What is $\pi_{31}(S^2)$, the 31st homotopy group of the 2-sphere ?

This question has a physics motivation:

1. There are relations between (2nd and 3rd) Hopf fibrations and (2- and 3-) qubits (quantum bits) entanglement; see Pinilla and Luthra - Hopf Fibration and Quantum Entanglement in Qubit Systems.

2. Maybe there are relations between classification of qubits entanglements and sphere homotopy groups, and we are interested in the classification of 4-qubits entanglements.

I tried fo find the solution on the net, with help of math fans, but without success.

Wikipedia gives only to the 22nd group homotopy of the 2-sphere.

This article of John Baez gives interesting references, like Allen Hatcher, Stable homotopy groups of spheres or a link with braids (Berrick, Cohen, Wong, and Wu - Configurations, braids, and homotopy groups). One speaks of a book of Kochman Stanley O.: Stable Homotopy Groups of Spheres: A Computer-Assisted Approach.

But I am totally unable to find the answer.

A subsidiary question would be: Until what rank do we know these high homotopy group of the 2-sphere?