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The energy spectrum of an electron confined to an arbitrary surface of revolution in an external magnetic field, parallel to the symmetry axis, is studied analytically and numerically. Via conformation mapping of the cross section of the circle, the problem is reduced to one on the surface of the sphere. The case of a spheroid is considered in details, and the dependence on parameters is discussed. In the high magnetic field limit a regular structure in the energy spectrum, resembling the Landau levels, is obtained.