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-71" raw="x^2 - x + 57" israw="0" ondblclick="ondouble(71)">\(x^{2} - x + 57\)</span>&nbsp;&nbsp;<span onclick="iconrawtset(71)"><img alt="Toggle raw display" src="/static/images/t2r.png" class="tset-icon" id="tset-raw-icon-71" style="position:relative;top: 2px"></span></span>

$\times$ \(\chi_{ 227 } ( 1, ·)\) \(\chi_{ 227 } ( 226, ·)\)
\(\chi_{ 227 }(1, ·)\) \(\chi_{ 227 } ( 1, ·)\) \(\chi_{ 227 } ( 226, ·)\)
\(\chi_{ 227 }(226, ·)\) \(\chi_{ 227 } ( 226, ·)\) \(\chi_{ 227 } ( 1, ·)\)