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: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/1 -20/3 -6/1 -16/3 -14/3 -22/5 -4/1 -26/7 -18/5 -7/2 -10/3 -42/13 -14/5 -12/5 -7/3 -2/1 -7/4 -14/9 -42/29 -7/5 -14/11 -7/6 0/1 1/1 7/6 14/11 7/5 42/29 3/2 14/9 7/4 2/1 28/13 7/3 112/47 12/5 56/23 5/2 28/11 8/3 14/5 3/1 42/13 56/17 10/3 84/25 7/2 196/55 18/5 112/31 11/3 26/7 56/15 4/1 13/3 22/5 84/19 9/2 14/3 24/5 5/1 16/3 11/2 28/5 6/1 19/3 32/5 13/2 20/3 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -1/4 -20/3 -2/9 0/1 -13/2 -1/4 -19/3 -7/30 -6/1 -1/5 -11/2 -3/16 -16/3 0/1 -5/1 -1/6 -14/3 -1/6 -23/5 -1/6 -32/7 0/1 -9/2 -1/8 -22/5 -1/7 -13/3 -1/6 -4/1 -2/13 0/1 -15/4 -1/6 -26/7 -1/7 -11/3 -1/6 -29/8 -3/26 -47/13 -1/16 -18/5 -1/5 -25/7 -3/20 -7/2 -1/7 -31/9 -1/6 -55/16 -9/64 -24/7 -2/15 -17/5 -1/10 -27/8 -5/32 -10/3 -1/7 -23/7 -5/38 -36/11 -2/15 -4/31 -13/4 -1/8 -42/13 -1/8 -29/9 -7/58 -16/5 0/1 -3/1 -1/8 -14/5 -1/9 -25/9 -5/46 -11/4 -1/10 -30/11 -1/9 -19/7 -1/8 -46/17 -1/9 -27/10 -13/120 -8/3 -2/19 -21/8 -1/10 -55/21 -3/26 -34/13 -3/29 -13/5 -1/10 -31/12 -5/48 -18/7 -5/49 -5/2 -1/10 -27/11 -17/176 -22/9 -7/73 -17/7 -11/116 -29/12 -19/202 -70/29 -3/32 -41/17 -3/32 -12/5 -2/21 -4/43 -31/13 -11/118 -50/21 -9/97 -19/8 -7/76 -26/11 -1/11 -7/3 -1/11 -30/13 -1/11 -83/36 -17/188 -53/23 -7/78 -23/10 -5/56 -16/7 -4/45 -25/11 -3/34 -34/15 -5/57 -9/4 -7/80 -29/13 -23/266 -20/9 -2/23 -8/93 -11/5 -7/82 -24/11 -6/71 -13/6 -1/12 -2/1 -1/13 -15/8 -1/14 -28/15 -1/14 -13/7 -1/14 -11/6 -7/100 -31/17 -5/72 -20/11 -8/115 -2/29 -29/16 -23/332 -9/5 -7/102 -25/14 -3/44 -16/9 -4/59 -23/13 -5/74 -7/4 -1/15 -33/19 -5/76 -59/34 -3/46 -26/15 -1/15 -19/11 -7/106 -50/29 -9/137 -81/47 -29/442 -112/65 -4/61 -31/18 -11/168 -43/25 -3/46 -12/7 -4/61 -2/31 -41/24 -3/46 -70/41 -3/46 -29/17 -19/292 -17/10 -11/170 -56/33 -2/31 -39/23 -25/388 -22/13 -7/109 -27/16 -17/266 -32/19 -4/63 -5/3 -1/16 -28/17 -1/16 -23/14 -1/16 -18/11 -5/81 -31/19 -5/82 -44/27 -2/33 0/1 -13/8 -1/16 -34/21 -3/49 -55/34 -3/52 -76/47 -2/31 0/1 -21/13 -1/16 -29/18 -15/244 -8/5 -2/33 -27/17 -13/218 -19/12 -1/18 -30/19 -1/17 -11/7 -1/16 -14/9 -1/17 -17/11 -5/86 -20/13 -2/35 0/1 -23/15 -1/16 -3/2 -1/18 -16/11 0/1 -29/20 -7/124 -42/29 -1/18 -13/9 -1/18 -36/25 -4/73 -2/37 -59/41 -1/18 -23/16 -5/92 -56/39 -2/37 -33/23 -7/130 -10/7 -1/19 -47/33 -9/170 -84/59 -1/19 -37/26 -7/134 -27/19 -5/98 -17/12 -1/16 -41/29 -1/18 -24/17 -2/37 -7/5 -1/19 -32/23 0/1 -57/41 -7/132 -196/141 -1/19 -139/100 -17/324 -82/59 -1/19 -25/18 -3/58 -18/13 -1/21 -65/47 -1/32 -112/81 0/1 -47/34 -1/10 -29/21 -3/52 -40/29 -2/37 -11/8 -1/20 -26/19 -1/19 -41/30 -3/58 -56/41 -2/39 -15/11 -1/20 -4/3 -2/39 0/1 -13/10 -1/20 -22/17 -1/19 -53/41 -1/20 -84/65 -1/20 -31/24 -1/20 -9/7 -1/18 -14/11 -1/20 -19/15 -3/62 -43/34 -1/20 -24/19 -2/41 -29/23 -5/106 -5/4 -1/20 -16/13 0/1 -27/22 -7/142 -11/9 -3/62 -28/23 -1/21 -17/14 -5/106 -6/5 -1/21 -19/16 -7/152 -32/27 -4/87 -13/11 -1/22 -20/17 -2/43 0/1 -27/23 -11/238 -7/6 -1/22 -8/7 -2/45 -1/1 -1/26 0/1 0/1 1/1 1/26 7/6 1/22 20/17 0/1 2/43 13/11 1/22 19/16 7/152 6/5 1/21 11/9 3/62 16/13 0/1 5/4 1/20 14/11 1/20 23/18 1/20 32/25 0/1 9/7 1/18 22/17 1/19 13/10 1/20 4/3 0/1 2/39 15/11 1/20 26/19 1/19 11/8 1/20 29/21 3/52 47/34 1/10 18/13 1/21 25/18 3/58 7/5 1/19 31/22 1/20 55/39 9/170 24/17 2/37 17/12 1/16 27/19 5/98 10/7 1/19 23/16 5/92 36/25 2/37 4/73 13/9 1/18 42/29 1/18 29/20 7/124 16/11 0/1 3/2 1/18 14/9 1/17 25/16 5/84 11/7 1/16 30/19 1/17 19/12 1/18 46/29 1/17 27/17 13/218 8/5 2/33 21/13 1/16 55/34 3/52 34/21 3/49 13/8 1/16 31/19 5/82 18/11 5/81 5/3 1/16 27/16 17/266 22/13 7/109 17/10 11/170 29/17 19/292 70/41 3/46 41/24 3/46 12/7 2/31 4/61 31/18 11/168 50/29 9/137 19/11 7/106 26/15 1/15 7/4 1/15 30/17 1/15 83/47 17/254 53/30 7/104 23/13 5/74 16/9 4/59 25/14 3/44 34/19 5/73 9/5 7/102 29/16 23/332 20/11 2/29 8/115 11/6 7/100 24/13 6/85 13/7 1/14 2/1 1/13 15/7 1/12 28/13 1/12 13/6 1/12 11/5 7/82 31/14 5/58 20/9 8/93 2/23 29/13 23/266 9/4 7/80 25/11 3/34 16/7 4/45 23/10 5/56 7/3 1/11 33/14 5/54 59/25 3/32 26/11 1/11 19/8 7/76 50/21 9/97 81/34 29/312 112/47 4/43 31/13 11/118 43/18 3/32 12/5 4/43 2/21 41/17 3/32 70/29 3/32 29/12 19/202 17/7 11/116 56/23 2/21 39/16 25/262 22/9 7/73 27/11 17/176 32/13 4/41 5/2 1/10 28/11 1/10 23/9 1/10 18/7 5/49 31/12 5/48 44/17 0/1 2/19 13/5 1/10 34/13 3/29 55/21 3/26 76/29 0/1 2/21 21/8 1/10 29/11 15/146 8/3 2/19 27/10 13/120 19/7 1/8 30/11 1/9 11/4 1/10 14/5 1/9 17/6 5/44 20/7 0/1 2/17 23/8 1/10 3/1 1/8 16/5 0/1 29/9 7/58 42/13 1/8 13/4 1/8 36/11 4/31 2/15 59/18 1/8 23/7 5/38 56/17 2/15 33/10 7/52 10/3 1/7 47/14 9/64 84/25 1/7 37/11 7/48 27/8 5/32 17/5 1/10 41/12 1/8 24/7 2/15 7/2 1/7 32/9 0/1 57/16 7/50 196/55 1/7 139/39 17/118 82/23 1/7 25/7 3/20 18/5 1/5 65/18 -1/6 112/31 0/1 47/13 1/16 29/8 3/26 40/11 2/15 11/3 1/6 26/7 1/7 41/11 3/20 56/15 2/13 15/4 1/6 4/1 0/1 2/13 13/3 1/6 22/5 1/7 53/12 1/6 84/19 1/6 31/7 1/6 9/2 1/8 14/3 1/6 19/4 3/16 43/9 1/6 24/5 2/11 29/6 5/24 5/1 1/6 16/3 0/1 27/5 7/40 11/2 3/16 28/5 1/5 17/3 5/24 6/1 1/5 19/3 7/30 32/5 4/17 13/2 1/4 20/3 0/1 2/9 27/4 11/48 7/1 1/4 8/1 2/7 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(29,224,-18,-139) (-7/1,1/0) -> (-21/13,-29/18) Hyperbolic Matrix(139,952,-86,-589) (-7/1,-20/3) -> (-76/47,-21/13) Hyperbolic Matrix(111,728,34,223) (-20/3,-13/2) -> (13/4,36/11) Hyperbolic Matrix(167,1064,-132,-841) (-13/2,-19/3) -> (-19/15,-43/34) Hyperbolic Matrix(169,1064,98,617) (-19/3,-6/1) -> (50/29,19/11) Hyperbolic Matrix(29,168,-24,-139) (-6/1,-11/2) -> (-17/14,-6/5) Hyperbolic Matrix(113,616,-82,-447) (-11/2,-16/3) -> (-40/29,-11/8) Hyperbolic Matrix(85,448,48,253) (-16/3,-5/1) -> (23/13,16/9) Hyperbolic Matrix(83,392,-18,-85) (-5/1,-14/3) -> (-14/3,-23/5) Parabolic Matrix(195,896,-116,-533) (-23/5,-32/7) -> (-32/19,-5/3) Hyperbolic Matrix(197,896,-166,-755) (-32/7,-9/2) -> (-19/16,-32/27) Hyperbolic Matrix(113,504,-50,-223) (-9/2,-22/5) -> (-34/15,-9/4) Hyperbolic Matrix(167,728,64,279) (-22/5,-13/3) -> (13/5,34/13) Hyperbolic Matrix(27,112,20,83) (-13/3,-4/1) -> (4/3,15/11) Hyperbolic Matrix(29,112,22,85) (-4/1,-15/4) -> (13/10,4/3) Hyperbolic Matrix(391,1456,-286,-1065) (-15/4,-26/7) -> (-26/19,-41/30) Hyperbolic Matrix(167,616,106,391) (-26/7,-11/3) -> (11/7,30/19) Hyperbolic Matrix(169,616,-138,-503) (-11/3,-29/8) -> (-27/22,-11/9) Hyperbolic Matrix(449,1624,248,897) (-29/8,-47/13) -> (9/5,29/16) Hyperbolic Matrix(559,2016,-404,-1457) (-47/13,-18/5) -> (-18/13,-65/47) Hyperbolic Matrix(281,1008,172,617) (-18/5,-25/7) -> (31/19,18/11) Hyperbolic Matrix(111,392,-32,-113) (-25/7,-7/2) -> (-7/2,-31/9) Parabolic Matrix(1595,5488,-692,-2381) (-31/9,-55/16) -> (-83/36,-53/23) Hyperbolic Matrix(587,2016,122,419) (-55/16,-24/7) -> (24/5,29/6) Hyperbolic Matrix(197,672,-90,-307) (-24/7,-17/5) -> (-11/5,-24/11) Hyperbolic Matrix(281,952,116,393) (-17/5,-27/8) -> (29/12,17/7) Hyperbolic Matrix(449,1512,-166,-559) (-27/8,-10/3) -> (-46/17,-27/10) Hyperbolic Matrix(169,560,-118,-391) (-10/3,-23/7) -> (-33/23,-10/7) Hyperbolic Matrix(393,1288,-256,-839) (-23/7,-36/11) -> (-20/13,-23/15) Hyperbolic Matrix(223,728,34,111) (-36/11,-13/4) -> (13/2,20/3) Hyperbolic Matrix(813,2632,476,1541) (-13/4,-42/13) -> (70/41,41/24) Hyperbolic Matrix(1007,3248,590,1903) (-42/13,-29/9) -> (29/17,70/41) Hyperbolic Matrix(279,896,52,167) (-29/9,-16/5) -> (16/3,27/5) Hyperbolic Matrix(141,448,62,197) (-16/5,-3/1) -> (25/11,16/7) Hyperbolic Matrix(139,392,-50,-141) (-3/1,-14/5) -> (-14/5,-25/9) Parabolic Matrix(223,616,-122,-337) (-25/9,-11/4) -> (-11/6,-31/17) Hyperbolic Matrix(225,616,164,449) (-11/4,-30/11) -> (26/19,11/8) Hyperbolic Matrix(391,1064,226,615) (-30/11,-19/7) -> (19/11,26/15) Hyperbolic Matrix(869,2352,-610,-1651) (-19/7,-46/17) -> (-10/7,-47/33) Hyperbolic Matrix(83,224,10,27) (-27/10,-8/3) -> (8/1,1/0) Hyperbolic Matrix(85,224,-74,-195) (-8/3,-21/8) -> (-7/6,-8/7) Hyperbolic Matrix(363,952,-310,-813) (-21/8,-55/21) -> (-27/23,-7/6) Hyperbolic Matrix(813,2128,332,869) (-55/21,-34/13) -> (22/9,27/11) Hyperbolic Matrix(279,728,64,167) (-34/13,-13/5) -> (13/3,22/5) Hyperbolic Matrix(671,1736,-390,-1009) (-13/5,-31/12) -> (-31/18,-43/25) Hyperbolic Matrix(391,1008,282,727) (-31/12,-18/7) -> (18/13,25/18) Hyperbolic Matrix(197,504,-120,-307) (-18/7,-5/2) -> (-23/14,-18/11) Hyperbolic Matrix(113,280,-90,-223) (-5/2,-27/11) -> (-29/23,-5/4) Hyperbolic Matrix(869,2128,332,813) (-27/11,-22/9) -> (34/13,55/21) Hyperbolic Matrix(505,1232,-298,-727) (-22/9,-17/7) -> (-39/23,-22/13) Hyperbolic Matrix(393,952,116,281) (-17/7,-29/12) -> (27/8,17/5) Hyperbolic Matrix(1345,3248,928,2241) (-29/12,-70/29) -> (42/29,29/20) Hyperbolic Matrix(1091,2632,754,1819) (-70/29,-41/17) -> (13/9,42/29) Hyperbolic Matrix(813,1960,314,757) (-41/17,-12/5) -> (44/17,13/5) Hyperbolic Matrix(727,1736,-446,-1065) (-12/5,-31/13) -> (-31/19,-44/27) Hyperbolic Matrix(2351,5600,-1364,-3249) (-31/13,-50/21) -> (-50/29,-81/47) Hyperbolic Matrix(447,1064,376,895) (-50/21,-19/8) -> (19/16,6/5) Hyperbolic Matrix(449,1064,284,673) (-19/8,-26/11) -> (30/19,19/12) Hyperbolic Matrix(167,392,-72,-169) (-26/11,-7/3) -> (-7/3,-30/13) Parabolic Matrix(4759,10976,-3424,-7897) (-30/13,-83/36) -> (-139/100,-82/59) Hyperbolic Matrix(559,1288,194,447) (-53/23,-23/10) -> (23/8,3/1) Hyperbolic Matrix(195,448,158,363) (-23/10,-16/7) -> (16/13,5/4) Hyperbolic Matrix(197,448,62,141) (-16/7,-25/11) -> (3/1,16/5) Hyperbolic Matrix(1037,2352,-802,-1819) (-25/11,-34/15) -> (-22/17,-53/41) Hyperbolic Matrix(727,1624,526,1175) (-9/4,-29/13) -> (29/21,47/34) Hyperbolic Matrix(503,1120,-428,-953) (-29/13,-20/9) -> (-20/17,-27/23) Hyperbolic Matrix(253,560,-164,-363) (-20/9,-11/5) -> (-17/11,-20/13) Hyperbolic Matrix(617,1344,-488,-1063) (-24/11,-13/6) -> (-43/34,-24/19) Hyperbolic Matrix(27,56,-14,-29) (-13/6,-2/1) -> (-2/1,-15/8) Parabolic Matrix(419,784,194,363) (-15/8,-28/15) -> (28/13,13/6) Hyperbolic Matrix(421,784,196,365) (-28/15,-13/7) -> (15/7,28/13) Hyperbolic Matrix(365,672,-258,-475) (-13/7,-11/6) -> (-17/12,-41/29) Hyperbolic Matrix(1261,2296,-876,-1595) (-31/17,-20/11) -> (-36/25,-59/41) Hyperbolic Matrix(1821,3304,-1126,-2043) (-20/11,-29/16) -> (-55/34,-76/47) Hyperbolic Matrix(897,1624,248,449) (-29/16,-9/5) -> (47/13,29/8) Hyperbolic Matrix(281,504,-218,-391) (-9/5,-25/14) -> (-31/24,-9/7) Hyperbolic Matrix(251,448,172,307) (-25/14,-16/9) -> (16/11,3/2) Hyperbolic Matrix(253,448,48,85) (-16/9,-23/13) -> (5/1,16/3) Hyperbolic Matrix(223,392,-128,-225) (-23/13,-7/4) -> (-7/4,-33/19) Parabolic Matrix(1903,3304,580,1007) (-33/19,-59/34) -> (59/18,23/7) Hyperbolic Matrix(3163,5488,-2276,-3949) (-59/34,-26/15) -> (-82/59,-25/18) Hyperbolic Matrix(615,1064,226,391) (-26/15,-19/11) -> (19/7,30/11) Hyperbolic Matrix(617,1064,98,169) (-19/11,-50/29) -> (6/1,19/3) Hyperbolic Matrix(7279,12544,3054,5263) (-81/47,-112/65) -> (112/47,31/13) Hyperbolic Matrix(7281,12544,3056,5265) (-112/65,-31/18) -> (81/34,112/47) Hyperbolic Matrix(587,1008,244,419) (-43/25,-12/7) -> (12/5,41/17) Hyperbolic Matrix(589,1008,246,421) (-12/7,-41/24) -> (43/18,12/5) Hyperbolic Matrix(1541,2632,476,813) (-41/24,-70/41) -> (42/13,13/4) Hyperbolic Matrix(1903,3248,590,1007) (-70/41,-29/17) -> (29/9,42/13) Hyperbolic Matrix(559,952,394,671) (-29/17,-17/10) -> (17/12,27/19) Hyperbolic Matrix(1847,3136,758,1287) (-17/10,-56/33) -> (56/23,39/16) Hyperbolic Matrix(1849,3136,760,1289) (-56/33,-39/23) -> (17/7,56/23) Hyperbolic Matrix(1259,2128,778,1315) (-22/13,-27/16) -> (55/34,34/21) Hyperbolic Matrix(1595,2688,448,755) (-27/16,-32/19) -> (32/9,57/16) Hyperbolic Matrix(475,784,186,307) (-5/3,-28/17) -> (28/11,23/9) Hyperbolic Matrix(477,784,188,309) (-28/17,-23/14) -> (5/2,28/11) Hyperbolic Matrix(617,1008,172,281) (-18/11,-31/19) -> (25/7,18/5) Hyperbolic Matrix(1203,1960,704,1147) (-44/27,-13/8) -> (41/24,12/7) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(1315,2128,778,1259) (-34/21,-55/34) -> (27/16,22/13) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(281,448,106,169) (-8/5,-27/17) -> (29/11,8/3) Hyperbolic Matrix(953,1512,-670,-1063) (-27/17,-19/12) -> (-37/26,-27/19) Hyperbolic Matrix(673,1064,284,449) (-19/12,-30/19) -> (26/11,19/8) Hyperbolic Matrix(391,616,106,167) (-30/19,-11/7) -> (11/3,26/7) Hyperbolic Matrix(251,392,-162,-253) (-11/7,-14/9) -> (-14/9,-17/11) Parabolic Matrix(841,1288,476,729) (-23/15,-3/2) -> (53/30,23/13) Hyperbolic Matrix(307,448,172,251) (-3/2,-16/11) -> (16/9,25/14) Hyperbolic Matrix(1119,1624,308,447) (-16/11,-29/20) -> (29/8,40/11) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(1819,2632,754,1091) (-42/29,-13/9) -> (41/17,70/29) Hyperbolic Matrix(505,728,428,617) (-13/9,-36/25) -> (20/17,13/11) Hyperbolic Matrix(2297,3304,974,1401) (-59/41,-23/16) -> (33/14,59/25) Hyperbolic Matrix(2183,3136,662,951) (-23/16,-56/39) -> (56/17,33/10) Hyperbolic Matrix(2185,3136,664,953) (-56/39,-33/23) -> (23/7,56/17) Hyperbolic Matrix(4955,7056,1474,2099) (-47/33,-84/59) -> (84/25,37/11) Hyperbolic Matrix(4957,7056,1476,2101) (-84/59,-37/26) -> (47/14,84/25) Hyperbolic Matrix(671,952,394,559) (-27/19,-17/12) -> (17/10,29/17) Hyperbolic Matrix(1149,1624,-970,-1371) (-41/29,-24/17) -> (-32/27,-13/11) Hyperbolic Matrix(279,392,-200,-281) (-24/17,-7/5) -> (-7/5,-32/23) Parabolic Matrix(1933,2688,786,1093) (-32/23,-57/41) -> (27/11,32/13) Hyperbolic Matrix(27635,38416,7754,10779) (-57/41,-196/141) -> (196/55,139/39) Hyperbolic Matrix(27637,38416,7756,10781) (-196/141,-139/100) -> (57/16,196/55) Hyperbolic Matrix(727,1008,282,391) (-25/18,-18/13) -> (18/7,31/12) Hyperbolic Matrix(9071,12544,2510,3471) (-65/47,-112/81) -> (112/31,47/13) Hyperbolic Matrix(9073,12544,2512,3473) (-112/81,-47/34) -> (65/18,112/31) Hyperbolic Matrix(1175,1624,526,727) (-47/34,-29/21) -> (29/13,9/4) Hyperbolic Matrix(1177,1624,366,505) (-29/21,-40/29) -> (16/5,29/9) Hyperbolic Matrix(449,616,164,225) (-11/8,-26/19) -> (30/11,11/4) Hyperbolic Matrix(2295,3136,614,839) (-41/30,-56/41) -> (56/15,15/4) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(83,112,20,27) (-15/11,-4/3) -> (4/1,13/3) Hyperbolic Matrix(85,112,22,29) (-4/3,-13/10) -> (15/4,4/1) Hyperbolic Matrix(561,728,346,449) (-13/10,-22/17) -> (34/21,13/8) Hyperbolic Matrix(5459,7056,1234,1595) (-53/41,-84/65) -> (84/19,31/7) Hyperbolic Matrix(5461,7056,1236,1597) (-84/65,-31/24) -> (53/12,84/19) Hyperbolic Matrix(307,392,-242,-309) (-9/7,-14/11) -> (-14/11,-19/15) Parabolic Matrix(1597,2016,1132,1429) (-24/19,-29/23) -> (55/39,24/17) Hyperbolic Matrix(363,448,158,195) (-5/4,-16/13) -> (16/7,23/10) Hyperbolic Matrix(729,896,502,617) (-16/13,-27/22) -> (29/20,16/11) Hyperbolic Matrix(643,784,114,139) (-11/9,-28/23) -> (28/5,17/3) Hyperbolic Matrix(645,784,116,141) (-28/23,-17/14) -> (11/2,28/5) Hyperbolic Matrix(895,1064,376,447) (-6/5,-19/16) -> (19/8,50/21) Hyperbolic Matrix(617,728,428,505) (-13/11,-20/17) -> (36/25,13/9) Hyperbolic Matrix(197,224,124,141) (-8/7,-1/1) -> (27/17,8/5) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(195,-224,74,-85) (1/1,7/6) -> (21/8,29/11) Hyperbolic Matrix(813,-952,310,-363) (7/6,20/17) -> (76/29,21/8) Hyperbolic Matrix(897,-1064,188,-223) (13/11,19/16) -> (19/4,43/9) Hyperbolic Matrix(139,-168,24,-29) (6/5,11/9) -> (17/3,6/1) Hyperbolic Matrix(503,-616,138,-169) (11/9,16/13) -> (40/11,11/3) Hyperbolic Matrix(309,-392,242,-307) (5/4,14/11) -> (14/11,23/18) Parabolic Matrix(701,-896,284,-363) (23/18,32/25) -> (32/13,5/2) Hyperbolic Matrix(699,-896,110,-141) (32/25,9/7) -> (19/3,32/5) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(1065,-1456,286,-391) (15/11,26/19) -> (26/7,41/11) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(3893,-5488,2204,-3107) (31/22,55/39) -> (83/47,53/30) Hyperbolic Matrix(475,-672,258,-365) (24/17,17/12) -> (11/6,24/13) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(391,-560,118,-169) (10/7,23/16) -> (33/10,10/3) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(253,-392,162,-251) (3/2,14/9) -> (14/9,25/16) Parabolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(1483,-2352,442,-701) (19/12,46/29) -> (10/3,47/14) Hyperbolic Matrix(139,-224,18,-29) (8/5,21/13) -> (7/1,8/1) Hyperbolic Matrix(589,-952,86,-139) (21/13,55/34) -> (27/4,7/1) Hyperbolic Matrix(1065,-1736,446,-727) (13/8,31/19) -> (31/13,43/18) Hyperbolic Matrix(307,-504,120,-197) (18/11,5/3) -> (23/9,18/7) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(727,-1232,298,-505) (22/13,17/10) -> (39/16,22/9) Hyperbolic Matrix(1009,-1736,390,-671) (12/7,31/18) -> (31/12,44/17) Hyperbolic Matrix(3249,-5600,1364,-2351) (31/18,50/29) -> (50/21,81/34) Hyperbolic Matrix(225,-392,128,-223) (26/15,7/4) -> (7/4,30/17) Parabolic Matrix(6217,-10976,1744,-3079) (30/17,83/47) -> (139/39,82/23) Hyperbolic Matrix(1315,-2352,298,-533) (25/14,34/19) -> (22/5,53/12) Hyperbolic Matrix(617,-1120,92,-167) (29/16,20/11) -> (20/3,27/4) Hyperbolic Matrix(307,-560,108,-197) (20/11,11/6) -> (17/6,20/7) Hyperbolic Matrix(727,-1344,152,-281) (24/13,13/7) -> (43/9,24/5) Hyperbolic Matrix(29,-56,14,-27) (13/7,2/1) -> (2/1,15/7) Parabolic Matrix(307,-672,90,-197) (13/6,11/5) -> (17/5,41/12) Hyperbolic Matrix(1035,-2296,316,-701) (31/14,20/9) -> (36/11,59/18) Hyperbolic Matrix(1483,-3304,566,-1261) (20/9,29/13) -> (55/21,76/29) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(2325,-5488,652,-1539) (59/25,26/11) -> (82/23,25/7) Hyperbolic Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(141,-392,50,-139) (11/4,14/5) -> (14/5,17/6) Parabolic Matrix(475,-1624,74,-253) (41/12,24/7) -> (32/5,13/2) Hyperbolic Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(85,-392,18,-83) (9/2,14/3) -> (14/3,19/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(29,224,-18,-139) -> Matrix(15,4,-244,-65) Matrix(139,952,-86,-589) -> Matrix(9,2,-140,-31) Matrix(111,728,34,223) -> Matrix(7,2,52,15) Matrix(167,1064,-132,-841) -> Matrix(9,2,-176,-39) Matrix(169,1064,98,617) -> Matrix(61,14,928,213) Matrix(29,168,-24,-139) -> Matrix(9,2,-194,-43) Matrix(113,616,-82,-447) -> Matrix(11,2,-204,-37) Matrix(85,448,48,253) -> Matrix(19,4,280,59) Matrix(83,392,-18,-85) -> Matrix(11,2,-72,-13) Matrix(195,896,-116,-533) -> Matrix(25,4,-394,-63) Matrix(197,896,-166,-755) -> Matrix(25,4,-544,-87) Matrix(113,504,-50,-223) -> Matrix(9,2,-104,-23) Matrix(167,728,64,279) -> Matrix(11,2,104,19) Matrix(27,112,20,83) -> Matrix(1,0,26,1) Matrix(29,112,22,85) -> Matrix(1,0,26,1) Matrix(391,1456,-286,-1065) -> Matrix(27,4,-520,-77) Matrix(167,616,106,391) -> Matrix(13,2,214,33) Matrix(169,616,-138,-503) -> Matrix(15,2,-308,-41) Matrix(449,1624,248,897) -> Matrix(25,2,362,29) Matrix(559,2016,-404,-1457) -> Matrix(1,0,-16,1) Matrix(281,1008,172,617) -> Matrix(25,4,406,65) Matrix(111,392,-32,-113) -> Matrix(13,2,-98,-15) Matrix(1595,5488,-692,-2381) -> Matrix(55,8,-612,-89) Matrix(587,2016,122,419) -> Matrix(29,4,152,21) Matrix(197,672,-90,-307) -> Matrix(33,4,-388,-47) Matrix(281,952,116,393) -> Matrix(9,2,94,21) Matrix(449,1512,-166,-559) -> Matrix(41,6,-376,-55) Matrix(169,560,-118,-391) -> Matrix(29,4,-544,-75) Matrix(393,1288,-256,-839) -> Matrix(15,2,-278,-37) Matrix(223,728,34,111) -> Matrix(15,2,52,7) Matrix(813,2632,476,1541) -> Matrix(77,10,1178,153) Matrix(1007,3248,590,1903) -> Matrix(163,20,2502,307) Matrix(279,896,52,167) -> Matrix(1,0,14,1) Matrix(141,448,62,197) -> Matrix(29,4,326,45) Matrix(139,392,-50,-141) -> Matrix(53,6,-486,-55) Matrix(223,616,-122,-337) -> Matrix(93,10,-1330,-143) Matrix(225,616,164,449) -> Matrix(19,2,370,39) Matrix(391,1064,226,615) -> Matrix(55,6,834,91) Matrix(869,2352,-610,-1651) -> Matrix(73,8,-1378,-151) Matrix(83,224,10,27) -> Matrix(37,4,120,13) Matrix(85,224,-74,-195) -> Matrix(39,4,-868,-89) Matrix(363,952,-310,-813) -> Matrix(21,2,-452,-43) Matrix(813,2128,332,869) -> Matrix(75,8,778,83) Matrix(279,728,64,167) -> Matrix(19,2,104,11) Matrix(671,1736,-390,-1009) -> Matrix(17,2,-264,-31) Matrix(391,1008,282,727) -> Matrix(39,4,770,79) Matrix(197,504,-120,-307) -> Matrix(99,10,-1594,-161) Matrix(113,280,-90,-223) -> Matrix(21,2,-410,-39) Matrix(869,2128,332,813) -> Matrix(83,8,778,75) Matrix(505,1232,-298,-727) -> Matrix(293,28,-4552,-435) Matrix(393,952,116,281) -> Matrix(21,2,94,9) Matrix(1345,3248,928,2241) -> Matrix(213,20,3802,357) Matrix(1091,2632,754,1819) -> Matrix(107,10,1958,183) Matrix(813,1960,314,757) -> Matrix(21,2,178,17) Matrix(727,1736,-446,-1065) -> Matrix(21,2,-368,-35) Matrix(2351,5600,-1364,-3249) -> Matrix(775,72,-11808,-1097) Matrix(447,1064,376,895) -> Matrix(151,14,3268,303) Matrix(449,1064,284,673) -> Matrix(65,6,1094,101) Matrix(167,392,-72,-169) -> Matrix(109,10,-1210,-111) Matrix(4759,10976,-3424,-7897) -> Matrix(1,0,-8,1) Matrix(559,1288,194,447) -> Matrix(67,6,614,55) Matrix(195,448,158,363) -> Matrix(45,4,956,85) Matrix(197,448,62,141) -> Matrix(45,4,326,29) Matrix(1037,2352,-802,-1819) -> Matrix(91,8,-1786,-157) Matrix(727,1624,526,1175) -> Matrix(23,2,310,27) Matrix(503,1120,-428,-953) -> Matrix(93,8,-1988,-171) Matrix(253,560,-164,-363) -> Matrix(93,8,-1616,-139) Matrix(617,1344,-488,-1063) -> Matrix(95,8,-1912,-161) Matrix(27,56,-14,-29) -> Matrix(25,2,-338,-27) Matrix(419,784,194,363) -> Matrix(335,24,4006,287) Matrix(421,784,196,365) -> Matrix(337,24,4058,289) Matrix(365,672,-258,-475) -> Matrix(57,4,-1012,-71) Matrix(1261,2296,-876,-1595) -> Matrix(259,18,-4734,-329) Matrix(1821,3304,-1126,-2043) -> Matrix(29,2,-392,-27) Matrix(897,1624,248,449) -> Matrix(29,2,362,25) Matrix(281,504,-218,-391) -> Matrix(29,2,-624,-43) Matrix(251,448,172,307) -> Matrix(59,4,1106,75) Matrix(253,448,48,85) -> Matrix(59,4,280,19) Matrix(223,392,-128,-225) -> Matrix(149,10,-2250,-151) Matrix(1903,3304,580,1007) -> Matrix(153,10,1178,77) Matrix(3163,5488,-2276,-3949) -> Matrix(1,0,-4,1) Matrix(615,1064,226,391) -> Matrix(91,6,834,55) Matrix(617,1064,98,169) -> Matrix(213,14,928,61) Matrix(7279,12544,3054,5263) -> Matrix(2439,160,26204,1719) Matrix(7281,12544,3056,5265) -> Matrix(2441,160,26256,1721) Matrix(587,1008,244,419) -> Matrix(1,0,26,1) Matrix(589,1008,246,421) -> Matrix(1,0,26,1) Matrix(1541,2632,476,813) -> Matrix(153,10,1178,77) Matrix(1903,3248,590,1007) -> Matrix(307,20,2502,163) Matrix(559,952,394,671) -> Matrix(31,2,666,43) Matrix(1847,3136,758,1287) -> Matrix(1115,72,11692,755) Matrix(1849,3136,760,1289) -> Matrix(1117,72,11744,757) Matrix(1259,2128,778,1315) -> Matrix(125,8,2078,133) Matrix(1595,2688,448,755) -> Matrix(63,4,488,31) Matrix(475,784,186,307) -> Matrix(255,16,2534,159) Matrix(477,784,188,309) -> Matrix(257,16,2586,161) Matrix(617,1008,172,281) -> Matrix(65,4,406,25) Matrix(1203,1960,704,1147) -> Matrix(35,2,542,31) Matrix(449,728,346,561) -> Matrix(33,2,676,41) Matrix(1315,2128,778,1259) -> Matrix(133,8,2078,125) Matrix(279,448,104,167) -> Matrix(131,8,1228,75) Matrix(281,448,106,169) -> Matrix(133,8,1280,77) Matrix(953,1512,-670,-1063) -> Matrix(101,6,-1936,-115) Matrix(673,1064,284,449) -> Matrix(101,6,1094,65) Matrix(391,616,106,167) -> Matrix(33,2,214,13) Matrix(251,392,-162,-253) -> Matrix(101,6,-1734,-103) Matrix(841,1288,476,729) -> Matrix(101,6,1498,89) Matrix(307,448,172,251) -> Matrix(75,4,1106,59) Matrix(1119,1624,308,447) -> Matrix(35,2,262,15) Matrix(2241,3248,928,1345) -> Matrix(357,20,3802,213) Matrix(1819,2632,754,1091) -> Matrix(183,10,1958,107) Matrix(505,728,428,617) -> Matrix(37,2,832,45) Matrix(2297,3304,974,1401) -> Matrix(183,10,1958,107) Matrix(2183,3136,662,951) -> Matrix(443,24,3304,179) Matrix(2185,3136,664,953) -> Matrix(445,24,3356,181) Matrix(4955,7056,1474,2099) -> Matrix(303,16,2102,111) Matrix(4957,7056,1476,2101) -> Matrix(305,16,2154,113) Matrix(671,952,394,559) -> Matrix(43,2,666,31) Matrix(1149,1624,-970,-1371) -> Matrix(109,6,-2380,-131) Matrix(279,392,-200,-281) -> Matrix(37,2,-722,-39) Matrix(1933,2688,786,1093) -> Matrix(73,4,748,41) Matrix(27635,38416,7754,10779) -> Matrix(455,24,3166,167) Matrix(27637,38416,7756,10781) -> Matrix(457,24,3218,169) Matrix(727,1008,282,391) -> Matrix(79,4,770,39) Matrix(9071,12544,2510,3471) -> Matrix(1,0,48,1) Matrix(9073,12544,2512,3473) -> Matrix(1,0,4,1) Matrix(1175,1624,526,727) -> Matrix(27,2,310,23) Matrix(1177,1624,366,505) -> Matrix(37,2,314,17) Matrix(449,616,164,225) -> Matrix(39,2,370,19) Matrix(2295,3136,614,839) -> Matrix(155,8,988,51) Matrix(2297,3136,616,841) -> Matrix(157,8,1040,53) Matrix(83,112,20,27) -> Matrix(1,0,26,1) Matrix(85,112,22,29) -> Matrix(1,0,26,1) Matrix(561,728,346,449) -> Matrix(41,2,676,33) Matrix(5459,7056,1234,1595) -> Matrix(159,8,934,47) Matrix(5461,7056,1236,1597) -> Matrix(161,8,986,49) Matrix(307,392,-242,-309) -> Matrix(39,2,-800,-41) Matrix(1597,2016,1132,1429) -> Matrix(83,4,1556,75) Matrix(363,448,158,195) -> Matrix(85,4,956,45) Matrix(729,896,502,617) -> Matrix(1,0,38,1) Matrix(643,784,114,139) -> Matrix(167,8,814,39) Matrix(645,784,116,141) -> Matrix(169,8,866,41) Matrix(895,1064,376,447) -> Matrix(303,14,3268,151) Matrix(617,728,428,505) -> Matrix(45,2,832,37) Matrix(197,224,124,141) -> Matrix(91,4,1524,67) Matrix(1,0,2,1) -> Matrix(1,0,52,1) Matrix(195,-224,74,-85) -> Matrix(89,-4,868,-39) Matrix(813,-952,310,-363) -> Matrix(43,-2,452,-21) Matrix(897,-1064,188,-223) -> Matrix(43,-2,280,-13) Matrix(139,-168,24,-29) -> Matrix(43,-2,194,-9) Matrix(503,-616,138,-169) -> Matrix(41,-2,308,-15) Matrix(309,-392,242,-307) -> Matrix(41,-2,800,-39) Matrix(701,-896,284,-363) -> Matrix(79,-4,810,-41) Matrix(699,-896,110,-141) -> Matrix(79,-4,336,-17) Matrix(391,-504,218,-281) -> Matrix(43,-2,624,-29) Matrix(1065,-1456,286,-391) -> Matrix(77,-4,520,-27) Matrix(447,-616,82,-113) -> Matrix(37,-2,204,-11) Matrix(1457,-2016,404,-559) -> Matrix(1,0,-16,1) Matrix(281,-392,200,-279) -> Matrix(39,-2,722,-37) Matrix(3893,-5488,2204,-3107) -> Matrix(153,-8,2276,-119) Matrix(475,-672,258,-365) -> Matrix(71,-4,1012,-57) Matrix(1063,-1512,670,-953) -> Matrix(115,-6,1936,-101) Matrix(391,-560,118,-169) -> Matrix(75,-4,544,-29) Matrix(895,-1288,312,-449) -> Matrix(37,-2,278,-15) Matrix(253,-392,162,-251) -> Matrix(103,-6,1734,-101) Matrix(393,-616,178,-279) -> Matrix(167,-10,1954,-117) Matrix(1483,-2352,442,-701) -> Matrix(135,-8,962,-57) Matrix(139,-224,18,-29) -> Matrix(65,-4,244,-15) Matrix(589,-952,86,-139) -> Matrix(31,-2,140,-9) Matrix(1065,-1736,446,-727) -> Matrix(35,-2,368,-21) Matrix(307,-504,120,-197) -> Matrix(161,-10,1594,-99) Matrix(167,-280,34,-57) -> Matrix(31,-2,202,-13) Matrix(727,-1232,298,-505) -> Matrix(435,-28,4552,-293) Matrix(1009,-1736,390,-671) -> Matrix(31,-2,264,-17) Matrix(3249,-5600,1364,-2351) -> Matrix(1097,-72,11808,-775) Matrix(225,-392,128,-223) -> Matrix(151,-10,2250,-149) Matrix(6217,-10976,1744,-3079) -> Matrix(1,0,-8,1) Matrix(1315,-2352,298,-533) -> Matrix(117,-8,746,-51) Matrix(617,-1120,92,-167) -> Matrix(115,-8,532,-37) Matrix(307,-560,108,-197) -> Matrix(115,-8,992,-69) Matrix(727,-1344,152,-281) -> Matrix(113,-8,664,-47) Matrix(29,-56,14,-27) -> Matrix(27,-2,338,-25) Matrix(307,-672,90,-197) -> Matrix(47,-4,388,-33) Matrix(1035,-2296,316,-701) -> Matrix(209,-18,1614,-139) Matrix(1483,-3304,566,-1261) -> Matrix(23,-2,288,-25) Matrix(223,-504,50,-113) -> Matrix(23,-2,104,-9) Matrix(169,-392,72,-167) -> Matrix(111,-10,1210,-109) Matrix(2325,-5488,652,-1539) -> Matrix(1,0,-4,1) Matrix(559,-1512,166,-449) -> Matrix(55,-6,376,-41) Matrix(141,-392,50,-139) -> Matrix(55,-6,486,-53) Matrix(475,-1624,74,-253) -> Matrix(47,-6,196,-25) Matrix(113,-392,32,-111) -> Matrix(15,-2,98,-13) Matrix(85,-392,18,-83) -> Matrix(13,-2,72,-11) 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): 96 Degree of the the map X: 96 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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 0/1 7/6 14/11 4/3 7/5 42/29 14/9 12/7 7/4 2/1 28/13 20/9 7/3 112/47 12/5 56/23 28/11 8/3 14/5 3/1 16/5 42/13 56/17 10/3 84/25 7/2 196/55 18/5 112/31 26/7 56/15 4/1 22/5 84/19 9/2 14/3 24/5 5/1 16/3 11/2 28/5 6/1 32/5 13/2 20/3 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/26 7/6 1/22 20/17 0/1 2/43 13/11 1/22 19/16 7/152 6/5 1/21 11/9 3/62 16/13 0/1 5/4 1/20 14/11 1/20 23/18 1/20 32/25 0/1 9/7 1/18 22/17 1/19 13/10 1/20 4/3 0/1 2/39 15/11 1/20 26/19 1/19 11/8 1/20 29/21 3/52 47/34 1/10 18/13 1/21 25/18 3/58 7/5 1/19 31/22 1/20 55/39 9/170 24/17 2/37 17/12 1/16 27/19 5/98 10/7 1/19 23/16 5/92 36/25 2/37 4/73 13/9 1/18 42/29 1/18 29/20 7/124 16/11 0/1 3/2 1/18 14/9 1/17 25/16 5/84 11/7 1/16 30/19 1/17 19/12 1/18 46/29 1/17 27/17 13/218 8/5 2/33 21/13 1/16 55/34 3/52 34/21 3/49 13/8 1/16 31/19 5/82 18/11 5/81 5/3 1/16 27/16 17/266 22/13 7/109 17/10 11/170 29/17 19/292 70/41 3/46 41/24 3/46 12/7 2/31 4/61 31/18 11/168 50/29 9/137 19/11 7/106 26/15 1/15 7/4 1/15 30/17 1/15 83/47 17/254 53/30 7/104 23/13 5/74 16/9 4/59 25/14 3/44 34/19 5/73 9/5 7/102 29/16 23/332 20/11 2/29 8/115 11/6 7/100 24/13 6/85 13/7 1/14 2/1 1/13 15/7 1/12 28/13 1/12 13/6 1/12 11/5 7/82 31/14 5/58 20/9 8/93 2/23 29/13 23/266 9/4 7/80 25/11 3/34 16/7 4/45 23/10 5/56 7/3 1/11 33/14 5/54 59/25 3/32 26/11 1/11 19/8 7/76 50/21 9/97 81/34 29/312 112/47 4/43 31/13 11/118 43/18 3/32 12/5 4/43 2/21 41/17 3/32 70/29 3/32 29/12 19/202 17/7 11/116 56/23 2/21 39/16 25/262 22/9 7/73 27/11 17/176 32/13 4/41 5/2 1/10 28/11 1/10 23/9 1/10 18/7 5/49 31/12 5/48 44/17 0/1 2/19 13/5 1/10 34/13 3/29 55/21 3/26 76/29 0/1 2/21 21/8 1/10 29/11 15/146 8/3 2/19 27/10 13/120 19/7 1/8 30/11 1/9 11/4 1/10 14/5 1/9 17/6 5/44 20/7 0/1 2/17 23/8 1/10 3/1 1/8 16/5 0/1 29/9 7/58 42/13 1/8 13/4 1/8 36/11 4/31 2/15 59/18 1/8 23/7 5/38 56/17 2/15 33/10 7/52 10/3 1/7 47/14 9/64 84/25 1/7 37/11 7/48 27/8 5/32 17/5 1/10 41/12 1/8 24/7 2/15 7/2 1/7 32/9 0/1 57/16 7/50 196/55 1/7 139/39 17/118 82/23 1/7 25/7 3/20 18/5 1/5 65/18 -1/6 112/31 0/1 47/13 1/16 29/8 3/26 40/11 2/15 11/3 1/6 26/7 1/7 41/11 3/20 56/15 2/13 15/4 1/6 4/1 0/1 2/13 13/3 1/6 22/5 1/7 53/12 1/6 84/19 1/6 31/7 1/6 9/2 1/8 14/3 1/6 19/4 3/16 43/9 1/6 24/5 2/11 29/6 5/24 5/1 1/6 16/3 0/1 27/5 7/40 11/2 3/16 28/5 1/5 17/3 5/24 6/1 1/5 19/3 7/30 32/5 4/17 13/2 1/4 20/3 0/1 2/9 27/4 11/48 7/1 1/4 8/1 2/7 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(195,-224,74,-85) (1/1,7/6) -> (21/8,29/11) Hyperbolic Matrix(813,-952,310,-363) (7/6,20/17) -> (76/29,21/8) Hyperbolic Matrix(617,-728,189,-223) (20/17,13/11) -> (13/4,36/11) Hyperbolic Matrix(897,-1064,188,-223) (13/11,19/16) -> (19/4,43/9) Hyperbolic Matrix(895,-1064,519,-617) (19/16,6/5) -> (50/29,19/11) Hyperbolic Matrix(139,-168,24,-29) (6/5,11/9) -> (17/3,6/1) Hyperbolic Matrix(503,-616,138,-169) (11/9,16/13) -> (40/11,11/3) Hyperbolic Matrix(363,-448,205,-253) (16/13,5/4) -> (23/13,16/9) Hyperbolic Matrix(309,-392,242,-307) (5/4,14/11) -> (14/11,23/18) Parabolic Matrix(701,-896,284,-363) (23/18,32/25) -> (32/13,5/2) Hyperbolic Matrix(699,-896,110,-141) (32/25,9/7) -> (19/3,32/5) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(561,-728,215,-279) (22/17,13/10) -> (13/5,34/13) Hyperbolic Matrix(85,-112,63,-83) (13/10,4/3) -> (4/3,15/11) Parabolic Matrix(1065,-1456,286,-391) (15/11,26/19) -> (26/7,41/11) Hyperbolic Matrix(449,-616,285,-391) (26/19,11/8) -> (11/7,30/19) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1175,-1624,649,-897) (29/21,47/34) -> (9/5,29/16) Hyperbolic Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(727,-1008,445,-617) (18/13,25/18) -> (31/19,18/11) Hyperbolic Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(3893,-5488,2204,-3107) (31/22,55/39) -> (83/47,53/30) Hyperbolic Matrix(1429,-2016,297,-419) (55/39,24/17) -> (24/5,29/6) Hyperbolic Matrix(475,-672,258,-365) (24/17,17/12) -> (11/6,24/13) Hyperbolic Matrix(671,-952,277,-393) (17/12,27/19) -> (29/12,17/7) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(391,-560,118,-169) (10/7,23/16) -> (33/10,10/3) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(505,-728,77,-111) (36/25,13/9) -> (13/2,20/3) Hyperbolic Matrix(1819,-2632,1065,-1541) (13/9,42/29) -> (70/41,41/24) Hyperbolic Matrix(2241,-3248,1313,-1903) (42/29,29/20) -> (29/17,70/41) Hyperbolic Matrix(617,-896,115,-167) (29/20,16/11) -> (16/3,27/5) Hyperbolic Matrix(307,-448,135,-197) (16/11,3/2) -> (25/11,16/7) Hyperbolic Matrix(253,-392,162,-251) (3/2,14/9) -> (14/9,25/16) Parabolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(673,-1064,389,-615) (30/19,19/12) -> (19/11,26/15) Hyperbolic Matrix(1483,-2352,442,-701) (19/12,46/29) -> (10/3,47/14) Hyperbolic Matrix(141,-224,17,-27) (27/17,8/5) -> (8/1,1/0) Hyperbolic Matrix(139,-224,18,-29) (8/5,21/13) -> (7/1,8/1) Hyperbolic Matrix(589,-952,86,-139) (21/13,55/34) -> (27/4,7/1) Hyperbolic Matrix(1315,-2128,537,-869) (55/34,34/21) -> (22/9,27/11) Hyperbolic Matrix(449,-728,103,-167) (34/21,13/8) -> (13/3,22/5) Hyperbolic Matrix(1065,-1736,446,-727) (13/8,31/19) -> (31/13,43/18) Hyperbolic Matrix(307,-504,120,-197) (18/11,5/3) -> (23/9,18/7) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(1259,-2128,481,-813) (27/16,22/13) -> (34/13,55/21) Hyperbolic Matrix(727,-1232,298,-505) (22/13,17/10) -> (39/16,22/9) Hyperbolic Matrix(559,-952,165,-281) (17/10,29/17) -> (27/8,17/5) Hyperbolic Matrix(1147,-1960,443,-757) (41/24,12/7) -> (44/17,13/5) Hyperbolic Matrix(1009,-1736,390,-671) (12/7,31/18) -> (31/12,44/17) Hyperbolic Matrix(3249,-5600,1364,-2351) (31/18,50/29) -> (50/21,81/34) Hyperbolic Matrix(225,-392,128,-223) (26/15,7/4) -> (7/4,30/17) Parabolic Matrix(6217,-10976,1744,-3079) (30/17,83/47) -> (139/39,82/23) Hyperbolic Matrix(729,-1288,253,-447) (53/30,23/13) -> (23/8,3/1) Hyperbolic Matrix(251,-448,79,-141) (16/9,25/14) -> (3/1,16/5) Hyperbolic Matrix(1315,-2352,298,-533) (25/14,34/19) -> (22/5,53/12) Hyperbolic Matrix(617,-1120,92,-167) (29/16,20/11) -> (20/3,27/4) Hyperbolic Matrix(307,-560,108,-197) (20/11,11/6) -> (17/6,20/7) Hyperbolic Matrix(727,-1344,152,-281) (24/13,13/7) -> (43/9,24/5) Hyperbolic Matrix(29,-56,14,-27) (13/7,2/1) -> (2/1,15/7) Parabolic Matrix(365,-784,169,-363) (15/7,28/13) -> (28/13,13/6) Parabolic Matrix(307,-672,90,-197) (13/6,11/5) -> (17/5,41/12) Hyperbolic Matrix(1035,-2296,316,-701) (31/14,20/9) -> (36/11,59/18) Hyperbolic Matrix(1483,-3304,566,-1261) (20/9,29/13) -> (55/21,76/29) Hyperbolic Matrix(727,-1624,201,-449) (29/13,9/4) -> (47/13,29/8) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(195,-448,37,-85) (16/7,23/10) -> (5/1,16/3) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1401,-3304,427,-1007) (33/14,59/25) -> (59/18,23/7) Hyperbolic Matrix(2325,-5488,652,-1539) (59/25,26/11) -> (82/23,25/7) Hyperbolic Matrix(449,-1064,165,-391) (26/11,19/8) -> (19/7,30/11) Hyperbolic Matrix(447,-1064,71,-169) (19/8,50/21) -> (6/1,19/3) Hyperbolic Matrix(5265,-12544,2209,-5263) (81/34,112/47) -> (112/47,31/13) Parabolic Matrix(421,-1008,175,-419) (43/18,12/5) -> (12/5,41/17) Parabolic Matrix(1091,-2632,337,-813) (41/17,70/29) -> (42/13,13/4) Hyperbolic Matrix(1345,-3248,417,-1007) (70/29,29/12) -> (29/9,42/13) Hyperbolic Matrix(1289,-3136,529,-1287) (17/7,56/23) -> (56/23,39/16) Parabolic Matrix(1093,-2688,307,-755) (27/11,32/13) -> (32/9,57/16) Hyperbolic Matrix(309,-784,121,-307) (5/2,28/11) -> (28/11,23/9) Parabolic Matrix(391,-1008,109,-281) (18/7,31/12) -> (25/7,18/5) Hyperbolic Matrix(169,-448,63,-167) (29/11,8/3) -> (8/3,27/10) Parabolic Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(225,-616,61,-167) (30/11,11/4) -> (11/3,26/7) Hyperbolic Matrix(141,-392,50,-139) (11/4,14/5) -> (14/5,17/6) Parabolic Matrix(505,-1624,139,-447) (16/5,29/9) -> (29/8,40/11) Hyperbolic Matrix(953,-3136,289,-951) (23/7,56/17) -> (56/17,33/10) Parabolic Matrix(2101,-7056,625,-2099) (47/14,84/25) -> (84/25,37/11) Parabolic Matrix(475,-1624,74,-253) (41/12,24/7) -> (32/5,13/2) Hyperbolic Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(10781,-38416,3025,-10779) (57/16,196/55) -> (196/55,139/39) Parabolic Matrix(3473,-12544,961,-3471) (65/18,112/31) -> (112/31,47/13) Parabolic Matrix(841,-3136,225,-839) (41/11,56/15) -> (56/15,15/4) Parabolic Matrix(29,-112,7,-27) (15/4,4/1) -> (4/1,13/3) Parabolic Matrix(1597,-7056,361,-1595) (53/12,84/19) -> (84/19,31/7) Parabolic Matrix(85,-392,18,-83) (9/2,14/3) -> (14/3,19/4) Parabolic Matrix(141,-784,25,-139) (11/2,28/5) -> (28/5,17/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,26,1) Matrix(195,-224,74,-85) -> Matrix(89,-4,868,-39) Matrix(813,-952,310,-363) -> Matrix(43,-2,452,-21) Matrix(617,-728,189,-223) -> Matrix(45,-2,338,-15) Matrix(897,-1064,188,-223) -> Matrix(43,-2,280,-13) Matrix(895,-1064,519,-617) -> Matrix(303,-14,4610,-213) Matrix(139,-168,24,-29) -> Matrix(43,-2,194,-9) Matrix(503,-616,138,-169) -> Matrix(41,-2,308,-15) Matrix(363,-448,205,-253) -> Matrix(85,-4,1254,-59) Matrix(309,-392,242,-307) -> Matrix(41,-2,800,-39) Matrix(701,-896,284,-363) -> Matrix(79,-4,810,-41) Matrix(699,-896,110,-141) -> Matrix(79,-4,336,-17) Matrix(391,-504,218,-281) -> Matrix(43,-2,624,-29) Matrix(561,-728,215,-279) -> Matrix(41,-2,390,-19) Matrix(85,-112,63,-83) -> Matrix(1,0,0,1) Matrix(1065,-1456,286,-391) -> Matrix(77,-4,520,-27) Matrix(449,-616,285,-391) -> Matrix(39,-2,644,-33) Matrix(447,-616,82,-113) -> Matrix(37,-2,204,-11) Matrix(1175,-1624,649,-897) -> Matrix(27,-2,392,-29) Matrix(1457,-2016,404,-559) -> Matrix(1,0,-16,1) Matrix(727,-1008,445,-617) -> Matrix(79,-4,1284,-65) Matrix(281,-392,200,-279) -> Matrix(39,-2,722,-37) Matrix(3893,-5488,2204,-3107) -> Matrix(153,-8,2276,-119) Matrix(1429,-2016,297,-419) -> Matrix(75,-4,394,-21) Matrix(475,-672,258,-365) -> Matrix(71,-4,1012,-57) Matrix(671,-952,277,-393) -> Matrix(43,-2,452,-21) Matrix(1063,-1512,670,-953) -> Matrix(115,-6,1936,-101) Matrix(391,-560,118,-169) -> Matrix(75,-4,544,-29) Matrix(895,-1288,312,-449) -> Matrix(37,-2,278,-15) Matrix(505,-728,77,-111) -> Matrix(37,-2,130,-7) Matrix(1819,-2632,1065,-1541) -> Matrix(183,-10,2800,-153) Matrix(2241,-3248,1313,-1903) -> Matrix(357,-20,5480,-307) Matrix(617,-896,115,-167) -> Matrix(1,0,-12,1) Matrix(307,-448,135,-197) -> Matrix(75,-4,844,-45) Matrix(253,-392,162,-251) -> Matrix(103,-6,1734,-101) Matrix(393,-616,178,-279) -> Matrix(167,-10,1954,-117) Matrix(673,-1064,389,-615) -> Matrix(101,-6,1532,-91) Matrix(1483,-2352,442,-701) -> Matrix(135,-8,962,-57) Matrix(141,-224,17,-27) -> Matrix(67,-4,218,-13) Matrix(139,-224,18,-29) -> Matrix(65,-4,244,-15) Matrix(589,-952,86,-139) -> Matrix(31,-2,140,-9) Matrix(1315,-2128,537,-869) -> Matrix(133,-8,1380,-83) Matrix(449,-728,103,-167) -> Matrix(33,-2,182,-11) Matrix(1065,-1736,446,-727) -> Matrix(35,-2,368,-21) Matrix(307,-504,120,-197) -> Matrix(161,-10,1594,-99) Matrix(167,-280,34,-57) -> Matrix(31,-2,202,-13) Matrix(1259,-2128,481,-813) -> Matrix(125,-8,1172,-75) Matrix(727,-1232,298,-505) -> Matrix(435,-28,4552,-293) Matrix(559,-952,165,-281) -> Matrix(31,-2,140,-9) Matrix(1147,-1960,443,-757) -> Matrix(31,-2,264,-17) Matrix(1009,-1736,390,-671) -> Matrix(31,-2,264,-17) Matrix(3249,-5600,1364,-2351) -> Matrix(1097,-72,11808,-775) Matrix(225,-392,128,-223) -> Matrix(151,-10,2250,-149) Matrix(6217,-10976,1744,-3079) -> Matrix(1,0,-8,1) Matrix(729,-1288,253,-447) -> Matrix(89,-6,816,-55) Matrix(251,-448,79,-141) -> Matrix(59,-4,428,-29) Matrix(1315,-2352,298,-533) -> Matrix(117,-8,746,-51) Matrix(617,-1120,92,-167) -> Matrix(115,-8,532,-37) Matrix(307,-560,108,-197) -> Matrix(115,-8,992,-69) Matrix(727,-1344,152,-281) -> Matrix(113,-8,664,-47) Matrix(29,-56,14,-27) -> Matrix(27,-2,338,-25) Matrix(365,-784,169,-363) -> Matrix(289,-24,3456,-287) Matrix(307,-672,90,-197) -> Matrix(47,-4,388,-33) Matrix(1035,-2296,316,-701) -> Matrix(209,-18,1614,-139) Matrix(1483,-3304,566,-1261) -> Matrix(23,-2,288,-25) Matrix(727,-1624,201,-449) -> Matrix(23,-2,288,-25) Matrix(223,-504,50,-113) -> Matrix(23,-2,104,-9) Matrix(195,-448,37,-85) -> Matrix(45,-4,214,-19) Matrix(169,-392,72,-167) -> Matrix(111,-10,1210,-109) Matrix(1401,-3304,427,-1007) -> Matrix(107,-10,824,-77) Matrix(2325,-5488,652,-1539) -> Matrix(1,0,-4,1) Matrix(449,-1064,165,-391) -> Matrix(65,-6,596,-55) Matrix(447,-1064,71,-169) -> Matrix(151,-14,658,-61) Matrix(5265,-12544,2209,-5263) -> Matrix(1721,-160,18490,-1719) Matrix(421,-1008,175,-419) -> Matrix(1,0,0,1) Matrix(1091,-2632,337,-813) -> Matrix(107,-10,824,-77) Matrix(1345,-3248,417,-1007) -> Matrix(213,-20,1736,-163) Matrix(1289,-3136,529,-1287) -> Matrix(757,-72,7938,-755) Matrix(1093,-2688,307,-755) -> Matrix(41,-4,318,-31) Matrix(309,-784,121,-307) -> Matrix(161,-16,1600,-159) Matrix(391,-1008,109,-281) -> Matrix(39,-4,244,-25) Matrix(169,-448,63,-167) -> Matrix(77,-8,722,-75) Matrix(559,-1512,166,-449) -> Matrix(55,-6,376,-41) Matrix(225,-616,61,-167) -> Matrix(19,-2,124,-13) Matrix(141,-392,50,-139) -> Matrix(55,-6,486,-53) Matrix(505,-1624,139,-447) -> Matrix(17,-2,128,-15) Matrix(953,-3136,289,-951) -> Matrix(181,-24,1350,-179) Matrix(2101,-7056,625,-2099) -> Matrix(113,-16,784,-111) Matrix(475,-1624,74,-253) -> Matrix(47,-6,196,-25) Matrix(113,-392,32,-111) -> Matrix(15,-2,98,-13) Matrix(10781,-38416,3025,-10779) -> Matrix(169,-24,1176,-167) Matrix(3473,-12544,961,-3471) -> Matrix(1,0,22,1) Matrix(841,-3136,225,-839) -> Matrix(53,-8,338,-51) Matrix(29,-112,7,-27) -> Matrix(1,0,0,1) Matrix(1597,-7056,361,-1595) -> Matrix(49,-8,288,-47) Matrix(85,-392,18,-83) -> Matrix(13,-2,72,-11) Matrix(141,-784,25,-139) -> Matrix(41,-8,200,-39) 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): 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 26 1 2/1 1/13 2 14 28/13 1/12 24 1 13/6 1/12 1 28 11/5 7/82 1 28 20/9 0 7 29/13 23/266 1 28 9/4 7/80 1 28 25/11 3/34 1 28 16/7 4/45 2 7 23/10 5/56 1 28 7/3 1/11 5 4 33/14 5/54 1 28 59/25 3/32 1 28 26/11 1/11 2 14 19/8 7/76 1 28 50/21 9/97 2 14 112/47 4/43 10 1 31/13 11/118 1 28 12/5 0 7 41/17 3/32 1 28 70/29 3/32 10 2 29/12 19/202 1 28 17/7 11/116 1 28 56/23 2/21 18 1 22/9 7/73 2 14 27/11 17/176 1 28 5/2 1/10 1 28 28/11 1/10 16 1 18/7 5/49 2 14 31/12 5/48 1 28 44/17 0 7 13/5 1/10 1 28 34/13 3/29 2 14 55/21 3/26 1 28 21/8 1/10 3 4 8/3 2/19 2 7 27/10 13/120 1 28 19/7 1/8 1 28 30/11 1/9 2 14 11/4 1/10 1 28 14/5 1/9 6 2 17/6 5/44 1 28 20/7 0 7 3/1 1/8 1 28 16/5 0/1 2 7 29/9 7/58 1 28 42/13 1/8 10 2 13/4 1/8 1 28 36/11 0 7 59/18 1/8 1 28 23/7 5/38 1 28 56/17 2/15 6 1 10/3 1/7 2 14 84/25 1/7 16 1 37/11 7/48 1 28 27/8 5/32 1 28 17/5 1/10 1 28 41/12 1/8 1 28 24/7 2/15 2 7 7/2 1/7 1 4 32/9 0/1 2 7 57/16 7/50 1 28 196/55 1/7 24 1 82/23 1/7 2 14 25/7 3/20 1 28 18/5 1/5 2 14 112/31 0/1 22 1 47/13 1/16 1 28 29/8 3/26 1 28 11/3 1/6 1 28 26/7 1/7 2 14 56/15 2/13 2 1 15/4 1/6 1 28 4/1 0 7 13/3 1/6 1 28 22/5 1/7 2 14 84/19 1/6 8 1 31/7 1/6 1 28 9/2 1/8 1 28 14/3 1/6 2 2 19/4 3/16 1 28 24/5 2/11 2 7 29/6 5/24 1 28 5/1 1/6 1 28 16/3 0/1 2 7 27/5 7/40 1 28 11/2 3/16 1 28 28/5 1/5 8 1 6/1 1/5 2 14 19/3 7/30 1 28 32/5 4/17 2 7 13/2 1/4 1 28 20/3 0 7 27/4 11/48 1 28 7/1 1/4 3 4 8/1 2/7 2 7 1/0 1/0 1 28 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(27,-56,13,-27) (2/1,28/13) -> (2/1,28/13) Reflection Matrix(337,-728,156,-337) (28/13,13/6) -> (28/13,13/6) Reflection Matrix(307,-672,90,-197) (13/6,11/5) -> (17/5,41/12) Hyperbolic Matrix(253,-560,89,-197) (11/5,20/9) -> (17/6,20/7) Glide Reflection Matrix(503,-1120,75,-167) (20/9,29/13) -> (20/3,27/4) Glide Reflection Matrix(727,-1624,201,-449) (29/13,9/4) -> (47/13,29/8) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(197,-448,62,-141) (25/11,16/7) -> (3/1,16/5) Glide Reflection Matrix(195,-448,37,-85) (16/7,23/10) -> (5/1,16/3) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1401,-3304,427,-1007) (33/14,59/25) -> (59/18,23/7) Hyperbolic Matrix(2325,-5488,652,-1539) (59/25,26/11) -> (82/23,25/7) Hyperbolic Matrix(449,-1064,165,-391) (26/11,19/8) -> (19/7,30/11) Hyperbolic Matrix(447,-1064,71,-169) (19/8,50/21) -> (6/1,19/3) Hyperbolic Matrix(2351,-5600,987,-2351) (50/21,112/47) -> (50/21,112/47) Reflection Matrix(2913,-6944,1222,-2913) (112/47,31/13) -> (112/47,31/13) Reflection Matrix(727,-1736,281,-671) (31/13,12/5) -> (31/12,44/17) Glide Reflection Matrix(813,-1960,314,-757) (12/5,41/17) -> (44/17,13/5) Glide Reflection Matrix(1091,-2632,337,-813) (41/17,70/29) -> (42/13,13/4) Hyperbolic Matrix(1345,-3248,417,-1007) (70/29,29/12) -> (29/9,42/13) Hyperbolic Matrix(393,-952,116,-281) (29/12,17/7) -> (27/8,17/5) Glide Reflection Matrix(783,-1904,322,-783) (17/7,56/23) -> (17/7,56/23) Reflection Matrix(505,-1232,207,-505) (56/23,22/9) -> (56/23,22/9) Reflection Matrix(869,-2128,332,-813) (22/9,27/11) -> (34/13,55/21) Glide Reflection Matrix(113,-280,23,-57) (27/11,5/2) -> (29/6,5/1) Glide Reflection Matrix(111,-280,44,-111) (5/2,28/11) -> (5/2,28/11) Reflection Matrix(197,-504,77,-197) (28/11,18/7) -> (28/11,18/7) Reflection Matrix(391,-1008,109,-281) (18/7,31/12) -> (25/7,18/5) Hyperbolic Matrix(279,-728,64,-167) (13/5,34/13) -> (13/3,22/5) Glide Reflection Matrix(363,-952,53,-139) (55/21,21/8) -> (27/4,7/1) Glide Reflection Matrix(85,-224,11,-29) (21/8,8/3) -> (7/1,8/1) Glide Reflection Matrix(83,-224,10,-27) (8/3,27/10) -> (8/1,1/0) Glide Reflection Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(225,-616,61,-167) (30/11,11/4) -> (11/3,26/7) Hyperbolic Matrix(141,-392,50,-139) (11/4,14/5) -> (14/5,17/6) Parabolic Matrix(449,-1288,137,-393) (20/7,3/1) -> (36/11,59/18) Glide Reflection Matrix(279,-896,52,-167) (16/5,29/9) -> (16/3,27/5) Glide Reflection Matrix(223,-728,34,-111) (13/4,36/11) -> (13/2,20/3) Glide Reflection Matrix(783,-2576,238,-783) (23/7,56/17) -> (23/7,56/17) Reflection Matrix(169,-560,51,-169) (56/17,10/3) -> (56/17,10/3) Reflection Matrix(251,-840,75,-251) (10/3,84/25) -> (10/3,84/25) Reflection Matrix(1849,-6216,550,-1849) (84/25,37/11) -> (84/25,37/11) Reflection Matrix(475,-1624,74,-253) (41/12,24/7) -> (32/5,13/2) Hyperbolic Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(645,-2296,134,-477) (32/9,57/16) -> (24/5,29/6) Glide Reflection Matrix(6271,-22344,1760,-6271) (57/16,196/55) -> (57/16,196/55) Reflection Matrix(4509,-16072,1265,-4509) (196/55,82/23) -> (196/55,82/23) Reflection Matrix(559,-2016,155,-559) (18/5,112/31) -> (18/5,112/31) Reflection Matrix(2913,-10528,806,-2913) (112/31,47/13) -> (112/31,47/13) Reflection Matrix(169,-616,31,-113) (29/8,11/3) -> (27/5,11/2) Glide Reflection Matrix(391,-1456,105,-391) (26/7,56/15) -> (26/7,56/15) Reflection Matrix(449,-1680,120,-449) (56/15,15/4) -> (56/15,15/4) Reflection Matrix(29,-112,7,-27) (15/4,4/1) -> (4/1,13/3) Parabolic Matrix(419,-1848,95,-419) (22/5,84/19) -> (22/5,84/19) Reflection Matrix(1177,-5208,266,-1177) (84/19,31/7) -> (84/19,31/7) Reflection Matrix(85,-392,18,-83) (9/2,14/3) -> (14/3,19/4) Parabolic Matrix(223,-1064,35,-167) (19/4,24/5) -> (19/3,32/5) Glide Reflection Matrix(111,-616,20,-111) (11/2,28/5) -> (11/2,28/5) Reflection Matrix(29,-168,5,-29) (28/5,6/1) -> (28/5,6/1) 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(1,0,26,-1) (0/1,2/1) -> (0/1,1/13) Matrix(27,-56,13,-27) -> Matrix(25,-2,312,-25) (2/1,28/13) -> (1/13,1/12) Matrix(337,-728,156,-337) -> Matrix(263,-22,3144,-263) (28/13,13/6) -> (1/12,11/131) Matrix(307,-672,90,-197) -> Matrix(47,-4,388,-33) Matrix(253,-560,89,-197) -> Matrix(93,-8,802,-69) Matrix(503,-1120,75,-167) -> Matrix(93,-8,430,-37) Matrix(727,-1624,201,-449) -> Matrix(23,-2,288,-25) 1/12 Matrix(223,-504,50,-113) -> Matrix(23,-2,104,-9) Matrix(197,-448,62,-141) -> Matrix(45,-4,326,-29) Matrix(195,-448,37,-85) -> Matrix(45,-4,214,-19) Matrix(169,-392,72,-167) -> Matrix(111,-10,1210,-109) 1/11 Matrix(1401,-3304,427,-1007) -> Matrix(107,-10,824,-77) Matrix(2325,-5488,652,-1539) -> Matrix(1,0,-4,1) 0/1 Matrix(449,-1064,165,-391) -> Matrix(65,-6,596,-55) Matrix(447,-1064,71,-169) -> Matrix(151,-14,658,-61) Matrix(2351,-5600,987,-2351) -> Matrix(775,-72,8342,-775) (50/21,112/47) -> (9/97,4/43) Matrix(2913,-6944,1222,-2913) -> Matrix(945,-88,10148,-945) (112/47,31/13) -> (4/43,11/118) Matrix(727,-1736,281,-671) -> Matrix(21,-2,178,-17) Matrix(813,-1960,314,-757) -> Matrix(21,-2,178,-17) Matrix(1091,-2632,337,-813) -> Matrix(107,-10,824,-77) Matrix(1345,-3248,417,-1007) -> Matrix(213,-20,1736,-163) Matrix(393,-952,116,-281) -> Matrix(21,-2,94,-9) Matrix(783,-1904,322,-783) -> Matrix(463,-44,4872,-463) (17/7,56/23) -> (11/116,2/21) Matrix(505,-1232,207,-505) -> Matrix(293,-28,3066,-293) (56/23,22/9) -> (2/21,7/73) Matrix(869,-2128,332,-813) -> Matrix(83,-8,778,-75) Matrix(113,-280,23,-57) -> Matrix(21,-2,136,-13) Matrix(111,-280,44,-111) -> Matrix(61,-6,620,-61) (5/2,28/11) -> (3/31,1/10) Matrix(197,-504,77,-197) -> Matrix(99,-10,980,-99) (28/11,18/7) -> (1/10,5/49) Matrix(391,-1008,109,-281) -> Matrix(39,-4,244,-25) Matrix(279,-728,64,-167) -> Matrix(19,-2,104,-11) Matrix(363,-952,53,-139) -> Matrix(21,-2,94,-9) Matrix(85,-224,11,-29) -> Matrix(39,-4,146,-15) Matrix(83,-224,10,-27) -> Matrix(37,-4,120,-13) Matrix(559,-1512,166,-449) -> Matrix(55,-6,376,-41) Matrix(225,-616,61,-167) -> Matrix(19,-2,124,-13) Matrix(141,-392,50,-139) -> Matrix(55,-6,486,-53) 1/9 Matrix(449,-1288,137,-393) -> Matrix(15,-2,112,-15) *** -> (1/8,1/7) Matrix(279,-896,52,-167) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(223,-728,34,-111) -> Matrix(15,-2,52,-7) Matrix(783,-2576,238,-783) -> Matrix(151,-20,1140,-151) (23/7,56/17) -> (5/38,2/15) Matrix(169,-560,51,-169) -> Matrix(29,-4,210,-29) (56/17,10/3) -> (2/15,1/7) Matrix(251,-840,75,-251) -> Matrix(15,-2,112,-15) (10/3,84/25) -> (1/8,1/7) Matrix(1849,-6216,550,-1849) -> Matrix(97,-14,672,-97) (84/25,37/11) -> (1/7,7/48) Matrix(475,-1624,74,-253) -> Matrix(47,-6,196,-25) Matrix(113,-392,32,-111) -> Matrix(15,-2,98,-13) 1/7 Matrix(645,-2296,134,-477) -> Matrix(15,-2,82,-11) Matrix(6271,-22344,1760,-6271) -> Matrix(99,-14,700,-99) (57/16,196/55) -> (7/50,1/7) Matrix(4509,-16072,1265,-4509) -> Matrix(69,-10,476,-69) (196/55,82/23) -> (1/7,5/34) Matrix(559,-2016,155,-559) -> Matrix(1,0,10,-1) (18/5,112/31) -> (0/1,1/5) Matrix(2913,-10528,806,-2913) -> Matrix(1,0,32,-1) (112/31,47/13) -> (0/1,1/16) Matrix(169,-616,31,-113) -> Matrix(15,-2,82,-11) Matrix(391,-1456,105,-391) -> Matrix(27,-4,182,-27) (26/7,56/15) -> (1/7,2/13) Matrix(449,-1680,120,-449) -> Matrix(25,-4,156,-25) (56/15,15/4) -> (2/13,1/6) Matrix(29,-112,7,-27) -> Matrix(1,0,0,1) Matrix(419,-1848,95,-419) -> Matrix(13,-2,84,-13) (22/5,84/19) -> (1/7,1/6) Matrix(1177,-5208,266,-1177) -> Matrix(35,-6,204,-35) (84/19,31/7) -> (1/6,3/17) Matrix(85,-392,18,-83) -> Matrix(13,-2,72,-11) 1/6 Matrix(223,-1064,35,-167) -> Matrix(13,-2,58,-9) Matrix(111,-616,20,-111) -> Matrix(31,-6,160,-31) (11/2,28/5) -> (3/16,1/5) Matrix(29,-168,5,-29) -> Matrix(9,-2,40,-9) (28/5,6/1) -> (1/5,1/4) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.