(1000 is close to the default for many plotting devices, we want to specify it explicitly so that the result do not depend on the output device.) Try...

(1000 is close to the default for many plotting devices, we want to specify it explicitly so that the result do not depend on the output device.) Try the recursive plot: ploth(t = 100, 110, real(zeta(0.5+I*t)), recursive) It takes approximately the same time. Now try specifying fewer points, but make PARI approximate the data by a smooth curve: ploth(t = 100, 110, real(zeta(0.5+I*t)), splines, 100) This takes much less time, and the output is practically the same. How to compare these two outputs? We will see it shortly. Right now let us plot both real and complex parts of On the same graph: f(t) = z=zeta(0.5+I*t); [real(z),imag(z)] ploth(t = 100, 110, f(t), , 1000) Note how one half of the roots of the real and imaginary parts coincide. Why did we define a function f(t)?