Given a positive integer $$n^{}_{}$$, it can be shown that every complex number of the form $$r+si^{}_{}$$, where $$r^{}_{}$$ and $$s^{}_{}$$ are integers, can be uniquely expressed in the base $$-n+i^{}_{}$$ using the integers $$1,2^{}_{},\ldots,n^2$$ as digits. That is, the equation $$r+si=a_m(-n+i)^m+a_{m-1}(-n+i)^{m-1}+\cdots +a_1(-n+i)+a_0$$ is true for a unique choice of non-negative integer $$m^{}_{}$$ and digits $$a_0,a_1^{},\ldots,a_m$$ chosen from the set $$\{0^{}_{},1,2,\ldots,n^2\}$$, with $$a_m\ne 0^{}){}$$. We write $$r+si=(a_ma_{m-1}\ldots a_1a_0)_{-n+i}$$ to denote the base $$-n+i^{}_{}$$ expansion of $$r+si^{}_{}$$. There are only finitely many integers $$k+0i^{}_{}$$ that have four-digit expansions $$k=(a_3a_2a_1a_0)_{-3+i^{}_{}}~~~~a_3\ne 0.$$ Find the sum of all such $$k^{}_{}$$.

(第七届AIME1989 第14题)