Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut +\mathstrut 10 x^{2} \) \(\mathstrut +\mathstrut 20 \)
| $\times$ | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 37, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 40 }(1, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 37, ·)\) |
| \(\chi_{ 40 }(9, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 13, ·)\) |
| \(\chi_{ 40 }(13, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 9, ·)\) | \(\chi_{ 40 } ( 1, ·)\) |
| \(\chi_{ 40 }(37, ·)\) | \(\chi_{ 40 } ( 37, ·)\) | \(\chi_{ 40 } ( 13, ·)\) | \(\chi_{ 40 } ( 1, ·)\) | \(\chi_{ 40 } ( 9, ·)\) |