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 -5/6 -3/4 -2/3 -23/36 -5/8 -1/2 -8/21 -3/8 -71/192 -1/3 -3/10 -6/23 -1/4 -2/9 -1/6 -2/13 -2/15 -1/8 -2/17 -1/9 -1/10 0/1 1/9 1/8 2/15 1/7 1/6 2/11 1/5 5/24 4/19 2/9 1/4 3/11 2/7 7/24 11/36 1/3 3/8 8/21 2/5 5/12 7/16 11/24 1/2 13/24 7/12 5/8 2/3 17/24 3/4 19/24 5/6 7/8 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/1 -6/7 3/2 2/1 -5/6 1/0 -4/5 1/2 1/1 -19/24 1/1 -15/19 1/1 8/7 -11/14 3/2 -18/23 1/1 1/0 -7/9 3/2 -17/22 7/4 -10/13 2/1 5/2 -13/17 1/1 2/1 -3/4 1/0 -17/23 -1/1 -4/5 -14/19 -1/2 0/1 -11/15 1/0 -8/11 0/1 1/2 -13/18 1/2 -18/25 1/1 1/0 -5/7 0/1 1/1 -17/24 1/1 -12/17 1/1 3/2 -7/10 1/0 -2/3 1/0 -9/14 1/0 -16/25 -1/1 -1/2 -23/36 -1/2 -7/11 -1/1 0/1 -12/19 0/1 1/0 -5/8 0/1 -18/29 0/1 1/2 -13/21 1/0 -8/13 0/1 1/0 -11/18 1/2 -14/23 3/4 1/1 -3/5 1/1 2/1 -13/22 7/2 -23/39 1/0 -10/17 5/1 1/0 -7/12 1/0 -4/7 -2/1 1/0 -13/23 -4/3 -1/1 -9/16 -1/1 -14/25 -1/1 -3/4 -5/9 -1/2 -6/11 -1/4 0/1 -13/24 0/1 -7/13 0/1 1/5 -1/2 1/0 -6/13 -1/6 0/1 -11/24 0/1 -5/11 0/1 1/5 -4/9 1/2 -11/25 2/3 1/1 -7/16 1/1 -10/23 1/1 1/0 -3/7 1/1 2/1 -11/26 5/2 -30/71 3/1 25/8 -19/45 7/2 -8/19 4/1 1/0 -5/12 1/0 -2/5 -1/1 1/0 -7/18 -1/2 -19/49 -1/3 -2/7 -31/80 0/1 -12/31 -1/2 -1/3 -5/13 -1/1 0/1 -23/60 -1/2 -18/47 -1/2 0/1 -13/34 -1/2 -8/21 -1/2 -3/8 0/1 -10/27 1/4 -27/73 8/25 1/3 -71/192 1/3 -44/119 1/3 13/38 -17/46 3/8 -7/19 0/1 1/1 -4/11 0/1 1/2 -13/36 1/2 -9/25 0/1 1/1 -5/14 1/2 -6/17 1/1 1/0 -1/3 1/0 -4/13 0/1 1/0 -11/36 1/0 -7/23 -2/1 -1/1 -10/33 1/0 -3/10 -1/2 -8/27 -1/2 -21/71 -1/3 -6/19 -13/44 -1/4 -5/17 -1/5 0/1 -7/24 0/1 -2/7 0/1 1/2 -5/18 1/0 -13/47 -4/3 -1/1 -8/29 0/1 1/0 -3/11 -1/1 0/1 -7/26 1/4 -11/41 0/1 1/1 -4/15 1/2 -9/34 3/4 -5/19 1/1 2/1 -6/23 3/4 1/1 -1/4 1/0 -6/25 -5/4 -1/1 -5/21 -1/2 -4/17 -1/1 -1/2 -3/13 -1/3 0/1 -2/9 1/0 -5/23 -1/1 0/1 -3/14 -1/2 -7/33 -1/2 -4/19 -1/4 0/1 -5/24 0/1 -1/5 0/1 1/1 -2/11 0/1 1/0 -1/6 1/0 -2/13 -1/2 0/1 -1/7 0/1 1/1 -2/15 1/0 -3/23 -2/1 -1/1 -1/8 0/1 -2/17 1/1 1/0 -1/9 1/0 -1/10 1/0 0/1 0/1 1/0 1/9 1/0 1/8 0/1 2/15 1/0 1/7 -1/1 0/1 1/6 1/0 2/11 0/1 1/0 1/5 -1/1 0/1 5/24 0/1 4/19 0/1 1/4 3/14 1/2 5/23 0/1 1/1 2/9 1/0 3/13 0/1 1/3 4/17 1/2 1/1 1/4 1/0 5/19 -2/1 -1/1 4/15 -1/2 7/26 -1/4 3/11 0/1 1/1 5/18 1/0 2/7 -1/2 0/1 7/24 0/1 5/17 0/1 1/5 8/27 1/2 3/10 1/2 10/33 1/0 17/56 0/1 7/23 1/1 2/1 11/36 1/0 4/13 0/1 1/0 1/3 1/0 5/14 -1/2 9/25 -1/1 0/1 13/36 -1/2 4/11 -1/2 0/1 7/19 -1/1 0/1 3/8 0/1 11/29 0/1 1/5 8/21 1/2 13/34 1/2 18/47 0/1 1/2 5/13 0/1 1/1 2/5 1/1 1/0 5/12 1/0 8/19 -4/1 1/0 11/26 -5/2 14/33 1/0 3/7 -2/1 -1/1 10/23 -1/1 1/0 7/16 -1/1 11/25 -1/1 -2/3 4/9 -1/2 5/11 -1/5 0/1 11/24 0/1 6/13 0/1 1/6 1/2 1/0 7/13 -1/5 0/1 13/24 0/1 6/11 0/1 1/4 5/9 1/2 14/25 3/4 1/1 9/16 1/1 4/7 2/1 1/0 7/12 1/0 10/17 -5/1 1/0 13/22 -7/2 29/49 -3/1 -26/9 16/27 -5/2 3/5 -2/1 -1/1 17/28 1/0 14/23 -1/1 -3/4 11/18 -1/2 19/31 -1/3 0/1 8/13 0/1 1/0 13/21 1/0 5/8 0/1 17/27 1/2 46/73 7/8 1/1 121/192 1/1 75/119 1/1 14/13 29/46 3/2 12/19 0/1 1/0 31/49 1/1 4/3 19/30 1/0 7/11 0/1 1/1 2/3 1/0 9/13 -2/1 -1/1 34/49 -2/1 -3/2 25/36 -3/2 16/23 -3/2 -1/1 7/10 1/0 19/27 -3/2 50/71 -1/1 -3/4 31/44 1/0 12/17 -3/2 -1/1 17/24 -1/1 5/7 -1/1 0/1 18/25 -1/1 1/0 13/18 -1/2 8/11 -1/2 0/1 11/15 1/0 36/49 0/1 1/0 25/34 1/0 14/19 0/1 1/2 17/23 4/5 1/1 3/4 1/0 19/25 -16/5 -3/1 16/21 -5/2 13/17 -2/1 -1/1 10/13 -5/2 -2/1 17/22 -7/4 24/31 -3/2 -1/1 31/40 -2/1 7/9 -3/2 18/23 -1/1 1/0 11/14 -3/2 26/33 -5/4 15/19 -8/7 -1/1 19/24 -1/1 4/5 -1/1 -1/2 9/11 -1/1 0/1 14/17 1/1 1/0 33/40 0/1 19/23 2/3 1/1 5/6 1/0 6/7 -2/1 -3/2 7/8 -1/1 1/1 -1/1 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(95,82,-168,-145) (-1/1,-6/7) -> (-4/7,-13/23) Hyperbolic Matrix(47,40,168,143) (-6/7,-5/6) -> (5/18,2/7) Hyperbolic Matrix(47,38,-120,-97) (-5/6,-4/5) -> (-2/5,-7/18) Hyperbolic Matrix(191,152,240,191) (-4/5,-19/24) -> (19/24,4/5) Hyperbolic Matrix(721,570,912,721) (-19/24,-15/19) -> (15/19,19/24) Hyperbolic Matrix(241,190,-912,-719) (-15/19,-11/14) -> (-9/34,-5/19) Hyperbolic Matrix(385,302,552,433) (-11/14,-18/23) -> (16/23,7/10) Hyperbolic Matrix(241,188,432,337) (-18/23,-7/9) -> (5/9,14/25) Hyperbolic Matrix(623,482,-1056,-817) (-7/9,-17/22) -> (-13/22,-23/39) Hyperbolic Matrix(145,112,312,241) (-17/22,-10/13) -> (6/13,1/2) Hyperbolic Matrix(383,294,624,479) (-10/13,-13/17) -> (19/31,8/13) Hyperbolic Matrix(241,184,-816,-623) (-13/17,-3/4) -> (-13/44,-5/17) Hyperbolic Matrix(383,284,-1296,-961) (-3/4,-17/23) -> (-21/71,-13/44) Hyperbolic Matrix(865,638,1368,1009) (-17/23,-14/19) -> (12/19,31/49) Hyperbolic Matrix(193,142,-912,-671) (-14/19,-11/15) -> (-7/33,-4/19) Hyperbolic Matrix(145,106,264,193) (-11/15,-8/11) -> (6/11,5/9) Hyperbolic Matrix(47,34,264,191) (-8/11,-13/18) -> (1/6,2/11) Hyperbolic Matrix(527,380,864,623) (-13/18,-18/25) -> (14/23,11/18) Hyperbolic Matrix(145,104,336,241) (-18/25,-5/7) -> (3/7,10/23) Hyperbolic Matrix(239,170,336,239) (-5/7,-17/24) -> (17/24,5/7) Hyperbolic Matrix(577,408,816,577) (-17/24,-12/17) -> (12/17,17/24) Hyperbolic Matrix(145,102,-408,-287) (-12/17,-7/10) -> (-5/14,-6/17) Hyperbolic Matrix(47,32,-72,-49) (-7/10,-2/3) -> (-2/3,-9/14) Parabolic Matrix(527,338,672,431) (-9/14,-16/25) -> (18/23,11/14) Hyperbolic Matrix(1201,768,1728,1105) (-16/25,-23/36) -> (25/36,16/23) Hyperbolic Matrix(433,276,-1128,-719) (-23/36,-7/11) -> (-5/13,-23/60) Hyperbolic Matrix(145,92,-528,-335) (-7/11,-12/19) -> (-8/29,-3/11) Hyperbolic Matrix(239,150,-384,-241) (-12/19,-5/8) -> (-5/8,-18/29) Parabolic Matrix(719,446,-1704,-1057) (-18/29,-13/21) -> (-19/45,-8/19) Hyperbolic Matrix(97,60,312,193) (-13/21,-8/13) -> (4/13,1/3) Hyperbolic Matrix(49,30,-312,-191) (-8/13,-11/18) -> (-1/6,-2/13) Hyperbolic Matrix(623,380,864,527) (-11/18,-14/23) -> (18/25,13/18) Hyperbolic Matrix(145,88,-552,-335) (-14/23,-3/5) -> (-5/19,-6/23) Hyperbolic Matrix(239,142,-648,-385) (-3/5,-13/22) -> (-17/46,-7/19) Hyperbolic Matrix(95,56,-816,-481) (-23/39,-10/17) -> (-2/17,-1/9) Hyperbolic Matrix(239,140,408,239) (-10/17,-7/12) -> (7/12,10/17) Hyperbolic Matrix(97,56,168,97) (-7/12,-4/7) -> (4/7,7/12) Hyperbolic Matrix(337,190,768,433) (-13/23,-9/16) -> (7/16,11/25) Hyperbolic Matrix(335,188,768,431) (-9/16,-14/25) -> (10/23,7/16) Hyperbolic Matrix(337,188,432,241) (-14/25,-5/9) -> (7/9,18/23) Hyperbolic Matrix(193,106,264,145) (-5/9,-6/11) -> (8/11,11/15) Hyperbolic Matrix(287,156,528,287) (-6/11,-13/24) -> (13/24,6/11) Hyperbolic Matrix(337,182,624,337) (-13/24,-7/13) -> (7/13,13/24) Hyperbolic Matrix(97,52,360,193) (-7/13,-1/2) -> (7/26,3/11) Hyperbolic Matrix(241,112,312,145) (-1/2,-6/13) -> (10/13,17/22) Hyperbolic Matrix(287,132,624,287) (-6/13,-11/24) -> (11/24,6/13) Hyperbolic Matrix(241,110,528,241) (-11/24,-5/11) -> (5/11,11/24) Hyperbolic Matrix(49,22,216,97) (-5/11,-4/9) -> (2/9,3/13) Hyperbolic Matrix(95,42,432,191) (-4/9,-11/25) -> (5/23,2/9) Hyperbolic Matrix(191,84,216,95) (-11/25,-7/16) -> (7/8,1/1) Hyperbolic Matrix(431,188,768,335) (-7/16,-10/23) -> (14/25,9/16) Hyperbolic Matrix(241,104,336,145) (-10/23,-3/7) -> (5/7,18/25) Hyperbolic Matrix(335,142,-1248,-529) (-3/7,-11/26) -> (-7/26,-11/41) Hyperbolic Matrix(2351,994,-6360,-2689) (-11/26,-30/71) -> (-44/119,-17/46) Hyperbolic Matrix(3599,1520,5112,2159) (-30/71,-19/45) -> (19/27,50/71) Hyperbolic Matrix(191,80,456,191) (-8/19,-5/12) -> (5/12,8/19) Hyperbolic Matrix(49,20,120,49) (-5/12,-2/5) -> (2/5,5/12) Hyperbolic Matrix(1489,578,2352,913) (-7/18,-19/49) -> (31/49,19/30) Hyperbolic Matrix(1393,540,4584,1777) (-19/49,-31/80) -> (17/56,7/23) Hyperbolic Matrix(2881,1116,3720,1441) (-31/80,-12/31) -> (24/31,31/40) Hyperbolic Matrix(145,56,624,241) (-12/31,-5/13) -> (3/13,4/17) Hyperbolic Matrix(3215,1232,4632,1775) (-23/60,-18/47) -> (34/49,25/36) Hyperbolic Matrix(47,18,-504,-193) (-18/47,-13/34) -> (-1/10,0/1) Hyperbolic Matrix(335,128,1128,431) (-13/34,-8/21) -> (8/27,3/10) Hyperbolic Matrix(143,54,-384,-145) (-8/21,-3/8) -> (-3/8,-10/27) Parabolic Matrix(1681,622,2208,817) (-10/27,-27/73) -> (19/25,16/21) Hyperbolic Matrix(23233,8592,36864,13633) (-27/73,-71/192) -> (121/192,75/119) Hyperbolic Matrix(23231,8590,36864,13631) (-71/192,-44/119) -> (46/73,121/192) Hyperbolic Matrix(49,18,264,97) (-7/19,-4/11) -> (2/11,1/5) Hyperbolic Matrix(287,104,792,287) (-4/11,-13/36) -> (13/36,4/11) Hyperbolic Matrix(527,190,1728,623) (-13/36,-9/25) -> (7/23,11/36) Hyperbolic Matrix(145,52,672,241) (-9/25,-5/14) -> (3/14,5/23) Hyperbolic Matrix(97,34,-408,-143) (-6/17,-1/3) -> (-5/21,-4/17) Hyperbolic Matrix(193,60,312,97) (-1/3,-4/13) -> (8/13,13/21) Hyperbolic Matrix(287,88,936,287) (-4/13,-11/36) -> (11/36,4/13) Hyperbolic Matrix(623,190,1728,527) (-11/36,-7/23) -> (9/25,13/36) Hyperbolic Matrix(145,44,-1104,-335) (-7/23,-10/33) -> (-2/15,-3/23) Hyperbolic Matrix(623,188,792,239) (-10/33,-3/10) -> (11/14,26/33) Hyperbolic Matrix(431,128,1128,335) (-3/10,-8/27) -> (8/21,13/34) Hyperbolic Matrix(1919,568,3240,959) (-8/27,-21/71) -> (29/49,16/27) Hyperbolic Matrix(239,70,816,239) (-5/17,-7/24) -> (7/24,5/17) Hyperbolic Matrix(97,28,336,97) (-7/24,-2/7) -> (2/7,7/24) Hyperbolic Matrix(143,40,168,47) (-2/7,-5/18) -> (5/6,6/7) Hyperbolic Matrix(577,160,696,193) (-5/18,-13/47) -> (19/23,5/6) Hyperbolic Matrix(1151,318,1560,431) (-13/47,-8/29) -> (14/19,17/23) Hyperbolic Matrix(193,52,360,97) (-3/11,-7/26) -> (1/2,7/13) Hyperbolic Matrix(97,26,720,193) (-11/41,-4/15) -> (2/15,1/7) Hyperbolic Matrix(385,102,1272,337) (-4/15,-9/34) -> (3/10,10/33) Hyperbolic Matrix(47,12,-192,-49) (-6/23,-1/4) -> (-1/4,-6/25) Parabolic Matrix(1391,332,2208,527) (-6/25,-5/21) -> (17/27,46/73) Hyperbolic Matrix(335,78,408,95) (-4/17,-3/13) -> (9/11,14/17) Hyperbolic Matrix(97,22,216,49) (-3/13,-2/9) -> (4/9,5/11) Hyperbolic Matrix(191,42,432,95) (-2/9,-5/23) -> (11/25,4/9) Hyperbolic Matrix(241,52,672,145) (-5/23,-3/14) -> (5/14,9/25) Hyperbolic Matrix(47,10,-456,-97) (-3/14,-7/33) -> (-1/9,-1/10) Hyperbolic Matrix(191,40,912,191) (-4/19,-5/24) -> (5/24,4/19) Hyperbolic Matrix(49,10,240,49) (-5/24,-1/5) -> (1/5,5/24) Hyperbolic Matrix(97,18,264,49) (-1/5,-2/11) -> (4/11,7/19) Hyperbolic Matrix(191,34,264,47) (-2/11,-1/6) -> (13/18,8/11) Hyperbolic Matrix(239,36,312,47) (-2/13,-1/7) -> (13/17,10/13) Hyperbolic Matrix(143,20,336,47) (-1/7,-2/15) -> (14/33,3/7) Hyperbolic Matrix(911,118,1104,143) (-3/23,-1/8) -> (33/40,19/23) Hyperbolic Matrix(673,80,816,97) (-1/8,-2/17) -> (14/17,33/40) Hyperbolic Matrix(335,-36,456,-49) (0/1,1/9) -> (11/15,36/49) Hyperbolic Matrix(335,-38,432,-49) (1/9,1/8) -> (31/40,7/9) Hyperbolic Matrix(335,-44,1104,-145) (1/8,2/15) -> (10/33,17/56) Hyperbolic Matrix(191,-30,312,-49) (1/7,1/6) -> (11/18,19/31) Hyperbolic Matrix(671,-142,912,-193) (4/19,3/14) -> (25/34,14/19) Hyperbolic Matrix(575,-136,816,-193) (4/17,1/4) -> (31/44,12/17) Hyperbolic Matrix(335,-88,552,-145) (1/4,5/19) -> (3/5,17/28) Hyperbolic Matrix(719,-190,912,-241) (5/19,4/15) -> (26/33,15/19) Hyperbolic Matrix(529,-142,1248,-335) (4/15,7/26) -> (11/26,14/33) Hyperbolic Matrix(335,-92,528,-145) (3/11,5/18) -> (19/30,7/11) Hyperbolic Matrix(623,-184,816,-241) (5/17,8/27) -> (16/21,13/17) Hyperbolic Matrix(287,-102,408,-145) (1/3,5/14) -> (7/10,19/27) Hyperbolic Matrix(145,-54,384,-143) (7/19,3/8) -> (3/8,11/29) Parabolic Matrix(527,-200,888,-337) (11/29,8/21) -> (16/27,3/5) Hyperbolic Matrix(2399,-918,3264,-1249) (13/34,18/47) -> (36/49,25/34) Hyperbolic Matrix(865,-332,1248,-479) (18/47,5/13) -> (9/13,34/49) Hyperbolic Matrix(97,-38,120,-47) (5/13,2/5) -> (4/5,9/11) Hyperbolic Matrix(863,-364,1368,-577) (8/19,11/26) -> (29/46,12/19) Hyperbolic Matrix(145,-82,168,-95) (9/16,4/7) -> (6/7,7/8) Hyperbolic Matrix(817,-482,1056,-623) (10/17,13/22) -> (17/22,24/31) Hyperbolic Matrix(3071,-1816,4872,-2881) (13/22,29/49) -> (75/119,29/46) Hyperbolic Matrix(2113,-1284,3000,-1823) (17/28,14/23) -> (50/71,31/44) Hyperbolic Matrix(241,-150,384,-239) (13/21,5/8) -> (5/8,17/27) Parabolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(145,-108,192,-143) (17/23,3/4) -> (3/4,19/25) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(95,82,-168,-145) -> Matrix(3,-4,-2,3) Matrix(47,40,168,143) -> Matrix(1,-2,0,1) Matrix(47,38,-120,-97) -> Matrix(1,0,-2,1) Matrix(191,152,240,191) -> Matrix(3,-2,-4,3) Matrix(721,570,912,721) -> Matrix(15,-16,-14,15) Matrix(241,190,-912,-719) -> Matrix(5,-6,6,-7) Matrix(385,302,552,433) -> Matrix(3,-4,-2,3) Matrix(241,188,432,337) -> Matrix(3,-4,4,-5) Matrix(623,482,-1056,-817) -> Matrix(9,-14,2,-3) Matrix(145,112,312,241) -> Matrix(1,-2,4,-7) Matrix(383,294,624,479) -> Matrix(1,-2,-2,5) Matrix(241,184,-816,-623) -> Matrix(1,-2,-4,9) Matrix(383,284,-1296,-961) -> Matrix(1,2,-4,-7) Matrix(865,638,1368,1009) -> Matrix(1,0,2,1) Matrix(193,142,-912,-671) -> Matrix(1,0,-2,1) Matrix(145,106,264,193) -> Matrix(1,0,2,1) Matrix(47,34,264,191) -> Matrix(1,0,-2,1) Matrix(527,380,864,623) -> Matrix(3,-2,-4,3) Matrix(145,104,336,241) -> Matrix(1,-2,0,1) Matrix(239,170,336,239) -> Matrix(1,0,-2,1) Matrix(577,408,816,577) -> Matrix(5,-6,-4,5) Matrix(145,102,-408,-287) -> Matrix(1,-2,2,-3) Matrix(47,32,-72,-49) -> Matrix(1,-2,0,1) Matrix(527,338,672,431) -> Matrix(3,2,-2,-1) Matrix(1201,768,1728,1105) -> Matrix(5,4,-4,-3) Matrix(433,276,-1128,-719) -> Matrix(1,0,0,1) Matrix(145,92,-528,-335) -> Matrix(1,0,0,1) Matrix(239,150,-384,-241) -> Matrix(1,0,2,1) Matrix(719,446,-1704,-1057) -> Matrix(7,-4,2,-1) Matrix(97,60,312,193) -> Matrix(1,0,0,1) Matrix(49,30,-312,-191) -> Matrix(1,0,-2,1) Matrix(623,380,864,527) -> Matrix(3,-2,-4,3) Matrix(145,88,-552,-335) -> Matrix(1,0,0,1) Matrix(239,142,-648,-385) -> Matrix(1,-2,2,-3) Matrix(95,56,-816,-481) -> Matrix(1,-4,0,1) Matrix(239,140,408,239) -> Matrix(1,-10,0,1) Matrix(97,56,168,97) -> Matrix(1,4,0,1) Matrix(337,190,768,433) -> Matrix(5,6,-6,-7) Matrix(335,188,768,431) -> Matrix(5,4,-4,-3) Matrix(337,188,432,241) -> Matrix(5,4,-4,-3) Matrix(193,106,264,145) -> Matrix(1,0,2,1) Matrix(287,156,528,287) -> Matrix(1,0,8,1) Matrix(337,182,624,337) -> Matrix(1,0,-10,1) Matrix(97,52,360,193) -> Matrix(1,0,-4,1) Matrix(241,112,312,145) -> Matrix(7,2,-4,-1) Matrix(287,132,624,287) -> Matrix(1,0,12,1) Matrix(241,110,528,241) -> Matrix(1,0,-10,1) Matrix(49,22,216,97) -> Matrix(1,0,-2,1) Matrix(95,42,432,191) -> Matrix(3,-2,2,-1) Matrix(191,84,216,95) -> Matrix(3,-2,-4,3) Matrix(431,188,768,335) -> Matrix(3,-4,4,-5) Matrix(241,104,336,145) -> Matrix(1,-2,0,1) Matrix(335,142,-1248,-529) -> Matrix(1,-2,2,-3) Matrix(2351,994,-6360,-2689) -> Matrix(5,-14,14,-39) Matrix(3599,1520,5112,2159) -> Matrix(5,-16,-4,13) Matrix(191,80,456,191) -> Matrix(1,-8,0,1) Matrix(49,20,120,49) -> Matrix(1,2,0,1) Matrix(1489,578,2352,913) -> Matrix(5,2,2,1) Matrix(1393,540,4584,1777) -> Matrix(1,0,4,1) Matrix(2881,1116,3720,1441) -> Matrix(7,2,-4,-1) Matrix(145,56,624,241) -> Matrix(1,0,4,1) Matrix(3215,1232,4632,1775) -> Matrix(7,2,-4,-1) Matrix(47,18,-504,-193) -> Matrix(1,0,2,1) Matrix(335,128,1128,431) -> Matrix(1,0,4,1) Matrix(143,54,-384,-145) -> Matrix(1,0,6,1) Matrix(1681,622,2208,817) -> Matrix(27,-8,-10,3) Matrix(23233,8592,36864,13633) -> Matrix(67,-22,64,-21) Matrix(23231,8590,36864,13631) -> Matrix(59,-20,62,-21) Matrix(49,18,264,97) -> Matrix(1,0,-2,1) Matrix(287,104,792,287) -> Matrix(1,0,-4,1) Matrix(527,190,1728,623) -> Matrix(3,-2,2,-1) Matrix(145,52,672,241) -> Matrix(1,0,0,1) Matrix(97,34,-408,-143) -> Matrix(1,0,-2,1) Matrix(193,60,312,97) -> Matrix(1,0,0,1) Matrix(287,88,936,287) -> Matrix(1,0,0,1) Matrix(623,190,1728,527) -> Matrix(1,2,-2,-3) Matrix(145,44,-1104,-335) -> Matrix(1,0,0,1) Matrix(623,188,792,239) -> Matrix(5,4,-4,-3) Matrix(431,128,1128,335) -> Matrix(1,0,4,1) Matrix(1919,568,3240,959) -> Matrix(21,8,-8,-3) Matrix(239,70,816,239) -> Matrix(1,0,10,1) Matrix(97,28,336,97) -> Matrix(1,0,-4,1) Matrix(143,40,168,47) -> Matrix(1,-2,0,1) Matrix(577,160,696,193) -> Matrix(1,2,0,1) Matrix(1151,318,1560,431) -> Matrix(1,0,2,1) Matrix(193,52,360,97) -> Matrix(1,0,-4,1) Matrix(97,26,720,193) -> Matrix(1,0,-2,1) Matrix(385,102,1272,337) -> Matrix(3,-2,2,-1) Matrix(47,12,-192,-49) -> Matrix(1,-2,0,1) Matrix(1391,332,2208,527) -> Matrix(3,2,4,3) Matrix(335,78,408,95) -> Matrix(1,0,2,1) Matrix(97,22,216,49) -> Matrix(1,0,-2,1) Matrix(191,42,432,95) -> Matrix(1,2,-2,-3) Matrix(241,52,672,145) -> Matrix(1,0,0,1) Matrix(47,10,-456,-97) -> Matrix(1,0,2,1) Matrix(191,40,912,191) -> Matrix(1,0,8,1) Matrix(49,10,240,49) -> Matrix(1,0,-2,1) Matrix(97,18,264,49) -> Matrix(1,0,-2,1) Matrix(191,34,264,47) -> Matrix(1,0,-2,1) Matrix(239,36,312,47) -> Matrix(1,-2,0,1) Matrix(143,20,336,47) -> Matrix(1,-2,0,1) Matrix(911,118,1104,143) -> Matrix(1,0,2,1) Matrix(673,80,816,97) -> Matrix(1,0,0,1) Matrix(335,-36,456,-49) -> Matrix(1,0,0,1) Matrix(335,-38,432,-49) -> Matrix(3,2,-2,-1) Matrix(335,-44,1104,-145) -> Matrix(1,0,0,1) Matrix(191,-30,312,-49) -> Matrix(1,0,-2,1) Matrix(671,-142,912,-193) -> Matrix(1,0,-2,1) Matrix(575,-136,816,-193) -> Matrix(1,-2,0,1) Matrix(335,-88,552,-145) -> Matrix(1,0,0,1) Matrix(719,-190,912,-241) -> Matrix(7,6,-6,-5) Matrix(529,-142,1248,-335) -> Matrix(3,2,-2,-1) Matrix(335,-92,528,-145) -> Matrix(1,0,0,1) Matrix(623,-184,816,-241) -> Matrix(9,-2,-4,1) Matrix(287,-102,408,-145) -> Matrix(3,2,-2,-1) Matrix(145,-54,384,-143) -> Matrix(1,0,6,1) Matrix(527,-200,888,-337) -> Matrix(9,-2,-4,1) Matrix(2399,-918,3264,-1249) -> Matrix(1,0,-2,1) Matrix(865,-332,1248,-479) -> Matrix(1,-2,0,1) Matrix(97,-38,120,-47) -> Matrix(1,0,-2,1) Matrix(863,-364,1368,-577) -> Matrix(1,4,0,1) Matrix(145,-82,168,-95) -> Matrix(3,-4,-2,3) Matrix(817,-482,1056,-623) -> Matrix(3,14,-2,-9) Matrix(3071,-1816,4872,-2881) -> Matrix(5,16,4,13) Matrix(2113,-1284,3000,-1823) -> Matrix(1,0,0,1) Matrix(241,-150,384,-239) -> Matrix(1,0,2,1) Matrix(49,-32,72,-47) -> Matrix(1,-2,0,1) Matrix(145,-108,192,-143) -> 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 0/1 (0/1,1/0) 0 24 1/9 1/0 1 8 1/8 0/1 1 3 2/15 1/0 2 8 1/7 (-1/1,0/1) 0 24 1/6 1/0 1 4 2/11 (0/1,1/0) 0 24 1/5 (-1/1,0/1) 0 24 5/24 0/1 5 1 4/19 (0/1,1/4) 0 24 3/14 1/2 1 12 5/23 (0/1,1/1) 0 24 2/9 1/0 2 8 3/13 (0/1,1/3) 0 24 4/17 (1/2,1/1) 0 24 1/4 1/0 1 6 5/19 (-2/1,-1/1) 0 24 4/15 -1/2 2 8 7/26 -1/4 1 12 3/11 (0/1,1/1) 0 24 5/18 1/0 2 4 2/7 (-1/2,0/1) 0 24 7/24 0/1 7 1 5/17 (0/1,1/5) 0 24 8/27 1/2 2 8 3/10 1/2 1 12 10/33 1/0 2 8 17/56 0/1 1 3 7/23 (1/1,2/1) 0 24 11/36 1/0 2 2 4/13 (0/1,1/0) 0 24 1/3 1/0 1 8 5/14 -1/2 1 12 9/25 (-1/1,0/1) 0 24 13/36 -1/2 2 2 4/11 (-1/2,0/1) 0 24 7/19 (-1/1,0/1) 0 24 3/8 0/1 3 3 11/29 (0/1,1/5) 0 24 8/21 1/2 2 8 13/34 1/2 1 12 18/47 (0/1,1/2) 0 24 5/13 (0/1,1/1) 0 24 2/5 (1/1,1/0) 0 24 5/12 1/0 5 2 8/19 (-4/1,1/0) 0 24 11/26 -5/2 1 12 14/33 1/0 2 8 3/7 (-2/1,-1/1) 0 24 10/23 (-1/1,1/0) 0 24 7/16 -1/1 5 3 11/25 (-1/1,-2/3) 0 24 4/9 -1/2 2 8 5/11 (-1/5,0/1) 0 24 11/24 0/1 11 1 6/13 (0/1,1/6) 0 24 1/2 1/0 1 12 7/13 (-1/5,0/1) 0 24 13/24 0/1 9 1 6/11 (0/1,1/4) 0 24 5/9 1/2 1 8 14/25 (3/4,1/1) 0 24 9/16 1/1 5 3 4/7 (2/1,1/0) 0 24 7/12 1/0 7 2 10/17 (-5/1,1/0) 0 24 13/22 -7/2 1 12 29/49 (-3/1,-26/9) 0 24 16/27 -5/2 2 8 3/5 (-2/1,-1/1) 0 24 17/28 1/0 1 6 14/23 (-1/1,-3/4) 0 24 11/18 -1/2 1 4 19/31 (-1/3,0/1) 0 24 8/13 (0/1,1/0) 0 24 13/21 1/0 1 8 5/8 0/1 1 3 17/27 1/2 1 8 46/73 (7/8,1/1) 0 24 121/192 1/1 21 1 75/119 (1/1,14/13) 0 24 29/46 3/2 1 12 12/19 (0/1,1/0) 0 24 31/49 (1/1,4/3) 0 24 19/30 1/0 2 4 7/11 (0/1,1/1) 0 24 2/3 1/0 2 8 9/13 (-2/1,-1/1) 0 24 34/49 (-2/1,-3/2) 0 24 25/36 -3/2 1 2 16/23 (-3/2,-1/1) 0 24 7/10 1/0 1 12 19/27 -3/2 1 8 50/71 (-1/1,-3/4) 0 24 31/44 1/0 1 6 12/17 (-3/2,-1/1) 0 24 17/24 -1/1 3 1 5/7 (-1/1,0/1) 0 24 18/25 (-1/1,1/0) 0 24 13/18 -1/2 1 4 8/11 (-1/2,0/1) 0 24 11/15 1/0 1 8 36/49 (0/1,1/0) 0 24 25/34 1/0 1 12 14/19 (0/1,1/2) 0 24 17/23 (4/5,1/1) 0 24 3/4 1/0 2 6 19/25 (-16/5,-3/1) 0 24 16/21 -5/2 2 8 13/17 (-2/1,-1/1) 0 24 10/13 (-5/2,-2/1) 0 24 17/22 -7/4 1 12 24/31 (-3/2,-1/1) 0 24 31/40 -2/1 1 3 7/9 -3/2 1 8 18/23 (-1/1,1/0) 0 24 11/14 -3/2 1 12 26/33 -5/4 2 8 15/19 (-8/7,-1/1) 0 24 19/24 -1/1 9 1 4/5 (-1/1,-1/2) 0 24 9/11 (-1/1,0/1) 0 24 14/17 (1/1,1/0) 0 24 33/40 0/1 1 3 19/23 (2/3,1/1) 0 24 5/6 1/0 2 4 6/7 (-2/1,-3/2) 0 24 7/8 -1/1 5 3 1/1 (-1/1,0/1) 0 24 1/0 0/1 1 1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(335,-36,456,-49) (0/1,1/9) -> (11/15,36/49) Hyperbolic Matrix(335,-38,432,-49) (1/9,1/8) -> (31/40,7/9) Hyperbolic Matrix(335,-44,1104,-145) (1/8,2/15) -> (10/33,17/56) Hyperbolic Matrix(143,-20,336,-47) (2/15,1/7) -> (14/33,3/7) Glide Reflection Matrix(191,-30,312,-49) (1/7,1/6) -> (11/18,19/31) Hyperbolic Matrix(191,-34,264,-47) (1/6,2/11) -> (13/18,8/11) Glide Reflection Matrix(97,-18,264,-49) (2/11,1/5) -> (4/11,7/19) Glide Reflection Matrix(49,-10,240,-49) (1/5,5/24) -> (1/5,5/24) Reflection Matrix(191,-40,912,-191) (5/24,4/19) -> (5/24,4/19) Reflection Matrix(671,-142,912,-193) (4/19,3/14) -> (25/34,14/19) Hyperbolic Matrix(241,-52,672,-145) (3/14,5/23) -> (5/14,9/25) Glide Reflection Matrix(191,-42,432,-95) (5/23,2/9) -> (11/25,4/9) Glide Reflection Matrix(97,-22,216,-49) (2/9,3/13) -> (4/9,5/11) Glide Reflection Matrix(335,-78,408,-95) (3/13,4/17) -> (9/11,14/17) Glide Reflection Matrix(575,-136,816,-193) (4/17,1/4) -> (31/44,12/17) Hyperbolic Matrix(335,-88,552,-145) (1/4,5/19) -> (3/5,17/28) Hyperbolic Matrix(719,-190,912,-241) (5/19,4/15) -> (26/33,15/19) Hyperbolic Matrix(529,-142,1248,-335) (4/15,7/26) -> (11/26,14/33) Hyperbolic Matrix(193,-52,360,-97) (7/26,3/11) -> (1/2,7/13) Glide Reflection Matrix(335,-92,528,-145) (3/11,5/18) -> (19/30,7/11) Hyperbolic Matrix(143,-40,168,-47) (5/18,2/7) -> (5/6,6/7) Glide Reflection Matrix(97,-28,336,-97) (2/7,7/24) -> (2/7,7/24) Reflection Matrix(239,-70,816,-239) (7/24,5/17) -> (7/24,5/17) Reflection Matrix(623,-184,816,-241) (5/17,8/27) -> (16/21,13/17) Hyperbolic Matrix(431,-128,1128,-335) (8/27,3/10) -> (8/21,13/34) Glide Reflection Matrix(623,-188,792,-239) (3/10,10/33) -> (11/14,26/33) Glide Reflection Matrix(1823,-554,2208,-671) (17/56,7/23) -> (33/40,19/23) Glide Reflection Matrix(623,-190,1728,-527) (7/23,11/36) -> (9/25,13/36) Glide Reflection Matrix(287,-88,936,-287) (11/36,4/13) -> (11/36,4/13) Reflection Matrix(193,-60,312,-97) (4/13,1/3) -> (8/13,13/21) Glide Reflection Matrix(287,-102,408,-145) (1/3,5/14) -> (7/10,19/27) Hyperbolic Matrix(287,-104,792,-287) (13/36,4/11) -> (13/36,4/11) Reflection Matrix(145,-54,384,-143) (7/19,3/8) -> (3/8,11/29) Parabolic Matrix(527,-200,888,-337) (11/29,8/21) -> (16/27,3/5) Hyperbolic Matrix(2399,-918,3264,-1249) (13/34,18/47) -> (36/49,25/34) Hyperbolic Matrix(865,-332,1248,-479) (18/47,5/13) -> (9/13,34/49) Hyperbolic Matrix(97,-38,120,-47) (5/13,2/5) -> (4/5,9/11) Hyperbolic Matrix(49,-20,120,-49) (2/5,5/12) -> (2/5,5/12) Reflection Matrix(191,-80,456,-191) (5/12,8/19) -> (5/12,8/19) Reflection Matrix(863,-364,1368,-577) (8/19,11/26) -> (29/46,12/19) Hyperbolic Matrix(241,-104,336,-145) (3/7,10/23) -> (5/7,18/25) Glide Reflection Matrix(431,-188,768,-335) (10/23,7/16) -> (14/25,9/16) Glide Reflection Matrix(191,-84,216,-95) (7/16,11/25) -> (7/8,1/1) Glide Reflection Matrix(241,-110,528,-241) (5/11,11/24) -> (5/11,11/24) Reflection Matrix(287,-132,624,-287) (11/24,6/13) -> (11/24,6/13) Reflection Matrix(241,-112,312,-145) (6/13,1/2) -> (10/13,17/22) Glide Reflection Matrix(337,-182,624,-337) (7/13,13/24) -> (7/13,13/24) Reflection Matrix(287,-156,528,-287) (13/24,6/11) -> (13/24,6/11) Reflection Matrix(193,-106,264,-145) (6/11,5/9) -> (8/11,11/15) Glide Reflection Matrix(337,-188,432,-241) (5/9,14/25) -> (7/9,18/23) Glide Reflection Matrix(145,-82,168,-95) (9/16,4/7) -> (6/7,7/8) Hyperbolic Matrix(97,-56,168,-97) (4/7,7/12) -> (4/7,7/12) Reflection Matrix(239,-140,408,-239) (7/12,10/17) -> (7/12,10/17) Reflection Matrix(817,-482,1056,-623) (10/17,13/22) -> (17/22,24/31) Hyperbolic Matrix(3071,-1816,4872,-2881) (13/22,29/49) -> (75/119,29/46) Hyperbolic Matrix(1297,-768,1704,-1009) (29/49,16/27) -> (19/25,16/21) Glide Reflection Matrix(2113,-1284,3000,-1823) (17/28,14/23) -> (50/71,31/44) Hyperbolic Matrix(623,-380,864,-527) (14/23,11/18) -> (18/25,13/18) Glide Reflection Matrix(479,-294,624,-383) (19/31,8/13) -> (13/17,10/13) Glide Reflection Matrix(241,-150,384,-239) (13/21,5/8) -> (5/8,17/27) Parabolic Matrix(2737,-1724,3888,-2449) (17/27,46/73) -> (19/27,50/71) Glide Reflection Matrix(17665,-11132,28032,-17665) (46/73,121/192) -> (46/73,121/192) Reflection Matrix(28799,-18150,45696,-28799) (121/192,75/119) -> (121/192,75/119) Reflection Matrix(1009,-638,1368,-865) (12/19,31/49) -> (14/19,17/23) Glide Reflection Matrix(815,-516,984,-623) (31/49,19/30) -> (19/23,5/6) Glide Reflection Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(2449,-1700,3528,-2449) (34/49,25/36) -> (34/49,25/36) Reflection Matrix(1151,-800,1656,-1151) (25/36,16/23) -> (25/36,16/23) Reflection Matrix(433,-302,552,-385) (16/23,7/10) -> (18/23,11/14) Glide Reflection Matrix(577,-408,816,-577) (12/17,17/24) -> (12/17,17/24) Reflection Matrix(239,-170,336,-239) (17/24,5/7) -> (17/24,5/7) Reflection Matrix(145,-108,192,-143) (17/23,3/4) -> (3/4,19/25) Parabolic Matrix(1583,-1226,1920,-1487) (24/31,31/40) -> (14/17,33/40) Glide Reflection Matrix(721,-570,912,-721) (15/19,19/24) -> (15/19,19/24) Reflection Matrix(191,-152,240,-191) (19/24,4/5) -> (19/24,4/5) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(335,-36,456,-49) -> Matrix(1,0,0,1) Matrix(335,-38,432,-49) -> Matrix(3,2,-2,-1) -1/1 Matrix(335,-44,1104,-145) -> Matrix(1,0,0,1) Matrix(143,-20,336,-47) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(191,-30,312,-49) -> Matrix(1,0,-2,1) 0/1 Matrix(191,-34,264,-47) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(97,-18,264,-49) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(49,-10,240,-49) -> Matrix(-1,0,2,1) (1/5,5/24) -> (-1/1,0/1) Matrix(191,-40,912,-191) -> Matrix(1,0,8,-1) (5/24,4/19) -> (0/1,1/4) Matrix(671,-142,912,-193) -> Matrix(1,0,-2,1) 0/1 Matrix(241,-52,672,-145) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(191,-42,432,-95) -> Matrix(1,-2,-2,3) Matrix(97,-22,216,-49) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(335,-78,408,-95) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(575,-136,816,-193) -> Matrix(1,-2,0,1) 1/0 Matrix(335,-88,552,-145) -> Matrix(1,0,0,1) Matrix(719,-190,912,-241) -> Matrix(7,6,-6,-5) -1/1 Matrix(529,-142,1248,-335) -> Matrix(3,2,-2,-1) -1/1 Matrix(193,-52,360,-97) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(335,-92,528,-145) -> Matrix(1,0,0,1) Matrix(143,-40,168,-47) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(97,-28,336,-97) -> Matrix(-1,0,4,1) (2/7,7/24) -> (-1/2,0/1) Matrix(239,-70,816,-239) -> Matrix(1,0,10,-1) (7/24,5/17) -> (0/1,1/5) Matrix(623,-184,816,-241) -> Matrix(9,-2,-4,1) Matrix(431,-128,1128,-335) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(623,-188,792,-239) -> Matrix(5,-4,-4,3) Matrix(1823,-554,2208,-671) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(623,-190,1728,-527) -> Matrix(1,-2,-2,3) Matrix(287,-88,936,-287) -> Matrix(1,0,0,-1) (11/36,4/13) -> (0/1,1/0) Matrix(193,-60,312,-97) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(287,-102,408,-145) -> Matrix(3,2,-2,-1) -1/1 Matrix(287,-104,792,-287) -> Matrix(-1,0,4,1) (13/36,4/11) -> (-1/2,0/1) Matrix(145,-54,384,-143) -> Matrix(1,0,6,1) 0/1 Matrix(527,-200,888,-337) -> Matrix(9,-2,-4,1) Matrix(2399,-918,3264,-1249) -> Matrix(1,0,-2,1) 0/1 Matrix(865,-332,1248,-479) -> Matrix(1,-2,0,1) 1/0 Matrix(97,-38,120,-47) -> Matrix(1,0,-2,1) 0/1 Matrix(49,-20,120,-49) -> Matrix(-1,2,0,1) (2/5,5/12) -> (1/1,1/0) Matrix(191,-80,456,-191) -> Matrix(1,8,0,-1) (5/12,8/19) -> (-4/1,1/0) Matrix(863,-364,1368,-577) -> Matrix(1,4,0,1) 1/0 Matrix(241,-104,336,-145) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(431,-188,768,-335) -> Matrix(3,4,4,5) Matrix(191,-84,216,-95) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(241,-110,528,-241) -> Matrix(-1,0,10,1) (5/11,11/24) -> (-1/5,0/1) Matrix(287,-132,624,-287) -> Matrix(1,0,12,-1) (11/24,6/13) -> (0/1,1/6) Matrix(241,-112,312,-145) -> Matrix(7,-2,-4,1) Matrix(337,-182,624,-337) -> Matrix(-1,0,10,1) (7/13,13/24) -> (-1/5,0/1) Matrix(287,-156,528,-287) -> Matrix(1,0,8,-1) (13/24,6/11) -> (0/1,1/4) Matrix(193,-106,264,-145) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(337,-188,432,-241) -> Matrix(5,-4,-4,3) Matrix(145,-82,168,-95) -> Matrix(3,-4,-2,3) Matrix(97,-56,168,-97) -> Matrix(-1,4,0,1) (4/7,7/12) -> (2/1,1/0) Matrix(239,-140,408,-239) -> Matrix(1,10,0,-1) (7/12,10/17) -> (-5/1,1/0) Matrix(817,-482,1056,-623) -> Matrix(3,14,-2,-9) Matrix(3071,-1816,4872,-2881) -> Matrix(5,16,4,13) Matrix(1297,-768,1704,-1009) -> Matrix(11,30,-4,-11) *** -> (-3/1,-5/2) Matrix(2113,-1284,3000,-1823) -> Matrix(1,0,0,1) Matrix(623,-380,864,-527) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(479,-294,624,-383) -> Matrix(5,2,-2,-1) Matrix(241,-150,384,-239) -> Matrix(1,0,2,1) 0/1 Matrix(2737,-1724,3888,-2449) -> Matrix(5,-4,-4,3) Matrix(17665,-11132,28032,-17665) -> Matrix(15,-14,16,-15) (46/73,121/192) -> (7/8,1/1) Matrix(28799,-18150,45696,-28799) -> Matrix(27,-28,26,-27) (121/192,75/119) -> (1/1,14/13) Matrix(1009,-638,1368,-865) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(815,-516,984,-623) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(49,-32,72,-47) -> Matrix(1,-2,0,1) 1/0 Matrix(2449,-1700,3528,-2449) -> Matrix(7,12,-4,-7) (34/49,25/36) -> (-2/1,-3/2) Matrix(1151,-800,1656,-1151) -> Matrix(5,6,-4,-5) (25/36,16/23) -> (-3/2,-1/1) Matrix(433,-302,552,-385) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(577,-408,816,-577) -> Matrix(5,6,-4,-5) (12/17,17/24) -> (-3/2,-1/1) Matrix(239,-170,336,-239) -> Matrix(-1,0,2,1) (17/24,5/7) -> (-1/1,0/1) Matrix(145,-108,192,-143) -> Matrix(1,-4,0,1) 1/0 Matrix(1583,-1226,1920,-1487) -> Matrix(1,2,2,3) Matrix(721,-570,912,-721) -> Matrix(15,16,-14,-15) (15/19,19/24) -> (-8/7,-1/1) Matrix(191,-152,240,-191) -> Matrix(3,2,-4,-3) (19/24,4/5) -> (-1/1,-1/2) Matrix(-1,2,0,1) -> Matrix(-1,0,2,1) (1/1,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.