Initial state for a 3-body problem to create Figure 8 [ restricted to 2D ]

Question

I've made an n-body simulation solution using the naive algorithm of O(n^2) in my library ChelseaaJS.
I was trying to make some pleasing 3 Body simulations.
I wanna do the 8 figure thing.
I know it's a 3D simulation restricted to 2D to create 8-figure as given in the famous research paper on the same.
I wanted to know if there is any particular initial state of the system in 2d i.e. given position and speed of masses.

Example of the n-body simulation:
This is just a basic solar system, nothing fancy. I will put it live if anyone wants to use it, tweak it.

EDIT : Here is the paper: https://arxiv.org/abs/math/0511219 [thanks to @PM 2Ring] and I want to make something like :

Answer 1

The initial condition are supposedly given in table 1 of Simó, C. (2001). New Families of Solutions in N-Body Problems, however I couldn't decipher the y position of the first and second bodies from there.

I found a slightly different version of the initial conditions in this website:

r[0][0] = 0.9700436;
r[0][1] = -0.24308753;
r[0][2] = 0;
v[0][0] = 0.466203685;
v[0][1] = 0.43236573;
v[0][2] = 0;

r[1][0] = -r[0][0];
r[1][1] = -r[0][1];
r[1][2] = -r[0][2];
v[1][0] = v[0][0];
v[1][1] = v[0][1];
v[1][2] = v[0][2];

r[2][0] = 0;
r[2][1] = 0;
r[2][2] = 0;
v[2][0] = -2*v[0][0];
v[2][1] = -2*v[0][1];
v[2][2] = -2*v[0][2];