Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{7} - x^{6} - 30 x^{5} - 3 x^{4} + 254 x^{3} + 246 x^{2} - 245 x - 137 \)
$\times$ | \(\chi_{ 71 } ( 1, ·)\) | \(\chi_{ 71 } ( 32, ·)\) | \(\chi_{ 71 } ( 20, ·)\) | \(\chi_{ 71 } ( 37, ·)\) | \(\chi_{ 71 } ( 48, ·)\) | \(\chi_{ 71 } ( 45, ·)\) | \(\chi_{ 71 } ( 30, ·)\) |
---|---|---|---|---|---|---|---|
\(\chi_{ 71 }(1, ·)\) | \(\chi_{ 71 } ( 1, ·)\) | \(\chi_{ 71 } ( 32, ·)\) | \(\chi_{ 71 } ( 20, ·)\) | \(\chi_{ 71 } ( 37, ·)\) | \(\chi_{ 71 } ( 48, ·)\) | \(\chi_{ 71 } ( 45, ·)\) | \(\chi_{ 71 } ( 30, ·)\) |
\(\chi_{ 71 }(32, ·)\) | \(\chi_{ 71 } ( 32, ·)\) | \(\chi_{ 71 } ( 30, ·)\) | \(\chi_{ 71 } ( 1, ·)\) | \(\chi_{ 71 } ( 48, ·)\) | \(\chi_{ 71 } ( 45, ·)\) | \(\chi_{ 71 } ( 20, ·)\) | \(\chi_{ 71 } ( 37, ·)\) |
\(\chi_{ 71 }(20, ·)\) | \(\chi_{ 71 } ( 20, ·)\) | \(\chi_{ 71 } ( 1, ·)\) | \(\chi_{ 71 } ( 45, ·)\) | \(\chi_{ 71 } ( 30, ·)\) | \(\chi_{ 71 } ( 37, ·)\) | \(\chi_{ 71 } ( 48, ·)\) | \(\chi_{ 71 } ( 32, ·)\) |
\(\chi_{ 71 }(37, ·)\) | \(\chi_{ 71 } ( 37, ·)\) | \(\chi_{ 71 } ( 48, ·)\) | \(\chi_{ 71 } ( 30, ·)\) | \(\chi_{ 71 } ( 20, ·)\) | \(\chi_{ 71 } ( 1, ·)\) | \(\chi_{ 71 } ( 32, ·)\) | \(\chi_{ 71 } ( 45, ·)\) |
\(\chi_{ 71 }(48, ·)\) | \(\chi_{ 71 } ( 48, ·)\) | \(\chi_{ 71 } ( 45, ·)\) | \(\chi_{ 71 } ( 37, ·)\) | \(\chi_{ 71 } ( 1, ·)\) | \(\chi_{ 71 } ( 32, ·)\) | \(\chi_{ 71 } ( 30, ·)\) | \(\chi_{ 71 } ( 20, ·)\) |
\(\chi_{ 71 }(45, ·)\) | \(\chi_{ 71 } ( 45, ·)\) | \(\chi_{ 71 } ( 20, ·)\) | \(\chi_{ 71 } ( 48, ·)\) | \(\chi_{ 71 } ( 32, ·)\) | \(\chi_{ 71 } ( 30, ·)\) | \(\chi_{ 71 } ( 37, ·)\) | \(\chi_{ 71 } ( 1, ·)\) |
\(\chi_{ 71 }(30, ·)\) | \(\chi_{ 71 } ( 30, ·)\) | \(\chi_{ 71 } ( 37, ·)\) | \(\chi_{ 71 } ( 32, ·)\) | \(\chi_{ 71 } ( 45, ·)\) | \(\chi_{ 71 } ( 20, ·)\) | \(\chi_{ 71 } ( 1, ·)\) | \(\chi_{ 71 } ( 48, ·)\) |