Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - x^{3} - 31x^{2} + 76x - 20 \)
| $\times$ | \(\chi_{ 483 } ( 1, ·)\) | \(\chi_{ 483 } ( 160, ·)\) | \(\chi_{ 483 } ( 461, ·)\) | \(\chi_{ 483 } ( 344, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 483 }(1, ·)\) | \(\chi_{ 483 } ( 1, ·)\) | \(\chi_{ 483 } ( 160, ·)\) | \(\chi_{ 483 } ( 461, ·)\) | \(\chi_{ 483 } ( 344, ·)\) |
| \(\chi_{ 483 }(160, ·)\) | \(\chi_{ 483 } ( 160, ·)\) | \(\chi_{ 483 } ( 1, ·)\) | \(\chi_{ 483 } ( 344, ·)\) | \(\chi_{ 483 } ( 461, ·)\) |
| \(\chi_{ 483 }(461, ·)\) | \(\chi_{ 483 } ( 461, ·)\) | \(\chi_{ 483 } ( 344, ·)\) | \(\chi_{ 483 } ( 1, ·)\) | \(\chi_{ 483 } ( 160, ·)\) |
| \(\chi_{ 483 }(344, ·)\) | \(\chi_{ 483 } ( 344, ·)\) | \(\chi_{ 483 } ( 461, ·)\) | \(\chi_{ 483 } ( 160, ·)\) | \(\chi_{ 483 } ( 1, ·)\) |