These Thurston maps all have degree 2. There is a choice of translation term b for which the resulting Thurston map is not a NET map. The postcritical set has 4 points if b = 0. The postcritical set has 4 points if b = lambda1. The postcritical set has 4 points if b = lambda2. The postcritical set has 3 points if b = lambda1+lambda2. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} These pure modular group Hurwitz classes each contain only finitely many Thurston equivalence classes. However, this modular group Hurwitz class contains infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 9. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/2, 1/2, 1/1 Every NET map in these pure modular group Hurwitz classes is rational because the modulo 2 correspondence graph has no loops. EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.000000) (-1.000000,infinity ) SLOPE FUNCTION INFORMATION There are no slope function fixed points because the mod 2 slope correspondence graph has no loops. 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=", "b=<1,c*d*c^-1>", "c=(1,2)", "d=(1,2)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=", "b=", "c=(1,2)", "d=(1,2)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,1>(1,2)", "b=(1,2)", "c=<1,c*d*c^-1>", "d=", "a*b*c*d");