Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{6} \) \(\mathstrut -\mathstrut x^{5} \) \(\mathstrut -\mathstrut 20 x^{4} \) \(\mathstrut +\mathstrut 20 x^{3} \) \(\mathstrut +\mathstrut 106 x^{2} \) \(\mathstrut -\mathstrut 106 x \) \(\mathstrut -\mathstrut 83 \)
$\times$ | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 76, ·)\) |
---|---|---|---|---|---|---|
\(\chi_{ 77 }(1, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 76, ·)\) |
\(\chi_{ 77 }(67, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 10, ·)\) |
\(\chi_{ 77 }(54, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 23, ·)\) |
\(\chi_{ 77 }(23, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 54, ·)\) |
\(\chi_{ 77 }(10, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 67, ·)\) |
\(\chi_{ 77 }(76, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 1, ·)\) |