Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut +\mathstrut 13 x^{4} \) \(\mathstrut +\mathstrut 50 x^{2} \) \(\mathstrut +\mathstrut 49 \)
| $\times$ | \(\chi_{ 76 } ( 1, ·)\) | \(\chi_{ 76 } ( 49, ·)\) | \(\chi_{ 76 } ( 7, ·)\) | \(\chi_{ 76 } ( 39, ·)\) | \(\chi_{ 76 } ( 11, ·)\) | \(\chi_{ 76 } ( 45, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 76 }(1, ·)\) | \(\chi_{ 76 } ( 1, ·)\) | \(\chi_{ 76 } ( 49, ·)\) | \(\chi_{ 76 } ( 7, ·)\) | \(\chi_{ 76 } ( 39, ·)\) | \(\chi_{ 76 } ( 11, ·)\) | \(\chi_{ 76 } ( 45, ·)\) |
| \(\chi_{ 76 }(49, ·)\) | \(\chi_{ 76 } ( 49, ·)\) | \(\chi_{ 76 } ( 45, ·)\) | \(\chi_{ 76 } ( 39, ·)\) | \(\chi_{ 76 } ( 11, ·)\) | \(\chi_{ 76 } ( 7, ·)\) | \(\chi_{ 76 } ( 1, ·)\) |
| \(\chi_{ 76 }(7, ·)\) | \(\chi_{ 76 } ( 7, ·)\) | \(\chi_{ 76 } ( 39, ·)\) | \(\chi_{ 76 } ( 49, ·)\) | \(\chi_{ 76 } ( 45, ·)\) | \(\chi_{ 76 } ( 1, ·)\) | \(\chi_{ 76 } ( 11, ·)\) |
| \(\chi_{ 76 }(39, ·)\) | \(\chi_{ 76 } ( 39, ·)\) | \(\chi_{ 76 } ( 11, ·)\) | \(\chi_{ 76 } ( 45, ·)\) | \(\chi_{ 76 } ( 1, ·)\) | \(\chi_{ 76 } ( 49, ·)\) | \(\chi_{ 76 } ( 7, ·)\) |
| \(\chi_{ 76 }(11, ·)\) | \(\chi_{ 76 } ( 11, ·)\) | \(\chi_{ 76 } ( 7, ·)\) | \(\chi_{ 76 } ( 1, ·)\) | \(\chi_{ 76 } ( 49, ·)\) | \(\chi_{ 76 } ( 45, ·)\) | \(\chi_{ 76 } ( 39, ·)\) |
| \(\chi_{ 76 }(45, ·)\) | \(\chi_{ 76 } ( 45, ·)\) | \(\chi_{ 76 } ( 1, ·)\) | \(\chi_{ 76 } ( 11, ·)\) | \(\chi_{ 76 } ( 7, ·)\) | \(\chi_{ 76 } ( 39, ·)\) | \(\chi_{ 76 } ( 49, ·)\) |