details/L8a3_0_515ff118.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(1/2, -3/2) (1/2, 1) x1^(-1/2)x2^(3/2) 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, 1, -1]}
(-9*q^(71/2) - 7*q^(69/2) - 12*q^(67/2) - 15*q^(65/2) - 21*q^(63/2) - 23*q^(61/2) - 29*q^(59/2) - 27*q^(57/2) - 26*q^(55/2) - 23*q^(53/2) - 21*q^(51/2) - 15*q^(49/2) - 13*q^(47/2) - 7*q^(45/2) - 4*q^(43/2) - 3*q^(41/2) - q^(39/2))*x1^(-17/2)*x2^(19/2) + (8*q^(55/2) + 6*q^(53/2) + 10*q^(51/2) + 12*q^(49/2) + 16*q^(47/2) + 16*q^(45/2) + 18*q^(43/2) + 12*q^(41/2) + 12*q^(39/2) + 8*q^(37/2) + 6*q^(35/2) + 2*q^(33/2) + 2*q^(31/2))*x1^(-15/2)*x2^(17/2) + (2*q^(69/2) + 4*q^(67/2) + 8*q^(65/2) + 14*q^(63/2) + 24*q^(61/2) + 38*q^(59/2) + 60*q^(57/2) + 106*q^(55/2) + 128*q^(53/2) + 164*q^(51/2) + 194*q^(49/2) + 222*q^(47/2) + 234*q^(45/2) + 238*q^(43/2) + 212*q^(41/2) + 188*q^(39/2) + 154*q^(37/2) + 120*q^(35/2) + 82*q^(33/2) + 56*q^(31/2) + 30*q^(29/2) + 16*q^(27/2) + 8*q^(25/2) + 2*q^(23/2))*x1^(-15/2)*x2^(19/2) + (-7*q^(41/2) - 5*q^(39/2) - 8*q^(37/2) - 9*q^(35/2) - 11*q^(33/2) - 9*q^(31/2) - 7*q^(29/2) - 4*q^(27/2) - 3*q^(25/2) - q^(23/2))*x1^(-13/2)*x2^(15/2) + (-2*q^(53/2) - 4*q^(51/2) - 8*q^(49/2) - 14*q^(47/2) - 24*q^(45/2) - 38*q^(43/2) - 74*q^(41/2) - 84*q^(39/2) - 106*q^(37/2) - 118*q^(35/2) - 128*q^(33/2) - 118*q^(31/2) - 104*q^(29/2) - 76*q^(27/2) - 58*q^(25/2) - 36*q^(23/2) - 20*q^(21/2) - 8*q^(19/2) - 4*q^(17/2))*x1^(-13/2)*x2^(17/2) + (-2*q^(65/2) - 2*q^(63/2) - 6*q^(61/2) - 8*q^(59/2) - 16*q^(57/2) - 22*q^(55/2) - 49*q^(53/2) - 79*q^(51/2) - 135*q^(49/2) - 202*q^(47/2) - 306*q^(45/2) - 430*q^(43/2) - 617*q^(41/2) - 749*q^(39/2) - 895*q^(37/2) - 990*q^(35/2) - 1055*q^(33/2) - 1028*q^(31/2) - 954*q^(29/2) - 807*q^(27/2) - 656*q^(25/2) - 491*q^(23/2) - 345*q^(21/2) - 217*q^(19/2) - 130*q^(17/2) - 66*q^(15/2) - 31*q^(13/2) - 13*q^(11/2) - 3*q^(9/2))*x1^(-13/2)*x2^(19/2) + (6*q^(29/2) + 4*q^(27/2) + 6*q^(25/2) + 6*q^(23/2) + 6*q^(21/2) + 2*q^(19/2) + 2*q^(17/2))*x1^(-11/2)*x2^(13/2) + (2*q^(39/2) + 4*q^(37/2) + 8*q^(35/2) + 14*q^(33/2) + 24*q^(31/2) + 50*q^(29/2) + 54*q^(27/2) + 64*q^(25/2) + 66*q^(23/2) + 62*q^(21/2) + 44*q^(19/2) + 30*q^(17/2) + 16*q^(15/2) + 8*q^(13/2) + 2*q^(11/2))*x1^(-11/2)*x2^(15/2) + (2*q^(49/2) + 2*q^(47/2) + 6*q^(45/2) + 8*q^(43/2) + 16*q^(41/2) + 32*q^(39/2) + 62*q^(37/2) + 98*q^(35/2) + 158*q^(33/2) + 232*q^(31/2) + 347*q^(29/2) + 412*q^(27/2) + 476*q^(25/2) + 493*q^(23/2) + 480*q^(21/2) + 403*q^(19/2) + 320*q^(17/2) + 218*q^(15/2) + 145*q^(13/2) + 78*q^(11/2) + 40*q^(9/2) + 14*q^(7/2) + 6*q^(5/2))*x1^(-11/2)*x2^(17/2) + (2*q^(59/2) + 2*q^(57/2) + 4*q^(55/2) + 8*q^(53/2) + 12*q^(51/2) + 24*q^(49/2) + 40*q^(47/2) + 70*q^(45/2) + 110*q^(43/2) + 188*q^(41/2) + 308*q^(39/2) + 504*q^(37/2) + 764*q^(35/2) + 1128*q^(33/2) + 1562*q^(31/2) + 2098*q^(29/2) + 2534*q^(27/2) + 2910*q^(25/2) + 3088*q^(23/2) + 3086*q^(21/2) + 2838*q^(19/2) + 2462*q^(17/2) + 1966*q^(15/2) + 1484*q^(13/2) + 1034*q^(11/2) + 676*q^(9/2) + 398*q^(7/2) + 222*q^(5/2) + 106*q^(3/2) + 46*q^(1/2) + 18*q^(-1/2) + 4*q^(-3/2))*x1^(-11/2)*x2^(19/2) + (-5*q^(19/2) - 3*q^(17/2) - 4*q^(15/2) - 3*q^(13/2) - q^(11/2))*x1^(-9/2)*x2^(11/2) + (-2*q^(27/2) - 4*q^(25/2) - 8*q^(23/2) - 14*q^(21/2) - 34*q^(19/2) - 32*q^(17/2) - 36*q^(15/2) - 30*q^(13/2) - 20*q^(11/2) - 8*q^(9/2) - 4*q^(7/2))*x1^(-9/2)*x2^(13/2) + (-2*q^(35/2) - 2*q^(33/2) - 6*q^(31/2) - 8*q^(29/2) - 25*q^(27/2) - 43*q^(25/2) - 77*q^(23/2) - 119*q^(21/2) - 192*q^(19/2) - 216*q^(17/2) - 235*q^(15/2) - 214*q^(13/2) - 172*q^(11/2) - 112*q^(9/2) - 66*q^(7/2) - 31*q^(5/2) - 13*q^(3/2) - 3*q^(1/2))*x1^(-9/2)*x2^(15/2) + (-2*q^(43/2) - 2*q^(41/2) - 4*q^(39/2) - 8*q^(37/2) - 18*q^(35/2) - 28*q^(33/2) - 58*q^(31/2) - 92*q^(29/2) - 180*q^(27/2) - 298*q^(25/2) - 488*q^(23/2) - 708*q^(21/2) - 1000*q^(19/2) - 1178*q^(17/2) - 1302*q^(15/2) - 1262*q^(13/2) - 1128*q^(11/2) - 886*q^(9/2) - 652*q^(7/2) - 414*q^(5/2) - 252*q^(3/2) - 128*q^(1/2) - 60*q^(-1/2) - 20*q^(-3/2) - 8*q^(-5/2))*x1^(-9/2)*x2^(17/2) + (-2*q^(51/2) - 2*q^(49/2) - 4*q^(47/2) - 6*q^(45/2) - 18*q^(43/2) - 24*q^(41/2) - 44*q^(39/2) - 74*q^(37/2) - 135*q^(35/2) - 217*q^(33/2) - 389*q^(31/2) - 623*q^(29/2) - 1064*q^(27/2) - 1680*q^(25/2) - 2570*q^(23/2) - 3602*q^(21/2) - 4795*q^(19/2) - 5725*q^(17/2) - 6408*q^(15/2) - 6559*q^(13/2) - 6264*q^(11/2) - 5515*q^(9/2) - 4572*q^(7/2) - 3492*q^(5/2) - 2520*q^(3/2) - 1681*q^(1/2) - 1048*q^(-1/2) - 597*q^(-3/2) - 319*q^(-5/2) - 146*q^(-7/2) - 61*q^(-9/2) - 23*q^(-11/2) - 5*q^(-13/2))*x1^(-9/2)*x2^(19/2) + (4*q^(11/2) + 2*q^(9/2) + 2*q^(7/2))*x1^(-7/2)*x2^(9/2) + (2*q^(17/2) + 4*q^(15/2) + 8*q^(13/2) + 22*q^(11/2) + 18*q^(9/2) + 16*q^(7/2) + 8*q^(5/2) + 2*q^(3/2))*x1^(-7/2)*x2^(11/2) + (2*q^(23/2) + 2*q^(21/2) + 6*q^(19/2) + 16*q^(17/2) + 34*q^(15/2) + 58*q^(13/2) + 103*q^(11/2) + 106*q^(9/2) + 100*q^(7/2) + 69*q^(5/2) + 40*q^(3/2) + 14*q^(1/2) + 6*q^(-1/2))*x1^(-7/2)*x2^(13/2) + (2*q^(29/2) + 2*q^(27/2) + 4*q^(25/2) + 14*q^(23/2) + 22*q^(21/2) + 48*q^(19/2) + 98*q^(17/2) + 190*q^(15/2) + 304*q^(13/2) + 454*q^(11/2) + 512*q^(9/2) + 516*q^(7/2) + 430*q^(5/2) + 316*q^(3/2) + 194*q^(1/2) + 106*q^(-1/2) + 46*q^(-3/2) + 18*q^(-5/2) + 4*q^(-7/2))*x1^(-7/2)*x2^(15/2) + (2*q^(35/2) + 2*q^(33/2) + 4*q^(31/2) + 12*q^(29/2) + 20*q^(27/2) + 36*q^(25/2) + 80*q^(23/2) + 140*q^(21/2) + 278*q^(19/2) + 519*q^(17/2) + 899*q^(15/2) + 1364*q^(13/2) + 1891*q^(11/2) + 2209*q^(9/2) + 2348*q^(7/2) + 2195*q^(5/2) + 1870*q^(3/2) + 1419*q^(1/2) + 1001*q^(-1/2) + 616*q^(-3/2) + 359*q^(-5/2) + 178*q^(-7/2) + 80*q^(-9/2) + 26*q^(-11/2) + 10*q^(-13/2))*x1^(-7/2)*x2^(17/2) + (2*q^(41/2) + 2*q^(39/2) + 4*q^(37/2) + 12*q^(35/2) + 18*q^(33/2) + 34*q^(31/2) + 68*q^(29/2) + 122*q^(27/2) + 216*q^(25/2) + 426*q^(23/2) + 764*q^(21/2) + 1414*q^(19/2) + 2426*q^(17/2) + 3876*q^(15/2) + 5586*q^(13/2) + 7446*q^(11/2) + 8872*q^(9/2) + 9772*q^(7/2) + 9846*q^(5/2) + 9218*q^(3/2) + 7972*q^(1/2) + 6476*q^(-1/2) + 4866*q^(-3/2) + 3444*q^(-5/2) + 2264*q^(-7/2) + 1390*q^(-9/2) + 778*q^(-11/2) + 410*q^(-13/2) + 186*q^(-15/2) + 76*q^(-17/2) + 28*q^(-19/2) + 6*q^(-21/2))*x1^(-7/2)*x2^(19/2) + (-3*q^(5/2) - q^(3/2))*x1^(-5/2)*x2^(7/2) + (-2*q^(9/2) - 4*q^(7/2) - 14*q^(5/2) - 8*q^(3/2) - 4*q^(1/2))*x1^(-5/2)*x2^(9/2) + (-2*q^(13/2) - 2*q^(11/2) - 13*q^(9/2) - 26*q^(7/2) - 53*q^(5/2) - 45*q^(3/2) - 31*q^(1/2) - 13*q^(-1/2) - 3*q^(-3/2))*x1^(-5/2)*x2^(11/2) + (-2*q^(17/2) - 2*q^(15/2) - 10*q^(13/2) - 20*q^(11/2) - 64*q^(9/2) - 116*q^(7/2) - 194*q^(5/2) - 194*q^(3/2) - 170*q^(1/2) - 108*q^(-1/2) - 60*q^(-3/2) - 20*q^(-5/2) - 8*q^(-7/2))*x1^(-5/2)*x2^(13/2) + (-2*q^(21/2) - 2*q^(19/2) - 10*q^(17/2) - 16*q^(15/2) - 54*q^(13/2) - 120*q^(11/2) - 272*q^(9/2) - 451*q^(7/2) - 675*q^(5/2) - 750*q^(3/2) - 737*q^(1/2) - 602*q^(-1/2) - 435*q^(-3/2) - 261*q^(-5/2) - 141*q^(-7/2) - 61*q^(-9/2) - 23*q^(-11/2) - 5*q^(-13/2))*x1^(-5/2)*x2^(15/2) + (-2*q^(25/2) - 2*q^(23/2) - 10*q^(21/2) - 16*q^(19/2) - 54*q^(17/2) - 112*q^(15/2) - 286*q^(13/2) - 564*q^(11/2) - 1054*q^(9/2) - 1622*q^(7/2) - 2284*q^(5/2) - 2668*q^(3/2) - 2842*q^(1/2) - 2648*q^(-1/2) - 2274*q^(-3/2) - 1718*q^(-5/2) - 1216*q^(-7/2) - 750*q^(-9/2) - 442*q^(-11/2) - 216*q^(-13/2) - 100*q^(-15/2) - 32*q^(-17/2) - 12*q^(-19/2))*x1^(-5/2)*x2^(17/2) + (-2*q^(29/2) - 2*q^(27/2) - 10*q^(25/2) - 19*q^(23/2) - 64*q^(21/2) - 133*q^(19/2) - 325*q^(17/2) - 657*q^(15/2) - 1335*q^(13/2) - 2336*q^(11/2) - 3838*q^(9/2) - 5587*q^(7/2) - 7551*q^(5/2) - 9060*q^(3/2) - 10089*q^(1/2) - 10252*q^(-1/2) - 9730*q^(-3/2) - 8498*q^(-5/2) - 6981*q^(-7/2) - 5301*q^(-9/2) - 3804*q^(-11/2) - 2524*q^(-13/2) - 1574*q^(-15/2) - 891*q^(-17/2) - 473*q^(-19/2) - 219*q^(-21/2) - 91*q^(-23/2) - 33*q^(-25/2) - 7*q^(-27/2))*x1^(-5/2)*x2^(19/2) + (2*q^(1/2))*x1^(-3/2)*x2^(5/2) + (2*q^(3/2) + 8*q^(1/2) + 2*q^(-1/2))*x1^(-3/2)*x2^(7/2) + (2*q^(5/2) + 10*q^(3/2) + 25*q^(1/2) + 14*q^(-1/2) + 6*q^(-3/2))*x1^(-3/2)*x2^(9/2) + (2*q^(7/2) + 14*q^(5/2) + 36*q^(3/2) + 72*q^(1/2) + 60*q^(-1/2) + 42*q^(-3/2) + 18*q^(-5/2) + 4*q^(-7/2))*x1^(-3/2)*x2^(11/2) + (4*q^(9/2) + 21*q^(7/2) + 58*q^(5/2) + 118*q^(3/2) + 202*q^(1/2) + 206*q^(-1/2) + 186*q^(-3/2) + 127*q^(-5/2) + 70*q^(-7/2) + 26*q^(-9/2) + 10*q^(-11/2))*x1^(-3/2)*x2^(13/2) + (4*q^(13/2) + 10*q^(11/2) + 42*q^(9/2) + 102*q^(7/2) + 212*q^(5/2) + 366*q^(3/2) + 566*q^(1/2) + 642*q^(-1/2) + 658*q^(-3/2) + 570*q^(-5/2) + 430*q^(-7/2) + 270*q^(-9/2) + 152*q^(-11/2) + 70*q^(-13/2) + 28*q^(-15/2) + 6*q^(-17/2))*x1^(-3/2)*x2^(15/2) + (2*q^(19/2) + 7*q^(17/2) + 16*q^(15/2) + 42*q^(13/2) + 99*q^(11/2) + 218*q^(9/2) + 414*q^(7/2) + 716*q^(5/2) + 1114*q^(3/2) + 1598*q^(1/2) + 1908*q^(-1/2) + 2099*q^(-3/2) + 2060*q^(-5/2) + 1846*q^(-7/2) + 1468*q^(-9/2) + 1080*q^(-11/2) + 702*q^(-13/2) + 431*q^(-15/2) + 226*q^(-17/2) + 106*q^(-19/2) + 38*q^(-21/2) + 14*q^(-23/2))*x1^(-3/2)*x2^(17/2) + (4*q^(25/2) + 6*q^(23/2) + 18*q^(21/2) + 38*q^(19/2) + 80*q^(17/2) + 146*q^(15/2) + 294*q^(13/2) + 528*q^(11/2) + 932*q^(9/2) + 1514*q^(7/2) + 2338*q^(5/2) + 3362*q^(3/2) + 4574*q^(1/2) + 5560*q^(-1/2) + 6350*q^(-3/2) + 6696*q^(-5/2) + 6604*q^(-7/2) + 6024*q^(-9/2) + 5158*q^(-11/2) + 4084*q^(-13/2) + 3060*q^(-15/2) + 2130*q^(-17/2) + 1384*q^(-19/2) + 822*q^(-21/2) + 458*q^(-23/2) + 220*q^(-25/2) + 98*q^(-27/2) + 38*q^(-29/2) + 8*q^(-31/2))*x1^(-3/2)*x2^(19/2) + (-q^(-1/2))*x1^(-1/2)*x2^(3/2) + (-4*q^(-1/2))*x1^(-1/2)*x2^(5/2) + (-q^(1/2) - 10*q^(-1/2) - 3*q^(-3/2))*x1^(-1/2)*x2^(7/2) + (-2*q^(3/2) - 4*q^(1/2) - 22*q^(-1/2) - 12*q^(-3/2) - 8*q^(-5/2))*x1^(-1/2)*x2^(9/2) + (-q^(7/2) - 3*q^(5/2) - 8*q^(3/2) - 14*q^(1/2) - 46*q^(-1/2) - 36*q^(-3/2) - 33*q^(-5/2) - 18*q^(-7/2) - 5*q^(-9/2))*x1^(-1/2)*x2^(11/2) + (-2*q^(11/2) - 2*q^(9/2) - 8*q^(7/2) - 14*q^(5/2) - 28*q^(3/2) - 42*q^(1/2) - 100*q^(-1/2) - 94*q^(-3/2) - 102*q^(-5/2) - 80*q^(-7/2) - 56*q^(-9/2) - 20*q^(-11/2) - 12*q^(-13/2))*x1^(-1/2)*x2^(13/2) + (-q^(17/2) - 3*q^(15/2) - 4*q^(13/2) - 11*q^(11/2) - 17*q^(9/2) - 34*q^(7/2) - 53*q^(5/2) - 87*q^(3/2) - 124*q^(1/2) - 225*q^(-1/2) - 242*q^(-3/2) - 276*q^(-5/2) - 261*q^(-7/2) - 230*q^(-9/2) - 158*q^(-11/2) - 102*q^(-13/2) - 51*q^(-15/2) - 26*q^(-17/2) - 7*q^(-19/2))*x1^(-1/2)*x2^(15/2) + (-2*q^(23/2) - 2*q^(21/2) - 6*q^(19/2) - 10*q^(17/2) - 20*q^(15/2) - 28*q^(13/2) - 54*q^(11/2) - 76*q^(9/2) - 126*q^(7/2) - 178*q^(5/2) - 264*q^(3/2) - 352*q^(1/2) - 544*q^(-1/2) - 616*q^(-3/2) - 726*q^(-5/2) - 746*q^(-7/2) - 742*q^(-9/2) - 632*q^(-11/2) - 526*q^(-13/2) - 356*q^(-15/2) - 254*q^(-17/2) - 144*q^(-19/2) - 80*q^(-21/2) - 28*q^(-23/2) - 16*q^(-25/2))*x1^(-1/2)*x2^(17/2) + (-q^(31/2) - 3*q^(29/2) - 4*q^(27/2) - 7*q^(25/2) - 17*q^(23/2) - 23*q^(21/2) - 41*q^(19/2) - 62*q^(17/2) - 98*q^(15/2) - 138*q^(13/2) - 215*q^(11/2) - 294*q^(9/2) - 425*q^(7/2) - 573*q^(5/2) - 780*q^(3/2) - 1003*q^(1/2) - 1379*q^(-1/2) - 1607*q^(-3/2) - 1890*q^(-5/2) - 2047*q^(-7/2) - 2146*q^(-9/2) - 2059*q^(-11/2) - 1918*q^(-13/2) - 1604*q^(-15/2) - 1303*q^(-17/2) - 976*q^(-19/2) - 699*q^(-21/2) - 442*q^(-23/2) - 280*q^(-25/2) - 142*q^(-27/2) - 69*q^(-29/2) - 34*q^(-31/2) - 9*q^(-33/2))*x1^(-1/2)*x2^(19/2)
(1/2, -3/2) (1/2, 1) x1^(-1/2)x2^(3/2) 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, 1, 1]}
(-9*q^(71/2) - 7*q^(69/2) - 12*q^(67/2) - 15*q^(65/2) - 21*q^(63/2) - 23*q^(61/2) - 29*q^(59/2) - 27*q^(57/2) - 26*q^(55/2) - 23*q^(53/2) - 21*q^(51/2) - 15*q^(49/2) - 13*q^(47/2) - 7*q^(45/2) - 4*q^(43/2) - 3*q^(41/2) - q^(39/2))*x1^(-17/2)*x2^(19/2) + (8*q^(55/2) + 6*q^(53/2) + 10*q^(51/2) + 12*q^(49/2) + 16*q^(47/2) + 16*q^(45/2) + 18*q^(43/2) + 12*q^(41/2) + 12*q^(39/2) + 8*q^(37/2) + 6*q^(35/2) + 2*q^(33/2) + 2*q^(31/2))*x1^(-15/2)*x2^(17/2) + (2*q^(69/2) + 4*q^(67/2) + 8*q^(65/2) + 14*q^(63/2) + 24*q^(61/2) + 38*q^(59/2) + 60*q^(57/2) + 106*q^(55/2) + 128*q^(53/2) + 164*q^(51/2) + 194*q^(49/2) + 222*q^(47/2) + 234*q^(45/2) + 238*q^(43/2) + 212*q^(41/2) + 188*q^(39/2) + 154*q^(37/2) + 120*q^(35/2) + 82*q^(33/2) + 56*q^(31/2) + 30*q^(29/2) + 16*q^(27/2) + 8*q^(25/2) + 2*q^(23/2))*x1^(-15/2)*x2^(19/2) + (-7*q^(41/2) - 5*q^(39/2) - 8*q^(37/2) - 9*q^(35/2) - 11*q^(33/2) - 9*q^(31/2) - 7*q^(29/2) - 4*q^(27/2) - 3*q^(25/2) - q^(23/2))*x1^(-13/2)*x2^(15/2) + (-2*q^(53/2) - 4*q^(51/2) - 8*q^(49/2) - 14*q^(47/2) - 24*q^(45/2) - 38*q^(43/2) - 74*q^(41/2) - 84*q^(39/2) - 106*q^(37/2) - 118*q^(35/2) - 128*q^(33/2) - 118*q^(31/2) - 104*q^(29/2) - 76*q^(27/2) - 58*q^(25/2) - 36*q^(23/2) - 20*q^(21/2) - 8*q^(19/2) - 4*q^(17/2))*x1^(-13/2)*x2^(17/2) + (-2*q^(65/2) - 2*q^(63/2) - 6*q^(61/2) - 8*q^(59/2) - 16*q^(57/2) - 22*q^(55/2) - 49*q^(53/2) - 79*q^(51/2) - 135*q^(49/2) - 202*q^(47/2) - 306*q^(45/2) - 430*q^(43/2) - 617*q^(41/2) - 749*q^(39/2) - 895*q^(37/2) - 990*q^(35/2) - 1055*q^(33/2) - 1028*q^(31/2) - 954*q^(29/2) - 807*q^(27/2) - 656*q^(25/2) - 491*q^(23/2) - 345*q^(21/2) - 217*q^(19/2) - 130*q^(17/2) - 66*q^(15/2) - 31*q^(13/2) - 13*q^(11/2) - 3*q^(9/2))*x1^(-13/2)*x2^(19/2) + (6*q^(29/2) + 4*q^(27/2) + 6*q^(25/2) + 6*q^(23/2) + 6*q^(21/2) + 2*q^(19/2) + 2*q^(17/2))*x1^(-11/2)*x2^(13/2) + (2*q^(39/2) + 4*q^(37/2) + 8*q^(35/2) + 14*q^(33/2) + 24*q^(31/2) + 50*q^(29/2) + 54*q^(27/2) + 64*q^(25/2) + 66*q^(23/2) + 62*q^(21/2) + 44*q^(19/2) + 30*q^(17/2) + 16*q^(15/2) + 8*q^(13/2) + 2*q^(11/2))*x1^(-11/2)*x2^(15/2) + (2*q^(49/2) + 2*q^(47/2) + 6*q^(45/2) + 8*q^(43/2) + 16*q^(41/2) + 32*q^(39/2) + 62*q^(37/2) + 98*q^(35/2) + 158*q^(33/2) + 232*q^(31/2) + 347*q^(29/2) + 412*q^(27/2) + 476*q^(25/2) + 493*q^(23/2) + 480*q^(21/2) + 403*q^(19/2) + 320*q^(17/2) + 218*q^(15/2) + 145*q^(13/2) + 78*q^(11/2) + 40*q^(9/2) + 14*q^(7/2) + 6*q^(5/2))*x1^(-11/2)*x2^(17/2) + (2*q^(59/2) + 2*q^(57/2) + 4*q^(55/2) + 8*q^(53/2) + 12*q^(51/2) + 24*q^(49/2) + 40*q^(47/2) + 70*q^(45/2) + 110*q^(43/2) + 188*q^(41/2) + 308*q^(39/2) + 504*q^(37/2) + 764*q^(35/2) + 1128*q^(33/2) + 1562*q^(31/2) + 2098*q^(29/2) + 2534*q^(27/2) + 2910*q^(25/2) + 3088*q^(23/2) + 3086*q^(21/2) + 2838*q^(19/2) + 2462*q^(17/2) + 1966*q^(15/2) + 1484*q^(13/2) + 1034*q^(11/2) + 676*q^(9/2) + 398*q^(7/2) + 222*q^(5/2) + 106*q^(3/2) + 46*q^(1/2) + 18*q^(-1/2) + 4*q^(-3/2))*x1^(-11/2)*x2^(19/2) + (-5*q^(19/2) - 3*q^(17/2) - 4*q^(15/2) - 3*q^(13/2) - q^(11/2))*x1^(-9/2)*x2^(11/2) + (-2*q^(27/2) - 4*q^(25/2) - 8*q^(23/2) - 14*q^(21/2) - 34*q^(19/2) - 32*q^(17/2) - 36*q^(15/2) - 30*q^(13/2) - 20*q^(11/2) - 8*q^(9/2) - 4*q^(7/2))*x1^(-9/2)*x2^(13/2) + (-2*q^(35/2) - 2*q^(33/2) - 6*q^(31/2) - 8*q^(29/2) - 25*q^(27/2) - 43*q^(25/2) - 77*q^(23/2) - 119*q^(21/2) - 192*q^(19/2) - 216*q^(17/2) - 235*q^(15/2) - 214*q^(13/2) - 172*q^(11/2) - 112*q^(9/2) - 66*q^(7/2) - 31*q^(5/2) - 13*q^(3/2) - 3*q^(1/2))*x1^(-9/2)*x2^(15/2) + (-2*q^(43/2) - 2*q^(41/2) - 4*q^(39/2) - 8*q^(37/2) - 18*q^(35/2) - 28*q^(33/2) - 58*q^(31/2) - 92*q^(29/2) - 180*q^(27/2) - 298*q^(25/2) - 488*q^(23/2) - 708*q^(21/2) - 1000*q^(19/2) - 1178*q^(17/2) - 1302*q^(15/2) - 1262*q^(13/2) - 1128*q^(11/2) - 886*q^(9/2) - 652*q^(7/2) - 414*q^(5/2) - 252*q^(3/2) - 128*q^(1/2) - 60*q^(-1/2) - 20*q^(-3/2) - 8*q^(-5/2))*x1^(-9/2)*x2^(17/2) + (-2*q^(51/2) - 2*q^(49/2) - 4*q^(47/2) - 6*q^(45/2) - 18*q^(43/2) - 24*q^(41/2) - 44*q^(39/2) - 74*q^(37/2) - 135*q^(35/2) - 217*q^(33/2) - 389*q^(31/2) - 623*q^(29/2) - 1064*q^(27/2) - 1680*q^(25/2) - 2570*q^(23/2) - 3602*q^(21/2) - 4795*q^(19/2) - 5725*q^(17/2) - 6408*q^(15/2) - 6559*q^(13/2) - 6264*q^(11/2) - 5515*q^(9/2) - 4572*q^(7/2) - 3492*q^(5/2) - 2520*q^(3/2) - 1681*q^(1/2) - 1048*q^(-1/2) - 597*q^(-3/2) - 319*q^(-5/2) - 146*q^(-7/2) - 61*q^(-9/2) - 23*q^(-11/2) - 5*q^(-13/2))*x1^(-9/2)*x2^(19/2) + (4*q^(11/2) + 2*q^(9/2) + 2*q^(7/2))*x1^(-7/2)*x2^(9/2) + (2*q^(17/2) + 4*q^(15/2) + 8*q^(13/2) + 22*q^(11/2) + 18*q^(9/2) + 16*q^(7/2) + 8*q^(5/2) + 2*q^(3/2))*x1^(-7/2)*x2^(11/2) + (2*q^(23/2) + 2*q^(21/2) + 6*q^(19/2) + 16*q^(17/2) + 34*q^(15/2) + 58*q^(13/2) + 103*q^(11/2) + 106*q^(9/2) + 100*q^(7/2) + 69*q^(5/2) + 40*q^(3/2) + 14*q^(1/2) + 6*q^(-1/2))*x1^(-7/2)*x2^(13/2) + (2*q^(29/2) + 2*q^(27/2) + 4*q^(25/2) + 14*q^(23/2) + 22*q^(21/2) + 48*q^(19/2) + 98*q^(17/2) + 190*q^(15/2) + 304*q^(13/2) + 454*q^(11/2) + 512*q^(9/2) + 516*q^(7/2) + 430*q^(5/2) + 316*q^(3/2) + 194*q^(1/2) + 106*q^(-1/2) + 46*q^(-3/2) + 18*q^(-5/2) + 4*q^(-7/2))*x1^(-7/2)*x2^(15/2) + (2*q^(35/2) + 2*q^(33/2) + 4*q^(31/2) + 12*q^(29/2) + 20*q^(27/2) + 36*q^(25/2) + 80*q^(23/2) + 140*q^(21/2) + 278*q^(19/2) + 519*q^(17/2) + 899*q^(15/2) + 1364*q^(13/2) + 1891*q^(11/2) + 2209*q^(9/2) + 2348*q^(7/2) + 2195*q^(5/2) + 1870*q^(3/2) + 1419*q^(1/2) + 1001*q^(-1/2) + 616*q^(-3/2) + 359*q^(-5/2) + 178*q^(-7/2) + 80*q^(-9/2) + 26*q^(-11/2) + 10*q^(-13/2))*x1^(-7/2)*x2^(17/2) + (2*q^(41/2) + 2*q^(39/2) + 4*q^(37/2) + 12*q^(35/2) + 18*q^(33/2) + 34*q^(31/2) + 68*q^(29/2) + 122*q^(27/2) + 216*q^(25/2) + 426*q^(23/2) + 764*q^(21/2) + 1414*q^(19/2) + 2426*q^(17/2) + 3876*q^(15/2) + 5586*q^(13/2) + 7446*q^(11/2) + 8872*q^(9/2) + 9772*q^(7/2) + 9846*q^(5/2) + 9218*q^(3/2) + 7972*q^(1/2) + 6476*q^(-1/2) + 4866*q^(-3/2) + 3444*q^(-5/2) + 2264*q^(-7/2) + 1390*q^(-9/2) + 778*q^(-11/2) + 410*q^(-13/2) + 186*q^(-15/2) + 76*q^(-17/2) + 28*q^(-19/2) + 6*q^(-21/2))*x1^(-7/2)*x2^(19/2) + (-3*q^(5/2) - q^(3/2))*x1^(-5/2)*x2^(7/2) + (-2*q^(9/2) - 4*q^(7/2) - 14*q^(5/2) - 8*q^(3/2) - 4*q^(1/2))*x1^(-5/2)*x2^(9/2) + (-2*q^(13/2) - 2*q^(11/2) - 13*q^(9/2) - 26*q^(7/2) - 53*q^(5/2) - 45*q^(3/2) - 31*q^(1/2) - 13*q^(-1/2) - 3*q^(-3/2))*x1^(-5/2)*x2^(11/2) + (-2*q^(17/2) - 2*q^(15/2) - 10*q^(13/2) - 20*q^(11/2) - 64*q^(9/2) - 116*q^(7/2) - 194*q^(5/2) - 194*q^(3/2) - 170*q^(1/2) - 108*q^(-1/2) - 60*q^(-3/2) - 20*q^(-5/2) - 8*q^(-7/2))*x1^(-5/2)*x2^(13/2) + (-2*q^(21/2) - 2*q^(19/2) - 10*q^(17/2) - 16*q^(15/2) - 54*q^(13/2) - 120*q^(11/2) - 272*q^(9/2) - 451*q^(7/2) - 675*q^(5/2) - 750*q^(3/2) - 737*q^(1/2) - 602*q^(-1/2) - 435*q^(-3/2) - 261*q^(-5/2) - 141*q^(-7/2) - 61*q^(-9/2) - 23*q^(-11/2) - 5*q^(-13/2))*x1^(-5/2)*x2^(15/2) + (-2*q^(25/2) - 2*q^(23/2) - 10*q^(21/2) - 16*q^(19/2) - 54*q^(17/2) - 112*q^(15/2) - 286*q^(13/2) - 564*q^(11/2) - 1054*q^(9/2) - 1622*q^(7/2) - 2284*q^(5/2) - 2668*q^(3/2) - 2842*q^(1/2) - 2648*q^(-1/2) - 2274*q^(-3/2) - 1718*q^(-5/2) - 1216*q^(-7/2) - 750*q^(-9/2) - 442*q^(-11/2) - 216*q^(-13/2) - 100*q^(-15/2) - 32*q^(-17/2) - 12*q^(-19/2))*x1^(-5/2)*x2^(17/2) + (-2*q^(29/2) - 2*q^(27/2) - 10*q^(25/2) - 19*q^(23/2) - 64*q^(21/2) - 133*q^(19/2) - 325*q^(17/2) - 657*q^(15/2) - 1335*q^(13/2) - 2336*q^(11/2) - 3838*q^(9/2) - 5587*q^(7/2) - 7551*q^(5/2) - 9060*q^(3/2) - 10089*q^(1/2) - 10252*q^(-1/2) - 9730*q^(-3/2) - 8498*q^(-5/2) - 6981*q^(-7/2) - 5301*q^(-9/2) - 3804*q^(-11/2) - 2524*q^(-13/2) - 1574*q^(-15/2) - 891*q^(-17/2) - 473*q^(-19/2) - 219*q^(-21/2) - 91*q^(-23/2) - 33*q^(-25/2) - 7*q^(-27/2))*x1^(-5/2)*x2^(19/2) + (2*q^(1/2))*x1^(-3/2)*x2^(5/2) + (2*q^(3/2) + 8*q^(1/2) + 2*q^(-1/2))*x1^(-3/2)*x2^(7/2) + (2*q^(5/2) + 10*q^(3/2) + 25*q^(1/2) + 14*q^(-1/2) + 6*q^(-3/2))*x1^(-3/2)*x2^(9/2) + (2*q^(7/2) + 14*q^(5/2) + 36*q^(3/2) + 72*q^(1/2) + 60*q^(-1/2) + 42*q^(-3/2) + 18*q^(-5/2) + 4*q^(-7/2))*x1^(-3/2)*x2^(11/2) + (4*q^(9/2) + 21*q^(7/2) + 58*q^(5/2) + 118*q^(3/2) + 202*q^(1/2) + 206*q^(-1/2) + 186*q^(-3/2) + 127*q^(-5/2) + 70*q^(-7/2) + 26*q^(-9/2) + 10*q^(-11/2))*x1^(-3/2)*x2^(13/2) + (4*q^(13/2) + 10*q^(11/2) + 42*q^(9/2) + 102*q^(7/2) + 212*q^(5/2) + 366*q^(3/2) + 566*q^(1/2) + 642*q^(-1/2) + 658*q^(-3/2) + 570*q^(-5/2) + 430*q^(-7/2) + 270*q^(-9/2) + 152*q^(-11/2) + 70*q^(-13/2) + 28*q^(-15/2) + 6*q^(-17/2))*x1^(-3/2)*x2^(15/2) + (2*q^(19/2) + 7*q^(17/2) + 16*q^(15/2) + 42*q^(13/2) + 99*q^(11/2) + 218*q^(9/2) + 414*q^(7/2) + 716*q^(5/2) + 1114*q^(3/2) + 1598*q^(1/2) + 1908*q^(-1/2) + 2099*q^(-3/2) + 2060*q^(-5/2) + 1846*q^(-7/2) + 1468*q^(-9/2) + 1080*q^(-11/2) + 702*q^(-13/2) + 431*q^(-15/2) + 226*q^(-17/2) + 106*q^(-19/2) + 38*q^(-21/2) + 14*q^(-23/2))*x1^(-3/2)*x2^(17/2) + (4*q^(25/2) + 6*q^(23/2) + 18*q^(21/2) + 38*q^(19/2) + 80*q^(17/2) + 146*q^(15/2) + 294*q^(13/2) + 528*q^(11/2) + 932*q^(9/2) + 1514*q^(7/2) + 2338*q^(5/2) + 3362*q^(3/2) + 4574*q^(1/2) + 5560*q^(-1/2) + 6350*q^(-3/2) + 6696*q^(-5/2) + 6604*q^(-7/2) + 6024*q^(-9/2) + 5158*q^(-11/2) + 4084*q^(-13/2) + 3060*q^(-15/2) + 2130*q^(-17/2) + 1384*q^(-19/2) + 822*q^(-21/2) + 458*q^(-23/2) + 220*q^(-25/2) + 98*q^(-27/2) + 38*q^(-29/2) + 8*q^(-31/2))*x1^(-3/2)*x2^(19/2) + (-q^(-1/2))*x1^(-1/2)*x2^(3/2) + (-4*q^(-1/2))*x1^(-1/2)*x2^(5/2) + (-q^(1/2) - 10*q^(-1/2) - 3*q^(-3/2))*x1^(-1/2)*x2^(7/2) + (-2*q^(3/2) - 4*q^(1/2) - 22*q^(-1/2) - 12*q^(-3/2) - 8*q^(-5/2))*x1^(-1/2)*x2^(9/2) + (-q^(7/2) - 3*q^(5/2) - 8*q^(3/2) - 14*q^(1/2) - 46*q^(-1/2) - 36*q^(-3/2) - 33*q^(-5/2) - 18*q^(-7/2) - 5*q^(-9/2))*x1^(-1/2)*x2^(11/2) + (-2*q^(11/2) - 2*q^(9/2) - 8*q^(7/2) - 14*q^(5/2) - 28*q^(3/2) - 42*q^(1/2) - 100*q^(-1/2) - 94*q^(-3/2) - 102*q^(-5/2) - 80*q^(-7/2) - 56*q^(-9/2) - 20*q^(-11/2) - 12*q^(-13/2))*x1^(-1/2)*x2^(13/2) + (-q^(17/2) - 3*q^(15/2) - 4*q^(13/2) - 11*q^(11/2) - 17*q^(9/2) - 34*q^(7/2) - 53*q^(5/2) - 87*q^(3/2) - 124*q^(1/2) - 225*q^(-1/2) - 242*q^(-3/2) - 276*q^(-5/2) - 261*q^(-7/2) - 230*q^(-9/2) - 158*q^(-11/2) - 102*q^(-13/2) - 51*q^(-15/2) - 26*q^(-17/2) - 7*q^(-19/2))*x1^(-1/2)*x2^(15/2) + (-2*q^(23/2) - 2*q^(21/2) - 6*q^(19/2) - 10*q^(17/2) - 20*q^(15/2) - 28*q^(13/2) - 54*q^(11/2) - 76*q^(9/2) - 126*q^(7/2) - 178*q^(5/2) - 264*q^(3/2) - 352*q^(1/2) - 544*q^(-1/2) - 616*q^(-3/2) - 726*q^(-5/2) - 746*q^(-7/2) - 742*q^(-9/2) - 632*q^(-11/2) - 526*q^(-13/2) - 356*q^(-15/2) - 254*q^(-17/2) - 144*q^(-19/2) - 80*q^(-21/2) - 28*q^(-23/2) - 16*q^(-25/2))*x1^(-1/2)*x2^(17/2) + (-q^(31/2) - 3*q^(29/2) - 4*q^(27/2) - 7*q^(25/2) - 17*q^(23/2) - 23*q^(21/2) - 41*q^(19/2) - 62*q^(17/2) - 98*q^(15/2) - 138*q^(13/2) - 215*q^(11/2) - 294*q^(9/2) - 425*q^(7/2) - 573*q^(5/2) - 780*q^(3/2) - 1003*q^(1/2) - 1379*q^(-1/2) - 1607*q^(-3/2) - 1890*q^(-5/2) - 2047*q^(-7/2) - 2146*q^(-9/2) - 2059*q^(-11/2) - 1918*q^(-13/2) - 1604*q^(-15/2) - 1303*q^(-17/2) - 976*q^(-19/2) - 699*q^(-21/2) - 442*q^(-23/2) - 280*q^(-25/2) - 142*q^(-27/2) - 69*q^(-29/2) - 34*q^(-31/2) - 9*q^(-33/2))*x1^(-1/2)*x2^(19/2)
(-1/2, 3/2) x1^(1/2)x2^(-3/2) q^(-1/2)
(-9*q^(71/2) - 7*q^(69/2) - 12*q^(67/2) - 15*q^(65/2) - 21*q^(63/2) - 23*q^(61/2) - 29*q^(59/2) - 27*q^(57/2) - 26*q^(55/2) - 23*q^(53/2) - 21*q^(51/2) - 15*q^(49/2) - 13*q^(47/2) - 7*q^(45/2) - 4*q^(43/2) - 3*q^(41/2) - q^(39/2))*x1^(17/2)*x2^(-19/2) + (8*q^(55/2) + 6*q^(53/2) + 10*q^(51/2) + 12*q^(49/2) + 16*q^(47/2) + 16*q^(45/2) + 18*q^(43/2) + 12*q^(41/2) + 12*q^(39/2) + 8*q^(37/2) + 6*q^(35/2) + 2*q^(33/2) + 2*q^(31/2))*x1^(15/2)*x2^(-17/2) + (2*q^(69/2) + 4*q^(67/2) + 8*q^(65/2) + 14*q^(63/2) + 24*q^(61/2) + 38*q^(59/2) + 60*q^(57/2) + 106*q^(55/2) + 128*q^(53/2) + 164*q^(51/2) + 194*q^(49/2) + 222*q^(47/2) + 234*q^(45/2) + 238*q^(43/2) + 212*q^(41/2) + 188*q^(39/2) + 154*q^(37/2) + 120*q^(35/2) + 82*q^(33/2) + 56*q^(31/2) + 30*q^(29/2) + 16*q^(27/2) + 8*q^(25/2) + 2*q^(23/2))*x1^(15/2)*x2^(-19/2) + (-7*q^(41/2) - 5*q^(39/2) - 8*q^(37/2) - 9*q^(35/2) - 11*q^(33/2) - 9*q^(31/2) - 7*q^(29/2) - 4*q^(27/2) - 3*q^(25/2) - q^(23/2))*x1^(13/2)*x2^(-15/2) + (-2*q^(53/2) - 4*q^(51/2) - 8*q^(49/2) - 14*q^(47/2) - 24*q^(45/2) - 38*q^(43/2) - 74*q^(41/2) - 84*q^(39/2) - 106*q^(37/2) - 118*q^(35/2) - 128*q^(33/2) - 118*q^(31/2) - 104*q^(29/2) - 76*q^(27/2) - 58*q^(25/2) - 36*q^(23/2) - 20*q^(21/2) - 8*q^(19/2) - 4*q^(17/2))*x1^(13/2)*x2^(-17/2) + (-2*q^(65/2) - 2*q^(63/2) - 6*q^(61/2) - 8*q^(59/2) - 16*q^(57/2) - 22*q^(55/2) - 49*q^(53/2) - 79*q^(51/2) - 135*q^(49/2) - 202*q^(47/2) - 306*q^(45/2) - 430*q^(43/2) - 617*q^(41/2) - 749*q^(39/2) - 895*q^(37/2) - 990*q^(35/2) - 1055*q^(33/2) - 1028*q^(31/2) - 954*q^(29/2) - 807*q^(27/2) - 656*q^(25/2) - 491*q^(23/2) - 345*q^(21/2) - 217*q^(19/2) - 130*q^(17/2) - 66*q^(15/2) - 31*q^(13/2) - 13*q^(11/2) - 3*q^(9/2))*x1^(13/2)*x2^(-19/2) + (6*q^(29/2) + 4*q^(27/2) + 6*q^(25/2) + 6*q^(23/2) + 6*q^(21/2) + 2*q^(19/2) + 2*q^(17/2))*x1^(11/2)*x2^(-13/2) + (2*q^(39/2) + 4*q^(37/2) + 8*q^(35/2) + 14*q^(33/2) + 24*q^(31/2) + 50*q^(29/2) + 54*q^(27/2) + 64*q^(25/2) + 66*q^(23/2) + 62*q^(21/2) + 44*q^(19/2) + 30*q^(17/2) + 16*q^(15/2) + 8*q^(13/2) + 2*q^(11/2))*x1^(11/2)*x2^(-15/2) + (2*q^(49/2) + 2*q^(47/2) + 6*q^(45/2) + 8*q^(43/2) + 16*q^(41/2) + 32*q^(39/2) + 62*q^(37/2) + 98*q^(35/2) + 158*q^(33/2) + 232*q^(31/2) + 347*q^(29/2) + 412*q^(27/2) + 476*q^(25/2) + 493*q^(23/2) + 480*q^(21/2) + 403*q^(19/2) + 320*q^(17/2) + 218*q^(15/2) + 145*q^(13/2) + 78*q^(11/2) + 40*q^(9/2) + 14*q^(7/2) + 6*q^(5/2))*x1^(11/2)*x2^(-17/2) + (2*q^(59/2) + 2*q^(57/2) + 4*q^(55/2) + 8*q^(53/2) + 12*q^(51/2) + 24*q^(49/2) + 40*q^(47/2) + 70*q^(45/2) + 110*q^(43/2) + 188*q^(41/2) + 308*q^(39/2) + 504*q^(37/2) + 764*q^(35/2) + 1128*q^(33/2) + 1562*q^(31/2) + 2098*q^(29/2) + 2534*q^(27/2) + 2910*q^(25/2) + 3088*q^(23/2) + 3086*q^(21/2) + 2838*q^(19/2) + 2462*q^(17/2) + 1966*q^(15/2) + 1484*q^(13/2) + 1034*q^(11/2) + 676*q^(9/2) + 398*q^(7/2) + 222*q^(5/2) + 106*q^(3/2) + 46*q^(1/2) + 18*q^(-1/2) + 4*q^(-3/2))*x1^(11/2)*x2^(-19/2) + (-5*q^(19/2) - 3*q^(17/2) - 4*q^(15/2) - 3*q^(13/2) - q^(11/2))*x1^(9/2)*x2^(-11/2) + (-2*q^(27/2) - 4*q^(25/2) - 8*q^(23/2) - 14*q^(21/2) - 34*q^(19/2) - 32*q^(17/2) - 36*q^(15/2) - 30*q^(13/2) - 20*q^(11/2) - 8*q^(9/2) - 4*q^(7/2))*x1^(9/2)*x2^(-13/2) + (-2*q^(35/2) - 2*q^(33/2) - 6*q^(31/2) - 8*q^(29/2) - 25*q^(27/2) - 43*q^(25/2) - 77*q^(23/2) - 119*q^(21/2) - 192*q^(19/2) - 216*q^(17/2) - 235*q^(15/2) - 214*q^(13/2) - 172*q^(11/2) - 112*q^(9/2) - 66*q^(7/2) - 31*q^(5/2) - 13*q^(3/2) - 3*q^(1/2))*x1^(9/2)*x2^(-15/2) + (-2*q^(43/2) - 2*q^(41/2) - 4*q^(39/2) - 8*q^(37/2) - 18*q^(35/2) - 28*q^(33/2) - 58*q^(31/2) - 92*q^(29/2) - 180*q^(27/2) - 298*q^(25/2) - 488*q^(23/2) - 708*q^(21/2) - 1000*q^(19/2) - 1178*q^(17/2) - 1302*q^(15/2) - 1262*q^(13/2) - 1128*q^(11/2) - 886*q^(9/2) - 652*q^(7/2) - 414*q^(5/2) - 252*q^(3/2) - 128*q^(1/2) - 60*q^(-1/2) - 20*q^(-3/2) - 8*q^(-5/2))*x1^(9/2)*x2^(-17/2) + (-2*q^(51/2) - 2*q^(49/2) - 4*q^(47/2) - 6*q^(45/2) - 18*q^(43/2) - 24*q^(41/2) - 44*q^(39/2) - 74*q^(37/2) - 135*q^(35/2) - 217*q^(33/2) - 389*q^(31/2) - 623*q^(29/2) - 1064*q^(27/2) - 1680*q^(25/2) - 2570*q^(23/2) - 3602*q^(21/2) - 4795*q^(19/2) - 5725*q^(17/2) - 6408*q^(15/2) - 6559*q^(13/2) - 6264*q^(11/2) - 5515*q^(9/2) - 4572*q^(7/2) - 3492*q^(5/2) - 2520*q^(3/2) - 1681*q^(1/2) - 1048*q^(-1/2) - 597*q^(-3/2) - 319*q^(-5/2) - 146*q^(-7/2) - 61*q^(-9/2) - 23*q^(-11/2) - 5*q^(-13/2))*x1^(9/2)*x2^(-19/2) + (4*q^(11/2) + 2*q^(9/2) + 2*q^(7/2))*x1^(7/2)*x2^(-9/2) + (2*q^(17/2) + 4*q^(15/2) + 8*q^(13/2) + 22*q^(11/2) + 18*q^(9/2) + 16*q^(7/2) + 8*q^(5/2) + 2*q^(3/2))*x1^(7/2)*x2^(-11/2) + (2*q^(23/2) + 2*q^(21/2) + 6*q^(19/2) + 16*q^(17/2) + 34*q^(15/2) + 58*q^(13/2) + 103*q^(11/2) + 106*q^(9/2) + 100*q^(7/2) + 69*q^(5/2) + 40*q^(3/2) + 14*q^(1/2) + 6*q^(-1/2))*x1^(7/2)*x2^(-13/2) + (2*q^(29/2) + 2*q^(27/2) + 4*q^(25/2) + 14*q^(23/2) + 22*q^(21/2) + 48*q^(19/2) + 98*q^(17/2) + 190*q^(15/2) + 304*q^(13/2) + 454*q^(11/2) + 512*q^(9/2) + 516*q^(7/2) + 430*q^(5/2) + 316*q^(3/2) + 194*q^(1/2) + 106*q^(-1/2) + 46*q^(-3/2) + 18*q^(-5/2) + 4*q^(-7/2))*x1^(7/2)*x2^(-15/2) + (2*q^(35/2) + 2*q^(33/2) + 4*q^(31/2) + 12*q^(29/2) + 20*q^(27/2) + 36*q^(25/2) + 80*q^(23/2) + 140*q^(21/2) + 278*q^(19/2) + 519*q^(17/2) + 899*q^(15/2) + 1364*q^(13/2) + 1891*q^(11/2) + 2209*q^(9/2) + 2348*q^(7/2) + 2195*q^(5/2) + 1870*q^(3/2) + 1419*q^(1/2) + 1001*q^(-1/2) + 616*q^(-3/2) + 359*q^(-5/2) + 178*q^(-7/2) + 80*q^(-9/2) + 26*q^(-11/2) + 10*q^(-13/2))*x1^(7/2)*x2^(-17/2) + (2*q^(41/2) + 2*q^(39/2) + 4*q^(37/2) + 12*q^(35/2) + 18*q^(33/2) + 34*q^(31/2) + 68*q^(29/2) + 122*q^(27/2) + 216*q^(25/2) + 426*q^(23/2) + 764*q^(21/2) + 1414*q^(19/2) + 2426*q^(17/2) + 3876*q^(15/2) + 5586*q^(13/2) + 7446*q^(11/2) + 8872*q^(9/2) + 9772*q^(7/2) + 9846*q^(5/2) + 9218*q^(3/2) + 7972*q^(1/2) + 6476*q^(-1/2) + 4866*q^(-3/2) + 3444*q^(-5/2) + 2264*q^(-7/2) + 1390*q^(-9/2) + 778*q^(-11/2) + 410*q^(-13/2) + 186*q^(-15/2) + 76*q^(-17/2) + 28*q^(-19/2) + 6*q^(-21/2))*x1^(7/2)*x2^(-19/2) + (-3*q^(5/2) - q^(3/2))*x1^(5/2)*x2^(-7/2) + (-2*q^(9/2) - 4*q^(7/2) - 14*q^(5/2) - 8*q^(3/2) - 4*q^(1/2))*x1^(5/2)*x2^(-9/2) + (-2*q^(13/2) - 2*q^(11/2) - 13*q^(9/2) - 26*q^(7/2) - 53*q^(5/2) - 45*q^(3/2) - 31*q^(1/2) - 13*q^(-1/2) - 3*q^(-3/2))*x1^(5/2)*x2^(-11/2) + (-2*q^(17/2) - 2*q^(15/2) - 10*q^(13/2) - 20*q^(11/2) - 64*q^(9/2) - 116*q^(7/2) - 194*q^(5/2) - 194*q^(3/2) - 170*q^(1/2) - 108*q^(-1/2) - 60*q^(-3/2) - 20*q^(-5/2) - 8*q^(-7/2))*x1^(5/2)*x2^(-13/2) + (-2*q^(21/2) - 2*q^(19/2) - 10*q^(17/2) - 16*q^(15/2) - 54*q^(13/2) - 120*q^(11/2) - 272*q^(9/2) - 451*q^(7/2) - 675*q^(5/2) - 750*q^(3/2) - 737*q^(1/2) - 602*q^(-1/2) - 435*q^(-3/2) - 261*q^(-5/2) - 141*q^(-7/2) - 61*q^(-9/2) - 23*q^(-11/2) - 5*q^(-13/2))*x1^(5/2)*x2^(-15/2) + (-2*q^(25/2) - 2*q^(23/2) - 10*q^(21/2) - 16*q^(19/2) - 54*q^(17/2) - 112*q^(15/2) - 286*q^(13/2) - 564*q^(11/2) - 1054*q^(9/2) - 1622*q^(7/2) - 2284*q^(5/2) - 2668*q^(3/2) - 2842*q^(1/2) - 2648*q^(-1/2) - 2274*q^(-3/2) - 1718*q^(-5/2) - 1216*q^(-7/2) - 750*q^(-9/2) - 442*q^(-11/2) - 216*q^(-13/2) - 100*q^(-15/2) - 32*q^(-17/2) - 12*q^(-19/2))*x1^(5/2)*x2^(-17/2) + (-2*q^(29/2) - 2*q^(27/2) - 10*q^(25/2) - 19*q^(23/2) - 64*q^(21/2) - 133*q^(19/2) - 325*q^(17/2) - 657*q^(15/2) - 1335*q^(13/2) - 2336*q^(11/2) - 3838*q^(9/2) - 5587*q^(7/2) - 7551*q^(5/2) - 9060*q^(3/2) - 10089*q^(1/2) - 10252*q^(-1/2) - 9730*q^(-3/2) - 8498*q^(-5/2) - 6981*q^(-7/2) - 5301*q^(-9/2) - 3804*q^(-11/2) - 2524*q^(-13/2) - 1574*q^(-15/2) - 891*q^(-17/2) - 473*q^(-19/2) - 219*q^(-21/2) - 91*q^(-23/2) - 33*q^(-25/2) - 7*q^(-27/2))*x1^(5/2)*x2^(-19/2) + (2*q^(1/2))*x1^(3/2)*x2^(-5/2) + (2*q^(3/2) + 8*q^(1/2) + 2*q^(-1/2))*x1^(3/2)*x2^(-7/2) + (2*q^(5/2) + 10*q^(3/2) + 25*q^(1/2) + 14*q^(-1/2) + 6*q^(-3/2))*x1^(3/2)*x2^(-9/2) + (2*q^(7/2) + 14*q^(5/2) + 36*q^(3/2) + 72*q^(1/2) + 60*q^(-1/2) + 42*q^(-3/2) + 18*q^(-5/2) + 4*q^(-7/2))*x1^(3/2)*x2^(-11/2) + (4*q^(9/2) + 21*q^(7/2) + 58*q^(5/2) + 118*q^(3/2) + 202*q^(1/2) + 206*q^(-1/2) + 186*q^(-3/2) + 127*q^(-5/2) + 70*q^(-7/2) + 26*q^(-9/2) + 10*q^(-11/2))*x1^(3/2)*x2^(-13/2) + (4*q^(13/2) + 10*q^(11/2) + 42*q^(9/2) + 102*q^(7/2) + 212*q^(5/2) + 366*q^(3/2) + 566*q^(1/2) + 642*q^(-1/2) + 658*q^(-3/2) + 570*q^(-5/2) + 430*q^(-7/2) + 270*q^(-9/2) + 152*q^(-11/2) + 70*q^(-13/2) + 28*q^(-15/2) + 6*q^(-17/2))*x1^(3/2)*x2^(-15/2) + (2*q^(19/2) + 7*q^(17/2) + 16*q^(15/2) + 42*q^(13/2) + 99*q^(11/2) + 218*q^(9/2) + 414*q^(7/2) + 716*q^(5/2) + 1114*q^(3/2) + 1598*q^(1/2) + 1908*q^(-1/2) + 2099*q^(-3/2) + 2060*q^(-5/2) + 1846*q^(-7/2) + 1468*q^(-9/2) + 1080*q^(-11/2) + 702*q^(-13/2) + 431*q^(-15/2) + 226*q^(-17/2) + 106*q^(-19/2) + 38*q^(-21/2) + 14*q^(-23/2))*x1^(3/2)*x2^(-17/2) + (4*q^(25/2) + 6*q^(23/2) + 18*q^(21/2) + 38*q^(19/2) + 80*q^(17/2) + 146*q^(15/2) + 294*q^(13/2) + 528*q^(11/2) + 932*q^(9/2) + 1514*q^(7/2) + 2338*q^(5/2) + 3362*q^(3/2) + 4574*q^(1/2) + 5560*q^(-1/2) + 6350*q^(-3/2) + 6696*q^(-5/2) + 6604*q^(-7/2) + 6024*q^(-9/2) + 5158*q^(-11/2) + 4084*q^(-13/2) + 3060*q^(-15/2) + 2130*q^(-17/2) + 1384*q^(-19/2) + 822*q^(-21/2) + 458*q^(-23/2) + 220*q^(-25/2) + 98*q^(-27/2) + 38*q^(-29/2) + 8*q^(-31/2))*x1^(3/2)*x2^(-19/2) + (-q^(-1/2))*x1^(1/2)*x2^(-3/2) + (-4*q^(-1/2))*x1^(1/2)*x2^(-5/2) + (-q^(1/2) - 10*q^(-1/2) - 3*q^(-3/2))*x1^(1/2)*x2^(-7/2) + (-2*q^(3/2) - 4*q^(1/2) - 22*q^(-1/2) - 12*q^(-3/2) - 8*q^(-5/2))*x1^(1/2)*x2^(-9/2) + (-q^(7/2) - 3*q^(5/2) - 8*q^(3/2) - 14*q^(1/2) - 46*q^(-1/2) - 36*q^(-3/2) - 33*q^(-5/2) - 18*q^(-7/2) - 5*q^(-9/2))*x1^(1/2)*x2^(-11/2) + (-2*q^(11/2) - 2*q^(9/2) - 8*q^(7/2) - 14*q^(5/2) - 28*q^(3/2) - 42*q^(1/2) - 100*q^(-1/2) - 94*q^(-3/2) - 102*q^(-5/2) - 80*q^(-7/2) - 56*q^(-9/2) - 20*q^(-11/2) - 12*q^(-13/2))*x1^(1/2)*x2^(-13/2) + (-q^(17/2) - 3*q^(15/2) - 4*q^(13/2) - 11*q^(11/2) - 17*q^(9/2) - 34*q^(7/2) - 53*q^(5/2) - 87*q^(3/2) - 124*q^(1/2) - 225*q^(-1/2) - 242*q^(-3/2) - 276*q^(-5/2) - 261*q^(-7/2) - 230*q^(-9/2) - 158*q^(-11/2) - 102*q^(-13/2) - 51*q^(-15/2) - 26*q^(-17/2) - 7*q^(-19/2))*x1^(1/2)*x2^(-15/2) + (-2*q^(23/2) - 2*q^(21/2) - 6*q^(19/2) - 10*q^(17/2) - 20*q^(15/2) - 28*q^(13/2) - 54*q^(11/2) - 76*q^(9/2) - 126*q^(7/2) - 178*q^(5/2) - 264*q^(3/2) - 352*q^(1/2) - 544*q^(-1/2) - 616*q^(-3/2) - 726*q^(-5/2) - 746*q^(-7/2) - 742*q^(-9/2) - 632*q^(-11/2) - 526*q^(-13/2) - 356*q^(-15/2) - 254*q^(-17/2) - 144*q^(-19/2) - 80*q^(-21/2) - 28*q^(-23/2) - 16*q^(-25/2))*x1^(1/2)*x2^(-17/2) + (-q^(31/2) - 3*q^(29/2) - 4*q^(27/2) - 7*q^(25/2) - 17*q^(23/2) - 23*q^(21/2) - 41*q^(19/2) - 62*q^(17/2) - 98*q^(15/2) - 138*q^(13/2) - 215*q^(11/2) - 294*q^(9/2) - 425*q^(7/2) - 573*q^(5/2) - 780*q^(3/2) - 1003*q^(1/2) - 1379*q^(-1/2) - 1607*q^(-3/2) - 1890*q^(-5/2) - 2047*q^(-7/2) - 2146*q^(-9/2) - 2059*q^(-11/2) - 1918*q^(-13/2) - 1604*q^(-15/2) - 1303*q^(-17/2) - 976*q^(-19/2) - 699*q^(-21/2) - 442*q^(-23/2) - 280*q^(-25/2) - 142*q^(-27/2) - 69*q^(-29/2) - 34*q^(-31/2) - 9*q^(-33/2))*x1^(1/2)*x2^(-19/2)

Braid

Braid word Components Crossings Strands
[2, -3, 2, -3, -4, 1, -2, 3, -4, -2, -1] 2 11 5

Multivariable Alexander polynomial

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

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, -1) no
(1, -3) yes
(1, 1) no
(-1, 3) yes
Dual Thurston polygon-10105h1h2

HFL polytope

Poincaré polynomial
2*m^(-2)*A1^(-1)*A2^(-1) + m^(-2)*A2^(-2) + 6*m^(-1)*A1^(-1) + 7*m^(-1)*A2^(-1) + m^(-1)*A1*A2^(-2) + 5*A1^(-1)*A2 + 12 + 5*A1*A2^(-1) + m*A1^(-1)*A2^2 + 7*m*A2 + 6*m*A1 + m^2*A2^2 + 2*m^2*A1*A2
VertexMaslovRank
(-1, -1)-22
(0, -2)-21
(1, -2)-11
(1, 1)22
(0, 2)21
(-1, 2)11
HFL polytope-101-202A1A2

Record

FL/HFL Links

orderOption(int) 55
namestring L8a3{0}
statusstring success
slugstring L8a3_0_515ff118
result_filestring details/L8a3_0_515ff118.json
complexity_scoreOption(int) 128
strandsOption(int) null
crossingsOption(int) 8
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 56
wall_secondsOption(float) 0.001647
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 13
vertex_countOption(int) 6
fibered_vertex_countOption(int) 2
polytope_statusstring computed
alexander_support_sizeOption(int) 6
alexander_vertex_countOption(int) 4
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks)
{
  "dataset": "FLHFLLinks",
  "key": "L8a3_0_515ff118"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L8a3_0_515ff118