details/L10a13_1_d16d8c2c.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^(3/2)
{"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^(3/2))*x1^(1/2)*x2^(5/2) + (-4*q^(3/2))*x1^(1/2)*x2^(7/2) + (2*q^(5/2))*x1^(3/2)*x2^(7/2) + (q^(5/2) - 10*q^(3/2))*x1^(1/2)*x2^(9/2) + (2*q^(7/2) + 8*q^(5/2) + q^(3/2))*x1^(3/2)*x2^(9/2) + (-3*q^(9/2) - q^(7/2))*x1^(5/2)*x2^(9/2) + (2*q^(7/2) + 4*q^(5/2) - 20*q^(3/2) + q^(-1/2))*x1^(1/2)*x2^(11/2) + (2*q^(9/2) + 6*q^(7/2) + 22*q^(5/2) + 4*q^(3/2) + q^(1/2))*x1^(3/2)*x2^(11/2) + (-2*q^(13/2) - 4*q^(11/2) - 14*q^(9/2) - 6*q^(7/2) - 2*q^(5/2))*x1^(5/2)*x2^(11/2) + (4*q^(15/2) + 2*q^(13/2) + 2*q^(11/2))*x1^(7/2)*x2^(11/2) + (2*q^(9/2) + 8*q^(7/2) + 11*q^(5/2) - 35*q^(3/2) + 5*q^(-1/2) + 3*q^(-3/2) - q^(-5/2))*x1^(1/2)*x2^(13/2) + (2*q^(11/2) + 2*q^(9/2) + 13*q^(7/2) + 47*q^(5/2) + 12*q^(3/2) + q^(1/2) + q^(-3/2))*x1^(3/2)*x2^(13/2) + (-2*q^(17/2) - 2*q^(15/2) - 13*q^(13/2) - 18*q^(11/2) - 43*q^(9/2) - 22*q^(7/2) - 10*q^(5/2) - 2*q^(3/2) - q^(1/2))*x1^(5/2)*x2^(13/2) + (2*q^(21/2) + 4*q^(19/2) + 8*q^(17/2) + 22*q^(15/2) + 15*q^(13/2) + 12*q^(11/2) + 4*q^(9/2) + q^(7/2))*x1^(7/2)*x2^(13/2) + (-5*q^(23/2) - 3*q^(21/2) - 4*q^(19/2) - 3*q^(17/2) - q^(15/2))*x1^(9/2)*x2^(13/2) + (-2*q^(13/2) + 2*q^(11/2) + 8*q^(9/2) + 22*q^(7/2) + 24*q^(5/2) - 55*q^(3/2) - q^(1/2) + 14*q^(-1/2) + 16*q^(-3/2) + 4*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(1/2)*x2^(15/2) + (2*q^(13/2) - 2*q^(11/2) - 6*q^(9/2) + 18*q^(7/2) + 86*q^(5/2) + 23*q^(3/2) - 4*q^(1/2) - 9*q^(-1/2) + q^(-3/2) + 4*q^(-5/2) + 2*q^(-7/2))*x1^(3/2)*x2^(15/2) + (-2*q^(21/2) - 2*q^(19/2) - 10*q^(17/2) - 14*q^(15/2) - 38*q^(13/2) - 50*q^(11/2) - 104*q^(9/2) - 60*q^(7/2) - 29*q^(5/2) - 7*q^(3/2) - 5*q^(1/2) - 3*q^(-1/2) - 2*q^(-3/2))*x1^(5/2)*x2^(15/2) + (2*q^(27/2) + 2*q^(25/2) + 6*q^(23/2) + 16*q^(21/2) + 32*q^(19/2) + 44*q^(17/2) + 82*q^(15/2) + 60*q^(13/2) + 49*q^(11/2) + 22*q^(9/2) + 10*q^(7/2) + 3*q^(5/2) + 2*q^(3/2))*x1^(7/2)*x2^(15/2) + (-2*q^(31/2) - 4*q^(29/2) - 8*q^(27/2) - 14*q^(25/2) - 34*q^(23/2) - 28*q^(21/2) - 30*q^(19/2) - 22*q^(17/2) - 12*q^(15/2) - 4*q^(13/2) - 2*q^(11/2))*x1^(9/2)*x2^(15/2) + (6*q^(33/2) + 4*q^(31/2) + 6*q^(29/2) + 6*q^(27/2) + 6*q^(25/2) + 2*q^(23/2) + 2*q^(21/2))*x1^(11/2)*x2^(15/2) + (-3*q^(17/2) - 3*q^(15/2) - 6*q^(13/2) + 7*q^(11/2) + 22*q^(9/2) + 48*q^(7/2) + 47*q^(5/2) - 83*q^(3/2) - 5*q^(1/2) + 28*q^(-1/2) + 47*q^(-3/2) + 31*q^(-5/2) + 2*q^(-7/2) - 14*q^(-9/2) - 8*q^(-11/2) - 3*q^(-13/2) - q^(-15/2))*x1^(1/2)*x2^(17/2) + (6*q^(15/2) - 5*q^(13/2) - 26*q^(11/2) - 42*q^(9/2) + 10*q^(7/2) + 132*q^(5/2) + 33*q^(3/2) - 33*q^(1/2) - 53*q^(-1/2) - 24*q^(-3/2) + 9*q^(-5/2) + 18*q^(-7/2) + 9*q^(-9/2) + 4*q^(-11/2) + q^(-13/2))*x1^(3/2)*x2^(17/2) + (-2*q^(25/2) - 2*q^(23/2) - 10*q^(21/2) - 10*q^(19/2) - 33*q^(17/2) - 32*q^(15/2) - 73*q^(13/2) - 99*q^(11/2) - 204*q^(9/2) - 123*q^(7/2) - 55*q^(5/2) - q^(3/2) - 4*q^(1/2) - 10*q^(-1/2) - 17*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - q^(-9/2))*x1^(5/2)*x2^(17/2) + (2*q^(33/2) + 2*q^(31/2) + 4*q^(29/2) + 14*q^(27/2) + 20*q^(25/2) + 40*q^(23/2) + 78*q^(21/2) + 120*q^(19/2) + 154*q^(17/2) + 229*q^(15/2) + 182*q^(13/2) + 143*q^(11/2) + 77*q^(9/2) + 39*q^(7/2) + 19*q^(5/2) + 16*q^(3/2) + 7*q^(1/2) + 4*q^(-1/2) + q^(-3/2))*x1^(7/2)*x2^(17/2) + (-2*q^(39/2) - 2*q^(37/2) - 6*q^(35/2) - 8*q^(33/2) - 25*q^(31/2) - 41*q^(29/2) - 71*q^(27/2) - 95*q^(25/2) - 154*q^(23/2) - 137*q^(21/2) - 134*q^(19/2) - 101*q^(17/2) - 65*q^(15/2) - 32*q^(13/2) - 19*q^(11/2) - 7*q^(9/2) - 4*q^(7/2) - q^(5/2))*x1^(9/2)*x2^(17/2) + (2*q^(43/2) + 4*q^(41/2) + 8*q^(39/2) + 14*q^(37/2) + 24*q^(35/2) + 50*q^(33/2) + 49*q^(31/2) + 56*q^(29/2) + 54*q^(27/2) + 47*q^(25/2) + 28*q^(23/2) + 19*q^(21/2) + 8*q^(19/2) + 4*q^(17/2) + q^(15/2))*x1^(11/2)*x2^(17/2) + (-7*q^(45/2) - 5*q^(43/2) - 8*q^(41/2) - 9*q^(39/2) - 11*q^(37/2) - 9*q^(35/2) - 7*q^(33/2) - 4*q^(31/2) - 3*q^(29/2) - q^(27/2))*x1^(13/2)*x2^(17/2) + (-2*q^(21/2) - 4*q^(19/2) - 16*q^(17/2) - 12*q^(15/2) - 16*q^(13/2) + 18*q^(11/2) + 47*q^(9/2) + 92*q^(7/2) + 80*q^(5/2) - 124*q^(3/2) - 23*q^(1/2) + 40*q^(-1/2) + 100*q^(-3/2) + 102*q^(-5/2) + 50*q^(-7/2) - 12*q^(-9/2) - 39*q^(-11/2) - 25*q^(-13/2) - 14*q^(-15/2) - 5*q^(-17/2) - 2*q^(-19/2) - 2*q^(-21/2))*x1^(1/2)*x2^(19/2) + (6*q^(19/2) + 14*q^(17/2) + 12*q^(15/2) - 38*q^(13/2) - 104*q^(11/2) - 140*q^(9/2) - 40*q^(7/2) + 176*q^(5/2) + 26*q^(3/2) - 116*q^(1/2) - 196*q^(-1/2) - 148*q^(-3/2) - 39*q^(-5/2) + 45*q^(-7/2) + 61*q^(-9/2) + 40*q^(-11/2) + 21*q^(-13/2) + 9*q^(-15/2) + 4*q^(-17/2) + 2*q^(-19/2))*x1^(3/2)*x2^(19/2) + (-2*q^(29/2) - 2*q^(27/2) - 10*q^(25/2) - 10*q^(23/2) - 28*q^(21/2) - 34*q^(19/2) - 56*q^(17/2) - 20*q^(15/2) - 70*q^(13/2) - 124*q^(11/2) - 312*q^(9/2) - 176*q^(7/2) - 34*q^(5/2) + 87*q^(3/2) + 71*q^(1/2) + 12*q^(-1/2) - 50*q^(-3/2) - 58*q^(-5/2) - 43*q^(-7/2) - 23*q^(-9/2) - 11*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(5/2)*x2^(19/2) + (2*q^(39/2) + 2*q^(37/2) + 4*q^(35/2) + 12*q^(33/2) + 18*q^(31/2) + 28*q^(29/2) + 66*q^(27/2) + 90*q^(25/2) + 156*q^(23/2) + 234*q^(21/2) + 320*q^(19/2) + 376*q^(17/2) + 513*q^(15/2) + 415*q^(13/2) + 320*q^(11/2) + 168*q^(9/2) + 88*q^(7/2) + 48*q^(5/2) + 59*q^(3/2) + 49*q^(1/2) + 39*q^(-1/2) + 23*q^(-3/2) + 11*q^(-5/2) + 4*q^(-7/2) + 2*q^(-9/2))*x1^(7/2)*x2^(19/2) + (-2*q^(47/2) - 2*q^(45/2) - 4*q^(43/2) - 8*q^(41/2) - 18*q^(39/2) - 26*q^(37/2) - 54*q^(35/2) - 78*q^(33/2) - 152*q^(31/2) - 226*q^(29/2) - 322*q^(27/2) - 394*q^(25/2) - 524*q^(23/2) - 476*q^(21/2) - 443*q^(19/2) - 343*q^(17/2) - 239*q^(15/2) - 138*q^(13/2) - 94*q^(11/2) - 54*q^(9/2) - 37*q^(7/2) - 21*q^(5/2) - 11*q^(3/2) - 4*q^(1/2) - 2*q^(-1/2))*x1^(9/2)*x2^(19/2) + (2*q^(53/2) + 2*q^(51/2) + 6*q^(49/2) + 8*q^(47/2) + 16*q^(45/2) + 32*q^(43/2) + 60*q^(41/2) + 92*q^(39/2) + 144*q^(37/2) + 192*q^(35/2) + 282*q^(33/2) + 286*q^(31/2) + 303*q^(29/2) + 276*q^(27/2) + 240*q^(25/2) + 163*q^(23/2) + 118*q^(21/2) + 67*q^(19/2) + 42*q^(17/2) + 20*q^(15/2) + 11*q^(13/2) + 4*q^(11/2) + 2*q^(9/2))*x1^(11/2)*x2^(19/2) + (-2*q^(57/2) - 4*q^(55/2) - 8*q^(53/2) - 14*q^(51/2) - 24*q^(49/2) - 38*q^(47/2) - 74*q^(45/2) - 78*q^(43/2) - 96*q^(41/2) - 102*q^(39/2) - 106*q^(37/2) - 90*q^(35/2) - 74*q^(33/2) - 50*q^(31/2) - 36*q^(29/2) - 20*q^(27/2) - 10*q^(25/2) - 4*q^(23/2) - 2*q^(21/2))*x1^(13/2)*x2^(19/2) + (8*q^(59/2) + 6*q^(57/2) + 10*q^(55/2) + 12*q^(53/2) + 16*q^(51/2) + 16*q^(49/2) + 18*q^(47/2) + 12*q^(45/2) + 12*q^(43/2) + 8*q^(41/2) + 6*q^(39/2) + 2*q^(37/2) + 2*q^(35/2))*x1^(15/2)*x2^(19/2)
(-1/2, -5/2) (1, 1) x1^(1/2)x2^(5/2) q^(3/2)
{"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^(3/2))*x1^(1/2)*x2^(5/2) + (-4*q^(3/2))*x1^(1/2)*x2^(7/2) + (2*q^(5/2))*x1^(3/2)*x2^(7/2) + (q^(5/2) - 10*q^(3/2))*x1^(1/2)*x2^(9/2) + (2*q^(7/2) + 8*q^(5/2) + q^(3/2))*x1^(3/2)*x2^(9/2) + (-3*q^(9/2) - q^(7/2))*x1^(5/2)*x2^(9/2) + (2*q^(7/2) + 4*q^(5/2) - 20*q^(3/2) + q^(-1/2))*x1^(1/2)*x2^(11/2) + (2*q^(9/2) + 6*q^(7/2) + 22*q^(5/2) + 4*q^(3/2) + q^(1/2))*x1^(3/2)*x2^(11/2) + (-2*q^(13/2) - 4*q^(11/2) - 14*q^(9/2) - 6*q^(7/2) - 2*q^(5/2))*x1^(5/2)*x2^(11/2) + (4*q^(15/2) + 2*q^(13/2) + 2*q^(11/2))*x1^(7/2)*x2^(11/2) + (2*q^(9/2) + 8*q^(7/2) + 11*q^(5/2) - 35*q^(3/2) + 5*q^(-1/2) + 3*q^(-3/2) - q^(-5/2))*x1^(1/2)*x2^(13/2) + (2*q^(11/2) + 2*q^(9/2) + 13*q^(7/2) + 47*q^(5/2) + 12*q^(3/2) + q^(1/2) + q^(-3/2))*x1^(3/2)*x2^(13/2) + (-2*q^(17/2) - 2*q^(15/2) - 13*q^(13/2) - 18*q^(11/2) - 43*q^(9/2) - 22*q^(7/2) - 10*q^(5/2) - 2*q^(3/2) - q^(1/2))*x1^(5/2)*x2^(13/2) + (2*q^(21/2) + 4*q^(19/2) + 8*q^(17/2) + 22*q^(15/2) + 15*q^(13/2) + 12*q^(11/2) + 4*q^(9/2) + q^(7/2))*x1^(7/2)*x2^(13/2) + (-5*q^(23/2) - 3*q^(21/2) - 4*q^(19/2) - 3*q^(17/2) - q^(15/2))*x1^(9/2)*x2^(13/2) + (-2*q^(13/2) + 2*q^(11/2) + 8*q^(9/2) + 22*q^(7/2) + 24*q^(5/2) - 55*q^(3/2) - q^(1/2) + 14*q^(-1/2) + 16*q^(-3/2) + 4*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(1/2)*x2^(15/2) + (2*q^(13/2) - 2*q^(11/2) - 6*q^(9/2) + 18*q^(7/2) + 86*q^(5/2) + 23*q^(3/2) - 4*q^(1/2) - 9*q^(-1/2) + q^(-3/2) + 4*q^(-5/2) + 2*q^(-7/2))*x1^(3/2)*x2^(15/2) + (-2*q^(21/2) - 2*q^(19/2) - 10*q^(17/2) - 14*q^(15/2) - 38*q^(13/2) - 50*q^(11/2) - 104*q^(9/2) - 60*q^(7/2) - 29*q^(5/2) - 7*q^(3/2) - 5*q^(1/2) - 3*q^(-1/2) - 2*q^(-3/2))*x1^(5/2)*x2^(15/2) + (2*q^(27/2) + 2*q^(25/2) + 6*q^(23/2) + 16*q^(21/2) + 32*q^(19/2) + 44*q^(17/2) + 82*q^(15/2) + 60*q^(13/2) + 49*q^(11/2) + 22*q^(9/2) + 10*q^(7/2) + 3*q^(5/2) + 2*q^(3/2))*x1^(7/2)*x2^(15/2) + (-2*q^(31/2) - 4*q^(29/2) - 8*q^(27/2) - 14*q^(25/2) - 34*q^(23/2) - 28*q^(21/2) - 30*q^(19/2) - 22*q^(17/2) - 12*q^(15/2) - 4*q^(13/2) - 2*q^(11/2))*x1^(9/2)*x2^(15/2) + (6*q^(33/2) + 4*q^(31/2) + 6*q^(29/2) + 6*q^(27/2) + 6*q^(25/2) + 2*q^(23/2) + 2*q^(21/2))*x1^(11/2)*x2^(15/2) + (-3*q^(17/2) - 3*q^(15/2) - 6*q^(13/2) + 7*q^(11/2) + 22*q^(9/2) + 48*q^(7/2) + 47*q^(5/2) - 83*q^(3/2) - 5*q^(1/2) + 28*q^(-1/2) + 47*q^(-3/2) + 31*q^(-5/2) + 2*q^(-7/2) - 14*q^(-9/2) - 8*q^(-11/2) - 3*q^(-13/2) - q^(-15/2))*x1^(1/2)*x2^(17/2) + (6*q^(15/2) - 5*q^(13/2) - 26*q^(11/2) - 42*q^(9/2) + 10*q^(7/2) + 132*q^(5/2) + 33*q^(3/2) - 33*q^(1/2) - 53*q^(-1/2) - 24*q^(-3/2) + 9*q^(-5/2) + 18*q^(-7/2) + 9*q^(-9/2) + 4*q^(-11/2) + q^(-13/2))*x1^(3/2)*x2^(17/2) + (-2*q^(25/2) - 2*q^(23/2) - 10*q^(21/2) - 10*q^(19/2) - 33*q^(17/2) - 32*q^(15/2) - 73*q^(13/2) - 99*q^(11/2) - 204*q^(9/2) - 123*q^(7/2) - 55*q^(5/2) - q^(3/2) - 4*q^(1/2) - 10*q^(-1/2) - 17*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - q^(-9/2))*x1^(5/2)*x2^(17/2) + (2*q^(33/2) + 2*q^(31/2) + 4*q^(29/2) + 14*q^(27/2) + 20*q^(25/2) + 40*q^(23/2) + 78*q^(21/2) + 120*q^(19/2) + 154*q^(17/2) + 229*q^(15/2) + 182*q^(13/2) + 143*q^(11/2) + 77*q^(9/2) + 39*q^(7/2) + 19*q^(5/2) + 16*q^(3/2) + 7*q^(1/2) + 4*q^(-1/2) + q^(-3/2))*x1^(7/2)*x2^(17/2) + (-2*q^(39/2) - 2*q^(37/2) - 6*q^(35/2) - 8*q^(33/2) - 25*q^(31/2) - 41*q^(29/2) - 71*q^(27/2) - 95*q^(25/2) - 154*q^(23/2) - 137*q^(21/2) - 134*q^(19/2) - 101*q^(17/2) - 65*q^(15/2) - 32*q^(13/2) - 19*q^(11/2) - 7*q^(9/2) - 4*q^(7/2) - q^(5/2))*x1^(9/2)*x2^(17/2) + (2*q^(43/2) + 4*q^(41/2) + 8*q^(39/2) + 14*q^(37/2) + 24*q^(35/2) + 50*q^(33/2) + 49*q^(31/2) + 56*q^(29/2) + 54*q^(27/2) + 47*q^(25/2) + 28*q^(23/2) + 19*q^(21/2) + 8*q^(19/2) + 4*q^(17/2) + q^(15/2))*x1^(11/2)*x2^(17/2) + (-7*q^(45/2) - 5*q^(43/2) - 8*q^(41/2) - 9*q^(39/2) - 11*q^(37/2) - 9*q^(35/2) - 7*q^(33/2) - 4*q^(31/2) - 3*q^(29/2) - q^(27/2))*x1^(13/2)*x2^(17/2) + (-2*q^(21/2) - 4*q^(19/2) - 16*q^(17/2) - 12*q^(15/2) - 16*q^(13/2) + 18*q^(11/2) + 47*q^(9/2) + 92*q^(7/2) + 80*q^(5/2) - 124*q^(3/2) - 23*q^(1/2) + 40*q^(-1/2) + 100*q^(-3/2) + 102*q^(-5/2) + 50*q^(-7/2) - 12*q^(-9/2) - 39*q^(-11/2) - 25*q^(-13/2) - 14*q^(-15/2) - 5*q^(-17/2) - 2*q^(-19/2) - 2*q^(-21/2))*x1^(1/2)*x2^(19/2) + (6*q^(19/2) + 14*q^(17/2) + 12*q^(15/2) - 38*q^(13/2) - 104*q^(11/2) - 140*q^(9/2) - 40*q^(7/2) + 176*q^(5/2) + 26*q^(3/2) - 116*q^(1/2) - 196*q^(-1/2) - 148*q^(-3/2) - 39*q^(-5/2) + 45*q^(-7/2) + 61*q^(-9/2) + 40*q^(-11/2) + 21*q^(-13/2) + 9*q^(-15/2) + 4*q^(-17/2) + 2*q^(-19/2))*x1^(3/2)*x2^(19/2) + (-2*q^(29/2) - 2*q^(27/2) - 10*q^(25/2) - 10*q^(23/2) - 28*q^(21/2) - 34*q^(19/2) - 56*q^(17/2) - 20*q^(15/2) - 70*q^(13/2) - 124*q^(11/2) - 312*q^(9/2) - 176*q^(7/2) - 34*q^(5/2) + 87*q^(3/2) + 71*q^(1/2) + 12*q^(-1/2) - 50*q^(-3/2) - 58*q^(-5/2) - 43*q^(-7/2) - 23*q^(-9/2) - 11*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(5/2)*x2^(19/2) + (2*q^(39/2) + 2*q^(37/2) + 4*q^(35/2) + 12*q^(33/2) + 18*q^(31/2) + 28*q^(29/2) + 66*q^(27/2) + 90*q^(25/2) + 156*q^(23/2) + 234*q^(21/2) + 320*q^(19/2) + 376*q^(17/2) + 513*q^(15/2) + 415*q^(13/2) + 320*q^(11/2) + 168*q^(9/2) + 88*q^(7/2) + 48*q^(5/2) + 59*q^(3/2) + 49*q^(1/2) + 39*q^(-1/2) + 23*q^(-3/2) + 11*q^(-5/2) + 4*q^(-7/2) + 2*q^(-9/2))*x1^(7/2)*x2^(19/2) + (-2*q^(47/2) - 2*q^(45/2) - 4*q^(43/2) - 8*q^(41/2) - 18*q^(39/2) - 26*q^(37/2) - 54*q^(35/2) - 78*q^(33/2) - 152*q^(31/2) - 226*q^(29/2) - 322*q^(27/2) - 394*q^(25/2) - 524*q^(23/2) - 476*q^(21/2) - 443*q^(19/2) - 343*q^(17/2) - 239*q^(15/2) - 138*q^(13/2) - 94*q^(11/2) - 54*q^(9/2) - 37*q^(7/2) - 21*q^(5/2) - 11*q^(3/2) - 4*q^(1/2) - 2*q^(-1/2))*x1^(9/2)*x2^(19/2) + (2*q^(53/2) + 2*q^(51/2) + 6*q^(49/2) + 8*q^(47/2) + 16*q^(45/2) + 32*q^(43/2) + 60*q^(41/2) + 92*q^(39/2) + 144*q^(37/2) + 192*q^(35/2) + 282*q^(33/2) + 286*q^(31/2) + 303*q^(29/2) + 276*q^(27/2) + 240*q^(25/2) + 163*q^(23/2) + 118*q^(21/2) + 67*q^(19/2) + 42*q^(17/2) + 20*q^(15/2) + 11*q^(13/2) + 4*q^(11/2) + 2*q^(9/2))*x1^(11/2)*x2^(19/2) + (-2*q^(57/2) - 4*q^(55/2) - 8*q^(53/2) - 14*q^(51/2) - 24*q^(49/2) - 38*q^(47/2) - 74*q^(45/2) - 78*q^(43/2) - 96*q^(41/2) - 102*q^(39/2) - 106*q^(37/2) - 90*q^(35/2) - 74*q^(33/2) - 50*q^(31/2) - 36*q^(29/2) - 20*q^(27/2) - 10*q^(25/2) - 4*q^(23/2) - 2*q^(21/2))*x1^(13/2)*x2^(19/2) + (8*q^(59/2) + 6*q^(57/2) + 10*q^(55/2) + 12*q^(53/2) + 16*q^(51/2) + 16*q^(49/2) + 18*q^(47/2) + 12*q^(45/2) + 12*q^(43/2) + 8*q^(41/2) + 6*q^(39/2) + 2*q^(37/2) + 2*q^(35/2))*x1^(15/2)*x2^(19/2)
(1/2, 5/2) x1^(-1/2)x2^(-5/2) q^(3/2)
(-q^(3/2))*x1^(-1/2)*x2^(-5/2) + (-4*q^(3/2))*x1^(-1/2)*x2^(-7/2) + (2*q^(5/2))*x1^(-3/2)*x2^(-7/2) + (q^(5/2) - 10*q^(3/2))*x1^(-1/2)*x2^(-9/2) + (2*q^(7/2) + 8*q^(5/2) + q^(3/2))*x1^(-3/2)*x2^(-9/2) + (-3*q^(9/2) - q^(7/2))*x1^(-5/2)*x2^(-9/2) + (2*q^(7/2) + 4*q^(5/2) - 20*q^(3/2) + q^(-1/2))*x1^(-1/2)*x2^(-11/2) + (2*q^(9/2) + 6*q^(7/2) + 22*q^(5/2) + 4*q^(3/2) + q^(1/2))*x1^(-3/2)*x2^(-11/2) + (-2*q^(13/2) - 4*q^(11/2) - 14*q^(9/2) - 6*q^(7/2) - 2*q^(5/2))*x1^(-5/2)*x2^(-11/2) + (4*q^(15/2) + 2*q^(13/2) + 2*q^(11/2))*x1^(-7/2)*x2^(-11/2) + (2*q^(9/2) + 8*q^(7/2) + 11*q^(5/2) - 35*q^(3/2) + 5*q^(-1/2) + 3*q^(-3/2) - q^(-5/2))*x1^(-1/2)*x2^(-13/2) + (2*q^(11/2) + 2*q^(9/2) + 13*q^(7/2) + 47*q^(5/2) + 12*q^(3/2) + q^(1/2) + q^(-3/2))*x1^(-3/2)*x2^(-13/2) + (-2*q^(17/2) - 2*q^(15/2) - 13*q^(13/2) - 18*q^(11/2) - 43*q^(9/2) - 22*q^(7/2) - 10*q^(5/2) - 2*q^(3/2) - q^(1/2))*x1^(-5/2)*x2^(-13/2) + (2*q^(21/2) + 4*q^(19/2) + 8*q^(17/2) + 22*q^(15/2) + 15*q^(13/2) + 12*q^(11/2) + 4*q^(9/2) + q^(7/2))*x1^(-7/2)*x2^(-13/2) + (-5*q^(23/2) - 3*q^(21/2) - 4*q^(19/2) - 3*q^(17/2) - q^(15/2))*x1^(-9/2)*x2^(-13/2) + (-2*q^(13/2) + 2*q^(11/2) + 8*q^(9/2) + 22*q^(7/2) + 24*q^(5/2) - 55*q^(3/2) - q^(1/2) + 14*q^(-1/2) + 16*q^(-3/2) + 4*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(-1/2)*x2^(-15/2) + (2*q^(13/2) - 2*q^(11/2) - 6*q^(9/2) + 18*q^(7/2) + 86*q^(5/2) + 23*q^(3/2) - 4*q^(1/2) - 9*q^(-1/2) + q^(-3/2) + 4*q^(-5/2) + 2*q^(-7/2))*x1^(-3/2)*x2^(-15/2) + (-2*q^(21/2) - 2*q^(19/2) - 10*q^(17/2) - 14*q^(15/2) - 38*q^(13/2) - 50*q^(11/2) - 104*q^(9/2) - 60*q^(7/2) - 29*q^(5/2) - 7*q^(3/2) - 5*q^(1/2) - 3*q^(-1/2) - 2*q^(-3/2))*x1^(-5/2)*x2^(-15/2) + (2*q^(27/2) + 2*q^(25/2) + 6*q^(23/2) + 16*q^(21/2) + 32*q^(19/2) + 44*q^(17/2) + 82*q^(15/2) + 60*q^(13/2) + 49*q^(11/2) + 22*q^(9/2) + 10*q^(7/2) + 3*q^(5/2) + 2*q^(3/2))*x1^(-7/2)*x2^(-15/2) + (-2*q^(31/2) - 4*q^(29/2) - 8*q^(27/2) - 14*q^(25/2) - 34*q^(23/2) - 28*q^(21/2) - 30*q^(19/2) - 22*q^(17/2) - 12*q^(15/2) - 4*q^(13/2) - 2*q^(11/2))*x1^(-9/2)*x2^(-15/2) + (6*q^(33/2) + 4*q^(31/2) + 6*q^(29/2) + 6*q^(27/2) + 6*q^(25/2) + 2*q^(23/2) + 2*q^(21/2))*x1^(-11/2)*x2^(-15/2) + (-3*q^(17/2) - 3*q^(15/2) - 6*q^(13/2) + 7*q^(11/2) + 22*q^(9/2) + 48*q^(7/2) + 47*q^(5/2) - 83*q^(3/2) - 5*q^(1/2) + 28*q^(-1/2) + 47*q^(-3/2) + 31*q^(-5/2) + 2*q^(-7/2) - 14*q^(-9/2) - 8*q^(-11/2) - 3*q^(-13/2) - q^(-15/2))*x1^(-1/2)*x2^(-17/2) + (6*q^(15/2) - 5*q^(13/2) - 26*q^(11/2) - 42*q^(9/2) + 10*q^(7/2) + 132*q^(5/2) + 33*q^(3/2) - 33*q^(1/2) - 53*q^(-1/2) - 24*q^(-3/2) + 9*q^(-5/2) + 18*q^(-7/2) + 9*q^(-9/2) + 4*q^(-11/2) + q^(-13/2))*x1^(-3/2)*x2^(-17/2) + (-2*q^(25/2) - 2*q^(23/2) - 10*q^(21/2) - 10*q^(19/2) - 33*q^(17/2) - 32*q^(15/2) - 73*q^(13/2) - 99*q^(11/2) - 204*q^(9/2) - 123*q^(7/2) - 55*q^(5/2) - q^(3/2) - 4*q^(1/2) - 10*q^(-1/2) - 17*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - q^(-9/2))*x1^(-5/2)*x2^(-17/2) + (2*q^(33/2) + 2*q^(31/2) + 4*q^(29/2) + 14*q^(27/2) + 20*q^(25/2) + 40*q^(23/2) + 78*q^(21/2) + 120*q^(19/2) + 154*q^(17/2) + 229*q^(15/2) + 182*q^(13/2) + 143*q^(11/2) + 77*q^(9/2) + 39*q^(7/2) + 19*q^(5/2) + 16*q^(3/2) + 7*q^(1/2) + 4*q^(-1/2) + q^(-3/2))*x1^(-7/2)*x2^(-17/2) + (-2*q^(39/2) - 2*q^(37/2) - 6*q^(35/2) - 8*q^(33/2) - 25*q^(31/2) - 41*q^(29/2) - 71*q^(27/2) - 95*q^(25/2) - 154*q^(23/2) - 137*q^(21/2) - 134*q^(19/2) - 101*q^(17/2) - 65*q^(15/2) - 32*q^(13/2) - 19*q^(11/2) - 7*q^(9/2) - 4*q^(7/2) - q^(5/2))*x1^(-9/2)*x2^(-17/2) + (2*q^(43/2) + 4*q^(41/2) + 8*q^(39/2) + 14*q^(37/2) + 24*q^(35/2) + 50*q^(33/2) + 49*q^(31/2) + 56*q^(29/2) + 54*q^(27/2) + 47*q^(25/2) + 28*q^(23/2) + 19*q^(21/2) + 8*q^(19/2) + 4*q^(17/2) + q^(15/2))*x1^(-11/2)*x2^(-17/2) + (-7*q^(45/2) - 5*q^(43/2) - 8*q^(41/2) - 9*q^(39/2) - 11*q^(37/2) - 9*q^(35/2) - 7*q^(33/2) - 4*q^(31/2) - 3*q^(29/2) - q^(27/2))*x1^(-13/2)*x2^(-17/2) + (-2*q^(21/2) - 4*q^(19/2) - 16*q^(17/2) - 12*q^(15/2) - 16*q^(13/2) + 18*q^(11/2) + 47*q^(9/2) + 92*q^(7/2) + 80*q^(5/2) - 124*q^(3/2) - 23*q^(1/2) + 40*q^(-1/2) + 100*q^(-3/2) + 102*q^(-5/2) + 50*q^(-7/2) - 12*q^(-9/2) - 39*q^(-11/2) - 25*q^(-13/2) - 14*q^(-15/2) - 5*q^(-17/2) - 2*q^(-19/2) - 2*q^(-21/2))*x1^(-1/2)*x2^(-19/2) + (6*q^(19/2) + 14*q^(17/2) + 12*q^(15/2) - 38*q^(13/2) - 104*q^(11/2) - 140*q^(9/2) - 40*q^(7/2) + 176*q^(5/2) + 26*q^(3/2) - 116*q^(1/2) - 196*q^(-1/2) - 148*q^(-3/2) - 39*q^(-5/2) + 45*q^(-7/2) + 61*q^(-9/2) + 40*q^(-11/2) + 21*q^(-13/2) + 9*q^(-15/2) + 4*q^(-17/2) + 2*q^(-19/2))*x1^(-3/2)*x2^(-19/2) + (-2*q^(29/2) - 2*q^(27/2) - 10*q^(25/2) - 10*q^(23/2) - 28*q^(21/2) - 34*q^(19/2) - 56*q^(17/2) - 20*q^(15/2) - 70*q^(13/2) - 124*q^(11/2) - 312*q^(9/2) - 176*q^(7/2) - 34*q^(5/2) + 87*q^(3/2) + 71*q^(1/2) + 12*q^(-1/2) - 50*q^(-3/2) - 58*q^(-5/2) - 43*q^(-7/2) - 23*q^(-9/2) - 11*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(-5/2)*x2^(-19/2) + (2*q^(39/2) + 2*q^(37/2) + 4*q^(35/2) + 12*q^(33/2) + 18*q^(31/2) + 28*q^(29/2) + 66*q^(27/2) + 90*q^(25/2) + 156*q^(23/2) + 234*q^(21/2) + 320*q^(19/2) + 376*q^(17/2) + 513*q^(15/2) + 415*q^(13/2) + 320*q^(11/2) + 168*q^(9/2) + 88*q^(7/2) + 48*q^(5/2) + 59*q^(3/2) + 49*q^(1/2) + 39*q^(-1/2) + 23*q^(-3/2) + 11*q^(-5/2) + 4*q^(-7/2) + 2*q^(-9/2))*x1^(-7/2)*x2^(-19/2) + (-2*q^(47/2) - 2*q^(45/2) - 4*q^(43/2) - 8*q^(41/2) - 18*q^(39/2) - 26*q^(37/2) - 54*q^(35/2) - 78*q^(33/2) - 152*q^(31/2) - 226*q^(29/2) - 322*q^(27/2) - 394*q^(25/2) - 524*q^(23/2) - 476*q^(21/2) - 443*q^(19/2) - 343*q^(17/2) - 239*q^(15/2) - 138*q^(13/2) - 94*q^(11/2) - 54*q^(9/2) - 37*q^(7/2) - 21*q^(5/2) - 11*q^(3/2) - 4*q^(1/2) - 2*q^(-1/2))*x1^(-9/2)*x2^(-19/2) + (2*q^(53/2) + 2*q^(51/2) + 6*q^(49/2) + 8*q^(47/2) + 16*q^(45/2) + 32*q^(43/2) + 60*q^(41/2) + 92*q^(39/2) + 144*q^(37/2) + 192*q^(35/2) + 282*q^(33/2) + 286*q^(31/2) + 303*q^(29/2) + 276*q^(27/2) + 240*q^(25/2) + 163*q^(23/2) + 118*q^(21/2) + 67*q^(19/2) + 42*q^(17/2) + 20*q^(15/2) + 11*q^(13/2) + 4*q^(11/2) + 2*q^(9/2))*x1^(-11/2)*x2^(-19/2) + (-2*q^(57/2) - 4*q^(55/2) - 8*q^(53/2) - 14*q^(51/2) - 24*q^(49/2) - 38*q^(47/2) - 74*q^(45/2) - 78*q^(43/2) - 96*q^(41/2) - 102*q^(39/2) - 106*q^(37/2) - 90*q^(35/2) - 74*q^(33/2) - 50*q^(31/2) - 36*q^(29/2) - 20*q^(27/2) - 10*q^(25/2) - 4*q^(23/2) - 2*q^(21/2))*x1^(-13/2)*x2^(-19/2) + (8*q^(59/2) + 6*q^(57/2) + 10*q^(55/2) + 12*q^(53/2) + 16*q^(51/2) + 16*q^(49/2) + 18*q^(47/2) + 12*q^(45/2) + 12*q^(43/2) + 8*q^(41/2) + 6*q^(39/2) + 2*q^(37/2) + 2*q^(35/2))*x1^(-15/2)*x2^(-19/2)

Braid

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

Multivariable Alexander polynomial

ΔL
A1^(1/2)*A2^(5/2) - 4*A1^(1/2)*A2^(3/2) + 7*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) + 7*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^(-6)*A1^(-1)*A2^(-3) + 5*m^(-5)*A1^(-1)*A2^(-2) + m^(-5)*A2^(-3) + 11*m^(-4)*A1^(-1)*A2^(-1) + 7*m^(-4)*A2^(-2) + 12*m^(-3)*A1^(-1) + 18*m^(-3)*A2^(-1) + 2*m^(-3)*A1*A2^(-2) + 7*m^(-2)*A1^(-1)*A2 + 24*m^(-2) + 7*m^(-2)*A1*A2^(-1) + 2*m^(-1)*A1^(-1)*A2^2 + 18*m^(-1)*A2 + 12*m^(-1)*A1 + 7*A2^2 + 11*A1*A2 + m*A2^3 + 5*m*A1*A2^2 + m^2*A1*A2^3
VertexMaslovRank
(-1, -3)-61
(0, -3)-51
(1, -2)-32
(1, 3)21
(0, 3)11
(-1, 2)-12
HFL polytope-10105A1A2

Record

FL/HFL Links

orderOption(int) 290
namestring L10a13{1}
statusstring success
slugstring L10a13_1_d16d8c2c
result_filestring details/L10a13_1_d16d8c2c.json
complexity_scoreOption(int) 200
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 152
wall_secondsOption(float) 0.003765
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": "L10a13_1_d16d8c2c"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10a13_1_d16d8c2c