  The distributions of event-by-event harmonic flow coefficients v_n for n=2-4
are measured in sqrt(s_NN)=2.76 TeV Pb+Pb collisions using the ATLAS detector
at the LHC. The measurements are performed using charged particles with
transverse momentum pT> 0.5 GeV and in the pseudorapidity range |eta|<2.5 in a
dataset of approximately 7 ub^-1 recorded in 2010. The shapes of the v_n
distributions are described by a two-dimensional Gaussian function for the
underlying flow vector in central collisions for v_2 and over most of the
measured centrality range for v_3 and v_4. Significant deviations from this
function are observed for v_2 in mid-central and peripheral collisions, and a
small deviation is observed for v_3 in mid-central collisions. It is shown that
the commonly used multi-particle cumulants are insensitive to the deviations
for v_2. The v_n distributions are also measured independently for charged
particles with 0.5<pT<1 GeV and pT>1 GeV. When these distributions are rescaled
to the same mean values, the adjusted shapes are found to be nearly the same
for these two pT ranges. The v_n distributions are compared with the
eccentricity distributions from two models for the initial collision geometry:
a Glauber model and a model that includes corrections to the initial geometry
due to gluon saturation effects. Both models fail to describe the experimental
data consistently over most of the measured centrality range.
