The equation $$x^{10}+(13x-1)^{10}=0\,$$ has 10 complex roots \(r_1, \overline{r_1}, r_2, \overline{r_2}, r_3, \overline{r_3}, r_4, \overline{r_4}, r_5, \overline{r_5},\,\) where the bar denotes complex conjugation. Find the value of $$\frac 1{r_1\overline{r_1}}+\frac 1{r_2\overline{r_2}}+\frac 1{r_3\overline{r_3}}+\frac 1{r_4\overline{r_4}}+\frac 1{r_5\overline{r_5}}.$$

(第十二届AIME1994 第13题)