Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - x^{2} + 1 \)
| $\times$ | \(\chi_{ 12 } ( 1, ·)\) | \(\chi_{ 12 } ( 11, ·)\) | \(\chi_{ 12 } ( 5, ·)\) | \(\chi_{ 12 } ( 7, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 12 }(1, ·)\) | \(\chi_{ 12 } ( 1, ·)\) | \(\chi_{ 12 } ( 11, ·)\) | \(\chi_{ 12 } ( 5, ·)\) | \(\chi_{ 12 } ( 7, ·)\) |
| \(\chi_{ 12 }(11, ·)\) | \(\chi_{ 12 } ( 11, ·)\) | \(\chi_{ 12 } ( 1, ·)\) | \(\chi_{ 12 } ( 7, ·)\) | \(\chi_{ 12 } ( 5, ·)\) |
| \(\chi_{ 12 }(5, ·)\) | \(\chi_{ 12 } ( 5, ·)\) | \(\chi_{ 12 } ( 7, ·)\) | \(\chi_{ 12 } ( 1, ·)\) | \(\chi_{ 12 } ( 11, ·)\) |
| \(\chi_{ 12 }(7, ·)\) | \(\chi_{ 12 } ( 7, ·)\) | \(\chi_{ 12 } ( 5, ·)\) | \(\chi_{ 12 } ( 11, ·)\) | \(\chi_{ 12 } ( 1, ·)\) |