Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by \( x^{16} - 31 x^{8} + 256 \)
$\times$ | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 57, ·)\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{ 112 }(1, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 57, ·)\) |
\(\chi_{ 112 }(69, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 13, ·)\) |
\(\chi_{ 112 }(71, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 15, ·)\) |
\(\chi_{ 112 }(13, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 69, ·)\) |
\(\chi_{ 112 }(15, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 71, ·)\) |
\(\chi_{ 112 }(83, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 27, ·)\) |
\(\chi_{ 112 }(85, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 29, ·)\) |
\(\chi_{ 112 }(27, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 83, ·)\) |
\(\chi_{ 112 }(29, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 85, ·)\) |
\(\chi_{ 112 }(97, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 41, ·)\) |
\(\chi_{ 112 }(99, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 43, ·)\) |
\(\chi_{ 112 }(41, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 97, ·)\) |
\(\chi_{ 112 }(43, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 99, ·)\) |
\(\chi_{ 112 }(111, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 55, ·)\) |
\(\chi_{ 112 }(55, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 1, ·)\) | \(\chi_{ 112 } ( 111, ·)\) |
\(\chi_{ 112 }(57, ·)\) | \(\chi_{ 112 } ( 57, ·)\) | \(\chi_{ 112 } ( 13, ·)\) | \(\chi_{ 112 } ( 15, ·)\) | \(\chi_{ 112 } ( 69, ·)\) | \(\chi_{ 112 } ( 71, ·)\) | \(\chi_{ 112 } ( 27, ·)\) | \(\chi_{ 112 } ( 29, ·)\) | \(\chi_{ 112 } ( 83, ·)\) | \(\chi_{ 112 } ( 85, ·)\) | \(\chi_{ 112 } ( 41, ·)\) | \(\chi_{ 112 } ( 43, ·)\) | \(\chi_{ 112 } ( 97, ·)\) | \(\chi_{ 112 } ( 99, ·)\) | \(\chi_{ 112 } ( 55, ·)\) | \(\chi_{ 112 } ( 111, ·)\) | \(\chi_{ 112 } ( 1, ·)\) |