Inverse fourier transform of Hermitian function, getting an imaginary part
A (near) sinusoid in one domain (zoom in off center, and you might see it) can indicate a shift away from symmetry in the other domain.  So your initial imaginary signal may be 1 or 1/2 samples off from exact circular symmetry around element 0 (maybe around element 1 in MatLab or Fortran weird array indexing)