Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} + 1 \)
$\times$ | \(\chi_{ 8 } ( 1, ·)\) | \(\chi_{ 8 } ( 3, ·)\) | \(\chi_{ 8 } ( 5, ·)\) | \(\chi_{ 8 } ( 7, ·)\) |
---|---|---|---|---|
\(\chi_{ 8 }(1, ·)\) | \(\chi_{ 8 } ( 1, ·)\) | \(\chi_{ 8 } ( 3, ·)\) | \(\chi_{ 8 } ( 5, ·)\) | \(\chi_{ 8 } ( 7, ·)\) |
\(\chi_{ 8 }(3, ·)\) | \(\chi_{ 8 } ( 3, ·)\) | \(\chi_{ 8 } ( 1, ·)\) | \(\chi_{ 8 } ( 7, ·)\) | \(\chi_{ 8 } ( 5, ·)\) |
\(\chi_{ 8 }(5, ·)\) | \(\chi_{ 8 } ( 5, ·)\) | \(\chi_{ 8 } ( 7, ·)\) | \(\chi_{ 8 } ( 1, ·)\) | \(\chi_{ 8 } ( 3, ·)\) |
\(\chi_{ 8 }(7, ·)\) | \(\chi_{ 8 } ( 7, ·)\) | \(\chi_{ 8 } ( 5, ·)\) | \(\chi_{ 8 } ( 3, ·)\) | \(\chi_{ 8 } ( 1, ·)\) |