Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} - x^{5} + 13 x^{4} + 34 x^{3} + 133 x^{2} + 132 x + 121 \)
$\times$ | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 100, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 10, ·)\) | \(\chi_{ 111 } ( 26, ·)\) | \(\chi_{ 111 } ( 47, ·)\) |
---|---|---|---|---|---|---|
\(\chi_{ 111 }(1, ·)\) | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 100, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 10, ·)\) | \(\chi_{ 111 } ( 26, ·)\) | \(\chi_{ 111 } ( 47, ·)\) |
\(\chi_{ 111 }(100, ·)\) | \(\chi_{ 111 } ( 100, ·)\) | \(\chi_{ 111 } ( 10, ·)\) | \(\chi_{ 111 } ( 26, ·)\) | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 47, ·)\) | \(\chi_{ 111 } ( 38, ·)\) |
\(\chi_{ 111 }(38, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 26, ·)\) | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 47, ·)\) | \(\chi_{ 111 } ( 100, ·)\) | \(\chi_{ 111 } ( 10, ·)\) |
\(\chi_{ 111 }(10, ·)\) | \(\chi_{ 111 } ( 10, ·)\) | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 47, ·)\) | \(\chi_{ 111 } ( 100, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 26, ·)\) |
\(\chi_{ 111 }(26, ·)\) | \(\chi_{ 111 } ( 26, ·)\) | \(\chi_{ 111 } ( 47, ·)\) | \(\chi_{ 111 } ( 100, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 10, ·)\) | \(\chi_{ 111 } ( 1, ·)\) |
\(\chi_{ 111 }(47, ·)\) | \(\chi_{ 111 } ( 47, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 10, ·)\) | \(\chi_{ 111 } ( 26, ·)\) | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 100, ·)\) |