details/L10a15_1_1198f09f.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-1/2, -5/2) (1, 1) x1^(1/2)x2^(5/2) q^(1/2)
{"0": [-1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1], "1": [1, -1, 1, 1, 1, -1]}
(-q^(1/2))*x1^(1/2)*x2^(5/2) + (-4*q^(1/2))*x1^(1/2)*x2^(7/2) + (2*q^(3/2))*x1^(3/2)*x2^(7/2) + (-q^(3/2) - 10*q^(1/2))*x1^(1/2)*x2^(9/2) + (2*q^(5/2) + 8*q^(3/2) + q^(1/2))*x1^(3/2)*x2^(9/2) + (-3*q^(7/2) - q^(5/2))*x1^(5/2)*x2^(9/2) + (-2*q^(5/2) - 4*q^(3/2) - 21*q^(1/2) - 2*q^(-3/2))*x1^(1/2)*x2^(11/2) + (2*q^(7/2) + 10*q^(5/2) + 23*q^(3/2) + 4*q^(1/2) + 2*q^(-1/2))*x1^(3/2)*x2^(11/2) + (-2*q^(11/2) - 4*q^(9/2) - 14*q^(7/2) - 6*q^(5/2) - 2*q^(3/2))*x1^(5/2)*x2^(11/2) + (4*q^(13/2) + 2*q^(11/2) + 2*q^(9/2))*x1^(7/2)*x2^(11/2) + (-q^(9/2) - 3*q^(7/2) - 8*q^(5/2) - 12*q^(3/2) - 39*q^(1/2) - 2*q^(-1/2) - 7*q^(-3/2) - 6*q^(-5/2) - q^(-7/2))*x1^(1/2)*x2^(13/2) + (2*q^(9/2) + 14*q^(7/2) + 34*q^(5/2) + 55*q^(3/2) + 16*q^(1/2) + 11*q^(-1/2) + 5*q^(-3/2) + q^(-5/2))*x1^(3/2)*x2^(13/2) + (-2*q^(15/2) - 2*q^(13/2) - 13*q^(11/2) - 24*q^(9/2) - 47*q^(7/2) - 24*q^(5/2) - 12*q^(3/2) - 4*q^(1/2) - q^(-1/2))*x1^(5/2)*x2^(13/2) + (2*q^(19/2) + 4*q^(17/2) + 8*q^(15/2) + 22*q^(13/2) + 15*q^(11/2) + 12*q^(9/2) + 4*q^(7/2) + q^(5/2))*x1^(7/2)*x2^(13/2) + (-5*q^(21/2) - 3*q^(19/2) - 4*q^(17/2) - 3*q^(15/2) - q^(13/2))*x1^(9/2)*x2^(13/2) + (-2*q^(13/2) - 2*q^(11/2) - 8*q^(9/2) - 13*q^(7/2) - 24*q^(5/2) - 28*q^(3/2) - 70*q^(1/2) - 9*q^(-1/2) - 21*q^(-3/2) - 23*q^(-5/2) - 14*q^(-7/2) - 2*q^(-9/2) - 2*q^(-11/2))*x1^(1/2)*x2^(15/2) + (4*q^(11/2) + 21*q^(9/2) + 56*q^(7/2) + 94*q^(5/2) + 124*q^(3/2) + 52*q^(1/2) + 45*q^(-1/2) + 33*q^(-3/2) + 16*q^(-5/2) + 4*q^(-7/2) + 2*q^(-9/2))*x1^(3/2)*x2^(15/2) + (-2*q^(19/2) - 2*q^(17/2) - 10*q^(15/2) - 18*q^(13/2) - 60*q^(11/2) - 94*q^(9/2) - 139*q^(7/2) - 83*q^(5/2) - 55*q^(3/2) - 29*q^(1/2) - 16*q^(-1/2) - 4*q^(-3/2) - 2*q^(-5/2))*x1^(5/2)*x2^(15/2) + (2*q^(25/2) + 2*q^(23/2) + 6*q^(21/2) + 16*q^(19/2) + 32*q^(17/2) + 52*q^(15/2) + 89*q^(13/2) + 68*q^(11/2) + 56*q^(9/2) + 27*q^(7/2) + 14*q^(5/2) + 4*q^(3/2) + 2*q^(1/2))*x1^(7/2)*x2^(15/2) + (-2*q^(29/2) - 4*q^(27/2) - 8*q^(25/2) - 14*q^(23/2) - 34*q^(21/2) - 28*q^(19/2) - 30*q^(17/2) - 22*q^(15/2) - 12*q^(13/2) - 4*q^(11/2) - 2*q^(9/2))*x1^(9/2)*x2^(15/2) + (6*q^(31/2) + 4*q^(29/2) + 6*q^(27/2) + 6*q^(25/2) + 6*q^(23/2) + 2*q^(21/2) + 2*q^(19/2))*x1^(11/2)*x2^(15/2) + (-q^(19/2) - 3*q^(17/2) - 4*q^(15/2) - 11*q^(13/2) - 15*q^(11/2) - 30*q^(9/2) - 40*q^(7/2) - 58*q^(5/2) - 63*q^(3/2) - 123*q^(1/2) - 33*q^(-1/2) - 56*q^(-3/2) - 67*q^(-5/2) - 53*q^(-7/2) - 26*q^(-9/2) - 9*q^(-11/2) - 4*q^(-13/2) - 3*q^(-15/2) - q^(-17/2))*x1^(1/2)*x2^(17/2) + (4*q^(15/2) + 10*q^(13/2) + 42*q^(11/2) + 97*q^(9/2) + 173*q^(7/2) + 235*q^(5/2) + 273*q^(3/2) + 156*q^(1/2) + 151*q^(-1/2) + 135*q^(-3/2) + 91*q^(-5/2) + 44*q^(-7/2) + 19*q^(-9/2) + 8*q^(-11/2) + 4*q^(-13/2) + q^(-15/2))*x1^(3/2)*x2^(17/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 14*q^(17/2) - 50*q^(15/2) - 102*q^(13/2) - 228*q^(11/2) - 310*q^(9/2) - 382*q^(7/2) - 270*q^(5/2) - 208*q^(3/2) - 150*q^(1/2) - 101*q^(-1/2) - 51*q^(-3/2) - 24*q^(-5/2) - 9*q^(-7/2) - 4*q^(-9/2) - q^(-11/2))*x1^(5/2)*x2^(17/2) + (2*q^(31/2) + 2*q^(29/2) + 4*q^(27/2) + 14*q^(25/2) + 20*q^(23/2) + 44*q^(21/2) + 88*q^(19/2) + 158*q^(17/2) + 231*q^(15/2) + 315*q^(13/2) + 266*q^(11/2) + 222*q^(9/2) + 142*q^(7/2) + 91*q^(5/2) + 49*q^(3/2) + 25*q^(1/2) + 9*q^(-1/2) + 4*q^(-3/2) + q^(-5/2))*x1^(7/2)*x2^(17/2) + (-2*q^(37/2) - 2*q^(35/2) - 6*q^(33/2) - 8*q^(31/2) - 25*q^(29/2) - 41*q^(27/2) - 71*q^(25/2) - 105*q^(23/2) - 164*q^(21/2) - 151*q^(19/2) - 152*q^(17/2) - 117*q^(15/2) - 77*q^(13/2) - 42*q^(11/2) - 23*q^(9/2) - 9*q^(7/2) - 4*q^(5/2) - q^(3/2))*x1^(9/2)*x2^(17/2) + (2*q^(41/2) + 4*q^(39/2) + 8*q^(37/2) + 14*q^(35/2) + 24*q^(33/2) + 50*q^(31/2) + 49*q^(29/2) + 56*q^(27/2) + 54*q^(25/2) + 47*q^(23/2) + 28*q^(21/2) + 19*q^(19/2) + 8*q^(17/2) + 4*q^(15/2) + q^(13/2))*x1^(11/2)*x2^(17/2) + (-7*q^(43/2) - 5*q^(41/2) - 8*q^(39/2) - 9*q^(37/2) - 11*q^(35/2) - 9*q^(33/2) - 7*q^(31/2) - 4*q^(29/2) - 3*q^(27/2) - q^(25/2))*x1^(13/2)*x2^(17/2) + (-2*q^(25/2) - 2*q^(23/2) - 6*q^(21/2) - 10*q^(19/2) - 19*q^(17/2) - 24*q^(15/2) - 46*q^(13/2) - 55*q^(11/2) - 88*q^(9/2) - 102*q^(7/2) - 133*q^(5/2) - 137*q^(3/2) - 226*q^(1/2) - 100*q^(-1/2) - 146*q^(-3/2) - 171*q^(-5/2) - 156*q^(-7/2) - 103*q^(-9/2) - 58*q^(-11/2) - 22*q^(-13/2) - 21*q^(-15/2) - 10*q^(-17/2) - 6*q^(-19/2) - 2*q^(-21/2) - 2*q^(-23/2))*x1^(1/2)*x2^(19/2) + (2*q^(21/2) + 7*q^(19/2) + 16*q^(17/2) + 42*q^(15/2) + 93*q^(13/2) + 198*q^(11/2) + 326*q^(9/2) + 466*q^(7/2) + 559*q^(5/2) + 610*q^(3/2) + 444*q^(1/2) + 459*q^(-1/2) + 446*q^(-3/2) + 359*q^(-5/2) + 229*q^(-7/2) + 127*q^(-9/2) + 65*q^(-11/2) + 41*q^(-13/2) + 20*q^(-15/2) + 10*q^(-17/2) + 4*q^(-19/2) + 2*q^(-21/2))*x1^(3/2)*x2^(19/2) + (-2*q^(27/2) - 2*q^(25/2) - 10*q^(23/2) - 14*q^(21/2) - 50*q^(19/2) - 94*q^(17/2) - 248*q^(15/2) - 445*q^(13/2) - 752*q^(11/2) - 915*q^(9/2) - 1027*q^(7/2) - 826*q^(5/2) - 724*q^(3/2) - 601*q^(1/2) - 475*q^(-1/2) - 304*q^(-3/2) - 184*q^(-5/2) - 91*q^(-7/2) - 53*q^(-9/2) - 24*q^(-11/2) - 12*q^(-13/2) - 4*q^(-15/2) - 2*q^(-17/2))*x1^(5/2)*x2^(19/2) + (2*q^(37/2) + 2*q^(35/2) + 4*q^(33/2) + 12*q^(31/2) + 18*q^(29/2) + 32*q^(27/2) + 72*q^(25/2) + 114*q^(23/2) + 226*q^(21/2) + 405*q^(19/2) + 651*q^(17/2) + 868*q^(15/2) + 1049*q^(13/2) + 939*q^(11/2) + 821*q^(9/2) + 625*q^(7/2) + 468*q^(5/2) + 313*q^(3/2) + 200*q^(1/2) + 103*q^(-1/2) + 57*q^(-3/2) + 26*q^(-5/2) + 12*q^(-7/2) + 4*q^(-9/2) + 2*q^(-11/2))*x1^(7/2)*x2^(19/2) + (-2*q^(45/2) - 2*q^(43/2) - 4*q^(41/2) - 8*q^(39/2) - 18*q^(37/2) - 26*q^(35/2) - 54*q^(33/2) - 82*q^(31/2) - 162*q^(29/2) - 248*q^(27/2) - 386*q^(25/2) - 520*q^(23/2) - 683*q^(21/2) - 669*q^(19/2) - 657*q^(17/2) - 536*q^(15/2) - 404*q^(13/2) - 270*q^(11/2) - 181*q^(9/2) - 99*q^(7/2) - 57*q^(5/2) - 26*q^(3/2) - 12*q^(1/2) - 4*q^(-1/2) - 2*q^(-3/2))*x1^(9/2)*x2^(19/2) + (2*q^(51/2) + 2*q^(49/2) + 6*q^(47/2) + 8*q^(45/2) + 16*q^(43/2) + 32*q^(41/2) + 60*q^(39/2) + 92*q^(37/2) + 144*q^(35/2) + 204*q^(33/2) + 295*q^(31/2) + 306*q^(29/2) + 332*q^(27/2) + 311*q^(25/2) + 272*q^(23/2) + 193*q^(21/2) + 142*q^(19/2) + 82*q^(17/2) + 51*q^(15/2) + 24*q^(13/2) + 12*q^(11/2) + 4*q^(9/2) + 2*q^(7/2))*x1^(11/2)*x2^(19/2) + (-2*q^(55/2) - 4*q^(53/2) - 8*q^(51/2) - 14*q^(49/2) - 24*q^(47/2) - 38*q^(45/2) - 74*q^(43/2) - 78*q^(41/2) - 96*q^(39/2) - 102*q^(37/2) - 106*q^(35/2) - 90*q^(33/2) - 74*q^(31/2) - 50*q^(29/2) - 36*q^(27/2) - 20*q^(25/2) - 10*q^(23/2) - 4*q^(21/2) - 2*q^(19/2))*x1^(13/2)*x2^(19/2) + (8*q^(57/2) + 6*q^(55/2) + 10*q^(53/2) + 12*q^(51/2) + 16*q^(49/2) + 16*q^(47/2) + 18*q^(45/2) + 12*q^(43/2) + 12*q^(41/2) + 8*q^(39/2) + 6*q^(37/2) + 2*q^(35/2) + 2*q^(33/2))*x1^(15/2)*x2^(19/2)
(-1/2, -5/2) (1, 1) x1^(1/2)x2^(5/2) q^(1/2)
{"0": [1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], "1": [1, -1, 1, 1, 1, -1]}
(-q^(1/2))*x1^(1/2)*x2^(5/2) + (-4*q^(1/2))*x1^(1/2)*x2^(7/2) + (2*q^(3/2))*x1^(3/2)*x2^(7/2) + (-q^(3/2) - 10*q^(1/2))*x1^(1/2)*x2^(9/2) + (2*q^(5/2) + 8*q^(3/2) + q^(1/2))*x1^(3/2)*x2^(9/2) + (-3*q^(7/2) - q^(5/2))*x1^(5/2)*x2^(9/2) + (-2*q^(5/2) - 4*q^(3/2) - 21*q^(1/2) - 2*q^(-3/2))*x1^(1/2)*x2^(11/2) + (2*q^(7/2) + 10*q^(5/2) + 23*q^(3/2) + 4*q^(1/2) + 2*q^(-1/2))*x1^(3/2)*x2^(11/2) + (-2*q^(11/2) - 4*q^(9/2) - 14*q^(7/2) - 6*q^(5/2) - 2*q^(3/2))*x1^(5/2)*x2^(11/2) + (4*q^(13/2) + 2*q^(11/2) + 2*q^(9/2))*x1^(7/2)*x2^(11/2) + (-q^(9/2) - 3*q^(7/2) - 8*q^(5/2) - 12*q^(3/2) - 39*q^(1/2) - 2*q^(-1/2) - 7*q^(-3/2) - 6*q^(-5/2) - q^(-7/2))*x1^(1/2)*x2^(13/2) + (2*q^(9/2) + 14*q^(7/2) + 34*q^(5/2) + 55*q^(3/2) + 16*q^(1/2) + 11*q^(-1/2) + 5*q^(-3/2) + q^(-5/2))*x1^(3/2)*x2^(13/2) + (-2*q^(15/2) - 2*q^(13/2) - 13*q^(11/2) - 24*q^(9/2) - 47*q^(7/2) - 24*q^(5/2) - 12*q^(3/2) - 4*q^(1/2) - q^(-1/2))*x1^(5/2)*x2^(13/2) + (2*q^(19/2) + 4*q^(17/2) + 8*q^(15/2) + 22*q^(13/2) + 15*q^(11/2) + 12*q^(9/2) + 4*q^(7/2) + q^(5/2))*x1^(7/2)*x2^(13/2) + (-5*q^(21/2) - 3*q^(19/2) - 4*q^(17/2) - 3*q^(15/2) - q^(13/2))*x1^(9/2)*x2^(13/2) + (-2*q^(13/2) - 2*q^(11/2) - 8*q^(9/2) - 13*q^(7/2) - 24*q^(5/2) - 28*q^(3/2) - 70*q^(1/2) - 9*q^(-1/2) - 21*q^(-3/2) - 23*q^(-5/2) - 14*q^(-7/2) - 2*q^(-9/2) - 2*q^(-11/2))*x1^(1/2)*x2^(15/2) + (4*q^(11/2) + 21*q^(9/2) + 56*q^(7/2) + 94*q^(5/2) + 124*q^(3/2) + 52*q^(1/2) + 45*q^(-1/2) + 33*q^(-3/2) + 16*q^(-5/2) + 4*q^(-7/2) + 2*q^(-9/2))*x1^(3/2)*x2^(15/2) + (-2*q^(19/2) - 2*q^(17/2) - 10*q^(15/2) - 18*q^(13/2) - 60*q^(11/2) - 94*q^(9/2) - 139*q^(7/2) - 83*q^(5/2) - 55*q^(3/2) - 29*q^(1/2) - 16*q^(-1/2) - 4*q^(-3/2) - 2*q^(-5/2))*x1^(5/2)*x2^(15/2) + (2*q^(25/2) + 2*q^(23/2) + 6*q^(21/2) + 16*q^(19/2) + 32*q^(17/2) + 52*q^(15/2) + 89*q^(13/2) + 68*q^(11/2) + 56*q^(9/2) + 27*q^(7/2) + 14*q^(5/2) + 4*q^(3/2) + 2*q^(1/2))*x1^(7/2)*x2^(15/2) + (-2*q^(29/2) - 4*q^(27/2) - 8*q^(25/2) - 14*q^(23/2) - 34*q^(21/2) - 28*q^(19/2) - 30*q^(17/2) - 22*q^(15/2) - 12*q^(13/2) - 4*q^(11/2) - 2*q^(9/2))*x1^(9/2)*x2^(15/2) + (6*q^(31/2) + 4*q^(29/2) + 6*q^(27/2) + 6*q^(25/2) + 6*q^(23/2) + 2*q^(21/2) + 2*q^(19/2))*x1^(11/2)*x2^(15/2) + (-q^(19/2) - 3*q^(17/2) - 4*q^(15/2) - 11*q^(13/2) - 15*q^(11/2) - 30*q^(9/2) - 40*q^(7/2) - 58*q^(5/2) - 63*q^(3/2) - 123*q^(1/2) - 33*q^(-1/2) - 56*q^(-3/2) - 67*q^(-5/2) - 53*q^(-7/2) - 26*q^(-9/2) - 9*q^(-11/2) - 4*q^(-13/2) - 3*q^(-15/2) - q^(-17/2))*x1^(1/2)*x2^(17/2) + (4*q^(15/2) + 10*q^(13/2) + 42*q^(11/2) + 97*q^(9/2) + 173*q^(7/2) + 235*q^(5/2) + 273*q^(3/2) + 156*q^(1/2) + 151*q^(-1/2) + 135*q^(-3/2) + 91*q^(-5/2) + 44*q^(-7/2) + 19*q^(-9/2) + 8*q^(-11/2) + 4*q^(-13/2) + q^(-15/2))*x1^(3/2)*x2^(17/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 14*q^(17/2) - 50*q^(15/2) - 102*q^(13/2) - 228*q^(11/2) - 310*q^(9/2) - 382*q^(7/2) - 270*q^(5/2) - 208*q^(3/2) - 150*q^(1/2) - 101*q^(-1/2) - 51*q^(-3/2) - 24*q^(-5/2) - 9*q^(-7/2) - 4*q^(-9/2) - q^(-11/2))*x1^(5/2)*x2^(17/2) + (2*q^(31/2) + 2*q^(29/2) + 4*q^(27/2) + 14*q^(25/2) + 20*q^(23/2) + 44*q^(21/2) + 88*q^(19/2) + 158*q^(17/2) + 231*q^(15/2) + 315*q^(13/2) + 266*q^(11/2) + 222*q^(9/2) + 142*q^(7/2) + 91*q^(5/2) + 49*q^(3/2) + 25*q^(1/2) + 9*q^(-1/2) + 4*q^(-3/2) + q^(-5/2))*x1^(7/2)*x2^(17/2) + (-2*q^(37/2) - 2*q^(35/2) - 6*q^(33/2) - 8*q^(31/2) - 25*q^(29/2) - 41*q^(27/2) - 71*q^(25/2) - 105*q^(23/2) - 164*q^(21/2) - 151*q^(19/2) - 152*q^(17/2) - 117*q^(15/2) - 77*q^(13/2) - 42*q^(11/2) - 23*q^(9/2) - 9*q^(7/2) - 4*q^(5/2) - q^(3/2))*x1^(9/2)*x2^(17/2) + (2*q^(41/2) + 4*q^(39/2) + 8*q^(37/2) + 14*q^(35/2) + 24*q^(33/2) + 50*q^(31/2) + 49*q^(29/2) + 56*q^(27/2) + 54*q^(25/2) + 47*q^(23/2) + 28*q^(21/2) + 19*q^(19/2) + 8*q^(17/2) + 4*q^(15/2) + q^(13/2))*x1^(11/2)*x2^(17/2) + (-7*q^(43/2) - 5*q^(41/2) - 8*q^(39/2) - 9*q^(37/2) - 11*q^(35/2) - 9*q^(33/2) - 7*q^(31/2) - 4*q^(29/2) - 3*q^(27/2) - q^(25/2))*x1^(13/2)*x2^(17/2) + (-2*q^(25/2) - 2*q^(23/2) - 6*q^(21/2) - 10*q^(19/2) - 19*q^(17/2) - 24*q^(15/2) - 46*q^(13/2) - 55*q^(11/2) - 88*q^(9/2) - 102*q^(7/2) - 133*q^(5/2) - 137*q^(3/2) - 226*q^(1/2) - 100*q^(-1/2) - 146*q^(-3/2) - 171*q^(-5/2) - 156*q^(-7/2) - 103*q^(-9/2) - 58*q^(-11/2) - 22*q^(-13/2) - 21*q^(-15/2) - 10*q^(-17/2) - 6*q^(-19/2) - 2*q^(-21/2) - 2*q^(-23/2))*x1^(1/2)*x2^(19/2) + (2*q^(21/2) + 7*q^(19/2) + 16*q^(17/2) + 42*q^(15/2) + 93*q^(13/2) + 198*q^(11/2) + 326*q^(9/2) + 466*q^(7/2) + 559*q^(5/2) + 610*q^(3/2) + 444*q^(1/2) + 459*q^(-1/2) + 446*q^(-3/2) + 359*q^(-5/2) + 229*q^(-7/2) + 127*q^(-9/2) + 65*q^(-11/2) + 41*q^(-13/2) + 20*q^(-15/2) + 10*q^(-17/2) + 4*q^(-19/2) + 2*q^(-21/2))*x1^(3/2)*x2^(19/2) + (-2*q^(27/2) - 2*q^(25/2) - 10*q^(23/2) - 14*q^(21/2) - 50*q^(19/2) - 94*q^(17/2) - 248*q^(15/2) - 445*q^(13/2) - 752*q^(11/2) - 915*q^(9/2) - 1027*q^(7/2) - 826*q^(5/2) - 724*q^(3/2) - 601*q^(1/2) - 475*q^(-1/2) - 304*q^(-3/2) - 184*q^(-5/2) - 91*q^(-7/2) - 53*q^(-9/2) - 24*q^(-11/2) - 12*q^(-13/2) - 4*q^(-15/2) - 2*q^(-17/2))*x1^(5/2)*x2^(19/2) + (2*q^(37/2) + 2*q^(35/2) + 4*q^(33/2) + 12*q^(31/2) + 18*q^(29/2) + 32*q^(27/2) + 72*q^(25/2) + 114*q^(23/2) + 226*q^(21/2) + 405*q^(19/2) + 651*q^(17/2) + 868*q^(15/2) + 1049*q^(13/2) + 939*q^(11/2) + 821*q^(9/2) + 625*q^(7/2) + 468*q^(5/2) + 313*q^(3/2) + 200*q^(1/2) + 103*q^(-1/2) + 57*q^(-3/2) + 26*q^(-5/2) + 12*q^(-7/2) + 4*q^(-9/2) + 2*q^(-11/2))*x1^(7/2)*x2^(19/2) + (-2*q^(45/2) - 2*q^(43/2) - 4*q^(41/2) - 8*q^(39/2) - 18*q^(37/2) - 26*q^(35/2) - 54*q^(33/2) - 82*q^(31/2) - 162*q^(29/2) - 248*q^(27/2) - 386*q^(25/2) - 520*q^(23/2) - 683*q^(21/2) - 669*q^(19/2) - 657*q^(17/2) - 536*q^(15/2) - 404*q^(13/2) - 270*q^(11/2) - 181*q^(9/2) - 99*q^(7/2) - 57*q^(5/2) - 26*q^(3/2) - 12*q^(1/2) - 4*q^(-1/2) - 2*q^(-3/2))*x1^(9/2)*x2^(19/2) + (2*q^(51/2) + 2*q^(49/2) + 6*q^(47/2) + 8*q^(45/2) + 16*q^(43/2) + 32*q^(41/2) + 60*q^(39/2) + 92*q^(37/2) + 144*q^(35/2) + 204*q^(33/2) + 295*q^(31/2) + 306*q^(29/2) + 332*q^(27/2) + 311*q^(25/2) + 272*q^(23/2) + 193*q^(21/2) + 142*q^(19/2) + 82*q^(17/2) + 51*q^(15/2) + 24*q^(13/2) + 12*q^(11/2) + 4*q^(9/2) + 2*q^(7/2))*x1^(11/2)*x2^(19/2) + (-2*q^(55/2) - 4*q^(53/2) - 8*q^(51/2) - 14*q^(49/2) - 24*q^(47/2) - 38*q^(45/2) - 74*q^(43/2) - 78*q^(41/2) - 96*q^(39/2) - 102*q^(37/2) - 106*q^(35/2) - 90*q^(33/2) - 74*q^(31/2) - 50*q^(29/2) - 36*q^(27/2) - 20*q^(25/2) - 10*q^(23/2) - 4*q^(21/2) - 2*q^(19/2))*x1^(13/2)*x2^(19/2) + (8*q^(57/2) + 6*q^(55/2) + 10*q^(53/2) + 12*q^(51/2) + 16*q^(49/2) + 16*q^(47/2) + 18*q^(45/2) + 12*q^(43/2) + 12*q^(41/2) + 8*q^(39/2) + 6*q^(37/2) + 2*q^(35/2) + 2*q^(33/2))*x1^(15/2)*x2^(19/2)
(1/2, 5/2) x1^(-1/2)x2^(-5/2) q^(1/2)
(-q^(1/2))*x1^(-1/2)*x2^(-5/2) + (-4*q^(1/2))*x1^(-1/2)*x2^(-7/2) + (2*q^(3/2))*x1^(-3/2)*x2^(-7/2) + (-q^(3/2) - 10*q^(1/2))*x1^(-1/2)*x2^(-9/2) + (2*q^(5/2) + 8*q^(3/2) + q^(1/2))*x1^(-3/2)*x2^(-9/2) + (-3*q^(7/2) - q^(5/2))*x1^(-5/2)*x2^(-9/2) + (-2*q^(5/2) - 4*q^(3/2) - 21*q^(1/2) - 2*q^(-3/2))*x1^(-1/2)*x2^(-11/2) + (2*q^(7/2) + 10*q^(5/2) + 23*q^(3/2) + 4*q^(1/2) + 2*q^(-1/2))*x1^(-3/2)*x2^(-11/2) + (-2*q^(11/2) - 4*q^(9/2) - 14*q^(7/2) - 6*q^(5/2) - 2*q^(3/2))*x1^(-5/2)*x2^(-11/2) + (4*q^(13/2) + 2*q^(11/2) + 2*q^(9/2))*x1^(-7/2)*x2^(-11/2) + (-q^(9/2) - 3*q^(7/2) - 8*q^(5/2) - 12*q^(3/2) - 39*q^(1/2) - 2*q^(-1/2) - 7*q^(-3/2) - 6*q^(-5/2) - q^(-7/2))*x1^(-1/2)*x2^(-13/2) + (2*q^(9/2) + 14*q^(7/2) + 34*q^(5/2) + 55*q^(3/2) + 16*q^(1/2) + 11*q^(-1/2) + 5*q^(-3/2) + q^(-5/2))*x1^(-3/2)*x2^(-13/2) + (-2*q^(15/2) - 2*q^(13/2) - 13*q^(11/2) - 24*q^(9/2) - 47*q^(7/2) - 24*q^(5/2) - 12*q^(3/2) - 4*q^(1/2) - q^(-1/2))*x1^(-5/2)*x2^(-13/2) + (2*q^(19/2) + 4*q^(17/2) + 8*q^(15/2) + 22*q^(13/2) + 15*q^(11/2) + 12*q^(9/2) + 4*q^(7/2) + q^(5/2))*x1^(-7/2)*x2^(-13/2) + (-5*q^(21/2) - 3*q^(19/2) - 4*q^(17/2) - 3*q^(15/2) - q^(13/2))*x1^(-9/2)*x2^(-13/2) + (-2*q^(13/2) - 2*q^(11/2) - 8*q^(9/2) - 13*q^(7/2) - 24*q^(5/2) - 28*q^(3/2) - 70*q^(1/2) - 9*q^(-1/2) - 21*q^(-3/2) - 23*q^(-5/2) - 14*q^(-7/2) - 2*q^(-9/2) - 2*q^(-11/2))*x1^(-1/2)*x2^(-15/2) + (4*q^(11/2) + 21*q^(9/2) + 56*q^(7/2) + 94*q^(5/2) + 124*q^(3/2) + 52*q^(1/2) + 45*q^(-1/2) + 33*q^(-3/2) + 16*q^(-5/2) + 4*q^(-7/2) + 2*q^(-9/2))*x1^(-3/2)*x2^(-15/2) + (-2*q^(19/2) - 2*q^(17/2) - 10*q^(15/2) - 18*q^(13/2) - 60*q^(11/2) - 94*q^(9/2) - 139*q^(7/2) - 83*q^(5/2) - 55*q^(3/2) - 29*q^(1/2) - 16*q^(-1/2) - 4*q^(-3/2) - 2*q^(-5/2))*x1^(-5/2)*x2^(-15/2) + (2*q^(25/2) + 2*q^(23/2) + 6*q^(21/2) + 16*q^(19/2) + 32*q^(17/2) + 52*q^(15/2) + 89*q^(13/2) + 68*q^(11/2) + 56*q^(9/2) + 27*q^(7/2) + 14*q^(5/2) + 4*q^(3/2) + 2*q^(1/2))*x1^(-7/2)*x2^(-15/2) + (-2*q^(29/2) - 4*q^(27/2) - 8*q^(25/2) - 14*q^(23/2) - 34*q^(21/2) - 28*q^(19/2) - 30*q^(17/2) - 22*q^(15/2) - 12*q^(13/2) - 4*q^(11/2) - 2*q^(9/2))*x1^(-9/2)*x2^(-15/2) + (6*q^(31/2) + 4*q^(29/2) + 6*q^(27/2) + 6*q^(25/2) + 6*q^(23/2) + 2*q^(21/2) + 2*q^(19/2))*x1^(-11/2)*x2^(-15/2) + (-q^(19/2) - 3*q^(17/2) - 4*q^(15/2) - 11*q^(13/2) - 15*q^(11/2) - 30*q^(9/2) - 40*q^(7/2) - 58*q^(5/2) - 63*q^(3/2) - 123*q^(1/2) - 33*q^(-1/2) - 56*q^(-3/2) - 67*q^(-5/2) - 53*q^(-7/2) - 26*q^(-9/2) - 9*q^(-11/2) - 4*q^(-13/2) - 3*q^(-15/2) - q^(-17/2))*x1^(-1/2)*x2^(-17/2) + (4*q^(15/2) + 10*q^(13/2) + 42*q^(11/2) + 97*q^(9/2) + 173*q^(7/2) + 235*q^(5/2) + 273*q^(3/2) + 156*q^(1/2) + 151*q^(-1/2) + 135*q^(-3/2) + 91*q^(-5/2) + 44*q^(-7/2) + 19*q^(-9/2) + 8*q^(-11/2) + 4*q^(-13/2) + q^(-15/2))*x1^(-3/2)*x2^(-17/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 14*q^(17/2) - 50*q^(15/2) - 102*q^(13/2) - 228*q^(11/2) - 310*q^(9/2) - 382*q^(7/2) - 270*q^(5/2) - 208*q^(3/2) - 150*q^(1/2) - 101*q^(-1/2) - 51*q^(-3/2) - 24*q^(-5/2) - 9*q^(-7/2) - 4*q^(-9/2) - q^(-11/2))*x1^(-5/2)*x2^(-17/2) + (2*q^(31/2) + 2*q^(29/2) + 4*q^(27/2) + 14*q^(25/2) + 20*q^(23/2) + 44*q^(21/2) + 88*q^(19/2) + 158*q^(17/2) + 231*q^(15/2) + 315*q^(13/2) + 266*q^(11/2) + 222*q^(9/2) + 142*q^(7/2) + 91*q^(5/2) + 49*q^(3/2) + 25*q^(1/2) + 9*q^(-1/2) + 4*q^(-3/2) + q^(-5/2))*x1^(-7/2)*x2^(-17/2) + (-2*q^(37/2) - 2*q^(35/2) - 6*q^(33/2) - 8*q^(31/2) - 25*q^(29/2) - 41*q^(27/2) - 71*q^(25/2) - 105*q^(23/2) - 164*q^(21/2) - 151*q^(19/2) - 152*q^(17/2) - 117*q^(15/2) - 77*q^(13/2) - 42*q^(11/2) - 23*q^(9/2) - 9*q^(7/2) - 4*q^(5/2) - q^(3/2))*x1^(-9/2)*x2^(-17/2) + (2*q^(41/2) + 4*q^(39/2) + 8*q^(37/2) + 14*q^(35/2) + 24*q^(33/2) + 50*q^(31/2) + 49*q^(29/2) + 56*q^(27/2) + 54*q^(25/2) + 47*q^(23/2) + 28*q^(21/2) + 19*q^(19/2) + 8*q^(17/2) + 4*q^(15/2) + q^(13/2))*x1^(-11/2)*x2^(-17/2) + (-7*q^(43/2) - 5*q^(41/2) - 8*q^(39/2) - 9*q^(37/2) - 11*q^(35/2) - 9*q^(33/2) - 7*q^(31/2) - 4*q^(29/2) - 3*q^(27/2) - q^(25/2))*x1^(-13/2)*x2^(-17/2) + (-2*q^(25/2) - 2*q^(23/2) - 6*q^(21/2) - 10*q^(19/2) - 19*q^(17/2) - 24*q^(15/2) - 46*q^(13/2) - 55*q^(11/2) - 88*q^(9/2) - 102*q^(7/2) - 133*q^(5/2) - 137*q^(3/2) - 226*q^(1/2) - 100*q^(-1/2) - 146*q^(-3/2) - 171*q^(-5/2) - 156*q^(-7/2) - 103*q^(-9/2) - 58*q^(-11/2) - 22*q^(-13/2) - 21*q^(-15/2) - 10*q^(-17/2) - 6*q^(-19/2) - 2*q^(-21/2) - 2*q^(-23/2))*x1^(-1/2)*x2^(-19/2) + (2*q^(21/2) + 7*q^(19/2) + 16*q^(17/2) + 42*q^(15/2) + 93*q^(13/2) + 198*q^(11/2) + 326*q^(9/2) + 466*q^(7/2) + 559*q^(5/2) + 610*q^(3/2) + 444*q^(1/2) + 459*q^(-1/2) + 446*q^(-3/2) + 359*q^(-5/2) + 229*q^(-7/2) + 127*q^(-9/2) + 65*q^(-11/2) + 41*q^(-13/2) + 20*q^(-15/2) + 10*q^(-17/2) + 4*q^(-19/2) + 2*q^(-21/2))*x1^(-3/2)*x2^(-19/2) + (-2*q^(27/2) - 2*q^(25/2) - 10*q^(23/2) - 14*q^(21/2) - 50*q^(19/2) - 94*q^(17/2) - 248*q^(15/2) - 445*q^(13/2) - 752*q^(11/2) - 915*q^(9/2) - 1027*q^(7/2) - 826*q^(5/2) - 724*q^(3/2) - 601*q^(1/2) - 475*q^(-1/2) - 304*q^(-3/2) - 184*q^(-5/2) - 91*q^(-7/2) - 53*q^(-9/2) - 24*q^(-11/2) - 12*q^(-13/2) - 4*q^(-15/2) - 2*q^(-17/2))*x1^(-5/2)*x2^(-19/2) + (2*q^(37/2) + 2*q^(35/2) + 4*q^(33/2) + 12*q^(31/2) + 18*q^(29/2) + 32*q^(27/2) + 72*q^(25/2) + 114*q^(23/2) + 226*q^(21/2) + 405*q^(19/2) + 651*q^(17/2) + 868*q^(15/2) + 1049*q^(13/2) + 939*q^(11/2) + 821*q^(9/2) + 625*q^(7/2) + 468*q^(5/2) + 313*q^(3/2) + 200*q^(1/2) + 103*q^(-1/2) + 57*q^(-3/2) + 26*q^(-5/2) + 12*q^(-7/2) + 4*q^(-9/2) + 2*q^(-11/2))*x1^(-7/2)*x2^(-19/2) + (-2*q^(45/2) - 2*q^(43/2) - 4*q^(41/2) - 8*q^(39/2) - 18*q^(37/2) - 26*q^(35/2) - 54*q^(33/2) - 82*q^(31/2) - 162*q^(29/2) - 248*q^(27/2) - 386*q^(25/2) - 520*q^(23/2) - 683*q^(21/2) - 669*q^(19/2) - 657*q^(17/2) - 536*q^(15/2) - 404*q^(13/2) - 270*q^(11/2) - 181*q^(9/2) - 99*q^(7/2) - 57*q^(5/2) - 26*q^(3/2) - 12*q^(1/2) - 4*q^(-1/2) - 2*q^(-3/2))*x1^(-9/2)*x2^(-19/2) + (2*q^(51/2) + 2*q^(49/2) + 6*q^(47/2) + 8*q^(45/2) + 16*q^(43/2) + 32*q^(41/2) + 60*q^(39/2) + 92*q^(37/2) + 144*q^(35/2) + 204*q^(33/2) + 295*q^(31/2) + 306*q^(29/2) + 332*q^(27/2) + 311*q^(25/2) + 272*q^(23/2) + 193*q^(21/2) + 142*q^(19/2) + 82*q^(17/2) + 51*q^(15/2) + 24*q^(13/2) + 12*q^(11/2) + 4*q^(9/2) + 2*q^(7/2))*x1^(-11/2)*x2^(-19/2) + (-2*q^(55/2) - 4*q^(53/2) - 8*q^(51/2) - 14*q^(49/2) - 24*q^(47/2) - 38*q^(45/2) - 74*q^(43/2) - 78*q^(41/2) - 96*q^(39/2) - 102*q^(37/2) - 106*q^(35/2) - 90*q^(33/2) - 74*q^(31/2) - 50*q^(29/2) - 36*q^(27/2) - 20*q^(25/2) - 10*q^(23/2) - 4*q^(21/2) - 2*q^(19/2))*x1^(-13/2)*x2^(-19/2) + (8*q^(57/2) + 6*q^(55/2) + 10*q^(53/2) + 12*q^(51/2) + 16*q^(49/2) + 16*q^(47/2) + 18*q^(45/2) + 12*q^(43/2) + 12*q^(41/2) + 8*q^(39/2) + 6*q^(37/2) + 2*q^(35/2) + 2*q^(33/2))*x1^(-15/2)*x2^(-19/2)

Braid

Braid word Components Crossings Strands
[-1, -1, 2, 2, -3, 2, -1, 2, 3, 2, 2, -1] 2 12 4

Multivariable Alexander polynomial

ΔL
-A1^(1/2)*A2^(5/2) + 4*A1^(1/2)*A2^(3/2) - 5*A1^(1/2)*A2^(1/2) + 5*A1^(1/2)*A2^(-1/2) - 2*A1^(1/2)*A2^(-3/2) - 2*A1^(-1/2)*A2^(3/2) + 5*A1^(-1/2)*A2^(1/2) - 5*A1^(-1/2)*A2^(-1/2) + 4*A1^(-1/2)*A2^(-3/2) - A1^(-1/2)*A2^(-5/2)

Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.

Newton Polygon of Alexander-0.500.5-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(-1, -5) yes
(1, -3) no
(1, 5) yes
(-1, 3) no
Dual Thurston polygon-101-505h1h2

HFL polytope

Poincaré polynomial
m^(-5)*A1^(-1)*A2^(-3) + 5*m^(-4)*A1^(-1)*A2^(-2) + m^(-4)*A2^(-3) + 9*m^(-3)*A1^(-1)*A2^(-1) + 7*m^(-3)*A2^(-2) + 10*m^(-2)*A1^(-1) + 16*m^(-2)*A2^(-1) + 2*m^(-2)*A1*A2^(-2) + 7*m^(-1)*A1^(-1)*A2 + 20*m^(-1) + 7*m^(-1)*A1*A2^(-1) + 2*A1^(-1)*A2^2 + 16*A2 + 10*A1 + 7*m*A2^2 + 9*m*A1*A2 + m^2*A2^3 + 5*m^2*A1*A2^2 + m^3*A1*A2^3
VertexMaslovRank
(-1, -3)-51
(0, -3)-41
(1, -2)-22
(1, 3)31
(0, 3)21
(-1, 2)02
HFL polytope-10105A1A2

Record

FL/HFL Links

orderOption(int) 294
namestring L10a15{1}
statusstring success
slugstring L10a15_1_1198f09f
result_filestring details/L10a15_1_1198f09f.json
complexity_scoreOption(int) 200
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 136
wall_secondsOption(float) 0.003685
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 19
vertex_countOption(int) 6
fibered_vertex_countOption(int) 2
polytope_statusstring computed
alexander_support_sizeOption(int) 10
alexander_vertex_countOption(int) 4
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks)
{
  "dataset": "FLHFLLinks",
  "key": "L10a15_1_1198f09f"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10a15_1_1198f09f