For any multiplicative congruential generator (d, z) with an odd modulus d and a multiplier z coprime to d, a computationally innovative method is presented as specialized forms of 2nd degree spectral tests of (d, z^i) with 2≦i≦6, at the least. Providing with sharp and powerful sieving tools, the method enables the excavation of the integer set (d, z) as a generator of uniform and independent random numbers of excellent statistics with sufficiently long periods for simulations, and furnishes the selected generator with ways of clear, unambiguous and quantitative specifications of its performance.