  The states of hydrogen atom with principal quantum number $n\le3$ and zero
magnetic quantum number in constant homogeneous magnetic field ${\cal H}$ are
considered. The coefficients of energy eigenvalues expansion up to 75th order
in powers of ${\cal H}^2$ are obtained for these states. The series for energy
eigenvalues and wave functions are summed up to ${\cal H}$ values of the order
of atomic magnetic field. The calculations are based on generalization of the
moment method, which may be used in other cases of the hydrogen atom
perturbation by a polynomial in coordinates potential.
