1.07 2.23 3.34 -1.06
 0.67 0.97 -2.8 11.3
 4.31 -1.3 -2.9 2.97
 -9.8 1.82 3.14 2.71

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.mlab import griddata

data = np.genfromtxt('Filename.dat')

x  = data[:,0] #extracts all data from 1st column (x-axis)
y  = data[:,1] #extracts all data from 2nd column (y-axis)
Fx = data[:,2] #extracts all data from 3rd column (x component of F)
Fy = data[:,3] #extracts all data from 4th column (y component of F)

xi = np.unique(x)
yi = np.unique(y)

X, Y = np.meshgrid(xi, yi)
Fxx = griddata(x, y, Fx, xi, yi, interp='linear')
Fyy = griddata(x, y, Fy, xi, yi, interp='linear')
plt.axes([0.065, 0.065, 0.9, 0.9])
plt.quiver(X,Y,Fxx,Fyy, alpha=.5)
plt.quiver(X,Y,Fxx,Fyy, edgecolor='k',facecolor='none', linewidth=.5)

plt.xlim(min(x)-1,max(x)+1)
plt.ylim(min(y)-1,max(y)+1)
plt.xticks(())
plt.yticks(())

plt.show()