Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut -\mathstrut 14 x^{4} \) \(\mathstrut +\mathstrut 9 x^{3} \) \(\mathstrut +\mathstrut 35 x^{2} \) \(\mathstrut -\mathstrut 16 x \) \(\mathstrut -\mathstrut 1 \)
| $\times$ | \(\chi_{ 91 } ( 1, ·)\) | \(\chi_{ 91 } ( 64, ·)\) | \(\chi_{ 91 } ( 51, ·)\) | \(\chi_{ 91 } ( 53, ·)\) | \(\chi_{ 91 } ( 25, ·)\) | \(\chi_{ 91 } ( 79, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 91 }(1, ·)\) | \(\chi_{ 91 } ( 1, ·)\) | \(\chi_{ 91 } ( 64, ·)\) | \(\chi_{ 91 } ( 51, ·)\) | \(\chi_{ 91 } ( 53, ·)\) | \(\chi_{ 91 } ( 25, ·)\) | \(\chi_{ 91 } ( 79, ·)\) |
| \(\chi_{ 91 }(64, ·)\) | \(\chi_{ 91 } ( 64, ·)\) | \(\chi_{ 91 } ( 1, ·)\) | \(\chi_{ 91 } ( 79, ·)\) | \(\chi_{ 91 } ( 25, ·)\) | \(\chi_{ 91 } ( 53, ·)\) | \(\chi_{ 91 } ( 51, ·)\) |
| \(\chi_{ 91 }(51, ·)\) | \(\chi_{ 91 } ( 51, ·)\) | \(\chi_{ 91 } ( 79, ·)\) | \(\chi_{ 91 } ( 53, ·)\) | \(\chi_{ 91 } ( 64, ·)\) | \(\chi_{ 91 } ( 1, ·)\) | \(\chi_{ 91 } ( 25, ·)\) |
| \(\chi_{ 91 }(53, ·)\) | \(\chi_{ 91 } ( 53, ·)\) | \(\chi_{ 91 } ( 25, ·)\) | \(\chi_{ 91 } ( 64, ·)\) | \(\chi_{ 91 } ( 79, ·)\) | \(\chi_{ 91 } ( 51, ·)\) | \(\chi_{ 91 } ( 1, ·)\) |
| \(\chi_{ 91 }(25, ·)\) | \(\chi_{ 91 } ( 25, ·)\) | \(\chi_{ 91 } ( 53, ·)\) | \(\chi_{ 91 } ( 1, ·)\) | \(\chi_{ 91 } ( 51, ·)\) | \(\chi_{ 91 } ( 79, ·)\) | \(\chi_{ 91 } ( 64, ·)\) |
| \(\chi_{ 91 }(79, ·)\) | \(\chi_{ 91 } ( 79, ·)\) | \(\chi_{ 91 } ( 51, ·)\) | \(\chi_{ 91 } ( 25, ·)\) | \(\chi_{ 91 } ( 1, ·)\) | \(\chi_{ 91 } ( 64, ·)\) | \(\chi_{ 91 } ( 53, ·)\) |