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 0/1, 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 13/1, 14/1, 17/1, 20/1, 23/1, 26/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.102961) (-1.102692,-1.102448) (-1.097667,-1.097445) (-1.095527,-1.094459) (-1.093111,-1.092907) (-1.089456,-1.088149) (-1.087931,-1.085811) (-1.085439,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 (-1.103299,-1.102863) -75/68 HST (-1.103109,-1.102612) -193/175 HST (-1.102805,-1.102802) -118/107 EXTENDED HST (-1.102494,-1.102395) -721/654 HST (-1.102439,-1.102206) -140/127 HST (-1.102274,-1.102271) -97/88 EXTENDED HST (-1.102220,-1.102160) -151/137 HST (-1.102288,-1.101944) -205/186 HST (-1.102054,-1.102027) -54/49 EXTENDED HST (-1.102033,-1.101738) -119/108 HST (-1.101750,-1.101643) -65/59 HST (-1.102648,-1.100832) -76/69 HST (-1.101160,-1.100393) -142/129 HST (-1.100426,-1.100359) -1403/1275 HST (-1.100391,-1.100391) -844/767 EXTENDED HST (-1.100389,-1.100383) -285/259 HST (-1.100516,-1.100215) -307/279 HST (-1.100305,-1.100134) -516/469 HST (-1.100184,-1.100081) -824/749 HST (-1.100132,-1.099873) -11/10 EXTENDED HST (-1.099905,-1.099796) -738/671 HST (-1.099849,-1.099848) -727/661 HST (-1.099849,-1.099842) -716/651 HST (-1.099844,-1.099844) -705/641 HST (-1.099842,-1.099842) -694/631 EXTENDED HST (-1.099839,-1.099838) -683/621 HST (-1.099838,-1.099669) -441/401 HST (-1.099746,-1.099500) -276/251 HST (-1.099588,-1.099582) -265/241 HST (-1.099585,-1.099196) -166/151 HST (-1.099300,-1.099281) -155/141 HST (-1.099242,-1.098515) -100/91 HST (-1.098793,-1.098736) -89/81 HST (-1.098752,-1.098072) -78/71 HST (-1.098409,-1.098309) -67/61 HST (-1.098086,-1.098052) -683/622 HST (-1.098054,-1.098049) -1747/1591 HST (-1.098055,-1.098044) -2195/1999 HST (-1.098044,-1.098043) -4995/4549 HST (-1.098043,-1.098042) -6171/5620 HST (-1.098049,-1.098035) -7683/6997 HST (-1.098042,-1.098037) -56/51 EXTENDED HST (-1.098080,-1.097897) -381/347 HST (-1.097975,-1.097944) -269/245 HST (-1.097939,-1.097937) -213/194 EXTENDED HST (-1.097929,-1.097874) -157/143 HST (-1.097888,-1.097846) -258/235 HST (-1.097866,-1.097819) -662/603 HST (-1.097828,-1.097825) -101/92 EXTENDED HST (-1.097839,-1.097762) -449/409 HST (-1.097796,-1.097759) -247/225 HST (-1.097760,-1.097749) -685/624 HST (-1.097779,-1.097719) -1999/1821 HST (-1.097745,-1.097743) -146/133 EXTENDED HST (-1.097734,-1.097706) -1202/1095 HST (-1.097716,-1.097703) -528/481 HST (-1.097705,-1.097702) -2820/2569 HST (-1.097702,-1.097700) -191/174 EXTENDED HST (-1.097715,-1.097616) -236/215 HST (-1.097460,-1.097197) -124/113 HST (-1.097274,-1.097072) -79/72 HST (-1.097139,-1.097034) -260/237 HST (-1.097035,-1.097018) -554/505 HST (-1.097022,-1.097013) -2759/2515 HST (-1.097016,-1.097013) -147/134 EXTENDED HST (-1.097015,-1.097009) -3121/2845 HST (-1.097012,-1.096996) -769/701 HST (-1.097003,-1.096935) -181/165 HST (-1.096941,-1.096891) -249/227 HST (-1.096906,-1.096866) -317/289 HST (-1.096866,-1.096838) -419/382 HST (-1.096842,-1.096825) -555/506 HST (-1.096836,-1.096815) -691/630 HST (-1.096821,-1.096804) -895/816 HST (-1.096809,-1.096798) -1201/1095 HST (-1.096802,-1.096793) -1507/1374 HST (-1.096796,-1.096789) -1915/1746 HST (-1.096791,-1.096786) -2425/2211 HST (-1.096788,-1.096784) -3003/2738 HST (-1.096785,-1.096782) -3785/3451 HST (-1.096782,-1.096782) -4669/4257 HST (-1.096783,-1.096780) -4839/4412 HST (-1.096781,-1.096768) -34/31 EXTENDED HST (-1.096768,-1.096766) -5123/4671 HST (-1.096767,-1.096764) -4171/3803 HST (-1.096766,-1.096762) -3389/3090 HST (-1.096764,-1.096763) -3219/2935 HST (-1.096763,-1.096758) -2607/2377 HST (-1.096761,-1.096755) -2131/1943 HST (-1.096757,-1.096750) -1757/1602 HST (-1.096754,-1.096743) -1417/1292 HST (-1.096749,-1.096742) -1281/1168 HST (-1.096746,-1.096735) -1077/982 HST (-1.096741,-1.096730) -941/858 HST (-1.096736,-1.096721) -771/703 HST (-1.096728,-1.096709) -635/579 HST (-1.096717,-1.096690) -533/486 HST (-1.096706,-1.096679) -465/424 HST (-1.096695,-1.096658) -397/362 HST (-1.096681,-1.096625) -329/300 HST (-1.096664,-1.096599) -261/238 HST (-1.096633,-1.096607) -227/207 HST (-1.096600,-1.096595) -806/735 HST (-1.096600,-1.096589) -1771/1615 HST (-1.096592,-1.096590) -193/176 EXTENDED HST (-1.096597,-1.096579) -2089/1905 HST (-1.096588,-1.096571) -738/673 HST (-1.096580,-1.096527) -159/145 HST (-1.096532,-1.096497) -284/259 HST (-1.096505,-1.096490) -3193/2912 HST (-1.096497,-1.096497) -1659/1513 HST (-1.096493,-1.096489) -125/114 EXTENDED HST (-1.096538,-1.096437) -966/881 HST (-1.096481,-1.096469) -591/539 HST (-1.096473,-1.096454) -466/425 HST (-1.096465,-1.096303) -91/83 HST (-1.096361,-1.096177) -148/135 HST (-1.096191,-1.096159) -946/863 HST (-1.096165,-1.096153) -3967/3619 HST (-1.096159,-1.096149) -57/52 EXTENDED HST (-1.096151,-1.096138) -2303/2101 HST (-1.096145,-1.096093) -593/541 HST (-1.096118,-1.096074) -422/385 HST (-1.096097,-1.096047) -251/229 HST (-1.096059,-1.095940) -137/125 HST (-1.096091,-1.095756) -377/344 HST (-1.095894,-1.095887) -80/73 EXTENDED HST (-1.095758,-1.095751) -1110/1013 HST (-1.095752,-1.095748) -1934/1765 HST (-1.095755,-1.095742) -3273/2987 HST (-1.095748,-1.095742) -103/94 EXTENDED HST (-1.095744,-1.095739) -3319/3029 HST (-1.095741,-1.095721) -950/867 HST (-1.095732,-1.095655) -229/209 HST (-1.095658,-1.095652) -3253/2969 HST (-1.095655,-1.095650) -126/115 EXTENDED HST (-1.095677,-1.095428) -149/136 HST -1.113834)(-1.094799 -35/32 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. 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,c*d*c^-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*d,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,a*b,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*d,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.