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Algebra Level 4

x4+3x3+4x2+3x+1=0x^4+3x^3+4x^2+3x+1=0

Let a,b,c,a,b,c, and dd be the not necessarily distinct roots of the equation above. Find the value of the expression below:

a1024+b1024+c1024+d1024+1a1024+1b1024+1c1024+1d1024.a^{1024}+b^{1024}+c^{1024}+d^{1024}+\frac{1}{a^{1024}}+\frac{1}{b^{1024}}+\frac{1}{c^{1024}}+\frac{1}{d^{1024}}.

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