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 5/43 2/17 -6/1 3/25 -5/1 1/8 -14/3 5/39 -9/2 1/8 -4/1 2/15 -11/3 2/15 1/7 -7/2 5/36 -10/3 1/7 -3/1 1/7 2/13 -14/5 3/19 -11/4 1/6 -30/11 1/7 -19/7 1/7 2/13 -8/3 2/13 -5/2 1/6 -12/5 4/23 -19/8 11/62 -7/3 2/11 1/5 -9/4 1/6 -2/1 1/5 -11/6 1/4 -20/11 0/1 -9/5 0/1 1/5 -7/4 3/14 -5/3 1/4 -13/8 5/18 -21/13 2/7 1/3 -8/5 2/7 -19/12 7/22 -30/19 1/3 -11/7 1/3 2/5 -14/9 1/3 -17/11 0/1 1/1 -20/13 0/1 -3/2 1/4 -10/7 1/3 -7/5 1/3 2/5 -11/8 1/2 -4/3 0/1 -9/7 0/1 1/3 -5/4 1/2 -11/9 2/3 1/1 -6/5 1/1 -13/11 -1/3 0/1 -20/17 0/1 -7/6 1/4 -1/1 0/1 1/1 0/1 0/1 1/1 0/1 1/19 7/6 1/16 6/5 1/19 5/4 1/18 14/11 1/17 9/7 0/1 1/17 4/3 0/1 11/8 1/18 7/5 2/35 1/17 10/7 1/17 3/2 1/16 14/9 1/17 11/7 2/35 1/17 30/19 1/17 19/12 7/118 8/5 2/33 5/3 1/16 12/7 2/31 19/11 3/47 2/31 7/4 3/46 9/5 0/1 1/15 2/1 1/15 11/5 1/15 2/29 20/9 2/29 9/4 1/14 7/3 1/15 2/29 5/2 1/14 13/5 5/69 4/55 21/8 13/178 8/3 2/27 19/7 2/27 1/13 30/11 1/13 11/4 1/14 14/5 3/41 17/6 5/68 20/7 2/27 3/1 2/27 1/13 10/3 1/13 7/2 5/64 11/3 1/13 2/25 4/1 2/25 9/2 1/12 5/1 1/12 11/2 1/12 6/1 3/35 13/2 9/104 20/3 2/23 7/1 2/23 5/57 1/0 1/10 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(87,-10,1192,-137) Matrix(19,120,-16,-101) -> Matrix(17,-2,-8,1) Matrix(19,100,-4,-21) -> Matrix(65,-8,512,-63) Matrix(61,280,22,101) -> Matrix(15,-2,218,-29) Matrix(19,80,14,59) -> Matrix(15,-2,278,-37) Matrix(21,80,16,61) -> Matrix(15,-2,248,-33) Matrix(39,140,22,79) -> Matrix(15,-2,218,-29) Matrix(41,140,12,41) -> Matrix(71,-10,916,-129) Matrix(19,60,6,19) -> Matrix(27,-4,358,-53) Matrix(99,280,-64,-181) -> Matrix(13,-2,20,-3) Matrix(79,220,14,39) -> Matrix(37,-6,438,-71) Matrix(241,660,88,241) -> Matrix(13,-2,176,-27) Matrix(419,1140,154,419) -> Matrix(27,-4,358,-53) Matrix(141,380,82,221) -> Matrix(25,-4,394,-63) Matrix(39,100,-16,-41) -> Matrix(37,-6,216,-35) Matrix(159,380,100,239) -> Matrix(57,-10,952,-167) Matrix(59,140,8,19) -> Matrix(45,-8,512,-91) Matrix(61,140,44,101) -> Matrix(1,0,12,1) Matrix(19,40,-10,-21) -> Matrix(11,-2,50,-9) Matrix(219,400,98,179) -> Matrix(7,-2,102,-29) Matrix(221,400,100,181) -> Matrix(11,-2,160,-29) Matrix(79,140,22,39) -> Matrix(11,-2,138,-25) Matrix(59,100,-36,-61) -> Matrix(17,-4,64,-15) Matrix(99,160,86,139) -> Matrix(7,-2,130,-37) Matrix(199,320,74,119) -> Matrix(1,0,10,1) Matrix(201,320,76,121) -> Matrix(27,-8,368,-109) Matrix(721,1140,456,721) -> Matrix(43,-14,728,-237) Matrix(419,660,266,419) -> Matrix(11,-4,190,-69) Matrix(179,280,140,219) -> Matrix(5,-2,88,-35) Matrix(259,400,90,139) -> Matrix(1,-2,14,-27) Matrix(261,400,92,141) -> Matrix(13,-2,176,-27) Matrix(41,60,28,41) -> Matrix(7,-2,116,-33) Matrix(99,140,70,99) -> Matrix(11,-4,190,-69) Matrix(101,140,44,61) -> Matrix(1,0,12,1) Matrix(59,80,14,19) -> Matrix(3,-2,38,-25) Matrix(61,80,16,21) -> Matrix(7,-2,88,-25) Matrix(79,100,-64,-81) -> Matrix(5,-2,8,-3) Matrix(181,220,116,141) -> Matrix(1,0,16,1) Matrix(339,400,50,59) -> Matrix(11,2,126,23) Matrix(341,400,52,61) -> Matrix(17,-2,196,-23) Matrix(121,140,70,81) -> Matrix(5,-2,78,-31) Matrix(1,0,2,1) -> Matrix(1,0,18,1) Matrix(101,-120,16,-19) -> Matrix(41,-2,472,-23) Matrix(81,-100,64,-79) -> Matrix(37,-2,648,-35) Matrix(181,-280,64,-99) -> Matrix(37,-2,500,-27) Matrix(61,-100,36,-59) -> Matrix(65,-4,1024,-63) Matrix(21,-40,10,-19) -> Matrix(31,-2,450,-29) Matrix(41,-100,16,-39) -> Matrix(85,-6,1176,-83) Matrix(21,-100,4,-19) -> Matrix(97,-8,1152,-95) 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 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 -4/1 -5/2 -2/1 -20/11 -5/4 0/1 1/1 5/4 10/7 3/2 5/3 2/1 5/2 3/1 10/3 7/2 4/1 9/2 5/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -5/1 1/8 -9/2 1/8 -4/1 2/15 -11/3 2/15 1/7 -7/2 5/36 -10/3 1/7 -3/1 1/7 2/13 -5/2 1/6 -7/3 2/11 1/5 -9/4 1/6 -2/1 1/5 -11/6 1/4 -20/11 0/1 -9/5 0/1 1/5 -7/4 3/14 -5/3 1/4 -3/2 1/4 -10/7 1/3 -7/5 1/3 2/5 -11/8 1/2 -4/3 0/1 -5/4 1/2 -6/5 1/1 -1/1 0/1 1/1 0/1 0/1 1/1 0/1 1/19 5/4 1/18 9/7 0/1 1/17 4/3 0/1 11/8 1/18 7/5 2/35 1/17 10/7 1/17 3/2 1/16 5/3 1/16 7/4 3/46 9/5 0/1 1/15 2/1 1/15 5/2 1/14 8/3 2/27 19/7 2/27 1/13 30/11 1/13 11/4 1/14 3/1 2/27 1/13 10/3 1/13 7/2 5/64 11/3 1/13 2/25 4/1 2/25 9/2 1/12 5/1 1/12 1/0 1/10 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,10,0,1) (-5/1,1/0) -> (5/1,1/0) Parabolic Matrix(19,90,4,19) (-5/1,-9/2) -> (9/2,5/1) 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(19,50,-8,-21) (-3/1,-5/2) -> (-5/2,-7/3) Parabolic 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(301,550,110,201) (-11/6,-20/11) -> (30/11,11/4) Hyperbolic Matrix(359,650,132,239) (-20/11,-9/5) -> (19/7,30/11) Hyperbolic Matrix(79,140,22,39) (-9/5,-7/4) -> (7/2,11/3) Hyperbolic Matrix(41,70,24,41) (-7/4,-5/3) -> (5/3,7/4) 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(99,140,70,99) (-10/7,-7/5) -> (7/5,10/7) Hyperbolic Matrix(79,110,28,39) (-7/5,-11/8) -> (11/4,3/1) Hyperbolic Matrix(59,80,14,19) (-11/8,-4/3) -> (4/1,9/2) Hyperbolic Matrix(39,50,-32,-41) (-4/3,-5/4) -> (-5/4,-6/5) Parabolic Matrix(59,70,16,19) (-6/5,-1/1) -> (11/3,4/1) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(41,-50,32,-39) (1/1,5/4) -> (5/4,9/7) Parabolic Matrix(59,-110,22,-41) (9/5,2/1) -> (8/3,19/7) Hyperbolic Matrix(21,-50,8,-19) (2/1,5/2) -> (5/2,8/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,10,0,1) -> Matrix(9,-1,100,-11) Matrix(19,90,4,19) -> Matrix(55,-7,668,-85) Matrix(19,80,14,59) -> Matrix(15,-2,278,-37) Matrix(21,80,16,61) -> Matrix(15,-2,248,-33) Matrix(39,140,22,79) -> Matrix(15,-2,218,-29) Matrix(41,140,12,41) -> Matrix(71,-10,916,-129) Matrix(19,60,6,19) -> Matrix(27,-4,358,-53) Matrix(19,50,-8,-21) -> Matrix(19,-3,108,-17) Matrix(61,140,44,101) -> Matrix(1,0,12,1) Matrix(19,40,-10,-21) -> Matrix(11,-2,50,-9) Matrix(301,550,110,201) -> Matrix(5,-1,66,-13) Matrix(359,650,132,239) -> Matrix(7,-1,92,-13) Matrix(79,140,22,39) -> Matrix(11,-2,138,-25) Matrix(41,70,24,41) -> Matrix(13,-3,204,-47) Matrix(19,30,12,19) -> Matrix(3,-1,52,-17) Matrix(41,60,28,41) -> Matrix(7,-2,116,-33) Matrix(99,140,70,99) -> Matrix(11,-4,190,-69) Matrix(79,110,28,39) -> Matrix(7,-3,96,-41) Matrix(59,80,14,19) -> Matrix(3,-2,38,-25) Matrix(39,50,-32,-41) -> Matrix(3,-1,4,-1) Matrix(59,70,16,19) -> Matrix(1,1,12,13) Matrix(1,0,2,1) -> Matrix(1,0,18,1) Matrix(41,-50,32,-39) -> Matrix(19,-1,324,-17) Matrix(59,-110,22,-41) -> Matrix(17,-1,222,-13) Matrix(21,-50,8,-19) -> Matrix(43,-3,588,-41) 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 1/1 (0/1,1/19) 0 10 5/4 1/18 1 2 9/7 (0/1,1/17) 0 10 4/3 0/1 1 5 11/8 1/18 1 10 7/5 (2/35,1/17) 0 10 10/7 1/17 3 1 3/2 1/16 1 10 5/3 1/16 2 2 7/4 3/46 1 10 9/5 (0/1,1/15) 0 10 2/1 1/15 1 5 5/2 1/14 3 2 8/3 2/27 1 5 19/7 (2/27,1/13) 0 10 30/11 1/13 1 1 11/4 1/14 1 10 3/1 (2/27,1/13) 0 10 10/3 1/13 7 1 7/2 5/64 1 10 11/3 (1/13,2/25) 0 10 4/1 2/25 1 5 9/2 1/12 1 10 5/1 1/12 4 2 1/0 1/10 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(41,-50,32,-39) (1/1,5/4) -> (5/4,9/7) Parabolic Matrix(61,-80,16,-21) (9/7,4/3) -> (11/3,4/1) Glide Reflection Matrix(59,-80,14,-19) (4/3,11/8) -> (4/1,9/2) Glide Reflection Matrix(79,-110,28,-39) (11/8,7/5) -> (11/4,3/1) Glide Reflection Matrix(99,-140,70,-99) (7/5,10/7) -> (7/5,10/7) Reflection Matrix(41,-60,28,-41) (10/7,3/2) -> (10/7,3/2) Reflection Matrix(19,-30,12,-19) (3/2,5/3) -> (3/2,5/3) Reflection Matrix(41,-70,24,-41) (5/3,7/4) -> (5/3,7/4) Reflection Matrix(79,-140,22,-39) (7/4,9/5) -> (7/2,11/3) Glide Reflection Matrix(59,-110,22,-41) (9/5,2/1) -> (8/3,19/7) Hyperbolic Matrix(21,-50,8,-19) (2/1,5/2) -> (5/2,8/3) 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(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(19,-90,4,-19) (9/2,5/1) -> (9/2,5/1) Reflection Matrix(-1,10,0,1) (5/1,1/0) -> (5/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,20,-1) (0/1,1/0) -> (0/1,1/10) Matrix(1,0,2,-1) -> Matrix(1,0,38,-1) (0/1,1/1) -> (0/1,1/19) Matrix(41,-50,32,-39) -> Matrix(19,-1,324,-17) 1/18 Matrix(61,-80,16,-21) -> Matrix(33,-2,412,-25) Matrix(59,-80,14,-19) -> Matrix(37,-2,462,-25) Matrix(79,-110,28,-39) -> Matrix(53,-3,724,-41) Matrix(99,-140,70,-99) -> Matrix(69,-4,1190,-69) (7/5,10/7) -> (2/35,1/17) Matrix(41,-60,28,-41) -> Matrix(33,-2,544,-33) (10/7,3/2) -> (1/17,1/16) Matrix(19,-30,12,-19) -> Matrix(17,-1,288,-17) (3/2,5/3) -> (1/18,1/16) Matrix(41,-70,24,-41) -> Matrix(47,-3,736,-47) (5/3,7/4) -> (1/16,3/46) Matrix(79,-140,22,-39) -> Matrix(29,-2,362,-25) Matrix(59,-110,22,-41) -> Matrix(17,-1,222,-13) Matrix(21,-50,8,-19) -> Matrix(43,-3,588,-41) 1/14 Matrix(419,-1140,154,-419) -> Matrix(53,-4,702,-53) (19/7,30/11) -> (2/27,1/13) Matrix(241,-660,88,-241) -> Matrix(27,-2,364,-27) (30/11,11/4) -> (1/14,1/13) Matrix(19,-60,6,-19) -> Matrix(53,-4,702,-53) (3/1,10/3) -> (2/27,1/13) Matrix(41,-140,12,-41) -> Matrix(129,-10,1664,-129) (10/3,7/2) -> (1/13,5/64) Matrix(19,-90,4,-19) -> Matrix(85,-7,1032,-85) (9/2,5/1) -> (7/86,1/12) Matrix(-1,10,0,1) -> Matrix(11,-1,120,-11) (5/1,1/0) -> (1/12,1/10) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.