Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{8} + 24x^{6} + 180x^{4} + 432x^{2} + 162 \)
| $\times$ | \(\chi_{ 96 } ( 1, ·)\) | \(\chi_{ 96 } ( 5, ·)\) | \(\chi_{ 96 } ( 73, ·)\) | \(\chi_{ 96 } ( 77, ·)\) | \(\chi_{ 96 } ( 49, ·)\) | \(\chi_{ 96 } ( 53, ·)\) | \(\chi_{ 96 } ( 25, ·)\) | \(\chi_{ 96 } ( 29, ·)\) |
|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 96 }(1, ·)\) | \(\chi_{ 96 } ( 1, ·)\) | \(\chi_{ 96 } ( 5, ·)\) | \(\chi_{ 96 } ( 73, ·)\) | \(\chi_{ 96 } ( 77, ·)\) | \(\chi_{ 96 } ( 49, ·)\) | \(\chi_{ 96 } ( 53, ·)\) | \(\chi_{ 96 } ( 25, ·)\) | \(\chi_{ 96 } ( 29, ·)\) |
| \(\chi_{ 96 }(5, ·)\) | \(\chi_{ 96 } ( 5, ·)\) | \(\chi_{ 96 } ( 25, ·)\) | \(\chi_{ 96 } ( 77, ·)\) | \(\chi_{ 96 } ( 1, ·)\) | \(\chi_{ 96 } ( 53, ·)\) | \(\chi_{ 96 } ( 73, ·)\) | \(\chi_{ 96 } ( 29, ·)\) | \(\chi_{ 96 } ( 49, ·)\) |
| \(\chi_{ 96 }(73, ·)\) | \(\chi_{ 96 } ( 73, ·)\) | \(\chi_{ 96 } ( 77, ·)\) | \(\chi_{ 96 } ( 49, ·)\) | \(\chi_{ 96 } ( 53, ·)\) | \(\chi_{ 96 } ( 25, ·)\) | \(\chi_{ 96 } ( 29, ·)\) | \(\chi_{ 96 } ( 1, ·)\) | \(\chi_{ 96 } ( 5, ·)\) |
| \(\chi_{ 96 }(77, ·)\) | \(\chi_{ 96 } ( 77, ·)\) | \(\chi_{ 96 } ( 1, ·)\) | \(\chi_{ 96 } ( 53, ·)\) | \(\chi_{ 96 } ( 73, ·)\) | \(\chi_{ 96 } ( 29, ·)\) | \(\chi_{ 96 } ( 49, ·)\) | \(\chi_{ 96 } ( 5, ·)\) | \(\chi_{ 96 } ( 25, ·)\) |
| \(\chi_{ 96 }(49, ·)\) | \(\chi_{ 96 } ( 49, ·)\) | \(\chi_{ 96 } ( 53, ·)\) | \(\chi_{ 96 } ( 25, ·)\) | \(\chi_{ 96 } ( 29, ·)\) | \(\chi_{ 96 } ( 1, ·)\) | \(\chi_{ 96 } ( 5, ·)\) | \(\chi_{ 96 } ( 73, ·)\) | \(\chi_{ 96 } ( 77, ·)\) |
| \(\chi_{ 96 }(53, ·)\) | \(\chi_{ 96 } ( 53, ·)\) | \(\chi_{ 96 } ( 73, ·)\) | \(\chi_{ 96 } ( 29, ·)\) | \(\chi_{ 96 } ( 49, ·)\) | \(\chi_{ 96 } ( 5, ·)\) | \(\chi_{ 96 } ( 25, ·)\) | \(\chi_{ 96 } ( 77, ·)\) | \(\chi_{ 96 } ( 1, ·)\) |
| \(\chi_{ 96 }(25, ·)\) | \(\chi_{ 96 } ( 25, ·)\) | \(\chi_{ 96 } ( 29, ·)\) | \(\chi_{ 96 } ( 1, ·)\) | \(\chi_{ 96 } ( 5, ·)\) | \(\chi_{ 96 } ( 73, ·)\) | \(\chi_{ 96 } ( 77, ·)\) | \(\chi_{ 96 } ( 49, ·)\) | \(\chi_{ 96 } ( 53, ·)\) |
| \(\chi_{ 96 }(29, ·)\) | \(\chi_{ 96 } ( 29, ·)\) | \(\chi_{ 96 } ( 49, ·)\) | \(\chi_{ 96 } ( 5, ·)\) | \(\chi_{ 96 } ( 25, ·)\) | \(\chi_{ 96 } ( 77, ·)\) | \(\chi_{ 96 } ( 1, ·)\) | \(\chi_{ 96 } ( 53, ·)\) | \(\chi_{ 96 } ( 73, ·)\) |