I have the characteristic function of a random variable $Y$ as
$$\psi_Y(t)=\sum_{m=0}^K{K\choose m}j^me^{-jmt}E_1^m(-jt)$$
where $j=\sqrt{-1}$, and $E_1(x)=\int_x^{\infty}\frac{e^{-z}}{z}\,dz$ is the exponential integral. I am trying to find the CDF from this characteristic function as (see this link)
$$F_Y(y)=\frac{1}{2}-\frac{1}{\pi}\int_0^{\infty}\frac{\text{Im}\left\{e^{-jty}\psi_Y(t)\right\}}{t}\,dt$$
where $\text{Im}(.)$ is the imaginary part of a complex number. However, evaluating this integral numerically gives me warning that the integral may not exist, and the result is not real and between 0 and 1. What could the problem be ? The characteristic function is not correct? The CDF formula given above is not correct?