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 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 0/29, 1/29, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 10/1, 11/1, 12/1 15/1, 16/1, 17/1, 19/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.144636) (-1.144342,-1.136433) (-1.134487,-1.132691) (-1.129202,-1.128808) (-1.122471,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 (-1.147326,-1.142691) -95/83 HST -1.135276)(-0.925330 -25/22 EXTENDED HST -> HST (-1.135313,-1.135218) -235/207 HST (-1.135366,-1.135074) -403/355 HST (-1.135154,-1.135116) -42/37 EXTENDED HST (-1.135145,-1.134957) -395/348 HST (-1.135053,-1.134630) -101/89 HST (-1.134820,-1.134197) -59/52 HST (-1.132693,-1.132664) -350/309 HST (-1.132669,-1.132658) -1127/995 HST (-1.132661,-1.132653) -2570/2269 HST (-1.132656,-1.132650) -111/98 EXTENDED HST (-1.132653,-1.132645) -2869/2533 HST (-1.132649,-1.132547) -205/181 HST (-1.132732,-1.132385) -863/762 HST (-1.132539,-1.132360) -94/83 HST (-1.132366,-1.132353) -2404/2123 HST (-1.132357,-1.132349) -77/68 EXTENDED HST (-1.132388,-1.132225) -445/393 HST (-1.132309,-1.132281) -291/257 HST (-1.132280,-1.132249) -214/189 HST (-1.132245,-1.132220) -137/121 HST (-1.132240,-1.132197) -745/658 HST (-1.132216,-1.132216) -608/537 EXTENDED HST (-1.132212,-1.132180) -334/295 HST (-1.132187,-1.132161) -197/174 HST (-1.132162,-1.132155) -257/227 HST (-1.132258,-1.132022) -317/280 HST (-1.132080,-1.132071) -60/53 EXTENDED HST (-1.132064,-1.131991) -403/356 HST (-1.131995,-1.131983) -1235/1091 HST (-1.131988,-1.131988) -729/644 EXTENDED HST (-1.131984,-1.131975) -223/197 HST (-1.132025,-1.131928) -386/341 HST (-1.131957,-1.131898) -163/144 HST (-1.131939,-1.131804) -103/91 HST (-1.132075,-1.131474) -146/129 HST (-1.131583,-1.131574) -43/38 EXTENDED HST (-1.131476,-1.131435) -284/251 HST (-1.131495,-1.131277) -112/99 HST (-1.131332,-1.131216) -1577/1394 HST (-1.131276,-1.130969) -69/61 HST (-1.130994,-1.130941) -829/733 HST (-1.130964,-1.130839) -95/84 HST (-1.130884,-1.130737) -510/451 HST (-1.130819,-1.130798) -389/344 HST (-1.130802,-1.130801) -268/237 EXTENDED HST (-1.130770,-1.130769) -147/130 EXTENDED HST (-1.130774,-1.130702) -493/436 HST (-1.130727,-1.130711) -173/153 HST (-1.130710,-1.130692) -1289/1140 HST (-1.130699,-1.130699) -372/329 EXTENDED HST (-1.130696,-1.130646) -199/176 HST (-1.130646,-1.130645) -2328/2059 HST (-1.130646,-1.130645) -7235/6399 HST (-1.130646,-1.130644) -16348/14459 HST (-1.130645,-1.130645) -701/620 EXTENDED HST (-1.130644,-1.130643) -1177/1041 HST (-1.130643,-1.130642) -2129/1883 HST (-1.130642,-1.130642) -3557/3146 HST (-1.130642,-1.130642) -6889/6093 HST (-1.130642,-1.130641) -11173/9882 HST (-1.130642,-1.130641) -18789/16618 HST (-1.130641,-1.130641) -30689/27143 HST (-1.130641,-1.130641) -476/421 EXTENDED HST (-1.130653,-1.130624) -1203/1064 HST (-1.130639,-1.130636) -727/643 HST (-1.130637,-1.130610) -251/222 HST (-1.130645,-1.130526) -303/268 HST (-1.130527,-1.130526) -537/475 HST (-1.130547,-1.130488) -563/498 HST (-1.130503,-1.130468) -927/820 HST (-1.130471,-1.130466) -7339/6492 HST (-1.130468,-1.130468) -1473/1303 HST (-1.130477,-1.130455) -1577/1395 HST (-1.130459,-1.130410) -26/23 EXTENDED HST (-1.130421,-1.130333) -867/767 HST (-1.130378,-1.130289) -477/422 HST (-1.130327,-1.130325) -451/399 HST (-1.130319,-1.130319) -425/376 EXTENDED HST (-1.130318,-1.130132) -217/192 HST (-1.130184,-1.130171) -191/169 HST (-1.130137,-1.130137) -165/146 EXTENDED HST (-1.130180,-1.130015) -304/269 HST (-1.130096,-1.128734) -61/54 HST (-1.128749,-1.128719) -605/536 HST (-1.128723,-1.128714) -1745/1546 HST (-1.128719,-1.128578) -114/101 HST (-1.128580,-1.128576) -12262/10865 HST (-1.128578,-1.128565) -79/70 EXTENDED HST (-1.128611,-1.128514) -1624/1439 HST (-1.128561,-1.128340) -123/109 HST (-1.128442,-1.128241) -1099/974 HST (-1.128336,-1.128267) -255/226 HST (-1.128242,-1.128239) -3264/2893 HST (-1.128240,-1.128240) -827/733 HST (-1.128276,-1.128205) -871/772 HST (-1.128229,-1.127777) -44/39 EXTENDED HST -> HST (-1.127891,-1.127382) -53/47 HST (-1.127624,-1.127023) -239/212 HST (-1.127281,-1.127264) -62/55 EXTENDED HST (-1.127203,-1.126733) -71/63 HST (-1.126780,-1.126362) -89/79 HST (-1.126493,-1.126122) -107/95 HST (-1.126129,-1.125829) -134/119 HST (-1.125908,-1.125658) -170/151 HST (-1.125759,-1.125545) -215/191 HST (-1.125764,-1.125248) -260/231 HST (-1.125288,-1.125201) -575/511 HST (-1.125236,-1.125165) -701/623 HST (-1.125303,-1.125012) -863/767 HST (-1.125101,-1.124892) -9/8 EXTENDED HST (-1.124902,-1.124630) -613/545 HST (-1.124770,-1.124070) -262/233 HST (-1.124445,-1.121873) -100/89 HST (-1.123591,-1.122434) -82/73 HST (-1.123190,-1.121451) -64/57 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,a*b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,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,a*b,c^-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,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,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,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,a*b,c^-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,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.