Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{4} - 15x^{2} + 1 \)
| $\times$ | \(\chi_{ 221 } ( 1, ·)\) | \(\chi_{ 221 } ( 220, ·)\) | \(\chi_{ 221 } ( 118, ·)\) | \(\chi_{ 221 } ( 103, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 221 }(1, ·)\) | \(\chi_{ 221 } ( 1, ·)\) | \(\chi_{ 221 } ( 220, ·)\) | \(\chi_{ 221 } ( 118, ·)\) | \(\chi_{ 221 } ( 103, ·)\) |
| \(\chi_{ 221 }(220, ·)\) | \(\chi_{ 221 } ( 220, ·)\) | \(\chi_{ 221 } ( 1, ·)\) | \(\chi_{ 221 } ( 103, ·)\) | \(\chi_{ 221 } ( 118, ·)\) |
| \(\chi_{ 221 }(118, ·)\) | \(\chi_{ 221 } ( 118, ·)\) | \(\chi_{ 221 } ( 103, ·)\) | \(\chi_{ 221 } ( 1, ·)\) | \(\chi_{ 221 } ( 220, ·)\) |
| \(\chi_{ 221 }(103, ·)\) | \(\chi_{ 221 } ( 103, ·)\) | \(\chi_{ 221 } ( 118, ·)\) | \(\chi_{ 221 } ( 220, ·)\) | \(\chi_{ 221 } ( 1, ·)\) |