Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{7} - x^{6} - 12 x^{5} + 7 x^{4} + 28 x^{3} - 14 x^{2} - 9 x - 1 \)
| $\times$ | \(\chi_{ 29 } ( 1, ·)\) | \(\chi_{ 29 } ( 16, ·)\) | \(\chi_{ 29 } ( 20, ·)\) | \(\chi_{ 29 } ( 7, ·)\) | \(\chi_{ 29 } ( 24, ·)\) | \(\chi_{ 29 } ( 25, ·)\) | \(\chi_{ 29 } ( 23, ·)\) |
|---|---|---|---|---|---|---|---|
| \(\chi_{ 29 }(1, ·)\) | \(\chi_{ 29 } ( 1, ·)\) | \(\chi_{ 29 } ( 16, ·)\) | \(\chi_{ 29 } ( 20, ·)\) | \(\chi_{ 29 } ( 7, ·)\) | \(\chi_{ 29 } ( 24, ·)\) | \(\chi_{ 29 } ( 25, ·)\) | \(\chi_{ 29 } ( 23, ·)\) |
| \(\chi_{ 29 }(16, ·)\) | \(\chi_{ 29 } ( 16, ·)\) | \(\chi_{ 29 } ( 24, ·)\) | \(\chi_{ 29 } ( 1, ·)\) | \(\chi_{ 29 } ( 25, ·)\) | \(\chi_{ 29 } ( 7, ·)\) | \(\chi_{ 29 } ( 23, ·)\) | \(\chi_{ 29 } ( 20, ·)\) |
| \(\chi_{ 29 }(20, ·)\) | \(\chi_{ 29 } ( 20, ·)\) | \(\chi_{ 29 } ( 1, ·)\) | \(\chi_{ 29 } ( 23, ·)\) | \(\chi_{ 29 } ( 24, ·)\) | \(\chi_{ 29 } ( 16, ·)\) | \(\chi_{ 29 } ( 7, ·)\) | \(\chi_{ 29 } ( 25, ·)\) |
| \(\chi_{ 29 }(7, ·)\) | \(\chi_{ 29 } ( 7, ·)\) | \(\chi_{ 29 } ( 25, ·)\) | \(\chi_{ 29 } ( 24, ·)\) | \(\chi_{ 29 } ( 20, ·)\) | \(\chi_{ 29 } ( 23, ·)\) | \(\chi_{ 29 } ( 1, ·)\) | \(\chi_{ 29 } ( 16, ·)\) |
| \(\chi_{ 29 }(24, ·)\) | \(\chi_{ 29 } ( 24, ·)\) | \(\chi_{ 29 } ( 7, ·)\) | \(\chi_{ 29 } ( 16, ·)\) | \(\chi_{ 29 } ( 23, ·)\) | \(\chi_{ 29 } ( 25, ·)\) | \(\chi_{ 29 } ( 20, ·)\) | \(\chi_{ 29 } ( 1, ·)\) |
| \(\chi_{ 29 }(25, ·)\) | \(\chi_{ 29 } ( 25, ·)\) | \(\chi_{ 29 } ( 23, ·)\) | \(\chi_{ 29 } ( 7, ·)\) | \(\chi_{ 29 } ( 1, ·)\) | \(\chi_{ 29 } ( 20, ·)\) | \(\chi_{ 29 } ( 16, ·)\) | \(\chi_{ 29 } ( 24, ·)\) |
| \(\chi_{ 29 }(23, ·)\) | \(\chi_{ 29 } ( 23, ·)\) | \(\chi_{ 29 } ( 20, ·)\) | \(\chi_{ 29 } ( 25, ·)\) | \(\chi_{ 29 } ( 16, ·)\) | \(\chi_{ 29 } ( 1, ·)\) | \(\chi_{ 29 } ( 24, ·)\) | \(\chi_{ 29 } ( 7, ·)\) |