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 -11/14 -5/7 -29/42 -9/14 -4/7 -1/2 -13/28 -3/7 -47/112 -5/12 -23/56 -11/28 -3/8 -5/14 -13/42 -17/56 -3/10 -25/84 -7/24 -2/7 -55/196 -5/18 -31/112 -7/26 -15/56 -1/4 -5/22 -19/84 -3/14 -5/24 -3/16 -5/28 -1/6 -3/20 -1/7 -1/8 0/1 1/7 3/20 2/13 1/6 2/11 3/16 1/5 3/14 2/9 5/22 3/13 1/4 7/26 3/11 5/18 2/7 3/10 13/42 1/3 5/14 2/5 5/12 3/7 1/2 5/9 4/7 9/14 2/3 29/42 5/7 11/14 6/7 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/2 -6/7 1/2 -17/20 3/5 -11/13 9/14 -16/19 3/4 -5/6 2/3 1/1 -9/11 3/2 -13/16 0/1 -4/5 1/0 -11/14 1/2 -18/23 5/8 -25/32 2/3 -7/9 1/2 -17/22 2/3 1/1 -10/13 7/8 -3/4 1/1 -11/15 5/6 -19/26 1/1 6/5 -8/11 1/0 -21/29 3/2 -34/47 7/4 -13/18 1/1 2/1 -18/25 1/0 -5/7 1/0 -22/31 1/0 -39/55 -1/2 -17/24 0/1 -12/17 1/0 -19/27 1/2 -7/10 0/1 1/1 -16/23 5/4 -25/36 1/1 -9/13 5/2 -29/42 1/0 -20/29 1/0 -11/16 0/1 -2/3 1/0 -9/14 1/0 -16/25 1/0 -7/11 -3/2 -19/30 -1/1 -2/3 -12/19 1/0 -29/46 -1/1 -2/3 -17/27 -1/2 -5/8 0/1 -13/21 1/0 -34/55 1/0 -21/34 -2/1 -1/1 -8/13 -3/4 -19/31 -1/2 -11/18 -1/3 0/1 -3/5 1/2 -16/27 1/0 -13/22 -1/1 0/1 -10/17 1/4 -17/29 1/2 -41/70 1/2 -24/41 7/12 -7/12 1/1 -18/31 1/0 -29/50 0/1 1/1 -11/19 1/2 -15/26 1/1 2/1 -4/7 1/0 -17/30 -1/1 0/1 -47/83 -1/2 -30/53 1/0 -13/23 -1/2 -9/16 0/1 -14/25 1/0 -19/34 -1/1 0/1 -5/9 -1/2 -16/29 1/0 -11/20 -1/1 -6/11 -1/4 -13/24 0/1 -7/13 -1/10 -1/2 0/1 1/1 -7/15 -1/10 -13/28 0/1 -6/13 1/12 -5/11 1/6 -14/31 1/4 -9/20 1/3 -13/29 1/2 -4/9 1/4 -11/25 1/2 -7/16 0/1 -10/23 1/4 -3/7 1/2 -14/33 3/4 -25/59 1/2 -11/26 2/3 1/1 -8/19 1/0 -21/50 0/1 1/1 -34/81 1/0 -47/112 0/1 -13/31 1/2 -18/43 3/8 -5/12 1/1 -17/41 7/2 -29/70 1/0 -12/29 1/0 -7/17 -1/2 -23/56 0/1 -16/39 1/8 -9/22 0/1 1/3 -11/27 1/2 -13/32 0/1 -2/5 1/0 -11/28 0/1 -9/23 1/10 -7/18 0/1 1/5 -12/31 1/4 -17/44 1/5 -5/13 3/10 -13/34 1/3 2/5 -21/55 1/2 -29/76 3/7 -8/21 1/2 -11/29 1/2 -3/8 0/1 -10/27 1/4 -7/19 1/2 -11/30 2/7 1/3 -4/11 3/8 -5/14 1/2 -6/17 5/8 -7/20 1/1 -8/23 1/0 -1/3 1/2 -5/16 0/1 -9/29 1/2 -13/42 1/2 -4/13 5/8 -11/36 1/1 -18/59 3/4 -7/23 5/6 -17/56 1/1 -10/33 5/4 -3/10 0/1 1/1 -14/47 3/4 -25/84 1/1 -11/37 3/2 -8/27 1/0 -5/17 1/2 -12/41 1/8 -7/24 0/1 -2/7 1/2 -9/32 2/3 -16/57 3/4 -55/196 1/1 -39/139 1/2 -23/82 2/3 1/1 -7/25 1/2 -5/18 2/3 1/1 -18/65 5/8 -31/112 2/3 -13/47 7/10 -8/29 3/4 -11/40 4/5 -3/11 1/2 -7/26 6/7 1/1 -11/41 17/18 -15/56 1/1 -4/15 5/4 -1/4 1/1 -3/13 7/6 -5/22 1/1 2/1 -12/53 1/0 -19/84 1/1 -7/31 3/2 -2/9 1/0 -3/14 1/0 -4/19 1/0 -9/43 -1/6 -5/24 0/1 -6/29 1/0 -1/5 1/2 -3/16 0/1 -5/27 1/2 -2/11 3/4 -5/28 1/1 -3/17 7/6 -1/6 1/1 2/1 -3/19 3/2 -5/32 2/1 -2/13 9/4 -3/20 3/1 -4/27 1/0 -1/7 1/0 -1/8 0/1 0/1 1/0 1/7 1/0 3/20 -3/1 2/13 -9/4 3/19 -3/2 1/6 -2/1 -1/1 2/11 -3/4 3/16 0/1 1/5 -1/2 3/14 1/0 5/23 -5/2 7/32 -2/1 2/9 1/0 5/22 -2/1 -1/1 3/13 -7/6 1/4 -1/1 4/15 -5/4 7/26 -1/1 -6/7 3/11 -1/2 8/29 -3/4 13/47 -7/10 5/18 -1/1 -2/3 7/25 -1/2 2/7 -1/2 9/31 -1/2 16/55 -1/4 7/24 0/1 5/17 -1/2 8/27 1/0 3/10 -1/1 0/1 7/23 -5/6 11/36 -1/1 4/13 -5/8 13/42 -1/2 9/29 -1/2 5/16 0/1 1/3 -1/2 5/14 -1/2 9/25 -1/2 4/11 -3/8 11/30 -1/3 -2/7 7/19 -1/2 17/46 -1/3 -2/7 10/27 -1/4 3/8 0/1 8/21 -1/2 21/55 -1/2 13/34 -2/5 -1/3 5/13 -3/10 12/31 -1/4 7/18 -1/5 0/1 2/5 1/0 11/27 -1/2 9/22 -1/3 0/1 7/17 1/2 12/29 1/0 29/70 1/0 17/41 -7/2 5/12 -1/1 13/31 -1/2 21/50 -1/1 0/1 8/19 1/0 11/26 -1/1 -2/3 3/7 -1/2 13/30 -1/3 0/1 36/83 -1/4 23/53 -1/2 10/23 -1/4 7/16 0/1 11/25 -1/2 15/34 -1/3 0/1 4/9 -1/4 13/29 -1/2 9/20 -1/3 5/11 -1/6 11/24 0/1 6/13 -1/12 1/2 -1/1 0/1 8/15 -1/12 15/28 0/1 7/13 1/10 6/11 1/4 17/31 1/2 11/20 1/1 16/29 1/0 5/9 1/2 14/25 1/0 9/16 0/1 13/23 1/2 4/7 1/0 19/33 -3/2 34/59 1/0 15/26 -2/1 -1/1 11/19 -1/2 29/50 -1/1 0/1 47/81 -1/2 65/112 0/1 18/31 1/0 25/43 3/2 7/12 -1/1 24/41 -7/12 41/70 -1/2 17/29 -1/2 10/17 -1/4 33/56 0/1 23/39 1/6 13/22 0/1 1/1 16/27 1/0 19/32 0/1 3/5 -1/2 17/28 0/1 14/23 1/8 11/18 0/1 1/3 19/31 1/2 27/44 1/3 8/13 3/4 21/34 1/1 2/1 34/55 1/0 47/76 3/1 13/21 1/0 18/29 1/0 5/8 0/1 17/27 1/2 12/19 1/0 19/30 2/3 1/1 7/11 3/2 9/14 1/0 11/17 -5/2 13/20 -1/1 15/23 -1/2 2/3 1/0 11/16 0/1 20/29 1/0 29/42 1/0 9/13 -5/2 25/36 -1/1 41/59 -3/2 16/23 -5/4 39/56 -1/1 23/33 -5/6 7/10 -1/1 0/1 33/47 -3/2 59/84 -1/1 26/37 -3/4 19/27 -1/2 12/17 1/0 29/41 1/6 17/24 0/1 5/7 1/0 23/32 -2/1 41/57 -3/2 141/196 -1/1 100/139 1/0 59/82 -2/1 -1/1 18/25 1/0 13/18 -2/1 -1/1 47/65 -5/2 81/112 -2/1 34/47 -7/4 21/29 -3/2 29/40 -4/3 8/11 1/0 19/26 -6/5 -1/1 30/41 -17/16 41/56 -1/1 11/15 -5/6 3/4 -1/1 10/13 -7/8 17/22 -1/1 -2/3 41/53 -1/2 65/84 -1/1 24/31 -3/4 7/9 -1/2 11/14 -1/2 15/19 -1/2 34/43 -1/8 19/24 0/1 23/29 -1/2 4/5 1/0 13/16 0/1 22/27 1/0 9/11 -3/2 23/28 -1/1 14/17 -7/8 5/6 -1/1 -2/3 16/19 -3/4 27/32 -2/3 11/13 -9/14 17/20 -3/5 23/27 -1/2 6/7 -1/2 7/8 0/1 1/1 -1/2 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(85,74,-224,-195) (-1/1,-6/7) -> (-8/21,-11/29) Hyperbolic Matrix(363,310,-952,-813) (-6/7,-17/20) -> (-29/76,-8/21) Hyperbolic Matrix(505,428,728,617) (-17/20,-11/13) -> (9/13,25/36) Hyperbolic Matrix(223,188,-1064,-897) (-11/13,-16/19) -> (-4/19,-9/43) Hyperbolic Matrix(447,376,1064,895) (-16/19,-5/6) -> (21/50,8/19) Hyperbolic Matrix(29,24,-168,-139) (-5/6,-9/11) -> (-3/17,-1/6) Hyperbolic Matrix(169,138,-616,-503) (-9/11,-13/16) -> (-11/40,-3/11) Hyperbolic Matrix(195,158,448,363) (-13/16,-4/5) -> (10/23,7/16) Hyperbolic Matrix(307,242,-392,-309) (-4/5,-11/14) -> (-11/14,-18/23) Parabolic Matrix(363,284,-896,-701) (-18/23,-25/32) -> (-13/32,-2/5) Hyperbolic Matrix(141,110,-896,-699) (-25/32,-7/9) -> (-3/19,-5/32) 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(29,22,112,85) (-10/13,-3/4) -> (1/4,4/15) Hyperbolic Matrix(27,20,112,83) (-3/4,-11/15) -> (3/13,1/4) 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(113,82,-616,-447) (-8/11,-21/29) -> (-5/27,-2/11) Hyperbolic Matrix(727,526,1624,1175) (-21/29,-34/47) -> (4/9,13/29) Hyperbolic Matrix(559,404,-2016,-1457) (-34/47,-13/18) -> (-5/18,-18/65) Hyperbolic Matrix(391,282,1008,727) (-13/18,-18/25) -> (12/31,7/18) Hyperbolic Matrix(279,200,-392,-281) (-18/25,-5/7) -> (-5/7,-22/31) Parabolic Matrix(3107,2204,-5488,-3893) (-22/31,-39/55) -> (-47/83,-30/53) Hyperbolic Matrix(1597,1132,2016,1429) (-39/55,-17/24) -> (19/24,23/29) Hyperbolic Matrix(365,258,-672,-475) (-17/24,-12/17) -> (-6/11,-13/24) Hyperbolic 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(169,118,-560,-391) (-7/10,-16/23) -> (-10/33,-3/10) Hyperbolic Matrix(449,312,-1288,-895) (-16/23,-25/36) -> (-7/20,-8/23) Hyperbolic Matrix(617,428,728,505) (-25/36,-9/13) -> (11/13,17/20) Hyperbolic Matrix(1091,754,2632,1819) (-9/13,-29/42) -> (29/70,17/41) 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(251,172,448,307) (-11/16,-2/3) -> (14/25,9/16) Hyperbolic Matrix(251,162,-392,-253) (-2/3,-9/14) -> (-9/14,-16/25) Parabolic Matrix(279,178,-616,-393) (-16/25,-7/11) -> (-5/11,-14/31) Hyperbolic Matrix(167,106,616,391) (-7/11,-19/30) -> (7/26,3/11) Hyperbolic Matrix(449,284,1064,673) (-19/30,-12/19) -> (8/19,11/26) Hyperbolic Matrix(701,442,-2352,-1483) (-12/19,-29/46) -> (-3/10,-14/47) Hyperbolic Matrix(197,124,224,141) (-17/27,-5/8) -> (7/8,1/1) Hyperbolic Matrix(29,18,-224,-139) (-5/8,-13/21) -> (-1/7,-1/8) Hyperbolic Matrix(139,86,-952,-589) (-13/21,-34/55) -> (-4/27,-1/7) Hyperbolic Matrix(1259,778,2128,1315) (-34/55,-21/34) -> (13/22,16/27) 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(197,120,-504,-307) (-11/18,-3/5) -> (-9/23,-7/18) Hyperbolic Matrix(57,34,-280,-167) (-3/5,-16/27) -> (-6/29,-1/5) Hyperbolic Matrix(1315,778,2128,1259) (-16/27,-13/22) -> (21/34,34/55) Hyperbolic Matrix(505,298,-1232,-727) (-13/22,-10/17) -> (-16/39,-9/22) Hyperbolic Matrix(671,394,952,559) (-10/17,-17/29) -> (19/27,12/17) Hyperbolic Matrix(1007,590,3248,1903) (-17/29,-41/70) -> (13/42,9/29) Hyperbolic Matrix(813,476,2632,1541) (-41/70,-24/41) -> (4/13,13/42) Hyperbolic Matrix(1203,704,1960,1147) (-24/41,-7/12) -> (27/44,8/13) Hyperbolic Matrix(671,390,-1736,-1009) (-7/12,-18/31) -> (-12/31,-17/44) Hyperbolic Matrix(2351,1364,-5600,-3249) (-18/31,-29/50) -> (-21/50,-34/81) Hyperbolic Matrix(169,98,1064,617) (-29/50,-11/19) -> (3/19,1/6) 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(841,476,1288,729) (-30/53,-13/23) -> (15/23,2/3) Hyperbolic Matrix(85,48,448,253) (-13/23,-9/16) -> (3/16,1/5) Hyperbolic Matrix(307,172,448,251) (-9/16,-14/25) -> (2/3,11/16) Hyperbolic Matrix(533,298,-2352,-1315) (-14/25,-19/34) -> (-5/22,-12/53) Hyperbolic Matrix(449,248,1624,897) (-5/9,-16/29) -> (8/29,13/47) Hyperbolic Matrix(167,92,-1120,-617) (-16/29,-11/20) -> (-3/20,-4/27) Hyperbolic Matrix(197,108,-560,-307) (-11/20,-6/11) -> (-6/17,-7/20) Hyperbolic Matrix(281,152,-1344,-727) (-13/24,-7/13) -> (-9/43,-5/24) Hyperbolic Matrix(27,14,-56,-29) (-7/13,-1/2) -> (-1/2,-7/15) Parabolic Matrix(421,196,784,365) (-7/15,-13/28) -> (15/28,7/13) Hyperbolic Matrix(419,194,784,363) (-13/28,-6/13) -> (8/15,15/28) Hyperbolic Matrix(197,90,-672,-307) (-6/13,-5/11) -> (-5/17,-12/41) Hyperbolic Matrix(701,316,-2296,-1035) (-14/31,-9/20) -> (-11/36,-18/59) Hyperbolic Matrix(1261,566,-3304,-1483) (-9/20,-13/29) -> (-21/55,-29/76) Hyperbolic Matrix(1175,526,1624,727) (-13/29,-4/9) -> (34/47,21/29) Hyperbolic Matrix(113,50,-504,-223) (-4/9,-11/25) -> (-7/31,-2/9) Hyperbolic Matrix(141,62,448,197) (-11/25,-7/16) -> (5/16,1/3) Hyperbolic Matrix(363,158,448,195) (-7/16,-10/23) -> (4/5,13/16) Hyperbolic Matrix(167,72,-392,-169) (-10/23,-3/7) -> (-3/7,-14/33) Parabolic Matrix(2297,974,3304,1401) (-14/33,-25/59) -> (41/59,16/23) Hyperbolic Matrix(1539,652,-5488,-2325) (-25/59,-11/26) -> (-23/82,-7/25) Hyperbolic Matrix(673,284,1064,449) (-11/26,-8/19) -> (12/19,19/30) Hyperbolic Matrix(895,376,1064,447) (-8/19,-21/50) -> (5/6,16/19) Hyperbolic Matrix(7281,3056,12544,5265) (-34/81,-47/112) -> (65/112,18/31) Hyperbolic Matrix(7279,3054,12544,5263) (-47/112,-13/31) -> (47/81,65/112) Hyperbolic Matrix(589,246,1008,421) (-18/43,-5/12) -> (7/12,24/41) Hyperbolic Matrix(587,244,1008,419) (-5/12,-17/41) -> (25/43,7/12) Hyperbolic Matrix(1819,754,2632,1091) (-17/41,-29/70) -> (29/42,9/13) 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(1849,760,3136,1289) (-7/17,-23/56) -> (33/56,23/39) Hyperbolic Matrix(1847,758,3136,1287) (-23/56,-16/39) -> (10/17,33/56) Hyperbolic Matrix(813,332,2128,869) (-9/22,-11/27) -> (21/55,13/34) Hyperbolic Matrix(1933,786,2688,1093) (-11/27,-13/32) -> (23/32,41/57) Hyperbolic Matrix(477,188,784,309) (-2/5,-11/28) -> (17/28,14/23) Hyperbolic Matrix(475,186,784,307) (-11/28,-9/23) -> (3/5,17/28) Hyperbolic Matrix(727,282,1008,391) (-7/18,-12/31) -> (18/25,13/18) Hyperbolic Matrix(813,314,1960,757) (-17/44,-5/13) -> (17/41,5/12) Hyperbolic Matrix(167,64,728,279) (-5/13,-13/34) -> (5/22,3/13) Hyperbolic Matrix(869,332,2128,813) (-13/34,-21/55) -> (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(139,50,-392,-141) (-4/11,-5/14) -> (-5/14,-6/17) Parabolic Matrix(559,194,1288,447) (-8/23,-1/3) -> (23/53,10/23) Hyperbolic Matrix(197,62,448,141) (-1/3,-5/16) -> (7/16,11/25) Hyperbolic Matrix(1177,366,1624,505) (-5/16,-9/29) -> (21/29,29/40) Hyperbolic Matrix(1903,590,3248,1007) (-9/29,-13/42) -> (41/70,17/29) Hyperbolic Matrix(1541,476,2632,813) (-13/42,-4/13) -> (24/41,41/70) 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(2185,664,3136,953) (-7/23,-17/56) -> (39/56,23/33) Hyperbolic Matrix(2183,662,3136,951) (-17/56,-10/33) -> (16/23,39/56) Hyperbolic Matrix(4957,1476,7056,2101) (-14/47,-25/84) -> (59/84,26/37) Hyperbolic Matrix(4955,1474,7056,2099) (-25/84,-11/37) -> (33/47,59/84) Hyperbolic Matrix(393,116,952,281) (-8/27,-5/17) -> (7/17,12/29) Hyperbolic Matrix(253,74,-1624,-475) (-12/41,-7/24) -> (-5/32,-2/13) Hyperbolic Matrix(111,32,-392,-113) (-7/24,-2/7) -> (-2/7,-9/32) Parabolic Matrix(1595,448,2688,755) (-9/32,-16/57) -> (16/27,19/32) Hyperbolic Matrix(27637,7756,38416,10781) (-16/57,-55/196) -> (141/196,100/139) Hyperbolic Matrix(27635,7754,38416,10779) (-55/196,-39/139) -> (41/57,141/196) 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(391,106,616,167) (-3/11,-7/26) -> (19/30,7/11) 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(85,22,112,29) (-4/15,-1/4) -> (3/4,10/13) Hyperbolic Matrix(83,20,112,27) (-1/4,-3/13) -> (11/15,3/4) Hyperbolic Matrix(279,64,728,167) (-3/13,-5/22) -> (13/34,5/13) Hyperbolic Matrix(5461,1236,7056,1597) (-12/53,-19/84) -> (65/84,24/31) Hyperbolic Matrix(5459,1234,7056,1595) (-19/84,-7/31) -> (41/53,65/84) Hyperbolic Matrix(83,18,-392,-85) (-2/9,-3/14) -> (-3/14,-4/19) Parabolic Matrix(587,122,2016,419) (-5/24,-6/29) -> (16/55,7/24) Hyperbolic Matrix(253,48,448,85) (-1/5,-3/16) -> (9/16,13/23) Hyperbolic Matrix(279,52,896,167) (-3/16,-5/27) -> (9/29,5/16) Hyperbolic Matrix(645,116,784,141) (-2/11,-5/28) -> (23/28,14/17) Hyperbolic Matrix(643,114,784,139) (-5/28,-3/17) -> (9/11,23/28) Hyperbolic Matrix(617,98,1064,169) (-1/6,-3/19) -> (11/19,29/50) Hyperbolic Matrix(223,34,728,111) (-2/13,-3/20) -> (11/36,4/13) Hyperbolic Matrix(83,10,224,27) (-1/8,0/1) -> (10/27,3/8) Hyperbolic Matrix(139,-18,224,-29) (0/1,1/7) -> (13/21,18/29) Hyperbolic Matrix(589,-86,952,-139) (1/7,3/20) -> (47/76,13/21) Hyperbolic Matrix(841,-132,1064,-167) (2/13,3/19) -> (15/19,34/43) Hyperbolic Matrix(139,-24,168,-29) (1/6,2/11) -> (14/17,5/6) Hyperbolic Matrix(447,-82,616,-113) (2/11,3/16) -> (29/40,8/11) Hyperbolic Matrix(85,-18,392,-83) (1/5,3/14) -> (3/14,5/23) Parabolic Matrix(533,-116,896,-195) (5/23,7/32) -> (19/32,3/5) Hyperbolic Matrix(755,-166,896,-197) (7/32,2/9) -> (16/19,27/32) Hyperbolic Matrix(223,-50,504,-113) (2/9,5/22) -> (15/34,4/9) Hyperbolic Matrix(1065,-286,1456,-391) (4/15,7/26) -> (19/26,30/41) 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(2381,-692,5488,-1595) (9/31,16/55) -> (36/83,23/53) Hyperbolic Matrix(307,-90,672,-197) (7/24,5/17) -> (5/11,11/24) Hyperbolic Matrix(559,-166,1512,-449) (8/27,3/10) -> (17/46,10/27) Hyperbolic Matrix(391,-118,560,-169) (3/10,7/23) -> (23/33,7/10) Hyperbolic Matrix(839,-256,1288,-393) (7/23,11/36) -> (13/20,15/23) Hyperbolic Matrix(141,-50,392,-139) (1/3,5/14) -> (5/14,9/25) Parabolic Matrix(337,-122,616,-223) (9/25,4/11) -> (6/11,17/31) Hyperbolic Matrix(1651,-610,2352,-869) (7/19,17/46) -> (7/10,33/47) Hyperbolic Matrix(195,-74,224,-85) (3/8,8/21) -> (6/7,7/8) Hyperbolic Matrix(813,-310,952,-363) (8/21,21/55) -> (23/27,6/7) Hyperbolic Matrix(1009,-390,1736,-671) (5/13,12/31) -> (18/31,25/43) Hyperbolic Matrix(307,-120,504,-197) (7/18,2/5) -> (14/23,11/18) Hyperbolic Matrix(223,-90,280,-113) (2/5,11/27) -> (23/29,4/5) Hyperbolic Matrix(727,-298,1232,-505) (9/22,7/17) -> (23/39,13/22) Hyperbolic Matrix(1065,-446,1736,-727) (5/12,13/31) -> (19/31,27/44) Hyperbolic Matrix(3249,-1364,5600,-2351) (13/31,21/50) -> (29/50,47/81) Hyperbolic Matrix(169,-72,392,-167) (11/26,3/7) -> (3/7,13/30) Parabolic Matrix(7897,-3424,10976,-4759) (13/30,36/83) -> (100/139,59/82) Hyperbolic Matrix(1819,-802,2352,-1037) (11/25,15/34) -> (17/22,41/53) Hyperbolic Matrix(953,-428,1120,-503) (13/29,9/20) -> (17/20,23/27) Hyperbolic Matrix(363,-164,560,-253) (9/20,5/11) -> (11/17,13/20) Hyperbolic Matrix(1063,-488,1344,-617) (11/24,6/13) -> (34/43,19/24) Hyperbolic Matrix(29,-14,56,-27) (6/13,1/2) -> (1/2,8/15) Parabolic Matrix(475,-258,672,-365) (7/13,6/11) -> (12/17,29/41) Hyperbolic Matrix(1595,-876,2296,-1261) (17/31,11/20) -> (25/36,41/59) Hyperbolic Matrix(2043,-1126,3304,-1821) (11/20,16/29) -> (34/55,47/76) Hyperbolic Matrix(391,-218,504,-281) (5/9,14/25) -> (24/31,7/9) Hyperbolic Matrix(225,-128,392,-223) (13/23,4/7) -> (4/7,19/33) Parabolic Matrix(3949,-2276,5488,-3163) (34/59,15/26) -> (59/82,18/25) Hyperbolic Matrix(1063,-670,1512,-953) (17/27,12/19) -> (26/37,19/27) Hyperbolic Matrix(253,-162,392,-251) (7/11,9/14) -> (9/14,11/17) Parabolic Matrix(1371,-970,1624,-1149) (29/41,17/24) -> (27/32,11/13) Hyperbolic Matrix(281,-200,392,-279) (17/24,5/7) -> (5/7,23/32) Parabolic Matrix(309,-242,392,-307) (7/9,11/14) -> (11/14,15/19) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(85,74,-224,-195) -> Matrix(1,0,0,1) Matrix(363,310,-952,-813) -> Matrix(11,-6,24,-13) Matrix(505,428,728,617) -> Matrix(13,-8,-8,5) Matrix(223,188,-1064,-897) -> Matrix(3,-2,-4,3) Matrix(447,376,1064,895) -> Matrix(3,-2,-4,3) Matrix(29,24,-168,-139) -> Matrix(5,-4,4,-3) Matrix(169,138,-616,-503) -> Matrix(3,-4,4,-5) Matrix(195,158,448,363) -> Matrix(1,0,-4,1) Matrix(307,242,-392,-309) -> Matrix(5,-2,8,-3) Matrix(363,284,-896,-701) -> Matrix(3,-2,8,-5) Matrix(141,110,-896,-699) -> Matrix(5,-4,4,-3) Matrix(281,218,-504,-391) -> Matrix(3,-2,-4,3) Matrix(449,346,728,561) -> Matrix(5,-4,4,-3) Matrix(29,22,112,85) -> Matrix(3,-2,-4,3) Matrix(27,20,112,83) -> Matrix(1,-2,0,1) Matrix(391,286,-1456,-1065) -> Matrix(11,-12,12,-13) Matrix(225,164,616,449) -> Matrix(3,-4,-8,11) Matrix(113,82,-616,-447) -> Matrix(3,-4,4,-5) Matrix(727,526,1624,1175) -> Matrix(1,-2,0,1) Matrix(559,404,-2016,-1457) -> Matrix(3,-4,4,-5) Matrix(391,282,1008,727) -> Matrix(1,-2,-4,9) Matrix(279,200,-392,-281) -> Matrix(1,-2,0,1) Matrix(3107,2204,-5488,-3893) -> Matrix(1,0,0,1) Matrix(1597,1132,2016,1429) -> Matrix(1,0,0,1) Matrix(365,258,-672,-475) -> Matrix(1,0,-4,1) Matrix(559,394,952,671) -> Matrix(1,0,-4,1) Matrix(953,670,-1512,-1063) -> Matrix(3,-2,-4,3) Matrix(169,118,-560,-391) -> Matrix(1,0,0,1) Matrix(449,312,-1288,-895) -> Matrix(3,-4,4,-5) Matrix(617,428,728,505) -> Matrix(5,-8,-8,13) Matrix(1091,754,2632,1819) -> Matrix(1,-6,0,1) Matrix(1345,928,3248,2241) -> Matrix(1,4,0,1) Matrix(729,502,896,617) -> Matrix(1,0,0,1) Matrix(251,172,448,307) -> Matrix(1,0,0,1) Matrix(251,162,-392,-253) -> Matrix(1,-4,0,1) Matrix(279,178,-616,-393) -> Matrix(1,2,4,9) Matrix(167,106,616,391) -> Matrix(3,4,-4,-5) Matrix(449,284,1064,673) -> Matrix(1,0,0,1) Matrix(701,442,-2352,-1483) -> Matrix(3,2,4,3) Matrix(197,124,224,141) -> Matrix(1,0,0,1) Matrix(29,18,-224,-139) -> Matrix(1,0,0,1) Matrix(139,86,-952,-589) -> Matrix(1,6,0,1) Matrix(1259,778,2128,1315) -> Matrix(1,2,0,1) Matrix(561,346,728,449) -> Matrix(3,4,-4,-5) Matrix(727,446,-1736,-1065) -> Matrix(1,0,4,1) Matrix(281,172,1008,617) -> Matrix(5,2,-8,-3) Matrix(197,120,-504,-307) -> Matrix(1,0,8,1) Matrix(57,34,-280,-167) -> Matrix(1,0,0,1) Matrix(1315,778,2128,1259) -> Matrix(1,2,0,1) Matrix(505,298,-1232,-727) -> Matrix(1,0,4,1) Matrix(671,394,952,559) -> Matrix(1,0,-4,1) Matrix(1007,590,3248,1903) -> Matrix(9,-4,-20,9) Matrix(813,476,2632,1541) -> Matrix(11,-6,-20,11) Matrix(1203,704,1960,1147) -> Matrix(3,-2,8,-5) Matrix(671,390,-1736,-1009) -> Matrix(1,0,4,1) Matrix(2351,1364,-5600,-3249) -> Matrix(1,0,0,1) Matrix(169,98,1064,617) -> Matrix(1,-2,0,1) Matrix(391,226,1064,615) -> Matrix(1,0,-4,1) Matrix(223,128,-392,-225) -> Matrix(1,-2,0,1) Matrix(3079,1744,-10976,-6217) -> Matrix(3,2,4,3) Matrix(841,476,1288,729) -> Matrix(1,0,0,1) Matrix(85,48,448,253) -> Matrix(1,0,0,1) Matrix(307,172,448,251) -> Matrix(1,0,0,1) Matrix(533,298,-2352,-1315) -> Matrix(1,2,0,1) Matrix(449,248,1624,897) -> Matrix(3,-2,-4,3) Matrix(167,92,-1120,-617) -> Matrix(1,4,0,1) Matrix(197,108,-560,-307) -> Matrix(3,2,4,3) Matrix(281,152,-1344,-727) -> Matrix(1,0,4,1) Matrix(27,14,-56,-29) -> Matrix(1,0,0,1) Matrix(421,196,784,365) -> Matrix(1,0,20,1) Matrix(419,194,784,363) -> Matrix(1,0,-24,1) Matrix(197,90,-672,-307) -> Matrix(1,0,-4,1) Matrix(701,316,-2296,-1035) -> Matrix(5,-2,8,-3) Matrix(1261,566,-3304,-1483) -> Matrix(3,-2,8,-5) Matrix(1175,526,1624,727) -> Matrix(1,-2,0,1) Matrix(113,50,-504,-223) -> Matrix(7,-2,4,-1) Matrix(141,62,448,197) -> Matrix(1,0,-4,1) Matrix(363,158,448,195) -> Matrix(1,0,-4,1) Matrix(167,72,-392,-169) -> Matrix(5,-2,8,-3) Matrix(2297,974,3304,1401) -> Matrix(1,-2,0,1) Matrix(1539,652,-5488,-2325) -> Matrix(1,0,0,1) Matrix(673,284,1064,449) -> Matrix(1,0,0,1) Matrix(895,376,1064,447) -> Matrix(3,-2,-4,3) Matrix(7281,3056,12544,5265) -> Matrix(1,0,0,1) Matrix(7279,3054,12544,5263) -> Matrix(1,0,-4,1) Matrix(589,246,1008,421) -> Matrix(3,-2,-4,3) Matrix(587,244,1008,419) -> Matrix(1,-2,0,1) Matrix(1819,754,2632,1091) -> Matrix(1,-6,0,1) Matrix(2241,928,3248,1345) -> Matrix(1,4,0,1) Matrix(281,116,952,393) -> Matrix(1,0,0,1) Matrix(1849,760,3136,1289) -> Matrix(1,0,8,1) Matrix(1847,758,3136,1287) -> Matrix(1,0,-12,1) Matrix(813,332,2128,869) -> Matrix(5,-2,-12,5) Matrix(1933,786,2688,1093) -> Matrix(1,-2,0,1) Matrix(477,188,784,309) -> Matrix(1,0,8,1) Matrix(475,186,784,307) -> Matrix(1,0,-12,1) Matrix(727,282,1008,391) -> Matrix(9,-2,-4,1) Matrix(813,314,1960,757) -> Matrix(9,-2,-4,1) Matrix(167,64,728,279) -> Matrix(11,-4,-8,3) Matrix(869,332,2128,813) -> Matrix(5,-2,-12,5) Matrix(281,106,448,169) -> Matrix(1,0,0,1) Matrix(279,104,448,167) -> Matrix(1,0,-4,1) Matrix(449,166,-1512,-559) -> Matrix(7,-2,4,-1) Matrix(615,226,1064,391) -> Matrix(1,0,-4,1) Matrix(449,164,616,225) -> Matrix(11,-4,-8,3) Matrix(139,50,-392,-141) -> Matrix(9,-4,16,-7) Matrix(559,194,1288,447) -> Matrix(1,0,-4,1) Matrix(197,62,448,141) -> Matrix(1,0,-4,1) Matrix(1177,366,1624,505) -> Matrix(11,-4,-8,3) Matrix(1903,590,3248,1007) -> Matrix(9,-4,-20,9) Matrix(1541,476,2632,813) -> Matrix(11,-6,-20,11) Matrix(111,34,728,223) -> Matrix(11,-8,-4,3) Matrix(1903,580,3304,1007) -> Matrix(3,-2,-4,3) Matrix(2185,664,3136,953) -> Matrix(11,-10,-12,11) Matrix(2183,662,3136,951) -> Matrix(9,-10,-8,9) Matrix(4957,1476,7056,2101) -> Matrix(7,-6,-8,7) Matrix(4955,1474,7056,2099) -> Matrix(5,-6,-4,5) Matrix(393,116,952,281) -> Matrix(1,0,0,1) Matrix(253,74,-1624,-475) -> Matrix(7,-2,4,-1) Matrix(111,32,-392,-113) -> Matrix(5,-2,8,-3) Matrix(1595,448,2688,755) -> Matrix(3,-2,-4,3) Matrix(27637,7756,38416,10781) -> Matrix(3,-2,-4,3) Matrix(27635,7754,38416,10779) -> Matrix(1,-2,0,1) Matrix(617,172,1008,281) -> Matrix(3,-2,8,-5) Matrix(9073,2512,12544,3473) -> Matrix(37,-24,-20,13) Matrix(9071,2510,12544,3471) -> Matrix(35,-24,-16,11) Matrix(897,248,1624,449) -> Matrix(3,-2,-4,3) Matrix(1119,308,1624,447) -> Matrix(5,-4,4,-3) Matrix(391,106,616,167) -> Matrix(5,-4,4,-3) Matrix(2297,616,3136,841) -> Matrix(23,-22,-24,23) Matrix(2295,614,3136,839) -> Matrix(21,-22,-20,21) Matrix(85,22,112,29) -> Matrix(3,-2,-4,3) Matrix(83,20,112,27) -> Matrix(1,-2,0,1) Matrix(279,64,728,167) -> Matrix(3,-4,-8,11) Matrix(5461,1236,7056,1597) -> Matrix(3,-2,-4,3) Matrix(5459,1234,7056,1595) -> Matrix(1,-2,0,1) Matrix(83,18,-392,-85) -> Matrix(1,-2,0,1) Matrix(587,122,2016,419) -> Matrix(1,0,-4,1) Matrix(253,48,448,85) -> Matrix(1,0,0,1) Matrix(279,52,896,167) -> Matrix(1,0,-4,1) Matrix(645,116,784,141) -> Matrix(11,-10,-12,11) Matrix(643,114,784,139) -> Matrix(9,-10,-8,9) Matrix(617,98,1064,169) -> Matrix(1,-2,0,1) Matrix(223,34,728,111) -> Matrix(3,-8,-4,11) Matrix(83,10,224,27) -> Matrix(1,0,-4,1) Matrix(139,-18,224,-29) -> Matrix(1,0,0,1) Matrix(589,-86,952,-139) -> Matrix(1,6,0,1) Matrix(841,-132,1064,-167) -> Matrix(1,2,-4,-7) Matrix(139,-24,168,-29) -> Matrix(3,4,-4,-5) Matrix(447,-82,616,-113) -> Matrix(5,4,-4,-3) Matrix(85,-18,392,-83) -> Matrix(1,-2,0,1) Matrix(533,-116,896,-195) -> Matrix(1,2,0,1) Matrix(755,-166,896,-197) -> Matrix(3,4,-4,-5) Matrix(223,-50,504,-113) -> Matrix(1,2,-4,-7) Matrix(1065,-286,1456,-391) -> Matrix(13,12,-12,-11) Matrix(503,-138,616,-169) -> Matrix(5,4,-4,-3) Matrix(1457,-404,2016,-559) -> Matrix(5,4,-4,-3) Matrix(113,-32,392,-111) -> Matrix(3,2,-8,-5) Matrix(2381,-692,5488,-1595) -> Matrix(1,0,0,1) Matrix(307,-90,672,-197) -> Matrix(1,0,-4,1) Matrix(559,-166,1512,-449) -> Matrix(1,2,-4,-7) Matrix(391,-118,560,-169) -> Matrix(1,0,0,1) Matrix(839,-256,1288,-393) -> Matrix(5,4,-4,-3) Matrix(141,-50,392,-139) -> Matrix(7,4,-16,-9) Matrix(337,-122,616,-223) -> Matrix(5,2,12,5) Matrix(1651,-610,2352,-869) -> Matrix(7,2,-4,-1) Matrix(195,-74,224,-85) -> Matrix(1,0,0,1) Matrix(813,-310,952,-363) -> Matrix(13,6,-24,-11) Matrix(1009,-390,1736,-671) -> Matrix(1,0,4,1) Matrix(307,-120,504,-197) -> Matrix(1,0,8,1) Matrix(223,-90,280,-113) -> Matrix(1,0,0,1) Matrix(727,-298,1232,-505) -> Matrix(1,0,4,1) Matrix(1065,-446,1736,-727) -> Matrix(1,0,4,1) Matrix(3249,-1364,5600,-2351) -> Matrix(1,0,0,1) Matrix(169,-72,392,-167) -> Matrix(3,2,-8,-5) Matrix(7897,-3424,10976,-4759) -> Matrix(7,2,-4,-1) Matrix(1819,-802,2352,-1037) -> Matrix(5,2,-8,-3) Matrix(953,-428,1120,-503) -> Matrix(9,4,-16,-7) Matrix(363,-164,560,-253) -> Matrix(7,2,-4,-1) Matrix(1063,-488,1344,-617) -> Matrix(1,0,4,1) Matrix(29,-14,56,-27) -> Matrix(1,0,0,1) Matrix(475,-258,672,-365) -> Matrix(1,0,-4,1) Matrix(1595,-876,2296,-1261) -> Matrix(1,-2,0,1) Matrix(2043,-1126,3304,-1821) -> Matrix(1,2,0,1) Matrix(391,-218,504,-281) -> Matrix(3,-2,-4,3) Matrix(225,-128,392,-223) -> Matrix(1,-2,0,1) Matrix(3949,-2276,5488,-3163) -> Matrix(1,0,0,1) Matrix(1063,-670,1512,-953) -> Matrix(3,-2,-4,3) Matrix(253,-162,392,-251) -> Matrix(1,-4,0,1) Matrix(1371,-970,1624,-1149) -> Matrix(3,-2,-4,3) Matrix(281,-200,392,-279) -> Matrix(1,-2,0,1) Matrix(309,-242,392,-307) -> Matrix(3,2,-8,-5) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 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): 288 Minimal number of generators: 49 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: 30 Genus: 10 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/7 1/6 2/11 1/5 3/14 2/9 3/13 1/4 2/7 3/10 1/3 5/14 3/8 5/12 3/7 1/2 4/7 7/12 17/28 5/8 29/42 5/7 81/112 41/56 3/4 65/84 23/28 6/7 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/0 1/7 1/0 1/6 -2/1 -1/1 2/11 -3/4 1/5 -1/2 3/14 1/0 2/9 1/0 5/22 -2/1 -1/1 3/13 -7/6 1/4 -1/1 4/15 -5/4 3/11 -1/2 2/7 -1/2 5/17 -1/2 8/27 1/0 3/10 -1/1 0/1 4/13 -5/8 5/16 0/1 1/3 -1/2 5/14 -1/2 4/11 -3/8 7/19 -1/2 17/46 -1/3 -2/7 10/27 -1/4 3/8 0/1 8/21 -1/2 5/13 -3/10 7/18 -1/5 0/1 2/5 1/0 7/17 1/2 12/29 1/0 5/12 -1/1 3/7 -1/2 7/16 0/1 11/25 -1/2 15/34 -1/3 0/1 4/9 -1/4 5/11 -1/6 6/13 -1/12 1/2 -1/1 0/1 6/11 1/4 5/9 1/2 4/7 1/0 11/19 -1/2 18/31 1/0 7/12 -1/1 24/41 -7/12 41/70 -1/2 17/29 -1/2 10/17 -1/4 3/5 -1/2 17/28 0/1 14/23 1/8 11/18 0/1 1/3 8/13 3/4 21/34 1/1 2/1 13/21 1/0 18/29 1/0 5/8 0/1 17/27 1/2 12/19 1/0 7/11 3/2 9/14 1/0 2/3 1/0 11/16 0/1 20/29 1/0 29/42 1/0 9/13 -5/2 7/10 -1/1 0/1 5/7 1/0 13/18 -2/1 -1/1 47/65 -5/2 81/112 -2/1 34/47 -7/4 21/29 -3/2 8/11 1/0 19/26 -6/5 -1/1 30/41 -17/16 41/56 -1/1 11/15 -5/6 3/4 -1/1 10/13 -7/8 17/22 -1/1 -2/3 41/53 -1/2 65/84 -1/1 24/31 -3/4 7/9 -1/2 11/14 -1/2 4/5 1/0 9/11 -3/2 23/28 -1/1 14/17 -7/8 5/6 -1/1 -2/3 11/13 -9/14 6/7 -1/2 7/8 0/1 1/1 -1/2 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(139,-18,224,-29) (0/1,1/7) -> (13/21,18/29) Hyperbolic Matrix(225,-34,364,-55) (1/7,1/6) -> (21/34,13/21) Hyperbolic Matrix(139,-24,168,-29) (1/6,2/11) -> (14/17,5/6) Hyperbolic Matrix(57,-11,140,-27) (2/11,1/5) -> (2/5,7/17) Hyperbolic Matrix(111,-23,140,-29) (1/5,3/14) -> (11/14,4/5) Hyperbolic Matrix(197,-43,252,-55) (3/14,2/9) -> (7/9,11/14) Hyperbolic Matrix(223,-50,504,-113) (2/9,5/22) -> (15/34,4/9) Hyperbolic Matrix(449,-103,728,-167) (5/22,3/13) -> (8/13,21/34) Hyperbolic Matrix(29,-7,112,-27) (3/13,1/4) -> (1/4,4/15) Parabolic Matrix(141,-38,308,-83) (4/15,3/11) -> (5/11,6/13) Hyperbolic Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(559,-165,952,-281) (5/17,8/27) -> (17/29,10/17) Hyperbolic Matrix(559,-166,1512,-449) (8/27,3/10) -> (17/46,10/27) Hyperbolic Matrix(141,-43,364,-111) (3/10,4/13) -> (5/13,7/18) Hyperbolic Matrix(475,-148,812,-253) (4/13,5/16) -> (7/12,24/41) Hyperbolic Matrix(309,-97,532,-167) (5/16,1/3) -> (18/31,7/12) Hyperbolic Matrix(55,-19,84,-29) (1/3,5/14) -> (9/14,2/3) Hyperbolic Matrix(197,-71,308,-111) (5/14,4/11) -> (7/11,9/14) Hyperbolic Matrix(139,-51,308,-113) (4/11,7/19) -> (4/9,5/11) Hyperbolic Matrix(2409,-890,3332,-1231) (7/19,17/46) -> (13/18,47/65) Hyperbolic Matrix(197,-73,224,-83) (10/27,3/8) -> (7/8,1/1) Hyperbolic Matrix(195,-74,224,-85) (3/8,8/21) -> (6/7,7/8) Hyperbolic Matrix(309,-118,364,-139) (8/21,5/13) -> (11/13,6/7) Hyperbolic Matrix(307,-120,504,-197) (7/18,2/5) -> (14/23,11/18) Hyperbolic Matrix(589,-243,812,-335) (7/17,12/29) -> (21/29,8/11) Hyperbolic Matrix(559,-232,812,-337) (12/29,5/12) -> (11/16,20/29) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(307,-135,448,-197) (7/16,11/25) -> (2/3,11/16) Hyperbolic Matrix(1819,-802,2352,-1037) (11/25,15/34) -> (17/22,41/53) Hyperbolic Matrix(307,-144,420,-197) (6/13,1/2) -> (19/26,30/41) Hyperbolic Matrix(225,-122,308,-167) (1/2,6/11) -> (8/11,19/26) Hyperbolic Matrix(195,-107,308,-169) (6/11,5/9) -> (12/19,7/11) Hyperbolic Matrix(113,-64,196,-111) (5/9,4/7) -> (4/7,11/19) Parabolic Matrix(673,-390,868,-503) (11/19,18/31) -> (24/31,7/9) Hyperbolic Matrix(1819,-1065,2632,-1541) (24/41,41/70) -> (29/42,9/13) Hyperbolic Matrix(2241,-1313,3248,-1903) (41/70,17/29) -> (20/29,29/42) Hyperbolic Matrix(113,-67,140,-83) (10/17,3/5) -> (4/5,9/11) Hyperbolic Matrix(477,-289,784,-475) (3/5,17/28) -> (17/28,14/23) Parabolic Matrix(253,-155,364,-223) (11/18,8/13) -> (9/13,7/10) Hyperbolic Matrix(281,-175,448,-279) (18/29,5/8) -> (5/8,17/27) Parabolic Matrix(1317,-830,1820,-1147) (17/27,12/19) -> (34/47,21/29) Hyperbolic Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic Matrix(9073,-6561,12544,-9071) (47/65,81/112) -> (81/112,34/47) Parabolic Matrix(2297,-1681,3136,-2295) (30/41,41/56) -> (41/56,11/15) Parabolic Matrix(85,-63,112,-83) (11/15,3/4) -> (3/4,10/13) Parabolic Matrix(307,-237,364,-281) (10/13,17/22) -> (5/6,11/13) Hyperbolic Matrix(5461,-4225,7056,-5459) (41/53,65/84) -> (65/84,24/31) Parabolic Matrix(645,-529,784,-643) (9/11,23/28) -> (23/28,14/17) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-2,1) Matrix(139,-18,224,-29) -> Matrix(1,0,0,1) Matrix(225,-34,364,-55) -> Matrix(1,3,0,1) Matrix(139,-24,168,-29) -> Matrix(3,4,-4,-5) Matrix(57,-11,140,-27) -> Matrix(1,1,-2,-1) Matrix(111,-23,140,-29) -> Matrix(1,1,-2,-1) Matrix(197,-43,252,-55) -> Matrix(1,3,-2,-5) Matrix(223,-50,504,-113) -> Matrix(1,2,-4,-7) Matrix(449,-103,728,-167) -> Matrix(3,4,2,3) Matrix(29,-7,112,-27) -> Matrix(1,2,-2,-3) Matrix(141,-38,308,-83) -> Matrix(1,1,-8,-7) Matrix(57,-16,196,-55) -> Matrix(1,1,-4,-3) Matrix(559,-165,952,-281) -> Matrix(1,0,-2,1) Matrix(559,-166,1512,-449) -> Matrix(1,2,-4,-7) Matrix(141,-43,364,-111) -> Matrix(1,1,-6,-5) Matrix(475,-148,812,-253) -> Matrix(3,1,-4,-1) Matrix(309,-97,532,-167) -> Matrix(1,1,-2,-1) Matrix(55,-19,84,-29) -> Matrix(1,1,-2,-1) Matrix(197,-71,308,-111) -> Matrix(7,3,2,1) Matrix(139,-51,308,-113) -> Matrix(3,1,-10,-3) Matrix(2409,-890,3332,-1231) -> Matrix(11,3,-4,-1) Matrix(197,-73,224,-83) -> Matrix(1,0,2,1) Matrix(195,-74,224,-85) -> Matrix(1,0,0,1) Matrix(309,-118,364,-139) -> Matrix(7,3,-12,-5) Matrix(307,-120,504,-197) -> Matrix(1,0,8,1) Matrix(589,-243,812,-335) -> Matrix(3,-1,-2,1) Matrix(559,-232,812,-337) -> Matrix(1,1,0,1) Matrix(85,-36,196,-83) -> Matrix(1,1,-4,-3) Matrix(307,-135,448,-197) -> Matrix(1,0,2,1) Matrix(1819,-802,2352,-1037) -> Matrix(5,2,-8,-3) Matrix(307,-144,420,-197) -> Matrix(5,-1,-4,1) Matrix(225,-122,308,-167) -> Matrix(5,-1,-4,1) Matrix(195,-107,308,-169) -> Matrix(1,-1,2,-1) Matrix(113,-64,196,-111) -> Matrix(1,-1,0,1) Matrix(673,-390,868,-503) -> Matrix(3,1,-4,-1) Matrix(1819,-1065,2632,-1541) -> Matrix(11,6,-2,-1) Matrix(2241,-1313,3248,-1903) -> Matrix(9,4,2,1) Matrix(113,-67,140,-83) -> Matrix(1,1,-2,-1) Matrix(477,-289,784,-475) -> Matrix(1,0,10,1) Matrix(253,-155,364,-223) -> Matrix(3,-1,-2,1) Matrix(281,-175,448,-279) -> Matrix(1,0,2,1) Matrix(1317,-830,1820,-1147) -> Matrix(7,-5,-4,3) Matrix(141,-100,196,-139) -> Matrix(1,-1,0,1) Matrix(9073,-6561,12544,-9071) -> Matrix(11,24,-6,-13) Matrix(2297,-1681,3136,-2295) -> Matrix(21,22,-22,-23) Matrix(85,-63,112,-83) -> Matrix(1,2,-2,-3) Matrix(307,-237,364,-281) -> Matrix(7,5,-10,-7) Matrix(5461,-4225,7056,-5459) -> Matrix(1,2,-2,-3) Matrix(645,-529,784,-643) -> Matrix(9,10,-10,-11) 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): 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 0/1 1/0 1 28 1/7 1/0 3 4 1/6 (-2/1,-1/1) 0 14 5/28 -1/1 10 1 2/11 -3/4 1 28 1/5 -1/2 1 28 3/14 1/0 2 2 2/9 1/0 1 28 5/22 (-2/1,-1/1) 0 14 3/13 -7/6 1 28 1/4 -1/1 2 7 4/15 -5/4 1 28 3/11 -1/2 1 28 2/7 -1/2 1 4 5/17 -1/2 1 28 8/27 1/0 1 28 3/10 (-1/1,0/1) 0 14 4/13 -5/8 1 28 5/16 0/1 2 7 1/3 -1/2 1 28 5/14 -1/2 4 2 4/11 -3/8 1 28 7/19 -1/2 1 28 31/84 -1/3 6 1 17/46 (-1/3,-2/7) 0 14 10/27 -1/4 1 28 3/8 0/1 2 7 11/29 -1/2 1 28 8/21 -1/2 3 4 13/34 (-2/5,-1/3) 0 14 5/13 -3/10 1 28 7/18 (-1/5,0/1) 0 14 11/28 0/1 10 1 2/5 1/0 1 28 7/17 1/2 1 28 12/29 1/0 1 28 29/70 1/0 10 2 17/41 -7/2 1 28 5/12 -1/1 2 7 3/7 -1/2 1 4 7/16 0/1 2 7 11/25 -1/2 1 28 37/84 -1/3 2 1 15/34 (-1/3,0/1) 0 14 4/9 -1/4 1 28 5/11 -1/6 1 28 6/13 -1/12 1 28 13/28 0/1 22 1 1/2 (-1/1,0/1) 0 14 1/0 0/1 2 1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(85,-11,224,-29) (0/1,1/7) -> (11/29,8/21) Glide Reflection Matrix(139,-21,364,-55) (1/7,1/6) -> (8/21,13/34) Glide Reflection Matrix(29,-5,168,-29) (1/6,5/28) -> (1/6,5/28) Reflection Matrix(111,-20,616,-111) (5/28,2/11) -> (5/28,2/11) Reflection Matrix(57,-11,140,-27) (2/11,1/5) -> (2/5,7/17) Hyperbolic Matrix(29,-6,140,-29) (1/5,3/14) -> (1/5,3/14) Reflection Matrix(55,-12,252,-55) (3/14,2/9) -> (3/14,2/9) Reflection Matrix(223,-50,504,-113) (2/9,5/22) -> (15/34,4/9) Hyperbolic Matrix(279,-64,728,-167) (5/22,3/13) -> (13/34,5/13) Glide Reflection Matrix(29,-7,112,-27) (3/13,1/4) -> (1/4,4/15) Parabolic Matrix(141,-38,308,-83) (4/15,3/11) -> (5/11,6/13) Hyperbolic Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(393,-116,952,-281) (5/17,8/27) -> (7/17,12/29) Glide Reflection Matrix(559,-166,1512,-449) (8/27,3/10) -> (17/46,10/27) Hyperbolic Matrix(141,-43,364,-111) (3/10,4/13) -> (5/13,7/18) Hyperbolic Matrix(337,-105,812,-253) (4/13,5/16) -> (17/41,5/12) Glide Reflection Matrix(197,-62,448,-141) (5/16,1/3) -> (7/16,11/25) Glide Reflection Matrix(29,-10,84,-29) (1/3,5/14) -> (1/3,5/14) Reflection Matrix(111,-40,308,-111) (5/14,4/11) -> (5/14,4/11) Reflection Matrix(139,-51,308,-113) (4/11,7/19) -> (4/9,5/11) Hyperbolic Matrix(1177,-434,3192,-1177) (7/19,31/84) -> (7/19,31/84) Reflection Matrix(1427,-527,3864,-1427) (31/84,17/46) -> (31/84,17/46) Reflection Matrix(169,-63,448,-167) (10/27,3/8) -> (3/8,11/29) Parabolic Matrix(197,-77,504,-197) (7/18,11/28) -> (7/18,11/28) Reflection Matrix(111,-44,280,-111) (11/28,2/5) -> (11/28,2/5) Reflection Matrix(1681,-696,4060,-1681) (12/29,29/70) -> (12/29,29/70) Reflection Matrix(2379,-986,5740,-2379) (29/70,17/41) -> (29/70,17/41) Reflection Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(1849,-814,4200,-1849) (11/25,37/84) -> (11/25,37/84) Reflection Matrix(1259,-555,2856,-1259) (37/84,15/34) -> (37/84,15/34) Reflection Matrix(337,-156,728,-337) (6/13,13/28) -> (6/13,13/28) Reflection Matrix(27,-13,56,-27) (13/28,1/2) -> (13/28,1/2) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(85,-11,224,-29) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(139,-21,364,-55) -> Matrix(1,3,-2,-7) Matrix(29,-5,168,-29) -> Matrix(3,4,-2,-3) (1/6,5/28) -> (-2/1,-1/1) Matrix(111,-20,616,-111) -> Matrix(7,6,-8,-7) (5/28,2/11) -> (-1/1,-3/4) Matrix(57,-11,140,-27) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(29,-6,140,-29) -> Matrix(1,1,0,-1) (1/5,3/14) -> (-1/2,1/0) Matrix(55,-12,252,-55) -> Matrix(1,3,0,-1) (3/14,2/9) -> (-3/2,1/0) Matrix(223,-50,504,-113) -> Matrix(1,2,-4,-7) Matrix(279,-64,728,-167) -> Matrix(3,4,-8,-11) Matrix(29,-7,112,-27) -> Matrix(1,2,-2,-3) -1/1 Matrix(141,-38,308,-83) -> Matrix(1,1,-8,-7) Matrix(57,-16,196,-55) -> Matrix(1,1,-4,-3) -1/2 Matrix(393,-116,952,-281) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(559,-166,1512,-449) -> Matrix(1,2,-4,-7) Matrix(141,-43,364,-111) -> Matrix(1,1,-6,-5) Matrix(337,-105,812,-253) -> Matrix(3,1,-2,-1) Matrix(197,-62,448,-141) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(29,-10,84,-29) -> Matrix(1,1,0,-1) (1/3,5/14) -> (-1/2,1/0) Matrix(111,-40,308,-111) -> Matrix(7,3,-16,-7) (5/14,4/11) -> (-1/2,-3/8) Matrix(139,-51,308,-113) -> Matrix(3,1,-10,-3) (-1/2,-1/4).(-1/3,0/1) Matrix(1177,-434,3192,-1177) -> Matrix(5,2,-12,-5) (7/19,31/84) -> (-1/2,-1/3) Matrix(1427,-527,3864,-1427) -> Matrix(13,4,-42,-13) (31/84,17/46) -> (-1/3,-2/7) Matrix(169,-63,448,-167) -> Matrix(1,0,2,1) 0/1 Matrix(197,-77,504,-197) -> Matrix(-1,0,10,1) (7/18,11/28) -> (-1/5,0/1) Matrix(111,-44,280,-111) -> Matrix(1,0,0,-1) (11/28,2/5) -> (0/1,1/0) Matrix(1681,-696,4060,-1681) -> Matrix(-1,3,0,1) (12/29,29/70) -> (3/2,1/0) Matrix(2379,-986,5740,-2379) -> Matrix(1,7,0,-1) (29/70,17/41) -> (-7/2,1/0) Matrix(85,-36,196,-83) -> Matrix(1,1,-4,-3) -1/2 Matrix(1849,-814,4200,-1849) -> Matrix(5,2,-12,-5) (11/25,37/84) -> (-1/2,-1/3) Matrix(1259,-555,2856,-1259) -> Matrix(-1,0,6,1) (37/84,15/34) -> (-1/3,0/1) Matrix(337,-156,728,-337) -> Matrix(-1,0,24,1) (6/13,13/28) -> (-1/12,0/1) Matrix(27,-13,56,-27) -> Matrix(-1,0,2,1) (13/28,1/2) -> (-1/1,0/1) Matrix(-1,1,0,1) -> Matrix(-1,0,2,1) (1/2,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.