Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} + 6x^{2} + 16 \)
| $\times$ | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 13, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 41, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 56 }(1, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 13, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 41, ·)\) |
| \(\chi_{ 56 }(13, ·)\) | \(\chi_{ 56 } ( 13, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 41, ·)\) | \(\chi_{ 56 } ( 29, ·)\) |
| \(\chi_{ 56 }(29, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 41, ·)\) | \(\chi_{ 56 } ( 1, ·)\) | \(\chi_{ 56 } ( 13, ·)\) |
| \(\chi_{ 56 }(41, ·)\) | \(\chi_{ 56 } ( 41, ·)\) | \(\chi_{ 56 } ( 29, ·)\) | \(\chi_{ 56 } ( 13, ·)\) | \(\chi_{ 56 } ( 1, ·)\) |