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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
8.2.5808919375.1	$x^{8} - x^{7} + x^{6} - 6 x^{5} - 17 x^{4} - 11 x^{3} + 2 x^{2} + 15 x + 11$	$8$	[2,3]	$-\,5^{4}\cdot 7^{6}\cdot 79$	$3$	$16.6154427584$	$85.53071012854735$			?	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$4$	$73.8704980818$
8.4.9191328125.1	$x^{8} - x^{7} - 13 x^{6} - 13 x^{5} + 25 x^{4} + 38 x^{3} - 33 x^{2} - 34 x + 11$	$8$	[4,2]	$5^{7}\cdot 7^{6}$	$2$	$17.5963375242$	$17.596337524163744$			?	$C_8:C_2$ (as 8T7)	trivial	$2$	$5$	$129.505077804$
8.0.12800211200.1	$x^{8} - 4 x^{7} + 9 x^{6} - 6 x^{5} + 2 x^{4} - 22 x^{3} + 30 x^{2} - 10 x + 1$	$8$	[0,4]	$2^{8}\cdot 5^{2}\cdot 7^{6}\cdot 17$	$4$	$18.3401186902$	$103.76669612493649$			?	$S_4\wr C_2$ (as 8T47)	$[4]$	$4$	$3$	$34.718649129$
8.4.16838513125.1	$x^{8} - 3 x^{7} + x^{6} + 3 x^{5} - 16 x^{4} + 26 x^{3} - 19 x^{2} + 4 x + 4$	$8$	[4,2]	$5^{4}\cdot 7^{6}\cdot 229$	$3$	$18.9796398631$	$145.62175921950228$				$S_4\wr C_2$ (as 8T47)	trivial	$2$	$5$	$210.497753896$
8.2.20220921875.1	$x^{8} - 2 x^{7} + 4 x^{6} - 13 x^{5} + x^{4} + 5 x^{3} - 5 x^{2} - 5 x - 5$	$8$	[2,3]	$-\,5^{6}\cdot 7^{6}\cdot 11$	$3$	$19.4189220714$	$47.725158108626026$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$4$	$103.277452002$
8.6.20220921875.1	$x^{8} - x^{7} - 6 x^{6} + 8 x^{5} + 4 x^{4} - 39 x^{3} - 19 x^{2} + 22 x + 11$	$8$	[6,1]	$-\,5^{6}\cdot 7^{6}\cdot 11$	$3$	$19.4189220714$	$47.725158108626026$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$6$	$195.782974638$
8.0.26293139712.1	$x^{8} - 2 x^{7} + x^{6} - 12 x^{5} + 49 x^{4} - 72 x^{3} + 50 x^{2} - 12 x + 1$	$8$	[0,4]	$2^{8}\cdot 3^{2}\cdot 7^{6}\cdot 97$	$4$	$20.0669009099$	$146.82500360141077$			?	$S_4\wr C_2$ (as 8T47)	$[4]$	$4$	$3$	$105.654393807$
8.2.34118210000.1	$x^{8} - 3 x^{7} + x^{6} + 3 x^{5} - 2 x^{4} + 5 x^{3} - 19 x^{2} - 10 x + 25$	$8$	[2,3]	$-\,2^{4}\cdot 5^{4}\cdot 7^{6}\cdot 29$	$4$	$20.7311445471$	$146.5725098572187$			?	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$4$	$203.709050283$
8.4.35888239205.1	$x^{8} - 2 x^{7} - 5 x^{6} + 4 x^{5} + 20 x^{4} + 4 x^{3} - 61 x^{2} + 33 x + 8$	$8$	[4,2]	$5\cdot 7^{6}\cdot 13^{2}\cdot 19^{2}$	$4$	$20.8626282216$	$151.23663605143227$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$640.422869397$
8.0.39153587200.1	$x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{5} - x^{4} - 10 x^{3} - 12 x^{2} - 16 x + 50$	$8$	[0,4]	$2^{10}\cdot 5^{2}\cdot 7^{6}\cdot 13$	$4$	$21.0909646954$	$128.32763854378362$			?	$S_4\wr C_2$ (as 8T47)	$[4]$	$4$	$3$	$173.458593684$
8.0.44486028125.1	$x^{8} - 3 x^{7} + x^{6} + 10 x^{5} + 5 x^{4} - 30 x^{3} - 5 x^{2} + 25 x + 25$	$8$	[0,4]	$5^{5}\cdot 7^{6}\cdot 11^{2}$	$3$	$21.430285359$	$47.725158108626026$			?	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28)	$[2]$	$2$	$3$	$64.6270064213$
8.4.44486028125.1	$x^{8} - 2 x^{7} - 3 x^{6} + 15 x^{5} - 6 x^{4} + 12 x^{3} - 33 x^{2} - 82 x + 79$	$8$	[4,2]	$5^{5}\cdot 7^{6}\cdot 11^{2}$	$3$	$21.430285359$	$47.725158108626026$			?	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28)	trivial	$2$	$5$	$245.026718105$
8.4.72885908480.1	$x^{8} - 2 x^{7} - 6 x^{6} + 16 x^{5} - 28 x^{4} - 16 x^{3} + 64 x^{2} - 40 x + 8$	$8$	[4,2]	$2^{10}\cdot 5\cdot 7^{6}\cdot 11^{2}$	$4$	$22.794519739$	$80.4226172057492$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$1021.26744479$
8.0.72885908480.1	$x^{8} + 8 x^{6} + 10 x^{4} - 14 x^{3} + 4 x^{2} - 14 x + 79$	$8$	[0,4]	$2^{10}\cdot 5\cdot 7^{6}\cdot 11^{2}$	$4$	$22.794519739$	$80.4226172057492$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$162.316495313$
8.6.76808796736.1	$x^{8} - 2 x^{7} - 5 x^{6} + 18 x^{5} - 78 x^{4} + 228 x^{3} - 264 x^{2} + 124 x - 20$	$8$	[6,1]	$-\,2^{6}\cdot 7^{6}\cdot 101^{2}$	$3$	$22.9443822962$	$108.9826953053031$				$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$6$	$2597.3767185$
8.2.76808796736.1	$x^{8} - 3 x^{7} + x^{6} - 25 x^{5} + 54 x^{4} - 72 x^{3} + 100 x^{2} - 80 x + 32$	$8$	[2,3]	$-\,2^{6}\cdot 7^{6}\cdot 101^{2}$	$3$	$22.944382296217274$	$108.9826953053031$				$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$1136.3646125056805$
8.6.130516859375.1	$x^{8} - x^{7} - 13 x^{6} - 13 x^{5} + 60 x^{4} + 213 x^{3} - 103 x^{2} - 454 x - 199$	$8$	[6,1]	$-\,5^{6}\cdot 7^{6}\cdot 71$	$3$	$24.5164919215$	$121.24957014770216$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$6$	$689.658877225$
8.2.130516859375.1	$x^{8} - 3 x^{7} + x^{6} - 4 x^{5} + 19 x^{4} - 2 x^{3} - 26 x^{2} - 66 x - 59$	$8$	[2,3]	$-\,5^{6}\cdot 7^{6}\cdot 71$	$3$	$24.5164919215$	$121.24957014770216$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$4$	$200.914030676$
8.0.139296416000.1	$x^{8} - 2 x^{7} + 7 x^{6} + 35 x^{4} - 14 x^{3} + 105 x^{2} + 96 x + 452$	$8$	[0,4]	$2^{8}\cdot 5^{3}\cdot 7^{6}\cdot 37$	$4$	$24.716814193$	$117.0683210408118$			?	$S_4\wr C_2$ (as 8T47)	$[4]$	$4$	$3$	$300.977047516$
8.0.147970441472.1	$x^{8} - 2 x^{7} + x^{6} - 26 x^{5} - 21 x^{4} + 180 x^{3} + 15 x^{2} - 68 x + 365$	$8$	[0,4]	$2^{8}\cdot 7^{6}\cdot 17^{3}$	$3$	$24.9041584705$	$72.0593294901264$			?	$C_4\wr C_2$ (as 8T17)	$[4]$	$4$	$3$	$124.978935536$
8.0.147970441472.2	$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 5 x^{4} - 26 x^{3} + 44 x^{2} - 18 x + 53$	$8$	[0,4]	$2^{8}\cdot 7^{6}\cdot 17^{3}$	$3$	$24.9041584705$	$72.0593294901264$			?	$C_4\wr C_2$ (as 8T17)	$[4]$	$4$	$3$	$104.538931014$
8.6.153617593472.1	$x^{8} - 3 x^{7} - 6 x^{6} + 3 x^{5} + 26 x^{4} + 5 x^{3} - 61 x^{2} + 46 x - 10$	$8$	[6,1]	$-\,2^{7}\cdot 7^{6}\cdot 101^{2}$	$3$	$25.0210263153$	$154.12480576473428$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$6$	$1537.80288179$
8.2.160348998656.1	$x^{8} + 8 x^{6} - 14 x^{5} + 10 x^{4} - 70 x^{3} + 4 x^{2} + 168 x - 117$	$8$	[2,3]	$-\,2^{10}\cdot 7^{6}\cdot 11^{3}$	$3$	$25.1555189743$	$65.50001077446599$			?	$Q_8:S_4$ (as 8T40)	trivial	$2$	$4$	$592.676016423$
8.2.160348998656.2	$x^{8} - 2 x^{7} + 2 x^{6} + 18 x^{5} + 6 x^{4} - 10 x^{3} - 26 x^{2} - 16 x - 6$	$8$	[2,3]	$-\,2^{10}\cdot 7^{6}\cdot 11^{3}$	$3$	$25.1555189743$	$65.50001077446599$			?	$Q_8:S_4$ (as 8T40)	trivial	$2$	$4$	$949.249393507$
8.6.174635234375.1	$x^{8} - x^{7} - 13 x^{6} + 22 x^{5} + 25 x^{4} - 102 x^{3} + 72 x^{2} + 106 x + 11$	$8$	[6,1]	$-\,5^{7}\cdot 7^{6}\cdot 19$	$3$	$25.425323297$	$76.70065704426244$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$6$	$688.162072619$
8.2.174635234375.1	$x^{8} - 2 x^{7} + 18 x^{6} - 34 x^{5} + 120 x^{4} - 184 x^{3} + 303 x^{2} - 362 x + 121$	$8$	[2,3]	$-\,5^{7}\cdot 7^{6}\cdot 19$	$3$	$25.425323297$	$76.70065704426244$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$4$	$192.095177682$
8.2.207062240000.1	$x^{8} - 4 x^{7} + 7 x^{6} - 63 x^{4} + 238 x^{3} - 469 x^{2} + 514 x - 229$	$8$	[2,3]	$-\,2^{8}\cdot 5^{4}\cdot 7^{6}\cdot 11$	$4$	$25.9724317367$	$107.35131462289476$			?	$S_4\wr C_2$ (as 8T47)	trivial	$2$	$4$	$378.291031786$
8.2.207062240000.2	$x^{8} - 2 x^{7} + 4 x^{6} - 20 x^{5} + 43 x^{4} + 12 x^{3} - 54 x^{2} + 30 x - 5$	$8$	[2,3]	$-\,2^{8}\cdot 5^{4}\cdot 7^{6}\cdot 11$	$4$	$25.9724317367$	$90.27133563916587$				$S_4\wr C_2$ (as 8T47)	trivial	$2$	$4$	$520.732520474$
8.2.233234907136.1	$x^{8} - 2 x^{7} + 4 x^{6} + 8 x^{5} + 8 x^{4} - 16 x^{3} + 58 x^{2} + 44 x - 54$	$8$	[2,3]	$-\,2^{14}\cdot 7^{6}\cdot 11^{2}$	$3$	$26.3617473657$	$71.4146754232608$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$1227.20480855$
8.2.233234907136.2	$x^{8} - 14 x^{6} + 56 x^{4} - 98 x^{2} - 49$	$8$	[2,3]	$-\,2^{14}\cdot 7^{6}\cdot 11^{2}$	$3$	$26.3617473657$	$71.4146754232608$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$783.213254955$
8.2.233234907136.3	$x^{8} + 14 x^{6} + 56 x^{4} + 98 x^{2} - 49$	$8$	[2,3]	$-\,2^{14}\cdot 7^{6}\cdot 11^{2}$	$3$	$26.3617473657$	$71.4146754232608$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$1393.69829873$
8.2.233234907136.4	$x^{8} - 2 x^{7} - 10 x^{6} + 8 x^{5} + 22 x^{4} + 40 x^{3} + 30 x^{2} + 16 x + 2$	$8$	[2,3]	$-\,2^{14}\cdot 7^{6}\cdot 11^{2}$	$3$	$26.3617473657$	$71.4146754232608$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$619.030211905$
8.6.277578109375.1	$x^{8} - 4 x^{7} + 14 x^{5} - 21 x^{4} + 14 x^{3} + 35 x^{2} - 39 x - 19$	$8$	[6,1]	$-\,5^{6}\cdot 7^{6}\cdot 151$	$3$	$26.9415855933$	$176.82330630796798$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$6$	$825.92073395$
8.0.291543633920.1	$x^{8} - 2 x^{7} + 8 x^{6} - 12 x^{5} + 28 x^{4} - 58 x^{3} + 50 x^{2} - 12 x + 71$	$8$	[0,4]	$2^{12}\cdot 5\cdot 7^{6}\cdot 11^{2}$	$4$	$27.1074050567$	$95.63914858821721$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$3$	$168.616842797$
8.4.291543633920.1	$x^{8} - 14 x^{4} - 196 x^{2} + 245$	$8$	[4,2]	$2^{12}\cdot 5\cdot 7^{6}\cdot 11^{2}$	$4$	$27.1074050567$	$95.63914858821721$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$2185.54957589$
8.2.307235186944.1	$x^{8} - x^{7} - 6 x^{6} + x^{5} + 32 x^{4} - 67 x^{3} - 194 x^{2} - 181 x - 73$	$8$	[2,3]	$-\,2^{8}\cdot 7^{6}\cdot 101^{2}$	$3$	$27.285622676004053$	$129.60299666924007$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$517.8018921499439$
8.6.307235186944.1	$x^{8} - 14 x^{6} + 28 x^{4} + 98 x^{2} - 49$	$8$	[6,1]	$-\,2^{8}\cdot 7^{6}\cdot 101^{2}$	$3$	$27.285622676$	$108.9826953053031$				$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$6$	$4490.68966201$
8.2.307235186944.2	$x^{8} - 4 x^{7} + 4 x^{6} + 2 x^{5} + 56 x^{4} + 62 x^{3} - 90 x^{2} - 136 x - 52$	$8$	[2,3]	$-\,2^{8}\cdot 7^{6}\cdot 101^{2}$	$3$	$27.285622676004053$	$129.60299666924007$			?	$C_2 \wr S_4$ (as 8T44)	$[2]$	$2$	$4$	$753.9602233421044$
8.6.307235186944.2	$x^{8} - 2 x^{7} - 3 x^{6} - 6 x^{5} + 8 x^{4} + 26 x^{3} - 26 x^{2} + 2 x + 2$	$8$	[6,1]	$-\,2^{8}\cdot 7^{6}\cdot 101^{2}$	$3$	$27.285622676$	$129.60299666924007$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$6$	$2009.20325773$
8.6.307235186944.3	$x^{8} - x^{7} - 13 x^{6} + 8 x^{5} + 32 x^{4} + 10 x^{3} + 2 x^{2} - 6 x - 10$	$8$	[6,1]	$-\,2^{8}\cdot 7^{6}\cdot 101^{2}$	$3$	$27.285622676$	$129.60299666924007$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$6$	$2428.33920253$
8.2.314437188128.1	$x^{8} - 4 x^{7} + 35 x^{4} - 14 x^{3} - 14 x^{2} - 60 x - 152$	$8$	[2,3]	$-\,2^{5}\cdot 7^{6}\cdot 17^{4}$	$3$	$27.3647659502$	$63.23191227961974$				$S_4\wr C_2$ (as 8T47)	trivial	$2$	$4$	$3149.67293746$
8.6.351108734375.1	$x^{8} - 3 x^{7} - 13 x^{6} + 45 x^{5} + 26 x^{4} - 205 x^{3} + 23 x^{2} + 291 x + 11$	$8$	[6,1]	$-\,5^{6}\cdot 7^{6}\cdot 191$	$3$	$27.7447109221$	$198.86928709587343$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$6$	$1432.5681937$
8.8.384043983680.1	$x^{8} - 2 x^{7} - 19 x^{6} + 18 x^{5} + 118 x^{4} + 4 x^{3} - 180 x^{2} - 72 x + 8$	$8$	[8,0]	$2^{6}\cdot 5\cdot 7^{6}\cdot 101^{2}$	$4$	$28.0574127292$	$217.10552747939172$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$7$	$2958.27242523$
8.8.384197515625.1	$x^{8} - 4 x^{7} - 14 x^{6} + 56 x^{5} + 56 x^{4} - 210 x^{3} - 35 x^{2} + 150 x - 5$	$8$	[8,0]	$5^{6}\cdot 7^{6}\cdot 11\cdot 19$	$4$	$28.0588145725$	$208.02914126000158$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$7$	$1950.21266255$
8.6.387874046875.1	$x^{8} - 3 x^{7} - 6 x^{6} + 38 x^{5} - 79 x^{4} + 5 x^{3} + 275 x^{2} - 325 x + 95$	$8$	[6,1]	$-\,5^{6}\cdot 7^{6}\cdot 211$	$3$	$28.0922380668$	$209.02212609719254$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$6$	$897.768601879$
8.6.441650581232.1	$x^{8} - x^{7} - 12 x^{6} + 2 x^{5} + 35 x^{4} + 31 x^{3} + 8 x^{2} - 48 x + 16$	$8$	[6,1]	$-\,2^{4}\cdot 7^{6}\cdot 23\cdot 101^{2}$	$4$	$28.551889278$	$329.25683461826776$				$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$6$	$9468.557263$
8.6.464030715204.1	$x^{8} - 3 x^{7} - 5 x^{6} + 13 x^{5} + 16 x^{4} - 6 x^{3} - 47 x^{2} - 18 x + 57$	$8$	[6,1]	$-\,2^{2}\cdot 3^{2}\cdot 7^{6}\cdot 331^{2}$	$4$	$28.7288565674$	$271.2240207887935$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$6$	$2944.51452426$
8.2.470596000000.1	$x^{8} + 7 x^{6} - 21 x^{4} - 147 x^{2} - 49$	$8$	[2,3]	$-\,2^{8}\cdot 5^{6}\cdot 7^{6}$	$3$	$28.779353183$	$52.78156645931917$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$4$	$562.893581212$
8.6.470596000000.1	$x^{8} - 14 x^{6} + 56 x^{4} - 49 x^{2} - 49$	$8$	[6,1]	$-\,2^{8}\cdot 5^{6}\cdot 7^{6}$	$3$	$28.779353183$	$52.78156645931917$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$6$	$1576.34772506$
8.6.470596000000.2	$x^{8} - 7 x^{6} - 21 x^{4} + 147 x^{2} - 49$	$8$	[6,1]	$-\,2^{8}\cdot 5^{6}\cdot 7^{6}$	$3$	$28.779353183$	$52.78156645931917$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	trivial	$2$	$6$	$714.942734872$

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