Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut +\mathstrut 176 x^{2} \) \(\mathstrut -\mathstrut 176 x \) \(\mathstrut +\mathstrut 6301 \)
| $\times$ | \(\chi_{ 705 } ( 1, ·)\) | \(\chi_{ 705 } ( 424, ·)\) | \(\chi_{ 705 } ( 563, ·)\) | \(\chi_{ 705 } ( 422, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 705 }(1, ·)\) | \(\chi_{ 705 } ( 1, ·)\) | \(\chi_{ 705 } ( 424, ·)\) | \(\chi_{ 705 } ( 563, ·)\) | \(\chi_{ 705 } ( 422, ·)\) |
| \(\chi_{ 705 }(424, ·)\) | \(\chi_{ 705 } ( 424, ·)\) | \(\chi_{ 705 } ( 1, ·)\) | \(\chi_{ 705 } ( 422, ·)\) | \(\chi_{ 705 } ( 563, ·)\) |
| \(\chi_{ 705 }(563, ·)\) | \(\chi_{ 705 } ( 563, ·)\) | \(\chi_{ 705 } ( 422, ·)\) | \(\chi_{ 705 } ( 424, ·)\) | \(\chi_{ 705 } ( 1, ·)\) |
| \(\chi_{ 705 }(422, ·)\) | \(\chi_{ 705 } ( 422, ·)\) | \(\chi_{ 705 } ( 563, ·)\) | \(\chi_{ 705 } ( 1, ·)\) | \(\chi_{ 705 } ( 424, ·)\) |