Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} - x^{5} - 20 x^{4} + 20 x^{3} + 106 x^{2} - 106 x - 83 \)
| $\times$ | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 76, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 77 }(1, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 76, ·)\) |
| \(\chi_{ 77 }(67, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 10, ·)\) |
| \(\chi_{ 77 }(54, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 23, ·)\) |
| \(\chi_{ 77 }(23, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 54, ·)\) |
| \(\chi_{ 77 }(10, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 1, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 67, ·)\) |
| \(\chi_{ 77 }(76, ·)\) | \(\chi_{ 77 } ( 76, ·)\) | \(\chi_{ 77 } ( 10, ·)\) | \(\chi_{ 77 } ( 23, ·)\) | \(\chi_{ 77 } ( 54, ·)\) | \(\chi_{ 77 } ( 67, ·)\) | \(\chi_{ 77 } ( 1, ·)\) |