Level
pending

Let **\(B\)** be the set of all integers. Given **\(2\)** polynomials

**\[p(x)=x^3+ax^2+bx+c\]**

with **\(a,b,c\)** are elements of **\(B\)** and

**\[q(x)=x^2-40x+2410\]**

Assuming that **\(p(x)=0\)** has **\(3\)** distinct integer roots, **\(p(2005)=-2005\)** and **\(p(q(x))=0\)** doesn't have any real roots, what are the last **\(3\)** digits of the absolute value of the sum of all possible values of **\(a\)**?

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