Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut +\mathstrut 5 x^{4} \) \(\mathstrut +\mathstrut 6 x^{3} \) \(\mathstrut +\mathstrut 15 x^{2} \) \(\mathstrut +\mathstrut 4 x \) \(\mathstrut +\mathstrut 1 \)
| $\times$ | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 35, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 29, ·)\) | \(\chi_{ 39 } ( 14, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 39 }(1, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 35, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 29, ·)\) | \(\chi_{ 39 } ( 14, ·)\) |
| \(\chi_{ 39 }(16, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 14, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 35, ·)\) | \(\chi_{ 39 } ( 29, ·)\) |
| \(\chi_{ 39 }(35, ·)\) | \(\chi_{ 39 } ( 35, ·)\) | \(\chi_{ 39 } ( 14, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 29, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 22, ·)\) |
| \(\chi_{ 39 }(22, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 29, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 14, ·)\) | \(\chi_{ 39 } ( 35, ·)\) |
| \(\chi_{ 39 }(29, ·)\) | \(\chi_{ 39 } ( 29, ·)\) | \(\chi_{ 39 } ( 35, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 14, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 16, ·)\) |
| \(\chi_{ 39 }(14, ·)\) | \(\chi_{ 39 } ( 14, ·)\) | \(\chi_{ 39 } ( 29, ·)\) | \(\chi_{ 39 } ( 22, ·)\) | \(\chi_{ 39 } ( 35, ·)\) | \(\chi_{ 39 } ( 16, ·)\) | \(\chi_{ 39 } ( 1, ·)\) |