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 0/1 1/1 -5/11 1/0 -4/9 1/2 1/1 -15/34 1/1 8/7 -11/25 3/2 -7/16 3/2 -10/23 2/1 5/2 -3/7 1/0 -8/19 0/1 1/2 -5/12 0/1 1/1 -12/29 1/1 3/2 -7/17 1/0 -2/5 1/0 -9/23 1/0 -7/18 -1/1 0/1 -12/31 0/1 1/0 -5/13 0/1 -8/21 0/1 1/0 -11/29 1/2 -3/8 1/1 2/1 -4/11 -2/1 1/0 -9/25 -1/1 -5/14 -1/2 -1/3 1/0 -4/13 1/2 -7/23 1/1 -3/10 1/1 2/1 -2/7 -1/1 1/0 -7/25 -1/2 -5/18 -1/1 0/1 -8/29 -1/2 -3/11 0/1 -4/15 0/1 1/2 -5/19 1/2 -6/23 1/1 1/0 -1/4 1/0 -3/13 -1/2 -5/22 -1/5 0/1 -2/9 0/1 1/2 -3/14 -1/1 0/1 -4/19 1/2 -5/24 1/1 2/1 -1/5 1/0 -2/11 1/0 -3/17 -1/2 -4/23 -1/4 0/1 -1/6 0/1 1/1 -1/7 1/0 -1/8 0/1 1/1 -1/9 0/1 -1/10 1/0 0/1 0/1 1/0 1/8 1/0 1/7 0/1 2/13 1/0 1/6 -1/1 0/1 1/5 1/0 3/14 -1/1 0/1 2/9 0/1 1/0 3/13 0/1 4/17 1/2 1/4 -1/1 0/1 5/19 0/1 9/34 0/1 1/9 4/15 0/1 1/4 3/11 1/2 8/29 0/1 1/2 5/18 0/1 1/1 2/7 1/0 5/17 -1/2 3/10 0/1 1/3 7/23 1/2 4/13 1/2 1/1 1/3 1/0 5/14 -2/1 -1/1 4/11 -1/2 7/19 -1/4 3/8 0/1 1/1 5/13 1/0 7/18 -2/1 -1/1 2/5 -1/2 0/1 7/17 0/1 12/29 0/1 1/12 5/12 0/1 1/5 8/19 1/2 11/26 0/1 1/3 14/33 0/1 1/2 3/7 1/2 13/30 1/1 4/3 10/23 1/0 17/39 0/1 7/16 1/1 2/1 11/25 1/0 4/9 0/1 1/0 5/11 0/1 6/13 0/1 1/2 1/2 1/0 5/9 -1/2 9/16 -1/1 0/1 13/23 -1/2 17/30 -1/3 0/1 4/7 -1/2 0/1 7/12 -1/1 0/1 3/5 0/1 11/18 0/1 1/5 8/13 1/2 21/34 -1/1 0/1 13/21 1/2 18/29 0/1 1/2 5/8 0/1 1/1 2/3 1/1 1/0 7/10 3/1 4/1 5/7 1/0 13/18 -7/1 -6/1 21/29 -11/2 29/40 -9/2 8/11 -4/1 1/0 11/15 -5/2 14/19 1/0 17/23 -2/1 3/4 -2/1 -1/1 10/13 -1/1 1/0 7/9 -1/1 18/23 -5/6 -4/5 11/14 -1/1 -2/3 15/19 -3/4 4/5 -1/2 9/11 -1/2 5/6 -1/5 0/1 11/13 0/1 6/7 0/1 1/6 7/8 1/2 1/1 1/0 9/8 -1/3 0/1 8/7 -1/2 7/6 -1/5 0/1 13/11 0/1 6/5 0/1 1/4 11/9 1/2 16/13 0/1 1/0 21/17 1/2 26/21 0/1 1/2 5/4 1/2 14/11 3/4 1/1 9/7 1/1 4/3 2/1 1/0 11/8 5/1 6/1 7/5 1/0 17/12 -9/1 -8/1 44/31 -15/2 27/19 -13/2 37/26 1/0 10/7 -5/1 1/0 13/9 -7/2 29/20 -3/1 -26/9 16/11 -5/2 3/2 -2/1 -1/1 17/11 1/0 14/9 -1/1 -3/4 25/16 -1/1 -2/3 11/7 -1/2 19/12 -1/3 0/1 46/29 1/0 27/17 -1/2 8/5 0/1 1/0 37/23 1/0 29/18 -2/1 -1/1 21/13 -1/2 13/8 1/0 5/3 0/1 17/10 1/2 46/27 7/8 1/1 121/71 1/1 75/44 1/1 14/13 29/17 3/2 12/7 0/1 1/0 43/25 1/2 74/43 3/4 31/18 1/1 4/3 50/29 1/1 1/0 19/11 1/0 7/4 0/1 1/1 2/1 1/0 9/4 -2/1 -1/1 34/15 -2/1 -3/2 25/11 -3/2 16/7 -3/2 -1/1 23/10 1/0 7/3 1/0 19/8 -3/2 69/29 -7/6 50/21 -1/1 -3/4 31/13 1/0 12/5 -3/2 -1/1 17/7 -1/1 22/9 -1/1 -3/4 5/2 -1/1 0/1 23/9 -1/1 18/7 -1/1 1/0 49/19 -3/4 31/12 -1/1 -4/5 13/5 -1/2 21/8 -1/1 0/1 8/3 -1/2 0/1 35/13 0/1 27/10 0/1 1/7 19/7 1/2 11/4 1/0 36/13 0/1 1/0 25/9 1/0 14/5 0/1 1/2 17/6 4/5 1/1 3/1 1/0 19/6 -16/5 -3/1 73/23 -3/1 54/17 -3/1 -47/16 35/11 -17/6 16/5 -5/2 13/4 -2/1 -1/1 23/7 1/0 10/3 -5/2 -2/1 37/11 -2/1 27/8 -2/1 -17/9 17/5 -7/4 24/7 -3/2 -1/1 55/16 -1/1 0/1 31/9 -2/1 7/2 -3/2 25/7 -1/1 18/5 -1/1 1/0 47/13 1/0 76/21 -2/1 1/0 29/8 -2/1 -1/1 11/3 -3/2 37/10 -6/5 -1/1 26/7 -5/4 15/4 -8/7 -1/1 19/5 -1/1 23/6 -1/1 -10/11 4/1 -1/1 -1/2 9/2 -1/1 0/1 23/5 1/2 60/13 5/6 1/1 37/8 1/0 14/3 1/1 1/0 47/10 1/0 33/7 0/1 52/11 1/2 19/4 2/3 1/1 5/1 1/0 21/4 -10/3 -3/1 16/3 -2/1 1/0 11/2 -3/1 -2/1 6/1 -2/1 -3/2 7/1 -1/1 8/1 -1/2 1/0 -1/1 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(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(1,0,2,1) Matrix(87,40,224,103) -> Matrix(1,-2,0,1) Matrix(85,38,-302,-135) -> Matrix(1,0,-2,1) Matrix(343,152,88,39) -> Matrix(3,-2,-4,3) Matrix(427,188,988,435) -> Matrix(3,-4,4,-5) Matrix(687,302,298,131) -> Matrix(3,-4,-2,3) Matrix(257,112,296,129) -> Matrix(1,-2,4,-7) Matrix(677,294,426,185) -> Matrix(1,-2,-2,5) Matrix(251,106,206,87) -> Matrix(1,0,2,1) Matrix(81,34,374,157) -> Matrix(1,0,-2,1) Matrix(409,170,166,69) -> Matrix(1,0,-2,1) Matrix(247,102,-942,-389) -> Matrix(1,-2,2,-3) Matrix(79,32,-200,-81) -> Matrix(1,-2,0,1) Matrix(865,338,238,93) -> Matrix(3,2,-2,-1) Matrix(629,244,116,45) -> Matrix(1,-2,0,1) Matrix(233,90,510,197) -> Matrix(1,0,2,1) Matrix(157,60,348,133) -> Matrix(1,0,0,1) Matrix(773,294,234,89) -> Matrix(5,-2,-2,1) Matrix(1003,380,388,147) -> Matrix(3,-2,-4,3) Matrix(153,56,112,41) -> Matrix(1,4,0,1) Matrix(527,190,674,243) -> Matrix(5,6,-6,-7) Matrix(525,188,148,53) -> Matrix(5,4,-4,-3) Matrix(299,106,110,39) -> Matrix(1,0,2,1) Matrix(71,22,242,75) -> Matrix(1,0,-2,1) Matrix(275,84,36,11) -> Matrix(3,-2,-4,3) Matrix(345,104,136,41) -> Matrix(1,-2,0,1) Matrix(69,20,100,29) -> Matrix(1,2,0,1) Matrix(201,56,664,185) -> Matrix(1,0,4,1) Matrix(463,128,1096,303) -> Matrix(1,0,4,1) Matrix(131,36,564,155) -> Matrix(1,0,4,1) Matrix(67,18,294,79) -> Matrix(1,0,-2,1) Matrix(197,52,716,189) -> Matrix(1,0,0,1) Matrix(907,236,196,51) -> Matrix(1,0,0,1) Matrix(253,60,156,37) -> Matrix(1,0,0,1) Matrix(559,128,904,207) -> Matrix(1,0,4,1) Matrix(309,70,746,169) -> Matrix(1,0,10,1) Matrix(183,40,32,7) -> Matrix(1,-2,0,1) Matrix(245,52,212,45) -> Matrix(1,0,-4,1) Matrix(487,102,1122,235) -> Matrix(3,-2,2,-1) Matrix(1331,276,516,107) -> Matrix(3,-2,-4,3) Matrix(119,22,146,27) -> Matrix(1,0,-2,1) Matrix(233,42,294,53) -> Matrix(1,2,-2,-3) Matrix(755,132,612,107) -> Matrix(1,0,4,1) Matrix(231,40,872,151) -> Matrix(1,0,8,1) Matrix(225,34,86,13) -> Matrix(1,0,-2,1) Matrix(275,36,84,11) -> Matrix(1,-2,0,1) Matrix(163,20,220,27) -> Matrix(1,-2,0,1) Matrix(753,80,160,17) -> Matrix(1,0,0,1) Matrix(265,26,214,21) -> Matrix(1,0,2,1) Matrix(299,-36,108,-13) -> Matrix(1,0,0,1) Matrix(297,-38,86,-11) -> Matrix(3,2,-2,-1) Matrix(291,-44,668,-101) -> Matrix(1,0,0,1) Matrix(165,-26,146,-23) -> Matrix(1,0,-2,1) Matrix(161,-30,102,-19) -> Matrix(1,0,-2,1) Matrix(279,-58,178,-37) -> Matrix(1,2,-2,-3) Matrix(465,-112,328,-79) -> Matrix(1,-8,0,1) Matrix(191,-50,722,-189) -> Matrix(1,0,10,1) Matrix(529,-142,190,-51) -> Matrix(1,0,-2,1) Matrix(565,-156,996,-275) -> Matrix(1,0,-4,1) Matrix(151,-42,18,-5) -> Matrix(1,0,-2,1) Matrix(629,-186,186,-55) -> Matrix(11,2,-6,-1) Matrix(1397,-426,810,-247) -> Matrix(3,-2,2,-1) Matrix(439,-136,184,-57) -> Matrix(1,-2,0,1) Matrix(247,-88,160,-57) -> Matrix(1,0,0,1) Matrix(529,-190,142,-51) -> Matrix(7,6,-6,-5) Matrix(387,-142,526,-193) -> Matrix(3,2,-2,-1) Matrix(665,-246,246,-91) -> Matrix(1,0,6,1) Matrix(243,-92,140,-53) -> Matrix(1,0,0,1) Matrix(379,-148,484,-189) -> Matrix(3,4,-4,-5) Matrix(239,-98,578,-237) -> Matrix(1,0,14,1) Matrix(439,-184,136,-57) -> Matrix(9,-2,-4,1) Matrix(2933,-1242,810,-343) -> Matrix(5,-2,-2,1) Matrix(875,-372,708,-301) -> Matrix(1,0,0,1) Matrix(2641,-1152,768,-335) -> Matrix(1,-2,0,1) Matrix(633,-278,1118,-491) -> Matrix(1,-2,-2,5) Matrix(533,-236,332,-147) -> Matrix(1,0,0,1) Matrix(393,-182,542,-251) -> Matrix(9,-4,-2,1) Matrix(185,-102,78,-43) -> Matrix(3,2,-2,-1) Matrix(339,-190,430,-241) -> Matrix(1,2,-2,-3) Matrix(1259,-710,782,-441) -> Matrix(3,2,-2,-1) Matrix(243,-140,92,-53) -> Matrix(1,0,0,1) Matrix(91,-54,150,-89) -> Matrix(1,0,6,1) Matrix(327,-200,224,-137) -> Matrix(9,-2,-4,1) Matrix(1811,-1118,1142,-705) -> Matrix(1,0,-2,1) Matrix(1481,-918,534,-331) -> Matrix(1,0,-2,1) Matrix(533,-332,236,-147) -> Matrix(1,-2,0,1) Matrix(59,-38,14,-9) -> Matrix(1,0,-2,1) Matrix(141,-100,196,-139) -> Matrix(1,-10,0,1) Matrix(279,-202,250,-181) -> Matrix(1,6,-2,-11) Matrix(3311,-2400,1392,-1009) -> Matrix(5,24,-4,-19) Matrix(499,-364,292,-213) -> Matrix(1,4,0,1) Matrix(1823,-1346,386,-285) -> Matrix(1,2,2,5) Matrix(381,-292,244,-187) -> Matrix(3,4,-4,-5) Matrix(487,-376,136,-105) -> Matrix(1,0,0,1) Matrix(237,-196,52,-43) -> Matrix(1,0,4,1) Matrix(573,-482,170,-143) -> Matrix(27,2,-14,-1) Matrix(389,-332,116,-99) -> Matrix(17,-2,-8,1) Matrix(253,-226,178,-159) -> Matrix(13,-6,-2,1) Matrix(507,-596,188,-221) -> Matrix(1,0,12,1) Matrix(263,-314,98,-117) -> Matrix(1,0,-6,1) Matrix(667,-820,388,-477) -> Matrix(1,0,0,1) Matrix(317,-402,138,-175) -> Matrix(1,0,-2,1) Matrix(379,-484,148,-189) -> Matrix(3,-2,-4,3) Matrix(63,-82,10,-13) -> Matrix(3,-4,-2,3) Matrix(141,-196,100,-139) -> Matrix(1,-14,0,1) Matrix(1389,-1972,436,-619) -> Matrix(11,80,-4,-29) Matrix(693,-988,148,-211) -> Matrix(1,6,0,1) Matrix(335,-482,98,-141) -> Matrix(3,14,-2,-9) Matrix(1255,-1816,736,-1065) -> Matrix(5,16,4,13) Matrix(1821,-2642,1058,-1535) -> Matrix(5,14,6,17) Matrix(829,-1284,348,-539) -> Matrix(1,0,0,1) Matrix(2505,-3976,1456,-2311) -> Matrix(3,2,4,3) Matrix(679,-1096,184,-297) -> Matrix(5,4,-4,-3) Matrix(91,-150,54,-89) -> Matrix(1,0,2,1) Matrix(1599,-2722,346,-589) -> Matrix(3,-2,2,-1) Matrix(5805,-9892,1828,-3115) -> Matrix(71,-68,-24,23) Matrix(4561,-7774,1438,-2451) -> Matrix(55,-58,-18,19) Matrix(2027,-3494,590,-1017) -> Matrix(3,-4,-2,3) Matrix(17,-32,8,-15) -> Matrix(1,-2,0,1) Matrix(1541,-3498,426,-967) -> Matrix(5,8,-2,-3) Matrix(527,-1202,146,-333) -> Matrix(1,2,-2,-3) Matrix(2301,-5476,724,-1723) -> Matrix(35,38,-12,-13) Matrix(239,-578,98,-237) -> Matrix(5,6,-6,-7) Matrix(1301,-3354,282,-727) -> Matrix(5,4,6,5) Matrix(201,-566,38,-107) -> Matrix(5,-2,-2,1) Matrix(37,-108,12,-35) -> Matrix(1,-4,0,1) Matrix(653,-2418,138,-511) -> Matrix(3,4,2,3) Matrix(191,-722,50,-189) -> Matrix(17,18,-18,-19) Matrix(41,-200,8,-39) -> Matrix(1,-4,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 43 Degree of the the map X: 43 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 (0/1,1/0) 0 24 1/8 1/0 1 8 1/7 0/1 1 3 2/13 1/0 2 8 1/6 (-1/1,0/1) 0 24 1/5 1/0 1 4 2/9 (0/1,1/0) 0 24 1/4 (-1/1,0/1) 0 24 5/19 0/1 5 1 4/15 (0/1,1/4) 0 24 3/11 1/2 1 12 5/18 (0/1,1/1) 0 24 2/7 1/0 2 8 3/10 (0/1,1/3) 0 24 4/13 (1/2,1/1) 0 24 1/3 1/0 1 6 5/14 (-2/1,-1/1) 0 24 4/11 -1/2 2 8 7/19 -1/4 1 12 3/8 (0/1,1/1) 0 24 5/13 1/0 2 4 2/5 (-1/2,0/1) 0 24 7/17 0/1 7 1 5/12 (0/1,1/5) 0 24 8/19 1/2 2 8 3/7 1/2 1 12 10/23 1/0 2 8 17/39 0/1 1 3 7/16 (1/1,2/1) 0 24 11/25 1/0 2 2 4/9 (0/1,1/0) 0 24 1/2 1/0 1 8 5/9 -1/2 1 12 9/16 (-1/1,0/1) 0 24 13/23 -1/2 2 2 4/7 (-1/2,0/1) 0 24 7/12 (-1/1,0/1) 0 24 3/5 0/1 3 3 11/18 (0/1,1/5) 0 24 8/13 1/2 2 8 13/21 1/2 1 12 18/29 (0/1,1/2) 0 24 5/8 (0/1,1/1) 0 24 2/3 (1/1,1/0) 0 24 5/7 1/0 5 2 8/11 (-4/1,1/0) 0 24 11/15 -5/2 1 12 14/19 1/0 2 8 3/4 (-2/1,-1/1) 0 24 10/13 (-1/1,1/0) 0 24 7/9 -1/1 5 3 11/14 (-1/1,-2/3) 0 24 4/5 -1/2 2 8 5/6 (-1/5,0/1) 0 24 11/13 0/1 11 1 6/7 (0/1,1/6) 0 24 1/1 1/0 1 12 7/6 (-1/5,0/1) 0 24 13/11 0/1 9 1 6/5 (0/1,1/4) 0 24 5/4 1/2 1 8 14/11 (3/4,1/1) 0 24 9/7 1/1 5 3 4/3 (2/1,1/0) 0 24 7/5 1/0 7 2 10/7 (-5/1,1/0) 0 24 13/9 -7/2 1 12 29/20 (-3/1,-26/9) 0 24 16/11 -5/2 2 8 3/2 (-2/1,-1/1) 0 24 17/11 1/0 1 6 14/9 (-1/1,-3/4) 0 24 11/7 -1/2 1 4 19/12 (-1/3,0/1) 0 24 8/5 (0/1,1/0) 0 24 13/8 1/0 1 8 5/3 0/1 1 3 17/10 1/2 1 8 46/27 (7/8,1/1) 0 24 121/71 1/1 21 1 75/44 (1/1,14/13) 0 24 29/17 3/2 1 12 12/7 (0/1,1/0) 0 24 31/18 (1/1,4/3) 0 24 19/11 1/0 2 4 7/4 (0/1,1/1) 0 24 2/1 1/0 2 8 9/4 (-2/1,-1/1) 0 24 34/15 (-2/1,-3/2) 0 24 25/11 -3/2 1 2 16/7 (-3/2,-1/1) 0 24 7/3 1/0 1 12 19/8 -3/2 1 8 50/21 (-1/1,-3/4) 0 24 31/13 1/0 1 6 12/5 (-3/2,-1/1) 0 24 17/7 -1/1 3 1 5/2 (-1/1,0/1) 0 24 18/7 (-1/1,1/0) 0 24 13/5 -1/2 1 4 8/3 (-1/2,0/1) 0 24 11/4 1/0 1 8 36/13 (0/1,1/0) 0 24 25/9 1/0 1 12 14/5 (0/1,1/2) 0 24 17/6 (4/5,1/1) 0 24 3/1 1/0 2 6 19/6 (-16/5,-3/1) 0 24 16/5 -5/2 2 8 13/4 (-2/1,-1/1) 0 24 10/3 (-5/2,-2/1) 0 24 17/5 -7/4 1 12 24/7 (-3/2,-1/1) 0 24 31/9 -2/1 1 3 7/2 -3/2 1 8 18/5 (-1/1,1/0) 0 24 11/3 -3/2 1 12 26/7 -5/4 2 8 15/4 (-8/7,-1/1) 0 24 19/5 -1/1 9 1 4/1 (-1/1,-1/2) 0 24 9/2 (-1/1,0/1) 0 24 14/3 (1/1,1/0) 0 24 33/7 0/1 1 3 19/4 (2/3,1/1) 0 24 5/1 1/0 2 4 6/1 (-2/1,-3/2) 0 24 7/1 -1/1 5 3 1/0 (-1/1,0/1) 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(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(123,-20,166,-27) (2/13,1/6) -> (14/19,3/4) Glide Reflection Matrix(161,-30,102,-19) (1/6,1/5) -> (11/7,19/12) Hyperbolic Matrix(157,-34,60,-13) (1/5,2/9) -> (13/5,8/3) Glide Reflection Matrix(79,-18,136,-31) (2/9,1/4) -> (4/7,7/12) Glide Reflection 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(75,-22,92,-27) (2/7,3/10) -> (4/5,5/6) Glide Reflection Matrix(257,-78,56,-17) (3/10,4/13) -> (9/2,14/3) Glide Reflection 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(141,-52,122,-45) (7/19,3/8) -> (1/1,7/6) Glide Reflection Matrix(243,-92,140,-53) (3/8,5/13) -> (19/11,7/4) Hyperbolic Matrix(103,-40,18,-7) (5/13,2/5) -> (5/1,6/1) 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(439,-184,136,-57) (5/12,8/19) -> (16/5,13/4) Hyperbolic Matrix(303,-128,490,-207) (8/19,3/7) -> (8/13,13/21) Glide Reflection Matrix(435,-188,118,-51) (3/7,10/23) -> (11/3,26/7) Glide Reflection Matrix(1269,-554,268,-117) (17/39,7/16) -> (33/7,19/4) Glide Reflection Matrix(433,-190,768,-337) (7/16,11/25) -> (9/16,13/23) Glide Reflection Matrix(199,-88,450,-199) (11/25,4/9) -> (11/25,4/9) Reflection Matrix(133,-60,82,-37) (4/9,1/2) -> (8/5,13/8) Glide Reflection Matrix(185,-102,78,-43) (1/2,5/9) -> (7/3,19/8) Hyperbolic Matrix(183,-104,322,-183) (13/23,4/7) -> (13/23,4/7) Reflection 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(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(29,-20,42,-29) (2/3,5/7) -> (2/3,5/7) Reflection Matrix(111,-80,154,-111) (5/7,8/11) -> (5/7,8/11) Reflection Matrix(499,-364,292,-213) (8/11,11/15) -> (29/17,12/7) Hyperbolic Matrix(137,-104,54,-41) (3/4,10/13) -> (5/2,18/7) Glide 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(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(129,-112,38,-33) (6/7,1/1) -> (10/3,17/5) 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(87,-106,32,-39) (6/5,5/4) -> (8/3,11/4) 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(99,-140,70,-99) (7/5,10/7) -> (7/5,10/7) Reflection 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(529,-768,166,-241) (29/20,16/11) -> (19/6,16/5) Glide Reflection Matrix(829,-1284,348,-539) (17/11,14/9) -> (50/21,31/13) Hyperbolic Matrix(243,-380,94,-147) (14/9,11/7) -> (18/7,13/5) Glide Reflection Matrix(185,-294,56,-89) (19/12,8/5) -> (13/4,10/3) 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(371,-638,132,-227) (12/7,31/18) -> (14/5,17/6) Glide Reflection Matrix(299,-516,62,-107) (31/18,19/11) -> (19/4,5/1) Glide Reflection Matrix(17,-32,8,-15) (7/4,2/1) -> (2/1,9/4) Parabolic Matrix(749,-1700,330,-749) (34/15,25/11) -> (34/15,25/11) 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(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(357,-1226,76,-261) (24/7,31/9) -> (14/3,33/7) Glide Reflection 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(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(-1,0,2,1) -> Matrix(1,0,0,-1) (-1/1,0/1) -> (0/1,1/0) Matrix(299,-36,108,-13) -> Matrix(1,0,0,1) Matrix(297,-38,86,-11) -> Matrix(3,2,-2,-1) -1/1 Matrix(291,-44,668,-101) -> Matrix(1,0,0,1) Matrix(123,-20,166,-27) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(161,-30,102,-19) -> Matrix(1,0,-2,1) 0/1 Matrix(157,-34,60,-13) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(79,-18,136,-31) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(39,-10,152,-39) -> Matrix(-1,0,2,1) (1/4,5/19) -> (-1/1,0/1) Matrix(151,-40,570,-151) -> Matrix(1,0,8,-1) (5/19,4/15) -> (0/1,1/4) Matrix(529,-142,190,-51) -> Matrix(1,0,-2,1) 0/1 Matrix(189,-52,338,-93) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(149,-42,188,-53) -> Matrix(1,-2,-2,3) Matrix(75,-22,92,-27) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(257,-78,56,-17) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(439,-136,184,-57) -> Matrix(1,-2,0,1) 1/0 Matrix(247,-88,160,-57) -> Matrix(1,0,0,1) Matrix(529,-190,142,-51) -> Matrix(7,6,-6,-5) -1/1 Matrix(387,-142,526,-193) -> Matrix(3,2,-2,-1) -1/1 Matrix(141,-52,122,-45) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(243,-92,140,-53) -> Matrix(1,0,0,1) Matrix(103,-40,18,-7) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(69,-28,170,-69) -> Matrix(-1,0,4,1) (2/5,7/17) -> (-1/2,0/1) Matrix(169,-70,408,-169) -> Matrix(1,0,10,-1) (7/17,5/12) -> (0/1,1/5) Matrix(439,-184,136,-57) -> Matrix(9,-2,-4,1) Matrix(303,-128,490,-207) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(435,-188,118,-51) -> Matrix(5,-4,-4,3) Matrix(1269,-554,268,-117) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(433,-190,768,-337) -> Matrix(1,-2,-2,3) Matrix(199,-88,450,-199) -> Matrix(1,0,0,-1) (11/25,4/9) -> (0/1,1/0) Matrix(133,-60,82,-37) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(185,-102,78,-43) -> Matrix(3,2,-2,-1) -1/1 Matrix(183,-104,322,-183) -> Matrix(-1,0,4,1) (13/23,4/7) -> (-1/2,0/1) Matrix(91,-54,150,-89) -> Matrix(1,0,6,1) 0/1 Matrix(327,-200,224,-137) -> Matrix(9,-2,-4,1) Matrix(1481,-918,534,-331) -> Matrix(1,0,-2,1) 0/1 Matrix(533,-332,236,-147) -> Matrix(1,-2,0,1) 1/0 Matrix(59,-38,14,-9) -> Matrix(1,0,-2,1) 0/1 Matrix(29,-20,42,-29) -> Matrix(-1,2,0,1) (2/3,5/7) -> (1/1,1/0) Matrix(111,-80,154,-111) -> Matrix(1,8,0,-1) (5/7,8/11) -> (-4/1,1/0) Matrix(499,-364,292,-213) -> Matrix(1,4,0,1) 1/0 Matrix(137,-104,54,-41) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(243,-188,190,-147) -> Matrix(3,4,4,5) Matrix(107,-84,14,-11) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(131,-110,156,-131) -> Matrix(-1,0,10,1) (5/6,11/13) -> (-1/5,0/1) Matrix(155,-132,182,-155) -> Matrix(1,0,12,-1) (11/13,6/7) -> (0/1,1/6) Matrix(129,-112,38,-33) -> Matrix(7,-2,-4,1) Matrix(155,-182,132,-155) -> Matrix(-1,0,10,1) (7/6,13/11) -> (-1/5,0/1) Matrix(131,-156,110,-131) -> Matrix(1,0,8,-1) (13/11,6/5) -> (0/1,1/4) Matrix(87,-106,32,-39) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(149,-188,42,-53) -> Matrix(5,-4,-4,3) Matrix(63,-82,10,-13) -> Matrix(3,-4,-2,3) Matrix(41,-56,30,-41) -> Matrix(-1,4,0,1) (4/3,7/5) -> (2/1,1/0) Matrix(99,-140,70,-99) -> Matrix(1,10,0,-1) (7/5,10/7) -> (-5/1,1/0) Matrix(335,-482,98,-141) -> Matrix(3,14,-2,-9) Matrix(1255,-1816,736,-1065) -> Matrix(5,16,4,13) Matrix(529,-768,166,-241) -> Matrix(11,30,-4,-11) *** -> (-3/1,-5/2) Matrix(829,-1284,348,-539) -> Matrix(1,0,0,1) Matrix(243,-380,94,-147) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(185,-294,56,-89) -> Matrix(5,2,-2,-1) Matrix(91,-150,54,-89) -> Matrix(1,0,2,1) 0/1 Matrix(1013,-1724,426,-725) -> Matrix(5,-4,-4,3) Matrix(6533,-11132,3834,-6533) -> Matrix(15,-14,16,-15) (46/27,121/71) -> (7/8,1/1) Matrix(10649,-18150,6248,-10649) -> Matrix(27,-28,26,-27) (121/71,75/44) -> (1/1,14/13) Matrix(371,-638,132,-227) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(299,-516,62,-107) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(17,-32,8,-15) -> Matrix(1,-2,0,1) 1/0 Matrix(749,-1700,330,-749) -> Matrix(7,12,-4,-7) (34/15,25/11) -> (-2/1,-3/2) Matrix(351,-800,154,-351) -> Matrix(5,6,-4,-5) (25/11,16/7) -> (-3/2,-1/1) Matrix(131,-302,36,-83) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(169,-408,70,-169) -> Matrix(5,6,-4,-5) (12/5,17/7) -> (-3/2,-1/1) Matrix(69,-170,28,-69) -> Matrix(-1,0,2,1) (17/7,5/2) -> (-1/1,0/1) Matrix(37,-108,12,-35) -> Matrix(1,-4,0,1) 1/0 Matrix(357,-1226,76,-261) -> Matrix(1,2,2,3) Matrix(151,-570,40,-151) -> Matrix(15,16,-14,-15) (15/4,19/5) -> (-8/7,-1/1) Matrix(39,-152,10,-39) -> Matrix(3,2,-4,-3) (19/5,4/1) -> (-1/1,-1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.