Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} + 39 x^{2} + 256\) 
| $\times$ | \(\chi_{ 497 } ( 1, ·)\) | \(\chi_{ 497 } ( 496, ·)\) | \(\chi_{ 497 } ( 356, ·)\) | \(\chi_{ 497 } ( 141, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 497 }(1, ·)\) | \(\chi_{ 497 } ( 1, ·)\) | \(\chi_{ 497 } ( 496, ·)\) | \(\chi_{ 497 } ( 356, ·)\) | \(\chi_{ 497 } ( 141, ·)\) |
| \(\chi_{ 497 }(496, ·)\) | \(\chi_{ 497 } ( 496, ·)\) | \(\chi_{ 497 } ( 1, ·)\) | \(\chi_{ 497 } ( 141, ·)\) | \(\chi_{ 497 } ( 356, ·)\) |
| \(\chi_{ 497 }(356, ·)\) | \(\chi_{ 497 } ( 356, ·)\) | \(\chi_{ 497 } ( 141, ·)\) | \(\chi_{ 497 } ( 1, ·)\) | \(\chi_{ 497 } ( 496, ·)\) |
| \(\chi_{ 497 }(141, ·)\) | \(\chi_{ 497 } ( 141, ·)\) | \(\chi_{ 497 } ( 356, ·)\) | \(\chi_{ 497 } ( 496, ·)\) | \(\chi_{ 497 } ( 1, ·)\) |