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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	Narrow class group	Unit group torsion	Unit group rank	Regulator	Unit signature rank	Max $p$
6.2.2774976002000.4	$x^{6} - x^{5} - 6 x^{4} - 53 x^{3} - 116 x^{2} - 95 x - 29$	$6$	(2, 2)	$2^{4}\cdot 5^{3}\cdot 193^{4}$	$3$	$118.543170533$	$149.3550358758861$				$\PGL(2,5)$ (as 6T14)	$[12]$	$[12]$	$2$	$3$	$718.346005805$	$2$	$193$
6.2.39023100028125.2	$x^{6} - 186245$	$6$	(2, 2)	$3^{2}\cdot 5^{5}\cdot 193^{4}$	$3$	$184.17059642$	$221.17727529708532$				$D_{6}$ (as 6T3)	$[6]$	$[6]$	$2$	$3$	$12823.162927877176$	$2$	$193$
6.0.117069300084375.1	$x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} + 325 x^{2} - 323 x + 6934$	$6$	(0, 3)	$-\,3^{3}\cdot 5^{5}\cdot 193^{4}$	$3$	$221.177275297$	$221.17727529708532$				$D_{6}$ (as 6T3)	$[2, 6]$	$[2, 6]$	$2$	$2$	$26647.647169287422$	$0$	$193$
6.0.152268483181744.1	$x^{6} - 2 x^{5} + 126 x^{4} + 148 x^{3} + 3885 x^{2} - 218 x + 112$	$6$	(0, 3)	$-\,2^{4}\cdot 19^{3}\cdot 193^{4}$	$3$	$231.083180833$	$291.1465638087653$			?	$\PGL(2,5)$ (as 6T14)	$[12]$	$[12]$	$2$	$2$	$8161.47808028$	$0$	$193$
6.2.539756419685017.2	$x^{6} - 2 x^{5} - 11 x^{4} + 588 x^{3} + 4570 x^{2} + 16619 x + 27610$	$6$	(2, 2)	$73^{3}\cdot 193^{4}$	$2$	$285.342395389$	$285.34239538916813$			?	$S_6$ (as 6T16)	$[6]$	$[6]$	$2$	$3$	$54325.1222986$	$2$	$193$
6.6.1137913596820125.1	$x^{6} - 3 x^{5} - 1158 x^{4} - 7329 x^{3} + 347979 x^{2} + 5209260 x + 20172745$	$6$	(6, 0)	$3^{8}\cdot 5^{3}\cdot 193^{4}$	$3$	$323.110854473$	$323.11085447286644$		✓	?	$C_6$ (as 6T1)	$[2, 6]$	$[2, 6]$	$2$	$5$	$52582.54098310857$	$6$	$193$
6.2.2022957505458000.1	$x^{6} - 3 x^{5} - 1539 x^{3} + 2316 x^{2} - 6951 x + 599071$	$6$	(2, 2)	$2^{4}\cdot 3^{6}\cdot 5^{3}\cdot 193^{4}$	$4$	$355.629511599$	$427.0886228306657$			?	$D_{6}$ (as 6T3)	$[3]$	$[3]$	$2$	$3$	$106326.49400516394$	$2$	$193$
6.0.2497478401800000.1	$x^{6} + 186245$	$6$	(0, 3)	$-\,2^{6}\cdot 3^{2}\cdot 5^{5}\cdot 193^{4}$	$4$	$368.3411928391708$	$442.35455059417063$				$D_{6}$ (as 6T3)	$[2, 6]$	$[2, 6]$	$2$	$2$	$111440.73944257524$	$0$	$193$
6.0.3413740790460375.1	$x^{6} - 3 x^{5} - 1143 x^{4} - 7359 x^{3} + 348039 x^{2} + 5353965 x + 21791115$	$6$	(0, 3)	$-\,3^{9}\cdot 5^{3}\cdot 193^{4}$	$3$	$388.035765755$	$388.0357657549607$	✓	✓	?	$C_6$ (as 6T1)	$[2, 4, 84]$	$[2, 4, 84]$	$2$	$2$	$593.4836090476081$	$0$	$193$
6.2.3747778526701125.1	$x^{6} - 3 x^{5} - 2697 x^{3} + 4053 x^{2} - 12162 x + 1830604$	$6$	(2, 2)	$3^{2}\cdot 5^{3}\cdot 7^{4}\cdot 193^{4}$	$4$	$394.1204649143205$	$473.31383110675466$				$D_{6}$ (as 6T3)	$[3, 15]$	$[3, 15]$	$2$	$3$	$16649.803370523765$	$2$	$193$
6.6.4589739545419949.1	$x^{6} - 381 x^{4} - 386 x^{3} + 25227 x^{2} + 16019 x - 102364$	$6$	(6, 0)	$149^{3}\cdot 193^{4}$	$2$	$407.659912457$	$407.65991245654726$			?	$\PGL(2,5)$ (as 6T14)	$[12]$	$[2, 24]$	$2$	$5$	$820569.669494$	$4$	$193$
6.0.5530327373713856.1	$x^{6} - x^{5} + 11 x^{4} + 275 x^{2} - 625 x + 15625$	$6$	(0, 3)	$-\,2^{6}\cdot 7^{2}\cdot 31\cdot 41\cdot 193^{4}$	$5$	$420.524987679$	$8909.876030989697$	✓		?	$S_4\times C_2$ (as 6T11)	$[6, 174]$	$[6, 174]$	$2$	$2$	$595.3999326113649$	$0$	$193$
6.0.6068872516374000.1	$x^{6} - 3 x^{5} + 15 x^{4} + 1519 x^{3} - 2256 x^{2} - 16260 x + 604540$	$6$	(0, 3)	$-\,2^{4}\cdot 3^{7}\cdot 5^{3}\cdot 193^{4}$	$4$	$427.088622831$	$427.0886228306657$			?	$D_{6}$ (as 6T3)	$[6]$	$[6]$	$2$	$2$	$220955.69657290576$	$0$	$193$
6.2.7492435205400000.1	$x^{6} - 5 x^{4} - 635 x^{2} - 7260$	$6$	(2, 2)	$2^{6}\cdot 3^{3}\cdot 5^{5}\cdot 193^{4}$	$4$	$442.354550594$	$442.35455059417063$			?	$D_{6}$ (as 6T3)	$[2, 6]$	$[2, 2, 6]$	$2$	$3$	$229950.95275094133$	$1$	$193$
6.0.7536213226807552.1	$x^{6} + 476 x^{4} + 10420 x^{2} + 6928$	$6$	(0, 3)	$-\,2^{8}\cdot 7^{2}\cdot 193^{4}\cdot 433$	$4$	$442.78428244391387$	$5200.472861325123$	✓		?	$S_4\times C_2$ (as 6T11)	$[2, 912]$	$[2, 912]$	$2$	$2$	$595.3999326113649$	$0$	$433$
6.0.9423529905287792.1	$x^{6} - 2 x^{5} + 5 x^{4} + 52 x^{3} + 49 x^{2} + 1846 x + 10216$	$6$	(0, 3)	$-\,2^{4}\cdot 7^{2}\cdot 193^{4}\cdot 8663$	$4$	$459.58826978$	$16448.187404881588$	✓		?	$S_4\times C_2$ (as 6T11)	$[3, 960]$	$[3, 960]$	$2$	$2$	$595.3999326113649$	$0$	$8663$
6.0.10387949227486875.1	$x^{6} - 3 x^{5} + 12 x^{4} + 9631 x^{3} - 14439 x^{2} - 72402 x + 23319252$	$6$	(0, 3)	$-\,3^{2}\cdot 5^{4}\cdot 11^{3}\cdot 193^{4}$	$4$	$467.11265827314304$	$560.9728535507171$				$D_{6}$ (as 6T3)	$[6]$	$[6]$	$2$	$2$	$470070.28304345196$	$0$	$193$
6.0.11169433806706112.1	$x^{6} - x^{5} - 7 x^{4} + 12 x^{3} - 133 x^{2} - 361 x + 6859$	$6$	(0, 3)	$-\,2^{6}\cdot 7^{2}\cdot 17\cdot 151\cdot 193^{4}$	$5$	$472.793894726$	$12662.27730888538$	✓		?	$S_4\times C_2$ (as 6T11)	$[6, 540]$	$[6, 540]$	$2$	$2$	$595.3999326113649$	$0$	$193$
6.0.11243335580103375.1	$x^{6} - 3 x^{5} + 5 x^{4} + 1346 x^{3} - 3149 x^{2} + 449 x + 541351$	$6$	(0, 3)	$-\,3^{3}\cdot 5^{3}\cdot 7^{4}\cdot 193^{4}$	$4$	$473.313831107$	$473.31383110675466$				$D_{6}$ (as 6T3)	$[3, 30]$	$[3, 30]$	$2$	$2$	$34599.738625420316$	$0$	$193$
6.0.13188373146913216.1	$x^{6} - x^{5} + 9 x^{4} + 130 x^{3} + 26 x^{2} + 2646 x + 12814$	$6$	(0, 3)	$-\,2^{6}\cdot 7^{3}\cdot 193^{4}\cdot 433$	$4$	$486.069686926$	$5200.472861325123$	✓		?	$S_4\times C_2$ (as 6T11)	$[2, 1176]$	$[2, 1176]$	$2$	$2$	$595.3999326113649$	$0$	$433$
6.0.19979827214400000.1	$x^{6} + 1489960$	$6$	(0, 3)	$-\,2^{9}\cdot 3^{2}\cdot 5^{5}\cdot 193^{4}$	$4$	$520.9131104938389$	$625.5838048277316$			?	$D_{6}$ (as 6T3)	$[2, 12]$	$[2, 12]$	$2$	$2$	$54828.73017770205$	$0$	$193$
6.2.19979827214400000.1	$x^{6} - 1489960$	$6$	(2, 2)	$2^{9}\cdot 3^{2}\cdot 5^{5}\cdot 193^{4}$	$4$	$520.9131104938389$	$625.5838048277316$				$D_{6}$ (as 6T3)	$[2, 42]$	$[2, 42]$	$2$	$3$	$55367.02366952273$	$2$	$193$
6.2.31163847682460625.1	$x^{6} - 3 x^{5} - 21 x^{4} - 9603 x^{3} + 14643 x^{2} - 246267 x + 23400738$	$6$	(2, 2)	$3^{3}\cdot 5^{4}\cdot 11^{3}\cdot 193^{4}$	$4$	$560.972853551$	$560.9728535507171$				$D_{6}$ (as 6T3)	$[6]$	$[2, 6]$	$2$	$3$	$1799508.2368575695$	$1$	$193$
6.6.36349511936822073.2	$x^{6} - 3 x^{5} - 1179 x^{4} - 7287 x^{3} + 348147 x^{2} + 5006421 x + 18003879$	$6$	(6, 0)	$3^{9}\cdot 11^{3}\cdot 193^{4}$	$3$	$575.550051786$	$575.5500517861893$		✓	?	$C_6$ (as 6T1)	$[3]$	$[6]$	$2$	$5$	$839349.0837944101$	$5$	$193$
6.0.52727385613426048.1	$x^{6} - 2 x^{5} + 6 x^{4} - 78 x^{3} + 138 x^{2} - 1058 x + 12167$	$6$	(0, 3)	$-\,2^{7}\cdot 7^{2}\cdot 73\cdot 83\cdot 193^{4}$	$5$	$612.358907695$	$27511.505722322032$	✓		?	$S_4\times C_2$ (as 6T11)	$[2, 1752]$	$[2, 1752]$	$2$	$2$	$595.3999326113649$	$0$	$193$
6.0.59939481643200000.1	$x^{6} + 10 x^{4} - 2540 x^{2} + 58080$	$6$	(0, 3)	$-\,2^{9}\cdot 3^{3}\cdot 5^{5}\cdot 193^{4}$	$4$	$625.583804828$	$625.5838048277316$			?	$D_{6}$ (as 6T3)	$[2, 2, 42]$	$[2, 2, 42]$	$2$	$2$	$30447.431316127022$	$0$	$193$
6.2.59939481643200000.1	$x^{6} - 10 x^{4} - 2540 x^{2} - 58080$	$6$	(2, 2)	$2^{9}\cdot 3^{3}\cdot 5^{5}\cdot 193^{4}$	$4$	$625.583804828$	$625.5838048277316$			?	$D_{6}$ (as 6T3)	$[2, 12]$	$[2, 2, 12]$	$2$	$3$	$169364.2974397667$	$1$	$193$
6.2.65870955385298973.1	$x^{6} - 3 x^{5} - 6 x^{4} - 2685 x^{3} + 4071 x^{2} - 28398 x + 1838684$	$6$	(2, 2)	$3^{2}\cdot 7^{4}\cdot 13^{3}\cdot 193^{4}$	$4$	$635.5001544037015$	$763.1956204434607$				$D_{6}$ (as 6T3)	$[3, 30]$	$[3, 30]$	$2$	$3$	$130599.8422382653$	$2$	$193$
6.2.117481384020672000.1	$x^{6} - 10 x^{4} - 1544 x^{3} - 2540 x^{2} - 15440 x + 537904$	$6$	(2, 2)	$2^{9}\cdot 3^{3}\cdot 5^{3}\cdot 7^{2}\cdot 193^{4}$	$5$	$699.8336848059901$	$1338.733678419882$			?	$S_3^2$ (as 6T9)	$[6]$	$[2, 6]$	$2$	$3$	$1011308.8537111565$	$1$	$193$
6.0.197612866155896919.1	$x^{6} - 3 x^{5} + 33 x^{4} + 2641 x^{3} - 3723 x^{2} - 77307 x + 1865380$	$6$	(0, 3)	$-\,3^{3}\cdot 7^{4}\cdot 13^{3}\cdot 193^{4}$	$4$	$763.195620443$	$763.1956204434607$				$D_{6}$ (as 6T3)	$[6, 60]$	$[6, 60]$	$2$	$2$	$109310.2301348145$	$0$	$193$
6.6.218479410589464000.1	$x^{6} - 1203 x^{4} - 9650 x^{3} + 335916 x^{2} + 5153100 x + 18509185$	$6$	(6, 0)	$2^{6}\cdot 3^{9}\cdot 5^{3}\cdot 193^{4}$	$4$	$776.07153151$	$776.0715315099214$		✓	?	$C_6$ (as 6T1)	$[2, 8, 24]$	$[2, 2, 8, 24]$	$2$	$5$	$45090.23312836668$	$5$	$193$
6.2.283684975291563408.1	$x^{6} - 3 x^{5} - 9 x^{4} - 13101 x^{3} + 19722 x^{2} - 177222 x + 43145086$	$6$	(2, 2)	$2^{4}\cdot 3^{2}\cdot 17^{5}\cdot 193^{4}$	$4$	$810.5989854417015$	$973.478277445114$			?	$D_{6}$ (as 6T3)	$[2, 24]$	$[2, 24]$	$2$	$3$	$191659.65018586442$	$2$	$193$
6.0.851054925874690224.1	$x^{6} - 3 x^{5} + 42 x^{4} + 13045 x^{3} - 19140 x^{2} - 492657 x + 43311397$	$6$	(0, 3)	$-\,2^{4}\cdot 3^{3}\cdot 17^{5}\cdot 193^{4}$	$4$	$973.478277445$	$973.478277445114$			?	$D_{6}$ (as 6T3)	$[2, 6, 24]$	$[2, 6, 24]$	$2$	$2$	$30498.958029104455$	$0$	$193$
6.2.214...000.1	$x^{6} - 3 x^{5} - 35 x^{4} - 11891 x^{3} + 148024 x^{2} - 602770 x + 479710$	$6$	(2, 2)	$2^{4}\cdot 3^{3}\cdot 5^{3}\cdot 31^{5}\cdot 193^{4}$	$5$	$3591.191607845464$	$3591.191607845464$			?	$S_3^2$ (as 6T9)	$[3, 6, 18]$	$[6, 6, 18]$	$2$	$3$	$2258509.699280877$	$1$	$193$
6.6.971...689.1	$x^{6} - x^{5} - 1746 x^{4} - 15298 x^{3} + 455701 x^{2} + 6379043 x + 20997564$	$6$	(6, 0)	$11^{3}\cdot 37^{3}\cdot 47^{3}\cdot 193^{4}$	$4$	$4619.03237506$	$4619.032375064658$			?	$S_6$ (as 6T16)	$[2, 6]$	$[2, 2, 2, 12]$	$2$	$5$	$253228342.941$	$3$	$193$
6.6.110...625.1	$x^{6} - 3 x^{5} - 6913 x^{4} - 246912 x^{3} - 759339 x^{2} + 29365831 x - 91052984$	$6$	(6, 0)	$5^{3}\cdot 193^{4}\cdot 3989^{3}$	$3$	$4716.52230918$	$4716.522309175281$			?	$S_6$ (as 6T16)	$[2, 6]$	$[4, 12]$	$2$	$5$	$161260364.719$	$4$	$3989$
8.2.582611761571904.1	$x^{8} + 21 x^{6} - 36 x^{4} - 2176 x^{2} - 9216$	$8$	(2, 3)	$-\,2^{6}\cdot 3^{8}\cdot 193^{4}$	$3$	$70.09263809904812$	$288.99913394774853$				$\textrm{GL(2,3)}$ (as 8T23)	$[2]$	$[2]$	$2$	$4$	$475280.9105082526$	$2$	$193$
8.2.582611761571904.2	$x^{8} - x^{7} + 12 x^{6} + 52 x^{5} + 11 x^{4} + 429 x^{3} + 704 x^{2} + 1240 x + 2400$	$8$	(2, 3)	$-\,2^{6}\cdot 3^{8}\cdot 193^{4}$	$3$	$70.09263809904812$	$288.99913394774853$				$\textrm{GL(2,3)}$ (as 8T23)	$[2]$	$[2]$	$2$	$4$	$475280.9105082526$	$2$	$193$
8.2.5243505854147136.1	$x^{8} + 21 x^{6} + 351 x^{4} - 753 x^{2} - 324$	$8$	(2, 3)	$-\,2^{6}\cdot 3^{10}\cdot 193^{4}$	$3$	$92.24709950144103$	$347.0697399717109$				$\textrm{GL(2,3)}$ (as 8T23)	$[2]$	$[2, 2]$	$2$	$4$	$202010.81600180932$	$1$	$193$
8.2.5243505854147136.2	$x^{8} - 21 x^{6} + 351 x^{4} + 753 x^{2} - 324$	$8$	(2, 3)	$-\,2^{6}\cdot 3^{10}\cdot 193^{4}$	$3$	$92.24709950144103$	$347.0697399717109$				$\textrm{GL(2,3)}$ (as 8T23)	$[2]$	$[2, 2]$	$2$	$4$	$202010.81600180932$	$1$	$193$
9.1.105...000.1	$x^{9} - 3 x^{8} + 18 x^{7} - 4039 x^{6} + 8106 x^{5} + 12579 x^{4} + 5924485 x^{3} - 6022308 x^{2} - 48750162 x - 2359541092$	$9$	(1, 4)	$2^{9}\cdot 3^{3}\cdot 5^{3}\cdot 7^{6}\cdot 193^{6}$	$5$	$602.7871441100574$	$1338.733678419882$				$S_3^2$ (as 9T8)	$[3, 15]$	$[3, 15]$	$2$	$4$	$266442963.49147534$	$1$	$193$
9.1.307...000.1	$x^{9} - 35898 x^{6} + 438793220 x^{3} - 1713353576696$	$9$	(1, 4)	$2^{6}\cdot 3^{3}\cdot 5^{3}\cdot 31^{7}\cdot 193^{6}$	$5$	$1889.6002608705849$	$3591.191607845464$			?	$S_3^2$ (as 9T8)	$[3, 3, 3, 18]$	$[3, 3, 3, 18]$	$2$	$4$	$1133178518.5725439$	$1$	$193$
10.0.68260824380205416.1	$x^{10} - 4 x^{9} + 9 x^{8} - 17 x^{7} + 25 x^{6} - 32 x^{5} + 75 x^{4} - 153 x^{3} + 243 x^{2} - 324 x + 243$	$10$	(0, 5)	$-\,2^{3}\cdot 149^{2}\cdot 193^{4}\cdot 277$	$4$	$48.2410945355$	$19190.349526794995$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[28]$	$[28]$	$2$	$4$	$1954.95474515$	$0$	$277$
10.2.165...000.1	$x^{10} - 2 x^{9} - 12 x^{8} + 12 x^{7} + 81 x^{6} + 110 x^{5} - 402 x^{4} - 384 x^{3} + 1124 x^{2} + 920 x - 296$	$10$	(2, 4)	$2^{8}\cdot 5^{3}\cdot 193^{6}$	$3$	$66.3512918964$	$149.3550358758861$				$S_5$ (as 10T13)	trivial	trivial	$2$	$5$	$3988763.38141$	$2$	$193$
10.4.907...096.1	$x^{10} - 2 x^{9} - 18 x^{8} + 24 x^{7} + 138 x^{6} - 332 x^{5} - 175 x^{4} + 364 x^{3} - 1356 x^{2} - 736 x + 988$	$10$	(4, 3)	$-\,2^{8}\cdot 19^{3}\cdot 193^{6}$	$3$	$99.0340322874$	$291.1465638087653$				$S_5$ (as 10T13)	trivial	trivial	$2$	$6$	$6101339.16922$	$4$	$193$
10.10.170...301.1	$x^{10} - 4 x^{9} - 30 x^{8} + 105 x^{7} + 255 x^{6} - 638 x^{5} - 941 x^{4} + 1448 x^{3} + 1632 x^{2} - 1113 x - 1115$	$10$	(10, 0)	$149^{3}\cdot 193^{6}$	$2$	$105.509184408$	$407.65991245654726$			?	$S_5$ (as 10T13)	trivial	$[2, 2]$	$2$	$9$	$14064578.1671$	$8$	$193$
12.0.524...625.1	$x^{12} - 3 x^{11} + 9 x^{10} + 240 x^{9} - 390 x^{8} + 1032 x^{7} + 21434 x^{6} - 16617 x^{5} - 43650 x^{4} + 1120470 x^{3} + 191904 x^{2} - 5197512 x + 25763851$	$12$	(0, 6)	$3^{18}\cdot 5^{10}\cdot 193^{4}$	$3$	$114.81782666084501$	$663.531825891256$			?	$C_6\times S_3$ (as 12T18)	$[3]$	$[3]$	$6$	$5$	$12179979.907511536$	$0$	$193$
12.0.215...000.1	$x^{12} + 30 x^{10} - 250 x^{9} + 375 x^{8} + 27775 x^{6} + 37500 x^{5} - 480000 x^{4} - 956250 x^{3} + 4809375 x^{2} + 18562500 x + 24043125$	$12$	(0, 6)	$2^{12}\cdot 3^{18}\cdot 5^{10}\cdot 193^{4}$	$4$	$229.63565332169003$	$1327.063651782512$			?	$C_6\times S_3$ (as 12T18)	$[3, 6]$	$[3, 6]$	$6$	$5$	$264410908.91586947$	$0$	$193$
12.0.371...625.1	$x^{12} - 6 x^{11} + 33 x^{10} + 140 x^{9} - 795 x^{8} + 1524 x^{7} + 24091 x^{6} - 87378 x^{5} - 144030 x^{4} + 1608780 x^{3} - 661077 x^{2} - 10445283 x + 28603479$	$12$	(0, 6)	$3^{18}\cdot 5^{8}\cdot 11^{6}\cdot 193^{4}$	$4$	$291.21293665414197$	$1682.9185606521512$			?	$C_6\times S_3$ (as 12T18)	$[3, 111]$	$[3, 111]$	$6$	$5$	$63667161.29898521$	$0$	$193$
12.4.331...000.1	$x^{12} - 6 x^{11} - 7 x^{10} - 2998 x^{9} + 21718 x^{8} - 5646 x^{7} + 222639 x^{6} + 1674850 x^{5} - 29162163 x^{4} + 129136052 x^{3} - 557281556 x^{2} + 1521001840 x - 2258382320$	$12$	(4, 4)	$2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 7^{8}\cdot 193^{8}$	$5$	$1338.733678419882$	$1851.5858891026116$				$S_3\times D_6$ (as 12T37)	$[3, 6]$	$[6, 12]$	$2$	$7$	$60377230801062.83$	$2$	$193$

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