L9a32{0} - HFL and FL

details/L9a32_0_c70eea0c.json

F_L expansions

Newt(Δ_L) vertex Exposing functional Leading x-power Leading q-power Inversion datum Inversion cycle F_L

Newt(Δ_L) vertex	Exposing functional	Leading x-power	Leading q-power	Inversion datum	Inversion cycle	F_L
`(1, -2)`	`(1/2, 1)`	`x1^(-1)x2^(2)`	`q^(-21/2)`	`{"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, -1, -1, 1, 1, 1, 1]}`		(3q^(53/2) - 3q^(43/2) + 3q^(41/2) - 6q^(37/2) - 15q^(35/2) - 15q^(33/2) - 27q^(31/2) - 18q^(29/2) - 12q^(27/2) + 3q^(25/2) + 3q^(23/2) + 3q^(21/2))x1^(-8)x2^(9) + (-3q^(39/2) + 3q^(31/2) - 4q^(29/2) + 9q^(27/2) + 16q^(25/2) + 9q^(23/2) + 3q^(21/2) + q^(19/2) - 6q^(17/2) - q^(15/2))x1^(-7)x2^(8) + (-3q^(51/2) - 3q^(49/2) - 3q^(47/2) - 3q^(45/2) - 3q^(43/2) - 3q^(41/2) - 12q^(39/2) - 3q^(37/2) + 12q^(33/2) + 24q^(31/2) + 42q^(29/2) + 87q^(27/2) + 93q^(25/2) + 33q^(23/2) - 21q^(21/2) - 51q^(19/2) - 57q^(17/2) - 33q^(15/2) - 12q^(13/2) - 3q^(11/2))x1^(-7)x2^(9) + (3q^(27/2) - 3q^(21/2) - 9q^(17/2) + 3q^(15/2) + 3q^(13/2) + 3q^(11/2))x1^(-6)x2^(7) + (3q^(37/2) + 3q^(35/2) + 3q^(33/2) + 3q^(31/2) + 3q^(29/2) + 12q^(27/2) + 3q^(25/2) - 12q^(23/2) - 21q^(21/2) - 12q^(19/2) - 9q^(17/2) + 39q^(15/2) + 45q^(13/2) + 33q^(11/2) + 12q^(9/2) + 3q^(7/2))x1^(-6)x2^(8) + (3q^(47/2) + 3q^(45/2) + 6q^(43/2) + 6q^(41/2) + 9q^(39/2) + 15q^(37/2) + 24q^(35/2) + 21q^(33/2) + 27q^(31/2) + 21q^(29/2) + 39q^(27/2) - 12q^(25/2) - 39q^(23/2) - 45q^(21/2) + 57q^(19/2) + 144q^(17/2) + 285q^(15/2) + 279q^(13/2) + 210q^(11/2) + 96q^(9/2) + 36q^(7/2) + 3q^(5/2))x1^(-6)x2^(9) + (-3q^(17/2) + 3q^(13/2) - 3q^(11/2) - 3q^(9/2) - 3q^(7/2))x1^(-5)x2^(6) + (-3q^(25/2) - 3q^(23/2) - 3q^(21/2) - 3q^(19/2) - 12q^(17/2) + 3q^(15/2) - 3q^(13/2) - 26q^(11/2) - 33q^(9/2) - 24q^(7/2) - 9q^(5/2) - q^(3/2))x1^(-5)x2^(7) + (-3q^(33/2) - 3q^(31/2) - 6q^(29/2) - 6q^(27/2) - 15q^(25/2) - 21q^(23/2) - 21q^(21/2) - 24q^(19/2) - 39q^(17/2) - 33q^(15/2) - 81q^(13/2) - 156q^(11/2) - 165q^(9/2) - 120q^(7/2) - 57q^(5/2) - 12q^(3/2))x1^(-5)x2^(8) + (-3q^(41/2) - 3q^(39/2) - 6q^(37/2) - 9q^(35/2) - 18q^(33/2) - 21q^(31/2) - 39q^(29/2) - 42q^(27/2) - 72q^(25/2) - 90q^(23/2) - 111q^(21/2) - 123q^(19/2) - 207q^(17/2) - 285q^(15/2) - 468q^(13/2) - 627q^(11/2) - 621q^(9/2) - 441q^(7/2) - 222q^(5/2) - 51q^(3/2) + 21q^(1/2) + 24q^(-1/2) + 12q^(-3/2) + 3q^(-5/2))x1^(-5)x2^(9) + (3q^(9/2) - q^(7/2) + 6q^(5/2) + q^(3/2))x1^(-4)x2^(5) + (3q^(15/2) + 3q^(13/2) + 3q^(11/2) + 12q^(9/2) + 12q^(7/2) + 27q^(5/2) + 12q^(3/2) + 3q^(1/2))x1^(-4)x2^(6) + (3q^(21/2) + 3q^(19/2) + 6q^(17/2) + 12q^(15/2) + 21q^(13/2) + 21q^(11/2) + 60q^(9/2) + 69q^(7/2) + 96q^(5/2) + 51q^(3/2) + 18q^(1/2))x1^(-4)x2^(7) + (3q^(27/2) + 3q^(25/2) + 6q^(23/2) + 15q^(21/2) + 18q^(19/2) + 33q^(17/2) + 54q^(15/2) + 80q^(13/2) + 117q^(11/2) + 214q^(9/2) + 248q^(7/2) + 273q^(5/2) + 164q^(3/2) + 57q^(1/2) - 7q^(-1/2) - 15q^(-3/2) - 9q^(-5/2) - q^(-7/2))x1^(-4)x2^(8) + (3q^(33/2) + 3q^(31/2) + 6q^(29/2) + 15q^(27/2) + 21q^(25/2) + 30q^(23/2) + 60q^(21/2) + 75q^(19/2) + 129q^(17/2) + 183q^(15/2) + 291q^(13/2) + 411q^(11/2) + 621q^(9/2) + 681q^(7/2) + 675q^(5/2) + 405q^(3/2) + 132q^(1/2) - 72q^(-1/2) - 120q^(-3/2) - 93q^(-5/2) - 42q^(-7/2) - 12q^(-9/2) - 3q^(-11/2))x1^(-4)x2^(9) + (-3q^(3/2) - 3q^(1/2))x1^(-3)x2^(4) + (-3q^(7/2) - 3q^(5/2) - 15q^(3/2) - 12q^(1/2) - 3q^(-1/2))x1^(-3)x2^(5) + (-3q^(11/2) - 3q^(9/2) - 12q^(7/2) - 21q^(5/2) - 45q^(3/2) - 36q^(1/2) - 12q^(-1/2))x1^(-3)x2^(6) + (-3q^(15/2) - 3q^(13/2) - 12q^(11/2) - 15q^(9/2) - 45q^(7/2) - 66q^(5/2) - 111q^(3/2) - 87q^(1/2) - 33q^(-1/2) + 3q^(-3/2) + 9q^(-5/2) + 3q^(-7/2))x1^(-3)x2^(7) + (-3q^(19/2) - 3q^(17/2) - 12q^(15/2) - 15q^(13/2) - 36q^(11/2) - 57q^(9/2) - 120q^(7/2) - 165q^(5/2) - 231q^(3/2) - 180q^(1/2) - 69q^(-1/2) + 24q^(-3/2) + 51q^(-5/2) + 39q^(-7/2) + 12q^(-9/2) + 3q^(-11/2))x1^(-3)x2^(8) + (-3q^(23/2) - 3q^(21/2) - 12q^(19/2) - 15q^(17/2) - 36q^(15/2) - 45q^(13/2) - 102q^(11/2) - 153q^(9/2) - 270q^(7/2) - 342q^(5/2) - 429q^(3/2) - 318q^(1/2) - 105q^(-1/2) + 102q^(-3/2) + 198q^(-5/2) + 186q^(-7/2) + 111q^(-9/2) + 39q^(-11/2) + 9q^(-13/2))x1^(-3)x2^(9) + (3q^(-1/2))x1^(-2)x2^(3) + (3q^(1/2) + 9q^(-1/2) + q^(-3/2))x1^(-2)x2^(4) + (3q^(3/2) + 9q^(1/2) + 21q^(-1/2) + 3q^(-3/2))x1^(-2)x2^(5) + (3q^(5/2) + 9q^(3/2) + 21q^(1/2) + 39q^(-1/2) + 9q^(-3/2) - 3q^(-5/2) - 3q^(-7/2))x1^(-2)x2^(6) + (3q^(7/2) + 9q^(5/2) + 21q^(3/2) + 39q^(1/2) + 66q^(-1/2) + 16q^(-3/2) - 9q^(-5/2) - 18q^(-7/2) - 9q^(-9/2) - q^(-11/2))x1^(-2)x2^(7) + (3q^(9/2) + 9q^(7/2) + 21q^(5/2) + 39q^(3/2) + 66q^(1/2) + 99q^(-1/2) + 24q^(-3/2) - 27q^(-5/2) - 54q^(-7/2) - 48q^(-9/2) - 21q^(-11/2) - 3q^(-13/2))x1^(-2)x2^(8) + (3q^(11/2) + 9q^(9/2) + 21q^(7/2) + 39q^(5/2) + 66q^(3/2) + 99q^(1/2) + 138q^(-1/2) + 24q^(-3/2) - 66q^(-5/2) - 132q^(-7/2) - 141q^(-9/2) - 102q^(-11/2) - 42q^(-13/2) - 3q^(-15/2) + 3q^(-17/2) + 3q^(-19/2))x1^(-2)x2^(9) + (-q^(-3/2))x1^(-1)x2^(2) + (-3q^(-3/2))x1^(-1)x2^(3) + (-6q^(-3/2))x1^(-1)x2^(4) + (-10q^(-3/2) + q^(-7/2))x1^(-1)x2^(5) + (-15q^(-3/2) + 3q^(-7/2) + 3q^(-9/2))x1^(-1)x2^(6) + (-21q^(-3/2) + 6q^(-7/2) + 9q^(-9/2) + 6q^(-11/2))x1^(-1)x2^(7) + (-28q^(-3/2) + 10q^(-7/2) + 18q^(-9/2) + 18q^(-11/2) + 10q^(-13/2) - q^(-17/2))x1^(-1)x2^(8) + (-36q^(-3/2) + 15q^(-7/2) + 30q^(-9/2) + 36q^(-11/2) + 30q^(-13/2) + 15q^(-15/2) - 3q^(-17/2) - 3q^(-19/2) - 3q^(-21/2))x1^(-1)*x2^(9)
`(-1, 2)`		`x1^(1)x2^(-2)`	`q^(-21/2)`			(3q^(53/2) - 3q^(43/2) + 3q^(41/2) - 6q^(37/2) - 15q^(35/2) - 15q^(33/2) - 27q^(31/2) - 18q^(29/2) - 12q^(27/2) + 3q^(25/2) + 3q^(23/2) + 3q^(21/2))x1^(8)x2^(-9) + (-3q^(39/2) + 3q^(31/2) - 4q^(29/2) + 9q^(27/2) + 16q^(25/2) + 9q^(23/2) + 3q^(21/2) + q^(19/2) - 6q^(17/2) - q^(15/2))x1^(7)x2^(-8) + (-3q^(51/2) - 3q^(49/2) - 3q^(47/2) - 3q^(45/2) - 3q^(43/2) - 3q^(41/2) - 12q^(39/2) - 3q^(37/2) + 12q^(33/2) + 24q^(31/2) + 42q^(29/2) + 87q^(27/2) + 93q^(25/2) + 33q^(23/2) - 21q^(21/2) - 51q^(19/2) - 57q^(17/2) - 33q^(15/2) - 12q^(13/2) - 3q^(11/2))x1^(7)x2^(-9) + (3q^(27/2) - 3q^(21/2) - 9q^(17/2) + 3q^(15/2) + 3q^(13/2) + 3q^(11/2))x1^(6)x2^(-7) + (3q^(37/2) + 3q^(35/2) + 3q^(33/2) + 3q^(31/2) + 3q^(29/2) + 12q^(27/2) + 3q^(25/2) - 12q^(23/2) - 21q^(21/2) - 12q^(19/2) - 9q^(17/2) + 39q^(15/2) + 45q^(13/2) + 33q^(11/2) + 12q^(9/2) + 3q^(7/2))x1^(6)x2^(-8) + (3q^(47/2) + 3q^(45/2) + 6q^(43/2) + 6q^(41/2) + 9q^(39/2) + 15q^(37/2) + 24q^(35/2) + 21q^(33/2) + 27q^(31/2) + 21q^(29/2) + 39q^(27/2) - 12q^(25/2) - 39q^(23/2) - 45q^(21/2) + 57q^(19/2) + 144q^(17/2) + 285q^(15/2) + 279q^(13/2) + 210q^(11/2) + 96q^(9/2) + 36q^(7/2) + 3q^(5/2))x1^(6)x2^(-9) + (-3q^(17/2) + 3q^(13/2) - 3q^(11/2) - 3q^(9/2) - 3q^(7/2))x1^(5)x2^(-6) + (-3q^(25/2) - 3q^(23/2) - 3q^(21/2) - 3q^(19/2) - 12q^(17/2) + 3q^(15/2) - 3q^(13/2) - 26q^(11/2) - 33q^(9/2) - 24q^(7/2) - 9q^(5/2) - q^(3/2))x1^(5)x2^(-7) + (-3q^(33/2) - 3q^(31/2) - 6q^(29/2) - 6q^(27/2) - 15q^(25/2) - 21q^(23/2) - 21q^(21/2) - 24q^(19/2) - 39q^(17/2) - 33q^(15/2) - 81q^(13/2) - 156q^(11/2) - 165q^(9/2) - 120q^(7/2) - 57q^(5/2) - 12q^(3/2))x1^(5)x2^(-8) + (-3q^(41/2) - 3q^(39/2) - 6q^(37/2) - 9q^(35/2) - 18q^(33/2) - 21q^(31/2) - 39q^(29/2) - 42q^(27/2) - 72q^(25/2) - 90q^(23/2) - 111q^(21/2) - 123q^(19/2) - 207q^(17/2) - 285q^(15/2) - 468q^(13/2) - 627q^(11/2) - 621q^(9/2) - 441q^(7/2) - 222q^(5/2) - 51q^(3/2) + 21q^(1/2) + 24q^(-1/2) + 12q^(-3/2) + 3q^(-5/2))x1^(5)x2^(-9) + (3q^(9/2) - q^(7/2) + 6q^(5/2) + q^(3/2))x1^(4)x2^(-5) + (3q^(15/2) + 3q^(13/2) + 3q^(11/2) + 12q^(9/2) + 12q^(7/2) + 27q^(5/2) + 12q^(3/2) + 3q^(1/2))x1^(4)x2^(-6) + (3q^(21/2) + 3q^(19/2) + 6q^(17/2) + 12q^(15/2) + 21q^(13/2) + 21q^(11/2) + 60q^(9/2) + 69q^(7/2) + 96q^(5/2) + 51q^(3/2) + 18q^(1/2))x1^(4)x2^(-7) + (3q^(27/2) + 3q^(25/2) + 6q^(23/2) + 15q^(21/2) + 18q^(19/2) + 33q^(17/2) + 54q^(15/2) + 80q^(13/2) + 117q^(11/2) + 214q^(9/2) + 248q^(7/2) + 273q^(5/2) + 164q^(3/2) + 57q^(1/2) - 7q^(-1/2) - 15q^(-3/2) - 9q^(-5/2) - q^(-7/2))x1^(4)x2^(-8) + (3q^(33/2) + 3q^(31/2) + 6q^(29/2) + 15q^(27/2) + 21q^(25/2) + 30q^(23/2) + 60q^(21/2) + 75q^(19/2) + 129q^(17/2) + 183q^(15/2) + 291q^(13/2) + 411q^(11/2) + 621q^(9/2) + 681q^(7/2) + 675q^(5/2) + 405q^(3/2) + 132q^(1/2) - 72q^(-1/2) - 120q^(-3/2) - 93q^(-5/2) - 42q^(-7/2) - 12q^(-9/2) - 3q^(-11/2))x1^(4)x2^(-9) + (-3q^(3/2) - 3q^(1/2))x1^(3)x2^(-4) + (-3q^(7/2) - 3q^(5/2) - 15q^(3/2) - 12q^(1/2) - 3q^(-1/2))x1^(3)x2^(-5) + (-3q^(11/2) - 3q^(9/2) - 12q^(7/2) - 21q^(5/2) - 45q^(3/2) - 36q^(1/2) - 12q^(-1/2))x1^(3)x2^(-6) + (-3q^(15/2) - 3q^(13/2) - 12q^(11/2) - 15q^(9/2) - 45q^(7/2) - 66q^(5/2) - 111q^(3/2) - 87q^(1/2) - 33q^(-1/2) + 3q^(-3/2) + 9q^(-5/2) + 3q^(-7/2))x1^(3)x2^(-7) + (-3q^(19/2) - 3q^(17/2) - 12q^(15/2) - 15q^(13/2) - 36q^(11/2) - 57q^(9/2) - 120q^(7/2) - 165q^(5/2) - 231q^(3/2) - 180q^(1/2) - 69q^(-1/2) + 24q^(-3/2) + 51q^(-5/2) + 39q^(-7/2) + 12q^(-9/2) + 3q^(-11/2))x1^(3)x2^(-8) + (-3q^(23/2) - 3q^(21/2) - 12q^(19/2) - 15q^(17/2) - 36q^(15/2) - 45q^(13/2) - 102q^(11/2) - 153q^(9/2) - 270q^(7/2) - 342q^(5/2) - 429q^(3/2) - 318q^(1/2) - 105q^(-1/2) + 102q^(-3/2) + 198q^(-5/2) + 186q^(-7/2) + 111q^(-9/2) + 39q^(-11/2) + 9q^(-13/2))x1^(3)x2^(-9) + (3q^(-1/2))x1^(2)x2^(-3) + (3q^(1/2) + 9q^(-1/2) + q^(-3/2))x1^(2)x2^(-4) + (3q^(3/2) + 9q^(1/2) + 21q^(-1/2) + 3q^(-3/2))x1^(2)x2^(-5) + (3q^(5/2) + 9q^(3/2) + 21q^(1/2) + 39q^(-1/2) + 9q^(-3/2) - 3q^(-5/2) - 3q^(-7/2))x1^(2)x2^(-6) + (3q^(7/2) + 9q^(5/2) + 21q^(3/2) + 39q^(1/2) + 66q^(-1/2) + 16q^(-3/2) - 9q^(-5/2) - 18q^(-7/2) - 9q^(-9/2) - q^(-11/2))x1^(2)x2^(-7) + (3q^(9/2) + 9q^(7/2) + 21q^(5/2) + 39q^(3/2) + 66q^(1/2) + 99q^(-1/2) + 24q^(-3/2) - 27q^(-5/2) - 54q^(-7/2) - 48q^(-9/2) - 21q^(-11/2) - 3q^(-13/2))x1^(2)x2^(-8) + (3q^(11/2) + 9q^(9/2) + 21q^(7/2) + 39q^(5/2) + 66q^(3/2) + 99q^(1/2) + 138q^(-1/2) + 24q^(-3/2) - 66q^(-5/2) - 132q^(-7/2) - 141q^(-9/2) - 102q^(-11/2) - 42q^(-13/2) - 3q^(-15/2) + 3q^(-17/2) + 3q^(-19/2))x1^(2)x2^(-9) + (-q^(-3/2))x1x2^(-2) + (-3q^(-3/2))x1x2^(-3) + (-6q^(-3/2))x1x2^(-4) + (-10q^(-3/2) + q^(-7/2))x1x2^(-5) + (-15q^(-3/2) + 3q^(-7/2) + 3q^(-9/2))x1x2^(-6) + (-21q^(-3/2) + 6q^(-7/2) + 9q^(-9/2) + 6q^(-11/2))x1x2^(-7) + (-28q^(-3/2) + 10q^(-7/2) + 18q^(-9/2) + 18q^(-11/2) + 10q^(-13/2) - q^(-17/2))x1x2^(-8) + (-36q^(-3/2) + 15q^(-7/2) + 30q^(-9/2) + 36q^(-11/2) + 30q^(-13/2) + 15q^(-15/2) - 3q^(-17/2) - 3q^(-19/2) - 3q^(-21/2))x1*x2^(-9)

(1, -2)

(1/2, 1)

x1^(-1)x2^(2)

q^(-21/2)

{"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, -1, -1, 1, 1, 1, 1]}

(3*q^(53/2) - 3*q^(43/2) + 3*q^(41/2) - 6*q^(37/2) - 15*q^(35/2) - 15*q^(33/2) - 27*q^(31/2) - 18*q^(29/2) - 12*q^(27/2) + 3*q^(25/2) + 3*q^(23/2) + 3*q^(21/2))*x1^(-8)*x2^(9) + (-3*q^(39/2) + 3*q^(31/2) - 4*q^(29/2) + 9*q^(27/2) + 16*q^(25/2) + 9*q^(23/2) + 3*q^(21/2) + q^(19/2) - 6*q^(17/2) - q^(15/2))*x1^(-7)*x2^(8) + (-3*q^(51/2) - 3*q^(49/2) - 3*q^(47/2) - 3*q^(45/2) - 3*q^(43/2) - 3*q^(41/2) - 12*q^(39/2) - 3*q^(37/2) + 12*q^(33/2) + 24*q^(31/2) + 42*q^(29/2) + 87*q^(27/2) + 93*q^(25/2) + 33*q^(23/2) - 21*q^(21/2) - 51*q^(19/2) - 57*q^(17/2) - 33*q^(15/2) - 12*q^(13/2) - 3*q^(11/2))*x1^(-7)*x2^(9) + (3*q^(27/2) - 3*q^(21/2) - 9*q^(17/2) + 3*q^(15/2) + 3*q^(13/2) + 3*q^(11/2))*x1^(-6)*x2^(7) + (3*q^(37/2) + 3*q^(35/2) + 3*q^(33/2) + 3*q^(31/2) + 3*q^(29/2) + 12*q^(27/2) + 3*q^(25/2) - 12*q^(23/2) - 21*q^(21/2) - 12*q^(19/2) - 9*q^(17/2) + 39*q^(15/2) + 45*q^(13/2) + 33*q^(11/2) + 12*q^(9/2) + 3*q^(7/2))*x1^(-6)*x2^(8) + (3*q^(47/2) + 3*q^(45/2) + 6*q^(43/2) + 6*q^(41/2) + 9*q^(39/2) + 15*q^(37/2) + 24*q^(35/2) + 21*q^(33/2) + 27*q^(31/2) + 21*q^(29/2) + 39*q^(27/2) - 12*q^(25/2) - 39*q^(23/2) - 45*q^(21/2) + 57*q^(19/2) + 144*q^(17/2) + 285*q^(15/2) + 279*q^(13/2) + 210*q^(11/2) + 96*q^(9/2) + 36*q^(7/2) + 3*q^(5/2))*x1^(-6)*x2^(9) + (-3*q^(17/2) + 3*q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - 3*q^(7/2))*x1^(-5)*x2^(6) + (-3*q^(25/2) - 3*q^(23/2) - 3*q^(21/2) - 3*q^(19/2) - 12*q^(17/2) + 3*q^(15/2) - 3*q^(13/2) - 26*q^(11/2) - 33*q^(9/2) - 24*q^(7/2) - 9*q^(5/2) - q^(3/2))*x1^(-5)*x2^(7) + (-3*q^(33/2) - 3*q^(31/2) - 6*q^(29/2) - 6*q^(27/2) - 15*q^(25/2) - 21*q^(23/2) - 21*q^(21/2) - 24*q^(19/2) - 39*q^(17/2) - 33*q^(15/2) - 81*q^(13/2) - 156*q^(11/2) - 165*q^(9/2) - 120*q^(7/2) - 57*q^(5/2) - 12*q^(3/2))*x1^(-5)*x2^(8) + (-3*q^(41/2) - 3*q^(39/2) - 6*q^(37/2) - 9*q^(35/2) - 18*q^(33/2) - 21*q^(31/2) - 39*q^(29/2) - 42*q^(27/2) - 72*q^(25/2) - 90*q^(23/2) - 111*q^(21/2) - 123*q^(19/2) - 207*q^(17/2) - 285*q^(15/2) - 468*q^(13/2) - 627*q^(11/2) - 621*q^(9/2) - 441*q^(7/2) - 222*q^(5/2) - 51*q^(3/2) + 21*q^(1/2) + 24*q^(-1/2) + 12*q^(-3/2) + 3*q^(-5/2))*x1^(-5)*x2^(9) + (3*q^(9/2) - q^(7/2) + 6*q^(5/2) + q^(3/2))*x1^(-4)*x2^(5) + (3*q^(15/2) + 3*q^(13/2) + 3*q^(11/2) + 12*q^(9/2) + 12*q^(7/2) + 27*q^(5/2) + 12*q^(3/2) + 3*q^(1/2))*x1^(-4)*x2^(6) + (3*q^(21/2) + 3*q^(19/2) + 6*q^(17/2) + 12*q^(15/2) + 21*q^(13/2) + 21*q^(11/2) + 60*q^(9/2) + 69*q^(7/2) + 96*q^(5/2) + 51*q^(3/2) + 18*q^(1/2))*x1^(-4)*x2^(7) + (3*q^(27/2) + 3*q^(25/2) + 6*q^(23/2) + 15*q^(21/2) + 18*q^(19/2) + 33*q^(17/2) + 54*q^(15/2) + 80*q^(13/2) + 117*q^(11/2) + 214*q^(9/2) + 248*q^(7/2) + 273*q^(5/2) + 164*q^(3/2) + 57*q^(1/2) - 7*q^(-1/2) - 15*q^(-3/2) - 9*q^(-5/2) - q^(-7/2))*x1^(-4)*x2^(8) + (3*q^(33/2) + 3*q^(31/2) + 6*q^(29/2) + 15*q^(27/2) + 21*q^(25/2) + 30*q^(23/2) + 60*q^(21/2) + 75*q^(19/2) + 129*q^(17/2) + 183*q^(15/2) + 291*q^(13/2) + 411*q^(11/2) + 621*q^(9/2) + 681*q^(7/2) + 675*q^(5/2) + 405*q^(3/2) + 132*q^(1/2) - 72*q^(-1/2) - 120*q^(-3/2) - 93*q^(-5/2) - 42*q^(-7/2) - 12*q^(-9/2) - 3*q^(-11/2))*x1^(-4)*x2^(9) + (-3*q^(3/2) - 3*q^(1/2))*x1^(-3)*x2^(4) + (-3*q^(7/2) - 3*q^(5/2) - 15*q^(3/2) - 12*q^(1/2) - 3*q^(-1/2))*x1^(-3)*x2^(5) + (-3*q^(11/2) - 3*q^(9/2) - 12*q^(7/2) - 21*q^(5/2) - 45*q^(3/2) - 36*q^(1/2) - 12*q^(-1/2))*x1^(-3)*x2^(6) + (-3*q^(15/2) - 3*q^(13/2) - 12*q^(11/2) - 15*q^(9/2) - 45*q^(7/2) - 66*q^(5/2) - 111*q^(3/2) - 87*q^(1/2) - 33*q^(-1/2) + 3*q^(-3/2) + 9*q^(-5/2) + 3*q^(-7/2))*x1^(-3)*x2^(7) + (-3*q^(19/2) - 3*q^(17/2) - 12*q^(15/2) - 15*q^(13/2) - 36*q^(11/2) - 57*q^(9/2) - 120*q^(7/2) - 165*q^(5/2) - 231*q^(3/2) - 180*q^(1/2) - 69*q^(-1/2) + 24*q^(-3/2) + 51*q^(-5/2) + 39*q^(-7/2) + 12*q^(-9/2) + 3*q^(-11/2))*x1^(-3)*x2^(8) + (-3*q^(23/2) - 3*q^(21/2) - 12*q^(19/2) - 15*q^(17/2) - 36*q^(15/2) - 45*q^(13/2) - 102*q^(11/2) - 153*q^(9/2) - 270*q^(7/2) - 342*q^(5/2) - 429*q^(3/2) - 318*q^(1/2) - 105*q^(-1/2) + 102*q^(-3/2) + 198*q^(-5/2) + 186*q^(-7/2) + 111*q^(-9/2) + 39*q^(-11/2) + 9*q^(-13/2))*x1^(-3)*x2^(9) + (3*q^(-1/2))*x1^(-2)*x2^(3) + (3*q^(1/2) + 9*q^(-1/2) + q^(-3/2))*x1^(-2)*x2^(4) + (3*q^(3/2) + 9*q^(1/2) + 21*q^(-1/2) + 3*q^(-3/2))*x1^(-2)*x2^(5) + (3*q^(5/2) + 9*q^(3/2) + 21*q^(1/2) + 39*q^(-1/2) + 9*q^(-3/2) - 3*q^(-5/2) - 3*q^(-7/2))*x1^(-2)*x2^(6) + (3*q^(7/2) + 9*q^(5/2) + 21*q^(3/2) + 39*q^(1/2) + 66*q^(-1/2) + 16*q^(-3/2) - 9*q^(-5/2) - 18*q^(-7/2) - 9*q^(-9/2) - q^(-11/2))*x1^(-2)*x2^(7) + (3*q^(9/2) + 9*q^(7/2) + 21*q^(5/2) + 39*q^(3/2) + 66*q^(1/2) + 99*q^(-1/2) + 24*q^(-3/2) - 27*q^(-5/2) - 54*q^(-7/2) - 48*q^(-9/2) - 21*q^(-11/2) - 3*q^(-13/2))*x1^(-2)*x2^(8) + (3*q^(11/2) + 9*q^(9/2) + 21*q^(7/2) + 39*q^(5/2) + 66*q^(3/2) + 99*q^(1/2) + 138*q^(-1/2) + 24*q^(-3/2) - 66*q^(-5/2) - 132*q^(-7/2) - 141*q^(-9/2) - 102*q^(-11/2) - 42*q^(-13/2) - 3*q^(-15/2) + 3*q^(-17/2) + 3*q^(-19/2))*x1^(-2)*x2^(9) + (-q^(-3/2))*x1^(-1)*x2^(2) + (-3*q^(-3/2))*x1^(-1)*x2^(3) + (-6*q^(-3/2))*x1^(-1)*x2^(4) + (-10*q^(-3/2) + q^(-7/2))*x1^(-1)*x2^(5) + (-15*q^(-3/2) + 3*q^(-7/2) + 3*q^(-9/2))*x1^(-1)*x2^(6) + (-21*q^(-3/2) + 6*q^(-7/2) + 9*q^(-9/2) + 6*q^(-11/2))*x1^(-1)*x2^(7) + (-28*q^(-3/2) + 10*q^(-7/2) + 18*q^(-9/2) + 18*q^(-11/2) + 10*q^(-13/2) - q^(-17/2))*x1^(-1)*x2^(8) + (-36*q^(-3/2) + 15*q^(-7/2) + 30*q^(-9/2) + 36*q^(-11/2) + 30*q^(-13/2) + 15*q^(-15/2) - 3*q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2))*x1^(-1)*x2^(9)

(-1, 2)

x1^(1)x2^(-2)

q^(-21/2)

(3*q^(53/2) - 3*q^(43/2) + 3*q^(41/2) - 6*q^(37/2) - 15*q^(35/2) - 15*q^(33/2) - 27*q^(31/2) - 18*q^(29/2) - 12*q^(27/2) + 3*q^(25/2) + 3*q^(23/2) + 3*q^(21/2))*x1^(8)*x2^(-9) + (-3*q^(39/2) + 3*q^(31/2) - 4*q^(29/2) + 9*q^(27/2) + 16*q^(25/2) + 9*q^(23/2) + 3*q^(21/2) + q^(19/2) - 6*q^(17/2) - q^(15/2))*x1^(7)*x2^(-8) + (-3*q^(51/2) - 3*q^(49/2) - 3*q^(47/2) - 3*q^(45/2) - 3*q^(43/2) - 3*q^(41/2) - 12*q^(39/2) - 3*q^(37/2) + 12*q^(33/2) + 24*q^(31/2) + 42*q^(29/2) + 87*q^(27/2) + 93*q^(25/2) + 33*q^(23/2) - 21*q^(21/2) - 51*q^(19/2) - 57*q^(17/2) - 33*q^(15/2) - 12*q^(13/2) - 3*q^(11/2))*x1^(7)*x2^(-9) + (3*q^(27/2) - 3*q^(21/2) - 9*q^(17/2) + 3*q^(15/2) + 3*q^(13/2) + 3*q^(11/2))*x1^(6)*x2^(-7) + (3*q^(37/2) + 3*q^(35/2) + 3*q^(33/2) + 3*q^(31/2) + 3*q^(29/2) + 12*q^(27/2) + 3*q^(25/2) - 12*q^(23/2) - 21*q^(21/2) - 12*q^(19/2) - 9*q^(17/2) + 39*q^(15/2) + 45*q^(13/2) + 33*q^(11/2) + 12*q^(9/2) + 3*q^(7/2))*x1^(6)*x2^(-8) + (3*q^(47/2) + 3*q^(45/2) + 6*q^(43/2) + 6*q^(41/2) + 9*q^(39/2) + 15*q^(37/2) + 24*q^(35/2) + 21*q^(33/2) + 27*q^(31/2) + 21*q^(29/2) + 39*q^(27/2) - 12*q^(25/2) - 39*q^(23/2) - 45*q^(21/2) + 57*q^(19/2) + 144*q^(17/2) + 285*q^(15/2) + 279*q^(13/2) + 210*q^(11/2) + 96*q^(9/2) + 36*q^(7/2) + 3*q^(5/2))*x1^(6)*x2^(-9) + (-3*q^(17/2) + 3*q^(13/2) - 3*q^(11/2) - 3*q^(9/2) - 3*q^(7/2))*x1^(5)*x2^(-6) + (-3*q^(25/2) - 3*q^(23/2) - 3*q^(21/2) - 3*q^(19/2) - 12*q^(17/2) + 3*q^(15/2) - 3*q^(13/2) - 26*q^(11/2) - 33*q^(9/2) - 24*q^(7/2) - 9*q^(5/2) - q^(3/2))*x1^(5)*x2^(-7) + (-3*q^(33/2) - 3*q^(31/2) - 6*q^(29/2) - 6*q^(27/2) - 15*q^(25/2) - 21*q^(23/2) - 21*q^(21/2) - 24*q^(19/2) - 39*q^(17/2) - 33*q^(15/2) - 81*q^(13/2) - 156*q^(11/2) - 165*q^(9/2) - 120*q^(7/2) - 57*q^(5/2) - 12*q^(3/2))*x1^(5)*x2^(-8) + (-3*q^(41/2) - 3*q^(39/2) - 6*q^(37/2) - 9*q^(35/2) - 18*q^(33/2) - 21*q^(31/2) - 39*q^(29/2) - 42*q^(27/2) - 72*q^(25/2) - 90*q^(23/2) - 111*q^(21/2) - 123*q^(19/2) - 207*q^(17/2) - 285*q^(15/2) - 468*q^(13/2) - 627*q^(11/2) - 621*q^(9/2) - 441*q^(7/2) - 222*q^(5/2) - 51*q^(3/2) + 21*q^(1/2) + 24*q^(-1/2) + 12*q^(-3/2) + 3*q^(-5/2))*x1^(5)*x2^(-9) + (3*q^(9/2) - q^(7/2) + 6*q^(5/2) + q^(3/2))*x1^(4)*x2^(-5) + (3*q^(15/2) + 3*q^(13/2) + 3*q^(11/2) + 12*q^(9/2) + 12*q^(7/2) + 27*q^(5/2) + 12*q^(3/2) + 3*q^(1/2))*x1^(4)*x2^(-6) + (3*q^(21/2) + 3*q^(19/2) + 6*q^(17/2) + 12*q^(15/2) + 21*q^(13/2) + 21*q^(11/2) + 60*q^(9/2) + 69*q^(7/2) + 96*q^(5/2) + 51*q^(3/2) + 18*q^(1/2))*x1^(4)*x2^(-7) + (3*q^(27/2) + 3*q^(25/2) + 6*q^(23/2) + 15*q^(21/2) + 18*q^(19/2) + 33*q^(17/2) + 54*q^(15/2) + 80*q^(13/2) + 117*q^(11/2) + 214*q^(9/2) + 248*q^(7/2) + 273*q^(5/2) + 164*q^(3/2) + 57*q^(1/2) - 7*q^(-1/2) - 15*q^(-3/2) - 9*q^(-5/2) - q^(-7/2))*x1^(4)*x2^(-8) + (3*q^(33/2) + 3*q^(31/2) + 6*q^(29/2) + 15*q^(27/2) + 21*q^(25/2) + 30*q^(23/2) + 60*q^(21/2) + 75*q^(19/2) + 129*q^(17/2) + 183*q^(15/2) + 291*q^(13/2) + 411*q^(11/2) + 621*q^(9/2) + 681*q^(7/2) + 675*q^(5/2) + 405*q^(3/2) + 132*q^(1/2) - 72*q^(-1/2) - 120*q^(-3/2) - 93*q^(-5/2) - 42*q^(-7/2) - 12*q^(-9/2) - 3*q^(-11/2))*x1^(4)*x2^(-9) + (-3*q^(3/2) - 3*q^(1/2))*x1^(3)*x2^(-4) + (-3*q^(7/2) - 3*q^(5/2) - 15*q^(3/2) - 12*q^(1/2) - 3*q^(-1/2))*x1^(3)*x2^(-5) + (-3*q^(11/2) - 3*q^(9/2) - 12*q^(7/2) - 21*q^(5/2) - 45*q^(3/2) - 36*q^(1/2) - 12*q^(-1/2))*x1^(3)*x2^(-6) + (-3*q^(15/2) - 3*q^(13/2) - 12*q^(11/2) - 15*q^(9/2) - 45*q^(7/2) - 66*q^(5/2) - 111*q^(3/2) - 87*q^(1/2) - 33*q^(-1/2) + 3*q^(-3/2) + 9*q^(-5/2) + 3*q^(-7/2))*x1^(3)*x2^(-7) + (-3*q^(19/2) - 3*q^(17/2) - 12*q^(15/2) - 15*q^(13/2) - 36*q^(11/2) - 57*q^(9/2) - 120*q^(7/2) - 165*q^(5/2) - 231*q^(3/2) - 180*q^(1/2) - 69*q^(-1/2) + 24*q^(-3/2) + 51*q^(-5/2) + 39*q^(-7/2) + 12*q^(-9/2) + 3*q^(-11/2))*x1^(3)*x2^(-8) + (-3*q^(23/2) - 3*q^(21/2) - 12*q^(19/2) - 15*q^(17/2) - 36*q^(15/2) - 45*q^(13/2) - 102*q^(11/2) - 153*q^(9/2) - 270*q^(7/2) - 342*q^(5/2) - 429*q^(3/2) - 318*q^(1/2) - 105*q^(-1/2) + 102*q^(-3/2) + 198*q^(-5/2) + 186*q^(-7/2) + 111*q^(-9/2) + 39*q^(-11/2) + 9*q^(-13/2))*x1^(3)*x2^(-9) + (3*q^(-1/2))*x1^(2)*x2^(-3) + (3*q^(1/2) + 9*q^(-1/2) + q^(-3/2))*x1^(2)*x2^(-4) + (3*q^(3/2) + 9*q^(1/2) + 21*q^(-1/2) + 3*q^(-3/2))*x1^(2)*x2^(-5) + (3*q^(5/2) + 9*q^(3/2) + 21*q^(1/2) + 39*q^(-1/2) + 9*q^(-3/2) - 3*q^(-5/2) - 3*q^(-7/2))*x1^(2)*x2^(-6) + (3*q^(7/2) + 9*q^(5/2) + 21*q^(3/2) + 39*q^(1/2) + 66*q^(-1/2) + 16*q^(-3/2) - 9*q^(-5/2) - 18*q^(-7/2) - 9*q^(-9/2) - q^(-11/2))*x1^(2)*x2^(-7) + (3*q^(9/2) + 9*q^(7/2) + 21*q^(5/2) + 39*q^(3/2) + 66*q^(1/2) + 99*q^(-1/2) + 24*q^(-3/2) - 27*q^(-5/2) - 54*q^(-7/2) - 48*q^(-9/2) - 21*q^(-11/2) - 3*q^(-13/2))*x1^(2)*x2^(-8) + (3*q^(11/2) + 9*q^(9/2) + 21*q^(7/2) + 39*q^(5/2) + 66*q^(3/2) + 99*q^(1/2) + 138*q^(-1/2) + 24*q^(-3/2) - 66*q^(-5/2) - 132*q^(-7/2) - 141*q^(-9/2) - 102*q^(-11/2) - 42*q^(-13/2) - 3*q^(-15/2) + 3*q^(-17/2) + 3*q^(-19/2))*x1^(2)*x2^(-9) + (-q^(-3/2))*x1*x2^(-2) + (-3*q^(-3/2))*x1*x2^(-3) + (-6*q^(-3/2))*x1*x2^(-4) + (-10*q^(-3/2) + q^(-7/2))*x1*x2^(-5) + (-15*q^(-3/2) + 3*q^(-7/2) + 3*q^(-9/2))*x1*x2^(-6) + (-21*q^(-3/2) + 6*q^(-7/2) + 9*q^(-9/2) + 6*q^(-11/2))*x1*x2^(-7) + (-28*q^(-3/2) + 10*q^(-7/2) + 18*q^(-9/2) + 18*q^(-11/2) + 10*q^(-13/2) - q^(-17/2))*x1*x2^(-8) + (-36*q^(-3/2) + 15*q^(-7/2) + 30*q^(-9/2) + 36*q^(-11/2) + 30*q^(-13/2) + 15*q^(-15/2) - 3*q^(-17/2) - 3*q^(-19/2) - 3*q^(-21/2))*x1*x2^(-9)

Braid

Braid word	Components	Crossings	Strands
`[-1, -2, -3, -4, -3, -3, -2, -2, -1, 2, 3, 4, -3, -2, -1, 2, 3]`	2	17	5

Multivariable Alexander polynomial

Δ_L
`-3A1 + 3A1A2^(-1) - A1A2^(-2) - 3A2 + 5 - 3A2^(-1) - A1^(-1)A2^(2) + 3A1^(-1)A2 - 3A1^(-1)`

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

Dual Thurston polytope

Vertex	Dual to fibered face
`(2, -4)`	yes
`(2, 0)`	no
`(-2, 4)`	yes
`(-2, 0)`	no

HFL polytope

Poincaré polynomial
`3m^(-1)A1^(-3/2)A2^(-1/2) + 3m^(-1)A1^(-1/2)A2^(-3/2) + m^(-1)A1^(1/2)A2^(-5/2) + 6A1^(-3/2)A2^(1/2) + 11A1^(-1/2)A2^(-1/2) + 7A1^(1/2)A2^(-3/2) + A1^(3/2)A2^(-5/2) + 4mA1^(-3/2)A2^(3/2) + 14mA1^(-1/2)A2^(1/2) + 14mA1^(1/2)A2^(-1/2) + 4mA1^(3/2)A2^(-3/2) + m^2A1^(-3/2)A2^(5/2) + 7m^2A1^(-1/2)A2^(3/2) + 11m^2A1^(1/2)A2^(1/2) + 6m^2A1^(3/2)A2^(-1/2) + m^3A1^(-1/2)A2^(5/2) + 3m^3A1^(1/2)A2^(3/2) + 3m^3A1^(3/2)A2^(1/2)`

Vertex	Maslov	Rank
`(-3/2, -1/2)`	-1	3
`(1/2, -5/2)`	-1	1
`(3/2, -5/2)`	0	1
`(3/2, 1/2)`	3	3
`(-1/2, 5/2)`	3	1
`(-3/2, 5/2)`	2	1

Record

FL/HFL Links

`orderOption(int)`	`125`
`namestring`	`L9a32{0}`
`statusstring`	`success`
`slugstring`	`L9a32_0_c70eea0c`
`result_filestring`	`details/L9a32_0_c70eea0c.json`
`complexity_scoreOption(int)`	`162`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`9`
`component_countOption(int)`	`2`
`girthOption(int)`	`6`
`total_rankOption(int)`	`100`
`wall_secondsOption(float)`	`0.003383`
`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`	`1`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L9a32_0_c70eea0c" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L9a32_0_c70eea0c`