details/L10a49_1_0173a314.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]}
|
|
(-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) + (-10*q^(-1/2))*x1^(1/2)*x2^(9/2) + (8*q^(3/2) + 16*q^(1/2) + 2*q^(-1/2))*x1^(3/2)*x2^(9/2) + (-9*q^(5/2) - 6*q^(3/2) - q^(1/2))*x1^(5/2)*x2^(9/2) + (-20*q^(-1/2) - 2*q^(-5/2))*x1^(1/2)*x2^(11/2) + (12*q^(5/2) + 32*q^(3/2) + 46*q^(1/2) + 8*q^(-1/2) + 4*q^(-3/2))*x1^(3/2)*x2^(11/2) + (-12*q^(9/2) - 28*q^(7/2) - 56*q^(5/2) - 34*q^(3/2) - 12*q^(1/2) - 2*q^(-1/2))*x1^(5/2)*x2^(11/2) + (16*q^(11/2) + 16*q^(9/2) + 20*q^(7/2) + 8*q^(5/2) + 4*q^(3/2))*x1^(7/2)*x2^(11/2) + (-35*q^(-1/2) - 7*q^(-5/2) - 5*q^(-7/2) - q^(-9/2))*x1^(1/2)*x2^(13/2) + (16*q^(7/2) + 48*q^(5/2) + 90*q^(3/2) + 104*q^(1/2) + 32*q^(-1/2) + 22*q^(-3/2) + 10*q^(-5/2) + 2*q^(-7/2))*x1^(3/2)*x2^(13/2) + (-16*q^(13/2) - 32*q^(11/2) - 106*q^(9/2) - 166*q^(7/2) - 212*q^(5/2) - 130*q^(3/2) - 62*q^(1/2) - 24*q^(-1/2) - 7*q^(-3/2) - q^(-5/2))*x1^(5/2)*x2^(13/2) + (16*q^(17/2) + 40*q^(15/2) + 88*q^(13/2) + 160*q^(11/2) + 164*q^(9/2) + 142*q^(7/2) + 78*q^(5/2) + 36*q^(3/2) + 10*q^(1/2) + 2*q^(-1/2))*x1^(7/2)*x2^(13/2) + (-25*q^(19/2) - 30*q^(17/2) - 49*q^(15/2) - 54*q^(13/2) - 44*q^(11/2) - 30*q^(9/2) - 17*q^(7/2) - 6*q^(5/2) - q^(3/2))*x1^(9/2)*x2^(13/2) + (-56*q^(-1/2) - 16*q^(-5/2) - 18*q^(-7/2) - 10*q^(-9/2) - 2*q^(-11/2) - 2*q^(-13/2))*x1^(1/2)*x2^(15/2) + (20*q^(9/2) + 64*q^(7/2) + 134*q^(5/2) + 200*q^(3/2) + 220*q^(1/2) + 98*q^(-1/2) + 90*q^(-3/2) + 62*q^(-5/2) + 29*q^(-7/2) + 8*q^(-9/2) + 4*q^(-11/2))*x1^(3/2)*x2^(15/2) + (-20*q^(17/2) - 40*q^(15/2) - 124*q^(13/2) - 242*q^(11/2) - 474*q^(9/2) - 594*q^(7/2) - 638*q^(5/2) - 424*q^(3/2) - 260*q^(1/2) - 146*q^(-1/2) - 78*q^(-3/2) - 28*q^(-5/2) - 10*q^(-7/2) - 2*q^(-9/2))*x1^(5/2)*x2^(15/2) + (20*q^(23/2) + 40*q^(21/2) + 112*q^(19/2) + 248*q^(17/2) + 470*q^(15/2) + 696*q^(13/2) + 908*q^(11/2) + 836*q^(9/2) + 680*q^(7/2) + 412*q^(5/2) + 234*q^(3/2) + 100*q^(1/2) + 44*q^(-1/2) + 12*q^(-3/2) + 4*q^(-5/2))*x1^(7/2)*x2^(15/2) + (-20*q^(27/2) - 52*q^(25/2) - 120*q^(23/2) - 232*q^(21/2) - 416*q^(19/2) - 512*q^(17/2) - 602*q^(15/2) - 566*q^(13/2) - 452*q^(11/2) - 306*q^(9/2) - 180*q^(7/2) - 82*q^(5/2) - 32*q^(3/2) - 10*q^(1/2) - 2*q^(-1/2))*x1^(9/2)*x2^(15/2) + (36*q^(29/2) + 48*q^(27/2) + 88*q^(25/2) + 120*q^(23/2) + 156*q^(21/2) + 144*q^(19/2) + 148*q^(17/2) + 112*q^(15/2) + 84*q^(13/2) + 48*q^(11/2) + 28*q^(9/2) + 8*q^(7/2) + 4*q^(5/2))*x1^(11/2)*x2^(15/2) + (-84*q^(-1/2) - 30*q^(-5/2) - 42*q^(-7/2) - 33*q^(-9/2) - 14*q^(-11/2) - 9*q^(-13/2) - 4*q^(-15/2) - 3*q^(-17/2) - q^(-19/2))*x1^(1/2)*x2^(17/2) + (24*q^(11/2) + 80*q^(9/2) + 178*q^(7/2) + 296*q^(5/2) + 408*q^(3/2) + 438*q^(1/2) + 272*q^(-1/2) + 282*q^(-3/2) + 240*q^(-5/2) + 150*q^(-7/2) + 74*q^(-9/2) + 36*q^(-11/2) + 16*q^(-13/2) + 8*q^(-15/2) + 2*q^(-17/2))*x1^(3/2)*x2^(17/2) + (-24*q^(21/2) - 48*q^(19/2) - 152*q^(17/2) - 274*q^(15/2) - 609*q^(13/2) - 996*q^(11/2) - 1517*q^(9/2) - 1708*q^(7/2) - 1717*q^(5/2) - 1285*q^(3/2) - 955*q^(1/2) - 683*q^(-1/2) - 454*q^(-3/2) - 246*q^(-5/2) - 121*q^(-7/2) - 50*q^(-9/2) - 21*q^(-11/2) - 7*q^(-13/2) - q^(-15/2))*x1^(5/2)*x2^(17/2) + (24*q^(29/2) + 48*q^(27/2) + 120*q^(25/2) + 288*q^(23/2) + 554*q^(21/2) + 1046*q^(19/2) + 1778*q^(17/2) + 2630*q^(15/2) + 3316*q^(13/2) + 3658*q^(11/2) + 3280*q^(9/2) + 2642*q^(7/2) + 1826*q^(5/2) + 1196*q^(3/2) + 704*q^(1/2) + 392*q^(-1/2) + 188*q^(-3/2) + 84*q^(-5/2) + 30*q^(-7/2) + 10*q^(-9/2) + 2*q^(-11/2))*x1^(7/2)*x2^(17/2) + (-24*q^(35/2) - 48*q^(33/2) - 136*q^(31/2) - 264*q^(29/2) - 594*q^(27/2) - 1046*q^(25/2) - 1756*q^(23/2) - 2552*q^(21/2) - 3400*q^(19/2) - 3786*q^(17/2) - 3876*q^(15/2) - 3426*q^(13/2) - 2707*q^(11/2) - 1901*q^(9/2) - 1211*q^(7/2) - 681*q^(5/2) - 356*q^(3/2) - 166*q^(1/2) - 69*q^(-1/2) - 25*q^(-3/2) - 7*q^(-5/2) - q^(-7/2))*x1^(9/2)*x2^(17/2) + (24*q^(39/2) + 64*q^(37/2) + 152*q^(35/2) + 304*q^(33/2) + 568*q^(31/2) + 968*q^(29/2) + 1342*q^(27/2) + 1748*q^(25/2) + 2046*q^(23/2) + 2168*q^(21/2) + 2034*q^(19/2) + 1790*q^(17/2) + 1392*q^(15/2) + 996*q^(13/2) + 630*q^(11/2) + 364*q^(9/2) + 180*q^(7/2) + 84*q^(5/2) + 30*q^(3/2) + 10*q^(1/2) + 2*q^(-1/2))*x1^(11/2)*x2^(17/2) + (-49*q^(41/2) - 70*q^(39/2) - 137*q^(37/2) - 206*q^(35/2) - 308*q^(33/2) - 380*q^(31/2) - 445*q^(29/2) - 468*q^(27/2) - 477*q^(25/2) - 432*q^(23/2) - 365*q^(21/2) - 284*q^(19/2) - 205*q^(17/2) - 132*q^(15/2) - 76*q^(13/2) - 38*q^(11/2) - 17*q^(9/2) - 6*q^(7/2) - q^(5/2))*x1^(13/2)*x2^(17/2) + (-120*q^(-1/2) - 50*q^(-5/2) - 80*q^(-7/2) - 76*q^(-9/2) - 46*q^(-11/2) - 30*q^(-13/2) - 16*q^(-15/2) - 18*q^(-17/2) - 10*q^(-19/2) - 6*q^(-21/2) - 2*q^(-23/2) - 2*q^(-25/2))*x1^(1/2)*x2^(19/2) + (28*q^(13/2) + 96*q^(11/2) + 222*q^(9/2) + 392*q^(7/2) + 596*q^(5/2) + 778*q^(3/2) + 860*q^(1/2) + 674*q^(-1/2) + 756*q^(-3/2) + 710*q^(-5/2) + 536*q^(-7/2) + 332*q^(-9/2) + 198*q^(-11/2) + 116*q^(-13/2) + 78*q^(-15/2) + 40*q^(-17/2) + 20*q^(-19/2) + 8*q^(-21/2) + 4*q^(-23/2))*x1^(3/2)*x2^(19/2) + (-28*q^(25/2) - 56*q^(23/2) - 180*q^(21/2) - 326*q^(19/2) - 694*q^(17/2) - 1190*q^(15/2) - 2142*q^(13/2) - 3062*q^(11/2) - 4070*q^(9/2) - 4390*q^(7/2) - 4398*q^(5/2) - 3704*q^(3/2) - 3174*q^(1/2) - 2594*q^(-1/2) - 1974*q^(-3/2) - 1294*q^(-5/2) - 788*q^(-7/2) - 430*q^(-9/2) - 242*q^(-11/2) - 124*q^(-13/2) - 60*q^(-15/2) - 24*q^(-17/2) - 10*q^(-19/2) - 2*q^(-21/2))*x1^(5/2)*x2^(19/2) + (28*q^(35/2) + 56*q^(33/2) + 140*q^(31/2) + 320*q^(29/2) + 626*q^(27/2) + 1162*q^(25/2) + 2160*q^(23/2) + 3560*q^(21/2) + 5690*q^(19/2) + 8166*q^(17/2) + 10582*q^(15/2) + 12038*q^(13/2) + 12420*q^(11/2) + 11158*q^(9/2) + 9396*q^(7/2) + 7244*q^(5/2) + 5409*q^(3/2) + 3754*q^(1/2) + 2484*q^(-1/2) + 1476*q^(-3/2) + 840*q^(-5/2) + 426*q^(-7/2) + 213*q^(-9/2) + 92*q^(-11/2) + 40*q^(-13/2) + 12*q^(-15/2) + 4*q^(-17/2))*x1^(7/2)*x2^(19/2) + (-28*q^(43/2) - 56*q^(41/2) - 140*q^(39/2) - 300*q^(37/2) - 632*q^(35/2) - 1154*q^(33/2) - 2162*q^(31/2) - 3622*q^(29/2) - 6014*q^(27/2) - 8968*q^(25/2) - 12526*q^(23/2) - 15794*q^(21/2) - 18398*q^(19/2) - 19076*q^(17/2) - 18342*q^(15/2) - 15946*q^(13/2) - 12846*q^(11/2) - 9568*q^(9/2) - 6728*q^(7/2) - 4394*q^(5/2) - 2750*q^(3/2) - 1598*q^(1/2) - 874*q^(-1/2) - 438*q^(-3/2) - 206*q^(-5/2) - 84*q^(-7/2) - 32*q^(-9/2) - 10*q^(-11/2) - 2*q^(-13/2))*x1^(9/2)*x2^(19/2) + (28*q^(49/2) + 56*q^(47/2) + 160*q^(45/2) + 312*q^(43/2) + 648*q^(41/2) + 1232*q^(39/2) + 2250*q^(37/2) + 3688*q^(35/2) + 5808*q^(33/2) + 8364*q^(31/2) + 11324*q^(29/2) + 13828*q^(27/2) + 15922*q^(25/2) + 16792*q^(23/2) + 16532*q^(21/2) + 14908*q^(19/2) + 12686*q^(17/2) + 9880*q^(15/2) + 7268*q^(13/2) + 4908*q^(11/2) + 3152*q^(9/2) + 1848*q^(7/2) + 1050*q^(5/2) + 528*q^(3/2) + 260*q^(1/2) + 108*q^(-1/2) + 44*q^(-3/2) + 12*q^(-5/2) + 4*q^(-7/2))*x1^(11/2)*x2^(19/2) + (-28*q^(53/2) - 76*q^(51/2) - 184*q^(49/2) - 376*q^(47/2) - 720*q^(45/2) - 1264*q^(43/2) - 2132*q^(41/2) - 3074*q^(39/2) - 4280*q^(37/2) - 5490*q^(35/2) - 6660*q^(33/2) - 7442*q^(31/2) - 7882*q^(29/2) - 7786*q^(27/2) - 7300*q^(25/2) - 6368*q^(23/2) - 5240*q^(21/2) - 4030*q^(19/2) - 2918*q^(17/2) - 1954*q^(15/2) - 1226*q^(13/2) - 708*q^(11/2) - 380*q^(9/2) - 184*q^(7/2) - 80*q^(5/2) - 30*q^(3/2) - 10*q^(1/2) - 2*q^(-1/2))*x1^(13/2)*x2^(19/2) + (64*q^(55/2) + 96*q^(53/2) + 196*q^(51/2) + 312*q^(49/2) + 500*q^(47/2) + 688*q^(45/2) + 944*q^(43/2) + 1112*q^(41/2) + 1336*q^(39/2) + 1456*q^(37/2) + 1552*q^(35/2) + 1512*q^(33/2) + 1460*q^(31/2) + 1280*q^(29/2) + 1112*q^(27/2) + 880*q^(25/2) + 680*q^(23/2) + 472*q^(21/2) + 328*q^(19/2) + 192*q^(17/2) + 116*q^(15/2) + 56*q^(13/2) + 28*q^(11/2) + 8*q^(9/2) + 4*q^(7/2))*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) + (-10*q^(-1/2))*x1^(1/2)*x2^(9/2) + (8*q^(3/2) + 16*q^(1/2) + 2*q^(-1/2))*x1^(3/2)*x2^(9/2) + (-9*q^(5/2) - 6*q^(3/2) - q^(1/2))*x1^(5/2)*x2^(9/2) + (-20*q^(-1/2) - 2*q^(-5/2))*x1^(1/2)*x2^(11/2) + (12*q^(5/2) + 32*q^(3/2) + 46*q^(1/2) + 8*q^(-1/2) + 4*q^(-3/2))*x1^(3/2)*x2^(11/2) + (-12*q^(9/2) - 28*q^(7/2) - 56*q^(5/2) - 34*q^(3/2) - 12*q^(1/2) - 2*q^(-1/2))*x1^(5/2)*x2^(11/2) + (16*q^(11/2) + 16*q^(9/2) + 20*q^(7/2) + 8*q^(5/2) + 4*q^(3/2))*x1^(7/2)*x2^(11/2) + (-35*q^(-1/2) - 7*q^(-5/2) - 5*q^(-7/2) - q^(-9/2))*x1^(1/2)*x2^(13/2) + (16*q^(7/2) + 48*q^(5/2) + 90*q^(3/2) + 104*q^(1/2) + 32*q^(-1/2) + 22*q^(-3/2) + 10*q^(-5/2) + 2*q^(-7/2))*x1^(3/2)*x2^(13/2) + (-16*q^(13/2) - 32*q^(11/2) - 106*q^(9/2) - 166*q^(7/2) - 212*q^(5/2) - 130*q^(3/2) - 62*q^(1/2) - 24*q^(-1/2) - 7*q^(-3/2) - q^(-5/2))*x1^(5/2)*x2^(13/2) + (16*q^(17/2) + 40*q^(15/2) + 88*q^(13/2) + 160*q^(11/2) + 164*q^(9/2) + 142*q^(7/2) + 78*q^(5/2) + 36*q^(3/2) + 10*q^(1/2) + 2*q^(-1/2))*x1^(7/2)*x2^(13/2) + (-25*q^(19/2) - 30*q^(17/2) - 49*q^(15/2) - 54*q^(13/2) - 44*q^(11/2) - 30*q^(9/2) - 17*q^(7/2) - 6*q^(5/2) - q^(3/2))*x1^(9/2)*x2^(13/2) + (-56*q^(-1/2) - 16*q^(-5/2) - 18*q^(-7/2) - 10*q^(-9/2) - 2*q^(-11/2) - 2*q^(-13/2))*x1^(1/2)*x2^(15/2) + (20*q^(9/2) + 64*q^(7/2) + 134*q^(5/2) + 200*q^(3/2) + 220*q^(1/2) + 98*q^(-1/2) + 90*q^(-3/2) + 62*q^(-5/2) + 29*q^(-7/2) + 8*q^(-9/2) + 4*q^(-11/2))*x1^(3/2)*x2^(15/2) + (-20*q^(17/2) - 40*q^(15/2) - 124*q^(13/2) - 242*q^(11/2) - 474*q^(9/2) - 594*q^(7/2) - 638*q^(5/2) - 424*q^(3/2) - 260*q^(1/2) - 146*q^(-1/2) - 78*q^(-3/2) - 28*q^(-5/2) - 10*q^(-7/2) - 2*q^(-9/2))*x1^(5/2)*x2^(15/2) + (20*q^(23/2) + 40*q^(21/2) + 112*q^(19/2) + 248*q^(17/2) + 470*q^(15/2) + 696*q^(13/2) + 908*q^(11/2) + 836*q^(9/2) + 680*q^(7/2) + 412*q^(5/2) + 234*q^(3/2) + 100*q^(1/2) + 44*q^(-1/2) + 12*q^(-3/2) + 4*q^(-5/2))*x1^(7/2)*x2^(15/2) + (-20*q^(27/2) - 52*q^(25/2) - 120*q^(23/2) - 232*q^(21/2) - 416*q^(19/2) - 512*q^(17/2) - 602*q^(15/2) - 566*q^(13/2) - 452*q^(11/2) - 306*q^(9/2) - 180*q^(7/2) - 82*q^(5/2) - 32*q^(3/2) - 10*q^(1/2) - 2*q^(-1/2))*x1^(9/2)*x2^(15/2) + (36*q^(29/2) + 48*q^(27/2) + 88*q^(25/2) + 120*q^(23/2) + 156*q^(21/2) + 144*q^(19/2) + 148*q^(17/2) + 112*q^(15/2) + 84*q^(13/2) + 48*q^(11/2) + 28*q^(9/2) + 8*q^(7/2) + 4*q^(5/2))*x1^(11/2)*x2^(15/2) + (-84*q^(-1/2) - 30*q^(-5/2) - 42*q^(-7/2) - 33*q^(-9/2) - 14*q^(-11/2) - 9*q^(-13/2) - 4*q^(-15/2) - 3*q^(-17/2) - q^(-19/2))*x1^(1/2)*x2^(17/2) + (24*q^(11/2) + 80*q^(9/2) + 178*q^(7/2) + 296*q^(5/2) + 408*q^(3/2) + 438*q^(1/2) + 272*q^(-1/2) + 282*q^(-3/2) + 240*q^(-5/2) + 150*q^(-7/2) + 74*q^(-9/2) + 36*q^(-11/2) + 16*q^(-13/2) + 8*q^(-15/2) + 2*q^(-17/2))*x1^(3/2)*x2^(17/2) + (-24*q^(21/2) - 48*q^(19/2) - 152*q^(17/2) - 274*q^(15/2) - 609*q^(13/2) - 996*q^(11/2) - 1517*q^(9/2) - 1708*q^(7/2) - 1717*q^(5/2) - 1285*q^(3/2) - 955*q^(1/2) - 683*q^(-1/2) - 454*q^(-3/2) - 246*q^(-5/2) - 121*q^(-7/2) - 50*q^(-9/2) - 21*q^(-11/2) - 7*q^(-13/2) - q^(-15/2))*x1^(5/2)*x2^(17/2) + (24*q^(29/2) + 48*q^(27/2) + 120*q^(25/2) + 288*q^(23/2) + 554*q^(21/2) + 1046*q^(19/2) + 1778*q^(17/2) + 2630*q^(15/2) + 3316*q^(13/2) + 3658*q^(11/2) + 3280*q^(9/2) + 2642*q^(7/2) + 1826*q^(5/2) + 1196*q^(3/2) + 704*q^(1/2) + 392*q^(-1/2) + 188*q^(-3/2) + 84*q^(-5/2) + 30*q^(-7/2) + 10*q^(-9/2) + 2*q^(-11/2))*x1^(7/2)*x2^(17/2) + (-24*q^(35/2) - 48*q^(33/2) - 136*q^(31/2) - 264*q^(29/2) - 594*q^(27/2) - 1046*q^(25/2) - 1756*q^(23/2) - 2552*q^(21/2) - 3400*q^(19/2) - 3786*q^(17/2) - 3876*q^(15/2) - 3426*q^(13/2) - 2707*q^(11/2) - 1901*q^(9/2) - 1211*q^(7/2) - 681*q^(5/2) - 356*q^(3/2) - 166*q^(1/2) - 69*q^(-1/2) - 25*q^(-3/2) - 7*q^(-5/2) - q^(-7/2))*x1^(9/2)*x2^(17/2) + (24*q^(39/2) + 64*q^(37/2) + 152*q^(35/2) + 304*q^(33/2) + 568*q^(31/2) + 968*q^(29/2) + 1342*q^(27/2) + 1748*q^(25/2) + 2046*q^(23/2) + 2168*q^(21/2) + 2034*q^(19/2) + 1790*q^(17/2) + 1392*q^(15/2) + 996*q^(13/2) + 630*q^(11/2) + 364*q^(9/2) + 180*q^(7/2) + 84*q^(5/2) + 30*q^(3/2) + 10*q^(1/2) + 2*q^(-1/2))*x1^(11/2)*x2^(17/2) + (-49*q^(41/2) - 70*q^(39/2) - 137*q^(37/2) - 206*q^(35/2) - 308*q^(33/2) - 380*q^(31/2) - 445*q^(29/2) - 468*q^(27/2) - 477*q^(25/2) - 432*q^(23/2) - 365*q^(21/2) - 284*q^(19/2) - 205*q^(17/2) - 132*q^(15/2) - 76*q^(13/2) - 38*q^(11/2) - 17*q^(9/2) - 6*q^(7/2) - q^(5/2))*x1^(13/2)*x2^(17/2) + (-120*q^(-1/2) - 50*q^(-5/2) - 80*q^(-7/2) - 76*q^(-9/2) - 46*q^(-11/2) - 30*q^(-13/2) - 16*q^(-15/2) - 18*q^(-17/2) - 10*q^(-19/2) - 6*q^(-21/2) - 2*q^(-23/2) - 2*q^(-25/2))*x1^(1/2)*x2^(19/2) + (28*q^(13/2) + 96*q^(11/2) + 222*q^(9/2) + 392*q^(7/2) + 596*q^(5/2) + 778*q^(3/2) + 860*q^(1/2) + 674*q^(-1/2) + 756*q^(-3/2) + 710*q^(-5/2) + 536*q^(-7/2) + 332*q^(-9/2) + 198*q^(-11/2) + 116*q^(-13/2) + 78*q^(-15/2) + 40*q^(-17/2) + 20*q^(-19/2) + 8*q^(-21/2) + 4*q^(-23/2))*x1^(3/2)*x2^(19/2) + (-28*q^(25/2) - 56*q^(23/2) - 180*q^(21/2) - 326*q^(19/2) - 694*q^(17/2) - 1190*q^(15/2) - 2142*q^(13/2) - 3062*q^(11/2) - 4070*q^(9/2) - 4390*q^(7/2) - 4398*q^(5/2) - 3704*q^(3/2) - 3174*q^(1/2) - 2594*q^(-1/2) - 1974*q^(-3/2) - 1294*q^(-5/2) - 788*q^(-7/2) - 430*q^(-9/2) - 242*q^(-11/2) - 124*q^(-13/2) - 60*q^(-15/2) - 24*q^(-17/2) - 10*q^(-19/2) - 2*q^(-21/2))*x1^(5/2)*x2^(19/2) + (28*q^(35/2) + 56*q^(33/2) + 140*q^(31/2) + 320*q^(29/2) + 626*q^(27/2) + 1162*q^(25/2) + 2160*q^(23/2) + 3560*q^(21/2) + 5690*q^(19/2) + 8166*q^(17/2) + 10582*q^(15/2) + 12038*q^(13/2) + 12420*q^(11/2) + 11158*q^(9/2) + 9396*q^(7/2) + 7244*q^(5/2) + 5409*q^(3/2) + 3754*q^(1/2) + 2484*q^(-1/2) + 1476*q^(-3/2) + 840*q^(-5/2) + 426*q^(-7/2) + 213*q^(-9/2) + 92*q^(-11/2) + 40*q^(-13/2) + 12*q^(-15/2) + 4*q^(-17/2))*x1^(7/2)*x2^(19/2) + (-28*q^(43/2) - 56*q^(41/2) - 140*q^(39/2) - 300*q^(37/2) - 632*q^(35/2) - 1154*q^(33/2) - 2162*q^(31/2) - 3622*q^(29/2) - 6014*q^(27/2) - 8968*q^(25/2) - 12526*q^(23/2) - 15794*q^(21/2) - 18398*q^(19/2) - 19076*q^(17/2) - 18342*q^(15/2) - 15946*q^(13/2) - 12846*q^(11/2) - 9568*q^(9/2) - 6728*q^(7/2) - 4394*q^(5/2) - 2750*q^(3/2) - 1598*q^(1/2) - 874*q^(-1/2) - 438*q^(-3/2) - 206*q^(-5/2) - 84*q^(-7/2) - 32*q^(-9/2) - 10*q^(-11/2) - 2*q^(-13/2))*x1^(9/2)*x2^(19/2) + (28*q^(49/2) + 56*q^(47/2) + 160*q^(45/2) + 312*q^(43/2) + 648*q^(41/2) + 1232*q^(39/2) + 2250*q^(37/2) + 3688*q^(35/2) + 5808*q^(33/2) + 8364*q^(31/2) + 11324*q^(29/2) + 13828*q^(27/2) + 15922*q^(25/2) + 16792*q^(23/2) + 16532*q^(21/2) + 14908*q^(19/2) + 12686*q^(17/2) + 9880*q^(15/2) + 7268*q^(13/2) + 4908*q^(11/2) + 3152*q^(9/2) + 1848*q^(7/2) + 1050*q^(5/2) + 528*q^(3/2) + 260*q^(1/2) + 108*q^(-1/2) + 44*q^(-3/2) + 12*q^(-5/2) + 4*q^(-7/2))*x1^(11/2)*x2^(19/2) + (-28*q^(53/2) - 76*q^(51/2) - 184*q^(49/2) - 376*q^(47/2) - 720*q^(45/2) - 1264*q^(43/2) - 2132*q^(41/2) - 3074*q^(39/2) - 4280*q^(37/2) - 5490*q^(35/2) - 6660*q^(33/2) - 7442*q^(31/2) - 7882*q^(29/2) - 7786*q^(27/2) - 7300*q^(25/2) - 6368*q^(23/2) - 5240*q^(21/2) - 4030*q^(19/2) - 2918*q^(17/2) - 1954*q^(15/2) - 1226*q^(13/2) - 708*q^(11/2) - 380*q^(9/2) - 184*q^(7/2) - 80*q^(5/2) - 30*q^(3/2) - 10*q^(1/2) - 2*q^(-1/2))*x1^(13/2)*x2^(19/2) + (64*q^(55/2) + 96*q^(53/2) + 196*q^(51/2) + 312*q^(49/2) + 500*q^(47/2) + 688*q^(45/2) + 944*q^(43/2) + 1112*q^(41/2) + 1336*q^(39/2) + 1456*q^(37/2) + 1552*q^(35/2) + 1512*q^(33/2) + 1460*q^(31/2) + 1280*q^(29/2) + 1112*q^(27/2) + 880*q^(25/2) + 680*q^(23/2) + 472*q^(21/2) + 328*q^(19/2) + 192*q^(17/2) + 116*q^(15/2) + 56*q^(13/2) + 28*q^(11/2) + 8*q^(9/2) + 4*q^(7/2))*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) + (-10*q^(-1/2))*x1^(-1/2)*x2^(-9/2) + (8*q^(3/2) + 16*q^(1/2) + 2*q^(-1/2))*x1^(-3/2)*x2^(-9/2) + (-9*q^(5/2) - 6*q^(3/2) - q^(1/2))*x1^(-5/2)*x2^(-9/2) + (-20*q^(-1/2) - 2*q^(-5/2))*x1^(-1/2)*x2^(-11/2) + (12*q^(5/2) + 32*q^(3/2) + 46*q^(1/2) + 8*q^(-1/2) + 4*q^(-3/2))*x1^(-3/2)*x2^(-11/2) + (-12*q^(9/2) - 28*q^(7/2) - 56*q^(5/2) - 34*q^(3/2) - 12*q^(1/2) - 2*q^(-1/2))*x1^(-5/2)*x2^(-11/2) + (16*q^(11/2) + 16*q^(9/2) + 20*q^(7/2) + 8*q^(5/2) + 4*q^(3/2))*x1^(-7/2)*x2^(-11/2) + (-35*q^(-1/2) - 7*q^(-5/2) - 5*q^(-7/2) - q^(-9/2))*x1^(-1/2)*x2^(-13/2) + (16*q^(7/2) + 48*q^(5/2) + 90*q^(3/2) + 104*q^(1/2) + 32*q^(-1/2) + 22*q^(-3/2) + 10*q^(-5/2) + 2*q^(-7/2))*x1^(-3/2)*x2^(-13/2) + (-16*q^(13/2) - 32*q^(11/2) - 106*q^(9/2) - 166*q^(7/2) - 212*q^(5/2) - 130*q^(3/2) - 62*q^(1/2) - 24*q^(-1/2) - 7*q^(-3/2) - q^(-5/2))*x1^(-5/2)*x2^(-13/2) + (16*q^(17/2) + 40*q^(15/2) + 88*q^(13/2) + 160*q^(11/2) + 164*q^(9/2) + 142*q^(7/2) + 78*q^(5/2) + 36*q^(3/2) + 10*q^(1/2) + 2*q^(-1/2))*x1^(-7/2)*x2^(-13/2) + (-25*q^(19/2) - 30*q^(17/2) - 49*q^(15/2) - 54*q^(13/2) - 44*q^(11/2) - 30*q^(9/2) - 17*q^(7/2) - 6*q^(5/2) - q^(3/2))*x1^(-9/2)*x2^(-13/2) + (-56*q^(-1/2) - 16*q^(-5/2) - 18*q^(-7/2) - 10*q^(-9/2) - 2*q^(-11/2) - 2*q^(-13/2))*x1^(-1/2)*x2^(-15/2) + (20*q^(9/2) + 64*q^(7/2) + 134*q^(5/2) + 200*q^(3/2) + 220*q^(1/2) + 98*q^(-1/2) + 90*q^(-3/2) + 62*q^(-5/2) + 29*q^(-7/2) + 8*q^(-9/2) + 4*q^(-11/2))*x1^(-3/2)*x2^(-15/2) + (-20*q^(17/2) - 40*q^(15/2) - 124*q^(13/2) - 242*q^(11/2) - 474*q^(9/2) - 594*q^(7/2) - 638*q^(5/2) - 424*q^(3/2) - 260*q^(1/2) - 146*q^(-1/2) - 78*q^(-3/2) - 28*q^(-5/2) - 10*q^(-7/2) - 2*q^(-9/2))*x1^(-5/2)*x2^(-15/2) + (20*q^(23/2) + 40*q^(21/2) + 112*q^(19/2) + 248*q^(17/2) + 470*q^(15/2) + 696*q^(13/2) + 908*q^(11/2) + 836*q^(9/2) + 680*q^(7/2) + 412*q^(5/2) + 234*q^(3/2) + 100*q^(1/2) + 44*q^(-1/2) + 12*q^(-3/2) + 4*q^(-5/2))*x1^(-7/2)*x2^(-15/2) + (-20*q^(27/2) - 52*q^(25/2) - 120*q^(23/2) - 232*q^(21/2) - 416*q^(19/2) - 512*q^(17/2) - 602*q^(15/2) - 566*q^(13/2) - 452*q^(11/2) - 306*q^(9/2) - 180*q^(7/2) - 82*q^(5/2) - 32*q^(3/2) - 10*q^(1/2) - 2*q^(-1/2))*x1^(-9/2)*x2^(-15/2) + (36*q^(29/2) + 48*q^(27/2) + 88*q^(25/2) + 120*q^(23/2) + 156*q^(21/2) + 144*q^(19/2) + 148*q^(17/2) + 112*q^(15/2) + 84*q^(13/2) + 48*q^(11/2) + 28*q^(9/2) + 8*q^(7/2) + 4*q^(5/2))*x1^(-11/2)*x2^(-15/2) + (-84*q^(-1/2) - 30*q^(-5/2) - 42*q^(-7/2) - 33*q^(-9/2) - 14*q^(-11/2) - 9*q^(-13/2) - 4*q^(-15/2) - 3*q^(-17/2) - q^(-19/2))*x1^(-1/2)*x2^(-17/2) + (24*q^(11/2) + 80*q^(9/2) + 178*q^(7/2) + 296*q^(5/2) + 408*q^(3/2) + 438*q^(1/2) + 272*q^(-1/2) + 282*q^(-3/2) + 240*q^(-5/2) + 150*q^(-7/2) + 74*q^(-9/2) + 36*q^(-11/2) + 16*q^(-13/2) + 8*q^(-15/2) + 2*q^(-17/2))*x1^(-3/2)*x2^(-17/2) + (-24*q^(21/2) - 48*q^(19/2) - 152*q^(17/2) - 274*q^(15/2) - 609*q^(13/2) - 996*q^(11/2) - 1517*q^(9/2) - 1708*q^(7/2) - 1717*q^(5/2) - 1285*q^(3/2) - 955*q^(1/2) - 683*q^(-1/2) - 454*q^(-3/2) - 246*q^(-5/2) - 121*q^(-7/2) - 50*q^(-9/2) - 21*q^(-11/2) - 7*q^(-13/2) - q^(-15/2))*x1^(-5/2)*x2^(-17/2) + (24*q^(29/2) + 48*q^(27/2) + 120*q^(25/2) + 288*q^(23/2) + 554*q^(21/2) + 1046*q^(19/2) + 1778*q^(17/2) + 2630*q^(15/2) + 3316*q^(13/2) + 3658*q^(11/2) + 3280*q^(9/2) + 2642*q^(7/2) + 1826*q^(5/2) + 1196*q^(3/2) + 704*q^(1/2) + 392*q^(-1/2) + 188*q^(-3/2) + 84*q^(-5/2) + 30*q^(-7/2) + 10*q^(-9/2) + 2*q^(-11/2))*x1^(-7/2)*x2^(-17/2) + (-24*q^(35/2) - 48*q^(33/2) - 136*q^(31/2) - 264*q^(29/2) - 594*q^(27/2) - 1046*q^(25/2) - 1756*q^(23/2) - 2552*q^(21/2) - 3400*q^(19/2) - 3786*q^(17/2) - 3876*q^(15/2) - 3426*q^(13/2) - 2707*q^(11/2) - 1901*q^(9/2) - 1211*q^(7/2) - 681*q^(5/2) - 356*q^(3/2) - 166*q^(1/2) - 69*q^(-1/2) - 25*q^(-3/2) - 7*q^(-5/2) - q^(-7/2))*x1^(-9/2)*x2^(-17/2) + (24*q^(39/2) + 64*q^(37/2) + 152*q^(35/2) + 304*q^(33/2) + 568*q^(31/2) + 968*q^(29/2) + 1342*q^(27/2) + 1748*q^(25/2) + 2046*q^(23/2) + 2168*q^(21/2) + 2034*q^(19/2) + 1790*q^(17/2) + 1392*q^(15/2) + 996*q^(13/2) + 630*q^(11/2) + 364*q^(9/2) + 180*q^(7/2) + 84*q^(5/2) + 30*q^(3/2) + 10*q^(1/2) + 2*q^(-1/2))*x1^(-11/2)*x2^(-17/2) + (-49*q^(41/2) - 70*q^(39/2) - 137*q^(37/2) - 206*q^(35/2) - 308*q^(33/2) - 380*q^(31/2) - 445*q^(29/2) - 468*q^(27/2) - 477*q^(25/2) - 432*q^(23/2) - 365*q^(21/2) - 284*q^(19/2) - 205*q^(17/2) - 132*q^(15/2) - 76*q^(13/2) - 38*q^(11/2) - 17*q^(9/2) - 6*q^(7/2) - q^(5/2))*x1^(-13/2)*x2^(-17/2) + (-120*q^(-1/2) - 50*q^(-5/2) - 80*q^(-7/2) - 76*q^(-9/2) - 46*q^(-11/2) - 30*q^(-13/2) - 16*q^(-15/2) - 18*q^(-17/2) - 10*q^(-19/2) - 6*q^(-21/2) - 2*q^(-23/2) - 2*q^(-25/2))*x1^(-1/2)*x2^(-19/2) + (28*q^(13/2) + 96*q^(11/2) + 222*q^(9/2) + 392*q^(7/2) + 596*q^(5/2) + 778*q^(3/2) + 860*q^(1/2) + 674*q^(-1/2) + 756*q^(-3/2) + 710*q^(-5/2) + 536*q^(-7/2) + 332*q^(-9/2) + 198*q^(-11/2) + 116*q^(-13/2) + 78*q^(-15/2) + 40*q^(-17/2) + 20*q^(-19/2) + 8*q^(-21/2) + 4*q^(-23/2))*x1^(-3/2)*x2^(-19/2) + (-28*q^(25/2) - 56*q^(23/2) - 180*q^(21/2) - 326*q^(19/2) - 694*q^(17/2) - 1190*q^(15/2) - 2142*q^(13/2) - 3062*q^(11/2) - 4070*q^(9/2) - 4390*q^(7/2) - 4398*q^(5/2) - 3704*q^(3/2) - 3174*q^(1/2) - 2594*q^(-1/2) - 1974*q^(-3/2) - 1294*q^(-5/2) - 788*q^(-7/2) - 430*q^(-9/2) - 242*q^(-11/2) - 124*q^(-13/2) - 60*q^(-15/2) - 24*q^(-17/2) - 10*q^(-19/2) - 2*q^(-21/2))*x1^(-5/2)*x2^(-19/2) + (28*q^(35/2) + 56*q^(33/2) + 140*q^(31/2) + 320*q^(29/2) + 626*q^(27/2) + 1162*q^(25/2) + 2160*q^(23/2) + 3560*q^(21/2) + 5690*q^(19/2) + 8166*q^(17/2) + 10582*q^(15/2) + 12038*q^(13/2) + 12420*q^(11/2) + 11158*q^(9/2) + 9396*q^(7/2) + 7244*q^(5/2) + 5409*q^(3/2) + 3754*q^(1/2) + 2484*q^(-1/2) + 1476*q^(-3/2) + 840*q^(-5/2) + 426*q^(-7/2) + 213*q^(-9/2) + 92*q^(-11/2) + 40*q^(-13/2) + 12*q^(-15/2) + 4*q^(-17/2))*x1^(-7/2)*x2^(-19/2) + (-28*q^(43/2) - 56*q^(41/2) - 140*q^(39/2) - 300*q^(37/2) - 632*q^(35/2) - 1154*q^(33/2) - 2162*q^(31/2) - 3622*q^(29/2) - 6014*q^(27/2) - 8968*q^(25/2) - 12526*q^(23/2) - 15794*q^(21/2) - 18398*q^(19/2) - 19076*q^(17/2) - 18342*q^(15/2) - 15946*q^(13/2) - 12846*q^(11/2) - 9568*q^(9/2) - 6728*q^(7/2) - 4394*q^(5/2) - 2750*q^(3/2) - 1598*q^(1/2) - 874*q^(-1/2) - 438*q^(-3/2) - 206*q^(-5/2) - 84*q^(-7/2) - 32*q^(-9/2) - 10*q^(-11/2) - 2*q^(-13/2))*x1^(-9/2)*x2^(-19/2) + (28*q^(49/2) + 56*q^(47/2) + 160*q^(45/2) + 312*q^(43/2) + 648*q^(41/2) + 1232*q^(39/2) + 2250*q^(37/2) + 3688*q^(35/2) + 5808*q^(33/2) + 8364*q^(31/2) + 11324*q^(29/2) + 13828*q^(27/2) + 15922*q^(25/2) + 16792*q^(23/2) + 16532*q^(21/2) + 14908*q^(19/2) + 12686*q^(17/2) + 9880*q^(15/2) + 7268*q^(13/2) + 4908*q^(11/2) + 3152*q^(9/2) + 1848*q^(7/2) + 1050*q^(5/2) + 528*q^(3/2) + 260*q^(1/2) + 108*q^(-1/2) + 44*q^(-3/2) + 12*q^(-5/2) + 4*q^(-7/2))*x1^(-11/2)*x2^(-19/2) + (-28*q^(53/2) - 76*q^(51/2) - 184*q^(49/2) - 376*q^(47/2) - 720*q^(45/2) - 1264*q^(43/2) - 2132*q^(41/2) - 3074*q^(39/2) - 4280*q^(37/2) - 5490*q^(35/2) - 6660*q^(33/2) - 7442*q^(31/2) - 7882*q^(29/2) - 7786*q^(27/2) - 7300*q^(25/2) - 6368*q^(23/2) - 5240*q^(21/2) - 4030*q^(19/2) - 2918*q^(17/2) - 1954*q^(15/2) - 1226*q^(13/2) - 708*q^(11/2) - 380*q^(9/2) - 184*q^(7/2) - 80*q^(5/2) - 30*q^(3/2) - 10*q^(1/2) - 2*q^(-1/2))*x1^(-13/2)*x2^(-19/2) + (64*q^(55/2) + 96*q^(53/2) + 196*q^(51/2) + 312*q^(49/2) + 500*q^(47/2) + 688*q^(45/2) + 944*q^(43/2) + 1112*q^(41/2) + 1336*q^(39/2) + 1456*q^(37/2) + 1552*q^(35/2) + 1512*q^(33/2) + 1460*q^(31/2) + 1280*q^(29/2) + 1112*q^(27/2) + 880*q^(25/2) + 680*q^(23/2) + 472*q^(21/2) + 328*q^(19/2) + 192*q^(17/2) + 116*q^(15/2) + 56*q^(13/2) + 28*q^(11/2) + 8*q^(9/2) + 4*q^(7/2))*x1^(-15/2)*x2^(-19/2)
|
Braid
| Braid word |
Components |
Crossings |
Strands |
[-1, 2, -3, -3, -3, 2, -1, 2, -3, 2] |
2 |
10 |
4 |
Multivariable Alexander polynomial
| ΔL |
A1^(1/2)*A2^(5/2) - 4*A1^(1/2)*A2^(3/2) + 6*A1^(1/2)*A2^(1/2) - 6*A1^(1/2)*A2^(-1/2) + 4*A1^(1/2)*A2^(-3/2) + 4*A1^(-1/2)*A2^(3/2) - 6*A1^(-1/2)*A2^(1/2) + 6*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^(-4)*A1^(-1)*A2^(-3) + 5*m^(-3)*A1^(-1)*A2^(-2) + m^(-3)*A2^(-3) + 10*m^(-2)*A1^(-1)*A2^(-1) + 9*m^(-2)*A2^(-2) + 12*m^(-1)*A1^(-1) + 20*m^(-1)*A2^(-1) + 4*m^(-1)*A1*A2^(-2) + 10*A1^(-1)*A2 + 24 + 10*A1*A2^(-1) + 4*m*A1^(-1)*A2^2 + 20*m*A2 + 12*m*A1 + 9*m^2*A2^2 + 10*m^2*A1*A2 + m^3*A2^3 + 5*m^3*A1*A2^2 + m^4*A1*A2^3 |
| Vertex | Maslov | Rank |
(-1, -3) | -4 | 1 |
(0, -3) | -3 | 1 |
(1, -2) | -1 | 4 |
(1, 3) | 4 | 1 |
(0, 3) | 3 | 1 |
(-1, 2) | 1 | 4 |
Record
FL/HFL Links
orderOption(int) |
368 |
namestring |
L10a49{1} |
statusstring |
success |
slugstring |
L10a49_1_0173a314 |
result_filestring |
details/L10a49_1_0173a314.json |
complexity_scoreOption(int) |
200 |
strandsOption(int) |
null |
crossingsOption(int) |
10 |
component_countOption(int) |
2 |
girthOption(int) |
6 |
total_rankOption(int) |
168 |
wall_secondsOption(float) |
0.002694 |
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": "L10a49_1_0173a314"
} |
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L10a49_1_0173a314 |