Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut 11 x^{2} \) \(\mathstrut +\mathstrut 9 \)
| $\times$ | \(\chi_{ 85 } ( 1, ·)\) | \(\chi_{ 85 } ( 16, ·)\) | \(\chi_{ 85 } ( 84, ·)\) | \(\chi_{ 85 } ( 69, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 85 }(1, ·)\) | \(\chi_{ 85 } ( 1, ·)\) | \(\chi_{ 85 } ( 16, ·)\) | \(\chi_{ 85 } ( 84, ·)\) | \(\chi_{ 85 } ( 69, ·)\) |
| \(\chi_{ 85 }(16, ·)\) | \(\chi_{ 85 } ( 16, ·)\) | \(\chi_{ 85 } ( 1, ·)\) | \(\chi_{ 85 } ( 69, ·)\) | \(\chi_{ 85 } ( 84, ·)\) |
| \(\chi_{ 85 }(84, ·)\) | \(\chi_{ 85 } ( 84, ·)\) | \(\chi_{ 85 } ( 69, ·)\) | \(\chi_{ 85 } ( 1, ·)\) | \(\chi_{ 85 } ( 16, ·)\) |
| \(\chi_{ 85 }(69, ·)\) | \(\chi_{ 85 } ( 69, ·)\) | \(\chi_{ 85 } ( 84, ·)\) | \(\chi_{ 85 } ( 16, ·)\) | \(\chi_{ 85 } ( 1, ·)\) |