Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{12} - x^{6} + 1 \)
| $\times$ | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 31, ·)\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 36 }(1, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 31, ·)\) |
| \(\chi_{ 36 }(35, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 5, ·)\) |
| \(\chi_{ 36 }(5, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 11, ·)\) |
| \(\chi_{ 36 }(7, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 1, ·)\) |
| \(\chi_{ 36 }(11, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 17, ·)\) |
| \(\chi_{ 36 }(13, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 7, ·)\) |
| \(\chi_{ 36 }(17, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 23, ·)\) |
| \(\chi_{ 36 }(19, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 13, ·)\) |
| \(\chi_{ 36 }(23, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 29, ·)\) |
| \(\chi_{ 36 }(25, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 19, ·)\) |
| \(\chi_{ 36 }(29, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 25, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 35, ·)\) |
| \(\chi_{ 36 }(31, ·)\) | \(\chi_{ 36 } ( 31, ·)\) | \(\chi_{ 36 } ( 5, ·)\) | \(\chi_{ 36 } ( 11, ·)\) | \(\chi_{ 36 } ( 1, ·)\) | \(\chi_{ 36 } ( 17, ·)\) | \(\chi_{ 36 } ( 7, ·)\) | \(\chi_{ 36 } ( 23, ·)\) | \(\chi_{ 36 } ( 13, ·)\) | \(\chi_{ 36 } ( 29, ·)\) | \(\chi_{ 36 } ( 19, ·)\) | \(\chi_{ 36 } ( 35, ·)\) | \(\chi_{ 36 } ( 25, ·)\) |