These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 39. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/3, 0/13, 0/39, 1/39, 1/13, 1/3, 2/3, 1/1, 3/3, 4/3, 5/3, 2/1, 6/3 8/3, 9/3, 4/1, 5/1, 7/1, 8/1, 10/1, 11/1, 14/1, 16/1, 17/1, 19/1, 20/1, 22/1 23/1, 31/1, 35/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-49.160128,-48.839872) (-47.160128,-46.839872) (-45.160128,-44.839872) (-43.160128,-42.839872) (-41.160128,-40.839872) (-39.160128,-38.839872) (-37.160128,-36.839872) (-35.160128,-34.839872) (-33.160128,-32.839872) (-31.160128,-30.839872) (-29.160128,-28.839872) (-27.160128,-26.839872) (-25.160128,-24.839872) (-23.160128,-22.839872) (-21.160128,-20.839872) (-19.160128,-18.839872) (-18.262594,-0.500000 ) ( -0.500000,-0.017029 ) ( 0.017029,0.500000 ) ( 0.500000,18.262594 ) ( 18.839872,19.160128 ) ( 20.839872,21.160128 ) ( 22.839872,23.160128 ) ( 24.839872,25.160128 ) ( 26.839872,27.160128 ) ( 28.839872,29.160128 ) ( 30.839872,31.160128 ) ( 32.839872,33.160128 ) ( 34.839872,35.160128 ) ( 36.839872,37.160128 ) ( 38.839872,39.160128 ) ( 40.839872,41.160128 ) ( 42.839872,43.160128 ) ( 44.839872,45.160128 ) ( 46.839872,47.160128 ) ( 48.839872,49.160128 ) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST ( -0.502053,-0.497947) -1/2 EXTENDED HST ( -0.019771,-0.014158) -1/59 HST ( -0.016340,-0.011829) -1/71 HST ( -0.013649,-0.009881) -1/85 HST ( -0.011263,-0.008154) -1/102 HST ( -0.008335,-0.007963) -3/368 HST ( -0.008148,-0.008112) -1/123 HST ( -0.009158,-0.006597) -1/126 HST ( -0.007667,-0.005574) -1/152 HST ( -0.006410,-0.004640) -1/180 HST ( -0.005346,-0.003870) -1/216 HST ( -0.004106,0.004106 ) 0/1 EXTENDED HST ( 0.004091,0.005668 ) 1/206 HST ( 0.004855,0.006706 ) 1/173 HST ( 0.005792,0.008001 ) 1/145 HST ( 0.006923,0.009613 ) 1/121 HST ( 0.008316,0.011486 ) 1/102 HST ( 0.009881,0.013649 ) 1/85 HST ( 0.011829,0.016340 ) 1/71 HST ( 0.014158,0.019771 ) 1/59 HST ( 0.497947,0.502053 ) 1/2 EXTENDED HST -10.816406)(9.817383 infinity EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points. Number of excluded intervals computed by the fixed point finder: 11441 No nontrivial cycles were found. The slope function maps some slope to the nonslope. The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50 ends in the nonslope. If the slope function maps slope p/q to slope p'/q', then |p'| <= |p| for every slope p/q with |p| <= 50 and |q| <= 50. If the slope function maps slope p/q to slope p'/q', then |q'| <= |q| for every slope p/q with |p| <= 50 and |q| <= 50. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "b=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d*c^-1>(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "c=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "d=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "b=<1,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "d=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "b=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d*c^-1>(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "d=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "b=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "c=<1,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "d=(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "a*b*c*d");