These Thurston maps are NET maps for every choice of translation term. They have degree 40. They are imprimitive, each factoring as a NET map with degree 20 followed by a Euclidean NET map with degree 2. 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 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/20, 0/40, 2/10, 2/8, 2/5, 2/4, 2/2, 6/4, 2/1, 4/2, 6/2, 6/1, 12/2, 14/1 18/1, 22/1, 34/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.000000) ( 0.000000,0.989130) ( 1.010870,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 (-0.011436,0.010936) 0/1 EXTENDED HST ( 0.965854,1.036653) 1/1 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points p/q with |p| <= 50 and |q| <= 50. The fixed point finder is unable to determine whether there are any slope function fixed points. Number of excluded intervals computed by the fixed point finder: 12842 Here is their union. There are no slope function fixed points whose negative reciprocals lie in any of the following intervals. EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION ( -infinity,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417359,0.417359) ( 0.417360,0.417360) ( 0.417360,0.417360) ( 0.417362,0.417362) ( 0.417367,0.417367) ( 0.417391,0.417392) ( 0.417474,0.417479) ( 0.417581,0.417583) ( 0.417701,0.417741) ( 0.417860,0.417960) ( 0.418177,0.418187) ( 0.418594,0.418614) ( 0.419118,0.419586) ( 0.421039,0.421066) ( 0.427682,0.429078) ( 0.499840,0.500160) ( 0.998724,1.001286) (1520.975610,infinity) 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=(2,40)(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=(1,40)(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,c^-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,c>(2,40)(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)", "d=(1,2)(3,40)(4,39)(5,38)(6,37)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,40)(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=(1,40)(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,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,c,c,c,c,c,c,c,c,c,c>(2,40)(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=(1,40)(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,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,c,c,c,c,c,c,c,c,c,c>(2,40)(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)", "c=(1,40)(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"); 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=(1,40)(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=(1,39)(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)(39,40)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about 157681/377810. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 157681/377810. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 157681/377810. Imminent integer overflow halted evaluation of the slope function at slope -98191573/40981159 while computing a fixed point excluded interval about 7423627/17787140. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 282735/677438. Imminent integer overflow halted evaluation of the slope function at slope -68082398/28414817 while computing a fixed point excluded interval about 4766671/11421027. Imminent integer overflow halted evaluation of the slope function at slope -6539623/2729372 while computing a fixed point excluded interval about 4766671/11421027. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 307090/735793. Imminent integer overflow halted evaluation of the slope function at slope -3267691/1363801 while computing a fixed point excluded interval about 307090/735793. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 324968/778629. Imminent integer overflow halted evaluation of the slope function at slope -4325837/1805428 while computing a fixed point excluded interval about 324968/778629. Imminent integer overflow halted evaluation of the slope function at slope -63210589/26381523 while computing a fixed point excluded interval about 2886128/6915213. Imminent integer overflow halted evaluation of the slope function at slope -74815479/31224931 while computing a fixed point excluded interval about 2886128/6915213. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 364840/874163. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 364840/874163. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 364840/874163. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 364840/874163. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 364840/874163. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 364840/874163. Imminent integer overflow halted evaluation of the slope function at slope -4669342/1948793 while computing a fixed point excluded interval about 1003423/2404219. Imminent integer overflow halted evaluation of the slope function at slope -61419427/25633965 while computing a fixed point excluded interval about 2803066/6716195. Imminent integer overflow halted evaluation of the slope function at slope -130837836/54606379 while computing a fixed point excluded interval about 7189633/17226486. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow halted evaluation of the slope function at slope -2702849/1128059 while computing a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow halted evaluation of the slope function at slope -4716359/1968416 while computing a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow halted evaluation of the slope function at slope -2884539/1203889 while computing a fixed point excluded interval about 287702/689339. Imminent integer overflow halted evaluation of the slope function at slope -5641895/2354697 while computing a fixed point excluded interval about 287702/689339. Imminent integer overflow halted evaluation of the slope function at slope -6349403/2649982 while computing a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow halted evaluation of the slope function at slope -4988894/2082161 while computing a fixed point excluded interval about 287702/689339. Imminent integer overflow halted evaluation of the slope function at slope -7437377/3104058 while computing a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 287702/689339. Imminent integer overflow halted evaluation of the slope function at slope -5314853/2218203 while computing a fixed point excluded interval about 287702/689339. Imminent integer overflow halted evaluation of the slope function at slope -8181223/3414509 while computing a fixed point excluded interval about 287702/689339.