### Visualize vector field with singularities

What's the best way to plot vector fields with singularities, for example if I take

```
var('x1 x2')
E1=vector([x1,x2])/(sqrt(x1^2+x2^2))^3
E2=E1.subs(x1=x1-1)
E=(E1-E2)
plot_vector_field(E,(x1,-3,3),(x2,-3,3))
```

I get the following ugly plot:

Is it possible to exclude a region around the singularities?