12n
0366
(K12n
0366
)
A knot diagram
1
Linearized knot diagam
3 5 8 10 2 11 3 4 12 7 5 9
Solving Sequence
4,9
8 3
1,7
12 10 5 2 6 11
c
8
c
3
c
7
c
12
c
9
c
4
c
2
c
5
c
11
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h8.60410 × 10
36
u
33
− 9.82765 × 10
36
u
32
+ ··· + 2.12256 × 10
38
b + 1.92039 × 10
38
,
3.53556 × 10
37
u
33
+ 3.38592 × 10
37
u
32
+ ··· + 8.49024 × 10
38
a − 2.51443 × 10
39
, u
34
− u
33
+ ··· + 14u − 4i
I
u
2
= h−41317u
19
+ 14868u
18
+ ··· + 102043b − 217021,
− 20816u
19
+ 54137u
18
+ ··· + 204086a + 123227, u
20
− 10u
18
+ ··· + 6u + 4i
* 2 irreducible components of dim
C
= 0, with total 54 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
= h8.60 × 10
36
u
33
− 9.83 × 10
36
u
32
+ · · · + 2.12 × 10
38
b + 1.92 × 10
38
, 3.54 ×
10
37
u
33
+3.39×10
37
u
32
+· · ·+8.49×10
38
a−2.51×10
39
, u
34
−u
33
+· · ·+14u−4i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
−0.0416427u
33
− 0.0398802u
32
+ ··· + 1.58286u + 2.96155
−0.0405364u
33
+ 0.0463009u
32
+ ··· + 1.98650u − 0.904754
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
12
=
−0.00110628u
33
− 0.0861811u
32
+ ··· − 0.403640u + 3.86631
−0.0405364u
33
+ 0.0463009u
32
+ ··· + 1.98650u − 0.904754
a
10
=
0.322523u
33
− 0.187269u
32
+ ··· − 12.1237u + 3.64934
−0.0561189u
33
+ 0.0359757u
32
+ ··· + 2.41252u − 0.0498318
a
5
=
0.309604u
33
− 0.157316u
32
+ ··· − 11.9411u + 1.11047
−0.115816u
33
− 0.0301325u
32
+ ··· + 2.98843u + 0.206879
a
2
=
0.0473120u
33
− 0.0631917u
32
+ ··· + 0.283713u + 3.39961
−0.0678345u
33
+ 0.0620244u
32
+ ··· + 2.72246u − 1.08024
a
6
=
−0.00781040u
33
+ 0.0389021u
32
+ ··· − 0.701468u − 1.89917
−0.203245u
33
− 0.107497u
32
+ ··· + 1.28592u − 0.355887
a
11
=
0.361377u
33
− 0.196045u
32
+ ··· − 11.6891u + 3.77920
−0.219182u
33
+ 0.0237395u
32
+ ··· + 3.96379u − 0.616850
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.349003u
33
+ 0.651298u
32
+ ··· − 1.59052u + 10.7798
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
+ 52u
33
+ ··· − 125583u + 7921
c
2
, c
5
u
34
+ 2u
33
+ ··· + 91u + 89
c
3
, c
7
, c
8
u
34
+ u
33
+ ··· − 14u − 4
c
4
u
34
− u
33
+ ··· − 1046u − 137
c
6
, c
10
u
34
− u
33
+ ··· + 75u + 17
c
9
, c
12
u
34
+ 3u
33
+ ··· + 11u + 1
c
11
u
34
+ u
33
+ ··· − 5852u + 764
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
− 152y
33
+ ··· − 3985291411y + 62742241
c
2
, c
5
y
34
+ 52y
33
+ ··· − 125583y + 7921
c
3
, c
7
, c
8
y
34
− 23y
33
+ ··· − 140y + 16
c
4
y
34
+ 11y
33
+ ··· − 925058y + 18769
c
6
, c
10
y
34
+ 57y
33
+ ··· − 16675y + 289
c
9
, c
12
y
34
+ 25y
33
+ ··· + 223y + 1
c
11
y
34
+ 73y
33
+ ··· + 16521896y + 583696
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.922036 + 0.452881I
a = −1.95374 + 1.73996I
b = 0.050107 − 0.380343I
−10.10770 − 1.83068I −1.32953 + 4.89170I
u = −0.922036 − 0.452881I
a = −1.95374 − 1.73996I
b = 0.050107 + 0.380343I
−10.10770 + 1.83068I −1.32953 − 4.89170I
u = 1.06806
a = −1.57173
b = −1.48329
5.61986 15.0470
u = −0.684975 + 0.829271I
a = 1.26384 − 0.77066I
b = 0.61689 − 1.83184I
−6.65191 − 3.35398I 5.96369 + 3.28451I
u = −0.684975 − 0.829271I
a = 1.26384 + 0.77066I
b = 0.61689 + 1.83184I
−6.65191 + 3.35398I 5.96369 − 3.28451I
u = 0.737579 + 0.460594I
a = −0.619611 + 0.405450I
b = 0.306540 − 0.990036I
−4.82144 − 1.46148I 3.54664 − 1.80098I
u = 0.737579 − 0.460594I
a = −0.619611 − 0.405450I
b = 0.306540 + 0.990036I
−4.82144 + 1.46148I 3.54664 + 1.80098I
u = −1.123130 + 0.394227I
a = 1.244230 − 0.472944I
b = 0.304757 − 1.086760I
0.20788 − 1.57648I 10.97463 + 0.65835I
u = −1.123130 − 0.394227I
a = 1.244230 + 0.472944I
b = 0.304757 + 1.086760I
0.20788 + 1.57648I 10.97463 − 0.65835I
u = 0.929580 + 0.767374I
a = 2.11679 − 0.95570I
b = 1.91672 − 0.56786I
−12.29770 + 2.91676I 6.61132 − 2.45322I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929580 − 0.767374I
a = 2.11679 + 0.95570I
b = 1.91672 + 0.56786I
−12.29770 − 2.91676I 6.61132 + 2.45322I
u = 1.21069
a = −2.25852
b = −1.75624
6.57930 4.63880
u = 1.083810 + 0.540124I
a = 1.67600 + 0.04657I
b = 0.496553 + 0.990924I
−3.48312 + 5.52227I 3.76620 − 5.89114I
u = 1.083810 − 0.540124I
a = 1.67600 − 0.04657I
b = 0.496553 − 0.990924I
−3.48312 − 5.52227I 3.76620 + 5.89114I
u = 1.25801
a = −1.22256
b = −1.08785
5.55227 15.4310
u = 0.553050 + 0.482320I
a = 0.680935 − 0.534063I
b = 0.442741 − 0.243060I
−2.01055 + 1.80457I 7.37027 − 4.67563I
u = 0.553050 − 0.482320I
a = 0.680935 + 0.534063I
b = 0.442741 + 0.243060I
−2.01055 − 1.80457I 7.37027 + 4.67563I
u = −0.399666 + 0.569326I
a = −1.124570 − 0.795239I
b = −0.495351 + 1.172960I
−2.05097 − 2.54093I 8.54961 + 2.56274I
u = −0.399666 − 0.569326I
a = −1.124570 + 0.795239I
b = −0.495351 − 1.172960I
−2.05097 + 2.54093I 8.54961 − 2.56274I
u = 1.271090 + 0.324893I
a = −1.326110 − 0.185075I
b = −0.562882 − 1.237790I
1.94144 + 5.55900I 17.2677 − 4.1054I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.271090 − 0.324893I
a = −1.326110 + 0.185075I
b = −0.562882 + 1.237790I
1.94144 − 5.55900I 17.2677 + 4.1054I
u = −1.133490 + 0.786019I
a = −1.17308 + 1.24490I
b = −0.45959 + 1.84212I
−5.26755 − 2.76815I 6.74305 + 1.96876I
u = −1.133490 − 0.786019I
a = −1.17308 − 1.24490I
b = −0.45959 − 1.84212I
−5.26755 + 2.76815I 6.74305 − 1.96876I
u = 0.088561 + 1.396340I
a = 0.226588 − 0.656943I
b = 0.51304 − 1.81326I
19.1288 − 5.4062I 6.05474 + 2.05125I
u = 0.088561 − 1.396340I
a = 0.226588 + 0.656943I
b = 0.51304 + 1.81326I
19.1288 + 5.4062I 6.05474 − 2.05125I
u = −1.51491 + 0.11448I
a = 0.207183 + 0.310262I
b = 0.0322077 − 0.0682113I
4.60570 − 3.56043I 15.4789 + 7.9563I
u = −1.51491 − 0.11448I
a = 0.207183 − 0.310262I
b = 0.0322077 + 0.0682113I
4.60570 + 3.56043I 15.4789 − 7.9563I
u = 1.47491 + 0.70325I
a = 1.73912 + 0.75900I
b = 0.93744 + 1.60343I
−16.0299 + 12.7557I 10.00000 − 5.13495I
u = 1.47491 − 0.70325I
a = 1.73912 − 0.75900I
b = 0.93744 − 1.60343I
−16.0299 − 12.7557I 10.00000 + 5.13495I
u = −0.345078
a = 0.490141
b = −0.241609
0.549407 18.2220
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.169258 + 0.230162I
a = 3.30928 − 1.57909I
b = −0.261095 + 0.870304I
−1.73764 − 2.47115I 11.65169 + 4.43713I
u = 0.169258 − 0.230162I
a = 3.30928 + 1.57909I
b = −0.261095 − 0.870304I
−1.73764 + 2.47115I 11.65169 − 4.43713I
u = −1.62548 + 0.63340I
a = −0.73552 + 1.36542I
b = −0.05359 + 1.57787I
−14.9890 − 1.9387I 0
u = −1.62548 − 0.63340I
a = −0.73552 − 1.36542I
b = −0.05359 − 1.57787I
−14.9890 + 1.9387I 0
8
II.
I
u
2
= h−4.13 × 10
4
u
19
+ 1.49 × 10
4
u
18
+ · · · + 1.02 × 10
5
b − 2.17 × 10
5
, −2.08 ×
10
4
u
19
+5.41×10
4
u
18
+· · ·+2.04×10
5
a+1.23×10
5
, u
20
−10u
18
+· · ·+6u+4i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
0.101996u
19
− 0.265266u
18
+ ··· − 1.49571u − 0.603799
0.404898u
19
− 0.145703u
18
+ ··· − 2.53587u + 2.12676
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
12
=
−0.302902u
19
− 0.119562u
18
+ ··· + 1.04016u − 2.73056
0.404898u
19
− 0.145703u
18
+ ··· − 2.53587u + 2.12676
a
10
=
0.992150u
19
− 0.400944u
18
+ ··· − 2.37768u + 4.62098
−0.0780847u
19
− 0.198152u
18
+ ··· − 3.56977u − 1.72914
a
5
=
−0.501860u
19
+ 0.227585u
18
+ ··· − 1.29265u − 2.70449
−0.400944u
19
− 0.417304u
18
+ ··· + 6.66808u + 0.0313985
a
2
=
0.0242741u
19
− 0.129666u
18
+ ··· + 0.735984u − 0.802951
0.810158u
19
+ 0.0423449u
18
+ ··· − 5.27028u + 1.78351
a
6
=
−0.554884u
19
− 0.0858119u
18
+ ··· + 1.98350u + 0.737253
−1.23375u
19
− 0.323609u
18
+ ··· + 12.8278u + 0.0295856
a
11
=
0.664975u
19
− 0.390840u
18
+ ··· − 3.07351u + 2.69337
−0.414012u
19
+ 0.324383u
18
+ ··· − 4.90638u − 4.90765
(ii) Obstruction class = 1
(iii) Cusp Shapes =
150899
102043
u
19
+
457156
102043
u
18
+ ··· −
3098728
102043
u −
1725625
102043
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 15u
19
+ ··· − 10u + 1
c
2
u
20
+ u
19
+ ··· + 2u − 1
c
3
u
20
− 10u
18
+ ··· − 6u + 4
c
4
u
20
− 3u
18
+ ··· + u − 1
c
5
u
20
− u
19
+ ··· − 2u − 1
c
6
u
20
+ 8u
18
+ ··· − 2u − 1
c
7
, c
8
u
20
− 10u
18
+ ··· + 6u + 4
c
9
u
20
+ 4u
19
+ ··· + 6u
2
+ 1
c
10
u
20
+ 8u
18
+ ··· + 2u − 1
c
11
u
20
+ 6u
18
+ ··· − 20u − 112
c
12
u
20
− 4u
19
+ ··· + 6u
2
+ 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 33y
19
+ ··· + 22y + 1
c
2
, c
5
y
20
+ 15y
19
+ ··· + 10y + 1
c
3
, c
7
, c
8
y
20
− 20y
19
+ ··· − 124y + 16
c
4
y
20
− 6y
19
+ ··· − 13y + 1
c
6
, c
10
y
20
+ 16y
19
+ ··· + 10y + 1
c
9
, c
12
y
20
+ 4y
19
+ ··· + 12y + 1
c
11
y
20
+ 12y
19
+ ··· − 34224y + 12544
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.612301 + 0.818596I
a = −0.067302 − 0.254585I
b = −0.401431 − 1.017480I
−3.53566 − 0.22064I 5.65649 + 1.54234I
u = −0.612301 − 0.818596I
a = −0.067302 + 0.254585I
b = −0.401431 + 1.017480I
−3.53566 + 0.22064I 5.65649 − 1.54234I
u = 1.002890 + 0.425695I
a = 1.91303 + 1.46841I
b = 0.629652 − 0.151473I
−9.59237 + 1.63826I 13.10729 + 0.49726I
u = 1.002890 − 0.425695I
a = 1.91303 − 1.46841I
b = 0.629652 + 0.151473I
−9.59237 − 1.63826I 13.10729 − 0.49726I
u = −1.207850 + 0.102646I
a = 2.03086 − 0.75278I
b = 0.745320 − 1.075030I
−2.13884 − 3.22223I 8.01422 + 2.52111I
u = −1.207850 − 0.102646I
a = 2.03086 + 0.75278I
b = 0.745320 + 1.075030I
−2.13884 + 3.22223I 8.01422 − 2.52111I
u = −1.039500 + 0.630586I
a = −1.55688 + 0.02679I
b = −0.738283 + 0.944855I
−2.28953 − 5.18286I 10.14826 + 4.21922I
u = −1.039500 − 0.630586I
a = −1.55688 − 0.02679I
b = −0.738283 − 0.944855I
−2.28953 + 5.18286I 10.14826 − 4.21922I
u = 1.22442
a = −2.03415
b = −1.74489
6.94299 27.7690
u = 0.733786
a = −2.65242
b = −1.84135
4.93941 2.40420
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.308800 + 0.304453I
a = −1.192490 − 0.050495I
b = −0.464800 − 1.223010I
1.37495 + 5.83178I 5.48272 − 8.86173I
u = 1.308800 − 0.304453I
a = −1.192490 + 0.050495I
b = −0.464800 + 1.223010I
1.37495 − 5.83178I 5.48272 + 8.86173I
u = 0.116813 + 0.627556I
a = 1.09932 − 1.18449I
b = −0.198146 + 0.916761I
−2.55287 − 2.35473I 1.50587 + 2.86724I
u = 0.116813 − 0.627556I
a = 1.09932 + 1.18449I
b = −0.198146 − 0.916761I
−2.55287 + 2.35473I 1.50587 − 2.86724I
u = −0.596398 + 0.154090I
a = −1.018880 + 0.068684I
b = 0.363803 + 1.056440I
−4.37423 + 2.18819I 9.13692 − 5.14183I
u = −0.596398 − 0.154090I
a = −1.018880 − 0.068684I
b = 0.363803 − 1.056440I
−4.37423 − 2.18819I 9.13692 + 5.14183I
u = −1.52607 + 0.20387I
a = 0.791649 − 0.377958I
b = −0.000385 − 0.551221I
3.15923 − 0.69222I 7.75845 + 0.32737I
u = −1.52607 − 0.20387I
a = 0.791649 + 0.377958I
b = −0.000385 + 0.551221I
3.15923 + 0.69222I 7.75845 − 0.32737I
u = 1.57451 + 0.13378I
a = −0.156023 + 0.726050I
b = −0.142609 + 0.648848I
4.13850 + 3.24894I 3.10320 + 0.10633I
u = 1.57451 − 0.13378I
a = −0.156023 − 0.726050I
b = −0.142609 − 0.648848I
4.13850 − 3.24894I 3.10320 − 0.10633I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 15u
19
+ ··· − 10u + 1)(u
34
+ 52u
33
+ ··· − 125583u + 7921)
c
2
(u
20
+ u
19
+ ··· + 2u − 1)(u
34
+ 2u
33
+ ··· + 91u + 89)
c
3
(u
20
− 10u
18
+ ··· − 6u + 4)(u
34
+ u
33
+ ··· − 14u − 4)
c
4
(u
20
− 3u
18
+ ··· + u − 1)(u
34
− u
33
+ ··· − 1046u − 137)
c
5
(u
20
− u
19
+ ··· − 2u − 1)(u
34
+ 2u
33
+ ··· + 91u + 89)
c
6
(u
20
+ 8u
18
+ ··· − 2u − 1)(u
34
− u
33
+ ··· + 75u + 17)
c
7
, c
8
(u
20
− 10u
18
+ ··· + 6u + 4)(u
34
+ u
33
+ ··· − 14u − 4)
c
9
(u
20
+ 4u
19
+ ··· + 6u
2
+ 1)(u
34
+ 3u
33
+ ··· + 11u + 1)
c
10
(u
20
+ 8u
18
+ ··· + 2u − 1)(u
34
− u
33
+ ··· + 75u + 17)
c
11
(u
20
+ 6u
18
+ ··· − 20u − 112)(u
34
+ u
33
+ ··· − 5852u + 764)
c
12
(u
20
− 4u
19
+ ··· + 6u
2
+ 1)(u
34
+ 3u
33
+ ··· + 11u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
− 33y
19
+ ··· + 22y + 1)
· (y
34
− 152y
33
+ ··· − 3985291411y + 62742241)
c
2
, c
5
(y
20
+ 15y
19
+ ··· + 10y + 1)(y
34
+ 52y
33
+ ··· − 125583y + 7921)
c
3
, c
7
, c
8
(y
20
− 20y
19
+ ··· − 124y + 16)(y
34
− 23y
33
+ ··· − 140y + 16)
c
4
(y
20
− 6y
19
+ ··· − 13y + 1)(y
34
+ 11y
33
+ ··· − 925058y + 18769)
c
6
, c
10
(y
20
+ 16y
19
+ ··· + 10y + 1)(y
34
+ 57y
33
+ ··· − 16675y + 289)
c
9
, c
12
(y
20
+ 4y
19
+ ··· + 12y + 1)(y
34
+ 25y
33
+ ··· + 223y + 1)
c
11
(y
20
+ 12y
19
+ ··· − 34224y + 12544)
· (y
34
+ 73y
33
+ ··· + 16521896y + 583696)
15
