prime powers checked: 217169 (4 <= q <= 3000000)
failures: 0
tight cases (first 12 of 291):
   (16, 'C8u tight: q0=4, |Y~|=187200 > M=65280, |PGU(3,q0)|=62400')
   (25, 'C5 tight: q0=5, |Y~|=1116000 > M=720000, |PGL(3,q0)|=372000')
   (49, 'C8u tight: q0=7, |Y~|=16990848 > M=11063808, |PGU(3,q0)|=5663616')
   (64, 'C5 tight: q0=8, |Y~|=49448448 > M=16773120, |PGL(3,q0)|=16482816')
   (121, 'C5 tight: q0=11, |Y~|=637282800 > M=421660800, |PGL(3,q0)|=212427600')
   (169, 'C8u tight: q0=13, |Y~|=2433819024 > M=1612211328, |PGU(3,q0)|=811273008')
   (256, 'C8u tight: q0=16, |Y~|=12837703680 > M=4294901760, |PGU(3,q0)|=4279234560')
   (289, 'C5 tight: q0=17, |Y~|=20850614784 > M=13855131648, |PGL(3,q0)|=6950204928')
   (361, 'C8u tight: q0=19, |Y~|=50816959200 > M=33779203200, |PGU(3,q0)|=16938986400')
   (529, 'C5 tight: q0=23, |Y~|=234469575648 > M=156030386688, |PGL(3,q0)|=78156525216')
   (625, 'C8u tight: q0=25, |Y~|=457060500000 > M=304200000000, |PGU(3,q0)|=152353500000')
   (841, 'C5 tight: q0=29, |Y~|=1498893308640 > M=998114947200, |PGL(3,q0)|=499631102880')
C9 cases (first 8 of 162568):
   (11, 'C9 L2(7) occurs, |Y~| = 168, M = 29040')
   (19, 'C9 3.A6 occurs, |Y~| = 1080, M = 259920')
   (23, 'C9 L2(7) occurs, |Y~| = 168, M = 558624')
   (29, 'C9 L2(7) occurs, |Y~| = 168, M = 1318688')
   (31, 'C9 3.A6 occurs, |Y~| = 1080, M = 1845120')
   (37, 'C9 L2(7) occurs, |Y~| = 504, M = 3548448')
   (43, 'C9 L2(7) occurs, |Y~| = 504, M = 6833904')
   (49, 'C9 3.A6 occurs, |Y~| = 1080, M = 11063808')
