Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - x^{3} + 16x^{2} - 16x + 61 \)
| $\times$ | \(\chi_{ 65 } ( 1, ·)\) | \(\chi_{ 65 } ( 12, ·)\) | \(\chi_{ 65 } ( 14, ·)\) | \(\chi_{ 65 } ( 38, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 65 }(1, ·)\) | \(\chi_{ 65 } ( 1, ·)\) | \(\chi_{ 65 } ( 12, ·)\) | \(\chi_{ 65 } ( 14, ·)\) | \(\chi_{ 65 } ( 38, ·)\) |
| \(\chi_{ 65 }(12, ·)\) | \(\chi_{ 65 } ( 12, ·)\) | \(\chi_{ 65 } ( 14, ·)\) | \(\chi_{ 65 } ( 38, ·)\) | \(\chi_{ 65 } ( 1, ·)\) |
| \(\chi_{ 65 }(14, ·)\) | \(\chi_{ 65 } ( 14, ·)\) | \(\chi_{ 65 } ( 38, ·)\) | \(\chi_{ 65 } ( 1, ·)\) | \(\chi_{ 65 } ( 12, ·)\) |
| \(\chi_{ 65 }(38, ·)\) | \(\chi_{ 65 } ( 38, ·)\) | \(\chi_{ 65 } ( 1, ·)\) | \(\chi_{ 65 } ( 12, ·)\) | \(\chi_{ 65 } ( 14, ·)\) |