INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -13/28 -5/11 -4/9 -11/26 -2/5 -3/8 -1/3 -2/7 -1/4 -1/6 0/1 2/13 1/5 1/4 7/23 1/3 4/11 7/18 3/7 1/2 11/19 7/11 2/3 13/17 4/5 7/8 1/1 8/7 11/9 5/4 17/13 29/21 7/5 3/2 46/29 13/8 5/3 151/89 19/11 29/16 13/7 2/1 31/14 7/3 19/8 5/2 13/5 11/4 31/11 3/1 19/6 23/7 10/3 27/8 31/9 7/2 11/3 19/5 23/6 4/1 17/4 13/3 9/2 37/8 19/4 5/1 21/4 11/2 17/3 23/4 6/1 13/2 7/1 15/2 8/1 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/2 -7/15 1/3 -13/28 1/2 -6/13 1/1 -5/11 0/1 -9/20 0/1 1/2 -4/9 1/2 -7/16 0/1 -17/39 1/1 -10/23 -1/1 -13/30 0/1 1/6 -3/7 1/3 -11/26 1/2 -19/45 3/5 -8/19 1/1 -5/12 0/1 1/1 -12/29 -1/1 -19/46 0/1 -7/17 0/1 -9/22 0/1 1/4 -11/27 1/3 -2/5 1/2 -9/23 1/1 -16/41 1/0 -7/18 0/1 1/0 -12/31 1/5 -17/44 0/1 -5/13 1/3 -23/60 1/3 3/8 -18/47 1/3 -13/34 2/5 -8/21 1/1 -3/8 1/2 -10/27 3/5 -7/19 1/2 -11/30 3/5 2/3 -4/11 1/1 -5/14 0/1 -11/31 1/2 -6/17 1/1 -7/20 0/1 1/2 -1/3 1/1 -5/16 0/1 1/2 -9/29 1/2 -4/13 1/2 -7/23 1/1 -10/33 1/1 -3/10 1/1 2/1 -8/27 1/1 -5/17 1/0 -7/24 -1/2 0/1 -9/31 -1/1 -11/38 0/1 -2/7 0/1 -9/32 1/3 1/2 -7/25 0/1 -5/18 2/5 1/2 -3/11 1/1 -10/37 1/2 -7/26 2/3 1/1 -4/15 1/1 -5/19 1/1 -1/4 0/1 -5/21 1/3 -4/17 1/1 -7/30 1/3 1/2 -3/13 1/2 -5/22 0/1 1/2 -2/9 1/1 -9/41 1/1 -7/32 1/0 -5/23 0/1 -3/14 0/1 1/0 -1/5 1/3 -2/11 1/2 -3/17 1/1 -1/6 1/2 1/0 -3/19 1/1 -2/13 1/3 -1/7 1/2 -2/15 3/5 -1/8 2/3 1/1 -1/9 1/1 0/1 1/1 1/7 1/1 2/13 1/1 3/19 1/1 1/6 1/1 2/1 1/5 1/0 4/19 -1/1 3/14 0/1 1/0 5/23 -1/1 7/32 0/1 2/9 -1/1 1/4 1/2 1/0 4/15 -1/1 3/11 1/1 5/18 1/1 3/2 12/43 2/1 19/68 2/1 7/25 1/1 9/32 1/1 2/1 2/7 1/0 7/24 1/1 1/0 5/17 1/1 3/10 4/1 1/0 7/23 1/0 4/13 -5/1 5/16 -2/1 1/3 -1/1 6/17 -1/1 5/14 -1/3 0/1 4/11 0/1 7/19 1/5 3/8 0/1 1/2 8/21 1/1 21/55 1/1 13/34 2/1 1/0 5/13 0/1 17/44 0/1 1/2 12/31 1/1 7/18 1/2 9/23 1/1 2/5 1/1 13/32 1/0 11/27 1/1 9/22 1/1 1/0 7/17 1/0 12/29 1/1 17/41 1/1 5/12 0/1 1/0 13/31 1/1 8/19 1/0 3/7 1/0 10/23 1/0 7/16 -1/1 1/0 4/9 1/1 1/2 0/1 6/11 1/3 5/9 1/1 14/25 1/0 9/16 1/2 1/0 22/39 1/1 13/23 0/1 4/7 1/1 11/19 1/1 18/31 1/1 7/12 1/1 2/1 10/17 1/0 33/56 1/1 1/0 23/39 1/1 13/22 1/0 16/27 -1/1 3/5 1/1 14/23 1/1 25/41 1/0 11/18 1/1 1/0 8/13 1/0 13/21 3/1 5/8 -2/1 1/0 12/19 -1/1 19/30 -1/2 0/1 7/11 0/1 23/36 0/1 1/0 16/25 1/1 25/39 -1/1 9/14 -1/1 1/0 11/17 -1/1 2/3 0/1 9/13 1/3 25/36 0/1 1/2 16/23 1/2 7/10 0/1 1/4 12/17 1/3 17/24 1/3 2/5 5/7 1/2 3/4 2/3 1/1 13/17 1/1 23/30 1/1 16/15 10/13 1/1 27/35 1/1 17/22 4/3 7/9 1/1 18/23 1/1 11/14 3/2 1/0 26/33 1/1 15/19 1/1 19/24 2/1 5/2 4/5 1/0 13/16 1/1 1/0 9/11 1/0 14/17 -1/1 5/6 0/1 1/0 11/13 0/1 28/33 1/1 17/20 1/1 1/0 6/7 -1/1 7/8 0/1 8/9 1/1 1/1 1/1 9/8 2/1 1/0 8/7 1/0 23/20 -2/1 1/0 15/13 -1/1 7/6 0/1 1/0 6/5 1/1 11/9 1/0 27/22 -2/1 1/0 16/13 -1/1 21/17 -1/1 5/4 0/1 14/11 1/2 23/18 2/3 1/1 32/25 1/2 9/7 1/1 22/17 1/2 35/27 1/1 13/10 3/4 1/1 17/13 1/1 4/3 1/1 19/14 2/1 34/25 1/1 15/11 1/1 26/19 2/1 11/8 2/1 3/1 40/29 1/0 69/50 2/1 1/0 29/21 2/1 76/55 3/1 47/34 2/1 18/13 3/1 43/31 3/1 25/18 7/2 4/1 7/5 1/0 3/2 1/0 11/7 1/0 30/19 -1/1 49/31 1/0 19/12 -1/1 1/0 46/29 1/0 27/17 -1/1 8/5 1/1 37/23 1/0 29/18 -8/1 1/0 21/13 -3/1 55/34 -3/1 1/0 34/21 1/0 47/29 -3/1 13/8 -2/1 57/35 -1/1 44/27 -1/1 31/19 -2/1 49/30 -2/1 -1/1 18/11 -1/1 23/14 -3/2 -1/1 51/31 -1/1 28/17 -1/1 5/3 -1/1 22/13 0/1 39/23 -1/1 95/56 -1/1 -1/2 151/89 -1/2 56/33 -1/3 17/10 0/1 46/27 -1/1 75/44 0/1 1/0 29/17 -1/1 12/7 -1/3 19/11 0/1 26/15 1/7 7/4 0/1 1/2 9/5 1/1 29/16 1/1 49/27 1/1 20/11 1/1 11/6 2/1 1/0 13/7 1/0 15/8 1/1 1/0 17/9 1/1 2/1 1/0 11/5 -1/1 31/14 -1/1 51/23 -1/1 20/9 -1/1 9/4 -1/2 0/1 34/15 -1/3 25/11 0/1 16/7 -1/3 7/3 0/1 26/11 1/3 45/19 1/3 64/27 1/3 83/35 1/1 19/8 0/1 50/21 1/5 31/13 1/3 74/31 1/2 43/18 0/1 1/2 12/5 1/3 41/17 1/3 70/29 1/2 29/12 0/1 1/3 46/19 1/2 63/26 1/3 1/2 17/7 1/2 5/2 0/1 1/1 13/5 1/0 34/13 -1/1 55/21 1/1 131/50 2/1 1/0 76/29 1/0 21/8 1/1 1/0 50/19 1/0 29/11 1/0 8/3 1/1 11/4 1/0 14/5 -3/1 59/21 -2/1 45/16 -2/1 1/0 31/11 -2/1 17/6 -1/1 1/0 20/7 1/0 23/8 -1/1 1/0 3/1 -1/1 22/7 -1/1 19/6 -1/2 1/0 16/5 -1/2 13/4 -1/4 0/1 23/7 0/1 33/10 0/1 1/10 10/3 1/3 47/14 0/1 1/2 37/11 0/1 27/8 1/2 71/21 1/1 186/55 1/3 301/89 1/2 115/34 1/2 1/1 44/13 1/2 17/5 1/1 24/7 1/1 31/9 1/0 7/2 0/1 18/5 1/1 47/13 1/1 29/8 1/1 3/2 11/3 1/1 26/7 1/0 15/4 1/1 2/1 49/13 1/1 34/9 1/1 19/5 1/0 23/6 1/1 1/0 4/1 1/0 25/6 -1/1 1/0 46/11 1/0 21/5 -1/1 17/4 -2/1 47/11 -1/1 30/7 -1/1 13/3 -1/1 9/2 0/1 1/0 23/5 -1/1 37/8 0/1 51/11 1/1 14/3 1/1 19/4 -1/1 1/0 24/5 -1/1 5/1 0/1 26/5 1/1 21/4 1/2 1/0 16/3 1/1 11/2 0/1 1/0 17/3 0/1 23/4 0/1 6/1 1/1 13/2 1/0 20/3 -1/1 7/1 -1/1 15/2 -1/2 0/1 8/1 1/0 17/2 -1/1 0/1 9/1 0/1 10/1 1/1 1/0 0/1 1/0 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(393,184,566,265) (-1/2,-7/15) -> (9/13,25/36) Hyperbolic Matrix(503,234,1236,575) (-7/15,-13/28) -> (13/32,11/27) Hyperbolic Matrix(225,104,556,257) (-13/28,-6/13) -> (2/5,13/32) Hyperbolic Matrix(501,230,220,101) (-6/13,-5/11) -> (25/11,16/7) Hyperbolic Matrix(275,124,326,147) (-5/11,-9/20) -> (5/6,11/13) Hyperbolic Matrix(383,172,-982,-441) (-9/20,-4/9) -> (-16/41,-7/18) Hyperbolic Matrix(269,118,212,93) (-4/9,-7/16) -> (5/4,14/11) Hyperbolic Matrix(531,232,428,187) (-7/16,-17/39) -> (21/17,5/4) Hyperbolic Matrix(693,302,1168,509) (-17/39,-10/23) -> (16/27,3/5) Hyperbolic Matrix(1059,460,320,139) (-10/23,-13/30) -> (33/10,10/3) Hyperbolic Matrix(583,252,738,319) (-13/30,-3/7) -> (15/19,19/24) Hyperbolic Matrix(571,242,-1352,-573) (-3/7,-11/26) -> (-11/26,-19/45) Parabolic Matrix(1195,504,1866,787) (-19/45,-8/19) -> (16/25,25/39) Hyperbolic Matrix(153,64,-514,-215) (-8/19,-5/12) -> (-3/10,-8/27) Hyperbolic Matrix(53,22,-412,-171) (-5/12,-12/29) -> (-2/15,-1/8) Hyperbolic Matrix(2609,1078,1532,633) (-12/29,-19/46) -> (17/10,46/27) Hyperbolic Matrix(1173,484,206,85) (-19/46,-7/17) -> (17/3,23/4) Hyperbolic Matrix(561,230,100,41) (-7/17,-9/22) -> (11/2,17/3) Hyperbolic Matrix(813,332,2128,869) (-9/22,-11/27) -> (21/55,13/34) Hyperbolic Matrix(909,370,710,289) (-11/27,-2/5) -> (32/25,9/7) Hyperbolic Matrix(249,98,592,233) (-2/5,-9/23) -> (13/31,8/19) Hyperbolic Matrix(2709,1058,1672,653) (-9/23,-16/41) -> (34/21,47/29) Hyperbolic Matrix(685,266,394,153) (-7/18,-12/31) -> (26/15,7/4) Hyperbolic Matrix(2789,1078,1172,453) (-12/31,-17/44) -> (19/8,50/21) Hyperbolic Matrix(539,208,-1858,-717) (-17/44,-5/13) -> (-9/31,-11/38) Hyperbolic Matrix(3359,1288,2042,783) (-5/13,-23/60) -> (23/14,51/31) Hyperbolic Matrix(2479,950,2920,1119) (-23/60,-18/47) -> (28/33,17/20) Hyperbolic Matrix(2821,1080,2040,781) (-18/47,-13/34) -> (47/34,18/13) Hyperbolic Matrix(241,92,778,297) (-13/34,-8/21) -> (4/13,5/16) Hyperbolic Matrix(143,54,-384,-145) (-8/21,-3/8) -> (-3/8,-10/27) Parabolic Matrix(997,368,382,141) (-10/27,-7/19) -> (13/5,34/13) Hyperbolic Matrix(473,174,666,245) (-7/19,-11/30) -> (17/24,5/7) Hyperbolic Matrix(235,86,664,243) (-11/30,-4/11) -> (6/17,5/14) Hyperbolic Matrix(329,118,92,33) (-4/11,-5/14) -> (7/2,18/5) Hyperbolic Matrix(651,232,188,67) (-5/14,-11/31) -> (31/9,7/2) Hyperbolic Matrix(1763,624,1116,395) (-11/31,-6/17) -> (30/19,49/31) Hyperbolic Matrix(833,292,368,129) (-6/17,-7/20) -> (9/4,34/15) Hyperbolic Matrix(321,112,278,97) (-7/20,-1/3) -> (15/13,7/6) Hyperbolic Matrix(395,124,86,27) (-1/3,-5/16) -> (9/2,23/5) Hyperbolic Matrix(959,298,782,243) (-5/16,-9/29) -> (11/9,27/22) Hyperbolic Matrix(1827,566,694,215) (-9/29,-4/13) -> (50/19,29/11) Hyperbolic Matrix(387,118,692,211) (-4/13,-7/23) -> (5/9,14/25) Hyperbolic Matrix(1119,340,260,79) (-7/23,-10/33) -> (30/7,13/3) Hyperbolic Matrix(859,260,1120,339) (-10/33,-3/10) -> (23/30,10/13) Hyperbolic Matrix(807,238,512,151) (-8/27,-5/17) -> (11/7,30/19) Hyperbolic Matrix(593,174,426,125) (-5/17,-7/24) -> (25/18,7/5) Hyperbolic Matrix(633,184,86,25) (-7/24,-9/31) -> (7/1,15/2) Hyperbolic Matrix(589,170,2110,609) (-11/38,-2/7) -> (12/43,19/68) Hyperbolic Matrix(419,118,1502,423) (-2/7,-9/32) -> (5/18,12/43) Hyperbolic Matrix(1417,398,502,141) (-9/32,-7/25) -> (31/11,17/6) Hyperbolic Matrix(415,116,1084,303) (-7/25,-5/18) -> (13/34,5/13) Hyperbolic Matrix(123,34,416,115) (-5/18,-3/11) -> (5/17,3/10) Hyperbolic Matrix(1113,302,328,89) (-3/11,-10/37) -> (44/13,17/5) Hyperbolic Matrix(1683,454,1316,355) (-10/37,-7/26) -> (23/18,32/25) Hyperbolic Matrix(573,154,986,265) (-7/26,-4/15) -> (18/31,7/12) Hyperbolic Matrix(447,118,572,151) (-4/15,-5/19) -> (7/9,18/23) Hyperbolic Matrix(39,10,-160,-41) (-5/19,-1/4) -> (-1/4,-5/21) Parabolic Matrix(1649,390,630,149) (-5/21,-4/17) -> (34/13,55/21) Hyperbolic Matrix(469,110,550,129) (-4/17,-7/30) -> (17/20,6/7) Hyperbolic Matrix(585,136,314,73) (-7/30,-3/13) -> (13/7,15/8) Hyperbolic Matrix(429,98,232,53) (-3/13,-5/22) -> (11/6,13/7) Hyperbolic Matrix(115,26,544,123) (-5/22,-2/9) -> (4/19,3/14) Hyperbolic Matrix(1653,364,386,85) (-2/9,-9/41) -> (47/11,30/7) Hyperbolic Matrix(3379,740,1000,219) (-9/41,-7/32) -> (27/8,71/21) Hyperbolic Matrix(1805,394,536,117) (-7/32,-5/23) -> (37/11,27/8) Hyperbolic Matrix(535,116,844,183) (-5/23,-3/14) -> (19/30,7/11) Hyperbolic Matrix(113,24,306,65) (-3/14,-1/5) -> (7/19,3/8) Hyperbolic Matrix(183,34,296,55) (-1/5,-2/11) -> (8/13,13/21) Hyperbolic Matrix(473,84,366,65) (-2/11,-3/17) -> (9/7,22/17) Hyperbolic Matrix(35,6,-216,-37) (-3/17,-1/6) -> (-1/6,-3/19) Parabolic Matrix(1353,212,568,89) (-3/19,-2/13) -> (50/21,31/13) Hyperbolic Matrix(175,26,424,63) (-2/13,-1/7) -> (7/17,12/29) Hyperbolic Matrix(523,72,138,19) (-1/7,-2/15) -> (34/9,19/5) Hyperbolic Matrix(33,4,206,25) (-1/8,-1/9) -> (3/19,1/6) Hyperbolic Matrix(165,16,134,13) (-1/9,0/1) -> (16/13,21/17) Hyperbolic Matrix(185,-24,54,-7) (0/1,1/7) -> (17/5,24/7) Hyperbolic Matrix(261,-38,158,-23) (1/7,2/13) -> (28/17,5/3) Hyperbolic Matrix(1195,-186,726,-113) (2/13,3/19) -> (51/31,28/17) Hyperbolic Matrix(127,-22,52,-9) (1/6,1/5) -> (17/7,5/2) Hyperbolic Matrix(545,-114,894,-187) (1/5,4/19) -> (14/23,25/41) Hyperbolic Matrix(221,-48,198,-43) (3/14,5/23) -> (1/1,9/8) Hyperbolic Matrix(1895,-414,444,-97) (5/23,7/32) -> (17/4,47/11) Hyperbolic Matrix(2855,-626,2066,-453) (7/32,2/9) -> (76/55,47/34) Hyperbolic Matrix(25,-6,96,-23) (2/9,1/4) -> (1/4,4/15) Parabolic Matrix(567,-152,332,-89) (4/15,3/11) -> (29/17,12/7) Hyperbolic Matrix(517,-142,142,-39) (3/11,5/18) -> (29/8,11/3) Hyperbolic Matrix(6119,-1710,2580,-721) (19/68,7/25) -> (83/35,19/8) Hyperbolic Matrix(1943,-546,516,-145) (7/25,9/32) -> (15/4,49/13) Hyperbolic Matrix(375,-106,46,-13) (9/32,2/7) -> (8/1,17/2) Hyperbolic Matrix(1347,-392,512,-149) (2/7,7/24) -> (21/8,50/19) Hyperbolic Matrix(417,-122,1022,-299) (7/24,5/17) -> (11/27,9/22) Hyperbolic Matrix(1037,-314,644,-195) (3/10,7/23) -> (37/23,29/18) Hyperbolic Matrix(665,-204,414,-127) (7/23,4/13) -> (8/5,37/23) Hyperbolic Matrix(387,-122,92,-29) (5/16,1/3) -> (21/5,17/4) Hyperbolic Matrix(843,-296,356,-125) (1/3,6/17) -> (26/11,45/19) Hyperbolic Matrix(485,-174,354,-127) (5/14,4/11) -> (26/19,11/8) Hyperbolic Matrix(659,-242,482,-177) (4/11,7/19) -> (15/11,26/19) Hyperbolic Matrix(217,-82,262,-99) (3/8,8/21) -> (14/17,5/6) Hyperbolic Matrix(2129,-812,1172,-447) (8/21,21/55) -> (49/27,20/11) Hyperbolic Matrix(1949,-752,692,-267) (5/13,17/44) -> (45/16,31/11) Hyperbolic Matrix(4349,-1682,2552,-987) (17/44,12/31) -> (46/27,75/44) Hyperbolic Matrix(691,-268,1168,-453) (12/31,7/18) -> (13/22,16/27) Hyperbolic Matrix(713,-278,1208,-471) (7/18,9/23) -> (23/39,13/22) Hyperbolic Matrix(365,-144,474,-187) (9/23,2/5) -> (10/13,27/35) Hyperbolic Matrix(809,-332,212,-87) (9/22,7/17) -> (19/5,23/6) Hyperbolic Matrix(3457,-1432,2122,-879) (12/29,17/41) -> (57/35,44/27) Hyperbolic Matrix(1123,-466,976,-405) (17/41,5/12) -> (23/20,15/13) Hyperbolic Matrix(1291,-540,930,-389) (5/12,13/31) -> (43/31,25/18) Hyperbolic Matrix(127,-54,294,-125) (8/19,3/7) -> (3/7,10/23) Parabolic Matrix(711,-310,250,-109) (10/23,7/16) -> (17/6,20/7) Hyperbolic Matrix(395,-174,84,-37) (7/16,4/9) -> (14/3,19/4) Hyperbolic Matrix(21,-10,40,-19) (4/9,1/2) -> (1/2,6/11) Parabolic Matrix(369,-202,232,-127) (6/11,5/9) -> (27/17,8/5) Hyperbolic Matrix(731,-410,230,-129) (14/25,9/16) -> (19/6,16/5) Hyperbolic Matrix(1093,-616,346,-195) (9/16,22/39) -> (22/7,19/6) Hyperbolic Matrix(1073,-606,1266,-715) (22/39,13/23) -> (11/13,28/33) Hyperbolic Matrix(957,-542,422,-239) (13/23,4/7) -> (34/15,25/11) Hyperbolic Matrix(419,-242,722,-417) (4/7,11/19) -> (11/19,18/31) Parabolic Matrix(567,-332,152,-89) (7/12,10/17) -> (26/7,15/4) Hyperbolic Matrix(3001,-1768,718,-423) (10/17,33/56) -> (25/6,46/11) Hyperbolic Matrix(5889,-3472,3472,-2047) (33/56,23/39) -> (39/23,95/56) Hyperbolic Matrix(261,-158,38,-23) (3/5,14/23) -> (20/3,7/1) Hyperbolic Matrix(2889,-1762,1192,-727) (25/41,11/18) -> (63/26,17/7) Hyperbolic Matrix(241,-148,298,-183) (11/18,8/13) -> (4/5,13/16) Hyperbolic Matrix(777,-482,482,-299) (13/21,5/8) -> (29/18,21/13) Hyperbolic Matrix(331,-208,148,-93) (5/8,12/19) -> (20/9,9/4) Hyperbolic Matrix(993,-628,808,-511) (12/19,19/30) -> (27/22,16/13) Hyperbolic Matrix(1849,-1180,550,-351) (7/11,23/36) -> (47/14,37/11) Hyperbolic Matrix(385,-246,36,-23) (23/36,16/25) -> (10/1,1/0) Hyperbolic Matrix(823,-528,438,-281) (25/39,9/14) -> (15/8,17/9) Hyperbolic Matrix(711,-458,548,-353) (9/14,11/17) -> (35/27,13/10) Hyperbolic Matrix(491,-320,290,-189) (11/17,2/3) -> (22/13,39/23) Hyperbolic Matrix(301,-208,178,-123) (2/3,9/13) -> (5/3,22/13) Hyperbolic Matrix(3027,-2104,2194,-1525) (25/36,16/23) -> (40/29,69/50) Hyperbolic Matrix(477,-332,602,-419) (16/23,7/10) -> (19/24,4/5) Hyperbolic Matrix(387,-272,212,-149) (7/10,12/17) -> (20/11,11/6) Hyperbolic Matrix(1265,-894,774,-547) (12/17,17/24) -> (49/30,18/11) Hyperbolic Matrix(87,-64,34,-25) (5/7,3/4) -> (5/2,13/5) Hyperbolic Matrix(443,-338,578,-441) (3/4,13/17) -> (13/17,23/30) Parabolic Matrix(1709,-1320,1050,-811) (27/35,17/22) -> (13/8,57/35) Hyperbolic Matrix(1151,-890,710,-549) (17/22,7/9) -> (47/29,13/8) Hyperbolic Matrix(707,-554,134,-105) (18/23,11/14) -> (21/4,16/3) Hyperbolic Matrix(1057,-832,202,-159) (11/14,26/33) -> (26/5,21/4) Hyperbolic Matrix(2701,-2130,1140,-899) (26/33,15/19) -> (45/19,64/27) Hyperbolic Matrix(993,-808,628,-511) (13/16,9/11) -> (49/31,19/12) Hyperbolic Matrix(791,-650,230,-189) (9/11,14/17) -> (24/7,31/9) Hyperbolic Matrix(113,-98,128,-111) (6/7,7/8) -> (7/8,8/9) Parabolic Matrix(475,-426,126,-113) (8/9,1/1) -> (49/13,34/9) Hyperbolic Matrix(225,-256,196,-223) (9/8,8/7) -> (8/7,23/20) Parabolic Matrix(151,-178,28,-33) (7/6,6/5) -> (16/3,11/2) Hyperbolic Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(1147,-1464,474,-605) (14/11,23/18) -> (29/12,46/19) Hyperbolic Matrix(2587,-3352,1072,-1389) (22/17,35/27) -> (41/17,70/29) Hyperbolic Matrix(847,-1104,234,-305) (13/10,17/13) -> (47/13,29/8) Hyperbolic Matrix(375,-494,104,-137) (17/13,4/3) -> (18/5,47/13) Hyperbolic Matrix(153,-206,26,-35) (4/3,19/14) -> (23/4,6/1) Hyperbolic Matrix(1209,-1642,712,-967) (19/14,34/25) -> (56/33,17/10) Hyperbolic Matrix(317,-432,102,-139) (34/25,15/11) -> (3/1,22/7) Hyperbolic Matrix(1401,-1930,580,-799) (11/8,40/29) -> (70/29,29/12) Hyperbolic Matrix(3895,-5376,1386,-1913) (69/50,29/21) -> (59/21,45/16) Hyperbolic Matrix(3539,-4890,1260,-1741) (29/21,76/55) -> (14/5,59/21) Hyperbolic Matrix(1283,-1778,578,-801) (18/13,43/31) -> (51/23,20/9) Hyperbolic Matrix(37,-54,24,-35) (7/5,3/2) -> (3/2,11/7) Parabolic Matrix(1521,-2410,580,-919) (19/12,46/29) -> (76/29,21/8) Hyperbolic Matrix(2157,-3424,904,-1435) (46/29,27/17) -> (31/13,74/31) Hyperbolic Matrix(401,-648,138,-223) (21/13,55/34) -> (23/8,3/1) Hyperbolic Matrix(2887,-4672,1192,-1929) (55/34,34/21) -> (46/19,63/26) Hyperbolic Matrix(433,-706,46,-75) (44/27,31/19) -> (9/1,10/1) Hyperbolic Matrix(593,-968,68,-111) (31/19,49/30) -> (17/2,9/1) Hyperbolic Matrix(545,-894,114,-187) (18/11,23/14) -> (19/4,24/5) Hyperbolic Matrix(27091,-45960,8010,-13589) (95/56,151/89) -> (301/89,115/34) Hyperbolic Matrix(26487,-44942,7832,-13289) (151/89,56/33) -> (186/55,301/89) Hyperbolic Matrix(4647,-7924,1774,-3025) (75/44,29/17) -> (55/21,131/50) Hyperbolic Matrix(419,-722,242,-417) (12/7,19/11) -> (19/11,26/15) Parabolic Matrix(97,-172,22,-39) (7/4,9/5) -> (13/3,9/2) Hyperbolic Matrix(929,-1682,512,-927) (9/5,29/16) -> (29/16,49/27) Parabolic Matrix(435,-824,104,-197) (17/9,2/1) -> (46/11,21/5) Hyperbolic Matrix(141,-308,38,-83) (2/1,11/5) -> (11/3,26/7) Hyperbolic Matrix(869,-1922,392,-867) (11/5,31/14) -> (31/14,51/23) Parabolic Matrix(127,-294,54,-125) (16/7,7/3) -> (7/3,26/11) Parabolic Matrix(8427,-19982,2492,-5909) (64/27,83/35) -> (71/21,186/55) Hyperbolic Matrix(5429,-12962,2072,-4947) (74/31,43/18) -> (131/50,76/29) Hyperbolic Matrix(415,-994,124,-297) (43/18,12/5) -> (10/3,47/14) Hyperbolic Matrix(493,-1186,106,-255) (12/5,41/17) -> (51/11,14/3) Hyperbolic Matrix(89,-242,32,-87) (8/3,11/4) -> (11/4,14/5) Parabolic Matrix(1157,-3312,342,-979) (20/7,23/8) -> (115/34,44/13) Hyperbolic Matrix(107,-344,14,-45) (16/5,13/4) -> (15/2,8/1) Hyperbolic Matrix(323,-1058,98,-321) (13/4,23/7) -> (23/7,33/10) Parabolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic Matrix(593,-2738,128,-591) (23/5,37/8) -> (37/8,51/11) Parabolic Matrix(51,-250,10,-49) (24/5,5/1) -> (5/1,26/5) Parabolic Matrix(53,-338,8,-51) (6/1,13/2) -> (13/2,20/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(393,184,566,265) -> Matrix(1,0,0,1) Matrix(503,234,1236,575) -> Matrix(1,0,-2,1) Matrix(225,104,556,257) -> Matrix(3,-2,2,-1) Matrix(501,230,220,101) -> Matrix(1,0,-4,1) Matrix(275,124,326,147) -> Matrix(1,0,-2,1) Matrix(383,172,-982,-441) -> Matrix(1,0,-2,1) Matrix(269,118,212,93) -> Matrix(1,0,0,1) Matrix(531,232,428,187) -> Matrix(1,0,-2,1) Matrix(693,302,1168,509) -> Matrix(1,0,0,1) Matrix(1059,460,320,139) -> Matrix(1,0,4,1) Matrix(583,252,738,319) -> Matrix(7,-2,4,-1) Matrix(571,242,-1352,-573) -> Matrix(9,-4,16,-7) Matrix(1195,504,1866,787) -> Matrix(3,-2,2,-1) Matrix(153,64,-514,-215) -> Matrix(3,-2,2,-1) Matrix(53,22,-412,-171) -> Matrix(1,-2,2,-3) Matrix(2609,1078,1532,633) -> Matrix(1,0,0,1) Matrix(1173,484,206,85) -> Matrix(1,0,2,1) Matrix(561,230,100,41) -> Matrix(1,0,-4,1) Matrix(813,332,2128,869) -> Matrix(7,-2,4,-1) Matrix(909,370,710,289) -> Matrix(5,-2,8,-3) Matrix(249,98,592,233) -> Matrix(3,-2,2,-1) Matrix(2709,1058,1672,653) -> Matrix(1,-4,0,1) Matrix(685,266,394,153) -> Matrix(1,0,2,1) Matrix(2789,1078,1172,453) -> Matrix(1,0,0,1) Matrix(539,208,-1858,-717) -> Matrix(1,0,-4,1) Matrix(3359,1288,2042,783) -> Matrix(17,-6,-14,5) Matrix(2479,950,2920,1119) -> Matrix(5,-2,8,-3) Matrix(2821,1080,2040,781) -> Matrix(21,-8,8,-3) Matrix(241,92,778,297) -> Matrix(9,-4,-2,1) Matrix(143,54,-384,-145) -> Matrix(5,-2,8,-3) Matrix(997,368,382,141) -> Matrix(3,-2,2,-1) Matrix(473,174,666,245) -> Matrix(7,-4,16,-9) Matrix(235,86,664,243) -> Matrix(3,-2,-4,3) Matrix(329,118,92,33) -> Matrix(1,0,0,1) Matrix(651,232,188,67) -> Matrix(1,0,-2,1) Matrix(1763,624,1116,395) -> Matrix(1,0,-2,1) Matrix(833,292,368,129) -> Matrix(1,0,-4,1) Matrix(321,112,278,97) -> Matrix(1,0,-2,1) Matrix(395,124,86,27) -> Matrix(1,0,-2,1) Matrix(959,298,782,243) -> Matrix(5,-2,-2,1) Matrix(1827,566,694,215) -> Matrix(3,-2,2,-1) Matrix(387,118,692,211) -> Matrix(3,-2,2,-1) Matrix(1119,340,260,79) -> Matrix(3,-2,-4,3) Matrix(859,260,1120,339) -> Matrix(15,-14,14,-13) Matrix(807,238,512,151) -> Matrix(1,-2,0,1) Matrix(593,174,426,125) -> Matrix(1,4,0,1) Matrix(633,184,86,25) -> Matrix(1,0,0,1) Matrix(589,170,2110,609) -> Matrix(1,2,0,1) Matrix(419,118,1502,423) -> Matrix(7,-2,4,-1) Matrix(1417,398,502,141) -> Matrix(5,-2,-2,1) Matrix(415,116,1084,303) -> Matrix(1,0,-2,1) Matrix(123,34,416,115) -> Matrix(3,-2,2,-1) Matrix(1113,302,328,89) -> Matrix(1,0,0,1) Matrix(1683,454,1316,355) -> Matrix(1,0,0,1) Matrix(573,154,986,265) -> Matrix(5,-4,4,-3) Matrix(447,118,572,151) -> Matrix(3,-2,2,-1) Matrix(39,10,-160,-41) -> Matrix(1,0,2,1) Matrix(1649,390,630,149) -> Matrix(1,0,-2,1) Matrix(469,110,550,129) -> Matrix(1,0,-2,1) Matrix(585,136,314,73) -> Matrix(1,0,-2,1) Matrix(429,98,232,53) -> Matrix(3,-2,2,-1) Matrix(115,26,544,123) -> Matrix(1,0,-2,1) Matrix(1653,364,386,85) -> Matrix(3,-4,-2,3) Matrix(3379,740,1000,219) -> Matrix(1,-2,2,-3) Matrix(1805,394,536,117) -> Matrix(1,0,2,1) Matrix(535,116,844,183) -> Matrix(1,0,-2,1) Matrix(113,24,306,65) -> Matrix(1,0,2,1) Matrix(183,34,296,55) -> Matrix(3,-2,2,-1) Matrix(473,84,366,65) -> Matrix(1,0,0,1) Matrix(35,6,-216,-37) -> Matrix(1,0,0,1) Matrix(1353,212,568,89) -> Matrix(1,0,2,1) Matrix(175,26,424,63) -> Matrix(1,0,-2,1) Matrix(523,72,138,19) -> Matrix(7,-4,2,-1) Matrix(33,4,206,25) -> Matrix(5,-4,4,-3) Matrix(165,16,134,13) -> Matrix(1,0,-2,1) Matrix(185,-24,54,-7) -> Matrix(1,0,0,1) Matrix(261,-38,158,-23) -> Matrix(1,0,-2,1) Matrix(1195,-186,726,-113) -> Matrix(9,-10,-8,9) Matrix(127,-22,52,-9) -> Matrix(1,-2,2,-3) Matrix(545,-114,894,-187) -> Matrix(1,2,0,1) Matrix(221,-48,198,-43) -> Matrix(1,2,0,1) Matrix(1895,-414,444,-97) -> Matrix(3,2,-2,-1) Matrix(2855,-626,2066,-453) -> Matrix(5,2,2,1) Matrix(25,-6,96,-23) -> Matrix(1,0,0,1) Matrix(567,-152,332,-89) -> Matrix(1,0,-2,1) Matrix(517,-142,142,-39) -> Matrix(1,0,0,1) Matrix(6119,-1710,2580,-721) -> Matrix(1,-2,2,-3) Matrix(1943,-546,516,-145) -> Matrix(1,0,0,1) Matrix(375,-106,46,-13) -> Matrix(1,-2,0,1) Matrix(1347,-392,512,-149) -> Matrix(1,0,0,1) Matrix(417,-122,1022,-299) -> Matrix(1,0,0,1) Matrix(1037,-314,644,-195) -> Matrix(1,-12,0,1) Matrix(665,-204,414,-127) -> Matrix(1,6,0,1) Matrix(387,-122,92,-29) -> Matrix(1,0,0,1) Matrix(843,-296,356,-125) -> Matrix(1,0,4,1) Matrix(485,-174,354,-127) -> Matrix(9,2,4,1) Matrix(659,-242,482,-177) -> Matrix(11,-2,6,-1) Matrix(217,-82,262,-99) -> Matrix(1,0,-2,1) Matrix(2129,-812,1172,-447) -> Matrix(7,-6,6,-5) Matrix(1949,-752,692,-267) -> Matrix(5,-2,-2,1) Matrix(4349,-1682,2552,-987) -> Matrix(1,0,-2,1) Matrix(691,-268,1168,-453) -> Matrix(1,0,-2,1) Matrix(713,-278,1208,-471) -> Matrix(3,-2,2,-1) Matrix(365,-144,474,-187) -> Matrix(7,-6,6,-5) Matrix(809,-332,212,-87) -> Matrix(1,0,0,1) Matrix(3457,-1432,2122,-879) -> Matrix(1,-2,0,1) Matrix(1123,-466,976,-405) -> Matrix(1,-2,0,1) Matrix(1291,-540,930,-389) -> Matrix(7,-4,2,-1) Matrix(127,-54,294,-125) -> Matrix(1,-2,0,1) Matrix(711,-310,250,-109) -> Matrix(1,0,0,1) Matrix(395,-174,84,-37) -> Matrix(1,0,0,1) Matrix(21,-10,40,-19) -> Matrix(1,0,2,1) Matrix(369,-202,232,-127) -> Matrix(1,0,-2,1) Matrix(731,-410,230,-129) -> Matrix(1,0,-2,1) Matrix(1093,-616,346,-195) -> Matrix(1,0,-2,1) Matrix(1073,-606,1266,-715) -> Matrix(1,0,0,1) Matrix(957,-542,422,-239) -> Matrix(1,0,-4,1) Matrix(419,-242,722,-417) -> Matrix(7,-6,6,-5) Matrix(567,-332,152,-89) -> Matrix(1,0,0,1) Matrix(3001,-1768,718,-423) -> Matrix(1,-2,0,1) Matrix(5889,-3472,3472,-2047) -> Matrix(1,0,-2,1) Matrix(261,-158,38,-23) -> Matrix(1,-2,0,1) Matrix(2889,-1762,1192,-727) -> Matrix(1,0,2,1) Matrix(241,-148,298,-183) -> Matrix(1,0,0,1) Matrix(777,-482,482,-299) -> Matrix(1,-6,0,1) Matrix(331,-208,148,-93) -> Matrix(1,2,-2,-3) Matrix(993,-628,808,-511) -> Matrix(3,2,-2,-1) Matrix(1849,-1180,550,-351) -> Matrix(1,0,2,1) Matrix(385,-246,36,-23) -> Matrix(1,0,0,1) Matrix(823,-528,438,-281) -> Matrix(1,2,0,1) Matrix(711,-458,548,-353) -> Matrix(3,2,4,3) Matrix(491,-320,290,-189) -> Matrix(1,0,0,1) Matrix(301,-208,178,-123) -> Matrix(1,0,-4,1) Matrix(3027,-2104,2194,-1525) -> Matrix(3,-2,2,-1) Matrix(477,-332,602,-419) -> Matrix(3,-2,2,-1) Matrix(387,-272,212,-149) -> Matrix(7,-2,4,-1) Matrix(1265,-894,774,-547) -> Matrix(11,-4,-8,3) Matrix(87,-64,34,-25) -> Matrix(3,-2,2,-1) Matrix(443,-338,578,-441) -> Matrix(19,-18,18,-17) Matrix(1709,-1320,1050,-811) -> Matrix(5,-6,-4,5) Matrix(1151,-890,710,-549) -> Matrix(7,-10,-2,3) Matrix(707,-554,134,-105) -> Matrix(1,-2,2,-3) Matrix(1057,-832,202,-159) -> Matrix(1,-2,2,-3) Matrix(2701,-2130,1140,-899) -> Matrix(1,-2,4,-7) Matrix(993,-808,628,-511) -> Matrix(1,-2,0,1) Matrix(791,-650,230,-189) -> Matrix(1,2,0,1) Matrix(113,-98,128,-111) -> Matrix(1,0,2,1) Matrix(475,-426,126,-113) -> Matrix(3,-2,2,-1) Matrix(225,-256,196,-223) -> Matrix(1,-4,0,1) Matrix(151,-178,28,-33) -> Matrix(1,0,0,1) Matrix(217,-262,82,-99) -> Matrix(1,0,0,1) Matrix(1147,-1464,474,-605) -> Matrix(3,-2,8,-5) Matrix(2587,-3352,1072,-1389) -> Matrix(3,-2,8,-5) Matrix(847,-1104,234,-305) -> Matrix(7,-6,6,-5) Matrix(375,-494,104,-137) -> Matrix(3,-4,4,-5) Matrix(153,-206,26,-35) -> Matrix(1,-2,2,-3) Matrix(1209,-1642,712,-967) -> Matrix(1,-2,-2,5) Matrix(317,-432,102,-139) -> Matrix(1,-2,0,1) Matrix(1401,-1930,580,-799) -> Matrix(1,-2,2,-3) Matrix(3895,-5376,1386,-1913) -> Matrix(1,-4,0,1) Matrix(3539,-4890,1260,-1741) -> Matrix(5,-12,-2,5) Matrix(1283,-1778,578,-801) -> Matrix(5,-14,-6,17) Matrix(37,-54,24,-35) -> Matrix(1,-2,0,1) Matrix(1521,-2410,580,-919) -> Matrix(1,2,0,1) Matrix(2157,-3424,904,-1435) -> Matrix(1,2,2,5) Matrix(401,-648,138,-223) -> Matrix(1,2,0,1) Matrix(2887,-4672,1192,-1929) -> Matrix(1,4,2,9) Matrix(433,-706,46,-75) -> Matrix(1,2,0,1) Matrix(593,-968,68,-111) -> Matrix(1,2,-2,-3) Matrix(545,-894,114,-187) -> Matrix(1,2,-2,-3) Matrix(27091,-45960,8010,-13589) -> Matrix(3,2,4,3) Matrix(26487,-44942,7832,-13289) -> Matrix(5,2,12,5) Matrix(4647,-7924,1774,-3025) -> Matrix(1,2,0,1) Matrix(419,-722,242,-417) -> Matrix(1,0,10,1) Matrix(97,-172,22,-39) -> Matrix(1,0,-2,1) Matrix(929,-1682,512,-927) -> Matrix(11,-10,10,-9) Matrix(435,-824,104,-197) -> Matrix(1,-2,0,1) Matrix(141,-308,38,-83) -> Matrix(1,2,0,1) Matrix(869,-1922,392,-867) -> Matrix(9,10,-10,-11) Matrix(127,-294,54,-125) -> Matrix(1,0,6,1) Matrix(8427,-19982,2492,-5909) -> Matrix(1,0,0,1) Matrix(5429,-12962,2072,-4947) -> Matrix(3,-2,2,-1) Matrix(415,-994,124,-297) -> Matrix(1,0,0,1) Matrix(493,-1186,106,-255) -> Matrix(1,0,-2,1) Matrix(89,-242,32,-87) -> Matrix(1,-4,0,1) Matrix(1157,-3312,342,-979) -> Matrix(1,0,2,1) Matrix(107,-344,14,-45) -> Matrix(1,0,2,1) Matrix(323,-1058,98,-321) -> Matrix(1,0,14,1) Matrix(49,-192,12,-47) -> Matrix(1,-2,0,1) Matrix(593,-2738,128,-591) -> Matrix(1,0,2,1) Matrix(51,-250,10,-49) -> Matrix(1,0,2,1) Matrix(53,-338,8,-51) -> Matrix(1,-2,0,1) 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): 44 Degree of the the map X: 44 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 -1/1 0/1 1 1 0/1 1/1 1 30 1/7 1/1 1 15 2/13 1/1 5 2 1/6 (1/1,2/1) 0 30 1/5 1/0 2 5 3/14 (0/1,1/0) 0 30 5/23 -1/1 1 15 7/32 0/1 2 10 2/9 -1/1 1 30 1/4 0 6 4/15 -1/1 1 30 3/11 1/1 1 15 5/18 (1/1,3/2) 0 30 7/25 1/1 1 15 9/32 (1/1,2/1) 0 30 2/7 1/0 1 10 3/10 (4/1,1/0) 0 30 7/23 1/0 9 1 4/13 -5/1 1 30 1/3 -1/1 1 15 5/14 (-1/3,0/1) 0 30 4/11 0/1 5 2 3/8 (0/1,1/2) 0 30 8/21 1/1 1 30 5/13 0/1 1 5 17/44 (0/1,1/2) 0 30 12/31 1/1 1 30 7/18 1/2 2 6 9/23 1/1 1 15 2/5 1/1 1 30 9/22 (1/1,1/0) 0 30 7/17 1/0 2 5 5/12 (0/1,1/0) 0 30 8/19 1/0 1 10 3/7 1/0 1 3 10/23 1/0 1 10 7/16 (-1/1,1/0) 0 30 4/9 1/1 1 30 1/2 0/1 2 10 6/11 1/3 1 30 5/9 1/1 1 15 9/16 0 6 22/39 1/1 1 30 13/23 0/1 1 5 4/7 1/1 1 30 11/19 1/1 3 1 7/12 (1/1,2/1) 0 30 10/17 1/0 1 10 33/56 (1/1,1/0) 0 30 23/39 1/1 1 15 13/22 1/0 2 6 3/5 1/1 1 15 14/23 1/1 1 30 11/18 (1/1,1/0) 0 30 8/13 1/0 1 10 5/8 (-2/1,1/0) 0 30 12/19 -1/1 1 30 7/11 0/1 1 5 23/36 (0/1,1/0) 0 30 16/25 1/1 1 30 9/14 (-1/1,1/0) 0 30 11/17 -1/1 1 15 2/3 0/1 2 6 9/13 1/3 1 15 16/23 1/2 1 10 7/10 (0/1,1/4) 0 30 12/17 1/3 1 30 5/7 1/2 2 5 3/4 (2/3,1/1) 0 30 13/17 1/1 9 1 10/13 1/1 1 30 27/35 1/1 1 15 17/22 4/3 2 10 7/9 1/1 1 15 11/14 0 6 26/33 1/1 1 30 15/19 1/1 1 15 4/5 1/0 1 10 13/16 (1/1,1/0) 0 30 9/11 1/0 2 3 14/17 -1/1 1 30 5/6 (0/1,1/0) 0 30 6/7 -1/1 1 30 7/8 0/1 2 2 8/9 1/1 1 30 1/1 1/1 1 15 9/8 (2/1,1/0) 0 30 8/7 1/0 2 2 7/6 (0/1,1/0) 0 30 6/5 1/1 1 30 11/9 1/0 2 3 16/13 -1/1 1 30 5/4 0/1 2 10 9/7 1/1 1 15 13/10 (3/4,1/1) 0 30 17/13 1/1 5 1 4/3 1/1 1 30 19/14 2/1 2 10 34/25 1/1 1 30 15/11 1/1 1 15 11/8 (2/1,3/1) 0 30 40/29 1/0 1 10 29/21 2/1 1 3 18/13 3/1 1 30 7/5 1/0 2 5 3/2 1/0 2 6 11/7 1/0 2 5 19/12 (-1/1,1/0) 0 30 46/29 1/0 1 2 27/17 -1/1 1 15 8/5 1/1 1 30 21/13 -3/1 1 15 55/34 (-3/1,1/0) 0 30 34/21 1/0 1 6 13/8 -2/1 2 10 44/27 -1/1 1 30 31/19 -2/1 1 3 18/11 -1/1 1 30 23/14 (-3/2,-1/1) 0 30 28/17 -1/1 5 2 5/3 -1/1 1 15 22/13 0/1 2 6 39/23 -1/1 1 15 95/56 (-1/1,-1/2) 0 30 151/89 -1/2 2 1 56/33 -1/3 1 30 17/10 0/1 2 10 29/17 -1/1 1 15 12/7 -1/3 1 30 19/11 0/1 5 1 7/4 (0/1,1/2) 0 30 9/5 1/1 1 15 29/16 1/1 10 2 20/11 1/1 1 30 11/6 (2/1,1/0) 0 30 2/1 1/0 1 10 11/5 -1/1 1 15 31/14 -1/1 10 2 20/9 -1/1 1 30 9/4 (-1/2,0/1) 0 30 16/7 -1/3 1 30 7/3 0/1 3 3 26/11 1/3 1 30 19/8 0/1 2 10 31/13 1/3 1 15 74/31 1/2 1 2 43/18 (0/1,1/2) 0 30 12/5 1/3 1 30 41/17 1/3 1 15 29/12 (0/1,1/3) 0 30 17/7 1/2 2 5 5/2 (0/1,1/1) 0 30 13/5 1/0 2 5 21/8 (1/1,1/0) 0 30 29/11 1/0 2 3 8/3 1/1 1 30 11/4 1/0 4 2 14/5 -3/1 1 30 17/6 (-1/1,1/0) 0 30 20/7 1/0 1 10 23/8 (-1/1,1/0) 0 30 3/1 -1/1 1 15 16/5 -1/2 1 10 13/4 (-1/4,0/1) 0 30 23/7 0/1 7 1 10/3 1/3 1 30 27/8 1/2 2 6 17/5 1/1 1 15 24/7 1/1 1 30 7/2 0/1 2 10 11/3 1/1 1 15 26/7 1/0 1 10 15/4 (1/1,2/1) 0 30 19/5 1/0 2 5 23/6 (1/1,1/0) 0 30 4/1 1/0 1 6 17/4 -2/1 2 10 13/3 -1/1 1 15 9/2 (0/1,1/0) 0 30 14/3 1/1 1 30 19/4 (-1/1,1/0) 0 30 24/5 -1/1 1 30 5/1 0/1 1 5 16/3 1/1 1 30 11/2 (0/1,1/0) 0 30 6/1 1/1 1 30 13/2 1/0 2 2 20/3 -1/1 1 30 7/1 -1/1 1 15 8/1 1/0 1 10 9/1 0/1 1 3 10/1 1/1 1 30 1/0 (0/1,1/0) 0 30 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(185,-24,54,-7) (0/1,1/7) -> (17/5,24/7) Hyperbolic Matrix(261,-38,158,-23) (1/7,2/13) -> (28/17,5/3) Hyperbolic Matrix(25,-4,156,-25) (2/13,1/6) -> (2/13,1/6) Reflection Matrix(127,-22,52,-9) (1/6,1/5) -> (17/7,5/2) Hyperbolic Matrix(123,-26,298,-63) (1/5,3/14) -> (7/17,5/12) Glide Reflection Matrix(221,-48,198,-43) (3/14,5/23) -> (1/1,9/8) Hyperbolic Matrix(1255,-274,1626,-355) (5/23,7/32) -> (27/35,17/22) Glide Reflection Matrix(1525,-334,936,-205) (7/32,2/9) -> (13/8,44/27) Glide Reflection Matrix(25,-6,96,-23) (2/9,1/4) -> (1/4,4/15) Parabolic Matrix(567,-152,332,-89) (4/15,3/11) -> (29/17,12/7) Hyperbolic Matrix(305,-84,236,-65) (3/11,5/18) -> (9/7,13/10) Glide Reflection Matrix(423,-118,656,-183) (5/18,7/25) -> (9/14,11/17) Glide Reflection Matrix(2037,-572,844,-237) (7/25,9/32) -> (41/17,29/12) Glide Reflection Matrix(1357,-382,984,-277) (9/32,2/7) -> (11/8,40/29) Glide Reflection Matrix(115,-34,186,-55) (2/7,3/10) -> (8/13,5/8) Glide Reflection Matrix(139,-42,460,-139) (3/10,7/23) -> (3/10,7/23) Reflection Matrix(183,-56,598,-183) (7/23,4/13) -> (7/23,4/13) Reflection Matrix(297,-92,184,-57) (4/13,1/3) -> (8/5,21/13) Glide Reflection Matrix(243,-86,178,-63) (1/3,5/14) -> (15/11,11/8) Glide Reflection Matrix(111,-40,308,-111) (5/14,4/11) -> (5/14,4/11) Reflection Matrix(65,-24,176,-65) (4/11,3/8) -> (4/11,3/8) Reflection Matrix(217,-82,262,-99) (3/8,8/21) -> (14/17,5/6) Hyperbolic Matrix(303,-116,478,-183) (8/21,5/13) -> (12/19,7/11) Glide Reflection Matrix(607,-234,952,-367) (5/13,17/44) -> (7/11,23/36) Glide Reflection Matrix(1861,-720,778,-301) (17/44,12/31) -> (43/18,12/5) Glide Reflection Matrix(1017,-394,302,-117) (12/31,7/18) -> (10/3,27/8) Glide Reflection Matrix(713,-278,1208,-471) (7/18,9/23) -> (23/39,13/22) Hyperbolic Matrix(365,-144,474,-187) (9/23,2/5) -> (10/13,27/35) Hyperbolic Matrix(363,-148,596,-243) (2/5,9/22) -> (14/23,11/18) Glide Reflection Matrix(809,-332,212,-87) (9/22,7/17) -> (19/5,23/6) Hyperbolic Matrix(233,-98,126,-53) (5/12,8/19) -> (11/6,2/1) Glide Reflection Matrix(127,-54,294,-125) (8/19,3/7) -> (3/7,10/23) Parabolic Matrix(711,-310,250,-109) (10/23,7/16) -> (17/6,20/7) Hyperbolic Matrix(395,-174,84,-37) (7/16,4/9) -> (14/3,19/4) Hyperbolic Matrix(21,-10,40,-19) (4/9,1/2) -> (1/2,6/11) Parabolic Matrix(369,-202,232,-127) (6/11,5/9) -> (27/17,8/5) Hyperbolic Matrix(211,-118,270,-151) (5/9,9/16) -> (7/9,11/14) Glide Reflection Matrix(845,-476,1074,-605) (9/16,22/39) -> (11/14,26/33) Glide Reflection Matrix(747,-422,154,-87) (22/39,13/23) -> (24/5,5/1) Glide Reflection Matrix(403,-228,76,-43) (13/23,4/7) -> (5/1,16/3) Glide Reflection Matrix(153,-88,266,-153) (4/7,11/19) -> (4/7,11/19) Reflection Matrix(265,-154,456,-265) (11/19,7/12) -> (11/19,7/12) Reflection Matrix(567,-332,152,-89) (7/12,10/17) -> (26/7,15/4) Hyperbolic Matrix(1511,-890,528,-311) (10/17,33/56) -> (20/7,23/8) Glide Reflection Matrix(5889,-3472,3472,-2047) (33/56,23/39) -> (39/23,95/56) Hyperbolic Matrix(509,-302,150,-89) (13/22,3/5) -> (27/8,17/5) Glide Reflection Matrix(261,-158,38,-23) (3/5,14/23) -> (20/3,7/1) Hyperbolic Matrix(241,-148,298,-183) (11/18,8/13) -> (4/5,13/16) Hyperbolic Matrix(331,-208,148,-93) (5/8,12/19) -> (20/9,9/4) Hyperbolic Matrix(385,-246,36,-23) (23/36,16/25) -> (10/1,1/0) Hyperbolic Matrix(621,-398,220,-141) (16/25,9/14) -> (14/5,17/6) Glide Reflection Matrix(491,-320,290,-189) (11/17,2/3) -> (22/13,39/23) Hyperbolic Matrix(301,-208,178,-123) (2/3,9/13) -> (5/3,22/13) Hyperbolic Matrix(265,-184,36,-25) (9/13,16/23) -> (7/1,8/1) Glide Reflection Matrix(459,-320,142,-99) (16/23,7/10) -> (16/5,13/4) Glide Reflection Matrix(387,-272,212,-149) (7/10,12/17) -> (20/11,11/6) Hyperbolic Matrix(245,-174,176,-125) (12/17,5/7) -> (18/13,7/5) Glide Reflection Matrix(87,-64,34,-25) (5/7,3/4) -> (5/2,13/5) Hyperbolic Matrix(103,-78,136,-103) (3/4,13/17) -> (3/4,13/17) Reflection Matrix(339,-260,442,-339) (13/17,10/13) -> (13/17,10/13) Reflection Matrix(439,-340,102,-79) (17/22,7/9) -> (17/4,13/3) Glide Reflection Matrix(1141,-900,838,-661) (26/33,15/19) -> (34/25,15/11) Glide Reflection Matrix(319,-252,100,-79) (15/19,4/5) -> (3/1,16/5) Glide Reflection Matrix(695,-566,264,-215) (13/16,9/11) -> (21/8,29/11) Glide Reflection Matrix(363,-298,296,-243) (9/11,14/17) -> (11/9,16/13) Glide Reflection Matrix(147,-124,32,-27) (5/6,6/7) -> (9/2,14/3) Glide Reflection Matrix(113,-98,128,-111) (6/7,7/8) -> (7/8,8/9) Parabolic Matrix(381,-340,158,-141) (8/9,1/1) -> (12/5,41/17) Glide Reflection Matrix(127,-144,112,-127) (9/8,8/7) -> (9/8,8/7) Reflection Matrix(97,-112,84,-97) (8/7,7/6) -> (8/7,7/6) Reflection Matrix(151,-178,28,-33) (7/6,6/5) -> (16/3,11/2) Hyperbolic Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(187,-232,54,-67) (16/13,5/4) -> (24/7,7/2) Glide Reflection Matrix(93,-118,26,-33) (5/4,9/7) -> (7/2,11/3) Glide Reflection Matrix(339,-442,260,-339) (13/10,17/13) -> (13/10,17/13) Reflection Matrix(103,-136,78,-103) (17/13,4/3) -> (17/13,4/3) Reflection Matrix(421,-570,178,-241) (4/3,19/14) -> (26/11,19/8) Glide Reflection Matrix(1209,-1642,712,-967) (19/14,34/25) -> (56/33,17/10) Hyperbolic Matrix(429,-592,50,-69) (40/29,29/21) -> (8/1,9/1) Glide Reflection Matrix(781,-1080,478,-661) (29/21,18/13) -> (31/19,18/11) Glide Reflection Matrix(37,-54,24,-35) (7/5,3/2) -> (3/2,11/7) Parabolic Matrix(303,-478,116,-183) (11/7,19/12) -> (13/5,21/8) Glide Reflection Matrix(1103,-1748,696,-1103) (19/12,46/29) -> (19/12,46/29) Reflection Matrix(2157,-3424,904,-1435) (46/29,27/17) -> (31/13,74/31) Hyperbolic Matrix(401,-648,138,-223) (21/13,55/34) -> (23/8,3/1) Hyperbolic Matrix(619,-1002,160,-259) (55/34,34/21) -> (23/6,4/1) Glide Reflection Matrix(389,-630,92,-149) (34/21,13/8) -> (4/1,17/4) Glide Reflection Matrix(433,-706,46,-75) (44/27,31/19) -> (9/1,10/1) Hyperbolic Matrix(545,-894,114,-187) (18/11,23/14) -> (19/4,24/5) Hyperbolic Matrix(783,-1288,476,-783) (23/14,28/17) -> (23/14,28/17) Reflection Matrix(16911,-28690,9968,-16911) (95/56,151/89) -> (95/56,151/89) Reflection Matrix(9967,-16912,5874,-9967) (151/89,56/33) -> (151/89,56/33) Reflection Matrix(633,-1078,266,-453) (17/10,29/17) -> (19/8,31/13) Glide Reflection Matrix(265,-456,154,-265) (12/7,19/11) -> (12/7,19/11) Reflection Matrix(153,-266,88,-153) (19/11,7/4) -> (19/11,7/4) Reflection Matrix(97,-172,22,-39) (7/4,9/5) -> (13/3,9/2) Hyperbolic Matrix(331,-598,150,-271) (9/5,29/16) -> (11/5,31/14) Glide Reflection Matrix(661,-1200,298,-541) (29/16,20/11) -> (31/14,20/9) Glide Reflection Matrix(141,-308,38,-83) (2/1,11/5) -> (11/3,26/7) Hyperbolic Matrix(101,-230,18,-41) (9/4,16/7) -> (11/2,6/1) Glide Reflection Matrix(127,-294,54,-125) (16/7,7/3) -> (7/3,26/11) Parabolic Matrix(2665,-6364,1116,-2665) (74/31,43/18) -> (74/31,43/18) Reflection Matrix(333,-806,88,-213) (29/12,17/7) -> (15/4,19/5) Glide Reflection Matrix(89,-242,32,-87) (8/3,11/4) -> (11/4,14/5) Parabolic Matrix(183,-598,56,-183) (13/4,23/7) -> (13/4,23/7) Reflection Matrix(139,-460,42,-139) (23/7,10/3) -> (23/7,10/3) Reflection Matrix(53,-338,8,-51) (6/1,13/2) -> (13/2,20/3) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,2,-1) (-1/1,0/1) -> (0/1,1/1) Matrix(185,-24,54,-7) -> Matrix(1,0,0,1) Matrix(261,-38,158,-23) -> Matrix(1,0,-2,1) 0/1 Matrix(25,-4,156,-25) -> Matrix(3,-4,2,-3) (2/13,1/6) -> (1/1,2/1) Matrix(127,-22,52,-9) -> Matrix(1,-2,2,-3) 1/1 Matrix(123,-26,298,-63) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(221,-48,198,-43) -> Matrix(1,2,0,1) 1/0 Matrix(1255,-274,1626,-355) -> Matrix(5,4,4,3) Matrix(1525,-334,936,-205) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(25,-6,96,-23) -> Matrix(1,0,0,1) Matrix(567,-152,332,-89) -> Matrix(1,0,-2,1) 0/1 Matrix(305,-84,236,-65) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(423,-118,656,-183) -> Matrix(1,-2,-2,3) Matrix(2037,-572,844,-237) -> Matrix(1,-2,2,-5) Matrix(1357,-382,984,-277) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(115,-34,186,-55) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(139,-42,460,-139) -> Matrix(-1,8,0,1) (3/10,7/23) -> (4/1,1/0) Matrix(183,-56,598,-183) -> Matrix(1,10,0,-1) (7/23,4/13) -> (-5/1,1/0) Matrix(297,-92,184,-57) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(243,-86,178,-63) -> Matrix(3,2,2,1) Matrix(111,-40,308,-111) -> Matrix(-1,0,6,1) (5/14,4/11) -> (-1/3,0/1) Matrix(65,-24,176,-65) -> Matrix(1,0,4,-1) (4/11,3/8) -> (0/1,1/2) Matrix(217,-82,262,-99) -> Matrix(1,0,-2,1) 0/1 Matrix(303,-116,478,-183) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(607,-234,952,-367) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1861,-720,778,-301) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(1017,-394,302,-117) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(713,-278,1208,-471) -> Matrix(3,-2,2,-1) 1/1 Matrix(365,-144,474,-187) -> Matrix(7,-6,6,-5) 1/1 Matrix(363,-148,596,-243) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(809,-332,212,-87) -> Matrix(1,0,0,1) Matrix(233,-98,126,-53) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(127,-54,294,-125) -> Matrix(1,-2,0,1) 1/0 Matrix(711,-310,250,-109) -> Matrix(1,0,0,1) Matrix(395,-174,84,-37) -> Matrix(1,0,0,1) Matrix(21,-10,40,-19) -> Matrix(1,0,2,1) 0/1 Matrix(369,-202,232,-127) -> Matrix(1,0,-2,1) 0/1 Matrix(211,-118,270,-151) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(845,-476,1074,-605) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(747,-422,154,-87) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(403,-228,76,-43) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(153,-88,266,-153) -> Matrix(3,-2,4,-3) (4/7,11/19) -> (1/2,1/1) Matrix(265,-154,456,-265) -> Matrix(3,-4,2,-3) (11/19,7/12) -> (1/1,2/1) Matrix(567,-332,152,-89) -> Matrix(1,0,0,1) Matrix(1511,-890,528,-311) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(5889,-3472,3472,-2047) -> Matrix(1,0,-2,1) 0/1 Matrix(509,-302,150,-89) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(261,-158,38,-23) -> Matrix(1,-2,0,1) 1/0 Matrix(241,-148,298,-183) -> Matrix(1,0,0,1) Matrix(331,-208,148,-93) -> Matrix(1,2,-2,-3) -1/1 Matrix(385,-246,36,-23) -> Matrix(1,0,0,1) Matrix(621,-398,220,-141) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(491,-320,290,-189) -> Matrix(1,0,0,1) Matrix(301,-208,178,-123) -> Matrix(1,0,-4,1) 0/1 Matrix(265,-184,36,-25) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(459,-320,142,-99) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(387,-272,212,-149) -> Matrix(7,-2,4,-1) Matrix(245,-174,176,-125) -> Matrix(9,-4,2,-1) Matrix(87,-64,34,-25) -> Matrix(3,-2,2,-1) 1/1 Matrix(103,-78,136,-103) -> Matrix(5,-4,6,-5) (3/4,13/17) -> (2/3,1/1) Matrix(339,-260,442,-339) -> Matrix(13,-14,12,-13) (13/17,10/13) -> (1/1,7/6) Matrix(439,-340,102,-79) -> Matrix(1,-2,-2,3) Matrix(1141,-900,838,-661) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(319,-252,100,-79) -> Matrix(1,-2,-2,3) Matrix(695,-566,264,-215) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(363,-298,296,-243) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(147,-124,32,-27) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(113,-98,128,-111) -> Matrix(1,0,2,1) 0/1 Matrix(381,-340,158,-141) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(127,-144,112,-127) -> Matrix(-1,4,0,1) (9/8,8/7) -> (2/1,1/0) Matrix(97,-112,84,-97) -> Matrix(1,0,0,-1) (8/7,7/6) -> (0/1,1/0) Matrix(151,-178,28,-33) -> Matrix(1,0,0,1) Matrix(217,-262,82,-99) -> Matrix(1,0,0,1) Matrix(187,-232,54,-67) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(93,-118,26,-33) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(339,-442,260,-339) -> Matrix(7,-6,8,-7) (13/10,17/13) -> (3/4,1/1) Matrix(103,-136,78,-103) -> Matrix(3,-4,2,-3) (17/13,4/3) -> (1/1,2/1) Matrix(421,-570,178,-241) -> Matrix(1,-2,2,-5) Matrix(1209,-1642,712,-967) -> Matrix(1,-2,-2,5) Matrix(429,-592,50,-69) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(781,-1080,478,-661) -> Matrix(3,-8,-2,5) Matrix(37,-54,24,-35) -> Matrix(1,-2,0,1) 1/0 Matrix(303,-478,116,-183) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1103,-1748,696,-1103) -> Matrix(1,2,0,-1) (19/12,46/29) -> (-1/1,1/0) Matrix(2157,-3424,904,-1435) -> Matrix(1,2,2,5) Matrix(401,-648,138,-223) -> Matrix(1,2,0,1) 1/0 Matrix(619,-1002,160,-259) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(389,-630,92,-149) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(433,-706,46,-75) -> Matrix(1,2,0,1) 1/0 Matrix(545,-894,114,-187) -> Matrix(1,2,-2,-3) -1/1 Matrix(783,-1288,476,-783) -> Matrix(5,6,-4,-5) (23/14,28/17) -> (-3/2,-1/1) Matrix(16911,-28690,9968,-16911) -> Matrix(3,2,-4,-3) (95/56,151/89) -> (-1/1,-1/2) Matrix(9967,-16912,5874,-9967) -> Matrix(5,2,-12,-5) (151/89,56/33) -> (-1/2,-1/3) Matrix(633,-1078,266,-453) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(265,-456,154,-265) -> Matrix(-1,0,6,1) (12/7,19/11) -> (-1/3,0/1) Matrix(153,-266,88,-153) -> Matrix(1,0,4,-1) (19/11,7/4) -> (0/1,1/2) Matrix(97,-172,22,-39) -> Matrix(1,0,-2,1) 0/1 Matrix(331,-598,150,-271) -> Matrix(3,-2,-2,1) Matrix(661,-1200,298,-541) -> Matrix(7,-8,-8,9) Matrix(141,-308,38,-83) -> Matrix(1,2,0,1) 1/0 Matrix(101,-230,18,-41) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(127,-294,54,-125) -> Matrix(1,0,6,1) 0/1 Matrix(2665,-6364,1116,-2665) -> Matrix(1,0,4,-1) (74/31,43/18) -> (0/1,1/2) Matrix(333,-806,88,-213) -> Matrix(5,-2,2,-1) Matrix(89,-242,32,-87) -> Matrix(1,-4,0,1) 1/0 Matrix(183,-598,56,-183) -> Matrix(-1,0,8,1) (13/4,23/7) -> (-1/4,0/1) Matrix(139,-460,42,-139) -> Matrix(1,0,6,-1) (23/7,10/3) -> (0/1,1/3) Matrix(53,-338,8,-51) -> Matrix(1,-2,0,1) 1/0 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.