Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut +\mathstrut 34 x^{2} \) \(\mathstrut +\mathstrut 272 \)
| $\times$ | \(\chi_{ 136 } ( 1, ·)\) | \(\chi_{ 136 } ( 115, ·)\) | \(\chi_{ 136 } ( 123, ·)\) | \(\chi_{ 136 } ( 33, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 136 }(1, ·)\) | \(\chi_{ 136 } ( 1, ·)\) | \(\chi_{ 136 } ( 115, ·)\) | \(\chi_{ 136 } ( 123, ·)\) | \(\chi_{ 136 } ( 33, ·)\) |
| \(\chi_{ 136 }(115, ·)\) | \(\chi_{ 136 } ( 115, ·)\) | \(\chi_{ 136 } ( 33, ·)\) | \(\chi_{ 136 } ( 1, ·)\) | \(\chi_{ 136 } ( 123, ·)\) |
| \(\chi_{ 136 }(123, ·)\) | \(\chi_{ 136 } ( 123, ·)\) | \(\chi_{ 136 } ( 1, ·)\) | \(\chi_{ 136 } ( 33, ·)\) | \(\chi_{ 136 } ( 115, ·)\) |
| \(\chi_{ 136 }(33, ·)\) | \(\chi_{ 136 } ( 33, ·)\) | \(\chi_{ 136 } ( 123, ·)\) | \(\chi_{ 136 } ( 115, ·)\) | \(\chi_{ 136 } ( 1, ·)\) |