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We present a measurement of the shape of the Z/γ* boson transverse momentum (qT) distribution in pp → Z/γ* → e+e- + X events at a center-of-mass energy of 1.96 TeVusing 0.98 fb-1 of data collected with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resummation prediction at low qT, but above the perturbative QCD calculation in the region of qT > 30 GeV/c. Using events with qT < 30 GeV/c, we extract the value of g2, one of the nonperturbative parameters for the resummation calculation. Data at large boson rapidity y are compared with the prediction of resummation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function.