Number field search results

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

Results (1-50 of 14315 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
16.2.13972911310408283.1	$x^{16} - 2 x^{15} + 2 x^{14} - 7 x^{13} + 10 x^{12} - 10 x^{11} + 19 x^{10} - 18 x^{9} + 18 x^{8} - 22 x^{7} + 13 x^{6} - 14 x^{5} + 8 x^{4} - 3 x^{3} + 4 x^{2} + x + 1$	$16$	[2,7]	$-\,4271\cdot 22247\cdot 147057059$	$3$	$10.2112857937$	$118207069.62956269$			✓	$S_{16}$ (as 16T1954)	trivial	$2$	$8$	$23.4808862884$
16.2.15968672198702159.1	$x^{16} - x^{14} + x^{12} - 3 x^{11} - 4 x^{10} + 5 x^{9} + 3 x^{8} - x^{7} - 2 x^{6} + 2 x^{5} - 5 x^{3} + 3 x^{2} + x - 1$	$16$	[2,7]	$-\,15968672198702159$	$1$	$10.2968479655$	$126367211.72322415$			?	$S_{16}$ (as 16T1954)	trivial	$2$	$8$	$25.3373214982$
16.2.17695129757421875.1	$x^{16} - x^{15} - 2 x^{14} + 5 x^{13} - 3 x^{12} - 7 x^{11} + 12 x^{10} + x^{9} - 15 x^{8} + 13 x^{7} + 8 x^{6} - 19 x^{5} + 2 x^{4} + 10 x^{3} - 3 x^{2} - 2 x + 1$	$16$	[2,7]	$-\,5^{8}\cdot 11^{4}\cdot 59\cdot 229^{2}$	$4$	$10.363127931$	$862.0353821044703$			?	$C_4^4.C_2\wr D_4$ (as 16T1823)	trivial	$2$	$8$	$26.9911896741$
16.2.17968112315819999.1	$x^{16} - x^{15} - 4 x^{14} + 5 x^{13} + 7 x^{12} - 9 x^{11} - 10 x^{10} + 11 x^{9} + 14 x^{8} - 14 x^{7} - 13 x^{6} + 17 x^{5} + 4 x^{4} - 11 x^{3} + 2 x^{2} + 3 x - 1$	$16$	[2,7]	$-\,43^{2}\cdot 71\cdot 369959^{2}$	$3$	$10.3730483776$	$33607.80901814339$			?	$C_2^8.S_8$ (as 16T1948)	trivial	$2$	$8$	$27.1389518265$
16.2.19666546293359375.1	$x^{16} - 3 x^{15} + 5 x^{14} - 4 x^{13} - x^{12} + 6 x^{11} - 6 x^{10} - 8 x^{9} + 20 x^{8} - 19 x^{7} + 11 x^{6} + 4 x^{5} - 14 x^{4} + 4 x^{3} + 5 x^{2} - x - 1$	$16$	[2,7]	$-\,5^{8}\cdot 31^{2}\cdot 71\cdot 859^{2}$	$4$	$10.4317700725$	$3074.621114869278$			?	$C_2^6.S_4^2:D_4$ (as 16T1905)	trivial	$2$	$8$	$28.6747805181$
16.2.21004976369198027.1	$x^{16} - 4 x^{15} + 6 x^{14} - x^{13} - 6 x^{12} + 2 x^{11} + 10 x^{10} - 18 x^{9} + 19 x^{8} - 18 x^{7} + 10 x^{6} + 2 x^{5} - 6 x^{4} - x^{3} + 6 x^{2} - 4 x + 1$	$16$	[2,7]	$-\,43^{2}\cdot 83\cdot 369959^{2}$	$3$	$10.4747854752$	$36337.083963906625$			?	$C_2^8.S_8$ (as 16T1948)	trivial	$2$	$8$	$29.604836305$
16.2.26611481600000000.1	$x^{16} - 2 x^{15} + 4 x^{13} - 2 x^{12} + 7 x^{10} - 20 x^{9} - 11 x^{8} + 28 x^{7} + x^{6} - 4 x^{5} + 11 x^{4} - 10 x^{3} - 5 x^{2} + 4 x - 1$	$16$	[2,7]	$-\,2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 71$	$4$	$10.6308212517$				?	$C_2^2.C_2^2\wr D_4$ (as 16T1719)	trivial	$2$	$8$	$34.2967522472$
16.2.32297047507421875.1	$x^{16} - 5 x^{15} + 13 x^{14} - 22 x^{13} + 26 x^{12} - 20 x^{11} + 4 x^{10} + 12 x^{9} - 19 x^{8} + 12 x^{7} + 4 x^{6} - 20 x^{5} + 26 x^{4} - 22 x^{3} + 13 x^{2} - 5 x + 1$	$16$	[2,7]	$-\,5^{8}\cdot 29^{6}\cdot 139$	$3$	$10.7602577971$	$329.45105355393224$			?	$C_2\wr D_4.C_4$ (as 16T1722)	trivial	$2$	$8$	$37.8934824391$
16.2.36286162879296875.1	$x^{16} - 2 x^{15} + x^{14} + 3 x^{13} - 11 x^{12} + 16 x^{11} - 17 x^{10} + 16 x^{9} - 13 x^{8} + 16 x^{7} - 17 x^{6} + 16 x^{5} - 11 x^{4} + 3 x^{3} + x^{2} - 2 x + 1$	$16$	[2,7]	$-\,5^{8}\cdot 31^{2}\cdot 131\cdot 859^{2}$	$4$	$10.8388652059$	$4176.361454663616$			?	$C_2^6.S_4^2:D_4$ (as 16T1905)	trivial	$2$	$8$	$40.8815236048$
16.2.36973431874322432.1	$x^{16} - 2 x^{15} + 3 x^{14} + 6 x^{13} - 9 x^{12} + 14 x^{11} + 6 x^{10} - 6 x^{9} + 21 x^{8} - 6 x^{7} + 6 x^{6} + 14 x^{5} - 9 x^{4} + 6 x^{3} + 3 x^{2} - 2 x + 1$	$16$	[2,7]	$-\,2^{16}\cdot 47\cdot 331^{4}$	$3$	$10.8515833424$				?	$C_2\wr C_2^3.S_4$ (as 16T1848)	trivial	$2$	$8$	$42.6664411408$
16.2.45287535480859375.1	$x^{16} - 3 x^{15} + 6 x^{14} - 11 x^{13} + 14 x^{12} - 16 x^{11} + 13 x^{10} - 8 x^{9} + 7 x^{8} - 8 x^{7} + 13 x^{6} - 16 x^{5} + 14 x^{4} - 11 x^{3} + 6 x^{2} - 3 x + 1$	$16$	[2,7]	$-\,5^{8}\cdot 11^{4}\cdot 151\cdot 229^{2}$	$4$	$10.9900246863$	$1379.0739646588938$			?	$C_4^4.C_2\wr D_4$ (as 16T1823)	trivial	$2$	$8$	$46.4808624$
16.2.46569375736056031.1	$x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 12 x^{12} - 17 x^{11} + 20 x^{10} - 23 x^{9} + 23 x^{8} - 23 x^{7} + 20 x^{6} - 17 x^{5} + 12 x^{4} - 8 x^{3} + 5 x^{2} - 2 x + 1$	$16$	[2,7]	$-\,37^{2}\cdot 199\cdot 643^{4}$	$3$	$11.0092130438$	$2175.869711172983$			✓	$C_4^4.C_2\wr S_4$ (as 16T1879)	trivial	$2$	$8$	$46.8877764419$
16.2.47375394326171875.1	$x^{16} - 5 x^{15} + 8 x^{14} + 4 x^{13} - 29 x^{12} + 31 x^{11} + 4 x^{10} - 19 x^{9} - 23 x^{8} + 59 x^{7} - 30 x^{6} - 16 x^{5} + 20 x^{4} - 6 x^{2} + x + 1$	$16$	[2,7]	$-\,5^{10}\cdot 19^{3}\cdot 29^{4}$	$3$	$11.021026645$	$163.86707546041302$			?	$C_4^2\wr C_2.D_4$ (as 16T1561)	trivial	$2$	$8$	$48.3314431778$
16.2.60840256363671875.1	$x^{16} - x^{15} + x^{14} - 2 x^{12} - 2 x^{11} + 3 x^{10} - 3 x^{9} + 3 x^{8} + 14 x^{7} - 22 x^{6} + 6 x^{5} + 5 x^{4} + 2 x^{3} - 5 x^{2} + 1$	$16$	[2,7]	$-\,5^{8}\cdot 29^{4}\cdot 41^{2}\cdot 131$	$4$	$11.194686597$	$882.4936260393046$			?	$C_4^4.C_2\wr D_4$ (as 16T1823)	trivial	$2$	$8$	$56.520400945$
16.2.63474986914349056.1	$x^{16} - 6 x^{15} + 15 x^{14} - 18 x^{13} + 5 x^{12} + 8 x^{11} + 4 x^{10} - 22 x^{9} + 25 x^{8} - 22 x^{7} + 4 x^{6} + 8 x^{5} + 5 x^{4} - 18 x^{3} + 15 x^{2} - 6 x + 1$	$16$	[2,7]	$-\,2^{16}\cdot 151\cdot 283^{4}$	$3$	$11.224387818$				?	$C_2\wr C_2^3.S_4$ (as 16T1848)	trivial	$2$	$8$	$56.3972659755$
16.2.66221484488898283.1	$x^{16} - x^{15} - 3 x^{13} + 10 x^{12} - 11 x^{11} + 17 x^{10} - 30 x^{9} + 27 x^{8} - 20 x^{7} + 47 x^{6} - 70 x^{5} + 35 x^{4} + 13 x^{3} - 21 x^{2} + 8 x - 1$	$16$	[2,7]	$-\,191^{2}\cdot 283^{5}$	$2$	$11.2541430731$	$953.5786309642566$			?	$C_2\wr Q_8.S_4$ (as 16T1847)	trivial	$2$	$8$	$61.1816013898$
16.2.67969704100000000.1	$x^{16} - 3 x^{14} + x^{12} + 3 x^{10} + 2 x^{8} - x^{6} - 9 x^{4} - 4 x^{2} - 1$	$16$	[2,7]	$-\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 31^{2}$	$4$	$11.2724861714$	$245.92126826496147$			?	$C_4^4.C_2\wr D_4$ (as 16T1823)	trivial	$2$	$8$	$62.5995169928$
16.2.75417294303354643.1	$x^{16} + 4 x^{14} - x^{13} + 7 x^{12} - 8 x^{11} + 3 x^{10} - 18 x^{9} - 7 x^{8} - 15 x^{7} - 4 x^{6} - 2 x^{5} - 7 x^{4} - 5 x^{3} + x^{2} - x - 1$	$16$	[2,7]	$-\,149^{2}\cdot 283\cdot 331^{4}$	$3$	$11.3459779239$	$3735.9439235620225$			?	$C_4^4.C_2\wr S_4$ (as 16T1879)	trivial	$2$	$8$	$62.5762180021$
16.2.80157081600000000.1	$x^{16} - 2 x^{15} + x^{14} - 3 x^{12} - 2 x^{11} + 19 x^{10} - 4 x^{9} - 37 x^{8} + 28 x^{7} + 19 x^{6} - 30 x^{5} + 6 x^{4} + 10 x^{3} - 6 x^{2} + 1$	$16$	[2,7]	$-\,2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 151$	$4$	$11.3892825843$				?	$C_2\wr D_4.C_2$ (as 16T1577)	trivial	$2$	$8$	$69.1847935897$
16.2.86899140707421875.1	$x^{16} - 5 x^{15} + 10 x^{14} - 9 x^{13} - 2 x^{12} + 17 x^{11} - 21 x^{10} + 11 x^{9} + x^{8} - 7 x^{7} + 2 x^{6} + 5 x^{5} - 12 x^{4} + 14 x^{3} - 9 x^{2} + 4 x - 1$	$16$	[2,7]	$-\,5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 131$	$4$	$11.4469152552$	$364.64366167534024$			?	$C_2^7.C_2\wr D_4$ (as 16T1778)	trivial	$2$	$8$	$67.4836755215$
16.2.98118744033289079.1	$x^{16} - 7 x^{15} + 27 x^{14} - 70 x^{13} + 129 x^{12} - 168 x^{11} + 134 x^{10} - 6 x^{9} - 152 x^{8} + 231 x^{7} - 187 x^{6} + 88 x^{5} - 18 x^{4} - 4 x^{3} + 5 x^{2} - 3 x + 1$	$16$	[2,7]	$-\,191\cdot 283^{6}$	$2$	$11.5341208847$	$953.5786309642566$			?	$C_2\wr Q_8.S_4$ (as 16T1849)	trivial	$2$	$8$	$77.7525923561$
16.2.98251000757421875.1	$x^{16} - x^{15} - x^{14} + 5 x^{13} - 2 x^{12} - 8 x^{11} + 13 x^{10} + 5 x^{9} - 24 x^{8} + 12 x^{7} + 28 x^{6} - 25 x^{5} - 21 x^{4} + 16 x^{3} + 8 x^{2} - 4 x - 1$	$16$	[2,7]	$-\,5^{8}\cdot 11^{2}\cdot 29^{4}\cdot 2939$	$4$	$11.5350919671$	$2165.1108516655677$			?	$C_4^4.C_2\wr D_4$ (as 16T1823)	trivial	$2$	$8$	$76.1400735821$
16.2.115558273191796875.1	$x^{16} + 2 x^{14} - 5 x^{13} - x^{12} - 10 x^{11} + 3 x^{10} - 4 x^{9} + 9 x^{8} - 4 x^{7} + 8 x^{6} - x^{5} + 7 x^{4} + 4 x^{2} - x + 1$	$16$	[2,7]	$-\,3^{4}\cdot 5^{8}\cdot 11^{4}\cdot 19^{2}\cdot 691$	$5$	$11.6526597417$	$1471.8304929576639$			?	$C_4^4.C_2\wr D_4$ (as 16T1823)	trivial	$2$	$8$	$84.8251848921$
16.2.117614702500000000.1	$x^{16} + 3 x^{14} - 5 x^{10} - x^{8} - x^{6} - 8 x^{4} - 7 x^{2} - 1$	$16$	[2,7]	$-\,2^{8}\cdot 5^{10}\cdot 19^{6}$	$3$	$11.6655132394$	$111.61535524130564$			?	$C_2^7.C_2\wr D_4$ (as 16T1774)	trivial	$2$	$8$	$81.4393135942$
16.2.118740047226171875.1	$x^{16} - x^{15} - 2 x^{14} + 3 x^{13} - x^{12} - 2 x^{11} - 2 x^{10} + 9 x^{9} + x^{8} + x^{7} - x^{6} - 2 x^{5} + 2 x^{4} + 10 x^{3} + 3 x^{2} - 2 x - 1$	$16$	[2,7]	$-\,5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 179$	$4$	$11.6724581656$	$426.24523457746716$			?	$C_2^7.C_2\wr D_4$ (as 16T1778)	trivial	$2$	$8$	$83.1594782248$
16.2.118893936100000000.1	$x^{16} - x^{14} - 4 x^{12} + 4 x^{10} + 7 x^{8} + 2 x^{6} - 4 x^{4} - 5 x^{2} - 1$	$16$	[2,7]	$-\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 41^{2}$	$4$	$11.6734030717$	$282.81808113862405$			?	$C_4^4.C_2\wr D_4$ (as 16T1823)	trivial	$2$	$8$	$83.2222937736$
16.2.122484747687109375.1	$x^{16} - 2 x^{15} - x^{14} + 3 x^{13} - 2 x^{10} - 6 x^{9} + 7 x^{8} + 6 x^{7} - 5 x^{6} + 2 x^{5} - 3 x^{3} - 1$	$16$	[2,7]	$-\,5^{8}\cdot 79\cdot 251^{4}$	$3$	$11.6951319407$	$314.8729902675045$			?	$C_{2440}.D_6$ (as 16T1759)	trivial	$2$	$8$	$82.9569002176$
16.2.125468737884127232.1	$x^{16} - 4 x^{15} + 20 x^{13} - 21 x^{12} - 32 x^{11} + 62 x^{10} + 4 x^{9} - 59 x^{8} + 20 x^{7} + 12 x^{6} + 8 x^{5} - 9 x^{4} - 8 x^{3} + 2 x^{2} + 4 x + 1$	$16$	[2,7]	$-\,2^{32}\cdot 7^{4}\cdot 23^{3}$	$3$	$11.7127391284$				?	$C_4^3.D_4^2$ (as 16T1567)	trivial	$2$	$8$	$84.135150286$
16.2.125468737884127232.2	$x^{16} - 4 x^{15} + 6 x^{14} - 8 x^{13} + 19 x^{12} - 40 x^{11} + 62 x^{10} - 76 x^{9} + 90 x^{8} - 104 x^{7} + 80 x^{6} - 12 x^{5} - 46 x^{4} + 52 x^{3} - 28 x^{2} + 8 x - 1$	$16$	[2,7]	$-\,2^{32}\cdot 7^{4}\cdot 23^{3}$	$3$	$11.7127391284$				?	$C_4^4.C_2\wr C_2^2$ (as 16T1781)	trivial	$2$	$8$	$83.7217340359$
16.2.125468737884127232.3	$x^{16} - 4 x^{15} + 6 x^{14} - 19 x^{12} + 44 x^{11} - 48 x^{10} + 8 x^{9} + 53 x^{8} - 76 x^{7} + 36 x^{6} + 28 x^{5} - 43 x^{4} + 12 x^{3} + 4 x^{2} - 1$	$16$	[2,7]	$-\,2^{32}\cdot 7^{4}\cdot 23^{3}$	$3$	$11.7127391284$				?	$C_4^4.C_2\wr C_2^2$ (as 16T1781)	trivial	$2$	$8$	$84.7108973406$
16.2.134673762004296875.1	$x^{16} - 3 x^{15} + 7 x^{14} - 9 x^{13} + 10 x^{12} - 9 x^{11} + 9 x^{10} - 12 x^{9} + 11 x^{8} - 12 x^{7} + 9 x^{6} - 9 x^{5} + 10 x^{4} - 9 x^{3} + 7 x^{2} - 3 x + 1$	$16$	[2,7]	$-\,5^{8}\cdot 29^{4}\cdot 61^{2}\cdot 131$	$4$	$11.76468184641966$	$1076.4269599002062$			?	$C_4^4.C_2\wr D_4$ (as 16T1823)	trivial	$2$	$8$	$91.09292559953064$
16.2.142966494557221347.1	$x^{16} - 2 x^{15} + x^{14} + 2 x^{13} - 3 x^{12} - 7 x^{11} + 38 x^{10} - 84 x^{9} + 105 x^{8} - 84 x^{7} + 38 x^{6} - 7 x^{5} - 3 x^{4} + 2 x^{3} + x^{2} - 2 x + 1$	$16$	[2,7]	$-\,3^{3}\cdot 19^{6}\cdot 103^{4}$	$3$	$11.8087014221$	$100.84081659346516$			?	$C_4^4:(C_2\times S_4)$ (as 16T1758)	trivial	$2$	$8$	$116.826344358$
16.2.145380128593826227.1	$x^{16} - x^{15} - 2 x^{14} + 2 x^{13} - 2 x^{12} + 7 x^{11} + 5 x^{10} - 24 x^{9} + x^{8} + 35 x^{7} - 15 x^{6} - 42 x^{5} + 36 x^{4} + 23 x^{3} - 28 x^{2} + 6 x - 1$	$16$	[2,7]	$-\,283^{7}$	$1$	$11.8210639157$	$68.99852815152498$			?	$C_2^7.\GL(2,3)$ (as 16T1691)	trivial	$2$	$8$	$96.9580135951$
16.2.145380128593826227.2	$x^{16} - 2 x^{15} + x^{14} - 5 x^{13} + 15 x^{12} - 13 x^{11} - 3 x^{10} + 9 x^{9} - x^{8} + 4 x^{7} - 17 x^{6} + 4 x^{5} + 16 x^{4} - 2 x^{3} - 9 x^{2} + 2 x + 1$	$16$	[2,7]	$-\,283^{7}$	$1$	$11.8210639157$	$68.99852815152498$			?	$C_2^7.\GL(2,3)$ (as 16T1692)	trivial	$2$	$8$	$103.008611429$
16.2.173942237590234375.1	$x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 2 x^{12} - 3 x^{11} + 2 x^{10} + x^{8} + 2 x^{6} - 3 x^{5} + 2 x^{4} - 4 x^{3} + 2 x^{2} - x + 1$	$16$	[2,7]	$-\,5^{8}\cdot 31\cdot 119851^{2}$	$3$	$11.9543320753$	$4310.093386459277$			✓	$C_2^6.S_4^2:D_4$ (as 16T1905)	trivial	$2$	$8$	$97.0131796811$
16.2.183992172742975744.1	$x^{16} + x^{14} + 3 x^{12} - 8 x^{10} + x^{8} + 14 x^{6} - 4 x^{2} - 1$	$16$	[2,7]	$-\,2^{8}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4}$	$4$	$11.9963729599$	$429.31461643061976$			?	$C_4^4.C_2\wr S_4$ (as 16T1879)	trivial	$2$	$8$	$121.328701657$
16.2.190802976100000000.1	$x^{16} - x^{15} - x^{14} - 3 x^{12} - 6 x^{11} + 5 x^{10} - x^{9} - 4 x^{8} - x^{7} + 5 x^{6} - 6 x^{5} - 3 x^{4} - x^{2} - x + 1$	$16$	[2,7]	$-\,2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 19^{4}$	$4$	$12.0236568043$	$118.57397717476675$			?	$C_2^2.C_2^2\wr D_4$ (as 16T1719)	trivial	$2$	$8$	$104.810498694$
16.2.194097037021484375.1	$x^{16} - 3 x^{15} + 3 x^{14} - 6 x^{12} + 10 x^{11} - 2 x^{10} - 6 x^{9} + 7 x^{8} + 9 x^{7} - 4 x^{6} - 12 x^{5} + 7 x^{4} + 7 x^{3} - 4 x^{2} - 3 x + 1$	$16$	[2,7]	$-\,5^{10}\cdot 101^{4}\cdot 191$	$3$	$12.0365266463$	$464.41354068302337$			?	$C_2^8.C_2\wr C_4$ (as 16T1776)	trivial	$2$	$8$	$134.861185173$
16.2.195238297600000000.1	$x^{16} - 4 x^{15} + 6 x^{14} - 6 x^{13} + 10 x^{12} - 26 x^{11} + 52 x^{10} - 54 x^{9} - 12 x^{8} + 82 x^{7} - 54 x^{6} - 24 x^{5} + 49 x^{4} - 32 x^{3} + 16 x^{2} - 6 x + 1$	$16$	[2,7]	$-\,2^{24}\cdot 5^{8}\cdot 31^{3}$	$3$	$12.0409378082$				?	$C_4^4:D_4$ (as 16T1477)	trivial	$2$	$8$	$106.032960978$
16.2.195238297600000000.2	$x^{16} - 6 x^{15} + 14 x^{14} - 14 x^{13} + 2 x^{12} - 4 x^{11} + 40 x^{10} - 78 x^{9} + 79 x^{8} - 52 x^{7} + 36 x^{6} - 34 x^{5} + 26 x^{4} - 18 x^{3} + 10 x^{2} - 4 x + 1$	$16$	[2,7]	$-\,2^{24}\cdot 5^{8}\cdot 31^{3}$	$3$	$12.0409378082$	$45.66643307539152$			?	$D_8\wr C_2$ (as 16T972)	trivial	$2$	$8$	$107.164441498$
16.2.195238297600000000.3	$x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 51 x^{12} - 46 x^{11} + 18 x^{10} - 4 x^{9} + 44 x^{8} - 118 x^{7} + 160 x^{6} - 138 x^{5} + 72 x^{4} - 16 x^{3} - 4 x^{2} + 4 x - 1$	$16$	[2,7]	$-\,2^{24}\cdot 5^{8}\cdot 31^{3}$	$3$	$12.0409378082$	$45.66643307539152$			?	$D_8\wr C_2$ (as 16T972)	trivial	$2$	$8$	$109.456398528$
16.2.199224773165828807.1	$x^{16} - 3 x^{15} + 6 x^{14} - 8 x^{13} + 7 x^{12} - 4 x^{11} + 3 x^{9} - 5 x^{8} + 3 x^{7} - 4 x^{5} + 7 x^{4} - 8 x^{3} + 6 x^{2} - 3 x + 1$	$16$	[2,7]	$-\,47\cdot 89^{2}\cdot 731531^{2}$	$3$	$12.0561587744$	$55317.21407482484$			✓	$C_2^8.S_8$ (as 16T1948)	trivial	$2$	$8$	$103.513307142$
16.2.217453542400000000.1	$x^{16} - 2 x^{15} - x^{14} + 4 x^{13} - 4 x^{12} + 4 x^{11} - x^{10} + 8 x^{9} - 14 x^{8} - 8 x^{7} + 14 x^{6} + 6 x^{5} - 4 x^{4} - 4 x^{3} - x^{2} + 2 x + 1$	$16$	[2,7]	$-\,2^{16}\cdot 5^{8}\cdot 31^{2}\cdot 8839$	$4$	$12.1223105454$				?	$C_4^4.C_2\wr D_4$ (as 16T1823)	trivial	$2$	$8$	$115.175792316$
16.2.284452595367842719.1	$x^{16} - x^{15} - 2 x^{14} - 4 x^{13} + 9 x^{12} + 4 x^{11} + 2 x^{10} - 11 x^{9} - 5 x^{8} - 5 x^{7} + 12 x^{6} + 2 x^{5} + 4 x^{4} - 6 x^{3} - x^{2} - x + 1$	$16$	[2,7]	$-\,1321^{2}\cdot 3347^{2}\cdot 14551$	$3$	$12.3275172465$	$253644.63770598423$			?	$C_2^8.S_8$ (as 16T1948)	trivial	$2$	$8$	$127.627660583$
16.2.300956572229230751.1	$x^{16} - 3 x^{15} + 3 x^{14} - x^{13} - x^{12} + 6 x^{11} - 12 x^{10} + 16 x^{9} - 17 x^{8} + 16 x^{7} - 12 x^{6} + 6 x^{5} - x^{4} - x^{3} + 3 x^{2} - 3 x + 1$	$16$	[2,7]	$-\,71\cdot 89^{2}\cdot 731531^{2}$	$3$	$12.3710479291$	$67989.29613549473$			?	$C_2^8.S_8$ (as 16T1948)	trivial	$2$	$8$	$130.183615174$
16.2.316940672000000000.1	$x^{16} - 4 x^{15} + 6 x^{14} - 2 x^{13} - 7 x^{12} + 37 x^{10} - 64 x^{9} + 32 x^{8} + 14 x^{7} + 8 x^{6} - 82 x^{5} + 119 x^{4} - 90 x^{3} + 40 x^{2} - 10 x + 1$	$16$	[2,7]	$-\,2^{16}\cdot 5^{9}\cdot 19^{5}$	$3$	$12.411124249$				?	$C_2^7.C_2\wr D_4$ (as 16T1782)	trivial	$2$	$8$	$160.345812218$
16.2.319040277384290048.1	$x^{16} - x^{15} + 2 x^{14} - 7 x^{13} + x^{12} + x^{11} + x^{10} + 13 x^{9} - 12 x^{8} - 11 x^{7} + 5 x^{6} - 8 x^{5} - 6 x^{4} - 8 x^{3} + 3 x^{2} - 6 x + 1$	$16$	[2,7]	$-\,2^{8}\cdot 47^{3}\cdot 331^{4}$	$3$	$12.4162470312$	$653.1566997847884$			?	$C_4^4:(C_2\times S_4)$ (as 16T1758)	trivial	$2$	$8$	$143.8650113$
16.2.319040277384290048.2	$x^{16} - 6 x^{15} + 15 x^{14} - 23 x^{13} + 29 x^{12} - 34 x^{11} + 28 x^{10} - 14 x^{9} + x^{8} + 40 x^{7} - 80 x^{6} + 58 x^{5} - 30 x^{4} + 29 x^{3} - 20 x^{2} + 6 x - 1$	$16$	[2,7]	$-\,2^{8}\cdot 47^{3}\cdot 331^{4}$	$3$	$12.4162470312$	$1098.4742548959503$			?	$C_2^7.C_2\wr S_4$ (as 16T1851)	trivial	$2$	$8$	$137.374267948$
16.2.320444825600000000.1	$x^{16} - 8 x^{15} + 36 x^{14} - 112 x^{13} + 260 x^{12} - 468 x^{11} + 658 x^{10} - 716 x^{9} + 574 x^{8} - 288 x^{7} + 8 x^{6} + 140 x^{5} - 145 x^{4} + 84 x^{3} - 32 x^{2} + 8 x - 1$	$16$	[2,7]	$-\,2^{32}\cdot 5^{8}\cdot 191$	$3$	$12.4196563444$				✓	$C_2^6.D_4^2$ (as 16T1590)	trivial	$2$	$8$	$139.323106415$
16.2.320501104309234339.1	$x^{16} - 3 x^{12} - 4 x^{11} - 10 x^{10} - 10 x^{9} - 22 x^{7} - 5 x^{6} + 5 x^{5} - 7 x^{4} + x^{3} + 7 x^{2} - 3 x + 1$	$16$	[2,7]	$-\,67^{2}\cdot 283^{4}\cdot 11131$	$3$	$12.4197926597$	$14527.728349607863$			?	$C_4^4.C_2\wr S_4$ (as 16T1879)	trivial	$2$	$8$	$149.317935997$