Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut 9 x^{2} \) \(\mathstrut +\mathstrut 4 \)
| $\times$ | \(\chi_{ 65 } ( 1, ·)\) | \(\chi_{ 65 } ( 64, ·)\) | \(\chi_{ 65 } ( 51, ·)\) | \(\chi_{ 65 } ( 14, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 65 }(1, ·)\) | \(\chi_{ 65 } ( 1, ·)\) | \(\chi_{ 65 } ( 64, ·)\) | \(\chi_{ 65 } ( 51, ·)\) | \(\chi_{ 65 } ( 14, ·)\) |
| \(\chi_{ 65 }(64, ·)\) | \(\chi_{ 65 } ( 64, ·)\) | \(\chi_{ 65 } ( 1, ·)\) | \(\chi_{ 65 } ( 14, ·)\) | \(\chi_{ 65 } ( 51, ·)\) |
| \(\chi_{ 65 }(51, ·)\) | \(\chi_{ 65 } ( 51, ·)\) | \(\chi_{ 65 } ( 14, ·)\) | \(\chi_{ 65 } ( 1, ·)\) | \(\chi_{ 65 } ( 64, ·)\) |
| \(\chi_{ 65 }(14, ·)\) | \(\chi_{ 65 } ( 14, ·)\) | \(\chi_{ 65 } ( 51, ·)\) | \(\chi_{ 65 } ( 64, ·)\) | \(\chi_{ 65 } ( 1, ·)\) |