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 -6/1 -5/1 -4/1 -3/1 -2/1 -9/5 -3/2 -4/3 -6/5 -1/1 -9/11 -3/4 -2/3 -3/5 0/1 1/2 3/5 2/3 3/4 9/11 1/1 6/5 5/4 4/3 3/2 12/7 9/5 2/1 24/11 11/5 7/3 12/5 5/2 3/1 11/3 4/1 5/1 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -6/1 1/0 -5/1 -2/1 1/0 -4/1 -1/1 -3/1 -1/1 -8/3 -1/1 -13/5 -1/1 1/0 -18/7 -1/1 -5/2 -1/2 -12/5 -1/1 -7/3 -1/1 -1/2 -9/4 0/1 -11/5 -1/1 -2/1 0/1 -13/7 1/1 -24/13 1/0 -11/6 1/0 -9/5 -1/1 1/1 -7/4 -1/2 -12/7 0/1 -5/3 1/1 -8/5 -1/1 -11/7 -1/1 -1/2 -3/2 0/1 -13/9 1/1 1/0 -36/25 1/0 -23/16 1/0 -10/7 0/1 -7/5 1/1 -18/13 1/0 -11/8 1/0 -15/11 -1/1 1/1 -4/3 1/0 -13/10 1/0 -9/7 -1/1 -5/4 1/0 -11/9 -1/1 -6/5 0/1 -1/1 0/1 1/0 -6/7 0/1 -5/6 1/0 -9/11 1/1 -4/5 1/0 -11/14 1/0 -7/9 -1/1 -3/4 0/1 -11/15 1/2 1/1 -8/11 1/1 -5/7 -1/1 -12/17 0/1 -7/10 1/2 -9/13 -1/1 1/1 -11/16 1/0 -2/3 0/1 -7/11 1/2 1/1 -12/19 1/1 -5/8 1/2 -3/5 1/1 -7/12 1/0 -11/19 1/1 3/2 -4/7 1/1 -5/9 2/1 1/0 -6/11 1/0 -7/13 1/1 -1/2 1/0 0/1 1/0 1/2 1/0 5/9 -5/1 4/7 -3/1 3/5 -3/1 -1/1 8/13 -3/1 5/8 1/0 7/11 -3/1 2/3 -2/1 9/13 -1/1 7/10 1/0 5/7 -2/1 -3/2 8/11 -1/1 3/4 -2/1 7/9 -5/3 -3/2 11/14 -3/2 4/5 -3/2 9/11 -7/5 -1/1 5/6 -5/4 1/1 -1/1 7/6 -3/2 6/5 -1/1 11/9 -1/1 -5/6 5/4 -3/4 9/7 -1/1 -3/5 13/10 -1/2 4/3 -1/2 15/11 -1/1 26/19 -2/3 11/8 -1/2 7/5 -1/2 -1/3 10/7 0/1 3/2 0/1 14/9 0/1 25/16 1/0 36/23 1/0 11/7 -1/1 19/12 1/0 8/5 -1/1 5/3 -1/2 0/1 17/10 -1/4 12/7 0/1 7/4 1/0 9/5 -1/1 11/6 -1/2 2/1 0/1 13/6 1/2 24/11 1/2 11/5 1/2 1/1 9/4 0/1 7/3 1/1 19/8 1/2 12/5 1/1 5/2 1/0 3/1 -1/1 1/1 7/2 1/0 18/5 0/1 11/3 1/1 15/4 0/1 4/1 1/1 5/1 3/1 11/2 1/0 6/1 1/0 13/2 1/0 7/1 -3/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,84,-8,-61) (-6/1,1/0) -> (-18/13,-11/8) Hyperbolic Matrix(11,60,-20,-109) (-6/1,-5/1) -> (-5/9,-6/11) Hyperbolic Matrix(13,60,8,37) (-5/1,-4/1) -> (8/5,5/3) Hyperbolic Matrix(11,36,-4,-13) (-4/1,-3/1) -> (-3/1,-8/3) Parabolic Matrix(73,192,-100,-263) (-8/3,-13/5) -> (-11/15,-8/11) Hyperbolic Matrix(107,276,88,227) (-13/5,-18/7) -> (6/5,11/9) Hyperbolic Matrix(61,156,52,133) (-18/7,-5/2) -> (7/6,6/5) 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(37,84,48,109) (-7/3,-9/4) -> (3/4,7/9) 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(395,732,252,467) (-13/7,-24/13) -> (36/23,11/7) 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(61,108,48,85) (-9/5,-7/4) -> (5/4,9/7) 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(37,60,8,13) (-5/3,-8/5) -> (4/1,5/1) Hyperbolic Matrix(83,132,-144,-229) (-8/5,-11/7) -> (-11/19,-4/7) Hyperbolic Matrix(47,72,-32,-49) (-11/7,-3/2) -> (-3/2,-13/9) Parabolic Matrix(491,708,224,323) (-13/9,-36/25) -> (24/11,11/5) Hyperbolic Matrix(1201,1728,768,1105) (-36/25,-23/16) -> (25/16,36/23) Hyperbolic Matrix(493,708,360,517) (-23/16,-10/7) -> (26/19,11/8) Hyperbolic Matrix(59,84,92,131) (-10/7,-7/5) -> (7/11,2/3) Hyperbolic Matrix(121,168,-224,-311) (-7/5,-18/13) -> (-6/11,-7/13) Hyperbolic Matrix(193,264,-280,-383) (-11/8,-15/11) -> (-9/13,-11/16) Hyperbolic Matrix(71,96,88,119) (-15/11,-4/3) -> (4/5,9/11) Hyperbolic Matrix(73,96,92,121) (-4/3,-13/10) -> (11/14,4/5) Hyperbolic Matrix(167,216,92,119) (-13/10,-9/7) -> (9/5,11/6) Hyperbolic Matrix(85,108,48,61) (-9/7,-5/4) -> (7/4,9/5) Hyperbolic Matrix(215,264,136,167) (-5/4,-11/9) -> (11/7,19/12) Hyperbolic Matrix(217,264,60,73) (-11/9,-6/5) -> (18/5,11/3) Hyperbolic Matrix(11,12,-12,-13) (-6/5,-1/1) -> (-1/1,-6/7) Parabolic Matrix(157,132,44,37) (-6/7,-5/6) -> (7/2,18/5) Hyperbolic Matrix(131,108,188,155) (-5/6,-9/11) -> (9/13,7/10) Hyperbolic Matrix(119,96,88,71) (-9/11,-4/5) -> (4/3,15/11) Hyperbolic Matrix(121,96,92,73) (-4/5,-11/14) -> (13/10,4/3) Hyperbolic Matrix(107,84,-200,-157) (-11/14,-7/9) -> (-7/13,-1/2) Hyperbolic Matrix(109,84,48,37) (-7/9,-3/4) -> (9/4,7/3) Hyperbolic Matrix(179,132,80,59) (-3/4,-11/15) -> (11/5,9/4) Hyperbolic Matrix(83,60,148,107) (-8/11,-5/7) -> (5/9,4/7) Hyperbolic Matrix(409,288,240,169) (-12/17,-7/10) -> (17/10,12/7) Hyperbolic Matrix(155,108,188,131) (-7/10,-9/13) -> (9/11,5/6) Hyperbolic Matrix(299,204,192,131) (-11/16,-2/3) -> (14/9,25/16) Hyperbolic Matrix(131,84,92,59) (-2/3,-7/11) -> (7/5,10/7) Hyperbolic Matrix(457,288,192,121) (-12/19,-5/8) -> (19/8,12/5) Hyperbolic Matrix(59,36,-100,-61) (-5/8,-3/5) -> (-3/5,-7/12) Parabolic Matrix(227,132,184,107) (-7/12,-11/19) -> (11/9,5/4) Hyperbolic Matrix(107,60,148,83) (-4/7,-5/9) -> (5/7,8/11) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(109,-60,20,-11) (1/2,5/9) -> (5/1,11/2) Hyperbolic Matrix(61,-36,100,-59) (4/7,3/5) -> (3/5,8/13) Parabolic Matrix(311,-192,196,-121) (8/13,5/8) -> (19/12,8/5) Hyperbolic Matrix(265,-168,112,-71) (5/8,7/11) -> (7/3,19/8) Hyperbolic Matrix(383,-264,280,-193) (2/3,9/13) -> (15/11,26/19) Hyperbolic Matrix(169,-120,100,-71) (7/10,5/7) -> (5/3,17/10) Hyperbolic Matrix(181,-132,48,-35) (8/11,3/4) -> (15/4,4/1) Hyperbolic Matrix(215,-168,32,-25) (7/9,11/14) -> (13/2,7/1) Hyperbolic Matrix(13,-12,12,-11) (5/6,1/1) -> (1/1,7/6) Parabolic Matrix(61,-84,8,-11) (11/8,7/5) -> (7/1,1/0) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(13,-36,4,-11) (5/2,3/1) -> (3/1,7/2) Parabolic Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(11,84,-8,-61) -> Matrix(1,2,0,1) Matrix(11,60,-20,-109) -> Matrix(1,4,0,1) Matrix(13,60,8,37) -> Matrix(1,2,-2,-3) Matrix(11,36,-4,-13) -> Matrix(1,2,-2,-3) Matrix(73,192,-100,-263) -> Matrix(1,0,2,1) Matrix(107,276,88,227) -> Matrix(5,6,-6,-7) Matrix(61,156,52,133) -> Matrix(5,4,-4,-3) Matrix(49,120,20,49) -> Matrix(1,0,2,1) Matrix(71,168,-112,-265) -> Matrix(3,2,4,3) Matrix(37,84,48,109) -> Matrix(7,2,-4,-1) Matrix(119,264,32,71) -> Matrix(1,0,2,1) Matrix(23,48,-12,-25) -> Matrix(1,0,2,1) Matrix(395,732,252,467) -> Matrix(1,-2,0,1) Matrix(313,576,144,265) -> Matrix(1,0,2,1) Matrix(119,216,92,167) -> Matrix(1,2,-2,-3) Matrix(61,108,48,85) -> Matrix(1,2,-2,-3) Matrix(97,168,56,97) -> Matrix(1,0,2,1) Matrix(71,120,-100,-169) -> Matrix(1,0,-2,1) Matrix(37,60,8,13) -> Matrix(1,2,0,1) Matrix(83,132,-144,-229) -> Matrix(1,2,0,1) Matrix(47,72,-32,-49) -> Matrix(1,0,2,1) Matrix(491,708,224,323) -> Matrix(1,-2,2,-3) Matrix(1201,1728,768,1105) -> Matrix(1,0,0,1) Matrix(493,708,360,517) -> Matrix(1,2,-2,-3) Matrix(59,84,92,131) -> Matrix(5,-2,-2,1) Matrix(121,168,-224,-311) -> Matrix(1,0,0,1) Matrix(193,264,-280,-383) -> Matrix(1,0,0,1) Matrix(71,96,88,119) -> Matrix(3,-4,-2,3) Matrix(73,96,92,121) -> Matrix(3,2,-2,-1) Matrix(167,216,92,119) -> Matrix(1,2,-2,-3) Matrix(85,108,48,61) -> Matrix(1,0,0,1) Matrix(215,264,136,167) -> Matrix(1,0,0,1) Matrix(217,264,60,73) -> Matrix(1,0,2,1) Matrix(11,12,-12,-13) -> Matrix(1,0,0,1) Matrix(157,132,44,37) -> Matrix(1,0,0,1) Matrix(131,108,188,155) -> Matrix(1,-2,0,1) Matrix(119,96,88,71) -> Matrix(1,0,-2,1) Matrix(121,96,92,73) -> Matrix(1,2,-2,-3) Matrix(107,84,-200,-157) -> Matrix(1,2,0,1) Matrix(109,84,48,37) -> Matrix(1,0,2,1) Matrix(179,132,80,59) -> Matrix(1,0,0,1) Matrix(83,60,148,107) -> Matrix(1,-4,0,1) Matrix(409,288,240,169) -> Matrix(1,0,-6,1) Matrix(155,108,188,131) -> Matrix(3,-4,-2,3) Matrix(299,204,192,131) -> Matrix(1,0,0,1) Matrix(131,84,92,59) -> Matrix(1,0,-4,1) Matrix(457,288,192,121) -> Matrix(1,0,0,1) Matrix(59,36,-100,-61) -> Matrix(3,-2,2,-1) Matrix(227,132,184,107) -> Matrix(3,-2,-4,3) Matrix(107,60,148,83) -> Matrix(3,-4,-2,3) Matrix(1,0,4,1) -> Matrix(1,-2,0,1) Matrix(109,-60,20,-11) -> Matrix(1,8,0,1) Matrix(61,-36,100,-59) -> Matrix(1,0,0,1) Matrix(311,-192,196,-121) -> Matrix(1,2,0,1) Matrix(265,-168,112,-71) -> Matrix(1,2,2,5) Matrix(383,-264,280,-193) -> Matrix(3,4,-4,-5) Matrix(169,-120,100,-71) -> Matrix(1,2,-4,-7) Matrix(181,-132,48,-35) -> Matrix(1,2,0,1) Matrix(215,-168,32,-25) -> Matrix(9,14,-2,-3) Matrix(13,-12,12,-11) -> Matrix(1,2,-2,-3) Matrix(61,-84,8,-11) -> Matrix(3,2,-2,-1) Matrix(49,-72,32,-47) -> Matrix(1,0,2,1) Matrix(25,-48,12,-23) -> Matrix(1,0,4,1) Matrix(13,-36,4,-11) -> Matrix(1,0,0,1) Matrix(25,-144,4,-23) -> Matrix(1,-12,0,1) 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): 16 Degree of the the map X: 16 Degree of the the map Y: 64 Permutation triple for Y: ((1,2)(3,10,37,62,38,11)(4,15,47,48,16,5)(6,21,58,61,34,22)(7,26,51,60,27,8)(9,32,57,20,56,33)(12,40,28,23,50,17)(13,35,25,24,44,14)(18,52,30,29,53,19)(31,45)(36,49)(39,46)(41,59)(42,43)(54,55)(63,64); (1,5,19,55,20,6)(2,8,30,31,9,3)(4,14)(7,25)(10,13,43,28,27,36)(11,12)(15,46,34,33,59,29)(16,49,21,24,41,17)(18,26,39,38,57,42)(22,23)(32,48)(35,61,63,47,40,54)(37,53)(44,62,64,51,50,45)(52,58)(56,60); (1,3,12,41,33,60,64,61,52,42,13,4)(2,6,23,43,57,48,63,62,53,59,24,7)(5,17,51,18)(8,28,47,29)(9,34,35,10)(11,39,15,14,45,30,58,49,27,56,55,40)(16,32,31,50,22,46,26,25,54,19,37,36)(20,38,44,21)) ----------------------------------------------------------------------- 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 -6/1 1/0 1 2 -5/1 (-2/1,1/0) 0 12 -4/1 -1/1 1 6 -3/1 -1/1 2 4 -8/3 -1/1 1 6 -13/5 (-1/1,1/0) 0 12 -5/2 -1/2 1 12 -12/5 -1/1 1 2 -7/3 (-1/1,-1/2) 0 12 -2/1 0/1 1 6 -11/6 1/0 1 12 -9/5 0 4 -7/4 -1/2 1 12 -12/7 0/1 5 2 -5/3 1/1 2 12 -8/5 -1/1 1 6 -11/7 (-1/1,-1/2) 0 12 -3/2 0/1 1 4 -7/5 1/1 2 12 -18/13 1/0 1 2 -11/8 1/0 1 12 -4/3 1/0 1 6 -9/7 -1/1 2 4 -5/4 1/0 1 12 -6/5 0/1 1 2 -1/1 (0/1,1/0) 0 12 0/1 1/0 1 2 1/1 -1/1 2 12 6/5 -1/1 5 2 11/9 (-1/1,-5/6) 0 12 5/4 -3/4 1 12 9/7 0 4 13/10 -1/2 1 12 4/3 -1/2 1 6 15/11 -1/1 2 4 11/8 -1/2 1 12 7/5 (-1/2,-1/3) 0 12 10/7 0/1 1 6 3/2 0/1 1 4 14/9 0/1 1 6 25/16 1/0 1 12 36/23 1/0 2 2 11/7 -1/1 2 12 8/5 -1/1 1 6 5/3 (-1/2,0/1) 0 12 12/7 0/1 5 2 7/4 1/0 1 12 9/5 -1/1 2 4 11/6 -1/2 1 12 2/1 0/1 2 6 13/6 1/2 1 12 24/11 1/2 2 2 11/5 (1/2,1/1) 0 12 9/4 0/1 1 4 7/3 1/1 2 12 12/5 1/1 1 2 5/2 1/0 1 12 3/1 0 4 7/2 1/0 1 12 18/5 0/1 1 2 11/3 1/1 2 12 4/1 1/1 1 6 5/1 3/1 2 12 6/1 1/0 6 2 7/1 (-3/1,1/0) 0 12 1/0 1/0 1 12 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,84,-8,-61) (-6/1,1/0) -> (-18/13,-11/8) Hyperbolic Matrix(11,60,-2,-11) (-6/1,-5/1) -> (-6/1,-5/1) Reflection Matrix(13,60,8,37) (-5/1,-4/1) -> (8/5,5/3) Hyperbolic Matrix(11,36,-4,-13) (-4/1,-3/1) -> (-3/1,-8/3) Parabolic Matrix(73,192,-46,-121) (-8/3,-13/5) -> (-8/5,-11/7) Glide Reflection Matrix(47,120,38,97) (-13/5,-5/2) -> (11/9,5/4) Glide Reflection Matrix(49,120,20,49) (-5/2,-12/5) -> (12/5,5/2) Hyperbolic Matrix(71,168,-30,-71) (-12/5,-7/3) -> (-12/5,-7/3) Reflection Matrix(37,84,26,59) (-7/3,-2/1) -> (7/5,10/7) Glide Reflection Matrix(109,204,70,131) (-2/1,-11/6) -> (14/9,25/16) Glide Reflection Matrix(119,216,92,167) (-11/6,-9/5) -> (9/7,13/10) Hyperbolic Matrix(61,108,48,85) (-9/5,-7/4) -> (5/4,9/7) Hyperbolic Matrix(97,168,56,97) (-7/4,-12/7) -> (12/7,7/4) Hyperbolic Matrix(71,120,-42,-71) (-12/7,-5/3) -> (-12/7,-5/3) Reflection Matrix(37,60,8,13) (-5/3,-8/5) -> (4/1,5/1) Hyperbolic Matrix(85,132,38,59) (-11/7,-3/2) -> (11/5,9/4) Glide Reflection Matrix(59,84,26,37) (-3/2,-7/5) -> (9/4,7/3) Glide Reflection Matrix(181,252,-130,-181) (-7/5,-18/13) -> (-7/5,-18/13) Reflection Matrix(71,96,54,73) (-11/8,-4/3) -> (13/10,4/3) Glide Reflection Matrix(73,96,54,71) (-4/3,-9/7) -> (4/3,15/11) Glide Reflection Matrix(85,108,48,61) (-9/7,-5/4) -> (7/4,9/5) Hyperbolic Matrix(107,132,30,37) (-5/4,-6/5) -> (7/2,18/5) Glide Reflection Matrix(11,12,-10,-11) (-6/5,-1/1) -> (-6/5,-1/1) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(11,-12,10,-11) (1/1,6/5) -> (1/1,6/5) Reflection Matrix(109,-132,90,-109) (6/5,11/9) -> (6/5,11/9) Reflection Matrix(193,-264,106,-145) (15/11,11/8) -> (9/5,11/6) Glide Reflection Matrix(61,-84,8,-11) (11/8,7/5) -> (7/1,1/0) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(683,-1068,314,-491) (25/16,36/23) -> (13/6,24/11) Glide Reflection Matrix(505,-792,322,-505) (36/23,11/7) -> (36/23,11/7) Reflection Matrix(83,-132,22,-35) (11/7,8/5) -> (11/3,4/1) Glide Reflection Matrix(71,-120,42,-71) (5/3,12/7) -> (5/3,12/7) Reflection Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(241,-528,110,-241) (24/11,11/5) -> (24/11,11/5) Reflection Matrix(71,-168,30,-71) (7/3,12/5) -> (7/3,12/5) Reflection Matrix(13,-36,4,-11) (5/2,3/1) -> (3/1,7/2) Parabolic Matrix(109,-396,30,-109) (18/5,11/3) -> (18/5,11/3) Reflection Matrix(11,-60,2,-11) (5/1,6/1) -> (5/1,6/1) Reflection Matrix(13,-84,2,-13) (6/1,7/1) -> (6/1,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(11,84,-8,-61) -> Matrix(1,2,0,1) 1/0 Matrix(11,60,-2,-11) -> Matrix(1,4,0,-1) (-6/1,-5/1) -> (-2/1,1/0) Matrix(13,60,8,37) -> Matrix(1,2,-2,-3) -1/1 Matrix(11,36,-4,-13) -> Matrix(1,2,-2,-3) -1/1 Matrix(73,192,-46,-121) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(47,120,38,97) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(49,120,20,49) -> Matrix(1,0,2,1) 0/1 Matrix(71,168,-30,-71) -> Matrix(3,2,-4,-3) (-12/5,-7/3) -> (-1/1,-1/2) Matrix(37,84,26,59) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(109,204,70,131) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(119,216,92,167) -> Matrix(1,2,-2,-3) -1/1 Matrix(61,108,48,85) -> Matrix(1,2,-2,-3) -1/1 Matrix(97,168,56,97) -> Matrix(1,0,2,1) 0/1 Matrix(71,120,-42,-71) -> Matrix(1,0,2,-1) (-12/7,-5/3) -> (0/1,1/1) Matrix(37,60,8,13) -> Matrix(1,2,0,1) 1/0 Matrix(85,132,38,59) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(59,84,26,37) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(181,252,-130,-181) -> Matrix(-1,2,0,1) (-7/5,-18/13) -> (1/1,1/0) Matrix(71,96,54,73) -> Matrix(1,-2,-2,3) Matrix(73,96,54,71) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(85,108,48,61) -> Matrix(1,0,0,1) Matrix(107,132,30,37) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(11,12,-10,-11) -> Matrix(1,0,0,-1) (-6/5,-1/1) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,0,-1) (-1/1,0/1) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,2,0,-1) (0/1,1/1) -> (-1/1,1/0) Matrix(11,-12,10,-11) -> Matrix(-1,0,2,1) (1/1,6/5) -> (-1/1,0/1) Matrix(109,-132,90,-109) -> Matrix(11,10,-12,-11) (6/5,11/9) -> (-1/1,-5/6) Matrix(193,-264,106,-145) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(61,-84,8,-11) -> Matrix(3,2,-2,-1) -1/1 Matrix(49,-72,32,-47) -> Matrix(1,0,2,1) 0/1 Matrix(683,-1068,314,-491) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(505,-792,322,-505) -> Matrix(1,2,0,-1) (36/23,11/7) -> (-1/1,1/0) Matrix(83,-132,22,-35) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(71,-120,42,-71) -> Matrix(-1,0,4,1) (5/3,12/7) -> (-1/2,0/1) Matrix(25,-48,12,-23) -> Matrix(1,0,4,1) 0/1 Matrix(241,-528,110,-241) -> Matrix(3,-2,4,-3) (24/11,11/5) -> (1/2,1/1) Matrix(71,-168,30,-71) -> Matrix(1,0,2,-1) (7/3,12/5) -> (0/1,1/1) Matrix(13,-36,4,-11) -> Matrix(1,0,0,1) Matrix(109,-396,30,-109) -> Matrix(1,0,2,-1) (18/5,11/3) -> (0/1,1/1) Matrix(11,-60,2,-11) -> Matrix(-1,6,0,1) (5/1,6/1) -> (3/1,1/0) Matrix(13,-84,2,-13) -> Matrix(1,6,0,-1) (6/1,7/1) -> (-3/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.