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 -9/1 -8/1 -7/1 -6/1 -17/3 -5/1 -19/4 -4/1 -11/3 -7/2 -3/1 -8/3 -43/18 -7/3 -9/4 -2/1 -1/1 -9/14 -3/5 -7/12 -6/11 -1/2 -4/9 -7/17 -3/8 -1/3 -2/7 -1/4 -3/13 -1/6 0/1 3/17 1/4 1/3 3/7 1/2 7/13 11/19 19/31 2/3 3/4 11/14 9/11 7/8 1/1 8/7 11/9 5/4 3/2 5/3 19/11 7/4 11/6 13/7 2/1 13/6 9/4 7/3 5/2 11/4 3/1 19/6 61/19 13/4 7/2 43/12 11/3 15/4 4/1 9/2 5/1 11/2 17/3 6/1 13/2 7/1 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 -1/2 1/0 -8/1 -1/2 1/0 -15/2 -1/1 0/1 -7/1 -1/2 1/0 -13/2 0/1 1/0 -6/1 -1/1 -17/3 -1/2 1/0 -28/5 -1/2 1/0 -11/2 -1/1 -1/2 -5/1 -1/2 1/0 -24/5 -1/2 -3/8 -19/4 0/1 -14/3 1/2 1/0 -9/2 -1/1 1/0 -4/1 -1/2 1/0 -19/5 -1/2 1/0 -15/4 -1/1 1/0 -26/7 -3/4 -1/2 -11/3 -1/2 1/0 -7/2 -1/1 -17/5 -3/4 -1/2 -10/3 -1/2 1/0 -13/4 -2/3 -1/2 -16/5 -1/2 -1/4 -3/1 -1/2 1/0 -17/6 -2/3 -1/2 -14/5 -1/2 -3/8 -11/4 -1/2 0/1 -30/11 -1/2 -1/4 -49/18 -1/3 -1/4 -68/25 -1/2 -1/4 -19/7 -1/2 -1/4 -27/10 -1/3 0/1 -8/3 0/1 -37/14 0/1 1/1 -29/11 -1/2 1/0 -21/8 -1/1 0/1 -55/21 -1/2 1/0 -34/13 -1/2 -1/4 -13/5 -1/2 1/0 -18/7 -1/2 1/0 -41/16 0/1 -23/9 -1/2 1/0 -28/11 -1/2 1/0 -5/2 -1/2 0/1 -12/5 1/2 1/0 -55/23 1/2 1/0 -43/18 1/1 -74/31 3/2 1/0 -31/13 1/2 1/0 -19/8 -1/1 1/0 -26/11 0/1 -33/14 1/1 1/0 -7/3 -1/2 1/0 -23/10 -1/1 0/1 -16/7 -1/2 -1/4 -9/4 0/1 -20/9 1/2 1/0 -11/5 1/2 1/0 -13/6 -1/1 1/0 -2/1 -1/2 1/0 -1/1 -1/2 1/0 -2/3 -1/2 1/0 -13/20 0/1 1/0 -11/17 -3/2 1/0 -9/14 -1/1 -25/39 -3/4 -1/2 -16/25 -3/4 -1/2 -7/11 -1/2 1/0 -26/41 -1/1 -19/30 0/1 1/0 -31/49 -3/2 1/0 -43/68 -2/1 -12/19 -3/2 1/0 -5/8 -1/1 -1/2 -28/45 -1/2 1/0 -23/37 -1/2 1/0 -18/29 -1/2 1/0 -13/21 -1/2 1/0 -34/55 -3/4 -1/2 -21/34 -1/1 0/1 -8/13 -1/1 -27/44 -1/1 -2/3 -19/31 -3/4 -1/2 -49/80 -3/4 -2/3 -30/49 -3/4 -1/2 -11/18 -1/1 -1/2 -14/23 -5/8 -1/2 -17/28 -1/2 -1/3 -3/5 -1/2 1/0 -10/17 -1/2 1/0 -7/12 0/1 -18/31 1/2 1/0 -11/19 -1/2 1/0 -26/45 -1/2 -1/4 -15/26 0/1 1/0 -19/33 -1/2 1/0 -4/7 -1/2 1/0 -9/16 0/1 1/0 -14/25 -3/2 1/0 -19/34 -1/1 -5/9 -1/2 1/0 -6/11 0/1 -13/24 -1/1 1/0 -7/13 -1/2 1/0 -15/28 -1/1 0/1 -8/15 -1/2 1/0 -9/17 -1/2 1/0 -1/2 -1/1 0/1 -7/15 -1/2 1/0 -6/13 -1/2 1/0 -5/11 -1/2 1/0 -4/9 0/1 -11/25 -1/2 1/0 -7/16 0/1 1/0 -10/23 -3/2 1/0 -3/7 -1/2 1/0 -5/12 -1/2 0/1 -12/29 -1/2 -1/4 -7/17 0/1 -9/22 0/1 1/1 -11/27 1/2 1/0 -2/5 -1/2 1/0 -7/18 -1/2 0/1 -5/13 -1/2 1/0 -3/8 0/1 -7/19 1/2 1/0 -18/49 1/2 1/0 -11/30 1/1 1/0 -15/41 1/2 1/0 -19/52 2/1 1/0 -4/11 -1/2 1/0 -9/25 1/2 1/0 -5/14 1/1 1/0 -6/17 -3/2 1/0 -1/3 -1/2 1/0 -3/10 -1/1 1/0 -5/17 -3/2 1/0 -12/41 -3/2 1/0 -7/24 -2/1 -1/1 -2/7 -1/1 -9/32 -1/1 -2/3 -7/25 -1/2 1/0 -12/43 -1/2 -1/4 -5/18 -1/1 0/1 -3/11 -1/2 1/0 -10/37 1/2 1/0 -7/26 -1/1 1/0 -18/67 -3/2 1/0 -11/41 -1/1 -4/15 -1/2 1/0 -5/19 -1/2 1/0 -1/4 -1/1 1/0 -4/17 -3/2 -5/4 -3/13 -1/1 -5/22 -1/1 -6/7 -7/31 -5/6 -3/4 -2/9 -3/4 -1/2 -3/14 -1/2 0/1 -1/5 -1/2 1/0 -3/16 -1/1 0/1 -5/27 -1/2 1/0 -2/11 -3/2 1/0 -1/6 -1/1 -2/13 -3/4 -1/2 -5/33 -3/4 -1/2 -3/20 -1/1 -2/3 -4/27 -3/4 -1/2 -1/7 -3/4 -1/2 0/1 -1/2 1/0 1/8 0/1 1/0 1/7 -1/2 1/0 1/6 -1/1 -1/2 3/17 -1/2 2/11 -1/2 -3/8 1/5 -1/2 -1/4 1/4 0/1 3/11 1/2 1/0 8/29 1/2 1/0 5/18 0/1 1/1 7/25 1/2 1/0 9/32 0/1 1/1 2/7 1/2 1/0 3/10 -1/1 0/1 7/23 0/1 4/13 1/2 1/0 5/16 -2/1 1/0 1/3 -1/2 1/0 5/14 -1/2 -1/3 9/25 -1/2 -1/4 4/11 0/1 3/8 -1/1 -1/2 5/13 -1/2 -1/4 17/44 -1/2 -4/9 12/31 -1/2 -3/8 7/18 -1/3 2/5 -1/2 -1/4 5/12 -1/7 0/1 3/7 0/1 7/16 0/1 1/7 11/25 1/6 1/4 4/9 1/4 1/2 1/2 0/1 1/0 8/15 1/2 1/0 7/13 1/0 6/11 -1/2 1/0 23/42 -1/1 17/31 -1/2 1/0 11/20 0/1 1/0 5/9 -1/2 1/0 4/7 -1/2 1/0 19/33 -1/2 1/0 15/26 -1/1 0/1 11/19 0/1 7/12 0/1 1/0 10/17 -3/2 1/0 3/5 -1/2 1/0 11/18 -1/2 0/1 30/49 -1/4 -1/6 19/31 0/1 46/75 1/4 1/2 27/44 0/1 1/2 8/13 1/2 1/0 21/34 -1/1 34/55 -1/2 1/0 13/21 -1/2 1/0 18/29 -1/2 1/0 5/8 -1/1 0/1 12/19 -3/4 -1/2 7/11 -1/2 1/0 2/3 0/1 9/13 1/4 1/2 25/36 4/9 1/2 41/59 1/2 16/23 1/2 7/12 23/33 1/2 3/4 7/10 0/1 1/1 12/17 1/2 1/0 5/7 1/2 1/0 13/18 1/2 1/1 8/11 1/2 1/0 11/15 3/2 1/0 25/34 1/1 1/0 14/19 5/2 1/0 17/23 1/0 3/4 0/1 1/0 7/9 1/2 1/0 25/32 0/1 1/3 18/23 1/2 5/8 11/14 1/1 26/33 3/2 7/4 15/19 3/2 1/0 4/5 3/2 1/0 9/11 1/0 14/17 -11/2 1/0 5/6 -2/1 1/0 6/7 -1/2 1/0 13/15 -1/2 1/0 7/8 0/1 15/17 1/2 1/0 8/9 1/2 1/0 1/1 -1/2 1/0 10/9 -9/2 1/0 9/8 -2/1 -1/1 8/7 -1/1 7/6 -1/1 0/1 6/5 1/2 1/0 17/14 3/1 1/0 11/9 1/0 16/13 -9/2 1/0 5/4 -2/1 1/0 24/19 -3/2 1/0 19/15 -3/2 1/0 33/26 -1/1 1/0 14/11 -2/1 9/7 -3/2 1/0 13/10 -4/3 -1/1 17/13 -1/1 4/3 -1/2 1/0 3/2 -1/1 8/5 -3/4 -1/2 45/28 -4/7 -1/2 37/23 -1/2 29/18 -1/2 -1/3 21/13 -1/2 1/0 34/21 -1/1 47/29 -3/4 -1/2 13/8 -1/2 0/1 31/19 0/1 49/30 -1/1 0/1 67/41 -1/2 1/0 18/11 -1/2 1/0 5/3 -1/2 1/0 17/10 -1/1 0/1 12/7 -3/2 1/0 31/18 -3/2 -1/1 19/11 -1/1 45/26 -1/1 -5/6 26/15 -5/6 -3/4 7/4 -1/1 -1/2 16/9 0/1 9/5 -1/2 1/0 20/11 -1/2 1/0 11/6 -1/1 0/1 24/13 -1/2 1/0 13/7 -1/2 1/0 2/1 -1/2 1/0 15/7 1/2 1/0 13/6 -3/1 1/0 11/5 -3/2 1/0 20/9 -1/2 1/0 9/4 -2/1 -1/1 7/3 -1/1 19/8 -1/1 -4/5 31/13 -5/6 -3/4 43/18 -7/9 -3/4 98/41 -3/4 -31/42 55/23 -3/4 -7/10 12/5 -3/4 -1/2 5/2 -1/1 -1/2 13/5 -3/4 -1/2 21/8 -3/5 -1/2 50/19 -13/24 -1/2 29/11 -1/2 8/3 -1/2 -1/4 19/7 -1/2 -1/4 11/4 0/1 25/9 1/2 1/0 39/14 0/1 1/1 14/5 3/2 1/0 59/21 1/0 45/16 -6/1 1/0 31/11 -5/2 1/0 17/6 -2/1 -1/1 3/1 -1/2 1/0 19/6 -1/1 16/5 -5/8 -1/2 61/19 -1/2 106/33 -1/2 -25/52 45/14 -1/2 -5/11 29/9 -1/2 -3/8 13/4 -1/3 0/1 10/3 1/2 1/0 17/5 1/2 1/0 24/7 3/2 1/0 31/9 1/0 7/2 -1/1 1/0 25/7 -1/2 1/0 68/19 -1/2 1/0 43/12 0/1 61/17 1/2 1/0 18/5 -1/2 1/0 47/13 1/0 76/21 -3/2 1/0 29/8 -1/1 1/0 11/3 -1/2 1/0 26/7 -3/2 1/0 15/4 0/1 1/0 4/1 -1/1 17/4 -2/3 -1/2 47/11 -1/2 -3/8 30/7 -1/2 -1/4 13/3 -1/2 1/0 9/2 -1/2 0/1 14/3 -1/2 1/0 33/7 -1/2 1/0 52/11 -1/2 1/0 19/4 -1/1 0/1 24/5 -1/2 1/0 5/1 -1/2 1/0 21/4 0/1 16/3 -3/2 1/0 11/2 -1/1 0/1 28/5 -1/2 1/0 17/3 -1/2 1/0 40/7 -1/2 1/0 23/4 -1/1 0/1 6/1 -1/2 1/0 13/2 -1/1 20/3 -1/2 1/0 27/4 -1/2 0/1 7/1 -1/2 1/0 8/1 -1/2 1/0 9/1 -1/1 10/1 -1/2 1/0 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(9,88,32,313) (-9/1,1/0) -> (7/25,9/32) Hyperbolic Matrix(67,548,-28,-229) (-9/1,-8/1) -> (-12/5,-55/23) Hyperbolic Matrix(67,508,12,91) (-8/1,-15/2) -> (11/2,28/5) Hyperbolic Matrix(89,648,32,233) (-15/2,-7/1) -> (25/9,39/14) Hyperbolic Matrix(53,352,-92,-611) (-7/1,-13/2) -> (-15/26,-19/33) Hyperbolic Matrix(71,452,-112,-713) (-13/2,-6/1) -> (-26/41,-19/30) Hyperbolic Matrix(123,704,76,435) (-6/1,-17/3) -> (21/13,34/21) Hyperbolic Matrix(199,1120,-320,-1801) (-17/3,-28/5) -> (-28/45,-23/37) Hyperbolic Matrix(381,2120,-140,-779) (-28/5,-11/2) -> (-49/18,-68/25) Hyperbolic Matrix(23,124,-64,-345) (-11/2,-5/1) -> (-9/25,-5/14) Hyperbolic Matrix(131,632,188,907) (-5/1,-24/5) -> (16/23,23/33) Hyperbolic Matrix(169,808,32,153) (-24/5,-19/4) -> (21/4,16/3) Hyperbolic Matrix(195,916,-76,-357) (-19/4,-14/3) -> (-18/7,-41/16) Hyperbolic Matrix(61,280,-100,-459) (-14/3,-9/2) -> (-11/18,-14/23) Hyperbolic Matrix(29,128,12,53) (-9/2,-4/1) -> (12/5,5/2) Hyperbolic Matrix(43,164,156,595) (-4/1,-19/5) -> (3/11,8/29) Hyperbolic Matrix(93,352,-172,-651) (-19/5,-15/4) -> (-13/24,-7/13) Hyperbolic Matrix(153,572,88,329) (-15/4,-26/7) -> (26/15,7/4) Hyperbolic Matrix(193,712,-312,-1151) (-26/7,-11/3) -> (-13/21,-34/55) Hyperbolic Matrix(55,196,-16,-57) (-11/3,-7/2) -> (-7/2,-17/5) Parabolic Matrix(59,200,100,339) (-17/5,-10/3) -> (10/17,3/5) Hyperbolic Matrix(61,200,-140,-459) (-10/3,-13/4) -> (-7/16,-10/23) Hyperbolic Matrix(89,288,72,233) (-13/4,-16/5) -> (16/13,5/4) Hyperbolic Matrix(47,148,-168,-529) (-16/5,-3/1) -> (-7/25,-12/43) Hyperbolic Matrix(205,584,-324,-923) (-3/1,-17/6) -> (-19/30,-31/49) Hyperbolic Matrix(109,308,132,373) (-17/6,-14/5) -> (14/17,5/6) Hyperbolic Matrix(101,280,-180,-499) (-14/5,-11/4) -> (-9/16,-14/25) Hyperbolic Matrix(151,412,-232,-633) (-11/4,-30/11) -> (-2/3,-13/20) Hyperbolic Matrix(963,2624,556,1515) (-30/11,-49/18) -> (45/26,26/15) Hyperbolic Matrix(431,1172,488,1327) (-68/25,-19/7) -> (15/17,8/9) Hyperbolic Matrix(105,284,376,1017) (-19/7,-27/10) -> (5/18,7/25) Hyperbolic Matrix(191,512,-72,-193) (-27/10,-8/3) -> (-8/3,-37/14) Parabolic Matrix(621,1640,220,581) (-37/14,-29/11) -> (31/11,17/6) Hyperbolic Matrix(73,192,-392,-1031) (-29/11,-21/8) -> (-3/16,-5/27) Hyperbolic Matrix(371,972,-692,-1813) (-21/8,-55/21) -> (-7/13,-15/28) Hyperbolic Matrix(741,1940,940,2461) (-55/21,-34/13) -> (26/33,15/19) Hyperbolic Matrix(273,712,-472,-1231) (-34/13,-13/5) -> (-11/19,-26/45) Hyperbolic Matrix(125,324,76,197) (-13/5,-18/7) -> (18/11,5/3) Hyperbolic Matrix(269,688,52,133) (-41/16,-23/9) -> (5/1,21/4) Hyperbolic Matrix(425,1084,336,857) (-23/9,-28/11) -> (24/19,19/15) Hyperbolic Matrix(27,68,52,131) (-28/11,-5/2) -> (1/2,8/15) Hyperbolic Matrix(13,32,28,69) (-5/2,-12/5) -> (4/9,1/2) Hyperbolic Matrix(835,1996,1524,3643) (-55/23,-43/18) -> (23/42,17/31) Hyperbolic Matrix(821,1960,1500,3581) (-43/18,-74/31) -> (6/11,23/42) Hyperbolic Matrix(1847,4408,432,1031) (-74/31,-31/13) -> (47/11,30/7) Hyperbolic Matrix(245,584,-404,-963) (-31/13,-19/8) -> (-17/28,-3/5) Hyperbolic Matrix(191,452,-352,-833) (-19/8,-26/11) -> (-6/11,-13/24) Hyperbolic Matrix(559,1320,440,1039) (-26/11,-33/14) -> (33/26,14/11) Hyperbolic Matrix(563,1324,236,555) (-33/14,-7/3) -> (31/13,43/18) Hyperbolic Matrix(137,316,-336,-775) (-7/3,-23/10) -> (-9/22,-11/27) Hyperbolic Matrix(155,356,-556,-1277) (-23/10,-16/7) -> (-12/43,-5/18) Hyperbolic Matrix(143,324,-64,-145) (-16/7,-9/4) -> (-9/4,-20/9) Parabolic Matrix(181,400,100,221) (-20/9,-11/5) -> (9/5,20/11) Hyperbolic Matrix(271,592,168,367) (-11/5,-13/6) -> (29/18,21/13) Hyperbolic Matrix(191,412,-312,-673) (-13/6,-2/1) -> (-30/49,-11/18) Hyperbolic Matrix(3,4,-4,-5) (-2/1,-1/1) -> (-1/1,-2/3) Parabolic Matrix(623,404,-1704,-1105) (-13/20,-11/17) -> (-15/41,-19/52) Hyperbolic Matrix(503,324,-784,-505) (-11/17,-9/14) -> (-9/14,-25/39) Parabolic Matrix(1061,680,220,141) (-25/39,-16/25) -> (24/5,5/1) Hyperbolic Matrix(495,316,224,143) (-16/25,-7/11) -> (11/5,20/9) Hyperbolic Matrix(2301,1460,1420,901) (-7/11,-26/41) -> (34/21,47/29) Hyperbolic Matrix(6255,3956,1744,1103) (-31/49,-43/68) -> (43/12,61/17) Hyperbolic Matrix(5441,3440,1520,961) (-43/68,-12/19) -> (68/19,43/12) Hyperbolic Matrix(51,32,-212,-133) (-12/19,-5/8) -> (-1/4,-4/17) Hyperbolic Matrix(1913,1192,528,329) (-5/8,-28/45) -> (76/21,29/8) Hyperbolic Matrix(1635,1016,2644,1643) (-23/37,-18/29) -> (34/55,13/21) Hyperbolic Matrix(581,360,-1580,-979) (-18/29,-13/21) -> (-7/19,-18/49) Hyperbolic Matrix(2621,1620,940,581) (-34/55,-21/34) -> (39/14,14/5) Hyperbolic Matrix(363,224,316,195) (-21/34,-8/13) -> (8/7,7/6) Hyperbolic Matrix(469,288,412,253) (-8/13,-27/44) -> (9/8,8/7) Hyperbolic Matrix(313,192,-2072,-1271) (-27/44,-19/31) -> (-5/33,-3/20) Hyperbolic Matrix(1397,856,204,125) (-19/31,-49/80) -> (27/4,7/1) Hyperbolic Matrix(5003,3064,8156,4995) (-49/80,-30/49) -> (46/75,27/44) Hyperbolic Matrix(1883,1144,716,435) (-14/23,-17/28) -> (21/8,50/19) Hyperbolic Matrix(339,200,100,59) (-3/5,-10/17) -> (10/3,17/5) Hyperbolic Matrix(335,196,-576,-337) (-10/17,-7/12) -> (-7/12,-18/31) Parabolic Matrix(283,164,-1044,-605) (-18/31,-11/19) -> (-3/11,-10/37) Hyperbolic Matrix(1275,736,2084,1203) (-26/45,-15/26) -> (11/18,30/49) Hyperbolic Matrix(139,80,-940,-541) (-19/33,-4/7) -> (-4/27,-1/7) Hyperbolic Matrix(227,128,-548,-309) (-4/7,-9/16) -> (-5/12,-12/29) Hyperbolic Matrix(1681,940,2720,1521) (-14/25,-19/34) -> (21/34,34/55) Hyperbolic Matrix(273,152,88,49) (-19/34,-5/9) -> (3/1,19/6) Hyperbolic Matrix(225,124,176,97) (-5/9,-6/11) -> (14/11,9/7) Hyperbolic Matrix(1465,784,256,137) (-15/28,-8/15) -> (40/7,23/4) Hyperbolic Matrix(1531,812,428,227) (-8/15,-9/17) -> (25/7,68/19) Hyperbolic Matrix(967,508,592,311) (-9/17,-1/2) -> (49/30,67/41) Hyperbolic Matrix(263,124,456,215) (-1/2,-7/15) -> (19/33,15/26) Hyperbolic Matrix(259,120,300,139) (-7/15,-6/13) -> (6/7,13/15) Hyperbolic Matrix(367,168,592,271) (-6/13,-5/11) -> (13/21,18/29) Hyperbolic Matrix(257,116,144,65) (-5/11,-4/9) -> (16/9,9/5) Hyperbolic Matrix(181,80,500,221) (-4/9,-11/25) -> (9/25,4/11) Hyperbolic Matrix(355,156,644,283) (-11/25,-7/16) -> (11/20,5/9) Hyperbolic Matrix(175,76,-776,-337) (-10/23,-3/7) -> (-7/31,-2/9) Hyperbolic Matrix(105,44,136,57) (-3/7,-5/12) -> (3/4,7/9) 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(875,356,204,83) (-11/27,-2/5) -> (30/7,13/3) Hyperbolic Matrix(297,116,64,25) (-2/5,-7/18) -> (9/2,14/3) Hyperbolic Matrix(197,76,324,125) (-7/18,-5/13) -> (3/5,11/18) Hyperbolic Matrix(95,36,-256,-97) (-5/13,-3/8) -> (-3/8,-7/19) Parabolic Matrix(883,324,-3284,-1205) (-18/49,-11/30) -> (-7/26,-18/67) Hyperbolic Matrix(1923,704,1516,555) (-11/30,-15/41) -> (19/15,33/26) Hyperbolic Matrix(911,332,568,207) (-19/52,-4/11) -> (8/5,45/28) Hyperbolic Matrix(221,80,500,181) (-4/11,-9/25) -> (11/25,4/9) Hyperbolic Matrix(373,132,308,109) (-5/14,-6/17) -> (6/5,17/14) Hyperbolic Matrix(91,32,-492,-173) (-6/17,-1/3) -> (-5/27,-2/11) Hyperbolic Matrix(145,44,56,17) (-1/3,-3/10) -> (5/2,13/5) Hyperbolic Matrix(27,8,172,51) (-3/10,-5/17) -> (1/7,1/6) Hyperbolic Matrix(847,248,1472,431) (-5/17,-12/41) -> (4/7,19/33) Hyperbolic Matrix(1355,396,284,83) (-12/41,-7/24) -> (19/4,24/5) Hyperbolic Matrix(111,32,-392,-113) (-7/24,-2/7) -> (-2/7,-9/32) Parabolic Matrix(1253,352,388,109) (-9/32,-7/25) -> (29/9,13/4) Hyperbolic Matrix(277,76,164,45) (-5/18,-3/11) -> (5/3,17/10) Hyperbolic Matrix(1289,348,1752,473) (-10/37,-7/26) -> (25/34,14/19) Hyperbolic Matrix(1013,272,108,29) (-18/67,-11/41) -> (9/1,10/1) Hyperbolic Matrix(463,124,56,15) (-11/41,-4/15) -> (8/1,9/1) Hyperbolic Matrix(301,80,380,101) (-4/15,-5/19) -> (15/19,4/5) Hyperbolic Matrix(595,156,164,43) (-5/19,-1/4) -> (29/8,11/3) Hyperbolic Matrix(341,80,260,61) (-4/17,-3/13) -> (17/13,4/3) Hyperbolic Matrix(543,124,416,95) (-3/13,-5/22) -> (13/10,17/13) Hyperbolic Matrix(723,164,1036,235) (-5/22,-7/31) -> (23/33,7/10) Hyperbolic Matrix(129,28,152,33) (-2/9,-3/14) -> (5/6,6/7) Hyperbolic Matrix(227,48,52,11) (-3/14,-1/5) -> (13/3,9/2) Hyperbolic Matrix(591,112,248,47) (-1/5,-3/16) -> (19/8,31/13) Hyperbolic Matrix(23,4,-144,-25) (-2/11,-1/6) -> (-1/6,-2/13) Parabolic Matrix(1465,224,896,137) (-2/13,-5/33) -> (67/41,18/11) Hyperbolic Matrix(1553,232,328,49) (-3/20,-4/27) -> (52/11,19/4) Hyperbolic Matrix(67,8,92,11) (-1/7,0/1) -> (8/11,11/15) Hyperbolic Matrix(91,-8,148,-13) (0/1,1/8) -> (27/44,8/13) Hyperbolic Matrix(213,-28,388,-51) (1/8,1/7) -> (17/31,11/20) Hyperbolic Matrix(715,-124,444,-77) (1/6,3/17) -> (37/23,29/18) Hyperbolic Matrix(425,-76,576,-103) (3/17,2/11) -> (14/19,17/23) Hyperbolic Matrix(251,-48,68,-13) (2/11,1/5) -> (11/3,26/7) Hyperbolic Matrix(17,-4,64,-15) (1/5,1/4) -> (1/4,3/11) Parabolic Matrix(751,-208,408,-113) (8/29,5/18) -> (11/6,24/13) Hyperbolic Matrix(327,-92,32,-9) (9/32,2/7) -> (10/1,1/0) Hyperbolic Matrix(109,-32,92,-27) (2/7,3/10) -> (7/6,6/5) Hyperbolic Matrix(413,-128,1068,-331) (4/13,5/16) -> (17/44,12/31) Hyperbolic Matrix(791,-248,488,-153) (5/16,1/3) -> (47/29,13/8) Hyperbolic Matrix(193,-68,88,-31) (1/3,5/14) -> (13/6,11/5) Hyperbolic Matrix(779,-280,1060,-381) (5/14,9/25) -> (11/15,25/34) 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(1949,-752,692,-267) (5/13,17/44) -> (45/16,31/11) Hyperbolic Matrix(763,-296,116,-45) (12/31,7/18) -> (13/2,20/3) Hyperbolic Matrix(173,-68,28,-11) (7/18,2/5) -> (6/1,13/2) Hyperbolic Matrix(185,-76,56,-23) (2/5,5/12) -> (13/4,10/3) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(737,-324,944,-415) (7/16,11/25) -> (7/9,25/32) Hyperbolic Matrix(1693,-908,468,-251) (8/15,7/13) -> (47/13,76/21) Hyperbolic Matrix(751,-408,208,-113) (7/13,6/11) -> (18/5,47/13) Hyperbolic Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(1737,-1004,1064,-615) (15/26,11/19) -> (31/19,49/30) Hyperbolic Matrix(619,-360,380,-221) (11/19,7/12) -> (13/8,31/19) Hyperbolic Matrix(567,-332,152,-89) (7/12,10/17) -> (26/7,15/4) Hyperbolic Matrix(2357,-1444,3844,-2355) (30/49,19/31) -> (19/31,46/75) Parabolic Matrix(791,-488,248,-153) (8/13,21/34) -> (19/6,16/5) Hyperbolic Matrix(715,-444,124,-77) (18/29,5/8) -> (23/4,6/1) Hyperbolic Matrix(331,-208,148,-93) (5/8,12/19) -> (20/9,9/4) 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(4779,-3320,1700,-1181) (25/36,41/59) -> (59/21,45/16) Hyperbolic Matrix(2347,-1632,732,-509) (41/59,16/23) -> (16/5,61/19) Hyperbolic Matrix(387,-272,212,-149) (7/10,12/17) -> (20/11,11/6) Hyperbolic Matrix(175,-124,24,-17) (12/17,5/7) -> (7/1,8/1) Hyperbolic Matrix(499,-360,140,-101) (5/7,13/18) -> (7/2,25/7) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(1183,-876,736,-545) (17/23,3/4) -> (45/28,37/23) Hyperbolic Matrix(527,-412,472,-369) (25/32,18/23) -> (10/9,9/8) Hyperbolic Matrix(617,-484,784,-615) (18/23,11/14) -> (11/14,26/33) Parabolic Matrix(233,-188,88,-71) (4/5,9/11) -> (29/11,8/3) Hyperbolic Matrix(1043,-856,396,-325) (9/11,14/17) -> (50/19,29/11) Hyperbolic Matrix(225,-196,256,-223) (13/15,7/8) -> (7/8,15/17) Parabolic 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(497,-604,144,-175) (17/14,11/9) -> (31/9,7/2) Hyperbolic Matrix(619,-760,180,-221) (11/9,16/13) -> (24/7,31/9) Hyperbolic Matrix(593,-748,88,-111) (5/4,24/19) -> (20/3,27/4) Hyperbolic Matrix(149,-192,52,-67) (9/7,13/10) -> (17/6,3/1) Hyperbolic Matrix(25,-36,16,-23) (4/3,3/2) -> (3/2,8/5) 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(793,-1468,168,-311) (24/13,13/7) -> (33/7,52/11) Hyperbolic Matrix(131,-248,28,-53) (13/7,2/1) -> (14/3,33/7) Hyperbolic Matrix(187,-392,52,-109) (2/1,15/7) -> (61/17,18/5) Hyperbolic Matrix(489,-1052,152,-327) (15/7,13/6) -> (45/14,29/9) Hyperbolic 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(177,-484,64,-175) (19/7,11/4) -> (11/4,25/9) Parabolic Matrix(2531,-7108,788,-2213) (14/5,59/21) -> (61/19,106/33) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(205,-1156,36,-203) (28/5,17/3) -> (17/3,40/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(9,88,32,313) -> Matrix(1,0,2,1) Matrix(67,548,-28,-229) -> Matrix(1,0,2,1) Matrix(67,508,12,91) -> Matrix(1,0,0,1) Matrix(89,648,32,233) -> Matrix(1,0,2,1) Matrix(53,352,-92,-611) -> Matrix(1,0,0,1) Matrix(71,452,-112,-713) -> Matrix(1,0,0,1) Matrix(123,704,76,435) -> Matrix(1,0,0,1) Matrix(199,1120,-320,-1801) -> Matrix(1,0,0,1) Matrix(381,2120,-140,-779) -> Matrix(1,0,-2,1) Matrix(23,124,-64,-345) -> Matrix(1,0,2,1) Matrix(131,632,188,907) -> Matrix(3,2,4,3) Matrix(169,808,32,153) -> Matrix(1,0,2,1) Matrix(195,916,-76,-357) -> Matrix(1,0,-2,1) Matrix(61,280,-100,-459) -> Matrix(1,2,-2,-3) Matrix(29,128,12,53) -> Matrix(1,2,-2,-3) Matrix(43,164,156,595) -> Matrix(1,0,2,1) Matrix(93,352,-172,-651) -> Matrix(1,0,0,1) Matrix(153,572,88,329) -> Matrix(1,2,-2,-3) Matrix(193,712,-312,-1151) -> Matrix(1,0,0,1) Matrix(55,196,-16,-57) -> Matrix(1,2,-2,-3) Matrix(59,200,100,339) -> Matrix(3,2,-2,-1) Matrix(61,200,-140,-459) -> Matrix(3,2,-2,-1) Matrix(89,288,72,233) -> Matrix(7,4,-2,-1) Matrix(47,148,-168,-529) -> Matrix(1,0,0,1) Matrix(205,584,-324,-923) -> Matrix(3,2,-2,-1) Matrix(109,308,132,373) -> Matrix(7,4,-2,-1) Matrix(101,280,-180,-499) -> Matrix(1,0,2,1) Matrix(151,412,-232,-633) -> Matrix(1,0,2,1) Matrix(963,2624,556,1515) -> Matrix(11,4,-14,-5) Matrix(431,1172,488,1327) -> Matrix(1,0,4,1) Matrix(105,284,376,1017) -> Matrix(1,0,4,1) Matrix(191,512,-72,-193) -> Matrix(1,0,4,1) Matrix(621,1640,220,581) -> Matrix(1,-2,0,1) Matrix(73,192,-392,-1031) -> Matrix(1,0,0,1) Matrix(371,972,-692,-1813) -> Matrix(1,0,0,1) Matrix(741,1940,940,2461) -> Matrix(1,2,0,1) Matrix(273,712,-472,-1231) -> Matrix(1,0,0,1) Matrix(125,324,76,197) -> Matrix(1,0,0,1) Matrix(269,688,52,133) -> Matrix(1,0,0,1) Matrix(425,1084,336,857) -> Matrix(3,2,-2,-1) Matrix(27,68,52,131) -> Matrix(1,0,2,1) Matrix(13,32,28,69) -> Matrix(1,0,2,1) Matrix(835,1996,1524,3643) -> Matrix(1,0,-2,1) Matrix(821,1960,1500,3581) -> Matrix(1,-2,0,1) Matrix(1847,4408,432,1031) -> Matrix(1,-2,-2,5) Matrix(245,584,-404,-963) -> Matrix(1,0,-2,1) Matrix(191,452,-352,-833) -> Matrix(1,0,0,1) Matrix(559,1320,440,1039) -> Matrix(1,-2,0,1) Matrix(563,1324,236,555) -> Matrix(3,4,-4,-5) Matrix(137,316,-336,-775) -> Matrix(1,0,2,1) Matrix(155,356,-556,-1277) -> Matrix(1,0,0,1) Matrix(143,324,-64,-145) -> Matrix(1,0,4,1) Matrix(181,400,100,221) -> Matrix(1,0,-2,1) Matrix(271,592,168,367) -> Matrix(1,0,-2,1) Matrix(191,412,-312,-673) -> Matrix(1,2,-2,-3) Matrix(3,4,-4,-5) -> Matrix(1,0,0,1) Matrix(623,404,-1704,-1105) -> Matrix(1,2,0,1) Matrix(503,324,-784,-505) -> Matrix(3,4,-4,-5) Matrix(1061,680,220,141) -> Matrix(3,2,-2,-1) Matrix(495,316,224,143) -> Matrix(3,2,-2,-1) Matrix(2301,1460,1420,901) -> Matrix(1,2,-2,-3) Matrix(6255,3956,1744,1103) -> Matrix(1,2,0,1) Matrix(5441,3440,1520,961) -> Matrix(1,2,-2,-3) Matrix(51,32,-212,-133) -> Matrix(3,2,-2,-1) Matrix(1913,1192,528,329) -> Matrix(3,2,-2,-1) Matrix(1635,1016,2644,1643) -> Matrix(1,0,0,1) Matrix(581,360,-1580,-979) -> Matrix(1,0,2,1) Matrix(2621,1620,940,581) -> Matrix(1,0,2,1) Matrix(363,224,316,195) -> Matrix(1,0,0,1) Matrix(469,288,412,253) -> Matrix(5,4,-4,-3) Matrix(313,192,-2072,-1271) -> Matrix(1,0,0,1) Matrix(1397,856,204,125) -> Matrix(3,2,-2,-1) Matrix(5003,3064,8156,4995) -> Matrix(3,2,10,7) Matrix(1883,1144,716,435) -> Matrix(9,4,-16,-7) Matrix(339,200,100,59) -> Matrix(1,0,2,1) Matrix(335,196,-576,-337) -> Matrix(1,0,2,1) Matrix(283,164,-1044,-605) -> Matrix(1,0,0,1) Matrix(1275,736,2084,1203) -> Matrix(1,0,-2,1) Matrix(139,80,-940,-541) -> Matrix(1,2,-2,-3) Matrix(227,128,-548,-309) -> Matrix(1,0,-2,1) Matrix(1681,940,2720,1521) -> Matrix(1,2,-2,-3) Matrix(273,152,88,49) -> Matrix(1,0,0,1) Matrix(225,124,176,97) -> Matrix(3,2,-2,-1) Matrix(1465,784,256,137) -> Matrix(1,0,0,1) Matrix(1531,812,428,227) -> Matrix(1,0,0,1) Matrix(967,508,592,311) -> Matrix(1,0,0,1) Matrix(263,124,456,215) -> Matrix(1,0,0,1) Matrix(259,120,300,139) -> Matrix(1,0,0,1) Matrix(367,168,592,271) -> Matrix(1,0,0,1) Matrix(257,116,144,65) -> Matrix(1,0,0,1) Matrix(181,80,500,221) -> Matrix(1,0,-2,1) Matrix(355,156,644,283) -> Matrix(1,0,0,1) Matrix(175,76,-776,-337) -> Matrix(3,4,-4,-5) Matrix(105,44,136,57) -> Matrix(1,0,2,1) Matrix(271,112,888,367) -> Matrix(1,0,4,1) Matrix(205,84,676,277) -> Matrix(1,0,-2,1) Matrix(875,356,204,83) -> Matrix(1,0,-2,1) Matrix(297,116,64,25) -> Matrix(1,0,0,1) Matrix(197,76,324,125) -> Matrix(1,0,0,1) Matrix(95,36,-256,-97) -> Matrix(1,0,2,1) Matrix(883,324,-3284,-1205) -> Matrix(1,-2,0,1) Matrix(1923,704,1516,555) -> Matrix(1,-2,0,1) Matrix(911,332,568,207) -> Matrix(1,2,-2,-3) Matrix(221,80,500,181) -> Matrix(1,0,4,1) Matrix(373,132,308,109) -> Matrix(1,2,0,1) Matrix(91,32,-492,-173) -> Matrix(1,0,0,1) Matrix(145,44,56,17) -> Matrix(1,2,-2,-3) Matrix(27,8,172,51) -> Matrix(1,2,-2,-3) Matrix(847,248,1472,431) -> Matrix(1,2,-2,-3) Matrix(1355,396,284,83) -> Matrix(1,2,-2,-3) Matrix(111,32,-392,-113) -> Matrix(3,4,-4,-5) Matrix(1253,352,388,109) -> Matrix(3,2,-8,-5) Matrix(277,76,164,45) -> Matrix(1,0,0,1) Matrix(1289,348,1752,473) -> Matrix(1,2,0,1) Matrix(1013,272,108,29) -> Matrix(1,2,-2,-3) Matrix(463,124,56,15) -> Matrix(1,0,0,1) Matrix(301,80,380,101) -> Matrix(1,2,0,1) Matrix(595,156,164,43) -> Matrix(1,0,0,1) Matrix(341,80,260,61) -> Matrix(3,4,-4,-5) Matrix(543,124,416,95) -> Matrix(11,10,-10,-9) Matrix(723,164,1036,235) -> Matrix(7,6,8,7) Matrix(129,28,152,33) -> Matrix(3,2,-2,-1) Matrix(227,48,52,11) -> Matrix(1,0,0,1) Matrix(591,112,248,47) -> Matrix(3,4,-4,-5) Matrix(23,4,-144,-25) -> Matrix(3,4,-4,-5) Matrix(1465,224,896,137) -> Matrix(3,2,-2,-1) Matrix(1553,232,328,49) -> Matrix(3,2,-2,-1) Matrix(67,8,92,11) -> Matrix(1,0,2,1) Matrix(91,-8,148,-13) -> Matrix(1,0,2,1) Matrix(213,-28,388,-51) -> Matrix(1,0,0,1) Matrix(715,-124,444,-77) -> Matrix(3,2,-8,-5) Matrix(425,-76,576,-103) -> Matrix(9,4,2,1) Matrix(251,-48,68,-13) -> Matrix(1,0,2,1) Matrix(17,-4,64,-15) -> Matrix(1,0,4,1) Matrix(751,-208,408,-113) -> Matrix(1,0,-2,1) Matrix(327,-92,32,-9) -> Matrix(1,0,-2,1) Matrix(109,-32,92,-27) -> Matrix(1,0,0,1) Matrix(413,-128,1068,-331) -> Matrix(1,-2,-2,5) Matrix(791,-248,488,-153) -> Matrix(1,2,-2,-3) Matrix(193,-68,88,-31) -> Matrix(3,2,-2,-1) Matrix(779,-280,1060,-381) -> Matrix(5,2,2,1) Matrix(205,-76,116,-43) -> Matrix(1,0,0,1) Matrix(377,-144,144,-55) -> Matrix(5,2,-8,-3) Matrix(1949,-752,692,-267) -> Matrix(3,2,-2,-1) Matrix(763,-296,116,-45) -> Matrix(5,2,-8,-3) Matrix(173,-68,28,-11) -> Matrix(1,0,2,1) Matrix(185,-76,56,-23) -> Matrix(1,0,4,1) Matrix(85,-36,196,-83) -> Matrix(1,0,14,1) Matrix(737,-324,944,-415) -> Matrix(1,0,-4,1) Matrix(1693,-908,468,-251) -> Matrix(1,-2,0,1) Matrix(751,-408,208,-113) -> Matrix(1,0,0,1) Matrix(205,-116,76,-43) -> Matrix(1,0,-2,1) Matrix(1737,-1004,1064,-615) -> Matrix(1,0,0,1) Matrix(619,-360,380,-221) -> Matrix(1,0,-2,1) Matrix(567,-332,152,-89) -> Matrix(1,0,0,1) Matrix(2357,-1444,3844,-2355) -> Matrix(1,0,8,1) Matrix(791,-488,248,-153) -> Matrix(1,2,-2,-3) Matrix(715,-444,124,-77) -> Matrix(1,0,0,1) Matrix(331,-208,148,-93) -> Matrix(3,2,-2,-1) Matrix(587,-372,172,-109) -> Matrix(1,0,2,1) Matrix(49,-32,72,-47) -> Matrix(1,0,4,1) Matrix(1913,-1328,448,-311) -> Matrix(5,-2,-12,5) Matrix(4779,-3320,1700,-1181) -> Matrix(21,-10,-2,1) Matrix(2347,-1632,732,-509) -> Matrix(11,-6,-20,11) Matrix(387,-272,212,-149) -> Matrix(1,0,-2,1) Matrix(175,-124,24,-17) -> Matrix(1,0,-2,1) Matrix(499,-360,140,-101) -> Matrix(1,0,-2,1) Matrix(557,-404,324,-235) -> Matrix(1,-2,0,1) Matrix(1183,-876,736,-545) -> Matrix(1,4,-2,-7) Matrix(527,-412,472,-369) -> Matrix(5,-2,-2,1) Matrix(617,-484,784,-615) -> Matrix(5,-4,4,-3) Matrix(233,-188,88,-71) -> Matrix(1,-2,-2,5) Matrix(1043,-856,396,-325) -> Matrix(1,12,-2,-23) Matrix(225,-196,256,-223) -> Matrix(1,0,2,1) Matrix(507,-452,212,-189) -> Matrix(3,-2,-4,3) Matrix(593,-648,248,-271) -> Matrix(3,-2,-4,3) Matrix(497,-604,144,-175) -> Matrix(1,-4,0,1) Matrix(619,-760,180,-221) -> Matrix(1,6,0,1) Matrix(593,-748,88,-111) -> Matrix(1,2,-2,-3) Matrix(149,-192,52,-67) -> Matrix(1,2,-2,-3) Matrix(25,-36,16,-23) -> Matrix(1,2,-2,-3) Matrix(237,-404,44,-75) -> Matrix(1,0,0,1) Matrix(837,-1444,484,-835) -> Matrix(7,8,-8,-9) Matrix(793,-1468,168,-311) -> Matrix(1,0,0,1) Matrix(131,-248,28,-53) -> Matrix(1,0,0,1) Matrix(187,-392,52,-109) -> Matrix(1,0,0,1) Matrix(489,-1052,152,-327) -> Matrix(1,-2,-2,5) Matrix(85,-196,36,-83) -> Matrix(5,6,-6,-7) Matrix(3753,-8968,1168,-2791) -> Matrix(29,22,-62,-47) Matrix(177,-484,64,-175) -> Matrix(1,0,4,1) Matrix(2531,-7108,788,-2213) -> Matrix(1,-14,-2,29) Matrix(33,-128,8,-31) -> Matrix(1,2,-2,-3) Matrix(205,-1156,36,-203) -> Matrix(1,0,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 33 Degree of the the map X: 33 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 -4/9 -3/7 -3/8 -1/3 -2/7 -1/6 0/1 1/7 3/17 1/4 1/3 3/7 1/2 7/13 3/5 2/3 9/11 7/8 1/1 11/9 3/2 5/3 19/11 9/5 13/7 2/1 7/3 5/2 11/4 3/1 61/19 13/4 7/2 15/4 4/1 13/3 9/2 5/1 21/4 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 -1/2 1/0 -1/2 -1/1 0/1 -7/15 -1/2 1/0 -6/13 -1/2 1/0 -5/11 -1/2 1/0 -4/9 0/1 -11/25 -1/2 1/0 -7/16 0/1 1/0 -3/7 -1/2 1/0 -5/12 -1/2 0/1 -2/5 -1/2 1/0 -7/18 -1/2 0/1 -5/13 -1/2 1/0 -3/8 0/1 -7/19 1/2 1/0 -4/11 -1/2 1/0 -9/25 1/2 1/0 -5/14 1/1 1/0 -6/17 -3/2 1/0 -1/3 -1/2 1/0 -3/10 -1/1 1/0 -5/17 -3/2 1/0 -7/24 -2/1 -1/1 -2/7 -1/1 -9/32 -1/1 -2/3 -7/25 -1/2 1/0 -5/18 -1/1 0/1 -3/11 -1/2 1/0 -4/15 -1/2 1/0 -5/19 -1/2 1/0 -1/4 -1/1 1/0 -2/9 -3/4 -1/2 -3/14 -1/2 0/1 -1/5 -1/2 1/0 -3/16 -1/1 0/1 -5/27 -1/2 1/0 -2/11 -3/2 1/0 -1/6 -1/1 -2/13 -3/4 -1/2 -1/7 -3/4 -1/2 0/1 -1/2 1/0 1/8 0/1 1/0 1/7 -1/2 1/0 1/6 -1/1 -1/2 3/17 -1/2 2/11 -1/2 -3/8 1/5 -1/2 -1/4 1/4 0/1 3/11 1/2 1/0 5/18 0/1 1/1 7/25 1/2 1/0 2/7 1/2 1/0 3/10 -1/1 0/1 1/3 -1/2 1/0 5/14 -1/2 -1/3 4/11 0/1 3/8 -1/1 -1/2 5/13 -1/2 -1/4 12/31 -1/2 -3/8 7/18 -1/3 2/5 -1/2 -1/4 5/12 -1/7 0/1 3/7 0/1 7/16 0/1 1/7 11/25 1/6 1/4 4/9 1/4 1/2 1/2 0/1 1/0 7/13 1/0 6/11 -1/2 1/0 17/31 -1/2 1/0 11/20 0/1 1/0 5/9 -1/2 1/0 4/7 -1/2 1/0 19/33 -1/2 1/0 15/26 -1/1 0/1 11/19 0/1 7/12 0/1 1/0 10/17 -3/2 1/0 3/5 -1/2 1/0 11/18 -1/2 0/1 8/13 1/2 1/0 13/21 -1/2 1/0 18/29 -1/2 1/0 5/8 -1/1 0/1 7/11 -1/2 1/0 2/3 0/1 9/13 1/4 1/2 25/36 4/9 1/2 41/59 1/2 16/23 1/2 7/12 7/10 0/1 1/1 12/17 1/2 1/0 5/7 1/2 1/0 13/18 1/2 1/1 8/11 1/2 1/0 11/15 3/2 1/0 3/4 0/1 1/0 7/9 1/2 1/0 25/32 0/1 1/3 18/23 1/2 5/8 11/14 1/1 15/19 3/2 1/0 4/5 3/2 1/0 9/11 1/0 5/6 -2/1 1/0 6/7 -1/2 1/0 13/15 -1/2 1/0 7/8 0/1 15/17 1/2 1/0 8/9 1/2 1/0 1/1 -1/2 1/0 7/6 -1/1 0/1 6/5 1/2 1/0 11/9 1/0 16/13 -9/2 1/0 5/4 -2/1 1/0 4/3 -1/2 1/0 3/2 -1/1 8/5 -3/4 -1/2 37/23 -1/2 29/18 -1/2 -1/3 21/13 -1/2 1/0 34/21 -1/1 13/8 -1/2 0/1 31/19 0/1 18/11 -1/2 1/0 5/3 -1/2 1/0 17/10 -1/1 0/1 12/7 -3/2 1/0 31/18 -3/2 -1/1 19/11 -1/1 45/26 -1/1 -5/6 26/15 -5/6 -3/4 7/4 -1/1 -1/2 16/9 0/1 9/5 -1/2 1/0 20/11 -1/2 1/0 11/6 -1/1 0/1 13/7 -1/2 1/0 2/1 -1/2 1/0 15/7 1/2 1/0 13/6 -3/1 1/0 11/5 -3/2 1/0 9/4 -2/1 -1/1 7/3 -1/1 19/8 -1/1 -4/5 31/13 -5/6 -3/4 12/5 -3/4 -1/2 5/2 -1/1 -1/2 13/5 -3/4 -1/2 21/8 -3/5 -1/2 29/11 -1/2 8/3 -1/2 -1/4 19/7 -1/2 -1/4 11/4 0/1 25/9 1/2 1/0 14/5 3/2 1/0 3/1 -1/2 1/0 16/5 -5/8 -1/2 61/19 -1/2 45/14 -1/2 -5/11 29/9 -1/2 -3/8 13/4 -1/3 0/1 10/3 1/2 1/0 7/2 -1/1 1/0 25/7 -1/2 1/0 18/5 -1/2 1/0 47/13 1/0 29/8 -1/1 1/0 11/3 -1/2 1/0 26/7 -3/2 1/0 15/4 0/1 1/0 4/1 -1/1 17/4 -2/3 -1/2 47/11 -1/2 -3/8 30/7 -1/2 -1/4 13/3 -1/2 1/0 9/2 -1/2 0/1 14/3 -1/2 1/0 33/7 -1/2 1/0 19/4 -1/1 0/1 5/1 -1/2 1/0 21/4 0/1 16/3 -3/2 1/0 11/2 -1/1 0/1 17/3 -1/2 1/0 23/4 -1/1 0/1 6/1 -1/2 1/0 13/2 -1/1 20/3 -1/2 1/0 7/1 -1/2 1/0 8/1 -1/2 1/0 9/1 -1/1 1/0 -1/1 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(263,124,456,215) (-1/2,-7/15) -> (19/33,15/26) Hyperbolic Matrix(259,120,300,139) (-7/15,-6/13) -> (6/7,13/15) Hyperbolic Matrix(367,168,592,271) (-6/13,-5/11) -> (13/21,18/29) Hyperbolic Matrix(257,116,144,65) (-5/11,-4/9) -> (16/9,9/5) Hyperbolic Matrix(1039,458,642,283) (-4/9,-11/25) -> (21/13,34/21) Hyperbolic Matrix(355,156,644,283) (-11/25,-7/16) -> (11/20,5/9) Hyperbolic Matrix(179,78,-498,-217) (-7/16,-3/7) -> (-9/25,-5/14) Hyperbolic Matrix(105,44,136,57) (-3/7,-5/12) -> (3/4,7/9) Hyperbolic Matrix(169,70,70,29) (-5/12,-2/5) -> (12/5,5/2) Hyperbolic Matrix(297,116,64,25) (-2/5,-7/18) -> (9/2,14/3) Hyperbolic Matrix(197,76,324,125) (-7/18,-5/13) -> (3/5,11/18) Hyperbolic Matrix(95,36,-256,-97) (-5/13,-3/8) -> (-3/8,-7/19) Parabolic Matrix(223,82,378,139) (-7/19,-4/11) -> (10/17,3/5) Hyperbolic Matrix(221,80,500,181) (-4/11,-9/25) -> (11/25,4/9) Hyperbolic Matrix(309,110,250,89) (-5/14,-6/17) -> (16/13,5/4) Hyperbolic Matrix(91,32,-492,-173) (-6/17,-1/3) -> (-5/27,-2/11) Hyperbolic Matrix(145,44,56,17) (-1/3,-3/10) -> (5/2,13/5) Hyperbolic Matrix(27,8,172,51) (-3/10,-5/17) -> (1/7,1/6) Hyperbolic Matrix(253,74,906,265) (-5/17,-7/24) -> (5/18,7/25) Hyperbolic Matrix(111,32,-392,-113) (-7/24,-2/7) -> (-2/7,-9/32) Parabolic Matrix(1253,352,388,109) (-9/32,-7/25) -> (29/9,13/4) 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(301,80,380,101) (-4/15,-5/19) -> (15/19,4/5) Hyperbolic Matrix(595,156,164,43) (-5/19,-1/4) -> (29/8,11/3) Hyperbolic Matrix(25,6,54,13) (-1/4,-2/9) -> (4/9,1/2) Hyperbolic Matrix(129,28,152,33) (-2/9,-3/14) -> (5/6,6/7) Hyperbolic Matrix(227,48,52,11) (-3/14,-1/5) -> (13/3,9/2) Hyperbolic Matrix(591,112,248,47) (-1/5,-3/16) -> (19/8,31/13) Hyperbolic Matrix(23,4,-144,-25) (-2/11,-1/6) -> (-1/6,-2/13) Parabolic Matrix(257,38,142,21) (-2/13,-1/7) -> (9/5,20/11) Hyperbolic Matrix(67,8,92,11) (-1/7,0/1) -> (8/11,11/15) 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(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(251,-48,68,-13) (2/11,1/5) -> (11/3,26/7) Hyperbolic Matrix(17,-4,64,-15) (1/5,1/4) -> (1/4,3/11) Parabolic Matrix(299,-82,62,-17) (3/11,5/18) -> (19/4,5/1) Hyperbolic Matrix(233,-66,406,-115) (7/25,2/7) -> (4/7,19/33) Hyperbolic Matrix(109,-32,92,-27) (2/7,3/10) -> (7/6,6/5) Hyperbolic Matrix(137,-42,62,-19) (3/10,1/3) -> (11/5,9/4) Hyperbolic Matrix(193,-68,88,-31) (1/3,5/14) -> (13/6,11/5) 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(763,-296,116,-45) (12/31,7/18) -> (13/2,20/3) Hyperbolic Matrix(173,-68,28,-11) (7/18,2/5) -> (6/1,13/2) Hyperbolic Matrix(185,-76,56,-23) (2/5,5/12) -> (13/4,10/3) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(737,-324,944,-415) (7/16,11/25) -> (7/9,25/32) 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(253,-146,26,-15) (15/26,11/19) -> (9/1,1/0) Hyperbolic Matrix(619,-360,380,-221) (11/19,7/12) -> (13/8,31/19) Hyperbolic Matrix(567,-332,152,-89) (7/12,10/17) -> (26/7,15/4) Hyperbolic Matrix(559,-342,322,-197) (11/18,8/13) -> (26/15,7/4) 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(85,-54,74,-47) (5/8,7/11) -> (1/1,7/6) 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(4851,-3370,1510,-1049) (25/36,41/59) -> (61/19,45/14) Hyperbolic Matrix(2347,-1632,732,-509) (41/59,16/23) -> (16/5,61/19) Hyperbolic Matrix(755,-526,966,-673) (16/23,7/10) -> (25/32,18/23) Hyperbolic Matrix(387,-272,212,-149) (7/10,12/17) -> (20/11,11/6) Hyperbolic Matrix(175,-124,24,-17) (12/17,5/7) -> (7/1,8/1) Hyperbolic Matrix(499,-360,140,-101) (5/7,13/18) -> (7/2,25/7) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(519,-382,322,-237) (11/15,3/4) -> (29/18,21/13) Hyperbolic Matrix(707,-554,134,-105) (18/23,11/14) -> (21/4,16/3) Hyperbolic Matrix(469,-370,90,-71) (11/14,15/19) -> (5/1,21/4) Hyperbolic Matrix(233,-188,88,-71) (4/5,9/11) -> (29/11,8/3) Hyperbolic Matrix(405,-334,154,-127) (9/11,5/6) -> (21/8,29/11) Hyperbolic Matrix(225,-196,256,-223) (13/15,7/8) -> (7/8,15/17) Parabolic Matrix(453,-406,106,-95) (8/9,1/1) -> (47/11,30/7) Hyperbolic Matrix(199,-242,162,-197) (6/5,11/9) -> (11/9,16/13) Parabolic Matrix(61,-78,18,-23) (5/4,4/3) -> (10/3,7/2) Hyperbolic Matrix(25,-36,16,-23) (4/3,3/2) -> (3/2,8/5) Parabolic Matrix(251,-410,30,-49) (31/19,18/11) -> (8/1,9/1) Hyperbolic 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(331,-610,70,-129) (11/6,13/7) -> (33/7,19/4) Hyperbolic Matrix(131,-248,28,-53) (13/7,2/1) -> (14/3,33/7) Hyperbolic Matrix(489,-1052,152,-327) (15/7,13/6) -> (45/14,29/9) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(455,-1086,106,-253) (31/13,12/5) -> (30/7,13/3) Hyperbolic Matrix(177,-484,64,-175) (19/7,11/4) -> (11/4,25/9) Parabolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) 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(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(1,1,-2,-1) Matrix(263,124,456,215) -> Matrix(1,0,0,1) Matrix(259,120,300,139) -> Matrix(1,0,0,1) Matrix(367,168,592,271) -> Matrix(1,0,0,1) Matrix(257,116,144,65) -> Matrix(1,0,0,1) Matrix(1039,458,642,283) -> Matrix(1,1,-2,-1) Matrix(355,156,644,283) -> Matrix(1,0,0,1) Matrix(179,78,-498,-217) -> Matrix(1,1,0,1) Matrix(105,44,136,57) -> Matrix(1,0,2,1) Matrix(169,70,70,29) -> Matrix(3,1,-4,-1) Matrix(297,116,64,25) -> Matrix(1,0,0,1) Matrix(197,76,324,125) -> Matrix(1,0,0,1) Matrix(95,36,-256,-97) -> Matrix(1,0,2,1) Matrix(223,82,378,139) -> Matrix(1,-1,0,1) Matrix(221,80,500,181) -> Matrix(1,0,4,1) Matrix(309,110,250,89) -> Matrix(1,-3,0,1) Matrix(91,32,-492,-173) -> Matrix(1,0,0,1) Matrix(145,44,56,17) -> Matrix(1,2,-2,-3) Matrix(27,8,172,51) -> Matrix(1,2,-2,-3) Matrix(253,74,906,265) -> Matrix(1,1,2,3) Matrix(111,32,-392,-113) -> Matrix(3,4,-4,-5) Matrix(1253,352,388,109) -> Matrix(3,2,-8,-5) Matrix(165,46,-886,-247) -> Matrix(1,1,-2,-1) Matrix(277,76,164,45) -> Matrix(1,0,0,1) Matrix(273,74,166,45) -> Matrix(1,1,-2,-1) Matrix(301,80,380,101) -> Matrix(1,2,0,1) Matrix(595,156,164,43) -> Matrix(1,0,0,1) Matrix(25,6,54,13) -> Matrix(1,1,0,1) Matrix(129,28,152,33) -> Matrix(3,2,-2,-1) Matrix(227,48,52,11) -> Matrix(1,0,0,1) Matrix(591,112,248,47) -> Matrix(3,4,-4,-5) Matrix(23,4,-144,-25) -> Matrix(3,4,-4,-5) Matrix(257,38,142,21) -> Matrix(1,1,-4,-3) Matrix(67,8,92,11) -> Matrix(1,0,2,1) Matrix(253,-26,146,-15) -> Matrix(5,1,-6,-1) Matrix(213,-28,388,-51) -> Matrix(1,0,0,1) Matrix(715,-124,444,-77) -> Matrix(3,2,-8,-5) Matrix(543,-98,338,-61) -> Matrix(7,3,-12,-5) Matrix(251,-48,68,-13) -> Matrix(1,0,2,1) Matrix(17,-4,64,-15) -> Matrix(1,0,4,1) Matrix(299,-82,62,-17) -> Matrix(1,-1,0,1) Matrix(233,-66,406,-115) -> Matrix(1,-1,0,1) Matrix(109,-32,92,-27) -> Matrix(1,0,0,1) Matrix(137,-42,62,-19) -> Matrix(1,-1,0,1) Matrix(193,-68,88,-31) -> Matrix(3,2,-2,-1) Matrix(619,-222,382,-137) -> Matrix(3,1,-4,-1) Matrix(205,-76,116,-43) -> Matrix(1,0,0,1) Matrix(377,-144,144,-55) -> Matrix(5,2,-8,-3) Matrix(491,-190,230,-89) -> Matrix(3,1,2,1) Matrix(763,-296,116,-45) -> Matrix(5,2,-8,-3) Matrix(173,-68,28,-11) -> Matrix(1,0,2,1) Matrix(185,-76,56,-23) -> Matrix(1,0,4,1) Matrix(85,-36,196,-83) -> Matrix(1,0,14,1) Matrix(737,-324,944,-415) -> Matrix(1,0,-4,1) Matrix(471,-250,130,-69) -> Matrix(1,-1,0,1) Matrix(751,-408,208,-113) -> Matrix(1,0,0,1) Matrix(413,-226,466,-255) -> Matrix(1,1,0,1) Matrix(205,-116,76,-43) -> Matrix(1,0,-2,1) Matrix(253,-146,26,-15) -> Matrix(1,1,-2,-1) Matrix(619,-360,380,-221) -> Matrix(1,0,-2,1) Matrix(567,-332,152,-89) -> Matrix(1,0,0,1) Matrix(559,-342,322,-197) -> Matrix(3,1,-4,-1) Matrix(619,-382,222,-137) -> Matrix(1,1,0,1) Matrix(715,-444,124,-77) -> Matrix(1,0,0,1) Matrix(85,-54,74,-47) -> Matrix(1,1,-2,-1) Matrix(49,-32,72,-47) -> Matrix(1,0,4,1) Matrix(1913,-1328,448,-311) -> Matrix(5,-2,-12,5) Matrix(4851,-3370,1510,-1049) -> Matrix(19,-9,-40,19) Matrix(2347,-1632,732,-509) -> Matrix(11,-6,-20,11) Matrix(755,-526,966,-673) -> Matrix(1,-1,4,-3) Matrix(387,-272,212,-149) -> Matrix(1,0,-2,1) Matrix(175,-124,24,-17) -> Matrix(1,0,-2,1) Matrix(499,-360,140,-101) -> Matrix(1,0,-2,1) Matrix(557,-404,324,-235) -> Matrix(1,-2,0,1) Matrix(519,-382,322,-237) -> Matrix(1,-1,-2,3) Matrix(707,-554,134,-105) -> Matrix(1,-1,2,-1) Matrix(469,-370,90,-71) -> Matrix(1,-1,-2,3) Matrix(233,-188,88,-71) -> Matrix(1,-2,-2,5) Matrix(405,-334,154,-127) -> Matrix(1,5,-2,-9) Matrix(225,-196,256,-223) -> Matrix(1,0,2,1) Matrix(453,-406,106,-95) -> Matrix(1,-1,-2,3) Matrix(199,-242,162,-197) -> Matrix(1,-5,0,1) Matrix(61,-78,18,-23) -> Matrix(1,1,0,1) Matrix(25,-36,16,-23) -> Matrix(1,2,-2,-3) Matrix(251,-410,30,-49) -> Matrix(1,1,-2,-1) Matrix(237,-404,44,-75) -> Matrix(1,0,0,1) Matrix(837,-1444,484,-835) -> Matrix(7,8,-8,-9) Matrix(331,-610,70,-129) -> Matrix(1,1,-2,-1) Matrix(131,-248,28,-53) -> Matrix(1,0,0,1) Matrix(489,-1052,152,-327) -> Matrix(1,-2,-2,5) Matrix(85,-196,36,-83) -> Matrix(5,6,-6,-7) Matrix(455,-1086,106,-253) -> Matrix(1,1,-6,-5) Matrix(177,-484,64,-175) -> Matrix(1,0,4,1) Matrix(31,-90,10,-29) -> Matrix(1,1,-2,-1) Matrix(175,-626,26,-93) -> Matrix(1,1,-2,-1) Matrix(33,-128,8,-31) -> Matrix(1,2,-2,-3) Matrix(103,-578,18,-101) -> Matrix(1,1,-2,-1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 33 ----------------------------------------------------------------------- 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 (-1/1,0/1).(-1/2,1/0) 0 2 0/1 (-1/2,1/0) 0 20 1/6 (-1/1,-1/2) 0 20 3/17 -1/2 5 2 2/11 (-1/2,-3/8) 0 20 1/5 0 10 1/4 0/1 4 4 3/11 0 10 5/18 (0/1,1/1) 0 20 2/7 (1/2,1/0) 0 20 3/10 (-1/1,0/1) 0 20 1/3 (-1/1,0/1).(-1/2,1/0) 0 10 5/14 (-1/2,-1/3) 0 20 4/11 0/1 1 4 3/8 (-1/1,-1/2) 0 20 5/13 0 10 12/31 (-1/2,-3/8) 0 20 7/18 -1/3 2 4 2/5 (-1/2,-1/4) 0 20 5/12 (-1/7,0/1) 0 20 3/7 0/1 7 2 1/2 (0/1,1/0) 0 20 7/13 1/0 1 2 6/11 (-1/2,1/0) 0 20 5/9 0 10 4/7 (-1/2,1/0) 0 20 15/26 (-1/1,0/1) 0 20 11/19 0/1 1 2 7/12 (0/1,1/0) 0 20 3/5 (-1/1,0/1).(-1/2,1/0) 0 10 8/13 (1/2,1/0) 0 20 13/21 0 10 5/8 (-1/1,0/1) 0 20 7/11 0 10 2/3 0/1 2 4 9/13 0 10 25/36 (4/9,1/2) 0 20 41/59 1/2 15 2 16/23 (1/2,7/12) 0 20 7/10 (0/1,1/1) 0 20 12/17 (1/2,1/0) 0 20 5/7 (0/1,1/1).(1/2,1/0) 0 10 13/18 (1/2,1/1) 0 20 8/11 (1/2,1/0) 0 20 3/4 (0/1,1/0) 0 20 4/5 (3/2,1/0) 0 20 9/11 1/0 7 2 5/6 (-2/1,1/0) 0 20 1/1 0 10 7/6 (-1/1,0/1) 0 20 6/5 (1/2,1/0) 0 20 11/9 1/0 5 2 5/4 (-2/1,1/0) 0 20 4/3 (-1/2,1/0) 0 20 3/2 -1/1 2 4 8/5 (-3/4,-1/2) 0 20 21/13 0 10 13/8 (-1/2,0/1) 0 20 5/3 (-1/1,0/1).(-1/2,1/0) 0 10 12/7 (-3/2,1/0) 0 20 31/18 (-3/2,-1/1) 0 20 19/11 -1/1 4 2 7/4 (-1/1,-1/2) 0 20 9/5 0 10 11/6 (-1/1,0/1) 0 20 13/7 (-1/1,0/1).(-1/2,1/0) 0 2 2/1 (-1/2,1/0) 0 20 15/7 0 10 13/6 (-3/1,1/0) 0 20 11/5 (-2/1,-1/1).(-3/2,1/0) 0 10 9/4 (-2/1,-1/1) 0 20 7/3 -1/1 3 2 5/2 (-1/1,-1/2) 0 20 8/3 (-1/2,-1/4) 0 20 19/7 0 10 11/4 0/1 4 4 25/9 0 10 14/5 (3/2,1/0) 0 20 3/1 (-1/1,0/1).(-1/2,1/0) 0 10 16/5 (-5/8,-1/2) 0 20 13/4 (-1/3,0/1) 0 20 10/3 (1/2,1/0) 0 20 7/2 (-1/1,1/0) 0 20 25/7 (-1/1,0/1).(-1/2,1/0) 0 10 18/5 (-1/2,1/0) 0 20 11/3 0 10 15/4 (0/1,1/0) 0 20 4/1 -1/1 1 4 9/2 (-1/2,0/1) 0 20 5/1 0 10 11/2 (-1/1,0/1) 0 20 17/3 (-1/1,0/1).(-1/2,1/0) 0 2 6/1 (-1/2,1/0) 0 20 13/2 -1/1 2 4 20/3 (-1/2,1/0) 0 20 7/1 (-1/1,0/1).(-1/2,1/0) 0 10 8/1 (-1/2,1/0) 0 20 1/0 (-1/1,0/1) 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(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(51,-8,70,-11) (0/1,1/6) -> (8/11,3/4) Glide Reflection Matrix(35,-6,204,-35) (1/6,3/17) -> (1/6,3/17) Reflection Matrix(67,-12,374,-67) (3/17,2/11) -> (3/17,2/11) Reflection Matrix(271,-50,168,-31) (2/11,1/5) -> (8/5,21/13) Glide Reflection Matrix(17,-4,64,-15) (1/5,1/4) -> (1/4,3/11) Parabolic Matrix(283,-78,156,-43) (3/11,5/18) -> (9/5,11/6) Glide Reflection Matrix(265,-74,376,-105) (5/18,2/7) -> (7/10,12/17) Glide Reflection Matrix(109,-32,92,-27) (2/7,3/10) -> (7/6,6/5) Hyperbolic Matrix(137,-42,62,-19) (3/10,1/3) -> (11/5,9/4) Hyperbolic Matrix(193,-68,88,-31) (1/3,5/14) -> (13/6,11/5) Hyperbolic Matrix(221,-80,58,-21) (5/14,4/11) -> (15/4,4/1) Glide Reflection Matrix(131,-48,30,-11) (4/11,3/8) -> (4/1,9/2) Glide Reflection Matrix(73,-28,86,-33) (3/8,5/13) -> (5/6,1/1) Glide Reflection Matrix(491,-190,230,-89) (5/13,12/31) -> (2/1,15/7) Hyperbolic Matrix(763,-296,116,-45) (12/31,7/18) -> (13/2,20/3) Hyperbolic Matrix(173,-68,28,-11) (7/18,2/5) -> (6/1,13/2) Hyperbolic Matrix(185,-76,56,-23) (2/5,5/12) -> (13/4,10/3) Hyperbolic Matrix(71,-30,168,-71) (5/12,3/7) -> (5/12,3/7) Reflection Matrix(13,-6,28,-13) (3/7,1/2) -> (3/7,1/2) Reflection Matrix(27,-14,52,-27) (1/2,7/13) -> (1/2,7/13) Reflection Matrix(155,-84,286,-155) (7/13,6/11) -> (7/13,6/11) Reflection Matrix(283,-156,78,-43) (6/11,5/9) -> (18/5,11/3) Glide Reflection Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(215,-124,26,-15) (4/7,15/26) -> (8/1,1/0) Glide Reflection Matrix(571,-330,988,-571) (15/26,11/19) -> (15/26,11/19) Reflection Matrix(265,-154,456,-265) (11/19,7/12) -> (11/19,7/12) Reflection Matrix(125,-74,76,-45) (7/12,3/5) -> (13/8,5/3) Glide Reflection Matrix(125,-76,74,-45) (3/5,8/13) -> (5/3,12/7) Glide Reflection Matrix(619,-382,222,-137) (8/13,13/21) -> (25/9,14/5) Hyperbolic Matrix(271,-168,50,-31) (13/21,5/8) -> (5/1,11/2) Glide Reflection Matrix(85,-54,74,-47) (5/8,7/11) -> (1/1,7/6) Hyperbolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(709,-492,330,-229) (9/13,25/36) -> (15/7,13/6) Glide Reflection Matrix(2951,-2050,4248,-2951) (25/36,41/59) -> (25/36,41/59) Reflection Matrix(1887,-1312,2714,-1887) (41/59,16/23) -> (41/59,16/23) Reflection Matrix(459,-320,142,-99) (16/23,7/10) -> (16/5,13/4) Glide Reflection Matrix(175,-124,24,-17) (12/17,5/7) -> (7/1,8/1) Hyperbolic Matrix(499,-360,140,-101) (5/7,13/18) -> (7/2,25/7) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(57,-44,22,-17) (3/4,4/5) -> (5/2,8/3) Glide Reflection Matrix(89,-72,110,-89) (4/5,9/11) -> (4/5,9/11) Reflection Matrix(109,-90,132,-109) (9/11,5/6) -> (9/11,5/6) 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(61,-78,18,-23) (5/4,4/3) -> (10/3,7/2) Hyperbolic Matrix(25,-36,16,-23) (4/3,3/2) -> (3/2,8/5) Parabolic Matrix(283,-458,76,-123) (21/13,13/8) -> (11/3,15/4) Glide Reflection Matrix(683,-1178,396,-683) (31/18,19/11) -> (31/18,19/11) Reflection Matrix(153,-266,88,-153) (19/11,7/4) -> (19/11,7/4) Reflection Matrix(65,-116,14,-25) (7/4,9/5) -> (9/2,5/1) Glide Reflection 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(55,-126,24,-55) (9/4,7/3) -> (9/4,7/3) Reflection Matrix(29,-70,12,-29) (7/3,5/2) -> (7/3,5/2) Reflection Matrix(177,-484,64,-175) (19/7,11/4) -> (11/4,25/9) Parabolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(175,-626,26,-93) (25/7,18/5) -> (20/3,7/1) Hyperbolic 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(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(-1,0,2,1) -> Matrix(1,1,0,-1) (-1/1,0/1) -> (-1/2,1/0) Matrix(51,-8,70,-11) -> Matrix(1,1,2,1) Matrix(35,-6,204,-35) -> Matrix(3,2,-4,-3) (1/6,3/17) -> (-1/1,-1/2) Matrix(67,-12,374,-67) -> Matrix(7,3,-16,-7) (3/17,2/11) -> (-1/2,-3/8) Matrix(271,-50,168,-31) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(17,-4,64,-15) -> Matrix(1,0,4,1) 0/1 Matrix(283,-78,156,-43) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(265,-74,376,-105) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(109,-32,92,-27) -> Matrix(1,0,0,1) Matrix(137,-42,62,-19) -> Matrix(1,-1,0,1) 1/0 Matrix(193,-68,88,-31) -> Matrix(3,2,-2,-1) -1/1 Matrix(221,-80,58,-21) -> Matrix(3,1,-2,-1) Matrix(131,-48,30,-11) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(73,-28,86,-33) -> Matrix(3,1,-2,-1) Matrix(491,-190,230,-89) -> Matrix(3,1,2,1) Matrix(763,-296,116,-45) -> Matrix(5,2,-8,-3) -1/2 Matrix(173,-68,28,-11) -> Matrix(1,0,2,1) 0/1 Matrix(185,-76,56,-23) -> Matrix(1,0,4,1) 0/1 Matrix(71,-30,168,-71) -> Matrix(-1,0,14,1) (5/12,3/7) -> (-1/7,0/1) Matrix(13,-6,28,-13) -> Matrix(1,0,0,-1) (3/7,1/2) -> (0/1,1/0) Matrix(27,-14,52,-27) -> Matrix(1,0,0,-1) (1/2,7/13) -> (0/1,1/0) Matrix(155,-84,286,-155) -> Matrix(1,1,0,-1) (7/13,6/11) -> (-1/2,1/0) Matrix(283,-156,78,-43) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(205,-116,76,-43) -> Matrix(1,0,-2,1) 0/1 Matrix(215,-124,26,-15) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(571,-330,988,-571) -> Matrix(-1,0,2,1) (15/26,11/19) -> (-1/1,0/1) Matrix(265,-154,456,-265) -> Matrix(1,0,0,-1) (11/19,7/12) -> (0/1,1/0) Matrix(125,-74,76,-45) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(125,-76,74,-45) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(619,-382,222,-137) -> Matrix(1,1,0,1) 1/0 Matrix(271,-168,50,-31) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(85,-54,74,-47) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(49,-32,72,-47) -> Matrix(1,0,4,1) 0/1 Matrix(709,-492,330,-229) -> Matrix(3,-1,2,-1) Matrix(2951,-2050,4248,-2951) -> Matrix(17,-8,36,-17) (25/36,41/59) -> (4/9,1/2) Matrix(1887,-1312,2714,-1887) -> Matrix(13,-7,24,-13) (41/59,16/23) -> (1/2,7/12) Matrix(459,-320,142,-99) -> Matrix(1,-1,-4,3) Matrix(175,-124,24,-17) -> Matrix(1,0,-2,1) 0/1 Matrix(499,-360,140,-101) -> Matrix(1,0,-2,1) 0/1 Matrix(557,-404,324,-235) -> Matrix(1,-2,0,1) 1/0 Matrix(57,-44,22,-17) -> Matrix(1,-1,-2,1) Matrix(89,-72,110,-89) -> Matrix(-1,3,0,1) (4/5,9/11) -> (3/2,1/0) Matrix(109,-90,132,-109) -> Matrix(1,4,0,-1) (9/11,5/6) -> (-2/1,1/0) Matrix(109,-132,90,-109) -> Matrix(-1,1,0,1) (6/5,11/9) -> (1/2,1/0) Matrix(89,-110,72,-89) -> Matrix(1,4,0,-1) (11/9,5/4) -> (-2/1,1/0) Matrix(61,-78,18,-23) -> Matrix(1,1,0,1) 1/0 Matrix(25,-36,16,-23) -> Matrix(1,2,-2,-3) -1/1 Matrix(283,-458,76,-123) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(683,-1178,396,-683) -> Matrix(5,6,-4,-5) (31/18,19/11) -> (-3/2,-1/1) Matrix(153,-266,88,-153) -> Matrix(3,2,-4,-3) (19/11,7/4) -> (-1/1,-1/2) Matrix(65,-116,14,-25) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(155,-286,84,-155) -> Matrix(-1,0,2,1) (11/6,13/7) -> (-1/1,0/1) Matrix(27,-52,14,-27) -> Matrix(1,1,0,-1) (13/7,2/1) -> (-1/2,1/0) Matrix(55,-126,24,-55) -> Matrix(3,4,-2,-3) (9/4,7/3) -> (-2/1,-1/1) Matrix(29,-70,12,-29) -> Matrix(3,2,-4,-3) (7/3,5/2) -> (-1/1,-1/2) Matrix(177,-484,64,-175) -> Matrix(1,0,4,1) 0/1 Matrix(31,-90,10,-29) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(175,-626,26,-93) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(67,-374,12,-67) -> Matrix(-1,0,2,1) (11/2,17/3) -> (-1/1,0/1) Matrix(35,-204,6,-35) -> Matrix(1,1,0,-1) (17/3,6/1) -> (-1/2,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.