Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} - 37 x^{2} + 256 \)
| $\times$ | \(\chi_{ 345 } ( 1, ·)\) | \(\chi_{ 345 } ( 344, ·)\) | \(\chi_{ 345 } ( 139, ·)\) | \(\chi_{ 345 } ( 206, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 345 }(1, ·)\) | \(\chi_{ 345 } ( 1, ·)\) | \(\chi_{ 345 } ( 344, ·)\) | \(\chi_{ 345 } ( 139, ·)\) | \(\chi_{ 345 } ( 206, ·)\) |
| \(\chi_{ 345 }(344, ·)\) | \(\chi_{ 345 } ( 344, ·)\) | \(\chi_{ 345 } ( 1, ·)\) | \(\chi_{ 345 } ( 206, ·)\) | \(\chi_{ 345 } ( 139, ·)\) |
| \(\chi_{ 345 }(139, ·)\) | \(\chi_{ 345 } ( 139, ·)\) | \(\chi_{ 345 } ( 206, ·)\) | \(\chi_{ 345 } ( 1, ·)\) | \(\chi_{ 345 } ( 344, ·)\) |
| \(\chi_{ 345 }(206, ·)\) | \(\chi_{ 345 } ( 206, ·)\) | \(\chi_{ 345 } ( 139, ·)\) | \(\chi_{ 345 } ( 344, ·)\) | \(\chi_{ 345 } ( 1, ·)\) |