↑

Properties

Label 2.2.4.22a1.48-1.2.9a
Base 2.2.4.22a1.48
Degree \(2\)
e \(2\)
f \(1\)
c \(9\)

Related objects

Downloads

Learn more

Defining polynomial

$x^{2} + \left(b_{15} \pi^{8} + b_{13} \pi^{7} + b_{11} \pi^{6} + b_{9} \pi^{5}\right) x + c_{16} \pi^{9} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $2$
Base field: 2.2.4.22a1.48
Ramification index $e$: $2$
Residue field degree $f$: $1$
Discriminant exponent $c$: $9$
Absolute Artin slopes: $[3,4,5]$
Swan slopes: $[8]$
Means: $\langle4\rangle$
Rams: $(8)$
Field count: $272$ (complete)
Ambiguity: $2$
Mass: $256$
Absolute Mass: $128$

Diagrams

Varying

These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.

Galois group: $(C_4\times C_8).D_4$ (show 4), $C_2^2.C_2\wr C_4$ (show 8), $D_4^2:C_4$ (show 4), $Q_8^2:C_8$ (show 16), $C_4^3.D_4$ (show 16), $(C_4\times \OD_{16}).D_4$ (show 8), $D_4^2:C_8$ (show 16), $Q_8^2:(C_2\times C_4)$ (show 4), $D_4^2:(C_2\times C_4)$ (show 4), $C_2^6.C_2\wr C_4$ (show 64), $C_2^7.C_2\wr C_4$ (show 64), $C_2^7.C_2\wr C_4$ (show 64) (incomplete)
Hidden Artin slopes: not computed (show 96), $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ (show 64), $[2,2,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ (show 32), $[2,2,\frac{7}{2},\frac{9}{2}]^{2}$ (show 16), $[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ (show 48), $[2,2,\frac{7}{2},\frac{9}{2}]$ (show 16) (incomplete)
Indices of inseparability: $[24,16,8,0]$
Associated inertia: $[1,1,1]$
Jump Set: $[1,3,7,15]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
Sort order Select

Showing 1-50 of 272

Next   displayed columns for results
Label Polynomial $/ \Q_p$ Galois group $/ \Q_p$ Galois degree $/ \Q_p$ $\#\Aut(K/\Q_p)$ Artin slope content $/ \Q_p$ Swan slope content $/ \Q_p$ Hidden Artin slopes $/ \Q_p$ Hidden Swan slopes $/ \Q_p$ Ind. of Insep. $/ \Q_p$ Assoc. Inertia $/ \Q_p$ Resid. Poly Jump Set
2.2.8.62a1.8341 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8342 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8343 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8344 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8345 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8346 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8347 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8348 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8349 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8350 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8351 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8352 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8353 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8354 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8355 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8356 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8357 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8358 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8359 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8360 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8361 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8362 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8363 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8364 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8365 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8366 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8367 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8368 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8369 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8370 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8371 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8372 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8373 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8374 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8375 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8376 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8377 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8378 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8379 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8380 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8381 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8382 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8383 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8384 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1698) $8192$ $2$ $[2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{17}{4}, \frac{19}{4}, 5]^{4}$ $[1,1,2,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{13}{4},\frac{15}{4},4]^{4}$ $[2,2,3,\frac{7}{2},\frac{7}{2},\frac{17}{4},\frac{17}{4},\frac{19}{4}]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},\frac{13}{4},\frac{13}{4},\frac{15}{4}]^{2}$ $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8385 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1727) $8192$ $2$ not computed not computed not computed not computed $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8386 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1727) $8192$ $2$ not computed not computed not computed not computed $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8387 $( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1727) $8192$ $2$ not computed not computed not computed not computed $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8388 $( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1727) $8192$ $2$ not computed not computed not computed not computed $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8389 $( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1727) $8192$ $2$ not computed not computed not computed not computed $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
2.2.8.62a1.8390 $( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ $C_2^7.C_2\wr C_4$ (as 16T1727) $8192$ $2$ not computed not computed not computed not computed $[24, 16, 8, 0]$ $[1, 1, 1]$ $z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15]$
Next   displayed columns for results