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): 1008 Minimal number of generators: 169 Number of equivalence classes of cusps: 60 Genus: 55 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -11/24 -9/22 -7/20 -1/3 -5/18 -3/16 -1/7 0/1 2/11 5/21 3/10 1/3 7/19 4/9 1/2 14/25 5/8 11/15 6/7 1/1 7/6 15/11 3/2 8/5 5/3 25/14 9/5 2/1 9/4 7/3 5/2 75/29 19/7 3/1 10/3 7/2 61/17 51/14 11/3 103/27 4/1 21/5 17/4 9/2 19/4 43/9 5/1 11/2 23/4 6/1 13/2 7/1 15/2 23/3 8/1 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/4 -8/17 0/1 1/2 -7/15 1/5 -6/13 1/5 1/4 -11/24 1/4 -5/11 1/3 -9/20 0/1 1/3 -13/29 1/1 -17/38 -1/4 0/1 -4/9 0/1 1/6 -11/25 1/5 -18/41 1/5 1/4 -7/16 1/5 1/4 -3/7 1/3 -14/33 1/1 1/0 -11/26 -1/2 0/1 -8/19 0/1 1/8 -13/31 1/7 -5/12 0/1 1/5 -7/17 1/5 -9/22 1/4 -11/27 3/11 -2/5 1/4 1/3 -9/23 1/3 -25/64 1/3 -16/41 0/1 1/2 -7/18 0/1 1/3 -5/13 1/3 -3/8 1/4 1/3 -7/19 1/3 -18/49 4/13 5/16 -11/30 8/25 1/3 -4/11 1/3 3/8 -9/25 1/3 -23/64 2/5 3/7 -14/39 2/5 1/2 -5/14 1/2 1/1 -16/45 1/2 1/1 -11/31 1/1 -17/48 -1/2 0/1 -23/65 1/3 -6/17 0/1 1/2 -7/20 0/1 -1/3 1/3 -5/16 0/1 1/5 -9/29 1/5 -4/13 2/9 1/4 -11/36 1/4 3/11 -7/23 1/3 -3/10 2/7 1/3 -8/27 1/3 5/14 -13/44 3/8 2/5 -5/17 1/3 -12/41 1/3 1/2 -7/24 2/5 1/2 -2/7 0/1 1/2 -5/18 0/1 -8/29 0/1 1/4 -3/11 1/3 -10/37 2/9 1/4 -7/26 0/1 1/3 -4/15 0/1 1/4 -9/34 1/4 1/3 -5/19 1/3 -6/23 0/1 1/2 -7/27 1/3 -8/31 1/4 1/3 -1/4 0/1 1/3 -3/13 1/3 -11/48 0/1 1/2 -8/35 2/5 1/2 -13/57 1/1 -18/79 -1/2 0/1 -5/22 0/1 1/4 -7/31 1/5 -2/9 1/3 1/2 -7/32 1/2 1/1 -12/55 4/9 1/2 -5/23 1/1 -3/14 0/1 1/1 -4/19 0/1 1/6 -5/24 0/1 1/5 -1/5 1/3 -3/16 1/3 -5/27 1/3 -2/11 2/5 1/2 -7/39 1/3 -5/28 1/3 1/2 -3/17 1/3 -1/6 1/3 1/2 -4/25 0/1 1/2 -7/44 0/1 1/2 -3/19 1/3 -5/32 1/2 1/1 -2/13 0/1 1/2 -3/20 0/1 1/4 -4/27 1/4 1/3 -5/34 1/3 1/2 -1/7 1/3 -1/8 1/3 2/5 -1/9 3/7 -2/19 8/17 1/2 -1/10 1/2 3/5 0/1 0/1 1/2 1/6 2/3 1/1 3/17 1/1 2/11 1/1 3/16 1/1 2/1 4/21 4/1 1/0 1/5 1/1 3/14 0/1 1/0 2/9 0/1 1/2 3/13 1/1 4/17 0/1 1/2 5/21 1/2 6/25 1/2 2/3 1/4 1/2 1/1 2/7 1/2 2/3 3/10 1/1 4/13 3/2 2/1 9/29 1/1 5/16 3/2 2/1 11/35 3/1 6/19 6/1 1/0 1/3 1/1 4/11 -1/2 0/1 7/19 0/1 10/27 0/1 1/8 3/8 0/1 1/3 2/5 1/2 1/1 7/17 -1/1 19/46 0/1 12/29 0/1 1/2 5/12 0/1 1/0 8/19 1/2 2/3 11/26 0/1 1/2 14/33 0/1 1/2 3/7 1/1 10/23 1/1 1/0 17/39 1/3 7/16 1/2 1/1 4/9 1/1 5/11 1/1 1/2 0/1 1/1 7/13 1/1 13/24 0/1 1/0 6/11 0/1 1/2 5/9 1/1 19/34 2/1 1/0 14/25 1/0 23/41 1/1 9/16 1/1 1/0 4/7 0/1 1/0 11/19 1/3 18/31 1/2 1/1 25/43 3/5 7/12 0/1 1/1 24/41 1/1 17/29 1/1 10/17 -2/1 1/0 13/22 -1/2 0/1 3/5 1/1 5/8 0/1 7/11 1/3 16/25 0/1 1/4 41/64 0/1 1/4 25/39 1/3 9/14 1/3 1/2 29/45 3/7 20/31 8/17 1/2 11/17 3/5 13/20 4/5 1/1 2/3 0/1 1/2 11/16 3/7 1/2 20/29 1/2 3/5 9/13 1/1 7/10 1/2 2/3 5/7 1/1 18/25 2/3 3/4 31/43 1/1 13/18 2/3 3/4 21/29 7/9 8/11 5/6 1/1 11/15 1/1 14/19 1/1 9/8 3/4 1/1 2/1 4/5 -2/1 1/0 5/6 -1/1 0/1 11/13 -1/3 6/7 0/1 13/15 1/7 7/8 0/1 1/4 15/17 1/3 8/9 0/1 1/2 1/1 1/1 7/6 0/1 13/11 1/5 19/16 0/1 1/4 6/5 0/1 1/2 17/14 0/1 1/6 28/23 1/4 4/15 11/9 1/3 5/4 1/3 1/2 14/11 1/2 2/3 9/7 1/1 22/17 1/1 13/10 1/2 1/1 4/3 3/4 1/1 15/11 1/1 26/19 1/1 19/18 11/8 1/1 8/7 7/5 1/1 17/12 1/1 1/0 10/7 0/1 1/0 3/2 1/1 1/0 11/7 1/1 8/5 1/0 21/13 -1/1 34/21 1/1 1/0 81/50 7/1 1/0 47/29 -3/1 13/8 0/1 1/0 44/27 1/1 3/2 31/19 3/1 80/49 14/1 1/0 129/79 1/0 49/30 -7/1 1/0 18/11 -1/1 1/0 41/25 -1/1 23/14 -1/2 0/1 28/17 1/1 1/0 5/3 1/1 17/10 1/1 1/0 46/27 -2/1 1/0 75/44 -2/1 1/0 29/17 -1/1 41/24 1/0 12/7 -1/1 1/0 7/4 0/1 1/1 16/9 0/1 1/2 25/14 1/1 34/19 2/1 1/0 43/24 0/1 1/0 9/5 1/1 11/6 0/1 1/0 13/7 1/1 2/1 1/1 1/0 9/4 1/0 16/7 -3/1 1/0 39/17 -5/1 23/10 -4/1 -3/1 53/23 -7/3 30/13 -5/2 -2/1 37/16 -2/1 1/0 44/19 -2/1 1/0 7/3 -1/1 26/11 0/1 1/0 19/8 1/1 1/0 31/13 1/1 12/5 -4/1 1/0 5/2 -1/1 0/1 18/7 -2/3 -1/2 31/12 -5/9 -1/2 75/29 -1/2 119/46 -1/2 -17/35 44/17 -1/2 -6/13 13/5 -1/3 34/13 -1/2 0/1 21/8 -1/2 -1/3 29/11 -1/3 66/25 -1/4 37/14 -1/4 0/1 8/3 -1/4 0/1 19/7 0/1 30/11 0/1 1/16 11/4 0/1 1/6 14/5 1/4 1/3 17/6 1/3 1/2 20/7 1/2 6/11 23/8 2/3 3/4 3/1 1/1 22/7 3/1 1/0 19/6 -3/1 1/0 16/5 0/1 1/0 13/4 2/1 1/0 10/3 1/0 27/8 -4/1 1/0 17/5 -3/1 7/2 -1/1 1/0 25/7 -1/1 43/12 -2/1 -1/1 61/17 -1/1 79/22 -1/1 0/1 18/5 -1/1 1/0 29/8 -2/1 -3/2 40/11 -3/2 -4/3 51/14 -1/1 11/3 -1/1 15/4 -1/1 -4/5 34/9 -2/3 -1/2 53/14 -3/4 -2/3 19/5 -3/5 61/16 -13/25 -1/2 103/27 -1/2 42/11 -1/2 -8/17 23/6 -1/2 -1/3 4/1 -1/2 0/1 21/5 0/1 38/9 0/1 1/18 17/4 0/1 1/8 30/7 0/1 1/4 13/3 1/3 22/5 0/1 1/2 9/2 0/1 1/1 14/3 1/2 2/3 19/4 1/2 1/1 43/9 1/1 67/14 1/1 3/2 24/5 1/1 1/0 5/1 1/1 11/2 1/0 17/3 -1/1 57/10 0/1 1/0 40/7 0/1 1/0 23/4 -3/1 1/0 6/1 -1/1 1/0 13/2 0/1 1/2 20/3 1/1 1/0 7/1 -1/1 15/2 -1/4 0/1 23/3 0/1 31/4 0/1 1/8 8/1 0/1 1/2 17/2 1/1 2/1 9/1 -1/1 10/1 0/1 1/0 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(689,326,298,141) (-1/2,-8/17) -> (30/13,37/16) Hyperbolic Matrix(491,230,-2154,-1009) (-8/17,-7/15) -> (-13/57,-18/79) Hyperbolic Matrix(485,226,294,137) (-7/15,-6/13) -> (28/17,5/3) Hyperbolic Matrix(821,378,480,221) (-6/13,-11/24) -> (41/24,12/7) Hyperbolic Matrix(1147,524,672,307) (-11/24,-5/11) -> (29/17,41/24) Hyperbolic Matrix(235,106,-756,-341) (-5/11,-9/20) -> (-5/16,-9/29) Hyperbolic Matrix(847,380,-2356,-1057) (-9/20,-13/29) -> (-9/25,-23/64) Hyperbolic Matrix(1367,612,-3862,-1729) (-13/29,-17/38) -> (-17/48,-23/65) Hyperbolic Matrix(1597,714,378,169) (-17/38,-4/9) -> (38/9,17/4) Hyperbolic Matrix(513,226,-1396,-615) (-4/9,-11/25) -> (-7/19,-18/49) Hyperbolic Matrix(2131,936,1300,571) (-11/25,-18/41) -> (18/11,41/25) Hyperbolic Matrix(461,202,-1294,-567) (-18/41,-7/16) -> (-5/14,-16/45) Hyperbolic Matrix(321,140,94,41) (-7/16,-3/7) -> (17/5,7/2) Hyperbolic Matrix(631,268,1448,615) (-3/7,-14/33) -> (10/23,17/39) Hyperbolic Matrix(1487,630,904,383) (-14/33,-11/26) -> (23/14,28/17) Hyperbolic Matrix(989,418,362,153) (-11/26,-8/19) -> (30/11,11/4) Hyperbolic Matrix(629,264,984,413) (-8/19,-13/31) -> (7/11,16/25) Hyperbolic Matrix(43,18,-356,-149) (-13/31,-5/12) -> (-1/8,-1/9) Hyperbolic Matrix(135,56,-446,-185) (-5/12,-7/17) -> (-7/23,-3/10) Hyperbolic Matrix(395,162,-968,-397) (-7/17,-9/22) -> (-9/22,-11/27) Parabolic Matrix(611,248,1052,427) (-11/27,-2/5) -> (18/31,25/43) Hyperbolic Matrix(301,118,-1028,-403) (-2/5,-9/23) -> (-5/17,-12/41) Hyperbolic Matrix(1877,734,514,201) (-9/23,-25/64) -> (51/14,11/3) Hyperbolic Matrix(4651,1816,1278,499) (-25/64,-16/41) -> (40/11,51/14) Hyperbolic Matrix(1195,466,-3326,-1297) (-16/41,-7/18) -> (-23/64,-14/39) Hyperbolic Matrix(129,50,-596,-231) (-7/18,-5/13) -> (-5/23,-3/14) Hyperbolic Matrix(127,48,82,31) (-5/13,-3/8) -> (3/2,11/7) Hyperbolic Matrix(43,16,-250,-93) (-3/8,-7/19) -> (-3/17,-1/6) Hyperbolic Matrix(697,256,1070,393) (-18/49,-11/30) -> (13/20,2/3) Hyperbolic Matrix(901,330,658,241) (-11/30,-4/11) -> (26/19,11/8) Hyperbolic Matrix(283,102,652,235) (-4/11,-9/25) -> (3/7,10/23) Hyperbolic Matrix(39,14,-404,-145) (-14/39,-5/14) -> (-1/10,0/1) Hyperbolic Matrix(563,200,-2176,-773) (-16/45,-11/31) -> (-7/27,-8/31) Hyperbolic Matrix(683,242,2176,771) (-11/31,-17/48) -> (5/16,11/35) Hyperbolic Matrix(2979,1054,1286,455) (-23/65,-6/17) -> (44/19,7/3) Hyperbolic Matrix(563,198,1362,479) (-6/17,-7/20) -> (19/46,12/29) Hyperbolic Matrix(197,68,478,165) (-7/20,-1/3) -> (7/17,19/46) Hyperbolic Matrix(191,60,226,71) (-1/3,-5/16) -> (5/6,11/13) Hyperbolic Matrix(149,46,-826,-255) (-9/29,-4/13) -> (-2/11,-7/39) Hyperbolic Matrix(523,160,-2396,-733) (-4/13,-11/36) -> (-7/32,-12/55) Hyperbolic Matrix(223,68,-1420,-433) (-11/36,-7/23) -> (-3/19,-5/32) Hyperbolic Matrix(221,66,298,89) (-3/10,-8/27) -> (14/19,3/4) Hyperbolic Matrix(2287,676,1404,415) (-8/27,-13/44) -> (13/8,44/27) Hyperbolic Matrix(481,142,1548,457) (-13/44,-5/17) -> (9/29,5/16) Hyperbolic Matrix(219,64,-1468,-429) (-12/41,-7/24) -> (-3/20,-4/27) Hyperbolic Matrix(475,138,148,43) (-7/24,-2/7) -> (16/5,13/4) Hyperbolic Matrix(179,50,-648,-181) (-2/7,-5/18) -> (-5/18,-8/29) Parabolic Matrix(751,206,288,79) (-8/29,-3/11) -> (13/5,34/13) Hyperbolic Matrix(569,154,-2494,-675) (-3/11,-10/37) -> (-8/35,-13/57) Hyperbolic Matrix(215,58,1138,307) (-10/37,-7/26) -> (3/16,4/21) Hyperbolic Matrix(179,48,-854,-229) (-7/26,-4/15) -> (-4/19,-5/24) Hyperbolic Matrix(143,38,-922,-245) (-4/15,-9/34) -> (-5/32,-2/13) Hyperbolic Matrix(953,252,1698,449) (-9/34,-5/19) -> (23/41,9/16) Hyperbolic Matrix(283,74,914,239) (-5/19,-6/23) -> (4/13,9/29) Hyperbolic Matrix(561,146,634,165) (-6/23,-7/27) -> (15/17,8/9) Hyperbolic Matrix(2521,650,702,181) (-8/31,-1/4) -> (79/22,18/5) Hyperbolic Matrix(33,8,70,17) (-1/4,-3/13) -> (5/11,1/2) Hyperbolic Matrix(235,54,-1484,-341) (-3/13,-11/48) -> (-7/44,-3/19) Hyperbolic Matrix(3137,718,1752,401) (-11/48,-8/35) -> (34/19,43/24) Hyperbolic Matrix(2625,598,338,77) (-18/79,-5/22) -> (31/4,8/1) Hyperbolic Matrix(875,198,738,167) (-5/22,-7/31) -> (13/11,19/16) Hyperbolic Matrix(1643,370,1008,227) (-7/31,-2/9) -> (44/27,31/19) Hyperbolic Matrix(399,88,68,15) (-2/9,-7/32) -> (23/4,6/1) Hyperbolic Matrix(101,22,-932,-203) (-12/55,-5/23) -> (-1/9,-2/19) Hyperbolic Matrix(197,42,530,113) (-3/14,-4/19) -> (10/27,3/8) Hyperbolic Matrix(1051,218,458,95) (-5/24,-1/5) -> (39/17,23/10) Hyperbolic Matrix(95,18,-512,-97) (-1/5,-3/16) -> (-3/16,-5/27) Parabolic Matrix(827,152,1148,211) (-5/27,-2/11) -> (18/25,31/43) Hyperbolic Matrix(223,40,-1522,-273) (-7/39,-5/28) -> (-5/34,-1/7) Hyperbolic Matrix(853,152,1330,237) (-5/28,-3/17) -> (25/39,9/14) Hyperbolic Matrix(61,10,250,41) (-1/6,-4/25) -> (6/25,1/4) Hyperbolic Matrix(3185,508,558,89) (-4/25,-7/44) -> (57/10,40/7) Hyperbolic Matrix(367,56,308,47) (-2/13,-3/20) -> (19/16,6/5) Hyperbolic Matrix(2625,388,548,81) (-4/27,-5/34) -> (67/14,24/5) Hyperbolic Matrix(31,4,178,23) (-1/7,-1/8) -> (1/6,3/17) Hyperbolic Matrix(2701,282,1044,109) (-2/19,-1/10) -> (119/46,44/17) Hyperbolic Matrix(113,-18,44,-7) (0/1,1/6) -> (5/2,18/7) Hyperbolic Matrix(595,-106,1016,-181) (3/17,2/11) -> (24/41,17/29) Hyperbolic Matrix(461,-86,788,-147) (2/11,3/16) -> (7/12,24/41) Hyperbolic Matrix(261,-50,830,-159) (4/21,1/5) -> (11/35,6/19) Hyperbolic Matrix(237,-50,128,-27) (1/5,3/14) -> (11/6,13/7) Hyperbolic Matrix(213,-46,514,-111) (3/14,2/9) -> (12/29,5/12) Hyperbolic Matrix(401,-92,170,-39) (2/9,3/13) -> (7/3,26/11) Hyperbolic Matrix(233,-54,548,-127) (3/13,4/17) -> (14/33,3/7) Hyperbolic Matrix(211,-50,882,-209) (4/17,5/21) -> (5/21,6/25) Parabolic Matrix(61,-16,42,-11) (1/4,2/7) -> (10/7,3/2) Hyperbolic Matrix(61,-18,200,-59) (2/7,3/10) -> (3/10,4/13) Parabolic Matrix(611,-194,948,-301) (6/19,1/3) -> (29/45,20/31) Hyperbolic Matrix(133,-48,230,-83) (1/3,4/11) -> (4/7,11/19) Hyperbolic Matrix(267,-98,722,-265) (4/11,7/19) -> (7/19,10/27) Parabolic Matrix(131,-50,76,-29) (3/8,2/5) -> (12/7,7/4) Hyperbolic Matrix(241,-98,332,-135) (2/5,7/17) -> (21/29,8/11) Hyperbolic Matrix(367,-154,622,-261) (5/12,8/19) -> (10/17,13/22) Hyperbolic Matrix(1591,-672,438,-185) (8/19,11/26) -> (29/8,40/11) Hyperbolic Matrix(3671,-1556,2154,-913) (11/26,14/33) -> (46/27,75/44) Hyperbolic Matrix(815,-356,1266,-553) (17/39,7/16) -> (9/14,29/45) Hyperbolic Matrix(469,-206,362,-159) (7/16,4/9) -> (22/17,13/10) Hyperbolic Matrix(323,-146,250,-113) (4/9,5/11) -> (9/7,22/17) Hyperbolic Matrix(609,-326,170,-91) (1/2,7/13) -> (25/7,43/12) Hyperbolic Matrix(1671,-902,980,-529) (7/13,13/24) -> (75/44,29/17) Hyperbolic Matrix(1399,-760,370,-201) (13/24,6/11) -> (34/9,53/14) Hyperbolic Matrix(217,-120,302,-167) (6/11,5/9) -> (5/7,18/25) Hyperbolic Matrix(1219,-680,1902,-1061) (5/9,19/34) -> (41/64,25/39) Hyperbolic Matrix(3169,-1772,1200,-671) (19/34,14/25) -> (66/25,37/14) Hyperbolic Matrix(3431,-1924,1300,-729) (14/25,23/41) -> (29/11,66/25) Hyperbolic Matrix(549,-310,232,-131) (9/16,4/7) -> (26/11,19/8) Hyperbolic Matrix(659,-382,954,-553) (11/19,18/31) -> (20/29,9/13) Hyperbolic Matrix(839,-488,98,-57) (25/43,7/12) -> (17/2,9/1) Hyperbolic Matrix(999,-586,820,-481) (17/29,10/17) -> (28/23,11/9) Hyperbolic Matrix(229,-136,32,-19) (13/22,3/5) -> (7/1,15/2) Hyperbolic Matrix(81,-50,128,-79) (3/5,5/8) -> (5/8,7/11) Parabolic Matrix(3741,-2396,1616,-1035) (16/25,41/64) -> (37/16,44/19) Hyperbolic Matrix(2321,-1500,1422,-919) (20/31,11/17) -> (31/19,80/49) Hyperbolic Matrix(1451,-942,630,-409) (11/17,13/20) -> (23/10,53/23) Hyperbolic Matrix(787,-540,462,-317) (2/3,11/16) -> (17/10,46/27) Hyperbolic Matrix(2893,-1994,1786,-1231) (11/16,20/29) -> (34/21,81/50) Hyperbolic Matrix(521,-362,154,-107) (9/13,7/10) -> (27/8,17/5) Hyperbolic Matrix(167,-118,92,-65) (7/10,5/7) -> (9/5,11/6) Hyperbolic Matrix(1043,-752,362,-261) (31/43,13/18) -> (23/8,3/1) Hyperbolic Matrix(1223,-884,754,-545) (13/18,21/29) -> (47/29,13/8) Hyperbolic Matrix(331,-242,450,-329) (8/11,11/15) -> (11/15,14/19) Parabolic Matrix(73,-56,30,-23) (3/4,4/5) -> (12/5,5/2) Hyperbolic Matrix(129,-106,28,-23) (4/5,5/6) -> (9/2,14/3) Hyperbolic Matrix(169,-144,196,-167) (11/13,6/7) -> (6/7,13/15) Parabolic Matrix(947,-822,250,-217) (13/15,7/8) -> (53/14,19/5) Hyperbolic Matrix(1105,-974,194,-171) (7/8,15/17) -> (17/3,57/10) Hyperbolic Matrix(507,-454,220,-197) (8/9,1/1) -> (53/23,30/13) Hyperbolic Matrix(85,-98,72,-83) (1/1,7/6) -> (7/6,13/11) Parabolic Matrix(505,-612,118,-143) (6/5,17/14) -> (17/4,30/7) Hyperbolic Matrix(809,-984,282,-343) (17/14,28/23) -> (20/7,23/8) Hyperbolic Matrix(163,-202,46,-57) (11/9,5/4) -> (7/2,25/7) Hyperbolic Matrix(413,-524,160,-203) (5/4,14/11) -> (18/7,31/12) Hyperbolic Matrix(297,-380,68,-87) (14/11,9/7) -> (13/3,22/5) Hyperbolic Matrix(191,-250,68,-89) (13/10,4/3) -> (14/5,17/6) Hyperbolic Matrix(331,-450,242,-329) (4/3,15/11) -> (15/11,26/19) Parabolic Matrix(163,-226,44,-61) (11/8,7/5) -> (11/3,15/4) Hyperbolic Matrix(453,-640,172,-243) (7/5,17/12) -> (21/8,29/11) Hyperbolic Matrix(301,-428,64,-91) (17/12,10/7) -> (14/3,19/4) Hyperbolic Matrix(161,-256,100,-159) (11/7,8/5) -> (8/5,21/13) Parabolic Matrix(407,-658,60,-97) (21/13,34/21) -> (20/3,7/1) Hyperbolic Matrix(2719,-4406,714,-1157) (81/50,47/29) -> (19/5,61/16) Hyperbolic Matrix(8365,-13658,2192,-3579) (80/49,129/79) -> (103/27,42/11) Hyperbolic Matrix(7909,-12916,2074,-3387) (129/79,49/30) -> (61/16,103/27) Hyperbolic Matrix(869,-1420,276,-451) (49/30,18/11) -> (22/7,19/6) Hyperbolic Matrix(1201,-1970,670,-1099) (41/25,23/14) -> (43/24,9/5) Hyperbolic Matrix(367,-622,154,-261) (5/3,17/10) -> (19/8,31/13) Hyperbolic Matrix(169,-298,38,-67) (7/4,16/9) -> (22/5,9/2) Hyperbolic Matrix(701,-1250,392,-699) (16/9,25/14) -> (25/14,34/19) Parabolic Matrix(173,-322,36,-67) (13/7,2/1) -> (24/5,5/1) Hyperbolic Matrix(73,-162,32,-71) (2/1,9/4) -> (9/4,16/7) Parabolic Matrix(395,-906,126,-289) (16/7,39/17) -> (3/1,22/7) Hyperbolic Matrix(637,-1520,246,-587) (31/13,12/5) -> (44/17,13/5) Hyperbolic Matrix(4351,-11250,1682,-4349) (31/12,75/29) -> (75/29,119/46) Parabolic Matrix(331,-866,86,-225) (34/13,21/8) -> (23/6,4/1) Hyperbolic Matrix(143,-378,14,-37) (37/14,8/3) -> (10/1,1/0) Hyperbolic Matrix(267,-722,98,-265) (8/3,19/7) -> (19/7,30/11) Parabolic Matrix(89,-248,14,-39) (11/4,14/5) -> (6/1,13/2) Hyperbolic Matrix(413,-1174,108,-307) (17/6,20/7) -> (42/11,23/6) Hyperbolic Matrix(355,-1128,62,-197) (19/6,16/5) -> (40/7,23/4) Hyperbolic Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(2075,-7442,578,-2073) (43/12,61/17) -> (61/17,79/22) Parabolic Matrix(225,-814,34,-123) (18/5,29/8) -> (13/2,20/3) Hyperbolic Matrix(185,-698,22,-83) (15/4,34/9) -> (8/1,17/2) Hyperbolic Matrix(211,-882,50,-209) (4/1,21/5) -> (21/5,38/9) Parabolic Matrix(93,-400,10,-43) (30/7,13/3) -> (9/1,10/1) Hyperbolic Matrix(775,-3698,162,-773) (19/4,43/9) -> (43/9,67/14) Parabolic Matrix(45,-242,8,-43) (5/1,11/2) -> (11/2,17/3) Parabolic Matrix(139,-1058,18,-137) (15/2,23/3) -> (23/3,31/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(689,326,298,141) -> Matrix(9,-2,-4,1) Matrix(491,230,-2154,-1009) -> Matrix(1,0,-4,1) Matrix(485,226,294,137) -> Matrix(1,0,-4,1) Matrix(821,378,480,221) -> Matrix(9,-2,-4,1) Matrix(1147,524,672,307) -> Matrix(1,0,-4,1) Matrix(235,106,-756,-341) -> Matrix(1,0,2,1) Matrix(847,380,-2356,-1057) -> Matrix(3,-2,8,-5) Matrix(1367,612,-3862,-1729) -> Matrix(1,0,2,1) Matrix(1597,714,378,169) -> Matrix(1,0,12,1) Matrix(513,226,-1396,-615) -> Matrix(19,-4,62,-13) Matrix(2131,936,1300,571) -> Matrix(9,-2,-4,1) Matrix(461,202,-1294,-567) -> Matrix(9,-2,14,-3) Matrix(321,140,94,41) -> Matrix(9,-2,-4,1) Matrix(631,268,1448,615) -> Matrix(1,0,0,1) Matrix(1487,630,904,383) -> Matrix(1,0,0,1) Matrix(989,418,362,153) -> Matrix(1,0,8,1) Matrix(629,264,984,413) -> Matrix(1,0,-4,1) Matrix(43,18,-356,-149) -> Matrix(11,-2,28,-5) Matrix(135,56,-446,-185) -> Matrix(9,-2,32,-7) Matrix(395,162,-968,-397) -> Matrix(17,-4,64,-15) Matrix(611,248,1052,427) -> Matrix(1,0,-2,1) Matrix(301,118,-1028,-403) -> Matrix(7,-2,18,-5) Matrix(1877,734,514,201) -> Matrix(5,-2,-2,1) Matrix(4651,1816,1278,499) -> Matrix(11,-4,-8,3) Matrix(1195,466,-3326,-1297) -> Matrix(3,-2,8,-5) Matrix(129,50,-596,-231) -> Matrix(1,0,-2,1) Matrix(127,48,82,31) -> Matrix(7,-2,4,-1) Matrix(43,16,-250,-93) -> Matrix(7,-2,18,-5) Matrix(697,256,1070,393) -> Matrix(13,-4,10,-3) Matrix(901,330,658,241) -> Matrix(49,-16,46,-15) Matrix(283,102,652,235) -> Matrix(5,-2,8,-3) Matrix(39,14,-404,-145) -> Matrix(5,-2,8,-3) Matrix(563,200,-2176,-773) -> Matrix(1,0,2,1) Matrix(683,242,2176,771) -> Matrix(1,2,0,1) Matrix(2979,1054,1286,455) -> Matrix(5,-2,-2,1) Matrix(563,198,1362,479) -> Matrix(1,0,0,1) Matrix(197,68,478,165) -> Matrix(1,0,-4,1) Matrix(191,60,226,71) -> Matrix(1,0,-6,1) Matrix(149,46,-826,-255) -> Matrix(1,0,-2,1) Matrix(523,160,-2396,-733) -> Matrix(7,-2,18,-5) Matrix(223,68,-1420,-433) -> Matrix(7,-2,18,-5) Matrix(221,66,298,89) -> Matrix(13,-4,10,-3) Matrix(2287,676,1404,415) -> Matrix(5,-2,8,-3) Matrix(481,142,1548,457) -> Matrix(1,0,-2,1) Matrix(219,64,-1468,-429) -> Matrix(5,-2,18,-7) Matrix(475,138,148,43) -> Matrix(1,0,-2,1) Matrix(179,50,-648,-181) -> Matrix(1,0,2,1) Matrix(751,206,288,79) -> Matrix(1,0,-6,1) Matrix(569,154,-2494,-675) -> Matrix(1,0,-2,1) Matrix(215,58,1138,307) -> Matrix(7,-2,4,-1) Matrix(179,48,-854,-229) -> Matrix(1,0,2,1) Matrix(143,38,-922,-245) -> Matrix(1,0,-2,1) Matrix(953,252,1698,449) -> Matrix(7,-2,4,-1) Matrix(283,74,914,239) -> Matrix(7,-2,4,-1) Matrix(561,146,634,165) -> Matrix(1,0,0,1) Matrix(2521,650,702,181) -> Matrix(1,0,-4,1) Matrix(33,8,70,17) -> Matrix(1,0,-2,1) Matrix(235,54,-1484,-341) -> Matrix(1,0,0,1) Matrix(3137,718,1752,401) -> Matrix(1,0,-2,1) Matrix(2625,598,338,77) -> Matrix(1,0,4,1) Matrix(875,198,738,167) -> Matrix(1,0,0,1) Matrix(1643,370,1008,227) -> Matrix(7,-2,4,-1) Matrix(399,88,68,15) -> Matrix(5,-2,-2,1) Matrix(101,22,-932,-203) -> Matrix(7,-4,16,-9) Matrix(197,42,530,113) -> Matrix(1,0,2,1) Matrix(1051,218,458,95) -> Matrix(17,-4,-4,1) Matrix(95,18,-512,-97) -> Matrix(13,-4,36,-11) Matrix(827,152,1148,211) -> Matrix(11,-4,14,-5) Matrix(223,40,-1522,-273) -> Matrix(1,0,0,1) Matrix(853,152,1330,237) -> Matrix(1,0,0,1) Matrix(61,10,250,41) -> Matrix(5,-2,8,-3) Matrix(3185,508,558,89) -> Matrix(1,0,-2,1) Matrix(367,56,308,47) -> Matrix(1,0,0,1) Matrix(2625,388,548,81) -> Matrix(7,-2,4,-1) Matrix(31,4,178,23) -> Matrix(11,-4,14,-5) Matrix(2701,282,1044,109) -> Matrix(29,-14,-60,29) Matrix(113,-18,44,-7) -> Matrix(3,-2,-4,3) Matrix(595,-106,1016,-181) -> Matrix(7,-6,6,-5) Matrix(461,-86,788,-147) -> Matrix(1,-2,2,-3) Matrix(261,-50,830,-159) -> Matrix(1,2,0,1) Matrix(237,-50,128,-27) -> Matrix(1,0,0,1) Matrix(213,-46,514,-111) -> Matrix(1,0,0,1) Matrix(401,-92,170,-39) -> Matrix(1,0,-2,1) Matrix(233,-54,548,-127) -> Matrix(1,0,0,1) Matrix(211,-50,882,-209) -> Matrix(5,-2,8,-3) Matrix(61,-16,42,-11) -> Matrix(3,-2,2,-1) Matrix(61,-18,200,-59) -> Matrix(5,-4,4,-3) Matrix(611,-194,948,-301) -> Matrix(1,2,2,5) Matrix(133,-48,230,-83) -> Matrix(1,0,2,1) Matrix(267,-98,722,-265) -> Matrix(1,0,10,1) Matrix(131,-50,76,-29) -> Matrix(1,0,-2,1) Matrix(241,-98,332,-135) -> Matrix(3,-4,4,-5) Matrix(367,-154,622,-261) -> Matrix(1,0,-2,1) Matrix(1591,-672,438,-185) -> Matrix(1,-2,0,1) Matrix(3671,-1556,2154,-913) -> Matrix(5,-2,-2,1) Matrix(815,-356,1266,-553) -> Matrix(3,-2,8,-5) Matrix(469,-206,362,-159) -> Matrix(1,0,0,1) Matrix(323,-146,250,-113) -> Matrix(1,-2,2,-3) Matrix(609,-326,170,-91) -> Matrix(1,-2,0,1) Matrix(1671,-902,980,-529) -> Matrix(1,-2,0,1) Matrix(1399,-760,370,-201) -> Matrix(3,-2,-4,3) Matrix(217,-120,302,-167) -> Matrix(1,-2,2,-3) Matrix(1219,-680,1902,-1061) -> Matrix(1,-2,4,-7) Matrix(3169,-1772,1200,-671) -> Matrix(1,-2,-4,9) Matrix(3431,-1924,1300,-729) -> Matrix(1,0,-4,1) Matrix(549,-310,232,-131) -> Matrix(1,0,0,1) Matrix(659,-382,954,-553) -> Matrix(5,-2,8,-3) Matrix(839,-488,98,-57) -> Matrix(3,-2,2,-1) Matrix(999,-586,820,-481) -> Matrix(1,-2,4,-7) Matrix(229,-136,32,-19) -> Matrix(1,0,-2,1) Matrix(81,-50,128,-79) -> Matrix(1,0,2,1) Matrix(3741,-2396,1616,-1035) -> Matrix(9,-2,-4,1) Matrix(2321,-1500,1422,-919) -> Matrix(11,-6,2,-1) Matrix(1451,-942,630,-409) -> Matrix(11,-8,-4,3) Matrix(787,-540,462,-317) -> Matrix(5,-2,-2,1) Matrix(2893,-1994,1786,-1231) -> Matrix(7,-4,2,-1) Matrix(521,-362,154,-107) -> Matrix(5,-2,-2,1) Matrix(167,-118,92,-65) -> Matrix(3,-2,2,-1) Matrix(1043,-752,362,-261) -> Matrix(1,0,0,1) Matrix(1223,-884,754,-545) -> Matrix(3,-2,-4,3) Matrix(331,-242,450,-329) -> Matrix(15,-14,14,-13) Matrix(73,-56,30,-23) -> Matrix(1,-2,0,1) Matrix(129,-106,28,-23) -> Matrix(1,0,2,1) Matrix(169,-144,196,-167) -> Matrix(1,0,10,1) Matrix(947,-822,250,-217) -> Matrix(11,-2,-16,3) Matrix(1105,-974,194,-171) -> Matrix(1,0,-4,1) Matrix(507,-454,220,-197) -> Matrix(9,-2,-4,1) Matrix(85,-98,72,-83) -> Matrix(1,0,4,1) Matrix(505,-612,118,-143) -> Matrix(1,0,2,1) Matrix(809,-984,282,-343) -> Matrix(9,-2,14,-3) Matrix(163,-202,46,-57) -> Matrix(5,-2,-2,1) Matrix(413,-524,160,-203) -> Matrix(7,-4,-12,7) Matrix(297,-380,68,-87) -> Matrix(3,-2,8,-5) Matrix(191,-250,68,-89) -> Matrix(3,-2,8,-5) Matrix(331,-450,242,-329) -> Matrix(23,-22,22,-21) Matrix(163,-226,44,-61) -> Matrix(3,-4,-2,3) Matrix(453,-640,172,-243) -> Matrix(1,-2,-2,5) Matrix(301,-428,64,-91) -> Matrix(1,-2,2,-3) Matrix(161,-256,100,-159) -> Matrix(1,-2,0,1) Matrix(407,-658,60,-97) -> Matrix(1,0,0,1) Matrix(2719,-4406,714,-1157) -> Matrix(1,6,-2,-11) Matrix(8365,-13658,2192,-3579) -> Matrix(1,-22,-2,45) Matrix(7909,-12916,2074,-3387) -> Matrix(1,20,-2,-39) Matrix(869,-1420,276,-451) -> Matrix(1,4,0,1) Matrix(1201,-1970,670,-1099) -> Matrix(1,0,2,1) Matrix(367,-622,154,-261) -> Matrix(1,0,0,1) Matrix(169,-298,38,-67) -> Matrix(1,0,0,1) Matrix(701,-1250,392,-699) -> Matrix(3,-2,2,-1) Matrix(173,-322,36,-67) -> Matrix(1,0,0,1) Matrix(73,-162,32,-71) -> Matrix(1,-4,0,1) Matrix(395,-906,126,-289) -> Matrix(1,6,0,1) Matrix(637,-1520,246,-587) -> Matrix(1,-2,-2,5) Matrix(4351,-11250,1682,-4349) -> Matrix(43,22,-88,-45) Matrix(331,-866,86,-225) -> Matrix(1,0,0,1) Matrix(143,-378,14,-37) -> Matrix(1,0,4,1) Matrix(267,-722,98,-265) -> Matrix(1,0,20,1) Matrix(89,-248,14,-39) -> Matrix(1,0,-4,1) Matrix(413,-1174,108,-307) -> Matrix(5,-2,-12,5) Matrix(355,-1128,62,-197) -> Matrix(1,0,0,1) Matrix(121,-400,36,-119) -> Matrix(1,-6,0,1) Matrix(2075,-7442,578,-2073) -> Matrix(1,2,-2,-3) Matrix(225,-814,34,-123) -> Matrix(1,2,0,1) Matrix(185,-698,22,-83) -> Matrix(3,2,4,3) Matrix(211,-882,50,-209) -> Matrix(1,0,20,1) Matrix(93,-400,10,-43) -> Matrix(1,0,-4,1) Matrix(775,-3698,162,-773) -> Matrix(5,-4,4,-3) Matrix(45,-242,8,-43) -> Matrix(1,-2,0,1) Matrix(139,-1058,18,-137) -> Matrix(1,0,12,1) 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): 44 Degree of the the map X: 44 Degree of the the map Y: 168 ----------------------------------------------------------------------- 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. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 0/1 2 1 0/1 (0/1,1/2) 0 26 1/6 (2/3,1/1) 0 26 2/11 1/1 4 2 3/16 (1/1,2/1) 0 26 1/5 1/1 1 13 3/14 (0/1,1/0) 0 26 2/9 (0/1,1/2) 0 26 3/13 1/1 1 13 4/17 (0/1,1/2) 0 26 5/21 1/2 1 1 1/4 (1/2,1/1) 0 26 2/7 (1/2,2/3) 0 26 3/10 1/1 4 2 4/13 (3/2,2/1) 0 26 5/16 (3/2,2/1) 0 26 6/19 (6/1,1/0) 0 26 1/3 1/1 1 13 4/11 (-1/2,0/1) 0 26 7/19 0/1 5 1 3/8 (0/1,1/3) 0 26 2/5 (1/2,1/1) 0 26 7/17 -1/1 1 13 12/29 (0/1,1/2) 0 26 5/12 (0/1,1/0) 0 26 8/19 (1/2,2/3) 0 26 11/26 (0/1,1/2) 0 26 14/33 (0/1,1/2) 0 26 3/7 1/1 1 13 7/16 (1/2,1/1) 0 26 4/9 1/1 1 2 1/2 (0/1,1/1) 0 26 7/13 1/1 1 13 13/24 (0/1,1/0) 0 26 6/11 (0/1,1/2) 0 26 5/9 1/1 1 13 19/34 (2/1,1/0) 0 26 14/25 1/0 1 2 9/16 (1/1,1/0) 0 26 4/7 (0/1,1/0) 0 26 11/19 1/3 1 13 18/31 (1/2,1/1) 0 26 7/12 (0/1,1/1) 0 26 17/29 1/1 1 13 10/17 (-2/1,1/0) 0 26 13/22 (-1/2,0/1) 0 26 3/5 1/1 1 13 5/8 0/1 2 2 7/11 1/3 1 13 9/14 (1/3,1/2) 0 26 20/31 (8/17,1/2) 0 26 11/17 3/5 1 13 2/3 (0/1,1/2) 0 26 11/16 (3/7,1/2) 0 26 20/29 (1/2,3/5) 0 26 9/13 1/1 1 13 7/10 (1/2,2/3) 0 26 5/7 1/1 1 13 18/25 (2/3,3/4) 0 26 13/18 (2/3,3/4) 0 26 21/29 7/9 1 13 8/11 (5/6,1/1) 0 26 11/15 1/1 7 1 3/4 (1/1,2/1) 0 26 4/5 (-2/1,1/0) 0 26 5/6 (-1/1,0/1) 0 26 6/7 0/1 5 2 7/8 (0/1,1/4) 0 26 8/9 (0/1,1/2) 0 26 1/1 1/1 1 13 7/6 0/1 4 2 13/11 1/5 1 13 6/5 (0/1,1/2) 0 26 17/14 (0/1,1/6) 0 26 28/23 (1/4,4/15) 0 26 11/9 1/3 1 13 5/4 (1/3,1/2) 0 26 14/11 (1/2,2/3) 0 26 9/7 1/1 1 13 13/10 (1/2,1/1) 0 26 4/3 (3/4,1/1) 0 26 15/11 1/1 11 1 11/8 (1/1,8/7) 0 26 7/5 1/1 1 13 17/12 (1/1,1/0) 0 26 10/7 (0/1,1/0) 0 26 3/2 (1/1,1/0) 0 26 8/5 1/0 1 2 13/8 (0/1,1/0) 0 26 31/19 3/1 1 13 80/49 (14/1,1/0) 0 26 129/79 1/0 21 1 49/30 (-7/1,1/0) 0 26 18/11 (-1/1,1/0) 0 26 23/14 (-1/2,0/1) 0 26 5/3 1/1 1 13 17/10 (1/1,1/0) 0 26 46/27 (-2/1,1/0) 0 26 75/44 (-2/1,1/0) 0 26 29/17 -1/1 1 13 12/7 (-1/1,1/0) 0 26 7/4 (0/1,1/1) 0 26 16/9 (0/1,1/2) 0 26 25/14 1/1 2 2 34/19 (2/1,1/0) 0 26 9/5 1/1 1 13 11/6 (0/1,1/0) 0 26 13/7 1/1 1 13 2/1 (1/1,1/0) 0 26 9/4 1/0 4 2 16/7 (-3/1,1/0) 0 26 23/10 (-4/1,-3/1) 0 26 30/13 (-5/2,-2/1) 0 26 7/3 -1/1 1 13 26/11 (0/1,1/0) 0 26 19/8 (1/1,1/0) 0 26 31/13 1/1 1 13 12/5 (-4/1,1/0) 0 26 5/2 (-1/1,0/1) 0 26 18/7 (-2/3,-1/2) 0 26 31/12 (-5/9,-1/2) 0 26 75/29 -1/2 11 1 44/17 (-1/2,-6/13) 0 26 13/5 -1/3 1 13 21/8 (-1/2,-1/3) 0 26 29/11 -1/3 1 13 37/14 (-1/4,0/1) 0 26 8/3 (-1/4,0/1) 0 26 19/7 0/1 10 1 11/4 (0/1,1/6) 0 26 14/5 (1/4,1/3) 0 26 17/6 (1/3,1/2) 0 26 20/7 (1/2,6/11) 0 26 3/1 1/1 1 13 13/4 (2/1,1/0) 0 26 10/3 1/0 3 2 7/2 (-1/1,1/0) 0 26 25/7 -1/1 1 13 43/12 (-2/1,-1/1) 0 26 61/17 -1/1 1 1 18/5 (-1/1,1/0) 0 26 29/8 (-2/1,-3/2) 0 26 40/11 (-3/2,-4/3) 0 26 11/3 -1/1 1 13 15/4 (-1/1,-4/5) 0 26 34/9 (-2/3,-1/2) 0 26 19/5 -3/5 1 13 4/1 (-1/2,0/1) 0 26 21/5 0/1 10 1 17/4 (0/1,1/8) 0 26 30/7 (0/1,1/4) 0 26 13/3 1/3 1 13 22/5 (0/1,1/2) 0 26 9/2 (0/1,1/1) 0 26 14/3 (1/2,2/3) 0 26 19/4 (1/2,1/1) 0 26 43/9 1/1 2 1 24/5 (1/1,1/0) 0 26 5/1 1/1 1 13 11/2 1/0 2 2 17/3 -1/1 1 13 6/1 (-1/1,1/0) 0 26 13/2 (0/1,1/2) 0 26 7/1 -1/1 1 13 15/2 (-1/4,0/1) 0 26 23/3 0/1 6 1 8/1 (0/1,1/2) 0 26 9/1 -1/1 1 13 10/1 (0/1,1/0) 0 26 1/0 (0/1,1/0) 0 26 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(113,-18,44,-7) (0/1,1/6) -> (5/2,18/7) Hyperbolic Matrix(23,-4,132,-23) (1/6,2/11) -> (1/6,2/11) Reflection Matrix(65,-12,352,-65) (2/11,3/16) -> (2/11,3/16) Reflection Matrix(307,-58,524,-99) (3/16,1/5) -> (7/12,17/29) Glide Reflection Matrix(237,-50,128,-27) (1/5,3/14) -> (11/6,13/7) Hyperbolic Matrix(213,-46,514,-111) (3/14,2/9) -> (12/29,5/12) Hyperbolic Matrix(401,-92,170,-39) (2/9,3/13) -> (7/3,26/11) Hyperbolic Matrix(233,-54,548,-127) (3/13,4/17) -> (14/33,3/7) Hyperbolic Matrix(169,-40,714,-169) (4/17,5/21) -> (4/17,5/21) Reflection Matrix(41,-10,168,-41) (5/21,1/4) -> (5/21,1/4) Reflection Matrix(61,-16,42,-11) (1/4,2/7) -> (10/7,3/2) Hyperbolic Matrix(61,-18,200,-59) (2/7,3/10) -> (3/10,4/13) Parabolic Matrix(457,-142,634,-197) (4/13,5/16) -> (18/25,13/18) Glide Reflection Matrix(771,-242,634,-199) (5/16,6/19) -> (17/14,28/23) Glide Reflection Matrix(117,-38,40,-13) (6/19,1/3) -> (20/7,3/1) Glide Reflection Matrix(133,-48,230,-83) (1/3,4/11) -> (4/7,11/19) Hyperbolic Matrix(153,-56,418,-153) (4/11,7/19) -> (4/11,7/19) Reflection Matrix(113,-42,304,-113) (7/19,3/8) -> (7/19,3/8) Reflection Matrix(131,-50,76,-29) (3/8,2/5) -> (12/7,7/4) Hyperbolic Matrix(241,-98,332,-135) (2/5,7/17) -> (21/29,8/11) Hyperbolic Matrix(479,-198,404,-167) (7/17,12/29) -> (13/11,6/5) Glide Reflection Matrix(367,-154,622,-261) (5/12,8/19) -> (10/17,13/22) Hyperbolic Matrix(1591,-672,438,-185) (8/19,11/26) -> (29/8,40/11) Hyperbolic Matrix(3671,-1556,2154,-913) (11/26,14/33) -> (46/27,75/44) Hyperbolic Matrix(235,-102,182,-79) (3/7,7/16) -> (9/7,13/10) Glide Reflection Matrix(127,-56,288,-127) (7/16,4/9) -> (7/16,4/9) Reflection Matrix(17,-8,36,-17) (4/9,1/2) -> (4/9,1/2) Reflection Matrix(609,-326,170,-91) (1/2,7/13) -> (25/7,43/12) Hyperbolic Matrix(1671,-902,980,-529) (7/13,13/24) -> (75/44,29/17) Hyperbolic Matrix(269,-146,304,-165) (13/24,6/11) -> (7/8,8/9) Glide Reflection Matrix(217,-120,302,-167) (6/11,5/9) -> (5/7,18/25) Hyperbolic Matrix(1319,-736,500,-279) (5/9,19/34) -> (29/11,37/14) Glide Reflection Matrix(951,-532,1700,-951) (19/34,14/25) -> (19/34,14/25) Reflection Matrix(449,-252,800,-449) (14/25,9/16) -> (14/25,9/16) Reflection Matrix(549,-310,232,-131) (9/16,4/7) -> (26/11,19/8) Hyperbolic Matrix(659,-382,954,-553) (11/19,18/31) -> (20/29,9/13) Hyperbolic Matrix(905,-526,394,-229) (18/31,7/12) -> (16/7,23/10) Glide Reflection Matrix(999,-586,820,-481) (17/29,10/17) -> (28/23,11/9) Hyperbolic Matrix(229,-136,32,-19) (13/22,3/5) -> (7/1,15/2) Hyperbolic Matrix(81,-50,128,-79) (3/5,5/8) -> (5/8,7/11) Parabolic Matrix(413,-264,158,-101) (7/11,9/14) -> (13/5,21/8) Glide Reflection Matrix(807,-520,284,-183) (9/14,20/31) -> (17/6,20/7) Glide Reflection Matrix(2321,-1500,1422,-919) (20/31,11/17) -> (31/19,80/49) Hyperbolic Matrix(125,-82,32,-21) (11/17,2/3) -> (19/5,4/1) Glide Reflection Matrix(787,-540,462,-317) (2/3,11/16) -> (17/10,46/27) Hyperbolic Matrix(1709,-1178,1046,-721) (11/16,20/29) -> (49/30,18/11) Glide Reflection Matrix(199,-138,62,-43) (9/13,7/10) -> (3/1,13/4) Glide Reflection Matrix(167,-118,92,-65) (7/10,5/7) -> (9/5,11/6) Hyperbolic Matrix(935,-676,574,-415) (13/18,21/29) -> (13/8,31/19) Glide Reflection Matrix(241,-176,330,-241) (8/11,11/15) -> (8/11,11/15) Reflection Matrix(89,-66,120,-89) (11/15,3/4) -> (11/15,3/4) Reflection Matrix(73,-56,30,-23) (3/4,4/5) -> (12/5,5/2) Hyperbolic Matrix(129,-106,28,-23) (4/5,5/6) -> (9/2,14/3) Hyperbolic Matrix(71,-60,84,-71) (5/6,6/7) -> (5/6,6/7) Reflection Matrix(97,-84,112,-97) (6/7,7/8) -> (6/7,7/8) Reflection Matrix(205,-186,54,-49) (8/9,1/1) -> (34/9,19/5) Glide Reflection Matrix(85,-98,72,-83) (1/1,7/6) -> (7/6,13/11) Parabolic Matrix(505,-612,118,-143) (6/5,17/14) -> (17/4,30/7) Hyperbolic Matrix(163,-202,46,-57) (11/9,5/4) -> (7/2,25/7) Hyperbolic Matrix(413,-524,160,-203) (5/4,14/11) -> (18/7,31/12) Hyperbolic Matrix(297,-380,68,-87) (14/11,9/7) -> (13/3,22/5) Hyperbolic Matrix(191,-250,68,-89) (13/10,4/3) -> (14/5,17/6) Hyperbolic Matrix(89,-120,66,-89) (4/3,15/11) -> (4/3,15/11) Reflection Matrix(241,-330,176,-241) (15/11,11/8) -> (15/11,11/8) Reflection Matrix(163,-226,44,-61) (11/8,7/5) -> (11/3,15/4) Hyperbolic Matrix(453,-640,172,-243) (7/5,17/12) -> (21/8,29/11) Hyperbolic Matrix(301,-428,64,-91) (17/12,10/7) -> (14/3,19/4) Hyperbolic Matrix(31,-48,20,-31) (3/2,8/5) -> (3/2,8/5) Reflection Matrix(129,-208,80,-129) (8/5,13/8) -> (8/5,13/8) Reflection Matrix(12641,-20640,7742,-12641) (80/49,129/79) -> (80/49,129/79) Reflection Matrix(7741,-12642,4740,-7741) (129/79,49/30) -> (129/79,49/30) Reflection Matrix(571,-936,158,-259) (18/11,23/14) -> (18/5,29/8) Glide Reflection Matrix(137,-226,20,-33) (23/14,5/3) -> (13/2,7/1) Glide Reflection Matrix(367,-622,154,-261) (5/3,17/10) -> (19/8,31/13) Hyperbolic Matrix(221,-378,38,-65) (29/17,12/7) -> (17/3,6/1) Glide Reflection Matrix(169,-298,38,-67) (7/4,16/9) -> (22/5,9/2) Hyperbolic Matrix(701,-1250,392,-699) (16/9,25/14) -> (25/14,34/19) Parabolic Matrix(409,-734,112,-201) (34/19,9/5) -> (40/11,11/3) Glide Reflection Matrix(173,-322,36,-67) (13/7,2/1) -> (24/5,5/1) Hyperbolic Matrix(73,-162,32,-71) (2/1,9/4) -> (9/4,16/7) Parabolic Matrix(535,-1232,142,-327) (23/10,30/13) -> (15/4,34/9) Glide Reflection Matrix(141,-326,16,-37) (30/13,7/3) -> (8/1,9/1) Glide Reflection Matrix(637,-1520,246,-587) (31/13,12/5) -> (44/17,13/5) Hyperbolic Matrix(1799,-4650,696,-1799) (31/12,75/29) -> (31/12,75/29) Reflection Matrix(2551,-6600,986,-2551) (75/29,44/17) -> (75/29,44/17) Reflection Matrix(143,-378,14,-37) (37/14,8/3) -> (10/1,1/0) Hyperbolic Matrix(113,-304,42,-113) (8/3,19/7) -> (8/3,19/7) Reflection Matrix(153,-418,56,-153) (19/7,11/4) -> (19/7,11/4) Reflection Matrix(89,-248,14,-39) (11/4,14/5) -> (6/1,13/2) Hyperbolic Matrix(79,-260,24,-79) (13/4,10/3) -> (13/4,10/3) Reflection Matrix(41,-140,12,-41) (10/3,7/2) -> (10/3,7/2) Reflection Matrix(1463,-5246,408,-1463) (43/12,61/17) -> (43/12,61/17) Reflection Matrix(611,-2196,170,-611) (61/17,18/5) -> (61/17,18/5) Reflection Matrix(41,-168,10,-41) (4/1,21/5) -> (4/1,21/5) Reflection Matrix(169,-714,40,-169) (21/5,17/4) -> (21/5,17/4) Reflection Matrix(93,-400,10,-43) (30/7,13/3) -> (9/1,10/1) Hyperbolic Matrix(343,-1634,72,-343) (19/4,43/9) -> (19/4,43/9) Reflection Matrix(431,-2064,90,-431) (43/9,24/5) -> (43/9,24/5) Reflection Matrix(45,-242,8,-43) (5/1,11/2) -> (11/2,17/3) Parabolic Matrix(91,-690,12,-91) (15/2,23/3) -> (15/2,23/3) Reflection Matrix(47,-368,6,-47) (23/3,8/1) -> (23/3,8/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,4,-1) (-1/1,0/1) -> (0/1,1/2) Matrix(113,-18,44,-7) -> Matrix(3,-2,-4,3) Matrix(23,-4,132,-23) -> Matrix(5,-4,6,-5) (1/6,2/11) -> (2/3,1/1) Matrix(65,-12,352,-65) -> Matrix(3,-4,2,-3) (2/11,3/16) -> (1/1,2/1) Matrix(307,-58,524,-99) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(237,-50,128,-27) -> Matrix(1,0,0,1) Matrix(213,-46,514,-111) -> Matrix(1,0,0,1) Matrix(401,-92,170,-39) -> Matrix(1,0,-2,1) 0/1 Matrix(233,-54,548,-127) -> Matrix(1,0,0,1) Matrix(169,-40,714,-169) -> Matrix(1,0,4,-1) (4/17,5/21) -> (0/1,1/2) Matrix(41,-10,168,-41) -> Matrix(3,-2,4,-3) (5/21,1/4) -> (1/2,1/1) Matrix(61,-16,42,-11) -> Matrix(3,-2,2,-1) 1/1 Matrix(61,-18,200,-59) -> Matrix(5,-4,4,-3) 1/1 Matrix(457,-142,634,-197) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(771,-242,634,-199) -> Matrix(1,-2,4,-9) Matrix(117,-38,40,-13) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(133,-48,230,-83) -> Matrix(1,0,2,1) 0/1 Matrix(153,-56,418,-153) -> Matrix(-1,0,4,1) (4/11,7/19) -> (-1/2,0/1) Matrix(113,-42,304,-113) -> Matrix(1,0,6,-1) (7/19,3/8) -> (0/1,1/3) Matrix(131,-50,76,-29) -> Matrix(1,0,-2,1) 0/1 Matrix(241,-98,332,-135) -> Matrix(3,-4,4,-5) 1/1 Matrix(479,-198,404,-167) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(367,-154,622,-261) -> Matrix(1,0,-2,1) 0/1 Matrix(1591,-672,438,-185) -> Matrix(1,-2,0,1) 1/0 Matrix(3671,-1556,2154,-913) -> Matrix(5,-2,-2,1) Matrix(235,-102,182,-79) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(127,-56,288,-127) -> Matrix(3,-2,4,-3) (7/16,4/9) -> (1/2,1/1) Matrix(17,-8,36,-17) -> Matrix(1,0,2,-1) (4/9,1/2) -> (0/1,1/1) Matrix(609,-326,170,-91) -> Matrix(1,-2,0,1) 1/0 Matrix(1671,-902,980,-529) -> Matrix(1,-2,0,1) 1/0 Matrix(269,-146,304,-165) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(217,-120,302,-167) -> Matrix(1,-2,2,-3) 1/1 Matrix(1319,-736,500,-279) -> Matrix(1,-2,-4,7) Matrix(951,-532,1700,-951) -> Matrix(-1,4,0,1) (19/34,14/25) -> (2/1,1/0) Matrix(449,-252,800,-449) -> Matrix(-1,2,0,1) (14/25,9/16) -> (1/1,1/0) Matrix(549,-310,232,-131) -> Matrix(1,0,0,1) Matrix(659,-382,954,-553) -> Matrix(5,-2,8,-3) 1/2 Matrix(905,-526,394,-229) -> Matrix(7,-4,-2,1) Matrix(999,-586,820,-481) -> Matrix(1,-2,4,-7) Matrix(229,-136,32,-19) -> Matrix(1,0,-2,1) 0/1 Matrix(81,-50,128,-79) -> Matrix(1,0,2,1) 0/1 Matrix(413,-264,158,-101) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(807,-520,284,-183) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(2321,-1500,1422,-919) -> Matrix(11,-6,2,-1) Matrix(125,-82,32,-21) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(787,-540,462,-317) -> Matrix(5,-2,-2,1) Matrix(1709,-1178,1046,-721) -> Matrix(7,-4,-2,1) Matrix(199,-138,62,-43) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(167,-118,92,-65) -> Matrix(3,-2,2,-1) 1/1 Matrix(935,-676,574,-415) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(241,-176,330,-241) -> Matrix(11,-10,12,-11) (8/11,11/15) -> (5/6,1/1) Matrix(89,-66,120,-89) -> Matrix(3,-4,2,-3) (11/15,3/4) -> (1/1,2/1) Matrix(73,-56,30,-23) -> Matrix(1,-2,0,1) 1/0 Matrix(129,-106,28,-23) -> Matrix(1,0,2,1) 0/1 Matrix(71,-60,84,-71) -> Matrix(-1,0,2,1) (5/6,6/7) -> (-1/1,0/1) Matrix(97,-84,112,-97) -> Matrix(1,0,8,-1) (6/7,7/8) -> (0/1,1/4) Matrix(205,-186,54,-49) -> Matrix(5,-2,-8,3) Matrix(85,-98,72,-83) -> Matrix(1,0,4,1) 0/1 Matrix(505,-612,118,-143) -> Matrix(1,0,2,1) 0/1 Matrix(163,-202,46,-57) -> Matrix(5,-2,-2,1) Matrix(413,-524,160,-203) -> Matrix(7,-4,-12,7) Matrix(297,-380,68,-87) -> Matrix(3,-2,8,-5) 1/2 Matrix(191,-250,68,-89) -> Matrix(3,-2,8,-5) 1/2 Matrix(89,-120,66,-89) -> Matrix(7,-6,8,-7) (4/3,15/11) -> (3/4,1/1) Matrix(241,-330,176,-241) -> Matrix(15,-16,14,-15) (15/11,11/8) -> (1/1,8/7) Matrix(163,-226,44,-61) -> Matrix(3,-4,-2,3) Matrix(453,-640,172,-243) -> Matrix(1,-2,-2,5) Matrix(301,-428,64,-91) -> Matrix(1,-2,2,-3) 1/1 Matrix(31,-48,20,-31) -> Matrix(-1,2,0,1) (3/2,8/5) -> (1/1,1/0) Matrix(129,-208,80,-129) -> Matrix(1,0,0,-1) (8/5,13/8) -> (0/1,1/0) Matrix(12641,-20640,7742,-12641) -> Matrix(-1,28,0,1) (80/49,129/79) -> (14/1,1/0) Matrix(7741,-12642,4740,-7741) -> Matrix(1,14,0,-1) (129/79,49/30) -> (-7/1,1/0) Matrix(571,-936,158,-259) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(137,-226,20,-33) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(367,-622,154,-261) -> Matrix(1,0,0,1) Matrix(221,-378,38,-65) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(169,-298,38,-67) -> Matrix(1,0,0,1) Matrix(701,-1250,392,-699) -> Matrix(3,-2,2,-1) 1/1 Matrix(409,-734,112,-201) -> Matrix(3,-2,-2,1) Matrix(173,-322,36,-67) -> Matrix(1,0,0,1) Matrix(73,-162,32,-71) -> Matrix(1,-4,0,1) 1/0 Matrix(535,-1232,142,-327) -> Matrix(3,8,-4,-11) Matrix(141,-326,16,-37) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(637,-1520,246,-587) -> Matrix(1,-2,-2,5) Matrix(1799,-4650,696,-1799) -> Matrix(19,10,-36,-19) (31/12,75/29) -> (-5/9,-1/2) Matrix(2551,-6600,986,-2551) -> Matrix(25,12,-52,-25) (75/29,44/17) -> (-1/2,-6/13) Matrix(143,-378,14,-37) -> Matrix(1,0,4,1) 0/1 Matrix(113,-304,42,-113) -> Matrix(-1,0,8,1) (8/3,19/7) -> (-1/4,0/1) Matrix(153,-418,56,-153) -> Matrix(1,0,12,-1) (19/7,11/4) -> (0/1,1/6) Matrix(89,-248,14,-39) -> Matrix(1,0,-4,1) 0/1 Matrix(79,-260,24,-79) -> Matrix(-1,4,0,1) (13/4,10/3) -> (2/1,1/0) Matrix(41,-140,12,-41) -> Matrix(1,2,0,-1) (10/3,7/2) -> (-1/1,1/0) Matrix(1463,-5246,408,-1463) -> Matrix(3,4,-2,-3) (43/12,61/17) -> (-2/1,-1/1) Matrix(611,-2196,170,-611) -> Matrix(1,2,0,-1) (61/17,18/5) -> (-1/1,1/0) Matrix(41,-168,10,-41) -> Matrix(-1,0,4,1) (4/1,21/5) -> (-1/2,0/1) Matrix(169,-714,40,-169) -> Matrix(1,0,16,-1) (21/5,17/4) -> (0/1,1/8) Matrix(93,-400,10,-43) -> Matrix(1,0,-4,1) 0/1 Matrix(343,-1634,72,-343) -> Matrix(3,-2,4,-3) (19/4,43/9) -> (1/2,1/1) Matrix(431,-2064,90,-431) -> Matrix(-1,2,0,1) (43/9,24/5) -> (1/1,1/0) Matrix(45,-242,8,-43) -> Matrix(1,-2,0,1) 1/0 Matrix(91,-690,12,-91) -> Matrix(-1,0,8,1) (15/2,23/3) -> (-1/4,0/1) Matrix(47,-368,6,-47) -> Matrix(1,0,4,-1) (23/3,8/1) -> (0/1,1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.