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 -1/2 -8/1 0/1 -15/2 1/2 -7/1 -1/2 -6/1 1/0 -11/2 -1/1 -1/2 -5/1 -1/2 -24/5 0/1 -19/4 0/1 1/0 -14/3 1/0 -23/5 -1/2 -9/2 -1/2 -13/3 1/2 -17/4 -3/2 -1/1 -4/1 -1/2 -19/5 -1/2 -15/4 -1/2 -26/7 -3/8 -11/3 -3/10 -18/5 -1/4 -7/2 -1/6 0/1 -24/7 0/1 -17/5 1/6 -27/8 1/2 -10/3 1/0 -33/10 -1/2 -56/17 0/1 -23/7 -1/2 -36/11 -1/2 -13/4 -1/2 0/1 -3/1 -1/2 -14/5 -1/4 -25/9 -1/2 -36/13 -1/2 -11/4 -1/2 -1/3 -19/7 -1/2 -8/3 -1/3 -29/11 -3/10 -21/8 -3/10 -34/13 -1/4 -47/18 -2/7 -1/4 -13/5 -3/10 -5/2 -1/3 -1/4 -12/5 -1/4 -19/8 -1/4 -4/17 -26/11 -1/4 -33/14 -5/22 -7/3 -3/14 -23/10 -1/4 -1/5 -16/7 -1/5 -25/11 -1/6 -9/4 -1/6 -11/5 -1/10 -24/11 0/1 -13/6 0/1 1/2 -2/1 -1/4 -13/7 -7/34 -24/13 -1/5 -11/6 -1/5 -5/26 -9/5 -1/6 -25/14 -1/4 -1/5 -16/9 -1/5 -7/4 -2/11 -1/6 -12/7 -1/6 -17/10 -1/6 -3/19 -22/13 -3/20 -49/29 -3/22 -27/16 -1/6 -5/3 -1/6 -28/17 -1/6 -23/14 -1/7 -1/8 -18/11 -1/8 -31/19 -1/10 -13/8 -1/6 0/1 -21/13 -1/6 -8/5 0/1 -27/17 -1/2 -73/46 -3/8 -1/3 -192/121 -1/3 -119/75 -7/22 -46/29 -1/4 -19/12 -1/4 0/1 -49/31 -3/10 -30/19 -1/4 -11/7 -1/6 -3/2 -1/6 -13/9 -1/6 -49/34 -2/13 -3/20 -36/25 -3/20 -23/16 -3/20 -1/7 -10/7 -3/20 -27/19 -5/34 -71/50 -3/20 -1/7 -44/31 -5/34 -17/12 -9/62 -1/7 -24/17 -1/7 -7/5 -3/22 -25/18 -1/7 -1/8 -18/13 -1/8 -11/8 -1/6 -1/7 -15/11 -3/22 -49/36 -2/15 -1/8 -34/25 -1/8 -19/14 -2/15 -1/8 -23/17 -1/6 -4/3 -1/8 -25/19 -3/26 -21/16 -1/10 -17/13 -1/6 -13/10 -1/10 0/1 -22/17 -1/4 -31/24 -1/6 -1/7 -40/31 0/1 -9/7 -1/6 -23/18 -1/7 -1/8 -14/11 -1/8 -33/26 -1/6 -19/15 -1/6 -24/19 -1/7 -5/4 -1/7 -1/8 -11/9 -3/22 -17/14 -3/23 -7/54 -40/33 -4/31 -23/19 -9/70 -6/5 -1/8 -7/6 -2/17 -3/26 -8/7 -1/9 -1/1 -1/10 0/1 0/1 1/1 1/10 7/6 3/26 2/17 6/5 1/8 5/4 1/8 1/7 24/19 1/7 19/15 1/6 14/11 1/8 23/18 1/8 1/7 9/7 1/6 22/17 1/4 13/10 0/1 1/10 17/13 1/6 4/3 1/8 23/17 1/6 19/14 1/8 2/15 15/11 3/22 11/8 1/7 1/6 18/13 1/8 25/18 1/8 1/7 7/5 3/22 24/17 1/7 17/12 1/7 9/62 10/7 3/20 3/2 1/6 14/9 1/4 25/16 1/5 1/4 36/23 1/4 11/7 1/6 19/12 0/1 1/4 8/5 0/1 29/18 0/1 1/8 21/13 1/6 13/8 0/1 1/6 18/11 1/8 23/14 1/8 1/7 5/3 1/6 22/13 3/20 39/23 1/6 17/10 3/19 1/6 12/7 1/6 7/4 1/6 2/11 23/13 5/26 16/9 1/5 25/14 1/5 1/4 9/5 1/6 11/6 5/26 1/5 24/13 1/5 13/7 7/34 2/1 1/4 13/6 -1/2 0/1 24/11 0/1 11/5 1/10 9/4 1/6 25/11 1/6 16/7 1/5 23/10 1/5 1/4 7/3 3/14 26/11 1/4 71/30 3/13 13/56 45/19 7/30 19/8 4/17 1/4 12/5 1/4 5/2 1/4 1/3 18/7 1/4 49/19 9/34 80/31 4/15 31/12 7/26 3/11 13/5 3/10 60/23 1/4 47/18 1/4 2/7 34/13 1/4 21/8 3/10 8/3 1/3 27/10 1/2 73/27 3/10 192/71 1/3 119/44 1/3 7/20 46/17 3/8 19/7 1/2 11/4 1/3 1/2 36/13 1/2 25/9 1/2 14/5 1/4 17/6 1/3 5/14 3/1 1/2 13/4 0/1 1/2 36/11 1/2 23/7 1/2 33/10 1/2 10/3 1/0 27/8 -1/2 71/21 -3/10 44/13 -1/4 17/5 -1/6 24/7 0/1 7/2 0/1 1/6 18/5 1/4 47/13 7/26 29/8 1/4 2/7 11/3 3/10 26/7 3/8 41/11 7/18 15/4 1/2 34/9 1/4 19/5 1/2 23/6 1/4 1/3 4/1 1/2 25/6 3/4 1/1 21/5 1/2 17/4 1/1 3/2 13/3 -1/2 9/2 1/2 23/5 1/2 14/3 1/0 33/7 1/2 19/4 0/1 1/0 24/5 0/1 5/1 1/2 11/2 1/2 1/1 6/1 1/0 13/2 -1/2 0/1 7/1 1/2 15/2 -1/2 23/3 -1/2 8/1 0/1 17/2 1/3 1/2 9/1 1/2 10/1 1/0 1/0 0/1 1/0 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(1,2,-8,-15) Matrix(49,432,-38,-335) -> Matrix(1,0,-4,1) Matrix(145,1104,-44,-335) -> Matrix(1,0,-4,1) Matrix(97,720,26,193) -> Matrix(3,-2,8,-5) Matrix(49,312,-30,-191) -> Matrix(1,0,-8,1) Matrix(47,264,34,191) -> Matrix(1,0,8,1) Matrix(49,264,18,97) -> Matrix(1,0,4,1) Matrix(49,240,10,49) -> Matrix(1,0,4,1) Matrix(191,912,40,191) -> Matrix(1,0,0,1) Matrix(193,912,-142,-671) -> Matrix(1,2,-8,-15) Matrix(145,672,52,241) -> Matrix(1,0,4,1) Matrix(95,432,42,191) -> Matrix(3,2,16,11) Matrix(49,216,22,97) -> Matrix(1,0,8,1) Matrix(145,624,56,241) -> Matrix(1,-2,4,-7) Matrix(193,816,-136,-575) -> Matrix(7,6,-48,-41) Matrix(145,552,-88,-335) -> Matrix(1,0,-4,1) Matrix(241,912,-190,-719) -> Matrix(1,0,-4,1) Matrix(335,1248,-142,-529) -> Matrix(21,8,-92,-35) Matrix(97,360,52,193) -> Matrix(11,4,52,19) Matrix(145,528,-92,-335) -> Matrix(7,2,-32,-9) Matrix(47,168,40,143) -> Matrix(9,2,76,17) Matrix(97,336,28,97) -> Matrix(1,0,12,1) Matrix(239,816,70,239) -> Matrix(1,0,-12,1) Matrix(241,816,-184,-623) -> Matrix(1,0,-12,1) Matrix(335,1128,128,431) -> Matrix(1,-2,4,-7) Matrix(385,1272,102,337) -> Matrix(1,0,4,1) Matrix(1393,4584,540,1777) -> Matrix(1,-4,4,-15) Matrix(527,1728,190,623) -> Matrix(1,0,4,1) Matrix(287,936,88,287) -> Matrix(1,0,4,1) Matrix(97,312,60,193) -> Matrix(1,0,8,1) Matrix(145,408,-102,-287) -> Matrix(13,4,-88,-27) Matrix(241,672,52,145) -> Matrix(1,0,4,1) Matrix(623,1728,190,527) -> Matrix(1,0,4,1) Matrix(287,792,104,287) -> Matrix(5,2,12,5) Matrix(97,264,18,49) -> Matrix(1,0,4,1) Matrix(143,384,-54,-145) -> Matrix(11,4,-36,-13) Matrix(337,888,-200,-527) -> Matrix(13,4,-88,-27) Matrix(431,1128,128,335) -> Matrix(7,2,-4,-1) Matrix(1249,3264,-918,-2399) -> Matrix(1,0,-4,1) Matrix(479,1248,-332,-865) -> Matrix(13,4,-88,-27) Matrix(47,120,-38,-97) -> Matrix(1,0,-4,1) Matrix(49,120,20,49) -> Matrix(7,2,24,7) Matrix(191,456,80,191) -> Matrix(33,8,136,33) Matrix(577,1368,-364,-863) -> Matrix(17,4,-64,-15) Matrix(143,336,20,47) -> Matrix(9,2,4,1) Matrix(145,336,104,241) -> Matrix(1,0,12,1) Matrix(335,768,188,431) -> Matrix(9,2,40,9) Matrix(337,768,190,433) -> Matrix(31,6,160,31) Matrix(191,432,42,95) -> Matrix(11,2,16,3) Matrix(97,216,22,49) -> Matrix(1,0,8,1) Matrix(241,528,110,241) -> Matrix(1,0,20,1) Matrix(287,624,132,287) -> Matrix(1,0,-4,1) Matrix(145,312,112,241) -> Matrix(1,0,8,1) Matrix(193,360,52,97) -> Matrix(19,4,52,11) Matrix(337,624,182,337) -> Matrix(69,14,340,69) Matrix(287,528,156,287) -> Matrix(51,10,260,51) Matrix(145,264,106,193) -> Matrix(21,4,152,29) Matrix(241,432,188,337) -> Matrix(1,0,12,1) Matrix(431,768,188,335) -> Matrix(9,2,40,9) Matrix(95,168,-82,-145) -> Matrix(21,4,-184,-35) Matrix(97,168,56,97) -> Matrix(23,4,132,23) Matrix(239,408,140,239) -> Matrix(37,6,228,37) Matrix(623,1056,-482,-817) -> Matrix(13,2,-72,-11) Matrix(2881,4872,-1816,-3071) -> Matrix(27,4,-88,-13) Matrix(1919,3240,568,959) -> Matrix(1,0,4,1) Matrix(1823,3000,-1284,-2113) -> Matrix(29,4,-196,-27) Matrix(527,864,380,623) -> Matrix(15,2,112,15) Matrix(383,624,294,479) -> Matrix(1,0,16,1) Matrix(193,312,60,97) -> Matrix(1,0,8,1) Matrix(239,384,-150,-241) -> Matrix(1,0,4,1) Matrix(1391,2208,332,527) -> Matrix(1,0,4,1) Matrix(23231,36864,8590,13631) -> Matrix(29,10,84,29) Matrix(23233,36864,8592,13633) -> Matrix(31,10,96,31) Matrix(865,1368,638,1009) -> Matrix(7,2,52,15) Matrix(1489,2352,578,913) -> Matrix(23,6,88,23) Matrix(47,72,-32,-49) -> Matrix(11,2,-72,-13) Matrix(3215,4632,1232,1775) -> Matrix(53,8,192,29) Matrix(1201,1728,768,1105) -> Matrix(27,4,128,19) Matrix(385,552,302,433) -> Matrix(13,2,84,13) Matrix(3599,5112,1520,2159) -> Matrix(151,22,652,95) Matrix(577,816,408,577) -> Matrix(125,18,868,125) Matrix(239,336,170,239) -> Matrix(43,6,308,43) Matrix(241,336,104,145) -> Matrix(1,0,12,1) Matrix(623,864,380,527) -> Matrix(15,2,112,15) Matrix(191,264,34,47) -> Matrix(1,0,8,1) Matrix(193,264,106,145) -> Matrix(29,4,152,21) Matrix(1151,1560,318,431) -> Matrix(31,4,116,15) Matrix(143,192,-108,-145) -> Matrix(15,2,-128,-17) Matrix(1681,2208,622,817) -> Matrix(1,0,12,1) Matrix(239,312,36,47) -> Matrix(1,0,8,1) Matrix(241,312,112,145) -> Matrix(1,0,8,1) Matrix(2881,3720,1116,1441) -> Matrix(31,4,116,15) Matrix(337,432,188,241) -> Matrix(1,0,12,1) Matrix(527,672,338,431) -> Matrix(1,0,12,1) Matrix(623,792,188,239) -> Matrix(1,0,8,1) Matrix(721,912,570,721) -> Matrix(13,2,84,13) Matrix(191,240,152,191) -> Matrix(15,2,112,15) Matrix(335,408,78,95) -> Matrix(15,2,-8,-1) Matrix(673,816,80,97) -> Matrix(31,4,116,15) Matrix(911,1104,118,143) -> Matrix(31,4,-132,-17) Matrix(577,696,160,193) -> Matrix(63,8,244,31) Matrix(143,168,40,47) -> Matrix(17,2,76,9) Matrix(191,216,84,95) -> Matrix(19,2,104,11) Matrix(1,0,2,1) -> Matrix(1,0,20,1) Matrix(145,-168,82,-95) -> Matrix(35,-4,184,-21) Matrix(97,-120,38,-47) -> Matrix(1,0,-4,1) Matrix(719,-912,190,-241) -> Matrix(1,0,-4,1) Matrix(817,-1056,482,-623) -> Matrix(11,-2,72,-13) Matrix(623,-816,184,-241) -> Matrix(1,0,-12,1) Matrix(961,-1296,284,-383) -> Matrix(15,-2,-52,7) Matrix(671,-912,142,-193) -> Matrix(15,-2,8,-1) Matrix(287,-408,102,-145) -> Matrix(27,-4,88,-13) Matrix(49,-72,32,-47) -> Matrix(13,-2,72,-11) Matrix(719,-1128,276,-433) -> Matrix(9,-2,32,-7) Matrix(335,-528,92,-145) -> Matrix(9,-2,32,-7) Matrix(241,-384,150,-239) -> Matrix(1,0,4,1) Matrix(1057,-1704,446,-719) -> Matrix(31,-4,132,-17) Matrix(191,-312,30,-49) -> Matrix(1,0,-8,1) Matrix(335,-552,88,-145) -> Matrix(1,0,-4,1) Matrix(385,-648,142,-239) -> Matrix(1,0,-4,1) Matrix(481,-816,56,-95) -> Matrix(13,-2,20,-3) Matrix(529,-1248,142,-335) -> Matrix(35,-8,92,-21) Matrix(2689,-6360,994,-2351) -> Matrix(35,-8,92,-21) Matrix(193,-504,18,-47) -> Matrix(7,-2,4,-1) Matrix(145,-384,54,-143) -> Matrix(13,-4,36,-11) Matrix(143,-408,34,-97) -> Matrix(5,-2,8,-3) Matrix(335,-1104,44,-145) -> Matrix(1,0,-4,1) Matrix(49,-192,12,-47) -> Matrix(5,-2,8,-3) Matrix(97,-456,10,-47) -> Matrix(1,0,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 24 Degree of the the map X: 48 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. ----------------------------------------------------------------------- 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): 384 Minimal number of generators: 65 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: 40 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/1 -9/2 -4/1 -10/3 -3/1 -8/3 -16/7 -2/1 -9/5 -3/2 -4/3 -6/5 0/1 1/1 6/5 4/3 3/2 36/23 12/7 9/5 2/1 24/11 12/5 5/2 8/3 3/1 36/11 10/3 24/7 7/2 11/3 4/1 9/2 24/5 5/1 11/2 6/1 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -1/2 -6/1 1/0 -5/1 -1/2 -14/3 1/0 -23/5 -1/2 -9/2 -1/2 -4/1 -1/2 -15/4 -1/2 -11/3 -3/10 -18/5 -1/4 -7/2 -1/6 0/1 -10/3 1/0 -3/1 -1/2 -14/5 -1/4 -25/9 -1/2 -36/13 -1/2 -11/4 -1/2 -1/3 -8/3 -1/3 -13/5 -3/10 -5/2 -1/3 -1/4 -12/5 -1/4 -7/3 -3/14 -23/10 -1/4 -1/5 -16/7 -1/5 -25/11 -1/6 -9/4 -1/6 -11/5 -1/10 -2/1 -1/4 -13/7 -7/34 -24/13 -1/5 -11/6 -1/5 -5/26 -9/5 -1/6 -25/14 -1/4 -1/5 -16/9 -1/5 -7/4 -2/11 -1/6 -12/7 -1/6 -5/3 -1/6 -18/11 -1/8 -13/8 -1/6 0/1 -8/5 0/1 -11/7 -1/6 -3/2 -1/6 -13/9 -1/6 -36/25 -3/20 -23/16 -3/20 -1/7 -10/7 -3/20 -17/12 -9/62 -1/7 -24/17 -1/7 -7/5 -3/22 -18/13 -1/8 -11/8 -1/6 -1/7 -4/3 -1/8 -13/10 -1/10 0/1 -9/7 -1/6 -23/18 -1/7 -1/8 -14/11 -1/8 -19/15 -1/6 -24/19 -1/7 -5/4 -1/7 -1/8 -11/9 -3/22 -6/5 -1/8 -7/6 -2/17 -3/26 -8/7 -1/9 -1/1 -1/10 0/1 0/1 1/1 1/10 7/6 3/26 2/17 6/5 1/8 5/4 1/8 1/7 14/11 1/8 23/18 1/8 1/7 9/7 1/6 4/3 1/8 15/11 3/22 11/8 1/7 1/6 18/13 1/8 7/5 3/22 10/7 3/20 3/2 1/6 14/9 1/4 25/16 1/5 1/4 36/23 1/4 11/7 1/6 8/5 0/1 13/8 0/1 1/6 5/3 1/6 12/7 1/6 7/4 1/6 2/11 23/13 5/26 16/9 1/5 25/14 1/5 1/4 9/5 1/6 11/6 5/26 1/5 2/1 1/4 13/6 -1/2 0/1 24/11 0/1 11/5 1/10 9/4 1/6 25/11 1/6 16/7 1/5 7/3 3/14 12/5 1/4 5/2 1/4 1/3 18/7 1/4 13/5 3/10 8/3 1/3 11/4 1/3 1/2 3/1 1/2 13/4 0/1 1/2 36/11 1/2 23/7 1/2 10/3 1/0 17/5 -1/6 24/7 0/1 7/2 0/1 1/6 18/5 1/4 11/3 3/10 4/1 1/2 13/3 -1/2 9/2 1/2 23/5 1/2 14/3 1/0 19/4 0/1 1/0 24/5 0/1 5/1 1/2 11/2 1/2 1/1 6/1 1/0 7/1 1/2 8/1 0/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(23,168,-10,-73) (-7/1,1/0) -> (-7/3,-23/10) Hyperbolic Matrix(25,168,18,121) (-7/1,-6/1) -> (18/13,7/5) Hyperbolic Matrix(23,120,-14,-73) (-6/1,-5/1) -> (-5/3,-18/11) Hyperbolic Matrix(71,336,-56,-265) (-5/1,-14/3) -> (-14/11,-19/15) Hyperbolic Matrix(119,552,36,167) (-14/3,-23/5) -> (23/7,10/3) Hyperbolic Matrix(95,432,42,191) (-23/5,-9/2) -> (9/4,25/11) Hyperbolic Matrix(23,96,-6,-25) (-9/2,-4/1) -> (-4/1,-15/4) Parabolic Matrix(71,264,32,119) (-15/4,-11/3) -> (11/5,9/4) Hyperbolic Matrix(119,432,46,167) (-11/3,-18/5) -> (18/7,13/5) Hyperbolic Matrix(47,168,40,143) (-18/5,-7/2) -> (7/6,6/5) Hyperbolic Matrix(71,240,-50,-169) (-7/2,-10/3) -> (-10/7,-17/12) Hyperbolic Matrix(23,72,-8,-25) (-10/3,-3/1) -> (-3/1,-14/5) Parabolic 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(313,864,96,265) (-36/13,-11/4) -> (13/4,36/11) Hyperbolic Matrix(71,192,44,119) (-11/4,-8/3) -> (8/5,13/8) Hyperbolic Matrix(73,192,46,121) (-8/3,-13/5) -> (11/7,8/5) 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(71,168,30,71) (-12/5,-7/3) -> (7/3,12/5) 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(23,48,-12,-25) (-11/5,-2/1) -> (-2/1,-13/7) Parabolic 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(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(121,216,14,25) (-25/14,-16/9) -> (8/1,1/0) 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(71,120,42,71) (-12/7,-5/3) -> (5/3,12/7) Hyperbolic Matrix(265,432,192,313) (-18/11,-13/8) -> (11/8,18/13) Hyperbolic Matrix(119,192,44,71) (-13/8,-8/5) -> (8/3,11/4) Hyperbolic Matrix(121,192,46,73) (-8/5,-11/7) -> (13/5,8/3) Hyperbolic Matrix(47,72,-32,-49) (-11/7,-3/2) -> (-3/2,-13/9) Parabolic Matrix(599,864,382,551) (-13/9,-36/25) -> (36/23,11/7) 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(407,576,118,167) (-17/12,-24/17) -> (24/7,7/2) Hyperbolic Matrix(409,576,120,169) (-24/17,-7/5) -> (17/5,24/7) Hyperbolic Matrix(121,168,18,25) (-7/5,-18/13) -> (6/1,7/1) Hyperbolic Matrix(191,264,34,47) (-18/13,-11/8) -> (11/2,6/1) Hyperbolic Matrix(71,96,-54,-73) (-11/8,-4/3) -> (-4/3,-13/10) Parabolic Matrix(167,216,92,119) (-13/10,-9/7) -> (9/5,11/6) 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(455,576,94,119) (-19/15,-24/19) -> (24/5,5/1) 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(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(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) Hyperbolic Matrix(73,-96,54,-71) (9/7,4/3) -> (4/3,15/11) Parabolic Matrix(169,-240,50,-71) (7/5,10/7) -> (10/3,17/5) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(73,-120,14,-23) (13/8,5/3) -> (5/1,11/2) Hyperbolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(73,-168,10,-23) (16/7,7/3) -> (7/1,8/1) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(25,-96,6,-23) (11/3,4/1) -> (4/1,13/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(23,168,-10,-73) -> Matrix(1,-1,-4,5) Matrix(25,168,18,121) -> Matrix(1,-1,8,-7) Matrix(23,120,-14,-73) -> Matrix(1,1,-8,-7) Matrix(71,336,-56,-265) -> Matrix(1,1,-8,-7) Matrix(119,552,36,167) -> Matrix(1,1,0,1) Matrix(95,432,42,191) -> Matrix(3,2,16,11) Matrix(23,96,-6,-25) -> Matrix(1,1,-4,-3) Matrix(71,264,32,119) -> Matrix(3,1,20,7) Matrix(119,432,46,167) -> Matrix(11,3,40,11) Matrix(47,168,40,143) -> Matrix(9,2,76,17) Matrix(71,240,-50,-169) -> Matrix(3,-1,-20,7) Matrix(23,72,-8,-25) -> Matrix(1,1,-4,-3) Matrix(241,672,52,145) -> Matrix(1,0,4,1) Matrix(623,1728,190,527) -> Matrix(1,0,4,1) Matrix(313,864,96,265) -> Matrix(3,1,8,3) Matrix(71,192,44,119) -> Matrix(3,1,20,7) Matrix(73,192,46,121) -> Matrix(3,1,8,3) Matrix(47,120,-38,-97) -> Matrix(1,0,-4,1) Matrix(49,120,20,49) -> Matrix(7,2,24,7) Matrix(71,168,30,71) -> Matrix(13,3,56,13) Matrix(335,768,188,431) -> Matrix(9,2,40,9) Matrix(337,768,190,433) -> Matrix(31,6,160,31) Matrix(191,432,42,95) -> Matrix(11,2,16,3) Matrix(97,216,22,49) -> Matrix(1,0,8,1) Matrix(23,48,-12,-25) -> Matrix(3,1,-16,-5) Matrix(311,576,142,263) -> Matrix(5,1,84,17) Matrix(313,576,144,265) -> Matrix(5,1,-36,-7) Matrix(145,264,106,193) -> Matrix(21,4,152,29) Matrix(241,432,188,337) -> Matrix(1,0,12,1) Matrix(121,216,14,25) -> Matrix(5,1,4,1) Matrix(95,168,-82,-145) -> Matrix(21,4,-184,-35) Matrix(97,168,56,97) -> Matrix(23,4,132,23) Matrix(71,120,42,71) -> Matrix(7,1,48,7) Matrix(265,432,192,313) -> Matrix(7,1,48,7) Matrix(119,192,44,71) -> Matrix(7,1,20,3) Matrix(121,192,46,73) -> Matrix(3,1,8,3) Matrix(47,72,-32,-49) -> Matrix(11,2,-72,-13) Matrix(599,864,382,551) -> Matrix(7,1,48,7) Matrix(1201,1728,768,1105) -> Matrix(27,4,128,19) Matrix(385,552,302,433) -> Matrix(13,2,84,13) Matrix(407,576,118,167) -> Matrix(7,1,104,15) Matrix(409,576,120,169) -> Matrix(7,1,-64,-9) Matrix(121,168,18,25) -> Matrix(7,1,-8,-1) Matrix(191,264,34,47) -> Matrix(1,0,8,1) Matrix(71,96,-54,-73) -> Matrix(7,1,-64,-9) Matrix(167,216,92,119) -> Matrix(5,1,24,5) Matrix(337,432,188,241) -> Matrix(1,0,12,1) Matrix(527,672,338,431) -> Matrix(1,0,12,1) Matrix(455,576,94,119) -> Matrix(7,1,20,3) Matrix(457,576,96,121) -> Matrix(7,1,-8,-1) Matrix(217,264,60,73) -> Matrix(23,3,84,11) Matrix(143,168,40,47) -> Matrix(17,2,76,9) Matrix(191,216,84,95) -> Matrix(19,2,104,11) Matrix(1,0,2,1) -> Matrix(1,0,20,1) Matrix(145,-168,82,-95) -> Matrix(35,-4,184,-21) Matrix(97,-120,38,-47) -> Matrix(1,0,-4,1) Matrix(265,-336,56,-71) -> Matrix(7,-1,8,-1) Matrix(73,-96,54,-71) -> Matrix(9,-1,64,-7) Matrix(169,-240,50,-71) -> Matrix(7,-1,-20,3) Matrix(49,-72,32,-47) -> Matrix(13,-2,72,-11) Matrix(73,-120,14,-23) -> Matrix(7,-1,8,-1) Matrix(25,-48,12,-23) -> Matrix(5,-1,16,-3) Matrix(73,-168,10,-23) -> Matrix(5,-1,-4,1) Matrix(25,-72,8,-23) -> Matrix(3,-1,4,-1) Matrix(25,-96,6,-23) -> Matrix(3,-1,4,-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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 24 ----------------------------------------------------------------------- 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 10 1 1/1 1/10 1 24 7/6 (3/26,2/17) 0 24 6/5 1/8 5 4 5/4 (1/8,1/7) 0 24 14/11 1/8 1 12 23/18 (1/8,1/7) 0 24 9/7 1/6 1 8 4/3 1/8 1 6 15/11 3/22 1 8 11/8 (1/7,1/6) 0 24 18/13 1/8 1 4 7/5 3/22 1 24 10/7 3/20 1 12 3/2 1/6 2 8 14/9 1/4 1 12 25/16 (1/5,1/4) 0 24 36/23 1/4 1 2 11/7 1/6 1 24 8/5 0/1 2 3 13/8 (0/1,1/6) 0 24 5/3 1/6 1 24 12/7 1/6 5 2 7/4 (1/6,2/11) 0 24 23/13 5/26 1 24 16/9 1/5 4 3 25/14 (1/5,1/4) 0 24 9/5 1/6 1 8 11/6 (5/26,1/5) 0 24 2/1 1/4 1 12 13/6 (-1/2,0/1) 0 24 24/11 0/1 12 1 11/5 1/10 1 24 9/4 1/6 2 8 25/11 1/6 1 24 16/7 1/5 4 3 7/3 3/14 1 24 12/5 1/4 5 2 5/2 (1/4,1/3) 0 24 18/7 1/4 5 4 13/5 3/10 1 24 8/3 1/3 2 3 11/4 (1/3,1/2) 0 24 3/1 1/2 1 8 13/4 (0/1,1/2) 0 24 36/11 1/2 1 2 23/7 1/2 1 24 10/3 1/0 1 12 17/5 -1/6 1 24 24/7 0/1 12 1 7/2 (0/1,1/6) 0 24 18/5 1/4 5 4 11/3 3/10 1 24 4/1 1/2 1 6 13/3 -1/2 1 24 9/2 1/2 2 8 23/5 1/2 1 24 14/3 1/0 1 12 19/4 (0/1,1/0) 0 24 24/5 0/1 2 1 5/1 1/2 1 24 11/2 (1/2,1/1) 0 24 6/1 1/0 1 4 7/1 1/2 1 24 8/1 0/1 4 3 1/0 (0/1,1/0) 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(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) 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(73,-96,54,-71) (9/7,4/3) -> (4/3,15/11) Parabolic 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(121,-168,18,-25) (18/13,7/5) -> (6/1,7/1) Glide Reflection Matrix(169,-240,50,-71) (7/5,10/7) -> (10/3,17/5) 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(505,-792,322,-505) (36/23,11/7) -> (36/23,11/7) Reflection Matrix(121,-192,46,-73) (11/7,8/5) -> (13/5,8/3) Glide Reflection Matrix(119,-192,44,-71) (8/5,13/8) -> (8/3,11/4) Glide Reflection Matrix(73,-120,14,-23) (13/8,5/3) -> (5/1,11/2) Hyperbolic Matrix(71,-120,42,-71) (5/3,12/7) -> (5/3,12/7) 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(121,-216,14,-25) (16/9,25/14) -> (8/1,1/0) 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(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(73,-168,10,-23) (16/7,7/3) -> (7/1,8/1) Hyperbolic Matrix(71,-168,30,-71) (7/3,12/5) -> (7/3,12/5) Reflection Matrix(49,-120,20,-49) (12/5,5/2) -> (12/5,5/2) Reflection Matrix(167,-432,46,-119) (18/7,13/5) -> (18/5,11/3) Glide Reflection Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(287,-936,88,-287) (13/4,36/11) -> (13/4,36/11) Reflection Matrix(505,-1656,154,-505) (36/11,23/7) -> (36/11,23/7) Reflection Matrix(167,-552,36,-119) (23/7,10/3) -> (23/5,14/3) 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(25,-96,6,-23) (11/3,4/1) -> (4/1,13/3) Parabolic 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(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,20,-1) (0/1,1/1) -> (0/1,1/10) Matrix(145,-168,82,-95) -> Matrix(35,-4,184,-21) Matrix(143,-168,40,-47) -> Matrix(17,-2,76,-9) Matrix(97,-120,38,-47) -> Matrix(1,0,-4,1) 0/1 Matrix(265,-336,56,-71) -> Matrix(7,-1,8,-1) Matrix(527,-672,338,-431) -> Matrix(1,0,12,-1) *** -> (0/1,1/6) Matrix(337,-432,188,-241) -> Matrix(1,0,12,-1) *** -> (0/1,1/6) Matrix(73,-96,54,-71) -> Matrix(9,-1,64,-7) 1/8 Matrix(193,-264,106,-145) -> Matrix(29,-4,152,-21) Matrix(191,-264,34,-47) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(121,-168,18,-25) -> Matrix(7,-1,-8,1) Matrix(169,-240,50,-71) -> Matrix(7,-1,-20,3) Matrix(49,-72,32,-47) -> Matrix(13,-2,72,-11) 1/6 Matrix(1151,-1800,736,-1151) -> Matrix(9,-2,40,-9) (25/16,36/23) -> (1/5,1/4) Matrix(505,-792,322,-505) -> Matrix(5,-1,24,-5) (36/23,11/7) -> (1/6,1/4) Matrix(121,-192,46,-73) -> Matrix(3,-1,8,-3) *** -> (1/4,1/2) Matrix(119,-192,44,-71) -> Matrix(7,-1,20,-3) Matrix(73,-120,14,-23) -> Matrix(7,-1,8,-1) Matrix(71,-120,42,-71) -> Matrix(7,-1,48,-7) (5/3,12/7) -> (1/8,1/6) Matrix(97,-168,56,-97) -> Matrix(23,-4,132,-23) (12/7,7/4) -> (1/6,2/11) Matrix(433,-768,190,-337) -> Matrix(31,-6,160,-31) *** -> (3/16,1/5) Matrix(121,-216,14,-25) -> Matrix(5,-1,4,-1) Matrix(25,-48,12,-23) -> Matrix(5,-1,16,-3) 1/4 Matrix(287,-624,132,-287) -> Matrix(-1,0,4,1) (13/6,24/11) -> (-1/2,0/1) Matrix(241,-528,110,-241) -> Matrix(1,0,20,-1) (24/11,11/5) -> (0/1,1/10) Matrix(97,-216,22,-49) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(191,-432,42,-95) -> Matrix(11,-2,16,-3) Matrix(73,-168,10,-23) -> Matrix(5,-1,-4,1) Matrix(71,-168,30,-71) -> Matrix(13,-3,56,-13) (7/3,12/5) -> (3/14,1/4) Matrix(49,-120,20,-49) -> Matrix(7,-2,24,-7) (12/5,5/2) -> (1/4,1/3) Matrix(167,-432,46,-119) -> Matrix(11,-3,40,-11) *** -> (1/4,3/10) Matrix(25,-72,8,-23) -> Matrix(3,-1,4,-1) 1/2 Matrix(287,-936,88,-287) -> Matrix(1,0,4,-1) (13/4,36/11) -> (0/1,1/2) Matrix(505,-1656,154,-505) -> Matrix(-1,1,0,1) (36/11,23/7) -> (1/2,1/0) Matrix(167,-552,36,-119) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(239,-816,70,-239) -> Matrix(-1,0,12,1) (17/5,24/7) -> (-1/6,0/1) Matrix(97,-336,28,-97) -> Matrix(1,0,12,-1) (24/7,7/2) -> (0/1,1/6) Matrix(25,-96,6,-23) -> Matrix(3,-1,4,-1) 1/2 Matrix(191,-912,40,-191) -> Matrix(1,0,0,-1) (19/4,24/5) -> (0/1,1/0) Matrix(49,-240,10,-49) -> Matrix(1,0,4,-1) (24/5,5/1) -> (0/1,1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.