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

$K$ is the global number field defined by \(x^{2} \) \(\mathstrut +\mathstrut 2505 \)

$\times$ \(\chi_{ 10020 } ( 1, ·)\) \(\chi_{ 10020 } ( 10019, ·)\)
\(\chi_{ 10020 }(1, ·)\) \(\chi_{ 10020 } ( 1, ·)\) \(\chi_{ 10020 } ( 10019, ·)\)
\(\chi_{ 10020 }(10019, ·)\) \(\chi_{ 10020 } ( 10019, ·)\) \(\chi_{ 10020 } ( 1, ·)\)