Characteristic polynomials

The characteristic polynomials of the first two Hecke operators are as follows:

$$\begin{eqnarray*}T_2&=&(x + 2)({x^{2} - {2}})({x^{3} - {4}x - {2}})(x^{6} + {3}x... ...-241030x^5 \\ &&+ 112365x^4 + 51018x^3 -28526x^2 + 3560x -100) \end{eqnarray*}$$