Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 2 x \) \(\mathstrut +\mathstrut 4 \)
| $\times$ | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 20, ·)\) | \(\chi_{ 21 } ( 13, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 21 }(1, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 20, ·)\) | \(\chi_{ 21 } ( 13, ·)\) |
| \(\chi_{ 21 }(8, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 13, ·)\) | \(\chi_{ 21 } ( 20, ·)\) |
| \(\chi_{ 21 }(20, ·)\) | \(\chi_{ 21 } ( 20, ·)\) | \(\chi_{ 21 } ( 13, ·)\) | \(\chi_{ 21 } ( 1, ·)\) | \(\chi_{ 21 } ( 8, ·)\) |
| \(\chi_{ 21 }(13, ·)\) | \(\chi_{ 21 } ( 13, ·)\) | \(\chi_{ 21 } ( 20, ·)\) | \(\chi_{ 21 } ( 8, ·)\) | \(\chi_{ 21 } ( 1, ·)\) |