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Mr. Xcoder
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Jelly, 8 bytes

ASŒRḅ@Ðḟ

Try it online!

##How?

ASŒRḅ@Ðḟ || Full program (monadic link).

AS        || Sum the absolute values.
  ŒR      || And create the symmetric inclusive range from its negative value.
       Ðḟ || And discard those that yield a truthy value...
     ḅ@   || When plugging them into the polynomial.

Based off Luis' answer.

Mr. Xcoder
  • 42.5k
  • 9
  • 81
  • 214