Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{16} + 175 x^{8} + 625 \)
| $\times$ | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 53, ·)\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 80 }(1, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 53, ·)\) |
| \(\chi_{ 80 }(3, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 79, ·)\) |
| \(\chi_{ 80 }(71, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 3, ·)\) |
| \(\chi_{ 80 }(9, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 77, ·)\) |
| \(\chi_{ 80 }(79, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 27, ·)\) |
| \(\chi_{ 80 }(13, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 49, ·)\) |
| \(\chi_{ 80 }(77, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 1, ·)\) |
| \(\chi_{ 80 }(67, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 31, ·)\) |
| \(\chi_{ 80 }(27, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 71, ·)\) |
| \(\chi_{ 80 }(31, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 43, ·)\) |
| \(\chi_{ 80 }(37, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 41, ·)\) |
| \(\chi_{ 80 }(39, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 67, ·)\) |
| \(\chi_{ 80 }(41, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 13, ·)\) |
| \(\chi_{ 80 }(43, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 39, ·)\) |
| \(\chi_{ 80 }(49, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 9, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 37, ·)\) |
| \(\chi_{ 80 }(53, ·)\) | \(\chi_{ 80 } ( 53, ·)\) | \(\chi_{ 80 } ( 79, ·)\) | \(\chi_{ 80 } ( 3, ·)\) | \(\chi_{ 80 } ( 77, ·)\) | \(\chi_{ 80 } ( 27, ·)\) | \(\chi_{ 80 } ( 49, ·)\) | \(\chi_{ 80 } ( 1, ·)\) | \(\chi_{ 80 } ( 31, ·)\) | \(\chi_{ 80 } ( 71, ·)\) | \(\chi_{ 80 } ( 43, ·)\) | \(\chi_{ 80 } ( 41, ·)\) | \(\chi_{ 80 } ( 67, ·)\) | \(\chi_{ 80 } ( 13, ·)\) | \(\chi_{ 80 } ( 39, ·)\) | \(\chi_{ 80 } ( 37, ·)\) | \(\chi_{ 80 } ( 9, ·)\) |