Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} + 76x^{2} + 722 \)
| $\times$ | \(\chi_{ 304 } ( 1, ·)\) | \(\chi_{ 304 } ( 153, ·)\) | \(\chi_{ 304 } ( 37, ·)\) | \(\chi_{ 304 } ( 189, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 304 }(1, ·)\) | \(\chi_{ 304 } ( 1, ·)\) | \(\chi_{ 304 } ( 153, ·)\) | \(\chi_{ 304 } ( 37, ·)\) | \(\chi_{ 304 } ( 189, ·)\) |
| \(\chi_{ 304 }(153, ·)\) | \(\chi_{ 304 } ( 153, ·)\) | \(\chi_{ 304 } ( 1, ·)\) | \(\chi_{ 304 } ( 189, ·)\) | \(\chi_{ 304 } ( 37, ·)\) |
| \(\chi_{ 304 }(37, ·)\) | \(\chi_{ 304 } ( 37, ·)\) | \(\chi_{ 304 } ( 189, ·)\) | \(\chi_{ 304 } ( 153, ·)\) | \(\chi_{ 304 } ( 1, ·)\) |
| \(\chi_{ 304 }(189, ·)\) | \(\chi_{ 304 } ( 189, ·)\) | \(\chi_{ 304 } ( 37, ·)\) | \(\chi_{ 304 } ( 1, ·)\) | \(\chi_{ 304 } ( 153, ·)\) |