Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$

$K$ is the global number field defined by \( x^{2} - x + 2501 \)

$\times$ \(\chi_{ 10003 } ( 1, ·)\) \(\chi_{ 10003 } ( 10002, ·)\)
\(\chi_{ 10003 }(1, ·)\) \(\chi_{ 10003 } ( 1, ·)\) \(\chi_{ 10003 } ( 10002, ·)\)
\(\chi_{ 10003 }(10002, ·)\) \(\chi_{ 10003 } ( 10002, ·)\) \(\chi_{ 10003 } ( 1, ·)\)