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The "color" in the colored Jones polynomial is an integer parameter. In thispaper, a periodic pattern of the values of the colored Jones polynomial at thesecond and the third roots of unity is found. If we substitute -1 to thecolored Jones polynomial, the value is alternately 1 or the determinant of thegiven link. When it comes to substituting the primitive third root of unity,another periodic pattern appears.

Periodicity Properties of the Colored Jones Polynomial