  We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters
using a biased random-walk sampling technique which allows us to measure
probabilities of random walkers hitting sections of clusters with unprecedented
accuracy; our results include probabilities as small as 10^(-80). We find the
multifractal D(q) spectrum including regions of small and negative q. Our
algorithm allows us to obtain the harmonic measure for clusters more than an
order of magnitude larger than those achieved using the method of iterative
conformal maps, which is the previous best method. We find a phase transition
in the singularity spectrum f(alpha) at alpha approximately equal to 14 and
also find a minimum q of D(q), q_{min} = 0.9 plus or minus 0.05.
