Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{16} + 1\) 
| $\times$ | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 31, ·)\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 32 }(1, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 31, ·)\) |
| \(\chi_{ 32 }(3, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 29, ·)\) |
| \(\chi_{ 32 }(5, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 27, ·)\) |
| \(\chi_{ 32 }(7, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 25, ·)\) |
| \(\chi_{ 32 }(9, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 23, ·)\) |
| \(\chi_{ 32 }(11, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 21, ·)\) |
| \(\chi_{ 32 }(13, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 19, ·)\) |
| \(\chi_{ 32 }(15, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 17, ·)\) |
| \(\chi_{ 32 }(17, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 15, ·)\) |
| \(\chi_{ 32 }(19, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 13, ·)\) |
| \(\chi_{ 32 }(21, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 11, ·)\) |
| \(\chi_{ 32 }(23, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 9, ·)\) |
| \(\chi_{ 32 }(25, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 7, ·)\) |
| \(\chi_{ 32 }(27, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 5, ·)\) |
| \(\chi_{ 32 }(29, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 1, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 3, ·)\) |
| \(\chi_{ 32 }(31, ·)\) | \(\chi_{ 32 } ( 31, ·)\) | \(\chi_{ 32 } ( 29, ·)\) | \(\chi_{ 32 } ( 27, ·)\) | \(\chi_{ 32 } ( 25, ·)\) | \(\chi_{ 32 } ( 23, ·)\) | \(\chi_{ 32 } ( 21, ·)\) | \(\chi_{ 32 } ( 19, ·)\) | \(\chi_{ 32 } ( 17, ·)\) | \(\chi_{ 32 } ( 15, ·)\) | \(\chi_{ 32 } ( 13, ·)\) | \(\chi_{ 32 } ( 11, ·)\) | \(\chi_{ 32 } ( 9, ·)\) | \(\chi_{ 32 } ( 7, ·)\) | \(\chi_{ 32 } ( 5, ·)\) | \(\chi_{ 32 } ( 3, ·)\) | \(\chi_{ 32 } ( 1, ·)\) |