Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut +\mathstrut x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut +\mathstrut x^{2} \) \(\mathstrut -\mathstrut x \) \(\mathstrut +\mathstrut 1 \)
| $\times$ | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 6, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 7 }(1, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 6, ·)\) |
| \(\chi_{ 7 }(2, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 5, ·)\) |
| \(\chi_{ 7 }(3, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 4, ·)\) |
| \(\chi_{ 7 }(4, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 3, ·)\) |
| \(\chi_{ 7 }(5, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 1, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 2, ·)\) |
| \(\chi_{ 7 }(6, ·)\) | \(\chi_{ 7 } ( 6, ·)\) | \(\chi_{ 7 } ( 5, ·)\) | \(\chi_{ 7 } ( 4, ·)\) | \(\chi_{ 7 } ( 3, ·)\) | \(\chi_{ 7 } ( 2, ·)\) | \(\chi_{ 7 } ( 1, ·)\) |