I'm doing an easy calculation. The problem is to write down the generators of the super-virasoro algebra in terms of the bosonic and fermionic oscillators. I'm following Polchinski. I'm trying to derive equation (10.2.12a)

We write $$T_{B}(z)=\sum_{n \in \mathbb{Z}}\frac{L_{n}}{z^n+2}$$

We invert to get $$L_{n}=\oint \frac{dz}{2\pi i}z^{n+2} T_{B}(z)$$

Now, $$T_{B}(z)=-\frac{1}{2}\psi \partial \psi $$+ contributions from bosons

I'm trying to calculate the $L_n$ in terms of the fermionic oscillators. I get

$$L_n=\frac{1}{4}\sum_{r\in \mathbb{Z}+\nu}(2r+1)\psi_{n-r}\psi_{r}$$

However, the correct formula is : $$L_n=\frac{1}{4}\sum_{r\in \mathbb{Z}+\nu}(2r-m)\psi_{n-r}\psi_{r}$$

Is this a typo? Or is my formula incorrect?