These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 31. 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 0/31, 1/31, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 10/1, 11/1, 12/1 13/1, 14/1, 15/1, 16/1, 19/1, 22/1, 25/1, 28/1, 29/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.034295) ( 0.034762,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 (0.033916,0.034411) 7/204 HST (0.034376,0.034440) 17/494 HST (0.034421,0.034453) 28/813 HST (0.034446,0.034461) 41/1190 HST (0.034456,0.034467) 56/1625 HST (0.034462,0.034470) 74/2147 HST (0.034468,0.034473) 97/2814 HST (0.034473,0.034474) 125/3626 HST (0.034472,0.034476) 131/3800 HST (0.034475,0.034490) 1/29 EXTENDED HST (0.034489,0.034491) 158/4581 HST (0.034490,0.034493) 135/3914 HST (0.034492,0.034494) 117/3392 HST (0.034493,0.034496) 102/2957 HST (0.034494,0.034498) 88/2551 HST (0.034496,0.034500) 76/2203 HST (0.034498,0.034505) 62/1797 HST (0.034502,0.034503) 60/1739 HST (0.034503,0.034506) 55/1594 HST (0.034505,0.034508) 50/1449 HST (0.034507,0.034510) 46/1333 HST (0.034509,0.034513) 42/1217 HST (0.034512,0.034513) 40/1159 HST (0.034513,0.034515) 38/1101 HST (0.034515,0.034517) 36/1043 HST (0.034515,0.034518) 176/5099 HST (0.034517,0.034519) 34/985 HST (0.034518,0.034519) 166/4809 HST (0.034519,0.034521) 32/927 HST (0.034520,0.034522) 156/4519 HST (0.034521,0.034522) 31/898 HST (0.034521,0.034524) 30/869 HST (0.034524,0.034524) 29/840 EXTENDED HST (0.034524,0.034524) 144/4171 HST (0.034524,0.034524) 86/2491 HST (0.034524,0.034525) 200/5793 HST (0.034525,0.034525) 57/1651 EXTENDED HST (0.034525,0.034525) 142/4113 HST (0.034525,0.034525) 567/16423 HST (0.034525,0.034525) 85/2462 EXTENDED HST (0.034525,0.034525) 623/18045 HST (0.034525,0.034525) 368/10659 HST (0.034525,0.034525) 198/5735 HST (0.034525,0.034525) 113/3273 EXTENDED HST (0.034525,0.034526) 28/811 HST (0.034525,0.034526) 362/10485 HST (0.034526,0.034526) 139/4026 HST (0.034526,0.034526) 111/3215 EXTENDED HST (0.034526,0.034526) 194/5619 HST (0.034525,0.034526) 360/10427 HST (0.034526,0.034526) 83/2404 EXTENDED HST (0.034526,0.034526) 55/1593 HST (0.034526,0.034527) 191/5532 HST (0.034526,0.034527) 109/3157 HST (0.034527,0.034527) 244/7067 HST (0.034527,0.034527) 406/11759 HST (0.034527,0.034527) 649/18797 HST (0.034527,0.034527) 3973/115070 HST (0.034527,0.034527) 1000/28963 HST (0.034527,0.034527) 1027/29745 HST (0.034527,0.034527) 27/782 EXTENDED HST (0.034527,0.034527) 242/7009 HST (0.034527,0.034528) 80/2317 HST (0.034528,0.034528) 928/26877 HST (0.034528,0.034528) 1140/33017 HST (0.034528,0.034528) 2518/72927 HST (0.034528,0.034528) 53/1535 EXTENDED HST (0.034528,0.034528) 556/16103 HST (0.034528,0.034528) 450/13033 HST (0.034528,0.034528) 344/9963 HST (0.034528,0.034528) 291/8428 HST (0.034528,0.034528) 132/3823 HST (0.034528,0.034528) 527/15263 HST (0.034528,0.034528) 79/2288 EXTENDED HST (0.034528,0.034528) 289/8370 HST (0.034528,0.034528) 105/3041 EXTENDED HST (0.034528,0.034528) 236/6835 HST (0.034528,0.034529) 26/753 HST (0.034529,0.034529) 336/9731 HST (0.034529,0.034529) 155/4489 HST (0.034529,0.034529) 129/3736 HST (0.034529,0.034530) 51/1477 HST (0.034530,0.034530) 25/724 EXTENDED HST (0.034530,0.034531) 524/15175 HST (0.034530,0.034531) 99/2867 HST (0.034531,0.034531) 74/2143 HST (0.034531,0.034531) 172/4981 HST (0.034531,0.034531) 49/1419 EXTENDED HST (0.034531,0.034531) 612/17723 HST (0.034531,0.034531) 514/14885 HST (0.034531,0.034532) 269/7790 HST (0.034531,0.034532) 122/3533 HST (0.034532,0.034532) 73/2114 HST (0.034532,0.034533) 24/695 HST (0.034531,0.034536) 71/2056 HST (0.034533,0.034534) 47/1361 HST (0.034534,0.034536) 23/666 HST (0.034536,0.034539) 22/637 HST (0.034538,0.034539) 64/1853 HST (0.034539,0.034542) 21/608 HST (0.034542,0.034543) 20/579 HST (0.034538,0.034556) 39/1129 HST (0.034544,0.034557) 18/521 HST (0.034550,0.034570) 16/463 HST (0.034559,0.034586) 14/405 HST (0.034568,0.034613) 13/376 HST (0.034580,0.034661) 11/318 HST (0.034599,0.034737) 9/260 HST (0.034622,0.035013) 7/202 HST (0.034664,0.039360) 5/144 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=<1,d*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>(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "b=(1,31)(2,30)(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)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "d=(1,2)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,31)(2,30)(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=(1,30)(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=(1,31)(2,30)(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)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,31)(2,30)(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=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "c=(1,31)(2,30)(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)", "d=(1,30)(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+lambda2: NewSphereMachine( "a=(1,30)(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=(1,31)(2,30)(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)", "c=(1,30)(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)(30,31)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow halted the computation of an excluded interval about the point 649/18797 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 3973/115070 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 3973/115070 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 3973/115070 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 3973/115070 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 1027/29745 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 1027/29745 during the supplemental half-space computation. Imminent integer overflow caused the modular group computation to abort.