Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} - x^{5} + 4 x^{4} - 3 x^{3} + 29 x^{2} - 4 x + 71 \)
| $\times$ | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 32, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 65, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 43, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 77 }(1, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 32, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 65, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 43, ·)\) |
| \(\chi_{ 77 }(32, ·)\) | \(\chi_{ 77 } ( 32, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 65, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 43, ·)\) | \(\chi_{ 77 } ( 67, ·)\) |
| \(\chi_{ 77 }(67, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 65, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 43, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 32, ·)\) |
| \(\chi_{ 77 }(65, ·)\) | \(\chi_{ 77 } ( 65, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 43, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 32, ·)\) | \(\chi_{ 77 } ( 23, ·)\) |
| \(\chi_{ 77 }(23, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 43, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 32, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 65, ·)\) |
| \(\chi_{ 77 }(43, ·)\) | \(\chi_{ 77 } ( 43, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 32, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 65, ·)\) | \(\chi_{ 77 } ( 1, ·)\) |