Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - 2x^{3} - 13x^{2} + 14x + 19 \)
| $\times$ | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 49, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 120 }(1, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 49, ·)\) |
| \(\chi_{ 120 }(11, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 59, ·)\) |
| \(\chi_{ 120 }(59, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 11, ·)\) |
| \(\chi_{ 120 }(49, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 1, ·)\) |