Definable E0 classes at arbitrary projective levels

Using a modification of the invariant Jensen forcing of [11], we define a model of ZFC, in which, for a given n≥3, there exists a lightface Πn1-set of reals, which is a E0-equivalence class, hence a countable set, and which does not contain any OD element, while every non-empty countable Σn1-set of reals is constructible, hence contains only OD reals.