Number field search results

Results (1-50 of 1217 matches)

  Download displayed columns for results to

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
21.1.238...101.1	$x^{21} - 6 x^{18} - 6 x^{16} + 8 x^{15} - 8 x^{14} + 17 x^{13} - 3 x^{12} + 23 x^{11} - 28 x^{10} - 11 x^{9} - 45 x^{8} - 14 x^{7} - 44 x^{6} - 17 x^{5} - 21 x^{4} - 4 x^{3} - 8 x^{2} - 1$	$21$	[1,10]	$23^{7}\cdot 41227^{3}$	$2$	$12.9783940136$	$973.7663990916918$			?	$D_7\wr S_3$ (as 21T62)	trivial	$2$	$10$	$952.218112417$
21.3.321...607.1	$x^{21} - 5 x^{14} - 8 x^{7} - 1$	$21$	[3,9]	$-\,7^{29}$	$1$	$14.6906208606$	$15.387268511758752$			?	$C_3\times D_7$ (as 21T3)	trivial	$2$	$11$	$6020.25035863$
21.3.396...527.1	$x^{21} - 5 x^{20} + 11 x^{19} - 20 x^{18} + 37 x^{17} - 68 x^{16} + 120 x^{15} - 168 x^{14} + 237 x^{13} - 331 x^{12} + 362 x^{11} - 431 x^{10} + 452 x^{9} - 381 x^{8} + 350 x^{7} - 238 x^{6} + 169 x^{5} - 90 x^{4} + 43 x^{3} + 6 x^{2} + 27$	$21$	[3,9]	$-\,13^{2}\cdot 1801^{2}\cdot 193327^{3}$	$3$	$14.8362250548$	$359846.7897340511$			?	$C_3^7.S_7$ (as 21T139)	trivial	$2$	$11$	$6158.71427835$
21.3.682...552.1	$x^{21} - 2 x^{20} - x^{19} - 3 x^{18} + 10 x^{17} + 13 x^{16} + x^{15} - 27 x^{14} - 16 x^{13} - 20 x^{12} + 55 x^{11} - 4 x^{10} + 8 x^{9} - 32 x^{8} - x^{7} + 70 x^{6} - 52 x^{5} - 4 x^{4} + 6 x^{3} + 2 x^{2} - 6 x + 1$	$21$	[3,9]	$-\,2^{21}\cdot 71^{10}$	$2$	$15.2258515194$	$23.83275057562597$			?	$S_3\times D_7$ (as 21T8)	trivial	$2$	$11$	$7666.61577427$
21.3.717...392.1	$x^{21} - 7 x^{20} + 21 x^{19} - 42 x^{18} + 77 x^{17} - 126 x^{16} + 168 x^{15} - 213 x^{14} + 266 x^{13} - 280 x^{12} + 259 x^{11} - 217 x^{10} + 133 x^{9} - 42 x^{8} - 53 x^{7} + 126 x^{6} - 112 x^{5} + 7 x^{4} + 63 x^{3} - 49 x^{2} + 14 x - 1$	$21$	[3,9]	$-\,2^{18}\cdot 7^{23}$	$2$	$15.2619237063$	$15.985663254345006$			?	$F_7$ (as 21T4)	trivial	$2$	$11$	$10096.3106241$
21.3.928...699.1	$x^{21} - 5 x^{20} + 11 x^{19} - 13 x^{18} + 7 x^{17} + 4 x^{16} - 16 x^{15} + 13 x^{14} - 6 x^{13} + 2 x^{12} - 2 x^{11} + 21 x^{10} - 28 x^{8} + 29 x^{7} - 16 x^{6} - 18 x^{5} + 17 x^{4} - 9 x^{3} - 2 x^{2} + 3 x - 1$	$21$	[3,9]	$-\,11^{9}\cdot 13^{14}$	$2$	$15.4504115563$	$18.336871607339905$			?	$F_7$ (as 21T4)	trivial	$2$	$11$	$10371.33223$
21.3.109...167.1	$x^{21} + x^{19} - 2 x^{18} - 2 x^{17} - 3 x^{16} - x^{15} + 4 x^{14} + 15 x^{13} + 3 x^{12} - 4 x^{11} - 29 x^{10} - 4 x^{9} + 12 x^{8} + 23 x^{7} + 16 x^{6} - 4 x^{5} - 7 x^{4} - 8 x^{3} - x^{2} + 1$	$21$	[3,9]	$-\,31^{8}\cdot 67^{3}\cdot 349^{3}$	$3$	$15.5692033983$	$851.3947380621987$			?	$S_3\times S_7$ (as 21T74)	trivial	$2$	$11$	$10492.3673171$
21.5.162...041.1	$x^{21} - x^{20} - 6 x^{19} + 8 x^{18} + 15 x^{17} - 28 x^{16} - 39 x^{15} + 74 x^{14} + 112 x^{13} - 127 x^{12} - 227 x^{11} + 89 x^{10} + 306 x^{9} + x^{8} - 244 x^{7} - 55 x^{6} + 122 x^{5} + 40 x^{4} - 41 x^{3} - 6 x^{2} + 8 x - 1$	$21$	[5,8]	$13^{8}\cdot 109^{8}$	$2$	$15.8679874279$	$37.64306044943742$			?	$\PSL(2,7)$ (as 21T14)	trivial	$2$	$12$	$17240.5464964$
21.1.214...721.1	$x^{21} - x^{20} - x^{19} + 2 x^{18} + 2 x^{17} + x^{16} - 5 x^{15} - x^{14} + 13 x^{13} + 9 x^{12} - 7 x^{11} - 16 x^{10} - x^{9} + 21 x^{8} + 17 x^{7} - 3 x^{6} - 11 x^{5} - 3 x^{4} + 4 x^{3} + 3 x^{2} - 1$	$21$	[1,10]	$23^{7}\cdot 184607^{3}$	$2$	$16.0779415343$	$2060.572978566884$			?	$S_3\times S_7$ (as 21T74)	trivial	$2$	$10$	$10455.3643856$
21.1.237...104.1	$x^{21} + x^{19} - 5 x^{18} + 8 x^{17} - 5 x^{16} + 11 x^{15} - 40 x^{14} + 33 x^{13} + 2 x^{12} + 62 x^{11} - 87 x^{10} - 12 x^{9} - 43 x^{8} + 76 x^{7} + 27 x^{6} - 15 x^{5} - 7 x^{4} - 10 x^{3} + 2 x^{2} + x + 1$	$21$	[1,10]	$2^{14}\cdot 11^{8}\cdot 41^{3}\cdot 461^{3}$	$4$	$16.1560089147$	$723.8113641062746$			?	$S_3\times S_7$ (as 21T74)	trivial	$2$	$10$	$11721.4726991$
21.5.267...304.1	$x^{21} - 5 x^{20} + 11 x^{19} - 16 x^{18} + 25 x^{17} - 38 x^{16} + 36 x^{15} - 25 x^{14} + 18 x^{13} - 4 x^{12} - 3 x^{11} - 17 x^{10} - 23 x^{9} - 12 x^{8} + 55 x^{7} + 18 x^{6} - 46 x^{5} - 17 x^{4} + 19 x^{3} + 9 x^{2} - 2 x - 1$	$21$	[5,8]	$2^{18}\cdot 317^{8}$	$2$	$16.2483846421$	$32.251902756545775$			?	$\PSL(2,7)$ (as 21T14)	trivial	$2$	$12$	$25357.2549184$
21.3.657...567.1	$x^{21} - 4 x^{20} + 12 x^{19} - 22 x^{18} + 41 x^{17} - 54 x^{16} + 79 x^{15} - 60 x^{14} + 57 x^{13} + 46 x^{12} - 70 x^{11} + 222 x^{10} - 182 x^{9} + 306 x^{8} - 168 x^{7} + 207 x^{6} - 48 x^{5} + 42 x^{4} + 5 x^{3} - 17 x^{2} - 15 x - 1$	$21$	[3,9]	$-\,3^{24}\cdot 7^{17}$	$2$	$16.959319372$	$21.898281770364438$			?	$C_3\times F_7$ (as 21T9)	trivial	$2$	$11$	$31647.6272279$
21.1.759...229.1	$x^{21} - x^{18} - 3 x^{15} + 2 x^{12} + 4 x^{9} - x^{6} - 2 x^{3} - 1$	$21$	[1,10]	$3^{21}\cdot 193607^{3}$	$2$	$17.0763753068$				✓	$C_3^6.(C_2\times S_7)$ (as 21T138)	trivial	$2$	$10$	$18363.369838$
21.5.855...849.1	$x^{21} - 4 x^{19} + 23 x^{17} - 4 x^{16} - 54 x^{15} + 19 x^{14} + 94 x^{13} - 41 x^{12} - 115 x^{11} + 59 x^{10} + 30 x^{9} - 81 x^{8} + 20 x^{7} + 46 x^{6} - 18 x^{5} - 5 x^{4} + 13 x^{3} - 3 x^{2} + 1$	$21$	[5,8]	$23^{8}\cdot 239^{3}\cdot 431^{3}$	$3$	$17.1742778909$	$1539.2228558594106$			?	$S_3\times S_7$ (as 21T74)	trivial	$2$	$12$	$45009.9851463$
21.3.108...223.1	$x^{21} - 9 x^{14} - 12 x^{7} + 1$	$21$	[3,9]	$-\,3^{28}\cdot 7^{15}$	$2$	$17.3701324536$	$21.898281770364438$			?	$C_3\times F_7$ (as 21T9)	trivial	$2$	$11$	$51151.7616302$
21.1.156...857.1	$x^{21} - x^{20} - x^{19} + 2 x^{18} + 5 x^{17} + 2 x^{16} - 10 x^{15} - 2 x^{14} + 23 x^{13} + 19 x^{12} - 11 x^{11} - 28 x^{10} + 8 x^{9} + 47 x^{8} + 23 x^{7} - 13 x^{6} - 24 x^{5} - 7 x^{4} + 11 x^{3} + 6 x^{2} - 1$	$21$	[1,10]	$23^{7}\cdot 71^{9}$	$2$	$17.672814291$	$40.4103947023535$			?	$S_3\times D_7$ (as 21T8)	trivial	$2$	$10$	$32527.0761402$
21.3.167...056.1	$x^{21} - 7 x^{20} + 23 x^{19} - 46 x^{18} + 59 x^{17} - 38 x^{16} - 51 x^{15} + 276 x^{14} - 725 x^{13} + 1392 x^{12} - 2056 x^{11} + 2397 x^{10} - 2311 x^{9} + 1987 x^{8} - 1615 x^{7} + 1208 x^{6} - 783 x^{5} + 436 x^{4} - 201 x^{3} + 66 x^{2} - 12 x + 1$	$21$	[3,9]	$-\,2^{18}\cdot 17^{6}\cdot 31^{9}$	$3$	$17.7311766635$	$92.75844411611145$			?	$S_3\times A_7$ (as 21T57)	trivial	$2$	$11$	$48967.484032$
21.3.188...059.1	$x^{21} - 3 x^{20} + 2 x^{19} - 4 x^{18} + 10 x^{17} - 9 x^{16} + 70 x^{15} - 167 x^{14} + 91 x^{13} + 110 x^{12} - 252 x^{11} + 50 x^{10} + 456 x^{9} - 519 x^{8} + x^{7} + 487 x^{6} - 548 x^{5} + 272 x^{4} - 48 x^{3} + x^{2} - 3 x + 1$	$21$	[3,9]	$-\,59^{8}\cdot 10859^{3}$	$2$	$17.8300144394$	$800.4255118372977$			?	$S_3\times S_7$ (as 21T74)	trivial	$2$	$11$	$47990.3401891$
21.3.214...807.1	$x^{21} - x^{20} - x^{19} + x^{18} - x^{17} + 6 x^{16} - 7 x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 9 x^{11} - 17 x^{10} + 11 x^{9} - 4 x^{8} - 3 x^{7} + 9 x^{6} - 6 x^{5} - x^{4} + 3 x^{3} - x^{2} - x + 1$	$21$	[3,9]	$-\,184607^{5}$	$1$	$17.9419073895$	$429.65916724771506$			?	$S_7$ (as 21T38)	trivial	$2$	$11$	$59489.8190642$
21.3.270...407.1	$x^{21} - 4 x^{18} - x^{17} + x^{16} + 7 x^{15} + x^{14} - 6 x^{13} - 11 x^{12} + 2 x^{11} + 10 x^{10} + 14 x^{9} - 2 x^{8} - 5 x^{7} - 6 x^{6} + 2 x^{5} - 2 x^{4} - 3 x^{3} + 2 x^{2} - 1$	$21$	[3,9]	$-\,193327^{5}$	$1$	$18.1401583673$	$439.68966328536766$			?	$S_7$ (as 21T38)	trivial	$2$	$11$	$75073.7253$
21.3.336...784.1	$x^{21} - 5 x^{20} + 11 x^{19} - 5 x^{18} - 29 x^{17} + 64 x^{16} - 22 x^{15} - 117 x^{14} + 218 x^{13} - 124 x^{12} - 76 x^{11} + 132 x^{10} - 38 x^{9} + 31 x^{8} - 168 x^{7} + 204 x^{6} - 47 x^{5} - 120 x^{4} + 134 x^{3} - 63 x^{2} + 13 x - 1$	$21$	[3,9]	$-\,2^{14}\cdot 11^{13}\cdot 29^{6}$	$3$	$18.3310070912$	$110.52127846308204$			?	$S_3\times A_7$ (as 21T57)	trivial	$2$	$11$	$73219.6797146$
21.3.930...607.1	$x^{21} - 5 x^{20} + 36 x^{18} - 35 x^{17} - 108 x^{16} + 155 x^{15} + 176 x^{14} - 338 x^{13} - 129 x^{12} + 413 x^{11} - 50 x^{10} - 234 x^{9} + 162 x^{8} - 66 x^{7} - 51 x^{6} + 196 x^{5} - 92 x^{4} - 98 x^{3} + 71 x^{2} - 10 x - 25$	$21$	[3,9]	$-\,151^{2}\cdot 2377^{2}\cdot 193327^{3}$	$3$	$19.2412307236$	$2220668.2086930433$			?	$C_3^7.S_7$ (as 21T139)	trivial	$2$	$11$	$99654.8309357$
21.1.126...441.1	$x^{21} + 3 x^{19} - x^{18} + x^{17} + 8 x^{16} - 7 x^{15} + 24 x^{14} - 15 x^{13} + 7 x^{12} + 25 x^{11} - 42 x^{10} + 46 x^{9} - 39 x^{8} - 12 x^{7} + 15 x^{6} - 14 x^{5} + x^{4} + 10 x^{3} - x^{2} + 2 x + 1$	$21$	[1,10]	$31^{7}\cdot 71^{9}$	$2$	$19.5216714707$	$46.9148164229596$			?	$S_3\times D_7$ (as 21T8)	trivial	$2$	$10$	$80948.9311635$
21.1.190...129.1	$x^{21} - x^{14} + 1$	$21$	[1,10]	$7^{21}\cdot 23^{7}$	$2$	$19.907068859$				✓	$C_7^2:(C_6\times S_3)$ (as 21T29)	trivial	$2$	$10$	$141151.982984$
21.9.252...441.1	$x^{21} - 9 x^{19} + 3 x^{17} + 66 x^{15} - 75 x^{14} - 90 x^{13} + 198 x^{12} - 21 x^{11} + 63 x^{9} - 177 x^{8} + 54 x^{7} + 45 x^{6} - 51 x^{5} + 18 x^{4} - 8 x^{3} - 3 x^{2} + 3$	$21$	[9,6]	$3^{34}\cdot 73^{6}$	$2$	$20.1771578454$				?	$C_3\times A_7$ (as 21T44)	trivial	$2$	$14$	$823613.327719$
21.9.332...609.1	$x^{21} - 6 x^{20} + 12 x^{19} - 2 x^{18} - 27 x^{17} + 36 x^{16} - 39 x^{15} + 180 x^{14} - 396 x^{13} + 183 x^{12} + 558 x^{11} - 738 x^{10} - 339 x^{9} + 1035 x^{8} + 27 x^{7} - 936 x^{6} + 27 x^{5} + 621 x^{4} + 99 x^{3} - 189 x^{2} - 81 x - 9$	$21$	[9,6]	$3^{36}\cdot 53^{6}$	$2$	$20.4443072604$				?	$C_3\times A_7$ (as 21T44)	trivial	$2$	$14$	$967276.035305$
21.3.426...007.1	$x^{21} - x^{20} - 7 x^{19} + 6 x^{18} + 16 x^{17} - 27 x^{16} + 3 x^{15} + 119 x^{14} + 23 x^{13} - 181 x^{12} - 153 x^{11} + 154 x^{10} + 417 x^{9} - 133 x^{8} - 395 x^{7} + 153 x^{6} + 61 x^{5} - 33 x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 1$	$21$	[3,9]	$-\,7^{14}\cdot 184607^{3}$	$2$	$20.6880644133$	$1572.2542440732786$			?	$C_3\times S_7$ (as 21T56)	trivial	$2$	$11$	$201933.335135$
21.3.429...912.1	$x^{21} - x^{20} + 9 x^{19} - 7 x^{18} + 35 x^{17} - 27 x^{16} + 83 x^{15} - 61 x^{14} + 123 x^{13} - 111 x^{12} + 163 x^{11} - 225 x^{10} + 213 x^{9} - 253 x^{8} + 177 x^{7} - 167 x^{6} + 192 x^{5} - 180 x^{4} + 136 x^{3} - 76 x^{2} - 12 x + 4$	$21$	[3,9]	$-\,2^{38}\cdot 3^{18}\cdot 7^{9}$	$3$	$20.6950697419$	$30.46083139496543$				$\PGL(2,7)$ (as 21T20)	trivial	$2$	$11$	$1790438.21987$
21.3.490...767.1	$x^{21} - x^{20} - 2 x^{19} + 9 x^{18} - 8 x^{17} - 16 x^{16} + 40 x^{15} + 25 x^{14} - 4 x^{13} - 178 x^{12} - 112 x^{11} + 286 x^{10} + 394 x^{9} - 392 x^{8} - 175 x^{7} + 201 x^{6} - 68 x^{5} - 36 x^{4} + 30 x^{3} - 4 x^{2} - 4 x + 1$	$21$	[3,9]	$-\,7^{14}\cdot 193327^{3}$	$2$	$20.8249198157$	$1608.9588954982237$			?	$C_3\times S_7$ (as 21T56)	trivial	$2$	$11$	$299129.54193$
21.1.573...421.1	$x^{21} - x - 1$	$21$	[1,10]	$1137694897331\cdot 5043293621028391$	$2$	$20.9818976857$	$75747801409585.36$			✓	$S_{21}$ (as 21T164)	trivial	$2$	$10$	$169158.997908$
21.1.594...421.1	$x^{21} + x - 1$	$21$	[1,10]	$11\cdot 17\cdot 1033\cdot 1583\cdot 159503\cdot 121937899012999$	$6$	$21.0177955058$	$77119677245084.36$			✓	$S_{21}$ (as 21T164)	trivial	$2$	$10$	$312816.601488$
21.3.714...224.1	$x^{21} - 3 x^{20} - 4 x^{19} + 16 x^{18} - 9 x^{17} - 33 x^{16} + 52 x^{15} + 12 x^{14} - 136 x^{13} + 96 x^{12} + 180 x^{11} - 260 x^{10} - 144 x^{9} + 312 x^{8} + 44 x^{7} - 220 x^{6} + 15 x^{5} + 59 x^{4} - 16 x^{3} + 36 x^{2} - 31 x + 1$	$21$	[3,9]	$-\,2^{64}\cdot 3^{18}$	$2$	$21.2024390858$	$31.63696468726565$				$\PGL(2,7)$ (as 21T20)	trivial	$2$	$11$	$3668230.07566$
21.1.739...928.1	$x^{21} - 2 x^{20} - x^{19} + 7 x^{18} - 3 x^{17} - 13 x^{16} + 14 x^{15} + 13 x^{14} - 28 x^{13} - 2 x^{12} + 34 x^{11} - 15 x^{10} - 25 x^{9} + 24 x^{8} + 7 x^{7} - 21 x^{6} + 6 x^{5} + 8 x^{4} - 7 x^{3} + 2 x - 1$	$21$	[1,10]	$2^{3}\cdot 101\cdot 1951\cdot 7481\cdot 35629381\cdot 17609300881$	$6$	$21.237517341$				✓	$S_{21}$ (as 21T164)	trivial	$2$	$10$	$564425.480379$
21.3.897...231.1	$x^{21} - x^{20} + 3 x^{19} + 4 x^{18} + 8 x^{17} - 12 x^{16} + 9 x^{15} + 113 x^{14} - 287 x^{13} + 404 x^{12} - 526 x^{11} + 1106 x^{10} - 2438 x^{9} + 2381 x^{8} - 2385 x^{7} + 3637 x^{6} - 6756 x^{5} + 4734 x^{4} - 3615 x^{3} + 1513 x^{2} - 2017 x - 1319$	$21$	[3,9]	$-\,7^{2}\cdot 13^{2}\cdot 71^{9}\cdot 4861^{2}$	$4$	$21.4332747759$	$48918.580904922295$			?	$C_3^7:D_7$ (as 21T76)	trivial	$2$	$11$	$277898.768894$
21.1.990...104.1	$x^{21} - 3 x^{20} - 2 x^{19} + 25 x^{18} - 40 x^{17} - 24 x^{16} + 156 x^{15} - 215 x^{14} + 131 x^{13} - 57 x^{12} + 294 x^{11} - 907 x^{10} + 1374 x^{9} - 1171 x^{8} + 439 x^{7} + 387 x^{6} - 847 x^{5} + 669 x^{4} - 179 x^{3} - 142 x^{2} + 156 x - 38$	$21$	[1,10]	$2^{14}\cdot 11^{10}\cdot 13^{12}$	$3$	$21.5341136548$	$29.107969279297173$			?	$C_{21}:C_6$ (as 21T10)	trivial	$2$	$10$	$637026.16318$
21.3.103...503.1	$x^{21} - 6 x^{20} - x^{19} + 72 x^{18} - 100 x^{17} - 299 x^{16} + 733 x^{15} + 386 x^{14} - 2195 x^{13} + 634 x^{12} + 3126 x^{11} - 2357 x^{10} - 2090 x^{9} + 2868 x^{8} + 87 x^{7} - 1535 x^{6} + 673 x^{5} + 170 x^{4} - 243 x^{3} + 89 x^{2} - 15 x + 1$	$21$	[3,9]	$-\,11^{4}\cdot 103^{4}\cdot 184607^{3}$	$3$	$21.5813816248$	$46695.75004699004$			✓	$C_3^6.S_7$ (as 21T130)	trivial	$2$	$11$	$361691.21971$
21.5.123...001.1	$x^{21} - 2 x^{19} - x^{18} - 8 x^{17} + 16 x^{15} + 16 x^{14} + 21 x^{13} - 27 x^{12} - 29 x^{11} - 63 x^{10} - 3 x^{9} + 86 x^{8} + 60 x^{7} + 11 x^{6} - 69 x^{5} - 49 x^{4} + 30 x^{3} + 16 x^{2} - 6 x - 1$	$21$	[5,8]	$7^{9}\cdot 12503^{5}$	$2$	$21.7602786875$	$295.8394835041462$			?	$S_7$ (as 21T38)	trivial	$2$	$12$	$564369.598704$
21.1.153...777.1	$x^{21} + x^{7} - 1$	$21$	[1,10]	$7^{21}\cdot 31^{7}$	$2$	$21.9896645667$				✓	$C_7^2:(C_6\times S_3)$ (as 21T29)	trivial	$2$	$10$	$472261.200133$
21.9.184...873.1	$x^{21} - 2 x^{20} - 2 x^{19} + 12 x^{18} - 25 x^{17} + x^{16} + 48 x^{15} - 91 x^{14} + 103 x^{13} - 12 x^{12} - 110 x^{11} + 272 x^{10} - 277 x^{9} - 78 x^{8} + 278 x^{7} - 46 x^{6} + 11 x^{5} - 114 x^{4} + 3 x^{3} + 93 x^{2} - 19 x - 23$	$21$	[9,6]	$71^{3}\cdot 8623^{3}\cdot 283573^{2}$	$3$	$22.1821586762$	$3377289.469795227$			?	$C_3^7.S_7$ (as 21T139)	trivial	$2$	$14$	$1614740.57391$
21.3.190...271.1	$x^{21} - 9 x^{20} + 23 x^{19} + 24 x^{18} - 196 x^{17} + 152 x^{16} + 587 x^{15} - 1008 x^{14} - 562 x^{13} + 2180 x^{12} - 404 x^{11} - 2259 x^{10} + 1317 x^{9} + 1079 x^{8} - 1081 x^{7} - 177 x^{6} + 477 x^{5} - 106 x^{4} - 81 x^{3} + 53 x^{2} - 12 x + 1$	$21$	[3,9]	$-\,67^{2}\cdot 71^{9}\cdot 9613^{2}$	$3$	$22.214074314$	$62842.242032253074$			?	$C_3^7:D_7$ (as 21T76)	trivial	$2$	$11$	$520928.798224$
21.3.207...824.1	$x^{21} - 4 x^{20} + 8 x^{19} - 12 x^{18} + 12 x^{17} - 16 x^{16} + 44 x^{15} - 94 x^{14} + 160 x^{13} - 200 x^{12} + 184 x^{11} - 132 x^{10} + 52 x^{9} - 8 x^{7} + 4 x^{6} + 16 x^{4} - 36 x^{3} + 32 x^{2} - 16 x + 4$	$21$	[3,9]	$-\,2^{20}\cdot 11^{7}\cdot 317^{6}$	$3$	$22.3056297787$	$114.26710056592353$			?	$S_3\times \GL(3,2)$ (as 21T27)	trivial	$2$	$11$	$999740.077738$
21.3.207...824.2	$x^{21} - 2 x^{20} + 2 x^{19} - 4 x^{16} - 6 x^{15} + 8 x^{14} - 16 x^{13} + 30 x^{12} - 24 x^{11} + 22 x^{10} - 48 x^{9} - 4 x^{8} - 30 x^{7} + 8 x^{6} - 4 x^{5} - 12 x^{4} - 10 x^{3} + 12 x^{2} - 4 x + 2$	$21$	[3,9]	$-\,2^{20}\cdot 11^{7}\cdot 317^{6}$	$3$	$22.3056297787$	$114.26710056592353$			?	$S_3\times \GL(3,2)$ (as 21T27)	trivial	$2$	$11$	$999740.077738$
21.5.279...288.1	$x^{21} - 2 x^{19} - 7 x^{18} - 5 x^{17} + 11 x^{16} + 17 x^{15} + 34 x^{14} - 32 x^{13} - 19 x^{12} - 120 x^{11} - 65 x^{10} - 276 x^{9} + 43 x^{8} + 539 x^{7} + 983 x^{6} + 606 x^{5} + 280 x^{4} + 121 x^{3} + 40 x^{2} - 13 x - 5$	$21$	[5,8]	$2^{27}\cdot 181^{9}$	$2$	$22.6263811101$	$38.05259518088089$				$\PGL(2,7)$ (as 21T20)	trivial	$2$	$12$	$2296254.50823$
21.3.310...319.1	$x^{21} - x^{20} - 7 x^{19} + 6 x^{18} + 3 x^{17} - 30 x^{16} + 72 x^{15} + 134 x^{14} - 49 x^{13} - 195 x^{12} - 375 x^{11} + 190 x^{10} + 878 x^{9} - 233 x^{8} - 491 x^{7} + 177 x^{6} + 32 x^{5} - 47 x^{4} + 21 x^{3} + 10 x^{2} - 4 x - 1$	$21$	[3,9]	$-\,7^{14}\cdot 71^{9}$	$2$	$22.7402444296$	$30.833857978493015$			?	$C_3\times D_7$ (as 21T3)	trivial	$2$	$11$	$725840.889095$
21.1.341...000.1	$x^{21} - 10 x^{18} + 36 x^{15} - 76 x^{12} - 224 x^{9} - 144 x^{6} - 32 x^{3} - 16$	$21$	[1,10]	$2^{20}\cdot 3^{34}\cdot 5^{9}$	$3$	$22.8420900179$	$28.700473627493697$			?	$S_3\times F_7$ (as 21T15)	trivial	$2$	$10$	$2085380.41806$
21.5.348...177.1	$x^{21} - 2 x^{20} - 5 x^{18} + 12 x^{17} - 5 x^{16} + 4 x^{15} - 27 x^{14} + 16 x^{13} - 8 x^{12} + 8 x^{11} - 22 x^{10} - 8 x^{9} - 2 x^{8} + 9 x^{7} + 15 x^{6} + 12 x^{5} + 13 x^{4} + 2 x^{3} - x^{2} - 2 x - 1$	$21$	[5,8]	$3^{8}\cdot 37^{5}\cdot 2381^{5}$	$3$	$22.8629450794$	$514.0924041454026$			?	$S_7$ (as 21T38)	trivial	$2$	$12$	$1358971.01083$
21.5.417...153.1	$x^{21} - 3 x^{19} - 2 x^{18} + 15 x^{17} + 6 x^{16} - 23 x^{15} - 30 x^{14} + 23 x^{13} + 44 x^{12} + 12 x^{11} - 43 x^{10} - 61 x^{9} + 51 x^{8} + 34 x^{7} - 5 x^{6} - 30 x^{5} - 9 x^{4} + 13 x^{3} + 7 x^{2} - 1$	$21$	[5,8]	$23^{7}\cdot 107^{3}\cdot 21557^{3}$	$3$	$23.062442084$	$7283.665080163969$			?	$S_3\times S_7$ (as 21T74)	trivial	$2$	$12$	$895675.424859$
21.1.753...068.1	$x^{21} - 2 x^{20} - x^{19} + 7 x^{18} - 3 x^{17} - 13 x^{16} + 14 x^{15} + 13 x^{14} - 28 x^{13} - 2 x^{12} + 34 x^{11} - 15 x^{10} - 25 x^{9} + 25 x^{8} + 7 x^{7} - 22 x^{6} + 6 x^{5} + 8 x^{4} - 7 x^{3} + 2 x - 1$	$21$	[1,10]	$2^{2}\cdot 11\cdot 29\cdot 1447\cdot 2579\cdot 4423\cdot 3578836676945557$	$7$	$23.7195344256$	$217907085144134.4$			✓	$S_{21}$ (as 21T164)	trivial	$2$	$10$	$2395762.98687$
21.9.778...553.1	$x^{21} - 8 x^{20} + 15 x^{19} + 42 x^{18} - 181 x^{17} + 43 x^{16} + 664 x^{15} - 785 x^{14} - 999 x^{13} + 2386 x^{12} - 12 x^{11} - 3337 x^{10} + 2186 x^{9} + 1818 x^{8} - 2845 x^{7} + 445 x^{6} + 1349 x^{5} - 754 x^{4} - 347 x^{3} + 279 x^{2} + 76 x + 1$	$21$	[9,6]	$71^{3}\cdot 157^{2}\cdot 3709^{2}\cdot 8623^{3}$	$4$	$23.7555403331$	$5456272.155977658$			?	$C_3^7.S_7$ (as 21T139)	trivial	$2$	$14$	$3400600.48543$
21.7.105...767.1	$x^{21} - x^{20} - 6 x^{19} + 11 x^{18} + 47 x^{17} - 45 x^{16} - 170 x^{15} + 162 x^{14} + 400 x^{13} - 307 x^{12} - 750 x^{11} + 395 x^{10} + 733 x^{9} - 371 x^{8} - 425 x^{7} + 197 x^{6} + 204 x^{5} - 78 x^{4} - 36 x^{3} + 17 x^{2} - 1$	$21$	[7,7]	$-\,17^{3}\cdot 23^{8}\cdot 64879^{3}$	$3$	$24.0976852901$	$5036.634689949233$			?	$S_3\times S_7$ (as 21T74)	trivial	$2$	$13$	$2726200.25314$

  Download displayed columns for results to