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): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -4/9 -3/7 -7/17 -3/8 -1/3 -2/7 -1/5 -1/6 -1/7 0/1 1/7 3/17 1/4 1/3 3/7 1/2 7/13 3/5 2/3 5/7 9/11 13/15 7/8 1/1 11/9 14/11 9/7 23/17 7/5 3/2 61/39 31/19 5/3 19/11 16/9 9/5 13/7 2/1 41/19 11/5 7/3 17/7 5/2 18/7 13/5 29/11 8/3 117/43 11/4 147/53 3/1 61/19 23/7 10/3 17/5 31/9 7/2 39/11 11/3 15/4 4/1 13/3 9/2 23/5 14/3 33/7 5/1 21/4 16/3 11/2 17/3 6/1 13/2 7/1 22/3 15/2 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/18 -7/15 0/1 -6/13 2/33 1/16 -5/11 0/1 2/31 -9/20 2/31 1/15 -13/29 2/31 -4/9 1/15 -11/25 0/1 2/29 -7/16 3/44 2/29 -10/23 3/43 4/57 -3/7 1/14 -14/33 1/14 2/27 -11/26 1/14 -8/19 5/68 2/27 -13/31 2/27 8/107 -31/74 2/27 1/13 -18/43 3/40 -5/12 2/27 1/13 -12/29 6/79 1/13 -7/17 1/13 -9/22 5/64 4/51 -11/27 2/25 -2/5 2/25 1/12 -9/23 6/71 4/47 -7/18 2/23 1/11 -5/13 2/23 -8/21 0/1 1/11 -19/50 5/58 2/23 -11/29 2/23 4/45 -3/8 1/11 -13/35 0/1 2/21 -10/27 1/11 2/21 -7/19 1/11 -25/68 5/53 2/21 -18/49 1/11 2/21 -11/30 1/11 2/21 -4/11 2/21 1/10 -9/25 0/1 -14/39 1/11 -5/14 2/21 1/10 -6/17 1/10 2/19 -7/20 0/1 1/8 -8/23 1/10 -1/3 0/1 2/19 -7/22 1/9 -6/19 0/1 1/11 -5/16 2/19 1/9 -4/13 1/9 2/17 -11/36 1/8 -7/23 0/1 -10/33 2/19 1/9 -3/10 1/9 2/17 -8/27 2/17 1/8 -13/44 2/17 1/8 -18/61 2/17 5/42 -5/17 1/8 -7/24 2/17 1/8 -2/7 1/8 -9/32 1/8 2/15 -7/25 4/31 2/15 -5/18 0/1 1/8 -3/11 2/15 -4/15 1/8 2/15 -9/34 3/22 -5/19 4/29 6/43 -1/4 1/7 2/13 -5/21 2/13 -9/38 2/13 3/19 -4/17 4/25 5/31 -3/13 1/6 -5/22 1/6 6/35 -7/31 4/23 -2/9 1/6 2/11 -9/41 4/23 -7/32 3/17 -12/55 1/6 2/11 -5/23 8/45 2/11 -8/37 13/72 2/11 -3/14 2/11 5/27 -7/33 10/53 4/21 -4/19 1/5 -5/24 2/11 1/5 -1/5 1/5 -3/16 4/19 3/14 -5/27 8/37 2/9 -7/38 11/50 2/9 -2/11 2/9 3/13 -3/17 0/1 2/9 -1/6 1/4 -3/19 2/7 -5/32 0/1 1/2 -2/13 1/4 2/7 -1/7 0/1 2/7 -1/8 1/3 2/5 -2/17 1/2 -1/9 0/1 0/1 0/1 1/1 1/8 -2/1 1/0 1/7 0/1 1/6 -2/1 -1/1 3/17 -1/1 2/11 -1/1 -4/5 1/5 -2/3 0/1 3/14 -2/3 -1/2 5/23 -1/2 2/9 -2/3 -1/2 3/13 -2/3 1/4 -1/2 5/19 -2/5 9/34 -3/7 -2/5 4/15 -1/2 -2/5 7/26 -3/7 -2/5 3/11 -2/5 0/1 8/29 -6/11 -1/2 5/18 -1/2 -6/13 7/25 -4/9 9/32 -4/9 -7/16 2/7 -3/7 -2/5 3/10 -3/8 -4/11 7/23 -1/3 4/13 -2/5 -1/3 1/3 -1/3 6/17 -1/3 -2/7 11/31 -4/13 -2/7 5/14 -1/3 -2/7 4/11 -1/3 3/8 -5/17 -2/7 5/13 -2/7 -8/29 12/31 -2/7 -1/4 7/18 -3/11 2/5 -2/7 -1/4 5/12 -6/23 -1/4 3/7 -1/4 7/16 -1/4 -6/25 18/41 -1/4 -6/25 11/25 -1/4 4/9 -5/21 -4/17 5/11 -2/9 6/13 -1/4 -2/9 1/2 -2/9 -1/5 7/13 -1/5 6/11 -1/5 -10/51 17/31 -8/41 11/20 -7/36 -6/31 5/9 -6/31 -4/21 4/7 -2/11 -1/6 19/33 -1/6 15/26 -1/6 0/1 11/19 -1/5 7/12 -1/5 -2/11 17/29 -2/11 0/1 10/17 -1/5 -4/21 3/5 -2/11 11/18 -2/11 -3/17 19/31 -1/6 27/44 -2/11 -1/6 8/13 -2/11 -1/6 13/21 -2/11 -4/23 18/29 -6/35 -1/6 5/8 -1/6 0/1 12/19 -5/27 -2/11 7/11 -2/11 -4/23 2/3 -1/6 9/13 -2/13 0/1 25/36 -2/13 -1/7 41/59 -1/7 16/23 -1/7 0/1 7/10 -1/6 -2/13 19/27 -2/13 0/1 12/17 -1/6 -2/13 17/24 -1/6 0/1 22/31 -1/3 0/1 5/7 -1/6 28/39 -4/25 -11/69 23/32 -3/19 18/25 -5/32 -2/13 13/18 -1/6 -2/13 8/11 -1/6 -2/13 27/37 -2/13 19/26 -1/6 11/15 -4/25 -2/13 3/4 -2/13 -1/7 7/9 0/1 25/32 -1/6 -2/13 18/23 -1/7 0/1 29/37 -2/9 0/1 11/14 -1/6 15/19 -4/25 -2/13 4/5 -2/13 -1/7 9/11 -1/7 14/17 -1/7 -6/43 5/6 -1/7 -2/15 6/7 -1/9 0/1 13/15 -1/6 20/23 -2/13 -3/20 7/8 -1/7 15/17 0/1 8/9 -1/7 -2/15 1/1 -2/15 0/1 10/9 -2/15 -1/8 9/8 -2/15 -1/8 8/7 -1/8 23/20 -3/25 -2/17 15/13 -1/9 7/6 -1/6 0/1 6/5 -2/15 -1/8 11/9 -1/8 16/13 -1/8 -6/49 5/4 -1/8 -2/17 24/19 -5/42 -2/17 19/15 -2/17 -4/35 33/26 -2/17 -1/9 14/11 -1/9 37/29 -2/21 0/1 60/47 -1/5 0/1 23/18 -1/8 0/1 9/7 0/1 22/17 -1/7 0/1 35/27 -2/15 0/1 13/10 -2/15 -1/8 4/3 -1/8 -2/17 23/17 -2/17 19/14 -2/17 -5/43 15/11 -2/17 -4/35 26/19 -1/9 11/8 -2/17 -1/9 29/21 -1/9 18/13 -2/17 -1/9 43/31 -4/33 -2/17 68/49 -9/76 -2/17 93/67 -2/17 25/18 -2/17 -5/43 7/5 -1/9 31/22 -1/12 0/1 86/61 -1/1 0/1 55/39 -2/13 0/1 24/17 -1/9 0/1 41/29 -1/8 17/12 -2/17 -1/9 27/19 -2/17 0/1 37/26 -1/8 -2/17 10/7 -2/17 -1/9 3/2 -1/9 14/9 -1/9 -2/19 39/25 -4/37 25/16 -4/37 -3/28 61/39 -3/28 36/23 -3/28 -2/19 47/30 -5/47 -2/19 11/7 -4/37 -2/19 8/5 -1/9 0/1 37/23 -1/9 29/18 -1/9 -6/55 21/13 -4/37 -2/19 76/47 -2/19 -5/48 55/34 -2/19 -1/10 34/21 -1/9 13/8 -1/9 -2/19 44/27 -1/9 -2/19 31/19 -1/9 80/49 -1/9 -6/55 49/30 -4/37 -3/28 18/11 -3/28 -2/19 5/3 -2/19 17/10 -4/39 -1/10 12/7 -2/19 -1/10 31/18 -2/19 -1/10 19/11 -1/10 45/26 -1/10 -2/21 26/15 -1/9 0/1 7/4 -1/9 -2/19 16/9 -3/29 25/14 -7/68 -4/39 59/33 -7/68 34/19 -19/185 -4/39 9/5 -4/39 -6/59 20/11 -6/59 -7/69 11/6 -10/99 -1/10 13/7 -1/10 15/8 -1/10 -14/141 2/1 -1/10 -2/21 15/7 -2/21 -4/43 28/13 -4/43 -1/11 41/19 -1/11 13/6 -2/21 -1/11 24/11 -1/11 11/5 -2/21 20/9 -2/21 -3/32 9/4 -4/43 -5/54 7/3 -1/11 19/8 -8/89 -7/78 31/13 -1/11 43/18 -1/11 -6/67 98/41 -6/67 -5/56 55/23 -6/67 -4/45 12/5 -1/11 -6/67 41/17 -6/67 -4/45 29/12 -5/56 -4/45 46/19 -1/11 17/7 -4/45 5/2 -1/11 -2/23 23/9 -4/45 41/16 -3/34 -2/23 18/7 -3/34 67/26 -19/216 -8/91 49/19 -5/57 31/12 -1/11 -2/23 44/17 -3/34 -2/23 101/39 -3/34 57/22 -3/34 -8/91 13/5 -8/91 -2/23 21/8 -13/149 -2/23 29/11 -2/23 37/14 -2/23 -23/265 8/3 -2/23 -5/58 19/7 -10/117 -4/47 68/25 -27/317 -4/47 117/43 -4/47 166/61 -4/47 -61/717 49/18 -4/47 -17/200 30/11 -4/47 -5/59 41/15 -4/47 11/4 -1/12 36/13 -1/11 -2/23 61/22 -5/57 -2/23 147/53 -2/23 86/31 -2/23 -9/104 25/9 -2/23 -4/47 14/5 -2/23 -1/12 3/1 -1/12 16/5 -1/12 -2/25 61/19 -2/25 106/33 -2/25 -3/38 45/14 -2/25 -1/13 29/9 -2/25 0/1 42/13 -1/12 13/4 -1/12 -2/25 23/7 -1/12 10/3 -4/49 -3/37 17/5 -8/99 -2/25 24/7 -11/137 -2/25 31/9 -2/25 38/11 -2/25 -17/213 7/2 -2/25 -3/38 39/11 -3/38 32/9 -7/89 -4/51 25/7 -4/51 18/5 -6/77 -1/13 47/13 -1/13 29/8 -1/13 -6/79 11/3 -2/25 0/1 37/10 -3/37 -2/25 63/17 -2/25 26/7 -2/25 -3/38 15/4 -2/25 -1/13 4/1 -1/13 17/4 -1/13 -2/27 47/11 -4/53 -2/27 30/7 -2/27 -1/14 13/3 -2/27 22/5 -1/15 0/1 9/2 -1/13 -2/27 32/7 -1/13 0/1 55/12 -1/10 0/1 23/5 -1/13 14/3 -1/13 -2/27 33/7 -2/27 52/11 -2/27 -3/41 19/4 -2/27 -1/14 5/1 -2/27 0/1 21/4 -1/14 16/3 -2/27 -1/14 11/2 -4/55 -1/14 17/3 -1/14 23/4 -1/14 -8/113 6/1 -1/14 -2/29 13/2 -1/15 33/5 -2/29 0/1 20/3 -2/29 -1/15 7/1 0/1 22/3 -1/14 15/2 -2/27 -1/14 8/1 -2/29 -1/15 9/1 -1/15 1/0 -1/16 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(149,70,530,249) (-1/2,-7/15) -> (7/25,9/32) Hyperbolic Matrix(147,68,-668,-309) (-7/15,-6/13) -> (-2/9,-9/41) Hyperbolic Matrix(367,168,592,271) (-6/13,-5/11) -> (13/21,18/29) Hyperbolic Matrix(727,328,512,231) (-5/11,-9/20) -> (17/12,27/19) Hyperbolic Matrix(361,162,-1522,-683) (-9/20,-13/29) -> (-5/21,-9/38) Hyperbolic Matrix(795,356,364,163) (-13/29,-4/9) -> (24/11,11/5) Hyperbolic Matrix(785,346,574,253) (-4/9,-11/25) -> (15/11,26/19) Hyperbolic Matrix(355,156,644,283) (-11/25,-7/16) -> (11/20,5/9) Hyperbolic Matrix(565,246,-1486,-647) (-7/16,-10/23) -> (-8/21,-19/50) Hyperbolic Matrix(281,122,638,277) (-10/23,-3/7) -> (11/25,4/9) Hyperbolic Matrix(489,208,1112,473) (-3/7,-14/33) -> (18/41,11/25) Hyperbolic Matrix(1109,470,210,89) (-14/33,-11/26) -> (21/4,16/3) Hyperbolic Matrix(275,116,-1036,-437) (-11/26,-8/19) -> (-4/15,-9/34) Hyperbolic Matrix(343,144,-1584,-665) (-8/19,-13/31) -> (-5/23,-8/37) Hyperbolic Matrix(2271,952,1448,607) (-13/31,-31/74) -> (47/30,11/7) Hyperbolic Matrix(1581,662,1378,577) (-31/74,-18/43) -> (8/7,23/20) Hyperbolic Matrix(67,28,-548,-229) (-18/43,-5/12) -> (-1/8,-2/17) Hyperbolic Matrix(207,86,-686,-285) (-5/12,-12/29) -> (-10/33,-3/10) Hyperbolic Matrix(271,112,888,367) (-12/29,-7/17) -> (7/23,4/13) Hyperbolic Matrix(205,84,676,277) (-7/17,-9/22) -> (3/10,7/23) Hyperbolic Matrix(201,82,-1282,-523) (-9/22,-11/27) -> (-3/19,-5/32) Hyperbolic Matrix(875,356,204,83) (-11/27,-2/5) -> (30/7,13/3) Hyperbolic Matrix(199,78,722,283) (-2/5,-9/23) -> (3/11,8/29) Hyperbolic Matrix(195,76,-916,-357) (-9/23,-7/18) -> (-3/14,-7/33) Hyperbolic Matrix(197,76,324,125) (-7/18,-5/13) -> (3/5,11/18) Hyperbolic Matrix(193,74,326,125) (-5/13,-8/21) -> (10/17,3/5) Hyperbolic Matrix(453,172,-2452,-931) (-19/50,-11/29) -> (-5/27,-7/38) Hyperbolic Matrix(191,72,-512,-193) (-11/29,-3/8) -> (-3/8,-13/35) Parabolic Matrix(1527,566,634,235) (-13/35,-10/27) -> (12/5,41/17) Hyperbolic Matrix(887,328,192,71) (-10/27,-7/19) -> (23/5,14/3) Hyperbolic Matrix(1457,536,1264,465) (-7/19,-25/68) -> (23/20,15/13) Hyperbolic Matrix(5437,1998,1962,721) (-25/68,-18/49) -> (36/13,61/22) Hyperbolic Matrix(1957,718,1202,441) (-18/49,-11/30) -> (13/8,44/27) Hyperbolic Matrix(945,346,254,93) (-11/30,-4/11) -> (26/7,15/4) Hyperbolic Matrix(127,46,-566,-205) (-4/11,-9/25) -> (-7/31,-2/9) Hyperbolic Matrix(1813,652,748,269) (-9/25,-14/39) -> (46/19,17/7) Hyperbolic Matrix(2621,940,1620,581) (-14/39,-5/14) -> (55/34,34/21) Hyperbolic Matrix(309,110,250,89) (-5/14,-6/17) -> (16/13,5/4) Hyperbolic Matrix(125,44,-804,-283) (-6/17,-7/20) -> (-5/32,-2/13) Hyperbolic Matrix(1901,662,738,257) (-7/20,-8/23) -> (18/7,67/26) Hyperbolic Matrix(793,274,246,85) (-8/23,-1/3) -> (29/9,42/13) Hyperbolic Matrix(765,244,116,37) (-1/3,-7/22) -> (13/2,33/5) Hyperbolic Matrix(1053,334,1466,465) (-7/22,-6/19) -> (28/39,23/32) Hyperbolic Matrix(235,74,-994,-313) (-6/19,-5/16) -> (-9/38,-4/17) Hyperbolic Matrix(289,90,350,109) (-5/16,-4/13) -> (14/17,5/6) Hyperbolic Matrix(1439,440,520,159) (-4/13,-11/36) -> (11/4,36/13) Hyperbolic Matrix(1729,528,632,193) (-11/36,-7/23) -> (41/15,11/4) Hyperbolic Matrix(1609,488,1032,313) (-7/23,-10/33) -> (14/9,39/25) Hyperbolic Matrix(229,68,852,253) (-3/10,-8/27) -> (4/15,7/26) Hyperbolic Matrix(1081,320,1760,521) (-8/27,-13/44) -> (27/44,8/13) Hyperbolic Matrix(6699,1978,4142,1223) (-13/44,-18/61) -> (76/47,55/34) Hyperbolic Matrix(1133,334,1306,385) (-18/61,-5/17) -> (13/15,20/23) Hyperbolic Matrix(171,50,790,231) (-5/17,-7/24) -> (3/14,5/23) Hyperbolic Matrix(111,32,-392,-113) (-7/24,-2/7) -> (-2/7,-9/32) Parabolic Matrix(1445,406,1114,313) (-9/32,-7/25) -> (35/27,13/10) Hyperbolic Matrix(165,46,-886,-247) (-7/25,-5/18) -> (-3/16,-5/27) Hyperbolic Matrix(277,76,164,45) (-5/18,-3/11) -> (5/3,17/10) Hyperbolic Matrix(273,74,166,45) (-3/11,-4/15) -> (18/11,5/3) Hyperbolic Matrix(1195,316,1524,403) (-9/34,-5/19) -> (29/37,11/14) Hyperbolic Matrix(595,156,164,43) (-5/19,-1/4) -> (29/8,11/3) Hyperbolic Matrix(209,50,790,189) (-1/4,-5/21) -> (5/19,9/34) Hyperbolic Matrix(521,122,158,37) (-4/17,-3/13) -> (23/7,10/3) Hyperbolic Matrix(675,154,206,47) (-3/13,-5/22) -> (13/4,23/7) Hyperbolic Matrix(929,210,1190,269) (-5/22,-7/31) -> (7/9,25/32) Hyperbolic Matrix(767,168,872,191) (-9/41,-7/32) -> (7/8,15/17) Hyperbolic Matrix(1025,224,1176,257) (-7/32,-12/55) -> (20/23,7/8) Hyperbolic Matrix(3275,714,766,167) (-12/55,-5/23) -> (47/11,30/7) Hyperbolic Matrix(1481,320,560,121) (-8/37,-3/14) -> (37/14,8/3) Hyperbolic Matrix(1165,246,914,193) (-7/33,-4/19) -> (14/11,37/29) Hyperbolic Matrix(963,202,758,159) (-4/19,-5/24) -> (33/26,14/11) Hyperbolic Matrix(959,198,402,83) (-5/24,-1/5) -> (31/13,43/18) Hyperbolic Matrix(591,112,248,47) (-1/5,-3/16) -> (19/8,31/13) Hyperbolic Matrix(1521,280,440,81) (-7/38,-2/11) -> (38/11,7/2) Hyperbolic Matrix(439,78,242,43) (-2/11,-3/17) -> (9/5,20/11) Hyperbolic Matrix(389,68,532,93) (-3/17,-1/6) -> (19/26,11/15) Hyperbolic Matrix(523,84,716,115) (-1/6,-3/19) -> (27/37,19/26) Hyperbolic Matrix(331,50,470,71) (-2/13,-1/7) -> (19/27,12/17) Hyperbolic Matrix(371,50,230,31) (-1/7,-1/8) -> (29/18,21/13) Hyperbolic Matrix(317,36,44,5) (-2/17,-1/9) -> (7/1,22/3) Hyperbolic Matrix(313,32,88,9) (-1/9,0/1) -> (32/9,25/7) Hyperbolic Matrix(253,-26,146,-15) (0/1,1/8) -> (45/26,26/15) Hyperbolic Matrix(213,-28,388,-51) (1/8,1/7) -> (17/31,11/20) Hyperbolic Matrix(173,-28,68,-11) (1/7,1/6) -> (5/2,23/9) Hyperbolic Matrix(715,-124,444,-77) (1/6,3/17) -> (37/23,29/18) Hyperbolic Matrix(543,-98,338,-61) (3/17,2/11) -> (8/5,37/23) Hyperbolic Matrix(237,-44,404,-75) (2/11,1/5) -> (17/29,10/17) Hyperbolic Matrix(165,-34,34,-7) (1/5,3/14) -> (19/4,5/1) Hyperbolic Matrix(263,-58,458,-101) (5/23,2/9) -> (4/7,19/33) Hyperbolic Matrix(359,-82,162,-37) (2/9,3/13) -> (11/5,20/9) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(1929,-512,1232,-327) (9/34,4/15) -> (36/23,47/30) Hyperbolic Matrix(693,-188,188,-51) (7/26,3/11) -> (11/3,37/10) Hyperbolic Matrix(471,-130,250,-69) (8/29,5/18) -> (15/8,2/1) Hyperbolic Matrix(1439,-402,562,-157) (5/18,7/25) -> (23/9,41/16) Hyperbolic Matrix(2903,-818,1778,-501) (9/32,2/7) -> (80/49,49/30) Hyperbolic Matrix(155,-46,246,-73) (2/7,3/10) -> (5/8,12/19) Hyperbolic Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(1181,-418,178,-63) (6/17,11/31) -> (33/5,20/3) Hyperbolic Matrix(1801,-640,560,-199) (11/31,5/14) -> (45/14,29/9) Hyperbolic Matrix(619,-222,382,-137) (5/14,4/11) -> (34/21,13/8) Hyperbolic Matrix(205,-76,116,-43) (4/11,3/8) -> (7/4,16/9) Hyperbolic Matrix(377,-144,144,-55) (3/8,5/13) -> (13/5,21/8) Hyperbolic Matrix(491,-190,230,-89) (5/13,12/31) -> (2/1,15/7) Hyperbolic Matrix(1037,-402,1442,-559) (12/31,7/18) -> (23/32,18/25) Hyperbolic Matrix(173,-68,28,-11) (7/18,2/5) -> (6/1,13/2) Hyperbolic Matrix(113,-46,86,-35) (2/5,5/12) -> (13/10,4/3) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(529,-232,472,-207) (7/16,18/41) -> (10/9,9/8) Hyperbolic Matrix(359,-162,82,-37) (4/9,5/11) -> (13/3,22/5) Hyperbolic Matrix(439,-202,602,-277) (5/11,6/13) -> (8/11,27/37) Hyperbolic Matrix(491,-230,190,-89) (6/13,1/2) -> (31/12,44/17) Hyperbolic Matrix(471,-250,130,-69) (1/2,7/13) -> (47/13,29/8) Hyperbolic Matrix(751,-408,208,-113) (7/13,6/11) -> (18/5,47/13) Hyperbolic Matrix(413,-226,466,-255) (6/11,17/31) -> (15/17,8/9) Hyperbolic Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(2359,-1360,1320,-761) (19/33,15/26) -> (25/14,59/33) Hyperbolic Matrix(253,-146,26,-15) (15/26,11/19) -> (9/1,1/0) Hyperbolic Matrix(557,-324,404,-235) (11/19,7/12) -> (11/8,29/21) Hyperbolic Matrix(1185,-694,934,-547) (7/12,17/29) -> (19/15,33/26) Hyperbolic Matrix(1265,-774,894,-547) (11/18,19/31) -> (41/29,17/12) Hyperbolic Matrix(1933,-1186,546,-335) (19/31,27/44) -> (7/2,39/11) Hyperbolic Matrix(619,-382,222,-137) (8/13,13/21) -> (25/9,14/5) Hyperbolic Matrix(715,-444,124,-77) (18/29,5/8) -> (23/4,6/1) Hyperbolic Matrix(587,-372,172,-109) (12/19,7/11) -> (17/5,24/7) Hyperbolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(1913,-1328,448,-311) (9/13,25/36) -> (17/4,47/11) Hyperbolic Matrix(2243,-1558,1038,-721) (25/36,41/59) -> (41/19,13/6) Hyperbolic Matrix(2595,-1804,1204,-837) (41/59,16/23) -> (28/13,41/19) Hyperbolic Matrix(755,-526,966,-673) (16/23,7/10) -> (25/32,18/23) Hyperbolic Matrix(1269,-892,892,-627) (7/10,19/27) -> (27/19,37/26) Hyperbolic Matrix(1265,-894,774,-547) (12/17,17/24) -> (49/30,18/11) Hyperbolic Matrix(2153,-1526,1686,-1195) (17/24,22/31) -> (60/47,23/18) Hyperbolic Matrix(351,-250,490,-349) (22/31,5/7) -> (5/7,28/39) Parabolic Matrix(557,-402,442,-319) (18/25,13/18) -> (5/4,24/19) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(345,-254,254,-187) (11/15,3/4) -> (19/14,15/11) Hyperbolic Matrix(113,-86,46,-35) (3/4,7/9) -> (17/7,5/2) Hyperbolic Matrix(2153,-1686,1526,-1195) (18/23,29/37) -> (55/39,24/17) Hyperbolic Matrix(469,-370,90,-71) (11/14,15/19) -> (5/1,21/4) Hyperbolic Matrix(557,-442,402,-319) (15/19,4/5) -> (18/13,43/31) Hyperbolic Matrix(199,-162,242,-197) (4/5,9/11) -> (9/11,14/17) Parabolic Matrix(195,-164,44,-37) (5/6,6/7) -> (22/5,9/2) Hyperbolic Matrix(923,-796,516,-445) (6/7,13/15) -> (59/33,34/19) Hyperbolic Matrix(507,-452,212,-189) (8/9,1/1) -> (55/23,12/5) Hyperbolic Matrix(593,-648,248,-271) (1/1,10/9) -> (98/41,55/23) Hyperbolic Matrix(281,-318,38,-43) (9/8,8/7) -> (22/3,15/2) Hyperbolic Matrix(853,-986,186,-215) (15/13,7/6) -> (55/12,23/5) Hyperbolic Matrix(165,-194,74,-87) (7/6,6/5) -> (20/9,9/4) Hyperbolic Matrix(199,-242,162,-197) (6/5,11/9) -> (11/9,16/13) Parabolic Matrix(1837,-2324,1324,-1675) (24/19,19/15) -> (43/31,68/49) Hyperbolic Matrix(5079,-6482,3602,-4597) (37/29,60/47) -> (86/61,55/39) Hyperbolic Matrix(877,-1122,562,-719) (23/18,9/7) -> (39/25,25/16) Hyperbolic Matrix(907,-1172,332,-429) (9/7,22/17) -> (30/11,41/15) Hyperbolic Matrix(1011,-1310,470,-609) (22/17,35/27) -> (15/7,28/13) Hyperbolic Matrix(631,-850,170,-229) (4/3,23/17) -> (63/17,26/7) Hyperbolic Matrix(1511,-2048,408,-553) (23/17,19/14) -> (37/10,63/17) Hyperbolic Matrix(439,-602,202,-277) (26/19,11/8) -> (13/6,24/11) Hyperbolic Matrix(285,-394,34,-47) (29/21,18/13) -> (8/1,9/1) Hyperbolic Matrix(12965,-17994,4674,-6487) (68/49,93/67) -> (147/53,86/31) Hyperbolic Matrix(6733,-9348,2428,-3371) (93/67,25/18) -> (61/22,147/53) Hyperbolic Matrix(1037,-1442,402,-559) (25/18,7/5) -> (49/19,31/12) Hyperbolic Matrix(1413,-1988,548,-771) (7/5,31/22) -> (67/26,49/19) Hyperbolic Matrix(6641,-9360,2440,-3439) (31/22,86/61) -> (166/61,49/18) Hyperbolic Matrix(1591,-2248,448,-633) (24/17,41/29) -> (39/11,32/9) Hyperbolic Matrix(1485,-2114,314,-447) (37/26,10/7) -> (52/11,19/4) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(3839,-6002,1482,-2317) (25/16,61/39) -> (101/39,57/22) Hyperbolic Matrix(4039,-6320,1560,-2441) (61/39,36/23) -> (44/17,101/39) Hyperbolic Matrix(155,-246,46,-73) (11/7,8/5) -> (10/3,17/5) Hyperbolic Matrix(2293,-3706,826,-1335) (21/13,76/47) -> (86/31,25/9) Hyperbolic Matrix(2357,-3844,1444,-2355) (44/27,31/19) -> (31/19,80/49) Parabolic Matrix(237,-404,44,-75) (17/10,12/7) -> (16/3,11/2) Hyperbolic Matrix(837,-1444,484,-835) (31/18,19/11) -> (19/11,45/26) Parabolic Matrix(263,-458,58,-101) (26/15,7/4) -> (9/2,32/7) Hyperbolic Matrix(905,-1614,374,-667) (16/9,25/14) -> (29/12,46/19) Hyperbolic Matrix(701,-1258,258,-463) (34/19,9/5) -> (19/7,68/25) Hyperbolic Matrix(213,-388,28,-51) (20/11,11/6) -> (15/2,8/1) Hyperbolic Matrix(183,-338,98,-181) (11/6,13/7) -> (13/7,15/8) Parabolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(3753,-8968,1168,-2791) (43/18,98/41) -> (106/33,45/14) Hyperbolic Matrix(1125,-2714,434,-1047) (41/17,29/12) -> (57/22,13/5) Hyperbolic Matrix(763,-1956,236,-605) (41/16,18/7) -> (42/13,13/4) Hyperbolic Matrix(639,-1682,242,-637) (21/8,29/11) -> (29/11,37/14) Parabolic Matrix(10063,-27378,3698,-10061) (68/25,117/43) -> (117/43,166/61) Parabolic Matrix(1181,-3218,258,-703) (49/18,30/11) -> (32/7,55/12) Hyperbolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(2319,-7442,722,-2317) (16/5,61/19) -> (61/19,106/33) Parabolic Matrix(559,-1922,162,-557) (24/7,31/9) -> (31/9,38/11) Parabolic Matrix(175,-626,26,-93) (25/7,18/5) -> (20/3,7/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(463,-2178,98,-461) (14/3,33/7) -> (33/7,52/11) Parabolic Matrix(103,-578,18,-101) (11/2,17/3) -> (17/3,23/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,34,1) Matrix(149,70,530,249) -> Matrix(65,-4,-146,9) Matrix(147,68,-668,-309) -> Matrix(65,-4,374,-23) Matrix(367,168,592,271) -> Matrix(63,-4,-362,23) Matrix(727,328,512,231) -> Matrix(1,0,-24,1) Matrix(361,162,-1522,-683) -> Matrix(63,-4,394,-25) Matrix(795,356,364,163) -> Matrix(1,0,-26,1) Matrix(785,346,574,253) -> Matrix(59,-4,-516,35) Matrix(355,156,644,283) -> Matrix(61,-4,-320,21) Matrix(565,246,-1486,-647) -> Matrix(57,-4,670,-47) Matrix(281,122,638,277) -> Matrix(113,-8,-466,33) Matrix(489,208,1112,473) -> Matrix(57,-4,-242,17) Matrix(1109,470,210,89) -> Matrix(55,-4,-756,55) Matrix(275,116,-1036,-437) -> Matrix(109,-8,804,-59) Matrix(343,144,-1584,-665) -> Matrix(215,-16,1196,-89) Matrix(2271,952,1448,607) -> Matrix(161,-12,-1516,113) Matrix(1581,662,1378,577) -> Matrix(107,-8,-896,67) Matrix(67,28,-548,-229) -> Matrix(53,-4,146,-11) Matrix(207,86,-686,-285) -> Matrix(53,-4,464,-35) Matrix(271,112,888,367) -> Matrix(53,-4,-172,13) Matrix(205,84,676,277) -> Matrix(103,-8,-296,23) Matrix(201,82,-1282,-523) -> Matrix(51,-4,166,-13) Matrix(875,356,204,83) -> Matrix(1,0,-26,1) Matrix(199,78,722,283) -> Matrix(47,-4,-82,7) Matrix(195,76,-916,-357) -> Matrix(93,-8,500,-43) Matrix(197,76,324,125) -> Matrix(47,-4,-270,23) Matrix(193,74,326,125) -> Matrix(45,-4,-236,21) Matrix(453,172,-2452,-931) -> Matrix(137,-12,628,-55) Matrix(191,72,-512,-193) -> Matrix(45,-4,484,-43) Matrix(1527,566,634,235) -> Matrix(45,-4,-506,45) Matrix(887,328,192,71) -> Matrix(1,0,-24,1) Matrix(1457,536,1264,465) -> Matrix(43,-4,-376,35) Matrix(5437,1998,1962,721) -> Matrix(1,0,-22,1) Matrix(1957,718,1202,441) -> Matrix(1,0,-20,1) Matrix(945,346,254,93) -> Matrix(43,-4,-548,51) Matrix(127,46,-566,-205) -> Matrix(41,-4,236,-23) Matrix(1813,652,748,269) -> Matrix(45,-4,-506,45) Matrix(2621,940,1620,581) -> Matrix(1,0,-20,1) Matrix(309,110,250,89) -> Matrix(41,-4,-338,33) Matrix(125,44,-804,-283) -> Matrix(1,0,-6,1) Matrix(1901,662,738,257) -> Matrix(83,-8,-944,91) Matrix(793,274,246,85) -> Matrix(1,0,-22,1) Matrix(765,244,116,37) -> Matrix(1,0,-24,1) Matrix(1053,334,1466,465) -> Matrix(33,-4,-206,25) Matrix(235,74,-994,-313) -> Matrix(39,-4,244,-25) Matrix(289,90,350,109) -> Matrix(37,-4,-268,29) Matrix(1439,440,520,159) -> Matrix(1,0,-20,1) Matrix(1729,528,632,193) -> Matrix(31,-4,-364,47) Matrix(1609,488,1032,313) -> Matrix(37,-4,-342,37) Matrix(229,68,852,253) -> Matrix(33,-4,-74,9) Matrix(1081,320,1760,521) -> Matrix(1,0,-14,1) Matrix(6699,1978,4142,1223) -> Matrix(1,0,-18,1) Matrix(1133,334,1306,385) -> Matrix(33,-4,-206,25) Matrix(171,50,790,231) -> Matrix(1,0,-10,1) Matrix(111,32,-392,-113) -> Matrix(33,-4,256,-31) Matrix(1445,406,1114,313) -> Matrix(31,-4,-240,31) Matrix(165,46,-886,-247) -> Matrix(29,-4,138,-19) Matrix(277,76,164,45) -> Matrix(31,-4,-302,39) Matrix(273,74,166,45) -> Matrix(29,-4,-268,37) Matrix(1195,316,1524,403) -> Matrix(29,-4,-152,21) Matrix(595,156,164,43) -> Matrix(29,-4,-384,53) Matrix(209,50,790,189) -> Matrix(25,-4,-56,9) Matrix(521,122,158,37) -> Matrix(49,-8,-594,97) Matrix(675,154,206,47) -> Matrix(23,-4,-270,47) Matrix(929,210,1190,269) -> Matrix(23,-4,-132,23) Matrix(767,168,872,191) -> Matrix(23,-4,-178,31) Matrix(1025,224,1176,257) -> Matrix(45,-8,-298,53) Matrix(3275,714,766,167) -> Matrix(23,-4,-316,55) Matrix(1481,320,560,121) -> Matrix(199,-36,-2294,415) Matrix(1165,246,914,193) -> Matrix(21,-4,-194,37) Matrix(963,202,758,159) -> Matrix(1,0,-14,1) Matrix(959,198,402,83) -> Matrix(41,-8,-456,89) Matrix(591,112,248,47) -> Matrix(21,-4,-236,45) Matrix(1521,280,440,81) -> Matrix(127,-28,-1592,351) Matrix(439,78,242,43) -> Matrix(15,-4,-146,39) Matrix(389,68,532,93) -> Matrix(17,-4,-106,25) Matrix(523,84,716,115) -> Matrix(1,0,-10,1) Matrix(331,50,470,71) -> Matrix(1,0,-10,1) Matrix(371,50,230,31) -> Matrix(13,-4,-120,37) Matrix(317,36,44,5) -> Matrix(1,0,-16,1) Matrix(313,32,88,9) -> Matrix(11,-4,-140,51) Matrix(253,-26,146,-15) -> Matrix(1,0,-10,1) Matrix(213,-28,388,-51) -> Matrix(7,8,-36,-41) Matrix(173,-28,68,-11) -> Matrix(3,4,-34,-45) Matrix(715,-124,444,-77) -> Matrix(7,8,-64,-73) Matrix(543,-98,338,-61) -> Matrix(5,4,-44,-35) Matrix(237,-44,404,-75) -> Matrix(1,0,-4,1) Matrix(165,-34,34,-7) -> Matrix(1,0,-12,1) Matrix(263,-58,458,-101) -> Matrix(1,0,-4,1) Matrix(359,-82,162,-37) -> Matrix(5,4,-54,-43) Matrix(33,-8,128,-31) -> Matrix(7,4,-16,-9) Matrix(1929,-512,1232,-327) -> Matrix(11,4,-102,-37) Matrix(693,-188,188,-51) -> Matrix(1,0,-10,1) Matrix(471,-130,250,-69) -> Matrix(15,8,-152,-81) Matrix(1439,-402,562,-157) -> Matrix(35,16,-396,-181) Matrix(2903,-818,1778,-501) -> Matrix(37,16,-340,-147) Matrix(155,-46,246,-73) -> Matrix(11,4,-58,-21) Matrix(31,-10,90,-29) -> Matrix(11,4,-36,-13) Matrix(1181,-418,178,-63) -> Matrix(13,4,-192,-59) Matrix(1801,-640,560,-199) -> Matrix(13,4,-166,-51) Matrix(619,-222,382,-137) -> Matrix(1,0,-6,1) Matrix(205,-76,116,-43) -> Matrix(27,8,-260,-77) Matrix(377,-144,144,-55) -> Matrix(57,16,-652,-183) Matrix(491,-190,230,-89) -> Matrix(15,4,-154,-41) Matrix(1037,-402,1442,-559) -> Matrix(43,12,-276,-77) Matrix(173,-68,28,-11) -> Matrix(15,4,-214,-57) Matrix(113,-46,86,-35) -> Matrix(15,4,-124,-33) Matrix(85,-36,196,-83) -> Matrix(47,12,-192,-49) Matrix(529,-232,472,-207) -> Matrix(33,8,-260,-63) Matrix(359,-162,82,-37) -> Matrix(17,4,-234,-55) Matrix(439,-202,602,-277) -> Matrix(1,0,-2,1) Matrix(491,-230,190,-89) -> Matrix(19,4,-214,-45) Matrix(471,-250,130,-69) -> Matrix(39,8,-512,-105) Matrix(751,-408,208,-113) -> Matrix(81,16,-1048,-207) Matrix(413,-226,466,-255) -> Matrix(41,8,-282,-55) Matrix(205,-116,76,-43) -> Matrix(43,8,-500,-93) Matrix(2359,-1360,1320,-761) -> Matrix(17,4,-166,-39) Matrix(253,-146,26,-15) -> Matrix(1,0,-10,1) Matrix(557,-324,404,-235) -> Matrix(21,4,-184,-35) Matrix(1185,-694,934,-547) -> Matrix(21,4,-184,-35) Matrix(1265,-774,894,-547) -> Matrix(23,4,-190,-33) Matrix(1933,-1186,546,-335) -> Matrix(21,4,-268,-51) Matrix(619,-382,222,-137) -> Matrix(1,0,-6,1) Matrix(715,-444,124,-77) -> Matrix(47,8,-664,-113) Matrix(587,-372,172,-109) -> Matrix(67,12,-832,-149) Matrix(49,-32,72,-47) -> Matrix(23,4,-144,-25) Matrix(1913,-1328,448,-311) -> Matrix(27,4,-358,-53) Matrix(2243,-1558,1038,-721) -> Matrix(1,0,-4,1) Matrix(2595,-1804,1204,-837) -> Matrix(29,4,-312,-43) Matrix(755,-526,966,-673) -> Matrix(1,0,0,1) Matrix(1269,-892,892,-627) -> Matrix(1,0,-2,1) Matrix(1265,-894,774,-547) -> Matrix(27,4,-250,-37) Matrix(2153,-1526,1686,-1195) -> Matrix(1,0,-2,1) Matrix(351,-250,490,-349) -> Matrix(23,4,-144,-25) Matrix(557,-402,442,-319) -> Matrix(1,0,-2,1) Matrix(557,-404,324,-235) -> Matrix(25,4,-244,-39) Matrix(345,-254,254,-187) -> Matrix(51,8,-440,-69) Matrix(113,-86,46,-35) -> Matrix(27,4,-304,-45) Matrix(2153,-1686,1526,-1195) -> Matrix(1,0,-2,1) Matrix(469,-370,90,-71) -> Matrix(25,4,-344,-55) Matrix(557,-442,402,-319) -> Matrix(1,0,-2,1) Matrix(199,-162,242,-197) -> Matrix(55,8,-392,-57) Matrix(195,-164,44,-37) -> Matrix(1,0,-6,1) Matrix(923,-796,516,-445) -> Matrix(17,4,-166,-39) Matrix(507,-452,212,-189) -> Matrix(27,4,-304,-45) Matrix(593,-648,248,-271) -> Matrix(27,4,-304,-45) Matrix(281,-318,38,-43) -> Matrix(1,0,-6,1) Matrix(853,-986,186,-215) -> Matrix(1,0,-4,1) Matrix(165,-194,74,-87) -> Matrix(29,4,-312,-43) Matrix(199,-242,162,-197) -> Matrix(63,8,-512,-65) Matrix(1837,-2324,1324,-1675) -> Matrix(69,8,-578,-67) Matrix(5079,-6482,3602,-4597) -> Matrix(1,0,4,1) Matrix(877,-1122,562,-719) -> Matrix(35,4,-324,-37) Matrix(907,-1172,332,-429) -> Matrix(33,4,-388,-47) Matrix(1011,-1310,470,-609) -> Matrix(29,4,-312,-43) Matrix(631,-850,170,-229) -> Matrix(67,8,-846,-101) Matrix(1511,-2048,408,-553) -> Matrix(137,16,-1704,-199) Matrix(439,-602,202,-277) -> Matrix(1,0,-2,1) Matrix(285,-394,34,-47) -> Matrix(1,0,-6,1) Matrix(12965,-17994,4674,-6487) -> Matrix(305,36,-3516,-415) Matrix(6733,-9348,2428,-3371) -> Matrix(171,20,-1958,-229) Matrix(1037,-1442,402,-559) -> Matrix(103,12,-1176,-137) Matrix(1413,-1988,548,-771) -> Matrix(77,8,-876,-91) Matrix(6641,-9360,2440,-3439) -> Matrix(65,4,-764,-47) Matrix(1591,-2248,448,-633) -> Matrix(29,4,-370,-51) Matrix(1485,-2114,314,-447) -> Matrix(33,4,-454,-55) Matrix(49,-72,32,-47) -> Matrix(35,4,-324,-37) Matrix(3839,-6002,1482,-2317) -> Matrix(335,36,-3806,-409) Matrix(4039,-6320,1560,-2441) -> Matrix(1,0,-2,1) Matrix(155,-246,46,-73) -> Matrix(39,4,-478,-49) Matrix(2293,-3706,826,-1335) -> Matrix(75,8,-872,-93) Matrix(2357,-3844,1444,-2355) -> Matrix(35,4,-324,-37) Matrix(237,-404,44,-75) -> Matrix(1,0,-4,1) Matrix(837,-1444,484,-835) -> Matrix(39,4,-400,-41) Matrix(263,-458,58,-101) -> Matrix(1,0,-4,1) Matrix(905,-1614,374,-667) -> Matrix(77,8,-876,-91) Matrix(701,-1258,258,-463) -> Matrix(313,32,-3668,-375) Matrix(213,-388,28,-51) -> Matrix(79,8,-1116,-113) Matrix(183,-338,98,-181) -> Matrix(239,24,-2400,-241) Matrix(85,-196,36,-83) -> Matrix(131,12,-1452,-133) Matrix(3753,-8968,1168,-2791) -> Matrix(89,8,-1146,-103) Matrix(1125,-2714,434,-1047) -> Matrix(313,28,-3566,-319) Matrix(763,-1956,236,-605) -> Matrix(45,4,-574,-51) Matrix(639,-1682,242,-637) -> Matrix(827,72,-9522,-829) Matrix(10063,-27378,3698,-10061) -> Matrix(4135,352,-48598,-4137) Matrix(1181,-3218,258,-703) -> Matrix(47,4,-670,-57) Matrix(31,-90,10,-29) -> Matrix(47,4,-576,-49) Matrix(2319,-7442,722,-2317) -> Matrix(99,8,-1250,-101) Matrix(559,-1922,162,-557) -> Matrix(699,56,-8750,-701) Matrix(175,-626,26,-93) -> Matrix(51,4,-778,-61) Matrix(33,-128,8,-31) -> Matrix(51,4,-676,-53) Matrix(463,-2178,98,-461) -> Matrix(107,8,-1458,-109) Matrix(103,-578,18,-101) -> Matrix(167,12,-2352,-169) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 Degree of the the map X: 64 Degree of the the map Y: 192 ----------------------------------------------------------------------- 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): 576 Minimal number of generators: 97 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: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/7 1/4 1/3 3/7 3/5 2/3 5/7 1/1 11/9 9/7 23/17 93/67 7/5 3/2 61/39 5/3 19/11 16/9 13/7 2/1 11/5 7/3 17/7 18/7 13/5 29/11 117/43 11/4 3/1 61/19 31/9 11/3 15/4 4/1 13/3 9/2 14/3 33/7 5/1 11/2 17/3 6/1 13/2 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 0/1 1/1 1/8 -2/1 1/0 1/7 0/1 1/6 -2/1 -1/1 3/17 -1/1 2/11 -1/1 -4/5 1/5 -2/3 0/1 3/14 -2/3 -1/2 2/9 -2/3 -1/2 3/13 -2/3 1/4 -1/2 5/19 -2/5 4/15 -1/2 -2/5 3/11 -2/5 0/1 5/18 -1/2 -6/13 7/25 -4/9 2/7 -3/7 -2/5 3/10 -3/8 -4/11 4/13 -2/5 -1/3 1/3 -1/3 6/17 -1/3 -2/7 11/31 -4/13 -2/7 5/14 -1/3 -2/7 4/11 -1/3 3/8 -5/17 -2/7 5/13 -2/7 -8/29 12/31 -2/7 -1/4 7/18 -3/11 2/5 -2/7 -1/4 5/12 -6/23 -1/4 3/7 -1/4 7/16 -1/4 -6/25 4/9 -5/21 -4/17 5/11 -2/9 6/13 -1/4 -2/9 1/2 -2/9 -1/5 7/13 -1/5 6/11 -1/5 -10/51 5/9 -6/31 -4/21 4/7 -2/11 -1/6 15/26 -1/6 0/1 11/19 -1/5 7/12 -1/5 -2/11 3/5 -2/11 8/13 -2/11 -1/6 13/21 -2/11 -4/23 5/8 -1/6 0/1 12/19 -5/27 -2/11 7/11 -2/11 -4/23 2/3 -1/6 9/13 -2/13 0/1 25/36 -2/13 -1/7 41/59 -1/7 16/23 -1/7 0/1 7/10 -1/6 -2/13 12/17 -1/6 -2/13 17/24 -1/6 0/1 22/31 -1/3 0/1 5/7 -1/6 23/32 -3/19 18/25 -5/32 -2/13 13/18 -1/6 -2/13 8/11 -1/6 -2/13 11/15 -4/25 -2/13 3/4 -2/13 -1/7 7/9 0/1 18/23 -1/7 0/1 11/14 -1/6 15/19 -4/25 -2/13 4/5 -2/13 -1/7 9/11 -1/7 5/6 -1/7 -2/15 6/7 -1/9 0/1 13/15 -1/6 7/8 -1/7 8/9 -1/7 -2/15 1/1 -2/15 0/1 9/8 -2/15 -1/8 8/7 -1/8 15/13 -1/9 7/6 -1/6 0/1 6/5 -2/15 -1/8 11/9 -1/8 5/4 -1/8 -2/17 24/19 -5/42 -2/17 19/15 -2/17 -4/35 14/11 -1/9 23/18 -1/8 0/1 9/7 0/1 22/17 -1/7 0/1 13/10 -2/15 -1/8 4/3 -1/8 -2/17 23/17 -2/17 19/14 -2/17 -5/43 15/11 -2/17 -4/35 11/8 -2/17 -1/9 29/21 -1/9 18/13 -2/17 -1/9 43/31 -4/33 -2/17 68/49 -9/76 -2/17 93/67 -2/17 25/18 -2/17 -5/43 7/5 -1/9 31/22 -1/12 0/1 24/17 -1/9 0/1 17/12 -2/17 -1/9 10/7 -2/17 -1/9 3/2 -1/9 14/9 -1/9 -2/19 25/16 -4/37 -3/28 61/39 -3/28 36/23 -3/28 -2/19 11/7 -4/37 -2/19 8/5 -1/9 0/1 21/13 -4/37 -2/19 34/21 -1/9 13/8 -1/9 -2/19 5/3 -2/19 12/7 -2/19 -1/10 31/18 -2/19 -1/10 19/11 -1/10 45/26 -1/10 -2/21 26/15 -1/9 0/1 7/4 -1/9 -2/19 16/9 -3/29 25/14 -7/68 -4/39 34/19 -19/185 -4/39 9/5 -4/39 -6/59 11/6 -10/99 -1/10 13/7 -1/10 2/1 -1/10 -2/21 15/7 -2/21 -4/43 13/6 -2/21 -1/11 11/5 -2/21 20/9 -2/21 -3/32 9/4 -4/43 -5/54 7/3 -1/11 19/8 -8/89 -7/78 12/5 -1/11 -6/67 29/12 -5/56 -4/45 17/7 -4/45 5/2 -1/11 -2/23 23/9 -4/45 41/16 -3/34 -2/23 18/7 -3/34 49/19 -5/57 31/12 -1/11 -2/23 44/17 -3/34 -2/23 13/5 -8/91 -2/23 21/8 -13/149 -2/23 29/11 -2/23 8/3 -2/23 -5/58 19/7 -10/117 -4/47 68/25 -27/317 -4/47 117/43 -4/47 49/18 -4/47 -17/200 30/11 -4/47 -5/59 11/4 -1/12 25/9 -2/23 -4/47 14/5 -2/23 -1/12 3/1 -1/12 16/5 -1/12 -2/25 61/19 -2/25 45/14 -2/25 -1/13 29/9 -2/25 0/1 13/4 -1/12 -2/25 10/3 -4/49 -3/37 17/5 -8/99 -2/25 24/7 -11/137 -2/25 31/9 -2/25 7/2 -2/25 -3/38 25/7 -4/51 18/5 -6/77 -1/13 11/3 -2/25 0/1 15/4 -2/25 -1/13 4/1 -1/13 17/4 -1/13 -2/27 13/3 -2/27 22/5 -1/15 0/1 9/2 -1/13 -2/27 14/3 -1/13 -2/27 33/7 -2/27 19/4 -2/27 -1/14 5/1 -2/27 0/1 11/2 -4/55 -1/14 17/3 -1/14 6/1 -1/14 -2/29 13/2 -1/15 20/3 -2/29 -1/15 7/1 0/1 8/1 -2/29 -1/15 9/1 -1/15 1/0 -1/16 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(253,-26,146,-15) (0/1,1/8) -> (45/26,26/15) Hyperbolic Matrix(70,-9,249,-32) (1/8,1/7) -> (7/25,2/7) Hyperbolic Matrix(173,-28,68,-11) (1/7,1/6) -> (5/2,23/9) Hyperbolic Matrix(204,-35,35,-6) (1/6,3/17) -> (17/3,6/1) Hyperbolic Matrix(374,-67,67,-12) (3/17,2/11) -> (11/2,17/3) Hyperbolic Matrix(168,-31,271,-50) (2/11,1/5) -> (13/21,5/8) Hyperbolic Matrix(165,-34,34,-7) (1/5,3/14) -> (19/4,5/1) Hyperbolic Matrix(328,-71,231,-50) (3/14,2/9) -> (17/12,10/7) Hyperbolic Matrix(359,-82,162,-37) (2/9,3/13) -> (11/5,20/9) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(412,-109,189,-50) (5/19,4/15) -> (13/6,11/5) Hyperbolic Matrix(346,-93,253,-68) (4/15,3/11) -> (15/11,11/8) Hyperbolic Matrix(156,-43,283,-78) (3/11,5/18) -> (6/11,5/9) Hyperbolic Matrix(1439,-402,562,-157) (5/18,7/25) -> (23/9,41/16) Hyperbolic Matrix(155,-46,246,-73) (2/7,3/10) -> (5/8,12/19) Hyperbolic Matrix(122,-37,277,-84) (3/10,4/13) -> (7/16,4/9) Hyperbolic Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(296,-105,265,-94) (6/17,11/31) -> (1/1,9/8) Hyperbolic Matrix(1801,-640,560,-199) (11/31,5/14) -> (45/14,29/9) Hyperbolic Matrix(619,-222,382,-137) (5/14,4/11) -> (34/21,13/8) Hyperbolic Matrix(205,-76,116,-43) (4/11,3/8) -> (7/4,16/9) Hyperbolic Matrix(377,-144,144,-55) (3/8,5/13) -> (13/5,21/8) Hyperbolic Matrix(491,-190,230,-89) (5/13,12/31) -> (2/1,15/7) Hyperbolic Matrix(1037,-402,1442,-559) (12/31,7/18) -> (23/32,18/25) Hyperbolic Matrix(173,-68,28,-11) (7/18,2/5) -> (6/1,13/2) Hyperbolic Matrix(113,-46,86,-35) (2/5,5/12) -> (13/10,4/3) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(359,-162,82,-37) (4/9,5/11) -> (13/3,22/5) Hyperbolic Matrix(356,-163,83,-38) (5/11,6/13) -> (17/4,13/3) Hyperbolic Matrix(491,-230,190,-89) (6/13,1/2) -> (31/12,44/17) Hyperbolic Matrix(52,-27,27,-14) (1/2,7/13) -> (13/7,2/1) Hyperbolic Matrix(286,-155,155,-84) (7/13,6/11) -> (11/6,13/7) Hyperbolic Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(610,-351,431,-248) (4/7,15/26) -> (24/17,17/12) Hyperbolic Matrix(253,-146,26,-15) (15/26,11/19) -> (9/1,1/0) Hyperbolic Matrix(557,-324,404,-235) (11/19,7/12) -> (11/8,29/21) Hyperbolic Matrix(76,-45,125,-74) (7/12,3/5) -> (3/5,8/13) Parabolic Matrix(619,-382,222,-137) (8/13,13/21) -> (25/9,14/5) Hyperbolic Matrix(587,-372,172,-109) (12/19,7/11) -> (17/5,24/7) Hyperbolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(1040,-721,401,-278) (9/13,25/36) -> (44/17,13/5) Hyperbolic Matrix(4320,-3001,2761,-1918) (25/36,41/59) -> (61/39,36/23) Hyperbolic Matrix(2878,-2001,1841,-1280) (41/59,16/23) -> (25/16,61/39) Hyperbolic Matrix(566,-395,235,-164) (16/23,7/10) -> (12/5,29/12) Hyperbolic Matrix(328,-231,71,-50) (7/10,12/17) -> (9/2,14/3) Hyperbolic Matrix(610,-431,351,-248) (12/17,17/24) -> (26/15,7/4) Hyperbolic Matrix(2106,-1493,773,-548) (17/24,22/31) -> (49/18,30/11) Hyperbolic Matrix(514,-365,445,-316) (22/31,5/7) -> (15/13,7/6) Hyperbolic Matrix(536,-385,465,-334) (5/7,23/32) -> (8/7,15/13) Hyperbolic Matrix(557,-402,442,-319) (18/25,13/18) -> (5/4,24/19) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(346,-253,93,-68) (8/11,11/15) -> (11/3,15/4) Hyperbolic Matrix(345,-254,254,-187) (11/15,3/4) -> (19/14,15/11) Hyperbolic Matrix(113,-86,46,-35) (3/4,7/9) -> (17/7,5/2) Hyperbolic Matrix(652,-509,269,-210) (7/9,18/23) -> (29/12,17/7) Hyperbolic Matrix(718,-563,403,-316) (18/23,11/14) -> (16/9,25/14) Hyperbolic Matrix(940,-741,581,-458) (11/14,15/19) -> (21/13,34/21) Hyperbolic Matrix(557,-442,402,-319) (15/19,4/5) -> (18/13,43/31) Hyperbolic Matrix(110,-89,89,-72) (4/5,9/11) -> (11/9,5/4) Hyperbolic Matrix(132,-109,109,-90) (9/11,5/6) -> (6/5,11/9) Hyperbolic Matrix(195,-164,44,-37) (5/6,6/7) -> (22/5,9/2) Hyperbolic Matrix(514,-445,365,-316) (6/7,13/15) -> (7/5,31/22) Hyperbolic Matrix(662,-577,257,-224) (13/15,7/8) -> (18/7,49/19) Hyperbolic Matrix(490,-431,191,-168) (7/8,8/9) -> (41/16,18/7) Hyperbolic Matrix(274,-245,85,-76) (8/9,1/1) -> (29/9,13/4) Hyperbolic Matrix(244,-277,37,-42) (9/8,8/7) -> (13/2,20/3) Hyperbolic Matrix(165,-194,74,-87) (7/6,6/5) -> (20/9,9/4) Hyperbolic Matrix(1837,-2324,1324,-1675) (24/19,19/15) -> (43/31,68/49) Hyperbolic Matrix(440,-559,159,-202) (19/15,14/11) -> (11/4,25/9) Hyperbolic Matrix(528,-673,193,-246) (14/11,23/18) -> (30/11,11/4) Hyperbolic Matrix(316,-405,245,-314) (23/18,9/7) -> (9/7,22/17) Parabolic Matrix(488,-633,313,-406) (22/17,13/10) -> (14/9,25/16) Hyperbolic Matrix(392,-529,289,-390) (4/3,23/17) -> (23/17,19/14) Parabolic Matrix(285,-394,34,-47) (29/21,18/13) -> (8/1,9/1) Hyperbolic Matrix(6232,-8649,4489,-6230) (68/49,93/67) -> (93/67,25/18) Parabolic Matrix(1037,-1442,402,-559) (25/18,7/5) -> (49/19,31/12) Hyperbolic Matrix(1128,-1591,631,-890) (31/22,24/17) -> (25/14,34/19) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(436,-683,203,-318) (36/23,11/7) -> (15/7,13/6) Hyperbolic Matrix(155,-246,46,-73) (11/7,8/5) -> (10/3,17/5) Hyperbolic Matrix(168,-271,31,-50) (8/5,21/13) -> (5/1,11/2) Hyperbolic Matrix(76,-125,45,-74) (13/8,5/3) -> (5/3,12/7) Parabolic Matrix(837,-1444,484,-835) (31/18,19/11) -> (19/11,45/26) Parabolic Matrix(701,-1258,258,-463) (34/19,9/5) -> (19/7,68/25) Hyperbolic Matrix(156,-283,43,-78) (9/5,11/6) -> (18/5,11/3) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(154,-367,47,-112) (19/8,12/5) -> (13/4,10/3) Hyperbolic Matrix(320,-841,121,-318) (21/8,29/11) -> (29/11,8/3) Parabolic Matrix(5032,-13689,1849,-5030) (68/25,117/43) -> (117/43,49/18) Parabolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(1160,-3721,361,-1158) (16/5,61/19) -> (61/19,45/14) Parabolic Matrix(280,-961,81,-278) (24/7,31/9) -> (31/9,7/2) Parabolic Matrix(70,-249,9,-32) (7/2,25/7) -> (7/1,8/1) Hyperbolic Matrix(175,-626,26,-93) (25/7,18/5) -> (20/3,7/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(232,-1089,49,-230) (14/3,33/7) -> (33/7,19/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,17,1) Matrix(253,-26,146,-15) -> Matrix(1,0,-10,1) Matrix(70,-9,249,-32) -> Matrix(3,4,-7,-9) Matrix(173,-28,68,-11) -> Matrix(3,4,-34,-45) Matrix(204,-35,35,-6) -> Matrix(3,4,-43,-57) Matrix(374,-67,67,-12) -> Matrix(9,8,-125,-111) Matrix(168,-31,271,-50) -> Matrix(5,4,-29,-23) Matrix(165,-34,34,-7) -> Matrix(1,0,-12,1) Matrix(328,-71,231,-50) -> Matrix(1,0,-7,1) Matrix(359,-82,162,-37) -> Matrix(5,4,-54,-43) Matrix(33,-8,128,-31) -> Matrix(7,4,-16,-9) Matrix(412,-109,189,-50) -> Matrix(9,4,-97,-43) Matrix(346,-93,253,-68) -> Matrix(9,4,-79,-35) Matrix(156,-43,283,-78) -> Matrix(7,4,-37,-21) Matrix(1439,-402,562,-157) -> Matrix(35,16,-396,-181) Matrix(155,-46,246,-73) -> Matrix(11,4,-58,-21) Matrix(122,-37,277,-84) -> Matrix(23,8,-95,-33) Matrix(31,-10,90,-29) -> Matrix(11,4,-36,-13) Matrix(296,-105,265,-94) -> Matrix(13,4,-101,-31) Matrix(1801,-640,560,-199) -> Matrix(13,4,-166,-51) Matrix(619,-222,382,-137) -> Matrix(1,0,-6,1) Matrix(205,-76,116,-43) -> Matrix(27,8,-260,-77) Matrix(377,-144,144,-55) -> Matrix(57,16,-652,-183) Matrix(491,-190,230,-89) -> Matrix(15,4,-154,-41) Matrix(1037,-402,1442,-559) -> Matrix(43,12,-276,-77) Matrix(173,-68,28,-11) -> Matrix(15,4,-214,-57) Matrix(113,-46,86,-35) -> Matrix(15,4,-124,-33) Matrix(85,-36,196,-83) -> Matrix(47,12,-192,-49) Matrix(359,-162,82,-37) -> Matrix(17,4,-234,-55) Matrix(356,-163,83,-38) -> Matrix(1,0,-9,1) Matrix(491,-230,190,-89) -> Matrix(19,4,-214,-45) Matrix(52,-27,27,-14) -> Matrix(19,4,-195,-41) Matrix(286,-155,155,-84) -> Matrix(101,20,-1005,-199) Matrix(205,-116,76,-43) -> Matrix(43,8,-500,-93) Matrix(610,-351,431,-248) -> Matrix(1,0,-3,1) Matrix(253,-146,26,-15) -> Matrix(1,0,-10,1) Matrix(557,-324,404,-235) -> Matrix(21,4,-184,-35) Matrix(76,-45,125,-74) -> Matrix(21,4,-121,-23) Matrix(619,-382,222,-137) -> Matrix(1,0,-6,1) Matrix(587,-372,172,-109) -> Matrix(67,12,-832,-149) Matrix(49,-32,72,-47) -> Matrix(23,4,-144,-25) Matrix(1040,-721,401,-278) -> Matrix(53,8,-603,-91) Matrix(4320,-3001,2761,-1918) -> Matrix(53,8,-497,-75) Matrix(2878,-2001,1841,-1280) -> Matrix(31,4,-287,-37) Matrix(566,-395,235,-164) -> Matrix(23,4,-259,-45) Matrix(328,-231,71,-50) -> Matrix(1,0,-7,1) Matrix(610,-431,351,-248) -> Matrix(1,0,-3,1) Matrix(2106,-1493,773,-548) -> Matrix(29,4,-341,-47) Matrix(514,-365,445,-316) -> Matrix(1,0,-3,1) Matrix(536,-385,465,-334) -> Matrix(25,4,-219,-35) Matrix(557,-402,442,-319) -> Matrix(1,0,-2,1) Matrix(557,-404,324,-235) -> Matrix(25,4,-244,-39) Matrix(346,-253,93,-68) -> Matrix(25,4,-319,-51) Matrix(345,-254,254,-187) -> Matrix(51,8,-440,-69) Matrix(113,-86,46,-35) -> Matrix(27,4,-304,-45) Matrix(652,-509,269,-210) -> Matrix(23,4,-259,-45) Matrix(718,-563,403,-316) -> Matrix(21,4,-205,-39) Matrix(940,-741,581,-458) -> Matrix(1,0,-3,1) Matrix(557,-442,402,-319) -> Matrix(1,0,-2,1) Matrix(110,-89,89,-72) -> Matrix(27,4,-223,-33) Matrix(132,-109,109,-90) -> Matrix(29,4,-225,-31) Matrix(195,-164,44,-37) -> Matrix(1,0,-6,1) Matrix(514,-445,365,-316) -> Matrix(1,0,-3,1) Matrix(662,-577,257,-224) -> Matrix(53,8,-603,-91) Matrix(490,-431,191,-168) -> Matrix(31,4,-349,-45) Matrix(274,-245,85,-76) -> Matrix(1,0,-5,1) Matrix(244,-277,37,-42) -> Matrix(1,0,-7,1) Matrix(165,-194,74,-87) -> Matrix(29,4,-312,-43) Matrix(1837,-2324,1324,-1675) -> Matrix(69,8,-578,-67) Matrix(440,-559,159,-202) -> Matrix(1,0,-3,1) Matrix(528,-673,193,-246) -> Matrix(37,4,-435,-47) Matrix(316,-405,245,-314) -> Matrix(1,0,1,1) Matrix(488,-633,313,-406) -> Matrix(31,4,-287,-37) Matrix(392,-529,289,-390) -> Matrix(101,12,-867,-103) Matrix(285,-394,34,-47) -> Matrix(1,0,-6,1) Matrix(6232,-8649,4489,-6230) -> Matrix(237,28,-2023,-239) Matrix(1037,-1442,402,-559) -> Matrix(103,12,-1176,-137) Matrix(1128,-1591,631,-890) -> Matrix(29,4,-283,-39) Matrix(49,-72,32,-47) -> Matrix(35,4,-324,-37) Matrix(436,-683,203,-318) -> Matrix(75,8,-797,-85) Matrix(155,-246,46,-73) -> Matrix(39,4,-478,-49) Matrix(168,-271,31,-50) -> Matrix(37,4,-509,-55) Matrix(76,-125,45,-74) -> Matrix(37,4,-361,-39) Matrix(837,-1444,484,-835) -> Matrix(39,4,-400,-41) Matrix(701,-1258,258,-463) -> Matrix(313,32,-3668,-375) Matrix(156,-283,43,-78) -> Matrix(39,4,-517,-53) Matrix(85,-196,36,-83) -> Matrix(131,12,-1452,-133) Matrix(154,-367,47,-112) -> Matrix(45,4,-529,-47) Matrix(320,-841,121,-318) -> Matrix(413,36,-4761,-415) Matrix(5032,-13689,1849,-5030) -> Matrix(2067,176,-24299,-2069) Matrix(31,-90,10,-29) -> Matrix(47,4,-576,-49) Matrix(1160,-3721,361,-1158) -> Matrix(49,4,-625,-51) Matrix(280,-961,81,-278) -> Matrix(349,28,-4375,-351) Matrix(70,-249,9,-32) -> Matrix(51,4,-727,-57) Matrix(175,-626,26,-93) -> Matrix(51,4,-778,-61) Matrix(33,-128,8,-31) -> Matrix(51,4,-676,-53) Matrix(232,-1089,49,-230) -> Matrix(53,4,-729,-55) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 ----------------------------------------------------------------------- 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 -1/1 0/1 17 1 1/1 (-2/15,0/1) 0 10 9/8 (-2/15,-1/8) 0 20 8/7 -1/8 2 4 15/13 -1/9 2 5 7/6 (-1/6,0/1) 0 20 6/5 (-2/15,-1/8) 0 20 11/9 -1/8 4 1 5/4 (-1/8,-2/17) 0 20 19/15 (-2/17,-4/35) 0 10 14/11 -1/9 2 4 23/18 (-1/8,0/1) 0 20 9/7 0/1 1 5 4/3 (-1/8,-2/17) 0 20 23/17 -2/17 3 1 15/11 (-2/17,-4/35) 0 10 11/8 (-2/17,-1/9) 0 20 18/13 (-2/17,-1/9) 0 20 43/31 (-4/33,-2/17) 0 10 93/67 -2/17 7 1 25/18 (-2/17,-5/43) 0 20 7/5 -1/9 2 5 31/22 (-1/12,0/1) 0 20 24/17 (-1/9,0/1) 0 20 17/12 (-2/17,-1/9) 0 20 10/7 (-2/17,-1/9) 0 20 3/2 -1/9 2 4 14/9 (-1/9,-2/19) 0 20 25/16 (-4/37,-3/28) 0 20 61/39 -3/28 2 1 36/23 (-3/28,-2/19) 0 20 11/7 (-4/37,-2/19) 0 10 8/5 (-1/9,0/1) 0 20 21/13 (-4/37,-2/19) 0 10 13/8 (-1/9,-2/19) 0 20 5/3 -2/19 1 5 12/7 (-2/19,-1/10) 0 20 31/18 (-2/19,-1/10) 0 20 19/11 -1/10 2 2 26/15 (-1/9,0/1) 0 20 7/4 (-1/9,-2/19) 0 20 9/5 (-4/39,-6/59) 0 10 11/6 (-10/99,-1/10) 0 20 13/7 -1/10 12 1 2/1 (-1/10,-2/21) 0 20 13/6 (-2/21,-1/11) 0 20 11/5 -2/21 1 5 9/4 (-4/43,-5/54) 0 20 7/3 -1/11 6 2 19/8 (-8/89,-7/78) 0 20 12/5 (-1/11,-6/67) 0 20 29/12 (-5/56,-4/45) 0 20 17/7 -4/45 1 5 5/2 (-1/11,-2/23) 0 20 18/7 -3/34 2 4 49/19 -5/57 2 5 31/12 (-1/11,-2/23) 0 20 44/17 (-3/34,-2/23) 0 20 13/5 (-8/91,-2/23) 0 10 29/11 -2/23 9 1 8/3 (-2/23,-5/58) 0 20 19/7 (-10/117,-4/47) 0 10 117/43 -4/47 11 1 49/18 (-4/47,-17/200) 0 20 30/11 (-4/47,-5/59) 0 20 11/4 -1/12 2 4 25/9 (-2/23,-4/47) 0 10 14/5 (-2/23,-1/12) 0 20 3/1 -1/12 2 5 16/5 (-1/12,-2/25) 0 20 61/19 -2/25 1 1 29/9 (-2/25,0/1) 0 10 13/4 (-1/12,-2/25) 0 20 10/3 (-4/49,-3/37) 0 20 17/5 (-8/99,-2/25) 0 10 31/9 -2/25 7 1 7/2 (-2/25,-3/38) 0 20 25/7 -4/51 1 5 18/5 (-6/77,-1/13) 0 20 11/3 (-2/25,0/1) 0 10 15/4 (-2/25,-1/13) 0 20 4/1 -1/13 2 4 17/4 (-1/13,-2/27) 0 20 13/3 -2/27 1 5 22/5 (-1/15,0/1) 0 20 9/2 (-1/13,-2/27) 0 20 14/3 (-1/13,-2/27) 0 20 33/7 -2/27 1 1 5/1 (-2/27,0/1) 0 10 11/2 (-4/55,-1/14) 0 20 17/3 -1/14 6 1 6/1 (-1/14,-2/29) 0 20 13/2 -1/15 2 4 20/3 (-2/29,-1/15) 0 20 7/1 0/1 1 5 8/1 (-2/29,-1/15) 0 20 9/1 -1/15 2 2 1/0 (-1/16,0/1) 0 20 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(245,-274,76,-85) (1/1,9/8) -> (29/9,13/4) Glide Reflection Matrix(244,-277,37,-42) (9/8,8/7) -> (13/2,20/3) Hyperbolic Matrix(577,-662,224,-257) (8/7,15/13) -> (18/7,49/19) Glide Reflection Matrix(445,-514,316,-365) (15/13,7/6) -> (7/5,31/22) Glide Reflection Matrix(164,-195,37,-44) (7/6,6/5) -> (22/5,9/2) Glide Reflection Matrix(109,-132,90,-109) (6/5,11/9) -> (6/5,11/9) Reflection Matrix(89,-110,72,-89) (11/9,5/4) -> (11/9,5/4) Reflection Matrix(442,-557,319,-402) (5/4,19/15) -> (18/13,43/31) Glide Reflection Matrix(440,-559,159,-202) (19/15,14/11) -> (11/4,25/9) Hyperbolic Matrix(528,-673,193,-246) (14/11,23/18) -> (30/11,11/4) Hyperbolic Matrix(509,-652,210,-269) (23/18,9/7) -> (29/12,17/7) Glide Reflection Matrix(86,-113,35,-46) (9/7,4/3) -> (17/7,5/2) Glide Reflection Matrix(137,-184,102,-137) (4/3,23/17) -> (4/3,23/17) Reflection Matrix(254,-345,187,-254) (23/17,15/11) -> (23/17,15/11) Reflection Matrix(253,-346,68,-93) (15/11,11/8) -> (11/3,15/4) Glide Reflection Matrix(404,-557,235,-324) (11/8,18/13) -> (12/7,31/18) Glide Reflection Matrix(2882,-3999,2077,-2882) (43/31,93/67) -> (43/31,93/67) Reflection Matrix(3349,-4650,2412,-3349) (93/67,25/18) -> (93/67,25/18) Reflection Matrix(1037,-1442,402,-559) (25/18,7/5) -> (49/19,31/12) Hyperbolic Matrix(1493,-2106,548,-773) (31/22,24/17) -> (49/18,30/11) Glide Reflection Matrix(431,-610,248,-351) (24/17,17/12) -> (26/15,7/4) Glide Reflection Matrix(231,-328,50,-71) (17/12,10/7) -> (9/2,14/3) Glide Reflection Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(453,-706,188,-293) (14/9,25/16) -> (12/5,29/12) Glide Reflection Matrix(1951,-3050,1248,-1951) (25/16,61/39) -> (25/16,61/39) Reflection Matrix(2807,-4392,1794,-2807) (61/39,36/23) -> (61/39,36/23) Reflection Matrix(607,-952,234,-367) (36/23,11/7) -> (44/17,13/5) Glide Reflection Matrix(155,-246,46,-73) (11/7,8/5) -> (10/3,17/5) Hyperbolic Matrix(168,-271,31,-50) (8/5,21/13) -> (5/1,11/2) Hyperbolic Matrix(382,-619,137,-222) (21/13,13/8) -> (25/9,14/5) Glide Reflection Matrix(76,-125,45,-74) (13/8,5/3) -> (5/3,12/7) Parabolic Matrix(250,-431,29,-50) (31/18,19/11) -> (8/1,9/1) Glide Reflection Matrix(146,-253,15,-26) (19/11,26/15) -> (9/1,1/0) Glide Reflection Matrix(116,-205,43,-76) (7/4,9/5) -> (8/3,19/7) Glide Reflection Matrix(156,-283,43,-78) (9/5,11/6) -> (18/5,11/3) Hyperbolic Matrix(155,-286,84,-155) (11/6,13/7) -> (11/6,13/7) Reflection Matrix(27,-52,14,-27) (13/7,2/1) -> (13/7,2/1) Reflection Matrix(230,-491,89,-190) (2/1,13/6) -> (31/12,44/17) Glide Reflection Matrix(163,-356,38,-83) (13/6,11/5) -> (17/4,13/3) Glide Reflection Matrix(162,-359,37,-82) (11/5,9/4) -> (13/3,22/5) Glide Reflection Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(154,-367,47,-112) (19/8,12/5) -> (13/4,10/3) Hyperbolic Matrix(68,-173,11,-28) (5/2,18/7) -> (6/1,13/2) Glide Reflection Matrix(144,-377,55,-144) (13/5,29/11) -> (13/5,29/11) Reflection Matrix(175,-464,66,-175) (29/11,8/3) -> (29/11,8/3) Reflection Matrix(818,-2223,301,-818) (19/7,117/43) -> (19/7,117/43) Reflection Matrix(4213,-11466,1548,-4213) (117/43,49/18) -> (117/43,49/18) Reflection Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(609,-1952,190,-609) (16/5,61/19) -> (16/5,61/19) Reflection Matrix(550,-1769,171,-550) (61/19,29/9) -> (61/19,29/9) Reflection Matrix(154,-527,45,-154) (17/5,31/9) -> (17/5,31/9) Reflection Matrix(125,-434,36,-125) (31/9,7/2) -> (31/9,7/2) Reflection Matrix(70,-249,9,-32) (7/2,25/7) -> (7/1,8/1) Hyperbolic Matrix(175,-626,26,-93) (25/7,18/5) -> (20/3,7/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(197,-924,42,-197) (14/3,33/7) -> (14/3,33/7) Reflection Matrix(34,-165,7,-34) (33/7,5/1) -> (33/7,5/1) Reflection Matrix(67,-374,12,-67) (11/2,17/3) -> (11/2,17/3) Reflection Matrix(35,-204,6,-35) (17/3,6/1) -> (17/3,6/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,32,1) (-1/1,1/0) -> (-1/16,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,15,1) (-1/1,1/1) -> (-2/15,0/1) Matrix(245,-274,76,-85) -> Matrix(-1,0,20,1) *** -> (-1/10,0/1) Matrix(244,-277,37,-42) -> Matrix(1,0,-7,1) 0/1 Matrix(577,-662,224,-257) -> Matrix(67,8,-762,-91) Matrix(445,-514,316,-365) -> Matrix(-1,0,18,1) *** -> (-1/9,0/1) Matrix(164,-195,37,-44) -> Matrix(-1,0,21,1) *** -> (-2/21,0/1) Matrix(109,-132,90,-109) -> Matrix(31,4,-240,-31) (6/5,11/9) -> (-2/15,-1/8) Matrix(89,-110,72,-89) -> Matrix(33,4,-272,-33) (11/9,5/4) -> (-1/8,-2/17) Matrix(442,-557,319,-402) -> Matrix(-1,0,17,1) *** -> (-2/17,0/1) Matrix(440,-559,159,-202) -> Matrix(1,0,-3,1) 0/1 Matrix(528,-673,193,-246) -> Matrix(37,4,-435,-47) Matrix(509,-652,210,-269) -> Matrix(37,4,-416,-45) Matrix(86,-113,35,-46) -> Matrix(33,4,-371,-45) Matrix(137,-184,102,-137) -> Matrix(33,4,-272,-33) (4/3,23/17) -> (-1/8,-2/17) Matrix(254,-345,187,-254) -> Matrix(69,8,-595,-69) (23/17,15/11) -> (-2/17,-4/35) Matrix(253,-346,68,-93) -> Matrix(35,4,-446,-51) Matrix(404,-557,235,-324) -> Matrix(35,4,-341,-39) Matrix(2882,-3999,2077,-2882) -> Matrix(67,8,-561,-67) (43/31,93/67) -> (-4/33,-2/17) Matrix(3349,-4650,2412,-3349) -> Matrix(171,20,-1462,-171) (93/67,25/18) -> (-2/17,-5/43) Matrix(1037,-1442,402,-559) -> Matrix(103,12,-1176,-137) Matrix(1493,-2106,548,-773) -> Matrix(31,4,-364,-47) Matrix(431,-610,248,-351) -> Matrix(-1,0,18,1) *** -> (-1/9,0/1) Matrix(231,-328,50,-71) -> Matrix(-1,0,22,1) *** -> (-1/11,0/1) Matrix(49,-72,32,-47) -> Matrix(35,4,-324,-37) -1/9 Matrix(453,-706,188,-293) -> Matrix(73,8,-812,-89) Matrix(1951,-3050,1248,-1951) -> Matrix(223,24,-2072,-223) (25/16,61/39) -> (-4/37,-3/28) Matrix(2807,-4392,1794,-2807) -> Matrix(113,12,-1064,-113) (61/39,36/23) -> (-3/28,-2/19) Matrix(607,-952,234,-367) -> Matrix(113,12,-1290,-137) Matrix(155,-246,46,-73) -> Matrix(39,4,-478,-49) Matrix(168,-271,31,-50) -> Matrix(37,4,-509,-55) Matrix(382,-619,137,-222) -> Matrix(-1,0,21,1) *** -> (-2/21,0/1) Matrix(76,-125,45,-74) -> Matrix(37,4,-361,-39) -2/19 Matrix(250,-431,29,-50) -> Matrix(39,4,-575,-59) Matrix(146,-253,15,-26) -> Matrix(-1,0,25,1) *** -> (-2/25,0/1) Matrix(116,-205,43,-76) -> Matrix(77,8,-895,-93) Matrix(156,-283,43,-78) -> Matrix(39,4,-517,-53) Matrix(155,-286,84,-155) -> Matrix(199,20,-1980,-199) (11/6,13/7) -> (-10/99,-1/10) Matrix(27,-52,14,-27) -> Matrix(41,4,-420,-41) (13/7,2/1) -> (-1/10,-2/21) Matrix(230,-491,89,-190) -> Matrix(41,4,-461,-45) Matrix(163,-356,38,-83) -> Matrix(-1,0,24,1) *** -> (-1/12,0/1) Matrix(162,-359,37,-82) -> Matrix(43,4,-591,-55) Matrix(85,-196,36,-83) -> Matrix(131,12,-1452,-133) -1/11 Matrix(154,-367,47,-112) -> Matrix(45,4,-529,-47) -2/23 Matrix(68,-173,11,-28) -> Matrix(45,4,-641,-57) Matrix(144,-377,55,-144) -> Matrix(183,16,-2093,-183) (13/5,29/11) -> (-8/91,-2/23) Matrix(175,-464,66,-175) -> Matrix(231,20,-2668,-231) (29/11,8/3) -> (-2/23,-5/58) Matrix(818,-2223,301,-818) -> Matrix(469,40,-5499,-469) (19/7,117/43) -> (-10/117,-4/47) Matrix(4213,-11466,1548,-4213) -> Matrix(1599,136,-18800,-1599) (117/43,49/18) -> (-4/47,-17/200) Matrix(31,-90,10,-29) -> Matrix(47,4,-576,-49) -1/12 Matrix(609,-1952,190,-609) -> Matrix(49,4,-600,-49) (16/5,61/19) -> (-1/12,-2/25) Matrix(550,-1769,171,-550) -> Matrix(-1,0,25,1) (61/19,29/9) -> (-2/25,0/1) Matrix(154,-527,45,-154) -> Matrix(199,16,-2475,-199) (17/5,31/9) -> (-8/99,-2/25) Matrix(125,-434,36,-125) -> Matrix(151,12,-1900,-151) (31/9,7/2) -> (-2/25,-3/38) Matrix(70,-249,9,-32) -> Matrix(51,4,-727,-57) Matrix(175,-626,26,-93) -> Matrix(51,4,-778,-61) Matrix(33,-128,8,-31) -> Matrix(51,4,-676,-53) -1/13 Matrix(197,-924,42,-197) -> Matrix(53,4,-702,-53) (14/3,33/7) -> (-1/13,-2/27) Matrix(34,-165,7,-34) -> Matrix(-1,0,27,1) (33/7,5/1) -> (-2/27,0/1) Matrix(67,-374,12,-67) -> Matrix(111,8,-1540,-111) (11/2,17/3) -> (-4/55,-1/14) Matrix(35,-204,6,-35) -> Matrix(57,4,-812,-57) (17/3,6/1) -> (-1/14,-2/29) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.