Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{6} - 3x^{5} + 12x^{4} - 17x^{3} + 87x^{2} - 114x + 323 \)
| $\times$ | \(\chi_{ 171 } ( 1, ·)\) | \(\chi_{ 171 } ( 115, ·)\) | \(\chi_{ 171 } ( 37, ·)\) | \(\chi_{ 171 } ( 151, ·)\) | \(\chi_{ 171 } ( 58, ·)\) | \(\chi_{ 171 } ( 94, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 171 }(1, ·)\) | \(\chi_{ 171 } ( 1, ·)\) | \(\chi_{ 171 } ( 115, ·)\) | \(\chi_{ 171 } ( 37, ·)\) | \(\chi_{ 171 } ( 151, ·)\) | \(\chi_{ 171 } ( 58, ·)\) | \(\chi_{ 171 } ( 94, ·)\) |
| \(\chi_{ 171 }(115, ·)\) | \(\chi_{ 171 } ( 115, ·)\) | \(\chi_{ 171 } ( 58, ·)\) | \(\chi_{ 171 } ( 151, ·)\) | \(\chi_{ 171 } ( 94, ·)\) | \(\chi_{ 171 } ( 1, ·)\) | \(\chi_{ 171 } ( 37, ·)\) |
| \(\chi_{ 171 }(37, ·)\) | \(\chi_{ 171 } ( 37, ·)\) | \(\chi_{ 171 } ( 151, ·)\) | \(\chi_{ 171 } ( 1, ·)\) | \(\chi_{ 171 } ( 115, ·)\) | \(\chi_{ 171 } ( 94, ·)\) | \(\chi_{ 171 } ( 58, ·)\) |
| \(\chi_{ 171 }(151, ·)\) | \(\chi_{ 171 } ( 151, ·)\) | \(\chi_{ 171 } ( 94, ·)\) | \(\chi_{ 171 } ( 115, ·)\) | \(\chi_{ 171 } ( 58, ·)\) | \(\chi_{ 171 } ( 37, ·)\) | \(\chi_{ 171 } ( 1, ·)\) |
| \(\chi_{ 171 }(58, ·)\) | \(\chi_{ 171 } ( 58, ·)\) | \(\chi_{ 171 } ( 1, ·)\) | \(\chi_{ 171 } ( 94, ·)\) | \(\chi_{ 171 } ( 37, ·)\) | \(\chi_{ 171 } ( 115, ·)\) | \(\chi_{ 171 } ( 151, ·)\) |
| \(\chi_{ 171 }(94, ·)\) | \(\chi_{ 171 } ( 94, ·)\) | \(\chi_{ 171 } ( 37, ·)\) | \(\chi_{ 171 } ( 58, ·)\) | \(\chi_{ 171 } ( 1, ·)\) | \(\chi_{ 171 } ( 151, ·)\) | \(\chi_{ 171 } ( 115, ·)\) |