Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{16} - x^{12} + x^{8} - x^{4} + 1 \)
| $\times$ | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 39, ·)\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 40 }(1, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 39, ·)\) |
| \(\chi_{ 40 }(3, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 37, ·)\) |
| \(\chi_{ 40 }(7, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 33, ·)\) |
| \(\chi_{ 40 }(9, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 31, ·)\) |
| \(\chi_{ 40 }(11, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 29, ·)\) |
| \(\chi_{ 40 }(13, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 27, ·)\) |
| \(\chi_{ 40 }(17, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 23, ·)\) |
| \(\chi_{ 40 }(19, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 21, ·)\) |
| \(\chi_{ 40 }(21, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 19, ·)\) |
| \(\chi_{ 40 }(23, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 17, ·)\) |
| \(\chi_{ 40 }(27, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 13, ·)\) |
| \(\chi_{ 40 }(29, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 11, ·)\) |
| \(\chi_{ 40 }(31, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 9, ·)\) |
| \(\chi_{ 40 }(33, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 7, ·)\) |
| \(\chi_{ 40 }(37, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 3, ·)\) |
| \(\chi_{ 40 }(39, ·)\) | \(\chi_{ 40 } ( 39, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 33, ·)\) | \(\chi_{ 40 } ( 31, ·)\) | \(\chi_{ 40 } ( 29, ·)\) | \(\chi_{ 40 } ( 27, ·)\) | \(\chi_{ 40 } ( 23, ·)\) | \(\chi_{ 40 } ( 21, ·)\) | \(\chi_{ 40 } ( 19, ·)\) | \(\chi_{ 40 } ( 17, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 11, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 7, ·)\) | \(\chi_{ 40 } ( 3, ·)\) | \(\chi_{ 40 } ( 1, ·)\) |