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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
8.4.5334402749.1	$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} - 2 x^{4} + 11 x^{3} - 7 x^{2} + x + 1$	$8$	[4,2]	$13\cdot 17^{7}$	$2$	$16.4393910096$	$43.014460711706995$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$5$	$50.4276582851$
8.2.19285917631.1	$x^{8} - 2 x^{7} + 6 x^{6} - 20 x^{5} + 36 x^{4} - 82 x^{3} + 91 x^{2} - 66 x + 52$	$8$	[2,3]	$-\,17^{7}\cdot 47$	$2$	$19.3043435745$	$81.7884043055344$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$4$	$89.4407401069$
8.2.26261675072.1	$x^{8} - x^{7} + 10 x^{6} - 11 x^{5} + 32 x^{4} - 61 x^{3} + 41 x^{2} - 132 x + 18$	$8$	[2,3]	$-\,2^{6}\cdot 17^{7}$	$2$	$20.063897614$	$23.86012979730628$				$D_{8}$ (as 8T6)	$[4]$	$2$	$4$	$83.109134679$
8.6.26261675072.1	$x^{8} - 3 x^{7} + 5 x^{6} - 8 x^{5} - 26 x^{4} + 52 x^{3} + 3 x^{2} - 7 x - 1$	$8$	[6,1]	$-\,2^{6}\cdot 17^{7}$	$2$	$20.063897614$	$47.72025959461256$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$196.99406069$
8.2.26261675072.2	$x^{8} - 3 x^{7} + 5 x^{6} + 9 x^{5} - 26 x^{4} + 18 x^{3} + 20 x^{2} - 24 x + 16$	$8$	[2,3]	$-\,2^{6}\cdot 17^{7}$	$2$	$20.063897614$	$23.86012979730628$				$QD_{16}$ (as 8T8)	$[4]$	$2$	$4$	$447.727402788$
8.0.26261675072.1	$x^{8} - 2 x^{7} + 6 x^{6} - 3 x^{5} + 19 x^{4} - 14 x^{3} + 6 x^{2} + 36 x + 52$	$8$	[0,4]	$2^{6}\cdot 17^{7}$	$2$	$20.063897614$	$33.74331915933294$	✓		?	$C_8:C_2$ (as 8T7)	$[2]$	$2$	$3$	$27.6959098582$
8.4.26261675072.1	$x^{8} - 3 x^{7} + 5 x^{6} - 25 x^{5} + 42 x^{4} - 33 x^{3} + 3 x^{2} + 10 x - 1$	$8$	[4,2]	$2^{6}\cdot 17^{7}$	$2$	$20.063897614$	$33.74331915933294$			?	$C_8:C_2$ (as 8T7)	$[2]$	$2$	$5$	$83.4829009987$
8.0.33237432513.1	$x^{8} - x^{7} + 10 x^{6} - 11 x^{5} + 15 x^{4} - 61 x^{3} + 58 x^{2} - 47 x + 103$	$8$	[0,4]	$3^{4}\cdot 17^{7}$	$2$	$20.6634785421$	$20.663478542061284$	✓	✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$3$	$27.6959098582$
8.4.36520141897.1	$x^{8} - x^{7} - 7 x^{6} + 6 x^{5} - 19 x^{4} + 24 x^{3} - 10 x^{2} + 4 x + 1$	$8$	[4,2]	$17^{7}\cdot 89$	$2$	$20.9081957294$	$112.54800715810448$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$5$	$92.0799928925$
8.0.61140462277.1	$x^{8} - 2 x^{7} + 6 x^{6} - 3 x^{5} + 19 x^{4} + 3 x^{3} + 57 x^{2} - 32 x + 52$	$8$	[0,4]	$17^{7}\cdot 149$	$2$	$22.2992927851$	$145.625000684722$	✓			$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[6]$	$2$	$3$	$27.6959098582$
8.4.64423171661.1	$x^{8} - x^{7} - 7 x^{6} - 11 x^{5} - 36 x^{4} - 44 x^{3} + 41 x^{2} + 106 x + 52$	$8$	[4,2]	$17^{7}\cdot 157$	$2$	$22.445550571$	$149.48328472546316$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$5$	$175.465370266$
8.0.69347235737.2	$x^{8} - 2 x^{7} + 6 x^{6} - 3 x^{5} + 2 x^{4} + 3 x^{3} + 6 x^{2} + 2 x + 1$	$8$	[0,4]	$13^{2}\cdot 17^{7}$	$2$	$22.6531522723$	$43.014460711706995$			?	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28)	$[8]$	$2$	$3$	$61.0235657638$
8.6.78374686543.1	$x^{8} - 2 x^{7} - 11 x^{6} + 48 x^{5} - 49 x^{4} - 48 x^{3} + 108 x^{2} - 32 x - 16$	$8$	[6,1]	$-\,17^{7}\cdot 191$	$2$	$23.0023378072$	$164.87677720297805$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$440.88950711$
8.2.85350443984.1	$x^{8} - 3 x^{7} + 5 x^{6} - 25 x^{5} + 42 x^{4} + x^{3} - 65 x^{2} + 95 x - 103$	$8$	[2,3]	$-\,2^{4}\cdot 13\cdot 17^{7}$	$3$	$23.248809723$	$121.66326743332137$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$4$	$88.6608656277$
8.6.85350443984.1	$x^{8} - 3 x^{7} - 12 x^{6} + 26 x^{5} + 42 x^{4} + x^{3} - 82 x^{2} - 24 x - 1$	$8$	[6,1]	$-\,2^{4}\cdot 13\cdot 17^{7}$	$3$	$23.248809723$	$121.66326743332137$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$247.6035496$
8.6.85350443984.2	$x^{8} - 3 x^{7} - 12 x^{6} + 43 x^{5} + 8 x^{4} - 135 x^{3} + 173 x^{2} - 92 x + 16$	$8$	[6,1]	$-\,2^{4}\cdot 13\cdot 17^{7}$	$3$	$23.248809723$	$121.66326743332137$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$327.388612675$
8.2.85350443984.2	$x^{8} - 2 x^{7} + 6 x^{6} - 20 x^{5} + 36 x^{4} - 48 x^{3} + 57 x^{2} - 134 x + 52$	$8$	[2,3]	$-\,2^{4}\cdot 13\cdot 17^{7}$	$3$	$23.248809723$	$121.66326743332137$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$4$	$194.25423704$
8.4.85350443984.1	$x^{8} - 2 x^{7} + 6 x^{6} - 3 x^{5} + 2 x^{4} - 48 x^{3} - 130 x^{2} - 15 x + 1$	$8$	[4,2]	$2^{4}\cdot 13\cdot 17^{7}$	$3$	$23.248809723$	$86.02892142341399$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$5$	$148.089767583$
8.4.85350443984.2	$x^{8} - 2 x^{7} - 11 x^{6} + 14 x^{5} + 19 x^{4} - 14 x^{3} - 45 x^{2} + 2 x + 52$	$8$	[4,2]	$2^{4}\cdot 13\cdot 17^{7}$	$3$	$23.248809723$	$86.02892142341399$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$5$	$230.308522105$
8.6.102995006923.1	$x^{8} - x^{7} - 7 x^{6} + 23 x^{5} - 2 x^{4} - 78 x^{3} + 75 x^{2} + 4 x - 16$	$8$	[6,1]	$-\,17^{7}\cdot 251$	$2$	$23.8013736034$	$189.00777383484788$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$339.047427299$
8.4.105046700288.2	$x^{8} - x^{7} - 7 x^{6} + 6 x^{5} - 19 x^{4} + 75 x^{3} - 27 x^{2} - 30 x - 16$	$8$	[4,2]	$2^{8}\cdot 17^{7}$	$2$	$23.8601297973$	$47.72025959461256$				$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28)	$[4]$	$2$	$5$	$581.963154925$
8.0.105046700288.2	$x^{8} - 2 x^{7} + 6 x^{6} - 20 x^{5} + 19 x^{4} + 20 x^{3} + 6 x^{2} + 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 17^{7}$	$2$	$23.8601297973$	$23.86012979730628$				$D_{8}$ (as 8T6)	$[16]$	$2$	$3$	$39.6756752079$
8.4.120229231189.1	$x^{8} - 2 x^{7} - 11 x^{6} + 31 x^{5} - 49 x^{4} + 54 x^{3} - 28 x^{2} + 19 x + 1$	$8$	[4,2]	$17^{7}\cdot 293$	$2$	$24.2661712833$	$204.20981711568174$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$5$	$200.796686037$
8.4.144849551569.1	$x^{8} - x^{7} + 10 x^{6} - 11 x^{5} - 53 x^{4} - 78 x^{3} + 24 x^{2} + 72 x - 16$	$8$	[4,2]	$17^{7}\cdot 353$	$2$	$24.8378868542$	$224.1455694756975$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$5$	$464.822491118$
8.4.148132260953.1	$x^{8} - x^{7} - 7 x^{6} + 6 x^{5} - 19 x^{4} + 24 x^{3} + 58 x^{2} + 106 x - 67$	$8$	[4,2]	$17^{7}\cdot 19^{2}$	$2$	$24.9075612203$	$52.00194728311084$			?	$C_8:C_2$ (as 8T7)	$[2]$	$2$	$5$	$177.70397323$
8.2.160852759816.1	$x^{8} - 2 x^{7} + 6 x^{6} - 3 x^{5} + 19 x^{4} - 14 x^{3} + 6 x^{2} + 19 x - 16$	$8$	[2,3]	$-\,2^{3}\cdot 7^{2}\cdot 17^{7}$	$3$	$25.1653841667$	$89.27643090547606$			?	$S_4\wr C_2$ (as 8T47)	$[4]$	$2$	$4$	$301.277854348$
8.4.172752581333.1	$x^{8} - 2 x^{7} - 11 x^{6} - 3 x^{5} + 19 x^{4} + 20 x^{3} + 23 x^{2} + 70 x + 52$	$8$	[4,2]	$17^{7}\cdot 421$	$2$	$25.3908984294$	$244.7844660362211$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$5$	$316.511046212$
8.2.189986805599.1	$x^{8} - 2 x^{7} + 6 x^{6} - 20 x^{5} + 19 x^{4} - 48 x^{3} + 125 x^{2} + 53 x - 271$	$8$	[2,3]	$-\,17^{7}\cdot 463$	$2$	$25.6945153292$	$256.7043935133426$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$4$	$93.2599687927$
8.6.214607125979.1	$x^{8} - 2 x^{7} - 11 x^{6} + 31 x^{5} + 19 x^{4} - 116 x^{3} + 40 x^{2} + 121 x - 67$	$8$	[6,1]	$-\,17^{7}\cdot 523$	$2$	$26.0888849348$	$272.83095967689883$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$476.710248178$
8.8.256461670625.1	$x^{8} - x^{7} - 24 x^{6} + 23 x^{5} + 151 x^{4} - 197 x^{3} - 214 x^{2} + 429 x - 169$	$8$	[8,0]	$5^{4}\cdot 17^{7}$	$2$	$26.6764360894$	$26.676436089372558$		✓	?	$C_8$ (as 8T1)	$[2]$	$2$	$7$	$636.601883042$
8.6.308574682096.1	$x^{8} - 3 x^{7} - 12 x^{6} + 43 x^{5} - 26 x^{4} - 101 x^{3} + 360 x^{2} - 347 x + 101$	$8$	[6,1]	$-\,2^{4}\cdot 17^{7}\cdot 47$	$3$	$27.3004644958$	$163.5768086110688$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$795.169478913$
8.8.308574682096.1	$x^{8} - 3 x^{7} - 12 x^{6} + 26 x^{5} + 59 x^{4} - 50 x^{3} - 116 x^{2} - 41 x - 1$	$8$	[8,0]	$2^{4}\cdot 17^{7}\cdot 47$	$3$	$27.3004644958$	$231.33254122748158$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$7$	$774.682519315$
8.6.357404984183.1	$x^{8} - 2 x^{7} - 11 x^{6} + 48 x^{5} - 100 x^{4} + 88 x^{3} + 176 x^{2} - 440 x + 239$	$8$	[6,1]	$-\,13\cdot 17^{7}\cdot 67$	$3$	$27.8064198295$	$352.0885352171694$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$438.580921132$
8.6.357404984183.2	$x^{8} - x^{7} - 7 x^{6} + 6 x^{5} - 19 x^{4} + 41 x^{3} + 109 x^{2} - 166 x + 52$	$8$	[6,1]	$-\,13\cdot 17^{7}\cdot 67$	$3$	$27.8064198295$	$352.0885352171694$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$951.924694467$
8.6.420186801152.1	$x^{8} - 17 x^{6} + 85 x^{4} - 102 x^{2} - 68$	$8$	[6,1]	$-\,2^{10}\cdot 17^{7}$	$2$	$28.3746361198$	$56.749272239690114$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$642.665212229$
8.2.420186801152.5	$x^{8} + 17 x^{6} + 51 x^{4} - 170 x^{2} - 68$	$8$	[2,3]	$-\,2^{10}\cdot 17^{7}$	$2$	$28.3746361198$	$47.72025959461256$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2]$	$2$	$4$	$148.380510799$
8.2.420186801152.6	$x^{8} + 17 x^{6} + 85 x^{4} + 102 x^{2} - 68$	$8$	[2,3]	$-\,2^{10}\cdot 17^{7}$	$2$	$28.3746361198$	$56.749272239690114$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$4$	$272.075725073$
8.4.420186801152.1	$x^{8} - 17 x^{4} + 68$	$8$	[4,2]	$2^{10}\cdot 17^{7}$	$2$	$28.3746361198$	$56.749272239690114$				$(C_8:C_2):C_2$ (as 8T16)	$[2]$	$2$	$5$	$558.352224922$
8.8.420186801152.1	$x^{8} - 17 x^{6} + 85 x^{4} - 136 x^{2} + 68$	$8$	[8,0]	$2^{10}\cdot 17^{7}$	$2$	$28.3746361198$	$47.72025959461256$				$C_8:C_2$ (as 8T7)	$[2]$	$2$	$7$	$1025.01963413$
8.4.420186801152.2	$x^{8} - 51 x^{4} + 34 x^{2} + 68$	$8$	[4,2]	$2^{10}\cdot 17^{7}$	$2$	$28.3746361198$	$47.72025959461256$				$C_8:C_2$ (as 8T7)	$[2]$	$2$	$5$	$448.460678046$
8.4.420186801152.3	$x^{8} - 17 x^{6} + 17 x^{4} + 170 x^{2} + 68$	$8$	[4,2]	$2^{10}\cdot 17^{7}$	$2$	$28.3746361198$	$56.749272239690114$				$(C_8:C_2):C_2$ (as 8T16)	$[2]$	$2$	$5$	$286.350086857$
8.0.472710151296.1	$x^{8} - x^{7} + 10 x^{6} - 28 x^{5} + 100 x^{4} - 180 x^{3} + 177 x^{2} - 81 x + 18$	$8$	[0,4]	$2^{7}\cdot 3^{2}\cdot 17^{7}$	$3$	$28.7954829033$	$82.65391416824514$				$C_2 \wr C_2\wr C_2$ (as 8T35)	$[4]$	$2$	$3$	$432.172374666$
8.0.472710151296.2	$x^{8} - 3 x^{7} + 22 x^{6} - 59 x^{5} + 93 x^{4} - 152 x^{3} + 122 x^{2} - 24 x + 152$	$8$	[0,4]	$2^{7}\cdot 3^{2}\cdot 17^{7}$	$3$	$28.7954829033$	$82.65391416824514$				$C_2 \wr C_2\wr C_2$ (as 8T35)	$[4]$	$2$	$3$	$678.755253096$
8.6.524823162767.1	$x^{8} - x^{7} - 7 x^{6} - 28 x^{5} - 19 x^{4} + 92 x^{3} + 92 x^{2} - 64 x - 67$	$8$	[6,1]	$-\,17^{7}\cdot 1279$	$2$	$29.1743792523$	$426.65621712766693$			?	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$540.11588047$
8.6.531798920208.1	$x^{8} - 3 x^{7} - 12 x^{6} + 43 x^{5} + 25 x^{4} - 186 x^{3} + 88 x^{2} + 248 x - 188$	$8$	[6,1]	$-\,2^{4}\cdot 3^{4}\cdot 17^{7}$	$3$	$29.2225716$	$58.445143199977$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$992.185267047$
8.4.531798920208.1	$x^{8} - 3 x^{7} - 12 x^{6} - 8 x^{5} + 25 x^{4} + 120 x^{3} - 14 x^{2} - 109 x + 169$	$8$	[4,2]	$2^{4}\cdot 3^{4}\cdot 17^{7}$	$3$	$29.2225716$	$41.32695708412257$			?	$C_8:C_2$ (as 8T7)	$[2]$	$2$	$5$	$509.394365486$
8.8.538774677649.1	$x^{8} - 4 x^{7} - 10 x^{6} + 44 x^{5} + 32 x^{4} - 142 x^{3} - 41 x^{2} + 120 x + 52$	$8$	[8,0]	$13\cdot 17^{7}\cdot 101$	$3$	$29.2702139537$	$432.28998006224646$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$7$	$1723.29151092$
8.0.538774677649.1	$x^{8} - x^{7} + 10 x^{6} - 11 x^{5} + 49 x^{4} - 44 x^{3} + 160 x^{2} - 64 x + 256$	$8$	[0,4]	$13\cdot 17^{7}\cdot 101$	$3$	$29.2702139537$	$432.28998006224646$	✓			$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 10]$	$2$	$3$	$27.6959098582$
8.6.549443483147.1	$x^{8} - x^{7} - 7 x^{6} - 11 x^{5} + 15 x^{4} + 92 x^{3} + 7 x^{2} - 132 x - 16$	$8$	[6,1]	$-\,13\cdot 17^{7}\cdot 103$	$3$	$29.3420449679$	$436.54909749403373$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$917.418921577$
8.6.549443483147.2	$x^{8} - x^{7} - 7 x^{6} + 23 x^{5} - 104 x^{4} + 24 x^{3} + 755 x^{2} - 1288 x + 596$	$8$	[6,1]	$-\,13\cdot 17^{7}\cdot 103$	$3$	$29.3420449679$	$436.54909749403373$				$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2]$	$2$	$6$	$833.149276258$

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