  We characterize non-Hermitian band structures by symmetry indicator
topological invariants. Enabled by crystalline inversion symmetry, these
indicators allow us to short-cut the calculation of conventional non-Hermitian
topological invariants. In particular, we express the three-dimensional winding
number of point-gapped non-Hermitian systems, which is defined as an integral
over the whole Brillouin zone, in terms of symmetry eigenvalues at
high-symmetry momenta. Furthermore, for time-reversal symmetric non-Hermitian
topological insulators, we find that symmetry indicators characterize the
associated Chern-Simons form, whose evaluation usually requires a
computationally expensive choice of smooth gauge. In each case, we discuss the
non-Hermitian surface states associated with nontrivial symmetry indicators.
