Nu is a Heegaard Floer theoretic invariant defined by Ozsvath-Szabo [2]. It is closely related to nu^+ and nu^-. It is a concordance invariant and takes integer values. Values of nu in this database were computed using a program written by Zoltan Szabo, available at [3].
[1] Hom, J., "A survey on Heegaard Floer homology and concordance," Journal of Knot Theory and Its Ramifications. Vol. 26, No. 02, 1740015 (2017). Arxiv preprint
[2] Ozsvath, P. and Szabo, Z., "Knot Floer homology and rational surgeries," Algebraic & Geometric Topology. 11 (2011), no. 1, 1-68. Arxiv preprint.
[3] Szabo, Z., Knot Floer Homology Calculator.