Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 2 x \) \(\mathstrut +\mathstrut 1 \)
$\times$ | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 4, ·)\) |
---|---|---|---|
\(\chi_{ 7 }(1, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 4, ·)\) |
\(\chi_{ 7 }(2, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 1, ·)\) |
\(\chi_{ 7 }(4, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 2, ·)\) |