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 1/1 5/4 15/11 3/2 5/3 9/5 2/1 15/7 20/9 12/5 5/2 3/1 10/3 7/2 15/4 4/1 30/7 9/2 5/1 6/1 7/1 15/2 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 0/1 -6/1 -1/1 -5/1 -1/1 -9/2 -1/2 -4/1 -1/3 -15/4 0/1 -11/3 0/1 -7/2 1/0 -10/3 -1/1 -1/3 -3/1 0/1 -5/2 0/1 -12/5 1/3 -7/3 0/1 -16/7 1/1 -9/4 1/2 -20/9 3/5 1/1 -11/5 2/3 -2/1 1/1 -15/8 1/1 -13/7 4/3 -11/6 3/2 -20/11 1/1 5/3 -9/5 2/1 -7/4 1/0 -19/11 2/1 -12/7 3/1 -5/3 1/0 -3/2 1/0 -10/7 -3/1 -1/1 -17/12 -3/2 -7/5 0/1 -18/13 1/1 -29/21 2/1 -40/29 1/1 3/1 -11/8 1/0 -15/11 1/0 -4/3 -3/1 -17/13 -2/1 -30/23 -3/1 -1/1 -13/10 1/0 -9/7 -2/1 -5/4 -1/1 -6/5 -1/1 -13/11 -2/3 -7/6 1/0 -15/13 -1/1 -8/7 -1/1 -1/1 0/1 0/1 -1/1 1/1 1/1 0/1 7/6 1/0 6/5 1/1 5/4 1/1 9/7 2/1 4/3 3/1 15/11 1/0 11/8 1/0 7/5 0/1 10/7 1/1 3/1 3/2 1/0 5/3 1/0 12/7 -3/1 7/4 1/0 16/9 -1/1 9/5 -2/1 20/11 -5/3 -1/1 11/6 -3/2 2/1 -1/1 15/7 -1/1 13/6 -3/4 11/5 -2/3 20/9 -1/1 -3/5 9/4 -1/2 7/3 0/1 19/8 -1/2 12/5 -1/3 5/2 0/1 3/1 0/1 10/3 1/3 1/1 17/5 2/3 7/2 1/0 18/5 -1/1 29/8 -1/2 40/11 -1/1 -1/3 11/3 0/1 15/4 0/1 4/1 1/3 17/4 1/2 30/7 1/3 1/1 13/3 0/1 9/2 1/2 5/1 1/1 6/1 1/1 13/2 3/2 7/1 0/1 15/2 1/1 8/1 1/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,90,-6,-49) (-7/1,1/0) -> (-13/7,-11/6) 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(19,90,4,19) (-5/1,-9/2) -> (9/2,5/1) Hyperbolic Matrix(41,180,-18,-79) (-9/2,-4/1) -> (-16/7,-9/4) Hyperbolic Matrix(31,120,8,31) (-4/1,-15/4) -> (15/4,4/1) Hyperbolic Matrix(89,330,24,89) (-15/4,-11/3) -> (11/3,15/4) Hyperbolic Matrix(59,210,-34,-121) (-11/3,-7/2) -> (-7/4,-19/11) Hyperbolic Matrix(71,240,-50,-169) (-7/2,-10/3) -> (-10/7,-17/12) Hyperbolic Matrix(19,60,6,19) (-10/3,-3/1) -> (3/1,10/3) Hyperbolic Matrix(11,30,4,11) (-3/1,-5/2) -> (5/2,3/1) Hyperbolic Matrix(49,120,20,49) (-5/2,-12/5) -> (12/5,5/2) Hyperbolic Matrix(89,210,-64,-151) (-12/5,-7/3) -> (-7/5,-18/13) Hyperbolic Matrix(131,300,-100,-229) (-7/3,-16/7) -> (-4/3,-17/13) Hyperbolic Matrix(161,360,72,161) (-9/4,-20/9) -> (20/9,9/4) Hyperbolic Matrix(461,1020,-334,-739) (-20/9,-11/5) -> (-29/21,-40/29) Hyperbolic Matrix(41,90,-36,-79) (-11/5,-2/1) -> (-8/7,-1/1) Hyperbolic Matrix(79,150,10,19) (-2/1,-15/8) -> (15/2,8/1) Hyperbolic Matrix(161,300,22,41) (-15/8,-13/7) -> (7/1,15/2) Hyperbolic Matrix(361,660,-262,-479) (-11/6,-20/11) -> (-40/29,-11/8) Hyperbolic Matrix(199,360,110,199) (-20/11,-9/5) -> (9/5,20/11) Hyperbolic Matrix(101,180,-78,-139) (-9/5,-7/4) -> (-13/10,-9/7) Hyperbolic Matrix(401,690,-290,-499) (-19/11,-12/7) -> (-18/13,-29/21) Hyperbolic Matrix(71,120,42,71) (-12/7,-5/3) -> (5/3,12/7) Hyperbolic Matrix(19,30,12,19) (-5/3,-3/2) -> (3/2,5/3) Hyperbolic Matrix(41,60,28,41) (-3/2,-10/7) -> (10/7,3/2) Hyperbolic Matrix(191,270,-162,-229) (-17/12,-7/5) -> (-13/11,-7/6) Hyperbolic Matrix(241,330,176,241) (-11/8,-15/11) -> (15/11,11/8) Hyperbolic Matrix(89,120,66,89) (-15/11,-4/3) -> (4/3,15/11) Hyperbolic Matrix(689,900,160,209) (-17/13,-30/23) -> (30/7,13/3) Hyperbolic Matrix(691,900,162,211) (-30/23,-13/10) -> (17/4,30/7) Hyperbolic Matrix(71,90,56,71) (-9/7,-5/4) -> (5/4,9/7) Hyperbolic Matrix(49,60,40,49) (-5/4,-6/5) -> (6/5,5/4) Hyperbolic Matrix(259,300,120,139) (-7/6,-15/13) -> (15/7,13/6) Hyperbolic Matrix(131,150,62,71) (-15/13,-8/7) -> (2/1,15/7) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(79,-90,36,-41) (1/1,7/6) -> (13/6,11/5) Hyperbolic Matrix(101,-120,16,-19) (7/6,6/5) -> (6/1,13/2) Hyperbolic Matrix(139,-180,78,-101) (9/7,4/3) -> (16/9,9/5) Hyperbolic Matrix(151,-210,64,-89) (11/8,7/5) -> (7/3,19/8) Hyperbolic Matrix(169,-240,50,-71) (7/5,10/7) -> (10/3,17/5) Hyperbolic Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(169,-300,40,-71) (7/4,16/9) -> (4/1,17/4) Hyperbolic Matrix(559,-1020,154,-281) (20/11,11/6) -> (29/8,40/11) Hyperbolic Matrix(49,-90,6,-11) (11/6,2/1) -> (8/1,1/0) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(289,-690,80,-191) (19/8,12/5) -> (18/5,29/8) Hyperbolic Matrix(79,-270,12,-41) (17/5,7/2) -> (13/2,7/1) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(11,90,-6,-49) -> Matrix(3,4,2,3) Matrix(19,120,-16,-101) -> Matrix(1,2,-2,-3) Matrix(11,60,2,11) -> Matrix(1,0,2,1) Matrix(19,90,4,19) -> Matrix(3,2,4,3) Matrix(41,180,-18,-79) -> Matrix(1,0,4,1) Matrix(31,120,8,31) -> Matrix(1,0,6,1) Matrix(89,330,24,89) -> Matrix(1,0,-6,1) Matrix(59,210,-34,-121) -> Matrix(1,2,0,1) Matrix(71,240,-50,-169) -> Matrix(3,2,-2,-1) Matrix(19,60,6,19) -> Matrix(1,0,4,1) Matrix(11,30,4,11) -> Matrix(1,0,-2,1) Matrix(49,120,20,49) -> Matrix(1,0,-6,1) Matrix(89,210,-64,-151) -> Matrix(1,0,-2,1) Matrix(131,300,-100,-229) -> Matrix(5,-2,-2,1) Matrix(161,360,72,161) -> Matrix(7,-4,-12,7) Matrix(461,1020,-334,-739) -> Matrix(7,-4,2,-1) Matrix(41,90,-36,-79) -> Matrix(3,-2,-4,3) Matrix(79,150,10,19) -> Matrix(3,-2,2,-1) Matrix(161,300,22,41) -> Matrix(3,-4,4,-5) Matrix(361,660,-262,-479) -> Matrix(5,-8,2,-3) Matrix(199,360,110,199) -> Matrix(7,-12,-4,7) Matrix(101,180,-78,-139) -> Matrix(1,-4,0,1) Matrix(401,690,-290,-499) -> Matrix(3,-8,2,-5) Matrix(71,120,42,71) -> Matrix(1,-6,0,1) Matrix(19,30,12,19) -> Matrix(1,-2,0,1) Matrix(41,60,28,41) -> Matrix(1,4,0,1) Matrix(191,270,-162,-229) -> Matrix(1,2,-2,-3) Matrix(241,330,176,241) -> Matrix(1,-6,0,1) Matrix(89,120,66,89) -> Matrix(1,6,0,1) Matrix(689,900,160,209) -> Matrix(1,2,2,5) Matrix(691,900,162,211) -> Matrix(1,2,2,5) Matrix(71,90,56,71) -> Matrix(3,4,2,3) Matrix(49,60,40,49) -> Matrix(1,2,0,1) Matrix(259,300,120,139) -> Matrix(3,4,-4,-5) Matrix(131,150,62,71) -> Matrix(3,2,-2,-1) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(79,-90,36,-41) -> Matrix(3,-2,-4,3) Matrix(101,-120,16,-19) -> Matrix(3,-2,2,-1) Matrix(139,-180,78,-101) -> Matrix(1,-4,0,1) Matrix(151,-210,64,-89) -> Matrix(1,0,-2,1) Matrix(169,-240,50,-71) -> Matrix(1,-2,2,-3) Matrix(121,-210,34,-59) -> Matrix(1,2,0,1) Matrix(169,-300,40,-71) -> Matrix(1,2,2,5) Matrix(559,-1020,154,-281) -> Matrix(1,2,-4,-7) Matrix(49,-90,6,-11) -> Matrix(3,4,2,3) Matrix(299,-660,82,-181) -> Matrix(3,2,-8,-5) Matrix(79,-180,18,-41) -> Matrix(1,0,4,1) Matrix(289,-690,80,-191) -> Matrix(5,2,-8,-3) Matrix(79,-270,12,-41) -> Matrix(3,-2,2,-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): 16 Degree of the the map X: 16 Degree of the the map Y: 48 Permutation triple for Y: ((2,6,20,43,45,34,12,4,3,11,33,48,38,21,7)(5,16,40,25,8,24,29,10,9,28,35,14,13,36,17)(15,39,26,27,37)(18,23,31)(19,30,32,22,41)(42,47,44); (1,4,14,37,33,47,30,29,24,41,44,38,15,5,2)(3,10,23,8,7)(6,12,19)(9,26,25)(11,32,13,31,27,45,43,39,18,17,22,21,40,46,28)(16,35,34,42,20); (1,2,8,26,43,42,41,17,36,32,47,34,27,9,3)(4,6,5,18,13)(7,22,11)(10,30,12,35,46,40,20,19,24,23,39,38,48,37,31)(14,16,15)(21,44,33,28,25)) ----------------------------------------------------------------------- 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: 16 Genus: 5 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 20/9 12/5 5/2 3/1 10/3 15/4 4/1 30/7 9/2 5/1 6/1 7/1 15/2 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/1 1/1 1/1 0/1 7/6 1/0 6/5 1/1 5/4 1/1 9/7 2/1 4/3 3/1 15/11 1/0 11/8 1/0 7/5 0/1 10/7 1/1 3/1 3/2 1/0 5/3 1/0 12/7 -3/1 7/4 1/0 16/9 -1/1 9/5 -2/1 20/11 -5/3 -1/1 11/6 -3/2 2/1 -1/1 15/7 -1/1 13/6 -3/4 11/5 -2/3 20/9 -1/1 -3/5 9/4 -1/2 7/3 0/1 19/8 -1/2 12/5 -1/3 5/2 0/1 3/1 0/1 10/3 1/3 1/1 17/5 2/3 7/2 1/0 18/5 -1/1 29/8 -1/2 40/11 -1/1 -1/3 11/3 0/1 15/4 0/1 4/1 1/3 17/4 1/2 30/7 1/3 1/1 13/3 0/1 9/2 1/2 5/1 1/1 6/1 1/1 13/2 3/2 7/1 0/1 15/2 1/1 8/1 1/1 1/0 1/0 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(79,-90,36,-41) (1/1,7/6) -> (13/6,11/5) 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(71,-90,15,-19) (5/4,9/7) -> (9/2,5/1) Hyperbolic Matrix(139,-180,78,-101) (9/7,4/3) -> (16/9,9/5) Hyperbolic Matrix(89,-120,23,-31) (4/3,15/11) -> (15/4,4/1) Hyperbolic Matrix(241,-330,65,-89) (15/11,11/8) -> (11/3,15/4) Hyperbolic Matrix(151,-210,64,-89) (11/8,7/5) -> (7/3,19/8) Hyperbolic Matrix(169,-240,50,-71) (7/5,10/7) -> (10/3,17/5) Hyperbolic Matrix(41,-60,13,-19) (10/7,3/2) -> (3/1,10/3) Hyperbolic Matrix(19,-30,7,-11) (3/2,5/3) -> (5/2,3/1) Hyperbolic Matrix(71,-120,29,-49) (5/3,12/7) -> (12/5,5/2) Hyperbolic Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(169,-300,40,-71) (7/4,16/9) -> (4/1,17/4) Hyperbolic Matrix(199,-360,89,-161) (9/5,20/11) -> (20/9,9/4) Hyperbolic Matrix(559,-1020,154,-281) (20/11,11/6) -> (29/8,40/11) Hyperbolic Matrix(49,-90,6,-11) (11/6,2/1) -> (8/1,1/0) Hyperbolic Matrix(71,-150,9,-19) (2/1,15/7) -> (15/2,8/1) Hyperbolic Matrix(139,-300,19,-41) (15/7,13/6) -> (7/1,15/2) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(289,-690,80,-191) (19/8,12/5) -> (18/5,29/8) Hyperbolic Matrix(79,-270,12,-41) (17/5,7/2) -> (13/2,7/1) Hyperbolic Matrix(211,-900,49,-209) (17/4,30/7) -> (30/7,13/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(0,-1,1,0) Matrix(79,-90,36,-41) -> Matrix(3,-2,-4,3) Matrix(101,-120,16,-19) -> Matrix(3,-2,2,-1) Matrix(49,-60,9,-11) -> Matrix(0,1,-1,2) Matrix(71,-90,15,-19) -> Matrix(2,-3,3,-4) Matrix(139,-180,78,-101) -> Matrix(1,-4,0,1) Matrix(89,-120,23,-31) -> Matrix(0,1,-1,6) Matrix(241,-330,65,-89) -> Matrix(0,-1,1,6) Matrix(151,-210,64,-89) -> Matrix(1,0,-2,1) Matrix(169,-240,50,-71) -> Matrix(1,-2,2,-3) Matrix(41,-60,13,-19) -> Matrix(0,1,-1,4) Matrix(19,-30,7,-11) -> Matrix(0,-1,1,2) Matrix(71,-120,29,-49) -> Matrix(0,-1,1,6) Matrix(121,-210,34,-59) -> Matrix(1,2,0,1) Matrix(169,-300,40,-71) -> Matrix(1,2,2,5) Matrix(199,-360,89,-161) -> Matrix(4,7,-7,-12) Matrix(559,-1020,154,-281) -> Matrix(1,2,-4,-7) Matrix(49,-90,6,-11) -> Matrix(3,4,2,3) Matrix(71,-150,9,-19) -> Matrix(2,3,1,2) Matrix(139,-300,19,-41) -> Matrix(4,3,5,4) Matrix(299,-660,82,-181) -> Matrix(3,2,-8,-5) Matrix(79,-180,18,-41) -> Matrix(1,0,4,1) Matrix(289,-690,80,-191) -> Matrix(5,2,-8,-3) Matrix(79,-270,12,-41) -> Matrix(3,-2,2,-1) Matrix(211,-900,49,-209) -> Matrix(2,-1,5,-2) 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 0/1 (-1/1,1/1).(0/1,1/0) 0 1 2/1 -1/1 1 15 11/5 -2/3 1 15 20/9 (-1/1,-3/5).(-2/3,-1/2) 0 3 9/4 -1/2 3 5 7/3 0/1 1 15 12/5 -1/3 3 5 5/2 0/1 2 3 3/1 0/1 3 5 10/3 (0/1,1/2).(1/3,1/1) 0 3 7/2 1/0 1 15 18/5 -1/1 3 5 40/11 (-1/1,-1/3).(-1/2,0/1) 0 3 11/3 0/1 1 15 15/4 0/1 6 1 4/1 1/3 1 15 30/7 (0/1,1/2).(1/3,1/1) 0 1 13/3 0/1 1 15 9/2 1/2 3 5 5/1 1/1 1 3 6/1 1/1 3 5 7/1 0/1 1 15 15/2 1/1 3 1 8/1 1/1 1 15 1/0 1/0 1 15 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(41,-90,5,-11) (2/1,11/5) -> (8/1,1/0) Glide Reflection Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(161,-360,72,-161) (20/9,9/4) -> (20/9,9/4) Reflection Matrix(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(89,-210,25,-59) (7/3,12/5) -> (7/2,18/5) Glide Reflection Matrix(49,-120,20,-49) (12/5,5/2) -> (12/5,5/2) Reflection Matrix(11,-30,4,-11) (5/2,3/1) -> (5/2,3/1) Reflection Matrix(19,-60,6,-19) (3/1,10/3) -> (3/1,10/3) Reflection Matrix(71,-240,21,-71) (10/3,24/7) -> (10/3,24/7) Reflection Matrix(61,-210,9,-31) (17/5,7/2) -> (13/2,7/1) Glide Reflection Matrix(199,-720,55,-199) (18/5,40/11) -> (18/5,40/11) Reflection Matrix(89,-330,24,-89) (11/3,15/4) -> (11/3,15/4) Reflection Matrix(31,-120,8,-31) (15/4,4/1) -> (15/4,4/1) Reflection Matrix(29,-120,7,-29) (4/1,30/7) -> (4/1,30/7) Reflection Matrix(181,-780,42,-181) (30/7,13/3) -> (30/7,13/3) Reflection Matrix(19,-90,4,-19) (9/2,5/1) -> (9/2,5/1) 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(29,-210,4,-29) (7/1,15/2) -> (7/1,15/2) Reflection Matrix(31,-240,4,-31) (15/2,8/1) -> (15/2,8/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(0,1,1,0) (0/1,2/1) -> (-1/1,1/1) Matrix(41,-90,5,-11) -> Matrix(4,3,3,2) Matrix(299,-660,82,-181) -> Matrix(3,2,-8,-5) -1/2 Matrix(161,-360,72,-161) -> Matrix(7,4,-12,-7) (20/9,9/4) -> (-2/3,-1/2) Matrix(79,-180,18,-41) -> Matrix(1,0,4,1) 0/1 Matrix(89,-210,25,-59) -> Matrix(2,1,1,0) Matrix(49,-120,20,-49) -> Matrix(-1,0,6,1) (12/5,5/2) -> (-1/3,0/1) Matrix(11,-30,4,-11) -> Matrix(-1,0,2,1) (5/2,3/1) -> (-1/1,0/1) Matrix(19,-60,6,-19) -> Matrix(1,0,4,-1) (3/1,10/3) -> (0/1,1/2) Matrix(71,-240,21,-71) -> Matrix(2,-1,3,-2) (10/3,24/7) -> (1/3,1/1) Matrix(61,-210,9,-31) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(199,-720,55,-199) -> Matrix(2,1,-3,-2) (18/5,40/11) -> (-1/1,-1/3) Matrix(89,-330,24,-89) -> Matrix(-1,0,6,1) (11/3,15/4) -> (-1/3,0/1) Matrix(31,-120,8,-31) -> Matrix(1,0,6,-1) (15/4,4/1) -> (0/1,1/3) Matrix(29,-120,7,-29) -> Matrix(2,-1,3,-2) (4/1,30/7) -> (1/3,1/1) Matrix(181,-780,42,-181) -> Matrix(1,0,4,-1) (30/7,13/3) -> (0/1,1/2) Matrix(19,-90,4,-19) -> Matrix(3,-2,4,-3) (9/2,5/1) -> (1/2,1/1) Matrix(11,-60,2,-11) -> Matrix(1,0,2,-1) (5/1,6/1) -> (0/1,1/1) Matrix(19,-120,3,-19) -> Matrix(2,-3,1,-2) (6/1,20/3) -> (1/1,3/1) Matrix(29,-210,4,-29) -> Matrix(1,0,2,-1) (7/1,15/2) -> (0/1,1/1) Matrix(31,-240,4,-31) -> Matrix(5,-6,4,-5) (15/2,8/1) -> (1/1,3/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.