These Thurston maps are NET maps for every choice of translation term. They have degree 36. They are imprimitive, each factoring as a NET map with degree 18 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 infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 7. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/36, 2/18, 2/12, 2/9, 2/6, 2/4, 2/3, 2/2, 4/4, 2/1, 8/4, 10/3, 10/2, 14/2 10/1, 14/1, 22/1, 26/1, 34/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.030039) (-0.028237,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 (-0.030041,-0.029944) -3/100 HST (-0.030229,-0.029775) -5/167 HST (-0.029854,-0.029848) -2/67 EXTENDED HST (-0.029907,-0.029618) -5/168 HST (-0.029750,-0.029572) -3/101 HST (-0.029590,-0.029507) -6/203 HST (-0.029522,-0.029483) -19/644 HST (-0.029502,-0.029495) -10/339 HST (-0.029487,-0.029472) -13/441 HST (-0.029482,-0.029454) -15/509 HST (-0.029454,-0.029449) -21/713 HST (-0.029455,-0.029439) -24/815 HST (-0.029444,-0.029381) -1/34 EXTENDED HST (-0.029390,-0.029364) -25/851 HST (-0.029377,-0.029337) -16/545 HST (-0.029356,-0.029343) -14/477 HST (-0.029349,-0.029326) -12/409 HST (-0.029336,-0.029330) -11/375 HST (-0.029328,-0.029236) -7/239 HST (-0.029278,-0.029172) -4/137 HST (-0.029222,-0.029132) -7/240 HST (-0.029167,-0.029101) -49/1682 HST (-0.029128,-0.029124) -3/103 EXTENDED HST (-0.029160,-0.029003) -11/378 HST (-0.029082,-0.029048) -5/172 HST (-0.029057,-0.028878) -2/69 HST (-0.028879,-0.028783) -3/104 HST (-0.028804,-0.028650) -4/139 HST (-0.028730,-0.028480) -11/384 HST (-0.028581,-0.028562) -1/35 EXTENDED HST (-0.028499,-0.028278) -6/211 HST (-0.028436,-0.028037) -3/106 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS FOUND: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 34/1 2 18 No No No No NUMBER OF EQUATORS FOUND: 0 0 0 0 The fixed point finder is unable to determine whether there are any more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 2582 Here is their union. There are no more slope function fixed points whose negative reciprocals lie in any of the following intervals. EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION (-infinity,-0.032282) (-0.032282,-0.029990) (-0.029990,-0.029990) (-0.029990,-0.029990) (-0.029990,-0.029990) (-0.029990,-0.029990) (-0.029989,-0.029988) (-0.029987,-0.029987) (-0.029985,-0.029985) (-0.029982,-0.029982) (-0.029979,-0.029979) (-0.029973,-0.029973) (-0.029966,-0.029959) (-0.029940,-0.029940) (-0.029851,-0.029851) (-0.029412,-0.029411) (-0.000792,0.000839 ) ( 2.324545,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 either one of the above cycles or 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=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "b=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "c=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "d=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "b=<1,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "c=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "d=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "b=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "c=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "d=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "b=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "c=<1,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "d=(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1779/51649. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -5705/165631. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -5705/165631. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -30150/875333. Imminent integer overflow halted evaluation of the slope function at slope 3081814/99301 while computing a fixed point excluded interval about -50349/1562585. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -2764/85781. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -29068/953359. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -29068/953359. Imminent integer overflow halted evaluation of the slope function at slope 3485348/106267 while computing a fixed point excluded interval about -215069/7053839. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -26317/864875. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -26317/864875. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -56641/1861435. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -56641/1861435. Imminent integer overflow halted evaluation of the slope function at slope 15534622/472697 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -6794/223277. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -7220/237277. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -29939/998299. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -29939/998299. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 2650449/79487 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 3683793/110477 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -29939/998299. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 3856017/115642 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 4854316/145581 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 5128674/153809 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 4200465/125972 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 5198764/155911 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 7195362/215789 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 4372689/131137 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow halted evaluation of the slope function at slope 8295795/248791 while computing a fixed point excluded interval about -29939/998299. Imminent integer overflow caused the modular group computation to abort.