Number field search results

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

Results (1-50 of 192 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
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	$2$	$11$	$10492.3673171$
21.3.657...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	$2$	$11$	$31647.6272279$
21.3.108...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	$2$	$11$	$51151.7616302$
21.3.167...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	$2$	$11$	$99654.8309357$
21.3.426...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	$2$	$11$	$299129.54193$
21.3.714...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	$2$	$11$	$3668230.07566$
21.3.897...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	$2$	$11$	$277898.768894$
21.3.103...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	$2$	$11$	$361691.21971$
21.3.190...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	$2$	$11$	$999740.077738$
21.3.310...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	$2$	$11$	$725840.889095$
21.3.142...751.1	$x^{21} + 2 x^{19} - 11 x^{17} - 27 x^{16} - 82 x^{15} - 60 x^{14} - 211 x^{13} - 21 x^{12} - 494 x^{11} + 177 x^{10} - 781 x^{9} + 699 x^{8} - 1096 x^{7} + 966 x^{6} - 737 x^{5} + 417 x^{4} - 128 x^{3} + 18 x^{2} + 18 x - 9$	$21$	[3,9]	$-\,3^{20}\cdot 151^{9}$	$2$	$24.4482882926$	$86.63712610377607$			?	$C_3^6.D_7$ (as 21T52)	trivial	$2$	$11$	$1758982.84323$
21.3.142...751.2	$x^{21} - 4 x^{19} - 2 x^{18} - 5 x^{17} + 58 x^{16} - 25 x^{15} - 201 x^{14} + 345 x^{13} - 93 x^{12} + 228 x^{11} + 426 x^{10} - 758 x^{9} - 54 x^{8} + 149 x^{7} - 473 x^{6} - 1772 x^{5} - 2981 x^{4} - 1405 x^{3} + 378 x^{2} + 18 x - 117$	$21$	[3,9]	$-\,3^{20}\cdot 151^{9}$	$2$	$24.4482882926$	$86.63712610377607$			?	$C_3^6.D_7$ (as 21T52)	trivial	$2$	$11$	$2184999.95298$
21.3.143...823.1	$x^{21} - 12 x^{19} - 4 x^{18} + 72 x^{17} + 21 x^{16} - 261 x^{15} - 72 x^{14} + 678 x^{13} + 58 x^{12} - 1062 x^{11} - 285 x^{10} + 513 x^{9} + 1188 x^{8} - 768 x^{7} - 2702 x^{6} + 792 x^{5} + 1485 x^{4} - 865 x^{3} - 342 x^{2} + 183 x - 47$	$21$	[3,9]	$-\,3^{28}\cdot 184607^{3}$	$2$	$24.4614861739$				?	$C_3^6.S_7$ (as 21T130)	trivial	$2$	$11$	$1049116.64407$
21.3.273...419.1	$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 51 x^{16} - 901 x^{15} - 354 x^{14} + 2589 x^{13} + 1292 x^{12} - 4479 x^{11} - 2667 x^{10} + 4522 x^{9} + 3132 x^{8} - 2424 x^{7} - 2026 x^{6} + 438 x^{5} + 534 x^{4} - 63 x^{2} - 15 x - 1$	$21$	[3,9]	$-\,23^{7}\cdot 113\cdot 710546119470924629$	$3$	$25.2203286314$	$42973356449.14105$			?	$S_7\wr C_3.C_2$ (as 21T162)	trivial	$2$	$11$	$2247653.20087$
21.3.378...943.1	$x^{21} - x^{14} - 2 x^{7} + 1$	$21$	[3,9]	$-\,7^{35}$	$1$	$25.6151399702$	$31.448918161367093$			✓	$C_7:F_7$ (as 21T16)	trivial	$2$	$11$	$2535367.84349$
21.3.378...943.2	$x^{21} - 4 x^{14} + 3 x^{7} + 1$	$21$	[3,9]	$-\,7^{35}$	$1$	$25.6151399702$	$31.448918161367093$			✓	$C_7:F_7$ (as 21T16)	trivial	$2$	$11$	$3187973.81132$
21.3.378...943.3	$x^{21} - x^{14} - 9 x^{7} + 1$	$21$	[3,9]	$-\,7^{35}$	$1$	$25.6151399702$	$26.829842007890413$				$F_7$ (as 21T4)	trivial	$2$	$11$	$5449377.399032222$
21.3.822...375.1	$x^{21} - 9 x^{20} + 39 x^{19} - 110 x^{18} + 212 x^{17} - 254 x^{16} + 72 x^{15} + 444 x^{14} - 1230 x^{13} + 2243 x^{12} - 3572 x^{11} + 5129 x^{10} - 6067 x^{9} + 5990 x^{8} - 5448 x^{7} + 5112 x^{6} - 4212 x^{5} + 3001 x^{4} - 1825 x^{3} + 903 x^{2} - 185 x + 211$	$21$	[3,9]	$-\,5^{9}\cdot 11^{7}\cdot 43^{10}$	$3$	$26.5785687175$	$48.63126566315131$			?	$S_3\times D_7$ (as 21T8)	trivial	$2$	$11$	$7898710.55939$
21.3.953...819.1	$x^{21} - 5 x^{20} + 14 x^{19} - 30 x^{18} + 81 x^{17} - 198 x^{16} + 312 x^{15} - 259 x^{14} - 31 x^{13} + 395 x^{12} - 455 x^{11} + 311 x^{10} + 131 x^{9} - 101 x^{8} + 292 x^{7} + 104 x^{6} + 29 x^{5} + 133 x^{4} + 67 x^{3} + 11 x^{2} + 4 x + 1$	$21$	[3,9]	$-\,3^{4}\cdot 11^{9}\cdot 13^{12}\cdot 463^{2}$	$4$	$26.76672916$	$4748.330187047302$			?	$C_3^7.F_7$ (as 21T98)	trivial	$2$	$11$	$6859502.52387$
21.3.107...936.2	$x^{21} - 3 x^{19} - 2 x^{18} - 9 x^{17} - 12 x^{16} - 4 x^{15} + 81 x^{13} + 216 x^{12} + 459 x^{11} + 906 x^{10} + 367 x^{9} - 2196 x^{8} - 6807 x^{7} - 14494 x^{6} - 22572 x^{5} - 23256 x^{4} - 15184 x^{3} - 6048 x^{2} - 1344 x - 128$	$21$	[3,9]	$-\,2^{14}\cdot 3^{21}\cdot 184607^{3}$	$3$	$26.9233492487$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$11$	$3523003.59392$
21.3.765...811.1	$x^{21} - 6 x^{20} + 19 x^{19} - 35 x^{18} + 34 x^{17} - 27 x^{16} + 33 x^{15} - 73 x^{14} + 37 x^{13} + 44 x^{12} + 137 x^{11} - 33 x^{10} + 60 x^{9} + 177 x^{8} + 243 x^{7} - 219 x^{6} - 876 x^{5} - 1332 x^{4} - 1192 x^{3} - 736 x^{2} - 288 x - 64$	$21$	[3,9]	$-\,7^{14}\cdot 29^{3}\cdot 77351^{3}$	$3$	$29.5573142604$	$5480.632208375353$			?	$D_7\wr C_3$ (as 21T45)	trivial	$2$	$11$	$14306648.6019$
21.3.772...983.1	$x^{21} - 7 x^{19} - 7 x^{18} + 42 x^{17} - 175 x^{15} + 280 x^{13} - 119 x^{12} - 588 x^{11} - 63 x^{10} + 448 x^{9} - 147 x^{8} - 637 x^{7} - 259 x^{6} + 147 x^{5} - 182 x^{3} - 147 x^{2} - 49 x - 7$	$21$	[3,9]	$-\,3^{24}\cdot 7^{23}$	$2$	$29.570931251626824$	$38.18269887824235$				$C_3\times F_7$ (as 21T9)	trivial	$2$	$11$	$27889140.491911642$
21.3.785...512.1	$x^{21} + 3 x^{19} + 18 x^{17} - 54 x^{16} + 58 x^{15} - 90 x^{14} - 75 x^{13} + 288 x^{12} - 486 x^{11} + 1380 x^{10} - 1915 x^{9} + 2988 x^{8} - 3399 x^{7} + 1690 x^{6} - 2232 x^{5} - 384 x^{4} - 1344 x^{3} - 384 x + 128$	$21$	[3,9]	$-\,2^{14}\cdot 3^{21}\cdot 71^{9}$	$3$	$29.5940466226$				?	$C_3^7:C_2\wr D_7$ (as 21T131)	trivial	$2$	$11$	$10907666.3389$
21.3.978...096.1	$x^{21} - x^{20} - 10 x^{19} + 8 x^{18} + 32 x^{17} - 59 x^{16} + 7 x^{15} + 422 x^{14} + 190 x^{13} - 795 x^{12} - 1054 x^{11} + 695 x^{10} + 3497 x^{9} - 381 x^{8} - 4108 x^{7} + 1137 x^{6} + 364 x^{5} - 117 x^{4} + x^{3} + 12 x^{2} - 3 x - 1$	$21$	[3,9]	$-\,2^{14}\cdot 37^{7}\cdot 184607^{3}$	$3$	$29.904857562$	$4148.695957657993$			?	$S_3\times S_7$ (as 21T74)	trivial	$2$	$11$	$11488244.7921$
21.3.112...376.1	$x^{21} - x^{20} - 3 x^{19} + 15 x^{18} - 14 x^{17} - 42 x^{16} + 112 x^{15} + 113 x^{14} + 10 x^{13} - 937 x^{12} - 860 x^{11} + 1848 x^{10} + 3892 x^{9} - 2944 x^{8} - 2961 x^{7} + 1339 x^{6} - 176 x^{5} - 182 x^{4} + 74 x^{3} - 4 x^{2} - 6 x + 1$	$21$	[3,9]	$-\,2^{14}\cdot 37^{7}\cdot 193327^{3}$	$3$	$30.1026837691$	$4245.548257194108$			?	$S_3\times S_7$ (as 21T74)	trivial	$2$	$11$	$13187708.2201$
21.3.127...727.1	$x^{21} - 3 x^{14} - 6 x^{7} - 1$	$21$	[3,9]	$-\,3^{28}\cdot 7^{21}$	$2$	$30.2872409765$	$38.18269887824235$			?	$C_7:(C_3\times F_7)$ (as 21T24)	trivial	$2$	$11$	$19109363.6324$
21.3.127...727.2	$x^{21} - 3 x^{7} - 1$	$21$	[3,9]	$-\,3^{28}\cdot 7^{21}$	$2$	$30.2872409765$	$38.18269887824235$			✓	$C_7:(C_3\times F_7)$ (as 21T24)	trivial	$2$	$11$	$20173681.1919$
21.3.127...727.3	$x^{21} - 9 x^{14} + 15 x^{7} + 1$	$21$	[3,9]	$-\,3^{28}\cdot 7^{21}$	$2$	$30.2872409765$	$38.18269887824235$				$C_3\times F_7$ (as 21T9)	trivial	$2$	$11$	$45076954.940072164$
21.3.172...648.1	$x^{21} - x^{20} - x^{19} - 26 x^{18} + 25 x^{17} + 28 x^{16} + 330 x^{15} - 125 x^{14} - 104 x^{13} - 2062 x^{12} - 109 x^{11} - 751 x^{10} + 5539 x^{9} + 340 x^{8} + 2923 x^{7} - 6382 x^{6} + 3416 x^{5} + 1031 x^{4} + 8397 x^{3} - 397 x^{2} - 1378 x - 2197$	$21$	[3,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{17}$	$3$	$30.720913770020566$	$39.667584012275974$			?	$C_3\times F_7$ (as 21T9)	trivial	$2$	$11$	$18296774.24958717$
21.3.172...648.2	$x^{21} - 6 x^{20} + 29 x^{19} - 77 x^{18} + 213 x^{17} - 414 x^{16} + 1128 x^{15} - 2157 x^{14} + 5178 x^{13} - 7411 x^{12} + 12573 x^{11} - 12131 x^{10} + 16268 x^{9} - 11658 x^{8} + 1875 x^{7} - 2158 x^{6} - 1110 x^{5} + 2269 x^{4} - 554 x^{3} - 279 x^{2} + 127 x - 13$	$21$	[3,9]	$-\,2^{18}\cdot 3^{24}\cdot 7^{17}$	$3$	$30.720913770020566$	$39.667584012275974$			?	$C_3\times F_7$ (as 21T9)	trivial	$2$	$11$	$19624254.06882178$
21.3.864...632.1	$x^{21} - 2 x^{18} - 18 x^{17} + 12 x^{16} + 93 x^{15} + 252 x^{14} + 756 x^{13} + 424 x^{12} - 846 x^{11} - 3942 x^{10} - 12420 x^{9} - 20592 x^{8} - 30729 x^{7} - 35272 x^{6} - 30168 x^{5} - 18600 x^{4} - 8512 x^{3} - 2880 x^{2} - 768 x - 128$	$21$	[3,9]	$-\,2^{14}\cdot 3^{21}\cdot 11\cdot 71^{9}$	$4$	$33.1737434361$				?	$C_3^7:C_2\wr D_7$ (as 21T131)	trivial	$2$	$11$	$48578716.598$
21.3.140...943.1	$x^{21} - 6 x^{20} + 12 x^{19} + 3 x^{18} - 60 x^{17} + 108 x^{16} - 18 x^{15} - 225 x^{14} + 357 x^{13} - 89 x^{12} - 387 x^{11} + 522 x^{10} - 121 x^{9} - 312 x^{8} + 315 x^{7} - 47 x^{6} - 108 x^{5} + 75 x^{4} - 8 x^{3} - 12 x^{2} + 6 x - 1$	$21$	[3,9]	$-\,3^{18}\cdot 23^{7}\cdot 10322161^{2}$	$3$	$33.9506825054$				?	$A_7\wr S_3$ (as 21T156)	trivial	$2$	$11$	$77801090.0541$
21.3.160...219.1	$x^{21} - 3 x^{20} + 3 x^{19} - 2 x^{18} - 3 x^{17} + 11 x^{16} - 25 x^{15} + 45 x^{14} - 52 x^{13} + 43 x^{12} + 51 x^{11} - 121 x^{10} + 143 x^{9} - 83 x^{8} - 62 x^{7} + 95 x^{6} - 203 x^{5} + 45 x^{4} - 50 x^{3} - 26 x^{2} + 3 x - 7$	$21$	[3,9]	$-\,11^{9}\cdot 13^{12}\cdot 37^{2}\cdot 1459^{2}$	$4$	$34.1618478127$	$26191.673890867773$			?	$C_3^7.F_7$ (as 21T98)	trivial	$2$	$11$	$54878271.2447$
21.3.171...583.1	$x^{21} - 6 x^{20} + 12 x^{19} + 5 x^{18} - 66 x^{17} + 108 x^{16} + 6 x^{15} - 261 x^{14} + 345 x^{13} - 11 x^{12} - 453 x^{11} + 474 x^{10} - 33 x^{9} - 336 x^{8} + 279 x^{7} - 19 x^{6} - 108 x^{5} + 69 x^{4} - 6 x^{3} - 12 x^{2} + 6 x - 1$	$21$	[3,9]	$-\,3^{18}\cdot 7^{4}\cdot 23^{7}\cdot 232801^{2}$	$4$	$34.2754229725$				?	$A_7\wr S_3$ (as 21T156)	trivial	$2$	$11$	$67378616.8716$
21.3.183...527.1	$x^{21} - 10 x^{20} + 55 x^{19} - 232 x^{18} + 778 x^{17} - 2176 x^{16} + 5171 x^{15} - 10560 x^{14} + 18589 x^{13} - 28136 x^{12} + 36163 x^{11} - 38416 x^{10} + 31475 x^{9} - 15502 x^{8} - 4692 x^{7} + 21382 x^{6} - 28506 x^{5} + 25066 x^{4} - 15737 x^{3} + 6646 x^{2} - 1564 x + 8$	$21$	[3,9]	$-\,7^{17}\cdot 31^{12}$	$2$	$34.38220037193264$	$49.94471001444876$				$C_3\times F_7$ (as 21T9)	trivial	$2$	$11$	$129961348.56213313$
21.3.372...096.1	$x^{21} + 11 x^{19} - 8 x^{18} + 72 x^{17} - 48 x^{16} + 204 x^{15} + 249 x^{13} + 376 x^{12} + 18 x^{11} + 62 x^{10} - 473 x^{9} - 1008 x^{8} - 975 x^{7} + 192 x^{6} - 324 x^{5} + 936 x^{4} + 368 x^{3} - 576 x^{2} - 128 x + 128$	$21$	[3,9]	$-\,2^{14}\cdot 3^{36}\cdot 73^{6}$	$3$	$35.5620488962$				?	$C_3^7.(C_2^7.A_7)$ (as 21T151)	trivial	$2$	$11$	$73916651.6702$