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Label 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 Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
3.1.12.22a1.1 $x^{12} + 3 x^{11} + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.2 $x^{12} + 3 x^{11} + 9 x^{4} + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.3 $x^{12} + 3 x^{11} + 18 x^{4} + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.4 $x^{12} + 3 x^{11} + 9 x^{2} + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{2} + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.5 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.6 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.10 $x^{12} + 3 x^{11} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.11 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.12 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.13 $x^{12} + 3 x^{11} + 9 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.14 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.15 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.16 $x^{12} + 3 x^{11} + 18 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.17 $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.18 $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ $[2, 14]$
3.1.12.22a1.19 $x^{12} + 6 x^{11} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.20 $x^{12} + 6 x^{11} + 9 x^{4} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x^{4} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.21 $x^{12} + 6 x^{11} + 18 x^{4} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 18 x^{4} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.22 $x^{12} + 6 x^{11} + 9 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.23 $x^{12} + 6 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.24 $x^{12} + 6 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.25 $x^{12} + 6 x^{11} + 18 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 18 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.26 $x^{12} + 6 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.27 $x^{12} + 6 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 3$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 3$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ $[2, 14]$
3.1.12.22a1.28 $x^{12} + 3 x^{11} + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.29 $x^{12} + 3 x^{11} + 9 x^{4} + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.30 $x^{12} + 3 x^{11} + 18 x^{4} + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.34 $x^{12} + 3 x^{11} + 18 x^{2} + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{2} + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.35 $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.36 $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{13}{8}, \frac{13}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{13}{8},\frac{13}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{5}{8},\frac{5}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.37 $x^{12} + 3 x^{11} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.38 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.39 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.40 $x^{12} + 3 x^{11} + 9 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.41 $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.42 $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.43 $x^{12} + 3 x^{11} + 18 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.44 $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.45 $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 3 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 2$ undefined
3.1.12.22a1.46 $x^{12} + 6 x^{11} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.47 $x^{12} + 6 x^{11} + 9 x^{4} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x^{4} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.48 $x^{12} + 6 x^{11} + 18 x^{4} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 18 x^{4} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.49 $x^{12} + 6 x^{11} + 9 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.50 $x^{12} + 6 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x^{4} + 9 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.51 $x^{12} + 6 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 18 x^{4} + 9 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.52 $x^{12} + 6 x^{11} + 18 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 18 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.53 $x^{12} + 6 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 9 x^{4} + 18 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
3.1.12.22a1.54 $x^{12} + 6 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 6$ $3$ $1$ $12$ $22$ $C_3^4:\SD_{16}$ (as 12T212) $2$ $8$ $[\frac{19}{8}]$ $[\frac{11}{8}]$ $[\frac{15}{8}, \frac{15}{8}, \frac{19}{8}, \frac{19}{8}]_{8}^{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8},\frac{11}{8}]_{8}^{2}$ $[\frac{15}{8},\frac{15}{8},\frac{19}{8}]^{2}_{2}$ $[\frac{7}{8},\frac{7}{8},\frac{11}{8}]^{2}_{2}$ $t + 1$ $x^{12} + 6 x^{11} + 18 x^{4} + 18 x^{2} + 9 x + 6$ $[11, 0]$ $[2, 1]$ $z^9 + z^6 + 1,z + 1$ undefined
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