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 -6/1 -5/1 -4/1 -8/3 -5/2 -2/1 -5/3 -5/4 0/1 1/1 5/4 10/7 3/2 30/19 5/3 2/1 20/9 5/2 8/3 30/11 20/7 3/1 10/3 7/2 11/3 4/1 9/2 5/1 6/1 20/3 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 0/1 1/1 -6/1 1/2 1/0 -5/1 0/1 -14/3 1/4 1/2 -9/2 1/3 1/2 -4/1 1/2 1/0 -11/3 2/1 1/0 -7/2 -1/1 0/1 -10/3 0/1 -3/1 0/1 1/2 -14/5 1/2 1/0 -11/4 1/2 1/1 -30/11 1/1 -19/7 0/1 1/1 -8/3 1/2 1/0 -5/2 0/1 -12/5 1/4 1/2 -19/8 0/1 1/3 -7/3 0/1 1/3 -9/4 3/7 1/2 -2/1 1/2 1/0 -11/6 3/7 1/2 -20/11 1/2 -9/5 1/2 4/7 -7/4 2/3 1/1 -5/3 1/1 -13/8 0/1 1/1 -21/13 0/1 1/1 -8/5 1/2 1/0 -19/12 0/1 1/1 -30/19 0/1 -11/7 0/1 1/2 -14/9 1/2 1/0 -17/11 0/1 1/2 -20/13 1/2 -3/2 1/2 1/1 -10/7 1/1 -7/5 1/1 2/1 -11/8 -1/1 1/0 -4/3 1/2 1/0 -9/7 1/2 2/3 -5/4 1/1 -11/9 0/1 1/0 -6/5 1/2 1/0 -13/11 0/1 1/1 -20/17 1/2 1/0 -7/6 0/1 1/1 -1/1 0/1 1/1 0/1 1/2 1/0 1/1 0/1 1/1 7/6 0/1 1/1 6/5 1/2 1/0 5/4 1/1 14/11 3/2 1/0 9/7 2/1 1/0 4/3 1/2 1/0 11/8 1/3 1/2 7/5 2/3 1/1 10/7 1/1 3/2 1/1 1/0 14/9 1/2 1/0 11/7 0/1 1/0 30/19 0/1 19/12 0/1 1/1 8/5 1/2 1/0 5/3 1/1 12/7 3/2 1/0 19/11 1/1 2/1 7/4 1/1 2/1 9/5 4/1 1/0 2/1 1/2 1/0 11/5 4/1 1/0 20/9 1/0 9/4 -3/1 1/0 7/3 -1/1 0/1 5/2 0/1 13/5 0/1 1/1 21/8 0/1 1/1 8/3 1/2 1/0 19/7 0/1 1/1 30/11 1/1 11/4 1/1 1/0 14/5 1/2 1/0 17/6 1/1 1/0 20/7 1/0 3/1 0/1 1/0 10/3 0/1 7/2 0/1 1/3 11/3 1/2 2/3 4/1 1/2 1/0 9/2 -1/1 1/0 5/1 0/1 11/2 1/2 1/1 6/1 1/2 1/0 13/2 0/1 1/1 20/3 1/2 1/0 7/1 0/1 1/1 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(19,100,-4,-21) (-6/1,-5/1) -> (-5/1,-14/3) Parabolic 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(39,140,22,79) (-11/3,-7/2) -> (7/4,9/5) Hyperbolic Matrix(41,140,12,41) (-7/2,-10/3) -> (10/3,7/2) Hyperbolic Matrix(19,60,6,19) (-10/3,-3/1) -> (3/1,10/3) Hyperbolic Matrix(99,280,-64,-181) (-3/1,-14/5) -> (-14/9,-17/11) Hyperbolic Matrix(79,220,14,39) (-14/5,-11/4) -> (11/2,6/1) Hyperbolic Matrix(241,660,88,241) (-11/4,-30/11) -> (30/11,11/4) Hyperbolic Matrix(419,1140,154,419) (-30/11,-19/7) -> (19/7,30/11) Hyperbolic Matrix(141,380,82,221) (-19/7,-8/3) -> (12/7,19/11) Hyperbolic Matrix(39,100,-16,-41) (-8/3,-5/2) -> (-5/2,-12/5) Parabolic Matrix(159,380,100,239) (-12/5,-19/8) -> (19/12,8/5) Hyperbolic Matrix(59,140,8,19) (-19/8,-7/3) -> (7/1,1/0) Hyperbolic Matrix(61,140,44,101) (-7/3,-9/4) -> (11/8,7/5) Hyperbolic Matrix(19,40,-10,-21) (-9/4,-2/1) -> (-2/1,-11/6) Parabolic Matrix(219,400,98,179) (-11/6,-20/11) -> (20/9,9/4) Hyperbolic Matrix(221,400,100,181) (-20/11,-9/5) -> (11/5,20/9) Hyperbolic Matrix(79,140,22,39) (-9/5,-7/4) -> (7/2,11/3) Hyperbolic Matrix(59,100,-36,-61) (-7/4,-5/3) -> (-5/3,-13/8) Parabolic 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(721,1140,456,721) (-19/12,-30/19) -> (30/19,19/12) Hyperbolic Matrix(419,660,266,419) (-30/19,-11/7) -> (11/7,30/19) 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(41,60,28,41) (-3/2,-10/7) -> (10/7,3/2) Hyperbolic Matrix(99,140,70,99) (-10/7,-7/5) -> (7/5,10/7) Hyperbolic Matrix(101,140,44,61) (-7/5,-11/8) -> (9/4,7/3) 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(79,100,-64,-81) (-9/7,-5/4) -> (-5/4,-11/9) Parabolic Matrix(181,220,116,141) (-11/9,-6/5) -> (14/9,11/7) 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(121,140,70,81) (-7/6,-1/1) -> (19/11,7/4) 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(81,-100,64,-79) (6/5,5/4) -> (5/4,14/11) Parabolic Matrix(181,-280,64,-99) (3/2,14/9) -> (14/5,17/6) Hyperbolic Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic Matrix(21,-40,10,-19) (9/5,2/1) -> (2/1,11/5) Parabolic Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(21,-100,4,-19) (9/2,5/1) -> (5/1,11/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(21,160,8,61) -> Matrix(1,0,0,1) Matrix(19,120,-16,-101) -> Matrix(1,0,0,1) Matrix(19,100,-4,-21) -> Matrix(1,0,2,1) Matrix(61,280,22,101) -> Matrix(1,0,-2,1) Matrix(19,80,14,59) -> Matrix(1,0,0,1) Matrix(21,80,16,61) -> Matrix(1,0,0,1) Matrix(39,140,22,79) -> Matrix(1,2,0,1) Matrix(41,140,12,41) -> Matrix(1,0,4,1) Matrix(19,60,6,19) -> Matrix(1,0,-2,1) Matrix(99,280,-64,-181) -> Matrix(1,0,0,1) Matrix(79,220,14,39) -> Matrix(1,0,0,1) Matrix(241,660,88,241) -> Matrix(3,-2,2,-1) Matrix(419,1140,154,419) -> Matrix(1,0,0,1) Matrix(141,380,82,221) -> Matrix(3,-2,2,-1) Matrix(39,100,-16,-41) -> Matrix(1,0,2,1) Matrix(159,380,100,239) -> Matrix(1,0,-2,1) Matrix(59,140,8,19) -> Matrix(1,0,-2,1) Matrix(61,140,44,101) -> Matrix(5,-2,8,-3) Matrix(19,40,-10,-21) -> Matrix(1,0,0,1) Matrix(219,400,98,179) -> Matrix(13,-6,-2,1) Matrix(221,400,100,181) -> Matrix(15,-8,2,-1) Matrix(79,140,22,39) -> Matrix(3,-2,8,-5) Matrix(59,100,-36,-61) -> Matrix(3,-2,2,-1) Matrix(99,160,86,139) -> Matrix(1,0,0,1) Matrix(199,320,74,119) -> Matrix(1,0,0,1) Matrix(201,320,76,121) -> Matrix(1,0,0,1) Matrix(721,1140,456,721) -> Matrix(1,0,0,1) Matrix(419,660,266,419) -> Matrix(1,0,-2,1) Matrix(179,280,140,219) -> Matrix(3,-2,2,-1) Matrix(259,400,90,139) -> Matrix(1,0,-2,1) Matrix(261,400,92,141) -> Matrix(3,-2,2,-1) Matrix(41,60,28,41) -> Matrix(3,-2,2,-1) Matrix(99,140,70,99) -> Matrix(3,-4,4,-5) Matrix(101,140,44,61) -> Matrix(1,-2,0,1) Matrix(59,80,14,19) -> Matrix(1,0,0,1) Matrix(61,80,16,21) -> Matrix(1,0,0,1) Matrix(79,100,-64,-81) -> Matrix(3,-2,2,-1) Matrix(181,220,116,141) -> Matrix(1,0,0,1) Matrix(339,400,50,59) -> Matrix(1,0,0,1) Matrix(341,400,52,61) -> Matrix(1,0,0,1) Matrix(121,140,70,81) -> Matrix(3,-2,2,-1) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(101,-120,16,-19) -> Matrix(1,0,0,1) Matrix(81,-100,64,-79) -> Matrix(3,-2,2,-1) Matrix(181,-280,64,-99) -> Matrix(1,0,0,1) Matrix(61,-100,36,-59) -> Matrix(3,-2,2,-1) Matrix(21,-40,10,-19) -> Matrix(1,0,0,1) Matrix(41,-100,16,-39) -> Matrix(1,0,2,1) Matrix(21,-100,4,-19) -> 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): 8 Degree of the the map X: 8 Degree of the the map Y: 48 Permutation triple for Y: ((2,6,23,24,7)(3,12,36,13,4)(5,18,10,9,19)(8,28,16,15,29)(11,34,22,21,35)(14,37,26,25,38)(17,42,30,33,39)(31,41,40,43,32); (1,4,16,41,34,46,37,17,5,2)(3,10,27,8,7,26,43,48,33,11)(6,22)(9,32)(12,35,42,47,31,25,24,15,20,19)(13,14)(18,39,38,44,21,40,28,36,45,23)(29,30); (1,2,8,30,35,44,38,31,9,3)(4,14,39,48,43,21,6,5,20,15)(7,25)(10,23,22,41,47,42,37,13,28,27)(11,12)(16,40)(17,18)(19,32,26,46,34,33,29,24,45,36)) ----------------------------------------------------------------------- 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 5/4 4/3 8/5 5/3 2/1 20/9 5/2 8/3 30/11 20/7 3/1 10/3 4/1 9/2 5/1 6/1 20/3 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/2 1/0 1/1 0/1 1/1 7/6 0/1 1/1 6/5 1/2 1/0 5/4 1/1 14/11 3/2 1/0 9/7 2/1 1/0 4/3 1/2 1/0 11/8 1/3 1/2 7/5 2/3 1/1 10/7 1/1 3/2 1/1 1/0 14/9 1/2 1/0 11/7 0/1 1/0 30/19 0/1 19/12 0/1 1/1 8/5 1/2 1/0 5/3 1/1 12/7 3/2 1/0 19/11 1/1 2/1 7/4 1/1 2/1 9/5 4/1 1/0 2/1 1/2 1/0 11/5 4/1 1/0 20/9 1/0 9/4 -3/1 1/0 7/3 -1/1 0/1 5/2 0/1 13/5 0/1 1/1 21/8 0/1 1/1 8/3 1/2 1/0 19/7 0/1 1/1 30/11 1/1 11/4 1/1 1/0 14/5 1/2 1/0 17/6 1/1 1/0 20/7 1/0 3/1 0/1 1/0 10/3 0/1 7/2 0/1 1/3 11/3 1/2 2/3 4/1 1/2 1/0 9/2 -1/1 1/0 5/1 0/1 11/2 1/2 1/1 6/1 1/2 1/0 13/2 0/1 1/1 20/3 1/2 1/0 7/1 0/1 1/1 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(81,-100,64,-79) (6/5,5/4) -> (5/4,14/11) Parabolic 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(101,-140,57,-79) (11/8,7/5) -> (7/4,9/5) Hyperbolic Matrix(99,-140,29,-41) (7/5,10/7) -> (10/3,7/2) Hyperbolic Matrix(41,-60,13,-19) (10/7,3/2) -> (3/1,10/3) Hyperbolic Matrix(181,-280,64,-99) (3/2,14/9) -> (14/5,17/6) Hyperbolic Matrix(141,-220,25,-39) (14/9,11/7) -> (11/2,6/1) Hyperbolic Matrix(419,-660,153,-241) (11/7,30/19) -> (30/11,11/4) Hyperbolic Matrix(721,-1140,265,-419) (30/19,19/12) -> (19/7,30/11) Hyperbolic Matrix(239,-380,139,-221) (19/12,8/5) -> (12/7,19/11) Hyperbolic Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic Matrix(81,-140,11,-19) (19/11,7/4) -> (7/1,1/0) Hyperbolic Matrix(21,-40,10,-19) (9/5,2/1) -> (2/1,11/5) Parabolic Matrix(181,-400,81,-179) (11/5,20/9) -> (20/9,9/4) Parabolic Matrix(61,-140,17,-39) (9/4,7/3) -> (7/2,11/3) Hyperbolic Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(121,-320,45,-119) (21/8,8/3) -> (8/3,19/7) Parabolic Matrix(141,-400,49,-139) (17/6,20/7) -> (20/7,3/1) Parabolic Matrix(21,-80,5,-19) (11/3,4/1) -> (4/1,9/2) Parabolic Matrix(21,-100,4,-19) (9/2,5/1) -> (5/1,11/2) 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,-1,2,-1) Matrix(139,-160,53,-61) -> Matrix(1,-1,2,-1) Matrix(101,-120,16,-19) -> Matrix(1,0,0,1) Matrix(81,-100,64,-79) -> Matrix(3,-2,2,-1) Matrix(219,-280,79,-101) -> Matrix(1,-1,0,1) Matrix(61,-80,45,-59) -> Matrix(1,-1,2,-1) Matrix(101,-140,57,-79) -> Matrix(5,-3,2,-1) Matrix(99,-140,29,-41) -> Matrix(1,-1,6,-5) Matrix(41,-60,13,-19) -> Matrix(1,-1,0,1) Matrix(181,-280,64,-99) -> Matrix(1,0,0,1) Matrix(141,-220,25,-39) -> Matrix(1,-1,2,-1) Matrix(419,-660,153,-241) -> Matrix(1,1,0,1) Matrix(721,-1140,265,-419) -> Matrix(1,-1,2,-1) Matrix(239,-380,139,-221) -> Matrix(1,1,0,1) Matrix(61,-100,36,-59) -> Matrix(3,-2,2,-1) Matrix(81,-140,11,-19) -> Matrix(1,-1,0,1) Matrix(21,-40,10,-19) -> Matrix(1,0,0,1) Matrix(181,-400,81,-179) -> Matrix(1,-7,0,1) Matrix(61,-140,17,-39) -> Matrix(1,1,2,3) Matrix(41,-100,16,-39) -> Matrix(1,0,2,1) Matrix(121,-320,45,-119) -> Matrix(1,-1,2,-1) Matrix(141,-400,49,-139) -> Matrix(1,-1,0,1) Matrix(21,-80,5,-19) -> Matrix(1,-1,2,-1) Matrix(21,-100,4,-19) -> Matrix(1,0,2,1) Matrix(61,-400,9,-59) -> Matrix(1,-1,2,-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): 8 ----------------------------------------------------------------------- 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 (0/1,1/1).(1/2,1/0) 0 1 2/1 (1/2,1/0) 0 5 20/9 1/0 7 1 9/4 (-3/1,1/0) 0 10 7/3 (-1/1,0/1) 0 10 5/2 0/1 1 2 13/5 (0/1,1/1) 0 10 21/8 (0/1,1/1) 0 10 8/3 (0/1,1/1).(1/2,1/0) 0 5 19/7 (0/1,1/1) 0 10 30/11 1/1 1 1 11/4 (1/1,1/0) 0 10 14/5 (1/2,1/0) 0 5 20/7 1/0 1 1 3/1 (0/1,1/0) 0 10 10/3 0/1 3 1 7/2 (0/1,1/3) 0 10 11/3 (1/2,2/3) 0 10 4/1 (0/1,1/1).(1/2,1/0) 0 5 9/2 (-1/1,1/0) 0 10 5/1 0/1 1 2 11/2 (1/2,1/1) 0 10 6/1 (1/2,1/0) 0 5 20/3 (0/1,1/1).(1/2,1/0) 0 1 7/1 (0/1,1/1) 0 10 1/0 (0/1,1/1) 0 10 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(19,-40,9,-19) (2/1,20/9) -> (2/1,20/9) Reflection Matrix(161,-360,72,-161) (20/9,9/4) -> (20/9,9/4) Reflection Matrix(61,-140,17,-39) (9/4,7/3) -> (7/2,11/3) Hyperbolic Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic 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(419,-1140,154,-419) (19/7,30/11) -> (19/7,30/11) Reflection Matrix(241,-660,88,-241) (30/11,11/4) -> (30/11,11/4) Reflection Matrix(79,-220,14,-39) (11/4,14/5) -> (11/2,6/1) 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(19,-60,6,-19) (3/1,10/3) -> (3/1,10/3) Reflection Matrix(41,-140,12,-41) (10/3,7/2) -> (10/3,7/2) Reflection Matrix(21,-80,5,-19) (11/3,4/1) -> (4/1,9/2) Parabolic Matrix(21,-100,4,-19) (9/2,5/1) -> (5/1,11/2) Parabolic 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(-1,1,0,1) (0/1,2/1) -> (1/2,1/0) Matrix(19,-40,9,-19) -> Matrix(-1,1,0,1) (2/1,20/9) -> (1/2,1/0) Matrix(161,-360,72,-161) -> Matrix(1,6,0,-1) (20/9,9/4) -> (-3/1,1/0) Matrix(61,-140,17,-39) -> Matrix(1,1,2,3) Matrix(41,-100,16,-39) -> Matrix(1,0,2,1) 0/1 Matrix(61,-160,8,-21) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(121,-320,45,-119) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(419,-1140,154,-419) -> Matrix(1,0,2,-1) (19/7,30/11) -> (0/1,1/1) Matrix(241,-660,88,-241) -> Matrix(-1,2,0,1) (30/11,11/4) -> (1/1,1/0) Matrix(79,-220,14,-39) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(99,-280,35,-99) -> Matrix(-1,1,0,1) (14/5,20/7) -> (1/2,1/0) Matrix(41,-120,14,-41) -> Matrix(1,0,0,-1) (20/7,3/1) -> (0/1,1/0) Matrix(19,-60,6,-19) -> Matrix(1,0,0,-1) (3/1,10/3) -> (0/1,1/0) Matrix(41,-140,12,-41) -> Matrix(1,0,6,-1) (10/3,7/2) -> (0/1,1/3) Matrix(21,-80,5,-19) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(21,-100,4,-19) -> Matrix(1,0,2,1) 0/1 Matrix(19,-120,3,-19) -> Matrix(-1,1,0,1) (6/1,20/3) -> (1/2,1/0) Matrix(41,-280,6,-41) -> Matrix(1,0,2,-1) (20/3,7/1) -> (0/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.