11a
253
(K11a
253
)
A knot diagram
1
Linearized knot diagam
4 7 1 2 8 3 10 11 5 6 9
Solving Sequence
7,10 3,8
2 6 11 5 4 1 9
c
7
c
2
c
6
c
10
c
5
c
4
c
1
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.29827 × 10
242
u
70
− 3.85213 × 10
243
u
69
+ ··· + 1.61478 × 10
243
b − 8.28511 × 10
242
,
− 1.44895 × 10
243
u
70
− 1.68032 × 10
244
u
69
+ ··· + 1.61478 × 10
243
a + 5.61105 × 10
243
,
u
71
+ 12u
70
+ ··· + 2u + 1i
I
u
2
= hb, −u
4
− u
3
− 3u
2
+ a − u − 2, 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−3.30 × 10
242
u
70
− 3.85 × 10
243
u
69
+ · · · + 1.61 × 10
243
b − 8.29 ×
10
242
, −1.45 × 10
243
u
70
− 1.68 × 10
244
u
69
+ · · · + 1.61 × 10
243
a + 5.61 ×
10
243
, u
71
+ 12u
70
+ · · · + 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
3
=
0.897301u
70
+ 10.4058u
69
+ ··· − 15.1406u − 3.47480
0.204255u
70
+ 2.38554u
69
+ ··· − 0.797246u + 0.513078
a
8
=
1
u
2
a
2
=
0.693047u
70
+ 8.02030u
69
+ ··· − 14.3434u − 3.98788
0.204255u
70
+ 2.38554u
69
+ ··· − 0.797246u + 0.513078
a
6
=
0.991671u
70
+ 11.2338u
69
+ ··· − 0.635568u + 2.82255
0.150636u
70
+ 1.87103u
69
+ ··· − 0.311046u + 0.838335
a
11
=
−3.05511u
70
− 38.0827u
69
+ ··· − 14.2425u + 2.92815
−0.251356u
70
− 2.91652u
69
+ ··· + 4.21504u + 0.652989
a
5
=
0.976661u
70
+ 11.0121u
69
+ ··· + 0.0163988u + 2.65051
0.218015u
70
+ 2.64923u
69
+ ··· − 0.212886u + 0.879910
a
4
=
0.0842423u
70
+ 1.02322u
69
+ ··· + 9.62101u + 4.52032
−0.0463985u
70
− 0.516278u
69
+ ··· + 0.435416u − 0.111771
a
1
=
0.658958u
70
+ 7.79572u
69
+ ··· − 9.48146u − 0.610030
0.0463985u
70
+ 0.516278u
69
+ ··· − 0.435416u + 0.111771
a
9
=
−3.25923u
70
− 40.5525u
69
+ ··· − 9.10450u + 3.81600
0.136311u
70
+ 1.50077u
69
+ ··· + 4.68772u + 1.32234
a
9
=
−3.25923u
70
− 40.5525u
69
+ ··· − 9.10450u + 3.81600
0.136311u
70
+ 1.50077u
69
+ ··· + 4.68772u + 1.32234
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.88170u
70
+ 58.5557u
69
+ ··· + 35.4740u + 5.13891
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
u
71
− 12u
70
+ ··· + 2u − 1
c
8
, c
11
u
71
+ 2u
70
+ ··· − 10u − 1
c
9
u
71
− 2u
70
+ ··· + 1044u + 216
c
10
u
71
+ 2u
70
+ ··· − 26u − 71
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
y
71
+ 60y
69
+ ··· + 10y −1
c
8
, c
11
y
71
− 48y
70
+ ··· + 10y −1
c
9
y
71
+ 48y
70
+ ··· + 5221584y −46656
c
10
y
71
+ 72y
70
+ ··· − 272958y −5041
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.703699 + 0.689890I
a = −0.550820 − 1.011170I
b = 0.82605 − 1.20952I
−3.47932 − 8.87997I 0
u = 0.703699 − 0.689890I
a = −0.550820 + 1.011170I
b = 0.82605 + 1.20952I
−3.47932 + 8.87997I 0
u = −0.864632 + 0.681430I
a = 0.08127 + 1.69538I
b = −0.422840 + 0.530363I
1.050550 − 0.525213I 0
u = −0.864632 − 0.681430I
a = 0.08127 − 1.69538I
b = −0.422840 − 0.530363I
1.050550 + 0.525213I 0
u = −0.370753 + 0.796394I
a = −0.1158600 − 0.0717373I
b = −0.967998 − 0.212799I
4.87893 + 2.71275I 9.31371 + 0.I
u = −0.370753 − 0.796394I
a = −0.1158600 + 0.0717373I
b = −0.967998 + 0.212799I
4.87893 − 2.71275I 9.31371 + 0.I
u = −1.083660 + 0.393419I
a = −0.02862 + 1.47352I
b = 0.15556 + 1.52316I
−8.97886 + 5.87062I 0
u = −1.083660 − 0.393419I
a = −0.02862 − 1.47352I
b = 0.15556 − 1.52316I
−8.97886 − 5.87062I 0
u = −0.624551 + 0.490472I
a = −1.12224 + 1.61022I
b = 0.563000 + 1.270970I
−6.53398 + 5.54394I −4.50504 − 1.63762I
u = −0.624551 − 0.490472I
a = −1.12224 − 1.61022I
b = 0.563000 − 1.270970I
−6.53398 − 5.54394I −4.50504 + 1.63762I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.092610 + 0.777088I
a = −0.51735 + 1.37351I
b = 0.371326 − 1.151650I
−4.63878 − 3.29846I −3.31669 + 7.32300I
u = 0.092610 − 0.777088I
a = −0.51735 − 1.37351I
b = 0.371326 + 1.151650I
−4.63878 + 3.29846I −3.31669 − 7.32300I
u = 0.626178 + 1.068960I
a = −0.272089 + 0.134473I
b = 0.555330 + 0.426705I
0.63691 − 2.06340I 0
u = 0.626178 − 1.068960I
a = −0.272089 − 0.134473I
b = 0.555330 − 0.426705I
0.63691 + 2.06340I 0
u = 0.999301 + 0.777975I
a = 0.28606 + 1.72412I
b = −0.182154 + 0.954080I
−2.76633 − 1.81907I 0
u = 0.999301 − 0.777975I
a = 0.28606 − 1.72412I
b = −0.182154 − 0.954080I
−2.76633 + 1.81907I 0
u = −0.799531 + 1.024210I
a = 0.0939270 − 0.0308360I
b = 0.919240 − 0.397727I
5.39522 + 6.50016I 0
u = −0.799531 − 1.024210I
a = 0.0939270 + 0.0308360I
b = 0.919240 + 0.397727I
5.39522 − 6.50016I 0
u = 0.563894 + 0.367730I
a = 3.33218 + 0.28298I
b = 0.497375 + 1.156290I
−3.73969 + 4.87336I −11.68238 + 4.88288I
u = 0.563894 − 0.367730I
a = 3.33218 − 0.28298I
b = 0.497375 − 1.156290I
−3.73969 − 4.87336I −11.68238 − 4.88288I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.977884 + 0.899474I
a = 0.50460 − 1.61337I
b = −0.434959 − 1.171370I
0.83262 + 6.84654I 0
u = −0.977884 − 0.899474I
a = 0.50460 + 1.61337I
b = −0.434959 + 1.171370I
0.83262 − 6.84654I 0
u = 0.466586 + 0.449196I
a = 0.441513 + 1.091590I
b = −0.78926 + 1.18254I
1.70771 − 3.92061I 2.90621 + 12.12775I
u = 0.466586 − 0.449196I
a = 0.441513 − 1.091590I
b = −0.78926 − 1.18254I
1.70771 + 3.92061I 2.90621 − 12.12775I
u = −0.647071
a = −1.79610
b = −0.259845
2.31401 2.89560
u = 0.107050 + 0.611923I
a = −0.276683 − 0.818069I
b = −0.363096 + 0.475061I
0.638942 − 1.236310I 4.36186 + 4.95807I
u = 0.107050 − 0.611923I
a = −0.276683 + 0.818069I
b = −0.363096 − 0.475061I
0.638942 + 1.236310I 4.36186 − 4.95807I
u = −0.794700 + 1.129040I
a = 1.12598 − 1.24645I
b = −0.782344 − 0.411126I
0.57965 − 2.48080I 0
u = −0.794700 − 1.129040I
a = 1.12598 + 1.24645I
b = −0.782344 + 0.411126I
0.57965 + 2.48080I 0
u = −0.532056 + 0.272808I
a = −0.08049 − 1.71128I
b = 0.091987 − 1.395920I
−0.50220 + 3.12016I −4.96274 − 11.92067I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.532056 − 0.272808I
a = −0.08049 + 1.71128I
b = 0.091987 + 1.395920I
−0.50220 − 3.12016I −4.96274 + 11.92067I
u = −0.44936 + 1.35350I
a = −0.0265873 + 0.0488917I
b = −0.040910 + 0.635562I
3.76322 + 4.31820I 0
u = −0.44936 − 1.35350I
a = −0.0265873 − 0.0488917I
b = −0.040910 − 0.635562I
3.76322 − 4.31820I 0
u = 1.39070 + 0.32345I
a = 0.116842 − 1.177400I
b = −0.116001 − 1.363920I
−10.36010 − 0.43943I 0
u = 1.39070 − 0.32345I
a = 0.116842 + 1.177400I
b = −0.116001 + 1.363920I
−10.36010 + 0.43943I 0
u = −0.071807 + 0.562576I
a = −2.05309 − 1.70487I
b = −0.158109 + 0.674265I
0.733207 − 1.164170I 5.75824 + 3.22185I
u = −0.071807 − 0.562576I
a = −2.05309 + 1.70487I
b = −0.158109 − 0.674265I
0.733207 + 1.164170I 5.75824 − 3.22185I
u = −1.06557 + 0.95974I
a = −0.1048880 + 0.0619005I
b = −1.204060 + 0.543396I
−0.14862 + 9.86900I 0
u = −1.06557 − 0.95974I
a = −0.1048880 − 0.0619005I
b = −1.204060 − 0.543396I
−0.14862 − 9.86900I 0
u = 0.484399 + 0.253838I
a = −1.69079 + 1.46053I
b = 0.384908 + 0.642002I
−2.06670 − 0.96031I −7.01026 − 0.44637I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.484399 − 0.253838I
a = −1.69079 − 1.46053I
b = 0.384908 − 0.642002I
−2.06670 + 0.96031I −7.01026 + 0.44637I
u = 0.524876 + 0.152599I
a = −0.238499 + 0.515412I
b = 1.078050 + 0.845687I
−1.94802 − 1.61598I −10.03099 + 8.04874I
u = 0.524876 − 0.152599I
a = −0.238499 − 0.515412I
b = 1.078050 − 0.845687I
−1.94802 + 1.61598I −10.03099 − 8.04874I
u = 1.13500 + 0.95032I
a = 0.267670 − 0.095830I
b = −1.049030 − 0.353850I
−3.94869 − 4.27443I 0
u = 1.13500 − 0.95032I
a = 0.267670 + 0.095830I
b = −1.049030 + 0.353850I
−3.94869 + 4.27443I 0
u = −0.510263
a = 0.359168
b = 1.45559
−2.44443 −13.2680
u = −1.09311 + 1.04884I
a = −0.65300 + 1.41019I
b = 0.639775 + 1.172900I
3.01535 + 12.24190I 0
u = −1.09311 − 1.04884I
a = −0.65300 − 1.41019I
b = 0.639775 − 1.172900I
3.01535 − 12.24190I 0
u = −0.380984 + 0.282605I
a = 1.31704 − 2.50803I
b = −0.342943 − 0.988238I
−0.62570 + 2.03170I −1.27918 − 2.72742I
u = −0.380984 − 0.282605I
a = 1.31704 + 2.50803I
b = −0.342943 + 0.988238I
−0.62570 − 2.03170I −1.27918 + 2.72742I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32159 + 0.77978I
a = −0.461978 + 1.215750I
b = 0.550290 + 0.713216I
3.94019 + 0.36090I 0
u = −1.32159 − 0.77978I
a = −0.461978 − 1.215750I
b = 0.550290 − 0.713216I
3.94019 − 0.36090I 0
u = 0.343738 + 0.223330I
a = −7.66838 + 0.46120I
b = −0.418183 − 0.830193I
1.53422 + 1.77853I −13.6461 + 18.0080I
u = 0.343738 − 0.223330I
a = −7.66838 − 0.46120I
b = −0.418183 + 0.830193I
1.53422 − 1.77853I −13.6461 − 18.0080I
u = −0.393942
a = 1.04989
b = 1.00143
−2.81001 −3.04700
u = 1.15700 + 1.12146I
a = −0.63710 − 1.29592I
b = 0.504028 − 1.050930I
−1.17091 − 6.36314I 0
u = 1.15700 − 1.12146I
a = −0.63710 + 1.29592I
b = 0.504028 + 1.050930I
−1.17091 + 6.36314I 0
u = 0.141965 + 0.325094I
a = −10.62010 − 3.90398I
b = 0.753769 − 0.149844I
−0.821815 + 0.287086I 15.6399 + 24.5037I
u = 0.141965 − 0.325094I
a = −10.62010 + 3.90398I
b = 0.753769 + 0.149844I
−0.821815 − 0.287086I 15.6399 − 24.5037I
u = −1.21755 + 1.11843I
a = 0.644457 − 1.245450I
b = −0.77537 − 1.24885I
−2.4732 + 16.9235I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.21755 − 1.11843I
a = 0.644457 + 1.245450I
b = −0.77537 + 1.24885I
−2.4732 − 16.9235I 0
u = −1.01851 + 1.30436I
a = −0.002774 − 0.719604I
b = 0.542577 − 0.884808I
3.42139 − 4.04641I 0
u = −1.01851 − 1.30436I
a = −0.002774 + 0.719604I
b = 0.542577 + 0.884808I
3.42139 + 4.04641I 0
u = 0.24162 + 1.73943I
a = 0.251256 − 0.242611I
b = −0.300612 − 1.059860I
−3.63710 − 0.29930I 0
u = 0.24162 − 1.73943I
a = 0.251256 + 0.242611I
b = −0.300612 + 1.059860I
−3.63710 + 0.29930I 0
u = 1.38157 + 1.26431I
a = 0.570316 + 1.053060I
b = −0.640749 + 1.227980I
−6.73040 − 10.34400I 0
u = 1.38157 − 1.26431I
a = 0.570316 − 1.053060I
b = −0.640749 − 1.227980I
−6.73040 + 10.34400I 0
u = −1.84457 + 0.68870I
a = 0.278706 − 0.975731I
b = −0.470368 − 1.055660I
−0.67110 + 3.32518I 0
u = −1.84457 − 0.68870I
a = 0.278706 + 0.975731I
b = −0.470368 + 1.055660I
−0.67110 − 3.32518I 0
u = −1.07373 + 1.68578I
a = 0.003009 + 0.521248I
b = −0.572860 + 1.122140I
−1.60491 − 7.59190I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.07373 − 1.68578I
a = 0.003009 − 0.521248I
b = −0.572860 − 1.122140I
−1.60491 + 7.59190I 0
12
II. I
u
2
= hb, −u
4
− u
3
− 3u
2
+ a − u − 2, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
3
=
u
4
+ u
3
+ 3u
2
+ u + 2
0
a
8
=
1
u
2
a
2
=
u
4
+ u
3
+ 3u
2
+ u + 2
0
a
6
=
1
0
a
11
=
−u
u
a
5
=
u
2
+ 1
u
4
a
4
=
u
4
+ u
3
+ 4u
2
+ u + 3
u
4
a
1
=
−u
2
− 1
−u
4
a
9
=
u
4
+ u
2
+ 1
−u
4
a
9
=
u
4
+ u
2
+ 1
−u
4
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
4
+ 5u
3
− 3u
2
+ 6u + 1
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
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
9
, c
11
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
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
10
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
8
, c
9
, c
11
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = 0.01014 + 1.59703I
b = 0
−1.31583 − 1.53058I 1.45754 + 4.40323I
u = 0.339110 − 0.822375I
a = 0.01014 − 1.59703I
b = 0
−1.31583 + 1.53058I 1.45754 − 4.40323I
u = −0.766826
a = 2.89210
b = 0
0.756147 −9.00270
u = −0.455697 + 1.200150I
a = 0.043806 − 0.365575I
b = 0
4.22763 + 4.40083I 10.04378 − 5.20937I
u = −0.455697 − 1.200150I
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
− 12u
70
+ ··· + 2u − 1)
c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
71
+ 2u
70
+ ··· − 10u − 1)
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
+ ··· − 26u − 71)
c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
71
+ 2u
70
+ ··· − 10u − 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
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
71
+ 60y
69
+ ··· + 10y −1)
c
8
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
71
− 48y
70
+ ··· + 10y −1)
c
9
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
71
+ 48y
70
+ ··· + 5221584y −46656)
c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
71
+ 72y
70
+ ··· − 272958y −5041)
18
