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 -1/1 -4/9 -3/8 -1/3 -2/7 0/1 1/4 1/3 3/7 1/2 11/19 2/3 1/1 11/9 3/2 5/3 19/11 9/5 13/7 2/1 7/3 5/2 8/3 11/4 3/1 7/2 4/1 5/1 17/3 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/1 -1/2 -1/1 -2/3 -5/11 -4/5 -4/9 -3/4 -3/7 -1/1 -5/12 -1/1 -2/3 -2/5 -3/4 -7/18 -1/1 -2/3 -5/13 -1/1 -3/8 -3/4 -7/19 -5/7 -4/11 -7/10 -1/3 -2/3 -3/10 -2/3 -3/5 -2/7 -1/2 -5/18 -1/1 0/1 -3/11 -1/1 -4/15 -5/6 -1/4 -1/1 -2/3 -2/9 -5/8 -1/5 -3/5 -1/6 -1/2 -1/7 0/1 0/1 -1/2 1/6 -1/1 0/1 1/5 -2/3 1/4 -1/2 3/11 -4/9 5/18 -4/9 -3/7 2/7 -5/12 1/3 -1/3 4/11 -1/4 3/8 -1/5 0/1 5/13 0/1 2/5 -1/4 3/7 0/1 4/9 1/2 1/2 -1/1 0/1 5/9 0/1 4/7 -3/2 11/19 -1/1 7/12 -1/1 -4/5 3/5 -1/1 2/3 -1/2 5/7 -1/3 13/18 -1/3 0/1 8/11 -1/2 11/15 -2/5 3/4 -1/3 0/1 7/9 -1/3 4/5 -1/6 1/1 0/1 6/5 -1/4 11/9 0/1 5/4 0/1 1/3 4/3 1/2 3/2 1/0 8/5 -3/2 29/18 -1/1 0/1 21/13 -2/1 13/8 -4/3 -1/1 31/19 -1/1 18/11 -3/4 5/3 -1/1 17/10 -1/1 0/1 12/7 -1/2 19/11 0/1 26/15 1/0 7/4 -1/1 0/1 16/9 1/0 9/5 0/1 11/6 -1/1 0/1 13/7 0/1 2/1 1/0 7/3 -1/1 12/5 -1/2 5/2 -1/1 0/1 13/5 0/1 21/8 -1/5 0/1 29/11 0/1 8/3 1/2 19/7 2/1 11/4 1/0 3/1 -1/1 10/3 1/0 7/2 0/1 1/1 4/1 1/0 9/2 -2/1 -1/1 14/3 1/0 33/7 -2/1 19/4 -2/1 -1/1 5/1 -2/1 11/2 -4/3 -1/1 17/3 -1/1 23/4 -1/1 -2/3 6/1 1/0 7/1 -1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(185,86,114,53) (-1/2,-5/11) -> (21/13,13/8) Hyperbolic Matrix(257,116,144,65) (-5/11,-4/9) -> (16/9,9/5) Hyperbolic Matrix(37,16,104,45) (-4/9,-3/7) -> (1/3,4/11) Hyperbolic Matrix(105,44,136,57) (-3/7,-5/12) -> (3/4,7/9) Hyperbolic Matrix(169,70,70,29) (-5/12,-2/5) -> (12/5,5/2) Hyperbolic Matrix(297,116,64,25) (-2/5,-7/18) -> (9/2,14/3) Hyperbolic Matrix(259,100,360,139) (-7/18,-5/13) -> (5/7,13/18) Hyperbolic Matrix(95,36,-256,-97) (-5/13,-3/8) -> (-3/8,-7/19) Parabolic Matrix(191,70,30,11) (-7/19,-4/11) -> (6/1,7/1) Hyperbolic Matrix(61,22,158,57) (-4/11,-1/3) -> (5/13,2/5) Hyperbolic Matrix(145,44,56,17) (-1/3,-3/10) -> (5/2,13/5) Hyperbolic Matrix(55,16,-196,-57) (-3/10,-2/7) -> (-2/7,-5/18) Parabolic Matrix(277,76,164,45) (-5/18,-3/11) -> (5/3,17/10) Hyperbolic Matrix(273,74,166,45) (-3/11,-4/15) -> (18/11,5/3) Hyperbolic Matrix(83,22,298,79) (-4/15,-1/4) -> (5/18,2/7) Hyperbolic Matrix(25,6,54,13) (-1/4,-2/9) -> (4/9,1/2) Hyperbolic Matrix(77,16,24,5) (-2/9,-1/5) -> (3/1,10/3) Hyperbolic Matrix(73,14,26,5) (-1/5,-1/6) -> (11/4,3/1) Hyperbolic Matrix(191,30,70,11) (-1/6,-1/7) -> (19/7,11/4) Hyperbolic Matrix(67,8,92,11) (-1/7,0/1) -> (8/11,11/15) Hyperbolic Matrix(89,-12,52,-7) (0/1,1/6) -> (17/10,12/7) Hyperbolic Matrix(85,-16,16,-3) (1/6,1/5) -> (5/1,11/2) Hyperbolic Matrix(17,-4,64,-15) (1/5,1/4) -> (1/4,3/11) Parabolic Matrix(299,-82,62,-17) (3/11,5/18) -> (19/4,5/1) Hyperbolic Matrix(61,-18,78,-23) (2/7,1/3) -> (7/9,4/5) Hyperbolic Matrix(205,-76,116,-43) (4/11,3/8) -> (7/4,16/9) Hyperbolic Matrix(377,-144,144,-55) (3/8,5/13) -> (13/5,21/8) Hyperbolic Matrix(43,-18,98,-41) (2/5,3/7) -> (3/7,4/9) Parabolic Matrix(117,-64,64,-35) (1/2,5/9) -> (9/5,11/6) Hyperbolic Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(559,-322,342,-197) (4/7,11/19) -> (31/19,18/11) Hyperbolic Matrix(619,-360,380,-221) (11/19,7/12) -> (13/8,31/19) Hyperbolic Matrix(89,-52,12,-7) (7/12,3/5) -> (7/1,1/0) Hyperbolic Matrix(25,-16,36,-23) (3/5,2/3) -> (2/3,5/7) Parabolic Matrix(545,-394,314,-227) (13/18,8/11) -> (26/15,7/4) Hyperbolic Matrix(519,-382,322,-237) (11/15,3/4) -> (29/18,21/13) Hyperbolic Matrix(11,-10,10,-9) (4/5,1/1) -> (1/1,6/5) Parabolic Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(305,-376,116,-143) (11/9,5/4) -> (21/8,29/11) Hyperbolic Matrix(61,-78,18,-23) (5/4,4/3) -> (10/3,7/2) Hyperbolic Matrix(25,-36,16,-23) (4/3,3/2) -> (3/2,8/5) Parabolic Matrix(223,-358,38,-61) (8/5,29/18) -> (23/4,6/1) Hyperbolic Matrix(419,-722,242,-417) (12/7,19/11) -> (19/11,26/15) Parabolic Matrix(331,-610,70,-129) (11/6,13/7) -> (33/7,19/4) Hyperbolic Matrix(131,-248,28,-53) (13/7,2/1) -> (14/3,33/7) Hyperbolic Matrix(43,-98,18,-41) (2/1,7/3) -> (7/3,12/5) Parabolic Matrix(17,-64,4,-15) (7/2,4/1) -> (4/1,9/2) Parabolic Matrix(103,-578,18,-101) (11/2,17/3) -> (17/3,23/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,2,-2,-3) Matrix(185,86,114,53) -> Matrix(7,6,-6,-5) Matrix(257,116,144,65) -> Matrix(5,4,-4,-3) Matrix(37,16,104,45) -> Matrix(3,2,-8,-5) Matrix(105,44,136,57) -> Matrix(3,2,-8,-5) Matrix(169,70,70,29) -> Matrix(3,2,-2,-1) Matrix(297,116,64,25) -> Matrix(5,4,-4,-3) Matrix(259,100,360,139) -> Matrix(3,2,-8,-5) Matrix(95,36,-256,-97) -> Matrix(23,18,-32,-25) Matrix(191,70,30,11) -> Matrix(17,12,-10,-7) Matrix(61,22,158,57) -> Matrix(3,2,-2,-1) Matrix(145,44,56,17) -> Matrix(3,2,-8,-5) Matrix(55,16,-196,-57) -> Matrix(3,2,-8,-5) Matrix(277,76,164,45) -> Matrix(1,0,0,1) Matrix(273,74,166,45) -> Matrix(3,2,-2,-1) Matrix(83,22,298,79) -> Matrix(13,10,-30,-23) Matrix(25,6,54,13) -> Matrix(3,2,-2,-1) Matrix(77,16,24,5) -> Matrix(3,2,-8,-5) Matrix(73,14,26,5) -> Matrix(7,4,-2,-1) Matrix(191,30,70,11) -> Matrix(5,2,2,1) Matrix(67,8,92,11) -> Matrix(3,2,-8,-5) Matrix(89,-12,52,-7) -> Matrix(1,0,0,1) Matrix(85,-16,16,-3) -> Matrix(5,4,-4,-3) Matrix(17,-4,64,-15) -> Matrix(11,6,-24,-13) Matrix(299,-82,62,-17) -> Matrix(5,2,2,1) Matrix(61,-18,78,-23) -> Matrix(5,2,-18,-7) Matrix(205,-76,116,-43) -> Matrix(1,0,4,1) Matrix(377,-144,144,-55) -> Matrix(1,0,0,1) Matrix(43,-18,98,-41) -> Matrix(1,0,6,1) Matrix(117,-64,64,-35) -> Matrix(1,0,0,1) Matrix(205,-116,76,-43) -> Matrix(1,2,0,1) Matrix(559,-322,342,-197) -> Matrix(5,6,-6,-7) Matrix(619,-360,380,-221) -> Matrix(9,8,-8,-7) Matrix(89,-52,12,-7) -> Matrix(5,4,-4,-3) Matrix(25,-16,36,-23) -> Matrix(3,2,-8,-5) Matrix(545,-394,314,-227) -> Matrix(1,0,2,1) Matrix(519,-382,322,-237) -> Matrix(1,0,2,1) Matrix(11,-10,10,-9) -> Matrix(1,0,2,1) Matrix(217,-262,82,-99) -> Matrix(1,0,6,1) Matrix(305,-376,116,-143) -> Matrix(1,0,-8,1) Matrix(61,-78,18,-23) -> Matrix(1,0,-2,1) Matrix(25,-36,16,-23) -> Matrix(1,-2,0,1) Matrix(223,-358,38,-61) -> Matrix(1,2,-2,-3) Matrix(419,-722,242,-417) -> Matrix(1,0,2,1) Matrix(331,-610,70,-129) -> Matrix(3,2,-2,-1) Matrix(131,-248,28,-53) -> Matrix(1,-2,0,1) Matrix(43,-98,18,-41) -> Matrix(1,2,-2,-3) Matrix(17,-64,4,-15) -> Matrix(1,-2,0,1) Matrix(103,-578,18,-101) -> Matrix(5,6,-6,-7) 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): 16 Degree of the the map X: 16 Degree of the the map Y: 48 Permutation triple for Y: ((1,6,22,39,38,44,43,23,7,2)(3,12,29,8,28,33,48,36,13,4)(5,17)(9,10)(11,34,18,45,40,46,21,16,42,35)(14,41,47,32,31,27,20,19,24,15)(25,26)(30,37); (1,4,15,16,5)(3,10,24,23,11)(6,20,30,29,21)(7,26,35,27,8)(9,32,22,46,33)(13,39,25,40,14)(17,44,28,31,18)(34,43,41,37,36); (1,2,8,30,41,40,45,31,9,3)(4,14)(5,18,36,48,46,25,7,24,19,6)(10,33,44,38,13,37,20,35,42,15)(11,26,39,32,47,43,17,16,29,12)(21,22)(23,34)(27,28)) ----------------------------------------------------------------------- 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 -1/1 -4/9 -1/3 -2/7 0/1 1/4 1/3 3/7 1/2 2/3 1/1 11/9 3/2 2/1 7/3 8/3 3/1 4/1 6/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/1 -1/2 -1/1 -2/3 -4/9 -3/4 -3/7 -1/1 -5/12 -1/1 -2/3 -2/5 -3/4 -1/3 -2/3 -2/7 -1/2 -3/11 -1/1 -1/4 -1/1 -2/3 -2/9 -5/8 -1/5 -3/5 0/1 -1/2 1/5 -2/3 1/4 -1/2 2/7 -5/12 1/3 -1/3 4/11 -1/4 3/8 -1/5 0/1 2/5 -1/4 3/7 0/1 4/9 1/2 1/2 -1/1 0/1 2/3 -1/2 3/4 -1/3 0/1 7/9 -1/3 4/5 -1/6 1/1 0/1 6/5 -1/4 11/9 0/1 5/4 0/1 1/3 4/3 1/2 3/2 1/0 8/5 -3/2 13/8 -4/3 -1/1 5/3 -1/1 2/1 1/0 7/3 -1/1 12/5 -1/2 5/2 -1/1 0/1 13/5 0/1 21/8 -1/5 0/1 29/11 0/1 8/3 1/2 11/4 1/0 3/1 -1/1 4/1 1/0 5/1 -2/1 6/1 1/0 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(35,16,94,43) (-1/2,-4/9) -> (4/11,3/8) Hyperbolic Matrix(37,16,104,45) (-4/9,-3/7) -> (1/3,4/11) Hyperbolic Matrix(105,44,136,57) (-3/7,-5/12) -> (3/4,7/9) Hyperbolic Matrix(169,70,70,29) (-5/12,-2/5) -> (12/5,5/2) Hyperbolic Matrix(31,12,18,7) (-2/5,-1/3) -> (5/3,2/1) Hyperbolic Matrix(27,8,-98,-29) (-1/3,-2/7) -> (-2/7,-3/11) Parabolic Matrix(107,28,42,11) (-3/11,-1/4) -> (5/2,13/5) Hyperbolic Matrix(25,6,54,13) (-1/4,-2/9) -> (4/9,1/2) Hyperbolic Matrix(75,16,14,3) (-2/9,-1/5) -> (5/1,6/1) Hyperbolic Matrix(1,0,10,1) (-1/5,0/1) -> (0/1,1/5) Parabolic Matrix(67,-14,24,-5) (1/5,1/4) -> (11/4,3/1) Hyperbolic Matrix(109,-30,40,-11) (1/4,2/7) -> (8/3,11/4) Hyperbolic Matrix(61,-18,78,-23) (2/7,1/3) -> (7/9,4/5) Hyperbolic Matrix(129,-50,80,-31) (3/8,2/5) -> (8/5,13/8) Hyperbolic Matrix(43,-18,98,-41) (2/5,3/7) -> (3/7,4/9) Parabolic Matrix(13,-8,18,-11) (1/2,2/3) -> (2/3,3/4) Parabolic Matrix(11,-10,10,-9) (4/5,1/1) -> (1/1,6/5) Parabolic Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(305,-376,116,-143) (11/9,5/4) -> (21/8,29/11) Hyperbolic Matrix(27,-34,4,-5) (5/4,4/3) -> (6/1,1/0) Hyperbolic Matrix(25,-36,16,-23) (4/3,3/2) -> (3/2,8/5) Parabolic Matrix(167,-274,64,-105) (13/8,5/3) -> (13/5,21/8) Hyperbolic Matrix(43,-98,18,-41) (2/1,7/3) -> (7/3,12/5) Parabolic Matrix(9,-32,2,-7) (3/1,4/1) -> (4/1,5/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,2,-2,-3) Matrix(35,16,94,43) -> Matrix(1,1,-8,-7) Matrix(37,16,104,45) -> Matrix(3,2,-8,-5) Matrix(105,44,136,57) -> Matrix(3,2,-8,-5) Matrix(169,70,70,29) -> Matrix(3,2,-2,-1) Matrix(31,12,18,7) -> Matrix(1,1,-4,-3) Matrix(27,8,-98,-29) -> Matrix(1,1,-4,-3) Matrix(107,28,42,11) -> Matrix(1,1,-4,-3) Matrix(25,6,54,13) -> Matrix(3,2,-2,-1) Matrix(75,16,14,3) -> Matrix(11,7,-8,-5) Matrix(1,0,10,1) -> Matrix(1,1,-4,-3) Matrix(67,-14,24,-5) -> Matrix(5,3,-2,-1) Matrix(109,-30,40,-11) -> Matrix(7,3,2,1) Matrix(61,-18,78,-23) -> Matrix(5,2,-18,-7) Matrix(129,-50,80,-31) -> Matrix(1,1,-2,-1) Matrix(43,-18,98,-41) -> Matrix(1,0,6,1) Matrix(13,-8,18,-11) -> Matrix(1,1,-4,-3) Matrix(11,-10,10,-9) -> Matrix(1,0,2,1) Matrix(217,-262,82,-99) -> Matrix(1,0,6,1) Matrix(305,-376,116,-143) -> Matrix(1,0,-8,1) Matrix(27,-34,4,-5) -> Matrix(3,-1,-2,1) Matrix(25,-36,16,-23) -> Matrix(1,-2,0,1) Matrix(167,-274,64,-105) -> Matrix(1,1,-2,-1) Matrix(43,-98,18,-41) -> Matrix(1,2,-2,-3) Matrix(9,-32,2,-7) -> Matrix(1,-1,0,1) 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): 16 ----------------------------------------------------------------------- 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 1 1 0/1 -1/2 1 10 1/4 -1/2 3 2 2/7 -5/12 1 10 1/3 -1/3 1 5 3/8 (-1/5,0/1) 0 10 2/5 -1/4 1 10 3/7 0/1 3 1 1/2 (-1/1,0/1) 0 10 2/3 -1/2 1 2 3/4 (-1/3,0/1) 0 10 4/5 -1/6 1 10 1/1 0/1 1 5 6/5 -1/4 1 10 11/9 0/1 7 1 5/4 (0/1,1/3) 0 10 4/3 1/2 1 10 3/2 1/0 1 2 2/1 1/0 1 10 7/3 -1/1 1 1 5/2 (-1/1,0/1) 0 10 8/3 1/2 1 10 3/1 -1/1 1 5 4/1 1/0 1 2 5/1 -2/1 1 5 1/0 (-1/1,0/1) 0 10 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(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(1,0,8,-1) (0/1,1/4) -> (0/1,1/4) Reflection Matrix(15,-4,56,-15) (1/4,2/7) -> (1/4,2/7) Reflection Matrix(45,-14,16,-5) (2/7,1/3) -> (8/3,3/1) Glide Reflection Matrix(43,-16,8,-3) (1/3,3/8) -> (5/1,1/0) Glide Reflection Matrix(57,-22,44,-17) (3/8,2/5) -> (5/4,4/3) Glide Reflection Matrix(29,-12,70,-29) (2/5,3/7) -> (2/5,3/7) Reflection Matrix(13,-6,28,-13) (3/7,1/2) -> (3/7,1/2) Reflection Matrix(13,-8,18,-11) (1/2,2/3) -> (2/3,3/4) Parabolic Matrix(57,-44,22,-17) (3/4,4/5) -> (5/2,8/3) Glide Reflection Matrix(11,-10,10,-9) (4/5,1/1) -> (1/1,6/5) Parabolic Matrix(109,-132,90,-109) (6/5,11/9) -> (6/5,11/9) Reflection Matrix(89,-110,72,-89) (11/9,5/4) -> (11/9,5/4) Reflection Matrix(17,-24,12,-17) (4/3,3/2) -> (4/3,3/2) Reflection Matrix(7,-12,4,-7) (3/2,2/1) -> (3/2,2/1) Reflection Matrix(13,-28,6,-13) (2/1,7/3) -> (2/1,7/3) Reflection Matrix(29,-70,12,-29) (7/3,5/2) -> (7/3,5/2) Reflection Matrix(9,-32,2,-7) (3/1,4/1) -> (4/1,5/1) Parabolic 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(-1,0,2,1) -> Matrix(3,2,-4,-3) (-1/1,0/1) -> (-1/1,-1/2) Matrix(1,0,8,-1) -> Matrix(1,1,0,-1) (0/1,1/4) -> (-1/2,1/0) Matrix(15,-4,56,-15) -> Matrix(11,5,-24,-11) (1/4,2/7) -> (-1/2,-5/12) Matrix(45,-14,16,-5) -> Matrix(5,2,-2,-1) Matrix(43,-16,8,-3) -> Matrix(5,1,-4,-1) Matrix(57,-22,44,-17) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(29,-12,70,-29) -> Matrix(-1,0,8,1) (2/5,3/7) -> (-1/4,0/1) Matrix(13,-6,28,-13) -> Matrix(-1,0,2,1) (3/7,1/2) -> (-1/1,0/1) Matrix(13,-8,18,-11) -> Matrix(1,1,-4,-3) -1/2 Matrix(57,-44,22,-17) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(11,-10,10,-9) -> Matrix(1,0,2,1) 0/1 Matrix(109,-132,90,-109) -> Matrix(-1,0,8,1) (6/5,11/9) -> (-1/4,0/1) Matrix(89,-110,72,-89) -> Matrix(1,0,6,-1) (11/9,5/4) -> (0/1,1/3) Matrix(17,-24,12,-17) -> Matrix(-1,1,0,1) (4/3,3/2) -> (1/2,1/0) Matrix(7,-12,4,-7) -> Matrix(1,1,0,-1) (3/2,2/1) -> (-1/2,1/0) Matrix(13,-28,6,-13) -> Matrix(1,2,0,-1) (2/1,7/3) -> (-1/1,1/0) Matrix(29,-70,12,-29) -> Matrix(-1,0,2,1) (7/3,5/2) -> (-1/1,0/1) Matrix(9,-32,2,-7) -> Matrix(1,-1,0,1) 1/0 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.