details/L10a49_0_c14c4e6e.json

FL expansions

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

Braid

Braid word Components Crossings Strands
[-1, 2, -1, -2, -3, -3, -3, -3, -2, -2, -1, 2, 3, -2] 2 14 4

Multivariable Alexander polynomial

ΔL
-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) - 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)

Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.

Newton Polygon of Alexander-0.500.5-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(-1, -3) no
(1, -5) yes
(1, 3) no
(-1, 5) yes
Dual Thurston polygon-101-505h1h2

HFL polytope

Poincaré polynomial
4*m^(-1)*A1^(-1)*A2^(-2) + m^(-1)*A2^(-3) + 10*A1^(-1)*A2^(-1) + 9*A2^(-2) + A1*A2^(-3) + 12*m*A1^(-1) + 20*m*A2^(-1) + 5*m*A1*A2^(-2) + 10*m^2*A1^(-1)*A2 + 24*m^2 + 10*m^2*A1*A2^(-1) + 5*m^3*A1^(-1)*A2^2 + 20*m^3*A2 + 12*m^3*A1 + m^4*A1^(-1)*A2^3 + 9*m^4*A2^2 + 10*m^4*A1*A2 + m^5*A2^3 + 4*m^5*A1*A2^2
VertexMaslovRank
(-1, -2)-14
(0, -3)-11
(1, -3)01
(1, 2)54
(0, 3)51
(-1, 3)41
HFL polytope-10105A1A2

Record

FL/HFL Links

orderOption(int) 367
namestring L10a49{0}
statusstring success
slugstring L10a49_0_c14c4e6e
result_filestring details/L10a49_0_c14c4e6e.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) 0.002835
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_0_c14c4e6e"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10a49_0_c14c4e6e