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 55)

Label	Polynomial	Discriminant	Galois group	Class group
27.27.706965049015104706497203195837614914543357369.1	x^27 - 27x^25 + 324x^23 - 2277x^21 + 10395x^19 - 32319x^17 + 69768x^15 - 104652x^13 + 107406x^11 - 72930x^9 + 30888x^7 - 7371x^5 + 819x^3 - 27x - 1	\( 3^{94} \)	$C_{27}$ (as 27T1)	Trivial (GRH)
27.27.93991579198394673195940551085616659931617170424829641.1	x^27 - x^26 - 52x^25 + 47x^24 + 1128x^23 - 914x^22 - 13369x^21 + 9612x^20 + 95357x^19 - 60102x^18 - 425693x^17 + 231576x^16 + 1201391x^15 - 553157x^14 - 2121177x^13 + 810403x^12 + 2271851x^11 - 706862x^10 - 1399735x^9 + 342875x^8 + 461618x^7 - 78149x^6 - 74294x^5 + 4948x^4 + 4861x^3 + 271x^2 - 34x - 1	\( 109^{26} \)	$C_{27}$ (as 27T1)	Trivial (GRH)
27.27.3287590482487420232312619225433719761322768037503974231209.1	x^27 - x^26 - 78x^25 + 175x^24 + 2388x^23 - 8354x^22 - 33013x^21 + 180016x^20 + 127774x^19 - 1968453x^18 + 1782518x^17 + 10489594x^16 - 23282154x^15 - 17166283x^14 + 103371060x^13 - 63556949x^12 - 176991137x^11 + 284942103x^10 + 20494295x^9 - 355135692x^8 + 239709074x^7 + 92044084x^6 - 184127684x^5 + 70412054x^4 + 8685910x^3 - 12922671x^2 + 3203525x - 255583	\( 163^{26} \)	$C_{27}$ (as 27T1)	$[2, 2]$ (GRH)
27.27.1151231499063623584349492991499498083339556847040831466248681.1	x^27 - 189x^25 + 15876x^23 - 781011x^21 + 24958395x^19 - 543185433x^17 + 8208135432x^15 - 86185422036x^13 + 619174216206x^11 - 2942988558510x^9 + 8725095491112x^7 - 14574875422653x^5 + 11336014217619x^3 - 2616003280989x - 315928389203	\( 3^{94}\cdot 7^{18} \)	$C_{27}$ (as 27T1)	$[3]$ (GRH)
27.27.1151231499063623584349492991499498083339556847040831466248681.2	x^27 - 189x^25 + 15876x^23 - 781011x^21 + 24958395x^19 - 543185433x^17 + 8208135432x^15 - 86185422036x^13 + 619174216206x^11 - 2942988558510x^9 + 8725095491112x^7 - 14574875422653x^5 + 11336014217619x^3 - 2616003280989x - 191719986857	\( 3^{94}\cdot 7^{18} \)	$C_{27}$ (as 27T1)	$[3]$ (GRH)
27.27.1808013057924621803706133777735157383417426695926299555844999521.1	x^27 - x^26 - 130x^25 + 97x^24 + 6904x^23 - 3280x^22 - 199218x^21 + 36137x^20 + 3502857x^19 + 387789x^18 - 39562422x^17 - 14938296x^16 + 292752760x^15 + 176273890x^14 - 1416926864x^13 - 1094616402x^12 + 4408831829x^11 + 3876101969x^10 - 8563493173x^9 - 7794039480x^8 + 9927852445x^7 + 8336484081x^6 - 6439483933x^5 - 4024809305x^4 + 2109337058x^3 + 601104909x^2 - 208051850x - 1762213	\( 271^{26} \)	$C_{27}$ (as 27T1)	Trivial (GRH)
27.27.79502042287804104995388608594472718525612115183651404436672117601.1	x^27 - 351x^25 + 54756x^23 - 5002569x^21 + 296891595x^19 - 11999818467x^17 + 336756810312x^15 - 6566757801084x^13 + 87614373819726x^11 - 773386139272890x^9 + 4258173096231912x^7 - 13210014264446727x^5 + 19081131715311939x^3 - 8177627877990831x - 2175481232872831	\( 3^{94}\cdot 13^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.79502042287804104995388608594472718525612115183651404436672117601.2	x^27 - 351x^25 + 54756x^23 - 5002569x^21 + 296891595x^19 - 11999818467x^17 + 336756810312x^15 - 6566757801084x^13 + 87614373819726x^11 - 773386139272890x^9 + 4258173096231912x^7 - 13210014264446727x^5 + 19081131715311939x^3 - 8177627877990831x - 920226642090821	\( 3^{94}\cdot 13^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.11082033513026159843197131857404812003970296978813351756002427720121.1	x^27 - x^26 - 182x^25 + 117x^24 + 13618x^23 - 9406x^22 - 563442x^21 + 525111x^20 + 14278105x^19 - 18161357x^18 - 227967713x^17 + 379632386x^16 + 2241789500x^15 - 4722897643x^14 - 12462752110x^13 + 33279114690x^12 + 31181666728x^11 - 119083238707x^10 - 8689190338x^9 + 181478462936x^8 - 57176007802x^7 - 75331044168x^6 + 18626907295x^5 + 11999475590x^4 - 1573415186x^3 - 576163073x^2 + 46387161x + 743723	\( 379^{26} \)	$C_{27}$ (as 27T1)	Trivial (GRH)
27.27.73614397307175798532497185733881845387702404681973260785482012855329.1	x^27 - 513x^25 + 116964x^23 - 15617943x^21 + 1354686795x^19 - 80025043581x^17 + 3282297025608x^15 - 93545465229828x^13 + 1824136571981646x^11 - 23533613799022470x^9 + 189376374570957288x^7 - 858649698338772249x^5 + 1812704918715185859x^3 - 1135430553480940593x - 319768342177193387	\( 3^{94}\cdot 19^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.73614397307175798532497185733881845387702404681973260785482012855329.2	x^27 - 513x^25 + 116964x^23 - 15617943x^21 + 1354686795x^19 - 80025043581x^17 + 3282297025608x^15 - 93545465229828x^13 + 1824136571981646x^11 - 23533613799022470x^9 + 189376374570957288x^7 - 858649698338772249x^5 + 1812704918715185859x^3 - 1135430553480940593x - 4600558507235203	\( 3^{94}\cdot 19^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.153057165655742785694240270408062158957719092936539775009144398818809.1	x^27 - x^26 - 270x^25 + 47x^24 + 29577x^23 + 3337x^22 - 1780259x^21 - 192801x^20 + 66361580x^19 - 4080349x^18 - 1617344119x^17 + 516991856x^16 + 26245873136x^15 - 16092388946x^14 - 281167865555x^13 + 254179800245x^12 + 1920886337379x^11 - 2242620213654x^10 - 7833979925097x^9 + 10946482266142x^8 + 16962632962667x^7 - 27783814512537x^6 - 14229439088616x^5 + 30919931451508x^4 - 2408923070548x^3 - 7952131380114x^2 + 1824983191615x - 89453361143	\( 7^{18}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.153057165655742785694240270408062158957719092936539775009144398818809.2	x^27 - x^26 - 270x^25 + 47x^24 + 29577x^23 + 17071x^22 - 1706248x^21 - 2065966x^20 + 56748543x^19 + 97784729x^18 - 1133435022x^17 - 2444680389x^16 + 13795117056x^15 + 35784378577x^14 - 100258381849x^13 - 319085698582x^12 + 393103177385x^11 + 1730848478672x^10 - 470512221204x^9 - 5450598257003x^8 - 2048147111227x^7 + 8688783015200x^6 + 7880177941710x^5 - 3967891227901x^4 - 7804346234595x^3 - 3131913897999x^2 - 284679967632x - 5532747569	\( 7^{18}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	$[3]$ (GRH)
27.27.353740923422167929660095172127764982174048848841031999908387732793569.1	x^27 - x^26 - 208x^25 + 123x^24 + 17870x^23 - 1088x^22 - 841786x^21 - 443292x^20 + 24039830x^19 + 27033889x^18 - 429353878x^17 - 739754812x^16 + 4721934257x^15 + 11204887862x^14 - 29627415002x^13 - 97647366531x^12 + 81012640811x^11 + 475857218485x^10 + 83530098447x^9 - 1173563894813x^8 - 978803617366x^7 + 1049934817162x^6 + 1660652330971x^5 + 298182116040x^4 - 410938972356x^3 - 136886280910x^2 + 26713087915x + 8539831241	\( 433^{26} \)	$C_{27}$ (as 27T1)	Trivial (GRH)
27.27.7511955241024825880501672185173495875424957194130773062050731864857009.1	x^27 - x^26 - 234x^25 + 451x^24 + 22410x^23 - 59336x^22 - 1146120x^21 + 3693810x^20 + 34438763x^19 - 128044212x^18 - 633592894x^17 + 2668309905x^16 + 7191540555x^15 - 34553534532x^14 - 49158187704x^13 + 278963008001x^12 + 190196186526x^11 - 1372095146729x^10 - 381761929893x^9 + 3905637763092x^8 + 497849168333x^7 - 5908214090044x^6 - 1034156707955x^5 + 4070335505780x^4 + 1245264135357x^3 - 878470562528x^2 - 387476751728x - 27950290933	\( 487^{26} \)	$C_{27}$ (as 27T1)	Trivial (GRH)
27.27.14107631800772057462614083047171090763038947897293819627757634951745561.1	x^27 - 327x^25 - 218x^24 + 43164x^23 + 43818x^22 - 3072165x^21 - 3647358x^20 + 131962812x^19 + 165292505x^18 - 3613267269x^17 - 4519002660x^16 + 64778023437x^15 + 78260935833x^14 - 767119231971x^13 - 876995136787x^12 + 5963472358983x^11 + 6362362120011x^10 - 29734911579460x^9 - 29277206700381x^8 + 90619763226495x^7 + 81336836424974x^6 - 153407836629198x^5 - 123198584898693x^4 + 115302813487550x^3 + 80431235416368x^2 - 13411789508832x - 7092040020823	\( 3^{36}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	$[3]$ (GRH)
27.27.14107631800772057462614083047171090763038947897293819627757634951745561.2	x^27 - 327x^25 - 218x^24 + 43164x^23 + 61476x^22 - 3018210x^21 - 6507954x^20 + 121903638x^19 + 347122817x^18 - 2891823192x^17 - 10299084090x^16 + 38866417215x^15 + 175020065793x^14 - 261230425254x^13 - 1695101848663x^12 + 460247647320x^11 + 9167918905077x^10 + 3708053868470x^9 - 27072768198312x^8 - 21922844820627x^7 + 41739348314777x^6 + 46953795423150x^5 - 28185634575723x^4 - 45243443721079x^3 + 1114518996171x^2 + 16368292431012x + 4826968628849	\( 3^{36}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	$[3]$ (GRH)
27.27.115645541170359168800904668451418896961215191921100766227083814325184041.1	x^27 - x^26 - 260x^25 + 127x^24 + 24978x^23 - 19668x^22 - 1241609x^21 + 1622160x^20 + 35778151x^19 - 67728086x^18 - 614779252x^17 + 1558672841x^16 + 6070505088x^15 - 20405620517x^14 - 29583496180x^13 + 148707111628x^12 + 27952037234x^11 - 564208979448x^10 + 257304955275x^9 + 1047941306021x^8 - 809764643713x^7 - 895854373113x^6 + 747910684042x^5 + 423859606824x^4 - 246881343980x^3 - 114088799811x^2 + 19932730946x + 9025899413	\( 541^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.494206476726811255379944367361178473261552448264840656699721419592855929.1	x^27 - 837x^25 + 311364x^23 - 67834107x^21 + 9600000795x^19 - 925265531169x^17 + 61919356816008x^15 - 2879250091944372x^13 + 91605614767388046x^11 - 1928241644177736030x^9 + 25316678528262981288x^7 - 187285883203400009301x^5 + 645095819922822254259x^3 - 659273750031016149957x - 254625961590055084699	\( 3^{94}\cdot 31^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.494206476726811255379944367361178473261552448264840656699721419592855929.2	x^27 - 837x^25 + 311364x^23 - 67834107x^21 + 9600000795x^19 - 925265531169x^17 + 61919356816008x^15 - 2879250091944372x^13 + 91605614767388046x^11 - 1928241644177736030x^9 + 25316678528262981288x^7 - 187285883203400009301x^5 + 645095819922822254259x^3 - 659273750031016149957x - 209910532282507790711	\( 3^{94}\cdot 31^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.11940677720052639937823094663962830546187812969131075398124270924891510801.1	x^27 - 999x^25 + 443556x^23 - 115336881x^21 + 19481903595x^19 - 2241127346283x^17 + 179005600103112x^15 - 9934810805722716x^13 + 377261368227838926x^11 - 9478109683254965610x^9 + 148527554095242519912x^7 - 1311430790136402704223x^5 + 5391437692782988895139x^3 - 6576369053834195245719x - 2893634395862792231483	\( 3^{94}\cdot 37^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.11940677720052639937823094663962830546187812969131075398124270924891510801.2	x^27 - 999x^25 + 443556x^23 - 115336881x^21 + 19481903595x^19 - 2241127346283x^17 + 179005600103112x^15 - 9934810805722716x^13 + 377261368227838926x^11 - 9478109683254965610x^9 + 148527554095242519912x^7 - 1311430790136402704223x^5 + 5391437692782988895139x^3 - 6576369053834195245719x - 894239309602828075753	\( 3^{94}\cdot 37^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.178578900240970840458250689871157457776932189215069373149025720786258346481.1	x^27 - 1161x^25 + 599076x^23 - 181037439x^21 + 35538436395x^19 - 4751165869317x^17 + 441028857202632x^15 - 28446361289569764x^13 + 1255382839016013006x^11 - 36654079188553959990x^9 + 667535465692723883112x^7 - 6849824153642382573297x^5 + 32726937622958050072419x^3 - 46393131355621851201561x - 22298685735659897360231	\( 3^{94}\cdot 43^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.178578900240970840458250689871157457776932189215069373149025720786258346481.2	x^27 - 1161x^25 + 599076x^23 - 181037439x^21 + 35538436395x^19 - 4751165869317x^17 + 441028857202632x^15 - 28446361289569764x^13 + 1255382839016013006x^11 - 36654079188553959990x^9 + 667535465692723883112x^7 - 6849824153642382573297x^5 + 32726937622958050072419x^3 - 46393131355621851201561x - 13967167800173896001791	\( 3^{94}\cdot 43^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.493449694474834715367307491089920591429543598652017227708295844390723767289.1	x^27 - 489x^25 - 326x^24 + 90954x^23 + 83130x^22 - 8577060x^21 - 8185860x^20 + 457201308x^19 + 385246262x^18 - 14492079306x^17 - 8421714480x^16 + 279857702460x^15 + 47349669510x^14 - 3313822863408x^13 + 1147496197436x^12 + 23285753737722x^11 - 21143039489730x^10 - 86802211852084x^9 + 132948531325152x^8 + 118272316935156x^7 - 329718615030309x^6 + 77698876603932x^5 + 245143951250058x^4 - 197708702495375x^3 + 29863417968666x^2 + 13068822764814x - 3091197936923	\( 3^{36}\cdot 163^{26} \)	$C_{27}$ (as 27T1)	$[2, 6]$ (GRH)
27.27.493449694474834715367307491089920591429543598652017227708295844390723767289.2	x^27 - 489x^25 - 326x^24 + 90954x^23 + 135942x^22 - 8327670x^21 - 21586905x^20 + 407434800x^19 + 1590643487x^18 - 10239551442x^17 - 59437041438x^16 + 94661845923x^15 + 1131991461396x^14 + 888897228816x^13 - 9943557891787x^12 - 24693521462100x^11 + 22733911982439x^10 + 164201192000225x^9 + 162818812310040x^8 - 280715203969491x^7 - 787809488325546x^6 - 492327500439375x^5 + 533351595404790x^4 + 1154685729661558x^3 + 872048463931521x^2 + 319734157042743x + 47584712719603	\( 3^{36}\cdot 163^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.718609355602660210319584878812136494786740645292210033727402940660065354649.1	x^27 - x^26 - 364x^25 + 103x^24 + 54397x^23 + 20889x^22 - 4319419x^21 - 4222885x^20 + 197554784x^19 + 291920915x^18 - 5296136455x^17 - 9934444834x^16 + 81671565089x^15 + 178480393873x^14 - 690978198420x^13 - 1710585763116x^12 + 2852693916452x^11 + 8291321681691x^10 - 4155692643926x^9 - 17383913593462x^8 + 395018931867x^7 + 13574520952295x^6 + 6524981901x^5 - 4239629686794x^4 + 189048734793x^3 + 495707735418x^2 - 23951734380x - 17999855161	\( 757^{26} \)	$C_{27}$ (as 27T1)	Trivial (GRH)
27.27.3463254175600113063839837232871102966170246194081956872095753304432278349849.1	x^27 - 513x^25 + 116964x^23 - 15617943x^21 + 1354686795x^19 - 3058506x^18 - 80025043581x^17 + 1046009052x^16 + 3282297025608x^15 - 149056289910x^14 - 93545465229828x^13 + 11454147789084x^12 + 1824136571981646x^11 - 512982190268262x^10 - 23529533875005090x^9 + 13495377620903508x^8 + 188678707563985308x^7 - 199431691508907396x^6 - 818882678941369389x^5 + 1476312521559444360x^4 + 973178953658903259x^3 - 4207490686444416426x^2 + 3649867447339870227x - 1053420808747042331	\( 3^{94}\cdot 19^{24} \)	$C_{27}$ (as 27T1)	$[9]$ (GRH)
27.27.3463254175600113063839837232871102966170246194081956872095753304432278349849.2	x^27 - 513x^25 + 116964x^23 - 15617943x^21 + 1354686795x^19 - 2334150x^18 - 80025043581x^17 + 798279300x^16 + 3282297025608x^15 - 113754800250x^14 - 93545465229828x^13 + 8741424428100x^12 + 1824136571981646x^11 - 391490936887050x^10 - 23530968709997016x^9 + 10299223108874700x^8 + 188924064347604654x^7 - 152199630386703900x^6 - 832868015607672111x^5 + 1126672588576899000x^4 + 1268424949947516279x^3 - 3211016877444162150x^2 + 1966965268494776013x - 342892963174292929	\( 3^{94}\cdot 19^{24} \)	$C_{27}$ (as 27T1)	n/a
27.27.3463254175600113063839837232871102966170246194081956872095753304432278349849.3	x^27 - 513x^25 + 116964x^23 - 15617943x^21 + 1354686795x^19 - 724356x^18 - 80025043581x^17 + 247729752x^16 + 3282297025608x^15 - 35301489660x^14 - 93545465229828x^13 + 2712723360984x^12 + 1824136571981646x^11 - 121491253381212x^10 - 23532675108670668x^9 + 3196154512028808x^8 + 189215858520799146x^7 - 47232061122203496x^6 - 849500283479758155x^5 + 349639932982545360x^4 + 1619550605024888319x^3 - 996473809000254276x^2 - 34450965446244615x - 53756552511721	\( 3^{94}\cdot 19^{24} \)	$C_{27}$ (as 27T1)	$[9]$ (GRH)
27.27.3463254175600113063839837232871102966170246194081956872095753304432278349849.4	x^27 - 513x^25 + 116964x^23 - 15617943x^21 + 1354686795x^19 - 768474x^18 - 80025043581x^17 + 262818108x^16 + 3282297025608x^15 - 37451580390x^14 - 93545465229828x^13 + 2877945888636x^12 + 1824136571981646x^11 - 128890862298198x^10 - 23533044355733718x^9 + 3390821146614132x^8 + 189278999768580696x^7 - 50108801388853284x^6 - 853099334603306505x^5 + 370935283008394440x^4 + 1695530573188686819x^3 - 1057165556573924154x^2 - 467536783979896065x + 18638104434069437	\( 3^{94}\cdot 19^{24} \)	$C_{27}$ (as 27T1)	n/a
27.27.3463254175600113063839837232871102966170246194081956872095753304432278349849.5	x^27 - 513x^25 + 116964x^23 - 15617943x^21 + 1354686795x^19 - 124146x^18 - 80025043581x^17 + 42457932x^16 + 3282297025608x^15 - 6050255310x^14 - 93545465229828x^13 + 464928508044x^12 + 1824136571981646x^11 - 20822155324542x^10 - 23533430642034312x^9 + 547782855461028x^8 + 189345054725982270x^7 - 8095013308479636x^6 - 856864467175196223x^5 + 59924124491342760x^4 + 1775016705261914199x^3 - 170783754800326866x^2 - 920607736797292131x + 249008793852866527	\( 3^{94}\cdot 19^{24} \)	$C_{27}$ (as 27T1)	$[9]$ (GRH)
27.27.3463254175600113063839837232871102966170246194081956872095753304432278349849.6	x^27 - 513x^25 + 116964x^23 - 15617943x^21 + 1354686795x^19 - 644328x^18 - 80025043581x^17 + 220360176x^16 + 3282297025608x^15 - 31401325080x^14 - 93545465229828x^13 + 2413017380592x^12 + 1824136571981646x^11 - 108068706973656x^10 - 23533855837754592x^9 + 2843038291153104x^8 + 189417763194150150x^7 - 42013788080373648x^6 - 861008849860765383x^5 + 311011158517051680x^4 + 1862509228623929799x^3 - 886381801773597288x^2 - 1419315119960781051x + 851940306004555639	\( 3^{94}\cdot 19^{24} \)	$C_{27}$ (as 27T1)	$[9]$ (GRH)
27.27.4310644515294872927421140184636954783440245428743294849809208125862657353561.1	x^27 - x^26 - 390x^25 + 631x^24 + 62487x^23 - 125051x^22 - 5461513x^21 + 11987778x^20 + 291724639x^19 - 652242171x^18 - 10104781105x^17 + 21752982180x^16 + 234561491462x^15 - 462871071073x^14 - 3699437470708x^13 + 6382397987484x^12 + 39482488248952x^11 - 56708916711397x^10 - 278381781984279x^9 + 315391810879847x^8 + 1232012669973146x^7 - 1030181727594079x^6 - 3102106712635726x^5 + 1730205865206149x^4 + 3613695941313439x^3 - 1068842915605065x^2 - 1080339624346363x - 21768517978327	\( 811^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.96679628704383224900411211844182831619287468040811424837360737394634888225089.1	x^27 - 1647x^25 + 1205604x^23 - 516835737x^21 + 143927517195x^19 - 27296507852019x^17 + 3594473478418248x^15 - 328894323275269692x^13 + 20590515659785963086x^11 - 852854074550393903130x^9 + 22033735855443117779688x^7 - 320741086713893566770231x^5 + 2173911809949723063664899x^3 - 4371712760668124402754687x - 2525651376607972493539559	\( 3^{94}\cdot 61^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.96679628704383224900411211844182831619287468040811424837360737394634888225089.2	x^27 - 1647x^25 + 1205604x^23 - 516835737x^21 + 143927517195x^19 - 27296507852019x^17 + 3594473478418248x^15 - 328894323275269692x^13 + 20590515659785963086x^11 - 852854074550393903130x^9 + 22033735855443117779688x^7 - 320741086713893566770231x^5 + 2173911809949723063664899x^3 - 4371712760668124402754687x - 1146875791564075382836381	\( 3^{94}\cdot 61^{18} \)	$C_{27}$ (as 27T1)	n/a
27.27.111225225787238495736527863011990180372275621447089344667888529197779462256081.1	x^27 - x^26 - 442x^25 + 57x^24 + 74120x^23 - 23792x^22 - 6491047x^21 + 6342342x^20 + 330851832x^19 - 609480375x^18 - 10054716230x^17 + 28281288192x^16 + 175097584226x^15 - 703058979520x^14 - 1504988947931x^13 + 9607454297019x^12 + 2167507434225x^11 - 71555147996156x^10 + 61821212164769x^9 + 272496425836143x^8 - 473016326020054x^7 - 401896444043157x^6 + 1367425404919687x^5 - 245718011944824x^4 - 1546434511258730x^3 + 1009917274857026x^2 + 397514834392024x - 384744919097023	\( 919^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.30636512167696967158640831949436414926745966008852301931537630975865004722034443609.1	x^27 - 999x^25 + 443556x^23 - 115336881x^21 + 19481903595x^19 - 43544412x^18 - 2241127346283x^17 + 29000578392x^16 + 179005600103112x^15 - 8047660503780x^14 - 9934810805722716x^13 + 1204287685165656x^12 + 377261368227838926x^11 - 105031090256233284x^10 - 9477154119242768340x^9 + 5380823546973182088x^8 + 148209351279180829002x^7 - 154848144296228240088x^6 - 1276110277553555013213x^5 + 2232226495698874629840x^4 + 3939372175488139375839x^3 - 12388857051128754195612x^2 + 9541558188138634418511x - 2080943940400297569469	\( 3^{94}\cdot 37^{24} \)	$C_{27}$ (as 27T1)	n/a
27.27.30636512167696967158640831949436414926745966008852301931537630975865004722034443609.2	x^27 - 999x^25 + 443556x^23 - 115336881x^21 + 19481903595x^19 - 16541442x^18 - 2241127346283x^17 + 11016600372x^16 + 179005600103112x^15 - 3057106603230x^14 - 9934810805722716x^13 + 457479019247796x^12 + 377261368227838926x^11 - 39898705892968494x^10 - 9477657404647124790x^9 + 2044041394209001308x^8 + 148376945318831526852x^7 - 58822969011125704308x^6 - 1294713215954782474563x^5 + 847967475355188724440x^4 + 4704159643094157231339x^3 - 4706219488221297420642x^2 + 1052417297711836222461x + 46181559728398496293	\( 3^{94}\cdot 37^{24} \)	$C_{27}$ (as 27T1)	$[9]$ (GRH)
27.27.30636512167696967158640831949436414926745966008852301931537630975865004722034443609.3	x^27 - 999x^25 + 443556x^23 - 115336881x^21 + 19481903595x^19 - 22791186x^18 - 2241127346283x^17 + 15178929876x^16 + 179005600103112x^15 - 4212153040590x^14 - 9934810805722716x^13 + 630325301674068x^12 + 377261368227838926x^11 - 54973370953145502x^10 - 9477769626051942234x^9 + 2816328081138069564x^8 + 148414315046635735704x^7 - 81047663668306668564x^6 - 1298861255741049657135x^5 + 1168349437296368858520x^4 + 4874690167640696959299x^3 - 6484339376994847164786x^2 - 840471524754754757895x + 1431296727003283447513	\( 3^{94}\cdot 37^{24} \)	$C_{27}$ (as 27T1)	n/a
27.27.30636512167696967158640831949436414926745966008852301931537630975865004722034443609.4	x^27 - 999x^25 + 443556x^23 - 115336881x^21 + 19481903595x^19 - 8551440x^18 - 2241127346283x^17 + 5695259040x^16 + 179005600103112x^15 - 1580434383600x^14 - 9934810805722716x^13 + 236503225314720x^12 + 377261368227838926x^11 - 20626459864948080x^10 - 9478067851112544048x^9 + 1056709405388878560x^8 + 148513623991816139766x^7 - 30409748443968838560x^6 - 1309884548656074508017x^5 + 438374295750719620800x^4 + 5327869987480607495559x^3 - 2432977341416493895440x^2 - 5870767524977761710381x + 3792769205762397922849	\( 3^{94}\cdot 37^{24} \)	$C_{27}$ (as 27T1)	n/a
27.27.30636512167696967158640831949436414926745966008852301931537630975865004722034443609.5	x^27 - 999x^25 + 443556x^23 - 115336881x^21 + 19481903595x^19 - 20753226x^18 - 2241127346283x^17 + 13821648516x^16 + 179005600103112x^15 - 3835507463190x^14 - 9934810805722716x^13 + 573962383491588x^12 + 377261368227838926x^11 - 50057719303087782x^10 - 9477982179287626548x^9 + 2564495465835112524x^8 + 148485095274118612266x^7 - 73800480627921571524x^6 - 1306717860991648955517x^5 + 1063877058402505771320x^4 + 5197683939054223670559x^3 - 5904517674133907030826x^2 - 4425702387444901252881x + 5039013988182624813037	\( 3^{94}\cdot 37^{24} \)	$C_{27}$ (as 27T1)	n/a
27.27.30636512167696967158640831949436414926745966008852301931537630975865004722034443609.6	x^27 - 999x^25 + 443556x^23 - 115336881x^21 + 19481903595x^19 - 25092882x^18 - 2241127346283x^17 + 16711859412x^16 + 179005600103112x^15 - 4637540986830x^14 - 9934810805722716x^13 + 693982244562516x^12 + 377261368227838926x^11 - 60525165757916574x^10 - 9478115594426938548x^9 + 3100750799597879868x^8 + 148529522515509508266x^7 - 89232717455094542868x^6 - 1311649284786038411517x^5 + 1286341771105908345240x^4 + 5400420250601345750559x^3 - 7139196829637791316082x^2 - 6676075445617956340881x + 10217831259149790606431	\( 3^{94}\cdot 37^{24} \)	$C_{27}$ (as 27T1)	n/a
27.27.2904636282635430627257935704503025621208529312293717639293800815805291320812817603089.1	x^27 - 981x^25 - 1962x^24 + 382590x^23 + 1502892x^22 - 76836171x^21 - 436152600x^20 + 8593793478x^19 + 63853614493x^18 - 538247668545x^17 - 5252980267026x^16 + 17240937970977x^15 + 255163612424409x^14 - 132413809696623x^13 - 7408499319197349x^12 - 8959346343291105x^11 + 124080882210161235x^10 + 316982487984654954x^9 - 1037038458999595329x^8 - 4405618310583782619x^7 + 1681015608216830466x^6 + 26342742980579439510x^5 + 27048463175169695061x^4 - 38812232925049188798x^3 - 95324677706378560338x^2 - 67082385110470102638x - 16138943926629514561	\( 3^{66}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.2904636282635430627257935704503025621208529312293717639293800815805291320812817603089.2	x^27 - 981x^25 - 1962x^24 + 382590x^23 + 1302768x^22 - 77704356x^21 - 341276166x^20 + 9085530519x^19 + 46242066805x^18 - 640020284352x^17 - 3580587873270x^16 + 27613039133250x^15 + 164576945137689x^14 - 729737997409152x^13 - 4515452537534952x^12 + 11800421536957974x^11 + 73180199137284495x^10 - 117578436400215843x^9 - 690714165440312325x^8 + 690099098631125814x^7 + 3669235005570784794x^6 - 1964343944326117491x^5 - 10291095715445447166x^4 + 1194656375883666906x^3 + 12404409711245032941x^2 + 3063320788537767798x - 1874520162296417917	\( 3^{66}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.2904636282635430627257935704503025621208529312293717639293800815805291320812817603089.3	x^27 - 981x^25 - 3924x^24 + 382590x^23 + 2805660x^22 - 73225110x^21 - 777428766x^20 + 6903675666x^19 + 108416615105x^18 - 232610440878x^17 - 8313083080686x^16 - 10743842518713x^15 + 356369675039019x^14 + 1267991081780472x^13 - 8109166737504153x^12 - 47356437284334108x^11 + 77344277257641249x^10 + 865257605899112586x^9 + 207644338670160276x^8 - 7923812360425415109x^7 - 8650195833611503449x^6 + 33977534604641591400x^5 + 43373094180308101017x^4 - 71561295489954712743x^3 - 56974306727633418045x^2 + 68809894376068855206x - 1699412318998420661	\( 3^{66}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.2904636282635430627257935704503025621208529312293717639293800815805291320812817603089.4	x^27 - 981x^25 - 981x^24 + 373761x^23 + 684738x^22 - 71877216x^21 - 179714295x^20 + 7529151456x^19 + 22336994059x^18 - 433214741421x^17 - 1374989293575x^16 + 13413197139192x^15 + 41364203974740x^14 - 223416498256713x^13 - 638856451127076x^12 + 1919829902996862x^11 + 5078544955694361x^10 - 7539868472088462x^9 - 19243512359549019x^8 + 10977970866234507x^7 + 28357598086884837x^6 - 6529678433587440x^5 - 14268854946745152x^4 + 2381897225559600x^3 + 2269088447893488x^2 - 427628571773184x + 13501336803776	\( 3^{66}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.2904636282635430627257935704503025621208529312293717639293800815805291320812817603089.5	x^27 - 981x^25 - 1962x^24 + 373761x^23 + 1393020x^22 - 70073157x^21 - 370235286x^20 + 6852111363x^19 + 47816065064x^18 - 334654866279x^17 - 3187424294262x^16 + 6206464972035x^15 + 109156644703548x^14 + 50084440827489x^13 - 1920679778347338x^12 - 3442346576482824x^11 + 16784501025746016x^10 + 47366059597665312x^9 - 60314381965065024x^8 - 270720680823631872x^7 - 4158047665852416x^6 + 586087104825974016x^5 + 349310299238051328x^4 - 173303709343893504x^3 - 97738973934280704x^2 + 23341809755455488x + 1938077279322112	\( 3^{66}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	$[9]$ (GRH)
27.27.2904636282635430627257935704503025621208529312293717639293800815805291320812817603089.6	x^27 - 981x^25 - 981x^24 + 373761x^23 + 708282x^22 - 71582916x^21 - 190520991x^20 + 7528668804x^19 + 24716174119x^18 - 443924177157x^17 - 1659494707047x^16 + 14482095775128x^15 + 58195882608228x^14 - 259786668484341x^13 - 1094416253548836x^12 + 2502136134254538x^11 + 11067766296130557x^10 - 12047180244214794x^9 - 57055730532335019x^8 + 27061786145990799x^7 + 130990295541684177x^6 - 49384592272051488x^5 - 124320658363397712x^4 + 59983368323472000x^3 + 29619759695053680x^2 - 20670342760256832x + 2723029543253312	\( 3^{66}\cdot 109^{26} \)	$C_{27}$ (as 27T1)	n/a
27.27.101596916227182385192221366107383951083708123828032373165177575777864460122174394998136561.1	x^27 - 1467x^25 - 5868x^24 + 880200x^23 + 6551622x^22 - 270579837x^21 - 2885233986x^20 + 44085669327x^19 + 644999384720x^18 - 3448527231303x^17 - 79721600074956x^16 + 48326300884575x^15 + 5633195024422557x^14 + 11722756835593800x^13 - 225363753591493305x^12 - 885777567591533238x^11 + 4794638783805720162x^10 + 27393004600121870850x^9 - 45879597049721326029x^8 - 411564370609290248289x^7 + 80459334094115940561x^6 + 2916568706309748047241x^5 + 761157212479400273814x^4 - 9009420285696855022620x^3 - 1109799760040952250707x^2 + 8048659263603645557385x - 2430775462661304142463	\( 3^{66}\cdot 163^{26} \)	$C_{27}$ (as 27T1)	n/a