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Atiyah says
$N(g,n) = - 2 g$
inAccording to lemma 4. of
M.F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414-452.
you could take $N(g,n) = - 2 g$.
in lemma 4.
According to lemma 4 of