Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General observations on series whose terms proceed as the sines and
  cosines of multiples of angles   Translated from the Latin original, "Observationes generales circa series,
quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur"
(1777). E655 in the Enestrom index. Euler looks at the binomial expansion
$(1+x)^n$ for $x=\cos \phi+i\sin\phi$. He does $n=$ positive and negative
integers, and $n={1/2}, -{1/2}$, and particular values of $\phi$.

4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess