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 -9/2 -4/1 -3/1 -21/8 -12/5 -24/11 -2/1 -9/5 -3/2 -15/11 -6/5 0/1 1/1 6/5 3/2 21/13 18/11 9/5 2/1 24/11 12/5 5/2 3/1 18/5 15/4 72/19 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 -1/1 -11/2 -1/2 -5/1 -2/3 -9/2 -1/2 1/0 -13/3 0/1 -4/1 -1/1 -1/3 -3/1 0/1 -8/3 -1/1 1/1 -29/11 -2/1 -21/8 -1/2 -55/21 -4/11 -34/13 -1/3 -13/5 0/1 -18/7 0/1 -5/2 1/4 -12/5 1/3 1/1 -7/3 2/3 -9/4 1/2 1/0 -11/5 0/1 -24/11 1/3 1/1 -13/6 1/2 -2/1 1/1 -13/7 2/1 -24/13 1/1 3/1 -11/6 1/0 -9/5 0/1 2/1 -7/4 3/2 -12/7 1/1 3/1 -5/3 4/1 -3/2 1/0 -7/5 2/1 -18/13 1/0 -11/8 1/0 -26/19 -5/1 -15/11 -4/1 -34/25 -3/1 -53/39 -22/7 -72/53 -3/1 -19/14 -5/2 -4/3 -3/1 -1/1 -17/13 0/1 -13/10 1/0 -9/7 -2/1 0/1 -5/4 -3/2 -6/5 -1/1 -7/6 1/0 -8/7 -1/1 -1/3 -1/1 0/1 0/1 -1/1 1/1 1/1 0/1 6/5 1/1 11/9 2/1 5/4 3/2 9/7 0/1 2/1 13/10 1/0 4/3 1/1 3/1 3/2 1/0 8/5 -1/1 1/1 29/18 1/2 21/13 2/1 55/34 11/4 34/21 3/1 13/8 1/0 18/11 1/0 5/3 -4/1 12/7 -3/1 -1/1 7/4 -3/2 9/5 -2/1 0/1 11/6 1/0 24/13 -3/1 -1/1 13/7 -2/1 2/1 -1/1 13/6 -1/2 24/11 -1/1 -1/3 11/5 0/1 9/4 -1/2 1/0 7/3 -2/3 12/5 -1/1 -1/3 5/2 -1/4 3/1 0/1 7/2 -1/2 18/5 0/1 11/3 0/1 26/7 1/5 15/4 1/4 34/9 1/3 53/14 7/22 72/19 1/3 19/5 2/5 4/1 1/3 1/1 17/4 1/0 13/3 0/1 9/2 1/2 1/0 5/1 2/3 6/1 1/1 7/1 0/1 8/1 1/1 3/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,72,-2,-13) (-6/1,1/0) -> (-6/1,-11/2) Parabolic Matrix(47,252,-36,-193) (-11/2,-5/1) -> (-17/13,-13/10) Hyperbolic Matrix(23,108,10,47) (-5/1,-9/2) -> (9/4,7/3) Hyperbolic Matrix(49,216,22,97) (-9/2,-13/3) -> (11/5,9/4) Hyperbolic Matrix(25,108,-22,-95) (-13/3,-4/1) -> (-8/7,-1/1) Hyperbolic Matrix(11,36,-4,-13) (-4/1,-3/1) -> (-3/1,-8/3) Parabolic Matrix(109,288,14,37) (-8/3,-29/11) -> (7/1,8/1) Hyperbolic Matrix(671,1764,-256,-673) (-29/11,-21/8) -> (-21/8,-55/21) Parabolic Matrix(1403,3672,-1032,-2701) (-55/21,-34/13) -> (-34/25,-53/39) Hyperbolic Matrix(179,468,96,251) (-34/13,-13/5) -> (13/7,2/1) Hyperbolic Matrix(167,432,46,119) (-13/5,-18/7) -> (18/5,11/3) Hyperbolic Matrix(85,216,24,61) (-18/7,-5/2) -> (7/2,18/5) Hyperbolic Matrix(59,144,34,83) (-5/2,-12/5) -> (12/7,7/4) Hyperbolic Matrix(61,144,36,85) (-12/5,-7/3) -> (5/3,12/7) Hyperbolic Matrix(47,108,10,23) (-7/3,-9/4) -> (9/2,5/1) Hyperbolic Matrix(97,216,22,49) (-9/4,-11/5) -> (13/3,9/2) Hyperbolic Matrix(263,576,142,311) (-11/5,-24/11) -> (24/13,13/7) Hyperbolic Matrix(265,576,144,313) (-24/11,-13/6) -> (11/6,24/13) Hyperbolic Matrix(217,468,134,289) (-13/6,-2/1) -> (34/21,13/8) Hyperbolic Matrix(193,360,52,97) (-2/1,-13/7) -> (11/3,26/7) Hyperbolic Matrix(311,576,142,263) (-13/7,-24/13) -> (24/11,11/5) 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(83,144,34,59) (-7/4,-12/7) -> (12/5,5/2) Hyperbolic Matrix(85,144,36,61) (-12/7,-5/3) -> (7/3,12/5) Hyperbolic Matrix(23,36,-16,-25) (-5/3,-3/2) -> (-3/2,-7/5) Parabolic Matrix(155,216,94,131) (-7/5,-18/13) -> (18/11,5/3) Hyperbolic Matrix(313,432,192,265) (-18/13,-11/8) -> (13/8,18/11) Hyperbolic Matrix(263,360,122,167) (-11/8,-26/19) -> (2/1,13/6) Hyperbolic Matrix(659,900,-484,-661) (-26/19,-15/11) -> (-15/11,-34/25) Parabolic Matrix(3815,5184,1006,1367) (-53/39,-72/53) -> (72/19,19/5) Hyperbolic Matrix(3817,5184,1008,1369) (-72/53,-19/14) -> (53/14,72/19) Hyperbolic Matrix(107,144,26,35) (-19/14,-4/3) -> (4/1,17/4) Hyperbolic Matrix(109,144,28,37) (-4/3,-17/13) -> (19/5,4/1) 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(59,72,-50,-61) (-5/4,-6/5) -> (-6/5,-7/6) Parabolic Matrix(251,288,156,179) (-7/6,-8/7) -> (8/5,29/18) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(61,-72,50,-59) (1/1,6/5) -> (6/5,11/9) Parabolic Matrix(205,-252,48,-59) (11/9,5/4) -> (17/4,13/3) Hyperbolic Matrix(83,-108,10,-13) (13/10,4/3) -> (8/1,1/0) Hyperbolic Matrix(25,-36,16,-23) (4/3,3/2) -> (3/2,8/5) Parabolic Matrix(1093,-1764,676,-1091) (29/18,21/13) -> (21/13,55/34) Parabolic Matrix(2269,-3672,600,-971) (55/34,34/21) -> (34/9,53/14) Hyperbolic Matrix(13,-36,4,-11) (5/2,3/1) -> (3/1,7/2) Parabolic Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) Parabolic Matrix(13,-72,2,-11) (5/1,6/1) -> (6/1,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(11,72,-2,-13) -> Matrix(1,2,-2,-3) Matrix(47,252,-36,-193) -> Matrix(3,2,-2,-1) Matrix(23,108,10,47) -> Matrix(1,0,0,1) Matrix(49,216,22,97) -> Matrix(1,0,0,1) Matrix(25,108,-22,-95) -> Matrix(1,0,0,1) Matrix(11,36,-4,-13) -> Matrix(1,0,2,1) Matrix(109,288,14,37) -> Matrix(1,2,0,1) Matrix(671,1764,-256,-673) -> Matrix(3,2,-8,-5) Matrix(1403,3672,-1032,-2701) -> Matrix(33,10,-10,-3) Matrix(179,468,96,251) -> Matrix(7,2,-4,-1) Matrix(167,432,46,119) -> Matrix(1,0,12,1) Matrix(85,216,24,61) -> Matrix(1,0,-6,1) Matrix(59,144,34,83) -> Matrix(5,-2,-2,1) Matrix(61,144,36,85) -> Matrix(5,-2,-2,1) Matrix(47,108,10,23) -> Matrix(1,0,0,1) Matrix(97,216,22,49) -> Matrix(1,0,0,1) Matrix(263,576,142,311) -> Matrix(5,-2,-2,1) Matrix(265,576,144,313) -> Matrix(5,-2,-2,1) Matrix(217,468,134,289) -> Matrix(7,-4,2,-1) Matrix(193,360,52,97) -> Matrix(1,-2,6,-11) Matrix(311,576,142,263) -> Matrix(1,-2,-2,5) Matrix(313,576,144,265) -> Matrix(1,-2,-2,5) Matrix(119,216,92,167) -> Matrix(1,0,0,1) Matrix(61,108,48,85) -> Matrix(1,0,0,1) Matrix(83,144,34,59) -> Matrix(1,-2,-2,5) Matrix(85,144,36,61) -> Matrix(1,-2,-2,5) Matrix(23,36,-16,-25) -> Matrix(1,-2,0,1) Matrix(155,216,94,131) -> Matrix(1,-6,0,1) Matrix(313,432,192,265) -> Matrix(1,12,0,1) Matrix(263,360,122,167) -> Matrix(1,6,-2,-11) Matrix(659,900,-484,-661) -> Matrix(7,32,-2,-9) Matrix(3815,5184,1006,1367) -> Matrix(9,28,26,81) Matrix(3817,5184,1008,1369) -> Matrix(9,26,28,81) Matrix(107,144,26,35) -> Matrix(1,2,2,5) Matrix(109,144,28,37) -> Matrix(1,2,2,5) Matrix(167,216,92,119) -> Matrix(1,0,0,1) Matrix(85,108,48,61) -> Matrix(1,0,0,1) Matrix(59,72,-50,-61) -> Matrix(1,2,-2,-3) Matrix(251,288,156,179) -> Matrix(1,0,2,1) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(61,-72,50,-59) -> Matrix(3,-2,2,-1) Matrix(205,-252,48,-59) -> Matrix(1,-2,2,-3) Matrix(83,-108,10,-13) -> Matrix(1,0,0,1) Matrix(25,-36,16,-23) -> Matrix(1,-2,0,1) Matrix(1093,-1764,676,-1091) -> Matrix(5,-8,2,-3) Matrix(2269,-3672,600,-971) -> Matrix(3,-10,10,-33) Matrix(13,-36,4,-11) -> Matrix(1,0,2,1) Matrix(241,-900,64,-239) -> Matrix(9,-2,32,-7) Matrix(13,-72,2,-11) -> 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: 48 Permutation triple for Y: ((2,6,19,39,43,46,40,20,7)(3,11,29,38,47,41,30,12,4)(5,16,36,27,10,9,26,37,17)(8,22,42,33,14,13,32,35,23); (1,4,14,34,26,40,45,41,22,28,27,39,44,29,35,15,5,2)(3,10)(6,17,31,13,12,21,20,9,25,42,47,48,43,36,24,23,11,18)(7,8)(16,30)(19,33)(32,46)(37,38); (1,2,8,24,36,30,45,40,32,31,17,38,44,39,33,25,9,3)(4,13)(5,6)(7,21,12,16,15,35,46,48,47,37,34,14,19,18,11,10,28,22)(20,26)(23,29)(27,43)(41,42)) ----------------------------------------------------------------------- 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 0/1 6/5 3/2 21/13 12/7 24/13 2/1 24/11 9/4 12/5 3/1 18/5 15/4 72/19 4/1 9/2 5/1 6/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/1 1/1 1/1 0/1 6/5 1/1 11/9 2/1 5/4 3/2 9/7 0/1 2/1 13/10 1/0 4/3 1/1 3/1 3/2 1/0 8/5 -1/1 1/1 29/18 1/2 21/13 2/1 55/34 11/4 34/21 3/1 13/8 1/0 18/11 1/0 5/3 -4/1 12/7 -3/1 -1/1 7/4 -3/2 9/5 -2/1 0/1 11/6 1/0 24/13 -3/1 -1/1 13/7 -2/1 2/1 -1/1 13/6 -1/2 24/11 -1/1 -1/3 11/5 0/1 9/4 -1/2 1/0 7/3 -2/3 12/5 -1/1 -1/3 5/2 -1/4 3/1 0/1 7/2 -1/2 18/5 0/1 11/3 0/1 26/7 1/5 15/4 1/4 34/9 1/3 53/14 7/22 72/19 1/3 19/5 2/5 4/1 1/3 1/1 17/4 1/0 13/3 0/1 9/2 1/2 1/0 5/1 2/3 6/1 1/1 7/1 0/1 8/1 1/1 3/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(61,-72,50,-59) (1/1,6/5) -> (6/5,11/9) Parabolic Matrix(205,-252,48,-59) (11/9,5/4) -> (17/4,13/3) Hyperbolic Matrix(85,-108,37,-47) (5/4,9/7) -> (9/4,7/3) Hyperbolic Matrix(167,-216,75,-97) (9/7,13/10) -> (11/5,9/4) Hyperbolic Matrix(83,-108,10,-13) (13/10,4/3) -> (8/1,1/0) Hyperbolic Matrix(25,-36,16,-23) (4/3,3/2) -> (3/2,8/5) Parabolic Matrix(179,-288,23,-37) (8/5,29/18) -> (7/1,8/1) Hyperbolic Matrix(1093,-1764,676,-1091) (29/18,21/13) -> (21/13,55/34) Parabolic Matrix(2269,-3672,600,-971) (55/34,34/21) -> (34/9,53/14) Hyperbolic Matrix(289,-468,155,-251) (34/21,13/8) -> (13/7,2/1) Hyperbolic Matrix(265,-432,73,-119) (13/8,18/11) -> (18/5,11/3) Hyperbolic Matrix(131,-216,37,-61) (18/11,5/3) -> (7/2,18/5) Hyperbolic Matrix(85,-144,49,-83) (5/3,12/7) -> (12/7,7/4) Parabolic Matrix(61,-108,13,-23) (7/4,9/5) -> (9/2,5/1) Hyperbolic Matrix(119,-216,27,-49) (9/5,11/6) -> (13/3,9/2) Hyperbolic Matrix(313,-576,169,-311) (11/6,24/13) -> (24/13,13/7) Parabolic Matrix(167,-360,45,-97) (2/1,13/6) -> (11/3,26/7) Hyperbolic Matrix(265,-576,121,-263) (13/6,24/11) -> (24/11,11/5) Parabolic Matrix(61,-144,25,-59) (7/3,12/5) -> (12/5,5/2) Parabolic Matrix(13,-36,4,-11) (5/2,3/1) -> (3/1,7/2) Parabolic Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) Parabolic Matrix(1369,-5184,361,-1367) (53/14,72/19) -> (72/19,19/5) Parabolic Matrix(37,-144,9,-35) (19/5,4/1) -> (4/1,17/4) Parabolic Matrix(13,-72,2,-11) (5/1,6/1) -> (6/1,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(0,-1,1,0) Matrix(61,-72,50,-59) -> Matrix(3,-2,2,-1) Matrix(205,-252,48,-59) -> Matrix(1,-2,2,-3) Matrix(85,-108,37,-47) -> Matrix(0,-1,1,0) Matrix(167,-216,75,-97) -> Matrix(0,-1,1,0) Matrix(83,-108,10,-13) -> Matrix(1,0,0,1) Matrix(25,-36,16,-23) -> Matrix(1,-2,0,1) Matrix(179,-288,23,-37) -> Matrix(2,-1,1,0) Matrix(1093,-1764,676,-1091) -> Matrix(5,-8,2,-3) Matrix(2269,-3672,600,-971) -> Matrix(3,-10,10,-33) Matrix(289,-468,155,-251) -> Matrix(2,-7,-1,4) Matrix(265,-432,73,-119) -> Matrix(0,1,-1,12) Matrix(131,-216,37,-61) -> Matrix(0,-1,1,6) Matrix(85,-144,49,-83) -> Matrix(2,5,-1,-2) Matrix(61,-108,13,-23) -> Matrix(0,-1,1,0) Matrix(119,-216,27,-49) -> Matrix(0,-1,1,0) Matrix(313,-576,169,-311) -> Matrix(2,5,-1,-2) Matrix(167,-360,45,-97) -> Matrix(2,1,11,6) Matrix(265,-576,121,-263) -> Matrix(2,1,-5,-2) Matrix(61,-144,25,-59) -> Matrix(2,1,-5,-2) Matrix(13,-36,4,-11) -> Matrix(1,0,2,1) Matrix(241,-900,64,-239) -> Matrix(9,-2,32,-7) Matrix(1369,-5184,361,-1367) -> Matrix(28,-9,81,-26) Matrix(37,-144,9,-35) -> Matrix(2,-1,5,-2) Matrix(13,-72,2,-11) -> Matrix(3,-2,2,-1) 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): 15 ----------------------------------------------------------------------- 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 (-1/1,1/1).(0/1,1/0) 0 1 2/1 -1/1 1 9 13/6 -1/2 1 18 24/11 (-1/1,-1/3).(-1/2,0/1) 0 3 11/5 0/1 1 18 9/4 0 2 7/3 -2/3 1 18 12/5 (-1/1,-1/3).(-1/2,0/1) 0 3 5/2 -1/4 1 18 3/1 0/1 3 6 7/2 -1/2 1 18 18/5 0/1 9 1 11/3 0/1 1 18 26/7 1/5 1 9 15/4 1/4 3 6 34/9 1/3 1 9 72/19 1/3 9 1 19/5 2/5 1 18 4/1 (0/1,1/2).(1/3,1/1) 0 9 13/3 0/1 1 18 9/2 0 2 5/1 2/3 1 18 6/1 1/1 3 3 7/1 0/1 1 18 8/1 (1/1,3/1).(2/1,1/0) 0 9 1/0 1/0 1 18 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(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(167,-360,45,-97) (2/1,13/6) -> (11/3,26/7) Hyperbolic Matrix(265,-576,121,-263) (13/6,24/11) -> (24/11,11/5) Parabolic Matrix(97,-216,22,-49) (11/5,9/4) -> (13/3,9/2) Glide Reflection Matrix(47,-108,10,-23) (9/4,7/3) -> (9/2,5/1) Glide Reflection Matrix(61,-144,25,-59) (7/3,12/5) -> (12/5,5/2) Parabolic Matrix(13,-36,4,-11) (5/2,3/1) -> (3/1,7/2) Parabolic Matrix(71,-252,20,-71) (7/2,18/5) -> (7/2,18/5) Reflection Matrix(109,-396,30,-109) (18/5,11/3) -> (18/5,11/3) Reflection Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) Parabolic Matrix(647,-2448,171,-647) (34/9,72/19) -> (34/9,72/19) Reflection Matrix(721,-2736,190,-721) (72/19,19/5) -> (72/19,19/5) Reflection Matrix(47,-180,6,-23) (19/5,4/1) -> (7/1,8/1) Glide Reflection Matrix(25,-108,3,-13) (4/1,13/3) -> (8/1,1/0) Glide Reflection Matrix(13,-72,2,-11) (5/1,6/1) -> (6/1,7/1) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(0,1,1,0) (0/1,2/1) -> (-1/1,1/1) Matrix(167,-360,45,-97) -> Matrix(2,1,11,6) Matrix(265,-576,121,-263) -> Matrix(2,1,-5,-2) (-1/1,-1/3).(-1/2,0/1) Matrix(97,-216,22,-49) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(47,-108,10,-23) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(61,-144,25,-59) -> Matrix(2,1,-5,-2) (-1/1,-1/3).(-1/2,0/1) Matrix(13,-36,4,-11) -> Matrix(1,0,2,1) 0/1 Matrix(71,-252,20,-71) -> Matrix(-1,0,4,1) (7/2,18/5) -> (-1/2,0/1) Matrix(109,-396,30,-109) -> Matrix(1,0,14,-1) (18/5,11/3) -> (0/1,1/7) Matrix(241,-900,64,-239) -> Matrix(9,-2,32,-7) 1/4 Matrix(647,-2448,171,-647) -> Matrix(16,-5,51,-16) (34/9,72/19) -> (5/17,1/3) Matrix(721,-2736,190,-721) -> Matrix(11,-4,30,-11) (72/19,19/5) -> (1/3,2/5) Matrix(47,-180,6,-23) -> Matrix(5,-2,2,-1) Matrix(25,-108,3,-13) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(13,-72,2,-11) -> Matrix(3,-2,2,-1) 1/1 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.