12n
0390
(K12n
0390
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 1 12 5 12 4 8 9
Solving Sequence
2,5
6 3
1,9
8 12 10 4 7 11
c
5
c
2
c
1
c
8
c
12
c
9
c
4
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.46294 × 10
29
u
46
+ 7.95784 × 10
29
u
45
+ ··· + 2.37042 × 10
29
b − 6.34182 × 10
30
,
1.94482 × 10
31
u
46
+ 4.33728 × 10
31
u
45
+ ··· + 2.60747 × 10
30
a − 2.49401 × 10
32
, u
47
+ 3u
46
+ ··· − 40u − 11i
I
u
2
= h−u
15
− u
14
+ 4u
13
+ 4u
12
− 9u
11
− 8u
10
+ 12u
9
+ 6u
8
− 11u
7
+ 2u
6
+ 6u
5
− 7u
4
− 2u
3
+ 3u
2
+ b,
− 2u
17
− 3u
16
+ ··· + a + 2, u
18
− 5u
16
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 65 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
=
h2.46×10
29
u
46
+7.96×10
29
u
45
+· · ·+2.37×10
29
b−6.34×10
30
, 1.94×10
31
u
46
+
4.34 × 10
31
u
45
+ · · · + 2.61 × 10
30
a − 2.49 × 10
32
, u
47
+ 3u
46
+ · · · − 40u − 11i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
−7.45865u
46
− 16.6341u
45
+ ··· + 241.132u + 95.6487
−1.03903u
46
− 3.35714u
45
+ ··· + 53.4137u + 26.7540
a
8
=
−6.41962u
46
− 13.2769u
45
+ ··· + 187.719u + 68.8947
−1.03903u
46
− 3.35714u
45
+ ··· + 53.4137u + 26.7540
a
12
=
3.75435u
46
+ 6.70383u
45
+ ··· − 90.9031u − 26.3287
1.22903u
46
+ 2.91014u
45
+ ··· − 45.7371u − 18.6251
a
10
=
−0.627376u
46
− 1.39884u
45
+ ··· + 11.2034u + 1.46172
−0.522819u
46
− 0.806804u
45
+ ··· + 8.68459u + 0.958907
a
4
=
−1.35192u
46
− 2.82554u
45
+ ··· + 39.1629u + 16.1387
4.70290u
46
+ 9.69022u
45
+ ··· − 140.178u − 52.4053
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
11
=
4.56620u
46
+ 7.93732u
45
+ ··· − 108.368u − 32.1734
3.91576u
46
+ 9.28160u
45
+ ··· − 146.560u − 60.9527
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.50908u
46
− 6.53790u
45
+ ··· + 87.7874u + 16.6803
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
47
+ 27u
46
+ ··· + 1050u + 121
c
2
, c
5
u
47
+ 3u
46
+ ··· − 40u − 11
c
3
u
47
+ u
46
+ ··· + 721u − 77
c
4
, c
10
u
47
+ 2u
46
+ ··· + 880u + 259
c
6
u
47
+ 9u
46
+ ··· − 2486u − 605
c
7
, c
11
u
47
+ 2u
46
+ ··· + 7139507u + 4293137
c
8
u
47
− 3u
46
+ ··· + 1235u + 319
c
9
, c
12
u
47
− 7u
46
+ ··· − 68u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
− 3y
46
+ ··· + 22454y −14641
c
2
, c
5
y
47
− 27y
46
+ ··· + 1050y −121
c
3
y
47
+ 89y
46
+ ··· + 1443379y −5929
c
4
, c
10
y
47
+ 70y
46
+ ··· + 827236y −67081
c
6
y
47
+ 39y
46
+ ··· + 7716896y −366025
c
7
, c
11
y
47
− 90y
46
+ ··· + 10351799467819y −18431025300769
c
8
y
47
+ y
46
+ ··· − 1880419y −101761
c
9
, c
12
y
47
+ 3y
46
+ ··· + 396y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.876077 + 0.495153I
a = 0.05861 − 1.54742I
b = 1.253340 − 0.133813I
2.96047 − 4.00527I 1.41913 + 7.02290I
u = 0.876077 − 0.495153I
a = 0.05861 + 1.54742I
b = 1.253340 + 0.133813I
2.96047 + 4.00527I 1.41913 − 7.02290I
u = −0.219784 + 0.989162I
a = −0.362101 − 0.066122I
b = 1.17874 − 1.23600I
−10.92830 − 8.41421I −3.04374 + 3.89039I
u = −0.219784 − 0.989162I
a = −0.362101 + 0.066122I
b = 1.17874 + 1.23600I
−10.92830 + 8.41421I −3.04374 − 3.89039I
u = −0.924941 + 0.211030I
a = −0.229367 − 0.697298I
b = −1.54763 + 0.11397I
0.99929 + 2.61967I −5.19015 − 2.74150I
u = −0.924941 − 0.211030I
a = −0.229367 + 0.697298I
b = −1.54763 − 0.11397I
0.99929 − 2.61967I −5.19015 + 2.74150I
u = −0.824634 + 0.426276I
a = −1.76007 − 2.37447I
b = 0.251649 + 0.584600I
−7.70591 + 1.80987I −3.91459 − 3.48681I
u = −0.824634 − 0.426276I
a = −1.76007 + 2.37447I
b = 0.251649 − 0.584600I
−7.70591 − 1.80987I −3.91459 + 3.48681I
u = 0.846874 + 0.360689I
a = −0.17435 + 2.83942I
b = 0.17024 + 1.41188I
−8.15375 − 1.57774I −0.80255 + 4.89499I
u = 0.846874 − 0.360689I
a = −0.17435 − 2.83942I
b = 0.17024 − 1.41188I
−8.15375 + 1.57774I −0.80255 − 4.89499I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.701499 + 0.543812I
a = 0.491865 + 0.673634I
b = −1.254340 + 0.037496I
3.47616 − 0.21144I 3.37728 + 0.59281I
u = 0.701499 − 0.543812I
a = 0.491865 − 0.673634I
b = −1.254340 − 0.037496I
3.47616 + 0.21144I 3.37728 − 0.59281I
u = −0.004113 + 0.880495I
a = 0.347513 + 0.070964I
b = 0.170930 + 0.679428I
−0.64377 + 2.79416I −3.76375 − 4.12382I
u = −0.004113 − 0.880495I
a = 0.347513 − 0.070964I
b = 0.170930 − 0.679428I
−0.64377 − 2.79416I −3.76375 + 4.12382I
u = −0.849942 + 0.204435I
a = 0.85944 + 2.33236I
b = 1.175050 + 0.465651I
1.244440 − 0.641998I −5.98611 − 0.69680I
u = −0.849942 − 0.204435I
a = 0.85944 − 2.33236I
b = 1.175050 − 0.465651I
1.244440 + 0.641998I −5.98611 + 0.69680I
u = 0.859362
a = −1.25271
b = 0.546195
−2.89515 3.43320
u = −0.027994 + 0.837881I
a = −1.018770 − 0.136305I
b = 1.20991 − 1.22321I
−10.84070 − 0.60465I −3.14085 − 0.02993I
u = −0.027994 − 0.837881I
a = −1.018770 + 0.136305I
b = 1.20991 + 1.22321I
−10.84070 + 0.60465I −3.14085 + 0.02993I
u = 1.141860 + 0.328010I
a = 0.41789 + 1.96075I
b = −0.288127 + 0.987319I
−5.30017 − 0.97973I −8.08906 + 2.35012I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.141860 − 0.328010I
a = 0.41789 − 1.96075I
b = −0.288127 − 0.987319I
−5.30017 + 0.97973I −8.08906 − 2.35012I
u = −1.140420 + 0.352854I
a = 0.648125 − 0.840786I
b = 0.492371 − 0.744957I
−2.56290 + 1.51479I −3.51596 − 1.49247I
u = −1.140420 − 0.352854I
a = 0.648125 + 0.840786I
b = 0.492371 + 0.744957I
−2.56290 − 1.51479I −3.51596 + 1.49247I
u = 0.272988 + 0.745917I
a = 0.438704 − 0.325162I
b = −0.907317 − 0.410716I
1.43547 + 1.61663I 2.81439 + 0.31096I
u = 0.272988 − 0.745917I
a = 0.438704 + 0.325162I
b = −0.907317 + 0.410716I
1.43547 − 1.61663I 2.81439 − 0.31096I
u = −1.123120 + 0.540873I
a = −1.11998 + 1.51248I
b = 0.158687 + 1.034900I
−3.78321 + 6.82193I 0. − 6.42288I
u = −1.123120 − 0.540873I
a = −1.11998 − 1.51248I
b = 0.158687 − 1.034900I
−3.78321 − 6.82193I 0. + 6.42288I
u = −0.279697 + 0.684332I
a = 0.221829 + 0.627921I
b = −0.076193 + 0.836935I
−1.37741 − 2.09664I −3.89707 + 2.40716I
u = −0.279697 − 0.684332I
a = 0.221829 − 0.627921I
b = −0.076193 − 0.836935I
−1.37741 + 2.09664I −3.89707 − 2.40716I
u = 1.144210 + 0.542382I
a = −0.25949 − 1.78790I
b = 0.996365 − 0.606031I
−1.11707 − 6.47946I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.144210 − 0.542382I
a = −0.25949 + 1.78790I
b = 0.996365 + 0.606031I
−1.11707 + 6.47946I 0
u = 1.237570 + 0.451956I
a = −1.43480 − 0.69587I
b = −1.27653 − 1.53747I
−14.6130 − 3.9696I 0
u = 1.237570 − 0.451956I
a = −1.43480 + 0.69587I
b = −1.27653 + 1.53747I
−14.6130 + 3.9696I 0
u = −1.231500 + 0.478844I
a = 0.44079 − 2.03120I
b = −1.48547 − 1.07528I
−14.4158 + 5.3399I 0
u = −1.231500 − 0.478844I
a = 0.44079 + 2.03120I
b = −1.48547 + 1.07528I
−14.4158 − 5.3399I 0
u = 1.248430 + 0.483208I
a = 0.306682 + 1.364460I
b = −0.358428 + 1.116070I
−4.37505 − 7.63882I 0
u = 1.248430 − 0.483208I
a = 0.306682 − 1.364460I
b = −0.358428 − 1.116070I
−4.37505 + 7.63882I 0
u = −0.523547 + 0.374959I
a = 0.632108 − 0.620727I
b = −0.111012 − 0.458273I
−0.431977 + 1.249080I −3.29232 − 5.98996I
u = −0.523547 − 0.374959I
a = 0.632108 + 0.620727I
b = −0.111012 + 0.458273I
−0.431977 − 1.249080I −3.29232 + 5.98996I
u = −1.298850 + 0.446921I
a = −0.302497 + 0.978434I
b = 0.474453 + 0.811864I
−4.60025 + 2.14253I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.298850 − 0.446921I
a = −0.302497 − 0.978434I
b = 0.474453 − 0.811864I
−4.60025 − 2.14253I 0
u = −1.244520 + 0.594030I
a = 0.50825 − 2.01870I
b = −1.35396 − 1.28721I
−14.0727 + 14.1097I 0
u = −1.244520 − 0.594030I
a = 0.50825 + 2.01870I
b = −1.35396 + 1.28721I
−14.0727 − 14.1097I 0
u = 1.367670 + 0.303326I
a = −1.12338 − 1.01518I
b = −0.94061 − 1.44352I
−16.2192 + 3.9265I 0
u = 1.367670 − 0.303326I
a = −1.12338 + 1.01518I
b = −0.94061 + 1.44352I
−16.2192 − 3.9265I 0
u = −1.07379 + 0.96465I
a = −0.324275 + 0.037659I
b = 0.294773 + 0.663976I
−5.13971 + 3.86765I 0
u = −1.07379 − 0.96465I
a = −0.324275 − 0.037659I
b = 0.294773 − 0.663976I
−5.13971 − 3.86765I 0
9
II.
I
u
2
= h−u
15
−u
14
+· · ·+3u
2
+b, −2u
17
−3u
16
+· · ·+a+2, u
18
−5u
16
+· · ·−u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
2u
17
+ 3u
16
+ ··· + 4u − 2
u
15
+ u
14
+ ··· + 2u
3
− 3u
2
a
8
=
2u
17
+ 3u
16
+ ··· + 4u − 2
u
15
+ u
14
+ ··· + 2u
3
− 3u
2
a
12
=
−u
17
− 2u
16
+ ··· − 3u − 2
−2u
17
+ 10u
15
+ ··· + 2u + 1
a
10
=
2u
17
+ 2u
16
+ ··· − 2u − 2
−u
17
+ u
16
+ ··· + 2u + 1
a
4
=
8u
17
+ 6u
16
+ ··· + 34u
2
− 9
u
17
+ u
16
+ ··· + u − 2
a
7
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
11
=
−3u
17
− 3u
16
+ ··· + 6u
4
− u
3
−u
17
− u
16
+ ··· + 6u
4
− 3u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12u
17
+ 12u
16
− 56u
15
− 55u
14
+ 146u
13
+ 130u
12
− 239u
11
−
151u
10
+ 274u
9
+ 56u
8
− 211u
7
+ 81u
6
+ 106u
5
− 112u
4
− 27u
3
+ 53u
2
− 16
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
u
18
− 10u
17
+ ··· − 7u + 1
c
2
u
18
− 5u
16
+ ··· + u + 1
c
3
u
18
− 2u
17
+ ··· − 16u + 101
c
4
u
18
+ u
17
+ ··· + 3u + 1
c
5
u
18
− 5u
16
+ ··· − u + 1
c
6
u
18
+ 2u
16
+ ··· − 3u + 1
c
7
u
18
+ u
17
+ ··· − 6u + 1
c
8
u
18
+ 2u
17
+ ··· + 4u + 1
c
9
u
18
− 6u
17
+ ··· + u + 1
c
10
u
18
− u
17
+ ··· − 3u + 1
c
11
u
18
− u
17
+ ··· + 6u + 1
c
12
u
18
+ 6u
17
+ ··· − u + 1
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 6y
17
+ ··· + 9y + 1
c
2
, c
5
y
18
− 10y
17
+ ··· − 7y + 1
c
3
y
18
+ 14y
17
+ ··· + 13884y + 10201
c
4
, c
10
y
18
+ 19y
17
+ ··· + 11y + 1
c
6
y
18
+ 4y
17
+ ··· − y + 1
c
7
, c
11
y
18
− 9y
17
+ ··· + 8y + 1
c
8
y
18
− 14y
17
+ ··· − 6y + 1
c
9
, c
12
y
18
+ 8y
17
+ ··· − 9y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.911423 + 0.313351I
a = −1.02137 + 3.11139I
b = 0.079988 + 1.151000I
−8.73578 − 1.31626I −13.91898 − 0.89713I
u = 0.911423 − 0.313351I
a = −1.02137 − 3.11139I
b = 0.079988 − 1.151000I
−8.73578 + 1.31626I −13.91898 + 0.89713I
u = −1.099540 + 0.219817I
a = 0.000777 − 0.869675I
b = 0.350991 − 0.272048I
−3.73137 + 0.34305I −6.94049 − 0.42724I
u = −1.099540 − 0.219817I
a = 0.000777 + 0.869675I
b = 0.350991 + 0.272048I
−3.73137 − 0.34305I −6.94049 + 0.42724I
u = −1.025280 + 0.454429I
a = 0.828326 + 0.479984I
b = 1.45038 − 0.24289I
0.84046 + 4.52433I −3.35223 − 6.04100I
u = −1.025280 − 0.454429I
a = 0.828326 − 0.479984I
b = 1.45038 + 0.24289I
0.84046 − 4.52433I −3.35223 + 6.04100I
u = 1.035030 + 0.480226I
a = −0.05553 − 1.64991I
b = 1.46258 − 0.02856I
1.04035 − 1.78617I −4.18125 + 2.75892I
u = 1.035030 − 0.480226I
a = −0.05553 + 1.64991I
b = 1.46258 + 0.02856I
1.04035 + 1.78617I −4.18125 − 2.75892I
u = 0.245321 + 0.787397I
a = 0.293070 − 0.605885I
b = −0.825077 − 0.167815I
0.99457 + 2.65474I 0.16626 − 4.79929I
u = 0.245321 − 0.787397I
a = 0.293070 + 0.605885I
b = −0.825077 + 0.167815I
0.99457 − 2.65474I 0.16626 + 4.79929I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.139670 + 0.550067I
a = −0.12667 − 1.72867I
b = 0.831035 − 0.381458I
−1.58532 − 7.59591I −3.31038 + 8.36386I
u = 1.139670 − 0.550067I
a = −0.12667 + 1.72867I
b = 0.831035 + 0.381458I
−1.58532 + 7.59591I −3.31038 − 8.36386I
u = −0.622208 + 0.347865I
a = −0.37175 − 1.66905I
b = −1.281030 − 0.281080I
2.26249 − 0.94977I 1.46449 + 1.20584I
u = −0.622208 − 0.347865I
a = −0.37175 + 1.66905I
b = −1.281030 + 0.281080I
2.26249 + 0.94977I 1.46449 − 1.20584I
u = 0.548147 + 0.424026I
a = 1.52770 + 1.26420I
b = −1.301760 + 0.008505I
2.59877 − 2.11586I −0.21775 + 2.73352I
u = 0.548147 − 0.424026I
a = 1.52770 − 1.26420I
b = −1.301760 − 0.008505I
2.59877 + 2.11586I −0.21775 − 2.73352I
u = −1.132560 + 0.827334I
a = −0.574547 + 0.086284I
b = 0.232885 + 0.649747I
−5.19872 + 3.58923I −11.70969 + 5.37750I
u = −1.132560 − 0.827334I
a = −0.574547 − 0.086284I
b = 0.232885 − 0.649747I
−5.19872 − 3.58923I −11.70969 − 5.37750I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 10u
17
+ ··· − 7u + 1)(u
47
+ 27u
46
+ ··· + 1050u + 121)
c
2
(u
18
− 5u
16
+ ··· + u + 1)(u
47
+ 3u
46
+ ··· − 40u − 11)
c
3
(u
18
− 2u
17
+ ··· − 16u + 101)(u
47
+ u
46
+ ··· + 721u − 77)
c
4
(u
18
+ u
17
+ ··· + 3u + 1)(u
47
+ 2u
46
+ ··· + 880u + 259)
c
5
(u
18
− 5u
16
+ ··· − u + 1)(u
47
+ 3u
46
+ ··· − 40u − 11)
c
6
(u
18
+ 2u
16
+ ··· − 3u + 1)(u
47
+ 9u
46
+ ··· − 2486u − 605)
c
7
(u
18
+ u
17
+ ··· − 6u + 1)(u
47
+ 2u
46
+ ··· + 7139507u + 4293137)
c
8
(u
18
+ 2u
17
+ ··· + 4u + 1)(u
47
− 3u
46
+ ··· + 1235u + 319)
c
9
(u
18
− 6u
17
+ ··· + u + 1)(u
47
− 7u
46
+ ··· − 68u + 7)
c
10
(u
18
− u
17
+ ··· − 3u + 1)(u
47
+ 2u
46
+ ··· + 880u + 259)
c
11
(u
18
− u
17
+ ··· + 6u + 1)(u
47
+ 2u
46
+ ··· + 7139507u + 4293137)
c
12
(u
18
+ 6u
17
+ ··· − u + 1)(u
47
− 7u
46
+ ··· − 68u + 7)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ 6y
17
+ ··· + 9y + 1)(y
47
− 3y
46
+ ··· + 22454y −14641)
c
2
, c
5
(y
18
− 10y
17
+ ··· − 7y + 1)(y
47
− 27y
46
+ ··· + 1050y −121)
c
3
(y
18
+ 14y
17
+ ··· + 13884y + 10201)
· (y
47
+ 89y
46
+ ··· + 1443379y −5929)
c
4
, c
10
(y
18
+ 19y
17
+ ··· + 11y + 1)(y
47
+ 70y
46
+ ··· + 827236y −67081)
c
6
(y
18
+ 4y
17
+ ··· − y + 1)(y
47
+ 39y
46
+ ··· + 7716896y −366025)
c
7
, c
11
(y
18
− 9y
17
+ ··· + 8y + 1)
· (y
47
− 90y
46
+ ··· + 10351799467819y −18431025300769)
c
8
(y
18
− 14y
17
+ ··· − 6y + 1)(y
47
+ y
46
+ ··· − 1880419y −101761)
c
9
, c
12
(y
18
+ 8y
17
+ ··· − 9y + 1)(y
47
+ 3y
46
+ ··· + 396y −49)
18
