Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} + 60x^{2} + 810 \)
| $\times$ | \(\chi_{ 240 } ( 1, ·)\) | \(\chi_{ 240 } ( 227, ·)\) | \(\chi_{ 240 } ( 203, ·)\) | \(\chi_{ 240 } ( 169, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 240 }(1, ·)\) | \(\chi_{ 240 } ( 1, ·)\) | \(\chi_{ 240 } ( 227, ·)\) | \(\chi_{ 240 } ( 203, ·)\) | \(\chi_{ 240 } ( 169, ·)\) |
| \(\chi_{ 240 }(227, ·)\) | \(\chi_{ 240 } ( 227, ·)\) | \(\chi_{ 240 } ( 169, ·)\) | \(\chi_{ 240 } ( 1, ·)\) | \(\chi_{ 240 } ( 203, ·)\) |
| \(\chi_{ 240 }(203, ·)\) | \(\chi_{ 240 } ( 203, ·)\) | \(\chi_{ 240 } ( 1, ·)\) | \(\chi_{ 240 } ( 169, ·)\) | \(\chi_{ 240 } ( 227, ·)\) |
| \(\chi_{ 240 }(169, ·)\) | \(\chi_{ 240 } ( 169, ·)\) | \(\chi_{ 240 } ( 203, ·)\) | \(\chi_{ 240 } ( 227, ·)\) | \(\chi_{ 240 } ( 1, ·)\) |