These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 40. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} Since no Thurston multiplier is 1, this modular group Hurwitz class contains only finitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/2, 0/10, 0/20, 1/20, 1/10, 1/4, 1/2, 3/4, 3/2, 4/2, 7/2, 8/2, 9/2, 11/2 17/2 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,infinity) The half-space computation determines rationality. The supplemental half-space computation is not needed. 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: 3539 NONTRIVIAL CYCLES 0/1 -> 1/1 -> 0/1 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 either one of the above cycles or the nonslope. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=<1,b,c^-1,1,c^-1,1,c^-1,1,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,c,1,c,1,c,1,c*d,1>(2,38)(3,39)(4,36)(5,37)(6,34)(7,35)(8,32)(9,33)(10,30)(11,31)(12,28)(13,29)(14,26)(15,27)(16,24)(17,25)(18,22)(19,23)", "b=(1,40)(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "c=(1,39)(2,40)(3,37)(4,38)(5,35)(6,36)(7,33)(8,34)(9,31)(10,32)(11,29)(12,30)(13,27)(14,28)(15,25)(16,26)(17,23)(18,24)(19,21)(20,22)", "d=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,40)(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "b=<1,c^-1,b,c^-1,1,c^-1,1,c^-1,1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,1,c,1,c,1,c,1,c*d,1,1>(2,38)(3,39)(4,36)(5,37)(6,34)(7,35)(8,32)(9,33)(10,30)(11,31)(12,28)(13,29)(14,26)(15,27)(16,24)(17,25)(18,22)(19,23)", "c=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "d=(1,39)(2,40)(3,37)(4,38)(5,35)(6,36)(7,33)(8,34)(9,31)(10,32)(11,29)(12,30)(13,27)(14,28)(15,25)(16,26)(17,23)(18,24)(19,21)(20,22)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "b=(1,39)(2,40)(3,37)(4,38)(5,35)(6,36)(7,33)(8,34)(9,31)(10,32)(11,29)(12,30)(13,27)(14,28)(15,25)(16,26)(17,23)(18,24)(19,21)(20,22)", "c=(1,40)(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "d=<1,1,c^-1*b,1,c^-1,1,c^-1,1,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,c,1,c,1,c,c*d*c^-1,c,1>(2,38)(3,39)(4,36)(5,37)(6,34)(7,35)(8,32)(9,33)(10,30)(11,31)(12,28)(13,29)(14,26)(15,27)(16,24)(17,25)(18,22)(19,23)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,39)(2,40)(3,37)(4,38)(5,35)(6,36)(7,33)(8,34)(9,31)(10,32)(11,29)(12,30)(13,27)(14,28)(15,25)(16,26)(17,23)(18,24)(19,21)(20,22)", "b=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "c=<1,c^-1,b,c^-1,1,c^-1,1,c^-1,1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,1,c,1,c,1,c,1,c*d,1,1>(2,38)(3,39)(4,36)(5,37)(6,34)(7,35)(8,32)(9,33)(10,30)(11,31)(12,28)(13,29)(14,26)(15,27)(16,24)(17,25)(18,22)(19,23)", "d=(1,40)(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.