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 1/0 -8/9 -2/1 1/0 -7/8 -3/2 -1/1 -20/23 -1/1 -13/15 -3/4 -6/7 -1/2 0/1 -11/13 1/0 -16/19 0/1 1/0 -21/25 1/0 -5/6 1/1 1/0 -19/23 1/0 -14/17 -6/1 1/0 -9/11 1/0 -13/16 -2/1 -1/1 -4/5 -2/1 1/0 -15/19 -3/2 -26/33 -4/3 -5/4 -11/14 -7/6 -1/1 -18/23 -1/1 -7/9 -3/4 -31/40 -3/5 -1/2 -24/31 -4/7 -1/2 -17/22 -1/1 -1/2 -10/13 -1/2 0/1 -13/17 -1/2 -3/4 -1/1 0/1 -17/23 0/1 -14/19 0/1 1/0 -11/15 1/0 -41/56 0/1 1/1 -30/41 0/1 1/0 -19/26 -2/1 -1/1 -8/11 0/1 1/0 -21/29 -3/4 -34/47 -4/7 -1/2 -13/18 -1/3 0/1 -31/43 1/0 -49/68 -1/1 1/0 -18/25 -1/2 0/1 -5/7 1/0 -22/31 -6/1 1/0 -17/24 -3/1 1/0 -12/17 -2/1 1/0 -31/44 -15/7 -2/1 -81/115 -2/1 -50/71 -2/1 -27/14 -19/27 -7/4 -45/64 -2/1 -5/3 -26/37 -2/1 -3/2 -33/47 -3/2 -7/10 -4/3 -1/1 -16/23 -1/1 -9/13 -5/6 -11/16 -5/7 -2/3 -2/3 -1/2 0/1 -15/23 0/1 -13/20 0/1 1/7 -11/17 1/2 -20/31 0/1 1/2 -29/45 1/2 -9/14 1/1 1/0 -25/39 1/0 -16/25 -1/2 0/1 -39/61 1/2 -23/36 0/1 1/1 -30/47 0/1 1/2 -7/11 1/0 -19/30 -1/1 0/1 -12/19 0/1 1/0 -5/8 1/1 1/0 -23/37 1/0 -18/29 0/1 1/0 -13/21 1/0 -21/34 3/1 1/0 -71/115 1/0 -50/81 -12/1 1/0 -29/47 1/0 -37/60 -7/2 -3/1 -8/13 -2/1 1/0 -19/31 -3/2 -30/49 -2/1 -3/2 -11/18 -4/3 -1/1 -14/23 -1/1 -3/5 -1/2 -13/22 -1/1 -1/2 -10/17 -1/2 0/1 -7/12 -1/1 -1/2 -25/43 -1/2 -18/31 -2/5 -3/8 -11/19 -3/10 -37/64 -1/3 -2/7 -26/45 -6/23 -1/4 -41/71 -1/4 -15/26 -1/5 0/1 -19/33 -1/4 -4/7 -1/6 0/1 -13/23 0/1 -9/16 0/1 1/11 -14/25 0/1 1/6 -5/9 1/2 -16/29 1/2 2/3 -11/20 1/1 2/1 -6/11 0/1 1/0 -7/13 -1/2 -1/2 -1/1 0/1 -7/15 1/4 -6/13 0/1 1/2 -11/24 1/3 1/2 -5/11 1/2 -9/20 -1/1 0/1 -13/29 1/4 -4/9 0/1 1/2 -19/43 1/2 -15/34 3/7 1/2 -11/25 1/2 -29/66 4/7 3/5 -18/41 1/2 2/3 -7/16 2/3 1/1 -10/23 1/1 -3/7 1/0 -11/26 -1/1 0/1 -30/71 0/1 1/0 -49/116 1/2 1/1 -68/161 1/1 -19/45 1/0 -8/19 0/1 1/0 -13/31 1/0 -18/43 0/1 1/0 -5/12 1/1 1/0 -12/29 0/1 1/0 -19/46 -1/1 1/1 -7/17 1/0 -9/22 3/1 1/0 -11/27 1/0 -2/5 -1/2 0/1 -9/23 0/1 -7/18 0/1 1/11 -19/49 1/8 -12/31 0/1 1/6 -17/44 0/1 1/5 -5/13 1/4 -18/47 1/4 2/7 -31/81 3/10 -44/115 1/3 -13/34 1/3 1/2 -34/89 0/1 1/2 -55/144 1/3 1/2 -21/55 1/0 -8/21 0/1 1/4 -19/50 0/1 1/3 -11/29 1/2 -14/37 0/1 1/4 -3/8 1/3 1/2 -10/27 0/1 1/2 -17/46 1/3 1/1 -7/19 1/2 -25/68 5/11 1/2 -18/49 1/2 2/3 -11/30 -1/1 0/1 -4/11 2/5 1/2 -17/47 1/2 -13/36 3/5 2/3 -22/61 0/1 1/2 -31/86 1/2 1/1 -9/25 1/2 -5/14 1/2 1/1 -16/45 0/1 1/2 -11/31 1/2 -17/48 11/17 2/3 -6/17 2/3 3/4 -7/20 6/7 1/1 -8/23 1/1 -1/3 1/0 -6/19 0/1 1/0 -5/16 -1/1 0/1 -19/61 1/0 -14/45 2/1 1/0 -9/29 -1/2 -4/13 -1/2 0/1 -7/23 0/1 -3/10 0/1 1/3 -11/37 1/2 -41/138 1/3 1/1 -30/101 0/1 1/2 -19/64 0/1 1/3 -8/27 0/1 1/2 -21/71 1/2 -34/115 1/1 -13/44 0/1 1/1 -18/61 0/1 1/2 -5/17 1/2 -7/24 1/2 3/5 -9/31 3/4 -2/7 0/1 1/2 -13/46 1/3 1/1 -11/39 1/2 -9/32 1/3 1/2 -7/25 1/2 -26/93 10/21 1/2 -45/161 1/2 -19/68 1/2 9/17 -12/43 1/2 2/3 -5/18 0/1 1/1 -18/65 0/1 1/2 -13/47 1/2 -8/29 2/5 1/2 -3/11 1/2 -7/26 2/3 5/7 -11/41 3/4 -37/138 5/7 1/1 -26/97 2/3 3/4 -15/56 2/3 5/7 -4/15 3/4 4/5 -5/19 9/10 -6/23 1/1 -1/4 1/1 2/1 -6/25 2/1 1/0 -11/46 1/1 3/1 -5/21 1/0 -4/17 2/1 1/0 -11/47 1/0 -18/77 0/1 1/0 -43/184 -1/1 1/1 -25/107 1/0 -7/30 -1/1 0/1 -3/13 3/2 -8/35 2/1 1/0 -21/92 1/1 3/1 -13/57 1/0 -5/22 3/1 1/0 -7/31 3/2 -9/40 3/1 1/0 -20/89 2/1 1/0 -31/138 1/1 3/1 -11/49 1/0 -2/9 2/1 1/0 -5/23 1/0 -3/14 -1/1 1/0 -10/47 -2/1 1/0 -7/33 1/0 -4/19 0/1 1/0 -9/43 1/0 -5/24 1/1 1/0 -1/5 1/0 -5/26 0/1 1/1 -4/21 0/1 1/0 -3/16 0/1 1/5 -2/11 1/2 2/3 -3/17 5/6 -4/23 1/1 -1/6 1/1 3/2 -5/31 7/4 -4/25 15/8 2/1 -3/19 5/2 -2/13 2/1 1/0 -7/46 1/1 3/1 -5/33 1/0 -3/20 1/1 2/1 -1/7 1/0 -2/15 8/1 1/0 -3/23 1/0 -1/8 -3/1 1/0 -1/9 1/0 -1/10 0/1 1/1 0/1 0/1 1/0 1/9 1/0 1/8 3/1 1/0 3/23 1/0 2/15 -8/1 1/0 1/7 1/0 2/13 -2/1 1/0 3/19 -5/2 4/25 -2/1 -15/8 1/6 -3/2 -1/1 4/23 -1/1 3/17 -5/6 2/11 -2/3 -1/2 3/16 -1/5 0/1 1/5 1/0 4/19 0/1 1/0 7/33 1/0 3/14 1/1 1/0 5/23 1/0 2/9 -2/1 1/0 9/40 -3/1 1/0 7/31 -3/2 5/22 -3/1 1/0 3/13 -3/2 4/17 -2/1 1/0 1/4 -2/1 -1/1 6/23 -1/1 5/19 -9/10 4/15 -4/5 -3/4 15/56 -5/7 -2/3 11/41 -3/4 7/26 -5/7 -2/3 3/11 -1/2 8/29 -1/2 -2/5 13/47 -1/2 5/18 -1/1 0/1 12/43 -2/3 -1/2 19/68 -9/17 -1/2 7/25 -1/2 2/7 -1/2 0/1 9/31 -3/4 7/24 -3/5 -1/2 5/17 -1/2 13/44 -1/1 0/1 34/115 -1/1 21/71 -1/2 8/27 -1/2 0/1 19/64 -1/3 0/1 11/37 -1/2 14/47 -1/2 0/1 3/10 -1/3 0/1 7/23 0/1 4/13 0/1 1/2 5/16 0/1 1/1 1/3 1/0 8/23 -1/1 7/20 -1/1 -6/7 6/17 -3/4 -2/3 11/31 -1/2 16/45 -1/2 0/1 5/14 -1/1 -1/2 14/39 -2/3 -1/2 9/25 -1/2 22/61 -1/2 0/1 13/36 -2/3 -3/5 17/47 -1/2 4/11 -1/2 -2/5 11/30 0/1 1/1 7/19 -1/2 3/8 -1/2 -1/3 14/37 -1/4 0/1 11/29 -1/2 8/21 -1/4 0/1 13/34 -1/2 -1/3 44/115 -1/3 31/81 -3/10 18/47 -2/7 -1/4 23/60 -1/3 -1/4 5/13 -1/4 12/31 -1/6 0/1 19/49 -1/8 7/18 -1/11 0/1 9/23 0/1 2/5 0/1 1/2 9/22 -3/1 1/0 7/17 1/0 5/12 -1/1 1/0 18/43 0/1 1/0 13/31 1/0 8/19 0/1 1/0 27/64 0/1 1/1 19/45 1/0 30/71 0/1 1/0 11/26 0/1 1/1 14/33 0/1 1/0 3/7 1/0 10/23 -1/1 7/16 -1/1 -2/3 11/25 -1/2 4/9 -1/2 0/1 13/29 -1/4 9/20 0/1 1/1 5/11 -1/2 6/13 -1/2 0/1 1/2 0/1 1/1 8/15 0/1 1/0 7/13 1/2 13/24 -1/1 1/0 6/11 0/1 1/0 11/20 -2/1 -1/1 16/29 -2/3 -1/2 5/9 -1/2 24/43 -1/4 0/1 19/34 -1/4 -1/5 14/25 -1/6 0/1 37/66 -1/7 0/1 23/41 -1/6 9/16 -1/11 0/1 13/23 0/1 4/7 0/1 1/6 15/26 0/1 1/5 41/71 1/4 67/116 13/53 1/4 93/161 1/4 26/45 1/4 6/23 11/19 3/10 18/31 3/8 2/5 25/43 1/2 7/12 1/2 1/1 17/29 1/2 27/46 1/3 1/1 10/17 0/1 1/2 13/22 1/2 1/1 16/27 0/1 1/2 3/5 1/2 14/23 1/1 11/18 1/1 4/3 30/49 3/2 2/1 19/31 3/2 27/44 2/1 7/3 8/13 2/1 1/0 29/47 1/0 50/81 12/1 1/0 71/115 1/0 21/34 -3/1 1/0 55/89 1/0 89/144 -1/1 1/0 34/55 0/1 1/0 13/21 1/0 31/50 0/1 1/1 18/29 0/1 1/0 23/37 1/0 5/8 -1/1 1/0 17/27 1/0 29/46 -1/1 1/1 12/19 0/1 1/0 43/68 -1/1 1/0 31/49 1/0 19/30 0/1 1/1 7/11 1/0 30/47 -1/2 0/1 23/36 -1/1 0/1 39/61 -1/2 55/86 -1/4 -1/5 16/25 0/1 1/2 9/14 -1/1 1/0 29/45 -1/2 20/31 -1/2 0/1 31/48 -1/1 0/1 11/17 -1/2 13/20 -1/7 0/1 15/23 0/1 2/3 0/1 1/2 13/19 1/2 11/16 2/3 5/7 42/61 2/3 3/4 31/45 3/4 20/29 3/4 4/5 9/13 5/6 16/23 1/1 7/10 1/1 4/3 26/37 3/2 2/1 97/138 1/1 5/3 71/101 3/2 45/64 5/3 2/1 19/27 7/4 50/71 27/14 2/1 81/115 2/1 31/44 2/1 15/7 43/61 5/2 12/17 2/1 1/0 17/24 3/1 1/0 22/31 6/1 1/0 5/7 1/0 33/46 -1/1 1/1 28/39 0/1 1/0 23/32 -1/1 1/0 18/25 0/1 1/2 67/93 1/2 116/161 1/1 49/68 1/1 1/0 31/43 1/0 13/18 0/1 1/3 47/65 1/4 34/47 1/2 4/7 21/29 3/4 8/11 0/1 1/0 19/26 1/1 2/1 30/41 0/1 1/0 101/138 -1/1 1/1 71/97 1/0 41/56 -1/1 0/1 11/15 1/0 14/19 0/1 1/0 17/23 0/1 3/4 0/1 1/1 19/25 1/0 35/46 -1/1 1/1 16/21 0/1 1/0 13/17 1/2 36/47 -2/1 1/0 59/77 1/0 141/184 -1/1 1/1 82/107 0/1 1/0 23/30 0/1 1/1 10/13 0/1 1/2 27/35 1/2 71/92 1/3 1/1 44/57 0/1 1/2 17/22 1/2 1/1 24/31 1/2 4/7 31/40 1/2 3/5 69/89 1/2 107/138 3/5 1/1 38/49 1/2 2/3 7/9 3/4 18/23 1/1 11/14 1/1 7/6 37/47 5/4 26/33 5/4 4/3 15/19 3/2 34/43 10/7 3/2 19/24 3/2 11/7 4/5 2/1 1/0 21/26 3/1 4/1 17/21 1/0 13/16 1/1 2/1 9/11 1/0 14/17 6/1 1/0 19/23 1/0 5/6 -1/1 1/0 26/31 -2/1 1/0 21/25 1/0 16/19 0/1 1/0 11/13 1/0 39/46 -1/1 1/1 28/33 0/1 1/0 17/20 0/1 1/1 6/7 0/1 1/2 13/15 3/4 20/23 1/1 7/8 1/1 3/2 8/9 2/1 1/0 9/10 3/1 4/1 1/1 1/0 1/0 -1/1 1/1 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(1,0,0,1) Matrix(323,290,-460,-413) -> Matrix(3,8,-2,-5) Matrix(139,122,368,323) -> Matrix(1,2,-4,-7) Matrix(321,280,368,321) -> Matrix(5,6,4,5) Matrix(599,520,690,599) -> Matrix(7,6,8,7) Matrix(93,80,322,277) -> Matrix(1,0,0,1) Matrix(185,158,-322,-275) -> Matrix(1,0,-4,1) Matrix(185,156,874,737) -> Matrix(1,0,0,1) Matrix(599,504,2024,1703) -> Matrix(1,0,-2,1) Matrix(829,696,-2300,-1931) -> Matrix(1,-2,2,-3) Matrix(229,190,276,229) -> Matrix(1,-2,0,1) Matrix(645,532,782,645) -> Matrix(1,12,0,1) Matrix(139,114,506,415) -> Matrix(1,4,-2,-7) Matrix(321,262,506,413) -> Matrix(1,2,0,1) Matrix(323,262,-736,-597) -> Matrix(1,0,2,1) Matrix(93,74,-230,-183) -> Matrix(1,2,-2,-3) Matrix(137,108,874,689) -> Matrix(11,14,-4,-5) Matrix(1333,1050,-2162,-1703) -> Matrix(11,14,-4,-5) Matrix(505,396,644,505) -> Matrix(13,14,12,13) Matrix(323,252,414,323) -> Matrix(7,6,8,7) Matrix(1335,1036,-3496,-2713) -> Matrix(3,2,4,3) Matrix(1841,1426,-5106,-3955) -> Matrix(7,4,12,7) Matrix(1011,782,1426,1103) -> Matrix(5,2,2,1) Matrix(275,212,-598,-461) -> Matrix(1,0,4,1) Matrix(185,142,-598,-459) -> Matrix(1,0,0,1) Matrix(367,280,-966,-737) -> Matrix(1,0,4,1) Matrix(137,102,184,137) -> Matrix(1,0,2,1) Matrix(645,476,874,645) -> Matrix(1,0,0,1) Matrix(367,270,874,643) -> Matrix(1,0,0,1) Matrix(2529,1852,3956,2897) -> Matrix(1,0,-2,1) Matrix(2071,1516,-7728,-5657) -> Matrix(3,2,4,3) Matrix(1657,1212,-3772,-2759) -> Matrix(1,-2,2,-3) Matrix(277,202,506,369) -> Matrix(1,0,0,1) Matrix(91,66,506,367) -> Matrix(1,2,-2,-3) Matrix(829,600,-2668,-1931) -> Matrix(3,2,-2,-1) Matrix(2207,1596,-3818,-2761) -> Matrix(5,2,-18,-7) Matrix(643,464,1656,1195) -> Matrix(1,0,-8,1) Matrix(3957,2852,6256,4509) -> Matrix(1,0,0,1) Matrix(3265,2352,-7728,-5567) -> Matrix(1,0,2,1) Matrix(737,530,-1150,-827) -> Matrix(1,0,0,1) Matrix(45,32,322,229) -> Matrix(1,-2,0,1) Matrix(1103,782,1426,1011) -> Matrix(1,2,2,5) Matrix(461,326,782,553) -> Matrix(1,2,2,5) Matrix(553,390,-1564,-1103) -> Matrix(3,8,4,11) Matrix(7129,5022,10120,7129) -> Matrix(29,60,14,29) Matrix(11501,8100,16330,11501) -> Matrix(55,108,28,55) Matrix(321,226,2024,1425) -> Matrix(13,24,-6,-11) Matrix(3359,2362,4646,3267) -> Matrix(1,2,0,1) Matrix(2623,1844,-8832,-6209) -> Matrix(1,2,0,1) Matrix(781,548,2162,1517) -> Matrix(7,10,-12,-17) Matrix(321,224,460,321) -> Matrix(7,8,6,7) Matrix(415,288,598,415) -> Matrix(11,10,12,11) Matrix(139,96,-598,-413) -> Matrix(3,2,4,3) Matrix(321,220,-874,-599) -> Matrix(3,2,4,3) Matrix(91,60,138,91) -> Matrix(1,0,4,1) Matrix(599,390,920,599) -> Matrix(1,0,-14,1) Matrix(413,268,920,597) -> Matrix(1,0,-6,1) Matrix(461,298,-1564,-1011) -> Matrix(1,0,0,1) Matrix(1151,742,-4922,-3173) -> Matrix(1,0,-2,1) Matrix(1013,652,1288,829) -> Matrix(7,-6,6,-5) Matrix(505,324,-1794,-1151) -> Matrix(1,0,2,1) Matrix(369,236,-2300,-1471) -> Matrix(11,-2,6,-1) Matrix(2897,1852,3956,2529) -> Matrix(1,0,-2,1) Matrix(645,412,2162,1381) -> Matrix(1,0,-4,1) Matrix(1655,1056,4324,2759) -> Matrix(3,-2,-10,7) Matrix(413,262,506,321) -> Matrix(1,2,0,1) Matrix(275,174,-874,-553) -> Matrix(1,0,0,1) Matrix(137,86,-368,-231) -> Matrix(1,0,2,1) Matrix(45,28,368,229) -> Matrix(1,2,0,1) Matrix(737,458,1334,829) -> Matrix(1,2,-2,-3) Matrix(229,142,-966,-599) -> Matrix(1,2,0,1) Matrix(689,426,-1564,-967) -> Matrix(1,0,2,1) Matrix(4829,2982,7820,4829) -> Matrix(1,-6,0,1) Matrix(11501,7100,18630,11501) -> Matrix(1,24,0,1) Matrix(1565,966,4324,2669) -> Matrix(1,10,-2,-19) Matrix(2163,1334,3358,2071) -> Matrix(1,4,-2,-7) Matrix(277,170,-598,-367) -> Matrix(1,2,2,5) Matrix(1195,732,2852,1747) -> Matrix(1,2,-2,-3) Matrix(461,282,1656,1013) -> Matrix(3,4,-4,-5) Matrix(505,308,828,505) -> Matrix(7,8,6,7) Matrix(139,84,230,139) -> Matrix(3,2,4,3) Matrix(47,28,-230,-137) -> Matrix(1,0,2,1) Matrix(553,326,782,461) -> Matrix(5,2,2,1) Matrix(229,134,-552,-323) -> Matrix(1,0,2,1) Matrix(873,508,-1978,-1151) -> Matrix(5,2,12,5) Matrix(1105,642,2852,1657) -> Matrix(5,2,-38,-15) Matrix(231,134,874,507) -> Matrix(17,6,-20,-7) Matrix(2071,1198,2944,1703) -> Matrix(29,8,18,5) Matrix(2161,1248,-7728,-4463) -> Matrix(17,4,38,9) Matrix(1933,1116,2392,1381) -> Matrix(17,4,4,1) Matrix(229,132,-1518,-875) -> Matrix(9,2,4,1) Matrix(183,104,322,183) -> Matrix(1,0,12,1) Matrix(415,234,736,415) -> Matrix(1,0,-22,1) Matrix(139,78,-736,-413) -> Matrix(1,0,-6,1) Matrix(597,334,-1564,-875) -> Matrix(1,0,-2,1) Matrix(829,458,1334,737) -> Matrix(3,-2,2,-1) Matrix(323,178,920,507) -> Matrix(5,-4,-6,5) Matrix(369,202,506,277) -> Matrix(1,0,0,1) Matrix(137,74,-598,-323) -> Matrix(1,2,0,1) Matrix(231,124,-598,-321) -> Matrix(1,0,6,1) Matrix(277,130,-782,-367) -> Matrix(9,-2,14,-3) Matrix(367,168,-1610,-737) -> Matrix(3,-2,2,-1) Matrix(137,62,506,229) -> Matrix(3,-2,-4,3) Matrix(597,268,920,413) -> Matrix(1,0,-6,1) Matrix(505,226,1334,597) -> Matrix(1,0,-6,1) Matrix(185,82,-828,-367) -> Matrix(3,-2,2,-1) Matrix(3081,1354,5336,2345) -> Matrix(7,-4,30,-17) Matrix(321,140,736,321) -> Matrix(5,-4,-6,5) Matrix(139,60,322,139) -> Matrix(1,-2,0,1) Matrix(47,20,-322,-137) -> Matrix(1,2,0,1) Matrix(2991,1264,5336,2255) -> Matrix(1,0,-6,1) Matrix(21345,9016,29624,12513) -> Matrix(3,-2,2,-1) Matrix(16007,6760,22218,9383) -> Matrix(1,-2,2,-3) Matrix(1057,446,-3818,-1611) -> Matrix(1,0,2,1) Matrix(643,270,874,367) -> Matrix(1,0,0,1) Matrix(1747,732,2852,1195) -> Matrix(3,-2,2,-1) Matrix(967,404,-2530,-1057) -> Matrix(1,0,2,1) Matrix(1243,514,2116,875) -> Matrix(1,0,2,1) Matrix(1241,512,2116,873) -> Matrix(1,0,2,1) Matrix(229,94,782,321) -> Matrix(1,0,-2,1) Matrix(829,338,-2254,-919) -> Matrix(1,2,2,5) Matrix(91,36,230,91) -> Matrix(1,0,4,1) Matrix(323,126,828,323) -> Matrix(1,0,-22,1) Matrix(1195,464,1656,643) -> Matrix(1,0,-8,1) Matrix(1657,642,2852,1105) -> Matrix(15,-2,38,-5) Matrix(1195,462,-4048,-1565) -> Matrix(1,0,-4,1) Matrix(459,176,-2162,-829) -> Matrix(1,0,-4,1) Matrix(2759,1056,4324,1655) -> Matrix(7,-2,-10,3) Matrix(7129,2728,18630,7129) -> Matrix(19,-6,-60,19) Matrix(2991,1144,7820,2991) -> Matrix(5,-2,-12,5) Matrix(3681,1406,-16376,-6255) -> Matrix(3,-2,2,-1) Matrix(321,122,-1334,-507) -> Matrix(7,-2,4,-1) Matrix(597,226,1334,505) -> Matrix(1,0,-6,1) Matrix(323,122,368,139) -> Matrix(7,-2,4,-1) Matrix(1335,494,2116,783) -> Matrix(1,0,-2,1) Matrix(1333,492,2116,781) -> Matrix(1,0,-2,1) Matrix(1747,642,6256,2299) -> Matrix(7,-4,-12,7) Matrix(93,34,506,185) -> Matrix(1,0,-4,1) Matrix(2669,966,4324,1565) -> Matrix(19,-10,2,-1) Matrix(459,166,506,183) -> Matrix(11,-6,2,-1) Matrix(1059,382,3956,1427) -> Matrix(5,-4,-6,5) Matrix(323,116,-1150,-413) -> Matrix(3,-2,8,-5) Matrix(1287,458,3358,1195) -> Matrix(3,-2,-10,7) Matrix(1289,458,-4140,-1471) -> Matrix(3,-2,2,-1) Matrix(507,178,920,323) -> Matrix(5,-4,-6,5) Matrix(321,112,920,321) -> Matrix(13,-12,-14,13) Matrix(47,16,138,47) -> Matrix(1,-2,0,1) Matrix(183,58,-874,-277) -> Matrix(1,0,0,1) Matrix(827,258,-3542,-1105) -> Matrix(1,0,0,1) Matrix(183,56,598,183) -> Matrix(1,0,4,1) Matrix(139,42,460,139) -> Matrix(1,0,-6,1) Matrix(47,14,-460,-137) -> Matrix(1,0,-2,1) Matrix(13387,3978,19044,5659) -> Matrix(7,-2,4,-1) Matrix(13385,3976,19044,5657) -> Matrix(7,-2,4,-1) Matrix(1241,368,2944,873) -> Matrix(1,0,-2,1) Matrix(1703,504,2024,599) -> Matrix(1,0,-2,1) Matrix(4829,1428,16330,4829) -> Matrix(3,-2,-4,3) Matrix(2991,884,10120,2991) -> Matrix(1,0,-2,1) Matrix(321,94,782,229) -> Matrix(1,0,-2,1) Matrix(323,94,1426,415) -> Matrix(1,0,-2,1) Matrix(277,80,322,93) -> Matrix(1,0,0,1) Matrix(1519,430,2116,599) -> Matrix(1,0,-2,1) Matrix(1517,428,2116,597) -> Matrix(1,0,-2,1) Matrix(12835,3588,22218,6211) -> Matrix(33,-16,130,-63) Matrix(17111,4782,29624,8279) -> Matrix(43,-22,174,-89) Matrix(3129,874,3956,1105) -> Matrix(29,-16,20,-11) Matrix(1013,282,1656,461) -> Matrix(5,-4,4,-3) Matrix(1379,382,4646,1287) -> Matrix(1,0,-4,1) Matrix(507,140,-2162,-597) -> Matrix(1,0,-2,1) Matrix(415,114,506,139) -> Matrix(7,-4,2,-1) Matrix(229,62,506,137) -> Matrix(3,-2,-4,3) Matrix(231,62,-1196,-321) -> Matrix(3,-2,-4,3) Matrix(13939,3738,19044,5107) -> Matrix(3,-2,-4,3) Matrix(13937,3736,19044,5105) -> Matrix(3,-2,-4,3) Matrix(1427,382,3956,1059) -> Matrix(5,-4,-6,5) Matrix(507,134,874,231) -> Matrix(7,-6,20,-17) Matrix(229,60,874,229) -> Matrix(19,-18,-20,19) Matrix(47,12,184,47) -> Matrix(3,-4,-2,3) Matrix(1611,386,2116,507) -> Matrix(1,-2,0,1) Matrix(1609,384,2116,505) -> Matrix(1,-2,0,1) Matrix(25945,6064,33856,7913) -> Matrix(1,0,0,1) Matrix(25943,6062,33856,7911) -> Matrix(1,0,0,1) Matrix(6533,1492,8464,1933) -> Matrix(1,-2,2,-3) Matrix(6531,1490,8464,1931) -> Matrix(1,-2,2,-3) Matrix(415,94,1426,323) -> Matrix(1,0,-2,1) Matrix(231,52,-1426,-321) -> Matrix(3,-8,2,-5) Matrix(14767,3318,19044,4279) -> Matrix(1,-4,2,-7) Matrix(14765,3316,19044,4277) -> Matrix(1,-4,2,-7) Matrix(91,20,414,91) -> Matrix(1,-4,0,1) Matrix(139,30,644,139) -> Matrix(1,2,0,1) Matrix(459,98,1288,275) -> Matrix(1,2,-2,-3) Matrix(737,156,874,185) -> Matrix(1,0,0,1) Matrix(2851,596,3956,827) -> Matrix(1,0,0,1) Matrix(1011,194,2392,459) -> Matrix(1,0,0,1) Matrix(185,34,506,93) -> Matrix(1,0,-4,1) Matrix(367,66,506,91) -> Matrix(3,-2,2,-1) Matrix(137,24,782,137) -> Matrix(11,-10,-12,11) Matrix(47,8,276,47) -> Matrix(5,-6,-4,5) Matrix(1425,226,2024,321) -> Matrix(11,-24,6,-13) Matrix(689,108,874,137) -> Matrix(5,-14,4,-11) Matrix(1795,274,2116,323) -> Matrix(1,-2,0,1) Matrix(1793,272,2116,321) -> Matrix(1,-2,0,1) Matrix(229,32,322,45) -> Matrix(1,-2,0,1) Matrix(91,12,690,91) -> Matrix(1,-16,0,1) Matrix(47,6,368,47) -> Matrix(1,6,0,1) Matrix(229,28,368,45) -> Matrix(1,2,0,1) Matrix(323,30,506,47) -> Matrix(1,0,-2,1) Matrix(137,-14,460,-47) -> Matrix(1,0,-2,1) Matrix(137,-20,322,-47) -> Matrix(1,2,0,1) Matrix(1471,-236,2300,-369) -> Matrix(1,2,-6,-11) Matrix(413,-78,736,-139) -> Matrix(1,0,-6,1) Matrix(137,-28,230,-47) -> Matrix(1,0,2,1) Matrix(829,-176,2162,-459) -> Matrix(1,0,-4,1) Matrix(2161,-484,3496,-783) -> Matrix(1,2,0,1) Matrix(3265,-736,5106,-1151) -> Matrix(1,2,-4,-7) Matrix(323,-74,598,-137) -> Matrix(1,2,0,1) Matrix(413,-96,598,-139) -> Matrix(3,2,4,3) Matrix(599,-142,966,-229) -> Matrix(1,2,0,1) Matrix(5657,-1516,7728,-2071) -> Matrix(3,2,4,3) Matrix(2115,-568,3772,-1013) -> Matrix(3,2,-14,-9) Matrix(1839,-508,2668,-737) -> Matrix(7,2,10,3) Matrix(1611,-446,3818,-1057) -> Matrix(1,0,2,1) Matrix(4463,-1248,7728,-2161) -> Matrix(9,4,38,17) Matrix(413,-116,1150,-323) -> Matrix(5,2,-8,-3) Matrix(1011,-298,1564,-461) -> Matrix(1,0,0,1) Matrix(6209,-1844,8832,-2623) -> Matrix(1,2,0,1) Matrix(459,-142,598,-185) -> Matrix(1,0,0,1) Matrix(553,-174,874,-275) -> Matrix(1,0,0,1) Matrix(1103,-390,1564,-553) -> Matrix(11,8,4,3) Matrix(3771,-1340,4922,-1749) -> Matrix(3,2,-2,-1) Matrix(1289,-462,1794,-643) -> Matrix(3,2,-2,-1) Matrix(1931,-696,2300,-829) -> Matrix(3,2,-2,-1) Matrix(599,-220,874,-321) -> Matrix(3,2,4,3) Matrix(231,-86,368,-137) -> Matrix(1,0,2,1) Matrix(737,-280,966,-367) -> Matrix(1,0,4,1) Matrix(875,-334,1564,-597) -> Matrix(1,0,-2,1) Matrix(321,-124,598,-231) -> Matrix(1,0,6,1) Matrix(183,-74,230,-93) -> Matrix(3,-2,2,-1) Matrix(323,-134,552,-229) -> Matrix(1,0,2,1) Matrix(1105,-462,1978,-827) -> Matrix(1,0,-4,1) Matrix(5567,-2352,7728,-3265) -> Matrix(1,0,2,1) Matrix(1289,-546,1518,-643) -> Matrix(1,0,0,1) Matrix(597,-262,736,-323) -> Matrix(1,0,2,1) Matrix(967,-426,1564,-689) -> Matrix(1,0,2,1) Matrix(461,-212,598,-275) -> Matrix(1,0,4,1) Matrix(367,-170,598,-277) -> Matrix(5,2,2,1) Matrix(505,-268,782,-415) -> Matrix(1,0,-2,1) Matrix(1243,-674,1610,-873) -> Matrix(1,0,2,1) Matrix(643,-358,828,-461) -> Matrix(7,2,10,3) Matrix(275,-158,322,-185) -> Matrix(1,0,-4,1) Matrix(2761,-1596,3818,-2207) -> Matrix(7,-2,18,-5) Matrix(1563,-910,2530,-1473) -> Matrix(5,-2,-2,1) Matrix(1425,-844,2254,-1335) -> Matrix(1,0,-2,1) Matrix(2853,-1750,4048,-2483) -> Matrix(9,-16,4,-7) Matrix(1703,-1050,2162,-1333) -> Matrix(5,-14,4,-11) Matrix(12695,-7846,16376,-10121) -> Matrix(1,-2,2,-3) Matrix(1013,-628,1334,-827) -> Matrix(1,0,0,1) Matrix(827,-530,1150,-737) -> Matrix(1,0,0,1) Matrix(2851,-1838,4140,-2669) -> Matrix(7,2,10,3) Matrix(691,-472,874,-597) -> Matrix(17,-10,12,-7) Matrix(2715,-1868,3542,-2437) -> Matrix(3,-2,-4,3) Matrix(413,-290,460,-323) -> Matrix(5,-8,2,-3) Matrix(1655,-1198,2162,-1565) -> Matrix(3,-2,2,-1) Matrix(965,-706,1196,-875) -> Matrix(1,2,0,1) Matrix(1195,-926,1426,-1105) -> Matrix(3,-2,2,-1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 66 Degree of the the map X: 66 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. Imminent integer overflow caused the modular group computation to abort.