These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 29. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain only finitely many Thurston equivalence classes. However, this modular group Hurwitz class contains 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 0/29, 1/29, 1/1, 2/1, 3/1, 5/1, 6/1, 7/1, 9/1, 10/1, 11/1, 13/1, 15/1, 16/1 17/1, 18/1, 20/1, 21/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.186150) (-1.183526,-1.180425) (-1.174282,-1.173578) (-1.171585,-1.171282) (-1.162791,-1.142857) (-1.141046,infinity ) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-1.186562,-1.185557) -51/43 HST (-1.186010,-1.183283) -32/27 EXTENDED HST -> HST (-1.180531,-1.174419) -33/28 EXTENDED HST -> HST (-1.176493,-1.176448) -20/17 EXTENDED HST (-1.174738,-1.173986) -101/86 HST (-1.173675,-1.172777) -88/75 HST (-1.173082,-1.173072) -61/52 EXTENDED HST (-1.172823,-1.172578) -129/110 HST (-1.172661,-1.171415) -34/29 EXTENDED HST -> HST (-1.171432,-1.171075) -212/181 HST (-1.171241,-1.169046) -48/41 EXTENDED HST -> HST (-1.169757,-1.168207) -83/71 HST (-1.168261,-1.167964) -132/113 HST (-1.168007,-1.167904) -452/387 HST (-1.167950,-1.167928) -153/131 HST (-1.168000,-1.167630) -160/137 HST (-1.167745,-1.167495) -202/173 HST (-1.167776,-1.167190) -237/203 HST (-1.167213,-1.167155) -377/323 HST (-1.167328,-1.166967) -398/341 HST (-1.167025,-1.166314) -7/6 EXTENDED HST (-1.166406,-1.166083) -456/391 HST (-1.166240,-1.166197) -435/373 HST (-1.166214,-1.165581) -260/223 HST (-1.165919,-1.165714) -232/199 HST (-1.165816,-1.165592) -204/175 HST (-1.165687,-1.165674) -197/169 HST (-1.165644,-1.165644) -190/163 EXTENDED HST (-1.165613,-1.165598) -183/157 HST (-1.165595,-1.164292) -106/91 HST (-1.164734,-1.161448) -50/43 EXTENDED HST -> HST (-1.142989,-1.142724) -8/7 EXTENDED HST (-1.144578,-1.136364) -145/127 HST (-1.141725,-1.141079) -121/106 HST (-1.141464,-1.140899) -97/85 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points because every loop multiplier of the mod 2 slope correspondence graph is at least 1 and the map is rational. 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. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "b=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "c=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "d=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "b=(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "c=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d,c*d>(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "d=<1,1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d>(1,2)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "b=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "c=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "d=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "b=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d,c*d>(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "c=(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "d=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.