  We report tests and results from a new approach to the spectral density and
the mode number distribution of the Dirac operator in lattice gauge theories.
The algorithm generates the spectral density of the lattice Dirac operator as a
continuous function over all scales of the complete eigenvalue spectrum. This
is distinct from an earlier method where the integrated spectral density (mode
number) was calculated efficiently for some preselected fixed range of the
integration. The new algorithm allows global studies like the chiral condensate
from the Dirac spectrum at any scale including the cutoff-dependent IR and UV
range of the spectrum. Physics applications include the scale-dependent mass
anomalous dimension, spectral representation of composite fermion operators,
and the crossover transition from the $\epsilon$-regime of Random Matrix Theory
to the p-regime in chiral perturbation theory. We present thorough tests of the
algorithm in the 2-flavor sextet SU(3) gauge theory that we continue to pursue
for its potential as a minimal realization of the composite Higgs scenario.
