details/L10n47_1_389e3295.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(0, -2) (1/2, 1) x1^(0)x2^(2) q^(5/2)
{"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]}
(2*q^(-27/2) + 2*q^(-29/2) + 6*q^(-31/2) + 8*q^(-33/2) + 12*q^(-35/2) + 12*q^(-37/2) + 18*q^(-39/2) + 16*q^(-41/2) + 16*q^(-43/2) + 12*q^(-45/2) + 10*q^(-47/2) + 6*q^(-49/2) + 8*q^(-51/2))*x1^(-7)*x2^(9) + (-q^(-19/2) - 3*q^(-21/2) - 4*q^(-23/2) - 7*q^(-25/2) - 9*q^(-27/2) - 11*q^(-29/2) - 9*q^(-31/2) - 8*q^(-33/2) - 5*q^(-35/2) - 7*q^(-37/2))*x1^(-6)*x2^(8) + (-2*q^(-19/2) - 8*q^(-21/2) - 16*q^(-23/2) - 30*q^(-25/2) - 46*q^(-27/2) - 66*q^(-29/2) - 78*q^(-31/2) - 86*q^(-33/2) - 84*q^(-35/2) - 86*q^(-37/2) - 68*q^(-39/2) - 52*q^(-41/2) - 36*q^(-43/2) - 24*q^(-45/2) - 14*q^(-47/2) - 8*q^(-49/2))*x1^(-6)*x2^(9) + (2*q^(-13/2) + 2*q^(-15/2) + 6*q^(-17/2) + 6*q^(-19/2) + 6*q^(-21/2) + 4*q^(-23/2) + 6*q^(-25/2))*x1^(-5)*x2^(7) + (4*q^(-13/2) + 8*q^(-15/2) + 20*q^(-17/2) + 31*q^(-19/2) + 40*q^(-21/2) + 44*q^(-23/2) + 49*q^(-25/2) + 40*q^(-27/2) + 29*q^(-29/2) + 20*q^(-31/2) + 12*q^(-33/2) + 7*q^(-35/2))*x1^(-5)*x2^(8) + (-q^(-5/2) - 4*q^(-7/2) - 8*q^(-9/2) - 15*q^(-11/2) - 18*q^(-13/2) - 21*q^(-15/2) - 3*q^(-17/2) + 22*q^(-19/2) + 63*q^(-21/2) + 97*q^(-23/2) + 148*q^(-25/2) + 169*q^(-27/2) + 182*q^(-29/2) + 166*q^(-31/2) + 149*q^(-33/2) + 118*q^(-35/2) + 84*q^(-37/2) + 50*q^(-39/2) + 32*q^(-41/2) + 14*q^(-43/2) + 8*q^(-45/2))*x1^(-5)*x2^(9) + (-q^(-7/2) - 3*q^(-9/2) - 4*q^(-11/2) - 3*q^(-13/2) - 5*q^(-15/2))*x1^(-4)*x2^(6) + (-2*q^(-7/2) - 8*q^(-9/2) - 16*q^(-11/2) - 20*q^(-13/2) - 28*q^(-15/2) - 22*q^(-17/2) - 16*q^(-19/2) - 10*q^(-21/2) - 6*q^(-23/2))*x1^(-4)*x2^(7) + (2*q^(-1/2) + 4*q^(-3/2) + 10*q^(-5/2) + 13*q^(-7/2) + 9*q^(-9/2) - 7*q^(-11/2) - 22*q^(-13/2) - 56*q^(-15/2) - 70*q^(-17/2) - 81*q^(-19/2) - 72*q^(-21/2) - 67*q^(-23/2) - 41*q^(-25/2) - 27*q^(-27/2) - 12*q^(-29/2) - 7*q^(-31/2))*x1^(-4)*x2^(8) + (2*q^(1/2) + 8*q^(-1/2) + 22*q^(-3/2) + 48*q^(-5/2) + 81*q^(-7/2) + 111*q^(-9/2) + 127*q^(-11/2) + 128*q^(-13/2) + 79*q^(-15/2) + 24*q^(-17/2) - 52*q^(-19/2) - 109*q^(-21/2) - 164*q^(-23/2) - 169*q^(-25/2) - 163*q^(-27/2) - 125*q^(-29/2) - 96*q^(-31/2) - 58*q^(-33/2) - 32*q^(-35/2) - 14*q^(-37/2) - 8*q^(-39/2))*x1^(-4)*x2^(9) + (2*q^(-3/2) + 2*q^(-5/2) + 4*q^(-7/2))*x1^(-3)*x2^(5) + (4*q^(-3/2) + 8*q^(-5/2) + 15*q^(-7/2) + 12*q^(-9/2) + 8*q^(-11/2) + 5*q^(-13/2))*x1^(-3)*x2^(6) + (-q^(3/2) - 4*q^(1/2) - 8*q^(-1/2) - 5*q^(-3/2) - q^(-5/2) + 20*q^(-7/2) + 28*q^(-9/2) + 35*q^(-11/2) + 32*q^(-13/2) + 22*q^(-15/2) + 10*q^(-17/2) + 6*q^(-19/2))*x1^(-3)*x2^(7) + (-q^(5/2) - 6*q^(3/2) - 18*q^(1/2) - 37*q^(-1/2) - 54*q^(-3/2) - 67*q^(-5/2) - 49*q^(-7/2) - 24*q^(-9/2) + 12*q^(-11/2) + 49*q^(-13/2) + 61*q^(-15/2) + 57*q^(-17/2) + 46*q^(-19/2) + 27*q^(-21/2) + 12*q^(-23/2) + 7*q^(-25/2))*x1^(-3)*x2^(8) + (2*q^(11/2) + 4*q^(9/2) + 11*q^(7/2) + 14*q^(5/2) + 13*q^(3/2) - 9*q^(1/2) - 50*q^(-1/2) - 119*q^(-3/2) - 198*q^(-5/2) - 250*q^(-7/2) - 275*q^(-9/2) - 245*q^(-11/2) - 162*q^(-13/2) - 70*q^(-15/2) + 6*q^(-17/2) + 66*q^(-19/2) + 79*q^(-21/2) + 71*q^(-23/2) + 52*q^(-25/2) + 30*q^(-27/2) + 14*q^(-29/2) + 8*q^(-31/2))*x1^(-3)*x2^(9) + (-q^(1/2) - 3*q^(-1/2))*x1^(-2)*x2^(4) + (-2*q^(1/2) - 8*q^(-1/2) - 6*q^(-3/2) - 4*q^(-5/2))*x1^(-2)*x2^(5) + (2*q^(5/2) + 4*q^(3/2) + 5*q^(1/2) - 7*q^(-1/2) - 11*q^(-3/2) - 17*q^(-5/2) - 8*q^(-7/2) - 5*q^(-9/2))*x1^(-2)*x2^(6) + (2*q^(7/2) + 8*q^(5/2) + 20*q^(3/2) + 31*q^(1/2) + 23*q^(-1/2) + 14*q^(-3/2) - 13*q^(-5/2) - 19*q^(-7/2) - 20*q^(-9/2) - 10*q^(-11/2) - 6*q^(-13/2))*x1^(-2)*x2^(7) + (-q^(13/2) - 4*q^(11/2) - 7*q^(9/2) - 7*q^(7/2) + 2*q^(5/2) + 31*q^(3/2) + 70*q^(1/2) + 94*q^(-1/2) + 108*q^(-3/2) + 72*q^(-5/2) + 36*q^(-7/2) - 7*q^(-9/2) - 16*q^(-11/2) - 21*q^(-13/2) - 10*q^(-15/2) - 7*q^(-17/2))*x1^(-2)*x2^(8) + (-q^(17/2) - 5*q^(15/2) - 15*q^(13/2) - 32*q^(11/2) - 61*q^(9/2) - 88*q^(7/2) - 103*q^(5/2) - 72*q^(3/2) + q^(1/2) + 105*q^(-1/2) + 211*q^(-3/2) + 251*q^(-5/2) + 240*q^(-7/2) + 162*q^(-9/2) + 89*q^(-11/2) + 25*q^(-13/2) + q^(-15/2) - 16*q^(-17/2) - 8*q^(-19/2) - 6*q^(-21/2))*x1^(-2)*x2^(9) + (2*q^(3/2))*x1^(-1)*x2^(3) + (4*q^(3/2) + 3*q^(1/2))*x1^(-1)*x2^(4) + (-q^(7/2) - 4*q^(5/2) + 3*q^(3/2) + 6*q^(1/2) + 4*q^(-1/2))*x1^(-1)*x2^(5) + (-q^(9/2) - 6*q^(7/2) - 14*q^(5/2) - 9*q^(3/2) + q^(1/2) + 6*q^(-1/2) + 5*q^(-3/2))*x1^(-1)*x2^(6) + (2*q^(13/2) + 3*q^(11/2) + 4*q^(9/2) - 8*q^(7/2) - 28*q^(5/2) - 36*q^(3/2) - 26*q^(1/2) - 9*q^(-1/2) + 4*q^(-3/2) + 4*q^(-5/2))*x1^(-1)*x2^(7) + (2*q^(17/2) + 6*q^(15/2) + 17*q^(13/2) + 30*q^(11/2) + 42*q^(9/2) + 30*q^(7/2) - 14*q^(5/2) - 54*q^(3/2) - 71*q^(1/2) - 60*q^(-1/2) - 28*q^(-3/2) - 7*q^(-5/2) + q^(-7/2) - 2*q^(-9/2))*x1^(-1)*x2^(8) + (-q^(23/2) - 2*q^(21/2) - 3*q^(19/2) + 4*q^(17/2) + 15*q^(15/2) + 56*q^(13/2) + 108*q^(11/2) + 170*q^(9/2) + 184*q^(7/2) + 132*q^(5/2) + 31*q^(3/2) - 58*q^(1/2) - 111*q^(-1/2) - 100*q^(-3/2) - 65*q^(-5/2) - 26*q^(-7/2) - 12*q^(-9/2) - 6*q^(-11/2) - 2*q^(-13/2))*x1^(-1)*x2^(9) + (-q^(5/2))*x2^(2) + (-2*q^(5/2))*x2^(3) + (2*q^(7/2) - 3*q^(5/2))*x2^(4) + (2*q^(9/2) + 6*q^(7/2) - 2*q^(5/2))*x2^(5) + (-q^(13/2) - 2*q^(11/2) + 4*q^(9/2) + 13*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x2^(6) + (-q^(17/2) - 5*q^(15/2) - 10*q^(13/2) - 15*q^(11/2) - q^(9/2) + 18*q^(7/2) + 10*q^(5/2) + 8*q^(3/2) + 2*q^(1/2))*x2^(7) + (q^(21/2) - q^(19/2) - 3*q^(17/2) - 21*q^(15/2) - 39*q^(13/2) - 54*q^(11/2) - 30*q^(9/2) + 8*q^(7/2) + 14*q^(5/2) + 17*q^(3/2) + 9*q^(1/2) + 2*q^(-1/2))*x2^(8) + (2*q^(27/2) + 5*q^(25/2) + 11*q^(23/2) + 21*q^(21/2) + 24*q^(19/2) + 17*q^(17/2) - 31*q^(15/2) - 86*q^(13/2) - 133*q^(11/2) - 108*q^(9/2) - 47*q^(7/2) - 9*q^(5/2) + 16*q^(3/2) + 18*q^(1/2) + 8*q^(-1/2) + 2*q^(-3/2))*x2^(9) + (-q^(9/2))*x1*x2^(4) + (-2*q^(9/2))*x1*x2^(5) + (2*q^(15/2) + 3*q^(13/2) - 3*q^(9/2))*x1*x2^(6) + (q^(19/2) + 2*q^(17/2) + 9*q^(15/2) + 8*q^(13/2) + 2*q^(11/2) - 4*q^(9/2))*x1*x2^(7) + (-q^(25/2) - 3*q^(23/2) - 5*q^(21/2) - 3*q^(19/2) + 8*q^(17/2) + 19*q^(15/2) + 18*q^(13/2) + 6*q^(11/2) - 3*q^(9/2))*x1*x2^(8) + (-q^(31/2) - 3*q^(29/2) - 6*q^(27/2) - 14*q^(25/2) - 27*q^(23/2) - 33*q^(21/2) - 21*q^(19/2) + 6*q^(17/2) + 31*q^(15/2) + 32*q^(13/2) + 16*q^(11/2) + 2*q^(7/2))*x1*x2^(9) + (-q^(17/2))*x1^(2)*x2^(6) + (-2*q^(17/2))*x1^(2)*x2^(7) + (2*q^(27/2) + 2*q^(25/2) + 3*q^(23/2) + q^(21/2) - 3*q^(17/2))*x1^(2)*x2^(8) + (q^(33/2) + q^(31/2) + 2*q^(29/2) + 7*q^(27/2) + 9*q^(25/2) + 10*q^(23/2) + 4*q^(21/2) - 4*q^(17/2))*x1^(2)*x2^(9) + (-q^(29/2))*x1^(3)*x2^(8) + (-2*q^(29/2))*x1^(3)*x2^(9)
(0, -2) (1/2, 1) x1^(0)x2^(2) q^(5/2)
{"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]}
(2*q^(-27/2) + 2*q^(-29/2) + 6*q^(-31/2) + 8*q^(-33/2) + 12*q^(-35/2) + 12*q^(-37/2) + 18*q^(-39/2) + 16*q^(-41/2) + 16*q^(-43/2) + 12*q^(-45/2) + 10*q^(-47/2) + 6*q^(-49/2) + 8*q^(-51/2))*x1^(-7)*x2^(9) + (-q^(-19/2) - 3*q^(-21/2) - 4*q^(-23/2) - 7*q^(-25/2) - 9*q^(-27/2) - 11*q^(-29/2) - 9*q^(-31/2) - 8*q^(-33/2) - 5*q^(-35/2) - 7*q^(-37/2))*x1^(-6)*x2^(8) + (-2*q^(-19/2) - 8*q^(-21/2) - 16*q^(-23/2) - 30*q^(-25/2) - 46*q^(-27/2) - 66*q^(-29/2) - 78*q^(-31/2) - 86*q^(-33/2) - 84*q^(-35/2) - 86*q^(-37/2) - 68*q^(-39/2) - 52*q^(-41/2) - 36*q^(-43/2) - 24*q^(-45/2) - 14*q^(-47/2) - 8*q^(-49/2))*x1^(-6)*x2^(9) + (2*q^(-13/2) + 2*q^(-15/2) + 6*q^(-17/2) + 6*q^(-19/2) + 6*q^(-21/2) + 4*q^(-23/2) + 6*q^(-25/2))*x1^(-5)*x2^(7) + (4*q^(-13/2) + 8*q^(-15/2) + 20*q^(-17/2) + 31*q^(-19/2) + 40*q^(-21/2) + 44*q^(-23/2) + 49*q^(-25/2) + 40*q^(-27/2) + 29*q^(-29/2) + 20*q^(-31/2) + 12*q^(-33/2) + 7*q^(-35/2))*x1^(-5)*x2^(8) + (-q^(-5/2) - 4*q^(-7/2) - 8*q^(-9/2) - 15*q^(-11/2) - 18*q^(-13/2) - 21*q^(-15/2) - 3*q^(-17/2) + 22*q^(-19/2) + 63*q^(-21/2) + 97*q^(-23/2) + 148*q^(-25/2) + 169*q^(-27/2) + 182*q^(-29/2) + 166*q^(-31/2) + 149*q^(-33/2) + 118*q^(-35/2) + 84*q^(-37/2) + 50*q^(-39/2) + 32*q^(-41/2) + 14*q^(-43/2) + 8*q^(-45/2))*x1^(-5)*x2^(9) + (-q^(-7/2) - 3*q^(-9/2) - 4*q^(-11/2) - 3*q^(-13/2) - 5*q^(-15/2))*x1^(-4)*x2^(6) + (-2*q^(-7/2) - 8*q^(-9/2) - 16*q^(-11/2) - 20*q^(-13/2) - 28*q^(-15/2) - 22*q^(-17/2) - 16*q^(-19/2) - 10*q^(-21/2) - 6*q^(-23/2))*x1^(-4)*x2^(7) + (2*q^(-1/2) + 4*q^(-3/2) + 10*q^(-5/2) + 13*q^(-7/2) + 9*q^(-9/2) - 7*q^(-11/2) - 22*q^(-13/2) - 56*q^(-15/2) - 70*q^(-17/2) - 81*q^(-19/2) - 72*q^(-21/2) - 67*q^(-23/2) - 41*q^(-25/2) - 27*q^(-27/2) - 12*q^(-29/2) - 7*q^(-31/2))*x1^(-4)*x2^(8) + (2*q^(1/2) + 8*q^(-1/2) + 22*q^(-3/2) + 48*q^(-5/2) + 81*q^(-7/2) + 111*q^(-9/2) + 127*q^(-11/2) + 128*q^(-13/2) + 79*q^(-15/2) + 24*q^(-17/2) - 52*q^(-19/2) - 109*q^(-21/2) - 164*q^(-23/2) - 169*q^(-25/2) - 163*q^(-27/2) - 125*q^(-29/2) - 96*q^(-31/2) - 58*q^(-33/2) - 32*q^(-35/2) - 14*q^(-37/2) - 8*q^(-39/2))*x1^(-4)*x2^(9) + (2*q^(-3/2) + 2*q^(-5/2) + 4*q^(-7/2))*x1^(-3)*x2^(5) + (4*q^(-3/2) + 8*q^(-5/2) + 15*q^(-7/2) + 12*q^(-9/2) + 8*q^(-11/2) + 5*q^(-13/2))*x1^(-3)*x2^(6) + (-q^(3/2) - 4*q^(1/2) - 8*q^(-1/2) - 5*q^(-3/2) - q^(-5/2) + 20*q^(-7/2) + 28*q^(-9/2) + 35*q^(-11/2) + 32*q^(-13/2) + 22*q^(-15/2) + 10*q^(-17/2) + 6*q^(-19/2))*x1^(-3)*x2^(7) + (-q^(5/2) - 6*q^(3/2) - 18*q^(1/2) - 37*q^(-1/2) - 54*q^(-3/2) - 67*q^(-5/2) - 49*q^(-7/2) - 24*q^(-9/2) + 12*q^(-11/2) + 49*q^(-13/2) + 61*q^(-15/2) + 57*q^(-17/2) + 46*q^(-19/2) + 27*q^(-21/2) + 12*q^(-23/2) + 7*q^(-25/2))*x1^(-3)*x2^(8) + (2*q^(11/2) + 4*q^(9/2) + 11*q^(7/2) + 14*q^(5/2) + 13*q^(3/2) - 9*q^(1/2) - 50*q^(-1/2) - 119*q^(-3/2) - 198*q^(-5/2) - 250*q^(-7/2) - 275*q^(-9/2) - 245*q^(-11/2) - 162*q^(-13/2) - 70*q^(-15/2) + 6*q^(-17/2) + 66*q^(-19/2) + 79*q^(-21/2) + 71*q^(-23/2) + 52*q^(-25/2) + 30*q^(-27/2) + 14*q^(-29/2) + 8*q^(-31/2))*x1^(-3)*x2^(9) + (-q^(1/2) - 3*q^(-1/2))*x1^(-2)*x2^(4) + (-2*q^(1/2) - 8*q^(-1/2) - 6*q^(-3/2) - 4*q^(-5/2))*x1^(-2)*x2^(5) + (2*q^(5/2) + 4*q^(3/2) + 5*q^(1/2) - 7*q^(-1/2) - 11*q^(-3/2) - 17*q^(-5/2) - 8*q^(-7/2) - 5*q^(-9/2))*x1^(-2)*x2^(6) + (2*q^(7/2) + 8*q^(5/2) + 20*q^(3/2) + 31*q^(1/2) + 23*q^(-1/2) + 14*q^(-3/2) - 13*q^(-5/2) - 19*q^(-7/2) - 20*q^(-9/2) - 10*q^(-11/2) - 6*q^(-13/2))*x1^(-2)*x2^(7) + (-q^(13/2) - 4*q^(11/2) - 7*q^(9/2) - 7*q^(7/2) + 2*q^(5/2) + 31*q^(3/2) + 70*q^(1/2) + 94*q^(-1/2) + 108*q^(-3/2) + 72*q^(-5/2) + 36*q^(-7/2) - 7*q^(-9/2) - 16*q^(-11/2) - 21*q^(-13/2) - 10*q^(-15/2) - 7*q^(-17/2))*x1^(-2)*x2^(8) + (-q^(17/2) - 5*q^(15/2) - 15*q^(13/2) - 32*q^(11/2) - 61*q^(9/2) - 88*q^(7/2) - 103*q^(5/2) - 72*q^(3/2) + q^(1/2) + 105*q^(-1/2) + 211*q^(-3/2) + 251*q^(-5/2) + 240*q^(-7/2) + 162*q^(-9/2) + 89*q^(-11/2) + 25*q^(-13/2) + q^(-15/2) - 16*q^(-17/2) - 8*q^(-19/2) - 6*q^(-21/2))*x1^(-2)*x2^(9) + (2*q^(3/2))*x1^(-1)*x2^(3) + (4*q^(3/2) + 3*q^(1/2))*x1^(-1)*x2^(4) + (-q^(7/2) - 4*q^(5/2) + 3*q^(3/2) + 6*q^(1/2) + 4*q^(-1/2))*x1^(-1)*x2^(5) + (-q^(9/2) - 6*q^(7/2) - 14*q^(5/2) - 9*q^(3/2) + q^(1/2) + 6*q^(-1/2) + 5*q^(-3/2))*x1^(-1)*x2^(6) + (2*q^(13/2) + 3*q^(11/2) + 4*q^(9/2) - 8*q^(7/2) - 28*q^(5/2) - 36*q^(3/2) - 26*q^(1/2) - 9*q^(-1/2) + 4*q^(-3/2) + 4*q^(-5/2))*x1^(-1)*x2^(7) + (2*q^(17/2) + 6*q^(15/2) + 17*q^(13/2) + 30*q^(11/2) + 42*q^(9/2) + 30*q^(7/2) - 14*q^(5/2) - 54*q^(3/2) - 71*q^(1/2) - 60*q^(-1/2) - 28*q^(-3/2) - 7*q^(-5/2) + q^(-7/2) - 2*q^(-9/2))*x1^(-1)*x2^(8) + (-q^(23/2) - 2*q^(21/2) - 3*q^(19/2) + 4*q^(17/2) + 15*q^(15/2) + 56*q^(13/2) + 108*q^(11/2) + 170*q^(9/2) + 184*q^(7/2) + 132*q^(5/2) + 31*q^(3/2) - 58*q^(1/2) - 111*q^(-1/2) - 100*q^(-3/2) - 65*q^(-5/2) - 26*q^(-7/2) - 12*q^(-9/2) - 6*q^(-11/2) - 2*q^(-13/2))*x1^(-1)*x2^(9) + (-q^(5/2))*x2^(2) + (-2*q^(5/2))*x2^(3) + (2*q^(7/2) - 3*q^(5/2))*x2^(4) + (2*q^(9/2) + 6*q^(7/2) - 2*q^(5/2))*x2^(5) + (-q^(13/2) - 2*q^(11/2) + 4*q^(9/2) + 13*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x2^(6) + (-q^(17/2) - 5*q^(15/2) - 10*q^(13/2) - 15*q^(11/2) - q^(9/2) + 18*q^(7/2) + 10*q^(5/2) + 8*q^(3/2) + 2*q^(1/2))*x2^(7) + (q^(21/2) - q^(19/2) - 3*q^(17/2) - 21*q^(15/2) - 39*q^(13/2) - 54*q^(11/2) - 30*q^(9/2) + 8*q^(7/2) + 14*q^(5/2) + 17*q^(3/2) + 9*q^(1/2) + 2*q^(-1/2))*x2^(8) + (2*q^(27/2) + 5*q^(25/2) + 11*q^(23/2) + 21*q^(21/2) + 24*q^(19/2) + 17*q^(17/2) - 31*q^(15/2) - 86*q^(13/2) - 133*q^(11/2) - 108*q^(9/2) - 47*q^(7/2) - 9*q^(5/2) + 16*q^(3/2) + 18*q^(1/2) + 8*q^(-1/2) + 2*q^(-3/2))*x2^(9) + (-q^(9/2))*x1*x2^(4) + (-2*q^(9/2))*x1*x2^(5) + (2*q^(15/2) + 3*q^(13/2) - 3*q^(9/2))*x1*x2^(6) + (q^(19/2) + 2*q^(17/2) + 9*q^(15/2) + 8*q^(13/2) + 2*q^(11/2) - 4*q^(9/2))*x1*x2^(7) + (-q^(25/2) - 3*q^(23/2) - 5*q^(21/2) - 3*q^(19/2) + 8*q^(17/2) + 19*q^(15/2) + 18*q^(13/2) + 6*q^(11/2) - 3*q^(9/2))*x1*x2^(8) + (-q^(31/2) - 3*q^(29/2) - 6*q^(27/2) - 14*q^(25/2) - 27*q^(23/2) - 33*q^(21/2) - 21*q^(19/2) + 6*q^(17/2) + 31*q^(15/2) + 32*q^(13/2) + 16*q^(11/2) + 2*q^(7/2))*x1*x2^(9) + (-q^(17/2))*x1^(2)*x2^(6) + (-2*q^(17/2))*x1^(2)*x2^(7) + (2*q^(27/2) + 2*q^(25/2) + 3*q^(23/2) + q^(21/2) - 3*q^(17/2))*x1^(2)*x2^(8) + (q^(33/2) + q^(31/2) + 2*q^(29/2) + 7*q^(27/2) + 9*q^(25/2) + 10*q^(23/2) + 4*q^(21/2) - 4*q^(17/2))*x1^(2)*x2^(9) + (-q^(29/2))*x1^(3)*x2^(8) + (-2*q^(29/2))*x1^(3)*x2^(9)
(0, 2) x1^(0)x2^(-2) q^(5/2)
(2*q^(-27/2) + 2*q^(-29/2) + 6*q^(-31/2) + 8*q^(-33/2) + 12*q^(-35/2) + 12*q^(-37/2) + 18*q^(-39/2) + 16*q^(-41/2) + 16*q^(-43/2) + 12*q^(-45/2) + 10*q^(-47/2) + 6*q^(-49/2) + 8*q^(-51/2))*x1^(7)*x2^(-9) + (-q^(-19/2) - 3*q^(-21/2) - 4*q^(-23/2) - 7*q^(-25/2) - 9*q^(-27/2) - 11*q^(-29/2) - 9*q^(-31/2) - 8*q^(-33/2) - 5*q^(-35/2) - 7*q^(-37/2))*x1^(6)*x2^(-8) + (-2*q^(-19/2) - 8*q^(-21/2) - 16*q^(-23/2) - 30*q^(-25/2) - 46*q^(-27/2) - 66*q^(-29/2) - 78*q^(-31/2) - 86*q^(-33/2) - 84*q^(-35/2) - 86*q^(-37/2) - 68*q^(-39/2) - 52*q^(-41/2) - 36*q^(-43/2) - 24*q^(-45/2) - 14*q^(-47/2) - 8*q^(-49/2))*x1^(6)*x2^(-9) + (2*q^(-13/2) + 2*q^(-15/2) + 6*q^(-17/2) + 6*q^(-19/2) + 6*q^(-21/2) + 4*q^(-23/2) + 6*q^(-25/2))*x1^(5)*x2^(-7) + (4*q^(-13/2) + 8*q^(-15/2) + 20*q^(-17/2) + 31*q^(-19/2) + 40*q^(-21/2) + 44*q^(-23/2) + 49*q^(-25/2) + 40*q^(-27/2) + 29*q^(-29/2) + 20*q^(-31/2) + 12*q^(-33/2) + 7*q^(-35/2))*x1^(5)*x2^(-8) + (-q^(-5/2) - 4*q^(-7/2) - 8*q^(-9/2) - 15*q^(-11/2) - 18*q^(-13/2) - 21*q^(-15/2) - 3*q^(-17/2) + 22*q^(-19/2) + 63*q^(-21/2) + 97*q^(-23/2) + 148*q^(-25/2) + 169*q^(-27/2) + 182*q^(-29/2) + 166*q^(-31/2) + 149*q^(-33/2) + 118*q^(-35/2) + 84*q^(-37/2) + 50*q^(-39/2) + 32*q^(-41/2) + 14*q^(-43/2) + 8*q^(-45/2))*x1^(5)*x2^(-9) + (-q^(-7/2) - 3*q^(-9/2) - 4*q^(-11/2) - 3*q^(-13/2) - 5*q^(-15/2))*x1^(4)*x2^(-6) + (-2*q^(-7/2) - 8*q^(-9/2) - 16*q^(-11/2) - 20*q^(-13/2) - 28*q^(-15/2) - 22*q^(-17/2) - 16*q^(-19/2) - 10*q^(-21/2) - 6*q^(-23/2))*x1^(4)*x2^(-7) + (2*q^(-1/2) + 4*q^(-3/2) + 10*q^(-5/2) + 13*q^(-7/2) + 9*q^(-9/2) - 7*q^(-11/2) - 22*q^(-13/2) - 56*q^(-15/2) - 70*q^(-17/2) - 81*q^(-19/2) - 72*q^(-21/2) - 67*q^(-23/2) - 41*q^(-25/2) - 27*q^(-27/2) - 12*q^(-29/2) - 7*q^(-31/2))*x1^(4)*x2^(-8) + (2*q^(1/2) + 8*q^(-1/2) + 22*q^(-3/2) + 48*q^(-5/2) + 81*q^(-7/2) + 111*q^(-9/2) + 127*q^(-11/2) + 128*q^(-13/2) + 79*q^(-15/2) + 24*q^(-17/2) - 52*q^(-19/2) - 109*q^(-21/2) - 164*q^(-23/2) - 169*q^(-25/2) - 163*q^(-27/2) - 125*q^(-29/2) - 96*q^(-31/2) - 58*q^(-33/2) - 32*q^(-35/2) - 14*q^(-37/2) - 8*q^(-39/2))*x1^(4)*x2^(-9) + (2*q^(-3/2) + 2*q^(-5/2) + 4*q^(-7/2))*x1^(3)*x2^(-5) + (4*q^(-3/2) + 8*q^(-5/2) + 15*q^(-7/2) + 12*q^(-9/2) + 8*q^(-11/2) + 5*q^(-13/2))*x1^(3)*x2^(-6) + (-q^(3/2) - 4*q^(1/2) - 8*q^(-1/2) - 5*q^(-3/2) - q^(-5/2) + 20*q^(-7/2) + 28*q^(-9/2) + 35*q^(-11/2) + 32*q^(-13/2) + 22*q^(-15/2) + 10*q^(-17/2) + 6*q^(-19/2))*x1^(3)*x2^(-7) + (-q^(5/2) - 6*q^(3/2) - 18*q^(1/2) - 37*q^(-1/2) - 54*q^(-3/2) - 67*q^(-5/2) - 49*q^(-7/2) - 24*q^(-9/2) + 12*q^(-11/2) + 49*q^(-13/2) + 61*q^(-15/2) + 57*q^(-17/2) + 46*q^(-19/2) + 27*q^(-21/2) + 12*q^(-23/2) + 7*q^(-25/2))*x1^(3)*x2^(-8) + (2*q^(11/2) + 4*q^(9/2) + 11*q^(7/2) + 14*q^(5/2) + 13*q^(3/2) - 9*q^(1/2) - 50*q^(-1/2) - 119*q^(-3/2) - 198*q^(-5/2) - 250*q^(-7/2) - 275*q^(-9/2) - 245*q^(-11/2) - 162*q^(-13/2) - 70*q^(-15/2) + 6*q^(-17/2) + 66*q^(-19/2) + 79*q^(-21/2) + 71*q^(-23/2) + 52*q^(-25/2) + 30*q^(-27/2) + 14*q^(-29/2) + 8*q^(-31/2))*x1^(3)*x2^(-9) + (-q^(1/2) - 3*q^(-1/2))*x1^(2)*x2^(-4) + (-2*q^(1/2) - 8*q^(-1/2) - 6*q^(-3/2) - 4*q^(-5/2))*x1^(2)*x2^(-5) + (2*q^(5/2) + 4*q^(3/2) + 5*q^(1/2) - 7*q^(-1/2) - 11*q^(-3/2) - 17*q^(-5/2) - 8*q^(-7/2) - 5*q^(-9/2))*x1^(2)*x2^(-6) + (2*q^(7/2) + 8*q^(5/2) + 20*q^(3/2) + 31*q^(1/2) + 23*q^(-1/2) + 14*q^(-3/2) - 13*q^(-5/2) - 19*q^(-7/2) - 20*q^(-9/2) - 10*q^(-11/2) - 6*q^(-13/2))*x1^(2)*x2^(-7) + (-q^(13/2) - 4*q^(11/2) - 7*q^(9/2) - 7*q^(7/2) + 2*q^(5/2) + 31*q^(3/2) + 70*q^(1/2) + 94*q^(-1/2) + 108*q^(-3/2) + 72*q^(-5/2) + 36*q^(-7/2) - 7*q^(-9/2) - 16*q^(-11/2) - 21*q^(-13/2) - 10*q^(-15/2) - 7*q^(-17/2))*x1^(2)*x2^(-8) + (-q^(17/2) - 5*q^(15/2) - 15*q^(13/2) - 32*q^(11/2) - 61*q^(9/2) - 88*q^(7/2) - 103*q^(5/2) - 72*q^(3/2) + q^(1/2) + 105*q^(-1/2) + 211*q^(-3/2) + 251*q^(-5/2) + 240*q^(-7/2) + 162*q^(-9/2) + 89*q^(-11/2) + 25*q^(-13/2) + q^(-15/2) - 16*q^(-17/2) - 8*q^(-19/2) - 6*q^(-21/2))*x1^(2)*x2^(-9) + (2*q^(3/2))*x1*x2^(-3) + (4*q^(3/2) + 3*q^(1/2))*x1*x2^(-4) + (-q^(7/2) - 4*q^(5/2) + 3*q^(3/2) + 6*q^(1/2) + 4*q^(-1/2))*x1*x2^(-5) + (-q^(9/2) - 6*q^(7/2) - 14*q^(5/2) - 9*q^(3/2) + q^(1/2) + 6*q^(-1/2) + 5*q^(-3/2))*x1*x2^(-6) + (2*q^(13/2) + 3*q^(11/2) + 4*q^(9/2) - 8*q^(7/2) - 28*q^(5/2) - 36*q^(3/2) - 26*q^(1/2) - 9*q^(-1/2) + 4*q^(-3/2) + 4*q^(-5/2))*x1*x2^(-7) + (2*q^(17/2) + 6*q^(15/2) + 17*q^(13/2) + 30*q^(11/2) + 42*q^(9/2) + 30*q^(7/2) - 14*q^(5/2) - 54*q^(3/2) - 71*q^(1/2) - 60*q^(-1/2) - 28*q^(-3/2) - 7*q^(-5/2) + q^(-7/2) - 2*q^(-9/2))*x1*x2^(-8) + (-q^(23/2) - 2*q^(21/2) - 3*q^(19/2) + 4*q^(17/2) + 15*q^(15/2) + 56*q^(13/2) + 108*q^(11/2) + 170*q^(9/2) + 184*q^(7/2) + 132*q^(5/2) + 31*q^(3/2) - 58*q^(1/2) - 111*q^(-1/2) - 100*q^(-3/2) - 65*q^(-5/2) - 26*q^(-7/2) - 12*q^(-9/2) - 6*q^(-11/2) - 2*q^(-13/2))*x1*x2^(-9) + (-q^(5/2))*x2^(-2) + (-2*q^(5/2))*x2^(-3) + (2*q^(7/2) - 3*q^(5/2))*x2^(-4) + (2*q^(9/2) + 6*q^(7/2) - 2*q^(5/2))*x2^(-5) + (-q^(13/2) - 2*q^(11/2) + 4*q^(9/2) + 13*q^(7/2) + 2*q^(5/2) + 2*q^(3/2))*x2^(-6) + (-q^(17/2) - 5*q^(15/2) - 10*q^(13/2) - 15*q^(11/2) - q^(9/2) + 18*q^(7/2) + 10*q^(5/2) + 8*q^(3/2) + 2*q^(1/2))*x2^(-7) + (q^(21/2) - q^(19/2) - 3*q^(17/2) - 21*q^(15/2) - 39*q^(13/2) - 54*q^(11/2) - 30*q^(9/2) + 8*q^(7/2) + 14*q^(5/2) + 17*q^(3/2) + 9*q^(1/2) + 2*q^(-1/2))*x2^(-8) + (2*q^(27/2) + 5*q^(25/2) + 11*q^(23/2) + 21*q^(21/2) + 24*q^(19/2) + 17*q^(17/2) - 31*q^(15/2) - 86*q^(13/2) - 133*q^(11/2) - 108*q^(9/2) - 47*q^(7/2) - 9*q^(5/2) + 16*q^(3/2) + 18*q^(1/2) + 8*q^(-1/2) + 2*q^(-3/2))*x2^(-9) + (-q^(9/2))*x1^(-1)*x2^(-4) + (-2*q^(9/2))*x1^(-1)*x2^(-5) + (2*q^(15/2) + 3*q^(13/2) - 3*q^(9/2))*x1^(-1)*x2^(-6) + (q^(19/2) + 2*q^(17/2) + 9*q^(15/2) + 8*q^(13/2) + 2*q^(11/2) - 4*q^(9/2))*x1^(-1)*x2^(-7) + (-q^(25/2) - 3*q^(23/2) - 5*q^(21/2) - 3*q^(19/2) + 8*q^(17/2) + 19*q^(15/2) + 18*q^(13/2) + 6*q^(11/2) - 3*q^(9/2))*x1^(-1)*x2^(-8) + (-q^(31/2) - 3*q^(29/2) - 6*q^(27/2) - 14*q^(25/2) - 27*q^(23/2) - 33*q^(21/2) - 21*q^(19/2) + 6*q^(17/2) + 31*q^(15/2) + 32*q^(13/2) + 16*q^(11/2) + 2*q^(7/2))*x1^(-1)*x2^(-9) + (-q^(17/2))*x1^(-2)*x2^(-6) + (-2*q^(17/2))*x1^(-2)*x2^(-7) + (2*q^(27/2) + 2*q^(25/2) + 3*q^(23/2) + q^(21/2) - 3*q^(17/2))*x1^(-2)*x2^(-8) + (q^(33/2) + q^(31/2) + 2*q^(29/2) + 7*q^(27/2) + 9*q^(25/2) + 10*q^(23/2) + 4*q^(21/2) - 4*q^(17/2))*x1^(-2)*x2^(-9) + (-q^(29/2))*x1^(-3)*x2^(-8) + (-2*q^(29/2))*x1^(-3)*x2^(-9)

Braid

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

Multivariable Alexander polynomial

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

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-101-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(-2, -2) no
(0, -4) yes
(2, 0) yes
(2, 2) no
(0, 4) yes
(-2, 0) yes
Dual Thurston polygon-202-505h1h2

HFL polytope

Poincaré polynomial
2*m^(-6)*A1^(-3/2)*A2^(-3/2) + m^(-6)*A1^(-1/2)*A2^(-5/2) + 3*m^(-5)*A1^(-3/2)*A2^(-1/2) + 5*m^(-5)*A1^(-1/2)*A2^(-3/2) + m^(-5)*A1^(1/2)*A2^(-5/2) + m^(-4)*A1^(-3/2)*A2^(1/2) + 8*m^(-4)*A1^(-1/2)*A2^(-1/2) + 3*m^(-4)*A1^(1/2)*A2^(-3/2) + 6*m^(-3)*A1^(-1/2)*A2^(1/2) + 6*m^(-3)*A1^(1/2)*A2^(-1/2) + 3*m^(-2)*A1^(-1/2)*A2^(3/2) + 8*m^(-2)*A1^(1/2)*A2^(1/2) + m^(-2)*A1^(3/2)*A2^(-1/2) + m^(-1)*A1^(-1/2)*A2^(5/2) + 5*m^(-1)*A1^(1/2)*A2^(3/2) + 3*m^(-1)*A1^(3/2)*A2^(1/2) + A1^(1/2)*A2^(5/2) + 2*A1^(3/2)*A2^(3/2)
VertexMaslovRank
(-3/2, -3/2)-62
(-1/2, -5/2)-61
(1/2, -5/2)-51
(3/2, -1/2)-21
(3/2, 3/2)02
(1/2, 5/2)01
(-1/2, 5/2)-11
(-3/2, 1/2)-41
HFL polytope-202-202A1A2

Record

FL/HFL Links

orderOption(int) 562
namestring L10n47{1}
statusstring success
slugstring L10n47_1_389e3295
result_filestring details/L10n47_1_389e3295.json
complexity_scoreOption(int) 200
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 60
wall_secondsOption(float) 0.003184
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 18
vertex_countOption(int) 8
fibered_vertex_countOption(int) 4
polytope_statusstring computed
alexander_support_sizeOption(int) 9
alexander_vertex_countOption(int) 6
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks)
{
  "dataset": "FLHFLLinks",
  "key": "L10n47_1_389e3295"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10n47_1_389e3295