L8n1{1} - HFL and FL

details/L8n1_1_51419213.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	F_L
`(1/2, -3/2)`	`(1, 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]}`	(-q^(-31/2) - 3q^(-33/2) - 4q^(-35/2) - 3q^(-37/2) - 5q^(-39/2))x1^(-9/2)x2^(19/2) + (-2q^(-19/2) - 2q^(-21/2) - 4q^(-23/2))x1^(-7/2)x2^(15/2) + (-q^(-15/2) - 4q^(-17/2) - 8q^(-19/2) - 11q^(-21/2) - 14q^(-23/2) - 8q^(-25/2) - 4q^(-27/2) - 2q^(-29/2))x1^(-7/2)x2^(17/2) + (-2q^(-11/2) - 4q^(-13/2) - 12q^(-15/2) - 20q^(-17/2) - 32q^(-19/2) - 38q^(-21/2) - 44q^(-23/2) - 32q^(-25/2) - 24q^(-27/2) - 12q^(-29/2) - 6q^(-31/2) - 2q^(-33/2) - 2q^(-35/2))x1^(-7/2)x2^(19/2) + (-q^(-9/2) - 3q^(-11/2))x1^(-5/2)x2^(11/2) + (-2q^(-7/2) - 4q^(-9/2) - 8q^(-11/2) - 4q^(-13/2) - 2q^(-15/2))x1^(-5/2)x2^(13/2) + (-q^(-3/2) - 4q^(-5/2) - 9q^(-7/2) - 14q^(-9/2) - 19q^(-11/2) - 13q^(-13/2) - 9q^(-15/2) - 2q^(-17/2) - 2q^(-19/2))x1^(-5/2)x2^(15/2) + (-2q^(1/2) - 4q^(-1/2) - 12q^(-3/2) - 20q^(-5/2) - 32q^(-7/2) - 38q^(-9/2) - 44q^(-11/2) - 32q^(-13/2) - 24q^(-15/2) - 12q^(-17/2) - 6q^(-19/2) - 2q^(-21/2) - 2q^(-23/2))x1^(-5/2)x2^(17/2) + (-q^(7/2) - 4q^(5/2) - 9q^(3/2) - 19q^(1/2) - 33q^(-1/2) - 53q^(-3/2) - 71q^(-5/2) - 88q^(-7/2) - 93q^(-9/2) - 94q^(-11/2) - 72q^(-13/2) - 55q^(-15/2) - 33q^(-17/2) - 21q^(-19/2) - 8q^(-21/2) - 6q^(-23/2) - 2q^(-25/2) - 2q^(-27/2))x1^(-5/2)x2^(19/2) + (-2q^(-3/2))x1^(-3/2)x2^(7/2) + (-q^(-1/2) - 4q^(-3/2) - 2q^(-5/2))x1^(-3/2)x2^(9/2) + (-2q^(1/2) - 4q^(-1/2) - 8q^(-3/2) - 4q^(-5/2) - 2q^(-7/2))x1^(-3/2)x2^(11/2) + (-q^(5/2) - 4q^(3/2) - 8q^(1/2) - 11q^(-1/2) - 14q^(-3/2) - 8q^(-5/2) - 4q^(-7/2) - 2q^(-9/2))x1^(-3/2)x2^(13/2) + (-2q^(9/2) - 4q^(7/2) - 10q^(5/2) - 16q^(3/2) - 22q^(1/2) - 22q^(-1/2) - 24q^(-3/2) - 14q^(-5/2) - 8q^(-7/2) - 4q^(-9/2) - 2q^(-11/2))x1^(-3/2)x2^(15/2) + (-q^(15/2) - 4q^(13/2) - 8q^(11/2) - 15q^(9/2) - 24q^(7/2) - 35q^(5/2) - 42q^(3/2) - 44q^(1/2) - 41q^(-1/2) - 38q^(-3/2) - 24q^(-5/2) - 14q^(-7/2) - 8q^(-9/2) - 4q^(-11/2) - 2q^(-13/2))x1^(-3/2)x2^(17/2) + (-2q^(21/2) - 4q^(19/2) - 10q^(17/2) - 18q^(15/2) - 30q^(13/2) - 42q^(11/2) - 60q^(9/2) - 72q^(7/2) - 84q^(5/2) - 84q^(3/2) - 80q^(1/2) - 68q^(-1/2) - 60q^(-3/2) - 38q^(-5/2) - 24q^(-7/2) - 14q^(-9/2) - 8q^(-11/2) - 4q^(-13/2) - 2q^(-15/2))x1^(-3/2)x2^(19/2) + (-q^(1/2))x1^(-1/2)x2^(3/2) + (-2q^(1/2))x1^(-1/2)x2^(5/2) + (-q^(3/2) - 3q^(1/2))x1^(-1/2)x2^(7/2) + (-2q^(5/2) - 2q^(3/2) - 4q^(1/2))x1^(-1/2)x2^(9/2) + (-q^(9/2) - 3q^(7/2) - 4q^(5/2) - 3q^(3/2) - 5q^(1/2))x1^(-1/2)x2^(11/2) + (-2q^(13/2) - 2q^(11/2) - 6q^(9/2) - 6q^(7/2) - 6q^(5/2) - 4q^(3/2) - 6q^(1/2))x1^(-1/2)x2^(13/2) + (-q^(19/2) - 3q^(17/2) - 4q^(15/2) - 7q^(13/2) - 9q^(11/2) - 11q^(9/2) - 9q^(7/2) - 8q^(5/2) - 5q^(3/2) - 7q^(1/2))x1^(-1/2)x2^(15/2) + (-2q^(25/2) - 2q^(23/2) - 6q^(21/2) - 8q^(19/2) - 12q^(17/2) - 12q^(15/2) - 18q^(13/2) - 16q^(11/2) - 16q^(9/2) - 12q^(7/2) - 10q^(5/2) - 6q^(3/2) - 8q^(1/2))x1^(-1/2)x2^(17/2) + (-q^(33/2) - 3q^(31/2) - 4q^(29/2) - 7q^(27/2) - 13q^(25/2) - 15q^(23/2) - 21q^(21/2) - 23q^(19/2) - 26q^(17/2) - 27q^(15/2) - 29q^(13/2) - 23q^(11/2) - 21q^(9/2) - 15q^(7/2) - 12q^(5/2) - 7q^(3/2) - 9q^(1/2))x1^(-1/2)x2^(19/2)
`(1/2, -3/2)`	`(1, 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]}`	(-q^(-31/2) - 3q^(-33/2) - 4q^(-35/2) - 3q^(-37/2) - 5q^(-39/2))x1^(-9/2)x2^(19/2) + (-2q^(-19/2) - 2q^(-21/2) - 4q^(-23/2))x1^(-7/2)x2^(15/2) + (-q^(-15/2) - 4q^(-17/2) - 8q^(-19/2) - 11q^(-21/2) - 14q^(-23/2) - 8q^(-25/2) - 4q^(-27/2) - 2q^(-29/2))x1^(-7/2)x2^(17/2) + (-2q^(-11/2) - 4q^(-13/2) - 12q^(-15/2) - 20q^(-17/2) - 32q^(-19/2) - 38q^(-21/2) - 44q^(-23/2) - 32q^(-25/2) - 24q^(-27/2) - 12q^(-29/2) - 6q^(-31/2) - 2q^(-33/2) - 2q^(-35/2))x1^(-7/2)x2^(19/2) + (-q^(-9/2) - 3q^(-11/2))x1^(-5/2)x2^(11/2) + (-2q^(-7/2) - 4q^(-9/2) - 8q^(-11/2) - 4q^(-13/2) - 2q^(-15/2))x1^(-5/2)x2^(13/2) + (-q^(-3/2) - 4q^(-5/2) - 9q^(-7/2) - 14q^(-9/2) - 19q^(-11/2) - 13q^(-13/2) - 9q^(-15/2) - 2q^(-17/2) - 2q^(-19/2))x1^(-5/2)x2^(15/2) + (-2q^(1/2) - 4q^(-1/2) - 12q^(-3/2) - 20q^(-5/2) - 32q^(-7/2) - 38q^(-9/2) - 44q^(-11/2) - 32q^(-13/2) - 24q^(-15/2) - 12q^(-17/2) - 6q^(-19/2) - 2q^(-21/2) - 2q^(-23/2))x1^(-5/2)x2^(17/2) + (-q^(7/2) - 4q^(5/2) - 9q^(3/2) - 19q^(1/2) - 33q^(-1/2) - 53q^(-3/2) - 71q^(-5/2) - 88q^(-7/2) - 93q^(-9/2) - 94q^(-11/2) - 72q^(-13/2) - 55q^(-15/2) - 33q^(-17/2) - 21q^(-19/2) - 8q^(-21/2) - 6q^(-23/2) - 2q^(-25/2) - 2q^(-27/2))x1^(-5/2)x2^(19/2) + (-2q^(-3/2))x1^(-3/2)x2^(7/2) + (-q^(-1/2) - 4q^(-3/2) - 2q^(-5/2))x1^(-3/2)x2^(9/2) + (-2q^(1/2) - 4q^(-1/2) - 8q^(-3/2) - 4q^(-5/2) - 2q^(-7/2))x1^(-3/2)x2^(11/2) + (-q^(5/2) - 4q^(3/2) - 8q^(1/2) - 11q^(-1/2) - 14q^(-3/2) - 8q^(-5/2) - 4q^(-7/2) - 2q^(-9/2))x1^(-3/2)x2^(13/2) + (-2q^(9/2) - 4q^(7/2) - 10q^(5/2) - 16q^(3/2) - 22q^(1/2) - 22q^(-1/2) - 24q^(-3/2) - 14q^(-5/2) - 8q^(-7/2) - 4q^(-9/2) - 2q^(-11/2))x1^(-3/2)x2^(15/2) + (-q^(15/2) - 4q^(13/2) - 8q^(11/2) - 15q^(9/2) - 24q^(7/2) - 35q^(5/2) - 42q^(3/2) - 44q^(1/2) - 41q^(-1/2) - 38q^(-3/2) - 24q^(-5/2) - 14q^(-7/2) - 8q^(-9/2) - 4q^(-11/2) - 2q^(-13/2))x1^(-3/2)x2^(17/2) + (-2q^(21/2) - 4q^(19/2) - 10q^(17/2) - 18q^(15/2) - 30q^(13/2) - 42q^(11/2) - 60q^(9/2) - 72q^(7/2) - 84q^(5/2) - 84q^(3/2) - 80q^(1/2) - 68q^(-1/2) - 60q^(-3/2) - 38q^(-5/2) - 24q^(-7/2) - 14q^(-9/2) - 8q^(-11/2) - 4q^(-13/2) - 2q^(-15/2))x1^(-3/2)x2^(19/2) + (-q^(1/2))x1^(-1/2)x2^(3/2) + (-2q^(1/2))x1^(-1/2)x2^(5/2) + (-q^(3/2) - 3q^(1/2))x1^(-1/2)x2^(7/2) + (-2q^(5/2) - 2q^(3/2) - 4q^(1/2))x1^(-1/2)x2^(9/2) + (-q^(9/2) - 3q^(7/2) - 4q^(5/2) - 3q^(3/2) - 5q^(1/2))x1^(-1/2)x2^(11/2) + (-2q^(13/2) - 2q^(11/2) - 6q^(9/2) - 6q^(7/2) - 6q^(5/2) - 4q^(3/2) - 6q^(1/2))x1^(-1/2)x2^(13/2) + (-q^(19/2) - 3q^(17/2) - 4q^(15/2) - 7q^(13/2) - 9q^(11/2) - 11q^(9/2) - 9q^(7/2) - 8q^(5/2) - 5q^(3/2) - 7q^(1/2))x1^(-1/2)x2^(15/2) + (-2q^(25/2) - 2q^(23/2) - 6q^(21/2) - 8q^(19/2) - 12q^(17/2) - 12q^(15/2) - 18q^(13/2) - 16q^(11/2) - 16q^(9/2) - 12q^(7/2) - 10q^(5/2) - 6q^(3/2) - 8q^(1/2))x1^(-1/2)x2^(17/2) + (-q^(33/2) - 3q^(31/2) - 4q^(29/2) - 7q^(27/2) - 13q^(25/2) - 15q^(23/2) - 21q^(21/2) - 23q^(19/2) - 26q^(17/2) - 27q^(15/2) - 29q^(13/2) - 23q^(11/2) - 21q^(9/2) - 15q^(7/2) - 12q^(5/2) - 7q^(3/2) - 9q^(1/2))x1^(-1/2)x2^(19/2)
`(-1/2, 3/2)`		`x1^(1/2)x2^(-3/2)`	`q^(1/2)`		(-q^(-31/2) - 3q^(-33/2) - 4q^(-35/2) - 3q^(-37/2) - 5q^(-39/2))x1^(9/2)x2^(-19/2) + (-2q^(-19/2) - 2q^(-21/2) - 4q^(-23/2))x1^(7/2)x2^(-15/2) + (-q^(-15/2) - 4q^(-17/2) - 8q^(-19/2) - 11q^(-21/2) - 14q^(-23/2) - 8q^(-25/2) - 4q^(-27/2) - 2q^(-29/2))x1^(7/2)x2^(-17/2) + (-2q^(-11/2) - 4q^(-13/2) - 12q^(-15/2) - 20q^(-17/2) - 32q^(-19/2) - 38q^(-21/2) - 44q^(-23/2) - 32q^(-25/2) - 24q^(-27/2) - 12q^(-29/2) - 6q^(-31/2) - 2q^(-33/2) - 2q^(-35/2))x1^(7/2)x2^(-19/2) + (-q^(-9/2) - 3q^(-11/2))x1^(5/2)x2^(-11/2) + (-2q^(-7/2) - 4q^(-9/2) - 8q^(-11/2) - 4q^(-13/2) - 2q^(-15/2))x1^(5/2)x2^(-13/2) + (-q^(-3/2) - 4q^(-5/2) - 9q^(-7/2) - 14q^(-9/2) - 19q^(-11/2) - 13q^(-13/2) - 9q^(-15/2) - 2q^(-17/2) - 2q^(-19/2))x1^(5/2)x2^(-15/2) + (-2q^(1/2) - 4q^(-1/2) - 12q^(-3/2) - 20q^(-5/2) - 32q^(-7/2) - 38q^(-9/2) - 44q^(-11/2) - 32q^(-13/2) - 24q^(-15/2) - 12q^(-17/2) - 6q^(-19/2) - 2q^(-21/2) - 2q^(-23/2))x1^(5/2)x2^(-17/2) + (-q^(7/2) - 4q^(5/2) - 9q^(3/2) - 19q^(1/2) - 33q^(-1/2) - 53q^(-3/2) - 71q^(-5/2) - 88q^(-7/2) - 93q^(-9/2) - 94q^(-11/2) - 72q^(-13/2) - 55q^(-15/2) - 33q^(-17/2) - 21q^(-19/2) - 8q^(-21/2) - 6q^(-23/2) - 2q^(-25/2) - 2q^(-27/2))x1^(5/2)x2^(-19/2) + (-2q^(-3/2))x1^(3/2)x2^(-7/2) + (-q^(-1/2) - 4q^(-3/2) - 2q^(-5/2))x1^(3/2)x2^(-9/2) + (-2q^(1/2) - 4q^(-1/2) - 8q^(-3/2) - 4q^(-5/2) - 2q^(-7/2))x1^(3/2)x2^(-11/2) + (-q^(5/2) - 4q^(3/2) - 8q^(1/2) - 11q^(-1/2) - 14q^(-3/2) - 8q^(-5/2) - 4q^(-7/2) - 2q^(-9/2))x1^(3/2)x2^(-13/2) + (-2q^(9/2) - 4q^(7/2) - 10q^(5/2) - 16q^(3/2) - 22q^(1/2) - 22q^(-1/2) - 24q^(-3/2) - 14q^(-5/2) - 8q^(-7/2) - 4q^(-9/2) - 2q^(-11/2))x1^(3/2)x2^(-15/2) + (-q^(15/2) - 4q^(13/2) - 8q^(11/2) - 15q^(9/2) - 24q^(7/2) - 35q^(5/2) - 42q^(3/2) - 44q^(1/2) - 41q^(-1/2) - 38q^(-3/2) - 24q^(-5/2) - 14q^(-7/2) - 8q^(-9/2) - 4q^(-11/2) - 2q^(-13/2))x1^(3/2)x2^(-17/2) + (-2q^(21/2) - 4q^(19/2) - 10q^(17/2) - 18q^(15/2) - 30q^(13/2) - 42q^(11/2) - 60q^(9/2) - 72q^(7/2) - 84q^(5/2) - 84q^(3/2) - 80q^(1/2) - 68q^(-1/2) - 60q^(-3/2) - 38q^(-5/2) - 24q^(-7/2) - 14q^(-9/2) - 8q^(-11/2) - 4q^(-13/2) - 2q^(-15/2))x1^(3/2)x2^(-19/2) + (-q^(1/2))x1^(1/2)x2^(-3/2) + (-2q^(1/2))x1^(1/2)x2^(-5/2) + (-q^(3/2) - 3q^(1/2))x1^(1/2)x2^(-7/2) + (-2q^(5/2) - 2q^(3/2) - 4q^(1/2))x1^(1/2)x2^(-9/2) + (-q^(9/2) - 3q^(7/2) - 4q^(5/2) - 3q^(3/2) - 5q^(1/2))x1^(1/2)x2^(-11/2) + (-2q^(13/2) - 2q^(11/2) - 6q^(9/2) - 6q^(7/2) - 6q^(5/2) - 4q^(3/2) - 6q^(1/2))x1^(1/2)x2^(-13/2) + (-q^(19/2) - 3q^(17/2) - 4q^(15/2) - 7q^(13/2) - 9q^(11/2) - 11q^(9/2) - 9q^(7/2) - 8q^(5/2) - 5q^(3/2) - 7q^(1/2))x1^(1/2)x2^(-15/2) + (-2q^(25/2) - 2q^(23/2) - 6q^(21/2) - 8q^(19/2) - 12q^(17/2) - 12q^(15/2) - 18q^(13/2) - 16q^(11/2) - 16q^(9/2) - 12q^(7/2) - 10q^(5/2) - 6q^(3/2) - 8q^(1/2))x1^(1/2)x2^(-17/2) + (-q^(33/2) - 3q^(31/2) - 4q^(29/2) - 7q^(27/2) - 13q^(25/2) - 15q^(23/2) - 21q^(21/2) - 23q^(19/2) - 26q^(17/2) - 27q^(15/2) - 29q^(13/2) - 23q^(11/2) - 21q^(9/2) - 15q^(7/2) - 12q^(5/2) - 7q^(3/2) - 9q^(1/2))x1^(1/2)x2^(-19/2)

(1/2, -3/2)

(1, 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]}

(-q^(-31/2) - 3*q^(-33/2) - 4*q^(-35/2) - 3*q^(-37/2) - 5*q^(-39/2))*x1^(-9/2)*x2^(19/2) + (-2*q^(-19/2) - 2*q^(-21/2) - 4*q^(-23/2))*x1^(-7/2)*x2^(15/2) + (-q^(-15/2) - 4*q^(-17/2) - 8*q^(-19/2) - 11*q^(-21/2) - 14*q^(-23/2) - 8*q^(-25/2) - 4*q^(-27/2) - 2*q^(-29/2))*x1^(-7/2)*x2^(17/2) + (-2*q^(-11/2) - 4*q^(-13/2) - 12*q^(-15/2) - 20*q^(-17/2) - 32*q^(-19/2) - 38*q^(-21/2) - 44*q^(-23/2) - 32*q^(-25/2) - 24*q^(-27/2) - 12*q^(-29/2) - 6*q^(-31/2) - 2*q^(-33/2) - 2*q^(-35/2))*x1^(-7/2)*x2^(19/2) + (-q^(-9/2) - 3*q^(-11/2))*x1^(-5/2)*x2^(11/2) + (-2*q^(-7/2) - 4*q^(-9/2) - 8*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(-5/2)*x2^(13/2) + (-q^(-3/2) - 4*q^(-5/2) - 9*q^(-7/2) - 14*q^(-9/2) - 19*q^(-11/2) - 13*q^(-13/2) - 9*q^(-15/2) - 2*q^(-17/2) - 2*q^(-19/2))*x1^(-5/2)*x2^(15/2) + (-2*q^(1/2) - 4*q^(-1/2) - 12*q^(-3/2) - 20*q^(-5/2) - 32*q^(-7/2) - 38*q^(-9/2) - 44*q^(-11/2) - 32*q^(-13/2) - 24*q^(-15/2) - 12*q^(-17/2) - 6*q^(-19/2) - 2*q^(-21/2) - 2*q^(-23/2))*x1^(-5/2)*x2^(17/2) + (-q^(7/2) - 4*q^(5/2) - 9*q^(3/2) - 19*q^(1/2) - 33*q^(-1/2) - 53*q^(-3/2) - 71*q^(-5/2) - 88*q^(-7/2) - 93*q^(-9/2) - 94*q^(-11/2) - 72*q^(-13/2) - 55*q^(-15/2) - 33*q^(-17/2) - 21*q^(-19/2) - 8*q^(-21/2) - 6*q^(-23/2) - 2*q^(-25/2) - 2*q^(-27/2))*x1^(-5/2)*x2^(19/2) + (-2*q^(-3/2))*x1^(-3/2)*x2^(7/2) + (-q^(-1/2) - 4*q^(-3/2) - 2*q^(-5/2))*x1^(-3/2)*x2^(9/2) + (-2*q^(1/2) - 4*q^(-1/2) - 8*q^(-3/2) - 4*q^(-5/2) - 2*q^(-7/2))*x1^(-3/2)*x2^(11/2) + (-q^(5/2) - 4*q^(3/2) - 8*q^(1/2) - 11*q^(-1/2) - 14*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(-3/2)*x2^(13/2) + (-2*q^(9/2) - 4*q^(7/2) - 10*q^(5/2) - 16*q^(3/2) - 22*q^(1/2) - 22*q^(-1/2) - 24*q^(-3/2) - 14*q^(-5/2) - 8*q^(-7/2) - 4*q^(-9/2) - 2*q^(-11/2))*x1^(-3/2)*x2^(15/2) + (-q^(15/2) - 4*q^(13/2) - 8*q^(11/2) - 15*q^(9/2) - 24*q^(7/2) - 35*q^(5/2) - 42*q^(3/2) - 44*q^(1/2) - 41*q^(-1/2) - 38*q^(-3/2) - 24*q^(-5/2) - 14*q^(-7/2) - 8*q^(-9/2) - 4*q^(-11/2) - 2*q^(-13/2))*x1^(-3/2)*x2^(17/2) + (-2*q^(21/2) - 4*q^(19/2) - 10*q^(17/2) - 18*q^(15/2) - 30*q^(13/2) - 42*q^(11/2) - 60*q^(9/2) - 72*q^(7/2) - 84*q^(5/2) - 84*q^(3/2) - 80*q^(1/2) - 68*q^(-1/2) - 60*q^(-3/2) - 38*q^(-5/2) - 24*q^(-7/2) - 14*q^(-9/2) - 8*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(-3/2)*x2^(19/2) + (-q^(1/2))*x1^(-1/2)*x2^(3/2) + (-2*q^(1/2))*x1^(-1/2)*x2^(5/2) + (-q^(3/2) - 3*q^(1/2))*x1^(-1/2)*x2^(7/2) + (-2*q^(5/2) - 2*q^(3/2) - 4*q^(1/2))*x1^(-1/2)*x2^(9/2) + (-q^(9/2) - 3*q^(7/2) - 4*q^(5/2) - 3*q^(3/2) - 5*q^(1/2))*x1^(-1/2)*x2^(11/2) + (-2*q^(13/2) - 2*q^(11/2) - 6*q^(9/2) - 6*q^(7/2) - 6*q^(5/2) - 4*q^(3/2) - 6*q^(1/2))*x1^(-1/2)*x2^(13/2) + (-q^(19/2) - 3*q^(17/2) - 4*q^(15/2) - 7*q^(13/2) - 9*q^(11/2) - 11*q^(9/2) - 9*q^(7/2) - 8*q^(5/2) - 5*q^(3/2) - 7*q^(1/2))*x1^(-1/2)*x2^(15/2) + (-2*q^(25/2) - 2*q^(23/2) - 6*q^(21/2) - 8*q^(19/2) - 12*q^(17/2) - 12*q^(15/2) - 18*q^(13/2) - 16*q^(11/2) - 16*q^(9/2) - 12*q^(7/2) - 10*q^(5/2) - 6*q^(3/2) - 8*q^(1/2))*x1^(-1/2)*x2^(17/2) + (-q^(33/2) - 3*q^(31/2) - 4*q^(29/2) - 7*q^(27/2) - 13*q^(25/2) - 15*q^(23/2) - 21*q^(21/2) - 23*q^(19/2) - 26*q^(17/2) - 27*q^(15/2) - 29*q^(13/2) - 23*q^(11/2) - 21*q^(9/2) - 15*q^(7/2) - 12*q^(5/2) - 7*q^(3/2) - 9*q^(1/2))*x1^(-1/2)*x2^(19/2)

(1/2, -3/2)

(1, 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]}

(-q^(-31/2) - 3*q^(-33/2) - 4*q^(-35/2) - 3*q^(-37/2) - 5*q^(-39/2))*x1^(-9/2)*x2^(19/2) + (-2*q^(-19/2) - 2*q^(-21/2) - 4*q^(-23/2))*x1^(-7/2)*x2^(15/2) + (-q^(-15/2) - 4*q^(-17/2) - 8*q^(-19/2) - 11*q^(-21/2) - 14*q^(-23/2) - 8*q^(-25/2) - 4*q^(-27/2) - 2*q^(-29/2))*x1^(-7/2)*x2^(17/2) + (-2*q^(-11/2) - 4*q^(-13/2) - 12*q^(-15/2) - 20*q^(-17/2) - 32*q^(-19/2) - 38*q^(-21/2) - 44*q^(-23/2) - 32*q^(-25/2) - 24*q^(-27/2) - 12*q^(-29/2) - 6*q^(-31/2) - 2*q^(-33/2) - 2*q^(-35/2))*x1^(-7/2)*x2^(19/2) + (-q^(-9/2) - 3*q^(-11/2))*x1^(-5/2)*x2^(11/2) + (-2*q^(-7/2) - 4*q^(-9/2) - 8*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(-5/2)*x2^(13/2) + (-q^(-3/2) - 4*q^(-5/2) - 9*q^(-7/2) - 14*q^(-9/2) - 19*q^(-11/2) - 13*q^(-13/2) - 9*q^(-15/2) - 2*q^(-17/2) - 2*q^(-19/2))*x1^(-5/2)*x2^(15/2) + (-2*q^(1/2) - 4*q^(-1/2) - 12*q^(-3/2) - 20*q^(-5/2) - 32*q^(-7/2) - 38*q^(-9/2) - 44*q^(-11/2) - 32*q^(-13/2) - 24*q^(-15/2) - 12*q^(-17/2) - 6*q^(-19/2) - 2*q^(-21/2) - 2*q^(-23/2))*x1^(-5/2)*x2^(17/2) + (-q^(7/2) - 4*q^(5/2) - 9*q^(3/2) - 19*q^(1/2) - 33*q^(-1/2) - 53*q^(-3/2) - 71*q^(-5/2) - 88*q^(-7/2) - 93*q^(-9/2) - 94*q^(-11/2) - 72*q^(-13/2) - 55*q^(-15/2) - 33*q^(-17/2) - 21*q^(-19/2) - 8*q^(-21/2) - 6*q^(-23/2) - 2*q^(-25/2) - 2*q^(-27/2))*x1^(-5/2)*x2^(19/2) + (-2*q^(-3/2))*x1^(-3/2)*x2^(7/2) + (-q^(-1/2) - 4*q^(-3/2) - 2*q^(-5/2))*x1^(-3/2)*x2^(9/2) + (-2*q^(1/2) - 4*q^(-1/2) - 8*q^(-3/2) - 4*q^(-5/2) - 2*q^(-7/2))*x1^(-3/2)*x2^(11/2) + (-q^(5/2) - 4*q^(3/2) - 8*q^(1/2) - 11*q^(-1/2) - 14*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(-3/2)*x2^(13/2) + (-2*q^(9/2) - 4*q^(7/2) - 10*q^(5/2) - 16*q^(3/2) - 22*q^(1/2) - 22*q^(-1/2) - 24*q^(-3/2) - 14*q^(-5/2) - 8*q^(-7/2) - 4*q^(-9/2) - 2*q^(-11/2))*x1^(-3/2)*x2^(15/2) + (-q^(15/2) - 4*q^(13/2) - 8*q^(11/2) - 15*q^(9/2) - 24*q^(7/2) - 35*q^(5/2) - 42*q^(3/2) - 44*q^(1/2) - 41*q^(-1/2) - 38*q^(-3/2) - 24*q^(-5/2) - 14*q^(-7/2) - 8*q^(-9/2) - 4*q^(-11/2) - 2*q^(-13/2))*x1^(-3/2)*x2^(17/2) + (-2*q^(21/2) - 4*q^(19/2) - 10*q^(17/2) - 18*q^(15/2) - 30*q^(13/2) - 42*q^(11/2) - 60*q^(9/2) - 72*q^(7/2) - 84*q^(5/2) - 84*q^(3/2) - 80*q^(1/2) - 68*q^(-1/2) - 60*q^(-3/2) - 38*q^(-5/2) - 24*q^(-7/2) - 14*q^(-9/2) - 8*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(-3/2)*x2^(19/2) + (-q^(1/2))*x1^(-1/2)*x2^(3/2) + (-2*q^(1/2))*x1^(-1/2)*x2^(5/2) + (-q^(3/2) - 3*q^(1/2))*x1^(-1/2)*x2^(7/2) + (-2*q^(5/2) - 2*q^(3/2) - 4*q^(1/2))*x1^(-1/2)*x2^(9/2) + (-q^(9/2) - 3*q^(7/2) - 4*q^(5/2) - 3*q^(3/2) - 5*q^(1/2))*x1^(-1/2)*x2^(11/2) + (-2*q^(13/2) - 2*q^(11/2) - 6*q^(9/2) - 6*q^(7/2) - 6*q^(5/2) - 4*q^(3/2) - 6*q^(1/2))*x1^(-1/2)*x2^(13/2) + (-q^(19/2) - 3*q^(17/2) - 4*q^(15/2) - 7*q^(13/2) - 9*q^(11/2) - 11*q^(9/2) - 9*q^(7/2) - 8*q^(5/2) - 5*q^(3/2) - 7*q^(1/2))*x1^(-1/2)*x2^(15/2) + (-2*q^(25/2) - 2*q^(23/2) - 6*q^(21/2) - 8*q^(19/2) - 12*q^(17/2) - 12*q^(15/2) - 18*q^(13/2) - 16*q^(11/2) - 16*q^(9/2) - 12*q^(7/2) - 10*q^(5/2) - 6*q^(3/2) - 8*q^(1/2))*x1^(-1/2)*x2^(17/2) + (-q^(33/2) - 3*q^(31/2) - 4*q^(29/2) - 7*q^(27/2) - 13*q^(25/2) - 15*q^(23/2) - 21*q^(21/2) - 23*q^(19/2) - 26*q^(17/2) - 27*q^(15/2) - 29*q^(13/2) - 23*q^(11/2) - 21*q^(9/2) - 15*q^(7/2) - 12*q^(5/2) - 7*q^(3/2) - 9*q^(1/2))*x1^(-1/2)*x2^(19/2)

(-1/2, 3/2)

x1^(1/2)x2^(-3/2)

q^(1/2)

(-q^(-31/2) - 3*q^(-33/2) - 4*q^(-35/2) - 3*q^(-37/2) - 5*q^(-39/2))*x1^(9/2)*x2^(-19/2) + (-2*q^(-19/2) - 2*q^(-21/2) - 4*q^(-23/2))*x1^(7/2)*x2^(-15/2) + (-q^(-15/2) - 4*q^(-17/2) - 8*q^(-19/2) - 11*q^(-21/2) - 14*q^(-23/2) - 8*q^(-25/2) - 4*q^(-27/2) - 2*q^(-29/2))*x1^(7/2)*x2^(-17/2) + (-2*q^(-11/2) - 4*q^(-13/2) - 12*q^(-15/2) - 20*q^(-17/2) - 32*q^(-19/2) - 38*q^(-21/2) - 44*q^(-23/2) - 32*q^(-25/2) - 24*q^(-27/2) - 12*q^(-29/2) - 6*q^(-31/2) - 2*q^(-33/2) - 2*q^(-35/2))*x1^(7/2)*x2^(-19/2) + (-q^(-9/2) - 3*q^(-11/2))*x1^(5/2)*x2^(-11/2) + (-2*q^(-7/2) - 4*q^(-9/2) - 8*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(5/2)*x2^(-13/2) + (-q^(-3/2) - 4*q^(-5/2) - 9*q^(-7/2) - 14*q^(-9/2) - 19*q^(-11/2) - 13*q^(-13/2) - 9*q^(-15/2) - 2*q^(-17/2) - 2*q^(-19/2))*x1^(5/2)*x2^(-15/2) + (-2*q^(1/2) - 4*q^(-1/2) - 12*q^(-3/2) - 20*q^(-5/2) - 32*q^(-7/2) - 38*q^(-9/2) - 44*q^(-11/2) - 32*q^(-13/2) - 24*q^(-15/2) - 12*q^(-17/2) - 6*q^(-19/2) - 2*q^(-21/2) - 2*q^(-23/2))*x1^(5/2)*x2^(-17/2) + (-q^(7/2) - 4*q^(5/2) - 9*q^(3/2) - 19*q^(1/2) - 33*q^(-1/2) - 53*q^(-3/2) - 71*q^(-5/2) - 88*q^(-7/2) - 93*q^(-9/2) - 94*q^(-11/2) - 72*q^(-13/2) - 55*q^(-15/2) - 33*q^(-17/2) - 21*q^(-19/2) - 8*q^(-21/2) - 6*q^(-23/2) - 2*q^(-25/2) - 2*q^(-27/2))*x1^(5/2)*x2^(-19/2) + (-2*q^(-3/2))*x1^(3/2)*x2^(-7/2) + (-q^(-1/2) - 4*q^(-3/2) - 2*q^(-5/2))*x1^(3/2)*x2^(-9/2) + (-2*q^(1/2) - 4*q^(-1/2) - 8*q^(-3/2) - 4*q^(-5/2) - 2*q^(-7/2))*x1^(3/2)*x2^(-11/2) + (-q^(5/2) - 4*q^(3/2) - 8*q^(1/2) - 11*q^(-1/2) - 14*q^(-3/2) - 8*q^(-5/2) - 4*q^(-7/2) - 2*q^(-9/2))*x1^(3/2)*x2^(-13/2) + (-2*q^(9/2) - 4*q^(7/2) - 10*q^(5/2) - 16*q^(3/2) - 22*q^(1/2) - 22*q^(-1/2) - 24*q^(-3/2) - 14*q^(-5/2) - 8*q^(-7/2) - 4*q^(-9/2) - 2*q^(-11/2))*x1^(3/2)*x2^(-15/2) + (-q^(15/2) - 4*q^(13/2) - 8*q^(11/2) - 15*q^(9/2) - 24*q^(7/2) - 35*q^(5/2) - 42*q^(3/2) - 44*q^(1/2) - 41*q^(-1/2) - 38*q^(-3/2) - 24*q^(-5/2) - 14*q^(-7/2) - 8*q^(-9/2) - 4*q^(-11/2) - 2*q^(-13/2))*x1^(3/2)*x2^(-17/2) + (-2*q^(21/2) - 4*q^(19/2) - 10*q^(17/2) - 18*q^(15/2) - 30*q^(13/2) - 42*q^(11/2) - 60*q^(9/2) - 72*q^(7/2) - 84*q^(5/2) - 84*q^(3/2) - 80*q^(1/2) - 68*q^(-1/2) - 60*q^(-3/2) - 38*q^(-5/2) - 24*q^(-7/2) - 14*q^(-9/2) - 8*q^(-11/2) - 4*q^(-13/2) - 2*q^(-15/2))*x1^(3/2)*x2^(-19/2) + (-q^(1/2))*x1^(1/2)*x2^(-3/2) + (-2*q^(1/2))*x1^(1/2)*x2^(-5/2) + (-q^(3/2) - 3*q^(1/2))*x1^(1/2)*x2^(-7/2) + (-2*q^(5/2) - 2*q^(3/2) - 4*q^(1/2))*x1^(1/2)*x2^(-9/2) + (-q^(9/2) - 3*q^(7/2) - 4*q^(5/2) - 3*q^(3/2) - 5*q^(1/2))*x1^(1/2)*x2^(-11/2) + (-2*q^(13/2) - 2*q^(11/2) - 6*q^(9/2) - 6*q^(7/2) - 6*q^(5/2) - 4*q^(3/2) - 6*q^(1/2))*x1^(1/2)*x2^(-13/2) + (-q^(19/2) - 3*q^(17/2) - 4*q^(15/2) - 7*q^(13/2) - 9*q^(11/2) - 11*q^(9/2) - 9*q^(7/2) - 8*q^(5/2) - 5*q^(3/2) - 7*q^(1/2))*x1^(1/2)*x2^(-15/2) + (-2*q^(25/2) - 2*q^(23/2) - 6*q^(21/2) - 8*q^(19/2) - 12*q^(17/2) - 12*q^(15/2) - 18*q^(13/2) - 16*q^(11/2) - 16*q^(9/2) - 12*q^(7/2) - 10*q^(5/2) - 6*q^(3/2) - 8*q^(1/2))*x1^(1/2)*x2^(-17/2) + (-q^(33/2) - 3*q^(31/2) - 4*q^(29/2) - 7*q^(27/2) - 13*q^(25/2) - 15*q^(23/2) - 21*q^(21/2) - 23*q^(19/2) - 26*q^(17/2) - 27*q^(15/2) - 29*q^(13/2) - 23*q^(11/2) - 21*q^(9/2) - 15*q^(7/2) - 12*q^(5/2) - 7*q^(3/2) - 9*q^(1/2))*x1^(1/2)*x2^(-19/2)

Braid

Braid word	Components	Crossings	Strands
`[1, 2, -1, 2, 1, 3, -2, 3]`	2	8	4

Multivariable Alexander polynomial

Δ_L
`2A1^(1/2)A2^(-1/2) - A1^(1/2)A2^(-3/2) - A1^(-1/2)A2^(3/2) + 2A1^(-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 F_L.

Dual Thurston polytope

Vertex	Dual to fibered face
`(1, -3)`	yes
`(1, -1)`	no
`(-1, 3)`	yes
`(-1, 1)`	no

HFL polytope

Poincaré polynomial
`m^(-3)A2^(-2) + 2m^(-2)A1^(-1) + 3m^(-2)A2^(-1) + m^(-2)A1A2^(-2) + 3m^(-1)A1^(-1)A2 + 4m^(-1) + 3m^(-1)A1A2^(-1) + A1^(-1)A2^2 + 3A2 + 2A1 + mA2^2`

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

Record

FL/HFL Links

`orderOption(int)`	`70`
`namestring`	`L8n1{1}`
`statusstring`	`success`
`slugstring`	`L8n1_1_51419213`
`result_filestring`	`details/L8n1_1_51419213.json`
`complexity_scoreOption(int)`	`128`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`8`
`component_countOption(int)`	`2`
`girthOption(int)`	`6`
`total_rankOption(int)`	`24`
`wall_secondsOption(float)`	`0.00153`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`2`
`support_sizeOption(int)`	`11`
`vertex_countOption(int)`	`6`
`fibered_vertex_countOption(int)`	`2`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`4`
`alexander_vertex_countOption(int)`	`4`
`alexander_relationstring`	`not_computed`
`fk_countint`	`2`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L8n1_1_51419213" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L8n1_1_51419213`

FL expansions

Braid

Multivariable Alexander polynomial

Dual Thurston polytope

HFL polytope

Record

F_L expansions