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 0/1 1/1 23/20 23/19 23/18 23/17 115/81 23/16 3/2 23/15 115/71 23/14 23/13 2/1 23/10 161/68 12/5 46/19 5/2 23/9 115/44 46/17 23/8 3/1 23/7 138/41 115/34 7/2 46/13 161/45 18/5 11/3 138/37 23/6 4/1 46/11 21/5 17/4 184/43 13/3 92/21 22/5 138/31 9/2 23/5 14/3 19/4 5/1 21/4 16/3 11/2 17/3 23/4 6/1 31/5 19/3 13/2 46/7 20/3 7/1 15/2 23/3 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 1/1 -8/1 -1/3 -23/3 0/1 -15/2 0/1 1/7 -7/1 1/1 -13/2 0/1 1/3 -19/3 -1/1 -25/4 0/1 1/3 -6/1 1/1 -23/4 1/0 -17/3 -1/1 -11/2 0/1 1/0 -16/3 -1/1 -5/1 -1/1 -19/4 -1/2 0/1 -33/7 -1/1 -14/3 -1/1 -23/5 -1/1 -9/2 -1/1 -1/2 -40/9 -1/1 -31/7 -3/5 -22/5 -3/5 -13/3 -1/1 -17/4 -1/3 -1/4 -4/1 -1/3 -23/6 0/1 -19/5 1/5 -15/4 0/1 1/1 -56/15 3/5 -41/11 1/1 -26/7 1/1 -11/3 -3/1 -29/8 -1/1 -5/6 -47/13 -1/1 -18/5 -1/1 -43/12 -1/1 -3/4 -68/19 -9/13 -25/7 -3/5 -7/2 -1/2 0/1 -31/9 -3/7 -24/7 -3/7 -17/5 -1/3 -44/13 -3/11 -115/34 -1/4 -71/21 -3/13 -27/8 -1/4 0/1 -64/19 -1/5 -37/11 -1/5 -47/14 -1/6 0/1 -10/3 -1/5 -23/7 0/1 -13/4 0/1 1/3 -16/5 1/1 -3/1 -1/1 -23/8 -1/2 -20/7 -3/7 -17/6 -1/2 -1/3 -31/11 -1/5 -45/16 -1/2 0/1 -14/5 -1/1 -39/14 -1/2 0/1 -25/9 -3/5 -61/22 -2/3 -3/5 -36/13 -5/9 -47/17 -7/13 -11/4 -1/2 -2/5 -30/11 -1/3 -19/7 -3/5 -8/3 -1/3 -37/14 -1/2 -3/7 -29/11 -3/7 -21/8 -2/5 -1/3 -34/13 -11/27 -115/44 -2/5 -81/31 -25/63 -47/18 -2/5 -7/18 -60/23 -5/13 -13/5 -5/13 -31/12 -4/11 -1/3 -49/19 -1/3 -18/7 -1/3 -23/9 -1/3 -5/2 -1/3 0/1 -22/9 -1/1 -17/7 -1/3 -12/5 -5/17 -43/18 -3/11 -1/4 -31/13 -5/19 -19/8 -1/4 -2/9 -64/27 -1/5 -45/19 -1/5 -71/30 -1/5 0/1 -26/11 -1/5 -33/14 -1/1 0/1 -7/3 -1/3 -23/10 -1/3 -16/7 -1/3 -25/11 -1/3 -9/4 -1/3 -1/4 -29/13 -1/3 -20/9 -1/3 -11/5 -5/19 -13/6 -2/9 -1/5 -2/1 -1/3 -15/8 -1/3 0/1 -13/7 -3/11 -24/13 -5/19 -11/6 -1/4 -4/17 -20/11 -1/5 -29/16 -1/4 -3/13 -9/5 -1/5 -43/24 -1/5 -1/6 -34/19 -1/9 -25/14 -1/3 0/1 -66/37 -1/3 -41/23 -1/3 -16/9 -1/3 -23/13 -1/4 -7/4 -1/4 -2/9 -26/15 -1/5 -71/41 -3/13 -116/67 -15/67 -161/93 -2/9 -45/26 -2/9 -3/14 -19/11 -3/13 -31/18 -2/9 -5/23 -43/25 -5/23 -12/7 -7/33 -29/17 -1/5 -46/27 -1/5 -17/10 -1/5 -3/16 -22/13 -1/5 -27/16 -1/4 -2/9 -5/3 -1/5 -23/14 -1/5 -18/11 -1/5 -49/30 -1/5 -7/36 -31/19 -13/67 -44/27 -11/57 -13/8 -1/5 -4/21 -47/29 -13/69 -81/50 -40/213 -3/16 -115/71 -3/16 -34/21 -17/91 -89/55 -5/27 -144/89 -5/27 -55/34 -3/16 -5/27 -21/13 -5/27 -50/31 -1/5 -29/18 -1/5 -3/16 -37/23 -5/27 -8/5 -3/17 -27/17 -7/41 -46/29 -1/6 -19/12 -1/6 -4/25 -68/43 -3/19 -49/31 -3/19 -30/19 -1/7 -11/7 -1/9 -47/30 0/1 1/0 -36/23 -1/1 -61/39 -1/3 -86/55 -1/5 -25/16 -1/3 0/1 -14/9 -1/5 -45/29 -1/7 -31/20 -1/3 0/1 -48/31 -1/3 -17/11 -1/5 -20/13 -1/5 -23/15 -1/5 -3/2 -1/5 -1/6 -19/13 -5/29 -16/11 -1/5 -61/42 -2/11 -11/61 -45/31 -3/17 -29/20 -3/17 -7/40 -13/9 -5/29 -23/16 -1/6 -10/7 -3/19 -37/26 -1/6 -3/19 -138/97 -3/19 -101/71 -3/19 -64/45 -3/19 -27/19 -1/7 -71/50 -7/45 -2/13 -115/81 -2/13 -44/31 -5/33 -61/43 -3/19 -17/12 -3/20 -1/7 -24/17 -1/7 -31/22 -1/11 0/1 -7/5 -1/5 -46/33 -1/6 -39/28 -1/6 -2/13 -32/23 -1/7 -25/18 -1/5 0/1 -93/67 -1/5 -161/116 -1/5 -68/49 -1/5 -43/31 -1/5 -18/13 -1/5 -65/47 -5/27 -47/34 -2/11 -1/6 -29/21 -3/17 -11/8 -2/11 -1/6 -26/19 -1/7 -41/30 -1/5 0/1 -138/101 -1/5 -97/71 -1/5 -56/41 -5/27 -15/11 -1/5 -19/14 -8/47 -1/6 -23/17 -1/6 -4/3 -3/19 -25/19 -7/45 -46/35 -2/13 -21/16 -2/13 -5/33 -17/13 -1/7 -47/36 -1/6 -2/13 -77/59 -7/45 -184/141 -2/13 -107/82 -2/13 -13/85 -30/23 -1/7 -13/10 -2/13 -5/33 -35/27 -23/153 -92/71 -3/20 -57/44 -3/20 -34/227 -22/17 -7/47 -31/24 -4/27 -9/61 -40/31 -1/7 -89/69 -1/7 -138/107 -1/7 -49/38 -3/20 -1/7 -9/7 -1/7 -23/18 -1/7 -14/11 -1/7 -47/37 -7/51 -33/26 -5/37 -2/15 -19/15 -3/23 -43/34 -1/8 -1/9 -24/19 -1/5 -5/4 -1/7 0/1 -26/21 -1/9 -21/17 -1/7 -16/13 -1/7 -11/9 -5/33 -17/14 -9/62 -1/7 -23/19 -1/7 -6/5 -1/7 -31/26 -4/29 -7/51 -25/21 -7/51 -19/16 -3/22 -2/15 -13/11 -5/37 -46/39 -2/15 -33/28 -2/15 -11/83 -20/17 -3/23 -7/6 -2/15 -1/8 -15/13 -5/39 -23/20 -1/8 -8/7 -1/9 -9/8 -1/7 -1/8 -10/9 -1/7 -1/1 -1/9 0/1 0/1 1/1 1/9 9/8 1/8 1/7 8/7 1/9 23/20 1/8 15/13 5/39 7/6 1/8 2/15 13/11 5/37 19/16 2/15 3/22 25/21 7/51 6/5 1/7 23/19 1/7 17/14 1/7 9/62 11/9 5/33 16/13 1/7 5/4 0/1 1/7 19/15 3/23 33/26 2/15 5/37 14/11 1/7 23/18 1/7 9/7 1/7 40/31 1/7 31/24 9/61 4/27 22/17 7/47 13/10 5/33 2/13 17/13 1/7 4/3 3/19 23/17 1/6 19/14 1/6 8/47 15/11 1/5 56/41 5/27 41/30 0/1 1/5 26/19 1/7 11/8 1/6 2/11 29/21 3/17 47/34 1/6 2/11 18/13 1/5 43/31 1/5 68/49 1/5 25/18 0/1 1/5 7/5 1/5 31/22 0/1 1/11 24/17 1/7 17/12 1/7 3/20 44/31 5/33 115/81 2/13 71/50 2/13 7/45 27/19 1/7 64/45 3/19 37/26 3/19 1/6 47/33 5/31 10/7 3/19 23/16 1/6 13/9 5/29 16/11 1/5 3/2 1/6 1/5 23/15 1/5 20/13 1/5 17/11 1/5 31/20 0/1 1/3 45/29 1/7 14/9 1/5 39/25 1/3 25/16 0/1 1/3 61/39 1/3 36/23 1/1 47/30 0/1 1/0 11/7 1/9 30/19 1/7 19/12 4/25 1/6 8/5 3/17 37/23 5/27 29/18 3/16 1/5 21/13 5/27 34/21 17/91 115/71 3/16 81/50 3/16 40/213 47/29 13/69 60/37 7/37 13/8 4/21 1/5 31/19 13/67 49/30 7/36 1/5 18/11 1/5 23/14 1/5 5/3 1/5 22/13 1/5 17/10 3/16 1/5 12/7 7/33 43/25 5/23 31/18 5/23 2/9 19/11 3/13 64/37 1/5 45/26 3/14 2/9 71/41 3/13 26/15 1/5 33/19 7/31 7/4 2/9 1/4 23/13 1/4 16/9 1/3 25/14 0/1 1/3 9/5 1/5 29/16 3/13 1/4 20/11 1/5 11/6 4/17 1/4 13/7 3/11 2/1 1/3 15/7 1/7 13/6 1/5 2/9 24/11 5/21 11/5 5/19 20/9 1/3 29/13 1/3 9/4 1/4 1/3 43/19 1/3 34/15 3/13 25/11 1/3 66/29 5/17 41/18 2/7 1/3 16/7 1/3 23/10 1/3 7/3 1/3 26/11 1/5 71/30 0/1 1/5 116/49 1/5 161/68 1/5 45/19 1/5 19/8 2/9 1/4 31/13 5/19 43/18 1/4 3/11 12/5 5/17 29/12 9/28 1/3 46/19 1/3 17/7 1/3 22/9 1/1 27/11 3/11 5/2 0/1 1/3 23/9 1/3 18/7 1/3 49/19 1/3 31/12 1/3 4/11 44/17 1/3 13/5 5/13 47/18 7/18 2/5 81/31 25/63 115/44 2/5 34/13 11/27 89/34 5/12 3/7 144/55 3/7 55/21 3/7 21/8 1/3 2/5 50/19 7/17 29/11 3/7 37/14 3/7 1/2 8/3 1/3 27/10 8/17 1/2 46/17 1/2 19/7 3/5 68/25 -1/1 49/18 1/3 1/2 30/11 1/3 11/4 2/5 1/2 47/17 7/13 36/13 5/9 61/22 3/5 2/3 86/31 1/1 25/9 3/5 14/5 1/1 45/16 0/1 1/2 31/11 1/5 48/17 1/1 17/6 1/3 1/2 20/7 3/7 23/8 1/2 3/1 1/1 19/6 2/1 1/0 16/5 -1/1 61/19 1/3 45/14 0/1 1/0 29/9 -1/1 13/4 -1/3 0/1 23/7 0/1 10/3 1/5 37/11 1/5 138/41 1/5 101/30 1/5 1/4 64/19 1/5 27/8 0/1 1/4 71/21 3/13 115/34 1/4 44/13 3/11 61/18 3/11 2/7 17/5 1/3 24/7 3/7 31/9 3/7 7/2 0/1 1/2 46/13 1/2 39/11 3/5 32/9 1/1 25/7 3/5 93/26 9/14 2/3 161/45 2/3 68/19 9/13 43/12 3/4 1/1 18/5 1/1 65/18 0/1 1/2 47/13 1/1 29/8 5/6 1/1 11/3 3/1 26/7 -1/1 41/11 -1/1 138/37 -1/1 97/26 -1/1 -4/5 56/15 -3/5 15/4 -1/1 0/1 19/5 -1/5 23/6 0/1 4/1 1/3 25/6 -1/1 0/1 46/11 0/1 21/5 1/5 17/4 1/4 1/3 47/11 1/3 77/18 9/23 2/5 184/43 2/5 107/25 11/27 30/7 3/7 13/3 1/1 35/8 6/13 1/2 92/21 1/2 57/13 13/25 22/5 3/5 31/7 3/5 40/9 1/1 89/20 3/4 1/1 138/31 1/1 49/11 1/1 9/2 1/2 1/1 23/5 1/1 14/3 1/1 47/10 0/1 1/0 33/7 1/1 19/4 0/1 1/2 43/9 1/1 24/5 1/1 5/1 1/1 26/5 1/1 21/4 1/1 2/1 16/3 1/1 11/2 0/1 1/0 17/3 1/1 23/4 1/0 6/1 -1/1 31/5 -1/3 25/4 -1/3 0/1 19/3 1/1 13/2 -1/3 0/1 46/7 0/1 33/5 1/5 20/3 1/1 7/1 -1/1 15/2 -1/7 0/1 23/3 0/1 8/1 1/3 9/1 -1/1 10/1 -1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(47,460,-14,-137) (-9/1,1/0) -> (-37/11,-47/14) Hyperbolic Matrix(45,368,28,229) (-9/1,-8/1) -> (8/5,37/23) Hyperbolic Matrix(47,368,6,47) (-8/1,-23/3) -> (23/3,8/1) Hyperbolic Matrix(91,690,12,91) (-23/3,-15/2) -> (15/2,23/3) Hyperbolic Matrix(45,322,32,229) (-15/2,-7/1) -> (7/5,31/22) Hyperbolic Matrix(47,322,-20,-137) (-7/1,-13/2) -> (-33/14,-7/3) Hyperbolic Matrix(137,874,108,689) (-13/2,-19/3) -> (19/15,33/26) Hyperbolic Matrix(321,2024,226,1425) (-19/3,-25/4) -> (71/50,27/19) Hyperbolic Matrix(369,2300,-236,-1471) (-25/4,-6/1) -> (-86/55,-25/16) Hyperbolic Matrix(47,276,8,47) (-6/1,-23/4) -> (23/4,6/1) Hyperbolic Matrix(137,782,24,137) (-23/4,-17/3) -> (17/3,23/4) Hyperbolic Matrix(91,506,66,367) (-17/3,-11/2) -> (11/8,29/21) Hyperbolic Matrix(93,506,34,185) (-11/2,-16/3) -> (30/11,11/4) Hyperbolic Matrix(139,736,-78,-413) (-16/3,-5/1) -> (-41/23,-16/9) Hyperbolic Matrix(47,230,-28,-137) (-5/1,-19/4) -> (-27/16,-5/3) Hyperbolic Matrix(185,874,156,737) (-19/4,-33/7) -> (13/11,19/16) Hyperbolic Matrix(459,2162,-176,-829) (-33/7,-14/3) -> (-60/23,-13/5) Hyperbolic Matrix(139,644,30,139) (-14/3,-23/5) -> (23/5,14/3) Hyperbolic Matrix(91,414,20,91) (-23/5,-9/2) -> (9/2,23/5) Hyperbolic Matrix(783,3496,-484,-2161) (-9/2,-40/9) -> (-144/89,-55/34) Hyperbolic Matrix(1151,5106,-736,-3265) (-40/9,-31/7) -> (-61/39,-86/55) Hyperbolic Matrix(323,1426,94,415) (-31/7,-22/5) -> (24/7,31/9) Hyperbolic Matrix(137,598,-74,-323) (-22/5,-13/3) -> (-13/7,-24/13) Hyperbolic Matrix(139,598,-96,-413) (-13/3,-17/4) -> (-29/20,-13/9) Hyperbolic Matrix(229,966,-142,-599) (-17/4,-4/1) -> (-50/31,-29/18) Hyperbolic Matrix(47,184,12,47) (-4/1,-23/6) -> (23/6,4/1) Hyperbolic Matrix(229,874,60,229) (-23/6,-19/5) -> (19/5,23/6) Hyperbolic Matrix(231,874,134,507) (-19/5,-15/4) -> (31/18,19/11) Hyperbolic Matrix(1059,3956,382,1427) (-15/4,-56/15) -> (36/13,61/22) Hyperbolic Matrix(2071,7728,-1516,-5657) (-56/15,-41/11) -> (-97/71,-56/41) Hyperbolic Matrix(1013,3772,-568,-2115) (-41/11,-26/7) -> (-66/37,-41/23) Hyperbolic Matrix(137,506,62,229) (-26/7,-11/3) -> (11/5,20/9) Hyperbolic Matrix(139,506,114,415) (-11/3,-29/8) -> (17/14,11/9) Hyperbolic Matrix(737,2668,-508,-1839) (-29/8,-47/13) -> (-45/31,-29/20) Hyperbolic Matrix(1057,3818,-446,-1611) (-47/13,-18/5) -> (-64/27,-45/19) Hyperbolic Matrix(461,1656,282,1013) (-18/5,-43/12) -> (49/30,18/11) Hyperbolic Matrix(1747,6256,642,2299) (-43/12,-68/19) -> (68/25,49/18) Hyperbolic Matrix(2161,7728,-1248,-4463) (-68/19,-25/7) -> (-71/41,-116/67) Hyperbolic Matrix(323,1150,-116,-413) (-25/7,-7/2) -> (-39/14,-25/9) Hyperbolic Matrix(93,322,80,277) (-7/2,-31/9) -> (15/13,7/6) Hyperbolic Matrix(415,1426,94,323) (-31/9,-24/7) -> (22/5,31/7) Hyperbolic Matrix(229,782,94,321) (-24/7,-17/5) -> (17/7,22/9) Hyperbolic Matrix(461,1564,-298,-1011) (-17/5,-44/13) -> (-48/31,-17/11) Hyperbolic Matrix(2991,10120,884,2991) (-44/13,-115/34) -> (115/34,44/13) Hyperbolic Matrix(4829,16330,1428,4829) (-115/34,-71/21) -> (71/21,115/34) Hyperbolic Matrix(599,2024,504,1703) (-71/21,-27/8) -> (19/16,25/21) Hyperbolic Matrix(1379,4646,382,1287) (-27/8,-64/19) -> (18/5,65/18) Hyperbolic Matrix(2623,8832,-1844,-6209) (-64/19,-37/11) -> (-101/71,-64/45) Hyperbolic Matrix(645,2162,412,1381) (-47/14,-10/3) -> (36/23,47/30) Hyperbolic Matrix(139,460,42,139) (-10/3,-23/7) -> (23/7,10/3) Hyperbolic Matrix(183,598,56,183) (-23/7,-13/4) -> (13/4,23/7) Hyperbolic Matrix(185,598,-142,-459) (-13/4,-16/5) -> (-30/23,-13/10) Hyperbolic Matrix(275,874,-174,-553) (-16/5,-3/1) -> (-49/31,-30/19) Hyperbolic Matrix(47,138,16,47) (-3/1,-23/8) -> (23/8,3/1) Hyperbolic Matrix(321,920,112,321) (-23/8,-20/7) -> (20/7,23/8) Hyperbolic Matrix(323,920,178,507) (-20/7,-17/6) -> (29/16,20/11) Hyperbolic Matrix(553,1564,-390,-1103) (-17/6,-31/11) -> (-61/43,-17/12) Hyperbolic Matrix(1749,4922,-1340,-3771) (-31/11,-45/16) -> (-47/36,-77/59) Hyperbolic Matrix(459,1288,98,275) (-45/16,-14/5) -> (14/3,47/10) Hyperbolic Matrix(643,1794,-462,-1289) (-14/5,-39/14) -> (-39/28,-32/23) Hyperbolic Matrix(829,2300,-696,-1931) (-25/9,-61/22) -> (-31/26,-25/21) Hyperbolic Matrix(1427,3956,382,1059) (-61/22,-36/13) -> (56/15,15/4) Hyperbolic Matrix(781,2162,548,1517) (-36/13,-47/17) -> (47/33,10/7) Hyperbolic Matrix(1565,4324,966,2669) (-47/17,-11/4) -> (81/50,47/29) Hyperbolic Matrix(185,506,34,93) (-11/4,-30/11) -> (16/3,11/2) Hyperbolic Matrix(321,874,-220,-599) (-30/11,-19/7) -> (-19/13,-16/11) Hyperbolic Matrix(137,368,-86,-231) (-19/7,-8/3) -> (-8/5,-27/17) Hyperbolic Matrix(139,368,122,323) (-8/3,-37/14) -> (9/8,8/7) Hyperbolic Matrix(505,1334,226,597) (-37/14,-29/11) -> (29/13,9/4) Hyperbolic Matrix(367,966,-280,-737) (-29/11,-21/8) -> (-21/16,-17/13) Hyperbolic Matrix(597,1564,-334,-875) (-21/8,-34/13) -> (-34/19,-25/14) Hyperbolic Matrix(2991,7820,1144,2991) (-34/13,-115/44) -> (115/44,34/13) Hyperbolic Matrix(7129,18630,2728,7129) (-115/44,-81/31) -> (81/31,115/44) Hyperbolic Matrix(1655,4324,1056,2759) (-81/31,-47/18) -> (47/30,11/7) Hyperbolic Matrix(1287,3358,458,1195) (-47/18,-60/23) -> (14/5,45/16) Hyperbolic Matrix(231,598,-124,-321) (-13/5,-31/12) -> (-15/8,-13/7) Hyperbolic Matrix(1105,2852,642,1657) (-31/12,-49/19) -> (43/25,31/18) Hyperbolic Matrix(643,1656,464,1195) (-49/19,-18/7) -> (18/13,43/31) Hyperbolic Matrix(323,828,126,323) (-18/7,-23/9) -> (23/9,18/7) Hyperbolic Matrix(91,230,36,91) (-23/9,-5/2) -> (5/2,23/9) Hyperbolic Matrix(93,230,-74,-183) (-5/2,-22/9) -> (-24/19,-5/4) Hyperbolic Matrix(321,782,94,229) (-22/9,-17/7) -> (17/5,24/7) Hyperbolic Matrix(229,552,-134,-323) (-17/7,-12/5) -> (-12/7,-29/17) Hyperbolic Matrix(827,1978,-462,-1105) (-12/5,-43/18) -> (-43/24,-34/19) Hyperbolic Matrix(1195,2852,732,1747) (-43/18,-31/13) -> (31/19,49/30) Hyperbolic Matrix(367,874,270,643) (-31/13,-19/8) -> (19/14,15/11) Hyperbolic Matrix(1241,2944,368,873) (-19/8,-64/27) -> (64/19,27/8) Hyperbolic Matrix(3265,7728,-2352,-5567) (-45/19,-71/30) -> (-25/18,-93/67) Hyperbolic Matrix(1011,2392,194,459) (-71/30,-26/11) -> (26/5,21/4) Hyperbolic Matrix(643,1518,-546,-1289) (-26/11,-33/14) -> (-33/28,-20/17) Hyperbolic Matrix(139,322,60,139) (-7/3,-23/10) -> (23/10,7/3) Hyperbolic Matrix(321,736,140,321) (-23/10,-16/7) -> (16/7,23/10) Hyperbolic Matrix(323,736,-262,-597) (-16/7,-25/11) -> (-21/17,-16/13) Hyperbolic Matrix(689,1564,-426,-967) (-25/11,-9/4) -> (-55/34,-21/13) Hyperbolic Matrix(597,1334,226,505) (-9/4,-29/13) -> (29/11,37/14) Hyperbolic Matrix(413,920,268,597) (-29/13,-20/9) -> (20/13,17/11) Hyperbolic Matrix(229,506,62,137) (-20/9,-11/5) -> (11/3,26/7) Hyperbolic Matrix(275,598,-212,-461) (-11/5,-13/6) -> (-13/10,-35/27) Hyperbolic Matrix(277,598,-170,-367) (-13/6,-2/1) -> (-44/27,-13/8) Hyperbolic Matrix(415,782,-268,-505) (-2/1,-15/8) -> (-31/20,-48/31) Hyperbolic Matrix(873,1610,-674,-1243) (-24/13,-11/6) -> (-57/44,-22/17) Hyperbolic Matrix(277,506,202,369) (-11/6,-20/11) -> (26/19,11/8) Hyperbolic Matrix(507,920,178,323) (-20/11,-29/16) -> (17/6,20/7) Hyperbolic Matrix(737,1334,458,829) (-29/16,-9/5) -> (37/23,29/18) Hyperbolic Matrix(461,828,-358,-643) (-9/5,-43/24) -> (-49/38,-9/7) Hyperbolic Matrix(2991,5336,1264,2255) (-25/14,-66/37) -> (26/11,71/30) Hyperbolic Matrix(415,736,234,415) (-16/9,-23/13) -> (23/13,16/9) Hyperbolic Matrix(183,322,104,183) (-23/13,-7/4) -> (7/4,23/13) Hyperbolic Matrix(185,322,-158,-275) (-7/4,-26/15) -> (-20/17,-7/6) Hyperbolic Matrix(3081,5336,1354,2345) (-26/15,-71/41) -> (25/11,66/29) Hyperbolic Matrix(17111,29624,4782,8279) (-116/67,-161/93) -> (161/45,68/19) Hyperbolic Matrix(12835,22218,3588,6211) (-161/93,-45/26) -> (93/26,161/45) Hyperbolic Matrix(2207,3818,-1596,-2761) (-45/26,-19/11) -> (-65/47,-47/34) Hyperbolic Matrix(507,874,134,231) (-19/11,-31/18) -> (15/4,19/5) Hyperbolic Matrix(1657,2852,642,1105) (-31/18,-43/25) -> (49/19,31/12) Hyperbolic Matrix(1473,2530,-910,-1563) (-43/25,-12/7) -> (-34/21,-89/55) Hyperbolic Matrix(1241,2116,512,873) (-29/17,-46/27) -> (46/19,17/7) Hyperbolic Matrix(1243,2116,514,875) (-46/27,-17/10) -> (29/12,46/19) Hyperbolic Matrix(461,782,326,553) (-17/10,-22/13) -> (24/17,17/12) Hyperbolic Matrix(1335,2254,-844,-1425) (-22/13,-27/16) -> (-19/12,-68/43) Hyperbolic Matrix(139,230,84,139) (-5/3,-23/14) -> (23/14,5/3) Hyperbolic Matrix(505,828,308,505) (-23/14,-18/11) -> (18/11,23/14) Hyperbolic Matrix(1013,1656,282,461) (-18/11,-49/30) -> (43/12,18/5) Hyperbolic Matrix(1747,2852,732,1195) (-49/30,-31/19) -> (31/13,43/18) Hyperbolic Matrix(2483,4048,-1750,-2853) (-31/19,-44/27) -> (-44/31,-61/43) Hyperbolic Matrix(1333,2162,-1050,-1703) (-13/8,-47/29) -> (-47/37,-33/26) Hyperbolic Matrix(2669,4324,966,1565) (-47/29,-81/50) -> (11/4,47/17) Hyperbolic Matrix(11501,18630,7100,11501) (-81/50,-115/71) -> (115/71,81/50) Hyperbolic Matrix(4829,7820,2982,4829) (-115/71,-34/21) -> (34/21,115/71) Hyperbolic Matrix(10121,16376,-7846,-12695) (-89/55,-144/89) -> (-40/31,-89/69) Hyperbolic Matrix(827,1334,-628,-1013) (-21/13,-50/31) -> (-4/3,-25/19) Hyperbolic Matrix(829,1334,458,737) (-29/18,-37/23) -> (9/5,29/16) Hyperbolic Matrix(229,368,28,45) (-37/23,-8/5) -> (8/1,9/1) Hyperbolic Matrix(1333,2116,492,781) (-27/17,-46/29) -> (46/17,19/7) Hyperbolic Matrix(1335,2116,494,783) (-46/29,-19/12) -> (27/10,46/17) Hyperbolic Matrix(3957,6256,2852,4509) (-68/43,-49/31) -> (43/31,68/49) Hyperbolic Matrix(321,506,262,413) (-30/19,-11/7) -> (11/9,16/13) Hyperbolic Matrix(2759,4324,1056,1655) (-11/7,-47/30) -> (47/18,81/31) Hyperbolic Matrix(323,506,30,47) (-47/30,-36/23) -> (10/1,1/0) Hyperbolic Matrix(2529,3956,1852,2897) (-36/23,-61/39) -> (15/11,56/41) Hyperbolic Matrix(737,1150,-530,-827) (-25/16,-14/9) -> (-32/23,-25/18) Hyperbolic Matrix(2163,3358,1334,2071) (-14/9,-45/29) -> (47/29,60/37) Hyperbolic Matrix(2669,4140,-1838,-2851) (-45/29,-31/20) -> (-61/42,-45/31) Hyperbolic Matrix(597,920,268,413) (-17/11,-20/13) -> (20/9,29/13) Hyperbolic Matrix(599,920,390,599) (-20/13,-23/15) -> (23/15,20/13) Hyperbolic Matrix(91,138,60,91) (-23/15,-3/2) -> (3/2,23/15) Hyperbolic Matrix(597,874,-472,-691) (-3/2,-19/13) -> (-19/15,-43/34) Hyperbolic Matrix(2437,3542,-1868,-2715) (-16/11,-61/42) -> (-107/82,-30/23) Hyperbolic Matrix(415,598,288,415) (-13/9,-23/16) -> (23/16,13/9) Hyperbolic Matrix(321,460,224,321) (-23/16,-10/7) -> (10/7,23/16) Hyperbolic Matrix(323,460,-290,-413) (-10/7,-37/26) -> (-9/8,-10/9) Hyperbolic Matrix(13385,19044,3976,5657) (-37/26,-138/97) -> (138/41,101/30) Hyperbolic Matrix(13387,19044,3978,5659) (-138/97,-101/71) -> (37/11,138/41) Hyperbolic Matrix(2071,2944,1198,1703) (-64/45,-27/19) -> (19/11,64/37) Hyperbolic Matrix(1425,2024,226,321) (-27/19,-71/50) -> (25/4,19/3) Hyperbolic Matrix(11501,16330,8100,11501) (-71/50,-115/81) -> (115/81,71/50) Hyperbolic Matrix(7129,10120,5022,7129) (-115/81,-44/31) -> (44/31,115/81) Hyperbolic Matrix(553,782,326,461) (-17/12,-24/17) -> (22/13,17/10) Hyperbolic Matrix(1011,1426,782,1103) (-24/17,-31/22) -> (31/24,22/17) Hyperbolic Matrix(229,322,32,45) (-31/22,-7/5) -> (7/1,15/2) Hyperbolic Matrix(1517,2116,428,597) (-7/5,-46/33) -> (46/13,39/11) Hyperbolic Matrix(1519,2116,430,599) (-46/33,-39/28) -> (7/2,46/13) Hyperbolic Matrix(16007,22218,6760,9383) (-93/67,-161/116) -> (161/68,45/19) Hyperbolic Matrix(21345,29624,9016,12513) (-161/116,-68/49) -> (116/49,161/68) Hyperbolic Matrix(2851,3956,596,827) (-68/49,-43/31) -> (43/9,24/5) Hyperbolic Matrix(1195,1656,464,643) (-43/31,-18/13) -> (18/7,49/19) Hyperbolic Matrix(3359,4646,2362,3267) (-18/13,-65/47) -> (27/19,64/45) Hyperbolic Matrix(1565,2162,-1198,-1655) (-47/34,-29/21) -> (-17/13,-47/36) Hyperbolic Matrix(367,506,66,91) (-29/21,-11/8) -> (11/2,17/3) Hyperbolic Matrix(369,506,202,277) (-11/8,-26/19) -> (20/11,11/6) Hyperbolic Matrix(875,1196,-706,-965) (-26/19,-41/30) -> (-5/4,-26/21) Hyperbolic Matrix(13937,19044,3736,5105) (-41/30,-138/101) -> (138/37,97/26) Hyperbolic Matrix(13939,19044,3738,5107) (-138/101,-97/71) -> (41/11,138/37) Hyperbolic Matrix(2897,3956,1852,2529) (-56/41,-15/11) -> (61/39,36/23) Hyperbolic Matrix(643,874,270,367) (-15/11,-19/14) -> (19/8,31/13) Hyperbolic Matrix(645,874,476,645) (-19/14,-23/17) -> (23/17,19/14) Hyperbolic Matrix(137,184,102,137) (-23/17,-4/3) -> (4/3,23/17) Hyperbolic Matrix(1609,2116,384,505) (-25/19,-46/35) -> (46/11,21/5) Hyperbolic Matrix(1611,2116,386,507) (-46/35,-21/16) -> (25/6,46/11) Hyperbolic Matrix(25943,33856,6062,7911) (-77/59,-184/141) -> (184/43,107/25) Hyperbolic Matrix(25945,33856,6064,7913) (-184/141,-107/82) -> (77/18,184/43) Hyperbolic Matrix(6531,8464,1490,1931) (-35/27,-92/71) -> (92/21,57/13) Hyperbolic Matrix(6533,8464,1492,1933) (-92/71,-57/44) -> (35/8,92/21) Hyperbolic Matrix(1103,1426,782,1011) (-22/17,-31/24) -> (31/22,24/17) Hyperbolic Matrix(1105,1426,-926,-1195) (-31/24,-40/31) -> (-6/5,-31/26) Hyperbolic Matrix(14765,19044,3316,4277) (-89/69,-138/107) -> (138/31,49/11) Hyperbolic Matrix(14767,19044,3318,4279) (-138/107,-49/38) -> (89/20,138/31) Hyperbolic Matrix(323,414,252,323) (-9/7,-23/18) -> (23/18,9/7) Hyperbolic Matrix(505,644,396,505) (-23/18,-14/11) -> (14/11,23/18) Hyperbolic Matrix(1013,1288,652,829) (-14/11,-47/37) -> (45/29,14/9) Hyperbolic Matrix(689,874,108,137) (-33/26,-19/15) -> (19/3,13/2) Hyperbolic Matrix(3129,3956,874,1105) (-43/34,-24/19) -> (68/19,43/12) Hyperbolic Matrix(1933,2392,1116,1381) (-26/21,-21/17) -> (71/41,26/15) Hyperbolic Matrix(413,506,262,321) (-16/13,-11/9) -> (11/7,30/19) Hyperbolic Matrix(415,506,114,139) (-11/9,-17/14) -> (29/8,11/3) Hyperbolic Matrix(645,782,532,645) (-17/14,-23/19) -> (23/19,17/14) Hyperbolic Matrix(229,276,190,229) (-23/19,-6/5) -> (6/5,23/19) Hyperbolic Matrix(1703,2024,504,599) (-25/21,-19/16) -> (27/8,71/21) Hyperbolic Matrix(737,874,156,185) (-19/16,-13/11) -> (33/7,19/4) Hyperbolic Matrix(1793,2116,272,321) (-13/11,-46/39) -> (46/7,33/5) Hyperbolic Matrix(1795,2116,274,323) (-46/39,-33/28) -> (13/2,46/7) Hyperbolic Matrix(277,322,80,93) (-7/6,-15/13) -> (31/9,7/2) Hyperbolic Matrix(599,690,520,599) (-15/13,-23/20) -> (23/20,15/13) Hyperbolic Matrix(321,368,280,321) (-23/20,-8/7) -> (8/7,23/20) Hyperbolic Matrix(323,368,122,139) (-8/7,-9/8) -> (37/14,8/3) Hyperbolic Matrix(459,506,166,183) (-10/9,-1/1) -> (47/17,36/13) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(413,-460,290,-323) (1/1,9/8) -> (37/26,47/33) Hyperbolic Matrix(275,-322,158,-185) (7/6,13/11) -> (33/19,7/4) Hyperbolic Matrix(1931,-2300,696,-829) (25/21,6/5) -> (86/31,25/9) Hyperbolic Matrix(597,-736,262,-323) (16/13,5/4) -> (41/18,16/7) Hyperbolic Matrix(183,-230,74,-93) (5/4,19/15) -> (27/11,5/2) Hyperbolic Matrix(1703,-2162,1050,-1333) (33/26,14/11) -> (60/37,13/8) Hyperbolic Matrix(2713,-3496,1036,-1335) (9/7,40/31) -> (144/55,55/21) Hyperbolic Matrix(3955,-5106,1426,-1841) (40/31,31/24) -> (61/22,86/31) Hyperbolic Matrix(461,-598,212,-275) (22/17,13/10) -> (13/6,24/11) Hyperbolic Matrix(459,-598,142,-185) (13/10,17/13) -> (29/9,13/4) Hyperbolic Matrix(737,-966,280,-367) (17/13,4/3) -> (50/19,29/11) Hyperbolic Matrix(5657,-7728,1516,-2071) (56/41,41/30) -> (97/26,56/15) Hyperbolic Matrix(2759,-3772,1212,-1657) (41/30,26/19) -> (66/29,41/18) Hyperbolic Matrix(1931,-2668,600,-829) (29/21,47/34) -> (45/14,29/9) Hyperbolic Matrix(2761,-3818,1596,-2207) (47/34,18/13) -> (64/37,45/26) Hyperbolic Matrix(5567,-7728,2352,-3265) (68/49,25/18) -> (71/30,116/49) Hyperbolic Matrix(827,-1150,530,-737) (25/18,7/5) -> (39/25,25/16) Hyperbolic Matrix(1103,-1564,390,-553) (17/12,44/31) -> (48/17,17/6) Hyperbolic Matrix(6209,-8832,1844,-2623) (64/45,37/26) -> (101/30,64/19) Hyperbolic Matrix(413,-598,96,-139) (13/9,16/11) -> (30/7,13/3) Hyperbolic Matrix(599,-874,220,-321) (16/11,3/2) -> (49/18,30/11) Hyperbolic Matrix(1011,-1564,298,-461) (17/11,31/20) -> (61/18,17/5) Hyperbolic Matrix(3173,-4922,742,-1151) (31/20,45/29) -> (47/11,77/18) Hyperbolic Matrix(1151,-1794,324,-505) (14/9,39/25) -> (39/11,32/9) Hyperbolic Matrix(1471,-2300,236,-369) (25/16,61/39) -> (31/5,25/4) Hyperbolic Matrix(553,-874,174,-275) (30/19,19/12) -> (19/6,16/5) Hyperbolic Matrix(231,-368,86,-137) (19/12,8/5) -> (8/3,27/10) Hyperbolic Matrix(599,-966,142,-229) (29/18,21/13) -> (21/5,17/4) Hyperbolic Matrix(967,-1564,426,-689) (21/13,34/21) -> (34/15,25/11) Hyperbolic Matrix(367,-598,170,-277) (13/8,31/19) -> (15/7,13/6) Hyperbolic Matrix(137,-230,28,-47) (5/3,22/13) -> (24/5,5/1) Hyperbolic Matrix(323,-552,134,-229) (17/10,12/7) -> (12/5,29/12) Hyperbolic Matrix(1151,-1978,508,-873) (12/7,43/25) -> (43/19,34/15) Hyperbolic Matrix(4463,-7728,1248,-2161) (45/26,71/41) -> (25/7,93/26) Hyperbolic Matrix(875,-1518,132,-229) (26/15,33/19) -> (33/5,20/3) Hyperbolic Matrix(413,-736,78,-139) (16/9,25/14) -> (21/4,16/3) Hyperbolic Matrix(875,-1564,334,-597) (25/14,9/5) -> (55/21,21/8) Hyperbolic Matrix(323,-598,74,-137) (11/6,13/7) -> (13/3,35/8) Hyperbolic Matrix(321,-598,124,-231) (13/7,2/1) -> (44/17,13/5) Hyperbolic Matrix(367,-782,130,-277) (2/1,15/7) -> (31/11,48/17) Hyperbolic Matrix(737,-1610,168,-367) (24/11,11/5) -> (57/13,22/5) Hyperbolic Matrix(367,-828,82,-185) (9/4,43/19) -> (49/11,9/2) Hyperbolic Matrix(137,-322,20,-47) (7/3,26/11) -> (20/3,7/1) Hyperbolic Matrix(1611,-3818,446,-1057) (45/19,19/8) -> (65/18,47/13) Hyperbolic Matrix(1057,-2530,404,-967) (43/18,12/5) -> (34/13,89/34) Hyperbolic Matrix(919,-2254,338,-829) (22/9,27/11) -> (19/7,68/25) Hyperbolic Matrix(1565,-4048,462,-1195) (31/12,44/17) -> (44/13,61/18) Hyperbolic Matrix(829,-2162,176,-459) (13/5,47/18) -> (47/10,33/7) Hyperbolic Matrix(6255,-16376,1406,-3681) (89/34,144/55) -> (40/9,89/20) Hyperbolic Matrix(507,-1334,122,-321) (21/8,50/19) -> (4/1,25/6) Hyperbolic Matrix(413,-1150,116,-323) (25/9,14/5) -> (32/9,25/7) Hyperbolic Matrix(1471,-4140,458,-1289) (45/16,31/11) -> (61/19,45/14) Hyperbolic Matrix(277,-874,58,-183) (3/1,19/6) -> (19/4,43/9) Hyperbolic Matrix(1105,-3542,258,-827) (16/5,61/19) -> (107/25,30/7) Hyperbolic Matrix(137,-460,14,-47) (10/3,37/11) -> (9/1,10/1) Hyperbolic Matrix(597,-2162,140,-507) (47/13,29/8) -> (17/4,47/11) Hyperbolic Matrix(321,-1196,62,-231) (26/7,41/11) -> (5/1,26/5) Hyperbolic Matrix(321,-1426,52,-231) (31/7,40/9) -> (6/1,31/5) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(47,460,-14,-137) -> Matrix(1,0,-6,1) Matrix(45,368,28,229) -> Matrix(3,2,16,11) Matrix(47,368,6,47) -> Matrix(1,0,6,1) Matrix(91,690,12,91) -> Matrix(1,0,-14,1) Matrix(45,322,32,229) -> Matrix(1,0,4,1) Matrix(47,322,-20,-137) -> Matrix(1,0,-4,1) Matrix(137,874,108,689) -> Matrix(1,-2,8,-15) Matrix(321,2024,226,1425) -> Matrix(1,2,6,13) Matrix(369,2300,-236,-1471) -> Matrix(1,0,-6,1) Matrix(47,276,8,47) -> Matrix(1,-2,0,1) Matrix(137,782,24,137) -> Matrix(1,2,0,1) Matrix(91,506,66,367) -> Matrix(1,-2,6,-11) Matrix(93,506,34,185) -> Matrix(1,2,2,5) Matrix(139,736,-78,-413) -> Matrix(1,2,-4,-7) Matrix(47,230,-28,-137) -> Matrix(3,2,-14,-9) Matrix(185,874,156,737) -> Matrix(7,2,52,15) Matrix(459,2162,-176,-829) -> Matrix(7,2,-18,-5) Matrix(139,644,30,139) -> Matrix(1,0,2,1) Matrix(91,414,20,91) -> Matrix(3,2,4,3) Matrix(783,3496,-484,-2161) -> Matrix(13,8,-70,-43) Matrix(1151,5106,-736,-3265) -> Matrix(3,2,-14,-9) Matrix(323,1426,94,415) -> Matrix(1,0,4,1) Matrix(137,598,-74,-323) -> Matrix(5,2,-18,-7) Matrix(139,598,-96,-413) -> Matrix(9,4,-52,-23) Matrix(229,966,-142,-599) -> Matrix(5,2,-28,-11) Matrix(47,184,12,47) -> Matrix(1,0,6,1) Matrix(229,874,60,229) -> Matrix(1,0,-10,1) Matrix(231,874,134,507) -> Matrix(7,-2,32,-9) Matrix(1059,3956,382,1427) -> Matrix(5,-2,8,-3) Matrix(2071,7728,-1516,-5657) -> Matrix(5,-4,-26,21) Matrix(1013,3772,-568,-2115) -> Matrix(1,0,-4,1) Matrix(137,506,62,229) -> Matrix(1,-2,4,-7) Matrix(139,506,114,415) -> Matrix(3,4,20,27) Matrix(737,2668,-508,-1839) -> Matrix(11,8,-62,-45) Matrix(1057,3818,-446,-1611) -> Matrix(3,2,-14,-9) Matrix(461,1656,282,1013) -> Matrix(11,10,56,51) Matrix(1747,6256,642,2299) -> Matrix(3,2,10,7) Matrix(2161,7728,-1248,-4463) -> Matrix(19,12,-84,-53) Matrix(323,1150,-116,-413) -> Matrix(1,0,0,1) Matrix(93,322,80,277) -> Matrix(3,2,22,15) Matrix(415,1426,94,323) -> Matrix(1,0,4,1) Matrix(229,782,94,321) -> Matrix(5,2,12,5) Matrix(461,1564,-298,-1011) -> Matrix(7,2,-32,-9) Matrix(2991,10120,884,2991) -> Matrix(23,6,88,23) Matrix(4829,16330,1428,4829) -> Matrix(25,6,104,25) Matrix(599,2024,504,1703) -> Matrix(11,2,82,15) Matrix(1379,4646,382,1287) -> Matrix(1,0,6,1) Matrix(2623,8832,-1844,-6209) -> Matrix(7,2,-46,-13) Matrix(645,2162,412,1381) -> Matrix(1,0,6,1) Matrix(139,460,42,139) -> Matrix(1,0,10,1) Matrix(183,598,56,183) -> Matrix(1,0,-6,1) Matrix(185,598,-142,-459) -> Matrix(1,-2,-6,13) Matrix(275,874,-174,-553) -> Matrix(1,-2,-6,13) Matrix(47,138,16,47) -> Matrix(3,2,4,3) Matrix(321,920,112,321) -> Matrix(13,6,28,13) Matrix(323,920,178,507) -> Matrix(9,4,38,17) Matrix(553,1564,-390,-1103) -> Matrix(7,2,-46,-13) Matrix(1749,4922,-1340,-3771) -> Matrix(3,2,-20,-13) Matrix(459,1288,98,275) -> Matrix(1,0,2,1) Matrix(643,1794,-462,-1289) -> Matrix(3,2,-20,-13) Matrix(829,2300,-696,-1931) -> Matrix(1,2,-8,-15) Matrix(1427,3956,382,1059) -> Matrix(3,2,-8,-5) Matrix(781,2162,548,1517) -> Matrix(3,2,16,11) Matrix(1565,4324,966,2669) -> Matrix(65,34,346,181) Matrix(185,506,34,93) -> Matrix(5,2,2,1) Matrix(321,874,-220,-599) -> Matrix(5,2,-28,-11) Matrix(137,368,-86,-231) -> Matrix(9,4,-52,-23) Matrix(139,368,122,323) -> Matrix(5,2,42,17) Matrix(505,1334,226,597) -> Matrix(5,2,22,9) Matrix(367,966,-280,-737) -> Matrix(19,8,-126,-53) Matrix(597,1564,-334,-875) -> Matrix(5,2,-18,-7) Matrix(2991,7820,1144,2991) -> Matrix(109,44,270,109) Matrix(7129,18630,2728,7129) -> Matrix(251,100,630,251) Matrix(1655,4324,1056,2759) -> Matrix(5,2,-18,-7) Matrix(1287,3358,458,1195) -> Matrix(5,2,-8,-3) Matrix(231,598,-124,-321) -> Matrix(11,4,-36,-13) Matrix(1105,2852,642,1657) -> Matrix(61,22,280,101) Matrix(643,1656,464,1195) -> Matrix(11,4,52,19) Matrix(323,828,126,323) -> Matrix(29,10,84,29) Matrix(91,230,36,91) -> Matrix(1,0,6,1) Matrix(93,230,-74,-183) -> Matrix(1,0,-4,1) Matrix(321,782,94,229) -> Matrix(5,2,12,5) Matrix(229,552,-134,-323) -> Matrix(19,6,-92,-29) Matrix(827,1978,-462,-1105) -> Matrix(7,2,-46,-13) Matrix(1195,2852,732,1747) -> Matrix(81,22,416,113) Matrix(367,874,270,643) -> Matrix(23,6,134,35) Matrix(1241,2944,368,873) -> Matrix(9,2,40,9) Matrix(3265,7728,-2352,-5567) -> Matrix(1,0,0,1) Matrix(1011,2392,194,459) -> Matrix(9,2,4,1) Matrix(643,1518,-546,-1289) -> Matrix(13,2,-98,-15) Matrix(139,322,60,139) -> Matrix(1,0,6,1) Matrix(321,736,140,321) -> Matrix(13,4,42,13) Matrix(323,736,-262,-597) -> Matrix(7,2,-46,-13) Matrix(689,1564,-426,-967) -> Matrix(29,8,-156,-43) Matrix(597,1334,226,505) -> Matrix(9,2,22,5) Matrix(413,920,268,597) -> Matrix(1,0,8,1) Matrix(229,506,62,137) -> Matrix(7,2,-4,-1) Matrix(275,598,-212,-461) -> Matrix(35,8,-232,-53) Matrix(277,598,-170,-367) -> Matrix(29,6,-150,-31) Matrix(415,782,-268,-505) -> Matrix(1,0,0,1) Matrix(873,1610,-674,-1243) -> Matrix(85,22,-568,-147) Matrix(277,506,202,369) -> Matrix(9,2,58,13) Matrix(507,920,178,323) -> Matrix(17,4,38,9) Matrix(737,1334,458,829) -> Matrix(35,8,188,43) Matrix(461,828,-358,-643) -> Matrix(21,4,-142,-27) Matrix(2991,5336,1264,2255) -> Matrix(1,0,8,1) Matrix(415,736,234,415) -> Matrix(7,2,24,7) Matrix(183,322,104,183) -> Matrix(17,4,72,17) Matrix(185,322,-158,-275) -> Matrix(17,4,-132,-31) Matrix(3081,5336,1354,2345) -> Matrix(35,8,118,27) Matrix(17111,29624,4782,8279) -> Matrix(215,48,318,71) Matrix(12835,22218,3588,6211) -> Matrix(109,24,168,37) Matrix(2207,3818,-1596,-2761) -> Matrix(19,4,-100,-21) Matrix(507,874,134,231) -> Matrix(9,2,-32,-7) Matrix(1657,2852,642,1105) -> Matrix(101,22,280,61) Matrix(1473,2530,-910,-1563) -> Matrix(139,30,-746,-161) Matrix(1241,2116,512,873) -> Matrix(69,14,202,41) Matrix(1243,2116,514,875) -> Matrix(61,12,188,37) Matrix(461,782,326,553) -> Matrix(1,0,12,1) Matrix(1335,2254,-844,-1425) -> Matrix(7,2,-46,-13) Matrix(139,230,84,139) -> Matrix(19,4,90,19) Matrix(505,828,308,505) -> Matrix(101,20,510,101) Matrix(1013,1656,282,461) -> Matrix(51,10,56,11) Matrix(1747,2852,732,1195) -> Matrix(113,22,416,81) Matrix(2483,4048,-1750,-2853) -> Matrix(41,8,-282,-55) Matrix(1333,2162,-1050,-1703) -> Matrix(95,18,-702,-133) Matrix(2669,4324,966,1565) -> Matrix(181,34,346,65) Matrix(11501,18630,7100,11501) -> Matrix(1279,240,6816,1279) Matrix(4829,7820,2982,4829) -> Matrix(545,102,2912,545) Matrix(10121,16376,-7846,-12695) -> Matrix(119,22,-806,-149) Matrix(827,1334,-628,-1013) -> Matrix(23,4,-144,-25) Matrix(829,1334,458,737) -> Matrix(43,8,188,35) Matrix(229,368,28,45) -> Matrix(11,2,16,3) Matrix(1333,2116,492,781) -> Matrix(59,10,112,19) Matrix(1335,2116,494,783) -> Matrix(73,12,152,25) Matrix(3957,6256,2852,4509) -> Matrix(13,2,84,13) Matrix(321,506,262,413) -> Matrix(13,2,84,13) Matrix(2759,4324,1056,1655) -> Matrix(7,-2,18,-5) Matrix(323,506,30,47) -> Matrix(1,0,0,1) Matrix(2529,3956,1852,2897) -> Matrix(7,2,38,11) Matrix(737,1150,-530,-827) -> Matrix(1,0,-2,1) Matrix(2163,3358,1334,2071) -> Matrix(57,10,302,53) Matrix(2669,4140,-1838,-2851) -> Matrix(17,2,-94,-11) Matrix(597,920,268,413) -> Matrix(1,0,8,1) Matrix(599,920,390,599) -> Matrix(19,4,90,19) Matrix(91,138,60,91) -> Matrix(11,2,60,11) Matrix(597,874,-472,-691) -> Matrix(11,2,-94,-17) Matrix(2437,3542,-1868,-2715) -> Matrix(21,4,-142,-27) Matrix(415,598,288,415) -> Matrix(59,10,348,59) Matrix(321,460,224,321) -> Matrix(37,6,228,37) Matrix(323,460,-290,-413) -> Matrix(25,4,-194,-31) Matrix(13385,19044,3976,5657) -> Matrix(25,4,106,17) Matrix(13387,19044,3978,5659) -> Matrix(13,2,84,13) Matrix(2071,2944,1198,1703) -> Matrix(25,4,106,17) Matrix(1425,2024,226,321) -> Matrix(13,2,6,1) Matrix(11501,16330,8100,11501) -> Matrix(181,28,1170,181) Matrix(7129,10120,5022,7129) -> Matrix(131,20,858,131) Matrix(553,782,326,461) -> Matrix(1,0,12,1) Matrix(1011,1426,782,1103) -> Matrix(35,4,236,27) Matrix(229,322,32,45) -> Matrix(1,0,4,1) Matrix(1517,2116,428,597) -> Matrix(23,4,40,7) Matrix(1519,2116,430,599) -> Matrix(13,2,32,5) Matrix(16007,22218,6760,9383) -> Matrix(9,2,40,9) Matrix(21345,29624,9016,12513) -> Matrix(11,2,60,11) Matrix(2851,3956,596,827) -> Matrix(11,2,16,3) Matrix(1195,1656,464,643) -> Matrix(19,4,52,11) Matrix(3359,4646,2362,3267) -> Matrix(43,8,274,51) Matrix(1565,2162,-1198,-1655) -> Matrix(23,4,-144,-25) Matrix(367,506,66,91) -> Matrix(11,2,-6,-1) Matrix(369,506,202,277) -> Matrix(13,2,58,9) Matrix(875,1196,-706,-965) -> Matrix(1,0,-2,1) Matrix(13937,19044,3736,5105) -> Matrix(19,4,-24,-5) Matrix(13939,19044,3738,5107) -> Matrix(31,6,-26,-5) Matrix(2897,3956,1852,2529) -> Matrix(11,2,38,7) Matrix(643,874,270,367) -> Matrix(35,6,134,23) Matrix(645,874,476,645) -> Matrix(95,16,564,95) Matrix(137,184,102,137) -> Matrix(37,6,228,37) Matrix(1609,2116,384,505) -> Matrix(13,2,110,17) Matrix(1611,2116,386,507) -> Matrix(13,2,-46,-7) Matrix(25943,33856,6062,7911) -> Matrix(233,36,576,89) Matrix(25945,33856,6064,7913) -> Matrix(287,44,724,111) Matrix(6531,8464,1490,1931) -> Matrix(413,62,806,121) Matrix(6533,8464,1492,1933) -> Matrix(347,52,714,107) Matrix(1103,1426,782,1011) -> Matrix(27,4,236,35) Matrix(1105,1426,-926,-1195) -> Matrix(55,8,-392,-57) Matrix(14765,19044,3316,4277) -> Matrix(41,6,34,5) Matrix(14767,19044,3318,4279) -> Matrix(1,0,8,1) Matrix(323,414,252,323) -> Matrix(69,10,476,69) Matrix(505,644,396,505) -> Matrix(71,10,504,71) Matrix(1013,1288,652,829) -> Matrix(29,4,152,21) Matrix(689,874,108,137) -> Matrix(15,2,-8,-1) Matrix(3129,3956,874,1105) -> Matrix(19,2,28,3) Matrix(1933,2392,1116,1381) -> Matrix(17,2,76,9) Matrix(413,506,262,321) -> Matrix(13,2,84,13) Matrix(415,506,114,139) -> Matrix(27,4,20,3) Matrix(645,782,532,645) -> Matrix(125,18,868,125) Matrix(229,276,190,229) -> Matrix(57,8,406,57) Matrix(1703,2024,504,599) -> Matrix(15,2,82,11) Matrix(737,874,156,185) -> Matrix(15,2,52,7) Matrix(1793,2116,272,321) -> Matrix(15,2,112,15) Matrix(1795,2116,274,323) -> Matrix(15,2,-128,-17) Matrix(277,322,80,93) -> Matrix(15,2,22,3) Matrix(599,690,520,599) -> Matrix(79,10,624,79) Matrix(321,368,280,321) -> Matrix(17,2,144,17) Matrix(323,368,122,139) -> Matrix(17,2,42,5) Matrix(459,506,166,183) -> Matrix(47,6,86,11) Matrix(1,0,2,1) -> Matrix(1,0,18,1) Matrix(413,-460,290,-323) -> Matrix(31,-4,194,-25) Matrix(275,-322,158,-185) -> Matrix(31,-4,132,-17) Matrix(1931,-2300,696,-829) -> Matrix(15,-2,8,-1) Matrix(597,-736,262,-323) -> Matrix(13,-2,46,-7) Matrix(183,-230,74,-93) -> Matrix(1,0,-4,1) Matrix(1703,-2162,1050,-1333) -> Matrix(133,-18,702,-95) Matrix(2713,-3496,1036,-1335) -> Matrix(95,-14,224,-33) Matrix(3955,-5106,1426,-1841) -> Matrix(41,-6,48,-7) Matrix(461,-598,212,-275) -> Matrix(53,-8,232,-35) Matrix(459,-598,142,-185) -> Matrix(13,-2,-6,1) Matrix(737,-966,280,-367) -> Matrix(53,-8,126,-19) Matrix(5657,-7728,1516,-2071) -> Matrix(21,-4,-26,5) Matrix(2759,-3772,1212,-1657) -> Matrix(9,-2,32,-7) Matrix(1931,-2668,600,-829) -> Matrix(11,-2,6,-1) Matrix(2761,-3818,1596,-2207) -> Matrix(21,-4,100,-19) Matrix(5567,-7728,2352,-3265) -> Matrix(1,0,0,1) Matrix(827,-1150,530,-737) -> Matrix(1,0,-2,1) Matrix(1103,-1564,390,-553) -> Matrix(13,-2,46,-7) Matrix(6209,-8832,1844,-2623) -> Matrix(13,-2,46,-7) Matrix(413,-598,96,-139) -> Matrix(23,-4,52,-9) Matrix(599,-874,220,-321) -> Matrix(11,-2,28,-5) Matrix(1011,-1564,298,-461) -> Matrix(9,-2,32,-7) Matrix(3173,-4922,742,-1151) -> Matrix(15,-2,38,-5) Matrix(1151,-1794,324,-505) -> Matrix(9,-2,14,-3) Matrix(1471,-2300,236,-369) -> Matrix(1,0,-6,1) Matrix(553,-874,174,-275) -> Matrix(13,-2,-6,1) Matrix(231,-368,86,-137) -> Matrix(23,-4,52,-9) Matrix(599,-966,142,-229) -> Matrix(11,-2,28,-5) Matrix(967,-1564,426,-689) -> Matrix(43,-8,156,-29) Matrix(367,-598,170,-277) -> Matrix(31,-6,150,-29) Matrix(137,-230,28,-47) -> Matrix(9,-2,14,-3) Matrix(323,-552,134,-229) -> Matrix(29,-6,92,-19) Matrix(1151,-1978,508,-873) -> Matrix(9,-2,50,-11) Matrix(4463,-7728,1248,-2161) -> Matrix(53,-12,84,-19) Matrix(875,-1518,132,-229) -> Matrix(9,-2,14,-3) Matrix(413,-736,78,-139) -> Matrix(7,-2,4,-1) Matrix(875,-1564,334,-597) -> Matrix(7,-2,18,-5) Matrix(323,-598,74,-137) -> Matrix(7,-2,18,-5) Matrix(321,-598,124,-231) -> Matrix(13,-4,36,-11) Matrix(367,-782,130,-277) -> Matrix(1,0,-2,1) Matrix(737,-1610,168,-367) -> Matrix(33,-8,62,-15) Matrix(367,-828,82,-185) -> Matrix(1,0,-2,1) Matrix(137,-322,20,-47) -> Matrix(1,0,-4,1) Matrix(1611,-3818,446,-1057) -> Matrix(9,-2,14,-3) Matrix(1057,-2530,404,-967) -> Matrix(43,-12,104,-29) Matrix(919,-2254,338,-829) -> Matrix(1,0,-2,1) Matrix(1565,-4048,462,-1195) -> Matrix(27,-10,100,-37) Matrix(829,-2162,176,-459) -> Matrix(5,-2,18,-7) Matrix(6255,-16376,1406,-3681) -> Matrix(9,-4,16,-7) Matrix(507,-1334,122,-321) -> Matrix(5,-2,-2,1) Matrix(413,-1150,116,-323) -> Matrix(1,0,0,1) Matrix(1471,-4140,458,-1289) -> Matrix(1,0,-2,1) Matrix(277,-874,58,-183) -> Matrix(1,-2,2,-3) Matrix(1105,-3542,258,-827) -> Matrix(5,2,12,5) Matrix(137,-460,14,-47) -> Matrix(1,0,-6,1) Matrix(597,-2162,140,-507) -> Matrix(5,-4,14,-11) Matrix(321,-1196,62,-231) -> Matrix(1,2,0,1) Matrix(321,-1426,52,-231) -> Matrix(3,-2,-4,3) 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): 92 Degree of the the map X: 92 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 1/1 23/20 23/19 23/18 23/17 23/16 3/2 23/15 23/14 23/13 2/1 23/10 161/68 5/2 23/9 115/44 23/8 3/1 23/7 115/34 7/2 11/3 23/6 4/1 25/6 46/11 17/4 92/21 9/2 23/5 19/4 5/1 11/2 23/4 6/1 13/2 7/1 15/2 23/3 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 1/1 -8/1 -1/3 -23/3 0/1 -15/2 0/1 1/7 -7/1 1/1 -13/2 0/1 1/3 -6/1 1/1 -11/2 0/1 1/0 -5/1 -1/1 -19/4 -1/2 0/1 -14/3 -1/1 -23/5 -1/1 -9/2 -1/1 -1/2 -22/5 -3/5 -13/3 -1/1 -4/1 -1/3 -15/4 0/1 1/1 -26/7 1/1 -11/3 -3/1 -7/2 -1/2 0/1 -17/5 -1/3 -44/13 -3/11 -27/8 -1/4 0/1 -10/3 -1/5 -23/7 0/1 -13/4 0/1 1/3 -16/5 1/1 -3/1 -1/1 -17/6 -1/2 -1/3 -14/5 -1/1 -11/4 -1/2 -2/5 -8/3 -1/3 -37/14 -1/2 -3/7 -29/11 -3/7 -21/8 -2/5 -1/3 -34/13 -11/27 -47/18 -2/5 -7/18 -13/5 -5/13 -31/12 -4/11 -1/3 -18/7 -1/3 -23/9 -1/3 -5/2 -1/3 0/1 -12/5 -5/17 -19/8 -1/4 -2/9 -45/19 -1/5 -26/11 -1/5 -7/3 -1/3 -9/4 -1/3 -1/4 -29/13 -1/3 -20/9 -1/3 -11/5 -5/19 -2/1 -1/3 -15/8 -1/3 0/1 -13/7 -3/11 -24/13 -5/19 -11/6 -1/4 -4/17 -9/5 -1/5 -25/14 -1/3 0/1 -16/9 -1/3 -23/13 -1/4 -7/4 -1/4 -2/9 -12/7 -7/33 -17/10 -1/5 -3/16 -22/13 -1/5 -27/16 -1/4 -2/9 -5/3 -1/5 -13/8 -1/5 -4/21 -21/13 -5/27 -29/18 -1/5 -3/16 -8/5 -3/17 -19/12 -1/6 -4/25 -11/7 -1/9 -25/16 -1/3 0/1 -14/9 -1/5 -31/20 -1/3 0/1 -48/31 -1/3 -17/11 -1/5 -20/13 -1/5 -23/15 -1/5 -3/2 -1/5 -1/6 -10/7 -3/19 -17/12 -3/20 -1/7 -24/17 -1/7 -31/22 -1/11 0/1 -7/5 -1/5 -25/18 -1/5 0/1 -43/31 -1/5 -18/13 -1/5 -11/8 -2/11 -1/6 -4/3 -3/19 -21/16 -2/13 -5/33 -17/13 -1/7 -13/10 -2/13 -5/33 -22/17 -7/47 -31/24 -4/27 -9/61 -9/7 -1/7 -5/4 -1/7 0/1 -6/5 -1/7 -7/6 -2/15 -1/8 -8/7 -1/9 -1/1 -1/9 0/1 0/1 1/1 1/9 9/8 1/8 1/7 8/7 1/9 23/20 1/8 15/13 5/39 7/6 1/8 2/15 6/5 1/7 23/19 1/7 17/14 1/7 9/62 11/9 5/33 5/4 0/1 1/7 14/11 1/7 23/18 1/7 9/7 1/7 31/24 9/61 4/27 22/17 7/47 13/10 5/33 2/13 17/13 1/7 4/3 3/19 23/17 1/6 19/14 1/6 8/47 15/11 1/5 11/8 1/6 2/11 18/13 1/5 43/31 1/5 68/49 1/5 25/18 0/1 1/5 7/5 1/5 31/22 0/1 1/11 24/17 1/7 17/12 1/7 3/20 44/31 5/33 115/81 2/13 71/50 2/13 7/45 27/19 1/7 10/7 3/19 23/16 1/6 13/9 5/29 3/2 1/6 1/5 23/15 1/5 20/13 1/5 17/11 1/5 31/20 0/1 1/3 14/9 1/5 25/16 0/1 1/3 11/7 1/9 19/12 4/25 1/6 8/5 3/17 37/23 5/27 29/18 3/16 1/5 21/13 5/27 34/21 17/91 115/71 3/16 81/50 3/16 40/213 47/29 13/69 13/8 4/21 1/5 18/11 1/5 23/14 1/5 5/3 1/5 22/13 1/5 17/10 3/16 1/5 12/7 7/33 7/4 2/9 1/4 23/13 1/4 16/9 1/3 25/14 0/1 1/3 9/5 1/5 11/6 4/17 1/4 13/7 3/11 2/1 1/3 13/6 1/5 2/9 24/11 5/21 11/5 5/19 20/9 1/3 29/13 1/3 9/4 1/4 1/3 16/7 1/3 23/10 1/3 7/3 1/3 26/11 1/5 71/30 0/1 1/5 116/49 1/5 161/68 1/5 45/19 1/5 19/8 2/9 1/4 12/5 5/17 29/12 9/28 1/3 46/19 1/3 17/7 1/3 5/2 0/1 1/3 23/9 1/3 18/7 1/3 49/19 1/3 31/12 1/3 4/11 44/17 1/3 13/5 5/13 47/18 7/18 2/5 81/31 25/63 115/44 2/5 34/13 11/27 21/8 1/3 2/5 50/19 7/17 29/11 3/7 37/14 3/7 1/2 8/3 1/3 27/10 8/17 1/2 46/17 1/2 19/7 3/5 11/4 2/5 1/2 14/5 1/1 31/11 1/5 17/6 1/3 1/2 20/7 3/7 23/8 1/2 3/1 1/1 16/5 -1/1 13/4 -1/3 0/1 23/7 0/1 10/3 1/5 37/11 1/5 27/8 0/1 1/4 71/21 3/13 115/34 1/4 44/13 3/11 61/18 3/11 2/7 17/5 1/3 7/2 0/1 1/2 11/3 3/1 26/7 -1/1 41/11 -1/1 15/4 -1/1 0/1 19/5 -1/5 23/6 0/1 4/1 1/3 25/6 -1/1 0/1 46/11 0/1 21/5 1/5 17/4 1/4 1/3 13/3 1/1 35/8 6/13 1/2 92/21 1/2 57/13 13/25 22/5 3/5 31/7 3/5 9/2 1/2 1/1 23/5 1/1 14/3 1/1 47/10 0/1 1/0 33/7 1/1 19/4 0/1 1/2 24/5 1/1 5/1 1/1 11/2 0/1 1/0 17/3 1/1 23/4 1/0 6/1 -1/1 13/2 -1/3 0/1 7/1 -1/1 15/2 -1/7 0/1 23/3 0/1 8/1 1/3 9/1 -1/1 10/1 -1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(47,437,10,93) (-9/1,1/0) -> (14/3,47/10) Hyperbolic Matrix(45,368,28,229) (-9/1,-8/1) -> (8/5,37/23) Hyperbolic Matrix(47,368,6,47) (-8/1,-23/3) -> (23/3,8/1) Hyperbolic Matrix(91,690,12,91) (-23/3,-15/2) -> (15/2,23/3) Hyperbolic Matrix(45,322,32,229) (-15/2,-7/1) -> (7/5,31/22) Hyperbolic Matrix(45,299,-14,-93) (-7/1,-13/2) -> (-13/4,-16/5) Hyperbolic Matrix(47,299,-36,-229) (-13/2,-6/1) -> (-17/13,-13/10) Hyperbolic Matrix(45,253,8,45) (-6/1,-11/2) -> (11/2,17/3) Hyperbolic Matrix(47,253,-34,-183) (-11/2,-5/1) -> (-18/13,-11/8) Hyperbolic Matrix(47,230,-28,-137) (-5/1,-19/4) -> (-27/16,-5/3) Hyperbolic Matrix(229,1081,68,321) (-19/4,-14/3) -> (37/11,27/8) Hyperbolic Matrix(139,644,30,139) (-14/3,-23/5) -> (23/5,14/3) Hyperbolic Matrix(91,414,20,91) (-23/5,-9/2) -> (9/2,23/5) Hyperbolic Matrix(47,207,42,185) (-9/2,-22/5) -> (1/1,9/8) Hyperbolic Matrix(137,598,-74,-323) (-22/5,-13/3) -> (-13/7,-24/13) Hyperbolic Matrix(91,391,64,275) (-13/3,-4/1) -> (27/19,10/7) Hyperbolic Matrix(91,345,24,91) (-4/1,-15/4) -> (15/4,19/5) Hyperbolic Matrix(413,1541,160,597) (-15/4,-26/7) -> (49/19,31/12) Hyperbolic Matrix(137,506,62,229) (-26/7,-11/3) -> (11/5,20/9) Hyperbolic Matrix(45,161,-26,-93) (-11/3,-7/2) -> (-7/4,-12/7) Hyperbolic Matrix(47,161,-40,-137) (-7/2,-17/5) -> (-6/5,-7/6) Hyperbolic Matrix(461,1564,-298,-1011) (-17/5,-44/13) -> (-48/31,-17/11) Hyperbolic Matrix(919,3105,272,919) (-44/13,-27/8) -> (27/8,71/21) Hyperbolic Matrix(321,1081,68,229) (-27/8,-10/3) -> (33/7,19/4) Hyperbolic Matrix(139,460,42,139) (-10/3,-23/7) -> (23/7,10/3) Hyperbolic Matrix(183,598,56,183) (-23/7,-13/4) -> (13/4,23/7) Hyperbolic Matrix(137,437,-58,-185) (-16/5,-3/1) -> (-26/11,-7/3) Hyperbolic Matrix(137,391,48,137) (-3/1,-17/6) -> (17/6,20/7) Hyperbolic Matrix(367,1035,228,643) (-17/6,-14/5) -> (37/23,29/18) Hyperbolic Matrix(91,253,-50,-139) (-14/5,-11/4) -> (-11/6,-9/5) Hyperbolic Matrix(93,253,68,185) (-11/4,-8/3) -> (15/11,11/8) Hyperbolic Matrix(139,368,122,323) (-8/3,-37/14) -> (9/8,8/7) Hyperbolic Matrix(505,1334,226,597) (-37/14,-29/11) -> (29/13,9/4) Hyperbolic Matrix(367,966,-280,-737) (-29/11,-21/8) -> (-21/16,-17/13) Hyperbolic Matrix(413,1081,-264,-691) (-21/8,-34/13) -> (-11/7,-25/16) Hyperbolic Matrix(2069,5405,792,2069) (-34/13,-47/18) -> (47/18,81/31) Hyperbolic Matrix(185,483,18,47) (-47/18,-13/5) -> (10/1,1/0) Hyperbolic Matrix(231,598,-124,-321) (-13/5,-31/12) -> (-15/8,-13/7) Hyperbolic Matrix(597,1541,160,413) (-31/12,-18/7) -> (41/11,15/4) Hyperbolic Matrix(323,828,126,323) (-18/7,-23/9) -> (23/9,18/7) Hyperbolic Matrix(91,230,36,91) (-23/9,-5/2) -> (5/2,23/9) Hyperbolic Matrix(47,115,38,93) (-5/2,-12/5) -> (11/9,5/4) Hyperbolic Matrix(183,437,-116,-277) (-12/5,-19/8) -> (-19/12,-11/7) Hyperbolic Matrix(689,1633,-408,-967) (-19/8,-45/19) -> (-22/13,-27/16) Hyperbolic Matrix(1565,3703,1128,2669) (-45/19,-26/11) -> (43/31,68/49) Hyperbolic Matrix(91,207,40,91) (-7/3,-9/4) -> (9/4,16/7) Hyperbolic Matrix(597,1334,226,505) (-9/4,-29/13) -> (29/11,37/14) Hyperbolic Matrix(413,920,268,597) (-29/13,-20/9) -> (20/13,17/11) Hyperbolic Matrix(229,506,62,137) (-20/9,-11/5) -> (11/3,26/7) Hyperbolic Matrix(139,299,86,185) (-11/5,-2/1) -> (21/13,34/21) Hyperbolic Matrix(415,782,-268,-505) (-2/1,-15/8) -> (-31/20,-48/31) Hyperbolic Matrix(1335,2461,824,1519) (-24/13,-11/6) -> (81/50,47/29) Hyperbolic Matrix(321,575,-206,-369) (-9/5,-25/14) -> (-25/16,-14/9) Hyperbolic Matrix(323,575,-232,-413) (-25/14,-16/9) -> (-7/5,-25/18) Hyperbolic Matrix(415,736,234,415) (-16/9,-23/13) -> (23/13,16/9) Hyperbolic Matrix(183,322,104,183) (-23/13,-7/4) -> (7/4,23/13) Hyperbolic Matrix(229,391,188,321) (-12/7,-17/10) -> (17/14,11/9) Hyperbolic Matrix(461,782,326,553) (-17/10,-22/13) -> (24/17,17/12) Hyperbolic Matrix(183,299,112,183) (-5/3,-13/8) -> (13/8,18/11) Hyperbolic Matrix(185,299,86,139) (-13/8,-21/13) -> (2/1,13/6) Hyperbolic Matrix(1013,1633,714,1151) (-21/13,-29/18) -> (17/12,44/31) Hyperbolic Matrix(643,1035,228,367) (-29/18,-8/5) -> (31/11,17/6) Hyperbolic Matrix(275,437,202,321) (-8/5,-19/12) -> (19/14,15/11) Hyperbolic Matrix(459,713,-356,-553) (-14/9,-31/20) -> (-31/24,-9/7) Hyperbolic Matrix(597,920,268,413) (-17/11,-20/13) -> (20/9,29/13) Hyperbolic Matrix(599,920,390,599) (-20/13,-23/15) -> (23/15,20/13) Hyperbolic Matrix(91,138,60,91) (-23/15,-3/2) -> (3/2,23/15) Hyperbolic Matrix(47,69,32,47) (-3/2,-10/7) -> (13/9,3/2) Hyperbolic Matrix(275,391,64,91) (-10/7,-17/12) -> (17/4,13/3) Hyperbolic Matrix(553,782,326,461) (-17/12,-24/17) -> (22/13,17/10) Hyperbolic Matrix(1011,1426,782,1103) (-24/17,-31/22) -> (31/24,22/17) Hyperbolic Matrix(229,322,32,45) (-31/22,-7/5) -> (7/1,15/2) Hyperbolic Matrix(2669,3703,1128,1565) (-25/18,-43/31) -> (26/11,71/30) Hyperbolic Matrix(1195,1656,464,643) (-43/31,-18/13) -> (18/7,49/19) Hyperbolic Matrix(185,253,68,93) (-11/8,-4/3) -> (19/7,11/4) Hyperbolic Matrix(645,851,454,599) (-4/3,-21/16) -> (71/50,27/19) Hyperbolic Matrix(691,897,426,553) (-13/10,-22/17) -> (47/29,13/8) Hyperbolic Matrix(1103,1426,782,1011) (-22/17,-31/24) -> (31/22,24/17) Hyperbolic Matrix(91,115,72,91) (-9/7,-5/4) -> (5/4,14/11) Hyperbolic Matrix(93,115,38,47) (-5/4,-6/5) -> (17/7,5/2) Hyperbolic Matrix(139,161,120,139) (-7/6,-8/7) -> (15/13,7/6) Hyperbolic Matrix(185,207,42,47) (-8/7,-1/1) -> (22/5,31/7) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(461,-529,400,-459) (8/7,23/20) -> (23/20,15/13) Parabolic Matrix(137,-161,40,-47) (7/6,6/5) -> (17/5,7/2) Hyperbolic Matrix(553,-667,228,-275) (6/5,23/19) -> (46/19,17/7) Hyperbolic Matrix(1195,-1449,494,-599) (23/19,17/14) -> (29/12,46/19) Hyperbolic Matrix(415,-529,324,-413) (14/11,23/18) -> (23/18,9/7) Parabolic Matrix(553,-713,356,-459) (9/7,31/24) -> (31/20,14/9) Hyperbolic Matrix(461,-598,212,-275) (22/17,13/10) -> (13/6,24/11) Hyperbolic Matrix(229,-299,36,-47) (13/10,17/13) -> (6/1,13/2) Hyperbolic Matrix(737,-966,280,-367) (17/13,4/3) -> (50/19,29/11) Hyperbolic Matrix(461,-621,170,-229) (4/3,23/17) -> (46/17,19/7) Hyperbolic Matrix(1103,-1495,408,-553) (23/17,19/14) -> (27/10,46/17) Hyperbolic Matrix(183,-253,34,-47) (11/8,18/13) -> (5/1,11/2) Hyperbolic Matrix(1609,-2231,432,-599) (18/13,43/31) -> (26/7,41/11) Hyperbolic Matrix(5567,-7728,2352,-3265) (68/49,25/18) -> (71/30,116/49) Hyperbolic Matrix(413,-575,232,-323) (25/18,7/5) -> (16/9,25/14) Hyperbolic Matrix(3127,-4439,746,-1059) (44/31,115/81) -> (46/11,21/5) Hyperbolic Matrix(4325,-6141,1036,-1471) (115/81,71/50) -> (25/6,46/11) Hyperbolic Matrix(369,-529,256,-367) (10/7,23/16) -> (23/16,13/9) Parabolic Matrix(1011,-1564,298,-461) (17/11,31/20) -> (61/18,17/5) Hyperbolic Matrix(369,-575,206,-321) (14/9,25/16) -> (25/14,9/5) Hyperbolic Matrix(691,-1081,264,-413) (25/16,11/7) -> (34/13,21/8) Hyperbolic Matrix(277,-437,116,-183) (11/7,19/12) -> (19/8,12/5) Hyperbolic Matrix(231,-368,86,-137) (19/12,8/5) -> (8/3,27/10) Hyperbolic Matrix(599,-966,142,-229) (29/18,21/13) -> (21/5,17/4) Hyperbolic Matrix(5979,-9683,1364,-2209) (34/21,115/71) -> (92/21,57/13) Hyperbolic Matrix(7085,-11477,1618,-2621) (115/71,81/50) -> (35/8,92/21) Hyperbolic Matrix(323,-529,196,-321) (18/11,23/14) -> (23/14,5/3) Parabolic Matrix(137,-230,28,-47) (5/3,22/13) -> (24/5,5/1) Hyperbolic Matrix(323,-552,134,-229) (17/10,12/7) -> (12/5,29/12) Hyperbolic Matrix(93,-161,26,-45) (12/7,7/4) -> (7/2,11/3) Hyperbolic Matrix(139,-253,50,-91) (9/5,11/6) -> (11/4,14/5) Hyperbolic Matrix(323,-598,74,-137) (11/6,13/7) -> (13/3,35/8) Hyperbolic Matrix(321,-598,124,-231) (13/7,2/1) -> (44/17,13/5) Hyperbolic Matrix(737,-1610,168,-367) (24/11,11/5) -> (57/13,22/5) Hyperbolic Matrix(231,-529,100,-229) (16/7,23/10) -> (23/10,7/3) Parabolic Matrix(185,-437,58,-137) (7/3,26/11) -> (3/1,16/5) Hyperbolic Matrix(10949,-25921,4624,-10947) (116/49,161/68) -> (161/68,45/19) Parabolic Matrix(553,-1311,116,-275) (45/19,19/8) -> (19/4,24/5) Hyperbolic Matrix(1565,-4048,462,-1195) (31/12,44/17) -> (44/13,61/18) Hyperbolic Matrix(829,-2162,176,-459) (13/5,47/18) -> (47/10,33/7) Hyperbolic Matrix(5061,-13225,1936,-5059) (81/31,115/44) -> (115/44,34/13) Parabolic Matrix(507,-1334,122,-321) (21/8,50/19) -> (4/1,25/6) Hyperbolic Matrix(461,-1219,104,-275) (37/14,8/3) -> (31/7,9/2) Hyperbolic Matrix(139,-391,16,-45) (14/5,31/11) -> (8/1,9/1) Hyperbolic Matrix(185,-529,64,-183) (20/7,23/8) -> (23/8,3/1) Parabolic Matrix(93,-299,14,-45) (16/5,13/4) -> (13/2,7/1) Hyperbolic Matrix(137,-460,14,-47) (10/3,37/11) -> (9/1,10/1) Hyperbolic Matrix(3911,-13225,1156,-3909) (71/21,115/34) -> (115/34,44/13) Parabolic Matrix(139,-529,36,-137) (19/5,23/6) -> (23/6,4/1) Parabolic Matrix(93,-529,16,-91) (17/3,23/4) -> (23/4,6/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(47,437,10,93) -> Matrix(1,0,0,1) Matrix(45,368,28,229) -> Matrix(3,2,16,11) Matrix(47,368,6,47) -> Matrix(1,0,6,1) Matrix(91,690,12,91) -> Matrix(1,0,-14,1) Matrix(45,322,32,229) -> Matrix(1,0,4,1) Matrix(45,299,-14,-93) -> Matrix(1,0,0,1) Matrix(47,299,-36,-229) -> Matrix(1,-2,-6,13) Matrix(45,253,8,45) -> Matrix(1,0,0,1) Matrix(47,253,-34,-183) -> Matrix(1,2,-6,-11) Matrix(47,230,-28,-137) -> Matrix(3,2,-14,-9) Matrix(229,1081,68,321) -> Matrix(1,0,6,1) Matrix(139,644,30,139) -> Matrix(1,0,2,1) Matrix(91,414,20,91) -> Matrix(3,2,4,3) Matrix(47,207,42,185) -> Matrix(3,2,22,15) Matrix(137,598,-74,-323) -> Matrix(5,2,-18,-7) Matrix(91,391,64,275) -> Matrix(5,2,32,13) Matrix(91,345,24,91) -> Matrix(1,0,-2,1) Matrix(413,1541,160,597) -> Matrix(5,-4,14,-11) Matrix(137,506,62,229) -> Matrix(1,-2,4,-7) Matrix(45,161,-26,-93) -> Matrix(3,2,-14,-9) Matrix(47,161,-40,-137) -> Matrix(5,2,-38,-15) Matrix(461,1564,-298,-1011) -> Matrix(7,2,-32,-9) Matrix(919,3105,272,919) -> Matrix(1,0,8,1) Matrix(321,1081,68,229) -> Matrix(1,0,6,1) Matrix(139,460,42,139) -> Matrix(1,0,10,1) Matrix(183,598,56,183) -> Matrix(1,0,-6,1) Matrix(137,437,-58,-185) -> Matrix(1,0,-4,1) Matrix(137,391,48,137) -> Matrix(5,2,12,5) Matrix(367,1035,228,643) -> Matrix(7,2,38,11) Matrix(91,253,-50,-139) -> Matrix(3,2,-14,-9) Matrix(93,253,68,185) -> Matrix(1,0,8,1) Matrix(139,368,122,323) -> Matrix(5,2,42,17) Matrix(505,1334,226,597) -> Matrix(5,2,22,9) Matrix(367,966,-280,-737) -> Matrix(19,8,-126,-53) Matrix(413,1081,-264,-691) -> Matrix(5,2,-18,-7) Matrix(2069,5405,792,2069) -> Matrix(71,28,180,71) Matrix(185,483,18,47) -> Matrix(5,2,-18,-7) Matrix(231,598,-124,-321) -> Matrix(11,4,-36,-13) Matrix(597,1541,160,413) -> Matrix(11,4,-14,-5) Matrix(323,828,126,323) -> Matrix(29,10,84,29) Matrix(91,230,36,91) -> Matrix(1,0,6,1) Matrix(47,115,38,93) -> Matrix(1,0,10,1) Matrix(183,437,-116,-277) -> Matrix(7,2,-46,-13) Matrix(689,1633,-408,-967) -> Matrix(1,0,0,1) Matrix(1565,3703,1128,2669) -> Matrix(1,0,10,1) Matrix(91,207,40,91) -> Matrix(7,2,24,7) Matrix(597,1334,226,505) -> Matrix(9,2,22,5) Matrix(413,920,268,597) -> Matrix(1,0,8,1) Matrix(229,506,62,137) -> Matrix(7,2,-4,-1) Matrix(139,299,86,185) -> Matrix(11,2,60,11) Matrix(415,782,-268,-505) -> Matrix(1,0,0,1) Matrix(1335,2461,824,1519) -> Matrix(109,28,580,149) Matrix(321,575,-206,-369) -> Matrix(1,0,0,1) Matrix(323,575,-232,-413) -> Matrix(1,0,-2,1) Matrix(415,736,234,415) -> Matrix(7,2,24,7) Matrix(183,322,104,183) -> Matrix(17,4,72,17) Matrix(229,391,188,321) -> Matrix(29,6,198,41) Matrix(461,782,326,553) -> Matrix(1,0,12,1) Matrix(183,299,112,183) -> Matrix(41,8,210,41) Matrix(185,299,86,139) -> Matrix(11,2,60,11) Matrix(1013,1633,714,1151) -> Matrix(1,0,12,1) Matrix(643,1035,228,367) -> Matrix(11,2,38,7) Matrix(275,437,202,321) -> Matrix(23,4,132,23) Matrix(459,713,-356,-553) -> Matrix(21,4,-142,-27) Matrix(597,920,268,413) -> Matrix(1,0,8,1) Matrix(599,920,390,599) -> Matrix(19,4,90,19) Matrix(91,138,60,91) -> Matrix(11,2,60,11) Matrix(47,69,32,47) -> Matrix(11,2,60,11) Matrix(275,391,64,91) -> Matrix(13,2,32,5) Matrix(553,782,326,461) -> Matrix(1,0,12,1) Matrix(1011,1426,782,1103) -> Matrix(35,4,236,27) Matrix(229,322,32,45) -> Matrix(1,0,4,1) Matrix(2669,3703,1128,1565) -> Matrix(1,0,10,1) Matrix(1195,1656,464,643) -> Matrix(19,4,52,11) Matrix(185,253,68,93) -> Matrix(1,0,8,1) Matrix(645,851,454,599) -> Matrix(25,4,156,25) Matrix(691,897,426,553) -> Matrix(119,18,628,95) Matrix(1103,1426,782,1011) -> Matrix(27,4,236,35) Matrix(91,115,72,91) -> Matrix(1,0,14,1) Matrix(93,115,38,47) -> Matrix(1,0,10,1) Matrix(139,161,120,139) -> Matrix(31,4,240,31) Matrix(185,207,42,47) -> Matrix(15,2,22,3) Matrix(1,0,2,1) -> Matrix(1,0,18,1) Matrix(461,-529,400,-459) -> Matrix(49,-6,384,-47) Matrix(137,-161,40,-47) -> Matrix(15,-2,38,-5) Matrix(553,-667,228,-275) -> Matrix(57,-8,164,-23) Matrix(1195,-1449,494,-599) -> Matrix(125,-18,382,-55) Matrix(415,-529,324,-413) -> Matrix(71,-10,490,-69) Matrix(553,-713,356,-459) -> Matrix(27,-4,142,-21) Matrix(461,-598,212,-275) -> Matrix(53,-8,232,-35) Matrix(229,-299,36,-47) -> Matrix(13,-2,-6,1) Matrix(737,-966,280,-367) -> Matrix(53,-8,126,-19) Matrix(461,-621,170,-229) -> Matrix(37,-6,68,-11) Matrix(1103,-1495,408,-553) -> Matrix(95,-16,196,-33) Matrix(183,-253,34,-47) -> Matrix(11,-2,6,-1) Matrix(1609,-2231,432,-599) -> Matrix(1,0,-6,1) Matrix(5567,-7728,2352,-3265) -> Matrix(1,0,0,1) Matrix(413,-575,232,-323) -> Matrix(1,0,-2,1) Matrix(3127,-4439,746,-1059) -> Matrix(13,-2,98,-15) Matrix(4325,-6141,1036,-1471) -> Matrix(13,-2,-58,9) Matrix(369,-529,256,-367) -> Matrix(49,-8,288,-47) Matrix(1011,-1564,298,-461) -> Matrix(9,-2,32,-7) Matrix(369,-575,206,-321) -> Matrix(1,0,0,1) Matrix(691,-1081,264,-413) -> Matrix(7,-2,18,-5) Matrix(277,-437,116,-183) -> Matrix(13,-2,46,-7) Matrix(231,-368,86,-137) -> Matrix(23,-4,52,-9) Matrix(599,-966,142,-229) -> Matrix(11,-2,28,-5) Matrix(5979,-9683,1364,-2209) -> Matrix(299,-56,582,-109) Matrix(7085,-11477,1618,-2621) -> Matrix(309,-58,634,-119) Matrix(323,-529,196,-321) -> Matrix(61,-12,300,-59) Matrix(137,-230,28,-47) -> Matrix(9,-2,14,-3) Matrix(323,-552,134,-229) -> Matrix(29,-6,92,-19) Matrix(93,-161,26,-45) -> Matrix(9,-2,14,-3) Matrix(139,-253,50,-91) -> Matrix(9,-2,14,-3) Matrix(323,-598,74,-137) -> Matrix(7,-2,18,-5) Matrix(321,-598,124,-231) -> Matrix(13,-4,36,-11) Matrix(737,-1610,168,-367) -> Matrix(33,-8,62,-15) Matrix(231,-529,100,-229) -> Matrix(7,-2,18,-5) Matrix(185,-437,58,-137) -> Matrix(1,0,-4,1) Matrix(10949,-25921,4624,-10947) -> Matrix(11,-2,50,-9) Matrix(553,-1311,116,-275) -> Matrix(9,-2,14,-3) Matrix(1565,-4048,462,-1195) -> Matrix(27,-10,100,-37) Matrix(829,-2162,176,-459) -> Matrix(5,-2,18,-7) Matrix(5061,-13225,1936,-5059) -> Matrix(181,-72,450,-179) Matrix(507,-1334,122,-321) -> Matrix(5,-2,-2,1) Matrix(461,-1219,104,-275) -> Matrix(9,-4,16,-7) Matrix(139,-391,16,-45) -> Matrix(1,0,-2,1) Matrix(185,-529,64,-183) -> Matrix(9,-4,16,-7) Matrix(93,-299,14,-45) -> Matrix(1,0,0,1) Matrix(137,-460,14,-47) -> Matrix(1,0,-6,1) Matrix(3911,-13225,1156,-3909) -> Matrix(25,-6,96,-23) Matrix(139,-529,36,-137) -> Matrix(1,0,8,1) Matrix(93,-529,16,-91) -> Matrix(1,-2,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 46 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 9 1 1/1 1/9 1 23 8/7 1/9 1 23 23/20 1/8 6 1 7/6 (1/8,2/15) 0 23 6/5 1/7 1 23 5/4 (0/1,1/7) 0 23 23/18 1/7 10 1 9/7 1/7 1 23 31/24 (9/61,4/27) 0 23 22/17 7/47 1 23 13/10 (5/33,2/13) 0 23 17/13 1/7 1 23 4/3 3/19 1 23 11/8 (1/6,2/11) 0 23 18/13 1/5 1 23 43/31 1/5 1 23 25/18 (0/1,1/5) 0 23 7/5 1/5 1 23 31/22 (0/1,1/11) 0 23 24/17 1/7 1 23 17/12 (1/7,3/20) 0 23 10/7 3/19 1 23 23/16 1/6 8 1 3/2 (1/6,1/5) 0 23 23/15 1/5 3 1 20/13 1/5 1 23 17/11 1/5 1 23 31/20 (0/1,1/3) 0 23 14/9 1/5 1 23 25/16 (0/1,1/3) 0 23 11/7 1/9 1 23 19/12 (4/25,1/6) 0 23 8/5 3/17 1 23 29/18 (3/16,1/5) 0 23 21/13 5/27 1 23 13/8 (4/21,1/5) 0 23 23/14 1/5 12 1 5/3 1/5 1 23 22/13 1/5 1 23 17/10 (3/16,1/5) 0 23 12/7 7/33 1 23 7/4 (2/9,1/4) 0 23 23/13 1/4 3 1 16/9 1/3 1 23 25/14 (0/1,1/3) 0 23 9/5 1/5 1 23 11/6 (4/17,1/4) 0 23 13/7 3/11 1 23 2/1 1/3 1 23 13/6 (1/5,2/9) 0 23 24/11 5/21 1 23 11/5 5/19 1 23 20/9 1/3 1 23 29/13 1/3 1 23 9/4 (1/4,1/3) 0 23 23/10 1/3 2 1 7/3 1/3 1 23 26/11 1/5 1 23 71/30 (0/1,1/5) 0 23 161/68 1/5 2 1 45/19 1/5 1 23 19/8 (2/9,1/4) 0 23 12/5 5/17 1 23 29/12 (9/28,1/3) 0 23 46/19 1/3 13 1 17/7 1/3 1 23 5/2 (0/1,1/3) 0 23 23/9 1/3 5 1 18/7 1/3 1 23 31/12 (1/3,4/11) 0 23 44/17 1/3 1 23 13/5 5/13 1 23 47/18 (7/18,2/5) 0 23 115/44 2/5 18 1 34/13 11/27 1 23 21/8 (1/3,2/5) 0 23 50/19 7/17 1 23 29/11 3/7 1 23 37/14 (3/7,1/2) 0 23 8/3 1/3 1 23 27/10 (8/17,1/2) 0 23 46/17 1/2 11 1 19/7 3/5 1 23 11/4 (2/5,1/2) 0 23 14/5 1/1 1 23 31/11 1/5 1 23 17/6 (1/3,1/2) 0 23 23/8 1/2 4 1 3/1 1/1 1 23 16/5 -1/1 1 23 13/4 (-1/3,0/1) 0 23 23/7 0/1 8 1 10/3 1/5 1 23 27/8 (0/1,1/4) 0 23 115/34 1/4 6 1 44/13 3/11 1 23 61/18 (3/11,2/7) 0 23 17/5 1/3 1 23 7/2 (0/1,1/2) 0 23 11/3 3/1 1 23 26/7 -1/1 1 23 41/11 -1/1 1 23 15/4 (-1/1,0/1) 0 23 23/6 0/1 8 1 4/1 1/3 1 23 25/6 (-1/1,0/1) 0 23 46/11 0/1 6 1 21/5 1/5 1 23 17/4 (1/4,1/3) 0 23 13/3 1/1 1 23 35/8 (6/13,1/2) 0 23 92/21 1/2 19 1 57/13 13/25 1 23 22/5 3/5 1 23 31/7 3/5 1 23 9/2 (1/2,1/1) 0 23 23/5 1/1 1 1 14/3 1/1 1 23 33/7 1/1 1 23 19/4 (0/1,1/2) 0 23 24/5 1/1 1 23 5/1 1/1 1 23 11/2 (0/1,1/0) 0 23 23/4 1/0 2 1 6/1 -1/1 1 23 13/2 (-1/3,0/1) 0 23 7/1 -1/1 1 23 15/2 (-1/7,0/1) 0 23 23/3 0/1 10 1 8/1 1/3 1 23 9/1 -1/1 1 23 10/1 -1/1 1 23 1/0 (0/1,1/0) 0 23 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(185,-207,42,-47) (1/1,8/7) -> (22/5,31/7) Glide Reflection Matrix(321,-368,280,-321) (8/7,23/20) -> (8/7,23/20) Reflection Matrix(139,-161,120,-139) (23/20,7/6) -> (23/20,7/6) Reflection Matrix(137,-161,40,-47) (7/6,6/5) -> (17/5,7/2) Hyperbolic Matrix(93,-115,38,-47) (6/5,5/4) -> (17/7,5/2) Glide Reflection Matrix(91,-115,72,-91) (5/4,23/18) -> (5/4,23/18) Reflection Matrix(323,-414,252,-323) (23/18,9/7) -> (23/18,9/7) Reflection Matrix(553,-713,356,-459) (9/7,31/24) -> (31/20,14/9) Hyperbolic Matrix(1103,-1426,782,-1011) (31/24,22/17) -> (31/22,24/17) Glide Reflection Matrix(461,-598,212,-275) (22/17,13/10) -> (13/6,24/11) Hyperbolic Matrix(229,-299,36,-47) (13/10,17/13) -> (6/1,13/2) Hyperbolic Matrix(737,-966,280,-367) (17/13,4/3) -> (50/19,29/11) Hyperbolic Matrix(185,-253,68,-93) (4/3,11/8) -> (19/7,11/4) Glide Reflection Matrix(183,-253,34,-47) (11/8,18/13) -> (5/1,11/2) Hyperbolic Matrix(1609,-2231,432,-599) (18/13,43/31) -> (26/7,41/11) Hyperbolic Matrix(2669,-3703,1128,-1565) (43/31,25/18) -> (26/11,71/30) Glide Reflection Matrix(413,-575,232,-323) (25/18,7/5) -> (16/9,25/14) Hyperbolic Matrix(229,-322,32,-45) (7/5,31/22) -> (7/1,15/2) Glide Reflection Matrix(553,-782,326,-461) (24/17,17/12) -> (22/13,17/10) Glide Reflection Matrix(275,-391,64,-91) (17/12,10/7) -> (17/4,13/3) Glide Reflection Matrix(321,-460,224,-321) (10/7,23/16) -> (10/7,23/16) Reflection Matrix(47,-69,32,-47) (23/16,3/2) -> (23/16,3/2) Reflection Matrix(91,-138,60,-91) (3/2,23/15) -> (3/2,23/15) Reflection Matrix(599,-920,390,-599) (23/15,20/13) -> (23/15,20/13) Reflection Matrix(597,-920,268,-413) (20/13,17/11) -> (20/9,29/13) Glide Reflection Matrix(1011,-1564,298,-461) (17/11,31/20) -> (61/18,17/5) Hyperbolic Matrix(369,-575,206,-321) (14/9,25/16) -> (25/14,9/5) Hyperbolic Matrix(691,-1081,264,-413) (25/16,11/7) -> (34/13,21/8) Hyperbolic Matrix(277,-437,116,-183) (11/7,19/12) -> (19/8,12/5) Hyperbolic Matrix(231,-368,86,-137) (19/12,8/5) -> (8/3,27/10) Hyperbolic Matrix(643,-1035,228,-367) (8/5,29/18) -> (31/11,17/6) Glide Reflection Matrix(599,-966,142,-229) (29/18,21/13) -> (21/5,17/4) Hyperbolic Matrix(185,-299,86,-139) (21/13,13/8) -> (2/1,13/6) Glide Reflection Matrix(183,-299,112,-183) (13/8,23/14) -> (13/8,23/14) Reflection Matrix(139,-230,84,-139) (23/14,5/3) -> (23/14,5/3) Reflection Matrix(137,-230,28,-47) (5/3,22/13) -> (24/5,5/1) Hyperbolic Matrix(323,-552,134,-229) (17/10,12/7) -> (12/5,29/12) Hyperbolic Matrix(93,-161,26,-45) (12/7,7/4) -> (7/2,11/3) Hyperbolic Matrix(183,-322,104,-183) (7/4,23/13) -> (7/4,23/13) Reflection Matrix(415,-736,234,-415) (23/13,16/9) -> (23/13,16/9) Reflection Matrix(139,-253,50,-91) (9/5,11/6) -> (11/4,14/5) Hyperbolic Matrix(323,-598,74,-137) (11/6,13/7) -> (13/3,35/8) Hyperbolic Matrix(321,-598,124,-231) (13/7,2/1) -> (44/17,13/5) Hyperbolic Matrix(737,-1610,168,-367) (24/11,11/5) -> (57/13,22/5) Hyperbolic Matrix(229,-506,62,-137) (11/5,20/9) -> (11/3,26/7) Glide Reflection Matrix(597,-1334,226,-505) (29/13,9/4) -> (29/11,37/14) Glide Reflection Matrix(91,-207,40,-91) (9/4,23/10) -> (9/4,23/10) Reflection Matrix(139,-322,60,-139) (23/10,7/3) -> (23/10,7/3) Reflection Matrix(185,-437,58,-137) (7/3,26/11) -> (3/1,16/5) Hyperbolic Matrix(4829,-11431,2040,-4829) (71/30,161/68) -> (71/30,161/68) Reflection Matrix(6119,-14490,2584,-6119) (161/68,45/19) -> (161/68,45/19) Reflection Matrix(553,-1311,116,-275) (45/19,19/8) -> (19/4,24/5) Hyperbolic Matrix(1103,-2668,456,-1103) (29/12,46/19) -> (29/12,46/19) Reflection Matrix(645,-1564,266,-645) (46/19,17/7) -> (46/19,17/7) Reflection Matrix(91,-230,36,-91) (5/2,23/9) -> (5/2,23/9) Reflection Matrix(323,-828,126,-323) (23/9,18/7) -> (23/9,18/7) Reflection Matrix(597,-1541,160,-413) (18/7,31/12) -> (41/11,15/4) Glide Reflection Matrix(1565,-4048,462,-1195) (31/12,44/17) -> (44/13,61/18) Hyperbolic Matrix(185,-483,18,-47) (13/5,47/18) -> (10/1,1/0) Glide Reflection Matrix(2069,-5405,792,-2069) (47/18,115/44) -> (47/18,115/44) Reflection Matrix(2991,-7820,1144,-2991) (115/44,34/13) -> (115/44,34/13) Reflection Matrix(507,-1334,122,-321) (21/8,50/19) -> (4/1,25/6) Hyperbolic Matrix(461,-1219,104,-275) (37/14,8/3) -> (31/7,9/2) Hyperbolic Matrix(919,-2484,340,-919) (27/10,46/17) -> (27/10,46/17) Reflection Matrix(645,-1748,238,-645) (46/17,19/7) -> (46/17,19/7) Reflection Matrix(139,-391,16,-45) (14/5,31/11) -> (8/1,9/1) Hyperbolic Matrix(137,-391,48,-137) (17/6,23/8) -> (17/6,23/8) Reflection Matrix(47,-138,16,-47) (23/8,3/1) -> (23/8,3/1) Reflection Matrix(93,-299,14,-45) (16/5,13/4) -> (13/2,7/1) Hyperbolic Matrix(183,-598,56,-183) (13/4,23/7) -> (13/4,23/7) Reflection Matrix(139,-460,42,-139) (23/7,10/3) -> (23/7,10/3) Reflection Matrix(321,-1081,68,-229) (10/3,27/8) -> (33/7,19/4) Glide Reflection Matrix(919,-3105,272,-919) (27/8,115/34) -> (27/8,115/34) Reflection Matrix(2991,-10120,884,-2991) (115/34,44/13) -> (115/34,44/13) Reflection Matrix(91,-345,24,-91) (15/4,23/6) -> (15/4,23/6) Reflection Matrix(47,-184,12,-47) (23/6,4/1) -> (23/6,4/1) Reflection Matrix(551,-2300,132,-551) (25/6,46/11) -> (25/6,46/11) Reflection Matrix(461,-1932,110,-461) (46/11,21/5) -> (46/11,21/5) Reflection Matrix(1471,-6440,336,-1471) (35/8,92/21) -> (35/8,92/21) Reflection Matrix(2393,-10488,546,-2393) (92/21,57/13) -> (92/21,57/13) Reflection Matrix(91,-414,20,-91) (9/2,23/5) -> (9/2,23/5) Reflection Matrix(139,-644,30,-139) (23/5,14/3) -> (23/5,14/3) Reflection Matrix(93,-437,10,-47) (14/3,33/7) -> (9/1,10/1) Glide Reflection Matrix(45,-253,8,-45) (11/2,23/4) -> (11/2,23/4) Reflection Matrix(47,-276,8,-47) (23/4,6/1) -> (23/4,6/1) Reflection Matrix(91,-690,12,-91) (15/2,23/3) -> (15/2,23/3) Reflection Matrix(47,-368,6,-47) (23/3,8/1) -> (23/3,8/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,18,-1) (0/1,1/1) -> (0/1,1/9) Matrix(185,-207,42,-47) -> Matrix(15,-2,22,-3) Matrix(321,-368,280,-321) -> Matrix(17,-2,144,-17) (8/7,23/20) -> (1/9,1/8) Matrix(139,-161,120,-139) -> Matrix(31,-4,240,-31) (23/20,7/6) -> (1/8,2/15) Matrix(137,-161,40,-47) -> Matrix(15,-2,38,-5) Matrix(93,-115,38,-47) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(91,-115,72,-91) -> Matrix(1,0,14,-1) (5/4,23/18) -> (0/1,1/7) Matrix(323,-414,252,-323) -> Matrix(69,-10,476,-69) (23/18,9/7) -> (1/7,5/34) Matrix(553,-713,356,-459) -> Matrix(27,-4,142,-21) Matrix(1103,-1426,782,-1011) -> Matrix(27,-4,236,-35) Matrix(461,-598,212,-275) -> Matrix(53,-8,232,-35) Matrix(229,-299,36,-47) -> Matrix(13,-2,-6,1) Matrix(737,-966,280,-367) -> Matrix(53,-8,126,-19) Matrix(185,-253,68,-93) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(183,-253,34,-47) -> Matrix(11,-2,6,-1) Matrix(1609,-2231,432,-599) -> Matrix(1,0,-6,1) 0/1 Matrix(2669,-3703,1128,-1565) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(413,-575,232,-323) -> Matrix(1,0,-2,1) 0/1 Matrix(229,-322,32,-45) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(553,-782,326,-461) -> Matrix(1,0,12,-1) *** -> (0/1,1/6) Matrix(275,-391,64,-91) -> Matrix(13,-2,32,-5) Matrix(321,-460,224,-321) -> Matrix(37,-6,228,-37) (10/7,23/16) -> (3/19,1/6) Matrix(47,-69,32,-47) -> Matrix(11,-2,60,-11) (23/16,3/2) -> (1/6,1/5) Matrix(91,-138,60,-91) -> Matrix(11,-2,60,-11) (3/2,23/15) -> (1/6,1/5) Matrix(599,-920,390,-599) -> Matrix(19,-4,90,-19) (23/15,20/13) -> (1/5,2/9) Matrix(597,-920,268,-413) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(1011,-1564,298,-461) -> Matrix(9,-2,32,-7) 1/4 Matrix(369,-575,206,-321) -> Matrix(1,0,0,1) Matrix(691,-1081,264,-413) -> Matrix(7,-2,18,-5) 1/3 Matrix(277,-437,116,-183) -> Matrix(13,-2,46,-7) Matrix(231,-368,86,-137) -> Matrix(23,-4,52,-9) Matrix(643,-1035,228,-367) -> Matrix(11,-2,38,-7) Matrix(599,-966,142,-229) -> Matrix(11,-2,28,-5) Matrix(185,-299,86,-139) -> Matrix(11,-2,60,-11) *** -> (1/6,1/5) Matrix(183,-299,112,-183) -> Matrix(41,-8,210,-41) (13/8,23/14) -> (4/21,1/5) Matrix(139,-230,84,-139) -> Matrix(19,-4,90,-19) (23/14,5/3) -> (1/5,2/9) Matrix(137,-230,28,-47) -> Matrix(9,-2,14,-3) Matrix(323,-552,134,-229) -> Matrix(29,-6,92,-19) Matrix(93,-161,26,-45) -> Matrix(9,-2,14,-3) Matrix(183,-322,104,-183) -> Matrix(17,-4,72,-17) (7/4,23/13) -> (2/9,1/4) Matrix(415,-736,234,-415) -> Matrix(7,-2,24,-7) (23/13,16/9) -> (1/4,1/3) Matrix(139,-253,50,-91) -> Matrix(9,-2,14,-3) Matrix(323,-598,74,-137) -> Matrix(7,-2,18,-5) 1/3 Matrix(321,-598,124,-231) -> Matrix(13,-4,36,-11) 1/3 Matrix(737,-1610,168,-367) -> Matrix(33,-8,62,-15) Matrix(229,-506,62,-137) -> Matrix(7,-2,-4,1) Matrix(597,-1334,226,-505) -> Matrix(9,-2,22,-5) Matrix(91,-207,40,-91) -> Matrix(7,-2,24,-7) (9/4,23/10) -> (1/4,1/3) Matrix(139,-322,60,-139) -> Matrix(1,0,6,-1) (23/10,7/3) -> (0/1,1/3) Matrix(185,-437,58,-137) -> Matrix(1,0,-4,1) 0/1 Matrix(4829,-11431,2040,-4829) -> Matrix(1,0,10,-1) (71/30,161/68) -> (0/1,1/5) Matrix(6119,-14490,2584,-6119) -> Matrix(9,-2,40,-9) (161/68,45/19) -> (1/5,1/4) Matrix(553,-1311,116,-275) -> Matrix(9,-2,14,-3) Matrix(1103,-2668,456,-1103) -> Matrix(55,-18,168,-55) (29/12,46/19) -> (9/28,1/3) Matrix(645,-1564,266,-645) -> Matrix(23,-8,66,-23) (46/19,17/7) -> (1/3,4/11) Matrix(91,-230,36,-91) -> Matrix(1,0,6,-1) (5/2,23/9) -> (0/1,1/3) Matrix(323,-828,126,-323) -> Matrix(29,-10,84,-29) (23/9,18/7) -> (1/3,5/14) Matrix(597,-1541,160,-413) -> Matrix(11,-4,-14,5) Matrix(1565,-4048,462,-1195) -> Matrix(27,-10,100,-37) Matrix(185,-483,18,-47) -> Matrix(5,-2,-18,7) Matrix(2069,-5405,792,-2069) -> Matrix(71,-28,180,-71) (47/18,115/44) -> (7/18,2/5) Matrix(2991,-7820,1144,-2991) -> Matrix(109,-44,270,-109) (115/44,34/13) -> (2/5,11/27) Matrix(507,-1334,122,-321) -> Matrix(5,-2,-2,1) Matrix(461,-1219,104,-275) -> Matrix(9,-4,16,-7) 1/2 Matrix(919,-2484,340,-919) -> Matrix(33,-16,68,-33) (27/10,46/17) -> (8/17,1/2) Matrix(645,-1748,238,-645) -> Matrix(11,-6,20,-11) (46/17,19/7) -> (1/2,3/5) Matrix(139,-391,16,-45) -> Matrix(1,0,-2,1) 0/1 Matrix(137,-391,48,-137) -> Matrix(5,-2,12,-5) (17/6,23/8) -> (1/3,1/2) Matrix(47,-138,16,-47) -> Matrix(3,-2,4,-3) (23/8,3/1) -> (1/2,1/1) Matrix(93,-299,14,-45) -> Matrix(1,0,0,1) Matrix(183,-598,56,-183) -> Matrix(-1,0,6,1) (13/4,23/7) -> (-1/3,0/1) Matrix(139,-460,42,-139) -> Matrix(1,0,10,-1) (23/7,10/3) -> (0/1,1/5) Matrix(321,-1081,68,-229) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(919,-3105,272,-919) -> Matrix(1,0,8,-1) (27/8,115/34) -> (0/1,1/4) Matrix(2991,-10120,884,-2991) -> Matrix(23,-6,88,-23) (115/34,44/13) -> (1/4,3/11) Matrix(91,-345,24,-91) -> Matrix(-1,0,2,1) (15/4,23/6) -> (-1/1,0/1) Matrix(47,-184,12,-47) -> Matrix(1,0,6,-1) (23/6,4/1) -> (0/1,1/3) Matrix(551,-2300,132,-551) -> Matrix(-1,0,2,1) (25/6,46/11) -> (-1/1,0/1) Matrix(461,-1932,110,-461) -> Matrix(1,0,10,-1) (46/11,21/5) -> (0/1,1/5) Matrix(1471,-6440,336,-1471) -> Matrix(25,-12,52,-25) (35/8,92/21) -> (6/13,1/2) Matrix(2393,-10488,546,-2393) -> Matrix(51,-26,100,-51) (92/21,57/13) -> (1/2,13/25) Matrix(91,-414,20,-91) -> Matrix(3,-2,4,-3) (9/2,23/5) -> (1/2,1/1) Matrix(139,-644,30,-139) -> Matrix(1,0,2,-1) (23/5,14/3) -> (0/1,1/1) Matrix(93,-437,10,-47) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(45,-253,8,-45) -> Matrix(1,0,0,-1) (11/2,23/4) -> (0/1,1/0) Matrix(47,-276,8,-47) -> Matrix(1,2,0,-1) (23/4,6/1) -> (-1/1,1/0) Matrix(91,-690,12,-91) -> Matrix(-1,0,14,1) (15/2,23/3) -> (-1/7,0/1) Matrix(47,-368,6,-47) -> Matrix(1,0,6,-1) (23/3,8/1) -> (0/1,1/3) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.