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 -10/13 -8/13 -1/2 -6/13 -5/12 -79/208 -14/39 -4/13 -1/4 -4/19 -4/23 -9/52 -1/6 -2/13 -2/15 -1/8 -2/17 -3/26 -1/10 -1/11 0/1 1/10 1/9 1/8 1/7 2/13 1/6 2/11 4/21 5/26 1/5 2/9 3/13 1/4 7/26 2/7 4/13 1/3 14/39 5/13 2/5 5/12 11/26 6/13 1/2 7/13 14/25 15/26 8/13 25/39 17/26 2/3 9/13 19/26 10/13 21/26 11/13 23/26 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -6/7 1/1 1/0 -11/13 1/0 -16/19 -6/1 1/0 -5/6 -5/2 1/0 -14/17 -2/1 -3/2 -9/11 -5/4 -13/16 -3/2 -5/4 -17/21 -9/8 -21/26 -1/1 -4/5 -1/1 -1/2 -7/9 1/0 -10/13 1/0 -13/17 1/0 -16/21 -5/2 -2/1 -19/25 1/0 -3/4 -3/2 1/0 -11/15 -9/8 -19/26 -1/1 -8/11 -1/1 -5/6 -5/7 1/0 -17/24 -3/4 -1/2 -29/41 -3/8 -12/17 -1/2 0/1 -19/27 1/0 -26/37 -2/1 -3/2 -33/47 -5/4 -7/10 -1/2 1/0 -16/23 0/1 1/0 -9/13 1/0 -2/3 -1/1 1/0 -13/20 -7/8 -5/6 -24/37 -6/7 -5/6 -11/17 -3/4 -9/14 -3/4 -1/2 -34/53 -2/3 -1/2 -25/39 -1/2 -16/25 -1/1 -1/2 -7/11 1/0 -19/30 -7/8 -5/6 -31/49 -7/8 -12/19 -4/5 -3/4 -29/46 -3/4 -13/18 -17/27 -3/4 -22/35 -7/10 -2/3 -5/8 -3/4 -1/2 -8/13 -1/2 -11/18 -1/2 -1/4 -14/23 0/1 1/0 -31/51 1/0 -17/28 -1/2 1/0 -3/5 1/0 -16/27 -1/1 -1/2 -29/49 -3/4 -13/22 -3/4 -1/2 -10/17 -1/2 0/1 -7/12 -3/2 1/0 -25/43 1/0 -18/31 -2/1 -3/2 -29/50 -3/2 1/0 -11/19 -5/4 -15/26 -1/1 -4/7 -1/1 -3/4 -5/9 -3/4 -6/11 -3/5 -1/2 -7/13 -1/2 -8/15 -1/2 -2/5 -9/17 -1/4 -1/2 -1/2 1/0 -6/13 -1/2 -11/24 -1/2 -11/24 -5/11 -5/12 -14/31 -2/5 -7/18 -23/51 -3/8 -9/20 -3/8 -5/14 -4/9 -1/2 -1/3 -11/25 -1/4 -7/16 -1/2 -1/4 -10/23 -1/4 0/1 -3/7 -1/4 -11/26 0/1 -8/19 0/1 1/4 -5/12 -1/2 1/0 -12/29 -1/4 0/1 -7/17 1/0 -2/5 -1/1 -1/2 -5/13 -1/2 -8/21 -1/2 -4/9 -19/50 -1/2 -7/16 -49/129 -7/16 -79/208 -3/7 -30/79 -1/2 -3/7 -11/29 -7/16 -14/37 -9/22 -2/5 -3/8 -1/2 -3/8 -10/27 -1/2 -1/3 -27/73 -3/8 -44/119 -1/2 0/1 -17/46 -1/2 -1/4 -7/19 -3/8 -4/11 -1/3 -3/10 -9/25 -1/4 -14/39 -1/4 -19/53 -1/4 -5/14 -1/4 -3/14 -6/17 -1/6 0/1 -7/20 -1/8 -1/10 -1/3 1/0 -4/13 -1/2 -7/23 -7/16 -10/33 -5/12 -2/5 -13/43 -5/12 -3/10 -1/2 -3/8 -11/37 -3/8 -8/27 -1/2 -1/3 -13/44 -1/2 -3/8 -5/17 -1/4 -2/7 -1/3 -1/4 -7/25 -1/4 -12/43 -3/14 -1/5 -29/104 -1/5 -17/61 -3/16 -5/18 -1/4 -1/6 -8/29 -1/8 0/1 -11/40 -1/4 -1/6 -14/51 -1/6 0/1 -3/11 -1/8 -7/26 0/1 -4/15 0/1 1/6 -5/19 1/0 -6/23 0/1 1/0 -7/27 1/0 -1/4 -1/2 1/0 -4/17 -2/3 -1/2 -3/13 -1/2 -2/9 -1/2 -1/3 -7/32 -3/8 -5/14 -12/55 -11/32 -1/3 -17/78 -1/3 -5/23 -5/16 -8/37 -2/7 -5/18 -11/51 -1/4 -3/14 -1/4 -1/6 -4/19 0/1 1/0 -9/43 1/0 -5/24 -1/2 -1/4 -1/5 -1/4 -5/26 0/1 -4/21 0/1 1/6 -7/37 1/0 -3/16 1/2 1/0 -5/27 1/0 -2/11 -1/1 -1/2 -3/17 -1/4 -4/23 -1/8 0/1 -9/52 0/1 -5/29 1/8 -1/6 -1/2 1/0 -2/13 -1/2 -3/20 -1/2 -3/8 -1/7 -1/4 -2/15 0/1 1/2 -1/8 -1/2 -1/4 -2/17 -1/6 0/1 -3/26 0/1 -1/9 1/0 -1/10 -1/2 -1/4 -1/11 -1/4 0/1 -1/2 0/1 1/10 -1/2 1/0 1/9 -1/4 1/8 -1/2 1/0 1/7 1/0 2/13 -1/2 3/19 -3/8 1/6 -1/2 -1/4 2/11 -1/2 -1/3 3/16 -1/4 -1/6 4/21 -1/10 0/1 5/26 0/1 1/5 1/0 3/14 1/2 1/0 8/37 -5/2 -2/1 5/23 -5/4 2/9 -1/1 -1/2 3/13 -1/2 4/17 -1/2 -2/5 1/4 -1/2 -1/4 5/19 -1/4 9/34 -1/4 -1/6 4/15 -1/10 0/1 7/26 0/1 3/11 1/4 8/29 0/1 1/4 5/18 1/2 1/0 2/7 -1/1 1/0 3/10 -3/4 -1/2 4/13 -1/2 5/16 -1/2 -5/12 11/35 -3/8 6/19 -2/5 -3/8 1/3 -1/4 5/14 3/2 1/0 14/39 1/0 23/64 -17/2 1/0 9/25 1/0 4/11 -3/2 -1/1 3/8 -3/4 -1/2 14/37 -2/3 -9/14 11/29 -7/12 30/79 -3/5 -1/2 19/50 -7/12 -1/2 8/21 -4/7 -1/2 5/13 -1/2 2/5 -1/2 -1/3 5/12 -1/2 -1/4 13/31 -1/4 21/50 -1/4 -1/6 29/69 -1/8 8/19 -1/8 0/1 11/26 0/1 3/7 1/0 13/30 1/2 1/0 23/53 1/0 10/23 0/1 1/0 7/16 -1/2 1/0 18/41 1/2 1/1 11/25 1/0 4/9 -1/1 -1/2 13/29 -5/4 9/20 -5/6 -3/4 14/31 -7/10 -2/3 19/42 -5/8 -1/2 5/11 -5/8 6/13 -1/2 7/15 -7/16 1/2 -1/2 -1/4 9/17 1/0 8/15 -2/3 -1/2 7/13 -1/2 6/11 -1/2 -3/7 11/20 -1/2 -5/12 5/9 -3/8 14/25 -1/2 -1/3 9/16 -1/2 -1/4 4/7 -3/8 -1/3 15/26 -1/3 11/19 -5/16 18/31 -3/10 -2/7 7/12 -3/10 -1/4 17/29 -1/8 10/17 -1/2 0/1 13/22 -1/2 -3/8 16/27 -1/2 -1/3 3/5 -1/4 8/13 -1/2 13/21 -5/12 31/50 -1/2 -5/12 80/129 -1/2 -3/7 129/208 -3/7 49/79 -5/12 18/29 -5/12 -2/5 5/8 -1/2 -3/8 17/27 -3/8 46/73 -1/2 -2/5 29/46 -13/34 -3/8 12/19 -3/8 -4/11 7/11 -1/4 16/25 -1/2 -1/3 25/39 -1/2 34/53 -1/2 -2/5 9/14 -1/2 -3/8 20/31 -1/2 -2/5 11/17 -3/8 24/37 -5/14 -6/17 13/20 -5/14 -7/20 15/23 -15/44 17/26 -1/3 2/3 -1/3 -1/4 9/13 -1/4 16/23 -1/4 0/1 7/10 -1/2 -1/4 26/37 -3/10 -2/7 45/64 -9/34 -1/4 19/27 -1/4 31/44 -1/4 -1/6 43/61 -1/8 55/78 0/1 12/17 -1/2 0/1 17/24 -1/2 -3/8 22/31 -1/2 -2/5 5/7 -1/4 23/32 -1/2 -3/8 41/57 -1/4 18/25 -1/2 -1/3 31/43 -3/8 13/18 -1/2 -1/4 8/11 -5/14 -1/3 19/26 -1/3 11/15 -9/28 14/19 -5/16 -4/13 17/23 -1/4 20/27 -1/3 -3/10 3/4 -3/10 -1/4 10/13 -1/4 17/22 -1/4 -5/22 41/53 -1/4 24/31 -2/9 -3/14 7/9 -1/4 25/32 -1/6 -1/8 18/23 0/1 1/0 29/37 1/0 69/88 -1/2 1/0 40/51 -1/2 0/1 11/14 -1/2 -1/4 4/5 -1/2 -1/3 21/26 -1/3 17/21 -9/28 47/58 -7/22 -5/16 30/37 -7/22 -6/19 13/16 -5/16 -3/10 22/27 -1/3 -3/10 9/11 -5/16 23/28 -3/10 -13/44 14/17 -3/10 -2/7 19/23 -15/52 43/52 -2/7 24/29 -2/7 -17/60 5/6 -5/18 -1/4 16/19 -6/23 -1/4 11/13 -1/4 6/7 -1/4 -1/5 7/8 -1/2 -1/4 15/17 -3/8 23/26 -1/3 8/9 -1/3 -3/10 1/1 -1/4 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(51,44,-182,-157) (-1/1,-6/7) -> (-2/7,-7/25) Hyperbolic Matrix(155,132,182,155) (-6/7,-11/13) -> (11/13,6/7) Hyperbolic Matrix(417,352,494,417) (-11/13,-16/19) -> (16/19,11/13) Hyperbolic Matrix(623,524,988,831) (-16/19,-5/6) -> (29/46,12/19) Hyperbolic Matrix(155,128,-442,-365) (-5/6,-14/17) -> (-6/17,-7/20) Hyperbolic Matrix(625,514,-884,-727) (-14/17,-9/11) -> (-29/41,-12/17) Hyperbolic Matrix(209,170,-702,-571) (-9/11,-13/16) -> (-3/10,-11/37) Hyperbolic Matrix(675,548,-962,-781) (-13/16,-17/21) -> (-33/47,-7/10) Hyperbolic Matrix(883,714,1092,883) (-17/21,-21/26) -> (21/26,17/21) Hyperbolic Matrix(209,168,260,209) (-21/26,-4/5) -> (4/5,21/26) Hyperbolic Matrix(53,42,-130,-103) (-4/5,-7/9) -> (-7/17,-2/5) Hyperbolic Matrix(259,200,-338,-261) (-7/9,-10/13) -> (-10/13,-13/17) Parabolic Matrix(571,436,884,675) (-13/17,-16/21) -> (20/31,11/17) Hyperbolic Matrix(1507,1146,2392,1819) (-16/21,-19/25) -> (17/27,46/73) Hyperbolic Matrix(417,316,962,729) (-19/25,-3/4) -> (13/30,23/53) Hyperbolic Matrix(313,230,-494,-363) (-3/4,-11/15) -> (-7/11,-19/30) Hyperbolic Matrix(571,418,780,571) (-11/15,-19/26) -> (19/26,11/15) Hyperbolic Matrix(417,304,572,417) (-19/26,-8/11) -> (8/11,19/26) Hyperbolic Matrix(105,76,-286,-207) (-8/11,-5/7) -> (-7/19,-4/11) Hyperbolic Matrix(467,332,-806,-573) (-5/7,-17/24) -> (-29/50,-11/19) Hyperbolic Matrix(209,148,442,313) (-17/24,-29/41) -> (7/15,1/2) Hyperbolic Matrix(883,622,-1404,-989) (-12/17,-19/27) -> (-17/27,-22/35) Hyperbolic Matrix(623,438,-2886,-2029) (-19/27,-26/37) -> (-8/37,-11/51) Hyperbolic Matrix(3067,2154,-8294,-5825) (-26/37,-33/47) -> (-27/73,-44/119) Hyperbolic Matrix(261,182,598,417) (-7/10,-16/23) -> (10/23,7/16) Hyperbolic Matrix(415,288,598,415) (-16/23,-9/13) -> (9/13,16/23) Hyperbolic Matrix(53,36,78,53) (-9/13,-2/3) -> (2/3,9/13) Hyperbolic Matrix(261,170,-1196,-779) (-2/3,-13/20) -> (-7/32,-12/55) Hyperbolic Matrix(1509,980,-4082,-2651) (-13/20,-24/37) -> (-44/119,-17/46) Hyperbolic Matrix(469,304,884,573) (-24/37,-11/17) -> (9/17,8/15) Hyperbolic Matrix(469,302,-806,-519) (-11/17,-9/14) -> (-7/12,-25/43) Hyperbolic Matrix(1143,734,1456,935) (-9/14,-34/53) -> (40/51,11/14) Hyperbolic Matrix(2651,1700,4134,2651) (-34/53,-25/39) -> (25/39,34/53) Hyperbolic Matrix(1249,800,1950,1249) (-25/39,-16/25) -> (16/25,25/39) Hyperbolic Matrix(363,232,-1222,-781) (-16/25,-7/11) -> (-11/37,-8/27) Hyperbolic Matrix(1507,954,-2548,-1613) (-19/30,-31/49) -> (-29/49,-13/22) Hyperbolic Matrix(313,198,988,625) (-31/49,-12/19) -> (6/19,1/3) Hyperbolic Matrix(831,524,988,623) (-12/19,-29/46) -> (5/6,16/19) Hyperbolic Matrix(1301,820,-2886,-1819) (-29/46,-17/27) -> (-23/51,-9/20) Hyperbolic Matrix(51,32,-416,-261) (-22/35,-5/8) -> (-1/8,-2/17) Hyperbolic Matrix(207,128,-338,-209) (-5/8,-8/13) -> (-8/13,-11/18) Parabolic Matrix(259,158,936,571) (-11/18,-14/23) -> (8/29,5/18) Hyperbolic Matrix(1039,632,2392,1455) (-14/23,-31/51) -> (23/53,10/23) Hyperbolic Matrix(2341,1422,-6162,-3743) (-31/51,-17/28) -> (-19/50,-49/129) Hyperbolic Matrix(469,284,1118,677) (-17/28,-3/5) -> (13/31,21/50) Hyperbolic Matrix(779,462,-2106,-1249) (-3/5,-16/27) -> (-10/27,-27/73) Hyperbolic Matrix(1767,1046,4654,2755) (-16/27,-29/49) -> (11/29,30/79) Hyperbolic Matrix(105,62,442,261) (-13/22,-10/17) -> (4/17,1/4) Hyperbolic Matrix(157,92,-442,-259) (-10/17,-7/12) -> (-5/14,-6/17) Hyperbolic Matrix(1249,726,1612,937) (-25/43,-18/31) -> (24/31,7/9) Hyperbolic Matrix(989,574,2600,1509) (-18/31,-29/50) -> (19/50,8/21) Hyperbolic Matrix(571,330,988,571) (-11/19,-15/26) -> (15/26,11/19) Hyperbolic Matrix(209,120,364,209) (-15/26,-4/7) -> (4/7,15/26) Hyperbolic Matrix(53,30,-182,-103) (-4/7,-5/9) -> (-5/17,-2/7) Hyperbolic Matrix(51,28,-286,-157) (-5/9,-6/11) -> (-2/11,-3/17) Hyperbolic Matrix(155,84,286,155) (-6/11,-7/13) -> (7/13,6/11) Hyperbolic Matrix(209,112,390,209) (-7/13,-8/15) -> (8/15,7/13) Hyperbolic Matrix(573,304,884,469) (-8/15,-9/17) -> (11/17,24/37) Hyperbolic Matrix(415,218,988,519) (-9/17,-1/2) -> (21/50,29/69) Hyperbolic Matrix(155,72,-338,-157) (-1/2,-6/13) -> (-6/13,-11/24) Parabolic Matrix(469,214,572,261) (-11/24,-5/11) -> (9/11,23/28) Hyperbolic Matrix(261,118,-1378,-623) (-5/11,-14/31) -> (-4/21,-7/37) Hyperbolic Matrix(2495,1126,3224,1455) (-14/31,-23/51) -> (41/53,24/31) Hyperbolic Matrix(103,46,-468,-209) (-9/20,-4/9) -> (-2/9,-7/32) Hyperbolic Matrix(363,160,-1300,-573) (-4/9,-11/25) -> (-7/25,-12/43) Hyperbolic Matrix(155,68,-832,-365) (-11/25,-7/16) -> (-3/16,-5/27) Hyperbolic Matrix(417,182,598,261) (-7/16,-10/23) -> (16/23,7/10) Hyperbolic Matrix(157,68,-598,-259) (-10/23,-3/7) -> (-5/19,-6/23) Hyperbolic Matrix(155,66,364,155) (-3/7,-11/26) -> (11/26,3/7) Hyperbolic Matrix(417,176,988,417) (-11/26,-8/19) -> (8/19,11/26) Hyperbolic Matrix(105,44,-494,-207) (-8/19,-5/12) -> (-3/14,-4/19) Hyperbolic Matrix(415,172,-1508,-625) (-5/12,-12/29) -> (-8/29,-11/40) Hyperbolic Matrix(155,64,-884,-365) (-12/29,-7/17) -> (-3/17,-4/23) Hyperbolic Matrix(51,20,130,51) (-2/5,-5/13) -> (5/13,2/5) Hyperbolic Matrix(209,80,546,209) (-5/13,-8/21) -> (8/21,5/13) Hyperbolic Matrix(1457,554,2054,781) (-8/21,-19/50) -> (17/24,22/31) Hyperbolic Matrix(26833,10192,43264,16433) (-49/129,-79/208) -> (129/208,49/79) Hyperbolic Matrix(26831,10190,43264,16431) (-79/208,-30/79) -> (80/129,129/208) Hyperbolic Matrix(1923,730,2600,987) (-30/79,-11/29) -> (17/23,20/27) Hyperbolic Matrix(417,158,1924,729) (-11/29,-14/37) -> (8/37,5/23) Hyperbolic Matrix(365,138,1378,521) (-14/37,-3/8) -> (9/34,4/15) Hyperbolic Matrix(415,154,-1404,-521) (-3/8,-10/27) -> (-8/27,-13/44) Hyperbolic Matrix(157,58,988,365) (-17/46,-7/19) -> (3/19,1/6) Hyperbolic Matrix(105,38,-572,-207) (-4/11,-9/25) -> (-5/27,-2/11) Hyperbolic Matrix(1091,392,-3042,-1093) (-9/25,-14/39) -> (-14/39,-19/53) Parabolic Matrix(2651,950,3770,1351) (-19/53,-5/14) -> (45/64,19/27) Hyperbolic Matrix(103,36,-598,-209) (-7/20,-1/3) -> (-5/29,-1/6) Hyperbolic Matrix(103,32,-338,-105) (-1/3,-4/13) -> (-4/13,-7/23) Parabolic Matrix(883,268,1196,363) (-7/23,-10/33) -> (14/19,17/23) Hyperbolic Matrix(1301,394,3094,937) (-10/33,-13/43) -> (29/69,8/19) Hyperbolic Matrix(53,16,520,157) (-13/43,-3/10) -> (1/10,1/9) Hyperbolic Matrix(833,246,-2990,-883) (-13/44,-5/17) -> (-17/61,-5/18) Hyperbolic Matrix(1821,508,2054,573) (-12/43,-29/104) -> (23/26,8/9) Hyperbolic Matrix(2963,826,3354,935) (-29/104,-17/61) -> (15/17,23/26) Hyperbolic Matrix(469,130,754,209) (-5/18,-8/29) -> (18/29,5/8) Hyperbolic Matrix(1819,500,2834,779) (-11/40,-14/51) -> (34/53,9/14) Hyperbolic Matrix(51,14,-572,-157) (-14/51,-3/11) -> (-1/11,0/1) Hyperbolic Matrix(155,42,572,155) (-3/11,-7/26) -> (7/26,3/11) Hyperbolic Matrix(209,56,780,209) (-7/26,-4/15) -> (4/15,7/26) Hyperbolic Matrix(53,14,-390,-103) (-4/15,-5/19) -> (-1/7,-2/15) Hyperbolic Matrix(1613,420,2600,677) (-6/23,-7/27) -> (49/79,18/29) Hyperbolic Matrix(623,160,806,207) (-7/27,-1/4) -> (17/22,41/53) Hyperbolic Matrix(261,62,442,105) (-1/4,-4/17) -> (10/17,13/22) Hyperbolic Matrix(103,24,442,103) (-4/17,-3/13) -> (3/13,4/17) Hyperbolic Matrix(53,12,234,53) (-3/13,-2/9) -> (2/9,3/13) Hyperbolic Matrix(1091,238,1664,363) (-12/55,-17/78) -> (17/26,2/3) Hyperbolic Matrix(1561,340,2392,521) (-17/78,-5/23) -> (15/23,17/26) Hyperbolic Matrix(729,158,1924,417) (-5/23,-8/37) -> (14/37,11/29) Hyperbolic Matrix(1299,280,3614,779) (-11/51,-3/14) -> (23/64,9/25) Hyperbolic Matrix(467,98,1482,311) (-4/19,-9/43) -> (11/35,6/19) Hyperbolic Matrix(259,54,494,103) (-9/43,-5/24) -> (1/2,9/17) Hyperbolic Matrix(467,96,754,155) (-5/24,-1/5) -> (13/21,31/50) Hyperbolic Matrix(51,10,260,51) (-1/5,-5/26) -> (5/26,1/5) Hyperbolic Matrix(209,40,1092,209) (-5/26,-4/21) -> (4/21,5/26) Hyperbolic Matrix(53,10,-546,-103) (-7/37,-3/16) -> (-1/10,-1/11) Hyperbolic Matrix(2237,388,2704,469) (-4/23,-9/52) -> (43/52,24/29) Hyperbolic Matrix(2235,386,2704,467) (-9/52,-5/29) -> (19/23,43/52) Hyperbolic Matrix(51,8,-338,-53) (-1/6,-2/13) -> (-2/13,-3/20) Parabolic Matrix(261,38,364,53) (-3/20,-1/7) -> (5/7,23/32) Hyperbolic Matrix(157,20,416,53) (-2/15,-1/8) -> (3/8,14/37) Hyperbolic Matrix(1247,146,1768,207) (-2/17,-3/26) -> (55/78,12/17) Hyperbolic Matrix(1613,184,2288,261) (-3/26,-1/9) -> (43/61,55/78) Hyperbolic Matrix(155,16,494,51) (-1/9,-1/10) -> (5/16,11/35) Hyperbolic Matrix(469,-40,598,-51) (0/1,1/10) -> (69/88,40/51) Hyperbolic Matrix(623,-74,884,-105) (1/9,1/8) -> (31/44,43/61) Hyperbolic Matrix(103,-14,390,-53) (1/8,1/7) -> (5/19,9/34) Hyperbolic Matrix(53,-8,338,-51) (1/7,2/13) -> (2/13,3/19) Parabolic Matrix(157,-28,286,-51) (1/6,2/11) -> (6/11,11/20) Hyperbolic Matrix(365,-68,832,-155) (2/11,3/16) -> (7/16,18/41) Hyperbolic Matrix(623,-118,1378,-261) (3/16,4/21) -> (14/31,19/42) Hyperbolic Matrix(207,-44,494,-105) (1/5,3/14) -> (5/12,13/31) Hyperbolic Matrix(2029,-438,2886,-623) (3/14,8/37) -> (26/37,45/64) Hyperbolic Matrix(209,-46,468,-103) (5/23,2/9) -> (4/9,13/29) Hyperbolic Matrix(259,-68,598,-157) (1/4,5/19) -> (3/7,13/30) Hyperbolic Matrix(1039,-286,1326,-365) (3/11,8/29) -> (18/23,29/37) Hyperbolic Matrix(157,-44,182,-51) (5/18,2/7) -> (6/7,7/8) Hyperbolic Matrix(103,-30,182,-53) (2/7,3/10) -> (9/16,4/7) Hyperbolic Matrix(105,-32,338,-103) (3/10,4/13) -> (4/13,5/16) Parabolic Matrix(259,-92,442,-157) (1/3,5/14) -> (7/12,17/29) Hyperbolic Matrix(1093,-392,3042,-1091) (5/14,14/39) -> (14/39,23/64) Parabolic Matrix(571,-206,1300,-469) (9/25,4/11) -> (18/41,11/25) Hyperbolic Matrix(207,-76,286,-105) (4/11,3/8) -> (13/18,8/11) Hyperbolic Matrix(6449,-2450,10400,-3951) (30/79,19/50) -> (31/50,80/129) Hyperbolic Matrix(103,-42,130,-53) (2/5,5/12) -> (11/14,4/5) Hyperbolic Matrix(209,-92,234,-103) (11/25,4/9) -> (8/9,1/1) Hyperbolic Matrix(677,-304,1040,-467) (13/29,9/20) -> (13/20,15/23) Hyperbolic Matrix(1819,-820,2886,-1301) (9/20,14/31) -> (46/73,29/46) Hyperbolic Matrix(1977,-896,2522,-1143) (19/42,5/11) -> (29/37,69/88) Hyperbolic Matrix(157,-72,338,-155) (5/11,6/13) -> (6/13,7/15) Parabolic Matrix(365,-202,468,-259) (11/20,5/9) -> (7/9,25/32) Hyperbolic Matrix(937,-524,1300,-727) (5/9,14/25) -> (18/25,31/43) Hyperbolic Matrix(677,-380,832,-467) (14/25,9/16) -> (13/16,22/27) Hyperbolic Matrix(573,-332,806,-467) (11/19,18/31) -> (22/31,5/7) Hyperbolic Matrix(519,-302,806,-469) (18/31,7/12) -> (9/14,20/31) Hyperbolic Matrix(729,-428,884,-519) (17/29,10/17) -> (14/17,19/23) Hyperbolic Matrix(521,-308,702,-415) (13/22,16/27) -> (20/27,3/4) Hyperbolic Matrix(1197,-710,1664,-987) (16/27,3/5) -> (41/57,18/25) Hyperbolic Matrix(209,-128,338,-207) (3/5,8/13) -> (8/13,13/21) Parabolic Matrix(989,-622,1404,-883) (5/8,17/27) -> (19/27,31/44) Hyperbolic Matrix(363,-230,494,-313) (12/19,7/11) -> (11/15,14/19) Hyperbolic Matrix(467,-298,572,-365) (7/11,16/25) -> (22/27,9/11) Hyperbolic Matrix(2339,-1518,2886,-1873) (24/37,13/20) -> (47/58,30/37) Hyperbolic Matrix(781,-548,962,-675) (7/10,26/37) -> (30/37,13/16) Hyperbolic Matrix(727,-514,884,-625) (12/17,17/24) -> (23/28,14/17) Hyperbolic Matrix(3223,-2318,3978,-2861) (23/32,41/57) -> (17/21,47/58) Hyperbolic Matrix(571,-412,650,-469) (31/43,13/18) -> (7/8,15/17) Hyperbolic Matrix(261,-200,338,-259) (3/4,10/13) -> (10/13,17/22) Parabolic Matrix(883,-690,1066,-833) (25/32,18/23) -> (24/29,5/6) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(51,44,-182,-157) -> Matrix(1,0,-4,1) Matrix(155,132,182,155) -> Matrix(1,-2,-4,9) Matrix(417,352,494,417) -> Matrix(1,12,-4,-47) Matrix(623,524,988,831) -> Matrix(3,14,-8,-37) Matrix(155,128,-442,-365) -> Matrix(1,2,-8,-15) Matrix(625,514,-884,-727) -> Matrix(1,2,-4,-7) Matrix(209,170,-702,-571) -> Matrix(1,2,-4,-7) Matrix(675,548,-962,-781) -> Matrix(3,4,-4,-5) Matrix(883,714,1092,883) -> Matrix(17,18,-52,-55) Matrix(209,168,260,209) -> Matrix(3,2,-8,-5) Matrix(53,42,-130,-103) -> Matrix(1,0,0,1) Matrix(259,200,-338,-261) -> Matrix(1,-4,0,1) Matrix(571,436,884,675) -> Matrix(3,8,-8,-21) Matrix(1507,1146,2392,1819) -> Matrix(3,8,-8,-21) Matrix(417,316,962,729) -> Matrix(1,2,0,1) Matrix(313,230,-494,-363) -> Matrix(7,8,-8,-9) Matrix(571,418,780,571) -> Matrix(17,18,-52,-55) Matrix(417,304,572,417) -> Matrix(11,10,-32,-29) Matrix(105,76,-286,-207) -> Matrix(3,2,-8,-5) Matrix(467,332,-806,-573) -> Matrix(5,4,-4,-3) Matrix(209,148,442,313) -> Matrix(3,2,-8,-5) Matrix(883,622,-1404,-989) -> Matrix(3,-2,-4,3) Matrix(623,438,-2886,-2029) -> Matrix(1,4,-4,-15) Matrix(3067,2154,-8294,-5825) -> Matrix(1,2,-4,-7) Matrix(261,182,598,417) -> Matrix(1,0,0,1) Matrix(415,288,598,415) -> Matrix(1,0,-4,1) Matrix(53,36,78,53) -> Matrix(1,2,-4,-7) Matrix(261,170,-1196,-779) -> Matrix(11,10,-32,-29) Matrix(1509,980,-4082,-2651) -> Matrix(7,6,-20,-17) Matrix(469,304,884,573) -> Matrix(5,4,-4,-3) Matrix(469,302,-806,-519) -> Matrix(5,4,-4,-3) Matrix(1143,734,1456,935) -> Matrix(3,2,-8,-5) Matrix(2651,1700,4134,2651) -> Matrix(7,4,-16,-9) Matrix(1249,800,1950,1249) -> Matrix(3,2,-8,-5) Matrix(363,232,-1222,-781) -> Matrix(3,2,-8,-5) Matrix(1507,954,-2548,-1613) -> Matrix(5,4,-4,-3) Matrix(313,198,988,625) -> Matrix(7,6,-20,-17) Matrix(831,524,988,623) -> Matrix(19,14,-72,-53) Matrix(1301,820,-2886,-1819) -> Matrix(17,12,-44,-31) Matrix(51,32,-416,-261) -> Matrix(3,2,-8,-5) Matrix(207,128,-338,-209) -> Matrix(3,2,-8,-5) Matrix(259,158,936,571) -> Matrix(1,0,4,1) Matrix(1039,632,2392,1455) -> Matrix(1,0,0,1) Matrix(2341,1422,-6162,-3743) -> Matrix(7,4,-16,-9) Matrix(469,284,1118,677) -> Matrix(1,0,-4,1) Matrix(779,462,-2106,-1249) -> Matrix(3,2,-8,-5) Matrix(1767,1046,4654,2755) -> Matrix(5,2,-8,-3) Matrix(105,62,442,261) -> Matrix(3,2,-8,-5) Matrix(157,92,-442,-259) -> Matrix(1,0,-4,1) Matrix(1249,726,1612,937) -> Matrix(1,0,-4,1) Matrix(989,574,2600,1509) -> Matrix(7,10,-12,-17) Matrix(571,330,988,571) -> Matrix(9,10,-28,-31) Matrix(209,120,364,209) -> Matrix(7,6,-20,-17) Matrix(53,30,-182,-103) -> Matrix(3,2,-8,-5) Matrix(51,28,-286,-157) -> Matrix(3,2,-8,-5) Matrix(155,84,286,155) -> Matrix(11,6,-24,-13) Matrix(209,112,390,209) -> Matrix(9,4,-16,-7) Matrix(573,304,884,469) -> Matrix(13,4,-36,-11) Matrix(415,218,988,519) -> Matrix(1,0,-4,1) Matrix(155,72,-338,-157) -> Matrix(11,6,-24,-13) Matrix(469,214,572,261) -> Matrix(23,10,-76,-33) Matrix(261,118,-1378,-623) -> Matrix(5,2,12,5) Matrix(2495,1126,3224,1455) -> Matrix(21,8,-92,-35) Matrix(103,46,-468,-209) -> Matrix(1,0,0,1) Matrix(363,160,-1300,-573) -> Matrix(7,2,-32,-9) Matrix(155,68,-832,-365) -> Matrix(1,0,4,1) Matrix(417,182,598,261) -> Matrix(1,0,0,1) Matrix(157,68,-598,-259) -> Matrix(1,0,4,1) Matrix(155,66,364,155) -> Matrix(1,0,4,1) Matrix(417,176,988,417) -> Matrix(1,0,-12,1) Matrix(105,44,-494,-207) -> Matrix(1,0,-4,1) Matrix(415,172,-1508,-625) -> Matrix(1,0,-4,1) Matrix(155,64,-884,-365) -> Matrix(1,0,-4,1) Matrix(51,20,130,51) -> Matrix(3,2,-8,-5) Matrix(209,80,546,209) -> Matrix(17,8,-32,-15) Matrix(1457,554,2054,781) -> Matrix(5,2,-8,-3) Matrix(26833,10192,43264,16433) -> Matrix(83,36,-196,-85) Matrix(26831,10190,43264,16431) -> Matrix(1,0,0,1) Matrix(1923,730,2600,987) -> Matrix(23,10,-76,-33) Matrix(417,158,1924,729) -> Matrix(19,8,-12,-5) Matrix(365,138,1378,521) -> Matrix(5,2,-28,-11) Matrix(415,154,-1404,-521) -> Matrix(1,0,0,1) Matrix(157,58,988,365) -> Matrix(1,0,0,1) Matrix(105,38,-572,-207) -> Matrix(7,2,-4,-1) Matrix(1091,392,-3042,-1093) -> Matrix(39,10,-160,-41) Matrix(2651,950,3770,1351) -> Matrix(25,6,-96,-23) Matrix(103,36,-598,-209) -> Matrix(1,0,8,1) Matrix(103,32,-338,-105) -> Matrix(7,4,-16,-9) Matrix(883,268,1196,363) -> Matrix(23,10,-76,-33) Matrix(1301,394,3094,937) -> Matrix(5,2,-28,-11) Matrix(53,16,520,157) -> Matrix(5,2,-8,-3) Matrix(833,246,-2990,-883) -> Matrix(5,2,-28,-11) Matrix(1821,508,2054,573) -> Matrix(29,6,-92,-19) Matrix(2963,826,3354,935) -> Matrix(31,6,-88,-17) Matrix(469,130,754,209) -> Matrix(11,2,-28,-5) Matrix(1819,500,2834,779) -> Matrix(11,2,-28,-5) Matrix(51,14,-572,-157) -> Matrix(1,0,4,1) Matrix(155,42,572,155) -> Matrix(1,0,12,1) Matrix(209,56,780,209) -> Matrix(1,0,-16,1) Matrix(53,14,-390,-103) -> Matrix(1,0,-4,1) Matrix(1613,420,2600,677) -> Matrix(5,-2,-12,5) Matrix(623,160,806,207) -> Matrix(1,-2,-4,9) Matrix(261,62,442,105) -> Matrix(3,2,-8,-5) Matrix(103,24,442,103) -> Matrix(7,4,-16,-9) Matrix(53,12,234,53) -> Matrix(5,2,-8,-3) Matrix(1091,238,1664,363) -> Matrix(35,12,-108,-37) Matrix(1561,340,2392,521) -> Matrix(61,20,-180,-59) Matrix(729,158,1924,417) -> Matrix(27,8,-44,-13) Matrix(1299,280,3614,779) -> Matrix(31,8,-4,-1) Matrix(467,98,1482,311) -> Matrix(3,2,-8,-5) Matrix(259,54,494,103) -> Matrix(1,0,0,1) Matrix(467,96,754,155) -> Matrix(3,2,-8,-5) Matrix(51,10,260,51) -> Matrix(1,0,4,1) Matrix(209,40,1092,209) -> Matrix(1,0,-16,1) Matrix(53,10,-546,-103) -> Matrix(1,0,-4,1) Matrix(2237,388,2704,469) -> Matrix(33,2,-116,-7) Matrix(2235,386,2704,467) -> Matrix(31,-2,-108,7) Matrix(51,8,-338,-53) -> Matrix(3,2,-8,-5) Matrix(261,38,364,53) -> Matrix(1,0,0,1) Matrix(157,20,416,53) -> Matrix(5,2,-8,-3) Matrix(1247,146,1768,207) -> Matrix(1,0,4,1) Matrix(1613,184,2288,261) -> Matrix(1,0,-8,1) Matrix(155,16,494,51) -> Matrix(3,2,-8,-5) Matrix(469,-40,598,-51) -> Matrix(1,0,0,1) Matrix(623,-74,884,-105) -> Matrix(1,0,-4,1) Matrix(103,-14,390,-53) -> Matrix(1,0,-4,1) Matrix(53,-8,338,-51) -> Matrix(3,2,-8,-5) Matrix(157,-28,286,-51) -> Matrix(3,2,-8,-5) Matrix(365,-68,832,-155) -> Matrix(1,0,4,1) Matrix(623,-118,1378,-261) -> Matrix(13,2,-20,-3) Matrix(207,-44,494,-105) -> Matrix(1,0,-4,1) Matrix(2029,-438,2886,-623) -> Matrix(1,4,-4,-15) Matrix(209,-46,468,-103) -> Matrix(1,0,0,1) Matrix(259,-68,598,-157) -> Matrix(1,0,4,1) Matrix(1039,-286,1326,-365) -> Matrix(1,0,-4,1) Matrix(157,-44,182,-51) -> Matrix(1,0,-4,1) Matrix(103,-30,182,-53) -> Matrix(3,2,-8,-5) Matrix(105,-32,338,-103) -> Matrix(7,4,-16,-9) Matrix(259,-92,442,-157) -> Matrix(1,0,-4,1) Matrix(1093,-392,3042,-1091) -> Matrix(1,-10,0,1) Matrix(571,-206,1300,-469) -> Matrix(1,2,0,1) Matrix(207,-76,286,-105) -> Matrix(3,2,-8,-5) Matrix(6449,-2450,10400,-3951) -> Matrix(11,6,-24,-13) Matrix(103,-42,130,-53) -> Matrix(1,0,0,1) Matrix(209,-92,234,-103) -> Matrix(1,2,-4,-7) Matrix(677,-304,1040,-467) -> Matrix(11,10,-32,-29) Matrix(1819,-820,2886,-1301) -> Matrix(17,12,-44,-31) Matrix(1977,-896,2522,-1143) -> Matrix(3,2,-8,-5) Matrix(157,-72,338,-155) -> Matrix(11,6,-24,-13) Matrix(365,-202,468,-259) -> Matrix(5,2,-28,-11) Matrix(937,-524,1300,-727) -> Matrix(1,0,0,1) Matrix(677,-380,832,-467) -> Matrix(11,4,-36,-13) Matrix(573,-332,806,-467) -> Matrix(13,4,-36,-11) Matrix(519,-302,806,-469) -> Matrix(13,4,-36,-11) Matrix(729,-428,884,-519) -> Matrix(1,2,-4,-7) Matrix(521,-308,702,-415) -> Matrix(11,4,-36,-13) Matrix(1197,-710,1664,-987) -> Matrix(1,0,0,1) Matrix(209,-128,338,-207) -> Matrix(3,2,-8,-5) Matrix(989,-622,1404,-883) -> Matrix(5,2,-28,-11) Matrix(363,-230,494,-313) -> Matrix(23,8,-72,-25) Matrix(467,-298,572,-365) -> Matrix(11,4,-36,-13) Matrix(2339,-1518,2886,-1873) -> Matrix(35,12,-108,-37) Matrix(781,-548,962,-675) -> Matrix(11,4,-36,-13) Matrix(727,-514,884,-625) -> Matrix(1,2,-4,-7) Matrix(3223,-2318,3978,-2861) -> Matrix(23,8,-72,-25) Matrix(571,-412,650,-469) -> Matrix(1,0,0,1) Matrix(261,-200,338,-259) -> Matrix(15,4,-64,-17) Matrix(883,-690,1066,-833) -> Matrix(17,2,-60,-7) 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): 28 Degree of the the map X: 56 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 -11/26 -7/26 -5/26 -9/52 -1/8 -3/26 -1/9 0/1 1/7 2/13 1/6 2/11 1/5 2/9 3/13 1/4 3/11 2/7 3/10 4/13 1/3 14/39 5/13 2/5 5/12 6/13 1/2 7/13 8/13 25/39 2/3 9/13 10/13 11/13 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -6/7 1/1 1/0 -11/13 1/0 -5/6 -5/2 1/0 -9/11 -5/4 -13/16 -3/2 -5/4 -4/5 -1/1 -1/2 -7/9 1/0 -10/13 1/0 -3/4 -3/2 1/0 -8/11 -1/1 -5/6 -5/7 1/0 -7/10 -1/2 1/0 -9/13 1/0 -2/3 -1/1 1/0 -9/14 -3/4 -1/2 -25/39 -1/2 -16/25 -1/1 -1/2 -7/11 1/0 -5/8 -3/4 -1/2 -8/13 -1/2 -3/5 1/0 -7/12 -3/2 1/0 -4/7 -1/1 -3/4 -5/9 -3/4 -6/11 -3/5 -1/2 -7/13 -1/2 -1/2 -1/2 1/0 -6/13 -1/2 -5/11 -5/12 -9/20 -3/8 -5/14 -4/9 -1/2 -1/3 -11/25 -1/4 -7/16 -1/2 -1/4 -3/7 -1/4 -11/26 0/1 -8/19 0/1 1/4 -5/12 -1/2 1/0 -12/29 -1/4 0/1 -7/17 1/0 -2/5 -1/1 -1/2 -5/13 -1/2 -3/8 -1/2 -3/8 -7/19 -3/8 -4/11 -1/3 -3/10 -9/25 -1/4 -14/39 -1/4 -5/14 -1/4 -3/14 -1/3 1/0 -4/13 -1/2 -3/10 -1/2 -3/8 -11/37 -3/8 -8/27 -1/2 -1/3 -5/17 -1/4 -2/7 -1/3 -1/4 -7/25 -1/4 -12/43 -3/14 -1/5 -5/18 -1/4 -1/6 -3/11 -1/8 -7/26 0/1 -4/15 0/1 1/6 -1/4 -1/2 1/0 -3/13 -1/2 -2/9 -1/2 -1/3 -7/32 -3/8 -5/14 -5/23 -5/16 -3/14 -1/4 -1/6 -1/5 -1/4 -5/26 0/1 -4/21 0/1 1/6 -3/16 1/2 1/0 -5/27 1/0 -2/11 -1/1 -1/2 -3/17 -1/4 -4/23 -1/8 0/1 -9/52 0/1 -5/29 1/8 -1/6 -1/2 1/0 -2/13 -1/2 -1/7 -1/4 -1/8 -1/2 -1/4 -2/17 -1/6 0/1 -3/26 0/1 -1/9 1/0 0/1 -1/2 0/1 1/7 1/0 2/13 -1/2 1/6 -1/2 -1/4 2/11 -1/2 -1/3 3/16 -1/4 -1/6 1/5 1/0 2/9 -1/1 -1/2 3/13 -1/2 1/4 -1/2 -1/4 3/11 1/4 2/7 -1/1 1/0 3/10 -3/4 -1/2 4/13 -1/2 1/3 -1/4 5/14 3/2 1/0 14/39 1/0 9/25 1/0 4/11 -3/2 -1/1 3/8 -3/4 -1/2 5/13 -1/2 2/5 -1/2 -1/3 5/12 -1/2 -1/4 3/7 1/0 4/9 -1/1 -1/2 5/11 -5/8 6/13 -1/2 1/2 -1/2 -1/4 7/13 -1/2 6/11 -1/2 -3/7 11/20 -1/2 -5/12 5/9 -3/8 14/25 -1/2 -1/3 9/16 -1/2 -1/4 4/7 -3/8 -1/3 15/26 -1/3 11/19 -5/16 7/12 -3/10 -1/4 17/29 -1/8 10/17 -1/2 0/1 3/5 -1/4 8/13 -1/2 5/8 -1/2 -3/8 12/19 -3/8 -4/11 7/11 -1/4 16/25 -1/2 -1/3 25/39 -1/2 9/14 -1/2 -3/8 2/3 -1/3 -1/4 9/13 -1/4 7/10 -1/2 -1/4 26/37 -3/10 -2/7 19/27 -1/4 12/17 -1/2 0/1 5/7 -1/4 18/25 -1/2 -1/3 31/43 -3/8 13/18 -1/2 -1/4 8/11 -5/14 -1/3 19/26 -1/3 11/15 -9/28 3/4 -3/10 -1/4 10/13 -1/4 7/9 -1/4 25/32 -1/6 -1/8 18/23 0/1 1/0 11/14 -1/2 -1/4 4/5 -1/2 -1/3 21/26 -1/3 17/21 -9/28 13/16 -5/16 -3/10 22/27 -1/3 -3/10 9/11 -5/16 14/17 -3/10 -2/7 19/23 -15/52 43/52 -2/7 24/29 -2/7 -17/60 5/6 -5/18 -1/4 11/13 -1/4 6/7 -1/4 -1/5 7/8 -1/2 -1/4 15/17 -3/8 23/26 -1/3 8/9 -1/3 -3/10 1/1 -1/4 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(51,44,-182,-157) (-1/1,-6/7) -> (-2/7,-7/25) Hyperbolic Matrix(155,132,182,155) (-6/7,-11/13) -> (11/13,6/7) Hyperbolic Matrix(131,110,156,131) (-11/13,-5/6) -> (5/6,11/13) Hyperbolic Matrix(129,106,-286,-235) (-5/6,-9/11) -> (-5/11,-9/20) Hyperbolic Matrix(209,170,-702,-571) (-9/11,-13/16) -> (-3/10,-11/37) Hyperbolic Matrix(79,64,-416,-337) (-13/16,-4/5) -> (-4/21,-3/16) Hyperbolic Matrix(53,42,-130,-103) (-4/5,-7/9) -> (-7/17,-2/5) Hyperbolic Matrix(181,140,234,181) (-7/9,-10/13) -> (10/13,7/9) Hyperbolic Matrix(79,60,104,79) (-10/13,-3/4) -> (3/4,10/13) Hyperbolic Matrix(27,20,-104,-77) (-3/4,-8/11) -> (-4/15,-1/4) Hyperbolic Matrix(105,76,-286,-207) (-8/11,-5/7) -> (-7/19,-4/11) Hyperbolic Matrix(79,56,-182,-129) (-5/7,-7/10) -> (-7/16,-3/7) Hyperbolic Matrix(181,126,260,181) (-7/10,-9/13) -> (9/13,7/10) Hyperbolic Matrix(53,36,78,53) (-9/13,-2/3) -> (2/3,9/13) Hyperbolic Matrix(183,118,-442,-285) (-2/3,-9/14) -> (-5/12,-12/29) Hyperbolic Matrix(701,450,1092,701) (-9/14,-25/39) -> (25/39,9/14) Hyperbolic Matrix(1249,800,1950,1249) (-25/39,-16/25) -> (16/25,25/39) Hyperbolic Matrix(363,232,-1222,-781) (-16/25,-7/11) -> (-11/37,-8/27) Hyperbolic Matrix(79,50,-286,-181) (-7/11,-5/8) -> (-5/18,-3/11) Hyperbolic Matrix(129,80,208,129) (-5/8,-8/13) -> (8/13,5/8) Hyperbolic Matrix(79,48,130,79) (-8/13,-3/5) -> (3/5,8/13) Hyperbolic Matrix(27,16,-130,-77) (-3/5,-7/12) -> (-3/14,-1/5) Hyperbolic Matrix(131,76,-312,-181) (-7/12,-4/7) -> (-8/19,-5/12) Hyperbolic Matrix(53,30,-182,-103) (-4/7,-5/9) -> (-5/17,-2/7) Hyperbolic Matrix(51,28,-286,-157) (-5/9,-6/11) -> (-2/11,-3/17) Hyperbolic Matrix(155,84,286,155) (-6/11,-7/13) -> (7/13,6/11) Hyperbolic Matrix(27,14,52,27) (-7/13,-1/2) -> (1/2,7/13) Hyperbolic Matrix(25,12,52,25) (-1/2,-6/13) -> (6/13,1/2) Hyperbolic Matrix(131,60,286,131) (-6/13,-5/11) -> (5/11,6/13) Hyperbolic Matrix(103,46,-468,-209) (-9/20,-4/9) -> (-2/9,-7/32) Hyperbolic Matrix(363,160,-1300,-573) (-4/9,-11/25) -> (-7/25,-12/43) Hyperbolic Matrix(155,68,-832,-365) (-11/25,-7/16) -> (-3/16,-5/27) Hyperbolic Matrix(391,166,676,287) (-3/7,-11/26) -> (15/26,11/19) Hyperbolic Matrix(389,164,676,285) (-11/26,-8/19) -> (4/7,15/26) Hyperbolic Matrix(155,64,-884,-365) (-12/29,-7/17) -> (-3/17,-4/23) Hyperbolic Matrix(51,20,130,51) (-2/5,-5/13) -> (5/13,2/5) Hyperbolic Matrix(79,30,208,79) (-5/13,-3/8) -> (3/8,5/13) Hyperbolic Matrix(27,10,-208,-77) (-3/8,-7/19) -> (-1/7,-1/8) Hyperbolic Matrix(105,38,-572,-207) (-4/11,-9/25) -> (-5/27,-2/11) Hyperbolic Matrix(701,252,1950,701) (-9/25,-14/39) -> (14/39,9/25) Hyperbolic Matrix(391,140,1092,391) (-14/39,-5/14) -> (5/14,14/39) Hyperbolic Matrix(79,28,-364,-129) (-5/14,-1/3) -> (-5/23,-3/14) Hyperbolic Matrix(25,8,78,25) (-1/3,-4/13) -> (4/13,1/3) Hyperbolic Matrix(79,24,260,79) (-4/13,-3/10) -> (3/10,4/13) Hyperbolic Matrix(27,8,-260,-77) (-8/27,-5/17) -> (-1/9,0/1) Hyperbolic Matrix(79,22,-650,-181) (-12/43,-5/18) -> (-1/8,-2/17) Hyperbolic Matrix(495,134,676,183) (-3/11,-7/26) -> (19/26,11/15) Hyperbolic Matrix(493,132,676,181) (-7/26,-4/15) -> (8/11,19/26) Hyperbolic Matrix(25,6,104,25) (-1/4,-3/13) -> (3/13,1/4) Hyperbolic Matrix(53,12,234,53) (-3/13,-2/9) -> (2/9,3/13) Hyperbolic Matrix(183,40,-1066,-233) (-7/32,-5/23) -> (-5/29,-1/6) Hyperbolic Matrix(547,106,676,131) (-1/5,-5/26) -> (21/26,17/21) Hyperbolic Matrix(545,104,676,129) (-5/26,-4/21) -> (4/5,21/26) Hyperbolic Matrix(2237,388,2704,469) (-4/23,-9/52) -> (43/52,24/29) Hyperbolic Matrix(2235,386,2704,467) (-9/52,-5/29) -> (19/23,43/52) Hyperbolic Matrix(25,4,156,25) (-1/6,-2/13) -> (2/13,1/6) Hyperbolic Matrix(27,4,182,27) (-2/13,-1/7) -> (1/7,2/13) Hyperbolic Matrix(599,70,676,79) (-2/17,-3/26) -> (23/26,8/9) Hyperbolic Matrix(597,68,676,77) (-3/26,-1/9) -> (15/17,23/26) Hyperbolic Matrix(131,-18,182,-25) (0/1,1/7) -> (5/7,18/25) Hyperbolic Matrix(157,-28,286,-51) (1/6,2/11) -> (6/11,11/20) Hyperbolic Matrix(493,-92,702,-131) (2/11,3/16) -> (7/10,26/37) Hyperbolic Matrix(337,-64,416,-79) (3/16,1/5) -> (17/21,13/16) Hyperbolic Matrix(77,-16,130,-27) (1/5,2/9) -> (10/17,3/5) Hyperbolic Matrix(77,-20,104,-27) (1/4,3/11) -> (11/15,3/4) Hyperbolic Matrix(181,-50,286,-79) (3/11,2/7) -> (12/19,7/11) Hyperbolic Matrix(103,-30,182,-53) (2/7,3/10) -> (9/16,4/7) Hyperbolic Matrix(259,-92,442,-157) (1/3,5/14) -> (7/12,17/29) Hyperbolic Matrix(859,-310,1222,-441) (9/25,4/11) -> (26/37,19/27) Hyperbolic Matrix(207,-76,286,-105) (4/11,3/8) -> (13/18,8/11) Hyperbolic Matrix(103,-42,130,-53) (2/5,5/12) -> (11/14,4/5) Hyperbolic Matrix(181,-76,312,-131) (5/12,3/7) -> (11/19,7/12) Hyperbolic Matrix(129,-56,182,-79) (3/7,4/9) -> (12/17,5/7) Hyperbolic Matrix(235,-106,286,-129) (4/9,5/11) -> (9/11,14/17) Hyperbolic Matrix(365,-202,468,-259) (11/20,5/9) -> (7/9,25/32) Hyperbolic Matrix(937,-524,1300,-727) (5/9,14/25) -> (18/25,31/43) Hyperbolic Matrix(677,-380,832,-467) (14/25,9/16) -> (13/16,22/27) Hyperbolic Matrix(729,-428,884,-519) (17/29,10/17) -> (14/17,19/23) Hyperbolic Matrix(181,-114,208,-131) (5/8,12/19) -> (6/7,7/8) Hyperbolic Matrix(467,-298,572,-365) (7/11,16/25) -> (22/27,9/11) Hyperbolic Matrix(285,-184,364,-235) (9/14,2/3) -> (18/23,11/14) Hyperbolic Matrix(233,-164,260,-183) (19/27,12/17) -> (8/9,1/1) Hyperbolic Matrix(571,-412,650,-469) (31/43,13/18) -> (7/8,15/17) Hyperbolic Matrix(883,-690,1066,-833) (25/32,18/23) -> (24/29,5/6) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(51,44,-182,-157) -> Matrix(1,0,-4,1) Matrix(155,132,182,155) -> Matrix(1,-2,-4,9) Matrix(131,110,156,131) -> Matrix(1,5,-4,-19) Matrix(129,106,-286,-235) -> Matrix(3,5,-8,-13) Matrix(209,170,-702,-571) -> Matrix(1,2,-4,-7) Matrix(79,64,-416,-337) -> Matrix(1,1,4,5) Matrix(53,42,-130,-103) -> Matrix(1,0,0,1) Matrix(181,140,234,181) -> Matrix(1,-1,-4,5) Matrix(79,60,104,79) -> Matrix(1,3,-4,-11) Matrix(27,20,-104,-77) -> Matrix(1,1,0,1) Matrix(105,76,-286,-207) -> Matrix(3,2,-8,-5) Matrix(79,56,-182,-129) -> Matrix(1,1,-4,-3) Matrix(181,126,260,181) -> Matrix(1,1,-4,-3) Matrix(53,36,78,53) -> Matrix(1,2,-4,-7) Matrix(183,118,-442,-285) -> Matrix(1,1,-4,-3) Matrix(701,450,1092,701) -> Matrix(5,3,-12,-7) Matrix(1249,800,1950,1249) -> Matrix(3,2,-8,-5) Matrix(363,232,-1222,-781) -> Matrix(3,2,-8,-5) Matrix(79,50,-286,-181) -> Matrix(1,1,-8,-7) Matrix(129,80,208,129) -> Matrix(5,3,-12,-7) Matrix(79,48,130,79) -> Matrix(1,1,-4,-3) Matrix(27,16,-130,-77) -> Matrix(1,1,-4,-3) Matrix(131,76,-312,-181) -> Matrix(1,1,0,1) Matrix(53,30,-182,-103) -> Matrix(3,2,-8,-5) Matrix(51,28,-286,-157) -> Matrix(3,2,-8,-5) Matrix(155,84,286,155) -> Matrix(11,6,-24,-13) Matrix(27,14,52,27) -> Matrix(1,1,-4,-3) Matrix(25,12,52,25) -> Matrix(1,1,-4,-3) Matrix(131,60,286,131) -> Matrix(11,5,-20,-9) Matrix(103,46,-468,-209) -> Matrix(1,0,0,1) Matrix(363,160,-1300,-573) -> Matrix(7,2,-32,-9) Matrix(155,68,-832,-365) -> Matrix(1,0,4,1) Matrix(391,166,676,287) -> Matrix(9,1,-28,-3) Matrix(389,164,676,285) -> Matrix(7,-1,-20,3) Matrix(155,64,-884,-365) -> Matrix(1,0,-4,1) Matrix(51,20,130,51) -> Matrix(3,2,-8,-5) Matrix(79,30,208,79) -> Matrix(7,3,-12,-5) Matrix(27,10,-208,-77) -> Matrix(3,1,-4,-1) Matrix(105,38,-572,-207) -> Matrix(7,2,-4,-1) Matrix(701,252,1950,701) -> Matrix(27,7,-4,-1) Matrix(391,140,1092,391) -> Matrix(13,3,4,1) Matrix(79,28,-364,-129) -> Matrix(5,1,-16,-3) Matrix(25,8,78,25) -> Matrix(1,1,-4,-3) Matrix(79,24,260,79) -> Matrix(7,3,-12,-5) Matrix(27,8,-260,-77) -> Matrix(3,1,-4,-1) Matrix(79,22,-650,-181) -> Matrix(5,1,-16,-3) Matrix(495,134,676,183) -> Matrix(17,1,-52,-3) Matrix(493,132,676,181) -> Matrix(11,-1,-32,3) Matrix(25,6,104,25) -> Matrix(1,1,-4,-3) Matrix(53,12,234,53) -> Matrix(5,2,-8,-3) Matrix(183,40,-1066,-233) -> Matrix(3,1,8,3) Matrix(547,106,676,131) -> Matrix(13,1,-40,-3) Matrix(545,104,676,129) -> Matrix(7,-1,-20,3) Matrix(2237,388,2704,469) -> Matrix(33,2,-116,-7) Matrix(2235,386,2704,467) -> Matrix(31,-2,-108,7) Matrix(25,4,156,25) -> Matrix(1,1,-4,-3) Matrix(27,4,182,27) -> Matrix(3,1,-4,-1) Matrix(599,70,676,79) -> Matrix(9,1,-28,-3) Matrix(597,68,676,77) -> Matrix(3,-1,-8,3) Matrix(131,-18,182,-25) -> Matrix(1,1,-4,-3) Matrix(157,-28,286,-51) -> Matrix(3,2,-8,-5) Matrix(493,-92,702,-131) -> Matrix(5,1,-16,-3) Matrix(337,-64,416,-79) -> Matrix(9,1,-28,-3) Matrix(77,-16,130,-27) -> Matrix(1,1,-4,-3) Matrix(77,-20,104,-27) -> Matrix(5,1,-16,-3) Matrix(181,-50,286,-79) -> Matrix(3,-1,-8,3) Matrix(103,-30,182,-53) -> Matrix(3,2,-8,-5) Matrix(259,-92,442,-157) -> Matrix(1,0,-4,1) Matrix(859,-310,1222,-441) -> Matrix(1,3,-4,-11) Matrix(207,-76,286,-105) -> Matrix(3,2,-8,-5) Matrix(103,-42,130,-53) -> Matrix(1,0,0,1) Matrix(181,-76,312,-131) -> Matrix(5,1,-16,-3) Matrix(129,-56,182,-79) -> Matrix(1,1,-4,-3) Matrix(235,-106,286,-129) -> Matrix(7,5,-24,-17) Matrix(365,-202,468,-259) -> Matrix(5,2,-28,-11) Matrix(937,-524,1300,-727) -> Matrix(1,0,0,1) Matrix(677,-380,832,-467) -> Matrix(11,4,-36,-13) Matrix(729,-428,884,-519) -> Matrix(1,2,-4,-7) Matrix(181,-114,208,-131) -> Matrix(3,1,-4,-1) Matrix(467,-298,572,-365) -> Matrix(11,4,-36,-13) Matrix(285,-184,364,-235) -> Matrix(3,1,-4,-1) Matrix(233,-164,260,-183) -> Matrix(5,1,-16,-3) Matrix(571,-412,650,-469) -> Matrix(1,0,0,1) Matrix(883,-690,1066,-833) -> Matrix(17,2,-60,-7) 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): 28 ----------------------------------------------------------------------- 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 (-1/2,0/1) 0 26 1/7 1/0 1 26 2/13 -1/2 2 2 1/6 (-1/2,-1/4) 0 13 2/11 (-1/2,-1/3) 0 26 3/16 (-1/4,-1/6) 0 13 1/5 1/0 1 26 2/9 (-1/1,-1/2) 0 26 3/13 -1/2 3 2 1/4 (-1/2,-1/4) 0 13 3/11 1/4 1 26 2/7 (-1/1,1/0) 0 26 3/10 (-3/4,-1/2) 0 13 4/13 -1/2 4 2 1/3 -1/4 1 26 5/14 (3/2,1/0) 0 13 14/39 1/0 10 2 9/25 1/0 1 26 4/11 (-3/2,-1/1) 0 26 3/8 (-3/4,-1/2) 0 13 5/13 -1/2 5 2 2/5 (-1/2,-1/3) 0 26 5/12 (-1/2,-1/4) 0 13 3/7 1/0 1 26 4/9 (-1/1,-1/2) 0 26 5/11 -5/8 1 26 6/13 -1/2 6 2 1/2 (-1/2,-1/4) 0 13 7/13 -1/2 5 2 6/11 (-1/2,-3/7) 0 26 11/20 (-1/2,-5/12) 0 13 5/9 -3/8 1 26 14/25 (-1/2,-1/3) 0 26 9/16 (-1/2,-1/4) 0 13 4/7 (-3/8,-1/3) 0 26 15/26 -1/3 8 1 11/19 -5/16 1 26 7/12 (-3/10,-1/4) 0 13 17/29 -1/8 1 26 10/17 (-1/2,0/1) 0 26 3/5 -1/4 1 26 8/13 -1/2 2 2 5/8 (-1/2,-3/8) 0 13 12/19 (-3/8,-4/11) 0 26 7/11 -1/4 1 26 16/25 (-1/2,-1/3) 0 26 25/39 -1/2 1 2 9/14 (-1/2,-3/8) 0 13 2/3 (-1/3,-1/4) 0 26 9/13 -1/4 1 2 7/10 (-1/2,-1/4) 0 13 26/37 (-3/10,-2/7) 0 26 19/27 -1/4 1 26 12/17 (-1/2,0/1) 0 26 5/7 -1/4 1 26 18/25 (-1/2,-1/3) 0 26 31/43 -3/8 1 26 13/18 (-1/2,-1/4) 0 13 8/11 (-5/14,-1/3) 0 26 19/26 -1/3 14 1 11/15 -9/28 1 26 3/4 (-3/10,-1/4) 0 13 10/13 -1/4 4 2 7/9 -1/4 1 26 25/32 (-1/6,-1/8) 0 13 18/23 (0/1,1/0) 0 26 11/14 (-1/2,-1/4) 0 13 4/5 (-1/2,-1/3) 0 26 21/26 -1/3 10 1 17/21 -9/28 1 26 13/16 (-5/16,-3/10) 0 13 22/27 (-1/3,-3/10) 0 26 9/11 -5/16 1 26 14/17 (-3/10,-2/7) 0 26 19/23 -15/52 1 26 43/52 -2/7 16 1 24/29 (-2/7,-17/60) 0 26 5/6 (-5/18,-1/4) 0 13 11/13 -1/4 7 2 6/7 (-1/4,-1/5) 0 26 7/8 (-1/2,-1/4) 0 13 15/17 -3/8 1 26 23/26 -1/3 6 1 8/9 (-1/3,-3/10) 0 26 1/1 -1/4 1 26 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(131,-18,182,-25) (0/1,1/7) -> (5/7,18/25) Hyperbolic Matrix(27,-4,182,-27) (1/7,2/13) -> (1/7,2/13) Reflection Matrix(25,-4,156,-25) (2/13,1/6) -> (2/13,1/6) Reflection Matrix(157,-28,286,-51) (1/6,2/11) -> (6/11,11/20) Hyperbolic Matrix(493,-92,702,-131) (2/11,3/16) -> (7/10,26/37) Hyperbolic Matrix(337,-64,416,-79) (3/16,1/5) -> (17/21,13/16) Hyperbolic Matrix(77,-16,130,-27) (1/5,2/9) -> (10/17,3/5) Hyperbolic Matrix(53,-12,234,-53) (2/9,3/13) -> (2/9,3/13) Reflection Matrix(25,-6,104,-25) (3/13,1/4) -> (3/13,1/4) Reflection Matrix(77,-20,104,-27) (1/4,3/11) -> (11/15,3/4) Hyperbolic Matrix(181,-50,286,-79) (3/11,2/7) -> (12/19,7/11) Hyperbolic Matrix(103,-30,182,-53) (2/7,3/10) -> (9/16,4/7) Hyperbolic Matrix(79,-24,260,-79) (3/10,4/13) -> (3/10,4/13) Reflection Matrix(25,-8,78,-25) (4/13,1/3) -> (4/13,1/3) Reflection Matrix(259,-92,442,-157) (1/3,5/14) -> (7/12,17/29) Hyperbolic Matrix(391,-140,1092,-391) (5/14,14/39) -> (5/14,14/39) Reflection Matrix(701,-252,1950,-701) (14/39,9/25) -> (14/39,9/25) Reflection Matrix(859,-310,1222,-441) (9/25,4/11) -> (26/37,19/27) Hyperbolic Matrix(207,-76,286,-105) (4/11,3/8) -> (13/18,8/11) Hyperbolic Matrix(79,-30,208,-79) (3/8,5/13) -> (3/8,5/13) Reflection Matrix(51,-20,130,-51) (5/13,2/5) -> (5/13,2/5) Reflection Matrix(103,-42,130,-53) (2/5,5/12) -> (11/14,4/5) Hyperbolic Matrix(181,-76,312,-131) (5/12,3/7) -> (11/19,7/12) Hyperbolic Matrix(129,-56,182,-79) (3/7,4/9) -> (12/17,5/7) Hyperbolic Matrix(235,-106,286,-129) (4/9,5/11) -> (9/11,14/17) Hyperbolic Matrix(131,-60,286,-131) (5/11,6/13) -> (5/11,6/13) Reflection Matrix(25,-12,52,-25) (6/13,1/2) -> (6/13,1/2) Reflection Matrix(27,-14,52,-27) (1/2,7/13) -> (1/2,7/13) Reflection Matrix(155,-84,286,-155) (7/13,6/11) -> (7/13,6/11) Reflection Matrix(365,-202,468,-259) (11/20,5/9) -> (7/9,25/32) Hyperbolic Matrix(937,-524,1300,-727) (5/9,14/25) -> (18/25,31/43) Hyperbolic Matrix(677,-380,832,-467) (14/25,9/16) -> (13/16,22/27) Hyperbolic Matrix(209,-120,364,-209) (4/7,15/26) -> (4/7,15/26) Reflection Matrix(571,-330,988,-571) (15/26,11/19) -> (15/26,11/19) Reflection Matrix(729,-428,884,-519) (17/29,10/17) -> (14/17,19/23) Hyperbolic Matrix(79,-48,130,-79) (3/5,8/13) -> (3/5,8/13) Reflection Matrix(129,-80,208,-129) (8/13,5/8) -> (8/13,5/8) Reflection Matrix(181,-114,208,-131) (5/8,12/19) -> (6/7,7/8) Hyperbolic Matrix(467,-298,572,-365) (7/11,16/25) -> (22/27,9/11) Hyperbolic Matrix(1249,-800,1950,-1249) (16/25,25/39) -> (16/25,25/39) Reflection Matrix(701,-450,1092,-701) (25/39,9/14) -> (25/39,9/14) Reflection Matrix(285,-184,364,-235) (9/14,2/3) -> (18/23,11/14) Hyperbolic Matrix(53,-36,78,-53) (2/3,9/13) -> (2/3,9/13) Reflection Matrix(181,-126,260,-181) (9/13,7/10) -> (9/13,7/10) Reflection Matrix(233,-164,260,-183) (19/27,12/17) -> (8/9,1/1) Hyperbolic Matrix(571,-412,650,-469) (31/43,13/18) -> (7/8,15/17) Hyperbolic Matrix(417,-304,572,-417) (8/11,19/26) -> (8/11,19/26) Reflection Matrix(571,-418,780,-571) (19/26,11/15) -> (19/26,11/15) Reflection Matrix(79,-60,104,-79) (3/4,10/13) -> (3/4,10/13) Reflection Matrix(181,-140,234,-181) (10/13,7/9) -> (10/13,7/9) Reflection Matrix(883,-690,1066,-833) (25/32,18/23) -> (24/29,5/6) Hyperbolic Matrix(209,-168,260,-209) (4/5,21/26) -> (4/5,21/26) Reflection Matrix(883,-714,1092,-883) (21/26,17/21) -> (21/26,17/21) Reflection Matrix(1977,-1634,2392,-1977) (19/23,43/52) -> (19/23,43/52) Reflection Matrix(2495,-2064,3016,-2495) (43/52,24/29) -> (43/52,24/29) Reflection Matrix(131,-110,156,-131) (5/6,11/13) -> (5/6,11/13) Reflection Matrix(155,-132,182,-155) (11/13,6/7) -> (11/13,6/7) Reflection Matrix(781,-690,884,-781) (15/17,23/26) -> (15/17,23/26) Reflection Matrix(415,-368,468,-415) (23/26,8/9) -> (23/26,8/9) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,4,1) (0/1,1/0) -> (-1/2,0/1) Matrix(131,-18,182,-25) -> Matrix(1,1,-4,-3) -1/2 Matrix(27,-4,182,-27) -> Matrix(1,1,0,-1) (1/7,2/13) -> (-1/2,1/0) Matrix(25,-4,156,-25) -> Matrix(3,1,-8,-3) (2/13,1/6) -> (-1/2,-1/4) Matrix(157,-28,286,-51) -> Matrix(3,2,-8,-5) -1/2 Matrix(493,-92,702,-131) -> Matrix(5,1,-16,-3) -1/4 Matrix(337,-64,416,-79) -> Matrix(9,1,-28,-3) Matrix(77,-16,130,-27) -> Matrix(1,1,-4,-3) -1/2 Matrix(53,-12,234,-53) -> Matrix(3,2,-4,-3) (2/9,3/13) -> (-1/1,-1/2) Matrix(25,-6,104,-25) -> Matrix(3,1,-8,-3) (3/13,1/4) -> (-1/2,-1/4) Matrix(77,-20,104,-27) -> Matrix(5,1,-16,-3) -1/4 Matrix(181,-50,286,-79) -> Matrix(3,-1,-8,3) Matrix(103,-30,182,-53) -> Matrix(3,2,-8,-5) -1/2 Matrix(79,-24,260,-79) -> Matrix(5,3,-8,-5) (3/10,4/13) -> (-3/4,-1/2) Matrix(25,-8,78,-25) -> Matrix(3,1,-8,-3) (4/13,1/3) -> (-1/2,-1/4) Matrix(259,-92,442,-157) -> Matrix(1,0,-4,1) 0/1 Matrix(391,-140,1092,-391) -> Matrix(-1,3,0,1) (5/14,14/39) -> (3/2,1/0) Matrix(701,-252,1950,-701) -> Matrix(1,7,0,-1) (14/39,9/25) -> (-7/2,1/0) Matrix(859,-310,1222,-441) -> Matrix(1,3,-4,-11) Matrix(207,-76,286,-105) -> Matrix(3,2,-8,-5) -1/2 Matrix(79,-30,208,-79) -> Matrix(5,3,-8,-5) (3/8,5/13) -> (-3/4,-1/2) Matrix(51,-20,130,-51) -> Matrix(5,2,-12,-5) (5/13,2/5) -> (-1/2,-1/3) Matrix(103,-42,130,-53) -> Matrix(1,0,0,1) Matrix(181,-76,312,-131) -> Matrix(5,1,-16,-3) -1/4 Matrix(129,-56,182,-79) -> Matrix(1,1,-4,-3) -1/2 Matrix(235,-106,286,-129) -> Matrix(7,5,-24,-17) Matrix(131,-60,286,-131) -> Matrix(9,5,-16,-9) (5/11,6/13) -> (-5/8,-1/2) Matrix(25,-12,52,-25) -> Matrix(3,1,-8,-3) (6/13,1/2) -> (-1/2,-1/4) Matrix(27,-14,52,-27) -> Matrix(3,1,-8,-3) (1/2,7/13) -> (-1/2,-1/4) Matrix(155,-84,286,-155) -> Matrix(13,6,-28,-13) (7/13,6/11) -> (-1/2,-3/7) Matrix(365,-202,468,-259) -> Matrix(5,2,-28,-11) Matrix(937,-524,1300,-727) -> Matrix(1,0,0,1) Matrix(677,-380,832,-467) -> Matrix(11,4,-36,-13) -1/3 Matrix(209,-120,364,-209) -> Matrix(17,6,-48,-17) (4/7,15/26) -> (-3/8,-1/3) Matrix(571,-330,988,-571) -> Matrix(31,10,-96,-31) (15/26,11/19) -> (-1/3,-5/16) Matrix(729,-428,884,-519) -> Matrix(1,2,-4,-7) Matrix(79,-48,130,-79) -> Matrix(3,1,-8,-3) (3/5,8/13) -> (-1/2,-1/4) Matrix(129,-80,208,-129) -> Matrix(7,3,-16,-7) (8/13,5/8) -> (-1/2,-3/8) Matrix(181,-114,208,-131) -> Matrix(3,1,-4,-1) -1/2 Matrix(467,-298,572,-365) -> Matrix(11,4,-36,-13) -1/3 Matrix(1249,-800,1950,-1249) -> Matrix(5,2,-12,-5) (16/25,25/39) -> (-1/2,-1/3) Matrix(701,-450,1092,-701) -> Matrix(7,3,-16,-7) (25/39,9/14) -> (-1/2,-3/8) Matrix(285,-184,364,-235) -> Matrix(3,1,-4,-1) -1/2 Matrix(53,-36,78,-53) -> Matrix(7,2,-24,-7) (2/3,9/13) -> (-1/3,-1/4) Matrix(181,-126,260,-181) -> Matrix(3,1,-8,-3) (9/13,7/10) -> (-1/2,-1/4) Matrix(233,-164,260,-183) -> Matrix(5,1,-16,-3) -1/4 Matrix(571,-412,650,-469) -> Matrix(1,0,0,1) Matrix(417,-304,572,-417) -> Matrix(29,10,-84,-29) (8/11,19/26) -> (-5/14,-1/3) Matrix(571,-418,780,-571) -> Matrix(55,18,-168,-55) (19/26,11/15) -> (-1/3,-9/28) Matrix(79,-60,104,-79) -> Matrix(11,3,-40,-11) (3/4,10/13) -> (-3/10,-1/4) Matrix(181,-140,234,-181) -> Matrix(5,1,-24,-5) (10/13,7/9) -> (-1/4,-1/6) Matrix(883,-690,1066,-833) -> Matrix(17,2,-60,-7) Matrix(209,-168,260,-209) -> Matrix(5,2,-12,-5) (4/5,21/26) -> (-1/2,-1/3) Matrix(883,-714,1092,-883) -> Matrix(55,18,-168,-55) (21/26,17/21) -> (-1/3,-9/28) Matrix(1977,-1634,2392,-1977) -> Matrix(209,60,-728,-209) (19/23,43/52) -> (-15/52,-2/7) Matrix(2495,-2064,3016,-2495) -> Matrix(239,68,-840,-239) (43/52,24/29) -> (-2/7,-17/60) Matrix(131,-110,156,-131) -> Matrix(19,5,-72,-19) (5/6,11/13) -> (-5/18,-1/4) Matrix(155,-132,182,-155) -> Matrix(9,2,-40,-9) (11/13,6/7) -> (-1/4,-1/5) Matrix(781,-690,884,-781) -> Matrix(17,6,-48,-17) (15/17,23/26) -> (-3/8,-1/3) Matrix(415,-368,468,-415) -> Matrix(19,6,-60,-19) (23/26,8/9) -> (-1/3,-3/10) Matrix(-1,2,0,1) -> Matrix(-1,0,8,1) (1/1,1/0) -> (-1/4,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.