If you do not like this plot, you can also try:
ROOT::Math::IntegratorOneDimOptions::SetDefaultIntegrator("Gauss");
TF1Convolution *f_conv = new TF1Convolution(f1, f1, emin, emax, false);
You will then have four different curves, so you should be able to pick one for you 
Well, you could try all different available ROOT’s “1-dim integrators”: “Gauss”, “GaussLegendre”, “Adaptive”, “AdaptiveSingular” and “NonAdaptive”. 
Seven different curves should be a “good many” to choose from