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 106)

Label	Polynomial	Discriminant	Galois group	Class group
27.27.7977212169716289044333767743376433611324896529.1	x^27 - x^26 - 42x^25 + 37x^24 + 728x^23 - 564x^22 - 6817x^21 + 4664x^20 + 37948x^19 - 23103x^18 - 130429x^17 + 71289x^16 + 279661x^15 - 138143x^14 - 372684x^13 + 166778x^12 + 305327x^11 - 124486x^10 - 150120x^9 + 56020x^8 + 42107x^7 - 14253x^6 - 6122x^5 + 1790x^4 + 395x^3 - 85x^2 - 10x + 1	\( 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.50323116815004832630295337440131512593194174521.1	x^27 - 45x^25 + 837x^23 - 8430x^21 + 50652x^19 - 193x^18 - 188811x^17 + 2934x^16 + 441720x^15 - 15822x^14 - 646731x^13 + 37506x^12 + 585063x^11 - 42453x^10 - 319331x^9 + 24462x^8 + 99963x^7 - 7245x^6 - 16119x^5 + 1080x^4 + 1059x^3 - 81x^2 - 18x + 1	\( 3^{66}\cdot 7^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.735278035529026786878794063569162978753987707441.1	x^27 - 51x^25 - 4x^24 + 1080x^23 + 156x^22 - 12356x^21 - 2448x^20 + 83283x^19 + 19984x^18 - 339003x^17 - 91596x^16 + 825846x^15 + 238428x^14 - 1168977x^13 - 344712x^12 + 930681x^11 + 259620x^10 - 414755x^9 - 102465x^8 + 101628x^7 + 20920x^6 - 12933x^5 - 2085x^4 + 755x^3 + 90x^2 - 15x - 1	\( 3^{36}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.550892378962365588304561118053988796799287710804809.1	x^27 - 6x^26 - 47x^25 + 302x^24 + 943x^23 - 6448x^22 - 10567x^21 + 76481x^20 + 71695x^19 - 556066x^18 - 291044x^17 + 2587104x^16 + 603975x^15 - 7811439x^14 - 35156x^13 + 15161145x^12 - 2848142x^11 - 18230502x^10 + 6439289x^9 + 12558384x^8 - 6282221x^7 - 4210683x^6 + 2778704x^5 + 421825x^4 - 457387x^3 + 20126x^2 + 21522x - 2699	\( 13^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.3475226802198116057554377769989579566636047832552241.1	x^27 - 9x^26 - 27x^25 + 420x^24 + 9x^23 - 8244x^22 + 7758x^21 + 88713x^20 - 125694x^19 - 570907x^18 + 991197x^17 + 2239173x^16 - 4595436x^15 - 5142816x^14 + 13108698x^13 + 5797086x^12 - 22773501x^11 - 112752x^10 + 22776726x^9 - 6585183x^8 - 11690658x^7 + 5812863x^6 + 2561958x^5 - 1837044x^4 - 142095x^3 + 213804x^2 - 7074x - 7019	\( 3^{66}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.70567721948812723604880306782225092911730957083793489.1	x^27 - 6x^26 - 53x^25 + 366x^24 + 982x^23 - 8844x^22 - 6757x^21 + 112446x^20 - 14683x^19 - 834075x^18 + 521672x^17 + 3777786x^16 - 3504440x^15 - 10646520x^14 + 12070299x^13 + 18475792x^12 - 24076806x^11 - 18615256x^10 + 28010042x^9 + 9025037x^8 - 17745073x^7 - 453885x^6 + 4979339x^5 - 862152x^4 - 251138x^3 + 61524x^2 - 1124x - 223	\( 7^{18}\cdot 37^{24} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.3217863581710817038235175421508758764893959268723195889.1	x^27 - 9x^26 - 45x^25 + 636x^24 + 27x^23 - 17460x^22 + 31872x^21 + 229473x^20 - 738450x^19 - 1345159x^18 + 7506369x^17 + 647631x^16 - 38801514x^15 + 30109320x^14 + 100880532x^13 - 138866430x^12 - 120638421x^11 + 261338922x^10 + 44503222x^9 - 240759207x^8 + 22047264x^7 + 115889073x^6 - 21421602x^5 - 28758384x^4 + 5399355x^3 + 3255948x^2 - 411264x - 105461	\( 3^{66}\cdot 19^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.6504389611606252637488188857147585077648657433962663281.1	x^27 - 3x^26 - 72x^25 + 194x^24 + 2136x^23 - 5166x^22 - 34511x^21 + 74439x^20 + 337788x^19 - 642199x^18 - 2109834x^17 + 3469977x^16 + 8634362x^15 - 11919870x^14 - 23358597x^13 + 25816709x^12 + 41360031x^11 - 34011447x^10 - 46156293x^9 + 25045044x^8 + 29760855x^7 - 8403372x^6 - 9106128x^5 + 587949x^4 + 751973x^3 + 31935x^2 - 14445x - 1153	\( 3^{36}\cdot 37^{24} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.3424497960405311916385247304908867275520984000621827548961.1	x^27 - 6x^26 - 101x^25 + 665x^24 + 4039x^23 - 30862x^22 - 78250x^21 + 781658x^20 + 631294x^19 - 11833279x^18 + 2312179x^17 + 110719275x^16 - 93223059x^15 - 644047317x^14 + 838327648x^13 + 2305955193x^12 - 3871097360x^11 - 4971409308x^10 + 10254915272x^9 + 6199663224x^8 - 15899447063x^7 - 4124731002x^6 + 13978784663x^5 + 1237075384x^4 - 6246677485x^3 - 134762902x^2 + 1023554967x + 16988281	\( 19^{24}\cdot 31^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.4873283973806953022959748626642827335637181614041911288969.1	x^27 - 6x^26 - 71x^25 + 442x^24 + 2014x^23 - 13298x^22 - 29833x^21 + 215668x^20 + 252089x^19 - 2090049x^18 - 1244428x^17 + 12673590x^16 + 3524558x^15 - 48977088x^14 - 5298545x^13 + 120468998x^12 + 3352006x^11 - 185148056x^10 - 486454x^9 + 171925849x^8 + 2045189x^7 - 92239753x^6 - 4261315x^5 + 26431312x^4 + 2604404x^3 - 3332540x^2 - 488126x + 70153	\( 13^{18}\cdot 37^{24} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.21602961940568681480203888396858143586678350003185405580489.1	x^27 - 9x^26 - 81x^25 + 933x^24 + 2007x^23 - 39807x^22 + 6678x^21 + 904248x^20 - 1262637x^19 - 11822536x^18 + 26844534x^17 + 89638254x^16 - 282749058x^15 - 371494179x^14 + 1710171315x^13 + 642477579x^12 - 6222060495x^11 + 686308842x^10 + 13853219952x^9 - 5005127394x^8 - 18850288581x^7 + 8789278983x^6 + 15172084575x^5 - 7014480921x^4 - 6523888629x^3 + 2434189824x^2 + 1093125672x - 273101111	\( 3^{66}\cdot 31^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.82740369509121494587249825446059868376844092109571921823609.1	x^27 - 6x^26 - 119x^25 + 588x^24 + 6703x^23 - 23664x^22 - 229513x^21 + 474063x^20 + 5090845x^19 - 3919676x^18 - 73206350x^17 - 21588434x^16 + 656954365x^15 + 787530733x^14 - 3325690822x^13 - 7213234613x^12 + 6583428950x^11 + 29933674810x^10 + 11963110633x^9 - 47377292870x^8 - 61123319381x^7 - 6523878607x^6 + 31218812642x^5 + 18121240371x^4 - 246741993x^3 - 2622725154x^2 - 602443376x - 28067027	\( 19^{24}\cdot 37^{18} \)	$C_3\times C_9$ (as 27T2)	$[2, 2]$ (GRH)
27.27.521955940438809922293374595854472560734963287885444907593441.1	x^27 - 9x^26 - 99x^25 + 906x^24 + 4833x^23 - 39654x^22 - 156102x^21 + 968139x^20 + 3563946x^19 - 13945195x^18 - 56219139x^17 + 112278861x^16 + 582670932x^15 - 354069522x^14 - 3707506512x^13 - 1396052364x^12 + 12836504439x^11 + 14919397542x^10 - 16968716582x^9 - 39300644385x^8 - 9891055872x^7 + 24100026927x^6 + 17213661954x^5 - 1129546062x^4 - 4247511909x^3 - 1269306432x^2 - 91305144x + 5272453	\( 3^{66}\cdot 37^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.854109127767918484727194550995844259867162076193861770225009.1	x^27 - 6x^26 - 101x^25 + 670x^24 + 3826x^23 - 29942x^22 - 65183x^21 + 701185x^20 + 356998x^19 - 9451534x^18 + 4123822x^17 + 75852203x^16 - 79731532x^15 - 361313257x^14 + 550432787x^13 + 983894056x^12 - 1975738003x^11 - 1390142439x^10 + 3935601510x^9 + 641980245x^8 - 4302987535x^7 + 676032279x^6 + 2333730233x^5 - 940006807x^4 - 414810580x^3 + 314793135x^2 - 56615545x + 2018477	\( 7^{18}\cdot 73^{24} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.1237424251695265996553186030546217359162421829813695859696729.1	x^27 - 6x^26 - 137x^25 + 709x^24 + 8599x^23 - 35066x^22 - 323554x^21 + 924610x^20 + 7956418x^19 - 13384023x^18 - 130806305x^17 + 86373179x^16 + 1422742061x^15 + 256596263x^14 - 9854606544x^13 - 8654405011x^12 + 40055307468x^11 + 61771660232x^10 - 77700458908x^9 - 199640506816x^8 + 13751584729x^7 + 280117270166x^6 + 129171933167x^5 - 142742440584x^4 - 115757033393x^3 + 8287037006x^2 + 20768956575x + 2265222521	\( 19^{24}\cdot 43^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.4512385497467278486124161046693886108531644910659813162128201.1	x^27 - 6x^26 - 89x^25 + 608x^24 + 2854x^23 - 24256x^22 - 37459x^21 + 502442x^20 + 38939x^19 - 5964855x^18 + 4517402x^17 + 42143562x^16 - 55948534x^15 - 176060310x^14 + 322170703x^13 + 406625862x^12 - 1018443104x^11 - 403762596x^10 + 1780570826x^9 - 109881561x^8 - 1631686473x^7 + 506463311x^6 + 712423287x^5 - 307934112x^4 - 139835954x^3 + 69450354x^2 + 9973258x - 5332589	\( 19^{18}\cdot 37^{24} \)	$C_3\times C_9$ (as 27T2)	$[2, 2]$ (GRH)
27.27.7806116202371923778076833319704235358304327213604702954864321.1	x^27 - 9x^26 - 117x^25 + 1077x^24 + 6363x^23 - 55647x^22 - 218118x^21 + 1616472x^20 + 5247171x^19 - 28705768x^18 - 90158310x^17 + 315512154x^16 + 1076463318x^15 - 2036139291x^14 - 8535335625x^13 + 6189476667x^12 + 42360771069x^11 + 3486053466x^10 - 120399207328x^9 - 77931984402x^8 + 167444847135x^7 + 186039613671x^6 - 81038691729x^5 - 162267197085x^4 - 14975802189x^3 + 44317649232x^2 + 9431461404x - 2809696843	\( 3^{66}\cdot 43^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.78725207281899442169440296957686289952130469188765531717705361.1	x^27 - 3x^26 - 120x^25 + 290x^24 + 6036x^23 - 11376x^22 - 167001x^21 + 234648x^20 + 2816421x^19 - 2737311x^18 - 30400659x^17 + 17664747x^16 + 214692790x^15 - 50437221x^14 - 994582143x^13 - 61951104x^12 + 2973052770x^11 + 928156266x^10 - 5490461910x^9 - 2877753387x^8 + 5691128145x^7 + 4106020983x^6 - 2585377374x^5 - 2591621310x^4 + 53422363x^3 + 491101713x^2 + 119304222x + 6213203	\( 3^{36}\cdot 73^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.151387227139400874793584512894425905310908185375198495733583209.1	x^27 - 171x^25 + 12312x^23 - 493905x^21 + 12316959x^19 - 144362x^18 - 201382767x^17 + 9162180x^16 + 2213413740x^15 - 239483790x^14 - 16451805348x^13 + 3352712412x^12 + 81769006062x^11 - 27287694702x^10 - 263091419295x^9 + 130647735324x^8 + 511737088221x^7 - 352985018796x^6 - 515019140298x^5 + 478960952040x^4 + 156639881529x^3 - 237404462490x^2 + 43969262832x + 3329578088	\( 3^{66}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.151387227139400874793584512894425905310908185375198495733583209.2	x^27 - 171x^25 + 12312x^23 - 493905x^21 + 12316959x^19 - 56221x^18 - 201382767x^17 + 3645378x^16 + 2213413740x^15 - 98688375x^14 - 16451805348x^13 + 1450706658x^12 + 81769006062x^11 - 12502317699x^10 - 263183382240x^9 + 63310449366x^8 + 513818842734x^7 - 177767378010x^6 - 531464834277x^5 + 237369275820x^4 + 211536642519x^3 - 96914645181x^2 - 25035315705x + 9868941829	\( 3^{66}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.1	x^27 - 3x^26 - 210x^25 + 278x^24 + 19929x^23 + 5937x^22 - 1083004x^21 - 1964481x^20 + 35357121x^19 + 118971079x^18 - 651688491x^17 - 3622053234x^16 + 4445915527x^15 + 60695501586x^14 + 61934493837x^13 - 500874109445x^12 - 1506251267832x^11 + 632120142195x^10 + 10208524999752x^9 + 17212808525700x^8 - 6295882065903x^7 - 67953265942575x^6 - 122172061784082x^5 - 118152234479289x^4 - 68213531737236x^3 - 22934996039574x^2 - 3986229684933x - 260162527969	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[2, 6]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.2	x^27 - 3x^26 - 210x^25 + 341x^24 + 19761x^23 - 5319x^22 - 1071027x^21 - 1072779x^20 + 35785290x^19 + 79547261x^18 - 727641144x^17 - 2617308423x^16 + 7915049615x^15 + 47517477258x^14 - 16231036935x^13 - 470794277397x^12 - 610037882562x^11 + 2029302136221x^10 + 6315551962953x^9 + 1612960677906x^8 - 17452227111315x^7 - 30692199651546x^6 - 18015765483522x^5 + 2873413735140x^4 + 6984224959239x^3 + 1384579835685x^2 - 495953919873x - 77502107663	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.3	x^27 - 234x^25 - 300x^24 + 21600x^23 + 49233x^22 - 1007250x^21 - 3087864x^20 + 25802124x^19 + 98166647x^18 - 368176113x^17 - 1747356537x^16 + 2750706459x^15 + 18094018455x^14 - 7767041349x^13 - 110231138950x^12 - 22064613804x^11 + 393523655928x^10 + 211466391591x^9 - 812037279015x^8 - 557167152231x^7 + 941607757277x^6 + 646172244414x^5 - 588923699037x^4 - 328067407732x^3 + 184625797869x^2 + 56808287184x - 23416482473	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.4	x^27 - 3x^26 - 162x^25 + 362x^24 + 11058x^23 - 17940x^22 - 417005x^21 + 475152x^20 + 9585783x^19 - 7334897x^18 - 140140161x^17 + 67545369x^16 + 1325068846x^15 - 360894987x^14 - 8127116829x^13 + 949692990x^12 + 32083489470x^11 + 34580448x^10 - 79891828714x^9 - 7402115451x^8 + 120762893079x^7 + 19715601263x^6 - 103424572098x^5 - 22163323110x^4 + 44013206071x^3 + 10730880483x^2 - 6912437058x - 1834540021	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.5	x^27 - 9x^26 - 153x^25 + 1380x^24 + 10011x^23 - 89964x^22 - 366086x^21 + 3289107x^20 + 8195640x^19 - 74863229x^18 - 115293333x^17 + 1111829427x^16 + 994569364x^15 - 10957304562x^14 - 4643357544x^13 + 71264766946x^12 + 4719112581x^11 - 297223405968x^10 + 61859763056x^9 + 747502977825x^8 - 308198445204x^7 - 1001646366449x^6 + 552392947014x^5 + 525970815906x^4 - 343918548357x^3 + 26874655680x^2 + 2448910590x - 226688239	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.6	x^27 - 9x^26 - 153x^25 + 1380x^24 + 10011x^23 - 86886x^22 - 383528x^21 + 2960787x^20 + 9796200x^19 - 59973575x^18 - 174434025x^17 + 738720423x^16 + 2134780606x^15 - 5368801578x^14 - 17089817922x^13 + 20633038024x^12 + 83517640365x^11 - 27094243584x^10 - 228532520050x^9 - 51466910463x^8 + 315859629984x^7 + 184866910465x^6 - 169543892730x^5 - 152909392110x^4 - 1004242821x^3 + 15202545204x^2 - 844847976x - 111053593	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.7	x^27 - 3x^26 - 162x^25 + 362x^24 + 11058x^23 - 16344x^22 - 417803x^21 + 322335x^20 + 9627678x^19 - 1383413x^18 - 140166894x^17 - 54908529x^16 + 1288690420x^15 + 1075653042x^14 - 7259510481x^13 - 8680107239x^12 + 23559312123x^11 + 35193844791x^10 - 40428696341x^9 - 70735013982x^8 + 36838185093x^7 + 69532031920x^6 - 22855569024x^5 - 32729761209x^4 + 11473645521x^3 + 5579986791x^2 - 2960472531x + 343950769	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.8	x^27 - 234x^25 - 249x^24 + 22626x^23 + 42558x^22 - 1176444x^21 - 2979873x^20 + 35915889x^19 + 111309958x^18 - 659712528x^17 - 2427785484x^16 + 7124089977x^15 + 31852073331x^14 - 40489809264x^13 - 249129898160x^12 + 64602332640x^11 + 1102440345990x^10 + 457955338088x^9 - 2397853291923x^8 - 2310077106372x^7 + 1456668702112x^6 + 2956555931049x^5 + 1371196307376x^4 + 149958202254x^3 - 31775939244x^2 - 3498281892x + 353597867	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[2, 6]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.9	x^27 - 234x^25 - 363x^24 + 21600x^23 + 58746x^22 - 1010232x^21 - 3754845x^20 + 25508145x^19 + 122869178x^18 - 334737288x^17 - 2243559090x^16 + 1661065767x^15 + 23417551341x^14 + 9070899120x^13 - 135972690394x^12 - 155269579194x^11 + 394444022466x^10 + 726143959982x^9 - 394126983513x^8 - 1382959296534x^7 - 230053380286x^6 + 1005649338285x^5 + 492843065832x^4 - 174788627574x^3 - 142021806498x^2 - 17497701342x + 1193490397	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[2, 6]$ (GRH)
27.27.1197336751300349460100016353165918520894496565611371829528951009.10	x^27 - 234x^25 - 15x^24 + 21600x^23 + 1923x^22 - 1048518x^21 - 36198x^20 + 30177957x^19 - 2255516x^18 - 546700113x^17 + 117546663x^16 + 6402152565x^15 - 2363379129x^14 - 48608855199x^13 + 25496147479x^12 + 234863069337x^11 - 157505340675x^10 - 690719521993x^9 + 551539138572x^8 + 1133759797215x^7 - 1025115854027x^6 - 857479276836x^5 + 846276915456x^4 + 160140482187x^3 - 159434629011x^2 - 16629567129x + 2164132187	\( 3^{36}\cdot 7^{18}\cdot 19^{24} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.4226100704227770327423556410760485273603323729873037153574412049.1	x^27 - 9x^26 - 171x^25 + 1662x^24 + 12105x^23 - 131490x^22 - 453414x^21 + 5848551x^20 + 9316386x^19 - 161570611x^18 - 87089931x^17 + 2896436709x^16 - 301799844x^15 - 34271005878x^14 + 17195762052x^13 + 267669198096x^12 - 196205674761x^11 - 1360829134422x^10 + 1139084249570x^9 + 4372192409787x^8 - 3630889722708x^7 - 8428513893225x^6 + 6048620755506x^5 + 8864208737262x^4 - 4498476763089x^3 - 4006776962952x^2 + 921282187860x + 173820270061	\( 3^{66}\cdot 61^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.12882515415852435459493331403759124565080304093640247033847689489.1	x^27 - 6x^26 - 149x^25 + 788x^24 + 9832x^23 - 42520x^22 - 381437x^21 + 1216319x^20 + 9582638x^19 - 19409897x^18 - 160108066x^17 + 155008644x^16 + 1756031318x^15 - 149163963x^14 - 12079333253x^13 - 7562465658x^12 + 47644690593x^11 + 58813589752x^10 - 88610606092x^9 - 177046464592x^8 + 27034763677x^7 + 205863517381x^6 + 81470197594x^5 - 63004124267x^4 - 47812852922x^3 - 8296111176x^2 - 149023054x + 24923387	\( 7^{18}\cdot 109^{24} \)	$C_3\times C_9$ (as 27T2)	$[2, 2]$ (GRH)
27.27.22874376238048151146999094376461057406235644645953493108395282961.1	x^27 - 9x^26 - 189x^25 + 1680x^24 + 16011x^23 - 135216x^22 - 811224x^21 + 6143229x^20 + 27534006x^19 - 173103583x^18 - 657009639x^17 + 3125053791x^16 + 11114099142x^15 - 35932528620x^14 - 130592837952x^13 + 250836674670x^12 + 1021415604147x^11 - 930934482786x^10 - 4988671858122x^9 + 1049534716941x^8 + 13954608198684x^7 + 2985430435785x^6 - 20357236188306x^5 - 8830845112932x^4 + 13243359313719x^3 + 6479388550764x^2 - 2750267537172x - 1151745452469	\( 3^{66}\cdot 67^{18} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.58983288808059104765952482916808157759827216339270579472138526889.1	x^27 - 6x^26 - 119x^25 + 746x^24 + 5530x^23 - 37564x^22 - 127355x^21 + 999299x^20 + 1505470x^19 - 15429798x^18 - 8000144x^17 + 144737679x^16 + 1202790x^15 - 849961797x^14 + 177434127x^13 + 3185085572x^12 - 727188729x^11 - 7601774021x^10 + 860974092x^9 + 11059085461x^8 + 854116693x^7 - 8633121087x^6 - 2479823783x^5 + 2520335249x^4 + 1318748708x^3 + 197825781x^2 + 11769907x + 241567	\( 13^{18}\cdot 73^{24} \)	$C_3\times C_9$ (as 27T2)	$[2, 2]$ (GRH)
27.27.107106121656197668357044180433735940609513745651269801273974583001.1	x^27 - 9x^26 - 207x^25 + 2112x^24 + 16893x^23 - 211032x^22 - 634038x^21 + 11704797x^20 + 5617746x^19 - 393140443x^18 + 437158845x^17 + 8144357769x^16 - 19135943232x^15 - 99785979396x^14 + 367193241090x^13 + 600310861842x^12 - 3835851698421x^11 + 107461159776x^10 + 21186874621942x^9 - 22126898435067x^8 - 48962930005890x^7 + 97874407378491x^6 + 741345334326x^5 - 93507662067480x^4 + 29359018756881x^3 + 28868873558292x^2 - 7673425487946x - 2813528454063	\( 3^{66}\cdot 73^{18} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.443905427170893592618091312247244421283763327307281442575957150569.1	x^27 - 9x^26 - 225x^25 + 1644x^24 + 25263x^23 - 122580x^22 - 1789356x^21 + 4127985x^20 + 83303766x^19 - 6907183x^18 - 2481341895x^17 - 4572350253x^16 + 42769856514x^15 + 169288875360x^14 - 275778124056x^13 - 2730350841870x^12 - 3198616042653x^11 + 16864294008150x^10 + 62786902579694x^9 + 45728358013593x^8 - 202686294270924x^7 - 677653689800451x^6 - 1034723340656082x^5 - 944724683324952x^4 - 533618215210377x^3 - 178295033152692x^2 - 31044631374180x - 2072482797673	\( 3^{66}\cdot 79^{18} \)	$C_3\times C_9$ (as 27T2)	n/a
27.27.504724077808035841778557530783708473162637353188340488433492146609.1	x^27 - 6x^26 - 173x^25 + 805x^24 + 12829x^23 - 41798x^22 - 525887x^21 + 1074049x^20 + 12931133x^19 - 14262294x^18 - 197099335x^17 + 84388495x^16 + 1886796975x^15 + 74350078x^14 - 11332953439x^13 - 4069183891x^12 + 42042763063x^11 + 24409158618x^10 - 92576569635x^9 - 68473588099x^8 + 111110219033x^7 + 95741259302x^6 - 60609893115x^5 - 59290655739x^4 + 10338086657x^3 + 12919246032x^2 - 475157373x - 885366943	\( 7^{18}\cdot 127^{24} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.1187411143908093381248555091925855631936617111126489321417190047281.1	x^27 - 3x^26 - 168x^25 + 572x^24 + 11610x^23 - 45264x^22 - 425713x^21 + 1939944x^20 + 8773131x^19 - 49261956x^18 - 94362513x^17 + 759872085x^16 + 275657276x^15 - 6982699857x^14 + 4569640299x^13 + 35528125026x^12 - 50785958448x^11 - 83218822605x^10 + 196283403790x^9 + 38975332611x^8 - 318723893835x^7 + 128423804151x^6 + 180395569233x^5 - 141722795001x^4 - 4007013731x^3 + 28531403934x^2 - 8074445220x + 668804824	\( 3^{36}\cdot 109^{24} \)	$C_3\times C_9$ (as 27T2)	Trivial (GRH)
27.27.5659106580522258442740055894009895600932750567734671570320232266209.1	x^27 - 180x^25 + 13581x^23 - 568500x^21 + 14742063x^19 - 174192x^18 - 249963084x^17 + 11243754x^16 + 2843438562x^15 - 300038904x^14 - 21840737832x^13 + 4313717772x^12 + 112040890065x^11 - 36374296608x^10 - 371584562893x^9 + 182892909312x^8 + 742994668764x^7 - 530201597184x^6 - 756546767280x^5 + 798056616960x^4 + 173258396544x^3 - 459871520256x^2 + 182205736704x - 21684382208	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.5659106580522258442740055894009895600932750567734671570320232266209.2	x^27 - 180x^25 + 13581x^23 - 560310x^21 + 13841163x^19 - 110106x^18 - 211280076x^17 + 8431398x^16 + 1997088057x^15 - 229078692x^14 - 11538409068x^13 + 2713319154x^12 + 40044205305x^11 - 14681285424x^10 - 81200156077x^9 + 39061121994x^8 + 90794275164x^7 - 50957966052x^6 - 49424314320x^5 + 28585642770x^4 + 10186413309x^3 - 3822753528x^2 - 1276399539x - 67976091	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.5659106580522258442740055894009895600932750567734671570320232266209.3	x^27 - 180x^25 + 13581x^23 - 560310x^21 + 13841163x^19 - 92880x^18 - 211280076x^17 + 7745112x^16 + 1997088057x^15 - 233589906x^14 - 11538409068x^13 + 3103240140x^12 + 40044205305x^11 - 18541949166x^10 - 79554132019x^9 + 53008275636x^8 + 81498609540x^7 - 72744969402x^6 - 31916666358x^5 + 42662749410x^4 - 2061705231x^3 - 6710328360x^2 + 969338907x + 230754987	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.5659106580522258442740055894009895600932750567734671570320232266209.4	x^27 - 180x^25 + 13581x^23 - 568500x^21 + 14742063x^19 - 173190x^18 - 249963084x^17 + 11056356x^16 + 2843438562x^15 - 289163682x^14 - 21840737832x^13 + 4026509760x^12 + 112040890065x^11 - 32469442902x^10 - 371871177991x^9 + 154371096648x^8 + 749302072020x^7 - 421068854304x^6 - 802318146192x^5 + 605250420480x^4 + 297429400704x^3 - 354965068800x^2 + 75168039168x + 1993642496	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.5659106580522258442740055894009895600932750567734671570320232266209.5	x^27 - 9x^26 - 189x^25 + 1770x^24 + 15075x^23 - 149400x^22 - 659574x^21 + 7112223x^20 + 17169588x^19 - 211132411x^18 - 267170931x^17 + 4084767207x^16 + 2275361346x^15 - 52402519296x^14 - 6034174794x^13 + 446404796160x^12 - 65737507815x^11 - 2499184727280x^10 + 703772052814x^9 + 8983662014547x^8 - 2901631249080x^7 - 19863323081169x^6 + 5926406371776x^5 + 24929372870136x^4 - 5674509280383x^3 - 15143291321652x^2 + 1878327723222x + 3142740871297	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.5659106580522258442740055894009895600932750567734671570320232266209.6	x^27 - 9x^26 - 261x^25 + 2058x^24 + 32067x^23 - 199422x^22 - 2430132x^21 + 10339083x^20 + 123276078x^19 - 285174031x^18 - 4239416871x^17 + 2545292439x^16 + 96103309782x^15 + 82399099806x^14 - 1330149204990x^13 - 2946031839456x^12 + 9081521720235x^11 + 37741694932692x^10 - 1312384302218x^9 - 189487015010469x^8 - 274189790401506x^7 + 84350717576493x^6 + 450767216583810x^5 + 188746081240014x^4 - 199876274766459x^3 - 126122964539436x^2 + 15086119963302x + 5057089505859	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	n/a
27.27.5659106580522258442740055894009895600932750567734671570320232266209.7	x^27 - 9x^26 - 189x^25 + 1770x^24 + 15075x^23 - 149400x^22 - 659574x^21 + 7112223x^20 + 17169588x^19 - 211111831x^18 - 267294411x^17 + 4084396767x^16 + 2286309906x^15 - 52467778476x^14 - 6381215334x^13 + 449758945140x^12 - 61101574695x^11 - 2565990000360x^10 + 683906165094x^9 + 9640483374987x^8 - 2952136236060x^7 - 23310660585549x^6 + 6532980509736x^5 + 34657732013436x^4 - 7255493877603x^3 - 28679264186472x^2 + 3190222769922x + 10071022217437	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	$[3]$ (GRH)
27.27.5659106580522258442740055894009895600932750567734671570320232266209.8	x^27 - 9x^26 - 261x^25 + 2877x^24 + 25515x^23 - 385335x^22 - 888774x^21 + 27904176x^20 - 30624669x^19 - 1158540616x^18 + 4183764714x^17 + 25557050754x^16 - 174741571434x^15 - 143798389803x^14 + 3671235722367x^13 - 6416274457389x^12 - 35021761608051x^11 + 155084845070178x^10 - 18670398026360x^9 - 1202353337008818x^8 + 2846666722896927x^7 + 52405731960495x^6 - 12365151517166049x^5 + 27636990777084987x^4 - 30918692573230389x^3 + 19464015249722088x^2 - 6490810357686540x + 878893626230101	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	n/a
27.27.5659106580522258442740055894009895600932750567734671570320232266209.9	x^27 - 9x^26 - 333x^25 + 2994x^24 + 48483x^23 - 434322x^22 - 4074096x^21 + 36210411x^20 + 219630546x^19 - 1923801079x^18 - 7986694239x^17 + 68210967663x^16 + 200583185334x^15 - 1642096841094x^14 - 3503200886262x^13 + 26759487401136x^12 + 42243715332927x^11 - 288687216994956x^10 - 343364658706698x^9 + 1968336232189875x^8 + 1787389461378522x^7 - 7789317328108479x^6 - 5379727037407434x^5 + 15167762481168378x^4 + 7574956000765869x^3 - 9665204246538732x^2 - 2609849224374930x + 1335980438165647	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	n/a
27.27.5659106580522258442740055894009895600932750567734671570320232266209.10	x^27 - 9x^26 - 333x^25 + 2994x^24 + 48483x^23 - 434322x^22 - 4074096x^21 + 36210411x^20 + 219630546x^19 - 1924262449x^18 - 7983926019x^17 + 68288477823x^16 + 200160570414x^15 - 1647554386824x^14 - 3477186538812x^13 + 26968936001406x^12 + 41414716489527x^11 - 293449181012676x^10 - 328865159417878x^9 + 2033775649158255x^8 + 1652493518068212x^7 - 8323967190730809x^6 - 4792095978290514x^5 + 17626794329742588x^4 + 6764432694563259x^3 - 15214678979277942x^2 - 3402078647206140x + 1914328354712957	\( 3^{66}\cdot 7^{18}\cdot 13^{18} \)	$C_3\times C_9$ (as 27T2)	n/a
27.27.17860517092005028417206516767820811734461334327640142959315501467081.1	x^27 - 9x^26 - 279x^25 + 3156x^24 + 28773x^23 - 460404x^22 - 955542x^21 + 35974809x^20 - 57567654x^19 - 1579631155x^18 + 7062218181x^17 + 34301043441x^16 - 306209006808x^15 - 6539221512x^14 + 6604533011718x^13 - 17817297444354x^12 - 55843161650181x^11 + 386037100051812x^10 - 379987896358162x^9 - 2701094621543055x^8 + 10001937729994218x^7 - 7711001730164253x^6 - 34488237931683786x^5 + 120712409085829428x^4 - 187652271757816539x^3 + 165535685719269948x^2 - 80461586519455374x + 16831477313082953	\( 3^{66}\cdot 97^{18} \)	$C_3\times C_9$ (as 27T2)	n/a
27.27.46521581790658445094934566845164072323103073629781639266605395671761.1	x^27 - 3x^26 - 192x^25 + 755x^24 + 14055x^23 - 68025x^22 - 494100x^21 + 2946153x^20 + 8585901x^19 - 69113725x^18 - 58476672x^17 + 926380305x^16 - 263176183x^15 - 7219642587x^14 + 7122066258x^13 + 32268931643x^12 - 48846266253x^11 - 78264957723x^10 + 163446427076x^9 + 85583050641x^8 - 284780543145x^7 - 3315665497x^6 + 245913582318x^5 - 61199808147x^4 - 89489663845x^3 + 33768425463x^2 + 7536057522x - 2784493637	\( 3^{36}\cdot 127^{24} \)	$C_3\times C_9$ (as 27T2)	$[2, 2]$ (GRH)