11a
127
(K11a
127
)
A knot diagram
1
Linearized knot diagam
5 1 10 8 2 9 3 11 7 4 6
Solving Sequence
2,5
6 1
3,8
4 7 11 9 10
c
5
c
1
c
2
c
4
c
7
c
11
c
8
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.48129 × 10
37
u
70
− 2.24416 × 10
37
u
69
+ ··· + 2.11503 × 10
37
b + 2.31427 × 10
37
,
1.02558 × 10
37
u
70
+ 1.31834 × 10
37
u
69
+ ··· + 9.61375 × 10
36
a − 1.17173 × 10
37
, u
71
+ 2u
70
+ ··· − 2u − 1i
I
u
2
= hb, 3u
2
+ 5a − 7u + 6, u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 74 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
= h−1.48×10
37
u
70
−2.24×10
37
u
69
+· · ·+2.12×10
37
b+2.31×10
37
, 1.03×
10
37
u
70
+1.32×10
37
u
69
+· · ·+9.61×10
36
a−1.17×10
37
, u
71
+2u
70
+· · ·−2u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
8
=
−1.06678u
70
− 1.37130u
69
+ ··· + 3.23612u + 1.21881
0.700363u
70
+ 1.06106u
69
+ ··· − 0.692179u − 1.09420
a
4
=
−2.15925u
70
− 2.76790u
69
+ ··· + 1.95352u + 2.23161
−0.0889259u
70
− 0.0397494u
69
+ ··· + 0.558128u − 0.272953
a
7
=
−0.0510485u
70
− 0.373547u
69
+ ··· + 2.27625u + 0.706786
1.65193u
70
+ 2.44250u
69
+ ··· − 2.69769u − 2.53117
a
11
=
u
3
u
5
− u
3
+ u
a
9
=
−1.48850u
70
− 2.21759u
69
+ ··· + 3.68765u + 1.74401
0.992194u
70
+ 1.60425u
69
+ ··· − 2.38134u − 1.45862
a
10
=
2.15925u
70
+ 2.76790u
69
+ ··· − 1.95352u − 2.23161
1.20977u
70
+ 1.41960u
69
+ ··· − 0.383830u − 1.82356
a
10
=
2.15925u
70
+ 2.76790u
69
+ ··· − 1.95352u − 2.23161
1.20977u
70
+ 1.41960u
69
+ ··· − 0.383830u − 1.82356
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.637188u
70
+ 2.00147u
69
+ ··· + 4.31419u − 9.38239
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
71
+ 2u
70
+ ··· − 2u − 1
c
2
u
71
+ 36u
70
+ ··· + 4u + 1
c
3
, c
10
u
71
+ 2u
70
+ ··· − 4u − 1
c
4
u
71
− 3u
70
+ ··· + 660u + 200
c
6
, c
9
u
71
− 4u
70
+ ··· + 21u − 25
c
7
5(5u
71
− 39u
70
+ ··· + 379583u + 94103)
c
8
5(5u
71
− 6u
70
+ ··· + 231980u − 42881)
c
11
u
71
+ 6u
70
+ ··· − 6402u − 847
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
71
− 36y
70
+ ··· + 4y −1
c
2
y
71
+ 72y
69
+ ··· + 16y −1
c
3
, c
10
y
71
− 48y
70
+ ··· + 4y −1
c
4
y
71
+ 21y
70
+ ··· − 606000y −40000
c
6
, c
9
y
71
− 58y
70
+ ··· + 79841y −625
c
7
25(25y
71
+ 959y
70
+ ··· − 1.81656 × 10
11
y −8.85537 × 10
9
)
c
8
25(25y
71
− 936y
70
+ ··· + 3.67278 × 10
10
y −1.83878 × 10
9
)
c
11
y
71
+ 36y
70
+ ··· + 22222860y −717409
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.756248 + 0.731356I
a = −0.319350 − 0.556979I
b = −0.609727 + 0.867860I
−4.07719 − 3.90151I −5.00000 + 3.54699I
u = −0.756248 − 0.731356I
a = −0.319350 + 0.556979I
b = −0.609727 − 0.867860I
−4.07719 + 3.90151I −5.00000 − 3.54699I
u = −0.815711 + 0.480281I
a = 0.851857 + 0.985100I
b = 0.795395 − 0.523783I
−0.567421 − 0.429034I −3.85529 − 0.87645I
u = −0.815711 − 0.480281I
a = 0.851857 − 0.985100I
b = 0.795395 + 0.523783I
−0.567421 + 0.429034I −3.85529 + 0.87645I
u = −0.270630 + 0.894068I
a = −0.243231 + 0.020060I
b = −0.051628 − 0.966961I
−7.01345 + 0.86966I −12.36097 − 1.34990I
u = −0.270630 − 0.894068I
a = −0.243231 − 0.020060I
b = −0.051628 + 0.966961I
−7.01345 − 0.86966I −12.36097 + 1.34990I
u = 0.916597 + 0.577342I
a = 0.034897 − 0.799407I
b = 0.811438 + 0.019369I
1.66910 − 3.91281I 0
u = 0.916597 − 0.577342I
a = 0.034897 + 0.799407I
b = 0.811438 − 0.019369I
1.66910 + 3.91281I 0
u = −0.836576 + 0.691781I
a = −0.894496 + 0.459599I
b = 0.799336 + 0.956428I
−4.32946 + 9.25395I 0
u = −0.836576 − 0.691781I
a = −0.894496 − 0.459599I
b = 0.799336 − 0.956428I
−4.32946 − 9.25395I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.222287 + 0.874807I
a = −0.288795 + 0.326260I
b = 0.664290 + 0.919235I
−2.91874 + 5.72330I −6.82100 − 5.17076I
u = 0.222287 − 0.874807I
a = −0.288795 − 0.326260I
b = 0.664290 − 0.919235I
−2.91874 − 5.72330I −6.82100 + 5.17076I
u = −0.730824 + 0.527079I
a = 0.753832 − 0.354136I
b = −0.968868 − 0.896754I
−0.33023 + 4.59723I −4.06867 − 6.98717I
u = −0.730824 − 0.527079I
a = 0.753832 + 0.354136I
b = −0.968868 + 0.896754I
−0.33023 − 4.59723I −4.06867 + 6.98717I
u = 0.852440 + 0.278118I
a = −0.491553 + 0.803598I
b = 0.441660 + 1.237110I
−4.80199 − 3.21094I −12.45295 + 5.85076I
u = 0.852440 − 0.278118I
a = −0.491553 − 0.803598I
b = 0.441660 − 1.237110I
−4.80199 + 3.21094I −12.45295 − 5.85076I
u = −0.234589 + 0.853865I
a = −0.554053 − 0.463968I
b = 1.02317 − 1.27672I
−7.77113 − 11.46490I −8.41846 + 5.96289I
u = −0.234589 − 0.853865I
a = −0.554053 + 0.463968I
b = 1.02317 + 1.27672I
−7.77113 + 11.46490I −8.41846 − 5.96289I
u = 0.640616 + 0.584471I
a = 0.569021 + 0.397714I
b = −0.836952 + 0.262697I
2.46408 − 0.68931I 1.74747 + 0.77475I
u = 0.640616 − 0.584471I
a = 0.569021 − 0.397714I
b = −0.836952 − 0.262697I
2.46408 + 0.68931I 1.74747 − 0.77475I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.859660
a = −0.477948
b = 1.49255
−6.41668 −15.8580
u = −1.099450 + 0.364554I
a = 0.87164 − 1.32285I
b = 0.420596 − 0.906615I
−2.63013 + 1.09669I 0
u = −1.099450 − 0.364554I
a = 0.87164 + 1.32285I
b = 0.420596 + 0.906615I
−2.63013 − 1.09669I 0
u = 1.087730 + 0.413641I
a = −1.09893 + 2.35531I
b = 0.001207 + 0.597493I
−5.31037 − 3.59883I 0
u = 1.087730 − 0.413641I
a = −1.09893 − 2.35531I
b = 0.001207 − 0.597493I
−5.31037 + 3.59883I 0
u = 0.862289 + 0.799421I
a = −0.285568 − 0.061148I
b = 0.121059 − 0.469128I
1.15814 − 2.98237I 0
u = 0.862289 − 0.799421I
a = −0.285568 + 0.061148I
b = 0.121059 + 0.469128I
1.15814 + 2.98237I 0
u = 1.145320 + 0.357313I
a = 1.92585 + 1.99482I
b = 0.70820 + 1.75526I
−6.26433 + 2.00466I 0
u = 1.145320 − 0.357313I
a = 1.92585 − 1.99482I
b = 0.70820 − 1.75526I
−6.26433 − 2.00466I 0
u = 1.130980 + 0.431488I
a = 0.67778 + 1.92019I
b = −0.795242 + 0.439034I
−5.35777 − 2.76405I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.130980 − 0.431488I
a = 0.67778 − 1.92019I
b = −0.795242 − 0.439034I
−5.35777 + 2.76405I 0
u = −1.115380 + 0.489220I
a = −1.63469 + 1.22563I
b = 0.059678 + 0.565014I
−4.70142 + 3.83162I 0
u = −1.115380 − 0.489220I
a = −1.63469 − 1.22563I
b = 0.059678 − 0.565014I
−4.70142 − 3.83162I 0
u = −1.137430 + 0.466202I
a = −0.643935 + 0.898772I
b = −0.720960 + 0.704286I
−5.10323 + 5.09404I 0
u = −1.137430 − 0.466202I
a = −0.643935 − 0.898772I
b = −0.720960 − 0.704286I
−5.10323 − 5.09404I 0
u = −1.162180 + 0.422674I
a = −0.53999 − 3.04221I
b = −1.93986 − 1.22986I
−10.03050 + 1.73926I 0
u = −1.162180 − 0.422674I
a = −0.53999 + 3.04221I
b = −1.93986 + 1.22986I
−10.03050 − 1.73926I 0
u = 1.131850 + 0.517529I
a = −0.60956 − 1.99402I
b = 0.809979 − 0.884446I
−1.51520 − 6.56162I 0
u = 1.131850 − 0.517529I
a = −0.60956 + 1.99402I
b = 0.809979 + 0.884446I
−1.51520 + 6.56162I 0
u = −0.201597 + 0.723825I
a = 0.407018 + 0.472911I
b = −0.99003 + 1.51453I
−2.41749 − 5.42731I −7.02359 + 6.01187I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.201597 − 0.723825I
a = 0.407018 − 0.472911I
b = −0.99003 − 1.51453I
−2.41749 + 5.42731I −7.02359 − 6.01187I
u = 1.163000 + 0.468877I
a = −2.63024 − 0.30133I
b = −1.65868 − 1.64014I
−9.70369 − 6.52499I 0
u = 1.163000 − 0.468877I
a = −2.63024 + 0.30133I
b = −1.65868 + 1.64014I
−9.70369 + 6.52499I 0
u = −0.686936 + 0.290469I
a = 0.31194 − 1.46125I
b = 0.142451 − 0.714960I
−1.21269 + 1.32793I −6.02554 − 4.52788I
u = −0.686936 − 0.290469I
a = 0.31194 + 1.46125I
b = 0.142451 + 0.714960I
−1.21269 − 1.32793I −6.02554 + 4.52788I
u = −1.152790 + 0.514748I
a = −0.96659 + 2.88563I
b = 1.14061 + 1.68141I
−5.16670 + 10.10120I 0
u = −1.152790 − 0.514748I
a = −0.96659 − 2.88563I
b = 1.14061 − 1.68141I
−5.16670 − 10.10120I 0
u = −0.736745
a = 1.06563
b = 0.319467
−1.23735 −7.42040
u = 0.254623 + 0.682236I
a = 0.490596 − 0.464241I
b = −0.733828 − 0.705892I
1.01632 + 1.94893I −0.27362 − 2.41499I
u = 0.254623 − 0.682236I
a = 0.490596 + 0.464241I
b = −0.733828 + 0.705892I
1.01632 − 1.94893I −0.27362 + 2.41499I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.237750 + 0.293203I
a = −1.24533 − 1.57655I
b = −0.89711 − 1.37506I
−12.4694 + 7.7567I 0
u = 1.237750 − 0.293203I
a = −1.24533 + 1.57655I
b = −0.89711 + 1.37506I
−12.4694 − 7.7567I 0
u = 1.253530 + 0.263632I
a = 0.02040 − 1.47913I
b = 0.199889 − 1.201490I
−12.02620 − 4.54379I 0
u = 1.253530 − 0.263632I
a = 0.02040 + 1.47913I
b = 0.199889 + 1.201490I
−12.02620 + 4.54379I 0
u = −1.256850 + 0.294449I
a = −0.74295 + 1.21599I
b = −0.466074 + 1.044560I
−7.69010 − 1.87443I 0
u = −1.256850 − 0.294449I
a = −0.74295 − 1.21599I
b = −0.466074 − 1.044560I
−7.69010 + 1.87443I 0
u = 0.066183 + 0.695054I
a = −0.405710 − 0.249698I
b = 1.56121 − 1.32211I
−6.61162 + 2.20383I −12.68569 − 3.07320I
u = 0.066183 − 0.695054I
a = −0.405710 + 0.249698I
b = 1.56121 + 1.32211I
−6.61162 − 2.20383I −12.68569 + 3.07320I
u = −1.186700 + 0.559365I
a = 0.89022 − 2.40681I
b = −1.10234 − 1.33333I
−10.6184 + 16.6559I 0
u = −1.186700 − 0.559365I
a = 0.89022 + 2.40681I
b = −1.10234 + 1.33333I
−10.6184 − 16.6559I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.196320 + 0.559287I
a = 0.61509 + 1.75869I
b = −0.769209 + 1.018600I
−5.84600 − 10.96250I 0
u = 1.196320 − 0.559287I
a = 0.61509 − 1.75869I
b = −0.769209 − 1.018600I
−5.84600 + 10.96250I 0
u = −1.198020 + 0.580415I
a = 1.025910 − 0.879632I
b = −0.129045 − 1.023280I
−9.82778 + 4.53798I 0
u = −1.198020 − 0.580415I
a = 1.025910 + 0.879632I
b = −0.129045 + 1.023280I
−9.82778 − 4.53798I 0
u = 0.654099
a = −2.68619
b = 0.513194
−2.37176 2.33790
u = −0.198330 + 0.594187I
a = 1.51239 + 0.35999I
b = 0.082687 + 0.549338I
−2.17011 + 0.43018I −7.12298 + 0.05912I
u = −0.198330 − 0.594187I
a = 1.51239 − 0.35999I
b = 0.082687 − 0.549338I
−2.17011 − 0.43018I −7.12298 − 0.05912I
u = −0.083118 + 0.598548I
a = −0.90282 + 1.22203I
b = 0.575442 + 0.552054I
−2.24291 − 0.96732I −4.89699 − 0.16722I
u = −0.083118 − 0.598548I
a = −0.90282 − 1.22203I
b = 0.575442 − 0.552054I
−2.24291 + 0.96732I −4.89699 + 0.16722I
u = 0.432980 + 0.381803I
a = 6.48861 + 2.17280I
b = −0.351355 + 0.254773I
−3.41757 + 0.22703I 4.7786 + 20.3751I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.432980 − 0.381803I
a = 6.48861 − 2.17280I
b = −0.351355 − 0.254773I
−3.41757 − 0.22703I 4.7786 − 20.3751I
12
II. I
u
2
= hb, 3u
2
+ 5a − 7u + 6, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
1
=
u
u
a
3
=
−u
2
+ 1
−u
2
+ u + 1
a
8
=
−
3
5
u
2
+
7
5
u −
6
5
0
a
4
=
1
0
a
7
=
−
2
5
u
2
+
8
5
u −
4
5
2
5
u
2
+
2
5
u −
1
5
a
11
=
u
2
− 1
−u
2
a
9
=
−
2
5
u
2
+
8
5
u −
9
5
−
3
5
u
2
+
2
5
u −
1
5
a
10
=
−1
−u
2
a
10
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
277
25
u
2
+
293
25
u −
119
25
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
, c
3
u
3
+ u
2
+ 2u + 1
c
4
u
3
c
5
u
3
− u
2
+ 1
c
6
(u − 1)
3
c
7
5(5u
3
− 4u
2
+ u − 1)
c
8
5(5u
3
− 11u
2
+ 6u − 1)
c
9
(u + 1)
3
c
10
u
3
− u
2
+ 2u − 1
c
11
u
3
+ 3u
2
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
3
− y
2
+ 2y −1
c
2
, c
3
, c
10
y
3
+ 3y
2
+ 2y −1
c
4
y
3
c
6
, c
9
(y −1)
3
c
7
25(25y
3
− 6y
2
− 7y −1)
c
8
25(25y
3
− 61y
2
+ 14y −1)
c
11
y
3
− 5y
2
+ 10y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.100634 + 0.258522I
b = 0
1.37919 − 2.82812I 3.14050 − 5.75335I
u = 0.877439 − 0.744862I
a = −0.100634 − 0.258522I
b = 0
1.37919 + 2.82812I 3.14050 + 5.75335I
u = −0.754878
a = −2.59873
b = 0
−2.75839 −19.9210
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)(u
71
+ 2u
70
+ ··· − 2u − 1)
c
2
(u
3
+ u
2
+ 2u + 1)(u
71
+ 36u
70
+ ··· + 4u + 1)
c
3
(u
3
+ u
2
+ 2u + 1)(u
71
+ 2u
70
+ ··· − 4u − 1)
c
4
u
3
(u
71
− 3u
70
+ ··· + 660u + 200)
c
5
(u
3
− u
2
+ 1)(u
71
+ 2u
70
+ ··· − 2u − 1)
c
6
((u − 1)
3
)(u
71
− 4u
70
+ ··· + 21u − 25)
c
7
25(5u
3
− 4u
2
+ u − 1)(5u
71
− 39u
70
+ ··· + 379583u + 94103)
c
8
25(5u
3
− 11u
2
+ 6u − 1)(5u
71
− 6u
70
+ ··· + 231980u − 42881)
c
9
((u + 1)
3
)(u
71
− 4u
70
+ ··· + 21u − 25)
c
10
(u
3
− u
2
+ 2u − 1)(u
71
+ 2u
70
+ ··· − 4u − 1)
c
11
(u
3
+ 3u
2
+ 2u − 1)(u
71
+ 6u
70
+ ··· − 6402u − 847)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
− y
2
+ 2y −1)(y
71
− 36y
70
+ ··· + 4y −1)
c
2
(y
3
+ 3y
2
+ 2y −1)(y
71
+ 72y
69
+ ··· + 16y −1)
c
3
, c
10
(y
3
+ 3y
2
+ 2y −1)(y
71
− 48y
70
+ ··· + 4y −1)
c
4
y
3
(y
71
+ 21y
70
+ ··· − 606000y −40000)
c
6
, c
9
((y −1)
3
)(y
71
− 58y
70
+ ··· + 79841y −625)
c
7
625(25y
3
− 6y
2
− 7y −1)
· (25y
71
+ 959y
70
+ ··· − 181655598053y −8855374609)
c
8
625(25y
3
− 61y
2
+ 14y −1)
· (25y
71
− 936y
70
+ ··· + 36727842568y −1838780161)
c
11
(y
3
− 5y
2
+ 10y −1)(y
71
+ 36y
70
+ ··· + 2.22229 × 10
7
y −717409)
18
