INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 768 Minimal number of generators: 129 Number of equivalence classes of cusps: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -5/11 -3/7 -2/5 -1/3 -3/11 -1/4 -1/5 0/1 1/7 1/5 5/19 1/3 7/17 5/11 1/2 13/23 3/5 5/7 4/5 1/1 8/7 13/11 5/4 7/5 16/11 3/2 5/3 2/1 25/11 7/3 17/7 5/2 13/5 8/3 3/1 73/23 16/5 10/3 37/11 7/2 25/7 18/5 11/3 26/7 19/5 4/1 9/2 14/3 33/7 5/1 16/3 6/1 7/1 8/1 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 1/4 -4/9 3/10 1/3 -15/34 7/20 -11/25 1/2 -7/16 1/2 -10/23 0/1 1/4 -3/7 1/4 -8/19 1/4 1/3 -5/12 5/16 -12/29 1/3 9/26 -7/17 1/2 -2/5 0/1 1/3 -9/23 1/2 -7/18 1/4 -12/31 2/7 3/10 -5/13 1/3 -8/21 3/8 2/5 -11/29 1/2 -3/8 3/8 -4/11 0/1 1/2 -9/25 1/3 -5/14 1/2 -1/3 1/2 -4/13 0/1 1/3 -7/23 1/3 -3/10 3/8 -2/7 1/2 1/1 -7/25 1/0 -5/18 1/0 -8/29 -1/1 0/1 -3/11 0/1 -4/15 1/5 1/4 -5/19 3/10 -6/23 1/3 5/14 -1/4 1/2 -3/13 -1/2 -5/22 -1/8 -2/9 0/1 1/6 -3/14 1/4 -4/19 0/1 1/3 -5/24 3/8 -1/5 1/2 -2/11 0/1 1/1 -3/17 -1/2 -4/23 -1/6 0/1 -1/6 1/4 -1/7 1/2 -1/8 1/4 -1/9 0/1 -1/10 1/2 0/1 0/1 1/2 1/8 1/2 1/7 0/1 2/13 0/1 1/3 1/6 1/0 1/5 1/2 3/14 3/4 2/9 1/1 1/0 3/13 0/1 4/17 0/1 1/3 1/4 1/0 5/19 0/1 9/34 1/20 4/15 0/1 1/10 3/11 1/6 8/29 3/13 1/4 5/18 1/4 2/7 0/1 1/3 5/17 1/2 3/10 1/4 7/23 1/4 4/13 3/10 1/3 1/3 1/2 5/14 3/4 4/11 0/1 1/1 7/19 1/2 3/8 1/0 5/13 1/0 7/18 1/0 2/5 -1/2 0/1 7/17 0/1 12/29 0/1 1/26 5/12 1/12 8/19 0/1 1/7 11/26 1/8 14/33 0/1 1/6 3/7 1/6 13/30 5/24 10/23 1/5 2/9 17/39 2/9 7/16 1/4 11/25 1/4 4/9 1/4 2/7 5/11 1/3 6/13 2/5 1/2 1/2 1/2 5/9 3/2 9/16 1/0 13/23 1/0 17/30 1/0 4/7 -1/1 1/0 7/12 1/0 3/5 0/1 11/18 1/8 8/13 0/1 1/5 21/34 1/0 13/21 1/6 18/29 0/1 1/6 5/8 1/4 2/3 1/3 1/2 7/10 7/16 5/7 1/2 13/18 13/24 21/29 1/2 29/40 1/2 8/11 1/2 4/7 11/15 1/2 14/19 3/5 2/3 17/23 2/3 3/4 3/4 10/13 1/2 1/1 7/9 1/1 18/23 3/2 2/1 11/14 1/0 15/19 -1/2 4/5 0/1 1/1 9/11 1/2 5/6 1/0 11/13 0/1 6/7 0/1 1/4 7/8 1/2 1/1 1/2 9/8 5/8 8/7 2/3 1/1 7/6 3/4 13/11 1/1 6/5 1/1 1/0 11/9 1/0 16/13 -1/2 0/1 21/17 1/2 26/21 0/1 1/2 5/4 1/2 14/11 1/2 1/1 9/7 1/1 4/3 0/1 1/2 11/8 3/8 7/5 1/2 17/12 9/16 44/31 4/7 3/5 27/19 1/2 37/26 1/2 10/7 1/2 3/5 13/9 1/2 29/20 5/8 16/11 3/5 2/3 3/2 3/4 17/11 1/2 14/9 1/2 1/1 25/16 3/4 11/7 1/2 19/12 5/8 46/29 2/3 5/7 27/17 3/4 8/5 2/3 3/4 37/23 3/4 29/18 3/4 21/13 11/14 13/8 5/6 5/3 1/1 17/10 3/2 46/27 1/1 3/2 121/71 1/1 75/44 5/4 29/17 3/2 12/7 3/2 2/1 43/25 1/0 74/43 2/1 3/1 31/18 1/0 50/29 5/2 3/1 19/11 1/0 7/4 1/0 2/1 0/1 1/1 9/4 1/0 34/15 0/1 1/2 25/11 1/2 16/7 1/2 1/1 23/10 1/2 7/3 1/2 19/8 5/6 69/29 5/6 50/21 5/6 1/1 31/13 5/6 12/5 9/10 1/1 17/7 1/1 22/9 1/1 19/18 5/2 5/4 23/9 1/1 18/7 1/1 3/2 49/19 3/2 31/12 5/4 13/5 3/2 21/8 1/0 8/3 1/1 1/0 35/13 1/1 27/10 5/4 19/7 3/2 11/4 3/2 36/13 3/2 2/1 25/9 3/2 14/5 2/1 5/2 17/6 1/0 3/1 1/0 19/6 1/0 73/23 -1/1 54/17 -1/1 -1/2 35/11 -1/2 16/5 -1/1 0/1 13/4 1/4 23/7 1/2 10/3 0/1 1/0 37/11 0/1 27/8 1/4 17/5 1/2 24/7 1/2 1/1 55/16 1/0 31/9 0/1 7/2 1/2 25/7 1/1 18/5 1/2 1/1 47/13 1/2 76/21 1/2 2/3 29/8 3/4 11/3 1/2 37/10 3/4 26/7 4/5 1/1 15/4 7/8 19/5 1/1 23/6 13/12 4/1 1/1 3/2 9/2 1/0 23/5 5/2 60/13 5/2 3/1 37/8 5/2 14/3 3/1 7/2 47/10 7/2 33/7 4/1 52/11 4/1 5/1 19/4 1/0 5/1 1/0 21/4 1/0 16/3 -2/1 -3/2 11/2 1/0 6/1 0/1 1/2 7/1 1/1 8/1 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(87,40,224,103) (-1/2,-5/11) -> (5/13,7/18) Hyperbolic Matrix(85,38,-302,-135) (-5/11,-4/9) -> (-2/7,-7/25) Hyperbolic Matrix(343,152,88,39) (-4/9,-15/34) -> (23/6,4/1) Hyperbolic Matrix(427,188,988,435) (-15/34,-11/25) -> (3/7,13/30) Hyperbolic Matrix(687,302,298,131) (-11/25,-7/16) -> (23/10,7/3) Hyperbolic Matrix(257,112,296,129) (-7/16,-10/23) -> (6/7,7/8) Hyperbolic Matrix(677,294,426,185) (-10/23,-3/7) -> (27/17,8/5) Hyperbolic Matrix(251,106,206,87) (-3/7,-8/19) -> (6/5,11/9) Hyperbolic Matrix(81,34,374,157) (-8/19,-5/12) -> (3/14,2/9) Hyperbolic Matrix(409,170,166,69) (-5/12,-12/29) -> (22/9,5/2) Hyperbolic Matrix(247,102,-942,-389) (-12/29,-7/17) -> (-5/19,-6/23) Hyperbolic Matrix(79,32,-200,-81) (-7/17,-2/5) -> (-2/5,-9/23) Parabolic Matrix(865,338,238,93) (-9/23,-7/18) -> (29/8,11/3) Hyperbolic Matrix(629,244,116,45) (-7/18,-12/31) -> (16/3,11/2) Hyperbolic Matrix(233,90,510,197) (-12/31,-5/13) -> (5/11,6/13) Hyperbolic Matrix(157,60,348,133) (-5/13,-8/21) -> (4/9,5/11) Hyperbolic Matrix(773,294,234,89) (-8/21,-11/29) -> (23/7,10/3) Hyperbolic Matrix(1003,380,388,147) (-11/29,-3/8) -> (31/12,13/5) Hyperbolic Matrix(153,56,112,41) (-3/8,-4/11) -> (4/3,11/8) Hyperbolic Matrix(527,190,674,243) (-4/11,-9/25) -> (7/9,18/23) Hyperbolic Matrix(525,188,148,53) (-9/25,-5/14) -> (7/2,25/7) Hyperbolic Matrix(299,106,110,39) (-5/14,-1/3) -> (19/7,11/4) Hyperbolic Matrix(71,22,242,75) (-1/3,-4/13) -> (2/7,5/17) Hyperbolic Matrix(275,84,36,11) (-4/13,-7/23) -> (7/1,8/1) Hyperbolic Matrix(345,104,136,41) (-7/23,-3/10) -> (5/2,23/9) Hyperbolic Matrix(69,20,100,29) (-3/10,-2/7) -> (2/3,7/10) Hyperbolic Matrix(201,56,664,185) (-7/25,-5/18) -> (3/10,7/23) Hyperbolic Matrix(463,128,1096,303) (-5/18,-8/29) -> (8/19,11/26) Hyperbolic Matrix(131,36,564,155) (-8/29,-3/11) -> (3/13,4/17) Hyperbolic Matrix(67,18,294,79) (-3/11,-4/15) -> (2/9,3/13) Hyperbolic Matrix(197,52,716,189) (-4/15,-5/19) -> (3/11,8/29) Hyperbolic Matrix(907,236,196,51) (-6/23,-1/4) -> (37/8,14/3) Hyperbolic Matrix(253,60,156,37) (-1/4,-3/13) -> (21/13,13/8) Hyperbolic Matrix(559,128,904,207) (-3/13,-5/22) -> (21/34,13/21) Hyperbolic Matrix(309,70,746,169) (-5/22,-2/9) -> (12/29,5/12) Hyperbolic Matrix(183,40,32,7) (-2/9,-3/14) -> (11/2,6/1) Hyperbolic Matrix(245,52,212,45) (-3/14,-4/19) -> (8/7,7/6) Hyperbolic Matrix(487,102,1122,235) (-4/19,-5/24) -> (13/30,10/23) Hyperbolic Matrix(1331,276,516,107) (-5/24,-1/5) -> (49/19,31/12) Hyperbolic Matrix(119,22,146,27) (-1/5,-2/11) -> (4/5,9/11) Hyperbolic Matrix(233,42,294,53) (-2/11,-3/17) -> (15/19,4/5) Hyperbolic Matrix(755,132,612,107) (-3/17,-4/23) -> (16/13,21/17) Hyperbolic Matrix(231,40,872,151) (-4/23,-1/6) -> (9/34,4/15) Hyperbolic Matrix(225,34,86,13) (-1/6,-1/7) -> (13/5,21/8) Hyperbolic Matrix(275,36,84,11) (-1/7,-1/8) -> (13/4,23/7) Hyperbolic Matrix(163,20,220,27) (-1/8,-1/9) -> (17/23,3/4) Hyperbolic Matrix(753,80,160,17) (-1/9,-1/10) -> (47/10,33/7) Hyperbolic Matrix(265,26,214,21) (-1/10,0/1) -> (26/21,5/4) Hyperbolic Matrix(299,-36,108,-13) (0/1,1/8) -> (11/4,36/13) Hyperbolic Matrix(297,-38,86,-11) (1/8,1/7) -> (31/9,7/2) Hyperbolic Matrix(291,-44,668,-101) (1/7,2/13) -> (10/23,17/39) Hyperbolic Matrix(165,-26,146,-23) (2/13,1/6) -> (9/8,8/7) Hyperbolic Matrix(161,-30,102,-19) (1/6,1/5) -> (11/7,19/12) Hyperbolic Matrix(279,-58,178,-37) (1/5,3/14) -> (25/16,11/7) Hyperbolic Matrix(465,-112,328,-79) (4/17,1/4) -> (17/12,44/31) Hyperbolic Matrix(191,-50,722,-189) (1/4,5/19) -> (5/19,9/34) Parabolic Matrix(529,-142,190,-51) (4/15,3/11) -> (25/9,14/5) Hyperbolic Matrix(565,-156,996,-275) (8/29,5/18) -> (17/30,4/7) Hyperbolic Matrix(151,-42,18,-5) (5/18,2/7) -> (8/1,1/0) Hyperbolic Matrix(629,-186,186,-55) (5/17,3/10) -> (27/8,17/5) Hyperbolic Matrix(1397,-426,810,-247) (7/23,4/13) -> (50/29,19/11) Hyperbolic Matrix(439,-136,184,-57) (4/13,1/3) -> (31/13,12/5) Hyperbolic Matrix(247,-88,160,-57) (1/3,5/14) -> (3/2,17/11) Hyperbolic Matrix(529,-190,142,-51) (5/14,4/11) -> (26/7,15/4) Hyperbolic Matrix(387,-142,526,-193) (4/11,7/19) -> (11/15,14/19) Hyperbolic Matrix(665,-246,246,-91) (7/19,3/8) -> (27/10,19/7) Hyperbolic Matrix(243,-92,140,-53) (3/8,5/13) -> (19/11,7/4) Hyperbolic Matrix(379,-148,484,-189) (7/18,2/5) -> (18/23,11/14) Hyperbolic Matrix(239,-98,578,-237) (2/5,7/17) -> (7/17,12/29) Parabolic Matrix(439,-184,136,-57) (5/12,8/19) -> (16/5,13/4) Hyperbolic Matrix(2933,-1242,810,-343) (11/26,14/33) -> (76/21,29/8) Hyperbolic Matrix(875,-372,708,-301) (14/33,3/7) -> (21/17,26/21) Hyperbolic Matrix(2641,-1152,768,-335) (17/39,7/16) -> (55/16,31/9) Hyperbolic Matrix(633,-278,1118,-491) (7/16,11/25) -> (13/23,17/30) Hyperbolic Matrix(533,-236,332,-147) (11/25,4/9) -> (8/5,37/23) Hyperbolic Matrix(393,-182,542,-251) (6/13,1/2) -> (29/40,8/11) Hyperbolic Matrix(185,-102,78,-43) (1/2,5/9) -> (7/3,19/8) Hyperbolic Matrix(339,-190,430,-241) (5/9,9/16) -> (11/14,15/19) Hyperbolic Matrix(1259,-710,782,-441) (9/16,13/23) -> (37/23,29/18) Hyperbolic Matrix(243,-140,92,-53) (4/7,7/12) -> (21/8,8/3) Hyperbolic Matrix(91,-54,150,-89) (7/12,3/5) -> (3/5,11/18) Parabolic Matrix(327,-200,224,-137) (11/18,8/13) -> (16/11,3/2) Hyperbolic Matrix(1811,-1118,1142,-705) (8/13,21/34) -> (19/12,46/29) Hyperbolic Matrix(1481,-918,534,-331) (13/21,18/29) -> (36/13,25/9) Hyperbolic Matrix(533,-332,236,-147) (18/29,5/8) -> (9/4,34/15) Hyperbolic Matrix(59,-38,14,-9) (5/8,2/3) -> (4/1,9/2) Hyperbolic Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic Matrix(279,-202,250,-181) (13/18,21/29) -> (1/1,9/8) Hyperbolic Matrix(3311,-2400,1392,-1009) (21/29,29/40) -> (19/8,69/29) Hyperbolic Matrix(499,-364,292,-213) (8/11,11/15) -> (29/17,12/7) Hyperbolic Matrix(1823,-1346,386,-285) (14/19,17/23) -> (33/7,52/11) Hyperbolic Matrix(381,-292,244,-187) (3/4,10/13) -> (14/9,25/16) Hyperbolic Matrix(487,-376,136,-105) (10/13,7/9) -> (25/7,18/5) Hyperbolic Matrix(237,-196,52,-43) (9/11,5/6) -> (9/2,23/5) Hyperbolic Matrix(573,-482,170,-143) (5/6,11/13) -> (37/11,27/8) Hyperbolic Matrix(389,-332,116,-99) (11/13,6/7) -> (10/3,37/11) Hyperbolic Matrix(253,-226,178,-159) (7/8,1/1) -> (27/19,37/26) Hyperbolic Matrix(507,-596,188,-221) (7/6,13/11) -> (35/13,27/10) Hyperbolic Matrix(263,-314,98,-117) (13/11,6/5) -> (8/3,35/13) Hyperbolic Matrix(667,-820,388,-477) (11/9,16/13) -> (12/7,43/25) Hyperbolic Matrix(317,-402,138,-175) (5/4,14/11) -> (16/7,23/10) Hyperbolic Matrix(379,-484,148,-189) (14/11,9/7) -> (23/9,18/7) Hyperbolic Matrix(63,-82,10,-13) (9/7,4/3) -> (6/1,7/1) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(1389,-1972,436,-619) (44/31,27/19) -> (35/11,16/5) Hyperbolic Matrix(693,-988,148,-211) (37/26,10/7) -> (14/3,47/10) Hyperbolic Matrix(335,-482,98,-141) (10/7,13/9) -> (17/5,24/7) Hyperbolic Matrix(1255,-1816,736,-1065) (13/9,29/20) -> (75/44,29/17) Hyperbolic Matrix(1821,-2642,1058,-1535) (29/20,16/11) -> (74/43,31/18) Hyperbolic Matrix(829,-1284,348,-539) (17/11,14/9) -> (50/21,31/13) Hyperbolic Matrix(2505,-3976,1456,-2311) (46/29,27/17) -> (43/25,74/43) Hyperbolic Matrix(679,-1096,184,-297) (29/18,21/13) -> (11/3,37/10) Hyperbolic Matrix(91,-150,54,-89) (13/8,5/3) -> (5/3,17/10) Parabolic Matrix(1599,-2722,346,-589) (17/10,46/27) -> (60/13,37/8) Hyperbolic Matrix(5805,-9892,1828,-3115) (46/27,121/71) -> (73/23,54/17) Hyperbolic Matrix(4561,-7774,1438,-2451) (121/71,75/44) -> (19/6,73/23) Hyperbolic Matrix(2027,-3494,590,-1017) (31/18,50/29) -> (24/7,55/16) Hyperbolic Matrix(17,-32,8,-15) (7/4,2/1) -> (2/1,9/4) Parabolic Matrix(1541,-3498,426,-967) (34/15,25/11) -> (47/13,76/21) Hyperbolic Matrix(527,-1202,146,-333) (25/11,16/7) -> (18/5,47/13) Hyperbolic Matrix(2301,-5476,724,-1723) (69/29,50/21) -> (54/17,35/11) Hyperbolic Matrix(239,-578,98,-237) (12/5,17/7) -> (17/7,22/9) Parabolic Matrix(1301,-3354,282,-727) (18/7,49/19) -> (23/5,60/13) Hyperbolic Matrix(201,-566,38,-107) (14/5,17/6) -> (21/4,16/3) Hyperbolic Matrix(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(653,-2418,138,-511) (37/10,26/7) -> (52/11,19/4) Hyperbolic Matrix(191,-722,50,-189) (15/4,19/5) -> (19/5,23/6) Parabolic Matrix(41,-200,8,-39) (19/4,5/1) -> (5/1,21/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(87,40,224,103) -> Matrix(1,0,-4,1) Matrix(85,38,-302,-135) -> Matrix(7,-2,4,-1) Matrix(343,152,88,39) -> Matrix(19,-6,16,-5) Matrix(427,188,988,435) -> Matrix(5,-2,28,-11) Matrix(687,302,298,131) -> Matrix(5,-2,8,-3) Matrix(257,112,296,129) -> Matrix(1,0,0,1) Matrix(677,294,426,185) -> Matrix(5,-2,8,-3) Matrix(251,106,206,87) -> Matrix(7,-2,4,-1) Matrix(81,34,374,157) -> Matrix(7,-2,4,-1) Matrix(409,170,166,69) -> Matrix(31,-10,28,-9) Matrix(247,102,-942,-389) -> Matrix(11,-4,36,-13) Matrix(79,32,-200,-81) -> Matrix(1,0,0,1) Matrix(865,338,238,93) -> Matrix(5,-2,8,-3) Matrix(629,244,116,45) -> Matrix(1,0,-4,1) Matrix(233,90,510,197) -> Matrix(13,-4,36,-11) Matrix(157,60,348,133) -> Matrix(11,-4,36,-13) Matrix(773,294,234,89) -> Matrix(5,-2,8,-3) Matrix(1003,380,388,147) -> Matrix(7,-2,4,-1) Matrix(153,56,112,41) -> Matrix(1,0,0,1) Matrix(527,190,674,243) -> Matrix(7,-2,4,-1) Matrix(525,188,148,53) -> Matrix(5,-2,8,-3) Matrix(299,106,110,39) -> Matrix(7,-2,4,-1) Matrix(71,22,242,75) -> Matrix(1,0,0,1) Matrix(275,84,36,11) -> Matrix(7,-2,4,-1) Matrix(345,104,136,41) -> Matrix(7,-2,4,-1) Matrix(69,20,100,29) -> Matrix(3,-2,8,-5) Matrix(201,56,664,185) -> Matrix(1,0,4,1) Matrix(463,128,1096,303) -> Matrix(1,0,8,1) Matrix(131,36,564,155) -> Matrix(1,0,4,1) Matrix(67,18,294,79) -> Matrix(1,0,-4,1) Matrix(197,52,716,189) -> Matrix(7,-2,32,-9) Matrix(907,236,196,51) -> Matrix(21,-8,8,-3) Matrix(253,60,156,37) -> Matrix(3,-4,4,-5) Matrix(559,128,904,207) -> Matrix(1,0,8,1) Matrix(309,70,746,169) -> Matrix(1,0,20,1) Matrix(183,40,32,7) -> Matrix(1,0,-4,1) Matrix(245,52,212,45) -> Matrix(5,-2,8,-3) Matrix(487,102,1122,235) -> Matrix(7,-2,32,-9) Matrix(1331,276,516,107) -> Matrix(7,-2,4,-1) Matrix(119,22,146,27) -> Matrix(1,0,0,1) Matrix(233,42,294,53) -> Matrix(1,0,0,1) Matrix(755,132,612,107) -> Matrix(1,0,4,1) Matrix(231,40,872,151) -> Matrix(1,0,16,1) Matrix(225,34,86,13) -> Matrix(7,-2,4,-1) Matrix(275,36,84,11) -> Matrix(1,0,0,1) Matrix(163,20,220,27) -> Matrix(5,-2,8,-3) Matrix(753,80,160,17) -> Matrix(15,-4,4,-1) Matrix(265,26,214,21) -> Matrix(1,0,0,1) Matrix(299,-36,108,-13) -> Matrix(7,-2,4,-1) Matrix(297,-38,86,-11) -> Matrix(1,0,0,1) Matrix(291,-44,668,-101) -> Matrix(7,-2,32,-9) Matrix(165,-26,146,-23) -> Matrix(5,-2,8,-3) Matrix(161,-30,102,-19) -> Matrix(5,-2,8,-3) Matrix(279,-58,178,-37) -> Matrix(1,0,0,1) Matrix(465,-112,328,-79) -> Matrix(9,-4,16,-7) Matrix(191,-50,722,-189) -> Matrix(1,0,20,1) Matrix(529,-142,190,-51) -> Matrix(15,-2,8,-1) Matrix(565,-156,996,-275) -> Matrix(17,-4,-4,1) Matrix(151,-42,18,-5) -> Matrix(7,-2,4,-1) Matrix(629,-186,186,-55) -> Matrix(1,0,0,1) Matrix(1397,-426,810,-247) -> Matrix(15,-4,4,-1) Matrix(439,-136,184,-57) -> Matrix(17,-6,20,-7) Matrix(247,-88,160,-57) -> Matrix(1,0,0,1) Matrix(529,-190,142,-51) -> Matrix(3,-4,4,-5) Matrix(387,-142,526,-193) -> Matrix(5,-2,8,-3) Matrix(665,-246,246,-91) -> Matrix(5,-4,4,-3) Matrix(243,-92,140,-53) -> Matrix(1,0,0,1) Matrix(379,-148,484,-189) -> Matrix(1,2,0,1) Matrix(239,-98,578,-237) -> Matrix(1,0,28,1) Matrix(439,-184,136,-57) -> Matrix(1,0,-8,1) Matrix(2933,-1242,810,-343) -> Matrix(13,-2,20,-3) Matrix(875,-372,708,-301) -> Matrix(1,0,-4,1) Matrix(2641,-1152,768,-335) -> Matrix(9,-2,-4,1) Matrix(633,-278,1118,-491) -> Matrix(33,-8,-4,1) Matrix(533,-236,332,-147) -> Matrix(29,-8,40,-11) Matrix(393,-182,542,-251) -> Matrix(13,-6,24,-11) Matrix(185,-102,78,-43) -> Matrix(3,-4,4,-5) Matrix(339,-190,430,-241) -> Matrix(1,-2,0,1) Matrix(1259,-710,782,-441) -> Matrix(3,-22,4,-29) Matrix(243,-140,92,-53) -> Matrix(1,2,0,1) Matrix(91,-54,150,-89) -> Matrix(1,0,8,1) Matrix(327,-200,224,-137) -> Matrix(13,-2,20,-3) Matrix(1811,-1118,1142,-705) -> Matrix(5,-2,8,-3) Matrix(1481,-918,534,-331) -> Matrix(15,-2,8,-1) Matrix(533,-332,236,-147) -> Matrix(1,0,-4,1) Matrix(59,-38,14,-9) -> Matrix(7,-2,4,-1) Matrix(141,-100,196,-139) -> Matrix(21,-10,40,-19) Matrix(279,-202,250,-181) -> Matrix(7,-4,16,-9) Matrix(3311,-2400,1392,-1009) -> Matrix(43,-24,52,-29) Matrix(499,-364,292,-213) -> Matrix(17,-10,12,-7) Matrix(1823,-1346,386,-285) -> Matrix(35,-22,8,-5) Matrix(381,-292,244,-187) -> Matrix(1,0,0,1) Matrix(487,-376,136,-105) -> Matrix(1,0,0,1) Matrix(237,-196,52,-43) -> Matrix(1,2,0,1) Matrix(573,-482,170,-143) -> Matrix(1,0,4,1) Matrix(389,-332,116,-99) -> Matrix(1,0,-4,1) Matrix(253,-226,178,-159) -> Matrix(9,-4,16,-7) Matrix(507,-596,188,-221) -> Matrix(9,-8,8,-7) Matrix(263,-314,98,-117) -> Matrix(1,0,0,1) Matrix(667,-820,388,-477) -> Matrix(1,2,0,1) Matrix(317,-402,138,-175) -> Matrix(1,0,0,1) Matrix(379,-484,148,-189) -> Matrix(5,-4,4,-3) Matrix(63,-82,10,-13) -> Matrix(1,0,0,1) Matrix(141,-196,100,-139) -> Matrix(13,-6,24,-11) Matrix(1389,-1972,436,-619) -> Matrix(7,-4,-12,7) Matrix(693,-988,148,-211) -> Matrix(41,-24,12,-7) Matrix(335,-482,98,-141) -> Matrix(3,-2,8,-5) Matrix(1255,-1816,736,-1065) -> Matrix(17,-10,12,-7) Matrix(1821,-2642,1058,-1535) -> Matrix(19,-12,8,-5) Matrix(829,-1284,348,-539) -> Matrix(3,-4,4,-5) Matrix(2505,-3976,1456,-2311) -> Matrix(5,-4,4,-3) Matrix(679,-1096,184,-297) -> Matrix(23,-18,32,-25) Matrix(91,-150,54,-89) -> Matrix(9,-8,8,-7) Matrix(1599,-2722,346,-589) -> Matrix(11,-14,4,-5) Matrix(5805,-9892,1828,-3115) -> Matrix(1,-2,0,1) Matrix(4561,-7774,1438,-2451) -> Matrix(5,-6,-4,5) Matrix(2027,-3494,590,-1017) -> Matrix(1,-2,0,1) Matrix(17,-32,8,-15) -> Matrix(1,0,0,1) Matrix(1541,-3498,426,-967) -> Matrix(5,-2,8,-3) Matrix(527,-1202,146,-333) -> Matrix(1,0,0,1) Matrix(2301,-5476,724,-1723) -> Matrix(7,-6,-8,7) Matrix(239,-578,98,-237) -> Matrix(29,-28,28,-27) Matrix(1301,-3354,282,-727) -> Matrix(11,-14,4,-5) Matrix(201,-566,38,-107) -> Matrix(1,-4,0,1) Matrix(37,-108,12,-35) -> Matrix(1,-2,0,1) Matrix(653,-2418,138,-511) -> Matrix(21,-16,4,-3) Matrix(191,-722,50,-189) -> Matrix(21,-20,20,-19) Matrix(41,-200,8,-39) -> Matrix(1,-6,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 21 Degree of the the map X: 42 Degree of the the map Y: 128 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- 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): 384 Minimal number of generators: 65 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: 40 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -5/11 -3/7 -2/5 -1/3 -1/4 -1/5 0/1 1/5 1/3 1/2 13/23 3/5 5/7 4/5 1/1 13/11 5/4 7/5 3/2 5/3 2/1 25/11 7/3 17/7 5/2 13/5 8/3 3/1 7/2 25/7 11/3 19/5 4/1 9/2 5/1 6/1 7/1 8/1 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 1/4 -4/9 3/10 1/3 -11/25 1/2 -7/16 1/2 -3/7 1/4 -8/19 1/4 1/3 -5/12 5/16 -7/17 1/2 -2/5 0/1 1/3 -5/13 1/3 -3/8 3/8 -4/11 0/1 1/2 -9/25 1/3 -5/14 1/2 -1/3 1/2 -4/13 0/1 1/3 -7/23 1/3 -3/10 3/8 -2/7 1/2 1/1 -3/11 0/1 -1/4 1/2 -3/13 -1/2 -5/22 -1/8 -2/9 0/1 1/6 -3/14 1/4 -1/5 1/2 -2/11 0/1 1/1 -3/17 -1/2 -4/23 -1/6 0/1 -1/6 1/4 -1/7 1/2 0/1 0/1 1/2 1/6 1/0 1/5 1/2 1/4 1/0 3/11 1/6 5/18 1/4 2/7 0/1 1/3 1/3 1/2 4/11 0/1 1/1 7/19 1/2 3/8 1/0 5/13 1/0 7/18 1/0 2/5 -1/2 0/1 3/7 1/6 1/2 1/2 5/9 3/2 9/16 1/0 13/23 1/0 4/7 -1/1 1/0 7/12 1/0 3/5 0/1 8/13 0/1 1/5 13/21 1/6 5/8 1/4 2/3 1/3 1/2 5/7 1/2 8/11 1/2 4/7 3/4 3/4 10/13 1/2 1/1 7/9 1/1 18/23 3/2 2/1 11/14 1/0 15/19 -1/2 4/5 0/1 1/1 9/11 1/2 5/6 1/0 1/1 1/2 7/6 3/4 13/11 1/1 6/5 1/1 1/0 11/9 1/0 5/4 1/2 14/11 1/2 1/1 9/7 1/1 4/3 0/1 1/2 7/5 1/2 10/7 1/2 3/5 3/2 3/4 11/7 1/2 19/12 5/8 8/5 2/3 3/4 37/23 3/4 29/18 3/4 21/13 11/14 13/8 5/6 5/3 1/1 12/7 3/2 2/1 19/11 1/0 7/4 1/0 2/1 0/1 1/1 9/4 1/0 25/11 1/2 16/7 1/2 1/1 23/10 1/2 7/3 1/2 12/5 9/10 1/1 17/7 1/1 22/9 1/1 19/18 5/2 5/4 23/9 1/1 18/7 1/1 3/2 13/5 3/2 21/8 1/0 8/3 1/1 1/0 3/1 1/0 10/3 0/1 1/0 37/11 0/1 27/8 1/4 17/5 1/2 7/2 1/2 25/7 1/1 18/5 1/2 1/1 47/13 1/2 29/8 3/4 11/3 1/2 15/4 7/8 19/5 1/1 23/6 13/12 4/1 1/1 3/2 9/2 1/0 5/1 1/0 11/2 1/0 6/1 0/1 1/2 7/1 1/1 8/1 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(87,40,224,103) (-1/2,-5/11) -> (5/13,7/18) Hyperbolic Matrix(303,136,176,79) (-5/11,-4/9) -> (12/7,19/11) Hyperbolic Matrix(127,56,-728,-321) (-4/9,-11/25) -> (-3/17,-4/23) Hyperbolic Matrix(687,302,298,131) (-11/25,-7/16) -> (23/10,7/3) Hyperbolic Matrix(211,92,172,75) (-7/16,-3/7) -> (11/9,5/4) Hyperbolic Matrix(251,106,206,87) (-3/7,-8/19) -> (6/5,11/9) Hyperbolic Matrix(457,192,288,121) (-8/19,-5/12) -> (19/12,8/5) Hyperbolic Matrix(121,50,-530,-219) (-5/12,-7/17) -> (-3/13,-5/22) Hyperbolic Matrix(201,82,326,133) (-7/17,-2/5) -> (8/13,13/21) Hyperbolic Matrix(119,46,194,75) (-2/5,-5/13) -> (3/5,8/13) Hyperbolic Matrix(115,44,196,75) (-5/13,-3/8) -> (7/12,3/5) Hyperbolic Matrix(113,42,78,29) (-3/8,-4/11) -> (10/7,3/2) Hyperbolic Matrix(527,190,674,243) (-4/11,-9/25) -> (7/9,18/23) Hyperbolic Matrix(525,188,148,53) (-9/25,-5/14) -> (7/2,25/7) Hyperbolic Matrix(259,92,76,27) (-5/14,-1/3) -> (17/5,7/2) Hyperbolic Matrix(103,32,280,87) (-1/3,-4/13) -> (4/11,7/19) Hyperbolic Matrix(275,84,36,11) (-4/13,-7/23) -> (7/1,8/1) Hyperbolic Matrix(345,104,136,41) (-7/23,-3/10) -> (5/2,23/9) Hyperbolic Matrix(101,30,138,41) (-3/10,-2/7) -> (8/11,3/4) Hyperbolic Matrix(167,46,98,27) (-2/7,-3/11) -> (5/3,12/7) Hyperbolic Matrix(163,44,100,27) (-3/11,-1/4) -> (13/8,5/3) Hyperbolic Matrix(253,60,156,37) (-1/4,-3/13) -> (21/13,13/8) Hyperbolic Matrix(529,120,216,49) (-5/22,-2/9) -> (22/9,5/2) Hyperbolic Matrix(183,40,32,7) (-2/9,-3/14) -> (11/2,6/1) Hyperbolic Matrix(151,32,184,39) (-3/14,-1/5) -> (9/11,5/6) Hyperbolic Matrix(119,22,146,27) (-1/5,-2/11) -> (4/5,9/11) Hyperbolic Matrix(233,42,294,53) (-2/11,-3/17) -> (15/19,4/5) Hyperbolic Matrix(553,96,144,25) (-4/23,-1/6) -> (23/6,4/1) Hyperbolic Matrix(225,34,86,13) (-1/6,-1/7) -> (13/5,21/8) Hyperbolic Matrix(139,18,54,7) (-1/7,0/1) -> (18/7,13/5) Hyperbolic Matrix(63,-10,82,-13) (0/1,1/6) -> (3/4,10/13) Hyperbolic Matrix(161,-30,102,-19) (1/6,1/5) -> (11/7,19/12) Hyperbolic Matrix(59,-14,38,-9) (1/5,1/4) -> (3/2,11/7) Hyperbolic Matrix(209,-56,56,-15) (1/4,3/11) -> (11/3,15/4) Hyperbolic Matrix(697,-192,432,-119) (3/11,5/18) -> (29/18,21/13) Hyperbolic Matrix(151,-42,18,-5) (5/18,2/7) -> (8/1,1/0) Hyperbolic Matrix(19,-6,54,-17) (2/7,1/3) -> (1/3,4/11) Parabolic Matrix(649,-240,192,-71) (7/19,3/8) -> (27/8,17/5) Hyperbolic Matrix(243,-92,140,-53) (3/8,5/13) -> (19/11,7/4) Hyperbolic Matrix(379,-148,484,-189) (7/18,2/5) -> (18/23,11/14) Hyperbolic Matrix(119,-50,50,-21) (2/5,3/7) -> (7/3,12/5) Hyperbolic Matrix(17,-8,32,-15) (3/7,1/2) -> (1/2,5/9) Parabolic Matrix(339,-190,430,-241) (5/9,9/16) -> (11/14,15/19) Hyperbolic Matrix(1259,-710,782,-441) (9/16,13/23) -> (37/23,29/18) Hyperbolic Matrix(443,-252,276,-157) (13/23,4/7) -> (8/5,37/23) Hyperbolic Matrix(243,-140,92,-53) (4/7,7/12) -> (21/8,8/3) Hyperbolic Matrix(697,-432,192,-119) (13/21,5/8) -> (29/8,11/3) Hyperbolic Matrix(59,-38,14,-9) (5/8,2/3) -> (4/1,9/2) Hyperbolic Matrix(71,-50,98,-69) (2/3,5/7) -> (5/7,8/11) Parabolic Matrix(487,-376,136,-105) (10/13,7/9) -> (25/7,18/5) Hyperbolic Matrix(13,-12,12,-11) (5/6,1/1) -> (1/1,7/6) Parabolic Matrix(519,-610,154,-181) (7/6,13/11) -> (37/11,27/8) Hyperbolic Matrix(295,-352,88,-105) (13/11,6/5) -> (10/3,37/11) Hyperbolic Matrix(317,-402,138,-175) (5/4,14/11) -> (16/7,23/10) Hyperbolic Matrix(379,-484,148,-189) (14/11,9/7) -> (23/9,18/7) Hyperbolic Matrix(63,-82,10,-13) (9/7,4/3) -> (6/1,7/1) Hyperbolic Matrix(71,-98,50,-69) (4/3,7/5) -> (7/5,10/7) Parabolic Matrix(17,-32,8,-15) (7/4,2/1) -> (2/1,9/4) Parabolic Matrix(507,-1148,140,-317) (9/4,25/11) -> (47/13,29/8) Hyperbolic Matrix(527,-1202,146,-333) (25/11,16/7) -> (18/5,47/13) Hyperbolic Matrix(239,-578,98,-237) (12/5,17/7) -> (17/7,22/9) Parabolic Matrix(19,-54,6,-17) (8/3,3/1) -> (3/1,10/3) Parabolic Matrix(191,-722,50,-189) (15/4,19/5) -> (19/5,23/6) Parabolic Matrix(21,-100,4,-19) (9/2,5/1) -> (5/1,11/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(87,40,224,103) -> Matrix(1,0,-4,1) Matrix(303,136,176,79) -> Matrix(11,-3,4,-1) Matrix(127,56,-728,-321) -> Matrix(3,-1,-8,3) Matrix(687,302,298,131) -> Matrix(5,-2,8,-3) Matrix(211,92,172,75) -> Matrix(3,-1,4,-1) Matrix(251,106,206,87) -> Matrix(7,-2,4,-1) Matrix(457,192,288,121) -> Matrix(17,-5,24,-7) Matrix(121,50,-530,-219) -> Matrix(3,-1,-8,3) Matrix(201,82,326,133) -> Matrix(3,-1,16,-5) Matrix(119,46,194,75) -> Matrix(3,-1,16,-5) Matrix(115,44,196,75) -> Matrix(3,-1,-8,3) Matrix(113,42,78,29) -> Matrix(7,-3,12,-5) Matrix(527,190,674,243) -> Matrix(7,-2,4,-1) Matrix(525,188,148,53) -> Matrix(5,-2,8,-3) Matrix(259,92,76,27) -> Matrix(3,-1,4,-1) Matrix(103,32,280,87) -> Matrix(3,-1,4,-1) Matrix(275,84,36,11) -> Matrix(7,-2,4,-1) Matrix(345,104,136,41) -> Matrix(7,-2,4,-1) Matrix(101,30,138,41) -> Matrix(7,-3,12,-5) Matrix(167,46,98,27) -> Matrix(1,1,0,1) Matrix(163,44,100,27) -> Matrix(7,-1,8,-1) Matrix(253,60,156,37) -> Matrix(3,-4,4,-5) Matrix(529,120,216,49) -> Matrix(13,1,12,1) Matrix(183,40,32,7) -> Matrix(1,0,-4,1) Matrix(151,32,184,39) -> Matrix(3,-1,4,-1) Matrix(119,22,146,27) -> Matrix(1,0,0,1) Matrix(233,42,294,53) -> Matrix(1,0,0,1) Matrix(553,96,144,25) -> Matrix(9,1,8,1) Matrix(225,34,86,13) -> Matrix(7,-2,4,-1) Matrix(139,18,54,7) -> Matrix(1,1,0,1) Matrix(63,-10,82,-13) -> Matrix(3,-1,4,-1) Matrix(161,-30,102,-19) -> Matrix(5,-2,8,-3) Matrix(59,-14,38,-9) -> Matrix(3,-1,4,-1) Matrix(209,-56,56,-15) -> Matrix(7,-1,8,-1) Matrix(697,-192,432,-119) -> Matrix(31,-7,40,-9) Matrix(151,-42,18,-5) -> Matrix(7,-2,4,-1) Matrix(19,-6,54,-17) -> Matrix(3,-1,4,-1) Matrix(649,-240,192,-71) -> Matrix(1,-1,4,-3) Matrix(243,-92,140,-53) -> Matrix(1,0,0,1) Matrix(379,-148,484,-189) -> Matrix(1,2,0,1) Matrix(119,-50,50,-21) -> Matrix(7,-1,8,-1) Matrix(17,-8,32,-15) -> Matrix(3,-1,4,-1) Matrix(339,-190,430,-241) -> Matrix(1,-2,0,1) Matrix(1259,-710,782,-441) -> Matrix(3,-22,4,-29) Matrix(443,-252,276,-157) -> Matrix(3,5,4,7) Matrix(243,-140,92,-53) -> Matrix(1,2,0,1) Matrix(697,-432,192,-119) -> Matrix(7,-1,8,-1) Matrix(59,-38,14,-9) -> Matrix(7,-2,4,-1) Matrix(71,-50,98,-69) -> Matrix(11,-5,20,-9) Matrix(487,-376,136,-105) -> Matrix(1,0,0,1) Matrix(13,-12,12,-11) -> Matrix(3,-1,4,-1) Matrix(519,-610,154,-181) -> Matrix(1,-1,8,-7) Matrix(295,-352,88,-105) -> Matrix(1,-1,0,1) Matrix(317,-402,138,-175) -> Matrix(1,0,0,1) Matrix(379,-484,148,-189) -> Matrix(5,-4,4,-3) Matrix(63,-82,10,-13) -> Matrix(1,0,0,1) Matrix(71,-98,50,-69) -> Matrix(7,-3,12,-5) Matrix(17,-32,8,-15) -> Matrix(1,0,0,1) Matrix(507,-1148,140,-317) -> Matrix(3,-1,4,-1) Matrix(527,-1202,146,-333) -> Matrix(1,0,0,1) Matrix(239,-578,98,-237) -> Matrix(29,-28,28,-27) Matrix(19,-54,6,-17) -> Matrix(1,-1,0,1) Matrix(191,-722,50,-189) -> Matrix(21,-20,20,-19) Matrix(21,-100,4,-19) -> Matrix(1,-3,0,1) 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 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): 21 ----------------------------------------------------------------------- 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 24 1/6 1/0 1 24 1/5 1/2 1 4 1/4 1/0 1 24 3/11 1/6 1 12 5/18 1/4 1 24 2/7 0 8 1/3 1/2 1 6 4/11 0 8 3/8 1/0 1 24 5/13 1/0 3 4 2/5 (-1/2,0/1) 0 24 3/7 1/6 1 12 1/2 1/2 1 8 5/9 3/2 1 12 9/16 1/0 1 24 13/23 1/0 9 2 4/7 (-1/1,1/0) 0 24 3/5 0/1 4 3 5/8 1/4 1 24 2/3 (1/3,1/2) 0 24 5/7 1/2 5 2 3/4 3/4 1 24 10/13 (1/2,1/1) 0 24 7/9 1/1 2 3 11/14 1/0 1 24 4/5 0 8 5/6 1/0 1 24 1/1 1/2 1 12 7/6 3/4 1 24 13/11 1/1 4 1 6/5 (1/1,1/0) 0 24 5/4 1/2 1 8 14/11 (1/2,1/1) 0 24 9/7 1/1 2 3 4/3 (0/1,1/2) 0 24 7/5 1/2 3 2 3/2 3/4 1 24 11/7 1/2 1 4 8/5 (2/3,3/4) 0 24 5/3 1/1 4 3 7/4 1/0 1 24 2/1 0 8 9/4 1/0 1 24 25/11 1/2 1 2 16/7 (1/2,1/1) 0 24 7/3 1/2 1 12 12/5 (9/10,1/1) 0 24 17/7 1/1 14 1 5/2 5/4 1 24 13/5 3/2 1 4 8/3 (1/1,1/0) 0 24 3/1 1/0 1 6 10/3 (0/1,1/0) 0 24 7/2 1/2 1 8 18/5 (1/2,1/1) 0 24 11/3 1/2 1 12 15/4 7/8 1 24 19/5 1/1 10 1 4/1 (1/1,3/2) 0 24 9/2 1/0 1 24 5/1 1/0 3 4 6/1 (0/1,1/2) 0 24 7/1 1/1 2 3 1/0 1/0 1 24 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(63,-10,82,-13) (0/1,1/6) -> (3/4,10/13) Hyperbolic Matrix(103,-18,40,-7) (1/6,1/5) -> (5/2,13/5) Glide Reflection Matrix(59,-14,38,-9) (1/5,1/4) -> (3/2,11/7) Hyperbolic Matrix(209,-56,56,-15) (1/4,3/11) -> (11/3,15/4) Hyperbolic Matrix(189,-52,338,-93) (3/11,5/18) -> (5/9,9/16) Glide Reflection Matrix(149,-42,188,-53) (5/18,2/7) -> (11/14,4/5) Glide Reflection Matrix(19,-6,54,-17) (2/7,1/3) -> (1/3,4/11) Parabolic Matrix(87,-32,106,-39) (4/11,3/8) -> (4/5,5/6) Glide Reflection Matrix(157,-60,34,-13) (3/8,5/13) -> (9/2,5/1) Glide Reflection Matrix(103,-40,18,-7) (5/13,2/5) -> (5/1,6/1) Glide Reflection Matrix(119,-50,50,-21) (2/5,3/7) -> (7/3,12/5) Hyperbolic Matrix(17,-8,32,-15) (3/7,1/2) -> (1/2,5/9) Parabolic Matrix(415,-234,736,-415) (9/16,13/23) -> (9/16,13/23) Reflection Matrix(183,-104,322,-183) (13/23,4/7) -> (13/23,4/7) Reflection Matrix(75,-44,46,-27) (4/7,3/5) -> (8/5,5/3) Glide Reflection Matrix(75,-46,44,-27) (3/5,5/8) -> (5/3,7/4) Glide Reflection Matrix(59,-38,14,-9) (5/8,2/3) -> (4/1,9/2) Hyperbolic Matrix(29,-20,42,-29) (2/3,5/7) -> (2/3,5/7) Reflection Matrix(41,-30,56,-41) (5/7,3/4) -> (5/7,3/4) Reflection Matrix(243,-188,190,-147) (10/13,7/9) -> (14/11,9/7) Glide Reflection Matrix(107,-84,14,-11) (7/9,11/14) -> (7/1,1/0) Glide Reflection Matrix(13,-12,12,-11) (5/6,1/1) -> (1/1,7/6) Parabolic Matrix(155,-182,132,-155) (7/6,13/11) -> (7/6,13/11) Reflection Matrix(131,-156,110,-131) (13/11,6/5) -> (13/11,6/5) Reflection Matrix(75,-92,22,-27) (6/5,5/4) -> (10/3,7/2) Glide Reflection Matrix(149,-188,42,-53) (5/4,14/11) -> (7/2,18/5) Glide Reflection Matrix(63,-82,10,-13) (9/7,4/3) -> (6/1,7/1) Hyperbolic Matrix(41,-56,30,-41) (4/3,7/5) -> (4/3,7/5) Reflection Matrix(29,-42,20,-29) (7/5,3/2) -> (7/5,3/2) Reflection Matrix(121,-192,46,-73) (11/7,8/5) -> (13/5,8/3) Glide Reflection Matrix(17,-32,8,-15) (7/4,2/1) -> (2/1,9/4) Parabolic Matrix(199,-450,88,-199) (9/4,25/11) -> (9/4,25/11) Reflection Matrix(351,-800,154,-351) (25/11,16/7) -> (25/11,16/7) Reflection Matrix(131,-302,36,-83) (16/7,7/3) -> (18/5,11/3) Glide Reflection Matrix(169,-408,70,-169) (12/5,17/7) -> (12/5,17/7) Reflection Matrix(69,-170,28,-69) (17/7,5/2) -> (17/7,5/2) Reflection Matrix(19,-54,6,-17) (8/3,3/1) -> (3/1,10/3) Parabolic Matrix(151,-570,40,-151) (15/4,19/5) -> (15/4,19/5) Reflection Matrix(39,-152,10,-39) (19/5,4/1) -> (19/5,4/1) 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(63,-10,82,-13) -> Matrix(3,-1,4,-1) 1/2 Matrix(103,-18,40,-7) -> Matrix(5,-1,4,-1) Matrix(59,-14,38,-9) -> Matrix(3,-1,4,-1) 1/2 Matrix(209,-56,56,-15) -> Matrix(7,-1,8,-1) Matrix(189,-52,338,-93) -> Matrix(9,-2,4,-1) Matrix(149,-42,188,-53) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(19,-6,54,-17) -> Matrix(3,-1,4,-1) 1/2 Matrix(87,-32,106,-39) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(157,-60,34,-13) -> Matrix(-1,3,0,1) *** -> (3/2,1/0) Matrix(103,-40,18,-7) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(119,-50,50,-21) -> Matrix(7,-1,8,-1) Matrix(17,-8,32,-15) -> Matrix(3,-1,4,-1) 1/2 Matrix(415,-234,736,-415) -> Matrix(-1,7,0,1) (9/16,13/23) -> (7/2,1/0) Matrix(183,-104,322,-183) -> Matrix(1,2,0,-1) (13/23,4/7) -> (-1/1,1/0) Matrix(75,-44,46,-27) -> Matrix(3,1,4,1) Matrix(75,-46,44,-27) -> Matrix(5,-1,4,-1) Matrix(59,-38,14,-9) -> Matrix(7,-2,4,-1) Matrix(29,-20,42,-29) -> Matrix(5,-2,12,-5) (2/3,5/7) -> (1/3,1/2) Matrix(41,-30,56,-41) -> Matrix(5,-3,8,-5) (5/7,3/4) -> (1/2,3/4) Matrix(243,-188,190,-147) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(107,-84,14,-11) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(13,-12,12,-11) -> Matrix(3,-1,4,-1) 1/2 Matrix(155,-182,132,-155) -> Matrix(7,-6,8,-7) (7/6,13/11) -> (3/4,1/1) Matrix(131,-156,110,-131) -> Matrix(-1,2,0,1) (13/11,6/5) -> (1/1,1/0) Matrix(75,-92,22,-27) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(149,-188,42,-53) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(63,-82,10,-13) -> Matrix(1,0,0,1) Matrix(41,-56,30,-41) -> Matrix(1,0,4,-1) (4/3,7/5) -> (0/1,1/2) Matrix(29,-42,20,-29) -> Matrix(5,-3,8,-5) (7/5,3/2) -> (1/2,3/4) Matrix(121,-192,46,-73) -> Matrix(7,-5,4,-3) Matrix(17,-32,8,-15) -> Matrix(1,0,0,1) Matrix(199,-450,88,-199) -> Matrix(-1,1,0,1) (9/4,25/11) -> (1/2,1/0) Matrix(351,-800,154,-351) -> Matrix(3,-2,4,-3) (25/11,16/7) -> (1/2,1/1) Matrix(131,-302,36,-83) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(169,-408,70,-169) -> Matrix(19,-18,20,-19) (12/5,17/7) -> (9/10,1/1) Matrix(69,-170,28,-69) -> Matrix(9,-10,8,-9) (17/7,5/2) -> (1/1,5/4) Matrix(19,-54,6,-17) -> Matrix(1,-1,0,1) 1/0 Matrix(151,-570,40,-151) -> Matrix(15,-14,16,-15) (15/4,19/5) -> (7/8,1/1) Matrix(39,-152,10,-39) -> Matrix(5,-6,4,-5) (19/5,4/1) -> (1/1,3/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.