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: 48 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 0/1 2/11 3/10 4/9 1/2 14/25 5/8 6/7 1/1 7/6 15/11 7/5 3/2 8/5 33/19 25/14 2/1 9/4 7/3 73/31 5/2 75/29 13/5 8/3 19/7 3/1 10/3 17/5 7/2 61/17 11/3 41/11 19/5 103/27 4/1 21/5 13/3 9/2 43/9 5/1 11/2 17/3 6/1 7/1 23/3 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 -1/2 -1/1 0/1 -6/13 -2/3 -3/5 -5/11 0/1 -14/31 -2/1 -1/1 -9/20 -1/1 0/1 -13/29 -1/1 1/0 -4/9 -1/1 -2/3 -15/34 -1/1 -2/3 -11/25 -2/3 -7/16 -2/3 -3/5 -3/7 -1/2 0/1 -8/19 -1/1 0/1 -13/31 0/1 -18/43 -2/1 -1/1 -5/12 -1/1 0/1 -17/41 -1/1 -1/2 -12/29 -2/1 -1/1 -19/46 -1/1 -2/3 -26/63 -1/1 -2/3 -7/17 -2/3 -2/5 -1/3 0/1 -11/28 0/1 1/1 -9/23 0/1 -16/41 -2/1 -1/1 -7/18 -1/1 0/1 -19/49 0/1 -12/31 0/1 1/1 -17/44 -2/1 -1/1 -22/57 -6/5 -1/1 -5/13 -1/1 -1/2 -3/8 -1/3 0/1 -10/27 -2/9 -1/5 -27/73 0/1 -17/46 -1/5 0/1 -7/19 -1/6 0/1 -4/11 0/1 1/3 -9/25 -1/1 1/0 -23/64 -1/1 0/1 -14/39 -2/1 -1/1 -19/53 0/1 -5/14 -1/1 0/1 -16/45 -1/5 0/1 -11/31 0/1 1/0 -17/48 -1/1 0/1 -23/65 0/1 -6/17 -1/1 0/1 -1/3 0/1 -5/16 -1/1 0/1 -14/45 -1/1 0/1 -9/29 -1/2 0/1 -4/13 -1/1 0/1 -11/36 -1/1 -2/3 -7/23 -1/1 -1/2 -3/10 -1/5 0/1 -8/27 0/1 1/13 -5/17 0/1 1/4 -12/41 0/1 1/3 -7/24 1/3 2/5 -2/7 0/1 1/1 -3/11 -1/1 1/0 -7/26 -1/3 0/1 -11/41 0/1 -15/56 -1/1 0/1 -4/15 -1/1 0/1 -9/34 -1/1 -2/3 -5/19 0/1 -1/4 0/1 1/1 -3/13 -2/1 -17/74 -2/1 -1/1 -14/61 -2/1 -1/1 -11/48 -2/1 -1/1 -8/35 -2/1 -1/1 -5/22 -1/1 -2/3 -7/31 -1/1 1/0 -2/9 -1/1 0/1 -7/32 -1/1 -2/3 -12/55 -1/1 0/1 -17/78 -1/1 0/1 -5/23 0/1 -3/14 -1/1 0/1 -4/19 0/1 1/1 -1/5 0/1 1/0 -2/11 -3/1 -2/1 -7/39 -5/2 -2/1 -12/67 -15/7 -2/1 -5/28 -2/1 -5/3 -3/17 -2/1 -7/40 -2/1 -1/1 -4/23 -2/1 -1/1 -1/6 -2/1 -1/1 -4/25 -1/1 -4/5 -3/19 -1/1 -1/2 -5/32 -1/1 -2/3 -2/13 -1/1 0/1 -3/20 -1/1 -2/3 -4/27 -1/1 0/1 -5/34 -1/1 0/1 -1/7 0/1 -1/8 -3/1 -2/1 -1/9 -3/2 -1/1 -2/19 -10/9 -1/1 -1/10 -1/1 -4/5 0/1 -1/1 0/1 1/6 -2/3 -3/5 4/23 -8/13 -3/5 3/17 -4/7 -1/2 2/11 -1/2 3/16 -3/7 -2/5 1/5 0/1 3/14 -2/1 -1/1 2/9 -1/1 0/1 3/13 -1/1 1/0 1/4 -1/1 -2/3 4/15 -1/1 -2/3 3/11 -2/3 2/7 -2/3 -3/5 7/24 -4/7 -5/9 19/65 -4/7 -9/16 12/41 -24/43 -5/9 5/17 -6/11 3/10 -1/2 4/13 -3/7 -2/5 1/3 -1/2 0/1 3/8 -1/1 0/1 8/21 -1/1 0/1 5/13 0/1 7/18 -2/1 -1/1 9/23 -2/3 -1/2 2/5 -1/1 0/1 9/22 -1/1 0/1 7/17 -1/1 -1/2 12/29 -1/1 0/1 5/12 -2/1 -1/1 8/19 -1/1 -2/3 11/26 -1/1 -2/3 3/7 -2/3 7/16 -4/7 -5/9 4/9 -1/2 5/11 -1/2 -3/7 6/13 -2/5 -5/13 7/15 -2/5 1/2 -1/3 0/1 6/11 0/1 1/1 5/9 0/1 19/34 1/1 2/1 14/25 1/0 23/41 -2/1 1/0 9/16 -2/1 -1/1 4/7 -1/1 0/1 11/19 0/1 7/12 0/1 1/1 10/17 -2/1 -1/1 13/22 -6/5 -1/1 3/5 -1/1 -1/2 8/13 -2/3 -3/5 5/8 -1/2 12/19 -4/9 -3/7 7/11 -2/5 16/25 -2/5 -1/3 41/64 -2/5 -1/3 25/39 -1/2 -2/5 9/14 -2/5 -1/3 29/45 -4/11 20/31 -10/29 -1/3 11/17 -1/3 -1/4 13/20 -1/3 0/1 2/3 -1/3 0/1 11/16 -4/11 -1/3 9/13 -2/7 7/10 -2/9 -1/5 19/27 0/1 12/17 -1/5 0/1 17/24 -1/5 0/1 22/31 -1/5 0/1 5/7 -1/6 0/1 3/4 0/1 1/3 13/17 0/1 23/30 6/7 1/1 10/13 1/1 2/1 7/9 -1/1 1/0 18/23 -1/1 0/1 11/14 -2/1 -1/1 15/19 0/1 4/5 -1/1 0/1 13/16 -1/5 0/1 9/11 0/1 1/0 23/28 -4/3 -1/1 14/17 -1/1 0/1 19/23 0/1 5/6 -1/1 0/1 16/19 -2/1 -1/1 11/13 -1/1 -1/2 6/7 -1/2 7/8 -1/3 0/1 1/1 0/1 8/7 0/1 1/1 7/6 1/0 20/17 -2/1 -1/1 13/11 -1/1 1/0 19/16 -1/1 -2/3 6/5 -1/1 0/1 17/14 -1/1 0/1 11/9 -1/2 0/1 5/4 -1/1 0/1 14/11 -1/1 -2/3 9/7 -1/1 -1/2 22/17 -1/2 13/10 -2/5 -1/3 4/3 -1/5 0/1 15/11 0/1 26/19 0/1 1/31 11/8 0/1 1/13 7/5 0/1 1/4 17/12 0/1 1/3 10/7 1/3 2/5 23/16 1/2 13/9 2/3 16/11 1/1 4/3 3/2 0/1 1/1 20/13 0/1 1/1 17/11 1/2 1/1 48/31 12/13 1/1 79/51 1/1 31/20 1/1 10/9 14/9 1/1 2/1 39/25 2/1 1/0 25/16 1/1 2/1 11/7 2/1 8/5 1/0 21/13 -4/1 34/21 -4/1 -3/1 81/50 -28/9 -3/1 47/29 -3/1 -5/2 13/8 -3/1 -2/1 5/3 -1/1 1/0 12/7 -1/3 0/1 31/18 -2/1 -1/1 50/29 -1/1 -6/7 19/11 0/1 26/15 -1/1 0/1 33/19 -1/2 1/0 40/23 -1/1 0/1 7/4 -1/1 0/1 16/9 -1/1 -2/3 57/32 -1/1 -2/3 41/23 -2/3 -1/2 25/14 -1/2 59/33 -1/2 -2/5 34/19 -2/5 -1/3 9/5 0/1 2/1 0/1 1/1 15/7 2/1 13/6 5/3 2/1 11/5 3/1 1/0 9/4 1/0 25/11 -7/1 1/0 16/7 -5/1 -4/1 7/3 -2/1 40/17 -2/1 -1/1 73/31 -3/2 1/0 106/45 -2/1 -1/1 33/14 -2/1 -1/1 26/11 -2/1 -1/1 19/8 -2/1 -1/1 12/5 -1/1 -2/3 17/7 -1/1 1/0 5/2 -1/1 0/1 28/11 1/0 23/9 -2/1 1/0 41/16 -2/1 -1/1 18/7 -1/1 -2/3 31/12 -1/1 0/1 75/29 -1/2 1/0 119/46 -1/1 0/1 44/17 -1/1 0/1 13/5 0/1 34/13 -2/1 -1/1 21/8 -1/1 0/1 29/11 0/1 1/0 66/25 1/0 37/14 -1/1 0/1 8/3 -1/1 0/1 19/7 0/1 30/11 0/1 1/3 11/4 0/1 1/1 3/1 0/1 1/0 13/4 2/1 3/1 10/3 1/0 27/8 -10/1 -9/1 17/5 -6/1 58/17 -16/3 -5/1 41/12 -5/1 -24/5 24/7 -5/1 -4/1 7/2 -3/1 -2/1 25/7 -5/2 -2/1 43/12 -15/7 -2/1 61/17 -2/1 79/22 -2/1 -25/13 18/5 -2/1 -5/3 11/3 -2/1 26/7 -2/1 -1/1 41/11 -3/2 1/0 56/15 -2/1 -1/1 15/4 -2/1 -1/1 19/5 -3/2 -1/1 61/16 -14/13 -1/1 103/27 -1/1 42/11 -1/1 -8/9 23/6 -1/1 0/1 4/1 -2/1 -1/1 21/5 -1/1 38/9 -1/1 -10/11 17/4 -1/1 -4/5 13/3 -1/1 -1/2 22/5 -1/1 -2/3 9/2 -1/1 0/1 32/7 1/0 23/5 -1/1 1/0 14/3 -1/1 -2/3 19/4 -1/1 0/1 43/9 -1/2 1/0 67/14 -1/1 0/1 24/5 -1/1 0/1 5/1 0/1 16/3 2/1 3/1 11/2 1/0 28/5 -6/1 -5/1 17/3 -4/1 1/0 40/7 -4/1 -3/1 23/4 -3/1 -8/3 6/1 -3/1 -2/1 7/1 -3/2 -1/1 15/2 -10/9 -1/1 23/3 -1/1 31/4 -1/1 -18/19 8/1 -1/1 -4/5 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(245,114,-634,-295) (-1/2,-6/13) -> (-12/31,-17/44) Hyperbolic Matrix(241,110,46,21) (-6/13,-5/11) -> (5/1,16/3) Hyperbolic Matrix(947,428,-2560,-1157) (-5/11,-14/31) -> (-10/27,-27/73) Hyperbolic Matrix(475,214,566,255) (-14/31,-9/20) -> (5/6,16/19) Hyperbolic Matrix(847,380,-2356,-1057) (-9/20,-13/29) -> (-9/25,-23/64) Hyperbolic Matrix(143,64,-896,-401) (-13/29,-4/9) -> (-4/25,-3/19) Hyperbolic Matrix(185,82,282,125) (-4/9,-15/34) -> (13/20,2/3) Hyperbolic Matrix(277,122,-1578,-695) (-15/34,-11/25) -> (-3/17,-7/40) Hyperbolic Matrix(419,184,-1068,-469) (-11/25,-7/16) -> (-11/28,-9/23) Hyperbolic Matrix(139,60,44,19) (-7/16,-3/7) -> (3/1,13/4) Hyperbolic Matrix(47,20,-228,-97) (-3/7,-8/19) -> (-4/19,-1/5) Hyperbolic Matrix(629,264,984,413) (-8/19,-13/31) -> (7/11,16/25) Hyperbolic Matrix(1251,524,-3488,-1461) (-13/31,-18/43) -> (-14/39,-19/53) Hyperbolic Matrix(91,38,534,223) (-18/43,-5/12) -> (1/6,4/23) Hyperbolic Matrix(665,276,1024,425) (-5/12,-17/41) -> (11/17,13/20) Hyperbolic Matrix(975,404,1156,479) (-17/41,-12/29) -> (16/19,11/13) Hyperbolic Matrix(1505,622,-3898,-1611) (-12/29,-19/46) -> (-17/44,-22/57) Hyperbolic Matrix(3319,1370,5182,2139) (-19/46,-26/63) -> (16/25,41/64) Hyperbolic Matrix(1551,640,-4384,-1809) (-26/63,-7/17) -> (-23/65,-6/17) Hyperbolic Matrix(307,126,134,55) (-7/17,-2/5) -> (16/7,7/3) Hyperbolic Matrix(473,186,-1330,-523) (-2/5,-11/28) -> (-5/14,-16/45) Hyperbolic Matrix(1151,450,642,251) (-9/23,-16/41) -> (34/19,9/5) Hyperbolic Matrix(1195,466,-3326,-1297) (-16/41,-7/18) -> (-23/64,-14/39) Hyperbolic Matrix(933,362,-3482,-1351) (-7/18,-19/49) -> (-11/41,-15/56) Hyperbolic Matrix(511,198,1102,427) (-19/49,-12/31) -> (6/13,7/15) Hyperbolic Matrix(83,32,-760,-293) (-22/57,-5/13) -> (-1/9,-2/19) Hyperbolic Matrix(209,80,128,49) (-5/13,-3/8) -> (13/8,5/3) Hyperbolic Matrix(205,76,704,261) (-3/8,-10/27) -> (2/7,7/24) Hyperbolic Matrix(411,152,-2804,-1037) (-27/73,-17/46) -> (-5/34,-1/7) Hyperbolic Matrix(1321,488,2060,761) (-17/46,-7/19) -> (25/39,9/14) Hyperbolic Matrix(207,76,-700,-257) (-7/19,-4/11) -> (-8/27,-5/17) Hyperbolic Matrix(205,74,446,161) (-4/11,-9/25) -> (5/11,6/13) Hyperbolic Matrix(971,348,-4456,-1597) (-19/53,-5/14) -> (-17/78,-5/23) Hyperbolic Matrix(687,244,-3832,-1361) (-16/45,-11/31) -> (-7/39,-12/67) Hyperbolic Matrix(1129,400,3864,1369) (-11/31,-17/48) -> (7/24,19/65) Hyperbolic Matrix(1249,442,-5434,-1923) (-17/48,-23/65) -> (-3/13,-17/74) Hyperbolic Matrix(41,14,38,13) (-6/17,-1/3) -> (1/1,8/7) Hyperbolic Matrix(37,12,40,13) (-1/3,-5/16) -> (7/8,1/1) Hyperbolic Matrix(719,224,-3136,-977) (-5/16,-14/45) -> (-14/61,-11/48) Hyperbolic Matrix(1925,598,338,105) (-14/45,-9/29) -> (17/3,40/7) 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(409,124,188,57) (-7/23,-3/10) -> (13/6,11/5) Hyperbolic Matrix(557,166,406,121) (-3/10,-8/27) -> (26/19,11/8) Hyperbolic Matrix(1837,538,1178,345) (-5/17,-12/41) -> (14/9,39/25) Hyperbolic Matrix(219,64,-1468,-429) (-12/41,-7/24) -> (-3/20,-4/27) Hyperbolic Matrix(625,182,182,53) (-7/24,-2/7) -> (24/7,7/2) Hyperbolic Matrix(109,30,178,49) (-2/7,-3/11) -> (3/5,8/13) Hyperbolic Matrix(37,10,-322,-87) (-3/11,-7/26) -> (-1/8,-1/9) Hyperbolic Matrix(923,248,428,115) (-7/26,-11/41) -> (15/7,13/6) Hyperbolic Matrix(2345,628,1348,361) (-15/56,-4/15) -> (40/23,7/4) Hyperbolic Matrix(143,38,-922,-245) (-4/15,-9/34) -> (-5/32,-2/13) Hyperbolic Matrix(531,140,952,251) (-9/34,-5/19) -> (5/9,19/34) Hyperbolic Matrix(107,28,-600,-157) (-5/19,-1/4) -> (-5/28,-3/17) Hyperbolic Matrix(103,24,236,55) (-1/4,-3/13) -> (3/7,7/16) Hyperbolic Matrix(9857,2264,4184,961) (-17/74,-14/61) -> (106/45,33/14) Hyperbolic Matrix(2763,632,1552,355) (-11/48,-8/35) -> (16/9,57/32) Hyperbolic Matrix(35,8,-372,-85) (-8/35,-5/22) -> (-1/10,0/1) Hyperbolic Matrix(875,198,738,167) (-5/22,-7/31) -> (13/11,19/16) Hyperbolic Matrix(773,174,502,113) (-7/31,-2/9) -> (20/13,17/11) Hyperbolic Matrix(399,88,68,15) (-2/9,-7/32) -> (23/4,6/1) Hyperbolic Matrix(9977,2176,3856,841) (-12/55,-17/78) -> (119/46,44/17) Hyperbolic Matrix(729,158,466,101) (-5/23,-3/14) -> (25/16,11/7) Hyperbolic Matrix(629,134,230,49) (-3/14,-4/19) -> (30/11,11/4) Hyperbolic Matrix(31,6,98,19) (-1/5,-2/11) -> (4/13,1/3) Hyperbolic Matrix(5797,1038,1614,289) (-12/67,-5/28) -> (79/22,18/5) Hyperbolic Matrix(2585,452,692,121) (-7/40,-4/23) -> (56/15,15/4) Hyperbolic Matrix(189,32,124,21) (-4/23,-1/6) -> (3/2,20/13) Hyperbolic Matrix(653,106,154,25) (-1/6,-4/25) -> (38/9,17/4) 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(29,4,152,21) (-1/7,-1/8) -> (3/16,1/5) Hyperbolic Matrix(669,70,86,9) (-2/19,-1/10) -> (31/4,8/1) Hyperbolic Matrix(67,-10,114,-17) (0/1,1/6) -> (7/12,10/17) Hyperbolic Matrix(641,-112,2192,-383) (4/23,3/17) -> (19/65,12/41) Hyperbolic Matrix(729,-130,286,-51) (3/17,2/11) -> (28/11,23/9) Hyperbolic Matrix(503,-94,198,-37) (2/11,3/16) -> (5/2,28/11) Hyperbolic Matrix(301,-64,428,-91) (1/5,3/14) -> (7/10,19/27) Hyperbolic Matrix(213,-46,514,-111) (3/14,2/9) -> (12/29,5/12) Hyperbolic Matrix(297,-68,380,-87) (2/9,3/13) -> (7/9,18/23) Hyperbolic Matrix(273,-64,64,-15) (3/13,1/4) -> (17/4,13/3) Hyperbolic Matrix(143,-38,350,-93) (1/4,4/15) -> (2/5,9/22) Hyperbolic Matrix(451,-122,122,-33) (4/15,3/11) -> (11/3,26/7) Hyperbolic Matrix(101,-28,184,-51) (3/11,2/7) -> (6/11,5/9) Hyperbolic Matrix(1529,-448,2372,-695) (12/41,5/17) -> (29/45,20/31) Hyperbolic Matrix(521,-154,362,-107) (5/17,3/10) -> (23/16,13/9) Hyperbolic Matrix(399,-122,278,-85) (3/10,4/13) -> (10/7,23/16) Hyperbolic Matrix(57,-20,20,-7) (1/3,3/8) -> (11/4,3/1) Hyperbolic Matrix(453,-172,640,-243) (3/8,8/21) -> (12/17,17/24) Hyperbolic Matrix(883,-338,546,-209) (8/21,5/13) -> (21/13,34/21) Hyperbolic Matrix(413,-160,524,-203) (5/13,7/18) -> (11/14,15/19) Hyperbolic Matrix(691,-270,842,-329) (7/18,9/23) -> (9/11,23/28) Hyperbolic Matrix(729,-286,130,-51) (9/23,2/5) -> (28/5,17/3) Hyperbolic Matrix(1255,-514,774,-317) (9/22,7/17) -> (47/29,13/8) Hyperbolic Matrix(717,-296,608,-251) (7/17,12/29) -> (20/17,13/11) Hyperbolic Matrix(367,-154,622,-261) (5/12,8/19) -> (10/17,13/22) Hyperbolic Matrix(895,-378,1262,-533) (8/19,11/26) -> (17/24,22/31) Hyperbolic Matrix(529,-224,640,-271) (11/26,3/7) -> (19/23,5/6) 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(193,-92,300,-143) (7/15,1/2) -> (9/14,29/45) Hyperbolic Matrix(151,-82,186,-101) (1/2,6/11) -> (4/5,13/16) 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(2081,-1168,3248,-1823) (23/41,9/16) -> (41/64,25/39) Hyperbolic Matrix(365,-206,466,-263) (9/16,4/7) -> (18/23,11/14) Hyperbolic Matrix(627,-362,362,-209) (4/7,11/19) -> (19/11,26/15) Hyperbolic Matrix(213,-124,280,-163) (11/19,7/12) -> (3/4,13/17) Hyperbolic Matrix(229,-136,32,-19) (13/22,3/5) -> (7/1,15/2) Hyperbolic Matrix(161,-100,256,-159) (8/13,5/8) -> (5/8,12/19) Parabolic Matrix(621,-394,238,-151) (12/19,7/11) -> (13/5,34/13) Hyperbolic Matrix(1343,-868,868,-561) (20/31,11/17) -> (17/11,48/31) Hyperbolic Matrix(293,-200,356,-243) (2/3,11/16) -> (23/28,14/17) Hyperbolic Matrix(507,-350,662,-457) (11/16,9/13) -> (13/17,23/30) Hyperbolic Matrix(521,-362,154,-107) (9/13,7/10) -> (27/8,17/5) Hyperbolic Matrix(733,-516,152,-107) (19/27,12/17) -> (24/5,5/1) Hyperbolic Matrix(2067,-1468,1156,-821) (22/31,5/7) -> (59/33,34/19) Hyperbolic Matrix(105,-76,76,-55) (5/7,3/4) -> (11/8,7/5) Hyperbolic Matrix(2073,-1592,1280,-983) (23/30,10/13) -> (34/21,81/50) Hyperbolic Matrix(469,-362,206,-159) (10/13,7/9) -> (25/11,16/7) Hyperbolic Matrix(901,-712,348,-275) (15/19,4/5) -> (44/17,13/5) Hyperbolic Matrix(873,-712,244,-199) (13/16,9/11) -> (25/7,43/12) Hyperbolic Matrix(1039,-858,442,-365) (14/17,19/23) -> (7/3,40/17) Hyperbolic Matrix(577,-490,126,-107) (11/13,6/7) -> (32/7,23/5) Hyperbolic Matrix(319,-278,70,-61) (6/7,7/8) -> (9/2,32/7) Hyperbolic Matrix(169,-196,144,-167) (8/7,7/6) -> (7/6,20/17) Parabolic Matrix(529,-640,224,-271) (6/5,17/14) -> (33/14,26/11) Hyperbolic Matrix(691,-842,270,-329) (17/14,11/9) -> (23/9,41/16) 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(213,-280,124,-163) (13/10,4/3) -> (12/7,31/18) Hyperbolic Matrix(331,-450,242,-329) (4/3,15/11) -> (15/11,26/19) Parabolic 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(659,-954,382,-553) (13/9,16/11) -> (50/29,19/11) Hyperbolic Matrix(487,-710,190,-277) (16/11,3/2) -> (41/16,18/7) Hyperbolic Matrix(5335,-8262,1398,-2165) (48/31,79/51) -> (103/27,42/11) Hyperbolic Matrix(5171,-8012,1356,-2101) (79/51,31/20) -> (61/16,103/27) Hyperbolic Matrix(1529,-2372,448,-695) (31/20,14/9) -> (58/17,41/12) Hyperbolic Matrix(2081,-3248,1168,-1823) (39/25,25/16) -> (57/32,41/23) Hyperbolic Matrix(161,-256,100,-159) (11/7,8/5) -> (8/5,21/13) Parabolic Matrix(2719,-4406,714,-1157) (81/50,47/29) -> (19/5,61/16) Hyperbolic Matrix(67,-114,10,-17) (5/3,12/7) -> (6/1,7/1) Hyperbolic Matrix(1423,-2452,372,-641) (31/18,50/29) -> (42/11,23/6) Hyperbolic Matrix(1255,-2178,722,-1253) (26/15,33/19) -> (33/19,40/23) Parabolic Matrix(169,-298,38,-67) (7/4,16/9) -> (22/5,9/2) Hyperbolic Matrix(1401,-2500,784,-1399) (41/23,25/14) -> (25/14,59/33) Parabolic Matrix(101,-184,28,-51) (9/5,2/1) -> (18/5,11/3) Hyperbolic Matrix(423,-904,124,-265) (2/1,15/7) -> (17/5,58/17) Hyperbolic Matrix(145,-324,64,-143) (11/5,9/4) -> (9/4,25/11) Parabolic Matrix(4527,-10658,1922,-4525) (40/17,73/31) -> (73/31,106/45) Parabolic Matrix(471,-1114,178,-421) (26/11,19/8) -> (37/14,8/3) Hyperbolic Matrix(69,-164,8,-19) (19/8,12/5) -> (8/1,1/0) Hyperbolic Matrix(213,-514,46,-111) (12/5,17/7) -> (23/5,14/3) Hyperbolic Matrix(143,-350,38,-93) (17/7,5/2) -> (15/4,19/5) 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(267,-722,98,-265) (8/3,19/7) -> (19/7,30/11) Parabolic Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(641,-2192,112,-383) (41/12,24/7) -> (40/7,23/4) Hyperbolic Matrix(2075,-7442,578,-2073) (43/12,61/17) -> (61/17,79/22) Parabolic Matrix(903,-3362,242,-901) (26/7,41/11) -> (41/11,56/15) Parabolic Matrix(211,-882,50,-209) (4/1,21/5) -> (21/5,38/9) Parabolic Matrix(775,-3698,162,-773) (19/4,43/9) -> (43/9,67/14) Parabolic Matrix(89,-484,16,-87) (16/3,11/2) -> (11/2,28/5) 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(1,0,0,1) Matrix(245,114,-634,-295) -> Matrix(3,2,-2,-1) Matrix(241,110,46,21) -> Matrix(1,0,2,1) Matrix(947,428,-2560,-1157) -> Matrix(1,0,-4,1) Matrix(475,214,566,255) -> Matrix(1,0,0,1) Matrix(847,380,-2356,-1057) -> Matrix(1,0,0,1) Matrix(143,64,-896,-401) -> Matrix(1,2,-2,-3) Matrix(185,82,282,125) -> Matrix(3,2,-8,-5) Matrix(277,122,-1578,-695) -> Matrix(5,4,-4,-3) Matrix(419,184,-1068,-469) -> Matrix(3,2,-2,-1) Matrix(139,60,44,19) -> Matrix(1,0,2,1) Matrix(47,20,-228,-97) -> Matrix(1,0,2,1) Matrix(629,264,984,413) -> Matrix(3,2,-8,-5) Matrix(1251,524,-3488,-1461) -> Matrix(1,0,0,1) Matrix(91,38,534,223) -> Matrix(5,2,-8,-3) Matrix(665,276,1024,425) -> Matrix(1,0,-2,1) Matrix(975,404,1156,479) -> Matrix(1,0,0,1) Matrix(1505,622,-3898,-1611) -> Matrix(5,4,-4,-3) Matrix(3319,1370,5182,2139) -> Matrix(5,4,-14,-11) Matrix(1551,640,-4384,-1809) -> Matrix(3,2,-2,-1) Matrix(307,126,134,55) -> Matrix(7,4,-2,-1) Matrix(473,186,-1330,-523) -> Matrix(1,0,-2,1) Matrix(1151,450,642,251) -> Matrix(1,0,-2,1) Matrix(1195,466,-3326,-1297) -> Matrix(1,0,0,1) Matrix(933,362,-3482,-1351) -> Matrix(1,0,0,1) Matrix(511,198,1102,427) -> Matrix(3,2,-8,-5) Matrix(83,32,-760,-293) -> Matrix(5,4,-4,-3) Matrix(209,80,128,49) -> Matrix(3,2,-2,-1) Matrix(205,76,704,261) -> Matrix(17,4,-30,-7) Matrix(411,152,-2804,-1037) -> Matrix(1,0,4,1) Matrix(1321,488,2060,761) -> Matrix(11,2,-28,-5) Matrix(207,76,-700,-257) -> Matrix(1,0,10,1) Matrix(205,74,446,161) -> Matrix(1,-2,-2,5) Matrix(971,348,-4456,-1597) -> Matrix(1,0,0,1) Matrix(687,244,-3832,-1361) -> Matrix(5,-2,-2,1) Matrix(1129,400,3864,1369) -> Matrix(9,4,-16,-7) Matrix(1249,442,-5434,-1923) -> Matrix(3,2,-2,-1) Matrix(41,14,38,13) -> Matrix(1,0,2,1) Matrix(37,12,40,13) -> Matrix(1,0,-2,1) Matrix(719,224,-3136,-977) -> Matrix(3,2,-2,-1) Matrix(1925,598,338,105) -> Matrix(7,4,-2,-1) Matrix(149,46,-826,-255) -> Matrix(1,-2,0,1) Matrix(523,160,-2396,-733) -> Matrix(1,0,0,1) Matrix(223,68,-1420,-433) -> Matrix(1,0,0,1) Matrix(409,124,188,57) -> Matrix(5,2,2,1) Matrix(557,166,406,121) -> Matrix(1,0,18,1) Matrix(1837,538,1178,345) -> Matrix(7,-2,4,-1) Matrix(219,64,-1468,-429) -> Matrix(1,0,-4,1) Matrix(625,182,182,53) -> Matrix(9,-4,-2,1) Matrix(109,30,178,49) -> Matrix(1,2,-2,-3) Matrix(37,10,-322,-87) -> Matrix(3,2,-2,-1) Matrix(923,248,428,115) -> Matrix(1,2,0,1) Matrix(2345,628,1348,361) -> Matrix(1,0,0,1) Matrix(143,38,-922,-245) -> Matrix(1,0,0,1) Matrix(531,140,952,251) -> Matrix(1,0,2,1) Matrix(107,28,-600,-157) -> Matrix(3,2,-2,-1) Matrix(103,24,236,55) -> Matrix(1,4,-2,-7) Matrix(9857,2264,4184,961) -> Matrix(1,0,0,1) Matrix(2763,632,1552,355) -> Matrix(3,4,-4,-5) Matrix(35,8,-372,-85) -> Matrix(1,2,-2,-3) Matrix(875,198,738,167) -> Matrix(1,0,0,1) Matrix(773,174,502,113) -> Matrix(1,0,2,1) Matrix(399,88,68,15) -> Matrix(1,-2,0,1) Matrix(9977,2176,3856,841) -> Matrix(1,0,0,1) Matrix(729,158,466,101) -> Matrix(1,2,0,1) Matrix(629,134,230,49) -> Matrix(1,0,2,1) Matrix(31,6,98,19) -> Matrix(1,0,-2,1) Matrix(5797,1038,1614,289) -> Matrix(19,40,-10,-21) Matrix(2585,452,692,121) -> Matrix(1,0,0,1) Matrix(189,32,124,21) -> Matrix(1,2,0,1) Matrix(653,106,154,25) -> Matrix(5,6,-6,-7) Matrix(367,56,308,47) -> Matrix(1,0,0,1) Matrix(2625,388,548,81) -> Matrix(1,0,0,1) Matrix(29,4,152,21) -> Matrix(1,0,-2,1) Matrix(669,70,86,9) -> Matrix(13,14,-14,-15) Matrix(67,-10,114,-17) -> Matrix(3,2,-2,-1) Matrix(641,-112,2192,-383) -> Matrix(55,32,-98,-57) Matrix(729,-130,286,-51) -> Matrix(11,6,-2,-1) Matrix(503,-94,198,-37) -> Matrix(5,2,2,1) Matrix(301,-64,428,-91) -> Matrix(1,0,-4,1) Matrix(213,-46,514,-111) -> Matrix(1,0,0,1) Matrix(297,-68,380,-87) -> Matrix(1,0,0,1) Matrix(273,-64,64,-15) -> Matrix(1,2,-2,-3) Matrix(143,-38,350,-93) -> Matrix(3,2,-2,-1) Matrix(451,-122,122,-33) -> Matrix(5,4,-4,-3) Matrix(101,-28,184,-51) -> Matrix(3,2,-2,-1) Matrix(1529,-448,2372,-695) -> Matrix(47,26,-132,-73) Matrix(521,-154,362,-107) -> Matrix(15,8,28,15) Matrix(399,-122,278,-85) -> Matrix(9,4,20,9) Matrix(57,-20,20,-7) -> Matrix(1,0,2,1) Matrix(453,-172,640,-243) -> Matrix(1,0,-4,1) Matrix(883,-338,546,-209) -> Matrix(7,4,-2,-1) Matrix(413,-160,524,-203) -> Matrix(1,0,0,1) Matrix(691,-270,842,-329) -> Matrix(3,2,-2,-1) Matrix(729,-286,130,-51) -> Matrix(11,6,-2,-1) Matrix(1255,-514,774,-317) -> Matrix(1,-2,0,1) Matrix(717,-296,608,-251) -> Matrix(3,2,-2,-1) Matrix(367,-154,622,-261) -> Matrix(5,4,-4,-3) Matrix(895,-378,1262,-533) -> Matrix(3,2,-14,-9) Matrix(529,-224,640,-271) -> Matrix(3,2,-2,-1) Matrix(469,-206,362,-159) -> Matrix(11,6,-24,-13) Matrix(323,-146,250,-113) -> Matrix(9,4,-16,-7) Matrix(193,-92,300,-143) -> Matrix(7,2,-18,-5) Matrix(151,-82,186,-101) -> Matrix(1,0,-2,1) Matrix(3169,-1772,1200,-671) -> Matrix(1,-2,0,1) Matrix(3431,-1924,1300,-729) -> Matrix(1,2,0,1) Matrix(2081,-1168,3248,-1823) -> Matrix(1,0,-2,1) Matrix(365,-206,466,-263) -> Matrix(1,0,0,1) Matrix(627,-362,362,-209) -> Matrix(1,0,0,1) Matrix(213,-124,280,-163) -> Matrix(1,0,2,1) Matrix(229,-136,32,-19) -> Matrix(5,4,-4,-3) Matrix(161,-100,256,-159) -> Matrix(11,6,-24,-13) Matrix(621,-394,238,-151) -> Matrix(5,2,2,1) Matrix(1343,-868,868,-561) -> Matrix(7,2,10,3) Matrix(293,-200,356,-243) -> Matrix(1,0,2,1) Matrix(507,-350,662,-457) -> Matrix(7,2,10,3) Matrix(521,-362,154,-107) -> Matrix(31,8,-4,-1) Matrix(733,-516,152,-107) -> Matrix(1,0,4,1) Matrix(2067,-1468,1156,-821) -> Matrix(11,2,-28,-5) Matrix(105,-76,76,-55) -> Matrix(1,0,10,1) Matrix(2073,-1592,1280,-983) -> Matrix(7,-10,-2,3) Matrix(469,-362,206,-159) -> Matrix(1,-6,0,1) Matrix(901,-712,348,-275) -> Matrix(1,0,0,1) Matrix(873,-712,244,-199) -> Matrix(5,-2,-2,1) Matrix(1039,-858,442,-365) -> Matrix(3,2,-2,-1) Matrix(577,-490,126,-107) -> Matrix(3,2,-2,-1) Matrix(319,-278,70,-61) -> Matrix(1,0,2,1) Matrix(169,-196,144,-167) -> Matrix(1,-2,0,1) Matrix(529,-640,224,-271) -> Matrix(3,2,-2,-1) Matrix(691,-842,270,-329) -> Matrix(3,2,-2,-1) Matrix(163,-202,46,-57) -> Matrix(1,-2,0,1) Matrix(413,-524,160,-203) -> Matrix(1,0,0,1) Matrix(297,-380,68,-87) -> Matrix(1,0,0,1) Matrix(213,-280,124,-163) -> Matrix(1,0,2,1) Matrix(331,-450,242,-329) -> Matrix(1,0,36,1) Matrix(453,-640,172,-243) -> Matrix(1,0,-4,1) Matrix(301,-428,64,-91) -> Matrix(1,0,-4,1) Matrix(659,-954,382,-553) -> Matrix(3,-2,-4,3) Matrix(487,-710,190,-277) -> Matrix(1,-2,0,1) Matrix(5335,-8262,1398,-2165) -> Matrix(21,-20,-22,21) Matrix(5171,-8012,1356,-2101) -> Matrix(23,-24,-22,23) Matrix(1529,-2372,448,-695) -> Matrix(21,-26,-4,5) Matrix(2081,-3248,1168,-1823) -> Matrix(1,0,-2,1) Matrix(161,-256,100,-159) -> Matrix(1,-6,0,1) Matrix(2719,-4406,714,-1157) -> Matrix(5,14,-4,-11) Matrix(67,-114,10,-17) -> Matrix(3,2,-2,-1) Matrix(1423,-2452,372,-641) -> Matrix(1,2,-2,-3) Matrix(1255,-2178,722,-1253) -> Matrix(1,0,0,1) Matrix(169,-298,38,-67) -> Matrix(1,0,0,1) Matrix(1401,-2500,784,-1399) -> Matrix(7,4,-16,-9) Matrix(101,-184,28,-51) -> Matrix(3,2,-2,-1) Matrix(423,-904,124,-265) -> Matrix(11,-16,-2,3) Matrix(145,-324,64,-143) -> Matrix(1,-10,0,1) Matrix(4527,-10658,1922,-4525) -> Matrix(1,0,0,1) Matrix(471,-1114,178,-421) -> Matrix(1,2,-2,-3) Matrix(69,-164,8,-19) -> Matrix(1,2,-2,-3) Matrix(213,-514,46,-111) -> Matrix(1,0,0,1) Matrix(143,-350,38,-93) -> Matrix(3,2,-2,-1) Matrix(4351,-11250,1682,-4349) -> Matrix(1,0,0,1) Matrix(331,-866,86,-225) -> Matrix(1,0,0,1) Matrix(267,-722,98,-265) -> Matrix(1,0,4,1) Matrix(121,-400,36,-119) -> Matrix(1,-12,0,1) Matrix(641,-2192,112,-383) -> Matrix(7,32,-2,-9) Matrix(2075,-7442,578,-2073) -> Matrix(39,80,-20,-41) Matrix(903,-3362,242,-901) -> Matrix(1,0,0,1) Matrix(211,-882,50,-209) -> Matrix(11,12,-12,-13) Matrix(775,-3698,162,-773) -> Matrix(1,0,0,1) Matrix(89,-484,16,-87) -> Matrix(1,-8,0,1) Matrix(139,-1058,18,-137) -> Matrix(27,28,-28,-29) 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): 42 Degree of the the map X: 42 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. ----------------------------------------------------------------------- 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): 504 Minimal number of generators: 85 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: 36 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/1 7/6 15/11 7/5 79/51 8/5 33/19 25/14 2/1 9/4 7/3 73/31 75/29 13/5 19/7 3/1 10/3 17/5 61/17 11/3 41/11 19/5 4/1 21/5 13/3 9/2 43/9 5/1 11/2 17/3 6/1 7/1 23/3 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 0/1 -1/1 0/1 1/6 -2/3 -3/5 3/17 -4/7 -1/2 2/11 -1/2 1/5 0/1 3/14 -2/1 -1/1 2/9 -1/1 0/1 3/13 -1/1 1/0 1/4 -1/1 -2/3 4/15 -1/1 -2/3 3/11 -2/3 2/7 -2/3 -3/5 5/17 -6/11 3/10 -1/2 1/3 -1/2 0/1 3/8 -1/1 0/1 8/21 -1/1 0/1 5/13 0/1 7/18 -2/1 -1/1 9/23 -2/3 -1/2 2/5 -1/1 0/1 9/22 -1/1 0/1 7/17 -1/1 -1/2 12/29 -1/1 0/1 5/12 -2/1 -1/1 8/19 -1/1 -2/3 11/26 -1/1 -2/3 3/7 -2/3 4/9 -1/2 5/11 -1/2 -3/7 1/2 -1/3 0/1 6/11 0/1 1/1 5/9 0/1 14/25 1/0 23/41 -2/1 1/0 9/16 -2/1 -1/1 4/7 -1/1 0/1 11/19 0/1 7/12 0/1 1/1 10/17 -2/1 -1/1 13/22 -6/5 -1/1 3/5 -1/1 -1/2 5/8 -1/2 7/11 -2/5 9/14 -2/5 -1/3 20/31 -10/29 -1/3 11/17 -1/3 -1/4 2/3 -1/3 0/1 11/16 -4/11 -1/3 9/13 -2/7 7/10 -2/9 -1/5 19/27 0/1 12/17 -1/5 0/1 17/24 -1/5 0/1 22/31 -1/5 0/1 5/7 -1/6 0/1 3/4 0/1 1/3 13/17 0/1 23/30 6/7 1/1 10/13 1/1 2/1 7/9 -1/1 1/0 18/23 -1/1 0/1 11/14 -2/1 -1/1 15/19 0/1 4/5 -1/1 0/1 13/16 -1/5 0/1 9/11 0/1 1/0 23/28 -4/3 -1/1 14/17 -1/1 0/1 19/23 0/1 5/6 -1/1 0/1 11/13 -1/1 -1/2 6/7 -1/2 1/1 0/1 7/6 1/0 13/11 -1/1 1/0 6/5 -1/1 0/1 17/14 -1/1 0/1 11/9 -1/2 0/1 5/4 -1/1 0/1 14/11 -1/1 -2/3 9/7 -1/1 -1/2 13/10 -2/5 -1/3 4/3 -1/5 0/1 15/11 0/1 11/8 0/1 1/13 7/5 0/1 1/4 17/12 0/1 1/3 10/7 1/3 2/5 13/9 2/3 16/11 1/1 4/3 3/2 0/1 1/1 17/11 1/2 1/1 48/31 12/13 1/1 79/51 1/1 31/20 1/1 10/9 14/9 1/1 2/1 11/7 2/1 8/5 1/0 5/3 -1/1 1/0 12/7 -1/3 0/1 31/18 -2/1 -1/1 50/29 -1/1 -6/7 19/11 0/1 26/15 -1/1 0/1 33/19 -1/2 1/0 7/4 -1/1 0/1 16/9 -1/1 -2/3 41/23 -2/3 -1/2 25/14 -1/2 9/5 0/1 2/1 0/1 1/1 11/5 3/1 1/0 9/4 1/0 7/3 -2/1 40/17 -2/1 -1/1 73/31 -3/2 1/0 33/14 -2/1 -1/1 26/11 -2/1 -1/1 19/8 -2/1 -1/1 12/5 -1/1 -2/3 17/7 -1/1 1/0 5/2 -1/1 0/1 23/9 -2/1 1/0 41/16 -2/1 -1/1 18/7 -1/1 -2/3 31/12 -1/1 0/1 75/29 -1/2 1/0 44/17 -1/1 0/1 13/5 0/1 21/8 -1/1 0/1 29/11 0/1 1/0 37/14 -1/1 0/1 8/3 -1/1 0/1 19/7 0/1 11/4 0/1 1/1 3/1 0/1 1/0 10/3 1/0 17/5 -6/1 7/2 -3/1 -2/1 25/7 -5/2 -2/1 43/12 -15/7 -2/1 61/17 -2/1 18/5 -2/1 -5/3 11/3 -2/1 26/7 -2/1 -1/1 41/11 -3/2 1/0 15/4 -2/1 -1/1 19/5 -3/2 -1/1 4/1 -2/1 -1/1 21/5 -1/1 17/4 -1/1 -4/5 13/3 -1/1 -1/2 22/5 -1/1 -2/3 9/2 -1/1 0/1 23/5 -1/1 1/0 14/3 -1/1 -2/3 19/4 -1/1 0/1 43/9 -1/2 1/0 24/5 -1/1 0/1 5/1 0/1 11/2 1/0 17/3 -4/1 1/0 6/1 -3/1 -2/1 7/1 -3/2 -1/1 15/2 -10/9 -1/1 23/3 -1/1 8/1 -1/1 -4/5 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(67,-10,114,-17) (0/1,1/6) -> (7/12,10/17) Hyperbolic Matrix(88,-15,223,-38) (1/6,3/17) -> (9/23,2/5) Hyperbolic Matrix(374,-67,67,-12) (3/17,2/11) -> (11/2,17/3) Hyperbolic Matrix(110,-21,21,-4) (2/11,1/5) -> (5/1,11/2) Hyperbolic Matrix(301,-64,428,-91) (1/5,3/14) -> (7/10,19/27) Hyperbolic Matrix(213,-46,514,-111) (3/14,2/9) -> (12/29,5/12) Hyperbolic Matrix(297,-68,380,-87) (2/9,3/13) -> (7/9,18/23) Hyperbolic Matrix(273,-64,64,-15) (3/13,1/4) -> (17/4,13/3) Hyperbolic Matrix(143,-38,350,-93) (1/4,4/15) -> (2/5,9/22) Hyperbolic Matrix(451,-122,122,-33) (4/15,3/11) -> (11/3,26/7) Hyperbolic Matrix(101,-28,184,-51) (3/11,2/7) -> (6/11,5/9) Hyperbolic Matrix(182,-53,261,-76) (2/7,5/17) -> (9/13,7/10) Hyperbolic Matrix(340,-101,101,-30) (5/17,3/10) -> (10/3,17/5) Hyperbolic Matrix(60,-19,19,-6) (3/10,1/3) -> (3/1,10/3) Hyperbolic Matrix(57,-20,20,-7) (1/3,3/8) -> (11/4,3/1) Hyperbolic Matrix(453,-172,640,-243) (3/8,8/21) -> (12/17,17/24) Hyperbolic Matrix(264,-101,413,-158) (8/21,5/13) -> (7/11,9/14) Hyperbolic Matrix(413,-160,524,-203) (5/13,7/18) -> (11/14,15/19) Hyperbolic Matrix(691,-270,842,-329) (7/18,9/23) -> (9/11,23/28) Hyperbolic Matrix(276,-113,425,-174) (9/22,7/17) -> (11/17,2/3) Hyperbolic Matrix(404,-167,479,-198) (7/17,12/29) -> (5/6,11/13) Hyperbolic Matrix(367,-154,622,-261) (5/12,8/19) -> (10/17,13/22) Hyperbolic Matrix(895,-378,1262,-533) (8/19,11/26) -> (17/24,22/31) Hyperbolic Matrix(529,-224,640,-271) (11/26,3/7) -> (19/23,5/6) Hyperbolic Matrix(126,-55,55,-24) (3/7,4/9) -> (9/4,7/3) Hyperbolic Matrix(198,-89,89,-40) (4/9,5/11) -> (11/5,9/4) Hyperbolic Matrix(124,-57,161,-74) (5/11,1/2) -> (10/13,7/9) Hyperbolic Matrix(151,-82,186,-101) (1/2,6/11) -> (4/5,13/16) Hyperbolic Matrix(450,-251,251,-140) (5/9,14/25) -> (25/14,9/5) Hyperbolic Matrix(2050,-1149,1149,-644) (14/25,23/41) -> (41/23,25/14) Hyperbolic Matrix(982,-551,1383,-776) (23/41,9/16) -> (22/31,5/7) Hyperbolic Matrix(365,-206,466,-263) (9/16,4/7) -> (18/23,11/14) Hyperbolic Matrix(627,-362,362,-209) (4/7,11/19) -> (19/11,26/15) Hyperbolic Matrix(213,-124,280,-163) (11/19,7/12) -> (3/4,13/17) Hyperbolic Matrix(229,-136,32,-19) (13/22,3/5) -> (7/1,15/2) Hyperbolic Matrix(80,-49,49,-30) (3/5,5/8) -> (8/5,5/3) Hyperbolic Matrix(176,-111,111,-70) (5/8,7/11) -> (11/7,8/5) Hyperbolic Matrix(632,-407,823,-530) (9/14,20/31) -> (23/30,10/13) Hyperbolic Matrix(1343,-868,868,-561) (20/31,11/17) -> (17/11,48/31) Hyperbolic Matrix(293,-200,356,-243) (2/3,11/16) -> (23/28,14/17) Hyperbolic Matrix(507,-350,662,-457) (11/16,9/13) -> (13/17,23/30) Hyperbolic Matrix(733,-516,152,-107) (19/27,12/17) -> (24/5,5/1) Hyperbolic Matrix(105,-76,76,-55) (5/7,3/4) -> (11/8,7/5) Hyperbolic Matrix(901,-712,348,-275) (15/19,4/5) -> (44/17,13/5) Hyperbolic Matrix(873,-712,244,-199) (13/16,9/11) -> (25/7,43/12) Hyperbolic Matrix(1039,-858,442,-365) (14/17,19/23) -> (7/3,40/17) Hyperbolic Matrix(182,-155,155,-132) (11/13,6/7) -> (7/6,13/11) Hyperbolic Matrix(14,-13,13,-12) (6/7,1/1) -> (1/1,7/6) Parabolic Matrix(214,-255,47,-56) (13/11,6/5) -> (9/2,23/5) Hyperbolic Matrix(529,-640,224,-271) (6/5,17/14) -> (33/14,26/11) Hyperbolic Matrix(691,-842,270,-329) (17/14,11/9) -> (23/9,41/16) 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(124,-161,57,-74) (9/7,13/10) -> (2/1,11/5) Hyperbolic Matrix(213,-280,124,-163) (13/10,4/3) -> (12/7,31/18) Hyperbolic Matrix(166,-225,121,-164) (4/3,15/11) -> (15/11,11/8) Parabolic 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(182,-261,53,-76) (10/7,13/9) -> (17/5,7/2) Hyperbolic Matrix(659,-954,382,-553) (13/9,16/11) -> (50/29,19/11) Hyperbolic Matrix(487,-710,190,-277) (16/11,3/2) -> (41/16,18/7) Hyperbolic Matrix(82,-125,21,-32) (3/2,17/11) -> (19/5,4/1) Hyperbolic Matrix(4030,-6241,2601,-4028) (48/31,79/51) -> (79/51,31/20) Parabolic Matrix(1070,-1661,621,-964) (31/20,14/9) -> (31/18,50/29) Hyperbolic Matrix(264,-413,101,-158) (14/9,11/7) -> (13/5,21/8) Hyperbolic Matrix(67,-114,10,-17) (5/3,12/7) -> (6/1,7/1) Hyperbolic Matrix(628,-1089,361,-626) (26/15,33/19) -> (33/19,7/4) Parabolic Matrix(169,-298,38,-67) (7/4,16/9) -> (22/5,9/2) Hyperbolic Matrix(1112,-1981,421,-750) (16/9,41/23) -> (29/11,37/14) Hyperbolic Matrix(101,-184,28,-51) (9/5,2/1) -> (18/5,11/3) Hyperbolic Matrix(2264,-5329,961,-2262) (40/17,73/31) -> (73/31,33/14) Parabolic Matrix(471,-1114,178,-421) (26/11,19/8) -> (37/14,8/3) Hyperbolic Matrix(69,-164,8,-19) (19/8,12/5) -> (8/1,1/0) Hyperbolic Matrix(213,-514,46,-111) (12/5,17/7) -> (23/5,14/3) Hyperbolic Matrix(143,-350,38,-93) (17/7,5/2) -> (15/4,19/5) Hyperbolic Matrix(88,-223,15,-38) (5/2,23/9) -> (17/3,6/1) Hyperbolic Matrix(2176,-5625,841,-2174) (31/12,75/29) -> (75/29,44/17) Parabolic Matrix(134,-361,49,-132) (8/3,19/7) -> (19/7,11/4) Parabolic Matrix(1038,-3721,289,-1036) (43/12,61/17) -> (61/17,18/5) Parabolic Matrix(452,-1681,121,-450) (26/7,41/11) -> (41/11,15/4) Parabolic Matrix(106,-441,25,-104) (4/1,21/5) -> (21/5,17/4) Parabolic Matrix(388,-1849,81,-386) (19/4,43/9) -> (43/9,24/5) Parabolic Matrix(70,-529,9,-68) (15/2,23/3) -> (23/3,8/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,0,1) Matrix(67,-10,114,-17) -> Matrix(3,2,-2,-1) Matrix(88,-15,223,-38) -> Matrix(3,2,-8,-5) Matrix(374,-67,67,-12) -> Matrix(15,8,-2,-1) Matrix(110,-21,21,-4) -> Matrix(1,0,2,1) Matrix(301,-64,428,-91) -> Matrix(1,0,-4,1) Matrix(213,-46,514,-111) -> Matrix(1,0,0,1) Matrix(297,-68,380,-87) -> Matrix(1,0,0,1) Matrix(273,-64,64,-15) -> Matrix(1,2,-2,-3) Matrix(143,-38,350,-93) -> Matrix(3,2,-2,-1) Matrix(451,-122,122,-33) -> Matrix(5,4,-4,-3) Matrix(101,-28,184,-51) -> Matrix(3,2,-2,-1) Matrix(182,-53,261,-76) -> Matrix(7,4,-30,-17) Matrix(340,-101,101,-30) -> Matrix(23,12,-2,-1) Matrix(60,-19,19,-6) -> Matrix(1,0,2,1) Matrix(57,-20,20,-7) -> Matrix(1,0,2,1) Matrix(453,-172,640,-243) -> Matrix(1,0,-4,1) Matrix(264,-101,413,-158) -> Matrix(3,2,-8,-5) Matrix(413,-160,524,-203) -> Matrix(1,0,0,1) Matrix(691,-270,842,-329) -> Matrix(3,2,-2,-1) Matrix(276,-113,425,-174) -> Matrix(1,0,-2,1) Matrix(404,-167,479,-198) -> Matrix(1,0,0,1) Matrix(367,-154,622,-261) -> Matrix(5,4,-4,-3) Matrix(895,-378,1262,-533) -> Matrix(3,2,-14,-9) Matrix(529,-224,640,-271) -> Matrix(3,2,-2,-1) Matrix(126,-55,55,-24) -> Matrix(7,4,-2,-1) Matrix(198,-89,89,-40) -> Matrix(13,6,2,1) Matrix(124,-57,161,-74) -> Matrix(5,2,2,1) Matrix(151,-82,186,-101) -> Matrix(1,0,-2,1) Matrix(450,-251,251,-140) -> Matrix(1,0,-2,1) Matrix(2050,-1149,1149,-644) -> Matrix(1,4,-2,-7) Matrix(982,-551,1383,-776) -> Matrix(1,2,-6,-11) Matrix(365,-206,466,-263) -> Matrix(1,0,0,1) Matrix(627,-362,362,-209) -> Matrix(1,0,0,1) Matrix(213,-124,280,-163) -> Matrix(1,0,2,1) Matrix(229,-136,32,-19) -> Matrix(5,4,-4,-3) Matrix(80,-49,49,-30) -> Matrix(3,2,-2,-1) Matrix(176,-111,111,-70) -> Matrix(9,4,2,1) Matrix(632,-407,823,-530) -> Matrix(11,4,8,3) Matrix(1343,-868,868,-561) -> Matrix(7,2,10,3) Matrix(293,-200,356,-243) -> Matrix(1,0,2,1) Matrix(507,-350,662,-457) -> Matrix(7,2,10,3) Matrix(733,-516,152,-107) -> Matrix(1,0,4,1) Matrix(105,-76,76,-55) -> Matrix(1,0,10,1) Matrix(901,-712,348,-275) -> Matrix(1,0,0,1) Matrix(873,-712,244,-199) -> Matrix(5,-2,-2,1) Matrix(1039,-858,442,-365) -> Matrix(3,2,-2,-1) Matrix(182,-155,155,-132) -> Matrix(3,2,-2,-1) Matrix(14,-13,13,-12) -> Matrix(1,0,2,1) Matrix(214,-255,47,-56) -> Matrix(1,0,0,1) Matrix(529,-640,224,-271) -> Matrix(3,2,-2,-1) Matrix(691,-842,270,-329) -> Matrix(3,2,-2,-1) Matrix(163,-202,46,-57) -> Matrix(1,-2,0,1) Matrix(413,-524,160,-203) -> Matrix(1,0,0,1) Matrix(297,-380,68,-87) -> Matrix(1,0,0,1) Matrix(124,-161,57,-74) -> Matrix(5,2,2,1) Matrix(213,-280,124,-163) -> Matrix(1,0,2,1) Matrix(166,-225,121,-164) -> Matrix(1,0,18,1) Matrix(453,-640,172,-243) -> Matrix(1,0,-4,1) Matrix(301,-428,64,-91) -> Matrix(1,0,-4,1) Matrix(182,-261,53,-76) -> Matrix(9,-4,-2,1) Matrix(659,-954,382,-553) -> Matrix(3,-2,-4,3) Matrix(487,-710,190,-277) -> Matrix(1,-2,0,1) Matrix(82,-125,21,-32) -> Matrix(1,-2,0,1) Matrix(4030,-6241,2601,-4028) -> Matrix(23,-22,22,-21) Matrix(1070,-1661,621,-964) -> Matrix(3,-4,-2,3) Matrix(264,-413,101,-158) -> Matrix(1,-2,0,1) Matrix(67,-114,10,-17) -> Matrix(3,2,-2,-1) Matrix(628,-1089,361,-626) -> Matrix(1,0,0,1) Matrix(169,-298,38,-67) -> Matrix(1,0,0,1) Matrix(1112,-1981,421,-750) -> Matrix(3,2,-2,-1) Matrix(101,-184,28,-51) -> Matrix(3,2,-2,-1) Matrix(2264,-5329,961,-2262) -> Matrix(1,0,0,1) Matrix(471,-1114,178,-421) -> Matrix(1,2,-2,-3) Matrix(69,-164,8,-19) -> Matrix(1,2,-2,-3) Matrix(213,-514,46,-111) -> Matrix(1,0,0,1) Matrix(143,-350,38,-93) -> Matrix(3,2,-2,-1) Matrix(88,-223,15,-38) -> Matrix(1,-2,0,1) Matrix(2176,-5625,841,-2174) -> Matrix(1,0,0,1) Matrix(134,-361,49,-132) -> Matrix(1,0,2,1) Matrix(1038,-3721,289,-1036) -> Matrix(19,40,-10,-21) Matrix(452,-1681,121,-450) -> Matrix(1,0,0,1) Matrix(106,-441,25,-104) -> Matrix(5,6,-6,-7) Matrix(388,-1849,81,-386) -> Matrix(1,0,0,1) Matrix(70,-529,9,-68) -> Matrix(13,14,-14,-15) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 21 ----------------------------------------------------------------------- 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 (-1/1,0/1) 0 1 1/1 0/1 2 13 7/6 1/0 1 2 13/11 (-1/1,1/0) 0 13 6/5 (-1/1,0/1) 0 26 17/14 (-1/1,0/1) 0 26 11/9 (-1/2,0/1) 0 13 5/4 (-1/1,0/1) 0 26 14/11 (-1/1,-2/3) 0 26 9/7 (-1/1,-1/2) 0 13 13/10 (-2/5,-1/3) 0 26 4/3 (-1/5,0/1) 0 26 15/11 0/1 18 1 7/5 (0/1,1/4) 0 13 17/12 (0/1,1/3) 0 26 10/7 (1/3,2/5) 0 26 13/9 2/3 2 13 16/11 (1/1,4/3) 0 26 3/2 (0/1,1/1) 0 26 17/11 (1/2,1/1) 0 13 79/51 1/1 22 1 31/20 (1/1,10/9) 0 26 14/9 (1/1,2/1) 0 26 11/7 2/1 2 13 8/5 1/0 3 2 5/3 (-1/1,1/0) 0 13 12/7 (-1/3,0/1) 0 26 31/18 (-2/1,-1/1) 0 26 50/29 (-1/1,-6/7) 0 26 19/11 0/1 2 13 33/19 (-1/1,0/1) 0 1 7/4 (-1/1,0/1) 0 26 16/9 (-1/1,-2/3) 0 26 41/23 (-2/3,-1/2) 0 13 25/14 -1/2 2 2 9/5 0/1 2 13 2/1 (0/1,1/1) 0 26 11/5 (3/1,1/0) 0 13 9/4 1/0 5 2 7/3 -2/1 2 13 73/31 (-2/1,-1/1) 0 1 33/14 (-2/1,-1/1) 0 26 26/11 (-2/1,-1/1) 0 26 19/8 (-2/1,-1/1) 0 26 12/5 (-1/1,-2/3) 0 26 17/7 (-1/1,1/0) 0 13 5/2 (-1/1,0/1) 0 26 23/9 (-2/1,1/0) 0 13 41/16 (-2/1,-1/1) 0 26 18/7 (-1/1,-2/3) 0 26 31/12 (-1/1,0/1) 0 26 75/29 (-1/1,0/1) 0 1 13/5 0/1 2 13 21/8 (-1/1,0/1) 0 26 29/11 (0/1,1/0) 0 13 37/14 (-1/1,0/1) 0 26 8/3 (-1/1,0/1) 0 26 19/7 0/1 2 1 3/1 (0/1,1/0) 0 13 10/3 1/0 6 2 17/5 -6/1 2 13 7/2 (-3/1,-2/1) 0 26 25/7 (-5/2,-2/1) 0 13 61/17 -2/1 10 1 18/5 (-2/1,-5/3) 0 26 11/3 -2/1 2 13 41/11 (-2/1,-1/1) 0 1 15/4 (-2/1,-1/1) 0 26 19/5 (-3/2,-1/1) 0 13 4/1 (-2/1,-1/1) 0 26 21/5 -1/1 6 1 13/3 (-1/1,-1/2) 0 13 22/5 (-1/1,-2/3) 0 26 9/2 (-1/1,0/1) 0 26 23/5 (-1/1,1/0) 0 13 14/3 (-1/1,-2/3) 0 26 19/4 (-1/1,0/1) 0 26 43/9 (-1/1,0/1) 0 1 5/1 0/1 2 13 11/2 1/0 4 2 17/3 (-4/1,1/0) 0 13 6/1 (-3/1,-2/1) 0 26 7/1 (-3/2,-1/1) 0 13 23/3 -1/1 14 1 8/1 (-1/1,-4/5) 0 26 1/0 (-1/1,0/1) 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(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(13,-14,12,-13) (1/1,7/6) -> (1/1,7/6) Reflection Matrix(155,-182,132,-155) (7/6,13/11) -> (7/6,13/11) Reflection Matrix(214,-255,47,-56) (13/11,6/5) -> (9/2,23/5) Hyperbolic Matrix(529,-640,224,-271) (6/5,17/14) -> (33/14,26/11) Hyperbolic Matrix(691,-842,270,-329) (17/14,11/9) -> (23/9,41/16) 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(124,-161,57,-74) (9/7,13/10) -> (2/1,11/5) Hyperbolic Matrix(213,-280,124,-163) (13/10,4/3) -> (12/7,31/18) Hyperbolic Matrix(89,-120,66,-89) (4/3,15/11) -> (4/3,15/11) Reflection Matrix(76,-105,55,-76) (15/11,7/5) -> (15/11,7/5) Reflection 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(182,-261,53,-76) (10/7,13/9) -> (17/5,7/2) Hyperbolic Matrix(659,-954,382,-553) (13/9,16/11) -> (50/29,19/11) Hyperbolic Matrix(487,-710,190,-277) (16/11,3/2) -> (41/16,18/7) Hyperbolic Matrix(82,-125,21,-32) (3/2,17/11) -> (19/5,4/1) Hyperbolic Matrix(868,-1343,561,-868) (17/11,79/51) -> (17/11,79/51) Reflection Matrix(3161,-4898,2040,-3161) (79/51,31/20) -> (79/51,31/20) Reflection Matrix(1070,-1661,621,-964) (31/20,14/9) -> (31/18,50/29) Hyperbolic Matrix(264,-413,101,-158) (14/9,11/7) -> (13/5,21/8) Hyperbolic Matrix(111,-176,70,-111) (11/7,8/5) -> (11/7,8/5) Reflection Matrix(49,-80,30,-49) (8/5,5/3) -> (8/5,5/3) Reflection Matrix(67,-114,10,-17) (5/3,12/7) -> (6/1,7/1) Hyperbolic Matrix(362,-627,209,-362) (19/11,33/19) -> (19/11,33/19) Reflection Matrix(265,-462,152,-265) (33/19,7/4) -> (33/19,7/4) Reflection Matrix(169,-298,38,-67) (7/4,16/9) -> (22/5,9/2) Hyperbolic Matrix(1112,-1981,421,-750) (16/9,41/23) -> (29/11,37/14) Hyperbolic Matrix(1149,-2050,644,-1149) (41/23,25/14) -> (41/23,25/14) Reflection Matrix(251,-450,140,-251) (25/14,9/5) -> (25/14,9/5) Reflection Matrix(101,-184,28,-51) (9/5,2/1) -> (18/5,11/3) Hyperbolic Matrix(89,-198,40,-89) (11/5,9/4) -> (11/5,9/4) Reflection Matrix(55,-126,24,-55) (9/4,7/3) -> (9/4,7/3) Reflection Matrix(218,-511,93,-218) (7/3,73/31) -> (7/3,73/31) Reflection Matrix(2045,-4818,868,-2045) (73/31,33/14) -> (73/31,33/14) Reflection Matrix(471,-1114,178,-421) (26/11,19/8) -> (37/14,8/3) Hyperbolic Matrix(69,-164,8,-19) (19/8,12/5) -> (8/1,1/0) Hyperbolic Matrix(213,-514,46,-111) (12/5,17/7) -> (23/5,14/3) Hyperbolic Matrix(143,-350,38,-93) (17/7,5/2) -> (15/4,19/5) Hyperbolic Matrix(88,-223,15,-38) (5/2,23/9) -> (17/3,6/1) Hyperbolic Matrix(1799,-4650,696,-1799) (31/12,75/29) -> (31/12,75/29) Reflection Matrix(376,-975,145,-376) (75/29,13/5) -> (75/29,13/5) Reflection Matrix(113,-304,42,-113) (8/3,19/7) -> (8/3,19/7) Reflection Matrix(20,-57,7,-20) (19/7,3/1) -> (19/7,3/1) Reflection Matrix(19,-60,6,-19) (3/1,10/3) -> (3/1,10/3) Reflection Matrix(101,-340,30,-101) (10/3,17/5) -> (10/3,17/5) Reflection Matrix(426,-1525,119,-426) (25/7,61/17) -> (25/7,61/17) Reflection Matrix(611,-2196,170,-611) (61/17,18/5) -> (61/17,18/5) Reflection Matrix(122,-451,33,-122) (11/3,41/11) -> (11/3,41/11) Reflection Matrix(329,-1230,88,-329) (41/11,15/4) -> (41/11,15/4) Reflection Matrix(41,-168,10,-41) (4/1,21/5) -> (4/1,21/5) Reflection Matrix(64,-273,15,-64) (21/5,13/3) -> (21/5,13/3) Reflection Matrix(343,-1634,72,-343) (19/4,43/9) -> (19/4,43/9) Reflection Matrix(44,-215,9,-44) (43/9,5/1) -> (43/9,5/1) Reflection Matrix(21,-110,4,-21) (5/1,11/2) -> (5/1,11/2) Reflection Matrix(67,-374,12,-67) (11/2,17/3) -> (11/2,17/3) Reflection Matrix(22,-161,3,-22) (7/1,23/3) -> (7/1,23/3) 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(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,2,1) (-1/1,1/1) -> (-1/1,0/1) Matrix(13,-14,12,-13) -> Matrix(1,0,0,-1) (1/1,7/6) -> (0/1,1/0) Matrix(155,-182,132,-155) -> Matrix(1,2,0,-1) (7/6,13/11) -> (-1/1,1/0) Matrix(214,-255,47,-56) -> Matrix(1,0,0,1) Matrix(529,-640,224,-271) -> Matrix(3,2,-2,-1) -1/1 Matrix(691,-842,270,-329) -> Matrix(3,2,-2,-1) -1/1 Matrix(163,-202,46,-57) -> Matrix(1,-2,0,1) 1/0 Matrix(413,-524,160,-203) -> Matrix(1,0,0,1) Matrix(297,-380,68,-87) -> Matrix(1,0,0,1) Matrix(124,-161,57,-74) -> Matrix(5,2,2,1) Matrix(213,-280,124,-163) -> Matrix(1,0,2,1) 0/1 Matrix(89,-120,66,-89) -> Matrix(-1,0,10,1) (4/3,15/11) -> (-1/5,0/1) Matrix(76,-105,55,-76) -> Matrix(1,0,8,-1) (15/11,7/5) -> (0/1,1/4) Matrix(453,-640,172,-243) -> Matrix(1,0,-4,1) 0/1 Matrix(301,-428,64,-91) -> Matrix(1,0,-4,1) 0/1 Matrix(182,-261,53,-76) -> Matrix(9,-4,-2,1) Matrix(659,-954,382,-553) -> Matrix(3,-2,-4,3) Matrix(487,-710,190,-277) -> Matrix(1,-2,0,1) 1/0 Matrix(82,-125,21,-32) -> Matrix(1,-2,0,1) 1/0 Matrix(868,-1343,561,-868) -> Matrix(3,-2,4,-3) (17/11,79/51) -> (1/2,1/1) Matrix(3161,-4898,2040,-3161) -> Matrix(19,-20,18,-19) (79/51,31/20) -> (1/1,10/9) Matrix(1070,-1661,621,-964) -> Matrix(3,-4,-2,3) Matrix(264,-413,101,-158) -> Matrix(1,-2,0,1) 1/0 Matrix(111,-176,70,-111) -> Matrix(-1,4,0,1) (11/7,8/5) -> (2/1,1/0) Matrix(49,-80,30,-49) -> Matrix(1,2,0,-1) (8/5,5/3) -> (-1/1,1/0) Matrix(67,-114,10,-17) -> Matrix(3,2,-2,-1) -1/1 Matrix(362,-627,209,-362) -> Matrix(-1,0,2,1) (19/11,33/19) -> (-1/1,0/1) Matrix(265,-462,152,-265) -> Matrix(-1,0,2,1) (33/19,7/4) -> (-1/1,0/1) Matrix(169,-298,38,-67) -> Matrix(1,0,0,1) Matrix(1112,-1981,421,-750) -> Matrix(3,2,-2,-1) -1/1 Matrix(1149,-2050,644,-1149) -> Matrix(7,4,-12,-7) (41/23,25/14) -> (-2/3,-1/2) Matrix(251,-450,140,-251) -> Matrix(-1,0,4,1) (25/14,9/5) -> (-1/2,0/1) Matrix(101,-184,28,-51) -> Matrix(3,2,-2,-1) -1/1 Matrix(89,-198,40,-89) -> Matrix(-1,6,0,1) (11/5,9/4) -> (3/1,1/0) Matrix(55,-126,24,-55) -> Matrix(1,4,0,-1) (9/4,7/3) -> (-2/1,1/0) Matrix(218,-511,93,-218) -> Matrix(3,4,-2,-3) (7/3,73/31) -> (-2/1,-1/1) Matrix(2045,-4818,868,-2045) -> Matrix(3,4,-2,-3) (73/31,33/14) -> (-2/1,-1/1) Matrix(471,-1114,178,-421) -> Matrix(1,2,-2,-3) -1/1 Matrix(69,-164,8,-19) -> Matrix(1,2,-2,-3) -1/1 Matrix(213,-514,46,-111) -> Matrix(1,0,0,1) Matrix(143,-350,38,-93) -> Matrix(3,2,-2,-1) -1/1 Matrix(88,-223,15,-38) -> Matrix(1,-2,0,1) 1/0 Matrix(1799,-4650,696,-1799) -> Matrix(-1,0,2,1) (31/12,75/29) -> (-1/1,0/1) Matrix(376,-975,145,-376) -> Matrix(-1,0,2,1) (75/29,13/5) -> (-1/1,0/1) Matrix(113,-304,42,-113) -> Matrix(-1,0,2,1) (8/3,19/7) -> (-1/1,0/1) Matrix(20,-57,7,-20) -> Matrix(1,0,0,-1) (19/7,3/1) -> (0/1,1/0) Matrix(19,-60,6,-19) -> Matrix(1,0,0,-1) (3/1,10/3) -> (0/1,1/0) Matrix(101,-340,30,-101) -> Matrix(1,12,0,-1) (10/3,17/5) -> (-6/1,1/0) Matrix(426,-1525,119,-426) -> Matrix(9,20,-4,-9) (25/7,61/17) -> (-5/2,-2/1) Matrix(611,-2196,170,-611) -> Matrix(11,20,-6,-11) (61/17,18/5) -> (-2/1,-5/3) Matrix(122,-451,33,-122) -> Matrix(3,4,-2,-3) (11/3,41/11) -> (-2/1,-1/1) Matrix(329,-1230,88,-329) -> Matrix(3,4,-2,-3) (41/11,15/4) -> (-2/1,-1/1) Matrix(41,-168,10,-41) -> Matrix(3,4,-2,-3) (4/1,21/5) -> (-2/1,-1/1) Matrix(64,-273,15,-64) -> Matrix(3,2,-4,-3) (21/5,13/3) -> (-1/1,-1/2) Matrix(343,-1634,72,-343) -> Matrix(-1,0,2,1) (19/4,43/9) -> (-1/1,0/1) Matrix(44,-215,9,-44) -> Matrix(-1,0,2,1) (43/9,5/1) -> (-1/1,0/1) Matrix(21,-110,4,-21) -> Matrix(1,0,0,-1) (5/1,11/2) -> (0/1,1/0) Matrix(67,-374,12,-67) -> Matrix(1,8,0,-1) (11/2,17/3) -> (-4/1,1/0) Matrix(22,-161,3,-22) -> Matrix(5,6,-4,-5) (7/1,23/3) -> (-3/2,-1/1) Matrix(47,-368,6,-47) -> Matrix(9,8,-10,-9) (23/3,8/1) -> (-1/1,-4/5) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.