Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$

$K$ is the global number field defined by \( x^{8} + 1 \) Copy content Toggle raw display

$\times$ \(\chi_{ 16 } ( 1, ·)\) \(\chi_{ 16 } ( 3, ·)\) \(\chi_{ 16 } ( 5, ·)\) \(\chi_{ 16 } ( 7, ·)\) \(\chi_{ 16 } ( 9, ·)\) \(\chi_{ 16 } ( 11, ·)\) \(\chi_{ 16 } ( 13, ·)\) \(\chi_{ 16 } ( 15, ·)\)
\(\chi_{ 16 }(1, ·)\) \(\chi_{ 16 } ( 1, ·)\) \(\chi_{ 16 } ( 3, ·)\) \(\chi_{ 16 } ( 5, ·)\) \(\chi_{ 16 } ( 7, ·)\) \(\chi_{ 16 } ( 9, ·)\) \(\chi_{ 16 } ( 11, ·)\) \(\chi_{ 16 } ( 13, ·)\) \(\chi_{ 16 } ( 15, ·)\)
\(\chi_{ 16 }(3, ·)\) \(\chi_{ 16 } ( 3, ·)\) \(\chi_{ 16 } ( 9, ·)\) \(\chi_{ 16 } ( 15, ·)\) \(\chi_{ 16 } ( 5, ·)\) \(\chi_{ 16 } ( 11, ·)\) \(\chi_{ 16 } ( 1, ·)\) \(\chi_{ 16 } ( 7, ·)\) \(\chi_{ 16 } ( 13, ·)\)
\(\chi_{ 16 }(5, ·)\) \(\chi_{ 16 } ( 5, ·)\) \(\chi_{ 16 } ( 15, ·)\) \(\chi_{ 16 } ( 9, ·)\) \(\chi_{ 16 } ( 3, ·)\) \(\chi_{ 16 } ( 13, ·)\) \(\chi_{ 16 } ( 7, ·)\) \(\chi_{ 16 } ( 1, ·)\) \(\chi_{ 16 } ( 11, ·)\)
\(\chi_{ 16 }(7, ·)\) \(\chi_{ 16 } ( 7, ·)\) \(\chi_{ 16 } ( 5, ·)\) \(\chi_{ 16 } ( 3, ·)\) \(\chi_{ 16 } ( 1, ·)\) \(\chi_{ 16 } ( 15, ·)\) \(\chi_{ 16 } ( 13, ·)\) \(\chi_{ 16 } ( 11, ·)\) \(\chi_{ 16 } ( 9, ·)\)
\(\chi_{ 16 }(9, ·)\) \(\chi_{ 16 } ( 9, ·)\) \(\chi_{ 16 } ( 11, ·)\) \(\chi_{ 16 } ( 13, ·)\) \(\chi_{ 16 } ( 15, ·)\) \(\chi_{ 16 } ( 1, ·)\) \(\chi_{ 16 } ( 3, ·)\) \(\chi_{ 16 } ( 5, ·)\) \(\chi_{ 16 } ( 7, ·)\)
\(\chi_{ 16 }(11, ·)\) \(\chi_{ 16 } ( 11, ·)\) \(\chi_{ 16 } ( 1, ·)\) \(\chi_{ 16 } ( 7, ·)\) \(\chi_{ 16 } ( 13, ·)\) \(\chi_{ 16 } ( 3, ·)\) \(\chi_{ 16 } ( 9, ·)\) \(\chi_{ 16 } ( 15, ·)\) \(\chi_{ 16 } ( 5, ·)\)
\(\chi_{ 16 }(13, ·)\) \(\chi_{ 16 } ( 13, ·)\) \(\chi_{ 16 } ( 7, ·)\) \(\chi_{ 16 } ( 1, ·)\) \(\chi_{ 16 } ( 11, ·)\) \(\chi_{ 16 } ( 5, ·)\) \(\chi_{ 16 } ( 15, ·)\) \(\chi_{ 16 } ( 9, ·)\) \(\chi_{ 16 } ( 3, ·)\)
\(\chi_{ 16 }(15, ·)\) \(\chi_{ 16 } ( 15, ·)\) \(\chi_{ 16 } ( 13, ·)\) \(\chi_{ 16 } ( 11, ·)\) \(\chi_{ 16 } ( 9, ·)\) \(\chi_{ 16 } ( 7, ·)\) \(\chi_{ 16 } ( 5, ·)\) \(\chi_{ 16 } ( 3, ·)\) \(\chi_{ 16 } ( 1, ·)\)