Calculation of values of L-functions associated to elliptic curves

We calculated numerically the values of L-functions of four typical elliptic curves in the critical strip in the range Im(s) ≤ 400. We found that all the non-trivial zeros in this range lie on the critical line Re(s) = 1 and are simple except the one at s = 1. The method we employed in this paper is the approximate functional equation with incomplete gamma functions in the coefficients. For incomplete gamma functions, we continued them holomorphically to the right half plane Re(s) > 0, which enables us to calculate for large Im(s). Furthermore we remark that a relation exists between Sato-Tate conjecture and the generalized Riemann Hypothesis.