Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{9} - x^{8} - 8x^{7} + 7x^{6} + 21x^{5} - 15x^{4} - 20x^{3} + 10x^{2} + 5x - 1 \)
| $\times$ | \(\chi_{ 19 } ( 1, ·)\) | \(\chi_{ 19 } ( 4, ·)\) | \(\chi_{ 19 } ( 5, ·)\) | \(\chi_{ 19 } ( 6, ·)\) | \(\chi_{ 19 } ( 7, ·)\) | \(\chi_{ 19 } ( 9, ·)\) | \(\chi_{ 19 } ( 11, ·)\) | \(\chi_{ 19 } ( 16, ·)\) | \(\chi_{ 19 } ( 17, ·)\) |
|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 19 }(1, ·)\) | \(\chi_{ 19 } ( 1, ·)\) | \(\chi_{ 19 } ( 4, ·)\) | \(\chi_{ 19 } ( 5, ·)\) | \(\chi_{ 19 } ( 6, ·)\) | \(\chi_{ 19 } ( 7, ·)\) | \(\chi_{ 19 } ( 9, ·)\) | \(\chi_{ 19 } ( 11, ·)\) | \(\chi_{ 19 } ( 16, ·)\) | \(\chi_{ 19 } ( 17, ·)\) |
| \(\chi_{ 19 }(4, ·)\) | \(\chi_{ 19 } ( 4, ·)\) | \(\chi_{ 19 } ( 16, ·)\) | \(\chi_{ 19 } ( 1, ·)\) | \(\chi_{ 19 } ( 5, ·)\) | \(\chi_{ 19 } ( 9, ·)\) | \(\chi_{ 19 } ( 17, ·)\) | \(\chi_{ 19 } ( 6, ·)\) | \(\chi_{ 19 } ( 7, ·)\) | \(\chi_{ 19 } ( 11, ·)\) |
| \(\chi_{ 19 }(5, ·)\) | \(\chi_{ 19 } ( 5, ·)\) | \(\chi_{ 19 } ( 1, ·)\) | \(\chi_{ 19 } ( 6, ·)\) | \(\chi_{ 19 } ( 11, ·)\) | \(\chi_{ 19 } ( 16, ·)\) | \(\chi_{ 19 } ( 7, ·)\) | \(\chi_{ 19 } ( 17, ·)\) | \(\chi_{ 19 } ( 4, ·)\) | \(\chi_{ 19 } ( 9, ·)\) |
| \(\chi_{ 19 }(6, ·)\) | \(\chi_{ 19 } ( 6, ·)\) | \(\chi_{ 19 } ( 5, ·)\) | \(\chi_{ 19 } ( 11, ·)\) | \(\chi_{ 19 } ( 17, ·)\) | \(\chi_{ 19 } ( 4, ·)\) | \(\chi_{ 19 } ( 16, ·)\) | \(\chi_{ 19 } ( 9, ·)\) | \(\chi_{ 19 } ( 1, ·)\) | \(\chi_{ 19 } ( 7, ·)\) |
| \(\chi_{ 19 }(7, ·)\) | \(\chi_{ 19 } ( 7, ·)\) | \(\chi_{ 19 } ( 9, ·)\) | \(\chi_{ 19 } ( 16, ·)\) | \(\chi_{ 19 } ( 4, ·)\) | \(\chi_{ 19 } ( 11, ·)\) | \(\chi_{ 19 } ( 6, ·)\) | \(\chi_{ 19 } ( 1, ·)\) | \(\chi_{ 19 } ( 17, ·)\) | \(\chi_{ 19 } ( 5, ·)\) |
| \(\chi_{ 19 }(9, ·)\) | \(\chi_{ 19 } ( 9, ·)\) | \(\chi_{ 19 } ( 17, ·)\) | \(\chi_{ 19 } ( 7, ·)\) | \(\chi_{ 19 } ( 16, ·)\) | \(\chi_{ 19 } ( 6, ·)\) | \(\chi_{ 19 } ( 5, ·)\) | \(\chi_{ 19 } ( 4, ·)\) | \(\chi_{ 19 } ( 11, ·)\) | \(\chi_{ 19 } ( 1, ·)\) |
| \(\chi_{ 19 }(11, ·)\) | \(\chi_{ 19 } ( 11, ·)\) | \(\chi_{ 19 } ( 6, ·)\) | \(\chi_{ 19 } ( 17, ·)\) | \(\chi_{ 19 } ( 9, ·)\) | \(\chi_{ 19 } ( 1, ·)\) | \(\chi_{ 19 } ( 4, ·)\) | \(\chi_{ 19 } ( 7, ·)\) | \(\chi_{ 19 } ( 5, ·)\) | \(\chi_{ 19 } ( 16, ·)\) |
| \(\chi_{ 19 }(16, ·)\) | \(\chi_{ 19 } ( 16, ·)\) | \(\chi_{ 19 } ( 7, ·)\) | \(\chi_{ 19 } ( 4, ·)\) | \(\chi_{ 19 } ( 1, ·)\) | \(\chi_{ 19 } ( 17, ·)\) | \(\chi_{ 19 } ( 11, ·)\) | \(\chi_{ 19 } ( 5, ·)\) | \(\chi_{ 19 } ( 9, ·)\) | \(\chi_{ 19 } ( 6, ·)\) |
| \(\chi_{ 19 }(17, ·)\) | \(\chi_{ 19 } ( 17, ·)\) | \(\chi_{ 19 } ( 11, ·)\) | \(\chi_{ 19 } ( 9, ·)\) | \(\chi_{ 19 } ( 7, ·)\) | \(\chi_{ 19 } ( 5, ·)\) | \(\chi_{ 19 } ( 1, ·)\) | \(\chi_{ 19 } ( 16, ·)\) | \(\chi_{ 19 } ( 6, ·)\) | \(\chi_{ 19 } ( 4, ·)\) |