Cyclotomic Polynomial Calculator

Minimal poly of e^{2πi/n}

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n (1–30)

Φ_7(x)

+x^6+x^5+x^4+x^3+x^2+x+1

deg = φ(7) = 6

Coefficients

[0]=1[1]=1[2]=1[3]=1[4]=1[5]=1[6]=1

x^7−1 = Π Φ_d

Φ_1Φ_7

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About Cyclotomic Polynomial Calculator

A cyclotomic polynomial calculator computing Φ_n(x), the minimal polynomial of primitive nth roots of unity. Degree = φ(n) (Euler totient). Φ_n divides x^n−1 and x^n−1 = Π_{d|n} Φ_d(x). Coefficients are always integers. Client-side.

Cyclotomic Polynomial Calculator Features

Φ_n(x) coefficients
Degree = φ(n)
Factorization
Root display
Divisor product

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