I have an integral
$$\int_\gamma e^{-z + z^3/3} dz,$$
where $\gamma$ is a contour in a complex plane going from infinity back to infinity (in some other direction). How can I figure out which contour deformations are allowed and which not?
Since both polynomials and the exponential function are entire functions it follows $e^{-z + z^3/3}$ is also entire. But somehow it seems I still can not change the contour of integration completely arbitrarily?