Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 1134 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
18.0.552...000.1	$x^{18} + 285 x^{16} + 34200 x^{14} + 2244375 x^{12} + 87530625 x^{10} + 2063221875 x^{8} + 28567687500 x^{6} + 214257656250 x^{4} + 730423828125 x^{2} + 730423828125$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 5^{9}\cdot 19^{17}$	$4$	$124.964702446$	$124.96470244562842$	✓	✓	?	$C_{18}$ (as 18T1)	$[2, 2, 2617972]$	$2$	$8$	$22305.895079162343$
18.0.184...043.1	$x^{18} - 9 x^{17} + 207 x^{16} - 1452 x^{15} + 18648 x^{14} - 105840 x^{13} + 976272 x^{12} - 4545126 x^{11} + 32991876 x^{10} - 125652506 x^{9} + 749248587 x^{8} - 2289051090 x^{7} + 11455485945 x^{6} - 26836628409 x^{5} + 113757248880 x^{4} - 185230785420 x^{3} + 665351396991 x^{2} - 576856453545 x + 1743009516489$	$18$	[0,9]	$-\,3^{44}\cdot 83^{9}$	$2$	$133.608917888$	$133.60891788772665$	✓	✓	?	$C_{18}$ (as 18T1)	$[10774323]$	$2$	$8$	$40934.03294431194$
18.0.237...543.1	$x^{18} - x^{17} + 240 x^{16} - 204 x^{15} + 25432 x^{14} - 17806 x^{13} + 1559289 x^{12} - 826496 x^{11} + 61315072 x^{10} - 21167725 x^{9} + 1619807322 x^{8} - 270891066 x^{7} + 28847771990 x^{6} - 914438490 x^{5} + 333576288008 x^{4} + 12164206228 x^{3} + 2271310237552 x^{2} + 89107859956 x + 6936762462491$	$18$	[0,9]	$-\,7^{15}\cdot 138041^{5}$	$2$	$135.52780156040677$	$1880.4094066508408$	✓		?	$S_3^3:C_6$ (as 18T283)	$[4, 3831240]$	$2$	$8$	$22017.76415264327$
18.0.421...091.1	$x^{18} - 9 x^{17} + 225 x^{16} - 1596 x^{15} + 22104 x^{14} - 127512 x^{13} + 1262352 x^{12} - 5986422 x^{11} + 46502352 x^{10} - 180492362 x^{9} + 1149875379 x^{8} - 3577518954 x^{7} + 19116861729 x^{6} - 45526465413 x^{5} + 206139713310 x^{4} - 340247545008 x^{3} + 1307472810363 x^{2} - 1144383031881 x + 3709960454951$	$18$	[0,9]	$-\,3^{44}\cdot 7^{9}\cdot 13^{9}$	$3$	$139.899800953$	$139.8998009532401$	✓	✓	?	$C_{18}$ (as 18T1)	$[7, 7, 249242]$	$2$	$8$	$40934.03294431194$
18.0.620...375.1	$x^{18} - 9 x^{17} + 234 x^{16} - 1668 x^{15} + 23940 x^{14} - 139104 x^{13} + 1424040 x^{12} - 6809130 x^{11} + 54623250 x^{10} - 213823058 x^{9} + 1405734741 x^{8} - 4409563914 x^{7} + 24309351321 x^{6} - 58323184659 x^{5} + 272500787439 x^{4} - 452550480084 x^{3} + 1795735413621 x^{2} - 1578496430709 x + 5291384827899$	$18$	[0,9]	$-\,3^{44}\cdot 5^{9}\cdot 19^{9}$	$3$	$142.941456515$	$142.94145651479022$	✓	✓	?	$C_{18}$ (as 18T1)	$[2, 2, 7697016]$	$2$	$8$	$40934.03294431194$
18.0.828...832.1	$x^{18} + 213 x^{16} - 6 x^{15} + 20232 x^{14} - 372 x^{13} + 1112048 x^{12} + 2232 x^{11} + 38661657 x^{10} + 1074518 x^{9} + 878462091 x^{8} + 49747296 x^{7} + 13080744725 x^{6} + 1198422450 x^{5} + 126327354123 x^{4} + 18837567282 x^{3} + 761687723085 x^{2} + 133856748120 x + 2131852243753$	$18$	[0,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{15}\cdot 11^{9}$	$4$	$145.256768372$	$145.25676837155686$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 2, 630, 1260]$	$2$	$8$	$54408.48888868202$
18.0.957...211.1	$x^{18} + 318 x^{16} - x^{15} + 39447 x^{14} - 321 x^{13} + 2500302 x^{12} - 133146 x^{11} + 89391399 x^{10} - 15798444 x^{9} + 1882862586 x^{8} - 809469819 x^{7} + 23827510937 x^{6} - 18496427643 x^{5} + 185880800082 x^{4} - 182182097162 x^{3} + 930282815520 x^{2} - 609765780432 x + 2780371629001$	$18$	[0,9]	$-\,3^{27}\cdot 7^{15}\cdot 31^{9}$	$3$	$146.423605184$	$146.42360518381108$	✓	✓	?	$C_6 \times C_3$ (as 18T2)	$[2, 4, 76, 16492]$	$2$	$8$	$54408.48888868202$
18.0.296...863.7	$x^{18} - 93 x^{16} - 48 x^{15} + 4050 x^{14} + 6240 x^{13} - 91658 x^{12} - 228384 x^{11} + 1071381 x^{10} + 4611968 x^{9} - 823257 x^{8} - 35960496 x^{7} - 77344856 x^{6} - 104708448 x^{5} - 4174416 x^{4} + 533722240 x^{3} + 4177096704 x^{2} + 12286132224 x + 10835984384$	$18$	[0,9]	$-\,3^{24}\cdot 7^{15}\cdot 19^{12}$	$3$	$155.923810734$	$155.9238107337415$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[4, 7372092]$	$2$	$8$	$10681224266.072006$
18.0.377...024.1	$x^{18} - 9 x^{17} + 258 x^{16} - 1706 x^{15} + 25692 x^{14} - 123246 x^{13} + 1221682 x^{12} - 4356336 x^{11} + 28639551 x^{10} - 81366637 x^{9} + 336386712 x^{8} - 771159882 x^{7} + 2020760692 x^{6} - 3333464652 x^{5} + 16394855484 x^{4} - 26333009892 x^{3} + 201734400000 x^{2} - 303589255200 x + 486213973000$	$18$	[0,9]	$-\,2^{12}\cdot 3^{21}\cdot 7^{14}\cdot 37^{9}$	$4$	$158.025606281$	$176.06675349561556$	✓		?	$S_3 \times C_6$ (as 18T6)	$[18, 54, 12312]$	$2$	$8$	$296124.35954857944$
18.0.540...959.7	$x^{18} - 3 x^{16} - 102 x^{15} + 306 x^{14} - 2904 x^{13} + 10306 x^{12} - 25956 x^{11} + 197229 x^{10} - 685960 x^{9} + 4076145 x^{8} - 16235718 x^{7} + 47843680 x^{6} - 129191472 x^{5} + 192346320 x^{4} - 242786912 x^{3} + 186484608 x^{2} + 741275136 x + 1196406784$	$18$	[0,9]	$-\,3^{27}\cdot 7^{12}\cdot 13^{15}$	$3$	$161.200617964$	$161.20061796425267$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[19, 1639092]$	$2$	$8$	$12689307150.302711$
18.0.462...023.1	$x^{18} + 318 x^{16} - 4 x^{15} + 31761 x^{14} - 5688 x^{13} + 1346987 x^{12} - 850383 x^{11} + 29343633 x^{10} - 33350634 x^{9} + 387929952 x^{8} - 516066921 x^{7} + 3633489894 x^{6} - 2896022691 x^{5} + 22810900296 x^{4} + 4904628409 x^{3} + 82416559734 x^{2} + 65824912344 x + 283790949688$	$18$	[0,9]	$-\,3^{27}\cdot 13^{15}\cdot 17^{9}$	$3$	$181.63204374$	$181.63204374014467$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 14, 14, 70952]$	$2$	$8$	$400417.1364448253$
18.0.465...000.1	$x^{18} - 6 x^{17} + 171 x^{16} - 866 x^{15} + 12825 x^{14} - 53706 x^{13} + 534596 x^{12} - 1842426 x^{11} + 13567536 x^{10} - 37365600 x^{9} + 219817671 x^{8} - 463924236 x^{7} + 2271460011 x^{6} - 3413556846 x^{5} + 15903607875 x^{4} - 10762099726 x^{3} + 82917294006 x^{2} + 893627904 x + 191108188441$	$18$	[0,9]	$-\,2^{27}\cdot 3^{27}\cdot 5^{9}\cdot 13^{12}$	$4$	$181.694080849$	$181.6940808491004$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 2, 90, 8190]$	$2$	$8$	$400417.1364448253$
18.0.669...352.1	$x^{18} + 108 x^{16} - 74 x^{15} + 4536 x^{14} - 4830 x^{13} + 124649 x^{12} - 107154 x^{11} + 2413434 x^{10} - 360170 x^{9} + 30463398 x^{8} + 5604570 x^{7} + 339507997 x^{6} + 2126142 x^{5} + 2908814970 x^{4} - 799917180 x^{3} + 10800077634 x^{2} - 5825746080 x + 18499563441$	$18$	[0,9]	$-\,2^{12}\cdot 3^{20}\cdot 7^{9}\cdot 47^{12}$	$4$	$185.396835308$	$271.6129929155886$	✓			$D_6\times S_4$ (as 18T111)	$[2, 2, 2511600]$	$2$	$8$	$12045005.94090459$
18.0.839...799.1	$x^{18} - 9 x^{17} + 60 x^{16} - 262 x^{15} + 1929 x^{14} - 10053 x^{13} + 71441 x^{12} - 309315 x^{11} + 1767420 x^{10} - 6349626 x^{9} + 33272703 x^{8} - 106851099 x^{7} + 497306862 x^{6} - 1307684628 x^{5} + 4889287872 x^{4} - 9029732096 x^{3} + 25896306432 x^{2} - 25618016256 x + 54730227712$	$18$	[0,9]	$-\,3^{21}\cdot 13^{9}\cdot 31^{14}$	$3$	$187.741863408$	$227.2032563448099$	✓			$S_3 \times C_6$ (as 18T6)	$[20, 1491440]$	$2$	$8$	$67295442.84873295$
18.0.861...944.2	$x^{18} - 7 x^{17} + 111 x^{16} - 570 x^{15} + 5575 x^{14} - 24157 x^{13} + 183489 x^{12} - 702801 x^{11} + 4348726 x^{10} - 14614200 x^{9} + 74356953 x^{8} - 212878813 x^{7} + 887867263 x^{6} - 2056738955 x^{5} + 6915161271 x^{4} - 11750894177 x^{3} + 30681517019 x^{2} - 29651248130 x + 55649538283$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 17^{9}\cdot 37^{14}$	$4$	$188.011408889$	$229.7769825137185$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 1940166]$	$2$	$8$	$615797.1340659427$
18.0.120...744.2	$x^{18} - 2 x^{17} + 164 x^{16} - 314 x^{15} + 13029 x^{14} - 21092 x^{13} + 651907 x^{12} - 798220 x^{11} + 22417227 x^{10} - 18246558 x^{9} + 545228110 x^{8} - 241380330 x^{7} + 9318786102 x^{6} - 1404347650 x^{5} + 107199772771 x^{4} + 3474292326 x^{3} + 747079319085 x^{2} + 64419294176 x + 2378782567897$	$18$	[0,9]	$-\,2^{24}\cdot 3^{9}\cdot 7^{9}\cdot 37^{14}$	$4$	$191.511750958$	$234.05490396037922$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 18, 18, 36, 468]$	$2$	$8$	$615797.1340659427$
18.0.169...000.1	$x^{18} - 7 x^{17} + 120 x^{16} - 626 x^{15} + 6531 x^{14} - 28695 x^{13} + 229872 x^{12} - 888043 x^{11} + 5767404 x^{10} - 19494767 x^{9} + 103972952 x^{8} - 299009263 x^{7} + 1307752076 x^{6} - 3039956271 x^{5} + 10743313753 x^{4} - 18290873776 x^{3} + 50489934410 x^{2} - 48726323693 x + 97992831511$	$18$	[0,9]	$-\,2^{12}\cdot 5^{9}\cdot 11^{9}\cdot 37^{14}$	$4$	$195.245242617$	$238.6177677391283$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 4, 28, 23436]$	$2$	$8$	$615797.1340659427$
18.0.178...056.1	$x^{18} - 6 x^{17} + 105 x^{16} - 470 x^{15} + 5088 x^{14} - 19992 x^{13} + 150340 x^{12} - 481404 x^{11} + 2729481 x^{10} - 7706476 x^{9} + 37870875 x^{8} - 94591272 x^{7} + 340487281 x^{6} - 646277772 x^{5} + 2508975903 x^{4} - 6699277158 x^{3} + 23166778845 x^{2} - 36740356506 x + 47051159113$	$18$	[0,9]	$-\,2^{18}\cdot 3^{27}\cdot 7^{9}\cdot 19^{12}$	$4$	$195.777734388$	$195.7777343883671$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 42, 84, 588]$	$2$	$8$	$1472619.082400847$
18.0.182...608.1	$x^{18} - 2 x^{17} + 173 x^{16} - 330 x^{15} + 14429 x^{14} - 23330 x^{13} + 755082 x^{12} - 929854 x^{11} + 27080080 x^{10} - 22449952 x^{9} + 685380987 x^{8} - 317287568 x^{7} + 12167724659 x^{6} - 2095429314 x^{5} + 145194850029 x^{4} + 2023454274 x^{3} + 1048817590026 x^{2} + 78764845432 x + 3461536818169$	$18$	[0,9]	$-\,2^{33}\cdot 11^{9}\cdot 37^{14}$	$3$	$196.018526409$	$239.56283175160974$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 14, 270774]$	$2$	$8$	$615797.1340659427$
18.0.319...216.1	$x^{18} - 7 x^{17} + 129 x^{16} - 682 x^{15} + 7559 x^{14} - 33625 x^{13} + 283423 x^{12} - 1103801 x^{11} + 7509688 x^{10} - 25521676 x^{9} + 142410717 x^{8} - 411169037 x^{7} + 1882145661 x^{6} - 4387355467 x^{5} + 16263505093 x^{4} - 27720649061 x^{3} + 80685361261 x^{2} - 77705750398 x + 166746964831$	$18$	[0,9]	$-\,2^{12}\cdot 37^{14}\cdot 59^{9}$	$3$	$202.220472891$	$247.14250235137513$	✓		?	$S_3 \times C_6$ (as 18T6)	$[6, 6, 649404]$	$2$	$8$	$615797.1340659427$
18.0.474...984.2	$x^{18} - 6 x^{17} + 117 x^{16} - 432 x^{15} + 7029 x^{14} - 4380 x^{13} + 269520 x^{12} + 360156 x^{11} + 6871230 x^{10} + 13600116 x^{9} + 121388427 x^{8} + 236256312 x^{7} + 1453703763 x^{6} + 2285310216 x^{5} + 11313506295 x^{4} + 12526883586 x^{3} + 52656339330 x^{2} + 33634384392 x + 143873586899$	$18$	[0,9]	$-\,2^{12}\cdot 3^{30}\cdot 7^{15}\cdot 17^{9}$	$4$	$206.71004539$	$219.7193566513441$	✓		?	$S_3 \times C_6$ (as 18T6)	$[3, 6, 126, 4410]$	$2$	$8$	$4695974.091249611$
18.0.100...368.1	$x^{18} - 7 x^{17} + 147 x^{16} - 794 x^{15} + 9831 x^{14} - 44661 x^{13} + 414045 x^{12} - 1636273 x^{11} + 12151554 x^{10} - 41702360 x^{9} + 253396625 x^{8} - 736480093 x^{7} + 3673658915 x^{6} - 8598059427 x^{5} + 34867471171 x^{4} - 59468160457 x^{3} + 191099338775 x^{2} - 183041086898 x + 442378829803$	$18$	[0,9]	$-\,2^{12}\cdot 37^{14}\cdot 67^{9}$	$3$	$215.494662209$	$263.3654708648976$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 6, 18, 211302]$	$2$	$8$	$615797.1340659427$
18.0.103...448.1	$x^{18} - 3 x^{17} + 6 x^{16} + 90 x^{15} - 39 x^{14} - 1401 x^{13} + 20406 x^{12} - 100113 x^{11} + 481848 x^{10} - 1697075 x^{9} + 6375792 x^{8} - 19367253 x^{7} + 59042850 x^{6} - 141091389 x^{5} + 317659023 x^{4} - 527232024 x^{3} + 800021124 x^{2} - 738392301 x + 619938747$	$18$	[0,9]	$-\,2^{12}\cdot 3^{30}\cdot 7^{14}\cdot 23^{9}$	$4$	$215.799855007$	$255.56876602031062$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 6, 6, 18, 11718]$	$2$	$8$	$4695974.091249611$
18.0.105...663.9	$x^{18} - 6 x^{17} - 45 x^{16} + 286 x^{15} + 1074 x^{14} - 8460 x^{13} + 3702 x^{12} + 21564 x^{11} + 216501 x^{10} - 1108894 x^{9} + 2166711 x^{8} - 741978 x^{7} + 5953192 x^{6} - 49153200 x^{5} + 88036464 x^{4} - 8290208 x^{3} - 445115136 x^{2} + 498077184 x + 921751552$	$18$	[0,9]	$-\,3^{24}\cdot 7^{15}\cdot 31^{12}$	$3$	$216.098209672$	$216.09820967240051$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[15926169]$	$2$	$8$	$219311185150.01114$
18.0.124...000.3	$x^{18} - 3 x^{17} - 60 x^{16} + 60 x^{15} + 1944 x^{14} + 1116 x^{13} - 22314 x^{12} - 19494 x^{11} + 210087 x^{10} + 301551 x^{9} + 816822 x^{8} + 5088618 x^{7} + 20836656 x^{6} + 36778968 x^{5} + 128208960 x^{4} + 167694048 x^{3} + 625363200 x^{2} + 242697600 x + 1721055744$	$18$	[0,9]	$-\,2^{18}\cdot 3^{31}\cdot 5^{9}\cdot 13^{14}$	$4$	$218.084204042$	$355.65175012690474$	✓			$S_3 \times C_6$ (as 18T6)	$[14, 2754192]$	$2$	$8$	$3533133948.6916637$
18.0.169...464.1	$x^{18} - 7 x^{17} + 156 x^{16} - 850 x^{15} + 11075 x^{14} - 50767 x^{13} + 492124 x^{12} - 1957691 x^{11} + 15151936 x^{10} - 52229455 x^{9} + 330391428 x^{8} - 962984783 x^{7} + 5002295088 x^{6} - 11724742015 x^{5} + 49602460501 x^{4} - 84577334312 x^{3} + 284676104674 x^{2} - 271819124605 x + 693932370643$	$18$	[0,9]	$-\,2^{12}\cdot 37^{14}\cdot 71^{9}$	$3$	$221.834091907$	$271.1131657289703$	✓		?	$S_3 \times C_6$ (as 18T6)	$[6, 42, 42, 7686]$	$2$	$8$	$615797.1340659427$
18.0.188...072.1	$x^{18} + 252 x^{16} + 26460 x^{14} + 1498224 x^{12} + 49441392 x^{10} + 958402368 x^{8} + 10435936896 x^{6} + 56923292160 x^{4} + 119538913536 x^{2} + 54965524992$	$18$	[0,9]	$-\,2^{27}\cdot 3^{45}\cdot 7^{15}$	$3$	$223.14979745$	$223.14979745003714$	✓	✓		$C_{18}$ (as 18T1)	$[2, 5642754]$	$2$	$8$	$10392888.21418944$
18.0.234...000.1	$x^{18} - 6 x^{17} + 57 x^{16} - 342 x^{15} + 2397 x^{14} - 8274 x^{13} + 73002 x^{12} - 114570 x^{11} + 1570920 x^{10} - 636788 x^{9} + 24975411 x^{8} + 9022440 x^{7} + 286583163 x^{6} + 206392410 x^{5} + 2169968997 x^{4} + 1548565326 x^{3} + 9411997182 x^{2} + 4225615884 x + 17320048361$	$18$	[0,9]	$-\,2^{33}\cdot 3^{30}\cdot 5^{9}\cdot 7^{14}$	$4$	$225.877979521$	$267.5041486729831$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 6, 6, 219198]$	$2$	$8$	$4695974.091249611$
18.0.300...672.1	$x^{18} - 7 x^{17} - 50 x^{16} + 520 x^{15} + 296 x^{14} - 14596 x^{13} + 31102 x^{12} + 144874 x^{11} - 651061 x^{10} - 156909 x^{9} + 5579540 x^{8} - 10349906 x^{7} - 6028004 x^{6} + 37023896 x^{5} + 14364176 x^{4} - 242844992 x^{3} + 517853824 x^{2} - 521534464 x + 242280448$	$18$	[0,9]	$-\,2^{18}\cdot 7^{9}\cdot 127^{14}$	$3$	$229.018622758$	$423.90035567675454$	✓			$S_3 \times C_6$ (as 18T6)	$[6, 6, 648144]$	$2$	$8$	$5546046730.2947445$
18.0.387...448.1	$x^{18} + 221 x^{16} + 18798 x^{14} + 773383 x^{12} + 15825836 x^{10} + 146193112 x^{8} + 451182511 x^{6} + 175757803 x^{4} + 11193715 x^{2} + 107653$	$18$	[0,9]	$-\,2^{18}\cdot 13^{15}\cdot 19^{16}$	$3$	$232.266186843$	$232.26618684296346$	✓	✓		$C_{18}$ (as 18T1)	$[3, 9, 909594]$	$2$	$8$	$107879432.94074221$
18.0.506...407.1	$x^{18} - x^{17} + 95 x^{16} - 786 x^{15} - 3197 x^{14} + 39408 x^{13} - 47312 x^{12} - 130372 x^{11} - 88308 x^{10} - 3107148 x^{9} + 43928444 x^{8} - 130864084 x^{7} + 152081560 x^{6} - 646274448 x^{5} + 2209461811 x^{4} - 1564440675 x^{3} - 1350313403 x^{2} - 452031866 x + 2852917793$	$18$	[0,9]	$-\,19^{15}\cdot 37^{15}$	$2$	$235.75600895$	$235.75600895005888$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 28, 67564]$	$2$	$8$	$57298269.80370742$
18.0.697...000.2	$x^{18} - 81 x^{16} + 3735 x^{14} - 95193 x^{12} + 1676052 x^{10} - 25382 x^{9} - 15545754 x^{8} + 6167826 x^{7} + 129779769 x^{6} - 281435616 x^{5} + 167351805 x^{4} + 3605893830 x^{3} + 7379910756 x^{2} - 10205696088 x + 65865831261$	$18$	[0,9]	$-\,2^{18}\cdot 3^{44}\cdot 5^{9}\cdot 7^{12}$	$4$	$239.999364426$	$239.9993644260504$	✓	✓	?	$C_{18}$ (as 18T1)	$[3, 3, 1858158]$	$2$	$8$	$4392158.291236831$
18.0.702...000.3	$x^{18} - 6 x^{17} + 237 x^{16} - 1302 x^{15} + 27597 x^{14} - 124314 x^{13} + 2042502 x^{12} - 6836730 x^{11} + 104127960 x^{10} - 234474428 x^{9} + 3743115171 x^{8} - 4993969080 x^{7} + 93909017643 x^{6} - 60571863750 x^{5} + 1569548611977 x^{4} - 315811185954 x^{3} + 15683707815702 x^{2} + 81200252004 x + 70597462733281$	$18$	[0,9]	$-\,2^{33}\cdot 3^{31}\cdot 5^{9}\cdot 7^{14}$	$4$	$240.093626067$	$267.5041486729831$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 2, 304, 10032]$	$2$	$8$	$4695974.091249611$
18.0.706...416.1	$x^{18} - 2 x^{17} + 98 x^{16} - 230 x^{15} + 7698 x^{14} - 11158 x^{13} + 451361 x^{12} - 483714 x^{11} + 19896362 x^{10} - 12565692 x^{9} + 686399371 x^{8} - 27166024 x^{7} + 17905672065 x^{6} + 7923669502 x^{5} + 323641640959 x^{4} + 201391197924 x^{3} + 3528664372527 x^{2} + 1687026042884 x + 17172029521969$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 7^{15}\cdot 19^{16}$	$4$	$240.164524772$	$240.16452477246145$	✓	✓	?	$C_{18}$ (as 18T1)	$[2, 2, 12, 598788]$	$2$	$8$	$4369063.348005476$
18.0.706...416.2	$x^{18} - 2 x^{17} + 98 x^{16} - 230 x^{15} + 7698 x^{14} - 12222 x^{13} + 450829 x^{12} - 294056 x^{11} + 20316110 x^{10} - 1036720 x^{9} + 691813801 x^{8} + 163570074 x^{7} + 17189420781 x^{6} + 4958427054 x^{5} + 301709383024 x^{4} + 51432868270 x^{3} + 3384649707670 x^{2} + 106026030264 x + 17934199170349$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 7^{15}\cdot 19^{16}$	$4$	$240.164524772$	$240.16452477246145$	✓	✓		$C_{18}$ (as 18T1)	$[2, 2, 228, 74556]$	$2$	$8$	$7595459.562747852$
18.0.722...659.1	$x^{18} + 294 x^{16} - 161 x^{15} + 32481 x^{14} - 21558 x^{13} + 1885484 x^{12} - 473373 x^{11} + 63962538 x^{10} + 40776861 x^{9} + 1386184545 x^{8} + 1712290440 x^{7} + 23514110103 x^{6} + 23995814184 x^{5} + 285834467088 x^{4} + 213915299096 x^{3} + 1630678178304 x^{2} + 1262975131200 x + 3320473161664$	$18$	[0,9]	$-\,3^{27}\cdot 7^{9}\cdot 31^{15}$	$3$	$240.454170291$	$240.45417029126355$	✓	✓	?	$C_6 \times C_3$ (as 18T2)	$[2, 4, 28, 58156]$	$2$	$8$	$4617140.625511786$
18.0.857...888.3	$x^{18} - 3 x^{17} - 78 x^{16} + 108 x^{15} + 2664 x^{14} - 12 x^{13} - 41898 x^{12} - 26646 x^{11} + 339819 x^{10} + 315807 x^{9} - 1018584 x^{8} + 613290 x^{7} + 6179676 x^{6} + 3729264 x^{5} + 5211552 x^{4} + 12964608 x^{3} + 42863616 x^{2} + 761856 x + 107610112$	$18$	[0,9]	$-\,2^{18}\cdot 3^{30}\cdot 7^{9}\cdot 13^{14}$	$4$	$242.762438923$	$420.8128257499555$	✓			$S_3 \times C_6$ (as 18T6)	$[5, 30, 442890]$	$2$	$8$	$3533133948.6916637$
18.0.882...823.10	$x^{18} - 201 x^{16} - 324 x^{15} + 17658 x^{14} + 54144 x^{13} - 814130 x^{12} - 3918456 x^{11} + 18110517 x^{10} + 145388304 x^{9} - 29319813 x^{8} - 2622648420 x^{7} - 6893038592 x^{6} + 11462360976 x^{5} + 109788683088 x^{4} + 298107348480 x^{3} + 389859017472 x^{2} + 168742637568 x + 25516048384$	$18$	[0,9]	$-\,3^{24}\cdot 7^{15}\cdot 37^{12}$	$3$	$243.152005351$	$243.1520053514046$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[3, 693, 9009]$	$2$	$8$	$958454033532.8324$
18.0.114...608.1	$x^{18} - 4 x^{17} + 73 x^{16} - 30 x^{15} + 3926 x^{14} - 2892 x^{13} + 101877 x^{12} + 389884 x^{11} + 727903 x^{10} + 6714132 x^{9} + 19205829 x^{8} + 49846322 x^{7} + 310395661 x^{6} + 187135216 x^{5} + 1909020302 x^{4} + 450056094 x^{3} + 3062291750 x^{2} + 337394588 x + 3057477097$	$18$	[0,9]	$-\,2^{18}\cdot 17^{9}\cdot 79^{14}$	$3$	$246.709934775$	$314.4925527816637$	✓			$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 4, 84, 5460]$	$2$	$8$	$9044146.559729666$
18.0.126...824.1	$x^{18} + 204 x^{16} - 6 x^{15} + 14787 x^{14} - 354 x^{13} + 387161 x^{12} - 51156 x^{11} + 863727 x^{10} - 952408 x^{9} + 18104562 x^{8} + 12264582 x^{7} + 50853848 x^{6} - 22106286 x^{5} + 191128917 x^{4} + 248399886 x^{3} + 1056948351 x^{2} + 752535174 x + 1084437811$	$18$	[0,9]	$-\,2^{27}\cdot 3^{24}\cdot 37^{15}$	$3$	$248.051259482$	$248.05125948216417$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 2, 2, 234, 8190]$	$2$	$8$	$8790607.764011372$
18.0.143...304.1	$x^{18} - 6 x^{17} + 211 x^{16} - 1138 x^{15} + 19464 x^{14} - 122114 x^{13} + 1096584 x^{12} - 6922760 x^{11} + 42834459 x^{10} - 241278252 x^{9} + 1081718019 x^{8} - 4152759542 x^{7} + 12730277207 x^{6} - 34293059272 x^{5} + 85309213333 x^{4} - 182185551544 x^{3} + 323539798141 x^{2} - 361298982396 x + 231928465789$	$18$	[0,9]	$-\,2^{18}\cdot 3^{9}\cdot 79^{8}\cdot 107^{9}$	$4$	$249.845959372$	$318.490188231914$	✓			$D_6\times S_4$ (as 18T111)	$[2, 2, 2, 8, 254848]$	$2$	$8$	$8859585.0138675$
18.0.149...304.1	$x^{18} + 434 x^{16} + 74648 x^{14} + 6681864 x^{12} + 343561344 x^{10} + 10535881216 x^{8} + 192490790912 x^{6} + 2009002082304 x^{4} + 10714677772288 x^{2} + 21429355544576$	$18$	[0,9]	$-\,2^{27}\cdot 7^{15}\cdot 31^{15}$	$3$	$250.377196167$	$250.37719616667974$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 18, 126, 16884]$	$2$	$8$	$2999047.7597124763$
18.0.151...416.2	$x^{18} - 3 x^{17} + 24 x^{16} + 42 x^{15} + 393 x^{14} - 1725 x^{13} + 32856 x^{12} - 157041 x^{11} + 983802 x^{10} - 3697991 x^{9} + 16474170 x^{8} - 51892869 x^{7} + 180078636 x^{6} - 449775009 x^{5} + 1169945709 x^{4} - 2071336188 x^{3} + 3760200192 x^{2} - 3727057221 x + 4059023093$	$18$	[0,9]	$-\,2^{12}\cdot 3^{30}\cdot 7^{14}\cdot 31^{9}$	$4$	$250.534810569$	$296.70489065000135$	✓		?	$S_3 \times C_6$ (as 18T6)	$[3, 12, 12, 137592]$	$2$	$8$	$4695974.091249611$
18.0.164...807.2	$x^{18} - 3 x^{17} + 66 x^{16} - 8 x^{15} + 7548 x^{14} + 51456 x^{13} + 277369 x^{12} + 1401495 x^{11} - 2483370 x^{10} - 5227070 x^{9} + 207680922 x^{8} - 291557100 x^{7} + 233470852 x^{6} - 171617115 x^{5} + 16443414363 x^{4} - 51037054889 x^{3} + 121351374567 x^{2} - 143569732788 x + 176288881193$	$18$	[0,9]	$-\,3^{24}\cdot 13^{9}\cdot 19^{17}$	$3$	$251.677901046$	$251.6779010456308$	✓	✓	?	$C_{18}$ (as 18T1)	$[3, 4280742]$	$2$	$8$	$15010229.973756868$
18.0.165...768.1	$x^{18} - 6 x^{17} + 264 x^{16} - 1446 x^{15} + 33861 x^{14} - 153312 x^{13} + 2737851 x^{12} - 9357396 x^{11} + 151699395 x^{10} - 356745098 x^{9} + 5906580054 x^{8} - 8515724286 x^{7} + 160131076710 x^{6} - 118816855266 x^{5} + 2888612355147 x^{4} - 789904049838 x^{3} + 31158412601505 x^{2} - 1029715188852 x + 151614141291361$	$18$	[0,9]	$-\,2^{24}\cdot 3^{31}\cdot 7^{14}\cdot 11^{9}$	$4$	$251.812319408$	$280.5607180504484$	✓		?	$S_3 \times C_6$ (as 18T6)	$[2, 2, 6, 6, 6, 12, 7884]$	$2$	$8$	$4695974.091249611$
18.0.233...831.2	$x^{18} - 9 x^{17} + 12 x^{16} + 32 x^{15} + 1686 x^{14} - 9846 x^{13} + 49286 x^{12} - 22440 x^{11} + 1331088 x^{10} - 4191132 x^{9} + 33730047 x^{8} - 34322004 x^{7} + 527869077 x^{6} - 1067345487 x^{5} + 7933667079 x^{4} - 8669431748 x^{3} + 68468181699 x^{2} - 104866576881 x + 427034554111$	$18$	[0,9]	$-\,3^{27}\cdot 13^{9}\cdot 19^{16}$	$3$	$256.639455833$	$256.6394558332278$	✓	✓		$C_{18}$ (as 18T1)	$[19, 1323084]$	$2$	$8$	$15010229.973756868$
18.0.240...736.1	$x^{18} + 372 x^{16} + 52452 x^{14} + 3732648 x^{12} + 148347648 x^{10} + 3427494912 x^{8} + 45983342592 x^{6} + 342643212288 x^{4} + 1265144168448 x^{2} + 1686858891264$	$18$	[0,9]	$-\,2^{27}\cdot 3^{27}\cdot 31^{15}$	$3$	$257.0563207$	$257.0563207002587$	✓	✓		$C_6 \times C_3$ (as 18T2)	$[2, 6, 342, 7182]$	$2$	$8$	$4617140.625511786$
18.0.257...248.1	$x^{18} - 6 x^{17} + 288 x^{16} - 1460 x^{15} + 31743 x^{14} - 144054 x^{13} + 1740469 x^{12} - 7439382 x^{11} + 52852089 x^{10} - 209920822 x^{9} + 948769365 x^{8} - 3201049386 x^{7} + 9952741960 x^{6} - 25214847156 x^{5} + 53555895597 x^{4} - 89435179422 x^{3} + 111698082474 x^{2} - 102868427688 x + 49809749944$	$18$	[0,9]	$-\,2^{18}\cdot 3^{21}\cdot 23^{8}\cdot 79^{9}$	$4$	$258.046145752$	$307.1488708964241$	✓			$D_6\times S_4$ (as 18T111)	$[2, 2, 2, 2, 4, 234900]$	$2$	$8$	$117603359.9309683$
18.0.330...159.1	$x^{18} + 315 x^{16} + 42903 x^{14} + 3235470 x^{12} + 145272897 x^{10} - 2063929 x^{9} + 3893509620 x^{8} - 888655572 x^{7} + 59407364016 x^{6} - 73024540848 x^{5} + 455759740800 x^{4} - 1761607827840 x^{3} + 1421970391296 x^{2} - 9636571236096 x + 18040528188928$	$18$	[0,9]	$-\,3^{45}\cdot 7^{15}\cdot 11^{9}$	$3$	$261.66633169$	$261.66633169026505$	✓	✓	?	$C_{18}$ (as 18T1)	$[3, 18, 1084806]$	$2$	$8$	$4392158.291236831$
18.0.330...159.2	$x^{18} + 315 x^{16} + 42903 x^{14} + 3235470 x^{12} + 145272897 x^{10} - 6297529 x^{9} + 3893509620 x^{8} - 600770772 x^{7} + 59407364016 x^{6} - 1188816048 x^{5} + 455759740800 x^{4} + 682703468160 x^{3} + 1421970391296 x^{2} + 7312629429504 x + 18089129916928$	$18$	[0,9]	$-\,3^{45}\cdot 7^{15}\cdot 11^{9}$	$3$	$261.66633169$	$261.66633169026505$	✓	✓	?	$C_{18}$ (as 18T1)	$[3, 18, 721278]$	$2$	$8$	$10392888.21418944$