Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{4} \) \(\mathstrut -\mathstrut x^{3} \) \(\mathstrut -\mathstrut 2 x^{2} \) \(\mathstrut -\mathstrut 3 x \) \(\mathstrut +\mathstrut 9 \)
$\times$ | \(\chi_{ 33 } ( 1, ·)\) | \(\chi_{ 33 } ( 32, ·)\) | \(\chi_{ 33 } ( 10, ·)\) | \(\chi_{ 33 } ( 23, ·)\) |
---|---|---|---|---|
\(\chi_{ 33 }(1, ·)\) | \(\chi_{ 33 } ( 1, ·)\) | \(\chi_{ 33 } ( 32, ·)\) | \(\chi_{ 33 } ( 10, ·)\) | \(\chi_{ 33 } ( 23, ·)\) |
\(\chi_{ 33 }(32, ·)\) | \(\chi_{ 33 } ( 32, ·)\) | \(\chi_{ 33 } ( 1, ·)\) | \(\chi_{ 33 } ( 23, ·)\) | \(\chi_{ 33 } ( 10, ·)\) |
\(\chi_{ 33 }(10, ·)\) | \(\chi_{ 33 } ( 10, ·)\) | \(\chi_{ 33 } ( 23, ·)\) | \(\chi_{ 33 } ( 1, ·)\) | \(\chi_{ 33 } ( 32, ·)\) |
\(\chi_{ 33 }(23, ·)\) | \(\chi_{ 33 } ( 23, ·)\) | \(\chi_{ 33 } ( 10, ·)\) | \(\chi_{ 33 } ( 32, ·)\) | \(\chi_{ 33 } ( 1, ·)\) |