Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - 21x^{2} + 16 \)
| $\times$ | \(\chi_{ 377 } ( 1, ·)\) | \(\chi_{ 377 } ( 144, ·)\) | \(\chi_{ 377 } ( 376, ·)\) | \(\chi_{ 377 } ( 233, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 377 }(1, ·)\) | \(\chi_{ 377 } ( 1, ·)\) | \(\chi_{ 377 } ( 144, ·)\) | \(\chi_{ 377 } ( 376, ·)\) | \(\chi_{ 377 } ( 233, ·)\) |
| \(\chi_{ 377 }(144, ·)\) | \(\chi_{ 377 } ( 144, ·)\) | \(\chi_{ 377 } ( 1, ·)\) | \(\chi_{ 377 } ( 233, ·)\) | \(\chi_{ 377 } ( 376, ·)\) |
| \(\chi_{ 377 }(376, ·)\) | \(\chi_{ 377 } ( 376, ·)\) | \(\chi_{ 377 } ( 233, ·)\) | \(\chi_{ 377 } ( 1, ·)\) | \(\chi_{ 377 } ( 144, ·)\) |
| \(\chi_{ 377 }(233, ·)\) | \(\chi_{ 377 } ( 233, ·)\) | \(\chi_{ 377 } ( 376, ·)\) | \(\chi_{ 377 } ( 144, ·)\) | \(\chi_{ 377 } ( 1, ·)\) |