Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{4} - x^{3} + 10 x^{2} + 9 x + 81 \)
| $\times$ | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 110, ·)\) | \(\chi_{ 111 } ( 73, ·)\) |
|---|---|---|---|---|
| \(\chi_{ 111 }(1, ·)\) | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 110, ·)\) | \(\chi_{ 111 } ( 73, ·)\) |
| \(\chi_{ 111 }(38, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 73, ·)\) | \(\chi_{ 111 } ( 110, ·)\) |
| \(\chi_{ 111 }(110, ·)\) | \(\chi_{ 111 } ( 110, ·)\) | \(\chi_{ 111 } ( 73, ·)\) | \(\chi_{ 111 } ( 1, ·)\) | \(\chi_{ 111 } ( 38, ·)\) |
| \(\chi_{ 111 }(73, ·)\) | \(\chi_{ 111 } ( 73, ·)\) | \(\chi_{ 111 } ( 110, ·)\) | \(\chi_{ 111 } ( 38, ·)\) | \(\chi_{ 111 } ( 1, ·)\) |