Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{9} - 9x^{7} + 27x^{5} - 30x^{3} + 9x - 1 \)
| $\times$ | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 25, ·)\) |
|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 27 }(1, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 25, ·)\) |
| \(\chi_{ 27 }(4, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 19, ·)\) |
| \(\chi_{ 27 }(7, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 13, ·)\) |
| \(\chi_{ 27 }(10, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 7, ·)\) |
| \(\chi_{ 27 }(13, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 1, ·)\) |
| \(\chi_{ 27 }(16, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 22, ·)\) |
| \(\chi_{ 27 }(19, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 16, ·)\) |
| \(\chi_{ 27 }(22, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 10, ·)\) |
| \(\chi_{ 27 }(25, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 4, ·)\) |