Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} + 27 x^{2} + 256 \)
| $\times$ | \(\chi_{ 295 } ( 1, ·)\) | \(\chi_{ 295 } ( 176, ·)\) | \(\chi_{ 295 } ( 294, ·)\) | \(\chi_{ 295 } ( 119, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 295 }(1, ·)\) | \(\chi_{ 295 } ( 1, ·)\) | \(\chi_{ 295 } ( 176, ·)\) | \(\chi_{ 295 } ( 294, ·)\) | \(\chi_{ 295 } ( 119, ·)\) |
| \(\chi_{ 295 }(176, ·)\) | \(\chi_{ 295 } ( 176, ·)\) | \(\chi_{ 295 } ( 1, ·)\) | \(\chi_{ 295 } ( 119, ·)\) | \(\chi_{ 295 } ( 294, ·)\) |
| \(\chi_{ 295 }(294, ·)\) | \(\chi_{ 295 } ( 294, ·)\) | \(\chi_{ 295 } ( 119, ·)\) | \(\chi_{ 295 } ( 1, ·)\) | \(\chi_{ 295 } ( 176, ·)\) |
| \(\chi_{ 295 }(119, ·)\) | \(\chi_{ 295 } ( 119, ·)\) | \(\chi_{ 295 } ( 294, ·)\) | \(\chi_{ 295 } ( 176, ·)\) | \(\chi_{ 295 } ( 1, ·)\) |