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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
6.0.18515.1	$x^{6} + 2 x^{4} - x^{3} + 2 x^{2} + 1$	$6$	[0,3]	$-\,5\cdot 7\cdot 23^{2}$	$3$	$5.14344325363$	$28.372521918222215$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$0.328780614749$
6.2.41069.1	$x^{6} - 2 x^{4} + 2 x^{2} - x - 1$	$6$	[2,2]	$7\cdot 5867$	$2$	$5.8737981937$	$202.6548790431654$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.632541712933$
6.0.54208.1	$x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,2^{6}\cdot 7\cdot 11^{2}$	$3$	$6.15191836841$	$19.699129000227927$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$0.956984205134$
6.0.54691.1	$x^{6} - x^{5} - 2 x^{3} + 2 x^{2} + 1$	$6$	[0,3]	$-\,7\cdot 13\cdot 601$	$3$	$6.16102036097$	$233.86106986841568$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.665616035351$
6.0.61131.1	$x^{6} - x^{5} - x^{4} + x^{2} + 1$	$6$	[0,3]	$-\,3\cdot 7\cdot 41\cdot 71$	$4$	$6.27639474378$	$247.24684022247888$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.857024077992$
6.0.80192.1	$x^{6} - 2 x^{5} + x^{4} + 2 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,2^{6}\cdot 7\cdot 179$	$3$	$6.56682093677$	$119.06333083375378$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.973589074988$
6.2.85169.1	$x^{6} - 3 x^{4} - 2 x^{3} + 6 x^{2} - 2 x - 1$	$6$	[2,2]	$7\cdot 23^{3}$	$2$	$6.63305489226$	$27.787207043050365$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$1.04071919564$
6.0.92575.1	$x^{6} - x^{5} + x^{4} + x^{3} - x^{2} + x + 5$	$6$	[0,3]	$-\,5^{2}\cdot 7\cdot 23^{2}$	$3$	$6.72587750482$	$28.372521918222215$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$1.01233395676$
6.2.97909.1	$x^{6} - x^{5} + 2 x^{3} - x^{2} - 3 x - 1$	$6$	[2,2]	$7\cdot 71\cdot 197$	$3$	$6.78896811771$	$312.90413867509005$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$1.32940738074$
6.2.116053.1	$x^{6} - x^{3} - 2 x^{2} - 1$	$6$	[2,2]	$7\cdot 59\cdot 281$	$3$	$6.98408305314$	$340.6655251122426$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$1.49133345911$
6.0.129647.1	$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} + x + 1$	$6$	[0,3]	$-\,7\cdot 18521$	$2$	$7.11421651826$	$360.06527186053364$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$1.43010815264$
6.0.137011.1	$x^{6} - 2 x^{4} - 4 x^{3} + 7 x + 5$	$6$	[0,3]	$-\,7\cdot 23^{2}\cdot 37$	$3$	$7.18002416696$	$77.18160402582988$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$1.23279835137$
6.2.143773.1	$x^{6} - 2 x^{5} + x^{4} - 2 x^{3} + 3 x^{2} - 3 x + 1$	$6$	[2,2]	$7\cdot 19\cdot 23\cdot 47$	$4$	$7.2379051768$	$379.1741024911907$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$1.41507891088$
6.2.149849.1	$x^{6} - x^{5} - 2 x^{4} - x^{3} + 3 x^{2} + x + 1$	$6$	[2,2]	$7\cdot 21407$	$2$	$7.28801025135$	$387.10334537433283$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.2244249143$
6.2.153461.1	$x^{6} - x^{5} - x^{4} + 4 x^{3} - 5 x^{2} + 4 x - 1$	$6$	[2,2]	$7\cdot 11\cdot 1993$	$3$	$7.31699913983$	$391.7409858567265$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$1.56581032058$
6.2.162589.1	$x^{6} - 2 x^{4} - x^{3} + 2 x^{2} + 2 x - 1$	$6$	[2,2]	$7\cdot 23227$	$2$	$7.38780107968$	$403.2232632177861$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$1.63772537788$
6.0.165263.1	$x^{6} - 2 x^{5} + 3 x^{4} - 5 x^{3} + 5 x^{2} - 3 x + 2$	$6$	[0,3]	$-\,7\cdot 23609$	$2$	$7.40791411615$	$406.5255219540343$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.34413156457$
6.0.176176.1	$x^{6} - x^{5} + 4 x^{4} - x^{3} + 4 x^{2} - x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 7\cdot 11^{2}\cdot 13$	$4$	$7.48728660143$	$50.22312158647186$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$1.36797583457$
6.0.178367.1	$x^{6} - x^{5} + 2 x^{4} - 3 x^{3} + 3 x^{2} - x + 2$	$6$	[0,3]	$-\,7\cdot 83\cdot 307$	$3$	$7.50272597176$	$422.33517494994425$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.45491360091$
6.0.198331.1	$x^{6} - 3 x^{5} + 6 x^{4} - 6 x^{3} + 3 x^{2} - x + 1$	$6$	[0,3]	$-\,7\cdot 29\cdot 977$	$3$	$7.63657169805$	$445.34368750438125$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$1.6604131879$
6.2.204169.1	$x^{6} - x^{5} - 2 x^{4} + 5 x^{3} - x^{2} - 3 x + 2$	$6$	[2,2]	$7\cdot 29167$	$2$	$7.67358486099$	$451.8506390390524$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.73826280744$
6.2.213549.1	$x^{6} - x^{5} + 2 x^{4} + x^{2} + 3 x + 1$	$6$	[2,2]	$3\cdot 7\cdot 10169$	$3$	$7.73124774578$	$462.113622391723$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.33272173634$
6.0.214088.1	$x^{6} - x^{5} + 2 x^{2} - x + 1$	$6$	[0,3]	$-\,2^{3}\cdot 7\cdot 3823$	$3$	$7.73449662294$	$462.6964447669768$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.74120724312$
6.2.214697.1	$x^{6} + x^{4} - x^{3} - 3 x^{2} + 1$	$6$	[2,2]	$7\cdot 30671$	$2$	$7.7381592408$	$463.3540762742894$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.00901423858$
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	$2$	$4$	$2.26354419685$
6.2.216832.1	$x^{6} - 2 x^{5} + 2 x^{4} - 6 x^{3} + 2 x^{2} + 4 x - 2$	$6$	[2,2]	$2^{8}\cdot 7\cdot 11^{2}$	$3$	$7.7509314496$	$26.29518248194094$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$2.84170170288$
6.2.218477.2	$x^{6} + x^{4} - 2 x^{3} - 3 x^{2} - 11 x - 5$	$6$	[2,2]	$7\cdot 23^{2}\cdot 59$	$3$	$7.76070104374$	$97.46281342132495$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$2.07044861804$
6.0.227248.1	$x^{6} - x^{5} - 2 x^{4} + x^{3} + 2 x^{2} + x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 7\cdot 2029$	$3$	$7.8117801383$	$189.18064738052297$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.02755127626$
6.2.227829.1	$x^{6} - x^{5} - 2 x^{4} + 2 x^{3} - 2 x - 1$	$6$	[2,2]	$3\cdot 7\cdot 19\cdot 571$	$4$	$7.81510529911$	$477.3143618203835$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.2917337147$
6.0.230384.1	$x^{6} - 3 x^{5} + x^{4} + 3 x^{3} - 2 x^{2} + 2$	$6$	[0,3]	$-\,2^{4}\cdot 7\cdot 11^{2}\cdot 17$	$4$	$7.82964465778$	$57.43233678534052$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$3.68263558859$
6.2.234892.1	$x^{6} - x^{5} - 2 x^{3} + x^{2} - 2 x + 2$	$6$	[2,2]	$2^{2}\cdot 7\cdot 8389$	$3$	$7.85497313958$	$484.6565794456937$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.99279483275$
6.0.236992.1	$x^{6} + x^{4} - x^{2} + 7$	$6$	[0,3]	$-\,2^{6}\cdot 7\cdot 23^{2}$	$3$	$7.86663405166$	$35.888716889852724$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$1.31783685997$
6.2.236992.2	$x^{6} - x^{4} - x^{2} - 7$	$6$	[2,2]	$2^{6}\cdot 7\cdot 23^{2}$	$3$	$7.86663405166$	$42.67911747373118$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$1.90994097731$
6.0.240667.1	$x^{6} + 3 x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,7\cdot 34381$	$2$	$7.88683504217$	$490.57823025486977$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.48234289246$
6.0.241451.1	$x^{6} - x^{3} + 2 x^{2} + 2 x + 1$	$6$	[0,3]	$-\,7\cdot 17\cdot 2029$	$3$	$7.89111128454$	$491.3766376212854$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$1.98247253147$
6.2.248101.1	$x^{6} - x^{5} - 4 x^{4} + 6 x^{3} + 8 x^{2} - 4 x - 5$	$6$	[2,2]	$7\cdot 23^{2}\cdot 67$	$3$	$7.92692506005$	$103.860483341837$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$2.22595602331$
6.0.252868.1	$x^{6} - x^{5} - x^{4} + x^{3} - x^{2} + 2$	$6$	[0,3]	$-\,2^{2}\cdot 7\cdot 11\cdot 821$	$4$	$7.9521087792$	$502.85982142143746$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.62716415772$
6.2.262864.1	$x^{6} - x^{5} - x^{3} + 2 x^{2} - 3 x - 1$	$6$	[2,2]	$2^{4}\cdot 7\cdot 2347$	$3$	$8.00365792544$	$203.4661786574018$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.78858903564$
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	$2$	$4$	$2.74371049773$
6.0.273791.1	$x^{6} - 3 x^{5} + 5 x^{4} - 3 x^{3} - 2 x^{2} + 2 x + 1$	$6$	[0,3]	$-\,7\cdot 39113$	$2$	$8.0581719058$	$523.2504180600337$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.23197126062$
6.0.276416.1	$x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} + 2 x^{2} + 2$	$6$	[0,3]	$-\,2^{6}\cdot 7\cdot 617$	$3$	$8.07099719434$	$185.88168279849415$			?	$S_6$ (as 6T16)	trivial	$2$	$2$	$3.60286293509$
6.0.282863.1	$x^{6} - 2 x^{5} + 2 x^{4} - x^{3} + x^{2} + x + 1$	$6$	[0,3]	$-\,7\cdot 17\cdot 2377$	$3$	$8.10207061165$	$531.8486626851665$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.24276903153$
6.0.283311.1	$x^{6} - 2 x^{5} + 5 x^{4} - 6 x^{3} + 8 x^{2} - 5 x + 2$	$6$	[0,3]	$-\,3^{3}\cdot 7\cdot 1499$	$3$	$8.10420788578$	$369.0551756460282$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$3.50593539383$
6.2.283801.1	$x^{6} - x^{5} - x^{4} - 2 x - 1$	$6$	[2,2]	$7\cdot 40543$	$2$	$8.10654230694$	$532.729762637681$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$3.38767135639$
6.2.298256.1	$x^{6} - x^{5} - 3 x^{4} + 2 x^{3} + 4 x^{2} - 2$	$6$	[2,2]	$2^{4}\cdot 7\cdot 2663$	$3$	$8.17394161913$	$306.5040834383146$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$3.83336331973$
6.0.298816.1	$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 2 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 7\cdot 23\cdot 29$	$4$	$8.17649749416$	$229.83408141909644$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$1.71482578443$
6.2.301133.1	$x^{6} + 3 x^{4} + x^{2} - 3 x + 1$	$6$	[2,2]	$7\cdot 43019$	$2$	$8.18703018858$	$548.7558655722962$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$3.32116132941$
6.0.304108.1	$x^{6} - x^{5} + 4 x^{4} - x^{3} + 4 x^{2} + 2 x + 1$	$6$	[0,3]	$-\,2^{2}\cdot 7\cdot 10861$	$3$	$8.20045546092$	$437.69399735513286$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$3.28911573447$
6.2.306341.1	$x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - x^{2} - 1$	$6$	[2,2]	$7\cdot 107\cdot 409$	$3$	$8.21046059224$	$553.4808036418247$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.54378008071$
6.0.311647.1	$x^{6} + x^{4} - 3 x^{3} + x^{2} + 1$	$6$	[0,3]	$-\,7\cdot 211^{2}$	$2$	$8.23399296806$	$38.43175770115127$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$1.99023333466$

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