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An application of Koike's Trace Formula
Koike's Trace Formula states that
\begin{equation}
\mbox{Tr}((U_p^{\kappa})^n) = - \sum_{0 \leq u < \sqrt{p^n}\\
(u,p)=1}H(u^2-4p^n)\frac{\gamma(u)^\kappa}{\gamma(u)^2 - p^n}-1,
\end{equation}
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