Number field search results

Results (1-50 of 288 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
27.9.675...923.1	x^27 - 18x^23 - 18x^22 - 18x^21 + 18x^20 + 135x^19 + 219x^18 - 162x^17 + 324x^16 - 153x^15 - 81x^14 - 675x^13 - 630x^12 - 540x^11 - 513x^10 - 405x^9 + 27x^8 + 243x^7 + 387x^6 + 162x^5 - 81x^4 - 135x^3 + 27x - 3	$27$	[9,9]	$-\,3^{73}$	$1$	$19.498199223768765$			not computed	$C_9\times S_3$ (as 27T12)	trivial	$2$	$17$	$13605448.556703938$
27.9.218...752.1	x^27 - 18x^25 - 9x^24 + 135x^23 + 63x^22 - 642x^21 - 135x^20 + 2133x^19 + 336x^18 - 6156x^17 - 270x^16 + 15525x^15 - 4347x^14 - 26667x^13 + 16194x^12 + 26730x^11 - 24912x^10 - 13179x^9 + 19197x^8 + 693x^7 - 6957x^6 + 1917x^5 + 648x^4 - 507x^3 + 135x^2 - 18x + 1	$27$	[9,9]	$-\,2^{18}\cdot 3^{69}$	$2$	$26.302470182986912$			not computed	$C_9\times S_3$ (as 27T12)	trivial	$2$	$17$	$932907706.847076$
27.1.437...027.1	x^27 - x - 1	$27$	[1,13]	$-\,23\cdot 3539\cdot 535391\cdot 10033918834509020645502251401$	$4$	$26.9860232809$			✓	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$289963252.83729804$
27.1.449...579.1	x^27 + x - 1	$27$	[1,13]	$-\,151\cdot 144512650291622071\cdot 20602820982951053299$	$3$	$27.0137911008$			✓	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$314436524.8339556$
27.9.656...256.1	x^27 - 9x^26 + 27x^25 - 24x^24 - 9x^23 - 63x^22 + 273x^21 + 144x^20 - 2376x^19 + 4050x^18 - 396x^17 - 3465x^16 - 141x^15 + 441x^14 + 17019x^13 - 33225x^12 + 12852x^11 + 17379x^10 - 14277x^9 + 1188x^8 + 1143x^7 - 501x^6 + 891x^5 + 216x^4 + 129x^3 + 18x^2 + 9x - 1	$27$	[9,9]	$-\,2^{18}\cdot 3^{70}$	$2$	$27.394772269463456$			not computed	$C_9\times S_3$ (as 27T12)	trivial	$2$	$17$	$1816757010.3045344$
27.1.800...063.1	x^27 - 9x^26 + 41x^25 - 116x^24 + 234x^23 - 347x^22 + 380x^21 - 274x^20 + 118x^19 - 121x^18 + 474x^17 - 1071x^16 + 1556x^15 - 1531x^14 + 964x^13 - 256x^12 + 122x^11 - 700x^10 + 1761x^9 - 2620x^8 + 2840x^7 - 2483x^6 + 1678x^5 - 860x^4 + 463x^3 - 60x^2 + 44x - 1	$27$	[1,13]	$-\,983^{13}$	$1$	$27.5968238300111$				$D_{27}$ (as 27T8)	trivial	$2$	$13$	$460164457.10213304$
27.9.162...375.1	x^27 - 9x^25 + 54x^23 - 63x^22 - 267x^21 + 513x^20 + 468x^19 - 981x^18 - 972x^17 - 1107x^16 + 9846x^15 - 4860x^14 - 24624x^13 + 41403x^12 - 9909x^11 - 43317x^10 + 67377x^9 - 45441x^8 - 4905x^7 + 46368x^6 - 47520x^5 + 19584x^4 + 1146x^3 - 3483x^2 + 594x + 107	$27$	[9,9]	$-\,3^{69}\cdot 5^{9}$	$2$	$28.333477097878134$			not computed	$C_9\times S_3$ (as 27T12)	trivial	$2$	$17$	$2153441387.4033856$
27.1.321...296.1	x^27 - 10x^26 + 38x^25 - 52x^24 - 84x^23 + 458x^22 - 715x^21 + 40x^20 + 1948x^19 - 3756x^18 + 1448x^17 + 4952x^16 - 7109x^15 + 94x^14 + 4978x^13 - 2352x^12 - 1300x^11 + 2422x^10 + 639x^9 - 3848x^8 - 28x^7 + 1728x^6 + 572x^5 - 368x^4 - 244x^3 + 48x^2 + 32x - 16	$27$	[1,13]	$-\,2^{18}\cdot 419^{13}$	$2$	$29.055888235511343$				$D_{27}$ (as 27T8)	trivial	$2$	$13$	$2806458409.197778$
27.1.149...191.1	x^27 - 4x^26 + 14x^25 - 10x^24 + 37x^22 - 3x^21 - x^20 + 139x^19 - 26x^18 + 76x^17 + 144x^16 - 117x^15 - 101x^14 + 12x^13 - 340x^12 + x^11 + 205x^10 + 307x^9 + 774x^8 + 909x^7 + 892x^6 + 864x^5 + 521x^4 + 327x^3 + 86x^2 + 71x + 1	$27$	[1,13]	$-\,1231^{13}$	$1$	$30.75402942005746$				$D_{27}$ (as 27T8)	trivial	$2$	$13$	$5105816638.575763$
27.9.177...912.1	x^27 - 18x^25 + 189x^23 - 63x^22 - 1062x^21 + 648x^20 + 4464x^19 - 2679x^18 - 14499x^17 + 7092x^16 + 36963x^15 - 21411x^14 - 74187x^13 + 24255x^12 + 61398x^11 - 36351x^10 - 17520x^9 + 66663x^8 + 42507x^7 - 11583x^6 - 18603x^5 - 10539x^4 - 6327x^3 - 2835x^2 - 639x - 53	$27$	[9,9]	$-\,2^{18}\cdot 3^{73}$	$2$	$30.95146195929607$			not computed	$C_9\times S_3$ (as 27T12)	trivial	$2$	$17$	$6360080771.530314$
27.9.177...912.2	x^27 - 9x^26 + 36x^25 - 54x^24 - 180x^23 + 1296x^22 - 3699x^21 + 5184x^20 + 1737x^19 - 28278x^18 + 81630x^17 - 152073x^16 + 206037x^15 - 206640x^14 + 143748x^13 - 36954x^12 - 70929x^11 + 125325x^10 - 106329x^9 + 53154x^8 - 10548x^7 - 9594x^6 + 13185x^5 - 9180x^4 + 4068x^3 - 1053x^2 - 207x + 163	$27$	[9,9]	$-\,2^{18}\cdot 3^{73}$	$2$	$30.95146195929607$			not computed	$C_9\times S_3$ (as 27T12)	trivial	$2$	$17$	$8061331492.668233$
27.1.252...624.1	x^27 - 9x^26 + 45x^25 - 154x^24 + 444x^23 - 1140x^22 + 2734x^21 - 5824x^20 + 11115x^19 - 18567x^18 + 29531x^17 - 43306x^16 + 56712x^15 - 56676x^14 + 52570x^13 - 50872x^12 + 59685x^11 - 40721x^10 + 10893x^9 + 10490x^8 - 13378x^7 + 7126x^6 - 3604x^5 - 204x^4 + 1348x^3 - 376x^2 + 8x + 8	$27$	[1,13]	$-\,2^{18}\cdot 491^{13}$	$2$	$31.361192438338826$				$D_{27}$ (as 27T8)	$[2]$	$2$	$13$	$4486112564.467699$
27.1.786...199.1	x^27 - x^26 + 6x^25 - 31x^24 + 97x^23 - 269x^22 + 599x^21 - 994x^20 + 1307x^19 - 1298x^18 + 592x^17 + 817x^16 - 2461x^15 + 4001x^14 - 4903x^13 + 4315x^12 - 2279x^11 - 512x^10 + 3872x^9 - 6814x^8 + 7826x^7 - 7115x^6 + 5689x^5 - 3842x^4 + 1951x^3 - 627x^2 + 101x - 1	$27$	[1,13]	$-\,1399^{13}$	$1$	$32.707923524616376$				$D_{27}$ (as 27T8)	$[2]$	$2$	$13$	$6401978481.787342$
27.1.149...032.1	x^27 - 7x^26 + 21x^25 - 50x^24 + 110x^23 - 244x^22 + 734x^21 - 2140x^20 + 5743x^19 - 13591x^18 + 28791x^17 - 54584x^16 + 93410x^15 - 138060x^14 + 176010x^13 - 189870x^12 + 169389x^11 - 127135x^10 + 89765x^9 - 72912x^8 + 70628x^7 - 65648x^6 + 50256x^5 - 29876x^4 + 13340x^3 - 4224x^2 + 848x - 80	$27$	[1,13]	$-\,2^{18}\cdot 563^{13}$	$2$	$33.49696971150064$				$D_{27}$ (as 27T8)	$[2]$	$2$	$13$	$14887194175.434155$
27.1.476...207.1	x^27 - 3x^26 - 11x^25 + 17x^24 + 38x^23 + x^22 + 157x^21 + 384x^20 + 124x^19 - 139x^18 + 318x^17 + 1284x^16 + 1757x^15 - 73x^14 - 3289x^13 - 3942x^12 - 2202x^11 - 2459x^10 - 3813x^9 - 1971x^8 + 2174x^7 + 7281x^6 + 9348x^5 + 4444x^4 - 209x^3 - 325x^2 + 132x + 1	$27$	[1,13]	$-\,1607^{13}$	$1$	$34.96530122267493$				$D_{27}$ (as 27T8)	trivial	$2$	$13$	$16112744313.230444$
27.1.154...079.1	x^27 - 6x^26 + 31x^25 - 80x^24 + 117x^23 - 51x^22 - 243x^21 + 807x^20 - 1350x^19 + 966x^18 + 1935x^17 - 9345x^16 + 23103x^15 - 43548x^14 + 68751x^13 - 94575x^12 + 115269x^11 - 125268x^10 + 121785x^9 - 105567x^8 + 81027x^7 - 54357x^6 + 31122x^5 - 14664x^4 + 5393x^3 - 1350x^2 + 179x - 1	$27$	[1,13]	$-\,1759^{13}$	$1$	$36.52038978810907$				$D_{27}$ (as 27T8)	trivial	$2$	$13$	$71844122831.24568$
27.1.363...239.1	x^27 - 2x^26 + x^25 + 18x^24 + 107x^23 + 180x^22 + 332x^21 + 290x^20 + 295x^19 - 179x^18 - 772x^17 - 1774x^16 - 2092x^15 - 2320x^14 - 811x^13 + 489x^12 + 3551x^11 + 5424x^10 + 7617x^9 + 6962x^8 + 6380x^7 + 2824x^6 + 2291x^5 - 521x^4 + 623x^3 - 221x^2 + 207x - 1	$27$	[1,13]	$-\,1879^{13}$	$1$	$37.69945885824853$				$D_{27}$ (as 27T8)	$[4]$	$2$	$13$	$25801652404.76311$
27.1.813...999.1	x^27 - 11x^26 + 70x^25 - 273x^24 + 723x^23 - 1456x^22 + 2649x^21 - 4775x^20 + 8022x^19 - 11719x^18 + 15552x^17 - 20687x^16 + 27099x^15 - 31222x^14 + 31020x^13 - 30638x^12 + 32802x^11 - 31588x^10 + 22446x^9 - 12521x^8 + 9384x^7 - 8740x^6 + 4644x^5 - 254x^4 - 460x^3 - 287x^2 + 245x + 1	$27$	[1,13]	$-\,1999^{13}$	$1$	$38.84009059236418$				$D_{27}$ (as 27T8)	$[5]$	$2$	$13$	$35248883953.15641$
27.1.536...079.1	x^27 - 5x^26 + 4x^25 - 53x^24 + 12x^23 - 178x^22 + 281x^21 - 251x^20 + 1170x^19 - 548x^18 + 1924x^17 - 3164x^16 + 1182x^15 - 5392x^14 + 2732x^13 - 5123x^12 + 7843x^11 + 5402x^10 + 11272x^9 - 9146x^8 - 13685x^7 - 8959x^6 + 8451x^5 + 8381x^4 + 1087x^3 - 2808x^2 - 714x - 59	$27$	[1,13]	$-\,31^{13}\cdot 89^{13}$	$2$	$45.35845217604604$			not computed	$D_{27}$ (as 27T8)	trivial	$2$	$13$	$438273503820.3111$
27.27.706...369.1	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	$27$	[27,0]	$3^{94}$	$1$	$45.823558579$		✓	✓	$C_{27}$ (as 27T1)	trivial	$2$	$26$	$68981171346332.37$
27.1.826...731.1	x^27 + 2x - 1	$27$	[1,13]	$-\,229351\cdot 36\!\cdots\!81$	$2$	$46.0889625063$			✓	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$657547065355.6862$
27.1.124...951.1	x^27 - 13x^26 + 64x^25 - 128x^24 - 64x^23 + 1031x^22 - 3598x^21 + 9810x^20 - 21567x^19 + 36061x^18 - 52129x^17 + 97285x^16 - 181966x^15 + 235897x^14 - 374052x^13 + 634209x^12 - 258724x^11 + 64070x^10 - 1005397x^9 + 111021x^8 + 1266741x^7 + 944398x^6 - 1133842x^5 - 1337690x^4 + 643480x^3 + 1031258x^2 - 50650x + 12587	$27$	[1,13]	$-\,7^{18}\cdot 199^{13}$	$2$	$46.800864812150095$				$D_{27}$ (as 27T8)	$[3, 3]$	$2$	$13$	$215328165314.12698$
27.1.128...351.1	x^27 - 4x^26 + 28x^25 - 42x^24 + 71x^23 + 267x^22 - 142x^21 + 385x^20 + 2210x^19 + 2329x^18 - 3315x^17 + 15117x^16 + 19014x^15 - 23157x^14 + 44479x^13 + 77004x^12 - 41903x^11 + 19829x^10 + 208952x^9 - 35302x^8 - 53453x^7 + 258838x^6 - 35701x^5 + 60990x^4 - 5393x^3 + 76227x^2 + 19031x + 2209	$27$	[1,13]	$-\,13^{13}\cdot 227^{13}$	$2$	$46.851760620993275$				$D_{27}$ (as 27T8)	trivial	$2$	$13$	$1184470448230.2556$
27.1.490...711.1	x^27 - 3x^26 + 15x^25 - 53x^24 + 106x^23 - 298x^22 + 714x^21 - 199x^20 + 2747x^19 + 4180x^18 + 4767x^17 + 27487x^16 - 7928x^15 + 93863x^14 - 80586x^13 + 257840x^12 - 253867x^11 + 459460x^10 - 363114x^9 + 981160x^8 + 143119x^7 - 202978x^6 + 143097x^5 + 629777x^4 + 25669x^3 - 205103x^2 - 65505x + 40293	$27$	[1,13]	$-\,3271^{13}$	$1$	$49.23269336712322$				$D_{27}$ (as 27T8)	$[2]$	$2$	$13$	$2789984396899.383$
27.27.797...529.1	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	$27$	[27,0]	$7^{18}\cdot 19^{24}$	$2$	$50.1266360901$		✓	not computed	$C_3\times C_9$ (as 27T2)	trivial	$2$	$26$	$173879598132270.75$
27.1.201...127.1	x^27 - 9x^26 + 43x^25 - 96x^24 + 144x^23 - 267x^22 + 429x^21 + 20x^20 - 947x^19 + 1263x^18 + 1070x^17 - 4443x^16 + 3518x^15 + 4729x^14 - 7874x^13 + 2497x^12 + 13136x^11 - 1996x^10 - 8600x^9 + 6002x^8 + 17843x^7 - 14482x^6 + 6811x^5 + 47488x^4 + 900x^3 - 46897x^2 + 24633x + 2075	$27$	[1,13]	$-\,7^{13}\cdot 521^{13}$	$2$	$51.88073357956727$				$D_{27}$ (as 27T8)	trivial	$2$	$13$	$16038112241729.484$
27.1.219...911.1	x^27 - 8x^26 + 46x^25 - 158x^24 + 412x^23 - 651x^22 + 948x^21 - 1384x^20 + 7521x^19 - 22249x^18 + 61004x^17 - 97499x^16 + 110127x^15 + 98440x^14 - 785239x^13 + 2068135x^12 - 3012058x^11 + 444932x^10 + 9236470x^9 - 28098698x^8 + 53493798x^7 - 76988059x^6 + 87553666x^5 - 79021445x^4 + 56695661x^3 - 30768538x^2 + 10754601x - 1715933	$27$	[1,13]	$-\,3671^{13}$	$1$	$52.04483866718473$			not computed	$D_{27}$ (as 27T8)	trivial	$2$	$13$	$1347745809122.2559$
27.1.281...936.1	x^27 - 4x - 4	$27$	[1,13]	$-\,2^{26}\cdot 263\cdot 15\!\cdots\!73$	$3$	$52.5200952866$			not computed	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$3583506363801.732$
27.1.289...864.1	x^27 - 2x - 2	$27$	[1,13]	$-\,2^{26}\cdot 239\cdot 911\cdot 1492637\cdot 10924843\cdot 125481509\cdot 967669291801$	$7$	$52.576487102$			✓	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$4511852311652.407$
27.1.297...016.1	x^27 - x - 2	$27$	[1,13]	$-\,2^{27}\cdot 47\cdot 47\!\cdots\!51$	$3$	$52.6313488922$			✓	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$6055111116377.756$
27.1.297...783.1	x^27 - x - 4	$27$	[1,13]	$-\,167\cdot 359\cdot 10245289151\cdot 48\!\cdots\!61$	$4$	$52.6313488926$			not computed	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$6097282211234.32$
27.1.297...792.1	x^27 - 2	$27$	[1,13]	$-\,2^{26}\cdot 3^{81}$	$2$	$52.6313488926$			✓	$C_9.(C_9\times S_3)$ (as 27T176)	trivial	$2$	$13$	$6049054674787.264$
27.1.305...720.1	x^27 + 2x - 2	$27$	[1,13]	$-\,2^{26}\cdot 5\cdot 7\cdot 11\cdot 80071\cdot 14\!\cdots\!13$	$6$	$52.6847629669$			✓	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$6660614872502.112$
27.1.314...648.1	x^27 + 4x - 4	$27$	[1,13]	$-\,2^{26}\cdot 1831\cdot 25\!\cdots\!97$	$3$	$52.7368051276$			not computed	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$8159276315394.001$
27.27.503...521.1	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	$27$	[27,0]	$3^{66}\cdot 7^{18}$	$2$	$53.6654893413$		✓	not computed	$C_3\times C_9$ (as 27T2)	trivial	$2$	$26$	$347763474421246.5$
27.1.556...943.1	x^27 - 6x^26 + 27x^25 - 119x^24 + 469x^23 - 1488x^22 + 4228x^21 - 11600x^20 + 26558x^19 - 54959x^18 + 133324x^17 - 272188x^16 + 522791x^15 - 983894x^14 + 1639478x^13 - 2435791x^12 + 3557436x^11 - 4633264x^10 + 5404652x^9 - 6079977x^8 + 6195381x^7 - 5327698x^6 + 4651935x^5 - 3835566x^4 + 2476602x^3 - 1723599x^2 + 1364445x - 459999	$27$	[1,13]	$-\,3943^{13}$	$1$	$53.86715065106362$				$D_{27}$ (as 27T8)	trivial	$2$	$13$	$29482123669434.47$
27.27.735...441.1	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	$27$	[27,0]	$3^{36}\cdot 19^{24}$	$2$	$59.2695377956$		✓	not computed	$C_3\times C_9$ (as 27T2)	trivial	$2$	$26$	$3059088874781005.5$
27.1.108...375.1	x^27 - 8x^26 + 11x^25 + 79x^24 - 318x^23 + 272x^22 + 1817x^21 - 11487x^20 + 27792x^19 - 5214x^18 - 88324x^17 + 101476x^16 + 384139x^15 - 2894444x^14 + 8285833x^13 - 7065937x^12 - 6208737x^11 - 6594753x^10 + 51530498x^9 - 40765921x^8 + 72314518x^7 - 318855243x^6 + 340132420x^5 + 140246505x^4 - 148040525x^3 - 594053575x^2 + 805097125x - 295863625	$27$	[1,13]	$-\,5^{13}\cdot 7^{18}\cdot 67^{13}$	$3$	$60.13966545010951$				$D_{27}$ (as 27T8)	$[3]$	$2$	$13$	$71364448730505.47$
27.1.356...663.1	x^27 - 10x^26 + 80x^25 - 447x^24 + 1863x^23 - 6240x^22 + 15201x^21 - 25896x^20 + 26931x^19 + 29922x^18 - 2157x^17 + 228x^16 + 1150141x^15 - 1553359x^14 + 3361193x^13 - 357518x^12 - 4399792x^11 - 5659177x^10 - 7694789x^9 - 6381628x^8 + 25148690x^7 + 37280366x^6 + 10154644x^5 - 4374482x^4 + 5689374x^3 + 3195477x^2 - 2094606x + 247941	$27$	[1,13]	$-\,7^{18}\cdot 367^{13}$	$2$	$62.8402507699084$				$D_{27}$ (as 27T8)	$[3]$	$2$	$13$	$67227716701120.3$
27.1.155...607.1	x^27 + 18x^25 - 54x^24 + 81x^23 - 729x^22 + 711x^21 - 2322x^20 + 7389x^19 - 646x^18 + 36288x^17 - 20349x^16 + 36072x^15 - 256311x^14 - 65700x^13 - 942516x^12 + 444744x^11 - 558486x^10 + 4867412x^9 + 1228689x^8 + 12312063x^7 - 3080772x^6 + 6516828x^5 - 31451760x^4 - 20430663x^3 - 52842915x^2 - 27379269x - 39209779	$27$	[1,13]	$-\,3^{66}\cdot 23^{13}$	$2$	$66.36561698613978$				$D_{27}$ (as 27T8)	$[9]$	$2$	$13$	$19566630112992.652$
27.1.199...291.1	x^27 - 2x^26 + 16x^25 + 62x^24 + 342x^23 + 1648x^22 + 6094x^21 + 15834x^20 + 34184x^19 + 61822x^18 + 112334x^17 + 237408x^16 + 637440x^15 + 1828206x^14 + 5099608x^13 + 12463122x^12 + 26430338x^11 + 48978608x^10 + 80603954x^9 + 116977534x^8 + 149538616x^7 + 167922122x^6 + 164525402x^5 + 137815936x^4 + 94764543x^3 + 50090044x^2 + 17954520x + 3418472	$27$	[1,13]	$-\,7^{18}\cdot 419^{13}$	$2$	$66.98016080949778$				$D_{27}$ (as 27T8)	$[3]$	$2$	$13$	$951820331630620.2$
27.1.432...211.1	x^27 - 3x - 3	$27$	[1,13]	$-\,3^{27}\cdot 71\cdot 337\cdot 14619373\cdot 78563389\cdot 206180539890995287$	$6$	$68.9213900506$			not computed	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$123801473306894.75$
27.3.469...109.1	x^27 - 3x - 1	$27$	[3,12]	$3^{27}\cdot 11\cdot 29\cdot 318911\cdot 7780103222533\cdot 7777884788734331$	$6$	$69.1334423852$			✓	$S_{27}$ (as 27T2392)	$[2]$	$2$	$14$	$77237424497237.73$
27.1.469...715.1	x^27 + 3x - 1	$27$	[1,13]	$-\,3^{27}\cdot 5\cdot 29573\cdot 718375177076041\cdot 57954924238599673$	$5$	$69.1334423853$			✓	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$179325593937769.6$
27.1.469...704.1	x^27 + 3x - 2	$27$	[1,13]	$-\,2^{27}\cdot 3^{27}\cdot 1592729\cdot 28815787221263522142841$	$4$	$69.1350649891$			✓	$S_{27}$ (as 27T2392)	trivial	$2$	$13$	$306797613214632.25$
27.1.863...271.1	x^27 - 9x^26 + 51x^25 - 157x^24 + 381x^23 + 94x^22 - 4772x^21 + 22385x^20 - 19633x^19 - 132957x^18 + 462384x^17 + 49228x^16 - 4729835x^15 + 16673567x^14 - 15312382x^13 - 102305328x^12 + 361800096x^11 - 196173035x^10 - 890969729x^9 + 1569260108x^8 - 437613721x^7 - 1278467664x^6 + 2134193061x^5 - 1922367953x^4 + 1085805378x^3 - 524572351x^2 + 152402636x - 24878621	$27$	[1,13]	$-\,13^{18}\cdot 199^{13}$	$2$	$70.71052902824587$				$D_{27}$ (as 27T8)	$[3]$	$2$	$13$	$174903583233230.53$
27.1.100...375.1	x^27 - 82x^24 - 9x^23 + 195x^22 + 2387x^21 + 810x^20 - 11814x^19 - 33683x^18 + 2520x^17 + 230379x^16 + 441880x^15 - 1170738x^14 - 529926x^13 - 6335185x^12 + 26111763x^11 - 28861455x^10 + 54201969x^9 - 172123947x^8 + 231730104x^7 - 172770969x^6 + 271759050x^5 - 338641350x^4 + 41402575x^3 + 177368400x^2 - 96664125x + 14269375	$27$	[1,13]	$-\,3^{36}\cdot 5^{13}\cdot 67^{13}$	$3$	$71.10890441561979$				$D_{27}$ (as 27T8)	$[3]$	$2$	$13$	$716753350335435.2$
27.1.119...311.1	x^27 - 9x^26 + 56x^25 - 273x^24 + 1290x^23 - 5604x^22 + 24003x^21 - 98346x^20 + 381168x^19 - 1383408x^18 + 4700958x^17 - 15265944x^16 + 47759673x^15 - 142609974x^14 + 403676163x^13 - 1071234237x^12 + 2616260829x^11 - 5766916275x^10 + 11330239941x^9 - 19648861461x^8 + 29452821249x^7 - 36679431165x^6 + 35809916697x^5 - 25389897726x^4 + 11811942110x^3 - 3328128234x^2 + 1063555192x - 565863243	$27$	[1,13]	$-\,19^{24}\cdot 31^{13}$	$2$	$71.57031114737545$				$D_{27}$ (as 27T8)	$[9]$	$2$	$13$	$111879013692337.2$
27.27.550...809.1	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	$27$	[27,0]	$13^{18}\cdot 19^{24}$	$2$	$75.7353730656$		✓	not computed	$C_3\times C_9$ (as 27T2)	trivial	$2$	$26$	$43333147066107930$
27.1.929...947.1	x^27 - 11x^26 + 7x^25 + 393x^24 - 1777x^23 - 1339x^22 + 33149x^21 - 122161x^20 + 301221x^19 - 901165x^18 + 2771309x^17 - 5696089x^16 + 7240134x^15 - 11573472x^14 + 45471960x^13 - 153604016x^12 + 357338624x^11 - 615897728x^10 + 876134656x^9 - 1154442240x^8 + 1414654976x^7 - 1520924672x^6 + 1526870016x^5 - 1494863872x^4 + 1216438272x^3 - 684785664x^2 + 248741888x - 73596928	$27$	[1,13]	$-\,7^{18}\cdot 563^{13}$	$2$	$77.21782241594255$				$D_{27}$ (as 27T8)	$[6]$	$2$	$13$	$5470716283346407.0$