We study numerically the development of singularities of vorticity field for 3D Euler equation on grids equivalent to up to $2048^3$ nodes. We examine nearly arbitrary smooth symmetric and non-symmetric initial data. We track the evolution for not only the global maximum of the vorticity field, but also for all of the local maximums. For several realizations of the initial data, both symmetric and non-symmetric, and as long as our simulations are reliable, we observe exponential development of singularities with time. To the end of our simulations we also observe the initial stage of formation of Kolmogorov energy spectrum $~k^(-5/3)$. Our results suggest that exponentially developing singularities may lead to formation of Kolmogorov energy spectrum even before viscosity comes in play.