These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 34. 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, 0/17, 0/34, 1/34, 1/17, 1/2, 1/1, 2/2, 3/2, 2/1, 4/2, 5/2, 3/1, 6/2 7/2, 8/2, 9/2, 5/1, 6/1, 13/2, 7/1, 10/1, 11/1, 13/1, 14/1, 15/1, 19/1, 22/1 25/1, 30/1, 31/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.099448) (-0.097313,-0.094151) (-0.092349,-0.089514) (-0.087883,-0.085296) (-0.081459,-0.079231) (-0.077951,-0.075922) (-0.074745,-0.072866) (-0.070047,-0.068394) (-0.067438,-0.065913) (-0.065025,-0.063598) (-0.061440,-0.060164) (-0.059423,-0.058236) (-0.057542,-0.056750) (-0.054411,-0.053702) (-0.053111,-0.052161) (-0.051603,-0.050965) (-0.049071,-0.048494) (-0.048011,-0.047233) (-0.046775,-0.046251) (-0.044685,-0.044206) (-0.043805,-0.043156) (-0.042774,-0.042335) (-0.041019,-0.040615) (-0.040276,-0.039727) (-0.037274,-0.036803) (-0.034688,-0.034280) (-0.032438,-0.032081) (-0.030461,-0.030146) (-0.028712,-0.028432) (-0.027153,-0.026902) (-0.025754,-0.025529) (-0.024493,-0.024289) (-0.023349,-0.023163) (-0.022307,-0.022138) (-0.021355,-0.021199) (-0.020480,-0.020337) ( 0.020337,0.020480 ) ( 0.021199,0.021355 ) ( 0.022138,0.022307 ) ( 0.023163,0.023349 ) ( 0.024289,0.024493 ) ( 0.025529,0.025754 ) ( 0.026902,0.027153 ) ( 0.028432,0.028712 ) ( 0.030146,0.030461 ) ( 0.032081,0.032438 ) ( 0.034280,0.034688 ) ( 0.036803,0.037274 ) ( 0.039727,0.040276 ) ( 0.040615,0.041019 ) ( 0.042335,0.042774 ) ( 0.043156,0.043805 ) ( 0.044206,0.044685 ) ( 0.046251,0.046775 ) ( 0.047233,0.048011 ) ( 0.048494,0.049071 ) ( 0.050965,0.051603 ) ( 0.052161,0.053111 ) ( 0.053702,0.054411 ) ( 0.056750,0.057542 ) ( 0.058236,0.059423 ) ( 0.060164,0.061440 ) ( 0.063598,0.065025 ) ( 0.065913,0.067438 ) ( 0.068394,0.070047 ) ( 0.072866,0.074745 ) ( 0.075922,0.077951 ) ( 0.079231,0.081459 ) ( 0.085296,0.087883 ) ( 0.089514,0.092349 ) ( 0.094151,0.097313 ) ( 0.098012,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 (-0.103173,-0.093988) -7/71 HST (-0.098370,-0.097711) -5/51 HST (-0.097585,-0.097537) -4/41 EXTENDED HST (-0.097057,-0.090852) -14/149 HST (-0.093771,-0.093729) -3/32 EXTENDED HST (-0.089878,-0.089229) -5/56 HST (-0.089260,-0.088958) -9/101 HST (-0.092690,-0.085211) -29/326 HST (-0.088909,-0.088869) -4/45 EXTENDED HST (-0.088254,-0.088217) -3/34 EXTENDED HST (-0.091028,-0.077941) -4/47 EXTENDED HST -> HST (-0.083383,-0.083284) -1/12 EXTENDED HST (-0.076183,-0.075717) -5/66 HST (-0.075739,-0.075521) -9/119 HST (-0.078685,-0.072347) -29/384 HST (-0.075486,-0.075457) -4/53 EXTENDED HST (-0.075013,-0.074987) -3/40 EXTENDED HST (-0.077906,-0.066640) -6/83 HST (-0.071465,-0.071392) -1/14 EXTENDED HST (-0.066110,-0.065759) -5/76 HST (-0.065776,-0.065611) -9/137 HST (-0.068357,-0.062857) -29/442 HST (-0.065585,-0.065563) -4/61 EXTENDED HST (-0.065228,-0.065207) -3/46 EXTENDED HST (-0.070215,-0.055397) -11/175 HST (-0.062528,-0.062472) -1/16 EXTENDED HST (-0.057741,-0.052488) -7/127 HST (-0.055049,-0.054842) -5/91 HST (-0.054802,-0.054787) -4/73 EXTENDED HST (-0.054716,-0.054376) -3/55 HST (-0.052284,-0.052064) -5/96 HST (-0.052075,-0.051972) -9/173 HST (-0.054144,-0.049794) -29/558 HST (-0.051955,-0.051941) -4/77 EXTENDED HST (-0.051731,-0.051718) -3/58 EXTENDED HST (-0.052015,-0.047270) -7/141 HST (-0.049589,-0.049421) -5/101 HST (-0.049389,-0.049377) -4/81 EXTENDED HST (-0.049319,-0.049042) -3/61 HST (-0.047334,-0.047154) -5/106 HST (-0.047163,-0.047078) -9/191 HST (-0.049045,-0.045107) -29/616 HST (-0.047064,-0.047053) -4/85 EXTENDED HST (-0.046880,-0.046870) -3/64 EXTENDED HST (-0.045115,-0.044976) -5/111 HST (-0.048353,-0.041543) -17/378 HST (-0.044949,-0.044939) -4/89 EXTENDED HST (-0.044891,-0.044662) -3/67 HST (-0.043406,-0.039431) -7/169 HST (-0.041381,-0.041264) -5/121 HST (-0.041241,-0.041233) -4/97 EXTENDED HST (-0.041193,-0.041000) -3/73 HST (-0.042014,-0.036719) -8/203 HST (-0.039403,-0.039030) -2/51 HST (-0.038472,-0.038451) -1/26 EXTENDED HST (-0.036773,-0.036661) -17/463 HST (-0.036701,-0.036694) -4/109 EXTENDED HST (-0.036682,-0.036616) -7/191 HST (-0.036621,-0.036597) -16/437 HST (-0.036882,-0.036309) -40/1093 HST (-0.036589,-0.036582) -3/82 EXTENDED HST (-0.036525,-0.036204) -2/55 HST (-0.036219,-0.036070) -3/83 HST (-0.038776,-0.033072) -4/111 HST (-0.035723,-0.035705) -1/28 EXTENDED HST (-0.033566,-0.032575) -21/635 HST (-0.033061,-0.033055) -4/121 EXTENDED HST (-0.033029,-0.032905) -3/91 HST (-0.032918,-0.032657) -2/61 HST (-0.032584,-0.032532) -7/215 HST (-0.032540,-0.032524) -23/707 HST (-0.032658,-0.032389) -75/2306 HST (-0.032523,-0.032518) -4/123 EXTENDED HST (-0.032127,-0.032044) -5/156 HST (-0.032048,-0.032009) -9/281 HST (-0.033344,-0.030672) -29/906 HST (-0.032003,-0.031997) -4/125 EXTENDED HST (-0.031917,-0.031912) -3/94 EXTENDED HST (-0.031869,-0.031624) -2/63 HST (-0.031257,-0.031243) -1/32 EXTENDED HST (-0.032505,-0.028771) -8/261 HST (-0.030614,-0.030610) -3/98 EXTENDED HST (-0.028774,-0.028763) -29/1008 HST (-0.028770,-0.028738) -9/313 HST (-0.028741,-0.028675) -5/174 HST (-0.028469,-0.028403) -5/176 HST (-0.028407,-0.028376) -9/317 HST (-0.029559,-0.027191) -29/1022 HST (-0.028371,-0.028367) -4/141 EXTENDED HST (-0.028304,-0.028300) -3/106 EXTENDED HST (-0.028266,-0.028073) -2/71 HST (-0.027783,-0.027772) -1/36 EXTENDED HST (-0.027204,-0.027176) -9/331 HST (-0.027179,-0.027120) -5/184 HST (-0.026935,-0.026877) -5/186 HST (-0.026879,-0.026852) -9/335 HST (-0.027971,-0.025731) -29/1080 HST (-0.026847,-0.026844) -4/149 EXTENDED HST (-0.026787,-0.026784) -3/112 EXTENDED HST (-0.026753,-0.026581) -2/75 HST (-0.026321,-0.026311) -1/38 EXTENDED HST (-0.025558,-0.025506) -5/196 HST (-0.025508,-0.025483) -9/353 HST (-0.026546,-0.024420) -29/1138 HST (-0.025479,-0.025476) -4/157 EXTENDED HST (-0.025425,-0.025422) -3/118 EXTENDED HST (-0.025394,-0.025239) -2/79 HST (-0.025004,-0.024996) -1/40 EXTENDED HST (-0.024315,-0.024268) -5/206 HST (-0.024270,-0.024248) -9/371 HST (-0.025258,-0.023236) -29/1196 HST (-0.024244,-0.024241) -4/165 EXTENDED HST (-0.024195,-0.024192) -3/124 EXTENDED HST (-0.024167,-0.024026) -2/83 HST (-0.023814,-0.023805) -1/42 EXTENDED HST (-0.023188,-0.023144) -5/216 HST (-0.023146,-0.023126) -9/389 HST (-0.024090,-0.022161) -29/1254 HST (-0.023123,-0.023120) -4/173 EXTENDED HST (-0.023078,-0.023076) -3/130 EXTENDED HST (-0.023053,-0.022925) -2/87 HST (-0.022731,-0.022724) -1/44 EXTENDED HST (-0.022160,-0.022120) -5/226 HST (-0.022122,-0.022104) -9/407 HST (-0.023025,-0.021182) -29/1312 HST (-0.022101,-0.022098) -4/181 EXTENDED HST (-0.022060,-0.022058) -3/136 EXTENDED HST (-0.022037,-0.021920) -2/91 HST (-0.021743,-0.021736) -1/46 EXTENDED HST (-0.021185,-0.021168) -9/425 HST (-0.022050,-0.020285) -29/1370 HST (-0.021165,-0.021163) -4/189 EXTENDED HST (-0.021128,-0.021126) -3/142 EXTENDED HST (-0.021107,-0.020999) -2/95 HST (-0.020836,-0.020830) -1/48 EXTENDED HST (-0.077693,0.084259 ) 0/1 EXTENDED HST ( 0.080039,0.088653 ) 7/83 HST ( 0.084500,0.084993 ) 5/59 HST ( 0.085088,0.085125 ) 4/47 EXTENDED HST ( 0.084101,0.093481 ) 11/124 HST ( 0.088869,0.088909 ) 4/45 EXTENDED HST ( 0.093410,0.093641 ) 13/139 HST ( 0.093607,0.093704 ) 28/299 HST ( 0.093204,0.094209 ) 64/683 HST ( 0.093729,0.093771 ) 3/32 EXTENDED HST ( 0.090051,0.106737 ) 4/41 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. Number of excluded intervals computed by the fixed point finder: 6851 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,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,c^-1*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*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "b=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "c=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c*d>(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(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)", "b=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,c^-1*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*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c*d>(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "d=<1,1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c>(1,2)(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)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,33)(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "b=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "c=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "d=(1,33)(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c*d>(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "c=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,c^-1*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*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "d=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.