We will define three similar but different notions of "spin" of an ideal in a number field, and we will show how a number-field version of Vinogradov's method (a sieve involving "sums of type I" and "sums of type II") can be used to prove that spins of prime ideals oscillate. Such equidistribution results have applications to the distribution of 16-ranks of class groups in certain one-prime-parameter families of quadratic number fields. Parts of this talk are joint work with Peter Koymans.