Polynomials are Awesome

Algebra Level 5

p(x)\large{p(x)} is a monic polynomial of degree 4, such that

p(2)=55p(3)=181p(4)=377p(5)=619.\begin{aligned} p(2)&=-55\\ p(3)&=-181\\ p(4)&=-377\\ p(5)&=-619. \end{aligned}

Then what is the value of p(ω)?p(\omega)?

Details and Assumptions

  • ω\omega represents cube root of unity.
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