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 -5/3 -3/2 -4/3 -11/9 -1/1 -5/6 -3/4 -2/3 -5/9 -1/2 -11/24 -5/11 -3/7 -1/3 -3/11 -1/4 -1/5 -1/6 -1/7 0/1 1/6 1/5 1/4 1/3 2/5 5/12 1/2 5/9 7/12 2/3 3/4 4/5 5/6 1/1 11/9 4/3 3/2 5/3 2/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -2/1 0/1 -9/5 0/1 1/1 -7/4 -1/1 1/1 -5/3 -1/2 1/0 -13/8 -1/1 1/1 -8/5 -2/1 -11/7 -1/1 0/1 -3/2 -1/1 -13/9 0/1 -10/7 -2/1 -7/5 -1/2 -11/8 -1/1 1/1 -4/3 -1/1 -9/7 -1/2 -14/11 0/1 -5/4 -1/1 -11/9 -1/2 1/0 -6/5 0/1 -1/1 -1/1 0/1 -6/7 0/1 -5/6 -1/1 -9/11 -1/2 -4/5 0/1 -7/9 -1/2 1/0 -10/13 0/1 -3/4 -1/1 -11/15 0/1 -19/26 -1/1 -8/11 0/1 -5/7 1/0 -7/10 -1/1 1/1 -2/3 -1/1 -9/14 -1/1 -3/5 -16/25 -2/3 -23/36 -1/1 -3/5 -7/11 -2/3 -1/2 -12/19 -2/5 -5/8 -1/1 -1/3 -3/5 1/0 -10/17 -4/3 -7/12 -1/1 -4/7 -2/3 -5/9 0/1 -6/11 0/1 -1/2 -1/1 -6/13 -2/3 -11/24 -1/1 -3/5 -5/11 -1/2 -4/9 -1/2 -3/7 -1/1 0/1 -8/19 -2/1 -5/12 -1/1 -2/5 -2/3 -1/3 -1/2 1/0 -2/7 -2/3 -5/18 -1/2 -3/11 -1/2 -2/5 -4/15 -1/3 -1/4 -1/1 -1/3 -1/5 -1/3 0/1 -2/11 0/1 -1/6 0/1 -2/13 0/1 -1/7 1/0 0/1 0/1 1/6 0/1 1/5 1/2 1/4 -1/1 1/1 1/3 0/1 3/8 1/3 1/1 5/13 1/2 7/18 1/1 2/5 0/1 5/12 1/1 3/7 1/0 4/9 1/1 5/11 0/1 1/0 1/2 -1/1 1/1 7/13 0/1 1/0 13/24 -1/1 1/1 6/11 0/1 5/9 1/2 1/0 4/7 0/1 7/12 1/1 3/5 1/1 2/1 5/8 1/1 3/1 7/11 1/0 2/3 1/0 9/13 1/0 25/36 -3/1 -1/1 16/23 -2/1 7/10 -1/1 5/7 -1/1 0/1 13/18 0/1 8/11 0/1 11/15 1/2 1/0 3/4 1/1 10/13 2/1 7/9 2/1 4/5 4/1 9/11 8/1 1/0 5/6 1/0 1/1 1/0 7/6 1/0 6/5 -6/1 11/9 -4/1 5/4 -3/1 14/11 -2/1 9/7 -2/1 -1/1 4/3 1/0 15/11 1/0 11/8 -5/1 -3/1 7/5 -4/1 -3/1 17/12 -3/1 10/7 -2/1 13/9 -5/2 1/0 16/11 -2/1 3/2 -3/1 -1/1 11/7 1/0 19/12 -3/1 8/5 -2/1 5/3 -2/1 12/7 -2/1 19/11 1/0 7/4 -3/1 -1/1 9/5 -5/2 11/6 -2/1 13/7 -2/1 -5/3 2/1 -2/1 1/0 -1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,4,0,1) (-2/1,1/0) -> (2/1,1/0) Parabolic Matrix(11,20,-60,-109) (-2/1,-9/5) -> (-1/5,-2/11) Hyperbolic Matrix(83,148,60,107) (-9/5,-7/4) -> (11/8,7/5) Hyperbolic Matrix(59,100,-36,-61) (-7/4,-5/3) -> (-5/3,-13/8) Parabolic Matrix(121,196,-192,-311) (-13/8,-8/5) -> (-12/19,-5/8) Hyperbolic Matrix(71,112,-168,-265) (-8/5,-11/7) -> (-3/7,-8/19) Hyperbolic Matrix(59,92,84,131) (-11/7,-3/2) -> (7/10,5/7) Hyperbolic Matrix(193,280,-264,-383) (-3/2,-13/9) -> (-11/15,-19/26) Hyperbolic Matrix(131,188,108,155) (-13/9,-10/7) -> (6/5,11/9) Hyperbolic Matrix(71,100,-120,-169) (-10/7,-7/5) -> (-3/5,-10/17) Hyperbolic Matrix(107,148,60,83) (-7/5,-11/8) -> (7/4,9/5) Hyperbolic Matrix(35,48,-132,-181) (-11/8,-4/3) -> (-4/15,-1/4) Hyperbolic Matrix(37,48,84,109) (-4/3,-9/7) -> (3/7,4/9) Hyperbolic Matrix(25,32,-168,-215) (-9/7,-14/11) -> (-2/13,-1/7) Hyperbolic Matrix(73,92,96,121) (-14/11,-5/4) -> (3/4,10/13) Hyperbolic Matrix(71,88,96,119) (-5/4,-11/9) -> (11/15,3/4) Hyperbolic Matrix(155,188,108,131) (-11/9,-6/5) -> (10/7,13/9) Hyperbolic Matrix(11,12,-12,-13) (-6/5,-1/1) -> (-1/1,-6/7) Parabolic Matrix(61,52,156,133) (-6/7,-5/6) -> (7/18,2/5) Hyperbolic Matrix(107,88,276,227) (-5/6,-9/11) -> (5/13,7/18) Hyperbolic Matrix(227,184,132,107) (-9/11,-4/5) -> (12/7,19/11) Hyperbolic Matrix(61,48,108,85) (-4/5,-7/9) -> (5/9,4/7) Hyperbolic Matrix(119,92,216,167) (-7/9,-10/13) -> (6/11,5/9) Hyperbolic Matrix(121,92,96,73) (-10/13,-3/4) -> (5/4,14/11) Hyperbolic Matrix(119,88,96,71) (-3/4,-11/15) -> (11/9,5/4) Hyperbolic Matrix(493,360,708,517) (-19/26,-8/11) -> (16/23,7/10) Hyperbolic Matrix(11,8,-84,-61) (-8/11,-5/7) -> (-1/7,0/1) Hyperbolic Matrix(131,92,84,59) (-5/7,-7/10) -> (3/2,11/7) Hyperbolic Matrix(47,32,-72,-49) (-7/10,-2/3) -> (-2/3,-9/14) Parabolic Matrix(299,192,204,131) (-9/14,-16/25) -> (16/11,3/2) Hyperbolic Matrix(1201,768,1728,1105) (-16/25,-23/36) -> (25/36,16/23) Hyperbolic Matrix(395,252,732,467) (-23/36,-7/11) -> (7/13,13/24) Hyperbolic Matrix(215,136,264,167) (-7/11,-12/19) -> (4/5,9/11) Hyperbolic Matrix(13,8,60,37) (-5/8,-3/5) -> (1/5,1/4) Hyperbolic Matrix(409,240,288,169) (-10/17,-7/12) -> (17/12,10/7) Hyperbolic Matrix(97,56,168,97) (-7/12,-4/7) -> (4/7,7/12) Hyperbolic Matrix(85,48,108,61) (-4/7,-5/9) -> (7/9,4/5) Hyperbolic Matrix(167,92,216,119) (-5/9,-6/11) -> (10/13,7/9) Hyperbolic Matrix(23,12,-48,-25) (-6/11,-1/2) -> (-1/2,-6/13) Parabolic Matrix(313,144,576,265) (-6/13,-11/24) -> (13/24,6/11) Hyperbolic Matrix(491,224,708,323) (-11/24,-5/11) -> (9/13,25/36) Hyperbolic Matrix(179,80,132,59) (-5/11,-4/9) -> (4/3,15/11) Hyperbolic Matrix(109,48,84,37) (-4/9,-3/7) -> (9/7,4/3) Hyperbolic Matrix(457,192,288,121) (-8/19,-5/12) -> (19/12,8/5) Hyperbolic Matrix(49,20,120,49) (-5/12,-2/5) -> (2/5,5/12) Hyperbolic Matrix(11,4,-36,-13) (-2/5,-1/3) -> (-1/3,-2/7) Parabolic Matrix(157,44,132,37) (-2/7,-5/18) -> (7/6,6/5) Hyperbolic Matrix(217,60,264,73) (-5/18,-3/11) -> (9/11,5/6) Hyperbolic Matrix(119,32,264,71) (-3/11,-4/15) -> (4/9,5/11) Hyperbolic Matrix(37,8,60,13) (-1/4,-1/5) -> (3/5,5/8) Hyperbolic Matrix(23,4,-144,-25) (-2/11,-1/6) -> (-1/6,-2/13) Parabolic Matrix(61,-8,84,-11) (0/1,1/6) -> (13/18,8/11) Hyperbolic Matrix(109,-20,60,-11) (1/6,1/5) -> (9/5,11/6) Hyperbolic Matrix(13,-4,36,-11) (1/4,1/3) -> (1/3,3/8) Parabolic Matrix(263,-100,192,-73) (3/8,5/13) -> (15/11,11/8) Hyperbolic Matrix(265,-112,168,-71) (5/12,3/7) -> (11/7,19/12) Hyperbolic Matrix(25,-12,48,-23) (5/11,1/2) -> (1/2,7/13) Parabolic Matrix(169,-100,120,-71) (7/12,3/5) -> (7/5,17/12) Hyperbolic Matrix(229,-144,132,-83) (5/8,7/11) -> (19/11,7/4) Hyperbolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(311,-224,168,-121) (5/7,13/18) -> (11/6,13/7) Hyperbolic Matrix(383,-280,264,-193) (8/11,11/15) -> (13/9,16/11) Hyperbolic Matrix(13,-12,12,-11) (5/6,1/1) -> (1/1,7/6) Parabolic Matrix(157,-200,84,-107) (14/11,9/7) -> (13/7,2/1) Hyperbolic Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(3,2,-2,-1) Matrix(11,20,-60,-109) -> Matrix(1,0,-4,1) Matrix(83,148,60,107) -> Matrix(1,-4,0,1) Matrix(59,100,-36,-61) -> Matrix(1,0,0,1) Matrix(121,196,-192,-311) -> Matrix(1,0,-2,1) Matrix(71,112,-168,-265) -> Matrix(1,0,0,1) Matrix(59,92,84,131) -> Matrix(1,0,0,1) Matrix(193,280,-264,-383) -> Matrix(1,0,0,1) Matrix(131,188,108,155) -> Matrix(1,-4,0,1) Matrix(71,100,-120,-169) -> Matrix(3,2,-2,-1) Matrix(107,148,60,83) -> Matrix(1,-2,0,1) Matrix(35,48,-132,-181) -> Matrix(1,0,-2,1) Matrix(37,48,84,109) -> Matrix(1,0,2,1) Matrix(25,32,-168,-215) -> Matrix(1,0,2,1) Matrix(73,92,96,121) -> Matrix(1,2,0,1) Matrix(71,88,96,119) -> Matrix(1,0,2,1) Matrix(155,188,108,131) -> Matrix(1,-2,0,1) Matrix(11,12,-12,-13) -> Matrix(1,0,0,1) Matrix(61,52,156,133) -> Matrix(1,0,2,1) Matrix(107,88,276,227) -> Matrix(3,2,4,3) Matrix(227,184,132,107) -> Matrix(3,2,-2,-1) Matrix(61,48,108,85) -> Matrix(1,0,2,1) Matrix(119,92,216,167) -> Matrix(1,0,2,1) Matrix(121,92,96,73) -> Matrix(1,-2,0,1) Matrix(119,88,96,71) -> Matrix(7,4,-2,-1) Matrix(493,360,708,517) -> Matrix(3,2,-2,-1) Matrix(11,8,-84,-61) -> Matrix(1,0,0,1) Matrix(131,92,84,59) -> Matrix(1,-2,0,1) Matrix(47,32,-72,-49) -> Matrix(1,2,-2,-3) Matrix(299,192,204,131) -> Matrix(7,4,-2,-1) Matrix(1201,768,1728,1105) -> Matrix(7,4,-2,-1) Matrix(395,252,732,467) -> Matrix(3,2,-2,-1) Matrix(215,136,264,167) -> Matrix(13,6,2,1) Matrix(13,8,60,37) -> Matrix(1,0,2,1) Matrix(409,240,288,169) -> Matrix(11,14,-4,-5) Matrix(97,56,168,97) -> Matrix(3,2,4,3) Matrix(85,48,108,61) -> Matrix(5,2,2,1) Matrix(167,92,216,119) -> Matrix(1,2,0,1) Matrix(23,12,-48,-25) -> Matrix(1,2,-2,-3) Matrix(313,144,576,265) -> Matrix(3,2,-2,-1) Matrix(491,224,708,323) -> Matrix(7,4,-2,-1) Matrix(179,80,132,59) -> Matrix(11,6,-2,-1) Matrix(109,48,84,37) -> Matrix(3,2,-2,-1) Matrix(457,192,288,121) -> Matrix(5,8,-2,-3) Matrix(49,20,120,49) -> Matrix(3,2,4,3) Matrix(11,4,-36,-13) -> Matrix(1,0,0,1) Matrix(157,44,132,37) -> Matrix(15,8,-2,-1) Matrix(217,60,264,73) -> Matrix(21,10,2,1) Matrix(119,32,264,71) -> Matrix(5,2,2,1) Matrix(37,8,60,13) -> Matrix(5,2,2,1) Matrix(23,4,-144,-25) -> Matrix(1,0,6,1) Matrix(61,-8,84,-11) -> Matrix(1,0,2,1) Matrix(109,-20,60,-11) -> Matrix(9,-2,-4,1) Matrix(13,-4,36,-11) -> Matrix(1,0,2,1) Matrix(263,-100,192,-73) -> Matrix(9,-4,-2,1) Matrix(265,-112,168,-71) -> Matrix(1,-4,0,1) Matrix(25,-12,48,-23) -> Matrix(1,0,0,1) Matrix(169,-100,120,-71) -> Matrix(7,-10,-2,3) Matrix(229,-144,132,-83) -> Matrix(1,-4,0,1) Matrix(49,-32,72,-47) -> Matrix(1,-4,0,1) Matrix(311,-224,168,-121) -> Matrix(7,2,-4,-1) Matrix(383,-280,264,-193) -> Matrix(5,-2,-2,1) Matrix(13,-12,12,-11) -> Matrix(1,-2,0,1) Matrix(157,-200,84,-107) -> Matrix(3,8,-2,-5) Matrix(61,-100,36,-59) -> Matrix(3,8,-2,-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): 16 Degree of the the map X: 16 Degree of the the map Y: 64 Permutation triple for Y: ((1,6,23,54,53,61,63,62,32,24,7,2)(3,12,41,59,52,60,64,56,48,42,13,4)(5,18,55,19)(8,25,50,49,38,46,45,35,58,22,21,26)(9,30,31,10)(11,36,57,37)(14,43,34,33,20,29,28,17,51,40,39,44)(15,47,27,16); (1,4,16,50,17,5)(2,10,34,35,11,3)(6,22)(7,8)(9,29,38,37,42,23)(12,40)(13,14)(15,46,20,19,24,41)(18,54,48,27,26,39)(21,36,59,32,31,44)(25,57,64,61,30,51)(28,52)(33,56)(43,55,63,60,47,58)(45,53)(49,62); (1,3)(2,8,27,60,28,9)(4,14,31,61,45,15)(5,20,56,57,21,6)(7,19,43,13,37,25)(10,32,49,16,48,33)(11,38,62,55,39,12)(17,52,36,35,53,18)(22,47,41,40,30,23)(24,59)(26,44)(29,46)(34,58)(42,54)(50,51)(63,64)) ----------------------------------------------------------------------- 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 (-1/1,0/1) 0 12 -5/6 -1/1 1 2 -4/5 0/1 1 12 -7/9 0 4 -3/4 -1/1 1 6 -8/11 0/1 1 12 -5/7 1/0 2 12 -2/3 -1/1 1 4 -7/11 (-2/3,-1/2) 0 12 -5/8 0 6 -3/5 1/0 2 12 -7/12 -1/1 5 2 -4/7 -2/3 1 12 -5/9 0/1 2 4 -6/11 0/1 1 12 -1/2 -1/1 1 6 -3/7 (-1/1,0/1) 0 12 -5/12 -1/1 3 2 -2/5 -2/3 1 12 -1/3 0 4 -2/7 -2/3 1 12 -3/11 (-1/2,-2/5) 0 12 -1/4 0 6 -1/5 (-1/3,0/1) 0 12 -1/6 0/1 3 2 -1/7 1/0 2 12 0/1 0/1 1 12 1/6 0/1 5 2 1/5 1/2 2 12 1/4 0 6 1/3 0/1 2 4 3/8 0 6 5/13 1/2 2 12 7/18 1/1 1 2 2/5 0/1 1 12 5/12 1/1 3 2 3/7 1/0 2 12 4/9 1/1 1 4 5/11 (0/1,1/0) 0 12 1/2 0 6 7/13 (0/1,1/0) 0 12 13/24 (0/1,1/0) 0 2 6/11 0/1 1 12 5/9 0 4 4/7 0/1 1 12 7/12 1/1 5 2 3/5 (1/1,2/1) 0 12 5/8 0 6 7/11 1/0 2 12 2/3 1/0 2 4 9/13 1/0 2 12 25/36 (-2/1,1/0) 0 2 16/23 -2/1 1 12 7/10 -1/1 1 6 5/7 (-1/1,0/1) 0 12 13/18 0/1 5 2 8/11 0/1 1 12 11/15 0 4 3/4 1/1 1 6 10/13 2/1 1 12 7/9 2/1 2 4 4/5 4/1 1 12 9/11 (8/1,1/0) 0 12 5/6 1/0 8 2 1/1 1/0 2 12 1/0 -1/1 1 2 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(11,10,-12,-11) (-1/1,-5/6) -> (-1/1,-5/6) Reflection Matrix(47,38,120,97) (-5/6,-4/5) -> (7/18,2/5) Glide Reflection Matrix(61,48,108,85) (-4/5,-7/9) -> (5/9,4/7) Hyperbolic Matrix(71,54,96,73) (-7/9,-3/4) -> (11/15,3/4) Glide Reflection Matrix(73,54,96,71) (-3/4,-8/11) -> (3/4,10/13) Glide Reflection Matrix(11,8,-84,-61) (-8/11,-5/7) -> (-1/7,0/1) Hyperbolic Matrix(37,26,84,59) (-5/7,-2/3) -> (3/7,4/9) Glide Reflection Matrix(59,38,132,85) (-2/3,-7/11) -> (4/9,5/11) Glide Reflection Matrix(35,22,-132,-83) (-7/11,-5/8) -> (-3/11,-1/4) Glide Reflection Matrix(13,8,60,37) (-5/8,-3/5) -> (1/5,1/4) Hyperbolic Matrix(71,42,-120,-71) (-3/5,-7/12) -> (-3/5,-7/12) Reflection Matrix(97,56,168,97) (-7/12,-4/7) -> (4/7,7/12) Hyperbolic Matrix(85,48,108,61) (-4/7,-5/9) -> (7/9,4/5) Hyperbolic Matrix(167,92,216,119) (-5/9,-6/11) -> (10/13,7/9) Hyperbolic Matrix(109,58,156,83) (-6/11,-1/2) -> (16/23,7/10) Glide Reflection Matrix(59,26,84,37) (-1/2,-3/7) -> (7/10,5/7) Glide Reflection Matrix(71,30,-168,-71) (-3/7,-5/12) -> (-3/7,-5/12) Reflection Matrix(49,20,120,49) (-5/12,-2/5) -> (2/5,5/12) Hyperbolic Matrix(11,4,-36,-13) (-2/5,-1/3) -> (-1/3,-2/7) Parabolic Matrix(107,30,132,37) (-2/7,-3/11) -> (4/5,9/11) Glide Reflection Matrix(37,8,60,13) (-1/4,-1/5) -> (3/5,5/8) Hyperbolic Matrix(11,2,-60,-11) (-1/5,-1/6) -> (-1/5,-1/6) Reflection Matrix(13,2,-84,-13) (-1/6,-1/7) -> (-1/6,-1/7) Reflection Matrix(61,-8,84,-11) (0/1,1/6) -> (13/18,8/11) Hyperbolic Matrix(11,-2,60,-11) (1/6,1/5) -> (1/6,1/5) Reflection Matrix(13,-4,36,-11) (1/4,1/3) -> (1/3,3/8) Parabolic Matrix(121,-46,192,-73) (3/8,5/13) -> (5/8,7/11) Glide Reflection Matrix(181,-70,468,-181) (5/13,7/18) -> (5/13,7/18) Reflection Matrix(71,-30,168,-71) (5/12,3/7) -> (5/12,3/7) Reflection Matrix(25,-12,48,-23) (5/11,1/2) -> (1/2,7/13) Parabolic Matrix(337,-182,624,-337) (7/13,13/24) -> (7/13,13/24) Reflection Matrix(659,-358,948,-515) (13/24,6/11) -> (25/36,16/23) Glide Reflection Matrix(193,-106,264,-145) (6/11,5/9) -> (8/11,11/15) Glide Reflection Matrix(71,-42,120,-71) (7/12,3/5) -> (7/12,3/5) Reflection Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(649,-450,936,-649) (9/13,25/36) -> (9/13,25/36) Reflection Matrix(181,-130,252,-181) (5/7,13/18) -> (5/7,13/18) Reflection Matrix(109,-90,132,-109) (9/11,5/6) -> (9/11,5/6) Reflection Matrix(11,-10,12,-11) (5/6,1/1) -> (5/6,1/1) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) 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) -> (-1/1,0/1) Matrix(11,10,-12,-11) -> Matrix(-1,0,2,1) (-1/1,-5/6) -> (-1/1,0/1) Matrix(47,38,120,97) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(61,48,108,85) -> Matrix(1,0,2,1) 0/1 Matrix(71,54,96,73) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(73,54,96,71) -> Matrix(3,2,2,1) Matrix(11,8,-84,-61) -> Matrix(1,0,0,1) Matrix(37,26,84,59) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(59,38,132,85) -> Matrix(3,2,2,1) Matrix(35,22,-132,-83) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(13,8,60,37) -> Matrix(1,0,2,1) 0/1 Matrix(71,42,-120,-71) -> Matrix(1,2,0,-1) (-3/5,-7/12) -> (-1/1,1/0) Matrix(97,56,168,97) -> Matrix(3,2,4,3) Matrix(85,48,108,61) -> Matrix(5,2,2,1) Matrix(167,92,216,119) -> Matrix(1,2,0,1) 1/0 Matrix(109,58,156,83) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(59,26,84,37) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(71,30,-168,-71) -> Matrix(-1,0,2,1) (-3/7,-5/12) -> (-1/1,0/1) Matrix(49,20,120,49) -> Matrix(3,2,4,3) Matrix(11,4,-36,-13) -> Matrix(1,0,0,1) Matrix(107,30,132,37) -> Matrix(11,6,2,1) Matrix(37,8,60,13) -> Matrix(5,2,2,1) Matrix(11,2,-60,-11) -> Matrix(-1,0,6,1) (-1/5,-1/6) -> (-1/3,0/1) Matrix(13,2,-84,-13) -> Matrix(1,0,0,-1) (-1/6,-1/7) -> (0/1,1/0) Matrix(61,-8,84,-11) -> Matrix(1,0,2,1) 0/1 Matrix(11,-2,60,-11) -> Matrix(1,0,4,-1) (1/6,1/5) -> (0/1,1/2) Matrix(13,-4,36,-11) -> Matrix(1,0,2,1) 0/1 Matrix(121,-46,192,-73) -> Matrix(5,-2,2,-1) Matrix(181,-70,468,-181) -> Matrix(3,-2,4,-3) (5/13,7/18) -> (1/2,1/1) Matrix(71,-30,168,-71) -> Matrix(-1,2,0,1) (5/12,3/7) -> (1/1,1/0) Matrix(25,-12,48,-23) -> Matrix(1,0,0,1) Matrix(337,-182,624,-337) -> Matrix(1,0,0,-1) (7/13,13/24) -> (0/1,1/0) Matrix(659,-358,948,-515) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(193,-106,264,-145) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(71,-42,120,-71) -> Matrix(3,-4,2,-3) (7/12,3/5) -> (1/1,2/1) Matrix(49,-32,72,-47) -> Matrix(1,-4,0,1) 1/0 Matrix(649,-450,936,-649) -> Matrix(1,4,0,-1) (9/13,25/36) -> (-2/1,1/0) Matrix(181,-130,252,-181) -> Matrix(-1,0,2,1) (5/7,13/18) -> (-1/1,0/1) Matrix(109,-90,132,-109) -> Matrix(-1,16,0,1) (9/11,5/6) -> (8/1,1/0) Matrix(11,-10,12,-11) -> Matrix(1,0,0,-1) (5/6,1/1) -> (0/1,1/0) Matrix(-1,2,0,1) -> Matrix(1,2,0,-1) (1/1,1/0) -> (-1/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.