Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 3334 x \) \(\mathstrut -\mathstrut 10744 \)
| $\times$ | \(\chi_{ 10003 } ( 1, ·)\) | \(\chi_{ 10003 } ( 2193, ·)\) | \(\chi_{ 10003 } ( 7809, ·)\) |
|---|---|---|---|
| \(\chi_{ 10003 }(1, ·)\) | \(\chi_{ 10003 } ( 1, ·)\) | \(\chi_{ 10003 } ( 2193, ·)\) | \(\chi_{ 10003 } ( 7809, ·)\) |
| \(\chi_{ 10003 }(2193, ·)\) | \(\chi_{ 10003 } ( 2193, ·)\) | \(\chi_{ 10003 } ( 7809, ·)\) | \(\chi_{ 10003 } ( 1, ·)\) |
| \(\chi_{ 10003 }(7809, ·)\) | \(\chi_{ 10003 } ( 7809, ·)\) | \(\chi_{ 10003 } ( 1, ·)\) | \(\chi_{ 10003 } ( 2193, ·)\) |