  Discriminant indicators with generalized inversion symmetry are computed only
from data at the high-symmetry points. They allow a systematic search for
exceptional points. In this paper, we propose discriminant indicators for two-
and three-dimensional systems with generalized $n$-fold rotational symmetry
($n=4$, $6$). As is the case for generalized inversion symmetry, the indicator
taking a nontrivial value predicts the emergence of exceptional points and
loops without ambiguity of the reference energy. A distinct difference from the
case of generalized inversion symmetry is that the indicator with generalized
$n$-fold rotational symmetry ($n=4$, $6$) can be computed only from data at two
of four high-symmetry points in the two-dimensional Brillouin zone. Such a
difference is also observed in three-dimensional systems. Furthermore, we also
propose how to fabricate a two-dimensional system with generalized four-fold
rotational symmetry for an electrical circuit.
