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: 24 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/2 7/12 7/10 3/4 1/1 7/6 5/4 7/5 3/2 7/4 2/1 7/3 5/2 21/8 14/5 3/1 7/2 4/1 14/3 5/1 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -5/1 1/1 -14/3 0/1 -9/2 0/1 1/1 -4/1 1/1 -7/2 1/0 -3/1 -1/1 -14/5 -1/1 -11/4 -1/1 -1/2 -8/3 -1/1 -21/8 -1/1 0/1 -13/5 -1/1 -5/2 -1/1 0/1 -7/3 0/1 -2/1 -1/1 -7/4 -1/1 0/1 -5/3 -1/1 -13/8 -1/2 0/1 -21/13 0/1 -8/5 1/1 -11/7 -1/1 -14/9 -1/1 -3/2 -1/1 0/1 -7/5 -1/1 -4/3 -1/1 -9/7 -1/1 -14/11 -2/3 -5/4 -2/3 -1/2 -6/5 -5/9 -7/6 -1/2 -1/1 -1/3 -5/6 -1/3 0/1 -4/5 -1/3 -7/9 -1/3 -3/4 -1/3 -1/4 -8/11 -1/3 -5/7 -3/11 -7/10 -1/4 -2/3 -1/5 -7/11 0/1 -5/8 -1/4 0/1 -8/13 -3/13 -3/5 -1/5 -7/12 -1/5 0/1 -4/7 -1/5 -5/9 -1/5 -6/11 -1/7 -7/13 0/1 -1/2 -1/5 0/1 0/1 0/1 1/2 0/1 1/5 5/9 1/5 4/7 1/5 7/12 0/1 1/5 3/5 1/5 8/13 3/13 5/8 0/1 1/4 2/3 1/5 7/10 1/4 5/7 3/11 13/18 3/11 2/7 8/11 1/3 3/4 1/4 1/3 4/5 1/3 5/6 0/1 1/3 1/1 1/3 7/6 1/2 6/5 5/9 5/4 1/2 2/3 14/11 2/3 9/7 1/1 4/3 1/1 11/8 3/4 1/1 7/5 1/1 3/2 0/1 1/1 14/9 1/1 11/7 1/1 8/5 -1/1 5/3 1/1 7/4 0/1 1/1 2/1 1/1 9/4 0/1 1/0 7/3 0/1 5/2 0/1 1/1 13/5 1/1 21/8 0/1 1/1 8/3 1/1 11/4 1/2 1/1 14/5 1/1 3/1 1/1 7/2 1/0 4/1 -1/1 9/2 -1/1 0/1 14/3 0/1 5/1 -1/1 6/1 -1/3 13/2 -1/5 0/1 7/1 0/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(13,70,-8,-43) (-5/1,1/0) -> (-5/3,-13/8) Hyperbolic Matrix(41,196,32,153) (-5/1,-14/3) -> (14/11,9/7) Hyperbolic Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(13,56,16,69) (-9/2,-4/1) -> (4/5,5/6) Hyperbolic Matrix(15,56,4,15) (-4/1,-7/2) -> (7/2,4/1) Hyperbolic Matrix(13,42,4,13) (-7/2,-3/1) -> (3/1,7/2) Hyperbolic Matrix(69,196,44,125) (-3/1,-14/5) -> (14/9,11/7) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(41,112,56,153) (-11/4,-8/3) -> (8/11,3/4) Hyperbolic Matrix(127,336,48,127) (-8/3,-21/8) -> (21/8,8/3) Hyperbolic Matrix(209,546,80,209) (-21/8,-13/5) -> (13/5,21/8) Hyperbolic Matrix(27,70,32,83) (-13/5,-5/2) -> (5/6,1/1) Hyperbolic Matrix(29,70,12,29) (-5/2,-7/3) -> (7/3,5/2) Hyperbolic Matrix(13,28,-20,-43) (-7/3,-2/1) -> (-2/3,-7/11) Hyperbolic Matrix(15,28,8,15) (-2/1,-7/4) -> (7/4,2/1) Hyperbolic Matrix(41,70,24,41) (-7/4,-5/3) -> (5/3,7/4) Hyperbolic Matrix(69,112,8,13) (-13/8,-21/13) -> (7/1,1/0) Hyperbolic Matrix(113,182,-208,-335) (-21/13,-8/5) -> (-6/11,-7/13) Hyperbolic Matrix(71,112,116,183) (-8/5,-11/7) -> (3/5,8/13) Hyperbolic Matrix(125,196,44,69) (-11/7,-14/9) -> (14/5,3/1) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(29,42,20,29) (-3/2,-7/5) -> (7/5,3/2) Hyperbolic Matrix(41,56,-52,-71) (-7/5,-4/3) -> (-4/5,-7/9) Hyperbolic Matrix(43,56,76,99) (-4/3,-9/7) -> (5/9,4/7) Hyperbolic Matrix(153,196,32,41) (-9/7,-14/11) -> (14/3,5/1) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(57,70,92,113) (-5/4,-6/5) -> (8/13,5/8) Hyperbolic Matrix(71,84,60,71) (-6/5,-7/6) -> (7/6,6/5) Hyperbolic Matrix(13,14,12,13) (-7/6,-1/1) -> (1/1,7/6) Hyperbolic Matrix(83,70,32,27) (-1/1,-5/6) -> (5/2,13/5) Hyperbolic Matrix(69,56,16,13) (-5/6,-4/5) -> (4/1,9/2) Hyperbolic Matrix(127,98,92,71) (-7/9,-3/4) -> (11/8,7/5) Hyperbolic Matrix(153,112,56,41) (-3/4,-8/11) -> (8/3,11/4) Hyperbolic Matrix(97,70,-176,-127) (-8/11,-5/7) -> (-5/9,-6/11) Hyperbolic Matrix(99,70,140,99) (-5/7,-7/10) -> (7/10,5/7) Hyperbolic Matrix(41,28,60,41) (-7/10,-2/3) -> (2/3,7/10) Hyperbolic Matrix(155,98,68,43) (-7/11,-5/8) -> (9/4,7/3) Hyperbolic Matrix(113,70,92,57) (-5/8,-8/13) -> (6/5,5/4) Hyperbolic Matrix(183,112,116,71) (-8/13,-3/5) -> (11/7,8/5) Hyperbolic Matrix(71,42,120,71) (-3/5,-7/12) -> (7/12,3/5) Hyperbolic Matrix(97,56,168,97) (-7/12,-4/7) -> (4/7,7/12) Hyperbolic Matrix(99,56,76,43) (-4/7,-5/9) -> (9/7,4/3) Hyperbolic Matrix(183,98,28,15) (-7/13,-1/2) -> (13/2,7/1) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(127,-70,176,-97) (1/2,5/9) -> (5/7,13/18) Hyperbolic Matrix(43,-28,20,-13) (5/8,2/3) -> (2/1,9/4) Hyperbolic Matrix(251,-182,40,-29) (13/18,8/11) -> (6/1,13/2) Hyperbolic Matrix(71,-56,52,-41) (3/4,4/5) -> (4/3,11/8) Hyperbolic Matrix(43,-70,8,-13) (8/5,5/3) -> (5/1,6/1) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(13,70,-8,-43) -> Matrix(1,0,-2,1) Matrix(41,196,32,153) -> Matrix(1,-2,2,-3) Matrix(55,252,12,55) -> Matrix(1,0,-2,1) Matrix(13,56,16,69) -> Matrix(1,0,2,1) Matrix(15,56,4,15) -> Matrix(1,-2,0,1) Matrix(13,42,4,13) -> Matrix(1,2,0,1) Matrix(69,196,44,125) -> Matrix(1,2,0,1) Matrix(111,308,40,111) -> Matrix(3,2,4,3) Matrix(41,112,56,153) -> Matrix(3,2,10,7) Matrix(127,336,48,127) -> Matrix(1,0,2,1) Matrix(209,546,80,209) -> Matrix(1,0,2,1) Matrix(27,70,32,83) -> Matrix(1,0,4,1) Matrix(29,70,12,29) -> Matrix(1,0,2,1) Matrix(13,28,-20,-43) -> Matrix(1,0,-4,1) Matrix(15,28,8,15) -> Matrix(1,0,2,1) Matrix(41,70,24,41) -> Matrix(1,0,2,1) Matrix(69,112,8,13) -> Matrix(1,0,2,1) Matrix(113,182,-208,-335) -> Matrix(1,0,-8,1) Matrix(71,112,116,183) -> Matrix(1,2,4,9) Matrix(125,196,44,69) -> Matrix(1,2,0,1) Matrix(55,84,36,55) -> Matrix(1,0,2,1) Matrix(29,42,20,29) -> Matrix(1,0,2,1) Matrix(41,56,-52,-71) -> Matrix(3,2,-8,-5) Matrix(43,56,76,99) -> Matrix(3,2,16,11) Matrix(153,196,32,41) -> Matrix(3,2,-2,-1) Matrix(111,140,88,111) -> Matrix(7,4,12,7) Matrix(57,70,92,113) -> Matrix(3,2,10,7) Matrix(71,84,60,71) -> Matrix(19,10,36,19) Matrix(13,14,12,13) -> Matrix(5,2,12,5) Matrix(83,70,32,27) -> Matrix(1,0,4,1) Matrix(69,56,16,13) -> Matrix(1,0,2,1) Matrix(127,98,92,71) -> Matrix(13,4,16,5) Matrix(153,112,56,41) -> Matrix(7,2,10,3) Matrix(97,70,-176,-127) -> Matrix(7,2,-46,-13) Matrix(99,70,140,99) -> Matrix(23,6,88,23) Matrix(41,28,60,41) -> Matrix(9,2,40,9) Matrix(155,98,68,43) -> Matrix(1,0,4,1) Matrix(113,70,92,57) -> Matrix(7,2,10,3) Matrix(183,112,116,71) -> Matrix(9,2,4,1) Matrix(71,42,120,71) -> Matrix(1,0,10,1) Matrix(97,56,168,97) -> Matrix(1,0,10,1) Matrix(99,56,76,43) -> Matrix(11,2,16,3) Matrix(183,98,28,15) -> Matrix(1,0,0,1) Matrix(1,0,4,1) -> Matrix(1,0,10,1) Matrix(127,-70,176,-97) -> Matrix(13,-2,46,-7) Matrix(43,-28,20,-13) -> Matrix(1,0,-4,1) Matrix(251,-182,40,-29) -> Matrix(7,-2,-24,7) Matrix(71,-56,52,-41) -> Matrix(5,-2,8,-3) Matrix(43,-70,8,-13) -> Matrix(1,0,-2,1) 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): 12 Degree of the the map X: 12 Degree of the the map Y: 48 Permutation triple for Y: ((1,2)(3,10,17,5,4,16,23,6,22,29,8,7,28,11)(9,34,24,26,25,20,19,21,39,12,14,13,32,31)(15,30,48,36,35,33,46,27,18,40,47,38,37,43)(41,45)(42,44); (1,5,20,46,33,9,3,2,8,32,43,37,21,6)(4,14,12,11,38,44,27,7,26,24,23,35,42,15)(10,36,39,45,25,30,29,22,47,34,41,13,18,17)(16,28)(19,31)(40,48); (1,3,12,36,40,13,4)(2,6,24,47,48,25,7)(5,18,44,35,10,9,19)(8,30,42,38,22,21,31)(11,16,15,32,41,39,37)(20,45,34,33,23,28,27)) ----------------------------------------------------------------------- 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: 18 Genus: 4 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/2 7/12 7/10 3/4 1/1 7/6 5/4 7/5 3/2 7/4 2/1 7/3 5/2 21/8 3/1 7/2 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -3/1 -1/1 -8/3 -1/1 -5/2 -1/1 0/1 -7/3 0/1 -2/1 -1/1 -3/2 -1/1 0/1 -7/5 -1/1 -4/3 -1/1 -5/4 -2/3 -1/2 -1/1 -1/3 -4/5 -1/3 -7/9 -1/3 -3/4 -1/3 -1/4 -2/3 -1/5 -7/11 0/1 -5/8 -1/4 0/1 -3/5 -1/5 -1/2 -1/5 0/1 0/1 0/1 1/2 0/1 1/5 4/7 1/5 7/12 0/1 1/5 3/5 1/5 5/8 0/1 1/4 2/3 1/5 7/10 1/4 5/7 3/11 3/4 1/4 1/3 4/5 1/3 1/1 1/3 7/6 1/2 6/5 5/9 5/4 1/2 2/3 4/3 1/1 11/8 3/4 1/1 7/5 1/1 3/2 0/1 1/1 5/3 1/1 7/4 0/1 1/1 2/1 1/1 9/4 0/1 1/0 7/3 0/1 5/2 0/1 1/1 13/5 1/1 21/8 0/1 1/1 8/3 1/1 3/1 1/1 7/2 1/0 4/1 -1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,7,0,1) (-3/1,1/0) -> (4/1,1/0) Parabolic Matrix(13,35,-16,-43) (-3/1,-8/3) -> (-1/1,-4/5) Hyperbolic Matrix(41,105,16,41) (-8/3,-5/2) -> (5/2,13/5) Hyperbolic Matrix(29,70,12,29) (-5/2,-7/3) -> (7/3,5/2) Hyperbolic Matrix(13,28,-20,-43) (-7/3,-2/1) -> (-2/3,-7/11) Hyperbolic Matrix(13,21,8,13) (-2/1,-3/2) -> (3/2,5/3) Hyperbolic Matrix(29,42,20,29) (-3/2,-7/5) -> (7/5,3/2) Hyperbolic Matrix(41,56,-52,-71) (-7/5,-4/3) -> (-4/5,-7/9) Hyperbolic Matrix(27,35,-44,-57) (-4/3,-5/4) -> (-5/8,-3/5) Hyperbolic Matrix(29,35,24,29) (-5/4,-1/1) -> (6/5,5/4) Hyperbolic Matrix(127,98,92,71) (-7/9,-3/4) -> (11/8,7/5) Hyperbolic Matrix(29,21,40,29) (-3/4,-2/3) -> (5/7,3/4) Hyperbolic Matrix(155,98,68,43) (-7/11,-5/8) -> (9/4,7/3) Hyperbolic Matrix(13,7,24,13) (-3/5,-1/2) -> (1/2,4/7) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(85,-49,144,-83) (4/7,7/12) -> (7/12,3/5) Parabolic Matrix(57,-35,44,-27) (3/5,5/8) -> (5/4,4/3) Hyperbolic Matrix(43,-28,20,-13) (5/8,2/3) -> (2/1,9/4) Hyperbolic Matrix(71,-49,100,-69) (2/3,7/10) -> (7/10,5/7) Parabolic Matrix(71,-56,52,-41) (3/4,4/5) -> (4/3,11/8) Hyperbolic Matrix(43,-35,16,-13) (4/5,1/1) -> (8/3,3/1) Hyperbolic Matrix(43,-49,36,-41) (1/1,7/6) -> (7/6,6/5) Parabolic Matrix(29,-49,16,-27) (5/3,7/4) -> (7/4,2/1) Parabolic Matrix(169,-441,64,-167) (13/5,21/8) -> (21/8,8/3) Parabolic Matrix(15,-49,4,-13) (3/1,7/2) -> (7/2,4/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,7,0,1) -> Matrix(1,0,0,1) Matrix(13,35,-16,-43) -> Matrix(1,0,-2,1) Matrix(41,105,16,41) -> Matrix(1,0,2,1) Matrix(29,70,12,29) -> Matrix(1,0,2,1) Matrix(13,28,-20,-43) -> Matrix(1,0,-4,1) Matrix(13,21,8,13) -> Matrix(1,0,2,1) Matrix(29,42,20,29) -> Matrix(1,0,2,1) Matrix(41,56,-52,-71) -> Matrix(3,2,-8,-5) Matrix(27,35,-44,-57) -> Matrix(3,2,-14,-9) Matrix(29,35,24,29) -> Matrix(7,4,12,7) Matrix(127,98,92,71) -> Matrix(13,4,16,5) Matrix(29,21,40,29) -> Matrix(7,2,24,7) Matrix(155,98,68,43) -> Matrix(1,0,4,1) Matrix(13,7,24,13) -> Matrix(1,0,10,1) Matrix(1,0,4,1) -> Matrix(1,0,10,1) Matrix(85,-49,144,-83) -> Matrix(1,0,0,1) Matrix(57,-35,44,-27) -> Matrix(9,-2,14,-3) Matrix(43,-28,20,-13) -> Matrix(1,0,-4,1) Matrix(71,-49,100,-69) -> Matrix(17,-4,64,-15) Matrix(71,-56,52,-41) -> Matrix(5,-2,8,-3) Matrix(43,-35,16,-13) -> Matrix(1,0,-2,1) Matrix(43,-49,36,-41) -> Matrix(13,-6,24,-11) Matrix(29,-49,16,-27) -> Matrix(1,0,0,1) Matrix(169,-441,64,-167) -> Matrix(1,0,0,1) Matrix(15,-49,4,-13) -> Matrix(1,-2,0,1) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 6 ----------------------------------------------------------------------- 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 0/1 0/1 5 2 1/2 (0/1,1/5) 0 14 7/12 (0/1,1/5) 0 2 3/5 1/5 1 14 5/8 (0/1,1/4) 0 14 2/3 1/5 1 14 7/10 1/4 8 2 3/4 (1/4,1/3) 0 14 4/5 1/3 1 14 1/1 1/3 1 14 7/6 1/2 12 2 5/4 (1/2,2/3) 0 14 4/3 1/1 1 14 11/8 (3/4,1/1) 0 14 7/5 1/1 3 2 3/2 (0/1,1/1) 0 14 7/4 (0/1,1/1) 0 2 2/1 1/1 1 14 9/4 (0/1,1/0) 0 14 7/3 0/1 1 2 5/2 (0/1,1/1) 0 14 21/8 (0/1,1/1) 0 2 8/3 1/1 1 14 3/1 1/1 1 14 7/2 1/0 4 2 1/0 (0/1,1/0) 0 14 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,4,-1) (0/1,1/2) -> (0/1,1/2) Reflection Matrix(13,-7,24,-13) (1/2,7/12) -> (1/2,7/12) Reflection Matrix(71,-42,120,-71) (7/12,3/5) -> (7/12,3/5) Reflection Matrix(57,-35,44,-27) (3/5,5/8) -> (5/4,4/3) Hyperbolic Matrix(43,-28,20,-13) (5/8,2/3) -> (2/1,9/4) Hyperbolic Matrix(41,-28,60,-41) (2/3,7/10) -> (2/3,7/10) Reflection Matrix(29,-21,40,-29) (7/10,3/4) -> (7/10,3/4) Reflection Matrix(71,-56,52,-41) (3/4,4/5) -> (4/3,11/8) Hyperbolic Matrix(43,-35,16,-13) (4/5,1/1) -> (8/3,3/1) Hyperbolic Matrix(13,-14,12,-13) (1/1,7/6) -> (1/1,7/6) Reflection Matrix(29,-35,24,-29) (7/6,5/4) -> (7/6,5/4) Reflection Matrix(111,-154,80,-111) (11/8,7/5) -> (11/8,7/5) Reflection Matrix(29,-42,20,-29) (7/5,3/2) -> (7/5,3/2) Reflection Matrix(13,-21,8,-13) (3/2,7/4) -> (3/2,7/4) Reflection Matrix(15,-28,8,-15) (7/4,2/1) -> (7/4,2/1) Reflection Matrix(55,-126,24,-55) (9/4,7/3) -> (9/4,7/3) Reflection Matrix(29,-70,12,-29) (7/3,5/2) -> (7/3,5/2) Reflection Matrix(41,-105,16,-41) (5/2,21/8) -> (5/2,21/8) Reflection Matrix(127,-336,48,-127) (21/8,8/3) -> (21/8,8/3) Reflection Matrix(13,-42,4,-13) (3/1,7/2) -> (3/1,7/2) Reflection Matrix(-1,7,0,1) (7/2,1/0) -> (7/2,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,4,-1) -> Matrix(1,0,10,-1) (0/1,1/2) -> (0/1,1/5) Matrix(13,-7,24,-13) -> Matrix(1,0,10,-1) (1/2,7/12) -> (0/1,1/5) Matrix(71,-42,120,-71) -> Matrix(1,0,10,-1) (7/12,3/5) -> (0/1,1/5) Matrix(57,-35,44,-27) -> Matrix(9,-2,14,-3) Matrix(43,-28,20,-13) -> Matrix(1,0,-4,1) 0/1 Matrix(41,-28,60,-41) -> Matrix(9,-2,40,-9) (2/3,7/10) -> (1/5,1/4) Matrix(29,-21,40,-29) -> Matrix(7,-2,24,-7) (7/10,3/4) -> (1/4,1/3) Matrix(71,-56,52,-41) -> Matrix(5,-2,8,-3) 1/2 Matrix(43,-35,16,-13) -> Matrix(1,0,-2,1) 0/1 Matrix(13,-14,12,-13) -> Matrix(5,-2,12,-5) (1/1,7/6) -> (1/3,1/2) Matrix(29,-35,24,-29) -> Matrix(7,-4,12,-7) (7/6,5/4) -> (1/2,2/3) Matrix(111,-154,80,-111) -> Matrix(7,-6,8,-7) (11/8,7/5) -> (3/4,1/1) Matrix(29,-42,20,-29) -> Matrix(1,0,2,-1) (7/5,3/2) -> (0/1,1/1) Matrix(13,-21,8,-13) -> Matrix(1,0,2,-1) (3/2,7/4) -> (0/1,1/1) Matrix(15,-28,8,-15) -> Matrix(1,0,2,-1) (7/4,2/1) -> (0/1,1/1) Matrix(55,-126,24,-55) -> Matrix(1,0,0,-1) (9/4,7/3) -> (0/1,1/0) Matrix(29,-70,12,-29) -> Matrix(1,0,2,-1) (7/3,5/2) -> (0/1,1/1) Matrix(41,-105,16,-41) -> Matrix(1,0,2,-1) (5/2,21/8) -> (0/1,1/1) Matrix(127,-336,48,-127) -> Matrix(1,0,2,-1) (21/8,8/3) -> (0/1,1/1) Matrix(13,-42,4,-13) -> Matrix(-1,2,0,1) (3/1,7/2) -> (1/1,1/0) Matrix(-1,7,0,1) -> Matrix(1,0,0,-1) (7/2,1/0) -> (0/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.