details/L10a33_1_2c75cf0d.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^(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^(1/2)*x2^(5/2) + (-4*q^(5/2))*x1^(1/2)*x2^(7/2) + (2*q^(7/2))*x1^(3/2)*x2^(7/2) + (q^(7/2) - 10*q^(5/2) - 3*q^(3/2))*x1^(1/2)*x2^(9/2) + (2*q^(9/2) + 8*q^(7/2) + 2*q^(5/2))*x1^(3/2)*x2^(9/2) + (-3*q^(11/2) - q^(9/2))*x1^(5/2)*x2^(9/2) + (4*q^(7/2) - 20*q^(5/2) - 12*q^(3/2) - 8*q^(1/2))*x1^(1/2)*x2^(11/2) + (2*q^(11/2) + 6*q^(9/2) + 24*q^(7/2) + 14*q^(5/2) + 6*q^(3/2))*x1^(3/2)*x2^(11/2) + (-2*q^(15/2) - 4*q^(13/2) - 14*q^(11/2) - 8*q^(9/2) - 4*q^(7/2))*x1^(5/2)*x2^(11/2) + (4*q^(17/2) + 2*q^(15/2) + 2*q^(13/2))*x1^(7/2)*x2^(11/2) + (-2*q^(11/2) + 10*q^(7/2) - 32*q^(5/2) - 30*q^(3/2) - 33*q^(1/2) - 18*q^(-1/2) - 5*q^(-3/2))*x1^(1/2)*x2^(13/2) + (2*q^(13/2) + 6*q^(11/2) + 16*q^(9/2) + 60*q^(7/2) + 56*q^(5/2) + 42*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(3/2)*x2^(13/2) + (-2*q^(19/2) - 2*q^(17/2) - 13*q^(15/2) - 20*q^(13/2) - 49*q^(11/2) - 43*q^(9/2) - 31*q^(7/2) - 13*q^(5/2) - 3*q^(3/2))*x1^(5/2)*x2^(13/2) + (2*q^(23/2) + 4*q^(21/2) + 8*q^(19/2) + 22*q^(17/2) + 18*q^(15/2) + 16*q^(13/2) + 8*q^(11/2) + 2*q^(9/2))*x1^(7/2)*x2^(13/2) + (-5*q^(25/2) - 3*q^(23/2) - 4*q^(21/2) - 3*q^(19/2) - q^(17/2))*x1^(9/2)*x2^(13/2) + (-2*q^(13/2) - 8*q^(11/2) - 2*q^(9/2) + 20*q^(7/2) - 44*q^(5/2) - 52*q^(3/2) - 84*q^(1/2) - 76*q^(-1/2) - 56*q^(-3/2) - 20*q^(-5/2) - 12*q^(-7/2))*x1^(1/2)*x2^(15/2) + (2*q^(15/2) + 10*q^(13/2) + 17*q^(11/2) + 38*q^(9/2) + 132*q^(7/2) + 162*q^(5/2) + 170*q^(3/2) + 124*q^(1/2) + 70*q^(-1/2) + 26*q^(-3/2) + 10*q^(-5/2))*x1^(3/2)*x2^(15/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 16*q^(17/2) - 48*q^(15/2) - 76*q^(13/2) - 156*q^(11/2) - 168*q^(9/2) - 160*q^(7/2) - 106*q^(5/2) - 60*q^(3/2) - 20*q^(1/2) - 8*q^(-1/2))*x1^(5/2)*x2^(15/2) + (2*q^(29/2) + 2*q^(27/2) + 6*q^(25/2) + 16*q^(23/2) + 34*q^(21/2) + 50*q^(19/2) + 96*q^(17/2) + 98*q^(15/2) + 96*q^(13/2) + 68*q^(11/2) + 40*q^(9/2) + 14*q^(7/2) + 6*q^(5/2))*x1^(7/2)*x2^(15/2) + (-2*q^(33/2) - 4*q^(31/2) - 8*q^(29/2) - 14*q^(27/2) - 34*q^(25/2) - 32*q^(23/2) - 36*q^(21/2) - 30*q^(19/2) - 20*q^(17/2) - 8*q^(15/2) - 4*q^(13/2))*x1^(9/2)*x2^(15/2) + (6*q^(35/2) + 4*q^(33/2) + 6*q^(31/2) + 6*q^(29/2) + 6*q^(27/2) + 2*q^(25/2) + 2*q^(23/2))*x1^(11/2)*x2^(15/2) + (2*q^(17/2) - 2*q^(15/2) - 8*q^(13/2) - 24*q^(11/2) - 14*q^(9/2) + 29*q^(7/2) - 54*q^(5/2) - 72*q^(3/2) - 152*q^(1/2) - 191*q^(-1/2) - 204*q^(-3/2) - 148*q^(-5/2) - 102*q^(-7/2) - 51*q^(-9/2) - 26*q^(-11/2) - 7*q^(-13/2))*x1^(1/2)*x2^(17/2) + (2*q^(17/2) + 14*q^(15/2) + 36*q^(13/2) + 50*q^(11/2) + 88*q^(9/2) + 264*q^(7/2) + 386*q^(5/2) + 494*q^(3/2) + 490*q^(1/2) + 402*q^(-1/2) + 262*q^(-3/2) + 152*q^(-5/2) + 70*q^(-7/2) + 28*q^(-9/2) + 6*q^(-11/2))*x1^(3/2)*x2^(17/2) + (-2*q^(27/2) - 2*q^(25/2) - 10*q^(23/2) - 12*q^(21/2) - 41*q^(19/2) - 72*q^(17/2) - 157*q^(15/2) - 247*q^(13/2) - 452*q^(11/2) - 558*q^(9/2) - 617*q^(7/2) - 542*q^(5/2) - 415*q^(3/2) - 255*q^(1/2) - 141*q^(-1/2) - 61*q^(-3/2) - 23*q^(-5/2) - 5*q^(-7/2))*x1^(5/2)*x2^(17/2) + (2*q^(35/2) + 2*q^(33/2) + 4*q^(31/2) + 14*q^(29/2) + 22*q^(27/2) + 44*q^(25/2) + 88*q^(23/2) + 160*q^(21/2) + 236*q^(19/2) + 372*q^(17/2) + 430*q^(15/2) + 456*q^(13/2) + 398*q^(11/2) + 304*q^(9/2) + 190*q^(7/2) + 106*q^(5/2) + 46*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(7/2)*x2^(17/2) + (-2*q^(41/2) - 2*q^(39/2) - 6*q^(37/2) - 8*q^(35/2) - 25*q^(33/2) - 43*q^(31/2) - 77*q^(29/2) - 109*q^(27/2) - 182*q^(25/2) - 202*q^(23/2) - 221*q^(21/2) - 204*q^(19/2) - 168*q^(17/2) - 110*q^(15/2) - 66*q^(13/2) - 31*q^(11/2) - 13*q^(9/2) - 3*q^(7/2))*x1^(9/2)*x2^(17/2) + (2*q^(45/2) + 4*q^(43/2) + 8*q^(41/2) + 14*q^(39/2) + 24*q^(37/2) + 50*q^(35/2) + 54*q^(33/2) + 64*q^(31/2) + 66*q^(29/2) + 62*q^(27/2) + 44*q^(25/2) + 30*q^(23/2) + 16*q^(21/2) + 8*q^(19/2) + 2*q^(17/2))*x1^(11/2)*x2^(17/2) + (-7*q^(47/2) - 5*q^(45/2) - 8*q^(43/2) - 9*q^(41/2) - 11*q^(39/2) - 9*q^(37/2) - 7*q^(35/2) - 4*q^(33/2) - 3*q^(31/2) - q^(29/2))*x1^(13/2)*x2^(17/2) + (2*q^(19/2) + 6*q^(17/2) - 6*q^(15/2) - 24*q^(13/2) - 62*q^(11/2) - 56*q^(9/2) + 14*q^(7/2) - 78*q^(5/2) - 88*q^(3/2) - 224*q^(1/2) - 344*q^(-1/2) - 480*q^(-3/2) - 480*q^(-5/2) - 456*q^(-7/2) - 328*q^(-9/2) - 248*q^(-11/2) - 144*q^(-13/2) - 80*q^(-15/2) - 28*q^(-17/2) - 16*q^(-19/2))*x1^(1/2)*x2^(19/2) + (-2*q^(19/2) + 17*q^(17/2) + 56*q^(15/2) + 118*q^(13/2) + 154*q^(11/2) + 218*q^(9/2) + 514*q^(7/2) + 807*q^(5/2) + 1172*q^(3/2) + 1402*q^(1/2) + 1454*q^(-1/2) + 1266*q^(-3/2) + 996*q^(-5/2) + 674*q^(-7/2) + 426*q^(-9/2) + 226*q^(-11/2) + 106*q^(-13/2) + 38*q^(-15/2) + 14*q^(-17/2))*x1^(3/2)*x2^(19/2) + (-2*q^(31/2) - 2*q^(29/2) - 10*q^(27/2) - 12*q^(25/2) - 36*q^(23/2) - 60*q^(21/2) - 150*q^(19/2) - 260*q^(17/2) - 480*q^(15/2) - 732*q^(13/2) - 1230*q^(11/2) - 1630*q^(9/2) - 1998*q^(7/2) - 2064*q^(5/2) - 1936*q^(3/2) - 1548*q^(1/2) - 1148*q^(-1/2) - 728*q^(-3/2) - 438*q^(-5/2) - 216*q^(-7/2) - 100*q^(-9/2) - 32*q^(-11/2) - 12*q^(-13/2))*x1^(5/2)*x2^(19/2) + (2*q^(41/2) + 2*q^(39/2) + 4*q^(37/2) + 12*q^(35/2) + 20*q^(33/2) + 32*q^(31/2) + 74*q^(29/2) + 120*q^(27/2) + 220*q^(25/2) + 384*q^(23/2) + 633*q^(21/2) + 920*q^(19/2) + 1342*q^(17/2) + 1633*q^(15/2) + 1854*q^(13/2) + 1836*q^(11/2) + 1654*q^(9/2) + 1306*q^(7/2) + 954*q^(5/2) + 600*q^(3/2) + 356*q^(1/2) + 178*q^(-1/2) + 80*q^(-3/2) + 26*q^(-5/2) + 10*q^(-7/2))*x1^(7/2)*x2^(19/2) + (-2*q^(49/2) - 2*q^(47/2) - 4*q^(45/2) - 8*q^(43/2) - 18*q^(41/2) - 28*q^(39/2) - 58*q^(37/2) - 88*q^(35/2) - 170*q^(33/2) - 276*q^(31/2) - 436*q^(29/2) - 598*q^(27/2) - 856*q^(25/2) - 1004*q^(23/2) - 1128*q^(21/2) - 1118*q^(19/2) - 1032*q^(17/2) - 830*q^(15/2) - 626*q^(13/2) - 404*q^(11/2) - 250*q^(9/2) - 128*q^(7/2) - 60*q^(5/2) - 20*q^(3/2) - 8*q^(1/2))*x1^(9/2)*x2^(19/2) + (2*q^(55/2) + 2*q^(53/2) + 6*q^(51/2) + 8*q^(49/2) + 16*q^(47/2) + 32*q^(45/2) + 62*q^(43/2) + 98*q^(41/2) + 158*q^(39/2) + 220*q^(37/2) + 334*q^(35/2) + 392*q^(33/2) + 452*q^(31/2) + 466*q^(29/2) + 460*q^(27/2) + 388*q^(25/2) + 312*q^(23/2) + 214*q^(21/2) + 144*q^(19/2) + 78*q^(17/2) + 40*q^(15/2) + 14*q^(13/2) + 6*q^(11/2))*x1^(11/2)*x2^(19/2) + (-2*q^(59/2) - 4*q^(57/2) - 8*q^(55/2) - 14*q^(53/2) - 24*q^(51/2) - 38*q^(49/2) - 74*q^(47/2) - 84*q^(45/2) - 106*q^(43/2) - 118*q^(41/2) - 128*q^(39/2) - 118*q^(37/2) - 104*q^(35/2) - 76*q^(33/2) - 58*q^(31/2) - 36*q^(29/2) - 20*q^(27/2) - 8*q^(25/2) - 4*q^(23/2))*x1^(13/2)*x2^(19/2) + (8*q^(61/2) + 6*q^(59/2) + 10*q^(57/2) + 12*q^(55/2) + 16*q^(53/2) + 16*q^(51/2) + 18*q^(49/2) + 12*q^(47/2) + 12*q^(45/2) + 8*q^(43/2) + 6*q^(41/2) + 2*q^(39/2) + 2*q^(37/2))*x1^(15/2)*x2^(19/2)
(-1/2, -5/2) (1, 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]}
(-q^(5/2))*x1^(1/2)*x2^(5/2) + (-4*q^(5/2))*x1^(1/2)*x2^(7/2) + (2*q^(7/2))*x1^(3/2)*x2^(7/2) + (q^(7/2) - 10*q^(5/2) - 3*q^(3/2))*x1^(1/2)*x2^(9/2) + (2*q^(9/2) + 8*q^(7/2) + 2*q^(5/2))*x1^(3/2)*x2^(9/2) + (-3*q^(11/2) - q^(9/2))*x1^(5/2)*x2^(9/2) + (4*q^(7/2) - 20*q^(5/2) - 12*q^(3/2) - 8*q^(1/2))*x1^(1/2)*x2^(11/2) + (2*q^(11/2) + 6*q^(9/2) + 24*q^(7/2) + 14*q^(5/2) + 6*q^(3/2))*x1^(3/2)*x2^(11/2) + (-2*q^(15/2) - 4*q^(13/2) - 14*q^(11/2) - 8*q^(9/2) - 4*q^(7/2))*x1^(5/2)*x2^(11/2) + (4*q^(17/2) + 2*q^(15/2) + 2*q^(13/2))*x1^(7/2)*x2^(11/2) + (-2*q^(11/2) + 10*q^(7/2) - 32*q^(5/2) - 30*q^(3/2) - 33*q^(1/2) - 18*q^(-1/2) - 5*q^(-3/2))*x1^(1/2)*x2^(13/2) + (2*q^(13/2) + 6*q^(11/2) + 16*q^(9/2) + 60*q^(7/2) + 56*q^(5/2) + 42*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(3/2)*x2^(13/2) + (-2*q^(19/2) - 2*q^(17/2) - 13*q^(15/2) - 20*q^(13/2) - 49*q^(11/2) - 43*q^(9/2) - 31*q^(7/2) - 13*q^(5/2) - 3*q^(3/2))*x1^(5/2)*x2^(13/2) + (2*q^(23/2) + 4*q^(21/2) + 8*q^(19/2) + 22*q^(17/2) + 18*q^(15/2) + 16*q^(13/2) + 8*q^(11/2) + 2*q^(9/2))*x1^(7/2)*x2^(13/2) + (-5*q^(25/2) - 3*q^(23/2) - 4*q^(21/2) - 3*q^(19/2) - q^(17/2))*x1^(9/2)*x2^(13/2) + (-2*q^(13/2) - 8*q^(11/2) - 2*q^(9/2) + 20*q^(7/2) - 44*q^(5/2) - 52*q^(3/2) - 84*q^(1/2) - 76*q^(-1/2) - 56*q^(-3/2) - 20*q^(-5/2) - 12*q^(-7/2))*x1^(1/2)*x2^(15/2) + (2*q^(15/2) + 10*q^(13/2) + 17*q^(11/2) + 38*q^(9/2) + 132*q^(7/2) + 162*q^(5/2) + 170*q^(3/2) + 124*q^(1/2) + 70*q^(-1/2) + 26*q^(-3/2) + 10*q^(-5/2))*x1^(3/2)*x2^(15/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 16*q^(17/2) - 48*q^(15/2) - 76*q^(13/2) - 156*q^(11/2) - 168*q^(9/2) - 160*q^(7/2) - 106*q^(5/2) - 60*q^(3/2) - 20*q^(1/2) - 8*q^(-1/2))*x1^(5/2)*x2^(15/2) + (2*q^(29/2) + 2*q^(27/2) + 6*q^(25/2) + 16*q^(23/2) + 34*q^(21/2) + 50*q^(19/2) + 96*q^(17/2) + 98*q^(15/2) + 96*q^(13/2) + 68*q^(11/2) + 40*q^(9/2) + 14*q^(7/2) + 6*q^(5/2))*x1^(7/2)*x2^(15/2) + (-2*q^(33/2) - 4*q^(31/2) - 8*q^(29/2) - 14*q^(27/2) - 34*q^(25/2) - 32*q^(23/2) - 36*q^(21/2) - 30*q^(19/2) - 20*q^(17/2) - 8*q^(15/2) - 4*q^(13/2))*x1^(9/2)*x2^(15/2) + (6*q^(35/2) + 4*q^(33/2) + 6*q^(31/2) + 6*q^(29/2) + 6*q^(27/2) + 2*q^(25/2) + 2*q^(23/2))*x1^(11/2)*x2^(15/2) + (2*q^(17/2) - 2*q^(15/2) - 8*q^(13/2) - 24*q^(11/2) - 14*q^(9/2) + 29*q^(7/2) - 54*q^(5/2) - 72*q^(3/2) - 152*q^(1/2) - 191*q^(-1/2) - 204*q^(-3/2) - 148*q^(-5/2) - 102*q^(-7/2) - 51*q^(-9/2) - 26*q^(-11/2) - 7*q^(-13/2))*x1^(1/2)*x2^(17/2) + (2*q^(17/2) + 14*q^(15/2) + 36*q^(13/2) + 50*q^(11/2) + 88*q^(9/2) + 264*q^(7/2) + 386*q^(5/2) + 494*q^(3/2) + 490*q^(1/2) + 402*q^(-1/2) + 262*q^(-3/2) + 152*q^(-5/2) + 70*q^(-7/2) + 28*q^(-9/2) + 6*q^(-11/2))*x1^(3/2)*x2^(17/2) + (-2*q^(27/2) - 2*q^(25/2) - 10*q^(23/2) - 12*q^(21/2) - 41*q^(19/2) - 72*q^(17/2) - 157*q^(15/2) - 247*q^(13/2) - 452*q^(11/2) - 558*q^(9/2) - 617*q^(7/2) - 542*q^(5/2) - 415*q^(3/2) - 255*q^(1/2) - 141*q^(-1/2) - 61*q^(-3/2) - 23*q^(-5/2) - 5*q^(-7/2))*x1^(5/2)*x2^(17/2) + (2*q^(35/2) + 2*q^(33/2) + 4*q^(31/2) + 14*q^(29/2) + 22*q^(27/2) + 44*q^(25/2) + 88*q^(23/2) + 160*q^(21/2) + 236*q^(19/2) + 372*q^(17/2) + 430*q^(15/2) + 456*q^(13/2) + 398*q^(11/2) + 304*q^(9/2) + 190*q^(7/2) + 106*q^(5/2) + 46*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(7/2)*x2^(17/2) + (-2*q^(41/2) - 2*q^(39/2) - 6*q^(37/2) - 8*q^(35/2) - 25*q^(33/2) - 43*q^(31/2) - 77*q^(29/2) - 109*q^(27/2) - 182*q^(25/2) - 202*q^(23/2) - 221*q^(21/2) - 204*q^(19/2) - 168*q^(17/2) - 110*q^(15/2) - 66*q^(13/2) - 31*q^(11/2) - 13*q^(9/2) - 3*q^(7/2))*x1^(9/2)*x2^(17/2) + (2*q^(45/2) + 4*q^(43/2) + 8*q^(41/2) + 14*q^(39/2) + 24*q^(37/2) + 50*q^(35/2) + 54*q^(33/2) + 64*q^(31/2) + 66*q^(29/2) + 62*q^(27/2) + 44*q^(25/2) + 30*q^(23/2) + 16*q^(21/2) + 8*q^(19/2) + 2*q^(17/2))*x1^(11/2)*x2^(17/2) + (-7*q^(47/2) - 5*q^(45/2) - 8*q^(43/2) - 9*q^(41/2) - 11*q^(39/2) - 9*q^(37/2) - 7*q^(35/2) - 4*q^(33/2) - 3*q^(31/2) - q^(29/2))*x1^(13/2)*x2^(17/2) + (2*q^(19/2) + 6*q^(17/2) - 6*q^(15/2) - 24*q^(13/2) - 62*q^(11/2) - 56*q^(9/2) + 14*q^(7/2) - 78*q^(5/2) - 88*q^(3/2) - 224*q^(1/2) - 344*q^(-1/2) - 480*q^(-3/2) - 480*q^(-5/2) - 456*q^(-7/2) - 328*q^(-9/2) - 248*q^(-11/2) - 144*q^(-13/2) - 80*q^(-15/2) - 28*q^(-17/2) - 16*q^(-19/2))*x1^(1/2)*x2^(19/2) + (-2*q^(19/2) + 17*q^(17/2) + 56*q^(15/2) + 118*q^(13/2) + 154*q^(11/2) + 218*q^(9/2) + 514*q^(7/2) + 807*q^(5/2) + 1172*q^(3/2) + 1402*q^(1/2) + 1454*q^(-1/2) + 1266*q^(-3/2) + 996*q^(-5/2) + 674*q^(-7/2) + 426*q^(-9/2) + 226*q^(-11/2) + 106*q^(-13/2) + 38*q^(-15/2) + 14*q^(-17/2))*x1^(3/2)*x2^(19/2) + (-2*q^(31/2) - 2*q^(29/2) - 10*q^(27/2) - 12*q^(25/2) - 36*q^(23/2) - 60*q^(21/2) - 150*q^(19/2) - 260*q^(17/2) - 480*q^(15/2) - 732*q^(13/2) - 1230*q^(11/2) - 1630*q^(9/2) - 1998*q^(7/2) - 2064*q^(5/2) - 1936*q^(3/2) - 1548*q^(1/2) - 1148*q^(-1/2) - 728*q^(-3/2) - 438*q^(-5/2) - 216*q^(-7/2) - 100*q^(-9/2) - 32*q^(-11/2) - 12*q^(-13/2))*x1^(5/2)*x2^(19/2) + (2*q^(41/2) + 2*q^(39/2) + 4*q^(37/2) + 12*q^(35/2) + 20*q^(33/2) + 32*q^(31/2) + 74*q^(29/2) + 120*q^(27/2) + 220*q^(25/2) + 384*q^(23/2) + 633*q^(21/2) + 920*q^(19/2) + 1342*q^(17/2) + 1633*q^(15/2) + 1854*q^(13/2) + 1836*q^(11/2) + 1654*q^(9/2) + 1306*q^(7/2) + 954*q^(5/2) + 600*q^(3/2) + 356*q^(1/2) + 178*q^(-1/2) + 80*q^(-3/2) + 26*q^(-5/2) + 10*q^(-7/2))*x1^(7/2)*x2^(19/2) + (-2*q^(49/2) - 2*q^(47/2) - 4*q^(45/2) - 8*q^(43/2) - 18*q^(41/2) - 28*q^(39/2) - 58*q^(37/2) - 88*q^(35/2) - 170*q^(33/2) - 276*q^(31/2) - 436*q^(29/2) - 598*q^(27/2) - 856*q^(25/2) - 1004*q^(23/2) - 1128*q^(21/2) - 1118*q^(19/2) - 1032*q^(17/2) - 830*q^(15/2) - 626*q^(13/2) - 404*q^(11/2) - 250*q^(9/2) - 128*q^(7/2) - 60*q^(5/2) - 20*q^(3/2) - 8*q^(1/2))*x1^(9/2)*x2^(19/2) + (2*q^(55/2) + 2*q^(53/2) + 6*q^(51/2) + 8*q^(49/2) + 16*q^(47/2) + 32*q^(45/2) + 62*q^(43/2) + 98*q^(41/2) + 158*q^(39/2) + 220*q^(37/2) + 334*q^(35/2) + 392*q^(33/2) + 452*q^(31/2) + 466*q^(29/2) + 460*q^(27/2) + 388*q^(25/2) + 312*q^(23/2) + 214*q^(21/2) + 144*q^(19/2) + 78*q^(17/2) + 40*q^(15/2) + 14*q^(13/2) + 6*q^(11/2))*x1^(11/2)*x2^(19/2) + (-2*q^(59/2) - 4*q^(57/2) - 8*q^(55/2) - 14*q^(53/2) - 24*q^(51/2) - 38*q^(49/2) - 74*q^(47/2) - 84*q^(45/2) - 106*q^(43/2) - 118*q^(41/2) - 128*q^(39/2) - 118*q^(37/2) - 104*q^(35/2) - 76*q^(33/2) - 58*q^(31/2) - 36*q^(29/2) - 20*q^(27/2) - 8*q^(25/2) - 4*q^(23/2))*x1^(13/2)*x2^(19/2) + (8*q^(61/2) + 6*q^(59/2) + 10*q^(57/2) + 12*q^(55/2) + 16*q^(53/2) + 16*q^(51/2) + 18*q^(49/2) + 12*q^(47/2) + 12*q^(45/2) + 8*q^(43/2) + 6*q^(41/2) + 2*q^(39/2) + 2*q^(37/2))*x1^(15/2)*x2^(19/2)
(1/2, 5/2) x1^(-1/2)x2^(-5/2) q^(5/2)
(-q^(5/2))*x1^(-1/2)*x2^(-5/2) + (-4*q^(5/2))*x1^(-1/2)*x2^(-7/2) + (2*q^(7/2))*x1^(-3/2)*x2^(-7/2) + (q^(7/2) - 10*q^(5/2) - 3*q^(3/2))*x1^(-1/2)*x2^(-9/2) + (2*q^(9/2) + 8*q^(7/2) + 2*q^(5/2))*x1^(-3/2)*x2^(-9/2) + (-3*q^(11/2) - q^(9/2))*x1^(-5/2)*x2^(-9/2) + (4*q^(7/2) - 20*q^(5/2) - 12*q^(3/2) - 8*q^(1/2))*x1^(-1/2)*x2^(-11/2) + (2*q^(11/2) + 6*q^(9/2) + 24*q^(7/2) + 14*q^(5/2) + 6*q^(3/2))*x1^(-3/2)*x2^(-11/2) + (-2*q^(15/2) - 4*q^(13/2) - 14*q^(11/2) - 8*q^(9/2) - 4*q^(7/2))*x1^(-5/2)*x2^(-11/2) + (4*q^(17/2) + 2*q^(15/2) + 2*q^(13/2))*x1^(-7/2)*x2^(-11/2) + (-2*q^(11/2) + 10*q^(7/2) - 32*q^(5/2) - 30*q^(3/2) - 33*q^(1/2) - 18*q^(-1/2) - 5*q^(-3/2))*x1^(-1/2)*x2^(-13/2) + (2*q^(13/2) + 6*q^(11/2) + 16*q^(9/2) + 60*q^(7/2) + 56*q^(5/2) + 42*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(-3/2)*x2^(-13/2) + (-2*q^(19/2) - 2*q^(17/2) - 13*q^(15/2) - 20*q^(13/2) - 49*q^(11/2) - 43*q^(9/2) - 31*q^(7/2) - 13*q^(5/2) - 3*q^(3/2))*x1^(-5/2)*x2^(-13/2) + (2*q^(23/2) + 4*q^(21/2) + 8*q^(19/2) + 22*q^(17/2) + 18*q^(15/2) + 16*q^(13/2) + 8*q^(11/2) + 2*q^(9/2))*x1^(-7/2)*x2^(-13/2) + (-5*q^(25/2) - 3*q^(23/2) - 4*q^(21/2) - 3*q^(19/2) - q^(17/2))*x1^(-9/2)*x2^(-13/2) + (-2*q^(13/2) - 8*q^(11/2) - 2*q^(9/2) + 20*q^(7/2) - 44*q^(5/2) - 52*q^(3/2) - 84*q^(1/2) - 76*q^(-1/2) - 56*q^(-3/2) - 20*q^(-5/2) - 12*q^(-7/2))*x1^(-1/2)*x2^(-15/2) + (2*q^(15/2) + 10*q^(13/2) + 17*q^(11/2) + 38*q^(9/2) + 132*q^(7/2) + 162*q^(5/2) + 170*q^(3/2) + 124*q^(1/2) + 70*q^(-1/2) + 26*q^(-3/2) + 10*q^(-5/2))*x1^(-3/2)*x2^(-15/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 16*q^(17/2) - 48*q^(15/2) - 76*q^(13/2) - 156*q^(11/2) - 168*q^(9/2) - 160*q^(7/2) - 106*q^(5/2) - 60*q^(3/2) - 20*q^(1/2) - 8*q^(-1/2))*x1^(-5/2)*x2^(-15/2) + (2*q^(29/2) + 2*q^(27/2) + 6*q^(25/2) + 16*q^(23/2) + 34*q^(21/2) + 50*q^(19/2) + 96*q^(17/2) + 98*q^(15/2) + 96*q^(13/2) + 68*q^(11/2) + 40*q^(9/2) + 14*q^(7/2) + 6*q^(5/2))*x1^(-7/2)*x2^(-15/2) + (-2*q^(33/2) - 4*q^(31/2) - 8*q^(29/2) - 14*q^(27/2) - 34*q^(25/2) - 32*q^(23/2) - 36*q^(21/2) - 30*q^(19/2) - 20*q^(17/2) - 8*q^(15/2) - 4*q^(13/2))*x1^(-9/2)*x2^(-15/2) + (6*q^(35/2) + 4*q^(33/2) + 6*q^(31/2) + 6*q^(29/2) + 6*q^(27/2) + 2*q^(25/2) + 2*q^(23/2))*x1^(-11/2)*x2^(-15/2) + (2*q^(17/2) - 2*q^(15/2) - 8*q^(13/2) - 24*q^(11/2) - 14*q^(9/2) + 29*q^(7/2) - 54*q^(5/2) - 72*q^(3/2) - 152*q^(1/2) - 191*q^(-1/2) - 204*q^(-3/2) - 148*q^(-5/2) - 102*q^(-7/2) - 51*q^(-9/2) - 26*q^(-11/2) - 7*q^(-13/2))*x1^(-1/2)*x2^(-17/2) + (2*q^(17/2) + 14*q^(15/2) + 36*q^(13/2) + 50*q^(11/2) + 88*q^(9/2) + 264*q^(7/2) + 386*q^(5/2) + 494*q^(3/2) + 490*q^(1/2) + 402*q^(-1/2) + 262*q^(-3/2) + 152*q^(-5/2) + 70*q^(-7/2) + 28*q^(-9/2) + 6*q^(-11/2))*x1^(-3/2)*x2^(-17/2) + (-2*q^(27/2) - 2*q^(25/2) - 10*q^(23/2) - 12*q^(21/2) - 41*q^(19/2) - 72*q^(17/2) - 157*q^(15/2) - 247*q^(13/2) - 452*q^(11/2) - 558*q^(9/2) - 617*q^(7/2) - 542*q^(5/2) - 415*q^(3/2) - 255*q^(1/2) - 141*q^(-1/2) - 61*q^(-3/2) - 23*q^(-5/2) - 5*q^(-7/2))*x1^(-5/2)*x2^(-17/2) + (2*q^(35/2) + 2*q^(33/2) + 4*q^(31/2) + 14*q^(29/2) + 22*q^(27/2) + 44*q^(25/2) + 88*q^(23/2) + 160*q^(21/2) + 236*q^(19/2) + 372*q^(17/2) + 430*q^(15/2) + 456*q^(13/2) + 398*q^(11/2) + 304*q^(9/2) + 190*q^(7/2) + 106*q^(5/2) + 46*q^(3/2) + 18*q^(1/2) + 4*q^(-1/2))*x1^(-7/2)*x2^(-17/2) + (-2*q^(41/2) - 2*q^(39/2) - 6*q^(37/2) - 8*q^(35/2) - 25*q^(33/2) - 43*q^(31/2) - 77*q^(29/2) - 109*q^(27/2) - 182*q^(25/2) - 202*q^(23/2) - 221*q^(21/2) - 204*q^(19/2) - 168*q^(17/2) - 110*q^(15/2) - 66*q^(13/2) - 31*q^(11/2) - 13*q^(9/2) - 3*q^(7/2))*x1^(-9/2)*x2^(-17/2) + (2*q^(45/2) + 4*q^(43/2) + 8*q^(41/2) + 14*q^(39/2) + 24*q^(37/2) + 50*q^(35/2) + 54*q^(33/2) + 64*q^(31/2) + 66*q^(29/2) + 62*q^(27/2) + 44*q^(25/2) + 30*q^(23/2) + 16*q^(21/2) + 8*q^(19/2) + 2*q^(17/2))*x1^(-11/2)*x2^(-17/2) + (-7*q^(47/2) - 5*q^(45/2) - 8*q^(43/2) - 9*q^(41/2) - 11*q^(39/2) - 9*q^(37/2) - 7*q^(35/2) - 4*q^(33/2) - 3*q^(31/2) - q^(29/2))*x1^(-13/2)*x2^(-17/2) + (2*q^(19/2) + 6*q^(17/2) - 6*q^(15/2) - 24*q^(13/2) - 62*q^(11/2) - 56*q^(9/2) + 14*q^(7/2) - 78*q^(5/2) - 88*q^(3/2) - 224*q^(1/2) - 344*q^(-1/2) - 480*q^(-3/2) - 480*q^(-5/2) - 456*q^(-7/2) - 328*q^(-9/2) - 248*q^(-11/2) - 144*q^(-13/2) - 80*q^(-15/2) - 28*q^(-17/2) - 16*q^(-19/2))*x1^(-1/2)*x2^(-19/2) + (-2*q^(19/2) + 17*q^(17/2) + 56*q^(15/2) + 118*q^(13/2) + 154*q^(11/2) + 218*q^(9/2) + 514*q^(7/2) + 807*q^(5/2) + 1172*q^(3/2) + 1402*q^(1/2) + 1454*q^(-1/2) + 1266*q^(-3/2) + 996*q^(-5/2) + 674*q^(-7/2) + 426*q^(-9/2) + 226*q^(-11/2) + 106*q^(-13/2) + 38*q^(-15/2) + 14*q^(-17/2))*x1^(-3/2)*x2^(-19/2) + (-2*q^(31/2) - 2*q^(29/2) - 10*q^(27/2) - 12*q^(25/2) - 36*q^(23/2) - 60*q^(21/2) - 150*q^(19/2) - 260*q^(17/2) - 480*q^(15/2) - 732*q^(13/2) - 1230*q^(11/2) - 1630*q^(9/2) - 1998*q^(7/2) - 2064*q^(5/2) - 1936*q^(3/2) - 1548*q^(1/2) - 1148*q^(-1/2) - 728*q^(-3/2) - 438*q^(-5/2) - 216*q^(-7/2) - 100*q^(-9/2) - 32*q^(-11/2) - 12*q^(-13/2))*x1^(-5/2)*x2^(-19/2) + (2*q^(41/2) + 2*q^(39/2) + 4*q^(37/2) + 12*q^(35/2) + 20*q^(33/2) + 32*q^(31/2) + 74*q^(29/2) + 120*q^(27/2) + 220*q^(25/2) + 384*q^(23/2) + 633*q^(21/2) + 920*q^(19/2) + 1342*q^(17/2) + 1633*q^(15/2) + 1854*q^(13/2) + 1836*q^(11/2) + 1654*q^(9/2) + 1306*q^(7/2) + 954*q^(5/2) + 600*q^(3/2) + 356*q^(1/2) + 178*q^(-1/2) + 80*q^(-3/2) + 26*q^(-5/2) + 10*q^(-7/2))*x1^(-7/2)*x2^(-19/2) + (-2*q^(49/2) - 2*q^(47/2) - 4*q^(45/2) - 8*q^(43/2) - 18*q^(41/2) - 28*q^(39/2) - 58*q^(37/2) - 88*q^(35/2) - 170*q^(33/2) - 276*q^(31/2) - 436*q^(29/2) - 598*q^(27/2) - 856*q^(25/2) - 1004*q^(23/2) - 1128*q^(21/2) - 1118*q^(19/2) - 1032*q^(17/2) - 830*q^(15/2) - 626*q^(13/2) - 404*q^(11/2) - 250*q^(9/2) - 128*q^(7/2) - 60*q^(5/2) - 20*q^(3/2) - 8*q^(1/2))*x1^(-9/2)*x2^(-19/2) + (2*q^(55/2) + 2*q^(53/2) + 6*q^(51/2) + 8*q^(49/2) + 16*q^(47/2) + 32*q^(45/2) + 62*q^(43/2) + 98*q^(41/2) + 158*q^(39/2) + 220*q^(37/2) + 334*q^(35/2) + 392*q^(33/2) + 452*q^(31/2) + 466*q^(29/2) + 460*q^(27/2) + 388*q^(25/2) + 312*q^(23/2) + 214*q^(21/2) + 144*q^(19/2) + 78*q^(17/2) + 40*q^(15/2) + 14*q^(13/2) + 6*q^(11/2))*x1^(-11/2)*x2^(-19/2) + (-2*q^(59/2) - 4*q^(57/2) - 8*q^(55/2) - 14*q^(53/2) - 24*q^(51/2) - 38*q^(49/2) - 74*q^(47/2) - 84*q^(45/2) - 106*q^(43/2) - 118*q^(41/2) - 128*q^(39/2) - 118*q^(37/2) - 104*q^(35/2) - 76*q^(33/2) - 58*q^(31/2) - 36*q^(29/2) - 20*q^(27/2) - 8*q^(25/2) - 4*q^(23/2))*x1^(-13/2)*x2^(-19/2) + (8*q^(61/2) + 6*q^(59/2) + 10*q^(57/2) + 12*q^(55/2) + 16*q^(53/2) + 16*q^(51/2) + 18*q^(49/2) + 12*q^(47/2) + 12*q^(45/2) + 8*q^(43/2) + 6*q^(41/2) + 2*q^(39/2) + 2*q^(37/2))*x1^(-15/2)*x2^(-19/2)

Braid

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

Multivariable Alexander polynomial

ΔL
-A1^(1/2)*A2^(5/2) + 4*A1^(1/2)*A2^(3/2) - 4*A1^(1/2)*A2^(1/2) + 4*A1^(1/2)*A2^(-1/2) - 2*A1^(1/2)*A2^(-3/2) - 2*A1^(-1/2)*A2^(3/2) + 4*A1^(-1/2)*A2^(1/2) - 4*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.

Newton Polygon of Alexander-0.500.5-202A1A2

Dual Thurston polytope

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

HFL polytope

Poincaré polynomial
m^(-7)*A1^(-1)*A2^(-3) + 5*m^(-6)*A1^(-1)*A2^(-2) + m^(-6)*A2^(-3) + 8*m^(-5)*A1^(-1)*A2^(-1) + 7*m^(-5)*A2^(-2) + 8*m^(-4)*A1^(-1) + 14*m^(-4)*A2^(-1) + 2*m^(-4)*A1*A2^(-2) + 6*m^(-3)*A1^(-1)*A2 + 16*m^(-3) + 6*m^(-3)*A1*A2^(-1) + 2*m^(-2)*A1^(-1)*A2^2 + 14*m^(-2)*A2 + 8*m^(-2)*A1 + 7*m^(-1)*A2^2 + 8*m^(-1)*A1*A2 + A2^3 + 5*A1*A2^2 + m*A1*A2^3
VertexMaslovRank
(-1, -3)-71
(0, -3)-61
(1, -2)-42
(1, 3)11
(0, 3)01
(-1, 2)-22
HFL polytope-10105A1A2

Record

FL/HFL Links

orderOption(int) 334
namestring L10a33{1}
statusstring success
slugstring L10a33_1_2c75cf0d
result_filestring details/L10a33_1_2c75cf0d.json
complexity_scoreOption(int) 200
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 120
wall_secondsOption(float) 0.003383
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": "L10a33_1_2c75cf0d"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10a33_1_2c75cf0d