| 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 |
| 2.2.8.56a3.521 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.522 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 8 x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.523 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.524 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.529 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.530 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.531 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.532 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.633 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.634 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.635 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.636 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.637 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.638 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 8 x^{2} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.639 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.640 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.645 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.646 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.647 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.648 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.653 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.654 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.655 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.656 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.761 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.762 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.763 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.764 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.765 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.766 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.767 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.768 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1573 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1574 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 4 t x^{4} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1575 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1576 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1617 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 4 t x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1618 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1619 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1620 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1621 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1622 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1623 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1624 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1629 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1630 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1631 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 4 t x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1632 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1733 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1734 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 28\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.(C_2\times C_4)$ (as 16T922) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
