Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} + 15x^{2} + 256 \)
| $\times$ | \(\chi_{ 799 } ( 1, ·)\) | \(\chi_{ 799 } ( 424, ·)\) | \(\chi_{ 799 } ( 798, ·)\) | \(\chi_{ 799 } ( 375, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 799 }(1, ·)\) | \(\chi_{ 799 } ( 1, ·)\) | \(\chi_{ 799 } ( 424, ·)\) | \(\chi_{ 799 } ( 798, ·)\) | \(\chi_{ 799 } ( 375, ·)\) |
| \(\chi_{ 799 }(424, ·)\) | \(\chi_{ 799 } ( 424, ·)\) | \(\chi_{ 799 } ( 1, ·)\) | \(\chi_{ 799 } ( 375, ·)\) | \(\chi_{ 799 } ( 798, ·)\) |
| \(\chi_{ 799 }(798, ·)\) | \(\chi_{ 799 } ( 798, ·)\) | \(\chi_{ 799 } ( 375, ·)\) | \(\chi_{ 799 } ( 1, ·)\) | \(\chi_{ 799 } ( 424, ·)\) |
| \(\chi_{ 799 }(375, ·)\) | \(\chi_{ 799 } ( 375, ·)\) | \(\chi_{ 799 } ( 798, ·)\) | \(\chi_{ 799 } ( 424, ·)\) | \(\chi_{ 799 } ( 1, ·)\) |