Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{7} - 609x^{5} - 609x^{4} + 104951x^{3} + 119770x^{2} - 5123720x - 9825577 \)
| $\times$ | \(\chi_{ 1421 } ( 1, ·)\) | \(\chi_{ 1421 } ( 547, ·)\) | \(\chi_{ 1421 } ( 372, ·)\) | \(\chi_{ 1421 } ( 806, ·)\) | \(\chi_{ 1421 } ( 281, ·)\) | \(\chi_{ 1421 } ( 799, ·)\) | \(\chi_{ 1421 } ( 239, ·)\) |
|---|---|---|---|---|---|---|---|
| \(\chi_{ 1421 }(1, ·)\) | \(\chi_{ 1421 } ( 1, ·)\) | \(\chi_{ 1421 } ( 547, ·)\) | \(\chi_{ 1421 } ( 372, ·)\) | \(\chi_{ 1421 } ( 806, ·)\) | \(\chi_{ 1421 } ( 281, ·)\) | \(\chi_{ 1421 } ( 799, ·)\) | \(\chi_{ 1421 } ( 239, ·)\) |
| \(\chi_{ 1421 }(547, ·)\) | \(\chi_{ 1421 } ( 547, ·)\) | \(\chi_{ 1421 } ( 799, ·)\) | \(\chi_{ 1421 } ( 281, ·)\) | \(\chi_{ 1421 } ( 372, ·)\) | \(\chi_{ 1421 } ( 239, ·)\) | \(\chi_{ 1421 } ( 806, ·)\) | \(\chi_{ 1421 } ( 1, ·)\) |
| \(\chi_{ 1421 }(372, ·)\) | \(\chi_{ 1421 } ( 372, ·)\) | \(\chi_{ 1421 } ( 281, ·)\) | \(\chi_{ 1421 } ( 547, ·)\) | \(\chi_{ 1421 } ( 1, ·)\) | \(\chi_{ 1421 } ( 799, ·)\) | \(\chi_{ 1421 } ( 239, ·)\) | \(\chi_{ 1421 } ( 806, ·)\) |
| \(\chi_{ 1421 }(806, ·)\) | \(\chi_{ 1421 } ( 806, ·)\) | \(\chi_{ 1421 } ( 372, ·)\) | \(\chi_{ 1421 } ( 1, ·)\) | \(\chi_{ 1421 } ( 239, ·)\) | \(\chi_{ 1421 } ( 547, ·)\) | \(\chi_{ 1421 } ( 281, ·)\) | \(\chi_{ 1421 } ( 799, ·)\) |
| \(\chi_{ 1421 }(281, ·)\) | \(\chi_{ 1421 } ( 281, ·)\) | \(\chi_{ 1421 } ( 239, ·)\) | \(\chi_{ 1421 } ( 799, ·)\) | \(\chi_{ 1421 } ( 547, ·)\) | \(\chi_{ 1421 } ( 806, ·)\) | \(\chi_{ 1421 } ( 1, ·)\) | \(\chi_{ 1421 } ( 372, ·)\) |
| \(\chi_{ 1421 }(799, ·)\) | \(\chi_{ 1421 } ( 799, ·)\) | \(\chi_{ 1421 } ( 806, ·)\) | \(\chi_{ 1421 } ( 239, ·)\) | \(\chi_{ 1421 } ( 281, ·)\) | \(\chi_{ 1421 } ( 1, ·)\) | \(\chi_{ 1421 } ( 372, ·)\) | \(\chi_{ 1421 } ( 547, ·)\) |
| \(\chi_{ 1421 }(239, ·)\) | \(\chi_{ 1421 } ( 239, ·)\) | \(\chi_{ 1421 } ( 1, ·)\) | \(\chi_{ 1421 } ( 806, ·)\) | \(\chi_{ 1421 } ( 799, ·)\) | \(\chi_{ 1421 } ( 372, ·)\) | \(\chi_{ 1421 } ( 547, ·)\) | \(\chi_{ 1421 } ( 281, ·)\) |