Euler tangent numbers modulo 720 and Genocchi numbers modulo 45

We establish congruences for higher order Euler polynomials modulo 720. apply this result constructing analogues of Stern secant numbers $E_{4n}\equiv 5(\mathrm{mod}\ 60), E_{4n+2}\equiv -1(\mathrm{mod}\ 60)$ to tangent and Genocchi numbers. prove that satisfy the following $E_{4n+1}\equiv 16(\mathrm{mod}\ 720)$, $E_{4n+3}\equiv -272(\mathrm{mod}\ 720)$. 12-periodic property 45.