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 1/2 -13/28 0/1 -6/13 0/1 1/2 -5/11 0/1 -9/20 0/1 1/1 -4/9 0/1 -7/16 0/1 1/2 1/1 -17/39 1/0 -10/23 -1/1 0/1 -13/30 0/1 1/6 -3/7 1/2 -11/26 0/1 -19/45 1/6 -8/19 0/1 1/4 -5/12 1/2 1/1 -12/29 -1/1 0/1 -19/46 -1/1 0/1 1/0 -7/17 0/1 -9/22 1/4 1/3 -11/27 1/2 -2/5 0/1 -9/23 1/2 -16/41 0/1 -7/18 0/1 1/1 -12/31 0/1 1/6 -17/44 0/1 1/5 1/4 -5/13 1/4 -23/60 1/3 1/2 -18/47 0/1 1/3 -13/34 0/1 1/4 1/3 -8/21 1/3 2/5 -3/8 1/3 1/1 -10/27 1/3 2/5 -7/19 1/3 -11/30 1/3 1/2 -4/11 2/5 1/2 -5/14 0/1 1/3 1/2 -11/31 1/3 -6/17 2/5 1/2 -7/20 3/7 1/2 -1/3 1/2 -5/16 2/3 1/1 -9/29 1/1 -4/13 0/1 -7/23 1/2 -10/33 6/13 1/2 -3/10 1/2 3/5 -8/27 2/3 3/4 -5/17 1/1 -7/24 0/1 1/0 -9/31 1/2 -11/38 0/1 1/3 1/2 -2/7 1/2 -9/32 1/2 3/5 -7/25 2/3 -5/18 3/4 1/1 -3/11 1/2 -10/37 0/1 -7/26 1/3 1/2 -4/15 1/2 2/3 -5/19 1/2 -1/4 0/1 1/2 1/1 -5/21 1/2 -4/17 0/1 1/1 -7/30 1/2 1/1 -3/13 1/1 -5/22 0/1 1/2 -2/9 0/1 1/2 -9/41 1/2 -7/32 3/5 1/1 -5/23 2/3 -3/14 2/3 1/1 -1/5 1/2 -2/11 0/1 -3/17 1/2 -1/6 1/1 -3/19 1/0 -2/13 0/1 1/2 -1/7 1/1 -2/15 -1/1 0/1 -1/8 1/2 1/1 -1/9 1/0 0/1 0/1 1/1 1/7 1/2 2/13 1/1 3/19 3/2 1/6 1/1 1/0 1/5 1/1 4/19 2/1 1/0 3/14 2/1 1/0 5/23 1/0 7/32 -1/1 0/1 1/0 2/9 0/1 1/0 1/4 1/1 4/15 3/2 2/1 3/11 1/0 5/18 -1/1 1/0 12/43 1/0 19/68 0/1 1/1 1/0 7/25 1/0 9/32 -1/1 1/0 2/7 0/1 7/24 0/1 1/1 5/17 1/2 3/10 3/4 1/1 7/23 1/1 4/13 1/1 6/5 5/16 1/1 4/3 3/2 1/3 1/0 6/17 0/1 1/2 5/14 1/2 1/1 4/11 1/1 7/19 3/2 3/8 1/1 2/1 8/21 1/1 2/1 21/55 3/2 13/34 1/1 1/0 5/13 2/1 17/44 2/1 1/0 12/31 1/1 2/1 7/18 1/1 3/1 9/23 1/0 2/5 0/1 1/0 13/32 0/1 11/27 1/2 9/22 0/1 1/1 7/17 1/1 12/29 2/1 1/0 17/41 1/0 5/12 0/1 1/0 13/31 1/0 8/19 0/1 3/7 1/1 10/23 2/1 7/16 1/1 1/0 4/9 0/1 1/1 1/2 0/1 1/1 1/0 6/11 0/1 1/1 5/9 1/0 14/25 0/1 9/16 1/1 22/39 1/1 2/1 13/23 2/1 4/7 2/1 1/0 11/19 1/0 18/31 -4/1 1/0 7/12 -1/1 1/0 10/17 0/1 33/56 0/1 1/1 23/39 1/0 13/22 -1/1 1/1 16/27 -1/1 0/1 3/5 1/0 14/23 0/1 1/2 25/41 1/1 11/18 0/1 1/1 8/13 0/1 13/21 1/2 5/8 1/1 3/2 12/19 1/1 2/1 19/30 1/1 2/1 7/11 2/1 23/36 2/1 1/0 16/25 2/1 1/0 25/39 5/2 9/14 3/1 1/0 11/17 1/0 2/3 1/0 9/13 1/0 25/36 0/1 1/0 16/23 0/1 7/10 0/1 1/2 12/17 0/1 1/1 17/24 1/2 1/1 5/7 1/1 3/4 3/1 1/0 13/17 1/0 23/30 -15/1 1/0 10/13 -6/1 1/0 27/35 1/0 17/22 -4/1 -3/1 1/0 7/9 1/0 18/23 -2/1 1/0 11/14 -1/1 26/33 -1/1 0/1 15/19 -1/2 19/24 0/1 1/2 4/5 0/1 13/16 0/1 1/1 9/11 1/1 14/17 1/1 2/1 5/6 1/1 2/1 11/13 2/1 28/33 2/1 3/1 17/20 3/1 1/0 6/7 3/1 4/1 7/8 1/0 8/9 -3/1 -2/1 1/1 1/0 9/8 2/1 1/0 8/7 1/0 23/20 -8/1 1/0 15/13 1/0 7/6 -3/1 1/0 6/5 -2/1 1/0 11/9 -1/1 27/22 -1/1 0/1 16/13 -1/1 0/1 21/17 -1/2 5/4 -1/1 0/1 1/0 14/11 0/1 23/18 1/1 1/0 32/25 0/1 9/7 1/0 22/17 2/1 35/27 1/0 13/10 3/1 1/0 17/13 1/0 4/3 -2/1 1/0 19/14 -2/1 -3/2 -1/1 34/25 -2/1 -1/1 15/11 -3/2 26/19 -1/1 11/8 -1/1 1/0 40/29 -2/1 69/50 -2/1 1/0 29/21 -2/1 76/55 -2/1 -3/2 47/34 -2/1 -3/2 -1/1 18/13 -2/1 -1/1 43/31 1/0 25/18 -2/1 1/0 7/5 -1/1 3/2 -1/1 1/1 11/7 -1/1 30/19 0/1 1/0 49/31 -1/1 19/12 -1/1 0/1 46/29 0/1 27/17 1/0 8/5 -2/1 -1/1 37/23 -1/1 29/18 -1/1 -7/8 21/13 -3/4 55/34 -1/1 -2/3 34/21 -2/3 47/29 -1/2 13/8 -1/1 -1/2 0/1 57/35 -1/2 44/27 -1/2 0/1 31/19 0/1 49/30 -1/1 1/0 18/11 -1/1 0/1 23/14 -1/1 1/0 51/31 -3/2 28/17 -1/1 5/3 -1/2 22/13 -1/2 39/23 -1/2 95/56 -2/5 -1/3 151/89 -1/3 56/33 -1/3 0/1 17/10 -1/2 -1/3 0/1 46/27 -1/3 0/1 75/44 -1/2 0/1 29/17 -1/2 12/7 -1/4 0/1 19/11 0/1 26/15 0/1 1/6 7/4 0/1 1/1 9/5 1/0 29/16 -1/1 49/27 -1/2 20/11 -1/1 0/1 11/6 0/1 1/0 13/7 -1/1 15/8 -1/1 -1/2 17/9 1/0 2/1 0/1 11/5 1/0 31/14 -1/1 51/23 -1/2 20/9 -1/1 0/1 9/4 -1/1 -1/2 34/15 -1/2 0/1 25/11 0/1 16/7 -1/2 0/1 7/3 0/1 26/11 0/1 1/4 45/19 1/2 64/27 0/1 1/3 83/35 1/2 19/8 0/1 1/3 1/2 50/21 0/1 1/4 31/13 1/2 74/31 0/1 43/18 0/1 1/2 12/5 0/1 1/3 41/17 1/2 70/29 2/3 29/12 1/2 1/1 46/19 2/3 63/26 2/3 1/1 17/7 1/1 5/2 1/1 1/0 13/5 -1/1 34/13 -1/1 -2/3 55/21 -1/2 131/50 -1/2 0/1 76/29 0/1 21/8 -1/1 0/1 50/19 0/1 29/11 -1/1 8/3 -1/2 0/1 11/4 0/1 14/5 0/1 1/2 59/21 0/1 45/16 0/1 1/2 31/11 0/1 17/6 1/2 1/1 20/7 0/1 23/8 0/1 1/1 3/1 1/0 22/7 -1/1 0/1 19/6 -1/1 16/5 0/1 13/4 -1/4 0/1 23/7 0/1 33/10 0/1 1/10 10/3 0/1 1/3 47/14 0/1 1/2 37/11 0/1 27/8 1/3 1/1 71/21 1/2 186/55 2/3 1/1 301/89 1/1 115/34 0/1 1/1 44/13 0/1 17/5 1/2 24/7 0/1 1/1 31/9 1/1 7/2 0/1 1/1 1/0 18/5 2/1 1/0 47/13 1/0 29/8 -3/1 1/0 11/3 1/0 26/7 0/1 15/4 -1/1 1/0 49/13 1/0 34/9 -3/1 -2/1 19/5 -1/1 23/6 -1/1 0/1 4/1 0/1 25/6 0/1 1/1 46/11 0/1 21/5 1/2 17/4 1/1 2/1 1/0 47/11 1/0 30/7 4/1 1/0 13/3 1/0 9/2 0/1 1/1 23/5 1/0 37/8 1/0 51/11 1/0 14/3 -2/1 -1/1 19/4 -1/1 1/0 24/5 -1/1 0/1 5/1 0/1 26/5 0/1 1/1 21/4 1/1 16/3 0/1 1/0 11/2 -1/1 1/0 17/3 0/1 23/4 0/1 1/2 1/1 6/1 0/1 1/0 13/2 0/1 20/3 0/1 1/2 7/1 1/0 15/2 -1/2 0/1 8/1 0/1 17/2 -1/1 1/0 9/1 0/1 10/1 0/1 1/0 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,-2,1) Matrix(503,234,1236,575) -> Matrix(1,0,0,1) Matrix(225,104,556,257) -> Matrix(1,0,-2,1) Matrix(501,230,220,101) -> Matrix(1,0,-4,1) Matrix(275,124,326,147) -> Matrix(3,-2,2,-1) Matrix(383,172,-982,-441) -> Matrix(1,0,0,1) Matrix(269,118,212,93) -> Matrix(1,0,-2,1) 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(1,0,-4,1) Matrix(571,242,-1352,-573) -> Matrix(1,0,4,1) Matrix(1195,504,1866,787) -> Matrix(7,-2,4,-1) Matrix(153,64,-514,-215) -> Matrix(5,-2,8,-3) Matrix(53,22,-412,-171) -> Matrix(1,0,0,1) Matrix(2609,1078,1532,633) -> Matrix(1,0,-2,1) 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(1,0,-2,1) Matrix(249,98,592,233) -> Matrix(1,0,-2,1) Matrix(2709,1058,1672,653) -> Matrix(3,-2,-4,3) Matrix(685,266,394,153) -> Matrix(1,0,0,1) Matrix(2789,1078,1172,453) -> Matrix(1,0,-2,1) Matrix(539,208,-1858,-717) -> Matrix(1,0,-2,1) Matrix(3359,1288,2042,783) -> Matrix(5,-2,-2,1) Matrix(2479,950,2920,1119) -> Matrix(3,-2,2,-1) Matrix(2821,1080,2040,781) -> Matrix(5,-2,-2,1) Matrix(241,92,778,297) -> Matrix(13,-4,10,-3) Matrix(143,54,-384,-145) -> Matrix(1,0,0,1) Matrix(997,368,382,141) -> Matrix(1,0,-4,1) Matrix(473,174,666,245) -> Matrix(5,-2,8,-3) Matrix(235,86,664,243) -> Matrix(5,-2,8,-3) Matrix(329,118,92,33) -> Matrix(1,0,-2,1) Matrix(651,232,188,67) -> Matrix(1,0,-2,1) Matrix(1763,624,1116,395) -> Matrix(5,-2,-2,1) Matrix(833,292,368,129) -> Matrix(5,-2,-12,5) Matrix(321,112,278,97) -> Matrix(13,-6,-2,1) Matrix(395,124,86,27) -> Matrix(3,-2,2,-1) Matrix(959,298,782,243) -> Matrix(3,-2,-4,3) Matrix(1827,566,694,215) -> Matrix(1,0,-2,1) Matrix(387,118,692,211) -> Matrix(1,0,-2,1) Matrix(1119,340,260,79) -> Matrix(5,-2,-2,1) Matrix(859,260,1120,339) -> Matrix(25,-12,-2,1) Matrix(807,238,512,151) -> Matrix(3,-2,-4,3) Matrix(593,174,426,125) -> Matrix(1,-2,0,1) Matrix(633,184,86,25) -> Matrix(1,0,-2,1) Matrix(589,170,2110,609) -> Matrix(1,0,-2,1) Matrix(419,118,1502,423) -> Matrix(3,-2,2,-1) Matrix(1417,398,502,141) -> Matrix(3,-2,8,-5) Matrix(415,116,1084,303) -> Matrix(5,-4,4,-3) Matrix(123,34,416,115) -> Matrix(1,0,0,1) Matrix(1113,302,328,89) -> Matrix(1,0,0,1) Matrix(1683,454,1316,355) -> Matrix(1,0,-2,1) Matrix(573,154,986,265) -> Matrix(5,-2,-2,1) Matrix(447,118,572,151) -> Matrix(1,0,-2,1) Matrix(39,10,-160,-41) -> Matrix(1,0,0,1) Matrix(1649,390,630,149) -> Matrix(3,-2,-4,3) Matrix(469,110,550,129) -> Matrix(7,-4,2,-1) Matrix(585,136,314,73) -> Matrix(3,-2,-4,3) Matrix(429,98,232,53) -> Matrix(1,0,-2,1) Matrix(115,26,544,123) -> Matrix(3,-2,2,-1) Matrix(1653,364,386,85) -> Matrix(7,-4,2,-1) Matrix(3379,740,1000,219) -> Matrix(3,-2,8,-5) Matrix(1805,394,536,117) -> Matrix(3,-2,8,-5) Matrix(535,116,844,183) -> Matrix(5,-4,4,-3) Matrix(113,24,306,65) -> Matrix(5,-4,4,-3) Matrix(183,34,296,55) -> Matrix(1,0,0,1) Matrix(473,84,366,65) -> Matrix(3,-2,2,-1) Matrix(35,6,-216,-37) -> Matrix(3,-2,2,-1) Matrix(1353,212,568,89) -> Matrix(1,0,2,1) Matrix(175,26,424,63) -> Matrix(3,-2,2,-1) Matrix(523,72,138,19) -> Matrix(1,-2,0,1) Matrix(33,4,206,25) -> Matrix(3,-2,2,-1) 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(3,-2,-4,3) Matrix(1195,-186,726,-113) -> Matrix(5,-6,-4,5) Matrix(127,-22,52,-9) -> Matrix(1,0,0,1) Matrix(545,-114,894,-187) -> Matrix(1,-2,2,-3) Matrix(221,-48,198,-43) -> Matrix(1,0,0,1) Matrix(1895,-414,444,-97) -> Matrix(1,2,0,1) Matrix(2855,-626,2066,-453) -> Matrix(3,2,-2,-1) Matrix(25,-6,96,-23) -> Matrix(3,-2,2,-1) Matrix(567,-152,332,-89) -> Matrix(1,-2,-2,5) Matrix(517,-142,142,-39) -> Matrix(1,-2,0,1) Matrix(6119,-1710,2580,-721) -> Matrix(1,0,2,1) Matrix(1943,-546,516,-145) -> Matrix(1,0,0,1) Matrix(375,-106,46,-13) -> Matrix(1,0,0,1) Matrix(1347,-392,512,-149) -> Matrix(1,0,-2,1) Matrix(417,-122,1022,-299) -> Matrix(1,0,0,1) Matrix(1037,-314,644,-195) -> Matrix(11,-10,-12,11) Matrix(665,-204,414,-127) -> Matrix(7,-8,-6,7) Matrix(387,-122,92,-29) -> Matrix(1,-2,2,-3) Matrix(843,-296,356,-125) -> Matrix(1,0,2,1) Matrix(485,-174,354,-127) -> Matrix(1,0,-2,1) Matrix(659,-242,482,-177) -> Matrix(5,-6,-4,5) Matrix(217,-82,262,-99) -> Matrix(1,0,0,1) Matrix(2129,-812,1172,-447) -> Matrix(1,-2,0,1) Matrix(1949,-752,692,-267) -> Matrix(1,-2,2,-3) Matrix(4349,-1682,2552,-987) -> Matrix(1,-2,-2,5) Matrix(691,-268,1168,-453) -> Matrix(1,-2,0,1) Matrix(713,-278,1208,-471) -> Matrix(1,-2,0,1) Matrix(365,-144,474,-187) -> Matrix(1,-6,0,1) Matrix(809,-332,212,-87) -> Matrix(1,0,-2,1) Matrix(3457,-1432,2122,-879) -> Matrix(1,-2,-2,5) Matrix(1123,-466,976,-405) -> Matrix(1,-8,0,1) Matrix(1291,-540,930,-389) -> Matrix(1,-2,0,1) Matrix(127,-54,294,-125) -> Matrix(3,-2,2,-1) Matrix(711,-310,250,-109) -> Matrix(1,-2,2,-3) Matrix(395,-174,84,-37) -> Matrix(1,-2,0,1) Matrix(21,-10,40,-19) -> Matrix(1,0,0,1) Matrix(369,-202,232,-127) -> Matrix(1,-2,0,1) Matrix(731,-410,230,-129) -> Matrix(1,0,-2,1) Matrix(1093,-616,346,-195) -> Matrix(1,-2,0,1) Matrix(1073,-606,1266,-715) -> Matrix(5,-8,2,-3) Matrix(957,-542,422,-239) -> Matrix(1,-2,-2,5) Matrix(419,-242,722,-417) -> Matrix(1,-6,0,1) Matrix(567,-332,152,-89) -> Matrix(1,0,0,1) Matrix(3001,-1768,718,-423) -> Matrix(1,0,0,1) Matrix(5889,-3472,3472,-2047) -> Matrix(1,-2,-2,5) Matrix(261,-158,38,-23) -> Matrix(1,0,0,1) Matrix(2889,-1762,1192,-727) -> Matrix(1,-2,2,-3) Matrix(241,-148,298,-183) -> Matrix(1,0,0,1) Matrix(777,-482,482,-299) -> Matrix(5,-4,-6,5) Matrix(331,-208,148,-93) -> Matrix(1,-2,0,1) Matrix(993,-628,808,-511) -> Matrix(1,-2,0,1) Matrix(1849,-1180,550,-351) -> Matrix(1,-2,2,-3) Matrix(385,-246,36,-23) -> Matrix(1,-2,0,1) Matrix(823,-528,438,-281) -> Matrix(1,-2,-2,5) Matrix(711,-458,548,-353) -> Matrix(1,0,0,1) Matrix(491,-320,290,-189) -> Matrix(1,-2,-2,5) Matrix(301,-208,178,-123) -> Matrix(1,0,-2,1) Matrix(3027,-2104,2194,-1525) -> Matrix(1,-2,0,1) Matrix(477,-332,602,-419) -> Matrix(1,0,0,1) Matrix(387,-272,212,-149) -> Matrix(1,0,-2,1) Matrix(1265,-894,774,-547) -> Matrix(1,0,-2,1) Matrix(87,-64,34,-25) -> Matrix(1,-2,0,1) Matrix(443,-338,578,-441) -> Matrix(1,-18,0,1) Matrix(1709,-1320,1050,-811) -> Matrix(1,4,-2,-7) Matrix(1151,-890,710,-549) -> Matrix(1,4,-2,-7) Matrix(707,-554,134,-105) -> Matrix(1,2,0,1) Matrix(1057,-832,202,-159) -> Matrix(1,0,2,1) Matrix(2701,-2130,1140,-899) -> Matrix(1,0,4,1) Matrix(993,-808,628,-511) -> Matrix(1,0,-2,1) Matrix(791,-650,230,-189) -> Matrix(1,-2,2,-3) Matrix(113,-98,128,-111) -> Matrix(1,-6,0,1) Matrix(475,-426,126,-113) -> Matrix(1,0,0,1) Matrix(225,-256,196,-223) -> Matrix(1,-10,0,1) Matrix(151,-178,28,-33) -> Matrix(1,2,0,1) Matrix(217,-262,82,-99) -> Matrix(1,2,-2,-3) Matrix(1147,-1464,474,-605) -> Matrix(1,-2,2,-3) Matrix(2587,-3352,1072,-1389) -> Matrix(1,-4,2,-7) Matrix(847,-1104,234,-305) -> Matrix(1,-6,0,1) Matrix(375,-494,104,-137) -> Matrix(1,4,0,1) Matrix(153,-206,26,-35) -> Matrix(1,2,0,1) Matrix(1209,-1642,712,-967) -> Matrix(1,2,-4,-7) Matrix(317,-432,102,-139) -> Matrix(1,2,-2,-3) Matrix(1401,-1930,580,-799) -> Matrix(1,0,2,1) Matrix(3895,-5376,1386,-1913) -> Matrix(1,2,2,5) Matrix(3539,-4890,1260,-1741) -> Matrix(1,2,0,1) Matrix(1283,-1778,578,-801) -> Matrix(1,2,-2,-3) Matrix(37,-54,24,-35) -> Matrix(1,0,0,1) Matrix(1521,-2410,580,-919) -> Matrix(1,0,0,1) Matrix(2157,-3424,904,-1435) -> Matrix(1,0,2,1) Matrix(401,-648,138,-223) -> Matrix(3,2,4,3) Matrix(2887,-4672,1192,-1929) -> Matrix(5,4,6,5) Matrix(433,-706,46,-75) -> Matrix(1,0,2,1) Matrix(593,-968,68,-111) -> Matrix(1,0,0,1) Matrix(545,-894,114,-187) -> Matrix(1,0,0,1) Matrix(27091,-45960,8010,-13589) -> Matrix(5,2,2,1) Matrix(26487,-44942,7832,-13289) -> Matrix(7,2,10,3) Matrix(4647,-7924,1774,-3025) -> Matrix(1,0,0,1) Matrix(419,-722,242,-417) -> Matrix(1,0,10,1) Matrix(97,-172,22,-39) -> Matrix(1,0,0,1) Matrix(929,-1682,512,-927) -> Matrix(1,2,-2,-3) Matrix(435,-824,104,-197) -> Matrix(1,0,2,1) Matrix(141,-308,38,-83) -> Matrix(1,0,0,1) Matrix(869,-1922,392,-867) -> Matrix(1,2,-2,-3) Matrix(127,-294,54,-125) -> Matrix(1,0,6,1) Matrix(8427,-19982,2492,-5909) -> Matrix(5,-2,8,-3) Matrix(5429,-12962,2072,-4947) -> Matrix(1,0,-4,1) Matrix(415,-994,124,-297) -> Matrix(1,0,0,1) Matrix(493,-1186,106,-255) -> Matrix(5,-2,-2,1) Matrix(89,-242,32,-87) -> Matrix(1,0,4,1) Matrix(1157,-3312,342,-979) -> Matrix(1,0,0,1) 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(1,0,2,1) Matrix(593,-2738,128,-591) -> Matrix(1,-6,0,1) Matrix(51,-250,10,-49) -> Matrix(1,0,2,1) Matrix(53,-338,8,-51) -> Matrix(1,0,2,1) 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): 38 Degree of the the map X: 38 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. Imminent integer overflow caused the modular group computation to abort.