Theorem 1.1(i), independent orbit computation (union-find over (F_q^*)^2, generators E12, E21)
  p  n     q    #y  #y ok  #orbits  tau(q-1)    #M bound viol.
  2  2     4     2      2        2         2   232           0
  2  3     8     6      6        2         2   232           0
  2  4    16    14     14        4         4   232           0
  2  5    32    30     30        2         2   232           0
  2  6    64    62     62        6         6   232           0
  2  7   128   126    126        2         2   232           0
  2  8   256   254    254        8         8   232           0
  2  9   512   510    510        4         4     -           -
  2 10  1024  1022   1022        8         8     -           -
  3  2     9     6      6        4         4   232           0
  3  3    27    24     24        4         4   232           0
  3  4    81    78     78       10        10   232           0
  3  5   243   240    240        6         6   232           0
  3  6   729   726    726       16        16     -           -
  5  1     5     2      2        3         3   232           0
  5  2    25    22     22        8         8   232           0
  5  3   125   122    122        6         6   232           0
  5  4   625   622    622       20        20     -           -
  7  1     7     4      4        4         4   232           0
  7  2    49    46     46       10        10   232           0
  7  3   343   340    340       12        12     -           -
 11  1    11     8      8        4         4   232           0
 11  2   121   118    118       16        16   232           0
 13  1    13    10     10        6         6   232           0
 13  2   169   166    166       16        16   232           0
 17  1    17    14     14        5         5   232           0
 17  2   289   286    286       18        18     -           -
 19  1    19    16     16        6         6   232           0
 19  2   361   358    358       24        24     -           -
 23  1    23    20     20        4         4   232           0
 23  2   529   526    526       20        20     -           -
 29  1    29    26     26        6         6   232           0
 29  2   841   838    838       32        32     -           -
 31  1    31    28     28        8         8   232           0
 31  2   961   958    958       28        28     -           -
 37  1    37    34     34        9         9   232           0
 41  1    41    38     38        8         8   232           0
 43  1    43    40     40        8         8   232           0
 47  1    47    44     44        4         4   232           0
 53  1    53    50     50        6         6   232           0
TOTAL: 40 fields, 7836 admissible y, c(y)^p in the SL_2(Z)-orbit of c(y) for 7836
orbit counts agree with tau(q-1) in every field; root-count bound (both signs) never violated
