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): 384 Minimal number of generators: 65 Number of equivalence classes of cusps: 40 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -11/2 -5/1 -4/1 -3/1 -5/2 -2/1 -1/1 -5/8 -1/2 -5/11 -2/5 -1/3 -1/4 0/1 1/5 1/4 1/3 1/2 5/7 3/4 4/5 1/1 13/11 5/4 7/5 3/2 11/7 5/3 7/4 2/1 7/3 5/2 11/4 3/1 7/2 4/1 9/2 5/1 6/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -6/1 1/0 -11/2 0/1 -5/1 0/1 -14/3 1/2 -9/2 1/1 1/0 -4/1 0/1 -11/3 1/1 -7/2 0/1 1/2 -10/3 1/2 -13/4 0/1 2/3 -3/1 1/1 -11/4 2/1 1/0 -8/3 1/0 -5/2 0/1 -12/5 1/2 -7/3 1/1 -9/4 1/2 1/1 -2/1 1/0 -1/1 0/1 -2/3 1/2 -9/14 0/1 1/4 -7/11 1/3 -5/8 0/1 2/5 -13/21 1/3 -8/13 1/2 -3/5 0/1 -13/22 0/1 -10/17 1/4 -7/12 1/4 1/3 -11/19 1/3 -4/7 1/3 -5/9 2/5 -6/11 1/2 -1/2 0/1 1/2 -5/11 1/2 -4/9 1/2 -3/7 2/3 -11/26 2/3 -8/19 1/2 -5/12 2/3 3/4 -7/17 1/1 -2/5 1/1 -3/8 1/1 1/0 -4/11 1/0 -1/3 0/1 -4/13 0/1 -3/10 1/3 1/2 -2/7 1/2 -1/4 0/1 2/3 -2/9 1/2 -3/14 1/2 1/1 -1/5 1/1 0/1 1/2 1/5 1/1 2/9 3/2 1/4 1/1 1/0 2/7 1/1 5/17 1/1 3/10 1/1 1/0 1/3 1/1 1/2 0/1 3/5 1/3 8/13 2/5 13/21 2/5 5/8 3/7 1/2 7/11 1/2 9/14 1/2 4/7 2/3 1/2 7/10 1/3 1/2 5/7 1/2 8/11 1/2 3/4 1/2 2/3 7/9 2/3 4/5 1/1 9/11 1/1 5/6 1/2 1/1 1/1 1/1 7/6 1/1 1/0 13/11 1/1 6/5 1/0 5/4 0/1 2/1 14/11 1/0 9/7 2/1 4/3 1/0 11/8 1/1 1/0 7/5 1/0 17/12 -1/1 1/0 10/7 1/0 3/2 0/1 1/0 14/9 -1/2 11/7 0/1 19/12 0/1 1/4 8/5 1/2 5/3 1/1 12/7 1/0 19/11 1/0 7/4 -1/1 1/0 2/1 0/1 9/4 1/2 1/1 25/11 1/1 16/7 1/0 23/10 0/1 7/3 0/1 12/5 1/2 17/7 1/2 5/2 1/2 1/1 18/7 3/4 13/5 1/1 8/3 1/0 35/13 1/1 27/10 1/1 1/0 19/7 1/1 11/4 0/1 2/1 14/5 1/0 3/1 0/1 13/4 0/1 1/0 23/7 0/1 10/3 1/2 7/2 0/1 18/5 1/4 47/13 1/3 29/8 1/3 1/2 11/3 0/1 4/1 1/2 13/3 1/1 9/2 1/2 1/1 5/1 1/1 11/2 1/1 1/0 6/1 1/0 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,12,0,1) (-6/1,1/0) -> (6/1,1/0) Parabolic Matrix(33,188,-56,-319) (-6/1,-11/2) -> (-13/22,-10/17) Hyperbolic Matrix(17,88,-40,-207) (-11/2,-5/1) -> (-3/7,-11/26) Hyperbolic Matrix(41,196,32,153) (-5/1,-14/3) -> (14/11,9/7) Hyperbolic Matrix(51,232,20,91) (-14/3,-9/2) -> (5/2,18/7) Hyperbolic Matrix(11,48,-36,-157) (-9/2,-4/1) -> (-4/13,-3/10) Hyperbolic Matrix(27,100,44,163) (-4/1,-11/3) -> (3/5,8/13) Hyperbolic Matrix(41,148,-64,-231) (-11/3,-7/2) -> (-9/14,-7/11) Hyperbolic Matrix(29,100,20,69) (-7/2,-10/3) -> (10/7,3/2) Hyperbolic Matrix(89,292,32,105) (-10/3,-13/4) -> (11/4,14/5) Hyperbolic Matrix(87,280,32,103) (-13/4,-3/1) -> (19/7,11/4) Hyperbolic Matrix(33,92,-80,-223) (-3/1,-11/4) -> (-5/12,-7/17) Hyperbolic Matrix(41,112,56,153) (-11/4,-8/3) -> (8/11,3/4) Hyperbolic Matrix(39,100,-16,-41) (-8/3,-5/2) -> (-5/2,-12/5) Parabolic Matrix(61,144,36,85) (-12/5,-7/3) -> (5/3,12/7) Hyperbolic Matrix(65,148,-112,-255) (-7/3,-9/4) -> (-7/12,-11/19) Hyperbolic Matrix(9,20,40,89) (-9/4,-2/1) -> (2/9,1/4) Hyperbolic Matrix(3,4,-4,-5) (-2/1,-1/1) -> (-1/1,-2/3) Parabolic Matrix(205,132,132,85) (-2/3,-9/14) -> (3/2,14/9) Hyperbolic Matrix(159,100,-256,-161) (-7/11,-5/8) -> (-5/8,-13/21) Parabolic Matrix(253,156,60,37) (-13/21,-8/13) -> (4/1,13/3) Hyperbolic Matrix(151,92,64,39) (-8/13,-3/5) -> (7/3,12/5) Hyperbolic Matrix(269,160,116,69) (-3/5,-13/22) -> (23/10,7/3) Hyperbolic Matrix(409,240,288,169) (-10/17,-7/12) -> (17/12,10/7) Hyperbolic Matrix(139,80,172,99) (-11/19,-4/7) -> (4/5,9/11) Hyperbolic Matrix(85,48,108,61) (-4/7,-5/9) -> (7/9,4/5) Hyperbolic Matrix(159,88,56,31) (-5/9,-6/11) -> (14/5,3/1) Hyperbolic Matrix(103,56,160,87) (-6/11,-1/2) -> (9/14,2/3) Hyperbolic Matrix(113,52,176,81) (-1/2,-5/11) -> (7/11,9/14) Hyperbolic Matrix(303,136,176,79) (-5/11,-4/9) -> (12/7,19/11) Hyperbolic Matrix(109,48,84,37) (-4/9,-3/7) -> (9/7,4/3) Hyperbolic Matrix(853,360,372,157) (-11/26,-8/19) -> (16/7,23/10) Hyperbolic Matrix(457,192,288,121) (-8/19,-5/12) -> (19/12,8/5) Hyperbolic Matrix(59,24,204,83) (-7/17,-2/5) -> (2/7,5/17) Hyperbolic Matrix(21,8,76,29) (-2/5,-3/8) -> (1/4,2/7) Hyperbolic Matrix(153,56,112,41) (-3/8,-4/11) -> (4/3,11/8) Hyperbolic Matrix(133,48,36,13) (-4/11,-1/3) -> (11/3,4/1) Hyperbolic Matrix(193,60,312,97) (-1/3,-4/13) -> (8/13,13/21) Hyperbolic Matrix(69,20,100,29) (-3/10,-2/7) -> (2/3,7/10) Hyperbolic Matrix(15,4,-64,-17) (-2/7,-1/4) -> (-1/4,-2/9) Parabolic Matrix(183,40,32,7) (-2/9,-3/14) -> (11/2,6/1) Hyperbolic Matrix(151,32,184,39) (-3/14,-1/5) -> (9/11,5/6) Hyperbolic Matrix(45,8,28,5) (-1/5,0/1) -> (8/5,5/3) Hyperbolic Matrix(53,-8,20,-3) (0/1,1/5) -> (13/5,8/3) Hyperbolic Matrix(207,-44,80,-17) (1/5,2/9) -> (18/7,13/5) Hyperbolic Matrix(649,-192,240,-71) (5/17,3/10) -> (27/10,19/7) Hyperbolic Matrix(157,-48,36,-11) (3/10,1/3) -> (13/3,9/2) Hyperbolic Matrix(9,-4,16,-7) (1/3,1/2) -> (1/2,3/5) Parabolic Matrix(697,-432,192,-119) (13/21,5/8) -> (29/8,11/3) Hyperbolic Matrix(229,-144,132,-83) (5/8,7/11) -> (19/11,7/4) Hyperbolic Matrix(205,-144,84,-59) (7/10,5/7) -> (17/7,5/2) Hyperbolic Matrix(271,-196,112,-81) (5/7,8/11) -> (12/5,17/7) Hyperbolic Matrix(129,-100,40,-31) (3/4,7/9) -> (3/1,13/4) Hyperbolic Matrix(13,-12,12,-11) (5/6,1/1) -> (1/1,7/6) Parabolic Matrix(507,-596,188,-221) (7/6,13/11) -> (35/13,27/10) Hyperbolic Matrix(433,-516,120,-143) (13/11,6/5) -> (18/5,47/13) Hyperbolic Matrix(81,-100,64,-79) (6/5,5/4) -> (5/4,14/11) Parabolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(277,-432,84,-131) (14/9,11/7) -> (23/7,10/3) Hyperbolic Matrix(367,-580,112,-177) (11/7,19/12) -> (13/4,23/7) Hyperbolic Matrix(17,-32,8,-15) (7/4,2/1) -> (2/1,9/4) Parabolic Matrix(507,-1148,140,-317) (9/4,25/11) -> (47/13,29/8) Hyperbolic Matrix(333,-760,124,-283) (25/11,16/7) -> (8/3,35/13) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(21,-100,4,-19) (9/2,5/1) -> (5/1,11/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,12,0,1) -> Matrix(1,0,0,1) Matrix(33,188,-56,-319) -> Matrix(1,0,4,1) Matrix(17,88,-40,-207) -> Matrix(1,-2,2,-3) Matrix(41,196,32,153) -> Matrix(3,-2,2,-1) Matrix(51,232,20,91) -> Matrix(1,-2,2,-3) Matrix(11,48,-36,-157) -> Matrix(1,0,2,1) Matrix(27,100,44,163) -> Matrix(3,-2,8,-5) Matrix(41,148,-64,-231) -> Matrix(1,0,2,1) Matrix(29,100,20,69) -> Matrix(1,0,-2,1) Matrix(89,292,32,105) -> Matrix(3,-2,2,-1) Matrix(87,280,32,103) -> Matrix(3,-2,2,-1) Matrix(33,92,-80,-223) -> Matrix(3,-4,4,-5) Matrix(41,112,56,153) -> Matrix(1,-4,2,-7) Matrix(39,100,-16,-41) -> Matrix(1,0,2,1) Matrix(61,144,36,85) -> Matrix(3,-2,2,-1) Matrix(65,148,-112,-255) -> Matrix(1,0,2,1) Matrix(9,20,40,89) -> Matrix(3,-2,2,-1) Matrix(3,4,-4,-5) -> Matrix(1,0,2,1) Matrix(205,132,132,85) -> Matrix(1,0,-4,1) Matrix(159,100,-256,-161) -> Matrix(1,0,0,1) Matrix(253,156,60,37) -> Matrix(5,-2,8,-3) Matrix(151,92,64,39) -> Matrix(1,0,0,1) Matrix(269,160,116,69) -> Matrix(1,0,-2,1) Matrix(409,240,288,169) -> Matrix(1,0,-4,1) Matrix(139,80,172,99) -> Matrix(1,0,-2,1) Matrix(85,48,108,61) -> Matrix(11,-4,14,-5) Matrix(159,88,56,31) -> Matrix(5,-2,-2,1) Matrix(103,56,160,87) -> Matrix(9,-4,16,-7) Matrix(113,52,176,81) -> Matrix(9,-4,16,-7) Matrix(303,136,176,79) -> Matrix(11,-6,2,-1) Matrix(109,48,84,37) -> Matrix(7,-4,2,-1) Matrix(853,360,372,157) -> Matrix(3,-2,2,-1) Matrix(457,192,288,121) -> Matrix(3,-2,8,-5) Matrix(59,24,204,83) -> Matrix(5,-4,4,-3) Matrix(21,8,76,29) -> Matrix(1,0,0,1) Matrix(153,56,112,41) -> Matrix(1,0,0,1) Matrix(133,48,36,13) -> Matrix(1,0,2,1) Matrix(193,60,312,97) -> Matrix(3,-2,8,-5) Matrix(69,20,100,29) -> Matrix(1,0,0,1) Matrix(15,4,-64,-17) -> Matrix(1,0,0,1) Matrix(183,40,32,7) -> Matrix(3,-2,2,-1) Matrix(151,32,184,39) -> Matrix(1,0,0,1) Matrix(45,8,28,5) -> Matrix(1,0,0,1) Matrix(53,-8,20,-3) -> Matrix(3,-2,2,-1) Matrix(207,-44,80,-17) -> Matrix(5,-6,6,-7) Matrix(649,-192,240,-71) -> Matrix(1,0,0,1) Matrix(157,-48,36,-11) -> Matrix(1,-2,2,-3) Matrix(9,-4,16,-7) -> Matrix(1,0,2,1) Matrix(697,-432,192,-119) -> Matrix(5,-2,8,-3) Matrix(229,-144,132,-83) -> Matrix(9,-4,-2,1) Matrix(205,-144,84,-59) -> Matrix(5,-2,8,-3) Matrix(271,-196,112,-81) -> Matrix(7,-4,16,-9) Matrix(129,-100,40,-31) -> Matrix(3,-2,2,-1) Matrix(13,-12,12,-11) -> Matrix(3,-2,2,-1) Matrix(507,-596,188,-221) -> Matrix(1,0,0,1) Matrix(433,-516,120,-143) -> Matrix(1,-2,4,-7) Matrix(81,-100,64,-79) -> Matrix(1,0,0,1) Matrix(141,-196,100,-139) -> Matrix(1,-2,0,1) Matrix(277,-432,84,-131) -> Matrix(1,0,4,1) Matrix(367,-580,112,-177) -> Matrix(1,0,-4,1) Matrix(17,-32,8,-15) -> Matrix(1,0,2,1) Matrix(507,-1148,140,-317) -> Matrix(3,-2,8,-5) Matrix(333,-760,124,-283) -> Matrix(1,0,0,1) Matrix(57,-196,16,-55) -> Matrix(1,0,2,1) Matrix(21,-100,4,-19) -> 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): 15 Degree of the the map X: 15 Degree of the the map Y: 64 Permutation triple for Y: ((1,7,25,15,47,64,50,61,52,18,8,2)(3,10,34,53,45,44,63,56,55,48,35,11)(4,16,17,5)(6,22,27,26,42,41,62,54,38,46,58,23)(9,24,60,29)(12,39,59,40)(13,43,33,49,37,36,51,30,20,19,28,14)(21,57,32,31); (1,5,20,56,21,6)(2,3)(4,14,45,31,46,15)(7,23,39,34,43,24)(8,27,59,44,28,9)(10,32,62,50,16,33)(11,37,60,47,38,12)(13,42)(17,36,35,57,26,18)(19,54)(22,49)(25,48)(29,61,41,40,55,30)(51,58)(52,53)(63,64); (1,3,12,41,13,4)(2,9,30,58,31,10)(5,18,53,39,38,19)(6,7)(8,26)(11,36)(14,44)(15,48,40,27,49,16)(17,50,63,59,23,51)(20,55)(21,45,52,29,37,22)(24,28,54,32,35,25)(33,34)(42,57,56,64,60,43)(46,47)(61,62)) ----------------------------------------------------------------------- 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- 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 -1/1 0/1 1 2 -1/2 (0/1,1/2) 0 12 -4/9 1/2 1 12 -3/7 2/3 1 6 -2/5 1/1 2 4 -3/8 (1/1,1/0) 0 12 -4/11 1/0 1 12 -1/3 0/1 1 6 -2/7 1/2 1 12 -1/4 0 4 -2/9 1/2 1 12 -1/5 1/1 1 6 0/1 1/2 1 12 1/5 1/1 4 2 1/4 (1/1,1/0) 0 12 2/7 1/1 2 4 3/10 (1/1,1/0) 0 12 1/3 1/1 1 6 1/2 0/1 2 4 3/5 1/3 1 6 5/8 (3/7,1/2) 0 12 7/11 1/2 7 2 9/14 (1/2,4/7) 0 12 2/3 1/2 1 12 7/10 (1/3,1/2) 0 12 5/7 1/2 3 2 3/4 (1/2,2/3) 0 12 7/9 2/3 1 6 4/5 1/1 2 4 5/6 (1/2,1/1) 0 12 1/1 1/1 1 6 7/6 (1/1,1/0) 0 12 13/11 1/1 2 2 6/5 1/0 1 12 5/4 0 4 9/7 2/1 1 6 4/3 1/0 1 12 11/8 (1/1,1/0) 0 12 7/5 1/0 1 2 3/2 (0/1,1/0) 0 12 11/7 0/1 4 2 19/12 (0/1,1/4) 0 12 8/5 1/2 1 12 5/3 1/1 1 6 7/4 (-1/1,1/0) 0 12 2/1 0/1 1 4 9/4 (1/2,1/1) 0 12 25/11 1/1 2 2 16/7 1/0 1 12 7/3 0/1 1 6 12/5 1/2 1 12 5/2 (1/2,1/1) 0 12 13/5 1/1 4 2 8/3 1/0 1 12 11/4 0 4 3/1 0/1 1 6 13/4 (0/1,1/0) 0 12 10/3 1/2 1 12 7/2 0/1 2 4 18/5 1/4 1 12 11/3 0/1 1 6 4/1 1/2 1 12 13/3 1/1 1 6 9/2 (1/2,1/1) 0 12 5/1 1/1 1 2 1/0 (0/1,1/1) 0 12 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(3,2,-4,-3) (-1/1,-1/2) -> (-1/1,-1/2) Reflection Matrix(85,38,132,59) (-1/2,-4/9) -> (9/14,2/3) Glide Reflection Matrix(109,48,84,37) (-4/9,-3/7) -> (9/7,4/3) Hyperbolic Matrix(63,26,80,33) (-3/7,-2/5) -> (7/9,4/5) Glide Reflection Matrix(21,8,76,29) (-2/5,-3/8) -> (1/4,2/7) Hyperbolic Matrix(153,56,112,41) (-3/8,-4/11) -> (4/3,11/8) Hyperbolic Matrix(133,48,36,13) (-4/11,-1/3) -> (11/3,4/1) Hyperbolic Matrix(85,26,36,11) (-1/3,-2/7) -> (7/3,12/5) Glide Reflection Matrix(15,4,-64,-17) (-2/7,-1/4) -> (-1/4,-2/9) Parabolic Matrix(137,30,32,7) (-2/9,-1/5) -> (4/1,13/3) Glide Reflection Matrix(45,8,28,5) (-1/5,0/1) -> (8/5,5/3) Hyperbolic Matrix(53,-8,20,-3) (0/1,1/5) -> (13/5,8/3) Hyperbolic Matrix(9,-2,40,-9) (1/5,1/4) -> (1/5,1/4) Reflection Matrix(75,-22,92,-27) (2/7,3/10) -> (4/5,5/6) Glide Reflection Matrix(157,-48,36,-11) (3/10,1/3) -> (13/3,9/2) Hyperbolic Matrix(9,-4,16,-7) (1/3,1/2) -> (1/2,3/5) Parabolic Matrix(75,-46,44,-27) (3/5,5/8) -> (5/3,7/4) Glide Reflection Matrix(111,-70,176,-111) (5/8,7/11) -> (5/8,7/11) Reflection Matrix(197,-126,308,-197) (7/11,9/14) -> (7/11,9/14) Reflection Matrix(135,-94,56,-39) (2/3,7/10) -> (12/5,5/2) Glide Reflection Matrix(99,-70,140,-99) (7/10,5/7) -> (7/10,5/7) Reflection Matrix(41,-30,56,-41) (5/7,3/4) -> (5/7,3/4) Reflection Matrix(129,-100,40,-31) (3/4,7/9) -> (3/1,13/4) Hyperbolic Matrix(13,-12,12,-11) (5/6,1/1) -> (1/1,7/6) Parabolic Matrix(155,-182,132,-155) (7/6,13/11) -> (7/6,13/11) Reflection Matrix(301,-358,132,-157) (13/11,6/5) -> (25/11,16/7) Glide Reflection Matrix(87,-106,32,-39) (6/5,5/4) -> (8/3,11/4) Glide Reflection Matrix(89,-114,32,-41) (5/4,9/7) -> (11/4,3/1) Glide Reflection Matrix(111,-154,80,-111) (11/8,7/5) -> (11/8,7/5) Reflection Matrix(29,-42,20,-29) (7/5,3/2) -> (7/5,3/2) Reflection Matrix(43,-66,28,-43) (3/2,11/7) -> (3/2,11/7) Reflection Matrix(265,-418,168,-265) (11/7,19/12) -> (11/7,19/12) Reflection Matrix(185,-294,56,-89) (19/12,8/5) -> (13/4,10/3) Glide Reflection Matrix(17,-32,8,-15) (7/4,2/1) -> (2/1,9/4) Parabolic Matrix(199,-450,88,-199) (9/4,25/11) -> (9/4,25/11) Reflection Matrix(131,-302,36,-83) (16/7,7/3) -> (18/5,11/3) Glide Reflection Matrix(51,-130,20,-51) (5/2,13/5) -> (5/2,13/5) Reflection Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic 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(1,2,0,-1) -> Matrix(1,0,2,-1) (-1/1,1/0) -> (0/1,1/1) Matrix(3,2,-4,-3) -> Matrix(1,0,4,-1) (-1/1,-1/2) -> (0/1,1/2) Matrix(85,38,132,59) -> Matrix(7,-4,12,-7) *** -> (1/2,2/3) Matrix(109,48,84,37) -> Matrix(7,-4,2,-1) Matrix(63,26,80,33) -> Matrix(5,-4,6,-5) *** -> (2/3,1/1) Matrix(21,8,76,29) -> Matrix(1,0,0,1) Matrix(153,56,112,41) -> Matrix(1,0,0,1) Matrix(133,48,36,13) -> Matrix(1,0,2,1) 0/1 Matrix(85,26,36,11) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(15,4,-64,-17) -> Matrix(1,0,0,1) Matrix(137,30,32,7) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(45,8,28,5) -> Matrix(1,0,0,1) Matrix(53,-8,20,-3) -> Matrix(3,-2,2,-1) 1/1 Matrix(9,-2,40,-9) -> Matrix(-1,2,0,1) (1/5,1/4) -> (1/1,1/0) Matrix(75,-22,92,-27) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(157,-48,36,-11) -> Matrix(1,-2,2,-3) 1/1 Matrix(9,-4,16,-7) -> Matrix(1,0,2,1) 0/1 Matrix(75,-46,44,-27) -> Matrix(5,-2,2,-1) Matrix(111,-70,176,-111) -> Matrix(13,-6,28,-13) (5/8,7/11) -> (3/7,1/2) Matrix(197,-126,308,-197) -> Matrix(15,-8,28,-15) (7/11,9/14) -> (1/2,4/7) Matrix(135,-94,56,-39) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(99,-70,140,-99) -> Matrix(5,-2,12,-5) (7/10,5/7) -> (1/3,1/2) Matrix(41,-30,56,-41) -> Matrix(7,-4,12,-7) (5/7,3/4) -> (1/2,2/3) Matrix(129,-100,40,-31) -> Matrix(3,-2,2,-1) 1/1 Matrix(13,-12,12,-11) -> Matrix(3,-2,2,-1) 1/1 Matrix(155,-182,132,-155) -> Matrix(-1,2,0,1) (7/6,13/11) -> (1/1,1/0) Matrix(301,-358,132,-157) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(87,-106,32,-39) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(89,-114,32,-41) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(111,-154,80,-111) -> Matrix(-1,2,0,1) (11/8,7/5) -> (1/1,1/0) Matrix(29,-42,20,-29) -> Matrix(1,0,0,-1) (7/5,3/2) -> (0/1,1/0) Matrix(43,-66,28,-43) -> Matrix(1,0,0,-1) (3/2,11/7) -> (0/1,1/0) Matrix(265,-418,168,-265) -> Matrix(1,0,8,-1) (11/7,19/12) -> (0/1,1/4) Matrix(185,-294,56,-89) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(17,-32,8,-15) -> Matrix(1,0,2,1) 0/1 Matrix(199,-450,88,-199) -> Matrix(3,-2,4,-3) (9/4,25/11) -> (1/2,1/1) Matrix(131,-302,36,-83) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(51,-130,20,-51) -> Matrix(3,-2,4,-3) (5/2,13/5) -> (1/2,1/1) Matrix(57,-196,16,-55) -> Matrix(1,0,2,1) 0/1 Matrix(19,-90,4,-19) -> Matrix(3,-2,4,-3) (9/2,5/1) -> (1/2,1/1) Matrix(-1,10,0,1) -> Matrix(1,0,2,-1) (5/1,1/0) -> (0/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.