  We present High Sensitivity Array observation of the water megamasers of NGC
1068. We obtain absolute astrometry with 0.3 mas precision that confirms the
association of the disk masers with the nuclear radio continuum source S1. The
new observations reveal two new blueshifted groups of disk masers. We also
detect the 22 GHz continuum on short interferometric baselines. The
position-velocity diagram of the disk masers shows a curve consistent with a
nonaxisymmetric distribution of maser spots. The curve is probably the result
of spiral arms with a constant pitch angle of roughly 5 degrees. The disk
kinematics are consistent with Keplerian rotation and low turbulent speeds. The
inferred central mass is 17 million solar masses. On the basis of disk
stability arguments, the mass of the molecular disk is roughly 110 thousand
solar masses. The disk masers further resolve into filamentary structures
suggesting an ordered magnetic field threading the maser disk. The magnetic
field strengths must be greater than 1.6 mG to withstand turbulent motions in
the partially ionized molecular gas. We note apparent asymmetries in the
molecular disk that might be explained by anisotropic heating by a misaligned
inner accretion disk. The new observations also detect the fainter jet masers
north of the disk masers. The distribution and kinematics of the jet masers are
consistent with an expanding ring of molecular gas.
