Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{8} \) \(\mathstrut +\mathstrut 1 \)
| $\times$ | \(\chi_{ 16 } ( 1, ·)\) | \(\chi_{ 16 } ( 3, ·)\) | \(\chi_{ 16 } ( 5, ·)\) | \(\chi_{ 16 } ( 7, ·)\) | \(\chi_{ 16 } ( 9, ·)\) | \(\chi_{ 16 } ( 11, ·)\) | \(\chi_{ 16 } ( 13, ·)\) | \(\chi_{ 16 } ( 15, ·)\) |
|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 16 }(1, ·)\) | \(\chi_{ 16 } ( 1, ·)\) | \(\chi_{ 16 } ( 3, ·)\) | \(\chi_{ 16 } ( 5, ·)\) | \(\chi_{ 16 } ( 7, ·)\) | \(\chi_{ 16 } ( 9, ·)\) | \(\chi_{ 16 } ( 11, ·)\) | \(\chi_{ 16 } ( 13, ·)\) | \(\chi_{ 16 } ( 15, ·)\) |
| \(\chi_{ 16 }(3, ·)\) | \(\chi_{ 16 } ( 3, ·)\) | \(\chi_{ 16 } ( 9, ·)\) | \(\chi_{ 16 } ( 15, ·)\) | \(\chi_{ 16 } ( 5, ·)\) | \(\chi_{ 16 } ( 11, ·)\) | \(\chi_{ 16 } ( 1, ·)\) | \(\chi_{ 16 } ( 7, ·)\) | \(\chi_{ 16 } ( 13, ·)\) |
| \(\chi_{ 16 }(5, ·)\) | \(\chi_{ 16 } ( 5, ·)\) | \(\chi_{ 16 } ( 15, ·)\) | \(\chi_{ 16 } ( 9, ·)\) | \(\chi_{ 16 } ( 3, ·)\) | \(\chi_{ 16 } ( 13, ·)\) | \(\chi_{ 16 } ( 7, ·)\) | \(\chi_{ 16 } ( 1, ·)\) | \(\chi_{ 16 } ( 11, ·)\) |
| \(\chi_{ 16 }(7, ·)\) | \(\chi_{ 16 } ( 7, ·)\) | \(\chi_{ 16 } ( 5, ·)\) | \(\chi_{ 16 } ( 3, ·)\) | \(\chi_{ 16 } ( 1, ·)\) | \(\chi_{ 16 } ( 15, ·)\) | \(\chi_{ 16 } ( 13, ·)\) | \(\chi_{ 16 } ( 11, ·)\) | \(\chi_{ 16 } ( 9, ·)\) |
| \(\chi_{ 16 }(9, ·)\) | \(\chi_{ 16 } ( 9, ·)\) | \(\chi_{ 16 } ( 11, ·)\) | \(\chi_{ 16 } ( 13, ·)\) | \(\chi_{ 16 } ( 15, ·)\) | \(\chi_{ 16 } ( 1, ·)\) | \(\chi_{ 16 } ( 3, ·)\) | \(\chi_{ 16 } ( 5, ·)\) | \(\chi_{ 16 } ( 7, ·)\) |
| \(\chi_{ 16 }(11, ·)\) | \(\chi_{ 16 } ( 11, ·)\) | \(\chi_{ 16 } ( 1, ·)\) | \(\chi_{ 16 } ( 7, ·)\) | \(\chi_{ 16 } ( 13, ·)\) | \(\chi_{ 16 } ( 3, ·)\) | \(\chi_{ 16 } ( 9, ·)\) | \(\chi_{ 16 } ( 15, ·)\) | \(\chi_{ 16 } ( 5, ·)\) |
| \(\chi_{ 16 }(13, ·)\) | \(\chi_{ 16 } ( 13, ·)\) | \(\chi_{ 16 } ( 7, ·)\) | \(\chi_{ 16 } ( 1, ·)\) | \(\chi_{ 16 } ( 11, ·)\) | \(\chi_{ 16 } ( 5, ·)\) | \(\chi_{ 16 } ( 15, ·)\) | \(\chi_{ 16 } ( 9, ·)\) | \(\chi_{ 16 } ( 3, ·)\) |
| \(\chi_{ 16 }(15, ·)\) | \(\chi_{ 16 } ( 15, ·)\) | \(\chi_{ 16 } ( 13, ·)\) | \(\chi_{ 16 } ( 11, ·)\) | \(\chi_{ 16 } ( 9, ·)\) | \(\chi_{ 16 } ( 7, ·)\) | \(\chi_{ 16 } ( 5, ·)\) | \(\chi_{ 16 } ( 3, ·)\) | \(\chi_{ 16 } ( 1, ·)\) |