We test a conjectural nonabelian refinement of the classical 2- adic Main Conjecture of Iwasawa theory. In the first part, we show how, in the special case that we study, the validity of this refinement is equivalent to a congruence condition on the coefficients of some power series. Then, in the second part, we explain how to compute the first coefficients of this power series and thus numerically check the conjecture in that setting.
"Numerical Evidence Toward a 2-adic Equivariant “Main Conjecture”." Experiment. Math. 20 (2) 169 - 176, 2011.