11a
29
(K11a
29
)
A knot diagram
1
Linearized knot diagam
5 1 10 2 9 3 11 4 6 8 7
Solving Sequence
1,5
2
3,9
6 7 10 4 8 11
c
1
c
2
c
5
c
6
c
9
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.99106 × 10
56
u
60
− 5.54013 × 10
56
u
59
+ ··· + 3.76009 × 10
57
b − 3.71146 × 10
57
,
− 3.10364 × 10
57
u
60
+ 5.28988 × 10
57
u
59
+ ··· + 1.12803 × 10
58
a − 3.91838 × 10
58
, u
61
− 3u
60
+ ··· − 5u + 9i
I
u
2
= h3b + 2u − 2, a + 1, u
2
+ u + 1i
I
u
3
= h3b − 2u − 1, a + u, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 65 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h4.99×10
56
u
60
−5.54×10
56
u
59
+· · ·+3.76×10
57
b−3.71×10
57
, −3.10×
10
57
u
60
+5.29×10
57
u
59
+· · ·+1.13×10
58
a−3.92×10
58
, u
61
−3u
60
+· · ·−5u+9i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
9
=
0.275139u
60
− 0.468950u
59
+ ··· + 4.47285u + 3.47366
−0.132738u
60
+ 0.147340u
59
+ ··· − 4.15830u + 0.987068
a
6
=
1.11106u
60
− 2.61700u
59
+ ··· + 5.79571u − 5.77693
−0.595122u
60
+ 2.16473u
59
+ ··· + 2.14031u + 12.7347
a
7
=
0.302897u
60
− 0.758393u
59
+ ··· + 2.22294u − 1.51536
−0.161015u
60
+ 0.635343u
59
+ ··· + 2.73852u + 5.59822
a
10
=
0.327154u
60
− 0.474281u
59
+ ··· + 10.9343u + 2.92153
−0.507182u
60
+ 1.24714u
59
+ ··· − 4.55730u + 2.94439
a
4
=
−u
u
3
+ u
a
8
=
0.849189u
60
− 1.82096u
59
+ ··· + 7.07757u + 2.72833
−0.575418u
60
+ 1.58164u
59
+ ··· − 3.44728u + 5.06368
a
11
=
−0.289728u
60
+ 0.616900u
59
+ ··· + 6.66475u + 2.26231
0.0110587u
60
− 0.250053u
59
+ ··· − 0.805308u − 1.89157
a
11
=
−0.289728u
60
+ 0.616900u
59
+ ··· + 6.66475u + 2.26231
0.0110587u
60
− 0.250053u
59
+ ··· − 0.805308u − 1.89157
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.51281u
60
− 3.43786u
59
+ ··· + 30.9340u − 2.78257
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
61
+ 3u
60
+ ··· − 5u − 9
c
2
u
61
+ 21u
60
+ ··· − 1505u − 81
c
3
u
61
− 3u
60
+ ··· − 1872u + 432
c
5
, c
9
u
61
− 3u
60
+ ··· + 3u − 1
c
6
9(9u
61
− 30u
60
+ ··· + 293350u − 68375)
c
7
, c
10
, c
11
u
61
− 3u
60
+ ··· + 3u − 1
c
8
9(9u
61
+ 57u
60
+ ··· − 10059u − 2801)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
61
+ 21y
60
+ ··· − 1505y −81
c
2
y
61
+ 41y
60
+ ··· + 37363y −6561
c
3
y
61
− 25y
60
+ ··· + 1897344y −186624
c
5
, c
9
y
61
− 39y
60
+ ··· − 13y −1
c
6
81(81y
61
+ 3546y
60
+ ··· − 9.00135 × 10
10
y −4.67514 × 10
9
)
c
7
, c
10
, c
11
y
61
+ 61y
60
+ ··· − 13y −1
c
8
81(81y
61
− 2259y
60
+ ··· + 1.36190 × 10
8
y −7845601)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.627295 + 0.781178I
a = 0.779915 + 0.938460I
b = −0.133545 − 0.868985I
0.680796 − 0.488788I 8.37952 + 2.33314I
u = 0.627295 − 0.781178I
a = 0.779915 − 0.938460I
b = −0.133545 + 0.868985I
0.680796 + 0.488788I 8.37952 − 2.33314I
u = −0.909616 + 0.468593I
a = −1.059460 − 0.502224I
b = 1.43290 − 0.75784I
4.73566 − 1.67644I 12.36420 + 3.79278I
u = −0.909616 − 0.468593I
a = −1.059460 + 0.502224I
b = 1.43290 + 0.75784I
4.73566 + 1.67644I 12.36420 − 3.79278I
u = 0.823832 + 0.641756I
a = −0.493457 − 0.867597I
b = 0.171205 + 0.613586I
8.40390 − 4.08328I 6.32782 + 2.17005I
u = 0.823832 − 0.641756I
a = −0.493457 + 0.867597I
b = 0.171205 − 0.613586I
8.40390 + 4.08328I 6.32782 − 2.17005I
u = 0.084826 + 0.951096I
a = 0.768701 − 0.355562I
b = −0.926574 − 0.590119I
−3.04092 − 0.55487I −5.63926 + 1.54785I
u = 0.084826 − 0.951096I
a = 0.768701 + 0.355562I
b = −0.926574 + 0.590119I
−3.04092 + 0.55487I −5.63926 − 1.54785I
u = 0.745313 + 0.734834I
a = −0.69455 + 1.28009I
b = 1.59810 + 0.54771I
5.33189 − 0.62357I 6.90078 + 0.I
u = 0.745313 − 0.734834I
a = −0.69455 − 1.28009I
b = 1.59810 − 0.54771I
5.33189 + 0.62357I 6.90078 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.592571 + 0.868966I
a = 0.643580 + 0.821069I
b = −3.23298 + 1.50658I
2.11702 − 2.33942I −10.06681 − 7.06956I
u = −0.592571 − 0.868966I
a = 0.643580 − 0.821069I
b = −3.23298 − 1.50658I
2.11702 + 2.33942I −10.06681 + 7.06956I
u = 0.869096 + 0.612382I
a = 0.840207 − 1.089160I
b = −1.66751 − 0.62148I
5.98865 − 5.78069I 6.25624 + 4.52312I
u = 0.869096 − 0.612382I
a = 0.840207 + 1.089160I
b = −1.66751 + 0.62148I
5.98865 + 5.78069I 6.25624 − 4.52312I
u = −0.510457 + 0.948104I
a = 0.221723 − 0.095163I
b = −0.197711 − 0.400616I
−0.17638 − 2.59422I 0
u = −0.510457 − 0.948104I
a = 0.221723 + 0.095163I
b = −0.197711 + 0.400616I
−0.17638 + 2.59422I 0
u = 0.642563 + 0.936820I
a = −0.882906 − 0.630814I
b = 0.433541 + 0.916219I
0.17275 + 5.47510I 0
u = 0.642563 − 0.936820I
a = −0.882906 + 0.630814I
b = 0.433541 − 0.916219I
0.17275 − 5.47510I 0
u = 0.318467 + 0.797607I
a = −1.256550 + 0.401471I
b = 1.24853 + 0.72368I
−0.53178 + 3.55128I −1.97116 + 0.53822I
u = 0.318467 − 0.797607I
a = −1.256550 − 0.401471I
b = 1.24853 − 0.72368I
−0.53178 − 3.55128I −1.97116 − 0.53822I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.541792 + 0.666328I
a = −0.443464 − 0.720747I
b = −1.80634 + 0.47653I
6.77383 − 1.39600I 1.94563 + 3.09396I
u = −0.541792 − 0.666328I
a = −0.443464 + 0.720747I
b = −1.80634 − 0.47653I
6.77383 + 1.39600I 1.94563 − 3.09396I
u = −0.105247 + 1.136650I
a = −0.528868 + 0.217428I
b = 0.733637 + 0.607458I
1.89473 − 3.39241I 0
u = −0.105247 − 1.136650I
a = −0.528868 − 0.217428I
b = 0.733637 − 0.607458I
1.89473 + 3.39241I 0
u = −0.430215 + 0.742658I
a = 0.120777 + 0.430167I
b = 0.656197 − 0.151023I
0.53014 − 1.40693I 5.62347 + 5.20497I
u = −0.430215 − 0.742658I
a = 0.120777 − 0.430167I
b = 0.656197 + 0.151023I
0.53014 + 1.40693I 5.62347 − 5.20497I
u = 0.769003 + 0.845851I
a = 1.196660 − 0.497619I
b = −2.31477 − 0.56610I
11.92950 + 1.96301I 0
u = 0.769003 − 0.845851I
a = 1.196660 + 0.497619I
b = −2.31477 + 0.56610I
11.92950 − 1.96301I 0
u = −0.035967 + 0.854814I
a = 0.563353 + 0.959661I
b = −0.057385 − 0.568156I
0.13425 − 1.52358I 1.52672 + 2.12846I
u = −0.035967 − 0.854814I
a = 0.563353 − 0.959661I
b = −0.057385 + 0.568156I
0.13425 + 1.52358I 1.52672 − 2.12846I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.757313 + 0.895285I
a = 0.456980 − 1.227760I
b = −1.41876 − 0.53071I
11.77860 + 3.79247I 0
u = 0.757313 − 0.895285I
a = 0.456980 + 1.227760I
b = −1.41876 + 0.53071I
11.77860 − 3.79247I 0
u = 1.008640 + 0.609371I
a = −0.801725 + 0.933371I
b = 1.70920 + 0.69780I
13.1909 − 9.2873I 0
u = 1.008640 − 0.609371I
a = −0.801725 − 0.933371I
b = 1.70920 − 0.69780I
13.1909 + 9.2873I 0
u = 0.699249 + 0.967906I
a = −1.098020 + 0.664109I
b = 2.41658 + 0.73364I
4.62247 + 6.13062I 0
u = 0.699249 − 0.967906I
a = −1.098020 − 0.664109I
b = 2.41658 − 0.73364I
4.62247 − 6.13062I 0
u = −0.312667 + 0.736573I
a = −0.52054 − 1.36729I
b = −0.76632 − 2.47025I
6.16730 − 1.44795I 6.66665 + 4.19132I
u = −0.312667 − 0.736573I
a = −0.52054 + 1.36729I
b = −0.76632 + 2.47025I
6.16730 + 1.44795I 6.66665 − 4.19132I
u = −0.141017 + 1.196910I
a = −0.409903 − 0.838432I
b = 0.617600 + 0.023876I
−1.00556 − 4.64477I 0
u = −0.141017 − 1.196910I
a = −0.409903 + 0.838432I
b = 0.617600 − 0.023876I
−1.00556 + 4.64477I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.657124 + 1.017530I
a = −0.322773 + 0.051413I
b = 0.113526 + 0.695926I
5.54533 − 3.61915I 0
u = −0.657124 − 1.017530I
a = −0.322773 − 0.051413I
b = 0.113526 − 0.695926I
5.54533 + 3.61915I 0
u = 0.711728 + 1.036980I
a = 0.745027 + 0.504667I
b = −0.521745 − 0.778989I
7.21133 + 9.84159I 0
u = 0.711728 − 1.036980I
a = 0.745027 − 0.504667I
b = −0.521745 + 0.778989I
7.21133 − 9.84159I 0
u = −0.602854 + 0.415244I
a = −0.754289 − 0.133208I
b = −0.631853 + 0.712874I
6.86257 − 1.40524I 4.78353 + 3.77219I
u = −0.602854 − 0.415244I
a = −0.754289 + 0.133208I
b = −0.631853 − 0.712874I
6.86257 + 1.40524I 4.78353 − 3.77219I
u = 0.717435 + 1.062890I
a = 0.966509 − 0.663460I
b = −2.53101 − 0.75950I
4.62032 + 11.67140I 0
u = 0.717435 − 1.062890I
a = 0.966509 + 0.663460I
b = −2.53101 + 0.75950I
4.62032 − 11.67140I 0
u = −0.736476 + 1.080940I
a = −0.590572 − 0.661323I
b = 2.05889 − 0.64346I
2.98645 − 4.33485I 0
u = −0.736476 − 1.080940I
a = −0.590572 + 0.661323I
b = 2.05889 + 0.64346I
2.98645 + 4.33485I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.762794 + 1.122440I
a = −0.897935 + 0.616455I
b = 2.61369 + 0.74270I
11.5735 + 15.7181I 0
u = 0.762794 − 1.122440I
a = −0.897935 − 0.616455I
b = 2.61369 − 0.74270I
11.5735 − 15.7181I 0
u = −1.265180 + 0.491129I
a = 0.862536 + 0.296472I
b = −1.81507 + 0.52494I
11.53690 − 2.05353I 0
u = −1.265180 − 0.491129I
a = 0.862536 − 0.296472I
b = −1.81507 − 0.52494I
11.53690 + 2.05353I 0
u = −0.23194 + 1.39578I
a = 0.368146 + 0.755457I
b = −0.844858 + 0.405684I
4.72211 − 7.08106I 0
u = −0.23194 − 1.39578I
a = 0.368146 − 0.755457I
b = −0.844858 − 0.405684I
4.72211 + 7.08106I 0
u = −0.91950 + 1.21328I
a = 0.561522 + 0.564425I
b = −1.88530 + 0.80608I
9.38339 − 5.57107I 0
u = −0.91950 − 1.21328I
a = 0.561522 − 0.564425I
b = −1.88530 − 0.80608I
9.38339 + 5.57107I 0
u = −0.408049
a = 2.87652
b = −0.0942688
2.58372 0.156380
u = 0.159087 + 0.350060I
a = 0.83224 + 1.41611I
b = 0.161959 − 0.489660I
0.145306 − 1.198500I 1.41714 + 6.05642I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.159087 − 0.350060I
a = 0.83224 − 1.41611I
b = 0.161959 + 0.489660I
0.145306 + 1.198500I 1.41714 − 6.05642I
11
II. I
u
2
= h3b + 2u − 2, a + 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
9
=
−1
−
2
3
u +
2
3
a
6
=
u
−
1
3
u −
2
3
a
7
=
4
3
u −
1
3
−u − 1
a
10
=
−u − 2
−u + 1
a
4
=
−u
u + 1
a
8
=
2
3
u −
2
3
−u
a
11
=
−
1
3
u −
2
3
−u
a
11
=
−
1
3
u −
2
3
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u +
28
3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
10
, c
11
u
2
+ u + 1
c
3
u
2
c
4
, c
7
, c
9
u
2
− u + 1
c
6
, c
8
3(3u
2
+ 3u + 1)
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
y
2
c
6
, c
8
9(9y
2
− 3y + 1)
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.00000
b = 1.000000 − 0.577350I
− 4.05977I 5.33333 + 6.92820I
u = −0.500000 − 0.866025I
a = −1.00000
b = 1.000000 + 0.577350I
4.05977I 5.33333 − 6.92820I
15
III. I
u
3
= h3b − 2u − 1, a + u, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
9
=
−u
2
3
u +
1
3
a
6
=
1
4
3
u −
1
3
a
7
=
−
1
3
u +
1
3
u
a
10
=
−2u − 1
u + 2
a
4
=
−u
u + 1
a
8
=
−
5
3
u −
1
3
u + 1
a
11
=
−
2
3
u +
2
3
u + 1
a
11
=
−
2
3
u +
2
3
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
8
3
u +
5
3
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
10
, c
11
u
2
+ u + 1
c
3
u
2
c
4
, c
7
, c
9
u
2
− u + 1
c
6
3(3u
2
+ 1)
c
8
3(3u
2
− 3u + 1)
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
y
2
c
6
9(3y + 1)
2
c
8
9(9y
2
− 3y + 1)
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 − 0.866025I
b = 0.577350I
0 0.33333 + 2.30940I
u = −0.500000 − 0.866025I
a = 0.500000 + 0.866025I
b = − 0.577350I
0 0.33333 − 2.30940I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
61
+ 3u
60
+ ··· − 5u − 9)
c
2
((u
2
+ u + 1)
2
)(u
61
+ 21u
60
+ ··· − 1505u − 81)
c
3
u
4
(u
61
− 3u
60
+ ··· − 1872u + 432)
c
4
((u
2
− u + 1)
2
)(u
61
+ 3u
60
+ ··· − 5u − 9)
c
5
((u
2
+ u + 1)
2
)(u
61
− 3u
60
+ ··· + 3u − 1)
c
6
81(3u
2
+ 1)(3u
2
+ 3u + 1)(9u
61
− 30u
60
+ ··· + 293350u − 68375)
c
7
((u
2
− u + 1)
2
)(u
61
− 3u
60
+ ··· + 3u − 1)
c
8
81(3u
2
− 3u + 1)(3u
2
+ 3u + 1)(9u
61
+ 57u
60
+ ··· − 10059u − 2801)
c
9
((u
2
− u + 1)
2
)(u
61
− 3u
60
+ ··· + 3u − 1)
c
10
, c
11
((u
2
+ u + 1)
2
)(u
61
− 3u
60
+ ··· + 3u − 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
61
+ 21y
60
+ ··· − 1505y −81)
c
2
((y
2
+ y + 1)
2
)(y
61
+ 41y
60
+ ··· + 37363y −6561)
c
3
y
4
(y
61
− 25y
60
+ ··· + 1897344y −186624)
c
5
, c
9
((y
2
+ y + 1)
2
)(y
61
− 39y
60
+ ··· − 13y −1)
c
6
6561(3y + 1)
2
(9y
2
− 3y + 1)
· (81y
61
+ 3546y
60
+ ··· − 90013453750y −4675140625)
c
7
, c
10
, c
11
((y
2
+ y + 1)
2
)(y
61
+ 61y
60
+ ··· − 13y −1)
c
8
6561(9y
2
− 3y + 1)
2
· (81y
61
− 2259y
60
+ ··· + 136190379y −7845601)
21
