Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{6} - x^{5} - 35x^{4} + 23x^{3} + 315x^{2} - 121x - 631 \)
| $\times$ | \(\chi_{ 287 } ( 1, ·)\) | \(\chi_{ 287 } ( 163, ·)\) | \(\chi_{ 287 } ( 165, ·)\) | \(\chi_{ 287 } ( 81, ·)\) | \(\chi_{ 287 } ( 247, ·)\) | \(\chi_{ 287 } ( 204, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 287 }(1, ·)\) | \(\chi_{ 287 } ( 1, ·)\) | \(\chi_{ 287 } ( 163, ·)\) | \(\chi_{ 287 } ( 165, ·)\) | \(\chi_{ 287 } ( 81, ·)\) | \(\chi_{ 287 } ( 247, ·)\) | \(\chi_{ 287 } ( 204, ·)\) |
| \(\chi_{ 287 }(163, ·)\) | \(\chi_{ 287 } ( 163, ·)\) | \(\chi_{ 287 } ( 165, ·)\) | \(\chi_{ 287 } ( 204, ·)\) | \(\chi_{ 287 } ( 1, ·)\) | \(\chi_{ 287 } ( 81, ·)\) | \(\chi_{ 287 } ( 247, ·)\) |
| \(\chi_{ 287 }(165, ·)\) | \(\chi_{ 287 } ( 165, ·)\) | \(\chi_{ 287 } ( 204, ·)\) | \(\chi_{ 287 } ( 247, ·)\) | \(\chi_{ 287 } ( 163, ·)\) | \(\chi_{ 287 } ( 1, ·)\) | \(\chi_{ 287 } ( 81, ·)\) |
| \(\chi_{ 287 }(81, ·)\) | \(\chi_{ 287 } ( 81, ·)\) | \(\chi_{ 287 } ( 1, ·)\) | \(\chi_{ 287 } ( 163, ·)\) | \(\chi_{ 287 } ( 247, ·)\) | \(\chi_{ 287 } ( 204, ·)\) | \(\chi_{ 287 } ( 165, ·)\) |
| \(\chi_{ 287 }(247, ·)\) | \(\chi_{ 287 } ( 247, ·)\) | \(\chi_{ 287 } ( 81, ·)\) | \(\chi_{ 287 } ( 1, ·)\) | \(\chi_{ 287 } ( 204, ·)\) | \(\chi_{ 287 } ( 165, ·)\) | \(\chi_{ 287 } ( 163, ·)\) |
| \(\chi_{ 287 }(204, ·)\) | \(\chi_{ 287 } ( 204, ·)\) | \(\chi_{ 287 } ( 247, ·)\) | \(\chi_{ 287 } ( 81, ·)\) | \(\chi_{ 287 } ( 165, ·)\) | \(\chi_{ 287 } ( 163, ·)\) | \(\chi_{ 287 } ( 1, ·)\) |