These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 37. 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 0/37, 1/37, 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, 17/1, 18/1, 19/1, 22/1, 25/1, 28/1, 31/1, 34/1, 35/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.028452) ( 0.028741,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 (0.028084,0.028523) 7/246 HST (0.028494,0.028543) 17/596 HST (0.028533,0.028552) 29/1016 HST (0.028547,0.028558) 43/1506 HST (0.028554,0.028561) 60/2101 HST (0.028558,0.028563) 78/2731 HST (0.028562,0.028565) 103/3606 HST (0.028564,0.028566) 131/4586 HST (0.028565,0.028567) 165/5776 HST (0.028567,0.028575) 1/35 EXTENDED HST (0.028575,0.028576) 207/7244 HST (0.028575,0.028577) 178/6229 HST (0.028576,0.028578) 149/5214 HST (0.028577,0.028578) 130/4549 HST (0.028578,0.028579) 114/3989 HST (0.028579,0.028580) 101/3534 HST (0.028580,0.028582) 89/3114 HST (0.028581,0.028583) 79/2764 HST (0.028582,0.028584) 73/2554 HST (0.028583,0.028583) 72/2519 HST (0.028583,0.028585) 67/2344 HST (0.028584,0.028585) 62/2169 HST (0.028585,0.028586) 59/2064 HST (0.028585,0.028587) 54/1889 HST (0.028587,0.028589) 49/1714 HST (0.028588,0.028590) 47/1644 HST (0.028589,0.028591) 44/1539 HST (0.028590,0.028591) 41/1434 HST (0.028591,0.028592) 40/1399 HST (0.028592,0.028592) 157/5491 HST (0.028592,0.028592) 39/1364 EXTENDED HST (0.028592,0.028593) 77/2693 HST (0.028593,0.028594) 37/1294 HST (0.028594,0.028595) 36/1259 HST (0.028595,0.028595) 35/1224 EXTENDED HST (0.028595,0.028595) 874/30565 HST (0.028595,0.028595) 279/9757 HST (0.028595,0.028595) 104/3637 HST (0.028595,0.028595) 725/25354 HST (0.028595,0.028595) 1622/56723 HST (0.028595,0.028595) 69/2413 EXTENDED HST (0.028595,0.028595) 1000/34971 HST (0.028595,0.028595) 103/3602 HST (0.028595,0.028596) 34/1189 HST (0.028596,0.028596) 3115/108933 HST (0.028596,0.028596) 237/8288 EXTENDED HST (0.028596,0.028596) 440/15387 HST (0.028596,0.028596) 2673/93476 HST (0.028596,0.028596) 203/7099 EXTENDED HST (0.028596,0.028596) 169/5910 HST (0.028596,0.028596) 101/3532 HST (0.028596,0.028596) 67/2343 EXTENDED HST (0.028596,0.028596) 100/3497 HST (0.028596,0.028596) 631/22066 HST (0.028596,0.028596) 166/5805 HST (0.028596,0.028596) 365/12764 HST (0.028596,0.028596) 199/6959 HST (0.028596,0.028596) 265/9267 HST (0.028596,0.028596) 496/17345 HST (0.028596,0.028596) 2247/78577 HST (0.028596,0.028596) 760/26577 HST (0.028596,0.028596) 793/27731 HST (0.028596,0.028596) 2015/70464 HST (0.028596,0.028596) 1024/35809 HST (0.028596,0.028596) 1321/46195 HST (0.028596,0.028596) 2047/71583 HST (0.028596,0.028596) 33/1154 EXTENDED HST (0.028596,0.028596) 659/23045 HST (0.028596,0.028596) 197/6889 HST (0.028596,0.028596) 164/5735 HST (0.028596,0.028596) 3704/129527 HST (0.028596,0.028596) 295/10316 EXTENDED HST (0.028596,0.028596) 721/25213 HST (0.028596,0.028596) 426/14897 HST (0.028596,0.028597) 98/3427 HST (0.028597,0.028597) 228/7973 HST (0.028597,0.028597) 293/10246 HST (0.028597,0.028597) 553/19338 HST (0.028597,0.028597) 65/2273 EXTENDED HST (0.028596,0.028597) 1722/60217 HST (0.028597,0.028597) 227/7938 HST (0.028597,0.028597) 162/5665 HST (0.028597,0.028597) 259/9057 HST (0.028597,0.028597) 97/3392 HST (0.028597,0.028597) 290/10141 HST (0.028597,0.028597) 161/5630 EXTENDED HST (0.028597,0.028597) 2125/74309 HST (0.028597,0.028597) 32/1119 HST (0.028597,0.028597) 223/7798 HST (0.028597,0.028598) 95/3322 HST (0.028597,0.028597) 63/2203 EXTENDED HST (0.028597,0.028598) 219/7658 HST (0.028598,0.028598) 469/16400 HST (0.028598,0.028598) 3344/116933 HST (0.028598,0.028598) 4094/143159 HST (0.028598,0.028598) 4969/173756 HST (0.028598,0.028598) 125/4371 EXTENDED HST (0.028598,0.028598) 281/9826 HST (0.028598,0.028598) 156/5455 HST (0.028598,0.028598) 218/7623 HST (0.028598,0.028598) 31/1084 HST (0.028598,0.028599) 30/1049 HST (0.028599,0.028599) 147/5140 HST (0.028599,0.028599) 235/8217 HST (0.028599,0.028599) 88/3077 HST (0.028599,0.028600) 117/4091 HST (0.028599,0.028600) 29/1014 HST (0.028600,0.028602) 28/979 HST (0.028601,0.028603) 27/944 HST (0.028602,0.028604) 26/909 HST (0.028604,0.028604) 25/874 EXTENDED HST (0.028604,0.028604) 399/13949 HST (0.028604,0.028605) 124/4335 HST (0.028604,0.028605) 74/2587 HST (0.028605,0.028605) 49/1713 HST (0.028605,0.028605) 315/11012 HST (0.028605,0.028605) 121/4230 HST (0.028605,0.028606) 24/839 HST (0.028604,0.028609) 71/2482 HST (0.028606,0.028613) 23/804 HST (0.028608,0.028619) 21/734 HST (0.028612,0.028626) 19/664 HST (0.028617,0.028634) 16/559 HST (0.028623,0.028643) 15/524 HST (0.028627,0.028671) 13/454 HST (0.028636,0.028702) 11/384 HST (0.028646,0.028784) 8/279 HST 0.027097)(0.028685 5/174 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,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,b^-1>(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=(1,37)(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,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^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(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)", "d=(1,2)(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: NewSphereMachine( "a=(1,37)(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=(1,36)(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=(1,37)(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=<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^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(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 lambda2: NewSphereMachine( "a=(1,37)(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,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^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(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)", "c=(1,37)(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=(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+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=(1,37)(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=(1,35)(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)(36,37)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow halted the computation of an excluded interval about the point 279/9757 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 2247/78577 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 2247/78577 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 793/27731 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 793/27731 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 2015/70464 during the supplemental half-space computation. Imminent integer overflow halted the computation of an excluded interval about the point 659/23045 during the supplemental half-space computation. Imminent integer overflow caused the modular group computation to abort.