Connes trace formula $$ \mathrm{Tr}\,{U(h)}=2h(1)\ln\Lambda + \sum_{v} \int d^{*}x \frac{h(u^{-1})}{|1-u|} $$
Weil's trace $$ \int_{C}h(u)|u|d^{*}u- \sum_{\rho}\int_{C}h(u)|u|^{\rho}d^{*}u+\int_{C}h(u)d^{*}u=\sum_{v} \int d^{*}x \frac{h(u^{-1})}{|1-u|} $$
in both cases the right side is quite similar. But are these two traces equivalent?