l1   m1   l2   m2     analytical value:         |        output of angint
                                                                          
  1    0    0    0         1/sqrt(3)             |        0.577350269
  1    0    1    0            0                  |        0.
  1    1    1    0            0                  |        0.
  1    1    1    1            0                  |        0.
  2    0    0    0            0                  |        0.
  2    0    1    0         2/sqrt(15)            |        0.516397779
  8    0    9    0         9/sqrt(323)           |        0.500773396
 11    0   10    0        11/sqrt(483)           |        0.500517331