Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} - x^{3} - 2 x^{2} - 3 x + 9 \)
| $\times$ | \(\chi_{ 33 } ( 1, ·)\) | \(\chi_{ 33 } ( 32, ·)\) | \(\chi_{ 33 } ( 10, ·)\) | \(\chi_{ 33 } ( 23, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 33 }(1, ·)\) | \(\chi_{ 33 } ( 1, ·)\) | \(\chi_{ 33 } ( 32, ·)\) | \(\chi_{ 33 } ( 10, ·)\) | \(\chi_{ 33 } ( 23, ·)\) |
| \(\chi_{ 33 }(32, ·)\) | \(\chi_{ 33 } ( 32, ·)\) | \(\chi_{ 33 } ( 1, ·)\) | \(\chi_{ 33 } ( 23, ·)\) | \(\chi_{ 33 } ( 10, ·)\) |
| \(\chi_{ 33 }(10, ·)\) | \(\chi_{ 33 } ( 10, ·)\) | \(\chi_{ 33 } ( 23, ·)\) | \(\chi_{ 33 } ( 1, ·)\) | \(\chi_{ 33 } ( 32, ·)\) |
| \(\chi_{ 33 }(23, ·)\) | \(\chi_{ 33 } ( 23, ·)\) | \(\chi_{ 33 } ( 10, ·)\) | \(\chi_{ 33 } ( 32, ·)\) | \(\chi_{ 33 } ( 1, ·)\) |