pp-adic field search results

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
23.8.0.1	$8$	$x^{8} + 3 x^{4} + 20 x^{3} + 5 x^{2} + 3 x + 5$	$23$	$1$	$8$	$0$	$C_8$ (as 8T1)	$8$	$1$	$[\ ]$	$[\ ]^{8}$	$t^{8} + 3 t^{4} + 20 t^{3} + 5 t^{2} + 3 t + 5$	$x - 23$	$[0]$	$[\ ]$
23.8.4.1	$8$	$x^{8} + 98 x^{6} + 38 x^{5} + 3331 x^{4} - 1634 x^{3} + 44919 x^{2} - 57494 x + 224528$	$23$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$t^{4} + 3 t^{2} + 19 t + 5$	$x^{2} + 23$	$[0]$	$[1]$
23.8.4.2	$8$	$x^{8} + 1587 x^{4} - 231173 x^{2} + 1399205$	$23$	$2$	$4$	$4$	$C_8$ (as 8T1)	$4$	$2$	$[\ ]$	$[\ ]_{2}^{4}$	$t^{4} + 3 t^{2} + 19 t + 5$	$x^{2} + 23 t$	$[0]$	$[1]$
23.8.6.1	$8$	$x^{8} - 138 x^{4} - 217948$	$23$	$4$	$2$	$6$	$Q_8$ (as 8T5)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 21 t + 5$	$x^{4} + 46 t + 414$	$[0]$	$[1]$
23.8.6.2	$8$	$x^{8} + 84 x^{7} + 2666 x^{6} + 38304 x^{5} + 221137 x^{4} + 193452 x^{3} + 126128 x^{2} + 833532 x + 4272507$	$23$	$4$	$2$	$6$	$D_4$ (as 8T4)	$2$	$4$	$[\ ]$	$[\ ]_{4}^{2}$	$t^{2} + 21 t + 5$	$x^{4} + 23$	$[0]$	$[1]$
23.8.6.3	$8$	$x^{8} - 483 x^{4} + 2645$	$23$	$4$	$2$	$6$	$C_8:C_2$ (as 8T7)	$4$	$4$	$[\ ]$	$[\ ]_{4}^{4}$	$t^{2} + 21 t + 5$	$x^{4} + 23 t$	$[0]$	$[1]$
23.8.7.1	$8$	$x^{8} + 23$	$23$	$8$	$1$	$7$	$D_{8}$ (as 8T6)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$t + 18$	$x^{8} + 23$	$[0]$	$[2]$
23.8.7.2	$8$	$x^{8} + 115$	$23$	$8$	$1$	$7$	$D_{8}$ (as 8T6)	$2$	$8$	$[\ ]$	$[\ ]_{8}^{2}$	$t + 18$	$x^{8} + 115$	$[0]$	$[2]$

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