INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1536 Minimal number of generators: 257 Number of equivalence classes of cusps: 96 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -7/15 -13/29 -3/7 -11/27 -5/13 -7/19 -9/25 -1/3 -7/23 -5/17 -3/11 -1/5 -1/7 -1/9 0/1 1/7 3/13 5/19 1/3 7/17 5/11 1/2 7/13 17/31 3/5 11/17 5/7 7/9 11/13 13/15 1/1 17/15 13/11 11/9 9/7 23/17 37/27 7/5 19/13 3/2 17/11 39/25 11/7 49/31 5/3 41/23 9/5 31/17 13/7 2/1 11/5 7/3 45/19 17/7 5/2 23/9 13/5 35/13 19/7 117/43 3/1 49/15 10/3 37/11 17/5 99/29 7/2 25/7 11/3 63/17 19/5 127/33 27/7 4/1 13/3 31/7 9/2 23/5 14/3 33/7 53/11 5/1 27/5 11/2 17/3 29/5 6/1 19/3 13/2 7/1 8/1 9/1 29/3 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/31 -7/15 1/28 -6/13 0/1 1/29 -11/24 4/109 1/27 -5/11 1/26 -14/31 4/109 1/27 -9/20 1/27 2/53 -13/29 1/26 -4/9 0/1 1/25 -15/34 7/179 2/51 -11/25 3/76 -7/16 1/25 4/99 -24/55 5/123 2/49 -17/39 5/122 -10/23 0/1 1/25 -3/7 1/24 -14/33 2/47 1/23 -11/26 2/47 1/23 -30/71 2/47 5/117 -19/45 1/22 -8/19 3/71 2/47 -21/50 7/163 4/93 -13/31 5/116 -5/12 1/23 4/91 -17/41 1/22 -12/29 1/23 4/91 -19/46 5/113 2/45 -7/17 1/22 -16/39 5/113 2/45 -9/22 4/89 5/111 -11/27 1/22 -2/5 2/43 1/21 -11/28 1/21 4/83 -9/23 3/62 -16/41 2/41 11/225 -7/18 2/41 3/61 -5/13 1/20 -13/34 4/79 3/59 -21/55 1/20 -29/76 4/79 3/59 -8/21 4/79 3/59 -19/50 3/59 2/39 -11/29 5/98 -14/37 2/39 13/253 -3/8 4/77 1/19 -13/35 9/170 -10/27 1/19 4/75 -17/46 9/169 4/75 -24/65 7/131 10/187 -7/19 3/56 -25/68 8/149 5/93 -18/49 1/19 2/37 -11/30 13/241 2/37 -15/41 9/166 -4/11 3/55 4/73 -9/25 1/18 -14/39 11/197 10/179 -5/14 5/89 4/71 -11/31 5/88 -6/17 2/35 9/157 -7/20 4/69 9/155 -8/23 14/239 1/17 -1/3 1/16 -8/25 16/241 1/15 -7/22 1/15 14/209 -6/19 9/133 4/59 -5/16 9/131 2/29 -9/29 5/72 -4/13 4/57 5/71 -7/23 1/14 -10/33 10/139 9/125 -3/10 4/55 3/41 -11/37 9/122 -19/64 31/419 2/27 -8/27 2/27 13/175 -13/44 2/27 1/13 -18/61 5/67 8/107 -5/17 3/40 -17/58 10/133 7/93 -12/41 4/53 9/119 -7/24 4/53 1/13 -9/31 9/118 -11/38 22/287 1/13 -2/7 1/13 4/51 -9/32 13/163 2/25 -16/57 2/25 23/287 -7/25 5/62 -12/43 2/25 3/37 -5/18 3/37 4/49 -3/11 1/12 -7/26 3/35 2/23 -11/41 1/12 -4/15 3/35 2/23 -9/34 11/127 2/23 -14/53 2/23 17/195 -5/19 3/34 -6/23 4/45 1/11 -1/4 1/11 2/21 -5/21 1/10 -4/17 5/49 4/39 -7/30 2/19 5/47 -3/13 1/10 -11/48 7/67 2/19 -8/35 2/19 5/47 -5/22 4/37 1/9 -7/31 1/10 -2/9 4/37 1/9 -7/32 1/9 14/125 -5/23 5/44 -8/37 4/35 7/61 -3/14 2/17 3/25 -7/33 1/10 -11/52 5/43 2/17 -4/19 1/9 2/17 -1/5 1/8 -4/21 0/1 1/7 -11/58 0/1 1/9 -7/37 1/8 -3/16 0/1 1/7 -5/27 5/38 -7/38 2/15 5/37 -2/11 4/29 1/7 -5/28 1/7 10/69 -3/17 3/20 -4/23 2/13 7/45 -1/6 0/1 1/7 -3/19 1/6 -2/13 2/11 1/5 -3/20 1/5 4/19 -1/7 1/6 -3/22 6/31 1/5 -2/15 1/5 4/19 -1/8 0/1 1/3 -1/9 1/4 0/1 0/1 1/1 1/10 -2/1 -1/1 1/9 -1/2 1/8 0/1 1/1 1/7 -1/2 2/13 -2/5 -1/3 3/19 -3/10 1/6 -1/1 0/1 3/17 -1/2 2/11 -4/11 -1/3 1/5 -1/4 4/19 -2/5 -1/3 7/33 -1/2 3/14 -4/11 -1/3 5/23 -3/10 7/32 -9/31 -2/7 2/9 -1/3 -2/7 3/13 -1/4 4/17 -5/21 -4/17 5/21 -5/22 1/4 -1/5 0/1 5/19 -1/4 4/15 -7/31 -2/9 3/11 -3/14 2/7 -1/5 -4/21 7/24 -5/27 -2/11 5/17 -5/28 8/27 -4/23 -5/29 11/37 -1/6 3/10 -1/5 0/1 1/3 -1/6 5/14 -2/13 -1/7 4/11 -2/13 -1/7 15/41 -1/6 11/30 -2/13 -5/33 7/19 -1/8 10/27 -1/5 -2/11 13/35 -1/6 3/8 -3/19 -2/13 14/37 -21/139 -8/53 11/29 -3/20 19/50 -7/47 -4/27 8/21 -7/47 -4/27 5/13 -5/34 2/5 -1/7 -4/29 11/27 -5/38 9/22 -1/7 -2/15 7/17 -1/8 19/46 -1/9 0/1 12/29 -1/7 -2/15 29/70 -1/11 0/1 17/41 -1/6 5/12 -1/7 -4/29 13/31 -3/22 21/50 -4/29 -7/51 8/19 -5/37 -2/15 3/7 -1/8 10/23 -5/37 -2/15 17/39 -1/8 7/16 -5/37 -2/15 18/41 -7/53 -12/91 11/25 -5/38 4/9 -4/31 -5/39 5/11 -1/8 6/13 -6/49 -5/41 7/15 -7/58 1/2 -2/17 -1/9 9/17 -9/82 8/15 -6/55 -11/101 7/13 -3/28 13/24 -5/47 -2/19 6/11 -1/9 -4/37 17/31 -3/28 11/20 -5/47 -2/19 16/29 -2/19 -7/67 5/9 -3/28 9/16 -2/19 -11/105 22/39 -2/19 -3/29 13/23 -5/48 17/30 -3/29 -16/155 4/7 -2/19 -3/29 3/5 -1/10 8/13 -4/41 -3/31 21/34 -1/11 0/1 34/55 -7/71 -6/61 13/21 -1/10 18/29 -4/41 -3/31 5/8 -4/41 -3/31 22/35 -8/83 -13/135 17/27 -5/52 29/46 -19/199 -2/21 41/65 -7/74 12/19 -3/31 -2/21 31/49 -1/10 19/30 -3/31 -2/21 26/41 -2/21 -1/11 7/11 -5/52 9/14 -2/21 -13/137 20/31 -19/201 -12/127 31/48 -5/53 -38/403 11/17 -3/32 24/37 -2/21 -1/11 13/20 -2/21 -1/11 2/3 -4/43 -1/11 9/13 -9/100 16/23 -6/67 -11/123 23/33 -5/56 7/10 -1/11 -4/45 26/37 -1/11 -4/45 19/27 -3/34 12/17 -9/101 -4/45 17/24 -7/79 -10/113 5/7 -3/34 23/32 -1/11 -4/45 18/25 -8/91 -5/57 13/18 -1/11 -2/23 34/47 -8/91 -5/57 21/29 -3/34 8/11 -13/149 -2/23 11/15 -9/104 14/19 -2/23 -3/35 17/23 -5/58 3/4 -3/35 -4/47 7/9 -1/12 11/14 -11/133 -10/121 26/33 -8/97 -7/85 15/19 -1/12 19/24 -8/97 -7/85 23/29 -1/12 4/5 -5/61 -4/49 13/16 -3/37 -20/247 9/11 -5/62 14/17 -7/87 -2/25 5/6 -2/25 -9/113 16/19 -8/101 -11/139 11/13 -3/38 28/33 -10/127 -7/89 17/20 -10/127 -7/89 6/7 -4/51 -9/115 13/15 -7/90 7/8 -14/181 -1/13 1/1 -1/14 9/8 -16/239 -1/15 17/15 -1/15 25/22 -1/15 -44/661 8/7 -1/15 -14/211 7/6 -9/137 -4/61 20/17 -7/107 -10/153 13/11 -3/46 32/27 -11/169 -8/123 19/16 -11/169 -8/123 6/5 -9/139 -2/31 23/19 -17/264 17/14 -2/31 -7/109 28/23 -16/249 -7/109 11/9 -5/78 27/22 -2/31 -3/47 16/13 -20/313 -3/47 21/17 -13/204 5/4 -4/63 -5/79 9/7 -1/16 13/10 -10/161 -9/145 43/33 -1/16 30/23 -7/113 -6/97 17/13 -1/16 55/42 -7/113 -6/97 38/29 -7/113 -6/97 21/16 -7/113 -6/97 25/19 -1/16 4/3 -4/65 -3/49 23/17 -5/82 42/31 -12/197 -7/115 19/14 -3/49 -2/33 53/39 -5/82 34/25 -3/49 -8/131 15/11 -9/148 26/19 -31/511 -2/33 37/27 -2/33 48/35 -2/33 -57/941 11/8 -2/33 -13/215 18/13 -2/33 -1/17 43/31 -7/116 25/18 -5/83 -8/133 7/5 -3/50 24/17 -10/167 -7/117 41/29 -11/184 17/12 -4/67 -9/151 10/7 -4/67 -1/17 43/30 -7/117 -4/67 33/23 -5/84 23/16 -11/185 -6/101 59/41 -7/118 95/66 -6/101 -13/219 36/25 -6/101 -13/219 13/9 -9/152 16/11 -22/373 -1/17 19/13 -1/17 22/15 -1/17 -30/511 3/2 -1/17 -4/69 20/13 -1/17 -2/35 17/11 -3/52 31/20 -12/209 -19/331 14/9 -13/227 -2/35 39/25 -2/35 64/41 -2/35 -59/1033 25/16 -2/35 -23/403 11/7 -5/88 41/26 -1/17 -2/35 30/19 -2/35 -3/53 49/31 -1/18 68/43 -1/17 0/1 19/12 -2/35 -3/53 65/41 -7/122 111/70 -33/577 -2/35 46/29 -2/35 -19/333 27/17 -5/88 35/22 -13/229 -8/141 8/5 -3/53 -4/71 5/3 -1/18 12/7 -3/55 -2/37 19/11 -1/18 83/48 -3/55 -2/37 64/37 -3/55 -2/37 45/26 -1/17 0/1 26/15 -6/109 -5/91 33/19 -1/18 7/4 -3/55 -2/37 30/17 -16/293 -3/55 53/30 -14/257 -25/459 23/13 -5/92 62/35 -3/55 -2/37 39/22 -3/55 -2/37 16/9 -11/203 -2/37 41/23 -2/37 66/37 -2/37 -45/833 25/14 -2/37 -17/315 9/5 -3/56 29/16 -7/129 -2/37 20/11 -2/37 -5/93 31/17 -3/56 42/23 -4/75 -1/19 11/6 -4/75 -1/19 24/13 -2/37 -5/93 37/20 -7/131 -4/75 13/7 -3/56 15/8 -11/207 -6/113 17/9 -9/170 19/10 -20/379 -1/19 2/1 -1/19 -2/39 11/5 -1/20 20/9 -9/181 -8/161 49/22 -8/161 -23/463 29/13 -13/262 9/4 -5/101 -4/81 25/11 -5/102 41/18 -12/245 -7/143 16/7 -2/41 -5/103 55/24 -2/41 -1/21 39/17 -1/20 23/10 -2/41 -5/103 30/13 -4/83 -1/21 67/29 -1/21 37/16 -1/21 -2/43 7/3 -1/20 26/11 -7/143 -2/41 45/19 -2/41 64/27 -2/41 -17/349 19/8 -2/41 -5/103 31/13 -3/62 43/18 -1/21 -2/43 12/5 -4/83 -1/21 41/17 -1/22 111/46 -1/27 0/1 70/29 -1/17 0/1 29/12 -2/41 -1/21 17/7 -1/20 22/9 -2/41 -1/21 49/20 -1/21 0/1 27/11 -5/102 5/2 -4/83 -1/21 23/9 -1/21 41/16 -1/21 -32/673 18/7 -1/21 -14/295 13/5 -5/106 47/18 -1/21 -4/85 81/31 -3/64 34/13 -1/21 -4/85 21/8 -4/85 -7/149 29/11 -3/64 8/3 -2/43 -3/65 35/13 -1/22 27/10 -2/45 -1/23 73/27 -1/22 46/17 -1/23 0/1 19/7 -1/20 68/25 -12/251 -1/21 117/43 -1/21 166/61 -1/21 -32/673 49/18 -1/21 -10/211 30/11 -5/107 -2/43 11/4 -1/21 -2/43 3/1 -1/22 13/4 -1/23 0/1 49/15 0/1 85/26 -1/19 0/1 36/11 -1/21 0/1 23/7 -1/22 10/3 -1/23 0/1 37/11 -1/22 27/8 -5/111 -4/89 44/13 -4/89 -11/245 17/5 -5/112 58/17 -31/697 -2/45 99/29 -2/45 140/41 -2/45 -73/1643 41/12 -2/45 -21/473 24/7 -2/45 -5/113 31/9 -3/68 7/2 -4/91 -1/23 25/7 -1/23 43/12 -1/23 -24/553 18/5 -1/23 -10/231 11/3 -3/70 37/10 -1/23 -4/93 63/17 -3/70 26/7 -5/117 -2/47 15/4 -2/47 -7/165 34/9 -4/95 -13/309 19/5 -1/24 23/6 -1/23 0/1 50/13 -1/23 0/1 127/33 -1/23 77/20 -1/23 -2/47 27/7 -1/24 4/1 -1/23 0/1 13/3 -1/24 22/5 -6/145 -5/121 53/12 -5/121 -4/97 31/7 -7/170 9/2 -2/49 -1/25 32/7 -2/49 -9/221 55/12 -2/49 -1/25 133/29 -3/74 78/17 -2/49 -1/25 23/5 -3/74 37/8 -11/273 -6/149 14/3 -1/25 -4/101 33/7 -1/26 52/11 -1/27 0/1 19/4 -1/25 -2/51 24/5 -1/29 0/1 53/11 0/1 82/17 -1/9 0/1 29/6 -1/19 0/1 5/1 -1/24 16/3 -6/149 -1/25 27/5 -1/25 38/7 -1/25 -14/351 11/2 -1/25 -4/101 28/5 -1/25 -2/51 17/3 -1/26 23/4 -2/51 -3/77 52/9 -2/51 -3/77 81/14 -2/51 -3/77 191/33 -3/77 110/19 -3/77 -4/103 29/5 -1/26 6/1 -1/27 0/1 25/4 -1/23 0/1 19/3 -3/74 13/2 -1/25 -2/51 7/1 -1/26 15/2 -1/27 0/1 8/1 -1/29 0/1 9/1 -1/26 19/2 -4/107 -1/27 29/3 -1/27 10/1 -1/27 -2/55 1/0 -1/29 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(423,200,184,87) (-1/2,-7/15) -> (39/17,23/10) Hyperbolic Matrix(539,250,774,359) (-7/15,-6/13) -> (16/23,23/33) Hyperbolic Matrix(593,272,944,433) (-6/13,-11/24) -> (5/8,22/35) Hyperbolic Matrix(57,26,-410,-187) (-11/24,-5/11) -> (-1/7,-3/22) Hyperbolic Matrix(1403,634,582,263) (-5/11,-14/31) -> (12/5,41/17) Hyperbolic Matrix(817,368,464,209) (-14/31,-9/20) -> (7/4,30/17) Hyperbolic Matrix(347,156,932,419) (-9/20,-13/29) -> (13/35,3/8) Hyperbolic Matrix(407,182,1098,491) (-13/29,-4/9) -> (10/27,13/35) Hyperbolic Matrix(743,328,632,279) (-4/9,-15/34) -> (7/6,20/17) Hyperbolic Matrix(1031,454,570,251) (-15/34,-11/25) -> (9/5,29/16) Hyperbolic Matrix(173,76,-972,-427) (-11/25,-7/16) -> (-5/28,-3/17) Hyperbolic Matrix(1877,820,396,173) (-7/16,-24/55) -> (52/11,19/4) Hyperbolic Matrix(2723,1188,4316,1883) (-24/55,-17/39) -> (41/65,12/19) Hyperbolic Matrix(395,172,852,371) (-17/39,-10/23) -> (6/13,7/15) Hyperbolic Matrix(167,72,-392,-169) (-10/23,-3/7) -> (-3/7,-14/33) Parabolic Matrix(1165,494,-3054,-1295) (-14/33,-11/26) -> (-29/76,-8/21) Hyperbolic Matrix(4321,1826,1886,797) (-11/26,-30/71) -> (16/7,55/24) Hyperbolic Matrix(999,422,1882,795) (-30/71,-19/45) -> (9/17,8/15) Hyperbolic Matrix(275,116,1164,491) (-19/45,-8/19) -> (4/17,5/21) Hyperbolic Matrix(661,278,554,233) (-8/19,-21/50) -> (19/16,6/5) Hyperbolic Matrix(1821,764,1156,485) (-21/50,-13/31) -> (11/7,41/26) Hyperbolic Matrix(277,116,-1268,-531) (-13/31,-5/12) -> (-7/32,-5/23) Hyperbolic Matrix(327,136,440,183) (-5/12,-17/41) -> (17/23,3/4) Hyperbolic Matrix(1531,634,326,135) (-17/41,-12/29) -> (14/3,33/7) Hyperbolic Matrix(653,270,1202,497) (-12/29,-19/46) -> (13/24,6/11) Hyperbolic Matrix(325,134,-1414,-583) (-19/46,-7/17) -> (-3/13,-11/48) Hyperbolic Matrix(487,200,56,23) (-7/17,-16/39) -> (8/1,9/1) Hyperbolic Matrix(1517,622,978,401) (-16/39,-9/22) -> (31/20,14/9) Hyperbolic Matrix(323,132,1084,443) (-9/22,-11/27) -> (11/37,3/10) Hyperbolic Matrix(271,110,914,371) (-11/27,-2/5) -> (8/27,11/37) Hyperbolic Matrix(583,230,474,187) (-2/5,-11/28) -> (27/22,16/13) Hyperbolic Matrix(1159,454,314,123) (-11/28,-9/23) -> (11/3,37/10) Hyperbolic Matrix(527,206,-1998,-781) (-9/23,-16/41) -> (-14/53,-5/19) Hyperbolic Matrix(945,368,208,81) (-16/41,-7/18) -> (9/2,32/7) Hyperbolic Matrix(259,100,-676,-261) (-7/18,-5/13) -> (-5/13,-13/34) Parabolic Matrix(1555,594,1966,751) (-13/34,-21/55) -> (15/19,19/24) Hyperbolic Matrix(1137,434,-6002,-2291) (-21/55,-29/76) -> (-11/58,-7/37) Hyperbolic Matrix(1757,668,1444,549) (-8/21,-19/50) -> (17/14,28/23) Hyperbolic Matrix(2013,764,772,293) (-19/50,-11/29) -> (13/5,47/18) Hyperbolic Matrix(723,274,-2578,-977) (-11/29,-14/37) -> (-16/57,-7/25) Hyperbolic Matrix(1645,622,722,273) (-14/37,-3/8) -> (41/18,16/7) Hyperbolic Matrix(457,170,-1578,-587) (-3/8,-13/35) -> (-9/31,-11/38) Hyperbolic Matrix(151,56,968,359) (-13/35,-10/27) -> (2/13,3/19) Hyperbolic Matrix(2487,920,1576,583) (-10/27,-17/46) -> (41/26,30/19) Hyperbolic Matrix(2437,900,5884,2173) (-17/46,-24/65) -> (12/29,29/70) Hyperbolic Matrix(1571,580,1980,731) (-24/65,-7/19) -> (23/29,4/5) Hyperbolic Matrix(1925,708,2428,893) (-7/19,-25/68) -> (19/24,23/29) Hyperbolic Matrix(49,18,558,205) (-25/68,-18/49) -> (0/1,1/10) Hyperbolic Matrix(2021,742,1114,409) (-18/49,-11/30) -> (29/16,20/11) Hyperbolic Matrix(1109,406,-3734,-1367) (-11/30,-15/41) -> (-11/37,-19/64) Hyperbolic Matrix(203,74,502,183) (-15/41,-4/11) -> (2/5,11/27) Hyperbolic Matrix(449,162,-1250,-451) (-4/11,-9/25) -> (-9/25,-14/39) Parabolic Matrix(1295,464,2096,751) (-14/39,-5/14) -> (21/34,34/55) Hyperbolic Matrix(647,230,346,123) (-5/14,-11/31) -> (13/7,15/8) Hyperbolic Matrix(1885,668,1188,421) (-11/31,-6/17) -> (46/29,27/17) Hyperbolic Matrix(935,328,248,87) (-6/17,-7/20) -> (15/4,34/9) Hyperbolic Matrix(1819,634,1030,359) (-7/20,-8/23) -> (30/17,53/30) Hyperbolic Matrix(47,16,-144,-49) (-8/23,-1/3) -> (-1/3,-8/25) Parabolic Matrix(801,256,704,225) (-8/25,-7/22) -> (25/22,8/7) Hyperbolic Matrix(1029,326,1594,505) (-7/22,-6/19) -> (20/31,31/48) Hyperbolic Matrix(281,88,744,233) (-6/19,-5/16) -> (3/8,14/37) Hyperbolic Matrix(1113,346,1766,549) (-5/16,-9/29) -> (17/27,29/46) Hyperbolic Matrix(323,100,604,187) (-9/29,-4/13) -> (8/15,7/13) Hyperbolic Matrix(321,98,-1058,-323) (-4/13,-7/23) -> (-7/23,-10/33) Parabolic Matrix(1745,528,1008,305) (-10/33,-3/10) -> (45/26,26/15) Hyperbolic Matrix(455,136,184,55) (-3/10,-11/37) -> (27/11,5/2) Hyperbolic Matrix(3369,1000,2456,729) (-19/64,-8/27) -> (48/35,11/8) Hyperbolic Matrix(1001,296,1816,537) (-8/27,-13/44) -> (11/20,16/29) Hyperbolic Matrix(501,148,44,13) (-13/44,-18/61) -> (10/1,1/0) Hyperbolic Matrix(3133,924,2404,709) (-18/61,-5/17) -> (43/33,30/23) Hyperbolic Matrix(2715,796,2084,611) (-5/17,-17/58) -> (13/10,43/33) Hyperbolic Matrix(5249,1538,2174,637) (-17/58,-12/41) -> (70/29,29/12) Hyperbolic Matrix(1403,410,2214,647) (-12/41,-7/24) -> (19/30,26/41) Hyperbolic Matrix(859,250,134,39) (-7/24,-9/31) -> (19/3,13/2) Hyperbolic Matrix(857,248,584,169) (-11/38,-2/7) -> (22/15,3/2) Hyperbolic Matrix(625,176,1424,401) (-2/7,-9/32) -> (7/16,18/41) Hyperbolic Matrix(3473,976,2224,625) (-9/32,-16/57) -> (64/41,25/16) Hyperbolic Matrix(1467,410,2086,583) (-7/25,-12/43) -> (26/37,19/27) Hyperbolic Matrix(977,272,176,49) (-12/43,-5/18) -> (11/2,28/5) Hyperbolic Matrix(131,36,-484,-133) (-5/18,-3/11) -> (-3/11,-7/26) Parabolic Matrix(305,82,-1618,-435) (-7/26,-11/41) -> (-7/37,-3/16) Hyperbolic Matrix(1485,398,1138,305) (-11/41,-4/15) -> (30/23,17/13) Hyperbolic Matrix(173,46,786,209) (-4/15,-9/34) -> (7/32,2/9) Hyperbolic Matrix(3569,944,2000,529) (-9/34,-14/53) -> (66/37,25/14) Hyperbolic Matrix(1129,296,1560,409) (-5/19,-6/23) -> (34/47,21/29) Hyperbolic Matrix(1037,270,434,113) (-6/23,-1/4) -> (43/18,12/5) Hyperbolic Matrix(715,172,212,51) (-1/4,-5/21) -> (37/11,27/8) Hyperbolic Matrix(839,198,250,59) (-5/21,-4/17) -> (10/3,37/11) Hyperbolic Matrix(753,176,1168,273) (-4/17,-7/30) -> (9/14,20/31) Hyperbolic Matrix(43,10,374,87) (-7/30,-3/13) -> (1/9,1/8) Hyperbolic Matrix(3737,856,1576,361) (-11/48,-8/35) -> (64/27,19/8) Hyperbolic Matrix(913,208,496,113) (-8/35,-5/22) -> (11/6,24/13) Hyperbolic Matrix(247,56,1160,263) (-5/22,-7/31) -> (7/33,3/14) Hyperbolic Matrix(331,74,246,55) (-7/31,-2/9) -> (4/3,23/17) Hyperbolic Matrix(945,208,368,81) (-2/9,-7/32) -> (41/16,18/7) Hyperbolic Matrix(857,186,1350,293) (-5/23,-8/37) -> (26/41,7/11) Hyperbolic Matrix(409,88,488,105) (-8/37,-3/14) -> (5/6,16/19) Hyperbolic Matrix(731,156,164,35) (-3/14,-7/33) -> (31/7,9/2) Hyperbolic Matrix(1379,292,732,155) (-7/33,-11/52) -> (15/8,17/9) Hyperbolic Matrix(1337,282,934,197) (-11/52,-4/19) -> (10/7,43/30) Hyperbolic Matrix(39,8,-200,-41) (-4/19,-1/5) -> (-1/5,-4/21) Parabolic Matrix(3873,736,1184,225) (-4/21,-11/58) -> (85/26,36/11) Hyperbolic Matrix(707,132,316,59) (-3/16,-5/27) -> (29/13,9/4) Hyperbolic Matrix(2983,550,1882,347) (-5/27,-7/38) -> (19/12,65/41) Hyperbolic Matrix(1805,332,1332,245) (-7/38,-2/11) -> (42/31,19/14) Hyperbolic Matrix(977,176,272,49) (-2/11,-5/28) -> (43/12,18/5) Hyperbolic Matrix(387,68,700,123) (-3/17,-4/23) -> (16/29,5/9) Hyperbolic Matrix(427,74,502,87) (-4/23,-1/6) -> (17/20,6/7) Hyperbolic Matrix(723,116,268,43) (-1/6,-3/19) -> (35/13,27/10) Hyperbolic Matrix(607,94,226,35) (-3/19,-2/13) -> (8/3,35/13) Hyperbolic Matrix(301,46,530,81) (-2/13,-3/20) -> (17/30,4/7) Hyperbolic Matrix(375,56,904,135) (-3/20,-1/7) -> (17/41,5/12) Hyperbolic Matrix(1001,136,184,25) (-3/22,-2/15) -> (38/7,11/2) Hyperbolic Matrix(589,78,370,49) (-2/15,-1/8) -> (35/22,8/5) Hyperbolic Matrix(471,56,328,39) (-1/8,-1/9) -> (33/23,23/16) Hyperbolic Matrix(107,10,246,23) (-1/9,0/1) -> (10/23,17/39) Hyperbolic Matrix(261,-28,28,-3) (1/10,1/9) -> (9/1,19/2) Hyperbolic Matrix(197,-26,538,-71) (1/8,1/7) -> (15/41,11/30) Hyperbolic Matrix(223,-34,610,-93) (1/7,2/13) -> (4/11,15/41) Hyperbolic Matrix(1105,-176,496,-79) (3/19,1/6) -> (49/22,29/13) Hyperbolic Matrix(435,-76,1036,-181) (1/6,3/17) -> (13/31,21/50) Hyperbolic Matrix(597,-106,490,-87) (3/17,2/11) -> (28/23,11/9) Hyperbolic Matrix(135,-26,26,-5) (2/11,1/5) -> (5/1,16/3) Hyperbolic Matrix(899,-188,636,-133) (1/5,4/19) -> (24/17,41/29) Hyperbolic Matrix(1823,-386,1346,-285) (4/19,7/33) -> (23/17,42/31) Hyperbolic Matrix(343,-74,394,-85) (3/14,5/23) -> (13/15,7/8) Hyperbolic Matrix(2417,-528,1680,-367) (5/23,7/32) -> (23/16,59/41) Hyperbolic Matrix(79,-18,338,-77) (2/9,3/13) -> (3/13,4/17) Parabolic Matrix(1137,-272,464,-111) (5/21,1/4) -> (49/20,27/11) Hyperbolic Matrix(405,-106,1066,-279) (1/4,5/19) -> (11/29,19/50) Hyperbolic Matrix(431,-114,1138,-301) (5/19,4/15) -> (14/37,11/29) Hyperbolic Matrix(403,-108,556,-149) (4/15,3/11) -> (21/29,8/11) Hyperbolic Matrix(275,-76,76,-21) (3/11,2/7) -> (18/5,11/3) Hyperbolic Matrix(421,-122,1018,-295) (2/7,7/24) -> (19/46,12/29) Hyperbolic Matrix(841,-246,694,-203) (7/24,5/17) -> (23/19,17/14) Hyperbolic Matrix(963,-284,668,-197) (5/17,8/27) -> (36/25,13/9) Hyperbolic Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(307,-110,494,-177) (5/14,4/11) -> (18/29,5/8) Hyperbolic Matrix(725,-266,586,-215) (11/30,7/19) -> (21/17,5/4) Hyperbolic Matrix(1051,-388,772,-285) (7/19,10/27) -> (34/25,15/11) Hyperbolic Matrix(2341,-890,1786,-679) (19/50,8/21) -> (38/29,21/16) Hyperbolic Matrix(555,-212,788,-301) (8/21,5/13) -> (19/27,12/17) Hyperbolic Matrix(299,-116,116,-45) (5/13,2/5) -> (18/7,13/5) Hyperbolic Matrix(2113,-862,478,-195) (11/27,9/22) -> (53/12,31/7) Hyperbolic Matrix(477,-196,1156,-475) (9/22,7/17) -> (7/17,19/46) Parabolic Matrix(7421,-3076,3076,-1275) (29/70,17/41) -> (41/17,111/46) Hyperbolic Matrix(969,-406,790,-331) (5/12,13/31) -> (11/9,27/22) Hyperbolic Matrix(4055,-1704,2344,-985) (21/50,8/19) -> (64/37,45/26) Hyperbolic Matrix(315,-134,134,-57) (8/19,3/7) -> (7/3,26/11) Hyperbolic Matrix(1115,-484,804,-349) (3/7,10/23) -> (18/13,43/31) Hyperbolic Matrix(2205,-962,1538,-671) (17/39,7/16) -> (43/30,33/23) Hyperbolic Matrix(3023,-1328,2224,-977) (18/41,11/25) -> (53/39,34/25) Hyperbolic Matrix(267,-118,310,-137) (11/25,4/9) -> (6/7,13/15) Hyperbolic Matrix(111,-50,242,-109) (4/9,5/11) -> (5/11,6/13) Parabolic Matrix(413,-194,66,-31) (7/15,1/2) -> (25/4,19/3) Hyperbolic Matrix(357,-188,188,-99) (1/2,9/17) -> (17/9,19/10) Hyperbolic Matrix(873,-472,664,-359) (7/13,13/24) -> (21/16,25/19) Hyperbolic Matrix(1945,-1064,744,-407) (6/11,17/31) -> (81/31,34/13) Hyperbolic Matrix(3077,-1690,1178,-647) (17/31,11/20) -> (47/18,81/31) Hyperbolic Matrix(369,-206,206,-115) (5/9,9/16) -> (25/14,9/5) Hyperbolic Matrix(2231,-1258,1002,-565) (9/16,22/39) -> (20/9,49/22) Hyperbolic Matrix(981,-554,1514,-855) (22/39,13/23) -> (11/17,24/37) Hyperbolic Matrix(1043,-590,1614,-913) (13/23,17/30) -> (31/48,11/17) Hyperbolic Matrix(61,-36,100,-59) (4/7,3/5) -> (3/5,8/13) Parabolic Matrix(911,-562,1266,-781) (8/13,21/34) -> (23/32,18/25) Hyperbolic Matrix(1721,-1064,296,-183) (34/55,13/21) -> (29/5,6/1) Hyperbolic Matrix(1423,-882,434,-269) (13/21,18/29) -> (36/11,23/7) Hyperbolic Matrix(983,-618,746,-469) (22/35,17/27) -> (25/19,4/3) Hyperbolic Matrix(10205,-6436,6436,-4059) (29/46,41/65) -> (65/41,111/70) Hyperbolic Matrix(2471,-1562,666,-421) (12/19,31/49) -> (63/17,26/7) Hyperbolic Matrix(3703,-2344,1000,-633) (31/49,19/30) -> (37/10,63/17) Hyperbolic Matrix(429,-274,274,-175) (7/11,9/14) -> (25/16,11/7) Hyperbolic Matrix(2795,-1814,2134,-1385) (24/37,13/20) -> (55/42,38/29) Hyperbolic Matrix(599,-392,136,-89) (13/20,2/3) -> (22/5,53/12) Hyperbolic Matrix(247,-170,170,-117) (2/3,9/13) -> (13/9,16/11) Hyperbolic Matrix(963,-668,284,-197) (9/13,16/23) -> (44/13,17/5) Hyperbolic Matrix(2205,-1538,962,-671) (23/33,7/10) -> (55/24,39/17) Hyperbolic Matrix(827,-580,452,-317) (7/10,26/37) -> (42/23,11/6) Hyperbolic Matrix(899,-636,188,-133) (12/17,17/24) -> (19/4,24/5) Hyperbolic Matrix(281,-200,392,-279) (17/24,5/7) -> (5/7,23/32) Parabolic Matrix(1115,-804,484,-349) (18/25,13/18) -> (23/10,30/13) Hyperbolic Matrix(2117,-1530,1338,-967) (13/18,34/47) -> (68/43,19/12) Hyperbolic Matrix(555,-406,406,-297) (8/11,11/15) -> (15/11,26/19) Hyperbolic Matrix(1051,-772,388,-285) (11/15,14/19) -> (46/17,19/7) Hyperbolic Matrix(1823,-1346,386,-285) (14/19,17/23) -> (33/7,52/11) Hyperbolic Matrix(127,-98,162,-125) (3/4,7/9) -> (7/9,11/14) Parabolic Matrix(1557,-1226,842,-663) (11/14,26/33) -> (24/13,37/20) Hyperbolic Matrix(967,-762,250,-197) (26/33,15/19) -> (27/7,4/1) Hyperbolic Matrix(725,-586,266,-215) (4/5,13/16) -> (49/18,30/11) Hyperbolic Matrix(969,-790,406,-331) (13/16,9/11) -> (31/13,43/18) Hyperbolic Matrix(597,-490,106,-87) (9/11,14/17) -> (28/5,17/3) Hyperbolic Matrix(841,-694,246,-203) (14/17,5/6) -> (41/12,24/7) Hyperbolic Matrix(573,-484,676,-571) (16/19,11/13) -> (11/13,28/33) Parabolic Matrix(1799,-1528,312,-265) (28/33,17/20) -> (23/4,52/9) Hyperbolic Matrix(17,-16,16,-15) (7/8,1/1) -> (1/1,9/8) Parabolic Matrix(511,-578,450,-509) (9/8,17/15) -> (17/15,25/22) Parabolic Matrix(343,-394,74,-85) (8/7,7/6) -> (37/8,14/3) Hyperbolic Matrix(573,-676,484,-571) (20/17,13/11) -> (13/11,32/27) Parabolic Matrix(3265,-3872,1888,-2239) (32/27,19/16) -> (83/48,64/37) Hyperbolic Matrix(1187,-1436,348,-421) (6/5,23/19) -> (17/5,58/17) Hyperbolic Matrix(1403,-1732,516,-637) (16/13,21/17) -> (19/7,68/25) Hyperbolic Matrix(127,-162,98,-125) (5/4,9/7) -> (9/7,13/10) Parabolic Matrix(2135,-2794,554,-725) (17/13,55/42) -> (77/20,27/7) Hyperbolic Matrix(4531,-6156,3148,-4277) (19/14,53/39) -> (59/41,95/66) Hyperbolic Matrix(1999,-2738,1458,-1997) (26/19,37/27) -> (37/27,48/35) Parabolic Matrix(403,-556,108,-149) (11/8,18/13) -> (26/7,15/4) Hyperbolic Matrix(1273,-1766,550,-763) (43/31,25/18) -> (37/16,7/3) Hyperbolic Matrix(629,-874,362,-503) (25/18,7/5) -> (33/19,7/4) Hyperbolic Matrix(691,-974,398,-561) (7/5,24/17) -> (26/15,33/19) Hyperbolic Matrix(901,-1274,186,-263) (41/29,17/12) -> (29/6,5/1) Hyperbolic Matrix(555,-788,212,-301) (17/12,10/7) -> (34/13,21/8) Hyperbolic Matrix(5457,-7856,944,-1359) (95/66,36/25) -> (52/9,81/14) Hyperbolic Matrix(495,-722,338,-493) (16/11,19/13) -> (19/13,22/15) Parabolic Matrix(681,-1046,278,-427) (3/2,20/13) -> (22/9,49/20) Hyperbolic Matrix(981,-1514,554,-855) (20/13,17/11) -> (23/13,62/35) Hyperbolic Matrix(1043,-1614,590,-913) (17/11,31/20) -> (53/30,23/13) Hyperbolic Matrix(1951,-3042,1250,-1949) (14/9,39/25) -> (39/25,64/41) Parabolic Matrix(3039,-4802,1922,-3037) (30/19,49/31) -> (49/31,68/43) Parabolic Matrix(10989,-17426,3218,-5103) (111/70,46/29) -> (140/41,41/12) Hyperbolic Matrix(915,-1454,494,-785) (27/17,35/22) -> (37/20,13/7) Hyperbolic Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic Matrix(271,-466,82,-141) (12/7,19/11) -> (23/7,10/3) Hyperbolic Matrix(6989,-12084,1524,-2635) (19/11,83/48) -> (55/12,133/29) Hyperbolic Matrix(1905,-3376,496,-879) (62/35,39/22) -> (23/6,50/13) Hyperbolic Matrix(357,-634,58,-103) (39/22,16/9) -> (6/1,25/4) Hyperbolic Matrix(1887,-3362,1058,-1885) (16/9,41/23) -> (41/23,66/37) Parabolic Matrix(1055,-1922,578,-1053) (20/11,31/17) -> (31/17,42/23) Parabolic Matrix(1709,-3252,628,-1195) (19/10,2/1) -> (166/61,49/18) Hyperbolic Matrix(111,-242,50,-109) (2/1,11/5) -> (11/5,20/9) Parabolic Matrix(499,-1132,108,-245) (9/4,25/11) -> (23/5,37/8) Hyperbolic Matrix(1611,-3668,596,-1357) (25/11,41/18) -> (27/10,73/27) Hyperbolic Matrix(667,-1540,68,-157) (30/13,67/29) -> (29/3,10/1) Hyperbolic Matrix(1015,-2346,106,-245) (67/29,37/16) -> (19/2,29/3) Hyperbolic Matrix(1711,-4050,722,-1709) (26/11,45/19) -> (45/19,64/27) Parabolic Matrix(435,-1036,76,-181) (19/8,31/13) -> (17/3,23/4) Hyperbolic Matrix(4613,-11132,956,-2307) (111/46,70/29) -> (82/17,29/6) Hyperbolic Matrix(421,-1018,122,-295) (29/12,17/7) -> (31/9,7/2) Hyperbolic Matrix(447,-1090,130,-317) (17/7,22/9) -> (24/7,31/9) Hyperbolic Matrix(415,-1058,162,-413) (5/2,23/9) -> (23/9,41/16) Parabolic Matrix(405,-1066,106,-279) (21/8,29/11) -> (19/5,23/6) Hyperbolic Matrix(431,-1138,114,-301) (29/11,8/3) -> (34/9,19/5) Hyperbolic Matrix(2497,-6752,544,-1471) (73/27,46/17) -> (78/17,23/5) Hyperbolic Matrix(10063,-27378,3698,-10061) (68/25,117/43) -> (117/43,166/61) Parabolic Matrix(197,-538,26,-71) (30/11,11/4) -> (15/2,8/1) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(1471,-4802,450,-1469) (13/4,49/15) -> (49/15,85/26) Parabolic Matrix(971,-3284,212,-717) (27/8,44/13) -> (32/7,55/12) Hyperbolic Matrix(5743,-19602,1682,-5741) (58/17,99/29) -> (99/29,140/41) Parabolic Matrix(351,-1250,98,-349) (7/2,25/7) -> (25/7,43/12) Parabolic Matrix(6113,-23520,1056,-4063) (50/13,127/33) -> (191/33,110/19) Hyperbolic Matrix(6493,-24994,1122,-4319) (127/33,77/20) -> (81/14,191/33) Hyperbolic Matrix(79,-338,18,-77) (4/1,13/3) -> (13/3,22/5) Parabolic Matrix(3683,-16892,636,-2917) (133/29,78/17) -> (110/19,29/5) Hyperbolic Matrix(1167,-5618,242,-1165) (24/5,53/11) -> (53/11,82/17) Parabolic Matrix(271,-1458,50,-269) (16/3,27/5) -> (27/5,38/7) Parabolic Matrix(29,-196,4,-27) (13/2,7/1) -> (7/1,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,60,1) Matrix(423,200,184,87) -> Matrix(57,-2,-1168,41) Matrix(539,250,774,359) -> Matrix(163,-6,-1820,67) Matrix(593,272,944,433) -> Matrix(219,-8,-2272,83) Matrix(57,26,-410,-187) -> Matrix(53,-2,292,-11) Matrix(1403,634,582,263) -> Matrix(1,0,-48,1) Matrix(817,368,464,209) -> Matrix(105,-4,-1916,73) Matrix(347,156,932,419) -> Matrix(105,-4,-656,25) Matrix(407,182,1098,491) -> Matrix(51,-2,-280,11) Matrix(743,328,632,279) -> Matrix(257,-10,-3932,153) Matrix(1031,454,570,251) -> Matrix(1,0,-44,1) Matrix(173,76,-972,-427) -> Matrix(151,-6,1032,-41) Matrix(1877,820,396,173) -> Matrix(49,-2,-1200,49) Matrix(2723,1188,4316,1883) -> Matrix(99,-4,-1064,43) Matrix(395,172,852,371) -> Matrix(145,-6,-1184,49) Matrix(167,72,-392,-169) -> Matrix(49,-2,1152,-47) Matrix(1165,494,-3054,-1295) -> Matrix(49,-2,956,-39) Matrix(4321,1826,1886,797) -> Matrix(1,0,-44,1) Matrix(999,422,1882,795) -> Matrix(185,-8,-1688,73) Matrix(275,116,1164,491) -> Matrix(49,-2,-220,9) Matrix(661,278,554,233) -> Matrix(281,-12,-4332,185) Matrix(1821,764,1156,485) -> Matrix(233,-10,-4124,177) Matrix(277,116,-1268,-531) -> Matrix(231,-10,2056,-89) Matrix(327,136,440,183) -> Matrix(181,-8,-2104,93) Matrix(1531,634,326,135) -> Matrix(1,0,-48,1) Matrix(653,270,1202,497) -> Matrix(1,0,-32,1) Matrix(325,134,-1414,-583) -> Matrix(89,-4,868,-39) Matrix(487,200,56,23) -> Matrix(45,-2,-1192,53) Matrix(1517,622,978,401) -> Matrix(359,-16,-6260,279) Matrix(323,132,1084,443) -> Matrix(89,-4,-556,25) Matrix(271,110,914,371) -> Matrix(131,-6,-764,35) Matrix(583,230,474,187) -> Matrix(291,-14,-4552,219) Matrix(1159,454,314,123) -> Matrix(1,0,-44,1) Matrix(527,206,-1998,-781) -> Matrix(247,-12,2820,-137) Matrix(945,368,208,81) -> Matrix(81,-4,-1964,97) Matrix(259,100,-676,-261) -> Matrix(121,-6,2400,-119) Matrix(1555,594,1966,751) -> Matrix(81,-4,-992,49) Matrix(1137,434,-6002,-2291) -> Matrix(79,-4,652,-33) Matrix(1757,668,1444,549) -> Matrix(391,-20,-6080,311) Matrix(2013,764,772,293) -> Matrix(197,-10,-4196,213) Matrix(723,274,-2578,-977) -> Matrix(391,-20,4868,-249) Matrix(1645,622,722,273) -> Matrix(311,-16,-6356,327) Matrix(457,170,-1578,-587) -> Matrix(341,-18,4452,-235) Matrix(151,56,968,359) -> Matrix(113,-6,-320,17) Matrix(2487,920,1576,583) -> Matrix(263,-14,-4640,247) Matrix(2437,900,5884,2173) -> Matrix(75,-4,-656,35) Matrix(1571,580,1980,731) -> Matrix(411,-22,-4988,267) Matrix(1925,708,2428,893) -> Matrix(299,-16,-3644,195) Matrix(49,18,558,205) -> Matrix(37,-2,56,-3) Matrix(2021,742,1114,409) -> Matrix(223,-12,-4144,223) Matrix(1109,406,-3734,-1367) -> Matrix(665,-36,8996,-487) Matrix(203,74,502,183) -> Matrix(147,-8,-1084,59) Matrix(449,162,-1250,-451) -> Matrix(253,-14,4536,-251) Matrix(1295,464,2096,751) -> Matrix(71,-4,-692,39) Matrix(647,230,346,123) -> Matrix(247,-14,-4640,263) Matrix(1885,668,1188,421) -> Matrix(351,-20,-6160,351) Matrix(935,328,248,87) -> Matrix(173,-10,-4100,237) Matrix(1819,634,1030,359) -> Matrix(445,-26,-8164,477) Matrix(47,16,-144,-49) -> Matrix(33,-2,512,-31) Matrix(801,256,704,225) -> Matrix(451,-30,-6780,451) Matrix(1029,326,1594,505) -> Matrix(475,-32,-5032,339) Matrix(281,88,744,233) -> Matrix(175,-12,-1152,79) Matrix(1113,346,1766,549) -> Matrix(289,-20,-3020,209) Matrix(323,100,604,187) -> Matrix(201,-14,-1852,129) Matrix(321,98,-1058,-323) -> Matrix(197,-14,2744,-195) Matrix(1745,528,1008,305) -> Matrix(55,-4,-976,71) Matrix(455,136,184,55) -> Matrix(109,-8,-2248,165) Matrix(3369,1000,2456,729) -> Matrix(1189,-88,-19632,1453) Matrix(1001,296,1816,537) -> Matrix(161,-12,-1516,113) Matrix(501,148,44,13) -> Matrix(27,-2,-796,59) Matrix(3133,924,2404,709) -> Matrix(347,-26,-5592,419) Matrix(2715,796,2084,611) -> Matrix(267,-20,-4312,323) Matrix(5249,1538,2174,637) -> Matrix(53,-4,-1020,77) Matrix(1403,410,2214,647) -> Matrix(185,-14,-1916,145) Matrix(859,250,134,39) -> Matrix(79,-6,-1988,151) Matrix(857,248,584,169) -> Matrix(339,-26,-5776,443) Matrix(625,176,1424,401) -> Matrix(201,-16,-1520,121) Matrix(3473,976,2224,625) -> Matrix(901,-72,-15780,1261) Matrix(1467,410,2086,583) -> Matrix(173,-14,-1940,157) Matrix(977,272,176,49) -> Matrix(99,-8,-2512,203) Matrix(131,36,-484,-133) -> Matrix(73,-6,864,-71) Matrix(305,82,-1618,-435) -> Matrix(23,-2,196,-17) Matrix(1485,398,1138,305) -> Matrix(49,-4,-796,65) Matrix(173,46,786,209) -> Matrix(47,-4,-176,15) Matrix(3569,944,2000,529) -> Matrix(645,-56,-11944,1037) Matrix(1129,296,1560,409) -> Matrix(137,-12,-1564,137) Matrix(1037,270,434,113) -> Matrix(1,0,-32,1) Matrix(715,172,212,51) -> Matrix(61,-6,-1352,133) Matrix(839,198,250,59) -> Matrix(39,-4,-848,87) Matrix(753,176,1168,273) -> Matrix(153,-16,-1616,169) Matrix(43,10,374,87) -> Matrix(19,-2,-28,3) Matrix(3737,856,1576,361) -> Matrix(229,-24,-4704,493) Matrix(913,208,496,113) -> Matrix(1,0,-28,1) Matrix(247,56,1160,263) -> Matrix(1,0,-12,1) Matrix(331,74,246,55) -> Matrix(75,-8,-1228,131) Matrix(945,208,368,81) -> Matrix(163,-18,-3432,379) Matrix(857,186,1350,293) -> Matrix(87,-10,-896,103) Matrix(409,88,488,105) -> Matrix(103,-12,-1296,151) Matrix(731,156,164,35) -> Matrix(33,-4,-800,97) Matrix(1379,292,732,155) -> Matrix(71,-8,-1340,151) Matrix(1337,282,934,197) -> Matrix(53,-6,-892,101) Matrix(39,8,-200,-41) -> Matrix(17,-2,128,-15) Matrix(3873,736,1184,225) -> Matrix(1,0,-28,1) Matrix(707,132,316,59) -> Matrix(33,-4,-668,81) Matrix(2983,550,1882,347) -> Matrix(29,-4,-500,69) Matrix(1805,332,1332,245) -> Matrix(119,-16,-1956,263) Matrix(977,176,272,49) -> Matrix(99,-14,-2284,323) Matrix(387,68,700,123) -> Matrix(1,0,-16,1) Matrix(427,74,502,87) -> Matrix(63,-10,-800,127) Matrix(723,116,268,43) -> Matrix(13,-2,-292,45) Matrix(607,94,226,35) -> Matrix(23,-4,-500,87) Matrix(301,46,530,81) -> Matrix(23,-4,-224,39) Matrix(375,56,904,135) -> Matrix(1,0,-12,1) Matrix(1001,136,184,25) -> Matrix(51,-10,-1280,251) Matrix(589,78,370,49) -> Matrix(37,-8,-652,141) Matrix(471,56,328,39) -> Matrix(29,-6,-488,101) Matrix(107,10,246,23) -> Matrix(7,-2,-52,15) Matrix(261,-28,28,-3) -> Matrix(3,2,-80,-53) Matrix(197,-26,538,-71) -> Matrix(3,2,-20,-13) Matrix(223,-34,610,-93) -> Matrix(1,0,-4,1) Matrix(1105,-176,496,-79) -> Matrix(31,8,-624,-161) Matrix(435,-76,1036,-181) -> Matrix(11,4,-80,-29) Matrix(597,-106,490,-87) -> Matrix(29,12,-452,-187) Matrix(135,-26,26,-5) -> Matrix(7,2,-172,-49) Matrix(899,-188,636,-133) -> Matrix(5,4,-84,-67) Matrix(1823,-386,1346,-285) -> Matrix(1,-2,-16,33) Matrix(343,-74,394,-85) -> Matrix(31,10,-400,-129) Matrix(2417,-528,1680,-367) -> Matrix(109,32,-1836,-539) Matrix(79,-18,338,-77) -> Matrix(23,6,-96,-25) Matrix(1137,-272,464,-111) -> Matrix(1,0,-16,1) Matrix(405,-106,1066,-279) -> Matrix(13,4,-88,-27) Matrix(431,-114,1138,-301) -> Matrix(59,14,-392,-93) Matrix(403,-108,556,-149) -> Matrix(55,12,-628,-137) Matrix(275,-76,76,-21) -> Matrix(29,6,-672,-139) Matrix(421,-122,1018,-295) -> Matrix(11,2,-72,-13) Matrix(841,-246,694,-203) -> Matrix(131,24,-2036,-373) Matrix(963,-284,668,-197) -> Matrix(125,22,-2108,-371) Matrix(25,-8,72,-23) -> Matrix(11,2,-72,-13) Matrix(307,-110,494,-177) -> Matrix(11,2,-116,-21) Matrix(725,-266,586,-215) -> Matrix(67,10,-1052,-157) Matrix(1051,-388,772,-285) -> Matrix(7,2,-116,-33) Matrix(2341,-890,1786,-679) -> Matrix(93,14,-1508,-227) Matrix(555,-212,788,-301) -> Matrix(55,8,-612,-89) Matrix(299,-116,116,-45) -> Matrix(69,10,-1456,-211) Matrix(2113,-862,478,-195) -> Matrix(47,6,-1136,-145) Matrix(477,-196,1156,-475) -> Matrix(15,2,-128,-17) Matrix(7421,-3076,3076,-1275) -> Matrix(1,0,-16,1) Matrix(969,-406,790,-331) -> Matrix(101,14,-1580,-219) Matrix(4055,-1704,2344,-985) -> Matrix(29,4,-544,-75) Matrix(315,-134,134,-57) -> Matrix(31,4,-628,-81) Matrix(1115,-484,804,-349) -> Matrix(89,12,-1476,-199) Matrix(2205,-962,1538,-671) -> Matrix(43,6,-724,-101) Matrix(3023,-1328,2224,-977) -> Matrix(151,20,-2484,-329) Matrix(267,-118,310,-137) -> Matrix(123,16,-1576,-205) Matrix(111,-50,242,-109) -> Matrix(79,10,-640,-81) Matrix(413,-194,66,-31) -> Matrix(17,2,-400,-47) Matrix(357,-188,188,-99) -> Matrix(163,18,-3088,-341) Matrix(873,-472,664,-359) -> Matrix(149,16,-2412,-259) Matrix(1945,-1064,744,-407) -> Matrix(1,0,-12,1) Matrix(3077,-1690,1178,-647) -> Matrix(169,18,-3596,-383) Matrix(369,-206,206,-115) -> Matrix(113,12,-2100,-223) Matrix(2231,-1258,1002,-565) -> Matrix(403,42,-8108,-845) Matrix(981,-554,1514,-855) -> Matrix(39,4,-400,-41) Matrix(1043,-590,1614,-913) -> Matrix(327,34,-3472,-361) Matrix(61,-36,100,-59) -> Matrix(59,6,-600,-61) Matrix(911,-562,1266,-781) -> Matrix(43,4,-484,-45) Matrix(1721,-1064,296,-183) -> Matrix(61,6,-1576,-155) Matrix(1423,-882,434,-269) -> Matrix(41,4,-892,-87) Matrix(983,-618,746,-469) -> Matrix(291,28,-4708,-453) Matrix(10205,-6436,6436,-4059) -> Matrix(295,28,-5152,-489) Matrix(2471,-1562,666,-421) -> Matrix(43,4,-1000,-93) Matrix(3703,-2344,1000,-633) -> Matrix(103,10,-2400,-233) Matrix(429,-274,274,-175) -> Matrix(209,20,-3668,-351) Matrix(2795,-1814,2134,-1385) -> Matrix(213,20,-3440,-323) Matrix(599,-392,136,-89) -> Matrix(149,14,-3608,-339) Matrix(247,-170,170,-117) -> Matrix(199,18,-3372,-305) Matrix(963,-668,284,-197) -> Matrix(245,22,-5468,-491) Matrix(2205,-1538,962,-671) -> Matrix(67,6,-1396,-125) Matrix(827,-580,452,-317) -> Matrix(89,8,-1680,-151) Matrix(899,-636,188,-133) -> Matrix(45,4,-1204,-107) Matrix(281,-200,392,-279) -> Matrix(203,18,-2312,-205) Matrix(1115,-804,484,-349) -> Matrix(137,12,-2820,-247) Matrix(2117,-1530,1338,-967) -> Matrix(91,8,-1604,-141) Matrix(555,-406,406,-297) -> Matrix(415,36,-6836,-593) Matrix(1051,-772,388,-285) -> Matrix(23,2,-564,-49) Matrix(1823,-1346,386,-285) -> Matrix(23,2,-656,-57) Matrix(127,-98,162,-125) -> Matrix(167,14,-2016,-169) Matrix(1557,-1226,842,-663) -> Matrix(315,26,-5876,-485) Matrix(967,-762,250,-197) -> Matrix(97,8,-2316,-191) Matrix(725,-586,266,-215) -> Matrix(123,10,-2620,-213) Matrix(969,-790,406,-331) -> Matrix(173,14,-3596,-291) Matrix(597,-490,106,-87) -> Matrix(149,12,-3812,-307) Matrix(841,-694,246,-203) -> Matrix(299,24,-6740,-541) Matrix(573,-484,676,-571) -> Matrix(683,54,-8664,-685) Matrix(1799,-1528,312,-265) -> Matrix(203,16,-5240,-413) Matrix(17,-16,16,-15) -> Matrix(27,2,-392,-29) Matrix(511,-578,450,-509) -> Matrix(899,60,-13500,-901) Matrix(343,-394,74,-85) -> Matrix(151,10,-3760,-249) Matrix(573,-676,484,-571) -> Matrix(827,54,-12696,-829) Matrix(3265,-3872,1888,-2239) -> Matrix(31,2,-512,-33) Matrix(1187,-1436,348,-421) -> Matrix(683,44,-15352,-989) Matrix(1403,-1732,516,-637) -> Matrix(251,16,-5224,-333) Matrix(127,-162,98,-125) -> Matrix(223,14,-3584,-225) Matrix(2135,-2794,554,-725) -> Matrix(129,8,-3080,-191) Matrix(4531,-6156,3148,-4277) -> Matrix(723,44,-12176,-741) Matrix(1999,-2738,1458,-1997) -> Matrix(2903,176,-47916,-2905) Matrix(403,-556,108,-149) -> Matrix(199,12,-4660,-281) Matrix(1273,-1766,550,-763) -> Matrix(33,2,-776,-47) Matrix(629,-874,362,-503) -> Matrix(233,14,-4244,-255) Matrix(691,-974,398,-561) -> Matrix(133,8,-2444,-147) Matrix(901,-1274,186,-263) -> Matrix(67,4,-1424,-85) Matrix(555,-788,212,-301) -> Matrix(135,8,-2852,-169) Matrix(5457,-7856,944,-1359) -> Matrix(135,8,-3392,-201) Matrix(495,-722,338,-493) -> Matrix(883,52,-15028,-885) Matrix(681,-1046,278,-427) -> Matrix(69,4,-1432,-83) Matrix(981,-1514,554,-855) -> Matrix(71,4,-1296,-73) Matrix(1043,-1614,590,-913) -> Matrix(591,34,-10864,-625) Matrix(1951,-3042,1250,-1949) -> Matrix(2519,144,-44100,-2521) Matrix(3039,-4802,1922,-3037) -> Matrix(35,2,-648,-37) Matrix(10989,-17426,3218,-5103) -> Matrix(1889,108,-42520,-2431) Matrix(915,-1454,494,-785) -> Matrix(71,4,-1296,-73) Matrix(61,-100,36,-59) -> Matrix(107,6,-1944,-109) Matrix(271,-466,82,-141) -> Matrix(37,2,-796,-43) Matrix(6989,-12084,1524,-2635) -> Matrix(147,8,-3620,-197) Matrix(1905,-3376,496,-879) -> Matrix(37,2,-796,-43) Matrix(357,-634,58,-103) -> Matrix(37,2,-796,-43) Matrix(1887,-3362,1058,-1885) -> Matrix(2071,112,-38332,-2073) Matrix(1055,-1922,578,-1053) -> Matrix(335,18,-6272,-337) Matrix(1709,-3252,628,-1195) -> Matrix(569,30,-11968,-631) Matrix(111,-242,50,-109) -> Matrix(199,10,-4000,-201) Matrix(499,-1132,108,-245) -> Matrix(285,14,-7064,-347) Matrix(1611,-3668,596,-1357) -> Matrix(41,2,-800,-39) Matrix(667,-1540,68,-157) -> Matrix(125,6,-3396,-163) Matrix(1015,-2346,106,-245) -> Matrix(127,6,-3408,-161) Matrix(1711,-4050,722,-1709) -> Matrix(983,48,-20172,-985) Matrix(435,-1036,76,-181) -> Matrix(83,4,-2096,-101) Matrix(4613,-11132,956,-2307) -> Matrix(1,0,8,1) Matrix(421,-1018,122,-295) -> Matrix(43,2,-968,-45) Matrix(447,-1090,130,-317) -> Matrix(163,8,-3688,-181) Matrix(415,-1058,162,-413) -> Matrix(755,36,-15876,-757) Matrix(405,-1066,106,-279) -> Matrix(85,4,-2104,-99) Matrix(431,-1138,114,-301) -> Matrix(299,14,-7112,-333) Matrix(2497,-6752,544,-1471) -> Matrix(47,2,-1152,-49) Matrix(10063,-27378,3698,-10061) -> Matrix(923,44,-19404,-925) Matrix(197,-538,26,-71) -> Matrix(43,2,-1140,-53) Matrix(25,-72,8,-23) -> Matrix(43,2,-968,-45) Matrix(1471,-4802,450,-1469) -> Matrix(1,0,4,1) Matrix(971,-3284,212,-717) -> Matrix(311,14,-7664,-345) Matrix(5743,-19602,1682,-5741) -> Matrix(4679,208,-105300,-4681) Matrix(351,-1250,98,-349) -> Matrix(643,28,-14812,-645) Matrix(6113,-23520,1056,-4063) -> Matrix(89,4,-2292,-103) Matrix(6493,-24994,1122,-4319) -> Matrix(187,8,-4792,-205) Matrix(79,-338,18,-77) -> Matrix(143,6,-3456,-145) Matrix(3683,-16892,636,-2917) -> Matrix(247,10,-6348,-257) Matrix(1167,-5618,242,-1165) -> Matrix(1,0,20,1) Matrix(271,-1458,50,-269) -> Matrix(499,20,-12500,-501) Matrix(29,-196,4,-27) -> Matrix(51,2,-1352,-53) 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): 64 Degree of the the map X: 128 Degree of the the map Y: 256 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 384 Minimal number of generators: 65 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 32 Genus: 17 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/7 1/3 3/5 5/7 1/1 9/7 37/27 19/13 5/3 31/17 2/1 11/5 7/3 45/19 23/9 13/5 19/7 3/1 49/15 23/7 17/5 25/7 11/3 4/1 13/3 5/1 27/5 17/3 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 0/1 1/1 1/7 -1/2 2/13 -2/5 -1/3 1/6 -1/1 0/1 2/11 -4/11 -1/3 1/5 -1/4 1/4 -1/5 0/1 3/11 -3/14 2/7 -1/5 -4/21 5/17 -5/28 3/10 -1/5 0/1 1/3 -1/6 5/14 -2/13 -1/7 4/11 -2/13 -1/7 7/19 -1/8 3/8 -3/19 -2/13 5/13 -5/34 2/5 -1/7 -4/29 9/22 -1/7 -2/15 7/17 -1/8 5/12 -1/7 -4/29 8/19 -5/37 -2/15 3/7 -1/8 1/2 -2/17 -1/9 6/11 -1/9 -4/37 5/9 -3/28 4/7 -2/19 -3/29 3/5 -1/10 8/13 -4/41 -3/31 21/34 -1/11 0/1 13/21 -1/10 18/29 -4/41 -3/31 5/8 -4/41 -3/31 12/19 -3/31 -2/21 7/11 -5/52 2/3 -4/43 -1/11 9/13 -9/100 16/23 -6/67 -11/123 7/10 -1/11 -4/45 12/17 -9/101 -4/45 17/24 -7/79 -10/113 5/7 -3/34 23/32 -1/11 -4/45 18/25 -8/91 -5/57 13/18 -1/11 -2/23 8/11 -13/149 -2/23 11/15 -9/104 14/19 -2/23 -3/35 3/4 -3/35 -4/47 1/1 -1/14 5/4 -4/63 -5/79 9/7 -1/16 13/10 -10/161 -9/145 17/13 -1/16 4/3 -4/65 -3/49 15/11 -9/148 26/19 -31/511 -2/33 37/27 -2/33 11/8 -2/33 -13/215 18/13 -2/33 -1/17 7/5 -3/50 17/12 -4/67 -9/151 10/7 -4/67 -1/17 13/9 -9/152 16/11 -22/373 -1/17 19/13 -1/17 3/2 -1/17 -4/69 11/7 -5/88 30/19 -2/35 -3/53 49/31 -1/18 19/12 -2/35 -3/53 8/5 -3/53 -4/71 5/3 -1/18 12/7 -3/55 -2/37 19/11 -1/18 26/15 -6/109 -5/91 7/4 -3/55 -2/37 9/5 -3/56 20/11 -2/37 -5/93 31/17 -3/56 11/6 -4/75 -1/19 2/1 -1/19 -2/39 11/5 -1/20 20/9 -9/181 -8/161 9/4 -5/101 -4/81 7/3 -1/20 26/11 -7/143 -2/41 45/19 -2/41 19/8 -2/41 -5/103 31/13 -3/62 12/5 -4/83 -1/21 17/7 -1/20 22/9 -2/41 -1/21 5/2 -4/83 -1/21 23/9 -1/21 18/7 -1/21 -14/295 13/5 -5/106 8/3 -2/43 -3/65 27/10 -2/45 -1/23 19/7 -1/20 30/11 -5/107 -2/43 11/4 -1/21 -2/43 3/1 -1/22 13/4 -1/23 0/1 49/15 0/1 36/11 -1/21 0/1 23/7 -1/22 10/3 -1/23 0/1 27/8 -5/111 -4/89 17/5 -5/112 24/7 -2/45 -5/113 7/2 -4/91 -1/23 25/7 -1/23 18/5 -1/23 -10/231 11/3 -3/70 4/1 -1/23 0/1 13/3 -1/24 22/5 -6/145 -5/121 9/2 -2/49 -1/25 5/1 -1/24 16/3 -6/149 -1/25 27/5 -1/25 11/2 -1/25 -4/101 17/3 -1/26 23/4 -2/51 -3/77 6/1 -1/27 0/1 13/2 -1/25 -2/51 7/1 -1/26 1/0 -1/29 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(42,-5,101,-12) (0/1,1/7) -> (7/17,5/12) Hyperbolic Matrix(154,-23,375,-56) (1/7,2/13) -> (9/22,7/17) Hyperbolic Matrix(250,-39,359,-56) (2/13,1/6) -> (16/23,7/10) Hyperbolic Matrix(259,-46,366,-65) (1/6,2/11) -> (12/17,17/24) Hyperbolic Matrix(135,-26,26,-5) (2/11,1/5) -> (5/1,16/3) Hyperbolic Matrix(65,-14,14,-3) (1/5,1/4) -> (9/2,5/1) Hyperbolic Matrix(64,-17,113,-30) (1/4,3/11) -> (5/9,4/7) Hyperbolic Matrix(275,-76,76,-21) (3/11,2/7) -> (18/5,11/3) Hyperbolic Matrix(335,-98,482,-141) (2/7,5/17) -> (9/13,16/23) Hyperbolic Matrix(629,-186,186,-55) (5/17,3/10) -> (27/8,17/5) Hyperbolic Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(307,-110,494,-177) (5/14,4/11) -> (18/29,5/8) Hyperbolic Matrix(387,-142,526,-193) (4/11,7/19) -> (11/15,14/19) Hyperbolic Matrix(665,-246,246,-91) (7/19,3/8) -> (27/10,19/7) Hyperbolic Matrix(82,-31,127,-48) (3/8,5/13) -> (7/11,2/3) Hyperbolic Matrix(299,-116,116,-45) (5/13,2/5) -> (18/7,13/5) Hyperbolic Matrix(136,-55,183,-74) (2/5,9/22) -> (14/19,3/4) Hyperbolic Matrix(463,-194,642,-269) (5/12,8/19) -> (18/25,13/18) Hyperbolic Matrix(315,-134,134,-57) (8/19,3/7) -> (7/3,26/11) Hyperbolic Matrix(77,-34,34,-15) (3/7,1/2) -> (9/4,7/3) Hyperbolic Matrix(114,-61,157,-84) (1/2,6/11) -> (13/18,8/11) Hyperbolic Matrix(279,-154,154,-85) (6/11,5/9) -> (9/5,20/11) Hyperbolic Matrix(61,-36,100,-59) (4/7,3/5) -> (3/5,8/13) Parabolic Matrix(911,-562,1266,-781) (8/13,21/34) -> (23/32,18/25) Hyperbolic Matrix(662,-409,505,-312) (21/34,13/21) -> (17/13,4/3) Hyperbolic Matrix(1423,-882,434,-269) (13/21,18/29) -> (36/11,23/7) Hyperbolic Matrix(284,-179,403,-254) (5/8,12/19) -> (7/10,12/17) Hyperbolic Matrix(539,-342,342,-217) (12/19,7/11) -> (11/7,30/19) Hyperbolic Matrix(247,-170,170,-117) (2/3,9/13) -> (13/9,16/11) Hyperbolic Matrix(281,-200,392,-279) (17/24,5/7) -> (5/7,23/32) Parabolic Matrix(555,-406,406,-297) (8/11,11/15) -> (15/11,26/19) Hyperbolic Matrix(9,-8,8,-7) (3/4,1/1) -> (1/1,5/4) Parabolic Matrix(127,-162,98,-125) (5/4,9/7) -> (9/7,13/10) Parabolic Matrix(528,-689,305,-398) (13/10,17/13) -> (19/11,26/15) Hyperbolic Matrix(387,-526,142,-193) (4/3,15/11) -> (19/7,30/11) Hyperbolic Matrix(1000,-1369,729,-998) (26/19,37/27) -> (37/27,11/8) Parabolic Matrix(114,-157,61,-84) (11/8,18/13) -> (11/6,2/1) Hyperbolic Matrix(463,-642,194,-269) (18/13,7/5) -> (31/13,12/5) Hyperbolic Matrix(259,-366,46,-65) (7/5,17/12) -> (11/2,17/3) Hyperbolic Matrix(284,-403,179,-254) (17/12,10/7) -> (19/12,8/5) Hyperbolic Matrix(335,-482,98,-141) (10/7,13/9) -> (17/5,24/7) Hyperbolic Matrix(248,-361,169,-246) (16/11,19/13) -> (19/13,3/2) Parabolic Matrix(82,-127,31,-48) (3/2,11/7) -> (13/5,8/3) Hyperbolic Matrix(930,-1469,509,-804) (30/19,49/31) -> (31/17,11/6) Hyperbolic Matrix(992,-1569,545,-862) (49/31,19/12) -> (20/11,31/17) Hyperbolic Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic Matrix(271,-466,82,-141) (12/7,19/11) -> (23/7,10/3) Hyperbolic Matrix(369,-640,64,-111) (26/15,7/4) -> (23/4,6/1) Hyperbolic Matrix(64,-113,17,-30) (7/4,9/5) -> (11/3,4/1) Hyperbolic Matrix(111,-242,50,-109) (2/1,11/5) -> (11/5,20/9) Parabolic Matrix(198,-443,59,-132) (20/9,9/4) -> (10/3,27/8) Hyperbolic Matrix(856,-2025,361,-854) (26/11,45/19) -> (45/19,19/8) Parabolic Matrix(435,-1036,76,-181) (19/8,31/13) -> (17/3,23/4) Hyperbolic Matrix(42,-101,5,-12) (12/5,17/7) -> (7/1,1/0) Hyperbolic Matrix(154,-375,23,-56) (17/7,22/9) -> (13/2,7/1) Hyperbolic Matrix(292,-715,107,-262) (22/9,5/2) -> (30/11,11/4) Hyperbolic Matrix(208,-529,81,-206) (5/2,23/9) -> (23/9,18/7) Parabolic Matrix(156,-419,35,-94) (8/3,27/10) -> (22/5,9/2) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(736,-2401,225,-734) (13/4,49/15) -> (49/15,36/11) Parabolic Matrix(68,-235,11,-38) (24/7,7/2) -> (6/1,13/2) Hyperbolic Matrix(176,-625,49,-174) (7/2,25/7) -> (25/7,18/5) Parabolic Matrix(79,-338,18,-77) (4/1,13/3) -> (13/3,22/5) Parabolic Matrix(136,-729,25,-134) (16/3,27/5) -> (27/5,11/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,30,1) Matrix(42,-5,101,-12) -> Matrix(3,1,-22,-7) Matrix(154,-23,375,-56) -> Matrix(7,3,-54,-23) Matrix(250,-39,359,-56) -> Matrix(17,6,-190,-67) Matrix(259,-46,366,-65) -> Matrix(17,7,-192,-79) Matrix(135,-26,26,-5) -> Matrix(7,2,-172,-49) Matrix(65,-14,14,-3) -> Matrix(3,1,-76,-25) Matrix(64,-17,113,-30) -> Matrix(13,3,-126,-29) Matrix(275,-76,76,-21) -> Matrix(29,6,-672,-139) Matrix(335,-98,482,-141) -> Matrix(71,13,-792,-145) Matrix(629,-186,186,-55) -> Matrix(29,5,-644,-111) Matrix(25,-8,72,-23) -> Matrix(11,2,-72,-13) Matrix(307,-110,494,-177) -> Matrix(11,2,-116,-21) Matrix(387,-142,526,-193) -> Matrix(47,7,-544,-81) Matrix(665,-246,246,-91) -> Matrix(7,1,-148,-21) Matrix(82,-31,127,-48) -> Matrix(33,5,-350,-53) Matrix(299,-116,116,-45) -> Matrix(69,10,-1456,-211) Matrix(136,-55,183,-74) -> Matrix(59,8,-686,-93) Matrix(463,-194,642,-269) -> Matrix(65,9,-744,-103) Matrix(315,-134,134,-57) -> Matrix(31,4,-628,-81) Matrix(77,-34,34,-15) -> Matrix(23,3,-468,-61) Matrix(114,-61,157,-84) -> Matrix(83,9,-950,-103) Matrix(279,-154,154,-85) -> Matrix(29,3,-532,-55) Matrix(61,-36,100,-59) -> Matrix(59,6,-600,-61) Matrix(911,-562,1266,-781) -> Matrix(43,4,-484,-45) Matrix(662,-409,505,-312) -> Matrix(29,3,-474,-49) Matrix(1423,-882,434,-269) -> Matrix(41,4,-892,-87) Matrix(284,-179,403,-254) -> Matrix(115,11,-1286,-123) Matrix(539,-342,342,-217) -> Matrix(51,5,-908,-89) Matrix(247,-170,170,-117) -> Matrix(199,18,-3372,-305) Matrix(281,-200,392,-279) -> Matrix(203,18,-2312,-205) Matrix(555,-406,406,-297) -> Matrix(415,36,-6836,-593) Matrix(9,-8,8,-7) -> Matrix(13,1,-196,-15) Matrix(127,-162,98,-125) -> Matrix(223,14,-3584,-225) Matrix(528,-689,305,-398) -> Matrix(65,4,-1154,-71) Matrix(387,-526,142,-193) -> Matrix(115,7,-2448,-149) Matrix(1000,-1369,729,-998) -> Matrix(1451,88,-23958,-1453) Matrix(114,-157,61,-84) -> Matrix(149,9,-2798,-169) Matrix(463,-642,194,-269) -> Matrix(149,9,-3096,-187) Matrix(259,-366,46,-65) -> Matrix(117,7,-2992,-179) Matrix(284,-403,179,-254) -> Matrix(185,11,-3246,-193) Matrix(335,-482,98,-141) -> Matrix(219,13,-4936,-293) Matrix(248,-361,169,-246) -> Matrix(441,26,-7514,-443) Matrix(82,-127,31,-48) -> Matrix(87,5,-1862,-107) Matrix(930,-1469,509,-804) -> Matrix(177,10,-3310,-187) Matrix(992,-1569,545,-862) -> Matrix(69,4,-1294,-75) Matrix(61,-100,36,-59) -> Matrix(107,6,-1944,-109) Matrix(271,-466,82,-141) -> Matrix(37,2,-796,-43) Matrix(369,-640,64,-111) -> Matrix(91,5,-2348,-129) Matrix(64,-113,17,-30) -> Matrix(55,3,-1302,-71) Matrix(111,-242,50,-109) -> Matrix(199,10,-4000,-201) Matrix(198,-443,59,-132) -> Matrix(81,4,-1762,-87) Matrix(856,-2025,361,-854) -> Matrix(491,24,-10086,-493) Matrix(435,-1036,76,-181) -> Matrix(83,4,-2096,-101) Matrix(42,-101,5,-12) -> Matrix(21,1,-526,-25) Matrix(154,-375,23,-56) -> Matrix(61,3,-1566,-77) Matrix(292,-715,107,-262) -> Matrix(61,3,-1322,-65) Matrix(208,-529,81,-206) -> Matrix(377,18,-7938,-379) Matrix(156,-419,35,-94) -> Matrix(87,4,-2110,-97) Matrix(25,-72,8,-23) -> Matrix(43,2,-968,-45) Matrix(736,-2401,225,-734) -> Matrix(1,0,2,1) Matrix(68,-235,11,-38) -> Matrix(23,1,-530,-23) Matrix(176,-625,49,-174) -> Matrix(321,14,-7406,-323) Matrix(79,-338,18,-77) -> Matrix(143,6,-3456,-145) Matrix(136,-729,25,-134) -> Matrix(249,10,-6250,-251) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 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: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 ----------------------------------------------------------------------- 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 -1/1 0/1 30 1 1/1 -1/14 2 16 9/7 -1/16 14 2 17/13 -1/16 2 16 4/3 (-4/65,-3/49) 0 32 15/11 -9/148 2 16 37/27 -2/33 22 1 11/8 (-2/33,-13/215) 0 32 18/13 (-2/33,-1/17) 0 32 7/5 -3/50 2 8 17/12 (-4/67,-9/151) 0 32 10/7 (-4/67,-1/17) 0 32 13/9 -9/152 2 16 19/13 -1/17 26 1 3/2 (-1/17,-4/69) 0 32 11/7 -5/88 2 16 49/31 -1/18 2 2 19/12 (-2/35,-3/53) 0 32 8/5 (-3/53,-4/71) 0 32 5/3 -1/18 6 4 12/7 (-3/55,-2/37) 0 32 19/11 -1/18 2 16 26/15 (-6/109,-5/91) 0 32 7/4 (-3/55,-2/37) 0 32 9/5 -3/56 2 16 31/17 -3/56 2 2 11/6 (-4/75,-1/19) 0 32 2/1 (-1/19,-2/39) 0 32 11/5 -1/20 10 2 7/3 -1/20 2 16 45/19 -2/41 6 1 19/8 (-2/41,-5/103) 0 32 31/13 -3/62 2 8 12/5 (-4/83,-1/21) 0 32 17/7 -1/20 2 4 22/9 (-2/41,-1/21) 0 32 5/2 (-4/83,-1/21) 0 32 23/9 -1/21 18 1 13/5 -5/106 2 16 8/3 (-2/43,-3/65) 0 32 19/7 -1/20 2 16 30/11 (-5/107,-2/43) 0 32 11/4 (-1/21,-2/43) 0 32 3/1 -1/22 2 8 13/4 (-1/23,0/1) 0 32 49/15 0/1 2 1 23/7 -1/22 2 16 10/3 (-1/23,0/1) 0 32 17/5 -5/112 2 16 24/7 (-2/45,-5/113) 0 32 7/2 (-4/91,-1/23) 0 32 25/7 -1/23 14 1 11/3 -3/70 2 16 4/1 (-1/23,0/1) 0 32 13/3 -1/24 6 2 5/1 -1/24 2 16 27/5 -1/25 10 1 11/2 (-1/25,-4/101) 0 32 17/3 -1/26 2 8 23/4 (-2/51,-3/77) 0 32 6/1 (-1/27,0/1) 0 32 13/2 (-1/25,-2/51) 0 32 7/1 -1/26 2 4 1/0 (-1/29,0/1) 0 32 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(8,-9,7,-8) (1/1,9/7) -> (1/1,9/7) Reflection Matrix(118,-153,91,-118) (9/7,17/13) -> (9/7,17/13) Reflection Matrix(395,-518,228,-299) (17/13,4/3) -> (19/11,26/15) Glide Reflection Matrix(387,-526,142,-193) (4/3,15/11) -> (19/7,30/11) Hyperbolic Matrix(406,-555,297,-406) (15/11,37/27) -> (15/11,37/27) Reflection Matrix(593,-814,432,-593) (37/27,11/8) -> (37/27,11/8) Reflection Matrix(114,-157,61,-84) (11/8,18/13) -> (11/6,2/1) Hyperbolic Matrix(463,-642,194,-269) (18/13,7/5) -> (31/13,12/5) Hyperbolic Matrix(259,-366,46,-65) (7/5,17/12) -> (11/2,17/3) Hyperbolic Matrix(284,-403,179,-254) (17/12,10/7) -> (19/12,8/5) Hyperbolic Matrix(335,-482,98,-141) (10/7,13/9) -> (17/5,24/7) Hyperbolic Matrix(170,-247,117,-170) (13/9,19/13) -> (13/9,19/13) Reflection Matrix(77,-114,52,-77) (19/13,3/2) -> (19/13,3/2) Reflection Matrix(82,-127,31,-48) (3/2,11/7) -> (13/5,8/3) Hyperbolic Matrix(342,-539,217,-342) (11/7,49/31) -> (11/7,49/31) Reflection Matrix(713,-1128,390,-617) (49/31,19/12) -> (31/17,11/6) Glide Reflection Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic Matrix(271,-466,82,-141) (12/7,19/11) -> (23/7,10/3) Hyperbolic Matrix(369,-640,64,-111) (26/15,7/4) -> (23/4,6/1) Hyperbolic Matrix(64,-113,17,-30) (7/4,9/5) -> (11/3,4/1) Hyperbolic Matrix(154,-279,85,-154) (9/5,31/17) -> (9/5,31/17) Reflection Matrix(87,-184,26,-55) (2/1,13/6) -> (10/3,27/8) Glide Reflection Matrix(76,-165,35,-76) (15/7,11/5) -> (15/7,11/5) Reflection Matrix(34,-77,15,-34) (11/5,7/3) -> (11/5,7/3) Reflection Matrix(134,-315,57,-134) (7/3,45/19) -> (7/3,45/19) Reflection Matrix(721,-1710,304,-721) (45/19,19/8) -> (45/19,19/8) Reflection Matrix(435,-1036,76,-181) (19/8,31/13) -> (17/3,23/4) Hyperbolic Matrix(42,-101,5,-12) (12/5,17/7) -> (7/1,1/0) Hyperbolic Matrix(154,-375,23,-56) (17/7,22/9) -> (13/2,7/1) Hyperbolic Matrix(292,-715,107,-262) (22/9,5/2) -> (30/11,11/4) Hyperbolic Matrix(91,-230,36,-91) (5/2,23/9) -> (5/2,23/9) Reflection Matrix(116,-299,45,-116) (23/9,13/5) -> (23/9,13/5) Reflection Matrix(91,-244,22,-59) (8/3,27/10) -> (4/1,17/4) Glide Reflection Matrix(246,-665,91,-246) (35/13,19/7) -> (35/13,19/7) Reflection Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(391,-1274,120,-391) (13/4,49/15) -> (13/4,49/15) Reflection Matrix(344,-1127,105,-344) (49/15,23/7) -> (49/15,23/7) Reflection Matrix(186,-629,55,-186) (37/11,17/5) -> (37/11,17/5) Reflection Matrix(68,-235,11,-38) (24/7,7/2) -> (6/1,13/2) 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(64,-273,15,-64) (21/5,13/3) -> (21/5,13/3) Reflection Matrix(14,-65,3,-14) (13/3,5/1) -> (13/3,5/1) Reflection Matrix(26,-135,5,-26) (5/1,27/5) -> (5/1,27/5) Reflection Matrix(109,-594,20,-109) (27/5,11/2) -> (27/5,11/2) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,58,1) (-1/1,1/0) -> (-1/29,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,28,1) (-1/1,1/1) -> (-1/14,0/1) Matrix(8,-9,7,-8) -> Matrix(15,1,-224,-15) (1/1,9/7) -> (-1/14,-1/16) Matrix(118,-153,91,-118) -> Matrix(209,13,-3360,-209) (9/7,17/13) -> (-1/16,-13/210) Matrix(395,-518,228,-299) -> Matrix(145,9,-2626,-163) Matrix(387,-526,142,-193) -> Matrix(115,7,-2448,-149) Matrix(406,-555,297,-406) -> Matrix(593,36,-9768,-593) (15/11,37/27) -> (-9/148,-2/33) Matrix(593,-814,432,-593) -> Matrix(859,52,-14190,-859) (37/27,11/8) -> (-2/33,-13/215) Matrix(114,-157,61,-84) -> Matrix(149,9,-2798,-169) Matrix(463,-642,194,-269) -> Matrix(149,9,-3096,-187) Matrix(259,-366,46,-65) -> Matrix(117,7,-2992,-179) Matrix(284,-403,179,-254) -> Matrix(185,11,-3246,-193) Matrix(335,-482,98,-141) -> Matrix(219,13,-4936,-293) Matrix(170,-247,117,-170) -> Matrix(305,18,-5168,-305) (13/9,19/13) -> (-9/152,-1/17) Matrix(77,-114,52,-77) -> Matrix(137,8,-2346,-137) (19/13,3/2) -> (-1/17,-4/69) Matrix(82,-127,31,-48) -> Matrix(87,5,-1862,-107) Matrix(342,-539,217,-342) -> Matrix(89,5,-1584,-89) (11/7,49/31) -> (-5/88,-1/18) Matrix(713,-1128,390,-617) -> Matrix(87,5,-1618,-93) Matrix(61,-100,36,-59) -> Matrix(107,6,-1944,-109) -1/18 Matrix(271,-466,82,-141) -> Matrix(37,2,-796,-43) Matrix(369,-640,64,-111) -> Matrix(91,5,-2348,-129) Matrix(64,-113,17,-30) -> Matrix(55,3,-1302,-71) Matrix(154,-279,85,-154) -> Matrix(55,3,-1008,-55) (9/5,31/17) -> (-1/18,-3/56) Matrix(87,-184,26,-55) -> Matrix(19,1,-398,-21) Matrix(76,-165,35,-76) -> Matrix(139,7,-2760,-139) (15/7,11/5) -> (-7/138,-1/20) Matrix(34,-77,15,-34) -> Matrix(61,3,-1240,-61) (11/5,7/3) -> (-1/20,-3/62) Matrix(134,-315,57,-134) -> Matrix(81,4,-1640,-81) (7/3,45/19) -> (-1/20,-2/41) Matrix(721,-1710,304,-721) -> Matrix(411,20,-8446,-411) (45/19,19/8) -> (-2/41,-5/103) Matrix(435,-1036,76,-181) -> Matrix(83,4,-2096,-101) Matrix(42,-101,5,-12) -> Matrix(21,1,-526,-25) Matrix(154,-375,23,-56) -> Matrix(61,3,-1566,-77) Matrix(292,-715,107,-262) -> Matrix(61,3,-1322,-65) Matrix(91,-230,36,-91) -> Matrix(167,8,-3486,-167) (5/2,23/9) -> (-4/83,-1/21) Matrix(116,-299,45,-116) -> Matrix(211,10,-4452,-211) (23/9,13/5) -> (-1/21,-5/106) Matrix(91,-244,22,-59) -> Matrix(65,3,-1538,-71) Matrix(246,-665,91,-246) -> Matrix(21,1,-440,-21) (35/13,19/7) -> (-1/20,-1/22) Matrix(25,-72,8,-23) -> Matrix(43,2,-968,-45) -1/22 Matrix(391,-1274,120,-391) -> Matrix(-1,0,46,1) (13/4,49/15) -> (-1/23,0/1) Matrix(344,-1127,105,-344) -> Matrix(-1,0,44,1) (49/15,23/7) -> (-1/22,0/1) Matrix(186,-629,55,-186) -> Matrix(111,5,-2464,-111) (37/11,17/5) -> (-1/22,-5/112) Matrix(68,-235,11,-38) -> Matrix(23,1,-530,-23) (-1/22,-1/24).(-1/23,0/1) Matrix(99,-350,28,-99) -> Matrix(183,8,-4186,-183) (7/2,25/7) -> (-4/91,-1/23) Matrix(76,-275,21,-76) -> Matrix(139,6,-3220,-139) (25/7,11/3) -> (-1/23,-3/70) Matrix(64,-273,15,-64) -> Matrix(119,5,-2832,-119) (21/5,13/3) -> (-5/118,-1/24) Matrix(14,-65,3,-14) -> Matrix(25,1,-624,-25) (13/3,5/1) -> (-1/24,-1/26) Matrix(26,-135,5,-26) -> Matrix(49,2,-1200,-49) (5/1,27/5) -> (-1/24,-1/25) Matrix(109,-594,20,-109) -> Matrix(201,8,-5050,-201) (27/5,11/2) -> (-1/25,-4/101) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.