$p$-adic field search results

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Label	$n$	Polynomial	$p$	$f$	$e$	$c$	Galois group	$u$	$t$	Visible Artin slopes	Visible Swan slopes	Artin slope content	Swan slope content	Hidden Artin slopes	Hidden Swan slopes	$\#\Aut(K/\Q_p)$	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia	Resid. Poly	Jump Set
2.4.4.44a1.81	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.82	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.83	$16$	$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t + 8\right) x^{3} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.84	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.85	$16$	$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.86	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t^{3} x^{3} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.87	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t x^{3} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.88	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.143	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t^{2} x^{3} + \left(8 t + 8\right) x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.144	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + \left(8 t + 8\right) x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.145	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t + 8\right) x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.146	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t^{3} x^{3} + \left(8 t + 8\right) x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.147	$16$	$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{2} + 8\right) x^{3} + \left(8 t + 8\right) x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.148	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + \left(8 t + 8\right) x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.149	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + \left(8 t + 8\right) x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.150	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + \left(8 t + 8\right) x + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.447	$16$	$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 4 t x^{2} + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.448	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.449	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.450	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.451	$16$	$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 4 t x^{2} + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.452	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.453	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t x^{3} + 4 t x^{2} + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.454	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + 24 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.695	$16$	$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 4 t x^{2} + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.696	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.697	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.698	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.699	$16$	$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 4 t x^{2} + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.700	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.701	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t x^{3} + 4 t x^{2} + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.702	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.743	$16$	$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 4 t x^{2} + 8 x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.744	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + 8 x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.745	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.746	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + 8 x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.747	$16$	$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 4 t x^{2} + 8 x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.748	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 8 x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.749	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.750	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1155)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1227	$16$	$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 4 x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1228	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t^{3} x^{3} + 4 x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1229	$16$	$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 t x^{3} + 4 x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1230	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1231	$16$	$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 4 x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1232	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1233	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1234	$16$	$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 x^{2} + 8 t^{2} x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1267	$16$	$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + 8 x^{3} + 4 x^{2} + \left(8 t^{2} + 8\right) x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$
2.4.4.44a1.1268	$16$	$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 8 x^{3} + 2$	$2$	$4$	$4$	$44$	$C_2^7.C_8$ (as 16T1223)	$4$	$1$	$[3, 4]$	$[2,3]$	$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$	$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$	$[2,2,2,2,\frac{7}{2},\frac{7}{2}]$	$[1,1,1,1,\frac{5}{2},\frac{5}{2}]$	$2$	$t^{4} + t + 1$	$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 x^{2} + \left(8 t^{2} + 8\right) x + 8 t^{3} + 2$	$[8, 4, 0]$	$[1, 1]$	$z^2 + 1,z + 1$	$[1, 3, 7]$

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