Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} + 25 \)
| $\times$ | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 31, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 40 }(1, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 31, ·)\) |
| \(\chi_{ 40 }(19, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 29, ·)\) |
| \(\chi_{ 40 }(29, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 19, ·)\) |
| \(\chi_{ 40 }(31, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 1, ·)\) |