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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
2.2.8.56a5.833 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.834 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 x^{3} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.835 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.836 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.837 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.838 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.839 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.840 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1817 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1818 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1819 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1820 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1821 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1822 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1823 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1824 $( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1825 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1826 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1827 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1828 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1829 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1830 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + 16 x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1831 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1832 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + 16 t x^{3} + 8 t x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1969 $( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1970 $( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1971 $( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1972 $( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1973 $( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1974 $( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1975 $( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.1976 $( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.2001 $( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + 16 x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.2002 $( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.2003 $( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.2004 $( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 t x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.2005 $( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.2006 $( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.2007 $( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
2.2.8.56a5.2008 $( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $2$ $2$ $8$ $56$ $C_2^5.C_2\wr C_4$ (as 16T1376) $4$ $1$ $[3, \frac{7}{2}, \frac{9}{2}]$ $[2,\frac{5}{2},\frac{7}{2}]$ $[2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{15}{4}, \frac{9}{2}]^{4}$ $[1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4},\frac{7}{2}]^{4}$ $[2,2,\frac{5}{2},\frac{7}{2},\frac{15}{4},\frac{15}{4}]^{2}$ $[1,1,\frac{3}{2},\frac{5}{2},\frac{11}{4},\frac{11}{4}]^{2}$ $t^{2} + t + 1$ $x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 8 t + 2$ $[21, 14, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + t,t z + (t + 1)$ $[1, 3, 7, 15]$
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