Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \(x^{9} - 63 x^{7} + 1323 x^{5} - 10290 x^{3} + 21609 x - 12691\) 
| $\times$ | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 130, ·)\) | \(\chi_{ 189 } ( 67, ·)\) | \(\chi_{ 189 } ( 4, ·)\) | \(\chi_{ 189 } ( 142, ·)\) | \(\chi_{ 189 } ( 79, ·)\) | \(\chi_{ 189 } ( 16, ·)\) | \(\chi_{ 189 } ( 127, ·)\) |
|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 189 }(1, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 130, ·)\) | \(\chi_{ 189 } ( 67, ·)\) | \(\chi_{ 189 } ( 4, ·)\) | \(\chi_{ 189 } ( 142, ·)\) | \(\chi_{ 189 } ( 79, ·)\) | \(\chi_{ 189 } ( 16, ·)\) | \(\chi_{ 189 } ( 127, ·)\) |
| \(\chi_{ 189 }(64, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 4, ·)\) | \(\chi_{ 189 } ( 130, ·)\) | \(\chi_{ 189 } ( 67, ·)\) | \(\chi_{ 189 } ( 16, ·)\) | \(\chi_{ 189 } ( 142, ·)\) | \(\chi_{ 189 } ( 79, ·)\) | \(\chi_{ 189 } ( 1, ·)\) |
| \(\chi_{ 189 }(130, ·)\) | \(\chi_{ 189 } ( 130, ·)\) | \(\chi_{ 189 } ( 4, ·)\) | \(\chi_{ 189 } ( 79, ·)\) | \(\chi_{ 189 } ( 16, ·)\) | \(\chi_{ 189 } ( 142, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 67, ·)\) |
| \(\chi_{ 189 }(67, ·)\) | \(\chi_{ 189 } ( 67, ·)\) | \(\chi_{ 189 } ( 130, ·)\) | \(\chi_{ 189 } ( 16, ·)\) | \(\chi_{ 189 } ( 142, ·)\) | \(\chi_{ 189 } ( 79, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 4, ·)\) |
| \(\chi_{ 189 }(4, ·)\) | \(\chi_{ 189 } ( 4, ·)\) | \(\chi_{ 189 } ( 67, ·)\) | \(\chi_{ 189 } ( 142, ·)\) | \(\chi_{ 189 } ( 79, ·)\) | \(\chi_{ 189 } ( 16, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 130, ·)\) |
| \(\chi_{ 189 }(142, ·)\) | \(\chi_{ 189 } ( 142, ·)\) | \(\chi_{ 189 } ( 16, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 130, ·)\) | \(\chi_{ 189 } ( 67, ·)\) | \(\chi_{ 189 } ( 4, ·)\) | \(\chi_{ 189 } ( 79, ·)\) |
| \(\chi_{ 189 }(79, ·)\) | \(\chi_{ 189 } ( 79, ·)\) | \(\chi_{ 189 } ( 142, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 67, ·)\) | \(\chi_{ 189 } ( 4, ·)\) | \(\chi_{ 189 } ( 130, ·)\) | \(\chi_{ 189 } ( 16, ·)\) |
| \(\chi_{ 189 }(16, ·)\) | \(\chi_{ 189 } ( 16, ·)\) | \(\chi_{ 189 } ( 79, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 4, ·)\) | \(\chi_{ 189 } ( 130, ·)\) | \(\chi_{ 189 } ( 67, ·)\) | \(\chi_{ 189 } ( 142, ·)\) |
| \(\chi_{ 189 }(127, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 67, ·)\) | \(\chi_{ 189 } ( 4, ·)\) | \(\chi_{ 189 } ( 130, ·)\) | \(\chi_{ 189 } ( 79, ·)\) | \(\chi_{ 189 } ( 16, ·)\) | \(\chi_{ 189 } ( 142, ·)\) | \(\chi_{ 189 } ( 64, ·)\) |