| 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 |
| 2.2.8.54a1.261 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.262 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.263 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.264 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.265 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.266 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.267 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.268 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(16 t + 2\right) x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.269 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.270 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.271 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.272 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.273 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.274 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.275 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.276 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(16 t + 2\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.425 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.426 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.427 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.428 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.429 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.430 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.431 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 2\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.432 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(24 t + 2\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.433 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.434 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.435 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.436 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.437 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.438 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.439 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 2\right) x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.440 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(24 t + 2\right) x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1434 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1435 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1436 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1437 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1438 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1439 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1440 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1441 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1442 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1443 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1444 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1445 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1446 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1447 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1448 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1449 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1494 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1495 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.Q_{16}$ (as 16T555) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,\frac{5}{2},3,4]$ |
$[1,\frac{3}{2},2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
