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

$K$ is the global number field defined by <span class="tset-container"><span class="tset-raw" id="tset-raw-165" raw="x^2 - 31" israw="0" ondblclick="ondouble(165)">\(x^{2} - 31\)</span>&nbsp;&nbsp;<span onclick="iconrawtset(165)"><img alt="Toggle raw display" src="/static/images/t2r.png" class="tset-icon" id="tset-raw-icon-165" style="position:relative;top: 2px"></span></span>

$\times$ \(\chi_{ 124 } ( 1, ·)\) \(\chi_{ 124 } ( 123, ·)\)
\(\chi_{ 124 }(1, ·)\) \(\chi_{ 124 } ( 1, ·)\) \(\chi_{ 124 } ( 123, ·)\)
\(\chi_{ 124 }(123, ·)\) \(\chi_{ 124 } ( 123, ·)\) \(\chi_{ 124 } ( 1, ·)\)