  We present inelastic neutron scattering experiments on a single-domain
crystal of lightly-doped La1.96Sr0.04CuO4. We find that the magnetic excitation
spectrum in this insulating phase with a diagonal incommensurate spin
modulation is remarkably similar to that in the superconducting regime, where
the spin modulation is bond parallel. In particular, we find that the
dispersion slope at low energy is essentially independent of doping and
temperature over a significant range. The energy at which the excitations cross
the commensurate antiferromagnetic wave vector increases roughly linearly with
doping through the underdoped regime.
