  A self-transverse immersion of the 2-sphere into 4-space with algebraic
number of self intersection points equal to -n induces an immersion of the
circle bundle over the 2-sphere of Euler class 2n into 4-space. Precomposing
the circle bundle immersions with their universal covering maps, we get for n>0
immersions g_n of the 3-sphere into 4-space. In this note, we compute the Smale
invariants of g_n. The computation is carried out by (partially) resolving the
singularities of the natural singular map of the punctured complex projective
plane which extends g_n.
  As an application, we determine the classes represented by g_n in the
cobordism group of immersions which is naturally identified with the stable
3-stem. It follows in particular that g_n represents a generator of the stable
3-stem if and only if n is divisible by 3.
