details/L10a78_0_d198ea41.json

FL expansions

Newt(ΔL) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle FL
(-1, -2) (1, 1) x1^(1)x2^(2) q^(-3/2)
{"0": [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], "1": [-1, 1, -1, 1, -1, 1]}
(-q^(-3/2))*x1*x2^(2) + (-4*q^(-3/2))*x1*x2^(3) + (4*q^(-5/2))*x1^(2)*x2^(3) + (-2*q^(-1/2) - 10*q^(-3/2))*x1*x2^(4) + (4*q^(-3/2) + 16*q^(-5/2) + 5*q^(-7/2))*x1^(2)*x2^(4) + (-q^(-5/2) - 6*q^(-7/2) - 5*q^(-9/2))*x1^(3)*x2^(4) + (-4*q^(1/2) - 8*q^(-1/2) - 20*q^(-3/2))*x1*x2^(5) + (9*q^(-1/2) + 24*q^(-3/2) + 48*q^(-5/2) + 20*q^(-7/2) + 7*q^(-9/2))*x1^(2)*x2^(5) + (-4*q^(-3/2) - 20*q^(-5/2) - 35*q^(-7/2) - 33*q^(-9/2) - 9*q^(-11/2) - 7*q^(-13/2))*x1^(3)*x2^(5) + (4*q^(-7/2) + 7*q^(-9/2) + 13*q^(-11/2) + q^(-13/2) + 7*q^(-15/2))*x1^(4)*x2^(5) + (-2*q^(5/2) - 6*q^(3/2) - 17*q^(1/2) - 20*q^(-1/2) - 35*q^(-3/2))*x1*x2^(6) + (4*q^(3/2) + 20*q^(1/2) + 56*q^(-1/2) + 91*q^(-3/2) + 122*q^(-5/2) + 62*q^(-7/2) + 28*q^(-9/2) + 9*q^(-11/2))*x1^(2)*x2^(6) + (-2*q^(1/2) - 18*q^(-1/2) - 58*q^(-3/2) - 117*q^(-5/2) - 154*q^(-7/2) - 136*q^(-9/2) - 70*q^(-11/2) - 44*q^(-13/2) - 16*q^(-15/2) - 9*q^(-17/2))*x1^(3)*x2^(6) + (4*q^(-3/2) + 20*q^(-5/2) + 52*q^(-7/2) + 80*q^(-9/2) + 92*q^(-11/2) + 50*q^(-13/2) + 46*q^(-15/2) + 23*q^(-17/2) + 16*q^(-19/2) + 9*q^(-21/2))*x1^(4)*x2^(6) + (-q^(-7/2) - 6*q^(-9/2) - 13*q^(-11/2) - 18*q^(-13/2) - 12*q^(-15/2) - 11*q^(-17/2) - 3*q^(-19/2) - 7*q^(-21/2) - 9*q^(-23/2))*x1^(5)*x2^(6) + (-4*q^(9/2) - 4*q^(7/2) - 16*q^(5/2) - 28*q^(3/2) - 44*q^(1/2) - 40*q^(-1/2) - 56*q^(-3/2))*x1*x2^(7) + (8*q^(7/2) + 18*q^(5/2) + 60*q^(3/2) + 128*q^(1/2) + 218*q^(-1/2) + 264*q^(-3/2) + 289*q^(-5/2) + 162*q^(-7/2) + 86*q^(-9/2) + 36*q^(-11/2) + 11*q^(-13/2))*x1^(2)*x2^(7) + (-4*q^(5/2) - 24*q^(3/2) - 72*q^(1/2) - 190*q^(-1/2) - 344*q^(-3/2) - 504*q^(-5/2) - 553*q^(-7/2) - 485*q^(-9/2) - 306*q^(-11/2) - 211*q^(-13/2) - 105*q^(-15/2) - 63*q^(-17/2) - 20*q^(-19/2) - 11*q^(-21/2))*x1^(3)*x2^(7) + (9*q^(1/2) + 32*q^(-1/2) + 110*q^(-3/2) + 222*q^(-5/2) + 384*q^(-7/2) + 476*q^(-9/2) + 493*q^(-11/2) + 358*q^(-13/2) + 295*q^(-15/2) + 189*q^(-17/2) + 155*q^(-19/2) + 91*q^(-21/2) + 47*q^(-23/2) + 20*q^(-25/2) + 11*q^(-27/2))*x1^(4)*x2^(7) + (-4*q^(-3/2) - 20*q^(-5/2) - 56*q^(-7/2) - 111*q^(-9/2) - 177*q^(-11/2) - 196*q^(-13/2) - 178*q^(-15/2) - 135*q^(-17/2) - 94*q^(-19/2) - 87*q^(-21/2) - 100*q^(-23/2) - 55*q^(-25/2) - 36*q^(-27/2) - 20*q^(-29/2) - 11*q^(-31/2))*x1^(5)*x2^(7) + (4*q^(-9/2) + 7*q^(-11/2) + 21*q^(-13/2) + 24*q^(-15/2) + 30*q^(-17/2) + 19*q^(-19/2) + 15*q^(-21/2) - q^(-23/2) + 23*q^(-25/2) + 14*q^(-27/2) + 16*q^(-29/2) + 9*q^(-31/2) + 11*q^(-33/2))*x1^(6)*x2^(7) + (-2*q^(15/2) - 6*q^(13/2) - 8*q^(11/2) - 22*q^(9/2) - 28*q^(7/2) - 62*q^(5/2) - 76*q^(3/2) - 90*q^(1/2) - 70*q^(-1/2) - 84*q^(-3/2))*x1*x2^(8) + (4*q^(13/2) + 16*q^(11/2) + 36*q^(9/2) + 88*q^(7/2) + 172*q^(5/2) + 330*q^(3/2) + 502*q^(1/2) + 646*q^(-1/2) + 675*q^(-3/2) + 640*q^(-5/2) + 390*q^(-7/2) + 222*q^(-9/2) + 110*q^(-11/2) + 44*q^(-13/2) + 13*q^(-15/2))*x1^(2)*x2^(8) + (-2*q^(11/2) - 14*q^(9/2) - 51*q^(7/2) - 132*q^(5/2) - 314*q^(3/2) - 614*q^(1/2) - 1055*q^(-1/2) - 1476*q^(-3/2) - 1784*q^(-5/2) - 1790*q^(-7/2) - 1544*q^(-9/2) - 1098*q^(-11/2) - 786*q^(-13/2) - 472*q^(-15/2) - 290*q^(-17/2) - 140*q^(-19/2) - 77*q^(-21/2) - 24*q^(-23/2) - 13*q^(-25/2))*x1^(3)*x2^(8) + (4*q^(7/2) + 24*q^(5/2) + 84*q^(3/2) + 232*q^(1/2) + 503*q^(-1/2) + 959*q^(-3/2) + 1487*q^(-5/2) + 2006*q^(-7/2) + 2246*q^(-9/2) + 2200*q^(-11/2) + 1804*q^(-13/2) + 1488*q^(-15/2) + 1113*q^(-17/2) + 872*q^(-19/2) + 614*q^(-21/2) + 390*q^(-23/2) + 223*q^(-25/2) + 128*q^(-27/2) + 57*q^(-29/2) + 24*q^(-31/2) + 13*q^(-33/2))*x1^(4)*x2^(8) + (-2*q^(3/2) - 18*q^(1/2) - 66*q^(-1/2) - 177*q^(-3/2) - 385*q^(-5/2) - 689*q^(-7/2) - 1038*q^(-9/2) - 1326*q^(-11/2) - 1419*q^(-13/2) - 1318*q^(-15/2) - 1101*q^(-17/2) - 888*q^(-19/2) - 793*q^(-21/2) - 749*q^(-23/2) - 589*q^(-25/2) - 442*q^(-27/2) - 300*q^(-29/2) - 187*q^(-31/2) - 95*q^(-33/2) - 57*q^(-35/2) - 24*q^(-37/2) - 13*q^(-39/2))*x1^(5)*x2^(8) + (4*q^(-3/2) + 20*q^(-5/2) + 56*q^(-7/2) + 128*q^(-9/2) + 224*q^(-11/2) + 336*q^(-13/2) + 401*q^(-15/2) + 424*q^(-17/2) + 353*q^(-19/2) + 276*q^(-21/2) + 203*q^(-23/2) + 258*q^(-25/2) + 261*q^(-27/2) + 263*q^(-29/2) + 233*q^(-31/2) + 186*q^(-33/2) + 110*q^(-35/2) + 71*q^(-37/2) + 44*q^(-39/2) + 24*q^(-41/2) + 13*q^(-43/2))*x1^(6)*x2^(8) + (-q^(-9/2) - 6*q^(-11/2) - 13*q^(-13/2) - 26*q^(-15/2) - 36*q^(-17/2) - 45*q^(-19/2) - 40*q^(-21/2) - 29*q^(-23/2) - 5*q^(-25/2) - 11*q^(-27/2) - 14*q^(-29/2) - 22*q^(-31/2) - 42*q^(-33/2) - 55*q^(-35/2) - 32*q^(-37/2) - 27*q^(-39/2) - 20*q^(-41/2) - 11*q^(-43/2) - 13*q^(-45/2))*x1^(7)*x2^(8) + (-4*q^(21/2) - 4*q^(19/2) - 12*q^(17/2) - 20*q^(15/2) - 36*q^(13/2) - 44*q^(11/2) - 84*q^(9/2) - 108*q^(7/2) - 160*q^(5/2) - 160*q^(3/2) - 160*q^(1/2) - 112*q^(-1/2) - 120*q^(-3/2))*x1*x2^(9) + (8*q^(19/2) + 16*q^(17/2) + 42*q^(15/2) + 88*q^(13/2) + 177*q^(11/2) + 302*q^(9/2) + 540*q^(7/2) + 836*q^(5/2) + 1224*q^(3/2) + 1506*q^(1/2) + 1657*q^(-1/2) + 1562*q^(-3/2) + 1365*q^(-5/2) + 868*q^(-7/2) + 526*q^(-9/2) + 282*q^(-11/2) + 134*q^(-13/2) + 52*q^(-15/2) + 15*q^(-17/2))*x1^(2)*x2^(9) + (-4*q^(17/2) - 20*q^(15/2) - 52*q^(13/2) - 144*q^(11/2) - 318*q^(9/2) - 660*q^(7/2) - 1211*q^(5/2) - 2089*q^(3/2) - 3162*q^(1/2) - 4352*q^(-1/2) - 5203*q^(-3/2) - 5629*q^(-5/2) - 5330*q^(-7/2) - 4578*q^(-9/2) - 3446*q^(-11/2) - 2557*q^(-13/2) - 1679*q^(-15/2) - 1100*q^(-17/2) - 615*q^(-19/2) - 365*q^(-21/2) - 168*q^(-23/2) - 91*q^(-25/2) - 28*q^(-27/2) - 15*q^(-29/2))*x1^(3)*x2^(9) + (8*q^(13/2) + 26*q^(11/2) + 100*q^(9/2) + 256*q^(7/2) + 618*q^(5/2) + 1247*q^(3/2) + 2331*q^(1/2) + 3790*q^(-1/2) + 5656*q^(-3/2) + 7376*q^(-5/2) + 8739*q^(-7/2) + 9134*q^(-9/2) + 8759*q^(-11/2) + 7545*q^(-13/2) + 6400*q^(-15/2) + 5088*q^(-17/2) + 4059*q^(-19/2) + 3014*q^(-21/2) + 2144*q^(-23/2) + 1385*q^(-25/2) + 890*q^(-27/2) + 499*q^(-29/2) + 286*q^(-31/2) + 152*q^(-33/2) + 67*q^(-35/2) + 28*q^(-37/2) + 15*q^(-39/2))*x1^(4)*x2^(9) + (-4*q^(9/2) - 24*q^(7/2) - 88*q^(5/2) - 248*q^(3/2) - 606*q^(1/2) - 1232*q^(-1/2) - 2250*q^(-3/2) - 3624*q^(-5/2) - 5237*q^(-7/2) - 6707*q^(-9/2) - 7761*q^(-11/2) - 7976*q^(-13/2) - 7559*q^(-15/2) - 6674*q^(-17/2) - 5831*q^(-19/2) - 5160*q^(-21/2) - 4679*q^(-23/2) - 3935*q^(-25/2) - 3203*q^(-27/2) - 2387*q^(-29/2) - 1691*q^(-31/2) - 1098*q^(-33/2) - 726*q^(-35/2) - 419*q^(-37/2) - 255*q^(-39/2) - 128*q^(-41/2) - 67*q^(-43/2) - 28*q^(-45/2) - 15*q^(-47/2))*x1^(5)*x2^(9) + (9*q^(3/2) + 32*q^(1/2) + 118*q^(-1/2) + 282*q^(-3/2) + 614*q^(-5/2) + 1102*q^(-7/2) + 1813*q^(-9/2) + 2541*q^(-11/2) + 3267*q^(-13/2) + 3635*q^(-15/2) + 3721*q^(-17/2) + 3342*q^(-19/2) + 2952*q^(-21/2) + 2560*q^(-23/2) + 2583*q^(-25/2) + 2546*q^(-27/2) + 2575*q^(-29/2) + 2348*q^(-31/2) + 2024*q^(-33/2) + 1515*q^(-35/2) + 1141*q^(-37/2) + 788*q^(-39/2) + 546*q^(-41/2) + 336*q^(-43/2) + 203*q^(-45/2) + 113*q^(-47/2) + 67*q^(-49/2) + 28*q^(-51/2) + 15*q^(-53/2))*x1^(6)*x2^(9) + (-4*q^(-3/2) - 20*q^(-5/2) - 56*q^(-7/2) - 132*q^(-9/2) - 255*q^(-11/2) - 421*q^(-13/2) - 600*q^(-15/2) - 762*q^(-17/2) - 826*q^(-19/2) - 790*q^(-21/2) - 642*q^(-23/2) - 490*q^(-25/2) - 416*q^(-27/2) - 450*q^(-29/2) - 550*q^(-31/2) - 739*q^(-33/2) - 834*q^(-35/2) - 773*q^(-37/2) - 657*q^(-39/2) - 542*q^(-41/2) - 408*q^(-43/2) - 318*q^(-45/2) - 199*q^(-47/2) - 136*q^(-49/2) - 85*q^(-51/2) - 52*q^(-53/2) - 28*q^(-55/2) - 15*q^(-57/2))*x1^(7)*x2^(9) + (4*q^(-11/2) + 7*q^(-13/2) + 21*q^(-15/2) + 32*q^(-17/2) + 54*q^(-19/2) + 58*q^(-21/2) + 70*q^(-23/2) + 42*q^(-25/2) + 28*q^(-27/2) - 8*q^(-29/2) - 15*q^(-31/2) - 30*q^(-33/2) + 21*q^(-35/2) + 51*q^(-37/2) + 104*q^(-39/2) + 101*q^(-41/2) + 111*q^(-43/2) + 95*q^(-45/2) + 88*q^(-47/2) + 54*q^(-49/2) + 51*q^(-51/2) + 33*q^(-53/2) + 24*q^(-55/2) + 13*q^(-57/2) + 15*q^(-59/2))*x1^(8)*x2^(9)
(-1, -2) (1, 1) x1^(1)x2^(2) q^(-3/2)
{"0": [1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1], "1": [-1, 1, -1, 1, -1, 1]}
(-q^(-3/2))*x1*x2^(2) + (-4*q^(-3/2))*x1*x2^(3) + (4*q^(-5/2))*x1^(2)*x2^(3) + (-2*q^(-1/2) - 10*q^(-3/2))*x1*x2^(4) + (4*q^(-3/2) + 16*q^(-5/2) + 5*q^(-7/2))*x1^(2)*x2^(4) + (-q^(-5/2) - 6*q^(-7/2) - 5*q^(-9/2))*x1^(3)*x2^(4) + (-4*q^(1/2) - 8*q^(-1/2) - 20*q^(-3/2))*x1*x2^(5) + (9*q^(-1/2) + 24*q^(-3/2) + 48*q^(-5/2) + 20*q^(-7/2) + 7*q^(-9/2))*x1^(2)*x2^(5) + (-4*q^(-3/2) - 20*q^(-5/2) - 35*q^(-7/2) - 33*q^(-9/2) - 9*q^(-11/2) - 7*q^(-13/2))*x1^(3)*x2^(5) + (4*q^(-7/2) + 7*q^(-9/2) + 13*q^(-11/2) + q^(-13/2) + 7*q^(-15/2))*x1^(4)*x2^(5) + (-2*q^(5/2) - 6*q^(3/2) - 17*q^(1/2) - 20*q^(-1/2) - 35*q^(-3/2))*x1*x2^(6) + (4*q^(3/2) + 20*q^(1/2) + 56*q^(-1/2) + 91*q^(-3/2) + 122*q^(-5/2) + 62*q^(-7/2) + 28*q^(-9/2) + 9*q^(-11/2))*x1^(2)*x2^(6) + (-2*q^(1/2) - 18*q^(-1/2) - 58*q^(-3/2) - 117*q^(-5/2) - 154*q^(-7/2) - 136*q^(-9/2) - 70*q^(-11/2) - 44*q^(-13/2) - 16*q^(-15/2) - 9*q^(-17/2))*x1^(3)*x2^(6) + (4*q^(-3/2) + 20*q^(-5/2) + 52*q^(-7/2) + 80*q^(-9/2) + 92*q^(-11/2) + 50*q^(-13/2) + 46*q^(-15/2) + 23*q^(-17/2) + 16*q^(-19/2) + 9*q^(-21/2))*x1^(4)*x2^(6) + (-q^(-7/2) - 6*q^(-9/2) - 13*q^(-11/2) - 18*q^(-13/2) - 12*q^(-15/2) - 11*q^(-17/2) - 3*q^(-19/2) - 7*q^(-21/2) - 9*q^(-23/2))*x1^(5)*x2^(6) + (-4*q^(9/2) - 4*q^(7/2) - 16*q^(5/2) - 28*q^(3/2) - 44*q^(1/2) - 40*q^(-1/2) - 56*q^(-3/2))*x1*x2^(7) + (8*q^(7/2) + 18*q^(5/2) + 60*q^(3/2) + 128*q^(1/2) + 218*q^(-1/2) + 264*q^(-3/2) + 289*q^(-5/2) + 162*q^(-7/2) + 86*q^(-9/2) + 36*q^(-11/2) + 11*q^(-13/2))*x1^(2)*x2^(7) + (-4*q^(5/2) - 24*q^(3/2) - 72*q^(1/2) - 190*q^(-1/2) - 344*q^(-3/2) - 504*q^(-5/2) - 553*q^(-7/2) - 485*q^(-9/2) - 306*q^(-11/2) - 211*q^(-13/2) - 105*q^(-15/2) - 63*q^(-17/2) - 20*q^(-19/2) - 11*q^(-21/2))*x1^(3)*x2^(7) + (9*q^(1/2) + 32*q^(-1/2) + 110*q^(-3/2) + 222*q^(-5/2) + 384*q^(-7/2) + 476*q^(-9/2) + 493*q^(-11/2) + 358*q^(-13/2) + 295*q^(-15/2) + 189*q^(-17/2) + 155*q^(-19/2) + 91*q^(-21/2) + 47*q^(-23/2) + 20*q^(-25/2) + 11*q^(-27/2))*x1^(4)*x2^(7) + (-4*q^(-3/2) - 20*q^(-5/2) - 56*q^(-7/2) - 111*q^(-9/2) - 177*q^(-11/2) - 196*q^(-13/2) - 178*q^(-15/2) - 135*q^(-17/2) - 94*q^(-19/2) - 87*q^(-21/2) - 100*q^(-23/2) - 55*q^(-25/2) - 36*q^(-27/2) - 20*q^(-29/2) - 11*q^(-31/2))*x1^(5)*x2^(7) + (4*q^(-9/2) + 7*q^(-11/2) + 21*q^(-13/2) + 24*q^(-15/2) + 30*q^(-17/2) + 19*q^(-19/2) + 15*q^(-21/2) - q^(-23/2) + 23*q^(-25/2) + 14*q^(-27/2) + 16*q^(-29/2) + 9*q^(-31/2) + 11*q^(-33/2))*x1^(6)*x2^(7) + (-2*q^(15/2) - 6*q^(13/2) - 8*q^(11/2) - 22*q^(9/2) - 28*q^(7/2) - 62*q^(5/2) - 76*q^(3/2) - 90*q^(1/2) - 70*q^(-1/2) - 84*q^(-3/2))*x1*x2^(8) + (4*q^(13/2) + 16*q^(11/2) + 36*q^(9/2) + 88*q^(7/2) + 172*q^(5/2) + 330*q^(3/2) + 502*q^(1/2) + 646*q^(-1/2) + 675*q^(-3/2) + 640*q^(-5/2) + 390*q^(-7/2) + 222*q^(-9/2) + 110*q^(-11/2) + 44*q^(-13/2) + 13*q^(-15/2))*x1^(2)*x2^(8) + (-2*q^(11/2) - 14*q^(9/2) - 51*q^(7/2) - 132*q^(5/2) - 314*q^(3/2) - 614*q^(1/2) - 1055*q^(-1/2) - 1476*q^(-3/2) - 1784*q^(-5/2) - 1790*q^(-7/2) - 1544*q^(-9/2) - 1098*q^(-11/2) - 786*q^(-13/2) - 472*q^(-15/2) - 290*q^(-17/2) - 140*q^(-19/2) - 77*q^(-21/2) - 24*q^(-23/2) - 13*q^(-25/2))*x1^(3)*x2^(8) + (4*q^(7/2) + 24*q^(5/2) + 84*q^(3/2) + 232*q^(1/2) + 503*q^(-1/2) + 959*q^(-3/2) + 1487*q^(-5/2) + 2006*q^(-7/2) + 2246*q^(-9/2) + 2200*q^(-11/2) + 1804*q^(-13/2) + 1488*q^(-15/2) + 1113*q^(-17/2) + 872*q^(-19/2) + 614*q^(-21/2) + 390*q^(-23/2) + 223*q^(-25/2) + 128*q^(-27/2) + 57*q^(-29/2) + 24*q^(-31/2) + 13*q^(-33/2))*x1^(4)*x2^(8) + (-2*q^(3/2) - 18*q^(1/2) - 66*q^(-1/2) - 177*q^(-3/2) - 385*q^(-5/2) - 689*q^(-7/2) - 1038*q^(-9/2) - 1326*q^(-11/2) - 1419*q^(-13/2) - 1318*q^(-15/2) - 1101*q^(-17/2) - 888*q^(-19/2) - 793*q^(-21/2) - 749*q^(-23/2) - 589*q^(-25/2) - 442*q^(-27/2) - 300*q^(-29/2) - 187*q^(-31/2) - 95*q^(-33/2) - 57*q^(-35/2) - 24*q^(-37/2) - 13*q^(-39/2))*x1^(5)*x2^(8) + (4*q^(-3/2) + 20*q^(-5/2) + 56*q^(-7/2) + 128*q^(-9/2) + 224*q^(-11/2) + 336*q^(-13/2) + 401*q^(-15/2) + 424*q^(-17/2) + 353*q^(-19/2) + 276*q^(-21/2) + 203*q^(-23/2) + 258*q^(-25/2) + 261*q^(-27/2) + 263*q^(-29/2) + 233*q^(-31/2) + 186*q^(-33/2) + 110*q^(-35/2) + 71*q^(-37/2) + 44*q^(-39/2) + 24*q^(-41/2) + 13*q^(-43/2))*x1^(6)*x2^(8) + (-q^(-9/2) - 6*q^(-11/2) - 13*q^(-13/2) - 26*q^(-15/2) - 36*q^(-17/2) - 45*q^(-19/2) - 40*q^(-21/2) - 29*q^(-23/2) - 5*q^(-25/2) - 11*q^(-27/2) - 14*q^(-29/2) - 22*q^(-31/2) - 42*q^(-33/2) - 55*q^(-35/2) - 32*q^(-37/2) - 27*q^(-39/2) - 20*q^(-41/2) - 11*q^(-43/2) - 13*q^(-45/2))*x1^(7)*x2^(8) + (-4*q^(21/2) - 4*q^(19/2) - 12*q^(17/2) - 20*q^(15/2) - 36*q^(13/2) - 44*q^(11/2) - 84*q^(9/2) - 108*q^(7/2) - 160*q^(5/2) - 160*q^(3/2) - 160*q^(1/2) - 112*q^(-1/2) - 120*q^(-3/2))*x1*x2^(9) + (8*q^(19/2) + 16*q^(17/2) + 42*q^(15/2) + 88*q^(13/2) + 177*q^(11/2) + 302*q^(9/2) + 540*q^(7/2) + 836*q^(5/2) + 1224*q^(3/2) + 1506*q^(1/2) + 1657*q^(-1/2) + 1562*q^(-3/2) + 1365*q^(-5/2) + 868*q^(-7/2) + 526*q^(-9/2) + 282*q^(-11/2) + 134*q^(-13/2) + 52*q^(-15/2) + 15*q^(-17/2))*x1^(2)*x2^(9) + (-4*q^(17/2) - 20*q^(15/2) - 52*q^(13/2) - 144*q^(11/2) - 318*q^(9/2) - 660*q^(7/2) - 1211*q^(5/2) - 2089*q^(3/2) - 3162*q^(1/2) - 4352*q^(-1/2) - 5203*q^(-3/2) - 5629*q^(-5/2) - 5330*q^(-7/2) - 4578*q^(-9/2) - 3446*q^(-11/2) - 2557*q^(-13/2) - 1679*q^(-15/2) - 1100*q^(-17/2) - 615*q^(-19/2) - 365*q^(-21/2) - 168*q^(-23/2) - 91*q^(-25/2) - 28*q^(-27/2) - 15*q^(-29/2))*x1^(3)*x2^(9) + (8*q^(13/2) + 26*q^(11/2) + 100*q^(9/2) + 256*q^(7/2) + 618*q^(5/2) + 1247*q^(3/2) + 2331*q^(1/2) + 3790*q^(-1/2) + 5656*q^(-3/2) + 7376*q^(-5/2) + 8739*q^(-7/2) + 9134*q^(-9/2) + 8759*q^(-11/2) + 7545*q^(-13/2) + 6400*q^(-15/2) + 5088*q^(-17/2) + 4059*q^(-19/2) + 3014*q^(-21/2) + 2144*q^(-23/2) + 1385*q^(-25/2) + 890*q^(-27/2) + 499*q^(-29/2) + 286*q^(-31/2) + 152*q^(-33/2) + 67*q^(-35/2) + 28*q^(-37/2) + 15*q^(-39/2))*x1^(4)*x2^(9) + (-4*q^(9/2) - 24*q^(7/2) - 88*q^(5/2) - 248*q^(3/2) - 606*q^(1/2) - 1232*q^(-1/2) - 2250*q^(-3/2) - 3624*q^(-5/2) - 5237*q^(-7/2) - 6707*q^(-9/2) - 7761*q^(-11/2) - 7976*q^(-13/2) - 7559*q^(-15/2) - 6674*q^(-17/2) - 5831*q^(-19/2) - 5160*q^(-21/2) - 4679*q^(-23/2) - 3935*q^(-25/2) - 3203*q^(-27/2) - 2387*q^(-29/2) - 1691*q^(-31/2) - 1098*q^(-33/2) - 726*q^(-35/2) - 419*q^(-37/2) - 255*q^(-39/2) - 128*q^(-41/2) - 67*q^(-43/2) - 28*q^(-45/2) - 15*q^(-47/2))*x1^(5)*x2^(9) + (9*q^(3/2) + 32*q^(1/2) + 118*q^(-1/2) + 282*q^(-3/2) + 614*q^(-5/2) + 1102*q^(-7/2) + 1813*q^(-9/2) + 2541*q^(-11/2) + 3267*q^(-13/2) + 3635*q^(-15/2) + 3721*q^(-17/2) + 3342*q^(-19/2) + 2952*q^(-21/2) + 2560*q^(-23/2) + 2583*q^(-25/2) + 2546*q^(-27/2) + 2575*q^(-29/2) + 2348*q^(-31/2) + 2024*q^(-33/2) + 1515*q^(-35/2) + 1141*q^(-37/2) + 788*q^(-39/2) + 546*q^(-41/2) + 336*q^(-43/2) + 203*q^(-45/2) + 113*q^(-47/2) + 67*q^(-49/2) + 28*q^(-51/2) + 15*q^(-53/2))*x1^(6)*x2^(9) + (-4*q^(-3/2) - 20*q^(-5/2) - 56*q^(-7/2) - 132*q^(-9/2) - 255*q^(-11/2) - 421*q^(-13/2) - 600*q^(-15/2) - 762*q^(-17/2) - 826*q^(-19/2) - 790*q^(-21/2) - 642*q^(-23/2) - 490*q^(-25/2) - 416*q^(-27/2) - 450*q^(-29/2) - 550*q^(-31/2) - 739*q^(-33/2) - 834*q^(-35/2) - 773*q^(-37/2) - 657*q^(-39/2) - 542*q^(-41/2) - 408*q^(-43/2) - 318*q^(-45/2) - 199*q^(-47/2) - 136*q^(-49/2) - 85*q^(-51/2) - 52*q^(-53/2) - 28*q^(-55/2) - 15*q^(-57/2))*x1^(7)*x2^(9) + (4*q^(-11/2) + 7*q^(-13/2) + 21*q^(-15/2) + 32*q^(-17/2) + 54*q^(-19/2) + 58*q^(-21/2) + 70*q^(-23/2) + 42*q^(-25/2) + 28*q^(-27/2) - 8*q^(-29/2) - 15*q^(-31/2) - 30*q^(-33/2) + 21*q^(-35/2) + 51*q^(-37/2) + 104*q^(-39/2) + 101*q^(-41/2) + 111*q^(-43/2) + 95*q^(-45/2) + 88*q^(-47/2) + 54*q^(-49/2) + 51*q^(-51/2) + 33*q^(-53/2) + 24*q^(-55/2) + 13*q^(-57/2) + 15*q^(-59/2))*x1^(8)*x2^(9)
(1, 2) x1^(-1)x2^(-2) q^(-3/2)
(-q^(-3/2))*x1^(-1)*x2^(-2) + (-4*q^(-3/2))*x1^(-1)*x2^(-3) + (4*q^(-5/2))*x1^(-2)*x2^(-3) + (-2*q^(-1/2) - 10*q^(-3/2))*x1^(-1)*x2^(-4) + (4*q^(-3/2) + 16*q^(-5/2) + 5*q^(-7/2))*x1^(-2)*x2^(-4) + (-q^(-5/2) - 6*q^(-7/2) - 5*q^(-9/2))*x1^(-3)*x2^(-4) + (-4*q^(1/2) - 8*q^(-1/2) - 20*q^(-3/2))*x1^(-1)*x2^(-5) + (9*q^(-1/2) + 24*q^(-3/2) + 48*q^(-5/2) + 20*q^(-7/2) + 7*q^(-9/2))*x1^(-2)*x2^(-5) + (-4*q^(-3/2) - 20*q^(-5/2) - 35*q^(-7/2) - 33*q^(-9/2) - 9*q^(-11/2) - 7*q^(-13/2))*x1^(-3)*x2^(-5) + (4*q^(-7/2) + 7*q^(-9/2) + 13*q^(-11/2) + q^(-13/2) + 7*q^(-15/2))*x1^(-4)*x2^(-5) + (-2*q^(5/2) - 6*q^(3/2) - 17*q^(1/2) - 20*q^(-1/2) - 35*q^(-3/2))*x1^(-1)*x2^(-6) + (4*q^(3/2) + 20*q^(1/2) + 56*q^(-1/2) + 91*q^(-3/2) + 122*q^(-5/2) + 62*q^(-7/2) + 28*q^(-9/2) + 9*q^(-11/2))*x1^(-2)*x2^(-6) + (-2*q^(1/2) - 18*q^(-1/2) - 58*q^(-3/2) - 117*q^(-5/2) - 154*q^(-7/2) - 136*q^(-9/2) - 70*q^(-11/2) - 44*q^(-13/2) - 16*q^(-15/2) - 9*q^(-17/2))*x1^(-3)*x2^(-6) + (4*q^(-3/2) + 20*q^(-5/2) + 52*q^(-7/2) + 80*q^(-9/2) + 92*q^(-11/2) + 50*q^(-13/2) + 46*q^(-15/2) + 23*q^(-17/2) + 16*q^(-19/2) + 9*q^(-21/2))*x1^(-4)*x2^(-6) + (-q^(-7/2) - 6*q^(-9/2) - 13*q^(-11/2) - 18*q^(-13/2) - 12*q^(-15/2) - 11*q^(-17/2) - 3*q^(-19/2) - 7*q^(-21/2) - 9*q^(-23/2))*x1^(-5)*x2^(-6) + (-4*q^(9/2) - 4*q^(7/2) - 16*q^(5/2) - 28*q^(3/2) - 44*q^(1/2) - 40*q^(-1/2) - 56*q^(-3/2))*x1^(-1)*x2^(-7) + (8*q^(7/2) + 18*q^(5/2) + 60*q^(3/2) + 128*q^(1/2) + 218*q^(-1/2) + 264*q^(-3/2) + 289*q^(-5/2) + 162*q^(-7/2) + 86*q^(-9/2) + 36*q^(-11/2) + 11*q^(-13/2))*x1^(-2)*x2^(-7) + (-4*q^(5/2) - 24*q^(3/2) - 72*q^(1/2) - 190*q^(-1/2) - 344*q^(-3/2) - 504*q^(-5/2) - 553*q^(-7/2) - 485*q^(-9/2) - 306*q^(-11/2) - 211*q^(-13/2) - 105*q^(-15/2) - 63*q^(-17/2) - 20*q^(-19/2) - 11*q^(-21/2))*x1^(-3)*x2^(-7) + (9*q^(1/2) + 32*q^(-1/2) + 110*q^(-3/2) + 222*q^(-5/2) + 384*q^(-7/2) + 476*q^(-9/2) + 493*q^(-11/2) + 358*q^(-13/2) + 295*q^(-15/2) + 189*q^(-17/2) + 155*q^(-19/2) + 91*q^(-21/2) + 47*q^(-23/2) + 20*q^(-25/2) + 11*q^(-27/2))*x1^(-4)*x2^(-7) + (-4*q^(-3/2) - 20*q^(-5/2) - 56*q^(-7/2) - 111*q^(-9/2) - 177*q^(-11/2) - 196*q^(-13/2) - 178*q^(-15/2) - 135*q^(-17/2) - 94*q^(-19/2) - 87*q^(-21/2) - 100*q^(-23/2) - 55*q^(-25/2) - 36*q^(-27/2) - 20*q^(-29/2) - 11*q^(-31/2))*x1^(-5)*x2^(-7) + (4*q^(-9/2) + 7*q^(-11/2) + 21*q^(-13/2) + 24*q^(-15/2) + 30*q^(-17/2) + 19*q^(-19/2) + 15*q^(-21/2) - q^(-23/2) + 23*q^(-25/2) + 14*q^(-27/2) + 16*q^(-29/2) + 9*q^(-31/2) + 11*q^(-33/2))*x1^(-6)*x2^(-7) + (-2*q^(15/2) - 6*q^(13/2) - 8*q^(11/2) - 22*q^(9/2) - 28*q^(7/2) - 62*q^(5/2) - 76*q^(3/2) - 90*q^(1/2) - 70*q^(-1/2) - 84*q^(-3/2))*x1^(-1)*x2^(-8) + (4*q^(13/2) + 16*q^(11/2) + 36*q^(9/2) + 88*q^(7/2) + 172*q^(5/2) + 330*q^(3/2) + 502*q^(1/2) + 646*q^(-1/2) + 675*q^(-3/2) + 640*q^(-5/2) + 390*q^(-7/2) + 222*q^(-9/2) + 110*q^(-11/2) + 44*q^(-13/2) + 13*q^(-15/2))*x1^(-2)*x2^(-8) + (-2*q^(11/2) - 14*q^(9/2) - 51*q^(7/2) - 132*q^(5/2) - 314*q^(3/2) - 614*q^(1/2) - 1055*q^(-1/2) - 1476*q^(-3/2) - 1784*q^(-5/2) - 1790*q^(-7/2) - 1544*q^(-9/2) - 1098*q^(-11/2) - 786*q^(-13/2) - 472*q^(-15/2) - 290*q^(-17/2) - 140*q^(-19/2) - 77*q^(-21/2) - 24*q^(-23/2) - 13*q^(-25/2))*x1^(-3)*x2^(-8) + (4*q^(7/2) + 24*q^(5/2) + 84*q^(3/2) + 232*q^(1/2) + 503*q^(-1/2) + 959*q^(-3/2) + 1487*q^(-5/2) + 2006*q^(-7/2) + 2246*q^(-9/2) + 2200*q^(-11/2) + 1804*q^(-13/2) + 1488*q^(-15/2) + 1113*q^(-17/2) + 872*q^(-19/2) + 614*q^(-21/2) + 390*q^(-23/2) + 223*q^(-25/2) + 128*q^(-27/2) + 57*q^(-29/2) + 24*q^(-31/2) + 13*q^(-33/2))*x1^(-4)*x2^(-8) + (-2*q^(3/2) - 18*q^(1/2) - 66*q^(-1/2) - 177*q^(-3/2) - 385*q^(-5/2) - 689*q^(-7/2) - 1038*q^(-9/2) - 1326*q^(-11/2) - 1419*q^(-13/2) - 1318*q^(-15/2) - 1101*q^(-17/2) - 888*q^(-19/2) - 793*q^(-21/2) - 749*q^(-23/2) - 589*q^(-25/2) - 442*q^(-27/2) - 300*q^(-29/2) - 187*q^(-31/2) - 95*q^(-33/2) - 57*q^(-35/2) - 24*q^(-37/2) - 13*q^(-39/2))*x1^(-5)*x2^(-8) + (4*q^(-3/2) + 20*q^(-5/2) + 56*q^(-7/2) + 128*q^(-9/2) + 224*q^(-11/2) + 336*q^(-13/2) + 401*q^(-15/2) + 424*q^(-17/2) + 353*q^(-19/2) + 276*q^(-21/2) + 203*q^(-23/2) + 258*q^(-25/2) + 261*q^(-27/2) + 263*q^(-29/2) + 233*q^(-31/2) + 186*q^(-33/2) + 110*q^(-35/2) + 71*q^(-37/2) + 44*q^(-39/2) + 24*q^(-41/2) + 13*q^(-43/2))*x1^(-6)*x2^(-8) + (-q^(-9/2) - 6*q^(-11/2) - 13*q^(-13/2) - 26*q^(-15/2) - 36*q^(-17/2) - 45*q^(-19/2) - 40*q^(-21/2) - 29*q^(-23/2) - 5*q^(-25/2) - 11*q^(-27/2) - 14*q^(-29/2) - 22*q^(-31/2) - 42*q^(-33/2) - 55*q^(-35/2) - 32*q^(-37/2) - 27*q^(-39/2) - 20*q^(-41/2) - 11*q^(-43/2) - 13*q^(-45/2))*x1^(-7)*x2^(-8) + (-4*q^(21/2) - 4*q^(19/2) - 12*q^(17/2) - 20*q^(15/2) - 36*q^(13/2) - 44*q^(11/2) - 84*q^(9/2) - 108*q^(7/2) - 160*q^(5/2) - 160*q^(3/2) - 160*q^(1/2) - 112*q^(-1/2) - 120*q^(-3/2))*x1^(-1)*x2^(-9) + (8*q^(19/2) + 16*q^(17/2) + 42*q^(15/2) + 88*q^(13/2) + 177*q^(11/2) + 302*q^(9/2) + 540*q^(7/2) + 836*q^(5/2) + 1224*q^(3/2) + 1506*q^(1/2) + 1657*q^(-1/2) + 1562*q^(-3/2) + 1365*q^(-5/2) + 868*q^(-7/2) + 526*q^(-9/2) + 282*q^(-11/2) + 134*q^(-13/2) + 52*q^(-15/2) + 15*q^(-17/2))*x1^(-2)*x2^(-9) + (-4*q^(17/2) - 20*q^(15/2) - 52*q^(13/2) - 144*q^(11/2) - 318*q^(9/2) - 660*q^(7/2) - 1211*q^(5/2) - 2089*q^(3/2) - 3162*q^(1/2) - 4352*q^(-1/2) - 5203*q^(-3/2) - 5629*q^(-5/2) - 5330*q^(-7/2) - 4578*q^(-9/2) - 3446*q^(-11/2) - 2557*q^(-13/2) - 1679*q^(-15/2) - 1100*q^(-17/2) - 615*q^(-19/2) - 365*q^(-21/2) - 168*q^(-23/2) - 91*q^(-25/2) - 28*q^(-27/2) - 15*q^(-29/2))*x1^(-3)*x2^(-9) + (8*q^(13/2) + 26*q^(11/2) + 100*q^(9/2) + 256*q^(7/2) + 618*q^(5/2) + 1247*q^(3/2) + 2331*q^(1/2) + 3790*q^(-1/2) + 5656*q^(-3/2) + 7376*q^(-5/2) + 8739*q^(-7/2) + 9134*q^(-9/2) + 8759*q^(-11/2) + 7545*q^(-13/2) + 6400*q^(-15/2) + 5088*q^(-17/2) + 4059*q^(-19/2) + 3014*q^(-21/2) + 2144*q^(-23/2) + 1385*q^(-25/2) + 890*q^(-27/2) + 499*q^(-29/2) + 286*q^(-31/2) + 152*q^(-33/2) + 67*q^(-35/2) + 28*q^(-37/2) + 15*q^(-39/2))*x1^(-4)*x2^(-9) + (-4*q^(9/2) - 24*q^(7/2) - 88*q^(5/2) - 248*q^(3/2) - 606*q^(1/2) - 1232*q^(-1/2) - 2250*q^(-3/2) - 3624*q^(-5/2) - 5237*q^(-7/2) - 6707*q^(-9/2) - 7761*q^(-11/2) - 7976*q^(-13/2) - 7559*q^(-15/2) - 6674*q^(-17/2) - 5831*q^(-19/2) - 5160*q^(-21/2) - 4679*q^(-23/2) - 3935*q^(-25/2) - 3203*q^(-27/2) - 2387*q^(-29/2) - 1691*q^(-31/2) - 1098*q^(-33/2) - 726*q^(-35/2) - 419*q^(-37/2) - 255*q^(-39/2) - 128*q^(-41/2) - 67*q^(-43/2) - 28*q^(-45/2) - 15*q^(-47/2))*x1^(-5)*x2^(-9) + (9*q^(3/2) + 32*q^(1/2) + 118*q^(-1/2) + 282*q^(-3/2) + 614*q^(-5/2) + 1102*q^(-7/2) + 1813*q^(-9/2) + 2541*q^(-11/2) + 3267*q^(-13/2) + 3635*q^(-15/2) + 3721*q^(-17/2) + 3342*q^(-19/2) + 2952*q^(-21/2) + 2560*q^(-23/2) + 2583*q^(-25/2) + 2546*q^(-27/2) + 2575*q^(-29/2) + 2348*q^(-31/2) + 2024*q^(-33/2) + 1515*q^(-35/2) + 1141*q^(-37/2) + 788*q^(-39/2) + 546*q^(-41/2) + 336*q^(-43/2) + 203*q^(-45/2) + 113*q^(-47/2) + 67*q^(-49/2) + 28*q^(-51/2) + 15*q^(-53/2))*x1^(-6)*x2^(-9) + (-4*q^(-3/2) - 20*q^(-5/2) - 56*q^(-7/2) - 132*q^(-9/2) - 255*q^(-11/2) - 421*q^(-13/2) - 600*q^(-15/2) - 762*q^(-17/2) - 826*q^(-19/2) - 790*q^(-21/2) - 642*q^(-23/2) - 490*q^(-25/2) - 416*q^(-27/2) - 450*q^(-29/2) - 550*q^(-31/2) - 739*q^(-33/2) - 834*q^(-35/2) - 773*q^(-37/2) - 657*q^(-39/2) - 542*q^(-41/2) - 408*q^(-43/2) - 318*q^(-45/2) - 199*q^(-47/2) - 136*q^(-49/2) - 85*q^(-51/2) - 52*q^(-53/2) - 28*q^(-55/2) - 15*q^(-57/2))*x1^(-7)*x2^(-9) + (4*q^(-11/2) + 7*q^(-13/2) + 21*q^(-15/2) + 32*q^(-17/2) + 54*q^(-19/2) + 58*q^(-21/2) + 70*q^(-23/2) + 42*q^(-25/2) + 28*q^(-27/2) - 8*q^(-29/2) - 15*q^(-31/2) - 30*q^(-33/2) + 21*q^(-35/2) + 51*q^(-37/2) + 104*q^(-39/2) + 101*q^(-41/2) + 111*q^(-43/2) + 95*q^(-45/2) + 88*q^(-47/2) + 54*q^(-49/2) + 51*q^(-51/2) + 33*q^(-53/2) + 24*q^(-55/2) + 13*q^(-57/2) + 15*q^(-59/2))*x1^(-8)*x2^(-9)

Braid

Braid word Components Crossings Strands
[1, -2, 3, -2, -2, -2, 1, -2, 3, -2] 2 10 4

Multivariable Alexander polynomial

ΔL
-A1*A2^(2) + 4*A1*A2 - 4*A1 - 4*A2 + 7 - 4*A2^(-1) - 4*A1^(-1) + 4*A1^(-1)*A2^(-1) - A1^(-1)*A2^(-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-101-202A1A2

Dual Thurston polytope

VertexDual to fibered face
(-2, -4) yes
(2, 0) no
(2, 4) yes
(-2, 0) no
Dual Thurston polygon-202-505h1h2

HFL polytope

Poincaré polynomial
m^(-3)*A1^(-3/2)*A2^(-5/2) + 5*m^(-2)*A1^(-3/2)*A2^(-3/2) + m^(-2)*A1^(-1/2)*A2^(-5/2) + 8*m^(-1)*A1^(-3/2)*A2^(-1/2) + 9*m^(-1)*A1^(-1/2)*A2^(-3/2) + 4*A1^(-3/2)*A2^(1/2) + 19*A1^(-1/2)*A2^(-1/2) + 4*A1^(1/2)*A2^(-3/2) + 15*m*A1^(-1/2)*A2^(1/2) + 15*m*A1^(1/2)*A2^(-1/2) + 4*m^2*A1^(-1/2)*A2^(3/2) + 19*m^2*A1^(1/2)*A2^(1/2) + 4*m^2*A1^(3/2)*A2^(-1/2) + 9*m^3*A1^(1/2)*A2^(3/2) + 8*m^3*A1^(3/2)*A2^(1/2) + m^4*A1^(1/2)*A2^(5/2) + 5*m^4*A1^(3/2)*A2^(3/2) + m^5*A1^(3/2)*A2^(5/2)
VertexMaslovRank
(-3/2, -5/2)-31
(-1/2, -5/2)-21
(3/2, -1/2)24
(3/2, 5/2)51
(1/2, 5/2)41
(-3/2, 1/2)04
HFL polytope-202-202A1A2

Record

FL/HFL Links

orderOption(int) 431
namestring L10a78{0}
statusstring success
slugstring L10a78_0_d198ea41
result_filestring details/L10a78_0_d198ea41.json
complexity_scoreOption(int) 200
strandsOption(int) null
crossingsOption(int) 10
component_countOption(int) 2
girthOption(int) 6
total_rankOption(int) 132
wall_secondsOption(float) 0.00237
backend_secondsOption(float) 0.0
errorstring
dimensionOption(int) 2
support_sizeOption(int) 18
vertex_countOption(int) 6
fibered_vertex_countOption(int) 2
polytope_statusstring computed
alexander_support_sizeOption(int) 9
alexander_vertex_countOption(int) 4
alexander_relationstring not_computed
fk_countint 2
detailsRowRef(FLHFLLinks)
{
  "dataset": "FLHFLLinks",
  "key": "L10a78_0_d198ea41"
}
detail_assetstring /api/v1/datasets/FLHFLLinks/assets/L10a78_0_d198ea41