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): 1440 Minimal number of generators: 241 Number of equivalence classes of cusps: 80 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -6/1 -11/2 -16/3 -24/5 -14/3 -4/1 -11/3 -18/5 -11/4 -12/5 -11/5 -2/1 -11/6 -11/7 -22/15 -33/23 -11/8 -11/9 -22/19 0/1 1/1 11/9 22/17 11/8 3/2 11/7 22/13 55/32 11/6 2/1 15/7 11/5 12/5 22/9 5/2 44/17 55/21 132/49 11/4 3/1 22/7 33/10 10/3 44/13 7/2 154/43 18/5 11/3 132/35 88/23 4/1 21/5 17/4 176/41 13/3 22/5 9/2 132/29 88/19 14/3 19/4 110/23 5/1 21/4 16/3 11/2 17/3 6/1 44/7 19/3 13/2 20/3 7/1 22/3 15/2 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 -1/4 -8/1 0/1 -7/1 -1/2 -13/2 -2/5 -1/3 -6/1 -1/1 -23/4 -1/1 -2/3 -17/3 -1/2 -11/2 -1/2 -27/5 -1/2 -43/8 -3/7 -2/5 -16/3 -2/5 -5/1 -1/4 -24/5 -2/1 -19/4 -2/3 -3/5 -14/3 -1/3 -23/5 -1/2 -32/7 -4/9 -9/2 -2/5 -1/3 -22/5 -1/3 -13/3 -3/10 -17/4 -2/7 -3/11 -21/5 -1/4 -4/1 0/1 -23/6 -1/3 -2/7 -19/5 -1/2 -34/9 -5/17 -49/13 -9/32 -15/4 -1/3 -2/7 -11/3 -1/4 -29/8 -5/21 -4/17 -47/13 -7/30 -18/5 -3/13 -7/2 -2/9 -1/5 -24/7 0/1 -17/5 -1/8 -10/3 -1/3 -13/4 -2/9 -1/5 -29/9 -9/40 -45/14 -2/9 -5/23 -16/5 -2/9 -3/1 -1/6 -17/6 -2/11 -3/17 -31/11 -3/16 -14/5 -3/17 -11/4 -1/6 -30/11 -5/31 -19/7 -7/44 -65/24 -3/19 -2/13 -46/17 -3/19 -27/10 -3/19 -8/51 -62/23 -11/71 -35/13 -7/46 -8/3 -2/13 -29/11 -7/50 -50/19 -1/7 -21/8 -1/7 0/1 -13/5 -1/8 -18/7 -1/5 -41/16 -1/5 0/1 -23/9 -1/6 -5/2 -2/13 -1/7 -22/9 -1/7 -17/7 -7/50 -46/19 -1/7 -29/12 -4/29 -7/51 -41/17 -5/36 -53/22 -4/29 -7/51 -12/5 -2/15 -55/23 -3/22 -43/18 -1/7 -2/15 -117/49 -15/112 -74/31 -3/23 -31/13 -3/22 -19/8 -2/15 -7/53 -7/3 -1/8 -23/10 -2/13 -1/7 -16/7 0/1 -25/11 -7/50 -34/15 -7/51 -9/4 -2/15 -3/23 -47/21 -3/22 -38/17 -3/23 -29/13 -13/100 -20/9 -4/31 -11/5 -1/8 -24/11 -6/49 -13/6 -3/25 -2/17 -15/7 -7/60 -2/1 -1/9 -15/8 -5/47 -2/19 -13/7 -1/10 -11/6 -1/10 -31/17 -1/10 -20/11 -6/61 -49/27 -17/174 -29/16 -4/41 -3/31 -9/5 -5/52 -43/24 -2/21 -5/53 -34/19 -1/11 -25/14 -4/43 -1/11 -66/37 -1/11 -41/23 -3/34 -16/9 0/1 -23/13 -1/10 -30/17 -3/31 -7/4 -2/21 -1/11 -26/15 -3/31 -71/41 -1/10 -45/26 -2/21 -1/11 -19/11 -5/52 -50/29 -9/95 -31/18 -12/127 -5/53 -43/25 -25/266 -55/32 -3/32 -12/7 -4/43 -41/24 -4/43 -9/97 -29/17 -17/184 -46/27 -1/11 -17/10 -10/109 -1/11 -22/13 -1/11 -5/3 -3/34 -28/17 0/1 -23/14 -2/21 -1/11 -41/25 -5/56 -18/11 -1/11 -31/19 -7/80 -44/27 -2/23 -13/8 -2/23 -3/35 -34/21 -5/59 -89/55 -21/250 -55/34 -1/12 -76/47 -4/49 -21/13 -1/12 -50/31 -1/13 -79/49 -3/34 -29/18 -1/11 0/1 -66/41 -1/11 -37/23 -3/34 -8/5 -2/23 -35/22 -19/223 -4/47 -132/83 -4/47 -97/61 -49/576 -62/39 -13/153 -27/17 -9/106 -46/29 -5/59 -19/12 -5/59 -6/71 -11/7 -1/12 -25/16 -9/109 -8/97 -14/9 -5/61 -17/11 -5/62 -20/13 -2/25 -23/15 -1/12 -3/2 -2/25 -1/13 -22/15 -1/13 -19/13 -13/170 -16/11 -6/79 -45/31 -31/410 -29/20 -4/53 -15/199 -13/9 -3/40 -23/16 -1/13 -2/27 -33/23 -3/40 -43/30 -5/67 -2/27 -10/7 -1/13 -27/19 -11/148 -44/31 -2/27 -17/12 -2/27 -7/95 -41/29 -5/68 -65/46 -26/355 -3/41 -24/17 -4/55 -31/22 -1/13 0/1 -7/5 -1/14 -25/18 -4/55 -13/179 -68/49 -24/331 -111/80 -74/1021 -5/69 -154/111 -5/69 -43/31 -31/428 -61/44 -28/387 -17/235 -18/13 -7/97 -11/8 -1/14 -26/19 -9/127 -41/30 -9/127 -8/113 -15/11 -11/156 -49/36 -21/299 -4/57 -132/97 -4/57 -83/61 -31/442 -34/25 -3/43 -19/14 -3/43 -2/29 -42/31 -3/43 -65/48 -3/43 -2/29 -88/65 -2/29 -23/17 -1/14 -4/3 -2/29 -21/16 -4/59 -1/15 -17/13 -3/44 -30/23 -11/163 -103/79 -65/964 -176/135 -6/89 -73/56 -6/89 -49/727 -43/33 -33/490 -13/10 -10/149 -1/15 -22/17 -1/15 -9/7 -7/106 -50/39 -9/137 -91/71 -21/320 -132/103 -4/61 -41/32 -4/61 -7/107 -32/25 -4/61 -55/43 -3/46 -23/18 -1/15 -2/31 -37/29 -5/76 -88/69 -4/61 -51/40 -4/61 -7/107 -14/11 -1/15 -19/15 -7/108 -43/34 -1/15 -2/31 -110/87 -1/15 -67/53 -3/46 -24/19 -2/31 -29/23 -17/262 -5/4 -2/31 -3/47 -21/17 -1/16 -16/13 -6/95 -11/9 -1/16 -28/23 -12/193 -45/37 -37/596 -17/14 -7/113 -6/97 -23/19 -1/16 -6/5 -3/49 -25/21 -17/280 -44/37 -2/33 -19/16 -2/33 -13/215 -13/11 -3/50 -20/17 -4/67 -7/6 -6/101 -1/17 -22/19 -1/17 -15/13 -13/222 -8/7 -4/69 -9/8 -2/35 -7/123 -10/9 -5/89 -1/1 -1/20 0/1 0/1 1/1 1/22 9/8 7/137 2/39 8/7 4/77 7/6 1/19 6/113 13/11 3/56 6/5 3/55 23/19 1/18 17/14 6/109 7/127 11/9 1/18 27/22 12/215 11/197 43/35 35/626 16/13 6/107 5/4 3/53 2/35 24/19 2/35 19/15 7/122 14/11 1/17 23/18 2/35 1/17 32/25 4/69 9/7 7/120 22/17 1/17 13/10 1/17 10/169 17/13 3/50 21/16 1/17 4/67 4/3 2/33 23/17 1/16 19/14 2/33 3/49 34/25 3/49 49/36 4/65 21/341 15/11 11/178 11/8 1/16 29/21 21/334 47/34 8/127 7/111 18/13 7/111 7/5 1/16 24/17 4/63 17/12 7/109 2/31 10/7 1/15 13/9 3/46 29/20 15/229 4/61 45/31 31/472 16/11 6/91 3/2 1/15 2/29 17/11 5/72 31/20 3/43 16/229 14/9 5/71 11/7 1/14 30/19 9/125 19/12 6/83 5/69 65/41 1/14 46/29 5/69 27/17 9/124 62/39 13/179 35/22 4/55 19/261 8/5 2/27 29/18 0/1 1/13 50/31 1/15 21/13 1/14 13/8 3/41 2/27 18/11 1/13 41/25 5/66 23/14 1/13 2/25 5/3 3/40 22/13 1/13 17/10 1/13 10/129 46/27 1/13 29/17 17/218 41/24 9/115 4/51 53/31 1/12 12/7 4/51 55/32 3/38 43/25 25/316 117/68 59/745 8/101 74/43 21/265 31/18 5/63 12/151 19/11 5/62 7/4 1/13 2/25 23/13 1/12 16/9 0/1 25/14 1/13 4/51 34/19 1/13 9/5 5/62 47/26 11/135 4/49 38/21 5/61 29/16 3/37 4/49 20/11 6/73 11/6 1/12 24/13 6/71 13/7 1/12 15/8 2/23 5/57 2/1 1/11 15/7 7/74 13/6 2/21 3/31 11/5 1/10 31/14 8/79 7/69 20/9 4/39 49/22 13/127 4/39 29/13 13/126 9/4 3/29 2/19 43/19 19/178 34/15 7/65 25/11 7/64 66/29 1/9 41/18 1/9 8/71 16/7 0/1 23/10 1/9 2/17 30/13 1/9 7/3 1/10 26/11 5/49 71/30 11/107 18/175 45/19 19/184 19/8 7/67 2/19 50/21 9/85 31/13 3/28 43/18 2/19 1/9 55/23 3/28 12/5 2/19 41/17 5/46 29/12 7/65 4/37 46/19 1/9 17/7 7/64 22/9 1/9 5/2 1/9 2/17 28/11 2/15 23/9 1/8 41/16 0/1 1/7 18/7 1/7 31/12 0/1 1/5 44/17 0/1 13/5 1/10 34/13 1/9 89/34 0/1 1/11 55/21 1/10 76/29 2/19 21/8 0/1 1/9 50/19 1/9 79/30 2/19 1/9 29/11 7/64 66/25 1/9 37/14 1/9 12/107 8/3 2/17 35/13 7/60 132/49 2/17 97/36 2/17 27/229 62/23 11/93 27/10 8/67 3/25 46/17 3/25 19/7 7/58 11/4 1/8 25/9 9/70 14/5 3/23 17/6 3/23 2/15 20/7 4/29 23/8 1/7 6/41 3/1 1/8 22/7 1/7 19/6 1/7 6/41 16/5 2/13 45/14 5/33 2/13 29/9 9/58 13/4 1/7 2/13 23/7 1/6 33/10 1/6 43/13 13/76 10/3 1/5 27/8 0/1 1/1 44/13 0/1 17/5 1/10 41/12 0/1 1/7 65/19 1/8 24/7 0/1 31/9 1/8 7/2 1/7 2/13 25/7 5/32 68/19 2/13 111/31 1/6 154/43 1/7 43/12 1/7 2/13 61/17 1/6 18/5 3/19 11/3 1/6 26/7 3/17 41/11 5/28 15/4 2/11 1/5 49/13 9/50 132/35 2/11 83/22 2/11 17/93 34/9 5/27 19/5 1/4 42/11 1/5 65/17 1/6 88/23 2/11 23/6 2/11 1/5 4/1 0/1 21/5 1/6 17/4 3/17 2/11 30/7 3/17 103/24 23/127 2/11 176/41 2/11 73/17 15/82 43/10 2/11 1/5 13/3 3/16 22/5 1/5 9/2 1/5 2/9 50/11 1/5 91/20 9/41 2/9 132/29 2/9 41/9 5/22 32/7 4/17 55/12 1/4 23/5 1/4 37/8 0/1 1/3 88/19 0/1 51/11 1/6 14/3 1/5 19/4 3/11 2/7 43/9 9/28 110/23 1/3 67/14 1/3 12/35 24/5 2/5 29/6 0/1 1/1 5/1 1/6 21/4 1/5 4/19 16/3 2/9 11/2 1/4 28/5 2/7 45/8 2/7 1/3 17/3 1/4 23/4 2/7 1/3 6/1 1/3 25/4 -1/5 0/1 44/7 0/1 19/3 1/10 13/2 1/5 2/9 20/3 2/7 7/1 1/4 22/3 1/3 15/2 1/3 2/5 8/1 0/1 9/1 1/6 10/1 1/3 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(43,396,-24,-221) (-9/1,1/0) -> (-9/5,-43/24) Hyperbolic Matrix(43,352,16,131) (-9/1,-8/1) -> (8/3,35/13) Hyperbolic Matrix(45,352,-28,-219) (-8/1,-7/1) -> (-37/23,-8/5) Hyperbolic Matrix(45,308,-32,-219) (-7/1,-13/2) -> (-31/22,-7/5) Hyperbolic Matrix(131,836,-76,-485) (-13/2,-6/1) -> (-50/29,-31/18) Hyperbolic Matrix(221,1276,84,485) (-6/1,-23/4) -> (21/8,50/19) Hyperbolic Matrix(131,748,100,571) (-23/4,-17/3) -> (17/13,21/16) Hyperbolic Matrix(87,484,-16,-89) (-17/3,-11/2) -> (-11/2,-27/5) Parabolic Matrix(703,3784,196,1055) (-27/5,-43/8) -> (43/12,61/17) Hyperbolic Matrix(263,1408,82,439) (-43/8,-16/3) -> (16/5,45/14) Hyperbolic Matrix(43,220,-26,-133) (-16/3,-5/1) -> (-5/3,-28/17) Hyperbolic Matrix(265,1276,-146,-703) (-5/1,-24/5) -> (-20/11,-49/27) Hyperbolic Matrix(397,1892,-286,-1363) (-24/5,-19/4) -> (-25/18,-68/49) Hyperbolic Matrix(177,836,112,529) (-19/4,-14/3) -> (30/19,19/12) Hyperbolic Matrix(219,1012,-124,-573) (-14/3,-23/5) -> (-23/13,-30/17) Hyperbolic Matrix(527,2420,-326,-1497) (-23/5,-32/7) -> (-76/47,-21/13) Hyperbolic Matrix(395,1804,-164,-749) (-32/7,-9/2) -> (-53/22,-12/5) Hyperbolic Matrix(89,396,20,89) (-9/2,-22/5) -> (22/5,9/2) Hyperbolic Matrix(131,572,30,131) (-22/5,-13/3) -> (13/3,22/5) Hyperbolic Matrix(175,748,-62,-265) (-13/3,-17/4) -> (-17/6,-31/11) Hyperbolic Matrix(177,748,146,617) (-17/4,-21/5) -> (23/19,17/14) Hyperbolic Matrix(43,176,32,131) (-21/5,-4/1) -> (4/3,23/17) Hyperbolic Matrix(45,176,34,133) (-4/1,-23/6) -> (21/16,4/3) Hyperbolic Matrix(439,1672,-162,-617) (-23/6,-19/5) -> (-19/7,-65/24) Hyperbolic Matrix(395,1496,174,659) (-19/5,-34/9) -> (34/15,25/11) Hyperbolic Matrix(1189,4488,-874,-3299) (-34/9,-49/13) -> (-83/61,-34/25) Hyperbolic Matrix(397,1496,82,309) (-49/13,-15/4) -> (29/6,5/1) Hyperbolic Matrix(131,484,-36,-133) (-15/4,-11/3) -> (-11/3,-29/8) Parabolic Matrix(705,2552,292,1057) (-29/8,-47/13) -> (41/17,29/12) Hyperbolic Matrix(439,1584,268,967) (-47/13,-18/5) -> (18/11,41/25) Hyperbolic Matrix(87,308,-50,-177) (-18/5,-7/2) -> (-7/4,-26/15) Hyperbolic Matrix(89,308,-76,-263) (-7/2,-24/7) -> (-20/17,-7/6) Hyperbolic Matrix(219,748,-142,-485) (-24/7,-17/5) -> (-17/11,-20/13) Hyperbolic Matrix(131,440,-92,-309) (-17/5,-10/3) -> (-10/7,-27/19) Hyperbolic Matrix(175,572,-108,-353) (-10/3,-13/4) -> (-13/8,-34/21) Hyperbolic Matrix(177,572,82,265) (-13/4,-29/9) -> (15/7,13/6) Hyperbolic Matrix(2025,6512,-848,-2727) (-29/9,-45/14) -> (-43/18,-117/49) Hyperbolic Matrix(617,1980,110,353) (-45/14,-16/5) -> (28/5,45/8) Hyperbolic Matrix(221,704,-124,-395) (-16/5,-3/1) -> (-41/23,-16/9) Hyperbolic Matrix(263,748,-186,-529) (-3/1,-17/6) -> (-17/12,-41/29) Hyperbolic Matrix(969,2728,-406,-1143) (-31/11,-14/5) -> (-74/31,-31/13) Hyperbolic Matrix(175,484,-64,-177) (-14/5,-11/4) -> (-11/4,-30/11) Parabolic Matrix(307,836,242,659) (-30/11,-19/7) -> (19/15,14/11) Hyperbolic Matrix(2113,5720,-1560,-4223) (-65/24,-46/17) -> (-42/31,-65/48) Hyperbolic Matrix(749,2024,440,1189) (-46/17,-27/10) -> (17/10,46/27) Hyperbolic Matrix(1893,5104,800,2157) (-27/10,-62/23) -> (26/11,71/30) Hyperbolic Matrix(3037,8184,-1910,-5147) (-62/23,-35/13) -> (-97/61,-62/39) Hyperbolic Matrix(131,352,16,43) (-35/13,-8/3) -> (8/1,9/1) Hyperbolic Matrix(133,352,-116,-307) (-8/3,-29/11) -> (-15/13,-8/7) Hyperbolic Matrix(969,2552,-434,-1143) (-29/11,-50/19) -> (-38/17,-29/13) Hyperbolic Matrix(485,1276,84,221) (-50/19,-21/8) -> (23/4,6/1) Hyperbolic Matrix(219,572,-152,-397) (-21/8,-13/5) -> (-13/9,-23/16) Hyperbolic Matrix(307,792,-188,-485) (-13/5,-18/7) -> (-18/11,-31/19) Hyperbolic Matrix(617,1584,446,1145) (-18/7,-41/16) -> (47/34,18/13) Hyperbolic Matrix(395,1012,-258,-661) (-41/16,-23/9) -> (-23/15,-3/2) Hyperbolic Matrix(87,220,-70,-177) (-23/9,-5/2) -> (-5/4,-21/17) Hyperbolic Matrix(89,220,36,89) (-5/2,-22/9) -> (22/9,5/2) Hyperbolic Matrix(307,748,126,307) (-22/9,-17/7) -> (17/7,22/9) Hyperbolic Matrix(835,2024,526,1275) (-17/7,-46/19) -> (46/29,27/17) Hyperbolic Matrix(309,748,164,397) (-46/19,-29/12) -> (15/8,2/1) Hyperbolic Matrix(747,1804,200,483) (-29/12,-41/17) -> (41/11,15/4) Hyperbolic Matrix(1187,2860,-530,-1277) (-41/17,-53/22) -> (-9/4,-47/21) Hyperbolic Matrix(2023,4840,772,1847) (-12/5,-55/23) -> (55/21,76/29) Hyperbolic Matrix(3037,7260,1160,2773) (-55/23,-43/18) -> (89/34,55/21) Hyperbolic Matrix(4663,11132,-3576,-8537) (-117/49,-74/31) -> (-30/23,-103/79) Hyperbolic Matrix(351,836,-296,-705) (-31/13,-19/8) -> (-19/16,-13/11) Hyperbolic Matrix(131,308,-94,-221) (-19/8,-7/3) -> (-7/5,-25/18) Hyperbolic Matrix(439,1012,-344,-793) (-7/3,-23/10) -> (-23/18,-37/29) Hyperbolic Matrix(441,1012,-268,-615) (-23/10,-16/7) -> (-28/17,-23/14) Hyperbolic Matrix(309,704,-212,-483) (-16/7,-25/11) -> (-19/13,-16/11) Hyperbolic Matrix(659,1496,174,395) (-25/11,-34/15) -> (34/9,19/5) Hyperbolic Matrix(175,396,-156,-353) (-34/15,-9/4) -> (-9/8,-10/9) Hyperbolic Matrix(2597,5808,-2026,-4531) (-47/21,-38/17) -> (-50/39,-91/71) Hyperbolic Matrix(573,1276,-454,-1011) (-29/13,-20/9) -> (-24/19,-29/23) Hyperbolic Matrix(219,484,-100,-221) (-20/9,-11/5) -> (-11/5,-24/11) Parabolic Matrix(263,572,40,87) (-24/11,-13/6) -> (13/2,20/3) Hyperbolic Matrix(265,572,82,177) (-13/6,-15/7) -> (29/9,13/4) Hyperbolic Matrix(351,748,206,439) (-15/7,-2/1) -> (46/27,29/17) Hyperbolic Matrix(397,748,164,309) (-2/1,-15/8) -> (29/12,46/19) Hyperbolic Matrix(307,572,212,395) (-15/8,-13/7) -> (13/9,29/20) Hyperbolic Matrix(263,484,-144,-265) (-13/7,-11/6) -> (-11/6,-31/17) Parabolic Matrix(749,1364,218,397) (-31/17,-20/11) -> (24/7,31/9) Hyperbolic Matrix(1189,2156,316,573) (-49/27,-29/16) -> (15/4,49/13) Hyperbolic Matrix(1409,2552,-874,-1583) (-29/16,-9/5) -> (-79/49,-29/18) Hyperbolic Matrix(2507,4488,958,1715) (-43/24,-34/19) -> (34/13,89/34) Hyperbolic Matrix(837,1496,616,1101) (-34/19,-25/14) -> (19/14,34/25) Hyperbolic Matrix(1011,1804,320,571) (-25/14,-66/37) -> (22/7,19/6) Hyperbolic Matrix(617,1100,198,353) (-66/37,-41/23) -> (3/1,22/7) Hyperbolic Matrix(397,704,-322,-571) (-16/9,-23/13) -> (-21/17,-16/13) Hyperbolic Matrix(923,1628,-724,-1277) (-30/17,-7/4) -> (-51/40,-14/11) Hyperbolic Matrix(2947,5104,1854,3211) (-26/15,-71/41) -> (27/17,62/39) Hyperbolic Matrix(2287,3960,406,703) (-71/41,-45/26) -> (45/8,17/3) Hyperbolic Matrix(967,1672,-764,-1321) (-45/26,-19/11) -> (-19/15,-43/34) Hyperbolic Matrix(791,1364,-664,-1145) (-19/11,-50/29) -> (-6/5,-25/21) Hyperbolic Matrix(1099,1892,-844,-1453) (-31/18,-43/25) -> (-43/33,-13/10) Hyperbolic Matrix(2201,3784,666,1145) (-43/25,-55/32) -> (33/10,43/13) Hyperbolic Matrix(1409,2420,308,529) (-55/32,-12/7) -> (32/7,55/12) Hyperbolic Matrix(1055,1804,-824,-1409) (-12/7,-41/24) -> (-41/32,-32/25) Hyperbolic Matrix(1495,2552,1082,1847) (-41/24,-29/17) -> (29/21,47/34) Hyperbolic Matrix(439,748,206,351) (-29/17,-46/27) -> (2/1,15/7) Hyperbolic Matrix(1189,2024,440,749) (-46/27,-17/10) -> (27/10,46/17) Hyperbolic Matrix(441,748,260,441) (-17/10,-22/13) -> (22/13,17/10) Hyperbolic Matrix(131,220,78,131) (-22/13,-5/3) -> (5/3,22/13) Hyperbolic Matrix(2199,3608,-1556,-2553) (-23/14,-41/25) -> (-41/29,-65/46) Hyperbolic Matrix(1101,1804,296,485) (-41/25,-18/11) -> (26/7,41/11) Hyperbolic Matrix(1187,1936,458,747) (-31/19,-44/27) -> (44/17,13/5) Hyperbolic Matrix(1189,1936,460,749) (-44/27,-13/8) -> (31/12,44/17) Hyperbolic Matrix(2773,4488,1224,1981) (-34/21,-89/55) -> (43/19,34/15) Hyperbolic Matrix(4487,7260,2610,4223) (-89/55,-55/34) -> (55/32,43/25) Hyperbolic Matrix(2993,4840,1742,2817) (-55/34,-76/47) -> (12/7,55/32) Hyperbolic Matrix(791,1276,654,1055) (-21/13,-50/31) -> (6/5,23/19) Hyperbolic Matrix(2729,4400,-2128,-3431) (-50/31,-79/49) -> (-9/7,-50/39) Hyperbolic Matrix(1011,1628,136,219) (-29/18,-66/41) -> (22/3,15/2) Hyperbolic Matrix(793,1276,110,177) (-66/41,-37/23) -> (7/1,22/3) Hyperbolic Matrix(221,352,194,309) (-8/5,-35/22) -> (9/8,8/7) Hyperbolic Matrix(10955,17424,4066,6467) (-35/22,-132/83) -> (132/49,97/36) Hyperbolic Matrix(10957,17424,4068,6469) (-132/83,-97/61) -> (35/13,132/49) Hyperbolic Matrix(2685,4268,748,1189) (-62/39,-27/17) -> (61/17,18/5) Hyperbolic Matrix(1275,2024,526,835) (-27/17,-46/29) -> (46/19,17/7) Hyperbolic Matrix(1055,1672,-778,-1233) (-46/29,-19/12) -> (-19/14,-42/31) Hyperbolic Matrix(307,484,-196,-309) (-19/12,-11/7) -> (-11/7,-25/16) Parabolic Matrix(395,616,84,131) (-25/16,-14/9) -> (14/3,19/4) Hyperbolic Matrix(483,748,-370,-573) (-14/9,-17/11) -> (-17/13,-30/23) Hyperbolic Matrix(1231,1892,-974,-1497) (-20/13,-23/15) -> (-67/53,-24/19) Hyperbolic Matrix(747,1100,328,483) (-3/2,-22/15) -> (66/29,41/18) Hyperbolic Matrix(1233,1804,542,793) (-22/15,-19/13) -> (25/11,66/29) Hyperbolic Matrix(969,1408,788,1145) (-16/11,-45/31) -> (43/35,16/13) Hyperbolic Matrix(3123,4532,-2396,-3477) (-45/31,-29/20) -> (-73/56,-43/33) Hyperbolic Matrix(395,572,212,307) (-29/20,-13/9) -> (13/7,15/8) Hyperbolic Matrix(1409,2024,-1102,-1583) (-23/16,-33/23) -> (-55/43,-23/18) Hyperbolic Matrix(2639,3784,1104,1583) (-33/23,-43/30) -> (43/18,55/23) Hyperbolic Matrix(307,440,30,43) (-43/30,-10/7) -> (10/1,1/0) Hyperbolic Matrix(1363,1936,402,571) (-27/19,-44/31) -> (44/13,17/5) Hyperbolic Matrix(1365,1936,404,573) (-44/31,-17/12) -> (27/8,44/13) Hyperbolic Matrix(5015,7084,-3614,-5105) (-65/46,-24/17) -> (-68/49,-111/80) Hyperbolic Matrix(967,1364,436,615) (-24/17,-31/22) -> (31/14,20/9) Hyperbolic Matrix(16237,22528,3394,4709) (-111/80,-154/111) -> (110/23,67/14) Hyperbolic Matrix(8183,11352,1712,2375) (-154/111,-43/31) -> (43/9,110/23) Hyperbolic Matrix(2729,3784,2222,3081) (-43/31,-61/44) -> (27/22,43/35) Hyperbolic Matrix(3079,4268,1142,1583) (-61/44,-18/13) -> (62/23,27/10) Hyperbolic Matrix(351,484,-256,-353) (-18/13,-11/8) -> (-11/8,-26/19) Parabolic Matrix(1319,1804,514,703) (-26/19,-41/30) -> (41/16,18/7) Hyperbolic Matrix(1321,1804,774,1057) (-41/30,-15/11) -> (29/17,41/24) Hyperbolic Matrix(1583,2156,710,967) (-15/11,-49/36) -> (49/22,29/13) Hyperbolic Matrix(12803,17424,3394,4619) (-49/36,-132/97) -> (132/35,83/22) Hyperbolic Matrix(12805,17424,3396,4621) (-132/97,-83/61) -> (49/13,132/35) Hyperbolic Matrix(1101,1496,616,837) (-34/25,-19/14) -> (25/14,34/19) Hyperbolic Matrix(5719,7744,1494,2023) (-65/48,-88/65) -> (88/23,23/6) Hyperbolic Matrix(5721,7744,1496,2025) (-88/65,-23/17) -> (65/17,88/23) Hyperbolic Matrix(131,176,32,43) (-23/17,-4/3) -> (4/1,21/5) Hyperbolic Matrix(133,176,34,45) (-4/3,-21/16) -> (23/6,4/1) Hyperbolic Matrix(571,748,100,131) (-21/16,-17/13) -> (17/3,23/4) Hyperbolic Matrix(23759,30976,5534,7215) (-103/79,-176/135) -> (176/41,73/17) Hyperbolic Matrix(23761,30976,5536,7217) (-176/135,-73/56) -> (103/24,176/41) Hyperbolic Matrix(441,572,340,441) (-13/10,-22/17) -> (22/17,13/10) Hyperbolic Matrix(307,396,238,307) (-22/17,-9/7) -> (9/7,22/17) Hyperbolic Matrix(13595,17424,2986,3827) (-91/71,-132/103) -> (132/29,41/9) Hyperbolic Matrix(13597,17424,2988,3829) (-132/103,-41/32) -> (91/20,132/29) Hyperbolic Matrix(1891,2420,790,1011) (-32/25,-55/43) -> (55/23,12/5) Hyperbolic Matrix(6071,7744,1310,1671) (-37/29,-88/69) -> (88/19,51/11) Hyperbolic Matrix(6073,7744,1312,1673) (-88/69,-51/40) -> (37/8,88/19) Hyperbolic Matrix(485,616,174,221) (-14/11,-19/15) -> (25/9,14/5) Hyperbolic Matrix(8977,11352,2506,3169) (-43/34,-110/87) -> (154/43,43/12) Hyperbolic Matrix(17819,22528,4976,6291) (-110/87,-67/53) -> (111/31,154/43) Hyperbolic Matrix(1187,1496,872,1099) (-29/23,-5/4) -> (49/36,15/11) Hyperbolic Matrix(395,484,-324,-397) (-16/13,-11/9) -> (-11/9,-28/23) Parabolic Matrix(1627,1980,1120,1363) (-28/23,-45/37) -> (45/31,16/11) Hyperbolic Matrix(3257,3960,1376,1673) (-45/37,-17/14) -> (71/30,45/19) Hyperbolic Matrix(617,748,146,177) (-17/14,-23/19) -> (21/5,17/4) Hyperbolic Matrix(1055,1276,654,791) (-23/19,-6/5) -> (50/31,21/13) Hyperbolic Matrix(1627,1936,258,307) (-25/21,-44/37) -> (44/7,19/3) Hyperbolic Matrix(1629,1936,260,309) (-44/37,-19/16) -> (25/4,44/7) Hyperbolic Matrix(485,572,262,309) (-13/11,-20/17) -> (24/13,13/7) Hyperbolic Matrix(1099,1276,416,483) (-7/6,-22/19) -> (66/25,37/14) Hyperbolic Matrix(1409,1628,534,617) (-22/19,-15/13) -> (29/11,66/25) Hyperbolic Matrix(309,352,194,221) (-8/7,-9/8) -> (35/22,8/5) Hyperbolic Matrix(397,440,120,133) (-10/9,-1/1) -> (43/13,10/3) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(353,-396,156,-175) (1/1,9/8) -> (9/4,43/19) Hyperbolic Matrix(307,-352,116,-133) (8/7,7/6) -> (37/14,8/3) Hyperbolic Matrix(263,-308,76,-89) (7/6,13/11) -> (31/9,7/2) Hyperbolic Matrix(705,-836,296,-351) (13/11,6/5) -> (50/21,31/13) Hyperbolic Matrix(397,-484,324,-395) (17/14,11/9) -> (11/9,27/22) Parabolic Matrix(177,-220,70,-87) (16/13,5/4) -> (5/2,28/11) Hyperbolic Matrix(1011,-1276,454,-573) (5/4,24/19) -> (20/9,49/22) Hyperbolic Matrix(1495,-1892,418,-529) (24/19,19/15) -> (25/7,68/19) Hyperbolic Matrix(793,-1012,344,-439) (14/11,23/18) -> (23/10,30/13) Hyperbolic Matrix(1893,-2420,722,-923) (23/18,32/25) -> (76/29,21/8) Hyperbolic Matrix(1409,-1804,824,-1055) (32/25,9/7) -> (53/31,12/7) Hyperbolic Matrix(573,-748,370,-483) (13/10,17/13) -> (17/11,31/20) Hyperbolic Matrix(1233,-1672,778,-1055) (23/17,19/14) -> (19/12,65/41) Hyperbolic Matrix(3299,-4488,874,-1189) (34/25,49/36) -> (83/22,34/9) Hyperbolic Matrix(353,-484,256,-351) (15/11,11/8) -> (11/8,29/21) Parabolic Matrix(221,-308,94,-131) (18/13,7/5) -> (7/3,26/11) Hyperbolic Matrix(219,-308,32,-45) (7/5,24/17) -> (20/3,7/1) Hyperbolic Matrix(529,-748,186,-263) (24/17,17/12) -> (17/6,20/7) Hyperbolic Matrix(309,-440,92,-131) (17/12,10/7) -> (10/3,27/8) Hyperbolic Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(4487,-6512,2608,-3785) (29/20,45/31) -> (43/25,117/68) Hyperbolic Matrix(483,-704,212,-309) (16/11,3/2) -> (41/18,16/7) Hyperbolic Matrix(485,-748,142,-219) (3/2,17/11) -> (17/5,41/12) Hyperbolic Matrix(1759,-2728,1022,-1585) (31/20,14/9) -> (74/43,31/18) Hyperbolic Matrix(309,-484,196,-307) (14/9,11/7) -> (11/7,30/19) Parabolic Matrix(3607,-5720,944,-1497) (65/41,46/29) -> (42/11,65/17) Hyperbolic Matrix(5147,-8184,1910,-3037) (62/39,35/22) -> (97/36,62/23) Hyperbolic Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(1583,-2552,874,-1409) (29/18,50/31) -> (38/21,29/16) Hyperbolic Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(485,-792,188,-307) (13/8,18/11) -> (18/7,31/12) Hyperbolic Matrix(617,-1012,214,-351) (41/25,23/14) -> (23/8,3/1) Hyperbolic Matrix(133,-220,26,-43) (23/14,5/3) -> (5/1,21/4) Hyperbolic Matrix(1673,-2860,926,-1583) (41/24,53/31) -> (9/5,47/26) Hyperbolic Matrix(6469,-11132,1508,-2595) (117/68,74/43) -> (30/7,103/24) Hyperbolic Matrix(485,-836,76,-131) (31/18,19/11) -> (19/3,13/2) Hyperbolic Matrix(177,-308,50,-87) (19/11,7/4) -> (7/2,25/7) Hyperbolic Matrix(573,-1012,124,-219) (7/4,23/13) -> (23/5,37/8) Hyperbolic Matrix(571,-1012,224,-397) (23/13,16/9) -> (28/11,23/9) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(221,-396,24,-43) (34/19,9/5) -> (9/1,10/1) Hyperbolic Matrix(3211,-5808,706,-1277) (47/26,38/21) -> (50/11,91/20) Hyperbolic Matrix(703,-1276,146,-265) (29/16,20/11) -> (24/5,29/6) Hyperbolic Matrix(265,-484,144,-263) (20/11,11/6) -> (11/6,24/13) Parabolic Matrix(221,-484,100,-219) (13/6,11/5) -> (11/5,31/14) Parabolic Matrix(1143,-2552,434,-969) (29/13,9/4) -> (79/30,29/11) Hyperbolic Matrix(307,-704,58,-133) (16/7,23/10) -> (21/4,16/3) Hyperbolic Matrix(705,-1628,152,-351) (30/13,7/3) -> (51/11,14/3) Hyperbolic Matrix(705,-1672,148,-351) (45/19,19/8) -> (19/4,43/9) Hyperbolic Matrix(573,-1364,92,-219) (19/8,50/21) -> (6/1,25/4) Hyperbolic Matrix(793,-1892,184,-439) (31/13,43/18) -> (43/10,13/3) Hyperbolic Matrix(749,-1804,164,-395) (12/5,41/17) -> (41/9,32/7) Hyperbolic Matrix(1409,-3608,412,-1055) (23/9,41/16) -> (41/12,65/19) Hyperbolic Matrix(1671,-4400,368,-969) (50/19,79/30) -> (9/2,50/11) Hyperbolic Matrix(617,-1672,162,-439) (46/17,19/7) -> (19/5,42/11) Hyperbolic Matrix(177,-484,64,-175) (19/7,11/4) -> (11/4,25/9) Parabolic Matrix(265,-748,62,-175) (14/5,17/6) -> (17/4,30/7) Hyperbolic Matrix(661,-1892,138,-395) (20/7,23/8) -> (67/14,24/5) Hyperbolic Matrix(1409,-4532,328,-1055) (45/14,29/9) -> (73/17,43/10) Hyperbolic Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(2069,-7084,578,-1979) (65/19,24/7) -> (68/19,111/31) Hyperbolic Matrix(133,-484,36,-131) (18/5,11/3) -> (11/3,26/7) Parabolic Matrix(89,-484,16,-87) (16/3,11/2) -> (11/2,28/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(43,396,-24,-221) -> Matrix(3,2,-32,-21) Matrix(43,352,16,131) -> Matrix(1,2,8,17) Matrix(45,352,-28,-219) -> Matrix(1,2,-12,-23) Matrix(45,308,-32,-219) -> Matrix(5,2,-68,-27) Matrix(131,836,-76,-485) -> Matrix(11,2,-116,-21) Matrix(221,1276,84,485) -> Matrix(3,2,28,19) Matrix(131,748,100,571) -> Matrix(1,2,16,33) Matrix(87,484,-16,-89) -> Matrix(7,4,-16,-9) Matrix(703,3784,196,1055) -> Matrix(9,4,56,25) Matrix(263,1408,82,439) -> Matrix(11,4,74,27) Matrix(43,220,-26,-133) -> Matrix(5,2,-58,-23) Matrix(265,1276,-146,-703) -> Matrix(1,-4,-10,41) Matrix(397,1892,-286,-1363) -> Matrix(19,14,-262,-193) Matrix(177,836,112,529) -> Matrix(15,8,208,111) Matrix(219,1012,-124,-573) -> Matrix(3,2,-32,-21) Matrix(527,2420,-326,-1497) -> Matrix(1,0,-10,1) Matrix(395,1804,-164,-749) -> Matrix(23,10,-168,-73) Matrix(89,396,20,89) -> Matrix(11,4,52,19) Matrix(131,572,30,131) -> Matrix(19,6,98,31) Matrix(175,748,-62,-265) -> Matrix(1,0,-2,1) Matrix(177,748,146,617) -> Matrix(17,4,310,73) Matrix(43,176,32,131) -> Matrix(9,2,148,33) Matrix(45,176,34,133) -> Matrix(5,2,82,33) Matrix(439,1672,-162,-617) -> Matrix(15,4,-94,-25) Matrix(395,1496,174,659) -> Matrix(19,6,174,55) Matrix(1189,4488,-874,-3299) -> Matrix(89,26,-1270,-371) Matrix(397,1496,82,309) -> Matrix(7,2,10,3) Matrix(131,484,-36,-133) -> Matrix(23,6,-96,-25) Matrix(705,2552,292,1057) -> Matrix(35,8,328,75) Matrix(439,1584,268,967) -> Matrix(35,8,468,107) Matrix(87,308,-50,-177) -> Matrix(1,0,-6,1) Matrix(89,308,-76,-263) -> Matrix(21,4,-352,-67) Matrix(219,748,-142,-485) -> Matrix(11,2,-138,-25) Matrix(131,440,-92,-309) -> Matrix(5,2,-68,-27) Matrix(175,572,-108,-353) -> Matrix(17,4,-200,-47) Matrix(177,572,82,265) -> Matrix(17,4,174,41) Matrix(2025,6512,-848,-2727) -> Matrix(55,12,-408,-89) Matrix(617,1980,110,353) -> Matrix(37,8,134,29) Matrix(221,704,-124,-395) -> Matrix(9,2,-104,-23) Matrix(263,748,-186,-529) -> Matrix(43,8,-586,-109) Matrix(969,2728,-406,-1143) -> Matrix(1,0,-2,1) Matrix(175,484,-64,-177) -> Matrix(47,8,-288,-49) Matrix(307,836,242,659) -> Matrix(87,14,1510,243) Matrix(2113,5720,-1560,-4223) -> Matrix(1,0,-8,1) Matrix(749,2024,440,1189) -> Matrix(139,22,1788,283) Matrix(1893,5104,800,2157) -> Matrix(219,34,2132,331) Matrix(3037,8184,-1910,-5147) -> Matrix(453,70,-5326,-823) Matrix(131,352,16,43) -> Matrix(13,2,32,5) Matrix(133,352,-116,-307) -> Matrix(41,6,-704,-103) Matrix(969,2552,-434,-1143) -> Matrix(59,8,-450,-61) Matrix(485,1276,84,221) -> Matrix(15,2,52,7) Matrix(219,572,-152,-397) -> Matrix(13,2,-176,-27) Matrix(307,792,-188,-485) -> Matrix(9,2,-104,-23) Matrix(617,1584,446,1145) -> Matrix(47,8,746,127) Matrix(395,1012,-258,-661) -> Matrix(11,2,-138,-25) Matrix(87,220,-70,-177) -> Matrix(25,4,-394,-63) Matrix(89,220,36,89) -> Matrix(27,4,236,35) Matrix(307,748,126,307) -> Matrix(99,14,898,127) Matrix(835,2024,526,1275) -> Matrix(187,26,2582,359) Matrix(309,748,164,397) -> Matrix(43,6,480,67) Matrix(747,1804,200,483) -> Matrix(73,10,416,57) Matrix(1187,2860,-530,-1277) -> Matrix(15,2,-98,-13) Matrix(2023,4840,772,1847) -> Matrix(29,4,268,37) Matrix(3037,7260,1160,2773) -> Matrix(15,2,172,23) Matrix(4663,11132,-3576,-8537) -> Matrix(303,40,-4492,-593) Matrix(351,836,-296,-705) -> Matrix(89,12,-1476,-199) Matrix(131,308,-94,-221) -> Matrix(17,2,-230,-27) Matrix(439,1012,-344,-793) -> Matrix(27,4,-412,-61) Matrix(441,1012,-268,-615) -> Matrix(1,0,-4,1) Matrix(309,704,-212,-483) -> Matrix(41,6,-540,-79) Matrix(659,1496,174,395) -> Matrix(43,6,222,31) Matrix(175,396,-156,-353) -> Matrix(59,8,-1040,-141) Matrix(2597,5808,-2026,-4531) -> Matrix(227,30,-3458,-457) Matrix(573,1276,-454,-1011) -> Matrix(109,14,-1674,-215) Matrix(219,484,-100,-221) -> Matrix(79,10,-640,-81) Matrix(263,572,40,87) -> Matrix(33,4,140,17) Matrix(265,572,82,177) -> Matrix(33,4,206,25) Matrix(351,748,206,439) -> Matrix(71,8,914,103) Matrix(397,748,164,309) -> Matrix(55,6,504,55) Matrix(307,572,212,395) -> Matrix(97,10,1484,153) Matrix(263,484,-144,-265) -> Matrix(119,12,-1200,-121) Matrix(749,1364,218,397) -> Matrix(61,6,498,49) Matrix(1189,2156,316,573) -> Matrix(21,2,136,13) Matrix(1409,2552,-874,-1583) -> Matrix(41,4,-482,-47) Matrix(2507,4488,958,1715) -> Matrix(21,2,178,17) Matrix(837,1496,616,1101) -> Matrix(107,10,1744,163) Matrix(1011,1804,320,571) -> Matrix(109,10,752,69) Matrix(617,1100,198,353) -> Matrix(45,4,326,29) Matrix(397,704,-322,-571) -> Matrix(61,6,-966,-95) Matrix(923,1628,-724,-1277) -> Matrix(103,10,-1576,-153) Matrix(2947,5104,1854,3211) -> Matrix(149,14,2054,193) Matrix(2287,3960,406,703) -> Matrix(1,0,14,1) Matrix(967,1672,-764,-1321) -> Matrix(43,4,-656,-61) Matrix(791,1364,-664,-1145) -> Matrix(253,24,-4164,-395) Matrix(1099,1892,-844,-1453) -> Matrix(403,38,-5992,-565) Matrix(2201,3784,666,1145) -> Matrix(341,32,2014,189) Matrix(1409,2420,308,529) -> Matrix(171,16,716,67) Matrix(1055,1804,-824,-1409) -> Matrix(87,8,-1316,-121) Matrix(1495,2552,1082,1847) -> Matrix(475,44,7546,699) Matrix(439,748,206,351) -> Matrix(87,8,946,87) Matrix(1189,2024,440,749) -> Matrix(239,22,1988,183) Matrix(441,748,260,441) -> Matrix(219,20,2836,259) Matrix(131,220,78,131) -> Matrix(67,6,882,79) Matrix(2199,3608,-1556,-2553) -> Matrix(223,20,-3044,-273) Matrix(1101,1804,296,485) -> Matrix(113,10,644,57) Matrix(1187,1936,458,747) -> Matrix(23,2,310,27) Matrix(1189,1936,460,749) -> Matrix(23,2,80,7) Matrix(2773,4488,1224,1981) -> Matrix(261,22,2432,205) Matrix(4487,7260,2610,4223) -> Matrix(525,44,6646,557) Matrix(2993,4840,1742,2817) -> Matrix(195,16,2474,203) Matrix(791,1276,654,1055) -> Matrix(49,4,894,73) Matrix(2729,4400,-2128,-3431) -> Matrix(43,4,-656,-61) Matrix(1011,1628,136,219) -> Matrix(21,2,52,5) Matrix(793,1276,110,177) -> Matrix(45,4,146,13) Matrix(221,352,194,309) -> Matrix(117,10,2258,193) Matrix(10955,17424,4066,6467) -> Matrix(1715,146,14554,1239) Matrix(10957,17424,4068,6469) -> Matrix(1481,126,12612,1073) Matrix(2685,4268,748,1189) -> Matrix(165,14,1096,93) Matrix(1275,2024,526,835) -> Matrix(307,26,2822,239) Matrix(1055,1672,-778,-1233) -> Matrix(95,8,-1342,-113) Matrix(307,484,-196,-309) -> Matrix(167,14,-2016,-169) Matrix(395,616,84,131) -> Matrix(73,6,304,25) Matrix(483,748,-370,-573) -> Matrix(173,14,-2558,-207) Matrix(1231,1892,-974,-1497) -> Matrix(51,4,-778,-61) Matrix(747,1100,328,483) -> Matrix(129,10,1148,89) Matrix(1233,1804,542,793) -> Matrix(261,20,2362,181) Matrix(969,1408,788,1145) -> Matrix(475,36,8484,643) Matrix(3123,4532,-2396,-3477) -> Matrix(1403,106,-20820,-1573) Matrix(395,572,212,307) -> Matrix(133,10,1556,117) Matrix(1409,2024,-1102,-1583) -> Matrix(1,0,-2,1) Matrix(2639,3784,1104,1583) -> Matrix(161,12,1516,113) Matrix(307,440,30,43) -> Matrix(27,2,94,7) Matrix(1363,1936,402,571) -> Matrix(27,2,418,31) Matrix(1365,1936,404,573) -> Matrix(27,2,-68,-5) Matrix(5015,7084,-3614,-5105) -> Matrix(1259,92,-17366,-1269) Matrix(967,1364,436,615) -> Matrix(111,8,1096,79) Matrix(16237,22528,3394,4709) -> Matrix(1849,134,5478,397) Matrix(8183,11352,1712,2375) -> Matrix(1049,76,3216,233) Matrix(2729,3784,2222,3081) -> Matrix(1437,104,25714,1861) Matrix(3079,4268,1142,1583) -> Matrix(719,52,6070,439) Matrix(351,484,-256,-353) -> Matrix(223,16,-3136,-225) Matrix(1319,1804,514,703) -> Matrix(113,8,918,65) Matrix(1321,1804,774,1057) -> Matrix(509,36,6518,461) Matrix(1583,2156,710,967) -> Matrix(455,32,4422,311) Matrix(12803,17424,3394,4619) -> Matrix(1567,110,8590,603) Matrix(12805,17424,3396,4621) -> Matrix(1397,98,7712,541) Matrix(1101,1496,616,837) -> Matrix(143,10,1816,127) Matrix(5719,7744,1494,2023) -> Matrix(115,8,618,43) Matrix(5721,7744,1496,2025) -> Matrix(1,0,20,1) Matrix(131,176,32,43) -> Matrix(29,2,188,13) Matrix(133,176,34,45) -> Matrix(29,2,130,9) Matrix(571,748,100,131) -> Matrix(29,2,72,5) Matrix(23759,30976,5534,7215) -> Matrix(3263,220,17902,1207) Matrix(23761,30976,5536,7217) -> Matrix(3501,236,19300,1301) Matrix(441,572,340,441) -> Matrix(299,20,5068,339) Matrix(307,396,238,307) -> Matrix(211,14,3602,239) Matrix(13595,17424,2986,3827) -> Matrix(945,62,4222,277) Matrix(13597,17424,2988,3829) -> Matrix(763,50,3464,227) Matrix(1891,2420,790,1011) -> Matrix(91,6,834,55) Matrix(6071,7744,1310,1671) -> Matrix(61,4,442,29) Matrix(6073,7744,1312,1673) -> Matrix(61,4,76,5) Matrix(485,616,174,221) -> Matrix(153,10,1178,77) Matrix(8977,11352,2506,3169) -> Matrix(1,0,22,1) Matrix(17819,22528,4976,6291) -> Matrix(31,2,232,15) Matrix(1187,1496,872,1099) -> Matrix(463,30,7516,487) Matrix(395,484,-324,-397) -> Matrix(287,18,-4608,-289) Matrix(1627,1980,1120,1363) -> Matrix(869,54,13212,821) Matrix(3257,3960,1376,1673) -> Matrix(967,60,9396,583) Matrix(617,748,146,177) -> Matrix(65,4,406,25) Matrix(1055,1276,654,791) -> Matrix(65,4,926,57) Matrix(1627,1936,258,307) -> Matrix(33,2,610,37) Matrix(1629,1936,260,309) -> Matrix(33,2,-380,-23) Matrix(485,572,262,309) -> Matrix(233,14,2746,165) Matrix(1099,1276,416,483) -> Matrix(305,18,2728,161) Matrix(1409,1628,534,617) -> Matrix(341,20,3086,181) Matrix(309,352,194,221) -> Matrix(173,10,2370,137) Matrix(397,440,120,133) -> Matrix(107,6,624,35) Matrix(1,0,2,1) -> Matrix(1,0,42,1) Matrix(353,-396,156,-175) -> Matrix(157,-8,1472,-75) Matrix(307,-352,116,-133) -> Matrix(115,-6,1016,-53) Matrix(263,-308,76,-89) -> Matrix(75,-4,544,-29) Matrix(705,-836,296,-351) -> Matrix(223,-12,2100,-113) Matrix(397,-484,324,-395) -> Matrix(325,-18,5832,-323) Matrix(177,-220,70,-87) -> Matrix(71,-4,586,-33) Matrix(1011,-1276,454,-573) -> Matrix(243,-14,2378,-137) Matrix(1495,-1892,418,-529) -> Matrix(69,-4,466,-27) Matrix(793,-1012,344,-439) -> Matrix(69,-4,604,-35) Matrix(1893,-2420,722,-923) -> Matrix(35,-2,298,-17) Matrix(1409,-1804,824,-1055) -> Matrix(137,-8,1764,-103) Matrix(573,-748,370,-483) -> Matrix(235,-14,3374,-201) Matrix(1233,-1672,778,-1055) -> Matrix(129,-8,1790,-111) Matrix(3299,-4488,874,-1189) -> Matrix(423,-26,2294,-141) Matrix(353,-484,256,-351) -> Matrix(257,-16,4096,-255) Matrix(221,-308,94,-131) -> Matrix(31,-2,326,-21) Matrix(219,-308,32,-45) -> Matrix(31,-2,140,-9) Matrix(529,-748,186,-263) -> Matrix(125,-8,922,-59) Matrix(309,-440,92,-131) -> Matrix(31,-2,140,-9) Matrix(397,-572,152,-219) -> Matrix(31,-2,264,-17) Matrix(4487,-6512,2608,-3785) -> Matrix(1767,-116,22316,-1465) Matrix(483,-704,212,-309) -> Matrix(91,-6,804,-53) Matrix(485,-748,142,-219) -> Matrix(29,-2,218,-15) Matrix(1759,-2728,1022,-1585) -> Matrix(629,-44,7934,-555) Matrix(309,-484,196,-307) -> Matrix(197,-14,2744,-195) Matrix(3607,-5720,944,-1497) -> Matrix(55,-4,344,-25) Matrix(5147,-8184,1910,-3037) -> Matrix(963,-70,8158,-593) Matrix(219,-352,28,-45) -> Matrix(27,-2,68,-5) Matrix(1583,-2552,874,-1409) -> Matrix(55,-4,674,-49) Matrix(353,-572,108,-175) -> Matrix(55,-4,344,-25) Matrix(485,-792,188,-307) -> Matrix(27,-2,176,-13) Matrix(617,-1012,214,-351) -> Matrix(53,-4,358,-27) Matrix(133,-220,26,-43) -> Matrix(27,-2,122,-9) Matrix(1673,-2860,926,-1583) -> Matrix(101,-8,1250,-99) Matrix(6469,-11132,1508,-2595) -> Matrix(833,-66,4632,-367) Matrix(485,-836,76,-131) -> Matrix(25,-2,188,-15) Matrix(177,-308,50,-87) -> Matrix(1,0,-6,1) Matrix(573,-1012,124,-219) -> Matrix(25,-2,88,-7) Matrix(571,-1012,224,-397) -> Matrix(25,-2,188,-15) Matrix(395,-704,124,-221) -> Matrix(27,-2,176,-13) Matrix(221,-396,24,-43) -> Matrix(25,-2,88,-7) Matrix(3211,-5808,706,-1277) -> Matrix(171,-14,794,-65) Matrix(703,-1276,146,-265) -> Matrix(49,-4,86,-7) Matrix(265,-484,144,-263) -> Matrix(145,-12,1728,-143) Matrix(221,-484,100,-219) -> Matrix(101,-10,1000,-99) Matrix(1143,-2552,434,-969) -> Matrix(77,-8,722,-75) Matrix(307,-704,58,-133) -> Matrix(19,-2,86,-9) Matrix(705,-1628,152,-351) -> Matrix(1,0,-4,1) Matrix(705,-1672,148,-351) -> Matrix(77,-8,260,-27) Matrix(573,-1364,92,-219) -> Matrix(19,-2,-28,3) Matrix(793,-1892,184,-439) -> Matrix(1,0,-4,1) Matrix(749,-1804,164,-395) -> Matrix(93,-10,400,-43) Matrix(1409,-3608,412,-1055) -> Matrix(1,0,0,1) Matrix(1671,-4400,368,-969) -> Matrix(37,-4,176,-19) Matrix(617,-1672,162,-439) -> Matrix(33,-4,190,-23) Matrix(177,-484,64,-175) -> Matrix(65,-8,512,-63) Matrix(265,-748,62,-175) -> Matrix(1,0,-2,1) Matrix(661,-1892,138,-395) -> Matrix(43,-6,122,-17) Matrix(1409,-4532,328,-1055) -> Matrix(79,-12,428,-65) Matrix(615,-2024,134,-441) -> Matrix(25,-4,94,-15) Matrix(2069,-7084,578,-1979) -> Matrix(15,-2,98,-13) Matrix(133,-484,36,-131) -> Matrix(37,-6,216,-35) Matrix(89,-484,16,-87) -> Matrix(17,-4,64,-15) 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): 120 Degree of the the map X: 120 Degree of the the map Y: 240 ----------------------------------------------------------------------- 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): 720 Minimal number of generators: 121 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: 50 Genus: 36 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -6/1 -4/1 -11/3 -10/3 -11/5 -15/7 -2/1 -11/7 -22/15 -33/23 -11/9 -22/19 0/1 1/1 11/9 22/17 11/8 3/2 11/7 22/13 9/5 11/6 2/1 11/5 22/9 5/2 55/21 11/4 3/1 22/7 23/7 33/10 10/3 7/2 11/3 19/5 88/23 4/1 13/3 22/5 9/2 5/1 11/2 17/3 6/1 7/1 22/3 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 0/1 -7/1 -1/2 -6/1 -1/1 -23/4 -1/1 -2/3 -17/3 -1/2 -11/2 -1/2 -5/1 -1/4 -9/2 -2/5 -1/3 -22/5 -1/3 -13/3 -3/10 -4/1 0/1 -11/3 -1/4 -18/5 -3/13 -7/2 -2/9 -1/5 -24/7 0/1 -17/5 -1/8 -10/3 -1/3 -13/4 -2/9 -1/5 -29/9 -9/40 -16/5 -2/9 -3/1 -1/6 -11/4 -1/6 -19/7 -7/44 -8/3 -2/13 -29/11 -7/50 -50/19 -1/7 -21/8 -1/7 0/1 -13/5 -1/8 -18/7 -1/5 -23/9 -1/6 -5/2 -2/13 -1/7 -22/9 -1/7 -17/7 -7/50 -12/5 -2/15 -7/3 -1/8 -16/7 0/1 -25/11 -7/50 -9/4 -2/15 -3/23 -11/5 -1/8 -13/6 -3/25 -2/17 -15/7 -7/60 -2/1 -1/9 -13/7 -1/10 -11/6 -1/10 -9/5 -5/52 -34/19 -1/11 -25/14 -4/43 -1/11 -66/37 -1/11 -41/23 -3/34 -16/9 0/1 -23/13 -1/10 -7/4 -2/21 -1/11 -26/15 -3/31 -45/26 -2/21 -1/11 -19/11 -5/52 -31/18 -12/127 -5/53 -43/25 -25/266 -12/7 -4/43 -29/17 -17/184 -46/27 -1/11 -17/10 -10/109 -1/11 -22/13 -1/11 -5/3 -3/34 -13/8 -2/23 -3/35 -34/21 -5/59 -89/55 -21/250 -55/34 -1/12 -21/13 -1/12 -29/18 -1/11 0/1 -66/41 -1/11 -37/23 -3/34 -8/5 -2/23 -11/7 -1/12 -14/9 -5/61 -17/11 -5/62 -20/13 -2/25 -3/2 -2/25 -1/13 -22/15 -1/13 -19/13 -13/170 -16/11 -6/79 -13/9 -3/40 -23/16 -1/13 -2/27 -33/23 -3/40 -10/7 -1/13 -7/5 -1/14 -11/8 -1/14 -15/11 -11/156 -34/25 -3/43 -19/14 -3/43 -2/29 -42/31 -3/43 -23/17 -1/14 -4/3 -2/29 -21/16 -4/59 -1/15 -17/13 -3/44 -30/23 -11/163 -13/10 -10/149 -1/15 -22/17 -1/15 -9/7 -7/106 -32/25 -4/61 -55/43 -3/46 -23/18 -1/15 -2/31 -14/11 -1/15 -19/15 -7/108 -43/34 -1/15 -2/31 -110/87 -1/15 -67/53 -3/46 -24/19 -2/31 -5/4 -2/31 -3/47 -11/9 -1/16 -17/14 -7/113 -6/97 -23/19 -1/16 -6/5 -3/49 -13/11 -3/50 -20/17 -4/67 -7/6 -6/101 -1/17 -22/19 -1/17 -15/13 -13/222 -8/7 -4/69 -9/8 -2/35 -7/123 -1/1 -1/20 0/1 0/1 1/1 1/22 9/8 7/137 2/39 8/7 4/77 7/6 1/19 6/113 13/11 3/56 6/5 3/55 11/9 1/18 16/13 6/107 5/4 3/53 2/35 14/11 1/17 23/18 2/35 1/17 32/25 4/69 9/7 7/120 22/17 1/17 13/10 1/17 10/169 17/13 3/50 21/16 1/17 4/67 4/3 2/33 19/14 2/33 3/49 15/11 11/178 11/8 1/16 7/5 1/16 10/7 1/15 13/9 3/46 16/11 6/91 3/2 1/15 2/29 11/7 1/14 19/12 6/83 5/69 27/17 9/124 35/22 4/55 19/261 8/5 2/27 29/18 0/1 1/13 21/13 1/14 13/8 3/41 2/27 5/3 3/40 22/13 1/13 17/10 1/13 10/129 46/27 1/13 29/17 17/218 41/24 9/115 4/51 12/7 4/51 43/25 25/316 31/18 5/63 12/151 19/11 5/62 7/4 1/13 2/25 23/13 1/12 16/9 0/1 25/14 1/13 4/51 34/19 1/13 9/5 5/62 11/6 1/12 13/7 1/12 2/1 1/11 11/5 1/10 20/9 4/39 29/13 13/126 9/4 3/29 2/19 25/11 7/64 66/29 1/9 41/18 1/9 8/71 16/7 0/1 7/3 1/10 12/5 2/19 17/7 7/64 22/9 1/9 5/2 1/9 2/17 28/11 2/15 23/9 1/8 41/16 0/1 1/7 18/7 1/7 13/5 1/10 34/13 1/9 55/21 1/10 76/29 2/19 21/8 0/1 1/9 50/19 1/9 29/11 7/64 66/25 1/9 37/14 1/9 12/107 8/3 2/17 27/10 8/67 3/25 46/17 3/25 19/7 7/58 11/4 1/8 3/1 1/8 22/7 1/7 19/6 1/7 6/41 16/5 2/13 29/9 9/58 13/4 1/7 2/13 23/7 1/6 33/10 1/6 43/13 13/76 10/3 1/5 17/5 1/10 41/12 0/1 1/7 65/19 1/8 24/7 0/1 31/9 1/8 7/2 1/7 2/13 11/3 1/6 15/4 2/11 1/5 19/5 1/4 42/11 1/5 65/17 1/6 88/23 2/11 23/6 2/11 1/5 4/1 0/1 13/3 3/16 22/5 1/5 9/2 1/5 2/9 5/1 1/6 11/2 1/4 17/3 1/4 23/4 2/7 1/3 6/1 1/3 7/1 1/4 22/3 1/3 15/2 1/3 2/5 8/1 0/1 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(23,198,18,155) (-8/1,1/0) -> (14/11,23/18) Hyperbolic Matrix(45,352,-28,-219) (-8/1,-7/1) -> (-37/23,-8/5) Hyperbolic Matrix(23,154,10,67) (-7/1,-6/1) -> (16/7,7/3) Hyperbolic Matrix(221,1276,84,485) (-6/1,-23/4) -> (21/8,50/19) Hyperbolic Matrix(131,748,100,571) (-23/4,-17/3) -> (17/13,21/16) Hyperbolic Matrix(67,374,12,67) (-17/3,-11/2) -> (11/2,17/3) Hyperbolic Matrix(21,110,4,21) (-11/2,-5/1) -> (5/1,11/2) Hyperbolic Matrix(23,110,14,67) (-5/1,-9/2) -> (13/8,5/3) Hyperbolic Matrix(89,396,20,89) (-9/2,-22/5) -> (22/5,9/2) Hyperbolic Matrix(131,572,30,131) (-22/5,-13/3) -> (13/3,22/5) Hyperbolic Matrix(67,286,26,111) (-13/3,-4/1) -> (18/7,13/5) Hyperbolic Matrix(65,242,-18,-67) (-4/1,-11/3) -> (-11/3,-18/5) Parabolic Matrix(87,308,-50,-177) (-18/5,-7/2) -> (-7/4,-26/15) Hyperbolic Matrix(89,308,-76,-263) (-7/2,-24/7) -> (-20/17,-7/6) Hyperbolic Matrix(219,748,-142,-485) (-24/7,-17/5) -> (-17/11,-20/13) Hyperbolic Matrix(111,374,46,155) (-17/5,-10/3) -> (12/5,17/7) Hyperbolic Matrix(175,572,-108,-353) (-10/3,-13/4) -> (-13/8,-34/21) Hyperbolic Matrix(197,638,88,285) (-13/4,-29/9) -> (29/13,9/4) Hyperbolic Matrix(595,1914,226,727) (-29/9,-16/5) -> (50/19,29/11) Hyperbolic Matrix(221,704,-124,-395) (-16/5,-3/1) -> (-41/23,-16/9) Hyperbolic Matrix(23,66,8,23) (-3/1,-11/4) -> (11/4,3/1) Hyperbolic Matrix(153,418,56,153) (-11/4,-19/7) -> (19/7,11/4) Hyperbolic Matrix(155,418,-122,-329) (-19/7,-8/3) -> (-14/11,-19/15) Hyperbolic Matrix(133,352,-116,-307) (-8/3,-29/11) -> (-15/13,-8/7) Hyperbolic Matrix(727,1914,226,595) (-29/11,-50/19) -> (16/5,29/9) Hyperbolic Matrix(485,1276,84,221) (-50/19,-21/8) -> (23/4,6/1) Hyperbolic Matrix(219,572,-152,-397) (-21/8,-13/5) -> (-13/9,-23/16) Hyperbolic Matrix(111,286,26,67) (-13/5,-18/7) -> (4/1,13/3) Hyperbolic Matrix(197,506,-146,-375) (-18/7,-23/9) -> (-23/17,-4/3) Hyperbolic Matrix(199,506,-164,-417) (-23/9,-5/2) -> (-17/14,-23/19) Hyperbolic Matrix(89,220,36,89) (-5/2,-22/9) -> (22/9,5/2) Hyperbolic Matrix(307,748,126,307) (-22/9,-17/7) -> (17/7,22/9) Hyperbolic Matrix(155,374,46,111) (-17/7,-12/5) -> (10/3,17/5) Hyperbolic Matrix(65,154,46,109) (-12/5,-7/3) -> (7/5,10/7) Hyperbolic Matrix(67,154,10,23) (-7/3,-16/7) -> (6/1,7/1) Hyperbolic Matrix(309,704,-212,-483) (-16/7,-25/11) -> (-19/13,-16/11) Hyperbolic Matrix(417,946,242,549) (-25/11,-9/4) -> (31/18,19/11) Hyperbolic Matrix(109,242,-50,-111) (-9/4,-11/5) -> (-11/5,-13/6) Parabolic Matrix(265,572,82,177) (-13/6,-15/7) -> (29/9,13/4) Hyperbolic Matrix(351,748,206,439) (-15/7,-2/1) -> (46/27,29/17) Hyperbolic Matrix(153,286,-130,-243) (-2/1,-13/7) -> (-13/11,-20/17) Hyperbolic Matrix(155,286,84,155) (-13/7,-11/6) -> (11/6,13/7) Hyperbolic Matrix(109,198,60,109) (-11/6,-9/5) -> (9/5,11/6) Hyperbolic Matrix(331,594,258,463) (-9/5,-34/19) -> (32/25,9/7) Hyperbolic Matrix(947,1694,554,991) (-34/19,-25/14) -> (41/24,12/7) Hyperbolic Matrix(1011,1804,320,571) (-25/14,-66/37) -> (22/7,19/6) Hyperbolic Matrix(617,1100,198,353) (-66/37,-41/23) -> (3/1,22/7) Hyperbolic Matrix(285,506,-236,-419) (-16/9,-23/13) -> (-23/19,-6/5) Hyperbolic Matrix(461,814,286,505) (-23/13,-7/4) -> (29/18,21/13) Hyperbolic Matrix(419,726,318,551) (-26/15,-45/26) -> (21/16,4/3) Hyperbolic Matrix(967,1672,-764,-1321) (-45/26,-19/11) -> (-19/15,-43/34) Hyperbolic Matrix(549,946,242,417) (-19/11,-31/18) -> (9/4,25/11) Hyperbolic Matrix(243,418,218,375) (-31/18,-43/25) -> (1/1,9/8) Hyperbolic Matrix(1473,2530,-910,-1563) (-43/25,-12/7) -> (-34/21,-89/55) Hyperbolic Matrix(683,1166,-502,-857) (-12/7,-29/17) -> (-15/11,-34/25) Hyperbolic Matrix(1123,1914,504,859) (-29/17,-46/27) -> (20/9,29/13) Hyperbolic Matrix(1189,2024,440,749) (-46/27,-17/10) -> (27/10,46/17) Hyperbolic Matrix(441,748,260,441) (-17/10,-22/13) -> (22/13,17/10) Hyperbolic Matrix(131,220,78,131) (-22/13,-5/3) -> (5/3,22/13) Hyperbolic Matrix(67,110,14,23) (-5/3,-13/8) -> (9/2,5/1) Hyperbolic Matrix(3277,5302,992,1605) (-89/55,-55/34) -> (33/10,43/13) Hyperbolic Matrix(1211,1958,368,595) (-55/34,-21/13) -> (23/7,33/10) Hyperbolic Matrix(505,814,286,461) (-21/13,-29/18) -> (7/4,23/13) Hyperbolic Matrix(1011,1628,136,219) (-29/18,-66/41) -> (22/3,15/2) Hyperbolic Matrix(793,1276,110,177) (-66/41,-37/23) -> (7/1,22/3) Hyperbolic Matrix(153,242,-98,-155) (-8/5,-11/7) -> (-11/7,-14/9) Parabolic Matrix(483,748,-370,-573) (-14/9,-17/11) -> (-17/13,-30/23) Hyperbolic Matrix(331,506,-244,-373) (-20/13,-3/2) -> (-19/14,-42/31) Hyperbolic Matrix(747,1100,328,483) (-3/2,-22/15) -> (66/29,41/18) Hyperbolic Matrix(1233,1804,542,793) (-22/15,-19/13) -> (25/11,66/29) Hyperbolic Matrix(197,286,166,241) (-16/11,-13/9) -> (13/11,6/5) Hyperbolic Matrix(1409,2024,-1102,-1583) (-23/16,-33/23) -> (-55/43,-23/18) Hyperbolic Matrix(1121,1606,-876,-1255) (-33/23,-10/7) -> (-32/25,-55/43) Hyperbolic Matrix(109,154,46,65) (-10/7,-7/5) -> (7/3,12/5) Hyperbolic Matrix(111,154,80,111) (-7/5,-11/8) -> (11/8,7/5) Hyperbolic Matrix(241,330,176,241) (-11/8,-15/11) -> (15/11,11/8) Hyperbolic Matrix(1101,1496,616,837) (-34/25,-19/14) -> (25/14,34/19) Hyperbolic Matrix(2485,3366,-1966,-2663) (-42/31,-23/17) -> (-67/53,-24/19) Hyperbolic Matrix(133,176,34,45) (-4/3,-21/16) -> (23/6,4/1) Hyperbolic Matrix(571,748,100,131) (-21/16,-17/13) -> (17/3,23/4) Hyperbolic Matrix(287,374,254,331) (-30/23,-13/10) -> (9/8,8/7) Hyperbolic Matrix(441,572,340,441) (-13/10,-22/17) -> (22/17,13/10) Hyperbolic Matrix(307,396,238,307) (-22/17,-9/7) -> (9/7,22/17) Hyperbolic Matrix(463,594,258,331) (-9/7,-32/25) -> (34/19,9/5) Hyperbolic Matrix(155,198,18,23) (-23/18,-14/11) -> (8/1,1/0) Hyperbolic Matrix(4993,6314,1304,1649) (-43/34,-110/87) -> (88/23,23/6) Hyperbolic Matrix(10319,13046,2698,3411) (-110/87,-67/53) -> (65/17,88/23) Hyperbolic Matrix(507,638,298,375) (-24/19,-5/4) -> (17/10,46/27) Hyperbolic Matrix(197,242,-162,-199) (-5/4,-11/9) -> (-11/9,-17/14) Parabolic Matrix(241,286,166,197) (-6/5,-13/11) -> (13/9,16/11) Hyperbolic Matrix(1099,1276,416,483) (-7/6,-22/19) -> (66/25,37/14) Hyperbolic Matrix(1409,1628,534,617) (-22/19,-15/13) -> (29/11,66/25) Hyperbolic Matrix(309,352,194,221) (-8/7,-9/8) -> (35/22,8/5) Hyperbolic Matrix(375,418,218,243) (-9/8,-1/1) -> (43/25,31/18) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(307,-352,116,-133) (8/7,7/6) -> (37/14,8/3) Hyperbolic Matrix(263,-308,76,-89) (7/6,13/11) -> (31/9,7/2) Hyperbolic Matrix(199,-242,162,-197) (6/5,11/9) -> (11/9,16/13) Parabolic Matrix(177,-220,70,-87) (16/13,5/4) -> (5/2,28/11) Hyperbolic Matrix(329,-418,122,-155) (5/4,14/11) -> (8/3,27/10) Hyperbolic Matrix(1893,-2420,722,-923) (23/18,32/25) -> (76/29,21/8) Hyperbolic Matrix(725,-946,456,-595) (13/10,17/13) -> (27/17,35/22) Hyperbolic Matrix(375,-506,146,-197) (4/3,19/14) -> (41/16,18/7) Hyperbolic Matrix(857,-1166,502,-683) (19/14,15/11) -> (29/17,41/24) Hyperbolic Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(483,-704,212,-309) (16/11,3/2) -> (41/18,16/7) Hyperbolic Matrix(155,-242,98,-153) (3/2,11/7) -> (11/7,19/12) Parabolic Matrix(901,-1430,264,-419) (19/12,27/17) -> (17/5,41/12) Hyperbolic Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(551,-946,166,-285) (12/7,43/25) -> (43/13,10/3) Hyperbolic Matrix(241,-418,64,-111) (19/11,7/4) -> (15/4,19/5) Hyperbolic Matrix(571,-1012,224,-397) (23/13,16/9) -> (28/11,23/9) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(199,-374,58,-109) (13/7,2/1) -> (24/7,31/9) Hyperbolic Matrix(111,-242,50,-109) (2/1,11/5) -> (11/5,20/9) Parabolic Matrix(1409,-3608,412,-1055) (23/9,41/16) -> (41/12,65/19) Hyperbolic Matrix(2311,-6050,882,-2309) (34/13,55/21) -> (55/21,76/29) Parabolic Matrix(617,-1672,162,-439) (46/17,19/7) -> (19/5,42/11) Hyperbolic Matrix(1253,-4290,328,-1123) (65/19,24/7) -> (42/11,65/17) Hyperbolic Matrix(67,-242,18,-65) (7/2,11/3) -> (11/3,15/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(23,198,18,155) -> Matrix(3,-1,52,-17) Matrix(45,352,-28,-219) -> Matrix(1,2,-12,-23) Matrix(23,154,10,67) -> Matrix(1,1,8,9) Matrix(221,1276,84,485) -> Matrix(3,2,28,19) Matrix(131,748,100,571) -> Matrix(1,2,16,33) Matrix(67,374,12,67) -> Matrix(5,3,18,11) Matrix(21,110,4,21) -> Matrix(3,1,14,5) Matrix(23,110,14,67) -> Matrix(1,1,12,13) Matrix(89,396,20,89) -> Matrix(11,4,52,19) Matrix(131,572,30,131) -> Matrix(19,6,98,31) Matrix(67,286,26,111) -> Matrix(3,1,20,7) Matrix(65,242,-18,-67) -> Matrix(11,3,-48,-13) Matrix(87,308,-50,-177) -> Matrix(1,0,-6,1) Matrix(89,308,-76,-263) -> Matrix(21,4,-352,-67) Matrix(219,748,-142,-485) -> Matrix(11,2,-138,-25) Matrix(111,374,46,155) -> Matrix(1,1,8,9) Matrix(175,572,-108,-353) -> Matrix(17,4,-200,-47) Matrix(197,638,88,285) -> Matrix(3,1,26,9) Matrix(595,1914,226,727) -> Matrix(23,5,216,47) Matrix(221,704,-124,-395) -> Matrix(9,2,-104,-23) Matrix(23,66,8,23) -> Matrix(5,1,34,7) Matrix(153,418,56,153) -> Matrix(43,7,350,57) Matrix(155,418,-122,-329) -> Matrix(45,7,-688,-107) Matrix(133,352,-116,-307) -> Matrix(41,6,-704,-103) Matrix(727,1914,226,595) -> Matrix(37,5,244,33) Matrix(485,1276,84,221) -> Matrix(15,2,52,7) Matrix(219,572,-152,-397) -> Matrix(13,2,-176,-27) Matrix(111,286,26,67) -> Matrix(5,1,24,5) Matrix(197,506,-146,-375) -> Matrix(17,3,-244,-43) Matrix(199,506,-164,-417) -> Matrix(29,5,-470,-81) Matrix(89,220,36,89) -> Matrix(27,4,236,35) Matrix(307,748,126,307) -> Matrix(99,14,898,127) Matrix(155,374,46,111) -> Matrix(7,1,20,3) Matrix(65,154,46,109) -> Matrix(23,3,360,47) Matrix(67,154,10,23) -> Matrix(7,1,20,3) Matrix(309,704,-212,-483) -> Matrix(41,6,-540,-79) Matrix(417,946,242,549) -> Matrix(65,9,816,113) Matrix(109,242,-50,-111) -> Matrix(39,5,-320,-41) Matrix(265,572,82,177) -> Matrix(33,4,206,25) Matrix(351,748,206,439) -> Matrix(71,8,914,103) Matrix(153,286,-130,-243) -> Matrix(67,7,-1120,-117) Matrix(155,286,84,155) -> Matrix(69,7,818,83) Matrix(109,198,60,109) -> Matrix(51,5,622,61) Matrix(331,594,258,463) -> Matrix(95,9,1636,155) Matrix(947,1694,554,991) -> Matrix(73,7,928,89) Matrix(1011,1804,320,571) -> Matrix(109,10,752,69) Matrix(617,1100,198,353) -> Matrix(45,4,326,29) Matrix(285,506,-236,-419) -> Matrix(29,3,-474,-49) Matrix(461,814,286,505) -> Matrix(11,1,164,15) Matrix(419,726,318,551) -> Matrix(73,7,1220,117) Matrix(967,1672,-764,-1321) -> Matrix(43,4,-656,-61) Matrix(549,946,242,417) -> Matrix(95,9,876,83) Matrix(243,418,218,375) -> Matrix(117,11,2308,217) Matrix(1473,2530,-910,-1563) -> Matrix(203,19,-2404,-225) Matrix(683,1166,-502,-857) -> Matrix(205,19,-2924,-271) Matrix(1123,1914,504,859) -> Matrix(293,27,2854,263) Matrix(1189,2024,440,749) -> Matrix(239,22,1988,183) Matrix(441,748,260,441) -> Matrix(219,20,2836,259) Matrix(131,220,78,131) -> Matrix(67,6,882,79) Matrix(67,110,14,23) -> Matrix(11,1,32,3) Matrix(3277,5302,992,1605) -> Matrix(203,17,1206,101) Matrix(1211,1958,368,595) -> Matrix(37,3,234,19) Matrix(505,814,286,461) -> Matrix(13,1,168,13) Matrix(1011,1628,136,219) -> Matrix(21,2,52,5) Matrix(793,1276,110,177) -> Matrix(45,4,146,13) Matrix(153,242,-98,-155) -> Matrix(83,7,-1008,-85) Matrix(483,748,-370,-573) -> Matrix(173,14,-2558,-207) Matrix(331,506,-244,-373) -> Matrix(11,1,-166,-15) Matrix(747,1100,328,483) -> Matrix(129,10,1148,89) Matrix(1233,1804,542,793) -> Matrix(261,20,2362,181) Matrix(197,286,166,241) -> Matrix(119,9,2208,167) Matrix(1409,2024,-1102,-1583) -> Matrix(1,0,-2,1) Matrix(1121,1606,-876,-1255) -> Matrix(121,9,-1842,-137) Matrix(109,154,46,65) -> Matrix(41,3,396,29) Matrix(111,154,80,111) -> Matrix(69,5,1090,79) Matrix(241,330,176,241) -> Matrix(155,11,2494,177) Matrix(1101,1496,616,837) -> Matrix(143,10,1816,127) Matrix(2485,3366,-1966,-2663) -> Matrix(101,7,-1544,-107) Matrix(133,176,34,45) -> Matrix(29,2,130,9) Matrix(571,748,100,131) -> Matrix(29,2,72,5) Matrix(287,374,254,331) -> Matrix(193,13,3756,253) Matrix(441,572,340,441) -> Matrix(299,20,5068,339) Matrix(307,396,238,307) -> Matrix(211,14,3602,239) Matrix(463,594,258,331) -> Matrix(137,9,1720,113) Matrix(155,198,18,23) -> Matrix(15,1,-16,-1) Matrix(4993,6314,1304,1649) -> Matrix(47,3,266,17) Matrix(10319,13046,2698,3411) -> Matrix(107,7,596,39) Matrix(507,638,298,375) -> Matrix(263,17,3388,219) Matrix(197,242,-162,-199) -> Matrix(143,9,-2304,-145) Matrix(241,286,166,197) -> Matrix(149,9,2268,137) Matrix(1099,1276,416,483) -> Matrix(305,18,2728,161) Matrix(1409,1628,534,617) -> Matrix(341,20,3086,181) Matrix(309,352,194,221) -> Matrix(173,10,2370,137) Matrix(375,418,218,243) -> Matrix(195,11,2464,139) Matrix(1,0,2,1) -> Matrix(1,0,42,1) Matrix(307,-352,116,-133) -> Matrix(115,-6,1016,-53) Matrix(263,-308,76,-89) -> Matrix(75,-4,544,-29) Matrix(199,-242,162,-197) -> Matrix(163,-9,2916,-161) Matrix(177,-220,70,-87) -> Matrix(71,-4,586,-33) Matrix(329,-418,122,-155) -> Matrix(121,-7,1020,-59) Matrix(1893,-2420,722,-923) -> Matrix(35,-2,298,-17) Matrix(725,-946,456,-595) -> Matrix(353,-21,4858,-289) Matrix(375,-506,146,-197) -> Matrix(49,-3,376,-23) Matrix(857,-1166,502,-683) -> Matrix(309,-19,3952,-243) Matrix(397,-572,152,-219) -> Matrix(31,-2,264,-17) Matrix(483,-704,212,-309) -> Matrix(91,-6,804,-53) Matrix(155,-242,98,-153) -> Matrix(99,-7,1372,-97) Matrix(901,-1430,264,-419) -> Matrix(69,-5,566,-41) Matrix(219,-352,28,-45) -> Matrix(27,-2,68,-5) Matrix(353,-572,108,-175) -> Matrix(55,-4,344,-25) Matrix(551,-946,166,-285) -> Matrix(89,-7,496,-39) Matrix(241,-418,64,-111) -> Matrix(37,-3,210,-17) Matrix(571,-1012,224,-397) -> Matrix(25,-2,188,-15) Matrix(395,-704,124,-221) -> Matrix(27,-2,176,-13) Matrix(199,-374,58,-109) -> Matrix(11,-1,100,-9) Matrix(111,-242,50,-109) -> Matrix(51,-5,500,-49) Matrix(1409,-3608,412,-1055) -> Matrix(1,0,0,1) Matrix(2311,-6050,882,-2309) -> Matrix(11,-1,100,-9) Matrix(617,-1672,162,-439) -> Matrix(33,-4,190,-23) Matrix(1253,-4290,328,-1123) -> Matrix(9,-1,46,-5) Matrix(67,-242,18,-65) -> Matrix(19,-3,108,-17) 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): 120 ----------------------------------------------------------------------- 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 21 1 1/1 1/22 1 22 9/8 (7/137,2/39) 0 22 8/7 4/77 1 11 7/6 (1/19,6/113) 0 22 13/11 3/56 1 22 6/5 3/55 1 11 11/9 1/18 9 2 16/13 6/107 1 11 5/4 (3/53,2/35) 0 22 14/11 1/17 1 11 23/18 (2/35,1/17) 0 22 32/25 4/69 1 11 9/7 7/120 1 22 22/17 1/17 17 1 13/10 (1/17,10/169) 0 22 17/13 3/50 1 22 21/16 (1/17,4/67) 0 22 4/3 2/33 1 11 19/14 (2/33,3/49) 0 22 15/11 11/178 1 22 11/8 1/16 8 2 7/5 1/16 1 22 10/7 1/15 1 11 13/9 3/46 1 22 16/11 6/91 1 11 3/2 (1/15,2/29) 0 22 11/7 1/14 7 2 19/12 (6/83,5/69) 0 22 27/17 9/124 1 22 35/22 (4/55,19/261) 0 22 8/5 2/27 1 11 29/18 (0/1,1/13) 0 22 21/13 1/14 1 22 13/8 (3/41,2/27) 0 22 5/3 3/40 1 22 22/13 1/13 13 1 17/10 (1/13,10/129) 0 22 46/27 1/13 1 11 29/17 17/218 1 22 41/24 (9/115,4/51) 0 22 12/7 4/51 1 11 43/25 25/316 1 22 31/18 (5/63,12/151) 0 22 19/11 5/62 1 22 7/4 (1/13,2/25) 0 22 23/13 1/12 1 22 16/9 0/1 1 11 25/14 (1/13,4/51) 0 22 34/19 1/13 1 11 9/5 5/62 1 22 11/6 1/12 6 2 13/7 1/12 1 22 2/1 1/11 1 11 11/5 1/10 5 2 20/9 4/39 1 11 29/13 13/126 1 22 9/4 (3/29,2/19) 0 22 25/11 7/64 1 22 66/29 1/9 15 1 41/18 (1/9,8/71) 0 22 16/7 0/1 1 11 7/3 1/10 1 22 12/5 2/19 1 11 17/7 7/64 1 22 22/9 1/9 9 1 5/2 (1/9,2/17) 0 22 28/11 2/15 1 11 23/9 1/8 1 22 41/16 (0/1,1/7) 0 22 18/7 1/7 1 11 13/5 1/10 1 22 34/13 1/9 1 11 55/21 1/10 1 2 76/29 2/19 1 11 21/8 (0/1,1/9) 0 22 50/19 1/9 1 11 29/11 7/64 1 22 66/25 1/9 19 1 37/14 (1/9,12/107) 0 22 8/3 2/17 1 11 27/10 (8/67,3/25) 0 22 46/17 3/25 1 11 19/7 7/58 1 22 11/4 1/8 4 2 3/1 1/8 1 22 22/7 1/7 7 1 19/6 (1/7,6/41) 0 22 16/5 2/13 1 11 29/9 9/58 1 22 13/4 (1/7,2/13) 0 22 23/7 1/6 1 22 33/10 1/6 10 2 43/13 13/76 1 22 10/3 1/5 1 11 17/5 1/10 1 22 41/12 (0/1,1/7) 0 22 65/19 1/8 1 22 24/7 0/1 1 11 31/9 1/8 1 22 7/2 (1/7,2/13) 0 22 11/3 1/6 3 2 15/4 (2/11,1/5) 0 22 19/5 1/4 1 22 42/11 1/5 1 11 65/17 1/6 1 22 88/23 2/11 1 1 23/6 (2/11,1/5) 0 22 4/1 0/1 1 11 13/3 3/16 1 22 22/5 1/5 5 1 9/2 (1/5,2/9) 0 22 5/1 1/6 1 22 11/2 1/4 2 2 17/3 1/4 1 22 23/4 (2/7,1/3) 0 22 6/1 1/3 1 11 7/1 1/4 1 22 22/3 1/3 3 1 15/2 (1/3,2/5) 0 22 8/1 0/1 1 11 1/0 (0/1,1/1) 0 22 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(375,-418,218,-243) (1/1,9/8) -> (43/25,31/18) Glide Reflection Matrix(309,-352,194,-221) (9/8,8/7) -> (35/22,8/5) Glide Reflection Matrix(307,-352,116,-133) (8/7,7/6) -> (37/14,8/3) Hyperbolic Matrix(263,-308,76,-89) (7/6,13/11) -> (31/9,7/2) Hyperbolic Matrix(241,-286,166,-197) (13/11,6/5) -> (13/9,16/11) Glide Reflection Matrix(199,-242,162,-197) (6/5,11/9) -> (11/9,16/13) Parabolic Matrix(177,-220,70,-87) (16/13,5/4) -> (5/2,28/11) Hyperbolic Matrix(329,-418,122,-155) (5/4,14/11) -> (8/3,27/10) Hyperbolic Matrix(155,-198,18,-23) (14/11,23/18) -> (8/1,1/0) Glide Reflection Matrix(1893,-2420,722,-923) (23/18,32/25) -> (76/29,21/8) Hyperbolic Matrix(463,-594,258,-331) (32/25,9/7) -> (34/19,9/5) Glide Reflection Matrix(307,-396,238,-307) (9/7,22/17) -> (9/7,22/17) Reflection Matrix(441,-572,340,-441) (22/17,13/10) -> (22/17,13/10) Reflection Matrix(725,-946,456,-595) (13/10,17/13) -> (27/17,35/22) Hyperbolic Matrix(571,-748,100,-131) (17/13,21/16) -> (17/3,23/4) Glide Reflection Matrix(133,-176,34,-45) (21/16,4/3) -> (23/6,4/1) Glide Reflection Matrix(375,-506,146,-197) (4/3,19/14) -> (41/16,18/7) Hyperbolic Matrix(857,-1166,502,-683) (19/14,15/11) -> (29/17,41/24) Hyperbolic Matrix(241,-330,176,-241) (15/11,11/8) -> (15/11,11/8) Reflection Matrix(111,-154,80,-111) (11/8,7/5) -> (11/8,7/5) Reflection Matrix(109,-154,46,-65) (7/5,10/7) -> (7/3,12/5) Glide Reflection Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(483,-704,212,-309) (16/11,3/2) -> (41/18,16/7) Hyperbolic Matrix(155,-242,98,-153) (3/2,11/7) -> (11/7,19/12) Parabolic Matrix(901,-1430,264,-419) (19/12,27/17) -> (17/5,41/12) Hyperbolic Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(505,-814,286,-461) (29/18,21/13) -> (7/4,23/13) Glide Reflection Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(67,-110,14,-23) (13/8,5/3) -> (9/2,5/1) Glide Reflection Matrix(131,-220,78,-131) (5/3,22/13) -> (5/3,22/13) Reflection Matrix(441,-748,260,-441) (22/13,17/10) -> (22/13,17/10) Reflection Matrix(1189,-2024,440,-749) (17/10,46/27) -> (27/10,46/17) Glide Reflection Matrix(1123,-1914,504,-859) (46/27,29/17) -> (20/9,29/13) Glide Reflection Matrix(991,-1694,554,-947) (41/24,12/7) -> (25/14,34/19) Glide Reflection Matrix(551,-946,166,-285) (12/7,43/25) -> (43/13,10/3) Hyperbolic Matrix(549,-946,242,-417) (31/18,19/11) -> (9/4,25/11) Glide Reflection Matrix(241,-418,64,-111) (19/11,7/4) -> (15/4,19/5) Hyperbolic Matrix(571,-1012,224,-397) (23/13,16/9) -> (28/11,23/9) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(109,-198,60,-109) (9/5,11/6) -> (9/5,11/6) Reflection Matrix(155,-286,84,-155) (11/6,13/7) -> (11/6,13/7) Reflection Matrix(199,-374,58,-109) (13/7,2/1) -> (24/7,31/9) Hyperbolic Matrix(111,-242,50,-109) (2/1,11/5) -> (11/5,20/9) Parabolic Matrix(285,-638,88,-197) (29/13,9/4) -> (29/9,13/4) Glide Reflection Matrix(1451,-3300,638,-1451) (25/11,66/29) -> (25/11,66/29) Reflection Matrix(2377,-5412,1044,-2377) (66/29,41/18) -> (66/29,41/18) Reflection Matrix(67,-154,10,-23) (16/7,7/3) -> (6/1,7/1) Glide Reflection Matrix(155,-374,46,-111) (12/5,17/7) -> (10/3,17/5) Glide Reflection Matrix(307,-748,126,-307) (17/7,22/9) -> (17/7,22/9) Reflection Matrix(89,-220,36,-89) (22/9,5/2) -> (22/9,5/2) Reflection Matrix(1409,-3608,412,-1055) (23/9,41/16) -> (41/12,65/19) Hyperbolic Matrix(111,-286,26,-67) (18/7,13/5) -> (4/1,13/3) Glide Reflection Matrix(2311,-6050,882,-2309) (34/13,55/21) -> (55/21,76/29) Parabolic Matrix(485,-1276,84,-221) (21/8,50/19) -> (23/4,6/1) Glide Reflection Matrix(727,-1914,226,-595) (50/19,29/11) -> (16/5,29/9) Glide Reflection Matrix(1451,-3828,550,-1451) (29/11,66/25) -> (29/11,66/25) Reflection Matrix(1849,-4884,700,-1849) (66/25,37/14) -> (66/25,37/14) Reflection Matrix(617,-1672,162,-439) (46/17,19/7) -> (19/5,42/11) Hyperbolic Matrix(153,-418,56,-153) (19/7,11/4) -> (19/7,11/4) Reflection Matrix(23,-66,8,-23) (11/4,3/1) -> (11/4,3/1) Reflection Matrix(43,-132,14,-43) (3/1,22/7) -> (3/1,22/7) Reflection Matrix(265,-836,84,-265) (22/7,19/6) -> (22/7,19/6) Reflection Matrix(461,-1518,140,-461) (23/7,33/10) -> (23/7,33/10) Reflection Matrix(859,-2838,260,-859) (33/10,43/13) -> (33/10,43/13) Reflection Matrix(1253,-4290,328,-1123) (65/19,24/7) -> (42/11,65/17) Hyperbolic Matrix(67,-242,18,-65) (7/2,11/3) -> (11/3,15/4) Parabolic Matrix(2991,-11440,782,-2991) (65/17,88/23) -> (65/17,88/23) Reflection Matrix(1057,-4048,276,-1057) (88/23,23/6) -> (88/23,23/6) Reflection Matrix(131,-572,30,-131) (13/3,22/5) -> (13/3,22/5) Reflection Matrix(89,-396,20,-89) (22/5,9/2) -> (22/5,9/2) Reflection Matrix(21,-110,4,-21) (5/1,11/2) -> (5/1,11/2) Reflection Matrix(67,-374,12,-67) (11/2,17/3) -> (11/2,17/3) Reflection Matrix(43,-308,6,-43) (7/1,22/3) -> (7/1,22/3) Reflection Matrix(89,-660,12,-89) (22/3,15/2) -> (22/3,15/2) 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) -> (0/1,1/1) Matrix(1,0,2,-1) -> Matrix(1,0,44,-1) (0/1,1/1) -> (0/1,1/22) Matrix(375,-418,218,-243) -> Matrix(217,-11,2742,-139) Matrix(309,-352,194,-221) -> Matrix(193,-10,2644,-137) Matrix(307,-352,116,-133) -> Matrix(115,-6,1016,-53) Matrix(263,-308,76,-89) -> Matrix(75,-4,544,-29) Matrix(241,-286,166,-197) -> Matrix(167,-9,2542,-137) Matrix(199,-242,162,-197) -> Matrix(163,-9,2916,-161) 1/18 Matrix(177,-220,70,-87) -> Matrix(71,-4,586,-33) Matrix(329,-418,122,-155) -> Matrix(121,-7,1020,-59) Matrix(155,-198,18,-23) -> Matrix(17,-1,-18,1) Matrix(1893,-2420,722,-923) -> Matrix(35,-2,298,-17) Matrix(463,-594,258,-331) -> Matrix(155,-9,1946,-113) Matrix(307,-396,238,-307) -> Matrix(239,-14,4080,-239) (9/7,22/17) -> (7/120,1/17) Matrix(441,-572,340,-441) -> Matrix(339,-20,5746,-339) (22/17,13/10) -> (1/17,10/169) Matrix(725,-946,456,-595) -> Matrix(353,-21,4858,-289) Matrix(571,-748,100,-131) -> Matrix(33,-2,82,-5) Matrix(133,-176,34,-45) -> Matrix(33,-2,148,-9) Matrix(375,-506,146,-197) -> Matrix(49,-3,376,-23) Matrix(857,-1166,502,-683) -> Matrix(309,-19,3952,-243) Matrix(241,-330,176,-241) -> Matrix(177,-11,2848,-177) (15/11,11/8) -> (11/178,1/16) Matrix(111,-154,80,-111) -> Matrix(79,-5,1248,-79) (11/8,7/5) -> (1/16,5/78) Matrix(109,-154,46,-65) -> Matrix(47,-3,454,-29) Matrix(397,-572,152,-219) -> Matrix(31,-2,264,-17) Matrix(483,-704,212,-309) -> Matrix(91,-6,804,-53) Matrix(155,-242,98,-153) -> Matrix(99,-7,1372,-97) 1/14 Matrix(901,-1430,264,-419) -> Matrix(69,-5,566,-41) Matrix(219,-352,28,-45) -> Matrix(27,-2,68,-5) Matrix(505,-814,286,-461) -> Matrix(15,-1,194,-13) Matrix(353,-572,108,-175) -> Matrix(55,-4,344,-25) Matrix(67,-110,14,-23) -> Matrix(13,-1,38,-3) Matrix(131,-220,78,-131) -> Matrix(79,-6,1040,-79) (5/3,22/13) -> (3/40,1/13) Matrix(441,-748,260,-441) -> Matrix(259,-20,3354,-259) (22/13,17/10) -> (1/13,10/129) Matrix(1189,-2024,440,-749) -> Matrix(283,-22,2354,-183) Matrix(1123,-1914,504,-859) -> Matrix(347,-27,3380,-263) Matrix(991,-1694,554,-947) -> Matrix(89,-7,1106,-87) Matrix(551,-946,166,-285) -> Matrix(89,-7,496,-39) Matrix(549,-946,242,-417) -> Matrix(113,-9,1042,-83) Matrix(241,-418,64,-111) -> Matrix(37,-3,210,-17) Matrix(571,-1012,224,-397) -> Matrix(25,-2,188,-15) Matrix(395,-704,124,-221) -> Matrix(27,-2,176,-13) Matrix(109,-198,60,-109) -> Matrix(61,-5,744,-61) (9/5,11/6) -> (5/62,1/12) Matrix(155,-286,84,-155) -> Matrix(83,-7,984,-83) (11/6,13/7) -> (1/12,7/82) Matrix(199,-374,58,-109) -> Matrix(11,-1,100,-9) 1/10 Matrix(111,-242,50,-109) -> Matrix(51,-5,500,-49) 1/10 Matrix(285,-638,88,-197) -> Matrix(9,-1,44,-5) Matrix(1451,-3300,638,-1451) -> Matrix(127,-14,1152,-127) (25/11,66/29) -> (7/64,1/9) Matrix(2377,-5412,1044,-2377) -> Matrix(143,-16,1278,-143) (66/29,41/18) -> (1/9,8/71) Matrix(67,-154,10,-23) -> Matrix(9,-1,26,-3) Matrix(155,-374,46,-111) -> Matrix(9,-1,26,-3) Matrix(307,-748,126,-307) -> Matrix(127,-14,1152,-127) (17/7,22/9) -> (7/64,1/9) Matrix(89,-220,36,-89) -> Matrix(35,-4,306,-35) (22/9,5/2) -> (1/9,2/17) Matrix(1409,-3608,412,-1055) -> Matrix(1,0,0,1) Matrix(111,-286,26,-67) -> Matrix(7,-1,34,-5) Matrix(2311,-6050,882,-2309) -> Matrix(11,-1,100,-9) 1/10 Matrix(485,-1276,84,-221) -> Matrix(19,-2,66,-7) Matrix(727,-1914,226,-595) -> Matrix(47,-5,310,-33) Matrix(1451,-3828,550,-1451) -> Matrix(127,-14,1152,-127) (29/11,66/25) -> (7/64,1/9) Matrix(1849,-4884,700,-1849) -> Matrix(215,-24,1926,-215) (66/25,37/14) -> (1/9,12/107) Matrix(617,-1672,162,-439) -> Matrix(33,-4,190,-23) Matrix(153,-418,56,-153) -> Matrix(57,-7,464,-57) (19/7,11/4) -> (7/58,1/8) Matrix(23,-66,8,-23) -> Matrix(7,-1,48,-7) (11/4,3/1) -> (1/8,1/6) Matrix(43,-132,14,-43) -> Matrix(15,-2,112,-15) (3/1,22/7) -> (1/8,1/7) Matrix(265,-836,84,-265) -> Matrix(83,-12,574,-83) (22/7,19/6) -> (1/7,6/41) Matrix(461,-1518,140,-461) -> Matrix(43,-7,264,-43) (23/7,33/10) -> (7/44,1/6) Matrix(859,-2838,260,-859) -> Matrix(77,-13,456,-77) (33/10,43/13) -> (1/6,13/76) Matrix(1253,-4290,328,-1123) -> Matrix(9,-1,46,-5) Matrix(67,-242,18,-65) -> Matrix(19,-3,108,-17) 1/6 Matrix(2991,-11440,782,-2991) -> Matrix(23,-4,132,-23) (65/17,88/23) -> (1/6,2/11) Matrix(1057,-4048,276,-1057) -> Matrix(21,-4,110,-21) (88/23,23/6) -> (2/11,1/5) Matrix(131,-572,30,-131) -> Matrix(31,-6,160,-31) (13/3,22/5) -> (3/16,1/5) Matrix(89,-396,20,-89) -> Matrix(19,-4,90,-19) (22/5,9/2) -> (1/5,2/9) Matrix(21,-110,4,-21) -> Matrix(5,-1,24,-5) (5/1,11/2) -> (1/6,1/4) Matrix(67,-374,12,-67) -> Matrix(11,-3,40,-11) (11/2,17/3) -> (1/4,3/10) Matrix(43,-308,6,-43) -> Matrix(7,-2,24,-7) (7/1,22/3) -> (1/4,1/3) Matrix(89,-660,12,-89) -> Matrix(11,-4,30,-11) (22/3,15/2) -> (1/3,2/5) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.