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): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 64 Genus: 65 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -4/9 -2/5 -3/8 -2/7 -1/4 -1/6 0/1 2/13 1/5 1/4 4/11 3/7 1/2 2/3 5/7 4/5 7/8 1/1 8/7 11/9 5/4 17/13 7/5 3/2 11/7 46/29 37/23 19/11 13/7 2/1 31/14 7/3 17/7 5/2 151/59 13/5 8/3 11/4 3/1 23/7 10/3 31/9 7/2 39/11 47/13 11/3 19/5 4/1 21/5 13/3 49/11 9/2 23/5 5/1 11/2 17/3 6/1 19/3 13/2 7/1 8/1 9/1 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 1/53 -6/13 0/1 1/50 -5/11 1/49 -9/20 3/146 2/97 -4/9 1/48 -11/25 1/48 -18/41 2/95 3/142 -7/16 0/1 2/95 -10/23 6/283 1/47 -3/7 1/47 1/46 -8/19 1/46 2/91 -13/31 1/45 -5/12 0/1 1/46 -7/17 1/45 -2/5 0/1 2/89 -11/28 0/1 1/45 -9/23 1/44 -16/41 1/44 -7/18 2/89 1/44 -5/13 1/44 1/43 -13/34 0/1 2/87 -21/55 1/44 -8/21 2/87 1/43 -11/29 1/43 -3/8 1/43 -10/27 1/43 4/171 -7/19 2/85 -11/30 4/169 1/42 -4/11 4/169 1/42 -9/25 1/42 5/209 -5/14 4/167 2/83 -11/31 2/83 -6/17 2/83 3/124 -7/20 6/247 1/41 -1/3 1/40 -6/19 1/39 6/233 -5/16 3/116 2/77 -9/29 2/77 -4/13 2/77 4/153 -7/23 5/191 1/38 -10/33 14/533 1/38 -3/10 1/38 4/151 -8/27 1/38 4/151 -5/17 2/75 -7/24 4/149 1/37 -2/7 1/37 -9/32 2/73 1/36 -7/25 1/37 -5/18 1/37 2/73 -18/65 2/73 3/109 -13/47 1/36 -8/29 0/1 2/73 -3/11 1/37 1/36 -7/26 4/145 1/36 -4/15 1/36 2/71 -5/19 1/36 -6/23 0/1 1/35 -1/4 0/1 2/71 -3/13 1/35 -2/9 0/1 1/34 -7/32 1/35 -5/23 1/35 -3/14 2/69 1/34 -1/5 1/34 1/33 -4/21 8/265 1/33 -3/16 1/33 6/197 -2/11 0/1 2/65 -5/28 3/98 2/65 -8/45 2/65 5/162 -3/17 1/32 -4/23 0/1 1/32 -1/6 1/32 -2/13 2/63 3/94 -1/7 1/31 -1/8 0/1 1/30 0/1 0/1 1/27 1/8 0/1 2/49 1/7 1/25 1/24 2/13 1/24 3/19 1/24 1/6 0/1 1/24 3/17 2/47 5/28 2/47 4/93 2/11 2/47 1/23 5/27 1/23 3/68 3/16 0/1 1/22 1/5 1/23 4/19 2/45 1/22 3/14 0/1 1/23 5/23 1/23 5/114 2/9 3/68 2/45 3/13 3/67 1/22 4/17 0/1 2/45 5/21 1/22 1/4 1/22 3/11 1/22 5/18 2/43 3/64 12/43 1/21 7/25 3/64 1/21 2/7 0/1 2/43 7/24 2/43 5/107 5/17 3/64 13/44 4/85 6/127 21/71 5/106 1/21 8/27 1/21 3/10 6/127 1/21 1/3 1/21 1/20 5/14 4/81 1/20 4/11 1/20 7/19 1/20 17/46 6/119 4/79 10/27 1/20 2/39 3/8 1/20 2/39 8/21 2/39 1/19 13/34 2/39 1/19 5/13 1/19 2/5 0/1 1/20 11/27 1/20 9/22 2/39 1/19 7/17 2/39 5/12 0/1 1/19 18/43 0/1 1/19 13/31 1/20 1/19 8/19 0/1 2/39 3/7 1/19 7/16 2/37 1/18 18/41 0/1 1/19 11/25 0/1 4/9 1/19 2/37 5/11 1/19 1/18 6/13 0/1 1/16 1/2 0/1 2/37 7/13 0/1 6/11 0/1 1/19 5/9 1/18 9/16 1/18 13/23 0/1 4/7 2/37 1/18 3/5 1/18 1/17 14/23 1/18 2/35 11/18 2/35 5/87 19/31 1/17 8/13 0/1 2/35 13/21 1/18 5/8 2/35 1/17 12/19 2/35 1/17 19/30 2/35 3/52 7/11 1/17 2/3 1/17 11/16 4/67 2/33 20/29 7/116 2/33 9/13 1/16 16/23 0/1 2/35 7/10 1/17 4/67 12/17 5/83 2/33 17/24 4/67 3/50 5/7 2/33 18/25 3/49 4/65 31/43 1/16 13/18 1/17 2/33 21/29 3/49 8/11 4/65 1/16 11/15 1/16 25/34 0/1 1/17 14/19 0/1 2/33 3/4 4/65 1/16 7/9 1/16 5/79 18/23 4/63 7/110 11/14 1/16 26/33 4/63 3/47 67/85 1/16 3/47 41/52 4/63 2/31 15/19 1/16 4/5 4/63 2/31 17/21 5/78 13/16 7/109 2/31 9/11 2/31 14/17 2/31 5/77 5/6 2/31 3/46 6/7 6/91 1/15 7/8 1/15 8/9 1/15 8/119 1/1 1/14 9/8 8/105 1/13 8/7 1/13 15/13 1/13 11/142 7/6 1/13 6/77 13/11 4/51 32/27 4/51 7/89 19/16 3/38 6/5 3/38 2/25 11/9 2/25 27/22 2/25 9/112 16/13 2/25 7/87 5/4 2/25 4/49 14/11 1/12 23/18 7/86 4/49 32/25 4/49 6/73 9/7 5/61 1/12 13/10 14/169 1/12 17/13 1/12 21/16 1/12 22/263 4/3 1/12 4/47 19/14 0/1 2/23 34/25 0/1 1/11 15/11 1/12 26/19 1/12 11/8 1/12 4/47 40/29 4/47 2/23 29/21 3/35 47/34 8/93 2/23 18/13 2/23 1/11 43/31 1/12 25/18 4/47 3/35 7/5 2/23 24/17 3/34 4/45 41/29 1/11 17/12 2/23 5/57 44/31 3/34 27/19 3/34 10/7 4/45 1/11 23/16 0/1 2/21 36/25 0/1 1/13 49/34 2/25 1/12 13/9 1/12 16/11 2/23 4/45 3/2 1/11 20/13 0/1 2/21 37/24 0/1 1/11 17/11 1/11 1/10 31/20 4/43 2/21 14/9 2/21 1/10 11/7 1/11 30/19 3/32 2/21 49/31 2/21 19/12 1/11 2/21 65/41 1/10 46/29 1/10 27/17 1/11 1/10 8/5 1/11 2/21 37/23 2/21 66/41 2/21 7/73 29/18 2/21 3/31 21/13 1/10 55/34 1/11 2/21 34/21 1/10 13/8 0/1 2/21 44/27 2/21 1/10 31/19 1/11 49/30 4/43 3/32 18/11 5/53 2/21 23/14 2/21 1/10 28/17 1/10 5/3 1/11 1/10 12/7 4/41 1/10 19/11 1/10 26/15 1/10 8/79 7/4 1/10 2/19 9/5 1/10 29/16 1/10 20/11 3/29 2/19 11/6 0/1 1/9 24/13 2/17 1/8 37/20 0/1 2/15 13/7 0/1 15/8 2/21 1/10 2/1 0/1 2/19 11/5 1/10 1/9 42/19 0/1 1/9 31/14 1/10 51/23 1/10 20/9 2/19 1/9 9/4 2/19 1/9 34/15 2/17 1/8 25/11 0/1 41/18 0/1 1/9 16/7 1/10 2/19 7/3 1/9 19/8 0/1 2/17 69/29 3/26 50/21 2/17 5/42 31/13 1/9 1/8 12/5 0/1 1/9 29/12 4/35 3/26 46/19 3/26 63/26 5/43 2/17 17/7 2/17 39/16 1/8 61/25 1/8 22/9 1/9 2/17 5/2 0/1 1/8 28/11 0/1 2/19 51/20 1/10 2/19 23/9 1/9 1/8 87/34 0/1 1/9 151/59 1/9 64/25 1/9 2/17 41/16 0/1 2/17 18/7 1/9 13/5 1/9 34/13 1/9 2/17 55/21 1/9 3/26 76/29 3/26 21/8 1/9 2/17 50/19 12/103 2/17 29/11 2/17 8/3 2/17 1/8 27/10 2/17 1/8 46/17 4/33 6/49 65/24 5/41 6/49 19/7 1/8 11/4 1/8 25/9 1/8 14/5 1/8 4/31 3/1 1/8 1/7 13/4 8/57 1/7 23/7 1/7 33/10 1/7 20/139 10/3 1/7 6/41 27/8 1/7 44/13 6/41 4/27 61/18 13/88 4/27 78/23 4/27 19/128 17/5 3/20 58/17 3/20 41/12 3/20 8/53 24/7 5/33 2/13 31/9 2/13 7/2 0/1 2/13 39/11 1/7 32/9 0/1 1/6 25/7 1/7 3/20 118/33 1/7 2/13 211/59 1/7 93/26 1/7 4/27 68/19 4/27 2/13 43/12 1/7 18/5 3/20 2/13 47/13 2/13 76/21 2/13 13/84 29/8 2/13 5/32 11/3 1/6 15/4 0/1 1/6 34/9 1/7 4/27 19/5 2/13 23/6 2/13 3/19 4/1 1/6 25/6 2/11 1/5 21/5 1/6 17/4 0/1 2/11 13/3 1/6 3/17 22/5 4/23 2/11 31/7 5/28 40/9 13/72 2/11 49/11 2/11 58/13 2/11 19/104 9/2 2/11 3/16 32/7 2/11 4/21 23/5 5/26 1/5 60/13 10/51 1/5 37/8 1/5 14/3 0/1 1/5 33/7 0/1 19/4 1/6 2/11 5/1 1/5 16/3 0/1 1/6 43/8 0/1 2/11 27/5 3/16 1/5 38/7 1/5 11/2 1/5 2/9 28/5 4/19 2/9 45/8 3/14 8/37 17/3 2/9 23/4 2/9 4/17 6/1 0/1 1/4 25/4 1/5 2/9 19/3 1/4 13/2 1/4 33/5 1/4 20/3 1/4 2/7 7/1 1/4 1/3 8/1 0/1 2/7 17/2 0/1 1/4 9/1 1/3 1/0 0/1 1/1 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(171,80,280,131) (-1/2,-6/13) -> (14/23,11/18) Hyperbolic Matrix(57,26,274,125) (-6/13,-5/11) -> (1/5,4/19) Hyperbolic Matrix(53,24,276,125) (-5/11,-9/20) -> (3/16,1/5) Hyperbolic Matrix(487,218,382,171) (-9/20,-4/9) -> (14/11,23/18) Hyperbolic Matrix(481,212,-1232,-543) (-4/9,-11/25) -> (-9/23,-16/41) Hyperbolic Matrix(323,142,-1822,-801) (-11/25,-18/41) -> (-8/45,-3/17) Hyperbolic Matrix(1495,656,964,423) (-18/41,-7/16) -> (31/20,14/9) Hyperbolic Matrix(689,300,480,209) (-7/16,-10/23) -> (10/7,23/16) Hyperbolic Matrix(51,22,-262,-113) (-10/23,-3/7) -> (-1/5,-4/21) Hyperbolic Matrix(155,66,54,23) (-3/7,-8/19) -> (14/5,3/1) Hyperbolic Matrix(1139,478,722,303) (-8/19,-13/31) -> (11/7,30/19) Hyperbolic Matrix(363,152,-1292,-541) (-13/31,-5/12) -> (-9/32,-7/25) Hyperbolic Matrix(155,64,356,147) (-5/12,-7/17) -> (3/7,7/16) Hyperbolic Matrix(151,62,358,147) (-7/17,-2/5) -> (8/19,3/7) Hyperbolic Matrix(839,330,150,59) (-2/5,-11/28) -> (11/2,28/5) Hyperbolic Matrix(1779,698,1282,503) (-11/28,-9/23) -> (43/31,25/18) Hyperbolic Matrix(2017,786,834,325) (-16/41,-7/18) -> (29/12,46/19) Hyperbolic Matrix(145,56,-536,-207) (-7/18,-5/13) -> (-3/11,-7/26) Hyperbolic Matrix(47,18,342,131) (-5/13,-13/34) -> (1/8,1/7) Hyperbolic Matrix(1649,630,390,149) (-13/34,-21/55) -> (21/5,17/4) Hyperbolic Matrix(1263,482,-4562,-1741) (-21/55,-8/21) -> (-18/65,-13/47) Hyperbolic Matrix(1259,478,482,183) (-8/21,-11/29) -> (13/5,34/13) Hyperbolic Matrix(243,92,-1112,-421) (-11/29,-3/8) -> (-7/32,-5/23) Hyperbolic Matrix(809,300,240,89) (-3/8,-10/27) -> (10/3,27/8) Hyperbolic Matrix(477,176,664,245) (-10/27,-7/19) -> (5/7,18/25) Hyperbolic Matrix(473,174,666,245) (-7/19,-11/30) -> (17/24,5/7) Hyperbolic Matrix(333,122,898,329) (-11/30,-4/11) -> (10/27,3/8) Hyperbolic Matrix(327,118,-1078,-389) (-4/11,-9/25) -> (-7/23,-10/33) Hyperbolic Matrix(607,218,142,51) (-9/25,-5/14) -> (17/4,13/3) Hyperbolic Matrix(651,232,188,67) (-5/14,-11/31) -> (31/9,7/2) Hyperbolic Matrix(1763,624,1116,395) (-11/31,-6/17) -> (30/19,49/31) Hyperbolic Matrix(833,292,368,129) (-6/17,-7/20) -> (9/4,34/15) Hyperbolic Matrix(47,16,44,15) (-7/20,-1/3) -> (1/1,9/8) Hyperbolic Matrix(43,14,46,15) (-1/3,-6/19) -> (8/9,1/1) Hyperbolic Matrix(829,260,220,69) (-6/19,-5/16) -> (15/4,34/9) Hyperbolic Matrix(959,298,782,243) (-5/16,-9/29) -> (11/9,27/22) Hyperbolic Matrix(1827,566,694,215) (-9/29,-4/13) -> (50/19,29/11) Hyperbolic Matrix(131,40,560,171) (-4/13,-7/23) -> (3/13,4/17) Hyperbolic Matrix(733,222,558,169) (-10/33,-3/10) -> (21/16,4/3) Hyperbolic Matrix(809,240,300,89) (-3/10,-8/27) -> (8/3,27/10) Hyperbolic Matrix(597,176,424,125) (-8/27,-5/17) -> (7/5,24/17) Hyperbolic Matrix(593,174,426,125) (-5/17,-7/24) -> (25/18,7/5) Hyperbolic Matrix(213,62,718,209) (-7/24,-2/7) -> (8/27,3/10) Hyperbolic Matrix(419,118,1502,423) (-2/7,-9/32) -> (5/18,12/43) Hyperbolic Matrix(415,116,1084,303) (-7/25,-5/18) -> (13/34,5/13) Hyperbolic Matrix(3073,852,1908,529) (-5/18,-18/65) -> (66/41,29/18) Hyperbolic Matrix(333,92,1408,389) (-13/47,-8/29) -> (4/17,5/21) Hyperbolic Matrix(291,80,40,11) (-8/29,-3/11) -> (7/1,8/1) Hyperbolic Matrix(781,210,450,121) (-7/26,-4/15) -> (26/15,7/4) Hyperbolic Matrix(121,32,-692,-183) (-4/15,-5/19) -> (-3/17,-4/23) Hyperbolic Matrix(1055,276,1464,383) (-5/19,-6/23) -> (18/25,31/43) Hyperbolic Matrix(123,32,688,179) (-6/23,-1/4) -> (5/28,2/11) Hyperbolic Matrix(275,64,116,27) (-1/4,-3/13) -> (7/3,19/8) Hyperbolic Matrix(271,62,118,27) (-3/13,-2/9) -> (16/7,7/3) Hyperbolic Matrix(963,212,268,59) (-2/9,-7/32) -> (43/12,18/5) Hyperbolic Matrix(535,116,844,183) (-5/23,-3/14) -> (19/30,7/11) Hyperbolic Matrix(39,8,112,23) (-3/14,-1/5) -> (1/3,5/14) Hyperbolic Matrix(853,162,258,49) (-4/21,-3/16) -> (33/10,10/3) Hyperbolic Matrix(333,62,478,89) (-3/16,-2/11) -> (16/23,7/10) Hyperbolic Matrix(839,150,330,59) (-2/11,-5/28) -> (5/2,28/11) Hyperbolic Matrix(3433,612,948,169) (-5/28,-8/45) -> (76/21,29/8) Hyperbolic Matrix(473,82,398,69) (-4/23,-1/6) -> (19/16,6/5) Hyperbolic Matrix(251,40,320,51) (-1/6,-2/13) -> (18/23,11/14) Hyperbolic Matrix(177,26,34,5) (-2/13,-1/7) -> (5/1,16/3) Hyperbolic Matrix(173,24,36,5) (-1/7,-1/8) -> (19/4,5/1) Hyperbolic Matrix(167,18,102,11) (-1/8,0/1) -> (18/11,23/14) Hyperbolic Matrix(191,-18,138,-13) (0/1,1/8) -> (47/34,18/13) Hyperbolic Matrix(261,-38,158,-23) (1/7,2/13) -> (28/17,5/3) Hyperbolic Matrix(1323,-208,388,-61) (2/13,3/19) -> (17/5,58/17) Hyperbolic Matrix(1009,-160,700,-111) (3/19,1/6) -> (49/34,13/9) Hyperbolic Matrix(333,-58,178,-31) (1/6,3/17) -> (13/7,15/8) Hyperbolic Matrix(993,-176,536,-95) (3/17,5/28) -> (37/20,13/7) Hyperbolic Matrix(1873,-346,406,-75) (2/11,5/27) -> (23/5,60/13) Hyperbolic Matrix(1745,-324,684,-127) (5/27,3/16) -> (51/20,23/9) Hyperbolic Matrix(545,-116,296,-63) (4/19,3/14) -> (11/6,24/13) Hyperbolic Matrix(371,-80,320,-69) (3/14,5/23) -> (15/13,7/6) Hyperbolic Matrix(961,-210,270,-59) (5/23,2/9) -> (32/9,25/7) Hyperbolic Matrix(123,-28,268,-61) (2/9,3/13) -> (5/11,6/13) Hyperbolic Matrix(1063,-256,436,-105) (5/21,1/4) -> (39/16,61/25) Hyperbolic Matrix(119,-32,212,-57) (1/4,3/11) -> (5/9,9/16) Hyperbolic Matrix(517,-142,142,-39) (3/11,5/18) -> (29/8,11/3) Hyperbolic Matrix(1103,-308,3728,-1041) (12/43,7/25) -> (21/71,8/27) Hyperbolic Matrix(961,-270,210,-59) (7/25,2/7) -> (32/7,23/5) Hyperbolic Matrix(1347,-392,512,-149) (2/7,7/24) -> (21/8,50/19) Hyperbolic Matrix(417,-122,1022,-299) (7/24,5/17) -> (11/27,9/22) Hyperbolic Matrix(3359,-992,1412,-417) (5/17,13/44) -> (19/8,69/29) Hyperbolic Matrix(5859,-1732,7432,-2197) (13/44,21/71) -> (67/85,41/52) Hyperbolic Matrix(69,-22,22,-7) (3/10,1/3) -> (3/1,13/4) Hyperbolic Matrix(485,-174,354,-127) (5/14,4/11) -> (26/19,11/8) Hyperbolic Matrix(659,-242,482,-177) (4/11,7/19) -> (15/11,26/19) Hyperbolic Matrix(1469,-542,1862,-687) (7/19,17/46) -> (41/52,15/19) Hyperbolic Matrix(2103,-778,1138,-421) (17/46,10/27) -> (24/13,37/20) Hyperbolic Matrix(217,-82,262,-99) (3/8,8/21) -> (14/17,5/6) Hyperbolic Matrix(717,-274,1714,-655) (8/21,13/34) -> (5/12,18/43) Hyperbolic Matrix(237,-92,152,-59) (5/13,2/5) -> (14/9,11/7) Hyperbolic Matrix(705,-286,106,-43) (2/5,11/27) -> (33/5,20/3) Hyperbolic Matrix(809,-332,212,-87) (9/22,7/17) -> (19/5,23/6) Hyperbolic Matrix(275,-114,234,-97) (7/17,5/12) -> (7/6,13/11) Hyperbolic Matrix(1775,-744,804,-337) (18/43,13/31) -> (11/5,42/19) Hyperbolic Matrix(1163,-488,908,-381) (13/31,8/19) -> (32/25,9/7) Hyperbolic Matrix(2585,-1134,1794,-787) (7/16,18/41) -> (36/25,49/34) Hyperbolic Matrix(1333,-586,1126,-495) (18/41,11/25) -> (13/11,32/27) Hyperbolic Matrix(1021,-450,270,-119) (11/25,4/9) -> (34/9,19/5) Hyperbolic Matrix(331,-148,208,-93) (4/9,5/11) -> (27/17,8/5) Hyperbolic Matrix(183,-86,266,-125) (6/13,1/2) -> (11/16,20/29) Hyperbolic Matrix(333,-178,58,-31) (1/2,7/13) -> (17/3,23/4) Hyperbolic Matrix(545,-296,116,-63) (7/13,6/11) -> (14/3,33/7) Hyperbolic Matrix(387,-212,272,-149) (6/11,5/9) -> (27/19,10/7) Hyperbolic Matrix(1169,-660,480,-271) (9/16,13/23) -> (17/7,39/16) Hyperbolic Matrix(957,-542,422,-239) (13/23,4/7) -> (34/15,25/11) Hyperbolic Matrix(95,-56,56,-33) (4/7,3/5) -> (5/3,12/7) Hyperbolic Matrix(261,-158,38,-23) (3/5,14/23) -> (20/3,7/1) Hyperbolic Matrix(1265,-774,894,-547) (11/18,19/31) -> (41/29,17/12) Hyperbolic Matrix(1617,-992,1172,-719) (19/31,8/13) -> (40/29,29/21) Hyperbolic Matrix(279,-172,352,-217) (8/13,13/21) -> (15/19,4/5) Hyperbolic Matrix(777,-482,482,-299) (13/21,5/8) -> (29/18,21/13) Hyperbolic Matrix(331,-208,148,-93) (5/8,12/19) -> (20/9,9/4) Hyperbolic Matrix(993,-628,808,-511) (12/19,19/30) -> (27/22,16/13) Hyperbolic Matrix(237,-152,92,-59) (7/11,2/3) -> (18/7,13/5) Hyperbolic Matrix(411,-280,160,-109) (2/3,11/16) -> (41/16,18/7) Hyperbolic Matrix(1419,-980,320,-221) (20/29,9/13) -> (31/7,40/9) Hyperbolic Matrix(443,-308,548,-381) (9/13,16/23) -> (4/5,17/21) Hyperbolic Matrix(387,-272,212,-149) (7/10,12/17) -> (20/11,11/6) Hyperbolic Matrix(1265,-894,774,-547) (12/17,17/24) -> (49/30,18/11) Hyperbolic Matrix(1987,-1434,1254,-905) (31/43,13/18) -> (19/12,65/41) Hyperbolic Matrix(191,-138,18,-13) (13/18,21/29) -> (9/1,1/0) Hyperbolic Matrix(1617,-1172,992,-719) (21/29,8/11) -> (44/27,31/19) Hyperbolic Matrix(485,-354,174,-127) (8/11,11/15) -> (25/9,14/5) Hyperbolic Matrix(1089,-800,260,-191) (11/15,25/34) -> (25/6,21/5) Hyperbolic Matrix(1383,-1018,898,-661) (25/34,14/19) -> (20/13,37/24) Hyperbolic Matrix(293,-216,156,-115) (14/19,3/4) -> (15/8,2/1) Hyperbolic Matrix(153,-118,118,-91) (3/4,7/9) -> (9/7,13/10) Hyperbolic Matrix(1163,-908,488,-381) (7/9,18/23) -> (50/21,31/13) Hyperbolic Matrix(1075,-846,906,-713) (11/14,26/33) -> (32/27,19/16) Hyperbolic Matrix(10855,-8556,3036,-2393) (26/33,67/85) -> (25/7,118/33) Hyperbolic Matrix(829,-672,132,-107) (17/21,13/16) -> (25/4,19/3) Hyperbolic Matrix(993,-808,628,-511) (13/16,9/11) -> (49/31,19/12) Hyperbolic Matrix(791,-650,230,-189) (9/11,14/17) -> (24/7,31/9) Hyperbolic Matrix(275,-234,114,-97) (5/6,6/7) -> (12/5,29/12) Hyperbolic Matrix(371,-320,80,-69) (6/7,7/8) -> (37/8,14/3) Hyperbolic Matrix(813,-716,176,-155) (7/8,8/9) -> (60/13,37/8) Hyperbolic Matrix(381,-430,70,-79) (9/8,8/7) -> (38/7,11/2) Hyperbolic Matrix(683,-786,126,-145) (8/7,15/13) -> (27/5,38/7) Hyperbolic Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(443,-548,308,-381) (16/13,5/4) -> (23/16,36/25) Hyperbolic Matrix(279,-352,172,-217) (5/4,14/11) -> (34/21,13/8) Hyperbolic Matrix(2317,-2964,684,-875) (23/18,32/25) -> (44/13,61/18) Hyperbolic Matrix(443,-578,338,-441) (13/10,17/13) -> (17/13,21/16) Parabolic Matrix(153,-206,26,-35) (4/3,19/14) -> (23/4,6/1) Hyperbolic Matrix(1921,-2610,750,-1019) (19/14,34/25) -> (64/25,41/16) Hyperbolic Matrix(1767,-2404,724,-985) (34/25,15/11) -> (61/25,22/9) Hyperbolic Matrix(1703,-2348,668,-921) (11/8,40/29) -> (28/11,51/20) Hyperbolic Matrix(1473,-2036,416,-575) (29/21,47/34) -> (7/2,39/11) Hyperbolic Matrix(1283,-1778,578,-801) (18/13,43/31) -> (51/23,20/9) Hyperbolic Matrix(1591,-2248,448,-633) (24/17,41/29) -> (39/11,32/9) Hyperbolic Matrix(1563,-2216,596,-845) (17/12,44/31) -> (76/29,21/8) Hyperbolic Matrix(2889,-4102,1822,-2587) (44/31,27/19) -> (65/41,46/29) Hyperbolic Matrix(539,-782,122,-177) (13/9,16/11) -> (22/5,31/7) Hyperbolic Matrix(73,-108,48,-71) (16/11,3/2) -> (3/2,20/13) Parabolic Matrix(1509,-2330,590,-911) (37/24,17/11) -> (23/9,87/34) Hyperbolic Matrix(1013,-1568,188,-291) (17/11,31/20) -> (43/8,27/5) Hyperbolic Matrix(2887,-4582,1102,-1749) (46/29,27/17) -> (55/21,76/29) Hyperbolic Matrix(1703,-2738,1058,-1701) (8/5,37/23) -> (37/23,66/41) Parabolic Matrix(1491,-2410,550,-889) (21/13,55/34) -> (65/24,19/7) Hyperbolic Matrix(2887,-4672,1192,-1929) (55/34,34/21) -> (46/19,63/26) Hyperbolic Matrix(1289,-2100,240,-391) (13/8,44/27) -> (16/3,43/8) Hyperbolic Matrix(593,-968,68,-111) (31/19,49/30) -> (17/2,9/1) Hyperbolic Matrix(1509,-2482,442,-727) (23/14,28/17) -> (58/17,41/12) Hyperbolic Matrix(419,-722,242,-417) (12/7,19/11) -> (19/11,26/15) Parabolic Matrix(119,-212,32,-57) (7/4,9/5) -> (11/3,15/4) Hyperbolic Matrix(971,-1758,438,-793) (9/5,29/16) -> (31/14,51/23) Hyperbolic Matrix(1013,-1838,458,-831) (29/16,20/11) -> (42/19,31/14) Hyperbolic Matrix(123,-268,28,-61) (2/1,11/5) -> (13/3,22/5) Hyperbolic Matrix(999,-2272,412,-937) (25/11,41/18) -> (63/26,17/7) Hyperbolic Matrix(283,-646,46,-105) (41/18,16/7) -> (6/1,25/4) Hyperbolic Matrix(2619,-6232,772,-1837) (69/29,50/21) -> (78/23,17/5) Hyperbolic Matrix(717,-1714,274,-655) (31/13,12/5) -> (34/13,55/21) Hyperbolic Matrix(417,-1022,122,-299) (22/9,5/2) -> (41/12,24/7) Hyperbolic Matrix(12661,-32400,3540,-9059) (87/34,151/59) -> (211/59,93/26) Hyperbolic Matrix(12237,-31322,3422,-8759) (151/59,64/25) -> (118/33,211/59) Hyperbolic Matrix(1045,-2826,186,-503) (27/10,46/17) -> (28/5,45/8) Hyperbolic Matrix(3213,-8698,898,-2431) (46/17,65/24) -> (93/26,68/19) Hyperbolic Matrix(177,-484,64,-175) (19/7,11/4) -> (11/4,25/9) Parabolic Matrix(323,-1058,98,-321) (13/4,23/7) -> (23/7,33/10) Parabolic Matrix(1103,-3728,308,-1041) (27/8,44/13) -> (68/19,43/12) Hyperbolic Matrix(1251,-4240,280,-949) (61/18,78/23) -> (58/13,9/2) Hyperbolic Matrix(1223,-4418,338,-1221) (18/5,47/13) -> (47/13,76/21) Parabolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic Matrix(1079,-4802,242,-1077) (40/9,49/11) -> (49/11,58/13) Parabolic Matrix(135,-616,16,-73) (9/2,32/7) -> (8/1,17/2) Hyperbolic Matrix(383,-1808,68,-321) (33/7,19/4) -> (45/8,17/3) Hyperbolic Matrix(105,-676,16,-103) (19/3,13/2) -> (13/2,33/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,52,1) Matrix(171,80,280,131) -> Matrix(101,-2,1768,-35) Matrix(57,26,274,125) -> Matrix(99,-2,2228,-45) Matrix(53,24,276,125) -> Matrix(97,-2,2280,-47) Matrix(487,218,382,171) -> Matrix(95,-2,1188,-25) Matrix(481,212,-1232,-543) -> Matrix(95,-2,4228,-89) Matrix(323,142,-1822,-801) -> Matrix(191,-4,6160,-129) Matrix(1495,656,964,423) -> Matrix(189,-4,2032,-43) Matrix(689,300,480,209) -> Matrix(95,-2,998,-21) Matrix(51,22,-262,-113) -> Matrix(93,-2,3116,-67) Matrix(155,66,54,23) -> Matrix(93,-2,698,-15) Matrix(1139,478,722,303) -> Matrix(181,-4,1946,-43) Matrix(363,152,-1292,-541) -> Matrix(91,-2,3322,-73) Matrix(155,64,356,147) -> Matrix(91,-2,1684,-37) Matrix(151,62,358,147) -> Matrix(89,-2,1736,-39) Matrix(839,330,150,59) -> Matrix(91,-2,410,-9) Matrix(1779,698,1282,503) -> Matrix(177,-4,2080,-47) Matrix(2017,786,834,325) -> Matrix(91,-2,774,-17) Matrix(145,56,-536,-207) -> Matrix(87,-2,3176,-73) Matrix(47,18,342,131) -> Matrix(87,-2,2132,-49) Matrix(1649,630,390,149) -> Matrix(1,0,-38,1) Matrix(1263,482,-4562,-1741) -> Matrix(175,-4,6344,-145) Matrix(1259,478,482,183) -> Matrix(173,-4,1514,-35) Matrix(243,92,-1112,-421) -> Matrix(87,-2,3002,-69) Matrix(809,300,240,89) -> Matrix(87,-2,566,-13) Matrix(477,176,664,245) -> Matrix(341,-8,5584,-131) Matrix(473,174,666,245) -> Matrix(339,-8,5636,-133) Matrix(333,122,898,329) -> Matrix(253,-6,5018,-119) Matrix(327,118,-1078,-389) -> Matrix(419,-10,15964,-381) Matrix(607,218,142,51) -> Matrix(83,-2,540,-13) Matrix(651,232,188,67) -> Matrix(167,-4,1044,-25) Matrix(1763,624,1116,395) -> Matrix(497,-12,5260,-127) Matrix(833,292,368,129) -> Matrix(165,-4,1444,-35) Matrix(47,16,44,15) -> Matrix(81,-2,1094,-27) Matrix(43,14,46,15) -> Matrix(79,-2,1146,-29) Matrix(829,260,220,69) -> Matrix(77,-2,578,-15) Matrix(959,298,782,243) -> Matrix(925,-24,11524,-299) Matrix(1827,566,694,215) -> Matrix(615,-16,5266,-137) Matrix(131,40,560,171) -> Matrix(77,-2,1656,-43) Matrix(733,222,558,169) -> Matrix(685,-18,8182,-215) Matrix(809,240,300,89) -> Matrix(227,-6,1854,-49) Matrix(597,176,424,125) -> Matrix(301,-8,3424,-91) Matrix(593,174,426,125) -> Matrix(299,-8,3476,-93) Matrix(213,62,718,209) -> Matrix(73,-2,1570,-43) Matrix(419,118,1502,423) -> Matrix(147,-4,3124,-85) Matrix(415,116,1084,303) -> Matrix(147,-4,2830,-77) Matrix(3073,852,1908,529) -> Matrix(293,-8,3040,-83) Matrix(333,92,1408,389) -> Matrix(1,0,-14,1) Matrix(291,80,40,11) -> Matrix(73,-2,256,-7) Matrix(781,210,450,121) -> Matrix(217,-6,2134,-59) Matrix(121,32,-692,-183) -> Matrix(71,-2,2308,-65) Matrix(1055,276,1464,383) -> Matrix(143,-4,2324,-65) Matrix(123,32,688,179) -> Matrix(69,-2,1622,-47) Matrix(275,64,116,27) -> Matrix(71,-2,604,-17) Matrix(271,62,118,27) -> Matrix(69,-2,656,-19) Matrix(963,212,268,59) -> Matrix(71,-2,462,-13) Matrix(535,116,844,183) -> Matrix(139,-4,2398,-69) Matrix(39,8,112,23) -> Matrix(67,-2,1374,-41) Matrix(853,162,258,49) -> Matrix(463,-14,3208,-97) Matrix(333,62,478,89) -> Matrix(65,-2,1138,-35) Matrix(839,150,330,59) -> Matrix(65,-2,618,-19) Matrix(3433,612,948,169) -> Matrix(521,-16,3354,-103) Matrix(473,82,398,69) -> Matrix(67,-2,838,-25) Matrix(251,40,320,51) -> Matrix(65,-2,1008,-31) Matrix(177,26,34,5) -> Matrix(63,-2,284,-9) Matrix(173,24,36,5) -> Matrix(61,-2,336,-11) Matrix(167,18,102,11) -> Matrix(59,-2,620,-21) Matrix(191,-18,138,-13) -> Matrix(53,-2,610,-23) Matrix(261,-38,158,-23) -> Matrix(1,0,-14,1) Matrix(1323,-208,388,-61) -> Matrix(237,-10,1588,-67) Matrix(1009,-160,700,-111) -> Matrix(47,-2,588,-25) Matrix(333,-58,178,-31) -> Matrix(47,-2,494,-21) Matrix(993,-176,536,-95) -> Matrix(47,-2,306,-13) Matrix(1873,-346,406,-75) -> Matrix(183,-8,938,-41) Matrix(1745,-324,684,-127) -> Matrix(45,-2,428,-19) Matrix(545,-116,296,-63) -> Matrix(1,0,-14,1) Matrix(371,-80,320,-69) -> Matrix(139,-6,1784,-77) Matrix(961,-210,270,-59) -> Matrix(45,-2,338,-15) Matrix(123,-28,268,-61) -> Matrix(45,-2,788,-35) Matrix(1063,-256,436,-105) -> Matrix(1,0,-14,1) Matrix(119,-32,212,-57) -> Matrix(43,-2,796,-37) Matrix(517,-142,142,-39) -> Matrix(87,-4,544,-25) Matrix(1103,-308,3728,-1041) -> Matrix(41,-2,882,-43) Matrix(961,-270,210,-59) -> Matrix(41,-2,226,-11) Matrix(1347,-392,512,-149) -> Matrix(257,-12,2206,-103) Matrix(417,-122,1022,-299) -> Matrix(171,-8,3356,-157) Matrix(3359,-992,1412,-417) -> Matrix(127,-6,1122,-53) Matrix(5859,-1732,7432,-2197) -> Matrix(297,-14,4646,-219) Matrix(69,-22,22,-7) -> Matrix(41,-2,308,-15) Matrix(485,-174,354,-127) -> Matrix(161,-8,1912,-95) Matrix(659,-242,482,-177) -> Matrix(79,-4,968,-49) Matrix(1469,-542,1862,-687) -> Matrix(39,-2,644,-33) Matrix(2103,-778,1138,-421) -> Matrix(79,-4,652,-33) Matrix(217,-82,262,-99) -> Matrix(157,-8,2414,-123) Matrix(717,-274,1714,-655) -> Matrix(39,-2,722,-37) Matrix(237,-92,152,-59) -> Matrix(39,-2,410,-21) Matrix(705,-286,106,-43) -> Matrix(41,-2,144,-7) Matrix(809,-332,212,-87) -> Matrix(79,-4,494,-25) Matrix(275,-114,234,-97) -> Matrix(115,-6,1476,-77) Matrix(1775,-744,804,-337) -> Matrix(1,0,-10,1) Matrix(1163,-488,908,-381) -> Matrix(119,-6,1448,-73) Matrix(2585,-1134,1794,-787) -> Matrix(1,0,-6,1) Matrix(1333,-586,1126,-495) -> Matrix(69,-4,880,-51) Matrix(1021,-450,270,-119) -> Matrix(39,-2,254,-13) Matrix(331,-148,208,-93) -> Matrix(1,0,-8,1) Matrix(183,-86,266,-125) -> Matrix(39,-2,644,-33) Matrix(333,-178,58,-31) -> Matrix(35,-2,158,-9) Matrix(545,-296,116,-63) -> Matrix(1,0,-14,1) Matrix(387,-212,272,-149) -> Matrix(75,-4,844,-45) Matrix(1169,-660,480,-271) -> Matrix(35,-2,298,-17) Matrix(957,-542,422,-239) -> Matrix(1,0,-10,1) Matrix(95,-56,56,-33) -> Matrix(35,-2,368,-21) Matrix(261,-158,38,-23) -> Matrix(1,0,-14,1) Matrix(1265,-774,894,-547) -> Matrix(1,0,-6,1) Matrix(1617,-992,1172,-719) -> Matrix(37,-2,426,-23) Matrix(279,-172,352,-217) -> Matrix(37,-2,574,-31) Matrix(777,-482,482,-299) -> Matrix(71,-4,728,-41) Matrix(331,-208,148,-93) -> Matrix(1,0,-8,1) Matrix(993,-628,808,-511) -> Matrix(211,-12,2620,-149) Matrix(237,-152,92,-59) -> Matrix(35,-2,298,-17) Matrix(411,-280,160,-109) -> Matrix(33,-2,314,-19) Matrix(1419,-980,320,-221) -> Matrix(197,-12,1100,-67) Matrix(443,-308,548,-381) -> Matrix(37,-2,574,-31) Matrix(387,-272,212,-149) -> Matrix(67,-4,620,-37) Matrix(1265,-894,774,-547) -> Matrix(1,0,-6,1) Matrix(1987,-1434,1254,-905) -> Matrix(1,0,-6,1) Matrix(191,-138,18,-13) -> Matrix(33,-2,50,-3) Matrix(1617,-1172,992,-719) -> Matrix(33,-2,314,-19) Matrix(485,-354,174,-127) -> Matrix(129,-8,1016,-63) Matrix(1089,-800,260,-191) -> Matrix(33,-2,182,-11) Matrix(1383,-1018,898,-661) -> Matrix(1,0,-6,1) Matrix(293,-216,156,-115) -> Matrix(33,-2,314,-19) Matrix(153,-118,118,-91) -> Matrix(159,-10,1924,-121) Matrix(1163,-908,488,-381) -> Matrix(95,-6,776,-49) Matrix(1075,-846,906,-713) -> Matrix(253,-16,3210,-203) Matrix(10855,-8556,3036,-2393) -> Matrix(157,-10,1052,-67) Matrix(829,-672,132,-107) -> Matrix(187,-12,826,-53) Matrix(993,-808,628,-511) -> Matrix(187,-12,1948,-125) Matrix(791,-650,230,-189) -> Matrix(309,-20,2024,-131) Matrix(275,-234,114,-97) -> Matrix(91,-6,804,-53) Matrix(371,-320,80,-69) -> Matrix(91,-6,440,-29) Matrix(813,-716,176,-155) -> Matrix(269,-18,1360,-91) Matrix(381,-430,70,-79) -> Matrix(131,-10,642,-49) Matrix(683,-786,126,-145) -> Matrix(181,-14,918,-71) Matrix(217,-262,82,-99) -> Matrix(101,-8,846,-67) Matrix(443,-548,308,-381) -> Matrix(25,-2,238,-19) Matrix(279,-352,172,-217) -> Matrix(25,-2,238,-19) Matrix(2317,-2964,684,-875) -> Matrix(293,-24,1990,-163) Matrix(443,-578,338,-441) -> Matrix(433,-36,5184,-431) Matrix(153,-206,26,-35) -> Matrix(47,-4,200,-17) Matrix(1921,-2610,750,-1019) -> Matrix(23,-2,196,-17) Matrix(1767,-2404,724,-985) -> Matrix(23,-2,196,-17) Matrix(1703,-2348,668,-921) -> Matrix(23,-2,242,-21) Matrix(1473,-2036,416,-575) -> Matrix(23,-2,196,-17) Matrix(1283,-1778,578,-801) -> Matrix(1,0,-2,1) Matrix(1591,-2248,448,-633) -> Matrix(45,-4,304,-27) Matrix(1563,-2216,596,-845) -> Matrix(137,-12,1176,-103) Matrix(2889,-4102,1822,-2587) -> Matrix(113,-10,1164,-103) Matrix(539,-782,122,-177) -> Matrix(91,-8,512,-45) Matrix(73,-108,48,-71) -> Matrix(45,-4,484,-43) Matrix(1509,-2330,590,-911) -> Matrix(1,0,-2,1) Matrix(1013,-1568,188,-291) -> Matrix(43,-4,226,-21) Matrix(2887,-4582,1102,-1749) -> Matrix(23,-2,196,-17) Matrix(1703,-2738,1058,-1701) -> Matrix(169,-16,1764,-167) Matrix(1491,-2410,550,-889) -> Matrix(39,-4,322,-33) Matrix(2887,-4672,1192,-1929) -> Matrix(83,-8,716,-69) Matrix(1289,-2100,240,-391) -> Matrix(21,-2,116,-11) Matrix(593,-968,68,-111) -> Matrix(43,-4,140,-13) Matrix(1509,-2482,442,-727) -> Matrix(143,-14,950,-93) Matrix(419,-722,242,-417) -> Matrix(121,-12,1200,-119) Matrix(119,-212,32,-57) -> Matrix(19,-2,124,-13) Matrix(971,-1758,438,-793) -> Matrix(21,-2,200,-19) Matrix(1013,-1838,458,-831) -> Matrix(19,-2,200,-21) Matrix(123,-268,28,-61) -> Matrix(21,-2,116,-11) Matrix(999,-2272,412,-937) -> Matrix(23,-2,196,-17) Matrix(283,-646,46,-105) -> Matrix(19,-2,86,-9) Matrix(2619,-6232,772,-1837) -> Matrix(155,-18,1042,-121) Matrix(717,-1714,274,-655) -> Matrix(19,-2,162,-17) Matrix(417,-1022,122,-299) -> Matrix(67,-8,444,-53) Matrix(12661,-32400,3540,-9059) -> Matrix(37,-4,250,-27) Matrix(12237,-31322,3422,-8759) -> Matrix(1,0,-2,1) Matrix(1045,-2826,186,-503) -> Matrix(115,-14,534,-65) Matrix(3213,-8698,898,-2431) -> Matrix(115,-14,764,-93) Matrix(177,-484,64,-175) -> Matrix(97,-12,768,-95) Matrix(323,-1058,98,-321) -> Matrix(197,-28,1372,-195) Matrix(1103,-3728,308,-1041) -> Matrix(13,-2,98,-15) Matrix(1251,-4240,280,-949) -> Matrix(257,-38,1400,-207) Matrix(1223,-4418,338,-1221) -> Matrix(209,-32,1352,-207) Matrix(49,-192,12,-47) -> Matrix(25,-4,144,-23) Matrix(1079,-4802,242,-1077) -> Matrix(353,-64,1936,-351) Matrix(135,-616,16,-73) -> Matrix(11,-2,28,-5) Matrix(383,-1808,68,-321) -> Matrix(15,-2,68,-9) Matrix(105,-676,16,-103) -> Matrix(33,-8,128,-31) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 Degree of the the map X: 64 Degree of the the map Y: 192 ----------------------------------------------------------------------- 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): 576 Minimal number of generators: 97 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: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/5 1/4 3/7 1/2 2/3 5/7 9/11 1/1 8/7 11/9 5/4 17/13 29/21 7/5 3/2 11/7 37/23 31/19 19/11 13/7 2/1 31/14 7/3 17/7 151/59 13/5 19/7 11/4 3/1 23/7 7/2 47/13 11/3 19/5 4/1 13/3 49/11 9/2 23/5 5/1 11/2 17/3 6/1 19/3 13/2 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 1/27 1/7 1/25 1/24 2/13 1/24 3/19 1/24 1/6 0/1 1/24 3/17 2/47 2/11 2/47 1/23 1/5 1/23 3/14 0/1 1/23 5/23 1/23 5/114 2/9 3/68 2/45 3/13 3/67 1/22 1/4 1/22 3/11 1/22 5/18 2/43 3/64 7/25 3/64 1/21 2/7 0/1 2/43 7/24 2/43 5/107 5/17 3/64 3/10 6/127 1/21 1/3 1/21 1/20 4/11 1/20 7/19 1/20 3/8 1/20 2/39 8/21 2/39 1/19 5/13 1/19 2/5 0/1 1/20 11/27 1/20 9/22 2/39 1/19 7/17 2/39 5/12 0/1 1/19 3/7 1/19 4/9 1/19 2/37 5/11 1/19 1/18 6/13 0/1 1/16 1/2 0/1 2/37 7/13 0/1 6/11 0/1 1/19 5/9 1/18 9/16 1/18 13/23 0/1 4/7 2/37 1/18 3/5 1/18 1/17 11/18 2/35 5/87 19/31 1/17 8/13 0/1 2/35 13/21 1/18 5/8 2/35 1/17 12/19 2/35 1/17 7/11 1/17 2/3 1/17 11/16 4/67 2/33 20/29 7/116 2/33 9/13 1/16 7/10 1/17 4/67 12/17 5/83 2/33 5/7 2/33 13/18 1/17 2/33 21/29 3/49 8/11 4/65 1/16 11/15 1/16 25/34 0/1 1/17 14/19 0/1 2/33 3/4 4/65 1/16 7/9 1/16 5/79 11/14 1/16 26/33 4/63 3/47 15/19 1/16 4/5 4/63 2/31 13/16 7/109 2/31 9/11 2/31 14/17 2/31 5/77 5/6 2/31 3/46 6/7 6/91 1/15 7/8 1/15 1/1 1/14 8/7 1/13 15/13 1/13 11/142 7/6 1/13 6/77 13/11 4/51 6/5 3/38 2/25 11/9 2/25 16/13 2/25 7/87 5/4 2/25 4/49 14/11 1/12 9/7 5/61 1/12 13/10 14/169 1/12 17/13 1/12 4/3 1/12 4/47 19/14 0/1 2/23 34/25 0/1 1/11 15/11 1/12 11/8 1/12 4/47 40/29 4/47 2/23 29/21 3/35 18/13 2/23 1/11 7/5 2/23 17/12 2/23 5/57 44/31 3/34 27/19 3/34 10/7 4/45 1/11 13/9 1/12 16/11 2/23 4/45 3/2 1/11 20/13 0/1 2/21 37/24 0/1 1/11 17/11 1/11 1/10 14/9 2/21 1/10 11/7 1/11 19/12 1/11 2/21 46/29 1/10 27/17 1/11 1/10 8/5 1/11 2/21 37/23 2/21 29/18 2/21 3/31 21/13 1/10 55/34 1/11 2/21 34/21 1/10 13/8 0/1 2/21 44/27 2/21 1/10 31/19 1/11 18/11 5/53 2/21 5/3 1/11 1/10 12/7 4/41 1/10 19/11 1/10 7/4 1/10 2/19 9/5 1/10 29/16 1/10 20/11 3/29 2/19 11/6 0/1 1/9 13/7 0/1 15/8 2/21 1/10 2/1 0/1 2/19 11/5 1/10 1/9 31/14 1/10 20/9 2/19 1/9 9/4 2/19 1/9 7/3 1/9 12/5 0/1 1/9 29/12 4/35 3/26 17/7 2/17 39/16 1/8 22/9 1/9 2/17 5/2 0/1 1/8 23/9 1/9 1/8 87/34 0/1 1/9 151/59 1/9 64/25 1/9 2/17 41/16 0/1 2/17 18/7 1/9 13/5 1/9 21/8 1/9 2/17 29/11 2/17 8/3 2/17 1/8 19/7 1/8 11/4 1/8 3/1 1/8 1/7 13/4 8/57 1/7 23/7 1/7 10/3 1/7 6/41 17/5 3/20 41/12 3/20 8/53 24/7 5/33 2/13 7/2 0/1 2/13 32/9 0/1 1/6 25/7 1/7 3/20 18/5 3/20 2/13 47/13 2/13 29/8 2/13 5/32 11/3 1/6 15/4 0/1 1/6 19/5 2/13 23/6 2/13 3/19 4/1 1/6 13/3 1/6 3/17 22/5 4/23 2/11 31/7 5/28 40/9 13/72 2/11 49/11 2/11 9/2 2/11 3/16 32/7 2/11 4/21 23/5 5/26 1/5 37/8 1/5 14/3 0/1 1/5 5/1 1/5 11/2 1/5 2/9 17/3 2/9 23/4 2/9 4/17 6/1 0/1 1/4 19/3 1/4 13/2 1/4 7/1 1/4 1/3 1/0 0/1 1/1 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(80,-11,131,-18) (0/1,1/7) -> (3/5,11/18) Hyperbolic Matrix(182,-27,27,-4) (1/7,2/13) -> (13/2,7/1) Hyperbolic Matrix(494,-77,77,-12) (2/13,3/19) -> (19/3,13/2) Hyperbolic Matrix(104,-17,257,-42) (3/19,1/6) -> (2/5,11/27) Hyperbolic Matrix(333,-58,178,-31) (1/6,3/17) -> (13/7,15/8) Hyperbolic Matrix(330,-59,179,-32) (3/17,2/11) -> (11/6,13/7) Hyperbolic Matrix(26,-5,125,-24) (2/11,1/5) -> (1/5,3/14) Parabolic Matrix(371,-80,320,-69) (3/14,5/23) -> (15/13,7/6) Hyperbolic Matrix(961,-210,270,-59) (5/23,2/9) -> (32/9,25/7) Hyperbolic Matrix(123,-28,268,-61) (2/9,3/13) -> (5/11,6/13) Hyperbolic Matrix(218,-51,171,-40) (3/13,1/4) -> (14/11,9/7) Hyperbolic Matrix(119,-32,212,-57) (1/4,3/11) -> (5/9,9/16) Hyperbolic Matrix(517,-142,142,-39) (3/11,5/18) -> (29/8,11/3) Hyperbolic Matrix(656,-183,423,-118) (5/18,7/25) -> (17/11,14/9) Hyperbolic Matrix(961,-270,210,-59) (7/25,2/7) -> (32/7,23/5) Hyperbolic Matrix(232,-67,187,-54) (2/7,7/24) -> (16/13,5/4) Hyperbolic Matrix(417,-122,1022,-299) (7/24,5/17) -> (11/27,9/22) Hyperbolic Matrix(300,-89,209,-62) (5/17,3/10) -> (10/7,13/9) Hyperbolic Matrix(69,-22,22,-7) (3/10,1/3) -> (3/1,13/4) Hyperbolic Matrix(66,-23,23,-8) (1/3,4/11) -> (11/4,3/1) Hyperbolic Matrix(418,-153,153,-56) (4/11,7/19) -> (19/7,11/4) Hyperbolic Matrix(240,-89,329,-122) (7/19,3/8) -> (8/11,11/15) Hyperbolic Matrix(217,-82,262,-99) (3/8,8/21) -> (14/17,5/6) Hyperbolic Matrix(478,-183,303,-116) (8/21,5/13) -> (11/7,19/12) Hyperbolic Matrix(237,-92,152,-59) (5/13,2/5) -> (14/9,11/7) Hyperbolic Matrix(809,-332,212,-87) (9/22,7/17) -> (19/5,23/6) Hyperbolic Matrix(275,-114,234,-97) (7/17,5/12) -> (7/6,13/11) Hyperbolic Matrix(64,-27,147,-62) (5/12,3/7) -> (3/7,4/9) Parabolic Matrix(331,-148,208,-93) (4/9,5/11) -> (27/17,8/5) Hyperbolic Matrix(183,-86,266,-125) (6/13,1/2) -> (11/16,20/29) Hyperbolic Matrix(333,-178,58,-31) (1/2,7/13) -> (17/3,23/4) Hyperbolic Matrix(330,-179,59,-32) (7/13,6/11) -> (11/2,17/3) Hyperbolic Matrix(387,-212,272,-149) (6/11,5/9) -> (27/19,10/7) Hyperbolic Matrix(1169,-660,480,-271) (9/16,13/23) -> (17/7,39/16) Hyperbolic Matrix(786,-445,325,-184) (13/23,4/7) -> (29/12,17/7) Hyperbolic Matrix(95,-56,56,-33) (4/7,3/5) -> (5/3,12/7) Hyperbolic Matrix(1080,-661,781,-478) (11/18,19/31) -> (29/21,18/13) Hyperbolic Matrix(1617,-992,1172,-719) (19/31,8/13) -> (40/29,29/21) Hyperbolic Matrix(279,-172,352,-217) (8/13,13/21) -> (15/19,4/5) Hyperbolic Matrix(777,-482,482,-299) (13/21,5/8) -> (29/18,21/13) Hyperbolic Matrix(331,-208,148,-93) (5/8,12/19) -> (20/9,9/4) Hyperbolic Matrix(478,-303,183,-116) (12/19,7/11) -> (13/5,21/8) Hyperbolic Matrix(237,-152,92,-59) (7/11,2/3) -> (18/7,13/5) Hyperbolic Matrix(411,-280,160,-109) (2/3,11/16) -> (41/16,18/7) Hyperbolic Matrix(1419,-980,320,-221) (20/29,9/13) -> (31/7,40/9) Hyperbolic Matrix(300,-209,89,-62) (9/13,7/10) -> (10/3,17/5) Hyperbolic Matrix(387,-272,212,-149) (7/10,12/17) -> (20/11,11/6) Hyperbolic Matrix(176,-125,245,-174) (12/17,5/7) -> (5/7,13/18) Parabolic Matrix(1080,-781,661,-478) (13/18,21/29) -> (31/19,18/11) Hyperbolic Matrix(1617,-1172,992,-719) (21/29,8/11) -> (44/27,31/19) Hyperbolic Matrix(900,-661,1141,-838) (11/15,25/34) -> (26/33,15/19) Hyperbolic Matrix(1383,-1018,898,-661) (25/34,14/19) -> (20/13,37/24) Hyperbolic Matrix(293,-216,156,-115) (14/19,3/4) -> (15/8,2/1) Hyperbolic Matrix(153,-118,118,-91) (3/4,7/9) -> (9/7,13/10) Hyperbolic Matrix(218,-171,51,-40) (7/9,11/14) -> (4/1,13/3) Hyperbolic Matrix(454,-357,117,-92) (11/14,26/33) -> (23/6,4/1) Hyperbolic Matrix(232,-187,67,-54) (4/5,13/16) -> (24/7,7/2) Hyperbolic Matrix(298,-243,363,-296) (13/16,9/11) -> (9/11,14/17) Parabolic Matrix(275,-234,114,-97) (5/6,6/7) -> (12/5,29/12) Hyperbolic Matrix(371,-320,80,-69) (6/7,7/8) -> (37/8,14/3) Hyperbolic Matrix(16,-15,15,-14) (7/8,1/1) -> (1/1,8/7) Parabolic Matrix(642,-739,139,-160) (8/7,15/13) -> (23/5,37/8) Hyperbolic Matrix(260,-309,69,-82) (13/11,6/5) -> (15/4,19/5) Hyperbolic Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(566,-695,215,-264) (11/9,16/13) -> (21/8,29/11) Hyperbolic Matrix(279,-352,172,-217) (5/4,14/11) -> (34/21,13/8) Hyperbolic Matrix(222,-289,169,-220) (13/10,17/13) -> (17/13,4/3) Parabolic Matrix(153,-206,26,-35) (4/3,19/14) -> (23/4,6/1) Hyperbolic Matrix(1921,-2610,750,-1019) (19/14,34/25) -> (64/25,41/16) Hyperbolic Matrix(1130,-1539,699,-952) (34/25,15/11) -> (21/13,55/34) Hyperbolic Matrix(240,-329,89,-122) (15/11,11/8) -> (8/3,19/7) Hyperbolic Matrix(984,-1357,277,-382) (11/8,40/29) -> (7/2,32/9) Hyperbolic Matrix(176,-245,125,-174) (18/13,7/5) -> (7/5,17/12) Parabolic Matrix(992,-1407,447,-634) (17/12,44/31) -> (31/14,20/9) Hyperbolic Matrix(830,-1179,459,-652) (44/31,27/19) -> (9/5,29/16) Hyperbolic Matrix(539,-782,122,-177) (13/9,16/11) -> (22/5,31/7) Hyperbolic Matrix(73,-108,48,-71) (16/11,3/2) -> (3/2,20/13) Parabolic Matrix(1509,-2330,590,-911) (37/24,17/11) -> (23/9,87/34) Hyperbolic Matrix(928,-1471,511,-810) (19/12,46/29) -> (29/16,20/11) Hyperbolic Matrix(846,-1343,383,-608) (46/29,27/17) -> (11/5,31/14) Hyperbolic Matrix(852,-1369,529,-850) (8/5,37/23) -> (37/23,29/18) Parabolic Matrix(1788,-2893,733,-1186) (55/34,34/21) -> (39/16,22/9) Hyperbolic Matrix(936,-1525,205,-334) (13/8,44/27) -> (9/2,32/7) Hyperbolic Matrix(80,-131,11,-18) (18/11,5/3) -> (7/1,1/0) Hyperbolic Matrix(210,-361,121,-208) (12/7,19/11) -> (19/11,7/4) Parabolic Matrix(119,-212,32,-57) (7/4,9/5) -> (11/3,15/4) Hyperbolic Matrix(123,-268,28,-61) (2/1,11/5) -> (13/3,22/5) Hyperbolic Matrix(64,-147,27,-62) (9/4,7/3) -> (7/3,12/5) Parabolic Matrix(417,-1022,122,-299) (22/9,5/2) -> (41/12,24/7) Hyperbolic Matrix(212,-539,59,-150) (5/2,23/9) -> (25/7,18/5) Hyperbolic Matrix(8910,-22801,3481,-8908) (87/34,151/59) -> (151/59,64/25) Parabolic Matrix(162,-529,49,-160) (13/4,23/7) -> (23/7,10/3) Parabolic Matrix(258,-881,41,-140) (17/5,41/12) -> (6/1,19/3) Hyperbolic Matrix(612,-2209,169,-610) (18/5,47/13) -> (47/13,29/8) Parabolic Matrix(540,-2401,121,-538) (40/9,49/11) -> (49/11,9/2) Parabolic Matrix(26,-125,5,-24) (14/3,5/1) -> (5/1,11/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,26,1) Matrix(80,-11,131,-18) -> Matrix(49,-2,858,-35) Matrix(182,-27,27,-4) -> Matrix(49,-2,172,-7) Matrix(494,-77,77,-12) -> Matrix(143,-6,596,-25) Matrix(104,-17,257,-42) -> Matrix(1,0,-4,1) Matrix(333,-58,178,-31) -> Matrix(47,-2,494,-21) Matrix(330,-59,179,-32) -> Matrix(47,-2,400,-17) Matrix(26,-5,125,-24) -> Matrix(47,-2,1058,-45) Matrix(371,-80,320,-69) -> Matrix(139,-6,1784,-77) Matrix(961,-210,270,-59) -> Matrix(45,-2,338,-15) Matrix(123,-28,268,-61) -> Matrix(45,-2,788,-35) Matrix(218,-51,171,-40) -> Matrix(43,-2,538,-25) Matrix(119,-32,212,-57) -> Matrix(43,-2,796,-37) Matrix(517,-142,142,-39) -> Matrix(87,-4,544,-25) Matrix(656,-183,423,-118) -> Matrix(85,-4,914,-43) Matrix(961,-270,210,-59) -> Matrix(41,-2,226,-11) Matrix(232,-67,187,-54) -> Matrix(87,-4,1066,-49) Matrix(417,-122,1022,-299) -> Matrix(171,-8,3356,-157) Matrix(300,-89,209,-62) -> Matrix(43,-2,452,-21) Matrix(69,-22,22,-7) -> Matrix(41,-2,308,-15) Matrix(66,-23,23,-8) -> Matrix(41,-2,308,-15) Matrix(418,-153,153,-56) -> Matrix(199,-10,1612,-81) Matrix(240,-89,329,-122) -> Matrix(119,-6,1924,-97) Matrix(217,-82,262,-99) -> Matrix(157,-8,2414,-123) Matrix(478,-183,303,-116) -> Matrix(77,-4,828,-43) Matrix(237,-92,152,-59) -> Matrix(39,-2,410,-21) Matrix(809,-332,212,-87) -> Matrix(79,-4,494,-25) Matrix(275,-114,234,-97) -> Matrix(115,-6,1476,-77) Matrix(64,-27,147,-62) -> Matrix(39,-2,722,-37) Matrix(331,-148,208,-93) -> Matrix(1,0,-8,1) Matrix(183,-86,266,-125) -> Matrix(39,-2,644,-33) Matrix(333,-178,58,-31) -> Matrix(35,-2,158,-9) Matrix(330,-179,59,-32) -> Matrix(39,-2,176,-9) Matrix(387,-212,272,-149) -> Matrix(75,-4,844,-45) Matrix(1169,-660,480,-271) -> Matrix(35,-2,298,-17) Matrix(786,-445,325,-184) -> Matrix(39,-2,332,-17) Matrix(95,-56,56,-33) -> Matrix(35,-2,368,-21) Matrix(1080,-661,781,-478) -> Matrix(139,-8,1616,-93) Matrix(1617,-992,1172,-719) -> Matrix(37,-2,426,-23) Matrix(279,-172,352,-217) -> Matrix(37,-2,574,-31) Matrix(777,-482,482,-299) -> Matrix(71,-4,728,-41) Matrix(331,-208,148,-93) -> Matrix(1,0,-8,1) Matrix(478,-303,183,-116) -> Matrix(69,-4,604,-35) Matrix(237,-152,92,-59) -> Matrix(35,-2,298,-17) Matrix(411,-280,160,-109) -> Matrix(33,-2,314,-19) Matrix(1419,-980,320,-221) -> Matrix(197,-12,1100,-67) Matrix(300,-209,89,-62) -> Matrix(35,-2,228,-13) Matrix(387,-272,212,-149) -> Matrix(67,-4,620,-37) Matrix(176,-125,245,-174) -> Matrix(133,-8,2178,-131) Matrix(1080,-781,661,-478) -> Matrix(131,-8,1392,-85) Matrix(1617,-1172,992,-719) -> Matrix(33,-2,314,-19) Matrix(900,-661,1141,-838) -> Matrix(65,-4,1024,-63) Matrix(1383,-1018,898,-661) -> Matrix(1,0,-6,1) Matrix(293,-216,156,-115) -> Matrix(33,-2,314,-19) Matrix(153,-118,118,-91) -> Matrix(159,-10,1924,-121) Matrix(218,-171,51,-40) -> Matrix(31,-2,202,-13) Matrix(454,-357,117,-92) -> Matrix(95,-6,586,-37) Matrix(232,-187,67,-54) -> Matrix(63,-4,394,-25) Matrix(298,-243,363,-296) -> Matrix(373,-24,5766,-371) Matrix(275,-234,114,-97) -> Matrix(91,-6,804,-53) Matrix(371,-320,80,-69) -> Matrix(91,-6,440,-29) Matrix(16,-15,15,-14) -> Matrix(29,-2,392,-27) Matrix(642,-739,139,-160) -> Matrix(207,-16,1048,-81) Matrix(260,-309,69,-82) -> Matrix(25,-2,188,-15) Matrix(217,-262,82,-99) -> Matrix(101,-8,846,-67) Matrix(566,-695,215,-264) -> Matrix(199,-16,1704,-137) Matrix(279,-352,172,-217) -> Matrix(25,-2,238,-19) Matrix(222,-289,169,-220) -> Matrix(217,-18,2592,-215) Matrix(153,-206,26,-35) -> Matrix(47,-4,200,-17) Matrix(1921,-2610,750,-1019) -> Matrix(23,-2,196,-17) Matrix(1130,-1539,699,-952) -> Matrix(23,-2,242,-21) Matrix(240,-329,89,-122) -> Matrix(71,-6,580,-49) Matrix(984,-1357,277,-382) -> Matrix(47,-4,294,-25) Matrix(176,-245,125,-174) -> Matrix(93,-8,1058,-91) Matrix(992,-1407,447,-634) -> Matrix(91,-8,876,-77) Matrix(830,-1179,459,-652) -> Matrix(23,-2,196,-17) Matrix(539,-782,122,-177) -> Matrix(91,-8,512,-45) Matrix(73,-108,48,-71) -> Matrix(45,-4,484,-43) Matrix(1509,-2330,590,-911) -> Matrix(1,0,-2,1) Matrix(928,-1471,511,-810) -> Matrix(41,-4,400,-39) Matrix(846,-1343,383,-608) -> Matrix(21,-2,200,-19) Matrix(852,-1369,529,-850) -> Matrix(85,-8,882,-83) Matrix(1788,-2893,733,-1186) -> Matrix(1,0,-2,1) Matrix(936,-1525,205,-334) -> Matrix(43,-4,226,-21) Matrix(80,-131,11,-18) -> Matrix(21,-2,74,-7) Matrix(210,-361,121,-208) -> Matrix(61,-6,600,-59) Matrix(119,-212,32,-57) -> Matrix(19,-2,124,-13) Matrix(123,-268,28,-61) -> Matrix(21,-2,116,-11) Matrix(64,-147,27,-62) -> Matrix(19,-2,162,-17) Matrix(417,-1022,122,-299) -> Matrix(67,-8,444,-53) Matrix(212,-539,59,-150) -> Matrix(19,-2,124,-13) Matrix(8910,-22801,3481,-8908) -> Matrix(19,-2,162,-17) Matrix(162,-529,49,-160) -> Matrix(99,-14,686,-97) Matrix(258,-881,41,-140) -> Matrix(53,-8,232,-35) Matrix(612,-2209,169,-610) -> Matrix(105,-16,676,-103) Matrix(540,-2401,121,-538) -> Matrix(177,-32,968,-175) Matrix(26,-125,5,-24) -> Matrix(11,-2,50,-9) 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): 32 ----------------------------------------------------------------------- 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 26 1 1/1 1/14 2 15 8/7 1/13 12 2 7/6 (1/13,6/77) 0 30 6/5 (3/38,2/25) 0 30 11/9 2/25 6 3 16/13 (2/25,7/87) 0 30 5/4 0 10 14/11 1/12 2 6 9/7 (5/61,1/12) 0 15 17/13 1/12 18 1 4/3 (1/12,4/47) 0 30 19/14 0 10 34/25 (0/1,1/11) 0 30 15/11 1/12 2 15 11/8 (1/12,4/47) 0 30 29/21 3/35 2 3 18/13 (2/23,1/11) 0 30 7/5 2/23 2 5 17/12 (2/23,5/57) 0 30 10/7 (4/45,1/11) 0 30 13/9 1/12 2 15 16/11 0 10 3/2 1/11 2 6 11/7 1/11 2 5 19/12 (1/11,2/21) 0 30 8/5 (1/11,2/21) 0 30 37/23 2/21 2 1 21/13 1/10 2 15 55/34 (1/11,2/21) 0 30 34/21 1/10 2 6 13/8 0 10 44/27 (2/21,1/10) 0 30 31/19 1/11 2 3 18/11 (5/53,2/21) 0 30 5/3 (1/11,1/10) 0 15 19/11 1/10 6 1 7/4 (1/10,2/19) 0 30 9/5 1/10 2 15 29/16 1/10 2 2 20/11 (3/29,2/19) 0 30 11/6 (0/1,1/9) 0 30 13/7 0/1 2 3 2/1 0 10 11/5 (1/10,1/9) 0 15 31/14 1/10 2 2 20/9 (2/19,1/9) 0 30 9/4 (2/19,1/9) 0 30 7/3 1/9 2 3 12/5 (0/1,1/9) 0 30 29/12 (4/35,3/26) 0 30 17/7 2/17 2 5 22/9 (1/9,2/17) 0 30 5/2 (0/1,1/8) 0 30 23/9 (1/9,1/8) 0 15 151/59 1/9 2 1 64/25 (1/9,2/17) 0 30 41/16 0 10 18/7 1/9 2 6 13/5 1/9 2 5 21/8 (1/9,2/17) 0 30 29/11 2/17 6 3 8/3 (2/17,1/8) 0 30 19/7 1/8 2 15 11/4 1/8 6 2 3/1 (1/8,1/7) 0 15 23/7 1/7 14 1 10/3 (1/7,6/41) 0 30 17/5 3/20 2 15 41/12 (3/20,8/53) 0 30 24/7 (5/33,2/13) 0 30 7/2 0 10 25/7 (1/7,3/20) 0 15 18/5 (3/20,2/13) 0 30 47/13 2/13 4 1 11/3 1/6 2 15 15/4 (0/1,1/6) 0 30 19/5 2/13 2 5 23/6 (2/13,3/19) 0 30 4/1 1/6 2 6 13/3 (1/6,3/17) 0 15 22/5 0 10 31/7 5/28 2 15 49/11 2/11 8 1 9/2 (2/11,3/16) 0 30 32/7 0 10 23/5 (5/26,1/5) 0 15 37/8 1/5 12 2 14/3 (0/1,1/5) 0 30 5/1 1/5 2 5 11/2 (1/5,2/9) 0 30 17/3 2/9 2 3 23/4 0 10 6/1 (0/1,1/4) 0 30 19/3 1/4 2 15 13/2 1/4 4 2 7/1 (1/4,1/3) 0 15 1/0 (0/1,1/1) 0 30 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(15,-16,14,-15) (1/1,8/7) -> (1/1,8/7) Reflection Matrix(320,-371,69,-80) (8/7,7/6) -> (37/8,14/3) Glide Reflection Matrix(234,-275,97,-114) (7/6,6/5) -> (12/5,29/12) Glide Reflection Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(566,-695,215,-264) (11/9,16/13) -> (21/8,29/11) Hyperbolic Matrix(187,-232,54,-67) (16/13,5/4) -> (24/7,7/2) Glide Reflection Matrix(279,-352,172,-217) (5/4,14/11) -> (34/21,13/8) Hyperbolic Matrix(171,-218,40,-51) (14/11,9/7) -> (4/1,13/3) Glide Reflection Matrix(118,-153,91,-118) (9/7,17/13) -> (9/7,17/13) Reflection Matrix(103,-136,78,-103) (17/13,4/3) -> (17/13,4/3) Reflection Matrix(153,-206,26,-35) (4/3,19/14) -> (23/4,6/1) Hyperbolic Matrix(1921,-2610,750,-1019) (19/14,34/25) -> (64/25,41/16) Hyperbolic Matrix(1130,-1539,699,-952) (34/25,15/11) -> (21/13,55/34) Hyperbolic Matrix(240,-329,89,-122) (15/11,11/8) -> (8/3,19/7) Hyperbolic Matrix(1172,-1617,719,-992) (11/8,29/21) -> (44/27,31/19) Glide Reflection Matrix(781,-1080,478,-661) (29/21,18/13) -> (31/19,18/11) Glide Reflection Matrix(176,-245,125,-174) (18/13,7/5) -> (7/5,17/12) Parabolic Matrix(272,-387,149,-212) (17/12,10/7) -> (20/11,11/6) Glide Reflection Matrix(209,-300,62,-89) (10/7,13/9) -> (10/3,17/5) Glide Reflection Matrix(539,-782,122,-177) (13/9,16/11) -> (22/5,31/7) Hyperbolic Matrix(280,-411,109,-160) (16/11,3/2) -> (41/16,18/7) Glide Reflection Matrix(152,-237,59,-92) (3/2,11/7) -> (18/7,13/5) Glide Reflection Matrix(303,-478,116,-183) (11/7,19/12) -> (13/5,21/8) Glide Reflection Matrix(208,-331,93,-148) (19/12,8/5) -> (20/9,9/4) Glide Reflection Matrix(369,-592,230,-369) (8/5,37/23) -> (8/5,37/23) Reflection Matrix(482,-777,299,-482) (37/23,21/13) -> (37/23,21/13) Reflection Matrix(619,-1002,160,-259) (55/34,34/21) -> (23/6,4/1) Glide Reflection Matrix(936,-1525,205,-334) (13/8,44/27) -> (9/2,32/7) Hyperbolic Matrix(80,-131,11,-18) (18/11,5/3) -> (7/1,1/0) Hyperbolic Matrix(56,-95,33,-56) (5/3,19/11) -> (5/3,19/11) Reflection Matrix(153,-266,88,-153) (19/11,7/4) -> (19/11,7/4) Reflection Matrix(119,-212,32,-57) (7/4,9/5) -> (11/3,15/4) Hyperbolic Matrix(289,-522,160,-289) (9/5,29/16) -> (9/5,29/16) Reflection Matrix(661,-1200,298,-541) (29/16,20/11) -> (31/14,20/9) Glide Reflection Matrix(179,-330,32,-59) (11/6,13/7) -> (11/2,17/3) Glide Reflection Matrix(178,-333,31,-58) (13/7,2/1) -> (17/3,23/4) Glide Reflection Matrix(123,-268,28,-61) (2/1,11/5) -> (13/3,22/5) Hyperbolic Matrix(309,-682,140,-309) (11/5,31/14) -> (11/5,31/14) Reflection Matrix(64,-147,27,-62) (9/4,7/3) -> (7/3,12/5) Parabolic Matrix(333,-806,88,-213) (29/12,17/7) -> (15/4,19/5) Glide Reflection Matrix(332,-809,87,-212) (17/7,22/9) -> (19/5,23/6) Glide Reflection Matrix(417,-1022,122,-299) (22/9,5/2) -> (41/12,24/7) Hyperbolic Matrix(212,-539,59,-150) (5/2,23/9) -> (25/7,18/5) Hyperbolic Matrix(1358,-3473,531,-1358) (23/9,151/59) -> (23/9,151/59) Reflection Matrix(7551,-19328,2950,-7551) (151/59,64/25) -> (151/59,64/25) Reflection Matrix(153,-418,56,-153) (19/7,11/4) -> (19/7,11/4) Reflection Matrix(23,-66,8,-23) (11/4,3/1) -> (11/4,3/1) Reflection Matrix(22,-69,7,-22) (3/1,23/7) -> (3/1,23/7) Reflection Matrix(139,-460,42,-139) (23/7,10/3) -> (23/7,10/3) Reflection Matrix(258,-881,41,-140) (17/5,41/12) -> (6/1,19/3) Hyperbolic Matrix(270,-961,59,-210) (7/2,25/7) -> (32/7,23/5) Glide Reflection Matrix(469,-1692,130,-469) (18/5,47/13) -> (18/5,47/13) Reflection Matrix(142,-517,39,-142) (47/13,11/3) -> (47/13,11/3) Reflection Matrix(342,-1519,77,-342) (31/7,49/11) -> (31/7,49/11) Reflection Matrix(197,-882,44,-197) (49/11,9/2) -> (49/11,9/2) Reflection Matrix(369,-1702,80,-369) (23/5,37/8) -> (23/5,37/8) Reflection Matrix(26,-125,5,-24) (14/3,5/1) -> (5/1,11/2) Parabolic Matrix(77,-494,12,-77) (19/3,13/2) -> (19/3,13/2) Reflection Matrix(27,-182,4,-27) (13/2,7/1) -> (13/2,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,2,-1) (-1/1,1/0) -> (0/1,1/1) Matrix(0,1,1,0) -> Matrix(1,0,28,-1) (-1/1,1/1) -> (0/1,1/14) Matrix(15,-16,14,-15) -> Matrix(27,-2,364,-27) (1/1,8/7) -> (1/14,1/13) Matrix(320,-371,69,-80) -> Matrix(77,-6,372,-29) Matrix(234,-275,97,-114) -> Matrix(77,-6,680,-53) Matrix(217,-262,82,-99) -> Matrix(101,-8,846,-67) Matrix(566,-695,215,-264) -> Matrix(199,-16,1704,-137) Matrix(187,-232,54,-67) -> Matrix(49,-4,306,-25) Matrix(279,-352,172,-217) -> Matrix(25,-2,238,-19) Matrix(171,-218,40,-51) -> Matrix(25,-2,162,-13) Matrix(118,-153,91,-118) -> Matrix(121,-10,1464,-121) (9/7,17/13) -> (5/61,1/12) Matrix(103,-136,78,-103) -> Matrix(95,-8,1128,-95) (17/13,4/3) -> (1/12,4/47) Matrix(153,-206,26,-35) -> Matrix(47,-4,200,-17) Matrix(1921,-2610,750,-1019) -> Matrix(23,-2,196,-17) Matrix(1130,-1539,699,-952) -> Matrix(23,-2,242,-21) 1/11 Matrix(240,-329,89,-122) -> Matrix(71,-6,580,-49) Matrix(1172,-1617,719,-992) -> Matrix(23,-2,218,-19) Matrix(781,-1080,478,-661) -> Matrix(93,-8,988,-85) Matrix(176,-245,125,-174) -> Matrix(93,-8,1058,-91) 2/23 Matrix(272,-387,149,-212) -> Matrix(45,-4,416,-37) Matrix(209,-300,62,-89) -> Matrix(21,-2,136,-13) Matrix(539,-782,122,-177) -> Matrix(91,-8,512,-45) Matrix(280,-411,109,-160) -> Matrix(23,-2,218,-19) Matrix(152,-237,59,-92) -> Matrix(21,-2,178,-17) Matrix(303,-478,116,-183) -> Matrix(43,-4,376,-35) Matrix(208,-331,93,-148) -> Matrix(1,0,20,-1) *** -> (0/1,1/10) Matrix(369,-592,230,-369) -> Matrix(43,-4,462,-43) (8/5,37/23) -> (1/11,2/21) Matrix(482,-777,299,-482) -> Matrix(41,-4,420,-41) (37/23,21/13) -> (2/21,1/10) Matrix(619,-1002,160,-259) -> Matrix(41,-4,256,-25) Matrix(936,-1525,205,-334) -> Matrix(43,-4,226,-21) Matrix(80,-131,11,-18) -> Matrix(21,-2,74,-7) Matrix(56,-95,33,-56) -> Matrix(21,-2,220,-21) (5/3,19/11) -> (1/11,1/10) Matrix(153,-266,88,-153) -> Matrix(39,-4,380,-39) (19/11,7/4) -> (1/10,2/19) Matrix(119,-212,32,-57) -> Matrix(19,-2,124,-13) Matrix(289,-522,160,-289) -> Matrix(19,-2,180,-19) (9/5,29/16) -> (1/10,1/9) Matrix(661,-1200,298,-541) -> Matrix(39,-4,380,-39) *** -> (1/10,2/19) Matrix(179,-330,32,-59) -> Matrix(17,-2,76,-9) Matrix(178,-333,31,-58) -> Matrix(21,-2,94,-9) Matrix(123,-268,28,-61) -> Matrix(21,-2,116,-11) Matrix(309,-682,140,-309) -> Matrix(19,-2,180,-19) (11/5,31/14) -> (1/10,1/9) Matrix(64,-147,27,-62) -> Matrix(19,-2,162,-17) 1/9 Matrix(333,-806,88,-213) -> Matrix(35,-4,236,-27) Matrix(332,-809,87,-212) -> Matrix(33,-4,206,-25) Matrix(417,-1022,122,-299) -> Matrix(67,-8,444,-53) Matrix(212,-539,59,-150) -> Matrix(19,-2,124,-13) Matrix(1358,-3473,531,-1358) -> Matrix(17,-2,144,-17) (23/9,151/59) -> (1/9,1/8) Matrix(7551,-19328,2950,-7551) -> Matrix(35,-4,306,-35) (151/59,64/25) -> (1/9,2/17) Matrix(153,-418,56,-153) -> Matrix(81,-10,656,-81) (19/7,11/4) -> (5/41,1/8) Matrix(23,-66,8,-23) -> Matrix(15,-2,112,-15) (11/4,3/1) -> (1/8,1/7) Matrix(22,-69,7,-22) -> Matrix(15,-2,112,-15) (3/1,23/7) -> (1/8,1/7) Matrix(139,-460,42,-139) -> Matrix(83,-12,574,-83) (23/7,10/3) -> (1/7,6/41) Matrix(258,-881,41,-140) -> Matrix(53,-8,232,-35) Matrix(270,-961,59,-210) -> Matrix(15,-2,82,-11) Matrix(469,-1692,130,-469) -> Matrix(79,-12,520,-79) (18/5,47/13) -> (3/20,2/13) Matrix(142,-517,39,-142) -> Matrix(25,-4,156,-25) (47/13,11/3) -> (2/13,1/6) Matrix(342,-1519,77,-342) -> Matrix(111,-20,616,-111) (31/7,49/11) -> (5/28,2/11) Matrix(197,-882,44,-197) -> Matrix(65,-12,352,-65) (49/11,9/2) -> (2/11,3/16) Matrix(369,-1702,80,-369) -> Matrix(51,-10,260,-51) (23/5,37/8) -> (5/26,1/5) Matrix(26,-125,5,-24) -> Matrix(11,-2,50,-9) 1/5 Matrix(77,-494,12,-77) -> Matrix(25,-6,104,-25) (19/3,13/2) -> (3/13,1/4) Matrix(27,-182,4,-27) -> Matrix(7,-2,24,-7) (13/2,7/1) -> (1/4,1/3) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.