  We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons
field coupled to $N_f$ fermions in the limit of large $N_f$ using conformal
truncation, i.e. with a truncated space of states corresponding to primary
operators with dimension below a maximum cutoff $\Delta_{\rm max}$. In both the
Chern-Simons theory, and in the $O(N)$ model at infinite $N$, we compute the
current spectral functions analytically as a function of $\Delta_{\rm max}$ and
reproduce previous results in the limit that the truncation $\Delta_{\rm max}$
is taken to $\infty$. Along the way, we determine how to preserve gauge
invariance and how to choose an optimal discrete basis for the momenta of
states in the truncation space.
