Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} + 7x^{2} + 9 \)
| $\times$ | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 27, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 25, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 52 }(1, ·)\) | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 27, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 25, ·)\) |
| \(\chi_{ 52 }(27, ·)\) | \(\chi_{ 52 } ( 27, ·)\) | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 25, ·)\) | \(\chi_{ 52 } ( 51, ·)\) |
| \(\chi_{ 52 }(51, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 25, ·)\) | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 27, ·)\) |
| \(\chi_{ 52 }(25, ·)\) | \(\chi_{ 52 } ( 25, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 27, ·)\) | \(\chi_{ 52 } ( 1, ·)\) |