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 -4/5 -11/15 -52/75 -3/5 -74/125 -7/15 -9/20 -21/50 -2/5 -49/125 -19/50 -8/25 -3/10 -27/100 -67/250 -4/15 -53/200 -13/50 -6/25 -5/21 -11/50 -5/24 -1/5 -4/21 -9/50 -4/23 -13/75 -4/25 -3/19 -3/20 -7/50 -3/22 -2/15 -3/25 -2/17 -1/10 0/1 1/10 1/9 1/8 2/15 1/7 3/20 2/13 1/6 3/17 2/11 3/16 1/5 4/19 3/14 5/23 2/9 3/13 1/4 4/15 3/11 5/18 7/25 2/7 3/10 23/75 1/3 9/25 2/5 5/12 11/25 9/20 7/15 1/2 14/25 3/5 16/25 2/3 17/25 18/25 11/15 19/25 4/5 62/75 21/25 22/25 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -9/10 -2/5 -8/9 -4/11 -5/14 -7/8 -1/3 -7/22 -13/15 -3/10 -6/7 -2/7 -5/18 -17/20 -4/15 -11/13 -1/4 -5/6 -1/4 -5/21 -14/17 -5/22 -2/9 -9/11 -7/32 -13/16 -3/14 -7/33 -4/5 -1/5 -15/19 -3/16 -11/14 -3/16 -5/27 -18/23 -3/16 -8/43 -7/9 -5/28 -31/40 -2/11 -24/31 -2/11 -5/28 -17/22 -3/17 -7/40 -61/79 -7/40 -105/136 -19/109 -23/132 -44/57 -4/23 -17/98 -27/35 -1/6 -10/13 -4/23 -1/6 -23/30 -4/23 -13/17 -13/76 -3/4 -1/6 -3/19 -14/19 -3/20 -4/27 -25/34 -1/6 -3/19 -36/49 -2/13 -3/20 -11/15 -3/20 -41/56 -3/20 -7/47 -30/41 -5/34 -6/41 -19/26 -3/20 -1/7 -8/11 -3/20 -4/27 -37/51 -37/252 -29/40 -6/41 -50/69 -6/41 -7/48 -21/29 -7/48 -55/76 -7/48 -1/7 -34/47 -7/48 -8/55 -47/65 -9/62 -13/18 -13/90 -1/7 -18/25 -1/7 -5/7 -5/36 -17/24 -1/7 -5/36 -29/41 -5/36 -12/17 -3/22 -2/15 -31/44 -1/8 -1/9 -81/115 -1/8 -50/71 -1/6 -2/13 -69/98 -7/48 -1/7 -88/125 -1/7 -19/27 -5/36 -7/10 -2/15 -16/23 -1/8 0/1 -25/36 -1/7 -1/8 -84/121 -5/38 -8/61 -59/85 -1/8 -34/49 -2/15 -1/8 -43/62 -5/38 -3/23 -52/75 -3/23 -9/13 -1/8 -11/16 -3/23 -7/54 -13/19 -1/8 -2/3 -1/8 -2/17 -13/20 -2/17 -11/17 -11/96 -9/14 -9/80 -1/9 -16/25 -1/9 -7/11 -7/64 -19/30 -4/37 -31/49 -31/288 -12/19 -3/28 -8/75 -29/46 -7/66 -9/85 -17/27 -5/48 -39/62 -1/10 -3/31 -22/35 -1/9 -5/8 -1/9 -1/10 -13/21 -5/48 -34/55 -3/29 -21/34 -1/9 -1/10 -8/13 -1/10 0/1 -19/31 -3/28 -30/49 -3/28 -2/19 -71/116 -7/66 -9/85 -41/67 -13/124 -11/18 -1/9 -1/10 -25/41 -13/124 -14/23 -5/48 -8/77 -3/5 -1/10 -16/27 -7/72 -10/103 -45/76 -43/444 -3/31 -74/125 -3/31 -29/49 -29/300 -13/22 -5/52 -7/73 -23/39 -11/116 -10/17 -1/10 -2/21 -17/29 -1/12 -24/41 -1/10 -2/21 -55/94 -1/12 -1/13 -31/53 -1/8 -7/12 -1/10 -3/31 -11/19 -3/32 -26/45 -1/11 -41/71 -3/32 -15/26 -3/32 -1/11 -4/7 -1/10 -2/21 -17/30 -4/43 -30/53 -3/32 -4/43 -43/76 -3/32 -1/11 -13/23 -3/32 -9/16 -9/98 -1/11 -14/25 -1/11 -5/9 -5/56 -16/29 -3/34 -14/159 -43/78 -13/148 -31/353 -27/49 -27/308 -11/20 -2/23 -6/11 -1/12 0/1 -13/24 -1/11 -1/12 -7/13 -1/12 -8/15 -1/11 -9/17 -9/104 -1/2 -1/12 -1/13 -8/17 -7/94 -2/27 -7/15 -1/14 -6/13 -1/14 0/1 -5/11 -1/12 -9/20 -2/27 -13/29 -5/68 -4/9 -4/55 -1/14 -11/25 -1/14 -7/16 -1/14 -7/99 -17/39 -7/100 -27/62 -1/14 -3/43 -10/23 -4/57 -7/100 -13/30 -2/29 -3/7 -3/44 -11/26 -3/44 -1/15 -8/19 -1/16 0/1 -21/50 0/1 -13/31 -1/12 -5/12 -1/14 -1/15 -22/53 -1/16 0/1 -17/41 -1/12 -12/29 -6/83 -1/14 -31/75 -1/14 -19/46 -1/14 -13/183 -7/17 -7/100 -9/22 -3/44 -1/15 -2/5 -1/15 -11/28 -1/15 -1/16 -20/51 -2/31 -1/16 -49/125 -1/16 -29/74 -1/15 -1/16 -9/23 -1/16 -7/18 -5/78 -3/47 -33/85 -7/110 -26/67 -23/362 -4/63 -19/49 -19/300 -12/31 -10/159 -1/16 -29/75 -1/16 -17/44 -1/16 -11/177 -5/13 -1/16 -13/34 -3/50 -1/17 -8/21 -1/18 0/1 -19/50 0/1 -11/29 -1/12 -3/8 -1/14 -1/15 -13/35 -3/46 -36/97 -7/108 -2/31 -23/62 -3/46 -5/77 -10/27 -7/108 -2/31 -7/19 -1/16 -18/49 -2/31 -1/16 -47/128 -1/15 -1/16 -29/79 -1/16 -11/30 -2/31 -4/11 -4/63 -1/16 -9/25 -1/16 -5/14 -1/16 -5/81 -11/31 -1/16 -17/48 -3/49 -11/180 -6/17 -2/33 -3/50 -7/20 -2/33 -8/23 -4/67 -5/84 -1/3 -1/16 -8/25 -1/17 -7/22 -1/17 -7/120 -6/19 -4/69 -3/52 -5/16 -3/53 -1/18 -4/13 -4/71 -1/18 -7/23 -3/56 -3/10 0/1 -8/27 -2/31 -1/16 -5/17 -5/84 -22/75 -1/17 -17/58 -1/17 -17/290 -12/41 -6/103 -5/86 -7/24 -1/17 -3/52 -2/7 -2/35 -1/18 -7/25 -1/18 -5/18 -1/18 -5/91 -23/83 -23/420 -18/65 -3/55 -31/112 -1/18 -7/127 -13/47 -7/128 -34/123 -16/293 -19/348 -21/76 -3/55 -17/312 -8/29 -1/18 -2/37 -27/98 -3/55 -17/312 -19/69 -5/92 -11/40 -2/37 -14/51 -2/37 -3/56 -17/62 -1/18 -1/19 -3/11 -3/56 -10/37 -1/18 -2/37 -27/100 -2/37 -17/63 -3/56 -7/26 -3/56 -1/19 -11/41 -3/56 -26/97 -5/92 -2/37 -67/250 -2/37 -41/153 -11/204 -15/56 -3/56 -1/19 -4/15 -1/19 -13/49 -13/252 -22/83 -19/370 -2/39 -53/200 -2/39 -31/117 -25/488 -9/34 -5/98 -3/59 -5/19 -1/20 -6/23 -1/24 0/1 -13/50 0/1 -7/27 -1/12 -1/4 -1/18 -1/19 -6/25 -1/19 -5/21 -5/96 -4/17 -3/58 -2/39 -7/30 -2/39 -3/13 -1/20 -8/35 -1/19 -5/22 -5/99 -1/20 -17/75 -1/20 -12/53 -1/20 -12/241 -7/31 -1/20 -9/40 -2/41 -2/9 -1/22 0/1 -11/50 0/1 -9/41 -1/8 -7/32 -1/14 -1/15 -5/23 -1/16 -8/37 -6/107 -1/18 -27/125 -1/18 -19/88 -1/18 -17/307 -11/51 -11/200 -14/65 -3/55 -3/14 -3/56 -1/19 -7/33 -7/136 -11/52 -5/99 -1/20 -15/71 -1/20 -4/19 -1/20 0/1 -5/24 -3/56 -1/19 -1/5 -1/20 -5/26 -5/104 -1/21 -4/21 -1/22 0/1 -3/16 -3/62 -1/21 -5/27 -3/64 -7/38 -7/153 -1/22 -9/49 -9/200 -2/11 -1/24 0/1 -9/50 0/1 -7/39 -1/8 -5/28 -1/16 -1/17 -3/17 -3/56 -4/23 -4/79 -1/20 -13/75 -1/20 -9/52 -1/20 -9/181 -5/29 -1/20 -11/64 -7/144 -5/103 -6/35 -1/21 -1/6 -1/20 -1/21 -4/25 -1/21 -3/19 -3/64 -2/13 -1/22 0/1 -3/20 0/1 -1/7 -1/24 -7/50 0/1 -6/43 -1/6 0/1 -5/36 -1/15 -1/16 -4/29 -2/35 -1/18 -3/22 -3/59 -1/20 -2/15 -1/21 -1/8 -1/21 -1/22 -3/25 -1/22 -2/17 -1/22 -2/45 -1/9 -1/24 -1/10 0/1 0/1 -1/24 0/1 1/10 0/1 1/9 -1/24 1/8 -1/26 -1/27 2/15 -1/27 1/7 -1/24 3/20 0/1 2/13 -1/26 0/1 1/6 -1/27 -1/28 3/17 -3/88 2/11 -1/24 0/1 3/16 -1/27 -3/82 1/5 -1/28 4/19 -1/28 0/1 3/14 -1/29 -3/88 5/23 -1/32 2/9 -1/26 0/1 9/40 -2/55 7/31 -1/28 5/22 -1/28 -5/141 18/79 -5/142 -12/341 31/136 -9/256 -11/313 13/57 -7/200 8/35 -1/29 3/13 -1/28 7/30 -2/57 4/17 -2/57 -3/86 1/4 -1/29 -1/30 5/19 -1/28 9/34 -3/85 -5/142 13/49 -13/372 4/15 -1/29 15/56 -1/29 -3/88 11/41 -3/88 7/26 -1/29 -3/88 3/11 -3/88 14/51 -3/88 -2/59 11/40 -2/59 19/69 -5/148 8/29 -2/59 -1/30 21/76 -17/504 -3/89 13/47 -7/208 18/65 -3/89 5/18 -5/149 -1/30 7/25 -1/30 2/7 -1/30 -2/61 7/24 -3/92 -1/31 12/41 -5/154 -6/185 5/17 -5/156 13/44 -3/95 -1/32 34/115 -3/95 21/71 -1/32 29/98 -11/351 -1/32 37/125 -1/32 8/27 -1/32 -2/65 3/10 0/1 7/23 -3/88 11/36 -3/89 -7/208 37/121 -9/268 26/85 -5/149 15/49 -15/448 19/62 -19/569 -1/30 23/75 -1/30 4/13 -1/30 -4/121 5/16 -1/30 -3/91 6/19 -3/92 -4/123 1/3 -1/32 7/20 -2/63 6/17 -3/94 -2/63 5/14 -5/159 -1/32 9/25 -1/32 4/11 -1/32 -4/129 11/30 -2/65 18/49 -1/32 -2/65 7/19 -1/32 17/46 -3/97 -5/162 10/27 -2/65 -7/228 23/62 -5/163 -3/98 13/35 -3/98 3/8 -1/33 -1/34 8/21 -1/30 0/1 21/55 -1/32 13/34 -1/31 -3/94 5/13 -1/32 12/31 -1/32 -10/321 19/49 -19/612 45/116 -21/677 -25/806 26/67 -4/129 -23/742 7/18 -3/97 -5/162 16/41 -2/65 -11/358 9/23 -1/32 2/5 -1/33 11/27 -3/100 31/76 -1/33 -3/100 51/125 -3/100 20/49 -3/100 -2/67 9/22 -1/33 -3/100 16/39 -2/67 -13/436 7/17 -7/236 12/29 -1/34 -6/205 17/41 -1/36 39/94 -1/35 -1/36 22/53 -1/32 0/1 5/12 -1/33 -1/34 8/19 -1/32 0/1 19/45 -1/32 30/71 -2/65 -3/98 11/26 -1/33 -3/100 3/7 -3/100 13/30 -2/67 23/53 -5/168 33/76 -29/976 -3/101 10/23 -7/236 -4/135 7/16 -7/237 -1/34 11/25 -1/34 4/9 -1/34 -4/137 13/29 -5/172 35/78 -3/103 -5/172 22/49 -5/172 -2/69 9/20 -2/69 5/11 -1/36 11/24 -1/35 -1/36 6/13 -1/34 0/1 7/15 -1/34 8/17 -2/69 -7/242 1/2 -1/35 -1/36 9/17 -9/328 8/15 -1/37 7/13 -1/36 6/11 -1/36 0/1 11/20 -2/73 16/29 -14/513 -3/110 5/9 -5/184 14/25 -1/37 9/16 -1/37 -9/334 22/39 -6/223 -17/632 35/62 -5/186 -29/1079 13/23 -3/112 17/30 -4/149 4/7 -2/75 -1/38 15/26 -1/37 -3/112 11/19 -3/112 29/50 -2/75 18/31 -2/75 -5/188 7/12 -3/113 -1/38 31/53 -1/40 24/41 -2/75 -1/38 17/29 -1/36 44/75 -1/37 27/46 -1/37 -5/186 10/17 -2/75 -1/38 13/22 -7/263 -5/188 3/5 -1/38 17/28 -11/421 -7/268 31/51 -31/1188 76/125 -3/115 45/74 -3/115 -41/1572 14/23 -8/307 -5/192 11/18 -1/38 -1/39 52/85 -3/115 41/67 -13/500 30/49 -2/77 -3/116 19/31 -3/116 46/75 -1/39 27/44 -1/39 -1/40 8/13 -1/38 0/1 21/34 -1/38 -1/39 13/21 -5/192 31/50 -2/77 18/29 -2/77 -7/270 5/8 -1/38 -1/39 22/35 -1/39 61/97 -1/40 39/62 -3/113 -1/38 17/27 -5/192 12/19 -8/309 -3/116 31/49 -31/1200 81/128 -57/2207 -25/968 50/79 -40/1549 -11/426 19/30 -4/155 7/11 -7/272 16/25 -1/39 9/14 -1/39 -9/352 20/31 -6/235 -5/196 31/48 -5/196 -19/745 11/17 -11/432 13/20 -2/79 15/23 -1/40 2/3 -2/79 -1/40 17/25 -1/40 15/22 -1/40 -15/601 13/19 -1/40 11/16 -7/282 -3/121 9/13 -1/40 16/23 -1/40 0/1 7/10 -2/81 19/27 -5/204 12/17 -2/81 -3/122 53/75 -3/122 41/58 -3/122 -7/285 29/41 -5/204 17/24 -5/204 -1/41 5/7 -5/204 18/25 -1/41 13/18 -1/41 -13/534 60/83 -10/411 -49/2014 47/65 -9/370 81/112 -1/41 -9/370 34/47 -8/329 -7/288 89/123 -7/288 55/76 -1/41 -7/288 21/29 -7/288 71/98 -7/288 -41/1687 50/69 -7/288 -6/247 29/40 -6/247 37/51 -37/1524 45/62 -5/206 -39/1607 8/11 -4/165 -3/124 27/37 -3/124 73/100 -2/83 46/63 -2/83 -1/42 19/26 -1/41 -3/124 30/41 -6/247 -5/206 71/97 -13/536 183/250 -4/165 112/153 -4/165 -19/784 41/56 -7/289 -3/124 11/15 -3/124 36/49 -3/124 -2/83 61/83 -19/788 147/200 -2/83 86/117 -2/83 -25/1038 25/34 -3/125 -1/42 14/19 -4/165 -3/124 17/23 -11/456 37/50 -2/83 20/27 -2/83 -13/540 3/4 -3/125 -1/42 19/25 -1/42 16/21 -1/42 -16/673 13/17 -13/548 23/30 -4/169 10/13 -1/42 -4/169 27/35 -1/42 17/22 -7/296 -3/127 58/75 -3/127 41/53 -17/720 24/31 -5/212 -2/85 31/40 -2/85 7/9 -5/212 39/50 -2/85 32/41 -2/85 -23/978 25/32 -9/383 -7/298 18/23 -8/341 -3/128 29/37 -3/128 98/125 -1/43 69/88 -1/42 -1/43 40/51 -2/85 -3/128 51/65 -3/128 11/14 -5/213 -3/128 26/33 -11/470 -4/171 41/52 -7/300 -1/43 56/71 -1/42 -2/85 15/19 -3/128 19/24 -3/128 -1/43 4/5 -1/43 21/26 -1/43 -5/216 17/21 -5/216 13/16 -7/303 -3/130 22/27 -7/304 -2/87 31/38 -3/130 -5/217 40/49 -7/304 -2/87 9/11 -7/304 41/50 -2/87 32/39 -2/87 -25/1088 23/28 -11/479 -9/392 14/17 -2/87 -5/218 19/23 -11/480 62/75 -3/131 43/52 -3/131 -25/1092 24/29 -10/437 -7/306 53/64 -5/219 -1/44 29/35 -1/44 5/6 -5/219 -1/44 21/25 -1/44 16/19 -1/44 -16/705 11/13 -1/44 17/20 -4/177 6/7 -5/222 -2/89 43/50 -2/89 37/43 -31/1380 31/36 -15/668 -13/579 25/29 -7/312 19/22 -7/312 -5/223 13/15 -3/134 7/8 -7/314 -1/45 22/25 -1/45 15/17 -15/676 8/9 -5/226 -4/181 9/10 -2/91 1/1 -1/48 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(399,362,550,499) (-1/1,-9/10) -> (29/40,37/51) Hyperbolic Matrix(101,90,450,401) (-9/10,-8/9) -> (2/9,9/40) Hyperbolic Matrix(249,220,-850,-751) (-8/9,-7/8) -> (-17/58,-12/41) Hyperbolic Matrix(149,130,400,349) (-7/8,-13/15) -> (13/35,3/8) Hyperbolic Matrix(849,734,-1100,-951) (-13/15,-6/7) -> (-44/57,-27/35) Hyperbolic Matrix(199,170,350,299) (-6/7,-17/20) -> (17/30,4/7) Hyperbolic Matrix(151,128,650,551) (-17/20,-11/13) -> (3/13,7/30) Hyperbolic Matrix(251,212,-650,-549) (-11/13,-5/6) -> (-17/44,-5/13) Hyperbolic Matrix(599,494,-850,-701) (-5/6,-14/17) -> (-12/17,-31/44) Hyperbolic Matrix(501,412,-850,-699) (-14/17,-9/11) -> (-23/39,-10/17) Hyperbolic Matrix(349,284,-800,-651) (-9/11,-13/16) -> (-7/16,-17/39) Hyperbolic Matrix(649,526,-1050,-851) (-13/16,-4/5) -> (-34/55,-21/34) Hyperbolic Matrix(549,434,-950,-751) (-4/5,-15/19) -> (-11/19,-26/45) Hyperbolic Matrix(249,196,-700,-551) (-15/19,-11/14) -> (-5/14,-11/31) Hyperbolic Matrix(799,626,-1150,-901) (-11/14,-18/23) -> (-16/23,-25/36) Hyperbolic Matrix(701,548,-1150,-899) (-18/23,-7/9) -> (-25/41,-14/23) Hyperbolic Matrix(49,38,450,349) (-7/9,-31/40) -> (1/10,1/9) Hyperbolic Matrix(2899,2246,4000,3099) (-31/40,-24/31) -> (50/69,29/40) Hyperbolic Matrix(349,270,-1100,-851) (-24/31,-17/22) -> (-7/22,-6/19) Hyperbolic Matrix(3051,2356,6800,5251) (-17/22,-61/79) -> (13/29,35/78) Hyperbolic Matrix(5901,4556,19300,14901) (-61/79,-105/136) -> (11/36,37/121) Hyperbolic Matrix(1101,850,-7900,-6099) (-105/136,-44/57) -> (-6/43,-5/36) Hyperbolic Matrix(301,232,650,501) (-27/35,-10/13) -> (6/13,7/15) Hyperbolic Matrix(99,76,650,499) (-10/13,-23/30) -> (3/20,2/13) Hyperbolic Matrix(551,422,850,651) (-23/30,-13/17) -> (11/17,13/20) Hyperbolic Matrix(351,268,-850,-649) (-13/17,-3/4) -> (-19/46,-7/17) Hyperbolic Matrix(599,442,-950,-701) (-3/4,-14/19) -> (-12/19,-29/46) Hyperbolic Matrix(299,220,950,699) (-14/19,-25/34) -> (5/16,6/19) Hyperbolic Matrix(4499,3306,-7350,-5401) (-25/34,-36/49) -> (-30/49,-71/116) Hyperbolic Matrix(3401,2498,-4900,-3599) (-36/49,-11/15) -> (-59/85,-34/49) Hyperbolic Matrix(5001,3662,-7100,-5199) (-11/15,-41/56) -> (-31/44,-81/115) Hyperbolic Matrix(3599,2634,-6150,-4501) (-41/56,-30/41) -> (-24/41,-55/94) Hyperbolic Matrix(599,438,2050,1499) (-30/41,-19/26) -> (7/24,12/41) Hyperbolic Matrix(299,218,-550,-401) (-19/26,-8/11) -> (-6/11,-13/24) Hyperbolic Matrix(201,146,-1100,-799) (-8/11,-37/51) -> (-9/49,-2/11) Hyperbolic Matrix(499,362,550,399) (-37/51,-29/40) -> (9/10,1/1) Hyperbolic Matrix(3099,2246,4000,2899) (-29/40,-50/69) -> (24/31,31/40) Hyperbolic Matrix(1151,834,-5450,-3949) (-50/69,-21/29) -> (-15/71,-4/19) Hyperbolic Matrix(1901,1376,2350,1701) (-21/29,-55/76) -> (21/26,17/21) Hyperbolic Matrix(4301,3112,-7600,-5499) (-55/76,-34/47) -> (-30/53,-43/76) Hyperbolic Matrix(2951,2134,-7950,-5749) (-34/47,-47/65) -> (-13/35,-36/97) Hyperbolic Matrix(1049,758,-2700,-1951) (-47/65,-13/18) -> (-7/18,-33/85) Hyperbolic Matrix(649,468,900,649) (-13/18,-18/25) -> (18/25,13/18) Hyperbolic Matrix(251,180,350,251) (-18/25,-5/7) -> (5/7,18/25) Hyperbolic Matrix(149,106,350,249) (-5/7,-17/24) -> (11/26,3/7) Hyperbolic Matrix(551,390,2050,1451) (-17/24,-29/41) -> (11/41,7/26) Hyperbolic Matrix(99,70,-850,-601) (-29/41,-12/17) -> (-2/17,-1/9) Hyperbolic Matrix(13849,9754,-19950,-14051) (-81/115,-50/71) -> (-84/121,-59/85) Hyperbolic Matrix(8399,5914,10650,7499) (-50/71,-69/98) -> (41/52,56/71) Hyperbolic Matrix(11451,8062,13850,9751) (-69/98,-88/125) -> (62/75,43/52) Hyperbolic Matrix(4049,2850,4900,3449) (-88/125,-19/27) -> (19/23,62/75) Hyperbolic Matrix(151,106,500,351) (-19/27,-7/10) -> (3/10,7/23) Hyperbolic Matrix(149,104,500,349) (-7/10,-16/23) -> (8/27,3/10) Hyperbolic Matrix(4399,3054,19300,13399) (-25/36,-84/121) -> (18/79,31/136) Hyperbolic Matrix(3999,2774,4900,3399) (-34/49,-43/62) -> (31/38,40/49) Hyperbolic Matrix(11251,7802,14350,9951) (-43/62,-52/75) -> (98/125,69/88) Hyperbolic Matrix(3449,2390,4400,3049) (-52/75,-9/13) -> (29/37,98/125) Hyperbolic Matrix(249,172,650,449) (-9/13,-11/16) -> (13/34,5/13) Hyperbolic Matrix(251,172,950,651) (-11/16,-13/19) -> (5/19,9/34) Hyperbolic Matrix(249,170,-1100,-751) (-13/19,-2/3) -> (-12/53,-7/31) Hyperbolic Matrix(651,424,-1150,-749) (-2/3,-13/20) -> (-17/30,-30/53) Hyperbolic Matrix(651,422,850,551) (-13/20,-11/17) -> (13/17,23/30) Hyperbolic Matrix(149,96,-700,-451) (-11/17,-9/14) -> (-3/14,-7/33) Hyperbolic Matrix(449,288,700,449) (-9/14,-16/25) -> (16/25,9/14) Hyperbolic Matrix(351,224,550,351) (-16/25,-7/11) -> (7/11,16/25) Hyperbolic Matrix(249,158,550,349) (-7/11,-19/30) -> (9/20,5/11) Hyperbolic Matrix(1349,854,-2450,-1551) (-19/30,-31/49) -> (-27/49,-11/20) Hyperbolic Matrix(949,600,2450,1549) (-31/49,-12/19) -> (12/31,19/49) Hyperbolic Matrix(349,220,-1350,-851) (-29/46,-17/27) -> (-7/27,-1/4) Hyperbolic Matrix(1751,1102,3100,1951) (-17/27,-39/62) -> (35/62,13/23) Hyperbolic Matrix(2201,1384,-7950,-4999) (-39/62,-22/35) -> (-18/65,-31/112) Hyperbolic Matrix(51,32,400,251) (-22/35,-5/8) -> (1/8,2/15) Hyperbolic Matrix(151,94,-400,-249) (-5/8,-13/21) -> (-11/29,-3/8) Hyperbolic Matrix(2801,1732,-4850,-2999) (-13/21,-34/55) -> (-26/45,-41/71) Hyperbolic Matrix(201,124,650,401) (-21/34,-8/13) -> (4/13,5/16) Hyperbolic Matrix(101,62,-650,-399) (-8/13,-19/31) -> (-3/19,-2/13) Hyperbolic Matrix(901,552,2450,1501) (-19/31,-30/49) -> (18/49,7/19) Hyperbolic Matrix(4199,2570,-15850,-9701) (-71/116,-41/67) -> (-31/117,-9/34) Hyperbolic Matrix(749,458,-2700,-1651) (-41/67,-11/18) -> (-5/18,-23/83) Hyperbolic Matrix(449,274,-2050,-1251) (-11/18,-25/41) -> (-9/41,-7/32) Hyperbolic Matrix(149,90,-250,-151) (-14/23,-3/5) -> (-3/5,-16/27) Parabolic Matrix(1651,978,3800,2251) (-16/27,-45/76) -> (33/76,10/23) Hyperbolic Matrix(11401,6750,18750,11101) (-45/76,-74/125) -> (76/125,45/74) Hyperbolic Matrix(7599,4498,12500,7399) (-74/125,-29/49) -> (31/51,76/125) Hyperbolic Matrix(2701,1598,-4900,-2899) (-29/49,-13/22) -> (-43/78,-27/49) Hyperbolic Matrix(349,206,-1950,-1151) (-13/22,-23/39) -> (-7/39,-5/28) Hyperbolic Matrix(201,118,-850,-499) (-10/17,-17/29) -> (-5/21,-4/17) Hyperbolic Matrix(649,380,1450,849) (-17/29,-24/41) -> (4/9,13/29) Hyperbolic Matrix(4649,2720,-17350,-10151) (-55/94,-31/53) -> (-41/153,-15/56) Hyperbolic Matrix(1799,1052,-6500,-3801) (-31/53,-7/12) -> (-31/112,-13/47) Hyperbolic Matrix(251,146,-600,-349) (-7/12,-11/19) -> (-13/31,-5/12) Hyperbolic Matrix(4451,2570,6150,3551) (-41/71,-15/26) -> (55/76,21/29) Hyperbolic Matrix(101,58,350,201) (-15/26,-4/7) -> (2/7,7/24) Hyperbolic Matrix(299,170,350,199) (-4/7,-17/30) -> (17/20,6/7) Hyperbolic Matrix(1549,876,3800,2149) (-43/76,-13/23) -> (11/27,31/76) Hyperbolic Matrix(149,84,-800,-451) (-13/23,-9/16) -> (-3/16,-5/27) Hyperbolic Matrix(449,252,800,449) (-9/16,-14/25) -> (14/25,9/16) Hyperbolic Matrix(251,140,450,251) (-14/25,-5/9) -> (5/9,14/25) Hyperbolic Matrix(601,332,1450,801) (-5/9,-16/29) -> (12/29,17/41) Hyperbolic Matrix(1549,854,6800,3749) (-16/29,-43/78) -> (5/22,18/79) Hyperbolic Matrix(201,110,550,301) (-11/20,-6/11) -> (4/11,11/30) Hyperbolic Matrix(499,270,-1850,-1001) (-13/24,-7/13) -> (-17/63,-7/26) Hyperbolic Matrix(149,80,650,349) (-7/13,-8/15) -> (8/35,3/13) Hyperbolic Matrix(651,346,-2350,-1249) (-8/15,-9/17) -> (-23/83,-18/65) Hyperbolic Matrix(549,290,850,449) (-9/17,-1/2) -> (31/48,11/17) Hyperbolic Matrix(749,354,950,449) (-1/2,-8/17) -> (26/33,41/52) Hyperbolic Matrix(951,446,-2450,-1149) (-8/17,-7/15) -> (-33/85,-26/67) Hyperbolic Matrix(501,232,650,301) (-7/15,-6/13) -> (10/13,27/35) Hyperbolic Matrix(149,68,-550,-251) (-6/13,-5/11) -> (-3/11,-10/37) Hyperbolic Matrix(349,158,550,249) (-5/11,-9/20) -> (19/30,7/11) Hyperbolic Matrix(899,404,-2450,-1101) (-9/20,-13/29) -> (-29/79,-11/30) Hyperbolic Matrix(849,380,1450,649) (-13/29,-4/9) -> (24/41,17/29) Hyperbolic Matrix(199,88,450,199) (-4/9,-11/25) -> (11/25,4/9) Hyperbolic Matrix(351,154,800,351) (-11/25,-7/16) -> (7/16,11/25) Hyperbolic Matrix(849,370,-3100,-1351) (-17/39,-27/62) -> (-17/62,-3/11) Hyperbolic Matrix(1149,500,3100,1349) (-27/62,-10/23) -> (10/27,23/62) Hyperbolic Matrix(401,174,-1150,-499) (-10/23,-13/30) -> (-7/20,-8/23) Hyperbolic Matrix(51,22,350,151) (-13/30,-3/7) -> (1/7,3/20) Hyperbolic Matrix(249,106,350,149) (-3/7,-11/26) -> (17/24,5/7) Hyperbolic Matrix(199,84,-950,-401) (-11/26,-8/19) -> (-4/19,-5/24) Hyperbolic Matrix(1451,610,2500,1051) (-8/19,-21/50) -> (29/50,18/31) Hyperbolic Matrix(1449,608,2500,1049) (-21/50,-13/31) -> (11/19,29/50) Hyperbolic Matrix(1651,686,-4450,-1849) (-5/12,-22/53) -> (-36/97,-23/62) Hyperbolic Matrix(1649,684,-6150,-2551) (-22/53,-17/41) -> (-11/41,-26/97) Hyperbolic Matrix(801,332,1450,601) (-17/41,-12/29) -> (16/29,5/9) Hyperbolic Matrix(1751,724,2300,951) (-12/29,-31/75) -> (19/25,16/21) Hyperbolic Matrix(1099,454,1450,599) (-31/75,-19/46) -> (3/4,19/25) Hyperbolic Matrix(151,62,-850,-349) (-7/17,-9/22) -> (-5/28,-3/17) Hyperbolic Matrix(99,40,-250,-101) (-9/22,-2/5) -> (-2/5,-11/28) Parabolic Matrix(2901,1138,-7900,-3099) (-11/28,-20/51) -> (-18/49,-47/128) Hyperbolic Matrix(5101,2000,12500,4901) (-20/51,-49/125) -> (51/125,20/49) Hyperbolic Matrix(7649,2998,18750,7349) (-49/125,-29/74) -> (31/76,51/125) Hyperbolic Matrix(7851,3076,10850,4251) (-29/74,-9/23) -> (89/123,55/76) Hyperbolic Matrix(251,98,-1150,-449) (-9/23,-7/18) -> (-7/32,-5/23) Hyperbolic Matrix(1949,756,-7350,-2851) (-26/67,-19/49) -> (-13/49,-22/83) Hyperbolic Matrix(1549,600,2450,949) (-19/49,-12/31) -> (12/19,31/49) Hyperbolic Matrix(1851,716,2200,851) (-12/31,-29/75) -> (21/25,16/19) Hyperbolic Matrix(1299,502,1550,599) (-29/75,-17/44) -> (5/6,21/25) Hyperbolic Matrix(449,172,650,249) (-5/13,-13/34) -> (11/16,9/13) Hyperbolic Matrix(199,76,-1050,-401) (-13/34,-8/21) -> (-4/21,-3/16) Hyperbolic Matrix(1551,590,2500,951) (-8/21,-19/50) -> (31/50,18/29) Hyperbolic Matrix(1549,588,2500,949) (-19/50,-11/29) -> (13/21,31/50) Hyperbolic Matrix(349,130,400,149) (-3/8,-13/35) -> (13/15,7/8) Hyperbolic Matrix(2201,816,2700,1001) (-23/62,-10/27) -> (22/27,31/38) Hyperbolic Matrix(249,92,-950,-351) (-10/27,-7/19) -> (-5/19,-6/23) Hyperbolic Matrix(1501,552,2450,901) (-7/19,-18/49) -> (30/49,19/31) Hyperbolic Matrix(4701,1726,5450,2001) (-47/128,-29/79) -> (25/29,19/22) Hyperbolic Matrix(301,110,550,201) (-11/30,-4/11) -> (6/11,11/20) Hyperbolic Matrix(199,72,550,199) (-4/11,-9/25) -> (9/25,4/11) Hyperbolic Matrix(251,90,700,251) (-9/25,-5/14) -> (5/14,9/25) Hyperbolic Matrix(1749,620,-6350,-2251) (-11/31,-17/48) -> (-27/98,-19/69) Hyperbolic Matrix(401,142,850,301) (-17/48,-6/17) -> (8/17,1/2) Hyperbolic Matrix(199,70,850,299) (-6/17,-7/20) -> (7/30,4/17) Hyperbolic Matrix(401,138,-1450,-499) (-8/23,-1/3) -> (-13/47,-34/123) Hyperbolic Matrix(1199,386,1550,499) (-1/3,-8/25) -> (58/75,41/53) Hyperbolic Matrix(1701,542,2200,701) (-8/25,-7/22) -> (17/22,58/75) Hyperbolic Matrix(699,220,950,299) (-6/19,-5/16) -> (25/34,14/19) Hyperbolic Matrix(401,124,650,201) (-5/16,-4/13) -> (8/13,21/34) Hyperbolic Matrix(249,76,-1150,-351) (-4/13,-7/23) -> (-5/23,-8/37) Hyperbolic Matrix(351,106,500,151) (-7/23,-3/10) -> (7/10,19/27) Hyperbolic Matrix(349,104,500,149) (-3/10,-8/27) -> (16/23,7/10) Hyperbolic Matrix(149,44,-850,-251) (-8/27,-5/17) -> (-3/17,-4/23) Hyperbolic Matrix(1499,440,1700,499) (-5/17,-22/75) -> (22/25,15/17) Hyperbolic Matrix(1801,528,2050,601) (-22/75,-17/58) -> (7/8,22/25) Hyperbolic Matrix(1499,438,2050,599) (-12/41,-7/24) -> (19/26,30/41) Hyperbolic Matrix(201,58,350,101) (-7/24,-2/7) -> (4/7,15/26) Hyperbolic Matrix(99,28,350,99) (-2/7,-7/25) -> (7/25,2/7) Hyperbolic Matrix(251,70,900,251) (-7/25,-5/18) -> (5/18,7/25) Hyperbolic Matrix(6599,1824,10850,2999) (-34/123,-21/76) -> (45/74,14/23) Hyperbolic Matrix(2599,718,6150,1699) (-21/76,-8/29) -> (30/71,11/26) Hyperbolic Matrix(3599,992,4350,1199) (-8/29,-27/98) -> (43/52,24/29) Hyperbolic Matrix(901,248,4000,1101) (-19/69,-11/40) -> (9/40,7/31) Hyperbolic Matrix(51,14,550,151) (-11/40,-14/51) -> (0/1,1/10) Hyperbolic Matrix(5999,1646,7650,2099) (-14/51,-17/62) -> (69/88,40/51) Hyperbolic Matrix(7301,1972,10000,2701) (-10/37,-27/100) -> (73/100,46/63) Hyperbolic Matrix(7299,1970,10000,2699) (-27/100,-17/63) -> (27/37,73/100) Hyperbolic Matrix(1451,390,2050,551) (-7/26,-11/41) -> (29/41,17/24) Hyperbolic Matrix(45751,12262,62500,16751) (-26/97,-67/250) -> (183/250,112/153) Hyperbolic Matrix(45749,12260,62500,16749) (-67/250,-41/153) -> (71/97,183/250) Hyperbolic Matrix(351,94,-2050,-549) (-15/56,-4/15) -> (-6/35,-1/6) Hyperbolic Matrix(851,226,-3950,-1049) (-4/15,-13/49) -> (-11/51,-14/65) Hyperbolic Matrix(29401,7792,40000,10601) (-22/83,-53/200) -> (147/200,86/117) Hyperbolic Matrix(29399,7790,40000,10599) (-53/200,-31/117) -> (61/83,147/200) Hyperbolic Matrix(651,172,950,251) (-9/34,-5/19) -> (13/19,11/16) Hyperbolic Matrix(1851,482,2500,651) (-6/23,-13/50) -> (37/50,20/27) Hyperbolic Matrix(1849,480,2500,649) (-13/50,-7/27) -> (17/23,37/50) Hyperbolic Matrix(851,206,1450,351) (-1/4,-6/25) -> (44/75,27/46) Hyperbolic Matrix(1349,322,2300,549) (-6/25,-5/21) -> (17/29,44/75) Hyperbolic Matrix(299,70,850,199) (-4/17,-7/30) -> (7/20,6/17) Hyperbolic Matrix(551,128,650,151) (-7/30,-3/13) -> (11/13,17/20) Hyperbolic Matrix(349,80,650,149) (-3/13,-8/35) -> (8/15,7/13) Hyperbolic Matrix(149,34,-1100,-251) (-8/35,-5/22) -> (-3/22,-2/15) Hyperbolic Matrix(1499,340,2200,499) (-5/22,-17/75) -> (17/25,15/22) Hyperbolic Matrix(1051,238,1550,351) (-17/75,-12/53) -> (2/3,17/25) Hyperbolic Matrix(1101,248,4000,901) (-7/31,-9/40) -> (11/40,19/69) Hyperbolic Matrix(401,90,450,101) (-9/40,-2/9) -> (8/9,9/10) Hyperbolic Matrix(1951,430,2500,551) (-2/9,-11/50) -> (39/50,32/41) Hyperbolic Matrix(1949,428,2500,549) (-11/50,-9/41) -> (7/9,39/50) Hyperbolic Matrix(1351,292,4400,951) (-8/37,-27/125) -> (23/75,4/13) Hyperbolic Matrix(4399,950,14350,3099) (-27/125,-19/88) -> (19/62,23/75) Hyperbolic Matrix(5551,1198,7650,1651) (-19/88,-11/51) -> (37/51,45/62) Hyperbolic Matrix(799,172,-4650,-1001) (-14/65,-3/14) -> (-11/64,-6/35) Hyperbolic Matrix(501,106,950,201) (-7/33,-11/52) -> (1/2,9/17) Hyperbolic Matrix(3151,666,10650,2251) (-11/52,-15/71) -> (21/71,29/98) Hyperbolic Matrix(49,10,-250,-51) (-5/24,-1/5) -> (-1/5,-5/26) Parabolic Matrix(649,124,2350,449) (-5/26,-4/21) -> (8/29,21/76) Hyperbolic Matrix(1699,314,2700,499) (-5/27,-7/38) -> (39/62,17/27) Hyperbolic Matrix(1501,276,4900,901) (-7/38,-9/49) -> (15/49,19/62) Hyperbolic Matrix(2051,370,2500,451) (-2/11,-9/50) -> (41/50,32/39) Hyperbolic Matrix(2049,368,2500,449) (-9/50,-7/39) -> (9/11,41/50) Hyperbolic Matrix(1451,252,4900,851) (-4/23,-13/75) -> (37/125,8/27) Hyperbolic Matrix(4099,710,13850,2399) (-13/75,-9/52) -> (29/98,37/125) Hyperbolic Matrix(3151,544,4350,751) (-9/52,-5/29) -> (21/29,71/98) Hyperbolic Matrix(2499,430,2900,499) (-5/29,-11/64) -> (31/36,25/29) Hyperbolic Matrix(951,154,1550,251) (-1/6,-4/25) -> (46/75,27/44) Hyperbolic Matrix(1349,214,2200,349) (-4/25,-3/19) -> (19/31,46/75) Hyperbolic Matrix(499,76,650,99) (-2/13,-3/20) -> (23/30,10/13) Hyperbolic Matrix(151,22,350,51) (-3/20,-1/7) -> (3/7,13/30) Hyperbolic Matrix(2151,302,2500,351) (-1/7,-7/50) -> (43/50,37/43) Hyperbolic Matrix(2149,300,2500,349) (-7/50,-6/43) -> (6/7,43/50) Hyperbolic Matrix(2401,332,2900,401) (-5/36,-4/29) -> (24/29,53/64) Hyperbolic Matrix(3449,474,5450,749) (-4/29,-3/22) -> (81/128,50/79) Hyperbolic Matrix(251,32,400,51) (-2/15,-1/8) -> (5/8,22/35) Hyperbolic Matrix(1449,176,2050,249) (-1/8,-3/25) -> (53/75,41/58) Hyperbolic Matrix(1201,142,1700,201) (-3/25,-2/17) -> (12/17,53/75) Hyperbolic Matrix(349,38,450,49) (-1/9,-1/10) -> (31/40,7/9) Hyperbolic Matrix(151,14,550,51) (-1/10,0/1) -> (14/51,11/40) Hyperbolic Matrix(601,-70,850,-99) (1/9,1/8) -> (41/58,29/41) Hyperbolic Matrix(251,-34,1100,-149) (2/15,1/7) -> (13/57,8/35) Hyperbolic Matrix(399,-62,650,-101) (2/13,1/6) -> (27/44,8/13) Hyperbolic Matrix(251,-44,850,-149) (1/6,3/17) -> (5/17,13/44) Hyperbolic Matrix(349,-62,850,-151) (3/17,2/11) -> (16/39,7/17) Hyperbolic Matrix(451,-84,800,-149) (2/11,3/16) -> (9/16,22/39) Hyperbolic Matrix(401,-76,1050,-199) (3/16,1/5) -> (21/55,13/34) Hyperbolic Matrix(401,-84,950,-199) (1/5,4/19) -> (8/19,19/45) Hyperbolic Matrix(451,-96,700,-149) (4/19,3/14) -> (9/14,20/31) Hyperbolic Matrix(351,-76,1150,-249) (3/14,5/23) -> (7/23,11/36) Hyperbolic Matrix(449,-98,1150,-251) (5/23,2/9) -> (16/41,9/23) Hyperbolic Matrix(751,-170,1100,-249) (7/31,5/22) -> (15/22,13/19) Hyperbolic Matrix(6799,-1550,7900,-1801) (31/136,13/57) -> (37/43,31/36) Hyperbolic Matrix(499,-118,850,-201) (4/17,1/4) -> (27/46,10/17) Hyperbolic Matrix(351,-92,950,-249) (1/4,5/19) -> (7/19,17/46) Hyperbolic Matrix(2851,-756,7350,-1949) (9/34,13/49) -> (19/49,45/116) Hyperbolic Matrix(1499,-398,4900,-1301) (13/49,4/15) -> (26/85,15/49) Hyperbolic Matrix(2099,-562,7100,-1901) (4/15,15/56) -> (13/44,34/115) Hyperbolic Matrix(2551,-684,6150,-1649) (15/56,11/41) -> (17/41,39/94) Hyperbolic Matrix(251,-68,550,-149) (7/26,3/11) -> (5/11,11/24) Hyperbolic Matrix(899,-246,1100,-301) (3/11,14/51) -> (40/49,9/11) Hyperbolic Matrix(4299,-1184,5450,-1501) (19/69,8/29) -> (56/71,15/19) Hyperbolic Matrix(3299,-912,7600,-2101) (21/76,13/47) -> (23/53,33/76) Hyperbolic Matrix(4999,-1384,7950,-2201) (13/47,18/65) -> (22/35,61/97) Hyperbolic Matrix(1651,-458,2700,-749) (18/65,5/18) -> (11/18,52/85) Hyperbolic Matrix(751,-220,850,-249) (12/41,5/17) -> (15/17,8/9) Hyperbolic Matrix(6101,-1804,19950,-5899) (34/115,21/71) -> (37/121,26/85) Hyperbolic Matrix(851,-270,1100,-349) (6/19,1/3) -> (41/53,24/31) Hyperbolic Matrix(499,-174,1150,-401) (1/3,7/20) -> (13/30,23/53) Hyperbolic Matrix(551,-196,700,-249) (6/17,5/14) -> (11/14,26/33) Hyperbolic Matrix(1101,-404,2450,-899) (11/30,18/49) -> (22/49,9/20) Hyperbolic Matrix(1001,-370,1350,-499) (17/46,10/27) -> (20/27,3/4) Hyperbolic Matrix(5749,-2134,7950,-2951) (23/62,13/35) -> (47/65,81/112) Hyperbolic Matrix(249,-94,400,-151) (3/8,8/21) -> (18/29,5/8) Hyperbolic Matrix(2049,-782,4850,-1851) (8/21,21/55) -> (19/45,30/71) Hyperbolic Matrix(549,-212,650,-251) (5/13,12/31) -> (16/19,11/13) Hyperbolic Matrix(11651,-4520,15850,-6149) (45/116,26/67) -> (86/117,25/34) Hyperbolic Matrix(1951,-758,2700,-1049) (26/67,7/18) -> (13/18,60/83) Hyperbolic Matrix(1601,-624,2050,-799) (7/18,16/41) -> (32/41,25/32) Hyperbolic Matrix(101,-40,250,-99) (9/23,2/5) -> (2/5,11/27) Parabolic Matrix(2199,-898,4900,-2001) (20/49,9/22) -> (35/78,22/49) Hyperbolic Matrix(1601,-656,1950,-799) (9/22,16/39) -> (32/39,23/28) Hyperbolic Matrix(649,-268,850,-351) (7/17,12/29) -> (16/21,13/17) Hyperbolic Matrix(12701,-5270,17350,-7199) (39/94,22/53) -> (112/153,41/56) Hyperbolic Matrix(4701,-1952,6500,-2699) (22/53,5/12) -> (81/112,34/47) Hyperbolic Matrix(349,-146,600,-251) (5/12,8/19) -> (18/31,7/12) Hyperbolic Matrix(651,-284,800,-349) (10/23,7/16) -> (13/16,22/27) Hyperbolic Matrix(1351,-620,1850,-849) (11/24,6/13) -> (46/63,19/26) Hyperbolic Matrix(1699,-796,2350,-1101) (7/15,8/17) -> (60/83,47/65) Hyperbolic Matrix(1499,-796,2450,-1301) (9/17,8/15) -> (52/85,41/67) Hyperbolic Matrix(401,-218,550,-299) (7/13,6/11) -> (8/11,27/37) Hyperbolic Matrix(1551,-854,2450,-1349) (11/20,16/29) -> (50/79,19/30) Hyperbolic Matrix(2251,-1270,3100,-1749) (22/39,35/62) -> (45/62,8/11) Hyperbolic Matrix(749,-424,1150,-651) (13/23,17/30) -> (13/20,15/23) Hyperbolic Matrix(751,-434,950,-549) (15/26,11/19) -> (15/19,19/24) Hyperbolic Matrix(2799,-1636,4450,-2601) (7/12,31/53) -> (61/97,39/62) Hyperbolic Matrix(4501,-2634,6150,-3599) (31/53,24/41) -> (30/41,71/97) Hyperbolic Matrix(699,-412,850,-501) (10/17,13/22) -> (23/28,14/17) Hyperbolic Matrix(151,-90,250,-149) (13/22,3/5) -> (3/5,17/28) Parabolic Matrix(4999,-3038,7900,-4801) (17/28,31/51) -> (31/49,81/128) Hyperbolic Matrix(899,-548,1150,-701) (14/23,11/18) -> (25/32,18/23) Hyperbolic Matrix(5401,-3306,7350,-4499) (41/67,30/49) -> (36/49,61/83) Hyperbolic Matrix(851,-526,1050,-649) (21/34,13/21) -> (17/21,13/16) Hyperbolic Matrix(701,-442,950,-599) (17/27,12/19) -> (14/19,17/23) Hyperbolic Matrix(4601,-2970,6350,-4099) (20/31,31/48) -> (71/98,50/69) Hyperbolic Matrix(1049,-688,1450,-951) (15/23,2/3) -> (34/47,89/123) Hyperbolic Matrix(901,-626,1150,-799) (9/13,16/23) -> (18/23,29/37) Hyperbolic Matrix(701,-494,850,-599) (19/27,12/17) -> (14/17,19/23) Hyperbolic Matrix(1699,-1244,2050,-1501) (41/56,11/15) -> (29/35,5/6) Hyperbolic Matrix(3099,-2276,3950,-2901) (11/15,36/49) -> (40/51,51/65) Hyperbolic Matrix(951,-734,1100,-849) (27/35,17/22) -> (19/22,13/15) Hyperbolic Matrix(3851,-3022,4650,-3649) (51/65,11/14) -> (53/64,29/35) Hyperbolic Matrix(201,-160,250,-199) (19/24,4/5) -> (4/5,21/26) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-48,1) Matrix(399,362,550,499) -> Matrix(37,16,-1524,-659) Matrix(101,90,450,401) -> Matrix(11,4,-300,-109) Matrix(249,220,-850,-751) -> Matrix(29,10,-496,-171) Matrix(149,130,400,349) -> Matrix(19,6,-624,-197) Matrix(849,734,-1100,-951) -> Matrix(47,14,-272,-81) Matrix(199,170,350,299) -> Matrix(29,8,-1084,-299) Matrix(151,128,650,551) -> Matrix(23,6,-648,-169) Matrix(251,212,-650,-549) -> Matrix(23,6,-372,-97) Matrix(599,494,-850,-701) -> Matrix(17,4,-132,-31) Matrix(501,412,-850,-699) -> Matrix(35,8,-372,-85) Matrix(349,284,-800,-651) -> Matrix(65,14,-924,-199) Matrix(649,526,-1050,-851) -> Matrix(47,10,-456,-97) Matrix(549,434,-950,-751) -> Matrix(31,6,-336,-65) Matrix(249,196,-700,-551) -> Matrix(53,10,-864,-163) Matrix(799,626,-1150,-901) -> Matrix(43,8,-328,-61) Matrix(701,548,-1150,-899) -> Matrix(87,16,-832,-153) Matrix(49,38,450,349) -> Matrix(11,2,-292,-53) Matrix(2899,2246,4000,3099) -> Matrix(245,44,-10084,-1811) Matrix(349,270,-1100,-851) -> Matrix(79,14,-1360,-241) Matrix(3051,2356,6800,5251) -> Matrix(35,6,-1196,-205) Matrix(5901,4556,19300,14901) -> Matrix(367,64,-10924,-1905) Matrix(1101,850,-7900,-6099) -> Matrix(23,4,-236,-41) Matrix(301,232,650,501) -> Matrix(23,4,-788,-137) Matrix(99,76,650,499) -> Matrix(23,4,-604,-105) Matrix(551,422,850,651) -> Matrix(81,14,-3188,-551) Matrix(351,268,-850,-649) -> Matrix(59,10,-832,-141) Matrix(599,442,-950,-701) -> Matrix(79,12,-744,-113) Matrix(299,220,950,699) -> Matrix(1,0,-24,1) Matrix(4499,3306,-7350,-5401) -> Matrix(79,12,-744,-113) Matrix(3401,2498,-4900,-3599) -> Matrix(27,4,-196,-29) Matrix(5001,3662,-7100,-5199) -> Matrix(27,4,-196,-29) Matrix(3599,2634,-6150,-4501) -> Matrix(27,4,-304,-45) Matrix(599,438,2050,1499) -> Matrix(1,0,-24,1) Matrix(299,218,-550,-401) -> Matrix(27,4,-304,-45) Matrix(201,146,-1100,-799) -> Matrix(27,4,-628,-93) Matrix(499,362,550,399) -> Matrix(109,16,-4980,-731) Matrix(3099,2246,4000,2899) -> Matrix(301,44,-12772,-1867) Matrix(1151,834,-5450,-3949) -> Matrix(41,6,-868,-127) Matrix(1901,1376,2350,1701) -> Matrix(83,12,-3576,-517) Matrix(4301,3112,-7600,-5499) -> Matrix(27,4,-304,-45) Matrix(2951,2134,-7950,-5749) -> Matrix(289,42,-4452,-647) Matrix(1049,758,-2700,-1951) -> Matrix(235,34,-3684,-533) Matrix(649,468,900,649) -> Matrix(181,26,-7428,-1067) Matrix(251,180,350,251) -> Matrix(71,10,-2904,-409) Matrix(149,106,350,249) -> Matrix(15,2,-488,-65) Matrix(551,390,2050,1451) -> Matrix(15,2,-428,-57) Matrix(99,70,-850,-601) -> Matrix(29,4,-660,-91) Matrix(13849,9754,-19950,-14051) -> Matrix(17,2,-128,-15) Matrix(8399,5914,10650,7499) -> Matrix(1,0,-36,1) Matrix(11451,8062,13850,9751) -> Matrix(319,46,-13932,-2009) Matrix(4049,2850,4900,3449) -> Matrix(185,26,-8076,-1135) Matrix(151,106,500,351) -> Matrix(15,2,-428,-57) Matrix(149,104,500,349) -> Matrix(15,2,-488,-65) Matrix(4399,3054,19300,13399) -> Matrix(151,20,-4296,-569) Matrix(3999,2774,4900,3399) -> Matrix(121,16,-5256,-695) Matrix(11251,7802,14350,9951) -> Matrix(15,2,-668,-89) Matrix(3449,2390,4400,3049) -> Matrix(77,10,-3288,-427) Matrix(249,172,650,449) -> Matrix(15,2,-488,-65) Matrix(251,172,950,651) -> Matrix(47,6,-1324,-169) Matrix(249,170,-1100,-751) -> Matrix(79,10,-1588,-201) Matrix(651,424,-1150,-749) -> Matrix(19,2,-200,-21) Matrix(651,422,850,551) -> Matrix(121,14,-5108,-591) Matrix(149,96,-700,-451) -> Matrix(53,6,-1016,-115) Matrix(449,288,700,449) -> Matrix(161,18,-6288,-703) Matrix(351,224,550,351) -> Matrix(127,14,-4944,-545) Matrix(249,158,550,349) -> Matrix(55,6,-1916,-209) Matrix(1349,854,-2450,-1551) -> Matrix(315,34,-3604,-389) Matrix(949,600,2450,1549) -> Matrix(205,22,-6588,-707) Matrix(349,220,-1350,-851) -> Matrix(19,2,-276,-29) Matrix(1751,1102,3100,1951) -> Matrix(135,14,-5024,-521) Matrix(2201,1384,-7950,-4999) -> Matrix(39,4,-712,-73) Matrix(51,32,400,251) -> Matrix(19,2,-504,-53) Matrix(151,94,-400,-249) -> Matrix(19,2,-276,-29) Matrix(2801,1732,-4850,-2999) -> Matrix(39,4,-400,-41) Matrix(201,124,650,401) -> Matrix(39,4,-1180,-121) Matrix(101,62,-650,-399) -> Matrix(1,0,-12,1) Matrix(901,552,2450,1501) -> Matrix(37,4,-1212,-131) Matrix(4199,2570,-15850,-9701) -> Matrix(227,24,-4436,-469) Matrix(749,458,-2700,-1651) -> Matrix(59,6,-1072,-109) Matrix(449,274,-2050,-1251) -> Matrix(19,2,-276,-29) Matrix(149,90,-250,-151) -> Matrix(59,6,-600,-61) Matrix(1651,978,3800,2251) -> Matrix(433,42,-14588,-1415) Matrix(11401,6750,18750,11101) -> Matrix(2603,252,-99792,-9661) Matrix(7599,4498,12500,7399) -> Matrix(1861,180,-71328,-6899) Matrix(2701,1598,-4900,-2899) -> Matrix(663,64,-7552,-729) Matrix(349,206,-1950,-1151) -> Matrix(21,2,-284,-27) Matrix(201,118,-850,-499) -> Matrix(43,4,-828,-77) Matrix(649,380,1450,849) -> Matrix(19,2,-656,-69) Matrix(4649,2720,-17350,-10151) -> Matrix(27,2,-500,-37) Matrix(1799,1052,-6500,-3801) -> Matrix(39,4,-712,-73) Matrix(251,146,-600,-349) -> Matrix(21,2,-284,-27) Matrix(4451,2570,6150,3551) -> Matrix(109,10,-4480,-411) Matrix(101,58,350,201) -> Matrix(1,0,-20,1) Matrix(299,170,350,199) -> Matrix(85,8,-3772,-355) Matrix(1549,876,3800,2149) -> Matrix(65,6,-2156,-199) Matrix(149,84,-800,-451) -> Matrix(65,6,-1376,-127) Matrix(449,252,800,449) -> Matrix(197,18,-7300,-667) Matrix(251,140,450,251) -> Matrix(111,10,-4096,-369) Matrix(601,332,1450,801) -> Matrix(45,4,-1564,-139) Matrix(1549,854,6800,3749) -> Matrix(387,34,-10984,-965) Matrix(201,110,550,301) -> Matrix(47,4,-1516,-129) Matrix(499,270,-1850,-1001) -> Matrix(45,4,-844,-75) Matrix(149,80,650,349) -> Matrix(23,2,-656,-57) Matrix(651,346,-2350,-1249) -> Matrix(113,10,-2068,-183) Matrix(549,290,850,449) -> Matrix(163,14,-6392,-549) Matrix(749,354,950,449) -> Matrix(79,6,-3384,-257) Matrix(951,446,-2450,-1149) -> Matrix(245,18,-3852,-283) Matrix(501,232,650,301) -> Matrix(55,4,-2324,-169) Matrix(149,68,-550,-251) -> Matrix(27,2,-500,-37) Matrix(349,158,550,249) -> Matrix(79,6,-3068,-233) Matrix(899,404,-2450,-1101) -> Matrix(109,8,-1676,-123) Matrix(849,380,1450,649) -> Matrix(27,2,-1040,-77) Matrix(199,88,450,199) -> Matrix(111,8,-3788,-273) Matrix(351,154,800,351) -> Matrix(197,14,-6684,-475) Matrix(849,370,-3100,-1351) -> Matrix(29,2,-508,-35) Matrix(1149,500,3100,1349) -> Matrix(199,14,-6496,-457) Matrix(401,174,-1150,-499) -> Matrix(115,8,-1912,-133) Matrix(51,22,350,151) -> Matrix(29,2,-740,-51) Matrix(249,106,350,149) -> Matrix(31,2,-1256,-81) Matrix(199,84,-950,-401) -> Matrix(1,0,-4,1) Matrix(1451,610,2500,1051) -> Matrix(37,2,-1388,-75) Matrix(1449,608,2500,1049) -> Matrix(21,2,-788,-75) Matrix(1651,686,-4450,-1849) -> Matrix(25,2,-388,-31) Matrix(1649,684,-6150,-2551) -> Matrix(27,2,-500,-37) Matrix(801,332,1450,601) -> Matrix(53,4,-1948,-147) Matrix(1751,724,2300,951) -> Matrix(307,22,-12908,-925) Matrix(1099,454,1450,599) -> Matrix(225,16,-9436,-671) Matrix(151,62,-850,-349) -> Matrix(29,2,-508,-35) Matrix(99,40,-250,-101) -> Matrix(59,4,-900,-61) Matrix(2901,1138,-7900,-3099) -> Matrix(1,0,0,1) Matrix(5101,2000,12500,4901) -> Matrix(125,8,-4172,-267) Matrix(7649,2998,18750,7349) -> Matrix(29,2,-972,-67) Matrix(7851,3076,10850,4251) -> Matrix(89,6,-3664,-247) Matrix(251,98,-1150,-449) -> Matrix(31,2,-512,-33) Matrix(1949,756,-7350,-2851) -> Matrix(473,30,-9192,-583) Matrix(1549,600,2450,949) -> Matrix(349,22,-13500,-851) Matrix(1851,716,2200,851) -> Matrix(415,26,-18276,-1145) Matrix(1299,502,1550,599) -> Matrix(257,16,-11292,-703) Matrix(449,172,650,249) -> Matrix(31,2,-1256,-81) Matrix(199,76,-1050,-401) -> Matrix(1,0,-4,1) Matrix(1551,590,2500,951) -> Matrix(43,2,-1656,-77) Matrix(1549,588,2500,949) -> Matrix(19,2,-732,-77) Matrix(349,130,400,149) -> Matrix(91,6,-4080,-269) Matrix(2201,816,2700,1001) -> Matrix(1,0,-28,1) Matrix(249,92,-950,-351) -> Matrix(31,2,-636,-41) Matrix(1501,552,2450,901) -> Matrix(61,4,-2364,-155) Matrix(4701,1726,5450,2001) -> Matrix(185,12,-8248,-535) Matrix(301,110,550,201) -> Matrix(63,4,-2284,-145) Matrix(199,72,550,199) -> Matrix(127,8,-4080,-257) Matrix(251,90,700,251) -> Matrix(161,10,-5136,-319) Matrix(1749,620,-6350,-2251) -> Matrix(293,18,-5388,-331) Matrix(401,142,850,301) -> Matrix(131,8,-4536,-277) Matrix(199,70,850,299) -> Matrix(1,0,-12,1) Matrix(401,138,-1450,-499) -> Matrix(71,4,-1296,-73) Matrix(1199,386,1550,499) -> Matrix(337,20,-14272,-847) Matrix(1701,542,2200,701) -> Matrix(479,28,-20272,-1185) Matrix(699,220,950,299) -> Matrix(1,0,-24,1) Matrix(401,124,650,201) -> Matrix(71,4,-2716,-153) Matrix(249,76,-1150,-351) -> Matrix(37,2,-648,-35) Matrix(351,106,500,151) -> Matrix(39,2,-1580,-81) Matrix(349,104,500,149) -> Matrix(31,2,-1256,-81) Matrix(149,44,-850,-251) -> Matrix(33,2,-644,-39) Matrix(1499,440,1700,499) -> Matrix(339,20,-15272,-901) Matrix(1801,528,2050,601) -> Matrix(409,24,-18388,-1079) Matrix(1499,438,2050,599) -> Matrix(1,0,-24,1) Matrix(201,58,350,101) -> Matrix(1,0,-20,1) Matrix(99,28,350,99) -> Matrix(71,4,-2148,-121) Matrix(251,70,900,251) -> Matrix(181,10,-5412,-299) Matrix(6599,1824,10850,2999) -> Matrix(1319,72,-50580,-2761) Matrix(2599,718,6150,1699) -> Matrix(147,8,-4796,-261) Matrix(3599,992,4350,1199) -> Matrix(439,24,-19188,-1049) Matrix(901,248,4000,1101) -> Matrix(221,12,-6096,-331) Matrix(51,14,550,151) -> Matrix(37,2,-944,-51) Matrix(5999,1646,7650,2099) -> Matrix(1,0,-24,1) Matrix(7301,1972,10000,2701) -> Matrix(73,4,-3048,-167) Matrix(7299,1970,10000,2699) -> Matrix(223,12,-9236,-497) Matrix(1451,390,2050,551) -> Matrix(39,2,-1580,-81) Matrix(45751,12262,62500,16751) -> Matrix(1071,58,-44188,-2393) Matrix(45749,12260,62500,16749) -> Matrix(1297,70,-53492,-2887) Matrix(351,94,-2050,-549) -> Matrix(37,2,-796,-43) Matrix(851,226,-3950,-1049) -> Matrix(193,10,-3532,-183) Matrix(29401,7792,40000,10601) -> Matrix(1715,88,-71192,-3653) Matrix(29399,7790,40000,10599) -> Matrix(1717,88,-71236,-3651) Matrix(651,172,950,251) -> Matrix(119,6,-4780,-241) Matrix(1851,482,2500,651) -> Matrix(61,2,-2532,-83) Matrix(1849,480,2500,649) -> Matrix(13,2,-540,-83) Matrix(851,206,1450,351) -> Matrix(113,6,-4200,-223) Matrix(1349,322,2300,549) -> Matrix(115,6,-4236,-221) Matrix(299,70,850,199) -> Matrix(1,0,-12,1) Matrix(551,128,650,151) -> Matrix(119,6,-5256,-265) Matrix(349,80,650,149) -> Matrix(39,2,-1424,-73) Matrix(149,34,-1100,-251) -> Matrix(39,2,-800,-41) Matrix(1499,340,2200,499) -> Matrix(399,20,-15980,-801) Matrix(1051,238,1550,351) -> Matrix(281,14,-11220,-559) Matrix(1101,248,4000,901) -> Matrix(245,12,-7248,-355) Matrix(401,90,450,101) -> Matrix(83,4,-3756,-181) Matrix(1951,430,2500,551) -> Matrix(67,2,-2848,-85) Matrix(1949,428,2500,549) -> Matrix(11,2,-468,-85) Matrix(1351,292,4400,951) -> Matrix(179,10,-5388,-301) Matrix(4399,950,14350,3099) -> Matrix(649,36,-19452,-1079) Matrix(5551,1198,7650,1651) -> Matrix(833,46,-34316,-1895) Matrix(799,172,-4650,-1001) -> Matrix(147,8,-3032,-165) Matrix(501,106,950,201) -> Matrix(79,4,-2864,-145) Matrix(3151,666,10650,2251) -> Matrix(121,6,-3852,-191) Matrix(49,10,-250,-51) -> Matrix(39,2,-800,-41) Matrix(649,124,2350,449) -> Matrix(45,2,-1328,-59) Matrix(1699,314,2700,499) -> Matrix(87,4,-3328,-153) Matrix(1501,276,4900,901) -> Matrix(265,12,-7928,-359) Matrix(2051,370,2500,451) -> Matrix(73,2,-3176,-87) Matrix(2049,368,2500,449) -> Matrix(9,2,-392,-87) Matrix(1451,252,4900,851) -> Matrix(119,6,-3828,-193) Matrix(4099,710,13850,2399) -> Matrix(401,20,-12812,-639) Matrix(3151,544,4350,751) -> Matrix(447,22,-18388,-905) Matrix(2499,430,2900,499) -> Matrix(327,16,-14572,-713) Matrix(951,154,1550,251) -> Matrix(41,2,-1620,-79) Matrix(1349,214,2200,349) -> Matrix(127,6,-4932,-233) Matrix(499,76,650,99) -> Matrix(87,4,-3676,-169) Matrix(151,22,350,51) -> Matrix(45,2,-1508,-67) Matrix(2151,302,2500,351) -> Matrix(79,2,-3516,-89) Matrix(2149,300,2500,349) -> Matrix(7,2,-312,-89) Matrix(2401,332,2900,401) -> Matrix(65,4,-2844,-175) Matrix(3449,474,5450,749) -> Matrix(335,18,-12972,-697) Matrix(251,32,400,51) -> Matrix(43,2,-1656,-77) Matrix(1449,176,2050,249) -> Matrix(217,10,-8832,-407) Matrix(1201,142,1700,201) -> Matrix(179,8,-7272,-325) Matrix(349,38,450,49) -> Matrix(43,2,-1828,-85) Matrix(151,14,550,51) -> Matrix(45,2,-1328,-59) Matrix(601,-70,850,-99) -> Matrix(101,4,-4116,-163) Matrix(251,-34,1100,-149) -> Matrix(55,2,-1568,-57) Matrix(399,-62,650,-101) -> Matrix(1,0,-12,1) Matrix(251,-44,850,-149) -> Matrix(57,2,-1796,-63) Matrix(349,-62,850,-151) -> Matrix(61,2,-2044,-67) Matrix(451,-84,800,-149) -> Matrix(161,6,-5984,-223) Matrix(401,-76,1050,-199) -> Matrix(1,0,-4,1) Matrix(401,-84,950,-199) -> Matrix(1,0,-4,1) Matrix(451,-96,700,-149) -> Matrix(173,6,-6776,-235) Matrix(351,-76,1150,-249) -> Matrix(61,2,-1800,-59) Matrix(449,-98,1150,-251) -> Matrix(63,2,-2048,-65) Matrix(751,-170,1100,-249) -> Matrix(279,10,-11188,-401) Matrix(6799,-1550,7900,-1801) -> Matrix(1367,48,-60860,-2137) Matrix(499,-118,850,-201) -> Matrix(115,4,-4284,-149) Matrix(351,-92,950,-249) -> Matrix(55,2,-1788,-65) Matrix(2851,-756,7350,-1949) -> Matrix(857,30,-27624,-967) Matrix(1499,-398,4900,-1301) -> Matrix(459,16,-13684,-477) Matrix(2099,-562,7100,-1901) -> Matrix(235,8,-7432,-253) Matrix(2551,-684,6150,-1649) -> Matrix(59,2,-2036,-69) Matrix(251,-68,550,-149) -> Matrix(59,2,-2036,-69) Matrix(899,-246,1100,-301) -> Matrix(237,8,-10280,-347) Matrix(4299,-1184,5450,-1501) -> Matrix(119,4,-5028,-169) Matrix(3299,-912,7600,-2101) -> Matrix(1069,36,-35960,-1211) Matrix(4999,-1384,7950,-2201) -> Matrix(119,4,-4552,-153) Matrix(1651,-458,2700,-749) -> Matrix(179,6,-6832,-229) Matrix(751,-220,850,-249) -> Matrix(309,10,-13936,-451) Matrix(6101,-1804,19950,-5899) -> Matrix(1015,32,-30228,-953) Matrix(851,-270,1100,-349) -> Matrix(431,14,-18256,-593) Matrix(499,-174,1150,-401) -> Matrix(251,8,-8440,-269) Matrix(551,-196,700,-249) -> Matrix(317,10,-13536,-427) Matrix(1101,-404,2450,-899) -> Matrix(261,8,-8972,-275) Matrix(1001,-370,1350,-499) -> Matrix(389,12,-16176,-499) Matrix(5749,-2134,7950,-2951) -> Matrix(1369,42,-56292,-1727) Matrix(249,-94,400,-151) -> Matrix(67,2,-2580,-77) Matrix(2049,-782,4850,-1851) -> Matrix(63,2,-2048,-65) Matrix(549,-212,650,-251) -> Matrix(191,6,-8436,-265) Matrix(11651,-4520,15850,-6149) -> Matrix(1741,54,-72316,-2243) Matrix(1951,-758,2700,-1049) -> Matrix(1099,34,-45156,-1397) Matrix(1601,-624,2050,-799) -> Matrix(779,24,-33140,-1021) Matrix(101,-40,250,-99) -> Matrix(131,4,-4356,-133) Matrix(2199,-898,4900,-2001) -> Matrix(135,4,-4624,-137) Matrix(1601,-656,1950,-799) -> Matrix(803,24,-34964,-1045) Matrix(649,-268,850,-351) -> Matrix(339,10,-14272,-421) Matrix(12701,-5270,17350,-7199) -> Matrix(147,4,-6064,-165) Matrix(4701,-1952,6500,-2699) -> Matrix(263,8,-10816,-329) Matrix(349,-146,600,-251) -> Matrix(69,2,-2588,-75) Matrix(651,-284,800,-349) -> Matrix(473,14,-20508,-607) Matrix(1351,-620,1850,-849) -> Matrix(69,2,-2864,-83) Matrix(1699,-796,2350,-1101) -> Matrix(961,28,-39504,-1151) Matrix(1499,-796,2450,-1301) -> Matrix(293,8,-11244,-307) Matrix(401,-218,550,-299) -> Matrix(147,4,-6064,-165) Matrix(1551,-854,2450,-1349) -> Matrix(1243,34,-48148,-1317) Matrix(2251,-1270,3100,-1749) -> Matrix(1859,50,-76628,-2061) Matrix(749,-424,1150,-651) -> Matrix(75,2,-2888,-77) Matrix(751,-434,950,-549) -> Matrix(223,6,-9552,-257) Matrix(2799,-1636,4450,-2601) -> Matrix(1,0,0,1) Matrix(4501,-2634,6150,-3599) -> Matrix(147,4,-6064,-165) Matrix(699,-412,850,-501) -> Matrix(299,8,-13044,-349) Matrix(151,-90,250,-149) -> Matrix(227,6,-8664,-229) Matrix(4999,-3038,7900,-4801) -> Matrix(4751,124,-183948,-4801) Matrix(899,-548,1150,-701) -> Matrix(615,16,-26176,-681) Matrix(5401,-3306,7350,-4499) -> Matrix(463,12,-19176,-497) Matrix(851,-526,1050,-649) -> Matrix(383,10,-16584,-433) Matrix(701,-442,950,-599) -> Matrix(463,12,-19176,-497) Matrix(4601,-2970,6350,-4099) -> Matrix(2821,72,-116092,-2963) Matrix(1049,-688,1450,-951) -> Matrix(233,6,-9592,-247) Matrix(901,-626,1150,-799) -> Matrix(323,8,-13768,-341) Matrix(701,-494,850,-599) -> Matrix(161,4,-7044,-175) Matrix(1699,-1244,2050,-1501) -> Matrix(331,8,-14440,-349) Matrix(3099,-2276,3950,-2901) -> Matrix(497,12,-21164,-511) Matrix(951,-734,1100,-849) -> Matrix(591,14,-26384,-625) Matrix(3851,-3022,4650,-3649) -> Matrix(427,10,-18660,-437) Matrix(201,-160,250,-199) -> Matrix(343,8,-14792,-345) 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): 75 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): 900 Minimal number of generators: 151 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 56 Genus: 48 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -4/5 -11/15 -3/5 -7/15 -21/50 -2/5 -19/50 -8/25 -3/10 -27/100 -13/50 -1/5 0/1 1/9 1/8 1/7 1/6 3/17 2/11 1/5 5/23 2/9 3/13 1/4 5/19 4/15 3/11 7/25 2/7 37/125 3/10 23/75 1/3 9/25 2/5 51/125 5/12 11/25 7/15 1/2 14/25 3/5 13/21 16/25 2/3 17/25 53/75 18/25 11/15 19/25 4/5 21/25 22/25 9/10 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -8/9 -4/11 -5/14 -7/8 -1/3 -7/22 -13/15 -3/10 -6/7 -2/7 -5/18 -5/6 -1/4 -5/21 -9/11 -7/32 -4/5 -1/5 -11/14 -3/16 -5/27 -7/9 -5/28 -24/31 -2/11 -5/28 -17/22 -3/17 -7/40 -27/35 -1/6 -10/13 -4/23 -1/6 -3/4 -1/6 -3/19 -14/19 -3/20 -4/27 -25/34 -1/6 -3/19 -11/15 -3/20 -30/41 -5/34 -6/41 -19/26 -3/20 -1/7 -8/11 -3/20 -4/27 -37/51 -37/252 -29/40 -6/41 -50/69 -6/41 -7/48 -21/29 -7/48 -55/76 -7/48 -1/7 -34/47 -7/48 -8/55 -13/18 -13/90 -1/7 -18/25 -1/7 -5/7 -5/36 -12/17 -3/22 -2/15 -19/27 -5/36 -7/10 -2/15 -16/23 -1/8 0/1 -9/13 -1/8 -2/3 -1/8 -2/17 -11/17 -11/96 -9/14 -9/80 -1/9 -16/25 -1/9 -7/11 -7/64 -12/19 -3/28 -8/75 -29/46 -7/66 -9/85 -17/27 -5/48 -5/8 -1/9 -1/10 -13/21 -5/48 -21/34 -1/9 -1/10 -8/13 -1/10 0/1 -3/5 -1/10 -7/12 -1/10 -3/31 -11/19 -3/32 -15/26 -3/32 -1/11 -4/7 -1/10 -2/21 -13/23 -3/32 -9/16 -9/98 -1/11 -14/25 -1/11 -5/9 -5/56 -6/11 -1/12 0/1 -13/24 -1/11 -1/12 -7/13 -1/12 -1/2 -1/12 -1/13 -7/15 -1/14 -6/13 -1/14 0/1 -5/11 -1/12 -4/9 -4/55 -1/14 -3/7 -3/44 -8/19 -1/16 0/1 -21/50 0/1 -13/31 -1/12 -5/12 -1/14 -1/15 -7/17 -7/100 -9/22 -3/44 -1/15 -2/5 -1/15 -11/28 -1/15 -1/16 -20/51 -2/31 -1/16 -9/23 -1/16 -7/18 -5/78 -3/47 -5/13 -1/16 -8/21 -1/18 0/1 -19/50 0/1 -11/29 -1/12 -3/8 -1/14 -1/15 -13/35 -3/46 -10/27 -7/108 -2/31 -7/19 -1/16 -4/11 -4/63 -1/16 -1/3 -1/16 -8/25 -1/17 -7/22 -1/17 -7/120 -6/19 -4/69 -3/52 -5/16 -3/53 -1/18 -4/13 -4/71 -1/18 -7/23 -3/56 -3/10 0/1 -8/27 -2/31 -1/16 -5/17 -5/84 -22/75 -1/17 -17/58 -1/17 -17/290 -12/41 -6/103 -5/86 -7/24 -1/17 -3/52 -2/7 -2/35 -1/18 -3/11 -3/56 -10/37 -1/18 -2/37 -27/100 -2/37 -17/63 -3/56 -7/26 -3/56 -1/19 -11/41 -3/56 -4/15 -1/19 -9/34 -5/98 -3/59 -5/19 -1/20 -6/23 -1/24 0/1 -13/50 0/1 -7/27 -1/12 -1/4 -1/18 -1/19 -3/13 -1/20 -2/9 -1/22 0/1 -5/23 -1/16 -8/37 -6/107 -1/18 -11/51 -11/200 -3/14 -3/56 -1/19 -1/5 -1/20 -2/11 -1/24 0/1 -3/17 -3/56 -4/23 -4/79 -1/20 -5/29 -1/20 -1/6 -1/20 -1/21 -1/7 -1/24 0/1 -1/24 0/1 1/9 -1/24 1/8 -1/26 -1/27 1/7 -1/24 1/6 -1/27 -1/28 3/17 -3/88 2/11 -1/24 0/1 1/5 -1/28 3/14 -1/29 -3/88 5/23 -1/32 2/9 -1/26 0/1 7/31 -1/28 5/22 -1/28 -5/141 3/13 -1/28 1/4 -1/29 -1/30 5/19 -1/28 9/34 -3/85 -5/142 13/49 -13/372 4/15 -1/29 15/56 -1/29 -3/88 11/41 -3/88 7/26 -1/29 -3/88 3/11 -3/88 5/18 -5/149 -1/30 7/25 -1/30 2/7 -1/30 -2/61 7/24 -3/92 -1/31 12/41 -5/154 -6/185 5/17 -5/156 13/44 -3/95 -1/32 21/71 -1/32 29/98 -11/351 -1/32 37/125 -1/32 8/27 -1/32 -2/65 3/10 0/1 7/23 -3/88 11/36 -3/89 -7/208 15/49 -15/448 19/62 -19/569 -1/30 23/75 -1/30 4/13 -1/30 -4/121 5/16 -1/30 -3/91 6/19 -3/92 -4/123 1/3 -1/32 5/14 -5/159 -1/32 9/25 -1/32 4/11 -1/32 -4/129 11/30 -2/65 18/49 -1/32 -2/65 7/19 -1/32 17/46 -3/97 -5/162 10/27 -2/65 -7/228 13/35 -3/98 3/8 -1/33 -1/34 8/21 -1/30 0/1 5/13 -1/32 12/31 -1/32 -10/321 7/18 -3/97 -5/162 9/23 -1/32 2/5 -1/33 11/27 -3/100 31/76 -1/33 -3/100 51/125 -3/100 20/49 -3/100 -2/67 9/22 -1/33 -3/100 7/17 -7/236 12/29 -1/34 -6/205 5/12 -1/33 -1/34 8/19 -1/32 0/1 3/7 -3/100 7/16 -7/237 -1/34 11/25 -1/34 4/9 -1/34 -4/137 13/29 -5/172 22/49 -5/172 -2/69 9/20 -2/69 5/11 -1/36 11/24 -1/35 -1/36 6/13 -1/34 0/1 7/15 -1/34 1/2 -1/35 -1/36 7/13 -1/36 6/11 -1/36 0/1 5/9 -5/184 14/25 -1/37 9/16 -1/37 -9/334 13/23 -3/112 4/7 -2/75 -1/38 15/26 -1/37 -3/112 11/19 -3/112 29/50 -2/75 18/31 -2/75 -5/188 7/12 -3/113 -1/38 3/5 -1/38 8/13 -1/38 0/1 21/34 -1/38 -1/39 13/21 -5/192 31/50 -2/77 18/29 -2/77 -7/270 5/8 -1/38 -1/39 17/27 -5/192 12/19 -8/309 -3/116 7/11 -7/272 16/25 -1/39 9/14 -1/39 -9/352 11/17 -11/432 2/3 -2/79 -1/40 17/25 -1/40 15/22 -1/40 -15/601 13/19 -1/40 11/16 -7/282 -3/121 9/13 -1/40 16/23 -1/40 0/1 7/10 -2/81 19/27 -5/204 12/17 -2/81 -3/122 53/75 -3/122 41/58 -3/122 -7/285 29/41 -5/204 17/24 -5/204 -1/41 5/7 -5/204 18/25 -1/41 13/18 -1/41 -13/534 47/65 -9/370 34/47 -8/329 -7/288 55/76 -1/41 -7/288 21/29 -7/288 50/69 -7/288 -6/247 29/40 -6/247 37/51 -37/1524 8/11 -4/165 -3/124 27/37 -3/124 73/100 -2/83 46/63 -2/83 -1/42 19/26 -1/41 -3/124 30/41 -6/247 -5/206 11/15 -3/124 25/34 -3/125 -1/42 14/19 -4/165 -3/124 17/23 -11/456 37/50 -2/83 20/27 -2/83 -13/540 3/4 -3/125 -1/42 19/25 -1/42 16/21 -1/42 -16/673 13/17 -13/548 10/13 -1/42 -4/169 27/35 -1/42 17/22 -7/296 -3/127 58/75 -3/127 41/53 -17/720 24/31 -5/212 -2/85 31/40 -2/85 7/9 -5/212 11/14 -5/213 -3/128 15/19 -3/128 19/24 -3/128 -1/43 4/5 -1/43 21/26 -1/43 -5/216 17/21 -5/216 13/16 -7/303 -3/130 9/11 -7/304 5/6 -5/219 -1/44 21/25 -1/44 16/19 -1/44 -16/705 11/13 -1/44 6/7 -5/222 -2/89 19/22 -7/312 -5/223 13/15 -3/134 7/8 -7/314 -1/45 22/25 -1/45 15/17 -15/676 8/9 -5/226 -4/181 9/10 -2/91 1/1 -1/48 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(126,113,475,426) (-1/1,-8/9) -> (9/34,13/49) Hyperbolic Matrix(249,220,-850,-751) (-8/9,-7/8) -> (-17/58,-12/41) Hyperbolic Matrix(149,130,400,349) (-7/8,-13/15) -> (13/35,3/8) Hyperbolic Matrix(524,451,725,624) (-13/15,-6/7) -> (13/18,47/65) Hyperbolic Matrix(126,107,325,276) (-6/7,-5/6) -> (12/31,7/18) Hyperbolic Matrix(174,143,-275,-226) (-5/6,-9/11) -> (-7/11,-12/19) Hyperbolic Matrix(124,101,275,224) (-9/11,-4/5) -> (9/20,5/11) Hyperbolic Matrix(174,137,475,374) (-4/5,-11/14) -> (4/11,11/30) Hyperbolic Matrix(124,97,-225,-176) (-11/14,-7/9) -> (-5/9,-6/11) Hyperbolic Matrix(476,369,1775,1376) (-7/9,-24/31) -> (15/56,11/41) Hyperbolic Matrix(349,270,-1100,-851) (-24/31,-17/22) -> (-7/22,-6/19) Hyperbolic Matrix(2224,1717,3075,2374) (-17/22,-27/35) -> (47/65,34/47) Hyperbolic Matrix(301,232,650,501) (-27/35,-10/13) -> (6/13,7/15) Hyperbolic Matrix(176,135,425,326) (-10/13,-3/4) -> (12/29,5/12) Hyperbolic Matrix(599,442,-950,-701) (-3/4,-14/19) -> (-12/19,-29/46) Hyperbolic Matrix(299,220,950,699) (-14/19,-25/34) -> (5/16,6/19) Hyperbolic Matrix(824,605,-1125,-826) (-25/34,-11/15) -> (-11/15,-30/41) Parabolic Matrix(599,438,2050,1499) (-30/41,-19/26) -> (7/24,12/41) Hyperbolic Matrix(299,218,-550,-401) (-19/26,-8/11) -> (-6/11,-13/24) Hyperbolic Matrix(274,199,-1275,-926) (-8/11,-37/51) -> (-11/51,-3/14) Hyperbolic Matrix(499,362,550,399) (-37/51,-29/40) -> (9/10,1/1) Hyperbolic Matrix(3099,2246,4000,2899) (-29/40,-50/69) -> (24/31,31/40) Hyperbolic Matrix(374,271,-2175,-1576) (-50/69,-21/29) -> (-5/29,-1/6) Hyperbolic Matrix(1901,1376,2350,1701) (-21/29,-55/76) -> (21/26,17/21) Hyperbolic Matrix(1776,1285,-4525,-3274) (-55/76,-34/47) -> (-11/28,-20/51) Hyperbolic Matrix(624,451,725,524) (-34/47,-13/18) -> (6/7,19/22) Hyperbolic Matrix(649,468,900,649) (-13/18,-18/25) -> (18/25,13/18) Hyperbolic Matrix(251,180,350,251) (-18/25,-5/7) -> (5/7,18/25) Hyperbolic Matrix(24,17,175,124) (-5/7,-12/17) -> (1/8,1/7) Hyperbolic Matrix(424,299,-675,-476) (-12/17,-19/27) -> (-17/27,-5/8) Hyperbolic Matrix(151,106,500,351) (-19/27,-7/10) -> (3/10,7/23) Hyperbolic Matrix(149,104,500,349) (-7/10,-16/23) -> (8/27,3/10) Hyperbolic Matrix(174,121,-325,-226) (-16/23,-9/13) -> (-7/13,-1/2) Hyperbolic Matrix(74,51,325,224) (-9/13,-2/3) -> (5/22,3/13) Hyperbolic Matrix(174,113,-425,-276) (-2/3,-11/17) -> (-7/17,-9/22) Hyperbolic Matrix(76,49,-425,-274) (-11/17,-9/14) -> (-2/11,-3/17) Hyperbolic Matrix(449,288,700,449) (-9/14,-16/25) -> (16/25,9/14) Hyperbolic Matrix(351,224,550,351) (-16/25,-7/11) -> (7/11,16/25) Hyperbolic Matrix(349,220,-1350,-851) (-29/46,-17/27) -> (-7/27,-1/4) Hyperbolic Matrix(151,94,-400,-249) (-5/8,-13/21) -> (-11/29,-3/8) Hyperbolic Matrix(526,325,1175,726) (-13/21,-21/34) -> (4/9,13/29) Hyperbolic Matrix(201,124,650,401) (-21/34,-8/13) -> (4/13,5/16) Hyperbolic Matrix(74,45,-125,-76) (-8/13,-3/5) -> (-3/5,-7/12) Parabolic Matrix(251,146,-600,-349) (-7/12,-11/19) -> (-13/31,-5/12) Hyperbolic Matrix(524,303,1425,824) (-11/19,-15/26) -> (18/49,7/19) Hyperbolic Matrix(101,58,350,201) (-15/26,-4/7) -> (2/7,7/24) Hyperbolic Matrix(224,127,-575,-326) (-4/7,-13/23) -> (-9/23,-7/18) Hyperbolic Matrix(126,71,-575,-324) (-13/23,-9/16) -> (-2/9,-5/23) Hyperbolic Matrix(449,252,800,449) (-9/16,-14/25) -> (14/25,9/16) Hyperbolic Matrix(251,140,450,251) (-14/25,-5/9) -> (5/9,14/25) Hyperbolic Matrix(499,270,-1850,-1001) (-13/24,-7/13) -> (-17/63,-7/26) Hyperbolic Matrix(176,83,-475,-224) (-1/2,-7/15) -> (-13/35,-10/27) Hyperbolic Matrix(501,232,650,301) (-7/15,-6/13) -> (10/13,27/35) Hyperbolic Matrix(149,68,-550,-251) (-6/13,-5/11) -> (-3/11,-10/37) Hyperbolic Matrix(224,101,275,124) (-5/11,-4/9) -> (13/16,9/11) Hyperbolic Matrix(76,33,175,76) (-4/9,-3/7) -> (3/7,7/16) Hyperbolic Matrix(26,11,-175,-74) (-3/7,-8/19) -> (-1/6,-1/7) Hyperbolic Matrix(1451,610,2500,1051) (-8/19,-21/50) -> (29/50,18/31) Hyperbolic Matrix(1449,608,2500,1049) (-21/50,-13/31) -> (11/19,29/50) Hyperbolic Matrix(326,135,425,176) (-5/12,-7/17) -> (13/17,10/13) Hyperbolic Matrix(99,40,-250,-101) (-9/22,-2/5) -> (-2/5,-11/28) Parabolic Matrix(1274,499,3125,1224) (-20/51,-9/23) -> (11/27,31/76) Hyperbolic Matrix(276,107,325,126) (-7/18,-5/13) -> (11/13,6/7) Hyperbolic Matrix(76,29,-325,-124) (-5/13,-8/21) -> (-1/4,-3/13) Hyperbolic Matrix(1551,590,2500,951) (-8/21,-19/50) -> (31/50,18/29) Hyperbolic Matrix(1549,588,2500,949) (-19/50,-11/29) -> (13/21,31/50) Hyperbolic Matrix(349,130,400,149) (-3/8,-13/35) -> (13/15,7/8) Hyperbolic Matrix(249,92,-950,-351) (-10/27,-7/19) -> (-5/19,-6/23) Hyperbolic Matrix(374,137,475,174) (-7/19,-4/11) -> (11/14,15/19) Hyperbolic Matrix(26,9,75,26) (-4/11,-1/3) -> (1/3,5/14) Hyperbolic Matrix(1199,386,1550,499) (-1/3,-8/25) -> (58/75,41/53) Hyperbolic Matrix(1701,542,2200,701) (-8/25,-7/22) -> (17/22,58/75) Hyperbolic Matrix(699,220,950,299) (-6/19,-5/16) -> (25/34,14/19) Hyperbolic Matrix(401,124,650,201) (-5/16,-4/13) -> (8/13,21/34) Hyperbolic Matrix(249,76,-1150,-351) (-4/13,-7/23) -> (-5/23,-8/37) Hyperbolic Matrix(351,106,500,151) (-7/23,-3/10) -> (7/10,19/27) Hyperbolic Matrix(349,104,500,149) (-3/10,-8/27) -> (16/23,7/10) Hyperbolic Matrix(149,44,-850,-251) (-8/27,-5/17) -> (-3/17,-4/23) Hyperbolic Matrix(1499,440,1700,499) (-5/17,-22/75) -> (22/25,15/17) Hyperbolic Matrix(1801,528,2050,601) (-22/75,-17/58) -> (7/8,22/25) Hyperbolic Matrix(1499,438,2050,599) (-12/41,-7/24) -> (19/26,30/41) Hyperbolic Matrix(201,58,350,101) (-7/24,-2/7) -> (4/7,15/26) Hyperbolic Matrix(76,21,275,76) (-2/7,-3/11) -> (3/11,5/18) Hyperbolic Matrix(7301,1972,10000,2701) (-10/37,-27/100) -> (73/100,46/63) Hyperbolic Matrix(7299,1970,10000,2699) (-27/100,-17/63) -> (27/37,73/100) Hyperbolic Matrix(1451,390,2050,551) (-7/26,-11/41) -> (29/41,17/24) Hyperbolic Matrix(1376,369,1775,476) (-11/41,-4/15) -> (31/40,7/9) Hyperbolic Matrix(426,113,475,126) (-4/15,-9/34) -> (8/9,9/10) Hyperbolic Matrix(651,172,950,251) (-9/34,-5/19) -> (13/19,11/16) Hyperbolic Matrix(1851,482,2500,651) (-6/23,-13/50) -> (37/50,20/27) Hyperbolic Matrix(1849,480,2500,649) (-13/50,-7/27) -> (17/23,37/50) Hyperbolic Matrix(224,51,325,74) (-3/13,-2/9) -> (11/16,9/13) Hyperbolic Matrix(1524,329,4975,1074) (-8/37,-11/51) -> (15/49,19/62) Hyperbolic Matrix(24,5,-125,-26) (-3/14,-1/5) -> (-1/5,-2/11) Parabolic Matrix(1324,229,4475,774) (-4/23,-5/29) -> (21/71,29/98) Hyperbolic Matrix(124,17,175,24) (-1/7,0/1) -> (17/24,5/7) Hyperbolic Matrix(74,-7,275,-26) (0/1,1/9) -> (11/41,7/26) Hyperbolic Matrix(601,-70,850,-99) (1/9,1/8) -> (41/58,29/41) Hyperbolic Matrix(74,-11,175,-26) (1/7,1/6) -> (8/19,3/7) Hyperbolic Matrix(251,-44,850,-149) (1/6,3/17) -> (5/17,13/44) Hyperbolic Matrix(274,-49,425,-76) (3/17,2/11) -> (9/14,11/17) Hyperbolic Matrix(26,-5,125,-24) (2/11,1/5) -> (1/5,3/14) Parabolic Matrix(351,-76,1150,-249) (3/14,5/23) -> (7/23,11/36) Hyperbolic Matrix(324,-71,575,-126) (5/23,2/9) -> (9/16,13/23) Hyperbolic Matrix(324,-73,1225,-276) (2/9,7/31) -> (5/19,9/34) Hyperbolic Matrix(751,-170,1100,-249) (7/31,5/22) -> (15/22,13/19) Hyperbolic Matrix(124,-29,325,-76) (3/13,1/4) -> (8/21,5/13) Hyperbolic Matrix(351,-92,950,-249) (1/4,5/19) -> (7/19,17/46) Hyperbolic Matrix(1976,-525,2725,-724) (13/49,4/15) -> (29/40,37/51) Hyperbolic Matrix(2374,-635,3275,-876) (4/15,15/56) -> (50/69,29/40) Hyperbolic Matrix(251,-68,550,-149) (7/26,3/11) -> (5/11,11/24) Hyperbolic Matrix(176,-49,625,-174) (5/18,7/25) -> (7/25,2/7) Parabolic Matrix(751,-220,850,-249) (12/41,5/17) -> (15/17,8/9) Hyperbolic Matrix(4474,-1323,6175,-1826) (13/44,21/71) -> (21/29,50/69) Hyperbolic Matrix(4626,-1369,15625,-4624) (29/98,37/125) -> (37/125,8/27) Parabolic Matrix(1724,-527,2375,-726) (11/36,15/49) -> (37/51,8/11) Hyperbolic Matrix(1726,-529,5625,-1724) (19/62,23/75) -> (23/75,4/13) Parabolic Matrix(851,-270,1100,-349) (6/19,1/3) -> (41/53,24/31) Hyperbolic Matrix(226,-81,625,-224) (5/14,9/25) -> (9/25,4/11) Parabolic Matrix(1101,-404,2450,-899) (11/30,18/49) -> (22/49,9/20) Hyperbolic Matrix(1001,-370,1350,-499) (17/46,10/27) -> (20/27,3/4) Hyperbolic Matrix(224,-83,475,-176) (10/27,13/35) -> (7/15,1/2) Hyperbolic Matrix(249,-94,400,-151) (3/8,8/21) -> (18/29,5/8) Hyperbolic Matrix(549,-212,650,-251) (5/13,12/31) -> (16/19,11/13) Hyperbolic Matrix(326,-127,575,-224) (7/18,9/23) -> (13/23,4/7) Hyperbolic Matrix(101,-40,250,-99) (9/23,2/5) -> (2/5,11/27) Parabolic Matrix(6376,-2601,15625,-6374) (31/76,51/125) -> (51/125,20/49) Parabolic Matrix(2876,-1175,3975,-1624) (20/49,9/22) -> (34/47,55/76) Hyperbolic Matrix(276,-113,425,-174) (9/22,7/17) -> (11/17,2/3) Hyperbolic Matrix(649,-268,850,-351) (7/17,12/29) -> (16/21,13/17) Hyperbolic Matrix(349,-146,600,-251) (5/12,8/19) -> (18/31,7/12) Hyperbolic Matrix(276,-121,625,-274) (7/16,11/25) -> (11/25,4/9) Parabolic Matrix(2624,-1177,3625,-1626) (13/29,22/49) -> (55/76,21/29) Hyperbolic Matrix(1351,-620,1850,-849) (11/24,6/13) -> (46/63,19/26) Hyperbolic Matrix(226,-121,325,-174) (1/2,7/13) -> (9/13,16/23) Hyperbolic Matrix(401,-218,550,-299) (7/13,6/11) -> (8/11,27/37) Hyperbolic Matrix(176,-97,225,-124) (6/11,5/9) -> (7/9,11/14) Hyperbolic Matrix(751,-434,950,-549) (15/26,11/19) -> (15/19,19/24) Hyperbolic Matrix(76,-45,125,-74) (7/12,3/5) -> (3/5,8/13) Parabolic Matrix(851,-526,1050,-649) (21/34,13/21) -> (17/21,13/16) Hyperbolic Matrix(476,-299,675,-424) (5/8,17/27) -> (19/27,12/17) Hyperbolic Matrix(701,-442,950,-599) (17/27,12/19) -> (14/19,17/23) Hyperbolic Matrix(226,-143,275,-174) (12/19,7/11) -> (9/11,5/6) Hyperbolic Matrix(426,-289,625,-424) (2/3,17/25) -> (17/25,15/22) Parabolic Matrix(3976,-2809,5625,-3974) (12/17,53/75) -> (53/75,41/58) Parabolic Matrix(826,-605,1125,-824) (30/41,11/15) -> (11/15,25/34) Parabolic Matrix(476,-361,625,-474) (3/4,19/25) -> (19/25,16/21) Parabolic Matrix(951,-734,1100,-849) (27/35,17/22) -> (19/22,13/15) Hyperbolic Matrix(201,-160,250,-199) (19/24,4/5) -> (4/5,21/26) Parabolic Matrix(526,-441,625,-524) (5/6,21/25) -> (21/25,16/19) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-48,1) Matrix(126,113,475,426) -> Matrix(13,5,-372,-143) Matrix(249,220,-850,-751) -> Matrix(29,10,-496,-171) Matrix(149,130,400,349) -> Matrix(19,6,-624,-197) Matrix(524,451,725,624) -> Matrix(73,21,-3000,-863) Matrix(126,107,325,276) -> Matrix(19,5,-612,-161) Matrix(174,143,-275,-226) -> Matrix(31,7,-288,-65) Matrix(124,101,275,224) -> Matrix(23,5,-796,-173) Matrix(174,137,475,374) -> Matrix(37,7,-1200,-227) Matrix(124,97,-225,-176) -> Matrix(27,5,-308,-57) Matrix(476,369,1775,1376) -> Matrix(5,1,-156,-31) Matrix(349,270,-1100,-851) -> Matrix(79,14,-1360,-241) Matrix(2224,1717,3075,2374) -> Matrix(201,35,-8264,-1439) Matrix(301,232,650,501) -> Matrix(23,4,-788,-137) Matrix(176,135,425,326) -> Matrix(17,3,-584,-103) Matrix(599,442,-950,-701) -> Matrix(79,12,-744,-113) Matrix(299,220,950,699) -> Matrix(1,0,-24,1) Matrix(824,605,-1125,-826) -> Matrix(59,9,-400,-61) Matrix(599,438,2050,1499) -> Matrix(1,0,-24,1) Matrix(299,218,-550,-401) -> Matrix(27,4,-304,-45) Matrix(274,199,-1275,-926) -> Matrix(61,9,-1132,-167) Matrix(499,362,550,399) -> Matrix(109,16,-4980,-731) Matrix(3099,2246,4000,2899) -> Matrix(301,44,-12772,-1867) Matrix(374,271,-2175,-1576) -> Matrix(89,13,-1828,-267) Matrix(1901,1376,2350,1701) -> Matrix(83,12,-3576,-517) Matrix(1776,1285,-4525,-3274) -> Matrix(103,15,-1600,-233) Matrix(624,451,725,524) -> Matrix(145,21,-6456,-935) Matrix(649,468,900,649) -> Matrix(181,26,-7428,-1067) Matrix(251,180,350,251) -> Matrix(71,10,-2904,-409) Matrix(24,17,175,124) -> Matrix(7,1,-204,-29) Matrix(424,299,-675,-476) -> Matrix(37,5,-348,-47) Matrix(151,106,500,351) -> Matrix(15,2,-428,-57) Matrix(149,104,500,349) -> Matrix(15,2,-488,-65) Matrix(174,121,-325,-226) -> Matrix(7,1,-92,-13) Matrix(74,51,325,224) -> Matrix(23,3,-652,-85) Matrix(174,113,-425,-276) -> Matrix(43,5,-628,-73) Matrix(76,49,-425,-274) -> Matrix(9,1,-136,-15) Matrix(449,288,700,449) -> Matrix(161,18,-6288,-703) Matrix(351,224,550,351) -> Matrix(127,14,-4944,-545) Matrix(349,220,-1350,-851) -> Matrix(19,2,-276,-29) Matrix(151,94,-400,-249) -> Matrix(19,2,-276,-29) Matrix(526,325,1175,726) -> Matrix(49,5,-1676,-171) Matrix(201,124,650,401) -> Matrix(39,4,-1180,-121) Matrix(74,45,-125,-76) -> Matrix(29,3,-300,-31) Matrix(251,146,-600,-349) -> Matrix(21,2,-284,-27) Matrix(524,303,1425,824) -> Matrix(53,5,-1728,-163) Matrix(101,58,350,201) -> Matrix(1,0,-20,1) Matrix(224,127,-575,-326) -> Matrix(75,7,-1168,-109) Matrix(126,71,-575,-324) -> Matrix(11,1,-144,-13) Matrix(449,252,800,449) -> Matrix(197,18,-7300,-667) Matrix(251,140,450,251) -> Matrix(111,10,-4096,-369) Matrix(499,270,-1850,-1001) -> Matrix(45,4,-844,-75) Matrix(176,83,-475,-224) -> Matrix(67,5,-1032,-77) Matrix(501,232,650,301) -> Matrix(55,4,-2324,-169) Matrix(149,68,-550,-251) -> Matrix(27,2,-500,-37) Matrix(224,101,275,124) -> Matrix(67,5,-2908,-217) Matrix(76,33,175,76) -> Matrix(43,3,-1448,-101) Matrix(26,11,-175,-74) -> Matrix(15,1,-316,-21) Matrix(1451,610,2500,1051) -> Matrix(37,2,-1388,-75) Matrix(1449,608,2500,1049) -> Matrix(21,2,-788,-75) Matrix(326,135,425,176) -> Matrix(41,3,-1736,-127) Matrix(99,40,-250,-101) -> Matrix(59,4,-900,-61) Matrix(1274,499,3125,1224) -> Matrix(77,5,-2572,-167) Matrix(276,107,325,126) -> Matrix(79,5,-3492,-221) Matrix(76,29,-325,-124) -> Matrix(17,1,-324,-19) Matrix(1551,590,2500,951) -> Matrix(43,2,-1656,-77) Matrix(1549,588,2500,949) -> Matrix(19,2,-732,-77) Matrix(349,130,400,149) -> Matrix(91,6,-4080,-269) Matrix(249,92,-950,-351) -> Matrix(31,2,-636,-41) Matrix(374,137,475,174) -> Matrix(109,7,-4656,-299) Matrix(26,9,75,26) -> Matrix(17,1,-528,-31) Matrix(1199,386,1550,499) -> Matrix(337,20,-14272,-847) Matrix(1701,542,2200,701) -> Matrix(479,28,-20272,-1185) Matrix(699,220,950,299) -> Matrix(1,0,-24,1) Matrix(401,124,650,201) -> Matrix(71,4,-2716,-153) Matrix(249,76,-1150,-351) -> Matrix(37,2,-648,-35) Matrix(351,106,500,151) -> Matrix(39,2,-1580,-81) Matrix(349,104,500,149) -> Matrix(31,2,-1256,-81) Matrix(149,44,-850,-251) -> Matrix(33,2,-644,-39) Matrix(1499,440,1700,499) -> Matrix(339,20,-15272,-901) Matrix(1801,528,2050,601) -> Matrix(409,24,-18388,-1079) Matrix(1499,438,2050,599) -> Matrix(1,0,-24,1) Matrix(201,58,350,101) -> Matrix(1,0,-20,1) Matrix(76,21,275,76) -> Matrix(55,3,-1632,-89) Matrix(7301,1972,10000,2701) -> Matrix(73,4,-3048,-167) Matrix(7299,1970,10000,2699) -> Matrix(223,12,-9236,-497) Matrix(1451,390,2050,551) -> Matrix(39,2,-1580,-81) Matrix(1376,369,1775,476) -> Matrix(17,1,-732,-43) Matrix(426,113,475,126) -> Matrix(97,5,-4404,-227) Matrix(651,172,950,251) -> Matrix(119,6,-4780,-241) Matrix(1851,482,2500,651) -> Matrix(61,2,-2532,-83) Matrix(1849,480,2500,649) -> Matrix(13,2,-540,-83) Matrix(224,51,325,74) -> Matrix(59,3,-2380,-121) Matrix(1524,329,4975,1074) -> Matrix(235,13,-7032,-389) Matrix(24,5,-125,-26) -> Matrix(19,1,-400,-21) Matrix(1324,229,4475,774) -> Matrix(141,7,-4492,-223) Matrix(124,17,175,24) -> Matrix(19,1,-780,-41) Matrix(74,-7,275,-26) -> Matrix(27,1,-784,-29) Matrix(601,-70,850,-99) -> Matrix(101,4,-4116,-163) Matrix(74,-11,175,-26) -> Matrix(27,1,-892,-33) Matrix(251,-44,850,-149) -> Matrix(57,2,-1796,-63) Matrix(274,-49,425,-76) -> Matrix(33,1,-1288,-39) Matrix(26,-5,125,-24) -> Matrix(27,1,-784,-29) Matrix(351,-76,1150,-249) -> Matrix(61,2,-1800,-59) Matrix(324,-71,575,-126) -> Matrix(35,1,-1296,-37) Matrix(324,-73,1225,-276) -> Matrix(83,3,-2352,-85) Matrix(751,-170,1100,-249) -> Matrix(279,10,-11188,-401) Matrix(124,-29,325,-76) -> Matrix(29,1,-900,-31) Matrix(351,-92,950,-249) -> Matrix(55,2,-1788,-65) Matrix(1976,-525,2725,-724) -> Matrix(661,23,-27216,-947) Matrix(2374,-635,3275,-876) -> Matrix(731,25,-30088,-1029) Matrix(251,-68,550,-149) -> Matrix(59,2,-2036,-69) Matrix(176,-49,625,-174) -> Matrix(209,7,-6300,-211) Matrix(751,-220,850,-249) -> Matrix(309,10,-13936,-451) Matrix(4474,-1323,6175,-1826) -> Matrix(857,27,-35264,-1111) Matrix(4626,-1369,15625,-4624) -> Matrix(415,13,-13312,-417) Matrix(1724,-527,2375,-726) -> Matrix(565,19,-23284,-783) Matrix(1726,-529,5625,-1724) -> Matrix(689,23,-20700,-691) Matrix(851,-270,1100,-349) -> Matrix(431,14,-18256,-593) Matrix(226,-81,625,-224) -> Matrix(287,9,-9216,-289) Matrix(1101,-404,2450,-899) -> Matrix(261,8,-8972,-275) Matrix(1001,-370,1350,-499) -> Matrix(389,12,-16176,-499) Matrix(224,-83,475,-176) -> Matrix(163,5,-5640,-173) Matrix(249,-94,400,-151) -> Matrix(67,2,-2580,-77) Matrix(549,-212,650,-251) -> Matrix(191,6,-8436,-265) Matrix(326,-127,575,-224) -> Matrix(227,7,-8464,-261) Matrix(101,-40,250,-99) -> Matrix(131,4,-4356,-133) Matrix(6376,-2601,15625,-6374) -> Matrix(299,9,-10000,-301) Matrix(2876,-1175,3975,-1624) -> Matrix(569,17,-23396,-699) Matrix(276,-113,425,-174) -> Matrix(167,5,-6580,-197) Matrix(649,-268,850,-351) -> Matrix(339,10,-14272,-421) Matrix(349,-146,600,-251) -> Matrix(69,2,-2588,-75) Matrix(276,-121,625,-274) -> Matrix(373,11,-12716,-375) Matrix(2624,-1177,3625,-1626) -> Matrix(655,19,-26924,-781) Matrix(1351,-620,1850,-849) -> Matrix(69,2,-2864,-83) Matrix(226,-121,325,-174) -> Matrix(35,1,-1436,-41) Matrix(401,-218,550,-299) -> Matrix(147,4,-6064,-165) Matrix(176,-97,225,-124) -> Matrix(183,5,-7796,-213) Matrix(751,-434,950,-549) -> Matrix(223,6,-9552,-257) Matrix(76,-45,125,-74) -> Matrix(113,3,-4332,-115) Matrix(851,-526,1050,-649) -> Matrix(383,10,-16584,-433) Matrix(476,-299,675,-424) -> Matrix(193,5,-7836,-203) Matrix(701,-442,950,-599) -> Matrix(463,12,-19176,-497) Matrix(226,-143,275,-174) -> Matrix(271,7,-11808,-305) Matrix(426,-289,625,-424) -> Matrix(679,17,-27200,-681) Matrix(3976,-2809,5625,-3974) -> Matrix(1097,27,-44652,-1099) Matrix(826,-605,1125,-824) -> Matrix(371,9,-15376,-373) Matrix(476,-361,625,-474) -> Matrix(797,19,-33516,-799) Matrix(951,-734,1100,-849) -> Matrix(591,14,-26384,-625) Matrix(201,-160,250,-199) -> Matrix(343,8,-14792,-345) Matrix(526,-441,625,-524) -> Matrix(923,21,-40656,-925) 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): 75 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (-1/24,0/1) 0 25 1/7 -1/24 1 25 1/6 (-1/27,-1/28) 0 25 3/17 -3/88 1 25 2/11 (-1/24,0/1) 0 25 1/5 -1/28 1 5 3/14 (-1/29,-3/88) 0 25 5/23 -1/32 1 25 2/9 (-1/26,0/1) 0 25 3/13 -1/28 1 25 1/4 (-1/29,-1/30) 0 25 5/19 -1/28 1 25 9/34 (-3/85,-5/142) 0 25 4/15 -1/29 4 5 11/41 -3/88 1 25 7/26 (-1/29,-3/88) 0 25 3/11 -3/88 1 25 7/25 -1/30 7 1 2/7 (-1/30,-2/61) 0 25 7/24 (-3/92,-1/31) 0 25 12/41 (-5/154,-6/185) 0 25 5/17 -5/156 1 25 13/44 (-3/95,-1/32) 0 25 21/71 -1/32 1 25 37/125 -1/32 13 1 8/27 (-1/32,-2/65) 0 25 3/10 0/1 2 5 7/23 -3/88 1 25 11/36 (-3/89,-7/208) 0 25 15/49 -15/448 1 25 23/75 -1/30 23 1 4/13 (-1/30,-4/121) 0 25 5/16 (-1/30,-3/91) 0 25 6/19 (-3/92,-4/123) 0 25 1/3 -1/32 1 25 9/25 -1/32 9 1 4/11 (-1/32,-4/129) 0 25 7/19 -1/32 1 25 17/46 (-3/97,-5/162) 0 25 10/27 (-2/65,-7/228) 0 25 13/35 -3/98 3 5 3/8 (-1/33,-1/34) 0 25 8/21 (-1/30,0/1) 0 25 5/13 -1/32 1 25 7/18 (-3/97,-5/162) 0 25 9/23 -1/32 1 25 2/5 -1/33 2 5 11/27 -3/100 1 25 51/125 -3/100 1 1 20/49 (-3/100,-2/67) 0 25 9/22 (-1/33,-3/100) 0 25 7/17 -7/236 1 25 5/12 (-1/33,-1/34) 0 25 8/19 (-1/32,0/1) 0 25 3/7 -3/100 1 25 11/25 -1/34 11 1 4/9 (-1/34,-4/137) 0 25 5/11 -1/36 1 25 11/24 (-1/35,-1/36) 0 25 6/13 (-1/34,0/1) 0 25 7/15 -1/34 3 5 1/2 (-1/35,-1/36) 0 25 7/13 -1/36 1 25 6/11 (-1/36,0/1) 0 25 5/9 -5/184 1 25 14/25 -1/37 14 1 9/16 (-1/37,-9/334) 0 25 13/23 -3/112 1 25 4/7 (-2/75,-1/38) 0 25 15/26 (-1/37,-3/112) 0 25 11/19 -3/112 1 25 29/50 -2/75 4 1 18/31 (-2/75,-5/188) 0 25 7/12 (-3/113,-1/38) 0 25 3/5 -1/38 3 5 8/13 (-1/38,0/1) 0 25 21/34 (-1/38,-1/39) 0 25 13/21 -5/192 1 25 31/50 -2/77 6 1 18/29 (-2/77,-7/270) 0 25 5/8 (-1/38,-1/39) 0 25 17/27 -5/192 1 25 12/19 (-8/309,-3/116) 0 25 7/11 -7/272 1 25 16/25 -1/39 16 1 9/14 (-1/39,-9/352) 0 25 11/17 -11/432 1 25 2/3 (-2/79,-1/40) 0 25 17/25 -1/40 17 1 13/19 -1/40 1 25 11/16 (-7/282,-3/121) 0 25 9/13 -1/40 1 25 16/23 (-1/40,0/1) 0 25 7/10 -2/81 2 5 19/27 -5/204 1 25 12/17 (-2/81,-3/122) 0 25 53/75 -3/122 3 1 29/41 -5/204 1 25 17/24 (-5/204,-1/41) 0 25 5/7 -5/204 1 25 18/25 -1/41 18 1 13/18 (-1/41,-13/534) 0 25 34/47 (-8/329,-7/288) 0 25 55/76 (-1/41,-7/288) 0 25 21/29 -7/288 1 25 50/69 (-7/288,-6/247) 0 25 29/40 -6/247 4 5 37/51 -37/1524 1 25 8/11 (-4/165,-3/124) 0 25 27/37 -3/124 1 25 73/100 -2/83 2 1 46/63 (-2/83,-1/42) 0 25 19/26 (-1/41,-3/124) 0 25 30/41 (-6/247,-5/206) 0 25 11/15 -3/124 1 5 25/34 (-3/125,-1/42) 0 25 14/19 (-4/165,-3/124) 0 25 17/23 -11/456 1 25 37/50 -2/83 12 1 20/27 (-2/83,-13/540) 0 25 3/4 (-3/125,-1/42) 0 25 19/25 -1/42 19 1 13/17 -13/548 1 25 10/13 (-1/42,-4/169) 0 25 27/35 -1/42 3 5 17/22 (-7/296,-3/127) 0 25 58/75 -3/127 8 1 41/53 -17/720 1 25 24/31 (-5/212,-2/85) 0 25 31/40 -2/85 4 5 7/9 -5/212 1 25 11/14 (-5/213,-3/128) 0 25 15/19 -3/128 1 25 19/24 (-3/128,-1/43) 0 25 4/5 -1/43 4 5 21/26 (-1/43,-5/216) 0 25 17/21 -5/216 1 25 13/16 (-7/303,-3/130) 0 25 9/11 -7/304 1 25 5/6 (-5/219,-1/44) 0 25 21/25 -1/44 21 1 11/13 -1/44 1 25 6/7 (-5/222,-2/89) 0 25 19/22 (-7/312,-5/223) 0 25 13/15 -3/134 3 5 7/8 (-7/314,-1/45) 0 25 22/25 -1/45 22 1 15/17 -15/676 1 25 8/9 (-5/226,-4/181) 0 25 9/10 -2/91 4 5 1/1 -1/48 1 25 1/0 0/1 24 1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(124,-17,175,-24) (0/1,1/7) -> (17/24,5/7) Glide Reflection Matrix(74,-11,175,-26) (1/7,1/6) -> (8/19,3/7) Hyperbolic Matrix(251,-44,850,-149) (1/6,3/17) -> (5/17,13/44) Hyperbolic Matrix(274,-49,425,-76) (3/17,2/11) -> (9/14,11/17) Hyperbolic Matrix(26,-5,125,-24) (2/11,1/5) -> (1/5,3/14) Parabolic Matrix(351,-76,1150,-249) (3/14,5/23) -> (7/23,11/36) Hyperbolic Matrix(324,-71,575,-126) (5/23,2/9) -> (9/16,13/23) Hyperbolic Matrix(224,-51,325,-74) (2/9,3/13) -> (11/16,9/13) Glide Reflection Matrix(124,-29,325,-76) (3/13,1/4) -> (8/21,5/13) Hyperbolic Matrix(351,-92,950,-249) (1/4,5/19) -> (7/19,17/46) Hyperbolic Matrix(651,-172,950,-251) (5/19,9/34) -> (13/19,11/16) Glide Reflection Matrix(426,-113,475,-126) (9/34,4/15) -> (8/9,9/10) Glide Reflection Matrix(1376,-369,1775,-476) (4/15,11/41) -> (31/40,7/9) Glide Reflection Matrix(1451,-390,2050,-551) (11/41,7/26) -> (29/41,17/24) Glide Reflection Matrix(251,-68,550,-149) (7/26,3/11) -> (5/11,11/24) Hyperbolic Matrix(76,-21,275,-76) (3/11,7/25) -> (3/11,7/25) Reflection Matrix(99,-28,350,-99) (7/25,2/7) -> (7/25,2/7) Reflection Matrix(201,-58,350,-101) (2/7,7/24) -> (4/7,15/26) Glide Reflection Matrix(1499,-438,2050,-599) (7/24,12/41) -> (19/26,30/41) Glide Reflection Matrix(751,-220,850,-249) (12/41,5/17) -> (15/17,8/9) Hyperbolic Matrix(4474,-1323,6175,-1826) (13/44,21/71) -> (21/29,50/69) Hyperbolic Matrix(2626,-777,8875,-2626) (21/71,37/125) -> (21/71,37/125) Reflection Matrix(1999,-592,6750,-1999) (37/125,8/27) -> (37/125,8/27) Reflection Matrix(349,-104,500,-149) (8/27,3/10) -> (16/23,7/10) Glide Reflection Matrix(351,-106,500,-151) (3/10,7/23) -> (7/10,19/27) Glide Reflection Matrix(1724,-527,2375,-726) (11/36,15/49) -> (37/51,8/11) Hyperbolic Matrix(1126,-345,3675,-1126) (15/49,23/75) -> (15/49,23/75) Reflection Matrix(599,-184,1950,-599) (23/75,4/13) -> (23/75,4/13) Reflection Matrix(401,-124,650,-201) (4/13,5/16) -> (8/13,21/34) Glide Reflection Matrix(699,-220,950,-299) (5/16,6/19) -> (25/34,14/19) Glide Reflection Matrix(851,-270,1100,-349) (6/19,1/3) -> (41/53,24/31) Hyperbolic Matrix(26,-9,75,-26) (1/3,9/25) -> (1/3,9/25) Reflection Matrix(199,-72,550,-199) (9/25,4/11) -> (9/25,4/11) Reflection Matrix(374,-137,475,-174) (4/11,7/19) -> (11/14,15/19) Glide Reflection Matrix(1001,-370,1350,-499) (17/46,10/27) -> (20/27,3/4) Hyperbolic Matrix(224,-83,475,-176) (10/27,13/35) -> (7/15,1/2) Hyperbolic Matrix(349,-130,400,-149) (13/35,3/8) -> (13/15,7/8) Glide Reflection Matrix(249,-94,400,-151) (3/8,8/21) -> (18/29,5/8) Hyperbolic Matrix(276,-107,325,-126) (5/13,7/18) -> (11/13,6/7) Glide Reflection Matrix(326,-127,575,-224) (7/18,9/23) -> (13/23,4/7) Hyperbolic Matrix(101,-40,250,-99) (9/23,2/5) -> (2/5,11/27) Parabolic Matrix(1376,-561,3375,-1376) (11/27,51/125) -> (11/27,51/125) Reflection Matrix(4999,-2040,12250,-4999) (51/125,20/49) -> (51/125,20/49) Reflection Matrix(2876,-1175,3975,-1624) (20/49,9/22) -> (34/47,55/76) Hyperbolic Matrix(276,-113,425,-174) (9/22,7/17) -> (11/17,2/3) Hyperbolic Matrix(326,-135,425,-176) (7/17,5/12) -> (13/17,10/13) Glide Reflection Matrix(349,-146,600,-251) (5/12,8/19) -> (18/31,7/12) Hyperbolic Matrix(76,-33,175,-76) (3/7,11/25) -> (3/7,11/25) Reflection Matrix(199,-88,450,-199) (11/25,4/9) -> (11/25,4/9) Reflection Matrix(224,-101,275,-124) (4/9,5/11) -> (13/16,9/11) Glide Reflection Matrix(1351,-620,1850,-849) (11/24,6/13) -> (46/63,19/26) Hyperbolic Matrix(501,-232,650,-301) (6/13,7/15) -> (10/13,27/35) Glide Reflection Matrix(226,-121,325,-174) (1/2,7/13) -> (9/13,16/23) Hyperbolic Matrix(401,-218,550,-299) (7/13,6/11) -> (8/11,27/37) Hyperbolic Matrix(176,-97,225,-124) (6/11,5/9) -> (7/9,11/14) Hyperbolic Matrix(251,-140,450,-251) (5/9,14/25) -> (5/9,14/25) Reflection Matrix(449,-252,800,-449) (14/25,9/16) -> (14/25,9/16) Reflection Matrix(751,-434,950,-549) (15/26,11/19) -> (15/19,19/24) Hyperbolic Matrix(1101,-638,1900,-1101) (11/19,29/50) -> (11/19,29/50) Reflection Matrix(1799,-1044,3100,-1799) (29/50,18/31) -> (29/50,18/31) Reflection Matrix(76,-45,125,-74) (7/12,3/5) -> (3/5,8/13) Parabolic Matrix(851,-526,1050,-649) (21/34,13/21) -> (17/21,13/16) Hyperbolic Matrix(1301,-806,2100,-1301) (13/21,31/50) -> (13/21,31/50) Reflection Matrix(1799,-1116,2900,-1799) (31/50,18/29) -> (31/50,18/29) Reflection Matrix(476,-299,675,-424) (5/8,17/27) -> (19/27,12/17) Hyperbolic Matrix(701,-442,950,-599) (17/27,12/19) -> (14/19,17/23) Hyperbolic Matrix(226,-143,275,-174) (12/19,7/11) -> (9/11,5/6) Hyperbolic Matrix(351,-224,550,-351) (7/11,16/25) -> (7/11,16/25) Reflection Matrix(449,-288,700,-449) (16/25,9/14) -> (16/25,9/14) Reflection Matrix(101,-68,150,-101) (2/3,17/25) -> (2/3,17/25) Reflection Matrix(324,-221,475,-324) (17/25,13/19) -> (17/25,13/19) Reflection Matrix(1801,-1272,2550,-1801) (12/17,53/75) -> (12/17,53/75) Reflection Matrix(2174,-1537,3075,-2174) (53/75,29/41) -> (53/75,29/41) Reflection Matrix(251,-180,350,-251) (5/7,18/25) -> (5/7,18/25) Reflection Matrix(649,-468,900,-649) (18/25,13/18) -> (18/25,13/18) Reflection Matrix(624,-451,725,-524) (13/18,34/47) -> (6/7,19/22) Glide Reflection Matrix(1901,-1376,2350,-1701) (55/76,21/29) -> (21/26,17/21) Glide Reflection Matrix(3099,-2246,4000,-2899) (50/69,29/40) -> (24/31,31/40) Glide Reflection Matrix(499,-362,550,-399) (29/40,37/51) -> (9/10,1/1) Glide Reflection Matrix(5401,-3942,7400,-5401) (27/37,73/100) -> (27/37,73/100) Reflection Matrix(9199,-6716,12600,-9199) (73/100,46/63) -> (73/100,46/63) Reflection Matrix(826,-605,1125,-824) (30/41,11/15) -> (11/15,25/34) Parabolic Matrix(1701,-1258,2300,-1701) (17/23,37/50) -> (17/23,37/50) Reflection Matrix(1999,-1480,2700,-1999) (37/50,20/27) -> (37/50,20/27) Reflection Matrix(151,-114,200,-151) (3/4,19/25) -> (3/4,19/25) Reflection Matrix(324,-247,425,-324) (19/25,13/17) -> (19/25,13/17) Reflection Matrix(951,-734,1100,-849) (27/35,17/22) -> (19/22,13/15) Hyperbolic Matrix(2551,-1972,3300,-2551) (17/22,58/75) -> (17/22,58/75) Reflection Matrix(6149,-4756,7950,-6149) (58/75,41/53) -> (58/75,41/53) Reflection Matrix(201,-160,250,-199) (19/24,4/5) -> (4/5,21/26) Parabolic Matrix(251,-210,300,-251) (5/6,21/25) -> (5/6,21/25) Reflection Matrix(274,-231,325,-274) (21/25,11/13) -> (21/25,11/13) Reflection Matrix(351,-308,400,-351) (7/8,22/25) -> (7/8,22/25) Reflection Matrix(749,-660,850,-749) (22/25,15/17) -> (22/25,15/17) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,48,1) (0/1,1/0) -> (-1/24,0/1) Matrix(124,-17,175,-24) -> Matrix(29,1,-1188,-41) Matrix(74,-11,175,-26) -> Matrix(27,1,-892,-33) Matrix(251,-44,850,-149) -> Matrix(57,2,-1796,-63) Matrix(274,-49,425,-76) -> Matrix(33,1,-1288,-39) Matrix(26,-5,125,-24) -> Matrix(27,1,-784,-29) -1/28 Matrix(351,-76,1150,-249) -> Matrix(61,2,-1800,-59) -1/30 Matrix(324,-71,575,-126) -> Matrix(35,1,-1296,-37) -1/36 Matrix(224,-51,325,-74) -> Matrix(85,3,-3428,-121) Matrix(124,-29,325,-76) -> Matrix(29,1,-900,-31) -1/30 Matrix(351,-92,950,-249) -> Matrix(55,2,-1788,-65) Matrix(651,-172,950,-251) -> Matrix(169,6,-6788,-241) Matrix(426,-113,475,-126) -> Matrix(143,5,-6492,-227) Matrix(1376,-369,1775,-476) -> Matrix(31,1,-1332,-43) Matrix(1451,-390,2050,-551) -> Matrix(57,2,-2308,-81) Matrix(251,-68,550,-149) -> Matrix(59,2,-2036,-69) Matrix(76,-21,275,-76) -> Matrix(89,3,-2640,-89) (3/11,7/25) -> (-3/88,-1/30) Matrix(99,-28,350,-99) -> Matrix(121,4,-3660,-121) (7/25,2/7) -> (-1/30,-2/61) Matrix(201,-58,350,-101) -> Matrix(-1,0,68,1) *** -> (-1/34,0/1) Matrix(1499,-438,2050,-599) -> Matrix(-1,0,72,1) *** -> (-1/36,0/1) Matrix(751,-220,850,-249) -> Matrix(309,10,-13936,-451) Matrix(4474,-1323,6175,-1826) -> Matrix(857,27,-35264,-1111) Matrix(2626,-777,8875,-2626) -> Matrix(287,9,-9152,-287) (21/71,37/125) -> (-9/286,-1/32) Matrix(1999,-592,6750,-1999) -> Matrix(129,4,-4160,-129) (37/125,8/27) -> (-1/32,-2/65) Matrix(349,-104,500,-149) -> Matrix(65,2,-2632,-81) Matrix(351,-106,500,-151) -> Matrix(57,2,-2308,-81) Matrix(1724,-527,2375,-726) -> Matrix(565,19,-23284,-783) Matrix(1126,-345,3675,-1126) -> Matrix(449,15,-13440,-449) (15/49,23/75) -> (-15/448,-1/30) Matrix(599,-184,1950,-599) -> Matrix(241,8,-7260,-241) (23/75,4/13) -> (-1/30,-4/121) Matrix(401,-124,650,-201) -> Matrix(121,4,-4628,-153) Matrix(699,-220,950,-299) -> Matrix(-1,0,72,1) *** -> (-1/36,0/1) Matrix(851,-270,1100,-349) -> Matrix(431,14,-18256,-593) Matrix(26,-9,75,-26) -> Matrix(31,1,-960,-31) (1/3,9/25) -> (-1/30,-1/32) Matrix(199,-72,550,-199) -> Matrix(257,8,-8256,-257) (9/25,4/11) -> (-1/32,-4/129) Matrix(374,-137,475,-174) -> Matrix(227,7,-9696,-299) Matrix(1001,-370,1350,-499) -> Matrix(389,12,-16176,-499) Matrix(224,-83,475,-176) -> Matrix(163,5,-5640,-173) Matrix(349,-130,400,-149) -> Matrix(197,6,-8832,-269) Matrix(249,-94,400,-151) -> Matrix(67,2,-2580,-77) Matrix(276,-107,325,-126) -> Matrix(161,5,-7116,-221) Matrix(326,-127,575,-224) -> Matrix(227,7,-8464,-261) Matrix(101,-40,250,-99) -> Matrix(131,4,-4356,-133) -1/33 Matrix(1376,-561,3375,-1376) -> Matrix(101,3,-3400,-101) (11/27,51/125) -> (-3/100,-1/34) Matrix(4999,-2040,12250,-4999) -> Matrix(401,12,-13400,-401) (51/125,20/49) -> (-3/100,-2/67) Matrix(2876,-1175,3975,-1624) -> Matrix(569,17,-23396,-699) Matrix(276,-113,425,-174) -> Matrix(167,5,-6580,-197) Matrix(326,-135,425,-176) -> Matrix(103,3,-4360,-127) Matrix(349,-146,600,-251) -> Matrix(69,2,-2588,-75) Matrix(76,-33,175,-76) -> Matrix(101,3,-3400,-101) (3/7,11/25) -> (-3/100,-1/34) Matrix(199,-88,450,-199) -> Matrix(273,8,-9316,-273) (11/25,4/9) -> (-1/34,-4/137) Matrix(224,-101,275,-124) -> Matrix(173,5,-7508,-217) Matrix(1351,-620,1850,-849) -> Matrix(69,2,-2864,-83) Matrix(501,-232,650,-301) -> Matrix(137,4,-5788,-169) Matrix(226,-121,325,-174) -> Matrix(35,1,-1436,-41) Matrix(401,-218,550,-299) -> Matrix(147,4,-6064,-165) Matrix(176,-97,225,-124) -> Matrix(183,5,-7796,-213) Matrix(251,-140,450,-251) -> Matrix(369,10,-13616,-369) (5/9,14/25) -> (-5/184,-1/37) Matrix(449,-252,800,-449) -> Matrix(667,18,-24716,-667) (14/25,9/16) -> (-1/37,-9/334) Matrix(751,-434,950,-549) -> Matrix(223,6,-9552,-257) Matrix(1101,-638,1900,-1101) -> Matrix(449,12,-16800,-449) (11/19,29/50) -> (-3/112,-2/75) Matrix(1799,-1044,3100,-1799) -> Matrix(751,20,-28200,-751) (29/50,18/31) -> (-2/75,-5/188) Matrix(76,-45,125,-74) -> Matrix(113,3,-4332,-115) -1/38 Matrix(851,-526,1050,-649) -> Matrix(383,10,-16584,-433) Matrix(1301,-806,2100,-1301) -> Matrix(769,20,-29568,-769) (13/21,31/50) -> (-5/192,-2/77) Matrix(1799,-1116,2900,-1799) -> Matrix(1079,28,-41580,-1079) (31/50,18/29) -> (-2/77,-7/270) Matrix(476,-299,675,-424) -> Matrix(193,5,-7836,-203) Matrix(701,-442,950,-599) -> Matrix(463,12,-19176,-497) Matrix(226,-143,275,-174) -> Matrix(271,7,-11808,-305) Matrix(351,-224,550,-351) -> Matrix(545,14,-21216,-545) (7/11,16/25) -> (-7/272,-1/39) Matrix(449,-288,700,-449) -> Matrix(703,18,-27456,-703) (16/25,9/14) -> (-1/39,-9/352) Matrix(101,-68,150,-101) -> Matrix(159,4,-6320,-159) (2/3,17/25) -> (-2/79,-1/40) Matrix(324,-221,475,-324) -> Matrix(521,13,-20880,-521) (17/25,13/19) -> (-1/40,-13/522) Matrix(1801,-1272,2550,-1801) -> Matrix(487,12,-19764,-487) (12/17,53/75) -> (-2/81,-3/122) Matrix(2174,-1537,3075,-2174) -> Matrix(611,15,-24888,-611) (53/75,29/41) -> (-3/122,-5/204) Matrix(251,-180,350,-251) -> Matrix(409,10,-16728,-409) (5/7,18/25) -> (-5/204,-1/41) Matrix(649,-468,900,-649) -> Matrix(1067,26,-43788,-1067) (18/25,13/18) -> (-1/41,-13/534) Matrix(624,-451,725,-524) -> Matrix(863,21,-38424,-935) Matrix(1901,-1376,2350,-1701) -> Matrix(493,12,-21240,-517) Matrix(3099,-2246,4000,-2899) -> Matrix(1811,44,-76844,-1867) Matrix(499,-362,550,-399) -> Matrix(659,16,-30108,-731) Matrix(5401,-3942,7400,-5401) -> Matrix(497,12,-20584,-497) (27/37,73/100) -> (-3/124,-2/83) Matrix(9199,-6716,12600,-9199) -> Matrix(167,4,-6972,-167) (73/100,46/63) -> (-2/83,-1/42) Matrix(826,-605,1125,-824) -> Matrix(371,9,-15376,-373) -3/124 Matrix(1701,-1258,2300,-1701) -> Matrix(1825,44,-75696,-1825) (17/23,37/50) -> (-11/456,-2/83) Matrix(1999,-1480,2700,-1999) -> Matrix(2159,52,-89640,-2159) (37/50,20/27) -> (-2/83,-13/540) Matrix(151,-114,200,-151) -> Matrix(251,6,-10500,-251) (3/4,19/25) -> (-3/125,-1/42) Matrix(324,-247,425,-324) -> Matrix(547,13,-23016,-547) (19/25,13/17) -> (-1/42,-13/548) Matrix(951,-734,1100,-849) -> Matrix(591,14,-26384,-625) Matrix(2551,-1972,3300,-2551) -> Matrix(1777,42,-75184,-1777) (17/22,58/75) -> (-7/296,-3/127) Matrix(6149,-4756,7950,-6149) -> Matrix(4319,102,-182880,-4319) (58/75,41/53) -> (-3/127,-17/720) Matrix(201,-160,250,-199) -> Matrix(343,8,-14792,-345) -1/43 Matrix(251,-210,300,-251) -> Matrix(439,10,-19272,-439) (5/6,21/25) -> (-5/219,-1/44) Matrix(274,-231,325,-274) -> Matrix(485,11,-21384,-485) (21/25,11/13) -> (-1/44,-11/486) Matrix(351,-308,400,-351) -> Matrix(629,14,-28260,-629) (7/8,22/25) -> (-7/314,-1/45) Matrix(749,-660,850,-749) -> Matrix(1351,30,-60840,-1351) (22/25,15/17) -> (-1/45,-15/676) Matrix(-1,2,0,1) -> Matrix(-1,0,96,1) (1/1,1/0) -> (-1/48,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.