Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut 5 x^{2} \) \(\mathstrut +\mathstrut 1 \)
| $\times$ | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 55, ·)\) | \(\chi_{ 84 } ( 41, ·)\) | \(\chi_{ 84 } ( 71, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 84 }(1, ·)\) | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 55, ·)\) | \(\chi_{ 84 } ( 41, ·)\) | \(\chi_{ 84 } ( 71, ·)\) |
| \(\chi_{ 84 }(55, ·)\) | \(\chi_{ 84 } ( 55, ·)\) | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 71, ·)\) | \(\chi_{ 84 } ( 41, ·)\) |
| \(\chi_{ 84 }(41, ·)\) | \(\chi_{ 84 } ( 41, ·)\) | \(\chi_{ 84 } ( 71, ·)\) | \(\chi_{ 84 } ( 1, ·)\) | \(\chi_{ 84 } ( 55, ·)\) |
| \(\chi_{ 84 }(71, ·)\) | \(\chi_{ 84 } ( 71, ·)\) | \(\chi_{ 84 } ( 41, ·)\) | \(\chi_{ 84 } ( 55, ·)\) | \(\chi_{ 84 } ( 1, ·)\) |