These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 29. 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 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/29, 1/29, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 11/1, 12/1, 13/1 14/1, 15/1, 16/1, 22/1, 23/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.204759) (-1.198288,-1.193291) (-1.190879,-1.190036) (-1.183971,-1.180626) (-1.174222,-1.173506) (-1.171846,-1.170929) (-1.163625,-1.145098) (-1.142734,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 (-1.207904,-1.201986) -53/44 HST (-1.202735,-1.201068) -125/104 HST (-1.201506,-1.200642) -227/189 HST (-1.200676,-1.200602) -377/314 HST (-1.200845,-1.200356) -401/334 HST (-1.200524,-1.199492) -6/5 EXTENDED HST (-1.205936,-1.195756) -145/121 HST (-1.196078,-1.189474) -31/26 EXTENDED HST -> HST (-1.189643,-1.189270) -113/95 HST (-1.189369,-1.189157) -421/354 HST (-1.189199,-1.189180) -44/37 EXTENDED HST (-1.189205,-1.188920) -283/238 HST (-1.189056,-1.188895) -151/127 HST (-1.188960,-1.188733) -107/90 HST (-1.188874,-1.188477) -63/53 HST (-1.188500,-1.188401) -309/260 HST (-1.188426,-1.188065) -82/69 HST (-1.188162,-1.187917) -139/117 HST (-1.188066,-1.187646) -196/165 HST (-1.187669,-1.187617) -519/437 HST (-1.187631,-1.187590) -652/549 HST (-1.187607,-1.187574) -823/693 HST (-1.187576,-1.187425) -19/16 EXTENDED HST (-1.187500,-1.186813) -222/187 HST (-1.187136,-1.186963) -165/139 HST (-1.187028,-1.186801) -127/107 HST (-1.186830,-1.186500) -89/75 HST (-1.186645,-1.186395) -70/59 HST (-1.186508,-1.186170) -261/220 HST (-1.186342,-1.186328) -191/161 HST (-1.186286,-1.186183) -121/102 HST (-1.186188,-1.186127) -223/188 HST (-1.186160,-1.185957) -51/43 HST (-1.186080,-1.185596) -185/156 HST (-1.185842,-1.185840) -134/113 EXTENDED HST (-1.185716,-1.185713) -83/70 EXTENDED HST (-1.185603,-1.185581) -428/361 HST (-1.185588,-1.185548) -115/97 HST (-1.185554,-1.185383) -147/124 HST (-1.185394,-1.185368) -1119/944 HST (-1.185379,-1.185379) -454/383 EXTENDED HST (-1.185370,-1.185362) -243/205 HST (-1.185365,-1.185315) -275/232 HST (-1.185328,-1.185288) -710/599 HST (-1.185305,-1.185302) -371/313 HST (-1.185521,-1.185123) -435/367 HST (-1.185221,-1.185150) -32/27 EXTENDED HST (-1.186901,-1.182953) -45/38 EXTENDED HST -> HST (-1.180662,-1.180542) -268/227 HST (-1.180587,-1.180314) -85/72 HST (-1.180335,-1.180321) -72/61 EXTENDED HST (-1.180431,-1.179968) -203/172 HST (-1.180229,-1.180138) -131/111 HST (-1.180008,-1.179992) -59/50 EXTENDED HST (-1.179977,-1.179921) -518/439 HST (-1.179952,-1.179838) -282/239 HST (-1.179897,-1.179662) -105/89 HST (-1.179702,-1.179582) -197/167 HST (-1.179597,-1.179537) -335/284 HST (-1.179619,-1.179448) -657/557 HST (-1.179504,-1.179470) -46/39 EXTENDED HST (-1.179465,-1.179338) -355/301 HST (-1.179390,-1.178811) -79/67 HST (-1.178880,-1.178660) -178/151 HST (-1.178709,-1.178611) -475/403 HST (-1.178719,-1.178502) -1102/935 HST (-1.178596,-1.178547) -33/28 EXTENDED HST (-1.178530,-1.178425) -449/381 HST (-1.178471,-1.178215) -152/129 HST (-1.178227,-1.177310) -53/45 HST (-1.177480,-1.176944) -93/79 HST (-1.177267,-1.176422) -153/130 HST (-1.176844,-1.172572) -20/17 EXTENDED HST -> HST (-1.172581,-1.171414) -34/29 EXTENDED HST -> HST (-1.171005,-1.170869) -185/158 HST (-1.170869,-1.170869) -4783/4085 HST (-1.170870,-1.170868) -7709/6584 HST (-1.170868,-1.170868) -418/357 EXTENDED HST (-1.170870,-1.170854) -651/556 HST (-1.170859,-1.170850) -233/199 HST (-1.171111,-1.170575) -281/240 HST (-1.170790,-1.169612) -48/41 EXTENDED HST -> HST (-1.169846,-1.169097) -69/59 HST (-1.169332,-1.168667) -83/71 HST (-1.168680,-1.168144) -104/89 HST (-1.168255,-1.167861) -132/113 HST (-1.167941,-1.167703) -167/143 HST (-1.167843,-1.167484) -188/161 HST (-1.167591,-1.167294) -244/209 HST (-1.167377,-1.167166) -314/269 HST (-1.167259,-1.167070) -391/335 HST (-1.167135,-1.166993) -482/413 HST (-1.167050,-1.166931) -601/515 HST (-1.166976,-1.166881) -741/635 HST (-1.166918,-1.166843) -909/779 HST (-1.166846,-1.166490) -7/6 EXTENDED HST (-1.166581,-1.166361) -1002/859 HST (-1.166472,-1.166384) -813/697 HST (-1.166426,-1.166301) -652/559 HST (-1.166365,-1.166217) -519/445 HST (-1.166289,-1.166121) -428/367 HST (-1.166211,-1.164959) -183/157 HST (-1.165574,-1.164990) -148/127 HST (-1.165341,-1.164510) -113/97 HST (-1.164885,-1.163837) -85/73 HST (-1.164269,-1.161892) -64/55 HST (-1.145659,-1.144176) -79/69 HST (-1.144607,-1.143673) -127/111 HST (-1.144766,-1.142463) -207/181 HST (-1.143536,-1.142141) -8/7 EXTENDED 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=(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=(1,29)(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)", "c=(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)", "d=<1,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(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: NewSphereMachine( "a=(1,2)(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=(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,a*b,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d,c*d>(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=<1,1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(1,2)(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)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "b=(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)", "c=(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)", "d=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(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)", "b=<1,a*b,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d,c*d>(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=(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)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.