Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{18} - x^{9} + 1 \)
| $\times$ | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 26, ·)\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 27 }(1, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 26, ·)\) |
| \(\chi_{ 27 }(2, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 25, ·)\) |
| \(\chi_{ 27 }(4, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 23, ·)\) |
| \(\chi_{ 27 }(5, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 22, ·)\) |
| \(\chi_{ 27 }(7, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 20, ·)\) |
| \(\chi_{ 27 }(8, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 19, ·)\) |
| \(\chi_{ 27 }(10, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 17, ·)\) |
| \(\chi_{ 27 }(11, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 16, ·)\) |
| \(\chi_{ 27 }(13, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 14, ·)\) |
| \(\chi_{ 27 }(14, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 13, ·)\) |
| \(\chi_{ 27 }(16, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 11, ·)\) |
| \(\chi_{ 27 }(17, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 10, ·)\) |
| \(\chi_{ 27 }(19, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 8, ·)\) |
| \(\chi_{ 27 }(20, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 7, ·)\) |
| \(\chi_{ 27 }(22, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 5, ·)\) |
| \(\chi_{ 27 }(23, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 4, ·)\) |
| \(\chi_{ 27 }(25, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 1, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 2, ·)\) |
| \(\chi_{ 27 }(26, ·)\) | \(\chi_{ 27 } ( 26, ·)\) | \(\chi_{ 27 } ( 25, ·)\) | \(\chi_{ 27 } ( 23, ·)\) | \(\chi_{ 27 } ( 22, ·)\) | \(\chi_{ 27 } ( 20, ·)\) | \(\chi_{ 27 } ( 19, ·)\) | \(\chi_{ 27 } ( 17, ·)\) | \(\chi_{ 27 } ( 16, ·)\) | \(\chi_{ 27 } ( 14, ·)\) | \(\chi_{ 27 } ( 13, ·)\) | \(\chi_{ 27 } ( 11, ·)\) | \(\chi_{ 27 } ( 10, ·)\) | \(\chi_{ 27 } ( 8, ·)\) | \(\chi_{ 27 } ( 7, ·)\) | \(\chi_{ 27 } ( 5, ·)\) | \(\chi_{ 27 } ( 4, ·)\) | \(\chi_{ 27 } ( 2, ·)\) | \(\chi_{ 27 } ( 1, ·)\) |