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 0/1 1/1 -8/9 1/1 2/1 -7/8 1/0 -13/15 -1/1 0/1 -6/7 0/1 1/1 -17/20 1/2 -11/13 4/5 1/1 -5/6 1/1 2/1 -19/23 1/1 2/1 -14/17 9/5 2/1 -23/28 5/2 -9/11 3/1 4/1 -13/16 1/0 -17/21 -3/1 -2/1 -4/5 0/1 1/1 -19/24 1/0 -15/19 0/1 1/1 -11/14 0/1 1/1 -7/9 1/1 2/1 -24/31 1/1 4/3 -17/22 1/1 2/1 -27/35 3/1 4/1 -10/13 0/1 1/1 -3/4 1/0 -14/19 -2/1 -1/1 -11/15 -1/1 0/1 -41/56 1/0 -30/41 -1/1 0/1 -19/26 0/1 1/1 -27/37 2/1 3/1 -8/11 -1/1 0/1 -29/40 1/0 -50/69 -2/1 -1/1 -21/29 -1/1 0/1 -13/18 -1/1 0/1 -5/7 0/1 1/1 -22/31 1/1 4/3 -17/24 1/0 -46/65 -1/1 -2/3 -29/41 -1/1 0/1 -12/17 0/1 1/3 -31/44 1/2 -50/71 0/1 1/1 -19/27 0/1 1/1 -7/10 0/1 1/1 -23/33 1/1 4/3 -16/23 1/1 2/1 -25/36 3/2 -9/13 2/1 3/1 -11/16 1/0 -13/19 -4/1 -3/1 -2/3 -1/1 0/1 -13/20 1/2 -11/17 0/1 1/3 -31/48 1/2 -20/31 0/1 1/1 -9/14 0/1 1/1 -16/25 0/1 1/1 -39/61 2/3 1/1 -23/36 1/0 -7/11 2/3 1/1 -5/8 1/0 -13/21 -4/3 -1/1 -34/55 -1/1 0/1 -21/34 -1/1 0/1 -29/47 -1/1 0/1 -8/13 -2/1 -1/1 -27/44 -1/2 -19/31 -1/1 -2/3 -49/80 -1/2 -30/49 -1/1 0/1 -11/18 -1/1 0/1 -14/23 -1/1 0/1 -17/28 1/0 -37/61 -4/3 -1/1 -20/33 -1/1 -6/7 -3/5 -1/3 0/1 -13/22 0/1 1/7 -23/39 0/1 1/5 -10/17 0/1 1/3 -27/46 0/1 1/3 -17/29 0/1 1/3 -24/41 0/1 1/3 -7/12 1/2 -32/55 2/3 1/1 -25/43 6/7 1/1 -18/31 0/1 1/1 -29/50 0/1 1/1 -11/19 0/1 1/1 -15/26 0/1 1/1 -19/33 1/1 4/3 -4/7 0/1 1/1 -9/16 1/0 -14/25 -2/1 -1/1 -33/59 -2/1 -1/1 -19/34 -1/1 0/1 -5/9 -1/1 0/1 -16/29 0/1 1/3 -11/20 1/0 -17/31 -2/1 -1/1 -6/11 -1/1 0/1 -13/24 -1/2 -7/13 -1/3 0/1 -15/28 -1/6 -8/15 -1/13 0/1 -1/2 0/1 1/1 -8/17 -1/13 0/1 -15/32 0/1 -7/15 0/1 1/15 -6/13 0/1 1/5 -11/24 1/4 -5/11 0/1 1/3 -19/42 0/1 1/3 -14/31 1/3 2/5 -9/20 1/2 -13/29 -1/1 0/1 -17/38 0/1 1/5 -4/9 0/1 1/3 -7/16 1/2 -10/23 2/3 1/1 -13/30 2/3 1/1 -42/97 1/1 12/11 -29/67 1/1 2/1 -16/37 0/1 1/1 -3/7 0/1 1/1 -14/33 4/5 1/1 -25/59 2/1 3/1 -11/26 0/1 1/1 -19/45 0/1 1/1 -27/64 1/2 1/0 -8/19 0/1 1/1 -13/31 0/1 1/1 -31/74 4/5 1/1 -18/43 1/1 6/5 -5/12 1/0 -17/41 -1/1 0/1 -29/70 -1/1 0/1 -12/29 -1/1 0/1 -7/17 -1/1 0/1 -16/39 -1/3 0/1 -25/61 -1/3 -2/7 -9/22 -1/5 0/1 -11/27 -1/15 0/1 -13/32 0/1 -2/5 0/1 1/5 -13/33 6/19 1/3 -11/28 1/2 -9/23 0/1 1/3 -25/64 1/4 1/2 -16/41 0/1 1/3 -7/18 0/1 1/3 -19/49 0/1 1/3 -31/80 1/4 -12/31 2/7 1/3 -17/44 1/4 -5/13 1/3 2/5 -3/8 1/2 -7/19 0/1 1/1 -11/30 2/3 1/1 -15/41 2/3 1/1 -19/52 3/4 -4/11 1/1 2/1 -13/36 1/2 -35/97 8/9 1/1 -22/61 1/1 2/1 -9/25 0/1 1/1 -23/64 1/2 1/0 -14/39 0/1 1/1 -5/14 0/1 1/1 -11/31 0/1 1/1 -17/48 1/0 -6/17 -1/1 0/1 -7/20 1/0 -1/3 0/1 1/3 -5/16 1/2 -9/29 6/11 5/9 -4/13 3/5 2/3 -11/36 3/4 -7/23 2/3 1/1 -10/33 4/5 1/1 -13/43 10/11 1/1 -29/96 1/1 -16/53 1/1 10/9 -3/10 0/1 1/1 -11/37 0/1 1/1 -19/64 1/2 1/0 -8/27 0/1 1/1 -13/44 1/0 -5/17 -1/1 0/1 -12/41 0/1 1/3 -7/24 1/2 -9/31 4/5 1/1 -2/7 0/1 1/1 -9/32 0/1 -7/25 0/1 1/5 -5/18 0/1 1/3 -13/47 0/1 1/3 -8/29 0/1 1/3 -11/40 1/2 -3/11 0/1 1/3 -10/37 3/5 2/3 -17/63 1/1 4/3 -7/26 0/1 1/1 -25/93 -1/5 0/1 -43/160 0/1 -18/67 0/1 1/7 -11/41 0/1 1/3 -4/15 0/1 1/3 -1/4 1/2 -4/17 2/3 1/1 -15/64 1/2 3/4 -11/47 2/3 1/1 -7/30 2/3 1/1 -3/13 0/1 1/1 -8/35 4/7 3/5 -13/57 3/5 2/3 -5/22 2/3 1/1 -17/75 2/3 1/1 -29/128 1/2 3/4 -12/53 2/3 1/1 -7/31 4/5 1/1 -9/40 1/2 -2/9 2/3 1/1 -7/32 1/1 -5/23 1/1 2/1 -3/14 0/1 1/1 -7/33 0/1 1/1 -4/19 0/1 1/1 -5/24 1/2 -6/29 2/3 1/1 -13/63 12/13 1/1 -33/160 1/1 -20/97 1/1 16/15 -7/34 1/1 2/1 -1/5 0/1 1/1 -3/16 1/2 -5/27 7/13 6/11 -2/11 4/7 3/5 -5/28 5/8 -8/45 11/17 2/3 -3/17 2/3 9/13 -4/23 2/3 1/1 -5/29 2/3 1/1 -11/64 1/2 3/4 -6/35 2/3 1/1 -1/6 2/3 1/1 -3/19 8/9 1/1 -5/32 1/1 -2/13 1/1 4/3 -3/20 1/0 -4/27 0/1 1/1 -1/7 0/1 1/1 -2/15 0/1 1/3 -1/8 1/2 -2/17 2/3 1/1 -1/9 2/3 1/1 0/1 0/1 1/1 1/9 1/1 2/1 1/8 1/0 2/15 -1/1 0/1 1/7 0/1 1/1 3/20 1/2 2/13 4/5 1/1 1/6 1/1 2/1 4/23 1/1 2/1 3/17 9/5 2/1 5/28 5/2 2/11 3/1 4/1 3/16 1/0 4/21 -3/1 -2/1 1/5 0/1 1/1 5/24 1/0 4/19 0/1 1/1 3/14 0/1 1/1 2/9 1/1 2/1 7/31 1/1 4/3 5/22 1/1 2/1 8/35 3/1 4/1 3/13 0/1 1/1 1/4 1/0 5/19 -2/1 -1/1 4/15 -1/1 0/1 15/56 1/0 11/41 -1/1 0/1 7/26 0/1 1/1 10/37 2/1 3/1 3/11 -1/1 0/1 11/40 1/0 19/69 -2/1 -1/1 8/29 -1/1 0/1 5/18 -1/1 0/1 2/7 0/1 1/1 9/31 1/1 4/3 7/24 1/0 19/65 -1/1 -2/3 12/41 -1/1 0/1 5/17 0/1 1/3 13/44 1/2 21/71 0/1 1/1 8/27 0/1 1/1 3/10 0/1 1/1 10/33 1/1 4/3 7/23 1/1 2/1 11/36 3/2 4/13 2/1 3/1 5/16 1/0 6/19 -4/1 -3/1 1/3 -1/1 0/1 7/20 1/2 6/17 0/1 1/3 17/48 1/2 11/31 0/1 1/1 5/14 0/1 1/1 9/25 0/1 1/1 22/61 2/3 1/1 13/36 1/0 4/11 2/3 1/1 3/8 1/0 8/21 -4/3 -1/1 21/55 -1/1 0/1 13/34 -1/1 0/1 18/47 -1/1 0/1 5/13 -2/1 -1/1 17/44 -1/2 12/31 -1/1 -2/3 31/80 -1/2 19/49 -1/1 0/1 7/18 -1/1 0/1 9/23 -1/1 0/1 11/28 1/0 24/61 -4/3 -1/1 13/33 -1/1 -6/7 2/5 -1/3 0/1 9/22 0/1 1/7 16/39 0/1 1/5 7/17 0/1 1/3 19/46 0/1 1/3 12/29 0/1 1/3 17/41 0/1 1/3 5/12 1/2 23/55 2/3 1/1 18/43 6/7 1/1 13/31 0/1 1/1 21/50 0/1 1/1 8/19 0/1 1/1 11/26 0/1 1/1 14/33 1/1 4/3 3/7 0/1 1/1 7/16 1/0 11/25 -2/1 -1/1 26/59 -2/1 -1/1 15/34 -1/1 0/1 4/9 -1/1 0/1 13/29 0/1 1/3 9/20 1/0 14/31 -2/1 -1/1 5/11 -1/1 0/1 11/24 -1/2 6/13 -1/3 0/1 13/28 -1/6 7/15 -1/13 0/1 1/2 0/1 1/1 9/17 -1/13 0/1 17/32 0/1 8/15 0/1 1/15 7/13 0/1 1/5 13/24 1/4 6/11 0/1 1/3 23/42 0/1 1/3 17/31 1/3 2/5 11/20 1/2 16/29 -1/1 0/1 21/38 0/1 1/5 5/9 0/1 1/3 9/16 1/2 13/23 2/3 1/1 17/30 2/3 1/1 55/97 1/1 12/11 38/67 1/1 2/1 21/37 0/1 1/1 4/7 0/1 1/1 19/33 4/5 1/1 34/59 2/1 3/1 15/26 0/1 1/1 26/45 0/1 1/1 37/64 1/2 1/0 11/19 0/1 1/1 18/31 0/1 1/1 43/74 4/5 1/1 25/43 1/1 6/5 7/12 1/0 24/41 -1/1 0/1 41/70 -1/1 0/1 17/29 -1/1 0/1 10/17 -1/1 0/1 23/39 -1/3 0/1 36/61 -1/3 -2/7 13/22 -1/5 0/1 16/27 -1/15 0/1 19/32 0/1 3/5 0/1 1/5 20/33 6/19 1/3 17/28 1/2 14/23 0/1 1/3 39/64 1/4 1/2 25/41 0/1 1/3 11/18 0/1 1/3 30/49 0/1 1/3 49/80 1/4 19/31 2/7 1/3 27/44 1/4 8/13 1/3 2/5 5/8 1/2 12/19 0/1 1/1 19/30 2/3 1/1 26/41 2/3 1/1 33/52 3/4 7/11 1/1 2/1 23/36 1/2 62/97 8/9 1/1 39/61 1/1 2/1 16/25 0/1 1/1 41/64 1/2 1/0 25/39 0/1 1/1 9/14 0/1 1/1 20/31 0/1 1/1 31/48 1/0 11/17 -1/1 0/1 13/20 1/0 2/3 0/1 1/3 11/16 1/2 20/29 6/11 5/9 9/13 3/5 2/3 25/36 3/4 16/23 2/3 1/1 23/33 4/5 1/1 30/43 10/11 1/1 67/96 1/1 37/53 1/1 10/9 7/10 0/1 1/1 26/37 0/1 1/1 45/64 1/2 1/0 19/27 0/1 1/1 31/44 1/0 12/17 -1/1 0/1 29/41 0/1 1/3 17/24 1/2 22/31 4/5 1/1 5/7 0/1 1/1 23/32 0/1 18/25 0/1 1/5 13/18 0/1 1/3 34/47 0/1 1/3 21/29 0/1 1/3 29/40 1/2 8/11 0/1 1/3 27/37 3/5 2/3 46/63 1/1 4/3 19/26 0/1 1/1 68/93 -1/5 0/1 117/160 0/1 49/67 0/1 1/7 30/41 0/1 1/3 11/15 0/1 1/3 3/4 1/2 13/17 2/3 1/1 49/64 1/2 3/4 36/47 2/3 1/1 23/30 2/3 1/1 10/13 0/1 1/1 27/35 4/7 3/5 44/57 3/5 2/3 17/22 2/3 1/1 58/75 2/3 1/1 99/128 1/2 3/4 41/53 2/3 1/1 24/31 4/5 1/1 31/40 1/2 7/9 2/3 1/1 25/32 1/1 18/23 1/1 2/1 11/14 0/1 1/1 26/33 0/1 1/1 15/19 0/1 1/1 19/24 1/2 23/29 2/3 1/1 50/63 12/13 1/1 127/160 1/1 77/97 1/1 16/15 27/34 1/1 2/1 4/5 0/1 1/1 13/16 1/2 22/27 7/13 6/11 9/11 4/7 3/5 23/28 5/8 37/45 11/17 2/3 14/17 2/3 9/13 19/23 2/3 1/1 24/29 2/3 1/1 53/64 1/2 3/4 29/35 2/3 1/1 5/6 2/3 1/1 16/19 8/9 1/1 27/32 1/1 11/13 1/1 4/3 17/20 1/0 23/27 0/1 1/1 6/7 0/1 1/1 13/15 0/1 1/3 7/8 1/2 15/17 2/3 1/1 8/9 2/3 1/1 1/1 0/1 1/1 1/0 1/2 1/0 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(1,0,0,1) Matrix(223,200,320,287) -> Matrix(3,-4,4,-5) Matrix(609,538,-832,-735) -> Matrix(1,-2,0,1) Matrix(703,610,-960,-833) -> Matrix(1,0,0,1) Matrix(289,250,704,609) -> Matrix(1,0,4,1) Matrix(1217,1036,-1728,-1471) -> Matrix(1,0,0,1) Matrix(321,272,832,705) -> Matrix(3,-2,-4,3) Matrix(31,26,-192,-161) -> Matrix(3,-4,4,-5) Matrix(769,636,-1856,-1535) -> Matrix(1,-2,0,1) Matrix(769,634,1088,897) -> Matrix(1,-2,4,-7) Matrix(479,394,-896,-737) -> Matrix(1,-2,-8,17) Matrix(449,368,704,577) -> Matrix(1,-2,0,1) Matrix(415,338,-512,-417) -> Matrix(1,-6,0,1) Matrix(225,182,832,673) -> Matrix(1,2,0,1) Matrix(1345,1066,-1856,-1471) -> Matrix(1,-2,0,1) Matrix(415,328,768,607) -> Matrix(1,0,4,1) Matrix(705,556,-1216,-959) -> Matrix(1,0,0,1) Matrix(97,76,-448,-351) -> Matrix(1,0,0,1) Matrix(1313,1018,-1856,-1439) -> Matrix(1,-2,0,1) Matrix(897,694,-1984,-1535) -> Matrix(1,-2,4,-7) Matrix(865,668,-2112,-1631) -> Matrix(1,-2,-4,9) Matrix(223,172,704,543) -> Matrix(1,-4,0,1) Matrix(95,72,-128,-97) -> Matrix(1,-2,0,1) Matrix(671,494,-1088,-801) -> Matrix(1,0,0,1) Matrix(801,586,-1792,-1311) -> Matrix(1,0,4,1) Matrix(1057,772,-2496,-1823) -> Matrix(1,0,0,1) Matrix(159,116,832,607) -> Matrix(1,-2,0,1) Matrix(383,278,704,511) -> Matrix(1,0,4,1) Matrix(2465,1786,-5696,-4127) -> Matrix(1,2,0,1) Matrix(1089,788,-1856,-1343) -> Matrix(1,0,4,1) Matrix(161,116,-576,-415) -> Matrix(1,0,4,1) Matrix(191,136,448,319) -> Matrix(1,0,0,1) Matrix(1631,1156,-2304,-1633) -> Matrix(1,-2,0,1) Matrix(897,634,1088,769) -> Matrix(3,2,4,3) Matrix(383,270,1088,767) -> Matrix(1,0,0,1) Matrix(1599,1126,2816,1983) -> Matrix(1,0,0,1) Matrix(191,134,-640,-449) -> Matrix(1,0,0,1) Matrix(1153,804,-2752,-1919) -> Matrix(3,-4,4,-5) Matrix(287,200,320,223) -> Matrix(3,-4,4,-5) Matrix(895,622,1472,1023) -> Matrix(1,-2,4,-7) Matrix(447,310,-832,-577) -> Matrix(1,-2,-4,9) Matrix(351,242,-512,-353) -> Matrix(1,-6,0,1) Matrix(161,110,704,481) -> Matrix(1,4,0,1) Matrix(353,230,640,417) -> Matrix(1,0,0,1) Matrix(321,208,1088,705) -> Matrix(1,0,0,1) Matrix(1439,930,3712,2399) -> Matrix(1,0,-4,1) Matrix(1537,992,3968,2561) -> Matrix(3,-2,-4,3) Matrix(705,454,896,577) -> Matrix(1,0,0,1) Matrix(321,206,-896,-575) -> Matrix(1,0,0,1) Matrix(3359,2148,4352,2783) -> Matrix(5,-2,8,-3) Matrix(2369,1514,-3904,-2495) -> Matrix(1,-2,0,1) Matrix(577,368,704,449) -> Matrix(5,-2,8,-3) Matrix(159,100,-256,-161) -> Matrix(1,-2,0,1) Matrix(2047,1266,-3520,-2177) -> Matrix(3,2,4,3) Matrix(961,594,2176,1345) -> Matrix(1,0,0,1) Matrix(703,434,-3008,-1857) -> Matrix(3,2,4,3) Matrix(127,78,832,511) -> Matrix(3,2,4,3) Matrix(1089,668,1984,1217) -> Matrix(1,0,4,1) Matrix(1407,862,3968,2431) -> Matrix(3,2,4,3) Matrix(1313,804,3712,2273) -> Matrix(1,0,4,1) Matrix(1249,764,1728,1057) -> Matrix(1,0,4,1) Matrix(449,274,-1152,-703) -> Matrix(1,0,4,1) Matrix(1023,622,1472,895) -> Matrix(3,2,4,3) Matrix(3519,2134,-8128,-4929) -> Matrix(5,6,4,5) Matrix(1121,678,1536,929) -> Matrix(3,2,4,3) Matrix(287,170,-704,-417) -> Matrix(1,0,-12,1) Matrix(481,284,-2112,-1247) -> Matrix(13,-2,20,-3) Matrix(95,56,704,415) -> Matrix(1,0,-4,1) Matrix(1567,920,2560,1503) -> Matrix(1,0,0,1) Matrix(321,188,-1856,-1087) -> Matrix(5,-2,8,-3) Matrix(671,392,-1152,-673) -> Matrix(5,-2,8,-3) Matrix(833,484,-2752,-1599) -> Matrix(3,-4,4,-5) Matrix(1279,742,1984,1151) -> Matrix(1,0,0,1) Matrix(703,406,-1664,-961) -> Matrix(1,0,0,1) Matrix(673,388,-2496,-1439) -> Matrix(1,0,0,1) Matrix(129,74,448,257) -> Matrix(1,0,0,1) Matrix(287,162,-512,-289) -> Matrix(1,-2,0,1) Matrix(929,520,1088,609) -> Matrix(1,2,0,1) Matrix(447,250,-2176,-1217) -> Matrix(1,2,0,1) Matrix(831,464,2176,1215) -> Matrix(1,0,0,1) Matrix(481,266,-1792,-991) -> Matrix(1,0,4,1) Matrix(417,230,640,353) -> Matrix(1,0,0,1) Matrix(1217,668,1984,1089) -> Matrix(1,0,4,1) Matrix(449,246,-1984,-1087) -> Matrix(3,2,4,3) Matrix(511,278,704,383) -> Matrix(1,0,4,1) Matrix(607,328,768,415) -> Matrix(1,0,4,1) Matrix(31,16,-64,-33) -> Matrix(1,0,0,1) Matrix(545,256,1024,481) -> Matrix(1,0,28,1) Matrix(543,254,1024,479) -> Matrix(1,0,-28,1) Matrix(159,74,-896,-417) -> Matrix(21,-2,32,-3) Matrix(161,74,768,353) -> Matrix(1,0,-4,1) Matrix(193,88,704,321) -> Matrix(1,0,-4,1) Matrix(769,348,-3392,-1535) -> Matrix(5,-2,8,-3) Matrix(767,346,1984,895) -> Matrix(1,0,-4,1) Matrix(223,100,640,287) -> Matrix(1,0,0,1) Matrix(1153,516,-4288,-1919) -> Matrix(1,0,-4,1) Matrix(223,98,-512,-225) -> Matrix(5,-2,8,-3) Matrix(1217,528,1920,833) -> Matrix(1,0,0,1) Matrix(1279,554,-6208,-2689) -> Matrix(5,-4,4,-3) Matrix(833,360,2816,1217) -> Matrix(1,0,0,1) Matrix(319,136,448,191) -> Matrix(1,0,0,1) Matrix(1279,542,2112,895) -> Matrix(1,-2,4,-7) Matrix(2369,1000,4096,1729) -> Matrix(1,0,0,1) Matrix(2367,998,4096,1727) -> Matrix(1,0,0,1) Matrix(257,108,-1216,-511) -> Matrix(1,0,0,1) Matrix(1313,550,-4352,-1823) -> Matrix(5,-4,4,-3) Matrix(865,362,-2368,-991) -> Matrix(3,-4,4,-5) Matrix(959,398,-2624,-1089) -> Matrix(3,2,4,3) Matrix(449,186,-2624,-1087) -> Matrix(3,2,4,3) Matrix(513,212,-1856,-767) -> Matrix(1,0,4,1) Matrix(609,250,704,289) -> Matrix(1,0,4,1) Matrix(2497,1024,3904,1601) -> Matrix(1,0,4,1) Matrix(609,248,1024,417) -> Matrix(1,0,20,1) Matrix(607,246,1024,415) -> Matrix(1,0,-20,1) Matrix(1217,480,2112,833) -> Matrix(7,-2,4,-1) Matrix(1409,554,-3904,-1535) -> Matrix(5,-2,8,-3) Matrix(449,176,1472,577) -> Matrix(7,-2,4,-1) Matrix(2497,976,4096,1601) -> Matrix(1,0,0,1) Matrix(2495,974,4096,1599) -> Matrix(1,0,0,1) Matrix(1057,410,2560,993) -> Matrix(1,0,0,1) Matrix(2399,930,3712,1439) -> Matrix(1,0,-4,1) Matrix(2561,992,3968,1537) -> Matrix(7,-2,4,-1) Matrix(895,346,1984,767) -> Matrix(1,0,-4,1) Matrix(705,272,832,321) -> Matrix(7,-2,4,-1) Matrix(95,36,-256,-97) -> Matrix(5,-2,8,-3) Matrix(223,82,-960,-353) -> Matrix(1,0,0,1) Matrix(1087,398,1920,703) -> Matrix(1,0,0,1) Matrix(127,46,704,255) -> Matrix(1,2,0,1) Matrix(1375,496,-6656,-2401) -> Matrix(3,-4,4,-5) Matrix(2303,830,3904,1407) -> Matrix(1,0,-4,1) Matrix(2625,944,4096,1473) -> Matrix(1,0,0,1) Matrix(2623,942,4096,1471) -> Matrix(1,0,0,1) Matrix(833,296,1984,705) -> Matrix(1,0,0,1) Matrix(2431,862,3968,1407) -> Matrix(1,-2,4,-7) Matrix(2273,804,3712,1313) -> Matrix(1,0,4,1) Matrix(767,270,1088,383) -> Matrix(1,0,0,1) Matrix(287,100,640,223) -> Matrix(1,0,0,1) Matrix(159,50,-512,-161) -> Matrix(13,-6,24,-11) Matrix(641,198,832,257) -> Matrix(3,-2,8,-5) Matrix(353,108,-1984,-607) -> Matrix(23,-16,36,-25) Matrix(577,176,1472,449) -> Matrix(3,-2,-4,3) Matrix(33,10,320,97) -> Matrix(5,-4,4,-3) Matrix(6433,1944,9216,2785) -> Matrix(21,-20,20,-19) Matrix(6431,1942,9216,2783) -> Matrix(19,-20,20,-21) Matrix(2881,856,4096,1217) -> Matrix(1,0,0,1) Matrix(2879,854,4096,1215) -> Matrix(1,0,0,1) Matrix(257,76,-1728,-511) -> Matrix(1,0,0,1) Matrix(705,208,1088,321) -> Matrix(1,0,0,1) Matrix(191,56,1088,319) -> Matrix(7,-2,4,-1) Matrix(417,122,-1856,-543) -> Matrix(5,-2,8,-3) Matrix(447,130,-1984,-577) -> Matrix(1,0,0,1) Matrix(257,74,448,129) -> Matrix(1,0,0,1) Matrix(737,208,1024,289) -> Matrix(1,0,4,1) Matrix(735,206,1024,287) -> Matrix(1,0,-4,1) Matrix(671,186,1728,479) -> Matrix(1,0,-4,1) Matrix(385,106,-1856,-511) -> Matrix(5,-2,8,-3) Matrix(321,88,704,193) -> Matrix(1,0,-4,1) Matrix(575,156,704,191) -> Matrix(9,-4,16,-7) Matrix(607,164,1536,415) -> Matrix(3,-2,-4,3) Matrix(18721,5032,25600,6881) -> Matrix(1,0,12,1) Matrix(18719,5030,25600,6879) -> Matrix(1,0,-12,1) Matrix(97,26,-832,-223) -> Matrix(5,-2,8,-3) Matrix(31,8,-128,-33) -> Matrix(5,-2,8,-3) Matrix(3137,736,4096,961) -> Matrix(1,0,0,1) Matrix(3135,734,4096,959) -> Matrix(1,0,0,1) Matrix(575,132,832,191) -> Matrix(5,-2,8,-3) Matrix(1569,358,4352,993) -> Matrix(3,-2,8,-5) Matrix(12673,2872,16384,3713) -> Matrix(1,0,0,1) Matrix(12671,2870,16384,3711) -> Matrix(1,0,0,1) Matrix(801,176,1024,225) -> Matrix(5,-4,4,-3) Matrix(799,174,1024,223) -> Matrix(3,-4,4,-5) Matrix(319,68,896,191) -> Matrix(1,0,0,1) Matrix(353,74,768,161) -> Matrix(1,0,-4,1) Matrix(20321,4192,25600,5281) -> Matrix(29,-28,28,-27) Matrix(20319,4190,25600,5279) -> Matrix(27,-28,28,-29) Matrix(95,18,-512,-97) -> Matrix(13,-6,24,-11) Matrix(513,94,704,129) -> Matrix(7,-4,16,-9) Matrix(255,46,704,127) -> Matrix(3,-2,8,-5) Matrix(319,56,1088,191) -> Matrix(3,-2,-4,3) Matrix(3393,584,4096,705) -> Matrix(1,0,0,1) Matrix(3391,582,4096,703) -> Matrix(1,0,0,1) Matrix(865,136,1024,161) -> Matrix(13,-12,12,-11) Matrix(863,134,1024,159) -> Matrix(11,-12,12,-13) Matrix(511,78,832,127) -> Matrix(1,-2,4,-7) Matrix(479,70,1088,159) -> Matrix(1,-2,0,1) Matrix(415,56,704,95) -> Matrix(1,0,-4,1) Matrix(31,4,-256,-33) -> Matrix(5,-2,8,-3) Matrix(97,10,320,33) -> Matrix(5,-4,4,-3) Matrix(223,-26,832,-97) -> Matrix(1,-2,0,1) Matrix(257,-34,960,-127) -> Matrix(1,0,0,1) Matrix(511,-76,1728,-257) -> Matrix(1,0,0,1) Matrix(161,-26,192,-31) -> Matrix(3,-4,4,-5) Matrix(1087,-188,1856,-321) -> Matrix(1,-2,0,1) Matrix(417,-74,896,-159) -> Matrix(1,-2,-8,17) Matrix(97,-18,512,-95) -> Matrix(1,-6,0,1) Matrix(511,-106,1856,-385) -> Matrix(1,-2,0,1) Matrix(511,-108,1216,-257) -> Matrix(1,0,0,1) Matrix(351,-76,448,-97) -> Matrix(1,0,0,1) Matrix(543,-122,1856,-417) -> Matrix(1,-2,0,1) Matrix(1087,-246,1984,-449) -> Matrix(1,-2,4,-7) Matrix(1247,-284,2112,-481) -> Matrix(1,-2,-4,9) Matrix(33,-8,128,-31) -> Matrix(1,-2,0,1) Matrix(417,-110,1088,-287) -> Matrix(1,0,0,1) Matrix(991,-266,1792,-481) -> Matrix(1,0,4,1) Matrix(1439,-388,2496,-673) -> Matrix(1,0,0,1) Matrix(3231,-890,5696,-1569) -> Matrix(1,2,0,1) Matrix(767,-212,1856,-513) -> Matrix(1,0,4,1) Matrix(415,-116,576,-161) -> Matrix(1,0,4,1) Matrix(673,-196,2304,-671) -> Matrix(1,-2,0,1) Matrix(449,-134,640,-191) -> Matrix(1,0,0,1) Matrix(1599,-484,2752,-833) -> Matrix(3,-4,4,-5) Matrix(385,-118,832,-255) -> Matrix(1,-2,-4,9) Matrix(161,-50,512,-159) -> Matrix(1,-6,0,1) Matrix(575,-206,896,-321) -> Matrix(1,0,0,1) Matrix(1535,-554,3904,-1409) -> Matrix(1,-2,0,1) Matrix(97,-36,256,-95) -> Matrix(1,-2,0,1) Matrix(1473,-562,3520,-1343) -> Matrix(3,2,4,3) Matrix(2305,-882,3008,-1151) -> Matrix(3,2,4,3) Matrix(703,-274,1152,-449) -> Matrix(1,0,4,1) Matrix(4609,-1814,8128,-3199) -> Matrix(5,6,4,5) Matrix(417,-170,704,-287) -> Matrix(1,0,-12,1) Matrix(1631,-668,2112,-865) -> Matrix(13,-2,20,-3) Matrix(1535,-636,1856,-769) -> Matrix(5,-2,8,-3) Matrix(481,-200,1152,-479) -> Matrix(5,-2,8,-3) Matrix(1919,-804,2752,-1153) -> Matrix(3,-4,4,-5) Matrix(961,-406,1664,-703) -> Matrix(1,0,0,1) Matrix(1823,-772,2496,-1057) -> Matrix(1,0,0,1) Matrix(225,-98,512,-223) -> Matrix(1,-2,0,1) Matrix(1729,-762,2176,-959) -> Matrix(1,2,0,1) Matrix(1311,-586,1792,-801) -> Matrix(1,0,4,1) Matrix(1535,-694,1984,-897) -> Matrix(3,2,4,3) Matrix(33,-16,64,-31) -> Matrix(1,0,0,1) Matrix(737,-394,896,-479) -> Matrix(21,-2,32,-3) Matrix(2623,-1436,3392,-1857) -> Matrix(5,-2,8,-3) Matrix(3135,-1732,4288,-2369) -> Matrix(1,0,-4,1) Matrix(289,-162,512,-287) -> Matrix(5,-2,8,-3) Matrix(4929,-2794,6208,-3519) -> Matrix(5,-4,4,-3) Matrix(959,-556,1216,-705) -> Matrix(1,0,0,1) Matrix(3039,-1766,4352,-2529) -> Matrix(5,-4,4,-3) Matrix(1503,-874,2368,-1377) -> Matrix(3,-4,4,-5) Matrix(1665,-974,2624,-1535) -> Matrix(3,2,4,3) Matrix(2175,-1274,2624,-1537) -> Matrix(3,2,4,3) Matrix(1343,-788,1856,-1089) -> Matrix(1,0,4,1) Matrix(2495,-1514,3904,-2369) -> Matrix(5,-2,8,-3) Matrix(161,-100,256,-159) -> Matrix(5,-2,8,-3) Matrix(737,-466,960,-607) -> Matrix(1,0,0,1) Matrix(5281,-3376,6656,-4255) -> Matrix(3,-4,4,-5) Matrix(353,-242,512,-351) -> Matrix(13,-6,24,-11) Matrix(1631,-1132,1984,-1377) -> Matrix(23,-16,36,-25) Matrix(1471,-1036,1728,-1217) -> Matrix(1,0,0,1) Matrix(1439,-1018,1856,-1313) -> Matrix(5,-2,8,-3) Matrix(1537,-1090,1984,-1407) -> Matrix(1,0,0,1) Matrix(1471,-1066,1856,-1345) -> Matrix(5,-2,8,-3) Matrix(735,-538,832,-609) -> Matrix(5,-2,8,-3) Matrix(97,-72,128,-95) -> Matrix(5,-2,8,-3) Matrix(417,-338,512,-415) -> Matrix(13,-6,24,-11) Matrix(225,-196,256,-223) -> Matrix(5,-2,8,-3) 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): 32 Degree of the the map X: 64 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: 40 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/8 1/7 1/6 5/28 3/16 1/5 1/4 7/24 3/10 5/16 1/3 3/8 31/80 11/28 5/12 7/16 9/20 11/24 1/2 17/32 13/24 11/20 9/16 37/64 7/12 19/32 5/8 41/64 9/14 31/48 11/16 45/64 17/24 3/4 25/32 13/16 27/32 7/8 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/8 1/0 2/15 -1/1 0/1 1/7 0/1 1/1 2/13 4/5 1/1 1/6 1/1 2/1 3/17 9/5 2/1 5/28 5/2 2/11 3/1 4/1 3/16 1/0 1/5 0/1 1/1 1/4 1/0 3/11 -1/1 0/1 11/40 1/0 8/29 -1/1 0/1 5/18 -1/1 0/1 2/7 0/1 1/1 7/24 1/0 12/41 -1/1 0/1 5/17 0/1 1/3 8/27 0/1 1/1 3/10 0/1 1/1 7/23 1/1 2/1 11/36 3/2 4/13 2/1 3/1 5/16 1/0 1/3 -1/1 0/1 3/8 1/0 5/13 -2/1 -1/1 17/44 -1/2 12/31 -1/1 -2/3 31/80 -1/2 19/49 -1/1 0/1 7/18 -1/1 0/1 9/23 -1/1 0/1 11/28 1/0 2/5 -1/3 0/1 9/22 0/1 1/7 7/17 0/1 1/3 5/12 1/2 13/31 0/1 1/1 21/50 0/1 1/1 8/19 0/1 1/1 11/26 0/1 1/1 3/7 0/1 1/1 7/16 1/0 4/9 -1/1 0/1 9/20 1/0 5/11 -1/1 0/1 11/24 -1/2 6/13 -1/3 0/1 13/28 -1/6 7/15 -1/13 0/1 1/2 0/1 1/1 9/17 -1/13 0/1 17/32 0/1 8/15 0/1 1/15 7/13 0/1 1/5 13/24 1/4 6/11 0/1 1/3 17/31 1/3 2/5 11/20 1/2 16/29 -1/1 0/1 5/9 0/1 1/3 9/16 1/2 4/7 0/1 1/1 19/33 4/5 1/1 15/26 0/1 1/1 26/45 0/1 1/1 37/64 1/2 1/0 11/19 0/1 1/1 7/12 1/0 17/29 -1/1 0/1 10/17 -1/1 0/1 23/39 -1/3 0/1 13/22 -1/5 0/1 16/27 -1/15 0/1 19/32 0/1 3/5 0/1 1/5 5/8 1/2 7/11 1/1 2/1 23/36 1/2 16/25 0/1 1/1 41/64 1/2 1/0 25/39 0/1 1/1 9/14 0/1 1/1 20/31 0/1 1/1 31/48 1/0 11/17 -1/1 0/1 13/20 1/0 2/3 0/1 1/3 11/16 1/2 9/13 3/5 2/3 25/36 3/4 16/23 2/3 1/1 23/33 4/5 1/1 7/10 0/1 1/1 26/37 0/1 1/1 45/64 1/2 1/0 19/27 0/1 1/1 31/44 1/0 12/17 -1/1 0/1 17/24 1/2 22/31 4/5 1/1 5/7 0/1 1/1 3/4 1/2 7/9 2/3 1/1 25/32 1/1 18/23 1/1 2/1 11/14 0/1 1/1 26/33 0/1 1/1 15/19 0/1 1/1 19/24 1/2 4/5 0/1 1/1 13/16 1/2 9/11 4/7 3/5 23/28 5/8 37/45 11/17 2/3 14/17 2/3 9/13 19/23 2/3 1/1 5/6 2/3 1/1 16/19 8/9 1/1 27/32 1/1 11/13 1/1 4/3 17/20 1/0 6/7 0/1 1/1 7/8 1/2 8/9 2/3 1/1 1/1 0/1 1/1 1/0 1/2 1/0 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(17,-2,128,-15) (0/1,1/8) -> (1/8,2/15) Parabolic Matrix(401,-55,576,-79) (2/15,1/7) -> (16/23,23/33) Hyperbolic Matrix(177,-26,320,-47) (1/7,2/13) -> (16/29,5/9) Hyperbolic Matrix(161,-26,192,-31) (2/13,1/6) -> (5/6,16/19) Hyperbolic Matrix(369,-64,640,-111) (1/6,3/17) -> (19/33,15/26) 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(49,-9,256,-47) (2/11,3/16) -> (3/16,1/5) Parabolic Matrix(17,-4,64,-15) (1/5,1/4) -> (1/4,3/11) Parabolic Matrix(383,-105,704,-193) (3/11,11/40) -> (13/24,6/11) Hyperbolic Matrix(657,-181,1216,-335) (11/40,8/29) -> (7/13,13/24) Hyperbolic Matrix(753,-208,1792,-495) (8/29,5/18) -> (21/50,8/19) Hyperbolic Matrix(401,-112,512,-143) (5/18,2/7) -> (18/23,11/14) Hyperbolic Matrix(337,-98,1152,-335) (2/7,7/24) -> (7/24,12/41) Parabolic Matrix(897,-263,1088,-319) (12/41,5/17) -> (14/17,19/23) Hyperbolic Matrix(561,-166,1024,-303) (5/17,8/27) -> (6/11,17/31) Hyperbolic Matrix(449,-134,640,-191) (8/27,3/10) -> (7/10,26/37) Hyperbolic Matrix(529,-160,896,-271) (3/10,7/23) -> (23/39,13/22) Hyperbolic Matrix(1105,-337,1728,-527) (7/23,11/36) -> (23/36,16/25) Hyperbolic Matrix(385,-118,832,-255) (11/36,4/13) -> (6/13,13/28) Hyperbolic Matrix(81,-25,256,-79) (4/13,5/16) -> (5/16,1/3) Parabolic Matrix(49,-18,128,-47) (1/3,3/8) -> (3/8,5/13) Parabolic Matrix(847,-327,1536,-593) (5/13,17/44) -> (11/20,16/29) Hyperbolic Matrix(1089,-421,1984,-767) (17/44,12/31) -> (17/31,11/20) Hyperbolic Matrix(2481,-961,6400,-2479) (12/31,31/80) -> (31/80,19/49) Parabolic Matrix(1007,-391,1280,-497) (19/49,7/18) -> (11/14,26/33) Hyperbolic Matrix(657,-256,1024,-399) (7/18,9/23) -> (25/39,9/14) Hyperbolic Matrix(1023,-401,1472,-577) (9/23,11/28) -> (25/36,16/23) Hyperbolic Matrix(367,-145,448,-177) (11/28,2/5) -> (9/11,23/28) Hyperbolic Matrix(417,-170,704,-287) (2/5,9/22) -> (13/22,16/27) Hyperbolic Matrix(625,-256,896,-367) (9/22,7/17) -> (23/33,7/10) Hyperbolic Matrix(241,-100,576,-239) (7/17,5/12) -> (5/12,13/31) Parabolic 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(529,-224,640,-271) (11/26,3/7) -> (19/23,5/6) Hyperbolic Matrix(113,-49,256,-111) (3/7,7/16) -> (7/16,4/9) Parabolic Matrix(273,-122,320,-143) (4/9,9/20) -> (17/20,6/7) Hyperbolic Matrix(721,-326,1024,-463) (9/20,5/11) -> (19/27,31/44) Hyperbolic Matrix(305,-139,384,-175) (5/11,11/24) -> (19/24,4/5) 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(145,-81,256,-143) (5/9,9/16) -> (9/16,4/7) Parabolic Matrix(319,-183,448,-257) (4/7,19/33) -> (22/31,5/7) Hyperbolic Matrix(2369,-1369,4096,-2367) (26/45,37/64) -> (37/64,11/19) Parabolic Matrix(337,-196,576,-335) (11/19,7/12) -> (7/12,17/29) Parabolic Matrix(1009,-592,1280,-751) (17/29,10/17) -> (26/33,15/19) Hyperbolic Matrix(175,-103,192,-113) (10/17,23/39) -> (8/9,1/1) Hyperbolic Matrix(609,-361,1024,-607) (16/27,19/32) -> (19/32,3/5) Parabolic Matrix(81,-50,128,-79) (3/5,5/8) -> (5/8,7/11) Parabolic Matrix(2625,-1681,4096,-2623) (16/25,41/64) -> (41/64,25/39) Parabolic Matrix(1489,-961,2304,-1487) (20/31,31/48) -> (31/48,11/17) Parabolic Matrix(767,-497,1088,-705) (11/17,13/20) -> (31/44,12/17) Hyperbolic Matrix(271,-177,320,-209) (13/20,2/3) -> (11/13,17/20) Hyperbolic Matrix(177,-121,256,-175) (2/3,11/16) -> (11/16,9/13) Parabolic Matrix(1631,-1132,1984,-1377) (9/13,25/36) -> (23/28,37/45) Hyperbolic Matrix(2881,-2025,4096,-2879) (26/37,45/64) -> (45/64,19/27) Parabolic Matrix(817,-578,1152,-815) (12/17,17/24) -> (17/24,22/31) Parabolic Matrix(49,-36,64,-47) (5/7,3/4) -> (3/4,7/9) Parabolic Matrix(801,-625,1024,-799) (7/9,25/32) -> (25/32,18/23) Parabolic Matrix(209,-169,256,-207) (4/5,13/16) -> (13/16,9/11) Parabolic Matrix(865,-729,1024,-863) (16/19,27/32) -> (27/32,11/13) Parabolic Matrix(113,-98,128,-111) (6/7,7/8) -> (7/8,8/9) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,0,1) Matrix(17,-2,128,-15) -> Matrix(1,-1,0,1) Matrix(401,-55,576,-79) -> Matrix(3,-1,4,-1) Matrix(177,-26,320,-47) -> Matrix(1,-1,4,-3) Matrix(161,-26,192,-31) -> Matrix(3,-4,4,-5) Matrix(369,-64,640,-111) -> Matrix(1,-1,0,1) Matrix(417,-74,896,-159) -> Matrix(1,-2,-8,17) Matrix(449,-81,704,-127) -> Matrix(1,-2,0,1) Matrix(49,-9,256,-47) -> Matrix(1,-3,0,1) Matrix(17,-4,64,-15) -> Matrix(1,-1,0,1) Matrix(383,-105,704,-193) -> Matrix(1,0,4,1) Matrix(657,-181,1216,-335) -> Matrix(1,1,4,5) Matrix(753,-208,1792,-495) -> Matrix(1,1,0,1) Matrix(401,-112,512,-143) -> Matrix(1,1,0,1) Matrix(337,-98,1152,-335) -> Matrix(1,-1,0,1) Matrix(897,-263,1088,-319) -> Matrix(3,2,4,3) Matrix(561,-166,1024,-303) -> Matrix(1,-1,4,-3) Matrix(449,-134,640,-191) -> Matrix(1,0,0,1) Matrix(529,-160,896,-271) -> Matrix(1,-1,-4,5) Matrix(1105,-337,1728,-527) -> Matrix(1,-1,0,1) Matrix(385,-118,832,-255) -> Matrix(1,-2,-4,9) Matrix(81,-25,256,-79) -> Matrix(1,-3,0,1) Matrix(49,-18,128,-47) -> Matrix(1,-1,0,1) Matrix(847,-327,1536,-593) -> Matrix(1,1,0,1) Matrix(1089,-421,1984,-767) -> Matrix(1,0,4,1) Matrix(2481,-961,6400,-2479) -> Matrix(1,1,-4,-3) Matrix(1007,-391,1280,-497) -> Matrix(1,1,0,1) Matrix(657,-256,1024,-399) -> Matrix(1,1,0,1) Matrix(1023,-401,1472,-577) -> Matrix(3,2,4,3) Matrix(367,-145,448,-177) -> Matrix(5,3,8,5) Matrix(417,-170,704,-287) -> Matrix(1,0,-12,1) Matrix(625,-256,896,-367) -> Matrix(7,-1,8,-1) Matrix(241,-100,576,-239) -> Matrix(3,-1,4,-1) Matrix(1279,-537,1984,-833) -> Matrix(1,0,0,1) Matrix(961,-406,1664,-703) -> Matrix(1,0,0,1) Matrix(529,-224,640,-271) -> Matrix(3,-1,4,-1) Matrix(113,-49,256,-111) -> Matrix(1,-1,0,1) Matrix(273,-122,320,-143) -> Matrix(1,1,0,1) Matrix(721,-326,1024,-463) -> Matrix(1,1,0,1) Matrix(305,-139,384,-175) -> Matrix(1,1,0,1) Matrix(607,-279,768,-353) -> Matrix(1,0,4,1) Matrix(33,-16,64,-31) -> Matrix(1,0,0,1) Matrix(545,-289,1024,-543) -> Matrix(1,0,28,1) Matrix(737,-394,896,-479) -> Matrix(21,-2,32,-3) Matrix(145,-81,256,-143) -> Matrix(3,-1,4,-1) Matrix(319,-183,448,-257) -> Matrix(1,0,0,1) Matrix(2369,-1369,4096,-2367) -> Matrix(1,0,0,1) Matrix(337,-196,576,-335) -> Matrix(1,-1,0,1) Matrix(1009,-592,1280,-751) -> Matrix(1,1,0,1) Matrix(175,-103,192,-113) -> Matrix(1,1,0,1) Matrix(609,-361,1024,-607) -> Matrix(1,0,20,1) Matrix(81,-50,128,-79) -> Matrix(3,-1,4,-1) Matrix(2625,-1681,4096,-2623) -> Matrix(1,0,0,1) Matrix(1489,-961,2304,-1487) -> Matrix(1,-1,0,1) Matrix(767,-497,1088,-705) -> Matrix(1,0,0,1) Matrix(271,-177,320,-209) -> Matrix(1,1,0,1) Matrix(177,-121,256,-175) -> Matrix(7,-3,12,-5) Matrix(1631,-1132,1984,-1377) -> Matrix(23,-16,36,-25) Matrix(2881,-2025,4096,-2879) -> Matrix(1,0,0,1) Matrix(817,-578,1152,-815) -> Matrix(3,-1,4,-1) Matrix(49,-36,64,-47) -> Matrix(3,-1,4,-1) Matrix(801,-625,1024,-799) -> Matrix(5,-4,4,-3) Matrix(209,-169,256,-207) -> Matrix(7,-3,12,-5) Matrix(865,-729,1024,-863) -> Matrix(13,-12,12,-11) Matrix(113,-98,128,-111) -> Matrix(3,-1,4,-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): 16 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (0/1,1/1) 0 32 1/8 1/0 2 4 2/15 (-1/1,0/1) 0 32 1/7 (0/1,1/1) 0 32 2/13 (4/5,1/1) 0 32 5/32 1/1 12 1 1/6 (1/1,2/1) 0 16 3/17 (9/5,2/1) 0 32 5/28 5/2 2 8 2/11 (3/1,4/1) 0 32 3/16 1/0 6 2 1/5 (0/1,1/1) 0 32 1/4 1/0 2 8 3/11 (-1/1,0/1) 0 32 11/40 1/0 2 4 8/29 (-1/1,0/1) 0 32 5/18 (-1/1,0/1) 0 16 9/32 0/1 4 1 2/7 (0/1,1/1) 0 32 7/24 1/0 2 4 12/41 (-1/1,0/1) 0 32 5/17 (0/1,1/3) 0 32 8/27 (0/1,1/1) 0 32 19/64 (0/1,1/1) 0 1 3/10 (0/1,1/1) 0 16 7/23 (1/1,2/1) 0 32 11/36 3/2 2 8 4/13 (2/1,3/1) 0 32 5/16 1/0 6 2 1/3 (-1/1,0/1) 0 32 3/8 1/0 2 4 5/13 (-2/1,-1/1) 0 32 17/44 -1/2 2 8 12/31 (-1/1,-2/3) 0 32 31/80 -1/2 2 2 19/49 (-1/1,0/1) 0 32 7/18 (-1/1,0/1) 0 16 25/64 (-1/1,0/1) 0 1 9/23 (-1/1,0/1) 0 32 11/28 1/0 2 8 2/5 (-1/3,0/1) 0 32 13/32 0/1 20 1 9/22 (0/1,1/7) 0 16 16/39 (0/1,1/5) 0 32 7/17 (0/1,1/3) 0 32 5/12 1/2 2 8 13/31 (0/1,1/1) 0 32 21/50 (0/1,1/1) 0 16 8/19 (0/1,1/1) 0 32 27/64 (0/1,1/1) 0 1 11/26 (0/1,1/1) 0 16 14/33 (1/1,4/3) 0 32 3/7 (0/1,1/1) 0 32 7/16 1/0 2 2 4/9 (-1/1,0/1) 0 32 13/29 (0/1,1/3) 0 32 9/20 1/0 2 8 14/31 (-2/1,-1/1) 0 32 5/11 (-1/1,0/1) 0 32 11/24 -1/2 2 4 6/13 (-1/3,0/1) 0 32 13/28 -1/6 2 8 7/15 (-1/13,0/1) 0 32 15/32 0/1 28 1 1/2 (0/1,1/1) 0 16 1/0 (0/1,1/1) 0 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(17,-2,128,-15) (0/1,1/8) -> (1/8,2/15) Parabolic Matrix(289,-39,704,-95) (2/15,1/7) -> (16/39,7/17) Hyperbolic Matrix(143,-21,320,-47) (1/7,2/13) -> (4/9,13/29) Glide Reflection 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(271,-47,640,-111) (1/6,3/17) -> (11/26,14/33) Glide Reflection Matrix(417,-74,896,-159) (3/17,5/28) -> (13/28,7/15) Hyperbolic Matrix(177,-32,448,-81) (5/28,2/11) -> (11/28,2/5) Glide Reflection Matrix(49,-9,256,-47) (2/11,3/16) -> (3/16,1/5) Parabolic Matrix(17,-4,64,-15) (1/5,1/4) -> (1/4,3/11) Parabolic Matrix(321,-88,704,-193) (3/11,11/40) -> (5/11,11/24) Glide Reflection Matrix(559,-154,1216,-335) (11/40,8/29) -> (11/24,6/13) Glide Reflection Matrix(753,-208,1792,-495) (8/29,5/18) -> (21/50,8/19) 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(337,-98,1152,-335) (2/7,7/24) -> (7/24,12/41) Parabolic Matrix(625,-183,1472,-431) (12/41,5/17) -> (14/33,3/7) Hyperbolic Matrix(463,-137,1024,-303) (5/17,8/27) -> (14/31,5/11) 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(367,-111,896,-271) (3/10,7/23) -> (9/22,16/39) 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(81,-25,256,-79) (4/13,5/16) -> (5/16,1/3) Parabolic Matrix(49,-18,128,-47) (1/3,3/8) -> (3/8,5/13) Parabolic Matrix(689,-266,1536,-593) (5/13,17/44) -> (13/29,9/20) Glide Reflection Matrix(895,-346,1984,-767) (17/44,12/31) -> (9/20,14/31) Glide Reflection Matrix(2481,-961,6400,-2479) (12/31,31/80) -> (31/80,19/49) Parabolic Matrix(1263,-490,3008,-1167) (19/49,7/18) -> (13/31,21/50) 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(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(241,-100,576,-239) (7/17,5/12) -> (5/12,13/31) Parabolic 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(113,-49,256,-111) (3/7,7/16) -> (7/16,4/9) Parabolic 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(1,0,2,-1) (0/1,1/0) -> (0/1,1/1) Matrix(17,-2,128,-15) -> Matrix(1,-1,0,1) 1/0 Matrix(289,-39,704,-95) -> Matrix(1,0,4,1) 0/1 Matrix(143,-21,320,-47) -> Matrix(1,-1,-2,1) Matrix(129,-20,832,-129) -> Matrix(9,-8,10,-9) (2/13,5/32) -> (4/5,1/1) Matrix(31,-5,192,-31) -> Matrix(3,-4,2,-3) (5/32,1/6) -> (1/1,2/1) Matrix(271,-47,640,-111) -> Matrix(1,-1,2,-3) Matrix(417,-74,896,-159) -> Matrix(1,-2,-8,17) Matrix(177,-32,448,-81) -> Matrix(1,-3,-2,5) Matrix(49,-9,256,-47) -> Matrix(1,-3,0,1) 1/0 Matrix(17,-4,64,-15) -> Matrix(1,-1,0,1) 1/0 Matrix(321,-88,704,-193) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(559,-154,1216,-335) -> Matrix(1,1,-2,-3) Matrix(753,-208,1792,-495) -> Matrix(1,1,0,1) 1/0 Matrix(161,-45,576,-161) -> Matrix(-1,0,2,1) (5/18,9/32) -> (-1/1,0/1) Matrix(127,-36,448,-127) -> Matrix(1,0,2,-1) (9/32,2/7) -> (0/1,1/1) Matrix(337,-98,1152,-335) -> Matrix(1,-1,0,1) 1/0 Matrix(625,-183,1472,-431) -> Matrix(1,1,0,1) 1/0 Matrix(463,-137,1024,-303) -> Matrix(1,-1,-2,1) Matrix(1025,-304,3456,-1025) -> Matrix(1,0,2,-1) (8/27,19/64) -> (0/1,1/1) Matrix(191,-57,640,-191) -> Matrix(1,0,2,-1) (19/64,3/10) -> (0/1,1/1) Matrix(367,-111,896,-271) -> Matrix(1,-1,6,-7) Matrix(577,-176,1472,-449) -> Matrix(1,-2,-2,3) Matrix(385,-118,832,-255) -> Matrix(1,-2,-4,9) Matrix(81,-25,256,-79) -> Matrix(1,-3,0,1) 1/0 Matrix(49,-18,128,-47) -> Matrix(1,-1,0,1) 1/0 Matrix(689,-266,1536,-593) -> Matrix(1,1,2,1) Matrix(895,-346,1984,-767) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(2481,-961,6400,-2479) -> Matrix(1,1,-4,-3) -1/2 Matrix(1263,-490,3008,-1167) -> Matrix(1,1,2,1) Matrix(449,-175,1152,-449) -> Matrix(-1,0,2,1) (7/18,25/64) -> (-1/1,0/1) Matrix(1151,-450,2944,-1151) -> Matrix(-1,0,2,1) (25/64,9/23) -> (-1/1,0/1) Matrix(129,-52,320,-129) -> Matrix(-1,0,6,1) (2/5,13/32) -> (-1/3,0/1) Matrix(287,-117,704,-287) -> Matrix(1,0,14,-1) (13/32,9/22) -> (0/1,1/7) Matrix(241,-100,576,-239) -> Matrix(3,-1,4,-1) 1/2 Matrix(1025,-432,2432,-1025) -> Matrix(1,0,2,-1) (8/19,27/64) -> (0/1,1/1) Matrix(703,-297,1664,-703) -> Matrix(1,0,2,-1) (27/64,11/26) -> (0/1,1/1) Matrix(113,-49,256,-111) -> Matrix(1,-1,0,1) 1/0 Matrix(449,-210,960,-449) -> Matrix(-1,0,26,1) (7/15,15/32) -> (-1/13,0/1) Matrix(31,-15,64,-31) -> Matrix(1,0,2,-1) (15/32,1/2) -> (0/1,1/1) Matrix(-1,1,0,1) -> Matrix(1,0,2,-1) (1/2,1/0) -> (0/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.