Lagrange interpolation of 2000 equidistant points on $\frac{1}{1+x^2}$ crashes mathematica/does not evaluate


My Code:

Points := Table[-5 + 10 j/2048, {j, 1, 2047}] Data := Table[1/(1 + x^2), {x, Points}] Data2 := Transpose[{Points, Data}] p[x_] = InterpolatingPolynomial[Data2, x] 

I am not sure why this crashes Mathematica. It seems it cannot handle this. I have a HW assignment that requires for me to find the interpolating polynomial of $ \frac{1}{1+x^2}$ at the points $ -5+10j/2048$ for $ j$ between 1 and 2047. The code above is my best attempt at doing so. I could not figure out how to make a table of the form $ \{\{x_1,y_1\}…\}$ so I just combined the two sets by transposition. Mathematica handles The first three lines properly. However, when trying to evaluate

p[x_] = InterpolatingPolynomial[Data2, x]

after about 2-3 minutes crashes. I am not sure what the issue is. Is this impossible for mathematica? I tried the command parallelize but that di not help. The goal of the problem is to find the error of this interpolatoin, and compare it to the error of interpolation using chebyshev points (which I will try doing after I can do this)