Akm[k_,m_]:=Piecewise[{{0, (k != 2 && k != 4) || (k != 4 && m != -2 && m != -1 && m != 0 && m != 1 && m != 2) || (m != -4 && m != -3 && m != -2 && m != -1 && m != 0 && m != 1 && m != 2 && m != 3 && m != 4)}, {A[2, 2], k == 2 && (m == -2 || m == 2)}, {-A[2, 1], k == 2 && m == -1}, {A[2, 0], k == 2 && m == 0}, {A[2, 1], k == 2 && m == 1}, {A[4, 4], k == 4 && (m == -4 || m == 4)}, {-A[4, 3], k == 4 && m == -3}, {A[4, 2], k == 4 && (m == -2 || m == 2)}, {-A[4, 1], k == 4 && m == -1}, {A[4, 0], k == 4 && m == 0}, {A[4, 1], k == 4 && m == 1}}, A[4, 3]]