Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{5} \) \(\mathstrut -\mathstrut x^{4} \) \(\mathstrut -\mathstrut 40 x^{3} \) \(\mathstrut -\mathstrut 93 x^{2} \) \(\mathstrut -\mathstrut 21 x \) \(\mathstrut +\mathstrut 17 \)
| $\times$ | \(\chi_{ 101 } ( 1, ·)\) | \(\chi_{ 101 } ( 87, ·)\) | \(\chi_{ 101 } ( 84, ·)\) | \(\chi_{ 101 } ( 36, ·)\) | \(\chi_{ 101 } ( 95, ·)\) |
|---|---|---|---|---|---|
| \(\chi_{ 101 }(1, ·)\) | \(\chi_{ 101 } ( 1, ·)\) | \(\chi_{ 101 } ( 87, ·)\) | \(\chi_{ 101 } ( 84, ·)\) | \(\chi_{ 101 } ( 36, ·)\) | \(\chi_{ 101 } ( 95, ·)\) |
| \(\chi_{ 101 }(87, ·)\) | \(\chi_{ 101 } ( 87, ·)\) | \(\chi_{ 101 } ( 95, ·)\) | \(\chi_{ 101 } ( 36, ·)\) | \(\chi_{ 101 } ( 1, ·)\) | \(\chi_{ 101 } ( 84, ·)\) |
| \(\chi_{ 101 }(84, ·)\) | \(\chi_{ 101 } ( 84, ·)\) | \(\chi_{ 101 } ( 36, ·)\) | \(\chi_{ 101 } ( 87, ·)\) | \(\chi_{ 101 } ( 95, ·)\) | \(\chi_{ 101 } ( 1, ·)\) |
| \(\chi_{ 101 }(36, ·)\) | \(\chi_{ 101 } ( 36, ·)\) | \(\chi_{ 101 } ( 1, ·)\) | \(\chi_{ 101 } ( 95, ·)\) | \(\chi_{ 101 } ( 84, ·)\) | \(\chi_{ 101 } ( 87, ·)\) |
| \(\chi_{ 101 }(95, ·)\) | \(\chi_{ 101 } ( 95, ·)\) | \(\chi_{ 101 } ( 84, ·)\) | \(\chi_{ 101 } ( 1, ·)\) | \(\chi_{ 101 } ( 87, ·)\) | \(\chi_{ 101 } ( 36, ·)\) |