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): 1536 Minimal number of generators: 257 Number of equivalence classes of cusps: 96 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/8 -13/16 -3/4 -17/24 -11/16 -31/48 -5/8 -17/28 -7/12 -9/16 -13/24 -15/28 -1/2 -15/32 -7/16 -13/30 -27/64 -5/12 -13/32 -25/64 -3/8 -23/64 -17/48 -7/20 -5/16 -29/96 -3/10 -19/64 -7/24 -9/32 -5/18 -7/26 -43/160 -1/4 -15/64 -7/30 -5/22 -29/128 -7/32 -3/14 -5/24 -33/160 -3/16 -5/28 -11/64 -1/6 -5/32 -3/20 -1/8 0/1 1/9 1/8 2/15 1/7 3/20 2/13 1/6 5/28 2/11 3/16 1/5 5/24 3/14 2/9 5/22 3/13 1/4 7/26 3/11 5/18 2/7 7/24 3/10 5/16 1/3 7/20 17/48 3/8 2/5 5/12 7/16 7/15 1/2 13/24 9/16 7/12 5/8 31/48 2/3 11/16 17/24 3/4 13/16 7/8 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/30 -8/9 5/132 -7/8 1/26 -13/15 1/26 -6/7 3/76 -17/20 3/76 -11/13 9/226 -5/6 1/25 2/49 -19/23 5/122 -14/17 1/24 -23/28 1/24 -9/11 7/170 -13/16 1/24 -17/21 13/310 -4/5 1/24 -19/24 1/24 -15/19 5/118 -11/14 4/93 1/23 -7/9 5/114 -24/31 17/384 -17/22 2/45 3/67 -27/35 1/22 -10/13 1/24 -3/4 1/22 -14/19 3/64 -11/15 1/22 -41/56 1/22 -30/41 3/64 -19/26 0/1 1/21 -27/37 1/22 -8/11 5/108 -29/40 3/64 -50/69 3/64 -21/29 1/22 -13/18 4/85 1/21 -5/7 3/62 -22/31 13/264 -17/24 1/20 -46/65 11/216 -29/41 1/18 -12/17 1/20 -31/44 1/20 -50/71 1/20 -19/27 1/18 -7/10 0/1 1/21 -23/33 13/270 -16/23 7/144 -25/36 1/20 -9/13 5/102 -11/16 1/20 -13/19 7/138 -2/3 1/20 -13/20 1/18 -11/17 1/18 -31/48 1/18 -20/31 9/160 -9/14 0/1 1/17 -16/25 1/24 -39/61 1/22 -23/36 1/20 -7/11 3/58 -5/8 1/18 -13/21 5/86 -34/55 1/16 -21/34 0/1 1/17 -29/47 1/18 -8/13 3/52 -27/44 3/50 -19/31 7/114 -49/80 1/16 -30/49 1/16 -11/18 0/1 1/15 -14/23 1/24 -17/28 1/20 -37/61 3/58 -20/33 7/132 -3/5 1/18 -13/22 1/17 2/33 -23/39 5/82 -10/17 1/16 -27/46 2/31 1/15 -17/29 1/14 -24/41 1/16 -7/12 1/16 -32/55 1/16 -25/43 7/106 -18/31 5/72 -29/50 2/27 1/13 -11/19 1/10 -15/26 0/1 1/21 -19/33 5/94 -4/7 1/16 -9/16 1/16 -14/25 1/16 -33/59 3/46 -19/34 0/1 1/15 -5/9 1/14 -16/29 3/44 -11/20 1/14 -17/31 3/34 -6/11 1/20 -13/24 1/16 -7/13 1/18 -15/28 1/16 -8/15 1/16 -1/2 0/1 1/15 -8/17 1/16 -15/32 1/15 -7/15 1/14 -6/13 1/12 -11/24 1/14 -5/11 1/10 -19/42 0/1 1/23 -14/31 3/56 -9/20 1/16 -13/29 3/46 -17/38 1/15 2/29 -4/9 1/16 -7/16 1/14 -10/23 3/40 -13/30 2/27 1/13 -42/97 13/168 -29/67 3/38 -16/37 1/12 -3/7 1/14 -14/33 5/56 -25/59 1/10 -11/26 0/1 1/9 -19/45 -1/2 -27/64 0/1 -8/19 1/20 -13/31 5/78 -31/74 6/91 1/15 -18/43 7/104 -5/12 1/14 -17/41 1/14 -29/70 0/1 1/11 -12/29 1/16 -7/17 1/14 -16/39 5/68 -25/61 1/14 -9/22 2/27 1/13 -11/27 5/66 -13/32 1/13 -2/5 1/12 -13/33 7/78 -11/28 1/10 -9/23 1/6 -25/64 0/1 -16/41 1/24 -7/18 0/1 1/15 -19/49 1/14 -31/80 1/14 -12/31 7/96 -17/44 3/40 -5/13 3/38 -3/8 1/12 -7/19 1/10 -11/30 2/23 1/11 -15/41 3/34 -19/52 3/34 -4/11 3/32 -13/36 1/10 -35/97 9/82 -22/61 1/8 -9/25 1/6 -23/64 0/1 -14/39 1/20 -5/14 0/1 1/13 -11/31 9/110 -17/48 1/12 -6/17 1/12 -7/20 1/12 -1/3 1/10 -5/16 1/10 -9/29 1/10 -4/13 5/48 -11/36 1/10 -7/23 7/66 -10/33 13/120 -13/43 13/118 -29/96 1/9 -16/53 13/116 -3/10 0/1 1/9 -11/37 1/6 -19/64 0/1 -8/27 1/12 -13/44 1/10 -5/17 1/10 -12/41 1/12 -7/24 1/10 -9/31 13/126 -2/7 3/28 -9/32 1/9 -7/25 11/98 -5/18 1/9 4/35 -13/47 3/26 -8/29 1/8 -11/40 3/26 -3/11 5/42 -10/37 1/8 -17/63 5/34 -7/26 0/1 1/9 -25/93 5/46 -43/160 1/9 -18/67 5/44 -11/41 3/26 -4/15 1/8 -1/4 1/8 -4/17 1/8 -15/64 2/15 -11/47 3/22 -7/30 2/15 1/7 -3/13 1/6 -8/35 1/8 -13/57 3/22 -5/22 3/23 2/15 -17/75 29/218 -29/128 2/15 -12/53 23/172 -7/31 17/126 -9/40 3/22 -2/9 5/36 -7/32 1/7 -5/23 13/90 -3/14 1/7 4/27 -7/33 19/126 -4/19 5/32 -5/24 1/6 -6/29 1/8 -13/63 11/78 -33/160 1/7 -20/97 19/132 -7/34 1/7 4/27 -1/5 1/6 -3/16 1/6 -5/27 1/6 -2/11 7/40 -5/28 1/6 -8/45 5/28 -3/17 1/6 -4/23 5/28 -5/29 9/50 -11/64 2/11 -6/35 11/60 -1/6 2/11 1/5 -3/19 13/66 -5/32 1/5 -2/13 9/44 -3/20 3/14 -4/27 1/4 -1/7 3/14 -2/15 1/4 -1/8 1/4 -2/17 1/4 -1/9 5/18 0/1 1/0 1/9 -5/18 1/8 -1/4 2/15 -1/4 1/7 -3/14 3/20 -3/14 2/13 -9/44 1/6 -1/5 -2/11 4/23 -5/28 3/17 -1/6 5/28 -1/6 2/11 -7/40 3/16 -1/6 4/21 -13/80 1/5 -1/6 5/24 -1/6 4/19 -5/32 3/14 -4/27 -1/7 2/9 -5/36 7/31 -17/126 5/22 -2/15 -3/23 8/35 -1/8 3/13 -1/6 1/4 -1/8 5/19 -3/26 4/15 -1/8 15/56 -1/8 11/41 -3/26 7/26 -1/9 0/1 10/37 -1/8 3/11 -5/42 11/40 -3/26 19/69 -3/26 8/29 -1/8 5/18 -4/35 -1/9 2/7 -3/28 9/31 -13/126 7/24 -1/10 19/65 -11/114 12/41 -1/12 5/17 -1/10 13/44 -1/10 21/71 -1/10 8/27 -1/12 3/10 -1/9 0/1 10/33 -13/120 7/23 -7/66 11/36 -1/10 4/13 -5/48 5/16 -1/10 6/19 -7/72 1/3 -1/10 7/20 -1/12 6/17 -1/12 17/48 -1/12 11/31 -9/110 5/14 -1/13 0/1 9/25 -1/6 22/61 -1/8 13/36 -1/10 4/11 -3/32 3/8 -1/12 8/21 -5/64 21/55 -1/14 13/34 -1/13 0/1 18/47 -1/12 5/13 -3/38 17/44 -3/40 12/31 -7/96 31/80 -1/14 19/49 -1/14 7/18 -1/15 0/1 9/23 -1/6 11/28 -1/10 24/61 -3/32 13/33 -7/78 2/5 -1/12 9/22 -1/13 -2/27 16/39 -5/68 7/17 -1/14 19/46 -2/29 -1/15 12/29 -1/16 17/41 -1/14 5/12 -1/14 23/55 -1/14 18/43 -7/104 13/31 -5/78 21/50 -2/33 -1/17 8/19 -1/20 11/26 -1/9 0/1 14/33 -5/56 3/7 -1/14 7/16 -1/14 11/25 -1/14 26/59 -3/44 15/34 -1/15 0/1 4/9 -1/16 13/29 -3/46 9/20 -1/16 14/31 -3/56 5/11 -1/10 11/24 -1/14 6/13 -1/12 13/28 -1/14 7/15 -1/14 1/2 -1/15 0/1 9/17 -1/14 17/32 -1/15 8/15 -1/16 7/13 -1/18 13/24 -1/16 6/11 -1/20 23/42 -1/7 0/1 17/31 -3/34 11/20 -1/14 16/29 -3/44 21/38 -1/15 -2/31 5/9 -1/14 9/16 -1/16 13/23 -3/50 17/30 -2/33 -1/17 55/97 -13/222 38/67 -3/52 21/37 -1/18 4/7 -1/16 19/33 -5/94 34/59 -1/20 15/26 -1/21 0/1 26/45 -1/32 37/64 0/1 11/19 -1/10 18/31 -5/72 43/74 -6/89 -1/15 25/43 -7/106 7/12 -1/16 24/41 -1/16 41/70 -1/19 0/1 17/29 -1/14 10/17 -1/16 23/39 -5/82 36/61 -1/16 13/22 -2/33 -1/17 16/27 -5/84 19/32 -1/17 3/5 -1/18 20/33 -7/132 17/28 -1/20 14/23 -1/24 39/64 0/1 25/41 -1/6 11/18 -1/15 0/1 30/49 -1/16 49/80 -1/16 19/31 -7/114 27/44 -3/50 8/13 -3/52 5/8 -1/18 12/19 -1/20 19/30 -2/37 -1/19 26/41 -3/56 33/52 -3/56 7/11 -3/58 23/36 -1/20 62/97 -9/188 39/61 -1/22 16/25 -1/24 41/64 0/1 25/39 -1/10 9/14 -1/17 0/1 20/31 -9/160 31/48 -1/18 11/17 -1/18 13/20 -1/18 2/3 -1/20 11/16 -1/20 20/29 -1/20 9/13 -5/102 25/36 -1/20 16/23 -7/144 23/33 -13/270 30/43 -13/272 67/96 -1/21 37/53 -13/274 7/10 -1/21 0/1 26/37 -1/24 45/64 0/1 19/27 -1/18 31/44 -1/20 12/17 -1/20 29/41 -1/18 17/24 -1/20 22/31 -13/264 5/7 -3/62 23/32 -1/21 18/25 -11/232 13/18 -1/21 -4/85 34/47 -3/64 21/29 -1/22 29/40 -3/64 8/11 -5/108 27/37 -1/22 46/63 -5/116 19/26 -1/21 0/1 68/93 -5/104 117/160 -1/21 49/67 -5/106 30/41 -3/64 11/15 -1/22 3/4 -1/22 13/17 -1/22 49/64 -2/45 36/47 -3/68 23/30 -2/45 -1/23 10/13 -1/24 27/35 -1/22 44/57 -3/68 17/22 -3/67 -2/45 58/75 -29/652 99/128 -2/45 41/53 -23/518 24/31 -17/384 31/40 -3/68 7/9 -5/114 25/32 -1/23 18/23 -13/300 11/14 -1/23 -4/93 26/33 -19/444 15/19 -5/118 19/24 -1/24 23/29 -1/22 50/63 -11/252 127/160 -1/23 77/97 -19/438 27/34 -1/23 -4/93 4/5 -1/24 13/16 -1/24 22/27 -1/24 9/11 -7/170 23/28 -1/24 37/45 -5/122 14/17 -1/24 19/23 -5/122 24/29 -9/220 53/64 -2/49 29/35 -11/270 5/6 -2/49 -1/25 16/19 -13/324 27/32 -1/25 11/13 -9/226 17/20 -3/76 23/27 -1/26 6/7 -3/76 13/15 -1/26 7/8 -1/26 15/17 -1/26 8/9 -5/132 1/1 -1/30 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(223,200,320,287) (-1/1,-8/9) -> (16/23,23/33) Hyperbolic Matrix(609,538,-832,-735) (-8/9,-7/8) -> (-41/56,-30/41) Hyperbolic Matrix(703,610,-960,-833) (-7/8,-13/15) -> (-11/15,-41/56) Hyperbolic Matrix(289,250,704,609) (-13/15,-6/7) -> (16/39,7/17) Hyperbolic Matrix(1217,1036,-1728,-1471) (-6/7,-17/20) -> (-31/44,-50/71) Hyperbolic Matrix(321,272,832,705) (-17/20,-11/13) -> (5/13,17/44) Hyperbolic Matrix(31,26,-192,-161) (-11/13,-5/6) -> (-1/6,-3/19) Hyperbolic Matrix(769,636,-1856,-1535) (-5/6,-19/23) -> (-17/41,-29/70) Hyperbolic Matrix(769,634,1088,897) (-19/23,-14/17) -> (12/17,29/41) Hyperbolic Matrix(479,394,-896,-737) (-14/17,-23/28) -> (-15/28,-8/15) Hyperbolic Matrix(449,368,704,577) (-23/28,-9/11) -> (7/11,23/36) Hyperbolic Matrix(415,338,-512,-417) (-9/11,-13/16) -> (-13/16,-17/21) Parabolic Matrix(225,182,832,673) (-17/21,-4/5) -> (10/37,3/11) Hyperbolic Matrix(1345,1066,-1856,-1471) (-4/5,-19/24) -> (-29/40,-50/69) Hyperbolic Matrix(415,328,768,607) (-19/24,-15/19) -> (7/13,13/24) Hyperbolic Matrix(705,556,-1216,-959) (-15/19,-11/14) -> (-29/50,-11/19) Hyperbolic Matrix(97,76,-448,-351) (-11/14,-7/9) -> (-5/23,-3/14) Hyperbolic Matrix(1313,1018,-1856,-1439) (-7/9,-24/31) -> (-46/65,-29/41) Hyperbolic Matrix(897,694,-1984,-1535) (-24/31,-17/22) -> (-19/42,-14/31) Hyperbolic Matrix(865,668,-2112,-1631) (-17/22,-27/35) -> (-25/61,-9/22) Hyperbolic Matrix(223,172,704,543) (-27/35,-10/13) -> (6/19,1/3) Hyperbolic Matrix(95,72,-128,-97) (-10/13,-3/4) -> (-3/4,-14/19) Parabolic Matrix(671,494,-1088,-801) (-14/19,-11/15) -> (-29/47,-8/13) Hyperbolic Matrix(801,586,-1792,-1311) (-30/41,-19/26) -> (-17/38,-4/9) Hyperbolic Matrix(1057,772,-2496,-1823) (-19/26,-27/37) -> (-25/59,-11/26) Hyperbolic Matrix(159,116,832,607) (-27/37,-8/11) -> (4/21,1/5) Hyperbolic Matrix(383,278,704,511) (-8/11,-29/40) -> (13/24,6/11) Hyperbolic Matrix(2465,1786,-5696,-4127) (-50/69,-21/29) -> (-29/67,-16/37) Hyperbolic Matrix(1089,788,-1856,-1343) (-21/29,-13/18) -> (-27/46,-17/29) Hyperbolic Matrix(161,116,-576,-415) (-13/18,-5/7) -> (-7/25,-5/18) Hyperbolic Matrix(191,136,448,319) (-5/7,-22/31) -> (14/33,3/7) Hyperbolic Matrix(1631,1156,-2304,-1633) (-22/31,-17/24) -> (-17/24,-46/65) Parabolic Matrix(897,634,1088,769) (-29/41,-12/17) -> (14/17,19/23) Hyperbolic Matrix(383,270,1088,767) (-12/17,-31/44) -> (7/20,6/17) Hyperbolic Matrix(1599,1126,2816,1983) (-50/71,-19/27) -> (21/37,4/7) Hyperbolic Matrix(191,134,-640,-449) (-19/27,-7/10) -> (-3/10,-11/37) Hyperbolic Matrix(1153,804,-2752,-1919) (-7/10,-23/33) -> (-13/31,-31/74) Hyperbolic Matrix(287,200,320,223) (-23/33,-16/23) -> (8/9,1/1) Hyperbolic Matrix(895,622,1472,1023) (-16/23,-25/36) -> (17/28,14/23) Hyperbolic Matrix(447,310,-832,-577) (-25/36,-9/13) -> (-7/13,-15/28) Hyperbolic Matrix(351,242,-512,-353) (-9/13,-11/16) -> (-11/16,-13/19) Parabolic Matrix(161,110,704,481) (-13/19,-2/3) -> (8/35,3/13) Hyperbolic Matrix(353,230,640,417) (-2/3,-13/20) -> (11/20,16/29) Hyperbolic Matrix(321,208,1088,705) (-13/20,-11/17) -> (5/17,13/44) Hyperbolic Matrix(1439,930,3712,2399) (-11/17,-31/48) -> (31/80,19/49) Hyperbolic Matrix(1537,992,3968,2561) (-31/48,-20/31) -> (12/31,31/80) Hyperbolic Matrix(705,454,896,577) (-20/31,-9/14) -> (11/14,26/33) Hyperbolic Matrix(321,206,-896,-575) (-9/14,-16/25) -> (-14/39,-5/14) Hyperbolic Matrix(3359,2148,4352,2783) (-16/25,-39/61) -> (27/35,44/57) Hyperbolic Matrix(2369,1514,-3904,-2495) (-39/61,-23/36) -> (-17/28,-37/61) Hyperbolic Matrix(577,368,704,449) (-23/36,-7/11) -> (9/11,23/28) Hyperbolic Matrix(159,100,-256,-161) (-7/11,-5/8) -> (-5/8,-13/21) Parabolic Matrix(2047,1266,-3520,-2177) (-13/21,-34/55) -> (-32/55,-25/43) Hyperbolic Matrix(961,594,2176,1345) (-34/55,-21/34) -> (15/34,4/9) Hyperbolic Matrix(703,434,-3008,-1857) (-21/34,-29/47) -> (-11/47,-7/30) Hyperbolic Matrix(127,78,832,511) (-8/13,-27/44) -> (3/20,2/13) Hyperbolic Matrix(1089,668,1984,1217) (-27/44,-19/31) -> (17/31,11/20) Hyperbolic Matrix(1407,862,3968,2431) (-19/31,-49/80) -> (17/48,11/31) Hyperbolic Matrix(1313,804,3712,2273) (-49/80,-30/49) -> (6/17,17/48) Hyperbolic Matrix(1249,764,1728,1057) (-30/49,-11/18) -> (13/18,34/47) Hyperbolic Matrix(449,274,-1152,-703) (-11/18,-14/23) -> (-16/41,-7/18) Hyperbolic Matrix(1023,622,1472,895) (-14/23,-17/28) -> (25/36,16/23) Hyperbolic Matrix(3519,2134,-8128,-4929) (-37/61,-20/33) -> (-42/97,-29/67) Hyperbolic Matrix(1121,678,1536,929) (-20/33,-3/5) -> (27/37,46/63) Hyperbolic Matrix(287,170,-704,-417) (-3/5,-13/22) -> (-9/22,-11/27) Hyperbolic Matrix(481,284,-2112,-1247) (-13/22,-23/39) -> (-13/57,-5/22) Hyperbolic Matrix(95,56,704,415) (-23/39,-10/17) -> (2/15,1/7) Hyperbolic Matrix(1567,920,2560,1503) (-10/17,-27/46) -> (11/18,30/49) Hyperbolic Matrix(321,188,-1856,-1087) (-17/29,-24/41) -> (-4/23,-5/29) Hyperbolic Matrix(671,392,-1152,-673) (-24/41,-7/12) -> (-7/12,-32/55) Parabolic Matrix(833,484,-2752,-1599) (-25/43,-18/31) -> (-10/33,-13/43) Hyperbolic Matrix(1279,742,1984,1151) (-18/31,-29/50) -> (9/14,20/31) Hyperbolic Matrix(703,406,-1664,-961) (-11/19,-15/26) -> (-11/26,-19/45) Hyperbolic Matrix(673,388,-2496,-1439) (-15/26,-19/33) -> (-17/63,-7/26) Hyperbolic Matrix(129,74,448,257) (-19/33,-4/7) -> (2/7,9/31) Hyperbolic Matrix(287,162,-512,-289) (-4/7,-9/16) -> (-9/16,-14/25) Parabolic Matrix(929,520,1088,609) (-14/25,-33/59) -> (23/27,6/7) Hyperbolic Matrix(447,250,-2176,-1217) (-33/59,-19/34) -> (-7/34,-1/5) Hyperbolic Matrix(831,464,2176,1215) (-19/34,-5/9) -> (21/55,13/34) Hyperbolic Matrix(481,266,-1792,-991) (-5/9,-16/29) -> (-18/67,-11/41) Hyperbolic Matrix(417,230,640,353) (-16/29,-11/20) -> (13/20,2/3) Hyperbolic Matrix(1217,668,1984,1089) (-11/20,-17/31) -> (19/31,27/44) Hyperbolic Matrix(449,246,-1984,-1087) (-17/31,-6/11) -> (-12/53,-7/31) Hyperbolic Matrix(511,278,704,383) (-6/11,-13/24) -> (29/40,8/11) Hyperbolic Matrix(607,328,768,415) (-13/24,-7/13) -> (15/19,19/24) Hyperbolic Matrix(31,16,-64,-33) (-8/15,-1/2) -> (-1/2,-8/17) Parabolic Matrix(545,256,1024,481) (-8/17,-15/32) -> (17/32,8/15) Hyperbolic Matrix(543,254,1024,479) (-15/32,-7/15) -> (9/17,17/32) Hyperbolic Matrix(159,74,-896,-417) (-7/15,-6/13) -> (-8/45,-3/17) Hyperbolic Matrix(161,74,768,353) (-6/13,-11/24) -> (5/24,4/19) Hyperbolic Matrix(193,88,704,321) (-11/24,-5/11) -> (3/11,11/40) Hyperbolic Matrix(769,348,-3392,-1535) (-5/11,-19/42) -> (-5/22,-17/75) Hyperbolic Matrix(767,346,1984,895) (-14/31,-9/20) -> (17/44,12/31) Hyperbolic Matrix(223,100,640,287) (-9/20,-13/29) -> (1/3,7/20) Hyperbolic Matrix(1153,516,-4288,-1919) (-13/29,-17/38) -> (-7/26,-25/93) Hyperbolic Matrix(223,98,-512,-225) (-4/9,-7/16) -> (-7/16,-10/23) Parabolic Matrix(1217,528,1920,833) (-10/23,-13/30) -> (19/30,26/41) Hyperbolic Matrix(1279,554,-6208,-2689) (-13/30,-42/97) -> (-20/97,-7/34) Hyperbolic Matrix(833,360,2816,1217) (-16/37,-3/7) -> (21/71,8/27) Hyperbolic Matrix(319,136,448,191) (-3/7,-14/33) -> (22/31,5/7) Hyperbolic Matrix(1279,542,2112,895) (-14/33,-25/59) -> (3/5,20/33) Hyperbolic Matrix(2369,1000,4096,1729) (-19/45,-27/64) -> (37/64,11/19) Hyperbolic Matrix(2367,998,4096,1727) (-27/64,-8/19) -> (26/45,37/64) Hyperbolic Matrix(257,108,-1216,-511) (-8/19,-13/31) -> (-7/33,-4/19) Hyperbolic Matrix(1313,550,-4352,-1823) (-31/74,-18/43) -> (-16/53,-3/10) Hyperbolic Matrix(865,362,-2368,-991) (-18/43,-5/12) -> (-19/52,-4/11) Hyperbolic Matrix(959,398,-2624,-1089) (-5/12,-17/41) -> (-15/41,-19/52) Hyperbolic Matrix(449,186,-2624,-1087) (-29/70,-12/29) -> (-6/35,-1/6) Hyperbolic Matrix(513,212,-1856,-767) (-12/29,-7/17) -> (-13/47,-8/29) Hyperbolic Matrix(609,250,704,289) (-7/17,-16/39) -> (6/7,13/15) Hyperbolic Matrix(2497,1024,3904,1601) (-16/39,-25/61) -> (39/61,16/25) Hyperbolic Matrix(609,248,1024,417) (-11/27,-13/32) -> (19/32,3/5) Hyperbolic Matrix(607,246,1024,415) (-13/32,-2/5) -> (16/27,19/32) Hyperbolic Matrix(1217,480,2112,833) (-2/5,-13/33) -> (19/33,34/59) Hyperbolic Matrix(1409,554,-3904,-1535) (-13/33,-11/28) -> (-13/36,-35/97) Hyperbolic Matrix(449,176,1472,577) (-11/28,-9/23) -> (7/23,11/36) Hyperbolic Matrix(2497,976,4096,1601) (-9/23,-25/64) -> (39/64,25/41) Hyperbolic Matrix(2495,974,4096,1599) (-25/64,-16/41) -> (14/23,39/64) Hyperbolic Matrix(1057,410,2560,993) (-7/18,-19/49) -> (7/17,19/46) Hyperbolic Matrix(2399,930,3712,1439) (-19/49,-31/80) -> (31/48,11/17) Hyperbolic Matrix(2561,992,3968,1537) (-31/80,-12/31) -> (20/31,31/48) Hyperbolic Matrix(895,346,1984,767) (-12/31,-17/44) -> (9/20,14/31) Hyperbolic Matrix(705,272,832,321) (-17/44,-5/13) -> (11/13,17/20) Hyperbolic Matrix(95,36,-256,-97) (-5/13,-3/8) -> (-3/8,-7/19) Parabolic Matrix(223,82,-960,-353) (-7/19,-11/30) -> (-7/30,-3/13) Hyperbolic Matrix(1087,398,1920,703) (-11/30,-15/41) -> (13/23,17/30) Hyperbolic Matrix(127,46,704,255) (-4/11,-13/36) -> (5/28,2/11) Hyperbolic Matrix(1375,496,-6656,-2401) (-35/97,-22/61) -> (-6/29,-13/63) Hyperbolic Matrix(2303,830,3904,1407) (-22/61,-9/25) -> (23/39,36/61) Hyperbolic Matrix(2625,944,4096,1473) (-9/25,-23/64) -> (41/64,25/39) Hyperbolic Matrix(2623,942,4096,1471) (-23/64,-14/39) -> (16/25,41/64) Hyperbolic Matrix(833,296,1984,705) (-5/14,-11/31) -> (13/31,21/50) Hyperbolic Matrix(2431,862,3968,1407) (-11/31,-17/48) -> (49/80,19/31) Hyperbolic Matrix(2273,804,3712,1313) (-17/48,-6/17) -> (30/49,49/80) Hyperbolic Matrix(767,270,1088,383) (-6/17,-7/20) -> (31/44,12/17) Hyperbolic Matrix(287,100,640,223) (-7/20,-1/3) -> (13/29,9/20) Hyperbolic Matrix(159,50,-512,-161) (-1/3,-5/16) -> (-5/16,-9/29) Parabolic Matrix(641,198,832,257) (-9/29,-4/13) -> (10/13,27/35) Hyperbolic Matrix(353,108,-1984,-607) (-4/13,-11/36) -> (-5/28,-8/45) Hyperbolic Matrix(577,176,1472,449) (-11/36,-7/23) -> (9/23,11/28) Hyperbolic Matrix(33,10,320,97) (-7/23,-10/33) -> (0/1,1/9) Hyperbolic Matrix(6433,1944,9216,2785) (-13/43,-29/96) -> (67/96,37/53) Hyperbolic Matrix(6431,1942,9216,2783) (-29/96,-16/53) -> (30/43,67/96) Hyperbolic Matrix(2881,856,4096,1217) (-11/37,-19/64) -> (45/64,19/27) Hyperbolic Matrix(2879,854,4096,1215) (-19/64,-8/27) -> (26/37,45/64) Hyperbolic Matrix(257,76,-1728,-511) (-8/27,-13/44) -> (-3/20,-4/27) Hyperbolic Matrix(705,208,1088,321) (-13/44,-5/17) -> (11/17,13/20) Hyperbolic Matrix(191,56,1088,319) (-5/17,-12/41) -> (4/23,3/17) Hyperbolic Matrix(417,122,-1856,-543) (-12/41,-7/24) -> (-9/40,-2/9) Hyperbolic Matrix(447,130,-1984,-577) (-7/24,-9/31) -> (-7/31,-9/40) Hyperbolic Matrix(257,74,448,129) (-9/31,-2/7) -> (4/7,19/33) Hyperbolic Matrix(737,208,1024,289) (-2/7,-9/32) -> (23/32,18/25) Hyperbolic Matrix(735,206,1024,287) (-9/32,-7/25) -> (5/7,23/32) Hyperbolic Matrix(671,186,1728,479) (-5/18,-13/47) -> (19/49,7/18) Hyperbolic Matrix(385,106,-1856,-511) (-8/29,-11/40) -> (-5/24,-6/29) Hyperbolic Matrix(321,88,704,193) (-11/40,-3/11) -> (5/11,11/24) Hyperbolic Matrix(575,156,704,191) (-3/11,-10/37) -> (22/27,9/11) Hyperbolic Matrix(607,164,1536,415) (-10/37,-17/63) -> (13/33,2/5) Hyperbolic Matrix(18721,5032,25600,6881) (-25/93,-43/160) -> (117/160,49/67) Hyperbolic Matrix(18719,5030,25600,6879) (-43/160,-18/67) -> (68/93,117/160) Hyperbolic Matrix(97,26,-832,-223) (-11/41,-4/15) -> (-2/17,-1/9) Hyperbolic Matrix(31,8,-128,-33) (-4/15,-1/4) -> (-1/4,-4/17) Parabolic Matrix(3137,736,4096,961) (-4/17,-15/64) -> (49/64,36/47) Hyperbolic Matrix(3135,734,4096,959) (-15/64,-11/47) -> (13/17,49/64) Hyperbolic Matrix(575,132,832,191) (-3/13,-8/35) -> (20/29,9/13) Hyperbolic Matrix(1569,358,4352,993) (-8/35,-13/57) -> (9/25,22/61) Hyperbolic Matrix(12673,2872,16384,3713) (-17/75,-29/128) -> (99/128,41/53) Hyperbolic Matrix(12671,2870,16384,3711) (-29/128,-12/53) -> (58/75,99/128) Hyperbolic Matrix(801,176,1024,225) (-2/9,-7/32) -> (25/32,18/23) Hyperbolic Matrix(799,174,1024,223) (-7/32,-5/23) -> (7/9,25/32) Hyperbolic Matrix(319,68,896,191) (-3/14,-7/33) -> (11/31,5/14) Hyperbolic Matrix(353,74,768,161) (-4/19,-5/24) -> (11/24,6/13) Hyperbolic Matrix(20321,4192,25600,5281) (-13/63,-33/160) -> (127/160,77/97) Hyperbolic Matrix(20319,4190,25600,5279) (-33/160,-20/97) -> (50/63,127/160) Hyperbolic Matrix(95,18,-512,-97) (-1/5,-3/16) -> (-3/16,-5/27) Parabolic Matrix(513,94,704,129) (-5/27,-2/11) -> (8/11,27/37) Hyperbolic Matrix(255,46,704,127) (-2/11,-5/28) -> (13/36,4/11) Hyperbolic Matrix(319,56,1088,191) (-3/17,-4/23) -> (12/41,5/17) Hyperbolic Matrix(3393,584,4096,705) (-5/29,-11/64) -> (53/64,29/35) Hyperbolic Matrix(3391,582,4096,703) (-11/64,-6/35) -> (24/29,53/64) Hyperbolic Matrix(865,136,1024,161) (-3/19,-5/32) -> (27/32,11/13) Hyperbolic Matrix(863,134,1024,159) (-5/32,-2/13) -> (16/19,27/32) Hyperbolic Matrix(511,78,832,127) (-2/13,-3/20) -> (27/44,8/13) Hyperbolic Matrix(479,70,1088,159) (-4/27,-1/7) -> (11/25,26/59) Hyperbolic Matrix(415,56,704,95) (-1/7,-2/15) -> (10/17,23/39) Hyperbolic Matrix(31,4,-256,-33) (-2/15,-1/8) -> (-1/8,-2/17) Parabolic Matrix(97,10,320,33) (-1/9,0/1) -> (10/33,7/23) Hyperbolic Matrix(223,-26,832,-97) (1/9,1/8) -> (15/56,11/41) Hyperbolic Matrix(257,-34,960,-127) (1/8,2/15) -> (4/15,15/56) Hyperbolic Matrix(511,-76,1728,-257) (1/7,3/20) -> (13/44,21/71) Hyperbolic Matrix(161,-26,192,-31) (2/13,1/6) -> (5/6,16/19) Hyperbolic Matrix(1087,-188,1856,-321) (1/6,4/23) -> (24/41,41/70) Hyperbolic Matrix(417,-74,896,-159) (3/17,5/28) -> (13/28,7/15) Hyperbolic Matrix(97,-18,512,-95) (2/11,3/16) -> (3/16,4/21) Parabolic Matrix(511,-106,1856,-385) (1/5,5/24) -> (11/40,19/69) Hyperbolic Matrix(511,-108,1216,-257) (4/19,3/14) -> (21/50,8/19) Hyperbolic Matrix(351,-76,448,-97) (3/14,2/9) -> (18/23,11/14) Hyperbolic Matrix(543,-122,1856,-417) (2/9,7/31) -> (19/65,12/41) Hyperbolic Matrix(1087,-246,1984,-449) (7/31,5/22) -> (23/42,17/31) Hyperbolic Matrix(1247,-284,2112,-481) (5/22,8/35) -> (36/61,13/22) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(417,-110,1088,-287) (5/19,4/15) -> (18/47,5/13) Hyperbolic Matrix(991,-266,1792,-481) (11/41,7/26) -> (21/38,5/9) Hyperbolic Matrix(1439,-388,2496,-673) (7/26,10/37) -> (34/59,15/26) Hyperbolic Matrix(3231,-890,5696,-1569) (19/69,8/29) -> (38/67,21/37) Hyperbolic Matrix(767,-212,1856,-513) (8/29,5/18) -> (19/46,12/29) Hyperbolic Matrix(415,-116,576,-161) (5/18,2/7) -> (18/25,13/18) Hyperbolic Matrix(673,-196,2304,-671) (9/31,7/24) -> (7/24,19/65) Parabolic Matrix(449,-134,640,-191) (8/27,3/10) -> (7/10,26/37) Hyperbolic Matrix(1599,-484,2752,-833) (3/10,10/33) -> (18/31,43/74) Hyperbolic Matrix(385,-118,832,-255) (11/36,4/13) -> (6/13,13/28) Hyperbolic Matrix(161,-50,512,-159) (4/13,5/16) -> (5/16,6/19) Parabolic Matrix(575,-206,896,-321) (5/14,9/25) -> (25/39,9/14) Hyperbolic Matrix(1535,-554,3904,-1409) (22/61,13/36) -> (11/28,24/61) Hyperbolic Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(1473,-562,3520,-1343) (8/21,21/55) -> (23/55,18/43) Hyperbolic Matrix(2305,-882,3008,-1151) (13/34,18/47) -> (36/47,23/30) Hyperbolic Matrix(703,-274,1152,-449) (7/18,9/23) -> (25/41,11/18) Hyperbolic Matrix(4609,-1814,8128,-3199) (24/61,13/33) -> (55/97,38/67) Hyperbolic Matrix(417,-170,704,-287) (2/5,9/22) -> (13/22,16/27) Hyperbolic Matrix(1631,-668,2112,-865) (9/22,16/39) -> (44/57,17/22) Hyperbolic Matrix(1535,-636,1856,-769) (12/29,17/41) -> (19/23,24/29) Hyperbolic Matrix(481,-200,1152,-479) (17/41,5/12) -> (5/12,23/55) Parabolic Matrix(1919,-804,2752,-1153) (18/43,13/31) -> (23/33,30/43) Hyperbolic Matrix(961,-406,1664,-703) (8/19,11/26) -> (15/26,26/45) Hyperbolic Matrix(1823,-772,2496,-1057) (11/26,14/33) -> (46/63,19/26) Hyperbolic Matrix(225,-98,512,-223) (3/7,7/16) -> (7/16,11/25) Parabolic Matrix(1729,-762,2176,-959) (26/59,15/34) -> (27/34,4/5) Hyperbolic Matrix(1311,-586,1792,-801) (4/9,13/29) -> (49/67,30/41) Hyperbolic Matrix(1535,-694,1984,-897) (14/31,5/11) -> (41/53,24/31) Hyperbolic Matrix(33,-16,64,-31) (7/15,1/2) -> (1/2,9/17) Parabolic Matrix(737,-394,896,-479) (8/15,7/13) -> (37/45,14/17) Hyperbolic Matrix(2623,-1436,3392,-1857) (6/11,23/42) -> (17/22,58/75) Hyperbolic Matrix(3135,-1732,4288,-2369) (16/29,21/38) -> (19/26,68/93) Hyperbolic Matrix(289,-162,512,-287) (5/9,9/16) -> (9/16,13/23) Parabolic Matrix(4929,-2794,6208,-3519) (17/30,55/97) -> (77/97,27/34) Hyperbolic Matrix(959,-556,1216,-705) (11/19,18/31) -> (26/33,15/19) Hyperbolic Matrix(3039,-1766,4352,-2529) (43/74,25/43) -> (37/53,7/10) Hyperbolic Matrix(1503,-874,2368,-1377) (25/43,7/12) -> (33/52,7/11) Hyperbolic Matrix(1665,-974,2624,-1535) (7/12,24/41) -> (26/41,33/52) Hyperbolic Matrix(2175,-1274,2624,-1537) (41/70,17/29) -> (29/35,5/6) Hyperbolic Matrix(1343,-788,1856,-1089) (17/29,10/17) -> (34/47,21/29) Hyperbolic Matrix(2495,-1514,3904,-2369) (20/33,17/28) -> (23/36,62/97) Hyperbolic Matrix(161,-100,256,-159) (8/13,5/8) -> (5/8,12/19) Parabolic Matrix(737,-466,960,-607) (12/19,19/30) -> (23/30,10/13) Hyperbolic Matrix(5281,-3376,6656,-4255) (62/97,39/61) -> (23/29,50/63) Hyperbolic Matrix(353,-242,512,-351) (2/3,11/16) -> (11/16,20/29) Parabolic Matrix(1631,-1132,1984,-1377) (9/13,25/36) -> (23/28,37/45) Hyperbolic Matrix(1471,-1036,1728,-1217) (19/27,31/44) -> (17/20,23/27) Hyperbolic Matrix(1439,-1018,1856,-1313) (29/41,17/24) -> (31/40,7/9) Hyperbolic Matrix(1537,-1090,1984,-1407) (17/24,22/31) -> (24/31,31/40) Hyperbolic Matrix(1471,-1066,1856,-1345) (21/29,29/40) -> (19/24,23/29) Hyperbolic Matrix(735,-538,832,-609) (30/41,11/15) -> (15/17,8/9) Hyperbolic Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(417,-338,512,-415) (4/5,13/16) -> (13/16,22/27) Parabolic Matrix(225,-196,256,-223) (13/15,7/8) -> (7/8,15/17) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-60,1) Matrix(223,200,320,287) -> Matrix(107,-4,-2220,83) Matrix(609,538,-832,-735) -> Matrix(105,-4,2284,-87) Matrix(703,610,-960,-833) -> Matrix(51,-2,1148,-45) Matrix(289,250,704,609) -> Matrix(103,-4,-1416,55) Matrix(1217,1036,-1728,-1471) -> Matrix(51,-2,944,-37) Matrix(321,272,832,705) -> Matrix(151,-6,-1988,79) Matrix(31,26,-192,-161) -> Matrix(99,-4,520,-21) Matrix(769,636,-1856,-1535) -> Matrix(49,-2,564,-23) Matrix(769,634,1088,897) -> Matrix(49,-2,-1004,41) Matrix(479,394,-896,-737) -> Matrix(49,-2,760,-31) Matrix(449,368,704,577) -> Matrix(49,-2,-1004,41) Matrix(415,338,-512,-417) -> Matrix(241,-10,5760,-239) Matrix(225,182,832,673) -> Matrix(95,-4,-736,31) Matrix(1345,1066,-1856,-1471) -> Matrix(45,-2,968,-43) Matrix(415,328,768,607) -> Matrix(47,-2,-728,31) Matrix(705,556,-1216,-959) -> Matrix(47,-2,588,-25) Matrix(97,76,-448,-351) -> Matrix(185,-8,1272,-55) Matrix(1313,1018,-1856,-1439) -> Matrix(91,-4,1752,-77) Matrix(897,694,-1984,-1535) -> Matrix(45,-2,968,-43) Matrix(865,668,-2112,-1631) -> Matrix(89,-4,1224,-55) Matrix(223,172,704,543) -> Matrix(89,-4,-912,41) Matrix(95,72,-128,-97) -> Matrix(45,-2,968,-43) Matrix(671,494,-1088,-801) -> Matrix(1,0,-4,1) Matrix(801,586,-1792,-1311) -> Matrix(43,-2,624,-29) Matrix(1057,772,-2496,-1823) -> Matrix(1,0,-12,1) Matrix(159,116,832,607) -> Matrix(89,-4,-556,25) Matrix(383,278,704,511) -> Matrix(43,-2,-752,35) Matrix(2465,1786,-5696,-4127) -> Matrix(85,-4,1084,-51) Matrix(1089,788,-1856,-1343) -> Matrix(43,-2,624,-29) Matrix(161,116,-576,-415) -> Matrix(169,-8,1500,-71) Matrix(191,136,448,319) -> Matrix(41,-2,-512,25) Matrix(1631,1156,-2304,-1633) -> Matrix(121,-6,2400,-119) Matrix(897,634,1088,769) -> Matrix(41,-2,-1004,49) Matrix(383,270,1088,767) -> Matrix(39,-2,-448,23) Matrix(1599,1126,2816,1983) -> Matrix(1,0,-36,1) Matrix(191,134,-640,-449) -> Matrix(1,0,-12,1) Matrix(1153,804,-2752,-1919) -> Matrix(125,-6,1896,-91) Matrix(287,200,320,223) -> Matrix(83,-4,-2220,107) Matrix(895,622,1472,1023) -> Matrix(41,-2,-840,41) Matrix(447,310,-832,-577) -> Matrix(41,-2,636,-31) Matrix(351,242,-512,-353) -> Matrix(121,-6,2400,-119) Matrix(161,110,704,481) -> Matrix(79,-4,-612,31) Matrix(353,230,640,417) -> Matrix(37,-2,-536,29) Matrix(321,208,1088,705) -> Matrix(37,-2,-388,21) Matrix(1439,930,3712,2399) -> Matrix(109,-6,-1544,85) Matrix(1537,992,3968,2561) -> Matrix(143,-8,-1984,111) Matrix(705,454,896,577) -> Matrix(69,-4,-1604,93) Matrix(321,206,-896,-575) -> Matrix(1,0,-4,1) Matrix(3359,2148,4352,2783) -> Matrix(45,-2,-1012,45) Matrix(2369,1514,-3904,-2495) -> Matrix(41,-2,800,-39) Matrix(577,368,704,449) -> Matrix(41,-2,-1004,49) Matrix(159,100,-256,-161) -> Matrix(37,-2,648,-35) Matrix(2047,1266,-3520,-2177) -> Matrix(33,-2,512,-31) Matrix(961,594,2176,1345) -> Matrix(1,0,-32,1) Matrix(703,434,-3008,-1857) -> Matrix(33,-2,248,-15) Matrix(127,78,832,511) -> Matrix(101,-6,-488,29) Matrix(1089,668,1984,1217) -> Matrix(33,-2,-412,25) Matrix(1407,862,3968,2431) -> Matrix(129,-8,-1564,97) Matrix(1313,804,3712,2273) -> Matrix(95,-6,-1124,71) Matrix(1249,764,1728,1057) -> Matrix(61,-4,-1296,85) Matrix(449,274,-1152,-703) -> Matrix(1,0,0,1) Matrix(1023,622,1472,895) -> Matrix(41,-2,-840,41) Matrix(3519,2134,-8128,-4929) -> Matrix(115,-6,1476,-77) Matrix(1121,678,1536,929) -> Matrix(37,-2,-832,45) Matrix(287,170,-704,-417) -> Matrix(67,-4,888,-53) Matrix(481,284,-2112,-1247) -> Matrix(65,-4,504,-31) Matrix(95,56,704,415) -> Matrix(65,-4,-276,17) Matrix(1567,920,2560,1503) -> Matrix(31,-2,-480,31) Matrix(321,188,-1856,-1087) -> Matrix(37,-2,204,-11) Matrix(671,392,-1152,-673) -> Matrix(33,-2,512,-31) Matrix(833,484,-2752,-1599) -> Matrix(89,-6,816,-55) Matrix(1279,742,1984,1151) -> Matrix(27,-2,-472,35) Matrix(703,406,-1664,-961) -> Matrix(1,0,-12,1) Matrix(673,388,-2496,-1439) -> Matrix(1,0,-12,1) Matrix(129,74,448,257) -> Matrix(35,-2,-332,19) Matrix(287,162,-512,-289) -> Matrix(33,-2,512,-31) Matrix(929,520,1088,609) -> Matrix(61,-4,-1540,101) Matrix(447,250,-2176,-1217) -> Matrix(61,-4,412,-27) Matrix(831,464,2176,1215) -> Matrix(1,0,-28,1) Matrix(481,266,-1792,-991) -> Matrix(31,-2,264,-17) Matrix(417,230,640,353) -> Matrix(29,-2,-536,37) Matrix(1217,668,1984,1089) -> Matrix(25,-2,-412,33) Matrix(449,246,-1984,-1087) -> Matrix(17,-2,128,-15) Matrix(511,278,704,383) -> Matrix(35,-2,-752,43) Matrix(607,328,768,415) -> Matrix(31,-2,-728,47) Matrix(31,16,-64,-33) -> Matrix(1,0,0,1) Matrix(545,256,1024,481) -> Matrix(31,-2,-480,31) Matrix(543,254,1024,479) -> Matrix(29,-2,-420,29) Matrix(159,74,-896,-417) -> Matrix(29,-2,160,-11) Matrix(161,74,768,353) -> Matrix(29,-2,-188,13) Matrix(193,88,704,321) -> Matrix(25,-2,-212,17) Matrix(769,348,-3392,-1535) -> Matrix(49,-2,368,-15) Matrix(767,346,1984,895) -> Matrix(35,-2,-472,27) Matrix(223,100,640,287) -> Matrix(31,-2,-356,23) Matrix(1153,516,-4288,-1919) -> Matrix(29,-2,276,-19) Matrix(223,98,-512,-225) -> Matrix(29,-2,392,-27) Matrix(1217,528,1920,833) -> Matrix(1,0,-32,1) Matrix(1279,554,-6208,-2689) -> Matrix(79,-6,540,-41) Matrix(833,360,2816,1217) -> Matrix(1,0,-24,1) Matrix(319,136,448,191) -> Matrix(25,-2,-512,41) Matrix(1279,542,2112,895) -> Matrix(21,-2,-388,37) Matrix(2369,1000,4096,1729) -> Matrix(1,0,-8,1) Matrix(2367,998,4096,1727) -> Matrix(1,0,-52,1) Matrix(257,108,-1216,-511) -> Matrix(35,-2,228,-13) Matrix(1313,550,-4352,-1823) -> Matrix(91,-6,804,-53) Matrix(865,362,-2368,-991) -> Matrix(59,-4,664,-45) Matrix(959,398,-2624,-1089) -> Matrix(25,-2,288,-23) Matrix(449,186,-2624,-1087) -> Matrix(21,-2,116,-11) Matrix(513,212,-1856,-767) -> Matrix(31,-2,264,-17) Matrix(609,250,704,289) -> Matrix(55,-4,-1416,103) Matrix(2497,1024,3904,1601) -> Matrix(27,-2,-580,43) Matrix(609,248,1024,417) -> Matrix(79,-6,-1356,103) Matrix(607,246,1024,415) -> Matrix(77,-6,-1296,101) Matrix(1217,480,2112,833) -> Matrix(23,-2,-448,39) Matrix(1409,554,-3904,-1535) -> Matrix(21,-2,200,-19) Matrix(449,176,1472,577) -> Matrix(19,-2,-180,19) Matrix(2497,976,4096,1601) -> Matrix(1,0,-12,1) Matrix(2495,974,4096,1599) -> Matrix(1,0,-48,1) Matrix(1057,410,2560,993) -> Matrix(29,-2,-420,29) Matrix(2399,930,3712,1439) -> Matrix(85,-6,-1544,109) Matrix(2561,992,3968,1537) -> Matrix(111,-8,-1984,143) Matrix(895,346,1984,767) -> Matrix(27,-2,-472,35) Matrix(705,272,832,321) -> Matrix(79,-6,-1988,151) Matrix(95,36,-256,-97) -> Matrix(25,-2,288,-23) Matrix(223,82,-960,-353) -> Matrix(1,0,-4,1) Matrix(1087,398,1920,703) -> Matrix(1,0,-28,1) Matrix(127,46,704,255) -> Matrix(19,-2,-104,11) Matrix(1375,496,-6656,-2401) -> Matrix(17,-2,128,-15) Matrix(2303,830,3904,1407) -> Matrix(17,-2,-280,33) Matrix(2625,944,4096,1473) -> Matrix(1,0,-16,1) Matrix(2623,942,4096,1471) -> Matrix(1,0,-44,1) Matrix(833,296,1984,705) -> Matrix(25,-2,-412,33) Matrix(2431,862,3968,1407) -> Matrix(97,-8,-1564,129) Matrix(2273,804,3712,1313) -> Matrix(71,-6,-1124,95) Matrix(767,270,1088,383) -> Matrix(23,-2,-448,39) Matrix(287,100,640,223) -> Matrix(23,-2,-356,31) Matrix(159,50,-512,-161) -> Matrix(61,-6,600,-59) Matrix(641,198,832,257) -> Matrix(19,-2,-408,43) Matrix(353,108,-1984,-607) -> Matrix(1,0,-4,1) Matrix(577,176,1472,449) -> Matrix(19,-2,-180,19) Matrix(33,10,320,97) -> Matrix(37,-4,-120,13) Matrix(6433,1944,9216,2785) -> Matrix(235,-26,-4944,547) Matrix(6431,1942,9216,2783) -> Matrix(233,-26,-4884,545) Matrix(2881,856,4096,1217) -> Matrix(1,0,-24,1) Matrix(2879,854,4096,1215) -> Matrix(1,0,-36,1) Matrix(257,76,-1728,-511) -> Matrix(23,-2,104,-9) Matrix(705,208,1088,321) -> Matrix(21,-2,-388,37) Matrix(191,56,1088,319) -> Matrix(19,-2,-104,11) Matrix(417,122,-1856,-543) -> Matrix(43,-4,312,-29) Matrix(447,130,-1984,-577) -> Matrix(137,-14,1008,-103) Matrix(257,74,448,129) -> Matrix(19,-2,-332,35) Matrix(737,208,1024,289) -> Matrix(127,-14,-2676,295) Matrix(735,206,1024,287) -> Matrix(125,-14,-2616,293) Matrix(671,186,1728,479) -> Matrix(35,-4,-516,59) Matrix(385,106,-1856,-511) -> Matrix(17,-2,128,-15) Matrix(321,88,704,193) -> Matrix(17,-2,-212,25) Matrix(575,156,704,191) -> Matrix(49,-6,-1184,145) Matrix(607,164,1536,415) -> Matrix(15,-2,-172,23) Matrix(18721,5032,25600,6881) -> Matrix(91,-10,-1920,211) Matrix(18719,5030,25600,6879) -> Matrix(89,-10,-1860,209) Matrix(97,26,-832,-223) -> Matrix(33,-4,124,-15) Matrix(31,8,-128,-33) -> Matrix(17,-2,128,-15) Matrix(3137,736,4096,961) -> Matrix(61,-8,-1380,181) Matrix(3135,734,4096,959) -> Matrix(59,-8,-1320,179) Matrix(575,132,832,191) -> Matrix(17,-2,-348,41) Matrix(1569,358,4352,993) -> Matrix(15,-2,-112,15) Matrix(12673,2872,16384,3713) -> Matrix(781,-104,-17580,2341) Matrix(12671,2870,16384,3711) -> Matrix(779,-104,-17520,2339) Matrix(801,176,1024,225) -> Matrix(127,-18,-2928,415) Matrix(799,174,1024,223) -> Matrix(125,-18,-2868,413) Matrix(319,68,896,191) -> Matrix(27,-4,-344,51) Matrix(353,74,768,161) -> Matrix(13,-2,-188,29) Matrix(20321,4192,25600,5281) -> Matrix(211,-30,-4860,691) Matrix(20319,4190,25600,5279) -> Matrix(209,-30,-4800,689) Matrix(95,18,-512,-97) -> Matrix(61,-10,360,-59) Matrix(513,94,704,129) -> Matrix(35,-6,-764,131) Matrix(255,46,704,127) -> Matrix(11,-2,-104,19) Matrix(319,56,1088,191) -> Matrix(11,-2,-104,19) Matrix(3393,584,4096,705) -> Matrix(221,-40,-5420,981) Matrix(3391,582,4096,703) -> Matrix(219,-40,-5360,979) Matrix(865,136,1024,161) -> Matrix(111,-22,-2780,551) Matrix(863,134,1024,159) -> Matrix(109,-22,-2720,549) Matrix(511,78,832,127) -> Matrix(29,-6,-488,101) Matrix(479,70,1088,159) -> Matrix(19,-4,-280,59) Matrix(415,56,704,95) -> Matrix(17,-4,-276,65) Matrix(31,4,-256,-33) -> Matrix(25,-6,96,-23) Matrix(97,10,320,33) -> Matrix(13,-4,-120,37) Matrix(223,-26,832,-97) -> Matrix(15,4,-124,-33) Matrix(257,-34,960,-127) -> Matrix(9,2,-68,-15) Matrix(511,-76,1728,-257) -> Matrix(9,2,-104,-23) Matrix(161,-26,192,-31) -> Matrix(21,4,-520,-99) Matrix(1087,-188,1856,-321) -> Matrix(11,2,-204,-37) Matrix(417,-74,896,-159) -> Matrix(11,2,-160,-29) Matrix(97,-18,512,-95) -> Matrix(59,10,-360,-61) Matrix(511,-106,1856,-385) -> Matrix(15,2,-128,-17) Matrix(511,-108,1216,-257) -> Matrix(13,2,-228,-35) Matrix(351,-76,448,-97) -> Matrix(55,8,-1272,-185) Matrix(543,-122,1856,-417) -> Matrix(29,4,-312,-43) Matrix(1087,-246,1984,-449) -> Matrix(15,2,-128,-17) Matrix(1247,-284,2112,-481) -> Matrix(31,4,-504,-65) Matrix(33,-8,128,-31) -> Matrix(15,2,-128,-17) Matrix(417,-110,1088,-287) -> Matrix(1,0,-4,1) Matrix(991,-266,1792,-481) -> Matrix(17,2,-264,-31) Matrix(1439,-388,2496,-673) -> Matrix(1,0,-12,1) Matrix(3231,-890,5696,-1569) -> Matrix(35,4,-604,-69) Matrix(767,-212,1856,-513) -> Matrix(17,2,-264,-31) Matrix(415,-116,576,-161) -> Matrix(71,8,-1500,-169) Matrix(673,-196,2304,-671) -> Matrix(59,6,-600,-61) Matrix(449,-134,640,-191) -> Matrix(1,0,-12,1) Matrix(1599,-484,2752,-833) -> Matrix(55,6,-816,-89) Matrix(385,-118,832,-255) -> Matrix(19,2,-276,-29) Matrix(161,-50,512,-159) -> Matrix(59,6,-600,-61) Matrix(575,-206,896,-321) -> Matrix(1,0,-4,1) Matrix(1535,-554,3904,-1409) -> Matrix(19,2,-200,-21) Matrix(97,-36,256,-95) -> Matrix(23,2,-288,-25) Matrix(1473,-562,3520,-1343) -> Matrix(27,2,-392,-29) Matrix(2305,-882,3008,-1151) -> Matrix(27,2,-608,-45) Matrix(703,-274,1152,-449) -> Matrix(1,0,0,1) Matrix(4609,-1814,8128,-3199) -> Matrix(65,6,-1116,-103) Matrix(417,-170,704,-287) -> Matrix(53,4,-888,-67) Matrix(1631,-668,2112,-865) -> Matrix(55,4,-1224,-89) Matrix(1535,-636,1856,-769) -> Matrix(23,2,-564,-49) Matrix(481,-200,1152,-479) -> Matrix(27,2,-392,-29) Matrix(1919,-804,2752,-1153) -> Matrix(91,6,-1896,-125) Matrix(961,-406,1664,-703) -> Matrix(1,0,-12,1) Matrix(1823,-772,2496,-1057) -> Matrix(1,0,-12,1) Matrix(225,-98,512,-223) -> Matrix(27,2,-392,-29) Matrix(1729,-762,2176,-959) -> Matrix(59,4,-1372,-93) Matrix(1311,-586,1792,-801) -> Matrix(29,2,-624,-43) Matrix(1535,-694,1984,-897) -> Matrix(43,2,-968,-45) Matrix(33,-16,64,-31) -> Matrix(1,0,0,1) Matrix(737,-394,896,-479) -> Matrix(31,2,-760,-49) Matrix(2623,-1436,3392,-1857) -> Matrix(11,2,-248,-45) Matrix(3135,-1732,4288,-2369) -> Matrix(31,2,-636,-41) Matrix(289,-162,512,-287) -> Matrix(31,2,-512,-33) Matrix(4929,-2794,6208,-3519) -> Matrix(101,6,-2340,-139) Matrix(959,-556,1216,-705) -> Matrix(25,2,-588,-47) Matrix(3039,-1766,4352,-2529) -> Matrix(89,6,-1884,-127) Matrix(1503,-874,2368,-1377) -> Matrix(61,4,-1144,-75) Matrix(1665,-974,2624,-1535) -> Matrix(35,2,-648,-37) Matrix(2175,-1274,2624,-1537) -> Matrix(39,2,-956,-49) Matrix(1343,-788,1856,-1089) -> Matrix(29,2,-624,-43) Matrix(2495,-1514,3904,-2369) -> Matrix(39,2,-800,-41) Matrix(161,-100,256,-159) -> Matrix(35,2,-648,-37) Matrix(737,-466,960,-607) -> Matrix(1,0,-4,1) Matrix(5281,-3376,6656,-4255) -> Matrix(43,2,-968,-45) Matrix(353,-242,512,-351) -> Matrix(119,6,-2400,-121) Matrix(1631,-1132,1984,-1377) -> Matrix(1,0,-4,1) Matrix(1471,-1036,1728,-1217) -> Matrix(37,2,-944,-51) Matrix(1439,-1018,1856,-1313) -> Matrix(77,4,-1752,-91) Matrix(1537,-1090,1984,-1407) -> Matrix(283,14,-6408,-317) Matrix(1471,-1066,1856,-1345) -> Matrix(43,2,-968,-45) Matrix(735,-538,832,-609) -> Matrix(87,4,-2284,-105) Matrix(97,-72,128,-95) -> Matrix(43,2,-968,-45) Matrix(417,-338,512,-415) -> Matrix(239,10,-5760,-241) Matrix(225,-196,256,-223) -> Matrix(155,6,-4056,-157) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 Degree of the the map X: 128 Degree of the the map Y: 256 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 384 Minimal number of generators: 65 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 32 Genus: 17 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/9 1/8 1/7 1/6 2/11 3/16 1/5 3/14 3/13 1/4 4/15 3/10 5/16 1/3 3/8 5/12 7/16 1/2 7/12 5/8 31/48 45/64 23/32 3/4 49/64 99/128 25/32 53/64 27/32 7/8 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/0 1/9 -5/18 1/8 -1/4 1/7 -3/14 1/6 -1/5 -2/11 2/11 -7/40 3/16 -1/6 1/5 -1/6 3/14 -4/27 -1/7 2/9 -5/36 3/13 -1/6 1/4 -1/8 5/19 -3/26 4/15 -1/8 3/11 -5/42 5/18 -4/35 -1/9 2/7 -3/28 7/24 -1/10 12/41 -1/12 5/17 -1/10 3/10 -1/9 0/1 4/13 -5/48 5/16 -1/10 1/3 -1/10 6/17 -1/12 5/14 -1/13 0/1 4/11 -3/32 3/8 -1/12 8/21 -5/64 5/13 -3/38 12/31 -7/96 7/18 -1/15 0/1 2/5 -1/12 9/22 -1/13 -2/27 7/17 -1/14 12/29 -1/16 5/12 -1/14 13/31 -5/78 8/19 -1/20 11/26 -1/9 0/1 3/7 -1/14 7/16 -1/14 4/9 -1/16 9/20 -1/16 5/11 -1/10 1/2 -1/15 0/1 8/15 -1/16 7/13 -1/18 6/11 -1/20 17/31 -3/34 11/20 -1/14 16/29 -3/44 5/9 -1/14 9/16 -1/16 4/7 -1/16 11/19 -1/10 18/31 -5/72 25/43 -7/106 7/12 -1/16 24/41 -1/16 17/29 -1/14 10/17 -1/16 3/5 -1/18 11/18 -1/15 0/1 30/49 -1/16 49/80 -1/16 19/31 -7/114 8/13 -3/52 5/8 -1/18 12/19 -1/20 19/30 -2/37 -1/19 7/11 -3/58 9/14 -1/17 0/1 20/31 -9/160 31/48 -1/18 11/17 -1/18 2/3 -1/20 11/16 -1/20 9/13 -5/102 16/23 -7/144 23/33 -13/270 30/43 -13/272 7/10 -1/21 0/1 26/37 -1/24 45/64 0/1 19/27 -1/18 12/17 -1/20 29/41 -1/18 17/24 -1/20 5/7 -3/62 23/32 -1/21 18/25 -11/232 13/18 -1/21 -4/85 8/11 -5/108 19/26 -1/21 0/1 49/67 -5/106 30/41 -3/64 11/15 -1/22 3/4 -1/22 13/17 -1/22 49/64 -2/45 36/47 -3/68 23/30 -2/45 -1/23 10/13 -1/24 17/22 -3/67 -2/45 58/75 -29/652 99/128 -2/45 41/53 -23/518 24/31 -17/384 7/9 -5/114 25/32 -1/23 18/23 -13/300 11/14 -1/23 -4/93 4/5 -1/24 13/16 -1/24 9/11 -7/170 14/17 -1/24 19/23 -5/122 24/29 -9/220 53/64 -2/49 29/35 -11/270 5/6 -2/49 -1/25 16/19 -13/324 27/32 -1/25 11/13 -9/226 6/7 -3/76 7/8 -1/26 8/9 -5/132 1/1 -1/30 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(223,-23,320,-33) (0/1,1/9) -> (16/23,23/33) Hyperbolic Matrix(159,-19,544,-65) (1/9,1/8) -> (7/24,12/41) Hyperbolic Matrix(65,-9,224,-31) (1/8,1/7) -> (2/7,7/24) Hyperbolic Matrix(95,-14,224,-33) (1/7,1/6) -> (11/26,3/7) Hyperbolic Matrix(257,-46,352,-63) (1/6,2/11) -> (8/11,19/26) Hyperbolic Matrix(287,-53,352,-65) (2/11,3/16) -> (13/16,9/11) Hyperbolic Matrix(129,-25,160,-31) (3/16,1/5) -> (4/5,13/16) Hyperbolic Matrix(63,-13,160,-33) (1/5,3/14) -> (7/18,2/5) Hyperbolic Matrix(351,-76,448,-97) (3/14,2/9) -> (18/23,11/14) Hyperbolic Matrix(289,-66,416,-95) (2/9,3/13) -> (9/13,16/23) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(257,-68,480,-127) (5/19,4/15) -> (8/15,7/13) Hyperbolic Matrix(289,-78,352,-95) (4/15,3/11) -> (9/11,14/17) Hyperbolic Matrix(127,-35,352,-97) (3/11,5/18) -> (5/14,4/11) Hyperbolic Matrix(415,-116,576,-161) (5/18,2/7) -> (18/25,13/18) Hyperbolic Matrix(897,-263,1088,-319) (12/41,5/17) -> (14/17,19/23) Hyperbolic Matrix(223,-66,544,-161) (5/17,3/10) -> (9/22,7/17) Hyperbolic Matrix(321,-98,416,-127) (3/10,4/13) -> (10/13,17/22) Hyperbolic Matrix(287,-89,416,-129) (4/13,5/16) -> (11/16,9/13) Hyperbolic Matrix(65,-21,96,-31) (5/16,1/3) -> (2/3,11/16) Hyperbolic Matrix(225,-79,544,-191) (1/3,6/17) -> (7/17,12/29) Hyperbolic Matrix(607,-216,992,-353) (6/17,5/14) -> (11/18,30/49) Hyperbolic Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(225,-86,416,-159) (8/21,5/13) -> (7/13,6/11) Hyperbolic Matrix(417,-161,992,-383) (5/13,12/31) -> (13/31,8/19) Hyperbolic Matrix(639,-248,992,-385) (12/31,7/18) -> (9/14,20/31) Hyperbolic Matrix(607,-248,864,-353) (2/5,9/22) -> (7/10,26/37) Hyperbolic Matrix(511,-212,928,-385) (12/29,5/12) -> (11/20,16/29) Hyperbolic Matrix(545,-228,992,-415) (5/12,13/31) -> (17/31,11/20) Hyperbolic Matrix(511,-216,608,-257) (8/19,11/26) -> (5/6,16/19) Hyperbolic Matrix(127,-55,224,-97) (3/7,7/16) -> (9/16,4/7) Hyperbolic Matrix(161,-71,288,-127) (7/16,4/9) -> (5/9,9/16) Hyperbolic Matrix(543,-244,928,-417) (4/9,9/20) -> (7/12,24/41) Hyperbolic Matrix(577,-260,992,-447) (9/20,5/11) -> (25/43,7/12) Hyperbolic Matrix(223,-102,352,-161) (5/11,1/2) -> (19/30,7/11) Hyperbolic Matrix(417,-220,544,-287) (1/2,8/15) -> (36/47,23/30) Hyperbolic Matrix(1183,-648,1696,-929) (6/11,17/31) -> (23/33,30/43) Hyperbolic Matrix(767,-424,928,-513) (16/29,5/9) -> (19/23,24/29) Hyperbolic Matrix(191,-110,224,-129) (4/7,11/19) -> (11/13,6/7) Hyperbolic Matrix(609,-353,992,-575) (11/19,18/31) -> (19/31,8/13) Hyperbolic Matrix(2303,-1338,2976,-1729) (18/31,25/43) -> (41/53,24/31) Hyperbolic Matrix(2879,-1686,3936,-2305) (24/41,17/29) -> (49/67,30/41) Hyperbolic Matrix(353,-207,544,-319) (17/29,10/17) -> (11/17,2/3) Hyperbolic Matrix(383,-226,544,-321) (10/17,3/5) -> (19/27,12/17) Hyperbolic Matrix(127,-77,160,-97) (3/5,11/18) -> (11/14,4/5) Hyperbolic Matrix(2399,-1469,3712,-2273) (30/49,49/80) -> (31/48,11/17) Hyperbolic Matrix(2561,-1569,3968,-2431) (49/80,19/31) -> (20/31,31/48) Hyperbolic Matrix(161,-100,256,-159) (8/13,5/8) -> (5/8,12/19) Parabolic Matrix(737,-466,960,-607) (12/19,19/30) -> (23/30,10/13) Hyperbolic Matrix(255,-163,352,-225) (7/11,9/14) -> (13/18,8/11) Hyperbolic Matrix(1311,-916,1696,-1185) (30/43,7/10) -> (17/22,58/75) Hyperbolic Matrix(2881,-2025,4096,-2879) (26/37,45/64) -> (45/64,19/27) Parabolic Matrix(961,-679,1312,-927) (12/17,29/41) -> (30/41,11/15) Hyperbolic Matrix(479,-339,544,-385) (29/41,17/24) -> (7/8,8/9) Hyperbolic Matrix(193,-137,224,-159) (17/24,5/7) -> (6/7,7/8) Hyperbolic Matrix(737,-529,1024,-735) (5/7,23/32) -> (23/32,18/25) Parabolic Matrix(1089,-796,1312,-959) (19/26,49/67) -> (29/35,5/6) Hyperbolic Matrix(97,-72,128,-95) (11/15,3/4) -> (3/4,13/17) Parabolic Matrix(3137,-2401,4096,-3135) (13/17,49/64) -> (49/64,36/47) Parabolic Matrix(12673,-9801,16384,-12671) (58/75,99/128) -> (99/128,41/53) Parabolic Matrix(257,-199,288,-223) (24/31,7/9) -> (8/9,1/1) Hyperbolic Matrix(801,-625,1024,-799) (7/9,25/32) -> (25/32,18/23) Parabolic Matrix(3393,-2809,4096,-3391) (24/29,53/64) -> (53/64,29/35) Parabolic Matrix(865,-729,1024,-863) (16/19,27/32) -> (27/32,11/13) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-30,1) Matrix(223,-23,320,-33) -> Matrix(13,4,-270,-83) Matrix(159,-19,544,-65) -> Matrix(11,3,-114,-31) Matrix(65,-9,224,-31) -> Matrix(13,3,-126,-29) Matrix(95,-14,224,-33) -> Matrix(5,1,-56,-11) Matrix(257,-46,352,-63) -> Matrix(5,1,-116,-23) Matrix(287,-53,352,-65) -> Matrix(41,7,-990,-169) Matrix(129,-25,160,-31) -> Matrix(19,3,-450,-71) Matrix(63,-13,160,-33) -> Matrix(7,1,-78,-11) Matrix(351,-76,448,-97) -> Matrix(55,8,-1272,-185) Matrix(289,-66,416,-95) -> Matrix(23,3,-468,-61) Matrix(33,-8,128,-31) -> Matrix(15,2,-128,-17) Matrix(257,-68,480,-127) -> Matrix(9,1,-136,-15) Matrix(289,-78,352,-95) -> Matrix(7,1,-176,-25) Matrix(127,-35,352,-97) -> Matrix(9,1,-82,-9) Matrix(415,-116,576,-161) -> Matrix(71,8,-1500,-169) Matrix(897,-263,1088,-319) -> Matrix(19,2,-466,-49) Matrix(223,-66,544,-161) -> Matrix(11,1,-144,-13) Matrix(321,-98,416,-127) -> Matrix(29,3,-648,-67) Matrix(287,-89,416,-129) -> Matrix(49,5,-990,-101) Matrix(65,-21,96,-31) -> Matrix(11,1,-210,-19) Matrix(225,-79,544,-191) -> Matrix(11,1,-166,-15) Matrix(607,-216,992,-353) -> Matrix(13,1,-196,-15) Matrix(97,-36,256,-95) -> Matrix(23,2,-288,-25) Matrix(225,-86,416,-159) -> Matrix(13,1,-196,-15) Matrix(417,-161,992,-383) -> Matrix(13,1,-222,-17) Matrix(639,-248,992,-385) -> Matrix(15,1,-256,-17) Matrix(607,-248,864,-353) -> Matrix(13,1,-300,-23) Matrix(511,-212,928,-385) -> Matrix(13,1,-196,-15) Matrix(545,-228,992,-415) -> Matrix(15,1,-196,-13) Matrix(511,-216,608,-257) -> Matrix(7,1,-176,-25) Matrix(127,-55,224,-97) -> Matrix(13,1,-222,-17) Matrix(161,-71,288,-127) -> Matrix(15,1,-226,-15) Matrix(543,-244,928,-417) -> Matrix(15,1,-256,-17) Matrix(577,-260,992,-447) -> Matrix(17,1,-256,-15) Matrix(223,-102,352,-161) -> Matrix(13,1,-248,-19) Matrix(417,-220,544,-287) -> Matrix(13,1,-300,-23) Matrix(1183,-648,1696,-929) -> Matrix(7,1,-148,-21) Matrix(767,-424,928,-513) -> Matrix(47,3,-1144,-73) Matrix(191,-110,224,-129) -> Matrix(19,1,-476,-25) Matrix(609,-353,992,-575) -> Matrix(13,1,-222,-17) Matrix(2303,-1338,2976,-1729) -> Matrix(133,9,-3000,-203) Matrix(2879,-1686,3936,-2305) -> Matrix(19,1,-400,-21) Matrix(353,-207,544,-319) -> Matrix(15,1,-286,-19) Matrix(383,-226,544,-321) -> Matrix(17,1,-324,-19) Matrix(127,-77,160,-97) -> Matrix(19,1,-438,-23) Matrix(2399,-1469,3712,-2273) -> Matrix(95,6,-1726,-109) Matrix(2561,-1569,3968,-2431) -> Matrix(129,8,-2306,-143) Matrix(161,-100,256,-159) -> Matrix(35,2,-648,-37) Matrix(737,-466,960,-607) -> Matrix(1,0,-4,1) Matrix(255,-163,352,-225) -> Matrix(21,1,-442,-21) Matrix(1311,-916,1696,-1185) -> Matrix(65,3,-1452,-67) Matrix(2881,-2025,4096,-2879) -> Matrix(1,0,6,1) Matrix(961,-679,1312,-927) -> Matrix(21,1,-442,-21) Matrix(479,-339,544,-385) -> Matrix(59,3,-1554,-79) Matrix(193,-137,224,-159) -> Matrix(61,3,-1566,-77) Matrix(737,-529,1024,-735) -> Matrix(293,14,-6174,-295) Matrix(1089,-796,1312,-959) -> Matrix(19,1,-476,-25) Matrix(97,-72,128,-95) -> Matrix(43,2,-968,-45) Matrix(3137,-2401,4096,-3135) -> Matrix(179,8,-4050,-181) Matrix(12673,-9801,16384,-12671) -> Matrix(2339,104,-52650,-2341) Matrix(257,-199,288,-223) -> Matrix(113,5,-3006,-133) Matrix(801,-625,1024,-799) -> Matrix(413,18,-9522,-415) Matrix(3393,-2809,4096,-3391) -> Matrix(979,40,-24010,-981) Matrix(865,-729,1024,-863) -> Matrix(549,22,-13750,-551) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 ----------------------------------------------------------------------- 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 1/0 1 32 1/9 -5/18 1 32 1/8 -1/4 6 4 1/7 -3/14 1 32 1/6 (-1/5,-2/11) 0 16 2/11 -7/40 1 32 3/16 -1/6 10 2 1/5 -1/6 1 32 3/14 (-4/27,-1/7) 0 16 7/32 -1/7 18 1 2/9 -5/36 1 32 3/13 -1/6 1 32 1/4 -1/8 2 8 5/19 -3/26 1 32 4/15 -1/8 1 32 11/41 -3/26 1 32 7/26 (-1/9,0/1) 0 16 3/11 -5/42 1 32 5/18 (-4/35,-1/9) 0 16 9/32 -1/9 14 1 2/7 -3/28 1 32 7/24 -1/10 6 4 12/41 -1/12 1 32 5/17 -1/10 1 32 3/10 (-1/9,0/1) 0 16 10/33 -13/120 1 32 7/23 -7/66 1 32 4/13 -5/48 1 32 5/16 -1/10 6 2 1/3 -1/10 1 32 6/17 -1/12 1 32 5/14 (-1/13,0/1) 0 16 4/11 -3/32 1 32 3/8 -1/12 2 4 8/21 -5/64 1 32 5/13 -3/38 1 32 12/31 -7/96 1 32 31/80 -1/14 14 2 19/49 -1/14 1 32 7/18 (-1/15,0/1) 0 16 2/5 -1/12 1 32 13/32 -1/13 6 1 9/22 (-1/13,-2/27) 0 16 7/17 -1/14 1 32 12/29 -1/16 1 32 5/12 -1/14 2 8 13/31 -5/78 1 32 8/19 -1/20 1 32 27/64 0/1 22 1 11/26 (-1/9,0/1) 0 16 3/7 -1/14 1 32 7/16 -1/14 2 2 4/9 -1/16 1 32 17/38 (-2/29,-1/15) 0 16 43/96 -1/15 10 1 13/29 -3/46 1 32 9/20 -1/16 2 8 14/31 -3/56 1 32 19/42 (-1/23,0/1) 0 16 29/64 0/1 26 1 5/11 -1/10 1 32 6/13 -1/12 1 32 7/15 -1/14 1 32 15/32 -1/15 2 1 1/2 (-1/15,0/1) 0 16 1/0 0/1 30 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(97,-10,320,-33) (0/1,1/9) -> (10/33,7/23) Glide Reflection Matrix(159,-19,544,-65) (1/9,1/8) -> (7/24,12/41) Hyperbolic Matrix(65,-9,224,-31) (1/8,1/7) -> (2/7,7/24) Hyperbolic Matrix(95,-14,224,-33) (1/7,1/6) -> (11/26,3/7) Hyperbolic Matrix(95,-17,352,-63) (1/6,2/11) -> (7/26,3/11) Glide Reflection Matrix(65,-12,352,-65) (2/11,3/16) -> (2/11,3/16) Reflection Matrix(31,-6,160,-31) (3/16,1/5) -> (3/16,1/5) Reflection Matrix(63,-13,160,-33) (1/5,3/14) -> (7/18,2/5) Hyperbolic Matrix(97,-21,448,-97) (3/14,7/32) -> (3/14,7/32) Reflection Matrix(127,-28,576,-127) (7/32,2/9) -> (7/32,2/9) Reflection Matrix(127,-29,416,-95) (2/9,3/13) -> (7/23,4/13) Glide Reflection Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(223,-59,480,-127) (5/19,4/15) -> (6/13,7/15) Glide Reflection Matrix(385,-103,1312,-351) (4/15,11/41) -> (12/41,5/17) Hyperbolic Matrix(801,-215,1792,-481) (11/41,7/26) -> (4/9,17/38) Glide Reflection Matrix(127,-35,352,-97) (3/11,5/18) -> (5/14,4/11) Hyperbolic Matrix(161,-45,576,-161) (5/18,9/32) -> (5/18,9/32) Reflection Matrix(127,-36,448,-127) (9/32,2/7) -> (9/32,2/7) Reflection Matrix(223,-66,544,-161) (5/17,3/10) -> (9/22,7/17) Hyperbolic Matrix(767,-232,1696,-513) (3/10,10/33) -> (14/31,19/42) Hyperbolic Matrix(129,-40,416,-129) (4/13,5/16) -> (4/13,5/16) Reflection Matrix(31,-10,96,-31) (5/16,1/3) -> (5/16,1/3) Reflection Matrix(225,-79,544,-191) (1/3,6/17) -> (7/17,12/29) Hyperbolic Matrix(385,-137,992,-353) (6/17,5/14) -> (19/49,7/18) Glide Reflection Matrix(97,-36,256,-95) (4/11,3/8) -> (3/8,8/21) Parabolic Matrix(191,-73,416,-159) (8/21,5/13) -> (5/11,6/13) Glide Reflection Matrix(417,-161,992,-383) (5/13,12/31) -> (13/31,8/19) Hyperbolic Matrix(1921,-744,4960,-1921) (12/31,31/80) -> (12/31,31/80) Reflection Matrix(3039,-1178,7840,-3039) (31/80,19/49) -> (31/80,19/49) Reflection Matrix(129,-52,320,-129) (2/5,13/32) -> (2/5,13/32) Reflection Matrix(287,-117,704,-287) (13/32,9/22) -> (13/32,9/22) Reflection Matrix(417,-173,928,-385) (12/29,5/12) -> (13/29,9/20) Glide Reflection Matrix(447,-187,992,-415) (5/12,13/31) -> (9/20,14/31) Glide Reflection Matrix(1025,-432,2432,-1025) (8/19,27/64) -> (8/19,27/64) Reflection Matrix(703,-297,1664,-703) (27/64,11/26) -> (27/64,11/26) Reflection Matrix(97,-42,224,-97) (3/7,7/16) -> (3/7,7/16) Reflection Matrix(127,-56,288,-127) (7/16,4/9) -> (7/16,4/9) Reflection Matrix(1633,-731,3648,-1633) (17/38,43/96) -> (17/38,43/96) Reflection Matrix(2495,-1118,5568,-2495) (43/96,13/29) -> (43/96,13/29) Reflection Matrix(1217,-551,2688,-1217) (19/42,29/64) -> (19/42,29/64) Reflection Matrix(639,-290,1408,-639) (29/64,5/11) -> (29/64,5/11) Reflection Matrix(449,-210,960,-449) (7/15,15/32) -> (7/15,15/32) Reflection Matrix(31,-15,64,-31) (15/32,1/2) -> (15/32,1/2) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) 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(97,-10,320,-33) -> Matrix(13,4,-120,-37) Matrix(159,-19,544,-65) -> Matrix(11,3,-114,-31) Matrix(65,-9,224,-31) -> Matrix(13,3,-126,-29) Matrix(95,-14,224,-33) -> Matrix(5,1,-56,-11) Matrix(95,-17,352,-63) -> Matrix(5,1,-34,-7) Matrix(65,-12,352,-65) -> Matrix(41,7,-240,-41) (2/11,3/16) -> (-7/40,-1/6) Matrix(31,-6,160,-31) -> Matrix(19,3,-120,-19) (3/16,1/5) -> (-1/6,-3/20) Matrix(63,-13,160,-33) -> Matrix(7,1,-78,-11) Matrix(97,-21,448,-97) -> Matrix(55,8,-378,-55) (3/14,7/32) -> (-4/27,-1/7) Matrix(127,-28,576,-127) -> Matrix(71,10,-504,-71) (7/32,2/9) -> (-1/7,-5/36) Matrix(127,-29,416,-95) -> Matrix(23,3,-222,-29) Matrix(33,-8,128,-31) -> Matrix(15,2,-128,-17) -1/8 Matrix(223,-59,480,-127) -> Matrix(9,1,-134,-15) Matrix(385,-103,1312,-351) -> Matrix(9,1,-82,-9) (-1/8,-1/10).(-1/9,0/1) Matrix(801,-215,1792,-481) -> Matrix(17,2,-246,-29) Matrix(127,-35,352,-97) -> Matrix(9,1,-82,-9) (-1/8,-1/10).(-1/9,0/1) Matrix(161,-45,576,-161) -> Matrix(71,8,-630,-71) (5/18,9/32) -> (-4/35,-1/9) Matrix(127,-36,448,-127) -> Matrix(55,6,-504,-55) (9/32,2/7) -> (-1/9,-3/28) Matrix(223,-66,544,-161) -> Matrix(11,1,-144,-13) -1/12 Matrix(767,-232,1696,-513) -> Matrix(9,1,-208,-23) Matrix(129,-40,416,-129) -> Matrix(49,5,-480,-49) (4/13,5/16) -> (-5/48,-1/10) Matrix(31,-10,96,-31) -> Matrix(11,1,-120,-11) (5/16,1/3) -> (-1/10,-1/12) Matrix(225,-79,544,-191) -> Matrix(11,1,-166,-15) Matrix(385,-137,992,-353) -> Matrix(13,1,-194,-15) Matrix(97,-36,256,-95) -> Matrix(23,2,-288,-25) -1/12 Matrix(191,-73,416,-159) -> Matrix(13,1,-194,-15) Matrix(417,-161,992,-383) -> Matrix(13,1,-222,-17) Matrix(1921,-744,4960,-1921) -> Matrix(97,7,-1344,-97) (12/31,31/80) -> (-7/96,-1/14) Matrix(3039,-1178,7840,-3039) -> Matrix(99,7,-1400,-99) (31/80,19/49) -> (-1/14,-7/100) Matrix(129,-52,320,-129) -> Matrix(25,2,-312,-25) (2/5,13/32) -> (-1/12,-1/13) Matrix(287,-117,704,-287) -> Matrix(53,4,-702,-53) (13/32,9/22) -> (-1/13,-2/27) Matrix(417,-173,928,-385) -> Matrix(13,1,-194,-15) Matrix(447,-187,992,-415) -> Matrix(15,1,-254,-17) Matrix(1025,-432,2432,-1025) -> Matrix(-1,0,40,1) (8/19,27/64) -> (-1/20,0/1) Matrix(703,-297,1664,-703) -> Matrix(-1,0,18,1) (27/64,11/26) -> (-1/9,0/1) Matrix(97,-42,224,-97) -> Matrix(13,1,-168,-13) (3/7,7/16) -> (-1/12,-1/14) Matrix(127,-56,288,-127) -> Matrix(15,1,-224,-15) (7/16,4/9) -> (-1/14,-1/16) Matrix(1633,-731,3648,-1633) -> Matrix(59,4,-870,-59) (17/38,43/96) -> (-2/29,-1/15) Matrix(2495,-1118,5568,-2495) -> Matrix(91,6,-1380,-91) (43/96,13/29) -> (-1/15,-3/46) Matrix(1217,-551,2688,-1217) -> Matrix(-1,0,46,1) (19/42,29/64) -> (-1/23,0/1) Matrix(639,-290,1408,-639) -> Matrix(-1,0,20,1) (29/64,5/11) -> (-1/10,0/1) Matrix(449,-210,960,-449) -> Matrix(29,2,-420,-29) (7/15,15/32) -> (-1/14,-1/15) Matrix(31,-15,64,-31) -> Matrix(-1,0,30,1) (15/32,1/2) -> (-1/15,0/1) Matrix(-1,1,0,1) -> Matrix(-1,0,30,1) (1/2,1/0) -> (-1/15,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.