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): 768 Minimal number of generators: 129 Number of equivalence classes of cusps: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/1 -8/1 -15/2 -6/1 -9/2 -4/1 -3/1 -8/3 -21/8 -16/7 -2/1 -8/5 -3/2 -4/3 -6/5 -8/7 0/1 1/1 6/5 24/19 4/3 24/17 3/2 36/23 8/5 12/7 24/13 2/1 24/11 12/5 5/2 21/8 8/3 192/71 3/1 36/11 10/3 24/7 7/2 11/3 23/6 4/1 9/2 19/4 24/5 5/1 11/2 6/1 13/2 7/1 15/2 8/1 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 1/0 -8/1 -1/1 -15/2 -1/2 -7/1 1/0 -6/1 -1/1 -11/2 -1/1 -2/3 -5/1 1/0 -24/5 -1/1 -19/4 -1/1 -6/7 -14/3 -1/1 -23/5 -1/2 -9/2 -1/2 -13/3 -1/2 -17/4 -2/3 -1/2 -4/1 0/1 -19/5 -1/2 -15/4 1/0 -26/7 -1/1 -11/3 1/0 -18/5 -1/1 -7/2 0/1 1/0 -24/7 1/0 -17/5 1/0 -27/8 1/0 -10/3 -1/1 -33/10 1/0 -56/17 -1/1 -23/7 -1/2 -36/11 0/1 -13/4 0/1 1/1 -3/1 1/0 -14/5 -3/1 -25/9 -5/2 -36/13 -2/1 -11/4 -2/1 -1/1 -19/7 -1/2 -8/3 1/0 -29/11 -5/2 -21/8 1/0 -34/13 -3/1 -47/18 -3/1 -2/1 -13/5 1/0 -5/2 -2/1 1/0 -12/5 -2/1 -19/8 -2/1 -9/5 -26/11 -5/3 -33/14 -7/4 -7/3 -3/2 -23/10 -2/1 1/0 -16/7 -2/1 -25/11 -3/2 -9/4 -3/2 -11/5 -3/2 -24/11 -1/1 -13/6 -2/1 -1/1 -2/1 -1/1 -13/7 1/0 -24/13 -2/1 -11/6 -2/1 -1/1 -9/5 1/0 -25/14 -2/1 1/0 -16/9 -2/1 -7/4 -2/1 1/0 -12/7 -2/1 -17/10 -2/1 -11/6 -22/13 -9/5 -49/29 -7/4 -27/16 -7/4 -5/3 -3/2 -28/17 -2/1 -23/14 -7/4 -12/7 -18/11 -5/3 -31/19 -13/8 -13/8 -5/3 -8/5 -21/13 -3/2 -8/5 -3/2 -27/17 -3/2 -73/46 -2/1 -3/2 -192/121 -3/2 -119/75 -3/2 -46/29 -7/5 -19/12 -4/3 -1/1 -49/31 -3/2 -30/19 -1/1 -11/7 -3/2 -3/2 -3/2 -13/9 -3/2 -49/34 -7/5 -4/3 -36/25 -4/3 -23/16 -3/2 -4/3 -10/7 -1/1 -27/19 -3/2 -71/50 -3/2 -4/3 -44/31 -2/1 -17/12 -8/5 -3/2 -24/17 -3/2 -7/5 -3/2 -25/18 -10/7 -17/12 -18/13 -7/5 -11/8 -7/5 -4/3 -15/11 -3/2 -49/36 -7/5 -4/3 -34/25 -7/5 -19/14 -7/5 -18/13 -23/17 -11/8 -4/3 -4/3 -25/19 -5/4 -21/16 -5/4 -17/13 -5/4 -13/10 -4/3 -1/1 -22/17 -1/1 -31/24 -4/3 -5/4 -40/31 -1/1 -9/7 -3/2 -23/18 -3/2 -4/3 -14/11 -7/5 -33/26 -11/8 -19/15 -19/14 -24/19 -4/3 -5/4 -4/3 -5/4 -11/9 -5/4 -17/14 -5/4 -6/5 -40/33 -1/1 -23/19 -5/4 -6/5 -1/1 -7/6 -3/2 -4/3 -8/7 -4/3 -1/1 -5/4 0/1 -1/1 1/1 -5/6 7/6 -4/5 -3/4 6/5 -1/1 5/4 -5/6 -4/5 24/19 -4/5 19/15 -19/24 14/11 -7/9 23/18 -4/5 -3/4 9/7 -3/4 22/17 -1/1 13/10 -1/1 -4/5 17/13 -5/6 4/3 -4/5 23/17 -11/14 19/14 -18/23 -7/9 15/11 -3/4 11/8 -4/5 -7/9 18/13 -7/9 25/18 -17/22 -10/13 7/5 -3/4 24/17 -3/4 17/12 -3/4 -8/11 10/7 -1/1 3/2 -3/4 14/9 -5/7 25/16 -3/4 -2/3 36/23 -2/3 11/7 -3/4 19/12 -1/1 -4/5 8/5 -3/4 29/18 -11/15 -8/11 21/13 -3/4 13/8 -8/11 -5/7 18/11 -5/7 23/14 -12/17 -7/10 5/3 -3/4 22/13 -9/13 39/23 -7/10 17/10 -11/16 -2/3 12/7 -2/3 7/4 -2/3 -1/2 23/13 -3/4 16/9 -2/3 25/14 -2/3 -1/2 9/5 -1/2 11/6 -1/1 -2/3 24/13 -2/3 13/7 -1/2 2/1 -1/1 13/6 -1/1 -2/3 24/11 -1/1 11/5 -3/4 9/4 -3/4 25/11 -3/4 16/7 -2/3 23/10 -2/3 -1/2 7/3 -3/4 26/11 -5/7 71/30 -7/10 -16/23 45/19 -7/10 19/8 -9/13 -2/3 12/5 -2/3 5/2 -2/3 -1/2 18/7 -3/5 49/19 -1/2 80/31 -3/5 31/12 -4/7 -1/2 13/5 -1/2 60/23 -2/3 47/18 -2/3 -3/5 34/13 -3/5 21/8 -1/2 8/3 -1/2 27/10 -1/2 73/27 -1/2 192/71 -1/2 119/44 -1/2 -4/9 46/17 -1/3 19/7 1/0 11/4 -1/1 -2/3 36/13 -2/3 25/9 -5/8 14/5 -3/5 17/6 -1/2 0/1 3/1 -1/2 13/4 -1/3 0/1 36/11 0/1 23/7 1/0 33/10 -1/2 10/3 -1/1 27/8 -1/2 71/21 -1/2 44/13 0/1 17/5 -1/2 24/7 -1/2 7/2 -1/2 0/1 18/5 -1/1 47/13 -1/2 29/8 -1/1 -2/3 11/3 -1/2 26/7 -1/1 41/11 1/0 15/4 -1/2 34/9 -1/3 19/5 1/0 23/6 -2/3 -1/2 4/1 0/1 25/6 2/1 1/0 21/5 1/0 17/4 -2/1 1/0 13/3 1/0 9/2 1/0 23/5 1/0 14/3 -1/1 33/7 -3/2 19/4 -6/5 -1/1 24/5 -1/1 5/1 -1/2 11/2 -2/1 -1/1 6/1 -1/1 13/2 -1/1 -2/3 7/1 -1/2 15/2 1/0 23/3 -3/2 8/1 -1/1 17/2 -3/4 -2/3 9/1 -1/2 10/1 -1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(49,456,-36,-335) (-9/1,1/0) -> (-15/11,-49/36) Hyperbolic Matrix(49,432,-38,-335) (-9/1,-8/1) -> (-40/31,-9/7) Hyperbolic Matrix(145,1104,-44,-335) (-8/1,-15/2) -> (-33/10,-56/17) Hyperbolic Matrix(97,720,26,193) (-15/2,-7/1) -> (41/11,15/4) Hyperbolic Matrix(49,312,-30,-191) (-7/1,-6/1) -> (-18/11,-31/19) Hyperbolic Matrix(47,264,34,191) (-6/1,-11/2) -> (11/8,18/13) Hyperbolic Matrix(49,264,18,97) (-11/2,-5/1) -> (19/7,11/4) Hyperbolic Matrix(49,240,10,49) (-5/1,-24/5) -> (24/5,5/1) Hyperbolic Matrix(191,912,40,191) (-24/5,-19/4) -> (19/4,24/5) Hyperbolic Matrix(193,912,-142,-671) (-19/4,-14/3) -> (-34/25,-19/14) Hyperbolic Matrix(145,672,52,241) (-14/3,-23/5) -> (25/9,14/5) Hyperbolic Matrix(95,432,42,191) (-23/5,-9/2) -> (9/4,25/11) Hyperbolic Matrix(49,216,22,97) (-9/2,-13/3) -> (11/5,9/4) Hyperbolic Matrix(145,624,56,241) (-13/3,-17/4) -> (31/12,13/5) Hyperbolic Matrix(193,816,-136,-575) (-17/4,-4/1) -> (-44/31,-17/12) Hyperbolic Matrix(145,552,-88,-335) (-4/1,-19/5) -> (-5/3,-28/17) Hyperbolic Matrix(241,912,-190,-719) (-19/5,-15/4) -> (-33/26,-19/15) Hyperbolic Matrix(335,1248,-142,-529) (-15/4,-26/7) -> (-26/11,-33/14) Hyperbolic Matrix(97,360,52,193) (-26/7,-11/3) -> (13/7,2/1) Hyperbolic Matrix(145,528,-92,-335) (-11/3,-18/5) -> (-30/19,-11/7) Hyperbolic Matrix(47,168,40,143) (-18/5,-7/2) -> (7/6,6/5) Hyperbolic Matrix(97,336,28,97) (-7/2,-24/7) -> (24/7,7/2) Hyperbolic Matrix(239,816,70,239) (-24/7,-17/5) -> (17/5,24/7) Hyperbolic Matrix(241,816,-184,-623) (-17/5,-27/8) -> (-21/16,-17/13) Hyperbolic Matrix(335,1128,128,431) (-27/8,-10/3) -> (34/13,21/8) Hyperbolic Matrix(385,1272,102,337) (-10/3,-33/10) -> (15/4,34/9) Hyperbolic Matrix(1393,4584,540,1777) (-56/17,-23/7) -> (49/19,80/31) Hyperbolic Matrix(527,1728,190,623) (-23/7,-36/11) -> (36/13,25/9) Hyperbolic Matrix(287,936,88,287) (-36/11,-13/4) -> (13/4,36/11) Hyperbolic Matrix(97,312,60,193) (-13/4,-3/1) -> (21/13,13/8) Hyperbolic Matrix(145,408,-102,-287) (-3/1,-14/5) -> (-10/7,-27/19) Hyperbolic Matrix(241,672,52,145) (-14/5,-25/9) -> (23/5,14/3) Hyperbolic Matrix(623,1728,190,527) (-25/9,-36/13) -> (36/11,23/7) Hyperbolic Matrix(287,792,104,287) (-36/13,-11/4) -> (11/4,36/13) Hyperbolic Matrix(97,264,18,49) (-11/4,-19/7) -> (5/1,11/2) Hyperbolic Matrix(143,384,-54,-145) (-19/7,-8/3) -> (-8/3,-29/11) Parabolic Matrix(337,888,-200,-527) (-29/11,-21/8) -> (-27/16,-5/3) Hyperbolic Matrix(431,1128,128,335) (-21/8,-34/13) -> (10/3,27/8) Hyperbolic Matrix(1249,3264,-918,-2399) (-34/13,-47/18) -> (-49/36,-34/25) Hyperbolic Matrix(479,1248,-332,-865) (-47/18,-13/5) -> (-13/9,-49/34) Hyperbolic Matrix(47,120,-38,-97) (-13/5,-5/2) -> (-5/4,-11/9) Hyperbolic Matrix(49,120,20,49) (-5/2,-12/5) -> (12/5,5/2) Hyperbolic Matrix(191,456,80,191) (-12/5,-19/8) -> (19/8,12/5) Hyperbolic Matrix(577,1368,-364,-863) (-19/8,-26/11) -> (-46/29,-19/12) Hyperbolic Matrix(143,336,20,47) (-33/14,-7/3) -> (7/1,15/2) Hyperbolic Matrix(145,336,104,241) (-7/3,-23/10) -> (25/18,7/5) Hyperbolic Matrix(335,768,188,431) (-23/10,-16/7) -> (16/9,25/14) Hyperbolic Matrix(337,768,190,433) (-16/7,-25/11) -> (23/13,16/9) Hyperbolic Matrix(191,432,42,95) (-25/11,-9/4) -> (9/2,23/5) Hyperbolic Matrix(97,216,22,49) (-9/4,-11/5) -> (13/3,9/2) Hyperbolic Matrix(241,528,110,241) (-11/5,-24/11) -> (24/11,11/5) Hyperbolic Matrix(287,624,132,287) (-24/11,-13/6) -> (13/6,24/11) Hyperbolic Matrix(145,312,112,241) (-13/6,-2/1) -> (22/17,13/10) Hyperbolic Matrix(193,360,52,97) (-2/1,-13/7) -> (11/3,26/7) Hyperbolic Matrix(337,624,182,337) (-13/7,-24/13) -> (24/13,13/7) Hyperbolic Matrix(287,528,156,287) (-24/13,-11/6) -> (11/6,24/13) Hyperbolic Matrix(145,264,106,193) (-11/6,-9/5) -> (15/11,11/8) Hyperbolic Matrix(241,432,188,337) (-9/5,-25/14) -> (23/18,9/7) Hyperbolic Matrix(431,768,188,335) (-25/14,-16/9) -> (16/7,23/10) Hyperbolic Matrix(95,168,-82,-145) (-16/9,-7/4) -> (-7/6,-8/7) Hyperbolic Matrix(97,168,56,97) (-7/4,-12/7) -> (12/7,7/4) Hyperbolic Matrix(239,408,140,239) (-12/7,-17/10) -> (17/10,12/7) Hyperbolic Matrix(623,1056,-482,-817) (-17/10,-22/13) -> (-22/17,-31/24) Hyperbolic Matrix(2881,4872,-1816,-3071) (-22/13,-49/29) -> (-119/75,-46/29) Hyperbolic Matrix(1919,3240,568,959) (-49/29,-27/16) -> (27/8,71/21) Hyperbolic Matrix(1823,3000,-1284,-2113) (-28/17,-23/14) -> (-71/50,-44/31) Hyperbolic Matrix(527,864,380,623) (-23/14,-18/11) -> (18/13,25/18) Hyperbolic Matrix(383,624,294,479) (-31/19,-13/8) -> (13/10,17/13) Hyperbolic Matrix(193,312,60,97) (-13/8,-21/13) -> (3/1,13/4) Hyperbolic Matrix(239,384,-150,-241) (-21/13,-8/5) -> (-8/5,-27/17) Parabolic Matrix(1391,2208,332,527) (-27/17,-73/46) -> (25/6,21/5) Hyperbolic Matrix(23231,36864,8590,13631) (-73/46,-192/121) -> (192/71,119/44) Hyperbolic Matrix(23233,36864,8592,13633) (-192/121,-119/75) -> (73/27,192/71) Hyperbolic Matrix(865,1368,638,1009) (-19/12,-49/31) -> (23/17,19/14) Hyperbolic Matrix(1489,2352,578,913) (-49/31,-30/19) -> (18/7,49/19) Hyperbolic Matrix(47,72,-32,-49) (-11/7,-3/2) -> (-3/2,-13/9) Parabolic Matrix(3215,4632,1232,1775) (-49/34,-36/25) -> (60/23,47/18) Hyperbolic Matrix(1201,1728,768,1105) (-36/25,-23/16) -> (25/16,36/23) Hyperbolic Matrix(385,552,302,433) (-23/16,-10/7) -> (14/11,23/18) Hyperbolic Matrix(3599,5112,1520,2159) (-27/19,-71/50) -> (71/30,45/19) Hyperbolic Matrix(577,816,408,577) (-17/12,-24/17) -> (24/17,17/12) Hyperbolic Matrix(239,336,170,239) (-24/17,-7/5) -> (7/5,24/17) Hyperbolic Matrix(241,336,104,145) (-7/5,-25/18) -> (23/10,7/3) Hyperbolic Matrix(623,864,380,527) (-25/18,-18/13) -> (18/11,23/14) Hyperbolic Matrix(191,264,34,47) (-18/13,-11/8) -> (11/2,6/1) Hyperbolic Matrix(193,264,106,145) (-11/8,-15/11) -> (9/5,11/6) Hyperbolic Matrix(1151,1560,318,431) (-19/14,-23/17) -> (47/13,29/8) Hyperbolic Matrix(143,192,-108,-145) (-23/17,-4/3) -> (-4/3,-25/19) Parabolic Matrix(1681,2208,622,817) (-25/19,-21/16) -> (27/10,73/27) Hyperbolic Matrix(239,312,36,47) (-17/13,-13/10) -> (13/2,7/1) Hyperbolic Matrix(241,312,112,145) (-13/10,-22/17) -> (2/1,13/6) Hyperbolic Matrix(2881,3720,1116,1441) (-31/24,-40/31) -> (80/31,31/12) Hyperbolic Matrix(337,432,188,241) (-9/7,-23/18) -> (25/14,9/5) Hyperbolic Matrix(527,672,338,431) (-23/18,-14/11) -> (14/9,25/16) Hyperbolic Matrix(623,792,188,239) (-14/11,-33/26) -> (33/10,10/3) Hyperbolic Matrix(721,912,570,721) (-19/15,-24/19) -> (24/19,19/15) Hyperbolic Matrix(191,240,152,191) (-24/19,-5/4) -> (5/4,24/19) Hyperbolic Matrix(335,408,78,95) (-11/9,-17/14) -> (17/4,13/3) Hyperbolic Matrix(673,816,80,97) (-17/14,-40/33) -> (8/1,17/2) Hyperbolic Matrix(911,1104,118,143) (-40/33,-23/19) -> (23/3,8/1) Hyperbolic Matrix(577,696,160,193) (-23/19,-6/5) -> (18/5,47/13) Hyperbolic Matrix(143,168,40,47) (-6/5,-7/6) -> (7/2,18/5) Hyperbolic Matrix(191,216,84,95) (-8/7,-1/1) -> (25/11,16/7) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(145,-168,82,-95) (1/1,7/6) -> (7/4,23/13) Hyperbolic Matrix(97,-120,38,-47) (6/5,5/4) -> (5/2,18/7) Hyperbolic Matrix(719,-912,190,-241) (19/15,14/11) -> (34/9,19/5) Hyperbolic Matrix(817,-1056,482,-623) (9/7,22/17) -> (22/13,39/23) Hyperbolic Matrix(623,-816,184,-241) (17/13,4/3) -> (44/13,17/5) Hyperbolic Matrix(961,-1296,284,-383) (4/3,23/17) -> (71/21,44/13) Hyperbolic Matrix(671,-912,142,-193) (19/14,15/11) -> (33/7,19/4) Hyperbolic Matrix(287,-408,102,-145) (17/12,10/7) -> (14/5,17/6) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(719,-1128,276,-433) (36/23,11/7) -> (13/5,60/23) Hyperbolic Matrix(335,-528,92,-145) (11/7,19/12) -> (29/8,11/3) Hyperbolic Matrix(241,-384,150,-239) (19/12,8/5) -> (8/5,29/18) Parabolic Matrix(1057,-1704,446,-719) (29/18,21/13) -> (45/19,19/8) Hyperbolic Matrix(191,-312,30,-49) (13/8,18/11) -> (6/1,13/2) Hyperbolic Matrix(335,-552,88,-145) (23/14,5/3) -> (19/5,23/6) Hyperbolic Matrix(385,-648,142,-239) (5/3,22/13) -> (46/17,19/7) Hyperbolic Matrix(481,-816,56,-95) (39/23,17/10) -> (17/2,9/1) Hyperbolic Matrix(529,-1248,142,-335) (7/3,26/11) -> (26/7,41/11) Hyperbolic Matrix(2689,-6360,994,-2351) (26/11,71/30) -> (119/44,46/17) Hyperbolic Matrix(193,-504,18,-47) (47/18,34/13) -> (10/1,1/0) Hyperbolic Matrix(145,-384,54,-143) (21/8,8/3) -> (8/3,27/10) Parabolic Matrix(143,-408,34,-97) (17/6,3/1) -> (21/5,17/4) Hyperbolic Matrix(335,-1104,44,-145) (23/7,33/10) -> (15/2,23/3) Hyperbolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic Matrix(97,-456,10,-47) (14/3,33/7) -> (9/1,10/1) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(49,456,-36,-335) -> Matrix(3,-4,-2,3) Matrix(49,432,-38,-335) -> Matrix(3,2,-2,-1) Matrix(145,1104,-44,-335) -> Matrix(3,2,-2,-1) Matrix(97,720,26,193) -> Matrix(1,0,0,1) Matrix(49,312,-30,-191) -> Matrix(13,18,-8,-11) Matrix(47,264,34,191) -> Matrix(25,18,-32,-23) Matrix(49,264,18,97) -> Matrix(1,0,0,1) Matrix(49,240,10,49) -> Matrix(1,2,-2,-3) Matrix(191,912,40,191) -> Matrix(13,12,-12,-11) Matrix(193,912,-142,-671) -> Matrix(31,24,-22,-17) Matrix(145,672,52,241) -> Matrix(11,8,-18,-13) Matrix(95,432,42,191) -> Matrix(13,8,-18,-11) Matrix(49,216,22,97) -> Matrix(1,2,-2,-3) Matrix(145,624,56,241) -> Matrix(5,2,-8,-3) Matrix(193,816,-136,-575) -> Matrix(7,2,-4,-1) Matrix(145,552,-88,-335) -> Matrix(7,2,-4,-1) Matrix(241,912,-190,-719) -> Matrix(11,-4,-8,3) Matrix(335,1248,-142,-529) -> Matrix(7,2,-4,-1) Matrix(97,360,52,193) -> Matrix(1,2,-2,-3) Matrix(145,528,-92,-335) -> Matrix(3,2,-2,-1) Matrix(47,168,40,143) -> Matrix(3,4,-4,-5) Matrix(97,336,28,97) -> Matrix(1,0,-2,1) Matrix(239,816,70,239) -> Matrix(1,2,-2,-3) Matrix(241,816,-184,-623) -> Matrix(5,4,-4,-3) Matrix(335,1128,128,431) -> Matrix(1,4,-2,-7) Matrix(385,1272,102,337) -> Matrix(1,0,-2,1) Matrix(1393,4584,540,1777) -> Matrix(5,2,-8,-3) Matrix(527,1728,190,623) -> Matrix(9,2,-14,-3) Matrix(287,936,88,287) -> Matrix(1,0,-4,1) Matrix(97,312,60,193) -> Matrix(3,-8,-4,11) Matrix(145,408,-102,-287) -> Matrix(3,8,-2,-5) Matrix(241,672,52,145) -> Matrix(3,8,-2,-5) Matrix(623,1728,190,527) -> Matrix(1,2,2,5) Matrix(287,792,104,287) -> Matrix(3,4,-4,-5) Matrix(97,264,18,49) -> Matrix(1,0,0,1) Matrix(143,384,-54,-145) -> Matrix(1,-2,0,1) Matrix(337,888,-200,-527) -> Matrix(7,16,-4,-9) Matrix(431,1128,128,335) -> Matrix(1,4,-2,-7) Matrix(1249,3264,-918,-2399) -> Matrix(3,2,-2,-1) Matrix(479,1248,-332,-865) -> Matrix(3,2,-2,-1) Matrix(47,120,-38,-97) -> Matrix(5,14,-4,-11) Matrix(49,120,20,49) -> Matrix(1,4,-2,-7) Matrix(191,456,80,191) -> Matrix(19,36,-28,-53) Matrix(577,1368,-364,-863) -> Matrix(19,34,-14,-25) Matrix(143,336,20,47) -> Matrix(1,2,-4,-7) Matrix(145,336,104,241) -> Matrix(17,24,-22,-31) Matrix(335,768,188,431) -> Matrix(1,4,-2,-7) Matrix(337,768,190,433) -> Matrix(7,12,-10,-17) Matrix(191,432,42,95) -> Matrix(5,8,-2,-3) Matrix(97,216,22,49) -> Matrix(1,2,-2,-3) Matrix(241,528,110,241) -> Matrix(5,6,-6,-7) Matrix(287,624,132,287) -> Matrix(3,4,-4,-5) Matrix(145,312,112,241) -> Matrix(5,6,-6,-7) Matrix(193,360,52,97) -> Matrix(1,2,-2,-3) Matrix(337,624,182,337) -> Matrix(1,4,-2,-7) Matrix(287,528,156,287) -> Matrix(3,4,-4,-5) Matrix(145,264,106,193) -> Matrix(3,10,-4,-13) Matrix(241,432,188,337) -> Matrix(3,10,-4,-13) Matrix(431,768,188,335) -> Matrix(1,4,-2,-7) Matrix(95,168,-82,-145) -> Matrix(3,2,-2,-1) Matrix(97,168,56,97) -> Matrix(1,4,-2,-7) Matrix(239,408,140,239) -> Matrix(23,44,-34,-65) Matrix(623,1056,-482,-817) -> Matrix(19,34,-14,-25) Matrix(2881,4872,-1816,-3071) -> Matrix(43,76,-30,-53) Matrix(1919,3240,568,959) -> Matrix(1,2,-6,-11) Matrix(1823,3000,-1284,-2113) -> Matrix(5,8,-2,-3) Matrix(527,864,380,623) -> Matrix(79,134,-102,-173) Matrix(383,624,294,479) -> Matrix(7,12,-10,-17) Matrix(193,312,60,97) -> Matrix(5,8,-12,-19) Matrix(239,384,-150,-241) -> Matrix(23,36,-16,-25) Matrix(1391,2208,332,527) -> Matrix(3,4,2,3) Matrix(23231,36864,8590,13631) -> Matrix(9,14,-20,-31) Matrix(23233,36864,8592,13633) -> Matrix(15,22,-28,-41) Matrix(865,1368,638,1009) -> Matrix(3,10,-4,-13) Matrix(1489,2352,578,913) -> Matrix(7,10,-12,-17) Matrix(47,72,-32,-49) -> Matrix(11,18,-8,-13) Matrix(3215,4632,1232,1775) -> Matrix(19,26,-30,-41) Matrix(1201,1728,768,1105) -> Matrix(5,6,-6,-7) Matrix(385,552,302,433) -> Matrix(17,24,-22,-31) Matrix(3599,5112,1520,2159) -> Matrix(11,20,-16,-29) Matrix(577,816,408,577) -> Matrix(31,48,-42,-65) Matrix(239,336,170,239) -> Matrix(41,60,-54,-79) Matrix(241,336,104,145) -> Matrix(17,24,-22,-31) Matrix(623,864,380,527) -> Matrix(95,134,-134,-189) Matrix(191,264,34,47) -> Matrix(13,18,-8,-11) Matrix(193,264,106,145) -> Matrix(7,10,-12,-17) Matrix(1151,1560,318,431) -> Matrix(3,4,2,3) Matrix(143,192,-108,-145) -> Matrix(47,64,-36,-49) Matrix(1681,2208,622,817) -> Matrix(3,4,-10,-13) Matrix(239,312,36,47) -> Matrix(5,6,-6,-7) Matrix(241,312,112,145) -> Matrix(5,6,-6,-7) Matrix(2881,3720,1116,1441) -> Matrix(13,16,-22,-27) Matrix(337,432,188,241) -> Matrix(7,10,-12,-17) Matrix(527,672,338,431) -> Matrix(5,6,-6,-7) Matrix(623,792,188,239) -> Matrix(3,4,2,3) Matrix(721,912,570,721) -> Matrix(113,152,-142,-191) Matrix(191,240,152,191) -> Matrix(31,40,-38,-49) Matrix(335,408,78,95) -> Matrix(3,4,-4,-5) Matrix(673,816,80,97) -> Matrix(7,8,-8,-9) Matrix(911,1104,118,143) -> Matrix(1,2,-2,-3) Matrix(577,696,160,193) -> Matrix(5,6,-6,-7) Matrix(143,168,40,47) -> Matrix(3,4,-4,-5) Matrix(191,216,84,95) -> Matrix(17,22,-24,-31) Matrix(1,0,2,1) -> Matrix(9,10,-10,-11) Matrix(145,-168,82,-95) -> Matrix(3,2,-2,-1) Matrix(97,-120,38,-47) -> Matrix(17,14,-28,-23) Matrix(719,-912,190,-241) -> Matrix(5,4,-24,-19) Matrix(817,-1056,482,-623) -> Matrix(43,34,-62,-49) Matrix(623,-816,184,-241) -> Matrix(5,4,-4,-3) Matrix(961,-1296,284,-383) -> Matrix(5,4,-24,-19) Matrix(671,-912,142,-193) -> Matrix(31,24,-22,-17) Matrix(287,-408,102,-145) -> Matrix(11,8,-18,-13) Matrix(49,-72,32,-47) -> Matrix(23,18,-32,-25) Matrix(719,-1128,276,-433) -> Matrix(11,8,-18,-13) Matrix(335,-528,92,-145) -> Matrix(3,2,-2,-1) Matrix(241,-384,150,-239) -> Matrix(47,36,-64,-49) Matrix(1057,-1704,446,-719) -> Matrix(69,50,-98,-71) Matrix(191,-312,30,-49) -> Matrix(25,18,-32,-23) Matrix(335,-552,88,-145) -> Matrix(3,2,4,3) Matrix(385,-648,142,-239) -> Matrix(3,2,4,3) Matrix(481,-816,56,-95) -> Matrix(23,16,-36,-25) Matrix(529,-1248,142,-335) -> Matrix(3,2,4,3) Matrix(2689,-6360,994,-2351) -> Matrix(17,12,-44,-31) Matrix(193,-504,18,-47) -> Matrix(3,2,-8,-5) Matrix(145,-384,54,-143) -> Matrix(3,2,-8,-5) Matrix(143,-408,34,-97) -> Matrix(3,2,-2,-1) Matrix(335,-1104,44,-145) -> Matrix(3,2,-2,-1) Matrix(49,-192,12,-47) -> Matrix(1,0,2,1) Matrix(97,-456,10,-47) -> Matrix(3,4,-4,-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): 35 Degree of the the map X: 35 Degree of the the map Y: 128 ----------------------------------------------------------------------- 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 -1/1 5 1 1/1 -5/6 1 24 7/6 (-4/5,-3/4) 0 24 6/5 -1/1 1 4 5/4 (-5/6,-4/5) 0 24 24/19 -4/5 6 1 19/15 -19/24 1 24 14/11 -7/9 1 12 23/18 (-4/5,-3/4) 0 24 9/7 -3/4 1 8 22/17 -1/1 1 12 13/10 (-1/1,-4/5) 0 24 17/13 -5/6 1 24 4/3 -4/5 2 6 23/17 -11/14 1 24 19/14 (-18/23,-7/9) 0 24 15/11 -3/4 1 8 11/8 (-4/5,-7/9) 0 24 18/13 -7/9 5 4 25/18 (-17/22,-10/13) 0 24 7/5 -3/4 1 24 24/17 -3/4 6 1 17/12 (-3/4,-8/11) 0 24 10/7 -1/1 1 12 3/2 -3/4 2 8 14/9 -5/7 1 12 25/16 (-3/4,-2/3) 0 24 36/23 -2/3 1 2 11/7 -3/4 1 24 19/12 (-1/1,-4/5) 0 24 8/5 -3/4 2 3 29/18 (-11/15,-8/11) 0 24 21/13 -3/4 1 8 13/8 (-8/11,-5/7) 0 24 18/11 -5/7 5 4 23/14 (-12/17,-7/10) 0 24 5/3 -3/4 1 24 22/13 -9/13 1 12 39/23 -7/10 1 8 17/10 (-11/16,-2/3) 0 24 12/7 -2/3 6 2 7/4 (-2/3,-1/2) 0 24 23/13 -3/4 1 24 16/9 -2/3 2 3 25/14 (-2/3,-1/2) 0 24 9/5 -1/2 1 8 11/6 (-1/1,-2/3) 0 24 24/13 -2/3 1 1 13/7 -1/2 1 24 2/1 -1/1 1 12 13/6 (-1/1,-2/3) 0 24 24/11 -1/1 1 1 11/5 -3/4 1 24 9/4 -3/4 2 8 25/11 -3/4 1 24 16/7 -2/3 2 3 23/10 (-2/3,-1/2) 0 24 7/3 -3/4 1 24 26/11 -5/7 1 12 71/30 (-7/10,-16/23) 0 24 45/19 -7/10 1 8 19/8 (-9/13,-2/3) 0 24 12/5 -2/3 5 2 5/2 (-2/3,-1/2) 0 24 18/7 -3/5 1 4 49/19 -1/2 1 24 80/31 -3/5 3 3 31/12 (-4/7,-1/2) 0 24 13/5 -1/2 1 24 60/23 -2/3 1 2 47/18 (-2/3,-3/5) 0 24 34/13 -3/5 1 12 21/8 -1/2 2 8 8/3 -1/2 1 3 27/10 -1/2 2 8 73/27 -1/2 1 24 192/71 -1/2 6 1 119/44 (-1/2,-4/9) 0 24 46/17 -1/3 1 12 19/7 1/0 1 24 11/4 (-1/1,-2/3) 0 24 36/13 -2/3 6 2 25/9 -5/8 1 24 14/5 -3/5 1 12 17/6 (-1/2,0/1) 0 24 3/1 -1/2 1 8 13/4 (-1/3,0/1) 0 24 36/11 0/1 6 2 23/7 1/0 1 24 33/10 -1/2 2 8 10/3 -1/1 1 12 27/8 -1/2 2 8 71/21 -1/2 1 24 44/13 0/1 2 6 17/5 -1/2 1 24 24/7 -1/2 1 1 7/2 (-1/2,0/1) 0 24 18/5 -1/1 1 4 47/13 -1/2 1 24 29/8 (-1/1,-2/3) 0 24 11/3 -1/2 1 24 26/7 -1/1 1 12 41/11 1/0 1 24 15/4 -1/2 2 8 34/9 -1/3 1 12 19/5 1/0 1 24 23/6 (-2/3,-1/2) 0 24 4/1 0/1 1 6 25/6 (2/1,1/0) 0 24 21/5 1/0 1 8 17/4 (-2/1,1/0) 0 24 13/3 1/0 1 24 9/2 1/0 2 8 23/5 1/0 1 24 14/3 -1/1 1 12 33/7 -3/2 1 8 19/4 (-6/5,-1/1) 0 24 24/5 -1/1 7 1 5/1 -1/2 1 24 11/2 (-2/1,-1/1) 0 24 6/1 -1/1 5 4 13/2 (-1/1,-2/3) 0 24 7/1 -1/2 1 24 15/2 1/0 2 8 23/3 -3/2 1 24 8/1 -1/1 3 3 17/2 (-3/4,-2/3) 0 24 9/1 -1/2 1 8 10/1 -1/1 1 12 1/0 (-1/1,0/1) 0 24 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(145,-168,82,-95) (1/1,7/6) -> (7/4,23/13) Hyperbolic Matrix(143,-168,40,-47) (7/6,6/5) -> (7/2,18/5) Glide Reflection Matrix(97,-120,38,-47) (6/5,5/4) -> (5/2,18/7) Hyperbolic Matrix(191,-240,152,-191) (5/4,24/19) -> (5/4,24/19) Reflection Matrix(721,-912,570,-721) (24/19,19/15) -> (24/19,19/15) Reflection Matrix(719,-912,190,-241) (19/15,14/11) -> (34/9,19/5) Hyperbolic Matrix(527,-672,338,-431) (14/11,23/18) -> (14/9,25/16) Glide Reflection Matrix(337,-432,188,-241) (23/18,9/7) -> (25/14,9/5) Glide Reflection Matrix(817,-1056,482,-623) (9/7,22/17) -> (22/13,39/23) Hyperbolic Matrix(241,-312,112,-145) (22/17,13/10) -> (2/1,13/6) Glide Reflection Matrix(239,-312,36,-47) (13/10,17/13) -> (13/2,7/1) Glide Reflection Matrix(623,-816,184,-241) (17/13,4/3) -> (44/13,17/5) Hyperbolic Matrix(961,-1296,284,-383) (4/3,23/17) -> (71/21,44/13) Hyperbolic Matrix(1151,-1560,318,-431) (23/17,19/14) -> (47/13,29/8) Glide Reflection Matrix(671,-912,142,-193) (19/14,15/11) -> (33/7,19/4) Hyperbolic Matrix(193,-264,106,-145) (15/11,11/8) -> (9/5,11/6) Glide Reflection Matrix(191,-264,34,-47) (11/8,18/13) -> (11/2,6/1) Glide Reflection Matrix(623,-864,380,-527) (18/13,25/18) -> (18/11,23/14) Glide Reflection Matrix(241,-336,104,-145) (25/18,7/5) -> (23/10,7/3) Glide Reflection Matrix(239,-336,170,-239) (7/5,24/17) -> (7/5,24/17) Reflection Matrix(577,-816,408,-577) (24/17,17/12) -> (24/17,17/12) Reflection Matrix(287,-408,102,-145) (17/12,10/7) -> (14/5,17/6) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(1151,-1800,736,-1151) (25/16,36/23) -> (25/16,36/23) Reflection Matrix(719,-1128,276,-433) (36/23,11/7) -> (13/5,60/23) Hyperbolic Matrix(335,-528,92,-145) (11/7,19/12) -> (29/8,11/3) Hyperbolic Matrix(241,-384,150,-239) (19/12,8/5) -> (8/5,29/18) Parabolic Matrix(1057,-1704,446,-719) (29/18,21/13) -> (45/19,19/8) Hyperbolic Matrix(193,-312,60,-97) (21/13,13/8) -> (3/1,13/4) Glide Reflection Matrix(191,-312,30,-49) (13/8,18/11) -> (6/1,13/2) Hyperbolic Matrix(335,-552,88,-145) (23/14,5/3) -> (19/5,23/6) Hyperbolic Matrix(385,-648,142,-239) (5/3,22/13) -> (46/17,19/7) Hyperbolic Matrix(481,-816,56,-95) (39/23,17/10) -> (17/2,9/1) Hyperbolic 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(433,-768,190,-337) (23/13,16/9) -> (25/11,16/7) Glide Reflection Matrix(431,-768,188,-335) (16/9,25/14) -> (16/7,23/10) Glide Reflection Matrix(287,-528,156,-287) (11/6,24/13) -> (11/6,24/13) Reflection Matrix(337,-624,182,-337) (24/13,13/7) -> (24/13,13/7) Reflection Matrix(193,-360,52,-97) (13/7,2/1) -> (11/3,26/7) Glide Reflection Matrix(287,-624,132,-287) (13/6,24/11) -> (13/6,24/11) Reflection Matrix(241,-528,110,-241) (24/11,11/5) -> (24/11,11/5) Reflection Matrix(97,-216,22,-49) (11/5,9/4) -> (13/3,9/2) Glide Reflection Matrix(191,-432,42,-95) (9/4,25/11) -> (9/2,23/5) Glide Reflection Matrix(529,-1248,142,-335) (7/3,26/11) -> (26/7,41/11) Hyperbolic Matrix(2689,-6360,994,-2351) (26/11,71/30) -> (119/44,46/17) Hyperbolic Matrix(1105,-2616,264,-625) (71/30,45/19) -> (25/6,21/5) Glide 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(671,-1728,186,-479) (18/7,49/19) -> (18/5,47/13) Glide Reflection Matrix(865,-2232,112,-289) (49/19,80/31) -> (23/3,8/1) Glide Reflection Matrix(623,-1608,74,-191) (80/31,31/12) -> (8/1,17/2) Glide Reflection Matrix(241,-624,56,-145) (31/12,13/5) -> (17/4,13/3) Glide Reflection Matrix(2161,-5640,828,-2161) (60/23,47/18) -> (60/23,47/18) Reflection Matrix(193,-504,18,-47) (47/18,34/13) -> (10/1,1/0) Hyperbolic Matrix(431,-1128,128,-335) (34/13,21/8) -> (10/3,27/8) Glide Reflection Matrix(145,-384,54,-143) (21/8,8/3) -> (8/3,27/10) Parabolic Matrix(1439,-3888,426,-1151) (27/10,73/27) -> (27/8,71/21) Glide Reflection Matrix(10367,-28032,3834,-10367) (73/27,192/71) -> (73/27,192/71) Reflection Matrix(16897,-45696,6248,-16897) (192/71,119/44) -> (192/71,119/44) Reflection Matrix(97,-264,18,-49) (19/7,11/4) -> (5/1,11/2) Glide Reflection Matrix(287,-792,104,-287) (11/4,36/13) -> (11/4,36/13) Reflection Matrix(623,-1728,190,-527) (36/13,25/9) -> (36/11,23/7) Glide Reflection Matrix(241,-672,52,-145) (25/9,14/5) -> (23/5,14/3) Glide Reflection Matrix(143,-408,34,-97) (17/6,3/1) -> (21/5,17/4) Hyperbolic Matrix(287,-936,88,-287) (13/4,36/11) -> (13/4,36/11) Reflection Matrix(335,-1104,44,-145) (23/7,33/10) -> (15/2,23/3) Hyperbolic Matrix(385,-1272,102,-337) (33/10,10/3) -> (15/4,34/9) Glide Reflection Matrix(239,-816,70,-239) (17/5,24/7) -> (17/5,24/7) Reflection Matrix(97,-336,28,-97) (24/7,7/2) -> (24/7,7/2) Reflection Matrix(193,-720,26,-97) (41/11,15/4) -> (7/1,15/2) Glide Reflection Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic Matrix(97,-456,10,-47) (14/3,33/7) -> (9/1,10/1) Hyperbolic Matrix(191,-912,40,-191) (19/4,24/5) -> (19/4,24/5) Reflection Matrix(49,-240,10,-49) (24/5,5/1) -> (24/5,5/1) 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(1,0,2,-1) -> Matrix(11,10,-12,-11) (0/1,1/1) -> (-1/1,-5/6) Matrix(145,-168,82,-95) -> Matrix(3,2,-2,-1) -1/1 Matrix(143,-168,40,-47) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(97,-120,38,-47) -> Matrix(17,14,-28,-23) Matrix(191,-240,152,-191) -> Matrix(49,40,-60,-49) (5/4,24/19) -> (-5/6,-4/5) Matrix(721,-912,570,-721) -> Matrix(191,152,-240,-191) (24/19,19/15) -> (-4/5,-19/24) Matrix(719,-912,190,-241) -> Matrix(5,4,-24,-19) Matrix(527,-672,338,-431) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(337,-432,188,-241) -> Matrix(13,10,-22,-17) Matrix(817,-1056,482,-623) -> Matrix(43,34,-62,-49) Matrix(241,-312,112,-145) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(239,-312,36,-47) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(623,-816,184,-241) -> Matrix(5,4,-4,-3) -1/1 Matrix(961,-1296,284,-383) -> Matrix(5,4,-24,-19) Matrix(1151,-1560,318,-431) -> Matrix(5,4,4,3) Matrix(671,-912,142,-193) -> Matrix(31,24,-22,-17) Matrix(193,-264,106,-145) -> Matrix(13,10,-22,-17) Matrix(191,-264,34,-47) -> Matrix(23,18,-14,-11) Matrix(623,-864,380,-527) -> Matrix(173,134,-244,-189) Matrix(241,-336,104,-145) -> Matrix(31,24,-40,-31) *** -> (-4/5,-3/4) Matrix(239,-336,170,-239) -> Matrix(79,60,-104,-79) (7/5,24/17) -> (-10/13,-3/4) Matrix(577,-816,408,-577) -> Matrix(65,48,-88,-65) (24/17,17/12) -> (-3/4,-8/11) Matrix(287,-408,102,-145) -> Matrix(11,8,-18,-13) -2/3 Matrix(49,-72,32,-47) -> Matrix(23,18,-32,-25) -3/4 Matrix(1151,-1800,736,-1151) -> Matrix(17,12,-24,-17) (25/16,36/23) -> (-3/4,-2/3) Matrix(719,-1128,276,-433) -> Matrix(11,8,-18,-13) -2/3 Matrix(335,-528,92,-145) -> Matrix(3,2,-2,-1) -1/1 Matrix(241,-384,150,-239) -> Matrix(47,36,-64,-49) -3/4 Matrix(1057,-1704,446,-719) -> Matrix(69,50,-98,-71) -5/7 Matrix(193,-312,60,-97) -> Matrix(11,8,-26,-19) Matrix(191,-312,30,-49) -> Matrix(25,18,-32,-23) -3/4 Matrix(335,-552,88,-145) -> Matrix(3,2,4,3) Matrix(385,-648,142,-239) -> Matrix(3,2,4,3) Matrix(481,-816,56,-95) -> Matrix(23,16,-36,-25) -2/3 Matrix(239,-408,140,-239) -> Matrix(65,44,-96,-65) (17/10,12/7) -> (-11/16,-2/3) Matrix(97,-168,56,-97) -> Matrix(7,4,-12,-7) (12/7,7/4) -> (-2/3,-1/2) Matrix(433,-768,190,-337) -> Matrix(17,12,-24,-17) *** -> (-3/4,-2/3) Matrix(431,-768,188,-335) -> Matrix(7,4,-12,-7) *** -> (-2/3,-1/2) Matrix(287,-528,156,-287) -> Matrix(5,4,-6,-5) (11/6,24/13) -> (-1/1,-2/3) Matrix(337,-624,182,-337) -> Matrix(7,4,-12,-7) (24/13,13/7) -> (-2/3,-1/2) Matrix(193,-360,52,-97) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(287,-624,132,-287) -> Matrix(5,4,-6,-5) (13/6,24/11) -> (-1/1,-2/3) Matrix(241,-528,110,-241) -> Matrix(7,6,-8,-7) (24/11,11/5) -> (-1/1,-3/4) Matrix(97,-216,22,-49) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(191,-432,42,-95) -> Matrix(11,8,-4,-3) Matrix(529,-1248,142,-335) -> Matrix(3,2,4,3) Matrix(2689,-6360,994,-2351) -> Matrix(17,12,-44,-31) Matrix(1105,-2616,264,-625) -> Matrix(3,2,-10,-7) Matrix(191,-456,80,-191) -> Matrix(53,36,-78,-53) (19/8,12/5) -> (-9/13,-2/3) Matrix(49,-120,20,-49) -> Matrix(7,4,-12,-7) (12/5,5/2) -> (-2/3,-1/2) Matrix(671,-1728,186,-479) -> Matrix(7,4,-12,-7) *** -> (-2/3,-1/2) Matrix(865,-2232,112,-289) -> Matrix(13,8,-8,-5) Matrix(623,-1608,74,-191) -> Matrix(17,10,-22,-13) Matrix(241,-624,56,-145) -> Matrix(3,2,2,1) Matrix(2161,-5640,828,-2161) -> Matrix(19,12,-30,-19) (60/23,47/18) -> (-2/3,-3/5) Matrix(193,-504,18,-47) -> Matrix(3,2,-8,-5) -1/2 Matrix(431,-1128,128,-335) -> Matrix(7,4,-12,-7) *** -> (-2/3,-1/2) Matrix(145,-384,54,-143) -> Matrix(3,2,-8,-5) -1/2 Matrix(1439,-3888,426,-1151) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(10367,-28032,3834,-10367) -> Matrix(7,4,-12,-7) (73/27,192/71) -> (-2/3,-1/2) Matrix(16897,-45696,6248,-16897) -> Matrix(17,8,-36,-17) (192/71,119/44) -> (-1/2,-4/9) Matrix(97,-264,18,-49) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(287,-792,104,-287) -> Matrix(5,4,-6,-5) (11/4,36/13) -> (-1/1,-2/3) Matrix(623,-1728,190,-527) -> Matrix(3,2,8,5) Matrix(241,-672,52,-145) -> Matrix(13,8,-8,-5) Matrix(143,-408,34,-97) -> Matrix(3,2,-2,-1) -1/1 Matrix(287,-936,88,-287) -> Matrix(-1,0,6,1) (13/4,36/11) -> (-1/3,0/1) Matrix(335,-1104,44,-145) -> Matrix(3,2,-2,-1) -1/1 Matrix(385,-1272,102,-337) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(239,-816,70,-239) -> Matrix(3,2,-4,-3) (17/5,24/7) -> (-1/1,-1/2) Matrix(97,-336,28,-97) -> Matrix(-1,0,4,1) (24/7,7/2) -> (-1/2,0/1) Matrix(193,-720,26,-97) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(49,-192,12,-47) -> Matrix(1,0,2,1) 0/1 Matrix(97,-456,10,-47) -> Matrix(3,4,-4,-5) -1/1 Matrix(191,-912,40,-191) -> Matrix(11,12,-10,-11) (19/4,24/5) -> (-6/5,-1/1) Matrix(49,-240,10,-49) -> Matrix(3,2,-4,-3) (24/5,5/1) -> (-1/1,-1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.