The Hard Way

When asking for zeta zero to infinity, the program produces
a conclusive sum with the error factored in. Those who play
with numbers, 1 to n, are producing what are called partial
sums.

Below, from Grapf, zeta for (.5 + i). Gives a -78° angle:

Here, using the analytic continuation formula for R between 0 and 1, and

n=10 000. The angle is 77°.