Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{16} + 47 x^{8} + 1 \)
| $\times$ | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 61, ·)\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 80 }(1, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 61, ·)\) |
| \(\chi_{ 80 }(69, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 49, ·)\) |
| \(\chi_{ 80 }(71, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 11, ·)\) |
| \(\chi_{ 80 }(9, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 69, ·)\) |
| \(\chi_{ 80 }(11, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 31, ·)\) |
| \(\chi_{ 80 }(79, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 19, ·)\) |
| \(\chi_{ 80 }(19, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 39, ·)\) |
| \(\chi_{ 80 }(21, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 1, ·)\) |
| \(\chi_{ 80 }(29, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 9, ·)\) |
| \(\chi_{ 80 }(31, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 51, ·)\) |
| \(\chi_{ 80 }(39, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 59, ·)\) |
| \(\chi_{ 80 }(41, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 21, ·)\) |
| \(\chi_{ 80 }(49, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 29, ·)\) |
| \(\chi_{ 80 }(51, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 71, ·)\) |
| \(\chi_{ 80 }(59, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 79, ·)\) |
| \(\chi_{ 80 }(61, ·)\) | \(\chi_{ 80 } ( 61, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 11, ·)\) | \(\chi_{ 80 } ( 69, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 19, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 51, ·)\) | \(\chi_{ 80 } ( 59, ·)\) | \(\chi_{ 80 } ( 21, ·)\) | \(\chi_{ 80 } ( 29, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 41, ·)\) |