Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut +\mathstrut 10 x^{4} \) \(\mathstrut -\mathstrut 7 x^{3} \) \(\mathstrut +\mathstrut 75 x^{2} \) \(\mathstrut -\mathstrut 16 x \) \(\mathstrut +\mathstrut 239 \)
| $\times$ | \(\chi_{ 133 } ( 1, ·)\) | \(\chi_{ 133 } ( 18, ·)\) | \(\chi_{ 133 } ( 113, ·)\) | \(\chi_{ 133 } ( 37, ·)\) | \(\chi_{ 133 } ( 39, ·)\) | \(\chi_{ 133 } ( 58, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 133 }(1, ·)\) | \(\chi_{ 133 } ( 1, ·)\) | \(\chi_{ 133 } ( 18, ·)\) | \(\chi_{ 133 } ( 113, ·)\) | \(\chi_{ 133 } ( 37, ·)\) | \(\chi_{ 133 } ( 39, ·)\) | \(\chi_{ 133 } ( 58, ·)\) |
| \(\chi_{ 133 }(18, ·)\) | \(\chi_{ 133 } ( 18, ·)\) | \(\chi_{ 133 } ( 58, ·)\) | \(\chi_{ 133 } ( 39, ·)\) | \(\chi_{ 133 } ( 1, ·)\) | \(\chi_{ 133 } ( 37, ·)\) | \(\chi_{ 133 } ( 113, ·)\) |
| \(\chi_{ 133 }(113, ·)\) | \(\chi_{ 133 } ( 113, ·)\) | \(\chi_{ 133 } ( 39, ·)\) | \(\chi_{ 133 } ( 1, ·)\) | \(\chi_{ 133 } ( 58, ·)\) | \(\chi_{ 133 } ( 18, ·)\) | \(\chi_{ 133 } ( 37, ·)\) |
| \(\chi_{ 133 }(37, ·)\) | \(\chi_{ 133 } ( 37, ·)\) | \(\chi_{ 133 } ( 1, ·)\) | \(\chi_{ 133 } ( 58, ·)\) | \(\chi_{ 133 } ( 39, ·)\) | \(\chi_{ 133 } ( 113, ·)\) | \(\chi_{ 133 } ( 18, ·)\) |
| \(\chi_{ 133 }(39, ·)\) | \(\chi_{ 133 } ( 39, ·)\) | \(\chi_{ 133 } ( 37, ·)\) | \(\chi_{ 133 } ( 18, ·)\) | \(\chi_{ 133 } ( 113, ·)\) | \(\chi_{ 133 } ( 58, ·)\) | \(\chi_{ 133 } ( 1, ·)\) |
| \(\chi_{ 133 }(58, ·)\) | \(\chi_{ 133 } ( 58, ·)\) | \(\chi_{ 133 } ( 113, ·)\) | \(\chi_{ 133 } ( 37, ·)\) | \(\chi_{ 133 } ( 18, ·)\) | \(\chi_{ 133 } ( 1, ·)\) | \(\chi_{ 133 } ( 39, ·)\) |