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 0/1 1/2 -8/9 1/4 -7/8 5/11 1/2 -20/23 1/2 -13/15 1/2 12/23 -6/7 7/12 -11/13 2/3 7/10 -16/19 3/4 -21/25 1/2 2/3 -5/6 3/4 1/1 -19/23 1/1 -14/17 5/4 -9/11 2/1 1/0 -13/16 1/1 1/0 -4/5 1/4 -15/19 2/5 5/12 -26/33 9/20 -11/14 7/15 1/2 -18/23 1/2 -7/9 1/2 6/11 -31/40 7/12 3/5 -24/31 7/12 -17/22 1/2 5/9 -10/13 7/12 -13/17 5/8 12/19 -3/4 3/4 1/1 -17/23 1/1 -14/19 9/8 -11/15 4/3 3/2 -41/56 9/5 11/6 -30/41 9/4 -19/26 3/1 1/0 -8/11 1/0 -21/29 -6/1 1/0 -34/47 1/0 -13/18 -3/2 -1/1 -31/43 -2/3 -5/8 -49/68 -9/17 -1/2 -18/25 -3/8 -5/7 0/1 1/4 -22/31 3/8 -17/24 3/7 1/2 -12/17 1/4 -31/44 7/22 1/3 -81/115 1/3 -50/71 15/44 -19/27 4/11 3/8 -45/64 5/13 7/18 -26/37 5/12 -33/47 2/5 1/2 -7/10 3/7 1/2 -16/23 1/2 -9/13 1/2 6/11 -11/16 7/12 3/5 -2/3 3/4 -15/23 1/1 -13/20 1/1 13/12 -11/17 5/4 4/3 -20/31 5/4 -29/45 3/2 2/1 -9/14 3/2 5/3 -25/39 2/1 17/8 -16/25 11/4 -39/61 7/2 18/5 -23/36 9/2 5/1 -30/47 1/0 -7/11 -2/1 1/0 -19/30 -1/1 1/0 -12/19 -1/4 -5/8 1/2 1/1 -23/37 0/1 1/2 -18/29 1/0 -13/21 0/1 1/6 -21/34 1/4 1/3 -71/115 1/3 -50/81 3/8 -29/47 2/5 1/2 -37/60 3/7 1/2 -8/13 1/4 -19/31 2/5 1/2 -30/49 5/12 -11/18 3/7 1/2 -14/23 1/2 -3/5 1/2 2/3 -13/22 1/2 5/9 -10/17 5/8 -7/12 3/4 1/1 -25/43 2/3 11/16 -18/31 3/4 -11/19 3/4 10/13 -37/64 5/6 1/1 -26/45 3/4 -41/71 11/14 4/5 -15/26 3/4 7/9 -19/33 4/5 21/26 -4/7 7/8 -13/23 1/1 -9/16 1/1 13/12 -14/25 19/16 -5/9 3/2 2/1 -16/29 1/0 -11/20 -1/1 1/0 -6/11 1/0 -7/13 1/2 2/3 -1/2 1/2 1/1 -7/15 4/3 3/2 -6/13 1/0 -11/24 3/2 5/3 -5/11 2/1 1/0 -9/20 3/4 1/1 -13/29 6/5 5/4 -4/9 1/0 -19/43 2/1 9/4 -15/34 1/1 1/0 -11/25 2/1 5/2 -29/66 3/1 1/0 -18/41 9/4 -7/16 3/1 1/0 -10/23 1/0 -3/7 0/1 1/0 -11/26 1/4 1/3 -30/71 9/20 -49/116 15/31 1/2 -68/161 1/2 -19/45 1/2 6/11 -8/19 3/4 -13/31 3/2 2/1 -18/43 7/4 -5/12 -1/1 1/0 -12/29 -1/4 -19/46 0/1 -7/17 0/1 1/4 -9/22 1/2 1/1 -11/27 0/1 1/4 -2/5 3/4 -9/23 1/1 -7/18 1/1 15/14 -19/49 31/28 10/9 -12/31 9/8 -17/44 1/1 7/6 -5/13 7/6 6/5 -18/47 5/4 -31/81 66/53 5/4 -44/115 5/4 -13/34 5/4 29/23 -34/89 61/48 -55/144 51/40 37/29 -21/55 23/18 32/25 -8/21 21/16 -19/50 27/20 23/17 -11/29 11/8 18/13 -14/37 17/12 -3/8 3/2 5/3 -10/27 15/8 -17/46 2/1 -7/19 2/1 9/4 -25/68 5/2 3/1 -18/49 9/4 -11/30 11/4 3/1 -4/11 1/0 -17/47 3/2 2/1 -13/36 3/2 5/3 -22/61 1/0 -31/86 1/1 1/0 -9/25 3/2 2/1 -5/14 5/2 3/1 -16/45 1/0 -11/31 2/1 5/2 -17/48 17/6 3/1 -6/17 1/0 -7/20 7/1 1/0 -8/23 1/0 -1/3 0/1 1/0 -6/19 5/8 -5/16 3/4 1/1 -19/61 2/3 7/10 -14/45 3/4 -9/29 3/4 10/13 -4/13 7/8 -7/23 1/1 -3/10 1/1 7/6 -11/37 13/10 4/3 -41/138 4/3 -30/101 27/20 -19/64 7/5 3/2 -8/27 5/4 -21/71 4/3 3/2 -34/115 3/2 -13/44 1/1 3/2 -18/61 5/4 -5/17 5/4 4/3 -7/24 7/5 3/2 -9/31 22/15 3/2 -2/7 7/4 -13/46 2/1 -11/39 2/1 33/16 -9/32 13/6 11/5 -7/25 2/1 5/2 -26/93 9/4 -45/161 7/3 -19/68 7/3 5/2 -12/43 1/0 -5/18 5/2 3/1 -18/65 9/4 -13/47 5/2 18/7 -8/29 11/4 -3/11 2/1 1/0 -7/26 3/1 13/4 -11/41 23/6 4/1 -37/138 4/1 -26/97 49/12 -15/56 13/3 9/2 -4/15 1/0 -5/19 10/1 1/0 -6/23 1/0 -1/4 -1/1 1/0 -6/25 -1/12 -11/46 0/1 -5/21 0/1 1/10 -4/17 1/4 -11/47 1/2 2/3 -18/77 1/0 -43/184 0/1 -25/107 0/1 1/6 -7/30 1/4 1/3 -3/13 1/2 2/3 -8/35 1/0 -21/92 0/1 -13/57 0/1 1/4 -5/22 1/2 1/1 -7/31 1/2 6/11 -9/40 5/8 7/11 -20/89 21/32 -31/138 2/3 -11/49 2/3 11/16 -2/9 3/4 -5/23 1/1 -3/14 1/1 7/6 -10/47 5/4 -7/33 13/10 4/3 -4/19 5/4 -9/43 17/12 10/7 -5/24 3/2 11/7 -1/5 3/2 2/1 -5/26 7/3 19/8 -4/21 21/8 -3/16 3/1 13/4 -2/11 1/0 -3/17 12/1 1/0 -4/23 1/0 -1/6 -3/1 1/0 -5/31 -3/2 -10/7 -4/25 -9/8 -3/19 -3/4 -2/3 -2/13 -1/4 -7/46 0/1 -5/33 0/1 1/10 -3/20 1/4 1/3 -1/7 0/1 1/0 -2/15 3/4 -3/23 1/1 -1/8 1/1 3/2 -1/9 3/2 2/1 -1/10 3/1 7/2 0/1 1/0 1/9 -2/1 -3/2 1/8 -3/2 -1/1 3/23 -1/1 2/15 -3/4 1/7 0/1 1/0 2/13 1/4 3/19 2/3 3/4 4/25 9/8 1/6 3/1 1/0 4/23 1/0 3/17 -12/1 1/0 2/11 1/0 3/16 -13/4 -3/1 1/5 -2/1 -3/2 4/19 -5/4 7/33 -4/3 -13/10 3/14 -7/6 -1/1 5/23 -1/1 2/9 -3/4 9/40 -7/11 -5/8 7/31 -6/11 -1/2 5/22 -1/1 -1/2 3/13 -2/3 -1/2 4/17 -1/4 1/4 1/1 1/0 6/23 1/0 5/19 -10/1 1/0 4/15 1/0 15/56 -9/2 -13/3 11/41 -4/1 -23/6 7/26 -13/4 -3/1 3/11 -2/1 1/0 8/29 -11/4 13/47 -18/7 -5/2 5/18 -3/1 -5/2 12/43 1/0 19/68 -5/2 -7/3 7/25 -5/2 -2/1 2/7 -7/4 9/31 -3/2 -22/15 7/24 -3/2 -7/5 5/17 -4/3 -5/4 13/44 -3/2 -1/1 34/115 -3/2 21/71 -3/2 -4/3 8/27 -5/4 19/64 -3/2 -7/5 11/37 -4/3 -13/10 14/47 -5/4 3/10 -7/6 -1/1 7/23 -1/1 4/13 -7/8 5/16 -1/1 -3/4 1/3 0/1 1/0 8/23 1/0 7/20 -7/1 1/0 6/17 1/0 11/31 -5/2 -2/1 16/45 1/0 5/14 -3/1 -5/2 14/39 -15/8 9/25 -2/1 -3/2 22/61 1/0 13/36 -5/3 -3/2 17/47 -2/1 -3/2 4/11 1/0 11/30 -3/1 -11/4 7/19 -9/4 -2/1 3/8 -5/3 -3/2 14/37 -17/12 11/29 -18/13 -11/8 8/21 -21/16 13/34 -29/23 -5/4 44/115 -5/4 31/81 -5/4 -66/53 18/47 -5/4 23/60 -27/22 -11/9 5/13 -6/5 -7/6 12/31 -9/8 19/49 -10/9 -31/28 7/18 -15/14 -1/1 9/23 -1/1 2/5 -3/4 9/22 -1/1 -1/2 7/17 -1/4 0/1 5/12 1/1 1/0 18/43 -7/4 13/31 -2/1 -3/2 8/19 -3/4 27/64 -3/5 -1/2 19/45 -6/11 -1/2 30/71 -9/20 11/26 -1/3 -1/4 14/33 1/4 3/7 0/1 1/0 10/23 1/0 7/16 -3/1 1/0 11/25 -5/2 -2/1 4/9 1/0 13/29 -5/4 -6/5 9/20 -1/1 -3/4 5/11 -2/1 1/0 6/13 1/0 1/2 -1/1 -1/2 8/15 1/0 7/13 -2/3 -1/2 13/24 -1/1 -1/2 6/11 1/0 11/20 1/1 1/0 16/29 1/0 5/9 -2/1 -3/2 24/43 -21/16 19/34 -19/15 -5/4 14/25 -19/16 37/66 -37/32 -15/13 23/41 -8/7 -25/22 9/16 -13/12 -1/1 13/23 -1/1 4/7 -7/8 15/26 -7/9 -3/4 41/71 -4/5 -11/14 67/116 -11/14 -7/9 93/161 -7/9 26/45 -3/4 11/19 -10/13 -3/4 18/31 -3/4 25/43 -11/16 -2/3 7/12 -1/1 -3/4 17/29 -11/16 -2/3 27/46 -2/3 10/17 -5/8 13/22 -5/9 -1/2 16/27 1/0 3/5 -2/3 -1/2 14/23 -1/2 11/18 -1/2 -3/7 30/49 -5/12 19/31 -1/2 -2/5 27/44 -1/3 -3/10 8/13 -1/4 29/47 -1/2 -2/5 50/81 -3/8 71/115 -1/3 21/34 -1/3 -1/4 55/89 -1/8 0/1 89/144 1/1 1/0 34/55 -1/4 13/21 -1/6 0/1 31/50 1/5 1/4 18/29 1/0 23/37 -1/2 0/1 5/8 -1/1 -1/2 17/27 -1/8 0/1 29/46 0/1 12/19 1/4 43/68 5/11 1/2 31/49 2/3 3/4 19/30 1/1 1/0 7/11 2/1 1/0 30/47 1/0 23/36 -5/1 -9/2 39/61 -18/5 -7/2 55/86 -23/7 -13/4 16/25 -11/4 9/14 -5/3 -3/2 29/45 -2/1 -3/2 20/31 -5/4 31/48 -3/2 -1/1 11/17 -4/3 -5/4 13/20 -13/12 -1/1 15/23 -1/1 2/3 -3/4 13/19 -3/4 -2/3 11/16 -3/5 -7/12 42/61 -9/16 31/45 -6/11 -1/2 20/29 -7/12 9/13 -6/11 -1/2 16/23 -1/2 7/10 -1/2 -3/7 26/37 -5/12 97/138 -2/5 71/101 -2/5 -15/38 45/64 -7/18 -5/13 19/27 -3/8 -4/11 50/71 -15/44 81/115 -1/3 31/44 -1/3 -7/22 43/61 -3/10 -2/7 12/17 -1/4 17/24 -1/2 -3/7 22/31 -3/8 5/7 -1/4 0/1 33/46 0/1 28/39 1/16 23/32 1/7 1/6 18/25 3/8 67/93 12/25 1/2 116/161 1/2 49/68 1/2 9/17 31/43 5/8 2/3 13/18 1/1 3/2 47/65 4/1 1/0 34/47 1/0 21/29 6/1 1/0 8/11 1/0 19/26 -3/1 1/0 30/41 -9/4 101/138 -2/1 71/97 -2/1 -27/14 41/56 -11/6 -9/5 11/15 -3/2 -4/3 14/19 -9/8 17/23 -1/1 3/4 -1/1 -3/4 19/25 -23/34 -2/3 35/46 -2/3 16/21 -21/32 13/17 -12/19 -5/8 36/47 -5/8 59/77 -21/34 -8/13 141/184 -8/13 82/107 -27/44 23/30 -5/8 -3/5 10/13 -7/12 27/35 -7/12 -4/7 71/92 -4/7 44/57 -9/16 17/22 -5/9 -1/2 24/31 -7/12 31/40 -3/5 -7/12 69/89 -39/68 -4/7 107/138 -4/7 38/49 -25/44 7/9 -6/11 -1/2 18/23 -1/2 11/14 -1/2 -7/15 37/47 -1/2 -6/13 26/33 -9/20 15/19 -5/12 -2/5 34/43 -5/12 19/24 -1/2 -1/3 4/5 -1/4 21/26 -1/1 1/0 17/21 -1/2 0/1 13/16 -1/1 1/0 9/11 -2/1 1/0 14/17 -5/4 19/23 -1/1 5/6 -1/1 -3/4 26/31 -3/4 21/25 -2/3 -1/2 16/19 -3/4 11/13 -7/10 -2/3 39/46 -2/3 28/33 -21/32 17/20 -7/11 -5/8 6/7 -7/12 13/15 -12/23 -1/2 20/23 -1/2 7/8 -1/2 -5/11 8/9 -1/4 9/10 -1/2 -1/3 1/1 -1/2 0/1 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,-4,1) Matrix(323,290,-460,-413) -> Matrix(3,-2,8,-5) Matrix(139,122,368,323) -> Matrix(23,-10,-16,7) Matrix(321,280,368,321) -> Matrix(21,-10,-44,21) Matrix(599,520,690,599) -> Matrix(47,-24,-92,47) Matrix(93,80,322,277) -> Matrix(25,-14,-16,9) Matrix(185,158,-322,-275) -> Matrix(23,-14,28,-17) Matrix(185,156,874,737) -> Matrix(1,-2,0,1) Matrix(599,504,2024,1703) -> Matrix(1,-2,0,1) Matrix(829,696,-2300,-1931) -> Matrix(5,-4,4,-3) Matrix(229,190,276,229) -> Matrix(7,-6,-8,7) Matrix(645,532,782,645) -> Matrix(9,-10,-8,9) Matrix(139,114,506,415) -> Matrix(1,-4,0,1) Matrix(321,262,506,413) -> Matrix(1,0,0,1) Matrix(323,262,-736,-597) -> Matrix(1,2,0,1) Matrix(93,74,-230,-183) -> Matrix(5,-2,8,-3) Matrix(137,108,874,689) -> Matrix(9,-4,16,-7) Matrix(1333,1050,-2162,-1703) -> Matrix(9,-4,16,-7) Matrix(505,396,644,505) -> Matrix(29,-14,-60,29) Matrix(323,252,414,323) -> Matrix(23,-12,-44,23) Matrix(1335,1036,-3496,-2713) -> Matrix(189,-106,148,-83) Matrix(1841,1426,-5106,-3955) -> Matrix(17,-10,12,-7) Matrix(1011,782,1426,1103) -> Matrix(3,-2,-4,3) Matrix(275,212,-598,-461) -> Matrix(17,-10,12,-7) Matrix(185,142,-598,-459) -> Matrix(23,-14,28,-17) Matrix(367,280,-966,-737) -> Matrix(65,-42,48,-31) Matrix(137,102,184,137) -> Matrix(7,-6,-8,7) Matrix(645,476,874,645) -> Matrix(17,-18,-16,17) Matrix(367,270,874,643) -> Matrix(5,-6,-4,5) Matrix(2529,1852,3956,2897) -> Matrix(15,-26,-4,7) Matrix(2071,1516,-7728,-5657) -> Matrix(33,-62,8,-15) Matrix(1657,1212,-3772,-2759) -> Matrix(1,0,0,1) Matrix(277,202,506,369) -> Matrix(1,-2,0,1) Matrix(91,66,506,367) -> Matrix(1,-6,0,1) Matrix(829,600,-2668,-1931) -> Matrix(3,8,4,11) Matrix(2207,1596,-3818,-2761) -> Matrix(3,2,4,3) Matrix(643,464,1656,1195) -> Matrix(13,12,-12,-11) Matrix(3957,2852,6256,4509) -> Matrix(7,4,12,7) Matrix(3265,2352,-7728,-5567) -> Matrix(13,6,28,13) Matrix(737,530,-1150,-827) -> Matrix(9,2,4,1) Matrix(45,32,322,229) -> Matrix(1,0,-4,1) Matrix(1103,782,1426,1011) -> Matrix(3,-2,-4,3) Matrix(461,326,782,553) -> Matrix(3,-2,-4,3) Matrix(553,390,-1564,-1103) -> Matrix(15,-4,4,-1) Matrix(7129,5022,10120,7129) -> Matrix(43,-14,-132,43) Matrix(11501,8100,16330,11501) -> Matrix(89,-30,-264,89) Matrix(321,226,2024,1425) -> Matrix(17,-6,20,-7) Matrix(3359,2362,4646,3267) -> Matrix(21,-8,8,-3) Matrix(2623,1844,-8832,-6209) -> Matrix(87,-34,64,-25) Matrix(781,548,2162,1517) -> Matrix(11,-4,-8,3) Matrix(321,224,460,321) -> Matrix(13,-6,-28,13) Matrix(415,288,598,415) -> Matrix(23,-12,-44,23) Matrix(139,96,-598,-413) -> Matrix(7,-4,16,-9) Matrix(321,220,-874,-599) -> Matrix(19,-12,8,-5) Matrix(91,60,138,91) -> Matrix(7,-6,-8,7) Matrix(599,390,920,599) -> Matrix(25,-26,-24,25) Matrix(413,268,920,597) -> Matrix(9,-10,-8,9) Matrix(461,298,-1564,-1011) -> Matrix(1,0,0,1) Matrix(1151,742,-4922,-3173) -> Matrix(3,-4,4,-5) Matrix(1013,652,1288,829) -> Matrix(11,-16,-24,35) Matrix(505,324,-1794,-1151) -> Matrix(17,-32,8,-15) Matrix(369,236,-2300,-1471) -> Matrix(5,-16,-4,13) Matrix(2897,1852,3956,2529) -> Matrix(7,-26,-4,15) Matrix(645,412,2162,1381) -> Matrix(5,-26,-4,21) Matrix(1655,1056,4324,2759) -> Matrix(5,-56,-4,45) Matrix(413,262,506,321) -> Matrix(1,0,0,1) Matrix(275,174,-874,-553) -> Matrix(3,2,4,3) Matrix(137,86,-368,-231) -> Matrix(7,-2,4,-1) Matrix(45,28,368,229) -> Matrix(1,-2,0,1) Matrix(737,458,1334,829) -> Matrix(1,-2,0,1) Matrix(229,142,-966,-599) -> Matrix(1,0,4,1) Matrix(689,426,-1564,-967) -> Matrix(7,-2,4,-1) Matrix(4829,2982,7820,4829) -> Matrix(7,-2,-24,7) Matrix(11501,7100,18630,11501) -> Matrix(17,-6,-48,17) Matrix(1565,966,4324,2669) -> Matrix(11,-4,-8,3) Matrix(2163,1334,3358,2071) -> Matrix(11,-4,-8,3) Matrix(277,170,-598,-367) -> Matrix(7,-2,4,-1) Matrix(1195,732,2852,1747) -> Matrix(11,-4,-8,3) Matrix(461,282,1656,1013) -> Matrix(29,-12,-12,5) Matrix(505,308,828,505) -> Matrix(13,-6,-28,13) Matrix(139,84,230,139) -> Matrix(7,-4,-12,7) Matrix(47,28,-230,-137) -> Matrix(5,-4,4,-3) Matrix(553,326,782,461) -> Matrix(3,-2,-4,3) Matrix(229,134,-552,-323) -> Matrix(3,-2,-4,3) Matrix(873,508,-1978,-1151) -> Matrix(5,-4,4,-3) Matrix(1105,642,2852,1657) -> Matrix(67,-48,-60,43) Matrix(231,134,874,507) -> Matrix(27,-20,-4,3) Matrix(2071,1198,2944,1703) -> Matrix(23,-18,-60,47) Matrix(2161,1248,-7728,-4463) -> Matrix(53,-42,24,-19) Matrix(1933,1116,2392,1381) -> Matrix(5,-4,4,-3) Matrix(229,132,-1518,-875) -> Matrix(5,-4,24,-19) Matrix(183,104,322,183) -> Matrix(15,-14,-16,15) Matrix(415,234,736,415) -> Matrix(25,-26,-24,25) Matrix(139,78,-736,-413) -> Matrix(23,-26,8,-9) Matrix(597,334,-1564,-875) -> Matrix(41,-50,32,-39) Matrix(829,458,1334,737) -> Matrix(1,-2,0,1) Matrix(323,178,920,507) -> Matrix(1,-6,0,1) Matrix(369,202,506,277) -> Matrix(1,-2,0,1) Matrix(137,74,-598,-323) -> Matrix(1,0,0,1) Matrix(231,124,-598,-321) -> Matrix(9,-8,8,-7) Matrix(277,130,-782,-367) -> Matrix(11,-14,4,-5) Matrix(367,168,-1610,-737) -> Matrix(1,-2,4,-7) Matrix(137,62,506,229) -> Matrix(1,-4,0,1) Matrix(597,268,920,413) -> Matrix(9,-10,-8,9) Matrix(505,226,1334,597) -> Matrix(17,-24,-12,17) Matrix(185,82,-828,-367) -> Matrix(3,-4,4,-5) Matrix(3081,1354,5336,2345) -> Matrix(3,-2,-4,3) Matrix(321,140,736,321) -> Matrix(1,-6,0,1) Matrix(139,60,322,139) -> Matrix(1,0,0,1) Matrix(47,20,-322,-137) -> Matrix(1,0,0,1) Matrix(2991,1264,5336,2255) -> Matrix(51,-22,-44,19) Matrix(21345,9016,29624,12513) -> Matrix(49,-24,96,-47) Matrix(16007,6760,22218,9383) -> Matrix(35,-18,72,-37) Matrix(1057,446,-3818,-1611) -> Matrix(19,-12,8,-5) Matrix(643,270,874,367) -> Matrix(5,-6,-4,5) Matrix(1747,732,2852,1195) -> Matrix(3,-4,-8,11) Matrix(967,404,-2530,-1057) -> Matrix(5,-24,4,-19) Matrix(1243,514,2116,875) -> Matrix(13,2,-20,-3) Matrix(1241,512,2116,873) -> Matrix(19,-2,-28,3) Matrix(229,94,782,321) -> Matrix(11,-4,-8,3) Matrix(829,338,-2254,-919) -> Matrix(1,2,0,1) Matrix(91,36,230,91) -> Matrix(7,-6,-8,7) Matrix(323,126,828,323) -> Matrix(29,-30,-28,29) Matrix(1195,464,1656,643) -> Matrix(11,-12,12,-13) Matrix(1657,642,2852,1105) -> Matrix(43,-48,-60,67) Matrix(1195,462,-4048,-1565) -> Matrix(3,-4,4,-5) Matrix(459,176,-2162,-829) -> Matrix(41,-50,32,-39) Matrix(2759,1056,4324,1655) -> Matrix(45,-56,-4,5) Matrix(7129,2728,18630,7129) -> Matrix(529,-660,-424,529) Matrix(2991,1144,7820,2991) -> Matrix(231,-290,-184,231) Matrix(3681,1406,-16376,-6255) -> Matrix(135,-172,208,-265) Matrix(321,122,-1334,-507) -> Matrix(3,-4,-20,27) Matrix(597,226,1334,505) -> Matrix(17,-24,-12,17) Matrix(323,122,368,139) -> Matrix(7,-10,-16,23) Matrix(1335,494,2116,783) -> Matrix(1,-2,12,-23) Matrix(1333,492,2116,781) -> Matrix(1,-2,-12,25) Matrix(1747,642,6256,2299) -> Matrix(9,-20,-4,9) Matrix(93,34,506,185) -> Matrix(1,-6,0,1) Matrix(2669,966,4324,1565) -> Matrix(3,-4,-8,11) Matrix(459,166,506,183) -> Matrix(1,-2,0,1) Matrix(1059,382,3956,1427) -> Matrix(1,-6,0,1) Matrix(323,116,-1150,-413) -> Matrix(9,-16,4,-7) Matrix(1287,458,3358,1195) -> Matrix(5,-26,-4,21) Matrix(1289,458,-4140,-1471) -> Matrix(3,-4,4,-5) Matrix(507,178,920,323) -> Matrix(1,-6,0,1) Matrix(321,112,920,321) -> Matrix(1,-14,0,1) Matrix(47,16,138,47) -> Matrix(1,0,0,1) Matrix(183,58,-874,-277) -> Matrix(17,-10,12,-7) Matrix(827,258,-3542,-1105) -> Matrix(3,-2,8,-5) Matrix(183,56,598,183) -> Matrix(15,-14,-16,15) Matrix(139,42,460,139) -> Matrix(13,-14,-12,13) Matrix(47,14,-460,-137) -> Matrix(11,-14,4,-5) Matrix(13387,3978,19044,5659) -> Matrix(65,-86,-164,217) Matrix(13385,3976,19044,5657) -> Matrix(55,-74,-136,183) Matrix(1241,368,2944,873) -> Matrix(1,-2,0,1) Matrix(1703,504,2024,599) -> Matrix(1,-2,0,1) Matrix(4829,1428,16330,4829) -> Matrix(17,-24,-12,17) Matrix(2991,884,10120,2991) -> Matrix(5,-6,-4,5) Matrix(321,94,782,229) -> Matrix(3,-4,-8,11) Matrix(323,94,1426,415) -> Matrix(3,-4,-8,11) Matrix(277,80,322,93) -> Matrix(9,-14,-16,25) Matrix(1519,430,2116,599) -> Matrix(1,-2,20,-39) Matrix(1517,428,2116,597) -> Matrix(1,-2,-20,41) Matrix(12835,3588,22218,6211) -> Matrix(37,-84,-48,109) Matrix(17111,4782,29624,8279) -> Matrix(47,-112,-60,143) Matrix(3129,874,3956,1105) -> Matrix(5,-12,-12,29) Matrix(1013,282,1656,461) -> Matrix(5,-12,-12,29) Matrix(1379,382,4646,1287) -> Matrix(11,-26,-8,19) Matrix(507,140,-2162,-597) -> Matrix(3,-8,8,-21) Matrix(415,114,506,139) -> Matrix(1,-4,0,1) Matrix(229,62,506,137) -> Matrix(1,-4,0,1) Matrix(231,62,-1196,-321) -> Matrix(9,-34,4,-15) Matrix(13939,3738,19044,5107) -> Matrix(39,-154,-20,79) Matrix(13937,3736,19044,5105) -> Matrix(33,-134,-16,65) Matrix(1427,382,3956,1059) -> Matrix(1,-6,0,1) Matrix(507,134,874,231) -> Matrix(3,-20,-4,27) Matrix(229,60,874,229) -> Matrix(1,-20,0,1) Matrix(47,12,184,47) -> Matrix(1,2,0,1) Matrix(1611,386,2116,507) -> Matrix(45,2,-68,-3) Matrix(1609,384,2116,505) -> Matrix(43,-2,-64,3) Matrix(25945,6064,33856,7913) -> Matrix(27,8,-44,-13) Matrix(25943,6062,33856,7911) -> Matrix(69,-8,-112,13) Matrix(6533,1492,8464,1933) -> Matrix(9,4,-16,-7) Matrix(6531,1490,8464,1931) -> Matrix(23,-4,-40,7) Matrix(415,94,1426,323) -> Matrix(11,-4,-8,3) Matrix(231,52,-1426,-321) -> Matrix(13,-8,-8,5) Matrix(14767,3318,19044,4279) -> Matrix(203,-134,-356,235) Matrix(14765,3316,19044,4277) -> Matrix(181,-122,-316,213) Matrix(91,20,414,91) -> Matrix(7,-6,-8,7) Matrix(139,30,644,139) -> Matrix(13,-14,-12,13) Matrix(459,98,1288,275) -> Matrix(13,-16,-4,5) Matrix(737,156,874,185) -> Matrix(1,-2,0,1) Matrix(2851,596,3956,827) -> Matrix(11,-16,20,-29) Matrix(1011,194,2392,459) -> Matrix(5,-12,-12,29) Matrix(185,34,506,93) -> Matrix(1,-6,0,1) Matrix(367,66,506,91) -> Matrix(1,-6,0,1) Matrix(137,24,782,137) -> Matrix(1,-24,0,1) Matrix(47,8,276,47) -> Matrix(1,6,0,1) Matrix(1425,226,2024,321) -> Matrix(7,6,-20,-17) Matrix(689,108,874,137) -> Matrix(7,4,-16,-9) Matrix(1795,274,2116,323) -> Matrix(29,2,-44,-3) Matrix(1793,272,2116,321) -> Matrix(27,-2,-40,3) Matrix(229,32,322,45) -> Matrix(1,0,-4,1) Matrix(91,12,690,91) -> Matrix(7,-6,-8,7) Matrix(47,6,368,47) -> Matrix(5,-6,-4,5) Matrix(229,28,368,45) -> Matrix(1,-2,0,1) Matrix(323,30,506,47) -> Matrix(1,-8,0,1) Matrix(137,-14,460,-47) -> Matrix(5,14,-4,-11) Matrix(137,-20,322,-47) -> Matrix(1,0,0,1) Matrix(1471,-236,2300,-369) -> Matrix(13,-16,-4,5) Matrix(413,-78,736,-139) -> Matrix(9,26,-8,-23) Matrix(137,-28,230,-47) -> Matrix(3,4,-4,-5) Matrix(829,-176,2162,-459) -> Matrix(39,50,-32,-41) Matrix(2161,-484,3496,-783) -> Matrix(3,2,-8,-5) Matrix(3265,-736,5106,-1151) -> Matrix(41,24,-12,-7) Matrix(323,-74,598,-137) -> Matrix(1,0,0,1) Matrix(413,-96,598,-139) -> Matrix(9,4,-16,-7) Matrix(599,-142,966,-229) -> Matrix(1,0,4,1) Matrix(5657,-1516,7728,-2071) -> Matrix(15,62,-8,-33) Matrix(2115,-568,3772,-1013) -> Matrix(23,84,-20,-73) Matrix(1839,-508,2668,-737) -> Matrix(5,12,-8,-19) Matrix(1611,-446,3818,-1057) -> Matrix(5,12,-8,-19) Matrix(4463,-1248,7728,-2161) -> Matrix(19,42,-24,-53) Matrix(413,-116,1150,-323) -> Matrix(7,16,-4,-9) Matrix(1011,-298,1564,-461) -> Matrix(1,0,0,1) Matrix(6209,-1844,8832,-2623) -> Matrix(25,34,-64,-87) Matrix(459,-142,598,-185) -> Matrix(17,14,-28,-23) Matrix(553,-174,874,-275) -> Matrix(3,2,4,3) Matrix(1103,-390,1564,-553) -> Matrix(1,4,-4,-15) Matrix(3771,-1340,4922,-1749) -> Matrix(5,2,-8,-3) Matrix(1289,-462,1794,-643) -> Matrix(1,2,8,17) Matrix(1931,-696,2300,-829) -> Matrix(3,4,-4,-5) Matrix(599,-220,874,-321) -> Matrix(5,12,-8,-19) Matrix(231,-86,368,-137) -> Matrix(1,2,-4,-7) Matrix(737,-280,966,-367) -> Matrix(31,42,-48,-65) Matrix(875,-334,1564,-597) -> Matrix(39,50,-32,-41) Matrix(321,-124,598,-231) -> Matrix(7,8,-8,-9) Matrix(183,-74,230,-93) -> Matrix(3,2,-8,-5) Matrix(323,-134,552,-229) -> Matrix(3,-2,-4,3) Matrix(1105,-462,1978,-827) -> Matrix(5,14,-4,-11) Matrix(5567,-2352,7728,-3265) -> Matrix(13,6,28,13) Matrix(1289,-546,1518,-643) -> Matrix(13,2,-20,-3) Matrix(597,-262,736,-323) -> Matrix(1,2,0,1) Matrix(967,-426,1564,-689) -> Matrix(1,2,-4,-7) Matrix(461,-212,598,-275) -> Matrix(7,10,-12,-17) Matrix(367,-170,598,-277) -> Matrix(1,2,-4,-7) Matrix(505,-268,782,-415) -> Matrix(5,4,-4,-3) Matrix(1243,-674,1610,-873) -> Matrix(9,4,-16,-7) Matrix(643,-358,828,-461) -> Matrix(11,16,-20,-29) Matrix(275,-158,322,-185) -> Matrix(17,14,-28,-23) Matrix(2761,-1596,3818,-2207) -> Matrix(3,2,4,3) Matrix(1563,-910,2530,-1473) -> Matrix(3,2,-8,-5) Matrix(1425,-844,2254,-1335) -> Matrix(1,0,4,1) Matrix(2853,-1750,4048,-2483) -> Matrix(11,4,-36,-13) Matrix(1703,-1050,2162,-1333) -> Matrix(7,4,-16,-9) Matrix(12695,-7846,16376,-10121) -> Matrix(7,-4,-12,7) Matrix(1013,-628,1334,-827) -> Matrix(11,-2,-16,3) Matrix(827,-530,1150,-737) -> Matrix(1,2,4,9) Matrix(2851,-1838,4140,-2669) -> Matrix(11,16,-20,-29) Matrix(691,-472,874,-597) -> Matrix(7,4,-16,-9) Matrix(2715,-1868,3542,-2437) -> Matrix(61,36,-100,-59) Matrix(413,-290,460,-323) -> Matrix(5,2,-8,-3) Matrix(1655,-1198,2162,-1565) -> Matrix(5,-18,-8,29) Matrix(965,-706,1196,-875) -> Matrix(1,2,0,1) Matrix(1195,-926,1426,-1105) -> Matrix(3,2,-8,-5) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 66 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 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): 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 1/6 4/23 2/11 1/5 4/19 5/23 2/9 4/17 1/4 6/23 3/11 2/7 34/115 3/10 7/23 1/3 8/23 8/21 44/115 9/23 2/5 10/23 1/2 13/23 14/23 15/23 2/3 16/23 116/161 17/23 35/46 71/92 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 0/1 1/2 -7/8 5/11 1/2 -6/7 7/12 -5/6 3/4 1/1 -4/5 1/4 -7/9 1/2 6/11 -24/31 7/12 -17/22 1/2 5/9 -10/13 7/12 -13/17 5/8 12/19 -3/4 3/4 1/1 -8/11 1/0 -13/18 -3/2 -1/1 -31/43 -2/3 -5/8 -18/25 -3/8 -5/7 0/1 1/4 -22/31 3/8 -17/24 3/7 1/2 -12/17 1/4 -7/10 3/7 1/2 -2/3 3/4 -15/23 1/1 -13/20 1/1 13/12 -11/17 5/4 4/3 -20/31 5/4 -9/14 3/2 5/3 -16/25 11/4 -7/11 -2/1 1/0 -12/19 -1/4 -5/8 1/2 1/1 -18/29 1/0 -13/21 0/1 1/6 -8/13 1/4 -3/5 1/2 2/3 -13/22 1/2 5/9 -10/17 5/8 -7/12 3/4 1/1 -4/7 7/8 -13/23 1/1 -9/16 1/1 13/12 -14/25 19/16 -5/9 3/2 2/1 -6/11 1/0 -7/13 1/2 2/3 -1/2 1/2 1/1 -5/11 2/1 1/0 -9/20 3/4 1/1 -13/29 6/5 5/4 -4/9 1/0 -3/7 0/1 1/0 -11/26 1/4 1/3 -19/45 1/2 6/11 -8/19 3/4 -5/12 -1/1 1/0 -2/5 3/4 -9/23 1/1 -7/18 1/1 15/14 -12/31 9/8 -17/44 1/1 7/6 -5/13 7/6 6/5 -18/47 5/4 -13/34 5/4 29/23 -8/21 21/16 -19/50 27/20 23/17 -11/29 11/8 18/13 -14/37 17/12 -3/8 3/2 5/3 -4/11 1/0 -5/14 5/2 3/1 -6/17 1/0 -1/3 0/1 1/0 -5/16 3/4 1/1 -4/13 7/8 -7/23 1/1 -3/10 1/1 7/6 -8/27 5/4 -13/44 1/1 3/2 -18/61 5/4 -5/17 5/4 4/3 -2/7 7/4 -3/11 2/1 1/0 -7/26 3/1 13/4 -4/15 1/0 -1/4 -1/1 1/0 -3/13 1/2 2/3 -8/35 1/0 -5/22 1/2 1/1 -2/9 3/4 -5/23 1/1 -3/14 1/1 7/6 -4/19 5/4 -5/24 3/2 11/7 -1/5 3/2 2/1 -2/11 1/0 -1/6 -3/1 1/0 -2/13 -1/4 -1/7 0/1 1/0 -2/15 3/4 -3/23 1/1 -1/8 1/1 3/2 -1/9 3/2 2/1 0/1 1/0 1/9 -2/1 -3/2 1/8 -3/2 -1/1 3/23 -1/1 2/15 -3/4 1/7 0/1 1/0 2/13 1/4 1/6 3/1 1/0 4/23 1/0 3/17 -12/1 1/0 2/11 1/0 1/5 -2/1 -3/2 4/19 -5/4 7/33 -4/3 -13/10 3/14 -7/6 -1/1 5/23 -1/1 2/9 -3/4 7/31 -6/11 -1/2 5/22 -1/1 -1/2 3/13 -2/3 -1/2 4/17 -1/4 1/4 1/1 1/0 6/23 1/0 5/19 -10/1 1/0 4/15 1/0 11/41 -4/1 -23/6 7/26 -13/4 -3/1 3/11 -2/1 1/0 2/7 -7/4 5/17 -4/3 -5/4 13/44 -3/2 -1/1 34/115 -3/2 21/71 -3/2 -4/3 8/27 -5/4 11/37 -4/3 -13/10 14/47 -5/4 3/10 -7/6 -1/1 7/23 -1/1 4/13 -7/8 5/16 -1/1 -3/4 1/3 0/1 1/0 8/23 1/0 7/20 -7/1 1/0 6/17 1/0 11/31 -5/2 -2/1 5/14 -3/1 -5/2 4/11 1/0 7/19 -9/4 -2/1 3/8 -5/3 -3/2 14/37 -17/12 11/29 -18/13 -11/8 8/21 -21/16 13/34 -29/23 -5/4 44/115 -5/4 31/81 -5/4 -66/53 18/47 -5/4 23/60 -27/22 -11/9 5/13 -6/5 -7/6 12/31 -9/8 19/49 -10/9 -31/28 7/18 -15/14 -1/1 9/23 -1/1 2/5 -3/4 7/17 -1/4 0/1 5/12 1/1 1/0 8/19 -3/4 19/45 -6/11 -1/2 30/71 -9/20 11/26 -1/3 -1/4 3/7 0/1 1/0 10/23 1/0 7/16 -3/1 1/0 4/9 1/0 13/29 -5/4 -6/5 9/20 -1/1 -3/4 5/11 -2/1 1/0 6/13 1/0 1/2 -1/1 -1/2 8/15 1/0 7/13 -2/3 -1/2 13/24 -1/1 -1/2 6/11 1/0 5/9 -2/1 -3/2 14/25 -19/16 9/16 -13/12 -1/1 13/23 -1/1 4/7 -7/8 7/12 -1/1 -3/4 17/29 -11/16 -2/3 27/46 -2/3 10/17 -5/8 13/22 -5/9 -1/2 16/27 1/0 3/5 -2/3 -1/2 14/23 -1/2 11/18 -1/2 -3/7 8/13 -1/4 29/47 -1/2 -2/5 50/81 -3/8 71/115 -1/3 21/34 -1/3 -1/4 13/21 -1/6 0/1 31/50 1/5 1/4 18/29 1/0 23/37 -1/2 0/1 5/8 -1/1 -1/2 17/27 -1/8 0/1 29/46 0/1 12/19 1/4 7/11 2/1 1/0 16/25 -11/4 9/14 -5/3 -3/2 20/31 -5/4 31/48 -3/2 -1/1 11/17 -4/3 -5/4 13/20 -13/12 -1/1 15/23 -1/1 2/3 -3/4 9/13 -6/11 -1/2 16/23 -1/2 7/10 -1/2 -3/7 19/27 -3/8 -4/11 50/71 -15/44 81/115 -1/3 31/44 -1/3 -7/22 12/17 -1/4 17/24 -1/2 -3/7 22/31 -3/8 5/7 -1/4 0/1 18/25 3/8 67/93 12/25 1/2 116/161 1/2 49/68 1/2 9/17 31/43 5/8 2/3 13/18 1/1 3/2 8/11 1/0 11/15 -3/2 -4/3 14/19 -9/8 17/23 -1/1 3/4 -1/1 -3/4 19/25 -23/34 -2/3 35/46 -2/3 16/21 -21/32 13/17 -12/19 -5/8 10/13 -7/12 27/35 -7/12 -4/7 71/92 -4/7 44/57 -9/16 17/22 -5/9 -1/2 24/31 -7/12 7/9 -6/11 -1/2 18/23 -1/2 11/14 -1/2 -7/15 4/5 -1/4 9/11 -2/1 1/0 14/17 -5/4 19/23 -1/1 5/6 -1/1 -3/4 6/7 -7/12 13/15 -12/23 -1/2 20/23 -1/2 7/8 -1/2 -5/11 8/9 -1/4 1/1 -1/2 0/1 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(47,42,207,185) (-1/1,-7/8) -> (7/31,5/22) Hyperbolic Matrix(139,120,161,139) (-7/8,-6/7) -> (6/7,13/15) Hyperbolic Matrix(47,40,-161,-137) (-6/7,-5/6) -> (-5/17,-2/7) Hyperbolic Matrix(47,38,115,93) (-5/6,-4/5) -> (2/5,7/17) Hyperbolic Matrix(91,72,115,91) (-4/5,-7/9) -> (11/14,4/5) Hyperbolic Matrix(459,356,-713,-553) (-7/9,-24/31) -> (-20/31,-9/14) Hyperbolic Matrix(1011,782,1426,1103) (-24/31,-17/22) -> (17/24,22/31) Hyperbolic Matrix(553,426,897,691) (-17/22,-10/13) -> (8/13,29/47) Hyperbolic Matrix(47,36,-299,-229) (-10/13,-13/17) -> (-1/6,-2/13) Hyperbolic Matrix(367,280,-966,-737) (-13/17,-3/4) -> (-19/50,-11/29) Hyperbolic Matrix(93,68,253,185) (-3/4,-8/11) -> (4/11,7/19) Hyperbolic Matrix(47,34,-253,-183) (-8/11,-13/18) -> (-1/5,-2/11) Hyperbolic Matrix(643,464,1656,1195) (-13/18,-31/43) -> (19/49,7/18) Hyperbolic Matrix(1565,1128,3703,2669) (-31/43,-18/25) -> (30/71,11/26) Hyperbolic Matrix(323,232,-575,-413) (-18/25,-5/7) -> (-9/16,-14/25) 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(91,64,391,275) (-12/17,-7/10) -> (3/13,4/17) Hyperbolic Matrix(47,32,69,47) (-7/10,-2/3) -> (2/3,9/13) 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(321,206,-575,-369) (-9/14,-16/25) -> (-14/25,-5/9) Hyperbolic Matrix(413,264,-1081,-691) (-16/25,-7/11) -> (-13/34,-8/21) Hyperbolic Matrix(183,116,-437,-277) (-7/11,-12/19) -> (-8/19,-5/12) Hyperbolic Matrix(321,202,437,275) (-12/19,-5/8) -> (11/15,14/19) Hyperbolic Matrix(367,228,1035,643) (-5/8,-18/29) -> (6/17,11/31) Hyperbolic Matrix(1151,714,1633,1013) (-18/29,-13/21) -> (31/44,12/17) Hyperbolic Matrix(139,86,299,185) (-13/21,-8/13) -> (6/13,1/2) Hyperbolic Matrix(183,112,299,183) (-8/13,-3/5) -> (11/18,8/13) 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(321,188,391,229) (-10/17,-7/12) -> (9/11,14/17) Hyperbolic Matrix(45,26,-161,-93) (-7/12,-4/7) -> (-2/7,-3/11) 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(91,50,-253,-139) (-5/9,-6/11) -> (-4/11,-5/14) 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(185,86,299,139) (-1/2,-5/11) -> (21/34,13/21) 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(91,40,207,91) (-4/9,-3/7) -> (7/16,4/9) Hyperbolic Matrix(137,58,-437,-185) (-3/7,-11/26) -> (-1/3,-5/16) Hyperbolic Matrix(2669,1128,3703,1565) (-11/26,-19/45) -> (49/68,31/43) Hyperbolic Matrix(275,116,-1311,-553) (-19/45,-8/19) -> (-4/19,-5/24) Hyperbolic Matrix(93,38,115,47) (-5/12,-2/5) -> (4/5,9/11) 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(413,160,1541,597) (-7/18,-12/31) -> (4/15,11/41) Hyperbolic Matrix(1195,462,-4048,-1565) (-12/31,-17/44) -> (-13/44,-18/61) Hyperbolic Matrix(323,124,1081,415) (-5/13,-18/47) -> (14/47,3/10) Hyperbolic Matrix(2069,792,5405,2069) (-18/47,-13/34) -> (31/81,18/47) Hyperbolic Matrix(2899,1102,4117,1565) (-8/21,-19/50) -> (19/27,50/71) 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(185,68,253,93) (-3/8,-4/11) -> (8/11,11/15) Hyperbolic Matrix(643,228,1035,367) (-5/14,-6/17) -> (18/29,23/37) Hyperbolic Matrix(137,48,391,137) (-6/17,-1/3) -> (7/20,6/17) Hyperbolic Matrix(45,14,-299,-93) (-5/16,-4/13) -> (-2/13,-1/7) 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(229,68,1081,321) (-3/10,-8/27) -> (4/19,7/33) Hyperbolic Matrix(919,272,3105,919) (-8/27,-13/44) -> (21/71,8/27) Hyperbolic Matrix(229,62,506,137) (-3/11,-7/26) -> (9/20,5/11) Hyperbolic Matrix(597,160,1541,413) (-7/26,-4/15) -> (12/31,19/49) Hyperbolic Matrix(91,24,345,91) (-4/15,-1/4) -> (5/19,4/15) Hyperbolic Matrix(275,64,391,91) (-1/4,-3/13) -> (7/10,19/27) Hyperbolic Matrix(2115,482,3427,781) (-8/35,-5/22) -> (29/47,50/81) Hyperbolic Matrix(185,42,207,47) (-5/22,-2/9) -> (8/9,1/1) 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(321,68,1081,229) (-3/14,-4/19) -> (8/27,11/37) Hyperbolic Matrix(45,8,253,45) (-2/11,-1/6) -> (3/17,2/11) 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(185,18,483,47) (-1/9,0/1) -> (18/47,23/60) Hyperbolic Matrix(137,-14,460,-47) (0/1,1/9) -> (11/37,14/47) Hyperbolic Matrix(139,-16,391,-45) (1/9,1/8) -> (11/31,5/14) Hyperbolic Matrix(93,-14,299,-45) (1/7,2/13) -> (4/13,5/16) Hyperbolic Matrix(229,-36,299,-47) (2/13,1/6) -> (13/17,10/13) Hyperbolic Matrix(93,-16,529,-91) (1/6,4/23) -> (4/23,3/17) Parabolic Matrix(183,-34,253,-47) (2/11,1/5) -> (13/18,8/11) 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(461,-104,1219,-275) (2/9,7/31) -> (3/8,14/37) Hyperbolic Matrix(323,-74,598,-137) (5/22,3/13) -> (7/13,13/24) Hyperbolic Matrix(599,-142,966,-229) (4/17,1/4) -> (31/50,18/29) Hyperbolic Matrix(139,-36,529,-137) (1/4,6/23) -> (6/23,5/19) Parabolic Matrix(1609,-432,2231,-599) (11/41,7/26) -> (31/43,13/18) Hyperbolic Matrix(93,-26,161,-45) (3/11,2/7) -> (4/7,7/12) Hyperbolic Matrix(137,-40,161,-47) (2/7,5/17) -> (5/6,6/7) Hyperbolic Matrix(1011,-298,1564,-461) (5/17,13/44) -> (31/48,11/17) Hyperbolic Matrix(3911,-1156,13225,-3909) (13/44,34/115) -> (34/115,21/71) Parabolic Matrix(185,-58,437,-137) (5/16,1/3) -> (11/26,3/7) Hyperbolic Matrix(185,-64,529,-183) (1/3,8/23) -> (8/23,7/20) Parabolic Matrix(139,-50,253,-91) (5/14,4/11) -> (6/11,5/9) 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(691,-264,1081,-413) (8/21,13/34) -> (7/11,16/25) Hyperbolic Matrix(5061,-1936,13225,-5059) (13/34,44/115) -> (44/115,31/81) Parabolic Matrix(321,-124,598,-231) (5/13,12/31) -> (8/15,7/13) Hyperbolic Matrix(323,-134,552,-229) (7/17,5/12) -> (7/12,17/29) Hyperbolic Matrix(277,-116,437,-183) (5/12,8/19) -> (12/19,7/11) Hyperbolic Matrix(967,-408,1633,-689) (8/19,19/45) -> (13/22,16/27) Hyperbolic Matrix(5567,-2352,7728,-3265) (19/45,30/71) -> (18/25,67/93) Hyperbolic Matrix(231,-100,529,-229) (3/7,10/23) -> (10/23,7/16) Parabolic Matrix(461,-212,598,-275) (5/11,6/13) -> (10/13,27/35) 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(369,-206,575,-321) (5/9,14/25) -> (16/25,9/14) Hyperbolic Matrix(413,-232,575,-323) (14/25,9/16) -> (5/7,18/25) Hyperbolic Matrix(781,-458,943,-553) (17/29,27/46) -> (19/23,5/6) Hyperbolic Matrix(967,-568,1173,-689) (27/46,10/17) -> (14/17,19/23) Hyperbolic Matrix(323,-196,529,-321) (3/5,14/23) -> (14/23,11/18) Parabolic Matrix(10811,-6674,14007,-8647) (50/81,71/115) -> (71/92,44/57) Hyperbolic Matrix(5519,-3408,7153,-4417) (71/115,21/34) -> (27/35,71/92) Hyperbolic Matrix(1013,-628,1334,-827) (13/21,31/50) -> (3/4,19/25) Hyperbolic Matrix(597,-376,805,-507) (17/27,29/46) -> (17/23,3/4) Hyperbolic Matrix(967,-610,1311,-827) (29/46,12/19) -> (14/19,17/23) Hyperbolic Matrix(553,-356,713,-459) (9/14,20/31) -> (24/31,7/9) Hyperbolic Matrix(369,-256,529,-367) (9/13,16/23) -> (16/23,7/10) Parabolic Matrix(4325,-3046,5681,-4001) (50/71,81/115) -> (35/46,16/21) Hyperbolic Matrix(3725,-2624,4899,-3451) (81/115,31/44) -> (19/25,35/46) Hyperbolic Matrix(18677,-13456,25921,-18675) (67/93,116/161) -> (116/161,49/68) Parabolic Matrix(415,-324,529,-413) (7/9,18/23) -> (18/23,11/14) Parabolic Matrix(461,-400,529,-459) (13/15,20/23) -> (20/23,7/8) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(47,42,207,185) -> Matrix(1,-1,0,1) Matrix(139,120,161,139) -> Matrix(13,-7,-24,13) Matrix(47,40,-161,-137) -> Matrix(11,-7,8,-5) Matrix(47,38,115,93) -> Matrix(1,-1,0,1) Matrix(91,72,115,91) -> Matrix(3,-1,-8,3) Matrix(459,356,-713,-553) -> Matrix(23,-13,16,-9) Matrix(1011,782,1426,1103) -> Matrix(3,-2,-4,3) Matrix(553,426,897,691) -> Matrix(5,-3,-8,5) Matrix(47,36,-299,-229) -> Matrix(5,-3,-8,5) Matrix(367,280,-966,-737) -> Matrix(65,-42,48,-31) Matrix(93,68,253,185) -> Matrix(1,-3,0,1) Matrix(47,34,-253,-183) -> Matrix(1,3,0,1) Matrix(643,464,1656,1195) -> Matrix(13,12,-12,-11) Matrix(1565,1128,3703,2669) -> Matrix(5,3,-12,-7) Matrix(323,232,-575,-413) -> Matrix(9,1,8,1) Matrix(45,32,322,229) -> Matrix(1,0,-4,1) Matrix(1103,782,1426,1011) -> Matrix(3,-2,-4,3) Matrix(461,326,782,553) -> Matrix(3,-2,-4,3) Matrix(91,64,391,275) -> Matrix(3,-1,-8,3) Matrix(47,32,69,47) -> Matrix(5,-3,-8,5) Matrix(91,60,138,91) -> Matrix(7,-6,-8,7) Matrix(599,390,920,599) -> Matrix(25,-26,-24,25) Matrix(413,268,920,597) -> Matrix(9,-10,-8,9) Matrix(461,298,-1564,-1011) -> Matrix(1,0,0,1) Matrix(321,206,-575,-369) -> Matrix(5,-9,4,-7) Matrix(413,264,-1081,-691) -> Matrix(5,-19,4,-15) Matrix(183,116,-437,-277) -> Matrix(1,1,0,1) Matrix(321,202,437,275) -> Matrix(5,-1,-4,1) Matrix(367,228,1035,643) -> Matrix(1,-3,0,1) Matrix(1151,714,1633,1013) -> Matrix(1,1,-4,-3) Matrix(139,86,299,185) -> Matrix(5,-1,-4,1) Matrix(183,112,299,183) -> Matrix(3,-1,-8,3) Matrix(47,28,-230,-137) -> Matrix(5,-4,4,-3) Matrix(553,326,782,461) -> Matrix(3,-2,-4,3) Matrix(321,188,391,229) -> Matrix(7,-5,-4,3) Matrix(45,26,-161,-93) -> Matrix(9,-7,4,-3) Matrix(183,104,322,183) -> Matrix(15,-14,-16,15) Matrix(415,234,736,415) -> Matrix(25,-26,-24,25) Matrix(91,50,-253,-139) -> Matrix(1,1,0,1) Matrix(137,74,-598,-323) -> Matrix(1,0,0,1) Matrix(231,124,-598,-321) -> Matrix(9,-8,8,-7) Matrix(185,86,299,139) -> Matrix(1,-1,-4,5) Matrix(137,62,506,229) -> Matrix(1,-4,0,1) Matrix(597,268,920,413) -> Matrix(9,-10,-8,9) Matrix(505,226,1334,597) -> Matrix(17,-24,-12,17) Matrix(91,40,207,91) -> Matrix(1,-3,0,1) Matrix(137,58,-437,-185) -> Matrix(3,-1,4,-1) Matrix(2669,1128,3703,1565) -> Matrix(7,-3,12,-5) Matrix(275,116,-1311,-553) -> Matrix(11,-7,8,-5) Matrix(93,38,115,47) -> Matrix(1,-1,0,1) Matrix(91,36,230,91) -> Matrix(7,-6,-8,7) Matrix(323,126,828,323) -> Matrix(29,-30,-28,29) Matrix(413,160,1541,597) -> Matrix(33,-37,-8,9) Matrix(1195,462,-4048,-1565) -> Matrix(3,-4,4,-5) Matrix(323,124,1081,415) -> Matrix(29,-35,-24,29) Matrix(2069,792,5405,2069) -> Matrix(149,-185,-120,149) Matrix(2899,1102,4117,1565) -> Matrix(29,-39,-84,113) Matrix(597,226,1334,505) -> Matrix(17,-24,-12,17) Matrix(323,122,368,139) -> Matrix(7,-10,-16,23) Matrix(185,68,253,93) -> Matrix(1,-3,0,1) Matrix(643,228,1035,367) -> Matrix(1,-3,0,1) Matrix(137,48,391,137) -> Matrix(1,-7,0,1) Matrix(45,14,-299,-93) -> Matrix(1,-1,4,-3) Matrix(183,56,598,183) -> Matrix(15,-14,-16,15) Matrix(139,42,460,139) -> Matrix(13,-14,-12,13) Matrix(229,68,1081,321) -> Matrix(11,-15,-8,11) Matrix(919,272,3105,919) -> Matrix(11,-15,-8,11) Matrix(229,62,506,137) -> Matrix(1,-4,0,1) Matrix(597,160,1541,413) -> Matrix(9,-37,-8,33) Matrix(91,24,345,91) -> Matrix(1,-9,0,1) Matrix(275,64,391,91) -> Matrix(3,-1,-8,3) Matrix(2115,482,3427,781) -> Matrix(3,-1,-8,3) Matrix(185,42,207,47) -> Matrix(1,-1,0,1) Matrix(91,20,414,91) -> Matrix(7,-6,-8,7) Matrix(139,30,644,139) -> Matrix(13,-14,-12,13) Matrix(321,68,1081,229) -> Matrix(11,-15,-8,11) Matrix(45,8,253,45) -> Matrix(1,-9,0,1) Matrix(229,32,322,45) -> Matrix(1,0,-4,1) Matrix(91,12,690,91) -> Matrix(7,-6,-8,7) Matrix(47,6,368,47) -> Matrix(5,-6,-4,5) Matrix(229,28,368,45) -> Matrix(1,-2,0,1) Matrix(185,18,483,47) -> Matrix(5,-21,-4,17) Matrix(137,-14,460,-47) -> Matrix(5,14,-4,-11) Matrix(139,-16,391,-45) -> Matrix(1,-1,0,1) Matrix(93,-14,299,-45) -> Matrix(3,1,-4,-1) Matrix(229,-36,299,-47) -> Matrix(5,-3,-8,5) Matrix(93,-16,529,-91) -> Matrix(1,-15,0,1) Matrix(183,-34,253,-47) -> Matrix(1,3,0,1) Matrix(137,-28,230,-47) -> Matrix(3,4,-4,-5) Matrix(829,-176,2162,-459) -> Matrix(39,50,-32,-41) Matrix(461,-104,1219,-275) -> Matrix(23,13,-16,-9) Matrix(323,-74,598,-137) -> Matrix(1,0,0,1) Matrix(599,-142,966,-229) -> Matrix(1,0,4,1) Matrix(139,-36,529,-137) -> Matrix(1,-11,0,1) Matrix(1609,-432,2231,-599) -> Matrix(3,11,4,15) Matrix(93,-26,161,-45) -> Matrix(3,7,-4,-9) Matrix(137,-40,161,-47) -> Matrix(5,7,-8,-11) Matrix(1011,-298,1564,-461) -> Matrix(1,0,0,1) Matrix(3911,-1156,13225,-3909) -> Matrix(5,9,-4,-7) Matrix(185,-58,437,-137) -> Matrix(1,1,-4,-3) Matrix(185,-64,529,-183) -> Matrix(1,-7,0,1) Matrix(139,-50,253,-91) -> Matrix(1,1,0,1) Matrix(231,-86,368,-137) -> Matrix(1,2,-4,-7) Matrix(737,-280,966,-367) -> Matrix(31,42,-48,-65) Matrix(691,-264,1081,-413) -> Matrix(15,19,-4,-5) Matrix(5061,-1936,13225,-5059) -> Matrix(379,475,-304,-381) Matrix(321,-124,598,-231) -> Matrix(7,8,-8,-9) Matrix(323,-134,552,-229) -> Matrix(3,-2,-4,3) Matrix(277,-116,437,-183) -> Matrix(1,1,0,1) Matrix(967,-408,1633,-689) -> Matrix(1,1,-4,-3) Matrix(5567,-2352,7728,-3265) -> Matrix(13,6,28,13) Matrix(231,-100,529,-229) -> Matrix(1,-3,0,1) Matrix(461,-212,598,-275) -> Matrix(7,10,-12,-17) Matrix(505,-268,782,-415) -> Matrix(5,4,-4,-3) Matrix(1243,-674,1610,-873) -> Matrix(9,4,-16,-7) Matrix(369,-206,575,-321) -> Matrix(7,9,-4,-5) Matrix(413,-232,575,-323) -> Matrix(1,1,8,9) Matrix(781,-458,943,-553) -> Matrix(25,17,-28,-19) Matrix(967,-568,1173,-689) -> Matrix(23,15,-20,-13) Matrix(323,-196,529,-321) -> Matrix(9,5,-20,-11) Matrix(10811,-6674,14007,-8647) -> Matrix(59,21,-104,-37) Matrix(5519,-3408,7153,-4417) -> Matrix(37,11,-64,-19) Matrix(1013,-628,1334,-827) -> Matrix(11,-2,-16,3) Matrix(597,-376,805,-507) -> Matrix(11,1,-12,-1) Matrix(967,-610,1311,-827) -> Matrix(13,-1,-12,1) Matrix(553,-356,713,-459) -> Matrix(9,13,-16,-23) Matrix(369,-256,529,-367) -> Matrix(17,9,-36,-19) Matrix(4325,-3046,5681,-4001) -> Matrix(151,51,-228,-77) Matrix(3725,-2624,4899,-3451) -> Matrix(113,37,-168,-55) Matrix(18677,-13456,25921,-18675) -> Matrix(43,-21,84,-41) Matrix(415,-324,529,-413) -> Matrix(25,13,-52,-27) Matrix(461,-400,529,-459) -> Matrix(33,17,-68,-35) 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 (-2/1,-3/2) 0 23 1/8 (-3/2,-1/1) 0 23 3/23 -1/1 6 1 2/15 -3/4 1 23 1/7 (0/1,1/0) 0 23 2/13 1/4 1 23 1/6 (3/1,1/0) 0 23 4/23 1/0 15 1 2/11 1/0 1 23 1/5 (-2/1,-3/2) 0 23 4/19 -5/4 1 23 3/14 (-7/6,-1/1) 0 23 5/23 -1/1 10 1 2/9 -3/4 1 23 5/22 (-1/1,-1/2) 0 23 3/13 (-2/3,-1/2) 0 23 1/4 (1/1,1/0) 0 23 6/23 1/0 11 1 4/15 1/0 1 23 7/26 (-13/4,-3/1) 0 23 3/11 (-2/1,1/0) 0 23 2/7 -7/4 1 23 5/17 (-4/3,-5/4) 0 23 13/44 (-3/2,-1/1) 0 23 34/115 -3/2 1 1 8/27 -5/4 1 23 11/37 (-4/3,-13/10) 0 23 3/10 (-7/6,-1/1) 0 23 7/23 -1/1 14 1 4/13 -7/8 1 23 5/16 (-1/1,-3/4) 0 23 1/3 (0/1,1/0) 0 23 8/23 1/0 7 1 6/17 1/0 1 23 5/14 (-3/1,-5/2) 0 23 4/11 1/0 1 23 3/8 (-5/3,-3/2) 0 23 14/37 -17/12 1 23 11/29 (-18/13,-11/8) 0 23 8/21 -21/16 1 23 13/34 (-29/23,-5/4) 0 23 44/115 -5/4 19 1 18/47 -5/4 1 23 23/60 (-27/22,-11/9) 0 23 5/13 (-6/5,-7/6) 0 23 12/31 -9/8 1 23 19/49 (-10/9,-31/28) 0 23 7/18 (-15/14,-1/1) 0 23 9/23 -1/1 18 1 2/5 -3/4 1 23 5/12 (1/1,1/0) 0 23 8/19 -3/4 1 23 19/45 (-6/11,-1/2) 0 23 11/26 (-1/3,-1/4) 0 23 3/7 (0/1,1/0) 0 23 10/23 1/0 3 1 4/9 1/0 1 23 13/29 (-5/4,-6/5) 0 23 9/20 (-1/1,-3/4) 0 23 5/11 (-2/1,1/0) 0 23 1/2 (-1/1,-1/2) 0 23 8/15 1/0 1 23 7/13 (-2/3,-1/2) 0 23 13/24 (-1/1,-1/2) 0 23 6/11 1/0 1 23 5/9 (-2/1,-3/2) 0 23 14/25 -19/16 1 23 9/16 (-13/12,-1/1) 0 23 13/23 -1/1 20 1 4/7 -7/8 1 23 7/12 (-1/1,-3/4) 0 23 10/17 -5/8 1 23 13/22 (-5/9,-1/2) 0 23 16/27 1/0 1 23 3/5 (-2/3,-1/2) 0 23 14/23 -1/2 5 1 8/13 -1/4 1 23 21/34 (-1/3,-1/4) 0 23 13/21 (-1/6,0/1) 0 23 18/29 1/0 1 23 23/37 (-1/2,0/1) 0 23 5/8 (-1/1,-1/2) 0 23 12/19 1/4 1 23 7/11 (2/1,1/0) 0 23 16/25 -11/4 1 23 9/14 (-5/3,-3/2) 0 23 20/31 -5/4 1 23 31/48 (-3/2,-1/1) 0 23 11/17 (-4/3,-5/4) 0 23 13/20 (-13/12,-1/1) 0 23 15/23 -1/1 16 1 2/3 -3/4 1 23 16/23 -1/2 9 1 7/10 (-1/2,-3/7) 0 23 19/27 (-3/8,-4/11) 0 23 31/44 (-1/3,-7/22) 0 23 12/17 -1/4 1 23 17/24 (-1/2,-3/7) 0 23 22/31 -3/8 1 23 5/7 (-1/4,0/1) 0 23 18/25 3/8 1 23 116/161 1/2 21 1 49/68 (1/2,9/17) 0 23 31/43 (5/8,2/3) 0 23 13/18 (1/1,3/2) 0 23 8/11 1/0 1 23 11/15 (-3/2,-4/3) 0 23 14/19 -9/8 1 23 17/23 -1/1 12 1 3/4 (-1/1,-3/4) 0 23 19/25 (-23/34,-2/3) 0 23 35/46 -2/3 22 1 16/21 -21/32 1 23 13/17 (-12/19,-5/8) 0 23 10/13 -7/12 1 23 27/35 (-7/12,-4/7) 0 23 71/92 -4/7 4 1 44/57 -9/16 1 23 17/22 (-5/9,-1/2) 0 23 24/31 -7/12 1 23 7/9 (-6/11,-1/2) 0 23 18/23 -1/2 13 1 4/5 -1/4 1 23 9/11 (-2/1,1/0) 0 23 14/17 -5/4 1 23 19/23 -1/1 8 1 5/6 (-1/1,-3/4) 0 23 6/7 -7/12 1 23 20/23 -1/2 17 1 7/8 (-1/2,-5/11) 0 23 8/9 -1/4 1 23 1/1 (-1/2,0/1) 0 23 1/0 0/1 2 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(185,-18,483,-47) (0/1,1/9) -> (18/47,23/60) Glide Reflection Matrix(229,-28,368,-45) (1/9,1/8) -> (23/37,5/8) Glide Reflection 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(229,-32,322,-45) (2/15,1/7) -> (22/31,5/7) Glide Reflection Matrix(93,-14,299,-45) (1/7,2/13) -> (4/13,5/16) Hyperbolic Matrix(229,-36,299,-47) (2/13,1/6) -> (13/17,10/13) Hyperbolic Matrix(47,-8,276,-47) (1/6,4/23) -> (1/6,4/23) Reflection Matrix(45,-8,253,-45) (4/23,2/11) -> (4/23,2/11) Reflection Matrix(183,-34,253,-47) (2/11,1/5) -> (13/18,8/11) Hyperbolic Matrix(137,-28,230,-47) (1/5,4/19) -> (16/27,3/5) Hyperbolic Matrix(321,-68,1081,-229) (4/19,3/14) -> (8/27,11/37) Glide Reflection 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(185,-42,207,-47) (2/9,5/22) -> (8/9,1/1) Glide Reflection Matrix(323,-74,598,-137) (5/22,3/13) -> (7/13,13/24) Hyperbolic Matrix(275,-64,391,-91) (3/13,1/4) -> (7/10,19/27) Glide Reflection Matrix(47,-12,184,-47) (1/4,6/23) -> (1/4,6/23) Reflection Matrix(91,-24,345,-91) (6/23,4/15) -> (6/23,4/15) Reflection Matrix(597,-160,1541,-413) (4/15,7/26) -> (12/31,19/49) Glide Reflection Matrix(229,-62,506,-137) (7/26,3/11) -> (9/20,5/11) Glide Reflection Matrix(93,-26,161,-45) (3/11,2/7) -> (4/7,7/12) Hyperbolic Matrix(137,-40,161,-47) (2/7,5/17) -> (5/6,6/7) Hyperbolic Matrix(1011,-298,1564,-461) (5/17,13/44) -> (31/48,11/17) Hyperbolic Matrix(2991,-884,10120,-2991) (13/44,34/115) -> (13/44,34/115) Reflection Matrix(919,-272,3105,-919) (34/115,8/27) -> (34/115,8/27) Reflection Matrix(415,-124,1081,-323) (11/37,3/10) -> (23/60,5/13) Glide Reflection 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(185,-58,437,-137) (5/16,1/3) -> (11/26,3/7) Hyperbolic Matrix(47,-16,138,-47) (1/3,8/23) -> (1/3,8/23) Reflection Matrix(137,-48,391,-137) (8/23,6/17) -> (8/23,6/17) Reflection Matrix(643,-228,1035,-367) (6/17,5/14) -> (18/29,23/37) Glide Reflection Matrix(139,-50,253,-91) (5/14,4/11) -> (6/11,5/9) Hyperbolic Matrix(185,-68,253,-93) (4/11,3/8) -> (8/11,11/15) Glide Reflection Matrix(323,-122,368,-139) (3/8,14/37) -> (7/8,8/9) Glide Reflection Matrix(597,-226,1334,-505) (14/37,11/29) -> (4/9,13/29) Glide Reflection Matrix(737,-280,966,-367) (11/29,8/21) -> (16/21,13/17) Hyperbolic Matrix(691,-264,1081,-413) (8/21,13/34) -> (7/11,16/25) Hyperbolic Matrix(2991,-1144,7820,-2991) (13/34,44/115) -> (13/34,44/115) Reflection Matrix(2069,-792,5405,-2069) (44/115,18/47) -> (44/115,18/47) Reflection Matrix(321,-124,598,-231) (5/13,12/31) -> (8/15,7/13) Hyperbolic Matrix(1195,-464,1656,-643) (19/49,7/18) -> (31/43,13/18) Glide Reflection 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(93,-38,115,-47) (2/5,5/12) -> (4/5,9/11) Glide Reflection Matrix(277,-116,437,-183) (5/12,8/19) -> (12/19,7/11) Hyperbolic Matrix(967,-408,1633,-689) (8/19,19/45) -> (13/22,16/27) Hyperbolic Matrix(2669,-1128,3703,-1565) (19/45,11/26) -> (49/68,31/43) Glide Reflection Matrix(139,-60,322,-139) (3/7,10/23) -> (3/7,10/23) Reflection Matrix(91,-40,207,-91) (10/23,4/9) -> (10/23,4/9) Reflection Matrix(597,-268,920,-413) (13/29,9/20) -> (11/17,13/20) Glide Reflection Matrix(185,-86,299,-139) (5/11,1/2) -> (21/34,13/21) Glide Reflection 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(369,-206,575,-321) (5/9,14/25) -> (16/25,9/14) Hyperbolic Matrix(413,-232,575,-323) (14/25,9/16) -> (5/7,18/25) Hyperbolic Matrix(415,-234,736,-415) (9/16,13/23) -> (9/16,13/23) Reflection Matrix(183,-104,322,-183) (13/23,4/7) -> (13/23,4/7) Reflection Matrix(321,-188,391,-229) (7/12,10/17) -> (9/11,14/17) Glide Reflection Matrix(553,-326,782,-461) (10/17,13/22) -> (12/17,17/24) Glide Reflection Matrix(139,-84,230,-139) (3/5,14/23) -> (3/5,14/23) Reflection Matrix(183,-112,299,-183) (14/23,8/13) -> (14/23,8/13) Reflection Matrix(691,-426,897,-553) (8/13,21/34) -> (10/13,27/35) Glide Reflection Matrix(1151,-714,1633,-1013) (13/21,18/29) -> (31/44,12/17) Glide Reflection Matrix(321,-202,437,-275) (5/8,12/19) -> (11/15,14/19) Glide Reflection Matrix(553,-356,713,-459) (9/14,20/31) -> (24/31,7/9) Hyperbolic Matrix(599,-390,920,-599) (13/20,15/23) -> (13/20,15/23) Reflection Matrix(91,-60,138,-91) (15/23,2/3) -> (15/23,2/3) Reflection Matrix(47,-32,69,-47) (2/3,16/23) -> (2/3,16/23) Reflection Matrix(321,-224,460,-321) (16/23,7/10) -> (16/23,7/10) Reflection Matrix(645,-454,851,-599) (19/27,31/44) -> (3/4,19/25) Glide Reflection Matrix(1103,-782,1426,-1011) (17/24,22/31) -> (17/22,24/31) Glide Reflection Matrix(2899,-2088,4025,-2899) (18/25,116/161) -> (18/25,116/161) Reflection Matrix(15777,-11368,21896,-15777) (116/161,49/68) -> (116/161,49/68) Reflection Matrix(645,-476,874,-645) (14/19,17/23) -> (14/19,17/23) Reflection Matrix(137,-102,184,-137) (17/23,3/4) -> (17/23,3/4) Reflection Matrix(1749,-1330,2300,-1749) (19/25,35/46) -> (19/25,35/46) Reflection Matrix(1471,-1120,1932,-1471) (35/46,16/21) -> (35/46,16/21) Reflection Matrix(4969,-3834,6440,-4969) (27/35,71/92) -> (27/35,71/92) Reflection Matrix(8095,-6248,10488,-8095) (71/92,44/57) -> (71/92,44/57) Reflection Matrix(323,-252,414,-323) (7/9,18/23) -> (7/9,18/23) Reflection Matrix(91,-72,115,-91) (18/23,4/5) -> (18/23,4/5) Reflection Matrix(645,-532,782,-645) (14/17,19/23) -> (14/17,19/23) Reflection Matrix(229,-190,276,-229) (19/23,5/6) -> (19/23,5/6) Reflection Matrix(139,-120,161,-139) (6/7,20/23) -> (6/7,20/23) Reflection Matrix(321,-280,368,-321) (20/23,7/8) -> (20/23,7/8) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) 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(185,-18,483,-47) -> Matrix(5,21,-4,-17) Matrix(229,-28,368,-45) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(47,-6,368,-47) -> Matrix(5,6,-4,-5) (1/8,3/23) -> (-3/2,-1/1) Matrix(91,-12,690,-91) -> Matrix(7,6,-8,-7) (3/23,2/15) -> (-1/1,-3/4) Matrix(229,-32,322,-45) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(93,-14,299,-45) -> Matrix(3,1,-4,-1) -1/2 Matrix(229,-36,299,-47) -> Matrix(5,-3,-8,5) Matrix(47,-8,276,-47) -> Matrix(-1,6,0,1) (1/6,4/23) -> (3/1,1/0) Matrix(45,-8,253,-45) -> Matrix(1,9,0,-1) (4/23,2/11) -> (-9/2,1/0) Matrix(183,-34,253,-47) -> Matrix(1,3,0,1) 1/0 Matrix(137,-28,230,-47) -> Matrix(3,4,-4,-5) -1/1 Matrix(321,-68,1081,-229) -> Matrix(11,15,-8,-11) *** -> (-3/2,-5/4) Matrix(139,-30,644,-139) -> Matrix(13,14,-12,-13) (3/14,5/23) -> (-7/6,-1/1) Matrix(91,-20,414,-91) -> Matrix(7,6,-8,-7) (5/23,2/9) -> (-1/1,-3/4) Matrix(185,-42,207,-47) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(323,-74,598,-137) -> Matrix(1,0,0,1) Matrix(275,-64,391,-91) -> Matrix(3,1,-8,-3) *** -> (-1/2,-1/4) Matrix(47,-12,184,-47) -> Matrix(-1,2,0,1) (1/4,6/23) -> (1/1,1/0) Matrix(91,-24,345,-91) -> Matrix(1,9,0,-1) (6/23,4/15) -> (-9/2,1/0) Matrix(597,-160,1541,-413) -> Matrix(9,37,-8,-33) Matrix(229,-62,506,-137) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(93,-26,161,-45) -> Matrix(3,7,-4,-9) Matrix(137,-40,161,-47) -> Matrix(5,7,-8,-11) Matrix(1011,-298,1564,-461) -> Matrix(1,0,0,1) Matrix(2991,-884,10120,-2991) -> Matrix(5,6,-4,-5) (13/44,34/115) -> (-3/2,-1/1) Matrix(919,-272,3105,-919) -> Matrix(11,15,-8,-11) (34/115,8/27) -> (-3/2,-5/4) Matrix(415,-124,1081,-323) -> Matrix(29,35,-24,-29) *** -> (-5/4,-7/6) Matrix(139,-42,460,-139) -> Matrix(13,14,-12,-13) (3/10,7/23) -> (-7/6,-1/1) Matrix(183,-56,598,-183) -> Matrix(15,14,-16,-15) (7/23,4/13) -> (-1/1,-7/8) Matrix(185,-58,437,-137) -> Matrix(1,1,-4,-3) -1/2 Matrix(47,-16,138,-47) -> Matrix(1,0,0,-1) (1/3,8/23) -> (0/1,1/0) Matrix(137,-48,391,-137) -> Matrix(1,7,0,-1) (8/23,6/17) -> (-7/2,1/0) Matrix(643,-228,1035,-367) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(139,-50,253,-91) -> Matrix(1,1,0,1) 1/0 Matrix(185,-68,253,-93) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(323,-122,368,-139) -> Matrix(7,10,-16,-23) Matrix(597,-226,1334,-505) -> Matrix(17,24,-12,-17) *** -> (-3/2,-4/3) Matrix(737,-280,966,-367) -> Matrix(31,42,-48,-65) Matrix(691,-264,1081,-413) -> Matrix(15,19,-4,-5) Matrix(2991,-1144,7820,-2991) -> Matrix(231,290,-184,-231) (13/34,44/115) -> (-29/23,-5/4) Matrix(2069,-792,5405,-2069) -> Matrix(149,185,-120,-149) (44/115,18/47) -> (-5/4,-37/30) Matrix(321,-124,598,-231) -> Matrix(7,8,-8,-9) -1/1 Matrix(1195,-464,1656,-643) -> Matrix(11,12,12,13) Matrix(323,-126,828,-323) -> Matrix(29,30,-28,-29) (7/18,9/23) -> (-15/14,-1/1) Matrix(91,-36,230,-91) -> Matrix(7,6,-8,-7) (9/23,2/5) -> (-1/1,-3/4) Matrix(93,-38,115,-47) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(277,-116,437,-183) -> Matrix(1,1,0,1) 1/0 Matrix(967,-408,1633,-689) -> Matrix(1,1,-4,-3) -1/2 Matrix(2669,-1128,3703,-1565) -> Matrix(7,3,12,5) Matrix(139,-60,322,-139) -> Matrix(1,0,0,-1) (3/7,10/23) -> (0/1,1/0) Matrix(91,-40,207,-91) -> Matrix(1,3,0,-1) (10/23,4/9) -> (-3/2,1/0) Matrix(597,-268,920,-413) -> Matrix(9,10,-8,-9) *** -> (-5/4,-1/1) Matrix(185,-86,299,-139) -> Matrix(1,1,-4,-5) Matrix(505,-268,782,-415) -> Matrix(5,4,-4,-3) -1/1 Matrix(1243,-674,1610,-873) -> Matrix(9,4,-16,-7) -1/2 Matrix(369,-206,575,-321) -> Matrix(7,9,-4,-5) -3/2 Matrix(413,-232,575,-323) -> Matrix(1,1,8,9) Matrix(415,-234,736,-415) -> Matrix(25,26,-24,-25) (9/16,13/23) -> (-13/12,-1/1) Matrix(183,-104,322,-183) -> Matrix(15,14,-16,-15) (13/23,4/7) -> (-1/1,-7/8) Matrix(321,-188,391,-229) -> Matrix(7,5,-4,-3) Matrix(553,-326,782,-461) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(139,-84,230,-139) -> Matrix(7,4,-12,-7) (3/5,14/23) -> (-2/3,-1/2) Matrix(183,-112,299,-183) -> Matrix(3,1,-8,-3) (14/23,8/13) -> (-1/2,-1/4) Matrix(691,-426,897,-553) -> Matrix(5,3,-8,-5) *** -> (-3/4,-1/2) Matrix(1151,-714,1633,-1013) -> Matrix(1,-1,-4,3) Matrix(321,-202,437,-275) -> Matrix(5,1,-4,-1) Matrix(553,-356,713,-459) -> Matrix(9,13,-16,-23) Matrix(599,-390,920,-599) -> Matrix(25,26,-24,-25) (13/20,15/23) -> (-13/12,-1/1) Matrix(91,-60,138,-91) -> Matrix(7,6,-8,-7) (15/23,2/3) -> (-1/1,-3/4) Matrix(47,-32,69,-47) -> Matrix(5,3,-8,-5) (2/3,16/23) -> (-3/4,-1/2) Matrix(321,-224,460,-321) -> Matrix(13,6,-28,-13) (16/23,7/10) -> (-1/2,-3/7) Matrix(645,-454,851,-599) -> Matrix(25,9,-36,-13) Matrix(1103,-782,1426,-1011) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(2899,-2088,4025,-2899) -> Matrix(7,-3,16,-7) (18/25,116/161) -> (3/8,1/2) Matrix(15777,-11368,21896,-15777) -> Matrix(35,-18,68,-35) (116/161,49/68) -> (1/2,9/17) Matrix(645,-476,874,-645) -> Matrix(17,18,-16,-17) (14/19,17/23) -> (-9/8,-1/1) Matrix(137,-102,184,-137) -> Matrix(7,6,-8,-7) (17/23,3/4) -> (-1/1,-3/4) Matrix(1749,-1330,2300,-1749) -> Matrix(137,92,-204,-137) (19/25,35/46) -> (-23/34,-2/3) Matrix(1471,-1120,1932,-1471) -> Matrix(127,84,-192,-127) (35/46,16/21) -> (-2/3,-21/32) Matrix(4969,-3834,6440,-4969) -> Matrix(97,56,-168,-97) (27/35,71/92) -> (-7/12,-4/7) Matrix(8095,-6248,10488,-8095) -> Matrix(127,72,-224,-127) (71/92,44/57) -> (-4/7,-9/16) Matrix(323,-252,414,-323) -> Matrix(23,12,-44,-23) (7/9,18/23) -> (-6/11,-1/2) Matrix(91,-72,115,-91) -> Matrix(3,1,-8,-3) (18/23,4/5) -> (-1/2,-1/4) Matrix(645,-532,782,-645) -> Matrix(9,10,-8,-9) (14/17,19/23) -> (-5/4,-1/1) Matrix(229,-190,276,-229) -> Matrix(7,6,-8,-7) (19/23,5/6) -> (-1/1,-3/4) Matrix(139,-120,161,-139) -> Matrix(13,7,-24,-13) (6/7,20/23) -> (-7/12,-1/2) Matrix(321,-280,368,-321) -> Matrix(21,10,-44,-21) (20/23,7/8) -> (-1/2,-5/11) Matrix(-1,2,0,1) -> Matrix(-1,0,4,1) (1/1,1/0) -> (-1/2,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.