Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - x^{3} - 11x^{2} - 9x + 3 \)
| $\times$ | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 8, ·)\) | \(\chi_{ 39 } ( 5, ·)\) | \(\chi_{ 39 } ( 25, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 39 }(1, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 8, ·)\) | \(\chi_{ 39 } ( 5, ·)\) | \(\chi_{ 39 } ( 25, ·)\) |
| \(\chi_{ 39 }(8, ·)\) | \(\chi_{ 39 } ( 8, ·)\) | \(\chi_{ 39 } ( 25, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 5, ·)\) |
| \(\chi_{ 39 }(5, ·)\) | \(\chi_{ 39 } ( 5, ·)\) | \(\chi_{ 39 } ( 1, ·)\) | \(\chi_{ 39 } ( 25, ·)\) | \(\chi_{ 39 } ( 8, ·)\) |
| \(\chi_{ 39 }(25, ·)\) | \(\chi_{ 39 } ( 25, ·)\) | \(\chi_{ 39 } ( 5, ·)\) | \(\chi_{ 39 } ( 8, ·)\) | \(\chi_{ 39 } ( 1, ·)\) |