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 1/2 -8/9 3/4 -7/8 0/1 2/3 -13/15 7/10 -6/7 3/4 -17/20 2/3 4/5 -11/13 5/6 -5/6 1/1 -19/23 1/2 -14/17 5/6 -23/28 0/1 2/1 -9/11 1/2 -13/16 1/1 -17/21 3/2 -4/5 1/0 -19/24 0/1 2/3 -15/19 1/0 -11/14 1/1 -7/9 1/0 -24/31 1/0 -17/22 1/1 -27/35 1/0 -10/13 1/0 -3/4 0/1 2/3 -14/19 1/0 -11/15 1/8 -41/56 0/1 2/9 -30/41 1/6 -19/26 1/3 -27/37 1/4 -8/11 1/2 -29/40 0/1 2/5 -50/69 3/8 -21/29 1/2 -13/18 1/3 -5/7 1/2 -22/31 1/2 -17/24 0/1 2/3 -46/65 1/2 -29/41 1/2 -12/17 3/2 -31/44 -2/1 0/1 -50/71 1/0 -19/27 -1/4 -7/10 1/3 -23/33 1/2 -16/23 1/0 -25/36 0/1 2/7 -9/13 1/2 -11/16 1/2 -13/19 1/2 -2/3 1/2 -13/20 4/7 2/3 -11/17 1/0 -31/48 1/2 -20/31 1/2 -9/14 3/5 -16/25 7/10 -39/61 3/4 -23/36 2/3 4/5 -7/11 1/2 -5/8 0/1 2/3 -13/21 1/2 -34/55 1/2 -21/34 7/11 -29/47 19/28 -8/13 3/4 -27/44 0/1 2/3 -19/31 1/2 -49/80 1/2 -30/49 9/16 -11/18 3/5 -14/23 11/16 -17/28 2/3 8/11 -37/61 3/4 -20/33 3/4 -3/5 3/4 -13/22 1/1 -23/39 1/2 -10/17 1/4 -27/46 1/1 -17/29 1/2 -24/41 1/2 -7/12 0/1 2/3 -32/55 1/2 -25/43 1/2 -18/31 1/2 -29/50 3/5 -11/19 5/8 -15/26 5/7 -19/33 3/4 -4/7 3/4 -9/16 1/1 -14/25 5/4 -33/59 11/8 -19/34 5/3 -5/9 1/0 -16/29 1/2 -11/20 0/1 2/3 -17/31 1/2 -6/11 3/4 -13/24 2/3 4/5 -7/13 5/6 -15/28 6/7 8/9 -8/15 13/14 -1/2 1/1 -8/17 11/12 -15/32 1/1 -7/15 13/12 -6/13 5/4 -11/24 4/3 2/1 -5/11 3/2 -19/42 3/1 -14/31 1/0 -9/20 0/1 2/1 -13/29 1/0 -17/38 -1/1 -4/9 1/2 -7/16 1/1 -10/23 7/6 -13/30 11/9 -42/97 5/4 -29/67 5/4 -16/37 13/10 -3/7 3/2 -14/33 3/2 -25/59 3/2 -11/26 5/3 -19/45 15/8 -27/64 2/1 -8/19 5/2 -13/31 1/0 -31/74 3/1 -18/43 1/0 -5/12 0/1 2/1 -17/41 1/0 -29/70 1/1 -12/29 1/0 -7/17 -1/2 -16/39 1/0 -25/61 1/2 -9/22 1/1 -11/27 5/6 -13/32 1/1 -2/5 3/2 -13/33 3/2 -11/28 8/5 2/1 -9/23 11/6 -25/64 2/1 -16/41 17/8 -7/18 3/1 -19/49 9/2 -31/80 1/0 -12/31 1/0 -17/44 0/1 2/1 -5/13 3/2 -3/8 0/1 2/1 -7/19 3/2 -11/30 7/3 -15/41 1/0 -19/52 2/1 4/1 -4/11 1/0 -13/36 4/3 2/1 -35/97 3/2 -22/61 3/2 -9/25 7/4 -23/64 2/1 -14/39 13/6 -5/14 3/1 -11/31 1/0 -17/48 1/0 -6/17 1/2 -7/20 2/1 4/1 -1/3 1/0 -5/16 1/0 -9/29 1/0 -4/13 1/0 -11/36 -2/3 0/1 -7/23 1/2 -10/33 1/0 -13/43 1/0 -29/96 1/0 -16/53 1/0 -3/10 -1/1 -11/37 -1/8 -19/64 0/1 -8/27 1/6 -13/44 0/1 2/5 -5/17 3/4 -12/41 1/0 -7/24 0/1 2/1 -9/31 1/0 -2/7 1/0 -9/32 1/0 -7/25 1/0 -5/18 -1/1 -13/47 -5/2 -8/29 1/0 -11/40 -2/1 0/1 -3/11 1/0 -10/37 -1/2 -17/63 -1/2 -7/26 -1/1 -25/93 -1/2 -43/160 -1/2 -18/67 -1/2 -11/41 -1/4 -4/15 -1/6 -1/4 0/1 2/1 -4/17 -1/6 -15/64 0/1 -11/47 1/20 -7/30 1/7 -3/13 1/2 -8/35 1/2 -13/57 3/4 -5/22 1/1 -17/75 -1/2 -29/128 0/1 -12/53 1/4 -7/31 1/2 -9/40 0/1 2/3 -2/9 1/2 -7/32 1/1 -5/23 3/2 -3/14 1/1 -7/33 1/0 -4/19 1/2 -5/24 0/1 2/1 -6/29 1/0 -13/63 1/0 -33/160 1/0 -20/97 1/0 -7/34 -3/1 -1/5 1/2 -3/16 1/1 -5/27 3/2 -2/11 1/0 -5/28 0/1 2/3 -8/45 3/4 -3/17 5/4 -4/23 1/0 -5/29 1/0 -11/64 0/1 -6/35 1/2 -1/6 1/1 -3/19 3/4 -5/32 1/1 -2/13 5/4 -3/20 4/3 2/1 -4/27 5/2 -1/7 3/2 -2/15 7/4 -1/8 0/1 2/1 -2/17 7/4 -1/9 3/2 0/1 1/0 1/9 -3/2 1/8 -2/1 0/1 2/15 -7/4 1/7 -3/2 3/20 -2/1 -4/3 2/13 -5/4 1/6 -1/1 4/23 1/0 3/17 -5/4 5/28 -2/3 0/1 2/11 1/0 3/16 -1/1 4/21 -3/4 1/5 -1/2 5/24 -2/1 0/1 4/19 -1/2 3/14 -1/1 2/9 -1/2 7/31 -1/2 5/22 -1/1 8/35 -1/2 3/13 -1/2 1/4 -2/1 0/1 5/19 -1/2 4/15 1/6 15/56 0/1 2/5 11/41 1/4 7/26 1/1 10/37 1/2 3/11 1/0 11/40 0/1 2/1 19/69 3/2 8/29 1/0 5/18 1/1 2/7 1/0 9/31 1/0 7/24 -2/1 0/1 19/65 1/0 12/41 1/0 5/17 -3/4 13/44 -2/5 0/1 21/71 -1/2 8/27 -1/6 3/10 1/1 10/33 1/0 7/23 -1/2 11/36 0/1 2/3 4/13 1/0 5/16 1/0 6/19 1/0 1/3 1/0 7/20 -4/1 -2/1 6/17 -1/2 17/48 1/0 11/31 1/0 5/14 -3/1 9/25 -7/4 22/61 -3/2 13/36 -2/1 -4/3 4/11 1/0 3/8 -2/1 0/1 8/21 1/0 21/55 1/0 13/34 -7/3 18/47 -19/10 5/13 -3/2 17/44 -2/1 0/1 12/31 1/0 31/80 1/0 19/49 -9/2 7/18 -3/1 9/23 -11/6 11/28 -2/1 -8/5 24/61 -3/2 13/33 -3/2 2/5 -3/2 9/22 -1/1 16/39 1/0 7/17 1/2 19/46 -1/1 12/29 1/0 17/41 1/0 5/12 -2/1 0/1 23/55 1/0 18/43 1/0 13/31 1/0 21/50 -3/1 8/19 -5/2 11/26 -5/3 14/33 -3/2 3/7 -3/2 7/16 -1/1 11/25 -5/6 26/59 -11/14 15/34 -5/7 4/9 -1/2 13/29 1/0 9/20 -2/1 0/1 14/31 1/0 5/11 -3/2 11/24 -2/1 -4/3 6/13 -5/4 13/28 -6/5 -8/7 7/15 -13/12 1/2 -1/1 9/17 -11/10 17/32 -1/1 8/15 -13/14 7/13 -5/6 13/24 -4/5 -2/3 6/11 -3/4 23/42 -3/5 17/31 -1/2 11/20 -2/3 0/1 16/29 -1/2 21/38 -1/3 5/9 1/0 9/16 -1/1 13/23 -7/8 17/30 -11/13 55/97 -5/6 38/67 -5/6 21/37 -13/16 4/7 -3/4 19/33 -3/4 34/59 -3/4 15/26 -5/7 26/45 -15/22 37/64 -2/3 11/19 -5/8 18/31 -1/2 43/74 -3/5 25/43 -1/2 7/12 -2/3 0/1 24/41 -1/2 41/70 -1/1 17/29 -1/2 10/17 -1/4 23/39 -1/2 36/61 1/0 13/22 -1/1 16/27 -5/4 19/32 -1/1 3/5 -3/4 20/33 -3/4 17/28 -8/11 -2/3 14/23 -11/16 39/64 -2/3 25/41 -17/26 11/18 -3/5 30/49 -9/16 49/80 -1/2 19/31 -1/2 27/44 -2/3 0/1 8/13 -3/4 5/8 -2/3 0/1 12/19 -3/4 19/30 -7/11 26/41 -1/2 33/52 -2/3 -4/7 7/11 -1/2 23/36 -4/5 -2/3 62/97 -3/4 39/61 -3/4 16/25 -7/10 41/64 -2/3 25/39 -13/20 9/14 -3/5 20/31 -1/2 31/48 -1/2 11/17 1/0 13/20 -2/3 -4/7 2/3 -1/2 11/16 -1/2 20/29 -1/2 9/13 -1/2 25/36 -2/7 0/1 16/23 1/0 23/33 -1/2 30/43 -1/2 67/96 -1/2 37/53 -1/2 7/10 -1/3 26/37 -1/10 45/64 0/1 19/27 1/4 31/44 0/1 2/1 12/17 -3/2 29/41 -1/2 17/24 -2/3 0/1 22/31 -1/2 5/7 -1/2 23/32 -1/2 18/25 -1/2 13/18 -1/3 34/47 -5/12 21/29 -1/2 29/40 -2/5 0/1 8/11 -1/2 27/37 -1/4 46/63 -1/4 19/26 -1/3 68/93 -1/4 117/160 -1/4 49/67 -1/4 30/41 -1/6 11/15 -1/8 3/4 -2/3 0/1 13/17 -1/8 49/64 0/1 36/47 1/18 23/30 1/5 10/13 1/0 27/35 1/0 44/57 -3/2 17/22 -1/1 58/75 -1/4 99/128 0/1 41/53 1/2 24/31 1/0 31/40 -2/1 0/1 7/9 1/0 25/32 -1/1 18/23 -3/4 11/14 -1/1 26/33 -1/2 15/19 1/0 19/24 -2/3 0/1 23/29 -1/2 50/63 -1/2 127/160 -1/2 77/97 -1/2 27/34 -3/7 4/5 1/0 13/16 -1/1 22/27 -3/4 9/11 -1/2 23/28 -2/1 0/1 37/45 -3/2 14/17 -5/6 19/23 -1/2 24/29 -1/2 53/64 0/1 29/35 1/0 5/6 -1/1 16/19 -3/2 27/32 -1/1 11/13 -5/6 17/20 -4/5 -2/3 23/27 -5/8 6/7 -3/4 13/15 -7/10 7/8 -2/3 0/1 15/17 -7/10 8/9 -3/4 1/1 -1/2 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,-4,1) Matrix(223,200,320,287) -> Matrix(3,-2,-4,3) Matrix(609,538,-832,-735) -> Matrix(3,-2,14,-9) Matrix(703,610,-960,-833) -> Matrix(3,-2,14,-9) Matrix(289,250,704,609) -> Matrix(3,-2,-4,3) Matrix(1217,1036,-1728,-1471) -> Matrix(3,-2,-4,3) Matrix(321,272,832,705) -> Matrix(3,-2,-4,3) Matrix(31,26,-192,-161) -> Matrix(3,-2,2,-1) Matrix(769,636,-1856,-1535) -> Matrix(3,-2,2,-1) Matrix(769,634,1088,897) -> Matrix(3,-2,-4,3) Matrix(479,394,-896,-737) -> Matrix(7,-8,8,-9) Matrix(449,368,704,577) -> Matrix(3,-2,-4,3) Matrix(415,338,-512,-417) -> Matrix(5,-4,4,-3) Matrix(225,182,832,673) -> Matrix(1,-2,2,-3) Matrix(1345,1066,-1856,-1471) -> Matrix(3,-2,8,-5) Matrix(415,328,768,607) -> Matrix(5,-4,-6,5) Matrix(705,556,-1216,-959) -> Matrix(5,-2,8,-3) Matrix(97,76,-448,-351) -> Matrix(3,-2,2,-1) Matrix(1313,1018,-1856,-1439) -> Matrix(1,-2,2,-3) Matrix(897,694,-1984,-1535) -> Matrix(1,2,0,1) Matrix(865,668,-2112,-1631) -> Matrix(1,-2,2,-3) Matrix(223,172,704,543) -> Matrix(1,-2,0,1) Matrix(95,72,-128,-97) -> Matrix(1,0,0,1) Matrix(671,494,-1088,-801) -> Matrix(3,2,4,3) Matrix(801,586,-1792,-1311) -> Matrix(1,0,-4,1) Matrix(1057,772,-2496,-1823) -> Matrix(11,-2,6,-1) Matrix(159,116,832,607) -> Matrix(7,-2,-10,3) Matrix(383,278,704,511) -> Matrix(7,-2,-10,3) Matrix(2465,1786,-5696,-4127) -> Matrix(33,-14,26,-11) Matrix(1089,788,-1856,-1343) -> Matrix(5,-2,8,-3) Matrix(161,116,-576,-415) -> Matrix(5,-2,-2,1) Matrix(191,136,448,319) -> Matrix(1,-2,0,1) Matrix(1631,1156,-2304,-1633) -> Matrix(1,0,0,1) Matrix(897,634,1088,769) -> Matrix(3,-2,-4,3) Matrix(383,270,1088,767) -> Matrix(1,-2,0,1) Matrix(1599,1126,2816,1983) -> Matrix(3,4,-4,-5) Matrix(191,134,-640,-449) -> Matrix(1,0,-4,1) Matrix(1153,804,-2752,-1919) -> Matrix(3,-2,2,-1) Matrix(287,200,320,223) -> Matrix(3,-2,-4,3) Matrix(895,622,1472,1023) -> Matrix(11,-2,-16,3) Matrix(447,310,-832,-577) -> Matrix(17,-6,20,-7) Matrix(351,242,-512,-353) -> Matrix(9,-4,16,-7) Matrix(161,110,704,481) -> Matrix(3,-2,-4,3) Matrix(353,230,640,417) -> Matrix(7,-4,-12,7) Matrix(321,208,1088,705) -> Matrix(3,-2,-4,3) Matrix(1439,930,3712,2399) -> Matrix(9,-4,-2,1) Matrix(1537,992,3968,2561) -> Matrix(7,-4,2,-1) Matrix(705,454,896,577) -> Matrix(7,-4,-12,7) Matrix(321,206,-896,-575) -> Matrix(19,-12,8,-5) Matrix(3359,2148,4352,2783) -> Matrix(11,-8,-4,3) Matrix(2369,1514,-3904,-2495) -> Matrix(23,-18,32,-25) Matrix(577,368,704,449) -> Matrix(3,-2,-4,3) Matrix(159,100,-256,-161) -> Matrix(1,0,0,1) Matrix(2047,1266,-3520,-2177) -> Matrix(3,-2,8,-5) Matrix(961,594,2176,1345) -> Matrix(7,-4,-12,7) Matrix(703,434,-3008,-1857) -> Matrix(3,-2,32,-21) Matrix(127,78,832,511) -> Matrix(1,-2,0,1) Matrix(1089,668,1984,1217) -> Matrix(3,-2,-4,3) Matrix(1407,862,3968,2431) -> Matrix(9,-4,-2,1) Matrix(1313,804,3712,2273) -> Matrix(7,-4,2,-1) Matrix(1249,764,1728,1057) -> Matrix(3,-2,-4,3) Matrix(449,274,-1152,-703) -> Matrix(19,-12,8,-5) Matrix(1023,622,1472,895) -> Matrix(3,-2,-16,11) Matrix(3519,2134,-8128,-4929) -> Matrix(111,-82,88,-65) Matrix(1121,678,1536,929) -> Matrix(5,-4,-16,13) Matrix(287,170,-704,-417) -> Matrix(1,-2,2,-3) Matrix(481,284,-2112,-1247) -> Matrix(1,-2,2,-3) Matrix(95,56,704,415) -> Matrix(1,-2,0,1) Matrix(1567,920,2560,1503) -> Matrix(7,-4,-12,7) Matrix(321,188,-1856,-1087) -> Matrix(3,-2,2,-1) Matrix(671,392,-1152,-673) -> Matrix(1,0,0,1) Matrix(833,484,-2752,-1599) -> Matrix(3,-2,2,-1) Matrix(1279,742,1984,1151) -> Matrix(11,-6,-20,11) Matrix(703,406,-1664,-961) -> Matrix(29,-20,16,-11) Matrix(673,388,-2496,-1439) -> Matrix(3,-2,-10,7) Matrix(129,74,448,257) -> Matrix(3,-2,-4,3) Matrix(287,162,-512,-289) -> Matrix(9,-8,8,-7) Matrix(929,520,1088,609) -> Matrix(1,-2,0,1) Matrix(447,250,-2176,-1217) -> Matrix(3,-4,-2,3) Matrix(831,464,2176,1215) -> Matrix(1,-4,0,1) Matrix(481,266,-1792,-991) -> Matrix(1,0,-4,1) Matrix(417,230,640,353) -> Matrix(7,-4,-12,7) Matrix(1217,668,1984,1089) -> Matrix(3,-2,-4,3) Matrix(449,246,-1984,-1087) -> Matrix(3,-2,8,-5) Matrix(511,278,704,383) -> Matrix(3,-2,-10,7) Matrix(607,328,768,415) -> Matrix(5,-4,-6,5) Matrix(31,16,-64,-33) -> Matrix(3,-2,2,-1) Matrix(545,256,1024,481) -> Matrix(25,-24,-26,25) Matrix(543,254,1024,479) -> Matrix(23,-24,-22,23) Matrix(159,74,-896,-417) -> Matrix(7,-8,8,-9) Matrix(161,74,768,353) -> Matrix(3,-4,-2,3) Matrix(193,88,704,321) -> Matrix(1,-2,2,-3) Matrix(769,348,-3392,-1535) -> Matrix(1,-2,0,1) Matrix(767,346,1984,895) -> Matrix(1,-2,0,1) Matrix(223,100,640,287) -> Matrix(1,-4,0,1) Matrix(1153,516,-4288,-1919) -> Matrix(1,2,-2,-3) Matrix(223,98,-512,-225) -> Matrix(9,-8,8,-7) Matrix(1217,528,1920,833) -> Matrix(17,-20,-28,33) Matrix(1279,554,-6208,-2689) -> Matrix(21,-26,-4,5) Matrix(833,360,2816,1217) -> Matrix(3,-4,-8,11) Matrix(319,136,448,191) -> Matrix(1,-2,0,1) Matrix(1279,542,2112,895) -> Matrix(11,-18,-14,23) Matrix(2369,1000,4096,1729) -> Matrix(21,-40,-32,61) Matrix(2367,998,4096,1727) -> Matrix(19,-40,-28,59) Matrix(257,108,-1216,-511) -> Matrix(1,-2,0,1) Matrix(1313,550,-4352,-1823) -> Matrix(1,-4,0,1) Matrix(865,362,-2368,-991) -> Matrix(1,2,0,1) Matrix(959,398,-2624,-1089) -> Matrix(1,2,0,1) Matrix(449,186,-2624,-1087) -> Matrix(1,-2,2,-3) Matrix(513,212,-1856,-767) -> Matrix(1,-2,0,1) Matrix(609,250,704,289) -> Matrix(3,-2,-4,3) Matrix(2497,1024,3904,1601) -> Matrix(7,-2,-10,3) Matrix(609,248,1024,417) -> Matrix(9,-8,-10,9) Matrix(607,246,1024,415) -> Matrix(7,-8,-6,7) Matrix(1217,480,2112,833) -> Matrix(13,-18,-18,25) Matrix(1409,554,-3904,-1535) -> Matrix(11,-18,8,-13) Matrix(449,176,1472,577) -> Matrix(1,-2,4,-7) Matrix(2497,976,4096,1601) -> Matrix(29,-56,-44,85) Matrix(2495,974,4096,1599) -> Matrix(27,-56,-40,83) Matrix(1057,410,2560,993) -> Matrix(1,-4,0,1) Matrix(2399,930,3712,1439) -> Matrix(1,-4,-2,9) Matrix(2561,992,3968,1537) -> Matrix(1,4,-2,-7) Matrix(895,346,1984,767) -> Matrix(1,-2,0,1) Matrix(705,272,832,321) -> Matrix(3,-2,-4,3) Matrix(95,36,-256,-97) -> Matrix(1,0,0,1) Matrix(223,82,-960,-353) -> Matrix(1,-2,4,-7) Matrix(1087,398,1920,703) -> Matrix(7,-20,-8,23) Matrix(127,46,704,255) -> Matrix(1,-2,0,1) Matrix(1375,496,-6656,-2401) -> Matrix(5,-8,2,-3) Matrix(2303,830,3904,1407) -> Matrix(1,-2,2,-3) Matrix(2625,944,4096,1473) -> Matrix(21,-40,-32,61) Matrix(2623,942,4096,1471) -> Matrix(19,-40,-28,59) Matrix(833,296,1984,705) -> Matrix(1,-6,0,1) Matrix(2431,862,3968,1407) -> Matrix(1,-4,-2,9) Matrix(2273,804,3712,1313) -> Matrix(1,4,-2,-7) Matrix(767,270,1088,383) -> Matrix(1,-2,0,1) Matrix(287,100,640,223) -> Matrix(1,-4,0,1) Matrix(159,50,-512,-161) -> Matrix(1,-4,0,1) Matrix(641,198,832,257) -> Matrix(1,2,0,1) Matrix(353,108,-1984,-607) -> Matrix(3,2,4,3) Matrix(577,176,1472,449) -> Matrix(7,2,-4,-1) Matrix(33,10,320,97) -> Matrix(1,-2,0,1) Matrix(6433,1944,9216,2785) -> Matrix(1,-8,-2,17) Matrix(6431,1942,9216,2783) -> Matrix(1,8,-2,-15) Matrix(2881,856,4096,1217) -> Matrix(1,0,12,1) Matrix(2879,854,4096,1215) -> Matrix(1,0,-16,1) Matrix(257,76,-1728,-511) -> Matrix(7,-2,4,-1) Matrix(705,208,1088,321) -> Matrix(3,-2,-4,3) Matrix(191,56,1088,319) -> Matrix(1,-2,0,1) Matrix(417,122,-1856,-543) -> Matrix(1,-2,2,-3) Matrix(447,130,-1984,-577) -> Matrix(1,-2,2,-3) Matrix(257,74,448,129) -> Matrix(3,-2,-4,3) Matrix(737,208,1024,289) -> Matrix(1,-4,-2,9) Matrix(735,206,1024,287) -> Matrix(1,4,-2,-7) Matrix(671,186,1728,479) -> Matrix(1,-2,0,1) Matrix(385,106,-1856,-511) -> Matrix(1,2,0,1) Matrix(321,88,704,193) -> Matrix(3,2,-2,-1) Matrix(575,156,704,191) -> Matrix(1,2,-2,-3) Matrix(607,164,1536,415) -> Matrix(5,4,-4,-3) Matrix(18721,5032,25600,6881) -> Matrix(15,8,-62,-33) Matrix(18719,5030,25600,6879) -> Matrix(17,8,-66,-31) Matrix(97,26,-832,-223) -> Matrix(5,2,2,1) Matrix(31,8,-128,-33) -> Matrix(1,0,0,1) Matrix(3137,736,4096,961) -> Matrix(1,0,24,1) Matrix(3135,734,4096,959) -> Matrix(1,0,-28,1) Matrix(575,132,832,191) -> Matrix(5,-2,-12,5) Matrix(1569,358,4352,993) -> Matrix(13,-8,-8,5) Matrix(12673,2872,16384,3713) -> Matrix(1,0,4,1) Matrix(12671,2870,16384,3711) -> Matrix(1,0,-8,1) Matrix(801,176,1024,225) -> Matrix(5,-4,-6,5) Matrix(799,174,1024,223) -> Matrix(3,-4,-2,3) Matrix(319,68,896,191) -> Matrix(1,-4,0,1) Matrix(353,74,768,161) -> Matrix(3,-4,-2,3) Matrix(20321,4192,25600,5281) -> Matrix(1,-24,-2,49) Matrix(20319,4190,25600,5279) -> Matrix(1,24,-2,-47) Matrix(95,18,-512,-97) -> Matrix(5,-4,4,-3) Matrix(513,94,704,129) -> Matrix(1,-2,-2,5) Matrix(255,46,704,127) -> Matrix(1,-2,0,1) Matrix(319,56,1088,191) -> Matrix(1,-2,0,1) Matrix(3393,584,4096,705) -> Matrix(1,0,0,1) Matrix(3391,582,4096,703) -> Matrix(1,0,-4,1) Matrix(865,136,1024,161) -> Matrix(9,-8,-10,9) Matrix(863,134,1024,159) -> Matrix(7,-8,-6,7) Matrix(511,78,832,127) -> Matrix(1,-2,0,1) Matrix(479,70,1088,159) -> Matrix(3,-2,-4,3) Matrix(415,56,704,95) -> Matrix(1,-2,0,1) Matrix(31,4,-256,-33) -> Matrix(1,0,0,1) Matrix(97,10,320,33) -> Matrix(1,-2,0,1) Matrix(223,-26,832,-97) -> Matrix(1,2,2,5) Matrix(257,-34,960,-127) -> Matrix(1,2,2,5) Matrix(511,-76,1728,-257) -> Matrix(1,2,-4,-7) Matrix(161,-26,192,-31) -> Matrix(1,2,-2,-3) Matrix(1087,-188,1856,-321) -> Matrix(1,2,-2,-3) Matrix(417,-74,896,-159) -> Matrix(9,8,-8,-7) Matrix(97,-18,512,-95) -> Matrix(3,4,-4,-5) Matrix(511,-106,1856,-385) -> Matrix(1,2,0,1) Matrix(511,-108,1216,-257) -> Matrix(1,-2,0,1) Matrix(351,-76,448,-97) -> Matrix(1,2,-2,-3) Matrix(543,-122,1856,-417) -> Matrix(3,2,-2,-1) Matrix(1087,-246,1984,-449) -> Matrix(5,2,-8,-3) Matrix(1247,-284,2112,-481) -> Matrix(3,2,-2,-1) Matrix(33,-8,128,-31) -> Matrix(1,0,0,1) Matrix(417,-110,1088,-287) -> Matrix(7,2,-4,-1) Matrix(991,-266,1792,-481) -> Matrix(1,0,-4,1) Matrix(1439,-388,2496,-673) -> Matrix(7,-2,-10,3) Matrix(3231,-890,5696,-1569) -> Matrix(5,-14,-6,17) Matrix(767,-212,1856,-513) -> Matrix(1,-2,0,1) Matrix(415,-116,576,-161) -> Matrix(1,-2,-2,5) Matrix(673,-196,2304,-671) -> Matrix(1,0,0,1) Matrix(449,-134,640,-191) -> Matrix(1,0,-4,1) Matrix(1599,-484,2752,-833) -> Matrix(1,2,-2,-3) Matrix(385,-118,832,-255) -> Matrix(5,-6,-4,5) Matrix(161,-50,512,-159) -> Matrix(1,-4,0,1) Matrix(575,-206,896,-321) -> Matrix(5,12,-8,-19) Matrix(1535,-554,3904,-1409) -> Matrix(13,18,-8,-11) Matrix(97,-36,256,-95) -> Matrix(1,0,0,1) Matrix(1473,-562,3520,-1343) -> Matrix(1,2,0,1) Matrix(2305,-882,3008,-1151) -> Matrix(1,2,8,17) Matrix(703,-274,1152,-449) -> Matrix(5,12,-8,-19) Matrix(4609,-1814,8128,-3199) -> Matrix(53,82,-64,-99) Matrix(417,-170,704,-287) -> Matrix(3,2,-2,-1) Matrix(1631,-668,2112,-865) -> Matrix(3,2,-2,-1) Matrix(1535,-636,1856,-769) -> Matrix(1,2,-2,-3) Matrix(481,-200,1152,-479) -> Matrix(1,0,0,1) Matrix(1919,-804,2752,-1153) -> Matrix(1,2,-2,-3) Matrix(961,-406,1664,-703) -> Matrix(11,20,-16,-29) Matrix(1823,-772,2496,-1057) -> Matrix(1,2,-6,-11) Matrix(225,-98,512,-223) -> Matrix(7,8,-8,-9) Matrix(1729,-762,2176,-959) -> Matrix(5,4,-14,-11) Matrix(1311,-586,1792,-801) -> Matrix(1,0,-4,1) Matrix(1535,-694,1984,-897) -> Matrix(1,2,0,1) Matrix(33,-16,64,-31) -> Matrix(1,2,-2,-3) Matrix(737,-394,896,-479) -> Matrix(9,8,-8,-7) Matrix(2623,-1436,3392,-1857) -> Matrix(3,2,-8,-5) Matrix(3135,-1732,4288,-2369) -> Matrix(5,2,-18,-7) Matrix(289,-162,512,-287) -> Matrix(7,8,-8,-9) Matrix(4929,-2794,6208,-3519) -> Matrix(31,26,-68,-57) Matrix(959,-556,1216,-705) -> Matrix(3,2,-8,-5) Matrix(3039,-1766,4352,-2529) -> Matrix(7,4,-16,-9) Matrix(1503,-874,2368,-1377) -> Matrix(5,2,-8,-3) Matrix(1665,-974,2624,-1535) -> Matrix(5,2,-8,-3) Matrix(2175,-1274,2624,-1537) -> Matrix(3,2,-2,-1) Matrix(1343,-788,1856,-1089) -> Matrix(3,2,-8,-5) Matrix(2495,-1514,3904,-2369) -> Matrix(25,18,-32,-23) Matrix(161,-100,256,-159) -> Matrix(1,0,0,1) Matrix(737,-466,960,-607) -> Matrix(3,2,4,3) Matrix(5281,-3376,6656,-4255) -> Matrix(11,8,-18,-13) Matrix(353,-242,512,-351) -> Matrix(7,4,-16,-9) Matrix(1631,-1132,1984,-1377) -> Matrix(7,2,-4,-1) Matrix(1471,-1036,1728,-1217) -> Matrix(3,-2,-4,3) Matrix(1439,-1018,1856,-1313) -> Matrix(3,2,-2,-1) Matrix(1537,-1090,1984,-1407) -> Matrix(3,2,-2,-1) Matrix(1471,-1066,1856,-1345) -> Matrix(5,2,-8,-3) Matrix(735,-538,832,-609) -> Matrix(9,2,-14,-3) Matrix(97,-72,128,-95) -> Matrix(1,0,0,1) Matrix(417,-338,512,-415) -> Matrix(3,4,-4,-5) Matrix(225,-196,256,-223) -> Matrix(1,0,0,1) 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): 84 Degree of the the map X: 84 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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): 768 Minimal number of generators: 129 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: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 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 5/22 1/4 7/26 5/18 7/24 3/10 5/16 1/3 17/48 3/8 11/28 5/12 7/16 9/20 11/24 1/2 17/32 9/16 17/30 37/64 7/12 19/32 39/64 5/8 41/64 31/48 11/16 67/96 45/64 17/24 23/32 117/160 3/4 49/64 99/128 25/32 127/160 13/16 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 -3/2 1/8 -2/1 0/1 2/15 -7/4 1/7 -3/2 3/20 -2/1 -4/3 2/13 -5/4 1/6 -1/1 4/23 1/0 3/17 -5/4 5/28 -2/3 0/1 2/11 1/0 3/16 -1/1 4/21 -3/4 1/5 -1/2 5/24 -2/1 0/1 4/19 -1/2 3/14 -1/1 2/9 -1/2 7/31 -1/2 5/22 -1/1 8/35 -1/2 3/13 -1/2 1/4 -2/1 0/1 5/19 -1/2 4/15 1/6 15/56 0/1 2/5 11/41 1/4 7/26 1/1 10/37 1/2 3/11 1/0 11/40 0/1 2/1 19/69 3/2 8/29 1/0 5/18 1/1 2/7 1/0 9/31 1/0 7/24 -2/1 0/1 19/65 1/0 12/41 1/0 5/17 -3/4 13/44 -2/5 0/1 21/71 -1/2 8/27 -1/6 3/10 1/1 10/33 1/0 7/23 -1/2 11/36 0/1 2/3 4/13 1/0 5/16 1/0 6/19 1/0 1/3 1/0 7/20 -4/1 -2/1 6/17 -1/2 17/48 1/0 11/31 1/0 5/14 -3/1 9/25 -7/4 22/61 -3/2 13/36 -2/1 -4/3 4/11 1/0 3/8 -2/1 0/1 8/21 1/0 21/55 1/0 13/34 -7/3 18/47 -19/10 5/13 -3/2 17/44 -2/1 0/1 12/31 1/0 31/80 1/0 19/49 -9/2 7/18 -3/1 9/23 -11/6 11/28 -2/1 -8/5 24/61 -3/2 13/33 -3/2 2/5 -3/2 9/22 -1/1 16/39 1/0 7/17 1/2 19/46 -1/1 12/29 1/0 17/41 1/0 5/12 -2/1 0/1 23/55 1/0 18/43 1/0 13/31 1/0 21/50 -3/1 8/19 -5/2 11/26 -5/3 14/33 -3/2 3/7 -3/2 7/16 -1/1 11/25 -5/6 26/59 -11/14 15/34 -5/7 4/9 -1/2 13/29 1/0 9/20 -2/1 0/1 14/31 1/0 5/11 -3/2 11/24 -2/1 -4/3 6/13 -5/4 13/28 -6/5 -8/7 7/15 -13/12 1/2 -1/1 9/17 -11/10 17/32 -1/1 8/15 -13/14 7/13 -5/6 13/24 -4/5 -2/3 6/11 -3/4 23/42 -3/5 17/31 -1/2 11/20 -2/3 0/1 16/29 -1/2 21/38 -1/3 5/9 1/0 9/16 -1/1 13/23 -7/8 17/30 -11/13 55/97 -5/6 38/67 -5/6 21/37 -13/16 4/7 -3/4 19/33 -3/4 34/59 -3/4 15/26 -5/7 26/45 -15/22 37/64 -2/3 11/19 -5/8 18/31 -1/2 43/74 -3/5 25/43 -1/2 7/12 -2/3 0/1 24/41 -1/2 41/70 -1/1 17/29 -1/2 10/17 -1/4 23/39 -1/2 36/61 1/0 13/22 -1/1 16/27 -5/4 19/32 -1/1 3/5 -3/4 20/33 -3/4 17/28 -8/11 -2/3 14/23 -11/16 39/64 -2/3 25/41 -17/26 11/18 -3/5 30/49 -9/16 49/80 -1/2 19/31 -1/2 27/44 -2/3 0/1 8/13 -3/4 5/8 -2/3 0/1 12/19 -3/4 19/30 -7/11 26/41 -1/2 33/52 -2/3 -4/7 7/11 -1/2 23/36 -4/5 -2/3 62/97 -3/4 39/61 -3/4 16/25 -7/10 41/64 -2/3 25/39 -13/20 9/14 -3/5 20/31 -1/2 31/48 -1/2 11/17 1/0 13/20 -2/3 -4/7 2/3 -1/2 11/16 -1/2 20/29 -1/2 9/13 -1/2 25/36 -2/7 0/1 16/23 1/0 23/33 -1/2 30/43 -1/2 67/96 -1/2 37/53 -1/2 7/10 -1/3 26/37 -1/10 45/64 0/1 19/27 1/4 31/44 0/1 2/1 12/17 -3/2 29/41 -1/2 17/24 -2/3 0/1 22/31 -1/2 5/7 -1/2 23/32 -1/2 18/25 -1/2 13/18 -1/3 34/47 -5/12 21/29 -1/2 29/40 -2/5 0/1 8/11 -1/2 27/37 -1/4 46/63 -1/4 19/26 -1/3 68/93 -1/4 117/160 -1/4 49/67 -1/4 30/41 -1/6 11/15 -1/8 3/4 -2/3 0/1 13/17 -1/8 49/64 0/1 36/47 1/18 23/30 1/5 10/13 1/0 27/35 1/0 44/57 -3/2 17/22 -1/1 58/75 -1/4 99/128 0/1 41/53 1/2 24/31 1/0 31/40 -2/1 0/1 7/9 1/0 25/32 -1/1 18/23 -3/4 11/14 -1/1 26/33 -1/2 15/19 1/0 19/24 -2/3 0/1 23/29 -1/2 50/63 -1/2 127/160 -1/2 77/97 -1/2 27/34 -3/7 4/5 1/0 13/16 -1/1 22/27 -3/4 9/11 -1/2 23/28 -2/1 0/1 37/45 -3/2 14/17 -5/6 19/23 -1/2 24/29 -1/2 53/64 0/1 29/35 1/0 5/6 -1/1 16/19 -3/2 27/32 -1/1 11/13 -5/6 17/20 -4/5 -2/3 23/27 -5/8 6/7 -3/4 13/15 -7/10 7/8 -2/3 0/1 15/17 -7/10 8/9 -3/4 1/1 -1/2 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(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(289,-39,704,-95) (2/15,1/7) -> (16/39,7/17) Hyperbolic Matrix(511,-76,1728,-257) (1/7,3/20) -> (13/44,21/71) Hyperbolic Matrix(321,-49,832,-127) (3/20,2/13) -> (5/13,17/44) 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(769,-135,1088,-191) (4/23,3/17) -> (12/17,29/41) Hyperbolic Matrix(417,-74,896,-159) (3/17,5/28) -> (13/28,7/15) Hyperbolic Matrix(449,-81,704,-127) (5/28,2/11) -> (7/11,23/36) Hyperbolic Matrix(97,-18,512,-95) (2/11,3/16) -> (3/16,4/21) Parabolic Matrix(225,-43,832,-159) (4/21,1/5) -> (10/37,3/11) Hyperbolic Matrix(511,-106,1856,-385) (1/5,5/24) -> (11/40,19/69) Hyperbolic Matrix(415,-87,768,-161) (5/24,4/19) -> (7/13,13/24) 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(223,-51,704,-161) (8/35,3/13) -> (6/19,1/3) 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(383,-105,704,-193) (3/11,11/40) -> (13/24,6/11) 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(191,-55,448,-129) (2/7,9/31) -> (14/33,3/7) Hyperbolic Matrix(673,-196,2304,-671) (9/31,7/24) -> (7/24,19/65) Parabolic Matrix(897,-263,1088,-319) (12/41,5/17) -> (14/17,19/23) Hyperbolic Matrix(383,-113,1088,-321) (5/17,13/44) -> (7/20,6/17) Hyperbolic Matrix(1599,-473,2816,-833) (21/71,8/27) -> (21/37,4/7) Hyperbolic 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(287,-87,320,-97) (10/33,7/23) -> (8/9,1/1) Hyperbolic Matrix(895,-273,1472,-449) (7/23,11/36) -> (17/28,14/23) 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(353,-123,640,-223) (1/3,7/20) -> (11/20,16/29) Hyperbolic Matrix(1439,-509,3712,-1313) (6/17,17/48) -> (31/80,19/49) Hyperbolic Matrix(1537,-545,3968,-1407) (17/48,11/31) -> (12/31,31/80) Hyperbolic Matrix(705,-251,896,-319) (11/31,5/14) -> (11/14,26/33) Hyperbolic Matrix(575,-206,896,-321) (5/14,9/25) -> (25/39,9/14) Hyperbolic Matrix(3359,-1211,4352,-1569) (9/25,22/61) -> (27/35,44/57) Hyperbolic Matrix(1535,-554,3904,-1409) (22/61,13/36) -> (11/28,24/61) Hyperbolic Matrix(577,-209,704,-255) (13/36,4/11) -> (9/11,23/28) 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(961,-367,2176,-831) (21/55,13/34) -> (15/34,4/9) Hyperbolic Matrix(2305,-882,3008,-1151) (13/34,18/47) -> (36/47,23/30) Hyperbolic Matrix(1089,-421,1984,-767) (17/44,12/31) -> (17/31,11/20) Hyperbolic Matrix(1249,-485,1728,-671) (19/49,7/18) -> (13/18,34/47) Hyperbolic Matrix(703,-274,1152,-449) (7/18,9/23) -> (25/41,11/18) Hyperbolic Matrix(1023,-401,1472,-577) (9/23,11/28) -> (25/36,16/23) Hyperbolic Matrix(4609,-1814,8128,-3199) (24/61,13/33) -> (55/97,38/67) Hyperbolic Matrix(1121,-443,1536,-607) (13/33,2/5) -> (27/37,46/63) 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(1567,-647,2560,-1057) (7/17,19/46) -> (11/18,30/49) 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(1279,-537,1984,-833) (13/31,21/50) -> (9/14,20/31) 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(929,-409,1088,-479) (11/25,26/59) -> (23/27,6/7) Hyperbolic 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(417,-187,640,-287) (13/29,9/20) -> (13/20,2/3) Hyperbolic Matrix(1217,-549,1984,-895) (9/20,14/31) -> (19/31,27/44) Hyperbolic Matrix(1535,-694,1984,-897) (14/31,5/11) -> (41/53,24/31) Hyperbolic Matrix(511,-233,704,-321) (5/11,11/24) -> (29/40,8/11) Hyperbolic Matrix(607,-279,768,-353) (11/24,6/13) -> (15/19,19/24) Hyperbolic Matrix(33,-16,64,-31) (7/15,1/2) -> (1/2,9/17) Parabolic Matrix(545,-289,1024,-543) (9/17,17/32) -> (17/32,8/15) 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(1217,-689,1920,-1087) (13/23,17/30) -> (19/30,26/41) Hyperbolic Matrix(4929,-2794,6208,-3519) (17/30,55/97) -> (77/97,27/34) Hyperbolic Matrix(319,-183,448,-257) (4/7,19/33) -> (22/31,5/7) Hyperbolic Matrix(1279,-737,2112,-1217) (19/33,34/59) -> (3/5,20/33) Hyperbolic Matrix(2369,-1369,4096,-2367) (26/45,37/64) -> (37/64,11/19) Parabolic 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(609,-359,704,-415) (10/17,23/39) -> (6/7,13/15) Hyperbolic Matrix(2497,-1473,3904,-2303) (23/39,36/61) -> (39/61,16/25) Hyperbolic Matrix(609,-361,1024,-607) (16/27,19/32) -> (19/32,3/5) Parabolic Matrix(2495,-1514,3904,-2369) (20/33,17/28) -> (23/36,62/97) Hyperbolic Matrix(2497,-1521,4096,-2495) (14/23,39/64) -> (39/64,25/41) Parabolic 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(705,-433,832,-511) (27/44,8/13) -> (11/13,17/20) 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(2625,-1681,4096,-2623) (16/25,41/64) -> (41/64,25/39) Parabolic Matrix(767,-497,1088,-705) (11/17,13/20) -> (31/44,12/17) Hyperbolic Matrix(353,-242,512,-351) (2/3,11/16) -> (11/16,20/29) Parabolic Matrix(641,-443,832,-575) (20/29,9/13) -> (10/13,27/35) Hyperbolic Matrix(1631,-1132,1984,-1377) (9/13,25/36) -> (23/28,37/45) Hyperbolic Matrix(6433,-4489,9216,-6431) (30/43,67/96) -> (67/96,37/53) Parabolic Matrix(2881,-2025,4096,-2879) (26/37,45/64) -> (45/64,19/27) Parabolic 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(737,-529,1024,-735) (5/7,23/32) -> (23/32,18/25) Parabolic Matrix(1471,-1066,1856,-1345) (21/29,29/40) -> (19/24,23/29) Hyperbolic Matrix(575,-419,704,-513) (8/11,27/37) -> (22/27,9/11) Hyperbolic Matrix(18721,-13689,25600,-18719) (68/93,117/160) -> (117/160,49/67) Parabolic 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(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(801,-625,1024,-799) (7/9,25/32) -> (25/32,18/23) Parabolic Matrix(20321,-16129,25600,-20319) (50/63,127/160) -> (127/160,77/97) Parabolic Matrix(417,-338,512,-415) (4/5,13/16) -> (13/16,22/27) 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 Matrix(225,-196,256,-223) (13/15,7/8) -> (7/8,15/17) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-2,1) Matrix(223,-23,320,-33) -> Matrix(1,2,-2,-3) Matrix(223,-26,832,-97) -> Matrix(1,2,2,5) Matrix(257,-34,960,-127) -> Matrix(1,2,2,5) Matrix(289,-39,704,-95) -> Matrix(1,2,-2,-3) Matrix(511,-76,1728,-257) -> Matrix(1,2,-4,-7) Matrix(321,-49,832,-127) -> Matrix(1,2,-2,-3) Matrix(161,-26,192,-31) -> Matrix(1,2,-2,-3) Matrix(1087,-188,1856,-321) -> Matrix(1,2,-2,-3) Matrix(769,-135,1088,-191) -> Matrix(1,2,-2,-3) Matrix(417,-74,896,-159) -> Matrix(9,8,-8,-7) Matrix(449,-81,704,-127) -> Matrix(1,2,-2,-3) Matrix(97,-18,512,-95) -> Matrix(3,4,-4,-5) Matrix(225,-43,832,-159) -> Matrix(3,2,4,3) Matrix(511,-106,1856,-385) -> Matrix(1,2,0,1) Matrix(415,-87,768,-161) -> Matrix(3,4,-4,-5) Matrix(511,-108,1216,-257) -> Matrix(1,-2,0,1) Matrix(351,-76,448,-97) -> Matrix(1,2,-2,-3) Matrix(543,-122,1856,-417) -> Matrix(3,2,-2,-1) Matrix(1087,-246,1984,-449) -> Matrix(5,2,-8,-3) Matrix(1247,-284,2112,-481) -> Matrix(3,2,-2,-1) Matrix(223,-51,704,-161) -> Matrix(3,2,-2,-1) Matrix(33,-8,128,-31) -> Matrix(1,0,0,1) Matrix(417,-110,1088,-287) -> Matrix(7,2,-4,-1) Matrix(991,-266,1792,-481) -> Matrix(1,0,-4,1) Matrix(1439,-388,2496,-673) -> Matrix(7,-2,-10,3) Matrix(383,-105,704,-193) -> Matrix(3,-2,-4,3) Matrix(3231,-890,5696,-1569) -> Matrix(5,-14,-6,17) Matrix(767,-212,1856,-513) -> Matrix(1,-2,0,1) Matrix(415,-116,576,-161) -> Matrix(1,-2,-2,5) Matrix(191,-55,448,-129) -> Matrix(3,2,-2,-1) Matrix(673,-196,2304,-671) -> Matrix(1,0,0,1) Matrix(897,-263,1088,-319) -> Matrix(1,2,-2,-3) Matrix(383,-113,1088,-321) -> Matrix(3,2,-2,-1) Matrix(1599,-473,2816,-833) -> Matrix(11,4,-14,-5) Matrix(449,-134,640,-191) -> Matrix(1,0,-4,1) Matrix(1599,-484,2752,-833) -> Matrix(1,2,-2,-3) Matrix(287,-87,320,-97) -> Matrix(1,2,-2,-3) Matrix(895,-273,1472,-449) -> Matrix(7,-2,-10,3) Matrix(385,-118,832,-255) -> Matrix(5,-6,-4,5) Matrix(161,-50,512,-159) -> Matrix(1,-4,0,1) Matrix(353,-123,640,-223) -> Matrix(1,4,-2,-7) Matrix(1439,-509,3712,-1313) -> Matrix(1,-4,0,1) Matrix(1537,-545,3968,-1407) -> Matrix(1,4,0,1) Matrix(705,-251,896,-319) -> Matrix(1,4,-2,-7) Matrix(575,-206,896,-321) -> Matrix(5,12,-8,-19) Matrix(3359,-1211,4352,-1569) -> Matrix(5,8,-2,-3) Matrix(1535,-554,3904,-1409) -> Matrix(13,18,-8,-11) Matrix(577,-209,704,-255) -> Matrix(1,2,-2,-3) Matrix(97,-36,256,-95) -> Matrix(1,0,0,1) Matrix(1473,-562,3520,-1343) -> Matrix(1,2,0,1) Matrix(961,-367,2176,-831) -> Matrix(1,4,-2,-7) Matrix(2305,-882,3008,-1151) -> Matrix(1,2,8,17) Matrix(1089,-421,1984,-767) -> Matrix(1,2,-2,-3) Matrix(1249,-485,1728,-671) -> Matrix(1,2,-2,-3) Matrix(703,-274,1152,-449) -> Matrix(5,12,-8,-19) Matrix(1023,-401,1472,-577) -> Matrix(1,2,-6,-11) Matrix(4609,-1814,8128,-3199) -> Matrix(53,82,-64,-99) Matrix(1121,-443,1536,-607) -> Matrix(3,4,-10,-13) Matrix(417,-170,704,-287) -> Matrix(3,2,-2,-1) Matrix(1631,-668,2112,-865) -> Matrix(3,2,-2,-1) Matrix(1567,-647,2560,-1057) -> Matrix(1,4,-2,-7) Matrix(1535,-636,1856,-769) -> Matrix(1,2,-2,-3) Matrix(481,-200,1152,-479) -> Matrix(1,0,0,1) Matrix(1919,-804,2752,-1153) -> Matrix(1,2,-2,-3) Matrix(1279,-537,1984,-833) -> Matrix(1,6,-2,-11) Matrix(961,-406,1664,-703) -> Matrix(11,20,-16,-29) Matrix(1823,-772,2496,-1057) -> Matrix(1,2,-6,-11) Matrix(225,-98,512,-223) -> Matrix(7,8,-8,-9) Matrix(929,-409,1088,-479) -> Matrix(3,2,-2,-1) Matrix(1729,-762,2176,-959) -> Matrix(5,4,-14,-11) Matrix(1311,-586,1792,-801) -> Matrix(1,0,-4,1) Matrix(417,-187,640,-287) -> Matrix(1,4,-2,-7) Matrix(1217,-549,1984,-895) -> Matrix(1,2,-2,-3) Matrix(1535,-694,1984,-897) -> Matrix(1,2,0,1) Matrix(511,-233,704,-321) -> Matrix(1,2,-4,-7) Matrix(607,-279,768,-353) -> Matrix(3,4,-4,-5) Matrix(33,-16,64,-31) -> Matrix(1,2,-2,-3) Matrix(545,-289,1024,-543) -> Matrix(23,24,-24,-25) Matrix(737,-394,896,-479) -> Matrix(9,8,-8,-7) Matrix(2623,-1436,3392,-1857) -> Matrix(3,2,-8,-5) Matrix(3135,-1732,4288,-2369) -> Matrix(5,2,-18,-7) Matrix(289,-162,512,-287) -> Matrix(7,8,-8,-9) Matrix(1217,-689,1920,-1087) -> Matrix(23,20,-38,-33) Matrix(4929,-2794,6208,-3519) -> Matrix(31,26,-68,-57) Matrix(319,-183,448,-257) -> Matrix(3,2,-2,-1) Matrix(1279,-737,2112,-1217) -> Matrix(25,18,-32,-23) Matrix(2369,-1369,4096,-2367) -> Matrix(59,40,-90,-61) Matrix(959,-556,1216,-705) -> Matrix(3,2,-8,-5) Matrix(3039,-1766,4352,-2529) -> Matrix(7,4,-16,-9) Matrix(1503,-874,2368,-1377) -> Matrix(5,2,-8,-3) Matrix(1665,-974,2624,-1535) -> Matrix(5,2,-8,-3) Matrix(2175,-1274,2624,-1537) -> Matrix(3,2,-2,-1) Matrix(1343,-788,1856,-1089) -> Matrix(3,2,-8,-5) Matrix(609,-359,704,-415) -> Matrix(1,2,-2,-3) Matrix(2497,-1473,3904,-2303) -> Matrix(3,-2,-4,3) Matrix(609,-361,1024,-607) -> Matrix(7,8,-8,-9) Matrix(2495,-1514,3904,-2369) -> Matrix(25,18,-32,-23) Matrix(2497,-1521,4096,-2495) -> Matrix(83,56,-126,-85) Matrix(2399,-1469,3712,-2273) -> Matrix(7,4,-16,-9) Matrix(2561,-1569,3968,-2431) -> Matrix(9,4,-16,-7) Matrix(705,-433,832,-511) -> Matrix(1,2,-2,-3) Matrix(161,-100,256,-159) -> Matrix(1,0,0,1) Matrix(737,-466,960,-607) -> Matrix(3,2,4,3) Matrix(5281,-3376,6656,-4255) -> Matrix(11,8,-18,-13) Matrix(2625,-1681,4096,-2623) -> Matrix(59,40,-90,-61) Matrix(767,-497,1088,-705) -> Matrix(3,2,-2,-1) Matrix(353,-242,512,-351) -> Matrix(7,4,-16,-9) Matrix(641,-443,832,-575) -> Matrix(5,2,2,1) Matrix(1631,-1132,1984,-1377) -> Matrix(7,2,-4,-1) Matrix(6433,-4489,9216,-6431) -> Matrix(15,8,-32,-17) Matrix(2881,-2025,4096,-2879) -> Matrix(1,0,14,1) Matrix(1471,-1036,1728,-1217) -> Matrix(3,-2,-4,3) Matrix(1439,-1018,1856,-1313) -> Matrix(3,2,-2,-1) Matrix(1537,-1090,1984,-1407) -> Matrix(3,2,-2,-1) Matrix(737,-529,1024,-735) -> Matrix(7,4,-16,-9) Matrix(1471,-1066,1856,-1345) -> Matrix(5,2,-8,-3) Matrix(575,-419,704,-513) -> Matrix(5,2,-8,-3) Matrix(18721,-13689,25600,-18719) -> Matrix(31,8,-128,-33) Matrix(735,-538,832,-609) -> Matrix(9,2,-14,-3) Matrix(97,-72,128,-95) -> Matrix(1,0,0,1) Matrix(3137,-2401,4096,-3135) -> Matrix(1,0,26,1) Matrix(12673,-9801,16384,-12671) -> Matrix(1,0,6,1) Matrix(801,-625,1024,-799) -> Matrix(3,4,-4,-5) Matrix(20321,-16129,25600,-20319) -> Matrix(47,24,-96,-49) Matrix(417,-338,512,-415) -> Matrix(3,4,-4,-5) Matrix(3393,-2809,4096,-3391) -> Matrix(1,0,2,1) Matrix(865,-729,1024,-863) -> Matrix(7,8,-8,-9) Matrix(225,-196,256,-223) -> Matrix(1,0,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 42 ----------------------------------------------------------------------- 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 -3/2 1 32 1/8 0 4 2/15 -7/4 1 32 1/7 -3/2 1 32 3/20 0 8 2/13 -5/4 1 32 5/32 -1/1 8 1 1/6 -1/1 2 16 4/23 1/0 1 32 3/17 -5/4 1 32 5/28 0 8 2/11 1/0 1 32 3/16 -1/1 4 2 4/21 -3/4 1 32 1/5 -1/2 1 32 5/24 0 4 4/19 -1/2 1 32 3/14 -1/1 2 16 7/32 -1/1 4 1 2/9 -1/2 1 32 7/31 -1/2 1 32 5/22 -1/1 2 16 8/35 -1/2 1 32 3/13 -1/2 1 32 1/4 0 8 5/19 -1/2 1 32 4/15 1/6 1 32 15/56 0 4 11/41 1/4 1 32 7/26 1/1 2 16 10/37 1/2 1 32 3/11 1/0 1 32 11/40 0 4 19/69 3/2 1 32 8/29 1/0 1 32 5/18 1/1 2 16 9/32 1/0 4 1 2/7 1/0 1 32 9/31 1/0 1 32 7/24 0 4 19/65 1/0 1 32 12/41 1/0 1 32 5/17 -3/4 1 32 13/44 0 8 21/71 -1/2 1 32 8/27 -1/6 1 32 19/64 0/1 14 1 3/10 1/1 2 16 10/33 1/0 1 32 7/23 -1/2 1 32 11/36 0 8 4/13 1/0 1 32 5/16 1/0 4 2 6/19 1/0 1 32 1/3 1/0 1 32 7/20 0 8 6/17 -1/2 1 32 17/48 1/0 8 2 11/31 1/0 1 32 5/14 -3/1 2 16 23/64 -2/1 10 1 9/25 -7/4 1 32 22/61 -3/2 1 32 13/36 0 8 4/11 1/0 1 32 3/8 0 4 8/21 1/0 1 32 21/55 1/0 1 32 13/34 -7/3 2 16 49/128 -2/1 26 1 18/47 -19/10 1 32 5/13 -3/2 1 32 17/44 0 8 12/31 1/0 1 32 31/80 1/0 8 2 19/49 -9/2 1 32 7/18 -3/1 2 16 25/64 -2/1 14 1 9/23 -11/6 1 32 11/28 0 8 24/61 -3/2 1 32 13/33 -3/2 1 32 2/5 -3/2 1 32 13/32 -1/1 8 1 9/22 -1/1 2 16 25/61 -1/2 1 32 16/39 1/0 1 32 7/17 1/2 1 32 19/46 -1/1 2 16 12/29 1/0 1 32 53/128 -2/1 2 1 29/70 -1/1 2 16 17/41 1/0 1 32 5/12 0 8 23/55 1/0 1 32 18/43 1/0 1 32 67/160 1/0 8 1 31/74 -3/1 2 16 13/31 1/0 1 32 21/50 -3/1 2 16 8/19 -5/2 1 32 27/64 -2/1 10 1 11/26 -5/3 2 16 25/59 -3/2 1 32 14/33 -3/2 1 32 3/7 -3/2 1 32 7/16 -1/1 8 2 11/25 -5/6 1 32 26/59 -11/14 1 32 41/93 -3/4 1 32 56/127 -3/4 1 32 127/288 -3/4 24 1 15/34 -5/7 2 16 4/9 -1/2 1 32 17/38 1/1 2 16 43/96 1/0 8 1 13/29 1/0 1 32 9/20 0 8 14/31 1/0 1 32 19/42 -3/1 2 16 29/64 -2/1 6 1 5/11 -3/2 1 32 11/24 0 4 6/13 -5/4 1 32 13/28 0 8 7/15 -13/12 1 32 15/32 -1/1 24 1 1/2 -1/1 2 16 1/0 0/1 2 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(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(289,-39,704,-95) (2/15,1/7) -> (16/39,7/17) Hyperbolic Matrix(511,-76,1728,-257) (1/7,3/20) -> (13/44,21/71) Hyperbolic Matrix(321,-49,832,-127) (3/20,2/13) -> (5/13,17/44) Hyperbolic Matrix(129,-20,832,-129) (2/13,5/32) -> (2/13,5/32) Reflection Matrix(31,-5,192,-31) (5/32,1/6) -> (5/32,1/6) Reflection Matrix(769,-133,1856,-321) (1/6,4/23) -> (29/70,17/41) Glide Reflection Matrix(319,-56,1088,-191) (4/23,3/17) -> (12/41,5/17) Glide Reflection Matrix(417,-74,896,-159) (3/17,5/28) -> (13/28,7/15) Hyperbolic Matrix(255,-46,704,-127) (5/28,2/11) -> (13/36,4/11) Glide Reflection Matrix(97,-18,512,-95) (2/11,3/16) -> (3/16,4/21) Parabolic Matrix(225,-43,832,-159) (4/21,1/5) -> (10/37,3/11) Hyperbolic Matrix(511,-106,1856,-385) (1/5,5/24) -> (11/40,19/69) Hyperbolic Matrix(353,-74,768,-161) (5/24,4/19) -> (11/24,6/13) Glide Reflection Matrix(511,-108,1216,-257) (4/19,3/14) -> (21/50,8/19) 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(543,-122,1856,-417) (2/9,7/31) -> (19/65,12/41) Hyperbolic Matrix(897,-203,1984,-449) (7/31,5/22) -> (14/31,19/42) Glide Reflection Matrix(865,-197,2112,-481) (5/22,8/35) -> (9/22,25/61) Glide Reflection Matrix(223,-51,704,-161) (8/35,3/13) -> (6/19,1/3) 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(801,-215,1792,-481) (11/41,7/26) -> (4/9,17/38) Glide Reflection Matrix(1057,-285,2496,-673) (7/26,10/37) -> (11/26,25/59) Glide Reflection Matrix(321,-88,704,-193) (3/11,11/40) -> (5/11,11/24) Glide Reflection Matrix(3583,-987,8128,-2239) (19/69,8/29) -> (26/59,41/93) Glide Reflection Matrix(767,-212,1856,-513) (8/29,5/18) -> (19/46,12/29) 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(191,-55,448,-129) (2/7,9/31) -> (14/33,3/7) Hyperbolic Matrix(673,-196,2304,-671) (9/31,7/24) -> (7/24,19/65) Parabolic Matrix(383,-113,1088,-321) (5/17,13/44) -> (7/20,6/17) Hyperbolic Matrix(2143,-634,4864,-1439) (21/71,8/27) -> (11/25,26/59) Glide Reflection Matrix(1025,-304,3456,-1025) (8/27,19/64) -> (8/27,19/64) Reflection Matrix(191,-57,640,-191) (19/64,3/10) -> (19/64,3/10) Reflection Matrix(1153,-349,2752,-833) (3/10,10/33) -> (31/74,13/31) Glide Reflection Matrix(577,-176,1472,-449) (7/23,11/36) -> (9/23,11/28) Glide Reflection 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(287,-100,640,-223) (1/3,7/20) -> (13/29,9/20) Glide Reflection Matrix(1439,-509,3712,-1313) (6/17,17/48) -> (31/80,19/49) Hyperbolic Matrix(1537,-545,3968,-1407) (17/48,11/31) -> (12/31,31/80) Hyperbolic Matrix(833,-296,1984,-705) (11/31,5/14) -> (13/31,21/50) Glide Reflection Matrix(321,-115,896,-321) (5/14,23/64) -> (5/14,23/64) Reflection Matrix(1151,-414,3200,-1151) (23/64,9/25) -> (23/64,9/25) Reflection Matrix(1601,-577,3904,-1407) (9/25,22/61) -> (25/61,16/39) 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(961,-367,2176,-831) (21/55,13/34) -> (15/34,4/9) Hyperbolic Matrix(1665,-637,4352,-1665) (13/34,49/128) -> (13/34,49/128) Reflection Matrix(4607,-1764,12032,-4607) (49/128,18/47) -> (49/128,18/47) Reflection Matrix(895,-346,1984,-767) (17/44,12/31) -> (9/20,14/31) Glide Reflection Matrix(1057,-410,2560,-993) (19/49,7/18) -> (7/17,19/46) Glide Reflection Matrix(449,-175,1152,-449) (7/18,25/64) -> (7/18,25/64) Reflection Matrix(1151,-450,2944,-1151) (25/64,9/23) -> (25/64,9/23) Reflection Matrix(4769,-1877,10816,-4257) (24/61,13/33) -> (41/93,56/127) Glide Reflection Matrix(895,-353,2112,-833) (13/33,2/5) -> (25/59,14/33) Hyperbolic 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(3073,-1272,7424,-3073) (12/29,53/128) -> (12/29,53/128) Reflection Matrix(3711,-1537,8960,-3711) (53/128,29/70) -> (53/128,29/70) Reflection Matrix(481,-200,1152,-479) (17/41,5/12) -> (5/12,23/55) Parabolic Matrix(5761,-2412,13760,-5761) (18/43,67/160) -> (18/43,67/160) Reflection Matrix(4959,-2077,11840,-4959) (67/160,31/74) -> (67/160,31/74) 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(225,-98,512,-223) (3/7,7/16) -> (7/16,11/25) Parabolic Matrix(32257,-14224,73152,-32257) (56/127,127/288) -> (56/127,127/288) Reflection Matrix(4319,-1905,9792,-4319) (127/288,15/34) -> (127/288,15/34) 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(1,2,0,-1) *** -> (-1/1,1/0) Matrix(223,-26,832,-97) -> Matrix(1,2,2,5) Matrix(257,-34,960,-127) -> Matrix(1,2,2,5) Matrix(289,-39,704,-95) -> Matrix(1,2,-2,-3) -1/1 Matrix(511,-76,1728,-257) -> Matrix(1,2,-4,-7) Matrix(321,-49,832,-127) -> Matrix(1,2,-2,-3) -1/1 Matrix(129,-20,832,-129) -> Matrix(9,10,-8,-9) (2/13,5/32) -> (-5/4,-1/1) Matrix(31,-5,192,-31) -> Matrix(1,2,0,-1) (5/32,1/6) -> (-1/1,1/0) Matrix(769,-133,1856,-321) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(319,-56,1088,-191) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(417,-74,896,-159) -> Matrix(9,8,-8,-7) -1/1 Matrix(255,-46,704,-127) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(97,-18,512,-95) -> Matrix(3,4,-4,-5) -1/1 Matrix(225,-43,832,-159) -> Matrix(3,2,4,3) Matrix(511,-106,1856,-385) -> Matrix(1,2,0,1) 1/0 Matrix(353,-74,768,-161) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(511,-108,1216,-257) -> Matrix(1,-2,0,1) 1/0 Matrix(97,-21,448,-97) -> Matrix(1,2,0,-1) (3/14,7/32) -> (-1/1,1/0) Matrix(127,-28,576,-127) -> Matrix(3,2,-4,-3) (7/32,2/9) -> (-1/1,-1/2) Matrix(543,-122,1856,-417) -> Matrix(3,2,-2,-1) -1/1 Matrix(897,-203,1984,-449) -> Matrix(5,2,-2,-1) Matrix(865,-197,2112,-481) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(223,-51,704,-161) -> Matrix(3,2,-2,-1) -1/1 Matrix(33,-8,128,-31) -> Matrix(1,0,0,1) Matrix(417,-110,1088,-287) -> Matrix(7,2,-4,-1) Matrix(801,-215,1792,-481) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1057,-285,2496,-673) -> Matrix(7,-2,-4,1) Matrix(321,-88,704,-193) -> Matrix(3,-2,-2,1) Matrix(3583,-987,8128,-2239) -> Matrix(3,-10,-4,13) Matrix(767,-212,1856,-513) -> Matrix(1,-2,0,1) 1/0 Matrix(161,-45,576,-161) -> Matrix(-1,2,0,1) (5/18,9/32) -> (1/1,1/0) Matrix(127,-36,448,-127) -> Matrix(1,2,0,-1) (9/32,2/7) -> (-1/1,1/0) Matrix(191,-55,448,-129) -> Matrix(3,2,-2,-1) -1/1 Matrix(673,-196,2304,-671) -> Matrix(1,0,0,1) Matrix(383,-113,1088,-321) -> Matrix(3,2,-2,-1) -1/1 Matrix(2143,-634,4864,-1439) -> Matrix(13,4,-16,-5) Matrix(1025,-304,3456,-1025) -> Matrix(-1,0,12,1) (8/27,19/64) -> (-1/6,0/1) Matrix(191,-57,640,-191) -> Matrix(1,0,2,-1) (19/64,3/10) -> (0/1,1/1) Matrix(1153,-349,2752,-833) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(577,-176,1472,-449) -> Matrix(7,-2,-4,1) Matrix(385,-118,832,-255) -> Matrix(5,-6,-4,5) Matrix(161,-50,512,-159) -> Matrix(1,-4,0,1) 1/0 Matrix(287,-100,640,-223) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(1439,-509,3712,-1313) -> Matrix(1,-4,0,1) 1/0 Matrix(1537,-545,3968,-1407) -> Matrix(1,4,0,1) 1/0 Matrix(833,-296,1984,-705) -> Matrix(1,6,0,-1) *** -> (-3/1,1/0) Matrix(321,-115,896,-321) -> Matrix(5,12,-2,-5) (5/14,23/64) -> (-3/1,-2/1) Matrix(1151,-414,3200,-1151) -> Matrix(15,28,-8,-15) (23/64,9/25) -> (-2/1,-7/4) Matrix(1601,-577,3904,-1407) -> Matrix(1,2,-4,-7) Matrix(1535,-554,3904,-1409) -> Matrix(13,18,-8,-11) -3/2 Matrix(97,-36,256,-95) -> Matrix(1,0,0,1) Matrix(1473,-562,3520,-1343) -> Matrix(1,2,0,1) 1/0 Matrix(961,-367,2176,-831) -> Matrix(1,4,-2,-7) Matrix(1665,-637,4352,-1665) -> Matrix(13,28,-6,-13) (13/34,49/128) -> (-7/3,-2/1) Matrix(4607,-1764,12032,-4607) -> Matrix(39,76,-20,-39) (49/128,18/47) -> (-2/1,-19/10) Matrix(895,-346,1984,-767) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(1057,-410,2560,-993) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(449,-175,1152,-449) -> Matrix(5,12,-2,-5) (7/18,25/64) -> (-3/1,-2/1) Matrix(1151,-450,2944,-1151) -> Matrix(23,44,-12,-23) (25/64,9/23) -> (-2/1,-11/6) Matrix(4769,-1877,10816,-4257) -> Matrix(35,54,-46,-71) Matrix(895,-353,2112,-833) -> Matrix(13,18,-8,-11) -3/2 Matrix(129,-52,320,-129) -> Matrix(5,6,-4,-5) (2/5,13/32) -> (-3/2,-1/1) Matrix(287,-117,704,-287) -> Matrix(3,2,-4,-3) (13/32,9/22) -> (-1/1,-1/2) Matrix(3073,-1272,7424,-3073) -> Matrix(1,4,0,-1) (12/29,53/128) -> (-2/1,1/0) Matrix(3711,-1537,8960,-3711) -> Matrix(3,4,-2,-3) (53/128,29/70) -> (-2/1,-1/1) Matrix(481,-200,1152,-479) -> Matrix(1,0,0,1) Matrix(5761,-2412,13760,-5761) -> Matrix(-1,2,0,1) (18/43,67/160) -> (1/1,1/0) Matrix(4959,-2077,11840,-4959) -> Matrix(1,6,0,-1) (67/160,31/74) -> (-3/1,1/0) Matrix(1025,-432,2432,-1025) -> Matrix(9,20,-4,-9) (8/19,27/64) -> (-5/2,-2/1) Matrix(703,-297,1664,-703) -> Matrix(11,20,-6,-11) (27/64,11/26) -> (-2/1,-5/3) Matrix(225,-98,512,-223) -> Matrix(7,8,-8,-9) -1/1 Matrix(32257,-14224,73152,-32257) -> Matrix(247,186,-328,-247) (56/127,127/288) -> (-31/41,-3/4) Matrix(4319,-1905,9792,-4319) -> Matrix(41,30,-56,-41) (127/288,15/34) -> (-3/4,-5/7) Matrix(1633,-731,3648,-1633) -> Matrix(-1,2,0,1) (17/38,43/96) -> (1/1,1/0) Matrix(2495,-1118,5568,-2495) -> Matrix(1,6,0,-1) (43/96,13/29) -> (-3/1,1/0) Matrix(1217,-551,2688,-1217) -> Matrix(5,12,-2,-5) (19/42,29/64) -> (-3/1,-2/1) Matrix(639,-290,1408,-639) -> Matrix(7,12,-4,-7) (29/64,5/11) -> (-2/1,-3/2) Matrix(449,-210,960,-449) -> Matrix(25,26,-24,-25) (7/15,15/32) -> (-13/12,-1/1) Matrix(31,-15,64,-31) -> Matrix(1,2,0,-1) (15/32,1/2) -> (-1/1,1/0) Matrix(-1,1,0,1) -> Matrix(-1,0,2,1) (1/2,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.