Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{3} - x^{2} - 4 x - 1\) 
| $\times$ | \(\chi_{ 13 } ( 1, ·)\) | \(\chi_{ 13 } ( 3, ·)\) | \(\chi_{ 13 } ( 9, ·)\) |
|---|---|---|---|
| \(\chi_{ 13 }(1, ·)\) | \(\chi_{ 13 } ( 1, ·)\) | \(\chi_{ 13 } ( 3, ·)\) | \(\chi_{ 13 } ( 9, ·)\) |
| \(\chi_{ 13 }(3, ·)\) | \(\chi_{ 13 } ( 3, ·)\) | \(\chi_{ 13 } ( 9, ·)\) | \(\chi_{ 13 } ( 1, ·)\) |
| \(\chi_{ 13 }(9, ·)\) | \(\chi_{ 13 } ( 9, ·)\) | \(\chi_{ 13 } ( 1, ·)\) | \(\chi_{ 13 } ( 3, ·)\) |