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 4/3 3/2 5/3 20/11 2/1 5/2 8/3 30/11 20/7 3/1 10/3 7/2 15/4 4/1 5/1 11/2 6/1 20/3 15/2 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 0/1 1/0 -7/1 2/1 1/0 -6/1 -2/1 1/0 -11/2 -3/2 -1/1 -5/1 -1/1 -4/1 -1/1 0/1 -15/4 0/1 -11/3 -2/1 -1/1 -7/2 -1/1 0/1 -10/3 -1/1 -3/1 -1/2 0/1 -14/5 0/1 1/0 -11/4 -1/1 -1/2 -8/3 -1/2 0/1 -5/2 0/1 -2/1 -1/1 0/1 -11/6 -3/2 -1/1 -20/11 -1/1 -9/5 -1/1 -4/5 -7/4 -1/1 -2/3 -19/11 -2/3 -3/5 -31/18 -2/3 -1/2 -12/7 -2/3 -1/2 -5/3 -1/2 -8/5 -1/2 0/1 -19/12 -1/1 -1/2 -30/19 -1/2 -41/26 -1/2 0/1 -11/7 -1/1 0/1 -25/16 -2/3 -14/9 -2/3 -1/2 -17/11 -6/11 -1/2 -20/13 -1/2 -3/2 -1/2 -1/3 -10/7 -1/3 -7/5 -1/2 0/1 -32/23 -1/2 -2/5 -25/18 -2/5 -18/13 -2/5 -1/3 -11/8 -1/3 -1/4 -15/11 -1/3 -4/3 -1/3 0/1 -5/4 0/1 -6/5 -1/2 0/1 -13/11 -1/4 0/1 -20/17 0/1 -7/6 -1/1 0/1 -1/1 -1/3 0/1 0/1 0/1 1/1 0/1 1/3 7/6 0/1 1/1 6/5 0/1 1/2 5/4 0/1 4/3 0/1 1/3 15/11 1/3 11/8 1/4 1/3 18/13 1/3 2/5 25/18 2/5 7/5 0/1 1/2 10/7 1/3 3/2 1/3 1/2 14/9 1/2 2/3 11/7 0/1 1/1 8/5 0/1 1/2 5/3 1/2 12/7 1/2 2/3 31/18 1/2 2/3 19/11 3/5 2/3 7/4 2/3 1/1 9/5 4/5 1/1 20/11 1/1 11/6 1/1 3/2 2/1 0/1 1/1 5/2 0/1 8/3 0/1 1/2 19/7 0/1 1/1 49/18 0/1 1/2 30/11 1/2 11/4 1/2 1/1 14/5 0/1 1/0 17/6 -1/1 0/1 20/7 0/1 3/1 0/1 1/2 10/3 1/1 7/2 0/1 1/1 11/3 1/1 2/1 26/7 0/1 1/0 15/4 0/1 4/1 0/1 1/1 5/1 1/1 11/2 1/1 3/2 6/1 2/1 1/0 13/2 5/1 1/0 20/3 1/0 7/1 -2/1 1/0 15/2 0/1 8/1 0/1 1/0 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(31,260,18,151) (-8/1,1/0) -> (12/7,31/18) Hyperbolic Matrix(39,280,-28,-201) (-8/1,-7/1) -> (-7/5,-32/23) Hyperbolic Matrix(31,200,-20,-129) (-7/1,-6/1) -> (-14/9,-17/11) Hyperbolic Matrix(39,220,14,79) (-6/1,-11/2) -> (11/4,14/5) Hyperbolic Matrix(41,220,30,161) (-11/2,-5/1) -> (15/11,11/8) Hyperbolic Matrix(9,40,2,9) (-5/1,-4/1) -> (4/1,5/1) Hyperbolic Matrix(31,120,8,31) (-4/1,-15/4) -> (15/4,4/1) Hyperbolic Matrix(119,440,-76,-281) (-15/4,-11/3) -> (-11/7,-25/16) 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(31,100,22,71) (-10/3,-3/1) -> (7/5,10/7) Hyperbolic Matrix(71,200,-60,-169) (-3/1,-14/5) -> (-6/5,-13/11) Hyperbolic Matrix(79,220,14,39) (-14/5,-11/4) -> (11/2,6/1) Hyperbolic Matrix(89,240,-56,-151) (-11/4,-8/3) -> (-8/5,-19/12) Hyperbolic Matrix(31,80,12,31) (-8/3,-5/2) -> (5/2,8/3) Hyperbolic Matrix(9,20,4,9) (-5/2,-2/1) -> (2/1,5/2) Hyperbolic Matrix(119,220,86,159) (-2/1,-11/6) -> (11/8,18/13) Hyperbolic Matrix(241,440,132,241) (-11/6,-20/11) -> (20/11,11/6) Hyperbolic Matrix(199,360,110,199) (-20/11,-9/5) -> (9/5,20/11) Hyperbolic Matrix(79,140,22,39) (-9/5,-7/4) -> (7/2,11/3) Hyperbolic Matrix(81,140,70,121) (-7/4,-19/11) -> (1/1,7/6) Hyperbolic Matrix(649,1120,-412,-711) (-19/11,-31/18) -> (-41/26,-11/7) Hyperbolic Matrix(151,260,18,31) (-31/18,-12/7) -> (8/1,1/0) Hyperbolic Matrix(71,120,42,71) (-12/7,-5/3) -> (5/3,12/7) Hyperbolic Matrix(49,80,30,49) (-5/3,-8/5) -> (8/5,5/3) Hyperbolic Matrix(569,900,208,329) (-19/12,-30/19) -> (30/11,11/4) Hyperbolic Matrix(1711,2700,628,991) (-30/19,-41/26) -> (49/18,30/11) Hyperbolic Matrix(551,860,148,231) (-25/16,-14/9) -> (26/7,15/4) Hyperbolic Matrix(311,480,46,71) (-17/11,-20/13) -> (20/3,7/1) Hyperbolic Matrix(209,320,32,49) (-20/13,-3/2) -> (13/2,20/3) Hyperbolic Matrix(41,60,28,41) (-3/2,-10/7) -> (10/7,3/2) Hyperbolic Matrix(71,100,22,31) (-10/7,-7/5) -> (3/1,10/3) Hyperbolic Matrix(489,680,64,89) (-32/23,-25/18) -> (15/2,8/1) Hyperbolic Matrix(649,900,468,649) (-25/18,-18/13) -> (18/13,25/18) Hyperbolic Matrix(159,220,86,119) (-18/13,-11/8) -> (11/6,2/1) Hyperbolic Matrix(161,220,30,41) (-11/8,-15/11) -> (5/1,11/2) Hyperbolic Matrix(89,120,66,89) (-15/11,-4/3) -> (4/3,15/11) Hyperbolic Matrix(31,40,24,31) (-4/3,-5/4) -> (5/4,4/3) Hyperbolic Matrix(49,60,40,49) (-5/4,-6/5) -> (6/5,5/4) Hyperbolic Matrix(271,320,94,111) (-13/11,-20/17) -> (20/7,3/1) Hyperbolic Matrix(409,480,144,169) (-20/17,-7/6) -> (17/6,20/7) 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(169,-200,60,-71) (7/6,6/5) -> (14/5,17/6) Hyperbolic Matrix(201,-280,28,-39) (25/18,7/5) -> (7/1,15/2) Hyperbolic Matrix(129,-200,20,-31) (3/2,14/9) -> (6/1,13/2) Hyperbolic Matrix(281,-440,76,-119) (14/9,11/7) -> (11/3,26/7) Hyperbolic Matrix(151,-240,56,-89) (11/7,8/5) -> (8/3,19/7) Hyperbolic Matrix(881,-1520,324,-559) (31/18,19/11) -> (19/7,49/18) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(31,260,18,151) -> Matrix(1,-2,2,-3) Matrix(39,280,-28,-201) -> Matrix(1,-2,-2,5) Matrix(31,200,-20,-129) -> Matrix(1,4,-2,-7) Matrix(39,220,14,79) -> Matrix(1,2,0,1) Matrix(41,220,30,161) -> Matrix(1,2,2,5) Matrix(9,40,2,9) -> Matrix(1,0,2,1) Matrix(31,120,8,31) -> Matrix(1,0,2,1) Matrix(119,440,-76,-281) -> Matrix(1,2,-2,-3) Matrix(39,140,22,79) -> Matrix(3,2,4,3) Matrix(41,140,12,41) -> Matrix(1,0,2,1) Matrix(31,100,22,71) -> Matrix(1,0,4,1) Matrix(71,200,-60,-169) -> Matrix(1,0,-2,1) Matrix(79,220,14,39) -> Matrix(1,2,0,1) Matrix(89,240,-56,-151) -> Matrix(1,0,0,1) Matrix(31,80,12,31) -> Matrix(1,0,4,1) Matrix(9,20,4,9) -> Matrix(1,0,2,1) Matrix(119,220,86,159) -> Matrix(1,2,2,5) Matrix(241,440,132,241) -> Matrix(5,6,4,5) Matrix(199,360,110,199) -> Matrix(9,8,10,9) Matrix(79,140,22,39) -> Matrix(3,2,4,3) Matrix(81,140,70,121) -> Matrix(3,2,4,3) Matrix(649,1120,-412,-711) -> Matrix(3,2,-8,-5) Matrix(151,260,18,31) -> Matrix(3,2,-2,-1) Matrix(71,120,42,71) -> Matrix(7,4,12,7) Matrix(49,80,30,49) -> Matrix(1,0,4,1) Matrix(569,900,208,329) -> Matrix(3,2,4,3) Matrix(1711,2700,628,991) -> Matrix(1,0,4,1) Matrix(551,860,148,231) -> Matrix(3,2,-2,-1) Matrix(311,480,46,71) -> Matrix(15,8,-2,-1) Matrix(209,320,32,49) -> Matrix(13,6,2,1) Matrix(41,60,28,41) -> Matrix(5,2,12,5) Matrix(71,100,22,31) -> Matrix(1,0,4,1) Matrix(489,680,64,89) -> Matrix(5,2,2,1) Matrix(649,900,468,649) -> Matrix(11,4,30,11) Matrix(159,220,86,119) -> Matrix(5,2,2,1) Matrix(161,220,30,41) -> Matrix(5,2,2,1) Matrix(89,120,66,89) -> Matrix(1,0,6,1) Matrix(31,40,24,31) -> Matrix(1,0,6,1) Matrix(49,60,40,49) -> Matrix(1,0,4,1) Matrix(271,320,94,111) -> Matrix(1,0,6,1) Matrix(409,480,144,169) -> Matrix(1,0,0,1) Matrix(121,140,70,81) -> Matrix(3,2,4,3) Matrix(1,0,2,1) -> Matrix(1,0,6,1) Matrix(169,-200,60,-71) -> Matrix(1,0,-2,1) Matrix(201,-280,28,-39) -> Matrix(5,-2,-2,1) Matrix(129,-200,20,-31) -> Matrix(7,-4,2,-1) Matrix(281,-440,76,-119) -> Matrix(3,-2,2,-1) Matrix(151,-240,56,-89) -> Matrix(1,0,0,1) Matrix(881,-1520,324,-559) -> Matrix(3,-2,8,-5) 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): 10 Degree of the the map X: 10 Degree of the the map Y: 48 Permutation triple for Y: ((2,6,21,34,38,31,12,4,3,7)(5,15,14,35,17)(8,24,28,10,9)(11,30,13,19,22)(16,37,27,26,33,40,39,25,29,36)(18,23)(20,32,44,45,42)(41,48); (1,4,15,36,42,41,19,40,24,31,43,21,28,33,30,48,32,16,5,2)(3,10,18,17,38,44,39,46,26,45,34,14,23,8,7,22,37,47,29,11)(6,13,12,20)(9,27,35,25); (1,2,8,25,44,48,42,26,9,3)(4,13,33,46,39,19,6,5,18,14)(7,11)(10,21,20,36,47,37,32,12,24,23)(15,16)(17,27,22,41,30,29,35,34,43,31)(28,40)(38,45)) ----------------------------------------------------------------------- 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: 12 Genus: 7 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/1 4/3 3/2 20/11 2/1 5/2 10/3 15/4 4/1 5/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -5/1 -1/1 -4/1 -1/1 0/1 -15/4 0/1 -11/3 -2/1 -1/1 -7/2 -1/1 0/1 -10/3 -1/1 -3/1 -1/2 0/1 -5/2 0/1 -2/1 -1/1 0/1 -11/6 -3/2 -1/1 -20/11 -1/1 -9/5 -1/1 -4/5 -7/4 -1/1 -2/3 -5/3 -1/2 -8/5 -1/2 0/1 -3/2 -1/2 -1/3 -10/7 -1/3 -7/5 -1/2 0/1 -25/18 -2/5 -18/13 -2/5 -1/3 -11/8 -1/3 -1/4 -4/3 -1/3 0/1 -5/4 0/1 -1/1 -1/3 0/1 0/1 0/1 1/1 0/1 1/3 4/3 0/1 1/3 7/5 0/1 1/2 10/7 1/3 3/2 1/3 1/2 14/9 1/2 2/3 11/7 0/1 1/1 8/5 0/1 1/2 5/3 1/2 7/4 2/3 1/1 9/5 4/5 1/1 20/11 1/1 11/6 1/1 3/2 2/1 0/1 1/1 5/2 0/1 8/3 0/1 1/2 3/1 0/1 1/2 10/3 1/1 7/2 0/1 1/1 11/3 1/1 2/1 26/7 0/1 1/0 15/4 0/1 4/1 0/1 1/1 5/1 1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(7,40,4,23) (-5/1,1/0) -> (5/3,7/4) Hyperbolic Matrix(9,40,2,9) (-5/1,-4/1) -> (4/1,5/1) Hyperbolic Matrix(31,120,8,31) (-4/1,-15/4) -> (15/4,4/1) Hyperbolic Matrix(103,380,-74,-273) (-15/4,-11/3) -> (-7/5,-25/18) 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(31,100,22,71) (-10/3,-3/1) -> (7/5,10/7) Hyperbolic Matrix(7,20,-6,-17) (-3/1,-5/2) -> (-5/4,-1/1) Hyperbolic Matrix(9,20,4,9) (-5/2,-2/1) -> (2/1,5/2) Hyperbolic Matrix(87,160,56,103) (-2/1,-11/6) -> (3/2,14/9) Hyperbolic Matrix(241,440,132,241) (-11/6,-20/11) -> (20/11,11/6) Hyperbolic Matrix(199,360,110,199) (-20/11,-9/5) -> (9/5,20/11) Hyperbolic Matrix(79,140,22,39) (-9/5,-7/4) -> (7/2,11/3) Hyperbolic Matrix(23,40,4,7) (-7/4,-5/3) -> (5/1,1/0) Hyperbolic Matrix(49,80,30,49) (-5/3,-8/5) -> (8/5,5/3) Hyperbolic Matrix(63,100,-46,-73) (-8/5,-3/2) -> (-11/8,-4/3) Hyperbolic Matrix(41,60,28,41) (-3/2,-10/7) -> (10/7,3/2) Hyperbolic Matrix(71,100,22,31) (-10/7,-7/5) -> (3/1,10/3) Hyperbolic Matrix(663,920,178,247) (-25/18,-18/13) -> (26/7,15/4) Hyperbolic Matrix(159,220,86,119) (-18/13,-11/8) -> (11/6,2/1) Hyperbolic Matrix(47,60,18,23) (-4/3,-5/4) -> (5/2,8/3) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(17,-20,6,-7) (1/1,4/3) -> (8/3,3/1) Hyperbolic Matrix(73,-100,46,-63) (4/3,7/5) -> (11/7,8/5) Hyperbolic Matrix(281,-440,76,-119) (14/9,11/7) -> (11/3,26/7) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(7,40,4,23) -> Matrix(1,2,1,3) Matrix(9,40,2,9) -> Matrix(1,0,2,1) Matrix(31,120,8,31) -> Matrix(1,0,2,1) Matrix(103,380,-74,-273) -> Matrix(1,2,-3,-5) Matrix(39,140,22,79) -> Matrix(3,2,4,3) Matrix(41,140,12,41) -> Matrix(1,0,2,1) Matrix(31,100,22,71) -> Matrix(1,0,4,1) Matrix(7,20,-6,-17) -> Matrix(1,0,-1,1) Matrix(9,20,4,9) -> Matrix(1,0,2,1) Matrix(87,160,56,103) -> Matrix(1,2,1,3) Matrix(241,440,132,241) -> Matrix(5,6,4,5) Matrix(199,360,110,199) -> Matrix(9,8,10,9) Matrix(79,140,22,39) -> Matrix(3,2,4,3) Matrix(23,40,4,7) -> Matrix(3,2,1,1) Matrix(49,80,30,49) -> Matrix(1,0,4,1) Matrix(63,100,-46,-73) -> Matrix(1,0,-1,1) Matrix(41,60,28,41) -> Matrix(5,2,12,5) Matrix(71,100,22,31) -> Matrix(1,0,4,1) Matrix(663,920,178,247) -> Matrix(5,2,-3,-1) Matrix(159,220,86,119) -> Matrix(5,2,2,1) Matrix(47,60,18,23) -> Matrix(1,0,5,1) Matrix(1,0,2,1) -> Matrix(1,0,6,1) Matrix(17,-20,6,-7) -> Matrix(1,0,-1,1) Matrix(73,-100,46,-63) -> Matrix(1,0,-1,1) Matrix(281,-440,76,-119) -> Matrix(3,-2,2,-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): 10 ----------------------------------------------------------------------- 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 3 1 1/1 (0/1,1/3) 0 20 4/3 (0/1,1/3) 0 5 7/5 (0/1,1/2) 0 20 10/7 1/3 1 2 3/2 (1/3,1/2) 0 20 14/9 (1/2,2/3) 0 10 11/7 (0/1,1/1) 0 20 8/5 (0/1,1/2) 0 5 5/3 1/2 2 4 7/4 (2/3,1/1) 0 20 9/5 (4/5,1/1) 0 20 20/11 1/1 7 1 11/6 (1/1,3/2) 0 20 2/1 (0/1,1/1) 0 10 5/2 0/1 2 4 8/3 (0/1,1/2) 0 5 3/1 (0/1,1/2) 0 20 10/3 1/1 1 2 7/2 (0/1,1/1) 0 20 11/3 (1/1,2/1) 0 20 26/7 (0/1,1/0) 0 10 15/4 0/1 2 4 4/1 (0/1,1/1) 0 5 5/1 1/1 2 4 1/0 (0/1,1/0) 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(17,-20,6,-7) (1/1,4/3) -> (8/3,3/1) Hyperbolic Matrix(73,-100,46,-63) (4/3,7/5) -> (11/7,8/5) Hyperbolic Matrix(71,-100,22,-31) (7/5,10/7) -> (3/1,10/3) Glide Reflection Matrix(41,-60,28,-41) (10/7,3/2) -> (10/7,3/2) Reflection Matrix(103,-160,56,-87) (3/2,14/9) -> (11/6,2/1) Glide Reflection Matrix(281,-440,76,-119) (14/9,11/7) -> (11/3,26/7) Hyperbolic Matrix(49,-80,30,-49) (8/5,5/3) -> (8/5,5/3) Reflection Matrix(23,-40,4,-7) (5/3,7/4) -> (5/1,1/0) Glide Reflection Matrix(79,-140,22,-39) (7/4,9/5) -> (7/2,11/3) Glide Reflection Matrix(199,-360,110,-199) (9/5,20/11) -> (9/5,20/11) Reflection Matrix(241,-440,132,-241) (20/11,11/6) -> (20/11,11/6) Reflection Matrix(9,-20,4,-9) (2/1,5/2) -> (2/1,5/2) Reflection Matrix(31,-80,12,-31) (5/2,8/3) -> (5/2,8/3) Reflection Matrix(41,-140,12,-41) (10/3,7/2) -> (10/3,7/2) Reflection Matrix(209,-780,56,-209) (26/7,15/4) -> (26/7,15/4) Reflection Matrix(31,-120,8,-31) (15/4,4/1) -> (15/4,4/1) Reflection Matrix(9,-40,2,-9) (4/1,5/1) -> (4/1,5/1) 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(1,0,2,-1) -> Matrix(1,0,6,-1) (0/1,1/1) -> (0/1,1/3) Matrix(17,-20,6,-7) -> Matrix(1,0,-1,1) 0/1 Matrix(73,-100,46,-63) -> Matrix(1,0,-1,1) 0/1 Matrix(71,-100,22,-31) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(41,-60,28,-41) -> Matrix(5,-2,12,-5) (10/7,3/2) -> (1/3,1/2) Matrix(103,-160,56,-87) -> Matrix(3,-2,1,-1) Matrix(281,-440,76,-119) -> Matrix(3,-2,2,-1) 1/1 Matrix(49,-80,30,-49) -> Matrix(1,0,4,-1) (8/5,5/3) -> (0/1,1/2) Matrix(23,-40,4,-7) -> Matrix(3,-2,1,-1) Matrix(79,-140,22,-39) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(199,-360,110,-199) -> Matrix(9,-8,10,-9) (9/5,20/11) -> (4/5,1/1) Matrix(241,-440,132,-241) -> Matrix(5,-6,4,-5) (20/11,11/6) -> (1/1,3/2) Matrix(9,-20,4,-9) -> Matrix(1,0,2,-1) (2/1,5/2) -> (0/1,1/1) Matrix(31,-80,12,-31) -> Matrix(1,0,4,-1) (5/2,8/3) -> (0/1,1/2) Matrix(41,-140,12,-41) -> Matrix(1,0,2,-1) (10/3,7/2) -> (0/1,1/1) Matrix(209,-780,56,-209) -> Matrix(1,0,0,-1) (26/7,15/4) -> (0/1,1/0) Matrix(31,-120,8,-31) -> Matrix(1,0,2,-1) (15/4,4/1) -> (0/1,1/1) Matrix(9,-40,2,-9) -> Matrix(1,0,2,-1) (4/1,5/1) -> (0/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.