Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut +\mathstrut 8 x^{4} \) \(\mathstrut -\mathstrut 8 x^{3} \) \(\mathstrut +\mathstrut 22 x^{2} \) \(\mathstrut -\mathstrut 22 x \) \(\mathstrut +\mathstrut 29 \)
| $\times$ | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 16, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 19, ·)\) | \(\chi_{ 35 } ( 24, ·)\) | \(\chi_{ 35 } ( 11, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 35 }(1, ·)\) | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 16, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 19, ·)\) | \(\chi_{ 35 } ( 24, ·)\) | \(\chi_{ 35 } ( 11, ·)\) |
| \(\chi_{ 35 }(16, ·)\) | \(\chi_{ 35 } ( 16, ·)\) | \(\chi_{ 35 } ( 11, ·)\) | \(\chi_{ 35 } ( 19, ·)\) | \(\chi_{ 35 } ( 24, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 1, ·)\) |
| \(\chi_{ 35 }(34, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 19, ·)\) | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 16, ·)\) | \(\chi_{ 35 } ( 11, ·)\) | \(\chi_{ 35 } ( 24, ·)\) |
| \(\chi_{ 35 }(19, ·)\) | \(\chi_{ 35 } ( 19, ·)\) | \(\chi_{ 35 } ( 24, ·)\) | \(\chi_{ 35 } ( 16, ·)\) | \(\chi_{ 35 } ( 11, ·)\) | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 34, ·)\) |
| \(\chi_{ 35 }(24, ·)\) | \(\chi_{ 35 } ( 24, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 11, ·)\) | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 16, ·)\) | \(\chi_{ 35 } ( 19, ·)\) |
| \(\chi_{ 35 }(11, ·)\) | \(\chi_{ 35 } ( 11, ·)\) | \(\chi_{ 35 } ( 1, ·)\) | \(\chi_{ 35 } ( 24, ·)\) | \(\chi_{ 35 } ( 34, ·)\) | \(\chi_{ 35 } ( 19, ·)\) | \(\chi_{ 35 } ( 16, ·)\) |