Equidistribution of shapes of complex cubic fields of fixed quadratic resolvent

We show that the shape of a complex cubic field lies on geodesic modular surface defined by field's trace-zero form. also prove general such statement for all orders in \'etale Q-algebras. Applying method Manjul Bhargava and Piper H to results Ariel Shnidman, we shapes lying fixed become equidistributed with respect hyperbolic measure as discriminant goes infinity. is complete invariant (within family fields).