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 1/4 -7/15 1/4 -6/13 2/7 1/3 -5/11 1/2 -9/20 1/4 -4/9 0/1 1/3 -11/25 1/4 -18/41 0/1 1/4 -7/16 1/4 -10/23 1/4 2/7 -3/7 1/4 -11/26 3/8 -19/45 3/8 -8/19 1/3 1/2 -13/31 1/2 -5/12 1/4 -12/29 0/1 1/3 -7/17 1/2 -16/39 0/1 1/2 -9/22 1/4 -2/5 0/1 1/3 -9/23 1/2 -7/18 1/2 -5/13 1/4 -13/34 3/10 -21/55 1/2 -8/21 0/1 1/2 -11/29 1/4 -14/37 0/1 1/4 -17/45 1/4 -3/8 1/4 -10/27 2/7 1/3 -7/19 3/10 -4/11 1/3 2/5 -17/47 3/8 -13/36 5/12 -9/25 1/2 -5/14 1/2 -11/31 1/2 -6/17 1/2 1/1 -1/3 1/4 -5/16 1/2 -4/13 1/2 1/1 -7/23 1/2 -10/33 0/1 1/0 -3/10 1/2 -5/17 1/4 -7/24 1/2 -2/7 0/1 1/3 -9/32 1/4 -7/25 1/4 -5/18 1/2 -8/29 1/3 2/5 -3/11 1/4 -4/15 1/3 3/8 -5/19 1/2 -1/4 1/2 -4/17 1/2 2/3 -7/30 1/2 -10/43 0/1 1/1 -13/56 1/2 -3/13 1/2 -5/22 3/4 -2/9 0/1 1/1 -5/23 1/0 -13/60 1/0 -8/37 -3/1 1/0 -3/14 1/0 -7/33 -1/2 -4/19 -1/4 0/1 -1/5 1/4 -5/26 5/16 -4/21 1/3 4/11 -3/16 3/8 -2/11 1/3 1/2 -5/28 3/8 -3/17 1/2 -1/6 1/2 -2/13 1/1 1/0 -1/7 1/0 -1/8 1/2 -2/17 0/1 1/0 -3/26 1/8 -1/9 1/4 0/1 0/1 1/2 1/7 1/0 1/6 1/2 3/17 1/0 2/11 -1/2 0/1 3/16 0/1 1/5 1/4 5/24 1/2 4/19 0/1 1/2 3/14 1/6 5/23 1/4 2/9 1/4 1/3 3/13 1/2 4/17 0/1 1/3 1/4 1/2 4/15 1/2 7/26 1/2 3/11 1/2 8/29 1/2 2/3 5/18 3/4 7/25 1/0 2/7 1/2 1/1 3/10 3/4 1/3 1/0 5/14 0/1 9/25 1/16 4/11 0/1 1/8 11/30 1/6 7/19 1/6 10/27 0/1 1/6 3/8 1/4 5/13 1/4 2/5 0/1 1/3 7/17 3/8 12/29 1/3 2/5 5/12 3/8 13/31 1/2 8/19 3/7 1/2 19/45 7/16 11/26 1/2 3/7 1/2 7/16 1/2 4/9 2/5 1/2 9/20 1/2 5/11 1/2 6/13 1/2 1/2 1/2 8/15 2/3 3/4 7/13 3/4 6/11 2/3 1/1 11/20 3/4 5/9 1/2 14/25 1/2 2/3 23/41 1/2 9/16 3/4 22/39 1/2 2/3 13/23 7/10 4/7 3/4 1/1 7/12 1/1 10/17 1/1 5/4 3/5 1/0 14/23 0/1 1/2 11/18 1/2 19/31 3/4 8/13 2/3 1/1 13/21 3/2 5/8 1/2 17/27 5/4 12/19 1/1 2/1 7/11 1/0 23/36 1/0 16/25 0/1 1/1 9/14 1/0 11/17 1/0 2/3 0/1 1/1 11/16 1/2 9/13 1/0 25/36 1/2 16/23 0/1 1/0 7/10 1/2 19/27 1/0 31/44 1/0 12/17 -1/1 1/0 29/41 -1/2 17/24 1/0 5/7 1/0 8/11 0/1 11/15 1/4 3/4 1/2 13/17 1/0 10/13 0/1 1/4 17/22 1/4 24/31 0/1 1/3 7/9 1/2 18/23 0/1 1/3 11/14 1/4 4/5 1/3 1/2 9/11 1/2 5/6 1/2 11/13 1/2 6/7 2/3 3/4 7/8 3/4 1/1 1/0 7/6 1/2 20/17 0/1 1/4 13/11 1/4 6/5 1/3 1/2 5/4 1/2 9/7 1/2 22/17 1/2 2/3 35/27 1/2 13/10 5/8 4/3 2/3 1/1 11/8 1/1 18/13 1/1 8/7 7/5 3/2 31/22 3/2 24/17 1/1 2/1 17/12 1/0 44/31 0/1 1/0 27/19 1/2 10/7 1/1 2/1 33/23 1/0 56/39 1/1 23/16 3/2 13/9 1/0 29/20 1/2 16/11 1/1 3/2 3/2 1/0 14/9 0/1 1/0 39/25 1/2 25/16 1/2 11/7 1/0 8/5 0/1 1/2 13/8 3/2 31/19 1/0 49/30 1/0 18/11 3/1 1/0 5/3 1/0 12/7 0/1 19/11 1/4 7/4 1/2 23/13 3/4 39/22 1/0 16/9 0/1 1/0 25/14 1/2 34/19 0/1 1/2 9/5 1/2 29/16 3/4 20/11 1/1 2/1 11/6 1/2 24/13 0/1 1/0 37/20 0/1 13/7 1/2 2/1 0/1 1/1 13/6 0/1 24/11 0/1 1/3 11/5 1/2 20/9 1/2 1/1 9/4 1/0 25/11 -1/2 66/29 0/1 41/18 1/6 16/7 0/1 1/2 23/10 1/2 53/23 0/1 83/36 1/4 30/13 0/1 1/3 7/3 1/2 40/17 1/2 33/14 1/2 26/11 1/2 2/3 71/30 5/8 45/19 1/2 19/8 3/4 31/13 1/2 43/18 5/6 55/23 9/10 12/5 0/1 1/1 53/22 1/2 94/39 1/1 41/17 1/0 29/12 1/2 17/7 1/2 22/9 4/5 1/1 27/11 1/1 32/13 1/1 6/5 5/2 1/0 23/9 -1/2 41/16 0/1 18/7 0/1 1/4 13/5 1/2 34/13 5/11 1/2 55/21 1/2 76/29 1/2 13/25 21/8 1/2 8/3 1/2 1/1 35/13 1/2 62/23 1/2 7/13 27/10 1/2 46/17 5/8 2/3 111/41 2/3 65/24 7/10 19/7 3/4 49/18 1/2 79/29 3/4 30/11 2/3 1/1 41/15 3/4 11/4 3/4 14/5 1/1 17/6 5/4 3/1 1/0 16/5 4/5 1/1 29/9 1/1 42/13 1/1 14/13 13/4 5/4 10/3 2/1 1/0 27/8 1/0 44/13 1/0 17/5 1/0 7/2 1/0 32/9 -1/1 0/1 89/25 0/1 57/16 1/0 25/7 -1/2 43/12 -1/4 104/29 0/1 61/17 1/4 18/5 0/1 1/0 47/13 1/2 29/8 1/0 69/19 -1/2 109/30 -1/4 149/41 0/1 40/11 0/1 1/2 11/3 1/0 15/4 0/1 19/5 1/2 4/1 0/1 1/1 17/4 1/0 47/11 1/0 77/18 0/1 30/7 0/1 1/2 13/3 1/2 22/5 3/4 1/1 31/7 1/1 40/9 1/1 5/4 9/2 1/0 32/7 0/1 1/2 55/12 1/2 78/17 1/2 23/5 1/2 14/3 2/3 1/1 47/10 1/1 80/17 1/1 16/15 33/7 7/6 19/4 3/2 24/5 1/1 1/0 29/6 1/0 63/13 0/1 34/7 0/1 1/1 5/1 1/2 16/3 1/1 27/5 11/10 11/2 5/4 17/3 3/2 6/1 1/1 2/1 13/2 7/4 33/5 2/1 53/8 25/12 20/3 2/1 9/4 7/1 1/0 8/1 5/1 1/0 17/2 1/0 26/3 -13/1 1/0 9/1 1/0 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(1,0,4,1) Matrix(503,236,714,335) -> Matrix(15,-4,4,-1) Matrix(281,130,-776,-359) -> Matrix(13,-4,36,-11) Matrix(353,162,560,257) -> Matrix(13,-4,10,-3) Matrix(829,374,348,157) -> Matrix(5,-2,8,-3) Matrix(139,62,204,91) -> Matrix(1,0,-2,1) Matrix(271,120,70,31) -> Matrix(1,0,-2,1) Matrix(1219,536,680,299) -> Matrix(1,0,-2,1) Matrix(269,118,1288,565) -> Matrix(1,0,-2,1) Matrix(271,118,604,263) -> Matrix(15,-4,34,-9) Matrix(539,234,-1412,-613) -> Matrix(7,-2,18,-5) Matrix(197,84,68,29) -> Matrix(7,-2,4,-1) Matrix(1577,666,1120,473) -> Matrix(1,0,-2,1) Matrix(721,304,1710,721) -> Matrix(3,-2,8,-5) Matrix(395,166,-1116,-469) -> Matrix(5,-2,8,-3) Matrix(67,28,390,163) -> Matrix(1,0,-2,1) Matrix(391,162,712,295) -> Matrix(5,-2,8,-3) Matrix(905,374,196,81) -> Matrix(5,-2,8,-3) Matrix(901,370,-2384,-979) -> Matrix(1,0,2,1) Matrix(835,342,1482,607) -> Matrix(5,-2,8,-3) Matrix(451,184,576,235) -> Matrix(1,0,0,1) Matrix(311,122,752,295) -> Matrix(7,-2,18,-5) Matrix(313,122,372,145) -> Matrix(5,-2,8,-3) Matrix(433,168,250,97) -> Matrix(1,0,0,1) Matrix(737,282,1048,401) -> Matrix(7,-2,4,-1) Matrix(309,118,-1600,-611) -> Matrix(5,-2,18,-7) Matrix(121,46,676,257) -> Matrix(1,0,-4,1) Matrix(491,186,916,347) -> Matrix(5,-2,8,-3) Matrix(609,230,-2624,-991) -> Matrix(1,0,-2,1) Matrix(59,22,244,91) -> Matrix(7,-2,18,-5) Matrix(665,246,1084,401) -> Matrix(1,0,-2,1) Matrix(419,154,302,111) -> Matrix(19,-6,16,-5) Matrix(177,64,-1546,-559) -> Matrix(5,-2,28,-11) Matrix(949,342,1368,493) -> Matrix(5,-2,-2,1) Matrix(295,106,654,235) -> Matrix(3,-2,8,-5) Matrix(473,168,-2182,-775) -> Matrix(7,-4,2,-1) Matrix(233,82,412,145) -> Matrix(1,-2,2,-3) Matrix(389,122,220,69) -> Matrix(5,-2,8,-3) Matrix(167,52,-774,-241) -> Matrix(5,-2,-2,1) Matrix(603,184,272,83) -> Matrix(1,0,0,1) Matrix(1965,596,544,165) -> Matrix(1,0,0,1) Matrix(53,16,-434,-131) -> Matrix(1,0,0,1) Matrix(161,48,218,65) -> Matrix(1,0,0,1) Matrix(965,282,592,173) -> Matrix(7,-2,4,-1) Matrix(215,62,52,15) -> Matrix(1,0,-2,1) Matrix(369,104,-1586,-447) -> Matrix(1,0,-2,1) Matrix(1587,446,580,163) -> Matrix(5,-2,8,-3) Matrix(581,162,104,29) -> Matrix(13,-4,10,-3) Matrix(159,44,-842,-233) -> Matrix(7,-2,18,-5) Matrix(893,246,628,173) -> Matrix(1,0,-2,1) Matrix(155,42,262,71) -> Matrix(7,-2,4,-1) Matrix(309,82,260,69) -> Matrix(5,-2,18,-7) Matrix(619,162,256,67) -> Matrix(5,-2,8,-3) Matrix(499,118,148,35) -> Matrix(7,-4,2,-1) Matrix(1143,268,644,151) -> Matrix(3,-2,2,-1) Matrix(5249,1220,2276,529) -> Matrix(1,0,2,1) Matrix(149,34,688,157) -> Matrix(3,-2,14,-9) Matrix(539,122,296,67) -> Matrix(3,-2,2,-1) Matrix(291,64,50,11) -> Matrix(3,-2,2,-1) Matrix(5337,1156,2036,441) -> Matrix(1,-10,2,-19) Matrix(1257,268,530,113) -> Matrix(3,2,4,3) Matrix(1203,254,772,163) -> Matrix(1,0,4,1) Matrix(191,40,530,111) -> Matrix(1,0,12,1) Matrix(1365,262,422,81) -> Matrix(31,-10,28,-9) Matrix(419,78,188,35) -> Matrix(5,-2,8,-3) Matrix(881,158,184,33) -> Matrix(1,0,-2,1) Matrix(1201,214,926,165) -> Matrix(9,-4,16,-7) Matrix(137,24,508,89) -> Matrix(13,-6,24,-11) Matrix(135,22,92,15) -> Matrix(3,-2,2,-1) Matrix(225,34,536,81) -> Matrix(1,2,2,5) Matrix(219,28,86,11) -> Matrix(1,0,-2,1) Matrix(1421,166,214,25) -> Matrix(9,2,4,1) Matrix(423,44,298,31) -> Matrix(1,0,-2,1) Matrix(101,-14,166,-23) -> Matrix(1,0,0,1) Matrix(99,-16,130,-21) -> Matrix(1,0,0,1) Matrix(739,-136,288,-53) -> Matrix(1,0,6,1) Matrix(573,-110,224,-43) -> Matrix(1,0,-6,1) Matrix(2141,-444,786,-163) -> Matrix(5,-2,8,-3) Matrix(1003,-212,440,-93) -> Matrix(1,0,0,1) Matrix(499,-110,186,-41) -> Matrix(1,0,-2,1) Matrix(403,-92,92,-21) -> Matrix(5,-2,8,-3) Matrix(431,-100,556,-129) -> Matrix(1,0,0,1) Matrix(121,-32,450,-119) -> Matrix(17,-8,32,-15) Matrix(597,-164,506,-139) -> Matrix(3,-2,14,-9) Matrix(1013,-280,1458,-403) -> Matrix(3,-2,2,-1) Matrix(1633,-456,684,-191) -> Matrix(1,-2,2,-3) Matrix(503,-142,712,-201) -> Matrix(1,0,-2,1) Matrix(117,-34,148,-43) -> Matrix(3,-2,8,-5) Matrix(145,-44,234,-71) -> Matrix(3,-2,2,-1) Matrix(141,-50,392,-139) -> Matrix(1,0,16,1) Matrix(251,-92,472,-173) -> Matrix(13,-2,20,-3) Matrix(1861,-684,1140,-419) -> Matrix(11,-2,6,-1) Matrix(887,-328,1582,-585) -> Matrix(13,-2,20,-3) Matrix(499,-186,110,-41) -> Matrix(1,0,-4,1) Matrix(137,-52,166,-63) -> Matrix(9,-2,14,-3) Matrix(191,-74,302,-117) -> Matrix(7,-2,4,-1) Matrix(459,-188,188,-77) -> Matrix(11,-4,14,-5) Matrix(859,-356,1344,-557) -> Matrix(5,-2,8,-3) Matrix(1633,-684,456,-191) -> Matrix(5,-2,-12,5) Matrix(3099,-1310,854,-361) -> Matrix(9,-4,-2,1) Matrix(241,-102,26,-11) -> Matrix(9,-4,-2,1) Matrix(239,-104,370,-161) -> Matrix(1,0,-2,1) Matrix(159,-70,184,-81) -> Matrix(11,-4,14,-5) Matrix(705,-322,208,-95) -> Matrix(13,-6,-2,1) Matrix(439,-206,130,-61) -> Matrix(11,-6,2,-1) Matrix(493,-268,344,-187) -> Matrix(5,-4,4,-3) Matrix(441,-244,244,-135) -> Matrix(1,0,0,1) Matrix(1073,-600,828,-463) -> Matrix(1,0,0,1) Matrix(2969,-1666,1096,-615) -> Matrix(13,-8,18,-11) Matrix(2793,-1576,778,-439) -> Matrix(3,-2,2,-1) Matrix(169,-98,288,-167) -> Matrix(9,-8,8,-7) Matrix(1227,-748,520,-317) -> Matrix(5,-2,8,-3) Matrix(1861,-1140,684,-419) -> Matrix(1,0,0,1) Matrix(375,-232,118,-73) -> Matrix(1,-2,2,-3) Matrix(513,-322,94,-59) -> Matrix(7,-6,6,-5) Matrix(1879,-1200,440,-281) -> Matrix(1,0,0,1) Matrix(1111,-712,788,-505) -> Matrix(3,-2,2,-1) Matrix(531,-344,230,-149) -> Matrix(1,0,2,1) Matrix(585,-404,404,-279) -> Matrix(1,0,0,1) Matrix(493,-344,268,-187) -> Matrix(1,0,0,1) Matrix(3187,-2246,1182,-833) -> Matrix(1,-6,2,-11) Matrix(2937,-2078,824,-583) -> Matrix(1,0,0,1) Matrix(1111,-788,712,-505) -> Matrix(1,0,2,1) Matrix(177,-128,242,-175) -> Matrix(1,0,4,1) Matrix(431,-330,64,-49) -> Matrix(1,2,0,1) Matrix(1073,-828,600,-463) -> Matrix(1,0,-2,1) Matrix(1907,-1476,792,-613) -> Matrix(1,0,-2,1) Matrix(469,-366,214,-167) -> Matrix(1,0,0,1) Matrix(439,-358,168,-137) -> Matrix(7,-4,16,-9) Matrix(597,-506,164,-139) -> Matrix(3,-2,2,-1) Matrix(283,-250,60,-53) -> Matrix(7,-6,6,-5) Matrix(159,-184,70,-81) -> Matrix(1,0,-2,1) Matrix(1363,-1602,576,-677) -> Matrix(9,-2,14,-3) Matrix(137,-166,52,-63) -> Matrix(5,-2,8,-3) Matrix(117,-148,34,-43) -> Matrix(3,-2,2,-1) Matrix(431,-556,100,-129) -> Matrix(3,-2,8,-5) Matrix(99,-130,16,-21) -> Matrix(5,-4,4,-3) Matrix(177,-242,128,-175) -> Matrix(11,-10,10,-9) Matrix(503,-712,142,-201) -> Matrix(1,-2,0,1) Matrix(2089,-2964,456,-647) -> Matrix(1,0,2,1) Matrix(3761,-5398,1560,-2239) -> Matrix(1,0,0,1) Matrix(3571,-5130,1482,-2129) -> Matrix(3,-4,4,-5) Matrix(1013,-1458,280,-403) -> Matrix(1,-2,2,-3) Matrix(899,-1304,202,-293) -> Matrix(3,-2,2,-1) Matrix(239,-370,104,-161) -> Matrix(1,0,2,1) Matrix(859,-1344,356,-557) -> Matrix(1,0,0,1) Matrix(191,-302,74,-117) -> Matrix(1,0,2,1) Matrix(145,-234,44,-71) -> Matrix(3,-2,2,-1) Matrix(1039,-1698,216,-353) -> Matrix(1,-2,0,1) Matrix(101,-166,14,-23) -> Matrix(1,2,0,1) Matrix(169,-288,98,-167) -> Matrix(1,0,4,1) Matrix(1769,-3134,740,-1311) -> Matrix(5,-6,6,-7) Matrix(887,-1582,328,-585) -> Matrix(5,-2,8,-3) Matrix(567,-1028,230,-417) -> Matrix(5,-4,4,-3) Matrix(1601,-2958,374,-691) -> Matrix(1,0,2,1) Matrix(1479,-2740,346,-641) -> Matrix(1,0,-2,1) Matrix(251,-472,92,-173) -> Matrix(1,-2,2,-3) Matrix(157,-338,72,-155) -> Matrix(1,0,2,1) Matrix(2913,-6626,812,-1847) -> Matrix(1,0,6,1) Matrix(3119,-7102,870,-1981) -> Matrix(1,0,-10,1) Matrix(2439,-5618,1058,-2437) -> Matrix(1,0,2,1) Matrix(625,-1466,136,-319) -> Matrix(1,0,0,1) Matrix(2027,-4774,442,-1041) -> Matrix(7,-4,16,-9) Matrix(4141,-9804,1140,-2699) -> Matrix(3,-2,-4,3) Matrix(2005,-4796,426,-1019) -> Matrix(17,-16,16,-15) Matrix(595,-1458,242,-593) -> Matrix(11,-10,10,-9) Matrix(2311,-6050,882,-2309) -> Matrix(37,-18,72,-35) Matrix(545,-1468,62,-167) -> Matrix(13,-6,-2,1) Matrix(4173,-11294,1148,-3107) -> Matrix(3,-2,14,-9) Matrix(8045,-21784,2214,-5995) -> Matrix(3,-2,-22,15) Matrix(1041,-2836,214,-583) -> Matrix(3,-2,2,-1) Matrix(141,-392,50,-139) -> Matrix(9,-8,8,-7) Matrix(523,-1682,162,-521) -> Matrix(19,-18,18,-17) Matrix(1417,-5042,292,-1039) -> Matrix(1,0,2,1) Matrix(1733,-6172,358,-1275) -> Matrix(1,0,0,1) Matrix(121,-450,32,-119) -> Matrix(1,0,2,1) Matrix(435,-1922,98,-433) -> Matrix(9,-8,8,-7) Matrix(941,-4418,200,-939) -> Matrix(19,-18,18,-17) Matrix(97,-512,18,-95) -> Matrix(13,-12,12,-11) Matrix(331,-2178,50,-329) -> Matrix(33,-64,16,-31) Matrix(69,-578,8,-67) -> Matrix(1,-18,0,1) 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): 48 Degree of the the map X: 48 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): 540 Minimal number of generators: 91 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: 36 Genus: 28 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 0/1 3/16 4/15 5/14 6/13 1/2 7/12 8/11 4/5 1/1 11/8 56/39 3/2 5/3 12/7 2/1 13/6 66/29 40/17 12/5 5/2 55/21 8/3 14/5 3/1 29/9 10/3 7/2 18/5 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 -1/2 1/4 -5/11 1/2 -4/9 0/1 1/3 -11/25 1/4 -18/41 0/1 1/4 -7/16 1/4 -10/23 1/4 2/7 -3/7 1/4 -5/12 1/4 -7/17 1/2 -9/22 1/4 -2/5 0/1 1/3 -3/8 1/4 -7/19 3/10 -4/11 1/3 2/5 -5/14 1/2 -1/3 1/4 -2/7 0/1 1/3 -5/18 1/2 -3/11 1/4 -4/15 1/3 3/8 -1/4 1/2 -3/13 1/2 -2/9 0/1 1/1 -5/23 1/0 -3/14 1/0 -7/33 -1/2 -4/19 -1/4 0/1 -1/5 1/4 -1/6 1/2 -1/7 1/0 -1/8 1/2 0/1 0/1 1/2 1/7 1/0 1/6 1/2 3/17 1/0 2/11 -1/2 0/1 3/16 0/1 1/5 1/4 5/24 1/2 4/19 0/1 1/2 3/14 1/6 5/23 1/4 2/9 1/4 1/3 1/4 1/2 4/15 1/2 3/11 1/2 5/18 3/4 7/25 1/0 2/7 1/2 1/1 3/10 3/4 1/3 1/0 5/14 0/1 9/25 1/16 4/11 0/1 1/8 7/19 1/6 3/8 1/4 5/13 1/4 2/5 0/1 1/3 3/7 1/2 4/9 2/5 1/2 9/20 1/2 5/11 1/2 6/13 1/2 1/2 1/2 7/13 3/4 6/11 2/3 1/1 11/20 3/4 5/9 1/2 4/7 3/4 1/1 7/12 1/1 10/17 1/1 5/4 3/5 1/0 14/23 0/1 1/2 11/18 1/2 19/31 3/4 8/13 2/3 1/1 13/21 3/2 5/8 1/2 2/3 0/1 1/1 7/10 1/2 19/27 1/0 31/44 1/0 12/17 -1/1 1/0 17/24 1/0 5/7 1/0 8/11 0/1 3/4 1/2 10/13 0/1 1/4 17/22 1/4 7/9 1/2 18/23 0/1 1/3 11/14 1/4 4/5 1/3 1/2 9/11 1/2 5/6 1/2 1/1 1/0 7/6 1/2 13/11 1/4 6/5 1/3 1/2 5/4 1/2 4/3 2/3 1/1 11/8 1/1 18/13 1/1 8/7 7/5 3/2 10/7 1/1 2/1 33/23 1/0 56/39 1/1 23/16 3/2 13/9 1/0 16/11 1/1 3/2 3/2 1/0 14/9 0/1 1/0 39/25 1/2 25/16 1/2 11/7 1/0 8/5 0/1 1/2 13/8 3/2 5/3 1/0 12/7 0/1 7/4 1/2 23/13 3/4 39/22 1/0 16/9 0/1 1/0 25/14 1/2 34/19 0/1 1/2 9/5 1/2 2/1 0/1 1/1 13/6 0/1 24/11 0/1 1/3 11/5 1/2 20/9 1/2 1/1 9/4 1/0 25/11 -1/2 66/29 0/1 41/18 1/6 16/7 0/1 1/2 7/3 1/2 40/17 1/2 33/14 1/2 26/11 1/2 2/3 45/19 1/2 19/8 3/4 31/13 1/2 43/18 5/6 55/23 9/10 12/5 0/1 1/1 5/2 1/0 23/9 -1/2 41/16 0/1 18/7 0/1 1/4 13/5 1/2 34/13 5/11 1/2 55/21 1/2 76/29 1/2 13/25 21/8 1/2 8/3 1/2 1/1 35/13 1/2 62/23 1/2 7/13 27/10 1/2 19/7 3/4 11/4 3/4 14/5 1/1 3/1 1/0 16/5 4/5 1/1 29/9 1/1 42/13 1/1 14/13 13/4 5/4 10/3 2/1 1/0 7/2 1/0 18/5 0/1 1/0 11/3 1/0 15/4 0/1 19/5 1/2 4/1 0/1 1/1 5/1 1/2 16/3 1/1 11/2 5/4 17/3 3/2 6/1 1/1 2/1 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(209,96,37,17) (-1/2,-5/11) -> (11/2,17/3) Hyperbolic Matrix(67,30,-239,-107) (-5/11,-4/9) -> (-2/7,-5/18) 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(1009,438,569,247) (-10/23,-3/7) -> (39/22,16/9) Hyperbolic Matrix(265,112,97,41) (-3/7,-5/12) -> (19/7,11/4) Hyperbolic Matrix(455,188,743,307) (-5/12,-7/17) -> (11/18,19/31) Hyperbolic Matrix(127,52,613,251) (-7/17,-9/22) -> (1/5,5/24) Hyperbolic Matrix(451,184,576,235) (-9/22,-2/5) -> (18/23,11/14) Hyperbolic Matrix(61,24,33,13) (-2/5,-3/8) -> (9/5,2/1) Hyperbolic Matrix(183,68,331,123) (-3/8,-7/19) -> (11/20,5/9) Hyperbolic Matrix(419,154,302,111) (-7/19,-4/11) -> (18/13,7/5) Hyperbolic Matrix(61,22,-269,-97) (-4/11,-5/14) -> (-3/13,-2/9) Hyperbolic Matrix(57,20,265,93) (-5/14,-1/3) -> (3/14,5/23) Hyperbolic Matrix(55,16,79,23) (-1/3,-2/7) -> (2/3,7/10) Hyperbolic Matrix(683,188,287,79) (-5/18,-3/11) -> (19/8,31/13) Hyperbolic Matrix(155,42,262,71) (-3/11,-4/15) -> (10/17,3/5) Hyperbolic Matrix(259,68,179,47) (-4/15,-1/4) -> (13/9,16/11) Hyperbolic Matrix(101,24,223,53) (-1/4,-3/13) -> (9/20,5/11) Hyperbolic Matrix(291,64,50,11) (-2/9,-5/23) -> (17/3,6/1) Hyperbolic Matrix(871,188,1237,267) (-5/23,-3/14) -> (19/27,31/44) 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(45,8,163,29) (-1/5,-1/6) -> (3/11,5/18) Hyperbolic Matrix(133,20,113,17) (-1/6,-1/7) -> (7/6,13/11) Hyperbolic Matrix(219,28,86,11) (-1/7,-1/8) -> (5/2,23/9) Hyperbolic Matrix(253,26,107,11) (-1/8,0/1) -> (26/11,45/19) Hyperbolic Matrix(101,-14,166,-23) (0/1,1/7) -> (3/5,14/23) Hyperbolic Matrix(67,-10,181,-27) (1/7,1/6) -> (7/19,3/8) Hyperbolic Matrix(485,-84,179,-31) (1/6,3/17) -> (27/10,19/7) Hyperbolic Matrix(547,-98,307,-55) (3/17,2/11) -> (16/9,25/14) 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(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(61,-14,109,-25) (2/9,1/4) -> (5/9,4/7) Hyperbolic Matrix(61,-16,225,-59) (1/4,4/15) -> (4/15,3/11) Parabolic Matrix(1633,-456,684,-191) (5/18,7/25) -> (31/13,43/18) Hyperbolic Matrix(563,-158,253,-71) (7/25,2/7) -> (20/9,9/4) 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(223,-82,291,-107) (4/11,7/19) -> (3/4,10/13) 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(79,-36,169,-77) (5/11,6/13) -> (6/13,1/2) Parabolic Matrix(125,-66,161,-85) (1/2,7/13) -> (17/22,7/9) Hyperbolic Matrix(493,-268,344,-187) (7/13,6/11) -> (10/7,33/23) Hyperbolic Matrix(369,-202,601,-329) (6/11,11/20) -> (19/31,8/13) 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(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(691,-486,391,-275) (7/10,19/27) -> (7/4,23/13) Hyperbolic Matrix(3187,-2246,1182,-833) (31/44,12/17) -> (62/23,27/10) Hyperbolic Matrix(667,-472,301,-213) (12/17,17/24) -> (11/5,20/9) Hyperbolic Matrix(1111,-788,712,-505) (17/24,5/7) -> (39/25,25/16) Hyperbolic Matrix(89,-64,121,-87) (5/7,8/11) -> (8/11,3/4) Parabolic Matrix(1073,-828,600,-463) (10/13,17/22) -> (25/14,34/19) 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(83,-70,51,-43) (5/6,1/1) -> (13/8,5/3) Hyperbolic Matrix(159,-184,70,-81) (1/1,7/6) -> (9/4,25/11) Hyperbolic Matrix(191,-226,131,-155) (13/11,6/5) -> (16/11,3/2) Hyperbolic Matrix(137,-166,52,-63) (6/5,5/4) -> (21/8,8/3) Hyperbolic Matrix(177,-242,128,-175) (4/3,11/8) -> (11/8,18/13) Parabolic Matrix(95,-134,39,-55) (7/5,10/7) -> (12/5,5/2) Hyperbolic Matrix(2185,-3136,1521,-2183) (33/23,56/39) -> (56/39,23/16) Parabolic Matrix(499,-718,319,-459) (23/16,13/9) -> (25/16,11/7) Hyperbolic Matrix(135,-208,37,-57) (3/2,14/9) -> (18/5,11/3) 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(85,-144,49,-83) (5/3,12/7) -> (12/7,7/4) Parabolic Matrix(1769,-3134,740,-1311) (23/13,39/22) -> (43/18,55/23) Hyperbolic Matrix(157,-338,72,-155) (2/1,13/6) -> (13/6,24/11) Parabolic Matrix(1915,-4356,841,-1913) (25/11,66/29) -> (66/29,41/18) Parabolic Matrix(103,-238,29,-67) (16/7,7/3) -> (7/2,18/5) Hyperbolic Matrix(681,-1600,289,-679) (7/3,40/17) -> (40/17,33/14) Parabolic Matrix(1031,-2466,319,-763) (55/23,12/5) -> (42/13,13/4) Hyperbolic Matrix(2311,-6050,882,-2309) (34/13,55/21) -> (55/21,76/29) Parabolic Matrix(1511,-3962,561,-1471) (76/29,21/8) -> (35/13,62/23) Hyperbolic Matrix(71,-196,25,-69) (11/4,14/5) -> (14/5,3/1) Parabolic Matrix(523,-1682,162,-521) (16/5,29/9) -> (29/9,42/13) Parabolic Matrix(121,-450,32,-119) (11/3,15/4) -> (15/4,19/5) Parabolic Matrix(49,-256,9,-47) (5/1,16/3) -> (16/3,11/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(209,96,37,17) -> Matrix(13,-4,10,-3) Matrix(67,30,-239,-107) -> Matrix(1,0,0,1) Matrix(271,120,70,31) -> Matrix(1,0,-2,1) Matrix(1219,536,680,299) -> Matrix(1,0,-2,1) Matrix(269,118,1288,565) -> Matrix(1,0,-2,1) Matrix(271,118,604,263) -> Matrix(15,-4,34,-9) Matrix(1009,438,569,247) -> Matrix(7,-2,4,-1) Matrix(265,112,97,41) -> Matrix(5,-2,8,-3) Matrix(455,188,743,307) -> Matrix(5,-2,8,-3) Matrix(127,52,613,251) -> Matrix(1,0,0,1) Matrix(451,184,576,235) -> Matrix(1,0,0,1) Matrix(61,24,33,13) -> Matrix(1,0,-2,1) Matrix(183,68,331,123) -> Matrix(1,0,-2,1) Matrix(419,154,302,111) -> Matrix(19,-6,16,-5) Matrix(61,22,-269,-97) -> Matrix(5,-2,8,-3) Matrix(57,20,265,93) -> Matrix(1,0,2,1) Matrix(55,16,79,23) -> Matrix(1,0,-2,1) Matrix(683,188,287,79) -> Matrix(5,-2,8,-3) Matrix(155,42,262,71) -> Matrix(7,-2,4,-1) Matrix(259,68,179,47) -> Matrix(1,0,-2,1) Matrix(101,24,223,53) -> Matrix(7,-4,16,-9) Matrix(291,64,50,11) -> Matrix(3,-2,2,-1) Matrix(871,188,1237,267) -> Matrix(1,2,0,1) Matrix(1257,268,530,113) -> Matrix(3,2,4,3) Matrix(1203,254,772,163) -> Matrix(1,0,4,1) Matrix(191,40,530,111) -> Matrix(1,0,12,1) Matrix(45,8,163,29) -> Matrix(5,-2,8,-3) Matrix(133,20,113,17) -> Matrix(1,0,2,1) Matrix(219,28,86,11) -> Matrix(1,0,-2,1) Matrix(253,26,107,11) -> Matrix(5,-2,8,-3) Matrix(101,-14,166,-23) -> Matrix(1,0,0,1) Matrix(67,-10,181,-27) -> Matrix(1,0,4,1) Matrix(485,-84,179,-31) -> Matrix(1,-2,2,-3) Matrix(547,-98,307,-55) -> Matrix(1,0,2,1) Matrix(739,-136,288,-53) -> Matrix(1,0,6,1) Matrix(573,-110,224,-43) -> Matrix(1,0,-6,1) Matrix(1003,-212,440,-93) -> Matrix(1,0,0,1) Matrix(499,-110,186,-41) -> Matrix(1,0,-2,1) Matrix(61,-14,109,-25) -> Matrix(5,-2,8,-3) Matrix(61,-16,225,-59) -> Matrix(9,-4,16,-7) Matrix(1633,-456,684,-191) -> Matrix(1,-2,2,-3) Matrix(563,-158,253,-71) -> Matrix(1,0,0,1) Matrix(117,-34,148,-43) -> Matrix(3,-2,8,-5) Matrix(145,-44,234,-71) -> Matrix(3,-2,2,-1) Matrix(141,-50,392,-139) -> Matrix(1,0,16,1) Matrix(223,-82,291,-107) -> Matrix(1,0,-4,1) Matrix(137,-52,166,-63) -> Matrix(9,-2,14,-3) Matrix(83,-32,13,-5) -> Matrix(7,-2,4,-1) Matrix(53,-22,41,-17) -> Matrix(5,-2,8,-3) Matrix(133,-58,39,-17) -> Matrix(1,0,-2,1) Matrix(79,-36,169,-77) -> Matrix(13,-6,24,-11) Matrix(125,-66,161,-85) -> Matrix(3,-2,8,-5) Matrix(493,-268,344,-187) -> Matrix(5,-4,4,-3) Matrix(369,-202,601,-329) -> Matrix(1,0,0,1) Matrix(169,-98,288,-167) -> Matrix(9,-8,8,-7) Matrix(1227,-748,520,-317) -> Matrix(5,-2,8,-3) Matrix(375,-232,118,-73) -> Matrix(1,-2,2,-3) Matrix(47,-30,11,-7) -> Matrix(1,0,0,1) Matrix(691,-486,391,-275) -> Matrix(1,-2,2,-3) Matrix(3187,-2246,1182,-833) -> Matrix(1,-6,2,-11) Matrix(667,-472,301,-213) -> Matrix(1,0,2,1) Matrix(1111,-788,712,-505) -> Matrix(1,0,2,1) Matrix(89,-64,121,-87) -> Matrix(1,0,2,1) Matrix(1073,-828,600,-463) -> Matrix(1,0,-2,1) Matrix(469,-366,214,-167) -> Matrix(1,0,0,1) Matrix(439,-358,168,-137) -> Matrix(7,-4,16,-9) Matrix(83,-70,51,-43) -> Matrix(3,-2,2,-1) Matrix(159,-184,70,-81) -> Matrix(1,0,-2,1) Matrix(191,-226,131,-155) -> Matrix(7,-2,4,-1) Matrix(137,-166,52,-63) -> Matrix(5,-2,8,-3) Matrix(177,-242,128,-175) -> Matrix(11,-10,10,-9) Matrix(95,-134,39,-55) -> Matrix(1,-2,2,-3) Matrix(2185,-3136,1521,-2183) -> Matrix(3,-2,2,-1) Matrix(499,-718,319,-459) -> Matrix(1,-2,2,-3) Matrix(135,-208,37,-57) -> Matrix(1,0,0,1) Matrix(191,-302,74,-117) -> Matrix(1,0,2,1) Matrix(145,-234,44,-71) -> Matrix(3,-2,2,-1) Matrix(85,-144,49,-83) -> Matrix(1,0,2,1) Matrix(1769,-3134,740,-1311) -> Matrix(5,-6,6,-7) Matrix(157,-338,72,-155) -> Matrix(1,0,2,1) Matrix(1915,-4356,841,-1913) -> Matrix(1,0,8,1) Matrix(103,-238,29,-67) -> Matrix(1,0,-2,1) Matrix(681,-1600,289,-679) -> Matrix(5,-2,8,-3) Matrix(1031,-2466,319,-763) -> Matrix(15,-14,14,-13) Matrix(2311,-6050,882,-2309) -> Matrix(37,-18,72,-35) Matrix(1511,-3962,561,-1471) -> Matrix(11,-6,24,-13) Matrix(71,-196,25,-69) -> Matrix(5,-4,4,-3) Matrix(523,-1682,162,-521) -> Matrix(19,-18,18,-17) Matrix(121,-450,32,-119) -> Matrix(1,0,2,1) Matrix(49,-256,9,-47) -> Matrix(7,-6,6,-5) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 24 ----------------------------------------------------------------------- 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 2 1 0/1 (0/1,1/2) 0 19 1/7 1/0 1 19 1/6 1/2 1 19 2/11 (-1/2,0/1) 0 19 3/16 0/1 6 1 1/5 1/4 1 19 2/9 (1/4,1/3) 0 19 1/4 1/2 1 19 4/15 1/2 4 1 2/7 (1/2,1/1) 0 19 3/10 3/4 1 19 1/3 1/0 1 19 5/14 0/1 8 1 4/11 (0/1,1/8) 0 19 7/19 1/6 1 19 3/8 1/4 1 19 5/13 1/4 1 19 2/5 (0/1,1/3) 0 19 3/7 1/2 1 19 4/9 (2/5,1/2) 0 19 6/13 1/2 6 1 1/2 1/2 1 19 5/9 1/2 1 19 4/7 (3/4,1/1) 0 19 7/12 1/1 4 1 3/5 1/0 1 19 8/13 (2/3,1/1) 0 19 13/21 3/2 1 19 5/8 1/2 1 19 2/3 (0/1,1/1) 0 19 8/11 0/1 2 1 3/4 1/2 1 19 10/13 (0/1,1/4) 0 19 7/9 1/2 1 19 11/14 1/4 1 19 4/5 (1/3,1/2) 0 19 9/11 1/2 1 19 5/6 1/2 1 19 1/1 1/0 1 19 7/6 1/2 1 19 6/5 (1/3,1/2) 0 19 5/4 1/2 1 19 4/3 (2/3,1/1) 0 19 11/8 1/1 5 1 7/5 3/2 1 19 10/7 (1/1,2/1) 0 19 56/39 1/1 2 1 23/16 3/2 1 19 13/9 1/0 1 19 3/2 1/0 1 19 14/9 (0/1,1/0) 0 19 25/16 1/2 1 19 11/7 1/0 1 19 8/5 (0/1,1/2) 0 19 13/8 3/2 1 19 5/3 1/0 1 19 12/7 0/1 2 1 2/1 (0/1,1/1) 0 19 13/6 0/1 1 1 11/5 1/2 1 19 9/4 1/0 1 19 25/11 -1/2 1 19 66/29 0/1 8 1 16/7 (0/1,1/2) 0 19 7/3 1/2 1 19 40/17 1/2 2 1 26/11 (1/2,2/3) 0 19 19/8 3/4 1 19 12/5 (0/1,1/1) 0 19 5/2 1/0 1 19 18/7 (0/1,1/4) 0 19 13/5 1/2 1 19 34/13 (5/11,1/2) 0 19 55/21 1/2 9 1 21/8 1/2 1 19 8/3 (1/2,1/1) 0 19 14/5 1/1 4 1 3/1 1/0 1 19 16/5 (4/5,1/1) 0 19 29/9 1/1 9 1 13/4 5/4 1 19 10/3 (2/1,1/0) 0 19 7/2 1/0 1 19 18/5 (0/1,1/0) 0 19 11/3 1/0 1 19 15/4 0/1 1 1 4/1 (0/1,1/1) 0 19 5/1 1/2 1 19 16/3 1/1 6 1 6/1 (1/1,2/1) 0 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(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(201,-26,85,-11) (0/1,1/7) -> (26/11,19/8) Glide Reflection Matrix(67,-10,181,-27) (1/7,1/6) -> (7/19,3/8) Hyperbolic Matrix(163,-28,64,-11) (1/6,2/11) -> (5/2,18/7) Glide Reflection Matrix(65,-12,352,-65) (2/11,3/16) -> (2/11,3/16) Reflection Matrix(31,-6,160,-31) (3/16,1/5) -> (3/16,1/5) Reflection Matrix(93,-20,79,-17) (1/5,2/9) -> (7/6,6/5) Glide Reflection Matrix(61,-14,109,-25) (2/9,1/4) -> (5/9,4/7) Hyperbolic Matrix(31,-8,120,-31) (1/4,4/15) -> (1/4,4/15) Reflection Matrix(29,-8,105,-29) (4/15,2/7) -> (4/15,2/7) Reflection 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(29,-10,84,-29) (1/3,5/14) -> (1/3,5/14) Reflection Matrix(111,-40,308,-111) (5/14,4/11) -> (5/14,4/11) Reflection Matrix(223,-82,291,-107) (4/11,7/19) -> (3/4,10/13) 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(53,-24,117,-53) (4/9,6/13) -> (4/9,6/13) Reflection Matrix(25,-12,52,-25) (6/13,1/2) -> (6/13,1/2) Reflection Matrix(123,-68,85,-47) (1/2,5/9) -> (13/9,3/2) Glide Reflection Matrix(97,-56,168,-97) (4/7,7/12) -> (4/7,7/12) Reflection Matrix(71,-42,120,-71) (7/12,3/5) -> (7/12,3/5) Reflection Matrix(307,-188,129,-79) (3/5,8/13) -> (19/8,12/5) Glide Reflection 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(23,-16,33,-23) (2/3,8/11) -> (2/3,8/11) Reflection Matrix(65,-48,88,-65) (8/11,3/4) -> (8/11,3/4) Reflection Matrix(451,-348,289,-223) (10/13,7/9) -> (14/9,25/16) Glide Reflection Matrix(235,-184,106,-83) (7/9,11/14) -> (11/5,9/4) Glide Reflection 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(159,-184,70,-81) (1/1,7/6) -> (9/4,25/11) Hyperbolic Matrix(137,-166,52,-63) (6/5,5/4) -> (21/8,8/3) Hyperbolic Matrix(65,-88,48,-65) (4/3,11/8) -> (4/3,11/8) Reflection Matrix(111,-154,80,-111) (11/8,7/5) -> (11/8,7/5) Reflection Matrix(95,-134,39,-55) (7/5,10/7) -> (12/5,5/2) Hyperbolic Matrix(391,-560,273,-391) (10/7,56/39) -> (10/7,56/39) Reflection Matrix(1793,-2576,1248,-1793) (56/39,23/16) -> (56/39,23/16) Reflection Matrix(499,-718,319,-459) (23/16,13/9) -> (25/16,11/7) Hyperbolic Matrix(135,-208,37,-57) (3/2,14/9) -> (18/5,11/3) 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(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(131,-286,60,-131) (13/6,11/5) -> (13/6,11/5) Reflection Matrix(1451,-3300,638,-1451) (25/11,66/29) -> (25/11,66/29) Reflection Matrix(463,-1056,203,-463) (66/29,16/7) -> (66/29,16/7) Reflection Matrix(103,-238,29,-67) (16/7,7/3) -> (7/2,18/5) Hyperbolic Matrix(239,-560,102,-239) (7/3,40/17) -> (7/3,40/17) Reflection Matrix(441,-1040,187,-441) (40/17,26/11) -> (40/17,26/11) Reflection Matrix(1429,-3740,546,-1429) (34/13,55/21) -> (34/13,55/21) 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(289,-928,90,-289) (16/5,29/9) -> (16/5,29/9) Reflection Matrix(233,-754,72,-233) (29/9,13/4) -> (29/9,13/4) Reflection Matrix(89,-330,24,-89) (11/3,15/4) -> (11/3,15/4) 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(-1,0,2,1) -> Matrix(1,0,4,-1) (-1/1,0/1) -> (0/1,1/2) Matrix(201,-26,85,-11) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(67,-10,181,-27) -> Matrix(1,0,4,1) 0/1 Matrix(163,-28,64,-11) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(65,-12,352,-65) -> Matrix(-1,0,4,1) (2/11,3/16) -> (-1/2,0/1) Matrix(31,-6,160,-31) -> Matrix(1,0,8,-1) (3/16,1/5) -> (0/1,1/4) Matrix(93,-20,79,-17) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(61,-14,109,-25) -> Matrix(5,-2,8,-3) 1/2 Matrix(31,-8,120,-31) -> Matrix(5,-2,12,-5) (1/4,4/15) -> (1/3,1/2) Matrix(29,-8,105,-29) -> Matrix(3,-2,4,-3) (4/15,2/7) -> (1/2,1/1) Matrix(117,-34,148,-43) -> Matrix(3,-2,8,-5) 1/2 Matrix(145,-44,234,-71) -> Matrix(3,-2,2,-1) 1/1 Matrix(29,-10,84,-29) -> Matrix(1,0,0,-1) (1/3,5/14) -> (0/1,1/0) Matrix(111,-40,308,-111) -> Matrix(1,0,16,-1) (5/14,4/11) -> (0/1,1/8) Matrix(223,-82,291,-107) -> Matrix(1,0,-4,1) 0/1 Matrix(137,-52,166,-63) -> Matrix(9,-2,14,-3) Matrix(83,-32,13,-5) -> Matrix(7,-2,4,-1) Matrix(53,-22,41,-17) -> Matrix(5,-2,8,-3) 1/2 Matrix(133,-58,39,-17) -> Matrix(1,0,-2,1) 0/1 Matrix(53,-24,117,-53) -> Matrix(9,-4,20,-9) (4/9,6/13) -> (2/5,1/2) Matrix(25,-12,52,-25) -> Matrix(3,-2,4,-3) (6/13,1/2) -> (1/2,1/1) Matrix(123,-68,85,-47) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(97,-56,168,-97) -> Matrix(7,-6,8,-7) (4/7,7/12) -> (3/4,1/1) Matrix(71,-42,120,-71) -> Matrix(-1,2,0,1) (7/12,3/5) -> (1/1,1/0) Matrix(307,-188,129,-79) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(375,-232,118,-73) -> Matrix(1,-2,2,-3) 1/1 Matrix(47,-30,11,-7) -> Matrix(1,0,0,1) Matrix(23,-16,33,-23) -> Matrix(1,0,2,-1) (2/3,8/11) -> (0/1,1/1) Matrix(65,-48,88,-65) -> Matrix(1,0,4,-1) (8/11,3/4) -> (0/1,1/2) Matrix(451,-348,289,-223) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(235,-184,106,-83) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(439,-358,168,-137) -> Matrix(7,-4,16,-9) 1/2 Matrix(83,-70,51,-43) -> Matrix(3,-2,2,-1) 1/1 Matrix(159,-184,70,-81) -> Matrix(1,0,-2,1) 0/1 Matrix(137,-166,52,-63) -> Matrix(5,-2,8,-3) 1/2 Matrix(65,-88,48,-65) -> Matrix(5,-4,6,-5) (4/3,11/8) -> (2/3,1/1) Matrix(111,-154,80,-111) -> Matrix(5,-6,4,-5) (11/8,7/5) -> (1/1,3/2) Matrix(95,-134,39,-55) -> Matrix(1,-2,2,-3) 1/1 Matrix(391,-560,273,-391) -> Matrix(3,-4,2,-3) (10/7,56/39) -> (1/1,2/1) Matrix(1793,-2576,1248,-1793) -> Matrix(5,-6,4,-5) (56/39,23/16) -> (1/1,3/2) Matrix(499,-718,319,-459) -> Matrix(1,-2,2,-3) 1/1 Matrix(135,-208,37,-57) -> Matrix(1,0,0,1) Matrix(191,-302,74,-117) -> Matrix(1,0,2,1) 0/1 Matrix(145,-234,44,-71) -> Matrix(3,-2,2,-1) 1/1 Matrix(71,-120,42,-71) -> Matrix(1,0,0,-1) (5/3,12/7) -> (0/1,1/0) Matrix(13,-24,7,-13) -> Matrix(1,0,2,-1) (12/7,2/1) -> (0/1,1/1) Matrix(25,-52,12,-25) -> Matrix(1,0,2,-1) (2/1,13/6) -> (0/1,1/1) Matrix(131,-286,60,-131) -> Matrix(1,0,4,-1) (13/6,11/5) -> (0/1,1/2) Matrix(1451,-3300,638,-1451) -> Matrix(-1,0,4,1) (25/11,66/29) -> (-1/2,0/1) Matrix(463,-1056,203,-463) -> Matrix(1,0,4,-1) (66/29,16/7) -> (0/1,1/2) Matrix(103,-238,29,-67) -> Matrix(1,0,-2,1) 0/1 Matrix(239,-560,102,-239) -> Matrix(3,-2,4,-3) (7/3,40/17) -> (1/2,1/1) Matrix(441,-1040,187,-441) -> Matrix(7,-4,12,-7) (40/17,26/11) -> (1/2,2/3) Matrix(1429,-3740,546,-1429) -> Matrix(21,-10,44,-21) (34/13,55/21) -> (5/11,1/2) Matrix(881,-2310,336,-881) -> Matrix(15,-8,28,-15) (55/21,21/8) -> (1/2,4/7) Matrix(41,-112,15,-41) -> Matrix(3,-2,4,-3) (8/3,14/5) -> (1/2,1/1) Matrix(29,-84,10,-29) -> Matrix(-1,2,0,1) (14/5,3/1) -> (1/1,1/0) Matrix(289,-928,90,-289) -> Matrix(9,-8,10,-9) (16/5,29/9) -> (4/5,1/1) Matrix(233,-754,72,-233) -> Matrix(9,-10,8,-9) (29/9,13/4) -> (1/1,5/4) Matrix(89,-330,24,-89) -> Matrix(1,0,0,-1) (11/3,15/4) -> (0/1,1/0) Matrix(31,-120,8,-31) -> Matrix(1,0,2,-1) (15/4,4/1) -> (0/1,1/1) Matrix(31,-160,6,-31) -> Matrix(3,-2,4,-3) (5/1,16/3) -> (1/2,1/1) Matrix(17,-96,3,-17) -> Matrix(3,-4,2,-3) (16/3,6/1) -> (1/1,2/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.