12a
1011
(K12a
1011
)
A knot diagram
1
Linearized knot diagam
4 6 1 9 10 11 12 2 5 3 7 8
Solving Sequence
4,9
5 10
2,6
1 3 11 8 12 7
c
4
c
9
c
5
c
1
c
3
c
10
c
8
c
12
c
7
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.77473 × 10
61
u
59
− 1.16877 × 10
62
u
58
+ ··· + 1.10219 × 10
62
b + 6.06781 × 10
61
,
− 4.84379 × 10
62
u
59
− 8.34198 × 10
62
u
58
+ ··· + 1.10219 × 10
62
a − 4.12695 × 10
62
, u
60
+ 3u
59
+ ··· − 3u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 60 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−7.77 × 10
61
u
59
− 1.17 × 10
62
u
58
+ · · · + 1.10 × 10
62
b + 6.07 ×
10
61
, −4.84 × 10
62
u
59
− 8.34 × 10
62
u
58
+ · · · + 1.10 × 10
62
a − 4.13 ×
10
62
, u
60
+ 3u
59
+ · · · − 3u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
10
=
−u
−u
3
+ u
a
2
=
4.39469u
59
+ 7.56854u
58
+ ··· + 8.66548u + 3.74431
0.705389u
59
+ 1.06041u
58
+ ··· − 0.422370u − 0.550522
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
5.10008u
59
+ 8.62895u
58
+ ··· + 8.24311u + 3.19379
0.705389u
59
+ 1.06041u
58
+ ··· − 0.422370u − 0.550522
a
3
=
4.47039u
59
+ 7.66384u
58
+ ··· + 8.64302u + 3.82572
0.718475u
59
+ 1.08549u
58
+ ··· − 0.368583u − 0.582231
a
11
=
20.7074u
59
+ 33.8191u
58
+ ··· − 16.5794u + 18.9472
5.56972u
59
+ 9.32309u
58
+ ··· − 1.10592u + 3.61027
a
8
=
−23.4227u
59
− 42.3566u
58
+ ··· + 10.6283u − 7.72848
−4.67738u
59
− 6.39518u
58
+ ··· + 4.40795u − 3.75191
a
12
=
−10.1429u
59
− 9.17229u
58
+ ··· + 11.5219u − 14.4523
−0.651171u
59
− 1.19686u
58
+ ··· − 0.432522u − 0.670575
a
7
=
−12.9717u
59
− 14.7561u
58
+ ··· + 10.0296u − 7.51652
−0.657819u
59
− 0.638710u
58
+ ··· + 0.0831336u − 0.551955
(ii) Obstruction class = −1
(iii) Cusp Shapes = −22.6173u
59
− 27.6772u
58
+ ··· + 28.8485u − 22.3361
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
60
− u
59
+ ··· − 66u + 1
c
2
u
60
− 5u
59
+ ··· + 4u + 1
c
4
, c
5
, c
9
u
60
− 3u
59
+ ··· − 3u
2
+ 1
c
6
, c
7
, c
11
c
12
u
60
+ u
59
+ ··· − 3u
2
+ 1
c
8
u
60
+ 47u
59
+ ··· + 11412u + 5859
c
10
u
60
− 51u
59
+ ··· + 30u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
60
− 39y
59
+ ··· − 3658y + 1
c
2
y
60
− 3y
59
+ ··· − 290y + 1
c
4
, c
5
, c
9
y
60
− 63y
59
+ ··· − 6y + 1
c
6
, c
7
, c
11
c
12
y
60
− 71y
59
+ ··· − 6y + 1
c
8
y
60
− 1879y
59
+ ··· + 397673874y + 34327881
c
10
y
60
− 1963y
59
+ ··· − 206y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.662817 + 0.762698I
a = −0.245728 + 1.250330I
b = 1.193830 − 0.447828I
−0.73206 + 8.12056I 0
u = −0.662817 − 0.762698I
a = −0.245728 − 1.250330I
b = 1.193830 + 0.447828I
−0.73206 − 8.12056I 0
u = −0.323840 + 0.957327I
a = −0.572957 − 0.024249I
b = 0.961555 + 0.221982I
0.23239 − 2.63217I 0
u = −0.323840 − 0.957327I
a = −0.572957 + 0.024249I
b = 0.961555 − 0.221982I
0.23239 + 2.63217I 0
u = 0.624560 + 0.748947I
a = −0.28039 − 1.52487I
b = 1.269310 + 0.591379I
7.64094 − 11.03190I 0
u = 0.624560 − 0.748947I
a = −0.28039 + 1.52487I
b = 1.269310 − 0.591379I
7.64094 + 11.03190I 0
u = 0.425213 + 0.838580I
a = −0.930124 + 0.154932I
b = 1.112760 − 0.474637I
8.24888 + 5.81523I 0
u = 0.425213 − 0.838580I
a = −0.930124 − 0.154932I
b = 1.112760 + 0.474637I
8.24888 − 5.81523I 0
u = 0.758315 + 0.809811I
a = −0.166292 − 0.849057I
b = 1.073790 + 0.249690I
−2.79981 − 3.45771I 0
u = 0.758315 − 0.809811I
a = −0.166292 + 0.849057I
b = 1.073790 − 0.249690I
−2.79981 + 3.45771I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.442644 + 0.577967I
a = −0.37374 + 1.43406I
b = 0.205523 − 1.112540I
11.00280 − 5.06190I 5.82530 + 5.53323I
u = 0.442644 − 0.577967I
a = −0.37374 − 1.43406I
b = 0.205523 + 1.112540I
11.00280 + 5.06190I 5.82530 − 5.53323I
u = 0.533556 + 0.494030I
a = 1.36268 − 1.13267I
b = 0.302652 + 0.710487I
10.70280 + 1.31241I 5.99165 + 2.38877I
u = 0.533556 − 0.494030I
a = 1.36268 + 1.13267I
b = 0.302652 − 0.710487I
10.70280 − 1.31241I 5.99165 − 2.38877I
u = −0.634510 + 0.307234I
a = 1.041510 + 0.447956I
b = 0.306128 − 0.284056I
1.84584 − 0.16634I 5.58998 − 1.16164I
u = −0.634510 − 0.307234I
a = 1.041510 − 0.447956I
b = 0.306128 + 0.284056I
1.84584 + 0.16634I 5.58998 + 1.16164I
u = −0.388734 + 0.547219I
a = −0.102961 − 1.234950I
b = 0.108665 + 0.851721I
2.57666 + 3.48003I 5.40845 − 7.70107I
u = −0.388734 − 0.547219I
a = −0.102961 + 1.234950I
b = 0.108665 − 0.851721I
2.57666 − 3.48003I 5.40845 + 7.70107I
u = −0.534688 + 0.300236I
a = 0.71450 − 1.75929I
b = −1.106720 + 0.780537I
5.77449 + 3.36958I −0.25480 − 6.43595I
u = −0.534688 − 0.300236I
a = 0.71450 + 1.75929I
b = −1.106720 − 0.780537I
5.77449 − 3.36958I −0.25480 + 6.43595I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.393360 + 0.104061I
a = 0.442020 + 0.476538I
b = −0.039469 − 0.361226I
−3.67380 − 0.55006I 0
u = 1.393360 − 0.104061I
a = 0.442020 − 0.476538I
b = −0.039469 + 0.361226I
−3.67380 + 0.55006I 0
u = 1.40808
a = 30.7026
b = −1.00235
2.29829 0
u = 0.590101
a = 0.794250
b = −1.54497
4.22265 −2.84470
u = −1.43641
a = 1.11782
b = 0.0164917
3.96509 0
u = −1.44502
a = −4.23868
b = −1.06556
−5.74141 0
u = −1.45489 + 0.12717I
a = −0.006934 − 0.704892I
b = −0.259620 + 0.860546I
−5.64401 + 3.03216I 0
u = −1.45489 − 0.12717I
a = −0.006934 + 0.704892I
b = −0.259620 − 0.860546I
−5.64401 − 3.03216I 0
u = 0.478326 + 0.237534I
a = 0.52704 + 1.65194I
b = −1.083170 − 0.489709I
−1.59831 − 2.29626I −3.55521 + 9.11938I
u = 0.478326 − 0.237534I
a = 0.52704 − 1.65194I
b = −1.083170 + 0.489709I
−1.59831 + 2.29626I −3.55521 − 9.11938I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.259388 + 0.444396I
a = 0.505889 + 0.793558I
b = −0.034493 − 0.340622I
0.027752 − 1.012700I 0.66910 + 6.22370I
u = 0.259388 − 0.444396I
a = 0.505889 − 0.793558I
b = −0.034493 + 0.340622I
0.027752 + 1.012700I 0.66910 − 6.22370I
u = 1.47743 + 0.15557I
a = −0.206202 + 0.601749I
b = −0.063839 − 1.211260I
−3.53480 − 5.95076I 0
u = 1.47743 − 0.15557I
a = −0.206202 − 0.601749I
b = −0.063839 + 1.211260I
−3.53480 + 5.95076I 0
u = −1.49269 + 0.17073I
a = −0.332630 − 0.562691I
b = 0.09351 + 1.43171I
4.66007 + 7.72555I 0
u = −1.49269 − 0.17073I
a = −0.332630 + 0.562691I
b = 0.09351 − 1.43171I
4.66007 − 7.72555I 0
u = 1.50347 + 0.02704I
a = −0.667227 + 0.507062I
b = −1.51372 − 0.34479I
−8.86338 − 0.56778I 0
u = 1.50347 − 0.02704I
a = −0.667227 − 0.507062I
b = −1.51372 + 0.34479I
−8.86338 + 0.56778I 0
u = −1.50768 + 0.05542I
a = −0.395766 − 0.775044I
b = −1.39878 + 0.72856I
−8.19989 + 3.27836I 0
u = −1.50768 − 0.05542I
a = −0.395766 + 0.775044I
b = −1.39878 − 0.72856I
−8.19989 − 3.27836I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42531 + 0.50921I
a = 0.093353 + 0.311150I
b = 0.942971 + 0.154173I
2.40478 − 1.15829I 0
u = −1.42531 − 0.50921I
a = 0.093353 − 0.311150I
b = 0.942971 − 0.154173I
2.40478 + 1.15829I 0
u = 1.52042 + 0.07500I
a = −0.249231 + 0.817995I
b = −1.37975 − 1.09877I
−1.05380 − 4.66299I 0
u = 1.52042 − 0.07500I
a = −0.249231 − 0.817995I
b = −1.37975 + 1.09877I
−1.05380 + 4.66299I 0
u = −1.52983
a = −0.336902
b = −1.95863
−2.82018 0
u = −0.436498 + 0.086603I
a = −0.399175 − 1.008990I
b = −1.189670 + 0.142954I
−2.36701 + 0.14297I −6.07641 + 3.65912I
u = −0.436498 − 0.086603I
a = −0.399175 + 1.008990I
b = −1.189670 − 0.142954I
−2.36701 − 0.14297I −6.07641 − 3.65912I
u = −0.158972 + 0.403171I
a = 4.83010 − 0.90232I
b = −1.027510 − 0.307952I
6.91858 − 0.97657I 7.47505 − 6.61019I
u = −0.158972 − 0.403171I
a = 4.83010 + 0.90232I
b = −1.027510 + 0.307952I
6.91858 + 0.97657I 7.47505 + 6.61019I
u = −1.57145 + 0.25178I
a = 0.575689 + 1.150720I
b = 1.41270 − 0.64234I
0.4156 + 14.7437I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57145 − 0.25178I
a = 0.575689 − 1.150720I
b = 1.41270 + 0.64234I
0.4156 − 14.7437I 0
u = 1.58219 + 0.25441I
a = 0.517989 − 1.039430I
b = 1.38366 + 0.52744I
−8.1120 − 11.9056I 0
u = 1.58219 − 0.25441I
a = 0.517989 + 1.039430I
b = 1.38366 − 0.52744I
−8.1120 + 11.9056I 0
u = −1.59853 + 0.26019I
a = 0.456687 + 0.894494I
b = 1.332230 − 0.391330I
−10.46850 + 7.42938I 0
u = −1.59853 − 0.26019I
a = 0.456687 − 0.894494I
b = 1.332230 + 0.391330I
−10.46850 − 7.42938I 0
u = 1.63860 + 0.26637I
a = 0.439098 − 0.662224I
b = 1.195760 + 0.242342I
−7.27899 − 2.94729I 0
u = 1.63860 − 0.26637I
a = 0.439098 + 0.662224I
b = 1.195760 − 0.242342I
−7.27899 + 2.94729I 0
u = 0.152092 + 0.297135I
a = 5.08934 + 3.12341I
b = −0.962464 + 0.100967I
−0.648981 + 0.439546I 0.5531 + 16.3580I
u = 0.152092 − 0.297135I
a = 5.08934 − 3.12341I
b = −0.962464 − 0.100967I
−0.648981 − 0.439546I 0.5531 − 16.3580I
u = −1.78480
a = 0.627868
b = 0.883346
3.12322 0
10
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
u
60
− u
59
+ ··· − 66u + 1
c
2
u
60
− 5u
59
+ ··· + 4u + 1
c
4
, c
5
, c
9
u
60
− 3u
59
+ ··· − 3u
2
+ 1
c
6
, c
7
, c
11
c
12
u
60
+ u
59
+ ··· − 3u
2
+ 1
c
8
u
60
+ 47u
59
+ ··· + 11412u + 5859
c
10
u
60
− 51u
59
+ ··· + 30u + 1
11
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
60
− 39y
59
+ ··· − 3658y + 1
c
2
y
60
− 3y
59
+ ··· − 290y + 1
c
4
, c
5
, c
9
y
60
− 63y
59
+ ··· − 6y + 1
c
6
, c
7
, c
11
c
12
y
60
− 71y
59
+ ··· − 6y + 1
c
8
y
60
− 1879y
59
+ ··· + 397673874y + 34327881
c
10
y
60
− 1963y
59
+ ··· − 206y + 1
12
