Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{2} - 19 \)
| $\times$ | \(\chi_{ 76 } ( 1, ·)\) | \(\chi_{ 76 } ( 75, ·)\) |
|---|---|---|
| \(\chi_{ 76 }(1, ·)\) | \(\chi_{ 76 } ( 1, ·)\) | \(\chi_{ 76 } ( 75, ·)\) |
| \(\chi_{ 76 }(75, ·)\) | \(\chi_{ 76 } ( 75, ·)\) | \(\chi_{ 76 } ( 1, ·)\) |