These Thurston maps are NET maps for every choice of translation term. They have degree 32. They are imprimitive, each factoring as a NET map with degree 16 followed by a Euclidean NET map with degree 2. 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 7. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/32, 2/16, 2/8, 2/4, 2/2, 6/4, 2/1, 6/2, 10/2, 6/1, 14/2, 10/1, 14/1, 18/1 22/1, 26/1, 30/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.034884) (-0.031833,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 (-0.035333,-0.034673) -3/86 HST (-0.034727,-0.034588) -7/202 HST (-0.034634,-0.033868) -1/29 EXTENDED HST -> HST (-0.034072,-0.033640) -13/384 HST (-0.033852,-0.033565) -3/89 HST (-0.033691,-0.033459) -29/864 HST (-0.033562,-0.033516) -5/149 HST (-0.033460,-0.033458) -71/2122 HST (-0.033459,-0.033444) -9/269 HST (-0.033482,-0.033401) -61/1824 HST (-0.033443,-0.033420) -11/329 HST (-0.033402,-0.033400) -33/988 HST (-0.033409,-0.033390) -67/2006 HST (-0.033399,-0.033395) -17/509 HST (-0.033395,-0.033387) -20/599 HST (-0.033407,-0.033366) -125/3744 HST (-0.033387,-0.033384) -21/629 HST (-0.033380,-0.033290) -1/30 EXTENDED HST (-0.033318,-0.033264) -25/751 HST (-0.033287,-0.033143) -8/241 HST (-0.033178,-0.033146) -6/181 HST (-0.033144,-0.032987) -4/121 HST (-0.033056,-0.032945) -19/576 HST (-0.032980,-0.032755) -2/61 HST (-0.032790,-0.032544) -7/214 HST (-0.032710,-0.032468) -3/92 HST (-0.032578,-0.032239) -5/154 HST (-0.032274,-0.032242) -1/31 EXTENDED HST (-0.032265,-0.031791) -7/218 HST (-0.032093,-0.031548) -3/94 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS FOUND: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 30/1 2 16 No No No No NUMBER OF EQUATORS FOUND: 0 0 0 0 The fixed point finder is unable to determine whether there are any more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 2398 Here is their union. There are no more slope function fixed points whose negative reciprocals lie in any of the following intervals. EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION (-infinity,-0.033701) (-0.033701,-0.033701) (-0.033701,-0.033701) (-0.033701,-0.033701) (-0.033701,-0.033701) (-0.033701,-0.033701) (-0.033701,-0.033701) (-0.033701,-0.033701) (-0.033700,-0.033700) (-0.033700,-0.033700) (-0.033699,-0.033699) (-0.033698,-0.033698) (-0.033698,-0.033697) (-0.033697,-0.033697) (-0.033696,-0.033695) (-0.033694,-0.033694) (-0.033694,-0.033692) (-0.033691,-0.033691) (-0.033690,-0.033686) (-0.033684,-0.033673) (-0.033670,-0.033670) (-0.033655,-0.033652) (-0.033614,-0.033613) (-0.033334,-0.033332) (-0.001005,0.001074 ) ( 2.372941,infinity ) 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 either one of the above cycles or 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=(1,31)(2,30)(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=(1,31)(2,30)(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)", "c=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "d=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(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,b,b,b,b,b,b,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,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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)", "c=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "d=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "b=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "c=(1,31)(2,30)(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)", "d=(1,31)(2,30)(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 lambda1+lambda2: NewSphereMachine( "a=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "b=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "c=<1,b,b,b,b,b,b,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,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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)", "d=(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"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about -6309/184397. Imminent integer overflow halted evaluation of the slope function at slope 2365186/80923 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -2746/81465. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -11877/352427. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -27140/805327. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -27140/805327. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -50894/1510181. Imminent integer overflow halted evaluation of the slope function at slope 4882970/164559 while computing a fixed point excluded interval about -50894/1510181. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -50894/1510181. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -89911/2667935. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -89911/2667935. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -89911/2667935. Imminent integer overflow halted evaluation of the slope function at slope 7198478/242593 while computing a fixed point excluded interval about -191699/5688297. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -191699/5688297. Imminent integer overflow halted evaluation of the slope function at slope 15554710/524203 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 11025710/371573 while computing a fixed point excluded interval about -312188/9263575. Imminent integer overflow halted evaluation of the slope function at slope 9616002/324065 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -44122/1309235. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -44122/1309235. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -44122/1309235. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -44122/1309235. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -44122/1309235. Imminent integer overflow halted evaluation of the slope function at slope 5488894/184979 while computing a fixed point excluded interval about -44122/1309235. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -44122/1309235. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -44122/1309235. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -44122/1309235. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow halted evaluation of the slope function at slope 11127726/375011 while computing a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow halted evaluation of the slope function at slope 13041342/439501 while computing a fixed point excluded interval about -67876/2014089. Imminent integer overflow halted evaluation of the slope function at slope 15860758/534517 while computing a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow halted evaluation of the slope function at slope 20593790/694023 while computing a fixed point excluded interval about -67876/2014089. Imminent integer overflow halted evaluation of the slope function at slope 6898602/232487 while computing a fixed point excluded interval about -67876/2014089. Imminent integer overflow halted evaluation of the slope function at slope 24621968/829775 while computing a fixed point excluded interval about -67876/2014089. Imminent integer overflow halted evaluation of the slope function at slope 25326822/853529 while computing a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -67876/2014089.