Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} + 39x^{2} + 117 \)
| $\times$ | \(\chi_{ 156 } ( 1, ·)\) | \(\chi_{ 156 } ( 83, ·)\) | \(\chi_{ 156 } ( 47, ·)\) | \(\chi_{ 156 } ( 25, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 156 }(1, ·)\) | \(\chi_{ 156 } ( 1, ·)\) | \(\chi_{ 156 } ( 83, ·)\) | \(\chi_{ 156 } ( 47, ·)\) | \(\chi_{ 156 } ( 25, ·)\) |
| \(\chi_{ 156 }(83, ·)\) | \(\chi_{ 156 } ( 83, ·)\) | \(\chi_{ 156 } ( 25, ·)\) | \(\chi_{ 156 } ( 1, ·)\) | \(\chi_{ 156 } ( 47, ·)\) |
| \(\chi_{ 156 }(47, ·)\) | \(\chi_{ 156 } ( 47, ·)\) | \(\chi_{ 156 } ( 1, ·)\) | \(\chi_{ 156 } ( 25, ·)\) | \(\chi_{ 156 } ( 83, ·)\) |
| \(\chi_{ 156 }(25, ·)\) | \(\chi_{ 156 } ( 25, ·)\) | \(\chi_{ 156 } ( 47, ·)\) | \(\chi_{ 156 } ( 83, ·)\) | \(\chi_{ 156 } ( 1, ·)\) |