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, 10/1, 11/1, 12/1 13/1, 14/1, 17/1, 23/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.219723) (-1.217755,-1.214768) (-1.212011,-1.204060) (-1.196098,-1.192616) (-1.192510,-1.188294) (-1.186131,-1.176881) (-1.174282,-1.173578) (-1.173061,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 (-1.220522,-1.217939) -50/41 EXTENDED HST -> HST (-1.218775,-1.218725) -39/32 EXTENDED HST (-1.218057,-1.217583) -123/101 HST (-1.214940,-1.214589) -181/149 HST (-1.214952,-1.214150) -300/247 HST (-1.214374,-1.214198) -17/14 EXTENDED HST (-1.214190,-1.213605) -227/187 HST (-1.213885,-1.211698) -40/33 EXTENDED HST -> HST (-1.204097,-1.202709) -65/54 HST (-1.202974,-1.202081) -89/74 HST (-1.202378,-1.201657) -119/99 HST (-1.201828,-1.201270) -149/124 HST (-1.201977,-1.200552) -191/159 HST (-1.200641,-1.200442) -437/364 HST (-1.201511,-1.199372) -545/454 HST (-1.200258,-1.199743) -6/5 EXTENDED HST (-1.199460,-1.199210) -361/301 HST (-1.199326,-1.199013) -295/246 HST (-1.199185,-1.198827) -241/201 HST (-1.198993,-1.198520) -199/166 HST (-1.198759,-1.195591) -91/76 HST (-1.197362,-1.196065) -79/66 HST (-1.196735,-1.195450) -67/56 HST (-1.192907,-1.192275) -161/135 HST (-1.190420,-1.186051) -101/85 HST (-1.187600,-1.187400) -19/16 EXTENDED HST (-1.178407,-1.175295) -173/147 HST (-1.176581,-1.176360) -20/17 EXTENDED HST (-1.176398,-1.174454) -47/40 EXTENDED HST -> HST (-1.174803,-1.174068) -478/407 HST (-1.174422,-1.174415) -101/86 EXTENDED HST (-1.178571,-1.166728) -61/52 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,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d>(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,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,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,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,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,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,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.