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,-1.015232) (-0.983966,-0.111336) (-0.110132,-0.098072) (-0.096351,-0.093250) (-0.088683,-0.086049) (-0.084542,-0.082159) (-0.080784,-0.078593) (-0.075323,-0.073415) (-0.072314,-0.070564) (-0.069547,-0.067917) (-0.065461,-0.064015) (-0.063177,-0.061837) (-0.061055,-0.059795) (-0.057542,-0.056750) (-0.056090,-0.055031) (-0.054411,-0.053702) (-0.051603,-0.050965) (-0.050432,-0.049575) (-0.049071,-0.048494) (-0.046775,-0.046251) (-0.045812,-0.045103) (-0.044685,-0.044206) (-0.042774,-0.042335) (-0.041967,-0.041371) (-0.041019,-0.040615) (-0.038717,-0.038210) (-0.035934,-0.035497) (-0.033525,-0.033144) (-0.031418,-0.031083) (-0.029561,-0.029264) (-0.027911,-0.027646) (-0.026435,-0.026198) (-0.025108,-0.024893) (-0.023907,-0.023713) (-0.022816,-0.022639) (-0.021820,-0.021658) (-0.020908,-0.020759) (-0.020069,-0.019932) ( 0.019932,0.020069 ) ( 0.020759,0.020908 ) ( 0.021658,0.021820 ) ( 0.022639,0.022816 ) ( 0.023713,0.023907 ) ( 0.024893,0.025108 ) ( 0.026198,0.026435 ) ( 0.027646,0.027911 ) ( 0.029264,0.029561 ) ( 0.031083,0.031418 ) ( 0.033144,0.033525 ) ( 0.035497,0.035934 ) ( 0.038210,0.038717 ) ( 0.040615,0.041019 ) ( 0.041371,0.041967 ) ( 0.042335,0.042774 ) ( 0.044206,0.044685 ) ( 0.045103,0.045812 ) ( 0.046251,0.046775 ) ( 0.048494,0.049071 ) ( 0.049575,0.050432 ) ( 0.050965,0.051603 ) ( 0.053702,0.054411 ) ( 0.055031,0.056090 ) ( 0.056750,0.057542 ) ( 0.059795,0.061055 ) ( 0.061837,0.063177 ) ( 0.064015,0.065461 ) ( 0.067917,0.069547 ) ( 0.070564,0.072314 ) ( 0.073415,0.075323 ) ( 0.078593,0.080784 ) ( 0.082159,0.084542 ) ( 0.086049,0.088683 ) ( 0.093250,0.096351 ) ( 0.096675,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 (-1.017796,-1.012521) -67/66 HST (-1.014675,-1.010334) -81/80 HST (-1.012589,-1.007948) -98/97 HST (-1.009336,-1.006549) -127/126 HST (-1.007185,-0.992917) -1/1 EXTENDED HST (-0.994075,-0.991642) -139/140 HST (-0.992847,-0.989916) -116/117 HST (-0.991431,-0.989084) -101/102 HST (-0.990117,-0.986082) -83/84 HST (-0.988023,-0.980201) -62/63 HST (-0.113665,-0.108977) -56/503 HST (-0.111199,-0.111023) -1/9 EXTENDED HST (-0.098753,-0.097971) -5/51 HST (-0.098009,-0.097644) -9/92 HST (-0.101744,-0.093527) -29/297 HST (-0.097585,-0.097537) -4/41 EXTENDED HST (-0.096796,-0.096752) -3/31 EXTENDED HST (-0.099399,-0.085163) -4/43 EXTENDED HST -> HST (-0.090968,-0.090850) -1/11 EXTENDED HST (-0.085185,-0.085121) -35/411 HST (-0.085125,-0.085088) -4/47 EXTENDED HST (-0.085367,-0.084800) -81/952 HST (-0.085084,-0.084984) -29/341 HST (-0.085043,-0.084769) -9/106 HST (-0.084797,-0.084219) -5/59 HST (-0.082466,-0.081920) -5/61 HST (-0.081946,-0.081691) -9/110 HST (-0.085115,-0.078254) -29/355 HST (-0.081649,-0.081616) -4/49 EXTENDED HST (-0.081097,-0.081065) -3/37 EXTENDED HST (-0.078335,-0.077916) -5/64 HST (-0.081125,-0.074392) -7/90 HST (-0.076965,-0.076881) -1/13 EXTENDED HST (-0.077640,-0.068997) -8/109 HST (-0.073183,-0.073158) -3/41 EXTENDED HST (-0.072668,-0.062135) -4/59 HST (-0.066698,-0.066635) -1/15 EXTENDED HST (-0.062011,-0.061701) -5/81 HST (-0.061716,-0.061572) -9/146 HST (-0.064147,-0.058989) -29/471 HST (-0.061548,-0.061529) -4/65 EXTENDED HST (-0.061233,-0.061216) -3/49 EXTENDED HST (-0.060243,-0.057718) -22/373 HST (-0.058848,-0.058799) -1/17 EXTENDED HST (-0.057883,-0.057503) -3/52 HST (-0.060078,-0.053306) -8/141 HST (-0.056611,-0.056596) -3/53 EXTENDED HST (-0.057725,-0.048858) -17/319 HST (-0.053289,-0.053095) -5/94 HST (-0.052651,-0.052612) -1/19 EXTENDED HST (-0.048521,-0.048254) -3/62 HST (-0.051780,-0.044205) -4/83 HST (-0.047635,-0.047603) -1/21 EXTENDED HST (-0.044229,-0.044007) -3/68 HST (-0.047253,-0.040326) -4/91 HST (-0.043492,-0.043465) -1/23 EXTENDED HST (-0.040378,-0.040267) -5/124 HST (-0.042077,-0.038372) -7/174 HST (-0.040011,-0.039989) -1/25 EXTENDED HST (-0.038276,-0.038158) -5/131 HST (-0.038163,-0.038108) -9/236 HST (-0.039698,-0.036515) -29/761 HST (-0.038099,-0.038092) -4/105 EXTENDED HST (-0.037978,-0.037971) -3/79 EXTENDED HST (-0.037909,-0.037564) -2/53 HST (-0.037047,-0.037027) -1/27 EXTENDED HST (-0.036525,-0.036204) -2/55 HST (-0.038376,-0.033985) -8/221 HST (-0.036148,-0.036141) -3/83 EXTENDED HST (-0.034038,-0.033760) -2/59 HST (-0.035790,-0.031688) -8/237 HST (-0.033711,-0.033705) -3/89 EXTENDED HST (-0.033707,-0.029571) -5/158 HST (-0.031581,-0.031577) -3/95 EXTENDED HST (-0.030394,-0.028741) -11/372 HST (-0.028764,-0.028707) -5/174 HST (-0.030031,-0.027340) -7/244 HST (-0.028577,-0.028566) -1/35 EXTENDED HST (-0.027489,-0.027307) -5/183 HST (-0.027315,-0.027230) -3/110 HST (-0.029312,-0.024982) -4/147 HST (-0.027032,-0.027022) -1/37 EXTENDED HST (-0.024921,-0.024871) -5/201 HST (-0.024874,-0.024850) -9/362 HST (-0.025886,-0.023813) -29/1167 HST (-0.024846,-0.024843) -4/161 EXTENDED HST (-0.024795,-0.024792) -3/121 EXTENDED HST (-0.024766,-0.024618) -2/81 HST (-0.024394,-0.024386) -1/41 EXTENDED HST (-0.023738,-0.023693) -5/211 HST (-0.023695,-0.023674) -9/380 HST (-0.024660,-0.022686) -29/1225 HST (-0.023670,-0.023667) -4/169 EXTENDED HST (-0.023623,-0.023621) -3/127 EXTENDED HST (-0.023597,-0.023462) -2/85 HST (-0.023260,-0.023252) -1/43 EXTENDED HST (-0.022662,-0.022621) -5/221 HST (-0.022623,-0.022603) -9/398 HST (-0.023545,-0.021660) -29/1283 HST (-0.022600,-0.022598) -4/177 EXTENDED HST (-0.022558,-0.022555) -3/133 EXTENDED HST (-0.022533,-0.022411) -2/89 HST (-0.022226,-0.022219) -1/45 EXTENDED HST (-0.021680,-0.021642) -5/231 HST (-0.021644,-0.021626) -9/416 HST (-0.022527,-0.020724) -29/1341 HST (-0.021623,-0.021620) -4/185 EXTENDED HST (-0.021584,-0.021582) -3/139 EXTENDED HST (-0.021562,-0.021449) -2/93 HST (-0.021280,-0.021273) -1/47 EXTENDED HST (-0.020724,-0.020718) -23/1110 HST (-0.020721,-0.020700) -7/338 HST (-0.020701,-0.020693) -16/773 HST (-0.020856,-0.020530) -40/1933 HST (-0.020691,-0.020689) -3/145 EXTENDED HST (-0.020670,-0.020567) -2/97 HST (-0.022115,-0.018838) -4/195 HST (-0.020411,-0.020405) -1/49 EXTENDED HST (-0.072092,0.092012 ) 0/1 EXTENDED HST ( 0.087395,0.096837 ) 7/76 HST ( 0.092299,0.092888 ) 5/54 HST ( 0.093001,0.093045 ) 4/43 EXTENDED 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: 7775 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=(1,33)(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: NewSphereMachine( "a=<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)", "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,a,d*a,d*a,d*a,d*a,d*a,d*a,d*a,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b,b,b,b,b,b,b,b,b,b*c,b*c,b*c,b*c,b*c,b*c,b*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,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)", "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,d*a*c*a*b,d*a,d*a,d*a,d*a,d*a,d*a,d*a,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b,b,b,b,b,b,b,b,b,b*c,b*c,b*c,b*c,b*c,b*c,b*c,c*d*b*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)", "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.