Firstly I will use Dwork's cohomology to compute half of the Newton polygon of the L-function under some conditions. Then I will introduce the dual theory and deformation theory to get the p-adic differential equation, which in modern name is the Gauss-Manin connection in my case. Then by analyzing the formal solutions at infinity, the irregular singular point, we are able to obtain a functional equation for the L-function when the base prime p large enough. The functional equation will give us the rest half of the Newton polygon. This explicit Newton polygon will be an evidence that satisfies Wan's limit conjecture.