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 -7/1 -6/1 -16/3 -5/1 -14/3 -13/3 -4/1 -11/3 -7/2 -3/1 -14/5 -8/3 -17/7 -7/3 -9/4 -11/5 -2/1 -1/1 -9/14 -8/13 -3/5 -6/11 -1/2 -4/9 -3/8 -1/3 -2/7 -1/4 -4/19 -1/6 0/1 3/17 1/5 1/4 1/3 3/7 1/2 11/19 2/3 3/4 9/11 1/1 8/7 11/9 5/4 14/11 4/3 7/5 3/2 5/3 19/11 16/9 13/7 2/1 7/3 12/5 46/19 5/2 18/7 8/3 14/5 48/17 3/1 61/19 10/3 27/8 7/2 4/1 41/9 14/3 33/7 5/1 16/3 17/3 6/1 7/1 22/3 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -2/1 -6/1 -2/1 0/1 -17/3 -2/1 -28/5 -2/1 -3/2 -11/2 1/0 -16/3 -2/1 1/0 -5/1 -1/1 -14/3 -3/2 -1/1 -9/2 -3/2 -22/5 -6/5 -1/1 -13/3 -1/1 -4/1 -1/1 1/0 -19/5 -1/1 -15/4 -1/2 -41/11 0/1 -26/7 0/1 1/0 -11/3 -1/1 -18/5 -2/1 -1/1 -25/7 -2/1 -7/2 -1/1 -31/9 -4/5 -24/7 -3/4 -2/3 -41/12 -1/2 -17/5 -2/3 -10/3 -1/2 0/1 -3/1 -1/1 -17/6 -1/2 -14/5 0/1 1/0 -11/4 1/0 -8/3 -1/1 -21/8 -1/2 -55/21 0/1 -34/13 -1/2 0/1 -13/5 -1/1 -18/7 -1/2 -1/3 -5/2 1/0 -22/9 -2/1 -1/1 -17/7 -1/1 -12/5 -1/1 -1/2 -7/3 0/1 -16/7 0/1 1/0 -25/11 0/1 -9/4 -1/1 -11/5 -1/1 -13/6 1/0 -15/7 0/1 -2/1 -1/1 0/1 -1/1 0/1 -2/3 0/1 1/1 -15/23 0/1 -13/20 1/0 -11/17 1/1 -9/14 1/1 -7/11 0/1 -12/19 1/2 1/1 -17/27 1/1 -5/8 1/0 -18/29 1/3 1/2 -13/21 1/1 -8/13 1/1 -19/31 1/1 -30/49 2/1 1/0 -11/18 1/0 -3/5 1/1 -10/17 0/1 1/2 -17/29 2/3 -41/70 1/2 -24/41 2/3 3/4 -7/12 1/1 -18/31 1/1 2/1 -11/19 1/1 -26/45 0/1 1/0 -41/71 0/1 -15/26 1/2 -19/33 1/1 -4/7 1/1 1/0 -13/23 1/1 -9/16 3/2 -14/25 1/1 3/2 -5/9 1/1 -11/20 1/0 -6/11 0/1 2/1 -13/24 1/0 -7/13 2/1 -1/2 1/0 -8/17 -4/1 1/0 -7/15 -2/1 -6/13 0/1 1/0 -5/11 -1/1 -4/9 1/0 -11/25 -3/1 -7/16 1/0 -10/23 -2/1 -1/1 -13/30 1/0 -3/7 -1/1 -14/33 -2/1 1/0 -11/26 -1/1 -8/19 -1/1 1/0 -13/31 -1/1 -31/74 -1/2 -18/43 0/1 -5/12 1/0 -2/5 -1/1 1/0 -11/28 -5/6 -9/23 -2/3 -7/18 -1/2 -5/13 -1/1 -18/47 -3/5 -1/2 -13/34 -1/2 -21/55 -1/3 -29/76 -1/4 -8/21 -1/2 0/1 -19/50 -1/2 -11/29 -1/1 -3/8 0/1 -13/35 1/1 -10/27 -1/1 0/1 -7/19 0/1 -18/49 2/1 1/0 -11/30 1/0 -15/41 0/1 -19/52 1/0 -4/11 -1/1 1/0 -9/25 0/1 -14/39 -2/1 0/1 -5/14 1/0 -6/17 -1/1 -1/2 -7/20 -1/2 -8/23 -1/1 -1/3 0/1 -6/19 -1/1 0/1 -5/16 -1/2 -4/13 0/1 1/0 -7/23 0/1 -10/33 -2/1 -1/1 -3/10 -1/2 -2/7 0/1 -5/18 1/2 -3/11 1/1 -10/37 1/1 2/1 -7/26 1/0 -4/15 -1/1 1/0 -9/34 -1/1 -5/19 -1/1 -1/4 1/0 -2/9 0/1 1/2 -5/23 1/1 -8/37 1/2 1/1 -3/14 1/0 -7/33 2/1 -4/19 1/0 -5/24 1/0 -1/5 0/1 -3/16 1/0 -2/11 0/1 1/0 -7/39 -2/1 -5/28 -3/2 -8/45 -1/1 -3/4 -3/17 -1/1 -1/6 0/1 -3/19 1/1 -2/13 1/1 1/0 -3/20 -1/2 -4/27 0/1 1/2 -1/7 0/1 -2/15 -1/1 0/1 -1/8 1/0 -2/17 0/1 -1/9 0/1 0/1 0/1 1/0 1/7 0/1 1/6 1/0 3/17 0/1 5/28 1/2 2/11 0/1 1/1 1/5 0/1 5/24 1/0 4/19 -1/2 0/1 3/14 1/2 2/9 -1/1 1/0 3/13 -1/1 1/4 0/1 5/19 1/3 9/34 1/2 4/15 1/2 1/1 3/11 1/1 8/29 3/4 1/1 5/18 3/2 2/7 0/1 1/0 5/17 1/1 3/10 1/0 1/3 0/1 5/14 1/0 4/11 1/0 3/8 1/0 5/13 -1/1 2/5 -1/2 0/1 5/12 -1/4 3/7 0/1 7/16 1/8 18/41 1/6 2/11 11/25 1/5 4/9 0/1 1/4 5/11 1/3 1/2 1/0 8/15 -1/4 0/1 7/13 0/1 6/11 0/1 1/3 5/9 1/1 4/7 1/1 1/0 15/26 1/0 11/19 1/0 7/12 1/0 24/41 1/0 17/29 -2/1 10/17 -2/1 -1/1 3/5 -1/1 2/3 0/1 5/7 1/3 13/18 1/2 8/11 1/3 1/2 19/26 0/1 11/15 1/3 14/19 2/5 1/2 3/4 1/2 13/17 1/1 10/13 1/1 2/1 27/35 3/1 17/22 1/0 7/9 0/1 11/14 1/1 26/33 0/1 1/0 15/19 0/1 19/24 3/2 4/5 0/1 1/0 13/16 -1/2 9/11 0/1 14/17 0/1 1/4 5/6 1/2 1/1 0/1 10/9 1/2 4/7 9/8 3/4 8/7 1/1 23/20 1/2 15/13 0/1 7/6 1/2 6/5 1/2 1/1 17/14 3/4 11/9 1/1 5/4 1/0 19/15 1/1 14/11 0/1 2/1 37/29 1/1 23/18 1/0 9/7 0/1 4/3 1/1 1/0 19/14 1/0 15/11 0/1 11/8 1/0 29/21 1/0 47/34 1/0 18/13 -2/1 1/0 25/18 -1/2 32/23 -1/1 39/28 -1/2 7/5 0/1 24/17 0/1 1/0 41/29 0/1 17/12 1/0 27/19 -1/1 10/7 0/1 1/1 3/2 0/1 14/9 0/1 1/3 39/25 2/5 25/16 1/2 61/39 1/2 36/23 1/2 5/9 47/30 1/2 11/7 1/1 30/19 0/1 1/0 49/31 0/1 19/12 1/2 27/17 1/1 8/5 0/1 1/2 45/28 1/0 37/23 0/1 29/18 1/4 21/13 1/3 55/34 1/2 34/21 0/1 2/5 13/8 1/2 31/19 1/2 49/30 1/2 18/11 1/2 3/5 5/3 1/1 17/10 1/2 12/7 1/2 1/1 31/18 1/2 19/11 1/1 45/26 1/0 71/41 0/1 26/15 0/1 1/1 33/19 0/1 7/4 1/2 16/9 1/2 25/14 1/2 34/19 3/5 2/3 9/5 2/3 20/11 2/3 3/4 11/6 5/6 24/13 11/12 1/1 13/7 1/1 28/15 1/1 13/12 15/8 7/6 2/1 1/1 1/0 9/4 1/0 7/3 1/0 19/8 1/0 31/13 0/1 43/18 1/0 12/5 0/1 1/0 41/17 2/1 29/12 1/0 46/19 -2/1 0/1 17/7 0/1 5/2 1/0 23/9 0/1 18/7 0/1 49/19 0/1 80/31 1/4 2/7 31/12 1/2 13/5 1/1 21/8 1/2 29/11 1/1 37/14 3/2 8/3 1/1 1/0 19/7 1/1 11/4 1/1 25/9 2/1 39/14 1/0 14/5 2/1 1/0 59/21 1/0 45/16 1/0 31/11 -2/1 48/17 -1/1 17/6 -1/2 3/1 1/1 19/6 2/1 16/5 3/1 1/0 61/19 1/0 45/14 1/0 29/9 -1/1 13/4 1/0 23/7 1/1 10/3 1/1 2/1 27/8 1/1 44/13 4/3 3/2 61/18 3/2 139/41 3/2 78/23 3/2 14/9 17/5 2/1 7/2 1/0 4/1 1/0 9/2 1/0 41/9 0/1 32/7 0/1 1/0 23/5 0/1 14/3 -1/1 0/1 33/7 0/1 52/11 0/1 1/6 19/4 1/2 5/1 1/1 16/3 1/1 1/0 11/2 1/0 28/5 5/1 1/0 17/3 1/0 40/7 -5/1 1/0 23/4 1/0 6/1 0/1 1/0 7/1 2/1 22/3 2/1 15/2 5/2 8/1 4/1 1/0 17/2 1/0 9/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,92,8,67) (-7/1,1/0) -> (15/11,11/8) Hyperbolic Matrix(23,144,-4,-25) (-7/1,-6/1) -> (-6/1,-17/3) Parabolic Matrix(17,96,-116,-655) (-17/3,-28/5) -> (-4/27,-1/7) Hyperbolic Matrix(253,1412,-432,-2411) (-28/5,-11/2) -> (-41/70,-24/41) Hyperbolic Matrix(73,392,-192,-1031) (-11/2,-16/3) -> (-8/21,-19/50) Hyperbolic Matrix(37,196,84,445) (-16/3,-5/1) -> (11/25,4/9) Hyperbolic Matrix(11,52,48,227) (-5/1,-14/3) -> (2/9,3/13) Hyperbolic Matrix(33,152,28,129) (-14/3,-9/2) -> (7/6,6/5) Hyperbolic Matrix(35,156,-116,-517) (-9/2,-22/5) -> (-10/33,-3/10) Hyperbolic Matrix(95,416,124,543) (-22/5,-13/3) -> (13/17,10/13) Hyperbolic Matrix(25,104,-44,-183) (-13/3,-4/1) -> (-4/7,-13/23) Hyperbolic Matrix(43,164,156,595) (-4/1,-19/5) -> (3/11,8/29) Hyperbolic Matrix(101,380,80,301) (-19/5,-15/4) -> (5/4,19/15) Hyperbolic Matrix(351,1312,248,927) (-15/4,-41/11) -> (41/29,17/12) Hyperbolic Matrix(573,2132,-992,-3691) (-41/11,-26/7) -> (-26/45,-41/71) Hyperbolic Matrix(223,824,-364,-1345) (-26/7,-11/3) -> (-19/31,-30/49) Hyperbolic Matrix(45,164,76,277) (-11/3,-18/5) -> (10/17,3/5) Hyperbolic Matrix(47,168,-148,-529) (-18/5,-25/7) -> (-1/3,-6/19) Hyperbolic Matrix(111,392,-32,-113) (-25/7,-7/2) -> (-7/2,-31/9) Parabolic Matrix(395,1356,164,563) (-31/9,-24/7) -> (12/5,41/17) Hyperbolic Matrix(83,284,396,1355) (-24/7,-41/12) -> (5/24,4/19) Hyperbolic Matrix(431,1472,248,847) (-41/12,-17/5) -> (33/19,7/4) Hyperbolic Matrix(51,172,8,27) (-17/5,-10/3) -> (6/1,7/1) Hyperbolic Matrix(17,56,44,145) (-10/3,-3/1) -> (5/13,2/5) Hyperbolic Matrix(85,244,-224,-643) (-3/1,-17/6) -> (-19/50,-11/29) Hyperbolic Matrix(109,308,132,373) (-17/6,-14/5) -> (14/17,5/6) Hyperbolic Matrix(23,64,-124,-345) (-14/5,-11/4) -> (-3/16,-2/11) Hyperbolic Matrix(95,256,-36,-97) (-11/4,-8/3) -> (-8/3,-21/8) Parabolic Matrix(519,1360,-1420,-3721) (-21/8,-55/21) -> (-15/41,-19/52) 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(25,64,116,297) (-18/7,-5/2) -> (3/14,2/9) Hyperbolic Matrix(137,336,-316,-775) (-5/2,-22/9) -> (-10/23,-13/30) Hyperbolic Matrix(277,676,84,205) (-22/9,-17/7) -> (23/7,10/3) Hyperbolic Matrix(169,408,-268,-647) (-17/7,-12/5) -> (-12/19,-17/27) Hyperbolic Matrix(57,136,44,105) (-12/5,-7/3) -> (9/7,4/3) Hyperbolic Matrix(61,140,-200,-459) (-7/3,-16/7) -> (-4/13,-7/23) Hyperbolic Matrix(283,644,156,355) (-16/7,-25/11) -> (9/5,20/11) Hyperbolic Matrix(221,500,80,181) (-25/11,-9/4) -> (11/4,25/9) Hyperbolic Matrix(131,292,48,107) (-9/4,-11/5) -> (19/7,11/4) Hyperbolic Matrix(271,592,168,367) (-11/5,-13/6) -> (29/18,21/13) Hyperbolic Matrix(139,300,120,259) (-13/6,-15/7) -> (15/13,7/6) Hyperbolic Matrix(215,456,124,263) (-15/7,-2/1) -> (26/15,33/19) Hyperbolic Matrix(3,4,-4,-5) (-2/1,-1/1) -> (-1/1,-2/3) Parabolic Matrix(811,532,468,307) (-2/3,-15/23) -> (71/41,26/15) Hyperbolic Matrix(1037,676,744,485) (-15/23,-13/20) -> (39/28,7/5) Hyperbolic Matrix(913,592,-2392,-1551) (-13/20,-11/17) -> (-21/55,-29/76) Hyperbolic Matrix(223,144,-844,-545) (-11/17,-9/14) -> (-9/34,-5/19) Hyperbolic Matrix(219,140,280,179) (-9/14,-7/11) -> (7/9,11/14) Hyperbolic Matrix(215,136,-596,-377) (-7/11,-12/19) -> (-4/11,-9/25) Hyperbolic Matrix(535,336,164,103) (-17/27,-5/8) -> (13/4,23/7) Hyperbolic Matrix(103,64,-684,-425) (-5/8,-18/29) -> (-2/13,-3/20) Hyperbolic Matrix(523,324,-1364,-845) (-18/29,-13/21) -> (-5/13,-18/47) Hyperbolic Matrix(415,256,-676,-417) (-13/21,-8/13) -> (-8/13,-19/31) Parabolic Matrix(2163,1324,776,475) (-30/49,-11/18) -> (39/14,14/5) Hyperbolic Matrix(105,64,356,217) (-11/18,-3/5) -> (5/17,3/10) Hyperbolic Matrix(95,56,-436,-257) (-3/5,-10/17) -> (-2/9,-5/23) Hyperbolic Matrix(293,172,-632,-371) (-10/17,-17/29) -> (-7/15,-6/13) Hyperbolic Matrix(6275,3676,3624,2123) (-17/29,-41/70) -> (45/26,71/41) Hyperbolic Matrix(1635,956,484,283) (-24/41,-7/12) -> (27/8,44/13) Hyperbolic Matrix(957,556,284,165) (-7/12,-18/31) -> (10/3,27/8) Hyperbolic Matrix(283,164,-1044,-605) (-18/31,-11/19) -> (-3/11,-10/37) Hyperbolic Matrix(1705,984,376,217) (-41/71,-15/26) -> (9/2,41/9) Hyperbolic Matrix(2361,1360,1460,841) (-15/26,-19/33) -> (21/13,55/34) Hyperbolic Matrix(285,164,-1604,-923) (-19/33,-4/7) -> (-8/45,-3/17) Hyperbolic Matrix(277,156,364,205) (-13/23,-9/16) -> (3/4,13/17) Hyperbolic Matrix(271,152,-772,-433) (-9/16,-14/25) -> (-6/17,-7/20) Hyperbolic Matrix(93,52,-592,-331) (-14/25,-5/9) -> (-3/19,-2/13) Hyperbolic Matrix(711,392,448,247) (-5/9,-11/20) -> (19/12,27/17) Hyperbolic Matrix(263,144,-484,-265) (-11/20,-6/11) -> (-6/11,-13/24) Parabolic Matrix(89,48,432,233) (-13/24,-7/13) -> (1/5,5/24) Hyperbolic Matrix(173,92,-472,-251) (-7/13,-1/2) -> (-11/30,-15/41) Hyperbolic Matrix(305,144,36,17) (-1/2,-8/17) -> (8/1,17/2) Hyperbolic Matrix(2033,952,788,369) (-8/17,-7/15) -> (49/19,80/31) Hyperbolic Matrix(297,136,404,185) (-6/13,-5/11) -> (11/15,14/19) Hyperbolic Matrix(143,64,-324,-145) (-5/11,-4/9) -> (-4/9,-11/25) Parabolic Matrix(857,376,604,265) (-11/25,-7/16) -> (17/12,27/19) Hyperbolic Matrix(211,92,-672,-293) (-7/16,-10/23) -> (-6/19,-5/16) Hyperbolic Matrix(213,92,808,349) (-13/30,-3/7) -> (5/19,9/34) Hyperbolic Matrix(489,208,1112,473) (-3/7,-14/33) -> (18/41,11/25) Hyperbolic Matrix(1039,440,1320,559) (-14/33,-11/26) -> (11/14,26/33) Hyperbolic Matrix(275,116,-1036,-437) (-11/26,-8/19) -> (-4/15,-9/34) Hyperbolic Matrix(343,144,-1584,-665) (-8/19,-13/31) -> (-5/23,-8/37) Hyperbolic Matrix(2271,952,1448,607) (-13/31,-31/74) -> (47/30,11/7) Hyperbolic Matrix(2273,952,308,129) (-31/74,-18/43) -> (22/3,15/2) Hyperbolic Matrix(67,28,-548,-229) (-18/43,-5/12) -> (-1/8,-2/17) Hyperbolic Matrix(69,28,32,13) (-5/12,-2/5) -> (2/1,9/4) Hyperbolic Matrix(131,52,68,27) (-2/5,-11/28) -> (15/8,2/1) Hyperbolic Matrix(857,336,1084,425) (-11/28,-9/23) -> (15/19,19/24) Hyperbolic Matrix(195,76,-916,-357) (-9/23,-7/18) -> (-3/14,-7/33) Hyperbolic Matrix(259,100,360,139) (-7/18,-5/13) -> (5/7,13/18) Hyperbolic Matrix(2915,1116,1784,683) (-18/47,-13/34) -> (49/30,18/11) Hyperbolic Matrix(2523,964,1976,755) (-13/34,-21/55) -> (37/29,23/18) Hyperbolic Matrix(1553,592,968,369) (-29/76,-8/21) -> (8/5,45/28) Hyperbolic Matrix(191,72,-512,-193) (-11/29,-3/8) -> (-3/8,-13/35) Parabolic Matrix(1079,400,1400,519) (-13/35,-10/27) -> (10/13,27/35) Hyperbolic Matrix(887,328,192,71) (-10/27,-7/19) -> (23/5,14/3) Hyperbolic Matrix(381,140,-2120,-779) (-7/19,-18/49) -> (-2/11,-7/39) Hyperbolic Matrix(2843,1044,2056,755) (-18/49,-11/30) -> (47/34,18/13) Hyperbolic Matrix(2333,852,408,149) (-19/52,-4/11) -> (40/7,23/4) Hyperbolic Matrix(1813,652,748,269) (-9/25,-14/39) -> (46/19,17/7) Hyperbolic Matrix(2621,940,1620,581) (-14/39,-5/14) -> (55/34,34/21) Hyperbolic Matrix(373,132,308,109) (-5/14,-6/17) -> (6/5,17/14) Hyperbolic Matrix(1537,536,1104,385) (-7/20,-8/23) -> (32/23,39/28) Hyperbolic Matrix(857,296,304,105) (-8/23,-1/3) -> (31/11,48/17) Hyperbolic Matrix(233,72,288,89) (-5/16,-4/13) -> (4/5,13/16) Hyperbolic Matrix(1609,488,1032,313) (-7/23,-10/33) -> (14/9,39/25) Hyperbolic Matrix(55,16,-196,-57) (-3/10,-2/7) -> (-2/7,-5/18) Parabolic Matrix(277,76,164,45) (-5/18,-3/11) -> (5/3,17/10) Hyperbolic Matrix(1809,488,1012,273) (-10/37,-7/26) -> (25/14,34/19) Hyperbolic Matrix(329,88,572,153) (-7/26,-4/15) -> (4/7,15/26) Hyperbolic Matrix(381,100,80,21) (-5/19,-1/4) -> (19/4,5/1) Hyperbolic Matrix(53,12,128,29) (-1/4,-2/9) -> (2/5,5/12) Hyperbolic Matrix(1481,320,560,121) (-8/37,-3/14) -> (37/14,8/3) Hyperbolic Matrix(1115,236,1904,403) (-7/33,-4/19) -> (24/41,17/29) Hyperbolic Matrix(709,148,1212,253) (-4/19,-5/24) -> (7/12,24/41) Hyperbolic Matrix(1061,220,680,141) (-5/24,-1/5) -> (39/25,25/16) Hyperbolic Matrix(591,112,248,47) (-1/5,-3/16) -> (19/8,31/13) Hyperbolic Matrix(1317,236,1144,205) (-7/39,-5/28) -> (23/20,15/13) Hyperbolic Matrix(1459,260,780,139) (-5/28,-8/45) -> (28/15,15/8) Hyperbolic Matrix(389,68,532,93) (-3/17,-1/6) -> (19/26,11/15) Hyperbolic Matrix(379,60,120,19) (-1/6,-3/19) -> (3/1,19/6) Hyperbolic Matrix(1553,232,328,49) (-3/20,-4/27) -> (52/11,19/4) Hyperbolic Matrix(373,52,208,29) (-1/7,-2/15) -> (34/19,9/5) Hyperbolic Matrix(91,12,508,67) (-2/15,-1/8) -> (5/28,2/11) Hyperbolic Matrix(317,36,44,5) (-2/17,-1/9) -> (7/1,22/3) Hyperbolic Matrix(311,32,68,7) (-1/9,0/1) -> (32/7,23/5) Hyperbolic Matrix(175,-24,124,-17) (0/1,1/7) -> (7/5,24/17) Hyperbolic Matrix(173,-28,68,-11) (1/7,1/6) -> (5/2,23/9) Hyperbolic Matrix(715,-124,444,-77) (1/6,3/17) -> (37/23,29/18) Hyperbolic Matrix(1801,-320,1120,-199) (3/17,5/28) -> (45/28,37/23) Hyperbolic Matrix(237,-44,404,-75) (2/11,1/5) -> (17/29,10/17) Hyperbolic Matrix(131,-28,248,-53) (4/19,3/14) -> (1/2,8/15) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(1929,-512,1232,-327) (9/34,4/15) -> (36/23,47/30) Hyperbolic Matrix(251,-68,48,-13) (4/15,3/11) -> (5/1,16/3) Hyperbolic Matrix(751,-208,408,-113) (8/29,5/18) -> (11/6,24/13) Hyperbolic Matrix(499,-140,360,-101) (5/18,2/7) -> (18/13,25/18) Hyperbolic Matrix(587,-172,372,-109) (2/7,5/17) -> (11/7,30/19) Hyperbolic Matrix(185,-56,76,-23) (3/10,1/3) -> (17/7,5/2) Hyperbolic Matrix(149,-52,192,-67) (1/3,5/14) -> (17/22,7/9) Hyperbolic Matrix(499,-180,280,-101) (5/14,4/11) -> (16/9,25/14) 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(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(529,-232,472,-207) (7/16,18/41) -> (10/9,9/8) Hyperbolic Matrix(331,-148,208,-93) (4/9,5/11) -> (27/17,8/5) Hyperbolic Matrix(193,-88,68,-31) (5/11,1/2) -> (17/6,3/1) Hyperbolic Matrix(1171,-628,248,-133) (8/15,7/13) -> (33/7,52/11) Hyperbolic Matrix(545,-296,116,-63) (7/13,6/11) -> (14/3,33/7) Hyperbolic Matrix(387,-212,272,-149) (6/11,5/9) -> (27/19,10/7) Hyperbolic Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(1647,-952,1192,-689) (15/26,11/19) -> (29/21,47/34) Hyperbolic Matrix(557,-324,404,-235) (11/19,7/12) -> (11/8,29/21) Hyperbolic Matrix(25,-16,36,-23) (3/5,2/3) -> (2/3,5/7) Parabolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(625,-456,196,-143) (8/11,19/26) -> (19/6,16/5) Hyperbolic Matrix(461,-340,80,-59) (14/19,3/4) -> (23/4,6/1) Hyperbolic Matrix(2213,-1708,688,-531) (27/35,17/22) -> (45/14,29/9) Hyperbolic Matrix(2075,-1644,804,-637) (19/24,4/5) -> (80/31,31/12) Hyperbolic Matrix(993,-808,628,-511) (13/16,9/11) -> (49/31,19/12) Hyperbolic Matrix(1163,-956,736,-605) (9/11,14/17) -> (30/19,49/31) Hyperbolic Matrix(109,-92,32,-27) (5/6,1/1) -> (17/5,7/2) Hyperbolic Matrix(231,-248,68,-73) (1/1,10/9) -> (78/23,17/5) Hyperbolic Matrix(225,-256,196,-223) (9/8,8/7) -> (8/7,23/20) Parabolic Matrix(739,-900,280,-341) (17/14,11/9) -> (29/11,37/14) Hyperbolic Matrix(305,-376,116,-143) (11/9,5/4) -> (21/8,29/11) Hyperbolic Matrix(617,-784,484,-615) (19/15,14/11) -> (14/11,37/29) Parabolic Matrix(859,-1100,360,-461) (23/18,9/7) -> (31/13,43/18) Hyperbolic Matrix(425,-576,76,-103) (4/3,19/14) -> (11/2,28/5) Hyperbolic Matrix(779,-1060,280,-381) (19/14,15/11) -> (25/9,39/14) Hyperbolic Matrix(1255,-1744,444,-617) (25/18,32/23) -> (48/17,17/6) Hyperbolic Matrix(1625,-2296,356,-503) (24/17,41/29) -> (41/9,32/7) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(2699,-4220,960,-1501) (25/16,61/39) -> (59/21,45/16) Hyperbolic Matrix(2027,-3172,632,-989) (61/39,36/23) -> (16/5,61/19) Hyperbolic Matrix(977,-1584,404,-655) (34/21,13/8) -> (29/12,46/19) Hyperbolic Matrix(91,-148,8,-13) (13/8,31/19) -> (9/1,1/0) Hyperbolic Matrix(593,-968,68,-111) (31/19,49/30) -> (17/2,9/1) 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(213,-388,28,-51) (20/11,11/6) -> (15/2,8/1) Hyperbolic Matrix(365,-676,196,-363) (24/13,13/7) -> (13/7,28/15) Parabolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(1097,-2624,324,-775) (43/18,12/5) -> (44/13,61/18) Hyperbolic Matrix(1137,-2744,404,-975) (41/17,29/12) -> (45/16,31/11) Hyperbolic Matrix(505,-1296,196,-503) (23/9,18/7) -> (18/7,49/19) Parabolic Matrix(413,-1068,128,-331) (31/12,13/5) -> (29/9,13/4) Hyperbolic Matrix(2333,-6548,688,-1931) (14/5,59/21) -> (139/41,78/23) Hyperbolic Matrix(3105,-9976,916,-2943) (61/19,45/14) -> (61/18,139/41) Hyperbolic Matrix(17,-64,4,-15) (7/2,4/1) -> (4/1,9/2) Parabolic Matrix(205,-1156,36,-203) (28/5,17/3) -> (17/3,40/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(11,92,8,67) -> Matrix(1,2,0,1) Matrix(23,144,-4,-25) -> Matrix(1,0,0,1) Matrix(17,96,-116,-655) -> Matrix(1,2,0,1) Matrix(253,1412,-432,-2411) -> Matrix(1,0,2,1) Matrix(73,392,-192,-1031) -> Matrix(1,2,-2,-3) Matrix(37,196,84,445) -> Matrix(1,2,4,9) Matrix(11,52,48,227) -> Matrix(1,2,-2,-3) Matrix(33,152,28,129) -> Matrix(1,2,0,1) Matrix(35,156,-116,-517) -> Matrix(3,4,-4,-5) Matrix(95,416,124,543) -> Matrix(7,8,6,7) Matrix(25,104,-44,-183) -> Matrix(1,2,0,1) Matrix(43,164,156,595) -> Matrix(3,2,4,3) Matrix(101,380,80,301) -> Matrix(1,0,2,1) Matrix(351,1312,248,927) -> Matrix(1,0,2,1) Matrix(573,2132,-992,-3691) -> Matrix(1,0,0,1) Matrix(223,824,-364,-1345) -> Matrix(1,2,0,1) Matrix(45,164,76,277) -> Matrix(1,0,0,1) Matrix(47,168,-148,-529) -> Matrix(1,2,-2,-3) Matrix(111,392,-32,-113) -> Matrix(5,6,-6,-7) Matrix(395,1356,164,563) -> Matrix(3,2,4,3) Matrix(83,284,396,1355) -> Matrix(3,2,-2,-1) Matrix(431,1472,248,847) -> Matrix(3,2,4,3) Matrix(51,172,8,27) -> Matrix(1,0,2,1) Matrix(17,56,44,145) -> Matrix(1,0,0,1) Matrix(85,244,-224,-643) -> Matrix(1,0,0,1) Matrix(109,308,132,373) -> Matrix(1,0,4,1) Matrix(23,64,-124,-345) -> Matrix(1,0,0,1) Matrix(95,256,-36,-97) -> Matrix(1,2,-2,-3) Matrix(519,1360,-1420,-3721) -> Matrix(1,0,2,1) Matrix(741,1940,940,2461) -> Matrix(1,0,2,1) Matrix(273,712,-472,-1231) -> Matrix(1,0,2,1) Matrix(125,324,76,197) -> Matrix(3,2,4,3) Matrix(25,64,116,297) -> Matrix(1,0,2,1) Matrix(137,336,-316,-775) -> Matrix(1,0,0,1) Matrix(277,676,84,205) -> Matrix(3,4,2,3) Matrix(169,408,-268,-647) -> Matrix(3,2,4,3) Matrix(57,136,44,105) -> Matrix(1,0,2,1) Matrix(61,140,-200,-459) -> Matrix(1,0,0,1) Matrix(283,644,156,355) -> Matrix(3,2,4,3) Matrix(221,500,80,181) -> Matrix(1,2,0,1) Matrix(131,292,48,107) -> Matrix(1,0,2,1) Matrix(271,592,168,367) -> Matrix(1,0,4,1) Matrix(139,300,120,259) -> Matrix(1,0,2,1) Matrix(215,456,124,263) -> Matrix(1,0,2,1) Matrix(3,4,-4,-5) -> Matrix(1,0,2,1) Matrix(811,532,468,307) -> Matrix(1,0,0,1) Matrix(1037,676,744,485) -> Matrix(1,0,-2,1) Matrix(913,592,-2392,-1551) -> Matrix(1,0,-4,1) Matrix(223,144,-844,-545) -> Matrix(1,0,-2,1) Matrix(219,140,280,179) -> Matrix(1,0,0,1) Matrix(215,136,-596,-377) -> Matrix(1,0,-2,1) Matrix(535,336,164,103) -> Matrix(1,0,0,1) Matrix(103,64,-684,-425) -> Matrix(1,0,-2,1) Matrix(523,324,-1364,-845) -> Matrix(3,-2,-4,3) Matrix(415,256,-676,-417) -> Matrix(3,-2,2,-1) Matrix(2163,1324,776,475) -> Matrix(1,0,0,1) Matrix(105,64,356,217) -> Matrix(1,0,0,1) Matrix(95,56,-436,-257) -> Matrix(1,0,0,1) Matrix(293,172,-632,-371) -> Matrix(1,0,-2,1) Matrix(6275,3676,3624,2123) -> Matrix(3,-2,2,-1) Matrix(1635,956,484,283) -> Matrix(7,-6,6,-5) Matrix(957,556,284,165) -> Matrix(1,0,0,1) Matrix(283,164,-1044,-605) -> Matrix(1,0,0,1) Matrix(1705,984,376,217) -> Matrix(1,0,-2,1) Matrix(2361,1360,1460,841) -> Matrix(3,-2,8,-5) Matrix(285,164,-1604,-923) -> Matrix(3,-2,-4,3) Matrix(277,156,364,205) -> Matrix(3,-4,4,-5) Matrix(271,152,-772,-433) -> Matrix(1,-2,0,1) Matrix(93,52,-592,-331) -> Matrix(1,-2,2,-3) Matrix(711,392,448,247) -> Matrix(1,-2,2,-3) Matrix(263,144,-484,-265) -> Matrix(1,0,0,1) Matrix(89,48,432,233) -> Matrix(1,-2,0,1) Matrix(173,92,-472,-251) -> Matrix(1,-2,0,1) Matrix(305,144,36,17) -> Matrix(1,8,0,1) Matrix(2033,952,788,369) -> Matrix(1,2,4,9) Matrix(297,136,404,185) -> Matrix(1,2,2,5) Matrix(143,64,-324,-145) -> Matrix(1,-2,0,1) Matrix(857,376,604,265) -> Matrix(1,2,0,1) Matrix(211,92,-672,-293) -> Matrix(1,2,-2,-3) Matrix(213,92,808,349) -> Matrix(1,2,2,5) Matrix(489,208,1112,473) -> Matrix(1,0,6,1) Matrix(1039,440,1320,559) -> Matrix(1,2,0,1) Matrix(275,116,-1036,-437) -> Matrix(1,0,0,1) Matrix(343,144,-1584,-665) -> Matrix(1,0,2,1) Matrix(2271,952,1448,607) -> Matrix(3,2,4,3) Matrix(2273,952,308,129) -> Matrix(9,2,4,1) Matrix(67,28,-548,-229) -> Matrix(1,0,0,1) Matrix(69,28,32,13) -> Matrix(1,2,0,1) Matrix(131,52,68,27) -> Matrix(1,2,0,1) Matrix(857,336,1084,425) -> Matrix(3,2,4,3) Matrix(195,76,-916,-357) -> Matrix(1,0,2,1) Matrix(259,100,360,139) -> Matrix(1,0,4,1) Matrix(2915,1116,1784,683) -> Matrix(11,6,20,11) Matrix(2523,964,1976,755) -> Matrix(5,2,2,1) Matrix(1553,592,968,369) -> Matrix(1,0,4,1) Matrix(191,72,-512,-193) -> Matrix(1,0,2,1) Matrix(1079,400,1400,519) -> Matrix(1,2,0,1) Matrix(887,328,192,71) -> Matrix(1,0,0,1) Matrix(381,140,-2120,-779) -> Matrix(1,-2,0,1) Matrix(2843,1044,2056,755) -> Matrix(1,-4,0,1) Matrix(2333,852,408,149) -> Matrix(1,-4,0,1) Matrix(1813,652,748,269) -> Matrix(1,0,0,1) Matrix(2621,940,1620,581) -> Matrix(1,2,2,5) Matrix(373,132,308,109) -> Matrix(3,2,4,3) Matrix(1537,536,1104,385) -> Matrix(1,0,0,1) Matrix(857,296,304,105) -> Matrix(3,2,-2,-1) Matrix(233,72,288,89) -> Matrix(1,0,0,1) Matrix(1609,488,1032,313) -> Matrix(1,2,2,5) Matrix(55,16,-196,-57) -> Matrix(1,0,4,1) Matrix(277,76,164,45) -> Matrix(1,0,0,1) Matrix(1809,488,1012,273) -> Matrix(1,-4,2,-7) Matrix(329,88,572,153) -> Matrix(1,2,0,1) Matrix(381,100,80,21) -> Matrix(1,0,2,1) Matrix(53,12,128,29) -> Matrix(1,0,-4,1) Matrix(1481,320,560,121) -> Matrix(3,-2,2,-1) Matrix(1115,236,1904,403) -> Matrix(1,-4,0,1) Matrix(709,148,1212,253) -> Matrix(1,-2,0,1) Matrix(1061,220,680,141) -> Matrix(1,2,2,5) Matrix(591,112,248,47) -> Matrix(1,0,0,1) Matrix(1317,236,1144,205) -> Matrix(1,2,0,1) Matrix(1459,260,780,139) -> Matrix(9,10,8,9) Matrix(389,68,532,93) -> Matrix(1,0,4,1) Matrix(379,60,120,19) -> Matrix(3,-2,2,-1) Matrix(1553,232,328,49) -> Matrix(1,0,4,1) Matrix(373,52,208,29) -> Matrix(1,-2,2,-3) Matrix(91,12,508,67) -> Matrix(1,0,2,1) Matrix(317,36,44,5) -> Matrix(1,2,0,1) Matrix(311,32,68,7) -> Matrix(1,0,0,1) Matrix(175,-24,124,-17) -> Matrix(1,0,0,1) Matrix(173,-28,68,-11) -> Matrix(1,0,0,1) Matrix(715,-124,444,-77) -> Matrix(1,0,4,1) Matrix(1801,-320,1120,-199) -> Matrix(1,0,-2,1) Matrix(237,-44,404,-75) -> Matrix(1,-2,0,1) Matrix(131,-28,248,-53) -> Matrix(1,0,-2,1) Matrix(33,-8,128,-31) -> Matrix(1,0,4,1) Matrix(1929,-512,1232,-327) -> Matrix(9,-4,16,-7) Matrix(251,-68,48,-13) -> Matrix(3,-2,2,-1) Matrix(751,-208,408,-113) -> Matrix(7,-8,8,-9) Matrix(499,-140,360,-101) -> Matrix(1,-2,0,1) Matrix(587,-172,372,-109) -> Matrix(1,0,0,1) Matrix(185,-56,76,-23) -> Matrix(1,0,0,1) Matrix(149,-52,192,-67) -> Matrix(1,0,0,1) Matrix(499,-180,280,-101) -> Matrix(1,-2,2,-3) Matrix(205,-76,116,-43) -> Matrix(1,0,2,1) Matrix(377,-144,144,-55) -> Matrix(1,0,2,1) Matrix(85,-36,196,-83) -> Matrix(1,0,12,1) Matrix(529,-232,472,-207) -> Matrix(13,-2,20,-3) Matrix(331,-148,208,-93) -> Matrix(1,0,-2,1) Matrix(193,-88,68,-31) -> Matrix(1,0,-2,1) Matrix(1171,-628,248,-133) -> Matrix(1,0,10,1) Matrix(545,-296,116,-63) -> Matrix(1,0,-4,1) Matrix(387,-212,272,-149) -> Matrix(1,0,-2,1) Matrix(205,-116,76,-43) -> Matrix(1,0,0,1) Matrix(1647,-952,1192,-689) -> Matrix(1,-8,0,1) Matrix(557,-324,404,-235) -> Matrix(1,2,0,1) Matrix(25,-16,36,-23) -> Matrix(1,0,4,1) Matrix(557,-404,324,-235) -> Matrix(5,-2,8,-3) Matrix(625,-456,196,-143) -> Matrix(3,-2,2,-1) Matrix(461,-340,80,-59) -> Matrix(5,-2,-2,1) Matrix(2213,-1708,688,-531) -> Matrix(1,-4,0,1) Matrix(2075,-1644,804,-637) -> Matrix(1,-2,4,-7) Matrix(993,-808,628,-511) -> Matrix(1,0,4,1) Matrix(1163,-956,736,-605) -> Matrix(1,0,-4,1) Matrix(109,-92,32,-27) -> Matrix(3,-2,2,-1) Matrix(231,-248,68,-73) -> Matrix(7,-2,4,-1) Matrix(225,-256,196,-223) -> Matrix(3,-2,2,-1) Matrix(739,-900,280,-341) -> Matrix(7,-6,6,-5) Matrix(305,-376,116,-143) -> Matrix(1,-2,2,-3) Matrix(617,-784,484,-615) -> Matrix(1,0,0,1) Matrix(859,-1100,360,-461) -> Matrix(1,0,0,1) Matrix(425,-576,76,-103) -> Matrix(1,4,0,1) Matrix(779,-1060,280,-381) -> Matrix(1,2,0,1) Matrix(1255,-1744,444,-617) -> Matrix(1,0,0,1) Matrix(1625,-2296,356,-503) -> Matrix(1,0,0,1) Matrix(49,-72,32,-47) -> Matrix(1,0,2,1) Matrix(2699,-4220,960,-1501) -> Matrix(17,-8,-2,1) Matrix(2027,-3172,632,-989) -> Matrix(15,-8,2,-1) Matrix(977,-1584,404,-655) -> Matrix(5,-2,-2,1) Matrix(91,-148,8,-13) -> Matrix(1,0,-2,1) Matrix(593,-968,68,-111) -> Matrix(27,-14,2,-1) Matrix(237,-404,44,-75) -> Matrix(3,-2,2,-1) Matrix(837,-1444,484,-835) -> Matrix(3,-2,2,-1) Matrix(213,-388,28,-51) -> Matrix(13,-10,4,-3) Matrix(365,-676,196,-363) -> Matrix(25,-24,24,-23) Matrix(85,-196,36,-83) -> Matrix(1,-2,0,1) Matrix(1097,-2624,324,-775) -> Matrix(3,4,2,3) Matrix(1137,-2744,404,-975) -> Matrix(1,-4,0,1) Matrix(505,-1296,196,-503) -> Matrix(1,0,4,1) Matrix(413,-1068,128,-331) -> Matrix(1,0,-2,1) Matrix(2333,-6548,688,-1931) -> Matrix(3,-20,2,-13) Matrix(3105,-9976,916,-2943) -> Matrix(3,22,2,15) Matrix(17,-64,4,-15) -> Matrix(1,-2,0,1) Matrix(205,-1156,36,-203) -> Matrix(1,-10,0,1) 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): 45 Degree of the the map X: 45 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- 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 -7/1 -2/1 1 10 -6/1 0 4 -17/3 -2/1 1 10 -11/2 1/0 1 20 -5/1 -1/1 1 10 -14/3 (-3/2,-1/1) 0 20 -9/2 -3/2 1 20 -13/3 -1/1 5 2 -4/1 (-1/1,1/0) 0 20 -19/5 -1/1 1 10 -15/4 -1/2 1 20 -41/11 0/1 2 2 -26/7 (0/1,1/0) 0 20 -11/3 -1/1 1 10 -18/5 (-2/1,-1/1) 0 20 -7/2 -1/1 3 4 -24/7 (-3/4,-2/3) 0 20 -41/12 -1/2 1 20 -17/5 -2/3 1 10 -10/3 (-1/2,0/1) 0 20 -3/1 -1/1 1 10 -11/4 1/0 1 20 -8/3 -1/1 2 4 -21/8 -1/2 1 20 -34/13 (-1/2,0/1) 0 20 -13/5 -1/1 1 10 -18/7 (-1/2,-1/3) 0 20 -5/2 1/0 1 20 -17/7 -1/1 3 2 -12/5 (-1/1,-1/2) 0 20 -7/3 0/1 1 10 -9/4 -1/1 1 4 -11/5 -1/1 1 10 -13/6 1/0 1 20 -15/7 0/1 1 10 -2/1 (-1/1,0/1) 0 20 -1/1 0/1 1 2 0/1 (0/1,1/0) 0 20 1/7 0/1 1 10 1/6 1/0 1 20 3/17 0/1 3 2 2/11 (0/1,1/1) 0 20 1/5 0/1 1 10 5/24 1/0 1 20 4/19 (-1/2,0/1) 0 20 3/14 1/2 1 20 2/9 (-1/1,1/0) 0 20 3/13 -1/1 1 10 1/4 0/1 2 4 5/19 1/3 1 10 4/15 (1/2,1/1) 0 20 3/11 1/1 1 10 8/29 (3/4,1/1) 0 20 5/18 3/2 1 20 2/7 (0/1,1/0) 0 20 5/17 1/1 1 10 3/10 1/0 1 20 1/3 0/1 1 10 5/14 1/0 1 20 4/11 1/0 2 4 3/8 1/0 1 20 5/13 -1/1 1 10 2/5 (-1/2,0/1) 0 20 3/7 0/1 6 2 4/9 (0/1,1/4) 0 20 5/11 1/3 1 10 1/2 1/0 1 20 8/15 (-1/4,0/1) 0 20 7/13 0/1 7 2 6/11 (0/1,1/3) 0 20 5/9 1/1 1 10 4/7 (1/1,1/0) 0 20 11/19 1/0 5 2 7/12 1/0 1 20 17/29 -2/1 1 10 10/17 (-2/1,-1/1) 0 20 3/5 -1/1 1 10 2/3 0/1 4 4 5/7 1/3 1 10 8/11 (1/3,1/2) 0 20 11/15 1/3 1 10 3/4 1/2 1 20 13/17 1/1 5 2 10/13 (1/1,2/1) 0 20 17/22 1/0 1 20 7/9 0/1 1 10 11/14 1/1 1 4 15/19 0/1 1 10 4/5 (0/1,1/0) 0 20 9/11 0/1 4 2 14/17 (0/1,1/4) 0 20 5/6 1/2 1 20 1/1 0/1 1 10 9/8 3/4 1 20 8/7 1/1 2 4 15/13 0/1 1 10 7/6 1/2 1 20 6/5 (1/2,1/1) 0 20 11/9 1/1 4 2 5/4 1/0 1 20 19/15 1/1 1 10 14/11 0 4 23/18 1/0 1 20 9/7 0/1 1 10 4/3 (1/1,1/0) 0 20 19/14 1/0 1 20 15/11 0/1 1 10 11/8 1/0 1 20 29/21 1/0 5 2 18/13 (-2/1,1/0) 0 20 25/18 -1/2 1 20 32/23 -1/1 2 4 7/5 0/1 1 10 24/17 (0/1,1/0) 0 20 41/29 0/1 2 2 17/12 1/0 1 20 10/7 (0/1,1/1) 0 20 3/2 0/1 1 4 14/9 (0/1,1/3) 0 20 25/16 1/2 1 20 61/39 1/2 15 2 36/23 (1/2,5/9) 0 20 11/7 1/1 1 10 30/19 (0/1,1/0) 0 20 19/12 1/2 1 20 27/17 1/1 1 10 8/5 (0/1,1/2) 0 20 37/23 0/1 3 2 29/18 1/4 1 20 21/13 1/3 1 10 34/21 0 4 13/8 1/2 1 20 31/19 1/2 7 2 18/11 (1/2,3/5) 0 20 5/3 1/1 1 10 12/7 (1/2,1/1) 0 20 19/11 1/1 1 2 26/15 (0/1,1/1) 0 20 33/19 0/1 1 10 7/4 1/2 1 20 16/9 1/2 2 4 25/14 1/2 1 20 9/5 2/3 1 10 20/11 (2/3,3/4) 0 20 11/6 5/6 1 20 24/13 (11/12,1/1) 0 20 13/7 1/1 12 2 2/1 (1/1,1/0) 0 20 7/3 1/0 1 2 12/5 (0/1,1/0) 0 20 41/17 2/1 1 10 29/12 1/0 1 20 17/7 0/1 1 10 5/2 1/0 1 20 23/9 0/1 1 10 18/7 0/1 4 4 49/19 0/1 1 10 31/12 1/2 1 20 13/5 1/1 1 10 21/8 1/2 1 20 29/11 1/1 4 2 8/3 (1/1,1/0) 0 20 19/7 1/1 1 10 11/4 1/1 1 4 25/9 2/1 1 10 39/14 1/0 1 20 14/5 (2/1,1/0) 0 20 59/21 1/0 15 2 45/16 1/0 1 20 31/11 -2/1 1 10 17/6 -1/2 1 20 3/1 1/1 1 10 16/5 (3/1,1/0) 0 20 29/9 -1/1 1 10 13/4 1/0 1 20 23/7 1/1 3 2 10/3 (1/1,2/1) 0 20 27/8 1/1 3 4 44/13 (4/3,3/2) 0 20 17/5 2/1 1 10 7/2 1/0 1 20 4/1 1/0 2 4 9/2 1/0 1 20 14/3 (-1/1,0/1) 0 20 5/1 1/1 1 10 11/2 1/0 1 20 28/5 (5/1,1/0) 0 20 17/3 1/0 5 2 6/1 (0/1,1/0) 0 20 7/1 2/1 1 10 15/2 5/2 1 20 8/1 (4/1,1/0) 0 20 9/1 1/0 7 2 1/0 1/0 1 20 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,92,8,67) (-7/1,1/0) -> (15/11,11/8) Hyperbolic Matrix(23,144,-4,-25) (-7/1,-6/1) -> (-6/1,-17/3) Parabolic Matrix(17,96,82,463) (-17/3,-11/2) -> (1/5,5/24) Glide Reflection Matrix(73,392,46,247) (-11/2,-5/1) -> (19/12,27/17) Glide Reflection Matrix(11,52,48,227) (-5/1,-14/3) -> (2/9,3/13) Hyperbolic Matrix(33,152,28,129) (-14/3,-9/2) -> (7/6,6/5) Hyperbolic Matrix(35,156,46,205) (-9/2,-13/3) -> (3/4,13/17) Glide Reflection Matrix(25,104,-6,-25) (-13/3,-4/1) -> (-13/3,-4/1) Reflection Matrix(43,164,156,595) (-4/1,-19/5) -> (3/11,8/29) Hyperbolic Matrix(101,380,80,301) (-19/5,-15/4) -> (5/4,19/15) Hyperbolic Matrix(351,1312,248,927) (-15/4,-41/11) -> (41/29,17/12) Hyperbolic Matrix(573,2132,-154,-573) (-41/11,-26/7) -> (-41/11,-26/7) Reflection Matrix(193,712,-74,-273) (-26/7,-11/3) -> (-34/13,-13/5) Glide Reflection Matrix(45,164,76,277) (-11/3,-18/5) -> (10/17,3/5) Hyperbolic Matrix(155,556,46,165) (-18/5,-7/2) -> (10/3,27/8) Glide Reflection Matrix(277,956,82,283) (-7/2,-24/7) -> (27/8,44/13) Glide Reflection Matrix(83,284,396,1355) (-24/7,-41/12) -> (5/24,4/19) Hyperbolic Matrix(431,1472,248,847) (-41/12,-17/5) -> (33/19,7/4) Hyperbolic Matrix(51,172,8,27) (-17/5,-10/3) -> (6/1,7/1) Hyperbolic Matrix(17,56,44,145) (-10/3,-3/1) -> (5/13,2/5) Hyperbolic Matrix(23,64,78,217) (-3/1,-11/4) -> (5/17,3/10) Glide Reflection Matrix(95,256,-36,-97) (-11/4,-8/3) -> (-8/3,-21/8) Parabolic Matrix(619,1620,222,581) (-21/8,-34/13) -> (39/14,14/5) Glide Reflection Matrix(125,324,76,197) (-13/5,-18/7) -> (18/11,5/3) Hyperbolic Matrix(25,64,116,297) (-18/7,-5/2) -> (3/14,2/9) Hyperbolic Matrix(137,336,42,103) (-5/2,-17/7) -> (13/4,23/7) Glide Reflection Matrix(169,408,-70,-169) (-17/7,-12/5) -> (-17/7,-12/5) Reflection Matrix(57,136,44,105) (-12/5,-7/3) -> (9/7,4/3) Hyperbolic Matrix(61,140,78,179) (-7/3,-9/4) -> (7/9,11/14) Glide Reflection Matrix(131,292,48,107) (-9/4,-11/5) -> (19/7,11/4) Hyperbolic Matrix(271,592,168,367) (-11/5,-13/6) -> (29/18,21/13) Hyperbolic Matrix(139,300,120,259) (-13/6,-15/7) -> (15/13,7/6) Hyperbolic Matrix(215,456,124,263) (-15/7,-2/1) -> (26/15,33/19) Hyperbolic Matrix(3,4,-2,-3) (-2/1,-1/1) -> (-2/1,-1/1) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(175,-24,124,-17) (0/1,1/7) -> (7/5,24/17) Hyperbolic Matrix(173,-28,68,-11) (1/7,1/6) -> (5/2,23/9) Hyperbolic Matrix(715,-124,444,-77) (1/6,3/17) -> (37/23,29/18) Hyperbolic Matrix(67,-12,374,-67) (3/17,2/11) -> (3/17,2/11) Reflection Matrix(237,-44,404,-75) (2/11,1/5) -> (17/29,10/17) Hyperbolic Matrix(131,-28,248,-53) (4/19,3/14) -> (1/2,8/15) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(349,-92,110,-29) (5/19,4/15) -> (3/1,16/5) Glide Reflection Matrix(253,-68,346,-93) (4/15,3/11) -> (8/11,11/15) Glide Reflection Matrix(751,-208,408,-113) (8/29,5/18) -> (11/6,24/13) Hyperbolic Matrix(499,-140,360,-101) (5/18,2/7) -> (18/13,25/18) Hyperbolic Matrix(587,-172,372,-109) (2/7,5/17) -> (11/7,30/19) Hyperbolic Matrix(185,-56,76,-23) (3/10,1/3) -> (17/7,5/2) Hyperbolic Matrix(149,-52,192,-67) (1/3,5/14) -> (17/22,7/9) Hyperbolic Matrix(499,-180,280,-101) (5/14,4/11) -> (16/9,25/14) 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(29,-12,70,-29) (2/5,3/7) -> (2/5,3/7) Reflection Matrix(55,-24,126,-55) (3/7,4/9) -> (3/7,4/9) Reflection Matrix(331,-148,208,-93) (4/9,5/11) -> (27/17,8/5) Hyperbolic Matrix(193,-88,68,-31) (5/11,1/2) -> (17/6,3/1) Hyperbolic Matrix(209,-112,390,-209) (8/15,7/13) -> (8/15,7/13) Reflection Matrix(155,-84,286,-155) (7/13,6/11) -> (7/13,6/11) Reflection Matrix(181,-100,38,-21) (6/11,5/9) -> (14/3,5/1) Glide Reflection Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(153,-88,266,-153) (4/7,11/19) -> (4/7,11/19) Reflection Matrix(557,-324,404,-235) (11/19,7/12) -> (11/8,29/21) Hyperbolic Matrix(833,-488,466,-273) (7/12,17/29) -> (25/14,9/5) Glide Reflection Matrix(25,-16,36,-23) (3/5,2/3) -> (2/3,5/7) Parabolic Matrix(139,-100,82,-59) (5/7,8/11) -> (5/3,12/7) Glide Reflection Matrix(185,-136,34,-25) (11/15,3/4) -> (5/1,11/2) Glide Reflection Matrix(339,-260,442,-339) (13/17,10/13) -> (13/17,10/13) Reflection Matrix(633,-488,406,-313) (10/13,17/22) -> (14/9,25/16) Glide Reflection Matrix(559,-440,202,-159) (11/14,15/19) -> (11/4,25/9) Glide Reflection Matrix(425,-336,234,-185) (15/19,4/5) -> (9/5,20/11) Glide Reflection Matrix(89,-72,110,-89) (4/5,9/11) -> (4/5,9/11) Reflection Matrix(307,-252,374,-307) (9/11,14/17) -> (9/11,14/17) Reflection Matrix(503,-416,318,-263) (14/17,5/6) -> (30/19,19/12) Glide Reflection Matrix(109,-92,32,-27) (5/6,1/1) -> (17/5,7/2) Hyperbolic Matrix(265,-296,94,-105) (1/1,9/8) -> (31/11,17/6) Glide Reflection Matrix(431,-488,310,-351) (9/8,8/7) -> (25/18,32/23) Glide Reflection Matrix(465,-536,334,-385) (8/7,15/13) -> (32/23,7/5) Glide Reflection Matrix(109,-132,90,-109) (6/5,11/9) -> (6/5,11/9) Reflection Matrix(305,-376,116,-143) (11/9,5/4) -> (21/8,29/11) Hyperbolic Matrix(741,-940,458,-581) (19/15,14/11) -> (21/13,34/21) Glide Reflection Matrix(755,-964,466,-595) (14/11,23/18) -> (34/21,13/8) Glide Reflection Matrix(509,-652,210,-269) (23/18,9/7) -> (29/12,17/7) Glide Reflection Matrix(425,-576,76,-103) (4/3,19/14) -> (11/2,28/5) Hyperbolic Matrix(779,-1060,280,-381) (19/14,15/11) -> (25/9,39/14) Hyperbolic Matrix(755,-1044,546,-755) (29/21,18/13) -> (29/21,18/13) Reflection Matrix(1393,-1968,986,-1393) (24/17,41/29) -> (24/17,41/29) Reflection Matrix(231,-328,50,-71) (17/12,10/7) -> (9/2,14/3) Glide Reflection Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(2699,-4220,960,-1501) (25/16,61/39) -> (59/21,45/16) Hyperbolic Matrix(2807,-4392,1794,-2807) (61/39,36/23) -> (61/39,36/23) Reflection Matrix(779,-1220,242,-379) (36/23,11/7) -> (16/5,29/9) Glide Reflection Matrix(369,-592,230,-369) (8/5,37/23) -> (8/5,37/23) Reflection Matrix(91,-148,8,-13) (13/8,31/19) -> (9/1,1/0) Hyperbolic Matrix(683,-1116,418,-683) (31/19,18/11) -> (31/19,18/11) Reflection Matrix(265,-456,154,-265) (12/7,19/11) -> (12/7,19/11) Reflection Matrix(571,-988,330,-571) (19/11,26/15) -> (19/11,26/15) Reflection Matrix(213,-388,28,-51) (20/11,11/6) -> (15/2,8/1) Hyperbolic Matrix(337,-624,182,-337) (24/13,13/7) -> (24/13,13/7) Reflection Matrix(27,-52,14,-27) (13/7,2/1) -> (13/7,2/1) Reflection Matrix(13,-28,6,-13) (2/1,7/3) -> (2/1,7/3) Reflection Matrix(71,-168,30,-71) (7/3,12/5) -> (7/3,12/5) Reflection Matrix(833,-2008,246,-593) (12/5,41/17) -> (44/13,17/5) Glide Reflection Matrix(1137,-2744,404,-975) (41/17,29/12) -> (45/16,31/11) Hyperbolic Matrix(505,-1296,196,-503) (23/9,18/7) -> (18/7,49/19) Parabolic Matrix(369,-952,50,-129) (49/19,31/12) -> (7/1,15/2) Glide Reflection Matrix(413,-1068,128,-331) (31/12,13/5) -> (29/9,13/4) Hyperbolic Matrix(175,-464,66,-175) (29/11,8/3) -> (29/11,8/3) Reflection Matrix(589,-1652,210,-589) (14/5,59/21) -> (14/5,59/21) Reflection Matrix(139,-460,42,-139) (23/7,10/3) -> (23/7,10/3) Reflection Matrix(17,-64,4,-15) (7/2,4/1) -> (4/1,9/2) Parabolic Matrix(169,-952,30,-169) (28/5,17/3) -> (28/5,17/3) Reflection Matrix(35,-204,6,-35) (17/3,6/1) -> (17/3,6/1) Reflection Matrix(17,-144,2,-17) (8/1,9/1) -> (8/1,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(11,92,8,67) -> Matrix(1,2,0,1) 1/0 Matrix(23,144,-4,-25) -> Matrix(1,0,0,1) Matrix(17,96,82,463) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(73,392,46,247) -> Matrix(1,2,2,3) Matrix(11,52,48,227) -> Matrix(1,2,-2,-3) -1/1 Matrix(33,152,28,129) -> Matrix(1,2,0,1) 1/0 Matrix(35,156,46,205) -> Matrix(3,4,4,5) Matrix(25,104,-6,-25) -> Matrix(1,2,0,-1) (-13/3,-4/1) -> (-1/1,1/0) Matrix(43,164,156,595) -> Matrix(3,2,4,3) Matrix(101,380,80,301) -> Matrix(1,0,2,1) 0/1 Matrix(351,1312,248,927) -> Matrix(1,0,2,1) 0/1 Matrix(573,2132,-154,-573) -> Matrix(1,0,0,-1) (-41/11,-26/7) -> (0/1,1/0) Matrix(193,712,-74,-273) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(45,164,76,277) -> Matrix(1,0,0,1) Matrix(155,556,46,165) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(277,956,82,283) -> Matrix(7,6,6,5) Matrix(83,284,396,1355) -> Matrix(3,2,-2,-1) -1/1 Matrix(431,1472,248,847) -> Matrix(3,2,4,3) Matrix(51,172,8,27) -> Matrix(1,0,2,1) 0/1 Matrix(17,56,44,145) -> Matrix(1,0,0,1) Matrix(23,64,78,217) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(95,256,-36,-97) -> Matrix(1,2,-2,-3) -1/1 Matrix(619,1620,222,581) -> Matrix(3,2,2,1) Matrix(125,324,76,197) -> Matrix(3,2,4,3) Matrix(25,64,116,297) -> Matrix(1,0,2,1) 0/1 Matrix(137,336,42,103) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(169,408,-70,-169) -> Matrix(3,2,-4,-3) (-17/7,-12/5) -> (-1/1,-1/2) Matrix(57,136,44,105) -> Matrix(1,0,2,1) 0/1 Matrix(61,140,78,179) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(131,292,48,107) -> Matrix(1,0,2,1) 0/1 Matrix(271,592,168,367) -> Matrix(1,0,4,1) 0/1 Matrix(139,300,120,259) -> Matrix(1,0,2,1) 0/1 Matrix(215,456,124,263) -> Matrix(1,0,2,1) 0/1 Matrix(3,4,-2,-3) -> Matrix(-1,0,2,1) (-2/1,-1/1) -> (-1/1,0/1) Matrix(-1,0,2,1) -> Matrix(1,0,0,-1) (-1/1,0/1) -> (0/1,1/0) Matrix(175,-24,124,-17) -> Matrix(1,0,0,1) Matrix(173,-28,68,-11) -> Matrix(1,0,0,1) Matrix(715,-124,444,-77) -> Matrix(1,0,4,1) 0/1 Matrix(67,-12,374,-67) -> Matrix(1,0,2,-1) (3/17,2/11) -> (0/1,1/1) Matrix(237,-44,404,-75) -> Matrix(1,-2,0,1) 1/0 Matrix(131,-28,248,-53) -> Matrix(1,0,-2,1) 0/1 Matrix(33,-8,128,-31) -> Matrix(1,0,4,1) 0/1 Matrix(349,-92,110,-29) -> Matrix(5,-2,2,-1) Matrix(253,-68,346,-93) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(751,-208,408,-113) -> Matrix(7,-8,8,-9) 1/1 Matrix(499,-140,360,-101) -> Matrix(1,-2,0,1) 1/0 Matrix(587,-172,372,-109) -> Matrix(1,0,0,1) Matrix(185,-56,76,-23) -> Matrix(1,0,0,1) Matrix(149,-52,192,-67) -> Matrix(1,0,0,1) Matrix(499,-180,280,-101) -> Matrix(1,-2,2,-3) 1/1 Matrix(205,-76,116,-43) -> Matrix(1,0,2,1) 0/1 Matrix(377,-144,144,-55) -> Matrix(1,0,2,1) 0/1 Matrix(29,-12,70,-29) -> Matrix(-1,0,4,1) (2/5,3/7) -> (-1/2,0/1) Matrix(55,-24,126,-55) -> Matrix(1,0,8,-1) (3/7,4/9) -> (0/1,1/4) Matrix(331,-148,208,-93) -> Matrix(1,0,-2,1) 0/1 Matrix(193,-88,68,-31) -> Matrix(1,0,-2,1) 0/1 Matrix(209,-112,390,-209) -> Matrix(-1,0,8,1) (8/15,7/13) -> (-1/4,0/1) Matrix(155,-84,286,-155) -> Matrix(1,0,6,-1) (7/13,6/11) -> (0/1,1/3) Matrix(181,-100,38,-21) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(205,-116,76,-43) -> Matrix(1,0,0,1) Matrix(153,-88,266,-153) -> Matrix(-1,2,0,1) (4/7,11/19) -> (1/1,1/0) Matrix(557,-324,404,-235) -> Matrix(1,2,0,1) 1/0 Matrix(833,-488,466,-273) -> Matrix(1,4,2,7) Matrix(25,-16,36,-23) -> Matrix(1,0,4,1) 0/1 Matrix(139,-100,82,-59) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(185,-136,34,-25) -> Matrix(5,-2,2,-1) Matrix(339,-260,442,-339) -> Matrix(3,-4,2,-3) (13/17,10/13) -> (1/1,2/1) Matrix(633,-488,406,-313) -> Matrix(1,-2,2,-5) Matrix(559,-440,202,-159) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(425,-336,234,-185) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(89,-72,110,-89) -> Matrix(1,0,0,-1) (4/5,9/11) -> (0/1,1/0) Matrix(307,-252,374,-307) -> Matrix(1,0,8,-1) (9/11,14/17) -> (0/1,1/4) Matrix(503,-416,318,-263) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(109,-92,32,-27) -> Matrix(3,-2,2,-1) 1/1 Matrix(265,-296,94,-105) -> Matrix(3,-2,-2,1) Matrix(431,-488,310,-351) -> Matrix(3,-2,-2,1) Matrix(465,-536,334,-385) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(109,-132,90,-109) -> Matrix(3,-2,4,-3) (6/5,11/9) -> (1/2,1/1) Matrix(305,-376,116,-143) -> Matrix(1,-2,2,-3) 1/1 Matrix(741,-940,458,-581) -> Matrix(1,-2,2,-5) Matrix(755,-964,466,-595) -> Matrix(1,-2,2,-5) Matrix(509,-652,210,-269) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(425,-576,76,-103) -> Matrix(1,4,0,1) 1/0 Matrix(779,-1060,280,-381) -> Matrix(1,2,0,1) 1/0 Matrix(755,-1044,546,-755) -> Matrix(1,4,0,-1) (29/21,18/13) -> (-2/1,1/0) Matrix(1393,-1968,986,-1393) -> Matrix(1,0,0,-1) (24/17,41/29) -> (0/1,1/0) Matrix(231,-328,50,-71) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(49,-72,32,-47) -> Matrix(1,0,2,1) 0/1 Matrix(2699,-4220,960,-1501) -> Matrix(17,-8,-2,1) Matrix(2807,-4392,1794,-2807) -> Matrix(19,-10,36,-19) (61/39,36/23) -> (1/2,5/9) Matrix(779,-1220,242,-379) -> Matrix(3,-2,-2,1) Matrix(369,-592,230,-369) -> Matrix(1,0,4,-1) (8/5,37/23) -> (0/1,1/2) Matrix(91,-148,8,-13) -> Matrix(1,0,-2,1) 0/1 Matrix(683,-1116,418,-683) -> Matrix(11,-6,20,-11) (31/19,18/11) -> (1/2,3/5) Matrix(265,-456,154,-265) -> Matrix(3,-2,4,-3) (12/7,19/11) -> (1/2,1/1) Matrix(571,-988,330,-571) -> Matrix(1,0,2,-1) (19/11,26/15) -> (0/1,1/1) Matrix(213,-388,28,-51) -> Matrix(13,-10,4,-3) Matrix(337,-624,182,-337) -> Matrix(23,-22,24,-23) (24/13,13/7) -> (11/12,1/1) Matrix(27,-52,14,-27) -> Matrix(-1,2,0,1) (13/7,2/1) -> (1/1,1/0) Matrix(13,-28,6,-13) -> Matrix(-1,2,0,1) (2/1,7/3) -> (1/1,1/0) Matrix(71,-168,30,-71) -> Matrix(1,0,0,-1) (7/3,12/5) -> (0/1,1/0) Matrix(833,-2008,246,-593) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(1137,-2744,404,-975) -> Matrix(1,-4,0,1) 1/0 Matrix(505,-1296,196,-503) -> Matrix(1,0,4,1) 0/1 Matrix(369,-952,50,-129) -> Matrix(9,-2,4,-1) Matrix(413,-1068,128,-331) -> Matrix(1,0,-2,1) 0/1 Matrix(175,-464,66,-175) -> Matrix(-1,2,0,1) (29/11,8/3) -> (1/1,1/0) Matrix(589,-1652,210,-589) -> Matrix(-1,4,0,1) (14/5,59/21) -> (2/1,1/0) Matrix(139,-460,42,-139) -> Matrix(3,-4,2,-3) (23/7,10/3) -> (1/1,2/1) Matrix(17,-64,4,-15) -> Matrix(1,-2,0,1) 1/0 Matrix(169,-952,30,-169) -> Matrix(-1,10,0,1) (28/5,17/3) -> (5/1,1/0) Matrix(35,-204,6,-35) -> Matrix(1,0,0,-1) (17/3,6/1) -> (0/1,1/0) Matrix(17,-144,2,-17) -> Matrix(-1,8,0,1) (8/1,9/1) -> (4/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.