Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut +\mathstrut 8 x^{4} \) \(\mathstrut -\mathstrut 9 x^{3} \) \(\mathstrut +\mathstrut 6 x^{2} \) \(\mathstrut +\mathstrut 10 x \) \(\mathstrut +\mathstrut 25 \)
| $\times$ | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 38, ·)\) | \(\chi_{ 39 } ( 17, ·)\) | \(\chi_{ 39 } ( 23, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 39 }(1, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 38, ·)\) | \(\chi_{ 39 } ( 17, ·)\) | \(\chi_{ 39 } ( 23, ·)\) |
| \(\chi_{ 39 }(16, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 23, ·)\) | \(\chi_{ 39 } ( 38, ·)\) | \(\chi_{ 39 } ( 17, ·)\) |
| \(\chi_{ 39 }(22, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 17, ·)\) | \(\chi_{ 39 } ( 23, ·)\) | \(\chi_{ 39 } ( 38, ·)\) |
| \(\chi_{ 39 }(38, ·)\) | \(\chi_{ 39 } ( 38, ·)\) | \(\chi_{ 39 } ( 23, ·)\) | \(\chi_{ 39 } ( 17, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 16, ·)\) |
| \(\chi_{ 39 }(17, ·)\) | \(\chi_{ 39 } ( 17, ·)\) | \(\chi_{ 39 } ( 38, ·)\) | \(\chi_{ 39 } ( 23, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 1, ·)\) |
| \(\chi_{ 39 }(23, ·)\) | \(\chi_{ 39 } ( 23, ·)\) | \(\chi_{ 39 } ( 17, ·)\) | \(\chi_{ 39 } ( 38, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 22, ·)\) |