Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} - x^{3} + 5 x^{2} + 2 x + 4 \)
| $\times$ | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 29, ·)\) | \(\chi_{ 35 } ( 6, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 35 }(1, ·)\) | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 29, ·)\) | \(\chi_{ 35 } ( 6, ·)\) |
| \(\chi_{ 35 }(34, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 6, ·)\) | \(\chi_{ 35 } ( 29, ·)\) |
| \(\chi_{ 35 }(29, ·)\) | \(\chi_{ 35 } ( 29, ·)\) | \(\chi_{ 35 } ( 6, ·)\) | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 34, ·)\) |
| \(\chi_{ 35 }(6, ·)\) | \(\chi_{ 35 } ( 6, ·)\) | \(\chi_{ 35 } ( 29, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 1, ·)\) |