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, 9/1, 10/1, 11/1, 12/1 13/1, 14/1, 18/1, 21/1, 24/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.391735) (-0.391642,-0.390939) (-0.390189,-0.208402) (-0.207714,-0.139165) (-0.135817,-0.134460) (-0.131496,-0.129390) (-0.128818,-0.127598) (-0.122506,-0.121401) (-0.120898,-0.119115) (-0.116783,-0.115779) (-0.113452,-0.108865) (-0.106805,-0.105964) (-0.104115,-0.102790) (-0.102429,-0.101656) (-0.097357,-0.096198) (-0.092470,-0.089400) (-0.086171,-0.085262) (-0.081490,-0.080676) (-0.078038,-0.075840) (-0.073504,-0.072841) (-0.070070,-0.069467) (-0.067502,-0.065851) (-0.064083,-0.063579) (-0.061457,-0.060993) (-0.059473,-0.058188) (-0.053151,-0.052122) (-0.048044,-0.047202) (-0.043832,-0.043130) (-0.040299,-0.039705) (-0.037294,-0.036784) (-0.034705,-0.034263) (-0.032452,-0.032066) (-0.030475,-0.030133) (-0.028724,-0.028421) (-0.027163,-0.026892) (-0.025764,-0.025520) (-0.024501,-0.024280) (-0.023357,-0.023156) (-0.022314,-0.022131) (-0.021361,-0.021193) (-0.020486,-0.020331) ( 0.020331,0.020486 ) ( 0.021193,0.021361 ) ( 0.022131,0.022314 ) ( 0.023156,0.023357 ) ( 0.024280,0.024501 ) ( 0.025520,0.025764 ) ( 0.026892,0.027163 ) ( 0.028421,0.028724 ) ( 0.030133,0.030475 ) ( 0.032066,0.032452 ) ( 0.034263,0.034705 ) ( 0.036784,0.037294 ) ( 0.039705,0.040299 ) ( 0.043130,0.043832 ) ( 0.047202,0.048044 ) ( 0.052122,0.053151 ) ( 0.058188,0.059473 ) ( 0.060993,0.061457 ) ( 0.063579,0.064083 ) ( 0.065851,0.067502 ) ( 0.069467,0.070070 ) ( 0.072841,0.073504 ) ( 0.075840,0.078038 ) ( 0.080676,0.081490 ) ( 0.085262,0.086171 ) ( 0.089400,0.092470 ) ( 0.096198,0.097357 ) ( 0.101656,0.102429 ) ( 0.102790,0.104115 ) ( 0.105964,0.106805 ) ( 0.108865,0.113452 ) ( 0.115779,0.116783 ) ( 0.119115,0.120898 ) ( 0.121401,0.122506 ) ( 0.127598,0.128818 ) ( 0.129390,0.131496 ) ( 0.133987,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 (-0.391968,-0.391297) -47/120 HST (-0.392420,-0.387192) -16/41 EXTENDED HST -> HST (-0.209063,-0.207738) -129/619 HST (-0.208389,-0.208278) -5/24 EXTENDED HST (-0.210374,-0.205061) -43/207 HST (-0.146133,-0.128568) -4/29 EXTENDED HST -> HST (-0.136403,-0.136324) -3/22 EXTENDED HST (-0.145081,-0.108853) -7/55 HST (-0.125100,-0.124900) -1/8 EXTENDED HST (-0.114386,-0.101112) -4/37 EXTENDED HST -> HST (-0.107167,-0.107118) -3/28 EXTENDED HST (-0.105077,-0.097153) -37/366 HST (-0.101090,-0.100746) -10/99 HST (-0.100064,-0.099936) -1/10 EXTENDED HST (-0.104210,-0.087269) -5/52 HST (-0.095267,-0.095209) -2/21 EXTENDED HST (-0.087357,-0.087140) -13/149 HST (-0.087204,-0.087070) -21/241 HST (-0.087894,-0.086223) -35/402 HST (-0.086981,-0.086932) -2/23 EXTENDED HST (-0.095371,-0.077427) -5/58 HST (-0.079740,-0.070851) -4/53 HST (-0.075012,-0.074988) -3/40 EXTENDED HST (-0.074092,-0.074057) -2/27 EXTENDED HST (-0.074181,-0.065878) -4/57 HST (-0.069252,-0.061629) -4/61 HST (-0.065226,-0.065208) -3/46 EXTENDED HST (-0.064529,-0.064503) -2/31 EXTENDED HST (-0.065129,-0.057722) -4/65 HST (-0.058260,-0.057177) -40/693 HST (-0.057699,-0.057685) -3/52 EXTENDED HST (-0.058030,-0.056322) -49/857 HST (-0.057153,-0.057132) -2/35 EXTENDED HST (-0.057267,-0.055332) -21/373 HST (-0.056297,-0.056063) -5/89 HST (-0.055575,-0.055536) -1/18 EXTENDED HST (-0.058046,-0.051363) -4/73 HST (-0.054730,-0.054362) -3/55 HST (-0.054063,-0.054045) -2/37 EXTENDED HST (-0.052452,-0.050266) -17/331 HST (-0.051290,-0.051274) -2/39 EXTENDED HST (-0.050271,-0.050186) -10/199 HST (-0.053660,-0.046644) -14/279 HST (-0.050016,-0.049984) -1/20 EXTENDED HST (-0.048603,-0.044665) -9/193 HST (-0.046519,-0.046505) -2/43 EXTENDED HST (-0.045468,-0.045441) -1/22 EXTENDED HST (-0.048912,-0.040188) -5/112 HST (-0.044451,-0.044438) -2/45 EXTENDED HST (-0.041778,-0.037332) -4/101 HST (-0.039477,-0.039470) -3/76 EXTENDED HST (-0.039221,-0.039211) -2/51 EXTENDED HST (-0.038471,-0.038452) -1/26 EXTENDED HST (-0.037342,-0.037314) -19/509 HST (-0.037315,-0.037312) -5/134 EXTENDED HST (-0.037405,-0.037218) -156/4181 HST (-0.037312,-0.037265) -16/429 HST (-0.038707,-0.034604) -4/109 HST (-0.036588,-0.036583) -3/82 EXTENDED HST (-0.036368,-0.036359) -2/55 EXTENDED HST (-0.035722,-0.035706) -1/28 EXTENDED HST (-0.036056,-0.032247) -4/117 HST (-0.034093,-0.034088) -3/88 EXTENDED HST (-0.033902,-0.033895) -2/59 EXTENDED HST (-0.033340,-0.033326) -1/30 EXTENDED HST (-0.033745,-0.030191) -4/125 HST (-0.031917,-0.031913) -3/94 EXTENDED HST (-0.031749,-0.031743) -2/63 EXTENDED HST (-0.031256,-0.031244) -1/32 EXTENDED HST (-0.031713,-0.028381) -4/133 HST (-0.030002,-0.029998) -3/100 EXTENDED HST (-0.029854,-0.029848) -2/67 EXTENDED HST (-0.029417,-0.029406) -1/34 EXTENDED HST (-0.029911,-0.026776) -4/141 HST (-0.028304,-0.028300) -3/106 EXTENDED HST (-0.028172,-0.028166) -2/71 EXTENDED HST (-0.027783,-0.027773) -1/36 EXTENDED HST (-0.026776,-0.026752) -14/523 HST (-0.026765,-0.026711) -5/187 HST (-0.027824,-0.025590) -9/337 HST (-0.026669,-0.026664) -2/75 EXTENDED HST (-0.026320,-0.026311) -1/38 EXTENDED HST (-0.026859,-0.024055) -4/157 HST (-0.025425,-0.025422) -3/118 EXTENDED HST (-0.025319,-0.025314) -2/79 EXTENDED HST (-0.025004,-0.024996) -1/40 EXTENDED HST (-0.026591,-0.021516) -5/208 HST (-0.024036,-0.023964) -3/125 HST (-0.023813,-0.023806) -1/42 EXTENDED HST (-0.021519,-0.021512) -23/1069 HST (-0.021709,-0.021313) -37/1720 HST (-0.021507,-0.021504) -2/93 EXTENDED HST (-0.022308,-0.019992) -4/189 HST (-0.021128,-0.021126) -3/142 EXTENDED HST (-0.021054,-0.021051) -2/95 EXTENDED HST (-0.020836,-0.020831) -1/48 EXTENDED HST (-0.140505,0.195494 ) 0/1 EXTENDED 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. 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=(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,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,c,c,c,c,c,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)", "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,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,c,c,c,c,c,c,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,d,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,c,c,c,c,c,c>(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,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,c,c,c,c,c,c,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)", "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.