Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut +\mathstrut 249 x^{2} \) \(\mathstrut +\mathstrut x \) \(\mathstrut +\mathstrut 15046 \)
| $\times$ | \(\chi_{ 1003 } ( 1, ·)\) | \(\chi_{ 1003 } ( 412, ·)\) | \(\chi_{ 1003 } ( 237, ·)\) | \(\chi_{ 1003 } ( 353, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 1003 }(1, ·)\) | \(\chi_{ 1003 } ( 1, ·)\) | \(\chi_{ 1003 } ( 412, ·)\) | \(\chi_{ 1003 } ( 237, ·)\) | \(\chi_{ 1003 } ( 353, ·)\) |
| \(\chi_{ 1003 }(412, ·)\) | \(\chi_{ 1003 } ( 412, ·)\) | \(\chi_{ 1003 } ( 237, ·)\) | \(\chi_{ 1003 } ( 353, ·)\) | \(\chi_{ 1003 } ( 1, ·)\) |
| \(\chi_{ 1003 }(237, ·)\) | \(\chi_{ 1003 } ( 237, ·)\) | \(\chi_{ 1003 } ( 353, ·)\) | \(\chi_{ 1003 } ( 1, ·)\) | \(\chi_{ 1003 } ( 412, ·)\) |
| \(\chi_{ 1003 }(353, ·)\) | \(\chi_{ 1003 } ( 353, ·)\) | \(\chi_{ 1003 } ( 1, ·)\) | \(\chi_{ 1003 } ( 412, ·)\) | \(\chi_{ 1003 } ( 237, ·)\) |