11a
251
(K11a
251
)
A knot diagram
1
Linearized knot diagam
4 7 1 2 11 3 10 5 6 8 9
Solving Sequence
7,10
8
3,11
2 6 5 4 9 1
c
7
c
10
c
2
c
6
c
5
c
4
c
9
c
11
c
1
, c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.68810 × 10
156
u
70
+ 1.55856 × 10
157
u
69
+ ··· + 7.93791 × 10
157
b + 3.59478 × 10
157
,
5.59936 × 10
157
u
70
− 8.12165 × 10
157
u
69
+ ··· + 7.93791 × 10
157
a − 4.78496 × 10
158
, u
71
− 2u
70
+ ··· − 10u + 1i
I
u
2
= hb, −u
4
+ 2u
3
+ u
2
+ a − 2u − 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 76 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−5.69 × 10
156
u
70
+ 1.56 × 10
157
u
69
+ · · · + 7.94 × 10
157
b + 3.59 ×
10
157
, 5.60 × 10
157
u
70
− 8.12 × 10
157
u
69
+ · · · + 7.94 × 10
157
a − 4.78 ×
10
158
, u
71
− 2u
70
+ · · · − 10u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
3
=
−0.705395u
70
+ 1.02315u
69
+ ··· − 20.4760u + 6.02799
0.0716575u
70
− 0.196344u
69
+ ··· + 0.865234u − 0.452863
a
11
=
u
−u
3
+ u
a
2
=
−0.777052u
70
+ 1.21949u
69
+ ··· − 21.3412u + 6.48085
0.0716575u
70
− 0.196344u
69
+ ··· + 0.865234u − 0.452863
a
6
=
0.821521u
70
− 0.920115u
69
+ ··· + 15.4811u − 2.91710
−0.201387u
70
+ 0.381284u
69
+ ··· − 10.7628u + 1.69056
a
5
=
0.801915u
70
− 0.815848u
69
+ ··· + 16.3688u − 3.09726
−0.209903u
70
+ 0.426666u
69
+ ··· − 10.5453u + 1.57546
a
4
=
−0.451816u
70
+ 0.954485u
69
+ ··· − 17.7677u + 5.06906
−0.0186479u
70
+ 0.0169092u
69
+ ··· − 2.19688u + 0.0640132
a
9
=
−0.725017u
70
+ 1.65402u
69
+ ··· + 4.00112u − 2.27250
0.271778u
70
− 0.315974u
69
+ ··· + 9.57483u − 0.629811
a
1
=
0.0982857u
70
− 0.0430280u
69
+ ··· + 3.63403u − 1.21756
0.0186479u
70
− 0.0169092u
69
+ ··· + 2.19688u − 0.0640132
a
1
=
0.0982857u
70
− 0.0430280u
69
+ ··· + 3.63403u − 1.21756
0.0186479u
70
− 0.0169092u
69
+ ··· + 2.19688u − 0.0640132
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.02243u
70
+ 6.21438u
69
+ ··· + 39.3412u − 7.45678
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
71
− 6u
70
+ ··· + 8u − 1
c
2
, c
6
u
71
− u
70
+ ··· + 160u − 32
c
5
u
71
+ 6u
70
+ ··· + 2u + 1
c
7
, c
10
u
71
+ 2u
70
+ ··· − 10u − 1
c
8
u
71
+ 2u
70
+ ··· − 26u − 71
c
9
u
71
− 2u
70
+ ··· + 1044u + 216
c
11
u
71
− 12u
70
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
y
71
− 64y
70
+ ··· + 192y −1
c
2
, c
6
y
71
+ 33y
70
+ ··· − 4608y −1024
c
5
y
71
− 12y
70
+ ··· + 6y −1
c
7
, c
10
y
71
− 48y
70
+ ··· + 10y −1
c
8
y
71
+ 72y
70
+ ··· − 272958y −5041
c
9
y
71
+ 48y
70
+ ··· + 5221584y −46656
c
11
y
71
+ 60y
69
+ ··· + 10y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.958690 + 0.052610I
a = 1.12357 + 3.37661I
b = −0.753769 − 0.149844I
−0.821815 − 0.287086I 15.6399 − 24.5037I
u = −0.958690 − 0.052610I
a = 1.12357 − 3.37661I
b = −0.753769 + 0.149844I
−0.821815 + 0.287086I 15.6399 + 24.5037I
u = −1.039170 + 0.068699I
a = −3.61770 + 0.29771I
b = 0.418183 − 0.830193I
1.53422 − 1.77853I 0
u = −1.039170 − 0.068699I
a = −3.61770 − 0.29771I
b = 0.418183 + 0.830193I
1.53422 + 1.77853I 0
u = 0.936141 + 0.181892I
a = −0.083967 + 0.975080I
b = −0.091987 + 1.395920I
−0.50220 + 3.12016I −4.96274 − 11.92067I
u = 0.936141 − 0.181892I
a = −0.083967 − 0.975080I
b = −0.091987 − 1.395920I
−0.50220 − 3.12016I −4.96274 + 11.92067I
u = 0.090337 + 1.044210I
a = −0.026334 + 0.752549I
b = 1.049030 + 0.353850I
−3.94869 − 4.27443I 0
u = 0.090337 − 1.044210I
a = −0.026334 − 0.752549I
b = 1.049030 − 0.353850I
−3.94869 + 4.27443I 0
u = 1.044140 + 0.187508I
a = −0.935314 + 0.664478I
b = 0.78926 + 1.18254I
1.70771 + 3.92061I 0
u = 1.044140 − 0.187508I
a = −0.935314 − 0.664478I
b = 0.78926 − 1.18254I
1.70771 − 3.92061I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.551309 + 0.934929I
a = −0.81004 + 1.24306I
b = 0.116001 + 1.363920I
−10.36010 − 0.43943I 0
u = 0.551309 − 0.934929I
a = −0.81004 − 1.24306I
b = 0.116001 − 1.363920I
−10.36010 + 0.43943I 0
u = 0.117174 + 0.888965I
a = 0.42606 − 1.98602I
b = 0.182154 − 0.954080I
−2.76633 − 1.81907I −5.04908 + 2.94377I
u = 0.117174 − 0.888965I
a = 0.42606 + 1.98602I
b = 0.182154 + 0.954080I
−2.76633 + 1.81907I −5.04908 − 2.94377I
u = −0.238708 + 0.856602I
a = −0.033528 − 0.750003I
b = −0.555330 − 0.426705I
0.63691 − 2.06340I 4.30464 + 4.04645I
u = −0.238708 − 0.856602I
a = −0.033528 + 0.750003I
b = −0.555330 + 0.426705I
0.63691 + 2.06340I 4.30464 − 4.04645I
u = 0.871168 + 0.127070I
a = 0.768608 − 0.123027I
b = −1.078050 + 0.845687I
−1.94802 + 1.61598I −10.03099 − 8.04874I
u = 0.871168 − 0.127070I
a = 0.768608 + 0.123027I
b = −1.078050 − 0.845687I
−1.94802 − 1.61598I −10.03099 + 8.04874I
u = −1.111760 + 0.154509I
a = 2.52899 − 0.19796I
b = −0.497375 + 1.156290I
−3.73969 − 4.87336I 0
u = −1.111760 − 0.154509I
a = 2.52899 + 0.19796I
b = −0.497375 − 1.156290I
−3.73969 + 4.87336I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.968505 + 0.574658I
a = 0.556618 − 1.072570I
b = −0.15556 − 1.52316I
−8.97886 + 5.87062I 0
u = 0.968505 − 0.574658I
a = 0.556618 + 1.072570I
b = −0.15556 + 1.52316I
−8.97886 − 5.87062I 0
u = 0.016654 + 1.134760I
a = 0.01069 + 1.54493I
b = −0.504028 + 1.050930I
−1.17091 − 6.36314I 0
u = 0.016654 − 1.134760I
a = 0.01069 − 1.54493I
b = −0.504028 − 1.050930I
−1.17091 + 6.36314I 0
u = −1.16582
a = 0.452000
b = 0.259845
2.31401 0
u = 0.827970
a = 0.602565
b = −1.45559
−2.44443 −13.2680
u = −0.795879 + 0.090569I
a = 1.76698 − 2.15625I
b = 0.158109 − 0.674265I
0.733207 − 1.164170I 5.75824 + 3.22185I
u = −0.795879 − 0.090569I
a = 1.76698 + 2.15625I
b = 0.158109 + 0.674265I
0.733207 + 1.164170I 5.75824 − 3.22185I
u = 1.152090 + 0.338633I
a = 1.033990 − 0.728304I
b = −0.82605 − 1.20952I
−3.47932 + 8.87997I 0
u = 1.152090 − 0.338633I
a = 1.033990 + 0.728304I
b = −0.82605 + 1.20952I
−3.47932 − 8.87997I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716396 + 0.338710I
a = −1.82350 − 1.16977I
b = −0.371326 − 1.151650I
−4.63878 + 3.29846I −3.31669 − 7.32300I
u = −0.716396 − 0.338710I
a = −1.82350 + 1.16977I
b = −0.371326 + 1.151650I
−4.63878 − 3.29846I −3.31669 + 7.32300I
u = 1.222350 + 0.171009I
a = −0.244405 + 0.071523I
b = 0.967998 + 0.212799I
4.87893 + 2.71275I 0
u = 1.222350 − 0.171009I
a = −0.244405 − 0.071523I
b = 0.967998 − 0.212799I
4.87893 − 2.71275I 0
u = −1.247410 + 0.331147I
a = −1.29926 − 2.06002I
b = 0.422840 − 0.530363I
1.050550 − 0.525213I 0
u = −1.247410 − 0.331147I
a = −1.29926 + 2.06002I
b = 0.422840 + 0.530363I
1.050550 + 0.525213I 0
u = 0.051066 + 1.301090I
a = 0.022365 − 1.283720I
b = 0.640749 − 1.227980I
−6.73040 − 10.34400I 0
u = 0.051066 − 1.301090I
a = 0.022365 + 1.283720I
b = 0.640749 + 1.227980I
−6.73040 + 10.34400I 0
u = −0.703062 + 1.112770I
a = 0.146447 + 0.850843I
b = 0.300612 + 1.059860I
−3.63710 − 0.29930I 0
u = −0.703062 − 1.112770I
a = 0.146447 − 0.850843I
b = 0.300612 − 1.059860I
−3.63710 + 0.29930I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.215620 + 0.579320I
a = −0.551017 + 0.353859I
b = 0.782344 + 0.411126I
0.57965 − 2.48080I 0
u = −1.215620 − 0.579320I
a = −0.551017 − 0.353859I
b = 0.782344 − 0.411126I
0.57965 + 2.48080I 0
u = 1.267920 + 0.491162I
a = −0.82403 + 1.37930I
b = 0.434959 + 1.171370I
0.83262 + 6.84654I 0
u = 1.267920 − 0.491162I
a = −0.82403 − 1.37930I
b = 0.434959 − 1.171370I
0.83262 − 6.84654I 0
u = 1.331280 + 0.393498I
a = 0.104491 − 0.201021I
b = −0.919240 + 0.397727I
5.39522 + 6.50016I 0
u = 1.331280 − 0.393498I
a = 0.104491 + 0.201021I
b = −0.919240 − 0.397727I
5.39522 − 6.50016I 0
u = 1.303720 + 0.536688I
a = −0.094492 + 0.280375I
b = 1.204060 − 0.543396I
−0.14862 + 9.86900I 0
u = 1.303720 − 0.536688I
a = −0.094492 − 0.280375I
b = 1.204060 + 0.543396I
−0.14862 − 9.86900I 0
u = 1.35249 + 0.54752I
a = 0.99301 − 1.24253I
b = −0.639775 − 1.172900I
3.01535 + 12.24190I 0
u = 1.35249 − 0.54752I
a = 0.99301 + 1.24253I
b = −0.639775 + 1.172900I
3.01535 − 12.24190I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.085901 + 0.499257I
a = −1.14561 + 1.25252I
b = −0.563000 + 1.270970I
−6.53398 − 5.54394I −4.50504 + 1.63762I
u = 0.085901 − 0.499257I
a = −1.14561 − 1.25252I
b = −0.563000 − 1.270970I
−6.53398 + 5.54394I −4.50504 − 1.63762I
u = −1.34861 + 0.66108I
a = 0.80494 + 1.17952I
b = −0.542577 + 0.884808I
3.42139 − 4.04641I 0
u = −1.34861 − 0.66108I
a = 0.80494 − 1.17952I
b = −0.542577 − 0.884808I
3.42139 + 4.04641I 0
u = 1.49354 + 0.21546I
a = 0.0543163 + 0.1174420I
b = 0.040910 − 0.635562I
3.76322 + 4.31820I 0
u = 1.49354 − 0.21546I
a = 0.0543163 − 0.1174420I
b = 0.040910 + 0.635562I
3.76322 − 4.31820I 0
u = 1.39546 + 0.60916I
a = −1.01075 + 1.10984I
b = 0.77537 + 1.24885I
−2.4732 + 16.9235I 0
u = 1.39546 − 0.60916I
a = −1.01075 − 1.10984I
b = 0.77537 − 1.24885I
−2.4732 − 16.9235I 0
u = −1.48233 + 0.37826I
a = 0.217114 − 0.286842I
b = −0.550290 − 0.713216I
3.94019 + 0.36090I 0
u = −1.48233 − 0.37826I
a = 0.217114 + 0.286842I
b = −0.550290 + 0.713216I
3.94019 − 0.36090I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.366011 + 0.204704I
a = 1.88485 − 0.59402I
b = 0.363096 − 0.475061I
0.638942 − 1.236310I 4.36186 + 4.95807I
u = −0.366011 − 0.204704I
a = 1.88485 + 0.59402I
b = 0.363096 + 0.475061I
0.638942 + 1.236310I 4.36186 − 4.95807I
u = −1.41055 + 0.85382I
a = −0.682852 − 0.955217I
b = 0.572860 − 1.122140I
−1.60491 − 7.59190I 0
u = −1.41055 − 0.85382I
a = −0.682852 + 0.955217I
b = 0.572860 + 1.122140I
−1.60491 + 7.59190I 0
u = 0.146576 + 0.246793I
a = 3.86257 − 1.93742I
b = −0.384908 − 0.642002I
−2.06670 − 0.96031I −7.01026 − 0.44637I
u = 0.146576 − 0.246793I
a = 3.86257 + 1.93742I
b = −0.384908 + 0.642002I
−2.06670 + 0.96031I −7.01026 + 0.44637I
u = −1.73227 + 0.32166I
a = −0.133229 + 0.168591I
b = 0.470368 + 1.055660I
−0.67110 + 3.32518I 0
u = −1.73227 − 0.32166I
a = −0.133229 − 0.168591I
b = 0.470368 − 1.055660I
−0.67110 − 3.32518I 0
u = 0.057931 + 0.208385I
a = 2.79535 − 0.71729I
b = 0.342943 − 0.988238I
−0.62570 − 2.03170I −1.27918 + 2.72742I
u = 0.057931 − 0.208385I
a = 2.79535 + 0.71729I
b = 0.342943 + 0.988238I
−0.62570 + 2.03170I −1.27918 − 2.72742I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.159227
a = 4.37555
b = −1.00143
−2.81001 −3.04700
12
II. I
u
2
= hb, −u
4
+ 2u
3
+ u
2
+ a − 2u − 1, u
5
− u
4
− 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
8
=
1
−u
2
a
3
=
u
4
− 2u
3
− u
2
+ 2u + 1
0
a
11
=
u
−u
3
+ u
a
2
=
u
4
− 2u
3
− u
2
+ 2u + 1
0
a
6
=
1
0
a
5
=
−u
4
+ u
2
+ 1
u
4
+ u
3
− u
2
− 2u − 1
a
4
=
−2u
3
+ 2u + 2
u
4
+ u
3
− u
2
− 2u − 1
a
9
=
−u
u
a
1
=
u
4
− u
2
− 1
−u
4
− u
3
+ u
2
+ 2u + 1
a
1
=
u
4
− u
2
− 1
−u
4
− u
3
+ u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
4
− u
3
+ 2u
2
+ 10u + 5
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
6
u
5
c
3
, c
4
(u + 1)
5
c
5
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
, c
11
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
9
, c
10
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
(y −1)
5
c
2
, c
6
y
5
c
5
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
7
, c
9
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21774
a = 2.89210
b = 0
0.756147 −9.00270
u = −0.309916 + 0.549911I
a = 0.01014 + 1.59703I
b = 0
−1.31583 − 1.53058I 1.45754 + 4.40323I
u = −0.309916 − 0.549911I
a = 0.01014 − 1.59703I
b = 0
−1.31583 + 1.53058I 1.45754 − 4.40323I
u = 1.41878 + 0.21917I
a = 0.043806 − 0.365575I
b = 0
4.22763 + 4.40083I 10.04378 − 5.20937I
u = 1.41878 − 0.21917I
a = 0.043806 + 0.365575I
b = 0
4.22763 − 4.40083I 10.04378 + 5.20937I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
71
− 6u
70
+ ··· + 8u − 1)
c
2
, c
6
u
5
(u
71
− u
70
+ ··· + 160u − 32)
c
3
, c
4
((u + 1)
5
)(u
71
− 6u
70
+ ··· + 8u − 1)
c
5
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
71
+ 6u
70
+ ··· + 2u + 1)
c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
71
+ 2u
70
+ ··· − 10u − 1)
c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
71
+ 2u
70
+ ··· − 26u − 71)
c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
71
− 2u
70
+ ··· + 1044u + 216)
c
10
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
71
+ 2u
70
+ ··· − 10u − 1)
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
71
− 12u
70
+ ··· + 2u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
((y −1)
5
)(y
71
− 64y
70
+ ··· + 192y −1)
c
2
, c
6
y
5
(y
71
+ 33y
70
+ ··· − 4608y −1024)
c
5
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
71
− 12y
70
+ ··· + 6y −1)
c
7
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
71
− 48y
70
+ ··· + 10y −1)
c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
71
+ 72y
70
+ ··· − 272958y −5041)
c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
71
+ 48y
70
+ ··· + 5221584y −46656)
c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
71
+ 60y
69
+ ··· + 10y −1)
18
