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 -8/1 -20/3 -6/1 -28/5 -16/3 -24/5 -14/3 -22/5 -4/1 -26/7 -18/5 -24/7 -10/3 -16/5 -20/7 -48/17 -8/3 -12/5 -16/7 -2/1 -24/13 -16/9 -12/7 -8/5 -48/31 -16/11 -24/17 -4/3 -16/13 -8/7 0/1 1/1 8/7 16/13 4/3 24/17 16/11 3/2 48/31 8/5 28/17 12/7 16/9 24/13 28/15 2/1 32/15 16/7 64/27 12/5 32/13 5/2 64/25 8/3 64/23 48/17 20/7 3/1 16/5 96/29 10/3 64/19 24/7 7/2 32/9 18/5 11/3 26/7 160/43 4/1 64/15 30/7 13/3 22/5 128/29 9/2 32/7 14/3 24/5 160/33 34/7 5/1 16/3 11/2 28/5 17/3 64/11 6/1 32/5 13/2 20/3 7/1 15/2 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 1/1 2/1 -8/1 1/0 -15/2 -1/1 0/1 -7/1 0/1 1/1 -20/3 1/2 -13/2 4/5 1/1 -6/1 1/1 2/1 -23/4 1/1 2/1 -17/3 9/5 2/1 -28/5 5/2 -11/2 3/1 4/1 -16/3 1/0 -21/4 -3/1 -2/1 -5/1 0/1 1/1 -24/5 1/0 -19/4 0/1 1/1 -14/3 0/1 1/1 -9/2 1/1 2/1 -31/7 1/1 4/3 -22/5 1/1 2/1 -35/8 3/1 4/1 -13/3 0/1 1/1 -4/1 1/0 -19/5 -2/1 -1/1 -15/4 -1/1 0/1 -56/15 1/0 -41/11 -1/1 0/1 -26/7 0/1 1/1 -37/10 2/1 3/1 -11/3 -1/1 0/1 -40/11 1/0 -69/19 -2/1 -1/1 -29/8 -1/1 0/1 -18/5 -1/1 0/1 -7/2 0/1 1/1 -31/9 1/1 4/3 -24/7 1/0 -65/19 -1/1 -2/3 -41/12 -1/1 0/1 -17/5 0/1 1/3 -44/13 1/2 -71/21 0/1 1/1 -27/8 0/1 1/1 -10/3 0/1 1/1 -33/10 1/1 4/3 -23/7 1/1 2/1 -36/11 3/2 -13/4 2/1 3/1 -16/5 1/0 -19/6 -4/1 -3/1 -3/1 -1/1 0/1 -20/7 1/2 -17/6 0/1 1/3 -48/17 1/2 -31/11 0/1 1/1 -14/5 0/1 1/1 -25/9 0/1 1/1 -61/22 2/3 1/1 -36/13 1/0 -11/4 2/3 1/1 -8/3 1/0 -21/8 -4/3 -1/1 -55/21 -1/1 0/1 -34/13 -1/1 0/1 -47/18 -1/1 0/1 -13/5 -2/1 -1/1 -44/17 -1/2 -31/12 -1/1 -2/3 -80/31 -1/2 -49/19 -1/1 0/1 -18/7 -1/1 0/1 -23/9 -1/1 0/1 -28/11 1/0 -61/24 -4/3 -1/1 -33/13 -1/1 -6/7 -5/2 -1/3 0/1 -22/9 0/1 1/7 -39/16 0/1 1/5 -17/7 0/1 1/3 -46/19 0/1 1/3 -29/12 0/1 1/3 -41/17 0/1 1/3 -12/5 1/2 -55/23 2/3 1/1 -43/18 6/7 1/1 -31/13 0/1 1/1 -50/21 0/1 1/1 -19/8 0/1 1/1 -26/11 0/1 1/1 -33/14 1/1 4/3 -7/3 0/1 1/1 -16/7 1/0 -25/11 -2/1 -1/1 -59/26 -2/1 -1/1 -34/15 -1/1 0/1 -9/4 -1/1 0/1 -29/13 0/1 1/3 -20/9 1/0 -31/14 -2/1 -1/1 -11/5 -1/1 0/1 -24/11 -1/2 -13/6 -1/3 0/1 -28/13 -1/6 -15/7 -1/13 0/1 -2/1 0/1 1/1 -17/9 -1/13 0/1 -32/17 0/1 -15/8 0/1 1/15 -13/7 0/1 1/5 -24/13 1/4 -11/6 0/1 1/3 -42/23 0/1 1/3 -31/17 1/3 2/5 -20/11 1/2 -29/16 -1/1 0/1 -38/21 0/1 1/5 -9/5 0/1 1/3 -16/9 1/2 -23/13 2/3 1/1 -30/17 2/3 1/1 -97/55 1/1 12/11 -67/38 1/1 2/1 -37/21 0/1 1/1 -7/4 0/1 1/1 -33/19 4/5 1/1 -59/34 2/1 3/1 -26/15 0/1 1/1 -45/26 0/1 1/1 -64/37 1/2 1/0 -19/11 0/1 1/1 -31/18 0/1 1/1 -74/43 4/5 1/1 -43/25 1/1 6/5 -12/7 1/0 -41/24 -1/1 0/1 -70/41 -1/1 0/1 -29/17 -1/1 0/1 -17/10 -1/1 0/1 -39/23 -1/3 0/1 -61/36 -1/3 -2/7 -22/13 -1/5 0/1 -27/16 -1/15 0/1 -32/19 0/1 -5/3 0/1 1/5 -33/20 6/19 1/3 -28/17 1/2 -23/14 0/1 1/3 -64/39 1/4 1/2 -41/25 0/1 1/3 -18/11 0/1 1/3 -49/30 0/1 1/3 -80/49 1/4 -31/19 2/7 1/3 -44/27 1/4 -13/8 1/3 2/5 -8/5 1/2 -19/12 0/1 1/1 -30/19 2/3 1/1 -41/26 2/3 1/1 -52/33 3/4 -11/7 1/1 2/1 -36/23 1/2 -97/62 8/9 1/1 -61/39 1/1 2/1 -25/16 0/1 1/1 -64/41 1/2 1/0 -39/25 0/1 1/1 -14/9 0/1 1/1 -31/20 0/1 1/1 -48/31 1/0 -17/11 -1/1 0/1 -20/13 1/0 -3/2 0/1 1/3 -16/11 1/2 -29/20 6/11 5/9 -13/9 3/5 2/3 -36/25 3/4 -23/16 2/3 1/1 -33/23 4/5 1/1 -43/30 10/11 1/1 -96/67 1/1 -53/37 1/1 10/9 -10/7 0/1 1/1 -37/26 0/1 1/1 -64/45 1/2 1/0 -27/19 0/1 1/1 -44/31 1/0 -17/12 -1/1 0/1 -41/29 0/1 1/3 -24/17 1/2 -31/22 4/5 1/1 -7/5 0/1 1/1 -32/23 0/1 -25/18 0/1 1/5 -18/13 0/1 1/3 -47/34 0/1 1/3 -29/21 0/1 1/3 -40/29 1/2 -11/8 0/1 1/3 -37/27 3/5 2/3 -63/46 1/1 4/3 -26/19 0/1 1/1 -93/68 -1/5 0/1 -160/117 0/1 -67/49 0/1 1/7 -41/30 0/1 1/3 -15/11 0/1 1/3 -4/3 1/2 -17/13 2/3 1/1 -64/49 1/2 3/4 -47/36 2/3 1/1 -30/23 2/3 1/1 -13/10 0/1 1/1 -35/27 4/7 3/5 -57/44 3/5 2/3 -22/17 2/3 1/1 -75/58 2/3 1/1 -128/99 1/2 3/4 -53/41 2/3 1/1 -31/24 4/5 1/1 -40/31 1/2 -9/7 2/3 1/1 -32/25 1/1 -23/18 1/1 2/1 -14/11 0/1 1/1 -33/26 0/1 1/1 -19/15 0/1 1/1 -24/19 1/2 -29/23 2/3 1/1 -63/50 12/13 1/1 -160/127 1/1 -97/77 1/1 16/15 -34/27 1/1 2/1 -5/4 0/1 1/1 -16/13 1/2 -27/22 7/13 6/11 -11/9 4/7 3/5 -28/23 5/8 -45/37 11/17 2/3 -17/14 2/3 9/13 -23/19 2/3 1/1 -29/24 2/3 1/1 -64/53 1/2 3/4 -35/29 2/3 1/1 -6/5 2/3 1/1 -19/16 8/9 1/1 -32/27 1/1 -13/11 1/1 4/3 -20/17 1/0 -27/23 0/1 1/1 -7/6 0/1 1/1 -15/13 0/1 1/3 -8/7 1/2 -17/15 2/3 1/1 -9/8 2/3 1/1 -1/1 0/1 1/1 0/1 1/2 1/0 1/1 0/1 1/1 9/8 1/1 2/1 8/7 1/0 15/13 -1/1 0/1 7/6 0/1 1/1 20/17 1/2 13/11 4/5 1/1 6/5 1/1 2/1 23/19 1/1 2/1 17/14 9/5 2/1 28/23 5/2 11/9 3/1 4/1 16/13 1/0 21/17 -3/1 -2/1 5/4 0/1 1/1 24/19 1/0 19/15 0/1 1/1 14/11 0/1 1/1 9/7 1/1 2/1 31/24 1/1 4/3 22/17 1/1 2/1 35/27 3/1 4/1 13/10 0/1 1/1 4/3 1/0 19/14 -2/1 -1/1 15/11 -1/1 0/1 56/41 1/0 41/30 -1/1 0/1 26/19 0/1 1/1 37/27 2/1 3/1 11/8 -1/1 0/1 40/29 1/0 69/50 -2/1 -1/1 29/21 -1/1 0/1 18/13 -1/1 0/1 7/5 0/1 1/1 31/22 1/1 4/3 24/17 1/0 65/46 -1/1 -2/3 41/29 -1/1 0/1 17/12 0/1 1/3 44/31 1/2 71/50 0/1 1/1 27/19 0/1 1/1 10/7 0/1 1/1 33/23 1/1 4/3 23/16 1/1 2/1 36/25 3/2 13/9 2/1 3/1 16/11 1/0 19/13 -4/1 -3/1 3/2 -1/1 0/1 20/13 1/2 17/11 0/1 1/3 48/31 1/2 31/20 0/1 1/1 14/9 0/1 1/1 25/16 0/1 1/1 61/39 2/3 1/1 36/23 1/0 11/7 2/3 1/1 8/5 1/0 21/13 -4/3 -1/1 55/34 -1/1 0/1 34/21 -1/1 0/1 47/29 -1/1 0/1 13/8 -2/1 -1/1 44/27 -1/2 31/19 -1/1 -2/3 80/49 -1/2 49/30 -1/1 0/1 18/11 -1/1 0/1 23/14 -1/1 0/1 28/17 1/0 61/37 -4/3 -1/1 33/20 -1/1 -6/7 5/3 -1/3 0/1 22/13 0/1 1/7 39/23 0/1 1/5 17/10 0/1 1/3 46/27 0/1 1/3 29/17 0/1 1/3 41/24 0/1 1/3 12/7 1/2 55/32 2/3 1/1 43/25 6/7 1/1 31/18 0/1 1/1 50/29 0/1 1/1 19/11 0/1 1/1 26/15 0/1 1/1 33/19 1/1 4/3 7/4 0/1 1/1 16/9 1/0 25/14 -2/1 -1/1 59/33 -2/1 -1/1 34/19 -1/1 0/1 9/5 -1/1 0/1 29/16 0/1 1/3 20/11 1/0 31/17 -2/1 -1/1 11/6 -1/1 0/1 24/13 -1/2 13/7 -1/3 0/1 28/15 -1/6 15/8 -1/13 0/1 2/1 0/1 1/1 17/8 -1/13 0/1 32/15 0/1 15/7 0/1 1/15 13/6 0/1 1/5 24/11 1/4 11/5 0/1 1/3 42/19 0/1 1/3 31/14 1/3 2/5 20/9 1/2 29/13 -1/1 0/1 38/17 0/1 1/5 9/4 0/1 1/3 16/7 1/2 23/10 2/3 1/1 30/13 2/3 1/1 97/42 1/1 12/11 67/29 1/1 2/1 37/16 0/1 1/1 7/3 0/1 1/1 33/14 4/5 1/1 59/25 2/1 3/1 26/11 0/1 1/1 45/19 0/1 1/1 64/27 1/2 1/0 19/8 0/1 1/1 31/13 0/1 1/1 74/31 4/5 1/1 43/18 1/1 6/5 12/5 1/0 41/17 -1/1 0/1 70/29 -1/1 0/1 29/12 -1/1 0/1 17/7 -1/1 0/1 39/16 -1/3 0/1 61/25 -1/3 -2/7 22/9 -1/5 0/1 27/11 -1/15 0/1 32/13 0/1 5/2 0/1 1/5 33/13 6/19 1/3 28/11 1/2 23/9 0/1 1/3 64/25 1/4 1/2 41/16 0/1 1/3 18/7 0/1 1/3 49/19 0/1 1/3 80/31 1/4 31/12 2/7 1/3 44/17 1/4 13/5 1/3 2/5 8/3 1/2 19/7 0/1 1/1 30/11 2/3 1/1 41/15 2/3 1/1 52/19 3/4 11/4 1/1 2/1 36/13 1/2 97/35 8/9 1/1 61/22 1/1 2/1 25/9 0/1 1/1 64/23 1/2 1/0 39/14 0/1 1/1 14/5 0/1 1/1 31/11 0/1 1/1 48/17 1/0 17/6 -1/1 0/1 20/7 1/0 3/1 0/1 1/3 16/5 1/2 29/9 6/11 5/9 13/4 3/5 2/3 36/11 3/4 23/7 2/3 1/1 33/10 4/5 1/1 43/13 10/11 1/1 96/29 1/1 53/16 1/1 10/9 10/3 0/1 1/1 37/11 0/1 1/1 64/19 1/2 1/0 27/8 0/1 1/1 44/13 1/0 17/5 -1/1 0/1 41/12 0/1 1/3 24/7 1/2 31/9 4/5 1/1 7/2 0/1 1/1 32/9 0/1 25/7 0/1 1/5 18/5 0/1 1/3 47/13 0/1 1/3 29/8 0/1 1/3 40/11 1/2 11/3 0/1 1/3 37/10 3/5 2/3 63/17 1/1 4/3 26/7 0/1 1/1 93/25 -1/5 0/1 160/43 0/1 67/18 0/1 1/7 41/11 0/1 1/3 15/4 0/1 1/3 4/1 1/2 17/4 2/3 1/1 64/15 1/2 3/4 47/11 2/3 1/1 30/7 2/3 1/1 13/3 0/1 1/1 35/8 4/7 3/5 57/13 3/5 2/3 22/5 2/3 1/1 75/17 2/3 1/1 128/29 1/2 3/4 53/12 2/3 1/1 31/7 4/5 1/1 40/9 1/2 9/2 2/3 1/1 32/7 1/1 23/5 1/1 2/1 14/3 0/1 1/1 33/7 0/1 1/1 19/4 0/1 1/1 24/5 1/2 29/6 2/3 1/1 63/13 12/13 1/1 160/33 1/1 97/20 1/1 16/15 34/7 1/1 2/1 5/1 0/1 1/1 16/3 1/2 27/5 7/13 6/11 11/2 4/7 3/5 28/5 5/8 45/8 11/17 2/3 17/3 2/3 9/13 23/4 2/3 1/1 29/5 2/3 1/1 64/11 1/2 3/4 35/6 2/3 1/1 6/1 2/3 1/1 19/3 8/9 1/1 32/5 1/1 13/2 1/1 4/3 20/3 1/0 27/4 0/1 1/1 7/1 0/1 1/1 15/2 0/1 1/3 8/1 1/2 17/2 2/3 1/1 9/1 2/3 1/1 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(33,320,10,97) (-9/1,1/0) -> (23/7,33/10) Hyperbolic Matrix(97,832,-26,-223) (-9/1,-8/1) -> (-56/15,-41/11) Hyperbolic Matrix(127,960,-34,-257) (-8/1,-15/2) -> (-15/4,-56/15) Hyperbolic Matrix(95,704,56,415) (-15/2,-7/1) -> (39/23,17/10) Hyperbolic Matrix(257,1728,-76,-511) (-7/1,-20/3) -> (-44/13,-71/21) Hyperbolic Matrix(127,832,78,511) (-20/3,-13/2) -> (13/8,44/27) Hyperbolic Matrix(31,192,-26,-161) (-13/2,-6/1) -> (-6/5,-19/16) Hyperbolic Matrix(321,1856,-188,-1087) (-6/1,-23/4) -> (-41/24,-70/41) Hyperbolic Matrix(191,1088,56,319) (-23/4,-17/3) -> (17/5,41/12) Hyperbolic Matrix(159,896,-74,-417) (-17/3,-28/5) -> (-28/13,-15/7) Hyperbolic Matrix(127,704,46,255) (-28/5,-11/2) -> (11/4,36/13) Hyperbolic Matrix(95,512,-18,-97) (-11/2,-16/3) -> (-16/3,-21/4) Parabolic Matrix(159,832,116,607) (-21/4,-5/1) -> (37/27,11/8) Hyperbolic Matrix(385,1856,-106,-511) (-5/1,-24/5) -> (-40/11,-69/19) Hyperbolic Matrix(161,768,74,353) (-24/5,-19/4) -> (13/6,24/11) Hyperbolic Matrix(257,1216,-108,-511) (-19/4,-14/3) -> (-50/21,-19/8) Hyperbolic Matrix(97,448,-76,-351) (-14/3,-9/2) -> (-23/18,-14/11) Hyperbolic Matrix(417,1856,-122,-543) (-9/2,-31/7) -> (-65/19,-41/12) Hyperbolic Matrix(449,1984,-246,-1087) (-31/7,-22/5) -> (-42/23,-31/17) Hyperbolic Matrix(481,2112,-284,-1247) (-22/5,-35/8) -> (-61/36,-22/13) Hyperbolic Matrix(161,704,110,481) (-35/8,-13/3) -> (19/13,3/2) Hyperbolic Matrix(31,128,-8,-33) (-13/3,-4/1) -> (-4/1,-19/5) Parabolic Matrix(287,1088,-110,-417) (-19/5,-15/4) -> (-47/18,-13/5) Hyperbolic Matrix(481,1792,-266,-991) (-41/11,-26/7) -> (-38/21,-9/5) Hyperbolic Matrix(673,2496,-388,-1439) (-26/7,-37/10) -> (-59/34,-26/15) Hyperbolic Matrix(225,832,182,673) (-37/10,-11/3) -> (21/17,5/4) Hyperbolic Matrix(193,704,88,321) (-11/3,-40/11) -> (24/11,11/5) Hyperbolic Matrix(1569,5696,-890,-3231) (-69/19,-29/8) -> (-67/38,-37/21) Hyperbolic Matrix(513,1856,-212,-767) (-29/8,-18/5) -> (-46/19,-29/12) Hyperbolic Matrix(161,576,-116,-415) (-18/5,-7/2) -> (-25/18,-18/13) Hyperbolic Matrix(129,448,74,257) (-7/2,-31/9) -> (33/19,7/4) Hyperbolic Matrix(671,2304,-196,-673) (-31/9,-24/7) -> (-24/7,-65/19) Parabolic Matrix(319,1088,56,191) (-41/12,-17/5) -> (17/3,23/4) Hyperbolic Matrix(321,1088,208,705) (-17/5,-44/13) -> (20/13,17/11) Hyperbolic Matrix(833,2816,360,1217) (-71/21,-27/8) -> (37/16,7/3) Hyperbolic Matrix(191,640,-134,-449) (-27/8,-10/3) -> (-10/7,-37/26) Hyperbolic Matrix(833,2752,-484,-1599) (-10/3,-33/10) -> (-31/18,-74/43) Hyperbolic Matrix(97,320,10,33) (-33/10,-23/7) -> (9/1,1/0) Hyperbolic Matrix(449,1472,176,577) (-23/7,-36/11) -> (28/11,23/9) Hyperbolic Matrix(255,832,-118,-385) (-36/11,-13/4) -> (-13/6,-28/13) Hyperbolic Matrix(159,512,-50,-161) (-13/4,-16/5) -> (-16/5,-19/6) Parabolic Matrix(223,704,172,543) (-19/6,-3/1) -> (35/27,13/10) Hyperbolic Matrix(223,640,100,287) (-3/1,-20/7) -> (20/9,29/13) Hyperbolic Matrix(383,1088,270,767) (-20/7,-17/6) -> (17/12,44/31) Hyperbolic Matrix(1313,3712,804,2273) (-17/6,-48/17) -> (80/49,49/30) Hyperbolic Matrix(1407,3968,862,2431) (-48/17,-31/11) -> (31/19,80/49) Hyperbolic Matrix(319,896,68,191) (-31/11,-14/5) -> (14/3,33/7) Hyperbolic Matrix(321,896,-206,-575) (-14/5,-25/9) -> (-39/25,-14/9) Hyperbolic Matrix(1569,4352,358,993) (-25/9,-61/22) -> (35/8,57/13) Hyperbolic Matrix(1409,3904,-554,-1535) (-61/22,-36/13) -> (-28/11,-61/24) Hyperbolic Matrix(255,704,46,127) (-36/13,-11/4) -> (11/2,28/5) Hyperbolic Matrix(95,256,-36,-97) (-11/4,-8/3) -> (-8/3,-21/8) Parabolic Matrix(1343,3520,-562,-1473) (-21/8,-55/21) -> (-55/23,-43/18) Hyperbolic Matrix(831,2176,464,1215) (-55/21,-34/13) -> (34/19,9/5) Hyperbolic Matrix(1151,3008,-882,-2305) (-34/13,-47/18) -> (-47/36,-30/23) Hyperbolic Matrix(321,832,272,705) (-13/5,-44/17) -> (20/17,13/11) Hyperbolic Matrix(767,1984,346,895) (-44/17,-31/12) -> (31/14,20/9) Hyperbolic Matrix(1537,3968,992,2561) (-31/12,-80/31) -> (48/31,31/20) Hyperbolic Matrix(1439,3712,930,2399) (-80/31,-49/19) -> (17/11,48/31) Hyperbolic Matrix(671,1728,186,479) (-49/19,-18/7) -> (18/5,47/13) Hyperbolic Matrix(449,1152,-274,-703) (-18/7,-23/9) -> (-41/25,-18/11) Hyperbolic Matrix(577,1472,176,449) (-23/9,-28/11) -> (36/11,23/7) Hyperbolic Matrix(3199,8128,-1814,-4609) (-61/24,-33/13) -> (-97/55,-67/38) Hyperbolic Matrix(607,1536,164,415) (-33/13,-5/2) -> (37/10,63/17) Hyperbolic Matrix(287,704,-170,-417) (-5/2,-22/9) -> (-22/13,-27/16) Hyperbolic Matrix(865,2112,-668,-1631) (-22/9,-39/16) -> (-57/44,-22/17) Hyperbolic Matrix(289,704,250,609) (-39/16,-17/7) -> (15/13,7/6) Hyperbolic Matrix(1057,2560,410,993) (-17/7,-46/19) -> (18/7,49/19) Hyperbolic Matrix(769,1856,-636,-1535) (-29/12,-41/17) -> (-23/19,-29/24) Hyperbolic Matrix(479,1152,-200,-481) (-41/17,-12/5) -> (-12/5,-55/23) Parabolic Matrix(1153,2752,-804,-1919) (-43/18,-31/13) -> (-33/23,-43/30) Hyperbolic Matrix(833,1984,296,705) (-31/13,-50/21) -> (14/5,31/11) Hyperbolic Matrix(703,1664,-406,-961) (-19/8,-26/11) -> (-26/15,-45/26) Hyperbolic Matrix(1057,2496,-772,-1823) (-26/11,-33/14) -> (-63/46,-26/19) Hyperbolic Matrix(191,448,136,319) (-33/14,-7/3) -> (7/5,31/22) Hyperbolic Matrix(223,512,-98,-225) (-7/3,-16/7) -> (-16/7,-25/11) Parabolic Matrix(479,1088,70,159) (-25/11,-59/26) -> (27/4,7/1) Hyperbolic Matrix(959,2176,-762,-1729) (-59/26,-34/15) -> (-34/27,-5/4) Hyperbolic Matrix(961,2176,594,1345) (-34/15,-9/4) -> (55/34,34/21) Hyperbolic Matrix(801,1792,-586,-1311) (-9/4,-29/13) -> (-67/49,-41/30) Hyperbolic Matrix(287,640,100,223) (-29/13,-20/9) -> (20/7,3/1) Hyperbolic Matrix(895,1984,346,767) (-20/9,-31/14) -> (31/12,44/17) Hyperbolic Matrix(897,1984,-694,-1535) (-31/14,-11/5) -> (-53/41,-31/24) Hyperbolic Matrix(321,704,88,193) (-11/5,-24/11) -> (40/11,11/3) Hyperbolic Matrix(353,768,74,161) (-24/11,-13/6) -> (19/4,24/5) Hyperbolic Matrix(31,64,-16,-33) (-15/7,-2/1) -> (-2/1,-17/9) Parabolic Matrix(543,1024,254,479) (-17/9,-32/17) -> (32/15,15/7) Hyperbolic Matrix(545,1024,256,481) (-32/17,-15/8) -> (17/8,32/15) Hyperbolic Matrix(479,896,-394,-737) (-15/8,-13/7) -> (-45/37,-17/14) Hyperbolic Matrix(415,768,328,607) (-13/7,-24/13) -> (24/19,19/15) Hyperbolic Matrix(383,704,278,511) (-24/13,-11/6) -> (11/8,40/29) Hyperbolic Matrix(1857,3392,-1436,-2623) (-11/6,-42/23) -> (-22/17,-75/58) Hyperbolic Matrix(1089,1984,668,1217) (-31/17,-20/11) -> (44/27,31/19) Hyperbolic Matrix(353,640,230,417) (-20/11,-29/16) -> (3/2,20/13) Hyperbolic Matrix(2369,4288,-1732,-3135) (-29/16,-38/21) -> (-26/19,-93/68) Hyperbolic Matrix(287,512,-162,-289) (-9/5,-16/9) -> (-16/9,-23/13) Parabolic Matrix(1087,1920,398,703) (-23/13,-30/17) -> (30/11,41/15) Hyperbolic Matrix(3519,6208,-2794,-4929) (-30/17,-97/55) -> (-97/77,-34/27) Hyperbolic Matrix(1599,2816,1126,1983) (-37/21,-7/4) -> (71/50,27/19) Hyperbolic Matrix(257,448,74,129) (-7/4,-33/19) -> (31/9,7/2) Hyperbolic Matrix(1217,2112,480,833) (-33/19,-59/34) -> (5/2,33/13) Hyperbolic Matrix(2367,4096,998,1727) (-45/26,-64/37) -> (64/27,19/8) Hyperbolic Matrix(2369,4096,1000,1729) (-64/37,-19/11) -> (45/19,64/27) Hyperbolic Matrix(705,1216,-556,-959) (-19/11,-31/18) -> (-33/26,-19/15) Hyperbolic Matrix(2529,4352,-1766,-3039) (-74/43,-43/25) -> (-53/37,-10/7) Hyperbolic Matrix(1377,2368,-874,-1503) (-43/25,-12/7) -> (-52/33,-11/7) Hyperbolic Matrix(1535,2624,-974,-1665) (-12/7,-41/24) -> (-41/26,-52/33) Hyperbolic Matrix(1537,2624,-1274,-2175) (-70/41,-29/17) -> (-35/29,-6/5) Hyperbolic Matrix(1089,1856,-788,-1343) (-29/17,-17/10) -> (-47/34,-29/21) Hyperbolic Matrix(415,704,56,95) (-17/10,-39/23) -> (7/1,15/2) Hyperbolic Matrix(2303,3904,830,1407) (-39/23,-61/36) -> (61/22,25/9) Hyperbolic Matrix(607,1024,246,415) (-27/16,-32/19) -> (32/13,5/2) Hyperbolic Matrix(609,1024,248,417) (-32/19,-5/3) -> (27/11,32/13) Hyperbolic Matrix(1279,2112,542,895) (-5/3,-33/20) -> (33/14,59/25) Hyperbolic Matrix(2369,3904,-1514,-2495) (-33/20,-28/17) -> (-36/23,-97/62) Hyperbolic Matrix(895,1472,622,1023) (-28/17,-23/14) -> (23/16,36/25) Hyperbolic Matrix(2495,4096,974,1599) (-23/14,-64/39) -> (64/25,41/16) Hyperbolic Matrix(2497,4096,976,1601) (-64/39,-41/25) -> (23/9,64/25) Hyperbolic Matrix(1567,2560,920,1503) (-18/11,-49/30) -> (17/10,46/27) Hyperbolic Matrix(2273,3712,804,1313) (-49/30,-80/49) -> (48/17,17/6) Hyperbolic Matrix(2431,3968,862,1407) (-80/49,-31/19) -> (31/11,48/17) Hyperbolic Matrix(1217,1984,668,1089) (-31/19,-44/27) -> (20/11,31/17) Hyperbolic Matrix(511,832,78,127) (-44/27,-13/8) -> (13/2,20/3) Hyperbolic Matrix(159,256,-100,-161) (-13/8,-8/5) -> (-8/5,-19/12) Parabolic Matrix(607,960,-466,-737) (-19/12,-30/19) -> (-30/23,-13/10) Hyperbolic Matrix(1217,1920,528,833) (-30/19,-41/26) -> (23/10,30/13) Hyperbolic Matrix(449,704,368,577) (-11/7,-36/23) -> (28/23,11/9) Hyperbolic Matrix(4255,6656,-3376,-5281) (-97/62,-61/39) -> (-29/23,-63/50) Hyperbolic Matrix(2497,3904,1024,1601) (-61/39,-25/16) -> (39/16,61/25) Hyperbolic Matrix(2623,4096,942,1471) (-25/16,-64/41) -> (64/23,39/14) Hyperbolic Matrix(2625,4096,944,1473) (-64/41,-39/25) -> (25/9,64/23) Hyperbolic Matrix(1279,1984,742,1151) (-14/9,-31/20) -> (31/18,50/29) Hyperbolic Matrix(2561,3968,992,1537) (-31/20,-48/31) -> (80/31,31/12) Hyperbolic Matrix(2399,3712,930,1439) (-48/31,-17/11) -> (49/19,80/31) Hyperbolic Matrix(705,1088,208,321) (-17/11,-20/13) -> (44/13,17/5) Hyperbolic Matrix(417,640,230,353) (-20/13,-3/2) -> (29/16,20/11) Hyperbolic Matrix(351,512,-242,-353) (-3/2,-16/11) -> (-16/11,-29/20) Parabolic Matrix(575,832,132,191) (-29/20,-13/9) -> (13/3,35/8) Hyperbolic Matrix(1377,1984,-1132,-1631) (-13/9,-36/25) -> (-28/23,-45/37) Hyperbolic Matrix(1023,1472,622,895) (-36/25,-23/16) -> (23/14,28/17) Hyperbolic Matrix(223,320,200,287) (-23/16,-33/23) -> (1/1,9/8) Hyperbolic Matrix(6431,9216,1942,2783) (-43/30,-96/67) -> (96/29,53/16) Hyperbolic Matrix(6433,9216,1944,2785) (-96/67,-53/37) -> (43/13,96/29) Hyperbolic Matrix(2879,4096,854,1215) (-37/26,-64/45) -> (64/19,27/8) Hyperbolic Matrix(2881,4096,856,1217) (-64/45,-27/19) -> (37/11,64/19) Hyperbolic Matrix(1217,1728,-1036,-1471) (-27/19,-44/31) -> (-20/17,-27/23) Hyperbolic Matrix(767,1088,270,383) (-44/31,-17/12) -> (17/6,20/7) Hyperbolic Matrix(769,1088,634,897) (-17/12,-41/29) -> (23/19,17/14) Hyperbolic Matrix(1313,1856,-1018,-1439) (-41/29,-24/17) -> (-40/31,-9/7) Hyperbolic Matrix(1407,1984,-1090,-1537) (-24/17,-31/22) -> (-31/24,-40/31) Hyperbolic Matrix(319,448,136,191) (-31/22,-7/5) -> (7/3,33/14) Hyperbolic Matrix(735,1024,206,287) (-7/5,-32/23) -> (32/9,25/7) Hyperbolic Matrix(737,1024,208,289) (-32/23,-25/18) -> (7/2,32/9) Hyperbolic Matrix(1249,1728,764,1057) (-18/13,-47/34) -> (49/30,18/11) Hyperbolic Matrix(1345,1856,-1066,-1471) (-29/21,-40/29) -> (-24/19,-29/23) Hyperbolic Matrix(511,704,278,383) (-40/29,-11/8) -> (11/6,24/13) Hyperbolic Matrix(513,704,94,129) (-11/8,-37/27) -> (27/5,11/2) Hyperbolic Matrix(1121,1536,678,929) (-37/27,-63/46) -> (33/20,5/3) Hyperbolic Matrix(18719,25600,5030,6879) (-93/68,-160/117) -> (160/43,67/18) Hyperbolic Matrix(18721,25600,5032,6881) (-160/117,-67/49) -> (93/25,160/43) Hyperbolic Matrix(609,832,-538,-735) (-41/30,-15/11) -> (-17/15,-9/8) Hyperbolic Matrix(95,128,-72,-97) (-15/11,-4/3) -> (-4/3,-17/13) Parabolic Matrix(3135,4096,734,959) (-17/13,-64/49) -> (64/15,47/11) Hyperbolic Matrix(3137,4096,736,961) (-64/49,-47/36) -> (17/4,64/15) Hyperbolic Matrix(641,832,198,257) (-13/10,-35/27) -> (29/9,13/4) Hyperbolic Matrix(3359,4352,2148,2783) (-35/27,-57/44) -> (25/16,61/39) Hyperbolic Matrix(12671,16384,2870,3711) (-75/58,-128/99) -> (128/29,53/12) Hyperbolic Matrix(12673,16384,2872,3713) (-128/99,-53/41) -> (75/17,128/29) Hyperbolic Matrix(799,1024,174,223) (-9/7,-32/25) -> (32/7,23/5) Hyperbolic Matrix(801,1024,176,225) (-32/25,-23/18) -> (9/2,32/7) Hyperbolic Matrix(705,896,454,577) (-14/11,-33/26) -> (31/20,14/9) Hyperbolic Matrix(607,768,328,415) (-19/15,-24/19) -> (24/13,13/7) Hyperbolic Matrix(20319,25600,4190,5279) (-63/50,-160/127) -> (160/33,97/20) Hyperbolic Matrix(20321,25600,4192,5281) (-160/127,-97/77) -> (63/13,160/33) Hyperbolic Matrix(415,512,-338,-417) (-5/4,-16/13) -> (-16/13,-27/22) Parabolic Matrix(575,704,156,191) (-27/22,-11/9) -> (11/3,37/10) Hyperbolic Matrix(577,704,368,449) (-11/9,-28/23) -> (36/23,11/7) Hyperbolic Matrix(897,1088,634,769) (-17/14,-23/19) -> (41/29,17/12) Hyperbolic Matrix(3391,4096,582,703) (-29/24,-64/53) -> (64/11,35/6) Hyperbolic Matrix(3393,4096,584,705) (-64/53,-35/29) -> (29/5,64/11) Hyperbolic Matrix(863,1024,134,159) (-19/16,-32/27) -> (32/5,13/2) Hyperbolic Matrix(865,1024,136,161) (-32/27,-13/11) -> (19/3,32/5) Hyperbolic Matrix(705,832,272,321) (-13/11,-20/17) -> (44/17,13/5) Hyperbolic Matrix(929,1088,520,609) (-27/23,-7/6) -> (25/14,59/33) Hyperbolic Matrix(609,704,250,289) (-7/6,-15/13) -> (17/7,39/16) Hyperbolic Matrix(223,256,-196,-225) (-15/13,-8/7) -> (-8/7,-17/15) Parabolic Matrix(287,320,200,223) (-9/8,-1/1) -> (33/23,23/16) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(735,-832,538,-609) (9/8,8/7) -> (56/41,41/30) Hyperbolic Matrix(833,-960,610,-703) (8/7,15/13) -> (15/11,56/41) Hyperbolic Matrix(1471,-1728,1036,-1217) (7/6,20/17) -> (44/31,71/50) Hyperbolic Matrix(161,-192,26,-31) (13/11,6/5) -> (6/1,19/3) Hyperbolic Matrix(1535,-1856,636,-769) (6/5,23/19) -> (41/17,70/29) Hyperbolic Matrix(737,-896,394,-479) (17/14,28/23) -> (28/15,15/8) Hyperbolic Matrix(417,-512,338,-415) (11/9,16/13) -> (16/13,21/17) Parabolic Matrix(1471,-1856,1066,-1345) (5/4,24/19) -> (40/29,69/50) Hyperbolic Matrix(959,-1216,556,-705) (19/15,14/11) -> (50/29,19/11) Hyperbolic Matrix(351,-448,76,-97) (14/11,9/7) -> (23/5,14/3) Hyperbolic Matrix(1439,-1856,1018,-1313) (9/7,31/24) -> (65/46,41/29) Hyperbolic Matrix(1535,-1984,694,-897) (31/24,22/17) -> (42/19,31/14) Hyperbolic Matrix(1631,-2112,668,-865) (22/17,35/27) -> (61/25,22/9) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(801,-1088,494,-671) (19/14,15/11) -> (47/29,13/8) Hyperbolic Matrix(1311,-1792,586,-801) (41/30,26/19) -> (38/17,9/4) Hyperbolic Matrix(1823,-2496,772,-1057) (26/19,37/27) -> (59/25,26/11) Hyperbolic Matrix(4127,-5696,1786,-2465) (69/50,29/21) -> (67/29,37/16) Hyperbolic Matrix(1343,-1856,788,-1089) (29/21,18/13) -> (46/27,29/17) Hyperbolic Matrix(415,-576,116,-161) (18/13,7/5) -> (25/7,18/5) Hyperbolic Matrix(1633,-2304,1156,-1631) (31/22,24/17) -> (24/17,65/46) Parabolic Matrix(449,-640,134,-191) (27/19,10/7) -> (10/3,37/11) Hyperbolic Matrix(1919,-2752,804,-1153) (10/7,33/23) -> (31/13,74/31) Hyperbolic Matrix(577,-832,310,-447) (36/25,13/9) -> (13/7,28/15) Hyperbolic Matrix(353,-512,242,-351) (13/9,16/11) -> (16/11,19/13) Parabolic Matrix(575,-896,206,-321) (14/9,25/16) -> (39/14,14/5) Hyperbolic Matrix(2495,-3904,1514,-2369) (61/39,36/23) -> (28/17,61/37) Hyperbolic Matrix(161,-256,100,-159) (11/7,8/5) -> (8/5,21/13) Parabolic Matrix(2177,-3520,1266,-2047) (21/13,55/34) -> (55/32,43/25) Hyperbolic Matrix(1857,-3008,434,-703) (34/21,47/29) -> (47/11,30/7) Hyperbolic Matrix(703,-1152,274,-449) (18/11,23/14) -> (41/16,18/7) Hyperbolic Matrix(4929,-8128,2134,-3519) (61/37,33/20) -> (97/42,67/29) Hyperbolic Matrix(417,-704,170,-287) (5/3,22/13) -> (22/9,27/11) Hyperbolic Matrix(1247,-2112,284,-481) (22/13,39/23) -> (57/13,22/5) Hyperbolic Matrix(1087,-1856,188,-321) (29/17,41/24) -> (23/4,29/5) Hyperbolic Matrix(673,-1152,392,-671) (41/24,12/7) -> (12/7,55/32) Parabolic Matrix(1599,-2752,484,-833) (43/25,31/18) -> (33/10,43/13) Hyperbolic Matrix(961,-1664,406,-703) (19/11,26/15) -> (26/11,45/19) Hyperbolic Matrix(1439,-2496,388,-673) (26/15,33/19) -> (63/17,26/7) Hyperbolic Matrix(289,-512,162,-287) (7/4,16/9) -> (16/9,25/14) Parabolic Matrix(1217,-2176,250,-447) (59/33,34/19) -> (34/7,5/1) Hyperbolic Matrix(991,-1792,266,-481) (9/5,29/16) -> (67/18,41/11) Hyperbolic Matrix(1087,-1984,246,-449) (31/17,11/6) -> (53/12,31/7) Hyperbolic Matrix(33,-64,16,-31) (15/8,2/1) -> (2/1,17/8) Parabolic Matrix(417,-896,74,-159) (15/7,13/6) -> (45/8,17/3) Hyperbolic Matrix(1535,-3392,348,-769) (11/5,42/19) -> (22/5,75/17) Hyperbolic Matrix(1919,-4288,516,-1153) (29/13,38/17) -> (26/7,93/25) Hyperbolic Matrix(225,-512,98,-223) (9/4,16/7) -> (16/7,23/10) Parabolic Matrix(2689,-6208,554,-1279) (30/13,97/42) -> (97/20,34/7) Hyperbolic Matrix(511,-1216,108,-257) (19/8,31/13) -> (33/7,19/4) Hyperbolic Matrix(1823,-4352,550,-1313) (74/31,43/18) -> (53/16,10/3) Hyperbolic Matrix(991,-2368,362,-865) (43/18,12/5) -> (52/19,11/4) Hyperbolic Matrix(1089,-2624,398,-959) (12/5,41/17) -> (41/15,52/19) Hyperbolic Matrix(1087,-2624,186,-449) (70/29,29/12) -> (35/6,6/1) Hyperbolic Matrix(767,-1856,212,-513) (29/12,17/7) -> (47/13,29/8) Hyperbolic Matrix(1535,-3904,554,-1409) (33/13,28/11) -> (36/13,97/35) Hyperbolic Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(353,-960,82,-223) (19/7,30/11) -> (30/7,13/3) Hyperbolic Matrix(2401,-6656,496,-1375) (97/35,61/22) -> (29/6,63/13) Hyperbolic Matrix(161,-512,50,-159) (3/1,16/5) -> (16/5,29/9) Parabolic Matrix(607,-1984,108,-353) (13/4,36/11) -> (28/5,45/8) Hyperbolic Matrix(511,-1728,76,-257) (27/8,44/13) -> (20/3,27/4) Hyperbolic Matrix(543,-1856,122,-417) (41/12,24/7) -> (40/9,9/2) Hyperbolic Matrix(577,-1984,130,-447) (24/7,31/9) -> (31/7,40/9) Hyperbolic Matrix(511,-1856,106,-385) (29/8,40/11) -> (24/5,29/6) Hyperbolic Matrix(223,-832,26,-97) (41/11,15/4) -> (17/2,9/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(97,-512,18,-95) (5/1,16/3) -> (16/3,27/5) Parabolic Matrix(33,-256,4,-31) (15/2,8/1) -> (8/1,17/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(33,320,10,97) -> Matrix(3,-4,4,-5) Matrix(97,832,-26,-223) -> Matrix(1,-2,0,1) Matrix(127,960,-34,-257) -> Matrix(1,0,0,1) Matrix(95,704,56,415) -> Matrix(1,0,4,1) Matrix(257,1728,-76,-511) -> Matrix(1,0,0,1) Matrix(127,832,78,511) -> Matrix(3,-2,-4,3) Matrix(31,192,-26,-161) -> Matrix(3,-4,4,-5) Matrix(321,1856,-188,-1087) -> Matrix(1,-2,0,1) Matrix(191,1088,56,319) -> Matrix(1,-2,4,-7) Matrix(159,896,-74,-417) -> Matrix(1,-2,-8,17) Matrix(127,704,46,255) -> Matrix(1,-2,0,1) Matrix(95,512,-18,-97) -> Matrix(1,-6,0,1) Matrix(159,832,116,607) -> Matrix(1,2,0,1) Matrix(385,1856,-106,-511) -> Matrix(1,-2,0,1) Matrix(161,768,74,353) -> Matrix(1,0,4,1) Matrix(257,1216,-108,-511) -> Matrix(1,0,0,1) Matrix(97,448,-76,-351) -> Matrix(1,0,0,1) Matrix(417,1856,-122,-543) -> Matrix(1,-2,0,1) Matrix(449,1984,-246,-1087) -> Matrix(1,-2,4,-7) Matrix(481,2112,-284,-1247) -> Matrix(1,-2,-4,9) Matrix(161,704,110,481) -> Matrix(1,-4,0,1) Matrix(31,128,-8,-33) -> Matrix(1,-2,0,1) Matrix(287,1088,-110,-417) -> Matrix(1,0,0,1) Matrix(481,1792,-266,-991) -> Matrix(1,0,4,1) Matrix(673,2496,-388,-1439) -> Matrix(1,0,0,1) Matrix(225,832,182,673) -> Matrix(1,-2,0,1) Matrix(193,704,88,321) -> Matrix(1,0,4,1) Matrix(1569,5696,-890,-3231) -> Matrix(1,2,0,1) Matrix(513,1856,-212,-767) -> Matrix(1,0,4,1) Matrix(161,576,-116,-415) -> Matrix(1,0,4,1) Matrix(129,448,74,257) -> Matrix(1,0,0,1) Matrix(671,2304,-196,-673) -> Matrix(1,-2,0,1) Matrix(319,1088,56,191) -> Matrix(3,2,4,3) Matrix(321,1088,208,705) -> Matrix(1,0,0,1) Matrix(833,2816,360,1217) -> Matrix(1,0,0,1) Matrix(191,640,-134,-449) -> Matrix(1,0,0,1) Matrix(833,2752,-484,-1599) -> Matrix(3,-4,4,-5) Matrix(97,320,10,33) -> Matrix(3,-4,4,-5) Matrix(449,1472,176,577) -> Matrix(1,-2,4,-7) Matrix(255,832,-118,-385) -> Matrix(1,-2,-4,9) Matrix(159,512,-50,-161) -> Matrix(1,-6,0,1) Matrix(223,704,172,543) -> Matrix(1,4,0,1) Matrix(223,640,100,287) -> Matrix(1,0,0,1) Matrix(383,1088,270,767) -> Matrix(1,0,0,1) Matrix(1313,3712,804,2273) -> Matrix(1,0,-4,1) Matrix(1407,3968,862,2431) -> Matrix(3,-2,-4,3) Matrix(319,896,68,191) -> Matrix(1,0,0,1) Matrix(321,896,-206,-575) -> Matrix(1,0,0,1) Matrix(1569,4352,358,993) -> Matrix(5,-2,8,-3) Matrix(1409,3904,-554,-1535) -> Matrix(1,-2,0,1) Matrix(255,704,46,127) -> Matrix(5,-2,8,-3) Matrix(95,256,-36,-97) -> Matrix(1,-2,0,1) Matrix(1343,3520,-562,-1473) -> Matrix(3,2,4,3) Matrix(831,2176,464,1215) -> Matrix(1,0,0,1) Matrix(1151,3008,-882,-2305) -> Matrix(3,2,4,3) Matrix(321,832,272,705) -> Matrix(3,2,4,3) Matrix(767,1984,346,895) -> Matrix(1,0,4,1) Matrix(1537,3968,992,2561) -> Matrix(3,2,4,3) Matrix(1439,3712,930,2399) -> Matrix(1,0,4,1) Matrix(671,1728,186,479) -> Matrix(1,0,4,1) Matrix(449,1152,-274,-703) -> Matrix(1,0,4,1) Matrix(577,1472,176,449) -> Matrix(3,2,4,3) Matrix(3199,8128,-1814,-4609) -> Matrix(5,6,4,5) Matrix(607,1536,164,415) -> Matrix(3,2,4,3) Matrix(287,704,-170,-417) -> Matrix(1,0,-12,1) Matrix(865,2112,-668,-1631) -> Matrix(13,-2,20,-3) Matrix(289,704,250,609) -> Matrix(1,0,-4,1) Matrix(1057,2560,410,993) -> Matrix(1,0,0,1) Matrix(769,1856,-636,-1535) -> Matrix(5,-2,8,-3) Matrix(479,1152,-200,-481) -> Matrix(5,-2,8,-3) Matrix(1153,2752,-804,-1919) -> Matrix(3,-4,4,-5) Matrix(833,1984,296,705) -> Matrix(1,0,0,1) Matrix(703,1664,-406,-961) -> Matrix(1,0,0,1) Matrix(1057,2496,-772,-1823) -> Matrix(1,0,0,1) Matrix(191,448,136,319) -> Matrix(1,0,0,1) Matrix(223,512,-98,-225) -> Matrix(1,-2,0,1) Matrix(479,1088,70,159) -> Matrix(1,2,0,1) Matrix(959,2176,-762,-1729) -> Matrix(1,2,0,1) Matrix(961,2176,594,1345) -> Matrix(1,0,0,1) Matrix(801,1792,-586,-1311) -> Matrix(1,0,4,1) Matrix(287,640,100,223) -> Matrix(1,0,0,1) Matrix(895,1984,346,767) -> Matrix(1,0,4,1) Matrix(897,1984,-694,-1535) -> Matrix(3,2,4,3) Matrix(321,704,88,193) -> Matrix(1,0,4,1) Matrix(353,768,74,161) -> Matrix(1,0,4,1) Matrix(31,64,-16,-33) -> Matrix(1,0,0,1) Matrix(543,1024,254,479) -> Matrix(1,0,28,1) Matrix(545,1024,256,481) -> Matrix(1,0,-28,1) Matrix(479,896,-394,-737) -> Matrix(21,-2,32,-3) Matrix(415,768,328,607) -> Matrix(1,0,-4,1) Matrix(383,704,278,511) -> Matrix(1,0,-4,1) Matrix(1857,3392,-1436,-2623) -> Matrix(5,-2,8,-3) Matrix(1089,1984,668,1217) -> Matrix(1,0,-4,1) Matrix(353,640,230,417) -> Matrix(1,0,0,1) Matrix(2369,4288,-1732,-3135) -> Matrix(1,0,-4,1) Matrix(287,512,-162,-289) -> Matrix(5,-2,8,-3) Matrix(1087,1920,398,703) -> Matrix(1,0,0,1) Matrix(3519,6208,-2794,-4929) -> Matrix(5,-4,4,-3) Matrix(1599,2816,1126,1983) -> Matrix(1,0,0,1) Matrix(257,448,74,129) -> Matrix(1,0,0,1) Matrix(1217,2112,480,833) -> Matrix(1,-2,4,-7) Matrix(2367,4096,998,1727) -> Matrix(1,0,0,1) Matrix(2369,4096,1000,1729) -> Matrix(1,0,0,1) Matrix(705,1216,-556,-959) -> Matrix(1,0,0,1) Matrix(2529,4352,-1766,-3039) -> Matrix(5,-4,4,-3) Matrix(1377,2368,-874,-1503) -> Matrix(3,-4,4,-5) Matrix(1535,2624,-974,-1665) -> Matrix(3,2,4,3) Matrix(1537,2624,-1274,-2175) -> Matrix(3,2,4,3) Matrix(1089,1856,-788,-1343) -> Matrix(1,0,4,1) Matrix(415,704,56,95) -> Matrix(1,0,4,1) Matrix(2303,3904,830,1407) -> Matrix(1,0,4,1) Matrix(607,1024,246,415) -> Matrix(1,0,20,1) Matrix(609,1024,248,417) -> Matrix(1,0,-20,1) Matrix(1279,2112,542,895) -> Matrix(7,-2,4,-1) Matrix(2369,3904,-1514,-2495) -> Matrix(5,-2,8,-3) Matrix(895,1472,622,1023) -> Matrix(7,-2,4,-1) Matrix(2495,4096,974,1599) -> Matrix(1,0,0,1) Matrix(2497,4096,976,1601) -> Matrix(1,0,0,1) Matrix(1567,2560,920,1503) -> Matrix(1,0,0,1) Matrix(2273,3712,804,1313) -> Matrix(1,0,-4,1) Matrix(2431,3968,862,1407) -> Matrix(7,-2,4,-1) Matrix(1217,1984,668,1089) -> Matrix(1,0,-4,1) Matrix(511,832,78,127) -> Matrix(7,-2,4,-1) Matrix(159,256,-100,-161) -> Matrix(5,-2,8,-3) Matrix(607,960,-466,-737) -> Matrix(1,0,0,1) Matrix(1217,1920,528,833) -> Matrix(1,0,0,1) Matrix(449,704,368,577) -> Matrix(1,2,0,1) Matrix(4255,6656,-3376,-5281) -> Matrix(3,-4,4,-5) Matrix(2497,3904,1024,1601) -> Matrix(1,0,-4,1) Matrix(2623,4096,942,1471) -> Matrix(1,0,0,1) Matrix(2625,4096,944,1473) -> Matrix(1,0,0,1) Matrix(1279,1984,742,1151) -> Matrix(1,0,0,1) Matrix(2561,3968,992,1537) -> Matrix(1,-2,4,-7) Matrix(2399,3712,930,1439) -> Matrix(1,0,4,1) Matrix(705,1088,208,321) -> Matrix(1,0,0,1) Matrix(417,640,230,353) -> Matrix(1,0,0,1) Matrix(351,512,-242,-353) -> Matrix(13,-6,24,-11) Matrix(575,832,132,191) -> Matrix(3,-2,8,-5) Matrix(1377,1984,-1132,-1631) -> Matrix(23,-16,36,-25) Matrix(1023,1472,622,895) -> Matrix(3,-2,-4,3) Matrix(223,320,200,287) -> Matrix(5,-4,4,-3) Matrix(6431,9216,1942,2783) -> Matrix(21,-20,20,-19) Matrix(6433,9216,1944,2785) -> Matrix(19,-20,20,-21) Matrix(2879,4096,854,1215) -> Matrix(1,0,0,1) Matrix(2881,4096,856,1217) -> Matrix(1,0,0,1) Matrix(1217,1728,-1036,-1471) -> Matrix(1,0,0,1) Matrix(767,1088,270,383) -> Matrix(1,0,0,1) Matrix(769,1088,634,897) -> Matrix(7,-2,4,-1) Matrix(1313,1856,-1018,-1439) -> Matrix(5,-2,8,-3) Matrix(1407,1984,-1090,-1537) -> Matrix(1,0,0,1) Matrix(319,448,136,191) -> Matrix(1,0,0,1) Matrix(735,1024,206,287) -> Matrix(1,0,4,1) Matrix(737,1024,208,289) -> Matrix(1,0,-4,1) Matrix(1249,1728,764,1057) -> Matrix(1,0,-4,1) Matrix(1345,1856,-1066,-1471) -> Matrix(5,-2,8,-3) Matrix(511,704,278,383) -> Matrix(1,0,-4,1) Matrix(513,704,94,129) -> Matrix(9,-4,16,-7) Matrix(1121,1536,678,929) -> Matrix(3,-2,-4,3) Matrix(18719,25600,5030,6879) -> Matrix(1,0,12,1) Matrix(18721,25600,5032,6881) -> Matrix(1,0,-12,1) Matrix(609,832,-538,-735) -> Matrix(5,-2,8,-3) Matrix(95,128,-72,-97) -> Matrix(5,-2,8,-3) Matrix(3135,4096,734,959) -> Matrix(1,0,0,1) Matrix(3137,4096,736,961) -> Matrix(1,0,0,1) Matrix(641,832,198,257) -> Matrix(5,-2,8,-3) Matrix(3359,4352,2148,2783) -> Matrix(3,-2,8,-5) Matrix(12671,16384,2870,3711) -> Matrix(1,0,0,1) Matrix(12673,16384,2872,3713) -> Matrix(1,0,0,1) Matrix(799,1024,174,223) -> Matrix(5,-4,4,-3) Matrix(801,1024,176,225) -> Matrix(3,-4,4,-5) Matrix(705,896,454,577) -> Matrix(1,0,0,1) Matrix(607,768,328,415) -> Matrix(1,0,-4,1) Matrix(20319,25600,4190,5279) -> Matrix(29,-28,28,-27) Matrix(20321,25600,4192,5281) -> Matrix(27,-28,28,-29) Matrix(415,512,-338,-417) -> Matrix(13,-6,24,-11) Matrix(575,704,156,191) -> Matrix(7,-4,16,-9) Matrix(577,704,368,449) -> Matrix(3,-2,8,-5) Matrix(897,1088,634,769) -> Matrix(3,-2,-4,3) Matrix(3391,4096,582,703) -> Matrix(1,0,0,1) Matrix(3393,4096,584,705) -> Matrix(1,0,0,1) Matrix(863,1024,134,159) -> Matrix(13,-12,12,-11) Matrix(865,1024,136,161) -> Matrix(11,-12,12,-13) Matrix(705,832,272,321) -> Matrix(1,-2,4,-7) Matrix(929,1088,520,609) -> Matrix(1,-2,0,1) Matrix(609,704,250,289) -> Matrix(1,0,-4,1) Matrix(223,256,-196,-225) -> Matrix(5,-2,8,-3) Matrix(287,320,200,223) -> Matrix(5,-4,4,-3) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(735,-832,538,-609) -> Matrix(1,-2,0,1) Matrix(833,-960,610,-703) -> Matrix(1,0,0,1) Matrix(1471,-1728,1036,-1217) -> Matrix(1,0,0,1) Matrix(161,-192,26,-31) -> Matrix(3,-4,4,-5) Matrix(1535,-1856,636,-769) -> Matrix(1,-2,0,1) Matrix(737,-896,394,-479) -> Matrix(1,-2,-8,17) Matrix(417,-512,338,-415) -> Matrix(1,-6,0,1) Matrix(1471,-1856,1066,-1345) -> Matrix(1,-2,0,1) Matrix(959,-1216,556,-705) -> Matrix(1,0,0,1) Matrix(351,-448,76,-97) -> Matrix(1,0,0,1) Matrix(1439,-1856,1018,-1313) -> Matrix(1,-2,0,1) Matrix(1535,-1984,694,-897) -> Matrix(1,-2,4,-7) Matrix(1631,-2112,668,-865) -> Matrix(1,-2,-4,9) Matrix(97,-128,72,-95) -> Matrix(1,-2,0,1) Matrix(801,-1088,494,-671) -> Matrix(1,0,0,1) Matrix(1311,-1792,586,-801) -> Matrix(1,0,4,1) Matrix(1823,-2496,772,-1057) -> Matrix(1,0,0,1) Matrix(4127,-5696,1786,-2465) -> Matrix(1,2,0,1) Matrix(1343,-1856,788,-1089) -> Matrix(1,0,4,1) Matrix(415,-576,116,-161) -> Matrix(1,0,4,1) Matrix(1633,-2304,1156,-1631) -> Matrix(1,-2,0,1) Matrix(449,-640,134,-191) -> Matrix(1,0,0,1) Matrix(1919,-2752,804,-1153) -> Matrix(3,-4,4,-5) Matrix(577,-832,310,-447) -> Matrix(1,-2,-4,9) Matrix(353,-512,242,-351) -> Matrix(1,-6,0,1) Matrix(575,-896,206,-321) -> Matrix(1,0,0,1) Matrix(2495,-3904,1514,-2369) -> Matrix(1,-2,0,1) Matrix(161,-256,100,-159) -> Matrix(1,-2,0,1) Matrix(2177,-3520,1266,-2047) -> Matrix(3,2,4,3) Matrix(1857,-3008,434,-703) -> Matrix(3,2,4,3) Matrix(703,-1152,274,-449) -> Matrix(1,0,4,1) Matrix(4929,-8128,2134,-3519) -> Matrix(5,6,4,5) Matrix(417,-704,170,-287) -> Matrix(1,0,-12,1) Matrix(1247,-2112,284,-481) -> Matrix(13,-2,20,-3) Matrix(1087,-1856,188,-321) -> Matrix(5,-2,8,-3) Matrix(673,-1152,392,-671) -> Matrix(5,-2,8,-3) Matrix(1599,-2752,484,-833) -> Matrix(3,-4,4,-5) Matrix(961,-1664,406,-703) -> Matrix(1,0,0,1) Matrix(1439,-2496,388,-673) -> Matrix(1,0,0,1) Matrix(289,-512,162,-287) -> Matrix(1,-2,0,1) Matrix(1217,-2176,250,-447) -> Matrix(1,2,0,1) Matrix(991,-1792,266,-481) -> Matrix(1,0,4,1) Matrix(1087,-1984,246,-449) -> Matrix(3,2,4,3) Matrix(33,-64,16,-31) -> Matrix(1,0,0,1) Matrix(417,-896,74,-159) -> Matrix(21,-2,32,-3) Matrix(1535,-3392,348,-769) -> Matrix(5,-2,8,-3) Matrix(1919,-4288,516,-1153) -> Matrix(1,0,-4,1) Matrix(225,-512,98,-223) -> Matrix(5,-2,8,-3) Matrix(2689,-6208,554,-1279) -> Matrix(5,-4,4,-3) Matrix(511,-1216,108,-257) -> Matrix(1,0,0,1) Matrix(1823,-4352,550,-1313) -> Matrix(5,-4,4,-3) Matrix(991,-2368,362,-865) -> Matrix(3,-4,4,-5) Matrix(1089,-2624,398,-959) -> Matrix(3,2,4,3) Matrix(1087,-2624,186,-449) -> Matrix(3,2,4,3) Matrix(767,-1856,212,-513) -> Matrix(1,0,4,1) Matrix(1535,-3904,554,-1409) -> Matrix(5,-2,8,-3) Matrix(97,-256,36,-95) -> Matrix(5,-2,8,-3) Matrix(353,-960,82,-223) -> Matrix(1,0,0,1) Matrix(2401,-6656,496,-1375) -> Matrix(3,-4,4,-5) Matrix(161,-512,50,-159) -> Matrix(13,-6,24,-11) Matrix(607,-1984,108,-353) -> Matrix(23,-16,36,-25) Matrix(511,-1728,76,-257) -> Matrix(1,0,0,1) Matrix(543,-1856,122,-417) -> Matrix(5,-2,8,-3) Matrix(577,-1984,130,-447) -> Matrix(1,0,0,1) Matrix(511,-1856,106,-385) -> Matrix(5,-2,8,-3) Matrix(223,-832,26,-97) -> Matrix(5,-2,8,-3) Matrix(33,-128,8,-31) -> Matrix(5,-2,8,-3) Matrix(97,-512,18,-95) -> Matrix(13,-6,24,-11) Matrix(33,-256,4,-31) -> 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 8/7 16/13 4/3 24/17 16/11 8/5 80/49 12/7 16/9 2/1 32/15 24/11 20/9 16/7 64/27 12/5 32/13 8/3 36/13 64/23 48/17 3/1 16/5 10/3 64/19 24/7 4/1 32/7 14/3 24/5 5/1 16/3 28/5 6/1 32/5 20/3 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/2 1/0 1/1 0/1 1/1 8/7 1/0 15/13 -1/1 0/1 7/6 0/1 1/1 13/11 4/5 1/1 6/5 1/1 2/1 17/14 9/5 2/1 28/23 5/2 11/9 3/1 4/1 16/13 1/0 5/4 0/1 1/1 4/3 1/0 11/8 -1/1 0/1 40/29 1/0 29/21 -1/1 0/1 18/13 -1/1 0/1 7/5 0/1 1/1 24/17 1/0 41/29 -1/1 0/1 17/12 0/1 1/3 27/19 0/1 1/1 10/7 0/1 1/1 23/16 1/1 2/1 36/25 3/2 13/9 2/1 3/1 16/11 1/0 3/2 -1/1 0/1 8/5 1/0 13/8 -2/1 -1/1 44/27 -1/2 31/19 -1/1 -2/3 80/49 -1/2 49/30 -1/1 0/1 18/11 -1/1 0/1 23/14 -1/1 0/1 28/17 1/0 5/3 -1/3 0/1 22/13 0/1 1/7 17/10 0/1 1/3 12/7 1/2 31/18 0/1 1/1 50/29 0/1 1/1 19/11 0/1 1/1 26/15 0/1 1/1 7/4 0/1 1/1 16/9 1/0 9/5 -1/1 0/1 20/11 1/0 11/6 -1/1 0/1 24/13 -1/2 13/7 -1/3 0/1 28/15 -1/6 15/8 -1/13 0/1 2/1 0/1 1/1 17/8 -1/13 0/1 32/15 0/1 15/7 0/1 1/15 13/6 0/1 1/5 24/11 1/4 11/5 0/1 1/3 31/14 1/3 2/5 20/9 1/2 29/13 -1/1 0/1 9/4 0/1 1/3 16/7 1/2 7/3 0/1 1/1 33/14 4/5 1/1 26/11 0/1 1/1 45/19 0/1 1/1 64/27 1/2 1/0 19/8 0/1 1/1 12/5 1/0 29/12 -1/1 0/1 17/7 -1/1 0/1 39/16 -1/3 0/1 22/9 -1/5 0/1 27/11 -1/15 0/1 32/13 0/1 5/2 0/1 1/5 8/3 1/2 11/4 1/1 2/1 36/13 1/2 25/9 0/1 1/1 64/23 1/2 1/0 39/14 0/1 1/1 14/5 0/1 1/1 31/11 0/1 1/1 48/17 1/0 17/6 -1/1 0/1 20/7 1/0 3/1 0/1 1/3 16/5 1/2 13/4 3/5 2/3 36/11 3/4 23/7 2/3 1/1 33/10 4/5 1/1 10/3 0/1 1/1 37/11 0/1 1/1 64/19 1/2 1/0 27/8 0/1 1/1 44/13 1/0 17/5 -1/1 0/1 24/7 1/2 31/9 4/5 1/1 7/2 0/1 1/1 4/1 1/2 9/2 2/3 1/1 32/7 1/1 23/5 1/1 2/1 14/3 0/1 1/1 33/7 0/1 1/1 19/4 0/1 1/1 24/5 1/2 5/1 0/1 1/1 16/3 1/2 11/2 4/7 3/5 28/5 5/8 45/8 11/17 2/3 17/3 2/3 9/13 23/4 2/3 1/1 6/1 2/3 1/1 19/3 8/9 1/1 32/5 1/1 13/2 1/1 4/3 20/3 1/0 7/1 0/1 1/1 8/1 1/2 9/1 2/3 1/1 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(113,-128,98,-111) (1/1,8/7) -> (8/7,15/13) Parabolic Matrix(497,-576,151,-175) (15/13,7/6) -> (23/7,33/10) Hyperbolic Matrix(273,-320,122,-143) (7/6,13/11) -> (29/13,9/4) Hyperbolic Matrix(161,-192,26,-31) (13/11,6/5) -> (6/1,19/3) Hyperbolic Matrix(529,-640,224,-271) (6/5,17/14) -> (33/14,26/11) Hyperbolic Matrix(737,-896,394,-479) (17/14,28/23) -> (28/15,15/8) Hyperbolic Matrix(577,-704,209,-255) (28/23,11/9) -> (11/4,36/13) Hyperbolic Matrix(209,-256,169,-207) (11/9,16/13) -> (16/13,5/4) Parabolic Matrix(49,-64,36,-47) (5/4,4/3) -> (4/3,11/8) Parabolic Matrix(511,-704,233,-321) (11/8,40/29) -> (24/11,11/5) Hyperbolic Matrix(881,-1216,405,-559) (40/29,29/21) -> (13/6,24/11) Hyperbolic Matrix(1297,-1792,752,-1039) (29/21,18/13) -> (50/29,19/11) Hyperbolic Matrix(369,-512,80,-111) (18/13,7/5) -> (23/5,14/3) Hyperbolic Matrix(817,-1152,578,-815) (7/5,24/17) -> (24/17,41/29) Parabolic Matrix(769,-1088,135,-191) (41/29,17/12) -> (17/3,23/4) Hyperbolic Matrix(721,-1024,326,-463) (17/12,27/19) -> (11/5,31/14) Hyperbolic Matrix(449,-640,134,-191) (27/19,10/7) -> (10/3,37/11) Hyperbolic Matrix(625,-896,256,-367) (10/7,23/16) -> (39/16,22/9) Hyperbolic Matrix(1201,-1728,433,-623) (23/16,36/25) -> (36/13,25/9) Hyperbolic Matrix(577,-832,310,-447) (36/25,13/9) -> (13/7,28/15) Hyperbolic Matrix(177,-256,121,-175) (13/9,16/11) -> (16/11,3/2) Parabolic Matrix(81,-128,50,-79) (3/2,8/5) -> (8/5,13/8) Parabolic Matrix(943,-1536,423,-689) (13/8,44/27) -> (20/9,29/13) Hyperbolic Matrix(1217,-1984,549,-895) (44/27,31/19) -> (31/14,20/9) Hyperbolic Matrix(3921,-6400,2401,-3919) (31/19,80/49) -> (80/49,49/30) Parabolic Matrix(783,-1280,167,-273) (49/30,18/11) -> (14/3,33/7) Hyperbolic Matrix(625,-1024,224,-367) (18/11,23/14) -> (39/14,14/5) Hyperbolic Matrix(895,-1472,273,-449) (23/14,28/17) -> (36/11,23/7) Hyperbolic Matrix(271,-448,49,-81) (28/17,5/3) -> (11/2,28/5) Hyperbolic Matrix(417,-704,170,-287) (5/3,22/13) -> (22/9,27/11) Hyperbolic Matrix(529,-896,160,-271) (22/13,17/10) -> (33/10,10/3) Hyperbolic Matrix(337,-576,196,-335) (17/10,12/7) -> (12/7,31/18) Parabolic Matrix(1151,-1984,409,-705) (31/18,50/29) -> (14/5,31/11) Hyperbolic Matrix(961,-1664,406,-703) (19/11,26/15) -> (26/11,45/19) Hyperbolic Matrix(369,-640,64,-111) (26/15,7/4) -> (23/4,6/1) Hyperbolic Matrix(145,-256,81,-143) (7/4,16/9) -> (16/9,9/5) Parabolic Matrix(177,-320,26,-47) (9/5,20/11) -> (20/3,7/1) Hyperbolic Matrix(561,-1024,166,-303) (20/11,11/6) -> (27/8,44/13) Hyperbolic Matrix(209,-384,43,-79) (11/6,24/13) -> (24/5,5/1) Hyperbolic Matrix(415,-768,87,-161) (24/13,13/7) -> (19/4,24/5) Hyperbolic Matrix(33,-64,16,-31) (15/8,2/1) -> (2/1,17/8) Parabolic Matrix(481,-1024,225,-479) (17/8,32/15) -> (32/15,15/7) Parabolic Matrix(417,-896,74,-159) (15/7,13/6) -> (45/8,17/3) Hyperbolic Matrix(113,-256,49,-111) (9/4,16/7) -> (16/7,7/3) Parabolic Matrix(191,-448,55,-129) (7/3,33/14) -> (31/9,7/2) Hyperbolic Matrix(1729,-4096,729,-1727) (45/19,64/27) -> (64/27,19/8) Parabolic Matrix(241,-576,100,-239) (19/8,12/5) -> (12/5,29/12) Parabolic Matrix(529,-1280,112,-271) (29/12,17/7) -> (33/7,19/4) Hyperbolic Matrix(79,-192,7,-17) (17/7,39/16) -> (9/1,1/0) Hyperbolic Matrix(417,-1024,169,-415) (27/11,32/13) -> (32/13,5/2) Parabolic Matrix(49,-128,18,-47) (5/2,8/3) -> (8/3,11/4) Parabolic Matrix(1473,-4096,529,-1471) (25/9,64/23) -> (64/23,39/14) Parabolic Matrix(817,-2304,289,-815) (31/11,48/17) -> (48/17,17/6) Parabolic Matrix(383,-1088,113,-321) (17/6,20/7) -> (44/13,17/5) Hyperbolic Matrix(111,-320,17,-49) (20/7,3/1) -> (13/2,20/3) Hyperbolic Matrix(81,-256,25,-79) (3/1,16/5) -> (16/5,13/4) Parabolic Matrix(607,-1984,108,-353) (13/4,36/11) -> (28/5,45/8) Hyperbolic Matrix(1217,-4096,361,-1215) (37/11,64/19) -> (64/19,27/8) Parabolic Matrix(337,-1152,98,-335) (17/5,24/7) -> (24/7,31/9) Parabolic Matrix(17,-64,4,-15) (7/2,4/1) -> (4/1,9/2) Parabolic Matrix(225,-1024,49,-223) (9/2,32/7) -> (32/7,23/5) Parabolic Matrix(49,-256,9,-47) (5/1,16/3) -> (16/3,11/2) Parabolic Matrix(161,-1024,25,-159) (19/3,32/5) -> (32/5,13/2) Parabolic Matrix(17,-128,2,-15) (7/1,8/1) -> (8/1,9/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,0,1) Matrix(113,-128,98,-111) -> Matrix(1,-1,0,1) Matrix(497,-576,151,-175) -> Matrix(3,-1,4,-1) Matrix(273,-320,122,-143) -> Matrix(1,-1,4,-3) Matrix(161,-192,26,-31) -> Matrix(3,-4,4,-5) Matrix(529,-640,224,-271) -> Matrix(1,-1,0,1) Matrix(737,-896,394,-479) -> Matrix(1,-2,-8,17) Matrix(577,-704,209,-255) -> Matrix(1,-2,0,1) Matrix(209,-256,169,-207) -> Matrix(1,-3,0,1) Matrix(49,-64,36,-47) -> Matrix(1,-1,0,1) Matrix(511,-704,233,-321) -> Matrix(1,0,4,1) Matrix(881,-1216,405,-559) -> Matrix(1,1,4,5) Matrix(1297,-1792,752,-1039) -> Matrix(1,1,0,1) Matrix(369,-512,80,-111) -> Matrix(1,1,0,1) Matrix(817,-1152,578,-815) -> Matrix(1,-1,0,1) Matrix(769,-1088,135,-191) -> Matrix(3,2,4,3) Matrix(721,-1024,326,-463) -> Matrix(1,-1,4,-3) Matrix(449,-640,134,-191) -> Matrix(1,0,0,1) Matrix(625,-896,256,-367) -> Matrix(1,-1,-4,5) Matrix(1201,-1728,433,-623) -> Matrix(1,-1,0,1) Matrix(577,-832,310,-447) -> Matrix(1,-2,-4,9) Matrix(177,-256,121,-175) -> Matrix(1,-3,0,1) Matrix(81,-128,50,-79) -> Matrix(1,-1,0,1) Matrix(943,-1536,423,-689) -> Matrix(1,1,0,1) Matrix(1217,-1984,549,-895) -> Matrix(1,0,4,1) Matrix(3921,-6400,2401,-3919) -> Matrix(1,1,-4,-3) Matrix(783,-1280,167,-273) -> Matrix(1,1,0,1) Matrix(625,-1024,224,-367) -> Matrix(1,1,0,1) Matrix(895,-1472,273,-449) -> Matrix(3,2,4,3) Matrix(271,-448,49,-81) -> Matrix(5,3,8,5) Matrix(417,-704,170,-287) -> Matrix(1,0,-12,1) Matrix(529,-896,160,-271) -> Matrix(7,-1,8,-1) Matrix(337,-576,196,-335) -> Matrix(3,-1,4,-1) Matrix(1151,-1984,409,-705) -> Matrix(1,0,0,1) Matrix(961,-1664,406,-703) -> Matrix(1,0,0,1) Matrix(369,-640,64,-111) -> Matrix(3,-1,4,-1) Matrix(145,-256,81,-143) -> Matrix(1,-1,0,1) Matrix(177,-320,26,-47) -> Matrix(1,1,0,1) Matrix(561,-1024,166,-303) -> Matrix(1,1,0,1) Matrix(209,-384,43,-79) -> Matrix(1,1,0,1) Matrix(415,-768,87,-161) -> Matrix(1,0,4,1) Matrix(33,-64,16,-31) -> Matrix(1,0,0,1) Matrix(481,-1024,225,-479) -> Matrix(1,0,28,1) Matrix(417,-896,74,-159) -> Matrix(21,-2,32,-3) Matrix(113,-256,49,-111) -> Matrix(3,-1,4,-1) Matrix(191,-448,55,-129) -> Matrix(1,0,0,1) Matrix(1729,-4096,729,-1727) -> Matrix(1,0,0,1) Matrix(241,-576,100,-239) -> Matrix(1,-1,0,1) Matrix(529,-1280,112,-271) -> Matrix(1,1,0,1) Matrix(79,-192,7,-17) -> Matrix(1,1,0,1) Matrix(417,-1024,169,-415) -> Matrix(1,0,20,1) Matrix(49,-128,18,-47) -> Matrix(3,-1,4,-1) Matrix(1473,-4096,529,-1471) -> Matrix(1,0,0,1) Matrix(817,-2304,289,-815) -> Matrix(1,-1,0,1) Matrix(383,-1088,113,-321) -> Matrix(1,0,0,1) Matrix(111,-320,17,-49) -> Matrix(1,1,0,1) Matrix(81,-256,25,-79) -> Matrix(7,-3,12,-5) Matrix(607,-1984,108,-353) -> Matrix(23,-16,36,-25) Matrix(1217,-4096,361,-1215) -> Matrix(1,0,0,1) Matrix(337,-1152,98,-335) -> Matrix(3,-1,4,-1) Matrix(17,-64,4,-15) -> Matrix(3,-1,4,-1) Matrix(225,-1024,49,-223) -> Matrix(5,-4,4,-3) Matrix(49,-256,9,-47) -> Matrix(7,-3,12,-5) Matrix(161,-1024,25,-159) -> Matrix(13,-12,12,-11) Matrix(17,-128,2,-15) -> 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 1 2/1 (0/1,1/1) 0 16 32/15 0/1 28 1 15/7 (0/1,1/15) 0 32 13/6 (0/1,1/5) 0 32 24/11 1/4 2 4 11/5 (0/1,1/3) 0 32 20/9 1/2 2 8 9/4 (0/1,1/3) 0 32 16/7 1/2 2 2 7/3 (0/1,1/1) 0 32 26/11 (0/1,1/1) 0 16 64/27 (0/1,1/1) 0 1 19/8 (0/1,1/1) 0 32 12/5 1/0 2 8 29/12 (-1/1,0/1) 0 32 17/7 (-1/1,0/1) 0 32 22/9 (-1/5,0/1) 0 16 32/13 0/1 20 1 5/2 (0/1,1/5) 0 32 8/3 1/2 2 4 11/4 (1/1,2/1) 0 32 36/13 1/2 2 8 25/9 (0/1,1/1) 0 32 64/23 (0/1,1/1) 0 1 14/5 (0/1,1/1) 0 16 31/11 (0/1,1/1) 0 32 48/17 1/0 2 2 17/6 (-1/1,0/1) 0 32 20/7 1/0 2 8 3/1 (0/1,1/3) 0 32 16/5 1/2 6 2 13/4 (3/5,2/3) 0 32 36/11 3/4 2 8 23/7 (2/3,1/1) 0 32 33/10 (4/5,1/1) 0 32 10/3 (0/1,1/1) 0 16 64/19 (0/1,1/1) 0 1 27/8 (0/1,1/1) 0 32 44/13 1/0 2 8 17/5 (-1/1,0/1) 0 32 24/7 1/2 2 4 31/9 (4/5,1/1) 0 32 7/2 (0/1,1/1) 0 32 4/1 1/2 2 8 9/2 (2/3,1/1) 0 32 32/7 1/1 4 1 14/3 (0/1,1/1) 0 16 33/7 (0/1,1/1) 0 32 19/4 (0/1,1/1) 0 32 24/5 1/2 2 4 5/1 (0/1,1/1) 0 32 16/3 1/2 6 2 11/2 (4/7,3/5) 0 32 28/5 5/8 2 8 45/8 (11/17,2/3) 0 32 17/3 (2/3,9/13) 0 32 23/4 (2/3,1/1) 0 32 6/1 (2/3,1/1) 0 16 32/5 1/1 12 1 13/2 (1/1,4/3) 0 32 20/3 1/0 2 8 7/1 (0/1,1/1) 0 32 8/1 1/2 2 4 9/1 (2/3,1/1) 0 32 1/0 (0/1,1/1) 0 32 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(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(31,-64,15,-31) (2/1,32/15) -> (2/1,32/15) Reflection Matrix(449,-960,210,-449) (32/15,15/7) -> (32/15,15/7) Reflection Matrix(417,-896,74,-159) (15/7,13/6) -> (45/8,17/3) Hyperbolic Matrix(353,-768,74,-161) (13/6,24/11) -> (19/4,24/5) Glide Reflection Matrix(175,-384,36,-79) (24/11,11/5) -> (24/5,5/1) Glide Reflection Matrix(463,-1024,137,-303) (11/5,20/9) -> (27/8,44/13) Glide Reflection Matrix(143,-320,21,-47) (20/9,9/4) -> (20/3,7/1) Glide Reflection Matrix(113,-256,49,-111) (9/4,16/7) -> (16/7,7/3) Parabolic Matrix(271,-640,47,-111) (7/3,26/11) -> (23/4,6/1) Glide Reflection Matrix(703,-1664,297,-703) (26/11,64/27) -> (26/11,64/27) Reflection Matrix(1025,-2432,432,-1025) (64/27,19/8) -> (64/27,19/8) Reflection Matrix(241,-576,100,-239) (19/8,12/5) -> (12/5,29/12) Parabolic Matrix(529,-1280,112,-271) (29/12,17/7) -> (33/7,19/4) Hyperbolic Matrix(367,-896,111,-271) (17/7,22/9) -> (33/10,10/3) Glide Reflection Matrix(287,-704,117,-287) (22/9,32/13) -> (22/9,32/13) Reflection Matrix(129,-320,52,-129) (32/13,5/2) -> (32/13,5/2) Reflection Matrix(49,-128,18,-47) (5/2,8/3) -> (8/3,11/4) Parabolic Matrix(255,-704,46,-127) (11/4,36/13) -> (11/2,28/5) Glide Reflection Matrix(623,-1728,190,-527) (36/13,25/9) -> (36/11,23/7) Glide Reflection Matrix(1151,-3200,414,-1151) (25/9,64/23) -> (25/9,64/23) Reflection Matrix(321,-896,115,-321) (64/23,14/5) -> (64/23,14/5) Reflection Matrix(319,-896,68,-191) (14/5,31/11) -> (14/3,33/7) Glide Reflection Matrix(817,-2304,289,-815) (31/11,48/17) -> (48/17,17/6) Parabolic Matrix(383,-1088,113,-321) (17/6,20/7) -> (44/13,17/5) Hyperbolic Matrix(111,-320,17,-49) (20/7,3/1) -> (13/2,20/3) Hyperbolic Matrix(81,-256,25,-79) (3/1,16/5) -> (16/5,13/4) Parabolic Matrix(607,-1984,108,-353) (13/4,36/11) -> (28/5,45/8) Hyperbolic Matrix(97,-320,10,-33) (23/7,33/10) -> (9/1,1/0) Glide Reflection Matrix(191,-640,57,-191) (10/3,64/19) -> (10/3,64/19) Reflection Matrix(1025,-3456,304,-1025) (64/19,27/8) -> (64/19,27/8) Reflection Matrix(337,-1152,98,-335) (17/5,24/7) -> (24/7,31/9) Parabolic Matrix(241,-832,42,-145) (31/9,7/2) -> (17/3,23/4) Glide Reflection Matrix(17,-64,4,-15) (7/2,4/1) -> (4/1,9/2) Parabolic Matrix(127,-576,28,-127) (9/2,32/7) -> (9/2,32/7) Reflection Matrix(97,-448,21,-97) (32/7,14/3) -> (32/7,14/3) Reflection Matrix(49,-256,9,-47) (5/1,16/3) -> (16/3,11/2) Parabolic Matrix(31,-192,5,-31) (6/1,32/5) -> (6/1,32/5) Reflection Matrix(129,-832,20,-129) (32/5,13/2) -> (32/5,13/2) Reflection Matrix(17,-128,2,-15) (7/1,8/1) -> (8/1,9/1) Parabolic 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(1,0,1,-1) -> Matrix(1,0,2,-1) (0/1,2/1) -> (0/1,1/1) Matrix(31,-64,15,-31) -> Matrix(1,0,2,-1) (2/1,32/15) -> (0/1,1/1) Matrix(449,-960,210,-449) -> Matrix(1,0,30,-1) (32/15,15/7) -> (0/1,1/15) Matrix(417,-896,74,-159) -> Matrix(21,-2,32,-3) Matrix(353,-768,74,-161) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(175,-384,36,-79) -> Matrix(3,-1,2,-1) Matrix(463,-1024,137,-303) -> Matrix(3,-1,2,-1) Matrix(143,-320,21,-47) -> Matrix(3,-1,2,-1) Matrix(113,-256,49,-111) -> Matrix(3,-1,4,-1) 1/2 Matrix(271,-640,47,-111) -> Matrix(1,1,2,1) Matrix(703,-1664,297,-703) -> Matrix(1,0,2,-1) (26/11,64/27) -> (0/1,1/1) Matrix(1025,-2432,432,-1025) -> Matrix(1,0,2,-1) (64/27,19/8) -> (0/1,1/1) Matrix(241,-576,100,-239) -> Matrix(1,-1,0,1) 1/0 Matrix(529,-1280,112,-271) -> Matrix(1,1,0,1) 1/0 Matrix(367,-896,111,-271) -> Matrix(5,1,6,1) Matrix(287,-704,117,-287) -> Matrix(-1,0,10,1) (22/9,32/13) -> (-1/5,0/1) Matrix(129,-320,52,-129) -> Matrix(1,0,10,-1) (32/13,5/2) -> (0/1,1/5) Matrix(49,-128,18,-47) -> Matrix(3,-1,4,-1) 1/2 Matrix(255,-704,46,-127) -> Matrix(1,2,2,3) Matrix(623,-1728,190,-527) -> Matrix(1,1,2,1) Matrix(1151,-3200,414,-1151) -> Matrix(1,0,2,-1) (25/9,64/23) -> (0/1,1/1) Matrix(321,-896,115,-321) -> Matrix(1,0,2,-1) (64/23,14/5) -> (0/1,1/1) Matrix(319,-896,68,-191) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(817,-2304,289,-815) -> Matrix(1,-1,0,1) 1/0 Matrix(383,-1088,113,-321) -> Matrix(1,0,0,1) Matrix(111,-320,17,-49) -> Matrix(1,1,0,1) 1/0 Matrix(81,-256,25,-79) -> Matrix(7,-3,12,-5) 1/2 Matrix(607,-1984,108,-353) -> Matrix(23,-16,36,-25) 2/3 Matrix(97,-320,10,-33) -> Matrix(5,-4,6,-5) *** -> (2/3,1/1) Matrix(191,-640,57,-191) -> Matrix(1,0,2,-1) (10/3,64/19) -> (0/1,1/1) Matrix(1025,-3456,304,-1025) -> Matrix(1,0,2,-1) (64/19,27/8) -> (0/1,1/1) Matrix(337,-1152,98,-335) -> Matrix(3,-1,4,-1) 1/2 Matrix(241,-832,42,-145) -> Matrix(1,1,2,1) Matrix(17,-64,4,-15) -> Matrix(3,-1,4,-1) 1/2 Matrix(127,-576,28,-127) -> Matrix(5,-4,6,-5) (9/2,32/7) -> (2/3,1/1) Matrix(97,-448,21,-97) -> Matrix(1,0,2,-1) (32/7,14/3) -> (0/1,1/1) Matrix(49,-256,9,-47) -> Matrix(7,-3,12,-5) 1/2 Matrix(31,-192,5,-31) -> Matrix(5,-4,6,-5) (6/1,32/5) -> (2/3,1/1) Matrix(129,-832,20,-129) -> Matrix(7,-8,6,-7) (32/5,13/2) -> (1/1,4/3) Matrix(17,-128,2,-15) -> Matrix(3,-1,4,-1) 1/2 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.