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: 32 Genus: 17 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/1 -5/1 -3/1 -2/1 -9/5 -6/5 -1/1 -2/3 0/1 1/2 2/3 3/4 1/1 6/5 5/4 4/3 3/2 12/7 9/5 2/1 9/4 12/5 5/2 8/3 3/1 4/1 9/2 24/5 5/1 6/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 1/0 -6/1 -1/1 -5/1 -3/4 -14/3 -1/2 -9/2 -2/3 -4/1 -1/2 -3/1 -1/2 1/0 -8/3 -1/1 0/1 -13/5 -1/2 -18/7 -1/1 -5/2 -1/2 -12/5 -1/2 -7/3 -1/2 -16/7 -1/1 0/1 -9/4 -1/1 -11/5 -3/4 -2/1 -1/2 -13/7 -5/12 -24/13 -2/5 -11/6 -3/8 -9/5 -1/2 -3/8 -16/9 -2/5 -1/3 -23/13 -3/8 -7/4 -2/5 -1/3 -12/7 -1/3 -5/3 -1/4 -13/8 -1/2 0/1 -8/5 -1/3 0/1 -3/2 0/1 -4/3 -1/2 -9/7 -1/2 -1/4 -14/11 -1/4 -19/15 -1/6 -24/19 0/1 -5/4 -1/2 0/1 -11/9 -1/4 -6/5 0/1 -7/6 1/0 -8/7 -1/1 0/1 -1/1 -1/2 -6/7 -1/3 -5/6 -1/4 -9/11 -1/2 -1/4 -4/5 -1/2 -3/4 -1/3 -8/11 -1/3 -2/7 -5/7 -1/4 -12/17 -1/3 -7/10 -3/10 -16/23 -1/3 -2/7 -9/13 -3/10 -1/4 -2/3 -1/4 -9/14 0/1 -16/25 -1/3 0/1 -7/11 -1/4 -12/19 -1/4 -5/8 -1/4 0/1 -8/13 -1/3 0/1 -3/5 -1/2 -1/4 -4/7 -1/4 -9/16 -1/5 -5/9 -1/4 -6/11 0/1 -1/2 -1/4 0/1 0/1 1/2 1/2 3/5 1/2 1/0 5/8 0/1 1/2 7/11 1/2 16/25 0/1 1/1 9/14 0/1 2/3 1/2 9/13 1/2 3/4 7/10 3/4 5/7 1/2 8/11 2/3 1/1 3/4 1/1 4/5 1/0 5/6 1/2 6/7 1/1 1/1 1/0 7/6 -1/2 6/5 0/1 5/4 0/1 1/0 14/11 1/2 9/7 1/2 1/0 13/10 1/2 4/3 1/0 3/2 0/1 8/5 0/1 1/1 13/8 0/1 1/0 18/11 0/1 5/3 1/2 17/10 3/4 12/7 1/1 7/4 1/1 2/1 16/9 1/1 2/1 25/14 1/0 9/5 3/2 1/0 11/6 3/2 2/1 1/0 13/6 -5/2 24/11 -2/1 11/5 -3/2 9/4 -1/1 16/7 -1/1 0/1 23/10 -1/2 7/3 1/0 19/8 0/1 1/0 12/5 1/0 5/2 1/0 13/5 1/0 8/3 -1/1 0/1 11/4 0/1 1/0 3/1 -1/2 1/0 7/2 1/0 18/5 0/1 11/3 1/0 15/4 1/1 4/1 1/0 9/2 -2/1 14/3 1/0 19/4 -5/2 -2/1 24/5 -2/1 5/1 -3/2 11/2 -3/2 6/1 -1/1 7/1 -1/2 8/1 -1/1 0/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(7,72,-4,-41) (-7/1,1/0) -> (-23/13,-7/4) Hyperbolic Matrix(7,48,8,55) (-7/1,-6/1) -> (6/7,1/1) Hyperbolic Matrix(31,168,-12,-65) (-6/1,-5/1) -> (-13/5,-18/7) Hyperbolic Matrix(71,336,-56,-265) (-5/1,-14/3) -> (-14/11,-19/15) Hyperbolic Matrix(31,144,48,223) (-14/3,-9/2) -> (9/14,2/3) Hyperbolic Matrix(17,72,4,17) (-9/2,-4/1) -> (4/1,9/2) Hyperbolic Matrix(7,24,-12,-41) (-4/1,-3/1) -> (-3/5,-4/7) Hyperbolic Matrix(17,48,-28,-79) (-3/1,-8/3) -> (-8/13,-3/5) Hyperbolic Matrix(55,144,76,199) (-8/3,-13/5) -> (5/7,8/11) Hyperbolic Matrix(47,120,56,143) (-18/7,-5/2) -> (5/6,6/7) Hyperbolic Matrix(49,120,20,49) (-5/2,-12/5) -> (12/5,5/2) Hyperbolic Matrix(71,168,-112,-265) (-12/5,-7/3) -> (-7/11,-12/19) Hyperbolic Matrix(31,72,-28,-65) (-7/3,-16/7) -> (-8/7,-1/1) Hyperbolic Matrix(127,288,56,127) (-16/7,-9/4) -> (9/4,16/7) Hyperbolic Matrix(119,264,32,71) (-9/4,-11/5) -> (11/3,15/4) Hyperbolic Matrix(23,48,-12,-25) (-11/5,-2/1) -> (-2/1,-13/7) Parabolic Matrix(233,432,48,89) (-13/7,-24/13) -> (24/5,5/1) Hyperbolic Matrix(313,576,144,265) (-24/13,-11/6) -> (13/6,24/11) Hyperbolic Matrix(119,216,92,167) (-11/6,-9/5) -> (9/7,13/10) Hyperbolic Matrix(161,288,-232,-415) (-9/5,-16/9) -> (-16/23,-9/13) Hyperbolic Matrix(271,480,424,751) (-16/9,-23/13) -> (7/11,16/25) Hyperbolic Matrix(97,168,56,97) (-7/4,-12/7) -> (12/7,7/4) Hyperbolic Matrix(71,120,-100,-169) (-12/7,-5/3) -> (-5/7,-12/17) Hyperbolic Matrix(103,168,-84,-137) (-5/3,-13/8) -> (-5/4,-11/9) Hyperbolic Matrix(119,192,44,71) (-13/8,-8/5) -> (8/3,11/4) Hyperbolic Matrix(31,48,20,31) (-8/5,-3/2) -> (3/2,8/5) Hyperbolic Matrix(17,24,12,17) (-3/2,-4/3) -> (4/3,3/2) Hyperbolic Matrix(55,72,-68,-89) (-4/3,-9/7) -> (-9/11,-4/5) Hyperbolic Matrix(113,144,164,209) (-9/7,-14/11) -> (2/3,9/13) Hyperbolic Matrix(569,720,260,329) (-19/15,-24/19) -> (24/11,11/5) Hyperbolic Matrix(457,576,96,121) (-24/19,-5/4) -> (19/4,24/5) Hyperbolic Matrix(217,264,60,73) (-11/9,-6/5) -> (18/5,11/3) Hyperbolic Matrix(143,168,40,47) (-6/5,-7/6) -> (7/2,18/5) Hyperbolic Matrix(271,312,152,175) (-7/6,-8/7) -> (16/9,25/14) Hyperbolic Matrix(55,48,8,7) (-1/1,-6/7) -> (6/1,7/1) Hyperbolic Matrix(113,96,20,17) (-6/7,-5/6) -> (11/2,6/1) Hyperbolic Matrix(175,144,96,79) (-5/6,-9/11) -> (9/5,11/6) Hyperbolic Matrix(31,24,40,31) (-4/5,-3/4) -> (3/4,4/5) Hyperbolic Matrix(65,48,88,65) (-3/4,-8/11) -> (8/11,3/4) Hyperbolic Matrix(199,144,76,55) (-8/11,-5/7) -> (13/5,8/3) Hyperbolic Matrix(409,288,240,169) (-12/17,-7/10) -> (17/10,12/7) Hyperbolic Matrix(689,480,300,209) (-7/10,-16/23) -> (16/7,23/10) Hyperbolic Matrix(209,144,164,113) (-9/13,-2/3) -> (14/11,9/7) Hyperbolic Matrix(223,144,48,31) (-2/3,-9/14) -> (9/2,14/3) Hyperbolic Matrix(449,288,700,449) (-9/14,-16/25) -> (16/25,9/14) Hyperbolic Matrix(263,168,36,23) (-16/25,-7/11) -> (7/1,8/1) Hyperbolic Matrix(457,288,192,121) (-12/19,-5/8) -> (19/8,12/5) Hyperbolic Matrix(233,144,144,89) (-5/8,-8/13) -> (8/5,13/8) Hyperbolic Matrix(169,96,44,25) (-4/7,-9/16) -> (15/4,4/1) Hyperbolic Matrix(257,144,116,65) (-9/16,-5/9) -> (11/5,9/4) Hyperbolic Matrix(217,120,132,73) (-5/9,-6/11) -> (18/11,5/3) Hyperbolic Matrix(89,48,76,41) (-6/11,-1/2) -> (7/6,6/5) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(41,-24,12,-7) (1/2,3/5) -> (3/1,7/2) Hyperbolic Matrix(79,-48,28,-17) (3/5,5/8) -> (11/4,3/1) Hyperbolic Matrix(265,-168,112,-71) (5/8,7/11) -> (7/3,19/8) Hyperbolic Matrix(415,-288,232,-161) (9/13,7/10) -> (25/14,9/5) Hyperbolic Matrix(169,-120,100,-71) (7/10,5/7) -> (5/3,17/10) Hyperbolic Matrix(89,-72,68,-55) (4/5,5/6) -> (13/10,4/3) Hyperbolic Matrix(65,-72,28,-31) (1/1,7/6) -> (23/10,7/3) Hyperbolic Matrix(137,-168,84,-103) (6/5,5/4) -> (13/8,18/11) Hyperbolic Matrix(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) Hyperbolic Matrix(41,-72,4,-7) (7/4,16/9) -> (8/1,1/0) Hyperbolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(65,-168,12,-31) (5/2,13/5) -> (5/1,11/2) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(7,72,-4,-41) -> Matrix(3,2,-8,-5) Matrix(7,48,8,55) -> Matrix(1,2,0,1) Matrix(31,168,-12,-65) -> Matrix(3,2,-2,-1) Matrix(71,336,-56,-265) -> Matrix(3,2,-14,-9) Matrix(31,144,48,223) -> Matrix(3,2,4,3) Matrix(17,72,4,17) -> Matrix(7,4,-2,-1) Matrix(7,24,-12,-41) -> Matrix(1,0,-2,1) Matrix(17,48,-28,-79) -> Matrix(1,0,-2,1) Matrix(55,144,76,199) -> Matrix(3,2,4,3) Matrix(47,120,56,143) -> Matrix(3,2,4,3) Matrix(49,120,20,49) -> Matrix(3,2,-2,-1) Matrix(71,168,-112,-265) -> Matrix(1,0,-2,1) Matrix(31,72,-28,-65) -> Matrix(1,0,0,1) Matrix(127,288,56,127) -> Matrix(1,0,0,1) Matrix(119,264,32,71) -> Matrix(3,2,4,3) Matrix(23,48,-12,-25) -> Matrix(7,4,-16,-9) Matrix(233,432,48,89) -> Matrix(39,16,-22,-9) Matrix(313,576,144,265) -> Matrix(41,16,-18,-7) Matrix(119,216,92,167) -> Matrix(5,2,2,1) Matrix(161,288,-232,-415) -> Matrix(11,4,-36,-13) Matrix(271,480,424,751) -> Matrix(5,2,2,1) Matrix(97,168,56,97) -> Matrix(11,4,8,3) Matrix(71,120,-100,-169) -> Matrix(1,0,0,1) Matrix(103,168,-84,-137) -> Matrix(1,0,0,1) Matrix(119,192,44,71) -> Matrix(1,0,2,1) Matrix(31,48,20,31) -> Matrix(1,0,4,1) Matrix(17,24,12,17) -> Matrix(1,0,2,1) Matrix(55,72,-68,-89) -> Matrix(1,0,0,1) Matrix(113,144,164,209) -> Matrix(7,2,10,3) Matrix(569,720,260,329) -> Matrix(15,2,-8,-1) Matrix(457,576,96,121) -> Matrix(1,-2,0,1) Matrix(217,264,60,73) -> Matrix(1,0,4,1) Matrix(143,168,40,47) -> Matrix(1,0,0,1) Matrix(271,312,152,175) -> Matrix(1,2,0,1) Matrix(55,48,8,7) -> Matrix(5,2,-8,-3) Matrix(113,96,20,17) -> Matrix(13,4,-10,-3) Matrix(175,144,96,79) -> Matrix(5,2,2,1) Matrix(31,24,40,31) -> Matrix(5,2,2,1) Matrix(65,48,88,65) -> Matrix(13,4,16,5) Matrix(199,144,76,55) -> Matrix(7,2,-4,-1) Matrix(409,288,240,169) -> Matrix(19,6,22,7) Matrix(689,480,300,209) -> Matrix(7,2,-4,-1) Matrix(209,144,164,113) -> Matrix(7,2,10,3) Matrix(223,144,48,31) -> Matrix(7,2,-4,-1) Matrix(449,288,700,449) -> Matrix(1,0,4,1) Matrix(263,168,36,23) -> Matrix(1,0,2,1) Matrix(457,288,192,121) -> Matrix(1,0,4,1) Matrix(233,144,144,89) -> Matrix(1,0,4,1) Matrix(169,96,44,25) -> Matrix(9,2,4,1) Matrix(257,144,116,65) -> Matrix(11,2,-6,-1) Matrix(217,120,132,73) -> Matrix(1,0,6,1) Matrix(89,48,76,41) -> Matrix(1,0,2,1) Matrix(1,0,4,1) -> Matrix(1,0,6,1) Matrix(41,-24,12,-7) -> Matrix(1,0,-2,1) Matrix(79,-48,28,-17) -> Matrix(1,0,-2,1) Matrix(265,-168,112,-71) -> Matrix(1,0,-2,1) Matrix(415,-288,232,-161) -> Matrix(5,-4,4,-3) Matrix(169,-120,100,-71) -> Matrix(1,0,0,1) Matrix(89,-72,68,-55) -> Matrix(1,0,0,1) Matrix(65,-72,28,-31) -> Matrix(1,0,0,1) Matrix(137,-168,84,-103) -> Matrix(1,0,0,1) Matrix(265,-336,56,-71) -> Matrix(5,-2,-2,1) Matrix(41,-72,4,-7) -> Matrix(1,-2,0,1) Matrix(25,-48,12,-23) -> Matrix(1,-4,0,1) Matrix(65,-168,12,-31) -> 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): 17 Degree of the the map X: 17 Degree of the the map Y: 64 Permutation triple for Y: ((1,2)(3,10,33,62,34,11)(4,16,46,47,17,5)(6,21,55,60,56,22)(7,25,41,52,26,8)(9,30,28,20,51,19)(12,23,42,14,13,37)(15,31,18,24,36,27)(29,43)(32,49)(35,44)(38,54)(39,40)(45,58,61,57,48,59)(50,53)(63,64); (1,5,19,53,45,16,44,56,61,54,20,6)(2,8,28,39,57,25,35,34,59,29,9,3)(4,14,22,15)(7,12,11,24)(10,31,43,42,62,63,41,13,40,27,26,32)(17,49,21,36,38,37,60,64,46,23,50,18)(30,55,48,47)(33,58,52,51); (1,3,12,38,61,33,32,17,48,39,13,4)(2,6,14,43,59,55,49,26,58,53,23,7)(5,18,10,9)(8,27,21,20)(11,35,16,15,40,28,47,64,62,51,54,36)(19,52,63,60,30,29,31,22,44,25,24,50)(34,42,46,45)(37,41,57,56)) ----------------------------------------------------------------------- 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 0/1 0/1 3 2 1/2 1/2 1 12 3/5 0 4 5/8 (0/1,1/2) 0 12 7/11 1/2 1 12 16/25 (0/1,1/1) 0 6 9/14 0/1 1 4 2/3 1/2 1 6 9/13 0 4 7/10 3/4 1 12 5/7 1/2 1 12 8/11 (2/3,1/1) 0 6 3/4 1/1 3 4 4/5 1/0 1 6 5/6 1/2 1 12 6/7 1/1 3 2 1/1 1/0 1 12 7/6 -1/2 1 12 6/5 0/1 2 2 5/4 (0/1,1/0) 0 12 14/11 1/2 1 6 9/7 0 4 13/10 1/2 1 12 4/3 1/0 1 6 3/2 0/1 1 4 8/5 (0/1,1/1) 0 6 13/8 (0/1,1/0) 0 12 18/11 0/1 2 2 5/3 1/2 1 12 17/10 3/4 1 12 12/7 1/1 5 2 7/4 (1/1,2/1) 0 12 16/9 (1/1,2/1) 0 6 25/14 1/0 1 12 9/5 0 4 11/6 3/2 1 12 2/1 1/0 2 6 13/6 -5/2 1 12 24/11 -2/1 8 2 11/5 -3/2 1 12 9/4 -1/1 3 4 16/7 (-1/1,0/1) 0 6 23/10 -1/2 1 12 7/3 1/0 1 12 19/8 (0/1,1/0) 0 12 12/5 1/0 1 2 5/2 1/0 1 12 13/5 1/0 1 12 8/3 (-1/1,0/1) 0 6 11/4 (0/1,1/0) 0 12 3/1 0 4 7/2 1/0 1 12 18/5 0/1 2 2 11/3 1/0 1 12 15/4 1/1 3 4 4/1 1/0 3 6 9/2 -2/1 1 4 14/3 1/0 1 6 19/4 (-5/2,-2/1) 0 12 24/5 -2/1 8 2 5/1 -3/2 1 12 11/2 -3/2 1 12 6/1 -1/1 3 2 7/1 -1/2 1 12 8/1 (-1/1,0/1) 0 6 1/0 (-1/1,0/1) 0 12 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(1,0,4,-1) (0/1,1/2) -> (0/1,1/2) Reflection Matrix(41,-24,12,-7) (1/2,3/5) -> (3/1,7/2) Hyperbolic Matrix(79,-48,28,-17) (3/5,5/8) -> (11/4,3/1) Hyperbolic Matrix(265,-168,112,-71) (5/8,7/11) -> (7/3,19/8) Hyperbolic Matrix(263,-168,36,-23) (7/11,16/25) -> (7/1,8/1) Glide Reflection Matrix(449,-288,700,-449) (16/25,9/14) -> (16/25,9/14) Reflection Matrix(223,-144,48,-31) (9/14,2/3) -> (9/2,14/3) Glide Reflection Matrix(209,-144,164,-113) (2/3,9/13) -> (14/11,9/7) Glide Reflection Matrix(415,-288,232,-161) (9/13,7/10) -> (25/14,9/5) Hyperbolic Matrix(169,-120,100,-71) (7/10,5/7) -> (5/3,17/10) Hyperbolic Matrix(199,-144,76,-55) (5/7,8/11) -> (13/5,8/3) Glide Reflection Matrix(65,-48,88,-65) (8/11,3/4) -> (8/11,3/4) Reflection Matrix(31,-24,40,-31) (3/4,4/5) -> (3/4,4/5) Reflection Matrix(89,-72,68,-55) (4/5,5/6) -> (13/10,4/3) Hyperbolic Matrix(113,-96,20,-17) (5/6,6/7) -> (11/2,6/1) Glide Reflection Matrix(55,-48,8,-7) (6/7,1/1) -> (6/1,7/1) Glide Reflection Matrix(65,-72,28,-31) (1/1,7/6) -> (23/10,7/3) Hyperbolic Matrix(143,-168,40,-47) (7/6,6/5) -> (7/2,18/5) Glide Reflection Matrix(137,-168,84,-103) (6/5,5/4) -> (13/8,18/11) Hyperbolic Matrix(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) Hyperbolic Matrix(167,-216,92,-119) (9/7,13/10) -> (9/5,11/6) Glide Reflection Matrix(17,-24,12,-17) (4/3,3/2) -> (4/3,3/2) Reflection Matrix(31,-48,20,-31) (3/2,8/5) -> (3/2,8/5) Reflection Matrix(119,-192,44,-71) (8/5,13/8) -> (8/3,11/4) Glide Reflection Matrix(175,-288,48,-79) (18/11,5/3) -> (18/5,11/3) Glide Reflection Matrix(239,-408,140,-239) (17/10,12/7) -> (17/10,12/7) Reflection Matrix(97,-168,56,-97) (12/7,7/4) -> (12/7,7/4) Reflection Matrix(41,-72,4,-7) (7/4,16/9) -> (8/1,1/0) Hyperbolic Matrix(431,-768,188,-335) (16/9,25/14) -> (16/7,23/10) Glide Reflection Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(287,-624,132,-287) (13/6,24/11) -> (13/6,24/11) Reflection Matrix(175,-384,36,-79) (24/11,11/5) -> (24/5,5/1) Glide Reflection Matrix(119,-264,32,-71) (11/5,9/4) -> (11/3,15/4) Glide Reflection Matrix(127,-288,56,-127) (9/4,16/7) -> (9/4,16/7) Reflection Matrix(191,-456,80,-191) (19/8,12/5) -> (19/8,12/5) Reflection Matrix(49,-120,20,-49) (12/5,5/2) -> (12/5,5/2) Reflection Matrix(65,-168,12,-31) (5/2,13/5) -> (5/1,11/2) Hyperbolic Matrix(31,-120,8,-31) (15/4,4/1) -> (15/4,4/1) Reflection Matrix(17,-72,4,-17) (4/1,9/2) -> (4/1,9/2) Reflection Matrix(191,-912,40,-191) (19/4,24/5) -> (19/4,24/5) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,4,-1) -> Matrix(1,0,4,-1) (0/1,1/2) -> (0/1,1/2) Matrix(41,-24,12,-7) -> Matrix(1,0,-2,1) 0/1 Matrix(79,-48,28,-17) -> Matrix(1,0,-2,1) 0/1 Matrix(265,-168,112,-71) -> Matrix(1,0,-2,1) 0/1 Matrix(263,-168,36,-23) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(449,-288,700,-449) -> Matrix(1,0,2,-1) (16/25,9/14) -> (0/1,1/1) Matrix(223,-144,48,-31) -> Matrix(3,-2,-2,1) Matrix(209,-144,164,-113) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(415,-288,232,-161) -> Matrix(5,-4,4,-3) 1/1 Matrix(169,-120,100,-71) -> Matrix(1,0,0,1) Matrix(199,-144,76,-55) -> Matrix(3,-2,-2,1) Matrix(65,-48,88,-65) -> Matrix(5,-4,6,-5) (8/11,3/4) -> (2/3,1/1) Matrix(31,-24,40,-31) -> Matrix(-1,2,0,1) (3/4,4/5) -> (1/1,1/0) Matrix(89,-72,68,-55) -> Matrix(1,0,0,1) Matrix(113,-96,20,-17) -> Matrix(5,-4,-4,3) Matrix(55,-48,8,-7) -> Matrix(1,-2,-2,3) Matrix(65,-72,28,-31) -> Matrix(1,0,0,1) Matrix(143,-168,40,-47) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(137,-168,84,-103) -> Matrix(1,0,0,1) Matrix(265,-336,56,-71) -> Matrix(5,-2,-2,1) Matrix(167,-216,92,-119) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(17,-24,12,-17) -> Matrix(1,0,0,-1) (4/3,3/2) -> (0/1,1/0) Matrix(31,-48,20,-31) -> Matrix(1,0,2,-1) (3/2,8/5) -> (0/1,1/1) Matrix(119,-192,44,-71) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(175,-288,48,-79) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(239,-408,140,-239) -> Matrix(7,-6,8,-7) (17/10,12/7) -> (3/4,1/1) Matrix(97,-168,56,-97) -> Matrix(3,-4,2,-3) (12/7,7/4) -> (1/1,2/1) Matrix(41,-72,4,-7) -> Matrix(1,-2,0,1) 1/0 Matrix(431,-768,188,-335) -> Matrix(1,-2,-2,3) Matrix(25,-48,12,-23) -> Matrix(1,-4,0,1) 1/0 Matrix(287,-624,132,-287) -> Matrix(9,20,-4,-9) (13/6,24/11) -> (-5/2,-2/1) Matrix(175,-384,36,-79) -> Matrix(7,12,-4,-7) *** -> (-2/1,-3/2) Matrix(119,-264,32,-71) -> Matrix(1,2,2,3) Matrix(127,-288,56,-127) -> Matrix(-1,0,2,1) (9/4,16/7) -> (-1/1,0/1) Matrix(191,-456,80,-191) -> Matrix(1,0,0,-1) (19/8,12/5) -> (0/1,1/0) Matrix(49,-120,20,-49) -> Matrix(1,2,0,-1) (12/5,5/2) -> (-1/1,1/0) Matrix(65,-168,12,-31) -> Matrix(3,2,-2,-1) -1/1 Matrix(31,-120,8,-31) -> Matrix(-1,2,0,1) (15/4,4/1) -> (1/1,1/0) Matrix(17,-72,4,-17) -> Matrix(1,4,0,-1) (4/1,9/2) -> (-2/1,1/0) Matrix(191,-912,40,-191) -> Matrix(9,20,-4,-9) (19/4,24/5) -> (-5/2,-2/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.