Fitting a plane ellipse in 3D space

Please define the number of points here
N= important: 8 <= n <= 100 !

Please define the parameters for generating the data in the following table.
You don't need to bother about the normalization requirement. This will be done internally. You must have λ₁, λ₂ >= 0.001 and their quotient in the range [0.001,1000].

a1=
a2 =
a3 =
a4 =
α =
β =
xc =
yc =
λ1 =
λ2 =

N angles will be chosen equidistantly
in [psi1,psi2] to generate the data points:

psi1 =
psi2 =

Please define the error level here. This is applied componentwise relative.
errlev =

Please specify the number of points: 8<=num<=100!

Please type the data points in the following textarea, simply as a series of 3*num numbers.
You may write several points in one line as you wish.

(x,y,z) =

0.002037965 0.004225765 0.002020202 0.005766671 0.007269193 0.004040404 0.010004802 0.00995638 0.006060606 0.03019849 0.01969697 0.014591289 0.038857283 0.022727273 0.017839321 0.045443501 0.024730475 0.02020202 0.051213405 0.026346492 0.02222222 0.162243245 0.039117883 0.054545455 0.178662839 0.03893748 0.058585859 0.195740664 0.038296774 0.062626263 0.222781268 0.036340005 0.068686869 0.251787024 0.033009003 0.074747475 0.455830971 -0.046969697 0.097166076 0.46279206 -0.068181818 0.091323015 0.407719192 -0.104545455 0.064554798 0.360058411 -0.11051623 0.050505051 0.352443612 -0.11084211 0.048484848 0.31150078 -0.110465333 0.038383838 0.212154519 -0.097501571 0.018181818 0.136529019 -0.077272727 0.006507255 0.103195122 -0.065151515 0.002507114 0.081719652 -0.056060606 0.000388246