Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} + 13 x^{4} + 26 x^{2} + 13 \)
$\times$ | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 23, ·)\) | \(\chi_{ 52 } ( 9, ·)\) | \(\chi_{ 52 } ( 43, ·)\) | \(\chi_{ 52 } ( 29, ·)\) |
---|---|---|---|---|---|---|
\(\chi_{ 52 }(1, ·)\) | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 23, ·)\) | \(\chi_{ 52 } ( 9, ·)\) | \(\chi_{ 52 } ( 43, ·)\) | \(\chi_{ 52 } ( 29, ·)\) |
\(\chi_{ 52 }(51, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 29, ·)\) | \(\chi_{ 52 } ( 43, ·)\) | \(\chi_{ 52 } ( 9, ·)\) | \(\chi_{ 52 } ( 23, ·)\) |
\(\chi_{ 52 }(23, ·)\) | \(\chi_{ 52 } ( 23, ·)\) | \(\chi_{ 52 } ( 29, ·)\) | \(\chi_{ 52 } ( 9, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 43, ·)\) |
\(\chi_{ 52 }(9, ·)\) | \(\chi_{ 52 } ( 9, ·)\) | \(\chi_{ 52 } ( 43, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 29, ·)\) | \(\chi_{ 52 } ( 23, ·)\) | \(\chi_{ 52 } ( 1, ·)\) |
\(\chi_{ 52 }(43, ·)\) | \(\chi_{ 52 } ( 43, ·)\) | \(\chi_{ 52 } ( 9, ·)\) | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 23, ·)\) | \(\chi_{ 52 } ( 29, ·)\) | \(\chi_{ 52 } ( 51, ·)\) |
\(\chi_{ 52 }(29, ·)\) | \(\chi_{ 52 } ( 29, ·)\) | \(\chi_{ 52 } ( 23, ·)\) | \(\chi_{ 52 } ( 43, ·)\) | \(\chi_{ 52 } ( 1, ·)\) | \(\chi_{ 52 } ( 51, ·)\) | \(\chi_{ 52 } ( 9, ·)\) |