details/L10a67_0_8d3156a4.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-1, -2) (1, 1) x1^(1)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]}
(-q^(-5/2))*x1*x2^(2) + (-4*q^(-5/2))*x1*x2^(3) + (2*q^(-7/2))*x1^(2)*x2^(3) + (-3*q^(-3/2) - 10*q^(-5/2) - q^(-7/2))*x1*x2^(4) + (2*q^(-5/2) + 8*q^(-7/2) + q^(-9/2))*x1^(2)*x2^(4) + (-q^(-9/2) - q^(-11/2))*x1^(3)*x2^(4) + (-8*q^(-1/2) - 12*q^(-3/2) - 22*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1*x2^(5) + (6*q^(-3/2) + 14*q^(-5/2) + 23*q^(-7/2) + 6*q^(-9/2) + q^(-11/2))*x1^(2)*x2^(5) + (-4*q^(-7/2) - 6*q^(-9/2) - 5*q^(-11/2) - q^(-15/2))*x1^(3)*x2^(5) + (q^(-13/2) - 2*q^(-15/2) + q^(-17/2))*x1^(4)*x2^(5) + (-5*q^(3/2) - 18*q^(1/2) - 33*q^(-1/2) - 36*q^(-3/2) - 46*q^(-5/2) - 14*q^(-7/2) - 8*q^(-9/2) - 3*q^(-11/2) - q^(-13/2))*x1*x2^(6) + (4*q^(1/2) + 18*q^(-1/2) + 42*q^(-3/2) + 54*q^(-5/2) + 61*q^(-7/2) + 23*q^(-9/2) + 9*q^(-11/2) + q^(-13/2))*x1^(2)*x2^(6) + (-3*q^(-3/2) - 13*q^(-5/2) - 25*q^(-7/2) - 27*q^(-9/2) - 18*q^(-11/2) - 4*q^(-13/2) - 4*q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(3)*x2^(6) + (2*q^(-9/2) + 4*q^(-11/2) + 4*q^(-13/2) - 6*q^(-15/2) + 2*q^(-17/2) + q^(-21/2) + q^(-23/2))*x1^(4)*x2^(6) + (q^(-17/2) + q^(-19/2) + 3*q^(-21/2) - q^(-25/2))*x1^(5)*x2^(6) + (-12*q^(7/2) - 20*q^(5/2) - 56*q^(3/2) - 80*q^(1/2) - 102*q^(-1/2) - 94*q^(-3/2) - 100*q^(-5/2) - 42*q^(-7/2) - 28*q^(-9/2) - 14*q^(-11/2) - 8*q^(-13/2) - 2*q^(-15/2) - 2*q^(-17/2))*x1*x2^(7) + (10*q^(5/2) + 26*q^(3/2) + 70*q^(1/2) + 123*q^(-1/2) + 168*q^(-3/2) + 172*q^(-5/2) + 160*q^(-7/2) + 79*q^(-9/2) + 39*q^(-11/2) + 14*q^(-13/2) + 3*q^(-15/2))*x1^(2)*x2^(7) + (-8*q^(1/2) - 20*q^(-1/2) - 56*q^(-3/2) - 87*q^(-5/2) - 112*q^(-7/2) - 96*q^(-9/2) - 66*q^(-11/2) - 27*q^(-13/2) - 18*q^(-15/2) - 7*q^(-17/2) - 5*q^(-19/2) - q^(-21/2) - q^(-23/2))*x1^(3)*x2^(7) + (6*q^(-5/2) + 11*q^(-7/2) + 24*q^(-9/2) + 23*q^(-11/2) + 14*q^(-13/2) - 10*q^(-15/2) + 4*q^(-17/2) + 2*q^(-19/2) + 7*q^(-21/2) + 5*q^(-23/2) + 2*q^(-25/2) + q^(-27/2) + q^(-29/2))*x1^(4)*x2^(7) + (-2*q^(-13/2) + 2*q^(-15/2) + 6*q^(-17/2) + 9*q^(-19/2) + 14*q^(-21/2) + 3*q^(-23/2) - 4*q^(-25/2) - q^(-27/2) - q^(-29/2) - q^(-31/2) - q^(-33/2))*x1^(5)*x2^(7) + (-q^(-21/2) - 2*q^(-23/2) - 4*q^(-25/2) - q^(-27/2) - q^(-29/2) + q^(-35/2))*x1^(6)*x2^(7) + (-7*q^(13/2) - 26*q^(11/2) - 51*q^(9/2) - 102*q^(7/2) - 158*q^(5/2) - 230*q^(3/2) - 261*q^(1/2) - 276*q^(-1/2) - 242*q^(-3/2) - 225*q^(-5/2) - 124*q^(-7/2) - 87*q^(-9/2) - 53*q^(-11/2) - 34*q^(-13/2) - 17*q^(-15/2) - 11*q^(-17/2) - 4*q^(-19/2) - 3*q^(-21/2) - q^(-23/2))*x1*x2^(8) + (6*q^(11/2) + 28*q^(9/2) + 70*q^(7/2) + 152*q^(5/2) + 260*q^(3/2) + 404*q^(1/2) + 505*q^(-1/2) + 553*q^(-3/2) + 507*q^(-5/2) + 430*q^(-7/2) + 252*q^(-9/2) + 147*q^(-11/2) + 71*q^(-13/2) + 31*q^(-15/2) + 8*q^(-17/2) + 4*q^(-19/2))*x1^(2)*x2^(8) + (-5*q^(7/2) - 23*q^(5/2) - 61*q^(3/2) - 131*q^(1/2) - 227*q^(-1/2) - 337*q^(-3/2) - 399*q^(-5/2) - 405*q^(-7/2) - 332*q^(-9/2) - 234*q^(-11/2) - 129*q^(-13/2) - 82*q^(-15/2) - 39*q^(-17/2) - 23*q^(-19/2) - 8*q^(-21/2) - 5*q^(-23/2) - q^(-25/2) - q^(-27/2))*x1^(3)*x2^(8) + (4*q^(1/2) + 18*q^(-1/2) + 38*q^(-3/2) + 78*q^(-5/2) + 108*q^(-7/2) + 128*q^(-9/2) + 98*q^(-11/2) + 61*q^(-13/2) + 2*q^(-15/2) + 22*q^(-17/2) + 21*q^(-19/2) + 33*q^(-21/2) + 25*q^(-23/2) + 15*q^(-25/2) + 8*q^(-27/2) + 6*q^(-29/2) + 2*q^(-31/2) + q^(-33/2) + q^(-35/2))*x1^(4)*x2^(8) + (-3*q^(-7/2) - 7*q^(-9/2) - 11*q^(-11/2) - 6*q^(-13/2) + 12*q^(-15/2) + 34*q^(-17/2) + 48*q^(-19/2) + 49*q^(-21/2) + 13*q^(-23/2) - 11*q^(-25/2) - 10*q^(-27/2) - 9*q^(-29/2) - 9*q^(-31/2) - 6*q^(-33/2) - 2*q^(-35/2) - 2*q^(-37/2) - q^(-39/2) - q^(-41/2))*x1^(5)*x2^(8) + (-2*q^(-17/2) - 4*q^(-19/2) - 14*q^(-21/2) - 22*q^(-23/2) - 25*q^(-25/2) - 13*q^(-27/2) - 8*q^(-29/2) - q^(-31/2) + 3*q^(-33/2) + 5*q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2) + q^(-43/2) + q^(-45/2))*x1^(6)*x2^(8) + (2*q^(-27/2) + 2*q^(-29/2) + 3*q^(-31/2) + 3*q^(-33/2) + q^(-35/2) - 3*q^(-37/2) + q^(-39/2) - q^(-47/2))*x1^(7)*x2^(8) + (-16*q^(19/2) - 28*q^(17/2) - 80*q^(15/2) - 144*q^(13/2) - 254*q^(11/2) - 356*q^(9/2) - 526*q^(7/2) - 632*q^(5/2) - 742*q^(3/2) - 746*q^(1/2) - 726*q^(-1/2) - 616*q^(-3/2) - 544*q^(-5/2) - 352*q^(-7/2) - 264*q^(-9/2) - 178*q^(-11/2) - 126*q^(-13/2) - 76*q^(-15/2) - 54*q^(-17/2) - 28*q^(-19/2) - 20*q^(-21/2) - 10*q^(-23/2) - 6*q^(-25/2) - 2*q^(-27/2) - 2*q^(-29/2))*x1*x2^(9) + (14*q^(17/2) + 38*q^(15/2) + 106*q^(13/2) + 226*q^(11/2) + 425*q^(9/2) + 674*q^(7/2) + 1010*q^(5/2) + 1328*q^(3/2) + 1606*q^(1/2) + 1712*q^(-1/2) + 1674*q^(-3/2) + 1457*q^(-5/2) + 1185*q^(-7/2) + 784*q^(-9/2) + 506*q^(-11/2) + 295*q^(-13/2) + 161*q^(-15/2) + 76*q^(-17/2) + 36*q^(-19/2) + 14*q^(-21/2) + 7*q^(-23/2) + 2*q^(-25/2))*x1^(2)*x2^(9) + (-12*q^(13/2) - 32*q^(11/2) - 100*q^(9/2) - 210*q^(7/2) - 409*q^(5/2) - 652*q^(3/2) - 980*q^(1/2) - 1256*q^(-1/2) - 1478*q^(-3/2) - 1494*q^(-5/2) - 1388*q^(-7/2) - 1114*q^(-9/2) - 822*q^(-11/2) - 524*q^(-13/2) - 345*q^(-15/2) - 191*q^(-17/2) - 110*q^(-19/2) - 50*q^(-21/2) - 26*q^(-23/2) - 8*q^(-25/2) - 5*q^(-27/2) - q^(-29/2) - q^(-31/2))*x1^(3)*x2^(9) + (10*q^(7/2) + 26*q^(5/2) + 75*q^(3/2) + 150*q^(1/2) + 271*q^(-1/2) + 392*q^(-3/2) + 531*q^(-5/2) + 569*q^(-7/2) + 543*q^(-9/2) + 410*q^(-11/2) + 278*q^(-13/2) + 136*q^(-15/2) + 148*q^(-17/2) + 133*q^(-19/2) + 143*q^(-21/2) + 115*q^(-23/2) + 80*q^(-25/2) + 47*q^(-27/2) + 31*q^(-29/2) + 15*q^(-31/2) + 9*q^(-33/2) + 6*q^(-35/2) + 2*q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(4)*x2^(9) + (-8*q^(-1/2) - 16*q^(-3/2) - 38*q^(-5/2) - 60*q^(-7/2) - 79*q^(-9/2) - 60*q^(-11/2) - 15*q^(-13/2) + 75*q^(-15/2) + 151*q^(-17/2) + 179*q^(-19/2) + 142*q^(-21/2) + 36*q^(-23/2) - 42*q^(-25/2) - 60*q^(-27/2) - 60*q^(-29/2) - 50*q^(-31/2) - 35*q^(-33/2) - 21*q^(-35/2) - 16*q^(-37/2) - 9*q^(-39/2) - 7*q^(-41/2) - 3*q^(-43/2) - 2*q^(-45/2) - q^(-47/2) - q^(-49/2))*x1^(5)*x2^(9) + (3*q^(-11/2) - 2*q^(-13/2) - 7*q^(-15/2) - 29*q^(-17/2) - 59*q^(-19/2) - 109*q^(-21/2) - 131*q^(-23/2) - 127*q^(-25/2) - 78*q^(-27/2) - 41*q^(-29/2) - q^(-31/2) + 18*q^(-33/2) + 24*q^(-35/2) + 13*q^(-37/2) + 12*q^(-39/2) + 10*q^(-41/2) + 9*q^(-43/2) + 6*q^(-45/2) + 3*q^(-47/2) + 2*q^(-49/2) + 2*q^(-51/2) + q^(-53/2) + q^(-55/2))*x1^(6)*x2^(9) + (2*q^(-21/2) + 6*q^(-23/2) + 14*q^(-25/2) + 24*q^(-27/2) + 28*q^(-29/2) + 31*q^(-31/2) + 24*q^(-33/2) + 8*q^(-35/2) - 9*q^(-37/2) - 2*q^(-41/2) - 2*q^(-43/2) - 2*q^(-45/2) - 4*q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2) - q^(-57/2) - q^(-59/2))*x1^(7)*x2^(9) + (-q^(-33/2) - 2*q^(-35/2) - 2*q^(-37/2) - q^(-39/2) + q^(-41/2) + q^(-43/2) + q^(-45/2) + 3*q^(-47/2) - q^(-51/2) + q^(-61/2))*x1^(8)*x2^(9)
(-1, -2) (1, 1) x1^(1)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]}
(-q^(-5/2))*x1*x2^(2) + (-4*q^(-5/2))*x1*x2^(3) + (2*q^(-7/2))*x1^(2)*x2^(3) + (-3*q^(-3/2) - 10*q^(-5/2) - q^(-7/2))*x1*x2^(4) + (2*q^(-5/2) + 8*q^(-7/2) + q^(-9/2))*x1^(2)*x2^(4) + (-q^(-9/2) - q^(-11/2))*x1^(3)*x2^(4) + (-8*q^(-1/2) - 12*q^(-3/2) - 22*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1*x2^(5) + (6*q^(-3/2) + 14*q^(-5/2) + 23*q^(-7/2) + 6*q^(-9/2) + q^(-11/2))*x1^(2)*x2^(5) + (-4*q^(-7/2) - 6*q^(-9/2) - 5*q^(-11/2) - q^(-15/2))*x1^(3)*x2^(5) + (q^(-13/2) - 2*q^(-15/2) + q^(-17/2))*x1^(4)*x2^(5) + (-5*q^(3/2) - 18*q^(1/2) - 33*q^(-1/2) - 36*q^(-3/2) - 46*q^(-5/2) - 14*q^(-7/2) - 8*q^(-9/2) - 3*q^(-11/2) - q^(-13/2))*x1*x2^(6) + (4*q^(1/2) + 18*q^(-1/2) + 42*q^(-3/2) + 54*q^(-5/2) + 61*q^(-7/2) + 23*q^(-9/2) + 9*q^(-11/2) + q^(-13/2))*x1^(2)*x2^(6) + (-3*q^(-3/2) - 13*q^(-5/2) - 25*q^(-7/2) - 27*q^(-9/2) - 18*q^(-11/2) - 4*q^(-13/2) - 4*q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(3)*x2^(6) + (2*q^(-9/2) + 4*q^(-11/2) + 4*q^(-13/2) - 6*q^(-15/2) + 2*q^(-17/2) + q^(-21/2) + q^(-23/2))*x1^(4)*x2^(6) + (q^(-17/2) + q^(-19/2) + 3*q^(-21/2) - q^(-25/2))*x1^(5)*x2^(6) + (-12*q^(7/2) - 20*q^(5/2) - 56*q^(3/2) - 80*q^(1/2) - 102*q^(-1/2) - 94*q^(-3/2) - 100*q^(-5/2) - 42*q^(-7/2) - 28*q^(-9/2) - 14*q^(-11/2) - 8*q^(-13/2) - 2*q^(-15/2) - 2*q^(-17/2))*x1*x2^(7) + (10*q^(5/2) + 26*q^(3/2) + 70*q^(1/2) + 123*q^(-1/2) + 168*q^(-3/2) + 172*q^(-5/2) + 160*q^(-7/2) + 79*q^(-9/2) + 39*q^(-11/2) + 14*q^(-13/2) + 3*q^(-15/2))*x1^(2)*x2^(7) + (-8*q^(1/2) - 20*q^(-1/2) - 56*q^(-3/2) - 87*q^(-5/2) - 112*q^(-7/2) - 96*q^(-9/2) - 66*q^(-11/2) - 27*q^(-13/2) - 18*q^(-15/2) - 7*q^(-17/2) - 5*q^(-19/2) - q^(-21/2) - q^(-23/2))*x1^(3)*x2^(7) + (6*q^(-5/2) + 11*q^(-7/2) + 24*q^(-9/2) + 23*q^(-11/2) + 14*q^(-13/2) - 10*q^(-15/2) + 4*q^(-17/2) + 2*q^(-19/2) + 7*q^(-21/2) + 5*q^(-23/2) + 2*q^(-25/2) + q^(-27/2) + q^(-29/2))*x1^(4)*x2^(7) + (-2*q^(-13/2) + 2*q^(-15/2) + 6*q^(-17/2) + 9*q^(-19/2) + 14*q^(-21/2) + 3*q^(-23/2) - 4*q^(-25/2) - q^(-27/2) - q^(-29/2) - q^(-31/2) - q^(-33/2))*x1^(5)*x2^(7) + (-q^(-21/2) - 2*q^(-23/2) - 4*q^(-25/2) - q^(-27/2) - q^(-29/2) + q^(-35/2))*x1^(6)*x2^(7) + (-7*q^(13/2) - 26*q^(11/2) - 51*q^(9/2) - 102*q^(7/2) - 158*q^(5/2) - 230*q^(3/2) - 261*q^(1/2) - 276*q^(-1/2) - 242*q^(-3/2) - 225*q^(-5/2) - 124*q^(-7/2) - 87*q^(-9/2) - 53*q^(-11/2) - 34*q^(-13/2) - 17*q^(-15/2) - 11*q^(-17/2) - 4*q^(-19/2) - 3*q^(-21/2) - q^(-23/2))*x1*x2^(8) + (6*q^(11/2) + 28*q^(9/2) + 70*q^(7/2) + 152*q^(5/2) + 260*q^(3/2) + 404*q^(1/2) + 505*q^(-1/2) + 553*q^(-3/2) + 507*q^(-5/2) + 430*q^(-7/2) + 252*q^(-9/2) + 147*q^(-11/2) + 71*q^(-13/2) + 31*q^(-15/2) + 8*q^(-17/2) + 4*q^(-19/2))*x1^(2)*x2^(8) + (-5*q^(7/2) - 23*q^(5/2) - 61*q^(3/2) - 131*q^(1/2) - 227*q^(-1/2) - 337*q^(-3/2) - 399*q^(-5/2) - 405*q^(-7/2) - 332*q^(-9/2) - 234*q^(-11/2) - 129*q^(-13/2) - 82*q^(-15/2) - 39*q^(-17/2) - 23*q^(-19/2) - 8*q^(-21/2) - 5*q^(-23/2) - q^(-25/2) - q^(-27/2))*x1^(3)*x2^(8) + (4*q^(1/2) + 18*q^(-1/2) + 38*q^(-3/2) + 78*q^(-5/2) + 108*q^(-7/2) + 128*q^(-9/2) + 98*q^(-11/2) + 61*q^(-13/2) + 2*q^(-15/2) + 22*q^(-17/2) + 21*q^(-19/2) + 33*q^(-21/2) + 25*q^(-23/2) + 15*q^(-25/2) + 8*q^(-27/2) + 6*q^(-29/2) + 2*q^(-31/2) + q^(-33/2) + q^(-35/2))*x1^(4)*x2^(8) + (-3*q^(-7/2) - 7*q^(-9/2) - 11*q^(-11/2) - 6*q^(-13/2) + 12*q^(-15/2) + 34*q^(-17/2) + 48*q^(-19/2) + 49*q^(-21/2) + 13*q^(-23/2) - 11*q^(-25/2) - 10*q^(-27/2) - 9*q^(-29/2) - 9*q^(-31/2) - 6*q^(-33/2) - 2*q^(-35/2) - 2*q^(-37/2) - q^(-39/2) - q^(-41/2))*x1^(5)*x2^(8) + (-2*q^(-17/2) - 4*q^(-19/2) - 14*q^(-21/2) - 22*q^(-23/2) - 25*q^(-25/2) - 13*q^(-27/2) - 8*q^(-29/2) - q^(-31/2) + 3*q^(-33/2) + 5*q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2) + q^(-43/2) + q^(-45/2))*x1^(6)*x2^(8) + (2*q^(-27/2) + 2*q^(-29/2) + 3*q^(-31/2) + 3*q^(-33/2) + q^(-35/2) - 3*q^(-37/2) + q^(-39/2) - q^(-47/2))*x1^(7)*x2^(8) + (-16*q^(19/2) - 28*q^(17/2) - 80*q^(15/2) - 144*q^(13/2) - 254*q^(11/2) - 356*q^(9/2) - 526*q^(7/2) - 632*q^(5/2) - 742*q^(3/2) - 746*q^(1/2) - 726*q^(-1/2) - 616*q^(-3/2) - 544*q^(-5/2) - 352*q^(-7/2) - 264*q^(-9/2) - 178*q^(-11/2) - 126*q^(-13/2) - 76*q^(-15/2) - 54*q^(-17/2) - 28*q^(-19/2) - 20*q^(-21/2) - 10*q^(-23/2) - 6*q^(-25/2) - 2*q^(-27/2) - 2*q^(-29/2))*x1*x2^(9) + (14*q^(17/2) + 38*q^(15/2) + 106*q^(13/2) + 226*q^(11/2) + 425*q^(9/2) + 674*q^(7/2) + 1010*q^(5/2) + 1328*q^(3/2) + 1606*q^(1/2) + 1712*q^(-1/2) + 1674*q^(-3/2) + 1457*q^(-5/2) + 1185*q^(-7/2) + 784*q^(-9/2) + 506*q^(-11/2) + 295*q^(-13/2) + 161*q^(-15/2) + 76*q^(-17/2) + 36*q^(-19/2) + 14*q^(-21/2) + 7*q^(-23/2) + 2*q^(-25/2))*x1^(2)*x2^(9) + (-12*q^(13/2) - 32*q^(11/2) - 100*q^(9/2) - 210*q^(7/2) - 409*q^(5/2) - 652*q^(3/2) - 980*q^(1/2) - 1256*q^(-1/2) - 1478*q^(-3/2) - 1494*q^(-5/2) - 1388*q^(-7/2) - 1114*q^(-9/2) - 822*q^(-11/2) - 524*q^(-13/2) - 345*q^(-15/2) - 191*q^(-17/2) - 110*q^(-19/2) - 50*q^(-21/2) - 26*q^(-23/2) - 8*q^(-25/2) - 5*q^(-27/2) - q^(-29/2) - q^(-31/2))*x1^(3)*x2^(9) + (10*q^(7/2) + 26*q^(5/2) + 75*q^(3/2) + 150*q^(1/2) + 271*q^(-1/2) + 392*q^(-3/2) + 531*q^(-5/2) + 569*q^(-7/2) + 543*q^(-9/2) + 410*q^(-11/2) + 278*q^(-13/2) + 136*q^(-15/2) + 148*q^(-17/2) + 133*q^(-19/2) + 143*q^(-21/2) + 115*q^(-23/2) + 80*q^(-25/2) + 47*q^(-27/2) + 31*q^(-29/2) + 15*q^(-31/2) + 9*q^(-33/2) + 6*q^(-35/2) + 2*q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(4)*x2^(9) + (-8*q^(-1/2) - 16*q^(-3/2) - 38*q^(-5/2) - 60*q^(-7/2) - 79*q^(-9/2) - 60*q^(-11/2) - 15*q^(-13/2) + 75*q^(-15/2) + 151*q^(-17/2) + 179*q^(-19/2) + 142*q^(-21/2) + 36*q^(-23/2) - 42*q^(-25/2) - 60*q^(-27/2) - 60*q^(-29/2) - 50*q^(-31/2) - 35*q^(-33/2) - 21*q^(-35/2) - 16*q^(-37/2) - 9*q^(-39/2) - 7*q^(-41/2) - 3*q^(-43/2) - 2*q^(-45/2) - q^(-47/2) - q^(-49/2))*x1^(5)*x2^(9) + (3*q^(-11/2) - 2*q^(-13/2) - 7*q^(-15/2) - 29*q^(-17/2) - 59*q^(-19/2) - 109*q^(-21/2) - 131*q^(-23/2) - 127*q^(-25/2) - 78*q^(-27/2) - 41*q^(-29/2) - q^(-31/2) + 18*q^(-33/2) + 24*q^(-35/2) + 13*q^(-37/2) + 12*q^(-39/2) + 10*q^(-41/2) + 9*q^(-43/2) + 6*q^(-45/2) + 3*q^(-47/2) + 2*q^(-49/2) + 2*q^(-51/2) + q^(-53/2) + q^(-55/2))*x1^(6)*x2^(9) + (2*q^(-21/2) + 6*q^(-23/2) + 14*q^(-25/2) + 24*q^(-27/2) + 28*q^(-29/2) + 31*q^(-31/2) + 24*q^(-33/2) + 8*q^(-35/2) - 9*q^(-37/2) - 2*q^(-41/2) - 2*q^(-43/2) - 2*q^(-45/2) - 4*q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2) - q^(-57/2) - q^(-59/2))*x1^(7)*x2^(9) + (-q^(-33/2) - 2*q^(-35/2) - 2*q^(-37/2) - q^(-39/2) + q^(-41/2) + q^(-43/2) + q^(-45/2) + 3*q^(-47/2) - q^(-51/2) + q^(-61/2))*x1^(8)*x2^(9)
(1, 2) x1^(-1)x2^(-2) q^(-5/2)
(-q^(-5/2))*x1^(-1)*x2^(-2) + (-4*q^(-5/2))*x1^(-1)*x2^(-3) + (2*q^(-7/2))*x1^(-2)*x2^(-3) + (-3*q^(-3/2) - 10*q^(-5/2) - q^(-7/2))*x1^(-1)*x2^(-4) + (2*q^(-5/2) + 8*q^(-7/2) + q^(-9/2))*x1^(-2)*x2^(-4) + (-q^(-9/2) - q^(-11/2))*x1^(-3)*x2^(-4) + (-8*q^(-1/2) - 12*q^(-3/2) - 22*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(-1)*x2^(-5) + (6*q^(-3/2) + 14*q^(-5/2) + 23*q^(-7/2) + 6*q^(-9/2) + q^(-11/2))*x1^(-2)*x2^(-5) + (-4*q^(-7/2) - 6*q^(-9/2) - 5*q^(-11/2) - q^(-15/2))*x1^(-3)*x2^(-5) + (q^(-13/2) - 2*q^(-15/2) + q^(-17/2))*x1^(-4)*x2^(-5) + (-5*q^(3/2) - 18*q^(1/2) - 33*q^(-1/2) - 36*q^(-3/2) - 46*q^(-5/2) - 14*q^(-7/2) - 8*q^(-9/2) - 3*q^(-11/2) - q^(-13/2))*x1^(-1)*x2^(-6) + (4*q^(1/2) + 18*q^(-1/2) + 42*q^(-3/2) + 54*q^(-5/2) + 61*q^(-7/2) + 23*q^(-9/2) + 9*q^(-11/2) + q^(-13/2))*x1^(-2)*x2^(-6) + (-3*q^(-3/2) - 13*q^(-5/2) - 25*q^(-7/2) - 27*q^(-9/2) - 18*q^(-11/2) - 4*q^(-13/2) - 4*q^(-15/2) - q^(-17/2) - q^(-19/2))*x1^(-3)*x2^(-6) + (2*q^(-9/2) + 4*q^(-11/2) + 4*q^(-13/2) - 6*q^(-15/2) + 2*q^(-17/2) + q^(-21/2) + q^(-23/2))*x1^(-4)*x2^(-6) + (q^(-17/2) + q^(-19/2) + 3*q^(-21/2) - q^(-25/2))*x1^(-5)*x2^(-6) + (-12*q^(7/2) - 20*q^(5/2) - 56*q^(3/2) - 80*q^(1/2) - 102*q^(-1/2) - 94*q^(-3/2) - 100*q^(-5/2) - 42*q^(-7/2) - 28*q^(-9/2) - 14*q^(-11/2) - 8*q^(-13/2) - 2*q^(-15/2) - 2*q^(-17/2))*x1^(-1)*x2^(-7) + (10*q^(5/2) + 26*q^(3/2) + 70*q^(1/2) + 123*q^(-1/2) + 168*q^(-3/2) + 172*q^(-5/2) + 160*q^(-7/2) + 79*q^(-9/2) + 39*q^(-11/2) + 14*q^(-13/2) + 3*q^(-15/2))*x1^(-2)*x2^(-7) + (-8*q^(1/2) - 20*q^(-1/2) - 56*q^(-3/2) - 87*q^(-5/2) - 112*q^(-7/2) - 96*q^(-9/2) - 66*q^(-11/2) - 27*q^(-13/2) - 18*q^(-15/2) - 7*q^(-17/2) - 5*q^(-19/2) - q^(-21/2) - q^(-23/2))*x1^(-3)*x2^(-7) + (6*q^(-5/2) + 11*q^(-7/2) + 24*q^(-9/2) + 23*q^(-11/2) + 14*q^(-13/2) - 10*q^(-15/2) + 4*q^(-17/2) + 2*q^(-19/2) + 7*q^(-21/2) + 5*q^(-23/2) + 2*q^(-25/2) + q^(-27/2) + q^(-29/2))*x1^(-4)*x2^(-7) + (-2*q^(-13/2) + 2*q^(-15/2) + 6*q^(-17/2) + 9*q^(-19/2) + 14*q^(-21/2) + 3*q^(-23/2) - 4*q^(-25/2) - q^(-27/2) - q^(-29/2) - q^(-31/2) - q^(-33/2))*x1^(-5)*x2^(-7) + (-q^(-21/2) - 2*q^(-23/2) - 4*q^(-25/2) - q^(-27/2) - q^(-29/2) + q^(-35/2))*x1^(-6)*x2^(-7) + (-7*q^(13/2) - 26*q^(11/2) - 51*q^(9/2) - 102*q^(7/2) - 158*q^(5/2) - 230*q^(3/2) - 261*q^(1/2) - 276*q^(-1/2) - 242*q^(-3/2) - 225*q^(-5/2) - 124*q^(-7/2) - 87*q^(-9/2) - 53*q^(-11/2) - 34*q^(-13/2) - 17*q^(-15/2) - 11*q^(-17/2) - 4*q^(-19/2) - 3*q^(-21/2) - q^(-23/2))*x1^(-1)*x2^(-8) + (6*q^(11/2) + 28*q^(9/2) + 70*q^(7/2) + 152*q^(5/2) + 260*q^(3/2) + 404*q^(1/2) + 505*q^(-1/2) + 553*q^(-3/2) + 507*q^(-5/2) + 430*q^(-7/2) + 252*q^(-9/2) + 147*q^(-11/2) + 71*q^(-13/2) + 31*q^(-15/2) + 8*q^(-17/2) + 4*q^(-19/2))*x1^(-2)*x2^(-8) + (-5*q^(7/2) - 23*q^(5/2) - 61*q^(3/2) - 131*q^(1/2) - 227*q^(-1/2) - 337*q^(-3/2) - 399*q^(-5/2) - 405*q^(-7/2) - 332*q^(-9/2) - 234*q^(-11/2) - 129*q^(-13/2) - 82*q^(-15/2) - 39*q^(-17/2) - 23*q^(-19/2) - 8*q^(-21/2) - 5*q^(-23/2) - q^(-25/2) - q^(-27/2))*x1^(-3)*x2^(-8) + (4*q^(1/2) + 18*q^(-1/2) + 38*q^(-3/2) + 78*q^(-5/2) + 108*q^(-7/2) + 128*q^(-9/2) + 98*q^(-11/2) + 61*q^(-13/2) + 2*q^(-15/2) + 22*q^(-17/2) + 21*q^(-19/2) + 33*q^(-21/2) + 25*q^(-23/2) + 15*q^(-25/2) + 8*q^(-27/2) + 6*q^(-29/2) + 2*q^(-31/2) + q^(-33/2) + q^(-35/2))*x1^(-4)*x2^(-8) + (-3*q^(-7/2) - 7*q^(-9/2) - 11*q^(-11/2) - 6*q^(-13/2) + 12*q^(-15/2) + 34*q^(-17/2) + 48*q^(-19/2) + 49*q^(-21/2) + 13*q^(-23/2) - 11*q^(-25/2) - 10*q^(-27/2) - 9*q^(-29/2) - 9*q^(-31/2) - 6*q^(-33/2) - 2*q^(-35/2) - 2*q^(-37/2) - q^(-39/2) - q^(-41/2))*x1^(-5)*x2^(-8) + (-2*q^(-17/2) - 4*q^(-19/2) - 14*q^(-21/2) - 22*q^(-23/2) - 25*q^(-25/2) - 13*q^(-27/2) - 8*q^(-29/2) - q^(-31/2) + 3*q^(-33/2) + 5*q^(-35/2) + q^(-37/2) + q^(-39/2) + q^(-41/2) + q^(-43/2) + q^(-45/2))*x1^(-6)*x2^(-8) + (2*q^(-27/2) + 2*q^(-29/2) + 3*q^(-31/2) + 3*q^(-33/2) + q^(-35/2) - 3*q^(-37/2) + q^(-39/2) - q^(-47/2))*x1^(-7)*x2^(-8) + (-16*q^(19/2) - 28*q^(17/2) - 80*q^(15/2) - 144*q^(13/2) - 254*q^(11/2) - 356*q^(9/2) - 526*q^(7/2) - 632*q^(5/2) - 742*q^(3/2) - 746*q^(1/2) - 726*q^(-1/2) - 616*q^(-3/2) - 544*q^(-5/2) - 352*q^(-7/2) - 264*q^(-9/2) - 178*q^(-11/2) - 126*q^(-13/2) - 76*q^(-15/2) - 54*q^(-17/2) - 28*q^(-19/2) - 20*q^(-21/2) - 10*q^(-23/2) - 6*q^(-25/2) - 2*q^(-27/2) - 2*q^(-29/2))*x1^(-1)*x2^(-9) + (14*q^(17/2) + 38*q^(15/2) + 106*q^(13/2) + 226*q^(11/2) + 425*q^(9/2) + 674*q^(7/2) + 1010*q^(5/2) + 1328*q^(3/2) + 1606*q^(1/2) + 1712*q^(-1/2) + 1674*q^(-3/2) + 1457*q^(-5/2) + 1185*q^(-7/2) + 784*q^(-9/2) + 506*q^(-11/2) + 295*q^(-13/2) + 161*q^(-15/2) + 76*q^(-17/2) + 36*q^(-19/2) + 14*q^(-21/2) + 7*q^(-23/2) + 2*q^(-25/2))*x1^(-2)*x2^(-9) + (-12*q^(13/2) - 32*q^(11/2) - 100*q^(9/2) - 210*q^(7/2) - 409*q^(5/2) - 652*q^(3/2) - 980*q^(1/2) - 1256*q^(-1/2) - 1478*q^(-3/2) - 1494*q^(-5/2) - 1388*q^(-7/2) - 1114*q^(-9/2) - 822*q^(-11/2) - 524*q^(-13/2) - 345*q^(-15/2) - 191*q^(-17/2) - 110*q^(-19/2) - 50*q^(-21/2) - 26*q^(-23/2) - 8*q^(-25/2) - 5*q^(-27/2) - q^(-29/2) - q^(-31/2))*x1^(-3)*x2^(-9) + (10*q^(7/2) + 26*q^(5/2) + 75*q^(3/2) + 150*q^(1/2) + 271*q^(-1/2) + 392*q^(-3/2) + 531*q^(-5/2) + 569*q^(-7/2) + 543*q^(-9/2) + 410*q^(-11/2) + 278*q^(-13/2) + 136*q^(-15/2) + 148*q^(-17/2) + 133*q^(-19/2) + 143*q^(-21/2) + 115*q^(-23/2) + 80*q^(-25/2) + 47*q^(-27/2) + 31*q^(-29/2) + 15*q^(-31/2) + 9*q^(-33/2) + 6*q^(-35/2) + 2*q^(-37/2) + q^(-39/2) + q^(-41/2))*x1^(-4)*x2^(-9) + (-8*q^(-1/2) - 16*q^(-3/2) - 38*q^(-5/2) - 60*q^(-7/2) - 79*q^(-9/2) - 60*q^(-11/2) - 15*q^(-13/2) + 75*q^(-15/2) + 151*q^(-17/2) + 179*q^(-19/2) + 142*q^(-21/2) + 36*q^(-23/2) - 42*q^(-25/2) - 60*q^(-27/2) - 60*q^(-29/2) - 50*q^(-31/2) - 35*q^(-33/2) - 21*q^(-35/2) - 16*q^(-37/2) - 9*q^(-39/2) - 7*q^(-41/2) - 3*q^(-43/2) - 2*q^(-45/2) - q^(-47/2) - q^(-49/2))*x1^(-5)*x2^(-9) + (3*q^(-11/2) - 2*q^(-13/2) - 7*q^(-15/2) - 29*q^(-17/2) - 59*q^(-19/2) - 109*q^(-21/2) - 131*q^(-23/2) - 127*q^(-25/2) - 78*q^(-27/2) - 41*q^(-29/2) - q^(-31/2) + 18*q^(-33/2) + 24*q^(-35/2) + 13*q^(-37/2) + 12*q^(-39/2) + 10*q^(-41/2) + 9*q^(-43/2) + 6*q^(-45/2) + 3*q^(-47/2) + 2*q^(-49/2) + 2*q^(-51/2) + q^(-53/2) + q^(-55/2))*x1^(-6)*x2^(-9) + (2*q^(-21/2) + 6*q^(-23/2) + 14*q^(-25/2) + 24*q^(-27/2) + 28*q^(-29/2) + 31*q^(-31/2) + 24*q^(-33/2) + 8*q^(-35/2) - 9*q^(-37/2) - 2*q^(-41/2) - 2*q^(-43/2) - 2*q^(-45/2) - 4*q^(-47/2) - q^(-49/2) - q^(-51/2) - q^(-53/2) - q^(-55/2) - q^(-57/2) - q^(-59/2))*x1^(-7)*x2^(-9) + (-q^(-33/2) - 2*q^(-35/2) - 2*q^(-37/2) - q^(-39/2) + q^(-41/2) + q^(-43/2) + q^(-45/2) + 3*q^(-47/2) - q^(-51/2) + q^(-61/2))*x1^(-8)*x2^(-9)

Braid

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

Multivariable Alexander polynomial

ΔL
A1*A2^(2) - 4*A1*A2 + 2*A1 + 2*A2 - 5 + 2*A2^(-1) + 2*A1^(-1) - 4*A1^(-1)*A2^(-1) + A1^(-1)*A2^(-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-101-202A1A2

Dual Thurston polytope

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

HFL polytope

Poincaré polynomial
m^(-2)*A1^(-3/2)*A2^(-5/2) + 5*m^(-1)*A1^(-3/2)*A2^(-3/2) + m^(-1)*A1^(-1/2)*A2^(-5/2) + 6*A1^(-3/2)*A2^(-1/2) + 7*A1^(-1/2)*A2^(-3/2) + 2*m*A1^(-3/2)*A2^(1/2) + 13*m*A1^(-1/2)*A2^(-1/2) + 2*m*A1^(1/2)*A2^(-3/2) + 9*m^2*A1^(-1/2)*A2^(1/2) + 9*m^2*A1^(1/2)*A2^(-1/2) + 2*m^3*A1^(-1/2)*A2^(3/2) + 13*m^3*A1^(1/2)*A2^(1/2) + 2*m^3*A1^(3/2)*A2^(-1/2) + 7*m^4*A1^(1/2)*A2^(3/2) + 6*m^4*A1^(3/2)*A2^(1/2) + m^5*A1^(1/2)*A2^(5/2) + 5*m^5*A1^(3/2)*A2^(3/2) + m^6*A1^(3/2)*A2^(5/2)
VertexMaslovRank
(-3/2, -5/2)-21
(-1/2, -5/2)-11
(3/2, -1/2)32
(3/2, 5/2)61
(1/2, 5/2)51
(-3/2, 1/2)12
HFL polytope-202-202A1A2

Record

FL/HFL Links

orderOption(int) 407
namestring L10a67{0}
statusstring success
slugstring L10a67_0_8d3156a4
result_filestring details/L10a67_0_8d3156a4.json
complexity_scoreOption(int) 200
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 92
wall_secondsOption(float) 0.002043
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 18
vertex_countOption(int) 6
fibered_vertex_countOption(int) 2
polytope_statusstring computed
alexander_support_sizeOption(int) 9
alexander_vertex_countOption(int) 4
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks)
{
  "dataset": "FLHFLLinks",
  "key": "L10a67_0_8d3156a4"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10a67_0_8d3156a4