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 -6/7 -17/21 -3/4 -5/7 -13/21 -7/12 -4/7 -47/84 -1/2 -3/7 -5/12 -3/8 -13/42 -3/10 -25/84 -2/7 -55/196 -31/112 -15/56 -7/27 -1/4 -5/21 -19/84 -1/6 -3/19 -1/7 -1/8 -1/9 0/1 1/8 1/7 2/13 1/6 3/17 5/28 2/11 1/5 3/14 5/23 2/9 3/13 5/21 1/4 3/11 7/25 2/7 3/10 1/3 5/14 3/8 11/28 2/5 5/12 3/7 1/2 15/28 4/7 7/12 17/28 13/21 9/14 2/3 29/42 5/7 11/15 3/4 11/14 17/21 23/28 6/7 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/0 -9/10 0/1 -8/9 0/1 1/2 -7/8 0/1 -13/15 0/1 1/1 -6/7 1/0 -5/6 0/1 -19/23 -1/3 0/1 -14/17 -1/6 0/1 -23/28 0/1 -9/11 0/1 1/4 -13/16 0/1 -17/21 0/1 -21/26 2/5 -4/5 1/1 1/0 -15/19 2/1 1/0 -11/14 1/0 -7/9 -1/1 1/0 -17/22 -2/1 -10/13 -3/2 -1/1 -23/30 -4/5 -36/47 -3/4 -2/3 -13/17 -1/1 -1/2 -3/4 0/1 -14/19 0/1 1/0 -25/34 0/1 -11/15 2/3 1/1 -19/26 4/3 -8/11 2/1 1/0 -5/7 1/0 -12/17 0/1 1/0 -19/27 1/1 1/0 -7/10 -2/1 -9/13 -1/1 0/1 -29/42 -1/1 -20/29 -1/2 0/1 -11/16 0/1 -2/3 0/1 1/0 -13/20 0/1 -24/37 0/1 1/2 -11/17 1/1 1/0 -9/14 1/0 -7/11 -2/1 1/0 -12/19 2/1 1/0 -29/46 -4/1 -17/27 -1/1 1/0 -5/8 -2/1 -18/29 -8/5 -3/2 -13/21 -1/1 -34/55 2/1 1/0 -55/89 -3/1 -2/1 -21/34 -2/1 -8/13 -1/1 1/0 -19/31 -2/1 -3/2 -11/18 -4/3 -25/41 -6/5 -1/1 -39/64 -6/5 -14/23 -9/8 -1/1 -17/28 -1/1 -3/5 -1/1 -1/2 -10/17 -1/2 0/1 -17/29 -1/2 -1/3 -7/12 0/1 -18/31 -1/2 0/1 -29/50 0/1 -11/19 -1/2 0/1 -15/26 -2/3 -4/7 0/1 -17/30 2/1 -47/83 -9/1 1/0 -30/53 -2/1 1/0 -13/23 -1/1 0/1 -22/39 0/1 1/2 -31/55 0/1 1/0 -9/16 0/1 -23/41 0/1 1/1 -37/66 2/1 -14/25 0/1 1/0 -47/84 0/1 -33/59 0/1 1/1 -19/34 0/1 -5/9 1/1 1/0 -11/20 -2/1 -6/11 -2/1 1/0 -7/13 -6/5 -1/1 -15/28 -1/1 -8/15 -1/1 -7/8 -1/2 0/1 -5/11 -2/3 -1/2 -4/9 -1/2 -2/5 -3/7 0/1 -8/19 -2/1 1/0 -13/31 0/1 1/0 -18/43 -1/1 -1/2 -23/55 -1/2 0/1 -5/12 0/1 -17/41 0/1 1/1 -29/70 1/1 -12/29 2/1 1/0 -7/17 1/1 1/0 -9/22 0/1 -11/27 3/1 1/0 -2/5 -1/1 1/0 -11/28 -1/1 -9/23 -1/1 -4/5 -7/18 -2/3 -5/13 -1/1 0/1 -13/34 -2/3 -8/21 -1/2 -27/71 -1/1 0/1 -19/50 -2/3 -11/29 -1/2 -1/3 -3/8 0/1 -10/27 -1/2 -2/5 -7/19 0/1 1/0 -11/30 -2/1 -4/11 -1/2 0/1 -13/36 0/1 -22/61 -1/1 -3/4 -31/86 -4/7 -9/25 -1/2 0/1 -5/14 0/1 -1/3 -1/1 0/1 -7/22 0/1 -6/19 -1/2 0/1 -17/54 -2/3 -11/35 0/1 -5/16 0/1 -9/29 -1/1 1/0 -13/42 1/0 -17/55 -2/1 1/0 -4/13 -1/1 1/0 -11/36 0/1 -18/59 0/1 1/0 -7/23 -2/1 -1/1 -3/10 0/1 -14/47 -1/4 0/1 -25/84 0/1 -11/37 0/1 1/2 -8/27 -2/1 1/0 -5/17 -1/1 1/0 -7/24 0/1 -2/7 -1/1 -9/32 -2/3 -16/57 -8/15 -1/2 -55/196 -1/2 -39/139 -1/2 -15/31 -23/82 -4/9 -7/25 -1/2 0/1 -5/18 -2/3 -18/65 -8/15 -1/2 -31/112 -1/2 -13/47 -1/2 -5/11 -8/29 -1/2 0/1 -11/40 0/1 -3/11 0/1 1/0 -7/26 -2/1 -11/41 -8/7 -1/1 -15/56 -1/1 -4/15 -1/1 -3/4 -5/19 -2/3 -1/2 -6/23 -1/1 -1/2 -7/27 -5/9 -1/2 -1/4 0/1 -7/29 5/1 1/0 -6/25 -2/1 1/0 -5/21 1/0 -14/59 -4/1 1/0 -9/38 -2/1 -13/55 -2/1 1/0 -4/17 -2/1 -3/2 -3/13 -1/1 -2/3 -5/22 0/1 -12/53 -1/2 0/1 -19/84 0/1 -7/31 0/1 1/0 -2/9 -2/1 1/0 -7/32 -2/1 -12/55 -3/2 -16/11 -5/23 -4/3 -1/1 -3/14 -1/1 -1/5 -1/1 -1/2 -2/11 -2/3 -1/2 -5/28 -1/2 -3/17 -1/2 -1/3 -1/6 0/1 -3/19 0/1 1/0 -2/13 -1/1 -1/2 -1/7 -1/1 -2/15 -1/1 -3/4 -1/8 -2/3 -1/9 -5/9 -1/2 0/1 -1/2 0/1 1/8 -2/5 1/7 -1/3 3/20 0/1 2/13 -1/2 -1/3 1/6 0/1 3/17 -1/1 -1/2 5/28 -1/2 2/11 -1/2 -2/5 1/5 -1/2 -1/3 3/14 -1/3 5/23 -1/3 -4/13 2/9 -2/7 -1/4 5/22 0/1 3/13 -2/5 -1/3 4/17 -3/10 -2/7 9/38 -2/7 5/21 -1/4 6/25 -2/7 -1/4 1/4 0/1 5/19 -1/2 -2/5 9/34 -2/5 4/15 -3/8 -1/3 3/11 -1/4 0/1 8/29 -1/2 0/1 13/47 -5/9 -1/2 5/18 -2/5 7/25 -1/2 0/1 2/7 -1/3 9/31 -2/7 -1/4 25/86 -6/23 16/55 -1/4 -6/25 7/24 0/1 5/17 -1/3 -1/4 8/27 -2/7 -1/4 3/10 0/1 7/23 -1/3 -2/7 11/36 0/1 4/13 -1/3 -1/4 5/16 0/1 6/19 -1/2 0/1 1/3 -1/3 0/1 5/14 0/1 9/25 -1/2 0/1 4/11 -1/2 0/1 11/30 -2/7 7/19 -1/4 0/1 31/84 0/1 24/65 0/1 1/2 17/46 0/1 10/27 -2/3 -1/2 3/8 0/1 11/29 -1/1 -1/2 19/50 -2/5 8/21 -1/2 5/13 -1/3 0/1 7/18 -2/5 9/23 -4/11 -1/3 11/28 -1/3 2/5 -1/3 -1/4 11/27 -1/4 -3/13 9/22 0/1 7/17 -1/4 -1/5 12/29 -1/4 -2/9 29/70 -1/5 17/41 -1/5 0/1 5/12 0/1 3/7 0/1 7/16 0/1 11/25 -1/2 0/1 15/34 0/1 4/9 -2/3 -1/2 5/11 -1/2 -2/5 6/13 -5/14 -1/3 1/2 0/1 8/15 -7/20 -1/3 15/28 -1/3 7/13 -1/3 -6/19 6/11 -2/7 -1/4 17/31 -2/7 -1/4 28/51 -1/2 -1/3 11/20 -2/7 16/29 -4/15 -1/4 5/9 -1/4 -1/5 14/25 -1/4 0/1 23/41 -1/5 0/1 9/16 0/1 31/55 -1/4 0/1 22/39 -1/6 0/1 13/23 -1/3 0/1 4/7 0/1 19/33 -1/1 0/1 34/59 -2/3 -1/2 49/85 -9/17 -1/2 113/196 -1/2 64/111 -1/2 -14/29 15/26 -2/5 11/19 -1/2 0/1 29/50 0/1 47/81 -1/4 0/1 65/112 0/1 18/31 -1/2 0/1 7/12 0/1 24/41 -1/1 -1/2 41/70 -1/2 17/29 -1/1 -1/2 10/17 -1/2 0/1 3/5 -1/2 -1/3 17/28 -1/3 14/23 -1/3 -9/28 25/41 -1/3 -6/19 36/59 -6/19 -5/16 47/77 -5/16 11/18 -4/13 19/31 -3/10 -2/7 27/44 -2/7 35/57 -2/7 -1/4 43/70 -1/4 8/13 -1/3 -1/4 21/34 -2/7 13/21 -1/3 31/50 -4/13 18/29 -3/10 -8/27 5/8 -2/7 17/27 -1/3 -1/4 12/19 -1/4 -2/9 7/11 -2/7 -1/4 9/14 -1/4 11/17 -1/4 -1/5 13/20 0/1 15/23 -1/3 -2/7 2/3 -1/4 0/1 11/16 0/1 20/29 -1/2 0/1 29/42 -1/3 9/13 -1/3 0/1 7/10 -2/7 5/7 -1/4 13/18 0/1 47/65 -7/27 -1/4 81/112 -1/4 34/47 -1/4 -6/25 21/29 -1/4 -3/13 8/11 -1/4 -2/9 19/26 -4/19 30/41 -9/44 -1/5 41/56 -1/5 11/15 -1/5 -2/11 25/34 0/1 39/53 -1/5 0/1 14/19 -1/4 0/1 17/23 -1/5 -2/11 20/27 -6/35 -1/6 3/4 0/1 13/17 -1/2 -1/3 36/47 -2/5 -3/8 23/30 -4/11 10/13 -1/3 -3/10 17/22 -2/7 41/53 -1/3 -2/7 65/84 -2/7 24/31 -2/7 -1/4 7/9 -1/3 -1/4 11/14 -1/4 15/19 -1/4 -2/9 19/24 0/1 42/53 -2/7 -1/4 23/29 -1/4 -5/21 4/5 -1/4 -1/5 25/31 -2/11 -1/6 21/26 -2/13 17/21 0/1 47/58 -2/9 30/37 -1/4 0/1 13/16 0/1 22/27 -1/6 0/1 9/11 -1/8 0/1 23/28 0/1 14/17 0/1 1/2 19/23 -1/1 0/1 24/29 -1/2 -4/9 5/6 0/1 11/13 -1/3 -2/7 6/7 -1/4 19/22 -2/9 13/15 -1/5 0/1 20/23 -1/5 -3/16 7/8 0/1 15/17 -1/4 -1/5 8/9 -1/6 0/1 9/10 0/1 10/11 -1/6 0/1 1/1 -1/4 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(139,126,-588,-533) (-1/1,-9/10) -> (-9/38,-13/55) Hyperbolic Matrix(393,352,1064,953) (-9/10,-8/9) -> (24/65,17/46) Hyperbolic Matrix(309,272,-476,-419) (-8/9,-7/8) -> (-13/20,-24/37) Hyperbolic Matrix(785,682,-1288,-1119) (-7/8,-13/15) -> (-25/41,-39/64) Hyperbolic Matrix(309,266,-812,-699) (-13/15,-6/7) -> (-8/21,-27/71) Hyperbolic Matrix(139,118,-364,-309) (-6/7,-5/6) -> (-13/34,-8/21) Hyperbolic Matrix(813,674,-1316,-1091) (-5/6,-19/23) -> (-55/89,-21/34) Hyperbolic Matrix(727,600,1288,1063) (-19/23,-14/17) -> (22/39,13/23) Hyperbolic Matrix(783,644,952,783) (-14/17,-23/28) -> (23/28,14/17) Hyperbolic Matrix(505,414,616,505) (-23/28,-9/11) -> (9/11,23/28) Hyperbolic Matrix(169,138,-616,-503) (-9/11,-13/16) -> (-11/40,-3/11) Hyperbolic Matrix(281,228,-896,-727) (-13/16,-17/21) -> (-11/35,-5/16) Hyperbolic Matrix(643,520,-2044,-1653) (-17/21,-21/26) -> (-17/54,-11/35) Hyperbolic Matrix(727,586,-2016,-1625) (-21/26,-4/5) -> (-22/61,-31/86) Hyperbolic Matrix(139,110,-532,-421) (-4/5,-15/19) -> (-5/19,-6/23) Hyperbolic Matrix(419,330,532,419) (-15/19,-11/14) -> (11/14,15/19) Hyperbolic Matrix(197,154,252,197) (-11/14,-7/9) -> (7/9,11/14) Hyperbolic Matrix(281,218,-504,-391) (-7/9,-17/22) -> (-19/34,-5/9) Hyperbolic Matrix(449,346,728,561) (-17/22,-10/13) -> (8/13,21/34) Hyperbolic Matrix(253,194,476,365) (-10/13,-23/30) -> (1/2,8/15) Hyperbolic Matrix(979,750,-3108,-2381) (-23/30,-36/47) -> (-6/19,-17/54) Hyperbolic Matrix(841,644,952,729) (-36/47,-13/17) -> (15/17,8/9) Hyperbolic Matrix(139,106,476,363) (-13/17,-3/4) -> (7/24,5/17) Hyperbolic Matrix(141,104,-644,-475) (-3/4,-14/19) -> (-2/9,-7/32) Hyperbolic Matrix(337,248,-1064,-783) (-14/19,-25/34) -> (-7/22,-6/19) Hyperbolic Matrix(1203,884,-3164,-2325) (-25/34,-11/15) -> (-27/71,-19/50) Hyperbolic Matrix(391,286,-1456,-1065) (-11/15,-19/26) -> (-7/26,-11/41) Hyperbolic Matrix(225,164,616,449) (-19/26,-8/11) -> (4/11,11/30) Hyperbolic Matrix(139,100,-196,-141) (-8/11,-5/7) -> (-5/7,-12/17) Parabolic Matrix(559,394,952,671) (-12/17,-19/27) -> (17/29,10/17) Hyperbolic Matrix(953,670,-1512,-1063) (-19/27,-7/10) -> (-29/46,-17/27) Hyperbolic Matrix(141,98,364,253) (-7/10,-9/13) -> (5/13,7/18) Hyperbolic Matrix(755,522,1092,755) (-9/13,-29/42) -> (29/42,9/13) Hyperbolic Matrix(1345,928,3248,2241) (-29/42,-20/29) -> (12/29,29/70) Hyperbolic Matrix(729,502,896,617) (-20/29,-11/16) -> (13/16,22/27) Hyperbolic Matrix(309,212,532,365) (-11/16,-2/3) -> (18/31,7/12) Hyperbolic Matrix(393,256,-1288,-839) (-2/3,-13/20) -> (-11/36,-18/59) Hyperbolic Matrix(1093,708,1428,925) (-24/37,-11/17) -> (13/17,36/47) Hyperbolic Matrix(307,198,476,307) (-11/17,-9/14) -> (9/14,11/17) Hyperbolic Matrix(197,126,308,197) (-9/14,-7/11) -> (7/11,9/14) Hyperbolic Matrix(139,88,308,195) (-7/11,-12/19) -> (4/9,5/11) Hyperbolic Matrix(923,582,-3332,-2101) (-12/19,-29/46) -> (-5/18,-18/65) Hyperbolic Matrix(169,106,448,281) (-17/27,-5/8) -> (3/8,11/29) Hyperbolic Matrix(167,104,448,279) (-5/8,-18/29) -> (10/27,3/8) Hyperbolic Matrix(1091,676,-1764,-1093) (-18/29,-13/21) -> (-13/21,-34/55) Parabolic Matrix(2715,1678,3668,2267) (-34/55,-55/89) -> (17/23,20/27) Hyperbolic Matrix(561,346,728,449) (-21/34,-8/13) -> (10/13,17/22) Hyperbolic Matrix(727,446,-1736,-1065) (-8/13,-19/31) -> (-13/31,-18/43) Hyperbolic Matrix(281,172,1008,617) (-19/31,-11/18) -> (5/18,7/25) Hyperbolic Matrix(1931,1178,-3444,-2101) (-11/18,-25/41) -> (-23/41,-37/66) Hyperbolic Matrix(2045,1246,3724,2269) (-39/64,-14/23) -> (28/51,11/20) Hyperbolic Matrix(783,476,1288,783) (-14/23,-17/28) -> (17/28,14/23) Hyperbolic Matrix(169,102,280,169) (-17/28,-3/5) -> (3/5,17/28) Hyperbolic Matrix(27,16,140,83) (-3/5,-10/17) -> (2/11,1/5) Hyperbolic Matrix(589,346,812,477) (-10/17,-17/29) -> (21/29,8/11) Hyperbolic Matrix(253,148,-812,-475) (-17/29,-7/12) -> (-5/16,-9/29) Hyperbolic Matrix(365,212,532,309) (-7/12,-18/31) -> (2/3,11/16) Hyperbolic Matrix(755,438,-3332,-1933) (-18/31,-29/50) -> (-5/22,-12/53) Hyperbolic Matrix(421,244,1596,925) (-29/50,-11/19) -> (5/19,9/34) Hyperbolic Matrix(391,226,1064,615) (-11/19,-15/26) -> (11/30,7/19) Hyperbolic Matrix(223,128,-392,-225) (-15/26,-4/7) -> (-4/7,-17/30) Parabolic Matrix(3079,1744,-10976,-6217) (-17/30,-47/83) -> (-39/139,-23/82) Hyperbolic Matrix(4705,2664,5936,3361) (-47/83,-30/53) -> (42/53,23/29) Hyperbolic Matrix(841,476,1288,729) (-30/53,-13/23) -> (15/23,2/3) Hyperbolic Matrix(1063,600,1288,727) (-13/23,-22/39) -> (14/17,19/23) Hyperbolic Matrix(727,410,-3080,-1737) (-22/39,-31/55) -> (-13/55,-4/17) Hyperbolic Matrix(2045,1152,3332,1877) (-31/55,-9/16) -> (27/44,35/57) Hyperbolic Matrix(477,268,1148,645) (-9/16,-23/41) -> (17/41,5/12) Hyperbolic Matrix(1149,644,-4844,-2715) (-37/66,-14/25) -> (-14/59,-9/38) Hyperbolic Matrix(3641,2038,4704,2633) (-14/25,-47/84) -> (65/84,24/31) Hyperbolic Matrix(7279,4072,9408,5263) (-47/84,-33/59) -> (41/53,65/84) Hyperbolic Matrix(2801,1566,3808,2129) (-33/59,-19/34) -> (25/34,39/53) Hyperbolic Matrix(29,16,-252,-139) (-5/9,-11/20) -> (-1/8,-1/9) Hyperbolic Matrix(223,122,-616,-337) (-11/20,-6/11) -> (-4/11,-13/36) Hyperbolic Matrix(85,46,364,197) (-6/11,-7/13) -> (3/13,4/17) Hyperbolic Matrix(391,210,728,391) (-7/13,-15/28) -> (15/28,7/13) Hyperbolic Matrix(449,240,840,449) (-15/28,-8/15) -> (8/15,15/28) Hyperbolic Matrix(365,194,476,253) (-8/15,-1/2) -> (23/30,10/13) Hyperbolic Matrix(83,38,-308,-141) (-1/2,-5/11) -> (-3/11,-7/26) Hyperbolic Matrix(195,88,308,139) (-5/11,-4/9) -> (12/19,7/11) Hyperbolic Matrix(83,36,-196,-85) (-4/9,-3/7) -> (-3/7,-8/19) Parabolic Matrix(195,82,-868,-365) (-8/19,-13/31) -> (-7/31,-2/9) Hyperbolic Matrix(951,398,-3080,-1289) (-18/43,-23/55) -> (-17/55,-4/13) Hyperbolic Matrix(867,362,1540,643) (-23/55,-5/12) -> (9/16,31/55) Hyperbolic Matrix(645,268,1148,477) (-5/12,-17/41) -> (23/41,9/16) Hyperbolic Matrix(2379,986,5740,2379) (-17/41,-29/70) -> (29/70,17/41) Hyperbolic Matrix(2241,928,3248,1345) (-29/70,-12/29) -> (20/29,29/42) Hyperbolic Matrix(281,116,952,393) (-12/29,-7/17) -> (5/17,8/27) Hyperbolic Matrix(83,34,476,195) (-7/17,-9/22) -> (1/6,3/17) Hyperbolic Matrix(755,308,1988,811) (-9/22,-11/27) -> (11/29,19/50) Hyperbolic Matrix(197,80,-756,-307) (-11/27,-2/5) -> (-6/23,-7/27) Hyperbolic Matrix(111,44,280,111) (-2/5,-11/28) -> (11/28,2/5) Hyperbolic Matrix(505,198,1288,505) (-11/28,-9/23) -> (9/23,11/28) Hyperbolic Matrix(195,76,644,251) (-9/23,-7/18) -> (3/10,7/23) Hyperbolic Matrix(253,98,364,141) (-7/18,-5/13) -> (9/13,7/10) Hyperbolic Matrix(167,64,728,279) (-5/13,-13/34) -> (5/22,3/13) Hyperbolic Matrix(811,308,1988,755) (-19/50,-11/29) -> (11/27,9/22) Hyperbolic Matrix(281,106,448,169) (-11/29,-3/8) -> (5/8,17/27) Hyperbolic Matrix(279,104,448,167) (-3/8,-10/27) -> (18/29,5/8) Hyperbolic Matrix(449,166,-1512,-559) (-10/27,-7/19) -> (-11/37,-8/27) Hyperbolic Matrix(615,226,1064,391) (-7/19,-11/30) -> (15/26,11/19) Hyperbolic Matrix(449,164,616,225) (-11/30,-4/11) -> (8/11,19/26) Hyperbolic Matrix(1147,414,1316,475) (-13/36,-22/61) -> (20/23,7/8) Hyperbolic Matrix(1399,504,4816,1735) (-31/86,-9/25) -> (9/31,25/86) Hyperbolic Matrix(251,90,700,251) (-9/25,-5/14) -> (5/14,9/25) Hyperbolic Matrix(29,10,84,29) (-5/14,-1/3) -> (1/3,5/14) Hyperbolic Matrix(953,304,1232,393) (-1/3,-7/22) -> (17/22,41/53) Hyperbolic Matrix(1903,590,3248,1007) (-9/29,-13/42) -> (41/70,17/29) Hyperbolic Matrix(3835,1186,6244,1931) (-13/42,-17/55) -> (35/57,43/70) Hyperbolic Matrix(111,34,728,223) (-4/13,-11/36) -> (3/20,2/13) Hyperbolic Matrix(1903,580,3304,1007) (-18/59,-7/23) -> (19/33,34/59) Hyperbolic Matrix(251,76,644,195) (-7/23,-3/10) -> (7/18,9/23) Hyperbolic Matrix(503,150,560,167) (-3/10,-14/47) -> (8/9,9/10) Hyperbolic Matrix(3473,1034,9408,2801) (-14/47,-25/84) -> (31/84,24/65) Hyperbolic Matrix(1735,516,4704,1399) (-25/84,-11/37) -> (7/19,31/84) Hyperbolic Matrix(393,116,952,281) (-8/27,-5/17) -> (7/17,12/29) Hyperbolic Matrix(363,106,476,139) (-5/17,-7/24) -> (3/4,13/17) Hyperbolic Matrix(111,32,-392,-113) (-7/24,-2/7) -> (-2/7,-9/32) Parabolic Matrix(811,228,1092,307) (-9/32,-16/57) -> (20/27,3/4) Hyperbolic Matrix(18985,5328,32928,9241) (-16/57,-55/196) -> (113/196,64/111) Hyperbolic Matrix(25311,7102,43904,12319) (-55/196,-39/139) -> (49/85,113/196) Hyperbolic Matrix(2575,722,3192,895) (-23/82,-7/25) -> (25/31,21/26) Hyperbolic Matrix(617,172,1008,281) (-7/25,-5/18) -> (11/18,19/31) Hyperbolic Matrix(9073,2512,12544,3473) (-18/65,-31/112) -> (81/112,34/47) Hyperbolic Matrix(9071,2510,12544,3471) (-31/112,-13/47) -> (47/65,81/112) Hyperbolic Matrix(897,248,1624,449) (-13/47,-8/29) -> (16/29,5/9) Hyperbolic Matrix(1119,308,1624,447) (-8/29,-11/40) -> (11/16,20/29) Hyperbolic Matrix(2297,616,3136,841) (-11/41,-15/56) -> (41/56,11/15) Hyperbolic Matrix(2295,614,3136,839) (-15/56,-4/15) -> (30/41,41/56) Hyperbolic Matrix(83,22,-532,-141) (-4/15,-5/19) -> (-3/19,-2/13) Hyperbolic Matrix(55,14,-224,-57) (-7/27,-1/4) -> (-1/4,-7/29) Parabolic Matrix(2211,532,3836,923) (-7/29,-6/25) -> (34/59,49/85) Hyperbolic Matrix(419,100,-1764,-421) (-6/25,-5/21) -> (-5/21,-14/59) Parabolic Matrix(197,46,364,85) (-4/17,-3/13) -> (7/13,6/11) Hyperbolic Matrix(307,70,364,83) (-3/13,-5/22) -> (5/6,11/13) Hyperbolic Matrix(4957,1122,8540,1933) (-12/53,-19/84) -> (65/112,18/31) Hyperbolic Matrix(5963,1348,10276,2323) (-19/84,-7/31) -> (47/81,65/112) Hyperbolic Matrix(897,196,3080,673) (-7/32,-12/55) -> (16/55,7/24) Hyperbolic Matrix(1597,348,1932,421) (-12/55,-5/23) -> (19/23,24/29) Hyperbolic Matrix(139,30,644,139) (-5/23,-3/14) -> (3/14,5/23) Hyperbolic Matrix(29,6,140,29) (-3/14,-1/5) -> (1/5,3/14) Hyperbolic Matrix(83,16,140,27) (-1/5,-2/11) -> (10/17,3/5) Hyperbolic Matrix(111,20,616,111) (-2/11,-5/28) -> (5/28,2/11) Hyperbolic Matrix(169,30,952,169) (-5/28,-3/17) -> (3/17,5/28) Hyperbolic Matrix(195,34,476,83) (-3/17,-1/6) -> (9/22,7/17) Hyperbolic Matrix(617,98,1064,169) (-1/6,-3/19) -> (11/19,29/50) Hyperbolic Matrix(27,4,-196,-29) (-2/13,-1/7) -> (-1/7,-2/15) Parabolic Matrix(197,26,644,85) (-2/15,-1/8) -> (11/36,4/13) Hyperbolic Matrix(85,8,308,29) (-1/9,0/1) -> (8/29,13/47) Hyperbolic Matrix(139,-16,252,-29) (0/1,1/8) -> (11/20,16/29) Hyperbolic Matrix(29,-4,196,-27) (1/8,1/7) -> (1/7,3/20) Parabolic Matrix(141,-22,532,-83) (2/13,1/6) -> (9/34,4/15) Hyperbolic Matrix(475,-104,644,-141) (5/23,2/9) -> (14/19,17/23) Hyperbolic Matrix(223,-50,504,-113) (2/9,5/22) -> (15/34,4/9) Hyperbolic Matrix(533,-126,588,-139) (4/17,9/38) -> (9/10,10/11) Hyperbolic Matrix(2017,-478,3304,-783) (9/38,5/21) -> (47/77,11/18) Hyperbolic Matrix(1931,-462,3164,-757) (5/21,6/25) -> (36/59,47/77) Hyperbolic Matrix(643,-156,812,-197) (6/25,1/4) -> (19/24,42/53) Hyperbolic Matrix(421,-110,532,-139) (1/4,5/19) -> (15/19,19/24) Hyperbolic Matrix(141,-38,308,-83) (4/15,3/11) -> (5/11,6/13) Hyperbolic Matrix(503,-138,616,-169) (3/11,8/29) -> (22/27,9/11) Hyperbolic Matrix(1457,-404,2016,-559) (13/47,5/18) -> (13/18,47/65) Hyperbolic Matrix(113,-32,392,-111) (7/25,2/7) -> (2/7,9/31) Parabolic Matrix(6329,-1840,10976,-3191) (25/86,16/55) -> (64/111,15/26) Hyperbolic Matrix(559,-166,1512,-449) (8/27,3/10) -> (17/46,10/27) Hyperbolic Matrix(839,-256,1288,-393) (7/23,11/36) -> (13/20,15/23) Hyperbolic Matrix(475,-148,812,-253) (4/13,5/16) -> (7/12,24/41) Hyperbolic Matrix(727,-228,896,-281) (5/16,6/19) -> (30/37,13/16) Hyperbolic Matrix(783,-248,1064,-337) (6/19,1/3) -> (39/53,14/19) Hyperbolic Matrix(337,-122,616,-223) (9/25,4/11) -> (6/11,17/31) Hyperbolic Matrix(699,-266,812,-309) (19/50,8/21) -> (6/7,19/22) Hyperbolic Matrix(309,-118,364,-139) (8/21,5/13) -> (11/13,6/7) Hyperbolic Matrix(223,-90,280,-113) (2/5,11/27) -> (23/29,4/5) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(979,-430,1596,-701) (7/16,11/25) -> (19/31,27/44) Hyperbolic Matrix(2323,-1024,4004,-1765) (11/25,15/34) -> (29/50,47/81) Hyperbolic Matrix(307,-144,420,-197) (6/13,1/2) -> (19/26,30/41) Hyperbolic Matrix(1399,-768,1736,-953) (17/31,28/51) -> (4/5,25/31) Hyperbolic Matrix(391,-218,504,-281) (5/9,14/25) -> (24/31,7/9) Hyperbolic Matrix(2101,-1178,3444,-1931) (14/25,23/41) -> (25/41,36/59) Hyperbolic Matrix(589,-332,644,-363) (31/55,22/39) -> (10/11,1/1) Hyperbolic Matrix(225,-128,392,-223) (13/23,4/7) -> (4/7,19/33) Parabolic Matrix(2323,-1360,3780,-2213) (24/41,41/70) -> (43/70,8/13) Hyperbolic Matrix(1119,-682,1288,-785) (14/23,25/41) -> (13/15,20/23) Hyperbolic Matrix(1093,-676,1764,-1091) (21/34,13/21) -> (13/21,31/50) Parabolic Matrix(1345,-834,1624,-1007) (31/50,18/29) -> (24/29,5/6) Hyperbolic Matrix(1317,-830,1820,-1147) (17/27,12/19) -> (34/47,21/29) Hyperbolic Matrix(419,-272,476,-309) (11/17,13/20) -> (7/8,15/17) Hyperbolic Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic Matrix(727,-534,840,-617) (11/15,25/34) -> (19/22,13/15) Hyperbolic Matrix(3109,-2382,3836,-2939) (36/47,23/30) -> (47/58,30/37) Hyperbolic Matrix(1429,-1156,1764,-1427) (21/26,17/21) -> (17/21,47/58) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(139,126,-588,-533) -> Matrix(1,-2,0,1) Matrix(393,352,1064,953) -> Matrix(1,0,0,1) Matrix(309,272,-476,-419) -> Matrix(1,0,0,1) Matrix(785,682,-1288,-1119) -> Matrix(5,-6,-4,5) Matrix(309,266,-812,-699) -> Matrix(1,0,-2,1) Matrix(139,118,-364,-309) -> Matrix(1,2,-2,-3) Matrix(813,674,-1316,-1091) -> Matrix(3,2,-2,-1) Matrix(727,600,1288,1063) -> Matrix(1,0,0,1) Matrix(783,644,952,783) -> Matrix(1,0,8,1) Matrix(505,414,616,505) -> Matrix(1,0,-12,1) Matrix(169,138,-616,-503) -> Matrix(1,0,-4,1) Matrix(281,228,-896,-727) -> Matrix(1,0,-2,1) Matrix(643,520,-2044,-1653) -> Matrix(1,0,-4,1) Matrix(727,586,-2016,-1625) -> Matrix(3,-2,-4,3) Matrix(139,110,-532,-421) -> Matrix(1,0,-2,1) Matrix(419,330,532,419) -> Matrix(1,-4,-4,17) Matrix(197,154,252,197) -> Matrix(1,2,-4,-7) Matrix(281,218,-504,-391) -> Matrix(1,2,0,1) Matrix(449,346,728,561) -> Matrix(3,4,-10,-13) Matrix(253,194,476,365) -> Matrix(5,4,-14,-11) Matrix(979,750,-3108,-2381) -> Matrix(3,2,-2,-1) Matrix(841,644,952,729) -> Matrix(3,2,-14,-9) Matrix(139,106,476,363) -> Matrix(1,0,-2,1) Matrix(141,104,-644,-475) -> Matrix(1,-2,0,1) Matrix(337,248,-1064,-783) -> Matrix(1,0,-2,1) Matrix(1203,884,-3164,-2325) -> Matrix(3,-2,-4,3) Matrix(391,286,-1456,-1065) -> Matrix(5,-6,-4,5) Matrix(225,164,616,449) -> Matrix(1,-2,-2,5) Matrix(139,100,-196,-141) -> Matrix(1,-2,0,1) Matrix(559,394,952,671) -> Matrix(1,0,-2,1) Matrix(953,670,-1512,-1063) -> Matrix(1,-2,0,1) Matrix(141,98,364,253) -> Matrix(1,0,-2,1) Matrix(755,522,1092,755) -> Matrix(1,0,-2,1) Matrix(1345,928,3248,2241) -> Matrix(3,2,-14,-9) Matrix(729,502,896,617) -> Matrix(1,0,-4,1) Matrix(309,212,532,365) -> Matrix(1,0,-2,1) Matrix(393,256,-1288,-839) -> Matrix(1,0,0,1) Matrix(1093,708,1428,925) -> Matrix(1,-2,-2,5) Matrix(307,198,476,307) -> Matrix(1,-2,-4,9) Matrix(197,126,308,197) -> Matrix(1,4,-4,-15) Matrix(139,88,308,195) -> Matrix(1,0,-2,1) Matrix(923,582,-3332,-2101) -> Matrix(1,6,-2,-11) Matrix(169,106,448,281) -> Matrix(1,2,-2,-3) Matrix(167,104,448,279) -> Matrix(1,2,-4,-7) Matrix(1091,676,-1764,-1093) -> Matrix(1,2,-2,-3) Matrix(2715,1678,3668,2267) -> Matrix(1,4,-6,-23) Matrix(561,346,728,449) -> Matrix(3,4,-10,-13) Matrix(727,446,-1736,-1065) -> Matrix(1,2,-2,-3) Matrix(281,172,1008,617) -> Matrix(1,2,-4,-7) Matrix(1931,1178,-3444,-2101) -> Matrix(5,6,4,5) Matrix(2045,1246,3724,2269) -> Matrix(7,8,-22,-25) Matrix(783,476,1288,783) -> Matrix(17,18,-52,-55) Matrix(169,102,280,169) -> Matrix(3,2,-8,-5) Matrix(27,16,140,83) -> Matrix(3,2,-8,-5) Matrix(589,346,812,477) -> Matrix(3,2,-14,-9) Matrix(253,148,-812,-475) -> Matrix(1,0,2,1) Matrix(365,212,532,309) -> Matrix(1,0,-2,1) Matrix(755,438,-3332,-1933) -> Matrix(1,0,0,1) Matrix(421,244,1596,925) -> Matrix(3,2,-8,-5) Matrix(391,226,1064,615) -> Matrix(1,0,-2,1) Matrix(223,128,-392,-225) -> Matrix(1,0,2,1) Matrix(3079,1744,-10976,-6217) -> Matrix(1,-6,-2,13) Matrix(4705,2664,5936,3361) -> Matrix(1,4,-4,-15) Matrix(841,476,1288,729) -> Matrix(1,2,-4,-7) Matrix(1063,600,1288,727) -> Matrix(1,0,0,1) Matrix(727,410,-3080,-1737) -> Matrix(1,-2,0,1) Matrix(2045,1152,3332,1877) -> Matrix(1,2,-4,-7) Matrix(477,268,1148,645) -> Matrix(1,0,-6,1) Matrix(1149,644,-4844,-2715) -> Matrix(1,-4,0,1) Matrix(3641,2038,4704,2633) -> Matrix(1,2,-4,-7) Matrix(7279,4072,9408,5263) -> Matrix(3,-2,-10,7) Matrix(2801,1566,3808,2129) -> Matrix(1,0,-6,1) Matrix(29,16,-252,-139) -> Matrix(1,4,-2,-7) Matrix(223,122,-616,-337) -> Matrix(1,2,-2,-3) Matrix(85,46,364,197) -> Matrix(3,4,-10,-13) Matrix(391,210,728,391) -> Matrix(11,12,-34,-37) Matrix(449,240,840,449) -> Matrix(15,14,-44,-41) Matrix(365,194,476,253) -> Matrix(5,4,-14,-11) Matrix(83,38,-308,-141) -> Matrix(3,2,-2,-1) Matrix(195,88,308,139) -> Matrix(1,0,-2,1) Matrix(83,36,-196,-85) -> Matrix(1,0,2,1) Matrix(195,82,-868,-365) -> Matrix(1,0,0,1) Matrix(951,398,-3080,-1289) -> Matrix(3,2,-2,-1) Matrix(867,362,1540,643) -> Matrix(1,0,-2,1) Matrix(645,268,1148,477) -> Matrix(1,0,-6,1) Matrix(2379,986,5740,2379) -> Matrix(1,0,-6,1) Matrix(2241,928,3248,1345) -> Matrix(1,-2,-2,5) Matrix(281,116,952,393) -> Matrix(1,0,-4,1) Matrix(83,34,476,195) -> Matrix(1,0,-2,1) Matrix(755,308,1988,811) -> Matrix(1,-2,-2,5) Matrix(197,80,-756,-307) -> Matrix(1,2,-2,-3) Matrix(111,44,280,111) -> Matrix(1,2,-4,-7) Matrix(505,198,1288,505) -> Matrix(9,8,-26,-23) Matrix(195,76,644,251) -> Matrix(3,2,-8,-5) Matrix(253,98,364,141) -> Matrix(1,0,-2,1) Matrix(167,64,728,279) -> Matrix(3,2,-8,-5) Matrix(811,308,1988,755) -> Matrix(3,2,-14,-9) Matrix(281,106,448,169) -> Matrix(5,2,-18,-7) Matrix(279,104,448,167) -> Matrix(1,2,-4,-7) Matrix(449,166,-1512,-559) -> Matrix(1,0,2,1) Matrix(615,226,1064,391) -> Matrix(1,0,-2,1) Matrix(449,164,616,225) -> Matrix(3,2,-14,-9) Matrix(1147,414,1316,475) -> Matrix(1,0,-4,1) Matrix(1399,504,4816,1735) -> Matrix(5,2,-18,-7) Matrix(251,90,700,251) -> Matrix(1,0,0,1) Matrix(29,10,84,29) -> Matrix(1,0,-2,1) Matrix(953,304,1232,393) -> Matrix(1,2,-4,-7) Matrix(1903,590,3248,1007) -> Matrix(1,2,-2,-3) Matrix(3835,1186,6244,1931) -> Matrix(1,4,-4,-15) Matrix(111,34,728,223) -> Matrix(1,0,-2,1) Matrix(1903,580,3304,1007) -> Matrix(1,2,-2,-3) Matrix(251,76,644,195) -> Matrix(3,2,-8,-5) Matrix(503,150,560,167) -> Matrix(1,0,-2,1) Matrix(3473,1034,9408,2801) -> Matrix(1,0,6,1) Matrix(1735,516,4704,1399) -> Matrix(1,0,-6,1) Matrix(393,116,952,281) -> Matrix(1,0,-4,1) Matrix(363,106,476,139) -> Matrix(1,0,-2,1) Matrix(111,32,-392,-113) -> Matrix(1,2,-2,-3) Matrix(811,228,1092,307) -> Matrix(3,2,-20,-13) Matrix(18985,5328,32928,9241) -> Matrix(43,22,-88,-45) Matrix(25311,7102,43904,12319) -> Matrix(49,24,-96,-47) Matrix(2575,722,3192,895) -> Matrix(5,2,-28,-11) Matrix(617,172,1008,281) -> Matrix(1,2,-4,-7) Matrix(9073,2512,12544,3473) -> Matrix(27,14,-110,-57) Matrix(9071,2510,12544,3471) -> Matrix(25,12,-98,-47) Matrix(897,248,1624,449) -> Matrix(9,4,-34,-15) Matrix(1119,308,1624,447) -> Matrix(1,0,0,1) Matrix(2297,616,3136,841) -> Matrix(9,10,-46,-51) Matrix(2295,614,3136,839) -> Matrix(13,12,-64,-59) Matrix(83,22,-532,-141) -> Matrix(3,2,-2,-1) Matrix(55,14,-224,-57) -> Matrix(1,0,2,1) Matrix(2211,532,3836,923) -> Matrix(1,4,-2,-7) Matrix(419,100,-1764,-421) -> Matrix(1,-2,0,1) Matrix(197,46,364,85) -> Matrix(3,4,-10,-13) Matrix(307,70,364,83) -> Matrix(1,0,-2,1) Matrix(4957,1122,8540,1933) -> Matrix(1,0,0,1) Matrix(5963,1348,10276,2323) -> Matrix(1,0,-4,1) Matrix(897,196,3080,673) -> Matrix(1,2,-6,-11) Matrix(1597,348,1932,421) -> Matrix(3,4,-4,-5) Matrix(139,30,644,139) -> Matrix(7,8,-22,-25) Matrix(29,6,140,29) -> Matrix(3,2,-8,-5) Matrix(83,16,140,27) -> Matrix(3,2,-8,-5) Matrix(111,20,616,111) -> Matrix(7,4,-16,-9) Matrix(169,30,952,169) -> Matrix(5,2,-8,-3) Matrix(195,34,476,83) -> Matrix(1,0,-2,1) Matrix(617,98,1064,169) -> Matrix(1,0,-2,1) Matrix(27,4,-196,-29) -> Matrix(1,2,-2,-3) Matrix(197,26,644,85) -> Matrix(3,2,-8,-5) Matrix(85,8,308,29) -> Matrix(1,0,0,1) Matrix(139,-16,252,-29) -> Matrix(9,4,-34,-15) Matrix(29,-4,196,-27) -> Matrix(5,2,-18,-7) Matrix(141,-22,532,-83) -> Matrix(7,2,-18,-5) Matrix(475,-104,644,-141) -> Matrix(7,2,-32,-9) Matrix(223,-50,504,-113) -> Matrix(1,0,2,1) Matrix(533,-126,588,-139) -> Matrix(7,2,-32,-9) Matrix(2017,-478,3304,-783) -> Matrix(51,14,-164,-45) Matrix(1931,-462,3164,-757) -> Matrix(11,4,-36,-13) Matrix(643,-156,812,-197) -> Matrix(1,0,0,1) Matrix(421,-110,532,-139) -> Matrix(1,0,-2,1) Matrix(141,-38,308,-83) -> Matrix(7,2,-18,-5) Matrix(503,-138,616,-169) -> Matrix(1,0,-4,1) Matrix(1457,-404,2016,-559) -> Matrix(5,2,-18,-7) Matrix(113,-32,392,-111) -> Matrix(5,2,-18,-7) Matrix(6329,-1840,10976,-3191) -> Matrix(31,8,-66,-17) Matrix(559,-166,1512,-449) -> Matrix(1,0,2,1) Matrix(839,-256,1288,-393) -> Matrix(1,0,0,1) Matrix(475,-148,812,-253) -> Matrix(1,0,2,1) Matrix(727,-228,896,-281) -> Matrix(1,0,-2,1) Matrix(783,-248,1064,-337) -> Matrix(1,0,-2,1) Matrix(337,-122,616,-223) -> Matrix(5,2,-18,-7) Matrix(699,-266,812,-309) -> Matrix(1,0,-2,1) Matrix(309,-118,364,-139) -> Matrix(5,2,-18,-7) Matrix(223,-90,280,-113) -> Matrix(7,2,-32,-9) Matrix(85,-36,196,-83) -> Matrix(1,0,2,1) Matrix(979,-430,1596,-701) -> Matrix(1,2,-4,-7) Matrix(2323,-1024,4004,-1765) -> Matrix(1,0,-2,1) Matrix(307,-144,420,-197) -> Matrix(13,4,-62,-19) Matrix(1399,-768,1736,-953) -> Matrix(1,0,-2,1) Matrix(391,-218,504,-281) -> Matrix(9,2,-32,-7) Matrix(2101,-1178,3444,-1931) -> Matrix(29,6,-92,-19) Matrix(589,-332,644,-363) -> Matrix(1,0,0,1) Matrix(225,-128,392,-223) -> Matrix(1,0,2,1) Matrix(2323,-1360,3780,-2213) -> Matrix(1,0,-2,1) Matrix(1119,-682,1288,-785) -> Matrix(19,6,-92,-29) Matrix(1093,-676,1764,-1091) -> Matrix(5,2,-18,-7) Matrix(1345,-834,1624,-1007) -> Matrix(13,4,-36,-11) Matrix(1317,-830,1820,-1147) -> Matrix(15,4,-64,-17) Matrix(419,-272,476,-309) -> Matrix(1,0,0,1) Matrix(141,-100,196,-139) -> Matrix(7,2,-32,-9) Matrix(727,-534,840,-617) -> Matrix(11,2,-50,-9) Matrix(3109,-2382,3836,-2939) -> Matrix(5,2,-28,-11) Matrix(1429,-1156,1764,-1427) -> Matrix(1,0,2,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 52 Degree of the the map X: 52 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. Imminent integer overflow caused the modular group computation to abort.