Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} + 9 x^{4} - 5 x^{3} + 36 x^{2} - 12 x + 8 \)
| $\times$ | \(\chi_{ 63 } ( 1, ·)\) | \(\chi_{ 63 } ( 34, ·)\) | \(\chi_{ 63 } ( 22, ·)\) | \(\chi_{ 63 } ( 55, ·)\) | \(\chi_{ 63 } ( 43, ·)\) | \(\chi_{ 63 } ( 13, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 63 }(1, ·)\) | \(\chi_{ 63 } ( 1, ·)\) | \(\chi_{ 63 } ( 34, ·)\) | \(\chi_{ 63 } ( 22, ·)\) | \(\chi_{ 63 } ( 55, ·)\) | \(\chi_{ 63 } ( 43, ·)\) | \(\chi_{ 63 } ( 13, ·)\) |
| \(\chi_{ 63 }(34, ·)\) | \(\chi_{ 63 } ( 34, ·)\) | \(\chi_{ 63 } ( 22, ·)\) | \(\chi_{ 63 } ( 55, ·)\) | \(\chi_{ 63 } ( 43, ·)\) | \(\chi_{ 63 } ( 13, ·)\) | \(\chi_{ 63 } ( 1, ·)\) |
| \(\chi_{ 63 }(22, ·)\) | \(\chi_{ 63 } ( 22, ·)\) | \(\chi_{ 63 } ( 55, ·)\) | \(\chi_{ 63 } ( 43, ·)\) | \(\chi_{ 63 } ( 13, ·)\) | \(\chi_{ 63 } ( 1, ·)\) | \(\chi_{ 63 } ( 34, ·)\) |
| \(\chi_{ 63 }(55, ·)\) | \(\chi_{ 63 } ( 55, ·)\) | \(\chi_{ 63 } ( 43, ·)\) | \(\chi_{ 63 } ( 13, ·)\) | \(\chi_{ 63 } ( 1, ·)\) | \(\chi_{ 63 } ( 34, ·)\) | \(\chi_{ 63 } ( 22, ·)\) |
| \(\chi_{ 63 }(43, ·)\) | \(\chi_{ 63 } ( 43, ·)\) | \(\chi_{ 63 } ( 13, ·)\) | \(\chi_{ 63 } ( 1, ·)\) | \(\chi_{ 63 } ( 34, ·)\) | \(\chi_{ 63 } ( 22, ·)\) | \(\chi_{ 63 } ( 55, ·)\) |
| \(\chi_{ 63 }(13, ·)\) | \(\chi_{ 63 } ( 13, ·)\) | \(\chi_{ 63 } ( 1, ·)\) | \(\chi_{ 63 } ( 34, ·)\) | \(\chi_{ 63 } ( 22, ·)\) | \(\chi_{ 63 } ( 55, ·)\) | \(\chi_{ 63 } ( 43, ·)\) |