  Let p be a prime number and C be the p-adic tame level 1 eigencurve
introduced by Coleman-Mazur. We prove that C is smooth at the evil Eisenstein
points and we give necessary and sufficient conditions for etaleness of the map
to the weight space at these points in terms of p-adic zeta values. A key step
is the determination at these points of the schematic reducibility locus of the
pseudo-character carried by C restricted to a decomposition group at p. Then,
the smoothness appears to be a consequence of the fact that the Dirichlet
L-functions only have simple zeros at integers.
