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 5/38 -6/1 2/15 4/29 -5/1 1/7 -14/3 4/27 2/13 -9/2 1/7 -4/1 2/13 -11/3 1/6 -7/2 3/19 -10/3 1/6 -3/1 1/6 -14/5 2/11 4/21 -11/4 1/5 -30/11 1/5 -19/7 5/24 -8/3 0/1 -5/2 1/5 -12/5 2/9 -19/8 3/11 -7/3 1/6 -9/4 1/5 -2/1 0/1 2/9 -11/6 1/5 -20/11 2/9 -9/5 1/4 -7/4 1/3 -5/3 1/4 -13/8 3/11 -21/13 5/16 -8/5 0/1 -19/12 5/21 -30/19 1/4 -11/7 1/4 -14/9 4/15 2/7 -17/11 5/18 -20/13 2/7 -3/2 1/3 -10/7 1/3 -7/5 3/8 -11/8 1/3 -4/3 2/5 -9/7 1/2 -5/4 1/2 -11/9 1/2 -6/5 4/7 2/3 -13/11 9/14 -20/17 2/3 -7/6 5/7 -1/1 1/0 0/1 0/1 1/1 1/18 7/6 5/83 6/5 2/33 4/65 5/4 1/16 14/11 4/63 2/31 9/7 1/16 4/3 2/31 11/8 1/15 7/5 3/46 10/7 1/15 3/2 1/15 14/9 2/29 4/57 11/7 1/14 30/19 1/14 19/12 5/69 8/5 0/1 5/3 1/14 12/7 2/27 19/11 3/38 7/4 1/15 9/5 1/14 2/1 0/1 2/27 11/5 1/14 20/9 2/27 9/4 1/13 7/3 1/12 5/2 1/13 13/5 3/38 21/8 5/61 8/3 0/1 19/7 5/66 30/11 1/13 11/4 1/13 14/5 4/51 2/25 17/6 5/63 20/7 2/25 3/1 1/12 10/3 1/12 7/2 3/35 11/3 1/12 4/1 2/23 9/2 1/11 5/1 1/11 11/2 1/11 6/1 4/43 2/21 13/2 9/95 20/3 2/21 7/1 5/52 1/0 1/9 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(31,-4,380,-49) Matrix(19,120,-16,-101) -> Matrix(59,-8,96,-13) Matrix(19,100,-4,-21) -> Matrix(43,-6,294,-41) Matrix(61,280,22,101) -> Matrix(1,0,6,1) Matrix(19,80,14,59) -> Matrix(27,-4,412,-61) Matrix(21,80,16,61) -> Matrix(25,-4,394,-63) Matrix(39,140,22,79) -> Matrix(13,-2,176,-27) Matrix(41,140,12,41) -> Matrix(37,-6,438,-71) Matrix(19,60,6,19) -> Matrix(11,-2,138,-25) Matrix(99,280,-64,-181) -> Matrix(43,-8,156,-29) Matrix(79,220,14,39) -> Matrix(31,-6,336,-65) Matrix(241,660,88,241) -> Matrix(31,-6,398,-77) Matrix(419,1140,154,419) -> Matrix(49,-10,642,-131) Matrix(141,380,82,221) -> Matrix(9,-2,122,-27) Matrix(39,100,-16,-41) -> Matrix(11,-2,50,-9) Matrix(159,380,100,239) -> Matrix(9,-2,122,-27) Matrix(59,140,8,19) -> Matrix(7,-2,74,-21) Matrix(61,140,44,101) -> Matrix(9,-2,140,-31) Matrix(19,40,-10,-21) -> Matrix(1,0,0,1) Matrix(219,400,98,179) -> Matrix(19,-4,252,-53) Matrix(221,400,100,181) -> Matrix(17,-4,234,-55) Matrix(79,140,22,39) -> Matrix(9,-2,104,-23) Matrix(59,100,-36,-61) -> Matrix(9,-2,32,-7) Matrix(99,160,86,139) -> Matrix(13,-4,218,-67) Matrix(199,320,74,119) -> Matrix(1,0,10,1) Matrix(201,320,76,121) -> Matrix(1,0,8,1) Matrix(721,1140,456,721) -> Matrix(41,-10,570,-139) Matrix(419,660,266,419) -> Matrix(23,-6,326,-85) Matrix(179,280,140,219) -> Matrix(1,0,12,1) Matrix(259,400,90,139) -> Matrix(43,-12,534,-149) Matrix(261,400,92,141) -> Matrix(41,-12,516,-151) Matrix(41,60,28,41) -> Matrix(7,-2,102,-29) Matrix(99,140,70,99) -> Matrix(17,-6,258,-91) Matrix(101,140,44,61) -> Matrix(5,-2,68,-27) Matrix(59,80,14,19) -> Matrix(11,-4,124,-45) Matrix(61,80,16,21) -> Matrix(9,-4,106,-47) Matrix(79,100,-64,-81) -> Matrix(13,-6,24,-11) Matrix(181,220,116,141) -> Matrix(11,-6,156,-85) Matrix(339,400,50,59) -> Matrix(43,-28,450,-293) Matrix(341,400,52,61) -> Matrix(41,-28,432,-295) Matrix(121,140,70,81) -> Matrix(3,-2,38,-25) Matrix(1,0,2,1) -> Matrix(1,0,18,1) Matrix(101,-120,16,-19) -> Matrix(131,-8,1392,-85) Matrix(81,-100,64,-79) -> Matrix(97,-6,1536,-95) Matrix(181,-280,64,-99) -> Matrix(115,-8,1452,-101) Matrix(61,-100,36,-59) -> Matrix(29,-2,392,-27) Matrix(21,-40,10,-19) -> Matrix(1,0,0,1) Matrix(41,-100,16,-39) -> Matrix(27,-2,338,-25) Matrix(21,-100,4,-19) -> Matrix(67,-6,726,-65) 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): 24 Degree of the the map X: 24 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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 0/1 1/1 1/18 7/6 5/83 6/5 2/33 4/65 5/4 1/16 14/11 4/63 2/31 9/7 1/16 4/3 2/31 11/8 1/15 7/5 3/46 10/7 1/15 3/2 1/15 14/9 2/29 4/57 11/7 1/14 30/19 1/14 19/12 5/69 8/5 0/1 5/3 1/14 12/7 2/27 19/11 3/38 7/4 1/15 9/5 1/14 2/1 0/1 2/27 11/5 1/14 20/9 2/27 9/4 1/13 7/3 1/12 5/2 1/13 13/5 3/38 21/8 5/61 8/3 0/1 19/7 5/66 30/11 1/13 11/4 1/13 14/5 4/51 2/25 17/6 5/63 20/7 2/25 3/1 1/12 10/3 1/12 7/2 3/35 11/3 1/12 4/1 2/23 9/2 1/11 5/1 1/11 11/2 1/11 6/1 4/43 2/21 13/2 9/95 20/3 2/21 7/1 5/52 1/0 1/9 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(1,0,9,1) Matrix(139,-160,53,-61) -> Matrix(67,-4,821,-49) Matrix(101,-120,16,-19) -> Matrix(131,-8,1392,-85) Matrix(81,-100,64,-79) -> Matrix(97,-6,1536,-95) Matrix(219,-280,79,-101) -> Matrix(1,0,-3,1) Matrix(61,-80,45,-59) -> Matrix(63,-4,961,-61) Matrix(101,-140,57,-79) -> Matrix(31,-2,419,-27) Matrix(99,-140,29,-41) -> Matrix(91,-6,1077,-71) Matrix(41,-60,13,-19) -> Matrix(29,-2,363,-25) Matrix(181,-280,64,-99) -> Matrix(115,-8,1452,-101) Matrix(141,-220,25,-39) -> Matrix(85,-6,921,-65) Matrix(419,-660,153,-241) -> Matrix(85,-6,1091,-77) Matrix(721,-1140,265,-419) -> Matrix(139,-10,1821,-131) Matrix(239,-380,139,-221) -> Matrix(27,-2,365,-27) Matrix(61,-100,36,-59) -> Matrix(29,-2,392,-27) Matrix(81,-140,11,-19) -> Matrix(25,-2,263,-21) Matrix(21,-40,10,-19) -> Matrix(1,0,0,1) Matrix(181,-400,81,-179) -> Matrix(55,-4,729,-53) Matrix(61,-140,17,-39) -> Matrix(27,-2,311,-23) Matrix(41,-100,16,-39) -> Matrix(27,-2,338,-25) Matrix(121,-320,45,-119) -> Matrix(1,0,1,1) Matrix(141,-400,49,-139) -> Matrix(151,-12,1875,-149) Matrix(21,-80,5,-19) -> Matrix(47,-4,529,-45) Matrix(21,-100,4,-19) -> Matrix(67,-6,726,-65) Matrix(61,-400,9,-59) -> Matrix(295,-28,3087,-293) 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): 24 ----------------------------------------------------------------------- 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 9 1 2/1 (0/1,2/27) 0 5 20/9 2/27 1 1 9/4 1/13 1 10 7/3 1/12 1 10 5/2 1/13 1 2 13/5 3/38 1 10 21/8 5/61 1 10 8/3 0/1 1 5 19/7 5/66 1 10 30/11 1/13 8 1 11/4 1/13 1 10 14/5 (4/51,2/25) 0 5 20/7 2/25 3 1 3/1 1/12 1 10 10/3 1/12 4 1 7/2 3/35 1 10 11/3 1/12 1 10 4/1 2/23 1 5 9/2 1/11 1 10 5/1 1/11 3 2 11/2 1/11 1 10 6/1 (4/43,2/21) 0 5 20/3 2/21 7 1 7/1 5/52 1 10 1/0 1/9 1 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(1,0,18,-1) (0/1,1/0) -> (0/1,1/9) Matrix(1,0,1,-1) -> Matrix(1,0,27,-1) (0/1,2/1) -> (0/1,2/27) Matrix(19,-40,9,-19) -> Matrix(1,0,27,-1) (2/1,20/9) -> (0/1,2/27) Matrix(161,-360,72,-161) -> Matrix(53,-4,702,-53) (20/9,9/4) -> (2/27,1/13) Matrix(61,-140,17,-39) -> Matrix(27,-2,311,-23) Matrix(41,-100,16,-39) -> Matrix(27,-2,338,-25) 1/13 Matrix(61,-160,8,-21) -> Matrix(49,-4,502,-41) Matrix(121,-320,45,-119) -> Matrix(1,0,1,1) 0/1 Matrix(419,-1140,154,-419) -> Matrix(131,-10,1716,-131) (19/7,30/11) -> (5/66,1/13) Matrix(241,-660,88,-241) -> Matrix(77,-6,988,-77) (30/11,11/4) -> (1/13,3/38) Matrix(79,-220,14,-39) -> Matrix(77,-6,834,-65) Matrix(99,-280,35,-99) -> Matrix(101,-8,1275,-101) (14/5,20/7) -> (4/51,2/25) Matrix(41,-120,14,-41) -> Matrix(49,-4,600,-49) (20/7,3/1) -> (2/25,1/12) Matrix(19,-60,6,-19) -> Matrix(25,-2,312,-25) (3/1,10/3) -> (1/13,1/12) Matrix(41,-140,12,-41) -> Matrix(71,-6,840,-71) (10/3,7/2) -> (1/12,3/35) Matrix(21,-80,5,-19) -> Matrix(47,-4,529,-45) 2/23 Matrix(21,-100,4,-19) -> Matrix(67,-6,726,-65) 1/11 Matrix(19,-120,3,-19) -> Matrix(85,-8,903,-85) (6/1,20/3) -> (4/43,2/21) Matrix(41,-280,6,-41) -> Matrix(209,-20,2184,-209) (20/3,7/1) -> (2/21,5/52) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.