Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - 19x^{2} + 1 \)
| $\times$ | \(\chi_{ 357 } ( 1, ·)\) | \(\chi_{ 357 } ( 188, ·)\) | \(\chi_{ 357 } ( 356, ·)\) | \(\chi_{ 357 } ( 169, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 357 }(1, ·)\) | \(\chi_{ 357 } ( 1, ·)\) | \(\chi_{ 357 } ( 188, ·)\) | \(\chi_{ 357 } ( 356, ·)\) | \(\chi_{ 357 } ( 169, ·)\) |
| \(\chi_{ 357 }(188, ·)\) | \(\chi_{ 357 } ( 188, ·)\) | \(\chi_{ 357 } ( 1, ·)\) | \(\chi_{ 357 } ( 169, ·)\) | \(\chi_{ 357 } ( 356, ·)\) |
| \(\chi_{ 357 }(356, ·)\) | \(\chi_{ 357 } ( 356, ·)\) | \(\chi_{ 357 } ( 169, ·)\) | \(\chi_{ 357 } ( 1, ·)\) | \(\chi_{ 357 } ( 188, ·)\) |
| \(\chi_{ 357 }(169, ·)\) | \(\chi_{ 357 } ( 169, ·)\) | \(\chi_{ 357 } ( 356, ·)\) | \(\chi_{ 357 } ( 188, ·)\) | \(\chi_{ 357 } ( 1, ·)\) |