You want the idoneal numbers, 
http://oeis.org/A000926  and http://en.wikipedia.org/wiki/Idoneal_number  

See also pages 81-82 in Duncan A. Buell, *Binary Quadratic Forms* 

Depending what you mean by 32, the primes represented by $x^2 + 8 y^2$ are, in fact, given by congruences. However, half of those same primes are represented by $x^2 + 32 y^2,$ while the other half are represented by $4 x^2 + 4 x y + 9 y^2.$ The condition saying which are which is not simply congruences.