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