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): 1800 Minimal number of generators: 301 Number of equivalence classes of cusps: 84 Genus: 109 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -15/2 -20/3 -5/1 -15/4 -10/3 -75/23 -5/2 -20/9 -15/7 -5/3 -25/17 -15/11 -25/19 -5/4 -75/62 -25/21 -25/22 0/1 1/1 5/4 15/11 25/18 75/52 3/2 25/16 5/3 125/74 25/14 2/1 15/7 20/9 25/11 50/21 12/5 5/2 125/49 50/19 25/9 3/1 25/8 10/3 7/2 25/7 18/5 11/3 100/27 250/67 15/4 200/53 50/13 4/1 25/6 21/5 13/3 9/2 50/11 23/5 14/3 19/4 24/5 5/1 21/4 16/3 11/2 50/9 17/3 23/4 75/13 6/1 25/4 19/3 13/2 20/3 7/1 50/7 22/3 15/2 8/1 25/3 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -2/1 -9/1 -1/1 -8/1 0/1 -15/2 1/0 -7/1 1/1 -20/3 2/1 -13/2 9/2 -6/1 -6/1 -17/3 -3/1 -11/2 -3/2 -16/3 -4/1 -5/1 -1/1 -19/4 1/4 -14/3 -2/1 -23/5 -1/3 -9/2 1/2 -40/9 0/1 -31/7 5/7 -22/5 6/5 -79/18 7/6 -136/31 4/3 -57/13 7/5 -35/8 3/2 -13/3 7/3 -30/7 4/1 -17/4 1/0 -4/1 -4/1 -19/5 -7/5 -34/9 -2/1 -49/13 -1/1 -15/4 1/0 -56/15 -12/5 -41/11 -3/1 -26/7 -2/1 -11/3 -1/1 -51/14 -3/2 -40/11 -4/3 -69/19 -3/1 -29/8 -11/8 -76/21 -4/3 -47/13 -7/5 -65/18 -5/4 -18/5 -6/5 -25/7 -1/1 -7/2 -1/2 -24/7 0/1 -41/12 1/0 -17/5 -1/1 -44/13 -4/1 -115/34 -3/2 -71/21 -7/5 -98/29 -10/9 -125/37 -1/1 -27/8 -3/4 -10/3 0/1 -23/7 3/5 -36/11 4/5 -121/37 11/13 -85/26 5/6 -49/15 1/1 -62/19 18/19 -75/23 1/1 -13/4 5/4 -16/5 4/1 -19/6 11/2 -3/1 -3/1 -20/7 -2/1 -17/6 -3/2 -14/5 -6/5 -25/9 -1/1 -11/4 -3/4 -30/11 -2/3 -49/18 -1/2 -19/7 -3/7 -46/17 -2/9 -27/10 1/2 -62/23 -6/1 -35/13 -1/1 -8/3 0/1 -21/8 1/8 -55/21 1/5 -34/13 2/7 -13/5 3/5 -31/12 9/8 -49/19 1/1 -116/45 4/3 -67/26 3/2 -18/7 2/1 -41/16 9/4 -23/9 1/1 -5/2 1/0 -27/11 -5/1 -76/31 -4/1 -125/51 -3/1 -49/20 1/0 -22/9 -6/1 -39/16 -15/4 -17/7 -3/1 -29/12 -23/8 -41/17 -19/7 -94/39 -62/23 -53/22 -37/14 -12/5 -12/5 -19/8 -15/8 -45/19 -5/3 -71/30 -11/6 -26/11 -2/1 -7/3 -1/1 -30/13 -4/3 -53/23 -7/5 -76/33 -4/3 -23/10 -3/2 -16/7 -8/7 -25/11 -1/1 -9/4 -3/4 -29/13 -3/7 -78/35 -2/5 -49/22 -1/2 -20/9 0/1 -11/5 -1/3 -24/11 0/1 -13/6 1/6 -15/7 1/1 -17/8 1/0 -2/1 -2/1 -17/9 -1/1 -15/8 -1/2 -13/7 -1/7 -11/6 1/2 -20/11 0/1 -29/16 3/4 -9/5 3/1 -25/14 1/0 -16/9 -8/1 -39/22 -11/2 -62/35 -34/7 -23/13 -3/1 -30/17 -4/1 -7/4 1/0 -26/15 -2/1 -19/11 -15/7 -50/29 -2/1 -31/18 -27/14 -12/7 -12/7 -53/31 -37/23 -41/24 -19/12 -29/17 -23/15 -75/44 -3/2 -46/27 -34/23 -17/10 -3/2 -22/13 -6/5 -5/3 -1/1 -28/17 0/1 -51/31 -1/1 -125/76 -3/4 -74/45 -2/3 -23/14 -1/2 -18/11 -2/3 -85/52 -1/2 -67/41 -3/5 -49/30 -1/2 -31/19 -9/17 -75/46 -1/2 -44/27 -12/25 -13/8 -3/8 -34/21 -2/9 -21/13 -1/9 -50/31 0/1 -29/18 1/10 -8/5 0/1 -35/22 1/0 -97/61 -7/3 -62/39 -6/5 -27/17 -1/3 -19/12 3/4 -49/31 1/1 -128/81 0/1 -79/50 1/2 -30/19 2/1 -11/7 3/1 -25/16 1/0 -14/9 -6/1 -31/20 -15/4 -48/31 -8/3 -17/11 -3/1 -20/13 -2/1 -23/15 -1/1 -3/2 -3/2 -25/17 -1/1 -22/15 -14/15 -19/13 -11/13 -16/11 -4/5 -13/9 -5/9 -23/16 -3/8 -10/7 0/1 -27/19 3/1 -17/12 1/0 -75/53 -1/1 -58/41 -2/3 -41/29 -1/1 -24/17 0/1 -7/5 1/1 -25/18 1/0 -18/13 -6/1 -83/60 1/0 -65/47 -5/1 -112/81 -40/9 -47/34 -7/2 -123/89 -3/1 -76/55 -4/1 -29/21 -11/3 -98/71 -14/5 -69/50 -3/2 -40/29 -4/1 -51/37 -3/1 -62/45 -26/9 -11/8 1/0 -37/27 -19/9 -100/73 -2/1 -63/46 -27/14 -26/19 -2/1 -41/30 -3/2 -97/71 -11/5 -250/183 -2/1 -153/112 -23/12 -56/41 -12/7 -15/11 -1/1 -49/36 1/0 -83/61 -3/1 -200/147 -2/1 -117/86 -3/2 -34/25 -2/1 -19/14 -7/2 -23/17 -11/5 -50/37 -2/1 -27/20 -15/8 -4/3 -4/3 -25/19 -1/1 -21/16 -15/16 -17/13 -1/1 -30/23 -4/5 -13/10 -7/10 -35/27 -3/5 -22/17 -6/11 -75/58 -1/2 -53/41 -11/23 -31/24 -5/12 -40/31 0/1 -9/7 -1/3 -50/39 0/1 -41/32 1/8 -32/25 0/1 -23/18 1/2 -37/29 7/1 -125/98 1/0 -88/69 -16/1 -51/40 1/0 -65/51 -3/1 -14/11 -2/1 -33/26 -1/2 -52/41 -4/7 -71/56 -5/12 -19/15 -1/5 -24/19 0/1 -5/4 1/0 -26/21 -2/1 -21/17 -7/3 -16/13 -4/3 -27/22 -1/2 -38/31 6/1 -49/40 1/0 -11/9 -3/1 -50/41 -2/1 -39/32 -15/8 -28/23 -12/7 -17/14 -3/2 -23/19 -11/7 -75/62 -3/2 -52/43 -28/19 -29/24 -17/12 -64/53 -4/3 -35/29 -7/5 -6/5 -6/5 -25/21 -1/1 -19/16 -15/16 -13/11 -9/11 -20/17 -2/3 -7/6 -1/2 -50/43 0/1 -43/37 1/5 -36/31 0/1 -29/25 3/1 -22/19 2/1 -15/13 -1/1 -8/7 0/1 -25/22 1/0 -17/15 -3/1 -9/8 1/0 -10/9 -2/1 -1/1 -1/1 0/1 0/1 1/1 1/1 10/9 2/1 9/8 1/0 8/7 0/1 15/13 1/1 7/6 1/2 20/17 2/3 13/11 9/11 6/5 6/5 17/14 3/2 11/9 3/1 16/13 4/3 5/4 1/0 19/15 1/5 14/11 2/1 23/18 -1/2 9/7 1/3 40/31 0/1 31/24 5/12 22/17 6/11 79/61 7/13 136/105 4/7 57/44 7/12 35/27 3/5 13/10 7/10 30/23 4/5 17/13 1/1 4/3 4/3 19/14 7/2 34/25 2/1 49/36 1/0 15/11 1/1 56/41 12/7 41/30 3/2 26/19 2/1 11/8 1/0 51/37 3/1 40/29 4/1 69/50 3/2 29/21 11/3 76/55 4/1 47/34 7/2 65/47 5/1 18/13 6/1 25/18 1/0 7/5 -1/1 24/17 0/1 41/29 1/1 17/12 1/0 44/31 4/3 115/81 3/1 71/50 7/2 98/69 10/1 125/88 1/0 27/19 -3/1 10/7 0/1 23/16 3/8 36/25 4/9 121/84 11/24 85/59 5/11 49/34 1/2 62/43 18/37 75/52 1/2 13/9 5/9 16/11 4/5 19/13 11/13 3/2 3/2 20/13 2/1 17/11 3/1 14/9 6/1 25/16 1/0 11/7 -3/1 30/19 -2/1 49/31 -1/1 19/12 -3/4 46/29 -2/7 27/17 1/3 62/39 6/5 35/22 1/0 8/5 0/1 21/13 1/9 55/34 1/6 34/21 2/9 13/8 3/8 31/19 9/17 49/30 1/2 116/71 4/7 67/41 3/5 18/11 2/3 41/25 9/13 23/14 1/2 5/3 1/1 27/16 5/4 76/45 4/3 125/74 3/2 49/29 1/1 22/13 6/5 39/23 15/11 17/10 3/2 29/17 23/15 41/24 19/12 94/55 62/39 53/31 37/23 12/7 12/7 19/11 15/7 45/26 5/2 71/41 11/5 26/15 2/1 7/4 1/0 30/17 4/1 53/30 7/2 76/43 4/1 23/13 3/1 16/9 8/1 25/14 1/0 9/5 -3/1 29/16 -3/4 78/43 -2/3 49/27 -1/1 20/11 0/1 11/6 -1/2 24/13 0/1 13/7 1/7 15/8 1/2 17/9 1/1 2/1 2/1 17/8 1/0 15/7 -1/1 13/6 -1/6 11/5 1/3 20/9 0/1 29/13 3/7 9/4 3/4 25/11 1/1 16/7 8/7 39/17 11/9 62/27 34/27 23/10 3/2 30/13 4/3 7/3 1/1 26/11 2/1 19/8 15/8 50/21 2/1 31/13 27/13 12/5 12/5 53/22 37/14 41/17 19/7 29/12 23/8 75/31 3/1 46/19 34/11 17/7 3/1 22/9 6/1 5/2 1/0 28/11 0/1 51/20 1/0 125/49 -3/1 74/29 -2/1 23/9 -1/1 18/7 -2/1 85/33 -1/1 67/26 -3/2 49/19 -1/1 31/12 -9/8 75/29 -1/1 44/17 -12/13 13/5 -3/5 34/13 -2/7 21/8 -1/8 50/19 0/1 29/11 1/11 8/3 0/1 35/13 1/1 97/36 7/4 62/23 6/1 27/10 -1/2 19/7 3/7 49/18 1/2 128/47 0/1 79/29 1/3 30/11 2/3 11/4 3/4 25/9 1/1 14/5 6/5 31/11 15/11 48/17 8/5 17/6 3/2 20/7 2/1 23/8 1/0 3/1 3/1 25/8 1/0 22/7 -14/1 19/6 -11/2 16/5 -4/1 13/4 -5/4 23/7 -3/5 10/3 0/1 27/8 3/4 17/5 1/1 75/22 1/0 58/17 -2/1 41/12 1/0 24/7 0/1 7/2 1/2 25/7 1/1 18/5 6/5 83/23 1/1 65/18 5/4 112/31 40/31 47/13 7/5 123/34 3/2 76/21 4/3 29/8 11/8 98/27 14/9 69/19 3/1 40/11 4/3 51/14 3/2 62/17 26/17 11/3 1/1 37/10 19/10 100/27 2/1 63/17 27/13 26/7 2/1 41/11 3/1 97/26 11/6 250/67 2/1 153/41 23/11 56/15 12/5 15/4 1/0 49/13 1/1 83/22 3/2 200/53 2/1 117/31 3/1 34/9 2/1 19/5 7/5 23/6 11/6 50/13 2/1 27/7 15/7 4/1 4/1 25/6 1/0 21/5 -15/1 17/4 1/0 30/7 -4/1 13/3 -7/3 35/8 -3/2 22/5 -6/5 75/17 -1/1 53/12 -11/12 31/7 -5/7 40/9 0/1 9/2 -1/2 50/11 0/1 41/9 1/9 32/7 0/1 23/5 1/3 37/8 7/8 125/27 1/1 88/19 16/15 51/11 1/1 65/14 3/2 14/3 2/1 33/7 -1/1 52/11 -4/3 71/15 -5/7 19/4 -1/4 24/5 0/1 5/1 1/1 26/5 2/1 21/4 7/4 16/3 4/1 27/5 -1/1 38/7 6/7 49/9 1/1 11/2 3/2 50/9 2/1 39/7 15/7 28/5 12/5 17/3 3/1 23/4 11/4 75/13 3/1 52/9 28/9 29/5 17/5 64/11 4/1 35/6 7/2 6/1 6/1 25/4 1/0 19/3 -15/1 13/2 -9/2 20/3 -2/1 7/1 -1/1 50/7 0/1 43/6 1/6 36/5 0/1 29/4 3/4 22/3 2/3 15/2 1/0 8/1 0/1 25/3 1/1 17/2 3/2 9/1 1/1 10/1 2/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(51,550,14,151) (-10/1,1/0) -> (40/11,51/14) Hyperbolic Matrix(49,450,38,349) (-10/1,-9/1) -> (9/7,40/31) Hyperbolic Matrix(99,850,-70,-601) (-9/1,-8/1) -> (-58/41,-41/29) Hyperbolic Matrix(51,400,32,251) (-8/1,-15/2) -> (35/22,8/5) Hyperbolic Matrix(149,1100,-34,-251) (-15/2,-7/1) -> (-57/13,-35/8) Hyperbolic Matrix(51,350,22,151) (-7/1,-20/3) -> (30/13,7/3) Hyperbolic Matrix(99,650,76,499) (-20/3,-13/2) -> (13/10,30/23) Hyperbolic Matrix(101,650,-62,-399) (-13/2,-6/1) -> (-44/27,-13/8) Hyperbolic Matrix(149,850,-44,-251) (-6/1,-17/3) -> (-17/5,-44/13) Hyperbolic Matrix(151,850,-62,-349) (-17/3,-11/2) -> (-39/16,-17/7) Hyperbolic Matrix(149,800,-84,-451) (-11/2,-16/3) -> (-16/9,-39/22) Hyperbolic Matrix(199,1050,-76,-401) (-16/3,-5/1) -> (-55/21,-34/13) Hyperbolic Matrix(199,950,-84,-401) (-5/1,-19/4) -> (-19/8,-45/19) Hyperbolic Matrix(149,700,-96,-451) (-19/4,-14/3) -> (-14/9,-31/20) Hyperbolic Matrix(249,1150,-76,-351) (-14/3,-23/5) -> (-23/7,-36/11) Hyperbolic Matrix(251,1150,-98,-449) (-23/5,-9/2) -> (-41/16,-23/9) Hyperbolic Matrix(101,450,90,401) (-9/2,-40/9) -> (10/9,9/8) Hyperbolic Matrix(901,4000,248,1101) (-40/9,-31/7) -> (69/19,40/11) Hyperbolic Matrix(249,1100,-170,-751) (-31/7,-22/5) -> (-22/15,-19/13) Hyperbolic Matrix(1549,6800,854,3749) (-22/5,-79/18) -> (29/16,78/43) Hyperbolic Matrix(4399,19300,3054,13399) (-79/18,-136/31) -> (36/25,121/84) Hyperbolic Matrix(1801,7900,-1550,-6799) (-136/31,-57/13) -> (-43/37,-36/31) Hyperbolic Matrix(149,650,80,349) (-35/8,-13/3) -> (13/7,15/8) Hyperbolic Matrix(151,650,128,551) (-13/3,-30/7) -> (20/17,13/11) Hyperbolic Matrix(199,850,70,299) (-30/7,-17/4) -> (17/6,20/7) Hyperbolic Matrix(201,850,-118,-499) (-17/4,-4/1) -> (-46/27,-17/10) Hyperbolic Matrix(249,950,-92,-351) (-4/1,-19/5) -> (-19/7,-46/17) Hyperbolic Matrix(251,950,172,651) (-19/5,-34/9) -> (16/11,19/13) Hyperbolic Matrix(1949,7350,-756,-2851) (-34/9,-49/13) -> (-49/19,-116/45) Hyperbolic Matrix(1301,4900,-398,-1499) (-49/13,-15/4) -> (-85/26,-49/15) Hyperbolic Matrix(1901,7100,-562,-2099) (-15/4,-56/15) -> (-44/13,-115/34) Hyperbolic Matrix(1649,6150,-684,-2551) (-56/15,-41/11) -> (-41/17,-94/39) Hyperbolic Matrix(551,2050,390,1451) (-41/11,-26/7) -> (24/17,41/29) Hyperbolic Matrix(149,550,-68,-251) (-26/7,-11/3) -> (-11/5,-24/11) Hyperbolic Matrix(301,1100,-246,-899) (-11/3,-51/14) -> (-49/40,-11/9) Hyperbolic Matrix(151,550,14,51) (-51/14,-40/11) -> (10/1,1/0) Hyperbolic Matrix(1101,4000,248,901) (-40/11,-69/19) -> (31/7,40/9) Hyperbolic Matrix(1501,5450,-1184,-4299) (-69/19,-29/8) -> (-71/56,-19/15) Hyperbolic Matrix(649,2350,124,449) (-29/8,-76/21) -> (26/5,21/4) Hyperbolic Matrix(2101,7600,-912,-3299) (-76/21,-47/13) -> (-53/23,-76/33) Hyperbolic Matrix(2201,7950,-1384,-4999) (-47/13,-65/18) -> (-35/22,-97/61) Hyperbolic Matrix(749,2700,-458,-1651) (-65/18,-18/5) -> (-18/11,-85/52) Hyperbolic Matrix(251,900,70,251) (-18/5,-25/7) -> (25/7,18/5) Hyperbolic Matrix(99,350,28,99) (-25/7,-7/2) -> (7/2,25/7) Hyperbolic Matrix(101,350,58,201) (-7/2,-24/7) -> (26/15,7/4) Hyperbolic Matrix(599,2050,438,1499) (-24/7,-41/12) -> (41/30,26/19) Hyperbolic Matrix(249,850,-220,-751) (-41/12,-17/5) -> (-17/15,-9/8) Hyperbolic Matrix(5899,19950,-1804,-6101) (-115/34,-71/21) -> (-121/37,-85/26) Hyperbolic Matrix(3151,10650,666,2251) (-71/21,-98/29) -> (52/11,71/15) Hyperbolic Matrix(4099,13850,710,2399) (-98/29,-125/37) -> (75/13,52/9) Hyperbolic Matrix(1451,4900,252,851) (-125/37,-27/8) -> (23/4,75/13) Hyperbolic Matrix(149,500,104,349) (-27/8,-10/3) -> (10/7,23/16) Hyperbolic Matrix(151,500,106,351) (-10/3,-23/7) -> (27/19,10/7) Hyperbolic Matrix(5901,19300,4556,14901) (-36/11,-121/37) -> (79/61,136/105) Hyperbolic Matrix(1501,4900,276,901) (-49/15,-62/19) -> (38/7,49/9) Hyperbolic Matrix(4399,14350,950,3099) (-62/19,-75/23) -> (125/27,88/19) Hyperbolic Matrix(1351,4400,292,951) (-75/23,-13/4) -> (37/8,125/27) Hyperbolic Matrix(201,650,124,401) (-13/4,-16/5) -> (34/21,13/8) Hyperbolic Matrix(299,950,220,699) (-16/5,-19/6) -> (19/14,34/25) Hyperbolic Matrix(349,1100,-270,-851) (-19/6,-3/1) -> (-53/41,-31/24) Hyperbolic Matrix(401,1150,-174,-499) (-3/1,-20/7) -> (-30/13,-53/23) Hyperbolic Matrix(299,850,70,199) (-20/7,-17/6) -> (17/4,30/7) Hyperbolic Matrix(249,700,-196,-551) (-17/6,-14/5) -> (-14/11,-33/26) Hyperbolic Matrix(251,700,90,251) (-14/5,-25/9) -> (25/9,14/5) Hyperbolic Matrix(199,550,72,199) (-25/9,-11/4) -> (11/4,25/9) Hyperbolic Matrix(201,550,110,301) (-11/4,-30/11) -> (20/11,11/6) Hyperbolic Matrix(899,2450,-404,-1101) (-30/11,-49/18) -> (-49/22,-20/9) Hyperbolic Matrix(901,2450,552,1501) (-49/18,-19/7) -> (31/19,49/30) Hyperbolic Matrix(499,1350,-370,-1001) (-46/17,-27/10) -> (-27/20,-4/3) Hyperbolic Matrix(1149,3100,500,1349) (-27/10,-62/23) -> (62/27,23/10) Hyperbolic Matrix(2951,7950,-2134,-5749) (-62/23,-35/13) -> (-65/47,-112/81) Hyperbolic Matrix(149,400,130,349) (-35/13,-8/3) -> (8/7,15/13) Hyperbolic Matrix(151,400,-94,-249) (-8/3,-21/8) -> (-29/18,-8/5) Hyperbolic Matrix(1851,4850,-782,-2049) (-21/8,-55/21) -> (-45/19,-71/30) Hyperbolic Matrix(249,650,172,449) (-34/13,-13/5) -> (13/9,16/11) Hyperbolic Matrix(251,650,-212,-549) (-13/5,-31/12) -> (-19/16,-13/11) Hyperbolic Matrix(949,2450,600,1549) (-31/12,-49/19) -> (49/31,19/12) Hyperbolic Matrix(6149,15850,-4520,-11651) (-116/45,-67/26) -> (-117/86,-34/25) Hyperbolic Matrix(1049,2700,-758,-1951) (-67/26,-18/7) -> (-18/13,-83/60) Hyperbolic Matrix(799,2050,-624,-1601) (-18/7,-41/16) -> (-41/32,-32/25) Hyperbolic Matrix(99,250,-40,-101) (-23/9,-5/2) -> (-5/2,-27/11) Parabolic Matrix(1549,3800,876,2149) (-27/11,-76/31) -> (76/43,23/13) Hyperbolic Matrix(7649,18750,2998,7349) (-76/31,-125/51) -> (125/49,74/29) Hyperbolic Matrix(5101,12500,2000,4901) (-125/51,-49/20) -> (51/20,125/49) Hyperbolic Matrix(2001,4900,-898,-2199) (-49/20,-22/9) -> (-78/35,-49/22) Hyperbolic Matrix(799,1950,-656,-1601) (-22/9,-39/16) -> (-39/32,-28/23) Hyperbolic Matrix(351,850,-268,-649) (-17/7,-29/12) -> (-21/16,-17/13) Hyperbolic Matrix(601,1450,332,801) (-29/12,-41/17) -> (9/5,29/16) Hyperbolic Matrix(7199,17350,-5270,-12701) (-94/39,-53/22) -> (-153/112,-56/41) Hyperbolic Matrix(2699,6500,-1952,-4701) (-53/22,-12/5) -> (-112/81,-47/34) Hyperbolic Matrix(251,600,-146,-349) (-12/5,-19/8) -> (-31/18,-12/7) Hyperbolic Matrix(2599,6150,718,1699) (-71/30,-26/11) -> (76/21,29/8) Hyperbolic Matrix(149,350,106,249) (-26/11,-7/3) -> (7/5,24/17) Hyperbolic Matrix(151,350,22,51) (-7/3,-30/13) -> (20/3,7/1) Hyperbolic Matrix(1651,3800,978,2251) (-76/33,-23/10) -> (27/16,76/45) Hyperbolic Matrix(349,800,-284,-651) (-23/10,-16/7) -> (-16/13,-27/22) Hyperbolic Matrix(351,800,154,351) (-16/7,-25/11) -> (25/11,16/7) Hyperbolic Matrix(199,450,88,199) (-25/11,-9/4) -> (9/4,25/11) Hyperbolic Matrix(649,1450,380,849) (-9/4,-29/13) -> (29/17,41/24) Hyperbolic Matrix(3051,6800,2356,5251) (-29/13,-78/35) -> (22/17,79/61) Hyperbolic Matrix(249,550,158,349) (-20/9,-11/5) -> (11/7,30/19) Hyperbolic Matrix(849,1850,-620,-1351) (-24/11,-13/6) -> (-63/46,-26/19) Hyperbolic Matrix(301,650,232,501) (-13/6,-15/7) -> (35/27,13/10) Hyperbolic Matrix(1101,2350,-796,-1699) (-15/7,-17/8) -> (-83/60,-65/47) Hyperbolic Matrix(401,850,142,301) (-17/8,-2/1) -> (48/17,17/6) Hyperbolic Matrix(501,950,106,201) (-2/1,-17/9) -> (33/7,52/11) Hyperbolic Matrix(1301,2450,-796,-1499) (-17/9,-15/8) -> (-85/52,-67/41) Hyperbolic Matrix(349,650,80,149) (-15/8,-13/7) -> (13/3,35/8) Hyperbolic Matrix(299,550,-218,-401) (-13/7,-11/6) -> (-11/8,-37/27) Hyperbolic Matrix(301,550,110,201) (-11/6,-20/11) -> (30/11,11/4) Hyperbolic Matrix(1349,2450,-854,-1551) (-20/11,-29/16) -> (-79/50,-30/19) Hyperbolic Matrix(801,1450,332,601) (-29/16,-9/5) -> (41/17,29/12) Hyperbolic Matrix(251,450,140,251) (-9/5,-25/14) -> (25/14,9/5) Hyperbolic Matrix(449,800,252,449) (-25/14,-16/9) -> (16/9,25/14) Hyperbolic Matrix(1749,3100,-1270,-2251) (-39/22,-62/35) -> (-62/45,-11/8) Hyperbolic Matrix(1751,3100,1102,1951) (-62/35,-23/13) -> (27/17,62/39) Hyperbolic Matrix(651,1150,-424,-749) (-23/13,-30/17) -> (-20/13,-23/15) Hyperbolic Matrix(199,350,170,299) (-30/17,-7/4) -> (7/6,20/17) Hyperbolic Matrix(201,350,58,101) (-7/4,-26/15) -> (24/7,7/2) Hyperbolic Matrix(549,950,-434,-751) (-26/15,-19/11) -> (-19/15,-24/19) Hyperbolic Matrix(1449,2500,608,1049) (-19/11,-50/29) -> (50/21,31/13) Hyperbolic Matrix(1451,2500,610,1051) (-50/29,-31/18) -> (19/8,50/21) Hyperbolic Matrix(2601,4450,-1636,-2799) (-12/7,-53/31) -> (-97/61,-62/39) Hyperbolic Matrix(3599,6150,-2634,-4501) (-53/31,-41/24) -> (-41/30,-97/71) Hyperbolic Matrix(849,1450,380,649) (-41/24,-29/17) -> (29/13,9/4) Hyperbolic Matrix(1349,2300,322,549) (-29/17,-75/44) -> (25/6,21/5) Hyperbolic Matrix(851,1450,206,351) (-75/44,-46/27) -> (4/1,25/6) Hyperbolic Matrix(501,850,-412,-699) (-17/10,-22/13) -> (-28/23,-17/14) Hyperbolic Matrix(149,250,-90,-151) (-22/13,-5/3) -> (-5/3,-28/17) Parabolic Matrix(4801,7900,-3038,-4999) (-28/17,-51/31) -> (-49/31,-128/81) Hyperbolic Matrix(7599,12500,4498,7399) (-51/31,-125/76) -> (125/74,49/29) Hyperbolic Matrix(11401,18750,6750,11101) (-125/76,-74/45) -> (76/45,125/74) Hyperbolic Matrix(6599,10850,1824,2999) (-74/45,-23/14) -> (123/34,76/21) Hyperbolic Matrix(701,1150,-548,-899) (-23/14,-18/11) -> (-32/25,-23/18) Hyperbolic Matrix(4499,7350,-3306,-5401) (-67/41,-49/30) -> (-49/36,-83/61) Hyperbolic Matrix(1501,2450,552,901) (-49/30,-31/19) -> (19/7,49/18) Hyperbolic Matrix(1349,2200,214,349) (-31/19,-75/46) -> (25/4,19/3) Hyperbolic Matrix(951,1550,154,251) (-75/46,-44/27) -> (6/1,25/4) Hyperbolic Matrix(401,650,124,201) (-13/8,-34/21) -> (16/5,13/4) Hyperbolic Matrix(649,1050,-526,-851) (-34/21,-21/13) -> (-21/17,-16/13) Hyperbolic Matrix(1549,2500,588,949) (-21/13,-50/31) -> (50/19,29/11) Hyperbolic Matrix(1551,2500,590,951) (-50/31,-29/18) -> (21/8,50/19) Hyperbolic Matrix(251,400,32,51) (-8/5,-35/22) -> (15/2,8/1) Hyperbolic Matrix(1699,2700,314,499) (-62/39,-27/17) -> (27/5,38/7) Hyperbolic Matrix(599,950,-442,-701) (-27/17,-19/12) -> (-19/14,-23/17) Hyperbolic Matrix(1549,2450,600,949) (-19/12,-49/31) -> (49/19,31/12) Hyperbolic Matrix(3449,5450,474,749) (-128/81,-79/50) -> (29/4,22/3) Hyperbolic Matrix(349,550,158,249) (-30/19,-11/7) -> (11/5,20/9) Hyperbolic Matrix(351,550,224,351) (-11/7,-25/16) -> (25/16,11/7) Hyperbolic Matrix(449,700,288,449) (-25/16,-14/9) -> (14/9,25/16) Hyperbolic Matrix(4099,6350,-2970,-4601) (-31/20,-48/31) -> (-98/71,-69/50) Hyperbolic Matrix(549,850,290,449) (-48/31,-17/11) -> (17/9,2/1) Hyperbolic Matrix(551,850,422,651) (-17/11,-20/13) -> (30/23,17/13) Hyperbolic Matrix(951,1450,-688,-1049) (-23/15,-3/2) -> (-47/34,-123/89) Hyperbolic Matrix(1051,1550,238,351) (-3/2,-25/17) -> (75/17,53/12) Hyperbolic Matrix(1499,2200,340,499) (-25/17,-22/15) -> (22/5,75/17) Hyperbolic Matrix(651,950,172,251) (-19/13,-16/11) -> (34/9,19/5) Hyperbolic Matrix(449,650,172,249) (-16/11,-13/9) -> (13/5,34/13) Hyperbolic Matrix(799,1150,-626,-901) (-13/9,-23/16) -> (-23/18,-37/29) Hyperbolic Matrix(349,500,104,149) (-23/16,-10/7) -> (10/3,27/8) Hyperbolic Matrix(351,500,106,151) (-10/7,-27/19) -> (23/7,10/3) Hyperbolic Matrix(599,850,-494,-701) (-27/19,-17/12) -> (-17/14,-23/19) Hyperbolic Matrix(1201,1700,142,201) (-17/12,-75/53) -> (25/3,17/2) Hyperbolic Matrix(1449,2050,176,249) (-75/53,-58/41) -> (8/1,25/3) Hyperbolic Matrix(1451,2050,390,551) (-41/29,-24/17) -> (26/7,41/11) Hyperbolic Matrix(249,350,106,149) (-24/17,-7/5) -> (7/3,26/11) Hyperbolic Matrix(251,350,180,251) (-7/5,-25/18) -> (25/18,7/5) Hyperbolic Matrix(649,900,468,649) (-25/18,-18/13) -> (18/13,25/18) Hyperbolic Matrix(7851,10850,3076,4251) (-123/89,-76/55) -> (74/29,23/9) Hyperbolic Matrix(4451,6150,2570,3551) (-76/55,-29/21) -> (71/41,26/15) Hyperbolic Matrix(3151,4350,544,751) (-29/21,-98/71) -> (52/9,29/5) Hyperbolic Matrix(2899,4000,2246,3099) (-69/50,-40/29) -> (40/31,31/24) Hyperbolic Matrix(399,550,362,499) (-40/29,-51/37) -> (1/1,10/9) Hyperbolic Matrix(5551,7650,1198,1651) (-51/37,-62/45) -> (88/19,51/11) Hyperbolic Matrix(7299,10000,1970,2699) (-37/27,-100/73) -> (100/27,63/17) Hyperbolic Matrix(7301,10000,1972,2701) (-100/73,-63/46) -> (37/10,100/27) Hyperbolic Matrix(1499,2050,438,599) (-26/19,-41/30) -> (41/12,24/7) Hyperbolic Matrix(45749,62500,12260,16749) (-97/71,-250/183) -> (250/67,153/41) Hyperbolic Matrix(45751,62500,12262,16751) (-250/183,-153/112) -> (97/26,250/67) Hyperbolic Matrix(1501,2050,-1244,-1699) (-56/41,-15/11) -> (-35/29,-6/5) Hyperbolic Matrix(2901,3950,-2276,-3099) (-15/11,-49/36) -> (-51/40,-65/51) Hyperbolic Matrix(29399,40000,7790,10599) (-83/61,-200/147) -> (200/53,117/31) Hyperbolic Matrix(29401,40000,7792,10601) (-200/147,-117/86) -> (83/22,200/53) Hyperbolic Matrix(699,950,220,299) (-34/25,-19/14) -> (19/6,16/5) Hyperbolic Matrix(1849,2500,480,649) (-23/17,-50/37) -> (50/13,27/7) Hyperbolic Matrix(1851,2500,482,651) (-50/37,-27/20) -> (23/6,50/13) Hyperbolic Matrix(1099,1450,454,599) (-4/3,-25/19) -> (75/31,46/19) Hyperbolic Matrix(1751,2300,724,951) (-25/19,-21/16) -> (29/12,75/31) Hyperbolic Matrix(651,850,422,551) (-17/13,-30/23) -> (20/13,17/11) Hyperbolic Matrix(499,650,76,99) (-30/23,-13/10) -> (13/2,20/3) Hyperbolic Matrix(501,650,232,301) (-13/10,-35/27) -> (15/7,13/6) Hyperbolic Matrix(849,1100,-734,-951) (-35/27,-22/17) -> (-22/19,-15/13) Hyperbolic Matrix(1701,2200,542,701) (-22/17,-75/58) -> (25/8,22/7) Hyperbolic Matrix(1199,1550,386,499) (-75/58,-53/41) -> (3/1,25/8) Hyperbolic Matrix(3099,4000,2246,2899) (-31/24,-40/31) -> (40/29,69/50) Hyperbolic Matrix(349,450,38,49) (-40/31,-9/7) -> (9/1,10/1) Hyperbolic Matrix(1949,2500,428,549) (-9/7,-50/39) -> (50/11,41/9) Hyperbolic Matrix(1951,2500,430,551) (-50/39,-41/32) -> (9/2,50/11) Hyperbolic Matrix(3449,4400,2390,3049) (-37/29,-125/98) -> (75/52,13/9) Hyperbolic Matrix(11251,14350,7802,9951) (-125/98,-88/69) -> (62/43,75/52) Hyperbolic Matrix(5999,7650,1646,2099) (-88/69,-51/40) -> (51/14,62/17) Hyperbolic Matrix(3649,4650,-3022,-3851) (-65/51,-14/11) -> (-64/53,-35/29) Hyperbolic Matrix(749,950,354,449) (-33/26,-52/41) -> (2/1,17/8) Hyperbolic Matrix(8399,10650,5914,7499) (-52/41,-71/56) -> (71/50,98/69) Hyperbolic Matrix(199,250,-160,-201) (-24/19,-5/4) -> (-5/4,-26/21) Parabolic Matrix(1901,2350,1376,1701) (-26/21,-21/17) -> (29/21,76/55) Hyperbolic Matrix(2201,2700,816,1001) (-27/22,-38/31) -> (62/23,27/10) Hyperbolic Matrix(3999,4900,2774,3399) (-38/31,-49/40) -> (49/34,62/43) Hyperbolic Matrix(2049,2500,368,449) (-11/9,-50/41) -> (50/9,39/7) Hyperbolic Matrix(2051,2500,370,451) (-50/41,-39/32) -> (11/2,50/9) Hyperbolic Matrix(4049,4900,2850,3449) (-23/19,-75/62) -> (125/88,27/19) Hyperbolic Matrix(11451,13850,8062,9751) (-75/62,-52/43) -> (98/69,125/88) Hyperbolic Matrix(3599,4350,992,1199) (-52/43,-29/24) -> (29/8,98/27) Hyperbolic Matrix(2401,2900,332,401) (-29/24,-64/53) -> (36/5,29/4) Hyperbolic Matrix(1299,1550,502,599) (-6/5,-25/21) -> (75/29,44/17) Hyperbolic Matrix(1851,2200,716,851) (-25/21,-19/16) -> (31/12,75/29) Hyperbolic Matrix(551,650,128,151) (-13/11,-20/17) -> (30/7,13/3) Hyperbolic Matrix(299,350,170,199) (-20/17,-7/6) -> (7/4,30/17) Hyperbolic Matrix(2149,2500,300,349) (-7/6,-50/43) -> (50/7,43/6) Hyperbolic Matrix(2151,2500,302,351) (-50/43,-43/37) -> (7/1,50/7) Hyperbolic Matrix(2499,2900,430,499) (-36/31,-29/25) -> (29/5,64/11) Hyperbolic Matrix(4701,5450,1726,2001) (-29/25,-22/19) -> (128/47,79/29) Hyperbolic Matrix(349,400,130,149) (-15/13,-8/7) -> (8/3,35/13) Hyperbolic Matrix(1801,2050,528,601) (-8/7,-25/22) -> (75/22,58/17) Hyperbolic Matrix(1499,1700,440,499) (-25/22,-17/15) -> (17/5,75/22) Hyperbolic Matrix(401,450,90,101) (-9/8,-10/9) -> (40/9,9/2) Hyperbolic Matrix(499,550,362,399) (-10/9,-1/1) -> (51/37,40/29) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(751,-850,220,-249) (9/8,8/7) -> (58/17,41/12) Hyperbolic Matrix(951,-1100,734,-849) (15/13,7/6) -> (57/44,35/27) Hyperbolic Matrix(549,-650,212,-251) (13/11,6/5) -> (44/17,13/5) Hyperbolic Matrix(701,-850,494,-599) (6/5,17/14) -> (17/12,44/31) Hyperbolic Matrix(699,-850,412,-501) (17/14,11/9) -> (39/23,17/10) Hyperbolic Matrix(651,-800,284,-349) (11/9,16/13) -> (16/7,39/17) Hyperbolic Matrix(851,-1050,526,-649) (16/13,5/4) -> (55/34,34/21) Hyperbolic Matrix(751,-950,434,-549) (5/4,19/15) -> (19/11,45/26) Hyperbolic Matrix(551,-700,196,-249) (19/15,14/11) -> (14/5,31/11) Hyperbolic Matrix(901,-1150,626,-799) (14/11,23/18) -> (23/16,36/25) Hyperbolic Matrix(899,-1150,548,-701) (23/18,9/7) -> (41/25,23/14) Hyperbolic Matrix(851,-1100,270,-349) (31/24,22/17) -> (22/7,19/6) Hyperbolic Matrix(6099,-7900,850,-1101) (136/105,57/44) -> (43/6,36/5) Hyperbolic Matrix(649,-850,268,-351) (17/13,4/3) -> (46/19,17/7) Hyperbolic Matrix(701,-950,442,-599) (4/3,19/14) -> (19/12,46/29) Hyperbolic Matrix(5401,-7350,3306,-4499) (34/25,49/36) -> (49/30,116/71) Hyperbolic Matrix(3599,-4900,2498,-3401) (49/36,15/11) -> (85/59,49/34) Hyperbolic Matrix(5199,-7100,3662,-5001) (15/11,56/41) -> (44/31,115/81) Hyperbolic Matrix(4501,-6150,2634,-3599) (56/41,41/30) -> (41/24,94/55) Hyperbolic Matrix(401,-550,218,-299) (26/19,11/8) -> (11/6,24/13) Hyperbolic Matrix(799,-1100,146,-201) (11/8,51/37) -> (49/9,11/2) Hyperbolic Matrix(3949,-5450,834,-1151) (69/50,29/21) -> (71/15,19/4) Hyperbolic Matrix(5499,-7600,3112,-4301) (76/55,47/34) -> (53/30,76/43) Hyperbolic Matrix(5749,-7950,2134,-2951) (47/34,65/47) -> (35/13,97/36) Hyperbolic Matrix(1951,-2700,758,-1049) (65/47,18/13) -> (18/7,85/33) Hyperbolic Matrix(601,-850,70,-99) (41/29,17/12) -> (17/2,9/1) Hyperbolic Matrix(14051,-19950,9754,-13849) (115/81,71/50) -> (121/84,85/59) Hyperbolic Matrix(751,-1100,170,-249) (19/13,3/2) -> (53/12,31/7) Hyperbolic Matrix(749,-1150,424,-651) (3/2,20/13) -> (30/17,53/30) Hyperbolic Matrix(451,-700,96,-149) (17/11,14/9) -> (14/3,33/7) Hyperbolic Matrix(1551,-2450,854,-1349) (30/19,49/31) -> (49/27,20/11) Hyperbolic Matrix(851,-1350,220,-349) (46/29,27/17) -> (27/7,4/1) Hyperbolic Matrix(4999,-7950,1384,-2201) (62/39,35/22) -> (65/18,112/31) Hyperbolic Matrix(249,-400,94,-151) (8/5,21/13) -> (29/11,8/3) Hyperbolic Matrix(2999,-4850,1732,-2801) (21/13,55/34) -> (45/26,71/41) Hyperbolic Matrix(399,-650,62,-101) (13/8,31/19) -> (19/3,13/2) Hyperbolic Matrix(9701,-15850,2570,-4199) (116/71,67/41) -> (117/31,34/9) Hyperbolic Matrix(1651,-2700,458,-749) (67/41,18/11) -> (18/5,83/23) Hyperbolic Matrix(1251,-2050,274,-449) (18/11,41/25) -> (41/9,32/7) Hyperbolic Matrix(151,-250,90,-149) (23/14,5/3) -> (5/3,27/16) Parabolic Matrix(2899,-4900,1598,-2701) (49/29,22/13) -> (78/43,49/27) Hyperbolic Matrix(1151,-1950,206,-349) (22/13,39/23) -> (39/7,28/5) Hyperbolic Matrix(499,-850,118,-201) (17/10,29/17) -> (21/5,17/4) Hyperbolic Matrix(10151,-17350,2720,-4649) (94/55,53/31) -> (153/41,56/15) Hyperbolic Matrix(3801,-6500,1052,-1799) (53/31,12/7) -> (112/31,47/13) Hyperbolic Matrix(349,-600,146,-251) (12/7,19/11) -> (31/13,12/5) Hyperbolic Matrix(451,-800,84,-149) (23/13,16/9) -> (16/3,27/5) Hyperbolic Matrix(1001,-1850,270,-499) (24/13,13/7) -> (63/17,26/7) Hyperbolic Matrix(1249,-2350,346,-651) (15/8,17/9) -> (83/23,65/18) Hyperbolic Matrix(1149,-2450,446,-951) (17/8,15/7) -> (85/33,67/26) Hyperbolic Matrix(251,-550,68,-149) (13/6,11/5) -> (11/3,37/10) Hyperbolic Matrix(1101,-2450,404,-899) (20/9,29/13) -> (79/29,30/11) Hyperbolic Matrix(1351,-3100,370,-849) (39/17,62/27) -> (62/17,11/3) Hyperbolic Matrix(499,-1150,174,-401) (23/10,30/13) -> (20/7,23/8) Hyperbolic Matrix(401,-950,84,-199) (26/11,19/8) -> (19/4,24/5) Hyperbolic Matrix(1849,-4450,686,-1651) (12/5,53/22) -> (97/36,62/23) Hyperbolic Matrix(2551,-6150,684,-1649) (53/22,41/17) -> (41/11,97/26) Hyperbolic Matrix(349,-850,62,-151) (17/7,22/9) -> (28/5,17/3) Hyperbolic Matrix(101,-250,40,-99) (22/9,5/2) -> (5/2,28/11) Parabolic Matrix(3099,-7900,1138,-2901) (28/11,51/20) -> (49/18,128/47) Hyperbolic Matrix(449,-1150,98,-251) (23/9,18/7) -> (32/7,23/5) Hyperbolic Matrix(2851,-7350,756,-1949) (67/26,49/19) -> (49/13,83/22) Hyperbolic Matrix(401,-1050,76,-199) (34/13,21/8) -> (21/4,16/3) Hyperbolic Matrix(351,-950,92,-249) (27/10,19/7) -> (19/5,23/6) Hyperbolic Matrix(2251,-6350,620,-1749) (31/11,48/17) -> (98/27,69/19) Hyperbolic Matrix(499,-1450,138,-401) (23/8,3/1) -> (47/13,123/34) Hyperbolic Matrix(351,-1150,76,-249) (13/4,23/7) -> (23/5,37/8) Hyperbolic Matrix(251,-850,44,-149) (27/8,17/5) -> (17/3,23/4) Hyperbolic Matrix(549,-2050,94,-351) (56/15,15/4) -> (35/6,6/1) Hyperbolic Matrix(1049,-3950,226,-851) (15/4,49/13) -> (51/11,65/14) Hyperbolic Matrix(251,-1100,34,-149) (35/8,22/5) -> (22/3,15/2) Hyperbolic Matrix(1001,-4650,172,-799) (65/14,14/3) -> (64/11,35/6) Hyperbolic Matrix(51,-250,10,-49) (24/5,5/1) -> (5/1,26/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(51,550,14,151) -> Matrix(3,10,2,7) Matrix(49,450,38,349) -> Matrix(1,2,2,5) Matrix(99,850,-70,-601) -> Matrix(1,2,-2,-3) Matrix(51,400,32,251) -> Matrix(1,0,0,1) Matrix(149,1100,-34,-251) -> Matrix(3,4,2,3) Matrix(51,350,22,151) -> Matrix(3,-2,2,-1) Matrix(99,650,76,499) -> Matrix(3,-10,4,-13) Matrix(101,650,-62,-399) -> Matrix(1,-6,-2,13) Matrix(149,850,-44,-251) -> Matrix(1,2,0,1) Matrix(151,850,-62,-349) -> Matrix(7,18,-2,-5) Matrix(149,800,-84,-451) -> Matrix(1,-4,0,1) Matrix(199,1050,-76,-401) -> Matrix(1,2,4,9) Matrix(199,950,-84,-401) -> Matrix(7,2,-4,-1) Matrix(149,700,-96,-451) -> Matrix(1,-4,0,1) Matrix(249,1150,-76,-351) -> Matrix(3,2,4,3) Matrix(251,1150,-98,-449) -> Matrix(5,2,2,1) Matrix(101,450,90,401) -> Matrix(3,-2,2,-1) Matrix(901,4000,248,1101) -> Matrix(5,-4,4,-3) Matrix(249,1100,-170,-751) -> Matrix(9,-8,-10,9) Matrix(1549,6800,854,3749) -> Matrix(3,-4,-2,3) Matrix(4399,19300,3054,13399) -> Matrix(19,-24,42,-53) Matrix(1801,7900,-1550,-6799) -> Matrix(3,-4,10,-13) Matrix(149,650,80,349) -> Matrix(1,-2,4,-7) Matrix(151,650,128,551) -> Matrix(3,-10,4,-13) Matrix(199,850,70,299) -> Matrix(3,-14,2,-9) Matrix(201,850,-118,-499) -> Matrix(3,-22,-2,15) Matrix(249,950,-92,-351) -> Matrix(1,2,-4,-7) Matrix(251,950,172,651) -> Matrix(3,2,4,3) Matrix(1949,7350,-756,-2851) -> Matrix(5,6,4,5) Matrix(1301,4900,-398,-1499) -> Matrix(5,4,6,5) Matrix(1901,7100,-562,-2099) -> Matrix(3,8,-2,-5) Matrix(1649,6150,-684,-2551) -> Matrix(11,14,-4,-5) Matrix(551,2050,390,1451) -> Matrix(1,2,2,5) Matrix(149,550,-68,-251) -> Matrix(1,2,-4,-7) Matrix(301,1100,-246,-899) -> Matrix(5,8,-2,-3) Matrix(151,550,14,51) -> Matrix(7,10,2,3) Matrix(1101,4000,248,901) -> Matrix(3,4,-4,-5) Matrix(1501,5450,-1184,-4299) -> Matrix(1,2,-4,-7) Matrix(649,2350,124,449) -> Matrix(5,6,4,5) Matrix(2101,7600,-912,-3299) -> Matrix(1,0,0,1) Matrix(2201,7950,-1384,-4999) -> Matrix(11,14,-4,-5) Matrix(749,2700,-458,-1651) -> Matrix(13,16,-22,-27) Matrix(251,900,70,251) -> Matrix(11,12,10,11) Matrix(99,350,28,99) -> Matrix(3,2,4,3) Matrix(101,350,58,201) -> Matrix(5,2,2,1) Matrix(599,2050,438,1499) -> Matrix(3,-2,2,-1) Matrix(249,850,-220,-751) -> Matrix(1,-2,0,1) Matrix(5899,19950,-1804,-6101) -> Matrix(3,2,4,3) Matrix(3151,10650,666,2251) -> Matrix(5,6,-6,-7) Matrix(4099,13850,710,2399) -> Matrix(55,58,18,19) Matrix(1451,4900,252,851) -> Matrix(23,20,8,7) Matrix(149,500,104,349) -> Matrix(1,0,4,1) Matrix(151,500,106,351) -> Matrix(1,0,-2,1) Matrix(5901,19300,4556,14901) -> Matrix(29,-24,52,-43) Matrix(1501,4900,276,901) -> Matrix(13,-12,12,-11) Matrix(4399,14350,950,3099) -> Matrix(35,-34,34,-33) Matrix(1351,4400,292,951) -> Matrix(11,-12,12,-13) Matrix(201,650,124,401) -> Matrix(1,-2,4,-7) Matrix(299,950,220,699) -> Matrix(1,-2,0,1) Matrix(349,1100,-270,-851) -> Matrix(1,-8,-2,17) Matrix(401,1150,-174,-499) -> Matrix(3,2,-2,-1) Matrix(299,850,70,199) -> Matrix(9,14,-2,-3) Matrix(249,700,-196,-551) -> Matrix(3,4,-4,-5) Matrix(251,700,90,251) -> Matrix(11,12,10,11) Matrix(199,550,72,199) -> Matrix(7,6,8,7) Matrix(201,550,110,301) -> Matrix(3,2,-2,-1) Matrix(899,2450,-404,-1101) -> Matrix(3,2,-8,-5) Matrix(901,2450,552,1501) -> Matrix(11,6,20,11) Matrix(499,1350,-370,-1001) -> Matrix(11,2,-6,-1) Matrix(1149,3100,500,1349) -> Matrix(5,-4,4,-3) Matrix(2951,7950,-2134,-5749) -> Matrix(9,14,-2,-3) Matrix(149,400,130,349) -> Matrix(1,0,2,1) Matrix(151,400,-94,-249) -> Matrix(1,0,2,1) Matrix(1851,4850,-782,-2049) -> Matrix(5,-2,-2,1) Matrix(249,650,172,449) -> Matrix(5,-2,8,-3) Matrix(251,650,-212,-549) -> Matrix(7,-6,-8,7) Matrix(949,2450,600,1549) -> Matrix(5,-6,-4,5) Matrix(6149,15850,-4520,-11651) -> Matrix(5,-6,-4,5) Matrix(1049,2700,-758,-1951) -> Matrix(11,-16,-2,3) Matrix(799,2050,-624,-1601) -> Matrix(1,-2,4,-7) Matrix(99,250,-40,-101) -> Matrix(1,-6,0,1) Matrix(1549,3800,876,2149) -> Matrix(1,8,0,1) Matrix(7649,18750,2998,7349) -> Matrix(5,18,-2,-7) Matrix(5101,12500,2000,4901) -> Matrix(1,0,0,1) Matrix(2001,4900,-898,-2199) -> Matrix(1,4,-2,-7) Matrix(799,1950,-656,-1601) -> Matrix(7,30,-4,-17) Matrix(351,850,-268,-649) -> Matrix(7,22,-8,-25) Matrix(601,1450,332,801) -> Matrix(5,14,-4,-11) Matrix(7199,17350,-5270,-12701) -> Matrix(41,110,-22,-59) Matrix(2699,6500,-1952,-4701) -> Matrix(35,92,-8,-21) Matrix(251,600,-146,-349) -> Matrix(11,24,-6,-13) Matrix(2599,6150,718,1699) -> Matrix(13,22,10,17) Matrix(149,350,106,249) -> Matrix(1,2,-2,-3) Matrix(151,350,22,51) -> Matrix(1,2,-2,-3) Matrix(1651,3800,978,2251) -> Matrix(7,8,6,7) Matrix(349,800,-284,-651) -> Matrix(3,4,-4,-5) Matrix(351,800,154,351) -> Matrix(15,16,14,15) Matrix(199,450,88,199) -> Matrix(7,6,8,7) Matrix(649,1450,380,849) -> Matrix(25,14,16,9) Matrix(3051,6800,2356,5251) -> Matrix(7,4,12,7) Matrix(249,550,158,349) -> Matrix(3,2,-2,-1) Matrix(849,1850,-620,-1351) -> Matrix(15,2,-8,-1) Matrix(301,650,232,501) -> Matrix(5,-2,8,-3) Matrix(1101,2350,-796,-1699) -> Matrix(1,-6,0,1) Matrix(401,850,142,301) -> Matrix(3,-2,2,-1) Matrix(501,950,106,201) -> Matrix(3,2,-2,-1) Matrix(1301,2450,-796,-1499) -> Matrix(5,2,-8,-3) Matrix(349,650,80,149) -> Matrix(7,2,-4,-1) Matrix(299,550,-218,-401) -> Matrix(5,-2,-2,1) Matrix(301,550,110,201) -> Matrix(1,-2,2,-3) Matrix(1349,2450,-854,-1551) -> Matrix(3,-2,2,-1) Matrix(801,1450,332,601) -> Matrix(11,-14,4,-5) Matrix(251,450,140,251) -> Matrix(1,-6,0,1) Matrix(449,800,252,449) -> Matrix(1,16,0,1) Matrix(1749,3100,-1270,-2251) -> Matrix(5,28,-2,-11) Matrix(1751,3100,1102,1951) -> Matrix(1,4,2,9) Matrix(651,1150,-424,-749) -> Matrix(1,2,0,1) Matrix(199,350,170,299) -> Matrix(1,2,2,5) Matrix(201,350,58,101) -> Matrix(1,2,2,5) Matrix(549,950,-434,-751) -> Matrix(1,2,2,5) Matrix(1449,2500,608,1049) -> Matrix(41,84,20,41) Matrix(1451,2500,610,1051) -> Matrix(43,84,22,43) Matrix(2601,4450,-1636,-2799) -> Matrix(11,18,-8,-13) Matrix(3599,6150,-2634,-4501) -> Matrix(9,14,-2,-3) Matrix(849,1450,380,649) -> Matrix(9,14,16,25) Matrix(1349,2300,322,549) -> Matrix(45,68,-2,-3) Matrix(851,1450,206,351) -> Matrix(31,46,2,3) Matrix(501,850,-412,-699) -> Matrix(13,18,-8,-11) Matrix(149,250,-90,-151) -> Matrix(5,6,-6,-7) Matrix(4801,7900,-3038,-4999) -> Matrix(1,0,2,1) Matrix(7599,12500,4498,7399) -> Matrix(1,0,2,1) Matrix(11401,18750,6750,11101) -> Matrix(25,18,18,13) Matrix(6599,10850,1824,2999) -> Matrix(1,2,0,1) Matrix(701,1150,-548,-899) -> Matrix(3,2,4,3) Matrix(4499,7350,-3306,-5401) -> Matrix(11,6,-2,-1) Matrix(1501,2450,552,901) -> Matrix(11,6,20,11) Matrix(1349,2200,214,349) -> Matrix(47,24,-2,-1) Matrix(951,1550,154,251) -> Matrix(37,18,2,1) Matrix(401,650,124,201) -> Matrix(7,2,-4,-1) Matrix(649,1050,-526,-851) -> Matrix(11,2,-6,-1) Matrix(1549,2500,588,949) -> Matrix(1,0,20,1) Matrix(1551,2500,590,951) -> Matrix(1,0,-18,1) Matrix(251,400,32,51) -> Matrix(1,0,0,1) Matrix(1699,2700,314,499) -> Matrix(1,0,2,1) Matrix(599,950,-442,-701) -> Matrix(5,-2,-2,1) Matrix(1549,2450,600,949) -> Matrix(5,-6,-4,5) Matrix(3449,5450,474,749) -> Matrix(1,-2,2,-3) Matrix(349,550,158,249) -> Matrix(1,-2,2,-3) Matrix(351,550,224,351) -> Matrix(1,-6,0,1) Matrix(449,700,288,449) -> Matrix(1,12,0,1) Matrix(4099,6350,-2970,-4601) -> Matrix(5,18,-2,-7) Matrix(549,850,290,449) -> Matrix(1,2,2,5) Matrix(551,850,422,651) -> Matrix(5,14,6,17) Matrix(951,1450,-688,-1049) -> Matrix(1,-2,0,1) Matrix(1051,1550,238,351) -> Matrix(13,14,-14,-15) Matrix(1499,2200,340,499) -> Matrix(21,20,-20,-19) Matrix(651,950,172,251) -> Matrix(3,2,4,3) Matrix(449,650,172,249) -> Matrix(3,2,-8,-5) Matrix(799,1150,-626,-901) -> Matrix(5,2,2,1) Matrix(349,500,104,149) -> Matrix(1,0,4,1) Matrix(351,500,106,151) -> Matrix(1,0,-2,1) Matrix(599,850,-494,-701) -> Matrix(3,2,-2,-1) Matrix(1201,1700,142,201) -> Matrix(3,4,2,3) Matrix(1449,2050,176,249) -> Matrix(3,2,4,3) Matrix(1451,2050,390,551) -> Matrix(5,2,2,1) Matrix(249,350,106,149) -> Matrix(3,-2,2,-1) Matrix(251,350,180,251) -> Matrix(1,-2,0,1) Matrix(649,900,468,649) -> Matrix(1,12,0,1) Matrix(7851,10850,3076,4251) -> Matrix(1,2,0,1) Matrix(4451,6150,2570,3551) -> Matrix(5,22,2,9) Matrix(3151,4350,544,751) -> Matrix(13,42,4,13) Matrix(2899,4000,2246,3099) -> Matrix(1,4,2,9) Matrix(399,550,362,499) -> Matrix(3,10,2,7) Matrix(5551,7650,1198,1651) -> Matrix(7,22,6,19) Matrix(7299,10000,1970,2699) -> Matrix(45,92,22,45) Matrix(7301,10000,1972,2701) -> Matrix(47,92,24,47) Matrix(1499,2050,438,599) -> Matrix(1,2,-2,-3) Matrix(45749,62500,12260,16749) -> Matrix(33,68,16,33) Matrix(45751,62500,12262,16751) -> Matrix(35,68,18,35) Matrix(1501,2050,-1244,-1699) -> Matrix(11,18,-8,-13) Matrix(2901,3950,-2276,-3099) -> Matrix(1,-2,0,1) Matrix(29399,40000,7790,10599) -> Matrix(5,12,2,5) Matrix(29401,40000,7792,10601) -> Matrix(7,12,4,7) Matrix(699,950,220,299) -> Matrix(1,-2,0,1) Matrix(1849,2500,480,649) -> Matrix(25,52,12,25) Matrix(1851,2500,482,651) -> Matrix(27,52,14,27) Matrix(1099,1450,454,599) -> Matrix(43,46,14,15) Matrix(1751,2300,724,951) -> Matrix(71,68,24,23) Matrix(651,850,422,551) -> Matrix(17,14,6,5) Matrix(499,650,76,99) -> Matrix(13,10,-4,-3) Matrix(501,650,232,301) -> Matrix(3,2,-8,-5) Matrix(849,1100,-734,-951) -> Matrix(7,4,-2,-1) Matrix(1701,2200,542,701) -> Matrix(39,20,-2,-1) Matrix(1199,1550,386,499) -> Matrix(29,14,2,1) Matrix(3099,4000,2246,2899) -> Matrix(9,4,2,1) Matrix(349,450,38,49) -> Matrix(5,2,2,1) Matrix(1949,2500,428,549) -> Matrix(1,0,12,1) Matrix(1951,2500,430,551) -> Matrix(1,0,-10,1) Matrix(3449,4400,2390,3049) -> Matrix(1,-12,2,-23) Matrix(11251,14350,7802,9951) -> Matrix(1,34,2,69) Matrix(5999,7650,1646,2099) -> Matrix(3,22,2,15) Matrix(3649,4650,-3022,-3851) -> Matrix(3,2,-2,-1) Matrix(749,950,354,449) -> Matrix(3,2,-2,-1) Matrix(8399,10650,5914,7499) -> Matrix(13,6,2,1) Matrix(199,250,-160,-201) -> Matrix(1,-2,0,1) Matrix(1901,2350,1376,1701) -> Matrix(1,6,0,1) Matrix(2201,2700,816,1001) -> Matrix(1,0,0,1) Matrix(3999,4900,2774,3399) -> Matrix(1,12,2,25) Matrix(2049,2500,368,449) -> Matrix(17,36,8,17) Matrix(2051,2500,370,451) -> Matrix(19,36,10,19) Matrix(4049,4900,2850,3449) -> Matrix(13,20,-2,-3) Matrix(11451,13850,8062,9751) -> Matrix(39,58,2,3) Matrix(3599,4350,992,1199) -> Matrix(29,42,20,29) Matrix(2401,2900,332,401) -> Matrix(3,4,8,11) Matrix(1299,1550,502,599) -> Matrix(17,18,-18,-19) Matrix(1851,2200,716,851) -> Matrix(25,24,-24,-23) Matrix(551,650,128,151) -> Matrix(13,10,-4,-3) Matrix(299,350,170,199) -> Matrix(5,2,2,1) Matrix(2149,2500,300,349) -> Matrix(1,0,8,1) Matrix(2151,2500,302,351) -> Matrix(1,0,-6,1) Matrix(2499,2900,430,499) -> Matrix(7,-4,2,-1) Matrix(4701,5450,1726,2001) -> Matrix(1,-2,2,-3) Matrix(349,400,130,149) -> Matrix(1,0,2,1) Matrix(1801,2050,528,601) -> Matrix(1,-2,0,1) Matrix(1499,1700,440,499) -> Matrix(1,4,0,1) Matrix(401,450,90,101) -> Matrix(1,2,-2,-3) Matrix(499,550,362,399) -> Matrix(7,10,2,3) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(751,-850,220,-249) -> Matrix(1,-2,0,1) Matrix(951,-1100,734,-849) -> Matrix(1,-4,2,-7) Matrix(549,-650,212,-251) -> Matrix(7,-6,-8,7) Matrix(701,-850,494,-599) -> Matrix(1,-2,2,-3) Matrix(699,-850,412,-501) -> Matrix(11,-18,8,-13) Matrix(651,-800,284,-349) -> Matrix(5,-4,4,-3) Matrix(851,-1050,526,-649) -> Matrix(1,-2,6,-11) Matrix(751,-950,434,-549) -> Matrix(5,2,2,1) Matrix(551,-700,196,-249) -> Matrix(5,-4,4,-3) Matrix(901,-1150,626,-799) -> Matrix(1,2,2,5) Matrix(899,-1150,548,-701) -> Matrix(3,2,4,3) Matrix(851,-1100,270,-349) -> Matrix(17,-8,-2,1) Matrix(6099,-7900,850,-1101) -> Matrix(7,-4,30,-17) Matrix(649,-850,268,-351) -> Matrix(25,-22,8,-7) Matrix(701,-950,442,-599) -> Matrix(1,-2,-2,5) Matrix(5401,-7350,3306,-4499) -> Matrix(1,-6,2,-11) Matrix(3599,-4900,2498,-3401) -> Matrix(1,4,2,9) Matrix(5199,-7100,3662,-5001) -> Matrix(5,-8,2,-3) Matrix(4501,-6150,2634,-3599) -> Matrix(3,-14,2,-9) Matrix(401,-550,218,-299) -> Matrix(1,-2,-2,5) Matrix(799,-1100,146,-201) -> Matrix(3,-8,2,-5) Matrix(3949,-5450,834,-1151) -> Matrix(1,-2,-2,5) Matrix(5499,-7600,3112,-4301) -> Matrix(1,0,0,1) Matrix(5749,-7950,2134,-2951) -> Matrix(3,-14,2,-9) Matrix(1951,-2700,758,-1049) -> Matrix(3,-16,-2,11) Matrix(601,-850,70,-99) -> Matrix(3,-2,2,-1) Matrix(14051,-19950,9754,-13849) -> Matrix(1,2,2,5) Matrix(751,-1100,170,-249) -> Matrix(9,-8,-10,9) Matrix(749,-1150,424,-651) -> Matrix(1,2,0,1) Matrix(451,-700,96,-149) -> Matrix(1,-4,0,1) Matrix(1551,-2450,854,-1349) -> Matrix(1,2,-2,-3) Matrix(851,-1350,220,-349) -> Matrix(9,2,4,1) Matrix(4999,-7950,1384,-2201) -> Matrix(5,-14,4,-11) Matrix(249,-400,94,-151) -> Matrix(1,0,2,1) Matrix(2999,-4850,1732,-2801) -> Matrix(7,-2,4,-1) Matrix(399,-650,62,-101) -> Matrix(13,-6,-2,1) Matrix(9701,-15850,2570,-4199) -> Matrix(11,-6,2,-1) Matrix(1651,-2700,458,-749) -> Matrix(27,-16,22,-13) Matrix(1251,-2050,274,-449) -> Matrix(3,-2,14,-9) Matrix(151,-250,90,-149) -> Matrix(7,-6,6,-5) Matrix(2899,-4900,1598,-2701) -> Matrix(3,-4,-2,3) Matrix(1151,-1950,206,-349) -> Matrix(23,-30,10,-13) Matrix(499,-850,118,-201) -> Matrix(15,-22,-2,3) Matrix(10151,-17350,2720,-4649) -> Matrix(69,-110,32,-51) Matrix(3801,-6500,1052,-1799) -> Matrix(57,-92,44,-71) Matrix(349,-600,146,-251) -> Matrix(13,-24,6,-11) Matrix(451,-800,84,-149) -> Matrix(1,-4,0,1) Matrix(1001,-1850,270,-499) -> Matrix(13,2,6,1) Matrix(1249,-2350,346,-651) -> Matrix(7,-6,6,-5) Matrix(1149,-2450,446,-951) -> Matrix(3,2,-2,-1) Matrix(251,-550,68,-149) -> Matrix(7,-2,4,-1) Matrix(1101,-2450,404,-899) -> Matrix(5,-2,8,-3) Matrix(1351,-3100,370,-849) -> Matrix(23,-28,14,-17) Matrix(499,-1150,174,-401) -> Matrix(1,-2,2,-3) Matrix(401,-950,84,-199) -> Matrix(1,-2,4,-7) Matrix(1849,-4450,686,-1651) -> Matrix(7,-18,2,-5) Matrix(2551,-6150,684,-1649) -> Matrix(5,-14,4,-11) Matrix(349,-850,62,-151) -> Matrix(5,-18,2,-7) Matrix(101,-250,40,-99) -> Matrix(1,-6,0,1) Matrix(3099,-7900,1138,-2901) -> Matrix(1,0,2,1) Matrix(449,-1150,98,-251) -> Matrix(1,2,2,5) Matrix(2851,-7350,756,-1949) -> Matrix(5,6,4,5) Matrix(401,-1050,76,-199) -> Matrix(9,2,4,1) Matrix(351,-950,92,-249) -> Matrix(7,-2,4,-1) Matrix(2251,-6350,620,-1749) -> Matrix(13,-18,8,-11) Matrix(499,-1450,138,-401) -> Matrix(3,-2,2,-1) Matrix(351,-1150,76,-249) -> Matrix(3,2,4,3) Matrix(251,-850,44,-149) -> Matrix(1,2,0,1) Matrix(549,-2050,94,-351) -> Matrix(7,-18,2,-5) Matrix(1049,-3950,226,-851) -> Matrix(3,-2,2,-1) Matrix(251,-1100,34,-149) -> Matrix(3,4,2,3) Matrix(1001,-4650,172,-799) -> Matrix(1,2,0,1) Matrix(51,-250,10,-49) -> Matrix(3,-2,2,-1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 150 Degree of the the map X: 150 Degree of the the map Y: 300 ----------------------------------------------------------------------- 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): 300 Minimal number of generators: 51 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: 28 Genus: 12 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 5/4 15/11 10/7 5/3 2/1 25/11 50/21 5/2 50/19 25/9 3/1 10/3 25/7 100/27 15/4 50/13 4/1 13/3 75/17 5/1 11/2 6/1 7/1 8/1 25/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/1 7/6 1/2 6/5 6/5 11/9 3/1 5/4 1/0 14/11 2/1 9/7 1/3 13/10 7/10 4/3 4/3 19/14 7/2 34/25 2/1 15/11 1/1 41/30 3/2 26/19 2/1 11/8 1/0 7/5 -1/1 24/17 0/1 41/29 1/1 17/12 1/0 27/19 -3/1 10/7 0/1 23/16 3/8 13/9 5/9 16/11 4/5 19/13 11/13 3/2 3/2 11/7 -3/1 19/12 -3/4 46/29 -2/7 27/17 1/3 8/5 0/1 21/13 1/9 13/8 3/8 5/3 1/1 12/7 12/7 19/11 15/7 7/4 1/0 9/5 -3/1 11/6 -1/2 24/13 0/1 13/7 1/7 2/1 2/1 13/6 -1/6 11/5 1/3 9/4 3/4 25/11 1/1 16/7 8/7 7/3 1/1 19/8 15/8 50/21 2/1 31/13 27/13 12/5 12/5 5/2 1/0 13/5 -3/5 21/8 -1/8 50/19 0/1 29/11 1/11 8/3 0/1 27/10 -1/2 19/7 3/7 11/4 3/4 25/9 1/1 14/5 6/5 3/1 3/1 13/4 -5/4 23/7 -3/5 10/3 0/1 27/8 3/4 17/5 1/1 7/2 1/2 25/7 1/1 18/5 6/5 11/3 1/1 37/10 19/10 100/27 2/1 63/17 27/13 26/7 2/1 41/11 3/1 15/4 1/0 34/9 2/1 19/5 7/5 23/6 11/6 50/13 2/1 27/7 15/7 4/1 4/1 13/3 -7/3 22/5 -6/5 75/17 -1/1 53/12 -11/12 31/7 -5/7 9/2 -1/2 14/3 2/1 5/1 1/1 11/2 3/2 6/1 6/1 7/1 -1/1 8/1 0/1 25/3 1/1 17/2 3/2 9/1 1/1 1/0 1/0 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(151,-175,107,-124) (1/1,7/6) -> (7/5,24/17) Hyperbolic Matrix(149,-175,86,-101) (7/6,6/5) -> (19/11,7/4) Hyperbolic Matrix(226,-275,143,-174) (6/5,11/9) -> (11/7,19/12) Hyperbolic Matrix(101,-125,80,-99) (11/9,5/4) -> (5/4,14/11) Parabolic Matrix(176,-225,97,-124) (14/11,9/7) -> (9/5,11/6) Hyperbolic Matrix(251,-325,173,-224) (9/7,13/10) -> (13/9,16/11) Hyperbolic Matrix(249,-325,154,-201) (13/10,4/3) -> (21/13,13/8) Hyperbolic Matrix(701,-950,442,-599) (4/3,19/14) -> (19/12,46/29) Hyperbolic Matrix(699,-950,479,-651) (19/14,34/25) -> (16/11,19/13) Hyperbolic Matrix(826,-1125,605,-824) (34/25,15/11) -> (15/11,41/30) Parabolic Matrix(1499,-2050,1061,-1451) (41/30,26/19) -> (24/17,41/29) Hyperbolic Matrix(401,-550,218,-299) (26/19,11/8) -> (11/6,24/13) Hyperbolic Matrix(199,-275,55,-76) (11/8,7/5) -> (18/5,11/3) Hyperbolic Matrix(601,-850,70,-99) (41/29,17/12) -> (17/2,9/1) Hyperbolic Matrix(476,-675,299,-424) (17/12,27/19) -> (27/17,8/5) Hyperbolic Matrix(351,-500,245,-349) (27/19,10/7) -> (10/7,23/16) Parabolic Matrix(226,-325,121,-174) (23/16,13/9) -> (13/7,2/1) Hyperbolic Matrix(751,-1100,170,-249) (19/13,3/2) -> (53/12,31/7) Hyperbolic Matrix(49,-75,17,-26) (3/2,11/7) -> (14/5,3/1) Hyperbolic Matrix(851,-1350,220,-349) (46/29,27/17) -> (27/7,4/1) Hyperbolic Matrix(249,-400,94,-151) (8/5,21/13) -> (29/11,8/3) Hyperbolic Matrix(76,-125,45,-74) (13/8,5/3) -> (5/3,12/7) Parabolic Matrix(349,-600,146,-251) (12/7,19/11) -> (31/13,12/5) Hyperbolic Matrix(99,-175,43,-76) (7/4,9/5) -> (16/7,7/3) Hyperbolic Matrix(1001,-1850,270,-499) (24/13,13/7) -> (63/17,26/7) Hyperbolic Matrix(151,-325,46,-99) (2/1,13/6) -> (13/4,23/7) Hyperbolic Matrix(251,-550,68,-149) (13/6,11/5) -> (11/3,37/10) Hyperbolic Matrix(101,-225,22,-49) (11/5,9/4) -> (9/2,14/3) Hyperbolic Matrix(276,-625,121,-274) (9/4,25/11) -> (25/11,16/7) Parabolic Matrix(74,-175,11,-26) (7/3,19/8) -> (6/1,7/1) Hyperbolic Matrix(1051,-2500,441,-1049) (19/8,50/21) -> (50/21,31/13) Parabolic Matrix(51,-125,20,-49) (12/5,5/2) -> (5/2,13/5) Parabolic Matrix(124,-325,29,-76) (13/5,21/8) -> (4/1,13/3) Hyperbolic Matrix(951,-2500,361,-949) (21/8,50/19) -> (50/19,29/11) Parabolic Matrix(251,-675,74,-199) (8/3,27/10) -> (27/8,17/5) Hyperbolic Matrix(351,-950,92,-249) (27/10,19/7) -> (19/5,23/6) Hyperbolic Matrix(101,-275,18,-49) (19/7,11/4) -> (11/2,6/1) Hyperbolic Matrix(226,-625,81,-224) (11/4,25/9) -> (25/9,14/5) Parabolic Matrix(101,-325,23,-74) (3/1,13/4) -> (13/3,22/5) Hyperbolic Matrix(151,-500,45,-149) (23/7,10/3) -> (10/3,27/8) Parabolic Matrix(51,-175,7,-24) (17/5,7/2) -> (7/1,8/1) Hyperbolic Matrix(176,-625,49,-174) (7/2,25/7) -> (25/7,18/5) Parabolic Matrix(2701,-10000,729,-2699) (37/10,100/27) -> (100/27,63/17) Parabolic Matrix(74,-275,7,-26) (26/7,41/11) -> (9/1,1/0) Hyperbolic Matrix(301,-1125,80,-299) (41/11,15/4) -> (15/4,34/9) Parabolic Matrix(324,-1225,73,-276) (34/9,19/5) -> (31/7,9/2) Hyperbolic Matrix(651,-2500,169,-649) (23/6,50/13) -> (50/13,27/7) Parabolic Matrix(1276,-5625,289,-1274) (22/5,75/17) -> (75/17,53/12) Parabolic Matrix(26,-125,5,-24) (14/3,5/1) -> (5/1,11/2) Parabolic Matrix(76,-625,9,-74) (8/1,25/3) -> (25/3,17/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,1,1) Matrix(151,-175,107,-124) -> Matrix(1,-1,1,0) Matrix(149,-175,86,-101) -> Matrix(5,-3,2,-1) Matrix(226,-275,143,-174) -> Matrix(2,-3,-1,2) Matrix(101,-125,80,-99) -> Matrix(1,-1,0,1) Matrix(176,-225,97,-124) -> Matrix(0,-1,1,0) Matrix(251,-325,173,-224) -> Matrix(5,-3,7,-4) Matrix(249,-325,154,-201) -> Matrix(1,-1,6,-5) Matrix(701,-950,442,-599) -> Matrix(1,-2,-2,5) Matrix(699,-950,479,-651) -> Matrix(1,2,1,3) Matrix(826,-1125,605,-824) -> Matrix(2,-1,1,0) Matrix(1499,-2050,1061,-1451) -> Matrix(1,-2,3,-5) Matrix(401,-550,218,-299) -> Matrix(1,-2,-2,5) Matrix(199,-275,55,-76) -> Matrix(1,-5,1,-4) Matrix(601,-850,70,-99) -> Matrix(3,-2,2,-1) Matrix(476,-675,299,-424) -> Matrix(0,-1,1,0) Matrix(351,-500,245,-349) -> Matrix(1,0,3,1) Matrix(226,-325,121,-174) -> Matrix(2,-1,5,-2) Matrix(751,-1100,170,-249) -> Matrix(9,-8,-10,9) Matrix(49,-75,17,-26) -> Matrix(1,-3,1,-2) Matrix(851,-1350,220,-349) -> Matrix(9,2,4,1) Matrix(249,-400,94,-151) -> Matrix(1,0,2,1) Matrix(76,-125,45,-74) -> Matrix(4,-3,3,-2) Matrix(349,-600,146,-251) -> Matrix(13,-24,6,-11) Matrix(99,-175,43,-76) -> Matrix(1,-5,1,-4) Matrix(1001,-1850,270,-499) -> Matrix(13,2,6,1) Matrix(151,-325,46,-99) -> Matrix(1,1,-2,-1) Matrix(251,-550,68,-149) -> Matrix(7,-2,4,-1) Matrix(101,-225,22,-49) -> Matrix(1,-1,2,-1) Matrix(276,-625,121,-274) -> Matrix(12,-11,11,-10) Matrix(74,-175,11,-26) -> Matrix(2,-3,-1,2) Matrix(1051,-2500,441,-1049) -> Matrix(43,-84,21,-41) Matrix(51,-125,20,-49) -> Matrix(1,-3,0,1) Matrix(124,-325,29,-76) -> Matrix(4,1,-1,0) Matrix(951,-2500,361,-949) -> Matrix(1,0,19,1) Matrix(251,-675,74,-199) -> Matrix(1,-1,2,-1) Matrix(351,-950,92,-249) -> Matrix(7,-2,4,-1) Matrix(101,-275,18,-49) -> Matrix(5,-3,2,-1) Matrix(226,-625,81,-224) -> Matrix(10,-9,9,-8) Matrix(101,-325,23,-74) -> Matrix(1,3,-1,-2) Matrix(151,-500,45,-149) -> Matrix(1,0,3,1) Matrix(51,-175,7,-24) -> Matrix(1,-1,1,0) Matrix(176,-625,49,-174) -> Matrix(8,-7,7,-6) Matrix(2701,-10000,729,-2699) -> Matrix(47,-92,23,-45) Matrix(74,-275,7,-26) -> Matrix(2,-5,1,-2) Matrix(301,-1125,80,-299) -> Matrix(1,-1,0,1) Matrix(324,-1225,73,-276) -> Matrix(0,-1,1,0) Matrix(651,-2500,169,-649) -> Matrix(27,-52,13,-25) Matrix(1276,-5625,289,-1274) -> Matrix(16,17,-17,-18) Matrix(26,-125,5,-24) -> Matrix(2,-1,1,0) Matrix(76,-625,9,-74) -> Matrix(4,-3,3,-2) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 1 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 1 Number of equivalence classes of cusps: 1 Genus: 0 Degree of H/liftables -> H/(image of liftables): 150 ----------------------------------------------------------------------- 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 2/1 2/1 1 25 13/6 -1/6 1 25 11/5 1/3 1 25 9/4 3/4 1 25 25/11 1/1 11 1 7/3 1/1 1 25 19/8 15/8 1 25 50/21 2/1 21 1 12/5 12/5 1 25 5/2 1/0 3 5 13/5 -3/5 1 25 21/8 -1/8 1 25 50/19 0/1 19 1 8/3 0/1 1 25 27/10 -1/2 1 25 19/7 3/7 1 25 11/4 3/4 1 25 25/9 1/1 9 1 3/1 3/1 1 25 13/4 -5/4 1 25 23/7 -3/5 1 25 10/3 0/1 3 5 27/8 3/4 1 25 17/5 1/1 1 25 7/2 1/2 1 25 25/7 1/1 7 1 11/3 1/1 1 25 37/10 19/10 1 25 100/27 2/1 23 1 26/7 2/1 1 25 41/11 3/1 1 25 15/4 1/0 1 5 34/9 2/1 1 25 19/5 7/5 1 25 23/6 11/6 1 25 50/13 2/1 13 1 4/1 4/1 1 25 13/3 -7/3 1 25 22/5 -6/5 1 25 75/17 -1/1 17 1 31/7 -5/7 1 25 9/2 -1/2 1 25 14/3 2/1 1 25 5/1 1/1 1 5 11/2 3/2 1 25 6/1 6/1 1 25 7/1 -1/1 1 25 8/1 0/1 1 25 25/3 1/1 3 1 9/1 1/1 1 25 1/0 1/0 1 25 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(151,-325,46,-99) (2/1,13/6) -> (13/4,23/7) Hyperbolic Matrix(251,-550,68,-149) (13/6,11/5) -> (11/3,37/10) Hyperbolic Matrix(101,-225,22,-49) (11/5,9/4) -> (9/2,14/3) Hyperbolic Matrix(199,-450,88,-199) (9/4,25/11) -> (9/4,25/11) Reflection Matrix(76,-175,33,-76) (25/11,7/3) -> (25/11,7/3) Reflection Matrix(74,-175,11,-26) (7/3,19/8) -> (6/1,7/1) Hyperbolic Matrix(799,-1900,336,-799) (19/8,50/21) -> (19/8,50/21) Reflection Matrix(251,-600,105,-251) (50/21,12/5) -> (50/21,12/5) Reflection Matrix(51,-125,20,-49) (12/5,5/2) -> (5/2,13/5) Parabolic Matrix(124,-325,29,-76) (13/5,21/8) -> (4/1,13/3) Hyperbolic Matrix(799,-2100,304,-799) (21/8,50/19) -> (21/8,50/19) Reflection Matrix(151,-400,57,-151) (50/19,8/3) -> (50/19,8/3) Reflection Matrix(251,-675,74,-199) (8/3,27/10) -> (27/8,17/5) Hyperbolic Matrix(351,-950,92,-249) (27/10,19/7) -> (19/5,23/6) Hyperbolic Matrix(101,-275,18,-49) (19/7,11/4) -> (11/2,6/1) Hyperbolic Matrix(199,-550,72,-199) (11/4,25/9) -> (11/4,25/9) Reflection Matrix(26,-75,9,-26) (25/9,3/1) -> (25/9,3/1) Reflection Matrix(101,-325,23,-74) (3/1,13/4) -> (13/3,22/5) Hyperbolic Matrix(151,-500,45,-149) (23/7,10/3) -> (10/3,27/8) Parabolic Matrix(51,-175,7,-24) (17/5,7/2) -> (7/1,8/1) Hyperbolic Matrix(99,-350,28,-99) (7/2,25/7) -> (7/2,25/7) Reflection Matrix(76,-275,21,-76) (25/7,11/3) -> (25/7,11/3) Reflection Matrix(1999,-7400,540,-1999) (37/10,100/27) -> (37/10,100/27) Reflection Matrix(701,-2600,189,-701) (100/27,26/7) -> (100/27,26/7) Reflection Matrix(74,-275,7,-26) (26/7,41/11) -> (9/1,1/0) Hyperbolic Matrix(301,-1125,80,-299) (41/11,15/4) -> (15/4,34/9) Parabolic Matrix(324,-1225,73,-276) (34/9,19/5) -> (31/7,9/2) Hyperbolic Matrix(599,-2300,156,-599) (23/6,50/13) -> (23/6,50/13) Reflection Matrix(51,-200,13,-51) (50/13,4/1) -> (50/13,4/1) Reflection Matrix(749,-3300,170,-749) (22/5,75/17) -> (22/5,75/17) Reflection Matrix(526,-2325,119,-526) (75/17,31/7) -> (75/17,31/7) Reflection Matrix(26,-125,5,-24) (14/3,5/1) -> (5/1,11/2) Parabolic Matrix(49,-400,6,-49) (8/1,25/3) -> (8/1,25/3) Reflection Matrix(26,-225,3,-26) (25/3,9/1) -> (25/3,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Matrix(151,-325,46,-99) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(251,-550,68,-149) -> Matrix(7,-2,4,-1) Matrix(101,-225,22,-49) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(199,-450,88,-199) -> Matrix(7,-6,8,-7) (9/4,25/11) -> (3/4,1/1) Matrix(76,-175,33,-76) -> Matrix(4,-5,3,-4) (25/11,7/3) -> (1/1,5/3) Matrix(74,-175,11,-26) -> Matrix(2,-3,-1,2) Matrix(799,-1900,336,-799) -> Matrix(31,-60,16,-31) (19/8,50/21) -> (15/8,2/1) Matrix(251,-600,105,-251) -> Matrix(11,-24,5,-11) (50/21,12/5) -> (2/1,12/5) Matrix(51,-125,20,-49) -> Matrix(1,-3,0,1) 1/0 Matrix(124,-325,29,-76) -> Matrix(4,1,-1,0) Matrix(799,-2100,304,-799) -> Matrix(-1,0,16,1) (21/8,50/19) -> (-1/8,0/1) Matrix(151,-400,57,-151) -> Matrix(1,0,3,-1) (50/19,8/3) -> (0/1,2/3) Matrix(251,-675,74,-199) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(351,-950,92,-249) -> Matrix(7,-2,4,-1) Matrix(101,-275,18,-49) -> Matrix(5,-3,2,-1) Matrix(199,-550,72,-199) -> Matrix(7,-6,8,-7) (11/4,25/9) -> (3/4,1/1) Matrix(26,-75,9,-26) -> Matrix(2,-3,1,-2) (25/9,3/1) -> (1/1,3/1) Matrix(101,-325,23,-74) -> Matrix(1,3,-1,-2) (-2/1,0/1).(-3/2,1/0).(-3/1,-1/1) Matrix(151,-500,45,-149) -> Matrix(1,0,3,1) 0/1 Matrix(51,-175,7,-24) -> Matrix(1,-1,1,0) (0/1,2/1).(1/2,1/0).(-1/1,1/1) Matrix(99,-350,28,-99) -> Matrix(3,-2,4,-3) (7/2,25/7) -> (1/2,1/1) Matrix(76,-275,21,-76) -> Matrix(4,-5,3,-4) (25/7,11/3) -> (1/1,5/3) Matrix(1999,-7400,540,-1999) -> Matrix(39,-76,20,-39) (37/10,100/27) -> (19/10,2/1) Matrix(701,-2600,189,-701) -> Matrix(7,-16,3,-7) (100/27,26/7) -> (2/1,8/3) Matrix(74,-275,7,-26) -> Matrix(2,-5,1,-2) (1/1,3/1).(2/1,1/0) Matrix(301,-1125,80,-299) -> Matrix(1,-1,0,1) 1/0 Matrix(324,-1225,73,-276) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(599,-2300,156,-599) -> Matrix(23,-44,12,-23) (23/6,50/13) -> (11/6,2/1) Matrix(51,-200,13,-51) -> Matrix(3,-8,1,-3) (50/13,4/1) -> (2/1,4/1) Matrix(749,-3300,170,-749) -> Matrix(11,12,-10,-11) (22/5,75/17) -> (-6/5,-1/1) Matrix(526,-2325,119,-526) -> Matrix(6,5,-7,-6) (75/17,31/7) -> (-1/1,-5/7) Matrix(26,-125,5,-24) -> Matrix(2,-1,1,0) 1/1 Matrix(49,-400,6,-49) -> Matrix(1,0,2,-1) (8/1,25/3) -> (0/1,1/1) Matrix(26,-225,3,-26) -> Matrix(2,-3,1,-2) (25/3,9/1) -> (1/1,3/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.