Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{2} + 17 \)
| $\times$ | \(\chi_{ 68 } ( 1, ·)\) | \(\chi_{ 68 } ( 67, ·)\) |
|---|---|---|
| \(\chi_{ 68 }(1, ·)\) | \(\chi_{ 68 } ( 1, ·)\) | \(\chi_{ 68 } ( 67, ·)\) |
| \(\chi_{ 68 }(67, ·)\) | \(\chi_{ 68 } ( 67, ·)\) | \(\chi_{ 68 } ( 1, ·)\) |