9
32
(K9a
6
)
A knot diagram
1
Linearized knot diagam
4 5 7 8 3 9 2 1 6
Solving Sequence
6,9
7
1,4
2 3 5 8
c
6
c
9
c
1
c
3
c
5
c
8
c
2
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h216472320u
28
− 196425840u
27
+ ··· + 2595371149b − 196454684,
− 230172u
28
− 27804388u
27
+ ··· + 370767307a − 679741065, u
29
− u
28
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 29 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
= h2.16 × 10
8
u
28
− 1.96 × 10
8
u
27
+ · · · + 2.60 × 10
9
b − 1.96 × 10
8
, −2.30 ×
10
5
u
28
− 2.78 × 10
7
u
27
+ · · · + 3.71 × 10
8
a − 6.80 × 10
8
, u
29
− u
28
+ · · · + 3u + 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
7
=
1
−u
2
a
1
=
u
u
a
4
=
0.000620799u
28
+ 0.0749915u
27
+ ··· − 3.83846u + 1.83334
−0.0834071u
28
+ 0.0756831u
27
+ ··· − 2.93896u + 0.0756943
a
2
=
−0.00281892u
28
− 0.833272u
27
+ ··· − 4.55210u − 0.116626
0.833292u
28
− 0.836091u
27
+ ··· − 3.22782u − 0.836111
a
3
=
−0.00528313u
28
+ 0.821590u
27
+ ··· − 0.672045u + 1.83325
−0.0166708u
28
+ 0.0163909u
27
+ ··· − 0.722782u + 0.816389
a
5
=
0.00446172u
28
+ 0.730031u
27
+ ··· − 2.03460u + 2.48337
0.0666831u
28
− 0.0655635u
27
+ ··· − 1.10887u + 0.734444
a
8
=
u
3
u
3
+ u
a
8
=
u
3
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
8357107928
2595371149
u
28
+
6279939276
2595371149
u
27
+ ··· +
20588201632
2595371149
u +
13962231674
2595371149
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
− 5u
28
+ ··· + u − 1
c
2
, c
5
u
29
+ u
28
+ ··· + 5u − 1
c
3
u
29
− u
28
+ ··· − u − 19
c
4
u
29
+ u
28
+ ··· + 21u − 11
c
6
, c
9
u
29
+ u
28
+ ··· + 3u − 1
c
7
u
29
+ 3u
28
+ ··· + u + 1
c
8
u
29
+ 11u
28
+ ··· + 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 3y
28
+ ··· − 5y −1
c
2
, c
5
y
29
− 21y
28
+ ··· − 5y −1
c
3
y
29
+ 15y
28
+ ··· + 1103y −361
c
4
y
29
+ 31y
28
+ ··· − 1869y −121
c
6
, c
9
y
29
+ 11y
28
+ ··· + 3y −1
c
7
y
29
− 5y
28
+ ··· + 3y −1
c
8
y
29
+ 15y
28
+ ··· + 175y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.647818 + 0.782212I
a = 1.174800 + 0.131909I
b = 1.35368 − 1.53216I
4.48635 + 0.55125I 10.94303 − 0.19758I
u = 0.647818 − 0.782212I
a = 1.174800 − 0.131909I
b = 1.35368 + 1.53216I
4.48635 − 0.55125I 10.94303 + 0.19758I
u = −0.559219 + 0.861588I
a = −2.56606 + 1.18824I
b = −2.19707 + 1.46012I
1.99105 − 2.23064I −15.0558 − 8.8774I
u = −0.559219 − 0.861588I
a = −2.56606 − 1.18824I
b = −2.19707 − 1.46012I
1.99105 + 2.23064I −15.0558 + 8.8774I
u = 0.099472 + 1.040710I
a = −0.040185 − 0.557055I
b = −0.559691 + 0.371807I
−3.62029 − 0.98610I −3.43918 + 1.15236I
u = 0.099472 − 1.040710I
a = −0.040185 + 0.557055I
b = −0.559691 − 0.371807I
−3.62029 + 0.98610I −3.43918 − 1.15236I
u = 0.923879 + 0.554080I
a = −1.061880 + 0.915307I
b = 0.170095 + 1.380090I
5.89129 − 7.10658I 7.40494 + 4.09137I
u = 0.923879 − 0.554080I
a = −1.061880 − 0.915307I
b = 0.170095 − 1.380090I
5.89129 + 7.10658I 7.40494 − 4.09137I
u = 0.644129 + 0.902940I
a = −1.03409 + 1.43901I
b = 0.565379 + 1.269170I
4.11625 + 4.48763I 9.60010 − 6.67821I
u = 0.644129 − 0.902940I
a = −1.03409 − 1.43901I
b = 0.565379 − 1.269170I
4.11625 − 4.48763I 9.60010 + 6.67821I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.528836 + 0.980105I
a = −0.540279 − 0.869458I
b = −0.347922 − 1.350220I
−0.15788 − 2.80514I 1.82209 + 1.85203I
u = −0.528836 − 0.980105I
a = −0.540279 + 0.869458I
b = −0.347922 + 1.350220I
−0.15788 + 2.80514I 1.82209 − 1.85203I
u = −1.034250 + 0.485851I
a = −0.549331 − 0.039451I
b = −0.348963 − 0.675392I
5.14963 − 1.80223I 13.69706 + 3.37820I
u = −1.034250 − 0.485851I
a = −0.549331 + 0.039451I
b = −0.348963 + 0.675392I
5.14963 + 1.80223I 13.69706 − 3.37820I
u = 0.641135 + 0.564919I
a = 1.42824 − 0.88660I
b = −0.129556 − 1.400390I
0.91572 − 2.15286I 5.11617 + 3.69479I
u = 0.641135 − 0.564919I
a = 1.42824 + 0.88660I
b = −0.129556 + 1.400390I
0.91572 + 2.15286I 5.11617 − 3.69479I
u = −0.447738 + 0.689000I
a = 1.79794 − 0.28016I
b = 1.170450 + 0.106145I
0.78940 − 1.37762I 5.11267 + 4.75149I
u = −0.447738 − 0.689000I
a = 1.79794 + 0.28016I
b = 1.170450 − 0.106145I
0.78940 + 1.37762I 5.11267 − 4.75149I
u = 0.618739 + 1.016340I
a = −1.74109 + 0.57301I
b = −1.33104 + 1.93207I
−0.38505 + 7.12556I 2.65443 − 8.10425I
u = 0.618739 − 1.016340I
a = −1.74109 − 0.57301I
b = −1.33104 − 1.93207I
−0.38505 − 7.12556I 2.65443 + 8.10425I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.111222 + 1.267020I
a = −0.303660 + 0.158824I
b = 0.107002 − 0.499750I
−1.26594 − 5.18635I 1.49328 + 7.03100I
u = −0.111222 − 1.267020I
a = −0.303660 − 0.158824I
b = 0.107002 + 0.499750I
−1.26594 + 5.18635I 1.49328 − 7.03100I
u = 0.708050 + 1.105240I
a = 1.56079 − 0.79326I
b = 1.27636 − 1.94848I
4.19521 + 13.09990I 5.01719 − 8.12211I
u = 0.708050 − 1.105240I
a = 1.56079 + 0.79326I
b = 1.27636 + 1.94848I
4.19521 − 13.09990I 5.01719 + 8.12211I
u = −0.770179 + 1.141350I
a = 0.718662 + 0.419411I
b = 0.461012 + 0.914365I
3.17430 − 4.69569I 8.95566 + 8.13169I
u = −0.770179 − 1.141350I
a = 0.718662 − 0.419411I
b = 0.461012 − 0.914365I
3.17430 + 4.69569I 8.95566 − 8.13169I
u = −0.195750 + 0.569252I
a = 1.95836 − 0.88135I
b = 0.778642 − 0.497191I
0.70687 − 1.36069I 4.42210 + 4.47976I
u = −0.195750 − 0.569252I
a = 1.95836 + 0.88135I
b = 0.778642 + 0.497191I
0.70687 + 1.36069I 4.42210 − 4.47976I
u = −0.272051
a = 3.39557
b = 1.06327
2.30899 2.51260
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
29
− 5u
28
+ ··· + u − 1
c
2
, c
5
u
29
+ u
28
+ ··· + 5u − 1
c
3
u
29
− u
28
+ ··· − u − 19
c
4
u
29
+ u
28
+ ··· + 21u − 11
c
6
, c
9
u
29
+ u
28
+ ··· + 3u − 1
c
7
u
29
+ 3u
28
+ ··· + u + 1
c
8
u
29
+ 11u
28
+ ··· + 3u − 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 3y
28
+ ··· − 5y −1
c
2
, c
5
y
29
− 21y
28
+ ··· − 5y −1
c
3
y
29
+ 15y
28
+ ··· + 1103y −361
c
4
y
29
+ 31y
28
+ ··· − 1869y −121
c
6
, c
9
y
29
+ 11y
28
+ ··· + 3y −1
c
7
y
29
− 5y
28
+ ··· + 3y −1
c
8
y
29
+ 15y
28
+ ··· + 175y −1
9
