Using the spherical basis of the spin-ν operator, together with an appropriate normalized complex (2ν +1)-spinor on S
3 we obtain spin-ν representation of the U(1) Hopf fibration S
3 → S
2 as well as its associated fuzzy version. Also, to realize the first Hopf map via the spherical basis of the spin-1 operator with even winding numbers, we present an appropriate normalized complex three-spinor. We put the winding numbers in one-to-one correspondence with the monopole charges corresponding to different associated complex vector bundles.