INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -13/7 -12/7 -11/7 -10/7 -9/7 -8/7 -1/1 -6/7 -5/7 -4/7 -1/2 -13/28 -3/7 -5/12 -11/28 -31/84 -1/3 -13/42 -3/10 -2/7 -3/11 -1/4 -3/13 -19/84 -1/5 -5/28 -1/6 -1/7 -1/8 -1/9 0/1 1/8 1/7 2/13 1/6 2/11 1/5 3/14 2/9 3/13 1/4 3/11 2/7 3/10 4/13 1/3 5/14 4/11 2/5 5/12 3/7 4/9 1/2 5/9 4/7 9/14 2/3 29/42 5/7 11/14 4/5 6/7 1/1 8/7 9/7 4/3 10/7 11/7 12/7 13/7 2/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -2/1 -2/1 1/0 -13/7 -2/1 -11/6 -3/2 1/0 -20/11 1/0 -9/5 -3/1 -2/1 1/0 -16/9 -3/2 -23/13 -1/1 0/1 1/0 -7/4 1/0 -19/11 -7/3 -9/4 -2/1 -12/7 -2/1 -29/17 -2/1 -9/5 -7/4 -46/27 -2/1 -7/4 -17/10 -7/4 -3/2 -22/13 -3/2 -1/1 -5/3 -2/1 -1/1 1/0 -18/11 -2/1 -7/4 -13/8 -3/2 -34/21 -1/1 -21/13 -2/1 -1/1 1/0 -8/5 1/0 -19/12 -5/2 -11/7 -2/1 -25/16 -11/6 -14/9 -2/1 -7/4 -17/11 -5/3 -8/5 -3/2 -3/2 -3/2 1/0 -13/9 -3/1 -2/1 1/0 -10/7 -2/1 -27/19 -2/1 -11/6 -9/5 -44/31 -7/4 -17/12 -7/4 -24/17 -3/2 -7/5 -2/1 -5/3 -3/2 -25/18 -3/2 1/0 -18/13 -5/3 -3/2 -29/21 -3/2 -11/8 -3/2 -26/19 -3/2 -4/3 -15/11 -5/4 -6/5 -1/1 -4/3 1/0 -13/10 -5/2 1/0 -9/7 -2/1 -23/18 -7/4 -3/2 -14/11 -2/1 -3/2 -19/15 -3/2 -4/3 -1/1 -5/4 -3/2 -11/9 -3/2 -4/3 -1/1 -6/5 -1/1 1/0 -7/6 -3/2 1/0 -8/7 -2/1 -1/1 -2/1 -1/1 1/0 -7/8 -3/2 -6/7 -1/1 -11/13 -1/1 -2/3 -1/2 -16/19 1/0 -5/6 -1/2 1/0 -9/11 -3/1 -2/1 1/0 -22/27 -2/1 1/0 -13/16 1/0 -4/5 -3/2 -11/14 -1/1 -18/23 -1/1 -3/4 -7/9 -1/1 -1/2 0/1 -24/31 1/0 -17/22 1/2 1/0 -10/13 -1/1 1/0 -13/17 -3/1 -5/2 -2/1 -3/4 -3/2 -11/15 -4/3 -9/7 -5/4 -19/26 -5/4 -17/14 -8/11 -7/6 -5/7 -1/1 -12/17 -5/6 -31/44 -3/4 -19/27 -1/1 -5/6 -4/5 -26/37 -4/5 -3/4 -7/10 -3/4 -1/2 -23/33 -2/3 -3/5 -1/2 -16/23 -1/2 -9/13 -1/1 -1/2 0/1 -11/16 1/0 -2/3 -1/1 1/0 -9/14 -1/1 -16/25 -7/8 -7/11 -1/1 -3/4 -2/3 -12/19 -1/2 -29/46 -1/2 1/0 -17/27 -1/1 0/1 1/0 -5/8 -1/2 -18/29 -1/2 0/1 -13/21 0/1 -21/34 1/2 1/0 -8/13 1/0 -11/18 -1/2 1/0 -3/5 -2/1 -1/1 1/0 -10/17 -3/2 -4/3 -27/46 -3/2 -5/4 -17/29 -3/2 -4/3 -1/1 -7/12 -5/4 -4/7 -1/1 -9/16 -5/6 -14/25 -1/1 -5/6 -19/34 -5/6 -3/4 -5/9 -1/1 -4/5 -3/4 -11/20 -3/4 -6/11 -2/3 -1/2 -7/13 -3/5 -4/7 -1/2 -1/2 -1/2 1/0 -7/15 2/1 3/1 1/0 -13/28 1/0 -6/13 -3/1 1/0 -5/11 -2/1 -3/2 -1/1 -4/9 1/0 -3/7 -1/1 -8/19 -3/4 -21/50 -3/4 -1/2 -34/81 -1/1 -3/4 -47/112 -3/4 -13/31 -1/1 -3/4 -2/3 -18/43 -1/1 -1/2 -23/55 -1/1 -3/4 -2/3 -5/12 -1/2 -17/41 -1/1 -3/4 -2/3 -29/70 -2/3 -12/29 -1/2 -7/17 -1/1 -2/3 -1/2 -16/39 -1/2 -9/22 -1/2 1/0 -2/5 -1/1 -1/2 -11/28 -1/2 -20/51 -1/2 -9/23 -1/2 -2/5 -1/3 -7/18 -1/2 -1/4 -12/31 -1/2 -17/44 -1/2 -22/57 -1/2 0/1 -27/70 0/1 -5/13 -1/1 -1/2 0/1 -13/34 -1/2 -1/4 -8/21 0/1 -11/29 -1/1 0/1 1/0 -14/37 -1/2 0/1 -3/8 -1/2 -10/27 -1/2 0/1 -17/46 -1/2 1/0 -24/65 -1/2 -31/84 -1/2 -7/19 -1/2 -1/3 0/1 -11/30 -1/2 1/0 -4/11 -1/4 -5/14 0/1 -6/17 0/1 1/4 -1/3 0/1 1/1 1/0 -6/19 0/1 1/0 -5/16 1/2 -9/29 0/1 1/1 1/0 -22/71 1/2 1/1 -13/42 1/1 -4/13 1/0 -3/10 1/2 1/0 -2/7 1/0 -5/18 -3/2 1/0 -18/65 0/1 1/0 -31/112 1/0 -13/47 -2/1 -1/1 1/0 -8/29 1/0 -3/11 -2/1 -1/1 1/0 -7/26 1/2 1/0 -11/41 3/1 4/1 1/0 -15/56 1/0 -4/15 1/0 -9/34 -3/2 1/0 -5/19 -2/1 -1/1 1/0 -1/4 1/0 -3/13 -1/2 -1/3 0/1 -5/22 -1/2 1/0 -12/53 -1/2 -19/84 -1/2 -7/31 -1/2 -1/3 0/1 -2/9 -1/2 0/1 -3/14 0/1 -4/19 1/4 -1/5 0/1 1/2 1/1 -2/11 2/1 1/0 -5/28 1/0 -8/45 1/0 -3/17 -1/1 0/1 1/0 -1/6 3/2 1/0 -2/13 3/1 1/0 -1/7 1/0 -1/8 1/0 -1/9 -1/1 0/1 1/0 0/1 1/0 1/8 1/0 1/7 1/0 2/13 -5/1 1/0 1/6 -7/2 1/0 2/11 -4/1 1/0 1/5 -3/1 -5/2 -2/1 3/14 -2/1 2/9 -2/1 -3/2 7/31 -2/1 -5/3 -3/2 5/22 -3/2 1/0 3/13 -2/1 -5/3 -3/2 1/4 1/0 4/15 1/0 7/26 -5/2 1/0 3/11 -1/1 0/1 1/0 2/7 1/0 5/17 -3/1 -2/1 1/0 8/27 1/0 11/37 -3/1 -2/1 1/0 3/10 -5/2 1/0 4/13 1/0 5/16 -5/2 1/3 -3/1 -2/1 1/0 5/14 -2/1 4/11 -7/4 7/19 -2/1 -5/3 -3/2 17/46 -3/2 1/0 10/27 -2/1 -3/2 3/8 -3/2 11/29 -2/1 -1/1 1/0 8/21 -2/1 13/34 -7/4 -3/2 5/13 -2/1 -3/2 -1/1 7/18 -7/4 -3/2 2/5 -3/2 -1/1 7/17 -3/2 -4/3 -1/1 12/29 -3/2 5/12 -3/2 3/7 -1/1 7/16 -1/2 11/25 -1/1 0/1 1/0 15/34 -1/2 1/0 4/9 1/0 5/11 -1/1 -1/2 0/1 6/13 1/1 1/0 1/2 -3/2 1/0 8/15 -3/2 15/28 -3/2 7/13 -3/2 -10/7 -7/5 6/11 -3/2 -4/3 5/9 -5/4 -6/5 -1/1 4/7 -1/1 11/19 -1/1 -5/6 -4/5 29/50 -5/6 -3/4 47/81 -1/1 -4/5 -3/4 65/112 -3/4 18/31 -1/1 -3/4 7/12 -3/4 24/41 -1/2 41/70 -1/1 17/29 -1/1 -2/3 -1/2 10/17 -2/3 -1/2 3/5 -1/1 0/1 1/0 17/28 1/0 14/23 -3/1 1/0 11/18 -3/2 1/0 8/13 1/0 21/34 -5/2 1/0 13/21 -2/1 18/29 -2/1 -3/2 5/8 -3/2 17/27 -2/1 -1/1 1/0 29/46 -3/2 1/0 41/65 -2/1 -5/3 -3/2 53/84 -3/2 12/19 -3/2 7/11 -4/3 -5/4 -1/1 9/14 -1/1 2/3 -1/1 1/0 11/16 1/0 20/29 1/0 29/42 -2/1 9/13 -2/1 -3/2 -1/1 7/10 -3/2 -5/4 5/7 -1/1 13/18 -9/10 -7/8 47/65 -1/1 -8/9 -7/8 81/112 -7/8 34/47 -7/8 -6/7 21/29 -1/1 -6/7 -5/6 8/11 -5/6 19/26 -11/14 -3/4 30/41 -13/17 -3/4 41/56 -3/4 11/15 -3/4 -5/7 -2/3 3/4 -1/2 10/13 -1/1 1/0 17/22 -5/2 1/0 41/53 -2/1 -1/1 1/0 65/84 1/0 24/31 1/0 7/9 -2/1 -3/2 -1/1 11/14 -1/1 4/5 -1/2 9/11 0/1 1/1 1/0 23/28 1/0 14/17 -2/1 1/0 5/6 -3/2 1/0 11/13 -3/2 -4/3 -1/1 6/7 -1/1 7/8 -1/2 1/1 -1/1 0/1 1/0 8/7 0/1 7/6 -1/2 1/0 13/11 -2/1 -1/1 1/0 6/5 -1/1 1/0 17/14 -1/1 11/9 -1/1 -2/3 -1/2 27/22 -3/4 -1/2 16/13 -1/2 5/4 -1/2 19/15 -1/1 -2/3 -1/2 14/11 -1/2 0/1 9/7 0/1 22/17 0/1 1/2 35/27 0/1 1/2 1/1 13/10 1/2 1/0 17/13 -1/1 0/1 1/0 21/16 1/0 4/3 1/0 19/14 -1/1 15/11 -1/1 -4/5 -3/4 26/19 -2/3 -1/2 37/27 -1/1 -3/4 -2/3 11/8 -1/2 29/21 -1/2 18/13 -1/2 -1/3 25/18 -1/2 1/0 7/5 -1/2 -1/3 0/1 24/17 -1/2 41/29 -1/2 -1/3 0/1 17/12 -1/4 10/7 0/1 23/16 1/2 36/25 1/2 13/9 0/1 1/1 1/0 16/11 1/2 3/2 -1/2 1/0 17/11 -1/2 -2/5 -1/3 14/9 -1/4 0/1 11/7 0/1 30/19 0/1 1/4 49/31 0/1 1/4 1/3 19/12 1/2 65/41 0/1 1/2 1/1 111/70 0/1 46/29 0/1 1/2 27/17 0/1 1/3 1/2 8/5 1/0 45/28 1/0 37/23 -3/1 -2/1 1/0 29/18 -3/2 1/0 21/13 -1/1 0/1 1/0 34/21 -1/1 13/8 -1/2 44/27 -1/2 31/19 -1/2 -2/5 -1/3 18/11 -1/4 0/1 23/14 0/1 5/3 -1/1 0/1 1/0 27/16 -1/2 49/29 -1/1 0/1 1/0 71/42 -1/1 22/13 -1/1 -1/2 17/10 -1/2 -1/4 12/7 0/1 31/18 1/6 1/4 50/29 0/1 1/4 19/11 0/1 1/4 1/3 26/15 1/2 1/1 7/4 1/0 23/13 -2/1 -1/1 1/0 39/22 -1/2 1/0 16/9 -1/2 25/14 0/1 9/5 0/1 1/1 1/0 20/11 1/0 51/28 1/0 31/17 -2/1 -1/1 1/0 11/6 -1/2 1/0 13/7 0/1 2/1 0/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,4,0,1) (-2/1,1/0) -> (2/1,1/0) Parabolic Matrix(139,260,224,419) (-2/1,-13/7) -> (13/21,18/29) Hyperbolic Matrix(225,416,364,673) (-13/7,-11/6) -> (21/34,13/21) Hyperbolic Matrix(195,356,-476,-869) (-11/6,-20/11) -> (-16/39,-9/22) Hyperbolic Matrix(197,356,140,253) (-20/11,-9/5) -> (7/5,24/17) Hyperbolic Matrix(29,52,-140,-251) (-9/5,-16/9) -> (-4/19,-1/5) Hyperbolic Matrix(307,544,-364,-645) (-16/9,-23/13) -> (-11/13,-16/19) Hyperbolic Matrix(141,248,112,197) (-23/13,-7/4) -> (5/4,19/15) Hyperbolic Matrix(85,148,-112,-195) (-7/4,-19/11) -> (-13/17,-3/4) Hyperbolic Matrix(335,576,-196,-337) (-19/11,-12/7) -> (-12/7,-29/17) Parabolic Matrix(1511,2576,952,1623) (-29/17,-46/27) -> (46/29,27/17) Hyperbolic Matrix(559,952,1512,2575) (-46/27,-17/10) -> (17/46,10/27) Hyperbolic Matrix(505,856,364,617) (-17/10,-22/13) -> (18/13,25/18) Hyperbolic Matrix(223,376,-532,-897) (-22/13,-5/3) -> (-13/31,-18/43) Hyperbolic Matrix(29,48,-84,-139) (-5/3,-18/11) -> (-6/17,-1/3) Hyperbolic Matrix(169,276,-308,-503) (-18/11,-13/8) -> (-11/20,-6/11) Hyperbolic Matrix(195,316,224,363) (-13/8,-34/21) -> (6/7,7/8) Hyperbolic Matrix(309,500,364,589) (-34/21,-21/13) -> (11/13,6/7) Hyperbolic Matrix(253,408,-364,-587) (-21/13,-8/5) -> (-16/23,-9/13) Hyperbolic Matrix(113,180,-140,-223) (-8/5,-19/12) -> (-13/16,-4/5) Hyperbolic Matrix(307,484,-196,-309) (-19/12,-11/7) -> (-11/7,-25/16) Parabolic Matrix(141,220,-448,-699) (-25/16,-14/9) -> (-6/19,-5/16) Hyperbolic Matrix(421,652,308,477) (-14/9,-17/11) -> (15/11,26/19) Hyperbolic Matrix(83,128,308,475) (-17/11,-3/2) -> (7/26,3/11) Hyperbolic Matrix(113,164,-308,-447) (-3/2,-13/9) -> (-7/19,-11/30) Hyperbolic Matrix(279,400,-196,-281) (-13/9,-10/7) -> (-10/7,-27/19) Parabolic Matrix(673,956,868,1233) (-27/19,-44/31) -> (24/31,7/9) Hyperbolic Matrix(699,992,532,755) (-44/31,-17/12) -> (21/16,4/3) Hyperbolic Matrix(671,948,-952,-1345) (-17/12,-24/17) -> (-12/17,-31/44) Hyperbolic Matrix(253,356,140,197) (-24/17,-7/5) -> (9/5,20/11) Hyperbolic Matrix(449,624,-644,-895) (-7/5,-25/18) -> (-7/10,-23/33) Hyperbolic Matrix(617,856,364,505) (-25/18,-18/13) -> (22/13,17/10) Hyperbolic Matrix(55,76,364,503) (-18/13,-29/21) -> (1/7,2/13) Hyperbolic Matrix(29,40,224,309) (-29/21,-11/8) -> (1/8,1/7) Hyperbolic Matrix(169,232,-448,-615) (-11/8,-26/19) -> (-14/37,-3/8) Hyperbolic Matrix(477,652,308,421) (-26/19,-15/11) -> (17/11,14/9) Hyperbolic Matrix(197,268,-308,-419) (-15/11,-4/3) -> (-16/25,-7/11) Hyperbolic Matrix(141,184,-364,-475) (-4/3,-13/10) -> (-7/18,-12/31) Hyperbolic Matrix(251,324,-196,-253) (-13/10,-9/7) -> (-9/7,-23/18) Parabolic Matrix(477,608,-812,-1035) (-23/18,-14/11) -> (-10/17,-27/46) Hyperbolic Matrix(167,212,308,391) (-14/11,-19/15) -> (7/13,6/11) Hyperbolic Matrix(197,248,112,141) (-19/15,-5/4) -> (7/4,23/13) Hyperbolic Matrix(29,36,-112,-139) (-5/4,-11/9) -> (-5/19,-1/4) Hyperbolic Matrix(197,240,-252,-307) (-11/9,-6/5) -> (-18/23,-7/9) Hyperbolic Matrix(57,68,-140,-167) (-6/5,-7/6) -> (-9/22,-2/5) Hyperbolic Matrix(139,160,364,419) (-7/6,-8/7) -> (8/21,13/34) Hyperbolic Matrix(85,96,224,253) (-8/7,-1/1) -> (11/29,8/21) Hyperbolic Matrix(141,124,224,197) (-1/1,-7/8) -> (5/8,17/27) Hyperbolic Matrix(363,316,224,195) (-7/8,-6/7) -> (34/21,13/8) Hyperbolic Matrix(589,500,364,309) (-6/7,-11/13) -> (21/13,34/21) Hyperbolic Matrix(309,260,700,589) (-16/19,-5/6) -> (15/34,4/9) Hyperbolic Matrix(29,24,-168,-139) (-5/6,-9/11) -> (-3/17,-1/6) Hyperbolic Matrix(1063,868,616,503) (-9/11,-22/27) -> (50/29,19/11) Hyperbolic Matrix(811,660,-2100,-1709) (-22/27,-13/16) -> (-17/44,-22/57) Hyperbolic Matrix(111,88,140,111) (-4/5,-11/14) -> (11/14,4/5) Hyperbolic Matrix(475,372,392,307) (-11/14,-18/23) -> (6/5,17/14) Hyperbolic Matrix(727,564,504,391) (-7/9,-24/31) -> (36/25,13/9) Hyperbolic Matrix(419,324,-1848,-1429) (-24/31,-17/22) -> (-5/22,-12/53) Hyperbolic Matrix(57,44,364,281) (-17/22,-10/13) -> (2/13,1/6) Hyperbolic Matrix(167,128,364,279) (-10/13,-13/17) -> (5/11,6/13) Hyperbolic Matrix(27,20,112,83) (-3/4,-11/15) -> (3/13,1/4) Hyperbolic Matrix(197,144,-420,-307) (-11/15,-19/26) -> (-1/2,-7/15) Hyperbolic Matrix(449,328,308,225) (-19/26,-8/11) -> (16/11,3/2) Hyperbolic Matrix(139,100,-196,-141) (-8/11,-5/7) -> (-5/7,-12/17) Parabolic Matrix(1147,808,-2744,-1933) (-31/44,-19/27) -> (-23/55,-5/12) Hyperbolic Matrix(2071,1456,1512,1063) (-19/27,-26/37) -> (26/19,37/27) Hyperbolic Matrix(365,256,-1316,-923) (-26/37,-7/10) -> (-5/18,-18/65) Hyperbolic Matrix(867,604,-2212,-1541) (-23/33,-16/23) -> (-20/51,-9/23) Hyperbolic Matrix(337,232,-812,-559) (-9/13,-11/16) -> (-5/12,-17/41) Hyperbolic Matrix(309,212,532,365) (-11/16,-2/3) -> (18/31,7/12) Hyperbolic Matrix(55,36,84,55) (-2/3,-9/14) -> (9/14,2/3) Hyperbolic Matrix(531,340,392,251) (-9/14,-16/25) -> (4/3,19/14) Hyperbolic Matrix(139,88,308,195) (-7/11,-12/19) -> (4/9,5/11) Hyperbolic Matrix(1427,900,-3864,-2437) (-12/19,-29/46) -> (-17/46,-24/65) Hyperbolic Matrix(1961,1236,1512,953) (-29/46,-17/27) -> (35/27,13/10) Hyperbolic Matrix(197,124,224,141) (-17/27,-5/8) -> (7/8,1/1) Hyperbolic Matrix(167,104,448,279) (-5/8,-18/29) -> (10/27,3/8) Hyperbolic Matrix(419,260,224,139) (-18/29,-13/21) -> (13/7,2/1) Hyperbolic Matrix(673,416,364,225) (-13/21,-21/34) -> (11/6,13/7) Hyperbolic Matrix(253,156,-952,-587) (-21/34,-8/13) -> (-4/15,-9/34) Hyperbolic Matrix(111,68,364,223) (-8/13,-11/18) -> (3/10,4/13) Hyperbolic Matrix(197,120,-504,-307) (-11/18,-3/5) -> (-9/23,-7/18) Hyperbolic Matrix(27,16,140,83) (-3/5,-10/17) -> (2/11,1/5) Hyperbolic Matrix(1623,952,2576,1511) (-27/46,-17/29) -> (17/27,29/46) Hyperbolic Matrix(253,148,-812,-475) (-17/29,-7/12) -> (-5/16,-9/29) Hyperbolic Matrix(111,64,-196,-113) (-7/12,-4/7) -> (-4/7,-9/16) Parabolic Matrix(307,172,448,251) (-9/16,-14/25) -> (2/3,11/16) Hyperbolic Matrix(1681,940,-4004,-2239) (-14/25,-19/34) -> (-21/50,-34/81) Hyperbolic Matrix(617,344,504,281) (-19/34,-5/9) -> (11/9,27/22) Hyperbolic Matrix(29,16,-252,-139) (-5/9,-11/20) -> (-1/8,-1/9) Hyperbolic Matrix(391,212,308,167) (-6/11,-7/13) -> (19/15,14/11) Hyperbolic Matrix(113,60,-420,-223) (-7/13,-1/2) -> (-7/26,-11/41) Hyperbolic Matrix(421,196,784,365) (-7/15,-13/28) -> (15/28,7/13) Hyperbolic Matrix(1373,636,1876,869) (-13/28,-6/13) -> (30/41,41/56) Hyperbolic Matrix(533,244,308,141) (-6/13,-5/11) -> (19/11,26/15) Hyperbolic Matrix(195,88,308,139) (-5/11,-4/9) -> (12/19,7/11) Hyperbolic Matrix(83,36,-196,-85) (-4/9,-3/7) -> (-3/7,-8/19) Parabolic Matrix(1541,648,868,365) (-8/19,-21/50) -> (39/22,16/9) Hyperbolic Matrix(7281,3056,12544,5265) (-34/81,-47/112) -> (65/112,18/31) Hyperbolic Matrix(6607,2772,8540,3583) (-47/112,-13/31) -> (41/53,65/84) Hyperbolic Matrix(1597,668,-5152,-2155) (-18/43,-23/55) -> (-9/29,-22/71) Hyperbolic Matrix(1457,604,-3780,-1567) (-17/41,-29/70) -> (-27/70,-5/13) Hyperbolic Matrix(2241,928,3248,1345) (-29/70,-12/29) -> (20/29,29/42) Hyperbolic Matrix(281,116,952,393) (-12/29,-7/17) -> (5/17,8/27) Hyperbolic Matrix(253,104,-1428,-587) (-7/17,-16/39) -> (-8/45,-3/17) Hyperbolic Matrix(477,188,784,309) (-2/5,-11/28) -> (17/28,14/23) Hyperbolic Matrix(2519,988,1568,615) (-11/28,-20/51) -> (8/5,45/28) Hyperbolic Matrix(2297,888,1596,617) (-12/31,-17/44) -> (23/16,36/25) Hyperbolic Matrix(9547,3684,6020,2323) (-22/57,-27/70) -> (111/70,46/29) Hyperbolic Matrix(167,64,728,279) (-5/13,-13/34) -> (5/22,3/13) Hyperbolic Matrix(419,160,364,139) (-13/34,-8/21) -> (8/7,7/6) Hyperbolic Matrix(253,96,224,85) (-8/21,-11/29) -> (1/1,8/7) Hyperbolic Matrix(1763,668,2436,923) (-11/29,-14/37) -> (34/47,21/29) Hyperbolic Matrix(279,104,448,167) (-3/8,-10/27) -> (18/29,5/8) Hyperbolic Matrix(3137,1160,1820,673) (-10/27,-17/46) -> (31/18,50/29) Hyperbolic Matrix(4453,1644,7056,2605) (-24/65,-31/84) -> (53/84,12/19) Hyperbolic Matrix(5487,2024,7588,2799) (-31/84,-7/19) -> (47/65,81/112) Hyperbolic Matrix(449,164,616,225) (-11/30,-4/11) -> (8/11,19/26) Hyperbolic Matrix(111,40,308,111) (-4/11,-5/14) -> (5/14,4/11) Hyperbolic Matrix(643,228,392,139) (-5/14,-6/17) -> (18/11,23/14) Hyperbolic Matrix(139,44,616,195) (-1/3,-6/19) -> (2/9,7/31) Hyperbolic Matrix(5965,1848,3528,1093) (-22/71,-13/42) -> (71/42,22/13) Hyperbolic Matrix(1541,476,2632,813) (-13/42,-4/13) -> (24/41,41/70) Hyperbolic Matrix(223,68,364,111) (-4/13,-3/10) -> (11/18,8/13) Hyperbolic Matrix(55,16,-196,-57) (-3/10,-2/7) -> (-2/7,-5/18) Parabolic Matrix(9073,2512,12544,3473) (-18/65,-31/112) -> (81/112,34/47) Hyperbolic Matrix(7083,1960,11228,3107) (-31/112,-13/47) -> (41/65,53/84) Hyperbolic Matrix(2967,820,1820,503) (-13/47,-8/29) -> (44/27,31/19) Hyperbolic Matrix(335,92,812,223) (-8/29,-3/11) -> (7/17,12/29) Hyperbolic Matrix(475,128,308,83) (-3/11,-7/26) -> (3/2,17/11) Hyperbolic Matrix(2297,616,3136,841) (-11/41,-15/56) -> (41/56,11/15) Hyperbolic Matrix(673,180,1260,337) (-15/56,-4/15) -> (8/15,15/28) Hyperbolic Matrix(925,244,1596,421) (-9/34,-5/19) -> (11/19,29/50) Hyperbolic Matrix(83,20,112,27) (-1/4,-3/13) -> (11/15,3/4) Hyperbolic Matrix(279,64,728,167) (-3/13,-5/22) -> (13/34,5/13) Hyperbolic Matrix(5461,1236,7056,1597) (-12/53,-19/84) -> (65/84,24/31) Hyperbolic Matrix(5963,1348,10276,2323) (-19/84,-7/31) -> (47/81,65/112) Hyperbolic Matrix(1371,308,868,195) (-7/31,-2/9) -> (30/19,49/31) Hyperbolic Matrix(55,12,252,55) (-2/9,-3/14) -> (3/14,2/9) Hyperbolic Matrix(699,148,392,83) (-3/14,-4/19) -> (16/9,25/14) Hyperbolic Matrix(83,16,140,27) (-1/5,-2/11) -> (10/17,3/5) Hyperbolic Matrix(645,116,784,141) (-2/11,-5/28) -> (23/28,14/17) Hyperbolic Matrix(2855,508,1568,279) (-5/28,-8/45) -> (20/11,51/28) Hyperbolic Matrix(281,44,364,57) (-1/6,-2/13) -> (10/13,17/22) Hyperbolic Matrix(503,76,364,55) (-2/13,-1/7) -> (29/21,18/13) Hyperbolic Matrix(309,40,224,29) (-1/7,-1/8) -> (11/8,29/21) Hyperbolic Matrix(83,8,280,27) (-1/9,0/1) -> (8/27,11/37) Hyperbolic Matrix(365,-44,224,-27) (0/1,1/8) -> (13/8,44/27) Hyperbolic Matrix(139,-24,168,-29) (1/6,2/11) -> (14/17,5/6) Hyperbolic Matrix(251,-52,140,-29) (1/5,3/14) -> (25/14,9/5) Hyperbolic Matrix(1429,-324,1848,-419) (7/31,5/22) -> (17/22,41/53) Hyperbolic Matrix(139,-36,112,-29) (1/4,4/15) -> (16/13,5/4) Hyperbolic Matrix(223,-60,420,-113) (4/15,7/26) -> (1/2,8/15) Hyperbolic Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(951,-284,1316,-393) (11/37,3/10) -> (13/18,47/65) Hyperbolic Matrix(475,-148,812,-253) (4/13,5/16) -> (7/12,24/41) Hyperbolic Matrix(841,-264,532,-167) (5/16,1/3) -> (49/31,19/12) Hyperbolic Matrix(139,-48,84,-29) (1/3,5/14) -> (23/14,5/3) Hyperbolic Matrix(447,-164,308,-113) (4/11,7/19) -> (13/9,16/11) Hyperbolic Matrix(2437,-900,3864,-1427) (7/19,17/46) -> (29/46,41/65) Hyperbolic Matrix(615,-232,448,-169) (3/8,11/29) -> (37/27,11/8) Hyperbolic Matrix(475,-184,364,-141) (5/13,7/18) -> (13/10,17/13) Hyperbolic Matrix(307,-120,504,-197) (7/18,2/5) -> (14/23,11/18) Hyperbolic Matrix(167,-68,140,-57) (2/5,7/17) -> (13/11,6/5) Hyperbolic Matrix(559,-232,812,-337) (12/29,5/12) -> (11/16,20/29) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(755,-332,448,-197) (7/16,11/25) -> (5/3,27/16) Hyperbolic Matrix(2323,-1024,4004,-1765) (11/25,15/34) -> (29/50,47/81) Hyperbolic Matrix(307,-144,420,-197) (6/13,1/2) -> (19/26,30/41) Hyperbolic Matrix(503,-276,308,-169) (6/11,5/9) -> (31/19,18/11) Hyperbolic Matrix(113,-64,196,-111) (5/9,4/7) -> (4/7,11/19) Parabolic Matrix(5489,-3216,3248,-1903) (41/70,17/29) -> (49/29,71/42) Hyperbolic Matrix(1233,-724,952,-559) (17/29,10/17) -> (22/17,35/27) Hyperbolic Matrix(1261,-764,784,-475) (3/5,17/28) -> (45/28,37/23) Hyperbolic Matrix(895,-552,728,-449) (8/13,21/34) -> (27/22,16/13) Hyperbolic Matrix(419,-268,308,-197) (7/11,9/14) -> (19/14,15/11) Hyperbolic Matrix(4173,-2884,2632,-1819) (29/42,9/13) -> (65/41,111/70) Hyperbolic Matrix(587,-408,364,-253) (9/13,7/10) -> (29/18,21/13) Hyperbolic Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic Matrix(1147,-832,812,-589) (21/29,8/11) -> (24/17,41/29) Hyperbolic Matrix(195,-148,112,-85) (3/4,10/13) -> (26/15,7/4) Hyperbolic Matrix(307,-240,252,-197) (7/9,11/14) -> (17/14,11/9) Hyperbolic Matrix(223,-180,140,-113) (4/5,9/11) -> (27/17,8/5) Hyperbolic Matrix(1429,-1172,784,-643) (9/11,23/28) -> (51/28,31/17) Hyperbolic Matrix(645,-544,364,-307) (5/6,11/13) -> (23/13,39/22) Hyperbolic Matrix(307,-360,168,-197) (7/6,13/11) -> (31/17,11/6) Hyperbolic Matrix(253,-324,196,-251) (14/11,9/7) -> (9/7,22/17) Parabolic Matrix(1287,-1688,812,-1065) (17/13,21/16) -> (19/12,65/41) Hyperbolic Matrix(811,-1128,504,-701) (25/18,7/5) -> (37/23,29/18) Hyperbolic Matrix(1371,-1940,812,-1149) (41/29,17/12) -> (27/16,49/29) Hyperbolic Matrix(281,-400,196,-279) (17/12,10/7) -> (10/7,23/16) Parabolic Matrix(309,-484,196,-307) (14/9,11/7) -> (11/7,30/19) Parabolic Matrix(337,-576,196,-335) (17/10,12/7) -> (12/7,31/18) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(1,2,0,1) Matrix(139,260,224,419) -> Matrix(3,8,-2,-5) Matrix(225,416,364,673) -> Matrix(5,8,-2,-3) Matrix(195,356,-476,-869) -> Matrix(1,2,-2,-3) Matrix(197,356,140,253) -> Matrix(1,2,-2,-3) Matrix(29,52,-140,-251) -> Matrix(1,2,2,5) Matrix(307,544,-364,-645) -> Matrix(1,2,-2,-3) Matrix(141,248,112,197) -> Matrix(1,2,-2,-3) Matrix(85,148,-112,-195) -> Matrix(3,8,-2,-5) Matrix(335,576,-196,-337) -> Matrix(15,32,-8,-17) Matrix(1511,2576,952,1623) -> Matrix(1,2,-2,-3) Matrix(559,952,1512,2575) -> Matrix(5,8,-2,-3) Matrix(505,856,364,617) -> Matrix(1,2,-4,-7) Matrix(223,376,-532,-897) -> Matrix(3,4,-4,-5) Matrix(29,48,-84,-139) -> Matrix(1,2,0,1) Matrix(169,276,-308,-503) -> Matrix(7,12,-10,-17) Matrix(195,316,224,363) -> Matrix(3,4,-4,-5) Matrix(309,500,364,589) -> Matrix(3,2,-2,-1) Matrix(253,408,-364,-587) -> Matrix(1,2,-2,-3) Matrix(113,180,-140,-223) -> Matrix(3,8,-2,-5) Matrix(307,484,-196,-309) -> Matrix(15,32,-8,-17) Matrix(141,220,-448,-699) -> Matrix(1,2,-4,-7) Matrix(421,652,308,477) -> Matrix(7,12,-10,-17) Matrix(83,128,308,475) -> Matrix(5,8,-2,-3) Matrix(113,164,-308,-447) -> Matrix(1,2,-2,-3) Matrix(279,400,-196,-281) -> Matrix(11,24,-6,-13) Matrix(673,956,868,1233) -> Matrix(9,16,-4,-7) Matrix(699,992,532,755) -> Matrix(1,2,-4,-7) Matrix(671,948,-952,-1345) -> Matrix(13,22,-16,-27) Matrix(253,356,140,197) -> Matrix(1,2,-2,-3) Matrix(449,624,-644,-895) -> Matrix(3,4,-4,-5) Matrix(617,856,364,505) -> Matrix(1,2,-4,-7) Matrix(55,76,364,503) -> Matrix(13,20,-2,-3) Matrix(29,40,224,309) -> Matrix(3,4,2,3) Matrix(169,232,-448,-615) -> Matrix(3,4,-4,-5) Matrix(477,652,308,421) -> Matrix(3,4,-10,-13) Matrix(197,268,-308,-419) -> Matrix(7,8,-8,-9) Matrix(141,184,-364,-475) -> Matrix(1,2,-2,-3) Matrix(251,324,-196,-253) -> Matrix(7,16,-4,-9) Matrix(477,608,-812,-1035) -> Matrix(11,18,-8,-13) Matrix(167,212,308,391) -> Matrix(11,18,-8,-13) Matrix(197,248,112,141) -> Matrix(1,2,-2,-3) Matrix(29,36,-112,-139) -> Matrix(1,2,-2,-3) Matrix(197,240,-252,-307) -> Matrix(3,4,-4,-5) Matrix(57,68,-140,-167) -> Matrix(1,2,-2,-3) Matrix(139,160,364,419) -> Matrix(3,8,-2,-5) Matrix(85,96,224,253) -> Matrix(1,0,0,1) Matrix(141,124,224,197) -> Matrix(1,0,0,1) Matrix(363,316,224,195) -> Matrix(3,4,-4,-5) Matrix(589,500,364,309) -> Matrix(3,2,-2,-1) Matrix(309,260,700,589) -> Matrix(1,0,0,1) Matrix(29,24,-168,-139) -> Matrix(1,2,0,1) Matrix(1063,868,616,503) -> Matrix(1,2,4,9) Matrix(811,660,-2100,-1709) -> Matrix(1,2,-2,-3) Matrix(111,88,140,111) -> Matrix(3,4,-4,-5) Matrix(475,372,392,307) -> Matrix(5,4,-4,-3) Matrix(727,564,504,391) -> Matrix(1,0,2,1) Matrix(419,324,-1848,-1429) -> Matrix(1,0,-2,1) Matrix(57,44,364,281) -> Matrix(1,-4,0,1) Matrix(167,128,364,279) -> Matrix(1,2,0,1) Matrix(27,20,112,83) -> Matrix(1,2,-2,-3) Matrix(197,144,-420,-307) -> Matrix(5,6,4,5) Matrix(449,328,308,225) -> Matrix(5,6,4,5) Matrix(139,100,-196,-141) -> Matrix(11,12,-12,-13) Matrix(1147,808,-2744,-1933) -> Matrix(3,2,-2,-1) Matrix(2071,1456,1512,1063) -> Matrix(3,2,-2,-1) Matrix(365,256,-1316,-923) -> Matrix(5,4,-4,-3) Matrix(867,604,-2212,-1541) -> Matrix(7,4,-16,-9) Matrix(337,232,-812,-559) -> Matrix(1,2,-2,-3) Matrix(309,212,532,365) -> Matrix(3,4,-4,-5) Matrix(55,36,84,55) -> Matrix(1,0,0,1) Matrix(531,340,392,251) -> Matrix(9,8,-8,-7) Matrix(139,88,308,195) -> Matrix(3,2,-2,-1) Matrix(1427,900,-3864,-2437) -> Matrix(1,0,0,1) Matrix(1961,1236,1512,953) -> Matrix(1,0,2,1) Matrix(197,124,224,141) -> Matrix(1,0,0,1) Matrix(167,104,448,279) -> Matrix(7,2,-4,-1) Matrix(419,260,224,139) -> Matrix(1,0,2,1) Matrix(673,416,364,225) -> Matrix(1,0,-2,1) Matrix(253,156,-952,-587) -> Matrix(1,-2,0,1) Matrix(111,68,364,223) -> Matrix(1,-2,0,1) Matrix(197,120,-504,-307) -> Matrix(1,0,-2,1) Matrix(27,16,140,83) -> Matrix(5,8,-2,-3) Matrix(1623,952,2576,1511) -> Matrix(1,2,-2,-3) Matrix(253,148,-812,-475) -> Matrix(3,4,2,3) Matrix(111,64,-196,-113) -> Matrix(9,10,-10,-11) Matrix(307,172,448,251) -> Matrix(7,6,-6,-5) Matrix(1681,940,-4004,-2239) -> Matrix(3,2,-2,-1) Matrix(617,344,504,281) -> Matrix(3,2,-2,-1) Matrix(29,16,-252,-139) -> Matrix(5,4,-4,-3) Matrix(391,212,308,167) -> Matrix(3,2,-8,-5) Matrix(113,60,-420,-223) -> Matrix(1,0,2,1) Matrix(421,196,784,365) -> Matrix(3,-16,-2,11) Matrix(1373,636,1876,869) -> Matrix(3,22,-4,-29) Matrix(533,244,308,141) -> Matrix(1,2,2,5) Matrix(195,88,308,139) -> Matrix(3,2,-2,-1) Matrix(83,36,-196,-85) -> Matrix(3,4,-4,-5) Matrix(1541,648,868,365) -> Matrix(3,2,-2,-1) Matrix(7281,3056,12544,5265) -> Matrix(1,0,0,1) Matrix(6607,2772,8540,3583) -> Matrix(5,4,-4,-3) Matrix(1597,668,-5152,-2155) -> Matrix(3,2,4,3) Matrix(1457,604,-3780,-1567) -> Matrix(3,2,-2,-1) Matrix(2241,928,3248,1345) -> Matrix(7,4,-2,-1) Matrix(281,116,952,393) -> Matrix(7,4,-2,-1) Matrix(253,104,-1428,-587) -> Matrix(3,2,-2,-1) Matrix(477,188,784,309) -> Matrix(7,4,-2,-1) Matrix(2519,988,1568,615) -> Matrix(9,4,2,1) Matrix(2297,888,1596,617) -> Matrix(1,0,4,1) Matrix(9547,3684,6020,2323) -> Matrix(1,0,4,1) Matrix(167,64,728,279) -> Matrix(7,2,-4,-1) Matrix(419,160,364,139) -> Matrix(1,0,2,1) Matrix(253,96,224,85) -> Matrix(1,0,0,1) Matrix(1763,668,2436,923) -> Matrix(5,6,-6,-7) Matrix(279,104,448,167) -> Matrix(7,2,-4,-1) Matrix(3137,1160,1820,673) -> Matrix(1,0,6,1) Matrix(4453,1644,7056,2605) -> Matrix(5,4,-4,-3) Matrix(5487,2024,7588,2799) -> Matrix(23,8,-26,-9) Matrix(449,164,616,225) -> Matrix(11,4,-14,-5) Matrix(111,40,308,111) -> Matrix(15,2,-8,-1) Matrix(643,228,392,139) -> Matrix(1,0,-8,1) Matrix(139,44,616,195) -> Matrix(3,2,-2,-1) Matrix(5965,1848,3528,1093) -> Matrix(3,-2,-4,3) Matrix(1541,476,2632,813) -> Matrix(1,0,-2,1) Matrix(223,68,364,111) -> Matrix(1,-2,0,1) Matrix(55,16,-196,-57) -> Matrix(1,-2,0,1) Matrix(9073,2512,12544,3473) -> Matrix(7,-6,-8,7) Matrix(7083,1960,11228,3107) -> Matrix(3,8,-2,-5) Matrix(2967,820,1820,503) -> Matrix(1,0,-2,1) Matrix(335,92,812,223) -> Matrix(3,2,-2,-1) Matrix(475,128,308,83) -> Matrix(1,0,-2,1) Matrix(2297,616,3136,841) -> Matrix(3,-14,-4,19) Matrix(673,180,1260,337) -> Matrix(3,14,-2,-9) Matrix(925,244,1596,421) -> Matrix(5,6,-6,-7) Matrix(83,20,112,27) -> Matrix(1,2,-2,-3) Matrix(279,64,728,167) -> Matrix(7,2,-4,-1) Matrix(5461,1236,7056,1597) -> Matrix(3,2,-2,-1) Matrix(5963,1348,10276,2323) -> Matrix(11,4,-14,-5) Matrix(1371,308,868,195) -> Matrix(1,0,6,1) Matrix(55,12,252,55) -> Matrix(7,2,-4,-1) Matrix(699,148,392,83) -> Matrix(1,0,-6,1) Matrix(83,16,140,27) -> Matrix(1,0,-2,1) Matrix(645,116,784,141) -> Matrix(1,-4,0,1) Matrix(2855,508,1568,279) -> Matrix(1,4,0,1) Matrix(281,44,364,57) -> Matrix(1,-4,0,1) Matrix(503,76,364,55) -> Matrix(1,-4,-2,9) Matrix(309,40,224,29) -> Matrix(1,4,-2,-7) Matrix(83,8,280,27) -> Matrix(1,-2,0,1) Matrix(365,-44,224,-27) -> Matrix(1,0,-2,1) Matrix(139,-24,168,-29) -> Matrix(1,2,0,1) Matrix(251,-52,140,-29) -> Matrix(1,2,2,5) Matrix(1429,-324,1848,-419) -> Matrix(5,8,-2,-3) Matrix(139,-36,112,-29) -> Matrix(1,2,-2,-3) Matrix(223,-60,420,-113) -> Matrix(3,8,-2,-5) Matrix(57,-16,196,-55) -> Matrix(1,-2,0,1) Matrix(951,-284,1316,-393) -> Matrix(7,22,-8,-25) Matrix(475,-148,812,-253) -> Matrix(1,4,-2,-7) Matrix(841,-264,532,-167) -> Matrix(1,2,4,9) Matrix(139,-48,84,-29) -> Matrix(1,2,0,1) Matrix(447,-164,308,-113) -> Matrix(1,2,-2,-3) Matrix(2437,-900,3864,-1427) -> Matrix(1,0,0,1) Matrix(615,-232,448,-169) -> Matrix(3,4,-4,-5) Matrix(475,-184,364,-141) -> Matrix(1,2,-2,-3) Matrix(307,-120,504,-197) -> Matrix(5,8,-2,-3) Matrix(167,-68,140,-57) -> Matrix(1,2,-2,-3) Matrix(559,-232,812,-337) -> Matrix(1,2,-2,-3) Matrix(85,-36,196,-83) -> Matrix(3,4,-4,-5) Matrix(755,-332,448,-197) -> Matrix(1,0,0,1) Matrix(2323,-1024,4004,-1765) -> Matrix(3,4,-4,-5) Matrix(307,-144,420,-197) -> Matrix(3,10,-4,-13) Matrix(503,-276,308,-169) -> Matrix(3,4,-10,-13) Matrix(113,-64,196,-111) -> Matrix(9,10,-10,-11) Matrix(5489,-3216,3248,-1903) -> Matrix(3,2,-2,-1) Matrix(1233,-724,952,-559) -> Matrix(3,2,4,3) Matrix(1261,-764,784,-475) -> Matrix(1,-2,0,1) Matrix(895,-552,728,-449) -> Matrix(1,4,-2,-7) Matrix(419,-268,308,-197) -> Matrix(7,8,-8,-9) Matrix(4173,-2884,2632,-1819) -> Matrix(1,2,0,1) Matrix(587,-408,364,-253) -> Matrix(1,2,-2,-3) Matrix(141,-100,196,-139) -> Matrix(11,12,-12,-13) Matrix(1147,-832,812,-589) -> Matrix(7,6,-20,-17) Matrix(195,-148,112,-85) -> Matrix(1,0,2,1) Matrix(307,-240,252,-197) -> Matrix(3,4,-4,-5) Matrix(223,-180,140,-113) -> Matrix(1,0,2,1) Matrix(1429,-1172,784,-643) -> Matrix(1,-2,0,1) Matrix(645,-544,364,-307) -> Matrix(1,2,-2,-3) Matrix(307,-360,168,-197) -> Matrix(1,0,0,1) Matrix(253,-324,196,-251) -> Matrix(1,0,4,1) Matrix(1287,-1688,812,-1065) -> Matrix(1,0,2,1) Matrix(811,-1128,504,-701) -> Matrix(3,2,-2,-1) Matrix(1371,-1940,812,-1149) -> Matrix(1,0,2,1) Matrix(281,-400,196,-279) -> Matrix(1,0,6,1) Matrix(309,-484,196,-307) -> Matrix(1,0,8,1) Matrix(337,-576,196,-335) -> Matrix(1,0,8,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 48 Degree of the the map X: 48 Degree of the the map Y: 192 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 1/0 1 14 1/8 1/0 1 14 1/7 1/0 4 2 2/13 (-5/1,1/0) 0 14 1/6 0 14 2/11 (-4/1,1/0) 0 14 1/5 0 14 3/14 -2/1 6 2 2/9 (-2/1,-3/2) 0 14 7/31 0 14 5/22 0 14 3/13 0 14 1/4 1/0 1 14 4/15 1/0 1 14 7/26 0 14 3/11 0 14 2/7 1/0 1 2 5/17 0 14 8/27 1/0 1 14 11/37 0 14 3/10 0 14 4/13 1/0 1 14 5/16 -5/2 1 14 1/3 0 14 5/14 -2/1 8 2 4/11 -7/4 1 14 7/19 0 14 17/46 0 14 10/27 (-2/1,-3/2) 0 14 3/8 -3/2 1 14 11/29 0 14 8/21 -2/1 1 2 13/34 0 14 5/13 0 14 7/18 0 14 2/5 (-3/2,-1/1) 0 14 7/17 0 14 12/29 -3/2 1 14 5/12 -3/2 1 14 3/7 -1/1 2 2 7/16 -1/2 1 14 11/25 0 14 15/34 0 14 4/9 1/0 1 14 5/11 0 14 6/13 (1/1,1/0) 0 14 1/2 0 14 8/15 -3/2 1 14 15/28 -3/2 11 2 7/13 0 14 6/11 (-3/2,-4/3) 0 14 5/9 0 14 4/7 -1/1 5 2 11/19 0 14 29/50 0 14 47/81 0 14 65/112 -3/4 1 2 18/31 (-1/1,-3/4) 0 14 7/12 -3/4 1 14 24/41 -1/2 1 14 41/70 -1/1 2 2 17/29 0 14 10/17 (-2/3,-1/2) 0 14 3/5 0 14 17/28 1/0 5 2 14/23 (-3/1,1/0) 0 14 11/18 0 14 8/13 1/0 1 14 21/34 0 14 13/21 -2/1 2 2 18/29 (-2/1,-3/2) 0 14 5/8 -3/2 1 14 17/27 0 14 29/46 0 14 41/65 0 14 53/84 -3/2 3 2 12/19 -3/2 1 14 7/11 0 14 9/14 -1/1 8 2 2/3 (-1/1,1/0) 0 14 11/16 1/0 1 14 20/29 1/0 1 14 29/42 -2/1 2 2 9/13 0 14 7/10 0 14 5/7 -1/1 6 2 13/18 0 14 47/65 0 14 81/112 -7/8 3 2 34/47 (-7/8,-6/7) 0 14 21/29 0 14 8/11 -5/6 1 14 19/26 0 14 30/41 (-13/17,-3/4) 0 14 41/56 -3/4 11 2 11/15 0 14 3/4 -1/2 1 14 10/13 (-1/1,1/0) 0 14 17/22 0 14 41/53 0 14 65/84 1/0 1 2 24/31 1/0 1 14 7/9 0 14 11/14 -1/1 6 2 4/5 -1/2 1 14 9/11 0 14 23/28 1/0 5 2 14/17 (-2/1,1/0) 0 14 5/6 0 14 11/13 0 14 6/7 -1/1 3 2 7/8 -1/2 1 14 1/1 0 14 8/7 0/1 1 2 7/6 0 14 13/11 0 14 6/5 (-1/1,1/0) 0 14 17/14 -1/1 6 2 11/9 0 14 27/22 0 14 16/13 -1/2 1 14 5/4 -1/2 1 14 19/15 0 14 14/11 (-1/2,0/1) 0 14 9/7 0/1 2 2 22/17 (0/1,1/2) 0 14 35/27 0 14 13/10 0 14 17/13 0 14 21/16 1/0 1 14 4/3 1/0 1 14 19/14 -1/1 8 2 15/11 0 14 26/19 (-2/3,-1/2) 0 14 37/27 0 14 11/8 -1/2 1 14 29/21 -1/2 4 2 18/13 (-1/2,-1/3) 0 14 25/18 0 14 7/5 0 14 24/17 -1/2 1 14 41/29 0 14 17/12 -1/4 1 14 10/7 0/1 3 2 23/16 1/2 1 14 36/25 1/2 1 14 13/9 0 14 16/11 1/2 1 14 3/2 0 14 17/11 0 14 14/9 (-1/4,0/1) 0 14 11/7 0/1 4 2 30/19 (0/1,1/4) 0 14 49/31 0 14 19/12 1/2 1 14 65/41 0 14 111/70 0/1 2 2 46/29 (0/1,1/2) 0 14 27/17 0 14 8/5 1/0 1 14 45/28 1/0 5 2 37/23 0 14 29/18 0 14 21/13 0 14 34/21 -1/1 3 2 13/8 -1/2 1 14 44/27 -1/2 1 14 31/19 0 14 18/11 (-1/4,0/1) 0 14 23/14 0/1 8 2 5/3 0 14 27/16 -1/2 1 14 49/29 0 14 71/42 -1/1 2 2 22/13 (-1/1,-1/2) 0 14 17/10 0 14 12/7 0/1 4 2 31/18 0 14 50/29 (0/1,1/4) 0 14 19/11 0 14 26/15 (1/2,1/1) 0 14 7/4 1/0 1 14 23/13 0 14 39/22 0 14 16/9 -1/2 1 14 25/14 0/1 6 2 9/5 0 14 20/11 1/0 1 14 51/28 1/0 5 2 31/17 0 14 11/6 0 14 13/7 0/1 2 2 2/1 (0/1,1/0) 0 14 1/0 1/0 1 2 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(365,-44,224,-27) (0/1,1/8) -> (13/8,44/27) Hyperbolic Matrix(309,-40,224,-29) (1/8,1/7) -> (11/8,29/21) Glide Reflection Matrix(503,-76,364,-55) (1/7,2/13) -> (29/21,18/13) Glide Reflection Matrix(281,-44,364,-57) (2/13,1/6) -> (10/13,17/22) Glide Reflection Matrix(139,-24,168,-29) (1/6,2/11) -> (14/17,5/6) Hyperbolic Matrix(83,-16,140,-27) (2/11,1/5) -> (10/17,3/5) Glide Reflection Matrix(251,-52,140,-29) (1/5,3/14) -> (25/14,9/5) Hyperbolic Matrix(55,-12,252,-55) (3/14,2/9) -> (3/14,2/9) Reflection Matrix(1371,-308,868,-195) (2/9,7/31) -> (30/19,49/31) Glide Reflection Matrix(1429,-324,1848,-419) (7/31,5/22) -> (17/22,41/53) Hyperbolic Matrix(279,-64,728,-167) (5/22,3/13) -> (13/34,5/13) Glide Reflection Matrix(83,-20,112,-27) (3/13,1/4) -> (11/15,3/4) Glide Reflection Matrix(139,-36,112,-29) (1/4,4/15) -> (16/13,5/4) Hyperbolic Matrix(223,-60,420,-113) (4/15,7/26) -> (1/2,8/15) Hyperbolic Matrix(475,-128,308,-83) (7/26,3/11) -> (3/2,17/11) Glide Reflection Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(393,-116,952,-281) (5/17,8/27) -> (7/17,12/29) Glide Reflection Matrix(2465,-732,1512,-449) (8/27,11/37) -> (44/27,31/19) Glide Reflection Matrix(951,-284,1316,-393) (11/37,3/10) -> (13/18,47/65) Hyperbolic Matrix(223,-68,364,-111) (3/10,4/13) -> (11/18,8/13) Glide Reflection Matrix(475,-148,812,-253) (4/13,5/16) -> (7/12,24/41) Hyperbolic Matrix(841,-264,532,-167) (5/16,1/3) -> (49/31,19/12) Hyperbolic Matrix(139,-48,84,-29) (1/3,5/14) -> (23/14,5/3) Hyperbolic Matrix(111,-40,308,-111) (5/14,4/11) -> (5/14,4/11) Reflection Matrix(447,-164,308,-113) (4/11,7/19) -> (13/9,16/11) Hyperbolic Matrix(2437,-900,3864,-1427) (7/19,17/46) -> (29/46,41/65) Hyperbolic Matrix(3137,-1160,1820,-673) (17/46,10/27) -> (31/18,50/29) Glide Reflection Matrix(279,-104,448,-167) (10/27,3/8) -> (18/29,5/8) Glide Reflection Matrix(615,-232,448,-169) (3/8,11/29) -> (37/27,11/8) Hyperbolic Matrix(253,-96,224,-85) (11/29,8/21) -> (1/1,8/7) Glide Reflection Matrix(419,-160,364,-139) (8/21,13/34) -> (8/7,7/6) Glide Reflection Matrix(475,-184,364,-141) (5/13,7/18) -> (13/10,17/13) Hyperbolic Matrix(307,-120,504,-197) (7/18,2/5) -> (14/23,11/18) Hyperbolic Matrix(167,-68,140,-57) (2/5,7/17) -> (13/11,6/5) Hyperbolic Matrix(559,-232,812,-337) (12/29,5/12) -> (11/16,20/29) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(755,-332,448,-197) (7/16,11/25) -> (5/3,27/16) Hyperbolic Matrix(2323,-1024,4004,-1765) (11/25,15/34) -> (29/50,47/81) Hyperbolic Matrix(895,-396,504,-223) (15/34,4/9) -> (39/22,16/9) Glide Reflection Matrix(195,-88,308,-139) (4/9,5/11) -> (12/19,7/11) Glide Reflection Matrix(533,-244,308,-141) (5/11,6/13) -> (19/11,26/15) Glide Reflection Matrix(307,-144,420,-197) (6/13,1/2) -> (19/26,30/41) Hyperbolic Matrix(449,-240,840,-449) (8/15,15/28) -> (8/15,15/28) Reflection Matrix(841,-452,1148,-617) (15/28,7/13) -> (41/56,11/15) Glide Reflection Matrix(391,-212,308,-167) (7/13,6/11) -> (19/15,14/11) Glide Reflection Matrix(503,-276,308,-169) (6/11,5/9) -> (31/19,18/11) Hyperbolic Matrix(113,-64,196,-111) (5/9,4/7) -> (4/7,11/19) Parabolic Matrix(1063,-616,868,-503) (11/19,29/50) -> (11/9,27/22) Glide Reflection Matrix(9857,-5720,12740,-7393) (47/81,65/112) -> (41/53,65/84) Glide Reflection Matrix(4031,-2340,6944,-4031) (65/112,18/31) -> (65/112,18/31) Reflection Matrix(365,-212,532,-309) (18/31,7/12) -> (2/3,11/16) Glide Reflection Matrix(3361,-1968,5740,-3361) (24/41,41/70) -> (24/41,41/70) Reflection Matrix(5489,-3216,3248,-1903) (41/70,17/29) -> (49/29,71/42) Hyperbolic Matrix(1233,-724,952,-559) (17/29,10/17) -> (22/17,35/27) Hyperbolic Matrix(1261,-764,784,-475) (3/5,17/28) -> (45/28,37/23) Hyperbolic Matrix(783,-476,1288,-783) (17/28,14/23) -> (17/28,14/23) Reflection Matrix(895,-552,728,-449) (8/13,21/34) -> (27/22,16/13) Hyperbolic Matrix(673,-416,364,-225) (21/34,13/21) -> (11/6,13/7) Glide Reflection Matrix(419,-260,224,-139) (13/21,18/29) -> (13/7,2/1) Glide Reflection Matrix(197,-124,224,-141) (5/8,17/27) -> (7/8,1/1) Glide Reflection Matrix(1961,-1236,1512,-953) (17/27,29/46) -> (35/27,13/10) Glide Reflection Matrix(9213,-5812,12740,-8037) (41/65,53/84) -> (47/65,81/112) Glide Reflection Matrix(2015,-1272,3192,-2015) (53/84,12/19) -> (53/84,12/19) Reflection Matrix(419,-268,308,-197) (7/11,9/14) -> (19/14,15/11) Hyperbolic Matrix(55,-36,84,-55) (9/14,2/3) -> (9/14,2/3) Reflection Matrix(1681,-1160,2436,-1681) (20/29,29/42) -> (20/29,29/42) Reflection Matrix(4173,-2884,2632,-1819) (29/42,9/13) -> (65/41,111/70) Hyperbolic Matrix(587,-408,364,-253) (9/13,7/10) -> (29/18,21/13) Hyperbolic Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic Matrix(7615,-5508,10528,-7615) (81/112,34/47) -> (81/112,34/47) Reflection Matrix(2493,-1804,1820,-1317) (34/47,21/29) -> (26/19,37/27) Glide Reflection Matrix(1147,-832,812,-589) (21/29,8/11) -> (24/17,41/29) Hyperbolic Matrix(449,-328,308,-225) (8/11,19/26) -> (16/11,3/2) Glide Reflection Matrix(3361,-2460,4592,-3361) (30/41,41/56) -> (30/41,41/56) Reflection Matrix(195,-148,112,-85) (3/4,10/13) -> (26/15,7/4) Hyperbolic Matrix(4031,-3120,5208,-4031) (65/84,24/31) -> (65/84,24/31) Reflection Matrix(727,-564,504,-391) (24/31,7/9) -> (36/25,13/9) Glide Reflection Matrix(307,-240,252,-197) (7/9,11/14) -> (17/14,11/9) Hyperbolic Matrix(111,-88,140,-111) (11/14,4/5) -> (11/14,4/5) Reflection Matrix(223,-180,140,-113) (4/5,9/11) -> (27/17,8/5) Hyperbolic Matrix(1429,-1172,784,-643) (9/11,23/28) -> (51/28,31/17) Hyperbolic Matrix(783,-644,952,-783) (23/28,14/17) -> (23/28,14/17) Reflection Matrix(645,-544,364,-307) (5/6,11/13) -> (23/13,39/22) Hyperbolic Matrix(589,-500,364,-309) (11/13,6/7) -> (21/13,34/21) Glide Reflection Matrix(363,-316,224,-195) (6/7,7/8) -> (34/21,13/8) Glide Reflection Matrix(307,-360,168,-197) (7/6,13/11) -> (31/17,11/6) Hyperbolic Matrix(169,-204,140,-169) (6/5,17/14) -> (6/5,17/14) Reflection Matrix(197,-248,112,-141) (5/4,19/15) -> (7/4,23/13) Glide Reflection Matrix(253,-324,196,-251) (14/11,9/7) -> (9/7,22/17) Parabolic Matrix(1287,-1688,812,-1065) (17/13,21/16) -> (19/12,65/41) Hyperbolic Matrix(645,-848,448,-589) (21/16,4/3) -> (23/16,36/25) Glide Reflection Matrix(113,-152,84,-113) (4/3,19/14) -> (4/3,19/14) Reflection Matrix(477,-652,308,-421) (15/11,26/19) -> (17/11,14/9) Glide Reflection Matrix(617,-856,364,-505) (18/13,25/18) -> (22/13,17/10) Glide Reflection Matrix(811,-1128,504,-701) (25/18,7/5) -> (37/23,29/18) Hyperbolic Matrix(253,-356,140,-197) (7/5,24/17) -> (9/5,20/11) Glide Reflection Matrix(1371,-1940,812,-1149) (41/29,17/12) -> (27/16,49/29) Hyperbolic Matrix(281,-400,196,-279) (17/12,10/7) -> (10/7,23/16) Parabolic Matrix(309,-484,196,-307) (14/9,11/7) -> (11/7,30/19) Parabolic Matrix(6439,-10212,4060,-6439) (111/70,46/29) -> (111/70,46/29) Reflection Matrix(1401,-2224,812,-1289) (46/29,27/17) -> (50/29,19/11) Glide Reflection Matrix(449,-720,280,-449) (8/5,45/28) -> (8/5,45/28) Reflection Matrix(505,-828,308,-505) (18/11,23/14) -> (18/11,23/14) Reflection Matrix(1847,-3124,1092,-1847) (71/42,22/13) -> (71/42,22/13) Reflection Matrix(337,-576,196,-335) (17/10,12/7) -> (12/7,31/18) Parabolic Matrix(449,-800,252,-449) (16/9,25/14) -> (16/9,25/14) Reflection Matrix(1121,-2040,616,-1121) (20/11,51/28) -> (20/11,51/28) Reflection Matrix(-1,4,0,1) (2/1,1/0) -> (2/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,2,0,-1) (0/1,1/0) -> (-1/1,1/0) Matrix(365,-44,224,-27) -> Matrix(1,0,-2,1) 0/1 Matrix(309,-40,224,-29) -> Matrix(1,-2,-2,3) Matrix(503,-76,364,-55) -> Matrix(1,6,-2,-13) Matrix(281,-44,364,-57) -> Matrix(1,6,0,-1) *** -> (-3/1,1/0) Matrix(139,-24,168,-29) -> Matrix(1,2,0,1) 1/0 Matrix(83,-16,140,-27) -> Matrix(1,2,-2,-5) Matrix(251,-52,140,-29) -> Matrix(1,2,2,5) Matrix(55,-12,252,-55) -> Matrix(7,12,-4,-7) (3/14,2/9) -> (-2/1,-3/2) Matrix(1371,-308,868,-195) -> Matrix(1,2,6,11) Matrix(1429,-324,1848,-419) -> Matrix(5,8,-2,-3) -2/1 Matrix(279,-64,728,-167) -> Matrix(7,12,-4,-7) *** -> (-2/1,-3/2) Matrix(83,-20,112,-27) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(139,-36,112,-29) -> Matrix(1,2,-2,-3) -1/1 Matrix(223,-60,420,-113) -> Matrix(3,8,-2,-5) -2/1 Matrix(475,-128,308,-83) -> Matrix(1,2,-2,-5) Matrix(57,-16,196,-55) -> Matrix(1,-2,0,1) 1/0 Matrix(393,-116,952,-281) -> Matrix(3,10,-2,-7) Matrix(2465,-732,1512,-449) -> Matrix(1,4,-2,-9) Matrix(951,-284,1316,-393) -> Matrix(7,22,-8,-25) Matrix(223,-68,364,-111) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(475,-148,812,-253) -> Matrix(1,4,-2,-7) Matrix(841,-264,532,-167) -> Matrix(1,2,4,9) Matrix(139,-48,84,-29) -> Matrix(1,2,0,1) 1/0 Matrix(111,-40,308,-111) -> Matrix(15,28,-8,-15) (5/14,4/11) -> (-2/1,-7/4) Matrix(447,-164,308,-113) -> Matrix(1,2,-2,-3) -1/1 Matrix(2437,-900,3864,-1427) -> Matrix(1,0,0,1) Matrix(3137,-1160,1820,-673) -> Matrix(1,2,6,11) Matrix(279,-104,448,-167) -> Matrix(7,12,-4,-7) *** -> (-2/1,-3/2) Matrix(615,-232,448,-169) -> Matrix(3,4,-4,-5) -1/1 Matrix(253,-96,224,-85) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(419,-160,364,-139) -> Matrix(1,2,2,3) Matrix(475,-184,364,-141) -> Matrix(1,2,-2,-3) -1/1 Matrix(307,-120,504,-197) -> Matrix(5,8,-2,-3) -2/1 Matrix(167,-68,140,-57) -> Matrix(1,2,-2,-3) -1/1 Matrix(559,-232,812,-337) -> Matrix(1,2,-2,-3) -1/1 Matrix(85,-36,196,-83) -> Matrix(3,4,-4,-5) -1/1 Matrix(755,-332,448,-197) -> Matrix(1,0,0,1) Matrix(2323,-1024,4004,-1765) -> Matrix(3,4,-4,-5) -1/1 Matrix(895,-396,504,-223) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(195,-88,308,-139) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(533,-244,308,-141) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(307,-144,420,-197) -> Matrix(3,10,-4,-13) Matrix(449,-240,840,-449) -> Matrix(31,48,-20,-31) (8/15,15/28) -> (-8/5,-3/2) Matrix(841,-452,1148,-617) -> Matrix(25,36,-34,-49) Matrix(391,-212,308,-167) -> Matrix(3,4,-8,-11) Matrix(503,-276,308,-169) -> Matrix(3,4,-10,-13) Matrix(113,-64,196,-111) -> Matrix(9,10,-10,-11) -1/1 Matrix(1063,-616,868,-503) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(9857,-5720,12740,-7393) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(4031,-2340,6944,-4031) -> Matrix(7,6,-8,-7) (65/112,18/31) -> (-1/1,-3/4) Matrix(365,-212,532,-309) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(3361,-1968,5740,-3361) -> Matrix(3,2,-4,-3) (24/41,41/70) -> (-1/1,-1/2) Matrix(5489,-3216,3248,-1903) -> Matrix(3,2,-2,-1) -1/1 Matrix(1233,-724,952,-559) -> Matrix(3,2,4,3) Matrix(1261,-764,784,-475) -> Matrix(1,-2,0,1) 1/0 Matrix(783,-476,1288,-783) -> Matrix(1,6,0,-1) (17/28,14/23) -> (-3/1,1/0) Matrix(895,-552,728,-449) -> Matrix(1,4,-2,-7) Matrix(673,-416,364,-225) -> Matrix(1,2,-2,-5) Matrix(419,-260,224,-139) -> Matrix(1,2,2,3) Matrix(197,-124,224,-141) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(1961,-1236,1512,-953) -> Matrix(1,2,2,3) Matrix(9213,-5812,12740,-8037) -> Matrix(23,38,-26,-43) Matrix(2015,-1272,3192,-2015) -> Matrix(5,6,-4,-5) (53/84,12/19) -> (-3/2,-1/1) Matrix(419,-268,308,-197) -> Matrix(7,8,-8,-9) -1/1 Matrix(55,-36,84,-55) -> Matrix(1,2,0,-1) (9/14,2/3) -> (-1/1,1/0) Matrix(1681,-1160,2436,-1681) -> Matrix(1,4,0,-1) (20/29,29/42) -> (-2/1,1/0) Matrix(4173,-2884,2632,-1819) -> Matrix(1,2,0,1) 1/0 Matrix(587,-408,364,-253) -> Matrix(1,2,-2,-3) -1/1 Matrix(141,-100,196,-139) -> Matrix(11,12,-12,-13) -1/1 Matrix(7615,-5508,10528,-7615) -> Matrix(97,84,-112,-97) (81/112,34/47) -> (-7/8,-6/7) Matrix(2493,-1804,1820,-1317) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(1147,-832,812,-589) -> Matrix(7,6,-20,-17) Matrix(449,-328,308,-225) -> Matrix(5,4,4,3) Matrix(3361,-2460,4592,-3361) -> Matrix(103,78,-136,-103) (30/41,41/56) -> (-13/17,-3/4) Matrix(195,-148,112,-85) -> Matrix(1,0,2,1) 0/1 Matrix(4031,-3120,5208,-4031) -> Matrix(1,4,0,-1) (65/84,24/31) -> (-2/1,1/0) Matrix(727,-564,504,-391) -> Matrix(1,2,2,3) Matrix(307,-240,252,-197) -> Matrix(3,4,-4,-5) -1/1 Matrix(111,-88,140,-111) -> Matrix(3,2,-4,-3) (11/14,4/5) -> (-1/1,-1/2) Matrix(223,-180,140,-113) -> Matrix(1,0,2,1) 0/1 Matrix(1429,-1172,784,-643) -> Matrix(1,-2,0,1) 1/0 Matrix(783,-644,952,-783) -> Matrix(1,4,0,-1) (23/28,14/17) -> (-2/1,1/0) Matrix(645,-544,364,-307) -> Matrix(1,2,-2,-3) -1/1 Matrix(589,-500,364,-309) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(363,-316,224,-195) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(307,-360,168,-197) -> Matrix(1,0,0,1) Matrix(169,-204,140,-169) -> Matrix(1,2,0,-1) (6/5,17/14) -> (-1/1,1/0) Matrix(197,-248,112,-141) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(253,-324,196,-251) -> Matrix(1,0,4,1) 0/1 Matrix(1287,-1688,812,-1065) -> Matrix(1,0,2,1) 0/1 Matrix(645,-848,448,-589) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(113,-152,84,-113) -> Matrix(1,2,0,-1) (4/3,19/14) -> (-1/1,1/0) Matrix(477,-652,308,-421) -> Matrix(3,2,-10,-7) Matrix(617,-856,364,-505) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(811,-1128,504,-701) -> Matrix(3,2,-2,-1) -1/1 Matrix(253,-356,140,-197) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1371,-1940,812,-1149) -> Matrix(1,0,2,1) 0/1 Matrix(281,-400,196,-279) -> Matrix(1,0,6,1) 0/1 Matrix(309,-484,196,-307) -> Matrix(1,0,8,1) 0/1 Matrix(6439,-10212,4060,-6439) -> Matrix(1,0,4,-1) (111/70,46/29) -> (0/1,1/2) Matrix(1401,-2224,812,-1289) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(449,-720,280,-449) -> Matrix(1,0,0,-1) (8/5,45/28) -> (0/1,1/0) Matrix(505,-828,308,-505) -> Matrix(-1,0,8,1) (18/11,23/14) -> (-1/4,0/1) Matrix(1847,-3124,1092,-1847) -> Matrix(3,2,-4,-3) (71/42,22/13) -> (-1/1,-1/2) Matrix(337,-576,196,-335) -> Matrix(1,0,8,1) 0/1 Matrix(449,-800,252,-449) -> Matrix(-1,0,4,1) (16/9,25/14) -> (-1/2,0/1) Matrix(1121,-2040,616,-1121) -> Matrix(-1,2,0,1) (20/11,51/28) -> (1/1,1/0) Matrix(-1,4,0,1) -> Matrix(1,0,0,-1) (2/1,1/0) -> (0/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.