Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 4 x \) \(\mathstrut -\mathstrut 1 \)
$\times$ | \(\chi_{ 13 } ( 1, ·)\) | \(\chi_{ 13 } ( 3, ·)\) | \(\chi_{ 13 } ( 9, ·)\) |
---|---|---|---|
\(\chi_{ 13 }(1, ·)\) | \(\chi_{ 13 } ( 1, ·)\) | \(\chi_{ 13 } ( 3, ·)\) | \(\chi_{ 13 } ( 9, ·)\) |
\(\chi_{ 13 }(3, ·)\) | \(\chi_{ 13 } ( 3, ·)\) | \(\chi_{ 13 } ( 9, ·)\) | \(\chi_{ 13 } ( 1, ·)\) |
\(\chi_{ 13 }(9, ·)\) | \(\chi_{ 13 } ( 9, ·)\) | \(\chi_{ 13 } ( 1, ·)\) | \(\chi_{ 13 } ( 3, ·)\) |