Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{6} - x^{5} + 249 x^{4} + 255 x^{3} + 6421 x^{2} + 6417 x + 51877 \)
| $\times$ | \(\chi_{ 1007 } ( 1, ·)\) | \(\chi_{ 1007 } ( 372, ·)\) | \(\chi_{ 1007 } ( 582, ·)\) | \(\chi_{ 1007 } ( 425, ·)\) | \(\chi_{ 1007 } ( 635, ·)\) | \(\chi_{ 1007 } ( 1006, ·)\) |
|---|---|---|---|---|---|---|
| \(\chi_{ 1007 }(1, ·)\) | \(\chi_{ 1007 } ( 1, ·)\) | \(\chi_{ 1007 } ( 372, ·)\) | \(\chi_{ 1007 } ( 582, ·)\) | \(\chi_{ 1007 } ( 425, ·)\) | \(\chi_{ 1007 } ( 635, ·)\) | \(\chi_{ 1007 } ( 1006, ·)\) |
| \(\chi_{ 1007 }(372, ·)\) | \(\chi_{ 1007 } ( 372, ·)\) | \(\chi_{ 1007 } ( 425, ·)\) | \(\chi_{ 1007 } ( 1006, ·)\) | \(\chi_{ 1007 } ( 1, ·)\) | \(\chi_{ 1007 } ( 582, ·)\) | \(\chi_{ 1007 } ( 635, ·)\) |
| \(\chi_{ 1007 }(582, ·)\) | \(\chi_{ 1007 } ( 582, ·)\) | \(\chi_{ 1007 } ( 1006, ·)\) | \(\chi_{ 1007 } ( 372, ·)\) | \(\chi_{ 1007 } ( 635, ·)\) | \(\chi_{ 1007 } ( 1, ·)\) | \(\chi_{ 1007 } ( 425, ·)\) |
| \(\chi_{ 1007 }(425, ·)\) | \(\chi_{ 1007 } ( 425, ·)\) | \(\chi_{ 1007 } ( 1, ·)\) | \(\chi_{ 1007 } ( 635, ·)\) | \(\chi_{ 1007 } ( 372, ·)\) | \(\chi_{ 1007 } ( 1006, ·)\) | \(\chi_{ 1007 } ( 582, ·)\) |
| \(\chi_{ 1007 }(635, ·)\) | \(\chi_{ 1007 } ( 635, ·)\) | \(\chi_{ 1007 } ( 582, ·)\) | \(\chi_{ 1007 } ( 1, ·)\) | \(\chi_{ 1007 } ( 1006, ·)\) | \(\chi_{ 1007 } ( 425, ·)\) | \(\chi_{ 1007 } ( 372, ·)\) |
| \(\chi_{ 1007 }(1006, ·)\) | \(\chi_{ 1007 } ( 1006, ·)\) | \(\chi_{ 1007 } ( 635, ·)\) | \(\chi_{ 1007 } ( 425, ·)\) | \(\chi_{ 1007 } ( 582, ·)\) | \(\chi_{ 1007 } ( 372, ·)\) | \(\chi_{ 1007 } ( 1, ·)\) |