Table of (integral) cohomology groups of K(Z,n) Can I find somewhere a table of the (first few) cohomology groups of $K(\mathbb{Z},n)$ with integer coefficients?
It seems like a natural counterpart to the table of the homotopy groups of spheres, but I couldn’t find anything. I’m aware of exposé 11, année 7 in the Cartan seminar where the homology of Eilenberg-MacLane spaces is computed, and I guess I could adapt it to the case where the group is $\mathbb{Z}$ and use the universal coefficient theorem to get the cohomology, but it’s not completely trivial, and I would be surprised that nobody thought about doing it before me.
 A: As far as I know, there is no complete source besides the Cartan seminar. Of course, the homology computation gives the cohomology computation immediately. However, if you are only interested in the first few groups, then you might be able to get away with just iteratively using the Serre spectral sequences for the fibrations $$K(\mathbb{Z},n-1)\rightarrow\star\rightarrow K(\mathbb{Z},n).$$ Since you know the integral cohomology of $K(\mathbb{Z},2)$ with its ring structure, and since the spectral sequences play well with the ring structure, it is not a difficult exercise to compute $H^*(K(\mathbb{Z},n),\mathbb{Z})$ for $*\leq 3n$ or so for any given $n\geq 3$.
A: There are several computations carried out explicitly in the paper
Samuel Eilenberg and Saunders Mac Lane, MR 65162 On the groups $H(\Pi,n)$. II. Methods of computation, Ann. of Math. (2) 60 (1954), 49--139.
For instance, I once wanted to know the groups $H_{4+i}(K(\mathbb{Z},4);\mathbb{Z})$ for $i\le 3$, and was able to extract the answer from Section 24. 
