^13 + 1993614817x^12 + 1740513231x^11 + 3580401840x^10 + 2916789821x^9 + 5006204397x^8 + 3581139363x^7 + 5853643895x^6 + 2918077776x^5 + 5636834421x^4 + 1219028741x^3 + 3957820605x^2 + 187966461x + 1759249171	\( 3^{54}\cdot 5^{27}\cdot 7^{30} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.31552276316229132122682846845993932976454945211245315153186594370879488.1	x^36 - 75x^34 - 12x^33 + 2466x^32 + 708x^31 - 46837x^30 - 17640x^29 + 571011x^28 + 242208x^27 - 4707315x^26 - 2006406x^25 + 26995916x^24 + 10295208x^23 - 109335657x^22 - 31916038x^21 + 314149779x^20 + 51886254x^19 - 635559496x^18 - 8009280x^17 + 884137635x^16 - 135354640x^15 - 806374134x^14 + 261081888x^13 + 440313718x^12 - 223846182x^11 - 116564358x^10 + 92545112x^9 + 3573618x^8 - 15365958x^7 + 3090085x^6 + 371922x^5 - 162048x^4 + 8268x^3 + 1335x^2 - 120x + 1	\( 2^{36}\cdot 3^{48}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.0.50263695010347434765870190422659414897457208738397988679495618135108933.1	x^36 - x^35 + 55x^34 - 56x^33 + 1322x^32 - 1379x^31 + 18345x^30 - 19781x^29 + 163941x^28 - 185158x^27 + 1002183x^26 - 1208558x^25 + 4408145x^24 - 5825079x^23 + 15017355x^22 - 22388250x^21 + 45074515x^20 - 76386185x^19 + 138221149x^18 - 246519877x^17 + 444193428x^16 - 703532376x^15 + 1351689873x^14 - 1601650713x^13 + 3605252587x^12 - 2754343527x^11 + 8327023718x^10 - 3127376355x^9 + 17005484365x^8 - 1760009807x^7 + 30454580477x^6 - 1674794190x^5 + 45670623647x^4 - 8083073282x^3 + 45711370125x^2 - 12457929369x + 21305513503	\( 3^{18}\cdot 7^{30}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.91153169226034327635845833383424381414975980898647673428058624267578125.1	x^36 - 9x^35 - 50x^34 + 617x^33 + 853x^32 - 18792x^31 - 857x^30 + 335261x^29 - 196141x^28 - 3888989x^27 + 3669506x^26 + 30780881x^25 - 36431516x^24 - 169652114x^23 + 234314708x^22 + 651588327x^21 - 1036003947x^20 - 1707996749x^19 + 3202795146x^18 + 2878146054x^17 - 6878941470x^16 - 2583494750x^15 + 9996118628x^14 - 21924592x^13 - 9335764683x^12 + 2679130010x^11 + 5110286208x^10 - 2690155249x^9 - 1371167792x^8 + 1122925954x^7 + 110647669x^6 - 212313517x^5 + 12391295x^4 + 16680904x^3 - 1356543x^2 - 505872x + 2521	\( 5^{27}\cdot 7^{30}\cdot 13^{24} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.36.235168055015185353161031494672207623739277412596389718353748321533203125.1	x^36 - 12x^35 - 18x^34 + 701x^33 - 1014x^32 - 17841x^31 + 46936x^30 + 258882x^29 - 903138x^28 - 2337941x^27 + 10357989x^26 + 13221999x^25 - 78595284x^24 - 41557041x^23 + 412140267x^22 + 15579817x^21 - 1517917803x^20 + 487842723x^19 + 3915786614x^18 - 2406058791x^17 - 6918173706x^16 + 6167942709x^15 + 7929872535x^14 - 9724914267x^13 - 5143540984x^12 + 9570453009x^11 + 944334231x^10 - 5631020628x^9 + 964975548x^8 + 1795533942x^7 - 646510065x^6 - 255756294x^5 + 139324140x^4 + 10150922x^3 - 10886424x^2 + 71286x + 288991	\( 3^{54}\cdot 5^{27}\cdot 13^{24} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.0.1078971204830304425585378172062472691337937003390705901956047673685421797.1	x^36 - 9x^35 + 16x^34 + 26x^33 + 181x^32 - 1445x^31 + 2604x^30 - 2755x^29 + 9910x^28 - 30401x^27 + 82223x^26 - 197798x^25 + 452764x^24 - 1456052x^23 + 2709150x^22 + 1162726x^21 - 8566260x^20 - 8520187x^19 + 71726367x^18 - 146575781x^17 + 219113520x^16 - 450921336x^15 + 971562775x^14 - 1564444576x^13 + 2406821450x^12 - 4029586993x^11 + 5513868716x^10 - 4668590893x^9 + 1306426495x^8 + 1351057679x^7 - 782004588x^6 - 648398298x^5 + 17515236x^4 + 769014408x^3 + 45608456x^2 - 600274541x + 239345231	\( 7^{24}\cdot 37^{33} \)	$C_3\times C_{12}$ (as 36T3)	$[3, 3, 117, 117]$ (GRH)
36.0.1751503182280629962324239137560707045640770185903918052149707794189453125.1	x^36 - 3x^35 + 9x^34 - 13x^33 + 153x^32 - 567x^31 + 1779x^30 - 3546x^29 + 13113x^28 - 47895x^27 + 161433x^26 - 415143x^25 + 1104025x^24 - 3273684x^23 + 10489914x^22 - 30772058x^21 + 84771678x^20 - 222454680x^19 + 611810329x^18 - 1550727096x^17 + 3898113045x^16 - 8261897447x^15 + 17439706425x^14 - 31141822035x^13 + 56950578528x^12 - 87157837233x^11 + 133566120075x^10 - 164805518158x^9 + 193914680868x^8 - 179069923941x^7 + 186530283006x^6 - 188488040397x^5 + 232594560831x^4 - 140326122819x^3 + 227273426838x^2 - 163796723415x + 254886323381	\( 3^{48}\cdot 5^{18}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.2911365736123781834882894128093567062854751804695669420063495635986328125.1	x^36 - 3x^35 + 33x^34 - 97x^33 + 744x^32 - 1893x^31 + 13664x^30 - 33576x^29 + 238560x^28 - 588745x^27 + 2734752x^26 - 6216015x^25 + 25176457x^24 - 48643407x^23 + 187250949x^22 - 366416386x^21 + 1263887211x^20 - 2483705709x^19 + 5333249622x^18 - 8164618602x^17 + 15104700468x^16 - 13400914841x^15 + 15331684227x^14 - 12098329740x^13 + 10527569472x^12 - 4556162778x^11 + 4668826305x^10 - 1640038211x^9 + 1696221807x^8 - 449229501x^7 + 699314280x^6 - 75367485x^5 + 187711800x^4 + 52035172x^3 + 18826488x^2 + 3495057x + 1874161	\( 3^{48}\cdot 5^{27}\cdot 19^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.3571176196381911298524292556211763388204839472594427825914130981966768013.1	x^36 - x^35 + 11x^34 - 13x^33 + 115x^32 - 157x^31 + 1203x^30 - 1853x^29 + 12627x^28 - 21533x^27 + 132979x^26 - 247293x^25 + 1404819x^24 + 345266x^23 + 11724580x^22 + 2966632x^21 + 117041296x^20 + 6421664x^19 + 1187724352x^18 - 187177344x^17 + 12115794176x^16 - 4485772800x^15 + 124146295808x^14 - 72077670400x^13 + 1277654446080x^12 - 1005260783616x^11 + 790941073408x^10 - 622313340928x^9 + 489637806080x^8 - 385242628096x^7 + 303113961472x^6 - 238437793792x^5 + 187636383744x^4 - 147102629888x^3 + 115964116992x^2 - 85899345920x + 68719476736	\( 13^{33}\cdot 31^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.3739759263561488214448481425151197673020924949514408774673938751220703125.1	x^36 - 9x^35 + 40x^34 - 93x^33 - 2x^32 + 978x^31 - 5277x^30 + 18201x^29 - 33611x^28 - 40454x^27 + 580156x^26 - 2428654x^25 + 6063184x^24 - 9282144x^23 + 10683683x^22 - 22090573x^21 + 50749698x^20 - 64733864x^19 + 165821771x^18 - 765022581x^17 + 2271992540x^16 - 3472565480x^15 + 1952471023x^14 + 519332948x^13 + 4974249937x^12 - 18527494830x^11 + 34673056498x^10 - 65961793774x^9 + 116764727313x^8 - 134118855581x^7 + 125862271939x^6 - 122395204267x^5 + 95870943525x^4 - 37664181986x^3 + 53097299592x^2 + 996547853x + 10152422981	\( 5^{27}\cdot 7^{24}\cdot 13^{30} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.7824257734407727258096221831729050732882821632000000000000000000000000000.1	x^36 - 105x^34 - 16x^33 + 4761x^32 + 1248x^31 - 123596x^30 - 41868x^29 + 2056674x^28 + 805868x^27 - 23292630x^26 - 9998316x^25 + 186077966x^24 + 84929628x^23 - 1071803142x^22 - 510857842x^21 + 4507244436x^20 + 2215904058x^19 - 13908705320x^18 - 6983909430x^17 + 31442289642x^16 + 15977803388x^15 - 51621469782x^14 - 26292514800x^13 + 60523405652x^12 + 30554706504x^11 - 49300418040x^10 - 24331055976x^9 + 26726967447x^8 + 12667223022x^7 - 9004822995x^6 - 4006725276x^5 + 1671476916x^4 + 681310144x^3 - 129046575x^2 - 47460006x + 405901	\( 2^{36}\cdot 3^{48}\cdot 5^{27}\cdot 7^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.8915622477387792008776526420485297744015759789756076873285322012614459392.1	x^36 + 91x^34 + 3731x^32 + 91364x^30 + 1493765x^28 + 17271618x^26 + 145978105x^24 + 919646455x^22 + 4365494770x^20 + 15684015256x^18 + 42607368076x^16 + 86981860147x^14 + 131846926939x^12 + 145558267218x^10 + 113655085362x^8 + 60003090875x^6 + 19902563681x^4 + 3618647942x^2 + 258474853	\( 2^{36}\cdot 7^{30}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.9685961927111642346915876016581426876940970357243365413693185450802413568.1	x^36 + 24x^34 - 12x^33 + 360x^32 - 84x^31 + 2630x^30 - 2412x^29 + 11523x^28 + 96x^27 + 91002x^26 - 46908x^25 - 220219x^24 - 320856x^23 + 4474812x^22 + 8165264x^21 - 7129761x^20 - 66767160x^19 - 67476264x^18 + 267892788x^17 + 928023510x^16 + 143463500x^15 - 3773616390x^14 - 5967524316x^13 + 4254421520x^12 + 24836211816x^11 + 27413396142x^10 - 22088255944x^9 - 97921001331x^8 - 98513884404x^7 + 41560681778x^6 + 245496957708x^5 + 373399441383x^4 + 324953099232x^3 + 191526766890x^2 + 65880963516x + 12160977767	\( 2^{99}\cdot 3^{48}\cdot 7^{24} \)	$C_3\times C_{12}$ (as 36T3)	$[3, 3, 234, 22698]$ (GRH)
36.36.9685961927111642346915876016581426876940970357243365413693185450802413568.1	x^36 - 96x^34 - 16x^33 + 3960x^32 + 1152x^31 - 93164x^30 - 35748x^29 + 1399617x^28 + 633928x^27 - 14244732x^26 - 7185408x^25 + 101630814x^24 + 55109544x^23 - 518477394x^22 - 295082980x^21 + 1910373432x^20 + 1121373960x^19 - 5094003336x^18 - 3042649560x^17 + 9770946912x^16 + 5873901604x^15 - 13272355962x^14 - 7951933872x^13 + 12401306684x^12 + 7325904048x^11 - 7580888508x^10 - 4344012424x^9 + 2779199601x^8 + 1490571564x^7 - 523046756x^6 - 234531744x^5 + 40444434x^4 + 8023128x^3 - 1974252x^2 + 134520x - 3023	\( 2^{99}\cdot 3^{48}\cdot 7^{24} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.0.18223999682577301331486554002999275479149290679843606302092196002570514037.1	x^36 - 9x^35 - 6x^34 + 302x^33 - 624x^32 - 3513x^31 + 13674x^30 + 14298x^29 - 120915x^28 + 16960x^27 + 705036x^26 - 447510x^25 - 3860961x^24 + 5881605x^23 + 13497015x^22 - 42557253x^21 - 7820376x^20 + 134349147x^19 + 12019540x^18 - 618372375x^17 + 715410807x^16 + 1940709560x^15 - 2960870652x^14 + 293208303x^13 + 14694026311x^12 - 2381175957x^11 - 10114588962x^10 + 31085975417x^9 + 12400497834x^8 - 49757150475x^7 - 290397941x^6 + 69843766965x^5 + 69916985034x^4 + 43030484656x^3 + 31088478201x^2 + 10559306385x + 6300259631	\( 3^{48}\cdot 7^{24}\cdot 13^{27} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.19865676195397711398725987827960270735894630080373118478444419023321956352.1	x^36 - 12x^35 + 120x^34 - 828x^33 + 5157x^32 - 26740x^31 + 128546x^30 - 546200x^29 + 2177147x^28 - 7884176x^27 + 26975312x^26 - 85116720x^25 + 254822270x^24 - 709486284x^23 + 1879297474x^22 - 4653122096x^21 + 10982223270x^20 - 24295546348x^19 + 51310501256x^18 - 101716601500x^17 + 192953738019x^16 - 343875076752x^15 + 588444243076x^14 - 945622774200x^13 + 1470275270855x^12 - 2150175684852x^11 + 3090474193456x^10 - 4158681286228x^9 + 5602128086021x^8 - 6986616644348x^7 + 9425727731754x^6 - 11556021388336x^5 + 15742746932912x^4 - 16012210942028x^3 + 15548809804884x^2 - 8434770285524x + 3561903327529	\( 2^{54}\cdot 7^{24}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.19865676195397711398725987827960270735894630080373118478444419023321956352.1	x^36 - 12x^35 - 36x^34 + 940x^33 - 927x^32 - 31316x^31 + 80914x^30 + 576272x^29 - 2182273x^28 - 6302752x^27 + 33144748x^26 + 39516048x^25 - 323192934x^24 - 95894188x^23 + 2132039314x^22 - 522495128x^21 - 9735028662x^20 + 5836708324x^19 + 30988574904x^18 - 26088563508x^17 - 68587862405x^16 + 69170933872x^15 + 104690525460x^14 - 116627921592x^13 - 109205998641x^12 + 126071424492x^11 + 77381360212x^10 - 85597408092x^9 - 36970755407x^8 + 34634932836x^7 + 11547553650x^6 - 7464917976x^5 - 2116489012x^4 + 652490564x^3 + 169180380x^2 - 2159532x - 771471	\( 2^{54}\cdot 7^{24}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.23001609434531037317435795350729577139835655058997834746673027296371146752.1	x^36 + 78x^34 + 2691x^32 + 54444x^30 + 722475x^28 + 6665490x^26 + 44226585x^24 + 215382726x^22 + 778931478x^20 + 2103342228x^18 + 4241564028x^16 + 6356268126x^14 + 7002607950x^12 + 5568808401x^10 + 3105527607x^8 + 1160101683x^6 + 269070984x^4 + 33633873x^2 + 1601613	\( 2^{36}\cdot 3^{54}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.249443392110565760356152376467177947898507670697337535040991674105418959533.1	x^36 - x^35 + 13x^34 - 36x^33 + 203x^32 - 778x^31 + 3610x^30 - 15179x^29 + 67057x^28 - 288915x^27 + 1260568x^26 - 5465175x^25 + 23770056x^24 + 93314596x^23 + 252043001x^22 + 606261535x^21 + 1391793921x^20 + 3110871488x^19 + 6921778679x^18 + 15098946046x^17 + 33742811734x^16 + 71304975349x^15 + 167520358953x^14 + 316968416161x^13 + 908921162436x^12 + 1051975883013x^11 + 1217338347379x^10 + 1408239461981x^9 + 1628085993424x^8 + 1880065729179x^7 + 2166332110118x^6 + 2485510712366x^5 + 2829751588081x^4 + 3166723749013x^3 + 3449677471933x^2 + 3423740047332x + 3138428376721	\( 13^{33}\cdot 37^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.449238657521288617873575771982141197761323383589614425066522712799093474917.1	x^36 - 3x^35 - 27x^34 + 137x^33 + 207x^32 - 1893x^31 + 1057x^30 + 9420x^29 - 18840x^28 + 12544x^27 + 65883x^26 - 229239x^25 + 159200x^24 + 167631x^23 - 2700417x^22 + 3836034x^21 + 19377618x^20 - 3061389x^19 - 51896833x^18 - 32759037x^17 + 96376791x^16 + 334585913x^15 + 313578288x^14 + 434132280x^13 + 951065917x^12 - 818916783x^11 - 3390929529x^10 - 4188723253x^9 - 861415446x^8 + 4170559728x^7 + 4762776347x^6 + 1981536447x^5 + 1704283443x^4 + 3516565010x^3 + 2834392743x^2 + 713505450x + 104897357	\( 3^{48}\cdot 37^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.494916467663075288417691500768863396509709128831881845460867298126220703125.1	x^36 - x^35 - 127x^34 + 126x^33 + 7328x^32 - 7203x^31 - 254655x^30 + 247577x^29 + 5956273x^28 - 5715774x^27 - 99258341x^26 + 93783066x^25 + 1216750731x^24 - 1128384881x^23 - 11167777905x^22 + 10123730642x^21 + 77372149977x^20 - 68170119347x^19 - 404867699989x^18 + 343756885869x^17 + 1590272002452x^16 - 1283637936946x^15 - 4628193618151x^14 + 3471389732603x^13 + 9777925862459x^12 - 6544984186949x^11 - 14568115911700x^10 + 8066810405369x^9 + 14716307928191x^8 - 5774232219857x^7 - 9516669187523x^6 + 1798484654352x^5 + 3510763848149x^4 + 66623171786x^3 - 532421593101x^2 - 84148737831x + 7203054951	\( 5^{18}\cdot 7^{30}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.747679671598239349782244492011516713922235706186072448481460365111232397117.1	x^36 - 3x^35 - 108x^34 + 314x^33 + 5133x^32 - 14553x^31 - 141455x^30 + 394602x^29 + 2507526x^28 - 6965157x^27 - 29988882x^26 + 84226455x^25 + 246806857x^24 - 714893316x^23 - 1398775770x^22 + 4292785887x^21 + 5364342456x^20 - 18168287730x^19 - 13333973109x^18 + 53510458269x^17 + 19430031183x^16 - 107555904357x^15 - 11332618518x^14 + 143867150712x^13 - 9214998883x^12 - 123510493746x^11 + 19994463534x^10 + 64078960801x^9 - 12437043336x^8 - 17931881889x^7 + 2702218315x^6 + 2080472373x^5 + 14312169x^4 - 34504929x^3 + 1294671x^2 + 21021x + 53	\( 3^{48}\cdot 7^{18}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.822654997589852745462607600081733488063942633416481504805386066436767578125.1	x^36 - 9x^35 - 74x^34 + 909x^33 + 1441x^32 - 38540x^31 + 29909x^30 + 883449x^29 - 1940661x^28 - 11622649x^27 + 41000690x^26 + 82185945x^25 - 475474126x^24 - 170531710x^23 + 3313200544x^22 - 1874661149x^21 - 14012133789x^20 + 17229198563x^19 + 34707820890x^18 - 66363236954x^17 - 44892472008x^16 + 142697506526x^15 + 15401207070x^14 - 183495454624x^13 + 32402227403x^12 + 145220963746x^11 - 46806011656x^10 - 71694298121x^9 + 27858490170x^8 + 21853214932x^7 - 8861546511x^6 - 3909998733x^5 + 1545247949x^4 + 363308426x^3 - 136694687x^2 - 12769152x + 4591091	\( 5^{27}\cdot 7^{30}\cdot 19^{24} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.36.1276845819882579242534370331281755436272121465523956260017136981964111328125.1	x^36 - 114x^34 - x^33 + 5859x^32 + 111x^31 - 180048x^30 - 5526x^29 + 3699240x^28 + 163470x^27 - 53820756x^26 - 3208830x^25 + 572790581x^24 + 44143254x^23 - 4540870752x^22 - 437624579x^21 + 27043916778x^20 + 3163735311x^19 - 121104847513x^18 - 16681810230x^17 + 405277633206x^16 + 63503538493x^15 - 1000011221073x^14 - 170766196161x^13 + 1779851366683x^12 + 312383052333x^11 - 2211527198037x^10 - 364422057685x^9 + 1829938769694x^8 + 239262351117x^7 - 941144446491x^6 - 61365660075x^5 + 268847902749x^4 - 9408191247x^3 - 32267765898x^2 + 5446221264x - 98828729	\( 3^{54}\cdot 5^{18}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.1326595912169561221084879732571729733056225211740623097203928593533001998853.1	x^36 - x^35 - 97x^34 + 98x^33 + 4058x^32 - 4149x^31 - 96839x^30 + 100351x^29 + 1472129x^28 - 1547896x^27 - 15099705x^26 + 16117232x^25 + 108034873x^24 - 116987282x^23 - 549690124x^22 + 602644282x^21 + 2008422826x^20 - 2221244124x^19 - 5280367442x^18 + 5859024782x^17 + 9939296148x^16 - 10975518510x^15 - 13230545958x^14 + 14360136230x^13 + 12203357336x^12 - 12756349726x^11 - 7568837976x^10 + 7354733074x^9 + 3020402597x^8 - 2560846304x^7 - 717542006x^6 + 475096085x^5 + 83002961x^4 - 35766984x^3 - 1884048x^2 + 471498x + 18773	\( 13^{33}\cdot 19^{30} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.0.1557079951247999724699376224646452411705566349268816543288528919219970703125.1	x^36 - 3x^35 - 3x^34 + 8x^33 - 15x^32 - 210x^31 - 385x^30 + 5415x^29 + 6351x^28 - 36200x^27 + 130713x^26 + 121467x^25 - 1894259x^24 + 441060x^23 + 14119596x^22 - 22878764x^21 - 43702461x^20 + 226149234x^19 - 26520393x^18 - 976832769x^17 + 3135439767x^16 - 4935139658x^15 + 2592680742x^14 + 2242273917x^13 + 11620240143x^12 - 26596418232x^11 + 69063367278x^10 - 65694612305x^9 + 136411565292x^8 - 109764491523x^7 + 123111472419x^6 - 18291665040x^5 + 69893697486x^4 - 64890324348x^3 + 101791204893x^2 - 51149414124x + 22848924331	\( 3^{48}\cdot 5^{27}\cdot 13^{30} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.2122385621634236957629629819380210388821114065623143007226288318634033203125.1	x^36 - 12x^35 - 42x^34 + 1061x^33 - 1350x^32 - 37617x^31 + 129380x^30 + 647814x^29 - 3761226x^28 - 4267081x^27 + 57623793x^26 - 33213237x^25 - 505422576x^24 + 881990283x^23 + 2405576283x^22 - 7520229251x^21 - 4085328615x^20 + 33458575323x^19 - 14028012138x^18 - 80883403815x^17 + 85769496648x^16 + 98511159201x^15 - 181248893193x^14 - 38964520557x^13 + 195904466188x^12 - 32629612377x^11 - 118260246567x^10 + 43807175472x^9 + 40452413076x^8 - 20325698838x^7 - 7481712385x^6 + 4554136782x^5 + 636738900x^4 - 467339570x^3 - 14193342x^2 + 15094344x + 143461	\( 3^{54}\cdot 5^{27}\cdot 19^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.5703883888383233171152145715330477984271576969728000000000000000000000000000.1	x^36 - 12x^35 + 132x^34 - 964x^33 + 6462x^32 - 35316x^31 + 178450x^30 - 786024x^29 + 3224823x^28 - 11908044x^27 + 41299005x^26 - 131377506x^25 + 394830604x^24 - 1099808568x^23 + 2908195344x^22 - 7183606822x^21 + 16934574060x^20 - 37490949888x^19 + 79573970631x^18 - 159170870298x^17 + 307045487688x^16 - 559522976788x^15 + 986494828509x^14 - 1636097978718x^13 + 2640055694434x^12 - 4009568149062x^11 + 6031372465950x^10 - 8462912247118x^9 + 11730030510336x^8 - 14696441624388x^7 + 19080633257687x^6 - 22224248926686x^5 + 28052657251047x^4 - 27230959523324x^3 + 25534530115587x^2 - 13710464052024x + 6311298334321	\( 2^{36}\cdot 3^{54}\cdot 5^{27}\cdot 7^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.7061066244864387270901673616087860193289967390430413386582332193634959491072.1	x^36 - 12x^35 + 114x^34 - 760x^33 + 4383x^32 - 21156x^31 + 90754x^30 - 342108x^29 + 1163349x^28 - 3564384x^27 + 10049106x^26 - 26143512x^25 + 63374392x^24 - 142650108x^23 + 302605242x^22 - 610491148x^21 + 1185262668x^20 - 2187042156x^19 + 3793817988x^18 - 6146155488x^17 + 9744782631x^16 - 15541129312x^15 + 23994963972x^14 - 33027263592x^13 + 41712329035x^12 - 53997803892x^11 + 81557728002x^10 - 120007128040x^9 + 143740618215x^8 - 131526335532x^7 + 150054670958x^6 - 234723540492x^5 + 430616836146x^4 - 504014501660x^3 + 443927747412x^2 - 219262177512x + 66191511889	\( 2^{99}\cdot 3^{54}\cdot 7^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.7061066244864387270901673616087860193289967390430413386582332193634959491072.1	x^36 - 12x^35 - 30x^34 + 872x^33 - 1233x^32 - 25380x^31 + 78226x^30 + 379620x^29 - 1758891x^28 - 2937888x^27 + 22076274x^26 + 6821832x^25 - 173279528x^24 + 79991748x^23 + 885664602x^22 - 877781932x^21 - 2962642644x^20 + 4262622420x^19 + 6317132340x^18 - 12265171104x^17 - 7935268665x^16 + 22118582240x^15 + 4488876612x^14 - 25142360904x^13 + 1143439675x^12 + 17833884876x^11 - 3207637326x^10 - 7708877992x^9 + 1857934743x^8 + 1926063060x^7 - 485300914x^6 - 247363308x^5 + 56713698x^4 + 12546916x^3 - 2193228x^2 - 170472x + 3457	\( 2^{99}\cdot 3^{54}\cdot 7^{24} \)	$C_3\times C_{12}$ (as 36T3)	Trivial (GRH)
36.36.8216251102044589607143313691057181287626972114083156077958643436431884765625.1	x^36 - 9x^35 - 65x^34 + 767x^33 + 1348x^32 - 27862x^31 + 1248x^30 + 570596x^29 - 539471x^28 - 7345274x^27 + 11035141x^26 + 62715081x^25 - 119635996x^24 - 365138709x^23 + 822660108x^22 + 1467238032x^21 - 3815197767x^20 - 4065525074x^19 + 12253153691x^18 + 7632713374x^17 - 27502514595x^16 - 9230490750x^15 + 42972000803x^14 + 6151376608x^13 - 45930613858x^12 - 541428095x^11 + 32430382933x^10 - 2537946464x^9 - 14234297497x^8 + 1972347494x^7 + 3506699274x^6 - 611541017x^5 - 408560825x^4 + 74320909x^3 + 14619917x^2 - 1560887x - 127399	\( 5^{27}\cdot 7^{24}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	$[2]$ (GRH)
36.36.8216251102044589607143313691057181287626972114083156077958643436431884765625.2	x^36 - 9x^35 - 65x^34 + 767x^33 + 1348x^32 - 27862x^31 + 1248x^30 + 570596x^29 - 539471x^28 - 7345079x^27 + 11033971x^26 + 62716641x^25 - 119639181x^24 - 365203449x^23 + 823243158x^22 + 1467032372x^21 - 3822699612x^20 - 4052765184x^19 + 12292532381x^18 + 7514841399x^17 - 27583235170x^16 - 8685061710x^15 + 42894256903x^14 + 4650174763x^13 - 45171089573x^12 + 2033087095x^11 + 30731222743x^10 - 5227780689x^9 - 12313025417x^8 + 3507716589x^7 + 2347697989x^6 - 949622917x^5 - 86946285x^4 + 56606849x^3 + 1187472x^2 - 996492x - 54664	\( 5^{27}\cdot 7^{24}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	$[2]$ (GRH)
36.0.8271239922641569611168572203596233566179805157456691895516946594759832502272.1	x^36 + 42x^34 - 12x^33 + 1062x^32 - 228x^31 + 18566x^30 - 3600x^29 + 244113x^28 - 26424x^27 + 2554524x^26 - 61164x^25 + 21412793x^24 + 1371384x^23 + 149530704x^22 + 27331592x^21 + 868074111x^20 + 236070696x^19 + 4266665390x^18 + 1820606652x^17 + 18620376480x^16 + 10373579276x^15 + 68331137634x^14 + 47710693968x^13 + 248970781930x^12 + 256259966832x^11 + 858443199054x^10 + 837202367648x^9 + 2334611060583x^8 + 3325143168012x^7 + 10600537969942x^6 + 18337221438216x^5 + 35763130408821x^4 + 38912147678040x^3 + 41429002968336x^2 + 21093689536332x + 9724193509447	\( 2^{54}\cdot 3^{48}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.8271239922641569611168572203596233566179805157456691895516946594759832502272.1	x^36 - 114x^34 - 12x^33 + 5742x^32 + 1020x^31 - 168842x^30 - 36360x^29 + 3229485x^28 + 703864x^27 - 42416064x^26 - 7921692x^25 + 393837365x^24 + 49313304x^23 - 2622544680x^22 - 102135304x^21 + 12569299335x^20 - 808250712x^19 - 43114770166x^18 + 7549082028x^17 + 104325807096x^16 - 29535704788x^15 - 174043844046x^14 + 65924502360x^13 + 194157715726x^12 - 88530910560x^11 - 139310773122x^10 + 71713506368x^9 + 60595492083x^8 - 33960132372x^7 - 14319635826x^6 + 8664074736x^5 + 1436547993x^4 - 990979704x^3 - 26527284x^2 + 33492924x - 126541	\( 2^{54}\cdot 3^{48}\cdot 13^{33} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.0.9191228435463896118643414243850705299591960444061012799480281884689056267053.1	x^36 - x^35 + 15x^34 - 37x^33 + 255x^32 - 893x^31 + 4759x^30 - 19301x^29 + 93071x^28 - 401357x^27 + 1858759x^26 - 8222325x^25 + 37455807x^24 + 144852694x^23 + 445307204x^22 + 1282984056x^21 + 3792495248x^20 + 10606823904x^19 + 32224237120x^18 + 85931335552x^17 + 280353392896x^16 + 664891407872x^15 + 2572605408256x^14 + 4493047158784x^13 + 26204297293824x^12 + 16117519663104x^11 + 9913428803584x^10 + 6097468129280x^9 + 3750377816064x^8 + 2306745565184x^7 + 1418798825472x^6 + 872616558592x^5 + 536602476544x^4 + 329638739968x^3 + 201863462912x^2 + 120259084288x + 68719476736	\( 13^{33}\cdot 43^{24} \)	$C_3\times C_{12}$ (as 36T3)	n/a
36.36.10924451324402501022100983006336490133035923719372600153527586154197811111957.1	x^36 - 9x^35 - 74x^34 + 906x^33 + 1465x^32 - 38375x^31 + 28176x^30 + 881049x^29 - 1892871x^28 - 11630750x^27 + 40364678x^26 + 82284019x^25 - 470447773x^24 - 160121713x^23 + 3263481172x^22 - 2057742341x^21 - 13374176751x^20 + 18261358636x^19 + 29791639547x^18 - 67146393883x^17 - 26075281081x^16 + 131524497452x^15 - 18736332340x^14 - 147685422825x^13 + 62851529470x^12 + 98707302558x^11 - 60074993232x^10 - 39397313544x^9 + 29752270500x^8 + 8975560111x^7 - 8221358547x^6 - 1005405651x^5 + 1224100668x^4 + 27696257x^3 - 85804113x^2 + 2030710x + 1923169	\( 3^{18}\cdot 13^{33}\cdot 19^{24} \)	$C_3\times C_{12}$ (as 36T3)	$[2, 2]$ (GRH)