Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut +\mathstrut 249 x^{2} \) \(\mathstrut +\mathstrut 251 x \) \(\mathstrut +\mathstrut 4943 \)
| $\times$ | \(\chi_{ 1001 } ( 1, ·)\) | \(\chi_{ 1001 } ( 538, ·)\) | \(\chi_{ 1001 } ( 307, ·)\) | \(\chi_{ 1001 } ( 155, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 1001 }(1, ·)\) | \(\chi_{ 1001 } ( 1, ·)\) | \(\chi_{ 1001 } ( 538, ·)\) | \(\chi_{ 1001 } ( 307, ·)\) | \(\chi_{ 1001 } ( 155, ·)\) |
| \(\chi_{ 1001 }(538, ·)\) | \(\chi_{ 1001 } ( 538, ·)\) | \(\chi_{ 1001 } ( 155, ·)\) | \(\chi_{ 1001 } ( 1, ·)\) | \(\chi_{ 1001 } ( 307, ·)\) |
| \(\chi_{ 1001 }(307, ·)\) | \(\chi_{ 1001 } ( 307, ·)\) | \(\chi_{ 1001 } ( 1, ·)\) | \(\chi_{ 1001 } ( 155, ·)\) | \(\chi_{ 1001 } ( 538, ·)\) |
| \(\chi_{ 1001 }(155, ·)\) | \(\chi_{ 1001 } ( 155, ·)\) | \(\chi_{ 1001 } ( 307, ·)\) | \(\chi_{ 1001 } ( 538, ·)\) | \(\chi_{ 1001 } ( 1, ·)\) |