11a
97
(K11a
97
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 2 3 11 5 4 7 8
Solving Sequence
7,10
11 8
1,4
3 2 6 9 5
c
10
c
7
c
11
c
3
c
2
c
6
c
9
c
4
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.35647 × 10
26
u
40
+ 3.41407 × 10
25
u
39
+ ··· + 4.76775 × 10
26
b + 1.22986 × 10
27
,
1.32011 × 10
27
u
40
− 3.91635 × 10
27
u
39
+ ··· + 5.72130 × 10
27
a + 9.91592 × 10
27
, u
41
+ 3u
40
+ ··· − 16u + 3i
I
u
2
= h−2a
3
− 3a
2
+ 5b − 15a − 7, a
4
+ 2a
3
+ 7a
2
+ 6a + 3, u − 1i
I
u
3
= hb, a
2
+ a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 47 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
=
h1.36×10
26
u
40
+3.41×10
25
u
39
+· · ·+4.77×10
26
b+1.23×10
27
, 1.32×10
27
u
40
−
3.92 × 10
27
u
39
+ · · · + 5.72 × 10
27
a + 9.92 × 10
27
, u
41
+ 3u
40
+ · · · − 16u + 3i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
8
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−0.230736u
40
+ 0.684521u
39
+ ··· + 27.5823u − 1.73316
−0.284509u
40
− 0.0716075u
39
+ ··· + 13.5631u − 2.57954
a
3
=
0.0537729u
40
+ 0.756128u
39
+ ··· + 14.0192u + 0.846378
−0.284509u
40
− 0.0716075u
39
+ ··· + 13.5631u − 2.57954
a
2
=
−0.417033u
40
+ 0.180050u
39
+ ··· + 24.6975u − 0.635993
−0.488200u
40
− 0.376850u
39
+ ··· + 16.4598u − 3.17299
a
6
=
−0.699060u
40
− 0.274328u
39
+ ··· + 36.6179u − 7.70938
−0.662144u
40
− 0.883819u
39
+ ··· + 14.3253u − 3.84461
a
9
=
2.14850u
40
+ 4.44463u
39
+ ··· + 10.3774u − 6.62221
0.866962u
40
+ 1.26216u
39
+ ··· − 10.7057u − 0.442876
a
5
=
0.516885u
40
+ 0.0710561u
39
+ ··· − 22.2661u + 0.886590
0.526631u
40
+ 0.306983u
39
+ ··· − 19.7993u + 3.74658
a
5
=
0.516885u
40
+ 0.0710561u
39
+ ··· − 22.2661u + 0.886590
0.526631u
40
+ 0.306983u
39
+ ··· − 19.7993u + 3.74658
(ii) Obstruction class = −1
(iii) Cusp Shapes =
559898241088593396717061691
238387645942441547003348479
u
40
+
403977182003809318732241725
86686416706342380728490356
u
39
+
··· −
465164699436934167876296904
238387645942441547003348479
u +
633526497906639455712438183
953550583769766188013393916
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
41
− 2u
40
+ ··· + 3u − 3
c
2
u
41
+ 22u
40
+ ··· − 33u − 9
c
3
, c
4
, c
8
c
9
u
41
− u
40
+ ··· + 8u + 4
c
6
u
41
+ 2u
40
+ ··· + 327u − 87
c
7
, c
10
, c
11
u
41
+ 3u
40
+ ··· − 16u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
41
+ 22y
40
+ ··· − 33y −9
c
2
y
41
− 2y
40
+ ··· + 423y −81
c
3
, c
4
, c
8
c
9
y
41
+ 51y
40
+ ··· − 128y −16
c
6
y
41
− 26y
40
+ ··· − 166425y −7569
c
7
, c
10
, c
11
y
41
− 43y
40
+ ··· + 4y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.997009 + 0.226554I
a = 0.0239968 + 0.0485183I
b = 0.302628 − 0.382168I
−2.03507 + 1.22420I −5.30574 + 2.47978I
u = −0.997009 − 0.226554I
a = 0.0239968 − 0.0485183I
b = 0.302628 + 0.382168I
−2.03507 − 1.22420I −5.30574 − 2.47978I
u = 0.549974 + 0.797423I
a = 0.960310 + 0.778214I
b = −0.05763 + 1.60436I
−7.81669 − 2.63616I −2.57791 + 2.58719I
u = 0.549974 − 0.797423I
a = 0.960310 − 0.778214I
b = −0.05763 − 1.60436I
−7.81669 + 2.63616I −2.57791 − 2.58719I
u = 0.507571 + 0.956182I
a = −0.888380 − 0.590788I
b = 0.09789 − 1.64453I
−10.92990 − 7.37639I −5.80773 + 5.55165I
u = 0.507571 − 0.956182I
a = −0.888380 + 0.590788I
b = 0.09789 + 1.64453I
−10.92990 + 7.37639I −5.80773 − 5.55165I
u = 0.762467 + 0.844946I
a = −0.710291 − 0.815437I
b = −0.00225 − 1.64871I
−11.70310 + 1.34196I −7.30625 − 0.70220I
u = 0.762467 − 0.844946I
a = −0.710291 + 0.815437I
b = −0.00225 + 1.64871I
−11.70310 − 1.34196I −7.30625 + 0.70220I
u = 1.137860 + 0.247744I
a = 0.169104 + 1.219170I
b = 0.12340 + 1.41903I
−7.87303 + 0.41748I −9.30153 + 0.50767I
u = 1.137860 − 0.247744I
a = 0.169104 − 1.219170I
b = 0.12340 − 1.41903I
−7.87303 − 0.41748I −9.30153 − 0.50767I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455355 + 0.700282I
a = −0.905605 − 0.022977I
b = 0.366148 + 0.772313I
−2.54750 + 5.63680I −3.76761 − 8.15870I
u = −0.455355 − 0.700282I
a = −0.905605 + 0.022977I
b = 0.366148 − 0.772313I
−2.54750 − 5.63680I −3.76761 + 8.15870I
u = −0.631099 + 0.496871I
a = −0.486895 − 0.221432I
b = 0.021123 + 0.779816I
−3.17977 − 1.35362I −6.58078 + 0.48937I
u = −0.631099 − 0.496871I
a = −0.486895 + 0.221432I
b = 0.021123 − 0.779816I
−3.17977 + 1.35362I −6.58078 − 0.48937I
u = 1.247250 + 0.042571I
a = −0.20681 − 1.71804I
b = 0.102712 − 0.658984I
−2.68106 − 2.54195I −5.78064 + 4.47516I
u = 1.247250 − 0.042571I
a = −0.20681 + 1.71804I
b = 0.102712 + 0.658984I
−2.68106 + 2.54195I −5.78064 − 4.47516I
u = −0.337954 + 0.540347I
a = 0.817560 − 0.128808I
b = −0.294187 − 0.599361I
−0.16445 + 1.48990I 0.43975 − 5.27239I
u = −0.337954 − 0.540347I
a = 0.817560 + 0.128808I
b = −0.294187 + 0.599361I
−0.16445 − 1.48990I 0.43975 + 5.27239I
u = −1.38121
a = −0.0677912
b = 0.707999
−3.43392 0
u = 1.45521 + 0.17025I
a = −0.414019 − 1.121630I
b = 0.508690 − 0.861076I
−6.01336 − 4.06181I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45521 − 0.17025I
a = −0.414019 + 1.121630I
b = 0.508690 + 0.861076I
−6.01336 + 4.06181I 0
u = −1.47695 + 0.04519I
a = −0.26335 + 2.90182I
b = 0.02320 + 1.62981I
−10.76740 + 2.97655I 0
u = −1.47695 − 0.04519I
a = −0.26335 − 2.90182I
b = 0.02320 − 1.62981I
−10.76740 − 2.97655I 0
u = −1.48592 + 0.10113I
a = 0.0860114 − 0.0153300I
b = −0.823123 + 0.103447I
−6.74821 + 4.23995I 0
u = −1.48592 − 0.10113I
a = 0.0860114 + 0.0153300I
b = −0.823123 − 0.103447I
−6.74821 − 4.23995I 0
u = 0.385648 + 0.302544I
a = −1.59375 − 0.01228I
b = 0.456373 + 0.089106I
−0.52713 − 2.73009I 3.23724 + 4.11462I
u = 0.385648 − 0.302544I
a = −1.59375 + 0.01228I
b = 0.456373 − 0.089106I
−0.52713 + 2.73009I 3.23724 − 4.11462I
u = 1.52169 + 0.06207I
a = 0.267867 + 1.067660I
b = −0.490449 + 1.028460I
−10.25760 − 0.21541I 0
u = 1.52169 − 0.06207I
a = 0.267867 − 1.067660I
b = −0.490449 − 1.028460I
−10.25760 + 0.21541I 0
u = 1.51624 + 0.23392I
a = 0.450012 + 1.020390I
b = −0.618443 + 0.860508I
−9.03060 − 9.03490I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51624 − 0.23392I
a = 0.450012 − 1.020390I
b = −0.618443 − 0.860508I
−9.03060 + 9.03490I 0
u = 0.046246 + 0.427515I
a = 1.224630 − 0.289199I
b = −0.391553 − 0.302388I
0.667792 + 1.033690I 4.88372 − 5.04725I
u = 0.046246 − 0.427515I
a = 1.224630 + 0.289199I
b = −0.391553 + 0.302388I
0.667792 − 1.033690I 4.88372 + 5.04725I
u = −1.55585 + 0.27915I
a = −0.94920 + 2.04202I
b = 0.14733 + 1.66702I
−14.7091 + 6.6164I 0
u = −1.55585 − 0.27915I
a = −0.94920 − 2.04202I
b = 0.14733 − 1.66702I
−14.7091 − 6.6164I 0
u = −1.57027 + 0.34811I
a = 1.02078 − 1.83166I
b = −0.18501 − 1.67298I
−17.6792 + 12.1700I 0
u = −1.57027 − 0.34811I
a = 1.02078 + 1.83166I
b = −0.18501 + 1.67298I
−17.6792 − 12.1700I 0
u = −1.64338 + 0.21292I
a = 0.60957 − 2.00064I
b = −0.11349 − 1.71534I
19.5976 + 2.5619I 0
u = −1.64338 − 0.21292I
a = 0.60957 + 2.00064I
b = −0.11349 + 1.71534I
19.5976 − 2.5619I 0
u = 0.214248 + 0.196206I
a = 3.15567 + 3.27078I
b = −0.02735 + 1.45336I
−4.91839 − 2.21626I 0.59639 + 3.86290I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.214248 − 0.196206I
a = 3.15567 − 3.27078I
b = −0.02735 − 1.45336I
−4.91839 + 2.21626I 0.59639 − 3.86290I
9
II. I
u
2
= h−2a
3
− 3a
2
+ 5b − 15a − 7, a
4
+ 2a
3
+ 7a
2
+ 6a + 3, u − 1i
(i) Arc colorings
a
7
=
0
1
a
10
=
1
0
a
11
=
1
1
a
8
=
−1
0
a
1
=
0
1
a
4
=
a
2
5
a
3
+
3
5
a
2
+ 3a +
7
5
a
3
=
−
2
5
a
3
−
3
5
a
2
− 2a −
7
5
2
5
a
3
+
3
5
a
2
+ 3a +
7
5
a
2
=
−
2
5
a
3
−
3
5
a
2
− 2a −
7
5
4
5
a
3
+
6
5
a
2
+ 5a +
14
5
a
6
=
2
5
a
3
+
3
5
a
2
+ 2a +
2
5
−
1
5
a
3
+
1
5
a
2
− a +
9
5
a
9
=
−
1
5
a
3
+
1
5
a
2
− a −
1
5
−2
a
5
=
2
5
a
3
+
3
5
a
2
+ 2a +
7
5
−
2
5
a
3
−
3
5
a
2
− 3a −
7
5
a
5
=
2
5
a
3
+
3
5
a
2
+ 2a +
7
5
−
2
5
a
3
−
3
5
a
2
− 3a −
7
5
(ii) Obstruction class = 1
(iii) Cusp Shapes =
8
5
a
3
+
12
5
a
2
+ 8a −
12
5
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
− u + 1)
2
c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
2
c
7
(u + 1)
4
c
10
, c
11
(u − 1)
4
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y + 2)
4
c
7
, c
10
, c
11
(y −1)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.500000 + 0.548188I
b = 1.414210I
−6.57974 − 2.02988I −6.00000 + 3.46410I
u = 1.00000
a = −0.500000 − 0.548188I
b = − 1.414210I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = 1.00000
a = −0.50000 + 2.28024I
b = 1.414210I
−6.57974 + 2.02988I −6.00000 − 3.46410I
u = 1.00000
a = −0.50000 − 2.28024I
b = − 1.414210I
−6.57974 − 2.02988I −6.00000 + 3.46410I
13
III. I
u
3
= hb, a
2
+ a + 1, u + 1i
(i) Arc colorings
a
7
=
0
−1
a
10
=
1
0
a
11
=
1
1
a
8
=
1
0
a
1
=
0
1
a
4
=
a
0
a
3
=
a
0
a
2
=
a
−a
a
6
=
a + 1
−1
a
9
=
1
0
a
5
=
a
0
a
5
=
a
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a − 2
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
c
5
u
2
− u + 1
c
7
(u − 1)
2
c
10
, c
11
(u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
c
7
, c
10
, c
11
(y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.500000 + 0.866025I
b = 0
−1.64493 + 2.02988I 0. − 3.46410I
u = −1.00000
a = −0.500000 − 0.866025I
b = 0
−1.64493 − 2.02988I 0. + 3.46410I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
41
− 2u
40
+ ··· + 3u − 3)
c
2
((u
2
+ u + 1)
3
)(u
41
+ 22u
40
+ ··· − 33u − 9)
c
3
, c
4
, c
8
c
9
u
2
(u
2
+ 2)
2
(u
41
− u
40
+ ··· + 8u + 4)
c
5
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
41
− 2u
40
+ ··· + 3u − 3)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
41
+ 2u
40
+ ··· + 327u − 87)
c
7
((u − 1)
2
)(u + 1)
4
(u
41
+ 3u
40
+ ··· − 16u + 3)
c
10
, c
11
((u − 1)
4
)(u + 1)
2
(u
41
+ 3u
40
+ ··· − 16u + 3)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
41
+ 22y
40
+ ··· − 33y −9)
c
2
((y
2
+ y + 1)
3
)(y
41
− 2y
40
+ ··· + 423y −81)
c
3
, c
4
, c
8
c
9
y
2
(y + 2)
4
(y
41
+ 51y
40
+ ··· − 128y −16)
c
6
((y
2
+ y + 1)
3
)(y
41
− 26y
40
+ ··· − 166425y −7569)
c
7
, c
10
, c
11
((y −1)
6
)(y
41
− 43y
40
+ ··· + 4y −9)
19
