| 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 |
| 2.2.8.56a5.817 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.818 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.819 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.820 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.821 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.822 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.823 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.824 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1793 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1794 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1795 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1796 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1797 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1798 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1799 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1800 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1889 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1890 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1891 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1892 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1893 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1894 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1895 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1896 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1977 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1978 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1979 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1980 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1981 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1982 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1983 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1984 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1985 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1986 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1987 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1988 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1989 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1990 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1991 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1992 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^5.C_2\wr C_4$ (as 16T1376) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, 4, \frac{9}{2}]^{4}$ |
$[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},3,\frac{7}{2}]^{4}$ |
$[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},4]^{2}$ |
$[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + 16 x^{3} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
