11a
22
(K11a
22
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 10 3 6 11 5 8 9
Solving Sequence
3,6
7 4
8,11
9 1 2 10 5
c
6
c
3
c
7
c
8
c
11
c
2
c
10
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.20922 × 10
53
u
57
+ 5.38010 × 10
53
u
56
+ ··· + 1.93523 × 10
52
b − 1.93917 × 10
54
,
8.75242 × 10
53
u
57
+ 2.15695 × 10
54
u
56
+ ··· + 3.87047 × 10
52
a − 7.51888 × 10
54
, u
58
+ 2u
57
+ ··· − 20u + 4i
I
u
2
= h−u
2
+ b, −u
5
+ 2u
3
+ a − 2u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 66 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
=
h2.21×10
53
u
57
+5.38×10
53
u
56
+· · ·+1.94×10
52
b−1.94×10
54
, 8.75×10
53
u
57
+
2.16 × 10
54
u
56
+ · · · + 3.87 × 10
52
a − 7.52 × 10
54
, u
58
+ 2u
57
+ · · · − 20u + 4i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
4
=
u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
2
a
11
=
−22.6133u
57
− 55.7283u
56
+ ··· − 545.664u + 194.263
−11.4158u
57
− 27.8007u
56
+ ··· − 276.503u + 100.203
a
9
=
−5.51590u
57
− 13.4288u
56
+ ··· − 123.425u + 47.3451
23.7116u
57
+ 58.8709u
56
+ ··· + 589.977u − 207.708
a
1
=
−4.78464u
57
− 12.0436u
56
+ ··· − 122.072u + 39.9544
24.1900u
57
+ 59.1862u
56
+ ··· + 587.084u − 206.905
a
2
=
−10.8746u
57
− 27.0241u
56
+ ··· − 269.732u + 91.6352
19.4239u
57
+ 47.5510u
56
+ ··· + 471.075u − 166.426
a
10
=
−33.5809u
57
− 82.6520u
56
+ ··· − 817.229u + 291.314
−8.47974u
57
− 20.5966u
56
+ ··· − 205.705u + 74.9209
a
5
=
−28.9747u
57
− 71.2298u
56
+ ··· − 709.155u + 246.859
−17.5651u
57
− 43.1972u
56
+ ··· − 437.372u + 153.783
a
5
=
−28.9747u
57
− 71.2298u
56
+ ··· − 709.155u + 246.859
−17.5651u
57
− 43.1972u
56
+ ··· − 437.372u + 153.783
(ii) Obstruction class = −1
(iii) Cusp Shapes = 11.5795u
57
+ 27.4881u
56
+ ··· + 286.625u − 124.569
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
58
− 4u
57
+ ··· − 14u + 1
c
2
u
58
+ 32u
57
+ ··· + 94u + 1
c
3
, c
6
u
58
− 2u
57
+ ··· + 20u + 4
c
5
, c
9
u
58
+ 2u
57
+ ··· + 128u + 64
c
7
u
58
− 18u
57
+ ··· − 360u + 16
c
8
, c
10
, c
11
u
58
− 8u
57
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
58
− 32y
57
+ ··· − 94y + 1
c
2
y
58
− 8y
57
+ ··· − 7838y + 1
c
3
, c
6
y
58
− 18y
57
+ ··· − 360y + 16
c
5
, c
9
y
58
− 42y
57
+ ··· − 8192y + 4096
c
7
y
58
+ 42y
57
+ ··· − 33056y + 256
c
8
, c
10
, c
11
y
58
− 60y
57
+ ··· − 36y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.751278 + 0.687165I
a = 0.397223 + 0.633477I
b = 0.489389 + 0.795565I
−2.18920 + 0.10128I −7.14023 + 0.I
u = 0.751278 − 0.687165I
a = 0.397223 − 0.633477I
b = 0.489389 − 0.795565I
−2.18920 − 0.10128I −7.14023 + 0.I
u = −0.938205 + 0.408426I
a = 0.231074 + 0.260146I
b = −0.593325 + 0.623788I
1.56893 − 1.49125I 1.52605 + 1.85258I
u = −0.938205 − 0.408426I
a = 0.231074 − 0.260146I
b = −0.593325 − 0.623788I
1.56893 + 1.49125I 1.52605 − 1.85258I
u = 0.975459
a = −1.52269
b = −0.110488
−8.12166 −10.1040
u = −1.025320 + 0.037106I
a = −0.086100 + 0.547603I
b = −0.554847 − 0.036376I
2.76529 + 0.01343I − 61.057430 + 0.10I
u = −1.025320 − 0.037106I
a = −0.086100 − 0.547603I
b = −0.554847 + 0.036376I
2.76529 − 0.01343I − 61.057430 + 0.10I
u = 0.141484 + 1.046590I
a = 1.95002 − 0.42418I
b = 0.327448 − 0.475424I
−6.51259 − 2.28009I −10.96046 + 3.19134I
u = 0.141484 − 1.046590I
a = 1.95002 + 0.42418I
b = 0.327448 + 0.475424I
−6.51259 + 2.28009I −10.96046 − 3.19134I
u = −0.907614 + 0.233881I
a = 0.452411 + 0.038868I
b = 1.68026 − 1.11227I
−1.05945 − 3.12017I −5.50127 + 4.47326I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.907614 − 0.233881I
a = 0.452411 − 0.038868I
b = 1.68026 + 1.11227I
−1.05945 + 3.12017I −5.50127 − 4.47326I
u = −0.766366 + 0.768934I
a = 0.43828 + 2.14321I
b = −1.37901 + 2.34528I
−13.34930 − 0.72037I −12.98227 + 3.28415I
u = −0.766366 − 0.768934I
a = 0.43828 − 2.14321I
b = −1.37901 − 2.34528I
−13.34930 + 0.72037I −12.98227 − 3.28415I
u = 1.056160 + 0.263793I
a = −0.226907 − 0.684770I
b = −0.294684 − 0.046749I
2.08472 + 4.56768I 0. − 7.20311I
u = 1.056160 − 0.263793I
a = −0.226907 + 0.684770I
b = −0.294684 + 0.046749I
2.08472 − 4.56768I 0. + 7.20311I
u = −0.816044 + 0.752910I
a = −1.43375 − 0.08308I
b = −0.202312 − 0.820966I
−5.71379 − 1.22939I 0
u = −0.816044 − 0.752910I
a = −1.43375 + 0.08308I
b = −0.202312 + 0.820966I
−5.71379 + 1.22939I 0
u = 0.531681 + 0.702789I
a = 1.041460 − 0.332937I
b = 0.178506 − 0.656257I
−2.16889 − 1.07216I −4.64986 + 0.67610I
u = 0.531681 − 0.702789I
a = 1.041460 + 0.332937I
b = 0.178506 + 0.656257I
−2.16889 + 1.07216I −4.64986 − 0.67610I
u = −0.871904 + 0.708903I
a = −1.62017 − 1.84549I
b = 0.60927 − 2.97487I
−3.98695 − 2.71614I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.871904 − 0.708903I
a = −1.62017 + 1.84549I
b = 0.60927 + 2.97487I
−3.98695 + 2.71614I 0
u = 0.646879 + 0.932661I
a = 1.23701 − 2.00036I
b = −0.50044 − 2.21446I
−9.34785 − 3.11893I 0
u = 0.646879 − 0.932661I
a = 1.23701 + 2.00036I
b = −0.50044 + 2.21446I
−9.34785 + 3.11893I 0
u = 0.786683 + 0.828955I
a = −2.61581 + 2.03754I
b = −0.16255 + 3.14290I
−7.78075 − 1.40297I 0
u = 0.786683 − 0.828955I
a = −2.61581 − 2.03754I
b = −0.16255 − 3.14290I
−7.78075 + 1.40297I 0
u = −0.733599 + 0.883254I
a = 0.012106 − 0.387354I
b = 0.049160 − 0.756342I
−5.55187 + 4.00580I 0
u = −0.733599 − 0.883254I
a = 0.012106 + 0.387354I
b = 0.049160 + 0.756342I
−5.55187 − 4.00580I 0
u = 0.844172 + 0.085017I
a = 0.986920 + 0.702481I
b = 1.49717 − 0.05675I
−0.629418 + 0.623631I −5.36343 − 3.54196I
u = 0.844172 − 0.085017I
a = 0.986920 − 0.702481I
b = 1.49717 + 0.05675I
−0.629418 − 0.623631I −5.36343 + 3.54196I
u = 0.959680 + 0.687124I
a = −0.783612 + 0.016039I
b = 0.095816 + 0.597900I
−1.54879 + 5.22529I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.959680 − 0.687124I
a = −0.783612 − 0.016039I
b = 0.095816 − 0.597900I
−1.54879 − 5.22529I 0
u = −0.925912 + 0.732408I
a = 0.191499 − 1.003200I
b = 0.468873 − 1.260970I
−5.37580 − 4.41103I 0
u = −0.925912 − 0.732408I
a = 0.191499 + 1.003200I
b = 0.468873 + 1.260970I
−5.37580 + 4.41103I 0
u = 1.032960 + 0.608744I
a = 0.192674 − 0.762403I
b = −0.660062 − 1.066530I
−0.69171 + 6.13139I 0
u = 1.032960 − 0.608744I
a = 0.192674 + 0.762403I
b = −0.660062 + 1.066530I
−0.69171 − 6.13139I 0
u = −0.970390 + 0.723923I
a = 1.94328 + 0.72453I
b = 0.47039 + 2.60152I
−12.71920 − 4.94560I 0
u = −0.970390 − 0.723923I
a = 1.94328 − 0.72453I
b = 0.47039 − 2.60152I
−12.71920 + 4.94560I 0
u = 0.971435 + 0.767699I
a = −1.37396 + 2.61714I
b = 0.85784 + 3.57871I
−7.20694 + 7.37757I 0
u = 0.971435 − 0.767699I
a = −1.37396 − 2.61714I
b = 0.85784 − 3.57871I
−7.20694 − 7.37757I 0
u = −0.749801 + 1.013650I
a = 1.42076 + 2.51991I
b = −0.31957 + 2.79288I
−12.3578 + 7.9362I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.749801 − 1.013650I
a = 1.42076 − 2.51991I
b = −0.31957 − 2.79288I
−12.3578 − 7.9362I 0
u = −1.260080 + 0.222648I
a = −1.043850 + 0.235063I
b = −1.069910 + 0.809848I
−1.33556 − 1.90763I 0
u = −1.260080 − 0.222648I
a = −1.043850 − 0.235063I
b = −1.069910 − 0.809848I
−1.33556 + 1.90763I 0
u = −1.021410 + 0.771092I
a = −0.608745 − 0.376035I
b = 0.332932 − 0.745316I
−4.65387 − 10.14070I 0
u = −1.021410 − 0.771092I
a = −0.608745 + 0.376035I
b = 0.332932 + 0.745316I
−4.65387 + 10.14070I 0
u = 0.117607 + 0.695097I
a = 0.967277 − 0.036072I
b = 0.433545 + 0.151204I
−1.14303 − 1.20148I −5.78859 + 5.55533I
u = 0.117607 − 0.695097I
a = 0.967277 + 0.036072I
b = 0.433545 − 0.151204I
−1.14303 + 1.20148I −5.78859 − 5.55533I
u = 1.249040 + 0.401910I
a = −0.605347 − 0.578787I
b = −0.98878 − 1.48797I
−2.57248 + 7.45358I 0
u = 1.249040 − 0.401910I
a = −0.605347 + 0.578787I
b = −0.98878 + 1.48797I
−2.57248 − 7.45358I 0
u = 1.073950 + 0.758891I
a = 1.50409 − 1.45263I
b = 0.04645 − 2.93251I
−8.03060 + 9.32855I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073950 − 0.758891I
a = 1.50409 + 1.45263I
b = 0.04645 + 2.93251I
−8.03060 − 9.32855I 0
u = −1.082250 + 0.829438I
a = 1.77158 + 1.93052I
b = 0.11809 + 3.30285I
−11.2723 − 14.6533I 0
u = −1.082250 − 0.829438I
a = 1.77158 − 1.93052I
b = 0.11809 − 3.30285I
−11.2723 + 14.6533I 0
u = −0.209439 + 0.468075I
a = −5.64495 + 2.38701I
b = −0.441139 − 0.581010I
−3.24157 + 0.49714I −10.0374 + 15.0443I
u = −0.209439 − 0.468075I
a = −5.64495 − 2.38701I
b = −0.441139 + 0.581010I
−3.24157 − 0.49714I −10.0374 − 15.0443I
u = 0.471619
a = 3.18461
b = −0.472950
−2.28699 3.94780
u = 0.459325
a = −0.198494
b = −2.04304
−10.2057 4.64730
u = 0.324240
a = 1.64764
b = 0.649452
−1.11333 −8.96690
10
II. I
u
2
= h−u
2
+ b, −u
5
+ 2u
3
+ a − 2u, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
4
=
u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
2
a
11
=
u
5
− 2u
3
+ 2u
u
2
a
9
=
u
5
− 2u
3
− u
2
+ 2u + 1
0
a
1
=
u
2
− 1
u
2
a
2
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
10
=
u
5
− 2u
3
− u
2
+ 2u + 1
0
a
5
=
1
0
a
5
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
5
− 5u
4
+ u
3
+ 7u
2
+ 4u − 12
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
2
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
c
3
, c
4
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
5
, c
9
u
6
c
7
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
8
(u − 1)
6
c
10
, c
11
(u + 1)
6
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
6
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
2
, c
7
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
5
, c
9
y
6
c
8
, c
10
, c
11
(y −1)
6
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = 0.686453 + 0.095369I
b = 0.917045 + 0.592379I
0.245672 + 0.924305I −3.44826 − 0.47256I
u = 1.002190 − 0.295542I
a = 0.686453 − 0.095369I
b = 0.917045 − 0.592379I
0.245672 − 0.924305I −3.44826 + 0.47256I
u = −0.428243 + 0.664531I
a = −1.91924 + 0.88792I
b = −0.258209 − 0.569162I
−3.53554 + 0.92430I −13.66012 − 2.42665I
u = −0.428243 − 0.664531I
a = −1.91924 − 0.88792I
b = −0.258209 + 0.569162I
−3.53554 − 0.92430I −13.66012 + 2.42665I
u = −1.073950 + 0.558752I
a = 0.232786 − 0.641391I
b = 0.84116 − 1.20014I
−1.64493 − 5.69302I −8.89162 + 3.92918I
u = −1.073950 − 0.558752I
a = 0.232786 + 0.641391I
b = 0.84116 + 1.20014I
−1.64493 + 5.69302I −8.89162 − 3.92918I
14
III. I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
(i) Arc colorings
a
3
=
v
0
a
6
=
1
0
a
7
=
1
0
a
4
=
v
0
a
8
=
1
0
a
11
=
0
−v − 2
a
9
=
1
v + 3
a
1
=
v + 2
v + 3
a
2
=
2v + 2
v + 3
a
10
=
−v − 2
−v − 2
a
5
=
−v − 2
−v − 3
a
5
=
−v − 2
−v − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −21
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
4
(u + 1)
2
c
3
, c
6
, c
7
u
2
c
5
, c
8
u
2
+ u − 1
c
9
, c
10
, c
11
u
2
− u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
, c
7
y
2
c
5
, c
8
, c
9
c
10
, c
11
y
2
− 3y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.381966
a = 0
b = −1.61803
−10.5276 −21.0000
v = −2.61803
a = 0
b = 0.618034
−2.63189 −21.0000
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
6
+ u
5
+ ··· + u + 1)(u
58
− 4u
57
+ ··· − 14u + 1)
c
2
(u + 1)
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
· (u
58
+ 32u
57
+ ··· + 94u + 1)
c
3
u
2
(u
6
− u
5
+ ··· − u + 1)(u
58
− 2u
57
+ ··· + 20u + 4)
c
4
((u + 1)
2
)(u
6
− u
5
+ ··· − u + 1)(u
58
− 4u
57
+ ··· − 14u + 1)
c
5
u
6
(u
2
+ u − 1)(u
58
+ 2u
57
+ ··· + 128u + 64)
c
6
u
2
(u
6
+ u
5
+ ··· + u + 1)(u
58
− 2u
57
+ ··· + 20u + 4)
c
7
u
2
(u
6
− 3u
5
+ ··· − u + 1)(u
58
− 18u
57
+ ··· − 360u + 16)
c
8
((u − 1)
6
)(u
2
+ u − 1)(u
58
− 8u
57
+ ··· − 4u + 1)
c
9
u
6
(u
2
− u − 1)(u
58
+ 2u
57
+ ··· + 128u + 64)
c
10
, c
11
((u + 1)
6
)(u
2
− u − 1)(u
58
− 8u
57
+ ··· − 4u + 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y − 1)
2
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
58
− 32y
57
+ ··· − 94y + 1)
c
2
((y − 1)
2
)(y
6
+ y
5
+ ··· + 3y + 1)(y
58
− 8y
57
+ ··· − 7838y + 1)
c
3
, c
6
y
2
(y
6
− 3y
5
+ ··· − y + 1)(y
58
− 18y
57
+ ··· − 360y + 16)
c
5
, c
9
y
6
(y
2
− 3y + 1)(y
58
− 42y
57
+ ··· − 8192y + 4096)
c
7
y
2
(y
6
+ y
5
+ ··· + 3y + 1)(y
58
+ 42y
57
+ ··· − 33056y + 256)
c
8
, c
10
, c
11
((y − 1)
6
)(y
2
− 3y + 1)(y
58
− 60y
57
+ ··· − 36y + 1)
20
