  The spectral test of random number generators (R.R. Coveyou and R.D.
McPherson, 1967) is generalized. The sequence of random numbers is analyzed
explicitly, not just via their n-tupel distributions. We find that the mixed
multiplicative generator with power of two modulus does not pass the extended
test with an ideal result. Best qualities has a new generator with the
recursion formula X(k+1)=a*X(k)+c*int(k/2) mod 2^d. We discuss the choice of
the parameters a, c for very large moduli 2^d and present an implementation of
the suggested generator with d=256, a=2^128+2^64+2^32+62181, c=(2^160+1)*11463.
