  Continuing previous work on the 3PN-accurate gravitational wave generation
from point particle binaries, we obtain the binary's 3PN mass-type quadrupole
and dipole moments for general (not necessarily circular) orbits in harmonic
coordinates. The final expressions are given in terms of their ``core'' parts,
resulting from the application of the pure Hadamard-Schwartz (pHS) self-field
regularization scheme, and augmented by an ``ambiguous'' part. In the case of
the 3PN quadrupole we find three ambiguity parameters, xi, kappa and zeta, but
only one for the 3PN dipole, in the form of the particular combination
xi+kappa. Requiring that the dipole moment agree with the center-of-mass
position deduced from the 3PN equations of motion in harmonic coordinates
yields the relation xi+kappa=-9871/9240. Our results will form the basis of the
complete calculation of the 3PN radiation field of compact binaries by means of
dimensional regularization.
