  We provide the time series and angular distributions of the neutrino and
gravitational-wave emissions of eleven state-of-the-art three-dimensional
non-rotating core-collapse supernova models and explore correlations between
these signatures and the real-time dynamics of the shock and the
proto-neutron-star core. The neutrino emissions are roughly isotropic on
average, with instantaneous excursions about the mean inferred luminosity of as
much as $\pm$20%. The deviation from isotropy is least for the
"$\nu_{\mu}$"-type neutrinos and the lowest-mass progenitors. Instantaneous
temporal luminosity variations along a given direction for exploding models
average $\sim$2$-$4%, but can be as high as $\sim$10%. For non-exploding
models, they can achieve $\sim$25%. The temporal variations in the neutrino
emissions correlate with the temporal and angular variations in the mass
accretion rate. We witness the LESA phenomenon in all our models and find that
the vector direction of the LESA dipole and that of the inner Y$_\mathrm{e}$
distribution are highly correlated. For our entire set of 3D models, we find
strong connections between the cumulative neutrino energy losses, the radius of
the proto-neutron star, and the $f$-mode frequency of the gravitational wave
emissions. When physically normalized, the progenitor-to-progenitor variation
in any of these quantities is no more than $\sim$10%. Moreover, the reduced
$f$-mode frequency is independent of time after bounce to better than
$\sim$10%. Therefore, simultaneous measurement of gravitational waves and
neutrinos from a given supernova event can be used synergistically to extract
real physical quantities of the supernova core.
