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 -2/1 -23/3 -1/1 -15/2 1/0 -7/1 -1/1 -13/2 1/0 -19/3 -1/1 -25/4 1/0 -6/1 -2/1 -23/4 -1/1 -17/3 -1/1 -11/2 1/0 -16/3 0/1 -5/1 -1/1 -19/4 1/0 -33/7 -1/1 -14/3 -2/1 -23/5 -1/1 -9/2 -1/2 -40/9 0/1 -31/7 -1/1 -22/5 -2/5 -13/3 -1/1 -17/4 -1/2 -4/1 0/1 -23/6 1/0 -19/5 -1/1 -15/4 1/0 -56/15 0/1 -41/11 -1/1 -26/7 0/1 -11/3 1/1 -29/8 1/0 -47/13 -1/1 -18/5 0/1 -43/12 1/0 -68/19 6/1 -25/7 -1/1 -7/2 1/0 -31/9 -1/1 -24/7 2/1 -17/5 -1/1 -44/13 0/1 -115/34 1/0 -71/21 -1/1 -27/8 1/0 -64/19 0/1 -37/11 1/1 -47/14 1/0 -10/3 0/1 -23/7 1/0 -13/4 1/0 -16/5 -2/1 -3/1 -1/1 -23/8 0/1 -20/7 0/1 -17/6 1/0 -31/11 -1/1 -45/16 1/0 -14/5 0/1 -39/14 1/0 -25/9 -1/1 -61/22 1/0 -36/13 -2/1 -47/17 -1/1 -11/4 -1/2 -30/11 0/1 -19/7 -1/3 -8/3 0/1 -37/14 1/0 -29/11 -1/1 -21/8 1/2 -34/13 2/1 -115/44 1/0 -81/31 -5/1 -47/18 1/0 -60/23 -2/1 -13/5 -1/1 -31/12 1/0 -49/19 -1/1 -18/7 0/1 -23/9 0/1 -5/2 1/0 -22/9 -4/1 -17/7 -1/1 -12/5 0/1 -43/18 1/0 -31/13 -1/1 -19/8 1/0 -64/27 -2/1 -45/19 -1/1 -71/30 -3/4 -26/11 0/1 -33/14 1/0 -7/3 -1/1 -23/10 -1/1 -16/7 -2/3 -25/11 -1/3 -9/4 -1/2 -29/13 -1/1 -20/9 0/1 -11/5 -1/3 -13/6 1/0 -2/1 0/1 -15/8 1/0 -13/7 -1/1 -24/13 -2/5 -11/6 1/2 -20/11 0/1 -29/16 1/0 -9/5 1/1 -43/24 1/0 -34/19 2/1 -25/14 1/2 -66/37 2/1 -41/23 1/1 -16/9 2/1 -23/13 1/0 -7/4 1/0 -26/15 0/1 -71/41 3/1 -116/67 10/1 -161/93 1/0 -45/26 1/0 -19/11 -1/1 -31/18 1/0 -43/25 -1/1 -12/7 0/1 -29/17 -1/1 -46/27 -2/1 0/1 -17/10 1/0 -22/13 -4/3 -27/16 1/0 -5/3 -1/1 -23/14 0/1 -18/11 0/1 -49/30 1/0 -31/19 -1/1 -44/27 0/1 -13/8 1/0 -47/29 -1/1 -81/50 -5/4 -115/71 -1/1 -34/21 -2/3 -89/55 -1/1 -144/89 0/1 -55/34 -1/2 -21/13 -1/3 -50/31 0/1 -29/18 1/0 -37/23 -1/1 -8/5 0/1 -27/17 -1/3 -46/29 0/1 -19/12 1/2 -68/43 4/5 -49/31 1/1 -30/19 0/1 -11/7 1/1 -47/30 1/0 -36/23 -2/1 -61/39 -1/1 -86/55 -2/1 -25/16 1/0 -14/9 0/1 -45/29 -1/1 -31/20 1/0 -48/31 0/1 -17/11 -1/1 -20/13 0/1 -23/15 0/1 -3/2 1/0 -19/13 -3/1 -16/11 -2/1 -61/42 -3/2 -45/31 -1/1 -29/20 1/0 -13/9 -1/1 -23/16 -1/1 -10/7 0/1 -37/26 -1/2 -138/97 0/1 -101/71 1/3 -64/45 0/1 -27/19 -1/1 -71/50 1/0 -115/81 -1/1 -44/31 0/1 -61/43 -1/1 -17/12 1/0 -24/17 -2/3 -31/22 1/0 -7/5 -1/1 -46/33 0/1 -39/28 1/0 -32/23 0/1 -25/18 1/0 -93/67 -1/1 -161/116 -1/1 -68/49 -6/7 -43/31 -1/1 -18/13 0/1 -65/47 1/1 -47/34 1/0 -29/21 -1/1 -11/8 -1/2 -26/19 0/1 -41/30 1/0 -138/101 -2/1 0/1 -97/71 -1/1 -56/41 0/1 -15/11 -1/1 -19/14 1/0 -23/17 -1/1 -4/3 0/1 -25/19 -1/5 -46/35 0/1 -21/16 1/4 -17/13 1/1 -47/36 1/0 -77/59 -1/1 -184/141 0/1 -107/82 1/2 -30/23 0/1 -13/10 1/0 -35/27 -1/3 -92/71 0/1 -57/44 1/6 -22/17 2/3 -31/24 1/0 -40/31 0/1 -89/69 1/1 -138/107 0/1 2/1 -49/38 1/0 -9/7 1/1 -23/18 1/0 -14/11 -2/1 -47/37 -1/1 -33/26 1/0 -19/15 -1/1 -43/34 1/0 -24/19 -4/1 -5/4 1/0 -26/21 0/1 -21/17 -3/1 -16/13 0/1 -11/9 -1/1 -17/14 1/0 -23/19 1/0 -6/5 -2/1 -31/26 1/0 -25/21 -1/1 -19/16 1/0 -13/11 -1/1 -46/39 -2/1 0/1 -33/28 1/0 -20/17 0/1 -7/6 1/0 -15/13 -1/1 -23/20 1/0 -8/7 -2/1 -9/8 1/0 -10/9 -2/1 -1/1 -1/1 0/1 0/1 1/1 1/1 9/8 1/0 8/7 2/1 23/20 1/0 15/13 1/1 7/6 1/0 13/11 1/1 19/16 1/0 25/21 1/1 6/5 2/1 23/19 1/0 17/14 1/0 11/9 1/1 16/13 0/1 5/4 1/0 19/15 1/1 33/26 1/0 14/11 2/1 23/18 1/0 9/7 -1/1 40/31 0/1 31/24 1/0 22/17 -2/3 13/10 1/0 17/13 -1/1 4/3 0/1 23/17 1/1 19/14 1/0 15/11 1/1 56/41 0/1 41/30 1/0 26/19 0/1 11/8 1/2 29/21 1/1 47/34 1/0 18/13 0/1 43/31 1/1 68/49 6/7 25/18 1/0 7/5 1/1 31/22 1/0 24/17 2/3 17/12 1/0 44/31 0/1 115/81 1/1 71/50 1/0 27/19 1/1 64/45 0/1 37/26 1/2 47/33 1/1 10/7 0/1 23/16 1/1 13/9 1/1 16/11 2/1 3/2 1/0 23/15 0/1 20/13 0/1 17/11 1/1 31/20 1/0 45/29 1/1 14/9 0/1 39/25 1/1 25/16 1/0 61/39 1/1 36/23 2/1 47/30 1/0 11/7 -1/1 30/19 0/1 19/12 -1/2 8/5 0/1 37/23 1/1 29/18 1/0 21/13 1/3 34/21 2/3 115/71 1/1 81/50 5/4 47/29 1/1 60/37 2/1 13/8 1/0 31/19 1/1 49/30 1/0 18/11 0/1 23/14 0/1 5/3 1/1 22/13 4/3 17/10 1/0 12/7 0/1 43/25 1/1 31/18 1/0 19/11 1/1 64/37 2/1 45/26 1/0 71/41 -3/1 26/15 0/1 33/19 1/1 7/4 1/0 23/13 1/0 16/9 -2/1 25/14 -1/2 9/5 -1/1 29/16 1/0 20/11 0/1 11/6 -1/2 13/7 1/1 2/1 0/1 15/7 1/1 13/6 1/0 24/11 -2/3 11/5 1/3 20/9 0/1 29/13 1/1 9/4 1/2 43/19 1/1 34/15 2/3 25/11 1/3 66/29 2/3 41/18 1/2 16/7 2/3 23/10 1/1 7/3 1/1 26/11 0/1 71/30 3/4 116/49 10/11 161/68 1/1 45/19 1/1 19/8 1/0 31/13 1/1 43/18 1/0 12/5 0/1 29/12 1/0 46/19 0/1 2/1 17/7 1/1 22/9 4/1 27/11 1/1 5/2 1/0 23/9 0/1 18/7 0/1 49/19 1/1 31/12 1/0 44/17 0/1 13/5 1/1 47/18 1/0 81/31 5/1 115/44 1/0 34/13 -2/1 89/34 1/0 144/55 0/1 55/21 -1/1 21/8 -1/2 50/19 0/1 29/11 1/1 37/14 1/0 8/3 0/1 27/10 -1/2 46/17 0/1 19/7 1/3 68/25 4/9 49/18 1/2 30/11 0/1 11/4 1/2 47/17 1/1 36/13 2/1 61/22 1/0 86/31 2/1 25/9 1/1 14/5 0/1 45/16 1/0 31/11 1/1 48/17 0/1 17/6 1/0 20/7 0/1 23/8 0/1 3/1 1/1 19/6 3/2 16/5 2/1 61/19 3/1 45/14 1/0 29/9 1/1 13/4 1/0 23/7 1/0 10/3 0/1 37/11 -1/1 138/41 0/1 101/30 1/4 64/19 0/1 27/8 1/0 71/21 1/1 115/34 1/0 44/13 0/1 61/18 1/0 17/5 1/1 24/7 -2/1 31/9 1/1 7/2 1/0 46/13 0/1 39/11 1/1 32/9 0/1 25/7 1/1 93/26 1/0 161/45 1/0 68/19 -6/1 43/12 1/0 18/5 0/1 65/18 1/2 47/13 1/1 29/8 1/0 11/3 -1/1 26/7 0/1 41/11 1/1 138/37 0/1 2/1 97/26 1/0 56/15 0/1 15/4 1/0 19/5 1/1 23/6 1/0 4/1 0/1 25/6 -1/4 46/11 0/1 21/5 1/5 17/4 1/2 47/11 1/1 77/18 1/0 184/43 0/1 107/25 1/3 30/7 0/1 13/3 1/1 35/8 -1/2 92/21 0/1 57/13 1/7 22/5 2/5 31/7 1/1 40/9 0/1 89/20 1/2 138/31 0/1 2/3 49/11 1/1 9/2 1/2 23/5 1/1 14/3 2/1 47/10 1/0 33/7 1/1 19/4 1/0 43/9 1/1 24/5 4/3 5/1 1/1 26/5 0/1 21/4 3/2 16/3 0/1 11/2 1/0 17/3 1/1 23/4 1/1 6/1 2/1 31/5 1/1 25/4 1/0 19/3 1/1 13/2 1/0 46/7 0/1 2/1 33/5 1/1 20/3 0/1 7/1 1/1 15/2 1/0 23/3 1/1 8/1 2/1 9/1 1/1 10/1 2/1 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(1,2,0,1) Matrix(45,368,28,229) -> Matrix(1,2,0,1) Matrix(47,368,6,47) -> Matrix(3,4,2,3) Matrix(91,690,12,91) -> Matrix(1,2,0,1) Matrix(45,322,32,229) -> Matrix(1,2,0,1) Matrix(47,322,-20,-137) -> Matrix(1,0,0,1) Matrix(137,874,108,689) -> Matrix(1,2,0,1) Matrix(321,2024,226,1425) -> Matrix(1,2,0,1) Matrix(369,2300,-236,-1471) -> Matrix(1,0,0,1) Matrix(47,276,8,47) -> Matrix(3,4,2,3) Matrix(137,782,24,137) -> Matrix(5,4,6,5) Matrix(91,506,66,367) -> Matrix(1,0,2,1) Matrix(93,506,34,185) -> Matrix(1,0,2,1) Matrix(139,736,-78,-413) -> Matrix(1,2,0,1) Matrix(47,230,-28,-137) -> Matrix(1,0,0,1) Matrix(185,874,156,737) -> Matrix(1,2,0,1) Matrix(459,2162,-176,-829) -> Matrix(1,0,0,1) Matrix(139,644,30,139) -> Matrix(3,4,2,3) Matrix(91,414,20,91) -> Matrix(3,2,4,3) Matrix(783,3496,-484,-2161) -> Matrix(1,0,0,1) Matrix(1151,5106,-736,-3265) -> Matrix(3,2,-2,-1) Matrix(323,1426,94,415) -> Matrix(1,0,2,1) Matrix(137,598,-74,-323) -> Matrix(1,0,0,1) Matrix(139,598,-96,-413) -> Matrix(3,2,-2,-1) Matrix(229,966,-142,-599) -> Matrix(1,0,2,1) Matrix(47,184,12,47) -> Matrix(1,0,0,1) Matrix(229,874,60,229) -> Matrix(1,2,0,1) Matrix(231,874,134,507) -> Matrix(1,2,0,1) Matrix(1059,3956,382,1427) -> Matrix(1,2,0,1) Matrix(2071,7728,-1516,-5657) -> Matrix(1,0,0,1) Matrix(1013,3772,-568,-2115) -> Matrix(1,2,0,1) Matrix(137,506,62,229) -> Matrix(1,0,2,1) Matrix(139,506,114,415) -> Matrix(1,0,0,1) Matrix(737,2668,-508,-1839) -> Matrix(1,0,0,1) Matrix(1057,3818,-446,-1611) -> Matrix(3,2,-2,-1) Matrix(461,1656,282,1013) -> Matrix(1,0,0,1) Matrix(1747,6256,642,2299) -> Matrix(1,-2,2,-3) Matrix(2161,7728,-1248,-4463) -> Matrix(1,4,0,1) Matrix(323,1150,-116,-413) -> Matrix(1,0,0,1) Matrix(93,322,80,277) -> Matrix(1,2,0,1) Matrix(415,1426,94,323) -> Matrix(1,0,2,1) Matrix(229,782,94,321) -> Matrix(1,2,0,1) Matrix(461,1564,-298,-1011) -> Matrix(1,0,0,1) Matrix(2991,10120,884,2991) -> Matrix(1,0,0,1) Matrix(4829,16330,1428,4829) -> Matrix(1,2,0,1) Matrix(599,2024,504,1703) -> Matrix(1,2,0,1) Matrix(1379,4646,382,1287) -> Matrix(1,0,2,1) Matrix(2623,8832,-1844,-6209) -> Matrix(1,0,2,1) Matrix(645,2162,412,1381) -> Matrix(1,2,0,1) Matrix(139,460,42,139) -> Matrix(1,0,0,1) Matrix(183,598,56,183) -> Matrix(1,4,0,1) Matrix(185,598,-142,-459) -> Matrix(1,2,0,1) Matrix(275,874,-174,-553) -> Matrix(1,2,0,1) Matrix(47,138,16,47) -> Matrix(1,0,2,1) Matrix(321,920,112,321) -> Matrix(1,0,0,1) Matrix(323,920,178,507) -> Matrix(1,0,0,1) Matrix(553,1564,-390,-1103) -> Matrix(1,0,0,1) Matrix(1749,4922,-1340,-3771) -> Matrix(1,0,0,1) Matrix(459,1288,98,275) -> Matrix(1,2,0,1) Matrix(643,1794,-462,-1289) -> Matrix(1,0,0,1) Matrix(829,2300,-696,-1931) -> Matrix(1,0,0,1) Matrix(1427,3956,382,1059) -> Matrix(1,2,0,1) Matrix(781,2162,548,1517) -> Matrix(1,2,0,1) Matrix(1565,4324,966,2669) -> Matrix(3,4,2,3) Matrix(185,506,34,93) -> Matrix(1,0,2,1) Matrix(321,874,-220,-599) -> Matrix(3,2,-2,-1) Matrix(137,368,-86,-231) -> Matrix(1,0,0,1) Matrix(139,368,122,323) -> Matrix(1,2,0,1) Matrix(505,1334,226,597) -> Matrix(1,0,2,1) Matrix(367,966,-280,-737) -> Matrix(1,0,2,1) Matrix(597,1564,-334,-875) -> Matrix(1,0,0,1) Matrix(2991,7820,1144,2991) -> Matrix(1,-4,0,1) Matrix(7129,18630,2728,7129) -> Matrix(1,10,0,1) Matrix(1655,4324,1056,2759) -> Matrix(1,4,0,1) Matrix(1287,3358,458,1195) -> Matrix(1,2,0,1) Matrix(231,598,-124,-321) -> Matrix(1,0,0,1) Matrix(1105,2852,642,1657) -> Matrix(1,2,0,1) Matrix(643,1656,464,1195) -> Matrix(1,0,2,1) Matrix(323,828,126,323) -> Matrix(1,0,2,1) Matrix(91,230,36,91) -> Matrix(1,0,0,1) Matrix(93,230,-74,-183) -> Matrix(1,0,0,1) Matrix(321,782,94,229) -> Matrix(1,2,0,1) Matrix(229,552,-134,-323) -> Matrix(1,0,0,1) Matrix(827,1978,-462,-1105) -> Matrix(1,2,0,1) Matrix(1195,2852,732,1747) -> Matrix(1,2,0,1) Matrix(367,874,270,643) -> Matrix(1,2,0,1) Matrix(1241,2944,368,873) -> Matrix(1,2,0,1) Matrix(3265,7728,-2352,-5567) -> Matrix(5,4,-4,-3) Matrix(1011,2392,194,459) -> Matrix(1,0,2,1) Matrix(643,1518,-546,-1289) -> Matrix(1,0,0,1) Matrix(139,322,60,139) -> Matrix(1,2,0,1) Matrix(321,736,140,321) -> Matrix(5,4,6,5) Matrix(323,736,-262,-597) -> Matrix(3,2,-2,-1) Matrix(689,1564,-426,-967) -> Matrix(1,0,0,1) Matrix(597,1334,226,505) -> Matrix(1,0,2,1) Matrix(413,920,268,597) -> Matrix(1,0,2,1) Matrix(229,506,62,137) -> Matrix(1,0,2,1) Matrix(275,598,-212,-461) -> Matrix(1,0,0,1) Matrix(277,598,-170,-367) -> Matrix(1,0,0,1) Matrix(415,782,-268,-505) -> Matrix(1,0,0,1) Matrix(873,1610,-674,-1243) -> Matrix(1,0,4,1) Matrix(277,506,202,369) -> Matrix(1,0,0,1) Matrix(507,920,178,323) -> Matrix(1,0,0,1) Matrix(737,1334,458,829) -> Matrix(1,0,0,1) Matrix(461,828,-358,-643) -> Matrix(1,0,0,1) Matrix(2991,5336,1264,2255) -> Matrix(1,-2,2,-3) Matrix(415,736,234,415) -> Matrix(1,-4,0,1) Matrix(183,322,104,183) -> Matrix(1,2,0,1) Matrix(185,322,-158,-275) -> Matrix(1,0,0,1) Matrix(3081,5336,1354,2345) -> Matrix(1,-2,2,-3) Matrix(17111,29624,4782,8279) -> Matrix(1,-16,0,1) Matrix(12835,22218,3588,6211) -> Matrix(1,14,0,1) Matrix(2207,3818,-1596,-2761) -> Matrix(1,2,0,1) Matrix(507,874,134,231) -> Matrix(1,2,0,1) Matrix(1657,2852,642,1105) -> Matrix(1,2,0,1) Matrix(1473,2530,-910,-1563) -> Matrix(1,2,-2,-3) Matrix(1241,2116,512,873) -> Matrix(1,2,0,1) Matrix(1243,2116,514,875) -> Matrix(1,2,0,1) Matrix(461,782,326,553) -> Matrix(1,2,0,1) Matrix(1335,2254,-844,-1425) -> Matrix(1,0,2,1) Matrix(139,230,84,139) -> Matrix(1,0,2,1) Matrix(505,828,308,505) -> Matrix(1,0,0,1) Matrix(1013,1656,282,461) -> Matrix(1,0,0,1) Matrix(1747,2852,732,1195) -> Matrix(1,2,0,1) Matrix(2483,4048,-1750,-2853) -> Matrix(1,0,0,1) Matrix(1333,2162,-1050,-1703) -> Matrix(1,0,0,1) Matrix(2669,4324,966,1565) -> Matrix(3,4,2,3) Matrix(11501,18630,7100,11501) -> Matrix(9,10,8,9) Matrix(4829,7820,2982,4829) -> Matrix(5,4,6,5) Matrix(10121,16376,-7846,-12695) -> Matrix(1,0,2,1) Matrix(827,1334,-628,-1013) -> Matrix(1,0,-2,1) Matrix(829,1334,458,737) -> Matrix(1,0,0,1) Matrix(229,368,28,45) -> Matrix(1,2,0,1) Matrix(1333,2116,492,781) -> Matrix(1,0,6,1) Matrix(1335,2116,494,783) -> Matrix(1,0,-4,1) Matrix(3957,6256,2852,4509) -> Matrix(1,-2,2,-3) Matrix(321,506,262,413) -> Matrix(1,0,0,1) Matrix(2759,4324,1056,1655) -> Matrix(1,4,0,1) Matrix(323,506,30,47) -> Matrix(1,4,0,1) Matrix(2529,3956,1852,2897) -> Matrix(1,2,0,1) Matrix(737,1150,-530,-827) -> Matrix(1,0,0,1) Matrix(2163,3358,1334,2071) -> Matrix(1,2,0,1) Matrix(2669,4140,-1838,-2851) -> Matrix(3,2,-2,-1) Matrix(597,920,268,413) -> Matrix(1,0,2,1) Matrix(599,920,390,599) -> Matrix(1,0,2,1) Matrix(91,138,60,91) -> Matrix(1,0,0,1) Matrix(597,874,-472,-691) -> Matrix(1,2,0,1) Matrix(2437,3542,-1868,-2715) -> Matrix(1,2,0,1) Matrix(415,598,288,415) -> Matrix(3,4,2,3) Matrix(321,460,224,321) -> Matrix(1,0,2,1) Matrix(323,460,-290,-413) -> Matrix(3,2,-2,-1) Matrix(13385,19044,3976,5657) -> Matrix(1,0,6,1) Matrix(13387,19044,3978,5659) -> Matrix(1,0,-4,1) Matrix(2071,2944,1198,1703) -> Matrix(1,2,0,1) Matrix(1425,2024,226,321) -> Matrix(1,2,0,1) Matrix(11501,16330,8100,11501) -> Matrix(1,2,0,1) Matrix(7129,10120,5022,7129) -> Matrix(1,0,2,1) Matrix(553,782,326,461) -> Matrix(1,2,0,1) Matrix(1011,1426,782,1103) -> Matrix(1,0,0,1) Matrix(229,322,32,45) -> Matrix(1,2,0,1) Matrix(1517,2116,428,597) -> Matrix(1,0,2,1) Matrix(1519,2116,430,599) -> Matrix(1,0,0,1) Matrix(16007,22218,6760,9383) -> Matrix(13,14,12,13) Matrix(21345,29624,9016,12513) -> Matrix(17,16,18,17) Matrix(2851,3956,596,827) -> Matrix(3,2,4,3) Matrix(1195,1656,464,643) -> Matrix(1,0,2,1) Matrix(3359,4646,2362,3267) -> Matrix(1,0,0,1) Matrix(1565,2162,-1198,-1655) -> Matrix(1,2,0,1) Matrix(367,506,66,91) -> Matrix(1,0,2,1) Matrix(369,506,202,277) -> Matrix(1,0,0,1) Matrix(875,1196,-706,-965) -> Matrix(1,0,0,1) Matrix(13937,19044,3736,5105) -> Matrix(1,2,0,1) Matrix(13939,19044,3738,5107) -> Matrix(1,2,0,1) Matrix(2897,3956,1852,2529) -> Matrix(1,2,0,1) Matrix(643,874,270,367) -> Matrix(1,2,0,1) Matrix(645,874,476,645) -> Matrix(1,2,0,1) Matrix(137,184,102,137) -> Matrix(1,0,2,1) Matrix(1609,2116,384,505) -> Matrix(1,0,10,1) Matrix(1611,2116,386,507) -> Matrix(1,0,-8,1) Matrix(25943,33856,6062,7911) -> Matrix(1,0,4,1) Matrix(25945,33856,6064,7913) -> Matrix(1,0,-2,1) Matrix(6531,8464,1490,1931) -> Matrix(1,0,10,1) Matrix(6533,8464,1492,1933) -> Matrix(1,0,-8,1) Matrix(1103,1426,782,1011) -> Matrix(1,0,0,1) Matrix(1105,1426,-926,-1195) -> Matrix(1,-2,0,1) Matrix(14765,19044,3316,4277) -> Matrix(1,-2,2,-3) Matrix(14767,19044,3318,4279) -> Matrix(1,-2,2,-3) Matrix(323,414,252,323) -> Matrix(1,-2,0,1) Matrix(505,644,396,505) -> Matrix(1,4,0,1) Matrix(1013,1288,652,829) -> Matrix(1,2,0,1) Matrix(689,874,108,137) -> Matrix(1,2,0,1) Matrix(3129,3956,874,1105) -> Matrix(1,-2,0,1) Matrix(1933,2392,1116,1381) -> Matrix(1,0,0,1) Matrix(413,506,262,321) -> Matrix(1,0,0,1) Matrix(415,506,114,139) -> Matrix(1,0,0,1) Matrix(645,782,532,645) -> Matrix(1,-4,0,1) Matrix(229,276,190,229) -> Matrix(1,4,0,1) Matrix(1703,2024,504,599) -> Matrix(1,2,0,1) Matrix(737,874,156,185) -> Matrix(1,2,0,1) Matrix(1793,2116,272,321) -> Matrix(1,2,0,1) Matrix(1795,2116,274,323) -> Matrix(1,2,0,1) Matrix(277,322,80,93) -> Matrix(1,2,0,1) Matrix(599,690,520,599) -> Matrix(1,2,0,1) Matrix(321,368,280,321) -> Matrix(1,4,0,1) Matrix(323,368,122,139) -> Matrix(1,2,0,1) Matrix(459,506,166,183) -> Matrix(3,4,2,3) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(413,-460,290,-323) -> Matrix(1,-2,2,-3) Matrix(275,-322,158,-185) -> Matrix(1,0,0,1) Matrix(1931,-2300,696,-829) -> Matrix(1,0,0,1) Matrix(597,-736,262,-323) -> Matrix(1,-2,2,-3) Matrix(183,-230,74,-93) -> Matrix(1,0,0,1) Matrix(1703,-2162,1050,-1333) -> Matrix(1,0,0,1) Matrix(2713,-3496,1036,-1335) -> Matrix(1,0,0,1) Matrix(3955,-5106,1426,-1841) -> Matrix(1,2,0,1) Matrix(461,-598,212,-275) -> Matrix(1,0,0,1) Matrix(459,-598,142,-185) -> Matrix(1,2,0,1) Matrix(737,-966,280,-367) -> Matrix(1,0,2,1) Matrix(5657,-7728,1516,-2071) -> Matrix(1,0,0,1) Matrix(2759,-3772,1212,-1657) -> Matrix(1,-2,2,-3) Matrix(1931,-2668,600,-829) -> Matrix(1,0,0,1) Matrix(2761,-3818,1596,-2207) -> Matrix(1,2,0,1) Matrix(5567,-7728,2352,-3265) -> Matrix(3,-4,4,-5) Matrix(827,-1150,530,-737) -> Matrix(1,0,0,1) Matrix(1103,-1564,390,-553) -> Matrix(1,0,0,1) Matrix(6209,-8832,1844,-2623) -> Matrix(1,0,2,1) Matrix(413,-598,96,-139) -> Matrix(1,-2,2,-3) Matrix(599,-874,220,-321) -> Matrix(1,-2,2,-3) Matrix(1011,-1564,298,-461) -> Matrix(1,0,0,1) Matrix(3173,-4922,742,-1151) -> Matrix(1,0,0,1) Matrix(1151,-1794,324,-505) -> Matrix(1,0,0,1) Matrix(1471,-2300,236,-369) -> Matrix(1,0,0,1) Matrix(553,-874,174,-275) -> Matrix(1,2,0,1) Matrix(231,-368,86,-137) -> Matrix(1,0,0,1) Matrix(599,-966,142,-229) -> Matrix(1,0,2,1) Matrix(967,-1564,426,-689) -> Matrix(1,0,0,1) Matrix(367,-598,170,-277) -> Matrix(1,0,0,1) Matrix(137,-230,28,-47) -> Matrix(1,0,0,1) Matrix(323,-552,134,-229) -> Matrix(1,0,0,1) Matrix(1151,-1978,508,-873) -> Matrix(1,-2,2,-3) Matrix(4463,-7728,1248,-2161) -> Matrix(1,4,0,1) Matrix(875,-1518,132,-229) -> Matrix(1,0,0,1) Matrix(413,-736,78,-139) -> Matrix(1,2,0,1) Matrix(875,-1564,334,-597) -> Matrix(1,0,0,1) Matrix(323,-598,74,-137) -> Matrix(1,0,0,1) Matrix(321,-598,124,-231) -> Matrix(1,0,0,1) Matrix(367,-782,130,-277) -> Matrix(1,0,0,1) Matrix(737,-1610,168,-367) -> Matrix(1,0,4,1) Matrix(367,-828,82,-185) -> Matrix(1,0,0,1) Matrix(137,-322,20,-47) -> Matrix(1,0,0,1) Matrix(1611,-3818,446,-1057) -> Matrix(1,-2,2,-3) Matrix(1057,-2530,404,-967) -> Matrix(1,-2,0,1) Matrix(919,-2254,338,-829) -> Matrix(1,0,2,1) Matrix(1565,-4048,462,-1195) -> Matrix(1,0,0,1) Matrix(829,-2162,176,-459) -> Matrix(1,0,0,1) Matrix(6255,-16376,1406,-3681) -> Matrix(1,0,2,1) Matrix(507,-1334,122,-321) -> Matrix(1,0,-2,1) Matrix(413,-1150,116,-323) -> Matrix(1,0,0,1) Matrix(1471,-4140,458,-1289) -> Matrix(1,2,0,1) Matrix(277,-874,58,-183) -> Matrix(1,-2,2,-3) Matrix(1105,-3542,258,-827) -> Matrix(1,-2,2,-3) Matrix(137,-460,14,-47) -> Matrix(1,2,0,1) Matrix(597,-2162,140,-507) -> Matrix(1,-2,2,-3) Matrix(321,-1196,62,-231) -> Matrix(1,0,0,1) Matrix(321,-1426,52,-231) -> Matrix(3,-2,2,-1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 48 Degree of the the map X: 48 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 2/1 23/10 12/5 46/19 23/9 115/44 46/17 23/8 3/1 23/7 138/41 115/34 46/13 161/45 18/5 138/37 23/6 4/1 46/11 184/43 92/21 22/5 138/31 23/5 14/3 5/1 21/4 16/3 11/2 17/3 23/4 6/1 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 0/1 0/1 1/1 1/1 9/8 1/0 8/7 2/1 23/20 1/0 15/13 1/1 7/6 1/0 13/11 1/1 19/16 1/0 25/21 1/1 6/5 2/1 23/19 1/0 17/14 1/0 11/9 1/1 16/13 0/1 5/4 1/0 19/15 1/1 33/26 1/0 14/11 2/1 23/18 1/0 9/7 -1/1 40/31 0/1 31/24 1/0 22/17 -2/3 13/10 1/0 17/13 -1/1 4/3 0/1 23/17 1/1 19/14 1/0 15/11 1/1 56/41 0/1 41/30 1/0 26/19 0/1 11/8 1/2 29/21 1/1 47/34 1/0 18/13 0/1 43/31 1/1 68/49 6/7 25/18 1/0 7/5 1/1 31/22 1/0 24/17 2/3 17/12 1/0 44/31 0/1 115/81 1/1 71/50 1/0 27/19 1/1 64/45 0/1 37/26 1/2 47/33 1/1 10/7 0/1 23/16 1/1 13/9 1/1 16/11 2/1 3/2 1/0 23/15 0/1 20/13 0/1 17/11 1/1 31/20 1/0 45/29 1/1 14/9 0/1 39/25 1/1 25/16 1/0 61/39 1/1 36/23 2/1 47/30 1/0 11/7 -1/1 30/19 0/1 19/12 -1/2 8/5 0/1 37/23 1/1 29/18 1/0 21/13 1/3 34/21 2/3 115/71 1/1 81/50 5/4 47/29 1/1 60/37 2/1 13/8 1/0 31/19 1/1 49/30 1/0 18/11 0/1 23/14 0/1 5/3 1/1 22/13 4/3 17/10 1/0 12/7 0/1 43/25 1/1 31/18 1/0 19/11 1/1 64/37 2/1 45/26 1/0 71/41 -3/1 26/15 0/1 33/19 1/1 7/4 1/0 23/13 1/0 16/9 -2/1 25/14 -1/2 9/5 -1/1 29/16 1/0 20/11 0/1 11/6 -1/2 13/7 1/1 2/1 0/1 15/7 1/1 13/6 1/0 24/11 -2/3 11/5 1/3 20/9 0/1 29/13 1/1 9/4 1/2 43/19 1/1 34/15 2/3 25/11 1/3 66/29 2/3 41/18 1/2 16/7 2/3 23/10 1/1 7/3 1/1 26/11 0/1 71/30 3/4 116/49 10/11 161/68 1/1 45/19 1/1 19/8 1/0 31/13 1/1 43/18 1/0 12/5 0/1 29/12 1/0 46/19 0/1 2/1 17/7 1/1 22/9 4/1 27/11 1/1 5/2 1/0 23/9 0/1 18/7 0/1 49/19 1/1 31/12 1/0 44/17 0/1 13/5 1/1 47/18 1/0 81/31 5/1 115/44 1/0 34/13 -2/1 89/34 1/0 144/55 0/1 55/21 -1/1 21/8 -1/2 50/19 0/1 29/11 1/1 37/14 1/0 8/3 0/1 27/10 -1/2 46/17 0/1 19/7 1/3 68/25 4/9 49/18 1/2 30/11 0/1 11/4 1/2 47/17 1/1 36/13 2/1 61/22 1/0 86/31 2/1 25/9 1/1 14/5 0/1 45/16 1/0 31/11 1/1 48/17 0/1 17/6 1/0 20/7 0/1 23/8 0/1 3/1 1/1 19/6 3/2 16/5 2/1 61/19 3/1 45/14 1/0 29/9 1/1 13/4 1/0 23/7 1/0 10/3 0/1 37/11 -1/1 138/41 0/1 101/30 1/4 64/19 0/1 27/8 1/0 71/21 1/1 115/34 1/0 44/13 0/1 61/18 1/0 17/5 1/1 24/7 -2/1 31/9 1/1 7/2 1/0 46/13 0/1 39/11 1/1 32/9 0/1 25/7 1/1 93/26 1/0 161/45 1/0 68/19 -6/1 43/12 1/0 18/5 0/1 65/18 1/2 47/13 1/1 29/8 1/0 11/3 -1/1 26/7 0/1 41/11 1/1 138/37 0/1 2/1 97/26 1/0 56/15 0/1 15/4 1/0 19/5 1/1 23/6 1/0 4/1 0/1 25/6 -1/4 46/11 0/1 21/5 1/5 17/4 1/2 47/11 1/1 77/18 1/0 184/43 0/1 107/25 1/3 30/7 0/1 13/3 1/1 35/8 -1/2 92/21 0/1 57/13 1/7 22/5 2/5 31/7 1/1 40/9 0/1 89/20 1/2 138/31 0/1 2/3 49/11 1/1 9/2 1/2 23/5 1/1 14/3 2/1 47/10 1/0 33/7 1/1 19/4 1/0 43/9 1/1 24/5 4/3 5/1 1/1 26/5 0/1 21/4 3/2 16/3 0/1 11/2 1/0 17/3 1/1 23/4 1/1 6/1 2/1 31/5 1/1 25/4 1/0 19/3 1/1 13/2 1/0 46/7 0/1 2/1 33/5 1/1 20/3 0/1 7/1 1/1 15/2 1/0 23/3 1/1 8/1 2/1 9/1 1/1 10/1 2/1 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(413,-460,290,-323) (1/1,9/8) -> (37/26,47/33) Hyperbolic Matrix(323,-368,201,-229) (9/8,8/7) -> (8/5,37/23) Hyperbolic Matrix(321,-368,41,-47) (8/7,23/20) -> (23/3,8/1) Hyperbolic Matrix(599,-690,79,-91) (23/20,15/13) -> (15/2,23/3) Hyperbolic Matrix(277,-322,197,-229) (15/13,7/6) -> (7/5,31/22) Hyperbolic Matrix(275,-322,158,-185) (7/6,13/11) -> (33/19,7/4) Hyperbolic Matrix(737,-874,581,-689) (13/11,19/16) -> (19/15,33/26) Hyperbolic Matrix(1703,-2024,1199,-1425) (19/16,25/21) -> (71/50,27/19) Hyperbolic Matrix(1931,-2300,696,-829) (25/21,6/5) -> (86/31,25/9) Hyperbolic Matrix(229,-276,39,-47) (6/5,23/19) -> (23/4,6/1) Hyperbolic Matrix(645,-782,113,-137) (23/19,17/14) -> (17/3,23/4) Hyperbolic Matrix(415,-506,301,-367) (17/14,11/9) -> (11/8,29/21) Hyperbolic Matrix(413,-506,151,-185) (11/9,16/13) -> (30/11,11/4) 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(505,-644,109,-139) (14/11,23/18) -> (23/5,14/3) Hyperbolic Matrix(323,-414,71,-91) (23/18,9/7) -> (9/2,23/5) 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(1103,-1426,321,-415) (31/24,22/17) -> (24/7,31/9) 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(137,-184,35,-47) (4/3,23/17) -> (23/6,4/1) Hyperbolic Matrix(645,-874,169,-229) (23/17,19/14) -> (19/5,23/6) Hyperbolic Matrix(643,-874,373,-507) (19/14,15/11) -> (31/18,19/11) Hyperbolic Matrix(2897,-3956,1045,-1427) (15/11,56/41) -> (36/13,61/22) 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(369,-506,167,-229) (26/19,11/8) -> (11/5,20/9) 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(1195,-1656,731,-1013) (18/13,43/31) -> (49/30,18/11) Hyperbolic Matrix(4509,-6256,1657,-2299) (43/31,68/49) -> (68/25,49/18) 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(1011,-1426,229,-323) (31/22,24/17) -> (22/5,31/7) Hyperbolic Matrix(553,-782,227,-321) (24/17,17/12) -> (17/7,22/9) Hyperbolic Matrix(1103,-1564,390,-553) (17/12,44/31) -> (48/17,17/6) Hyperbolic Matrix(7129,-10120,2107,-2991) (44/31,115/81) -> (115/34,44/13) Hyperbolic Matrix(11501,-16330,3401,-4829) (115/81,71/50) -> (71/21,115/34) Hyperbolic Matrix(3267,-4646,905,-1287) (27/19,64/45) -> (18/5,65/18) Hyperbolic Matrix(6209,-8832,1844,-2623) (64/45,37/26) -> (101/30,64/19) Hyperbolic Matrix(1517,-2162,969,-1381) (47/33,10/7) -> (36/23,47/30) Hyperbolic Matrix(321,-460,97,-139) (10/7,23/16) -> (23/7,10/3) Hyperbolic Matrix(415,-598,127,-183) (23/16,13/9) -> (13/4,23/7) 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(91,-138,31,-47) (3/2,23/15) -> (23/8,3/1) Hyperbolic Matrix(599,-920,209,-321) (23/15,20/13) -> (20/7,23/8) Hyperbolic Matrix(597,-920,329,-507) (20/13,17/11) -> (29/16,20/11) 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(829,-1288,177,-275) (45/29,14/9) -> (14/3,47/10) 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(2529,-3956,677,-1059) (61/39,36/23) -> (56/15,15/4) Hyperbolic Matrix(2759,-4324,1703,-2669) (47/30,11/7) -> (81/50,47/29) Hyperbolic Matrix(321,-506,59,-93) (11/7,30/19) -> (16/3,11/2) 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(829,-1334,371,-597) (37/23,29/18) -> (29/13,9/4) 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(4829,-7820,1847,-2991) (34/21,115/71) -> (115/44,34/13) Hyperbolic Matrix(11501,-18630,4401,-7129) (115/71,81/50) -> (81/31,115/44) Hyperbolic Matrix(2071,-3358,737,-1195) (47/29,60/37) -> (14/5,45/16) Hyperbolic Matrix(367,-598,170,-277) (13/8,31/19) -> (15/7,13/6) Hyperbolic Matrix(1747,-2852,1015,-1657) (31/19,49/30) -> (43/25,31/18) Hyperbolic Matrix(505,-828,197,-323) (18/11,23/14) -> (23/9,18/7) Hyperbolic Matrix(139,-230,55,-91) (23/14,5/3) -> (5/2,23/9) Hyperbolic Matrix(137,-230,28,-47) (5/3,22/13) -> (24/5,5/1) Hyperbolic Matrix(461,-782,135,-229) (22/13,17/10) -> (17/5,24/7) 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(1703,-2944,505,-873) (19/11,64/37) -> (64/19,27/8) Hyperbolic Matrix(4463,-7728,1248,-2161) (45/26,71/41) -> (25/7,93/26) Hyperbolic Matrix(1381,-2392,265,-459) (71/41,26/15) -> (26/5,21/4) Hyperbolic Matrix(875,-1518,132,-229) (26/15,33/19) -> (33/5,20/3) Hyperbolic Matrix(183,-322,79,-139) (7/4,23/13) -> (23/10,7/3) Hyperbolic Matrix(415,-736,181,-321) (23/13,16/9) -> (16/7,23/10) 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(737,-1334,279,-505) (9/5,29/16) -> (29/11,37/14) Hyperbolic Matrix(277,-506,75,-137) (20/11,11/6) -> (11/3,26/7) 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(413,-920,145,-323) (20/9,29/13) -> (17/6,20/7) Hyperbolic Matrix(367,-828,82,-185) (9/4,43/19) -> (49/11,9/2) Hyperbolic Matrix(2345,-5336,991,-2255) (25/11,66/29) -> (26/11,71/30) Hyperbolic Matrix(137,-322,20,-47) (7/3,26/11) -> (20/3,7/1) Hyperbolic Matrix(12513,-29624,3497,-8279) (116/49,161/68) -> (161/45,68/19) Hyperbolic Matrix(9383,-22218,2623,-6211) (161/68,45/19) -> (93/26,161/45) Hyperbolic Matrix(1611,-3818,446,-1057) (45/19,19/8) -> (65/18,47/13) Hyperbolic Matrix(367,-874,97,-231) (19/8,31/13) -> (15/4,19/5) Hyperbolic Matrix(1195,-2852,463,-1105) (31/13,43/18) -> (49/19,31/12) Hyperbolic Matrix(1057,-2530,404,-967) (43/18,12/5) -> (34/13,89/34) Hyperbolic Matrix(875,-2116,361,-873) (29/12,46/19) -> (46/19,17/7) Parabolic Matrix(919,-2254,338,-829) (22/9,27/11) -> (19/7,68/25) Hyperbolic Matrix(643,-1656,179,-461) (18/7,49/19) -> (43/12,18/5) 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(1655,-4324,599,-1565) (47/18,81/31) -> (11/4,47/17) 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(139,-368,17,-45) (37/14,8/3) -> (8/1,9/1) Hyperbolic Matrix(783,-2116,289,-781) (27/10,46/17) -> (46/17,19/7) Parabolic Matrix(183,-506,17,-47) (47/17,36/13) -> (10/1,1/0) 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(5659,-19044,1681,-5657) (37/11,138/41) -> (138/41,101/30) Parabolic Matrix(599,-2024,95,-321) (27/8,71/21) -> (25/4,19/3) Hyperbolic Matrix(93,-322,13,-45) (31/9,7/2) -> (7/1,15/2) Hyperbolic Matrix(599,-2116,169,-597) (7/2,46/13) -> (46/13,39/11) Parabolic Matrix(1105,-3956,231,-827) (68/19,43/12) -> (43/9,24/5) Hyperbolic Matrix(597,-2162,140,-507) (47/13,29/8) -> (17/4,47/11) Hyperbolic Matrix(139,-506,25,-91) (29/8,11/3) -> (11/2,17/3) Hyperbolic Matrix(321,-1196,62,-231) (26/7,41/11) -> (5/1,26/5) Hyperbolic Matrix(5107,-19044,1369,-5105) (41/11,138/37) -> (138/37,97/26) Parabolic Matrix(507,-2116,121,-505) (25/6,46/11) -> (46/11,21/5) Parabolic Matrix(7913,-33856,1849,-7911) (77/18,184/43) -> (184/43,107/25) Parabolic Matrix(1933,-8464,441,-1931) (35/8,92/21) -> (92/21,57/13) Parabolic Matrix(321,-1426,52,-231) (31/7,40/9) -> (6/1,31/5) Hyperbolic Matrix(4279,-19044,961,-4277) (89/20,138/31) -> (138/31,49/11) Parabolic Matrix(185,-874,29,-137) (33/7,19/4) -> (19/3,13/2) Hyperbolic Matrix(323,-2116,49,-321) (13/2,46/7) -> (46/7,33/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,1,1) Matrix(413,-460,290,-323) -> Matrix(1,-2,2,-3) Matrix(323,-368,201,-229) -> Matrix(1,-2,1,-1) Matrix(321,-368,41,-47) -> Matrix(1,-4,1,-3) Matrix(599,-690,79,-91) -> Matrix(1,-2,1,-1) Matrix(277,-322,197,-229) -> Matrix(1,-2,1,-1) Matrix(275,-322,158,-185) -> Matrix(1,0,0,1) Matrix(737,-874,581,-689) -> Matrix(1,-2,1,-1) Matrix(1703,-2024,1199,-1425) -> Matrix(1,-2,1,-1) Matrix(1931,-2300,696,-829) -> Matrix(1,0,0,1) Matrix(229,-276,39,-47) -> Matrix(1,-4,1,-3) Matrix(645,-782,113,-137) -> Matrix(1,4,1,5) Matrix(415,-506,301,-367) -> Matrix(1,0,1,1) Matrix(413,-506,151,-185) -> Matrix(1,0,1,1) Matrix(597,-736,262,-323) -> Matrix(1,-2,2,-3) Matrix(183,-230,74,-93) -> Matrix(1,0,0,1) Matrix(1703,-2162,1050,-1333) -> Matrix(1,0,0,1) Matrix(505,-644,109,-139) -> Matrix(1,-4,1,-3) Matrix(323,-414,71,-91) -> Matrix(1,2,1,3) Matrix(2713,-3496,1036,-1335) -> Matrix(1,0,0,1) Matrix(3955,-5106,1426,-1841) -> Matrix(1,2,0,1) Matrix(1103,-1426,321,-415) -> Matrix(1,0,1,1) Matrix(461,-598,212,-275) -> Matrix(1,0,0,1) Matrix(459,-598,142,-185) -> Matrix(1,2,0,1) Matrix(737,-966,280,-367) -> Matrix(1,0,2,1) Matrix(137,-184,35,-47) -> Matrix(1,0,-1,1) Matrix(645,-874,169,-229) -> Matrix(1,-2,1,-1) Matrix(643,-874,373,-507) -> Matrix(1,-2,1,-1) Matrix(2897,-3956,1045,-1427) -> Matrix(1,-2,1,-1) Matrix(5657,-7728,1516,-2071) -> Matrix(1,0,0,1) Matrix(2759,-3772,1212,-1657) -> Matrix(1,-2,2,-3) Matrix(369,-506,167,-229) -> Matrix(1,0,1,1) Matrix(1931,-2668,600,-829) -> Matrix(1,0,0,1) Matrix(2761,-3818,1596,-2207) -> Matrix(1,2,0,1) Matrix(1195,-1656,731,-1013) -> Matrix(1,0,-1,1) Matrix(4509,-6256,1657,-2299) -> Matrix(3,-2,5,-3) Matrix(5567,-7728,2352,-3265) -> Matrix(3,-4,4,-5) Matrix(827,-1150,530,-737) -> Matrix(1,0,0,1) Matrix(1011,-1426,229,-323) -> Matrix(1,0,1,1) Matrix(553,-782,227,-321) -> Matrix(1,-2,1,-1) Matrix(1103,-1564,390,-553) -> Matrix(1,0,0,1) Matrix(7129,-10120,2107,-2991) -> Matrix(1,0,-1,1) Matrix(11501,-16330,3401,-4829) -> Matrix(1,-2,1,-1) Matrix(3267,-4646,905,-1287) -> Matrix(1,0,1,1) Matrix(6209,-8832,1844,-2623) -> Matrix(1,0,2,1) Matrix(1517,-2162,969,-1381) -> Matrix(1,-2,1,-1) Matrix(321,-460,97,-139) -> Matrix(1,0,-1,1) Matrix(415,-598,127,-183) -> Matrix(3,-4,1,-1) Matrix(413,-598,96,-139) -> Matrix(1,-2,2,-3) Matrix(599,-874,220,-321) -> Matrix(1,-2,2,-3) Matrix(91,-138,31,-47) -> Matrix(1,0,1,1) Matrix(599,-920,209,-321) -> Matrix(1,0,-1,1) Matrix(597,-920,329,-507) -> Matrix(1,0,-1,1) Matrix(1011,-1564,298,-461) -> Matrix(1,0,0,1) Matrix(3173,-4922,742,-1151) -> Matrix(1,0,0,1) Matrix(829,-1288,177,-275) -> Matrix(1,-2,1,-1) Matrix(1151,-1794,324,-505) -> Matrix(1,0,0,1) Matrix(1471,-2300,236,-369) -> Matrix(1,0,0,1) Matrix(2529,-3956,677,-1059) -> Matrix(1,-2,1,-1) Matrix(2759,-4324,1703,-2669) -> Matrix(1,-4,1,-3) Matrix(321,-506,59,-93) -> Matrix(1,0,1,1) Matrix(553,-874,174,-275) -> Matrix(1,2,0,1) Matrix(231,-368,86,-137) -> Matrix(1,0,0,1) Matrix(829,-1334,371,-597) -> Matrix(1,0,1,1) Matrix(599,-966,142,-229) -> Matrix(1,0,2,1) Matrix(967,-1564,426,-689) -> Matrix(1,0,0,1) Matrix(4829,-7820,1847,-2991) -> Matrix(5,-4,-1,1) Matrix(11501,-18630,4401,-7129) -> Matrix(9,-10,1,-1) Matrix(2071,-3358,737,-1195) -> Matrix(1,-2,1,-1) Matrix(367,-598,170,-277) -> Matrix(1,0,0,1) Matrix(1747,-2852,1015,-1657) -> Matrix(1,-2,1,-1) Matrix(505,-828,197,-323) -> Matrix(1,0,1,1) Matrix(139,-230,55,-91) -> Matrix(1,0,-1,1) Matrix(137,-230,28,-47) -> Matrix(1,0,0,1) Matrix(461,-782,135,-229) -> Matrix(1,-2,1,-1) Matrix(323,-552,134,-229) -> Matrix(1,0,0,1) Matrix(1151,-1978,508,-873) -> Matrix(1,-2,2,-3) Matrix(1703,-2944,505,-873) -> Matrix(1,-2,1,-1) Matrix(4463,-7728,1248,-2161) -> Matrix(1,4,0,1) Matrix(1381,-2392,265,-459) -> Matrix(1,0,1,1) Matrix(875,-1518,132,-229) -> Matrix(1,0,0,1) Matrix(183,-322,79,-139) -> Matrix(1,-2,1,-1) Matrix(415,-736,181,-321) -> Matrix(1,4,1,5) Matrix(413,-736,78,-139) -> Matrix(1,2,0,1) Matrix(875,-1564,334,-597) -> Matrix(1,0,0,1) Matrix(737,-1334,279,-505) -> Matrix(1,0,1,1) Matrix(277,-506,75,-137) -> Matrix(1,0,1,1) Matrix(323,-598,74,-137) -> Matrix(1,0,0,1) Matrix(321,-598,124,-231) -> Matrix(1,0,0,1) Matrix(367,-782,130,-277) -> Matrix(1,0,0,1) Matrix(737,-1610,168,-367) -> Matrix(1,0,4,1) Matrix(413,-920,145,-323) -> Matrix(1,0,-1,1) Matrix(367,-828,82,-185) -> Matrix(1,0,0,1) Matrix(2345,-5336,991,-2255) -> Matrix(3,-2,5,-3) Matrix(137,-322,20,-47) -> Matrix(1,0,0,1) Matrix(12513,-29624,3497,-8279) -> Matrix(17,-16,-1,1) Matrix(9383,-22218,2623,-6211) -> Matrix(13,-14,1,-1) Matrix(1611,-3818,446,-1057) -> Matrix(1,-2,2,-3) Matrix(367,-874,97,-231) -> Matrix(1,-2,1,-1) Matrix(1195,-2852,463,-1105) -> Matrix(1,-2,1,-1) Matrix(1057,-2530,404,-967) -> Matrix(1,-2,0,1) Matrix(875,-2116,361,-873) -> Matrix(1,-2,1,-1) Matrix(919,-2254,338,-829) -> Matrix(1,0,2,1) Matrix(643,-1656,179,-461) -> Matrix(1,0,-1,1) Matrix(1565,-4048,462,-1195) -> Matrix(1,0,0,1) Matrix(829,-2162,176,-459) -> Matrix(1,0,0,1) Matrix(1655,-4324,599,-1565) -> Matrix(1,-4,1,-3) Matrix(6255,-16376,1406,-3681) -> Matrix(1,0,2,1) Matrix(507,-1334,122,-321) -> Matrix(1,0,-2,1) Matrix(139,-368,17,-45) -> Matrix(1,-2,1,-1) Matrix(783,-2116,289,-781) -> Matrix(1,0,5,1) Matrix(183,-506,17,-47) -> Matrix(3,-4,1,-1) Matrix(413,-1150,116,-323) -> Matrix(1,0,0,1) Matrix(1471,-4140,458,-1289) -> Matrix(1,2,0,1) Matrix(277,-874,58,-183) -> Matrix(1,-2,2,-3) Matrix(1105,-3542,258,-827) -> Matrix(1,-2,2,-3) Matrix(137,-460,14,-47) -> Matrix(1,2,0,1) Matrix(5659,-19044,1681,-5657) -> Matrix(1,0,5,1) Matrix(599,-2024,95,-321) -> Matrix(1,-2,1,-1) Matrix(93,-322,13,-45) -> Matrix(1,-2,1,-1) Matrix(599,-2116,169,-597) -> Matrix(1,0,1,1) Matrix(1105,-3956,231,-827) -> Matrix(1,2,1,3) Matrix(597,-2162,140,-507) -> Matrix(1,-2,2,-3) Matrix(139,-506,25,-91) -> Matrix(1,0,1,1) Matrix(321,-1196,62,-231) -> Matrix(1,0,0,1) Matrix(5107,-19044,1369,-5105) -> Matrix(1,-2,1,-1) Matrix(507,-2116,121,-505) -> Matrix(1,0,9,1) Matrix(7913,-33856,1849,-7911) -> Matrix(1,0,3,1) Matrix(1933,-8464,441,-1931) -> Matrix(1,0,9,1) Matrix(321,-1426,52,-231) -> Matrix(3,-2,2,-1) Matrix(4279,-19044,961,-4277) -> Matrix(3,-2,5,-3) Matrix(185,-874,29,-137) -> Matrix(1,-2,1,-1) Matrix(323,-2116,49,-321) -> Matrix(1,-2,1,-1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 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: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 48 ----------------------------------------------------------------------- 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 1 1 2/1 0/1 1 23 13/6 1/0 1 23 11/5 1/3 1 23 20/9 0/1 1 23 29/13 1/1 1 23 9/4 1/2 1 23 25/11 1/3 1 23 16/7 2/3 1 23 23/10 1/1 3 1 7/3 1/1 1 23 26/11 0/1 1 23 71/30 3/4 1 23 45/19 1/1 1 23 19/8 1/0 1 23 31/13 1/1 1 23 43/18 1/0 1 23 12/5 0/1 1 23 46/19 (0/1,2/1).(1/1,1/0) 0 1 17/7 1/1 1 23 22/9 4/1 1 23 5/2 1/0 1 23 23/9 0/1 1 1 18/7 0/1 1 23 49/19 1/1 1 23 31/12 1/0 1 23 44/17 0/1 1 23 13/5 1/1 1 23 47/18 1/0 1 23 81/31 5/1 1 23 115/44 1/0 7 1 34/13 -2/1 1 23 89/34 1/0 1 23 55/21 -1/1 1 23 21/8 -1/2 1 23 29/11 1/1 1 23 37/14 1/0 1 23 8/3 0/1 1 23 46/17 0/1 5 1 19/7 1/3 1 23 30/11 0/1 1 23 11/4 1/2 1 23 47/17 1/1 1 23 36/13 2/1 1 23 61/22 1/0 1 23 25/9 1/1 1 23 14/5 0/1 1 23 45/16 1/0 1 23 31/11 1/1 1 23 17/6 1/0 1 23 20/7 0/1 1 23 23/8 0/1 1 1 3/1 1/1 1 23 19/6 3/2 1 23 16/5 2/1 1 23 13/4 1/0 1 23 23/7 1/0 2 1 10/3 0/1 1 23 37/11 -1/1 1 23 138/41 0/1 5 1 64/19 0/1 1 23 27/8 1/0 1 23 71/21 1/1 1 23 115/34 1/0 1 1 44/13 0/1 1 23 61/18 1/0 1 23 17/5 1/1 1 23 24/7 -2/1 1 23 31/9 1/1 1 23 7/2 1/0 1 23 46/13 0/1 1 1 32/9 0/1 1 23 25/7 1/1 1 23 93/26 1/0 1 23 161/45 1/0 15 1 68/19 -6/1 1 23 43/12 1/0 1 23 18/5 0/1 1 23 65/18 1/2 1 23 47/13 1/1 1 23 29/8 1/0 1 23 11/3 -1/1 1 23 26/7 0/1 1 23 41/11 1/1 1 23 138/37 (0/1,2/1).(1/1,1/0) 0 1 56/15 0/1 1 23 15/4 1/0 1 23 19/5 1/1 1 23 23/6 1/0 1 1 4/1 0/1 1 23 46/11 0/1 9 1 21/5 1/5 1 23 17/4 1/2 1 23 47/11 1/1 1 23 77/18 1/0 1 23 184/43 0/1 3 1 30/7 0/1 1 23 13/3 1/1 1 23 35/8 -1/2 1 23 92/21 0/1 9 1 22/5 2/5 1 23 31/7 1/1 1 23 40/9 0/1 1 23 138/31 (0/1,2/3).(1/2,1/1) 0 1 49/11 1/1 1 23 9/2 1/2 1 23 23/5 1/1 3 1 14/3 2/1 1 23 47/10 1/0 1 23 33/7 1/1 1 23 19/4 1/0 1 23 43/9 1/1 1 23 24/5 4/3 1 23 5/1 1/1 1 23 26/5 0/1 1 23 21/4 3/2 1 23 16/3 0/1 1 23 11/2 1/0 1 23 17/3 1/1 1 23 23/4 1/1 4 1 6/1 2/1 1 23 31/5 1/1 1 23 25/4 1/0 1 23 19/3 1/1 1 23 13/2 1/0 1 23 46/7 (0/1,2/1).(1/1,1/0) 0 1 20/3 0/1 1 23 7/1 1/1 1 23 15/2 1/0 1 23 23/3 1/1 1 1 8/1 2/1 1 23 9/1 1/1 1 23 10/1 2/1 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(277,-598,107,-231) (2/1,13/6) -> (44/17,13/5) Glide Reflection Matrix(275,-598,63,-137) (13/6,11/5) -> (13/3,35/8) Glide Reflection Matrix(229,-506,62,-137) (11/5,20/9) -> (11/3,26/7) Glide Reflection Matrix(413,-920,145,-323) (20/9,29/13) -> (17/6,20/7) Hyperbolic Matrix(597,-1334,226,-505) (29/13,9/4) -> (29/11,37/14) Glide Reflection Matrix(689,-1564,263,-597) (9/4,25/11) -> (55/21,21/8) Glide Reflection Matrix(323,-736,61,-139) (25/11,16/7) -> (21/4,16/3) Glide Reflection Matrix(321,-736,140,-321) (16/7,23/10) -> (16/7,23/10) Reflection Matrix(139,-322,60,-139) (23/10,7/3) -> (23/10,7/3) Reflection Matrix(137,-322,20,-47) (7/3,26/11) -> (20/3,7/1) Hyperbolic Matrix(1011,-2392,194,-459) (26/11,71/30) -> (26/5,21/4) Glide Reflection Matrix(3265,-7728,913,-2161) (71/30,45/19) -> (25/7,93/26) Glide Reflection Matrix(1611,-3818,446,-1057) (45/19,19/8) -> (65/18,47/13) Hyperbolic Matrix(367,-874,97,-231) (19/8,31/13) -> (15/4,19/5) Hyperbolic Matrix(1195,-2852,463,-1105) (31/13,43/18) -> (49/19,31/12) Hyperbolic Matrix(1057,-2530,404,-967) (43/18,12/5) -> (34/13,89/34) Hyperbolic Matrix(229,-552,95,-229) (12/5,46/19) -> (12/5,46/19) Reflection Matrix(645,-1564,266,-645) (46/19,17/7) -> (46/19,17/7) Reflection Matrix(321,-782,94,-229) (17/7,22/9) -> (17/5,24/7) Glide Reflection Matrix(93,-230,19,-47) (22/9,5/2) -> (24/5,5/1) Glide 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(643,-1656,179,-461) (18/7,49/19) -> (43/12,18/5) 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(1655,-4324,599,-1565) (47/18,81/31) -> (11/4,47/17) Hyperbolic Matrix(7129,-18630,2728,-7129) (81/31,115/44) -> (81/31,115/44) Reflection Matrix(2991,-7820,1144,-2991) (115/44,34/13) -> (115/44,34/13) Reflection Matrix(1335,-3496,299,-783) (89/34,55/21) -> (49/11,9/2) Glide Reflection Matrix(367,-966,87,-229) (21/8,29/11) -> (21/5,17/4) Glide Reflection Matrix(139,-368,17,-45) (37/14,8/3) -> (8/1,9/1) Hyperbolic Matrix(137,-368,51,-137) (8/3,46/17) -> (8/3,46/17) Reflection Matrix(645,-1748,238,-645) (46/17,19/7) -> (46/17,19/7) Reflection Matrix(321,-874,101,-275) (19/7,30/11) -> (19/6,16/5) Glide Reflection Matrix(185,-506,34,-93) (30/11,11/4) -> (16/3,11/2) Glide Reflection Matrix(183,-506,17,-47) (47/17,36/13) -> (10/1,1/0) Hyperbolic Matrix(1427,-3956,382,-1059) (36/13,61/22) -> (56/15,15/4) Glide Reflection Matrix(829,-2300,133,-369) (61/22,25/9) -> (31/5,25/4) Glide Reflection Matrix(413,-1150,116,-323) (25/9,14/5) -> (32/9,25/7) Hyperbolic Matrix(459,-1288,98,-275) (14/5,45/16) -> (14/3,47/10) Glide Reflection Matrix(1749,-4922,409,-1151) (45/16,31/11) -> (47/11,77/18) Glide Reflection Matrix(553,-1564,163,-461) (31/11,17/6) -> (61/18,17/5) Glide Reflection Matrix(321,-920,112,-321) (20/7,23/8) -> (20/7,23/8) Reflection Matrix(47,-138,16,-47) (23/8,3/1) -> (23/8,3/1) Reflection Matrix(277,-874,58,-183) (3/1,19/6) -> (19/4,43/9) Hyperbolic Matrix(185,-598,43,-139) (16/5,13/4) -> (30/7,13/3) Glide Reflection 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(137,-460,14,-47) (10/3,37/11) -> (9/1,10/1) Hyperbolic Matrix(3035,-10212,902,-3035) (37/11,138/41) -> (37/11,138/41) Reflection Matrix(2623,-8832,779,-2623) (138/41,64/19) -> (138/41,64/19) Reflection Matrix(1379,-4646,382,-1287) (64/19,27/8) -> (18/5,65/18) Glide Reflection Matrix(599,-2024,95,-321) (27/8,71/21) -> (25/4,19/3) Hyperbolic Matrix(4829,-16330,1428,-4829) (71/21,115/34) -> (71/21,115/34) Reflection Matrix(2991,-10120,884,-2991) (115/34,44/13) -> (115/34,44/13) Reflection Matrix(415,-1426,94,-323) (24/7,31/9) -> (22/5,31/7) Glide Reflection Matrix(93,-322,13,-45) (31/9,7/2) -> (7/1,15/2) Hyperbolic Matrix(183,-644,52,-183) (7/2,46/13) -> (7/2,46/13) Reflection Matrix(415,-1472,117,-415) (46/13,32/9) -> (46/13,32/9) Reflection Matrix(8371,-29946,2340,-8371) (93/26,161/45) -> (93/26,161/45) Reflection Matrix(6119,-21896,1710,-6119) (161/45,68/19) -> (161/45,68/19) Reflection Matrix(1105,-3956,231,-827) (68/19,43/12) -> (43/9,24/5) Hyperbolic Matrix(597,-2162,140,-507) (47/13,29/8) -> (17/4,47/11) Hyperbolic Matrix(139,-506,25,-91) (29/8,11/3) -> (11/2,17/3) Hyperbolic Matrix(321,-1196,62,-231) (26/7,41/11) -> (5/1,26/5) Hyperbolic Matrix(3035,-11316,814,-3035) (41/11,138/37) -> (41/11,138/37) Reflection Matrix(2071,-7728,555,-2071) (138/37,56/15) -> (138/37,56/15) Reflection Matrix(229,-874,60,-229) (19/5,23/6) -> (19/5,23/6) 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(6623,-28336,1548,-6623) (77/18,184/43) -> (77/18,184/43) Reflection Matrix(1289,-5520,301,-1289) (184/43,30/7) -> (184/43,30/7) 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(321,-1426,52,-231) (31/7,40/9) -> (6/1,31/5) Hyperbolic Matrix(1241,-5520,279,-1241) (40/9,138/31) -> (40/9,138/31) Reflection Matrix(3037,-13524,682,-3037) (138/31,49/11) -> (138/31,49/11) 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(185,-874,29,-137) (33/7,19/4) -> (19/3,13/2) Hyperbolic Matrix(137,-782,24,-137) (17/3,23/4) -> (17/3,23/4) Reflection Matrix(47,-276,8,-47) (23/4,6/1) -> (23/4,6/1) Reflection Matrix(183,-1196,28,-183) (13/2,46/7) -> (13/2,46/7) Reflection Matrix(139,-920,21,-139) (46/7,20/3) -> (46/7,20/3) 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(1,0,1,-1) -> Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Matrix(277,-598,107,-231) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(275,-598,63,-137) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(229,-506,62,-137) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(413,-920,145,-323) -> Matrix(1,0,-1,1) 0/1 Matrix(597,-1334,226,-505) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(689,-1564,263,-597) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(323,-736,61,-139) -> Matrix(3,-2,1,-1) Matrix(321,-736,140,-321) -> Matrix(5,-4,6,-5) (16/7,23/10) -> (2/3,1/1) Matrix(139,-322,60,-139) -> Matrix(-1,2,0,1) (23/10,7/3) -> (1/1,1/0) Matrix(137,-322,20,-47) -> Matrix(1,0,0,1) Matrix(1011,-2392,194,-459) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(3265,-7728,913,-2161) -> Matrix(5,-4,1,-1) Matrix(1611,-3818,446,-1057) -> Matrix(1,-2,2,-3) 1/1 Matrix(367,-874,97,-231) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(1195,-2852,463,-1105) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(1057,-2530,404,-967) -> Matrix(1,-2,0,1) 1/0 Matrix(229,-552,95,-229) -> Matrix(1,0,1,-1) (12/5,46/19) -> (0/1,2/1) Matrix(645,-1564,266,-645) -> Matrix(-1,2,0,1) (46/19,17/7) -> (1/1,1/0) Matrix(321,-782,94,-229) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(93,-230,19,-47) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(91,-230,36,-91) -> Matrix(1,0,0,-1) (5/2,23/9) -> (0/1,1/0) Matrix(323,-828,126,-323) -> Matrix(1,0,2,-1) (23/9,18/7) -> (0/1,1/1) Matrix(643,-1656,179,-461) -> Matrix(1,0,-1,1) 0/1 Matrix(1565,-4048,462,-1195) -> Matrix(1,0,0,1) Matrix(829,-2162,176,-459) -> Matrix(1,0,0,1) Matrix(1655,-4324,599,-1565) -> Matrix(1,-4,1,-3) 2/1 Matrix(7129,-18630,2728,-7129) -> Matrix(-1,10,0,1) (81/31,115/44) -> (5/1,1/0) Matrix(2991,-7820,1144,-2991) -> Matrix(1,4,0,-1) (115/44,34/13) -> (-2/1,1/0) Matrix(1335,-3496,299,-783) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(367,-966,87,-229) -> Matrix(1,0,3,-1) *** -> (0/1,2/3) Matrix(139,-368,17,-45) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(137,-368,51,-137) -> Matrix(1,0,1,-1) (8/3,46/17) -> (0/1,2/1) Matrix(645,-1748,238,-645) -> Matrix(1,0,6,-1) (46/17,19/7) -> (0/1,1/3) Matrix(321,-874,101,-275) -> Matrix(3,-2,1,-1) Matrix(185,-506,34,-93) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(183,-506,17,-47) -> Matrix(3,-4,1,-1) 2/1 Matrix(1427,-3956,382,-1059) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(829,-2300,133,-369) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(413,-1150,116,-323) -> Matrix(1,0,0,1) Matrix(459,-1288,98,-275) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1749,-4922,409,-1151) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(553,-1564,163,-461) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(321,-920,112,-321) -> Matrix(1,0,0,-1) (20/7,23/8) -> (0/1,1/0) Matrix(47,-138,16,-47) -> Matrix(1,0,2,-1) (23/8,3/1) -> (0/1,1/1) Matrix(277,-874,58,-183) -> Matrix(1,-2,2,-3) 1/1 Matrix(185,-598,43,-139) -> Matrix(1,-2,1,-3) Matrix(183,-598,56,-183) -> Matrix(-1,4,0,1) (13/4,23/7) -> (2/1,1/0) Matrix(139,-460,42,-139) -> Matrix(1,0,0,-1) (23/7,10/3) -> (0/1,1/0) Matrix(137,-460,14,-47) -> Matrix(1,2,0,1) 1/0 Matrix(3035,-10212,902,-3035) -> Matrix(-1,0,2,1) (37/11,138/41) -> (-1/1,0/1) Matrix(2623,-8832,779,-2623) -> Matrix(1,0,3,-1) (138/41,64/19) -> (0/1,2/3) Matrix(1379,-4646,382,-1287) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(599,-2024,95,-321) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(4829,-16330,1428,-4829) -> Matrix(-1,2,0,1) (71/21,115/34) -> (1/1,1/0) Matrix(2991,-10120,884,-2991) -> Matrix(1,0,0,-1) (115/34,44/13) -> (0/1,1/0) Matrix(415,-1426,94,-323) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(93,-322,13,-45) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(183,-644,52,-183) -> Matrix(1,0,0,-1) (7/2,46/13) -> (0/1,1/0) Matrix(415,-1472,117,-415) -> Matrix(1,0,1,-1) (46/13,32/9) -> (0/1,2/1) Matrix(8371,-29946,2340,-8371) -> Matrix(-1,18,0,1) (93/26,161/45) -> (9/1,1/0) Matrix(6119,-21896,1710,-6119) -> Matrix(1,12,0,-1) (161/45,68/19) -> (-6/1,1/0) Matrix(1105,-3956,231,-827) -> Matrix(1,2,1,3) Matrix(597,-2162,140,-507) -> Matrix(1,-2,2,-3) 1/1 Matrix(139,-506,25,-91) -> Matrix(1,0,1,1) 0/1 Matrix(321,-1196,62,-231) -> Matrix(1,0,0,1) Matrix(3035,-11316,814,-3035) -> Matrix(-1,2,0,1) (41/11,138/37) -> (1/1,1/0) Matrix(2071,-7728,555,-2071) -> Matrix(1,0,1,-1) (138/37,56/15) -> (0/1,2/1) Matrix(229,-874,60,-229) -> Matrix(-1,2,0,1) (19/5,23/6) -> (1/1,1/0) Matrix(47,-184,12,-47) -> Matrix(1,0,0,-1) (23/6,4/1) -> (0/1,1/0) Matrix(45,-184,11,-45) -> Matrix(1,0,1,-1) (4/1,46/11) -> (0/1,2/1) Matrix(461,-1932,110,-461) -> Matrix(1,0,10,-1) (46/11,21/5) -> (0/1,1/5) Matrix(6623,-28336,1548,-6623) -> Matrix(1,0,0,-1) (77/18,184/43) -> (0/1,1/0) Matrix(1289,-5520,301,-1289) -> Matrix(1,0,3,-1) (184/43,30/7) -> (0/1,2/3) Matrix(1471,-6440,336,-1471) -> Matrix(-1,0,4,1) (35/8,92/21) -> (-1/2,0/1) Matrix(461,-2024,105,-461) -> Matrix(1,0,5,-1) (92/21,22/5) -> (0/1,2/5) Matrix(321,-1426,52,-231) -> Matrix(3,-2,2,-1) 1/1 Matrix(1241,-5520,279,-1241) -> Matrix(1,0,3,-1) (40/9,138/31) -> (0/1,2/3) Matrix(3037,-13524,682,-3037) -> Matrix(3,-2,4,-3) (138/31,49/11) -> (1/2,1/1) Matrix(91,-414,20,-91) -> Matrix(3,-2,4,-3) (9/2,23/5) -> (1/2,1/1) Matrix(139,-644,30,-139) -> Matrix(3,-4,2,-3) (23/5,14/3) -> (1/1,2/1) Matrix(185,-874,29,-137) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(137,-782,24,-137) -> Matrix(5,-4,6,-5) (17/3,23/4) -> (2/3,1/1) Matrix(47,-276,8,-47) -> Matrix(3,-4,2,-3) (23/4,6/1) -> (1/1,2/1) Matrix(183,-1196,28,-183) -> Matrix(-1,2,0,1) (13/2,46/7) -> (1/1,1/0) Matrix(139,-920,21,-139) -> Matrix(1,0,1,-1) (46/7,20/3) -> (0/1,2/1) Matrix(91,-690,12,-91) -> Matrix(-1,2,0,1) (15/2,23/3) -> (1/1,1/0) Matrix(47,-368,6,-47) -> Matrix(3,-4,2,-3) (23/3,8/1) -> (1/1,2/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.