| 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 |
| 2.2.8.56a1.380 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.381 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.382 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.383 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.384 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.385 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.390 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.391 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.392 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.393 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.394 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.395 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.407 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.408 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.409 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.410 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.411 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.412 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.413 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.414 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.471 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.472 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.473 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.474 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.485 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.486 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.487 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.488 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.489 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.490 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.491 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.492 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.533 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.534 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.535 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.536 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.573 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.574 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.575 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.576 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.577 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.578 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.579 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.580 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.617 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 16 t x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.618 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 16 t x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.619 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.620 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.621 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 16 t x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.622 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{15}{4}]^{2}$ |
$[1,1,1,2,\frac{11}{4}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 16 t x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
