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): 1080 Minimal number of generators: 181 Number of equivalence classes of cusps: 54 Genus: 64 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 0/1 3/16 4/15 5/14 6/13 1/2 7/12 8/11 1/1 11/8 7/5 56/39 3/2 12/7 2/1 13/6 66/29 53/23 40/17 27/11 5/2 55/21 8/3 111/41 14/5 3/1 29/9 13/4 10/3 7/2 11/3 15/4 4/1 77/18 13/3 31/7 9/2 14/3 47/10 63/13 5/1 16/3 11/2 17/3 6/1 13/2 33/5 20/3 7/1 8/1 17/2 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/34 -7/15 2/63 -6/13 1/31 -5/11 4/123 -9/20 3/92 -4/9 3/91 -11/25 8/239 -18/41 3/89 -7/16 5/148 -10/23 1/31 -3/7 2/59 -11/26 7/202 -19/45 4/115 -8/19 1/29 -13/31 8/227 -5/12 1/28 -12/29 1/29 -7/17 4/115 -16/39 1/29 -9/22 5/142 -2/5 1/27 -9/23 0/1 -7/18 3/82 -5/13 2/53 -13/34 1/26 -21/55 0/1 -8/21 3/79 -11/29 4/101 -14/37 1/23 -17/45 2/45 -3/8 1/28 -10/27 1/27 -7/19 2/53 -4/11 1/25 -17/47 0/1 -13/36 1/28 -9/25 2/51 -5/14 1/22 -11/31 2/59 -6/17 1/27 -1/3 0/1 -5/16 1/24 -4/13 1/29 -7/23 2/51 -10/33 1/23 -3/10 1/26 -5/17 2/49 -7/24 1/24 -2/7 1/23 -9/32 1/28 -7/25 4/103 -5/18 3/74 -8/29 1/25 -3/11 2/49 -4/15 3/71 -5/19 0/1 -1/4 1/24 -4/17 5/113 -7/30 1/22 -10/43 9/203 -13/56 13/292 -3/13 4/89 -5/22 1/22 -2/9 1/23 -5/23 8/181 -13/60 19/428 -8/37 11/247 -3/14 1/22 -7/33 4/89 -4/19 7/155 -1/5 2/43 -5/26 1/22 -4/21 1/21 -3/16 1/20 -2/11 5/107 -5/28 3/64 -3/17 8/169 -1/6 3/62 -2/13 3/61 -1/7 4/81 -1/8 1/20 -2/17 7/137 -3/26 11/214 -1/9 2/39 0/1 1/17 1/7 2/29 1/6 1/14 3/17 14/199 2/11 9/127 3/16 1/14 1/5 4/55 5/24 1/12 4/19 1/13 3/14 1/14 5/23 2/29 2/9 3/41 3/13 2/27 4/17 1/13 1/4 3/40 4/15 1/13 7/26 19/246 3/11 8/103 8/29 21/269 5/18 3/38 7/25 6/77 2/7 5/63 3/10 1/14 1/3 2/25 5/14 1/12 9/25 16/191 4/11 7/83 11/30 9/106 7/19 4/47 10/27 17/199 3/8 1/12 5/13 8/91 2/5 1/11 7/17 2/25 12/29 1/13 5/12 1/12 13/31 2/25 8/19 1/13 19/45 2/25 11/26 7/86 3/7 4/47 7/16 1/12 4/9 5/57 9/20 11/124 5/11 6/67 6/13 1/11 1/2 1/10 8/15 3/35 7/13 6/67 6/11 1/11 11/20 3/32 5/9 0/1 14/25 11/117 23/41 2/21 9/16 5/52 22/39 1/11 13/23 2/21 4/7 3/31 7/12 1/10 10/17 7/69 3/5 2/19 14/23 9/83 11/18 3/26 19/31 0/1 8/13 1/9 13/21 0/1 5/8 3/28 17/27 10/89 12/19 1/9 7/11 4/33 23/36 1/8 16/25 3/23 9/14 1/6 11/17 2/11 2/3 1/11 11/16 1/8 9/13 0/1 25/36 5/52 16/23 7/71 7/10 1/10 19/27 0/1 31/44 5/52 12/17 5/49 29/41 8/77 17/24 3/28 5/7 2/19 8/11 1/9 11/15 4/35 3/4 1/8 13/17 0/1 10/13 1/11 17/22 5/46 24/31 1/9 7/9 2/17 18/23 5/39 11/14 3/22 4/5 1/5 9/11 2/25 5/6 1/10 11/13 2/17 6/7 1/11 7/8 1/8 1/1 0/1 7/6 1/6 20/17 3/31 13/11 2/17 6/5 1/7 5/4 1/12 9/7 2/17 22/17 5/39 35/27 4/29 13/10 1/6 4/3 1/9 11/8 1/8 18/13 5/39 7/5 2/15 31/22 1/6 24/17 3/23 17/12 5/36 44/31 5/33 27/19 0/1 10/7 1/7 33/23 10/71 56/39 1/7 23/16 7/48 13/9 0/1 29/20 1/4 16/11 1/9 3/2 1/6 14/9 1/11 39/25 2/19 25/16 3/28 11/7 4/35 8/5 3/23 13/8 1/8 31/19 0/1 49/30 1/6 18/11 3/25 5/3 2/15 12/7 1/7 19/11 8/55 7/4 3/20 23/13 2/13 39/22 1/6 16/9 5/33 25/14 11/70 34/19 5/31 9/5 0/1 29/16 3/20 20/11 3/19 11/6 1/6 24/13 11/67 37/20 1/6 13/7 6/35 2/1 1/7 13/6 1/6 24/11 13/77 11/5 6/35 20/9 11/63 9/4 5/28 25/11 2/11 66/29 1/5 41/18 1/6 16/7 1/5 23/10 9/50 53/23 2/11 83/36 35/192 30/13 13/71 7/3 4/21 40/17 1/5 33/14 11/54 26/11 7/33 71/30 11/50 45/19 2/9 19/8 1/4 31/13 2/9 43/18 1/6 55/23 0/1 12/5 1/5 53/22 9/46 94/39 1/5 41/17 8/39 29/12 1/4 17/7 2/9 22/9 1/3 27/11 0/1 32/13 1/9 5/2 1/6 23/9 6/37 41/16 1/6 18/7 7/41 13/5 8/45 34/13 19/105 55/21 2/11 76/29 41/225 21/8 11/60 8/3 1/5 35/13 14/75 62/23 31/165 27/10 17/90 46/17 23/121 111/41 4/21 65/24 29/152 19/7 4/21 49/18 1/6 79/29 10/53 30/11 9/47 41/15 26/135 11/4 7/36 14/5 1/5 17/6 11/54 3/1 2/9 16/5 1/5 29/9 2/9 42/13 3/13 13/4 1/4 10/3 1/3 27/8 3/16 44/13 1/5 17/5 4/19 7/2 5/22 32/9 11/47 89/25 4/17 57/16 17/72 25/7 6/25 43/12 1/4 104/29 3/13 61/17 4/17 18/5 3/13 47/13 14/59 29/8 21/88 69/19 6/25 109/30 59/246 149/41 6/25 40/11 19/79 11/3 8/33 15/4 1/4 19/5 14/55 4/1 3/11 17/4 1/4 47/11 8/33 77/18 1/4 30/7 9/35 13/3 2/7 22/5 7/25 31/7 2/7 40/9 13/45 9/2 3/10 32/7 11/35 55/12 13/40 78/17 1/3 23/5 2/5 14/3 1/3 47/10 1/4 80/17 3/11 33/7 2/7 19/4 1/4 24/5 1/5 29/6 5/18 63/13 2/7 34/7 9/31 5/1 4/13 16/3 1/3 27/5 22/65 11/2 9/26 17/3 14/39 6/1 1/3 13/2 7/18 33/5 2/5 53/8 29/72 20/3 11/27 7/1 2/5 8/1 7/15 17/2 1/2 26/3 23/45 9/1 8/15 1/0 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(503,236,714,335) (-1/2,-7/15) -> (19/27,31/44) Hyperbolic Matrix(281,130,-776,-359) (-7/15,-6/13) -> (-4/11,-17/47) Hyperbolic Matrix(353,162,560,257) (-6/13,-5/11) -> (17/27,12/19) Hyperbolic Matrix(829,374,348,157) (-5/11,-9/20) -> (19/8,31/13) Hyperbolic Matrix(139,62,204,91) (-9/20,-4/9) -> (2/3,11/16) Hyperbolic Matrix(271,120,70,31) (-4/9,-11/25) -> (19/5,4/1) Hyperbolic Matrix(1219,536,680,299) (-11/25,-18/41) -> (34/19,9/5) Hyperbolic Matrix(269,118,1288,565) (-18/41,-7/16) -> (5/24,4/19) Hyperbolic Matrix(271,118,604,263) (-7/16,-10/23) -> (4/9,9/20) Hyperbolic Matrix(539,234,-1412,-613) (-10/23,-3/7) -> (-21/55,-8/21) Hyperbolic Matrix(197,84,68,29) (-3/7,-11/26) -> (17/6,3/1) Hyperbolic Matrix(1577,666,1120,473) (-11/26,-19/45) -> (7/5,31/22) Hyperbolic Matrix(721,304,1710,721) (-19/45,-8/19) -> (8/19,19/45) Hyperbolic Matrix(395,166,-1116,-469) (-8/19,-13/31) -> (-11/31,-6/17) Hyperbolic Matrix(67,28,390,163) (-13/31,-5/12) -> (1/6,3/17) Hyperbolic Matrix(391,162,712,295) (-5/12,-12/29) -> (6/11,11/20) Hyperbolic Matrix(905,374,196,81) (-12/29,-7/17) -> (23/5,14/3) Hyperbolic Matrix(901,370,-2384,-979) (-7/17,-16/39) -> (-14/37,-17/45) Hyperbolic Matrix(835,342,1482,607) (-16/39,-9/22) -> (9/16,22/39) Hyperbolic Matrix(451,184,576,235) (-9/22,-2/5) -> (18/23,11/14) Hyperbolic Matrix(311,122,752,295) (-2/5,-9/23) -> (7/17,12/29) Hyperbolic Matrix(313,122,372,145) (-9/23,-7/18) -> (5/6,11/13) Hyperbolic Matrix(433,168,250,97) (-7/18,-5/13) -> (19/11,7/4) Hyperbolic Matrix(737,282,1048,401) (-5/13,-13/34) -> (7/10,19/27) Hyperbolic Matrix(309,118,-1600,-611) (-13/34,-21/55) -> (-1/5,-5/26) Hyperbolic Matrix(121,46,676,257) (-8/21,-11/29) -> (3/17,2/11) Hyperbolic Matrix(491,186,916,347) (-11/29,-14/37) -> (8/15,7/13) Hyperbolic Matrix(609,230,-2624,-991) (-17/45,-3/8) -> (-13/56,-3/13) Hyperbolic Matrix(59,22,244,91) (-3/8,-10/27) -> (4/17,1/4) Hyperbolic Matrix(665,246,1084,401) (-10/27,-7/19) -> (19/31,8/13) Hyperbolic Matrix(419,154,302,111) (-7/19,-4/11) -> (18/13,7/5) Hyperbolic Matrix(177,64,-1546,-559) (-17/47,-13/36) -> (-3/26,-1/9) Hyperbolic Matrix(949,342,1368,493) (-13/36,-9/25) -> (9/13,25/36) Hyperbolic Matrix(295,106,654,235) (-9/25,-5/14) -> (9/20,5/11) Hyperbolic Matrix(473,168,-2182,-775) (-5/14,-11/31) -> (-5/23,-13/60) Hyperbolic Matrix(233,82,412,145) (-6/17,-1/3) -> (13/23,4/7) Hyperbolic Matrix(389,122,220,69) (-1/3,-5/16) -> (7/4,23/13) Hyperbolic Matrix(167,52,-774,-241) (-5/16,-4/13) -> (-8/37,-3/14) Hyperbolic Matrix(603,184,272,83) (-4/13,-7/23) -> (11/5,20/9) Hyperbolic Matrix(1965,596,544,165) (-7/23,-10/33) -> (18/5,47/13) Hyperbolic Matrix(53,16,-434,-131) (-10/33,-3/10) -> (-1/8,-2/17) Hyperbolic Matrix(161,48,218,65) (-3/10,-5/17) -> (11/15,3/4) Hyperbolic Matrix(965,282,592,173) (-5/17,-7/24) -> (13/8,31/19) Hyperbolic Matrix(215,62,52,15) (-7/24,-2/7) -> (4/1,17/4) Hyperbolic Matrix(369,104,-1586,-447) (-2/7,-9/32) -> (-7/30,-10/43) Hyperbolic Matrix(1587,446,580,163) (-9/32,-7/25) -> (41/15,11/4) Hyperbolic Matrix(581,162,104,29) (-7/25,-5/18) -> (11/2,17/3) Hyperbolic Matrix(159,44,-842,-233) (-5/18,-8/29) -> (-4/21,-3/16) Hyperbolic Matrix(893,246,628,173) (-8/29,-3/11) -> (27/19,10/7) Hyperbolic Matrix(155,42,262,71) (-3/11,-4/15) -> (10/17,3/5) Hyperbolic Matrix(309,82,260,69) (-4/15,-5/19) -> (13/11,6/5) Hyperbolic Matrix(619,162,256,67) (-5/19,-1/4) -> (29/12,17/7) Hyperbolic Matrix(499,118,148,35) (-1/4,-4/17) -> (10/3,27/8) Hyperbolic Matrix(1143,268,644,151) (-4/17,-7/30) -> (39/22,16/9) Hyperbolic Matrix(5249,1220,2276,529) (-10/43,-13/56) -> (83/36,30/13) Hyperbolic Matrix(149,34,688,157) (-3/13,-5/22) -> (3/14,5/23) Hyperbolic Matrix(539,122,296,67) (-5/22,-2/9) -> (20/11,11/6) Hyperbolic Matrix(291,64,50,11) (-2/9,-5/23) -> (17/3,6/1) Hyperbolic Matrix(5337,1156,2036,441) (-13/60,-8/37) -> (76/29,21/8) Hyperbolic Matrix(1257,268,530,113) (-3/14,-7/33) -> (45/19,19/8) Hyperbolic Matrix(1203,254,772,163) (-7/33,-4/19) -> (14/9,39/25) Hyperbolic Matrix(191,40,530,111) (-4/19,-1/5) -> (9/25,4/11) Hyperbolic Matrix(1365,262,422,81) (-5/26,-4/21) -> (42/13,13/4) Hyperbolic Matrix(419,78,188,35) (-3/16,-2/11) -> (20/9,9/4) Hyperbolic Matrix(881,158,184,33) (-2/11,-5/28) -> (19/4,24/5) Hyperbolic Matrix(1201,214,926,165) (-5/28,-3/17) -> (35/27,13/10) Hyperbolic Matrix(137,24,508,89) (-3/17,-1/6) -> (7/26,3/11) Hyperbolic Matrix(135,22,92,15) (-1/6,-2/13) -> (16/11,3/2) Hyperbolic Matrix(225,34,536,81) (-2/13,-1/7) -> (13/31,8/19) Hyperbolic Matrix(219,28,86,11) (-1/7,-1/8) -> (5/2,23/9) Hyperbolic Matrix(1421,166,214,25) (-2/17,-3/26) -> (53/8,20/3) Hyperbolic Matrix(423,44,298,31) (-1/9,0/1) -> (44/31,27/19) Hyperbolic Matrix(101,-14,166,-23) (0/1,1/7) -> (3/5,14/23) Hyperbolic Matrix(99,-16,130,-21) (1/7,1/6) -> (3/4,13/17) Hyperbolic Matrix(739,-136,288,-53) (2/11,3/16) -> (41/16,18/7) Hyperbolic Matrix(573,-110,224,-43) (3/16,1/5) -> (23/9,41/16) Hyperbolic Matrix(2141,-444,786,-163) (1/5,5/24) -> (49/18,79/29) Hyperbolic Matrix(1003,-212,440,-93) (4/19,3/14) -> (41/18,16/7) Hyperbolic Matrix(499,-110,186,-41) (5/23,2/9) -> (8/3,35/13) Hyperbolic Matrix(403,-92,92,-21) (2/9,3/13) -> (13/3,22/5) Hyperbolic Matrix(431,-100,556,-129) (3/13,4/17) -> (24/31,7/9) Hyperbolic Matrix(121,-32,450,-119) (1/4,4/15) -> (4/15,7/26) Parabolic Matrix(597,-164,506,-139) (3/11,8/29) -> (20/17,13/11) Hyperbolic Matrix(1013,-280,1458,-403) (8/29,5/18) -> (25/36,16/23) Hyperbolic Matrix(1633,-456,684,-191) (5/18,7/25) -> (31/13,43/18) Hyperbolic Matrix(503,-142,712,-201) (7/25,2/7) -> (12/17,29/41) Hyperbolic Matrix(117,-34,148,-43) (2/7,3/10) -> (11/14,4/5) Hyperbolic Matrix(145,-44,234,-71) (3/10,1/3) -> (13/21,5/8) Hyperbolic Matrix(141,-50,392,-139) (1/3,5/14) -> (5/14,9/25) Parabolic Matrix(251,-92,472,-173) (4/11,11/30) -> (1/2,8/15) Hyperbolic Matrix(1861,-684,1140,-419) (11/30,7/19) -> (31/19,49/30) Hyperbolic Matrix(887,-328,1582,-585) (7/19,10/27) -> (14/25,23/41) Hyperbolic Matrix(499,-186,110,-41) (10/27,3/8) -> (9/2,32/7) Hyperbolic Matrix(137,-52,166,-63) (3/8,5/13) -> (9/11,5/6) Hyperbolic Matrix(191,-74,302,-117) (5/13,2/5) -> (12/19,7/11) Hyperbolic Matrix(459,-188,188,-77) (2/5,7/17) -> (17/7,22/9) Hyperbolic Matrix(859,-356,1344,-557) (12/29,5/12) -> (23/36,16/25) Hyperbolic Matrix(1633,-684,456,-191) (5/12,13/31) -> (25/7,43/12) Hyperbolic Matrix(3099,-1310,854,-361) (19/45,11/26) -> (29/8,69/19) Hyperbolic Matrix(241,-102,26,-11) (11/26,3/7) -> (9/1,1/0) Hyperbolic Matrix(239,-104,370,-161) (3/7,7/16) -> (9/14,11/17) Hyperbolic Matrix(159,-70,184,-81) (7/16,4/9) -> (6/7,7/8) Hyperbolic Matrix(705,-322,208,-95) (5/11,6/13) -> (44/13,17/5) Hyperbolic Matrix(439,-206,130,-61) (6/13,1/2) -> (27/8,44/13) Hyperbolic Matrix(493,-268,344,-187) (7/13,6/11) -> (10/7,33/23) Hyperbolic Matrix(441,-244,244,-135) (11/20,5/9) -> (9/5,29/16) Hyperbolic Matrix(1073,-600,828,-463) (5/9,14/25) -> (22/17,35/27) Hyperbolic Matrix(2969,-1666,1096,-615) (23/41,9/16) -> (65/24,19/7) Hyperbolic Matrix(2793,-1576,778,-439) (22/39,13/23) -> (61/17,18/5) Hyperbolic Matrix(169,-98,288,-167) (4/7,7/12) -> (7/12,10/17) Parabolic Matrix(1227,-748,520,-317) (14/23,11/18) -> (33/14,26/11) Hyperbolic Matrix(1861,-1140,684,-419) (11/18,19/31) -> (19/7,49/18) Hyperbolic Matrix(375,-232,118,-73) (8/13,13/21) -> (3/1,16/5) Hyperbolic Matrix(513,-322,94,-59) (5/8,17/27) -> (27/5,11/2) Hyperbolic Matrix(1879,-1200,440,-281) (7/11,23/36) -> (17/4,47/11) Hyperbolic Matrix(1111,-712,788,-505) (16/25,9/14) -> (31/22,24/17) Hyperbolic Matrix(531,-344,230,-149) (11/17,2/3) -> (30/13,7/3) Hyperbolic Matrix(585,-404,404,-279) (11/16,9/13) -> (13/9,29/20) Hyperbolic Matrix(493,-344,268,-187) (16/23,7/10) -> (11/6,24/13) Hyperbolic Matrix(3187,-2246,1182,-833) (31/44,12/17) -> (62/23,27/10) Hyperbolic Matrix(2937,-2078,824,-583) (29/41,17/24) -> (57/16,25/7) Hyperbolic Matrix(1111,-788,712,-505) (17/24,5/7) -> (39/25,25/16) Hyperbolic Matrix(177,-128,242,-175) (5/7,8/11) -> (8/11,11/15) Parabolic Matrix(431,-330,64,-49) (13/17,10/13) -> (20/3,7/1) Hyperbolic Matrix(1073,-828,600,-463) (10/13,17/22) -> (25/14,34/19) Hyperbolic Matrix(1907,-1476,792,-613) (17/22,24/31) -> (12/5,53/22) Hyperbolic Matrix(469,-366,214,-167) (7/9,18/23) -> (24/11,11/5) Hyperbolic Matrix(439,-358,168,-137) (4/5,9/11) -> (13/5,34/13) Hyperbolic Matrix(597,-506,164,-139) (11/13,6/7) -> (40/11,11/3) Hyperbolic Matrix(283,-250,60,-53) (7/8,1/1) -> (33/7,19/4) Hyperbolic Matrix(159,-184,70,-81) (1/1,7/6) -> (9/4,25/11) Hyperbolic Matrix(1363,-1602,576,-677) (7/6,20/17) -> (26/11,71/30) Hyperbolic Matrix(137,-166,52,-63) (6/5,5/4) -> (21/8,8/3) Hyperbolic Matrix(117,-148,34,-43) (5/4,9/7) -> (17/5,7/2) Hyperbolic Matrix(431,-556,100,-129) (9/7,22/17) -> (30/7,13/3) Hyperbolic Matrix(99,-130,16,-21) (13/10,4/3) -> (6/1,13/2) Hyperbolic Matrix(177,-242,128,-175) (4/3,11/8) -> (11/8,18/13) Parabolic Matrix(503,-712,142,-201) (24/17,17/12) -> (7/2,32/9) Hyperbolic Matrix(2089,-2964,456,-647) (17/12,44/31) -> (32/7,55/12) Hyperbolic Matrix(3761,-5398,1560,-2239) (33/23,56/39) -> (94/39,41/17) Hyperbolic Matrix(3571,-5130,1482,-2129) (56/39,23/16) -> (53/22,94/39) Hyperbolic Matrix(1013,-1458,280,-403) (23/16,13/9) -> (47/13,29/8) Hyperbolic Matrix(899,-1304,202,-293) (29/20,16/11) -> (40/9,9/2) Hyperbolic Matrix(239,-370,104,-161) (3/2,14/9) -> (16/7,23/10) Hyperbolic Matrix(859,-1344,356,-557) (25/16,11/7) -> (41/17,29/12) Hyperbolic Matrix(191,-302,74,-117) (11/7,8/5) -> (18/7,13/5) Hyperbolic Matrix(145,-234,44,-71) (8/5,13/8) -> (13/4,10/3) Hyperbolic Matrix(1039,-1698,216,-353) (49/30,18/11) -> (24/5,29/6) Hyperbolic Matrix(101,-166,14,-23) (18/11,5/3) -> (7/1,8/1) Hyperbolic Matrix(169,-288,98,-167) (5/3,12/7) -> (12/7,19/11) Parabolic Matrix(1769,-3134,740,-1311) (23/13,39/22) -> (43/18,55/23) Hyperbolic Matrix(887,-1582,328,-585) (16/9,25/14) -> (27/10,46/17) Hyperbolic Matrix(567,-1028,230,-417) (29/16,20/11) -> (32/13,5/2) Hyperbolic Matrix(1601,-2958,374,-691) (24/13,37/20) -> (77/18,30/7) Hyperbolic Matrix(1479,-2740,346,-641) (37/20,13/7) -> (47/11,77/18) Hyperbolic Matrix(251,-472,92,-173) (13/7,2/1) -> (30/11,41/15) Hyperbolic Matrix(157,-338,72,-155) (2/1,13/6) -> (13/6,24/11) Parabolic Matrix(2913,-6626,812,-1847) (25/11,66/29) -> (104/29,61/17) Hyperbolic Matrix(3119,-7102,870,-1981) (66/29,41/18) -> (43/12,104/29) Hyperbolic Matrix(2439,-5618,1058,-2437) (23/10,53/23) -> (53/23,83/36) Parabolic Matrix(625,-1466,136,-319) (7/3,40/17) -> (78/17,23/5) Hyperbolic Matrix(2027,-4774,442,-1041) (40/17,33/14) -> (55/12,78/17) Hyperbolic Matrix(4141,-9804,1140,-2699) (71/30,45/19) -> (69/19,109/30) Hyperbolic Matrix(2005,-4796,426,-1019) (55/23,12/5) -> (80/17,33/7) Hyperbolic Matrix(595,-1458,242,-593) (22/9,27/11) -> (27/11,32/13) Parabolic Matrix(2311,-6050,882,-2309) (34/13,55/21) -> (55/21,76/29) Parabolic Matrix(545,-1468,62,-167) (35/13,62/23) -> (26/3,9/1) Hyperbolic Matrix(4173,-11294,1148,-3107) (46/17,111/41) -> (149/41,40/11) Hyperbolic Matrix(8045,-21784,2214,-5995) (111/41,65/24) -> (109/30,149/41) Hyperbolic Matrix(1041,-2836,214,-583) (79/29,30/11) -> (34/7,5/1) Hyperbolic Matrix(141,-392,50,-139) (11/4,14/5) -> (14/5,17/6) Parabolic Matrix(523,-1682,162,-521) (16/5,29/9) -> (29/9,42/13) Parabolic Matrix(1417,-5042,292,-1039) (32/9,89/25) -> (63/13,34/7) Hyperbolic Matrix(1733,-6172,358,-1275) (89/25,57/16) -> (29/6,63/13) Hyperbolic Matrix(121,-450,32,-119) (11/3,15/4) -> (15/4,19/5) Parabolic Matrix(435,-1922,98,-433) (22/5,31/7) -> (31/7,40/9) Parabolic Matrix(941,-4418,200,-939) (14/3,47/10) -> (47/10,80/17) Parabolic Matrix(97,-512,18,-95) (5/1,16/3) -> (16/3,27/5) Parabolic Matrix(331,-2178,50,-329) (13/2,33/5) -> (33/5,53/8) Parabolic Matrix(69,-578,8,-67) (8/1,17/2) -> (17/2,26/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,34,1) Matrix(503,236,714,335) -> Matrix(63,-2,662,-21) Matrix(281,130,-776,-359) -> Matrix(63,-2,1544,-49) Matrix(353,162,560,257) -> Matrix(187,-6,1652,-53) Matrix(829,374,348,157) -> Matrix(61,-2,336,-11) Matrix(139,62,204,91) -> Matrix(61,-2,580,-19) Matrix(271,120,70,31) -> Matrix(181,-6,694,-23) Matrix(1219,536,680,299) -> Matrix(239,-8,1464,-49) Matrix(269,118,1288,565) -> Matrix(59,-2,856,-29) Matrix(271,118,604,263) -> Matrix(57,-2,656,-23) Matrix(539,234,-1412,-613) -> Matrix(59,-2,1564,-53) Matrix(197,84,68,29) -> Matrix(117,-4,556,-19) Matrix(1577,666,1120,473) -> Matrix(173,-6,1240,-43) Matrix(721,304,1710,721) -> Matrix(57,-2,770,-27) Matrix(395,166,-1116,-469) -> Matrix(57,-2,1568,-55) Matrix(67,28,390,163) -> Matrix(55,-2,798,-29) Matrix(391,162,712,295) -> Matrix(59,-2,620,-21) Matrix(905,374,196,81) -> Matrix(57,-2,200,-7) Matrix(901,370,-2384,-979) -> Matrix(57,-2,1340,-47) Matrix(835,342,1482,607) -> Matrix(1,0,-18,1) Matrix(451,184,576,235) -> Matrix(113,-4,876,-31) Matrix(311,122,752,295) -> Matrix(55,-2,688,-25) Matrix(313,122,372,145) -> Matrix(55,-2,468,-17) Matrix(433,168,250,97) -> Matrix(163,-6,1114,-41) Matrix(737,282,1048,401) -> Matrix(53,-2,504,-19) Matrix(309,118,-1600,-611) -> Matrix(53,-2,1140,-43) Matrix(121,46,676,257) -> Matrix(155,-6,2196,-85) Matrix(491,186,916,347) -> Matrix(49,-2,564,-23) Matrix(609,230,-2624,-991) -> Matrix(43,-2,968,-45) Matrix(59,22,244,91) -> Matrix(53,-2,716,-27) Matrix(665,246,1084,401) -> Matrix(53,-2,504,-19) Matrix(419,154,302,111) -> Matrix(105,-4,814,-31) Matrix(177,64,-1546,-559) -> Matrix(45,-2,878,-39) Matrix(949,342,1368,493) -> Matrix(51,-2,536,-21) Matrix(295,106,654,235) -> Matrix(99,-4,1114,-45) Matrix(473,168,-2182,-775) -> Matrix(63,-2,1418,-45) Matrix(233,82,412,145) -> Matrix(51,-2,536,-21) Matrix(389,122,220,69) -> Matrix(51,-2,332,-13) Matrix(167,52,-774,-241) -> Matrix(47,-2,1058,-45) Matrix(603,184,272,83) -> Matrix(105,-4,604,-23) Matrix(1965,596,544,165) -> Matrix(95,-4,404,-17) Matrix(53,16,-434,-131) -> Matrix(53,-2,1034,-39) Matrix(161,48,218,65) -> Matrix(51,-2,434,-17) Matrix(965,282,592,173) -> Matrix(49,-2,368,-15) Matrix(215,62,52,15) -> Matrix(49,-2,172,-7) Matrix(369,104,-1586,-447) -> Matrix(55,-2,1238,-45) Matrix(1587,446,580,163) -> Matrix(161,-6,832,-31) Matrix(581,162,104,29) -> Matrix(151,-6,428,-17) Matrix(159,44,-842,-233) -> Matrix(49,-2,1054,-43) Matrix(893,246,628,173) -> Matrix(49,-2,368,-15) Matrix(155,42,262,71) -> Matrix(97,-4,946,-39) Matrix(309,82,260,69) -> Matrix(47,-2,400,-17) Matrix(619,162,256,67) -> Matrix(47,-2,212,-9) Matrix(499,118,148,35) -> Matrix(45,-2,248,-11) Matrix(1143,268,644,151) -> Matrix(1,0,-16,1) Matrix(5249,1220,2276,529) -> Matrix(991,-44,5428,-241) Matrix(149,34,688,157) -> Matrix(45,-2,608,-27) Matrix(539,122,296,67) -> Matrix(43,-2,280,-13) Matrix(291,64,50,11) -> Matrix(47,-2,118,-5) Matrix(5337,1156,2036,441) -> Matrix(1351,-60,7408,-329) Matrix(1257,268,530,113) -> Matrix(45,-2,158,-7) Matrix(1203,254,772,163) -> Matrix(133,-6,1308,-59) Matrix(191,40,530,111) -> Matrix(309,-14,3686,-167) Matrix(1365,262,422,81) -> Matrix(87,-4,370,-17) Matrix(419,78,188,35) -> Matrix(45,-2,248,-11) Matrix(881,158,184,33) -> Matrix(43,-2,108,-5) Matrix(1201,214,926,165) -> Matrix(85,-4,574,-27) Matrix(137,24,508,89) -> Matrix(337,-16,4360,-207) Matrix(135,22,92,15) -> Matrix(41,-2,308,-15) Matrix(225,34,536,81) -> Matrix(41,-2,472,-23) Matrix(219,28,86,11) -> Matrix(39,-2,254,-13) Matrix(1421,166,214,25) -> Matrix(703,-36,1738,-89) Matrix(423,44,298,31) -> Matrix(39,-2,254,-13) Matrix(101,-14,166,-23) -> Matrix(59,-4,546,-37) Matrix(99,-16,130,-21) -> Matrix(29,-2,218,-15) Matrix(739,-136,288,-53) -> Matrix(225,-16,1336,-95) Matrix(573,-110,224,-43) -> Matrix(139,-10,848,-61) Matrix(2141,-444,786,-163) -> Matrix(25,-2,138,-11) Matrix(1003,-212,440,-93) -> Matrix(1,0,-8,1) Matrix(499,-110,186,-41) -> Matrix(109,-8,586,-43) Matrix(403,-92,92,-21) -> Matrix(107,-8,388,-29) Matrix(431,-100,556,-129) -> Matrix(53,-4,464,-35) Matrix(121,-32,450,-119) -> Matrix(287,-22,3718,-285) Matrix(597,-164,506,-139) -> Matrix(77,-6,706,-55) Matrix(1013,-280,1458,-403) -> Matrix(179,-14,1854,-145) Matrix(1633,-456,684,-191) -> Matrix(51,-4,268,-21) Matrix(503,-142,712,-201) -> Matrix(127,-10,1232,-97) Matrix(117,-34,148,-43) -> Matrix(25,-2,188,-15) Matrix(145,-44,234,-71) -> Matrix(25,-2,238,-19) Matrix(141,-50,392,-139) -> Matrix(217,-18,2592,-215) Matrix(251,-92,472,-173) -> Matrix(47,-4,576,-49) Matrix(1861,-684,1140,-419) -> Matrix(47,-4,388,-33) Matrix(887,-328,1582,-585) -> Matrix(305,-26,3226,-275) Matrix(499,-186,110,-41) -> Matrix(93,-8,314,-27) Matrix(137,-52,166,-63) -> Matrix(23,-2,242,-21) Matrix(191,-74,302,-117) -> Matrix(45,-4,394,-35) Matrix(459,-188,188,-77) -> Matrix(1,0,-8,1) Matrix(859,-356,1344,-557) -> Matrix(49,-4,380,-31) Matrix(1633,-684,456,-191) -> Matrix(47,-4,200,-17) Matrix(3099,-1310,854,-361) -> Matrix(347,-28,1450,-117) Matrix(241,-102,26,-11) -> Matrix(49,-4,86,-7) Matrix(239,-104,370,-161) -> Matrix(23,-2,150,-13) Matrix(159,-70,184,-81) -> Matrix(23,-2,196,-17) Matrix(705,-322,208,-95) -> Matrix(111,-10,544,-49) Matrix(439,-206,130,-61) -> Matrix(43,-4,226,-21) Matrix(493,-268,344,-187) -> Matrix(43,-4,312,-29) Matrix(441,-244,244,-135) -> Matrix(1,0,-4,1) Matrix(1073,-600,828,-463) -> Matrix(43,-4,312,-29) Matrix(2969,-1666,1096,-615) -> Matrix(401,-38,2100,-199) Matrix(2793,-1576,778,-439) -> Matrix(19,-2,86,-9) Matrix(169,-98,288,-167) -> Matrix(101,-10,1000,-99) Matrix(1227,-748,520,-317) -> Matrix(73,-8,356,-39) Matrix(1861,-1140,684,-419) -> Matrix(35,-4,184,-21) Matrix(375,-232,118,-73) -> Matrix(19,-2,86,-9) Matrix(513,-322,94,-59) -> Matrix(109,-12,318,-35) Matrix(1879,-1200,440,-281) -> Matrix(31,-4,132,-17) Matrix(1111,-712,788,-505) -> Matrix(1,0,0,1) Matrix(531,-344,230,-149) -> Matrix(9,-2,50,-11) Matrix(585,-404,404,-279) -> Matrix(1,0,-4,1) Matrix(493,-344,268,-187) -> Matrix(39,-4,244,-25) Matrix(3187,-2246,1182,-833) -> Matrix(163,-16,866,-85) Matrix(2937,-2078,824,-583) -> Matrix(211,-22,892,-93) Matrix(1111,-788,712,-505) -> Matrix(1,0,0,1) Matrix(177,-128,242,-175) -> Matrix(55,-6,486,-53) Matrix(431,-330,64,-49) -> Matrix(11,-2,28,-5) Matrix(1073,-828,600,-463) -> Matrix(39,-4,244,-25) Matrix(1907,-1476,792,-613) -> Matrix(35,-4,184,-21) Matrix(469,-366,214,-167) -> Matrix(65,-8,382,-47) Matrix(439,-358,168,-137) -> Matrix(29,-2,160,-11) Matrix(597,-506,164,-139) -> Matrix(47,-6,196,-25) Matrix(283,-250,60,-53) -> Matrix(17,-2,60,-7) Matrix(159,-184,70,-81) -> Matrix(17,-2,94,-11) Matrix(1363,-1602,576,-677) -> Matrix(23,-2,104,-9) Matrix(137,-166,52,-63) -> Matrix(13,-2,72,-11) Matrix(117,-148,34,-43) -> Matrix(19,-2,86,-9) Matrix(431,-556,100,-129) -> Matrix(33,-4,124,-15) Matrix(99,-130,16,-21) -> Matrix(19,-2,48,-5) Matrix(177,-242,128,-175) -> Matrix(49,-6,384,-47) Matrix(503,-712,142,-201) -> Matrix(73,-10,314,-43) Matrix(2089,-2964,456,-647) -> Matrix(55,-8,172,-25) Matrix(3761,-5398,1560,-2239) -> Matrix(127,-18,628,-89) Matrix(3571,-5130,1482,-2129) -> Matrix(111,-16,562,-81) Matrix(1013,-1458,280,-403) -> Matrix(93,-14,392,-59) Matrix(899,-1304,202,-293) -> Matrix(5,-2,18,-7) Matrix(239,-370,104,-161) -> Matrix(21,-2,116,-11) Matrix(859,-1344,356,-557) -> Matrix(37,-4,176,-19) Matrix(191,-302,74,-117) -> Matrix(33,-4,190,-23) Matrix(145,-234,44,-71) -> Matrix(15,-2,68,-9) Matrix(1039,-1698,216,-353) -> Matrix(17,-2,60,-7) Matrix(101,-166,14,-23) -> Matrix(31,-4,70,-9) Matrix(169,-288,98,-167) -> Matrix(71,-10,490,-69) Matrix(1769,-3134,740,-1311) -> Matrix(13,-2,72,-11) Matrix(887,-1582,328,-585) -> Matrix(167,-26,880,-137) Matrix(567,-1028,230,-417) -> Matrix(13,-2,98,-15) Matrix(1601,-2958,374,-691) -> Matrix(121,-20,478,-79) Matrix(1479,-2740,346,-641) -> Matrix(83,-14,338,-57) Matrix(251,-472,92,-173) -> Matrix(19,-4,100,-21) Matrix(157,-338,72,-155) -> Matrix(85,-14,504,-83) Matrix(2913,-6626,812,-1847) -> Matrix(53,-10,228,-43) Matrix(3119,-7102,870,-1981) -> Matrix(23,-4,98,-17) Matrix(2439,-5618,1058,-2437) -> Matrix(485,-88,2662,-483) Matrix(625,-1466,136,-319) -> Matrix(31,-6,88,-17) Matrix(2027,-4774,442,-1041) -> Matrix(119,-24,362,-73) Matrix(4141,-9804,1140,-2699) -> Matrix(231,-52,964,-217) Matrix(2005,-4796,426,-1019) -> Matrix(13,-2,46,-7) Matrix(595,-1458,242,-593) -> Matrix(1,0,6,1) Matrix(2311,-6050,882,-2309) -> Matrix(661,-120,3630,-659) Matrix(545,-1468,62,-167) -> Matrix(203,-38,390,-73) Matrix(4173,-11294,1148,-3107) -> Matrix(1125,-214,4684,-891) Matrix(8045,-21784,2214,-5995) -> Matrix(2151,-410,8966,-1709) Matrix(1041,-2836,214,-583) -> Matrix(95,-18,322,-61) Matrix(141,-392,50,-139) -> Matrix(91,-18,450,-89) Matrix(523,-1682,162,-521) -> Matrix(37,-8,162,-35) Matrix(1417,-5042,292,-1039) -> Matrix(247,-58,856,-201) Matrix(1733,-6172,358,-1275) -> Matrix(229,-54,810,-191) Matrix(121,-450,32,-119) -> Matrix(89,-22,352,-87) Matrix(435,-1922,98,-433) -> Matrix(141,-40,490,-139) Matrix(941,-4418,200,-939) -> Matrix(9,-2,32,-7) Matrix(97,-512,18,-95) -> Matrix(79,-26,234,-77) Matrix(331,-2178,50,-329) -> Matrix(181,-72,450,-179) Matrix(69,-578,8,-67) -> Matrix(61,-30,120,-59) 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): 90 Degree of the the map X: 90 Degree of the the map Y: 180 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 180 Minimal number of generators: 31 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 18 Genus: 7 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/1 11/8 5/3 12/7 2/1 13/6 55/21 14/5 3/1 29/9 7/2 15/4 4/1 5/1 16/3 6/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 1/17 1/6 1/14 1/5 4/55 1/4 3/40 2/7 5/63 3/10 1/14 1/3 2/25 3/8 1/12 5/13 8/91 2/5 1/11 3/7 4/47 4/9 5/57 1/2 1/10 3/5 2/19 8/13 1/9 13/21 0/1 5/8 3/28 2/3 1/11 3/4 1/8 4/5 1/5 9/11 2/25 5/6 1/10 1/1 0/1 6/5 1/7 5/4 1/12 4/3 1/9 11/8 1/8 7/5 2/15 3/2 1/6 8/5 3/23 13/8 1/8 5/3 2/15 12/7 1/7 7/4 3/20 2/1 1/7 13/6 1/6 11/5 6/35 9/4 5/28 7/3 4/21 5/2 1/6 13/5 8/45 34/13 19/105 55/21 2/11 21/8 11/60 8/3 1/5 11/4 7/36 14/5 1/5 3/1 2/9 16/5 1/5 29/9 2/9 13/4 1/4 10/3 1/3 7/2 5/22 11/3 8/33 15/4 1/4 4/1 3/11 5/1 4/13 16/3 1/3 11/2 9/26 6/1 1/3 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(83,-13,32,-5) (0/1,1/6) -> (5/2,13/5) Hyperbolic Matrix(96,-17,17,-3) (1/6,1/5) -> (11/2,6/1) Hyperbolic Matrix(47,-11,30,-7) (1/5,1/4) -> (3/2,8/5) Hyperbolic Matrix(105,-29,29,-8) (1/4,2/7) -> (7/2,11/3) Hyperbolic Matrix(133,-39,58,-17) (2/7,3/10) -> (9/4,7/3) Hyperbolic Matrix(145,-44,234,-71) (3/10,1/3) -> (13/21,5/8) Hyperbolic Matrix(112,-41,41,-15) (1/3,3/8) -> (8/3,11/4) Hyperbolic Matrix(137,-52,166,-63) (3/8,5/13) -> (9/11,5/6) Hyperbolic Matrix(83,-32,13,-5) (5/13,2/5) -> (6/1,1/0) Hyperbolic Matrix(53,-22,41,-17) (2/5,3/7) -> (5/4,4/3) Hyperbolic Matrix(133,-58,39,-17) (3/7,4/9) -> (10/3,7/2) Hyperbolic Matrix(117,-53,53,-24) (4/9,1/2) -> (11/5,9/4) Hyperbolic Matrix(24,-13,13,-7) (1/2,3/5) -> (7/4,2/1) Hyperbolic Matrix(83,-51,70,-43) (3/5,8/13) -> (1/1,6/5) Hyperbolic Matrix(375,-232,118,-73) (8/13,13/21) -> (3/1,16/5) Hyperbolic Matrix(47,-30,11,-7) (5/8,2/3) -> (4/1,5/1) Hyperbolic Matrix(33,-23,23,-16) (2/3,3/4) -> (7/5,3/2) Hyperbolic Matrix(53,-41,22,-17) (3/4,4/5) -> (7/3,5/2) Hyperbolic Matrix(439,-358,168,-137) (4/5,9/11) -> (13/5,34/13) Hyperbolic Matrix(83,-70,51,-43) (5/6,1/1) -> (13/8,5/3) Hyperbolic Matrix(137,-166,52,-63) (6/5,5/4) -> (21/8,8/3) Hyperbolic Matrix(89,-121,64,-87) (4/3,11/8) -> (11/8,7/5) Parabolic Matrix(145,-234,44,-71) (8/5,13/8) -> (13/4,10/3) Hyperbolic Matrix(85,-144,49,-83) (5/3,12/7) -> (12/7,7/4) Parabolic Matrix(79,-169,36,-77) (2/1,13/6) -> (13/6,11/5) Parabolic Matrix(1156,-3025,441,-1154) (34/13,55/21) -> (55/21,21/8) Parabolic Matrix(71,-196,25,-69) (11/4,14/5) -> (14/5,3/1) Parabolic Matrix(262,-841,81,-260) (16/5,29/9) -> (29/9,13/4) Parabolic Matrix(61,-225,16,-59) (11/3,15/4) -> (15/4,4/1) Parabolic Matrix(49,-256,9,-47) (5/1,16/3) -> (16/3,11/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,17,1) Matrix(83,-13,32,-5) -> Matrix(43,-3,244,-17) Matrix(96,-17,17,-3) -> Matrix(71,-5,199,-14) Matrix(47,-11,30,-7) -> Matrix(13,-1,118,-9) Matrix(105,-29,29,-8) -> Matrix(64,-5,269,-21) Matrix(133,-39,58,-17) -> Matrix(37,-3,210,-17) Matrix(145,-44,234,-71) -> Matrix(25,-2,238,-19) Matrix(112,-41,41,-15) -> Matrix(59,-5,307,-26) Matrix(137,-52,166,-63) -> Matrix(23,-2,242,-21) Matrix(83,-32,13,-5) -> Matrix(34,-3,91,-8) Matrix(53,-22,41,-17) -> Matrix(12,-1,97,-8) Matrix(133,-58,39,-17) -> Matrix(34,-3,159,-14) Matrix(117,-53,53,-24) -> Matrix(56,-5,325,-29) Matrix(24,-13,13,-7) -> Matrix(11,-1,67,-6) Matrix(83,-51,70,-43) -> Matrix(9,-1,82,-9) Matrix(375,-232,118,-73) -> Matrix(19,-2,86,-9) Matrix(47,-30,11,-7) -> Matrix(8,-1,33,-4) Matrix(33,-23,23,-16) -> Matrix(10,-1,71,-7) Matrix(53,-41,22,-17) -> Matrix(9,-1,46,-5) Matrix(439,-358,168,-137) -> Matrix(29,-2,160,-11) Matrix(83,-70,51,-43) -> Matrix(8,-1,65,-8) Matrix(137,-166,52,-63) -> Matrix(13,-2,72,-11) Matrix(89,-121,64,-87) -> Matrix(25,-3,192,-23) Matrix(145,-234,44,-71) -> Matrix(15,-2,68,-9) Matrix(85,-144,49,-83) -> Matrix(36,-5,245,-34) Matrix(79,-169,36,-77) -> Matrix(43,-7,252,-41) Matrix(1156,-3025,441,-1154) -> Matrix(331,-60,1815,-329) Matrix(71,-196,25,-69) -> Matrix(46,-9,225,-44) Matrix(262,-841,81,-260) -> Matrix(19,-4,81,-17) Matrix(61,-225,16,-59) -> Matrix(45,-11,176,-43) Matrix(49,-256,9,-47) -> Matrix(40,-13,117,-38) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 1 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 1 Number of equivalence classes of cusps: 1 Genus: 0 Degree of H/liftables -> H/(image of liftables): 90 ----------------------------------------------------------------------- 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 17 1 1/1 0/1 1 19 6/5 1/7 1 19 5/4 1/12 1 19 4/3 1/9 1 19 11/8 1/8 3 1 3/2 1/6 1 19 8/5 3/23 1 19 13/8 1/8 1 19 5/3 2/15 1 19 12/7 1/7 5 1 2/1 1/7 1 19 13/6 1/6 7 1 9/4 5/28 1 19 7/3 4/21 1 19 5/2 1/6 1 19 13/5 8/45 1 19 55/21 2/11 15 1 21/8 11/60 1 19 8/3 1/5 1 19 14/5 1/5 9 1 3/1 2/9 1 19 29/9 2/9 1 1 13/4 1/4 1 19 10/3 1/3 1 19 7/2 5/22 1 19 15/4 1/4 11 1 4/1 3/11 1 19 5/1 4/13 1 19 16/3 1/3 13 1 6/1 1/3 1 19 1/0 1/0 1 19 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(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(70,-83,43,-51) (1/1,6/5) -> (13/8,5/3) Glide Reflection Matrix(137,-166,52,-63) (6/5,5/4) -> (21/8,8/3) Hyperbolic Matrix(41,-53,17,-22) (5/4,4/3) -> (7/3,5/2) Glide Reflection Matrix(65,-88,48,-65) (4/3,11/8) -> (4/3,11/8) Reflection Matrix(23,-33,16,-23) (11/8,3/2) -> (11/8,3/2) Reflection Matrix(30,-47,7,-11) (3/2,8/5) -> (4/1,5/1) Glide Reflection Matrix(145,-234,44,-71) (8/5,13/8) -> (13/4,10/3) Hyperbolic Matrix(71,-120,42,-71) (5/3,12/7) -> (5/3,12/7) Reflection Matrix(13,-24,7,-13) (12/7,2/1) -> (12/7,2/1) Reflection Matrix(25,-52,12,-25) (2/1,13/6) -> (2/1,13/6) Reflection Matrix(53,-117,24,-53) (13/6,9/4) -> (13/6,9/4) Reflection Matrix(58,-133,17,-39) (9/4,7/3) -> (10/3,7/2) Glide Reflection Matrix(32,-83,5,-13) (5/2,13/5) -> (6/1,1/0) Glide Reflection Matrix(274,-715,105,-274) (13/5,55/21) -> (13/5,55/21) Reflection Matrix(881,-2310,336,-881) (55/21,21/8) -> (55/21,21/8) Reflection Matrix(41,-112,15,-41) (8/3,14/5) -> (8/3,14/5) Reflection Matrix(29,-84,10,-29) (14/5,3/1) -> (14/5,3/1) Reflection Matrix(28,-87,9,-28) (3/1,29/9) -> (3/1,29/9) Reflection Matrix(233,-754,72,-233) (29/9,13/4) -> (29/9,13/4) Reflection Matrix(29,-105,8,-29) (7/2,15/4) -> (7/2,15/4) Reflection Matrix(31,-120,8,-31) (15/4,4/1) -> (15/4,4/1) Reflection Matrix(31,-160,6,-31) (5/1,16/3) -> (5/1,16/3) Reflection Matrix(17,-96,3,-17) (16/3,6/1) -> (16/3,6/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(0,1,1,0) -> Matrix(1,0,17,-1) (-1/1,1/1) -> (0/1,2/17) Matrix(70,-83,43,-51) -> Matrix(9,-1,71,-8) Matrix(137,-166,52,-63) -> Matrix(13,-2,72,-11) 1/6 Matrix(41,-53,17,-22) -> Matrix(8,-1,39,-5) Matrix(65,-88,48,-65) -> Matrix(17,-2,144,-17) (4/3,11/8) -> (1/9,1/8) Matrix(23,-33,16,-23) -> Matrix(7,-1,48,-7) (11/8,3/2) -> (1/8,1/6) Matrix(30,-47,7,-11) -> Matrix(9,-1,35,-4) Matrix(145,-234,44,-71) -> Matrix(15,-2,68,-9) Matrix(71,-120,42,-71) -> Matrix(29,-4,210,-29) (5/3,12/7) -> (2/15,1/7) Matrix(13,-24,7,-13) -> Matrix(6,-1,35,-6) (12/7,2/1) -> (1/7,1/5) Matrix(25,-52,12,-25) -> Matrix(13,-2,84,-13) (2/1,13/6) -> (1/7,1/6) Matrix(53,-117,24,-53) -> Matrix(29,-5,168,-29) (13/6,9/4) -> (1/6,5/28) Matrix(58,-133,17,-39) -> Matrix(17,-3,79,-14) Matrix(32,-83,5,-13) -> Matrix(17,-3,45,-8) Matrix(274,-715,105,-274) -> Matrix(89,-16,495,-89) (13/5,55/21) -> (8/45,2/11) Matrix(881,-2310,336,-881) -> Matrix(241,-44,1320,-241) (55/21,21/8) -> (2/11,11/60) Matrix(41,-112,15,-41) -> Matrix(26,-5,135,-26) (8/3,14/5) -> (5/27,1/5) Matrix(29,-84,10,-29) -> Matrix(19,-4,90,-19) (14/5,3/1) -> (1/5,2/9) Matrix(28,-87,9,-28) -> Matrix(1,0,9,-1) (3/1,29/9) -> (0/1,2/9) Matrix(233,-754,72,-233) -> Matrix(17,-4,72,-17) (29/9,13/4) -> (2/9,1/4) Matrix(29,-105,8,-29) -> Matrix(21,-5,88,-21) (7/2,15/4) -> (5/22,1/4) Matrix(31,-120,8,-31) -> Matrix(23,-6,88,-23) (15/4,4/1) -> (1/4,3/11) Matrix(31,-160,6,-31) -> Matrix(25,-8,78,-25) (5/1,16/3) -> (4/13,1/3) Matrix(17,-96,3,-17) -> Matrix(14,-5,39,-14) (16/3,6/1) -> (1/3,5/13) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.