Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{7} - x^{6} - 48 x^{5} - 37 x^{4} + 312 x^{3} + 12 x^{2} - 49 x + 1 \)
$\times$ | \(\chi_{ 113 } ( 1, ·)\) | \(\chi_{ 113 } ( 16, ·)\) | \(\chi_{ 113 } ( 49, ·)\) | \(\chi_{ 113 } ( 106, ·)\) | \(\chi_{ 113 } ( 28, ·)\) | \(\chi_{ 113 } ( 109, ·)\) | \(\chi_{ 113 } ( 30, ·)\) |
---|---|---|---|---|---|---|---|
\(\chi_{ 113 }(1, ·)\) | \(\chi_{ 113 } ( 1, ·)\) | \(\chi_{ 113 } ( 16, ·)\) | \(\chi_{ 113 } ( 49, ·)\) | \(\chi_{ 113 } ( 106, ·)\) | \(\chi_{ 113 } ( 28, ·)\) | \(\chi_{ 113 } ( 109, ·)\) | \(\chi_{ 113 } ( 30, ·)\) |
\(\chi_{ 113 }(16, ·)\) | \(\chi_{ 113 } ( 16, ·)\) | \(\chi_{ 113 } ( 30, ·)\) | \(\chi_{ 113 } ( 106, ·)\) | \(\chi_{ 113 } ( 1, ·)\) | \(\chi_{ 113 } ( 109, ·)\) | \(\chi_{ 113 } ( 49, ·)\) | \(\chi_{ 113 } ( 28, ·)\) |
\(\chi_{ 113 }(49, ·)\) | \(\chi_{ 113 } ( 49, ·)\) | \(\chi_{ 113 } ( 106, ·)\) | \(\chi_{ 113 } ( 28, ·)\) | \(\chi_{ 113 } ( 109, ·)\) | \(\chi_{ 113 } ( 16, ·)\) | \(\chi_{ 113 } ( 30, ·)\) | \(\chi_{ 113 } ( 1, ·)\) |
\(\chi_{ 113 }(106, ·)\) | \(\chi_{ 113 } ( 106, ·)\) | \(\chi_{ 113 } ( 1, ·)\) | \(\chi_{ 113 } ( 109, ·)\) | \(\chi_{ 113 } ( 49, ·)\) | \(\chi_{ 113 } ( 30, ·)\) | \(\chi_{ 113 } ( 28, ·)\) | \(\chi_{ 113 } ( 16, ·)\) |
\(\chi_{ 113 }(28, ·)\) | \(\chi_{ 113 } ( 28, ·)\) | \(\chi_{ 113 } ( 109, ·)\) | \(\chi_{ 113 } ( 16, ·)\) | \(\chi_{ 113 } ( 30, ·)\) | \(\chi_{ 113 } ( 106, ·)\) | \(\chi_{ 113 } ( 1, ·)\) | \(\chi_{ 113 } ( 49, ·)\) |
\(\chi_{ 113 }(109, ·)\) | \(\chi_{ 113 } ( 109, ·)\) | \(\chi_{ 113 } ( 49, ·)\) | \(\chi_{ 113 } ( 30, ·)\) | \(\chi_{ 113 } ( 28, ·)\) | \(\chi_{ 113 } ( 1, ·)\) | \(\chi_{ 113 } ( 16, ·)\) | \(\chi_{ 113 } ( 106, ·)\) |
\(\chi_{ 113 }(30, ·)\) | \(\chi_{ 113 } ( 30, ·)\) | \(\chi_{ 113 } ( 28, ·)\) | \(\chi_{ 113 } ( 1, ·)\) | \(\chi_{ 113 } ( 16, ·)\) | \(\chi_{ 113 } ( 49, ·)\) | \(\chi_{ 113 } ( 106, ·)\) | \(\chi_{ 113 } ( 109, ·)\) |