L10a25{0} - HFL and FL

details/L10a25_0_9bef87ee.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, -5/2)`	`(1/2, 1)`	`x1^(-1/2)x2^(5/2)`	`q^(-17/2)`	`{"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]}`		(8q^(53/2) + 6q^(51/2) + 10q^(49/2) + 12q^(47/2) + 16q^(45/2) + 16q^(43/2) + 18q^(41/2) + 12q^(39/2) + 12q^(37/2) + 8q^(35/2) + 6q^(33/2) + 2q^(31/2) + 2q^(29/2))x1^(-15/2)x2^(19/2) + (-7q^(39/2) - 5q^(37/2) - 8q^(35/2) - 9q^(33/2) - 11q^(31/2) - 9q^(29/2) - 7q^(27/2) - 4q^(25/2) - 3q^(23/2) - q^(21/2))x1^(-13/2)x2^(17/2) + (-2q^(51/2) - 4q^(49/2) - 8q^(47/2) - 14q^(45/2) - 24q^(43/2) - 38q^(41/2) - 74q^(39/2) - 72q^(37/2) - 86q^(35/2) - 86q^(33/2) - 84q^(31/2) - 62q^(29/2) - 44q^(27/2) - 24q^(25/2) - 14q^(23/2) - 4q^(21/2))x1^(-13/2)x2^(19/2) + (6q^(27/2) + 4q^(25/2) + 6q^(23/2) + 6q^(21/2) + 6q^(19/2) + 2q^(17/2) + 2q^(15/2))x1^(-11/2)x2^(15/2) + (2q^(37/2) + 4q^(35/2) + 8q^(33/2) + 14q^(31/2) + 24q^(29/2) + 50q^(27/2) + 44q^(25/2) + 48q^(23/2) + 42q^(21/2) + 32q^(19/2) + 12q^(17/2) + 8q^(15/2))x1^(-11/2)x2^(17/2) + (2q^(47/2) + 2q^(45/2) + 6q^(43/2) + 8q^(41/2) + 16q^(39/2) + 32q^(37/2) + 58q^(35/2) + 86q^(33/2) + 130q^(31/2) + 176q^(29/2) + 238q^(27/2) + 204q^(25/2) + 194q^(23/2) + 146q^(21/2) + 94q^(19/2) + 32q^(17/2) + 18q^(15/2) - 2q^(13/2))x1^(-11/2)x2^(19/2) + (-5q^(17/2) - 3q^(15/2) - 4q^(13/2) - 3q^(11/2) - q^(9/2))x1^(-9/2)x2^(13/2) + (-2q^(25/2) - 4q^(23/2) - 8q^(21/2) - 14q^(19/2) - 34q^(17/2) - 24q^(15/2) - 24q^(13/2) - 14q^(11/2) - 4q^(9/2))x1^(-9/2)x2^(15/2) + (-2q^(33/2) - 2q^(31/2) - 6q^(29/2) - 8q^(27/2) - 25q^(25/2) - 39q^(23/2) - 65q^(21/2) - 91q^(19/2) - 132q^(17/2) - 90q^(15/2) - 75q^(13/2) - 35q^(11/2) - 7q^(9/2) + q^(7/2))x1^(-9/2)x2^(17/2) + (-2q^(41/2) - 2q^(39/2) - 4q^(37/2) - 8q^(35/2) - 18q^(33/2) - 24q^(31/2) - 50q^(29/2) - 72q^(27/2) - 142q^(25/2) - 196q^(23/2) - 282q^(21/2) - 326q^(19/2) - 368q^(17/2) - 232q^(15/2) - 164q^(13/2) - 68q^(11/2) - 18q^(9/2) - 12q^(7/2) - 16q^(5/2) - 8q^(3/2) - 4q^(1/2))x1^(-9/2)x2^(19/2) + (4q^(9/2) + 2q^(7/2) + 2q^(5/2))x1^(-7/2)x2^(11/2) + (2q^(15/2) + 4q^(13/2) + 8q^(11/2) + 22q^(9/2) + 12q^(7/2) + 8q^(5/2))x1^(-7/2)x2^(13/2) + (2q^(21/2) + 2q^(19/2) + 6q^(17/2) + 16q^(15/2) + 30q^(13/2) + 46q^(11/2) + 72q^(9/2) + 34q^(7/2) + 18q^(5/2) - 2q^(3/2))x1^(-7/2)x2^(15/2) + (2q^(27/2) + 2q^(25/2) + 4q^(23/2) + 14q^(21/2) + 18q^(19/2) + 40q^(17/2) + 76q^(15/2) + 124q^(13/2) + 150q^(11/2) + 172q^(9/2) + 66q^(7/2) + 28q^(5/2) - 2q^(3/2) + 8q^(1/2) + 8q^(-1/2) + 2q^(-3/2))x1^(-7/2)x2^(17/2) + (2q^(33/2) + 2q^(31/2) + 4q^(29/2) + 12q^(27/2) + 16q^(25/2) + 28q^(23/2) + 62q^(21/2) + 88q^(19/2) + 168q^(17/2) + 272q^(15/2) + 364q^(13/2) + 362q^(11/2) + 330q^(9/2) + 110q^(7/2) + 63q^(5/2) + 52q^(3/2) + 82q^(1/2) + 69q^(-1/2) + 32q^(-3/2) + 6q^(-5/2))x1^(-7/2)x2^(19/2) + (-3q^(3/2) - q^(1/2))x1^(-5/2)x2^(9/2) + (-2q^(7/2) - 4q^(5/2) - 14q^(3/2) - 4q^(1/2))x1^(-5/2)x2^(11/2) + (-2q^(11/2) - 2q^(9/2) - 13q^(7/2) - 22q^(5/2) - 39q^(3/2) - 7q^(1/2) + q^(-1/2))x1^(-5/2)x2^(13/2) + (-2q^(15/2) - 2q^(13/2) - 10q^(11/2) - 16q^(9/2) - 54q^(7/2) - 66q^(5/2) - 80q^(3/2) - 6q^(1/2) + 4q^(-1/2) - 4q^(-3/2) - 4q^(-5/2))x1^(-5/2)x2^(15/2) + (-2q^(19/2) - 2q^(17/2) - 10q^(15/2) - 12q^(13/2) - 44q^(11/2) - 78q^(9/2) - 154q^(7/2) - 143q^(5/2) - 133q^(3/2) - 4q^(-1/2) - 38q^(-3/2) - 32q^(-5/2) - 12q^(-7/2))x1^(-5/2)x2^(17/2) + (-2q^(23/2) - 2q^(21/2) - 10q^(19/2) - 12q^(17/2) - 44q^(15/2) - 66q^(13/2) - 172q^(11/2) - 242q^(9/2) - 334q^(7/2) - 250q^(5/2) - 200q^(3/2) - 22q^(1/2) - 94q^(-1/2) - 186q^(-3/2) - 160q^(-5/2) - 76q^(-7/2) - 16q^(-9/2) + 4q^(-11/2))x1^(-5/2)x2^(19/2) + (2q^(-1/2))x1^(-3/2)x2^(7/2) + (2q^(1/2) + 8q^(-1/2))x1^(-3/2)x2^(9/2) + (2q^(3/2) + 10q^(1/2) + 20q^(-1/2) - 2q^(-3/2))x1^(-3/2)x2^(11/2) + (2q^(5/2) + 14q^(3/2) + 28q^(1/2) + 38q^(-1/2) - 8q^(-3/2) + 2q^(-7/2))x1^(-3/2)x2^(13/2) + (4q^(7/2) + 20q^(5/2) + 44q^(3/2) + 58q^(1/2) + 60q^(-1/2) - 20q^(-3/2) + 5q^(-5/2) + 16q^(-7/2) + 6q^(-9/2))x1^(-3/2)x2^(15/2) + (4q^(11/2) + 8q^(9/2) + 36q^(7/2) + 68q^(5/2) + 98q^(3/2) + 96q^(1/2) + 84q^(-1/2) - 32q^(-3/2) + 34q^(-5/2) + 68q^(-7/2) + 40q^(-9/2) + 10q^(-11/2) - 2q^(-13/2))x1^(-3/2)x2^(17/2) + (2q^(17/2) + 6q^(15/2) + 12q^(13/2) + 30q^(11/2) + 62q^(9/2) + 120q^(7/2) + 156q^(5/2) + 170q^(3/2) + 139q^(1/2) + 122q^(-1/2) - 10q^(-3/2) + 142q^(-5/2) + 218q^(-7/2) + 152q^(-9/2) + 59q^(-11/2) - 2q^(-13/2) - 6q^(-15/2))x1^(-3/2)x2^(19/2) + (-q^(-3/2))x1^(-1/2)x2^(5/2) + (-4q^(-3/2))x1^(-1/2)x2^(7/2) + (-q^(-1/2) - 10q^(-3/2) + q^(-5/2))x1^(-1/2)x2^(9/2) + (-2q^(1/2) - 4q^(-1/2) - 20q^(-3/2) + 4q^(-5/2))x1^(-1/2)x2^(11/2) + (-q^(5/2) - 3q^(3/2) - 8q^(1/2) - 10q^(-1/2) - 34q^(-3/2) + 10q^(-5/2) - 4q^(-9/2))x1^(-1/2)x2^(13/2) + (-2q^(9/2) - 2q^(7/2) - 8q^(5/2) - 12q^(3/2) - 20q^(1/2) - 18q^(-1/2) - 52q^(-3/2) + 20q^(-5/2) - 2q^(-7/2) - 16q^(-9/2) - 8q^(-11/2))x1^(-1/2)x2^(15/2) + (-q^(15/2) - 3q^(13/2) - 4q^(11/2) - 11q^(9/2) - 13q^(7/2) - 26q^(5/2) - 29q^(3/2) - 37q^(1/2) - 27q^(-1/2) - 74q^(-3/2) + 31q^(-5/2) - 12q^(-7/2) - 46q^(-9/2) - 32q^(-11/2) - 12q^(-13/2) + 4q^(-15/2))x1^(-1/2)x2^(17/2) + (-2q^(21/2) - 2q^(19/2) - 6q^(17/2) - 10q^(15/2) - 18q^(13/2) - 20q^(11/2) - 38q^(9/2) - 38q^(7/2) - 58q^(5/2) - 52q^(3/2) - 58q^(1/2) - 38q^(-1/2) - 108q^(-3/2) + 32q^(-5/2) - 48q^(-7/2) - 112q^(-9/2) - 90q^(-11/2) - 46q^(-13/2) + 8q^(-17/2))x1^(-1/2)*x2^(19/2)
`(-1/2, 5/2)`		`x1^(1/2)x2^(-5/2)`	`q^(-17/2)`			(8q^(53/2) + 6q^(51/2) + 10q^(49/2) + 12q^(47/2) + 16q^(45/2) + 16q^(43/2) + 18q^(41/2) + 12q^(39/2) + 12q^(37/2) + 8q^(35/2) + 6q^(33/2) + 2q^(31/2) + 2q^(29/2))x1^(15/2)x2^(-19/2) + (-7q^(39/2) - 5q^(37/2) - 8q^(35/2) - 9q^(33/2) - 11q^(31/2) - 9q^(29/2) - 7q^(27/2) - 4q^(25/2) - 3q^(23/2) - q^(21/2))x1^(13/2)x2^(-17/2) + (-2q^(51/2) - 4q^(49/2) - 8q^(47/2) - 14q^(45/2) - 24q^(43/2) - 38q^(41/2) - 74q^(39/2) - 72q^(37/2) - 86q^(35/2) - 86q^(33/2) - 84q^(31/2) - 62q^(29/2) - 44q^(27/2) - 24q^(25/2) - 14q^(23/2) - 4q^(21/2))x1^(13/2)x2^(-19/2) + (6q^(27/2) + 4q^(25/2) + 6q^(23/2) + 6q^(21/2) + 6q^(19/2) + 2q^(17/2) + 2q^(15/2))x1^(11/2)x2^(-15/2) + (2q^(37/2) + 4q^(35/2) + 8q^(33/2) + 14q^(31/2) + 24q^(29/2) + 50q^(27/2) + 44q^(25/2) + 48q^(23/2) + 42q^(21/2) + 32q^(19/2) + 12q^(17/2) + 8q^(15/2))x1^(11/2)x2^(-17/2) + (2q^(47/2) + 2q^(45/2) + 6q^(43/2) + 8q^(41/2) + 16q^(39/2) + 32q^(37/2) + 58q^(35/2) + 86q^(33/2) + 130q^(31/2) + 176q^(29/2) + 238q^(27/2) + 204q^(25/2) + 194q^(23/2) + 146q^(21/2) + 94q^(19/2) + 32q^(17/2) + 18q^(15/2) - 2q^(13/2))x1^(11/2)x2^(-19/2) + (-5q^(17/2) - 3q^(15/2) - 4q^(13/2) - 3q^(11/2) - q^(9/2))x1^(9/2)x2^(-13/2) + (-2q^(25/2) - 4q^(23/2) - 8q^(21/2) - 14q^(19/2) - 34q^(17/2) - 24q^(15/2) - 24q^(13/2) - 14q^(11/2) - 4q^(9/2))x1^(9/2)x2^(-15/2) + (-2q^(33/2) - 2q^(31/2) - 6q^(29/2) - 8q^(27/2) - 25q^(25/2) - 39q^(23/2) - 65q^(21/2) - 91q^(19/2) - 132q^(17/2) - 90q^(15/2) - 75q^(13/2) - 35q^(11/2) - 7q^(9/2) + q^(7/2))x1^(9/2)x2^(-17/2) + (-2q^(41/2) - 2q^(39/2) - 4q^(37/2) - 8q^(35/2) - 18q^(33/2) - 24q^(31/2) - 50q^(29/2) - 72q^(27/2) - 142q^(25/2) - 196q^(23/2) - 282q^(21/2) - 326q^(19/2) - 368q^(17/2) - 232q^(15/2) - 164q^(13/2) - 68q^(11/2) - 18q^(9/2) - 12q^(7/2) - 16q^(5/2) - 8q^(3/2) - 4q^(1/2))x1^(9/2)x2^(-19/2) + (4q^(9/2) + 2q^(7/2) + 2q^(5/2))x1^(7/2)x2^(-11/2) + (2q^(15/2) + 4q^(13/2) + 8q^(11/2) + 22q^(9/2) + 12q^(7/2) + 8q^(5/2))x1^(7/2)x2^(-13/2) + (2q^(21/2) + 2q^(19/2) + 6q^(17/2) + 16q^(15/2) + 30q^(13/2) + 46q^(11/2) + 72q^(9/2) + 34q^(7/2) + 18q^(5/2) - 2q^(3/2))x1^(7/2)x2^(-15/2) + (2q^(27/2) + 2q^(25/2) + 4q^(23/2) + 14q^(21/2) + 18q^(19/2) + 40q^(17/2) + 76q^(15/2) + 124q^(13/2) + 150q^(11/2) + 172q^(9/2) + 66q^(7/2) + 28q^(5/2) - 2q^(3/2) + 8q^(1/2) + 8q^(-1/2) + 2q^(-3/2))x1^(7/2)x2^(-17/2) + (2q^(33/2) + 2q^(31/2) + 4q^(29/2) + 12q^(27/2) + 16q^(25/2) + 28q^(23/2) + 62q^(21/2) + 88q^(19/2) + 168q^(17/2) + 272q^(15/2) + 364q^(13/2) + 362q^(11/2) + 330q^(9/2) + 110q^(7/2) + 63q^(5/2) + 52q^(3/2) + 82q^(1/2) + 69q^(-1/2) + 32q^(-3/2) + 6q^(-5/2))x1^(7/2)x2^(-19/2) + (-3q^(3/2) - q^(1/2))x1^(5/2)x2^(-9/2) + (-2q^(7/2) - 4q^(5/2) - 14q^(3/2) - 4q^(1/2))x1^(5/2)x2^(-11/2) + (-2q^(11/2) - 2q^(9/2) - 13q^(7/2) - 22q^(5/2) - 39q^(3/2) - 7q^(1/2) + q^(-1/2))x1^(5/2)x2^(-13/2) + (-2q^(15/2) - 2q^(13/2) - 10q^(11/2) - 16q^(9/2) - 54q^(7/2) - 66q^(5/2) - 80q^(3/2) - 6q^(1/2) + 4q^(-1/2) - 4q^(-3/2) - 4q^(-5/2))x1^(5/2)x2^(-15/2) + (-2q^(19/2) - 2q^(17/2) - 10q^(15/2) - 12q^(13/2) - 44q^(11/2) - 78q^(9/2) - 154q^(7/2) - 143q^(5/2) - 133q^(3/2) - 4q^(-1/2) - 38q^(-3/2) - 32q^(-5/2) - 12q^(-7/2))x1^(5/2)x2^(-17/2) + (-2q^(23/2) - 2q^(21/2) - 10q^(19/2) - 12q^(17/2) - 44q^(15/2) - 66q^(13/2) - 172q^(11/2) - 242q^(9/2) - 334q^(7/2) - 250q^(5/2) - 200q^(3/2) - 22q^(1/2) - 94q^(-1/2) - 186q^(-3/2) - 160q^(-5/2) - 76q^(-7/2) - 16q^(-9/2) + 4q^(-11/2))x1^(5/2)x2^(-19/2) + (2q^(-1/2))x1^(3/2)x2^(-7/2) + (2q^(1/2) + 8q^(-1/2))x1^(3/2)x2^(-9/2) + (2q^(3/2) + 10q^(1/2) + 20q^(-1/2) - 2q^(-3/2))x1^(3/2)x2^(-11/2) + (2q^(5/2) + 14q^(3/2) + 28q^(1/2) + 38q^(-1/2) - 8q^(-3/2) + 2q^(-7/2))x1^(3/2)x2^(-13/2) + (4q^(7/2) + 20q^(5/2) + 44q^(3/2) + 58q^(1/2) + 60q^(-1/2) - 20q^(-3/2) + 5q^(-5/2) + 16q^(-7/2) + 6q^(-9/2))x1^(3/2)x2^(-15/2) + (4q^(11/2) + 8q^(9/2) + 36q^(7/2) + 68q^(5/2) + 98q^(3/2) + 96q^(1/2) + 84q^(-1/2) - 32q^(-3/2) + 34q^(-5/2) + 68q^(-7/2) + 40q^(-9/2) + 10q^(-11/2) - 2q^(-13/2))x1^(3/2)x2^(-17/2) + (2q^(17/2) + 6q^(15/2) + 12q^(13/2) + 30q^(11/2) + 62q^(9/2) + 120q^(7/2) + 156q^(5/2) + 170q^(3/2) + 139q^(1/2) + 122q^(-1/2) - 10q^(-3/2) + 142q^(-5/2) + 218q^(-7/2) + 152q^(-9/2) + 59q^(-11/2) - 2q^(-13/2) - 6q^(-15/2))x1^(3/2)x2^(-19/2) + (-q^(-3/2))x1^(1/2)x2^(-5/2) + (-4q^(-3/2))x1^(1/2)x2^(-7/2) + (-q^(-1/2) - 10q^(-3/2) + q^(-5/2))x1^(1/2)x2^(-9/2) + (-2q^(1/2) - 4q^(-1/2) - 20q^(-3/2) + 4q^(-5/2))x1^(1/2)x2^(-11/2) + (-q^(5/2) - 3q^(3/2) - 8q^(1/2) - 10q^(-1/2) - 34q^(-3/2) + 10q^(-5/2) - 4q^(-9/2))x1^(1/2)x2^(-13/2) + (-2q^(9/2) - 2q^(7/2) - 8q^(5/2) - 12q^(3/2) - 20q^(1/2) - 18q^(-1/2) - 52q^(-3/2) + 20q^(-5/2) - 2q^(-7/2) - 16q^(-9/2) - 8q^(-11/2))x1^(1/2)x2^(-15/2) + (-q^(15/2) - 3q^(13/2) - 4q^(11/2) - 11q^(9/2) - 13q^(7/2) - 26q^(5/2) - 29q^(3/2) - 37q^(1/2) - 27q^(-1/2) - 74q^(-3/2) + 31q^(-5/2) - 12q^(-7/2) - 46q^(-9/2) - 32q^(-11/2) - 12q^(-13/2) + 4q^(-15/2))x1^(1/2)x2^(-17/2) + (-2q^(21/2) - 2q^(19/2) - 6q^(17/2) - 10q^(15/2) - 18q^(13/2) - 20q^(11/2) - 38q^(9/2) - 38q^(7/2) - 58q^(5/2) - 52q^(3/2) - 58q^(1/2) - 38q^(-1/2) - 108q^(-3/2) + 32q^(-5/2) - 48q^(-7/2) - 112q^(-9/2) - 90q^(-11/2) - 46q^(-13/2) + 8q^(-17/2))x1^(1/2)*x2^(-19/2)

(1/2, -5/2)

(1/2, 1)

x1^(-1/2)x2^(5/2)

q^(-17/2)

{"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]}

(8*q^(53/2) + 6*q^(51/2) + 10*q^(49/2) + 12*q^(47/2) + 16*q^(45/2) + 16*q^(43/2) + 18*q^(41/2) + 12*q^(39/2) + 12*q^(37/2) + 8*q^(35/2) + 6*q^(33/2) + 2*q^(31/2) + 2*q^(29/2))*x1^(-15/2)*x2^(19/2) + (-7*q^(39/2) - 5*q^(37/2) - 8*q^(35/2) - 9*q^(33/2) - 11*q^(31/2) - 9*q^(29/2) - 7*q^(27/2) - 4*q^(25/2) - 3*q^(23/2) - q^(21/2))*x1^(-13/2)*x2^(17/2) + (-2*q^(51/2) - 4*q^(49/2) - 8*q^(47/2) - 14*q^(45/2) - 24*q^(43/2) - 38*q^(41/2) - 74*q^(39/2) - 72*q^(37/2) - 86*q^(35/2) - 86*q^(33/2) - 84*q^(31/2) - 62*q^(29/2) - 44*q^(27/2) - 24*q^(25/2) - 14*q^(23/2) - 4*q^(21/2))*x1^(-13/2)*x2^(19/2) + (6*q^(27/2) + 4*q^(25/2) + 6*q^(23/2) + 6*q^(21/2) + 6*q^(19/2) + 2*q^(17/2) + 2*q^(15/2))*x1^(-11/2)*x2^(15/2) + (2*q^(37/2) + 4*q^(35/2) + 8*q^(33/2) + 14*q^(31/2) + 24*q^(29/2) + 50*q^(27/2) + 44*q^(25/2) + 48*q^(23/2) + 42*q^(21/2) + 32*q^(19/2) + 12*q^(17/2) + 8*q^(15/2))*x1^(-11/2)*x2^(17/2) + (2*q^(47/2) + 2*q^(45/2) + 6*q^(43/2) + 8*q^(41/2) + 16*q^(39/2) + 32*q^(37/2) + 58*q^(35/2) + 86*q^(33/2) + 130*q^(31/2) + 176*q^(29/2) + 238*q^(27/2) + 204*q^(25/2) + 194*q^(23/2) + 146*q^(21/2) + 94*q^(19/2) + 32*q^(17/2) + 18*q^(15/2) - 2*q^(13/2))*x1^(-11/2)*x2^(19/2) + (-5*q^(17/2) - 3*q^(15/2) - 4*q^(13/2) - 3*q^(11/2) - q^(9/2))*x1^(-9/2)*x2^(13/2) + (-2*q^(25/2) - 4*q^(23/2) - 8*q^(21/2) - 14*q^(19/2) - 34*q^(17/2) - 24*q^(15/2) - 24*q^(13/2) - 14*q^(11/2) - 4*q^(9/2))*x1^(-9/2)*x2^(15/2) + (-2*q^(33/2) - 2*q^(31/2) - 6*q^(29/2) - 8*q^(27/2) - 25*q^(25/2) - 39*q^(23/2) - 65*q^(21/2) - 91*q^(19/2) - 132*q^(17/2) - 90*q^(15/2) - 75*q^(13/2) - 35*q^(11/2) - 7*q^(9/2) + q^(7/2))*x1^(-9/2)*x2^(17/2) + (-2*q^(41/2) - 2*q^(39/2) - 4*q^(37/2) - 8*q^(35/2) - 18*q^(33/2) - 24*q^(31/2) - 50*q^(29/2) - 72*q^(27/2) - 142*q^(25/2) - 196*q^(23/2) - 282*q^(21/2) - 326*q^(19/2) - 368*q^(17/2) - 232*q^(15/2) - 164*q^(13/2) - 68*q^(11/2) - 18*q^(9/2) - 12*q^(7/2) - 16*q^(5/2) - 8*q^(3/2) - 4*q^(1/2))*x1^(-9/2)*x2^(19/2) + (4*q^(9/2) + 2*q^(7/2) + 2*q^(5/2))*x1^(-7/2)*x2^(11/2) + (2*q^(15/2) + 4*q^(13/2) + 8*q^(11/2) + 22*q^(9/2) + 12*q^(7/2) + 8*q^(5/2))*x1^(-7/2)*x2^(13/2) + (2*q^(21/2) + 2*q^(19/2) + 6*q^(17/2) + 16*q^(15/2) + 30*q^(13/2) + 46*q^(11/2) + 72*q^(9/2) + 34*q^(7/2) + 18*q^(5/2) - 2*q^(3/2))*x1^(-7/2)*x2^(15/2) + (2*q^(27/2) + 2*q^(25/2) + 4*q^(23/2) + 14*q^(21/2) + 18*q^(19/2) + 40*q^(17/2) + 76*q^(15/2) + 124*q^(13/2) + 150*q^(11/2) + 172*q^(9/2) + 66*q^(7/2) + 28*q^(5/2) - 2*q^(3/2) + 8*q^(1/2) + 8*q^(-1/2) + 2*q^(-3/2))*x1^(-7/2)*x2^(17/2) + (2*q^(33/2) + 2*q^(31/2) + 4*q^(29/2) + 12*q^(27/2) + 16*q^(25/2) + 28*q^(23/2) + 62*q^(21/2) + 88*q^(19/2) + 168*q^(17/2) + 272*q^(15/2) + 364*q^(13/2) + 362*q^(11/2) + 330*q^(9/2) + 110*q^(7/2) + 63*q^(5/2) + 52*q^(3/2) + 82*q^(1/2) + 69*q^(-1/2) + 32*q^(-3/2) + 6*q^(-5/2))*x1^(-7/2)*x2^(19/2) + (-3*q^(3/2) - q^(1/2))*x1^(-5/2)*x2^(9/2) + (-2*q^(7/2) - 4*q^(5/2) - 14*q^(3/2) - 4*q^(1/2))*x1^(-5/2)*x2^(11/2) + (-2*q^(11/2) - 2*q^(9/2) - 13*q^(7/2) - 22*q^(5/2) - 39*q^(3/2) - 7*q^(1/2) + q^(-1/2))*x1^(-5/2)*x2^(13/2) + (-2*q^(15/2) - 2*q^(13/2) - 10*q^(11/2) - 16*q^(9/2) - 54*q^(7/2) - 66*q^(5/2) - 80*q^(3/2) - 6*q^(1/2) + 4*q^(-1/2) - 4*q^(-3/2) - 4*q^(-5/2))*x1^(-5/2)*x2^(15/2) + (-2*q^(19/2) - 2*q^(17/2) - 10*q^(15/2) - 12*q^(13/2) - 44*q^(11/2) - 78*q^(9/2) - 154*q^(7/2) - 143*q^(5/2) - 133*q^(3/2) - 4*q^(-1/2) - 38*q^(-3/2) - 32*q^(-5/2) - 12*q^(-7/2))*x1^(-5/2)*x2^(17/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 12*q^(17/2) - 44*q^(15/2) - 66*q^(13/2) - 172*q^(11/2) - 242*q^(9/2) - 334*q^(7/2) - 250*q^(5/2) - 200*q^(3/2) - 22*q^(1/2) - 94*q^(-1/2) - 186*q^(-3/2) - 160*q^(-5/2) - 76*q^(-7/2) - 16*q^(-9/2) + 4*q^(-11/2))*x1^(-5/2)*x2^(19/2) + (2*q^(-1/2))*x1^(-3/2)*x2^(7/2) + (2*q^(1/2) + 8*q^(-1/2))*x1^(-3/2)*x2^(9/2) + (2*q^(3/2) + 10*q^(1/2) + 20*q^(-1/2) - 2*q^(-3/2))*x1^(-3/2)*x2^(11/2) + (2*q^(5/2) + 14*q^(3/2) + 28*q^(1/2) + 38*q^(-1/2) - 8*q^(-3/2) + 2*q^(-7/2))*x1^(-3/2)*x2^(13/2) + (4*q^(7/2) + 20*q^(5/2) + 44*q^(3/2) + 58*q^(1/2) + 60*q^(-1/2) - 20*q^(-3/2) + 5*q^(-5/2) + 16*q^(-7/2) + 6*q^(-9/2))*x1^(-3/2)*x2^(15/2) + (4*q^(11/2) + 8*q^(9/2) + 36*q^(7/2) + 68*q^(5/2) + 98*q^(3/2) + 96*q^(1/2) + 84*q^(-1/2) - 32*q^(-3/2) + 34*q^(-5/2) + 68*q^(-7/2) + 40*q^(-9/2) + 10*q^(-11/2) - 2*q^(-13/2))*x1^(-3/2)*x2^(17/2) + (2*q^(17/2) + 6*q^(15/2) + 12*q^(13/2) + 30*q^(11/2) + 62*q^(9/2) + 120*q^(7/2) + 156*q^(5/2) + 170*q^(3/2) + 139*q^(1/2) + 122*q^(-1/2) - 10*q^(-3/2) + 142*q^(-5/2) + 218*q^(-7/2) + 152*q^(-9/2) + 59*q^(-11/2) - 2*q^(-13/2) - 6*q^(-15/2))*x1^(-3/2)*x2^(19/2) + (-q^(-3/2))*x1^(-1/2)*x2^(5/2) + (-4*q^(-3/2))*x1^(-1/2)*x2^(7/2) + (-q^(-1/2) - 10*q^(-3/2) + q^(-5/2))*x1^(-1/2)*x2^(9/2) + (-2*q^(1/2) - 4*q^(-1/2) - 20*q^(-3/2) + 4*q^(-5/2))*x1^(-1/2)*x2^(11/2) + (-q^(5/2) - 3*q^(3/2) - 8*q^(1/2) - 10*q^(-1/2) - 34*q^(-3/2) + 10*q^(-5/2) - 4*q^(-9/2))*x1^(-1/2)*x2^(13/2) + (-2*q^(9/2) - 2*q^(7/2) - 8*q^(5/2) - 12*q^(3/2) - 20*q^(1/2) - 18*q^(-1/2) - 52*q^(-3/2) + 20*q^(-5/2) - 2*q^(-7/2) - 16*q^(-9/2) - 8*q^(-11/2))*x1^(-1/2)*x2^(15/2) + (-q^(15/2) - 3*q^(13/2) - 4*q^(11/2) - 11*q^(9/2) - 13*q^(7/2) - 26*q^(5/2) - 29*q^(3/2) - 37*q^(1/2) - 27*q^(-1/2) - 74*q^(-3/2) + 31*q^(-5/2) - 12*q^(-7/2) - 46*q^(-9/2) - 32*q^(-11/2) - 12*q^(-13/2) + 4*q^(-15/2))*x1^(-1/2)*x2^(17/2) + (-2*q^(21/2) - 2*q^(19/2) - 6*q^(17/2) - 10*q^(15/2) - 18*q^(13/2) - 20*q^(11/2) - 38*q^(9/2) - 38*q^(7/2) - 58*q^(5/2) - 52*q^(3/2) - 58*q^(1/2) - 38*q^(-1/2) - 108*q^(-3/2) + 32*q^(-5/2) - 48*q^(-7/2) - 112*q^(-9/2) - 90*q^(-11/2) - 46*q^(-13/2) + 8*q^(-17/2))*x1^(-1/2)*x2^(19/2)

(-1/2, 5/2)

x1^(1/2)x2^(-5/2)

q^(-17/2)

(8*q^(53/2) + 6*q^(51/2) + 10*q^(49/2) + 12*q^(47/2) + 16*q^(45/2) + 16*q^(43/2) + 18*q^(41/2) + 12*q^(39/2) + 12*q^(37/2) + 8*q^(35/2) + 6*q^(33/2) + 2*q^(31/2) + 2*q^(29/2))*x1^(15/2)*x2^(-19/2) + (-7*q^(39/2) - 5*q^(37/2) - 8*q^(35/2) - 9*q^(33/2) - 11*q^(31/2) - 9*q^(29/2) - 7*q^(27/2) - 4*q^(25/2) - 3*q^(23/2) - q^(21/2))*x1^(13/2)*x2^(-17/2) + (-2*q^(51/2) - 4*q^(49/2) - 8*q^(47/2) - 14*q^(45/2) - 24*q^(43/2) - 38*q^(41/2) - 74*q^(39/2) - 72*q^(37/2) - 86*q^(35/2) - 86*q^(33/2) - 84*q^(31/2) - 62*q^(29/2) - 44*q^(27/2) - 24*q^(25/2) - 14*q^(23/2) - 4*q^(21/2))*x1^(13/2)*x2^(-19/2) + (6*q^(27/2) + 4*q^(25/2) + 6*q^(23/2) + 6*q^(21/2) + 6*q^(19/2) + 2*q^(17/2) + 2*q^(15/2))*x1^(11/2)*x2^(-15/2) + (2*q^(37/2) + 4*q^(35/2) + 8*q^(33/2) + 14*q^(31/2) + 24*q^(29/2) + 50*q^(27/2) + 44*q^(25/2) + 48*q^(23/2) + 42*q^(21/2) + 32*q^(19/2) + 12*q^(17/2) + 8*q^(15/2))*x1^(11/2)*x2^(-17/2) + (2*q^(47/2) + 2*q^(45/2) + 6*q^(43/2) + 8*q^(41/2) + 16*q^(39/2) + 32*q^(37/2) + 58*q^(35/2) + 86*q^(33/2) + 130*q^(31/2) + 176*q^(29/2) + 238*q^(27/2) + 204*q^(25/2) + 194*q^(23/2) + 146*q^(21/2) + 94*q^(19/2) + 32*q^(17/2) + 18*q^(15/2) - 2*q^(13/2))*x1^(11/2)*x2^(-19/2) + (-5*q^(17/2) - 3*q^(15/2) - 4*q^(13/2) - 3*q^(11/2) - q^(9/2))*x1^(9/2)*x2^(-13/2) + (-2*q^(25/2) - 4*q^(23/2) - 8*q^(21/2) - 14*q^(19/2) - 34*q^(17/2) - 24*q^(15/2) - 24*q^(13/2) - 14*q^(11/2) - 4*q^(9/2))*x1^(9/2)*x2^(-15/2) + (-2*q^(33/2) - 2*q^(31/2) - 6*q^(29/2) - 8*q^(27/2) - 25*q^(25/2) - 39*q^(23/2) - 65*q^(21/2) - 91*q^(19/2) - 132*q^(17/2) - 90*q^(15/2) - 75*q^(13/2) - 35*q^(11/2) - 7*q^(9/2) + q^(7/2))*x1^(9/2)*x2^(-17/2) + (-2*q^(41/2) - 2*q^(39/2) - 4*q^(37/2) - 8*q^(35/2) - 18*q^(33/2) - 24*q^(31/2) - 50*q^(29/2) - 72*q^(27/2) - 142*q^(25/2) - 196*q^(23/2) - 282*q^(21/2) - 326*q^(19/2) - 368*q^(17/2) - 232*q^(15/2) - 164*q^(13/2) - 68*q^(11/2) - 18*q^(9/2) - 12*q^(7/2) - 16*q^(5/2) - 8*q^(3/2) - 4*q^(1/2))*x1^(9/2)*x2^(-19/2) + (4*q^(9/2) + 2*q^(7/2) + 2*q^(5/2))*x1^(7/2)*x2^(-11/2) + (2*q^(15/2) + 4*q^(13/2) + 8*q^(11/2) + 22*q^(9/2) + 12*q^(7/2) + 8*q^(5/2))*x1^(7/2)*x2^(-13/2) + (2*q^(21/2) + 2*q^(19/2) + 6*q^(17/2) + 16*q^(15/2) + 30*q^(13/2) + 46*q^(11/2) + 72*q^(9/2) + 34*q^(7/2) + 18*q^(5/2) - 2*q^(3/2))*x1^(7/2)*x2^(-15/2) + (2*q^(27/2) + 2*q^(25/2) + 4*q^(23/2) + 14*q^(21/2) + 18*q^(19/2) + 40*q^(17/2) + 76*q^(15/2) + 124*q^(13/2) + 150*q^(11/2) + 172*q^(9/2) + 66*q^(7/2) + 28*q^(5/2) - 2*q^(3/2) + 8*q^(1/2) + 8*q^(-1/2) + 2*q^(-3/2))*x1^(7/2)*x2^(-17/2) + (2*q^(33/2) + 2*q^(31/2) + 4*q^(29/2) + 12*q^(27/2) + 16*q^(25/2) + 28*q^(23/2) + 62*q^(21/2) + 88*q^(19/2) + 168*q^(17/2) + 272*q^(15/2) + 364*q^(13/2) + 362*q^(11/2) + 330*q^(9/2) + 110*q^(7/2) + 63*q^(5/2) + 52*q^(3/2) + 82*q^(1/2) + 69*q^(-1/2) + 32*q^(-3/2) + 6*q^(-5/2))*x1^(7/2)*x2^(-19/2) + (-3*q^(3/2) - q^(1/2))*x1^(5/2)*x2^(-9/2) + (-2*q^(7/2) - 4*q^(5/2) - 14*q^(3/2) - 4*q^(1/2))*x1^(5/2)*x2^(-11/2) + (-2*q^(11/2) - 2*q^(9/2) - 13*q^(7/2) - 22*q^(5/2) - 39*q^(3/2) - 7*q^(1/2) + q^(-1/2))*x1^(5/2)*x2^(-13/2) + (-2*q^(15/2) - 2*q^(13/2) - 10*q^(11/2) - 16*q^(9/2) - 54*q^(7/2) - 66*q^(5/2) - 80*q^(3/2) - 6*q^(1/2) + 4*q^(-1/2) - 4*q^(-3/2) - 4*q^(-5/2))*x1^(5/2)*x2^(-15/2) + (-2*q^(19/2) - 2*q^(17/2) - 10*q^(15/2) - 12*q^(13/2) - 44*q^(11/2) - 78*q^(9/2) - 154*q^(7/2) - 143*q^(5/2) - 133*q^(3/2) - 4*q^(-1/2) - 38*q^(-3/2) - 32*q^(-5/2) - 12*q^(-7/2))*x1^(5/2)*x2^(-17/2) + (-2*q^(23/2) - 2*q^(21/2) - 10*q^(19/2) - 12*q^(17/2) - 44*q^(15/2) - 66*q^(13/2) - 172*q^(11/2) - 242*q^(9/2) - 334*q^(7/2) - 250*q^(5/2) - 200*q^(3/2) - 22*q^(1/2) - 94*q^(-1/2) - 186*q^(-3/2) - 160*q^(-5/2) - 76*q^(-7/2) - 16*q^(-9/2) + 4*q^(-11/2))*x1^(5/2)*x2^(-19/2) + (2*q^(-1/2))*x1^(3/2)*x2^(-7/2) + (2*q^(1/2) + 8*q^(-1/2))*x1^(3/2)*x2^(-9/2) + (2*q^(3/2) + 10*q^(1/2) + 20*q^(-1/2) - 2*q^(-3/2))*x1^(3/2)*x2^(-11/2) + (2*q^(5/2) + 14*q^(3/2) + 28*q^(1/2) + 38*q^(-1/2) - 8*q^(-3/2) + 2*q^(-7/2))*x1^(3/2)*x2^(-13/2) + (4*q^(7/2) + 20*q^(5/2) + 44*q^(3/2) + 58*q^(1/2) + 60*q^(-1/2) - 20*q^(-3/2) + 5*q^(-5/2) + 16*q^(-7/2) + 6*q^(-9/2))*x1^(3/2)*x2^(-15/2) + (4*q^(11/2) + 8*q^(9/2) + 36*q^(7/2) + 68*q^(5/2) + 98*q^(3/2) + 96*q^(1/2) + 84*q^(-1/2) - 32*q^(-3/2) + 34*q^(-5/2) + 68*q^(-7/2) + 40*q^(-9/2) + 10*q^(-11/2) - 2*q^(-13/2))*x1^(3/2)*x2^(-17/2) + (2*q^(17/2) + 6*q^(15/2) + 12*q^(13/2) + 30*q^(11/2) + 62*q^(9/2) + 120*q^(7/2) + 156*q^(5/2) + 170*q^(3/2) + 139*q^(1/2) + 122*q^(-1/2) - 10*q^(-3/2) + 142*q^(-5/2) + 218*q^(-7/2) + 152*q^(-9/2) + 59*q^(-11/2) - 2*q^(-13/2) - 6*q^(-15/2))*x1^(3/2)*x2^(-19/2) + (-q^(-3/2))*x1^(1/2)*x2^(-5/2) + (-4*q^(-3/2))*x1^(1/2)*x2^(-7/2) + (-q^(-1/2) - 10*q^(-3/2) + q^(-5/2))*x1^(1/2)*x2^(-9/2) + (-2*q^(1/2) - 4*q^(-1/2) - 20*q^(-3/2) + 4*q^(-5/2))*x1^(1/2)*x2^(-11/2) + (-q^(5/2) - 3*q^(3/2) - 8*q^(1/2) - 10*q^(-1/2) - 34*q^(-3/2) + 10*q^(-5/2) - 4*q^(-9/2))*x1^(1/2)*x2^(-13/2) + (-2*q^(9/2) - 2*q^(7/2) - 8*q^(5/2) - 12*q^(3/2) - 20*q^(1/2) - 18*q^(-1/2) - 52*q^(-3/2) + 20*q^(-5/2) - 2*q^(-7/2) - 16*q^(-9/2) - 8*q^(-11/2))*x1^(1/2)*x2^(-15/2) + (-q^(15/2) - 3*q^(13/2) - 4*q^(11/2) - 11*q^(9/2) - 13*q^(7/2) - 26*q^(5/2) - 29*q^(3/2) - 37*q^(1/2) - 27*q^(-1/2) - 74*q^(-3/2) + 31*q^(-5/2) - 12*q^(-7/2) - 46*q^(-9/2) - 32*q^(-11/2) - 12*q^(-13/2) + 4*q^(-15/2))*x1^(1/2)*x2^(-17/2) + (-2*q^(21/2) - 2*q^(19/2) - 6*q^(17/2) - 10*q^(15/2) - 18*q^(13/2) - 20*q^(11/2) - 38*q^(9/2) - 38*q^(7/2) - 58*q^(5/2) - 52*q^(3/2) - 58*q^(1/2) - 38*q^(-1/2) - 108*q^(-3/2) + 32*q^(-5/2) - 48*q^(-7/2) - 112*q^(-9/2) - 90*q^(-11/2) - 46*q^(-13/2) + 8*q^(-17/2))*x1^(1/2)*x2^(-19/2)

Braid

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

Multivariable Alexander polynomial

Δ_L
`2A1^(1/2)A2^(3/2) - 6A1^(1/2)A2^(1/2) + 6A1^(1/2)A2^(-1/2) - 4A1^(1/2)A2^(-3/2) + A1^(1/2)A2^(-5/2) + A1^(-1/2)A2^(5/2) - 4A1^(-1/2)A2^(3/2) + 6A1^(-1/2)A2^(1/2) - 6A1^(-1/2)A2^(-1/2) + 2A1^(-1/2)A2^(-3/2)`

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)`	no
`(1, -5)`	yes
`(1, 3)`	no
`(-1, 5)`	yes

HFL polytope

Poincaré polynomial
`2m^(-2)A1^(-1)A2^(-2) + m^(-2)A2^(-3) + 8m^(-1)A1^(-1)A2^(-1) + 7m^(-1)A2^(-2) + m^(-1)A1A2^(-3) + 12A1^(-1) + 18A2^(-1) + 5A1A2^(-2) + 10mA1^(-1)A2 + 24m + 10mA1A2^(-1) + 5m^2A1^(-1)A2^2 + 18m^2A2 + 12m^2A1 + m^3A1^(-1)A2^3 + 7m^3A2^2 + 8m^3A1A2 + m^4A2^3 + 2m^4A1A2^2`

Vertex	Maslov	Rank
`(-1, -2)`	-2	2
`(0, -3)`	-2	1
`(1, -3)`	-1	1
`(1, 2)`	4	2
`(0, 3)`	4	1
`(-1, 3)`	3	1

Record

FL/HFL Links

`orderOption(int)`	`315`
`namestring`	`L10a25{0}`
`statusstring`	`success`
`slugstring`	`L10a25_0_9bef87ee`
`result_filestring`	`details/L10a25_0_9bef87ee.json`
`complexity_scoreOption(int)`	`200`
`strandsOption(int)`	`null`
`crossingsOption(int)`	`10`
`component_countOption(int)`	`2`
`girthOption(int)`	`6`
`total_rankOption(int)`	`152`
`wall_secondsOption(float)`	`0.003595`
`backend_secondsOption(float)`	`0.0`
`errorstring`
`dimensionOption(int)`	`2`
`support_sizeOption(int)`	`19`
`vertex_countOption(int)`	`6`
`fibered_vertex_countOption(int)`	`2`
`polytope_statusstring`	`computed`
`alexander_support_sizeOption(int)`	`10`
`alexander_vertex_countOption(int)`	`4`
`alexander_relationstring`	`not_computed`
`fk_countint`	`1`
`detailsRowRef(FLHFLLinks)`	{ "dataset": "FLHFLLinks", "key": "L10a25_0_9bef87ee" }
`detail_assetstring`	`/api/v1/datasets/FLHFLLinks/assets/L10a25_0_9bef87ee`