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 0/1 1/2 -7/15 1/0 -6/13 1/2 -5/11 1/4 -9/20 1/4 1/3 -4/9 1/2 -11/25 1/2 -18/41 3/4 -7/16 1/2 1/1 -10/23 3/4 -3/7 1/0 -11/26 0/1 1/8 -19/45 1/6 -8/19 1/4 -13/31 1/4 -5/12 0/1 1/3 -12/29 3/8 -7/17 1/2 -16/39 1/2 -9/22 2/5 1/2 -2/5 1/2 -9/23 1/2 -7/18 3/4 1/1 -5/13 1/0 -13/34 2/3 1/1 -21/55 3/2 -8/21 1/2 -11/29 1/0 -14/37 1/0 -17/45 1/0 -3/8 0/1 1/1 -10/27 1/2 -7/19 1/0 -4/11 1/2 -17/47 1/0 -13/36 0/1 1/4 -9/25 1/2 -5/14 1/3 1/2 -11/31 1/2 -6/17 1/2 -1/3 1/0 -5/16 1/3 1/2 -4/13 1/2 -7/23 1/2 -10/33 5/8 -3/10 2/3 1/1 -5/17 3/2 -7/24 1/1 2/1 -2/7 1/0 -9/32 0/1 1/0 -7/25 1/0 -5/18 0/1 1/2 -8/29 3/2 -3/11 1/0 -4/15 1/2 -5/19 1/2 -1/4 0/1 1/1 -4/17 1/0 -7/30 0/1 1/2 -10/43 1/2 -13/56 0/1 1/3 -3/13 1/2 -5/22 0/1 1/1 -2/9 1/0 -5/23 1/2 -13/60 5/11 1/2 -8/37 1/2 -3/14 1/2 1/1 -7/33 3/4 -4/19 3/4 -1/5 1/0 -5/26 4/5 1/1 -4/21 5/4 -3/16 2/1 1/0 -2/11 1/0 -5/28 0/1 1/0 -3/17 1/0 -1/6 0/1 1/1 -2/13 1/0 -1/7 1/2 -1/8 1/1 2/1 -2/17 7/4 -3/26 2/1 9/4 -1/9 1/0 0/1 1/0 1/7 1/0 1/6 -2/1 -1/1 3/17 -3/2 2/11 -5/4 3/16 -1/1 1/5 -1/2 5/24 -1/1 1/0 4/19 -3/2 3/14 -1/1 -2/3 5/23 -1/2 2/9 1/0 3/13 -1/2 4/17 1/0 1/4 -1/1 0/1 4/15 0/1 7/26 0/1 1/1 3/11 1/0 8/29 1/0 5/18 0/1 1/0 7/25 1/2 2/7 1/0 3/10 -2/1 1/0 1/3 1/0 5/14 -1/1 9/25 -7/8 4/11 -3/4 11/30 -1/1 -2/3 7/19 -3/4 10/27 -1/2 3/8 -1/1 -1/2 5/13 -1/2 2/5 1/0 7/17 -1/2 12/29 -1/2 5/12 -1/1 0/1 13/31 -1/2 8/19 -3/4 19/45 -1/2 11/26 -2/3 -1/2 3/7 -1/2 7/16 -1/2 0/1 4/9 1/0 9/20 -1/1 -1/2 5/11 -1/2 6/13 0/1 1/2 -1/1 0/1 8/15 -1/2 7/13 -1/2 6/11 -1/2 11/20 -2/1 -1/1 5/9 -1/2 14/25 -1/2 23/41 -1/4 9/16 0/1 1/0 22/39 1/0 13/23 -3/4 4/7 -1/2 7/12 0/1 10/17 1/2 3/5 1/0 14/23 1/0 11/18 -3/1 1/0 19/31 1/0 8/13 -3/2 13/21 -1/2 5/8 -1/2 0/1 17/27 1/4 12/19 1/2 7/11 1/0 23/36 -1/1 0/1 16/25 -1/2 9/14 0/1 1/0 11/17 1/0 2/3 1/0 11/16 -3/2 -1/1 9/13 1/0 25/36 -2/1 -3/2 16/23 -3/2 7/10 -2/1 -1/1 19/27 -1/2 31/44 0/1 1/0 12/17 1/0 29/41 -3/2 17/24 -2/1 -1/1 5/7 -3/2 8/11 -1/1 11/15 -7/8 3/4 -1/1 -2/3 13/17 -3/4 10/13 -5/8 17/22 -2/3 -1/2 24/31 -5/8 7/9 -1/2 18/23 -1/2 11/14 -1/2 0/1 4/5 -1/2 9/11 -1/2 5/6 -1/2 -1/3 11/13 -1/4 6/7 -1/2 7/8 -1/4 0/1 1/1 1/0 7/6 -3/4 -2/3 20/17 -1/2 13/11 -1/2 6/5 -1/2 5/4 -1/2 -1/3 9/7 -1/2 22/17 -1/4 35/27 -1/4 13/10 -1/4 0/1 4/3 -1/2 11/8 0/1 18/13 1/2 7/5 1/0 31/22 0/1 1/2 24/17 1/0 17/12 1/1 1/0 44/31 1/0 27/19 1/0 10/7 -1/2 33/23 -1/2 56/39 0/1 23/16 0/1 1/0 13/9 1/0 29/20 -3/2 -1/1 16/11 -1/2 3/2 -1/1 0/1 14/9 1/0 39/25 1/0 25/16 -1/1 0/1 11/7 1/0 8/5 -1/2 13/8 -1/1 -2/3 31/19 -3/4 49/30 -1/1 -2/3 18/11 -1/2 5/3 1/0 12/7 -1/1 19/11 -7/8 7/4 -1/1 -3/4 23/13 -7/10 39/22 -2/3 -1/2 16/9 -3/4 25/14 -2/3 -1/2 34/19 -5/8 9/5 -1/2 29/16 -2/1 -1/1 20/11 -3/4 11/6 -1/1 -2/3 24/13 -1/2 37/20 -1/1 13/7 -3/4 2/1 -1/2 13/6 -1/2 24/11 -1/2 11/5 -1/2 20/9 -1/2 9/4 -1/2 -2/5 25/11 -5/14 66/29 -1/3 41/18 -1/3 -4/13 16/7 -1/2 23/10 -1/3 0/1 53/23 0/1 83/36 -1/1 0/1 30/13 -1/2 7/3 -1/2 40/17 -1/2 33/14 -1/2 -9/19 26/11 -1/2 71/30 -9/20 -4/9 45/19 -7/16 19/8 -1/2 -3/7 31/13 -1/2 43/18 -5/12 -2/5 55/23 -13/32 12/5 -3/8 53/22 -1/2 -2/5 94/39 -2/5 41/17 -3/8 29/12 -2/5 -1/3 17/7 -3/8 22/9 -5/14 27/11 -1/3 32/13 -5/16 5/2 -1/3 0/1 23/9 -3/8 41/16 -1/3 18/7 -3/10 13/5 -1/4 34/13 -1/4 55/21 -1/4 76/29 -1/4 21/8 -1/4 -3/13 8/3 -1/4 35/13 -1/6 62/23 -1/6 27/10 -1/6 0/1 46/17 -1/8 111/41 0/1 65/24 -1/2 0/1 19/7 -1/6 49/18 -1/6 -1/7 79/29 -1/8 30/11 -1/6 41/15 -1/8 11/4 -1/8 0/1 14/5 0/1 17/6 0/1 1/8 3/1 1/0 16/5 -5/4 29/9 -1/1 42/13 -13/14 13/4 -1/1 -4/5 10/3 -3/4 27/8 -1/1 -2/3 44/13 -2/3 17/5 -1/2 7/2 -1/1 -1/2 32/9 -1/2 89/25 0/1 57/16 -1/1 0/1 25/7 1/0 43/12 -2/1 -1/1 104/29 -1/1 61/17 -7/8 18/5 -3/4 47/13 -1/2 29/8 -2/3 -1/2 69/19 -1/2 109/30 -7/10 -2/3 149/41 -2/3 40/11 -5/8 11/3 -1/2 15/4 -1/2 19/5 -1/2 4/1 -1/2 17/4 -1/3 0/1 47/11 -1/2 77/18 -1/3 30/7 -1/4 13/3 -1/2 22/5 -3/8 31/7 -1/3 40/9 -5/16 9/2 -1/3 -1/4 32/7 -1/4 55/12 -7/27 -1/4 78/17 -1/4 23/5 -1/4 14/3 -1/6 47/10 0/1 80/17 1/10 33/7 1/2 19/4 -1/2 0/1 24/5 -1/2 29/6 -1/3 0/1 63/13 0/1 34/7 -1/2 5/1 -1/4 16/3 0/1 27/5 1/8 11/2 0/1 1/2 17/3 1/0 6/1 -1/2 13/2 -1/4 0/1 33/5 0/1 53/8 0/1 1/12 20/3 1/4 7/1 1/0 8/1 -1/2 17/2 -1/2 26/3 -1/2 9/1 -1/2 1/0 -1/2 0/1 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(1,0,-2,1) Matrix(281,130,-776,-359) -> Matrix(1,0,0,1) Matrix(353,162,560,257) -> Matrix(1,0,0,1) Matrix(829,374,348,157) -> Matrix(9,-2,-22,5) Matrix(139,62,204,91) -> Matrix(5,-2,-2,1) Matrix(271,120,70,31) -> Matrix(5,-2,-12,5) Matrix(1219,536,680,299) -> Matrix(7,-4,-12,7) Matrix(269,118,1288,565) -> Matrix(1,0,-2,1) Matrix(271,118,604,263) -> Matrix(3,-2,-4,3) Matrix(539,234,-1412,-613) -> Matrix(3,-2,2,-1) Matrix(197,84,68,29) -> Matrix(1,0,0,1) Matrix(1577,666,1120,473) -> Matrix(1,0,-6,1) Matrix(721,304,1710,721) -> Matrix(11,-2,-16,3) Matrix(395,166,-1116,-469) -> Matrix(9,-2,14,-3) Matrix(67,28,390,163) -> Matrix(5,-2,-2,1) Matrix(391,162,712,295) -> Matrix(5,-2,-2,1) Matrix(905,374,196,81) -> Matrix(5,-2,-22,9) Matrix(901,370,-2384,-979) -> Matrix(1,0,-2,1) Matrix(835,342,1482,607) -> Matrix(5,-2,-2,1) Matrix(451,184,576,235) -> Matrix(5,-2,-12,5) Matrix(311,122,752,295) -> Matrix(3,-2,-4,3) Matrix(313,122,372,145) -> Matrix(3,-2,-10,7) Matrix(433,168,250,97) -> Matrix(7,-6,-8,7) Matrix(737,282,1048,401) -> Matrix(1,0,-2,1) Matrix(309,118,-1600,-611) -> Matrix(1,-2,2,-3) Matrix(121,46,676,257) -> Matrix(3,-4,-2,3) Matrix(491,186,916,347) -> Matrix(1,0,-2,1) Matrix(609,230,-2624,-991) -> Matrix(1,0,2,1) Matrix(59,22,244,91) -> Matrix(1,0,-2,1) Matrix(665,246,1084,401) -> Matrix(1,-2,0,1) Matrix(419,154,302,111) -> Matrix(1,0,0,1) Matrix(177,64,-1546,-559) -> Matrix(1,2,0,1) Matrix(949,342,1368,493) -> Matrix(5,-2,-2,1) Matrix(295,106,654,235) -> Matrix(1,0,-4,1) Matrix(473,168,-2182,-775) -> Matrix(7,-4,16,-9) Matrix(233,82,412,145) -> Matrix(3,-2,-4,3) Matrix(389,122,220,69) -> Matrix(7,-2,-10,3) Matrix(167,52,-774,-241) -> Matrix(5,-2,8,-3) Matrix(603,184,272,83) -> Matrix(5,-2,-12,5) Matrix(1965,596,544,165) -> Matrix(7,-4,-12,7) Matrix(53,16,-434,-131) -> Matrix(5,-4,4,-3) Matrix(161,48,218,65) -> Matrix(5,-4,-6,5) Matrix(965,282,592,173) -> Matrix(1,0,-2,1) Matrix(215,62,52,15) -> Matrix(1,-2,-2,5) Matrix(369,104,-1586,-447) -> Matrix(1,0,2,1) Matrix(1587,446,580,163) -> Matrix(1,0,-8,1) Matrix(581,162,104,29) -> Matrix(1,0,0,1) Matrix(159,44,-842,-233) -> Matrix(3,-2,2,-1) Matrix(893,246,628,173) -> Matrix(1,-2,0,1) Matrix(155,42,262,71) -> Matrix(1,0,0,1) Matrix(309,82,260,69) -> Matrix(3,-2,-4,3) Matrix(619,162,256,67) -> Matrix(1,-2,-2,5) Matrix(499,118,148,35) -> Matrix(3,-2,-4,3) Matrix(1143,268,644,151) -> Matrix(3,-2,-4,3) Matrix(5249,1220,2276,529) -> Matrix(1,0,-4,1) Matrix(149,34,688,157) -> Matrix(3,-2,-4,3) Matrix(539,122,296,67) -> Matrix(3,-2,-4,3) Matrix(291,64,50,11) -> Matrix(1,0,-2,1) Matrix(5337,1156,2036,441) -> Matrix(17,-8,-70,33) Matrix(1257,268,530,113) -> Matrix(5,-2,-12,5) Matrix(1203,254,772,163) -> Matrix(3,-2,-4,3) Matrix(191,40,530,111) -> Matrix(7,-6,-8,7) Matrix(1365,262,422,81) -> Matrix(9,-8,-10,9) Matrix(419,78,188,35) -> Matrix(1,-4,-2,9) Matrix(881,158,184,33) -> Matrix(1,0,-2,1) Matrix(1201,214,926,165) -> Matrix(1,0,-4,1) Matrix(137,24,508,89) -> Matrix(1,0,0,1) Matrix(135,22,92,15) -> Matrix(1,0,-2,1) Matrix(225,34,536,81) -> Matrix(3,-2,-4,3) Matrix(219,28,86,11) -> Matrix(1,-2,-2,5) Matrix(1421,166,214,25) -> Matrix(1,-2,8,-15) Matrix(423,44,298,31) -> Matrix(1,-4,0,1) Matrix(101,-14,166,-23) -> Matrix(1,2,0,1) Matrix(99,-16,130,-21) -> Matrix(3,4,-4,-5) Matrix(739,-136,288,-53) -> Matrix(7,8,-22,-25) Matrix(573,-110,224,-43) -> Matrix(5,4,-14,-11) Matrix(2141,-444,786,-163) -> Matrix(1,0,-6,1) Matrix(1003,-212,440,-93) -> Matrix(1,2,-4,-7) Matrix(499,-110,186,-41) -> Matrix(1,0,-4,1) Matrix(403,-92,92,-21) -> Matrix(3,2,-8,-5) Matrix(431,-100,556,-129) -> Matrix(5,2,-8,-3) Matrix(121,-32,450,-119) -> Matrix(1,0,2,1) Matrix(597,-164,506,-139) -> Matrix(1,2,-2,-3) Matrix(1013,-280,1458,-403) -> Matrix(3,2,-2,-1) Matrix(1633,-456,684,-191) -> Matrix(5,-2,-12,5) Matrix(503,-142,712,-201) -> Matrix(1,-2,0,1) Matrix(117,-34,148,-43) -> Matrix(1,2,-2,-3) Matrix(145,-44,234,-71) -> Matrix(1,2,-2,-3) Matrix(141,-50,392,-139) -> Matrix(7,8,-8,-9) Matrix(251,-92,472,-173) -> Matrix(3,2,-2,-1) Matrix(1861,-684,1140,-419) -> Matrix(1,0,0,1) Matrix(887,-328,1582,-585) -> Matrix(3,2,-8,-5) Matrix(499,-186,110,-41) -> Matrix(1,0,-2,1) Matrix(137,-52,166,-63) -> Matrix(3,2,-8,-5) Matrix(191,-74,302,-117) -> Matrix(1,0,2,1) Matrix(459,-188,188,-77) -> Matrix(5,4,-14,-11) Matrix(859,-356,1344,-557) -> Matrix(1,0,0,1) Matrix(1633,-684,456,-191) -> Matrix(3,2,-2,-1) Matrix(3099,-1310,854,-361) -> Matrix(1,0,0,1) Matrix(241,-102,26,-11) -> Matrix(3,2,-8,-5) Matrix(239,-104,370,-161) -> Matrix(1,0,2,1) Matrix(159,-70,184,-81) -> Matrix(1,0,-2,1) Matrix(705,-322,208,-95) -> Matrix(5,2,-8,-3) Matrix(439,-206,130,-61) -> Matrix(1,2,-2,-3) Matrix(493,-268,344,-187) -> Matrix(1,0,0,1) Matrix(441,-244,244,-135) -> Matrix(1,0,0,1) Matrix(1073,-600,828,-463) -> Matrix(1,0,-2,1) Matrix(2969,-1666,1096,-615) -> Matrix(1,0,-2,1) Matrix(2793,-1576,778,-439) -> Matrix(3,4,-4,-5) Matrix(169,-98,288,-167) -> Matrix(1,0,4,1) Matrix(1227,-748,520,-317) -> Matrix(1,-6,-2,13) Matrix(1861,-1140,684,-419) -> Matrix(1,2,-6,-11) Matrix(375,-232,118,-73) -> Matrix(3,2,-2,-1) Matrix(513,-322,94,-59) -> Matrix(1,0,4,1) Matrix(1879,-1200,440,-281) -> Matrix(1,0,-2,1) Matrix(1111,-712,788,-505) -> Matrix(1,0,2,1) 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(3,4,-4,-5) Matrix(3187,-2246,1182,-833) -> Matrix(1,0,-6,1) Matrix(2937,-2078,824,-583) -> Matrix(1,2,-2,-3) Matrix(1111,-788,712,-505) -> Matrix(1,2,-2,-3) Matrix(177,-128,242,-175) -> Matrix(9,10,-10,-11) Matrix(431,-330,64,-49) -> Matrix(3,2,4,3) Matrix(1073,-828,600,-463) -> Matrix(1,0,0,1) Matrix(1907,-1476,792,-613) -> Matrix(7,4,-16,-9) Matrix(469,-366,214,-167) -> Matrix(15,8,-32,-17) Matrix(439,-358,168,-137) -> Matrix(9,4,-34,-15) Matrix(597,-506,164,-139) -> Matrix(9,2,-14,-3) Matrix(283,-250,60,-53) -> Matrix(1,0,2,1) Matrix(159,-184,70,-81) -> Matrix(5,4,-14,-11) Matrix(1363,-1602,576,-677) -> Matrix(11,6,-24,-13) Matrix(137,-166,52,-63) -> Matrix(3,2,-14,-9) Matrix(117,-148,34,-43) -> Matrix(5,2,-8,-3) Matrix(431,-556,100,-129) -> Matrix(1,0,0,1) Matrix(99,-130,16,-21) -> Matrix(1,0,0,1) Matrix(177,-242,128,-175) -> Matrix(1,0,4,1) Matrix(503,-712,142,-201) -> Matrix(1,0,-2,1) Matrix(2089,-2964,456,-647) -> Matrix(1,6,-4,-23) Matrix(3761,-5398,1560,-2239) -> Matrix(7,2,-18,-5) Matrix(3571,-5130,1482,-2129) -> Matrix(1,-2,-2,5) Matrix(1013,-1458,280,-403) -> Matrix(1,2,-2,-3) Matrix(899,-1304,202,-293) -> Matrix(3,4,-10,-13) Matrix(239,-370,104,-161) -> Matrix(1,0,-2,1) Matrix(859,-1344,356,-557) -> Matrix(3,2,-8,-5) Matrix(191,-302,74,-117) -> Matrix(1,2,-4,-7) Matrix(145,-234,44,-71) -> Matrix(1,2,-2,-3) Matrix(1039,-1698,216,-353) -> Matrix(3,2,-8,-5) Matrix(101,-166,14,-23) -> Matrix(1,0,0,1) Matrix(169,-288,98,-167) -> Matrix(7,8,-8,-9) Matrix(1769,-3134,740,-1311) -> Matrix(19,12,-46,-29) Matrix(887,-1582,328,-585) -> Matrix(3,2,-20,-13) Matrix(567,-1028,230,-417) -> Matrix(1,2,-4,-7) Matrix(1601,-2958,374,-691) -> Matrix(1,0,-2,1) Matrix(1479,-2740,346,-641) -> Matrix(5,4,-14,-11) Matrix(251,-472,92,-173) -> Matrix(3,2,-20,-13) Matrix(157,-338,72,-155) -> Matrix(23,12,-48,-25) Matrix(2913,-6626,812,-1847) -> Matrix(35,12,-38,-13) Matrix(3119,-7102,870,-1981) -> Matrix(19,6,-16,-5) Matrix(2439,-5618,1058,-2437) -> Matrix(1,0,2,1) Matrix(625,-1466,136,-319) -> Matrix(3,2,-14,-9) Matrix(2027,-4774,442,-1041) -> Matrix(33,16,-130,-63) Matrix(4141,-9804,1140,-2699) -> Matrix(23,10,-30,-13) Matrix(2005,-4796,426,-1019) -> Matrix(5,2,42,17) Matrix(595,-1458,242,-593) -> Matrix(29,10,-90,-31) Matrix(2311,-6050,882,-2309) -> Matrix(71,18,-288,-73) Matrix(545,-1468,62,-167) -> Matrix(11,2,-28,-5) Matrix(4173,-11294,1148,-3107) -> Matrix(21,2,-32,-3) Matrix(8045,-21784,2214,-5995) -> Matrix(3,-2,-4,3) Matrix(1041,-2836,214,-583) -> Matrix(1,0,4,1) Matrix(141,-392,50,-139) -> Matrix(1,0,16,1) Matrix(523,-1682,162,-521) -> Matrix(17,18,-18,-19) Matrix(1417,-5042,292,-1039) -> Matrix(1,0,0,1) Matrix(1733,-6172,358,-1275) -> Matrix(1,0,-2,1) Matrix(121,-450,32,-119) -> Matrix(15,8,-32,-17) Matrix(435,-1922,98,-433) -> Matrix(23,8,-72,-25) Matrix(941,-4418,200,-939) -> Matrix(1,0,16,1) Matrix(97,-512,18,-95) -> Matrix(1,0,12,1) Matrix(331,-2178,50,-329) -> Matrix(1,0,16,1) Matrix(69,-578,8,-67) -> Matrix(7,4,-16,-9) 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 1/1 11/8 3/2 12/7 37/20 2/1 13/6 5/2 55/21 11/4 14/5 3/1 29/9 13/4 7/2 15/4 4/1 9/2 47/10 5/1 16/3 11/2 6/1 7/1 8/1 17/2 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/2 -6/13 1/2 -5/11 1/4 -4/9 1/2 -3/7 1/0 -11/26 0/1 1/8 -19/45 1/6 -8/19 1/4 -13/31 1/4 -5/12 0/1 1/3 -7/17 1/2 -2/5 1/2 -7/18 3/4 1/1 -5/13 1/0 -8/21 1/2 -3/8 0/1 1/1 -1/3 1/0 -4/13 1/2 -3/10 2/3 1/1 -5/17 3/2 -2/7 1/0 -1/4 0/1 1/1 -4/17 1/0 -3/13 1/2 -2/9 1/0 -1/5 1/0 -3/16 2/1 1/0 -2/11 1/0 -5/28 0/1 1/0 -3/17 1/0 -1/6 0/1 1/1 -1/7 1/2 0/1 1/0 1/6 -2/1 -1/1 3/17 -3/2 2/11 -5/4 3/16 -1/1 1/5 -1/2 1/4 -1/1 0/1 4/15 0/1 7/26 0/1 1/1 3/11 1/0 5/18 0/1 1/0 2/7 1/0 3/10 -2/1 1/0 1/3 1/0 5/14 -1/1 4/11 -3/4 7/19 -3/4 10/27 -1/2 3/8 -1/1 -1/2 5/13 -1/2 2/5 1/0 5/12 -1/1 0/1 13/31 -1/2 8/19 -3/4 19/45 -1/2 11/26 -2/3 -1/2 3/7 -1/2 7/16 -1/2 0/1 4/9 1/0 9/20 -1/1 -1/2 5/11 -1/2 6/13 0/1 1/2 -1/1 0/1 5/9 -1/2 14/25 -1/2 9/16 0/1 1/0 22/39 1/0 13/23 -3/4 4/7 -1/2 7/12 0/1 3/5 1/0 8/13 -3/2 13/21 -1/2 5/8 -1/2 0/1 17/27 1/4 12/19 1/2 7/11 1/0 16/25 -1/2 9/14 0/1 1/0 2/3 1/0 11/16 -3/2 -1/1 9/13 1/0 16/23 -3/2 7/10 -2/1 -1/1 5/7 -3/2 8/11 -1/1 11/15 -7/8 3/4 -1/1 -2/3 4/5 -1/2 9/11 -1/2 5/6 -1/2 -1/3 11/13 -1/4 6/7 -1/2 7/8 -1/4 0/1 1/1 1/0 6/5 -1/2 5/4 -1/2 -1/3 9/7 -1/2 22/17 -1/4 35/27 -1/4 13/10 -1/4 0/1 4/3 -1/2 11/8 0/1 7/5 1/0 31/22 0/1 1/2 24/17 1/0 17/12 1/1 1/0 44/31 1/0 27/19 1/0 10/7 -1/2 3/2 -1/1 0/1 8/5 -1/2 13/8 -1/1 -2/3 31/19 -3/4 18/11 -1/2 5/3 1/0 12/7 -1/1 19/11 -7/8 7/4 -1/1 -3/4 9/5 -1/2 20/11 -3/4 11/6 -1/1 -2/3 24/13 -1/2 37/20 -1/1 13/7 -3/4 2/1 -1/2 13/6 -1/2 11/5 -1/2 20/9 -1/2 9/4 -1/2 -2/5 7/3 -1/2 5/2 -1/3 0/1 13/5 -1/4 34/13 -1/4 55/21 -1/4 76/29 -1/4 21/8 -1/4 -3/13 8/3 -1/4 19/7 -1/6 11/4 -1/8 0/1 14/5 0/1 17/6 0/1 1/8 3/1 1/0 16/5 -5/4 29/9 -1/1 42/13 -13/14 13/4 -1/1 -4/5 10/3 -3/4 27/8 -1/1 -2/3 44/13 -2/3 17/5 -1/2 7/2 -1/1 -1/2 25/7 1/0 43/12 -2/1 -1/1 61/17 -7/8 18/5 -3/4 11/3 -1/2 15/4 -1/2 4/1 -1/2 9/2 -1/3 -1/4 32/7 -1/4 55/12 -7/27 -1/4 23/5 -1/4 14/3 -1/6 47/10 0/1 33/7 1/2 19/4 -1/2 0/1 24/5 -1/2 5/1 -1/4 16/3 0/1 27/5 1/8 11/2 0/1 1/2 17/3 1/0 6/1 -1/2 7/1 1/0 8/1 -1/2 17/2 -1/2 9/1 -1/2 1/0 -1/2 0/1 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(181,85,428,201) (-1/2,-6/13) -> (19/45,11/26) Hyperbolic Matrix(353,162,560,257) (-6/13,-5/11) -> (17/27,12/19) Hyperbolic Matrix(175,79,206,93) (-5/11,-4/9) -> (11/13,6/7) Hyperbolic Matrix(239,105,66,29) (-4/9,-3/7) -> (18/5,11/3) 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(1673,703,1178,495) (-8/19,-13/31) -> (44/31,27/19) Hyperbolic Matrix(67,28,390,163) (-13/31,-5/12) -> (1/6,3/17) Hyperbolic Matrix(99,41,-326,-135) (-5/12,-7/17) -> (-4/13,-3/10) Hyperbolic Matrix(287,117,130,53) (-7/17,-2/5) -> (11/5,20/9) Hyperbolic Matrix(217,85,314,123) (-2/5,-7/18) -> (11/16,9/13) Hyperbolic Matrix(433,168,250,97) (-7/18,-5/13) -> (19/11,7/4) Hyperbolic Matrix(337,129,802,307) (-5/13,-8/21) -> (13/31,8/19) Hyperbolic Matrix(29,11,-182,-69) (-8/21,-3/8) -> (-1/6,-1/7) Hyperbolic Matrix(89,33,62,23) (-3/8,-1/3) -> (10/7,3/2) Hyperbolic Matrix(251,79,54,17) (-1/3,-4/13) -> (23/5,14/3) Hyperbolic Matrix(161,48,218,65) (-3/10,-5/17) -> (11/15,3/4) Hyperbolic Matrix(293,85,162,47) (-5/17,-2/7) -> (9/5,20/11) Hyperbolic Matrix(27,7,50,13) (-2/7,-1/4) -> (1/2,5/9) Hyperbolic Matrix(499,118,148,35) (-1/4,-4/17) -> (10/3,27/8) Hyperbolic Matrix(473,111,98,23) (-4/17,-3/13) -> (24/5,5/1) Hyperbolic Matrix(565,129,346,79) (-3/13,-2/9) -> (31/19,18/11) Hyperbolic Matrix(71,15,194,41) (-2/9,-1/5) -> (4/11,7/19) Hyperbolic Matrix(397,75,704,133) (-1/5,-3/16) -> (9/16,22/39) 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(23,3,130,17) (-1/7,0/1) -> (3/17,2/11) Hyperbolic Matrix(83,-13,32,-5) (0/1,1/6) -> (5/2,13/5) Hyperbolic Matrix(49,-9,256,-47) (2/11,3/16) -> (3/16,1/5) Parabolic Matrix(47,-11,30,-7) (1/5,1/4) -> (3/2,8/5) Hyperbolic Matrix(121,-32,450,-119) (1/4,4/15) -> (4/15,7/26) Parabolic Matrix(135,-37,208,-57) (3/11,5/18) -> (9/14,2/3) Hyperbolic Matrix(103,-29,238,-67) (5/18,2/7) -> (3/7,7/16) 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(71,-25,196,-69) (1/3,5/14) -> (5/14,4/11) Parabolic Matrix(485,-179,84,-31) (7/19,10/27) -> (17/3,6/1) 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(95,-39,134,-55) (2/5,5/12) -> (7/10,5/7) Hyperbolic Matrix(1633,-684,456,-191) (5/12,13/31) -> (25/7,43/12) Hyperbolic Matrix(241,-102,26,-11) (11/26,3/7) -> (9/1,1/0) Hyperbolic Matrix(159,-70,184,-81) (7/16,4/9) -> (6/7,7/8) Hyperbolic Matrix(563,-253,158,-71) (4/9,9/20) -> (7/2,25/7) Hyperbolic Matrix(667,-301,472,-213) (9/20,5/11) -> (24/17,17/12) 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(1073,-600,828,-463) (5/9,14/25) -> (22/17,35/27) Hyperbolic Matrix(547,-307,98,-55) (14/25,9/16) -> (11/2,17/3) Hyperbolic Matrix(2793,-1576,778,-439) (22/39,13/23) -> (61/17,18/5) Hyperbolic Matrix(691,-391,486,-275) (13/23,4/7) -> (27/19,10/7) Hyperbolic Matrix(85,-49,144,-83) (4/7,7/12) -> (7/12,3/5) Parabolic 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(513,-322,94,-59) (5/8,17/27) -> (27/5,11/2) Hyperbolic Matrix(499,-319,718,-459) (7/11,16/25) -> (9/13,16/23) Hyperbolic Matrix(1111,-712,788,-505) (16/25,9/14) -> (31/22,24/17) Hyperbolic Matrix(191,-131,226,-155) (2/3,11/16) -> (5/6,11/13) Hyperbolic Matrix(493,-344,268,-187) (16/23,7/10) -> (11/6,24/13) Hyperbolic Matrix(177,-128,242,-175) (5/7,8/11) -> (8/11,11/15) Parabolic 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(283,-250,60,-53) (7/8,1/1) -> (33/7,19/4) 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(125,-161,66,-85) (9/7,22/17) -> (13/7,2/1) Hyperbolic Matrix(223,-291,82,-107) (13/10,4/3) -> (19/7,11/4) Hyperbolic Matrix(89,-121,64,-87) (4/3,11/8) -> (11/8,7/5) Parabolic Matrix(2089,-2964,456,-647) (17/12,44/31) -> (32/7,55/12) Hyperbolic Matrix(145,-234,44,-71) (8/5,13/8) -> (13/4,10/3) Hyperbolic Matrix(369,-601,202,-329) (13/8,31/19) -> (20/11,11/6) 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(61,-109,14,-25) (7/4,9/5) -> (4/1,9/2) Hyperbolic Matrix(741,-1369,400,-739) (24/13,37/20) -> (37/20,13/7) Parabolic Matrix(79,-169,36,-77) (2/1,13/6) -> (13/6,11/5) Parabolic Matrix(2311,-6050,882,-2309) (34/13,55/21) -> (55/21,76/29) Parabolic Matrix(1779,-4663,388,-1017) (76/29,21/8) -> (55/12,23/5) Hyperbolic Matrix(67,-181,10,-27) (8/3,19/7) -> (6/1,7/1) 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(803,-2599,224,-725) (42/13,13/4) -> (43/12,61/17) Hyperbolic Matrix(61,-225,16,-59) (11/3,15/4) -> (15/4,4/1) Parabolic Matrix(471,-2209,100,-469) (14/3,47/10) -> (47/10,33/7) Parabolic Matrix(97,-512,18,-95) (5/1,16/3) -> (16/3,27/5) Parabolic Matrix(35,-289,4,-33) (8/1,17/2) -> (17/2,9/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(181,85,428,201) -> Matrix(3,-2,-4,3) Matrix(353,162,560,257) -> Matrix(1,0,0,1) Matrix(175,79,206,93) -> Matrix(1,0,-6,1) Matrix(239,105,66,29) -> Matrix(3,-2,-4,3) Matrix(197,84,68,29) -> Matrix(1,0,0,1) Matrix(1577,666,1120,473) -> Matrix(1,0,-6,1) Matrix(721,304,1710,721) -> Matrix(11,-2,-16,3) Matrix(1673,703,1178,495) -> Matrix(9,-2,-4,1) Matrix(67,28,390,163) -> Matrix(5,-2,-2,1) Matrix(99,41,-326,-135) -> Matrix(5,-2,8,-3) Matrix(287,117,130,53) -> Matrix(9,-4,-20,9) Matrix(217,85,314,123) -> Matrix(1,0,-2,1) Matrix(433,168,250,97) -> Matrix(7,-6,-8,7) Matrix(337,129,802,307) -> Matrix(3,-2,-4,3) Matrix(29,11,-182,-69) -> Matrix(1,0,0,1) Matrix(89,33,62,23) -> Matrix(1,0,-2,1) Matrix(251,79,54,17) -> Matrix(1,0,-6,1) Matrix(161,48,218,65) -> Matrix(5,-4,-6,5) Matrix(293,85,162,47) -> Matrix(1,0,-2,1) Matrix(27,7,50,13) -> Matrix(1,0,-2,1) Matrix(499,118,148,35) -> Matrix(3,-2,-4,3) Matrix(473,111,98,23) -> Matrix(1,0,-4,1) Matrix(565,129,346,79) -> Matrix(3,-2,-4,3) Matrix(71,15,194,41) -> Matrix(3,-2,-4,3) Matrix(397,75,704,133) -> Matrix(1,-2,0,1) Matrix(419,78,188,35) -> Matrix(1,-4,-2,9) Matrix(881,158,184,33) -> Matrix(1,0,-2,1) Matrix(1201,214,926,165) -> Matrix(1,0,-4,1) Matrix(137,24,508,89) -> Matrix(1,0,0,1) Matrix(23,3,130,17) -> Matrix(3,-4,-2,3) Matrix(83,-13,32,-5) -> Matrix(1,2,-4,-7) Matrix(49,-9,256,-47) -> Matrix(5,6,-6,-7) Matrix(47,-11,30,-7) -> Matrix(1,0,0,1) Matrix(121,-32,450,-119) -> Matrix(1,0,2,1) Matrix(135,-37,208,-57) -> Matrix(1,0,0,1) Matrix(103,-29,238,-67) -> Matrix(1,0,-2,1) Matrix(133,-39,58,-17) -> Matrix(1,0,-2,1) Matrix(145,-44,234,-71) -> Matrix(1,2,-2,-3) Matrix(71,-25,196,-69) -> Matrix(3,4,-4,-5) Matrix(485,-179,84,-31) -> Matrix(3,2,-2,-1) Matrix(499,-186,110,-41) -> Matrix(1,0,-2,1) Matrix(137,-52,166,-63) -> Matrix(3,2,-8,-5) Matrix(191,-74,302,-117) -> Matrix(1,0,2,1) Matrix(95,-39,134,-55) -> Matrix(3,2,-2,-1) Matrix(1633,-684,456,-191) -> Matrix(3,2,-2,-1) Matrix(241,-102,26,-11) -> Matrix(3,2,-8,-5) Matrix(159,-70,184,-81) -> Matrix(1,0,-2,1) Matrix(563,-253,158,-71) -> Matrix(1,0,0,1) Matrix(667,-301,472,-213) -> Matrix(1,0,2,1) Matrix(705,-322,208,-95) -> Matrix(5,2,-8,-3) Matrix(439,-206,130,-61) -> Matrix(1,2,-2,-3) Matrix(1073,-600,828,-463) -> Matrix(1,0,-2,1) Matrix(547,-307,98,-55) -> Matrix(1,0,2,1) Matrix(2793,-1576,778,-439) -> Matrix(3,4,-4,-5) Matrix(691,-391,486,-275) -> Matrix(3,2,-2,-1) Matrix(85,-49,144,-83) -> Matrix(1,0,2,1) Matrix(83,-51,70,-43) -> Matrix(1,2,-2,-3) Matrix(375,-232,118,-73) -> Matrix(3,2,-2,-1) Matrix(513,-322,94,-59) -> Matrix(1,0,4,1) Matrix(499,-319,718,-459) -> Matrix(3,2,-2,-1) Matrix(1111,-712,788,-505) -> Matrix(1,0,2,1) Matrix(191,-131,226,-155) -> Matrix(1,2,-4,-7) Matrix(493,-344,268,-187) -> Matrix(3,4,-4,-5) Matrix(177,-128,242,-175) -> Matrix(9,10,-10,-11) Matrix(53,-41,22,-17) -> Matrix(3,2,-8,-5) Matrix(439,-358,168,-137) -> Matrix(9,4,-34,-15) Matrix(283,-250,60,-53) -> Matrix(1,0,2,1) Matrix(137,-166,52,-63) -> Matrix(3,2,-14,-9) Matrix(117,-148,34,-43) -> Matrix(5,2,-8,-3) Matrix(125,-161,66,-85) -> Matrix(5,2,-8,-3) Matrix(223,-291,82,-107) -> Matrix(1,0,-4,1) Matrix(89,-121,64,-87) -> Matrix(1,0,2,1) Matrix(2089,-2964,456,-647) -> Matrix(1,6,-4,-23) Matrix(145,-234,44,-71) -> Matrix(1,2,-2,-3) Matrix(369,-601,202,-329) -> Matrix(1,0,0,1) Matrix(101,-166,14,-23) -> Matrix(1,0,0,1) Matrix(169,-288,98,-167) -> Matrix(7,8,-8,-9) Matrix(61,-109,14,-25) -> Matrix(3,2,-8,-5) Matrix(741,-1369,400,-739) -> Matrix(1,2,-2,-3) Matrix(79,-169,36,-77) -> Matrix(11,6,-24,-13) Matrix(2311,-6050,882,-2309) -> Matrix(71,18,-288,-73) Matrix(1779,-4663,388,-1017) -> Matrix(41,10,-160,-39) Matrix(67,-181,10,-27) -> Matrix(1,0,4,1) Matrix(141,-392,50,-139) -> Matrix(1,0,16,1) Matrix(523,-1682,162,-521) -> Matrix(17,18,-18,-19) Matrix(803,-2599,224,-725) -> Matrix(7,6,-6,-5) Matrix(61,-225,16,-59) -> Matrix(7,4,-16,-9) Matrix(471,-2209,100,-469) -> Matrix(1,0,8,1) Matrix(97,-512,18,-95) -> Matrix(1,0,12,1) Matrix(35,-289,4,-33) -> Matrix(3,2,-8,-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 1/0 1 19 1/6 (-2/1,-1/1) 0 19 3/16 -1/1 6 1 1/5 -1/2 1 19 1/4 (-1/1,0/1) 0 19 4/15 0/1 1 1 3/11 1/0 1 19 5/18 (0/1,1/0) 0 19 2/7 1/0 1 19 3/10 (-2/1,1/0) 0 19 1/3 1/0 1 19 5/14 -1/1 4 1 3/8 (-1/1,-1/2) 0 19 5/13 -1/2 1 19 2/5 1/0 1 19 5/12 (-1/1,0/1) 0 19 3/7 -1/2 1 19 7/16 (-1/2,0/1) 0 19 4/9 1/0 1 19 5/11 -1/2 1 19 6/13 0/1 1 1 1/2 (-1/1,0/1) 0 19 7/12 0/1 2 1 3/5 1/0 1 19 8/13 -3/2 1 19 13/21 -1/2 1 19 5/8 (-1/2,0/1) 0 19 12/19 1/2 1 19 7/11 1/0 1 19 9/14 (0/1,1/0) 0 19 2/3 1/0 1 19 7/10 (-2/1,-1/1) 0 19 5/7 -3/2 1 19 8/11 -1/1 5 1 3/4 (-1/1,-2/3) 0 19 4/5 -1/2 1 19 9/11 -1/2 1 19 5/6 (-1/2,-1/3) 0 19 1/1 1/0 1 19 6/5 -1/2 1 19 5/4 (-1/2,-1/3) 0 19 9/7 -1/2 1 19 22/17 -1/4 1 19 13/10 (-1/4,0/1) 0 19 4/3 -1/2 1 19 11/8 0/1 2 1 3/2 (-1/1,0/1) 0 19 8/5 -1/2 1 19 13/8 (-1/1,-2/3) 0 19 18/11 -1/2 1 19 5/3 1/0 1 19 12/7 -1/1 4 1 7/4 (-1/1,-3/4) 0 19 9/5 -1/2 1 19 11/6 (-1/1,-2/3) 0 19 37/20 -1/1 2 1 13/7 -3/4 1 19 2/1 -1/2 1 19 13/6 -1/2 6 1 9/4 (-1/2,-2/5) 0 19 7/3 -1/2 1 19 5/2 (-1/3,0/1) 0 19 13/5 -1/4 1 19 34/13 -1/4 1 19 55/21 -1/4 9 1 21/8 (-1/4,-3/13) 0 19 8/3 -1/4 1 19 19/7 -1/6 1 19 11/4 (-1/8,0/1) 0 19 14/5 0/1 8 1 3/1 1/0 1 19 16/5 -5/4 1 19 29/9 -1/1 9 1 13/4 (-1/1,-4/5) 0 19 10/3 -3/4 1 19 17/5 -1/2 1 19 7/2 (-1/1,-1/2) 0 19 15/4 -1/2 4 1 4/1 -1/2 1 19 9/2 (-1/3,-1/4) 0 19 14/3 -1/6 1 19 47/10 0/1 8 1 19/4 (-1/2,0/1) 0 19 5/1 -1/4 1 19 16/3 0/1 6 1 11/2 (0/1,1/2) 0 19 6/1 -1/2 1 19 7/1 1/0 1 19 8/1 -1/2 1 19 17/2 -1/2 2 1 1/0 (-1/2,0/1) 0 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(83,-13,32,-5) (0/1,1/6) -> (5/2,13/5) Hyperbolic Matrix(17,-3,96,-17) (1/6,3/16) -> (1/6,3/16) Reflection Matrix(31,-6,160,-31) (3/16,1/5) -> (3/16,1/5) Reflection Matrix(47,-11,30,-7) (1/5,1/4) -> (3/2,8/5) Hyperbolic Matrix(31,-8,120,-31) (1/4,4/15) -> (1/4,4/15) Reflection Matrix(89,-24,330,-89) (4/15,3/11) -> (4/15,3/11) Reflection Matrix(135,-37,208,-57) (3/11,5/18) -> (9/14,2/3) Hyperbolic Matrix(103,-29,238,-67) (5/18,2/7) -> (3/7,7/16) 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(29,-10,84,-29) (1/3,5/14) -> (1/3,5/14) Reflection Matrix(41,-15,112,-41) (5/14,3/8) -> (5/14,3/8) Reflection 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(95,-39,134,-55) (2/5,5/12) -> (7/10,5/7) Hyperbolic Matrix(307,-129,188,-79) (5/12,3/7) -> (13/8,18/11) Glide Reflection Matrix(251,-111,52,-23) (7/16,4/9) -> (19/4,5/1) Glide Reflection Matrix(263,-118,78,-35) (4/9,5/11) -> (10/3,17/5) Glide Reflection Matrix(131,-60,286,-131) (5/11,6/13) -> (5/11,6/13) Reflection Matrix(25,-12,52,-25) (6/13,1/2) -> (6/13,1/2) Reflection Matrix(13,-7,24,-13) (1/2,7/12) -> (1/2,7/12) Reflection Matrix(71,-42,120,-71) (7/12,3/5) -> (7/12,3/5) Reflection 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(257,-162,46,-29) (5/8,12/19) -> (11/2,6/1) Glide Reflection Matrix(451,-289,348,-223) (7/11,9/14) -> (22/17,13/10) Glide Reflection Matrix(123,-85,68,-47) (2/3,7/10) -> (9/5,11/6) Glide Reflection Matrix(111,-80,154,-111) (5/7,8/11) -> (5/7,8/11) Reflection Matrix(65,-48,88,-65) (8/11,3/4) -> (8/11,3/4) Reflection 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(93,-79,20,-17) (5/6,1/1) -> (9/2,14/3) Glide Reflection 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(125,-161,66,-85) (9/7,22/17) -> (13/7,2/1) Hyperbolic Matrix(223,-291,82,-107) (13/10,4/3) -> (19/7,11/4) Hyperbolic 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(145,-234,44,-71) (8/5,13/8) -> (13/4,10/3) Hyperbolic Matrix(101,-166,14,-23) (18/11,5/3) -> (7/1,8/1) Hyperbolic Matrix(71,-120,42,-71) (5/3,12/7) -> (5/3,12/7) Reflection Matrix(97,-168,56,-97) (12/7,7/4) -> (12/7,7/4) Reflection Matrix(61,-109,14,-25) (7/4,9/5) -> (4/1,9/2) Hyperbolic Matrix(221,-407,120,-221) (11/6,37/20) -> (11/6,37/20) Reflection Matrix(519,-962,280,-519) (37/20,13/7) -> (37/20,13/7) 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(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(67,-181,10,-27) (8/3,19/7) -> (6/1,7/1) Hyperbolic Matrix(111,-308,40,-111) (11/4,14/5) -> (11/4,14/5) 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(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(281,-1316,60,-281) (14/3,47/10) -> (14/3,47/10) Reflection Matrix(189,-893,40,-189) (47/10,19/4) -> (47/10,19/4) Reflection Matrix(31,-160,6,-31) (5/1,16/3) -> (5/1,16/3) Reflection Matrix(65,-352,12,-65) (16/3,11/2) -> (16/3,11/2) Reflection Matrix(33,-272,4,-33) (8/1,17/2) -> (8/1,17/2) Reflection Matrix(-1,17,0,1) (17/2,1/0) -> (17/2,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,4,1) (-1/1,1/0) -> (-1/2,0/1) Matrix(-1,0,2,1) -> Matrix(1,0,0,-1) (-1/1,0/1) -> (0/1,1/0) Matrix(83,-13,32,-5) -> Matrix(1,2,-4,-7) Matrix(17,-3,96,-17) -> Matrix(3,4,-2,-3) (1/6,3/16) -> (-2/1,-1/1) Matrix(31,-6,160,-31) -> Matrix(3,2,-4,-3) (3/16,1/5) -> (-1/1,-1/2) Matrix(47,-11,30,-7) -> Matrix(1,0,0,1) Matrix(31,-8,120,-31) -> Matrix(-1,0,2,1) (1/4,4/15) -> (-1/1,0/1) Matrix(89,-24,330,-89) -> Matrix(1,0,0,-1) (4/15,3/11) -> (0/1,1/0) Matrix(135,-37,208,-57) -> Matrix(1,0,0,1) Matrix(103,-29,238,-67) -> Matrix(1,0,-2,1) 0/1 Matrix(133,-39,58,-17) -> Matrix(1,0,-2,1) 0/1 Matrix(145,-44,234,-71) -> Matrix(1,2,-2,-3) -1/1 Matrix(29,-10,84,-29) -> Matrix(1,2,0,-1) (1/3,5/14) -> (-1/1,1/0) Matrix(41,-15,112,-41) -> Matrix(3,2,-4,-3) (5/14,3/8) -> (-1/1,-1/2) Matrix(137,-52,166,-63) -> Matrix(3,2,-8,-5) -1/2 Matrix(191,-74,302,-117) -> Matrix(1,0,2,1) 0/1 Matrix(95,-39,134,-55) -> Matrix(3,2,-2,-1) -1/1 Matrix(307,-129,188,-79) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(251,-111,52,-23) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(263,-118,78,-35) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(131,-60,286,-131) -> Matrix(-1,0,4,1) (5/11,6/13) -> (-1/2,0/1) Matrix(25,-12,52,-25) -> Matrix(-1,0,2,1) (6/13,1/2) -> (-1/1,0/1) Matrix(13,-7,24,-13) -> Matrix(-1,0,2,1) (1/2,7/12) -> (-1/1,0/1) Matrix(71,-42,120,-71) -> Matrix(1,0,0,-1) (7/12,3/5) -> (0/1,1/0) Matrix(83,-51,70,-43) -> Matrix(1,2,-2,-3) -1/1 Matrix(375,-232,118,-73) -> Matrix(3,2,-2,-1) -1/1 Matrix(257,-162,46,-29) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(451,-289,348,-223) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(123,-85,68,-47) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(111,-80,154,-111) -> Matrix(5,6,-4,-5) (5/7,8/11) -> (-3/2,-1/1) Matrix(65,-48,88,-65) -> Matrix(5,4,-6,-5) (8/11,3/4) -> (-1/1,-2/3) Matrix(53,-41,22,-17) -> Matrix(3,2,-8,-5) -1/2 Matrix(439,-358,168,-137) -> Matrix(9,4,-34,-15) Matrix(93,-79,20,-17) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(137,-166,52,-63) -> Matrix(3,2,-14,-9) Matrix(117,-148,34,-43) -> Matrix(5,2,-8,-3) -1/2 Matrix(125,-161,66,-85) -> Matrix(5,2,-8,-3) -1/2 Matrix(223,-291,82,-107) -> Matrix(1,0,-4,1) 0/1 Matrix(65,-88,48,-65) -> Matrix(-1,0,4,1) (4/3,11/8) -> (-1/2,0/1) Matrix(23,-33,16,-23) -> Matrix(-1,0,2,1) (11/8,3/2) -> (-1/1,0/1) Matrix(145,-234,44,-71) -> Matrix(1,2,-2,-3) -1/1 Matrix(101,-166,14,-23) -> Matrix(1,0,0,1) Matrix(71,-120,42,-71) -> Matrix(1,2,0,-1) (5/3,12/7) -> (-1/1,1/0) Matrix(97,-168,56,-97) -> Matrix(7,6,-8,-7) (12/7,7/4) -> (-1/1,-3/4) Matrix(61,-109,14,-25) -> Matrix(3,2,-8,-5) -1/2 Matrix(221,-407,120,-221) -> Matrix(5,4,-6,-5) (11/6,37/20) -> (-1/1,-2/3) Matrix(519,-962,280,-519) -> Matrix(7,6,-8,-7) (37/20,13/7) -> (-1/1,-3/4) Matrix(25,-52,12,-25) -> Matrix(3,2,-4,-3) (2/1,13/6) -> (-1/1,-1/2) Matrix(53,-117,24,-53) -> Matrix(9,4,-20,-9) (13/6,9/4) -> (-1/2,-2/5) Matrix(1429,-3740,546,-1429) -> Matrix(47,12,-184,-47) (34/13,55/21) -> (-6/23,-1/4) Matrix(881,-2310,336,-881) -> Matrix(25,6,-104,-25) (55/21,21/8) -> (-1/4,-3/13) Matrix(67,-181,10,-27) -> Matrix(1,0,4,1) 0/1 Matrix(111,-308,40,-111) -> Matrix(-1,0,16,1) (11/4,14/5) -> (-1/8,0/1) Matrix(29,-84,10,-29) -> Matrix(1,0,0,-1) (14/5,3/1) -> (0/1,1/0) Matrix(289,-928,90,-289) -> Matrix(9,10,-8,-9) (16/5,29/9) -> (-5/4,-1/1) Matrix(233,-754,72,-233) -> Matrix(9,8,-10,-9) (29/9,13/4) -> (-1/1,-4/5) Matrix(29,-105,8,-29) -> Matrix(3,2,-4,-3) (7/2,15/4) -> (-1/1,-1/2) Matrix(31,-120,8,-31) -> Matrix(5,2,-12,-5) (15/4,4/1) -> (-1/2,-1/3) Matrix(281,-1316,60,-281) -> Matrix(-1,0,12,1) (14/3,47/10) -> (-1/6,0/1) Matrix(189,-893,40,-189) -> Matrix(-1,0,4,1) (47/10,19/4) -> (-1/2,0/1) Matrix(31,-160,6,-31) -> Matrix(-1,0,8,1) (5/1,16/3) -> (-1/4,0/1) Matrix(65,-352,12,-65) -> Matrix(1,0,4,-1) (16/3,11/2) -> (0/1,1/2) Matrix(33,-272,4,-33) -> Matrix(3,2,-4,-3) (8/1,17/2) -> (-1/1,-1/2) Matrix(-1,17,0,1) -> Matrix(-1,0,4,1) (17/2,1/0) -> (-1/2,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.