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 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 14. 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, 2/1, 7/3, 4/1 5/1, 7/1, 8/1, 9/1, 10/1, 11/1, 15/1, 27/1, 33/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.201992) (-1.196396,-1.017140) (-0.982008,-0.858991) (-0.856130,-0.507904) (-0.492002,-0.252304) (-0.245887,-0.166806) (-0.166164,-0.037548) ( 0.037305,0.248870 ) ( 0.250249,0.494500 ) ( 0.504149,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 (-1.202544,-1.197519) -6/5 EXTENDED HST (-1.204971,-1.187656) -67/56 HST (-1.019119,-1.013696) -60/59 HST (-1.015892,-1.011505) -149/147 HST (-1.013564,-1.013463) -75/74 HST (-1.013384,-1.009618) -88/87 HST (-1.009641,-1.009590) -105/104 HST (-1.011083,-1.007974) -106/105 HST (-1.009135,-1.006613) -127/126 HST (-1.007683,-1.005562) -305/303 HST (-1.006591,-1.006567) -153/152 HST (-1.006313,-1.004768) -181/180 HST (-1.005498,-1.003980) -211/210 HST (-1.004140,-0.995894) -1/1 EXTENDED HST (-0.996544,-0.995226) -241/242 HST (-0.995856,-0.994294) -203/204 HST (-0.995088,-0.993216) -170/171 HST (-0.994138,-0.994098) -169/170 HST (-0.994114,-0.991905) -142/143 HST (-0.992971,-0.992944) -141/142 HST (-0.992942,-0.990251) -118/119 HST (-0.991597,-0.991453) -117/118 HST (-0.991516,-0.988282) -98/99 HST (-0.989881,-0.986023) -82/83 HST (-0.987846,-0.987763) -81/82 HST (-0.987771,-0.983264) -67/68 HST (-0.985182,-0.979761) -55/56 HST (-0.859878,-0.857913) -67/78 HST (-0.858413,-0.855849) -6/7 EXTENDED HST (-0.509868,-0.505535) -33/65 HST (-0.505903,-0.505146) -137/271 HST (-0.505514,-0.505475) -46/91 HST (-0.505801,-0.504401) -99/196 HST (-0.505067,-0.505034) -50/99 HST (-0.505666,-0.503190) -115/228 HST (-0.504360,-0.504336) -58/115 HST (-0.503600,-0.502728) -79/157 HST (-0.503457,-0.501950) -93/185 HST (-0.502053,-0.497947) -1/2 EXTENDED HST (-0.498192,-0.497606) -119/239 HST (-0.497893,-0.497887) -118/237 HST (-0.497889,-0.495900) -79/159 HST (-0.496850,-0.494460) -57/115 HST (-0.495586,-0.491427) -37/75 HST (-0.493285,-0.491085) -31/63 HST (-0.253695,-0.250810) -28/111 HST (-0.251026,-0.248974) -1/4 EXTENDED HST (-0.249614,-0.248240) -60/241 HST (-0.248947,-0.247946) -42/169 HST (-0.248500,-0.247071) -30/121 HST (-0.247868,-0.246255) -21/85 HST (-0.247025,-0.244789) -15/61 HST (-0.167351,-0.165982) -1/6 EXTENDED HST (-0.084614,0.101880 ) 0/1 EXTENDED HST ( 0.248463,0.251543 ) 1/4 EXTENDED HST ( 0.493003,0.496017 ) 45/91 HST ( 0.495911,0.504123 ) 1/2 EXTENDED HST ( 0.501458,0.506686 ) 61/121 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: 11092 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 |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=(1,39)(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=(1,39)(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=(1,38)(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: NewSphereMachine( "a=<1,d,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c>(1,2)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "b=(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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c,c>(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=(1,2)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c,c>(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=(1,39)(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=(1,39)(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=(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"); 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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c,c>(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=(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=(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"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.