  We use self-consistent Hartree-Fock calculations performed in the full
$\pi$-band Hilbert space to assess the nature of the recently discovered
correlated insulator states in magic-angle twisted bilayer graphene (TBG). We
find that gaps between the flat conduction and valence bands open at neutrality
over a wide range of twist angles, sometimes without breaking the system's
valley projected ${\cal C}_{2}{\cal T}$ symmetry. Broken spin/valley flavor
symmetries then enable gapped states to form not only at neutrality, but also
at total moir\'e band filling $n = \pm p/4$ with integer $p = 1, 2, 3$, when
the twist angle is close to the magic value at which the flat bands are most
narrow. Because the magic-angle flat band quasiparticles are isolated from
remote band quasiparticles only for effective dielectric constants larger than
$ \sim 20$, the gapped states do not necessarily break \CT symmetry and as a
consequence the insulating states at $n = \pm 1/4$ and $n = \pm 3/4$ need not
exhibit a quantized anomalous Hall effect.
