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 -5/13 -8/1 -6/17 -23/3 -1/3 -15/2 -11/34 -7/1 -1/3 -13/2 -5/18 -19/3 -3/11 -25/4 -1/4 -6/1 -4/15 -23/4 -1/4 -17/3 -11/45 -11/2 -7/30 -16/3 -2/9 -5/1 -1/5 -19/4 -5/24 -33/7 -9/43 -14/3 -8/39 -23/5 -1/5 -9/2 -5/26 -40/9 -10/53 -31/7 -13/69 -22/5 -12/65 -13/3 -3/17 -17/4 -3/16 -4/1 -2/11 -23/6 -1/6 -19/5 -9/55 -15/4 -7/44 -56/15 -2/13 -41/11 -1/7 -26/7 -4/25 -11/3 -5/33 -29/8 -5/36 -47/13 -5/39 -18/5 0/1 -43/12 -3/20 -68/19 -10/69 -25/7 -1/7 -7/2 -1/6 -31/9 -9/55 -24/7 -10/63 -17/5 -5/33 -44/13 -2/13 -115/34 -3/20 -71/21 -1/7 -27/8 -3/20 -64/19 -2/13 -37/11 -9/59 -47/14 -19/126 -10/3 -4/27 -23/7 -1/7 -13/4 -5/36 -16/5 -2/15 -3/1 -1/7 -23/8 -1/8 -20/7 -6/49 -17/6 -5/42 -31/11 -7/59 -45/16 -13/112 -14/5 0/1 -39/14 -3/26 -25/9 -1/9 -61/22 -1/10 -36/13 -2/17 -47/17 -13/115 -11/4 -3/28 -30/11 0/1 -19/7 -1/13 -8/3 -2/15 -37/14 -3/26 -29/11 -1/7 -21/8 -1/8 -34/13 -4/31 -115/44 -1/8 -81/31 -15/121 -47/18 -11/90 -60/23 -10/83 -13/5 -1/9 -31/12 -7/60 -49/19 -5/43 -18/7 -4/35 -23/9 -1/9 -5/2 -1/10 -22/9 -4/45 -17/7 -1/15 -12/5 -2/15 -43/18 -3/26 -31/13 -5/43 -19/8 -3/28 -64/27 -2/19 -45/19 -7/69 -71/30 -1/10 -26/11 0/1 -33/14 -1/6 -7/3 -1/9 -23/10 -1/10 -16/7 -2/21 -25/11 -1/11 -9/4 -1/12 -29/13 -3/31 -20/9 -2/23 -11/5 -1/15 -13/6 -1/10 -2/1 0/1 -15/8 -1/8 -13/7 -1/11 -24/13 -2/31 -11/6 -1/6 -20/11 -2/19 -29/16 -3/32 -9/5 -1/9 -43/24 -1/8 -34/19 -4/39 -25/14 -1/10 -66/37 -4/41 -41/23 -1/11 -16/9 -2/21 -23/13 -1/11 -7/4 -1/12 -26/15 0/1 -71/41 -1/11 -116/67 -14/153 -161/93 -1/11 -45/26 -7/78 -19/11 -3/35 -31/18 -5/62 -43/25 -3/37 -12/7 -2/27 -29/17 -1/21 -46/27 0/1 -17/10 -1/6 -22/13 -4/39 -27/16 -3/32 -5/3 -1/11 -23/14 -1/12 -18/11 -4/49 -49/30 -5/62 -31/19 -7/87 -44/27 -2/25 -13/8 -1/12 -47/29 -11/141 -81/50 -15/194 -115/71 -1/13 -34/21 -4/53 -89/55 -1/15 -144/89 -2/23 -55/34 -1/14 -21/13 -1/13 -50/31 0/1 -29/18 -1/14 -37/23 -3/37 -8/5 -2/27 -27/17 -1/19 -46/29 0/1 -19/12 -1/8 -68/43 -6/59 -49/31 -1/11 -30/19 0/1 -11/7 -3/35 -47/30 -13/158 -36/23 -2/25 -61/39 -1/11 -86/55 0/1 -25/16 -1/12 -14/9 0/1 -45/29 -13/161 -31/20 -7/88 -48/31 -2/25 -17/11 -5/63 -20/13 -6/77 -23/15 -1/13 -3/2 -1/14 -19/13 -5/67 -16/11 -2/27 -61/42 -17/230 -45/31 -17/231 -29/20 -7/96 -13/9 -5/69 -23/16 -1/14 -10/7 -4/57 -37/26 -9/130 -138/97 -2/29 -101/71 -17/247 -64/45 -2/29 -27/19 -3/43 -71/50 -1/14 -115/81 -3/43 -44/31 -2/29 -61/43 -7/101 -17/12 -5/72 -24/17 -10/147 -31/22 -9/134 -7/5 -1/15 -46/33 0/1 -39/28 -1/12 -32/23 -2/27 -25/18 -1/14 -93/67 -11/153 -161/116 -1/14 -68/49 -10/141 -43/31 -3/43 -18/13 0/1 -65/47 -1/11 -47/34 -5/66 -29/21 -5/69 -11/8 -5/72 -26/19 -4/59 -41/30 -1/14 -138/101 -2/29 -97/71 -9/131 -56/41 -2/29 -15/11 -7/103 -19/14 -9/134 -23/17 -1/15 -4/3 -2/31 -25/19 -1/15 -46/35 -2/31 -21/16 -1/16 -17/13 -3/47 -47/36 -3/52 -77/59 -1/23 -184/141 0/1 -107/82 -1/6 -30/23 0/1 -13/10 -3/46 -35/27 -13/201 -92/71 -2/31 -57/44 -25/388 -22/17 -12/187 -31/24 -13/204 -40/31 -10/157 -89/69 -19/299 -138/107 -4/63 -49/38 -9/142 -9/7 -5/79 -23/18 -1/16 -14/11 -8/129 -47/37 -27/437 -33/26 -9/146 -19/15 -5/81 -43/34 -7/114 -24/19 -14/229 -5/4 -1/16 -26/21 -4/67 -21/17 -1/17 -16/13 -2/33 -11/9 -7/117 -17/14 -11/186 -23/19 -1/17 -6/5 -4/69 -31/26 -5/86 -25/21 -1/17 -19/16 -3/52 -13/11 -5/87 -46/39 -2/35 -33/28 -13/228 -20/17 -2/35 -7/6 -1/18 -15/13 -11/197 -23/20 -1/18 -8/7 -6/109 -9/8 -5/92 -10/9 -4/75 -1/1 -1/21 0/1 0/1 1/1 1/21 9/8 5/92 8/7 6/109 23/20 1/18 15/13 11/197 7/6 1/18 13/11 5/87 19/16 3/52 25/21 1/17 6/5 4/69 23/19 1/17 17/14 11/186 11/9 7/117 16/13 2/33 5/4 1/16 19/15 5/81 33/26 9/146 14/11 8/129 23/18 1/16 9/7 5/79 40/31 10/157 31/24 13/204 22/17 12/187 13/10 3/46 17/13 3/47 4/3 2/31 23/17 1/15 19/14 9/134 15/11 7/103 56/41 2/29 41/30 1/14 26/19 4/59 11/8 5/72 29/21 5/69 47/34 5/66 18/13 0/1 43/31 3/43 68/49 10/141 25/18 1/14 7/5 1/15 31/22 9/134 24/17 10/147 17/12 5/72 44/31 2/29 115/81 3/43 71/50 1/14 27/19 3/43 64/45 2/29 37/26 9/130 47/33 19/273 10/7 4/57 23/16 1/14 13/9 5/69 16/11 2/27 3/2 1/14 23/15 1/13 20/13 6/77 17/11 5/63 31/20 7/88 45/29 13/161 14/9 0/1 39/25 3/37 25/16 1/12 61/39 1/11 36/23 2/25 47/30 13/158 11/7 3/35 30/19 0/1 19/12 1/8 8/5 2/27 37/23 3/37 29/18 1/14 21/13 1/13 34/21 4/53 115/71 1/13 81/50 15/194 47/29 11/141 60/37 10/127 13/8 1/12 31/19 7/87 49/30 5/62 18/11 4/49 23/14 1/12 5/3 1/11 22/13 4/39 17/10 1/6 12/7 2/27 43/25 3/37 31/18 5/62 19/11 3/35 64/37 2/23 45/26 7/78 71/41 1/11 26/15 0/1 33/19 1/15 7/4 1/12 23/13 1/11 16/9 2/21 25/14 1/10 9/5 1/9 29/16 3/32 20/11 2/19 11/6 1/6 13/7 1/11 2/1 0/1 15/7 1/13 13/6 1/10 24/11 2/11 11/5 1/15 20/9 2/23 29/13 3/31 9/4 1/12 43/19 1/13 34/15 4/45 25/11 1/11 66/29 4/43 41/18 1/10 16/7 2/21 23/10 1/10 7/3 1/9 26/11 0/1 71/30 1/10 116/49 14/141 161/68 1/10 45/19 7/69 19/8 3/28 31/13 5/43 43/18 3/26 12/5 2/15 29/12 1/0 46/19 0/1 17/7 1/15 22/9 4/45 27/11 3/31 5/2 1/10 23/9 1/9 18/7 4/35 49/19 5/43 31/12 7/60 44/17 2/17 13/5 1/9 47/18 11/90 81/31 15/121 115/44 1/8 34/13 4/31 89/34 1/6 144/55 2/19 55/21 1/7 21/8 1/8 50/19 0/1 29/11 1/7 37/14 3/26 8/3 2/15 27/10 1/2 46/17 0/1 19/7 1/13 68/25 6/67 49/18 1/10 30/11 0/1 11/4 3/28 47/17 13/115 36/13 2/17 61/22 1/10 86/31 0/1 25/9 1/9 14/5 0/1 45/16 13/112 31/11 7/59 48/17 2/17 17/6 5/42 20/7 6/49 23/8 1/8 3/1 1/7 19/6 5/38 16/5 2/15 61/19 17/127 45/14 17/126 29/9 7/51 13/4 5/36 23/7 1/7 10/3 4/27 37/11 9/59 138/41 2/13 101/30 17/110 64/19 2/13 27/8 3/20 71/21 1/7 115/34 3/20 44/13 2/13 61/18 7/46 17/5 5/33 24/7 10/63 31/9 9/55 7/2 1/6 46/13 0/1 39/11 1/9 32/9 2/15 25/7 1/7 93/26 11/78 161/45 1/7 68/19 10/69 43/12 3/20 18/5 0/1 65/18 1/10 47/13 5/39 29/8 5/36 11/3 5/33 26/7 4/25 41/11 1/7 138/37 2/13 97/26 9/58 56/15 2/13 15/4 7/44 19/5 9/55 23/6 1/6 4/1 2/11 25/6 1/6 46/11 2/11 21/5 1/5 17/4 3/16 47/11 3/11 77/18 -1/2 184/43 0/1 107/25 1/15 30/7 0/1 13/3 3/17 35/8 13/72 92/21 2/11 57/13 25/137 22/5 12/65 31/7 13/69 40/9 10/53 89/20 19/100 138/31 4/21 49/11 9/47 9/2 5/26 23/5 1/5 14/3 8/39 47/10 27/130 33/7 9/43 19/4 5/24 43/9 7/33 24/5 14/65 5/1 1/5 26/5 4/17 21/4 1/4 16/3 2/9 11/2 7/30 17/3 11/45 23/4 1/4 6/1 4/15 31/5 5/19 25/4 1/4 19/3 3/11 13/2 5/18 46/7 2/7 33/5 13/45 20/3 2/7 7/1 1/3 15/2 11/34 23/3 1/3 8/1 6/17 9/1 5/13 10/1 4/9 1/0 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(19,8,-126,-53) Matrix(45,368,28,229) -> Matrix(11,4,140,51) Matrix(47,368,6,47) -> Matrix(35,12,102,35) Matrix(91,690,12,91) -> Matrix(67,22,204,67) Matrix(45,322,32,229) -> Matrix(7,2,108,31) Matrix(47,322,-20,-137) -> Matrix(7,2,-60,-17) Matrix(137,874,108,689) -> Matrix(9,2,148,33) Matrix(321,2024,226,1425) -> Matrix(1,0,18,1) Matrix(369,2300,-236,-1471) -> Matrix(15,4,-184,-49) Matrix(47,276,8,47) -> Matrix(31,8,120,31) Matrix(137,782,24,137) -> Matrix(89,22,360,89) Matrix(91,506,66,367) -> Matrix(25,6,354,85) Matrix(93,506,34,185) -> Matrix(9,2,94,21) Matrix(139,736,-78,-413) -> Matrix(1,0,-6,1) Matrix(47,230,-28,-137) -> Matrix(9,2,-104,-23) Matrix(185,874,156,737) -> Matrix(9,2,148,33) Matrix(459,2162,-176,-829) -> Matrix(67,14,-560,-117) Matrix(139,644,30,139) -> Matrix(79,16,390,79) Matrix(91,414,20,91) -> Matrix(51,10,260,51) Matrix(783,3496,-484,-2161) -> Matrix(21,4,-268,-51) Matrix(1151,5106,-736,-3265) -> Matrix(53,10,-652,-123) Matrix(323,1426,94,415) -> Matrix(75,14,466,87) Matrix(137,598,-74,-323) -> Matrix(11,2,-138,-25) Matrix(139,598,-96,-413) -> Matrix(13,2,-176,-27) Matrix(229,966,-142,-599) -> Matrix(11,2,-138,-25) Matrix(47,184,12,47) -> Matrix(23,4,132,23) Matrix(229,874,60,229) -> Matrix(109,18,660,109) Matrix(231,874,134,507) -> Matrix(37,6,450,73) Matrix(1059,3956,382,1427) -> Matrix(25,4,206,33) Matrix(2071,7728,-1516,-5657) -> Matrix(103,16,-1500,-233) Matrix(1013,3772,-568,-2115) -> Matrix(1,0,-4,1) Matrix(137,506,62,229) -> Matrix(13,2,162,25) Matrix(139,506,114,415) -> Matrix(41,6,690,101) Matrix(737,2668,-508,-1839) -> Matrix(59,8,-804,-109) Matrix(1057,3818,-446,-1611) -> Matrix(17,2,-162,-19) Matrix(461,1656,282,1013) -> Matrix(25,4,306,49) Matrix(1747,6256,642,2299) -> Matrix(27,4,290,43) Matrix(2161,7728,-1248,-4463) -> Matrix(29,4,-312,-43) Matrix(323,1150,-116,-413) -> Matrix(15,2,-128,-17) Matrix(93,322,80,277) -> Matrix(11,2,192,35) Matrix(415,1426,94,323) -> Matrix(87,14,466,75) Matrix(229,782,94,321) -> Matrix(13,2,162,25) Matrix(461,1564,-298,-1011) -> Matrix(1,0,-6,1) Matrix(2991,10120,884,2991) -> Matrix(79,12,520,79) Matrix(4829,16330,1428,4829) -> Matrix(41,6,280,41) Matrix(599,2024,504,1703) -> Matrix(1,0,24,1) Matrix(1379,4646,382,1287) -> Matrix(13,2,110,17) Matrix(2623,8832,-1844,-6209) -> Matrix(103,16,-1500,-233) Matrix(645,2162,412,1381) -> Matrix(67,10,824,123) Matrix(139,460,42,139) -> Matrix(55,8,378,55) Matrix(183,598,56,183) -> Matrix(71,10,504,71) Matrix(185,598,-142,-459) -> Matrix(15,2,-218,-29) Matrix(275,874,-174,-553) -> Matrix(15,2,-158,-21) Matrix(47,138,16,47) -> Matrix(15,2,112,15) Matrix(321,920,112,321) -> Matrix(97,12,784,97) Matrix(323,920,178,507) -> Matrix(33,4,338,41) Matrix(553,1564,-390,-1103) -> Matrix(1,0,-6,1) Matrix(1749,4922,-1340,-3771) -> Matrix(17,2,-332,-39) Matrix(459,1288,98,275) -> Matrix(71,8,346,39) Matrix(643,1794,-462,-1289) -> Matrix(17,2,-230,-27) Matrix(829,2300,-696,-1931) -> Matrix(35,4,-604,-69) Matrix(1427,3956,382,1059) -> Matrix(33,4,206,25) Matrix(781,2162,548,1517) -> Matrix(87,10,1244,143) Matrix(1565,4324,966,2669) -> Matrix(107,12,1382,155) Matrix(185,506,34,93) -> Matrix(21,2,94,9) Matrix(321,874,-220,-599) -> Matrix(21,2,-284,-27) Matrix(137,368,-86,-231) -> Matrix(1,0,-6,1) Matrix(139,368,122,323) -> Matrix(33,4,602,73) Matrix(505,1334,226,597) -> Matrix(17,2,178,21) Matrix(367,966,-280,-737) -> Matrix(17,2,-264,-31) Matrix(597,1564,-334,-875) -> Matrix(1,0,-2,1) Matrix(2991,7820,1144,2991) -> Matrix(63,8,496,63) Matrix(7129,18630,2728,7129) -> Matrix(241,30,1936,241) Matrix(1655,4324,1056,2759) -> Matrix(97,12,1172,145) Matrix(1287,3358,458,1195) -> Matrix(83,10,722,87) Matrix(231,598,-124,-321) -> Matrix(17,2,-196,-23) Matrix(1105,2852,642,1657) -> Matrix(35,4,446,51) Matrix(643,1656,464,1195) -> Matrix(35,4,516,59) Matrix(323,828,126,323) -> Matrix(71,8,630,71) Matrix(91,230,36,91) -> Matrix(19,2,180,19) Matrix(93,230,-74,-183) -> Matrix(19,2,-314,-33) Matrix(321,782,94,229) -> Matrix(25,2,162,13) Matrix(229,552,-134,-323) -> Matrix(1,0,-6,1) Matrix(827,1978,-462,-1105) -> Matrix(17,2,-162,-19) Matrix(1195,2852,732,1747) -> Matrix(33,4,404,49) Matrix(367,874,270,643) -> Matrix(53,6,786,89) Matrix(1241,2944,368,873) -> Matrix(1,0,16,1) Matrix(3265,7728,-2352,-5567) -> Matrix(41,4,-564,-55) Matrix(1011,2392,194,459) -> Matrix(41,4,174,17) Matrix(643,1518,-546,-1289) -> Matrix(25,2,-438,-35) Matrix(139,322,60,139) -> Matrix(19,2,180,19) Matrix(321,736,140,321) -> Matrix(41,4,420,41) Matrix(323,736,-262,-597) -> Matrix(1,0,-6,1) Matrix(689,1564,-426,-967) -> Matrix(1,0,-2,1) Matrix(597,1334,226,505) -> Matrix(21,2,178,17) Matrix(413,920,268,597) -> Matrix(43,4,548,51) Matrix(229,506,62,137) -> Matrix(25,2,162,13) Matrix(275,598,-212,-461) -> Matrix(17,2,-264,-31) Matrix(277,598,-170,-367) -> Matrix(19,2,-238,-25) Matrix(415,782,-268,-505) -> Matrix(23,2,-288,-25) Matrix(873,1610,-674,-1243) -> Matrix(37,2,-574,-31) Matrix(277,506,202,369) -> Matrix(17,2,246,29) Matrix(507,920,178,323) -> Matrix(41,4,338,33) Matrix(737,1334,458,829) -> Matrix(21,2,262,25) Matrix(461,828,-358,-643) -> Matrix(41,4,-646,-63) Matrix(2991,5336,1264,2255) -> Matrix(41,4,420,41) Matrix(415,736,234,415) -> Matrix(43,4,462,43) Matrix(183,322,104,183) -> Matrix(23,2,264,23) Matrix(185,322,-158,-275) -> Matrix(25,2,-438,-35) Matrix(3081,5336,1354,2345) -> Matrix(43,4,462,43) Matrix(17111,29624,4782,8279) -> Matrix(263,24,1830,167) Matrix(12835,22218,3588,6211) -> Matrix(199,18,1404,127) Matrix(2207,3818,-1596,-2761) -> Matrix(23,2,-288,-25) Matrix(507,874,134,231) -> Matrix(73,6,450,37) Matrix(1657,2852,642,1105) -> Matrix(51,4,446,35) Matrix(1473,2530,-910,-1563) -> Matrix(25,2,-338,-27) Matrix(1241,2116,512,873) -> Matrix(1,0,36,1) Matrix(1243,2116,514,875) -> Matrix(1,0,6,1) Matrix(461,782,326,553) -> Matrix(17,2,246,29) Matrix(1335,2254,-844,-1425) -> Matrix(21,2,-200,-19) Matrix(139,230,84,139) -> Matrix(23,2,264,23) Matrix(505,828,308,505) -> Matrix(97,8,1176,97) Matrix(1013,1656,282,461) -> Matrix(49,4,306,25) Matrix(1747,2852,732,1195) -> Matrix(49,4,404,33) Matrix(2483,4048,-1750,-2853) -> Matrix(1,0,-2,1) Matrix(1333,2162,-1050,-1703) -> Matrix(177,14,-2870,-227) Matrix(2669,4324,966,1565) -> Matrix(155,12,1382,107) Matrix(11501,18630,7100,11501) -> Matrix(389,30,5044,389) Matrix(4829,7820,2982,4829) -> Matrix(105,8,1378,105) Matrix(10121,16376,-7846,-12695) -> Matrix(41,4,-646,-63) Matrix(827,1334,-628,-1013) -> Matrix(25,2,-388,-31) Matrix(829,1334,458,737) -> Matrix(25,2,262,21) Matrix(229,368,28,45) -> Matrix(51,4,140,11) Matrix(1333,2116,492,781) -> Matrix(1,0,32,1) Matrix(1335,2116,494,783) -> Matrix(1,0,10,1) Matrix(3957,6256,2852,4509) -> Matrix(41,4,584,57) Matrix(321,506,262,413) -> Matrix(21,2,346,33) Matrix(2759,4324,1056,1655) -> Matrix(145,12,1172,97) Matrix(323,506,30,47) -> Matrix(73,6,158,13) Matrix(2529,3956,1852,2897) -> Matrix(51,4,752,59) Matrix(737,1150,-530,-827) -> Matrix(25,2,-338,-27) Matrix(2163,3358,1334,2071) -> Matrix(123,10,1562,127) Matrix(2669,4140,-1838,-2851) -> Matrix(249,20,-3374,-271) Matrix(597,920,268,413) -> Matrix(51,4,548,43) Matrix(599,920,390,599) -> Matrix(155,12,2002,155) Matrix(91,138,60,91) -> Matrix(27,2,364,27) Matrix(597,874,-472,-691) -> Matrix(133,10,-2168,-163) Matrix(2437,3542,-1868,-2715) -> Matrix(27,2,-392,-29) Matrix(415,598,288,415) -> Matrix(139,10,1932,139) Matrix(321,460,224,321) -> Matrix(113,8,1596,113) Matrix(323,460,-290,-413) -> Matrix(115,8,-2142,-149) Matrix(13385,19044,3976,5657) -> Matrix(753,52,4880,337) Matrix(13387,19044,3978,5659) -> Matrix(755,52,4922,339) Matrix(2071,2944,1198,1703) -> Matrix(1,0,26,1) Matrix(1425,2024,226,321) -> Matrix(1,0,18,1) Matrix(11501,16330,8100,11501) -> Matrix(85,6,1204,85) Matrix(7129,10120,5022,7129) -> Matrix(173,12,2494,173) Matrix(553,782,326,461) -> Matrix(29,2,246,17) Matrix(1011,1426,782,1103) -> Matrix(207,14,3238,219) Matrix(229,322,32,45) -> Matrix(31,2,108,7) Matrix(1517,2116,428,597) -> Matrix(1,0,24,1) Matrix(1519,2116,430,599) -> Matrix(1,0,18,1) Matrix(16007,22218,6760,9383) -> Matrix(251,18,2496,179) Matrix(21345,29624,9016,12513) -> Matrix(337,24,3384,241) Matrix(2851,3956,596,827) -> Matrix(227,16,1064,75) Matrix(1195,1656,464,643) -> Matrix(59,4,516,35) Matrix(3359,4646,2362,3267) -> Matrix(25,2,362,29) Matrix(1565,2162,-1198,-1655) -> Matrix(27,2,-446,-33) Matrix(367,506,66,91) -> Matrix(85,6,354,25) Matrix(369,506,202,277) -> Matrix(29,2,246,17) Matrix(875,1196,-706,-965) -> Matrix(1,0,-2,1) Matrix(13937,19044,3736,5105) -> Matrix(289,20,1864,129) Matrix(13939,19044,3738,5107) -> Matrix(291,20,1906,131) Matrix(2897,3956,1852,2529) -> Matrix(59,4,752,51) Matrix(643,874,270,367) -> Matrix(89,6,786,53) Matrix(645,874,476,645) -> Matrix(269,18,4020,269) Matrix(137,184,102,137) -> Matrix(61,4,930,61) Matrix(1609,2116,384,505) -> Matrix(61,4,320,21) Matrix(1611,2116,386,507) -> Matrix(63,4,362,23) Matrix(25943,33856,6062,7911) -> Matrix(1,0,38,1) Matrix(25945,33856,6064,7913) -> Matrix(1,0,4,1) Matrix(6531,8464,1490,1931) -> Matrix(1177,76,6458,417) Matrix(6533,8464,1492,1933) -> Matrix(1179,76,6500,419) Matrix(1103,1426,782,1011) -> Matrix(219,14,3238,207) Matrix(1105,1426,-926,-1195) -> Matrix(31,2,-574,-37) Matrix(14765,19044,3316,4277) -> Matrix(1763,112,9240,587) Matrix(14767,19044,3318,4279) -> Matrix(1765,112,9282,589) Matrix(323,414,252,323) -> Matrix(159,10,2528,159) Matrix(505,644,396,505) -> Matrix(257,16,4128,257) Matrix(1013,1288,652,829) -> Matrix(129,8,1564,97) Matrix(689,874,108,137) -> Matrix(33,2,148,9) Matrix(3129,3956,874,1105) -> Matrix(261,16,1778,109) Matrix(1933,2392,1116,1381) -> Matrix(67,4,720,43) Matrix(413,506,262,321) -> Matrix(33,2,346,21) Matrix(415,506,114,139) -> Matrix(101,6,690,41) Matrix(645,782,532,645) -> Matrix(373,22,6324,373) Matrix(229,276,190,229) -> Matrix(137,8,2346,137) Matrix(1703,2024,504,599) -> Matrix(1,0,24,1) Matrix(737,874,156,185) -> Matrix(33,2,148,9) Matrix(1793,2116,272,321) -> Matrix(629,36,2184,125) Matrix(1795,2116,274,323) -> Matrix(631,36,2226,127) Matrix(277,322,80,93) -> Matrix(35,2,192,11) Matrix(599,690,520,599) -> Matrix(395,22,7092,395) Matrix(321,368,280,321) -> Matrix(217,12,3924,217) Matrix(323,368,122,139) -> Matrix(73,4,602,33) Matrix(459,506,166,183) -> Matrix(113,6,998,53) Matrix(1,0,2,1) -> Matrix(1,0,42,1) Matrix(413,-460,290,-323) -> Matrix(149,-8,2142,-115) Matrix(275,-322,158,-185) -> Matrix(35,-2,438,-25) Matrix(1931,-2300,696,-829) -> Matrix(69,-4,604,-35) Matrix(597,-736,262,-323) -> Matrix(1,0,-6,1) Matrix(183,-230,74,-93) -> Matrix(33,-2,314,-19) Matrix(1703,-2162,1050,-1333) -> Matrix(227,-14,2870,-177) Matrix(2713,-3496,1036,-1335) -> Matrix(63,-4,520,-33) Matrix(3955,-5106,1426,-1841) -> Matrix(157,-10,1366,-87) Matrix(461,-598,212,-275) -> Matrix(31,-2,264,-17) Matrix(459,-598,142,-185) -> Matrix(29,-2,218,-15) Matrix(737,-966,280,-367) -> Matrix(31,-2,264,-17) Matrix(5657,-7728,1516,-2071) -> Matrix(233,-16,1500,-103) Matrix(2759,-3772,1212,-1657) -> Matrix(1,0,-4,1) Matrix(1931,-2668,600,-829) -> Matrix(109,-8,804,-59) Matrix(2761,-3818,1596,-2207) -> Matrix(25,-2,288,-23) Matrix(5567,-7728,2352,-3265) -> Matrix(55,-4,564,-41) Matrix(827,-1150,530,-737) -> Matrix(27,-2,338,-25) Matrix(1103,-1564,390,-553) -> Matrix(1,0,-6,1) Matrix(6209,-8832,1844,-2623) -> Matrix(233,-16,1500,-103) Matrix(413,-598,96,-139) -> Matrix(27,-2,176,-13) Matrix(599,-874,220,-321) -> Matrix(27,-2,284,-21) Matrix(1011,-1564,298,-461) -> Matrix(1,0,-6,1) Matrix(3173,-4922,742,-1151) -> Matrix(25,-2,38,-3) Matrix(1151,-1794,324,-505) -> Matrix(25,-2,188,-15) Matrix(1471,-2300,236,-369) -> Matrix(49,-4,184,-15) Matrix(553,-874,174,-275) -> Matrix(21,-2,158,-15) Matrix(231,-368,86,-137) -> Matrix(1,0,-6,1) Matrix(599,-966,142,-229) -> Matrix(25,-2,138,-11) Matrix(967,-1564,426,-689) -> Matrix(1,0,-2,1) Matrix(367,-598,170,-277) -> Matrix(25,-2,238,-19) Matrix(137,-230,28,-47) -> Matrix(23,-2,104,-9) Matrix(323,-552,134,-229) -> Matrix(1,0,-6,1) Matrix(1151,-1978,508,-873) -> Matrix(25,-2,288,-23) Matrix(4463,-7728,1248,-2161) -> Matrix(43,-4,312,-29) Matrix(875,-1518,132,-229) -> Matrix(17,-2,60,-7) Matrix(413,-736,78,-139) -> Matrix(1,0,-6,1) Matrix(875,-1564,334,-597) -> Matrix(1,0,-2,1) Matrix(323,-598,74,-137) -> Matrix(25,-2,138,-11) Matrix(321,-598,124,-231) -> Matrix(23,-2,196,-17) Matrix(367,-782,130,-277) -> Matrix(19,-2,162,-17) Matrix(737,-1610,168,-367) -> Matrix(5,-2,28,-11) Matrix(367,-828,82,-185) -> Matrix(43,-4,226,-21) Matrix(137,-322,20,-47) -> Matrix(17,-2,60,-7) Matrix(1611,-3818,446,-1057) -> Matrix(19,-2,162,-17) Matrix(1057,-2530,404,-967) -> Matrix(17,-2,128,-15) Matrix(919,-2254,338,-829) -> Matrix(21,-2,242,-23) Matrix(1565,-4048,462,-1195) -> Matrix(1,0,-2,1) Matrix(829,-2162,176,-459) -> Matrix(117,-14,560,-67) Matrix(6255,-16376,1406,-3681) -> Matrix(43,-4,226,-21) Matrix(507,-1334,122,-321) -> Matrix(17,-2,94,-11) Matrix(413,-1150,116,-323) -> Matrix(17,-2,128,-15) Matrix(1471,-4140,458,-1289) -> Matrix(171,-20,1274,-149) Matrix(277,-874,58,-183) -> Matrix(77,-10,362,-47) Matrix(1105,-3542,258,-827) -> Matrix(15,-2,98,-13) Matrix(137,-460,14,-47) -> Matrix(53,-8,126,-19) Matrix(597,-2162,140,-507) -> Matrix(15,-2,68,-9) Matrix(321,-1196,62,-231) -> Matrix(1,0,-2,1) Matrix(321,-1426,52,-231) -> Matrix(11,-2,28,-5) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 132 Degree of the the map X: 132 Degree of the the map Y: 264 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 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): 264 Minimal number of generators: 45 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: 22 Genus: 12 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 23/10 23/9 23/8 3/1 23/7 10/3 23/6 4/1 46/11 92/21 23/5 5/1 11/2 23/4 6/1 7/1 23/3 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/21 8/7 6/109 7/6 1/18 6/5 4/69 5/4 1/16 9/7 5/79 31/24 13/204 22/17 12/187 13/10 3/46 4/3 2/31 11/8 5/72 7/5 1/15 17/12 5/72 27/19 3/43 10/7 4/57 3/2 1/14 17/11 5/63 14/9 0/1 11/7 3/35 19/12 1/8 8/5 2/27 37/23 3/37 29/18 1/14 21/13 1/13 13/8 1/12 5/3 1/11 17/10 1/6 12/7 2/27 7/4 1/12 9/5 1/9 11/6 1/6 13/7 1/11 2/1 0/1 11/5 1/15 9/4 1/12 16/7 2/21 23/10 1/10 7/3 1/9 12/5 2/15 5/2 1/10 23/9 1/9 18/7 4/35 13/5 1/9 47/18 11/90 34/13 4/31 21/8 1/8 50/19 0/1 29/11 1/7 8/3 2/15 11/4 3/28 14/5 0/1 31/11 7/59 17/6 5/42 20/7 6/49 23/8 1/8 3/1 1/7 13/4 5/36 23/7 1/7 10/3 4/27 17/5 5/33 7/2 1/6 11/3 5/33 15/4 7/44 19/5 9/55 23/6 1/6 4/1 2/11 25/6 1/6 46/11 2/11 21/5 1/5 17/4 3/16 13/3 3/17 35/8 13/72 92/21 2/11 57/13 25/137 22/5 12/65 9/2 5/26 23/5 1/5 14/3 8/39 5/1 1/5 11/2 7/30 17/3 11/45 23/4 1/4 6/1 4/15 7/1 1/3 15/2 11/34 23/3 1/3 8/1 6/17 9/1 5/13 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(185,-207,143,-160) (1/1,8/7) -> (31/24,22/17) Hyperbolic Matrix(139,-161,19,-22) (8/7,7/6) -> (7/1,15/2) Hyperbolic Matrix(137,-161,40,-47) (7/6,6/5) -> (17/5,7/2) Hyperbolic Matrix(93,-115,55,-68) (6/5,5/4) -> (5/3,17/10) Hyperbolic Matrix(91,-115,19,-24) (5/4,9/7) -> (14/3,5/1) Hyperbolic Matrix(944,-1219,587,-758) (9/7,31/24) -> (8/5,37/23) Hyperbolic Matrix(691,-897,265,-344) (22/17,13/10) -> (13/5,47/18) Hyperbolic Matrix(300,-391,211,-275) (13/10,4/3) -> (27/19,10/7) Hyperbolic Matrix(185,-253,117,-160) (4/3,11/8) -> (11/7,19/12) Hyperbolic Matrix(116,-161,49,-68) (11/8,7/5) -> (7/3,12/5) Hyperbolic Matrix(114,-161,17,-24) (7/5,17/12) -> (6/1,7/1) Hyperbolic Matrix(1151,-1633,437,-620) (17/12,27/19) -> (50/19,29/11) Hyperbolic Matrix(47,-69,15,-22) (10/7,3/2) -> (3/1,13/4) Hyperbolic Matrix(254,-391,89,-137) (3/2,17/11) -> (17/6,20/7) Hyperbolic Matrix(668,-1035,415,-643) (17/11,14/9) -> (37/23,29/18) Hyperbolic Matrix(162,-253,73,-114) (14/9,11/7) -> (11/5,9/4) Hyperbolic Matrix(275,-437,73,-116) (19/12,8/5) -> (15/4,19/5) Hyperbolic Matrix(599,-966,142,-229) (29/18,21/13) -> (21/5,17/4) Hyperbolic Matrix(185,-299,99,-160) (21/13,13/8) -> (13/7,2/1) Hyperbolic Matrix(183,-299,71,-116) (13/8,5/3) -> (18/7,13/5) Hyperbolic Matrix(229,-391,41,-70) (17/10,12/7) -> (11/2,17/3) Hyperbolic Matrix(93,-161,26,-45) (12/7,7/4) -> (7/2,11/3) Hyperbolic Matrix(116,-207,51,-91) (7/4,9/5) -> (9/4,16/7) 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(139,-299,53,-114) (2/1,11/5) -> (34/13,21/8) Hyperbolic Matrix(231,-529,100,-229) (16/7,23/10) -> (23/10,7/3) Parabolic Matrix(47,-115,9,-22) (12/5,5/2) -> (5/1,11/2) Hyperbolic Matrix(208,-529,81,-206) (5/2,23/9) -> (23/9,18/7) Parabolic Matrix(1312,-3427,299,-781) (47/18,34/13) -> (57/13,22/5) Hyperbolic Matrix(507,-1334,122,-321) (21/8,50/19) -> (4/1,25/6) Hyperbolic Matrix(392,-1035,139,-367) (29/11,8/3) -> (31/11,17/6) Hyperbolic Matrix(93,-253,25,-68) (8/3,11/4) -> (11/3,15/4) 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(162,-529,49,-160) (13/4,23/7) -> (23/7,10/3) Parabolic Matrix(116,-391,27,-91) (10/3,17/5) -> (17/4,13/3) Hyperbolic Matrix(139,-529,36,-137) (19/5,23/6) -> (23/6,4/1) Parabolic Matrix(507,-2116,121,-505) (25/6,46/11) -> (46/11,21/5) Parabolic Matrix(1933,-8464,441,-1931) (35/8,92/21) -> (92/21,57/13) Parabolic Matrix(47,-207,5,-22) (22/5,9/2) -> (9/1,1/0) Hyperbolic Matrix(116,-529,25,-114) (9/2,23/5) -> (23/5,14/3) Parabolic Matrix(93,-529,16,-91) (17/3,23/4) -> (23/4,6/1) Parabolic Matrix(70,-529,9,-68) (15/2,23/3) -> (23/3,8/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,21,1) Matrix(185,-207,143,-160) -> Matrix(93,-5,1451,-78) Matrix(139,-161,19,-22) -> Matrix(89,-5,285,-16) Matrix(137,-161,40,-47) -> Matrix(53,-3,336,-19) Matrix(93,-115,55,-68) -> Matrix(17,-1,171,-10) Matrix(91,-115,19,-24) -> Matrix(49,-3,229,-14) Matrix(944,-1219,587,-758) -> Matrix(110,-7,1383,-88) Matrix(691,-897,265,-344) -> Matrix(77,-5,647,-42) Matrix(300,-391,211,-275) -> Matrix(14,-1,211,-15) Matrix(185,-253,117,-160) -> Matrix(15,-1,151,-10) Matrix(116,-161,49,-68) -> Matrix(14,-1,141,-10) Matrix(114,-161,17,-24) -> Matrix(44,-3,147,-10) Matrix(1151,-1633,437,-620) -> Matrix(43,-3,373,-26) Matrix(47,-69,15,-22) -> Matrix(13,-1,105,-8) Matrix(254,-391,89,-137) -> Matrix(64,-5,525,-41) Matrix(668,-1035,415,-643) -> Matrix(38,-3,469,-37) Matrix(162,-253,73,-114) -> Matrix(12,-1,145,-12) Matrix(275,-437,73,-116) -> Matrix(17,-1,103,-6) Matrix(599,-966,142,-229) -> Matrix(25,-2,138,-11) Matrix(185,-299,99,-160) -> Matrix(13,-1,131,-10) Matrix(183,-299,71,-116) -> Matrix(37,-3,321,-26) Matrix(229,-391,41,-70) -> Matrix(17,-1,69,-4) Matrix(93,-161,26,-45) -> Matrix(11,-1,78,-7) Matrix(116,-207,51,-91) -> Matrix(10,-1,111,-11) Matrix(139,-253,50,-91) -> Matrix(9,-1,82,-9) Matrix(323,-598,74,-137) -> Matrix(25,-2,138,-11) Matrix(139,-299,53,-114) -> Matrix(11,-1,89,-8) Matrix(231,-529,100,-229) -> Matrix(31,-3,300,-29) Matrix(47,-115,9,-22) -> Matrix(11,-1,45,-4) Matrix(208,-529,81,-206) -> Matrix(46,-5,405,-44) Matrix(1312,-3427,299,-781) -> Matrix(138,-17,755,-93) Matrix(507,-1334,122,-321) -> Matrix(17,-2,94,-11) Matrix(392,-1035,139,-367) -> Matrix(26,-3,217,-25) Matrix(93,-253,25,-68) -> Matrix(11,-1,67,-6) Matrix(139,-391,16,-45) -> Matrix(43,-5,112,-13) Matrix(185,-529,64,-183) -> Matrix(57,-7,448,-55) Matrix(162,-529,49,-160) -> Matrix(64,-9,441,-62) Matrix(116,-391,27,-91) -> Matrix(6,-1,43,-7) Matrix(139,-529,36,-137) -> Matrix(67,-11,396,-65) Matrix(507,-2116,121,-505) -> Matrix(23,-4,121,-21) Matrix(1933,-8464,441,-1931) -> Matrix(419,-76,2299,-417) Matrix(47,-207,5,-22) -> Matrix(27,-5,65,-12) Matrix(116,-529,25,-114) -> Matrix(66,-13,325,-64) Matrix(93,-529,16,-91) -> Matrix(61,-15,240,-59) Matrix(70,-529,9,-68) -> Matrix(52,-17,153,-50) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 1 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 1 Number of equivalence classes of cusps: 1 Genus: 0 Degree of H/liftables -> H/(image of liftables): 132 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 21 1 2/1 0/1 1 23 11/5 1/15 1 23 9/4 1/12 1 23 23/10 1/10 3 1 7/3 1/9 1 23 12/5 2/15 1 23 5/2 1/10 1 23 23/9 1/9 5 1 13/5 1/9 1 23 34/13 4/31 1 23 21/8 1/8 1 23 29/11 1/7 1 23 8/3 2/15 1 23 11/4 3/28 1 23 14/5 0/1 1 23 31/11 7/59 1 23 17/6 5/42 1 23 23/8 1/8 7 1 3/1 1/7 1 23 23/7 1/7 9 1 10/3 4/27 1 23 17/5 5/33 1 23 7/2 1/6 1 23 11/3 5/33 1 23 15/4 7/44 1 23 23/6 1/6 11 1 4/1 2/11 1 23 46/11 2/11 1 1 21/5 1/5 1 23 17/4 3/16 1 23 13/3 3/17 1 23 35/8 13/72 1 23 92/21 2/11 19 1 22/5 12/65 1 23 9/2 5/26 1 23 23/5 1/5 13 1 5/1 1/5 1 23 11/2 7/30 1 23 23/4 1/4 15 1 6/1 4/15 1 23 7/1 1/3 1 23 23/3 1/3 17 1 8/1 6/17 1 23 9/1 5/13 1 23 1/0 1/0 1 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(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(139,-299,53,-114) (2/1,11/5) -> (34/13,21/8) Hyperbolic Matrix(114,-253,41,-91) (11/5,9/4) -> (11/4,14/5) 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(68,-161,19,-45) (7/3,12/5) -> (7/2,11/3) Glide Reflection Matrix(47,-115,9,-22) (12/5,5/2) -> (5/1,11/2) Hyperbolic Matrix(91,-230,36,-91) (5/2,23/9) -> (5/2,23/9) Reflection Matrix(116,-299,45,-116) (23/9,13/5) -> (23/9,13/5) Reflection Matrix(344,-897,79,-206) (13/5,34/13) -> (13/3,35/8) Glide Reflection Matrix(367,-966,87,-229) (21/8,29/11) -> (21/5,17/4) Glide Reflection Matrix(392,-1035,139,-367) (29/11,8/3) -> (31/11,17/6) Hyperbolic Matrix(93,-253,25,-68) (8/3,11/4) -> (11/3,15/4) Hyperbolic 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(22,-69,7,-22) (3/1,23/7) -> (3/1,23/7) Reflection Matrix(139,-460,42,-139) (23/7,10/3) -> (23/7,10/3) Reflection Matrix(116,-391,27,-91) (10/3,17/5) -> (17/4,13/3) Hyperbolic Matrix(47,-161,7,-24) (17/5,7/2) -> (6/1,7/1) Glide 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(45,-184,11,-45) (4/1,46/11) -> (4/1,46/11) 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(461,-2024,105,-461) (92/21,22/5) -> (92/21,22/5) Reflection Matrix(47,-207,5,-22) (22/5,9/2) -> (9/1,1/0) Hyperbolic Matrix(91,-414,20,-91) (9/2,23/5) -> (9/2,23/5) Reflection Matrix(24,-115,5,-24) (23/5,5/1) -> (23/5,5/1) 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(22,-161,3,-22) (7/1,23/3) -> (7/1,23/3) 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(1,0,1,-1) -> Matrix(1,0,21,-1) (0/1,2/1) -> (0/1,2/21) Matrix(139,-299,53,-114) -> Matrix(11,-1,89,-8) Matrix(114,-253,41,-91) -> Matrix(12,-1,107,-9) Matrix(91,-207,40,-91) -> Matrix(11,-1,120,-11) (9/4,23/10) -> (1/12,1/10) Matrix(139,-322,60,-139) -> Matrix(19,-2,180,-19) (23/10,7/3) -> (1/10,1/9) Matrix(68,-161,19,-45) -> Matrix(10,-1,69,-7) Matrix(47,-115,9,-22) -> Matrix(11,-1,45,-4) Matrix(91,-230,36,-91) -> Matrix(19,-2,180,-19) (5/2,23/9) -> (1/10,1/9) Matrix(116,-299,45,-116) -> Matrix(26,-3,225,-26) (23/9,13/5) -> (1/9,3/25) Matrix(344,-897,79,-206) -> Matrix(42,-5,235,-28) Matrix(367,-966,87,-229) -> Matrix(17,-2,93,-11) Matrix(392,-1035,139,-367) -> Matrix(26,-3,217,-25) (0/1,2/17).(1/9,3/25).(3/26,1/8) Matrix(93,-253,25,-68) -> Matrix(11,-1,67,-6) Matrix(139,-391,16,-45) -> Matrix(43,-5,112,-13) Matrix(137,-391,48,-137) -> Matrix(41,-5,336,-41) (17/6,23/8) -> (5/42,1/8) Matrix(47,-138,16,-47) -> Matrix(15,-2,112,-15) (23/8,3/1) -> (1/8,1/7) Matrix(22,-69,7,-22) -> Matrix(8,-1,63,-8) (3/1,23/7) -> (1/9,1/7) Matrix(139,-460,42,-139) -> Matrix(55,-8,378,-55) (23/7,10/3) -> (1/7,4/27) Matrix(116,-391,27,-91) -> Matrix(6,-1,43,-7) (1/7,1/5).(0/1,2/13).(1/8,1/6) Matrix(47,-161,7,-24) -> Matrix(19,-3,63,-10) Matrix(91,-345,24,-91) -> Matrix(43,-7,264,-43) (15/4,23/6) -> (7/44,1/6) Matrix(47,-184,12,-47) -> Matrix(23,-4,132,-23) (23/6,4/1) -> (1/6,2/11) Matrix(45,-184,11,-45) -> Matrix(1,0,11,-1) (4/1,46/11) -> (0/1,2/11) Matrix(461,-1932,110,-461) -> Matrix(21,-4,110,-21) (46/11,21/5) -> (2/11,1/5) Matrix(1471,-6440,336,-1471) -> Matrix(287,-52,1584,-287) (35/8,92/21) -> (13/72,2/11) Matrix(461,-2024,105,-461) -> Matrix(131,-24,715,-131) (92/21,22/5) -> (2/11,12/65) Matrix(47,-207,5,-22) -> Matrix(27,-5,65,-12) Matrix(91,-414,20,-91) -> Matrix(51,-10,260,-51) (9/2,23/5) -> (5/26,1/5) Matrix(24,-115,5,-24) -> Matrix(14,-3,65,-14) (23/5,5/1) -> (1/5,3/13) Matrix(45,-253,8,-45) -> Matrix(29,-7,120,-29) (11/2,23/4) -> (7/30,1/4) Matrix(47,-276,8,-47) -> Matrix(31,-8,120,-31) (23/4,6/1) -> (1/4,4/15) Matrix(22,-161,3,-22) -> Matrix(16,-5,51,-16) (7/1,23/3) -> (5/17,1/3) Matrix(47,-368,6,-47) -> Matrix(35,-12,102,-35) (23/3,8/1) -> (1/3,6/17) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.