12a
1009
(K12a
1009
)
A knot diagram
1
Linearized knot diagam
4 6 12 1 9 10 11 3 2 7 8 5
Solving Sequence
7,10
11 8 12
2,6
3 4 1 9 5
c
10
c
7
c
11
c
6
c
2
c
3
c
1
c
9
c
5
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.83377 × 10
70
u
70
− 9.54793 × 10
70
u
69
+ ··· + 1.77999 × 10
69
b + 4.28601 × 10
70
,
− 1.01200 × 10
71
u
70
− 3.39563 × 10
71
u
69
+ ··· + 5.33996 × 10
69
a + 1.38029 × 10
71
,
u
71
+ 4u
70
+ ··· − 11u − 1i
I
u
2
= hb − a, a
3
− a
2
+ 1, u + 1i
* 2 irreducible components of dim
C
= 0, with total 74 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−2.83 × 10
70
u
70
− 9.55 × 10
70
u
69
+ · · · + 1.78 × 10
69
b + 4.29 ×
10
70
, −1.01 × 10
71
u
70
− 3.40 × 10
71
u
69
+ · · · + 5.34 × 10
69
a + 1.38 ×
10
71
, u
71
+ 4u
70
+ · · · − 11u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
8
=
−u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
18.9514u
70
+ 63.5891u
69
+ ··· − 271.927u − 25.8484
15.9202u
70
+ 53.6404u
69
+ ··· − 234.194u − 24.0789
a
6
=
u
u
a
3
=
17.2006u
70
+ 58.3127u
69
+ ··· − 251.019u − 23.6721
14.1693u
70
+ 48.3641u
69
+ ··· − 213.286u − 21.9026
a
4
=
19.8181u
70
+ 66.3472u
69
+ ··· − 282.283u − 27.5349
18.5251u
70
+ 62.2805u
69
+ ··· − 268.012u − 27.5305
a
1
=
1.01917u
70
+ 3.16140u
69
+ ··· − 3.40337u + 1.44731
1.16536u
70
+ 3.78779u
69
+ ··· − 5.87924u − 0.221025
a
9
=
5.05082u
70
+ 17.2412u
69
+ ··· − 52.3212u − 5.84505
6.62995u
70
+ 22.6456u
69
+ ··· − 101.441u − 10.8064
a
5
=
2.46549u
70
+ 7.58181u
69
+ ··· − 26.3911u − 4.12137
2.46549u
70
+ 7.58181u
69
+ ··· − 26.3911u − 3.12137
(ii) Obstruction class = −1
(iii) Cusp Shapes = −97.9174u
70
− 336.151u
69
+ ··· + 1510.09u + 154.499
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
71
− 2u
70
+ ··· − 8u − 1
c
2
u
71
− 5u
70
+ ··· + 12u − 8
c
3
u
71
+ 2u
70
+ ··· − 14304u − 929
c
5
u
71
− 4u
70
+ ··· + 3u − 1
c
6
, c
7
, c
10
c
11
u
71
+ 4u
70
+ ··· − 11u − 1
c
8
u
71
− 22u
69
+ ··· − 460924u − 201793
c
9
u
71
− 2u
70
+ ··· − 1978u − 169
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
71
+ 60y
70
+ ··· + 40y −1
c
2
y
71
+ 21y
70
+ ··· + 720y −64
c
3
y
71
− 36y
70
+ ··· + 30160512y −863041
c
5
y
71
+ 2y
70
+ ··· − 3y −1
c
6
, c
7
, c
10
c
11
y
71
− 86y
70
+ ··· − 3y −1
c
8
y
71
− 44y
70
+ ··· − 833663350352y −40720414849
c
9
y
71
− 96y
70
+ ··· + 7503396y −28561
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.916330 + 0.404967I
a = 1.41839 − 0.68949I
b = 1.089920 + 0.667509I
−2.48396 − 4.29702I 0
u = 0.916330 − 0.404967I
a = 1.41839 + 0.68949I
b = 1.089920 − 0.667509I
−2.48396 + 4.29702I 0
u = −0.797905 + 0.667654I
a = 0.407468 + 0.747440I
b = 0.939564 + 0.123379I
−0.64412 + 3.87490I 0
u = −0.797905 − 0.667654I
a = 0.407468 − 0.747440I
b = 0.939564 − 0.123379I
−0.64412 − 3.87490I 0
u = 0.919544 + 0.509968I
a = −1.38427 + 0.50220I
b = −1.18719 − 0.81000I
−4.93660 − 8.62281I 0
u = 0.919544 − 0.509968I
a = −1.38427 − 0.50220I
b = −1.18719 + 0.81000I
−4.93660 + 8.62281I 0
u = 0.899669 + 0.567468I
a = 1.343630 − 0.396527I
b = 1.21545 + 0.90921I
0.03199 − 12.75630I 0
u = 0.899669 − 0.567468I
a = 1.343630 + 0.396527I
b = 1.21545 − 0.90921I
0.03199 + 12.75630I 0
u = −0.902665 + 0.602685I
a = −0.299774 − 0.774692I
b = −0.802092 − 0.207826I
−4.42813 + 0.27103I 0
u = −0.902665 − 0.602685I
a = −0.299774 + 0.774692I
b = −0.802092 + 0.207826I
−4.42813 − 0.27103I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16620
a = −0.362381
b = 0.0637371
−2.18683 0
u = −1.013430 + 0.583657I
a = 0.183762 + 0.842968I
b = 0.696701 + 0.328940I
−0.31480 − 3.35362I 0
u = −1.013430 − 0.583657I
a = 0.183762 − 0.842968I
b = 0.696701 − 0.328940I
−0.31480 + 3.35362I 0
u = 0.811667 + 0.167450I
a = 1.56180 − 1.25295I
b = 0.749957 + 0.379899I
−1.94355 − 3.45136I 0
u = 0.811667 − 0.167450I
a = 1.56180 + 1.25295I
b = 0.749957 − 0.379899I
−1.94355 + 3.45136I 0
u = 0.012443 + 0.826554I
a = 0.185238 − 0.013310I
b = −0.906553 + 0.727576I
2.73486 + 8.14282I 0
u = 0.012443 − 0.826554I
a = 0.185238 + 0.013310I
b = −0.906553 − 0.727576I
2.73486 − 8.14282I 0
u = 0.788810 + 0.056736I
a = −2.20931 − 1.28447I
b = −0.586607 − 0.039795I
−3.91288 − 1.17863I −20.7772 + 5.1029I
u = 0.788810 − 0.056736I
a = −2.20931 + 1.28447I
b = −0.586607 + 0.039795I
−3.91288 + 1.17863I −20.7772 − 5.1029I
u = 0.750230 + 0.210776I
a = 2.28809 + 0.97667I
b = 0.475905 + 0.328068I
1.15173 − 5.50599I −6.00000 + 10.13859I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.750230 − 0.210776I
a = 2.28809 − 0.97667I
b = 0.475905 − 0.328068I
1.15173 + 5.50599I −6.00000 − 10.13859I
u = −0.057589 + 0.774983I
a = −0.130444 + 0.204956I
b = 0.917161 − 0.614056I
−1.95781 + 4.36004I −9.73775 − 6.33857I
u = −0.057589 − 0.774983I
a = −0.130444 − 0.204956I
b = 0.917161 + 0.614056I
−1.95781 − 4.36004I −9.73775 + 6.33857I
u = 0.642028 + 0.410757I
a = −0.750353 + 0.843964I
b = −0.684830 − 0.915401I
5.36047 − 4.61297I −2.63206 + 7.81095I
u = 0.642028 − 0.410757I
a = −0.750353 − 0.843964I
b = −0.684830 + 0.915401I
5.36047 + 4.61297I −2.63206 − 7.81095I
u = −0.221305 + 0.702040I
a = −0.093157 − 0.497861I
b = −0.965469 + 0.417790I
0.956547 + 0.819716I −7.05042 − 3.17652I
u = −0.221305 − 0.702040I
a = −0.093157 + 0.497861I
b = −0.965469 − 0.417790I
0.956547 − 0.819716I −7.05042 + 3.17652I
u = −1.253580 + 0.245545I
a = 0.451351 − 0.533518I
b = −0.095832 − 0.256473I
1.87673 + 1.66795I 0
u = −1.253580 − 0.245545I
a = 0.451351 + 0.533518I
b = −0.095832 + 0.256473I
1.87673 − 1.66795I 0
u = −0.689252 + 0.066561I
a = 3.77196 − 0.35800I
b = 3.28529 − 0.34701I
1.80845 + 2.97035I 27.2900 + 10.8535I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.689252 − 0.066561I
a = 3.77196 + 0.35800I
b = 3.28529 + 0.34701I
1.80845 − 2.97035I 27.2900 − 10.8535I
u = −0.674572
a = −3.82901
b = −3.39142
−2.27556 45.0080
u = −0.649970 + 0.157969I
a = 0.715941 + 0.100560I
b = 0.728948 − 0.515381I
−1.239550 + 0.397962I −8.72729 − 0.25235I
u = −0.649970 − 0.157969I
a = 0.715941 − 0.100560I
b = 0.728948 + 0.515381I
−1.239550 − 0.397962I −8.72729 + 0.25235I
u = 0.248104 + 0.573900I
a = −1.127820 + 0.073338I
b = 0.440596 − 0.654495I
6.54466 + 1.22183I 0.937262 − 0.719785I
u = 0.248104 − 0.573900I
a = −1.127820 − 0.073338I
b = 0.440596 + 0.654495I
6.54466 − 1.22183I 0.937262 + 0.719785I
u = −0.418442 + 0.184487I
a = −2.67657 + 0.89298I
b = −1.54879 + 0.72191I
2.23688 − 2.23181I −2.34161 + 7.40187I
u = −0.418442 − 0.184487I
a = −2.67657 − 0.89298I
b = −1.54879 − 0.72191I
2.23688 + 2.23181I −2.34161 − 7.40187I
u = 1.54364 + 0.03606I
a = 2.07634 + 0.16337I
b = 1.72830 + 0.61768I
−4.29068 − 2.11335I 0
u = 1.54364 − 0.03606I
a = 2.07634 − 0.16337I
b = 1.72830 − 0.61768I
−4.29068 + 2.11335I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.027766 + 0.439550I
a = 0.616350 − 1.062520I
b = −0.655258 + 0.345763I
0.73320 + 1.40973I −1.20605 − 3.84392I
u = −0.027766 − 0.439550I
a = 0.616350 + 1.062520I
b = −0.655258 − 0.345763I
0.73320 − 1.40973I −1.20605 + 3.84392I
u = −1.60578 + 0.08607I
a = 1.287790 − 0.085996I
b = 0.851120 − 1.100430I
−2.34616 + 6.29316I 0
u = −1.60578 − 0.08607I
a = 1.287790 + 0.085996I
b = 0.851120 + 1.100430I
−2.34616 − 6.29316I 0
u = 1.62936 + 0.03391I
a = −1.093500 − 0.875100I
b = −0.96393 − 1.30038I
−9.26887 − 1.05823I 0
u = 1.62936 − 0.03391I
a = −1.093500 + 0.875100I
b = −0.96393 + 1.30038I
−9.26887 + 1.05823I 0
u = 1.63403
a = 3.86249
b = 3.49963
−10.4426 0
u = 1.63409 + 0.02399I
a = −3.55343 + 0.22314I
b = −3.14434 + 0.32055I
−6.38831 − 3.34830I 0
u = 1.63409 − 0.02399I
a = −3.55343 − 0.22314I
b = −3.14434 − 0.32055I
−6.38831 + 3.34830I 0
u = −1.64131 + 0.04793I
a = −1.75205 + 0.63284I
b = −0.658185 − 0.009831I
−7.20909 + 6.42648I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.64131 − 0.04793I
a = −1.75205 − 0.63284I
b = −0.658185 + 0.009831I
−7.20909 − 6.42648I 0
u = −1.65355 + 0.01136I
a = 1.75280 − 0.69764I
b = 0.698957 + 0.215320I
−12.50500 + 1.41291I 0
u = −1.65355 − 0.01136I
a = 1.75280 + 0.69764I
b = 0.698957 − 0.215320I
−12.50500 − 1.41291I 0
u = −1.65390 + 0.03334I
a = −1.55282 − 0.51867I
b = −0.800340 + 0.545581I
−10.56950 + 4.14320I 0
u = −1.65390 − 0.03334I
a = −1.55282 + 0.51867I
b = −0.800340 − 0.545581I
−10.56950 − 4.14320I 0
u = −1.67951 + 0.11538I
a = −1.84477 − 0.04028I
b = −1.28310 + 0.83407I
−11.49190 + 6.36006I 0
u = −1.67951 − 0.11538I
a = −1.84477 + 0.04028I
b = −1.28310 − 0.83407I
−11.49190 − 6.36006I 0
u = 1.67267 + 0.19634I
a = −1.242390 + 0.481250I
b = −1.087260 − 0.168561I
−9.10774 − 7.22720I 0
u = 1.67267 − 0.19634I
a = −1.242390 − 0.481250I
b = −1.087260 + 0.168561I
−9.10774 + 7.22720I 0
u = −1.67935 + 0.16443I
a = −2.00330 + 0.17615I
b = −1.48667 + 0.99930I
−8.8172 + 15.6243I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.67935 − 0.16443I
a = −2.00330 − 0.17615I
b = −1.48667 − 0.99930I
−8.8172 − 15.6243I 0
u = −1.68414 + 0.14421I
a = 1.95556 − 0.07671I
b = 1.41912 − 0.91577I
−13.9245 + 11.1963I 0
u = −1.68414 − 0.14421I
a = 1.95556 + 0.07671I
b = 1.41912 + 0.91577I
−13.9245 − 11.1963I 0
u = 1.69608 + 0.16003I
a = 1.070460 − 0.423461I
b = 0.938968 + 0.203592I
−13.44530 − 3.25448I 0
u = 1.69608 − 0.16003I
a = 1.070460 + 0.423461I
b = 0.938968 − 0.203592I
−13.44530 + 3.25448I 0
u = −0.008362 + 0.294687I
a = −2.44024 − 0.48075I
b = −0.419854 + 1.049640I
3.27067 + 3.66399I −0.860825 − 0.895430I
u = −0.008362 − 0.294687I
a = −2.44024 + 0.48075I
b = −0.419854 − 1.049640I
3.27067 − 3.66399I −0.860825 + 0.895430I
u = 1.72348 + 0.11551I
a = −0.803597 + 0.371179I
b = −0.707949 − 0.235462I
−10.04190 + 0.66192I 0
u = 1.72348 − 0.11551I
a = −0.803597 − 0.371179I
b = −0.707949 + 0.235462I
−10.04190 − 0.66192I 0
u = −0.146978 + 0.147957I
a = 3.53532 − 0.76333I
b = 0.722322 − 0.678600I
−1.35611 + 0.52258I −7.48776 + 0.18415I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.146978 − 0.147957I
a = 3.53532 + 0.76333I
b = 0.722322 + 0.678600I
−1.35611 − 0.52258I −7.48776 − 0.18415I
12
II. I
u
2
= hb − a, a
3
− a
2
+ 1, u + 1i
(i) Arc colorings
a
7
=
0
−1
a
10
=
1
0
a
11
=
1
1
a
8
=
1
0
a
12
=
0
1
a
2
=
a
a
a
6
=
−1
−1
a
3
=
a
a
a
4
=
a
2a
a
1
=
−a
2
+ a + 1
−2a
2
+ a + 2
a
9
=
−a
2
+ 1
−a
2
a
5
=
−a
2
−a
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −a
2
+ 5a − 11
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
3
− u
2
+ 2u − 1
c
2
u
3
c
3
, c
8
, c
9
u
3
− u
2
+ 1
c
4
u
3
+ u
2
+ 2u + 1
c
5
, c
6
, c
7
(u − 1)
3
c
10
, c
11
(u + 1)
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
y
3
c
3
, c
8
, c
9
y
3
− y
2
+ 2y −1
c
5
, c
6
, c
7
c
10
, c
11
(y −1)
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.877439 + 0.744862I
b = 0.877439 + 0.744862I
1.37919 − 2.82812I −6.82789 + 2.41717I
u = −1.00000
a = 0.877439 − 0.744862I
b = 0.877439 − 0.744862I
1.37919 + 2.82812I −6.82789 − 2.41717I
u = −1.00000
a = −0.754878
b = −0.754878
−2.75839 −15.3440
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
3
− u
2
+ 2u − 1)(u
71
− 2u
70
+ ··· − 8u − 1)
c
2
u
3
(u
71
− 5u
70
+ ··· + 12u − 8)
c
3
(u
3
− u
2
+ 1)(u
71
+ 2u
70
+ ··· − 14304u − 929)
c
4
(u
3
+ u
2
+ 2u + 1)(u
71
− 2u
70
+ ··· − 8u − 1)
c
5
((u − 1)
3
)(u
71
− 4u
70
+ ··· + 3u − 1)
c
6
, c
7
((u − 1)
3
)(u
71
+ 4u
70
+ ··· − 11u − 1)
c
8
(u
3
− u
2
+ 1)(u
71
− 22u
69
+ ··· − 460924u − 201793)
c
9
(u
3
− u
2
+ 1)(u
71
− 2u
70
+ ··· − 1978u − 169)
c
10
, c
11
((u + 1)
3
)(u
71
+ 4u
70
+ ··· − 11u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
3
+ 3y
2
+ 2y −1)(y
71
+ 60y
70
+ ··· + 40y −1)
c
2
y
3
(y
71
+ 21y
70
+ ··· + 720y −64)
c
3
(y
3
− y
2
+ 2y −1)(y
71
− 36y
70
+ ··· + 3.01605 × 10
7
y −863041)
c
5
((y −1)
3
)(y
71
+ 2y
70
+ ··· − 3y −1)
c
6
, c
7
, c
10
c
11
((y −1)
3
)(y
71
− 86y
70
+ ··· − 3y −1)
c
8
(y
3
− y
2
+ 2y −1)
· (y
71
− 44y
70
+ ··· − 833663350352y −40720414849)
c
9
(y
3
− y
2
+ 2y −1)(y
71
− 96y
70
+ ··· + 7503396y −28561)
18
