details/L10a43_0_451cb26d.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]}
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(-q^(1/2))*x1^(1/2)*x2^(5/2) + (-4*q^(1/2))*x1^(1/2)*x2^(7/2) + (4*q^(-1/2))*x1^(3/2)*x2^(7/2) + (2*q^(3/2) - 10*q^(1/2))*x1^(1/2)*x2^(9/2) + (16*q^(-1/2) + 8*q^(-3/2))*x1^(3/2)*x2^(9/2) + (-q^(-1/2) - 6*q^(-3/2) - 9*q^(-5/2))*x1^(5/2)*x2^(9/2) + (4*q^(5/2) + 8*q^(3/2) - 20*q^(1/2))*x1^(1/2)*x2^(11/2) + (-4*q^(3/2) - 8*q^(1/2) + 40*q^(-1/2) + 32*q^(-3/2) + 12*q^(-5/2))*x1^(3/2)*x2^(11/2) + (-4*q^(-1/2) - 28*q^(-3/2) - 56*q^(-5/2) - 28*q^(-7/2) - 12*q^(-9/2))*x1^(5/2)*x2^(11/2) + (4*q^(-3/2) + 8*q^(-5/2) + 20*q^(-7/2) + 16*q^(-9/2) + 16*q^(-11/2))*x1^(7/2)*x2^(11/2) + (4*q^(7/2) + 15*q^(5/2) + 20*q^(3/2) - 35*q^(1/2))*x1^(1/2)*x2^(13/2) + (-8*q^(5/2) - 32*q^(3/2) - 44*q^(1/2) + 64*q^(-1/2) + 80*q^(-3/2) + 48*q^(-5/2) + 16*q^(-7/2))*x1^(3/2)*x2^(13/2) + (4*q^(3/2) + 18*q^(1/2) + 14*q^(-1/2) - 58*q^(-3/2) - 180*q^(-5/2) - 156*q^(-7/2) - 106*q^(-9/2) - 32*q^(-11/2) - 16*q^(-13/2))*x1^(5/2)*x2^(13/2) + (16*q^(-3/2) + 48*q^(-5/2) + 120*q^(-7/2) + 152*q^(-9/2) + 160*q^(-11/2) + 88*q^(-13/2) + 40*q^(-15/2) + 16*q^(-17/2))*x1^(7/2)*x2^(13/2) + (-q^(-3/2) - 6*q^(-5/2) - 17*q^(-7/2) - 30*q^(-9/2) - 44*q^(-11/2) - 54*q^(-13/2) - 49*q^(-15/2) - 30*q^(-17/2) - 25*q^(-19/2))*x1^(9/2)*x2^(13/2) + (-4*q^(11/2) + 4*q^(9/2) + 12*q^(7/2) + 36*q^(5/2) + 40*q^(3/2) - 56*q^(1/2))*x1^(1/2)*x2^(15/2) + (4*q^(9/2) - 7*q^(7/2) - 44*q^(5/2) - 124*q^(3/2) - 160*q^(1/2) + 56*q^(-1/2) + 136*q^(-3/2) + 120*q^(-5/2) + 64*q^(-7/2) + 20*q^(-9/2))*x1^(3/2)*x2^(15/2) + (8*q^(5/2) + 52*q^(3/2) + 136*q^(1/2) + 180*q^(-1/2) + 16*q^(-3/2) - 344*q^(-5/2) - 452*q^(-7/2) - 432*q^(-9/2) - 228*q^(-11/2) - 124*q^(-13/2) - 40*q^(-15/2) - 20*q^(-17/2))*x1^(5/2)*x2^(15/2) + (-4*q^(3/2) - 20*q^(1/2) - 48*q^(-1/2) - 36*q^(-3/2) + 60*q^(-5/2) + 344*q^(-7/2) + 592*q^(-9/2) + 788*q^(-11/2) + 648*q^(-13/2) + 456*q^(-15/2) + 248*q^(-17/2) + 112*q^(-19/2) + 40*q^(-21/2) + 20*q^(-23/2))*x1^(7/2)*x2^(15/2) + (-4*q^(-3/2) - 28*q^(-5/2) - 96*q^(-7/2) - 208*q^(-9/2) - 352*q^(-11/2) - 492*q^(-13/2) - 560*q^(-15/2) - 492*q^(-17/2) - 416*q^(-19/2) - 232*q^(-21/2) - 120*q^(-23/2) - 52*q^(-25/2) - 20*q^(-27/2))*x1^(9/2)*x2^(15/2) + (4*q^(-5/2) + 8*q^(-7/2) + 28*q^(-9/2) + 48*q^(-11/2) + 84*q^(-13/2) + 112*q^(-15/2) + 148*q^(-17/2) + 144*q^(-19/2) + 156*q^(-21/2) + 120*q^(-23/2) + 88*q^(-25/2) + 48*q^(-27/2) + 36*q^(-29/2))*x1^(11/2)*x2^(15/2) + (-6*q^(15/2) - 6*q^(13/2) - 12*q^(11/2) + 8*q^(9/2) + 24*q^(7/2) + 70*q^(5/2) + 70*q^(3/2) - 84*q^(1/2))*x1^(1/2)*x2^(17/2) + (8*q^(13/2) + 16*q^(11/2) + 28*q^(9/2) - 16*q^(7/2) - 132*q^(5/2) - 340*q^(3/2) - 440*q^(1/2) - 64*q^(-1/2) + 156*q^(-3/2) + 208*q^(-5/2) + 160*q^(-7/2) + 80*q^(-9/2) + 24*q^(-11/2))*x1^(3/2)*x2^(17/2) + (-2*q^(11/2) - 10*q^(9/2) - 12*q^(7/2) + 44*q^(5/2) + 243*q^(3/2) + 590*q^(1/2) + 860*q^(-1/2) + 618*q^(-3/2) - 219*q^(-5/2) - 784*q^(-7/2) - 1083*q^(-9/2) - 818*q^(-11/2) - 555*q^(-13/2) - 256*q^(-15/2) - 152*q^(-17/2) - 48*q^(-19/2) - 24*q^(-21/2))*x1^(5/2)*x2^(17/2) + (-8*q^(5/2) - 56*q^(3/2) - 192*q^(1/2) - 436*q^(-1/2) - 632*q^(-3/2) - 544*q^(-5/2) + 168*q^(-7/2) + 1168*q^(-9/2) + 2224*q^(-11/2) + 2484*q^(-13/2) + 2240*q^(-15/2) + 1624*q^(-17/2) + 992*q^(-19/2) + 536*q^(-21/2) + 288*q^(-23/2) + 120*q^(-25/2) + 48*q^(-27/2) + 24*q^(-29/2))*x1^(7/2)*x2^(17/2) + (4*q^(3/2) + 20*q^(1/2) + 58*q^(-1/2) + 110*q^(-3/2) + 126*q^(-5/2) - 36*q^(-7/2) - 440*q^(-9/2) - 1148*q^(-11/2) - 2030*q^(-13/2) - 2808*q^(-15/2) - 3082*q^(-17/2) - 3036*q^(-19/2) - 2384*q^(-21/2) - 1692*q^(-23/2) - 1028*q^(-25/2) - 594*q^(-27/2) - 264*q^(-29/2) - 136*q^(-31/2) - 48*q^(-33/2) - 24*q^(-35/2))*x1^(9/2)*x2^(17/2) + (16*q^(-5/2) + 48*q^(-7/2) + 160*q^(-9/2) + 344*q^(-11/2) + 648*q^(-13/2) + 1016*q^(-15/2) + 1440*q^(-17/2) + 1728*q^(-19/2) + 1952*q^(-21/2) + 1912*q^(-23/2) + 1680*q^(-25/2) + 1312*q^(-27/2) + 968*q^(-29/2) + 568*q^(-31/2) + 304*q^(-33/2) + 152*q^(-35/2) + 64*q^(-37/2) + 24*q^(-39/2))*x1^(11/2)*x2^(17/2) + (-q^(-5/2) - 6*q^(-7/2) - 17*q^(-9/2) - 38*q^(-11/2) - 76*q^(-13/2) - 132*q^(-15/2) - 205*q^(-17/2) - 284*q^(-19/2) - 365*q^(-21/2) - 432*q^(-23/2) - 477*q^(-25/2) - 468*q^(-27/2) - 445*q^(-29/2) - 380*q^(-31/2) - 308*q^(-33/2) - 206*q^(-35/2) - 137*q^(-37/2) - 70*q^(-39/2) - 49*q^(-41/2))*x1^(13/2)*x2^(17/2) + (-4*q^(19/2) - 8*q^(17/2) - 32*q^(15/2) - 16*q^(13/2) - 36*q^(11/2) + 8*q^(9/2) + 40*q^(7/2) + 120*q^(5/2) + 112*q^(3/2) - 120*q^(1/2))*x1^(1/2)*x2^(19/2) + (8*q^(17/2) + 24*q^(15/2) + 78*q^(13/2) + 108*q^(11/2) + 152*q^(9/2) + 34*q^(7/2) - 260*q^(5/2) - 740*q^(3/2) - 996*q^(1/2) - 420*q^(-1/2) + 32*q^(-3/2) + 256*q^(-5/2) + 280*q^(-7/2) + 200*q^(-9/2) + 96*q^(-11/2) + 28*q^(-13/2))*x1^(3/2)*x2^(19/2) + (-4*q^(15/2) - 24*q^(13/2) - 68*q^(11/2) - 148*q^(9/2) - 172*q^(7/2) - 4*q^(5/2) + 656*q^(3/2) + 1752*q^(1/2) + 2800*q^(-1/2) + 2740*q^(-3/2) + 1216*q^(-5/2) - 384*q^(-7/2) - 1708*q^(-9/2) - 1860*q^(-11/2) - 1620*q^(-13/2) - 968*q^(-15/2) - 628*q^(-17/2) - 304*q^(-19/2) - 180*q^(-21/2) - 56*q^(-23/2) - 28*q^(-25/2))*x1^(5/2)*x2^(19/2) + (8*q^(11/2) + 21*q^(9/2) + 52*q^(7/2) + 20*q^(5/2) - 194*q^(3/2) - 856*q^(1/2) - 2028*q^(-1/2) - 3371*q^(-3/2) - 4076*q^(-5/2) - 3052*q^(-7/2) - 492*q^(-9/2) + 3116*q^(-11/2) + 5580*q^(-13/2) + 6688*q^(-15/2) + 6084*q^(-17/2) + 4672*q^(-19/2) + 3104*q^(-21/2) + 1984*q^(-23/2) + 1096*q^(-25/2) + 604*q^(-27/2) + 320*q^(-29/2) + 140*q^(-31/2) + 56*q^(-33/2) + 28*q^(-35/2))*x1^(7/2)*x2^(19/2) + (8*q^(5/2) + 56*q^(3/2) + 212*q^(1/2) + 568*q^(-1/2) + 1172*q^(-3/2) + 1872*q^(-5/2) + 2220*q^(-7/2) + 1692*q^(-9/2) - 232*q^(-11/2) - 3516*q^(-13/2) - 7432*q^(-15/2) - 10584*q^(-17/2) - 12576*q^(-19/2) - 12200*q^(-21/2) - 10540*q^(-23/2) - 7976*q^(-25/2) - 5584*q^(-27/2) - 3432*q^(-29/2) - 2096*q^(-31/2) - 1132*q^(-33/2) - 632*q^(-35/2) - 300*q^(-37/2) - 140*q^(-39/2) - 56*q^(-41/2) - 28*q^(-43/2))*x1^(9/2)*x2^(19/2) + (-4*q^(3/2) - 20*q^(1/2) - 60*q^(-1/2) - 144*q^(-3/2) - 240*q^(-5/2) - 320*q^(-7/2) - 156*q^(-9/2) + 368*q^(-11/2) + 1592*q^(-13/2) + 3468*q^(-15/2) + 6064*q^(-17/2) + 8672*q^(-19/2) + 11228*q^(-21/2) + 12712*q^(-23/2) + 13068*q^(-25/2) + 12032*q^(-27/2) + 10348*q^(-29/2) + 7880*q^(-31/2) + 5592*q^(-33/2) + 3608*q^(-35/2) + 2228*q^(-37/2) + 1232*q^(-39/2) + 648*q^(-41/2) + 312*q^(-43/2) + 160*q^(-45/2) + 56*q^(-47/2) + 28*q^(-49/2))*x1^(11/2)*x2^(19/2) + (-4*q^(-5/2) - 28*q^(-7/2) - 96*q^(-9/2) - 248*q^(-11/2) - 544*q^(-13/2) - 1040*q^(-15/2) - 1780*q^(-17/2) - 2728*q^(-19/2) - 3844*q^(-21/2) - 4992*q^(-23/2) - 6044*q^(-25/2) - 6724*q^(-27/2) - 7048*q^(-29/2) - 6852*q^(-31/2) - 6292*q^(-33/2) - 5280*q^(-35/2) - 4180*q^(-37/2) - 3032*q^(-39/2) - 2132*q^(-41/2) - 1264*q^(-43/2) - 720*q^(-45/2) - 376*q^(-47/2) - 184*q^(-49/2) - 76*q^(-51/2) - 28*q^(-53/2))*x1^(13/2)*x2^(19/2) + (4*q^(-7/2) + 8*q^(-9/2) + 28*q^(-11/2) + 56*q^(-13/2) + 116*q^(-15/2) + 192*q^(-17/2) + 328*q^(-19/2) + 472*q^(-21/2) + 680*q^(-23/2) + 880*q^(-25/2) + 1112*q^(-27/2) + 1280*q^(-29/2) + 1460*q^(-31/2) + 1512*q^(-33/2) + 1552*q^(-35/2) + 1456*q^(-37/2) + 1336*q^(-39/2) + 1112*q^(-41/2) + 944*q^(-43/2) + 688*q^(-45/2) + 500*q^(-47/2) + 312*q^(-49/2) + 196*q^(-51/2) + 96*q^(-53/2) + 64*q^(-55/2))*x1^(15/2)*x2^(19/2)
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(-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]}
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(-q^(1/2))*x1^(1/2)*x2^(5/2) + (-4*q^(1/2))*x1^(1/2)*x2^(7/2) + (4*q^(-1/2))*x1^(3/2)*x2^(7/2) + (2*q^(3/2) - 10*q^(1/2))*x1^(1/2)*x2^(9/2) + (16*q^(-1/2) + 8*q^(-3/2))*x1^(3/2)*x2^(9/2) + (-q^(-1/2) - 6*q^(-3/2) - 9*q^(-5/2))*x1^(5/2)*x2^(9/2) + (4*q^(5/2) + 8*q^(3/2) - 20*q^(1/2))*x1^(1/2)*x2^(11/2) + (-4*q^(3/2) - 8*q^(1/2) + 40*q^(-1/2) + 32*q^(-3/2) + 12*q^(-5/2))*x1^(3/2)*x2^(11/2) + (-4*q^(-1/2) - 28*q^(-3/2) - 56*q^(-5/2) - 28*q^(-7/2) - 12*q^(-9/2))*x1^(5/2)*x2^(11/2) + (4*q^(-3/2) + 8*q^(-5/2) + 20*q^(-7/2) + 16*q^(-9/2) + 16*q^(-11/2))*x1^(7/2)*x2^(11/2) + (4*q^(7/2) + 15*q^(5/2) + 20*q^(3/2) - 35*q^(1/2))*x1^(1/2)*x2^(13/2) + (-8*q^(5/2) - 32*q^(3/2) - 44*q^(1/2) + 64*q^(-1/2) + 80*q^(-3/2) + 48*q^(-5/2) + 16*q^(-7/2))*x1^(3/2)*x2^(13/2) + (4*q^(3/2) + 18*q^(1/2) + 14*q^(-1/2) - 58*q^(-3/2) - 180*q^(-5/2) - 156*q^(-7/2) - 106*q^(-9/2) - 32*q^(-11/2) - 16*q^(-13/2))*x1^(5/2)*x2^(13/2) + (16*q^(-3/2) + 48*q^(-5/2) + 120*q^(-7/2) + 152*q^(-9/2) + 160*q^(-11/2) + 88*q^(-13/2) + 40*q^(-15/2) + 16*q^(-17/2))*x1^(7/2)*x2^(13/2) + (-q^(-3/2) - 6*q^(-5/2) - 17*q^(-7/2) - 30*q^(-9/2) - 44*q^(-11/2) - 54*q^(-13/2) - 49*q^(-15/2) - 30*q^(-17/2) - 25*q^(-19/2))*x1^(9/2)*x2^(13/2) + (-4*q^(11/2) + 4*q^(9/2) + 12*q^(7/2) + 36*q^(5/2) + 40*q^(3/2) - 56*q^(1/2))*x1^(1/2)*x2^(15/2) + (4*q^(9/2) - 7*q^(7/2) - 44*q^(5/2) - 124*q^(3/2) - 160*q^(1/2) + 56*q^(-1/2) + 136*q^(-3/2) + 120*q^(-5/2) + 64*q^(-7/2) + 20*q^(-9/2))*x1^(3/2)*x2^(15/2) + (8*q^(5/2) + 52*q^(3/2) + 136*q^(1/2) + 180*q^(-1/2) + 16*q^(-3/2) - 344*q^(-5/2) - 452*q^(-7/2) - 432*q^(-9/2) - 228*q^(-11/2) - 124*q^(-13/2) - 40*q^(-15/2) - 20*q^(-17/2))*x1^(5/2)*x2^(15/2) + (-4*q^(3/2) - 20*q^(1/2) - 48*q^(-1/2) - 36*q^(-3/2) + 60*q^(-5/2) + 344*q^(-7/2) + 592*q^(-9/2) + 788*q^(-11/2) + 648*q^(-13/2) + 456*q^(-15/2) + 248*q^(-17/2) + 112*q^(-19/2) + 40*q^(-21/2) + 20*q^(-23/2))*x1^(7/2)*x2^(15/2) + (-4*q^(-3/2) - 28*q^(-5/2) - 96*q^(-7/2) - 208*q^(-9/2) - 352*q^(-11/2) - 492*q^(-13/2) - 560*q^(-15/2) - 492*q^(-17/2) - 416*q^(-19/2) - 232*q^(-21/2) - 120*q^(-23/2) - 52*q^(-25/2) - 20*q^(-27/2))*x1^(9/2)*x2^(15/2) + (4*q^(-5/2) + 8*q^(-7/2) + 28*q^(-9/2) + 48*q^(-11/2) + 84*q^(-13/2) + 112*q^(-15/2) + 148*q^(-17/2) + 144*q^(-19/2) + 156*q^(-21/2) + 120*q^(-23/2) + 88*q^(-25/2) + 48*q^(-27/2) + 36*q^(-29/2))*x1^(11/2)*x2^(15/2) + (-6*q^(15/2) - 6*q^(13/2) - 12*q^(11/2) + 8*q^(9/2) + 24*q^(7/2) + 70*q^(5/2) + 70*q^(3/2) - 84*q^(1/2))*x1^(1/2)*x2^(17/2) + (8*q^(13/2) + 16*q^(11/2) + 28*q^(9/2) - 16*q^(7/2) - 132*q^(5/2) - 340*q^(3/2) - 440*q^(1/2) - 64*q^(-1/2) + 156*q^(-3/2) + 208*q^(-5/2) + 160*q^(-7/2) + 80*q^(-9/2) + 24*q^(-11/2))*x1^(3/2)*x2^(17/2) + (-2*q^(11/2) - 10*q^(9/2) - 12*q^(7/2) + 44*q^(5/2) + 243*q^(3/2) + 590*q^(1/2) + 860*q^(-1/2) + 618*q^(-3/2) - 219*q^(-5/2) - 784*q^(-7/2) - 1083*q^(-9/2) - 818*q^(-11/2) - 555*q^(-13/2) - 256*q^(-15/2) - 152*q^(-17/2) - 48*q^(-19/2) - 24*q^(-21/2))*x1^(5/2)*x2^(17/2) + (-8*q^(5/2) - 56*q^(3/2) - 192*q^(1/2) - 436*q^(-1/2) - 632*q^(-3/2) - 544*q^(-5/2) + 168*q^(-7/2) + 1168*q^(-9/2) + 2224*q^(-11/2) + 2484*q^(-13/2) + 2240*q^(-15/2) + 1624*q^(-17/2) + 992*q^(-19/2) + 536*q^(-21/2) + 288*q^(-23/2) + 120*q^(-25/2) + 48*q^(-27/2) + 24*q^(-29/2))*x1^(7/2)*x2^(17/2) + (4*q^(3/2) + 20*q^(1/2) + 58*q^(-1/2) + 110*q^(-3/2) + 126*q^(-5/2) - 36*q^(-7/2) - 440*q^(-9/2) - 1148*q^(-11/2) - 2030*q^(-13/2) - 2808*q^(-15/2) - 3082*q^(-17/2) - 3036*q^(-19/2) - 2384*q^(-21/2) - 1692*q^(-23/2) - 1028*q^(-25/2) - 594*q^(-27/2) - 264*q^(-29/2) - 136*q^(-31/2) - 48*q^(-33/2) - 24*q^(-35/2))*x1^(9/2)*x2^(17/2) + (16*q^(-5/2) + 48*q^(-7/2) + 160*q^(-9/2) + 344*q^(-11/2) + 648*q^(-13/2) + 1016*q^(-15/2) + 1440*q^(-17/2) + 1728*q^(-19/2) + 1952*q^(-21/2) + 1912*q^(-23/2) + 1680*q^(-25/2) + 1312*q^(-27/2) + 968*q^(-29/2) + 568*q^(-31/2) + 304*q^(-33/2) + 152*q^(-35/2) + 64*q^(-37/2) + 24*q^(-39/2))*x1^(11/2)*x2^(17/2) + (-q^(-5/2) - 6*q^(-7/2) - 17*q^(-9/2) - 38*q^(-11/2) - 76*q^(-13/2) - 132*q^(-15/2) - 205*q^(-17/2) - 284*q^(-19/2) - 365*q^(-21/2) - 432*q^(-23/2) - 477*q^(-25/2) - 468*q^(-27/2) - 445*q^(-29/2) - 380*q^(-31/2) - 308*q^(-33/2) - 206*q^(-35/2) - 137*q^(-37/2) - 70*q^(-39/2) - 49*q^(-41/2))*x1^(13/2)*x2^(17/2) + (-4*q^(19/2) - 8*q^(17/2) - 32*q^(15/2) - 16*q^(13/2) - 36*q^(11/2) + 8*q^(9/2) + 40*q^(7/2) + 120*q^(5/2) + 112*q^(3/2) - 120*q^(1/2))*x1^(1/2)*x2^(19/2) + (8*q^(17/2) + 24*q^(15/2) + 78*q^(13/2) + 108*q^(11/2) + 152*q^(9/2) + 34*q^(7/2) - 260*q^(5/2) - 740*q^(3/2) - 996*q^(1/2) - 420*q^(-1/2) + 32*q^(-3/2) + 256*q^(-5/2) + 280*q^(-7/2) + 200*q^(-9/2) + 96*q^(-11/2) + 28*q^(-13/2))*x1^(3/2)*x2^(19/2) + (-4*q^(15/2) - 24*q^(13/2) - 68*q^(11/2) - 148*q^(9/2) - 172*q^(7/2) - 4*q^(5/2) + 656*q^(3/2) + 1752*q^(1/2) + 2800*q^(-1/2) + 2740*q^(-3/2) + 1216*q^(-5/2) - 384*q^(-7/2) - 1708*q^(-9/2) - 1860*q^(-11/2) - 1620*q^(-13/2) - 968*q^(-15/2) - 628*q^(-17/2) - 304*q^(-19/2) - 180*q^(-21/2) - 56*q^(-23/2) - 28*q^(-25/2))*x1^(5/2)*x2^(19/2) + (8*q^(11/2) + 21*q^(9/2) + 52*q^(7/2) + 20*q^(5/2) - 194*q^(3/2) - 856*q^(1/2) - 2028*q^(-1/2) - 3371*q^(-3/2) - 4076*q^(-5/2) - 3052*q^(-7/2) - 492*q^(-9/2) + 3116*q^(-11/2) + 5580*q^(-13/2) + 6688*q^(-15/2) + 6084*q^(-17/2) + 4672*q^(-19/2) + 3104*q^(-21/2) + 1984*q^(-23/2) + 1096*q^(-25/2) + 604*q^(-27/2) + 320*q^(-29/2) + 140*q^(-31/2) + 56*q^(-33/2) + 28*q^(-35/2))*x1^(7/2)*x2^(19/2) + (8*q^(5/2) + 56*q^(3/2) + 212*q^(1/2) + 568*q^(-1/2) + 1172*q^(-3/2) + 1872*q^(-5/2) + 2220*q^(-7/2) + 1692*q^(-9/2) - 232*q^(-11/2) - 3516*q^(-13/2) - 7432*q^(-15/2) - 10584*q^(-17/2) - 12576*q^(-19/2) - 12200*q^(-21/2) - 10540*q^(-23/2) - 7976*q^(-25/2) - 5584*q^(-27/2) - 3432*q^(-29/2) - 2096*q^(-31/2) - 1132*q^(-33/2) - 632*q^(-35/2) - 300*q^(-37/2) - 140*q^(-39/2) - 56*q^(-41/2) - 28*q^(-43/2))*x1^(9/2)*x2^(19/2) + (-4*q^(3/2) - 20*q^(1/2) - 60*q^(-1/2) - 144*q^(-3/2) - 240*q^(-5/2) - 320*q^(-7/2) - 156*q^(-9/2) + 368*q^(-11/2) + 1592*q^(-13/2) + 3468*q^(-15/2) + 6064*q^(-17/2) + 8672*q^(-19/2) + 11228*q^(-21/2) + 12712*q^(-23/2) + 13068*q^(-25/2) + 12032*q^(-27/2) + 10348*q^(-29/2) + 7880*q^(-31/2) + 5592*q^(-33/2) + 3608*q^(-35/2) + 2228*q^(-37/2) + 1232*q^(-39/2) + 648*q^(-41/2) + 312*q^(-43/2) + 160*q^(-45/2) + 56*q^(-47/2) + 28*q^(-49/2))*x1^(11/2)*x2^(19/2) + (-4*q^(-5/2) - 28*q^(-7/2) - 96*q^(-9/2) - 248*q^(-11/2) - 544*q^(-13/2) - 1040*q^(-15/2) - 1780*q^(-17/2) - 2728*q^(-19/2) - 3844*q^(-21/2) - 4992*q^(-23/2) - 6044*q^(-25/2) - 6724*q^(-27/2) - 7048*q^(-29/2) - 6852*q^(-31/2) - 6292*q^(-33/2) - 5280*q^(-35/2) - 4180*q^(-37/2) - 3032*q^(-39/2) - 2132*q^(-41/2) - 1264*q^(-43/2) - 720*q^(-45/2) - 376*q^(-47/2) - 184*q^(-49/2) - 76*q^(-51/2) - 28*q^(-53/2))*x1^(13/2)*x2^(19/2) + (4*q^(-7/2) + 8*q^(-9/2) + 28*q^(-11/2) + 56*q^(-13/2) + 116*q^(-15/2) + 192*q^(-17/2) + 328*q^(-19/2) + 472*q^(-21/2) + 680*q^(-23/2) + 880*q^(-25/2) + 1112*q^(-27/2) + 1280*q^(-29/2) + 1460*q^(-31/2) + 1512*q^(-33/2) + 1552*q^(-35/2) + 1456*q^(-37/2) + 1336*q^(-39/2) + 1112*q^(-41/2) + 944*q^(-43/2) + 688*q^(-45/2) + 500*q^(-47/2) + 312*q^(-49/2) + 196*q^(-51/2) + 96*q^(-53/2) + 64*q^(-55/2))*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) + (4*q^(-1/2))*x1^(-3/2)*x2^(-7/2) + (2*q^(3/2) - 10*q^(1/2))*x1^(-1/2)*x2^(-9/2) + (16*q^(-1/2) + 8*q^(-3/2))*x1^(-3/2)*x2^(-9/2) + (-q^(-1/2) - 6*q^(-3/2) - 9*q^(-5/2))*x1^(-5/2)*x2^(-9/2) + (4*q^(5/2) + 8*q^(3/2) - 20*q^(1/2))*x1^(-1/2)*x2^(-11/2) + (-4*q^(3/2) - 8*q^(1/2) + 40*q^(-1/2) + 32*q^(-3/2) + 12*q^(-5/2))*x1^(-3/2)*x2^(-11/2) + (-4*q^(-1/2) - 28*q^(-3/2) - 56*q^(-5/2) - 28*q^(-7/2) - 12*q^(-9/2))*x1^(-5/2)*x2^(-11/2) + (4*q^(-3/2) + 8*q^(-5/2) + 20*q^(-7/2) + 16*q^(-9/2) + 16*q^(-11/2))*x1^(-7/2)*x2^(-11/2) + (4*q^(7/2) + 15*q^(5/2) + 20*q^(3/2) - 35*q^(1/2))*x1^(-1/2)*x2^(-13/2) + (-8*q^(5/2) - 32*q^(3/2) - 44*q^(1/2) + 64*q^(-1/2) + 80*q^(-3/2) + 48*q^(-5/2) + 16*q^(-7/2))*x1^(-3/2)*x2^(-13/2) + (4*q^(3/2) + 18*q^(1/2) + 14*q^(-1/2) - 58*q^(-3/2) - 180*q^(-5/2) - 156*q^(-7/2) - 106*q^(-9/2) - 32*q^(-11/2) - 16*q^(-13/2))*x1^(-5/2)*x2^(-13/2) + (16*q^(-3/2) + 48*q^(-5/2) + 120*q^(-7/2) + 152*q^(-9/2) + 160*q^(-11/2) + 88*q^(-13/2) + 40*q^(-15/2) + 16*q^(-17/2))*x1^(-7/2)*x2^(-13/2) + (-q^(-3/2) - 6*q^(-5/2) - 17*q^(-7/2) - 30*q^(-9/2) - 44*q^(-11/2) - 54*q^(-13/2) - 49*q^(-15/2) - 30*q^(-17/2) - 25*q^(-19/2))*x1^(-9/2)*x2^(-13/2) + (-4*q^(11/2) + 4*q^(9/2) + 12*q^(7/2) + 36*q^(5/2) + 40*q^(3/2) - 56*q^(1/2))*x1^(-1/2)*x2^(-15/2) + (4*q^(9/2) - 7*q^(7/2) - 44*q^(5/2) - 124*q^(3/2) - 160*q^(1/2) + 56*q^(-1/2) + 136*q^(-3/2) + 120*q^(-5/2) + 64*q^(-7/2) + 20*q^(-9/2))*x1^(-3/2)*x2^(-15/2) + (8*q^(5/2) + 52*q^(3/2) + 136*q^(1/2) + 180*q^(-1/2) + 16*q^(-3/2) - 344*q^(-5/2) - 452*q^(-7/2) - 432*q^(-9/2) - 228*q^(-11/2) - 124*q^(-13/2) - 40*q^(-15/2) - 20*q^(-17/2))*x1^(-5/2)*x2^(-15/2) + (-4*q^(3/2) - 20*q^(1/2) - 48*q^(-1/2) - 36*q^(-3/2) + 60*q^(-5/2) + 344*q^(-7/2) + 592*q^(-9/2) + 788*q^(-11/2) + 648*q^(-13/2) + 456*q^(-15/2) + 248*q^(-17/2) + 112*q^(-19/2) + 40*q^(-21/2) + 20*q^(-23/2))*x1^(-7/2)*x2^(-15/2) + (-4*q^(-3/2) - 28*q^(-5/2) - 96*q^(-7/2) - 208*q^(-9/2) - 352*q^(-11/2) - 492*q^(-13/2) - 560*q^(-15/2) - 492*q^(-17/2) - 416*q^(-19/2) - 232*q^(-21/2) - 120*q^(-23/2) - 52*q^(-25/2) - 20*q^(-27/2))*x1^(-9/2)*x2^(-15/2) + (4*q^(-5/2) + 8*q^(-7/2) + 28*q^(-9/2) + 48*q^(-11/2) + 84*q^(-13/2) + 112*q^(-15/2) + 148*q^(-17/2) + 144*q^(-19/2) + 156*q^(-21/2) + 120*q^(-23/2) + 88*q^(-25/2) + 48*q^(-27/2) + 36*q^(-29/2))*x1^(-11/2)*x2^(-15/2) + (-6*q^(15/2) - 6*q^(13/2) - 12*q^(11/2) + 8*q^(9/2) + 24*q^(7/2) + 70*q^(5/2) + 70*q^(3/2) - 84*q^(1/2))*x1^(-1/2)*x2^(-17/2) + (8*q^(13/2) + 16*q^(11/2) + 28*q^(9/2) - 16*q^(7/2) - 132*q^(5/2) - 340*q^(3/2) - 440*q^(1/2) - 64*q^(-1/2) + 156*q^(-3/2) + 208*q^(-5/2) + 160*q^(-7/2) + 80*q^(-9/2) + 24*q^(-11/2))*x1^(-3/2)*x2^(-17/2) + (-2*q^(11/2) - 10*q^(9/2) - 12*q^(7/2) + 44*q^(5/2) + 243*q^(3/2) + 590*q^(1/2) + 860*q^(-1/2) + 618*q^(-3/2) - 219*q^(-5/2) - 784*q^(-7/2) - 1083*q^(-9/2) - 818*q^(-11/2) - 555*q^(-13/2) - 256*q^(-15/2) - 152*q^(-17/2) - 48*q^(-19/2) - 24*q^(-21/2))*x1^(-5/2)*x2^(-17/2) + (-8*q^(5/2) - 56*q^(3/2) - 192*q^(1/2) - 436*q^(-1/2) - 632*q^(-3/2) - 544*q^(-5/2) + 168*q^(-7/2) + 1168*q^(-9/2) + 2224*q^(-11/2) + 2484*q^(-13/2) + 2240*q^(-15/2) + 1624*q^(-17/2) + 992*q^(-19/2) + 536*q^(-21/2) + 288*q^(-23/2) + 120*q^(-25/2) + 48*q^(-27/2) + 24*q^(-29/2))*x1^(-7/2)*x2^(-17/2) + (4*q^(3/2) + 20*q^(1/2) + 58*q^(-1/2) + 110*q^(-3/2) + 126*q^(-5/2) - 36*q^(-7/2) - 440*q^(-9/2) - 1148*q^(-11/2) - 2030*q^(-13/2) - 2808*q^(-15/2) - 3082*q^(-17/2) - 3036*q^(-19/2) - 2384*q^(-21/2) - 1692*q^(-23/2) - 1028*q^(-25/2) - 594*q^(-27/2) - 264*q^(-29/2) - 136*q^(-31/2) - 48*q^(-33/2) - 24*q^(-35/2))*x1^(-9/2)*x2^(-17/2) + (16*q^(-5/2) + 48*q^(-7/2) + 160*q^(-9/2) + 344*q^(-11/2) + 648*q^(-13/2) + 1016*q^(-15/2) + 1440*q^(-17/2) + 1728*q^(-19/2) + 1952*q^(-21/2) + 1912*q^(-23/2) + 1680*q^(-25/2) + 1312*q^(-27/2) + 968*q^(-29/2) + 568*q^(-31/2) + 304*q^(-33/2) + 152*q^(-35/2) + 64*q^(-37/2) + 24*q^(-39/2))*x1^(-11/2)*x2^(-17/2) + (-q^(-5/2) - 6*q^(-7/2) - 17*q^(-9/2) - 38*q^(-11/2) - 76*q^(-13/2) - 132*q^(-15/2) - 205*q^(-17/2) - 284*q^(-19/2) - 365*q^(-21/2) - 432*q^(-23/2) - 477*q^(-25/2) - 468*q^(-27/2) - 445*q^(-29/2) - 380*q^(-31/2) - 308*q^(-33/2) - 206*q^(-35/2) - 137*q^(-37/2) - 70*q^(-39/2) - 49*q^(-41/2))*x1^(-13/2)*x2^(-17/2) + (-4*q^(19/2) - 8*q^(17/2) - 32*q^(15/2) - 16*q^(13/2) - 36*q^(11/2) + 8*q^(9/2) + 40*q^(7/2) + 120*q^(5/2) + 112*q^(3/2) - 120*q^(1/2))*x1^(-1/2)*x2^(-19/2) + (8*q^(17/2) + 24*q^(15/2) + 78*q^(13/2) + 108*q^(11/2) + 152*q^(9/2) + 34*q^(7/2) - 260*q^(5/2) - 740*q^(3/2) - 996*q^(1/2) - 420*q^(-1/2) + 32*q^(-3/2) + 256*q^(-5/2) + 280*q^(-7/2) + 200*q^(-9/2) + 96*q^(-11/2) + 28*q^(-13/2))*x1^(-3/2)*x2^(-19/2) + (-4*q^(15/2) - 24*q^(13/2) - 68*q^(11/2) - 148*q^(9/2) - 172*q^(7/2) - 4*q^(5/2) + 656*q^(3/2) + 1752*q^(1/2) + 2800*q^(-1/2) + 2740*q^(-3/2) + 1216*q^(-5/2) - 384*q^(-7/2) - 1708*q^(-9/2) - 1860*q^(-11/2) - 1620*q^(-13/2) - 968*q^(-15/2) - 628*q^(-17/2) - 304*q^(-19/2) - 180*q^(-21/2) - 56*q^(-23/2) - 28*q^(-25/2))*x1^(-5/2)*x2^(-19/2) + (8*q^(11/2) + 21*q^(9/2) + 52*q^(7/2) + 20*q^(5/2) - 194*q^(3/2) - 856*q^(1/2) - 2028*q^(-1/2) - 3371*q^(-3/2) - 4076*q^(-5/2) - 3052*q^(-7/2) - 492*q^(-9/2) + 3116*q^(-11/2) + 5580*q^(-13/2) + 6688*q^(-15/2) + 6084*q^(-17/2) + 4672*q^(-19/2) + 3104*q^(-21/2) + 1984*q^(-23/2) + 1096*q^(-25/2) + 604*q^(-27/2) + 320*q^(-29/2) + 140*q^(-31/2) + 56*q^(-33/2) + 28*q^(-35/2))*x1^(-7/2)*x2^(-19/2) + (8*q^(5/2) + 56*q^(3/2) + 212*q^(1/2) + 568*q^(-1/2) + 1172*q^(-3/2) + 1872*q^(-5/2) + 2220*q^(-7/2) + 1692*q^(-9/2) - 232*q^(-11/2) - 3516*q^(-13/2) - 7432*q^(-15/2) - 10584*q^(-17/2) - 12576*q^(-19/2) - 12200*q^(-21/2) - 10540*q^(-23/2) - 7976*q^(-25/2) - 5584*q^(-27/2) - 3432*q^(-29/2) - 2096*q^(-31/2) - 1132*q^(-33/2) - 632*q^(-35/2) - 300*q^(-37/2) - 140*q^(-39/2) - 56*q^(-41/2) - 28*q^(-43/2))*x1^(-9/2)*x2^(-19/2) + (-4*q^(3/2) - 20*q^(1/2) - 60*q^(-1/2) - 144*q^(-3/2) - 240*q^(-5/2) - 320*q^(-7/2) - 156*q^(-9/2) + 368*q^(-11/2) + 1592*q^(-13/2) + 3468*q^(-15/2) + 6064*q^(-17/2) + 8672*q^(-19/2) + 11228*q^(-21/2) + 12712*q^(-23/2) + 13068*q^(-25/2) + 12032*q^(-27/2) + 10348*q^(-29/2) + 7880*q^(-31/2) + 5592*q^(-33/2) + 3608*q^(-35/2) + 2228*q^(-37/2) + 1232*q^(-39/2) + 648*q^(-41/2) + 312*q^(-43/2) + 160*q^(-45/2) + 56*q^(-47/2) + 28*q^(-49/2))*x1^(-11/2)*x2^(-19/2) + (-4*q^(-5/2) - 28*q^(-7/2) - 96*q^(-9/2) - 248*q^(-11/2) - 544*q^(-13/2) - 1040*q^(-15/2) - 1780*q^(-17/2) - 2728*q^(-19/2) - 3844*q^(-21/2) - 4992*q^(-23/2) - 6044*q^(-25/2) - 6724*q^(-27/2) - 7048*q^(-29/2) - 6852*q^(-31/2) - 6292*q^(-33/2) - 5280*q^(-35/2) - 4180*q^(-37/2) - 3032*q^(-39/2) - 2132*q^(-41/2) - 1264*q^(-43/2) - 720*q^(-45/2) - 376*q^(-47/2) - 184*q^(-49/2) - 76*q^(-51/2) - 28*q^(-53/2))*x1^(-13/2)*x2^(-19/2) + (4*q^(-7/2) + 8*q^(-9/2) + 28*q^(-11/2) + 56*q^(-13/2) + 116*q^(-15/2) + 192*q^(-17/2) + 328*q^(-19/2) + 472*q^(-21/2) + 680*q^(-23/2) + 880*q^(-25/2) + 1112*q^(-27/2) + 1280*q^(-29/2) + 1460*q^(-31/2) + 1512*q^(-33/2) + 1552*q^(-35/2) + 1456*q^(-37/2) + 1336*q^(-39/2) + 1112*q^(-41/2) + 944*q^(-43/2) + 688*q^(-45/2) + 500*q^(-47/2) + 312*q^(-49/2) + 196*q^(-51/2) + 96*q^(-53/2) + 64*q^(-55/2))*x1^(-15/2)*x2^(-19/2)
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Braid
| Braid word |
Components |
Crossings |
Strands |
[1, -2, 3, 3, -2, 1, -2, 3, -2, 1] |
2 |
10 |
4 |
Multivariable Alexander polynomial
| ΔL |
-A1^(1/2)*A2^(5/2) + 4*A1^(1/2)*A2^(3/2) - 8*A1^(1/2)*A2^(1/2) + 8*A1^(1/2)*A2^(-1/2) - 4*A1^(1/2)*A2^(-3/2) - 4*A1^(-1/2)*A2^(3/2) + 8*A1^(-1/2)*A2^(1/2) - 8*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.
Dual Thurston polytope
| Vertex | Dual to fibered face |
(-1, -5) |
yes |
(1, -3) |
no |
(1, 5) |
yes |
(-1, 3) |
no |
HFL polytope
| Poincaré polynomial |
m^(-5)*A1^(-1)*A2^(-3) + 5*m^(-4)*A1^(-1)*A2^(-2) + m^(-4)*A2^(-3) + 12*m^(-3)*A1^(-1)*A2^(-1) + 9*m^(-3)*A2^(-2) + 16*m^(-2)*A1^(-1) + 24*m^(-2)*A2^(-1) + 4*m^(-2)*A1*A2^(-2) + 12*m^(-1)*A1^(-1)*A2 + 32*m^(-1) + 12*m^(-1)*A1*A2^(-1) + 4*A1^(-1)*A2^2 + 24*A2 + 16*A1 + 9*m*A2^2 + 12*m*A1*A2 + m^2*A2^3 + 5*m^2*A1*A2^2 + m^3*A1*A2^3 |
| Vertex | Maslov | Rank |
(-1, -3) | -5 | 1 |
(0, -3) | -4 | 1 |
(1, -2) | -2 | 4 |
(1, 3) | 3 | 1 |
(0, 3) | 2 | 1 |
(-1, 2) | 0 | 4 |
Record
FL/HFL Links
orderOption(int) |
355 |
namestring |
L10a43{0} |
statusstring |
success |
slugstring |
L10a43_0_451cb26d |
result_filestring |
details/L10a43_0_451cb26d.json |
complexity_scoreOption(int) |
200 |
strandsOption(int) |
null |
crossingsOption(int) |
10 |
component_countOption(int) |
2 |
girthOption(int) |
6 |
total_rankOption(int) |
200 |
wall_secondsOption(float) |
0.003625 |
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": "L10a43_0_451cb26d"
} |
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L10a43_0_451cb26d |