Listing 3

 before transform:
0.500000 0.000000
0.778801 0.000000
0.606531 0.000000
0.472367 0.000000
0.367879 0.000000
0.286505 0.000000
0.223130 0.000000
0.173774 0.000000
0.135335 0.000000
0.105399 0.000000
0.082085 0.000000
0.063928 0.000000
0.049787 0.000000
0.038774 0.000000
0.030197 0.000000
0.023518 0.000000
 w factors:
1.000000 0.0000001.000000 -0.000000
0.923880 0.3826830.923880 -0.382683
0.707107 0.7071070.707107 -0.707107
0.382683 0.9238800.382683 -0.923880
0.000000 1.0000000.000000 -1.000000
-0.382683 0.923880-0.382683 -0.923880
-0.707107 0.707107-0.707107 -0.707107
-0.923880 0.382683-0.923880 -0.382683
-1.000000 0.000000-1.000000 -0.000000
-0.923880 -0.382683-0.923880 0.382683
-0.707107 -0.707107-0.707107 0.707107
-0.382683 -0.923880-0.382683 0.923880
-0.000000 -1.000000-0.000000 1.000000
0.382683 -0.9238800.382683 0.923880
0.707107 -0.7071070.707107 0.707107
0.923880 -0.3826830.923880 0.382683
 transformed:
3.938010 0.000000
1.143903 -1.746777
0.373174 -1.070216
0.181974 -0.699026
0.111059 -0.475893
0.078526 -0.320685
0.062163 -0.199640
0.054256 -0.096066
0.051880 0.000000
0.054256 0.096066
0.062163 0.199640
0.078526 0.320685
0.111059 0.475893
0.181974 0.699026
0.373174 1.070216
1.143903 1.746777
 scaled by dt and compared to analytic answer:
 0.984503 0.000000 1.000000 -0.000000
 0.285976 -0.436694 0.288400 -0.453018
 0.093294 -0.267554 0.092000 -0.289025
 0.045493 -0.174757 0.043091 -0.203062
 0.027765 -0.118973 0.024705 -0.155223
 0.019631 -0.080171 0.015953 -0.125293
 0.015541 -0.049910 0.011133 -0.104922
 0.013564 -0.024017 0.008203 -0.090200
 0.012970 0.000000 0.006293 -0.079077
 0.013564 0.024017 0.004979 -0.070383
 0.015541 0.049910 0.004036 -0.063405
 0.019631 0.080171 0.003338 -0.057681
 0.027765 0.118973 0.002807 -0.052903
 0.045493 0.174757 0.002392 -0.048854
 0.093294 0.267554 0.002064 -0.045379
 0.285976 0.436694 0.001798 -0.042365
 transformed back and scaled by 1/N:
0.500000 0.000000
0.778801 -0.000000
0.606531 0.000000
0.472367 -0.000000
0.367879 -0.000000
0.286505 -0.000000
0.223130 0.000000
0.173774 0.000000
0.135335 0.000000
0.105399 0.000000
0.082085 -0.000000
0.063928 0.000000
0.049787 0.000000
0.038774 0.000000
0.030197 -0.000000
0.023518 -0.000000