These Thurston maps are NET maps for every choice of translation term. They have degree 38. They are imprimitive, each factoring as a NET map with degree 19 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 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/19, 0/38, 2/19, 2/2, 2/1, 4/2, 6/2, 8/2, 10/2, 6/1, 16/2, 10/1, 14/1, 18/1 26/1, 34/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.027911) ( 0.030080,0.030751) ( 0.032558,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 (0.027879,0.028166) 3/107 HST (0.028164,0.028174) 2/71 EXTENDED HST (0.028171,0.028317) 3/106 HST (0.028297,0.028339) 16/565 HST (0.028321,0.028332) 10/353 HST (0.028335,0.028346) 7/247 HST (0.028295,0.028388) 11/388 HST (0.028354,0.028425) 4/141 HST (0.028405,0.028444) 17/598 HST (0.028430,0.028464) 6/211 HST (0.028448,0.028479) 8/281 HST (0.028458,0.028508) 9/316 HST (0.028499,0.028523) 13/456 HST (0.028517,0.028533) 17/596 HST (0.028530,0.028540) 22/771 HST (0.028538,0.028546) 27/946 HST (0.028542,0.028551) 32/1121 HST (0.028548,0.028555) 40/1401 HST (0.028553,0.028555) 49/1716 HST (0.028553,0.028558) 51/1786 HST (0.028557,0.028561) 63/2206 HST (0.028559,0.028562) 227/7948 HST (0.028561,0.028561) 76/2661 HST (0.028561,0.028564) 91/3186 HST (0.028563,0.028565) 110/3851 HST (0.028564,0.028578) 1/35 EXTENDED HST (0.028578,0.028580) 107/3744 HST (0.028579,0.028579) 105/3674 HST (0.028579,0.028582) 88/3079 HST (0.028581,0.028585) 73/2554 HST (0.028583,0.028587) 62/2169 HST (0.028585,0.028590) 52/1819 HST (0.028587,0.028593) 44/1539 HST (0.028590,0.028597) 37/1294 HST (0.028594,0.028603) 31/1084 HST (0.028598,0.028604) 28/979 HST (0.028601,0.028611) 24/839 HST (0.028607,0.028620) 20/699 HST (0.028613,0.028628) 17/594 HST (0.028622,0.028643) 14/489 HST (0.028630,0.028655) 12/419 HST (0.028641,0.028704) 8/279 HST (0.028686,0.028708) 7/244 HST (0.028708,0.028709) 6/209 EXTENDED HST (0.028708,0.028731) 11/383 HST (0.028721,0.028738) 36/1253 HST (0.028735,0.028736) 5/174 EXTENDED HST (0.028734,0.028747) 24/835 HST (0.028743,0.028763) 9/313 HST (0.028698,0.028807) 17/591 HST (0.028776,0.028778) 4/139 EXTENDED HST (0.028778,0.028833) 7/243 HST (0.028813,0.029003) 3/104 HST (0.028980,0.028991) 2/69 EXTENDED HST (0.028998,0.029022) 21/724 HST (0.029006,0.029031) 15/517 HST (0.029016,0.029030) 11/379 HST (0.029023,0.029037) 56/1929 HST (0.029032,0.029032) 9/310 EXTENDED HST (0.029033,0.029087) 5/172 HST (0.029078,0.029112) 8/275 HST (0.029092,0.029154) 3/103 HST (0.029065,0.029321) 4/137 HST (0.029238,0.029522) 10/341 HST (0.029401,0.029423) 1/34 EXTENDED HST (0.029513,0.029921) 4/135 HST (0.029669,0.029945) 3/101 HST (0.029847,0.029855) 2/67 EXTENDED HST (0.029915,0.030612) 3/100 HST (0.030457,0.032787) 1/32 EXTENDED HST -> HST (0.031361,0.038295) 1/31 EXTENDED HST -> 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. 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,c^-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*d^-1>(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=(1,38)(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)", "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,c>(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=(1,2)(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: 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=(1,37)(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=(1,38)(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)", "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,c>(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 lambda2: 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,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,c>(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=(1,38)(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)", "d=(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)", "a*b*c*d"); When the translation term of the affine map is lambda1+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=(1,38)(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)", "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)(37,38)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.