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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
8.0.47775744.1	$x^{8} + 3 x^{4} + 9$	$8$	[0,4]	$2^{16}\cdot 3^{6}$	$2$	$9.11802822782$	$9.11802822781911$		✓	?	$D_4$ (as 8T4)	trivial	$12$	$3$	$20.8957982344$
8.0.55115776.3	$x^{8} - 4 x^{5} - x^{4} + 4 x^{3} + 8 x^{2} + 4 x + 1$	$8$	[0,4]	$2^{16}\cdot 29^{2}$	$2$	$9.28238314842$	$21.540659228538015$			?	$S_4\times C_2$ (as 8T24)	trivial	$4$	$3$	$8.52019638775$
8.0.321978368.4	$x^{8} - 4 x^{6} + 11 x^{4} - 20 x^{2} + 17$	$8$	[0,4]	$2^{16}\cdot 17^{3}$	$2$	$11.5738629877$	$16.492422502470642$			?	$D_{8}$ (as 8T6)	trivial	$4$	$3$	$20.282622579$
8.0.375455744.1	$x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 22 x^{4} - 16 x^{3} + 20 x^{2} - 8 x + 4$	$8$	[0,4]	$2^{16}\cdot 17\cdot 337$	$3$	$11.7983111155$	$302.76063152266016$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$22.7577294403$
8.0.430505984.1	$x^{8} - 4 x^{7} + 12 x^{6} - 20 x^{5} + 23 x^{4} - 20 x^{3} + 20 x^{2} - 8 x + 1$	$8$	[0,4]	$2^{16}\cdot 6569$	$2$	$12.0018280145$	$324.1974706872341$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$25.0864433646$
8.0.451477504.5	$x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 21 x^{4} - 20 x^{3} + 20 x^{2} - 12 x + 5$	$8$	[0,4]	$2^{16}\cdot 83^{2}$	$2$	$12.0733979172$	$36.4417343165772$			?	$S_4\times C_2$ (as 8T24)	trivial	$4$	$3$	$35.694160127$
8.0.481361920.1	$x^{8} + 2 x^{6} - 8 x^{5} + x^{4} - 12 x^{3} + 16 x^{2} + 13$	$8$	[0,4]	$2^{16}\cdot 5\cdot 13\cdot 113$	$4$	$12.1705152911$	$342.81190177705327$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$29.9300203392$
8.0.514916352.6	$x^{8} - 8 x^{6} + 2 x^{4} + 56 x^{2} + 97$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 97$	$3$	$12.273462089$	$68.23488843692792$			?	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31)	trivial	$12$	$3$	$53.6338974265$
8.0.536412160.1	$x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 14 x^{4} - 4 x^{3} - 10 x^{2} + 8 x + 5$	$8$	[0,4]	$2^{16}\cdot 5\cdot 1637$	$3$	$12.3363683032$	$361.88395930187346$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$34.747638937$
8.0.642318336.9	$x^{8} - 12 x^{6} + 59 x^{4} - 132 x^{2} + 121$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 11^{2}$	$3$	$12.6173685821$	$22.978250586152114$			?	$D_4\times C_2$ (as 8T9)	trivial	$12$	$3$	$85.4809876926$
8.0.750321664.3	$x^{8} - 6 x^{6} - 4 x^{5} + 14 x^{4} + 32 x^{3} - 34 x^{2} - 60 x + 61$	$8$	[0,4]	$2^{16}\cdot 107^{2}$	$2$	$12.8648858108$	$41.376321731154405$			?	$S_4\times C_2$ (as 8T24)	trivial	$4$	$3$	$29.8794137621$
8.0.881917952.2	$x^{8} - 2 x^{6} - 8 x^{5} + 14 x^{4} - 4 x^{2} + 8 x + 4$	$8$	[0,4]	$2^{16}\cdot 13457$	$2$	$13.127394082$	$464.0172410589934$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$45.7293913147$
8.0.897122304.10	$x^{8} - 8 x^{6} + 51 x^{4} - 104 x^{2} + 169$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 13^{2}$	$3$	$13.1554726719$	$24.979991993593593$	✓		?	$D_4\times C_2$ (as 8T9)	trivial	$12$	$3$	$80.5956958474$
8.0.921763840.1	$x^{8} - 4 x^{7} + 6 x^{6} - 14 x^{4} + 16 x^{3} + 4 x^{2} - 24 x + 20$	$8$	[0,4]	$2^{16}\cdot 5\cdot 29\cdot 97$	$4$	$13.2001072061$	$474.3838108536167$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$47.8521365508$
8.0.1024000000.6	$x^{8} + 4 x^{6} + 16 x^{4} - 56 x^{2} + 36$	$8$	[0,4]	$2^{16}\cdot 5^{6}$	$2$	$13.3748060995$	$13.37480609952844$		✓		$D_4$ (as 8T4)	$[2]$	$4$	$3$	$24.6646630038$
8.0.1145110528.2	$x^{8} - 4 x^{6} + 9 x^{4} - 4 x^{3} - 2 x^{2} - 4 x + 5$	$8$	[0,4]	$2^{16}\cdot 101\cdot 173$	$3$	$13.5630051276$	$528.7419030112897$			✓	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$37.7270188141$
8.0.1174470656.1	$x^{8} + 4 x^{6} - 4 x^{5} + x^{4} - 8 x^{3} + 2 x^{2} + 8 x + 13$	$8$	[0,4]	$2^{16}\cdot 17921$	$2$	$13.6059938809$	$535.4773571309995$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$43.7260685499$
8.0.1266221056.1	$x^{8} - 4 x^{6} - 4 x^{5} + 25 x^{4} + 8 x^{3} - 38 x^{2} - 24 x + 45$	$8$	[0,4]	$2^{16}\cdot 139^{2}$	$2$	$13.7345264921$	$47.15930449020638$				$S_4\times C_2$ (as 8T24)	trivial	$4$	$3$	$55.5478932997$
8.0.1364787200.1	$x^{8} + 2 x^{6} - 12 x^{5} + 22 x^{4} - 16 x^{3} + 6 x^{2} - 4 x + 5$	$8$	[0,4]	$2^{16}\cdot 5^{2}\cdot 7^{2}\cdot 17$	$4$	$13.8638265914$	$127.58907089700965$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$54.2440615096$
8.0.1382612992.4	$x^{8} - 4 x^{6} + 11 x^{4} + 4 x^{2} + 73$	$8$	[0,4]	$2^{16}\cdot 17^{2}\cdot 73$	$3$	$13.8863331145$	$140.91131963046828$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$4$	$3$	$63.3566161084$
8.0.1506344960.1	$x^{8} - 4 x^{5} + 5 x^{4} + 2 x^{2} - 8 x + 5$	$8$	[0,4]	$2^{16}\cdot 5\cdot 4597$	$3$	$14.0359093548$	$606.4321891192782$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$75.0156014077$
8.0.1560346624.1	$x^{8} + 4 x^{6} - 4 x^{5} + 15 x^{4} - 20 x^{3} + 12 x^{2} - 4 x + 1$	$8$	[0,4]	$2^{16}\cdot 29\cdot 821$	$3$	$14.0978418946$	$617.2066104636275$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$55.7849224907$
8.0.1615396864.3	$x^{8} - 4 x^{7} + 8 x^{6} - 8 x^{5} + 13 x^{4} - 12 x^{3} + 6 x^{2} - 8 x + 5$	$8$	[0,4]	$2^{16}\cdot 157^{2}$	$2$	$14.1590757247$	$50.11985634456667$			?	$S_4\times C_2$ (as 8T24)	trivial	$4$	$3$	$73.2862051196$
8.0.1629552640.1	$x^{8} - 4 x^{7} + 10 x^{6} - 8 x^{5} - 2 x^{4} + 20 x^{3} - 10 x^{2} - 8 x + 5$	$8$	[0,4]	$2^{16}\cdot 5\cdot 4973$	$3$	$14.1745261433$	$630.7455905513727$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$52.8989617706$
8.0.1637941248.2	$x^{8} + 4 x^{6} + x^{4} - 4 x^{3} - 2 x^{2} - 4 x + 5$	$8$	[0,4]	$2^{16}\cdot 3^{2}\cdot 2777$	$3$	$14.1836266172$	$365.09724731912183$			✓	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$61.0440450374$
8.0.1698234368.3	$x^{8} - 4 x^{7} + 16 x^{6} - 32 x^{5} + 59 x^{4} - 56 x^{3} + 48 x^{2} - 4 x + 1$	$8$	[0,4]	$2^{16}\cdot 25913$	$2$	$14.2478621038$	$643.9006134490012$			✓	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$54.2092673956$
8.2.1863254016.1	$x^{8} - 6 x^{6} - 12 x^{5} - 18 x^{4} - 24 x^{3} - 18 x^{2} - 12 x - 3$	$8$	[2,3]	$-\,2^{16}\cdot 3^{7}\cdot 13$	$3$	$14.4139830907$	$37.71488305085648$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$2$	$4$	$45.6290093489$
8.0.1916338176.6	$x^{8} - 37 x^{4} + 361$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 19^{2}$	$3$	$14.4646862838$	$30.199337741083$			?	$D_4\times C_2$ (as 8T9)	trivial	$12$	$3$	$150.856250519$
8.0.2062614528.1	$x^{8} + 4 x^{6} + 9 x^{4} - 36 x^{3} + 46 x^{2} - 36 x + 13$	$8$	[0,4]	$2^{16}\cdot 3^{2}\cdot 13\cdot 269$	$4$	$14.598299151$	$409.70233096725235$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$55.8690749893$
8.0.2096168960.1	$x^{8} - 4 x^{7} + 2 x^{6} + 14 x^{4} - 4 x^{3} - 2 x^{2} - 8 x + 5$	$8$	[0,4]	$2^{16}\cdot 5\cdot 6397$	$3$	$14.6277754775$	$715.3740280440715$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$75.6061907174$
8.0.2163802112.1	$x^{8} - 4 x^{7} + 6 x^{6} - 6 x^{4} + 8 x^{3} + 12 x^{2} - 24 x + 20$	$8$	[0,4]	$2^{16}\cdot 137\cdot 241$	$3$	$14.6859549802$	$726.8232247252422$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$51.1032575152$
8.0.2298544128.3	$x^{8} - 4 x^{6} - 21 x^{4} + 140 x^{2} + 433$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 433$	$3$	$14.7972702539$	$144.1665703275208$			?	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31)	trivial	$12$	$3$	$157.057924835$
8.0.2341011456.19	$x^{8} - 4 x^{7} + 8 x^{6} - 8 x^{5} + 11 x^{4} - 16 x^{3} + 8 x^{2} + 4 x + 1$	$8$	[0,4]	$2^{16}\cdot 3^{6}\cdot 7^{2}$	$3$	$14.8311710043$	$38.12856628395392$			?	$S_4\times C_2$ (as 8T24)	trivial	$4$	$3$	$58.704350859$
8.0.2357264384.1	$x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} - 10 x^{4} - 4 x^{3} + 30 x^{2} - 32 x + 13$	$8$	[0,4]	$2^{16}\cdot 35969$	$2$	$14.8440031149$	$758.6197993725184$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$55.9164140875$
8.0.2553348096.6	$x^{8} - 16 x^{6} + 107 x^{4} - 344 x^{2} + 481$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 13\cdot 37$	$4$	$14.9930073271$	$151.94735930578062$			?	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31)	trivial	$12$	$3$	$149.879530135$
8.0.2636185600.1	$x^{8} + 2 x^{6} - 8 x^{5} + 2 x^{4} - 8 x^{3} + 36 x^{2} + 24 x + 52$	$8$	[0,4]	$2^{16}\cdot 5^{2}\cdot 1609$	$3$	$15.0529631311$	$469.1568009271788$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$72.8785050392$
8.0.2723217408.3	$x^{8} - 6 x^{6} - 12 x^{5} + 6 x^{4} + 48 x^{3} + 78 x^{2} + 60 x + 21$	$8$	[0,4]	$2^{16}\cdot 3^{7}\cdot 19$	$3$	$15.1142043351$	$45.595070303079446$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2]$	$6$	$3$	$61.2644178686$
8.0.2746286080.3	$x^{8} - 8 x^{6} + 34 x^{4} - 104 x^{2} + 145$	$8$	[0,4]	$2^{16}\cdot 5\cdot 17^{2}\cdot 29$	$4$	$15.1301495931$	$198.59506539690256$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$4$	$3$	$54.4782307065$
8.0.2775646208.2	$x^{8} - 4 x^{6} - 4 x^{5} + 7 x^{4} + 12 x^{3} + 4 x^{2} - 4 x + 1$	$8$	[0,4]	$2^{16}\cdot 41\cdot 1033$	$3$	$15.1502749166$	$823.1937803457944$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$63.3440411985$
8.0.2780364800.1	$x^{8} - 6 x^{6} - 8 x^{5} + 10 x^{4} + 24 x^{3} + 4 x^{2} + 8 x + 20$	$8$	[0,4]	$2^{16}\cdot 5^{2}\cdot 1697$	$3$	$15.1534919536$	$481.8156644618649$			?	$S_4\wr C_2$ (as 8T47)	trivial	$4$	$3$	$87.4600906248$
8.0.2872115200.1	$x^{8} - 4 x^{6} - 4 x^{5} + 17 x^{4} - 16 x^{3} + 18 x^{2} - 16 x + 5$	$8$	[0,4]	$2^{16}\cdot 5^{2}\cdot 1753$	$3$	$15.2151147443$	$374.4863148367374$			?	$S_4\wr C_2$ (as 8T47)	$[2]$	$4$	$3$	$31.8474482789$
8.0.2917728256.2	$x^{8} + 6 x^{6} - 12 x^{5} + 13 x^{4} - 24 x^{3} + 44 x^{2} - 36 x + 13$	$8$	[0,4]	$2^{16}\cdot 211^{2}$	$2$	$15.2451115031$	$58.1033561853358$			?	$S_4\times C_2$ (as 8T24)	trivial	$4$	$3$	$73.1642624161$
8.2.3031367680.1	$x^{8} - 4 x^{7} + 6 x^{6} - 2 x^{4} - 20 x^{3} + 2 x^{2} + 8 x - 3$	$8$	[2,3]	$-\,2^{16}\cdot 5\cdot 11\cdot 29^{2}$	$4$	$15.3180974118$	$159.74980438172688$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$4$	$79.3357626143$
8.0.3436773376.5	$x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} - 3 x^{4} - 12 x^{3} + 4 x^{2} + 4 x + 5$	$8$	[0,4]	$2^{16}\cdot 229^{2}$	$2$	$15.5603321046$	$60.530983801686226$			?	$S_4\times C_2$ (as 8T24)	trivial	$4$	$3$	$85.124441204$
8.0.3503882240.6	$x^{8} - 21 x^{4} - 16 x^{2} + 185$	$8$	[0,4]	$2^{16}\cdot 5\cdot 17^{2}\cdot 37$	$4$	$15.5979918011$	$224.32119828495925$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$4$	$3$	$52.7367208067$
8.0.3572563968.1	$x^{8} - 24 x^{6} + 194 x^{4} - 600 x^{2} + 673$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 673$	$3$	$15.6358862286$	$179.73313550928776$			?	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31)	trivial	$12$	$3$	$187.714428389$
8.4.3582525440.1	$x^{8} - 6 x^{6} - 8 x^{5} - 3 x^{4} + 20 x^{3} + 36 x^{2} - 27$	$8$	[4,2]	$2^{16}\cdot 5\cdot 13\cdot 29^{2}$	$4$	$15.6413293351$	$173.6663467687393$			?	$C_2 \wr S_4$ (as 8T44)	trivial	$2$	$5$	$77.1972984677$
8.0.3619225600.2	$x^{8} + 2 x^{6} + 15 x^{4} - 2 x^{2} + 9$	$8$	[0,4]	$2^{16}\cdot 5^{2}\cdot 47^{2}$	$3$	$15.6612692802$	$61.318838867023565$				$S_4\times C_2$ (as 8T24)	trivial	$4$	$3$	$149.280568435$
8.0.3645440000.13	$x^{8} - 4 x^{6} + 3 x^{4} - 28 x^{2} + 89$	$8$	[0,4]	$2^{16}\cdot 5^{4}\cdot 89$	$3$	$15.6754040602$	$84.38009243891595$			?	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31)	$[2]$	$4$	$3$	$41.7020798514$
8.0.3655401472.4	$x^{8} - 8 x^{6} + 27 x^{4} - 64 x^{2} + 193$	$8$	[0,4]	$2^{16}\cdot 17^{2}\cdot 193$	$3$	$15.6807519654$	$229.12005586591496$			?	$C_2 \wr C_2\wr C_2$ (as 8T35)	trivial	$4$	$3$	$52.743171598$

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