Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} + 255 x^{2} + 13005 \)
| $\times$ | \(\chi_{ 1020 } ( 1, ·)\) | \(\chi_{ 1020 } ( 409, ·)\) | \(\chi_{ 1020 } ( 203, ·)\) | \(\chi_{ 1020 } ( 407, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 1020 }(1, ·)\) | \(\chi_{ 1020 } ( 1, ·)\) | \(\chi_{ 1020 } ( 409, ·)\) | \(\chi_{ 1020 } ( 203, ·)\) | \(\chi_{ 1020 } ( 407, ·)\) |
| \(\chi_{ 1020 }(409, ·)\) | \(\chi_{ 1020 } ( 409, ·)\) | \(\chi_{ 1020 } ( 1, ·)\) | \(\chi_{ 1020 } ( 407, ·)\) | \(\chi_{ 1020 } ( 203, ·)\) |
| \(\chi_{ 1020 }(203, ·)\) | \(\chi_{ 1020 } ( 203, ·)\) | \(\chi_{ 1020 } ( 407, ·)\) | \(\chi_{ 1020 } ( 409, ·)\) | \(\chi_{ 1020 } ( 1, ·)\) |
| \(\chi_{ 1020 }(407, ·)\) | \(\chi_{ 1020 } ( 407, ·)\) | \(\chi_{ 1020 } ( 203, ·)\) | \(\chi_{ 1020 } ( 1, ·)\) | \(\chi_{ 1020 } ( 409, ·)\) |