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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
6.4.92779.1	$x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - x^{2} - 2 x + 1$	$6$	[4,1]	$-\,92779$	$1$	$6.72834545134$	$304.59645434574577$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$1.26271099409$
6.4.94363.1	$x^{6} - 2 x^{4} - 2 x^{3} + 3 x + 1$	$6$	[4,1]	$-\,197\cdot 479$	$2$	$6.74735597692$	$307.18561164221217$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$1.27706633779$
6.4.103243.1	$x^{6} - x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + 3 x - 1$	$6$	[4,1]	$-\,7^{4}\cdot 43$	$2$	$6.84925658504$	$23.99567223510292$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$4$	$1.35989705552$
6.4.104483.1	$x^{6} - x^{5} - x^{4} + 2 x^{3} - 2 x^{2} - x + 1$	$6$	[4,1]	$-\,163\cdot 641$	$2$	$6.86289897071$	$323.2383021858641$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$1.37161676762$
6.4.104875.1	$x^{6} - 2 x^{5} - x^{4} + x^{3} + 2 x^{2} + x - 1$	$6$	[4,1]	$-\,5^{3}\cdot 839$	$2$	$6.86718365572$	$64.7688196588451$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$1.37486382678$
6.4.118987.1	$x^{6} - x^{5} + 4 x^{3} - 2 x^{2} - 2 x + 1$	$6$	[4,1]	$-\,11\cdot 29\cdot 373$	$3$	$7.01320584053$	$344.9449231399123$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$1.49736951283$
6.4.124659.1	$x^{6} - 3 x^{4} - 2 x^{3} + 3 x^{2} + 3 x - 1$	$6$	[4,1]	$-\,3^{8}\cdot 19$	$2$	$7.06784917257$	$18.859860385004858$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$4$	$1.54949123381$
6.4.133787.1	$x^{6} - 3 x^{5} + 2 x^{4} - x^{2} + 3 x - 1$	$6$	[4,1]	$-\,353\cdot 379$	$2$	$7.15158523749$	$365.7690528188518$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$1.64177118637$
6.4.144875.1	$x^{6} - 2 x^{5} - x^{4} + 5 x^{3} - 2 x^{2} - 3 x + 1$	$6$	[4,1]	$-\,5^{3}\cdot 19\cdot 61$	$3$	$7.24712204036$	$76.12489737267302$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$1.71537174718$
6.4.149875.1	$x^{6} - 3 x^{4} - 2 x^{3} + x^{2} + 3 x + 1$	$6$	[4,1]	$-\,5^{3}\cdot 11\cdot 109$	$3$	$7.2882209908$	$77.42738533619743$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$1.75141750738$
6.4.153664.1	$x^{6} - x^{4} - 2 x^{2} + 1$	$6$	[4,1]	$-\,2^{6}\cdot 7^{4}$	$2$	$7.31861142005$	$12.308388215503062$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$4$	$1.79006336385$
6.4.158875.1	$x^{6} - 2 x^{3} - 5 x^{2} + 1$	$6$	[4,1]	$-\,5^{3}\cdot 31\cdot 41$	$3$	$7.35940314298$	$79.71825386948713$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$1.90094666627$
6.4.161939.1	$x^{6} - 2 x^{5} + x^{4} - 2 x^{3} - x^{2} + 3 x - 1$	$6$	[4,1]	$-\,67\cdot 2417$	$2$	$7.38287035521$	$402.41645095597175$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$1.84655694102$
6.4.170471.1	$x^{6} - 3 x^{5} + x^{4} + 3 x^{3} - 3 x^{2} + x + 1$	$6$	[4,1]	$-\,7^{4}\cdot 71$	$2$	$7.44632095503$	$30.833857978493015$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$4$	$1.93594594089$
6.4.174875.1	$x^{6} - x^{5} - 2 x^{4} + 4 x^{3} + x^{2} - 3 x - 1$	$6$	[4,1]	$-\,5^{3}\cdot 1399$	$2$	$7.47804293959$	$83.63611660042568$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$1.9447304322$
6.4.187904.1	$x^{6} - 4 x^{4} - 2 x^{3} + 3 x^{2} + 2 x - 1$	$6$	[4,1]	$-\,2^{9}\cdot 367$	$2$	$7.56814314074$	$54.18486873657626$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$2.0498560296$
6.4.188875.1	$x^{6} - x^{5} - 4 x^{3} + 2 x^{2} + 2 x - 1$	$6$	[4,1]	$-\,5^{3}\cdot 1511$	$2$	$7.57464725461$	$86.91950298983537$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$2.13795426682$
6.4.195379.1	$x^{6} + x^{4} - 2 x^{3} - 3 x^{2} + x + 1$	$6$	[4,1]	$-\,47\cdot 4157$	$2$	$7.61750907714$	$442.01696800009836$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.18581014238$
6.4.199283.1	$x^{6} - 2 x^{5} + x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1$	$6$	[4,1]	$-\,7^{4}\cdot 83$	$2$	$7.6426688442$	$33.33786161694775$			?	$A_4\times C_2$ (as 6T6)	trivial	$2$	$4$	$2.17772456899$
6.4.202375.1	$x^{6} - 2 x^{5} - 2 x^{4} + 5 x^{3} - x^{2} - 3 x + 1$	$6$	[4,1]	$-\,5^{3}\cdot 1619$	$2$	$7.6623057369$	$89.97221793420455$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$2.31736654503$
6.4.209107.1	$x^{6} - x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} + 2 x + 1$	$6$	[4,1]	$-\,67\cdot 3121$	$2$	$7.70420969891$	$457.28218858818457$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.28226788919$
6.4.214747.1	$x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 3 x + 1$	$6$	[4,1]	$-\,13\cdot 16519$	$2$	$7.7384595636$	$463.4080275523936$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.24299199866$
6.4.214875.1	$x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 3 x^{2} + 2 x + 1$	$6$	[4,1]	$-\,3^{2}\cdot 5^{3}\cdot 191$	$3$	$7.73922812452$	$53.52569476429054$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$2.2308508208$
6.4.215811.1	$x^{6} - x^{5} - 2 x^{4} - 2 x^{3} + x^{2} + 3 x + 1$	$6$	[4,1]	$-\,3^{3}\cdot 7993$	$2$	$7.74483666021$	$154.85154180698365$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.33005230908$
6.4.216587.1	$x^{6} - x^{5} - x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 1$	$6$	[4,1]	$-\,7\cdot 30941$	$2$	$7.74947112329$	$465.38908453035293$			?	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.26354419685$
6.4.217024.1	$x^{6} - 2 x^{3} - 3 x^{2} + 4 x - 1$	$6$	[4,1]	$-\,2^{6}\cdot 3391$	$2$	$7.75207490788$	$164.7057983193063$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.36664754095$
6.4.218491.1	$x^{6} - 3 x^{5} + 2 x^{4} + x^{3} - 3 x^{2} + 2 x + 1$	$6$	[4,1]	$-\,7^{5}\cdot 13$	$2$	$7.76078392578$	$18.248200448594663$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$4$	$2.26526479968$
6.4.221875.1	$x^{6} - 2 x^{5} + 3 x - 1$	$6$	[4,1]	$-\,5^{5}\cdot 71$	$2$	$7.78068909224$	$32.21841549588632$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$2.37085301879$
6.4.225403.1	$x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + 2 x^{2} - 2 x + 1$	$6$	[4,1]	$-\,17\cdot 13259$	$2$	$7.8011737127$	$474.766258278745$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.38764499459$
6.4.228544.1	$x^{6} - 2 x^{5} + 4 x^{3} - 3 x^{2} - 2 x + 1$	$6$	[4,1]	$-\,2^{6}\cdot 3571$	$2$	$7.81918767923$	$169.0207087903728$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.31022927669$
6.4.233003.1	$x^{6} - 3 x^{4} - 3 x^{3} + 4 x^{2} + x - 1$	$6$	[4,1]	$-\,41\cdot 5683$	$2$	$7.84440941257$	$482.7038429513484$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.76165730795$
6.4.237179.1	$x^{6} - x^{5} - 3 x^{4} + 2 x^{2} + 3 x + 1$	$6$	[4,1]	$-\,237179$	$1$	$7.86766824772$	$487.0102668322301$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.79317933194$
6.4.238507.1	$x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + 4 x^{2} - 2 x - 1$	$6$	[4,1]	$-\,19\cdot 12553$	$2$	$7.87499321532$	$488.37178460676864$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.39438395261$
6.4.242467.1	$x^{6} - x^{4} - x^{3} - 2 x^{2} + x + 1$	$6$	[4,1]	$-\,242467$	$1$	$7.89663576524$	$492.40938252636903$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.56408503955$
6.4.254875.1	$x^{6} - x^{5} - 4 x^{4} + 5 x^{3} + 3 x^{2} - 4 x - 1$	$6$	[4,1]	$-\,5^{3}\cdot 2039$	$2$	$7.96259340397$	$100.97029266076235$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$2.46166362305$
6.4.255179.1	$x^{6} - 2 x^{5} - x^{4} + 3 x^{2} + 3 x - 1$	$6$	[4,1]	$-\,255179$	$1$	$7.96417550388$	$505.1524522359562$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.9352576377$
6.4.255823.1	$x^{6} - x^{5} - x^{4} + 3 x^{3} - 2 x^{2} - 2 x + 1$	$6$	[4,1]	$-\,109\cdot 2347$	$2$	$7.96752187643$	$505.78948189933726$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.70194889575$
6.4.257339.1	$x^{6} - 2 x^{5} - x^{4} + 4 x^{3} - 3 x^{2} - x + 1$	$6$	[4,1]	$-\,257339$	$1$	$7.97537173511$	$507.2859154362557$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.9470809923$
6.4.257344.1	$x^{6} - 2 x^{5} + 2 x^{3} - 3 x^{2} + 1$	$6$	[4,1]	$-\,2^{6}\cdot 4021$	$2$	$7.97539756131$	$213.28952593697076$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.63979925599$
6.4.259283.1	$x^{6} - 2 x^{5} - x^{4} + 3 x^{3} - 2 x^{2} + x + 1$	$6$	[4,1]	$-\,251\cdot 1033$	$2$	$7.98538158332$	$509.19838962824696$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.95993014505$
6.4.262375.1	$x^{6} - 2 x^{5} - x^{4} + 5 x^{3} - 7 x^{2} + 2 x + 1$	$6$	[4,1]	$-\,5^{3}\cdot 2099$	$2$	$8.0011744956$	$102.44510725261603$			?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$2.75446819831$
6.4.264931.1	$x^{6} - x^{5} - 3 x^{4} + 2 x^{3} + x^{2} + 2 x - 1$	$6$	[4,1]	$-\,264931$	$1$	$8.01411302547$	$514.7144839617397$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.7129897559$
6.4.269395.1	$x^{6} - x^{5} - 2 x^{4} + 2 x + 1$	$6$	[4,1]	$-\,5\cdot 7\cdot 43\cdot 179$	$4$	$8.03646248686$	$519.0327542650849$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.74371049773$
6.4.288576.1	$x^{6} - 2 x^{5} - x^{2} + 2 x + 1$	$6$	[4,1]	$-\,2^{6}\cdot 3^{3}\cdot 167$	$3$	$8.12911688664$	$44.76605857119878$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$2.68447846766$
6.4.295643.1	$x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + 2 x^{2} - 4 x + 1$	$6$	[4,1]	$-\,239\cdot 1237$	$2$	$8.16196259421$	$543.7306318389649$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.69270782388$
6.4.302123.1	$x^{6} - x^{5} - x^{4} - 2 x^{3} - x^{2} + 2 x + 1$	$6$	[4,1]	$-\,302123$	$1$	$8.19150998072$	$549.6571658770583$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.79405767396$
6.4.302375.1	$x^{6} - x^{4} - 3 x^{3} - x^{2} + 4 x + 1$	$6$	[4,1]	$-\,5^{3}\cdot 41\cdot 59$	$3$	$8.19264833798$	$109.97727037892875$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$4$	$3.0340297267$
6.4.303619.1	$x^{6} - x^{5} - 2 x^{4} - x^{3} + 3 x^{2} + 2 x - 1$	$6$	[4,1]	$-\,303619$	$1$	$8.19825629043$	$551.0163336961981$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.8613939594$
6.4.304859.1	$x^{6} - x^{4} - 3 x^{3} + 3 x - 1$	$6$	[4,1]	$-\,83\cdot 3673$	$2$	$8.20382718778$	$552.1403807004157$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.92624389541$
6.4.304927.1	$x^{6} - 2 x^{5} + 2 x^{3} - 7 x^{2} + 6 x - 1$	$6$	[4,1]	$-\,7^{4}\cdot 127$	$2$	$8.2041321421$	$41.23828102000196$			?	$A_4\times C_2$ (as 6T6)	trivial	$2$	$4$	$2.80736740928$

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