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 -7/15 -5/11 -3/7 -2/5 -1/3 -1/4 0/1 1/5 5/19 1/3 7/17 1/2 13/23 3/5 5/7 4/5 11/13 1/1 13/11 5/4 9/7 7/5 3/2 5/3 2/1 11/5 25/11 7/3 17/7 5/2 13/5 8/3 11/4 3/1 7/2 25/7 15/4 19/5 4/1 97/23 17/4 13/3 9/2 19/4 5/1 11/2 17/3 23/4 6/1 13/2 7/1 15/2 8/1 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 -8/17 0/1 -7/15 0/1 -6/13 0/1 1/1 -5/11 0/1 -4/9 0/1 1/1 -15/34 0/1 1/6 -11/25 1/4 -7/16 0/1 1/3 1/2 -3/7 0/1 -14/33 2/7 1/3 -11/26 1/3 2/5 1/2 -8/19 1/2 2/3 -5/12 0/1 1/0 -12/29 0/1 1/7 -7/17 1/4 -2/5 0/1 -9/23 1/2 -7/18 1/3 1/2 -5/13 0/1 -13/34 0/1 1/4 1/3 -8/21 0/1 1/4 -3/8 1/3 1/2 -4/11 0/1 1/3 -9/25 1/3 -5/14 1/3 2/5 1/2 -1/3 1/2 -4/13 2/3 -7/23 1/1 -3/10 0/1 1/2 -2/7 2/3 1/1 -7/25 0/1 -5/18 1/2 1/1 -3/11 1/2 -7/26 1/2 2/3 -4/15 1/2 2/3 -1/4 0/1 1/2 1/1 -4/17 1/2 2/3 -3/13 1/2 -8/35 2/3 -5/22 3/4 1/1 -2/9 0/1 1/1 -3/14 1/3 1/2 -1/5 1/1 -3/16 1/3 1/2 -2/11 2/3 -3/17 3/4 -4/23 8/9 1/1 -1/6 1/1 1/0 -2/13 0/1 1/2 -1/7 1/1 0/1 0/1 1/1 1/6 0/1 1/0 2/11 1/2 2/3 3/16 1/2 2/3 1/5 1/1 1/4 1/2 1/1 5/19 1/1 9/34 1/1 17/16 4/15 1/1 8/7 3/11 3/2 8/29 3/2 2/1 5/18 1/1 2/1 2/7 2/1 5/17 1/0 3/10 -1/1 1/0 7/23 0/1 4/13 -1/1 0/1 1/3 1/1 6/17 1/1 2/1 5/14 3/2 2/1 4/11 2/1 7/19 1/0 3/8 -1/1 1/0 5/13 0/1 12/31 2/3 1/1 19/49 0/1 7/18 0/1 1/1 2/5 0/1 1/1 7/17 1/1 12/29 1/1 6/5 5/12 1/1 3/2 3/7 1/0 1/2 0/1 1/1 1/0 5/9 1/0 9/16 1/1 2/1 22/39 3/2 2/1 13/23 2/1 4/7 2/1 1/0 7/12 2/1 1/0 3/5 1/0 11/18 0/1 1/0 8/13 0/1 13/21 1/2 18/29 0/1 1/1 5/8 1/1 1/0 7/11 0/1 9/14 0/1 1/1 2/3 1/1 2/1 9/13 1/0 16/23 2/1 7/10 3/1 1/0 5/7 1/0 13/18 -3/1 1/0 21/29 1/0 8/11 -2/1 -1/1 3/4 0/1 1/0 10/13 0/1 1/1 7/9 1/1 18/23 1/1 2/1 11/14 1/1 2/1 15/19 1/0 4/5 2/1 17/21 1/0 13/16 2/1 5/2 9/11 3/1 5/6 5/1 1/0 11/13 1/0 6/7 -4/1 1/0 7/8 -1/1 0/1 1/0 1/1 1/0 9/8 -1/1 1/0 8/7 0/1 7/6 3/1 1/0 13/11 1/0 6/5 -4/1 1/0 11/9 -2/1 5/4 -2/1 -1/1 1/0 14/11 -2/1 -1/1 9/7 -1/1 22/17 0/1 13/10 -1/1 0/1 4/3 -1/1 0/1 15/11 1/0 41/30 -1/1 0/1 26/19 0/1 11/8 0/1 1/0 7/5 1/0 17/12 -2/1 1/0 27/19 1/0 10/7 -2/1 -1/1 3/2 -1/1 1/0 11/7 -1/1 41/26 -3/4 -2/3 30/19 -1/1 -2/3 49/31 -2/3 68/43 -2/3 19/12 -1/1 -1/2 46/29 -2/3 73/46 -1/1 -2/3 27/17 -2/3 8/5 -1/2 0/1 37/23 0/1 29/18 -1/2 0/1 21/13 -1/2 34/21 0/1 1/1 13/8 -1/1 -1/2 0/1 5/3 0/1 17/10 0/1 1/1 1/0 46/27 0/1 1/1 121/71 1/1 75/44 1/1 2/1 29/17 1/0 12/7 -1/1 0/1 19/11 0/1 7/4 -1/1 1/0 23/13 -1/1 16/9 -1/1 0/1 25/14 -1/1 -1/2 0/1 9/5 1/0 11/6 -1/1 -1/2 2/1 0/1 15/7 1/0 13/6 0/1 1/0 11/5 1/0 9/4 -1/1 1/0 34/15 -2/1 -1/1 25/11 -1/1 16/7 -1/1 0/1 23/10 -1/1 0/1 1/0 30/13 -4/3 -1/1 7/3 -1/2 40/17 0/1 33/14 -1/2 0/1 59/25 0/1 26/11 -1/2 0/1 19/8 -1/2 -1/3 0/1 50/21 -1/3 0/1 31/13 -1/3 12/5 -1/5 0/1 17/7 0/1 22/9 0/1 1/9 5/2 0/1 1/2 23/9 1/1 18/7 0/1 1/1 13/5 1/1 34/13 1/1 2/1 55/21 1/1 21/8 2/1 1/0 8/3 2/1 1/0 35/13 1/0 27/10 -7/1 1/0 19/7 1/0 30/11 -3/1 -2/1 41/15 -2/1 11/4 -2/1 -1/1 1/0 47/17 -2/1 36/13 -2/1 -1/1 25/9 -3/2 14/5 -1/1 -2/3 17/6 -1/1 0/1 3/1 0/1 19/6 0/1 1/1 35/11 1/0 16/5 0/1 13/4 1/1 1/0 36/11 0/1 1/1 23/7 1/1 10/3 2/1 1/0 37/11 1/0 27/8 -5/1 1/0 17/5 1/0 7/2 -1/1 0/1 1/0 25/7 -1/1 18/5 -1/1 0/1 47/13 -1/1 29/8 -1/1 -1/2 11/3 -1/2 26/7 0/1 15/4 -1/4 0/1 19/5 0/1 23/6 0/1 1/6 4/1 0/1 1/1 21/5 1/0 59/14 -2/1 -1/1 97/23 -1/1 38/9 -1/1 0/1 17/4 -1/1 0/1 1/0 13/3 0/1 9/2 1/1 1/0 14/3 -1/1 0/1 19/4 -1/1 0/1 5/1 0/1 11/2 1/1 1/0 17/3 -1/1 40/7 -1/1 0/1 23/4 -1/1 -1/2 0/1 6/1 0/1 1/1 19/3 1/0 13/2 -1/1 0/1 1/0 20/3 -1/1 0/1 7/1 0/1 22/3 0/1 1/1 15/2 1/1 1/0 8/1 0/1 9/1 1/0 1/0 0/1 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(641,304,272,129) (-1/2,-8/17) -> (40/17,33/14) Hyperbolic Matrix(1853,868,1172,549) (-8/17,-7/15) -> (49/31,68/43) Hyperbolic Matrix(983,456,360,167) (-7/15,-6/13) -> (30/11,41/15) Hyperbolic Matrix(135,62,442,203) (-6/13,-5/11) -> (7/23,4/13) Hyperbolic Matrix(303,136,176,79) (-5/11,-4/9) -> (12/7,19/11) Hyperbolic Matrix(343,152,88,39) (-4/9,-15/34) -> (23/6,4/1) Hyperbolic Matrix(903,398,1114,491) (-15/34,-11/25) -> (17/21,13/16) Hyperbolic Matrix(769,338,430,189) (-11/25,-7/16) -> (25/14,9/5) Hyperbolic Matrix(211,92,172,75) (-7/16,-3/7) -> (11/9,5/4) Hyperbolic Matrix(711,302,1834,779) (-3/7,-14/33) -> (12/31,19/49) Hyperbolic Matrix(1539,652,668,283) (-14/33,-11/26) -> (23/10,30/13) Hyperbolic Matrix(289,122,334,141) (-11/26,-8/19) -> (6/7,7/8) Hyperbolic Matrix(43,18,246,103) (-8/19,-5/12) -> (1/6,2/11) Hyperbolic Matrix(409,170,166,69) (-5/12,-12/29) -> (22/9,5/2) Hyperbolic Matrix(1187,490,734,303) (-12/29,-7/17) -> (21/13,34/21) Hyperbolic Matrix(201,82,326,133) (-7/17,-2/5) -> (8/13,13/21) Hyperbolic Matrix(199,78,-870,-341) (-2/5,-9/23) -> (-3/13,-8/35) Hyperbolic Matrix(865,338,238,93) (-9/23,-7/18) -> (29/8,11/3) Hyperbolic Matrix(351,136,80,31) (-7/18,-5/13) -> (13/3,9/2) Hyperbolic Matrix(663,254,154,59) (-5/13,-13/34) -> (17/4,13/3) Hyperbolic Matrix(1283,490,542,207) (-13/34,-8/21) -> (26/11,19/8) Hyperbolic Matrix(37,14,-230,-87) (-8/21,-3/8) -> (-1/6,-2/13) 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(623,190,482,147) (-4/13,-7/23) -> (9/7,22/17) 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(335,94,866,243) (-2/7,-7/25) -> (5/13,12/31) Hyperbolic Matrix(201,56,664,185) (-7/25,-5/18) -> (3/10,7/23) Hyperbolic Matrix(297,82,134,37) (-5/18,-3/11) -> (11/5,9/4) Hyperbolic Matrix(429,116,196,53) (-3/11,-7/26) -> (13/6,11/5) Hyperbolic Matrix(97,26,526,141) (-7/26,-4/15) -> (2/11,3/16) Hyperbolic Matrix(31,8,-128,-33) (-4/15,-1/4) -> (-1/4,-4/17) Parabolic Matrix(155,36,564,131) (-4/17,-3/13) -> (3/11,8/29) Hyperbolic Matrix(1677,382,1058,241) (-8/35,-5/22) -> (19/12,46/29) Hyperbolic Matrix(309,70,746,169) (-5/22,-2/9) -> (12/29,5/12) Hyperbolic Matrix(277,60,60,13) (-2/9,-3/14) -> (9/2,14/3) Hyperbolic Matrix(151,32,184,39) (-3/14,-1/5) -> (9/11,5/6) Hyperbolic Matrix(327,62,58,11) (-1/5,-3/16) -> (11/2,17/3) Hyperbolic Matrix(205,38,178,33) (-3/16,-2/11) -> (8/7,7/6) Hyperbolic Matrix(233,42,294,53) (-2/11,-3/17) -> (15/19,4/5) Hyperbolic Matrix(671,118,290,51) (-3/17,-4/23) -> (30/13,7/3) Hyperbolic Matrix(231,40,872,151) (-4/23,-1/6) -> (9/34,4/15) Hyperbolic Matrix(369,56,112,17) (-2/13,-1/7) -> (23/7,10/3) 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(381,-74,242,-47) (3/16,1/5) -> (11/7,41/26) Hyperbolic Matrix(59,-14,38,-9) (1/5,1/4) -> (3/2,11/7) 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(657,-182,1166,-323) (8/29,5/18) -> (9/16,22/39) Hyperbolic Matrix(487,-136,376,-105) (5/18,2/7) -> (22/17,13/10) Hyperbolic Matrix(335,-98,482,-141) (2/7,5/17) -> (9/13,16/23) Hyperbolic Matrix(629,-186,186,-55) (5/17,3/10) -> (27/8,17/5) Hyperbolic Matrix(439,-136,184,-57) (4/13,1/3) -> (31/13,12/5) Hyperbolic Matrix(677,-236,284,-99) (1/3,6/17) -> (50/21,31/13) Hyperbolic Matrix(1117,-396,708,-251) (6/17,5/14) -> (41/26,30/19) Hyperbolic Matrix(529,-190,142,-51) (5/14,4/11) -> (26/7,15/4) 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(4063,-1576,2560,-993) (19/49,7/18) -> (73/46,27/17) 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(185,-78,102,-43) (5/12,3/7) -> (9/5,11/6) 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(2899,-1636,1228,-693) (22/39,13/23) -> (59/25,26/11) 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(91,-54,150,-89) (7/12,3/5) -> (3/5,11/18) Parabolic Matrix(611,-374,446,-273) (11/18,8/13) -> (26/19,11/8) 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(161,-102,30,-19) (5/8,7/11) -> (5/1,11/2) Hyperbolic Matrix(279,-178,58,-37) (7/11,9/14) -> (19/4,5/1) Hyperbolic Matrix(247,-160,88,-57) (9/14,2/3) -> (14/5,17/6) Hyperbolic Matrix(243,-166,142,-97) (2/3,9/13) -> (29/17,12/7) Hyperbolic Matrix(425,-296,56,-39) (16/23,7/10) -> (15/2,8/1) 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(347,-252,84,-61) (21/29,8/11) -> (4/1,21/5) Hyperbolic Matrix(487,-376,136,-105) (10/13,7/9) -> (25/7,18/5) Hyperbolic Matrix(875,-708,372,-301) (4/5,17/21) -> (7/3,40/17) Hyperbolic Matrix(1111,-904,424,-345) (13/16,9/11) -> (55/21,21/8) Hyperbolic Matrix(561,-472,208,-175) (5/6,11/13) -> (35/13,27/10) Hyperbolic Matrix(349,-298,130,-111) (11/13,6/7) -> (8/3,35/13) Hyperbolic Matrix(165,-146,26,-23) (7/8,1/1) -> (19/3,13/2) Hyperbolic Matrix(677,-764,428,-483) (9/8,8/7) -> (68/43,19/12) Hyperbolic 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(207,-250,130,-157) (6/5,11/9) -> (27/17,8/5) Hyperbolic Matrix(339,-430,190,-241) (5/4,14/11) -> (16/9,25/14) Hyperbolic Matrix(379,-484,148,-189) (14/11,9/7) -> (23/9,18/7) Hyperbolic Matrix(197,-258,42,-55) (13/10,4/3) -> (14/3,19/4) Hyperbolic Matrix(387,-526,142,-193) (4/3,15/11) -> (19/7,30/11) Hyperbolic Matrix(1695,-2314,994,-1357) (15/11,41/30) -> (75/44,29/17) Hyperbolic Matrix(2767,-3784,1744,-2385) (41/30,26/19) -> (46/29,73/46) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(427,-606,198,-281) (17/12,27/19) -> (15/7,13/6) Hyperbolic Matrix(247,-352,40,-57) (27/19,10/7) -> (6/1,19/3) Hyperbolic Matrix(2009,-3174,726,-1147) (30/19,49/31) -> (47/17,36/13) Hyperbolic Matrix(1821,-2932,772,-1243) (37/23,29/18) -> (33/14,59/25) Hyperbolic Matrix(175,-282,18,-29) (29/18,21/13) -> (9/1,1/0) Hyperbolic Matrix(531,-860,92,-149) (34/21,13/8) -> (23/4,6/1) Hyperbolic Matrix(91,-150,54,-89) (13/8,5/3) -> (5/3,17/10) Parabolic Matrix(1021,-1738,178,-303) (17/10,46/27) -> (40/7,23/4) Hyperbolic Matrix(5317,-9060,1260,-2147) (46/27,121/71) -> (97/23,38/9) Hyperbolic Matrix(8457,-14414,2006,-3419) (121/71,75/44) -> (59/14,97/23) Hyperbolic Matrix(565,-996,156,-275) (7/4,23/13) -> (47/13,29/8) Hyperbolic Matrix(667,-1182,294,-521) (23/13,16/9) -> (34/15,25/11) Hyperbolic Matrix(109,-202,34,-63) (11/6,2/1) -> (16/5,13/4) Hyperbolic Matrix(147,-310,46,-97) (2/1,15/7) -> (35/11,16/5) Hyperbolic Matrix(527,-1202,146,-333) (25/11,16/7) -> (18/5,47/13) Hyperbolic Matrix(291,-668,44,-101) (16/7,23/10) -> (13/2,20/3) Hyperbolic Matrix(661,-1572,156,-371) (19/8,50/21) -> (38/9,17/4) Hyperbolic Matrix(239,-578,98,-237) (12/5,17/7) -> (17/7,22/9) Parabolic Matrix(479,-1250,146,-381) (13/5,34/13) -> (36/11,23/7) Hyperbolic Matrix(1061,-2778,186,-487) (34/13,55/21) -> (17/3,40/7) Hyperbolic Matrix(353,-968,128,-351) (41/15,11/4) -> (11/4,47/17) Parabolic Matrix(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(775,-2464,184,-585) (19/6,35/11) -> (21/5,59/14) Hyperbolic Matrix(253,-826,34,-111) (13/4,36/11) -> (22/3,15/2) Hyperbolic Matrix(87,-322,10,-37) (11/3,26/7) -> (8/1,9/1) Hyperbolic Matrix(191,-722,50,-189) (15/4,19/5) -> (19/5,23/6) Parabolic Matrix(43,-294,6,-41) (20/3,7/1) -> (7/1,22/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(641,304,272,129) -> Matrix(1,0,-4,1) Matrix(1853,868,1172,549) -> Matrix(3,-2,-4,3) Matrix(983,456,360,167) -> Matrix(5,-2,-2,1) Matrix(135,62,442,203) -> Matrix(1,0,-2,1) Matrix(303,136,176,79) -> Matrix(1,0,-2,1) Matrix(343,152,88,39) -> Matrix(1,0,0,1) Matrix(903,398,1114,491) -> Matrix(7,-2,4,-1) Matrix(769,338,430,189) -> Matrix(1,0,-4,1) Matrix(211,92,172,75) -> Matrix(5,-2,-2,1) Matrix(711,302,1834,779) -> Matrix(1,0,-2,1) Matrix(1539,652,668,283) -> Matrix(5,-2,-2,1) Matrix(289,122,334,141) -> Matrix(5,-2,-2,1) Matrix(43,18,246,103) -> Matrix(1,0,0,1) Matrix(409,170,166,69) -> Matrix(1,0,2,1) Matrix(1187,490,734,303) -> Matrix(1,0,-6,1) Matrix(201,82,326,133) -> Matrix(1,0,-2,1) Matrix(199,78,-870,-341) -> Matrix(5,-2,8,-3) Matrix(865,338,238,93) -> Matrix(1,0,-4,1) Matrix(351,136,80,31) -> Matrix(1,0,-2,1) Matrix(663,254,154,59) -> Matrix(1,0,-4,1) Matrix(1283,490,542,207) -> Matrix(1,0,-6,1) Matrix(37,14,-230,-87) -> Matrix(1,0,-2,1) Matrix(113,42,78,29) -> Matrix(5,-2,-2,1) Matrix(527,190,674,243) -> Matrix(7,-2,4,-1) Matrix(525,188,148,53) -> Matrix(5,-2,-2,1) Matrix(259,92,76,27) -> Matrix(5,-2,-2,1) Matrix(103,32,280,87) -> Matrix(7,-4,2,-1) Matrix(623,190,482,147) -> Matrix(3,-2,-4,3) Matrix(345,104,136,41) -> Matrix(1,0,0,1) Matrix(101,30,138,41) -> Matrix(1,0,-2,1) Matrix(335,94,866,243) -> Matrix(1,0,0,1) Matrix(201,56,664,185) -> Matrix(1,0,-2,1) Matrix(297,82,134,37) -> Matrix(1,0,-2,1) Matrix(429,116,196,53) -> Matrix(3,-2,2,-1) Matrix(97,26,526,141) -> Matrix(1,0,0,1) Matrix(31,8,-128,-33) -> Matrix(1,0,0,1) Matrix(155,36,564,131) -> Matrix(5,-4,4,-3) Matrix(1677,382,1058,241) -> Matrix(5,-4,-6,5) Matrix(309,70,746,169) -> Matrix(7,-6,6,-5) Matrix(277,60,60,13) -> Matrix(1,0,-2,1) Matrix(151,32,184,39) -> Matrix(7,-4,2,-1) Matrix(327,62,58,11) -> Matrix(1,0,-2,1) Matrix(205,38,178,33) -> Matrix(3,-2,2,-1) Matrix(233,42,294,53) -> Matrix(5,-4,4,-3) Matrix(671,118,290,51) -> Matrix(5,-4,-6,5) Matrix(231,40,872,151) -> Matrix(17,-16,16,-15) Matrix(369,56,112,17) -> Matrix(3,-2,2,-1) Matrix(139,18,54,7) -> Matrix(1,0,0,1) Matrix(63,-10,82,-13) -> Matrix(1,0,0,1) Matrix(381,-74,242,-47) -> Matrix(5,-4,-6,5) Matrix(59,-14,38,-9) -> Matrix(1,0,-2,1) Matrix(191,-50,722,-189) -> Matrix(19,-18,18,-17) Matrix(529,-142,190,-51) -> Matrix(5,-6,-4,5) Matrix(657,-182,1166,-323) -> Matrix(1,0,0,1) Matrix(487,-136,376,-105) -> Matrix(1,-2,0,1) Matrix(335,-98,482,-141) -> Matrix(1,0,0,1) Matrix(629,-186,186,-55) -> Matrix(1,-4,0,1) Matrix(439,-136,184,-57) -> Matrix(1,0,-4,1) Matrix(677,-236,284,-99) -> Matrix(1,-2,-2,5) Matrix(1117,-396,708,-251) -> Matrix(1,0,-2,1) Matrix(529,-190,142,-51) -> Matrix(1,-2,-2,5) Matrix(665,-246,246,-91) -> Matrix(1,-6,0,1) Matrix(243,-92,140,-53) -> Matrix(1,0,0,1) Matrix(4063,-1576,2560,-993) -> Matrix(3,-2,-4,3) Matrix(379,-148,484,-189) -> Matrix(3,-2,2,-1) Matrix(239,-98,578,-237) -> Matrix(7,-6,6,-5) Matrix(185,-78,102,-43) -> Matrix(1,-2,0,1) Matrix(17,-8,32,-15) -> Matrix(1,0,0,1) Matrix(339,-190,430,-241) -> Matrix(1,0,0,1) Matrix(2899,-1636,1228,-693) -> Matrix(1,-2,0,1) Matrix(443,-252,276,-157) -> Matrix(1,-2,-2,5) Matrix(243,-140,92,-53) -> Matrix(1,0,0,1) Matrix(91,-54,150,-89) -> Matrix(1,-2,0,1) Matrix(611,-374,446,-273) -> Matrix(1,0,0,1) Matrix(1481,-918,534,-331) -> Matrix(1,-2,0,1) Matrix(533,-332,236,-147) -> Matrix(1,-2,0,1) Matrix(161,-102,30,-19) -> Matrix(1,0,0,1) Matrix(279,-178,58,-37) -> Matrix(1,0,-2,1) Matrix(247,-160,88,-57) -> Matrix(1,0,-2,1) Matrix(243,-166,142,-97) -> Matrix(1,-2,0,1) Matrix(425,-296,56,-39) -> Matrix(1,-2,0,1) Matrix(141,-100,196,-139) -> Matrix(1,-6,0,1) Matrix(279,-202,250,-181) -> Matrix(1,2,0,1) Matrix(347,-252,84,-61) -> Matrix(1,2,0,1) Matrix(487,-376,136,-105) -> Matrix(1,0,-2,1) Matrix(875,-708,372,-301) -> Matrix(1,-2,-2,5) Matrix(1111,-904,424,-345) -> Matrix(3,-8,2,-5) Matrix(561,-472,208,-175) -> Matrix(1,-12,0,1) Matrix(349,-298,130,-111) -> Matrix(1,6,0,1) Matrix(165,-146,26,-23) -> Matrix(1,0,0,1) Matrix(677,-764,428,-483) -> Matrix(1,2,-2,-3) Matrix(519,-610,154,-181) -> Matrix(1,-8,0,1) Matrix(295,-352,88,-105) -> Matrix(1,6,0,1) Matrix(207,-250,130,-157) -> Matrix(1,4,-2,-7) Matrix(339,-430,190,-241) -> Matrix(1,2,-2,-3) Matrix(379,-484,148,-189) -> Matrix(1,2,0,1) Matrix(197,-258,42,-55) -> Matrix(1,0,0,1) Matrix(387,-526,142,-193) -> Matrix(1,-2,0,1) Matrix(1695,-2314,994,-1357) -> Matrix(1,2,0,1) Matrix(2767,-3784,1744,-2385) -> Matrix(1,2,-2,-3) Matrix(141,-196,100,-139) -> Matrix(1,-2,0,1) Matrix(427,-606,198,-281) -> Matrix(1,2,0,1) Matrix(247,-352,40,-57) -> Matrix(1,2,0,1) Matrix(2009,-3174,726,-1147) -> Matrix(5,4,-4,-3) Matrix(1821,-2932,772,-1243) -> Matrix(1,0,0,1) Matrix(175,-282,18,-29) -> Matrix(1,0,2,1) Matrix(531,-860,92,-149) -> Matrix(1,0,0,1) Matrix(91,-150,54,-89) -> Matrix(1,0,2,1) Matrix(1021,-1738,178,-303) -> Matrix(1,0,-2,1) Matrix(5317,-9060,1260,-2147) -> Matrix(1,0,-2,1) Matrix(8457,-14414,2006,-3419) -> Matrix(3,-4,-2,3) Matrix(565,-996,156,-275) -> Matrix(1,2,-2,-3) Matrix(667,-1182,294,-521) -> Matrix(3,2,-2,-1) Matrix(109,-202,34,-63) -> Matrix(1,0,2,1) Matrix(147,-310,46,-97) -> Matrix(1,0,0,1) Matrix(527,-1202,146,-333) -> Matrix(1,0,0,1) Matrix(291,-668,44,-101) -> Matrix(1,0,0,1) Matrix(661,-1572,156,-371) -> Matrix(1,0,2,1) Matrix(239,-578,98,-237) -> Matrix(1,0,14,1) Matrix(479,-1250,146,-381) -> Matrix(1,-2,2,-3) Matrix(1061,-2778,186,-487) -> Matrix(1,-2,0,1) Matrix(353,-968,128,-351) -> Matrix(1,0,0,1) Matrix(37,-108,12,-35) -> Matrix(1,0,2,1) Matrix(775,-2464,184,-585) -> Matrix(1,-2,0,1) Matrix(253,-826,34,-111) -> Matrix(1,0,0,1) Matrix(87,-322,10,-37) -> Matrix(1,0,2,1) Matrix(191,-722,50,-189) -> Matrix(1,0,10,1) Matrix(43,-294,6,-41) -> Matrix(1,0,2,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 26 Degree of the the map X: 26 Degree of the the map Y: 128 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- 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 1 1 0/1 (0/1,1/1) 0 24 1/6 (0/1,1/0) 0 24 1/5 1/1 2 4 1/4 (1/2,1/1) 0 24 5/19 1/1 9 1 4/15 (1/1,8/7) 0 24 3/11 3/2 1 12 5/18 (1/1,2/1) 0 24 2/7 2/1 1 8 5/17 1/0 1 12 3/10 (-1/1,1/0) 0 24 4/13 (-1/1,0/1) 0 24 1/3 1/1 1 6 6/17 (1/1,2/1) 0 24 5/14 (3/2,2/1) 0 24 4/11 2/1 1 8 3/8 (-1/1,1/0) 0 24 5/13 0/1 1 4 7/18 (0/1,1/1) 0 24 2/5 (0/1,1/1) 0 24 7/17 1/1 3 1 5/12 (1/1,3/2) 0 24 3/7 1/0 1 12 1/2 0 8 5/9 1/0 1 12 9/16 (1/1,2/1) 0 24 13/23 2/1 1 2 4/7 (2/1,1/0) 0 24 7/12 (2/1,1/0) 0 24 3/5 1/0 1 3 11/18 (0/1,1/0) 0 24 8/13 0/1 1 8 5/8 (1/1,1/0) 0 24 7/11 0/1 1 4 9/14 (0/1,1/1) 0 24 2/3 (1/1,2/1) 0 24 9/13 1/0 1 12 16/23 2/1 1 8 7/10 (3/1,1/0) 0 24 5/7 1/0 3 2 3/4 (0/1,1/0) 0 24 10/13 (0/1,1/1) 0 24 7/9 1/1 2 3 11/14 (1/1,2/1) 0 24 4/5 2/1 1 8 5/6 (5/1,1/0) 0 24 11/13 1/0 9 1 6/7 (-4/1,1/0) 0 24 1/1 1/0 1 12 7/6 (3/1,1/0) 0 24 13/11 1/0 7 1 6/5 (-4/1,1/0) 0 24 5/4 0 8 14/11 (-2/1,-1/1) 0 24 9/7 -1/1 2 3 13/10 (-1/1,0/1) 0 24 4/3 (-1/1,0/1) 0 24 15/11 1/0 1 12 41/30 (-1/1,0/1) 0 24 26/19 0/1 1 8 11/8 (0/1,1/0) 0 24 7/5 1/0 1 2 3/2 (-1/1,1/0) 0 24 11/7 -1/1 2 4 30/19 (-1/1,-2/3) 0 24 49/31 -2/3 1 3 19/12 (-1/1,-1/2) 0 24 8/5 (-1/2,0/1) 0 24 37/23 0/1 1 2 29/18 (-1/2,0/1) 0 24 21/13 -1/2 1 12 13/8 0 8 5/3 0/1 1 3 17/10 0 8 46/27 (0/1,1/1) 0 24 121/71 1/1 2 1 75/44 (1/1,2/1) 0 24 29/17 1/0 1 12 12/7 (-1/1,0/1) 0 24 7/4 (-1/1,1/0) 0 24 23/13 -1/1 2 2 16/9 (-1/1,0/1) 0 24 9/5 1/0 1 12 11/6 (-1/1,-1/2) 0 24 2/1 0/1 1 8 9/4 (-1/1,1/0) 0 24 25/11 -1/1 2 2 16/7 (-1/1,0/1) 0 24 23/10 0 8 7/3 -1/2 1 12 19/8 0 8 50/21 (-1/3,0/1) 0 24 31/13 -1/3 1 6 12/5 (-1/5,0/1) 0 24 17/7 0/1 7 1 5/2 (0/1,1/2) 0 24 13/5 1/1 2 4 34/13 (1/1,2/1) 0 24 21/8 (2/1,1/0) 0 24 8/3 (2/1,1/0) 0 24 19/7 1/0 1 12 30/11 (-3/1,-2/1) 0 24 11/4 0 8 25/9 -3/2 1 12 14/5 (-1/1,-2/3) 0 24 17/6 (-1/1,0/1) 0 24 3/1 0/1 1 6 19/6 (0/1,1/1) 0 24 16/5 0/1 1 8 13/4 (1/1,1/0) 0 24 10/3 (2/1,1/0) 0 24 7/2 0 8 18/5 (-1/1,0/1) 0 24 11/3 -1/2 1 12 26/7 0/1 1 8 15/4 (-1/4,0/1) 0 24 19/5 0/1 5 1 4/1 (0/1,1/1) 0 24 9/2 (1/1,1/0) 0 24 5/1 0/1 1 4 11/2 (1/1,1/0) 0 24 6/1 (0/1,1/1) 0 24 13/2 0 8 20/3 (-1/1,0/1) 0 24 7/1 0/1 1 3 15/2 (1/1,1/0) 0 24 8/1 0/1 1 8 9/1 1/0 1 12 1/0 (0/1,1/0) 0 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(39,-10,152,-39) (1/4,5/19) -> (1/4,5/19) Reflection Matrix(151,-40,570,-151) (5/19,4/15) -> (5/19,4/15) Reflection Matrix(529,-142,190,-51) (4/15,3/11) -> (25/9,14/5) 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(335,-98,482,-141) (2/7,5/17) -> (9/13,16/23) Hyperbolic Matrix(129,-38,112,-33) (5/17,3/10) -> (1/1,7/6) Glide Reflection Matrix(203,-62,36,-11) (3/10,4/13) -> (11/2,6/1) Glide Reflection Matrix(439,-136,184,-57) (4/13,1/3) -> (31/13,12/5) Hyperbolic Matrix(677,-236,284,-99) (1/3,6/17) -> (50/21,31/13) Hyperbolic Matrix(833,-296,318,-113) (6/17,5/14) -> (34/13,21/8) Glide Reflection Matrix(529,-190,142,-51) (5/14,4/11) -> (26/7,15/4) Hyperbolic 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(243,-94,380,-147) (5/13,7/18) -> (7/11,9/14) Glide Reflection Matrix(137,-54,104,-41) (7/18,2/5) -> (13/10,4/3) Glide Reflection Matrix(69,-28,170,-69) (2/5,7/17) -> (2/5,7/17) Reflection Matrix(169,-70,408,-169) (7/17,5/12) -> (7/17,5/12) Reflection Matrix(185,-78,102,-43) (5/12,3/7) -> (9/5,11/6) 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(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(91,-54,150,-89) (7/12,3/5) -> (3/5,11/18) Parabolic Matrix(611,-374,446,-273) (11/18,8/13) -> (26/19,11/8) Hyperbolic Matrix(133,-82,60,-37) (8/13,5/8) -> (2/1,9/4) Glide Reflection Matrix(161,-102,30,-19) (5/8,7/11) -> (5/1,11/2) Hyperbolic Matrix(247,-160,88,-57) (9/14,2/3) -> (14/5,17/6) Hyperbolic Matrix(243,-166,142,-97) (2/3,9/13) -> (29/17,12/7) Hyperbolic Matrix(425,-296,56,-39) (16/23,7/10) -> (15/2,8/1) Hyperbolic Matrix(99,-70,140,-99) (7/10,5/7) -> (7/10,5/7) 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(243,-190,188,-147) (7/9,11/14) -> (9/7,13/10) Glide Reflection Matrix(131,-110,156,-131) (5/6,11/13) -> (5/6,11/13) Reflection Matrix(155,-132,182,-155) (11/13,6/7) -> (11/13,6/7) Reflection Matrix(141,-122,52,-45) (6/7,1/1) -> (8/3,19/7) Glide Reflection 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(387,-526,142,-193) (4/3,15/11) -> (19/7,30/11) Hyperbolic Matrix(1695,-2314,994,-1357) (15/11,41/30) -> (75/44,29/17) Hyperbolic Matrix(841,-1150,264,-361) (41/30,26/19) -> (19/6,16/5) Glide Reflection Matrix(111,-154,80,-111) (11/8,7/5) -> (11/8,7/5) Reflection Matrix(29,-42,20,-29) (7/5,3/2) -> (7/5,3/2) Reflection Matrix(485,-764,186,-293) (11/7,30/19) -> (13/5,34/13) Glide Reflection Matrix(753,-1190,112,-177) (30/19,49/31) -> (20/3,7/1) Glide Reflection Matrix(549,-868,74,-117) (49/31,19/12) -> (7/1,15/2) Glide Reflection Matrix(185,-294,56,-89) (19/12,8/5) -> (13/4,10/3) Glide Reflection Matrix(1333,-2146,828,-1333) (37/23,29/18) -> (37/23,29/18) Reflection Matrix(175,-282,18,-29) (29/18,21/13) -> (9/1,1/0) Hyperbolic Matrix(303,-490,128,-207) (21/13,13/8) -> (7/3,19/8) Glide Reflection Matrix(91,-150,54,-89) (13/8,5/3) -> (5/3,17/10) Parabolic Matrix(1013,-1724,426,-725) (17/10,46/27) -> (19/8,50/21) Glide Reflection Matrix(6533,-11132,3834,-6533) (46/27,121/71) -> (46/27,121/71) Reflection Matrix(10649,-18150,6248,-10649) (121/71,75/44) -> (121/71,75/44) Reflection Matrix(79,-136,18,-31) (12/7,7/4) -> (4/1,9/2) Glide Reflection Matrix(183,-322,104,-183) (7/4,23/13) -> (7/4,23/13) Reflection Matrix(433,-768,190,-337) (23/13,16/9) -> (25/11,16/7) Glide Reflection Matrix(189,-338,52,-93) (16/9,9/5) -> (18/5,11/3) Glide Reflection Matrix(109,-202,34,-63) (11/6,2/1) -> (16/5,13/4) Hyperbolic Matrix(199,-450,88,-199) (9/4,25/11) -> (9/4,25/11) Reflection Matrix(291,-668,44,-101) (16/7,23/10) -> (13/2,20/3) Hyperbolic Matrix(283,-652,102,-235) (23/10,7/3) -> (11/4,25/9) 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(167,-456,26,-71) (30/11,11/4) -> (6/1,13/2) Glide Reflection Matrix(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(87,-322,10,-37) (11/3,26/7) -> (8/1,9/1) Hyperbolic 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(1,0,2,-1) (-1/1,0/1) -> (0/1,1/1) Matrix(63,-10,82,-13) -> Matrix(1,0,0,1) Matrix(103,-18,40,-7) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(59,-14,38,-9) -> Matrix(1,0,-2,1) 0/1 Matrix(39,-10,152,-39) -> Matrix(3,-2,4,-3) (1/4,5/19) -> (1/2,1/1) Matrix(151,-40,570,-151) -> Matrix(15,-16,14,-15) (5/19,4/15) -> (1/1,8/7) Matrix(529,-142,190,-51) -> Matrix(5,-6,-4,5) Matrix(189,-52,338,-93) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(149,-42,188,-53) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(335,-98,482,-141) -> Matrix(1,0,0,1) Matrix(129,-38,112,-33) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(203,-62,36,-11) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(439,-136,184,-57) -> Matrix(1,0,-4,1) 0/1 Matrix(677,-236,284,-99) -> Matrix(1,-2,-2,5) Matrix(833,-296,318,-113) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(529,-190,142,-51) -> Matrix(1,-2,-2,5) Matrix(87,-32,106,-39) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(157,-60,34,-13) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(243,-94,380,-147) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(137,-54,104,-41) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(69,-28,170,-69) -> Matrix(1,0,2,-1) (2/5,7/17) -> (0/1,1/1) Matrix(169,-70,408,-169) -> Matrix(5,-6,4,-5) (7/17,5/12) -> (1/1,3/2) Matrix(185,-78,102,-43) -> Matrix(1,-2,0,1) 1/0 Matrix(17,-8,32,-15) -> Matrix(1,0,0,1) Matrix(415,-234,736,-415) -> Matrix(3,-4,2,-3) (9/16,13/23) -> (1/1,2/1) Matrix(443,-252,276,-157) -> Matrix(1,-2,-2,5) Matrix(243,-140,92,-53) -> Matrix(1,0,0,1) Matrix(91,-54,150,-89) -> Matrix(1,-2,0,1) 1/0 Matrix(611,-374,446,-273) -> Matrix(1,0,0,1) Matrix(133,-82,60,-37) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(161,-102,30,-19) -> Matrix(1,0,0,1) Matrix(247,-160,88,-57) -> Matrix(1,0,-2,1) 0/1 Matrix(243,-166,142,-97) -> Matrix(1,-2,0,1) 1/0 Matrix(425,-296,56,-39) -> Matrix(1,-2,0,1) 1/0 Matrix(99,-70,140,-99) -> Matrix(-1,6,0,1) (7/10,5/7) -> (3/1,1/0) Matrix(41,-30,56,-41) -> Matrix(1,0,0,-1) (5/7,3/4) -> (0/1,1/0) Matrix(243,-188,190,-147) -> Matrix(3,-2,-2,1) Matrix(243,-190,188,-147) -> Matrix(1,-2,-2,3) Matrix(131,-110,156,-131) -> Matrix(-1,10,0,1) (5/6,11/13) -> (5/1,1/0) Matrix(155,-132,182,-155) -> Matrix(1,8,0,-1) (11/13,6/7) -> (-4/1,1/0) Matrix(141,-122,52,-45) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(155,-182,132,-155) -> Matrix(-1,6,0,1) (7/6,13/11) -> (3/1,1/0) Matrix(131,-156,110,-131) -> Matrix(1,8,0,-1) (13/11,6/5) -> (-4/1,1/0) Matrix(75,-92,22,-27) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(149,-188,42,-53) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(387,-526,142,-193) -> Matrix(1,-2,0,1) 1/0 Matrix(1695,-2314,994,-1357) -> Matrix(1,2,0,1) 1/0 Matrix(841,-1150,264,-361) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(111,-154,80,-111) -> Matrix(1,0,0,-1) (11/8,7/5) -> (0/1,1/0) Matrix(29,-42,20,-29) -> Matrix(1,2,0,-1) (7/5,3/2) -> (-1/1,1/0) Matrix(485,-764,186,-293) -> Matrix(5,4,4,3) Matrix(753,-1190,112,-177) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(549,-868,74,-117) -> Matrix(3,2,2,1) Matrix(185,-294,56,-89) -> Matrix(3,2,2,1) Matrix(1333,-2146,828,-1333) -> Matrix(-1,0,4,1) (37/23,29/18) -> (-1/2,0/1) Matrix(175,-282,18,-29) -> Matrix(1,0,2,1) 0/1 Matrix(303,-490,128,-207) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(91,-150,54,-89) -> Matrix(1,0,2,1) 0/1 Matrix(1013,-1724,426,-725) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(6533,-11132,3834,-6533) -> Matrix(1,0,2,-1) (46/27,121/71) -> (0/1,1/1) Matrix(10649,-18150,6248,-10649) -> Matrix(3,-4,2,-3) (121/71,75/44) -> (1/1,2/1) Matrix(79,-136,18,-31) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(183,-322,104,-183) -> Matrix(1,2,0,-1) (7/4,23/13) -> (-1/1,1/0) Matrix(433,-768,190,-337) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(189,-338,52,-93) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(109,-202,34,-63) -> Matrix(1,0,2,1) 0/1 Matrix(199,-450,88,-199) -> Matrix(1,2,0,-1) (9/4,25/11) -> (-1/1,1/0) Matrix(291,-668,44,-101) -> Matrix(1,0,0,1) Matrix(283,-652,102,-235) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(169,-408,70,-169) -> Matrix(-1,0,10,1) (12/5,17/7) -> (-1/5,0/1) Matrix(69,-170,28,-69) -> Matrix(1,0,4,-1) (17/7,5/2) -> (0/1,1/2) Matrix(167,-456,26,-71) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(37,-108,12,-35) -> Matrix(1,0,2,1) 0/1 Matrix(87,-322,10,-37) -> Matrix(1,0,2,1) 0/1 Matrix(151,-570,40,-151) -> Matrix(-1,0,8,1) (15/4,19/5) -> (-1/4,0/1) Matrix(39,-152,10,-39) -> Matrix(1,0,2,-1) (19/5,4/1) -> (0/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.