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): 1584 Minimal number of generators: 265 Number of equivalence classes of cusps: 66 Genus: 100 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/15 -68/161 -19/46 -17/46 -41/138 -13/46 -45/161 -37/138 -11/46 -5/21 -43/184 -21/92 -31/138 -4/21 -7/46 -3/20 -1/10 0/1 1/9 1/8 3/23 2/15 1/7 2/13 3/19 1/6 4/23 3/17 2/11 3/16 1/5 4/19 3/14 5/23 2/9 5/22 3/13 4/17 1/4 6/23 3/11 5/18 2/7 34/115 7/23 1/3 8/23 44/115 9/23 2/5 5/12 10/23 1/2 13/23 14/23 71/115 15/23 2/3 16/23 81/115 17/23 18/23 19/23 20/23 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/22 -8/9 7/136 -7/8 6/115 1/19 -20/23 1/19 -13/15 11/208 -6/7 3/56 -11/13 9/166 -16/19 1/18 -21/25 1/18 -5/6 4/73 1/18 -19/23 1/18 -14/17 1/18 -9/11 1/18 -13/16 1/18 2/35 -4/5 3/52 -15/19 3/52 -26/33 13/224 -11/14 8/137 1/17 -18/23 1/17 -7/9 5/84 -31/40 2/33 1/16 -24/31 3/52 -17/22 1/17 4/67 -10/13 1/16 -13/17 3/50 -3/4 2/33 1/16 -17/23 1/16 -14/19 1/16 -11/15 7/110 -41/56 7/109 2/31 -30/41 7/108 -19/26 0/1 1/16 -8/11 1/16 -21/29 1/16 -34/47 21/332 -13/18 4/63 3/47 -31/43 7/110 -49/68 22/345 3/47 -18/25 5/78 -5/7 3/46 -22/31 5/74 -17/24 2/31 1/15 -12/17 1/16 -31/44 2/31 1/15 -81/115 1/15 -50/71 1/16 -19/27 1/16 -45/64 7/109 2/31 -26/37 11/170 -33/47 19/292 -7/10 4/61 1/15 -16/23 1/15 -9/13 5/74 -11/16 2/29 1/14 -2/3 1/14 -15/23 1/14 -13/20 1/14 6/83 -11/17 1/14 -20/31 9/122 -29/45 13/174 -9/14 0/1 1/13 -25/39 1/18 -16/25 1/14 -39/61 5/74 -23/36 2/29 3/43 -30/47 13/184 -7/11 1/14 -19/30 1/14 4/55 -12/19 5/68 -5/8 2/27 1/13 -23/37 5/62 -18/29 1/12 -13/21 1/16 -21/34 4/57 1/14 -71/115 1/14 -50/81 1/14 -29/47 11/152 -37/60 10/137 3/41 -8/13 3/40 -19/31 7/94 -30/49 5/66 -11/18 4/53 1/13 -14/23 1/13 -3/5 1/12 -13/22 1/13 4/51 -10/17 3/38 -7/12 2/25 1/12 -25/43 1/14 -18/31 5/62 -11/19 1/12 -37/64 2/23 5/57 -26/45 7/78 -41/71 5/54 -15/26 0/1 1/10 -19/33 1/18 -4/7 1/12 -13/23 1/12 -9/16 1/12 2/23 -14/25 1/10 -5/9 1/10 -16/29 1/12 -11/20 1/12 2/23 -6/11 1/12 -7/13 1/10 -1/2 0/1 1/11 -7/15 1/14 -6/13 1/12 -11/24 1/11 2/21 -5/11 1/10 -9/20 2/21 1/10 -13/29 1/10 -4/9 1/12 -19/43 5/52 -15/34 4/41 1/10 -11/25 1/12 -29/66 4/43 3/32 -18/41 5/52 -7/16 2/21 1/10 -10/23 1/10 -3/7 1/10 -11/26 0/1 1/12 -30/71 5/56 -49/116 14/155 1/11 -68/161 1/11 -19/45 7/76 -8/19 1/10 -13/31 5/48 -18/43 1/8 -5/12 1/10 2/19 -12/29 5/48 -19/46 2/19 -7/17 3/28 -9/22 4/37 1/9 -11/27 1/10 -2/5 1/10 -9/23 1/9 -7/18 1/9 4/35 -19/49 5/44 -12/31 7/60 -17/44 1/9 2/17 -5/13 3/26 -18/47 11/90 -31/81 1/8 -44/115 1/8 -13/34 1/8 4/31 -34/89 5/38 -55/144 2/15 3/22 -21/55 1/6 -8/21 1/6 -19/50 0/1 1/12 -11/29 1/10 -14/37 5/48 -3/8 1/9 2/17 -10/27 7/60 -17/46 2/17 -7/19 5/42 -25/68 14/117 3/25 -18/49 1/8 -11/30 4/33 1/8 -4/11 1/8 -17/47 13/102 -13/36 3/23 2/15 -22/61 5/36 -31/86 0/1 1/8 -9/25 1/8 -5/14 0/1 1/9 -16/45 13/112 -11/31 9/76 -17/48 2/17 3/25 -6/17 1/8 -7/20 6/49 1/8 -8/23 1/8 -1/3 1/8 -6/19 1/6 -5/16 1/8 2/15 -19/61 19/142 -14/45 17/126 -9/29 3/22 -4/13 5/36 -7/23 1/7 -3/10 1/7 4/27 -11/37 11/72 -41/138 2/13 -30/101 25/162 -19/64 2/13 7/45 -8/27 1/6 -21/71 1/6 -34/115 1/7 -13/44 1/7 2/13 -18/61 7/46 -5/17 1/6 -7/24 1/7 2/13 -9/31 5/36 -2/7 3/20 -13/46 2/13 -11/39 17/110 -9/32 2/13 7/45 -7/25 5/32 -26/93 41/260 -45/161 3/19 -19/68 3/19 22/139 -12/43 7/44 -5/18 3/19 4/25 -18/65 9/56 -13/47 21/130 -8/29 1/6 -3/11 1/6 -7/26 0/1 1/6 -11/41 7/46 -37/138 2/13 -26/97 21/136 -15/56 2/13 7/45 -4/15 7/44 -5/19 1/6 -6/23 1/6 -1/4 1/6 2/11 -6/25 13/72 -11/46 2/11 -5/21 11/60 -4/17 3/16 -11/47 25/132 -18/77 35/184 -43/184 4/21 -25/107 45/236 -7/30 4/21 5/26 -3/13 1/6 -8/35 3/16 -21/92 4/21 -13/57 5/26 -5/22 4/21 1/5 -7/31 3/14 -9/40 1/6 2/11 -20/89 9/50 -31/138 2/11 -11/49 7/38 -2/9 5/26 -5/23 1/5 -3/14 1/5 8/39 -10/47 27/130 -7/33 13/62 -4/19 3/14 -9/43 1/4 -5/24 1/5 6/29 -1/5 3/14 -5/26 5/22 8/35 -4/21 7/30 -3/16 2/9 1/4 -2/11 1/4 -3/17 1/4 -4/23 1/4 -1/6 1/4 4/15 -5/31 11/40 -4/25 1/4 -3/19 1/4 -2/13 9/32 -7/46 2/7 -5/33 23/80 -3/20 2/7 7/24 -1/7 3/10 -2/15 11/34 -3/23 1/3 -1/8 1/3 6/17 -1/9 7/18 -1/10 3/7 4/9 0/1 1/0 1/9 -7/18 1/8 -6/17 -1/3 3/23 -1/3 2/15 -11/34 1/7 -3/10 2/13 -9/32 3/19 -1/4 4/25 -1/4 1/6 -4/15 -1/4 4/23 -1/4 3/17 -1/4 2/11 -1/4 3/16 -1/4 -2/9 1/5 -3/14 4/19 -3/14 7/33 -13/62 3/14 -8/39 -1/5 5/23 -1/5 2/9 -5/26 9/40 -2/11 -1/6 7/31 -3/14 5/22 -1/5 -4/21 3/13 -1/6 4/17 -3/16 1/4 -2/11 -1/6 6/23 -1/6 5/19 -1/6 4/15 -7/44 15/56 -7/45 -2/13 11/41 -7/46 7/26 -1/6 0/1 3/11 -1/6 8/29 -1/6 13/47 -21/130 5/18 -4/25 -3/19 12/43 -7/44 19/68 -22/139 -3/19 7/25 -5/32 2/7 -3/20 9/31 -5/36 7/24 -2/13 -1/7 5/17 -1/6 13/44 -2/13 -1/7 34/115 -1/7 21/71 -1/6 8/27 -1/6 19/64 -7/45 -2/13 11/37 -11/72 14/47 -19/126 3/10 -4/27 -1/7 7/23 -1/7 4/13 -5/36 5/16 -2/15 -1/8 1/3 -1/8 8/23 -1/8 7/20 -1/8 -6/49 6/17 -1/8 11/31 -9/76 16/45 -13/112 5/14 -1/9 0/1 14/39 -1/4 9/25 -1/8 22/61 -5/36 13/36 -2/15 -3/23 17/47 -13/102 4/11 -1/8 11/30 -1/8 -4/33 7/19 -5/42 3/8 -2/17 -1/9 14/37 -5/48 11/29 -1/10 8/21 -1/6 13/34 -4/31 -1/8 44/115 -1/8 31/81 -1/8 18/47 -11/90 23/60 -10/83 -3/25 5/13 -3/26 12/31 -7/60 19/49 -5/44 7/18 -4/35 -1/9 9/23 -1/9 2/5 -1/10 9/22 -1/9 -4/37 7/17 -3/28 5/12 -2/19 -1/10 18/43 -1/8 13/31 -5/48 8/19 -1/10 27/64 -2/21 -5/53 19/45 -7/76 30/71 -5/56 11/26 -1/12 0/1 14/33 -1/4 3/7 -1/10 10/23 -1/10 7/16 -1/10 -2/21 11/25 -1/12 4/9 -1/12 13/29 -1/10 9/20 -1/10 -2/21 5/11 -1/10 6/13 -1/12 1/2 -1/11 0/1 8/15 -1/8 7/13 -1/10 13/24 -1/11 -2/23 6/11 -1/12 11/20 -2/23 -1/12 16/29 -1/12 5/9 -1/10 24/43 -5/58 19/34 -4/47 -1/12 14/25 -1/10 37/66 -4/45 -3/34 23/41 -5/58 9/16 -2/23 -1/12 13/23 -1/12 4/7 -1/12 15/26 -1/10 0/1 41/71 -5/54 67/116 -14/153 -1/11 93/161 -1/11 26/45 -7/78 11/19 -1/12 18/31 -5/62 25/43 -1/14 7/12 -1/12 -2/25 17/29 -5/62 27/46 -2/25 10/17 -3/38 13/22 -4/51 -1/13 16/27 -1/12 3/5 -1/12 14/23 -1/13 11/18 -1/13 -4/53 30/49 -5/66 19/31 -7/94 27/44 -1/13 -2/27 8/13 -3/40 29/47 -11/152 50/81 -1/14 71/115 -1/14 21/34 -1/14 -4/57 55/89 -5/72 89/144 -2/29 -3/44 34/55 -1/16 13/21 -1/16 31/50 -1/10 0/1 18/29 -1/12 23/37 -5/62 5/8 -1/13 -2/27 17/27 -7/94 29/46 -2/27 12/19 -5/68 43/68 -14/191 -3/41 31/49 -1/14 19/30 -4/55 -1/14 7/11 -1/14 30/47 -13/184 23/36 -3/43 -2/29 39/61 -5/74 55/86 -1/14 0/1 16/25 -1/14 9/14 -1/13 0/1 29/45 -13/174 20/31 -9/122 31/48 -2/27 -3/41 11/17 -1/14 13/20 -6/83 -1/14 15/23 -1/14 2/3 -1/14 13/19 -1/16 11/16 -1/14 -2/29 42/61 -19/276 31/45 -17/248 20/29 -3/44 9/13 -5/74 16/23 -1/15 7/10 -1/15 -4/61 26/37 -11/170 97/138 -2/31 71/101 -25/388 45/64 -2/31 -7/109 19/27 -1/16 50/71 -1/16 81/115 -1/15 31/44 -1/15 -2/31 43/61 -7/108 12/17 -1/16 17/24 -1/15 -2/31 22/31 -5/74 5/7 -3/46 33/46 -2/31 28/39 -17/264 23/32 -2/31 -7/109 18/25 -5/78 67/93 -41/642 116/161 -3/47 49/68 -3/47 -22/345 31/43 -7/110 13/18 -3/47 -4/63 47/65 -9/142 34/47 -21/332 21/29 -1/16 8/11 -1/16 19/26 -1/16 0/1 30/41 -7/108 101/138 -2/31 71/97 -21/326 41/56 -2/31 -7/109 11/15 -7/110 14/19 -1/16 17/23 -1/16 3/4 -1/16 -2/33 19/25 -13/214 35/46 -2/33 16/21 -11/182 13/17 -3/50 36/47 -25/418 59/77 -35/586 141/184 -4/67 82/107 -45/754 23/30 -4/67 -5/84 10/13 -1/16 27/35 -3/50 71/92 -4/67 44/57 -5/84 17/22 -4/67 -1/17 24/31 -3/52 31/40 -1/16 -2/33 69/89 -9/148 107/138 -2/33 38/49 -7/116 7/9 -5/84 18/23 -1/17 11/14 -1/17 -8/137 37/47 -27/464 26/33 -13/224 15/19 -3/52 34/43 -1/18 19/24 -1/17 -6/103 4/5 -3/52 21/26 -5/88 -8/141 17/21 -7/124 13/16 -2/35 -1/18 9/11 -1/18 14/17 -1/18 19/23 -1/18 5/6 -1/18 -4/73 26/31 -11/202 21/25 -1/18 16/19 -1/18 11/13 -9/166 39/46 -2/37 28/33 -23/426 17/20 -2/37 -7/130 6/7 -3/56 13/15 -11/208 20/23 -1/19 7/8 -1/19 -6/115 8/9 -7/136 9/10 -3/59 -4/79 1/1 -1/22 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(323,290,-460,-413) (-1/1,-8/9) -> (-26/37,-33/47) Hyperbolic Matrix(139,122,368,323) (-8/9,-7/8) -> (3/8,14/37) Hyperbolic Matrix(321,280,368,321) (-7/8,-20/23) -> (20/23,7/8) Hyperbolic Matrix(599,520,690,599) (-20/23,-13/15) -> (13/15,20/23) Hyperbolic Matrix(93,80,322,277) (-13/15,-6/7) -> (2/7,9/31) Hyperbolic Matrix(185,158,-322,-275) (-6/7,-11/13) -> (-19/33,-4/7) Hyperbolic Matrix(185,156,874,737) (-11/13,-16/19) -> (4/19,7/33) Hyperbolic Matrix(599,504,2024,1703) (-16/19,-21/25) -> (21/71,8/27) Hyperbolic Matrix(829,696,-2300,-1931) (-21/25,-5/6) -> (-31/86,-9/25) Hyperbolic Matrix(229,190,276,229) (-5/6,-19/23) -> (19/23,5/6) Hyperbolic Matrix(645,532,782,645) (-19/23,-14/17) -> (14/17,19/23) Hyperbolic Matrix(139,114,506,415) (-14/17,-9/11) -> (3/11,8/29) Hyperbolic Matrix(321,262,506,413) (-9/11,-13/16) -> (19/30,7/11) Hyperbolic Matrix(323,262,-736,-597) (-13/16,-4/5) -> (-18/41,-7/16) Hyperbolic Matrix(93,74,-230,-183) (-4/5,-15/19) -> (-11/27,-2/5) Hyperbolic Matrix(137,108,874,689) (-15/19,-26/33) -> (2/13,3/19) Hyperbolic Matrix(1333,1050,-2162,-1703) (-26/33,-11/14) -> (-37/60,-8/13) Hyperbolic Matrix(505,396,644,505) (-11/14,-18/23) -> (18/23,11/14) Hyperbolic Matrix(323,252,414,323) (-18/23,-7/9) -> (7/9,18/23) Hyperbolic Matrix(1335,1036,-3496,-2713) (-7/9,-31/40) -> (-55/144,-21/55) Hyperbolic Matrix(1841,1426,-5106,-3955) (-31/40,-24/31) -> (-22/61,-31/86) Hyperbolic Matrix(1011,782,1426,1103) (-24/31,-17/22) -> (17/24,22/31) Hyperbolic Matrix(275,212,-598,-461) (-17/22,-10/13) -> (-6/13,-11/24) Hyperbolic Matrix(185,142,-598,-459) (-10/13,-13/17) -> (-9/29,-4/13) Hyperbolic Matrix(367,280,-966,-737) (-13/17,-3/4) -> (-19/50,-11/29) Hyperbolic Matrix(137,102,184,137) (-3/4,-17/23) -> (17/23,3/4) Hyperbolic Matrix(645,476,874,645) (-17/23,-14/19) -> (14/19,17/23) Hyperbolic Matrix(367,270,874,643) (-14/19,-11/15) -> (13/31,8/19) Hyperbolic Matrix(2529,1852,3956,2897) (-11/15,-41/56) -> (23/36,39/61) Hyperbolic Matrix(2071,1516,-7728,-5657) (-41/56,-30/41) -> (-26/97,-15/56) Hyperbolic Matrix(1657,1212,-3772,-2759) (-30/41,-19/26) -> (-29/66,-18/41) Hyperbolic Matrix(277,202,506,369) (-19/26,-8/11) -> (6/11,11/20) Hyperbolic Matrix(91,66,506,367) (-8/11,-21/29) -> (3/17,2/11) Hyperbolic Matrix(829,600,-2668,-1931) (-21/29,-34/47) -> (-14/45,-9/29) Hyperbolic Matrix(2207,1596,-3818,-2761) (-34/47,-13/18) -> (-37/64,-26/45) Hyperbolic Matrix(643,464,1656,1195) (-13/18,-31/43) -> (19/49,7/18) Hyperbolic Matrix(3957,2852,6256,4509) (-31/43,-49/68) -> (43/68,31/49) Hyperbolic Matrix(3265,2352,-7728,-5567) (-49/68,-18/25) -> (-30/71,-49/116) Hyperbolic Matrix(737,530,-1150,-827) (-18/25,-5/7) -> (-25/39,-16/25) Hyperbolic Matrix(45,32,322,229) (-5/7,-22/31) -> (2/15,1/7) Hyperbolic Matrix(1103,782,1426,1011) (-22/31,-17/24) -> (17/22,24/31) Hyperbolic Matrix(461,326,782,553) (-17/24,-12/17) -> (10/17,13/22) Hyperbolic Matrix(553,390,-1564,-1103) (-12/17,-31/44) -> (-17/48,-6/17) Hyperbolic Matrix(7129,5022,10120,7129) (-31/44,-81/115) -> (81/115,31/44) Hyperbolic Matrix(11501,8100,16330,11501) (-81/115,-50/71) -> (50/71,81/115) Hyperbolic Matrix(321,226,2024,1425) (-50/71,-19/27) -> (3/19,4/25) Hyperbolic Matrix(3359,2362,4646,3267) (-19/27,-45/64) -> (13/18,47/65) Hyperbolic Matrix(2623,1844,-8832,-6209) (-45/64,-26/37) -> (-30/101,-19/64) Hyperbolic Matrix(781,548,2162,1517) (-33/47,-7/10) -> (13/36,17/47) Hyperbolic Matrix(321,224,460,321) (-7/10,-16/23) -> (16/23,7/10) Hyperbolic Matrix(415,288,598,415) (-16/23,-9/13) -> (9/13,16/23) Hyperbolic Matrix(139,96,-598,-413) (-9/13,-11/16) -> (-7/30,-3/13) Hyperbolic Matrix(321,220,-874,-599) (-11/16,-2/3) -> (-18/49,-11/30) Hyperbolic Matrix(91,60,138,91) (-2/3,-15/23) -> (15/23,2/3) Hyperbolic Matrix(599,390,920,599) (-15/23,-13/20) -> (13/20,15/23) Hyperbolic Matrix(413,268,920,597) (-13/20,-11/17) -> (13/29,9/20) Hyperbolic Matrix(461,298,-1564,-1011) (-11/17,-20/31) -> (-18/61,-5/17) Hyperbolic Matrix(1151,742,-4922,-3173) (-20/31,-29/45) -> (-11/47,-18/77) Hyperbolic Matrix(1013,652,1288,829) (-29/45,-9/14) -> (11/14,37/47) Hyperbolic Matrix(505,324,-1794,-1151) (-9/14,-25/39) -> (-11/39,-9/32) Hyperbolic Matrix(369,236,-2300,-1471) (-16/25,-39/61) -> (-5/31,-4/25) Hyperbolic Matrix(2897,1852,3956,2529) (-39/61,-23/36) -> (41/56,11/15) Hyperbolic Matrix(645,412,2162,1381) (-23/36,-30/47) -> (14/47,3/10) Hyperbolic Matrix(1655,1056,4324,2759) (-30/47,-7/11) -> (31/81,18/47) Hyperbolic Matrix(413,262,506,321) (-7/11,-19/30) -> (13/16,9/11) Hyperbolic Matrix(275,174,-874,-553) (-19/30,-12/19) -> (-6/19,-5/16) Hyperbolic Matrix(137,86,-368,-231) (-12/19,-5/8) -> (-3/8,-10/27) Hyperbolic Matrix(45,28,368,229) (-5/8,-23/37) -> (1/9,1/8) Hyperbolic Matrix(737,458,1334,829) (-23/37,-18/29) -> (16/29,5/9) Hyperbolic Matrix(229,142,-966,-599) (-18/29,-13/21) -> (-5/21,-4/17) Hyperbolic Matrix(689,426,-1564,-967) (-13/21,-21/34) -> (-15/34,-11/25) Hyperbolic Matrix(4829,2982,7820,4829) (-21/34,-71/115) -> (71/115,21/34) Hyperbolic Matrix(11501,7100,18630,11501) (-71/115,-50/81) -> (50/81,71/115) Hyperbolic Matrix(1565,966,4324,2669) (-50/81,-29/47) -> (17/47,4/11) Hyperbolic Matrix(2163,1334,3358,2071) (-29/47,-37/60) -> (9/14,29/45) Hyperbolic Matrix(277,170,-598,-367) (-8/13,-19/31) -> (-7/15,-6/13) Hyperbolic Matrix(1195,732,2852,1747) (-19/31,-30/49) -> (18/43,13/31) Hyperbolic Matrix(461,282,1656,1013) (-30/49,-11/18) -> (5/18,12/43) Hyperbolic Matrix(505,308,828,505) (-11/18,-14/23) -> (14/23,11/18) Hyperbolic Matrix(139,84,230,139) (-14/23,-3/5) -> (3/5,14/23) Hyperbolic Matrix(47,28,-230,-137) (-3/5,-13/22) -> (-5/24,-1/5) Hyperbolic Matrix(553,326,782,461) (-13/22,-10/17) -> (12/17,17/24) Hyperbolic Matrix(229,134,-552,-323) (-10/17,-7/12) -> (-5/12,-12/29) Hyperbolic Matrix(873,508,-1978,-1151) (-7/12,-25/43) -> (-19/43,-15/34) Hyperbolic Matrix(1105,642,2852,1657) (-25/43,-18/31) -> (12/31,19/49) Hyperbolic Matrix(231,134,874,507) (-18/31,-11/19) -> (5/19,4/15) Hyperbolic Matrix(2071,1198,2944,1703) (-11/19,-37/64) -> (45/64,19/27) Hyperbolic Matrix(2161,1248,-7728,-4463) (-26/45,-41/71) -> (-7/25,-26/93) Hyperbolic Matrix(1933,1116,2392,1381) (-41/71,-15/26) -> (21/26,17/21) Hyperbolic Matrix(229,132,-1518,-875) (-15/26,-19/33) -> (-5/33,-3/20) Hyperbolic Matrix(183,104,322,183) (-4/7,-13/23) -> (13/23,4/7) Hyperbolic Matrix(415,234,736,415) (-13/23,-9/16) -> (9/16,13/23) Hyperbolic Matrix(139,78,-736,-413) (-9/16,-14/25) -> (-4/21,-3/16) Hyperbolic Matrix(597,334,-1564,-875) (-14/25,-5/9) -> (-21/55,-8/21) Hyperbolic Matrix(829,458,1334,737) (-5/9,-16/29) -> (18/29,23/37) Hyperbolic Matrix(323,178,920,507) (-16/29,-11/20) -> (7/20,6/17) Hyperbolic Matrix(369,202,506,277) (-11/20,-6/11) -> (8/11,19/26) Hyperbolic Matrix(137,74,-598,-323) (-6/11,-7/13) -> (-3/13,-8/35) Hyperbolic Matrix(231,124,-598,-321) (-7/13,-1/2) -> (-17/44,-5/13) Hyperbolic Matrix(277,130,-782,-367) (-1/2,-7/15) -> (-11/31,-17/48) Hyperbolic Matrix(367,168,-1610,-737) (-11/24,-5/11) -> (-13/57,-5/22) Hyperbolic Matrix(137,62,506,229) (-5/11,-9/20) -> (7/26,3/11) Hyperbolic Matrix(597,268,920,413) (-9/20,-13/29) -> (11/17,13/20) Hyperbolic Matrix(505,226,1334,597) (-13/29,-4/9) -> (14/37,11/29) Hyperbolic Matrix(185,82,-828,-367) (-4/9,-19/43) -> (-11/49,-2/9) Hyperbolic Matrix(3081,1354,5336,2345) (-11/25,-29/66) -> (15/26,41/71) Hyperbolic Matrix(321,140,736,321) (-7/16,-10/23) -> (10/23,7/16) Hyperbolic Matrix(139,60,322,139) (-10/23,-3/7) -> (3/7,10/23) Hyperbolic Matrix(47,20,-322,-137) (-3/7,-11/26) -> (-3/20,-1/7) Hyperbolic Matrix(2991,1264,5336,2255) (-11/26,-30/71) -> (14/25,37/66) Hyperbolic Matrix(21345,9016,29624,12513) (-49/116,-68/161) -> (116/161,49/68) Hyperbolic Matrix(16007,6760,22218,9383) (-68/161,-19/45) -> (67/93,116/161) Hyperbolic Matrix(1057,446,-3818,-1611) (-19/45,-8/19) -> (-18/65,-13/47) Hyperbolic Matrix(643,270,874,367) (-8/19,-13/31) -> (11/15,14/19) Hyperbolic Matrix(1747,732,2852,1195) (-13/31,-18/43) -> (30/49,19/31) Hyperbolic Matrix(967,404,-2530,-1057) (-18/43,-5/12) -> (-13/34,-34/89) Hyperbolic Matrix(1243,514,2116,875) (-12/29,-19/46) -> (27/46,10/17) Hyperbolic Matrix(1241,512,2116,873) (-19/46,-7/17) -> (17/29,27/46) Hyperbolic Matrix(229,94,782,321) (-7/17,-9/22) -> (7/24,5/17) Hyperbolic Matrix(829,338,-2254,-919) (-9/22,-11/27) -> (-7/19,-25/68) Hyperbolic Matrix(91,36,230,91) (-2/5,-9/23) -> (9/23,2/5) Hyperbolic Matrix(323,126,828,323) (-9/23,-7/18) -> (7/18,9/23) Hyperbolic Matrix(1195,464,1656,643) (-7/18,-19/49) -> (31/43,13/18) Hyperbolic Matrix(1657,642,2852,1105) (-19/49,-12/31) -> (18/31,25/43) Hyperbolic Matrix(1195,462,-4048,-1565) (-12/31,-17/44) -> (-13/44,-18/61) Hyperbolic Matrix(459,176,-2162,-829) (-5/13,-18/47) -> (-10/47,-7/33) Hyperbolic Matrix(2759,1056,4324,1655) (-18/47,-31/81) -> (7/11,30/47) Hyperbolic Matrix(7129,2728,18630,7129) (-31/81,-44/115) -> (44/115,31/81) Hyperbolic Matrix(2991,1144,7820,2991) (-44/115,-13/34) -> (13/34,44/115) Hyperbolic Matrix(3681,1406,-16376,-6255) (-34/89,-55/144) -> (-9/40,-20/89) Hyperbolic Matrix(321,122,-1334,-507) (-8/21,-19/50) -> (-1/4,-6/25) Hyperbolic Matrix(597,226,1334,505) (-11/29,-14/37) -> (4/9,13/29) Hyperbolic Matrix(323,122,368,139) (-14/37,-3/8) -> (7/8,8/9) Hyperbolic Matrix(1335,494,2116,783) (-10/27,-17/46) -> (29/46,12/19) Hyperbolic Matrix(1333,492,2116,781) (-17/46,-7/19) -> (17/27,29/46) Hyperbolic Matrix(1747,642,6256,2299) (-25/68,-18/49) -> (12/43,19/68) Hyperbolic Matrix(93,34,506,185) (-11/30,-4/11) -> (2/11,3/16) Hyperbolic Matrix(2669,966,4324,1565) (-4/11,-17/47) -> (29/47,50/81) Hyperbolic Matrix(459,166,506,183) (-17/47,-13/36) -> (9/10,1/1) Hyperbolic Matrix(1059,382,3956,1427) (-13/36,-22/61) -> (4/15,15/56) Hyperbolic Matrix(323,116,-1150,-413) (-9/25,-5/14) -> (-9/32,-7/25) Hyperbolic Matrix(1287,458,3358,1195) (-5/14,-16/45) -> (18/47,23/60) Hyperbolic Matrix(1289,458,-4140,-1471) (-16/45,-11/31) -> (-19/61,-14/45) Hyperbolic Matrix(507,178,920,323) (-6/17,-7/20) -> (11/20,16/29) Hyperbolic Matrix(321,112,920,321) (-7/20,-8/23) -> (8/23,7/20) Hyperbolic Matrix(47,16,138,47) (-8/23,-1/3) -> (1/3,8/23) Hyperbolic Matrix(183,58,-874,-277) (-1/3,-6/19) -> (-4/19,-9/43) Hyperbolic Matrix(827,258,-3542,-1105) (-5/16,-19/61) -> (-25/107,-7/30) Hyperbolic Matrix(183,56,598,183) (-4/13,-7/23) -> (7/23,4/13) Hyperbolic Matrix(139,42,460,139) (-7/23,-3/10) -> (3/10,7/23) Hyperbolic Matrix(47,14,-460,-137) (-3/10,-11/37) -> (-1/9,-1/10) Hyperbolic Matrix(13387,3978,19044,5659) (-11/37,-41/138) -> (97/138,71/101) Hyperbolic Matrix(13385,3976,19044,5657) (-41/138,-30/101) -> (26/37,97/138) Hyperbolic Matrix(1241,368,2944,873) (-19/64,-8/27) -> (8/19,27/64) Hyperbolic Matrix(1703,504,2024,599) (-8/27,-21/71) -> (21/25,16/19) Hyperbolic Matrix(4829,1428,16330,4829) (-21/71,-34/115) -> (34/115,21/71) Hyperbolic Matrix(2991,884,10120,2991) (-34/115,-13/44) -> (13/44,34/115) Hyperbolic Matrix(321,94,782,229) (-5/17,-7/24) -> (9/22,7/17) Hyperbolic Matrix(323,94,1426,415) (-7/24,-9/31) -> (7/31,5/22) Hyperbolic Matrix(277,80,322,93) (-9/31,-2/7) -> (6/7,13/15) Hyperbolic Matrix(1519,430,2116,599) (-2/7,-13/46) -> (33/46,28/39) Hyperbolic Matrix(1517,428,2116,597) (-13/46,-11/39) -> (5/7,33/46) Hyperbolic Matrix(12835,3588,22218,6211) (-26/93,-45/161) -> (93/161,26/45) Hyperbolic Matrix(17111,4782,29624,8279) (-45/161,-19/68) -> (67/116,93/161) Hyperbolic Matrix(3129,874,3956,1105) (-19/68,-12/43) -> (34/43,19/24) Hyperbolic Matrix(1013,282,1656,461) (-12/43,-5/18) -> (11/18,30/49) Hyperbolic Matrix(1379,382,4646,1287) (-5/18,-18/65) -> (8/27,19/64) Hyperbolic Matrix(507,140,-2162,-597) (-13/47,-8/29) -> (-4/17,-11/47) Hyperbolic Matrix(415,114,506,139) (-8/29,-3/11) -> (9/11,14/17) Hyperbolic Matrix(229,62,506,137) (-3/11,-7/26) -> (9/20,5/11) Hyperbolic Matrix(231,62,-1196,-321) (-7/26,-11/41) -> (-1/5,-5/26) Hyperbolic Matrix(13939,3738,19044,5107) (-11/41,-37/138) -> (101/138,71/97) Hyperbolic Matrix(13937,3736,19044,5105) (-37/138,-26/97) -> (30/41,101/138) Hyperbolic Matrix(1427,382,3956,1059) (-15/56,-4/15) -> (22/61,13/36) Hyperbolic Matrix(507,134,874,231) (-4/15,-5/19) -> (11/19,18/31) Hyperbolic Matrix(229,60,874,229) (-5/19,-6/23) -> (6/23,5/19) Hyperbolic Matrix(47,12,184,47) (-6/23,-1/4) -> (1/4,6/23) Hyperbolic Matrix(1611,386,2116,507) (-6/25,-11/46) -> (35/46,16/21) Hyperbolic Matrix(1609,384,2116,505) (-11/46,-5/21) -> (19/25,35/46) Hyperbolic Matrix(25945,6064,33856,7913) (-18/77,-43/184) -> (141/184,82/107) Hyperbolic Matrix(25943,6062,33856,7911) (-43/184,-25/107) -> (59/77,141/184) Hyperbolic Matrix(6533,1492,8464,1933) (-8/35,-21/92) -> (71/92,44/57) Hyperbolic Matrix(6531,1490,8464,1931) (-21/92,-13/57) -> (27/35,71/92) Hyperbolic Matrix(415,94,1426,323) (-5/22,-7/31) -> (9/31,7/24) Hyperbolic Matrix(231,52,-1426,-321) (-7/31,-9/40) -> (-1/6,-5/31) Hyperbolic Matrix(14767,3318,19044,4279) (-20/89,-31/138) -> (107/138,38/49) Hyperbolic Matrix(14765,3316,19044,4277) (-31/138,-11/49) -> (69/89,107/138) Hyperbolic Matrix(91,20,414,91) (-2/9,-5/23) -> (5/23,2/9) Hyperbolic Matrix(139,30,644,139) (-5/23,-3/14) -> (3/14,5/23) Hyperbolic Matrix(459,98,1288,275) (-3/14,-10/47) -> (16/45,5/14) Hyperbolic Matrix(737,156,874,185) (-7/33,-4/19) -> (16/19,11/13) Hyperbolic Matrix(2851,596,3956,827) (-9/43,-5/24) -> (49/68,31/43) Hyperbolic Matrix(1011,194,2392,459) (-5/26,-4/21) -> (30/71,11/26) Hyperbolic Matrix(185,34,506,93) (-3/16,-2/11) -> (4/11,11/30) Hyperbolic Matrix(367,66,506,91) (-2/11,-3/17) -> (21/29,8/11) Hyperbolic Matrix(137,24,782,137) (-3/17,-4/23) -> (4/23,3/17) Hyperbolic Matrix(47,8,276,47) (-4/23,-1/6) -> (1/6,4/23) Hyperbolic Matrix(1425,226,2024,321) (-4/25,-3/19) -> (19/27,50/71) Hyperbolic Matrix(689,108,874,137) (-3/19,-2/13) -> (26/33,15/19) Hyperbolic Matrix(1795,274,2116,323) (-2/13,-7/46) -> (39/46,28/33) Hyperbolic Matrix(1793,272,2116,321) (-7/46,-5/33) -> (11/13,39/46) Hyperbolic Matrix(229,32,322,45) (-1/7,-2/15) -> (22/31,5/7) Hyperbolic Matrix(91,12,690,91) (-2/15,-3/23) -> (3/23,2/15) Hyperbolic Matrix(47,6,368,47) (-3/23,-1/8) -> (1/8,3/23) Hyperbolic Matrix(229,28,368,45) (-1/8,-1/9) -> (23/37,5/8) Hyperbolic Matrix(323,30,506,47) (-1/10,0/1) -> (30/47,23/36) Hyperbolic Matrix(137,-14,460,-47) (0/1,1/9) -> (11/37,14/47) Hyperbolic Matrix(137,-20,322,-47) (1/7,2/13) -> (14/33,3/7) Hyperbolic Matrix(1471,-236,2300,-369) (4/25,1/6) -> (55/86,16/25) Hyperbolic Matrix(413,-78,736,-139) (3/16,1/5) -> (23/41,9/16) Hyperbolic Matrix(137,-28,230,-47) (1/5,4/19) -> (16/27,3/5) Hyperbolic Matrix(829,-176,2162,-459) (7/33,3/14) -> (23/60,5/13) Hyperbolic Matrix(2161,-484,3496,-783) (2/9,9/40) -> (89/144,34/55) Hyperbolic Matrix(3265,-736,5106,-1151) (9/40,7/31) -> (39/61,55/86) Hyperbolic Matrix(323,-74,598,-137) (5/22,3/13) -> (7/13,13/24) Hyperbolic Matrix(413,-96,598,-139) (3/13,4/17) -> (20/29,9/13) Hyperbolic Matrix(599,-142,966,-229) (4/17,1/4) -> (31/50,18/29) Hyperbolic Matrix(5657,-1516,7728,-2071) (15/56,11/41) -> (71/97,41/56) Hyperbolic Matrix(2115,-568,3772,-1013) (11/41,7/26) -> (37/66,23/41) Hyperbolic Matrix(1839,-508,2668,-737) (8/29,13/47) -> (31/45,20/29) Hyperbolic Matrix(1611,-446,3818,-1057) (13/47,5/18) -> (27/64,19/45) Hyperbolic Matrix(4463,-1248,7728,-2161) (19/68,7/25) -> (41/71,67/116) Hyperbolic Matrix(413,-116,1150,-323) (7/25,2/7) -> (14/39,9/25) Hyperbolic Matrix(1011,-298,1564,-461) (5/17,13/44) -> (31/48,11/17) Hyperbolic Matrix(6209,-1844,8832,-2623) (19/64,11/37) -> (71/101,45/64) Hyperbolic Matrix(459,-142,598,-185) (4/13,5/16) -> (23/30,10/13) Hyperbolic Matrix(553,-174,874,-275) (5/16,1/3) -> (31/49,19/30) Hyperbolic Matrix(1103,-390,1564,-553) (6/17,11/31) -> (43/61,12/17) Hyperbolic Matrix(3771,-1340,4922,-1749) (11/31,16/45) -> (36/47,59/77) Hyperbolic Matrix(1289,-462,1794,-643) (5/14,14/39) -> (28/39,23/32) Hyperbolic Matrix(1931,-696,2300,-829) (9/25,22/61) -> (26/31,21/25) Hyperbolic Matrix(599,-220,874,-321) (11/30,7/19) -> (13/19,11/16) Hyperbolic Matrix(231,-86,368,-137) (7/19,3/8) -> (5/8,17/27) Hyperbolic Matrix(737,-280,966,-367) (11/29,8/21) -> (16/21,13/17) Hyperbolic Matrix(875,-334,1564,-597) (8/21,13/34) -> (19/34,14/25) Hyperbolic Matrix(321,-124,598,-231) (5/13,12/31) -> (8/15,7/13) Hyperbolic Matrix(183,-74,230,-93) (2/5,9/22) -> (19/24,4/5) Hyperbolic Matrix(323,-134,552,-229) (7/17,5/12) -> (7/12,17/29) Hyperbolic Matrix(1105,-462,1978,-827) (5/12,18/43) -> (24/43,19/34) Hyperbolic Matrix(5567,-2352,7728,-3265) (19/45,30/71) -> (18/25,67/93) Hyperbolic Matrix(1289,-546,1518,-643) (11/26,14/33) -> (28/33,17/20) Hyperbolic Matrix(597,-262,736,-323) (7/16,11/25) -> (17/21,13/16) Hyperbolic Matrix(967,-426,1564,-689) (11/25,4/9) -> (34/55,13/21) Hyperbolic Matrix(461,-212,598,-275) (5/11,6/13) -> (10/13,27/35) Hyperbolic Matrix(367,-170,598,-277) (6/13,1/2) -> (27/44,8/13) Hyperbolic Matrix(505,-268,782,-415) (1/2,8/15) -> (20/31,31/48) Hyperbolic Matrix(1243,-674,1610,-873) (13/24,6/11) -> (44/57,17/22) Hyperbolic Matrix(643,-358,828,-461) (5/9,24/43) -> (38/49,7/9) Hyperbolic Matrix(275,-158,322,-185) (4/7,15/26) -> (17/20,6/7) Hyperbolic Matrix(2761,-1596,3818,-2207) (26/45,11/19) -> (47/65,34/47) Hyperbolic Matrix(1563,-910,2530,-1473) (25/43,7/12) -> (21/34,55/89) Hyperbolic Matrix(1425,-844,2254,-1335) (13/22,16/27) -> (12/19,43/68) Hyperbolic Matrix(2853,-1750,4048,-2483) (19/31,27/44) -> (31/44,43/61) Hyperbolic Matrix(1703,-1050,2162,-1333) (8/13,29/47) -> (37/47,26/33) Hyperbolic Matrix(12695,-7846,16376,-10121) (55/89,89/144) -> (31/40,69/89) Hyperbolic Matrix(1013,-628,1334,-827) (13/21,31/50) -> (3/4,19/25) Hyperbolic Matrix(827,-530,1150,-737) (16/25,9/14) -> (23/32,18/25) Hyperbolic Matrix(2851,-1838,4140,-2669) (29/45,20/31) -> (42/61,31/45) Hyperbolic Matrix(691,-472,874,-597) (2/3,13/19) -> (15/19,34/43) Hyperbolic Matrix(2715,-1868,3542,-2437) (11/16,42/61) -> (82/107,23/30) Hyperbolic Matrix(413,-290,460,-323) (7/10,26/37) -> (8/9,9/10) Hyperbolic Matrix(1655,-1198,2162,-1565) (34/47,21/29) -> (13/17,36/47) Hyperbolic Matrix(965,-706,1196,-875) (19/26,30/41) -> (4/5,21/26) Hyperbolic Matrix(1195,-926,1426,-1105) (24/31,31/40) -> (5/6,26/31) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-44,1) Matrix(323,290,-460,-413) -> Matrix(157,-8,2414,-123) Matrix(139,122,368,323) -> Matrix(77,-4,-712,37) Matrix(321,280,368,321) -> Matrix(229,-12,-4370,229) Matrix(599,520,690,599) -> Matrix(417,-22,-7904,417) Matrix(93,80,322,277) -> Matrix(113,-6,-772,41) Matrix(185,158,-322,-275) -> Matrix(37,-2,500,-27) Matrix(185,156,874,737) -> Matrix(183,-10,-860,47) Matrix(599,504,2024,1703) -> Matrix(73,-4,-456,25) Matrix(829,696,-2300,-1931) -> Matrix(73,-4,566,-31) Matrix(229,190,276,229) -> Matrix(145,-8,-2628,145) Matrix(645,532,782,645) -> Matrix(395,-22,-7092,395) Matrix(139,114,506,415) -> Matrix(35,-2,-192,11) Matrix(321,262,506,413) -> Matrix(107,-6,-1480,83) Matrix(323,262,-736,-597) -> Matrix(71,-4,728,-41) Matrix(93,74,-230,-183) -> Matrix(35,-2,298,-17) Matrix(137,108,874,689) -> Matrix(173,-10,-640,37) Matrix(1333,1050,-2162,-1703) -> Matrix(241,-14,3288,-191) Matrix(505,396,644,505) -> Matrix(273,-16,-4658,273) Matrix(323,252,414,323) -> Matrix(169,-10,-2856,169) Matrix(1335,1036,-3496,-2713) -> Matrix(67,-4,486,-29) Matrix(1841,1426,-5106,-3955) -> Matrix(33,-2,248,-15) Matrix(1011,782,1426,1103) -> Matrix(33,-2,-478,29) Matrix(275,212,-598,-461) -> Matrix(33,-2,380,-23) Matrix(185,142,-598,-459) -> Matrix(101,-6,724,-43) Matrix(367,280,-966,-737) -> Matrix(33,-2,380,-23) Matrix(137,102,184,137) -> Matrix(65,-4,-1056,65) Matrix(645,476,874,645) -> Matrix(287,-18,-4576,287) Matrix(367,270,874,643) -> Matrix(95,-6,-934,59) Matrix(2529,1852,3956,2897) -> Matrix(125,-8,-1828,117) Matrix(2071,1516,-7728,-5657) -> Matrix(435,-28,2812,-181) Matrix(1657,1212,-3772,-2759) -> Matrix(61,-4,656,-43) Matrix(277,202,506,369) -> Matrix(31,-2,-356,23) Matrix(91,66,506,367) -> Matrix(33,-2,-148,9) Matrix(829,600,-2668,-1931) -> Matrix(317,-20,2330,-147) Matrix(2207,1596,-3818,-2761) -> Matrix(221,-14,2510,-159) Matrix(643,464,1656,1195) -> Matrix(125,-8,-1078,69) Matrix(3957,2852,6256,4509) -> Matrix(377,-24,-5168,329) Matrix(3265,2352,-7728,-5567) -> Matrix(313,-20,3490,-223) Matrix(737,530,-1150,-827) -> Matrix(31,-2,512,-33) Matrix(45,32,322,229) -> Matrix(91,-6,-288,19) Matrix(1103,782,1426,1011) -> Matrix(29,-2,-478,33) Matrix(461,326,782,553) -> Matrix(29,-2,-362,25) Matrix(553,390,-1564,-1103) -> Matrix(63,-4,520,-33) Matrix(7129,5022,10120,7129) -> Matrix(61,-4,-930,61) Matrix(11501,8100,16330,11501) -> Matrix(31,-2,-480,31) Matrix(321,226,2024,1425) -> Matrix(63,-4,-236,15) Matrix(3359,2362,4646,3267) -> Matrix(343,-22,-5410,347) Matrix(2623,1844,-8832,-6209) -> Matrix(435,-28,2812,-181) Matrix(781,548,2162,1517) -> Matrix(153,-10,-1178,77) Matrix(321,224,460,321) -> Matrix(121,-8,-1830,121) Matrix(415,288,598,415) -> Matrix(149,-10,-2220,149) Matrix(139,96,-598,-413) -> Matrix(89,-6,460,-31) Matrix(321,220,-874,-599) -> Matrix(27,-2,230,-17) Matrix(91,60,138,91) -> Matrix(29,-2,-420,29) Matrix(599,390,920,599) -> Matrix(167,-12,-2324,167) Matrix(413,268,920,597) -> Matrix(55,-4,-536,39) Matrix(461,298,-1564,-1011) -> Matrix(55,-4,344,-25) Matrix(1151,742,-4922,-3173) -> Matrix(457,-34,2406,-179) Matrix(1013,652,1288,829) -> Matrix(105,-8,-1798,137) Matrix(505,324,-1794,-1151) -> Matrix(19,-2,124,-13) Matrix(369,236,-2300,-1471) -> Matrix(57,-4,214,-15) Matrix(2897,1852,3956,2529) -> Matrix(117,-8,-1828,125) Matrix(645,412,2162,1381) -> Matrix(143,-10,-958,67) Matrix(1655,1056,4324,2759) -> Matrix(169,-12,-1366,97) Matrix(413,262,506,321) -> Matrix(83,-6,-1480,107) Matrix(275,174,-874,-553) -> Matrix(27,-2,230,-17) Matrix(137,86,-368,-231) -> Matrix(53,-4,464,-35) Matrix(45,28,368,229) -> Matrix(51,-4,-140,11) Matrix(737,458,1334,829) -> Matrix(25,-2,-312,25) Matrix(229,142,-966,-599) -> Matrix(21,-2,116,-11) Matrix(689,426,-1564,-967) -> Matrix(1,0,-4,1) Matrix(4829,2982,7820,4829) -> Matrix(113,-8,-1596,113) Matrix(11501,7100,18630,11501) -> Matrix(419,-30,-5852,419) Matrix(1565,966,4324,2669) -> Matrix(167,-12,-1322,95) Matrix(2163,1334,3358,2071) -> Matrix(137,-10,-1822,133) Matrix(277,170,-598,-367) -> Matrix(27,-2,284,-21) Matrix(1195,732,2852,1747) -> Matrix(53,-4,-490,37) Matrix(461,282,1656,1013) -> Matrix(107,-8,-682,51) Matrix(505,308,828,505) -> Matrix(105,-8,-1378,105) Matrix(139,84,230,139) -> Matrix(25,-2,-312,25) Matrix(47,28,-230,-137) -> Matrix(27,-2,122,-9) Matrix(553,326,782,461) -> Matrix(25,-2,-362,29) Matrix(229,134,-552,-323) -> Matrix(49,-4,478,-39) Matrix(873,508,-1978,-1151) -> Matrix(23,-2,242,-21) Matrix(1105,642,2852,1657) -> Matrix(51,-4,-446,35) Matrix(231,134,874,507) -> Matrix(73,-6,-450,37) Matrix(2071,1198,2944,1703) -> Matrix(47,-4,-740,63) Matrix(2161,1248,-7728,-4463) -> Matrix(217,-20,1378,-127) Matrix(1933,1116,2392,1381) -> Matrix(85,-8,-1498,141) Matrix(229,132,-1518,-875) -> Matrix(13,-2,46,-7) Matrix(183,104,322,183) -> Matrix(25,-2,-312,25) Matrix(415,234,736,415) -> Matrix(47,-4,-552,47) Matrix(139,78,-736,-413) -> Matrix(47,-4,200,-17) Matrix(597,334,-1564,-875) -> Matrix(1,0,-4,1) Matrix(829,458,1334,737) -> Matrix(25,-2,-312,25) Matrix(323,178,920,507) -> Matrix(49,-4,-404,33) Matrix(369,202,506,277) -> Matrix(23,-2,-356,31) Matrix(137,74,-598,-323) -> Matrix(21,-2,116,-11) Matrix(231,124,-598,-321) -> Matrix(23,-2,196,-17) Matrix(277,130,-782,-367) -> Matrix(19,-2,162,-17) Matrix(367,168,-1610,-737) -> Matrix(65,-6,336,-31) Matrix(137,62,506,229) -> Matrix(21,-2,-136,13) Matrix(597,268,920,413) -> Matrix(39,-4,-536,55) Matrix(505,226,1334,597) -> Matrix(19,-2,-180,19) Matrix(185,82,-828,-367) -> Matrix(43,-4,226,-21) Matrix(3081,1354,5336,2345) -> Matrix(43,-4,-462,43) Matrix(321,140,736,321) -> Matrix(41,-4,-420,41) Matrix(139,60,322,139) -> Matrix(19,-2,-180,19) Matrix(47,20,-322,-137) -> Matrix(17,-2,60,-7) Matrix(2991,1264,5336,2255) -> Matrix(45,-4,-506,45) Matrix(21345,9016,29624,12513) -> Matrix(707,-64,-11080,1003) Matrix(16007,6760,22218,9383) -> Matrix(679,-62,-10634,971) Matrix(1057,446,-3818,-1611) -> Matrix(149,-14,926,-87) Matrix(643,270,874,367) -> Matrix(59,-6,-934,95) Matrix(1747,732,2852,1195) -> Matrix(37,-4,-490,53) Matrix(967,404,-2530,-1057) -> Matrix(21,-2,158,-15) Matrix(1243,514,2116,875) -> Matrix(153,-16,-1922,201) Matrix(1241,512,2116,873) -> Matrix(151,-16,-1878,199) Matrix(229,94,782,321) -> Matrix(19,-2,-142,15) Matrix(829,338,-2254,-919) -> Matrix(15,-2,128,-17) Matrix(91,36,230,91) -> Matrix(19,-2,-180,19) Matrix(323,126,828,323) -> Matrix(71,-8,-630,71) Matrix(1195,464,1656,643) -> Matrix(69,-8,-1078,125) Matrix(1657,642,2852,1105) -> Matrix(35,-4,-446,51) Matrix(1195,462,-4048,-1565) -> Matrix(1,0,-2,1) Matrix(459,176,-2162,-829) -> Matrix(117,-14,560,-67) Matrix(2759,1056,4324,1655) -> Matrix(97,-12,-1366,169) Matrix(7129,2728,18630,7129) -> Matrix(241,-30,-1936,241) Matrix(2991,1144,7820,2991) -> Matrix(63,-8,-496,63) Matrix(3681,1406,-16376,-6255) -> Matrix(59,-8,332,-45) Matrix(321,122,-1334,-507) -> Matrix(25,-2,138,-11) Matrix(597,226,1334,505) -> Matrix(19,-2,-180,19) Matrix(323,122,368,139) -> Matrix(37,-4,-712,77) Matrix(1335,494,2116,783) -> Matrix(205,-24,-2776,325) Matrix(1333,492,2116,781) -> Matrix(203,-24,-2732,323) Matrix(1747,642,6256,2299) -> Matrix(199,-24,-1252,151) Matrix(93,34,506,185) -> Matrix(49,-6,-204,25) Matrix(2669,966,4324,1565) -> Matrix(95,-12,-1322,167) Matrix(459,166,506,183) -> Matrix(47,-6,-932,119) Matrix(1059,382,3956,1427) -> Matrix(59,-8,-376,51) Matrix(323,116,-1150,-413) -> Matrix(11,-2,72,-13) Matrix(1287,458,3358,1195) -> Matrix(87,-10,-722,83) Matrix(1289,458,-4140,-1471) -> Matrix(171,-20,1274,-149) Matrix(507,178,920,323) -> Matrix(33,-4,-404,49) Matrix(321,112,920,321) -> Matrix(97,-12,-784,97) Matrix(47,16,138,47) -> Matrix(15,-2,-112,15) Matrix(183,58,-874,-277) -> Matrix(15,-2,68,-9) Matrix(827,258,-3542,-1105) -> Matrix(107,-14,558,-73) Matrix(183,56,598,183) -> Matrix(71,-10,-504,71) Matrix(139,42,460,139) -> Matrix(55,-8,-378,55) Matrix(47,14,-460,-137) -> Matrix(53,-8,126,-19) Matrix(13387,3978,19044,5659) -> Matrix(469,-72,-7276,1117) Matrix(13385,3976,19044,5657) -> Matrix(467,-72,-7232,1115) Matrix(1241,368,2944,873) -> Matrix(25,-4,-256,41) Matrix(1703,504,2024,599) -> Matrix(25,-4,-456,73) Matrix(4829,1428,16330,4829) -> Matrix(13,-2,-84,13) Matrix(2991,884,10120,2991) -> Matrix(27,-4,-182,27) Matrix(321,94,782,229) -> Matrix(15,-2,-142,19) Matrix(323,94,1426,415) -> Matrix(15,-2,-82,11) Matrix(277,80,322,93) -> Matrix(41,-6,-772,113) Matrix(1519,430,2116,599) -> Matrix(261,-40,-4052,621) Matrix(1517,428,2116,597) -> Matrix(259,-40,-4008,619) Matrix(12835,3588,22218,6211) -> Matrix(393,-62,-4342,685) Matrix(17111,4782,29624,8279) -> Matrix(405,-64,-4436,701) Matrix(3129,874,3956,1105) -> Matrix(25,-4,-406,65) Matrix(1013,282,1656,461) -> Matrix(51,-8,-682,107) Matrix(1379,382,4646,1287) -> Matrix(137,-22,-878,141) Matrix(507,140,-2162,-597) -> Matrix(135,-22,718,-117) Matrix(415,114,506,139) -> Matrix(11,-2,-192,35) Matrix(229,62,506,137) -> Matrix(13,-2,-136,21) Matrix(231,62,-1196,-321) -> Matrix(53,-8,232,-35) Matrix(13939,3738,19044,5107) -> Matrix(365,-56,-5664,869) Matrix(13937,3736,19044,5105) -> Matrix(363,-56,-5620,867) Matrix(1427,382,3956,1059) -> Matrix(51,-8,-376,59) Matrix(507,134,874,231) -> Matrix(37,-6,-450,73) Matrix(229,60,874,229) -> Matrix(109,-18,-660,109) Matrix(47,12,184,47) -> Matrix(23,-4,-132,23) Matrix(1611,386,2116,507) -> Matrix(265,-48,-4378,793) Matrix(1609,384,2116,505) -> Matrix(263,-48,-4334,791) Matrix(25945,6064,33856,7913) -> Matrix(1681,-320,-28162,5361) Matrix(25943,6062,33856,7911) -> Matrix(1679,-320,-28118,5359) Matrix(6533,1492,8464,1933) -> Matrix(169,-32,-2836,537) Matrix(6531,1490,8464,1931) -> Matrix(167,-32,-2792,535) Matrix(415,94,1426,323) -> Matrix(11,-2,-82,15) Matrix(231,52,-1426,-321) -> Matrix(13,-2,46,-7) Matrix(14767,3318,19044,4279) -> Matrix(177,-32,-2926,529) Matrix(14765,3316,19044,4277) -> Matrix(175,-32,-2882,527) Matrix(91,20,414,91) -> Matrix(51,-10,-260,51) Matrix(139,30,644,139) -> Matrix(79,-16,-390,79) Matrix(459,98,1288,275) -> Matrix(39,-8,-346,71) Matrix(737,156,874,185) -> Matrix(47,-10,-860,183) Matrix(2851,596,3956,827) -> Matrix(23,-4,-362,63) Matrix(1011,194,2392,459) -> Matrix(35,-8,-398,91) Matrix(185,34,506,93) -> Matrix(25,-6,-204,49) Matrix(367,66,506,91) -> Matrix(9,-2,-148,33) Matrix(137,24,782,137) -> Matrix(89,-22,-360,89) Matrix(47,8,276,47) -> Matrix(31,-8,-120,31) Matrix(1425,226,2024,321) -> Matrix(15,-4,-236,63) Matrix(689,108,874,137) -> Matrix(37,-10,-640,173) Matrix(1795,274,2116,323) -> Matrix(225,-64,-4166,1185) Matrix(1793,272,2116,321) -> Matrix(223,-64,-4122,1183) Matrix(229,32,322,45) -> Matrix(19,-6,-288,91) Matrix(91,12,690,91) -> Matrix(67,-22,-204,67) Matrix(47,6,368,47) -> Matrix(35,-12,-102,35) Matrix(229,28,368,45) -> Matrix(11,-4,-140,51) Matrix(323,30,506,47) -> Matrix(13,-6,-184,85) Matrix(137,-14,460,-47) -> Matrix(19,8,-126,-53) Matrix(137,-20,322,-47) -> Matrix(7,2,-60,-17) Matrix(1471,-236,2300,-369) -> Matrix(15,4,-214,-57) Matrix(413,-78,736,-139) -> Matrix(17,4,-200,-47) Matrix(137,-28,230,-47) -> Matrix(9,2,-122,-27) Matrix(829,-176,2162,-459) -> Matrix(67,14,-560,-117) Matrix(2161,-484,3496,-783) -> Matrix(21,4,-310,-59) Matrix(3265,-736,5106,-1151) -> Matrix(11,2,-160,-29) Matrix(323,-74,598,-137) -> Matrix(11,2,-116,-21) Matrix(413,-96,598,-139) -> Matrix(31,6,-460,-89) Matrix(599,-142,966,-229) -> Matrix(11,2,-116,-21) Matrix(5657,-1516,7728,-2071) -> Matrix(181,28,-2812,-435) Matrix(2115,-568,3772,-1013) -> Matrix(27,4,-304,-45) Matrix(1839,-508,2668,-737) -> Matrix(123,20,-1802,-293) Matrix(1611,-446,3818,-1057) -> Matrix(87,14,-926,-149) Matrix(4463,-1248,7728,-2161) -> Matrix(127,20,-1378,-217) Matrix(413,-116,1150,-323) -> Matrix(13,2,-72,-11) Matrix(1011,-298,1564,-461) -> Matrix(25,4,-344,-55) Matrix(6209,-1844,8832,-2623) -> Matrix(181,28,-2812,-435) Matrix(459,-142,598,-185) -> Matrix(43,6,-724,-101) Matrix(553,-174,874,-275) -> Matrix(17,2,-230,-27) Matrix(1103,-390,1564,-553) -> Matrix(33,4,-520,-63) Matrix(3771,-1340,4922,-1749) -> Matrix(291,34,-4870,-569) Matrix(1289,-462,1794,-643) -> Matrix(25,2,-388,-31) Matrix(1931,-696,2300,-829) -> Matrix(31,4,-566,-73) Matrix(599,-220,874,-321) -> Matrix(17,2,-230,-27) Matrix(231,-86,368,-137) -> Matrix(35,4,-464,-53) Matrix(737,-280,966,-367) -> Matrix(23,2,-380,-33) Matrix(875,-334,1564,-597) -> Matrix(1,0,-4,1) Matrix(321,-124,598,-231) -> Matrix(17,2,-196,-23) Matrix(183,-74,230,-93) -> Matrix(17,2,-298,-35) Matrix(323,-134,552,-229) -> Matrix(39,4,-478,-49) Matrix(1105,-462,1978,-827) -> Matrix(21,2,-242,-23) Matrix(5567,-2352,7728,-3265) -> Matrix(223,20,-3490,-313) Matrix(1289,-546,1518,-643) -> Matrix(31,2,-574,-37) Matrix(597,-262,736,-323) -> Matrix(41,4,-728,-71) Matrix(967,-426,1564,-689) -> Matrix(1,0,-4,1) Matrix(461,-212,598,-275) -> Matrix(23,2,-380,-33) Matrix(367,-170,598,-277) -> Matrix(21,2,-284,-27) Matrix(505,-268,782,-415) -> Matrix(25,2,-338,-27) Matrix(1243,-674,1610,-873) -> Matrix(67,6,-1128,-101) Matrix(643,-358,828,-461) -> Matrix(45,4,-754,-67) Matrix(275,-158,322,-185) -> Matrix(27,2,-500,-37) Matrix(2761,-1596,3818,-2207) -> Matrix(159,14,-2510,-221) Matrix(1563,-910,2530,-1473) -> Matrix(23,2,-334,-29) Matrix(1425,-844,2254,-1335) -> Matrix(29,2,-392,-27) Matrix(2853,-1750,4048,-2483) -> Matrix(1,0,-2,1) Matrix(1703,-1050,2162,-1333) -> Matrix(191,14,-3288,-241) Matrix(12695,-7846,16376,-10121) -> Matrix(117,8,-1916,-131) Matrix(1013,-628,1334,-827) -> Matrix(19,2,-314,-33) Matrix(827,-530,1150,-737) -> Matrix(33,2,-512,-31) Matrix(2851,-1838,4140,-2669) -> Matrix(269,20,-3914,-291) Matrix(691,-472,874,-597) -> Matrix(29,2,-508,-35) Matrix(2715,-1868,3542,-2437) -> Matrix(201,14,-3374,-235) Matrix(413,-290,460,-323) -> Matrix(123,8,-2414,-157) Matrix(1655,-1198,2162,-1565) -> Matrix(349,22,-5822,-367) Matrix(965,-706,1196,-875) -> Matrix(123,8,-2168,-141) Matrix(1195,-926,1426,-1105) -> Matrix(31,2,-574,-37) 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): 132 Degree of the the map X: 132 Degree of the the map Y: 264 ----------------------------------------------------------------------- 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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): 792 Minimal number of generators: 133 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: 44 Genus: 45 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/9 1/8 3/23 2/15 1/7 2/13 3/19 1/6 4/23 3/17 2/11 3/16 1/5 3/14 5/23 5/22 1/4 6/23 5/18 34/115 3/10 7/23 1/3 8/23 7/20 8/21 44/115 9/23 5/12 10/23 1/2 93/161 27/46 29/46 97/138 33/46 101/138 35/46 141/184 71/92 107/138 39/46 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/0 1/9 -7/18 1/8 -6/17 -1/3 3/23 -1/3 2/15 -11/34 1/7 -3/10 2/13 -9/32 3/19 -1/4 4/25 -1/4 1/6 -4/15 -1/4 4/23 -1/4 3/17 -1/4 2/11 -1/4 3/16 -1/4 -2/9 1/5 -3/14 4/19 -3/14 7/33 -13/62 3/14 -8/39 -1/5 5/23 -1/5 2/9 -5/26 9/40 -2/11 -1/6 7/31 -3/14 5/22 -1/5 -4/21 3/13 -1/6 4/17 -3/16 1/4 -2/11 -1/6 6/23 -1/6 5/19 -1/6 4/15 -7/44 15/56 -7/45 -2/13 11/41 -7/46 7/26 -1/6 0/1 3/11 -1/6 8/29 -1/6 13/47 -21/130 5/18 -4/25 -3/19 12/43 -7/44 19/68 -22/139 -3/19 7/25 -5/32 2/7 -3/20 9/31 -5/36 7/24 -2/13 -1/7 5/17 -1/6 13/44 -2/13 -1/7 34/115 -1/7 21/71 -1/6 8/27 -1/6 19/64 -7/45 -2/13 11/37 -11/72 14/47 -19/126 3/10 -4/27 -1/7 7/23 -1/7 4/13 -5/36 5/16 -2/15 -1/8 1/3 -1/8 8/23 -1/8 7/20 -1/8 -6/49 6/17 -1/8 11/31 -9/76 16/45 -13/112 5/14 -1/9 0/1 14/39 -1/4 9/25 -1/8 22/61 -5/36 13/36 -2/15 -3/23 17/47 -13/102 4/11 -1/8 11/30 -1/8 -4/33 7/19 -5/42 3/8 -2/17 -1/9 14/37 -5/48 11/29 -1/10 8/21 -1/6 13/34 -4/31 -1/8 44/115 -1/8 31/81 -1/8 18/47 -11/90 23/60 -10/83 -3/25 5/13 -3/26 12/31 -7/60 19/49 -5/44 7/18 -4/35 -1/9 9/23 -1/9 2/5 -1/10 9/22 -1/9 -4/37 7/17 -3/28 5/12 -2/19 -1/10 18/43 -1/8 13/31 -5/48 8/19 -1/10 27/64 -2/21 -5/53 19/45 -7/76 30/71 -5/56 11/26 -1/12 0/1 14/33 -1/4 3/7 -1/10 10/23 -1/10 7/16 -1/10 -2/21 11/25 -1/12 4/9 -1/12 13/29 -1/10 9/20 -1/10 -2/21 5/11 -1/10 6/13 -1/12 1/2 -1/11 0/1 8/15 -1/8 7/13 -1/10 13/24 -1/11 -2/23 6/11 -1/12 11/20 -2/23 -1/12 16/29 -1/12 5/9 -1/10 24/43 -5/58 19/34 -4/47 -1/12 14/25 -1/10 37/66 -4/45 -3/34 23/41 -5/58 9/16 -2/23 -1/12 13/23 -1/12 4/7 -1/12 15/26 -1/10 0/1 41/71 -5/54 67/116 -14/153 -1/11 93/161 -1/11 26/45 -7/78 11/19 -1/12 18/31 -5/62 25/43 -1/14 7/12 -1/12 -2/25 17/29 -5/62 27/46 -2/25 10/17 -3/38 13/22 -4/51 -1/13 16/27 -1/12 3/5 -1/12 14/23 -1/13 11/18 -1/13 -4/53 30/49 -5/66 19/31 -7/94 27/44 -1/13 -2/27 8/13 -3/40 29/47 -11/152 50/81 -1/14 71/115 -1/14 21/34 -1/14 -4/57 55/89 -5/72 89/144 -2/29 -3/44 34/55 -1/16 13/21 -1/16 31/50 -1/10 0/1 18/29 -1/12 23/37 -5/62 5/8 -1/13 -2/27 17/27 -7/94 29/46 -2/27 12/19 -5/68 43/68 -14/191 -3/41 31/49 -1/14 19/30 -4/55 -1/14 7/11 -1/14 30/47 -13/184 23/36 -3/43 -2/29 39/61 -5/74 55/86 -1/14 0/1 16/25 -1/14 9/14 -1/13 0/1 29/45 -13/174 20/31 -9/122 31/48 -2/27 -3/41 11/17 -1/14 13/20 -6/83 -1/14 15/23 -1/14 2/3 -1/14 13/19 -1/16 11/16 -1/14 -2/29 42/61 -19/276 31/45 -17/248 20/29 -3/44 9/13 -5/74 16/23 -1/15 7/10 -1/15 -4/61 26/37 -11/170 97/138 -2/31 71/101 -25/388 45/64 -2/31 -7/109 19/27 -1/16 50/71 -1/16 81/115 -1/15 31/44 -1/15 -2/31 43/61 -7/108 12/17 -1/16 17/24 -1/15 -2/31 22/31 -5/74 5/7 -3/46 33/46 -2/31 28/39 -17/264 23/32 -2/31 -7/109 18/25 -5/78 67/93 -41/642 116/161 -3/47 49/68 -3/47 -22/345 31/43 -7/110 13/18 -3/47 -4/63 47/65 -9/142 34/47 -21/332 21/29 -1/16 8/11 -1/16 19/26 -1/16 0/1 30/41 -7/108 101/138 -2/31 71/97 -21/326 41/56 -2/31 -7/109 11/15 -7/110 14/19 -1/16 17/23 -1/16 3/4 -1/16 -2/33 19/25 -13/214 35/46 -2/33 16/21 -11/182 13/17 -3/50 36/47 -25/418 59/77 -35/586 141/184 -4/67 82/107 -45/754 23/30 -4/67 -5/84 10/13 -1/16 27/35 -3/50 71/92 -4/67 44/57 -5/84 17/22 -4/67 -1/17 24/31 -3/52 31/40 -1/16 -2/33 69/89 -9/148 107/138 -2/33 38/49 -7/116 7/9 -5/84 18/23 -1/17 11/14 -1/17 -8/137 37/47 -27/464 26/33 -13/224 15/19 -3/52 34/43 -1/18 19/24 -1/17 -6/103 4/5 -3/52 21/26 -5/88 -8/141 17/21 -7/124 13/16 -2/35 -1/18 9/11 -1/18 14/17 -1/18 19/23 -1/18 5/6 -1/18 -4/73 26/31 -11/202 21/25 -1/18 16/19 -1/18 11/13 -9/166 39/46 -2/37 28/33 -23/426 17/20 -2/37 -7/130 6/7 -3/56 13/15 -11/208 20/23 -1/19 7/8 -1/19 -6/115 8/9 -7/136 9/10 -3/59 -4/79 1/1 -1/22 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(137,-14,460,-47) (0/1,1/9) -> (11/37,14/47) Hyperbolic Matrix(139,-17,368,-45) (1/9,1/8) -> (3/8,14/37) Hyperbolic Matrix(321,-41,368,-47) (1/8,3/23) -> (20/23,7/8) Hyperbolic Matrix(599,-79,690,-91) (3/23,2/15) -> (13/15,20/23) Hyperbolic Matrix(93,-13,322,-45) (2/15,1/7) -> (2/7,9/31) Hyperbolic Matrix(137,-20,322,-47) (1/7,2/13) -> (14/33,3/7) Hyperbolic Matrix(185,-29,874,-137) (2/13,3/19) -> (4/19,7/33) Hyperbolic Matrix(599,-95,2024,-321) (3/19,4/25) -> (21/71,8/27) Hyperbolic Matrix(1471,-236,2300,-369) (4/25,1/6) -> (55/86,16/25) Hyperbolic Matrix(229,-39,276,-47) (1/6,4/23) -> (19/23,5/6) Hyperbolic Matrix(645,-113,782,-137) (4/23,3/17) -> (14/17,19/23) Hyperbolic Matrix(139,-25,506,-91) (3/17,2/11) -> (3/11,8/29) Hyperbolic Matrix(321,-59,506,-93) (2/11,3/16) -> (19/30,7/11) Hyperbolic Matrix(413,-78,736,-139) (3/16,1/5) -> (23/41,9/16) Hyperbolic Matrix(137,-28,230,-47) (1/5,4/19) -> (16/27,3/5) Hyperbolic Matrix(829,-176,2162,-459) (7/33,3/14) -> (23/60,5/13) Hyperbolic Matrix(505,-109,644,-139) (3/14,5/23) -> (18/23,11/14) Hyperbolic Matrix(323,-71,414,-91) (5/23,2/9) -> (7/9,18/23) Hyperbolic Matrix(2161,-484,3496,-783) (2/9,9/40) -> (89/144,34/55) Hyperbolic Matrix(3265,-736,5106,-1151) (9/40,7/31) -> (39/61,55/86) Hyperbolic Matrix(1011,-229,1426,-323) (7/31,5/22) -> (17/24,22/31) Hyperbolic Matrix(323,-74,598,-137) (5/22,3/13) -> (7/13,13/24) Hyperbolic Matrix(413,-96,598,-139) (3/13,4/17) -> (20/29,9/13) Hyperbolic Matrix(599,-142,966,-229) (4/17,1/4) -> (31/50,18/29) Hyperbolic Matrix(137,-35,184,-47) (1/4,6/23) -> (17/23,3/4) Hyperbolic Matrix(645,-169,874,-229) (6/23,5/19) -> (14/19,17/23) Hyperbolic Matrix(367,-97,874,-231) (5/19,4/15) -> (13/31,8/19) Hyperbolic Matrix(2529,-677,3956,-1059) (4/15,15/56) -> (23/36,39/61) Hyperbolic Matrix(5657,-1516,7728,-2071) (15/56,11/41) -> (71/97,41/56) Hyperbolic Matrix(2115,-568,3772,-1013) (11/41,7/26) -> (37/66,23/41) Hyperbolic Matrix(277,-75,506,-137) (7/26,3/11) -> (6/11,11/20) Hyperbolic Matrix(1839,-508,2668,-737) (8/29,13/47) -> (31/45,20/29) Hyperbolic Matrix(1611,-446,3818,-1057) (13/47,5/18) -> (27/64,19/45) Hyperbolic Matrix(643,-179,1656,-461) (5/18,12/43) -> (19/49,7/18) Hyperbolic Matrix(3957,-1105,6256,-1747) (12/43,19/68) -> (43/68,31/49) Hyperbolic Matrix(4463,-1248,7728,-2161) (19/68,7/25) -> (41/71,67/116) Hyperbolic Matrix(413,-116,1150,-323) (7/25,2/7) -> (14/39,9/25) Hyperbolic Matrix(1103,-321,1426,-415) (9/31,7/24) -> (17/22,24/31) Hyperbolic Matrix(461,-135,782,-229) (7/24,5/17) -> (10/17,13/22) Hyperbolic Matrix(1011,-298,1564,-461) (5/17,13/44) -> (31/48,11/17) Hyperbolic Matrix(7129,-2107,10120,-2991) (13/44,34/115) -> (81/115,31/44) Hyperbolic Matrix(11501,-3401,16330,-4829) (34/115,21/71) -> (50/71,81/115) Hyperbolic Matrix(3359,-997,4646,-1379) (8/27,19/64) -> (13/18,47/65) Hyperbolic Matrix(6209,-1844,8832,-2623) (19/64,11/37) -> (71/101,45/64) Hyperbolic Matrix(781,-233,2162,-645) (14/47,3/10) -> (13/36,17/47) Hyperbolic Matrix(321,-97,460,-139) (3/10,7/23) -> (16/23,7/10) Hyperbolic Matrix(415,-127,598,-183) (7/23,4/13) -> (9/13,16/23) Hyperbolic Matrix(459,-142,598,-185) (4/13,5/16) -> (23/30,10/13) Hyperbolic Matrix(553,-174,874,-275) (5/16,1/3) -> (31/49,19/30) Hyperbolic Matrix(91,-31,138,-47) (1/3,8/23) -> (15/23,2/3) Hyperbolic Matrix(599,-209,920,-321) (8/23,7/20) -> (13/20,15/23) Hyperbolic Matrix(413,-145,920,-323) (7/20,6/17) -> (13/29,9/20) Hyperbolic Matrix(1103,-390,1564,-553) (6/17,11/31) -> (43/61,12/17) Hyperbolic Matrix(3771,-1340,4922,-1749) (11/31,16/45) -> (36/47,59/77) Hyperbolic Matrix(1013,-361,1288,-459) (16/45,5/14) -> (11/14,37/47) Hyperbolic Matrix(1289,-462,1794,-643) (5/14,14/39) -> (28/39,23/32) Hyperbolic Matrix(1931,-696,2300,-829) (9/25,22/61) -> (26/31,21/25) Hyperbolic Matrix(2897,-1045,3956,-1427) (22/61,13/36) -> (41/56,11/15) Hyperbolic Matrix(1655,-599,4324,-1565) (17/47,4/11) -> (31/81,18/47) Hyperbolic Matrix(413,-151,506,-185) (4/11,11/30) -> (13/16,9/11) Hyperbolic Matrix(599,-220,874,-321) (11/30,7/19) -> (13/19,11/16) Hyperbolic Matrix(231,-86,368,-137) (7/19,3/8) -> (5/8,17/27) Hyperbolic Matrix(737,-279,1334,-505) (14/37,11/29) -> (16/29,5/9) Hyperbolic Matrix(737,-280,966,-367) (11/29,8/21) -> (16/21,13/17) Hyperbolic Matrix(875,-334,1564,-597) (8/21,13/34) -> (19/34,14/25) Hyperbolic Matrix(4829,-1847,7820,-2991) (13/34,44/115) -> (71/115,21/34) Hyperbolic Matrix(11501,-4401,18630,-7129) (44/115,31/81) -> (50/81,71/115) Hyperbolic Matrix(2163,-829,3358,-1287) (18/47,23/60) -> (9/14,29/45) Hyperbolic Matrix(321,-124,598,-231) (5/13,12/31) -> (8/15,7/13) Hyperbolic Matrix(1195,-463,2852,-1105) (12/31,19/49) -> (18/43,13/31) Hyperbolic Matrix(505,-197,828,-323) (7/18,9/23) -> (14/23,11/18) Hyperbolic Matrix(139,-55,230,-91) (9/23,2/5) -> (3/5,14/23) Hyperbolic Matrix(183,-74,230,-93) (2/5,9/22) -> (19/24,4/5) Hyperbolic Matrix(553,-227,782,-321) (9/22,7/17) -> (12/17,17/24) Hyperbolic Matrix(323,-134,552,-229) (7/17,5/12) -> (7/12,17/29) Hyperbolic Matrix(1105,-462,1978,-827) (5/12,18/43) -> (24/43,19/34) Hyperbolic Matrix(2071,-873,2944,-1241) (8/19,27/64) -> (45/64,19/27) Hyperbolic Matrix(5567,-2352,7728,-3265) (19/45,30/71) -> (18/25,67/93) Hyperbolic Matrix(1933,-817,2392,-1011) (30/71,11/26) -> (21/26,17/21) Hyperbolic Matrix(1289,-546,1518,-643) (11/26,14/33) -> (28/33,17/20) Hyperbolic Matrix(183,-79,322,-139) (3/7,10/23) -> (13/23,4/7) Hyperbolic Matrix(415,-181,736,-321) (10/23,7/16) -> (9/16,13/23) Hyperbolic Matrix(597,-262,736,-323) (7/16,11/25) -> (17/21,13/16) Hyperbolic Matrix(967,-426,1564,-689) (11/25,4/9) -> (34/55,13/21) Hyperbolic Matrix(829,-371,1334,-597) (4/9,13/29) -> (18/29,23/37) Hyperbolic Matrix(369,-167,506,-229) (9/20,5/11) -> (8/11,19/26) Hyperbolic Matrix(461,-212,598,-275) (5/11,6/13) -> (10/13,27/35) Hyperbolic Matrix(367,-170,598,-277) (6/13,1/2) -> (27/44,8/13) Hyperbolic Matrix(505,-268,782,-415) (1/2,8/15) -> (20/31,31/48) Hyperbolic Matrix(1243,-674,1610,-873) (13/24,6/11) -> (44/57,17/22) Hyperbolic Matrix(597,-329,920,-507) (11/20,16/29) -> (11/17,13/20) Hyperbolic Matrix(643,-358,828,-461) (5/9,24/43) -> (38/49,7/9) Hyperbolic Matrix(3081,-1727,5336,-2991) (14/25,37/66) -> (15/26,41/71) Hyperbolic Matrix(275,-158,322,-185) (4/7,15/26) -> (17/20,6/7) Hyperbolic Matrix(21345,-12329,29624,-17111) (67/116,93/161) -> (116/161,49/68) Hyperbolic Matrix(16007,-9247,22218,-12835) (93/161,26/45) -> (67/93,116/161) Hyperbolic Matrix(2761,-1596,3818,-2207) (26/45,11/19) -> (47/65,34/47) Hyperbolic Matrix(643,-373,874,-507) (11/19,18/31) -> (11/15,14/19) Hyperbolic Matrix(1747,-1015,2852,-1657) (18/31,25/43) -> (30/49,19/31) Hyperbolic Matrix(1563,-910,2530,-1473) (25/43,7/12) -> (21/34,55/89) Hyperbolic Matrix(1243,-729,2116,-1241) (17/29,27/46) -> (27/46,10/17) Parabolic Matrix(1425,-844,2254,-1335) (13/22,16/27) -> (12/19,43/68) Hyperbolic Matrix(1195,-731,1656,-1013) (11/18,30/49) -> (31/43,13/18) Hyperbolic Matrix(2853,-1750,4048,-2483) (19/31,27/44) -> (31/44,43/61) Hyperbolic Matrix(1703,-1050,2162,-1333) (8/13,29/47) -> (37/47,26/33) Hyperbolic Matrix(2759,-1703,4324,-2669) (29/47,50/81) -> (7/11,30/47) Hyperbolic Matrix(12695,-7846,16376,-10121) (55/89,89/144) -> (31/40,69/89) Hyperbolic Matrix(1013,-628,1334,-827) (13/21,31/50) -> (3/4,19/25) Hyperbolic Matrix(323,-201,368,-229) (23/37,5/8) -> (7/8,8/9) Hyperbolic Matrix(1335,-841,2116,-1333) (17/27,29/46) -> (29/46,12/19) Parabolic Matrix(459,-293,506,-323) (30/47,23/36) -> (9/10,1/1) Hyperbolic Matrix(827,-530,1150,-737) (16/25,9/14) -> (23/32,18/25) Hyperbolic Matrix(2851,-1838,4140,-2669) (29/45,20/31) -> (42/61,31/45) Hyperbolic Matrix(691,-472,874,-597) (2/3,13/19) -> (15/19,34/43) Hyperbolic Matrix(2715,-1868,3542,-2437) (11/16,42/61) -> (82/107,23/30) Hyperbolic Matrix(413,-290,460,-323) (7/10,26/37) -> (8/9,9/10) Hyperbolic Matrix(13387,-9409,19044,-13385) (26/37,97/138) -> (97/138,71/101) Parabolic Matrix(1703,-1199,2024,-1425) (19/27,50/71) -> (21/25,16/19) Hyperbolic Matrix(277,-197,322,-229) (22/31,5/7) -> (6/7,13/15) Hyperbolic Matrix(1519,-1089,2116,-1517) (5/7,33/46) -> (33/46,28/39) Parabolic Matrix(3129,-2255,3956,-2851) (49/68,31/43) -> (34/43,19/24) Hyperbolic Matrix(1655,-1198,2162,-1565) (34/47,21/29) -> (13/17,36/47) Hyperbolic Matrix(415,-301,506,-367) (21/29,8/11) -> (9/11,14/17) Hyperbolic Matrix(965,-706,1196,-875) (19/26,30/41) -> (4/5,21/26) Hyperbolic Matrix(13939,-10201,19044,-13937) (30/41,101/138) -> (101/138,71/97) Parabolic Matrix(1611,-1225,2116,-1609) (19/25,35/46) -> (35/46,16/21) Parabolic Matrix(25945,-19881,33856,-25943) (59/77,141/184) -> (141/184,82/107) Parabolic Matrix(6533,-5041,8464,-6531) (27/35,71/92) -> (71/92,44/57) Parabolic Matrix(1195,-926,1426,-1105) (24/31,31/40) -> (5/6,26/31) Hyperbolic Matrix(14767,-11449,19044,-14765) (69/89,107/138) -> (107/138,38/49) Parabolic Matrix(737,-581,874,-689) (26/33,15/19) -> (16/19,11/13) Hyperbolic Matrix(1795,-1521,2116,-1793) (11/13,39/46) -> (39/46,28/33) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-22,1) Matrix(137,-14,460,-47) -> Matrix(19,8,-126,-53) Matrix(139,-17,368,-45) -> Matrix(11,4,-102,-37) Matrix(321,-41,368,-47) -> Matrix(35,12,-668,-229) Matrix(599,-79,690,-91) -> Matrix(67,22,-1270,-417) Matrix(93,-13,322,-45) -> Matrix(19,6,-130,-41) Matrix(137,-20,322,-47) -> Matrix(7,2,-60,-17) Matrix(185,-29,874,-137) -> Matrix(37,10,-174,-47) Matrix(599,-95,2024,-321) -> Matrix(15,4,-94,-25) Matrix(1471,-236,2300,-369) -> Matrix(15,4,-214,-57) Matrix(229,-39,276,-47) -> Matrix(31,8,-562,-145) Matrix(645,-113,782,-137) -> Matrix(89,22,-1598,-395) Matrix(139,-25,506,-91) -> Matrix(9,2,-50,-11) Matrix(321,-59,506,-93) -> Matrix(25,6,-346,-83) Matrix(413,-78,736,-139) -> Matrix(17,4,-200,-47) Matrix(137,-28,230,-47) -> Matrix(9,2,-122,-27) Matrix(829,-176,2162,-459) -> Matrix(67,14,-560,-117) Matrix(505,-109,644,-139) -> Matrix(79,16,-1348,-273) Matrix(323,-71,414,-91) -> Matrix(51,10,-862,-169) Matrix(2161,-484,3496,-783) -> Matrix(21,4,-310,-59) Matrix(3265,-736,5106,-1151) -> Matrix(11,2,-160,-29) Matrix(1011,-229,1426,-323) -> Matrix(11,2,-160,-29) Matrix(323,-74,598,-137) -> Matrix(11,2,-116,-21) Matrix(413,-96,598,-139) -> Matrix(31,6,-460,-89) Matrix(599,-142,966,-229) -> Matrix(11,2,-116,-21) Matrix(137,-35,184,-47) -> Matrix(23,4,-374,-65) Matrix(645,-169,874,-229) -> Matrix(109,18,-1738,-287) Matrix(367,-97,874,-231) -> Matrix(37,6,-364,-59) Matrix(2529,-677,3956,-1059) -> Matrix(51,8,-746,-117) Matrix(5657,-1516,7728,-2071) -> Matrix(181,28,-2812,-435) Matrix(2115,-568,3772,-1013) -> Matrix(27,4,-304,-45) Matrix(277,-75,506,-137) -> Matrix(13,2,-150,-23) Matrix(1839,-508,2668,-737) -> Matrix(123,20,-1802,-293) Matrix(1611,-446,3818,-1057) -> Matrix(87,14,-926,-149) Matrix(643,-179,1656,-461) -> Matrix(51,8,-440,-69) Matrix(3957,-1105,6256,-1747) -> Matrix(151,24,-2070,-329) Matrix(4463,-1248,7728,-2161) -> Matrix(127,20,-1378,-217) Matrix(413,-116,1150,-323) -> Matrix(13,2,-72,-11) Matrix(1103,-321,1426,-415) -> Matrix(15,2,-248,-33) Matrix(461,-135,782,-229) -> Matrix(15,2,-188,-25) Matrix(1011,-298,1564,-461) -> Matrix(25,4,-344,-55) Matrix(7129,-2107,10120,-2991) -> Matrix(27,4,-412,-61) Matrix(11501,-3401,16330,-4829) -> Matrix(13,2,-202,-31) Matrix(3359,-997,4646,-1379) -> Matrix(141,22,-2224,-347) Matrix(6209,-1844,8832,-2623) -> Matrix(181,28,-2812,-435) Matrix(781,-233,2162,-645) -> Matrix(67,10,-516,-77) Matrix(321,-97,460,-139) -> Matrix(55,8,-832,-121) Matrix(415,-127,598,-183) -> Matrix(71,10,-1058,-149) Matrix(459,-142,598,-185) -> Matrix(43,6,-724,-101) Matrix(553,-174,874,-275) -> Matrix(17,2,-230,-27) Matrix(91,-31,138,-47) -> Matrix(15,2,-218,-29) Matrix(599,-209,920,-321) -> Matrix(97,12,-1350,-167) Matrix(413,-145,920,-323) -> Matrix(33,4,-322,-39) Matrix(1103,-390,1564,-553) -> Matrix(33,4,-520,-63) Matrix(3771,-1340,4922,-1749) -> Matrix(291,34,-4870,-569) Matrix(1013,-361,1288,-459) -> Matrix(71,8,-1216,-137) Matrix(1289,-462,1794,-643) -> Matrix(25,2,-388,-31) Matrix(1931,-696,2300,-829) -> Matrix(31,4,-566,-73) Matrix(2897,-1045,3956,-1427) -> Matrix(59,8,-922,-125) Matrix(1655,-599,4324,-1565) -> Matrix(95,12,-768,-97) Matrix(413,-151,506,-185) -> Matrix(49,6,-874,-107) Matrix(599,-220,874,-321) -> Matrix(17,2,-230,-27) Matrix(231,-86,368,-137) -> Matrix(35,4,-464,-53) Matrix(737,-279,1334,-505) -> Matrix(19,2,-238,-25) Matrix(737,-280,966,-367) -> Matrix(23,2,-380,-33) Matrix(875,-334,1564,-597) -> Matrix(1,0,-4,1) Matrix(4829,-1847,7820,-2991) -> Matrix(63,8,-890,-113) Matrix(11501,-4401,18630,-7129) -> Matrix(241,30,-3366,-419) Matrix(2163,-829,3358,-1287) -> Matrix(83,10,-1104,-133) Matrix(321,-124,598,-231) -> Matrix(17,2,-196,-23) Matrix(1195,-463,2852,-1105) -> Matrix(35,4,-324,-37) Matrix(505,-197,828,-323) -> Matrix(71,8,-932,-105) Matrix(139,-55,230,-91) -> Matrix(19,2,-238,-25) Matrix(183,-74,230,-93) -> Matrix(17,2,-298,-35) Matrix(553,-227,782,-321) -> Matrix(19,2,-276,-29) Matrix(323,-134,552,-229) -> Matrix(39,4,-478,-49) Matrix(1105,-462,1978,-827) -> Matrix(21,2,-242,-23) Matrix(2071,-873,2944,-1241) -> Matrix(41,4,-646,-63) Matrix(5567,-2352,7728,-3265) -> Matrix(223,20,-3490,-313) Matrix(1933,-817,2392,-1011) -> Matrix(91,8,-1604,-141) Matrix(1289,-546,1518,-643) -> Matrix(31,2,-574,-37) Matrix(183,-79,322,-139) -> Matrix(19,2,-238,-25) Matrix(415,-181,736,-321) -> Matrix(41,4,-482,-47) Matrix(597,-262,736,-323) -> Matrix(41,4,-728,-71) Matrix(967,-426,1564,-689) -> Matrix(1,0,-4,1) Matrix(829,-371,1334,-597) -> Matrix(19,2,-238,-25) Matrix(369,-167,506,-229) -> Matrix(21,2,-326,-31) Matrix(461,-212,598,-275) -> Matrix(23,2,-380,-33) Matrix(367,-170,598,-277) -> Matrix(21,2,-284,-27) Matrix(505,-268,782,-415) -> Matrix(25,2,-338,-27) Matrix(1243,-674,1610,-873) -> Matrix(67,6,-1128,-101) Matrix(597,-329,920,-507) -> Matrix(49,4,-674,-55) Matrix(643,-358,828,-461) -> Matrix(45,4,-754,-67) Matrix(3081,-1727,5336,-2991) -> Matrix(45,4,-484,-43) Matrix(275,-158,322,-185) -> Matrix(27,2,-500,-37) Matrix(21345,-12329,29624,-17111) -> Matrix(701,64,-10986,-1003) Matrix(16007,-9247,22218,-12835) -> Matrix(685,62,-10728,-971) Matrix(2761,-1596,3818,-2207) -> Matrix(159,14,-2510,-221) Matrix(643,-373,874,-507) -> Matrix(73,6,-1156,-95) Matrix(1747,-1015,2852,-1657) -> Matrix(51,4,-676,-53) Matrix(1563,-910,2530,-1473) -> Matrix(23,2,-334,-29) Matrix(1243,-729,2116,-1241) -> Matrix(199,16,-2500,-201) Matrix(1425,-844,2254,-1335) -> Matrix(29,2,-392,-27) Matrix(1195,-731,1656,-1013) -> Matrix(107,8,-1672,-125) Matrix(2853,-1750,4048,-2483) -> Matrix(1,0,-2,1) Matrix(1703,-1050,2162,-1333) -> Matrix(191,14,-3288,-241) Matrix(2759,-1703,4324,-2669) -> Matrix(167,12,-2352,-169) Matrix(12695,-7846,16376,-10121) -> Matrix(117,8,-1916,-131) Matrix(1013,-628,1334,-827) -> Matrix(19,2,-314,-33) Matrix(323,-201,368,-229) -> Matrix(51,4,-982,-77) Matrix(1335,-841,2116,-1333) -> Matrix(323,24,-4374,-325) Matrix(459,-293,506,-323) -> Matrix(85,6,-1686,-119) Matrix(827,-530,1150,-737) -> Matrix(33,2,-512,-31) Matrix(2851,-1838,4140,-2669) -> Matrix(269,20,-3914,-291) Matrix(691,-472,874,-597) -> Matrix(29,2,-508,-35) Matrix(2715,-1868,3542,-2437) -> Matrix(201,14,-3374,-235) Matrix(413,-290,460,-323) -> Matrix(123,8,-2414,-157) Matrix(13387,-9409,19044,-13385) -> Matrix(1115,72,-17298,-1117) Matrix(1703,-1199,2024,-1425) -> Matrix(63,4,-1150,-73) Matrix(277,-197,322,-229) -> Matrix(91,6,-1714,-113) Matrix(1519,-1089,2116,-1517) -> Matrix(619,40,-9610,-621) Matrix(3129,-2255,3956,-2851) -> Matrix(63,4,-1024,-65) Matrix(1655,-1198,2162,-1565) -> Matrix(349,22,-5822,-367) Matrix(415,-301,506,-367) -> Matrix(33,2,-578,-35) Matrix(965,-706,1196,-875) -> Matrix(123,8,-2168,-141) Matrix(13939,-10201,19044,-13937) -> Matrix(867,56,-13454,-869) Matrix(1611,-1225,2116,-1609) -> Matrix(791,48,-13068,-793) Matrix(25945,-19881,33856,-25943) -> Matrix(5359,320,-89780,-5361) Matrix(6533,-5041,8464,-6531) -> Matrix(535,32,-8978,-537) Matrix(1195,-926,1426,-1105) -> Matrix(31,2,-574,-37) Matrix(14767,-11449,19044,-14765) -> Matrix(527,32,-8712,-529) Matrix(737,-581,874,-689) -> Matrix(173,10,-3166,-183) Matrix(1795,-1521,2116,-1793) -> Matrix(1183,64,-21904,-1185) 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): 66 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 1/0 1 23 1/9 -7/18 1 23 1/8 (-6/17,-1/3) 0 23 3/23 -1/3 17 1 2/15 -11/34 1 23 1/7 -3/10 1 23 2/13 -9/32 1 23 3/19 -1/4 1 23 4/25 -1/4 1 23 1/6 (-4/15,-1/4) 0 23 4/23 -1/4 15 1 3/17 -1/4 1 23 2/11 -1/4 1 23 3/16 (-1/4,-2/9) 0 23 1/5 -3/14 1 23 4/19 -3/14 1 23 7/33 -13/62 1 23 3/14 (-8/39,-1/5) 0 23 5/23 -1/5 13 1 2/9 -5/26 1 23 9/40 (-2/11,-1/6) 0 23 7/31 -3/14 1 23 5/22 (-1/5,-4/21) 0 23 3/13 -1/6 1 23 4/17 -3/16 1 23 1/4 (-2/11,-1/6) 0 23 6/23 -1/6 11 1 5/19 -1/6 1 23 4/15 -7/44 1 23 15/56 (-7/45,-2/13) 0 23 37/138 -2/13 14 1 11/41 -7/46 1 23 7/26 (-1/6,0/1) 0 23 3/11 -1/6 1 23 8/29 -1/6 1 23 13/47 -21/130 1 23 5/18 (-4/25,-3/19) 0 23 12/43 -7/44 1 23 19/68 (-22/139,-3/19) 0 23 7/25 -5/32 1 23 2/7 -3/20 1 23 9/31 -5/36 1 23 7/24 (-2/13,-1/7) 0 23 5/17 -1/6 1 23 13/44 (-2/13,-1/7) 0 23 34/115 -1/7 1 1 21/71 -1/6 1 23 8/27 -1/6 1 23 19/64 (-7/45,-2/13) 0 23 41/138 -2/13 18 1 11/37 -11/72 1 23 14/47 -19/126 1 23 3/10 (-4/27,-1/7) 0 23 7/23 -1/7 9 1 4/13 -5/36 1 23 9/29 -3/22 1 23 14/45 -17/126 1 23 5/16 (-2/15,-1/8) 0 23 1/3 -1/8 1 23 8/23 -1/8 7 1 7/20 (-1/8,-6/49) 0 23 6/17 -1/8 1 23 11/31 -9/76 1 23 49/138 -2/17 20 1 27/76 (-2/17,-11/94) 0 23 16/45 -13/112 1 23 5/14 (-1/9,0/1) 0 23 33/92 0/1 10 1 14/39 -1/4 1 23 9/25 -1/8 1 23 31/86 (-1/8,0/1) 0 23 22/61 -5/36 1 23 13/36 (-2/15,-3/23) 0 23 17/47 -13/102 1 23 4/11 -1/8 1 23 11/30 (-1/8,-4/33) 0 23 18/49 -1/8 1 23 7/19 -5/42 1 23 17/46 -2/17 6 1 3/8 (-2/17,-1/9) 0 23 14/37 -5/48 1 23 11/29 -1/10 1 23 19/50 (-1/12,0/1) 0 23 35/92 0/1 12 1 8/21 -1/6 1 23 13/34 (-4/31,-1/8) 0 23 44/115 -1/8 19 1 31/81 -1/8 1 23 18/47 -11/90 1 23 23/60 (-10/83,-3/25) 0 23 5/13 -3/26 1 23 12/31 -7/60 1 23 19/49 -5/44 1 23 7/18 (-4/35,-1/9) 0 23 9/23 -1/9 5 1 2/5 -1/10 1 23 11/27 -1/10 1 23 20/49 -1/8 1 23 9/22 (-1/9,-4/37) 0 23 7/17 -3/28 1 23 19/46 -2/19 4 1 5/12 (-2/19,-1/10) 0 23 18/43 -1/8 1 23 13/31 -5/48 1 23 8/19 -1/10 1 23 27/64 (-2/21,-5/53) 0 23 19/45 -7/76 1 23 68/161 -1/11 21 1 49/116 (-1/11,-14/155) 0 23 30/71 -5/56 1 23 11/26 (-1/12,0/1) 0 23 39/92 0/1 16 1 14/33 -1/4 1 23 3/7 -1/10 1 23 10/23 -1/10 3 1 7/16 (-1/10,-2/21) 0 23 18/41 -5/52 1 23 29/66 (-3/32,-4/43) 0 23 11/25 -1/12 1 23 15/34 (-1/10,-4/41) 0 23 19/43 -5/52 1 23 61/138 -2/21 8 1 23/52 (-2/21,-3/32) 0 23 4/9 -1/12 1 23 13/29 -1/10 1 23 9/20 (-1/10,-2/21) 0 23 5/11 -1/10 1 23 21/46 -2/21 2 1 11/24 (-2/21,-1/11) 0 23 6/13 -1/12 1 23 7/15 -1/14 1 23 8/17 -1/10 1 23 1/2 (-1/11,0/1) 0 23 1/0 0/1 22 1 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(137,-14,460,-47) (0/1,1/9) -> (11/37,14/47) Hyperbolic Matrix(139,-17,368,-45) (1/9,1/8) -> (3/8,14/37) Hyperbolic Matrix(47,-6,368,-47) (1/8,3/23) -> (1/8,3/23) Reflection Matrix(91,-12,690,-91) (3/23,2/15) -> (3/23,2/15) Reflection Matrix(93,-13,322,-45) (2/15,1/7) -> (2/7,9/31) Hyperbolic Matrix(137,-20,322,-47) (1/7,2/13) -> (14/33,3/7) Hyperbolic Matrix(185,-29,874,-137) (2/13,3/19) -> (4/19,7/33) Hyperbolic Matrix(599,-95,2024,-321) (3/19,4/25) -> (21/71,8/27) Hyperbolic Matrix(829,-133,2300,-369) (4/25,1/6) -> (9/25,31/86) Glide Reflection Matrix(47,-8,276,-47) (1/6,4/23) -> (1/6,4/23) Reflection Matrix(137,-24,782,-137) (4/23,3/17) -> (4/23,3/17) Reflection Matrix(139,-25,506,-91) (3/17,2/11) -> (3/11,8/29) Hyperbolic Matrix(185,-34,506,-93) (2/11,3/16) -> (4/11,11/30) Glide Reflection Matrix(323,-61,736,-139) (3/16,1/5) -> (7/16,18/41) Glide Reflection Matrix(93,-19,230,-47) (1/5,4/19) -> (2/5,11/27) Glide Reflection Matrix(829,-176,2162,-459) (7/33,3/14) -> (23/60,5/13) Hyperbolic Matrix(139,-30,644,-139) (3/14,5/23) -> (3/14,5/23) Reflection Matrix(91,-20,414,-91) (5/23,2/9) -> (5/23,2/9) Reflection Matrix(367,-82,828,-185) (2/9,9/40) -> (23/52,4/9) Hyperbolic Matrix(1841,-415,5106,-1151) (9/40,7/31) -> (31/86,22/61) Glide Reflection Matrix(415,-94,1426,-323) (7/31,5/22) -> (9/31,7/24) Glide Reflection Matrix(275,-63,598,-137) (5/22,3/13) -> (11/24,6/13) Glide Reflection Matrix(185,-43,598,-139) (3/13,4/17) -> (4/13,9/29) Glide Reflection Matrix(367,-87,966,-229) (4/17,1/4) -> (11/29,19/50) Glide Reflection Matrix(47,-12,184,-47) (1/4,6/23) -> (1/4,6/23) Reflection Matrix(229,-60,874,-229) (6/23,5/19) -> (6/23,5/19) Reflection Matrix(367,-97,874,-231) (5/19,4/15) -> (13/31,8/19) Hyperbolic Matrix(1427,-382,3956,-1059) (4/15,15/56) -> (22/61,13/36) Glide Reflection Matrix(2071,-555,7728,-2071) (15/56,37/138) -> (15/56,37/138) Reflection Matrix(3035,-814,11316,-3035) (37/138,11/41) -> (37/138,11/41) Reflection Matrix(1657,-445,3772,-1013) (11/41,7/26) -> (18/41,29/66) Glide Reflection Matrix(229,-62,506,-137) (7/26,3/11) -> (9/20,5/11) Glide Reflection Matrix(829,-229,2668,-737) (8/29,13/47) -> (9/29,14/45) Glide Reflection Matrix(1611,-446,3818,-1057) (13/47,5/18) -> (27/64,19/45) Hyperbolic Matrix(643,-179,1656,-461) (5/18,12/43) -> (19/49,7/18) Hyperbolic Matrix(1747,-488,4278,-1195) (12/43,19/68) -> (20/49,9/22) Glide Reflection Matrix(3265,-913,7728,-2161) (19/68,7/25) -> (49/116,30/71) Glide Reflection Matrix(413,-116,1150,-323) (7/25,2/7) -> (14/39,9/25) Hyperbolic Matrix(321,-94,782,-229) (7/24,5/17) -> (9/22,7/17) Glide Reflection Matrix(369,-109,782,-231) (5/17,13/44) -> (8/17,1/2) Glide Reflection Matrix(2991,-884,10120,-2991) (13/44,34/115) -> (13/44,34/115) Reflection Matrix(4829,-1428,16330,-4829) (34/115,21/71) -> (34/115,21/71) Reflection Matrix(1241,-368,2944,-873) (8/27,19/64) -> (8/19,27/64) Glide Reflection Matrix(2623,-779,8832,-2623) (19/64,41/138) -> (19/64,41/138) Reflection Matrix(3035,-902,10212,-3035) (41/138,11/37) -> (41/138,11/37) Reflection Matrix(781,-233,2162,-645) (14/47,3/10) -> (13/36,17/47) Hyperbolic Matrix(139,-42,460,-139) (3/10,7/23) -> (3/10,7/23) Reflection Matrix(183,-56,598,-183) (7/23,4/13) -> (7/23,4/13) Reflection Matrix(1471,-458,4140,-1289) (14/45,5/16) -> (27/76,16/45) Hyperbolic Matrix(321,-101,874,-275) (5/16,1/3) -> (11/30,18/49) Glide Reflection Matrix(47,-16,138,-47) (1/3,8/23) -> (1/3,8/23) Reflection Matrix(321,-112,920,-321) (8/23,7/20) -> (8/23,7/20) Reflection Matrix(413,-145,920,-323) (7/20,6/17) -> (13/29,9/20) Hyperbolic Matrix(367,-130,782,-277) (6/17,11/31) -> (7/15,8/17) Hyperbolic Matrix(3037,-1078,8556,-3037) (11/31,49/138) -> (11/31,49/138) Reflection Matrix(3725,-1323,10488,-3725) (49/138,27/76) -> (49/138,27/76) Reflection Matrix(1287,-458,3358,-1195) (16/45,5/14) -> (18/47,23/60) Glide Reflection Matrix(461,-165,1288,-461) (5/14,33/92) -> (5/14,33/92) Reflection Matrix(2575,-924,7176,-2575) (33/92,14/39) -> (33/92,14/39) Reflection Matrix(1655,-599,4324,-1565) (17/47,4/11) -> (31/81,18/47) Hyperbolic Matrix(919,-338,2254,-829) (18/49,7/19) -> (11/27,20/49) Hyperbolic Matrix(645,-238,1748,-645) (7/19,17/46) -> (7/19,17/46) Reflection Matrix(137,-51,368,-137) (17/46,3/8) -> (17/46,3/8) Reflection Matrix(597,-226,1334,-505) (14/37,11/29) -> (4/9,13/29) Glide Reflection Matrix(1749,-665,4600,-1749) (19/50,35/92) -> (19/50,35/92) Reflection Matrix(1471,-560,3864,-1471) (35/92,8/21) -> (35/92,8/21) Reflection Matrix(689,-263,1564,-597) (8/21,13/34) -> (11/25,15/34) Glide Reflection Matrix(2991,-1144,7820,-2991) (13/34,44/115) -> (13/34,44/115) Reflection Matrix(7129,-2728,18630,-7129) (44/115,31/81) -> (44/115,31/81) Reflection Matrix(277,-107,598,-231) (5/13,12/31) -> (6/13,7/15) Glide Reflection Matrix(1195,-463,2852,-1105) (12/31,19/49) -> (18/43,13/31) Hyperbolic Matrix(323,-126,828,-323) (7/18,9/23) -> (7/18,9/23) Reflection Matrix(91,-36,230,-91) (9/23,2/5) -> (9/23,2/5) Reflection Matrix(645,-266,1564,-645) (7/17,19/46) -> (7/17,19/46) Reflection Matrix(229,-95,552,-229) (19/46,5/12) -> (19/46,5/12) Reflection Matrix(873,-365,1978,-827) (5/12,18/43) -> (15/34,19/43) Glide Reflection Matrix(6119,-2584,14490,-6119) (19/45,68/161) -> (19/45,68/161) Reflection Matrix(15777,-6664,37352,-15777) (68/161,49/116) -> (68/161,49/116) Reflection Matrix(2345,-991,5336,-2255) (30/71,11/26) -> (29/66,11/25) Hyperbolic Matrix(1013,-429,2392,-1013) (11/26,39/92) -> (11/26,39/92) Reflection Matrix(2575,-1092,6072,-2575) (39/92,14/33) -> (39/92,14/33) Reflection Matrix(139,-60,322,-139) (3/7,10/23) -> (3/7,10/23) Reflection Matrix(321,-140,736,-321) (10/23,7/16) -> (10/23,7/16) Reflection Matrix(5245,-2318,11868,-5245) (19/43,61/138) -> (19/43,61/138) Reflection Matrix(3173,-1403,7176,-3173) (61/138,23/52) -> (61/138,23/52) Reflection Matrix(461,-210,1012,-461) (5/11,21/46) -> (5/11,21/46) Reflection Matrix(505,-231,1104,-505) (21/46,11/24) -> (21/46,11/24) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) 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(137,-14,460,-47) -> Matrix(19,8,-126,-53) Matrix(139,-17,368,-45) -> Matrix(11,4,-102,-37) Matrix(47,-6,368,-47) -> Matrix(35,12,-102,-35) (1/8,3/23) -> (-6/17,-1/3) Matrix(91,-12,690,-91) -> Matrix(67,22,-204,-67) (3/23,2/15) -> (-1/3,-11/34) Matrix(93,-13,322,-45) -> Matrix(19,6,-130,-41) Matrix(137,-20,322,-47) -> Matrix(7,2,-60,-17) Matrix(185,-29,874,-137) -> Matrix(37,10,-174,-47) Matrix(599,-95,2024,-321) -> Matrix(15,4,-94,-25) Matrix(829,-133,2300,-369) -> Matrix(15,4,-116,-31) Matrix(47,-8,276,-47) -> Matrix(31,8,-120,-31) (1/6,4/23) -> (-4/15,-1/4) Matrix(137,-24,782,-137) -> Matrix(89,22,-360,-89) (4/23,3/17) -> (-1/4,-11/45) Matrix(139,-25,506,-91) -> Matrix(9,2,-50,-11) -1/5 Matrix(185,-34,506,-93) -> Matrix(25,6,-204,-49) Matrix(323,-61,736,-139) -> Matrix(17,4,-174,-41) Matrix(93,-19,230,-47) -> Matrix(9,2,-76,-17) Matrix(829,-176,2162,-459) -> Matrix(67,14,-560,-117) Matrix(139,-30,644,-139) -> Matrix(79,16,-390,-79) (3/14,5/23) -> (-8/39,-1/5) Matrix(91,-20,414,-91) -> Matrix(51,10,-260,-51) (5/23,2/9) -> (-1/5,-5/26) Matrix(367,-82,828,-185) -> Matrix(21,4,-226,-43) Matrix(1841,-415,5106,-1151) -> Matrix(11,2,-82,-15) Matrix(415,-94,1426,-323) -> Matrix(11,2,-82,-15) Matrix(275,-63,598,-137) -> Matrix(11,2,-126,-23) Matrix(185,-43,598,-139) -> Matrix(31,6,-222,-43) Matrix(367,-87,966,-229) -> Matrix(11,2,-126,-23) Matrix(47,-12,184,-47) -> Matrix(23,4,-132,-23) (1/4,6/23) -> (-2/11,-1/6) Matrix(229,-60,874,-229) -> Matrix(109,18,-660,-109) (6/23,5/19) -> (-1/6,-9/55) Matrix(367,-97,874,-231) -> Matrix(37,6,-364,-59) Matrix(1427,-382,3956,-1059) -> Matrix(51,8,-376,-59) Matrix(2071,-555,7728,-2071) -> Matrix(181,28,-1170,-181) (15/56,37/138) -> (-7/45,-2/13) Matrix(3035,-814,11316,-3035) -> Matrix(183,28,-1196,-183) (37/138,11/41) -> (-2/13,-7/46) Matrix(1657,-445,3772,-1013) -> Matrix(27,4,-290,-43) Matrix(229,-62,506,-137) -> Matrix(13,2,-136,-21) Matrix(829,-229,2668,-737) -> Matrix(123,20,-904,-147) Matrix(1611,-446,3818,-1057) -> Matrix(87,14,-926,-149) Matrix(643,-179,1656,-461) -> Matrix(51,8,-440,-69) Matrix(1747,-488,4278,-1195) -> Matrix(63,10,-548,-87) Matrix(3265,-913,7728,-2161) -> Matrix(127,20,-1416,-223) Matrix(413,-116,1150,-323) -> Matrix(13,2,-72,-11) -1/6 Matrix(321,-94,782,-229) -> Matrix(15,2,-142,-19) Matrix(369,-109,782,-231) -> Matrix(13,2,-136,-21) Matrix(2991,-884,10120,-2991) -> Matrix(27,4,-182,-27) (13/44,34/115) -> (-2/13,-1/7) Matrix(4829,-1428,16330,-4829) -> Matrix(13,2,-84,-13) (34/115,21/71) -> (-1/6,-1/7) Matrix(1241,-368,2944,-873) -> Matrix(25,4,-256,-41) Matrix(2623,-779,8832,-2623) -> Matrix(181,28,-1170,-181) (19/64,41/138) -> (-7/45,-2/13) Matrix(3035,-902,10212,-3035) -> Matrix(287,44,-1872,-287) (41/138,11/37) -> (-2/13,-11/72) Matrix(781,-233,2162,-645) -> Matrix(67,10,-516,-77) Matrix(139,-42,460,-139) -> Matrix(55,8,-378,-55) (3/10,7/23) -> (-4/27,-1/7) Matrix(183,-56,598,-183) -> Matrix(71,10,-504,-71) (7/23,4/13) -> (-1/7,-5/36) Matrix(1471,-458,4140,-1289) -> Matrix(149,20,-1274,-171) Matrix(321,-101,874,-275) -> Matrix(17,2,-144,-17) *** -> (-1/8,-1/9) Matrix(47,-16,138,-47) -> Matrix(15,2,-112,-15) (1/3,8/23) -> (-1/7,-1/8) Matrix(321,-112,920,-321) -> Matrix(97,12,-784,-97) (8/23,7/20) -> (-1/8,-6/49) Matrix(413,-145,920,-323) -> Matrix(33,4,-322,-39) Matrix(367,-130,782,-277) -> Matrix(17,2,-162,-19) -1/9 Matrix(3037,-1078,8556,-3037) -> Matrix(305,36,-2584,-305) (11/31,49/138) -> (-9/76,-2/17) Matrix(3725,-1323,10488,-3725) -> Matrix(375,44,-3196,-375) (49/138,27/76) -> (-2/17,-11/94) Matrix(1287,-458,3358,-1195) -> Matrix(87,10,-722,-83) Matrix(461,-165,1288,-461) -> Matrix(-1,0,18,1) (5/14,33/92) -> (-1/9,0/1) Matrix(2575,-924,7176,-2575) -> Matrix(-1,0,8,1) (33/92,14/39) -> (-1/4,0/1) Matrix(1655,-599,4324,-1565) -> Matrix(95,12,-768,-97) -1/8 Matrix(919,-338,2254,-829) -> Matrix(17,2,-128,-15) -1/8 Matrix(645,-238,1748,-645) -> Matrix(169,20,-1428,-169) (7/19,17/46) -> (-5/42,-2/17) Matrix(137,-51,368,-137) -> Matrix(35,4,-306,-35) (17/46,3/8) -> (-2/17,-1/9) Matrix(597,-226,1334,-505) -> Matrix(19,2,-180,-19) *** -> (-1/9,-1/10) Matrix(1749,-665,4600,-1749) -> Matrix(-1,0,24,1) (19/50,35/92) -> (-1/12,0/1) Matrix(1471,-560,3864,-1471) -> Matrix(-1,0,12,1) (35/92,8/21) -> (-1/6,0/1) Matrix(689,-263,1564,-597) -> Matrix(-1,0,18,1) *** -> (-1/9,0/1) Matrix(2991,-1144,7820,-2991) -> Matrix(63,8,-496,-63) (13/34,44/115) -> (-4/31,-1/8) Matrix(7129,-2728,18630,-7129) -> Matrix(241,30,-1936,-241) (44/115,31/81) -> (-1/8,-15/121) Matrix(277,-107,598,-231) -> Matrix(17,2,-178,-21) Matrix(1195,-463,2852,-1105) -> Matrix(35,4,-324,-37) -1/9 Matrix(323,-126,828,-323) -> Matrix(71,8,-630,-71) (7/18,9/23) -> (-4/35,-1/9) Matrix(91,-36,230,-91) -> Matrix(19,2,-180,-19) (9/23,2/5) -> (-1/9,-1/10) Matrix(645,-266,1564,-645) -> Matrix(113,12,-1064,-113) (7/17,19/46) -> (-3/28,-2/19) Matrix(229,-95,552,-229) -> Matrix(39,4,-380,-39) (19/46,5/12) -> (-2/19,-1/10) Matrix(873,-365,1978,-827) -> Matrix(21,2,-220,-21) *** -> (-1/10,-1/11) Matrix(6119,-2584,14490,-6119) -> Matrix(153,14,-1672,-153) (19/45,68/161) -> (-7/76,-1/11) Matrix(15777,-6664,37352,-15777) -> Matrix(309,28,-3410,-309) (68/161,49/116) -> (-1/11,-14/155) Matrix(2345,-991,5336,-2255) -> Matrix(45,4,-484,-43) -1/11 Matrix(1013,-429,2392,-1013) -> Matrix(-1,0,24,1) (11/26,39/92) -> (-1/12,0/1) Matrix(2575,-1092,6072,-2575) -> Matrix(-1,0,8,1) (39/92,14/33) -> (-1/4,0/1) Matrix(139,-60,322,-139) -> Matrix(19,2,-180,-19) (3/7,10/23) -> (-1/9,-1/10) Matrix(321,-140,736,-321) -> Matrix(41,4,-420,-41) (10/23,7/16) -> (-1/10,-2/21) Matrix(5245,-2318,11868,-5245) -> Matrix(209,20,-2184,-209) (19/43,61/138) -> (-5/52,-2/21) Matrix(3173,-1403,7176,-3173) -> Matrix(127,12,-1344,-127) (61/138,23/52) -> (-2/21,-3/32) Matrix(461,-210,1012,-461) -> Matrix(41,4,-420,-41) (5/11,21/46) -> (-1/10,-2/21) Matrix(505,-231,1104,-505) -> Matrix(43,4,-462,-43) (21/46,11/24) -> (-2/21,-1/11) Matrix(-1,1,0,1) -> Matrix(-1,0,22,1) (1/2,1/0) -> (-1/11,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.