Sum of Reciprocals

Algebra Level 3

Given

\[\begin{align} a+b+c +d & = 0 \\ abcd & = 1 \\ a^3 + b^3 + c^3 + d^3 & = 1983 \\ \end{align} \]

What is the value of \( \frac {1}{a} + \frac {1}{b} + \frac {1}{c} + \frac {1}{d} \)?

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