11a
152
(K11a
152
)
A knot diagram
1
Linearized knot diagam
6 1 11 10 2 9 5 3 7 4 8
Solving Sequence
5,10
4
8,11
1 3 2 7 9 6
c
4
c
10
c
11
c
3
c
2
c
7
c
9
c
6
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h3.06173 × 10
60
u
58
− 4.84579 × 10
60
u
57
+ ··· + 7.53869 × 10
60
b − 6.50731 × 10
60
,
3.66584 × 10
60
u
58
− 7.89631 × 10
60
u
57
+ ··· + 7.53869 × 10
60
a − 4.93339 × 10
60
, u
59
− 2u
58
+ ··· − 2u + 1i
I
u
2
= h3b − 2, 3a − 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 60 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
= h3.06 × 10
60
u
58
− 4.85 × 10
60
u
57
+ · · · + 7.54 × 10
60
b − 6.51 × 10
60
, 3.67 ×
10
60
u
58
−7.90×10
60
u
57
+· · ·+7.54×10
60
a−4.93×10
60
, u
59
−2u
58
+· · ·−2u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
8
=
−0.486270u
58
+ 1.04744u
57
+ ··· − 3.97604u + 0.654410
−0.406136u
58
+ 0.642788u
57
+ ··· + 0.0112412u + 0.863189
a
11
=
u
u
3
+ u
a
1
=
0.162396u
58
− 0.0414876u
57
+ ··· − 0.620453u + 0.289562
0.264365u
58
− 0.566519u
57
+ ··· − 0.385454u − 0.631376
a
3
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
−0.418108u
58
+ 0.310255u
57
+ ··· − 0.686190u + 0.663142
−0.104972u
58
+ 0.436443u
57
+ ··· − 0.736202u + 0.995922
a
7
=
−0.892406u
58
+ 1.69023u
57
+ ··· − 3.96480u + 1.51760
−0.406136u
58
+ 0.642788u
57
+ ··· + 0.0112412u + 0.863189
a
9
=
−0.855262u
58
+ 1.72021u
57
+ ··· − 3.82594u + 1.72628
−0.432378u
58
+ 0.672814u
57
+ ··· + 1.00305u + 0.933233
a
6
=
−0.0187345u
58
− 0.208269u
57
+ ··· − 0.169215u − 0.637633
−0.0593368u
58
+ 0.0928833u
57
+ ··· − 1.26241u − 0.102333
a
6
=
−0.0187345u
58
− 0.208269u
57
+ ··· − 0.169215u − 0.637633
−0.0593368u
58
+ 0.0928833u
57
+ ··· − 1.26241u − 0.102333
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.834501u
58
− 3.42749u
57
+ ··· − 17.5070u − 8.87218
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
59
− 2u
58
+ ··· + 2u − 1
c
2
u
59
+ 24u
58
+ ··· − 4u − 1
c
3
, c
4
, c
10
u
59
+ 2u
58
+ ··· − 2u − 1
c
6
, c
9
u
59
− 2u
58
+ ··· − 32u − 9
c
7
3(3u
59
+ 29u
58
+ ··· + 96336u − 7216)
c
8
3(3u
59
− 44u
58
+ ··· − 96u − 64)
c
11
u
59
− 5u
58
+ ··· + 108u − 18
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
59
+ 24y
58
+ ··· − 4y −1
c
2
y
59
+ 16y
58
+ ··· − 76y −1
c
3
, c
4
, c
10
y
59
+ 60y
58
+ ··· − 4y −1
c
6
, c
9
y
59
− 44y
58
+ ··· + 3472y −81
c
7
9(9y
59
− 787y
58
+ ··· + 4.57874 × 10
9
y −5.20707 × 10
7
)
c
8
9(9y
59
− 424y
58
+ ··· − 148480y −4096)
c
11
y
59
+ 9y
58
+ ··· − 6300y −324
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772835 + 0.630169I
a = 0.486457 + 0.408560I
b = −1.20441 + 0.80693I
−2.98475 + 11.82370I 0. − 9.15160I
u = 0.772835 − 0.630169I
a = 0.486457 − 0.408560I
b = −1.20441 − 0.80693I
−2.98475 − 11.82370I 0. + 9.15160I
u = 0.893809 + 0.462202I
a = −0.354680 + 0.593555I
b = −0.839382 − 0.317177I
−2.42227 − 6.38133I 0
u = 0.893809 − 0.462202I
a = −0.354680 − 0.593555I
b = −0.839382 + 0.317177I
−2.42227 + 6.38133I 0
u = −0.769320 + 0.665358I
a = −0.399111 + 0.329878I
b = 1.017530 + 0.758404I
−0.73398 − 6.05254I 0
u = −0.769320 − 0.665358I
a = −0.399111 − 0.329878I
b = 1.017530 − 0.758404I
−0.73398 + 6.05254I 0
u = 0.871014 + 0.643445I
a = 0.171049 + 0.483786I
b = −1.045410 + 0.327693I
−7.08101 + 2.98588I 0
u = 0.871014 − 0.643445I
a = 0.171049 − 0.483786I
b = −1.045410 − 0.327693I
−7.08101 − 2.98588I 0
u = −1.058830 + 0.406799I
a = 0.273276 + 0.303483I
b = 0.621331 − 0.083380I
0.196305 + 0.379080I 0
u = −1.058830 − 0.406799I
a = 0.273276 − 0.303483I
b = 0.621331 + 0.083380I
0.196305 − 0.379080I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.421425 + 0.652253I
a = −0.229200 − 0.191547I
b = 0.073389 + 0.936603I
1.67726 − 2.08783I 6.30981 + 5.41216I
u = −0.421425 − 0.652253I
a = −0.229200 + 0.191547I
b = 0.073389 − 0.936603I
1.67726 + 2.08783I 6.30981 − 5.41216I
u = 0.538558 + 0.434252I
a = −1.52889 − 0.28560I
b = 0.560561 − 0.856660I
1.09865 + 6.46666I 3.55713 − 8.78536I
u = 0.538558 − 0.434252I
a = −1.52889 + 0.28560I
b = 0.560561 + 0.856660I
1.09865 − 6.46666I 3.55713 + 8.78536I
u = −0.564831 + 0.382666I
a = 1.263980 − 0.143409I
b = −0.352394 − 0.726889I
2.45484 − 1.46486I 7.14865 + 3.00711I
u = −0.564831 − 0.382666I
a = 1.263980 + 0.143409I
b = −0.352394 + 0.726889I
2.45484 + 1.46486I 7.14865 − 3.00711I
u = 0.407938 + 0.495194I
a = 0.234399 − 0.376842I
b = 0.290086 + 1.044180I
0.82881 − 3.06030I 4.18689 + 0.59937I
u = 0.407938 − 0.495194I
a = 0.234399 + 0.376842I
b = 0.290086 − 1.044180I
0.82881 + 3.06030I 4.18689 − 0.59937I
u = −0.133674 + 1.400600I
a = 1.029390 − 0.297689I
b = −0.654687 + 0.290826I
−3.80970 − 2.30389I 0
u = −0.133674 − 1.400600I
a = 1.029390 + 0.297689I
b = −0.654687 − 0.290826I
−3.80970 + 2.30389I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.065188 + 1.410510I
a = −0.86471 − 1.34195I
b = 0.80222 + 1.22589I
−5.12435 − 1.84537I 0
u = 0.065188 − 1.410510I
a = −0.86471 + 1.34195I
b = 0.80222 − 1.22589I
−5.12435 + 1.84537I 0
u = −0.240543 + 0.535915I
a = 1.08834 − 2.33107I
b = −1.011390 + 0.003314I
−3.33182 − 4.55345I −4.30626 + 8.52736I
u = −0.240543 − 0.535915I
a = 1.08834 + 2.33107I
b = −1.011390 − 0.003314I
−3.33182 + 4.55345I −4.30626 − 8.52736I
u = 0.01950 + 1.43251I
a = −6.58810 + 3.57964I
b = 6.56362 − 4.27440I
−6.55441 + 2.12552I 0
u = 0.01950 − 1.43251I
a = −6.58810 − 3.57964I
b = 6.56362 + 4.27440I
−6.55441 − 2.12552I 0
u = −0.087504 + 0.546858I
a = 0.39073 − 2.81411I
b = −0.423741 + 0.227336I
−4.10264 + 1.33087I −6.62416 − 1.43922I
u = −0.087504 − 0.546858I
a = 0.39073 + 2.81411I
b = −0.423741 − 0.227336I
−4.10264 − 1.33087I −6.62416 + 1.43922I
u = −0.541912
a = 0.611273
b = −0.123892
0.892681 11.5980
u = 0.356131 + 0.401711I
a = −0.91403 − 1.19911I
b = 0.886772 − 0.315941I
−1.79094 + 1.03849I −2.00439 − 5.37844I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356131 − 0.401711I
a = −0.91403 + 1.19911I
b = 0.886772 + 0.315941I
−1.79094 − 1.03849I −2.00439 + 5.37844I
u = −0.15816 + 1.47252I
a = 1.59643 + 0.26788I
b = −0.817080 − 0.366010I
−3.60110 − 3.99693I 0
u = −0.15816 − 1.47252I
a = 1.59643 − 0.26788I
b = −0.817080 + 0.366010I
−3.60110 + 3.99693I 0
u = 0.10761 + 1.48343I
a = −1.90601 − 0.15341I
b = 1.253580 − 0.326367I
−7.99699 + 2.70852I 0
u = 0.10761 − 1.48343I
a = −1.90601 + 0.15341I
b = 1.253580 + 0.326367I
−7.99699 − 2.70852I 0
u = 0.04741 + 1.49720I
a = −1.53150 − 0.05275I
b = 1.18789 − 0.84677I
−8.07186 + 1.71448I 0
u = 0.04741 − 1.49720I
a = −1.53150 + 0.05275I
b = 1.18789 + 0.84677I
−8.07186 − 1.71448I 0
u = 0.15594 + 1.49285I
a = −1.83827 + 0.36366I
b = 0.915367 − 0.530137I
−5.23405 + 8.92854I 0
u = 0.15594 − 1.49285I
a = −1.83827 − 0.36366I
b = 0.915367 + 0.530137I
−5.23405 − 8.92854I 0
u = −0.05816 + 1.52227I
a = 1.62424 − 0.57913I
b = −1.082160 − 0.473836I
−10.18440 − 5.57197I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05816 − 1.52227I
a = 1.62424 + 0.57913I
b = −1.082160 + 0.473836I
−10.18440 + 5.57197I 0
u = −0.02356 + 1.52322I
a = 0.755412 − 0.573027I
b = −0.529705 − 0.615962I
−10.99430 + 0.93911I 0
u = −0.02356 − 1.52322I
a = 0.755412 + 0.573027I
b = −0.529705 + 0.615962I
−10.99430 − 0.93911I 0
u = 0.226157 + 0.399881I
a = −0.44978 − 1.85794I
b = 0.880240 − 0.289353I
−1.71907 + 0.84714I −1.58416 − 2.44825I
u = 0.226157 − 0.399881I
a = −0.44978 + 1.85794I
b = 0.880240 + 0.289353I
−1.71907 − 0.84714I −1.58416 + 2.44825I
u = 0.338130 + 0.233977I
a = 0.284402 − 0.906149I
b = 1.53304 + 0.15644I
−1.34852 + 1.21434I −0.61490 − 9.36280I
u = 0.338130 − 0.233977I
a = 0.284402 + 0.906149I
b = 1.53304 − 0.15644I
−1.34852 − 1.21434I −0.61490 + 9.36280I
u = 0.25843 + 1.57442I
a = 1.86661 − 0.09363I
b = −1.66038 + 1.05895I
−10.2296 + 15.6414I 0
u = 0.25843 − 1.57442I
a = 1.86661 + 0.09363I
b = −1.66038 − 1.05895I
−10.2296 − 15.6414I 0
u = −0.25542 + 1.58255I
a = −1.69347 − 0.15977I
b = 1.51201 + 1.06731I
−8.11873 − 9.85959I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.25542 − 1.58255I
a = −1.69347 + 0.15977I
b = 1.51201 − 1.06731I
−8.11873 + 9.85959I 0
u = 0.27503 + 1.58999I
a = 1.46114 + 0.16066I
b = −1.41360 + 0.76345I
−14.4364 + 7.1649I 0
u = 0.27503 − 1.58999I
a = 1.46114 − 0.16066I
b = −1.41360 − 0.76345I
−14.4364 − 7.1649I 0
u = −0.359471 + 0.100084I
a = −0.622900 − 0.492336I
b = −2.26496 + 0.09975I
−2.01075 + 2.52108I 10.02369 + 7.46616I
u = −0.359471 − 0.100084I
a = −0.622900 + 0.492336I
b = −2.26496 − 0.09975I
−2.01075 − 2.52108I 10.02369 − 7.46616I
u = 0.34658 + 1.62518I
a = 0.678378 + 0.241908I
b = −0.828238 + 0.485899I
−9.14972 − 1.51752I 0
u = 0.34658 − 1.62518I
a = 0.678378 − 0.241908I
b = −0.828238 − 0.485899I
−9.14972 + 1.51752I 0
u = −0.27841 + 1.64508I
a = −0.922544 − 0.098475I
b = 0.925175 + 0.826150I
−7.26563 − 4.89851I 0
u = −0.27841 − 1.64508I
a = −0.922544 + 0.098475I
b = 0.925175 − 0.826150I
−7.26563 + 4.89851I 0
10
II. I
u
2
= h3b − 2, 3a − 1, u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
1
a
4
=
1
1
a
8
=
0.333333
0.666667
a
11
=
1
2
a
1
=
1
2
a
3
=
2
3
a
2
=
1
1
a
7
=
1
0.666667
a
9
=
1
1.66667
a
6
=
0
−1
a
6
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7.11111
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
, c
10
u + 1
c
2
, c
3
, c
4
c
5
, c
6
u − 1
c
7
3(3u + 2)
c
8
3(3u + 1)
c
11
u
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
9
, c
10
y −1
c
7
9(9y −4)
c
8
9(9y −1)
c
11
y
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.333333
b = 0.666667
0 −7.11110
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
59
− 2u
58
+ ··· + 2u − 1)
c
2
(u − 1)(u
59
+ 24u
58
+ ··· − 4u − 1)
c
3
, c
4
(u − 1)(u
59
+ 2u
58
+ ··· − 2u − 1)
c
5
(u − 1)(u
59
− 2u
58
+ ··· + 2u − 1)
c
6
(u − 1)(u
59
− 2u
58
+ ··· − 32u − 9)
c
7
9(3u + 2)(3u
59
+ 29u
58
+ ··· + 96336u − 7216)
c
8
9(3u + 1)(3u
59
− 44u
58
+ ··· − 96u − 64)
c
9
(u + 1)(u
59
− 2u
58
+ ··· − 32u − 9)
c
10
(u + 1)(u
59
+ 2u
58
+ ··· − 2u − 1)
c
11
u(u
59
− 5u
58
+ ··· + 108u − 18)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)(y
59
+ 24y
58
+ ··· − 4y −1)
c
2
(y −1)(y
59
+ 16y
58
+ ··· − 76y −1)
c
3
, c
4
, c
10
(y −1)(y
59
+ 60y
58
+ ··· − 4y −1)
c
6
, c
9
(y −1)(y
59
− 44y
58
+ ··· + 3472y −81)
c
7
81(9y −4)(9y
59
− 787y
58
+ ··· + 4.57874 × 10
9
y −5.20707 × 10
7
)
c
8
81(9y −1)(9y
59
− 424y
58
+ ··· − 148480y −4096)
c
11
y(y
59
+ 9y
58
+ ··· − 6300y −324)
16
