The governing equation locating component centers in the degree- n bifurcation set is a polynomial with a very high degree and its root-finding lacks numerical accuracy. The equation is transformed to have its degree reduced by a factor (n - 1) . Newton's method applied to the transformed equation improves the accuracy with properly chosen initial values. The numerical implementation is done with Maple V using a large number of computational precision digits. Many cases are studied for 2\leq n \leq 25 and show a remarkably improved computation. Our study extends the results given by Peitgen and Richter [11].