Mathematica - Countour plot problem

[asynja]

Hello! I'm trying to plot some eigenfunctions (for a semicircle) in Mathematica. Functions are of the following form:
$$g_{ms}=J_{2m+1}(y_{ms}x) sin ((2m+1)\varphi)$$
For example, for m=0 and s=1 it should look like what I drew in the attached file "Snapshot". Well, I don't have much experience with Mathematica and the "code" I wrote so far doesn't give me the right result.
Here's my try:

m = 0;
s = 1;
dat = Table[{x = RandomReal[{-1, 1}], y = RandomReal[{0, 1}],
    BesselJ[(2*m + 1), BesselJZero[m, s]*x]*
     Sin[(2*m + 1)*ArcTan[x, y]]}, {1000}];
ListContourPlot[dat]

The plot I get is in the attached file "Wrongplot". What am I doing wrong?

 

[RUber]

It seems like you might be using the wrong coordinates. Could this be the polar form?
Where you have x in $g_{ms} = J_{2m+1}(y_{ms} x) \sin ((2m+1)\varphi)$, you might try using r = $\sqrt(x^2+y^2)$.