Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} - x^{3} + 2 x^{2} + x + 1 \)
$\times$ | \(\chi_{ 15 } ( 1, ·)\) | \(\chi_{ 15 } ( 11, ·)\) | \(\chi_{ 15 } ( 4, ·)\) | \(\chi_{ 15 } ( 14, ·)\) |
---|---|---|---|---|
\(\chi_{ 15 }(1, ·)\) | \(\chi_{ 15 } ( 1, ·)\) | \(\chi_{ 15 } ( 11, ·)\) | \(\chi_{ 15 } ( 4, ·)\) | \(\chi_{ 15 } ( 14, ·)\) |
\(\chi_{ 15 }(11, ·)\) | \(\chi_{ 15 } ( 11, ·)\) | \(\chi_{ 15 } ( 1, ·)\) | \(\chi_{ 15 } ( 14, ·)\) | \(\chi_{ 15 } ( 4, ·)\) |
\(\chi_{ 15 }(4, ·)\) | \(\chi_{ 15 } ( 4, ·)\) | \(\chi_{ 15 } ( 14, ·)\) | \(\chi_{ 15 } ( 1, ·)\) | \(\chi_{ 15 } ( 11, ·)\) |
\(\chi_{ 15 }(14, ·)\) | \(\chi_{ 15 } ( 14, ·)\) | \(\chi_{ 15 } ( 4, ·)\) | \(\chi_{ 15 } ( 11, ·)\) | \(\chi_{ 15 } ( 1, ·)\) |