Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 32 x \) \(\mathstrut +\mathstrut 79 \)
| $\times$ | \(\chi_{ 97 } ( 1, ·)\) | \(\chi_{ 97 } ( 35, ·)\) | \(\chi_{ 97 } ( 61, ·)\) |
|---|---|---|---|
| \(\chi_{ 97 }(1, ·)\) | \(\chi_{ 97 } ( 1, ·)\) | \(\chi_{ 97 } ( 35, ·)\) | \(\chi_{ 97 } ( 61, ·)\) |
| \(\chi_{ 97 }(35, ·)\) | \(\chi_{ 97 } ( 35, ·)\) | \(\chi_{ 97 } ( 61, ·)\) | \(\chi_{ 97 } ( 1, ·)\) |
| \(\chi_{ 97 }(61, ·)\) | \(\chi_{ 97 } ( 61, ·)\) | \(\chi_{ 97 } ( 1, ·)\) | \(\chi_{ 97 } ( 35, ·)\) |