| 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 |
| 3.1.9.9a1.1 |
$9$ |
$x^{9} + 3 x + 3$ |
$3$ |
$1$ |
$9$ |
$9$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{9}{8}, \frac{9}{8}]$ |
$[\frac{1}{8},\frac{1}{8}]$ |
$[\frac{9}{8}, \frac{9}{8}]_{8}^{2}$ |
$[\frac{1}{8},\frac{1}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x + 3$ |
$[1, 1, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.1.9.9a1.2 |
$9$ |
$x^{9} + 6 x + 3$ |
$3$ |
$1$ |
$9$ |
$9$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{9}{8}, \frac{9}{8}]$ |
$[\frac{1}{8},\frac{1}{8}]$ |
$[\frac{9}{8}, \frac{9}{8}]_{8}^{2}$ |
$[\frac{1}{8},\frac{1}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x + 3$ |
$[1, 1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.1.9.10a1.1 |
$9$ |
$x^{9} + 3 x^{2} + 3$ |
$3$ |
$1$ |
$9$ |
$10$ |
$C_3^2:Q_8$ (as 9T14) |
$2$ |
$4$ |
$[\frac{5}{4}, \frac{5}{4}]$ |
$[\frac{1}{4},\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\ ]^{2}_{4}$ |
$[\ ]^{2}_{4}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{2} + 3$ |
$[2, 2, 0]$ |
$[2]$ |
$z^2 + 1$ |
undefined |
| 3.1.9.10a2.1 |
$9$ |
$x^{9} + 6 x^{2} + 3$ |
$3$ |
$1$ |
$9$ |
$10$ |
$S_3^2:C_2$ (as 9T16) |
$2$ |
$4$ |
$[\frac{5}{4}, \frac{5}{4}]$ |
$[\frac{1}{4},\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\ ]^{2}_{4}$ |
$[\ ]^{2}_{4}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{2} + 3$ |
$[2, 2, 0]$ |
$[1]$ |
$z^2 + 2$ |
undefined |
| 3.1.9.12a1.1 |
$9$ |
$x^{9} + 6 x^{4} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$C_3^2:C_4$ (as 9T9) |
$2$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{4} + 3$ |
$[4, 4, 0]$ |
$[2]$ |
$z^4 + 1$ |
undefined |
| 3.1.9.12a2.1 |
$9$ |
$x^{9} + 3 x^{4} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{4} + 3$ |
$[4, 4, 0]$ |
$[2]$ |
$z^4 + 2$ |
undefined |
| 3.1.9.12a3.1 |
$9$ |
$x^{9} + 6 x^{4} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$C_3^2 : C_6$ (as 9T11) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{4} + 3 x^{3} + 3$ |
$[4, 3, 0]$ |
$[3]$ |
$z^4 + 2 z + 1$ |
undefined |
| 3.1.9.12a3.2 |
$9$ |
$x^{9} + 6 x^{4} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$C_3^2 : C_6$ (as 9T11) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{4} + 6 x^{3} + 3$ |
$[4, 3, 0]$ |
$[3]$ |
$z^4 + z + 1$ |
undefined |
| 3.1.9.12a4.1 |
$9$ |
$x^{9} + 3 x^{4} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$C_3^2:C_8$ (as 9T15) |
$4$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\ ]^{4}_{2}$ |
$[\ ]^{4}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{4} + 3 x^{3} + 3$ |
$[4, 3, 0]$ |
$[4]$ |
$z^4 + 2 z + 2$ |
undefined |
| 3.1.9.12a4.2 |
$9$ |
$x^{9} + 3 x^{4} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$C_3^2:C_8$ (as 9T15) |
$4$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\ ]^{4}_{2}$ |
$[\ ]^{4}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{4} + 6 x^{3} + 3$ |
$[4, 3, 0]$ |
$[4]$ |
$z^4 + z + 2$ |
undefined |
| 3.1.9.13a1.1 |
$9$ |
$x^{9} + 3 x^{5} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{13}{8}, \frac{13}{8}]$ |
$[\frac{5}{8},\frac{5}{8}]$ |
$[\frac{13}{8}, \frac{13}{8}]_{8}^{2}$ |
$[\frac{5}{8},\frac{5}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{5} + 3$ |
$[5, 5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.1.9.13a1.2 |
$9$ |
$x^{9} + 6 x^{5} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{13}{8}, \frac{13}{8}]$ |
$[\frac{5}{8},\frac{5}{8}]$ |
$[\frac{13}{8}, \frac{13}{8}]_{8}^{2}$ |
$[\frac{5}{8},\frac{5}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{5} + 3$ |
$[5, 5, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.1.9.13b1.1 |
$9$ |
$x^{9} + 6 x^{5} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$[\frac{1}{2},\frac{2}{3}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{3}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{2}{3}]_{2}^{2}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{5} + 3 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + 2$ |
undefined |
| 3.1.9.13b1.2 |
$9$ |
$x^{9} + 3 x^{5} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$[\frac{1}{2},\frac{2}{3}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{3}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{2}{3}]_{2}^{2}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{5} + 6 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 2]$ |
$z^3 + 1,z^2 + 1$ |
undefined |
| 3.1.9.13b2.1 |
$9$ |
$x^{9} + 3 x^{5} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$[\frac{1}{2},\frac{2}{3}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{3}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{2}{3}]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{5} + 3 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.13b2.2 |
$9$ |
$x^{9} + 3 x^{6} + 3 x^{5} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$[\frac{1}{2},\frac{2}{3}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{3}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{2}{3}]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{6} + 3 x^{5} + 3 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.13b2.3 |
$9$ |
$x^{9} + 6 x^{6} + 3 x^{5} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$[\frac{1}{2},\frac{2}{3}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{3}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{2}{3}]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 3 x^{5} + 3 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.13b2.4 |
$9$ |
$x^{9} + 6 x^{5} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$[\frac{1}{2},\frac{2}{3}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{3}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{2}{3}]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{5} + 6 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.13b2.5 |
$9$ |
$x^{9} + 3 x^{6} + 6 x^{5} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$[\frac{1}{2},\frac{2}{3}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{3}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{2}{3}]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{6} + 6 x^{5} + 6 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.13b2.6 |
$9$ |
$x^{9} + 6 x^{6} + 6 x^{5} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{5}{3}]$ |
$[\frac{1}{2},\frac{2}{3}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{3}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{2}{3}]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 6 x^{5} + 6 x^{3} + 3$ |
$[5, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.15a1.1 |
$9$ |
$x^{9} + 3 x^{7} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{15}{8}, \frac{15}{8}]$ |
$[\frac{7}{8},\frac{7}{8}]$ |
$[\frac{15}{8}, \frac{15}{8}]_{8}^{2}$ |
$[\frac{7}{8},\frac{7}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{7} + 3$ |
$[7, 7, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.1.9.15a1.2 |
$9$ |
$x^{9} + 6 x^{7} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{15}{8}, \frac{15}{8}]$ |
$[\frac{7}{8},\frac{7}{8}]$ |
$[\frac{15}{8}, \frac{15}{8}]_{8}^{2}$ |
$[\frac{7}{8},\frac{7}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{7} + 3$ |
$[7, 7, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.1.9.15a1.3 |
$9$ |
$x^{9} + 3 x^{7} + 3 x^{6} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{15}{8}, \frac{15}{8}]$ |
$[\frac{7}{8},\frac{7}{8}]$ |
$[\frac{15}{8}, \frac{15}{8}]_{8}^{2}$ |
$[\frac{7}{8},\frac{7}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{7} + 3 x^{6} + 3$ |
$[7, 6, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.1.9.15a1.4 |
$9$ |
$x^{9} + 6 x^{7} + 3 x^{6} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{15}{8}, \frac{15}{8}]$ |
$[\frac{7}{8},\frac{7}{8}]$ |
$[\frac{15}{8}, \frac{15}{8}]_{8}^{2}$ |
$[\frac{7}{8},\frac{7}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{7} + 3 x^{6} + 3$ |
$[7, 6, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.1.9.15a1.5 |
$9$ |
$x^{9} + 3 x^{7} + 6 x^{6} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{15}{8}, \frac{15}{8}]$ |
$[\frac{7}{8},\frac{7}{8}]$ |
$[\frac{15}{8}, \frac{15}{8}]_{8}^{2}$ |
$[\frac{7}{8},\frac{7}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{7} + 6 x^{6} + 3$ |
$[7, 6, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.1.9.15a1.6 |
$9$ |
$x^{9} + 6 x^{7} + 6 x^{6} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{15}{8}, \frac{15}{8}]$ |
$[\frac{7}{8},\frac{7}{8}]$ |
$[\frac{15}{8}, \frac{15}{8}]_{8}^{2}$ |
$[\frac{7}{8},\frac{7}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{7} + 6 x^{6} + 3$ |
$[7, 6, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.1.9.15b1.1 |
$9$ |
$x^{9} + 3 x^{7} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{2}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{7} + 3 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + 2$ |
undefined |
| 3.1.9.15b1.2 |
$9$ |
$x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{2}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + 2$ |
undefined |
| 3.1.9.15b1.3 |
$9$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, 2]_{2}^{2}$ |
$[\frac{1}{2},1]_{2}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 3 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + 2$ |
undefined |
| 3.1.9.15b1.4 |
$9$ |
$x^{9} + 6 x^{7} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{2}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{7} + 6 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 2]$ |
$z^3 + 1,z^2 + 1$ |
undefined |
| 3.1.9.15b1.5 |
$9$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{2}$ |
$[\frac{3}{2}]^{2}_{2}$ |
$[\frac{1}{2}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 6 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 2]$ |
$z^3 + 1,z^2 + 1$ |
undefined |
| 3.1.9.15b1.6 |
$9$ |
$x^{9} + 6 x^{8} + 6 x^{7} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, 2]_{2}^{2}$ |
$[\frac{1}{2},1]_{2}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{8} + 6 x^{7} + 6 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 2]$ |
$z^3 + 1,z^2 + 1$ |
undefined |
| 3.1.9.15b2.1 |
$9$ |
$x^{9} + 6 x^{7} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{7} + 3 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.15b2.2 |
$9$ |
$x^{9} + 6 x^{7} + 3 x^{3} + 12$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{7} + 3 x^{3} + 12$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.15b2.3 |
$9$ |
$x^{9} + 6 x^{7} + 3 x^{3} + 21$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{7} + 3 x^{3} + 21$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.15b2.4 |
$9$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 3 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.15b2.5 |
$9$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 3 x^{3} + 12$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 3 x^{3} + 12$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.15b2.6 |
$9$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 3 x^{3} + 21$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 3 x^{3} + 21$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.15b2.7 |
$9$ |
$x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$S_3\times C_3$ (as 9T4) |
$1$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, 2]_{2}$ |
$[\frac{1}{2},1]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.15b2.8 |
$9$ |
$x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{3} + 12$ |
$3$ |
$1$ |
$9$ |
$15$ |
$S_3\times C_3$ (as 9T4) |
$1$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, 2]_{2}$ |
$[\frac{1}{2},1]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{3} + 12$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.15b2.9 |
$9$ |
$x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{3} + 21$ |
$3$ |
$1$ |
$9$ |
$15$ |
$S_3\times C_3$ (as 9T4) |
$1$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, 2]_{2}$ |
$[\frac{1}{2},1]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{3} + 21$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.9.15b2.10 |
$9$ |
$x^{9} + 3 x^{7} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{7} + 6 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.15b2.11 |
$9$ |
$x^{9} + 3 x^{7} + 6 x^{3} + 12$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{7} + 6 x^{3} + 12$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.15b2.12 |
$9$ |
$x^{9} + 3 x^{7} + 6 x^{3} + 21$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{7} + 6 x^{3} + 21$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.15b2.13 |
$9$ |
$x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.15b2.14 |
$9$ |
$x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{3} + 12$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{3} + 12$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.15b2.15 |
$9$ |
$x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{3} + 21$ |
$3$ |
$1$ |
$9$ |
$15$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, \frac{3}{2}, 2]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},1]_{2}^{3}$ |
$[\frac{3}{2}]^{3}_{2}$ |
$[\frac{1}{2}]^{3}_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{3} + 21$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.15b2.16 |
$9$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$15$ |
$S_3\times C_3$ (as 9T4) |
$1$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, 2]_{2}$ |
$[\frac{1}{2},1]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 6 x^{3} + 3$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.15b2.17 |
$9$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 6 x^{3} + 12$ |
$3$ |
$1$ |
$9$ |
$15$ |
$S_3\times C_3$ (as 9T4) |
$1$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, 2]_{2}$ |
$[\frac{1}{2},1]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 6 x^{3} + 12$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
| 3.1.9.15b2.18 |
$9$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 6 x^{3} + 21$ |
$3$ |
$1$ |
$9$ |
$15$ |
$S_3\times C_3$ (as 9T4) |
$1$ |
$2$ |
$[\frac{3}{2}, 2]$ |
$[\frac{1}{2},1]$ |
$[\frac{3}{2}, 2]_{2}$ |
$[\frac{1}{2},1]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t + 1$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 6 x^{3} + 21$ |
$[7, 3, 0]$ |
$[1, 1]$ |
$z^3 + 1,z^2 + 2$ |
undefined |
