  Lattice QCD calculations are presented for the spectra of N* excited states
with spins up to J = 7/2. Ambiguities of the standard method of spin
identification are shown to be overcome by the use of lattice operators that
transform according to SU(2) symmetry restricted to the lattice. Such operators
are labeled by their continuum spins. Overlaps of the operators with the states
obtained by diagonalizing matrices of correlation functions provide a clear
link between continuum spins and lattice states, allowing spins to be
identified. Evidence for an approximate realization of rotational symmetry in
the N* spectrum is presented. In simulations with pion mass = 392 MeV, the
low-lying excited states of lattice QCD are found to have the same quantum
numbers as the states of SU(6)xO(3) symmetry. The lattice spectra are
inconsistent with either a quark-diquark model or parity doubling of states and
they suggest that the J = 1/2 Roper resonance may have a complex structure
consisting of contributions from L=0, 1 and 2.
