Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{2} - 10 \)
| $\times$ | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 29, ·)\) |
|---|---|---|
| \(\chi_{ 40 }(1, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 29, ·)\) |
| \(\chi_{ 40 }(29, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 1, ·)\) |