Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} + 9 x^{2} + 16 \)
| $\times$ | \(\chi_{ 68 } ( 1, ·)\) | \(\chi_{ 68 } ( 67, ·)\) | \(\chi_{ 68 } ( 35, ·)\) | \(\chi_{ 68 } ( 33, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 68 }(1, ·)\) | \(\chi_{ 68 } ( 1, ·)\) | \(\chi_{ 68 } ( 67, ·)\) | \(\chi_{ 68 } ( 35, ·)\) | \(\chi_{ 68 } ( 33, ·)\) |
| \(\chi_{ 68 }(67, ·)\) | \(\chi_{ 68 } ( 67, ·)\) | \(\chi_{ 68 } ( 1, ·)\) | \(\chi_{ 68 } ( 33, ·)\) | \(\chi_{ 68 } ( 35, ·)\) |
| \(\chi_{ 68 }(35, ·)\) | \(\chi_{ 68 } ( 35, ·)\) | \(\chi_{ 68 } ( 33, ·)\) | \(\chi_{ 68 } ( 1, ·)\) | \(\chi_{ 68 } ( 67, ·)\) |
| \(\chi_{ 68 }(33, ·)\) | \(\chi_{ 68 } ( 33, ·)\) | \(\chi_{ 68 } ( 35, ·)\) | \(\chi_{ 68 } ( 67, ·)\) | \(\chi_{ 68 } ( 1, ·)\) |