Combining several techniques, we propose an efficient and numerically reliable method to perform the quantum number projection and configuration mixing for most general meanfield states, i.e., the Hartree-Fock-Bogoliubov (HFB) type product states without symmetry restrictions. As for the example of calculations, we show the results of the simultaneous parity, number and angular-momentum projection from HFB type states generated from the cranked Woods-Saxon mean-field with a very large basis that is composed of N max = 20 spherical harmonic oscillator shells. that all the states connected by the symmetry operation, e.g., rotation of the system, are degenerate. Superposition of all these degenerate states gives a better quantum mechanical description in the variational sense, as it is clear in the formulation of the generator coordinate method (GCM). Since the symmetry requires the specific form of weight functions for superposition, the procedure restores the symmetry at the same time, i.e., projects out the states with good quantum numbers.The most important symmetry-breaking in nuclear structure is the spatial deformation, e.g., the quadrupole shape, so that the projection of the angular momentum is necessary to obtain the eigenstates of the angular momentum operators, especially for calculating the electromagnetic transition probabilities. There is a long history in the angular momentum projection calculations. Except for some special calculations intended for very light nuclei, the general framework of the projection from the (HFB-like) general product-type mean-field wave functions has been developed by Hara and his collaborators in Refs. 9)-11), where the calculation is restricted to the axially symmetric shape, but extended to the triaxially deformed and cranked (for high spins) cases in Ref. 12) (see also the review paper, 13) and a more recent application 14) ). Based on the angular momentum projection, the variation after projection calculations from general mean-field states have also been performed for the G-matrix based realistic interactions (see e.g. Refs. 15) and 16)). However, relatively small model spaces are used in these works, e.g., the two or three harmonic oscillator shells. Recently, the angular momentum projection with much larger space has been attempted with restriction of axially symmetry, intending to employ the Skyrme (or more general) energy functional, 17) where the GCM calculation with respect to the quadrupole deformed coordinates on top of it is performed (see also Ref. 18) for the similar type calculation with the finite range Gogny interaction). The restriction of axial symmetry has been lifted in more recent works for the Skyrme, 19) the relativistic mean-field, 20), 21) and the Gogny 22) approaches, although still the time-reversal invariance (no-cranking) and the D 2 symmetry of deformation are imposed in such calculations.In this paper, we discuss an efficient method of general quantum number projection, i.e., rather technical aspect of projection. We intend to perform the...