f^{*}(e_{1})=(1-t-t^{2})(-1)+(1-t-t^{2})(1)+(1-t-t^{2})(1)(0)=1-1+1=1=\alpha_1
\\ f^{*}(e_{2})=0+2+1=3=\alpha_2
\\ f^{*}(e_{3})=-2+0+0=-2=\alpha_3
\\ f^{*}(e_{4})=-2+2+0=0=\alpha_4