Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{3} - x^{2} - 342 x - 989 \)
| $\times$ | \(\chi_{ 1027 } ( 1, ·)\) | \(\chi_{ 1027 } ( 529, ·)\) | \(\chi_{ 1027 } ( 497, ·)\) |
|---|---|---|---|
| \(\chi_{ 1027 }(1, ·)\) | \(\chi_{ 1027 } ( 1, ·)\) | \(\chi_{ 1027 } ( 529, ·)\) | \(\chi_{ 1027 } ( 497, ·)\) |
| \(\chi_{ 1027 }(529, ·)\) | \(\chi_{ 1027 } ( 529, ·)\) | \(\chi_{ 1027 } ( 497, ·)\) | \(\chi_{ 1027 } ( 1, ·)\) |
| \(\chi_{ 1027 }(497, ·)\) | \(\chi_{ 1027 } ( 497, ·)\) | \(\chi_{ 1027 } ( 1, ·)\) | \(\chi_{ 1027 } ( 529, ·)\) |