Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{6} - x^{3} + 1 \)
| $\times$ | \(\chi_{ 9 } ( 1, ·)\) | \(\chi_{ 9 } ( 2, ·)\) | \(\chi_{ 9 } ( 4, ·)\) | \(\chi_{ 9 } ( 5, ·)\) | \(\chi_{ 9 } ( 7, ·)\) | \(\chi_{ 9 } ( 8, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 9 }(1, ·)\) | \(\chi_{ 9 } ( 1, ·)\) | \(\chi_{ 9 } ( 2, ·)\) | \(\chi_{ 9 } ( 4, ·)\) | \(\chi_{ 9 } ( 5, ·)\) | \(\chi_{ 9 } ( 7, ·)\) | \(\chi_{ 9 } ( 8, ·)\) |
| \(\chi_{ 9 }(2, ·)\) | \(\chi_{ 9 } ( 2, ·)\) | \(\chi_{ 9 } ( 4, ·)\) | \(\chi_{ 9 } ( 8, ·)\) | \(\chi_{ 9 } ( 1, ·)\) | \(\chi_{ 9 } ( 5, ·)\) | \(\chi_{ 9 } ( 7, ·)\) |
| \(\chi_{ 9 }(4, ·)\) | \(\chi_{ 9 } ( 4, ·)\) | \(\chi_{ 9 } ( 8, ·)\) | \(\chi_{ 9 } ( 7, ·)\) | \(\chi_{ 9 } ( 2, ·)\) | \(\chi_{ 9 } ( 1, ·)\) | \(\chi_{ 9 } ( 5, ·)\) |
| \(\chi_{ 9 }(5, ·)\) | \(\chi_{ 9 } ( 5, ·)\) | \(\chi_{ 9 } ( 1, ·)\) | \(\chi_{ 9 } ( 2, ·)\) | \(\chi_{ 9 } ( 7, ·)\) | \(\chi_{ 9 } ( 8, ·)\) | \(\chi_{ 9 } ( 4, ·)\) |
| \(\chi_{ 9 }(7, ·)\) | \(\chi_{ 9 } ( 7, ·)\) | \(\chi_{ 9 } ( 5, ·)\) | \(\chi_{ 9 } ( 1, ·)\) | \(\chi_{ 9 } ( 8, ·)\) | \(\chi_{ 9 } ( 4, ·)\) | \(\chi_{ 9 } ( 2, ·)\) |
| \(\chi_{ 9 }(8, ·)\) | \(\chi_{ 9 } ( 8, ·)\) | \(\chi_{ 9 } ( 7, ·)\) | \(\chi_{ 9 } ( 5, ·)\) | \(\chi_{ 9 } ( 4, ·)\) | \(\chi_{ 9 } ( 2, ·)\) | \(\chi_{ 9 } ( 1, ·)\) |