Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} - 17 x^{2} + 36 \)
| $\times$ | \(\chi_{ 145 } ( 1, ·)\) | \(\chi_{ 145 } ( 144, ·)\) | \(\chi_{ 145 } ( 59, ·)\) | \(\chi_{ 145 } ( 86, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 145 }(1, ·)\) | \(\chi_{ 145 } ( 1, ·)\) | \(\chi_{ 145 } ( 144, ·)\) | \(\chi_{ 145 } ( 59, ·)\) | \(\chi_{ 145 } ( 86, ·)\) |
| \(\chi_{ 145 }(144, ·)\) | \(\chi_{ 145 } ( 144, ·)\) | \(\chi_{ 145 } ( 1, ·)\) | \(\chi_{ 145 } ( 86, ·)\) | \(\chi_{ 145 } ( 59, ·)\) |
| \(\chi_{ 145 }(59, ·)\) | \(\chi_{ 145 } ( 59, ·)\) | \(\chi_{ 145 } ( 86, ·)\) | \(\chi_{ 145 } ( 1, ·)\) | \(\chi_{ 145 } ( 144, ·)\) |
| \(\chi_{ 145 }(86, ·)\) | \(\chi_{ 145 } ( 86, ·)\) | \(\chi_{ 145 } ( 59, ·)\) | \(\chi_{ 145 } ( 144, ·)\) | \(\chi_{ 145 } ( 1, ·)\) |