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 1/0 -6/1 1/1 -5/1 1/0 -9/2 -3/1 -4/1 -2/1 -1/1 -15/4 -1/1 -11/3 -1/1 -2/3 -7/2 -1/1 0/1 -10/3 1/0 -3/1 -1/1 -5/2 -1/1 0/1 -12/5 -1/1 -7/3 -1/2 0/1 -16/7 0/1 1/1 -9/4 -1/1 -20/9 -1/2 -11/5 -1/3 0/1 -2/1 0/1 1/0 -15/8 -1/1 1/1 -13/7 0/1 1/0 -11/6 0/1 1/0 -20/11 1/0 -9/5 -1/1 -7/4 0/1 1/1 -19/11 1/1 2/1 -12/7 1/1 -5/3 1/0 -3/2 -1/1 -10/7 -1/2 -17/12 -1/3 0/1 -7/5 -1/2 0/1 -18/13 -1/1 -29/21 -1/1 -2/3 -40/29 -1/2 -11/8 -1/2 0/1 -15/11 0/1 -4/3 -1/1 0/1 -17/13 -1/4 0/1 -30/23 0/1 -13/10 0/1 1/1 -9/7 -1/1 -5/4 -1/1 0/1 -6/5 -1/1 -13/11 -1/2 0/1 -7/6 -1/3 0/1 -15/13 0/1 -8/7 0/1 1/2 -1/1 -1/1 0/1 0/1 0/1 1/1 0/1 1/1 7/6 0/1 1/3 6/5 1/1 5/4 0/1 1/1 9/7 1/1 4/3 0/1 1/1 15/11 0/1 11/8 0/1 1/2 7/5 0/1 1/2 10/7 1/2 3/2 1/1 5/3 1/0 12/7 -1/1 7/4 -1/1 0/1 16/9 0/1 1/1 9/5 1/1 20/11 1/0 11/6 0/1 1/0 2/1 0/1 1/0 15/7 0/1 13/6 0/1 1/5 11/5 0/1 1/3 20/9 1/2 9/4 1/1 7/3 0/1 1/2 19/8 0/1 1/2 12/5 1/1 5/2 0/1 1/1 3/1 1/1 10/3 1/0 17/5 0/1 1/0 7/2 0/1 1/1 18/5 1/1 29/8 0/1 1/2 40/11 1/2 11/3 2/3 1/1 15/4 1/1 4/1 1/1 2/1 17/4 5/3 2/1 30/7 2/1 13/3 2/1 5/2 9/2 3/1 5/1 1/0 6/1 -1/1 13/2 0/1 1/1 7/1 0/1 1/0 15/2 -1/1 1/1 8/1 0/1 1/0 1/0 0/1 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(1,0,0,1) Matrix(19,120,-16,-101) -> Matrix(1,0,-2,1) Matrix(11,60,2,11) -> Matrix(1,-2,0,1) Matrix(19,90,4,19) -> Matrix(1,6,0,1) Matrix(41,180,-18,-79) -> Matrix(1,2,0,1) Matrix(31,120,8,31) -> Matrix(3,4,2,3) Matrix(89,330,24,89) -> Matrix(5,4,6,5) Matrix(59,210,-34,-121) -> Matrix(1,0,2,1) Matrix(71,240,-50,-169) -> Matrix(1,0,-2,1) Matrix(19,60,6,19) -> Matrix(1,2,0,1) Matrix(11,30,4,11) -> Matrix(1,0,2,1) Matrix(49,120,20,49) -> Matrix(1,0,2,1) Matrix(89,210,-64,-151) -> Matrix(1,0,0,1) Matrix(131,300,-100,-229) -> Matrix(1,0,-2,1) Matrix(161,360,72,161) -> Matrix(3,2,4,3) Matrix(461,1020,-334,-739) -> Matrix(5,2,-8,-3) Matrix(41,90,-36,-79) -> Matrix(1,0,2,1) Matrix(79,150,10,19) -> Matrix(1,0,0,1) Matrix(161,300,22,41) -> Matrix(1,0,0,1) Matrix(361,660,-262,-479) -> Matrix(1,0,-2,1) Matrix(199,360,110,199) -> Matrix(1,2,0,1) Matrix(101,180,-78,-139) -> Matrix(1,0,0,1) Matrix(401,690,-290,-499) -> Matrix(1,0,-2,1) Matrix(71,120,42,71) -> Matrix(1,-2,0,1) Matrix(19,30,12,19) -> Matrix(1,2,0,1) Matrix(41,60,28,41) -> Matrix(3,2,4,3) Matrix(191,270,-162,-229) -> Matrix(1,0,0,1) Matrix(241,330,176,241) -> Matrix(1,0,4,1) Matrix(89,120,66,89) -> Matrix(1,0,2,1) Matrix(689,900,160,209) -> Matrix(13,2,6,1) Matrix(691,900,162,211) -> Matrix(7,-2,4,-1) Matrix(71,90,56,71) -> Matrix(1,0,2,1) Matrix(49,60,40,49) -> Matrix(1,0,2,1) Matrix(259,300,120,139) -> Matrix(1,0,8,1) Matrix(131,150,62,71) -> Matrix(1,0,-2,1) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(79,-90,36,-41) -> Matrix(1,0,2,1) Matrix(101,-120,16,-19) -> Matrix(1,0,-2,1) Matrix(139,-180,78,-101) -> Matrix(1,0,0,1) Matrix(151,-210,64,-89) -> Matrix(1,0,0,1) Matrix(169,-240,50,-71) -> Matrix(1,0,-2,1) Matrix(121,-210,34,-59) -> Matrix(1,0,2,1) Matrix(169,-300,40,-71) -> Matrix(3,-2,2,-1) Matrix(559,-1020,154,-281) -> Matrix(1,0,2,1) Matrix(49,-90,6,-11) -> Matrix(1,0,0,1) Matrix(299,-660,82,-181) -> Matrix(5,-2,8,-3) Matrix(79,-180,18,-41) -> Matrix(1,2,0,1) Matrix(289,-690,80,-191) -> Matrix(1,0,0,1) Matrix(79,-270,12,-41) -> Matrix(1,0,0,1) 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 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: ((2,6,20,43,45,34,12,4,3,11,33,48,38,21,7)(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 1/1 5/4 3/2 5/3 2/1 15/7 5/2 3/1 7/2 15/4 9/2 5/1 6/1 15/2 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -6/1 1/1 -5/1 1/0 -9/2 -3/1 -4/1 -2/1 -1/1 -7/2 -1/1 0/1 -3/1 -1/1 -5/2 -1/1 0/1 -2/1 0/1 1/0 -9/5 -1/1 -7/4 0/1 1/1 -5/3 1/0 -3/2 -1/1 -1/1 -1/1 0/1 0/1 0/1 1/1 0/1 1/1 7/6 0/1 1/3 6/5 1/1 5/4 0/1 1/1 9/7 1/1 4/3 0/1 1/1 3/2 1/1 5/3 1/0 12/7 -1/1 7/4 -1/1 0/1 16/9 0/1 1/1 9/5 1/1 11/6 0/1 1/0 2/1 0/1 1/0 15/7 0/1 13/6 0/1 1/5 11/5 0/1 1/3 9/4 1/1 7/3 0/1 1/2 5/2 0/1 1/1 3/1 1/1 10/3 1/0 7/2 0/1 1/1 11/3 2/3 1/1 15/4 1/1 4/1 1/1 2/1 17/4 5/3 2/1 30/7 2/1 13/3 2/1 5/2 9/2 3/1 5/1 1/0 6/1 -1/1 7/1 0/1 1/0 15/2 -1/1 1/1 8/1 0/1 1/0 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,75,6,41) (-6/1,1/0) -> (9/5,11/6) 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(31,135,14,61) (-9/2,-4/1) -> (11/5,9/4) Hyperbolic Matrix(29,105,8,29) (-4/1,-7/2) -> (7/2,11/3) Hyperbolic Matrix(31,105,18,61) (-7/2,-3/1) -> (12/7,7/4) Hyperbolic Matrix(11,30,4,11) (-3/1,-5/2) -> (5/2,3/1) Hyperbolic Matrix(19,45,8,19) (-5/2,-2/1) -> (7/3,5/2) Hyperbolic Matrix(41,75,6,11) (-2/1,-9/5) -> (6/1,7/1) Hyperbolic Matrix(59,105,50,89) (-9/5,-7/4) -> (7/6,6/5) Hyperbolic Matrix(61,105,18,31) (-7/4,-5/3) -> (10/3,7/2) Hyperbolic Matrix(19,30,12,19) (-5/3,-3/2) -> (3/2,5/3) Hyperbolic Matrix(11,15,8,11) (-3/2,-1/1) -> (4/3,3/2) 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(61,-75,48,-59) (6/5,5/4) -> (5/4,9/7) Parabolic Matrix(139,-180,78,-101) (9/7,4/3) -> (16/9,9/5) Hyperbolic Matrix(79,-135,24,-41) (5/3,12/7) -> (3/1,10/3) Hyperbolic Matrix(169,-300,40,-71) (7/4,16/9) -> (4/1,17/4) Hyperbolic Matrix(49,-90,6,-11) (11/6,2/1) -> (8/1,1/0) Hyperbolic Matrix(121,-255,28,-59) (2/1,15/7) -> (30/7,13/3) Hyperbolic Matrix(299,-645,70,-151) (15/7,13/6) -> (17/4,30/7) Hyperbolic Matrix(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(61,-225,16,-59) (11/3,15/4) -> (15/4,4/1) Parabolic Matrix(31,-225,4,-29) (7/1,15/2) -> (15/2,8/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(11,75,6,41) -> Matrix(1,0,0,1) Matrix(11,60,2,11) -> Matrix(1,-2,0,1) Matrix(19,90,4,19) -> Matrix(1,6,0,1) Matrix(31,135,14,61) -> Matrix(1,2,2,5) Matrix(29,105,8,29) -> Matrix(1,0,2,1) Matrix(31,105,18,61) -> Matrix(1,0,0,1) Matrix(11,30,4,11) -> Matrix(1,0,2,1) Matrix(19,45,8,19) -> Matrix(1,0,2,1) Matrix(41,75,6,11) -> Matrix(1,0,0,1) Matrix(59,105,50,89) -> Matrix(1,0,2,1) Matrix(61,105,18,31) -> Matrix(1,0,0,1) Matrix(19,30,12,19) -> Matrix(1,2,0,1) Matrix(11,15,8,11) -> Matrix(1,0,2,1) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(79,-90,36,-41) -> Matrix(1,0,2,1) Matrix(61,-75,48,-59) -> Matrix(1,0,0,1) Matrix(139,-180,78,-101) -> Matrix(1,0,0,1) Matrix(79,-135,24,-41) -> Matrix(1,2,0,1) Matrix(169,-300,40,-71) -> Matrix(3,-2,2,-1) Matrix(49,-90,6,-11) -> Matrix(1,0,0,1) Matrix(121,-255,28,-59) -> Matrix(5,2,2,1) Matrix(299,-645,70,-151) -> Matrix(15,-2,8,-1) Matrix(79,-180,18,-41) -> Matrix(1,2,0,1) Matrix(61,-225,16,-59) -> Matrix(5,-4,4,-3) Matrix(31,-225,4,-29) -> Matrix(1,0,0,1) 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 1 1 1/1 (0/1,1/1) 0 15 6/5 1/1 1 5 5/4 (0/1,1/1) 0 3 3/2 1/1 2 5 5/3 1/0 2 3 7/4 (-1/1,0/1) 0 15 16/9 (0/1,1/1) 0 15 9/5 1/1 1 5 2/1 (0/1,1/0) 0 15 9/4 1/1 2 5 5/2 (0/1,1/1) 0 3 3/1 1/1 1 5 10/3 1/0 2 3 7/2 (0/1,1/1) 0 15 15/4 1/1 4 1 4/1 (1/1,2/1) 0 15 17/4 (5/3,2/1) 0 15 30/7 2/1 5 1 13/3 (2/1,5/2) 0 15 9/2 3/1 2 5 5/1 1/0 4 3 6/1 -1/1 1 5 7/1 (0/1,1/0) 0 15 15/2 (0/1,1/0) 0 1 1/0 (0/1,1/0) 0 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(89,-105,50,-59) (1/1,6/5) -> (16/9,9/5) Glide Reflection Matrix(49,-60,40,-49) (6/5,5/4) -> (6/5,5/4) Reflection Matrix(11,-15,8,-11) (5/4,3/2) -> (5/4,3/2) Reflection Matrix(19,-30,12,-19) (3/2,5/3) -> (3/2,5/3) Reflection Matrix(61,-105,18,-31) (5/3,7/4) -> (10/3,7/2) Glide Reflection Matrix(169,-300,40,-71) (7/4,16/9) -> (4/1,17/4) Hyperbolic Matrix(41,-75,6,-11) (9/5,2/1) -> (6/1,7/1) Glide Reflection Matrix(61,-135,14,-31) (2/1,9/4) -> (13/3,9/2) Glide Reflection Matrix(19,-45,8,-19) (9/4,5/2) -> (9/4,5/2) 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(29,-105,8,-29) (7/2,15/4) -> (7/2,15/4) Reflection Matrix(31,-120,8,-31) (15/4,4/1) -> (15/4,4/1) Reflection Matrix(239,-1020,56,-239) (17/4,30/7) -> (17/4,30/7) 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(29,-210,4,-29) (7/1,15/2) -> (7/1,15/2) Reflection Matrix(-1,15,0,1) (15/2,1/0) -> (15/2,1/0) 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(1,0,2,-1) -> Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Matrix(89,-105,50,-59) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(49,-60,40,-49) -> Matrix(1,0,2,-1) (6/5,5/4) -> (0/1,1/1) Matrix(11,-15,8,-11) -> Matrix(1,0,2,-1) (5/4,3/2) -> (0/1,1/1) Matrix(19,-30,12,-19) -> Matrix(-1,2,0,1) (3/2,5/3) -> (1/1,1/0) Matrix(61,-105,18,-31) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(169,-300,40,-71) -> Matrix(3,-2,2,-1) 1/1 Matrix(41,-75,6,-11) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(61,-135,14,-31) -> Matrix(5,-2,2,-1) Matrix(19,-45,8,-19) -> Matrix(1,0,2,-1) (9/4,5/2) -> (0/1,1/1) Matrix(11,-30,4,-11) -> Matrix(1,0,2,-1) (5/2,3/1) -> (0/1,1/1) Matrix(19,-60,6,-19) -> Matrix(-1,2,0,1) (3/1,10/3) -> (1/1,1/0) Matrix(29,-105,8,-29) -> Matrix(1,0,2,-1) (7/2,15/4) -> (0/1,1/1) Matrix(31,-120,8,-31) -> Matrix(3,-4,2,-3) (15/4,4/1) -> (1/1,2/1) Matrix(239,-1020,56,-239) -> Matrix(11,-20,6,-11) (17/4,30/7) -> (5/3,2/1) Matrix(181,-780,42,-181) -> Matrix(9,-20,4,-9) (30/7,13/3) -> (2/1,5/2) Matrix(19,-90,4,-19) -> Matrix(-1,6,0,1) (9/2,5/1) -> (3/1,1/0) Matrix(11,-60,2,-11) -> Matrix(1,2,0,-1) (5/1,6/1) -> (-1/1,1/0) Matrix(29,-210,4,-29) -> Matrix(1,0,0,-1) (7/1,15/2) -> (0/1,1/0) Matrix(-1,15,0,1) -> Matrix(1,0,0,-1) (15/2,1/0) -> (0/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.