# What are the correct eigenvalues to use in controlled rotation in HHL?

I'm studying the HHL algorithm from the qiskit textbook, but I don't understand what $$\lambda$$ we have to use. If my matrix $$A$$ has eigenvalues that can be written in a binary representation, then, after QPE, in that register we just have an $$n$$-bit representation of the eigenvalues. Otherwise, in that register, we have an $$n$$-bit approximation, $$2^n \frac{\lambda t}{2\pi}$$. When I do controlled rotation, I have to calculate $$2\arcsin(C/\lambda_j)$$. My question is, which $$\lambda_j$$'s are the real eigenvalues of $$A$$: the values stored in the register or only $$\frac{\lambda t}{2\pi}$$? My question arises because in this paper the authors use the exact eigenvalues, which can be written in a binary representation, but, the textbook uses $$\frac{\lambda t}{2\pi}$$, wherein this case, the eigenvalues cannot be written in a binary notation. Can't I always use the value inside the register $$(2^n \frac{\lambda t}{2\pi})$$ regardless of the representation?