INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 288 Minimal number of generators: 49 Number of equivalence classes of cusps: 32 Genus: 9 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/5 -7/5 -1/1 -4/5 -7/9 -3/5 -5/9 -1/2 -3/7 -2/5 -1/3 -1/4 -1/5 -1/7 0/1 1/5 1/4 3/10 1/3 2/5 9/20 1/2 3/5 2/3 7/10 4/5 1/1 4/3 7/5 9/5 2/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -2/1 -1/1 -9/5 1/0 -7/4 -2/1 -12/7 -3/1 -5/3 -3/2 -3/2 0/1 -7/5 1/0 -11/8 -2/1 -4/3 -1/1 -9/7 -3/2 -5/4 -4/3 -1/1 -1/1 0/1 -5/6 -4/3 -4/5 -1/1 -11/14 -14/15 -7/9 -9/10 -3/4 -4/5 -11/15 -3/4 -8/11 -5/7 -5/7 -3/4 -12/17 -5/7 -7/10 -2/3 -2/3 -1/1 -3/5 -1/2 -4/7 -1/3 -9/16 0/1 -5/9 -1/3 0/1 -11/20 0/1 -6/11 1/1 -1/2 0/1 -5/11 -5/2 -9/20 -2/1 -4/9 -5/3 -3/7 -4/3 -1/1 -2/5 -1/1 -5/13 -1/1 -10/11 -8/21 -17/19 -3/8 -6/7 -1/3 -3/4 -4/13 -9/13 -3/10 -2/3 -2/7 -3/5 -5/18 -2/3 -3/11 -2/3 -3/5 -1/4 -2/3 -1/5 -1/2 -1/6 -2/5 -1/7 -1/2 0/1 -1/1 1/5 -1/2 2/9 -5/11 1/4 -2/5 3/11 -3/10 2/7 -1/5 3/10 0/1 1/3 -1/1 0/1 2/5 -1/1 3/7 -3/4 4/9 -5/7 9/20 -2/3 5/11 -2/3 -3/5 1/2 -2/3 3/5 -1/2 5/8 -6/13 12/19 -13/29 19/30 -4/9 7/11 -7/16 2/3 -1/3 7/10 0/1 5/7 -1/1 0/1 8/11 -3/5 3/4 0/1 7/9 -1/1 0/1 4/5 -1/1 1/1 -1/2 6/5 -1/3 11/9 -1/3 0/1 5/4 0/1 14/11 -3/7 9/7 -1/3 0/1 13/10 0/1 4/3 -1/1 7/5 -1/2 10/7 -7/15 13/9 -9/20 3/2 -2/5 14/9 -5/13 11/7 -3/8 8/5 -1/3 5/3 -1/3 0/1 17/10 0/1 12/7 1/1 19/11 -3/2 7/4 -2/3 9/5 -1/2 11/6 -4/9 2/1 -1/3 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,4,0,1) (-2/1,1/0) -> (2/1,1/0) Parabolic Matrix(51,94,-70,-129) (-2/1,-9/5) -> (-11/15,-8/11) Hyperbolic Matrix(59,104,-80,-141) (-9/5,-7/4) -> (-3/4,-11/15) Hyperbolic Matrix(79,136,-140,-241) (-7/4,-12/7) -> (-4/7,-9/16) Hyperbolic Matrix(19,32,-60,-101) (-12/7,-5/3) -> (-1/3,-4/13) Hyperbolic Matrix(11,18,-30,-49) (-5/3,-3/2) -> (-3/8,-1/3) Hyperbolic Matrix(69,98,-50,-71) (-3/2,-7/5) -> (-7/5,-11/8) Parabolic Matrix(31,42,-110,-149) (-11/8,-4/3) -> (-2/7,-5/18) Hyperbolic Matrix(99,128,-140,-181) (-4/3,-9/7) -> (-5/7,-12/17) Hyperbolic Matrix(11,14,-70,-89) (-9/7,-5/4) -> (-1/6,-1/7) Hyperbolic Matrix(9,10,-10,-11) (-5/4,-1/1) -> (-1/1,-5/6) Parabolic Matrix(79,64,-100,-81) (-5/6,-4/5) -> (-4/5,-11/14) Parabolic Matrix(329,258,190,149) (-11/14,-7/9) -> (19/11,7/4) Hyperbolic Matrix(21,16,80,61) (-7/9,-3/4) -> (1/4,3/11) Hyperbolic Matrix(61,44,140,101) (-8/11,-5/7) -> (3/7,4/9) Hyperbolic Matrix(261,184,200,141) (-12/17,-7/10) -> (13/10,4/3) Hyperbolic Matrix(41,28,60,41) (-7/10,-2/3) -> (2/3,7/10) Hyperbolic Matrix(29,18,-50,-31) (-2/3,-3/5) -> (-3/5,-4/7) Parabolic Matrix(221,124,180,101) (-9/16,-5/9) -> (11/9,5/4) Hyperbolic Matrix(181,100,400,221) (-5/9,-11/20) -> (9/20,5/11) Hyperbolic Matrix(449,246,710,389) (-11/20,-6/11) -> (12/19,19/30) Hyperbolic Matrix(61,32,40,21) (-6/11,-1/2) -> (3/2,14/9) Hyperbolic Matrix(59,28,40,19) (-1/2,-5/11) -> (13/9,3/2) Hyperbolic Matrix(349,158,550,249) (-5/11,-9/20) -> (19/30,7/11) Hyperbolic Matrix(161,72,360,161) (-9/20,-4/9) -> (4/9,9/20) Hyperbolic Matrix(101,44,140,61) (-4/9,-3/7) -> (5/7,8/11) Hyperbolic Matrix(39,16,-100,-41) (-3/7,-2/5) -> (-2/5,-5/13) Parabolic Matrix(371,142,290,111) (-5/13,-8/21) -> (14/11,9/7) Hyperbolic Matrix(201,76,320,121) (-8/21,-3/8) -> (5/8,12/19) Hyperbolic Matrix(341,104,200,61) (-4/13,-3/10) -> (17/10,12/7) Hyperbolic Matrix(41,12,140,41) (-3/10,-2/7) -> (2/7,3/10) Hyperbolic Matrix(101,28,220,61) (-5/18,-3/11) -> (5/11,1/2) Hyperbolic Matrix(61,16,80,21) (-3/11,-1/4) -> (3/4,7/9) Hyperbolic Matrix(9,2,-50,-11) (-1/4,-1/5) -> (-1/5,-1/6) Parabolic Matrix(109,14,70,9) (-1/7,0/1) -> (14/9,11/7) Hyperbolic Matrix(11,-2,50,-9) (0/1,1/5) -> (1/5,2/9) Parabolic Matrix(101,-24,80,-19) (2/9,1/4) -> (5/4,14/11) Hyperbolic Matrix(201,-56,140,-39) (3/11,2/7) -> (10/7,13/9) Hyperbolic Matrix(101,-32,60,-19) (3/10,1/3) -> (5/3,17/10) Hyperbolic Matrix(49,-18,30,-11) (1/3,2/5) -> (8/5,5/3) Hyperbolic Matrix(111,-46,70,-29) (2/5,3/7) -> (11/7,8/5) Hyperbolic Matrix(31,-18,50,-29) (1/2,3/5) -> (3/5,5/8) Parabolic Matrix(189,-122,110,-71) (7/11,2/3) -> (12/7,19/11) Hyperbolic Matrix(181,-128,140,-99) (7/10,5/7) -> (9/7,13/10) Hyperbolic Matrix(129,-94,70,-51) (8/11,3/4) -> (11/6,2/1) Hyperbolic Matrix(109,-86,90,-71) (7/9,4/5) -> (6/5,11/9) Hyperbolic Matrix(11,-10,10,-9) (4/5,1/1) -> (1/1,6/5) Parabolic Matrix(71,-98,50,-69) (4/3,7/5) -> (7/5,10/7) Parabolic Matrix(91,-162,50,-89) (7/4,9/5) -> (9/5,11/6) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(1,0,-2,1) Matrix(51,94,-70,-129) -> Matrix(3,-2,-4,3) Matrix(59,104,-80,-141) -> Matrix(3,10,-4,-13) Matrix(79,136,-140,-241) -> Matrix(1,2,-2,-3) Matrix(19,32,-60,-101) -> Matrix(7,12,-10,-17) Matrix(11,18,-30,-49) -> Matrix(5,6,-6,-7) Matrix(69,98,-50,-71) -> Matrix(1,-2,0,1) Matrix(31,42,-110,-149) -> Matrix(1,4,-2,-7) Matrix(99,128,-140,-181) -> Matrix(7,12,-10,-17) Matrix(11,14,-70,-89) -> Matrix(1,2,-4,-7) Matrix(9,10,-10,-11) -> Matrix(1,0,0,1) Matrix(79,64,-100,-81) -> Matrix(17,18,-18,-19) Matrix(329,258,190,149) -> Matrix(13,12,-12,-11) Matrix(21,16,80,61) -> Matrix(7,6,-20,-17) Matrix(61,44,140,101) -> Matrix(1,0,0,1) Matrix(261,184,200,141) -> Matrix(3,2,4,3) Matrix(41,28,60,41) -> Matrix(3,2,-8,-5) Matrix(29,18,-50,-31) -> Matrix(3,2,-8,-5) Matrix(221,124,180,101) -> Matrix(1,0,0,1) Matrix(181,100,400,221) -> Matrix(9,2,-14,-3) Matrix(449,246,710,389) -> Matrix(17,-4,-38,9) Matrix(61,32,40,21) -> Matrix(3,2,-8,-5) Matrix(59,28,40,19) -> Matrix(1,-2,-2,5) Matrix(349,158,550,249) -> Matrix(15,34,-34,-77) Matrix(161,72,360,161) -> Matrix(11,20,-16,-29) Matrix(101,44,140,61) -> Matrix(3,4,-4,-5) Matrix(39,16,-100,-41) -> Matrix(13,14,-14,-15) Matrix(371,142,290,111) -> Matrix(11,10,-32,-29) Matrix(201,76,320,121) -> Matrix(41,36,-90,-79) Matrix(341,104,200,61) -> Matrix(3,2,16,11) Matrix(41,12,140,41) -> Matrix(3,2,-20,-13) Matrix(101,28,220,61) -> Matrix(1,0,0,1) Matrix(61,16,80,21) -> Matrix(3,2,-8,-5) Matrix(9,2,-50,-11) -> Matrix(7,4,-16,-9) Matrix(109,14,70,9) -> Matrix(7,2,-18,-5) Matrix(11,-2,50,-9) -> Matrix(11,6,-24,-13) Matrix(101,-24,80,-19) -> Matrix(5,2,-8,-3) Matrix(201,-56,140,-39) -> Matrix(23,6,-50,-13) Matrix(101,-32,60,-19) -> Matrix(1,0,-2,1) Matrix(49,-18,30,-11) -> Matrix(1,0,-2,1) Matrix(111,-46,70,-29) -> Matrix(7,6,-20,-17) Matrix(31,-18,50,-29) -> Matrix(15,8,-32,-17) Matrix(189,-122,110,-71) -> Matrix(5,2,2,1) Matrix(181,-128,140,-99) -> Matrix(1,0,-2,1) Matrix(129,-94,70,-51) -> Matrix(7,4,-16,-9) Matrix(109,-86,90,-71) -> Matrix(1,0,-2,1) Matrix(11,-10,10,-9) -> Matrix(3,2,-8,-5) Matrix(71,-98,50,-69) -> Matrix(15,8,-32,-17) Matrix(91,-162,50,-89) -> Matrix(11,6,-24,-13) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 24 Degree of the the map X: 24 Degree of the the map Y: 48 Permutation triple for Y: ((1,6,22,43,45,48,40,23,7,2)(3,12,36,30,46,47,27,37,13,4)(5,18,29,10,9,28,35,39,38,19)(8,26)(11,33,42,16,15,41,21,25,24,34)(14,20)(17,44)(31,32); (1,4,16,17,5)(2,10,32,11,3)(6,14,13,39,21)(7,25,35,12,8)(18,27,26,43,42)(20,30,29,33,40)(24,44,28,48,46)(31,41,47,45,38); (1,3)(2,8,27,41,15,4,14,40,28,9)(5,19,45,26,12,11,34,46,20,6)(7,23,33,32,38,13,37,18,17,24)(10,30,36,35,44,16,43,22,21,31)(25,39)(29,42)(47,48)) ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 144 Minimal number of generators: 25 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 20 Genus: 3 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/5 -1/1 -4/5 -7/9 -3/5 -1/2 -2/5 -1/3 -1/5 0/1 1/5 1/3 2/5 3/7 1/2 3/5 1/1 9/5 2/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -2/1 -1/1 -5/3 -3/2 -3/2 0/1 -7/5 1/0 -4/3 -1/1 -5/4 -4/3 -1/1 -1/1 0/1 -5/6 -4/3 -4/5 -1/1 -11/14 -14/15 -7/9 -9/10 -3/4 -4/5 -8/11 -5/7 -5/7 -3/4 -2/3 -1/1 -3/5 -1/2 -1/2 0/1 -3/7 -4/3 -1/1 -2/5 -1/1 -3/8 -6/7 -1/3 -3/4 -1/4 -2/3 -1/5 -1/2 -1/6 -2/5 0/1 -1/1 1/5 -1/2 1/4 -2/5 3/11 -3/10 2/7 -1/5 3/10 0/1 1/3 -1/1 0/1 2/5 -1/1 3/7 -3/4 4/9 -5/7 1/2 -2/3 3/5 -1/2 5/8 -6/13 7/11 -7/16 2/3 -1/3 1/1 -1/2 3/2 -2/5 11/7 -3/8 8/5 -1/3 5/3 -1/3 0/1 12/7 1/1 19/11 -3/2 7/4 -2/3 9/5 -1/2 2/1 -1/3 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,4,0,1) (-2/1,1/0) -> (2/1,1/0) Parabolic Matrix(4,7,-15,-26) (-2/1,-5/3) -> (-1/3,-1/4) Hyperbolic Matrix(11,18,-30,-49) (-5/3,-3/2) -> (-3/8,-1/3) Hyperbolic Matrix(34,49,-25,-36) (-3/2,-7/5) -> (-7/5,-4/3) Parabolic Matrix(16,21,35,46) (-4/3,-5/4) -> (4/9,1/2) Hyperbolic Matrix(9,10,-10,-11) (-5/4,-1/1) -> (-1/1,-5/6) Parabolic Matrix(79,64,-100,-81) (-5/6,-4/5) -> (-4/5,-11/14) Parabolic Matrix(329,258,190,149) (-11/14,-7/9) -> (19/11,7/4) Hyperbolic Matrix(21,16,80,61) (-7/9,-3/4) -> (1/4,3/11) Hyperbolic Matrix(4,3,-35,-26) (-3/4,-8/11) -> (-1/6,0/1) Hyperbolic Matrix(61,44,140,101) (-8/11,-5/7) -> (3/7,4/9) Hyperbolic Matrix(54,37,35,24) (-5/7,-2/3) -> (3/2,11/7) Hyperbolic Matrix(14,9,-25,-16) (-2/3,-3/5) -> (-3/5,-1/2) Parabolic Matrix(94,41,55,24) (-1/2,-3/7) -> (5/3,12/7) Hyperbolic Matrix(26,11,85,36) (-3/7,-2/5) -> (3/10,1/3) Hyperbolic Matrix(34,13,115,44) (-2/5,-3/8) -> (2/7,3/10) Hyperbolic Matrix(9,2,-50,-11) (-1/4,-1/5) -> (-1/5,-1/6) Parabolic Matrix(6,-1,25,-4) (0/1,1/5) -> (1/5,1/4) Parabolic Matrix(104,-29,165,-46) (3/11,2/7) -> (5/8,7/11) Hyperbolic Matrix(49,-18,30,-11) (1/3,2/5) -> (8/5,5/3) Hyperbolic Matrix(111,-46,70,-29) (2/5,3/7) -> (11/7,8/5) Hyperbolic Matrix(31,-18,50,-29) (1/2,3/5) -> (3/5,5/8) Parabolic Matrix(189,-122,110,-71) (7/11,2/3) -> (12/7,19/11) Hyperbolic Matrix(6,-5,5,-4) (2/3,1/1) -> (1/1,3/2) Parabolic Matrix(46,-81,25,-44) (7/4,9/5) -> (9/5,2/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(1,0,-2,1) Matrix(4,7,-15,-26) -> Matrix(1,3,-2,-5) Matrix(11,18,-30,-49) -> Matrix(5,6,-6,-7) Matrix(34,49,-25,-36) -> Matrix(1,-1,0,1) Matrix(16,21,35,46) -> Matrix(1,3,-2,-5) Matrix(9,10,-10,-11) -> Matrix(1,0,0,1) Matrix(79,64,-100,-81) -> Matrix(17,18,-18,-19) Matrix(329,258,190,149) -> Matrix(13,12,-12,-11) Matrix(21,16,80,61) -> Matrix(7,6,-20,-17) Matrix(4,3,-35,-26) -> Matrix(1,1,-6,-5) Matrix(61,44,140,101) -> Matrix(1,0,0,1) Matrix(54,37,35,24) -> Matrix(5,3,-12,-7) Matrix(14,9,-25,-16) -> Matrix(1,1,-4,-3) Matrix(94,41,55,24) -> Matrix(1,1,0,1) Matrix(26,11,85,36) -> Matrix(1,1,2,3) Matrix(34,13,115,44) -> Matrix(1,1,-12,-11) Matrix(9,2,-50,-11) -> Matrix(7,4,-16,-9) Matrix(6,-1,25,-4) -> Matrix(5,3,-12,-7) Matrix(104,-29,165,-46) -> Matrix(19,5,-42,-11) Matrix(49,-18,30,-11) -> Matrix(1,0,-2,1) Matrix(111,-46,70,-29) -> Matrix(7,6,-20,-17) Matrix(31,-18,50,-29) -> Matrix(15,8,-32,-17) Matrix(189,-122,110,-71) -> Matrix(5,2,2,1) Matrix(6,-5,5,-4) -> Matrix(1,1,-4,-3) Matrix(46,-81,25,-44) -> Matrix(5,3,-12,-7) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 24 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 (-1/1,0/1) 0 10 -4/5 -1/1 9 2 -7/9 -9/10 2 10 -3/4 -4/5 1 10 -5/7 -3/4 2 10 -2/3 -1/1 1 10 -3/5 -1/2 2 2 -1/2 0/1 1 10 -3/7 (-4/3,-1/1) 0 10 -2/5 -1/1 7 2 -1/3 -3/4 2 10 -1/5 -1/2 4 2 0/1 -1/1 1 10 1/5 -1/2 6 2 1/4 -2/5 1 10 3/11 -3/10 2 10 2/7 -1/5 1 10 1/3 (-1/1,0/1) 0 10 2/5 -1/1 3 2 3/7 -3/4 2 10 1/2 -2/3 1 10 5/9 -9/16 2 10 3/5 -1/2 8 2 1/1 -1/2 2 10 1/0 0/1 1 2 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(9,8,-10,-9) (-1/1,-4/5) -> (-1/1,-4/5) Reflection Matrix(71,56,-90,-71) (-4/5,-7/9) -> (-4/5,-7/9) Reflection Matrix(21,16,80,61) (-7/9,-3/4) -> (1/4,3/11) Hyperbolic Matrix(4,3,-35,-26) (-3/4,-8/11) -> (-1/6,0/1) Hyperbolic Matrix(76,55,-105,-76) (-11/15,-5/7) -> (-11/15,-5/7) Reflection Matrix(16,11,35,24) (-5/7,-2/3) -> (3/7,1/2) Glide Reflection Matrix(14,9,-25,-16) (-2/3,-3/5) -> (-3/5,-1/2) Parabolic Matrix(16,7,55,24) (-1/2,-3/7) -> (2/7,1/3) Glide Reflection Matrix(29,12,-70,-29) (-3/7,-2/5) -> (-3/7,-2/5) Reflection Matrix(11,4,-30,-11) (-2/5,-1/3) -> (-2/5,-1/3) Reflection Matrix(4,1,-15,-4) (-1/3,-1/5) -> (-1/3,-1/5) Reflection Matrix(6,1,-35,-6) (-1/5,-1/7) -> (-1/5,-1/7) Reflection Matrix(6,-1,25,-4) (0/1,1/5) -> (1/5,1/4) Parabolic Matrix(46,-13,85,-24) (3/11,2/7) -> (1/2,5/9) Hyperbolic Matrix(11,-4,30,-11) (1/3,2/5) -> (1/3,2/5) Reflection Matrix(29,-12,70,-29) (2/5,3/7) -> (2/5,3/7) Reflection Matrix(26,-15,45,-26) (5/9,3/5) -> (5/9,3/5) Reflection Matrix(4,-3,5,-4) (3/5,1/1) -> (3/5,1/1) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(9,8,-10,-9) -> Matrix(-1,0,2,1) (-1/1,-4/5) -> (-1/1,0/1) Matrix(71,56,-90,-71) -> Matrix(19,18,-20,-19) (-4/5,-7/9) -> (-1/1,-9/10) Matrix(21,16,80,61) -> Matrix(7,6,-20,-17) Matrix(4,3,-35,-26) -> Matrix(1,1,-6,-5) Matrix(76,55,-105,-76) -> Matrix(5,3,-8,-5) (-11/15,-5/7) -> (-3/4,-1/2) Matrix(16,11,35,24) -> Matrix(5,3,-8,-5) *** -> (-3/4,-1/2) Matrix(14,9,-25,-16) -> Matrix(1,1,-4,-3) -1/2 Matrix(16,7,55,24) -> Matrix(1,1,-4,-5) Matrix(29,12,-70,-29) -> Matrix(7,8,-6,-7) (-3/7,-2/5) -> (-4/3,-1/1) Matrix(11,4,-30,-11) -> Matrix(7,6,-8,-7) (-2/5,-1/3) -> (-1/1,-3/4) Matrix(4,1,-15,-4) -> Matrix(5,3,-8,-5) (-1/3,-1/5) -> (-3/4,-1/2) Matrix(6,1,-35,-6) -> Matrix(3,1,-8,-3) (-1/5,-1/7) -> (-1/2,-1/4) Matrix(6,-1,25,-4) -> Matrix(5,3,-12,-7) -1/2 Matrix(46,-13,85,-24) -> Matrix(13,3,-22,-5) Matrix(11,-4,30,-11) -> Matrix(-1,0,2,1) (1/3,2/5) -> (-1/1,0/1) Matrix(29,-12,70,-29) -> Matrix(7,6,-8,-7) (2/5,3/7) -> (-1/1,-3/4) Matrix(26,-15,45,-26) -> Matrix(17,9,-32,-17) (5/9,3/5) -> (-9/16,-1/2) Matrix(4,-3,5,-4) -> Matrix(1,1,0,-1) (3/5,1/1) -> (-1/2,1/0) Matrix(-1,2,0,1) -> Matrix(-1,0,4,1) (1/1,1/0) -> (-1/2,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.