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): 768 Minimal number of generators: 129 Number of equivalence classes of cusps: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/1 -9/2 -4/1 -10/3 -3/1 -8/3 -16/7 -2/1 -9/5 -8/5 -3/2 -15/11 -4/3 -6/5 -8/7 0/1 1/1 8/7 6/5 24/19 4/3 24/17 3/2 36/23 8/5 12/7 9/5 24/13 2/1 24/11 12/5 27/11 5/2 8/3 192/71 3/1 36/11 10/3 24/7 7/2 11/3 19/5 4/1 21/5 13/3 9/2 23/5 33/7 24/5 5/1 11/2 17/3 6/1 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 0/1 1/0 -6/1 1/1 -5/1 1/2 1/1 -24/5 1/1 -19/4 1/1 8/7 -14/3 3/2 -23/5 1/1 2/1 -9/2 2/1 -22/5 1/0 -13/3 -1/1 1/0 -17/4 -1/1 0/1 -4/1 1/1 -23/6 1/1 2/1 -19/5 3/2 2/1 -15/4 2/1 -11/3 -1/1 1/0 -18/5 0/1 -25/7 0/1 1/1 -7/2 0/1 1/1 -24/7 1/1 -17/5 1/1 3/2 -10/3 1/0 -3/1 0/1 1/1 1/0 -14/5 1/0 -25/9 1/1 2/1 -36/13 2/1 -11/4 2/1 1/0 -19/7 2/1 1/0 -8/3 1/0 -29/11 0/1 1/0 -21/8 0/1 -13/5 1/1 1/0 -18/7 0/1 -23/9 0/1 1/1 -5/2 1/1 2/1 -22/9 1/0 -39/16 2/1 -17/7 3/1 1/0 -12/5 1/0 -7/3 0/1 1/0 -23/10 0/1 1/1 -16/7 1/1 -25/11 1/1 2/1 -9/4 2/1 -11/5 5/1 1/0 -24/11 1/0 -13/6 -4/1 1/0 -2/1 1/0 -13/7 3/1 1/0 -24/13 1/0 -11/6 -4/1 1/0 -9/5 -2/1 -1/1 1/0 -25/14 -2/1 -1/1 -16/9 -1/1 -23/13 -1/1 0/1 -7/4 -1/1 0/1 -26/15 1/0 -71/41 -1/1 0/1 -45/26 0/1 -19/11 0/1 1/0 -12/7 1/0 -5/3 -1/1 1/0 -18/11 -1/1 -49/30 -1/1 -2/3 -80/49 -2/3 -31/19 -1/1 -1/2 -13/8 -1/2 0/1 -60/37 0/1 -47/29 -1/2 0/1 -34/21 -1/2 -21/13 -1/1 -1/2 0/1 -8/5 0/1 -27/17 0/1 1/1 1/0 -73/46 0/1 1/1 -192/121 1/1 -119/75 1/1 2/1 -46/29 1/0 -19/12 -1/1 0/1 -11/7 -1/1 1/0 -36/23 -1/1 -25/16 -1/1 0/1 -14/9 1/0 -17/11 -1/1 -1/2 -3/2 0/1 -13/9 -1/1 1/0 -36/25 -1/1 -23/16 -1/1 0/1 -33/23 -1/1 0/1 1/0 -10/7 -1/2 -27/19 -1/2 -1/3 0/1 -71/50 -1/3 0/1 -44/31 -1/3 -17/12 -1/5 0/1 -24/17 0/1 -7/5 0/1 1/2 -18/13 1/1 -47/34 1/1 2/1 -29/21 2/1 1/0 -11/8 2/1 1/0 -26/19 1/0 -41/30 -3/1 -2/1 -15/11 -2/1 -1/1 1/0 -34/25 -3/2 -19/14 -1/1 -2/3 -23/17 -1/1 0/1 -4/3 0/1 -25/19 0/1 1/1 -21/16 0/1 -17/13 1/1 1/0 -13/10 2/1 1/0 -9/7 -1/1 0/1 1/0 -23/18 -1/1 0/1 -14/11 -1/2 -33/26 0/1 -19/15 -1/4 0/1 -24/19 0/1 -5/4 0/1 1/1 -11/9 1/1 1/0 -6/5 0/1 -13/11 1/1 1/0 -7/6 0/1 1/1 -15/13 -1/1 0/1 1/0 -23/20 -1/1 0/1 -8/7 0/1 -17/15 1/1 1/0 -9/8 0/1 -10/9 1/0 -1/1 0/1 1/0 0/1 0/1 1/1 0/1 1/2 9/8 0/1 8/7 0/1 15/13 0/1 1/3 1/2 7/6 0/1 1/1 6/5 0/1 11/9 1/2 1/1 5/4 0/1 1/1 24/19 0/1 19/15 0/1 1/6 14/11 1/4 23/18 0/1 1/3 9/7 0/1 1/3 1/2 13/10 1/2 2/3 17/13 1/2 1/1 4/3 0/1 19/14 2/7 1/3 15/11 1/3 2/5 1/2 26/19 1/2 11/8 1/2 2/3 18/13 1/1 7/5 0/1 1/0 24/17 0/1 17/12 0/1 1/7 27/19 0/1 1/5 1/4 10/7 1/4 33/23 0/1 1/3 1/2 56/39 0/1 23/16 0/1 1/3 36/25 1/3 13/9 1/3 1/2 3/2 0/1 14/9 1/2 25/16 0/1 1/3 36/23 1/3 11/7 1/3 1/2 19/12 0/1 1/3 8/5 0/1 29/18 0/1 1/5 21/13 0/1 1/4 1/3 34/21 1/4 47/29 0/1 1/4 13/8 0/1 1/4 5/3 1/3 1/2 12/7 1/2 19/11 0/1 1/2 26/15 1/2 33/19 0/1 1/2 1/1 7/4 0/1 1/3 23/13 0/1 1/3 16/9 1/3 25/14 1/3 2/5 9/5 1/3 2/5 1/2 11/6 4/9 1/2 24/13 1/2 13/7 1/2 3/5 2/1 1/2 13/6 4/9 1/2 24/11 1/2 11/5 1/2 5/9 9/4 2/3 25/11 2/3 1/1 16/7 1/1 7/3 0/1 1/2 12/5 1/2 17/7 1/2 3/5 22/9 1/2 49/20 3/5 2/3 27/11 1/2 3/5 2/3 5/2 2/3 1/1 28/11 0/1 23/9 0/1 1/1 18/7 0/1 31/12 0/1 1/1 13/5 1/2 1/1 21/8 0/1 8/3 1/2 27/10 2/3 73/27 2/3 1/1 192/71 1/1 119/44 0/1 1/1 46/17 1/2 19/7 1/2 2/3 49/18 2/3 1/1 30/11 1/1 11/4 1/2 2/3 3/1 0/1 1/2 1/1 13/4 1/2 2/3 49/15 1/2 2/3 36/11 2/3 23/7 2/3 1/1 10/3 1/2 27/8 2/3 71/21 2/3 1/1 44/13 2/3 17/5 3/4 1/1 24/7 1/1 7/2 0/1 1/1 25/7 0/1 1/1 18/5 0/1 11/3 1/3 1/2 15/4 2/3 49/13 1/2 2/3 34/9 1/2 19/5 2/3 3/4 23/6 2/3 1/1 4/1 1/1 25/6 0/1 1/1 21/5 0/1 1/1 1/0 17/4 0/1 1/3 13/3 1/3 1/2 22/5 1/2 31/7 1/2 3/5 40/9 2/3 9/2 2/3 23/5 2/3 1/1 14/3 3/4 33/7 4/5 5/6 1/1 19/4 8/9 1/1 24/5 1/1 5/1 1/1 1/0 11/2 0/1 1/2 17/3 1/2 1/1 40/7 2/3 23/4 2/3 1/1 6/1 1/1 7/1 0/1 1/2 8/1 1/1 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(23,168,-10,-73) (-7/1,1/0) -> (-7/3,-23/10) Hyperbolic Matrix(25,168,18,121) (-7/1,-6/1) -> (18/13,7/5) Hyperbolic Matrix(23,120,-14,-73) (-6/1,-5/1) -> (-5/3,-18/11) Hyperbolic Matrix(49,240,10,49) (-5/1,-24/5) -> (24/5,5/1) Hyperbolic Matrix(191,912,40,191) (-24/5,-19/4) -> (19/4,24/5) Hyperbolic Matrix(193,912,-142,-671) (-19/4,-14/3) -> (-34/25,-19/14) Hyperbolic Matrix(119,552,36,167) (-14/3,-23/5) -> (23/7,10/3) Hyperbolic Matrix(95,432,42,191) (-23/5,-9/2) -> (9/4,25/11) Hyperbolic Matrix(239,1056,-98,-433) (-9/2,-22/5) -> (-22/9,-39/16) Hyperbolic Matrix(71,312,38,167) (-22/5,-13/3) -> (13/7,2/1) Hyperbolic Matrix(145,624,56,241) (-13/3,-17/4) -> (31/12,13/5) Hyperbolic Matrix(193,816,-136,-575) (-17/4,-4/1) -> (-44/31,-17/12) Hyperbolic Matrix(335,1296,-236,-913) (-4/1,-23/6) -> (-71/50,-44/31) Hyperbolic Matrix(359,1368,132,503) (-23/6,-19/5) -> (19/7,49/18) Hyperbolic Matrix(241,912,-190,-719) (-19/5,-15/4) -> (-33/26,-19/15) Hyperbolic Matrix(71,264,32,119) (-15/4,-11/3) -> (11/5,9/4) Hyperbolic Matrix(73,264,60,217) (-11/3,-18/5) -> (6/5,11/9) Hyperbolic Matrix(241,864,94,337) (-18/5,-25/7) -> (23/9,18/7) Hyperbolic Matrix(95,336,54,191) (-25/7,-7/2) -> (7/4,23/13) Hyperbolic Matrix(97,336,28,97) (-7/2,-24/7) -> (24/7,7/2) Hyperbolic Matrix(239,816,70,239) (-24/7,-17/5) -> (17/5,24/7) Hyperbolic Matrix(121,408,-78,-263) (-17/5,-10/3) -> (-14/9,-17/11) Hyperbolic Matrix(23,72,-8,-25) (-10/3,-3/1) -> (-3/1,-14/5) Parabolic Matrix(241,672,52,145) (-14/5,-25/9) -> (23/5,14/3) Hyperbolic Matrix(623,1728,190,527) (-25/9,-36/13) -> (36/11,23/7) Hyperbolic Matrix(409,1128,-252,-695) (-36/13,-11/4) -> (-13/8,-60/37) Hyperbolic Matrix(193,528,-140,-383) (-11/4,-19/7) -> (-29/21,-11/8) Hyperbolic Matrix(143,384,-54,-145) (-19/7,-8/3) -> (-8/3,-29/11) Parabolic Matrix(647,1704,-374,-985) (-29/11,-21/8) -> (-45/26,-19/11) Hyperbolic Matrix(119,312,82,215) (-21/8,-13/5) -> (13/9,3/2) Hyperbolic Matrix(121,312,-102,-263) (-13/5,-18/7) -> (-6/5,-13/11) Hyperbolic Matrix(337,864,94,241) (-18/7,-23/9) -> (25/7,18/5) Hyperbolic Matrix(217,552,-160,-407) (-23/9,-5/2) -> (-19/14,-23/17) Hyperbolic Matrix(263,648,-166,-409) (-5/2,-22/9) -> (-46/29,-19/12) Hyperbolic Matrix(335,816,-296,-721) (-39/16,-17/7) -> (-17/15,-9/8) Hyperbolic Matrix(169,408,70,169) (-17/7,-12/5) -> (12/5,17/7) Hyperbolic Matrix(71,168,30,71) (-12/5,-7/3) -> (7/3,12/5) Hyperbolic Matrix(335,768,188,431) (-23/10,-16/7) -> (16/9,25/14) Hyperbolic Matrix(337,768,190,433) (-16/7,-25/11) -> (23/13,16/9) Hyperbolic Matrix(191,432,42,95) (-25/11,-9/4) -> (9/2,23/5) Hyperbolic Matrix(119,264,32,71) (-9/4,-11/5) -> (11/3,15/4) Hyperbolic Matrix(241,528,110,241) (-11/5,-24/11) -> (24/11,11/5) Hyperbolic Matrix(287,624,132,287) (-24/11,-13/6) -> (13/6,24/11) Hyperbolic Matrix(167,360,122,263) (-13/6,-2/1) -> (26/19,11/8) Hyperbolic Matrix(167,312,38,71) (-2/1,-13/7) -> (13/3,22/5) Hyperbolic Matrix(337,624,182,337) (-13/7,-24/13) -> (24/13,13/7) Hyperbolic Matrix(287,528,156,287) (-24/13,-11/6) -> (11/6,24/13) Hyperbolic Matrix(119,216,92,167) (-11/6,-9/5) -> (9/7,13/10) Hyperbolic Matrix(241,432,188,337) (-9/5,-25/14) -> (23/18,9/7) Hyperbolic Matrix(121,216,14,25) (-25/14,-16/9) -> (8/1,1/0) Hyperbolic Matrix(433,768,190,337) (-16/9,-23/13) -> (25/11,16/7) Hyperbolic Matrix(191,336,54,95) (-23/13,-7/4) -> (7/2,25/7) Hyperbolic Matrix(719,1248,-526,-913) (-7/4,-26/15) -> (-26/19,-41/30) Hyperbolic Matrix(3671,6360,-2314,-4009) (-26/15,-71/41) -> (-119/75,-46/29) Hyperbolic Matrix(2953,5112,874,1513) (-71/41,-45/26) -> (27/8,71/21) Hyperbolic Matrix(265,456,154,265) (-19/11,-12/7) -> (12/7,19/11) Hyperbolic Matrix(71,120,42,71) (-12/7,-5/3) -> (5/3,12/7) Hyperbolic Matrix(1439,2352,528,863) (-18/11,-49/30) -> (49/18,30/11) Hyperbolic Matrix(2807,4584,1954,3191) (-49/30,-80/49) -> (56/39,23/16) Hyperbolic Matrix(2279,3720,514,839) (-80/49,-31/19) -> (31/7,40/9) Hyperbolic Matrix(383,624,294,479) (-31/19,-13/8) -> (13/10,17/13) Hyperbolic Matrix(2857,4632,874,1417) (-60/37,-47/29) -> (49/15,36/11) Hyperbolic Matrix(311,504,-282,-457) (-47/29,-34/21) -> (-10/9,-1/1) Hyperbolic Matrix(697,1128,490,793) (-34/21,-21/13) -> (27/19,10/7) Hyperbolic Matrix(239,384,-150,-241) (-21/13,-8/5) -> (-8/5,-27/17) Parabolic Matrix(1391,2208,332,527) (-27/17,-73/46) -> (25/6,21/5) Hyperbolic Matrix(23231,36864,8590,13631) (-73/46,-192/121) -> (192/71,119/44) Hyperbolic Matrix(23233,36864,8592,13633) (-192/121,-119/75) -> (73/27,192/71) Hyperbolic Matrix(167,264,136,215) (-19/12,-11/7) -> (11/9,5/4) Hyperbolic Matrix(505,792,322,505) (-11/7,-36/23) -> (36/23,11/7) Hyperbolic Matrix(1105,1728,768,1201) (-36/23,-25/16) -> (23/16,36/25) Hyperbolic Matrix(431,672,338,527) (-25/16,-14/9) -> (14/11,23/18) Hyperbolic Matrix(265,408,-202,-311) (-17/11,-3/2) -> (-21/16,-17/13) Hyperbolic Matrix(215,312,82,119) (-3/2,-13/9) -> (13/5,21/8) Hyperbolic Matrix(649,936,450,649) (-13/9,-36/25) -> (36/25,13/9) Hyperbolic Matrix(1201,1728,768,1105) (-36/25,-23/16) -> (25/16,36/23) Hyperbolic Matrix(769,1104,-668,-959) (-23/16,-33/23) -> (-15/13,-23/20) Hyperbolic Matrix(553,792,118,169) (-33/23,-10/7) -> (14/3,33/7) Hyperbolic Matrix(793,1128,490,697) (-10/7,-27/19) -> (21/13,34/21) Hyperbolic Matrix(2281,3240,930,1321) (-27/19,-71/50) -> (49/20,27/11) Hyperbolic Matrix(577,816,408,577) (-17/12,-24/17) -> (24/17,17/12) Hyperbolic Matrix(239,336,170,239) (-24/17,-7/5) -> (7/5,24/17) Hyperbolic Matrix(121,168,18,25) (-7/5,-18/13) -> (6/1,7/1) Hyperbolic Matrix(503,696,86,119) (-18/13,-47/34) -> (23/4,6/1) Hyperbolic Matrix(1129,1560,296,409) (-47/34,-29/21) -> (19/5,23/6) Hyperbolic Matrix(263,360,122,167) (-11/8,-26/19) -> (2/1,13/6) Hyperbolic Matrix(527,720,456,623) (-41/30,-15/11) -> (15/13,7/6) Hyperbolic Matrix(935,1272,652,887) (-15/11,-34/25) -> (10/7,33/23) Hyperbolic Matrix(143,192,-108,-145) (-23/17,-4/3) -> (-4/3,-25/19) Parabolic Matrix(1681,2208,622,817) (-25/19,-21/16) -> (27/10,73/27) Hyperbolic Matrix(313,408,56,73) (-17/13,-13/10) -> (11/2,17/3) Hyperbolic Matrix(167,216,92,119) (-13/10,-9/7) -> (9/5,11/6) Hyperbolic Matrix(337,432,188,241) (-9/7,-23/18) -> (25/14,9/5) Hyperbolic Matrix(527,672,338,431) (-23/18,-14/11) -> (14/9,25/16) Hyperbolic Matrix(359,456,-322,-409) (-14/11,-33/26) -> (-9/8,-10/9) Hyperbolic Matrix(721,912,570,721) (-19/15,-24/19) -> (24/19,19/15) Hyperbolic Matrix(191,240,152,191) (-24/19,-5/4) -> (5/4,24/19) Hyperbolic Matrix(215,264,136,167) (-5/4,-11/9) -> (11/7,19/12) Hyperbolic Matrix(217,264,60,73) (-11/9,-6/5) -> (18/5,11/3) Hyperbolic Matrix(265,312,62,73) (-13/11,-7/6) -> (17/4,13/3) Hyperbolic Matrix(289,336,166,193) (-7/6,-15/13) -> (33/19,7/4) Hyperbolic Matrix(961,1104,168,193) (-23/20,-8/7) -> (40/7,23/4) Hyperbolic Matrix(719,816,126,143) (-8/7,-17/15) -> (17/3,40/7) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(407,-456,108,-121) (1/1,9/8) -> (15/4,49/13) Hyperbolic Matrix(383,-432,86,-97) (9/8,8/7) -> (40/9,9/2) Hyperbolic Matrix(959,-1104,668,-769) (8/7,15/13) -> (33/23,56/39) Hyperbolic Matrix(263,-312,102,-121) (7/6,6/5) -> (18/7,31/12) Hyperbolic Matrix(719,-912,190,-241) (19/15,14/11) -> (34/9,19/5) Hyperbolic Matrix(623,-816,184,-241) (17/13,4/3) -> (44/13,17/5) Hyperbolic Matrix(407,-552,160,-217) (4/3,19/14) -> (5/2,28/11) Hyperbolic Matrix(671,-912,142,-193) (19/14,15/11) -> (33/7,19/4) Hyperbolic Matrix(913,-1248,526,-719) (15/11,26/19) -> (26/15,33/19) Hyperbolic Matrix(383,-528,140,-193) (11/8,18/13) -> (30/11,11/4) Hyperbolic Matrix(575,-816,136,-193) (17/12,27/19) -> (21/5,17/4) Hyperbolic Matrix(263,-408,78,-121) (3/2,14/9) -> (10/3,27/8) Hyperbolic Matrix(241,-384,150,-239) (19/12,8/5) -> (8/5,29/18) Parabolic Matrix(551,-888,224,-361) (29/18,21/13) -> (27/11,5/2) Hyperbolic Matrix(2015,-3264,534,-865) (34/21,47/29) -> (49/13,34/9) Hyperbolic Matrix(769,-1248,236,-383) (47/29,13/8) -> (13/4,49/15) Hyperbolic Matrix(73,-120,14,-23) (13/8,5/3) -> (5/1,11/2) Hyperbolic Matrix(791,-1368,292,-505) (19/11,26/15) -> (46/17,19/7) Hyperbolic Matrix(73,-168,10,-23) (16/7,7/3) -> (7/1,8/1) Hyperbolic Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(1991,-4872,736,-1801) (22/9,49/20) -> (119/44,46/17) Hyperbolic Matrix(1177,-3000,348,-887) (28/11,23/9) -> (71/21,44/13) Hyperbolic Matrix(145,-384,54,-143) (21/8,8/3) -> (8/3,27/10) Parabolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(23,168,-10,-73) -> Matrix(1,0,0,1) Matrix(25,168,18,121) -> Matrix(1,0,0,1) Matrix(23,120,-14,-73) -> Matrix(1,0,-2,1) Matrix(49,240,10,49) -> Matrix(3,-2,2,-1) Matrix(191,912,40,191) -> Matrix(15,-16,16,-17) Matrix(193,912,-142,-671) -> Matrix(5,-6,-4,5) Matrix(119,552,36,167) -> Matrix(3,-4,4,-5) Matrix(95,432,42,191) -> Matrix(3,-4,4,-5) Matrix(239,1056,-98,-433) -> Matrix(1,0,0,1) Matrix(71,312,38,167) -> Matrix(1,-2,2,-3) Matrix(145,624,56,241) -> Matrix(1,0,2,1) Matrix(193,816,-136,-575) -> Matrix(1,0,-4,1) Matrix(335,1296,-236,-913) -> Matrix(1,-2,-2,5) Matrix(359,1368,132,503) -> Matrix(3,-4,4,-5) Matrix(241,912,-190,-719) -> Matrix(1,-2,-2,5) Matrix(71,264,32,119) -> Matrix(1,-4,2,-7) Matrix(73,264,60,217) -> Matrix(1,0,2,1) Matrix(241,864,94,337) -> Matrix(1,0,0,1) Matrix(95,336,54,191) -> Matrix(1,0,2,1) Matrix(97,336,28,97) -> Matrix(1,0,0,1) Matrix(239,816,70,239) -> Matrix(5,-6,6,-7) Matrix(121,408,-78,-263) -> Matrix(1,-2,0,1) Matrix(23,72,-8,-25) -> Matrix(1,0,0,1) Matrix(241,672,52,145) -> Matrix(3,-4,4,-5) Matrix(623,1728,190,527) -> Matrix(3,-4,4,-5) Matrix(409,1128,-252,-695) -> Matrix(1,-2,-2,5) Matrix(193,528,-140,-383) -> Matrix(1,0,0,1) Matrix(143,384,-54,-145) -> Matrix(1,-2,0,1) Matrix(647,1704,-374,-985) -> Matrix(1,0,0,1) Matrix(119,312,82,215) -> Matrix(1,0,2,1) Matrix(121,312,-102,-263) -> Matrix(1,0,0,1) Matrix(337,864,94,241) -> Matrix(1,0,0,1) Matrix(217,552,-160,-407) -> Matrix(1,0,-2,1) Matrix(263,648,-166,-409) -> Matrix(1,-2,0,1) Matrix(335,816,-296,-721) -> Matrix(1,-2,0,1) Matrix(169,408,70,169) -> Matrix(1,-6,2,-11) Matrix(71,168,30,71) -> Matrix(1,0,2,1) Matrix(335,768,188,431) -> Matrix(3,-2,8,-5) Matrix(337,768,190,433) -> Matrix(1,-2,4,-7) Matrix(191,432,42,95) -> Matrix(3,-4,4,-5) Matrix(119,264,32,71) -> Matrix(1,-4,2,-7) Matrix(241,528,110,241) -> Matrix(1,-10,2,-19) Matrix(287,624,132,287) -> Matrix(1,8,2,17) Matrix(167,360,122,263) -> Matrix(1,2,2,5) Matrix(167,312,38,71) -> Matrix(1,-2,2,-3) Matrix(337,624,182,337) -> Matrix(1,-6,2,-11) Matrix(287,528,156,287) -> Matrix(1,8,2,17) Matrix(119,216,92,167) -> Matrix(1,2,2,5) Matrix(241,432,188,337) -> Matrix(1,2,2,5) Matrix(121,216,14,25) -> Matrix(1,2,0,1) Matrix(433,768,190,337) -> Matrix(3,2,4,3) Matrix(191,336,54,95) -> Matrix(1,0,2,1) Matrix(719,1248,-526,-913) -> Matrix(1,-2,0,1) Matrix(3671,6360,-2314,-4009) -> Matrix(1,2,0,1) Matrix(2953,5112,874,1513) -> Matrix(3,2,4,3) Matrix(265,456,154,265) -> Matrix(1,0,2,1) Matrix(71,120,42,71) -> Matrix(1,2,2,5) Matrix(1439,2352,528,863) -> Matrix(5,4,6,5) Matrix(2807,4584,1954,3191) -> Matrix(3,2,10,7) Matrix(2279,3720,514,839) -> Matrix(7,4,12,7) Matrix(383,624,294,479) -> Matrix(3,2,4,3) Matrix(2857,4632,874,1417) -> Matrix(3,2,4,3) Matrix(311,504,-282,-457) -> Matrix(1,0,2,1) Matrix(697,1128,490,793) -> Matrix(1,0,6,1) Matrix(239,384,-150,-241) -> Matrix(1,0,2,1) Matrix(1391,2208,332,527) -> Matrix(1,0,0,1) Matrix(23231,36864,8590,13631) -> Matrix(1,0,0,1) Matrix(23233,36864,8592,13633) -> Matrix(3,-4,4,-5) Matrix(167,264,136,215) -> Matrix(1,0,2,1) Matrix(505,792,322,505) -> Matrix(1,2,2,5) Matrix(1105,1728,768,1201) -> Matrix(1,0,4,1) Matrix(431,672,338,527) -> Matrix(1,0,4,1) Matrix(265,408,-202,-311) -> Matrix(1,0,2,1) Matrix(215,312,82,119) -> Matrix(1,0,2,1) Matrix(649,936,450,649) -> Matrix(1,2,2,5) Matrix(1201,1728,768,1105) -> Matrix(1,0,4,1) Matrix(769,1104,-668,-959) -> Matrix(1,0,0,1) Matrix(553,792,118,169) -> Matrix(5,4,6,5) Matrix(793,1128,490,697) -> Matrix(1,0,6,1) Matrix(2281,3240,930,1321) -> Matrix(3,2,4,3) Matrix(577,816,408,577) -> Matrix(1,0,12,1) Matrix(239,336,170,239) -> Matrix(1,0,-2,1) Matrix(121,168,18,25) -> Matrix(1,0,0,1) Matrix(503,696,86,119) -> Matrix(3,-4,4,-5) Matrix(1129,1560,296,409) -> Matrix(3,-4,4,-5) Matrix(263,360,122,167) -> Matrix(1,2,2,5) Matrix(527,720,456,623) -> Matrix(1,2,2,5) Matrix(935,1272,652,887) -> Matrix(1,2,2,5) Matrix(143,192,-108,-145) -> Matrix(1,0,2,1) Matrix(1681,2208,622,817) -> Matrix(1,-2,2,-3) Matrix(313,408,56,73) -> Matrix(1,-2,2,-3) Matrix(167,216,92,119) -> Matrix(1,2,2,5) Matrix(337,432,188,241) -> Matrix(1,2,2,5) Matrix(527,672,338,431) -> Matrix(1,0,4,1) Matrix(359,456,-322,-409) -> Matrix(1,0,2,1) Matrix(721,912,570,721) -> Matrix(1,0,10,1) Matrix(191,240,152,191) -> Matrix(1,0,0,1) Matrix(215,264,136,167) -> Matrix(1,0,2,1) Matrix(217,264,60,73) -> Matrix(1,0,2,1) Matrix(265,312,62,73) -> Matrix(1,0,2,1) Matrix(289,336,166,193) -> Matrix(1,0,2,1) Matrix(961,1104,168,193) -> Matrix(3,2,4,3) Matrix(719,816,126,143) -> Matrix(1,-2,2,-3) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(407,-456,108,-121) -> Matrix(5,-2,8,-3) Matrix(383,-432,86,-97) -> Matrix(5,-2,8,-3) Matrix(959,-1104,668,-769) -> Matrix(1,0,0,1) Matrix(263,-312,102,-121) -> Matrix(1,0,0,1) Matrix(719,-912,190,-241) -> Matrix(9,-2,14,-3) Matrix(623,-816,184,-241) -> Matrix(1,-2,2,-3) Matrix(407,-552,160,-217) -> Matrix(1,0,-2,1) Matrix(671,-912,142,-193) -> Matrix(17,-6,20,-7) Matrix(913,-1248,526,-719) -> Matrix(5,-2,8,-3) Matrix(383,-528,140,-193) -> Matrix(1,0,0,1) Matrix(575,-816,136,-193) -> Matrix(1,0,-4,1) Matrix(263,-408,78,-121) -> Matrix(5,-2,8,-3) Matrix(241,-384,150,-239) -> Matrix(1,0,2,1) Matrix(551,-888,224,-361) -> Matrix(9,-2,14,-3) Matrix(2015,-3264,534,-865) -> Matrix(9,-2,14,-3) Matrix(769,-1248,236,-383) -> Matrix(9,-2,14,-3) Matrix(73,-120,14,-23) -> Matrix(1,0,-2,1) Matrix(791,-1368,292,-505) -> Matrix(5,-2,8,-3) Matrix(73,-168,10,-23) -> Matrix(1,0,0,1) Matrix(433,-1056,98,-239) -> Matrix(1,0,0,1) Matrix(1991,-4872,736,-1801) -> Matrix(3,-2,8,-5) Matrix(1177,-3000,348,-887) -> Matrix(1,-2,2,-3) Matrix(145,-384,54,-143) -> Matrix(5,-2,8,-3) Matrix(25,-72,8,-23) -> Matrix(1,0,0,1) Matrix(49,-192,12,-47) -> Matrix(3,-2,2,-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): 26 Degree of the the map X: 26 Degree of the the map Y: 128 ----------------------------------------------------------------------- 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.