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The sum of

If you multiply all the primitive roots of unity for the first $n$ primes is by $-n$, -i$, then add them, you get$in$, whose degree is$1$2$ and whose absolute value is $n$, rational and unbounded.

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No, because the

The sum over of all quadratic residues $a$ mod $p$ the primitive roots of unity for the first $e^{2\pi i a/p}$ n$primes is$(-1+\sqrt{p})/2$or -n$, whose degree is $(-1+i\sqrt{p})/2$, by the theory of Gauss sums, which 1$and whose absolute value is unbounded but has degree$2$.n$, rational and unbounded.

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No, because the sum over all quadratic residues $a$ mod $p$ of $e^{2\pi i a/p}$ is $(-1+\sqrt{p})/2$ or $(-1+i\sqrt{p})/2$, by the theory of Gauss sums, which is unbounded but has degree $2$.