Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{3} - x^{2} - 336 x + 1719 \)
| $\times$ | \(\chi_{ 1009 } ( 1, ·)\) | \(\chi_{ 1009 } ( 634, ·)\) | \(\chi_{ 1009 } ( 374, ·)\) |
|---|---|---|---|
| \(\chi_{ 1009 }(1, ·)\) | \(\chi_{ 1009 } ( 1, ·)\) | \(\chi_{ 1009 } ( 634, ·)\) | \(\chi_{ 1009 } ( 374, ·)\) |
| \(\chi_{ 1009 }(634, ·)\) | \(\chi_{ 1009 } ( 634, ·)\) | \(\chi_{ 1009 } ( 374, ·)\) | \(\chi_{ 1009 } ( 1, ·)\) |
| \(\chi_{ 1009 }(374, ·)\) | \(\chi_{ 1009 } ( 374, ·)\) | \(\chi_{ 1009 } ( 1, ·)\) | \(\chi_{ 1009 } ( 634, ·)\) |