Differential measurements of the elliptic (upsilon(2)) and hexadecapole (upsilon(4)) Fourier flow coefficients are reported for charged hadrons as a function of transverse momentum (p(T)) and collision centrality or number of participant nucleons (N-part) for Au + Au collisions at root s(NN) = 200 GeV/ The upsilon(2,4) measurements at pseudorapidity vertical bar eta vertical bar <= 0.35, obtained with four separate reaction-plane detectors positioned in the range 1.0 < vertical bar eta vertical bar < 3.9, show good agreement, indicating the absence of significant Delta eta-dependent nonflow correlations. Sizable values for upsilon(4)(p(T)) are observed with a ratio upsilon(4)(p(T), N-part)/upsilon(2)(2)(p(T), N-part) approximate to 0.8 for 50 less than or similar to N-part less than or similar to 200, which is compatible with the combined effects of a finite viscosity and initial eccentricity fluctuations. For N-part greater than or similar to 200 this ratio increases up to 1.7 in the most central collisions.