Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} - x^{5} + 28 x^{4} - 19 x^{3} + 357 x^{2} - 100 x + 1847 \)
| $\times$ | \(\chi_{ 301 } ( 1, ·)\) | \(\chi_{ 301 } ( 128, ·)\) | \(\chi_{ 301 } ( 130, ·)\) | \(\chi_{ 301 } ( 85, ·)\) | \(\chi_{ 301 } ( 214, ·)\) | \(\chi_{ 301 } ( 44, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 301 }(1, ·)\) | \(\chi_{ 301 } ( 1, ·)\) | \(\chi_{ 301 } ( 128, ·)\) | \(\chi_{ 301 } ( 130, ·)\) | \(\chi_{ 301 } ( 85, ·)\) | \(\chi_{ 301 } ( 214, ·)\) | \(\chi_{ 301 } ( 44, ·)\) |
| \(\chi_{ 301 }(128, ·)\) | \(\chi_{ 301 } ( 128, ·)\) | \(\chi_{ 301 } ( 130, ·)\) | \(\chi_{ 301 } ( 85, ·)\) | \(\chi_{ 301 } ( 44, ·)\) | \(\chi_{ 301 } ( 1, ·)\) | \(\chi_{ 301 } ( 214, ·)\) |
| \(\chi_{ 301 }(130, ·)\) | \(\chi_{ 301 } ( 130, ·)\) | \(\chi_{ 301 } ( 85, ·)\) | \(\chi_{ 301 } ( 44, ·)\) | \(\chi_{ 301 } ( 214, ·)\) | \(\chi_{ 301 } ( 128, ·)\) | \(\chi_{ 301 } ( 1, ·)\) |
| \(\chi_{ 301 }(85, ·)\) | \(\chi_{ 301 } ( 85, ·)\) | \(\chi_{ 301 } ( 44, ·)\) | \(\chi_{ 301 } ( 214, ·)\) | \(\chi_{ 301 } ( 1, ·)\) | \(\chi_{ 301 } ( 130, ·)\) | \(\chi_{ 301 } ( 128, ·)\) |
| \(\chi_{ 301 }(214, ·)\) | \(\chi_{ 301 } ( 214, ·)\) | \(\chi_{ 301 } ( 1, ·)\) | \(\chi_{ 301 } ( 128, ·)\) | \(\chi_{ 301 } ( 130, ·)\) | \(\chi_{ 301 } ( 44, ·)\) | \(\chi_{ 301 } ( 85, ·)\) |
| \(\chi_{ 301 }(44, ·)\) | \(\chi_{ 301 } ( 44, ·)\) | \(\chi_{ 301 } ( 214, ·)\) | \(\chi_{ 301 } ( 1, ·)\) | \(\chi_{ 301 } ( 128, ·)\) | \(\chi_{ 301 } ( 85, ·)\) | \(\chi_{ 301 } ( 130, ·)\) |