  We calculate the $N$ interval replicated negativity for the Ising and free
compact boson conformal field theory using correlation functions of branch
point twist fields. For some subset $P\subset N$, this is a calculation of
$\rm{Tr}(\rho_A^{T_P})^n$ where $n$ is the replica index. This can be
reformulated as a calculation of partition functions over superelliptic Riemann
surfaces, and for the models in question, this partition function can be
expressed in terms of the period matrix of this surface. We detail how to
construct the period matrices for these surfaces, giving an analytic expression
for $\rm{Tr}(\rho_A^{T_P})^n$. The results are expressed such that when $P =
\emptyset$, which corresponds to calculating the R\'enyi entropy, the formulas
aligns with known results for the $N$ interval R\'enyi entropy.
