Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut 2 x^{5} \) \(\mathstrut -\mathstrut x^{4} \) \(\mathstrut -\mathstrut 2 x^{3} \) \(\mathstrut +\mathstrut 34 x^{2} \) \(\mathstrut +\mathstrut 28 x \) \(\mathstrut +\mathstrut 73 \)
| $\times$ | \(\chi_{ 104 } ( 1, ·)\) | \(\chi_{ 104 } ( 3, ·)\) | \(\chi_{ 104 } ( 35, ·)\) | \(\chi_{ 104 } ( 81, ·)\) | \(\chi_{ 104 } ( 9, ·)\) | \(\chi_{ 104 } ( 27, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 104 }(1, ·)\) | \(\chi_{ 104 } ( 1, ·)\) | \(\chi_{ 104 } ( 3, ·)\) | \(\chi_{ 104 } ( 35, ·)\) | \(\chi_{ 104 } ( 81, ·)\) | \(\chi_{ 104 } ( 9, ·)\) | \(\chi_{ 104 } ( 27, ·)\) |
| \(\chi_{ 104 }(3, ·)\) | \(\chi_{ 104 } ( 3, ·)\) | \(\chi_{ 104 } ( 9, ·)\) | \(\chi_{ 104 } ( 1, ·)\) | \(\chi_{ 104 } ( 35, ·)\) | \(\chi_{ 104 } ( 27, ·)\) | \(\chi_{ 104 } ( 81, ·)\) |
| \(\chi_{ 104 }(35, ·)\) | \(\chi_{ 104 } ( 35, ·)\) | \(\chi_{ 104 } ( 1, ·)\) | \(\chi_{ 104 } ( 81, ·)\) | \(\chi_{ 104 } ( 27, ·)\) | \(\chi_{ 104 } ( 3, ·)\) | \(\chi_{ 104 } ( 9, ·)\) |
| \(\chi_{ 104 }(81, ·)\) | \(\chi_{ 104 } ( 81, ·)\) | \(\chi_{ 104 } ( 35, ·)\) | \(\chi_{ 104 } ( 27, ·)\) | \(\chi_{ 104 } ( 9, ·)\) | \(\chi_{ 104 } ( 1, ·)\) | \(\chi_{ 104 } ( 3, ·)\) |
| \(\chi_{ 104 }(9, ·)\) | \(\chi_{ 104 } ( 9, ·)\) | \(\chi_{ 104 } ( 27, ·)\) | \(\chi_{ 104 } ( 3, ·)\) | \(\chi_{ 104 } ( 1, ·)\) | \(\chi_{ 104 } ( 81, ·)\) | \(\chi_{ 104 } ( 35, ·)\) |
| \(\chi_{ 104 }(27, ·)\) | \(\chi_{ 104 } ( 27, ·)\) | \(\chi_{ 104 } ( 81, ·)\) | \(\chi_{ 104 } ( 9, ·)\) | \(\chi_{ 104 } ( 3, ·)\) | \(\chi_{ 104 } ( 35, ·)\) | \(\chi_{ 104 } ( 1, ·)\) |