Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{6} - x^{5} - 62x^{4} + 55x^{3} + 631x^{2} + 48x - 944 \)
| $\times$ | \(\chi_{ 273 } ( 1, ·)\) | \(\chi_{ 273 } ( 256, ·)\) | \(\chi_{ 273 } ( 68, ·)\) | \(\chi_{ 273 } ( 16, ·)\) | \(\chi_{ 273 } ( 209, ·)\) | \(\chi_{ 273 } ( 269, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 273 }(1, ·)\) | \(\chi_{ 273 } ( 1, ·)\) | \(\chi_{ 273 } ( 256, ·)\) | \(\chi_{ 273 } ( 68, ·)\) | \(\chi_{ 273 } ( 16, ·)\) | \(\chi_{ 273 } ( 209, ·)\) | \(\chi_{ 273 } ( 269, ·)\) |
| \(\chi_{ 273 }(256, ·)\) | \(\chi_{ 273 } ( 256, ·)\) | \(\chi_{ 273 } ( 16, ·)\) | \(\chi_{ 273 } ( 209, ·)\) | \(\chi_{ 273 } ( 1, ·)\) | \(\chi_{ 273 } ( 269, ·)\) | \(\chi_{ 273 } ( 68, ·)\) |
| \(\chi_{ 273 }(68, ·)\) | \(\chi_{ 273 } ( 68, ·)\) | \(\chi_{ 273 } ( 209, ·)\) | \(\chi_{ 273 } ( 256, ·)\) | \(\chi_{ 273 } ( 269, ·)\) | \(\chi_{ 273 } ( 16, ·)\) | \(\chi_{ 273 } ( 1, ·)\) |
| \(\chi_{ 273 }(16, ·)\) | \(\chi_{ 273 } ( 16, ·)\) | \(\chi_{ 273 } ( 1, ·)\) | \(\chi_{ 273 } ( 269, ·)\) | \(\chi_{ 273 } ( 256, ·)\) | \(\chi_{ 273 } ( 68, ·)\) | \(\chi_{ 273 } ( 209, ·)\) |
| \(\chi_{ 273 }(209, ·)\) | \(\chi_{ 273 } ( 209, ·)\) | \(\chi_{ 273 } ( 269, ·)\) | \(\chi_{ 273 } ( 16, ·)\) | \(\chi_{ 273 } ( 68, ·)\) | \(\chi_{ 273 } ( 1, ·)\) | \(\chi_{ 273 } ( 256, ·)\) |
| \(\chi_{ 273 }(269, ·)\) | \(\chi_{ 273 } ( 269, ·)\) | \(\chi_{ 273 } ( 68, ·)\) | \(\chi_{ 273 } ( 1, ·)\) | \(\chi_{ 273 } ( 209, ·)\) | \(\chi_{ 273 } ( 256, ·)\) | \(\chi_{ 273 } ( 16, ·)\) |