| 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 |
| 2.2.8.56a2.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.9 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.10 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.11 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.12 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.13 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.14 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.15 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.16 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.17 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.18 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.19 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.20 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.21 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.22 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.23 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.24 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.25 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:D_8$ (as 16T988) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.26 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:D_8$ (as 16T988) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.27 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:D_8$ (as 16T988) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.28 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:D_8$ (as 16T988) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.29 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:D_8$ (as 16T988) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.30 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:D_8$ (as 16T988) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.31 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:D_8$ (as 16T988) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.32 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:D_8$ (as 16T988) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.33 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.34 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.35 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.36 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.37 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.38 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.39 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.40 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5:\SD_{16}$ (as 16T970) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 t x^{5} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.41 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.42 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.43 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.44 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.45 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.46 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.47 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.48 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 16 x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.145 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + 8 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a2.146 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.(C_2\times D_4)$ (as 16T1000) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{11}{4},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 3, 7, 15]$ |
