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: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -8/1 -7/1 -6/1 -16/3 -21/4 -4/1 -7/2 -8/3 -21/8 -7/3 -2/1 -7/4 -12/7 -7/5 -4/3 -21/16 -7/6 0/1 1/1 7/6 28/23 14/11 21/16 4/3 7/5 3/2 14/9 84/53 28/17 12/7 7/4 2/1 28/13 7/3 196/83 112/47 5/2 28/11 70/27 21/8 8/3 14/5 3/1 42/13 7/2 112/31 56/15 4/1 13/3 84/19 9/2 14/3 19/4 29/6 5/1 31/6 21/4 16/3 11/2 28/5 23/4 6/1 13/2 7/1 15/2 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -2/1 -9/1 -1/1 -3/4 -8/1 -1/1 -15/2 0/1 1/0 -7/1 -2/1 0/1 -6/1 -2/1 -23/4 -4/3 -5/4 -17/3 -7/6 -1/1 -28/5 -1/1 -11/2 -1/1 -2/3 -16/3 1/0 -21/4 -2/1 0/1 -26/5 0/1 -5/1 -1/1 1/0 -19/4 -3/1 -2/1 -14/3 -2/1 -9/2 -2/1 -3/2 -22/5 -4/3 -13/3 -3/2 -1/1 -30/7 -2/1 -47/11 -5/4 -1/1 -17/4 -2/1 -3/2 -4/1 -1/1 -19/5 -7/4 -5/3 -34/9 -2/1 -15/4 -2/1 -3/2 -26/7 -2/1 -11/3 -5/3 -3/2 -7/2 -2/1 -4/3 -17/5 -5/3 -3/2 -27/8 -2/1 -3/2 -10/3 -4/3 -13/4 -7/5 -4/3 -42/13 -4/3 -29/9 -21/16 -17/13 -16/5 -5/4 -3/1 -3/2 -1/1 -20/7 -7/5 -37/13 -7/5 -25/18 -17/6 -11/8 -4/3 -14/5 -4/3 -11/4 -4/3 -9/7 -19/7 -19/15 -5/4 -46/17 -6/5 -27/10 -4/3 -5/4 -8/3 -5/4 -29/11 -9/7 -5/4 -21/8 -4/3 -6/5 -55/21 -9/7 -5/4 -89/34 -6/5 -7/6 -34/13 -4/3 -13/5 -5/4 -1/1 -31/12 -4/3 -1/1 -18/7 -6/5 -41/16 -6/5 -7/6 -64/25 -1/1 -23/9 -7/6 -1/1 -28/11 -1/1 -5/2 -4/3 -1/1 -17/7 -5/4 -11/9 -29/12 -5/4 -6/5 -12/5 -5/4 -31/13 -7/6 -1/1 -50/21 -4/3 -19/8 -6/5 -1/1 -26/11 -4/3 -7/3 -4/3 -6/5 -30/13 -4/3 -83/36 -5/4 -26/21 -53/23 -5/4 -11/9 -23/10 -5/4 -6/5 -39/17 -3/2 -1/1 -55/24 -4/3 -1/1 -16/7 -1/1 -41/18 -4/3 -13/10 -66/29 -4/3 -25/11 -9/7 -5/4 -84/37 -5/4 -59/26 -5/4 -16/13 -34/15 -6/5 -9/4 -4/3 -5/4 -20/9 -11/9 -11/5 -7/6 -1/1 -13/6 -6/5 -1/1 -28/13 -1/1 -15/7 -5/4 -1/1 -2/1 -6/5 -11/6 -6/5 -1/1 -9/5 -7/6 -15/13 -7/4 -6/5 -8/7 -19/11 -7/6 -15/13 -31/18 -6/5 -1/1 -43/25 -7/6 -1/1 -55/32 -8/7 -1/1 -12/7 -1/1 -41/24 -17/14 -6/5 -70/41 -6/5 -29/17 -25/21 -19/16 -17/10 -20/17 -7/6 -22/13 -8/7 -27/16 -6/5 -7/6 -5/3 -7/6 -1/1 -28/17 -7/6 -23/14 -7/6 -22/19 -18/11 -8/7 -13/8 -8/7 -1/1 -34/21 -8/7 -21/13 -6/5 -8/7 -71/44 -6/5 -7/6 -50/31 -6/5 -29/18 -7/6 -8/7 -8/5 -7/6 -27/17 -7/6 -29/25 -19/12 -15/13 -38/33 -30/19 -8/7 -11/7 -23/20 -31/27 -36/23 -47/41 -61/39 -47/41 -55/48 -86/55 -102/89 -25/16 -63/55 -8/7 -14/9 -8/7 -3/2 -8/7 -9/8 -22/15 -10/9 -19/13 -11/10 -1/1 -54/37 -8/7 -35/24 -8/7 -10/9 -16/11 -9/8 -29/20 -9/8 -10/9 -42/29 -10/9 -55/38 -10/9 -1/1 -13/9 -9/8 -1/1 -36/25 -1/1 -59/41 -17/15 -9/8 -23/16 -8/7 -9/8 -10/7 -10/9 -47/33 -15/14 -1/1 -84/59 -1/1 -37/26 -4/3 -1/1 -27/19 -7/6 -15/13 -17/12 -9/8 -10/9 -24/17 -1/1 -7/5 -8/7 -10/9 -32/23 -1/1 -57/41 -35/31 -9/8 -196/141 -9/8 -139/100 -9/8 -82/73 -82/59 -28/25 -25/18 -10/9 -1/1 -18/13 -8/7 -65/47 -53/47 -9/8 -112/81 -9/8 -47/34 -9/8 -46/41 -29/21 -19/17 -29/26 -40/29 -11/10 -11/8 -8/7 -1/1 -26/19 -8/7 -41/30 -8/7 -9/8 -56/41 -9/8 -15/11 -9/8 -1/1 -19/14 -8/7 -1/1 -23/17 -17/15 -9/8 -27/20 -26/23 -9/8 -4/3 -9/8 -29/22 -8/7 -9/8 -25/19 -9/8 -19/17 -21/16 -28/25 -10/9 -59/45 -9/8 -19/17 -38/29 -28/25 -55/42 -19/17 -10/9 -17/13 -19/17 -29/26 -13/10 -19/17 -10/9 -22/17 -10/9 -53/41 -47/42 -19/17 -84/65 -19/17 -31/24 -19/17 -48/43 -9/7 -29/26 -39/35 -32/25 -59/53 -55/43 -69/62 -217/195 -23/18 -89/80 -10/9 -14/11 -10/9 -5/4 -10/9 -21/19 -11/9 -43/39 -11/10 -28/23 -11/10 -17/14 -11/10 -56/51 -6/5 -12/11 -19/16 -10/9 -1/1 -13/11 -11/10 -1/1 -7/6 -10/9 -12/11 -15/13 -11/10 -1/1 -8/7 -1/1 -9/8 -32/29 -11/10 -1/1 -13/12 -1/1 0/1 -1/1 1/1 -1/1 -13/14 8/7 -1/1 7/6 -12/13 -10/11 20/17 -1/1 13/11 -1/1 -11/12 6/5 -12/13 17/14 -56/61 -11/12 28/23 -11/12 11/9 -11/12 -43/47 5/4 -21/23 -10/11 14/11 -10/11 23/18 -10/11 -89/98 9/7 -39/43 -29/32 22/17 -10/11 13/10 -10/11 -19/21 17/13 -29/32 -19/21 38/29 -28/31 21/16 -10/11 -28/31 25/19 -19/21 -9/10 4/3 -9/10 19/14 -1/1 -8/9 34/25 -10/11 15/11 -1/1 -9/10 11/8 -1/1 -8/9 29/21 -29/32 -19/21 47/34 -46/51 -9/10 18/13 -8/9 25/18 -1/1 -10/11 7/5 -10/11 -8/9 31/22 -1/1 -10/11 86/61 -28/31 55/39 -9/10 -35/39 24/17 -1/1 17/12 -10/11 -9/10 27/19 -15/17 -7/8 10/7 -10/11 23/16 -9/10 -8/9 36/25 -1/1 13/9 -1/1 -9/10 16/11 -9/10 19/13 -1/1 -11/12 3/2 -9/10 -8/9 14/9 -8/9 25/16 -8/9 -63/71 11/7 -31/35 -23/26 30/19 -8/9 19/12 -38/43 -15/17 84/53 -15/17 65/41 -15/17 -127/144 46/29 -52/59 27/17 -29/33 -7/8 8/5 -7/8 29/18 -8/9 -7/8 50/31 -6/7 21/13 -8/9 -6/7 13/8 -1/1 -8/9 18/11 -8/9 23/14 -22/25 -7/8 28/17 -7/8 5/3 -1/1 -7/8 27/16 -7/8 -6/7 22/13 -8/9 17/10 -7/8 -20/23 29/17 -19/22 -25/29 70/41 -6/7 41/24 -6/7 -17/20 12/7 -1/1 7/4 -8/9 -6/7 16/9 -1/1 25/14 -1/1 -6/7 34/19 -8/9 9/5 -15/17 -7/8 11/6 -1/1 -6/7 13/7 -1/1 -7/8 2/1 -6/7 15/7 -1/1 -5/6 28/13 -1/1 13/6 -1/1 -6/7 11/5 -1/1 -7/8 31/14 -6/7 -23/27 51/23 -17/20 -11/13 20/9 -11/13 29/13 -11/13 -27/32 9/4 -5/6 -4/5 25/11 -5/6 -9/11 41/18 -13/16 -4/5 16/7 -1/1 55/24 -1/1 -4/5 39/17 -1/1 -3/4 23/10 -6/7 -5/6 7/3 -6/7 -4/5 33/14 -6/7 -5/6 59/25 -11/13 -5/6 85/36 -26/31 -5/6 196/83 -5/6 111/47 -5/6 -39/47 26/11 -4/5 19/8 -1/1 -6/7 50/21 -4/5 81/34 -1/1 -2/3 112/47 -1/1 31/13 -1/1 -7/8 12/5 -5/6 41/17 -1/1 -5/6 70/29 -6/7 29/12 -6/7 -5/6 17/7 -11/13 -5/6 5/2 -1/1 -4/5 28/11 -1/1 23/9 -1/1 -7/8 41/16 -7/8 -6/7 59/23 -1/1 -5/6 77/30 -6/7 -4/5 18/7 -6/7 31/12 -1/1 -4/5 44/17 -1/1 57/22 -1/1 -6/7 70/27 -6/7 13/5 -1/1 -5/6 34/13 -4/5 21/8 -6/7 -4/5 50/19 -4/5 29/11 -5/6 -9/11 8/3 -5/6 27/10 -5/6 -4/5 19/7 -5/6 -19/23 11/4 -9/11 -4/5 14/5 -4/5 17/6 -4/5 -11/14 20/7 -7/9 23/8 -4/5 -3/4 3/1 -1/1 -3/4 16/5 -5/6 29/9 -17/21 -21/26 42/13 -4/5 13/4 -4/5 -7/9 10/3 -4/5 7/2 -4/5 -2/3 18/5 -4/5 65/18 -22/29 -3/4 112/31 -3/4 47/13 -3/4 -11/15 29/8 -3/4 -2/3 11/3 -3/4 -5/7 26/7 -2/3 41/11 -1/1 -3/4 56/15 -3/4 15/4 -3/4 -2/3 34/9 -2/3 53/14 -3/4 -8/11 19/5 -5/7 -7/10 23/6 -2/3 -5/8 27/7 -5/9 -1/2 4/1 -1/1 17/4 -3/4 -2/3 47/11 -1/1 -5/6 30/7 -2/3 13/3 -1/1 -3/4 22/5 -4/5 53/12 -10/13 -3/4 84/19 -3/4 31/7 -3/4 -5/7 9/2 -3/4 -2/3 14/3 -2/3 19/4 -2/3 -3/5 24/5 -1/2 53/11 -3/5 -1/2 29/6 -1/2 0/1 5/1 -1/1 -1/2 31/6 -2/3 -3/5 26/5 0/1 21/4 -2/3 0/1 58/11 0/1 37/7 -1/1 -3/4 16/3 -1/2 27/5 1/2 1/1 11/2 -2/1 -1/1 28/5 -1/1 17/3 -1/1 -7/8 23/4 -5/6 -4/5 29/5 -3/4 -5/7 6/1 -2/3 13/2 -1/1 -2/3 7/1 -2/3 0/1 22/3 0/1 15/2 -1/2 0/1 23/3 -1/1 -1/2 8/1 -1/1 17/2 0/1 1/0 9/1 -3/2 -1/1 10/1 -2/3 11/1 -1/1 1/0 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(55,588,-42,-449) (-10/1,1/0) -> (-38/29,-55/42) Hyperbolic Matrix(111,1064,70,671) (-10/1,-9/1) -> (65/41,46/29) Hyperbolic Matrix(57,476,-20,-167) (-9/1,-8/1) -> (-20/7,-37/13) Hyperbolic Matrix(169,1288,-66,-503) (-8/1,-15/2) -> (-41/16,-64/25) Hyperbolic Matrix(113,812,-70,-503) (-15/2,-7/1) -> (-21/13,-71/44) Hyperbolic Matrix(55,364,-34,-225) (-7/1,-6/1) -> (-34/21,-21/13) Hyperbolic Matrix(225,1316,-86,-503) (-6/1,-23/4) -> (-89/34,-34/13) Hyperbolic Matrix(225,1288,98,561) (-23/4,-17/3) -> (39/17,23/10) Hyperbolic Matrix(169,952,30,169) (-17/3,-28/5) -> (28/5,17/3) Hyperbolic Matrix(111,616,20,111) (-28/5,-11/2) -> (11/2,28/5) Hyperbolic Matrix(113,616,-82,-447) (-11/2,-16/3) -> (-40/29,-11/8) Hyperbolic Matrix(169,896,-116,-615) (-16/3,-21/4) -> (-35/24,-16/11) Hyperbolic Matrix(391,2044,-268,-1401) (-21/4,-26/5) -> (-54/37,-35/24) Hyperbolic Matrix(391,2016,-250,-1289) (-26/5,-5/1) -> (-61/39,-86/55) Hyperbolic Matrix(111,532,-82,-393) (-5/1,-19/4) -> (-19/14,-23/17) Hyperbolic Matrix(113,532,24,113) (-19/4,-14/3) -> (14/3,19/4) Hyperbolic Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(113,504,-50,-223) (-9/2,-22/5) -> (-34/15,-9/4) Hyperbolic Matrix(167,728,64,279) (-22/5,-13/3) -> (13/5,34/13) Hyperbolic Matrix(111,476,52,223) (-13/3,-30/7) -> (2/1,15/7) Hyperbolic Matrix(727,3108,-498,-2129) (-30/7,-47/11) -> (-19/13,-54/37) Hyperbolic Matrix(223,952,26,111) (-47/11,-17/4) -> (17/2,9/1) Hyperbolic Matrix(113,476,80,337) (-17/4,-4/1) -> (24/17,17/12) Hyperbolic Matrix(169,644,-132,-503) (-4/1,-19/5) -> (-9/7,-32/25) Hyperbolic Matrix(281,1064,-192,-727) (-19/5,-34/9) -> (-22/15,-19/13) Hyperbolic Matrix(839,3164,-520,-1961) (-34/9,-15/4) -> (-71/44,-50/31) Hyperbolic Matrix(391,1456,-286,-1065) (-15/4,-26/7) -> (-26/19,-41/30) Hyperbolic Matrix(167,616,106,391) (-26/7,-11/3) -> (11/7,30/19) Hyperbolic Matrix(55,196,-16,-57) (-11/3,-7/2) -> (-7/2,-17/5) Parabolic Matrix(281,952,116,393) (-17/5,-27/8) -> (29/12,17/7) Hyperbolic Matrix(449,1512,-166,-559) (-27/8,-10/3) -> (-46/17,-27/10) Hyperbolic Matrix(111,364,68,223) (-10/3,-13/4) -> (13/8,18/11) Hyperbolic Matrix(337,1092,104,337) (-13/4,-42/13) -> (42/13,13/4) Hyperbolic Matrix(1007,3248,590,1903) (-42/13,-29/9) -> (29/17,70/41) Hyperbolic Matrix(279,896,52,167) (-29/9,-16/5) -> (16/3,27/5) Hyperbolic Matrix(167,532,70,223) (-16/5,-3/1) -> (31/13,12/5) Hyperbolic Matrix(449,1288,-312,-895) (-3/1,-20/7) -> (-36/25,-59/41) Hyperbolic Matrix(503,1428,118,335) (-37/13,-17/6) -> (17/4,47/11) Hyperbolic Matrix(169,476,60,169) (-17/6,-14/5) -> (14/5,17/6) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,62,169) (-11/4,-19/7) -> (9/5,11/6) Hyperbolic Matrix(1231,3332,-890,-2409) (-19/7,-46/17) -> (-18/13,-65/47) Hyperbolic Matrix(167,448,104,279) (-27/10,-8/3) -> (8/5,29/18) Hyperbolic Matrix(169,448,106,281) (-8/3,-29/11) -> (27/17,8/5) Hyperbolic Matrix(671,1764,-256,-673) (-29/11,-21/8) -> (-21/8,-55/21) Parabolic Matrix(1401,3668,364,953) (-55/21,-89/34) -> (23/6,27/7) Hyperbolic Matrix(279,728,64,167) (-34/13,-13/5) -> (13/3,22/5) Hyperbolic Matrix(671,1736,-390,-1009) (-13/5,-31/12) -> (-31/18,-43/25) Hyperbolic Matrix(391,1008,282,727) (-31/12,-18/7) -> (18/13,25/18) Hyperbolic Matrix(1343,3444,-590,-1513) (-18/7,-41/16) -> (-41/18,-66/29) Hyperbolic Matrix(1455,3724,656,1679) (-64/25,-23/9) -> (51/23,20/9) Hyperbolic Matrix(505,1288,198,505) (-23/9,-28/11) -> (28/11,23/9) Hyperbolic Matrix(111,280,44,111) (-28/11,-5/2) -> (5/2,28/11) Hyperbolic Matrix(57,140,46,113) (-5/2,-17/7) -> (11/9,5/4) Hyperbolic Matrix(335,812,92,223) (-17/7,-29/12) -> (29/8,11/3) Hyperbolic Matrix(337,812,-232,-559) (-29/12,-12/5) -> (-16/11,-29/20) Hyperbolic Matrix(223,532,70,167) (-12/5,-31/13) -> (3/1,16/5) Hyperbolic Matrix(1399,3332,-1082,-2577) (-31/13,-50/21) -> (-22/17,-53/41) Hyperbolic Matrix(671,1596,494,1175) (-50/21,-19/8) -> (19/14,34/25) Hyperbolic Matrix(449,1064,284,673) (-19/8,-26/11) -> (30/19,19/12) Hyperbolic Matrix(167,392,-72,-169) (-26/11,-7/3) -> (-7/3,-30/13) Parabolic Matrix(4759,10976,-3424,-7897) (-30/13,-83/36) -> (-139/100,-82/59) Hyperbolic Matrix(2575,5936,534,1231) (-83/36,-53/23) -> (53/11,29/6) Hyperbolic Matrix(559,1288,194,447) (-53/23,-23/10) -> (23/8,3/1) Hyperbolic Matrix(561,1288,98,225) (-23/10,-39/17) -> (17/3,23/4) Hyperbolic Matrix(1343,3080,-1026,-2353) (-39/17,-55/24) -> (-55/42,-17/13) Hyperbolic Matrix(1455,3332,562,1287) (-55/24,-16/7) -> (44/17,57/22) Hyperbolic Matrix(503,1148,294,671) (-16/7,-41/18) -> (41/24,12/7) Hyperbolic Matrix(2129,4844,-1624,-3695) (-66/29,-25/11) -> (-59/45,-38/29) Hyperbolic Matrix(2071,4704,468,1063) (-25/11,-84/37) -> (84/19,31/7) Hyperbolic Matrix(4145,9408,938,2129) (-84/37,-59/26) -> (53/12,84/19) Hyperbolic Matrix(1679,3808,444,1007) (-59/26,-34/15) -> (34/9,53/14) Hyperbolic Matrix(113,252,-100,-223) (-9/4,-20/9) -> (-8/7,-9/8) Hyperbolic Matrix(279,616,-178,-393) (-20/9,-11/5) -> (-11/7,-36/23) Hyperbolic Matrix(167,364,128,279) (-11/5,-13/6) -> (13/10,17/13) Hyperbolic Matrix(337,728,156,337) (-13/6,-28/13) -> (28/13,13/6) Hyperbolic Matrix(391,840,182,391) (-28/13,-15/7) -> (15/7,28/13) Hyperbolic Matrix(223,476,52,111) (-15/7,-2/1) -> (30/7,13/3) Hyperbolic Matrix(167,308,-122,-225) (-2/1,-11/6) -> (-11/8,-26/19) Hyperbolic Matrix(169,308,62,113) (-11/6,-9/5) -> (19/7,11/4) Hyperbolic Matrix(111,196,-64,-113) (-9/5,-7/4) -> (-7/4,-19/11) Parabolic Matrix(503,868,-390,-673) (-19/11,-31/18) -> (-31/24,-9/7) Hyperbolic Matrix(1791,3080,-1238,-2129) (-43/25,-55/32) -> (-55/38,-13/9) Hyperbolic Matrix(897,1540,392,673) (-55/32,-12/7) -> (16/7,55/24) Hyperbolic Matrix(671,1148,294,503) (-12/7,-41/24) -> (41/18,16/7) Hyperbolic Matrix(3361,5740,1968,3361) (-41/24,-70/41) -> (70/41,41/24) Hyperbolic Matrix(1903,3248,590,1007) (-70/41,-29/17) -> (29/9,42/13) Hyperbolic Matrix(559,952,394,671) (-29/17,-17/10) -> (17/12,27/19) Hyperbolic Matrix(281,476,232,393) (-17/10,-22/13) -> (6/5,17/14) Hyperbolic Matrix(1177,1988,730,1233) (-22/13,-27/16) -> (29/18,50/31) Hyperbolic Matrix(449,756,-332,-559) (-27/16,-5/3) -> (-23/17,-27/20) Hyperbolic Matrix(169,280,102,169) (-5/3,-28/17) -> (28/17,5/3) Hyperbolic Matrix(783,1288,476,783) (-28/17,-23/14) -> (23/14,28/17) Hyperbolic Matrix(393,644,274,449) (-23/14,-18/11) -> (10/7,23/16) Hyperbolic Matrix(223,364,68,111) (-18/11,-13/8) -> (13/4,10/3) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(1233,1988,730,1177) (-50/31,-29/18) -> (27/16,22/13) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(281,448,106,169) (-8/5,-27/17) -> (29/11,8/3) Hyperbolic Matrix(953,1512,-670,-1063) (-27/17,-19/12) -> (-37/26,-27/19) Hyperbolic Matrix(673,1064,284,449) (-19/12,-30/19) -> (26/11,19/8) Hyperbolic Matrix(391,616,106,167) (-30/19,-11/7) -> (11/3,26/7) Hyperbolic Matrix(841,1316,108,169) (-36/23,-61/39) -> (23/3,8/1) Hyperbolic Matrix(3081,4816,2186,3417) (-86/55,-25/16) -> (31/22,86/61) Hyperbolic Matrix(449,700,288,449) (-25/16,-14/9) -> (14/9,25/16) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(839,1232,190,279) (-3/2,-22/15) -> (22/5,53/12) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(4313,6244,1664,2409) (-42/29,-55/38) -> (57/22,70/27) Hyperbolic Matrix(505,728,428,617) (-13/9,-36/25) -> (20/17,13/11) Hyperbolic Matrix(2297,3304,974,1401) (-59/41,-23/16) -> (33/14,59/25) Hyperbolic Matrix(449,644,274,393) (-23/16,-10/7) -> (18/11,23/14) Hyperbolic Matrix(393,560,40,57) (-10/7,-47/33) -> (9/1,10/1) Hyperbolic Matrix(6607,9408,4168,5935) (-47/33,-84/59) -> (84/53,65/41) Hyperbolic Matrix(3305,4704,2086,2969) (-84/59,-37/26) -> (19/12,84/53) Hyperbolic Matrix(671,952,394,559) (-27/19,-17/12) -> (17/10,29/17) Hyperbolic Matrix(337,476,80,113) (-17/12,-24/17) -> (4/1,17/4) Hyperbolic Matrix(279,392,-200,-281) (-24/17,-7/5) -> (-7/5,-32/23) Parabolic Matrix(785,1092,202,281) (-32/23,-57/41) -> (27/7,4/1) Hyperbolic Matrix(23687,32928,10030,13943) (-57/41,-196/141) -> (196/83,111/47) Hyperbolic Matrix(31585,43904,13376,18593) (-196/141,-139/100) -> (85/36,196/83) Hyperbolic Matrix(2297,3192,444,617) (-82/59,-25/18) -> (31/6,26/5) Hyperbolic Matrix(727,1008,282,391) (-25/18,-18/13) -> (18/7,31/12) Hyperbolic Matrix(9071,12544,2510,3471) (-65/47,-112/81) -> (112/31,47/13) Hyperbolic Matrix(9073,12544,2512,3473) (-112/81,-47/34) -> (65/18,112/31) Hyperbolic Matrix(1175,1624,526,727) (-47/34,-29/21) -> (29/13,9/4) Hyperbolic Matrix(1177,1624,366,505) (-29/21,-40/29) -> (16/5,29/9) Hyperbolic Matrix(2295,3136,614,839) (-41/30,-56/41) -> (56/15,15/4) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(391,532,-330,-449) (-15/11,-19/14) -> (-19/16,-13/11) Hyperbolic Matrix(167,224,-126,-169) (-27/20,-4/3) -> (-4/3,-29/22) Parabolic Matrix(2913,3836,1234,1625) (-29/22,-25/19) -> (59/25,85/36) Hyperbolic Matrix(1343,1764,-1024,-1345) (-25/19,-21/16) -> (-21/16,-59/45) Parabolic Matrix(279,364,128,167) (-17/13,-13/10) -> (13/6,11/5) Hyperbolic Matrix(281,364,44,57) (-13/10,-22/17) -> (6/1,13/2) Hyperbolic Matrix(6607,8540,2772,3583) (-53/41,-84/65) -> (112/47,31/13) Hyperbolic Matrix(7953,10276,3338,4313) (-84/65,-31/24) -> (81/34,112/47) Hyperbolic Matrix(2407,3080,1706,2183) (-32/25,-55/43) -> (55/39,24/17) Hyperbolic Matrix(1511,1932,262,335) (-55/43,-23/18) -> (23/4,29/5) Hyperbolic Matrix(505,644,396,505) (-23/18,-14/11) -> (14/11,23/18) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(113,140,46,57) (-5/4,-11/9) -> (17/7,5/2) Hyperbolic Matrix(505,616,414,505) (-11/9,-28/23) -> (28/23,11/9) Hyperbolic Matrix(783,952,644,783) (-28/23,-17/14) -> (17/14,28/23) Hyperbolic Matrix(393,476,232,281) (-17/14,-6/5) -> (22/13,17/10) Hyperbolic Matrix(895,1064,376,447) (-6/5,-19/16) -> (19/8,50/21) Hyperbolic Matrix(167,196,-144,-169) (-13/11,-7/6) -> (-7/6,-15/13) Parabolic Matrix(559,644,388,447) (-15/13,-8/7) -> (36/25,13/9) Hyperbolic Matrix(279,308,202,223) (-9/8,-1/1) -> (29/21,47/34) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(223,-252,100,-113) (1/1,8/7) -> (20/9,29/13) Hyperbolic Matrix(169,-196,144,-167) (8/7,7/6) -> (7/6,20/17) Parabolic Matrix(449,-532,330,-391) (13/11,6/5) -> (34/25,15/11) Hyperbolic Matrix(503,-644,132,-169) (23/18,9/7) -> (19/5,23/6) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(449,-588,42,-55) (17/13,38/29) -> (10/1,11/1) Hyperbolic Matrix(2521,-3304,982,-1287) (38/29,21/16) -> (77/30,18/7) Hyperbolic Matrix(2407,-3164,938,-1233) (21/16,25/19) -> (59/23,77/30) Hyperbolic Matrix(615,-812,128,-169) (25/19,4/3) -> (24/5,53/11) Hyperbolic Matrix(393,-532,82,-111) (4/3,19/14) -> (19/4,24/5) Hyperbolic Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(7785,-10976,3296,-4647) (86/61,55/39) -> (111/47,26/11) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(615,-896,116,-169) (16/11,19/13) -> (37/7,16/3) Hyperbolic Matrix(727,-1064,192,-281) (19/13,3/2) -> (53/14,19/5) Hyperbolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(503,-812,70,-113) (50/31,21/13) -> (7/1,22/3) Hyperbolic Matrix(225,-364,34,-55) (21/13,13/8) -> (13/2,7/1) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(895,-1596,346,-617) (16/9,25/14) -> (31/12,44/17) Hyperbolic Matrix(2239,-4004,940,-1681) (25/14,34/19) -> (50/21,81/34) Hyperbolic Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(783,-1736,152,-337) (31/14,51/23) -> (5/1,31/6) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(1513,-3444,590,-1343) (25/11,41/18) -> (41/16,59/23) Hyperbolic Matrix(281,-644,24,-55) (55/24,39/17) -> (11/1,1/0) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1567,-3780,604,-1457) (41/17,70/29) -> (70/27,13/5) Hyperbolic Matrix(503,-1288,66,-169) (23/9,41/16) -> (15/2,23/3) Hyperbolic Matrix(673,-1764,256,-671) (34/13,21/8) -> (21/8,50/19) Parabolic Matrix(617,-1624,106,-279) (50/19,29/11) -> (29/5,6/1) Hyperbolic Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(167,-476,20,-57) (17/6,20/7) -> (8/1,17/2) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(223,-840,30,-113) (15/4,34/9) -> (22/3,15/2) Hyperbolic Matrix(897,-3836,170,-727) (47/11,30/7) -> (58/11,37/7) Hyperbolic Matrix(337,-1764,64,-335) (26/5,21/4) -> (21/4,58/11) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(55,588,-42,-449) -> Matrix(9,-10,-8,9) Matrix(111,1064,70,671) -> Matrix(67,82,-76,-93) Matrix(57,476,-20,-167) -> Matrix(3,-4,-2,3) Matrix(169,1288,-66,-503) -> Matrix(7,6,-6,-5) Matrix(113,812,-70,-503) -> Matrix(7,6,-6,-5) Matrix(55,364,-34,-225) -> Matrix(7,6,-6,-5) Matrix(225,1316,-86,-503) -> Matrix(3,2,-2,-1) Matrix(225,1288,98,561) -> Matrix(9,10,-10,-11) Matrix(169,952,30,169) -> Matrix(13,14,-14,-15) Matrix(111,616,20,111) -> Matrix(5,4,-4,-3) Matrix(113,616,-82,-447) -> Matrix(11,10,-10,-9) Matrix(169,896,-116,-615) -> Matrix(9,8,-8,-7) Matrix(391,2044,-268,-1401) -> Matrix(9,8,-8,-7) Matrix(391,2016,-250,-1289) -> Matrix(55,102,-48,-89) Matrix(111,532,-82,-393) -> Matrix(9,26,-8,-23) Matrix(113,532,24,113) -> Matrix(5,12,-8,-19) Matrix(55,252,12,55) -> Matrix(7,12,-10,-17) Matrix(113,504,-50,-223) -> Matrix(3,2,-2,-1) Matrix(167,728,64,279) -> Matrix(7,8,-8,-9) Matrix(111,476,52,223) -> Matrix(7,8,-8,-9) Matrix(727,3108,-498,-2129) -> Matrix(7,6,-6,-5) Matrix(223,952,26,111) -> Matrix(1,2,-2,-3) Matrix(113,476,80,337) -> Matrix(11,12,-12,-13) Matrix(169,644,-132,-503) -> Matrix(69,128,-62,-115) Matrix(281,1064,-192,-727) -> Matrix(29,48,-26,-43) Matrix(839,3164,-520,-1961) -> Matrix(5,4,-4,-3) Matrix(391,1456,-286,-1065) -> Matrix(7,6,-6,-5) Matrix(167,616,106,391) -> Matrix(7,22,-8,-25) Matrix(55,196,-16,-57) -> Matrix(1,0,0,1) Matrix(281,952,116,393) -> Matrix(7,8,-8,-9) Matrix(449,1512,-166,-559) -> Matrix(3,2,-2,-1) Matrix(111,364,68,223) -> Matrix(37,52,-42,-59) Matrix(337,1092,104,337) -> Matrix(41,56,-52,-71) Matrix(1007,3248,590,1903) -> Matrix(153,202,-178,-235) Matrix(279,896,52,167) -> Matrix(3,4,-10,-13) Matrix(167,532,70,223) -> Matrix(9,10,-10,-11) Matrix(449,1288,-312,-895) -> Matrix(43,60,-38,-53) Matrix(503,1428,118,335) -> Matrix(7,10,-12,-17) Matrix(169,476,60,169) -> Matrix(65,88,-82,-111) Matrix(111,308,40,111) -> Matrix(55,72,-68,-89) Matrix(113,308,62,169) -> Matrix(45,58,-52,-67) Matrix(1231,3332,-890,-2409) -> Matrix(77,94,-68,-83) Matrix(167,448,104,279) -> Matrix(11,12,-12,-13) Matrix(169,448,106,281) -> Matrix(67,82,-76,-93) Matrix(671,1764,-256,-673) -> Matrix(1,0,0,1) Matrix(1401,3668,364,953) -> Matrix(13,16,-22,-27) Matrix(279,728,64,167) -> Matrix(7,8,-8,-9) Matrix(671,1736,-390,-1009) -> Matrix(3,2,-2,-1) Matrix(391,1008,282,727) -> Matrix(13,14,-14,-15) Matrix(1343,3444,-590,-1513) -> Matrix(41,50,-32,-39) Matrix(1455,3724,656,1679) -> Matrix(49,60,-58,-71) Matrix(505,1288,198,505) -> Matrix(13,14,-14,-15) Matrix(111,280,44,111) -> Matrix(7,8,-8,-9) Matrix(57,140,46,113) -> Matrix(73,94,-80,-103) Matrix(335,812,92,223) -> Matrix(7,8,-8,-9) Matrix(337,812,-232,-559) -> Matrix(5,4,-4,-3) Matrix(223,532,70,167) -> Matrix(9,10,-10,-11) Matrix(1399,3332,-1082,-2577) -> Matrix(67,86,-60,-77) Matrix(671,1596,494,1175) -> Matrix(13,14,-14,-15) Matrix(449,1064,284,673) -> Matrix(37,52,-42,-59) Matrix(167,392,-72,-169) -> Matrix(1,0,0,1) Matrix(4759,10976,-3424,-7897) -> Matrix(139,176,-124,-157) Matrix(2575,5936,534,1231) -> Matrix(21,26,-38,-47) Matrix(559,1288,194,447) -> Matrix(31,38,-40,-49) Matrix(561,1288,98,225) -> Matrix(9,10,-10,-11) Matrix(1343,3080,-1026,-2353) -> Matrix(67,86,-60,-77) Matrix(1455,3332,562,1287) -> Matrix(9,10,-10,-11) Matrix(503,1148,294,671) -> Matrix(9,10,-10,-11) Matrix(2129,4844,-1624,-3695) -> Matrix(139,176,-124,-157) Matrix(2071,4704,468,1063) -> Matrix(41,52,-56,-71) Matrix(4145,9408,938,2129) -> Matrix(79,98,-104,-129) Matrix(1679,3808,444,1007) -> Matrix(7,8,-8,-9) Matrix(113,252,-100,-223) -> Matrix(95,116,-86,-105) Matrix(279,616,-178,-393) -> Matrix(163,194,-142,-169) Matrix(167,364,128,279) -> Matrix(85,104,-94,-115) Matrix(337,728,156,337) -> Matrix(11,12,-12,-13) Matrix(391,840,182,391) -> Matrix(9,10,-10,-11) Matrix(223,476,52,111) -> Matrix(7,8,-8,-9) Matrix(167,308,-122,-225) -> Matrix(3,2,-2,-1) Matrix(169,308,62,113) -> Matrix(49,58,-60,-71) Matrix(111,196,-64,-113) -> Matrix(1,0,0,1) Matrix(503,868,-390,-673) -> Matrix(143,162,-128,-145) Matrix(1791,3080,-1238,-2129) -> Matrix(3,2,-2,-1) Matrix(897,1540,392,673) -> Matrix(11,12,-12,-13) Matrix(671,1148,294,503) -> Matrix(9,10,-10,-11) Matrix(3361,5740,1968,3361) -> Matrix(169,204,-198,-239) Matrix(1903,3248,590,1007) -> Matrix(169,202,-210,-251) Matrix(559,952,394,671) -> Matrix(93,110,-104,-123) Matrix(281,476,232,393) -> Matrix(149,172,-162,-187) Matrix(1177,1988,730,1233) -> Matrix(13,14,-14,-15) Matrix(449,756,-332,-559) -> Matrix(111,128,-98,-113) Matrix(169,280,102,169) -> Matrix(13,14,-14,-15) Matrix(783,1288,476,783) -> Matrix(265,308,-302,-351) Matrix(393,644,274,449) -> Matrix(123,142,-136,-157) Matrix(223,364,68,111) -> Matrix(45,52,-58,-67) Matrix(449,728,346,561) -> Matrix(123,142,-136,-157) Matrix(1233,1988,730,1177) -> Matrix(13,14,-14,-15) Matrix(279,448,104,167) -> Matrix(11,12,-12,-13) Matrix(281,448,106,169) -> Matrix(71,82,-84,-97) Matrix(953,1512,-670,-1063) -> Matrix(85,98,-72,-83) Matrix(673,1064,284,449) -> Matrix(45,52,-58,-67) Matrix(391,616,106,167) -> Matrix(19,22,-32,-37) Matrix(841,1316,108,169) -> Matrix(7,8,34,39) Matrix(3081,4816,2186,3417) -> Matrix(543,622,-598,-685) Matrix(449,700,288,449) -> Matrix(881,1008,-992,-1135) Matrix(55,84,36,55) -> Matrix(127,144,-142,-161) Matrix(839,1232,190,279) -> Matrix(59,66,-76,-85) Matrix(2241,3248,928,1345) -> Matrix(93,104,-110,-123) Matrix(4313,6244,1664,2409) -> Matrix(15,16,-16,-17) Matrix(505,728,428,617) -> Matrix(19,20,-20,-21) Matrix(2297,3304,974,1401) -> Matrix(13,14,-14,-15) Matrix(449,644,274,393) -> Matrix(127,142,-144,-161) Matrix(393,560,40,57) -> Matrix(11,12,-12,-13) Matrix(6607,9408,4168,5935) -> Matrix(337,352,-382,-399) Matrix(3305,4704,2086,2969) -> Matrix(7,22,-8,-25) Matrix(671,952,394,559) -> Matrix(97,110,-112,-127) Matrix(337,476,80,113) -> Matrix(11,12,-12,-13) Matrix(279,392,-200,-281) -> Matrix(1,0,0,1) Matrix(785,1092,202,281) -> Matrix(9,10,-10,-11) Matrix(23687,32928,10030,13943) -> Matrix(467,526,-562,-633) Matrix(31585,43904,13376,18593) -> Matrix(573,644,-686,-771) Matrix(2297,3192,444,617) -> Matrix(25,28,-42,-47) Matrix(727,1008,282,391) -> Matrix(13,14,-14,-15) Matrix(9071,12544,2510,3471) -> Matrix(229,258,-308,-347) Matrix(9073,12544,2512,3473) -> Matrix(299,336,-396,-445) Matrix(1175,1624,526,727) -> Matrix(173,194,-206,-231) Matrix(1177,1624,366,505) -> Matrix(85,94,-104,-115) Matrix(2295,3136,614,839) -> Matrix(37,42,-52,-59) Matrix(2297,3136,616,841) -> Matrix(11,12,-12,-13) Matrix(391,532,-330,-449) -> Matrix(3,2,-2,-1) Matrix(167,224,-126,-169) -> Matrix(143,162,-128,-145) Matrix(2913,3836,1234,1625) -> Matrix(173,194,-206,-231) Matrix(1343,1764,-1024,-1345) -> Matrix(1,0,0,1) Matrix(279,364,128,167) -> Matrix(93,104,-110,-123) Matrix(281,364,44,57) -> Matrix(25,28,-42,-47) Matrix(6607,8540,2772,3583) -> Matrix(161,180,-178,-199) Matrix(7953,10276,3338,4313) -> Matrix(9,10,8,9) Matrix(2407,3080,1706,2183) -> Matrix(415,462,-468,-521) Matrix(1511,1932,262,335) -> Matrix(275,306,-346,-385) Matrix(505,644,396,505) -> Matrix(1601,1780,-1762,-1959) Matrix(111,140,88,111) -> Matrix(379,420,-416,-461) Matrix(113,140,46,57) -> Matrix(85,94,-104,-115) Matrix(505,616,414,505) -> Matrix(859,946,-938,-1033) Matrix(783,952,644,783) -> Matrix(1121,1232,-1222,-1343) Matrix(393,476,232,281) -> Matrix(157,172,-178,-195) Matrix(895,1064,376,447) -> Matrix(15,16,-16,-17) Matrix(167,196,-144,-169) -> Matrix(1,0,0,1) Matrix(559,644,388,447) -> Matrix(19,20,-20,-21) Matrix(279,308,202,223) -> Matrix(199,218,-220,-241) Matrix(1,0,2,1) -> Matrix(25,26,-26,-27) Matrix(223,-252,100,-113) -> Matrix(127,116,-150,-137) Matrix(169,-196,144,-167) -> Matrix(1,0,0,1) Matrix(449,-532,330,-391) -> Matrix(3,2,-2,-1) Matrix(503,-644,132,-169) -> Matrix(141,128,-206,-187) Matrix(391,-504,218,-281) -> Matrix(179,162,-200,-181) Matrix(449,-588,42,-55) -> Matrix(11,10,-32,-29) Matrix(2521,-3304,982,-1287) -> Matrix(95,86,-116,-105) Matrix(2407,-3164,938,-1233) -> Matrix(95,86,-116,-105) Matrix(615,-812,128,-169) -> Matrix(9,8,-8,-7) Matrix(393,-532,82,-111) -> Matrix(29,26,-48,-43) Matrix(225,-308,122,-167) -> Matrix(3,2,-2,-1) Matrix(447,-616,82,-113) -> Matrix(11,10,-10,-9) Matrix(1457,-2016,404,-559) -> Matrix(67,60,-86,-77) Matrix(281,-392,200,-279) -> Matrix(1,0,0,1) Matrix(7785,-10976,3296,-4647) -> Matrix(195,176,-236,-213) Matrix(1063,-1512,670,-953) -> Matrix(113,98,-128,-111) Matrix(895,-1288,312,-449) -> Matrix(67,60,-86,-77) Matrix(559,-812,232,-337) -> Matrix(5,4,-4,-3) Matrix(615,-896,116,-169) -> Matrix(9,8,-8,-7) Matrix(727,-1064,192,-281) -> Matrix(53,48,-74,-67) Matrix(393,-616,178,-279) -> Matrix(219,194,-254,-225) Matrix(503,-812,70,-113) -> Matrix(7,6,-6,-5) Matrix(225,-364,34,-55) -> Matrix(7,6,-6,-5) Matrix(167,-280,34,-57) -> Matrix(7,6,-6,-5) Matrix(113,-196,64,-111) -> Matrix(1,0,0,1) Matrix(895,-1596,346,-617) -> Matrix(3,2,-2,-1) Matrix(2239,-4004,940,-1681) -> Matrix(5,4,-4,-3) Matrix(223,-420,60,-113) -> Matrix(5,4,-4,-3) Matrix(783,-1736,152,-337) -> Matrix(33,28,-46,-39) Matrix(223,-504,50,-113) -> Matrix(3,2,-2,-1) Matrix(1513,-3444,590,-1343) -> Matrix(61,50,-72,-59) Matrix(281,-644,24,-55) -> Matrix(5,4,-4,-3) Matrix(169,-392,72,-167) -> Matrix(1,0,0,1) Matrix(1567,-3780,604,-1457) -> Matrix(1,0,0,1) Matrix(503,-1288,66,-169) -> Matrix(7,6,-6,-5) Matrix(673,-1764,256,-671) -> Matrix(1,0,0,1) Matrix(617,-1624,106,-279) -> Matrix(3,2,-2,-1) Matrix(673,-1820,186,-503) -> Matrix(3,2,-2,-1) Matrix(167,-476,20,-57) -> Matrix(5,4,-14,-11) Matrix(57,-196,16,-55) -> Matrix(1,0,0,1) Matrix(223,-840,30,-113) -> Matrix(3,2,-2,-1) Matrix(897,-3836,170,-727) -> Matrix(3,2,-2,-1) Matrix(337,-1764,64,-335) -> Matrix(1,0,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 48 Degree of the the map X: 48 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 -7/1 -6/1 -4/1 -7/2 -10/3 -12/5 -7/3 -2/1 -7/4 -42/29 -7/5 -7/6 0/1 1/1 7/6 14/11 7/5 3/2 14/9 7/4 9/5 2/1 7/3 12/5 5/2 28/11 8/3 14/5 3/1 42/13 10/3 7/2 112/31 11/3 56/15 4/1 13/3 84/19 9/2 14/3 5/1 11/2 28/5 6/1 13/2 7/1 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -2/1 0/1 -6/1 -2/1 -11/2 -1/1 -2/3 -5/1 -1/1 1/0 -14/3 -2/1 -9/2 -2/1 -3/2 -22/5 -4/3 -13/3 -3/2 -1/1 -4/1 -1/1 -15/4 -2/1 -3/2 -11/3 -5/3 -3/2 -7/2 -2/1 -4/3 -17/5 -5/3 -3/2 -27/8 -2/1 -3/2 -10/3 -4/3 -13/4 -7/5 -4/3 -16/5 -5/4 -3/1 -3/2 -1/1 -14/5 -4/3 -11/4 -4/3 -9/7 -19/7 -19/15 -5/4 -46/17 -6/5 -27/10 -4/3 -5/4 -8/3 -5/4 -21/8 -4/3 -6/5 -13/5 -5/4 -1/1 -18/7 -6/5 -5/2 -4/3 -1/1 -17/7 -5/4 -11/9 -29/12 -5/4 -6/5 -12/5 -5/4 -7/3 -4/3 -6/5 -16/7 -1/1 -25/11 -9/7 -5/4 -34/15 -6/5 -9/4 -4/3 -5/4 -11/5 -7/6 -1/1 -13/6 -6/5 -1/1 -2/1 -6/5 -11/6 -6/5 -1/1 -9/5 -7/6 -15/13 -7/4 -6/5 -8/7 -19/11 -7/6 -15/13 -31/18 -6/5 -1/1 -12/7 -1/1 -41/24 -17/14 -6/5 -70/41 -6/5 -29/17 -25/21 -19/16 -17/10 -20/17 -7/6 -5/3 -7/6 -1/1 -28/17 -7/6 -23/14 -7/6 -22/19 -18/11 -8/7 -13/8 -8/7 -1/1 -34/21 -8/7 -21/13 -6/5 -8/7 -29/18 -7/6 -8/7 -8/5 -7/6 -27/17 -7/6 -29/25 -19/12 -15/13 -38/33 -11/7 -23/20 -31/27 -14/9 -8/7 -3/2 -8/7 -9/8 -16/11 -9/8 -29/20 -9/8 -10/9 -42/29 -10/9 -13/9 -9/8 -1/1 -10/7 -10/9 -7/5 -8/7 -10/9 -18/13 -8/7 -65/47 -53/47 -9/8 -112/81 -9/8 -47/34 -9/8 -46/41 -29/21 -19/17 -29/26 -11/8 -8/7 -1/1 -26/19 -8/7 -41/30 -8/7 -9/8 -56/41 -9/8 -15/11 -9/8 -1/1 -4/3 -9/8 -13/10 -19/17 -10/9 -22/17 -10/9 -53/41 -47/42 -19/17 -84/65 -19/17 -31/24 -19/17 -48/43 -9/7 -29/26 -39/35 -14/11 -10/9 -5/4 -10/9 -21/19 -11/9 -43/39 -11/10 -28/23 -11/10 -17/14 -11/10 -56/51 -6/5 -12/11 -13/11 -11/10 -1/1 -7/6 -10/9 -12/11 -8/7 -1/1 -1/1 -13/12 -1/1 0/1 -1/1 1/1 -1/1 -13/14 7/6 -12/13 -10/11 6/5 -12/13 11/9 -11/12 -43/47 5/4 -21/23 -10/11 14/11 -10/11 9/7 -39/43 -29/32 22/17 -10/11 13/10 -10/11 -19/21 4/3 -9/10 15/11 -1/1 -9/10 11/8 -1/1 -8/9 7/5 -10/11 -8/9 17/12 -10/11 -9/10 27/19 -15/17 -7/8 10/7 -10/11 13/9 -1/1 -9/10 16/11 -9/10 3/2 -9/10 -8/9 14/9 -8/9 11/7 -31/35 -23/26 19/12 -38/43 -15/17 46/29 -52/59 27/17 -29/33 -7/8 8/5 -7/8 21/13 -8/9 -6/7 13/8 -1/1 -8/9 18/11 -8/9 5/3 -1/1 -7/8 17/10 -7/8 -20/23 29/17 -19/22 -25/29 12/7 -1/1 7/4 -8/9 -6/7 16/9 -1/1 25/14 -1/1 -6/7 34/19 -8/9 9/5 -15/17 -7/8 11/6 -1/1 -6/7 13/7 -1/1 -7/8 2/1 -6/7 11/5 -1/1 -7/8 9/4 -5/6 -4/5 7/3 -6/7 -4/5 19/8 -1/1 -6/7 31/13 -1/1 -7/8 12/5 -5/6 41/17 -1/1 -5/6 70/29 -6/7 29/12 -6/7 -5/6 17/7 -11/13 -5/6 5/2 -1/1 -4/5 28/11 -1/1 23/9 -1/1 -7/8 18/7 -6/7 13/5 -1/1 -5/6 34/13 -4/5 21/8 -6/7 -4/5 29/11 -5/6 -9/11 8/3 -5/6 27/10 -5/6 -4/5 19/7 -5/6 -19/23 11/4 -9/11 -4/5 14/5 -4/5 3/1 -1/1 -3/4 16/5 -5/6 29/9 -17/21 -21/26 42/13 -4/5 13/4 -4/5 -7/9 10/3 -4/5 7/2 -4/5 -2/3 18/5 -4/5 65/18 -22/29 -3/4 112/31 -3/4 47/13 -3/4 -11/15 29/8 -3/4 -2/3 11/3 -3/4 -5/7 26/7 -2/3 41/11 -1/1 -3/4 56/15 -3/4 15/4 -3/4 -2/3 4/1 -1/1 13/3 -1/1 -3/4 22/5 -4/5 53/12 -10/13 -3/4 84/19 -3/4 31/7 -3/4 -5/7 9/2 -3/4 -2/3 14/3 -2/3 5/1 -1/1 -1/2 11/2 -2/1 -1/1 28/5 -1/1 17/3 -1/1 -7/8 6/1 -2/3 13/2 -1/1 -2/3 7/1 -2/3 0/1 8/1 -1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(29,224,-18,-139) (-7/1,1/0) -> (-21/13,-29/18) Hyperbolic Matrix(55,364,-34,-225) (-7/1,-6/1) -> (-34/21,-21/13) Hyperbolic Matrix(29,168,-24,-139) (-6/1,-11/2) -> (-17/14,-6/5) Hyperbolic Matrix(27,140,16,83) (-11/2,-5/1) -> (5/3,17/10) Hyperbolic Matrix(29,140,6,29) (-5/1,-14/3) -> (14/3,5/1) Hyperbolic Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(113,504,-50,-223) (-9/2,-22/5) -> (-34/15,-9/4) Hyperbolic Matrix(167,728,64,279) (-22/5,-13/3) -> (13/5,34/13) Hyperbolic Matrix(27,112,20,83) (-13/3,-4/1) -> (4/3,15/11) Hyperbolic Matrix(29,112,22,85) (-4/1,-15/4) -> (13/10,4/3) Hyperbolic Matrix(83,308,-38,-141) (-15/4,-11/3) -> (-11/5,-13/6) Hyperbolic Matrix(55,196,-16,-57) (-11/3,-7/2) -> (-7/2,-17/5) Parabolic Matrix(281,952,116,393) (-17/5,-27/8) -> (29/12,17/7) Hyperbolic Matrix(449,1512,-166,-559) (-27/8,-10/3) -> (-46/17,-27/10) Hyperbolic Matrix(111,364,68,223) (-10/3,-13/4) -> (13/8,18/11) Hyperbolic Matrix(253,812,-148,-475) (-13/4,-16/5) -> (-12/7,-41/24) Hyperbolic Matrix(167,532,70,223) (-16/5,-3/1) -> (31/13,12/5) Hyperbolic Matrix(29,84,10,29) (-3/1,-14/5) -> (14/5,3/1) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,62,169) (-11/4,-19/7) -> (9/5,11/6) Hyperbolic Matrix(1231,3332,-890,-2409) (-19/7,-46/17) -> (-18/13,-65/47) Hyperbolic Matrix(83,224,10,27) (-27/10,-8/3) -> (8/1,1/0) Hyperbolic Matrix(85,224,-74,-195) (-8/3,-21/8) -> (-7/6,-8/7) Hyperbolic Matrix(139,364,-118,-309) (-21/8,-13/5) -> (-13/11,-7/6) Hyperbolic Matrix(141,364,98,253) (-13/5,-18/7) -> (10/7,13/9) Hyperbolic Matrix(197,504,-120,-307) (-18/7,-5/2) -> (-23/14,-18/11) Hyperbolic Matrix(57,140,46,113) (-5/2,-17/7) -> (11/9,5/4) Hyperbolic Matrix(335,812,92,223) (-17/7,-29/12) -> (29/8,11/3) Hyperbolic Matrix(337,812,-232,-559) (-29/12,-12/5) -> (-16/11,-29/20) Hyperbolic Matrix(83,196,-36,-85) (-12/5,-7/3) -> (-7/3,-16/7) Parabolic Matrix(197,448,62,141) (-16/7,-25/11) -> (3/1,16/5) Hyperbolic Matrix(1037,2352,-802,-1819) (-25/11,-34/15) -> (-22/17,-53/41) Hyperbolic Matrix(139,308,88,195) (-9/4,-11/5) -> (11/7,19/12) Hyperbolic Matrix(197,420,-144,-307) (-13/6,-2/1) -> (-26/19,-41/30) Hyperbolic Matrix(167,308,-122,-225) (-2/1,-11/6) -> (-11/8,-26/19) Hyperbolic Matrix(169,308,62,113) (-11/6,-9/5) -> (19/7,11/4) Hyperbolic Matrix(111,196,-64,-113) (-9/5,-7/4) -> (-7/4,-19/11) Parabolic Matrix(503,868,-390,-673) (-19/11,-31/18) -> (-31/24,-9/7) Hyperbolic Matrix(309,532,212,365) (-31/18,-12/7) -> (16/11,3/2) Hyperbolic Matrix(1541,2632,476,813) (-41/24,-70/41) -> (42/13,13/4) Hyperbolic Matrix(1903,3248,590,1007) (-70/41,-29/17) -> (29/9,42/13) Hyperbolic Matrix(559,952,394,671) (-29/17,-17/10) -> (17/12,27/19) Hyperbolic Matrix(83,140,16,27) (-17/10,-5/3) -> (5/1,11/2) Hyperbolic Matrix(475,784,186,307) (-5/3,-28/17) -> (28/11,23/9) Hyperbolic Matrix(477,784,188,309) (-28/17,-23/14) -> (5/2,28/11) Hyperbolic Matrix(223,364,68,111) (-18/11,-13/8) -> (13/4,10/3) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(281,448,106,169) (-8/5,-27/17) -> (29/11,8/3) Hyperbolic Matrix(1147,1820,-830,-1317) (-27/17,-19/12) -> (-47/34,-29/21) Hyperbolic Matrix(195,308,88,139) (-19/12,-11/7) -> (11/5,9/4) Hyperbolic Matrix(197,308,126,197) (-11/7,-14/9) -> (14/9,11/7) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(307,448,172,251) (-3/2,-16/11) -> (16/9,25/14) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(1819,2632,754,1091) (-42/29,-13/9) -> (41/17,70/29) Hyperbolic Matrix(253,364,98,141) (-13/9,-10/7) -> (18/7,13/5) Hyperbolic Matrix(139,196,-100,-141) (-10/7,-7/5) -> (-7/5,-18/13) Parabolic Matrix(9071,12544,2510,3471) (-65/47,-112/81) -> (112/31,47/13) Hyperbolic Matrix(9073,12544,2512,3473) (-112/81,-47/34) -> (65/18,112/31) Hyperbolic Matrix(589,812,346,477) (-29/21,-11/8) -> (17/10,29/17) Hyperbolic Matrix(2295,3136,614,839) (-41/30,-56/41) -> (56/15,15/4) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(83,112,20,27) (-15/11,-4/3) -> (4/1,13/3) Hyperbolic Matrix(85,112,22,29) (-4/3,-13/10) -> (15/4,4/1) Hyperbolic Matrix(281,364,44,57) (-13/10,-22/17) -> (6/1,13/2) Hyperbolic Matrix(5459,7056,1234,1595) (-53/41,-84/65) -> (84/19,31/7) Hyperbolic Matrix(5461,7056,1236,1597) (-84/65,-31/24) -> (53/12,84/19) Hyperbolic Matrix(197,252,154,197) (-9/7,-14/11) -> (14/11,9/7) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(113,140,46,57) (-5/4,-11/9) -> (17/7,5/2) Hyperbolic Matrix(643,784,114,139) (-11/9,-28/23) -> (28/5,17/3) Hyperbolic Matrix(645,784,116,141) (-28/23,-17/14) -> (11/2,28/5) Hyperbolic Matrix(307,364,70,83) (-6/5,-13/11) -> (13/3,22/5) Hyperbolic Matrix(197,224,124,141) (-8/7,-1/1) -> (27/17,8/5) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(195,-224,74,-85) (1/1,7/6) -> (21/8,29/11) Hyperbolic Matrix(309,-364,118,-139) (7/6,6/5) -> (34/13,21/8) Hyperbolic Matrix(139,-168,24,-29) (6/5,11/9) -> (17/3,6/1) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(2101,-3332,582,-923) (19/12,46/29) -> (18/5,65/18) Hyperbolic Matrix(139,-224,18,-29) (8/5,21/13) -> (7/1,8/1) Hyperbolic Matrix(225,-364,34,-55) (21/13,13/8) -> (13/2,7/1) Hyperbolic Matrix(307,-504,120,-197) (18/11,5/3) -> (23/9,18/7) Hyperbolic Matrix(475,-812,148,-253) (29/17,12/7) -> (16/5,29/9) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(1315,-2352,298,-533) (25/14,34/19) -> (22/5,53/12) Hyperbolic Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(141,-308,38,-83) (2/1,11/5) -> (11/3,26/7) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(365,-868,82,-195) (19/8,31/13) -> (31/7,9/2) Hyperbolic Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(29,224,-18,-139) -> Matrix(1,8,-1,-7) Matrix(55,364,-34,-225) -> Matrix(7,6,-6,-5) Matrix(29,168,-24,-139) -> Matrix(23,34,-21,-31) Matrix(27,140,16,83) -> Matrix(1,-6,-1,7) Matrix(29,140,6,29) -> Matrix(1,0,-1,1) Matrix(55,252,12,55) -> Matrix(7,12,-10,-17) Matrix(113,504,-50,-223) -> Matrix(3,2,-2,-1) Matrix(167,728,64,279) -> Matrix(7,8,-8,-9) Matrix(27,112,20,83) -> Matrix(17,26,-19,-29) Matrix(29,112,22,85) -> Matrix(1,-8,-1,9) Matrix(83,308,-38,-141) -> Matrix(11,16,-9,-13) Matrix(55,196,-16,-57) -> Matrix(1,0,0,1) Matrix(281,952,116,393) -> Matrix(7,8,-8,-9) Matrix(449,1512,-166,-559) -> Matrix(3,2,-2,-1) Matrix(111,364,68,223) -> Matrix(37,52,-42,-59) Matrix(253,812,-148,-475) -> Matrix(21,26,-17,-21) Matrix(167,532,70,223) -> Matrix(9,10,-10,-11) Matrix(29,84,10,29) -> Matrix(5,8,-7,-11) Matrix(111,308,40,111) -> Matrix(55,72,-68,-89) Matrix(113,308,62,169) -> Matrix(45,58,-52,-67) Matrix(1231,3332,-890,-2409) -> Matrix(77,94,-68,-83) Matrix(83,224,10,27) -> Matrix(3,4,-7,-9) Matrix(85,224,-74,-195) -> Matrix(45,56,-41,-51) Matrix(139,364,-118,-309) -> Matrix(45,56,-41,-51) Matrix(141,364,98,253) -> Matrix(35,44,-39,-49) Matrix(197,504,-120,-307) -> Matrix(43,50,-37,-43) Matrix(57,140,46,113) -> Matrix(73,94,-80,-103) Matrix(335,812,92,223) -> Matrix(7,8,-8,-9) Matrix(337,812,-232,-559) -> Matrix(5,4,-4,-3) Matrix(83,196,-36,-85) -> Matrix(21,26,-17,-21) Matrix(197,448,62,141) -> Matrix(19,24,-23,-29) Matrix(1037,2352,-802,-1819) -> Matrix(55,64,-49,-57) Matrix(139,308,88,195) -> Matrix(107,130,-121,-147) Matrix(197,420,-144,-307) -> Matrix(37,46,-33,-41) Matrix(167,308,-122,-225) -> Matrix(3,2,-2,-1) Matrix(169,308,62,113) -> Matrix(49,58,-60,-71) Matrix(111,196,-64,-113) -> Matrix(1,0,0,1) Matrix(503,868,-390,-673) -> Matrix(143,162,-128,-145) Matrix(309,532,212,365) -> Matrix(53,62,-59,-69) Matrix(1541,2632,476,813) -> Matrix(91,110,-115,-139) Matrix(1903,3248,590,1007) -> Matrix(169,202,-210,-251) Matrix(559,952,394,671) -> Matrix(93,110,-104,-123) Matrix(83,140,16,27) -> Matrix(5,6,-11,-13) Matrix(475,784,186,307) -> Matrix(41,48,-47,-55) Matrix(477,784,188,309) -> Matrix(5,6,-11,-13) Matrix(223,364,68,111) -> Matrix(45,52,-58,-67) Matrix(449,728,346,561) -> Matrix(123,142,-136,-157) Matrix(279,448,104,167) -> Matrix(11,12,-12,-13) Matrix(281,448,106,169) -> Matrix(71,82,-84,-97) Matrix(1147,1820,-830,-1317) -> Matrix(301,348,-269,-311) Matrix(195,308,88,139) -> Matrix(113,130,-133,-153) Matrix(197,308,126,197) -> Matrix(377,432,-425,-487) Matrix(55,84,36,55) -> Matrix(127,144,-142,-161) Matrix(307,448,172,251) -> Matrix(55,62,-63,-71) Matrix(2241,3248,928,1345) -> Matrix(93,104,-110,-123) Matrix(1819,2632,754,1091) -> Matrix(39,44,-47,-53) Matrix(253,364,98,141) -> Matrix(39,44,-47,-53) Matrix(139,196,-100,-141) -> Matrix(73,82,-65,-73) Matrix(9071,12544,2510,3471) -> Matrix(229,258,-308,-347) Matrix(9073,12544,2512,3473) -> Matrix(299,336,-396,-445) Matrix(589,812,346,477) -> Matrix(69,76,-79,-87) Matrix(2295,3136,614,839) -> Matrix(37,42,-52,-59) Matrix(2297,3136,616,841) -> Matrix(11,12,-12,-13) Matrix(83,112,20,27) -> Matrix(23,26,-31,-35) Matrix(85,112,22,29) -> Matrix(7,8,-15,-17) Matrix(281,364,44,57) -> Matrix(25,28,-42,-47) Matrix(5459,7056,1234,1595) -> Matrix(211,236,-287,-321) Matrix(5461,7056,1236,1597) -> Matrix(299,334,-393,-439) Matrix(197,252,154,197) -> Matrix(611,680,-673,-749) Matrix(111,140,88,111) -> Matrix(379,420,-416,-461) Matrix(113,140,46,57) -> Matrix(85,94,-104,-115) Matrix(643,784,114,139) -> Matrix(109,120,-119,-131) Matrix(645,784,116,141) -> Matrix(71,78,-61,-67) Matrix(307,364,70,83) -> Matrix(29,32,-39,-43) Matrix(197,224,124,141) -> Matrix(55,62,-63,-71) Matrix(1,0,2,1) -> Matrix(25,26,-26,-27) Matrix(195,-224,74,-85) -> Matrix(61,56,-73,-67) Matrix(309,-364,118,-139) -> Matrix(61,56,-73,-67) Matrix(139,-168,24,-29) -> Matrix(37,34,-49,-45) Matrix(391,-504,218,-281) -> Matrix(179,162,-200,-181) Matrix(225,-308,122,-167) -> Matrix(3,2,-2,-1) Matrix(141,-196,100,-139) -> Matrix(91,82,-101,-91) Matrix(1063,-1512,670,-953) -> Matrix(113,98,-128,-111) Matrix(559,-812,232,-337) -> Matrix(5,4,-4,-3) Matrix(2101,-3332,582,-923) -> Matrix(245,216,-321,-283) Matrix(139,-224,18,-29) -> Matrix(9,8,-17,-15) Matrix(225,-364,34,-55) -> Matrix(7,6,-6,-5) Matrix(307,-504,120,-197) -> Matrix(57,50,-65,-57) Matrix(475,-812,148,-253) -> Matrix(31,26,-37,-31) Matrix(113,-196,64,-111) -> Matrix(1,0,0,1) Matrix(1315,-2352,298,-533) -> Matrix(31,28,-41,-37) Matrix(223,-420,60,-113) -> Matrix(5,4,-4,-3) Matrix(141,-308,38,-83) -> Matrix(19,16,-25,-21) Matrix(85,-196,36,-83) -> Matrix(31,26,-37,-31) Matrix(365,-868,82,-195) -> Matrix(19,16,-25,-21) Matrix(673,-1820,186,-503) -> Matrix(3,2,-2,-1) Matrix(57,-196,16,-55) -> Matrix(1,0,0,1) 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): 48 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 -1/1 13 1 1/1 (-1/1,-13/14).(-14/15,-12/13) 0 28 7/6 0 4 6/5 -12/13 1 14 11/9 (-11/12,-43/47).(-54/59,-32/35) 0 28 5/4 (-21/23,-10/11) 0 28 14/11 -10/11 11 2 9/7 (-10/11,-68/75).(-39/43,-29/32) 0 28 22/17 -10/11 1 14 13/10 (-10/11,-19/21) 0 28 4/3 -9/10 1 7 15/11 (-1/1,-9/10).(-10/11,-8/9) 0 28 11/8 (-1/1,-8/9) 0 28 7/5 (-1/1,-9/10).(-10/11,-8/9) 0 4 17/12 (-10/11,-9/10) 0 28 27/19 (-8/9,-22/25).(-15/17,-7/8) 0 28 10/7 -10/11 1 14 13/9 (-1/1,-9/10).(-10/11,-8/9) 0 28 16/11 -9/10 1 7 3/2 (-9/10,-8/9) 0 28 14/9 -8/9 9 2 11/7 (-8/9,-54/61).(-31/35,-23/26) 0 28 19/12 (-38/43,-15/17) 0 28 46/29 -52/59 1 14 27/17 (-22/25,-36/41).(-29/33,-7/8) 0 28 8/5 -7/8 1 7 21/13 (-1/1,-7/8).(-8/9,-6/7) 0 4 13/8 (-1/1,-8/9) 0 28 18/11 -8/9 1 14 5/3 (-1/1,-7/8).(-8/9,-6/7) 0 28 17/10 (-7/8,-20/23) 0 28 29/17 (-19/22,-25/29).(-44/51,-6/7) 0 28 12/7 -1/1 1 7 7/4 0 4 16/9 -1/1 1 7 25/14 (-1/1,-6/7) 0 28 34/19 -8/9 1 14 9/5 (-8/9,-22/25).(-15/17,-7/8) 0 28 11/6 (-1/1,-6/7) 0 28 13/7 (-1/1,-7/8).(-8/9,-6/7) 0 28 2/1 -6/7 1 14 11/5 (-1/1,-7/8).(-8/9,-6/7) 0 28 9/4 (-5/6,-4/5) 0 28 7/3 (-1/1,-5/6).(-6/7,-4/5) 0 4 19/8 (-1/1,-6/7) 0 28 31/13 (-1/1,-7/8).(-8/9,-6/7) 0 28 12/5 -5/6 1 7 41/17 (-1/1,-5/6).(-6/7,-4/5) 0 28 70/29 -6/7 1 2 29/12 (-6/7,-5/6) 0 28 17/7 (-6/7,-16/19).(-11/13,-5/6) 0 28 5/2 (-1/1,-4/5) 0 28 28/11 -1/1 3 1 23/9 (-1/1,-7/8).(-8/9,-6/7) 0 28 18/7 -6/7 1 14 13/5 (-1/1,-5/6).(-6/7,-4/5) 0 28 34/13 -4/5 1 14 21/8 0 4 29/11 (-5/6,-9/11).(-14/17,-4/5) 0 28 8/3 -5/6 1 7 27/10 (-5/6,-4/5) 0 28 19/7 (-5/6,-19/23).(-24/29,-14/17) 0 28 11/4 (-9/11,-4/5) 0 28 14/5 -4/5 5 2 3/1 (-1/1,-3/4).(-4/5,-2/3) 0 28 16/5 -5/6 1 7 29/9 (-17/21,-21/26).(-38/47,-4/5) 0 28 42/13 -4/5 13 2 13/4 (-4/5,-7/9) 0 28 10/3 -4/5 1 14 7/2 0 4 18/5 -4/5 1 14 65/18 (-22/29,-3/4) 0 28 112/31 -3/4 11 1 47/13 (-3/4,-11/15).(-14/19,-8/11) 0 28 29/8 (-3/4,-2/3) 0 28 11/3 (-3/4,-5/7).(-8/11,-2/3) 0 28 26/7 -2/3 1 14 41/11 (-1/1,-3/4).(-4/5,-2/3) 0 28 56/15 -3/4 1 1 15/4 (-3/4,-2/3) 0 28 4/1 -1/1 1 7 13/3 (-1/1,-3/4).(-4/5,-2/3) 0 28 22/5 -4/5 1 14 53/12 (-10/13,-3/4) 0 28 84/19 -3/4 5 1 31/7 (-3/4,-5/7).(-8/11,-2/3) 0 28 9/2 (-3/4,-2/3) 0 28 14/3 -2/3 3 2 5/1 (-1/1,-1/2).(-2/3,0/1) 0 28 11/2 (-2/1,-1/1) 0 28 28/5 -1/1 9 1 17/3 (-1/1,-7/8).(-8/9,-6/7) 0 28 6/1 -2/3 1 14 13/2 (-1/1,-2/3) 0 28 7/1 (-1/1,-1/2).(-2/3,0/1) 0 4 8/1 -1/1 1 7 1/0 (-1/1,0/1) 0 28 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(195,-224,74,-85) (1/1,7/6) -> (21/8,29/11) Hyperbolic Matrix(309,-364,118,-139) (7/6,6/5) -> (34/13,21/8) Hyperbolic Matrix(139,-168,24,-29) (6/5,11/9) -> (17/3,6/1) Hyperbolic Matrix(113,-140,46,-57) (11/9,5/4) -> (17/7,5/2) Glide Reflection Matrix(111,-140,88,-111) (5/4,14/11) -> (5/4,14/11) Reflection Matrix(197,-252,154,-197) (14/11,9/7) -> (14/11,9/7) Reflection Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(281,-364,44,-57) (22/17,13/10) -> (6/1,13/2) Glide Reflection Matrix(85,-112,22,-29) (13/10,4/3) -> (15/4,4/1) Glide Reflection Matrix(83,-112,20,-27) (4/3,15/11) -> (4/1,13/3) Glide Reflection Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(671,-952,394,-559) (17/12,27/19) -> (17/10,29/17) Glide Reflection Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(253,-364,98,-141) (10/7,13/9) -> (18/7,13/5) Glide Reflection Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(307,-448,172,-251) (16/11,3/2) -> (16/9,25/14) Glide Reflection Matrix(55,-84,36,-55) (3/2,14/9) -> (3/2,14/9) Reflection Matrix(197,-308,126,-197) (14/9,11/7) -> (14/9,11/7) Reflection Matrix(195,-308,88,-139) (11/7,19/12) -> (11/5,9/4) Glide Reflection Matrix(2101,-3332,582,-923) (19/12,46/29) -> (18/5,65/18) Hyperbolic Matrix(281,-448,106,-169) (27/17,8/5) -> (29/11,8/3) Glide Reflection Matrix(139,-224,18,-29) (8/5,21/13) -> (7/1,8/1) Hyperbolic Matrix(225,-364,34,-55) (21/13,13/8) -> (13/2,7/1) Hyperbolic Matrix(223,-364,68,-111) (13/8,18/11) -> (13/4,10/3) Glide Reflection Matrix(307,-504,120,-197) (18/11,5/3) -> (23/9,18/7) Hyperbolic Matrix(83,-140,16,-27) (5/3,17/10) -> (5/1,11/2) Glide Reflection Matrix(475,-812,148,-253) (29/17,12/7) -> (16/5,29/9) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(1315,-2352,298,-533) (25/14,34/19) -> (22/5,53/12) Hyperbolic Matrix(169,-308,62,-113) (9/5,11/6) -> (19/7,11/4) Glide Reflection Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(141,-308,38,-83) (2/1,11/5) -> (11/3,26/7) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(365,-868,82,-195) (19/8,31/13) -> (31/7,9/2) Hyperbolic Matrix(223,-532,70,-167) (31/13,12/5) -> (3/1,16/5) Glide Reflection Matrix(2379,-5740,986,-2379) (41/17,70/29) -> (41/17,70/29) Reflection Matrix(1681,-4060,696,-1681) (70/29,29/12) -> (70/29,29/12) Reflection Matrix(335,-812,92,-223) (29/12,17/7) -> (29/8,11/3) Glide Reflection Matrix(111,-280,44,-111) (5/2,28/11) -> (5/2,28/11) Reflection Matrix(505,-1288,198,-505) (28/11,23/9) -> (28/11,23/9) Reflection Matrix(279,-728,64,-167) (13/5,34/13) -> (13/3,22/5) Glide Reflection Matrix(83,-224,10,-27) (8/3,27/10) -> (8/1,1/0) Glide Reflection Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(111,-308,40,-111) (11/4,14/5) -> (11/4,14/5) Reflection Matrix(29,-84,10,-29) (14/5,3/1) -> (14/5,3/1) Reflection Matrix(755,-2436,234,-755) (29/9,42/13) -> (29/9,42/13) Reflection Matrix(337,-1092,104,-337) (42/13,13/4) -> (42/13,13/4) Reflection Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(4031,-14560,1116,-4031) (65/18,112/31) -> (65/18,112/31) Reflection Matrix(2913,-10528,806,-2913) (112/31,47/13) -> (112/31,47/13) Reflection Matrix(1231,-4592,330,-1231) (41/11,56/15) -> (41/11,56/15) Reflection Matrix(449,-1680,120,-449) (56/15,15/4) -> (56/15,15/4) Reflection Matrix(2015,-8904,456,-2015) (53/12,84/19) -> (53/12,84/19) Reflection Matrix(1177,-5208,266,-1177) (84/19,31/7) -> (84/19,31/7) Reflection Matrix(55,-252,12,-55) (9/2,14/3) -> (9/2,14/3) Reflection Matrix(29,-140,6,-29) (14/3,5/1) -> (14/3,5/1) Reflection Matrix(111,-616,20,-111) (11/2,28/5) -> (11/2,28/5) Reflection Matrix(169,-952,30,-169) (28/5,17/3) -> (28/5,17/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,2,-1) -> Matrix(27,26,-28,-27) (0/1,1/1) -> (-1/1,-13/14) Matrix(195,-224,74,-85) -> Matrix(61,56,-73,-67) Matrix(309,-364,118,-139) -> Matrix(61,56,-73,-67) Matrix(139,-168,24,-29) -> Matrix(37,34,-49,-45) Matrix(113,-140,46,-57) -> Matrix(103,94,-126,-115) Matrix(111,-140,88,-111) -> Matrix(461,420,-506,-461) (5/4,14/11) -> (-21/23,-10/11) Matrix(197,-252,154,-197) -> Matrix(749,680,-825,-749) (14/11,9/7) -> (-10/11,-68/75) Matrix(391,-504,218,-281) -> Matrix(179,162,-200,-181) -9/10 Matrix(281,-364,44,-57) -> Matrix(31,28,-52,-47) Matrix(85,-112,22,-29) -> Matrix(9,8,-19,-17) Matrix(83,-112,20,-27) -> Matrix(29,26,-39,-35) Matrix(225,-308,122,-167) -> Matrix(3,2,-2,-1) -1/1 Matrix(141,-196,100,-139) -> Matrix(91,82,-101,-91) (-1/1,-9/10).(-10/11,-8/9) Matrix(671,-952,394,-559) -> Matrix(123,110,-142,-127) Matrix(1063,-1512,670,-953) -> Matrix(113,98,-128,-111) -7/8 Matrix(253,-364,98,-141) -> Matrix(49,44,-59,-53) Matrix(559,-812,232,-337) -> Matrix(5,4,-4,-3) -1/1 Matrix(307,-448,172,-251) -> Matrix(69,62,-79,-71) Matrix(55,-84,36,-55) -> Matrix(161,144,-180,-161) (3/2,14/9) -> (-9/10,-8/9) Matrix(197,-308,126,-197) -> Matrix(487,432,-549,-487) (14/9,11/7) -> (-8/9,-54/61) Matrix(195,-308,88,-139) -> Matrix(147,130,-173,-153) Matrix(2101,-3332,582,-923) -> Matrix(245,216,-321,-283) Matrix(281,-448,106,-169) -> Matrix(93,82,-110,-97) Matrix(139,-224,18,-29) -> Matrix(9,8,-17,-15) Matrix(225,-364,34,-55) -> Matrix(7,6,-6,-5) -1/1 Matrix(223,-364,68,-111) -> Matrix(59,52,-76,-67) Matrix(307,-504,120,-197) -> Matrix(57,50,-65,-57) (-1/1,-7/8).(-8/9,-6/7) Matrix(83,-140,16,-27) -> Matrix(7,6,-15,-13) Matrix(475,-812,148,-253) -> Matrix(31,26,-37,-31) (-1/1,-5/6).(-6/7,-4/5) Matrix(113,-196,64,-111) -> Matrix(1,0,0,1) Matrix(1315,-2352,298,-533) -> Matrix(31,28,-41,-37) Matrix(169,-308,62,-113) -> Matrix(67,58,-82,-71) Matrix(223,-420,60,-113) -> Matrix(5,4,-4,-3) -1/1 Matrix(141,-308,38,-83) -> Matrix(19,16,-25,-21) -4/5 Matrix(85,-196,36,-83) -> Matrix(31,26,-37,-31) (-1/1,-5/6).(-6/7,-4/5) Matrix(365,-868,82,-195) -> Matrix(19,16,-25,-21) -4/5 Matrix(223,-532,70,-167) -> Matrix(11,10,-12,-11) *** -> (-1/1,-5/6) Matrix(2379,-5740,986,-2379) -> Matrix(29,24,-35,-29) (41/17,70/29) -> (-6/7,-4/5) Matrix(1681,-4060,696,-1681) -> Matrix(71,60,-84,-71) (70/29,29/12) -> (-6/7,-5/6) Matrix(335,-812,92,-223) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(111,-280,44,-111) -> Matrix(9,8,-10,-9) (5/2,28/11) -> (-1/1,-4/5) Matrix(505,-1288,198,-505) -> Matrix(15,14,-16,-15) (28/11,23/9) -> (-1/1,-7/8) Matrix(279,-728,64,-167) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(83,-224,10,-27) -> Matrix(5,4,-11,-9) Matrix(673,-1820,186,-503) -> Matrix(3,2,-2,-1) -1/1 Matrix(111,-308,40,-111) -> Matrix(89,72,-110,-89) (11/4,14/5) -> (-9/11,-4/5) Matrix(29,-84,10,-29) -> Matrix(11,8,-15,-11) (14/5,3/1) -> (-4/5,-2/3) Matrix(755,-2436,234,-755) -> Matrix(189,152,-235,-189) (29/9,42/13) -> (-38/47,-4/5) Matrix(337,-1092,104,-337) -> Matrix(71,56,-90,-71) (42/13,13/4) -> (-4/5,-7/9) Matrix(57,-196,16,-55) -> Matrix(1,0,0,1) Matrix(4031,-14560,1116,-4031) -> Matrix(175,132,-232,-175) (65/18,112/31) -> (-22/29,-3/4) Matrix(2913,-10528,806,-2913) -> Matrix(89,66,-120,-89) (112/31,47/13) -> (-3/4,-11/15) Matrix(1231,-4592,330,-1231) -> Matrix(7,6,-8,-7) (41/11,56/15) -> (-1/1,-3/4) Matrix(449,-1680,120,-449) -> Matrix(17,12,-24,-17) (56/15,15/4) -> (-3/4,-2/3) Matrix(2015,-8904,456,-2015) -> Matrix(79,60,-104,-79) (53/12,84/19) -> (-10/13,-3/4) Matrix(1177,-5208,266,-1177) -> Matrix(41,30,-56,-41) (84/19,31/7) -> (-3/4,-5/7) Matrix(55,-252,12,-55) -> Matrix(17,12,-24,-17) (9/2,14/3) -> (-3/4,-2/3) Matrix(29,-140,6,-29) -> Matrix(-1,0,3,1) (14/3,5/1) -> (-2/3,0/1) Matrix(111,-616,20,-111) -> Matrix(3,4,-2,-3) (11/2,28/5) -> (-2/1,-1/1) Matrix(169,-952,30,-169) -> Matrix(15,14,-16,-15) (28/5,17/3) -> (-1/1,-7/8) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.