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 -4/1 -10/3 -30/11 -8/3 0/1 1/1 5/4 3/2 5/3 2/1 5/2 8/3 30/11 20/7 3/1 10/3 18/5 40/11 4/1 14/3 5/1 6/1 20/3 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 5/1 1/0 -6/1 -1/1 1/0 -5/1 -2/1 0/1 -14/3 -1/1 1/0 -9/2 -2/1 -1/1 -4/1 -1/1 0/1 1/0 -11/3 -2/1 -1/1 -18/5 -1/1 -2/3 -7/2 -1/2 -1/3 -10/3 0/1 -3/1 -1/1 1/0 -14/5 -1/1 -1/2 -11/4 -1/1 -2/3 -30/11 -2/3 0/1 -19/7 -1/1 -2/3 -8/3 -1/1 -1/2 0/1 -21/8 -1/1 -2/3 -13/5 -1/2 -3/7 -18/7 -1/3 0/1 -5/2 0/1 -2/1 -1/1 0/1 -5/3 0/1 -18/11 0/1 1/1 -13/8 3/1 1/0 -21/13 -2/1 -1/1 -8/5 -1/1 0/1 1/0 -19/12 -2/1 -1/1 -30/19 -2/1 0/1 -11/7 -2/1 -1/1 -14/9 -1/1 1/0 -17/11 -3/2 -1/1 -20/13 -1/1 -3/2 -1/1 -1/2 -10/7 0/1 -7/5 1/1 1/0 -18/13 -2/1 -1/1 -29/21 -6/5 -1/1 -40/29 -1/1 -11/8 -1/1 -2/3 -4/3 -1/1 -1/2 0/1 -9/7 -1/1 -2/3 -14/11 -1/1 -1/2 -5/4 -2/3 0/1 -6/5 -1/1 -1/2 -13/11 -7/13 -1/2 -20/17 -1/2 -7/6 -1/2 -5/11 -1/1 -1/3 0/1 0/1 0/1 1/1 0/1 1/5 7/6 5/21 1/4 6/5 1/4 1/3 5/4 0/1 2/7 14/11 1/4 1/3 9/7 2/7 1/3 4/3 0/1 1/4 1/3 11/8 2/7 1/3 18/13 1/3 2/5 7/5 1/2 1/1 10/7 0/1 3/2 1/4 1/3 14/9 1/3 1/2 11/7 1/3 2/5 30/19 0/1 2/5 19/12 1/3 2/5 8/5 0/1 1/3 1/2 21/13 1/3 2/5 13/8 1/2 3/5 18/11 0/1 1/1 5/3 0/1 2/1 0/1 1/3 5/2 0/1 18/7 0/1 1/5 13/5 3/13 1/4 21/8 2/7 1/3 8/3 0/1 1/4 1/3 19/7 2/7 1/3 30/11 0/1 2/7 11/4 2/7 1/3 14/5 1/4 1/3 17/6 3/10 1/3 20/7 1/3 3/1 1/3 1/2 10/3 0/1 7/2 1/5 1/4 18/5 2/7 1/3 29/8 6/19 1/3 40/11 1/3 11/3 1/3 2/5 4/1 0/1 1/3 1/2 9/2 1/3 2/5 14/3 1/3 1/2 5/1 0/1 2/5 6/1 1/3 1/2 13/2 7/15 1/2 20/3 1/2 7/1 1/2 5/9 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(21,160,8,61) (-7/1,1/0) -> (13/5,21/8) Hyperbolic Matrix(19,120,-16,-101) (-7/1,-6/1) -> (-6/5,-13/11) Hyperbolic Matrix(11,60,2,11) (-6/1,-5/1) -> (5/1,6/1) Hyperbolic Matrix(29,140,6,29) (-5/1,-14/3) -> (14/3,5/1) Hyperbolic Matrix(61,280,22,101) (-14/3,-9/2) -> (11/4,14/5) Hyperbolic Matrix(19,80,14,59) (-9/2,-4/1) -> (4/3,11/8) Hyperbolic Matrix(21,80,16,61) (-4/1,-11/3) -> (9/7,4/3) Hyperbolic Matrix(199,720,-144,-521) (-11/3,-18/5) -> (-18/13,-29/21) Hyperbolic Matrix(101,360,62,221) (-18/5,-7/2) -> (13/8,18/11) Hyperbolic Matrix(29,100,20,69) (-7/2,-10/3) -> (10/7,3/2) Hyperbolic Matrix(31,100,22,71) (-10/3,-3/1) -> (7/5,10/7) Hyperbolic Matrix(99,280,-64,-181) (-3/1,-14/5) -> (-14/9,-17/11) Hyperbolic Matrix(101,280,22,61) (-14/5,-11/4) -> (9/2,14/3) Hyperbolic Matrix(329,900,208,569) (-11/4,-30/11) -> (30/19,19/12) Hyperbolic Matrix(331,900,210,571) (-30/11,-19/7) -> (11/7,30/19) Hyperbolic Matrix(119,320,74,199) (-19/7,-8/3) -> (8/5,21/13) Hyperbolic Matrix(121,320,76,201) (-8/3,-21/8) -> (19/12,8/5) Hyperbolic Matrix(61,160,8,21) (-21/8,-13/5) -> (7/1,1/0) Hyperbolic Matrix(139,360,100,259) (-13/5,-18/7) -> (18/13,7/5) Hyperbolic Matrix(71,180,28,71) (-18/7,-5/2) -> (5/2,18/7) Hyperbolic Matrix(9,20,4,9) (-5/2,-2/1) -> (2/1,5/2) Hyperbolic Matrix(11,20,6,11) (-2/1,-5/3) -> (5/3,2/1) Hyperbolic Matrix(109,180,66,109) (-5/3,-18/11) -> (18/11,5/3) Hyperbolic Matrix(221,360,62,101) (-18/11,-13/8) -> (7/2,18/5) Hyperbolic Matrix(99,160,86,139) (-13/8,-21/13) -> (1/1,7/6) Hyperbolic Matrix(199,320,74,119) (-21/13,-8/5) -> (8/3,19/7) Hyperbolic Matrix(201,320,76,121) (-8/5,-19/12) -> (21/8,8/3) Hyperbolic Matrix(569,900,208,329) (-19/12,-30/19) -> (30/11,11/4) Hyperbolic Matrix(571,900,210,331) (-30/19,-11/7) -> (19/7,30/11) Hyperbolic Matrix(179,280,140,219) (-11/7,-14/9) -> (14/11,9/7) Hyperbolic Matrix(259,400,90,139) (-17/11,-20/13) -> (20/7,3/1) Hyperbolic Matrix(261,400,92,141) (-20/13,-3/2) -> (17/6,20/7) Hyperbolic Matrix(69,100,20,29) (-3/2,-10/7) -> (10/3,7/2) Hyperbolic Matrix(71,100,22,31) (-10/7,-7/5) -> (3/1,10/3) Hyperbolic Matrix(259,360,100,139) (-7/5,-18/13) -> (18/7,13/5) Hyperbolic Matrix(1159,1600,318,439) (-29/21,-40/29) -> (40/11,11/3) Hyperbolic Matrix(1161,1600,320,441) (-40/29,-11/8) -> (29/8,40/11) Hyperbolic Matrix(59,80,14,19) (-11/8,-4/3) -> (4/1,9/2) Hyperbolic Matrix(61,80,16,21) (-4/3,-9/7) -> (11/3,4/1) Hyperbolic Matrix(219,280,140,179) (-9/7,-14/11) -> (14/9,11/7) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(49,60,40,49) (-5/4,-6/5) -> (6/5,5/4) Hyperbolic Matrix(339,400,50,59) (-13/11,-20/17) -> (20/3,7/1) Hyperbolic Matrix(341,400,52,61) (-20/17,-7/6) -> (13/2,20/3) Hyperbolic Matrix(139,160,86,99) (-7/6,-1/1) -> (21/13,13/8) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(101,-120,16,-19) (7/6,6/5) -> (6/1,13/2) Hyperbolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(181,-280,64,-99) (3/2,14/9) -> (14/5,17/6) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(21,160,8,61) -> Matrix(1,-2,4,-7) Matrix(19,120,-16,-101) -> Matrix(1,2,-2,-3) Matrix(11,60,2,11) -> Matrix(1,2,2,5) Matrix(29,140,6,29) -> Matrix(1,2,2,5) Matrix(61,280,22,101) -> Matrix(1,0,4,1) Matrix(19,80,14,59) -> Matrix(1,0,4,1) Matrix(21,80,16,61) -> Matrix(1,0,4,1) Matrix(199,720,-144,-521) -> Matrix(5,4,-4,-3) Matrix(101,360,62,221) -> Matrix(3,2,4,3) Matrix(29,100,20,69) -> Matrix(1,0,6,1) Matrix(31,100,22,71) -> Matrix(1,0,2,1) Matrix(99,280,-64,-181) -> Matrix(3,2,-2,-1) Matrix(101,280,22,61) -> Matrix(1,0,4,1) Matrix(329,900,208,569) -> Matrix(1,0,4,1) Matrix(331,900,210,571) -> Matrix(1,0,4,1) Matrix(119,320,74,199) -> Matrix(1,0,4,1) Matrix(121,320,76,201) -> Matrix(1,0,4,1) Matrix(61,160,8,21) -> Matrix(3,2,4,3) Matrix(139,360,100,259) -> Matrix(5,2,12,5) Matrix(71,180,28,71) -> Matrix(1,0,8,1) Matrix(9,20,4,9) -> Matrix(1,0,4,1) Matrix(11,20,6,11) -> Matrix(1,0,4,1) Matrix(109,180,66,109) -> Matrix(1,0,0,1) Matrix(221,360,62,101) -> Matrix(1,-2,4,-7) Matrix(99,160,86,139) -> Matrix(1,2,4,9) Matrix(199,320,74,119) -> Matrix(1,0,4,1) Matrix(201,320,76,121) -> Matrix(1,0,4,1) Matrix(569,900,208,329) -> Matrix(1,0,4,1) Matrix(571,900,210,331) -> Matrix(1,0,4,1) Matrix(179,280,140,219) -> Matrix(1,0,4,1) Matrix(259,400,90,139) -> Matrix(3,4,8,11) Matrix(261,400,92,141) -> Matrix(5,4,16,13) Matrix(69,100,20,29) -> Matrix(1,0,6,1) Matrix(71,100,22,31) -> Matrix(1,0,2,1) Matrix(259,360,100,139) -> Matrix(1,2,4,9) Matrix(1159,1600,318,439) -> Matrix(7,8,20,23) Matrix(1161,1600,320,441) -> Matrix(9,8,28,25) Matrix(59,80,14,19) -> Matrix(1,0,4,1) Matrix(61,80,16,21) -> Matrix(1,0,4,1) Matrix(219,280,140,179) -> Matrix(1,0,4,1) Matrix(111,140,88,111) -> Matrix(3,2,10,7) Matrix(49,60,40,49) -> Matrix(3,2,10,7) Matrix(339,400,50,59) -> Matrix(23,12,44,23) Matrix(341,400,52,61) -> Matrix(25,12,52,25) Matrix(139,160,86,99) -> Matrix(5,2,12,5) Matrix(1,0,2,1) -> Matrix(1,0,8,1) Matrix(101,-120,16,-19) -> Matrix(7,-2,18,-5) Matrix(521,-720,144,-199) -> Matrix(11,-4,36,-13) Matrix(181,-280,64,-99) -> Matrix(5,-2,18,-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): 12 Degree of the the map X: 12 Degree of the the map Y: 48 Permutation triple for Y: ((2,6,4,3,7)(5,16,10,9,17)(8,24,14,13,25)(11,31,20,19,32)(12,35,22,21,36)(15,41,26,27,40)(28,30,37,39,43)(29,38,33,42,34); (1,4,14,40,31,44,19,39,24,42,47,29,16,37,36,45,35,15,5,2)(3,10,18,17,33,32,41,46,27,21,38,13,23,8,7,22,43,48,30,11)(6,20,34,12)(9,26,25,28); (1,2,8,26,32,44,31,30,25,38,47,42,17,28,22,45,36,27,9,3)(4,12,37,48,43,19,6,5,18,10,29,20,40,46,41,35,34,24,23,13)(7,11,33,21)(14,39,16,15)) ----------------------------------------------------------------------- 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 0/1 4/3 10/7 30/19 8/5 2/1 5/2 8/3 30/11 20/7 3/1 10/3 18/5 40/11 4/1 14/3 5/1 6/1 20/3 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 0/1 1/5 7/6 5/21 1/4 6/5 1/4 1/3 5/4 0/1 2/7 14/11 1/4 1/3 9/7 2/7 1/3 4/3 0/1 1/4 1/3 11/8 2/7 1/3 18/13 1/3 2/5 7/5 1/2 1/1 10/7 0/1 3/2 1/4 1/3 14/9 1/3 1/2 11/7 1/3 2/5 30/19 0/1 2/5 19/12 1/3 2/5 8/5 0/1 1/3 1/2 21/13 1/3 2/5 13/8 1/2 3/5 18/11 0/1 1/1 5/3 0/1 2/1 0/1 1/3 5/2 0/1 18/7 0/1 1/5 13/5 3/13 1/4 21/8 2/7 1/3 8/3 0/1 1/4 1/3 19/7 2/7 1/3 30/11 0/1 2/7 11/4 2/7 1/3 14/5 1/4 1/3 17/6 3/10 1/3 20/7 1/3 3/1 1/3 1/2 10/3 0/1 7/2 1/5 1/4 18/5 2/7 1/3 29/8 6/19 1/3 40/11 1/3 11/3 1/3 2/5 4/1 0/1 1/3 1/2 9/2 1/3 2/5 14/3 1/3 1/2 5/1 0/1 2/5 6/1 1/3 1/2 13/2 7/15 1/2 20/3 1/2 7/1 1/2 5/9 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(139,-160,53,-61) (1/1,7/6) -> (13/5,21/8) Hyperbolic Matrix(101,-120,16,-19) (7/6,6/5) -> (6/1,13/2) Hyperbolic Matrix(49,-60,9,-11) (6/5,5/4) -> (5/1,6/1) Hyperbolic Matrix(111,-140,23,-29) (5/4,14/11) -> (14/3,5/1) Hyperbolic Matrix(219,-280,79,-101) (14/11,9/7) -> (11/4,14/5) Hyperbolic Matrix(61,-80,45,-59) (9/7,4/3) -> (4/3,11/8) Parabolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(259,-360,159,-221) (18/13,7/5) -> (13/8,18/11) Hyperbolic Matrix(71,-100,49,-69) (7/5,10/7) -> (10/7,3/2) Parabolic Matrix(181,-280,64,-99) (3/2,14/9) -> (14/5,17/6) Hyperbolic Matrix(179,-280,39,-61) (14/9,11/7) -> (9/2,14/3) Hyperbolic Matrix(571,-900,361,-569) (11/7,30/19) -> (30/19,19/12) Parabolic Matrix(201,-320,125,-199) (19/12,8/5) -> (8/5,21/13) Parabolic Matrix(99,-160,13,-21) (21/13,13/8) -> (7/1,1/0) Hyperbolic Matrix(109,-180,43,-71) (18/11,5/3) -> (5/2,18/7) Hyperbolic Matrix(11,-20,5,-9) (5/3,2/1) -> (2/1,5/2) Parabolic Matrix(139,-360,39,-101) (18/7,13/5) -> (7/2,18/5) Hyperbolic Matrix(121,-320,45,-119) (21/8,8/3) -> (8/3,19/7) Parabolic Matrix(331,-900,121,-329) (19/7,30/11) -> (30/11,11/4) Parabolic Matrix(141,-400,49,-139) (17/6,20/7) -> (20/7,3/1) Parabolic Matrix(31,-100,9,-29) (3/1,10/3) -> (10/3,7/2) Parabolic Matrix(441,-1600,121,-439) (29/8,40/11) -> (40/11,11/3) Parabolic Matrix(21,-80,5,-19) (11/3,4/1) -> (4/1,9/2) Parabolic Matrix(61,-400,9,-59) (13/2,20/3) -> (20/3,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,4,1) Matrix(139,-160,53,-61) -> Matrix(9,-2,32,-7) Matrix(101,-120,16,-19) -> Matrix(7,-2,18,-5) Matrix(49,-60,9,-11) -> Matrix(7,-2,18,-5) Matrix(111,-140,23,-29) -> Matrix(7,-2,18,-5) Matrix(219,-280,79,-101) -> Matrix(1,0,0,1) Matrix(61,-80,45,-59) -> Matrix(1,0,0,1) Matrix(521,-720,144,-199) -> Matrix(11,-4,36,-13) Matrix(259,-360,159,-221) -> Matrix(5,-2,8,-3) Matrix(71,-100,49,-69) -> Matrix(1,0,2,1) Matrix(181,-280,64,-99) -> Matrix(5,-2,18,-7) Matrix(179,-280,39,-61) -> Matrix(1,0,0,1) Matrix(571,-900,361,-569) -> Matrix(1,0,0,1) Matrix(201,-320,125,-199) -> Matrix(1,0,0,1) Matrix(99,-160,13,-21) -> Matrix(5,-2,8,-3) Matrix(109,-180,43,-71) -> Matrix(1,0,4,1) Matrix(11,-20,5,-9) -> Matrix(1,0,0,1) Matrix(139,-360,39,-101) -> Matrix(9,-2,32,-7) Matrix(121,-320,45,-119) -> Matrix(1,0,0,1) Matrix(331,-900,121,-329) -> Matrix(1,0,0,1) Matrix(141,-400,49,-139) -> Matrix(13,-4,36,-11) Matrix(31,-100,9,-29) -> Matrix(1,0,2,1) Matrix(441,-1600,121,-439) -> Matrix(25,-8,72,-23) Matrix(21,-80,5,-19) -> Matrix(1,0,0,1) Matrix(61,-400,9,-59) -> Matrix(25,-12,48,-23) 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 4 1 2/1 (0/1,1/3) 0 10 5/2 0/1 2 4 18/7 (0/1,1/5) 0 10 13/5 (3/13,1/4) 0 20 21/8 (2/7,1/3) 0 20 8/3 0 5 19/7 (2/7,1/3) 0 20 30/11 0 2 11/4 (2/7,1/3) 0 20 14/5 (1/4,1/3) 0 10 20/7 1/3 4 1 3/1 (1/3,1/2) 0 20 10/3 0/1 4 2 7/2 (1/5,1/4) 0 20 18/5 (2/7,1/3) 0 10 40/11 1/3 8 1 11/3 (1/3,2/5) 0 20 4/1 0 5 9/2 (1/3,2/5) 0 20 14/3 (1/3,1/2) 0 10 5/1 (1/3,1/2) 0 4 6/1 (1/3,1/2) 0 10 20/3 1/2 12 1 7/1 (1/2,5/9) 0 20 1/0 (0/1,1/1) 0 20 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(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(9,-20,4,-9) (2/1,5/2) -> (2/1,5/2) Reflection Matrix(71,-180,28,-71) (5/2,18/7) -> (5/2,18/7) Reflection Matrix(139,-360,39,-101) (18/7,13/5) -> (7/2,18/5) Hyperbolic Matrix(61,-160,8,-21) (13/5,21/8) -> (7/1,1/0) Glide Reflection Matrix(121,-320,45,-119) (21/8,8/3) -> (8/3,19/7) Parabolic Matrix(331,-900,121,-329) (19/7,30/11) -> (30/11,11/4) Parabolic Matrix(101,-280,22,-61) (11/4,14/5) -> (9/2,14/3) Glide Reflection Matrix(99,-280,35,-99) (14/5,20/7) -> (14/5,20/7) Reflection Matrix(41,-120,14,-41) (20/7,3/1) -> (20/7,3/1) Reflection Matrix(31,-100,9,-29) (3/1,10/3) -> (10/3,7/2) Parabolic Matrix(199,-720,55,-199) (18/5,40/11) -> (18/5,40/11) Reflection Matrix(241,-880,66,-241) (40/11,11/3) -> (40/11,11/3) Reflection Matrix(21,-80,5,-19) (11/3,4/1) -> (4/1,9/2) Parabolic Matrix(29,-140,6,-29) (14/3,5/1) -> (14/3,5/1) Reflection Matrix(11,-60,2,-11) (5/1,6/1) -> (5/1,6/1) Reflection Matrix(19,-120,3,-19) (6/1,20/3) -> (6/1,20/3) Reflection Matrix(41,-280,6,-41) (20/3,7/1) -> (20/3,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,2,-1) (0/1,1/0) -> (0/1,1/1) Matrix(1,0,1,-1) -> Matrix(1,0,6,-1) (0/1,2/1) -> (0/1,1/3) Matrix(9,-20,4,-9) -> Matrix(1,0,6,-1) (2/1,5/2) -> (0/1,1/3) Matrix(71,-180,28,-71) -> Matrix(1,0,10,-1) (5/2,18/7) -> (0/1,1/5) Matrix(139,-360,39,-101) -> Matrix(9,-2,32,-7) 1/4 Matrix(61,-160,8,-21) -> Matrix(7,-2,10,-3) Matrix(121,-320,45,-119) -> Matrix(1,0,0,1) Matrix(331,-900,121,-329) -> Matrix(1,0,0,1) Matrix(101,-280,22,-61) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(99,-280,35,-99) -> Matrix(7,-2,24,-7) (14/5,20/7) -> (1/4,1/3) Matrix(41,-120,14,-41) -> Matrix(5,-2,12,-5) (20/7,3/1) -> (1/3,1/2) Matrix(31,-100,9,-29) -> Matrix(1,0,2,1) 0/1 Matrix(199,-720,55,-199) -> Matrix(13,-4,42,-13) (18/5,40/11) -> (2/7,1/3) Matrix(241,-880,66,-241) -> Matrix(11,-4,30,-11) (40/11,11/3) -> (1/3,2/5) Matrix(21,-80,5,-19) -> Matrix(1,0,0,1) Matrix(29,-140,6,-29) -> Matrix(5,-2,12,-5) (14/3,5/1) -> (1/3,1/2) Matrix(11,-60,2,-11) -> Matrix(5,-2,12,-5) (5/1,6/1) -> (1/3,1/2) Matrix(19,-120,3,-19) -> Matrix(5,-2,12,-5) (6/1,20/3) -> (1/3,1/2) Matrix(41,-280,6,-41) -> Matrix(19,-10,36,-19) (20/3,7/1) -> (1/2,5/9) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.