12n
0506
(K12n
0506
)
A knot diagram
1
Linearized knot diagam
3 5 7 12 2 9 11 3 5 8 4 10
Solving Sequence
4,11
12
5,8
7 3 2 6 10 1 9
c
11
c
4
c
7
c
3
c
2
c
5
c
10
c
12
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.92307 × 10
57
u
49
− 8.25153 × 10
56
u
48
+ ··· + 4.65772 × 10
58
b + 1.19662 × 10
58
,
− 3.65030 × 10
58
u
49
− 7.49016 × 10
57
u
48
+ ··· + 9.31544 × 10
58
a − 2.43552 × 10
59
, u
50
− 2u
49
+ ··· + 4u − 4i
I
u
2
= h38499u
20
− 7436u
19
+ ··· + 35558b − 156754, 37681u
20
+ 484u
19
+ ··· + 35558a − 142970,
u
21
+ u
20
+ ··· − 4u − 4i
* 2 irreducible components of dim
C
= 0, with total 71 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−2.92×10
57
u
49
−8.25×10
56
u
48
+· · ·+4.66×10
58
b+1.20×10
58
, −3.65×
10
58
u
49
−7.49×10
57
u
48
+· · ·+9.32×10
58
a−2.44×10
59
, u
50
−2u
49
+· · ·+4u−4i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
8
=
0.391855u
49
+ 0.0804058u
48
+ ··· + 18.2311u + 2.61450
0.0627575u
49
+ 0.0177158u
48
+ ··· + 6.02426u − 0.256911
a
7
=
0.329097u
49
+ 0.0626900u
48
+ ··· + 12.2069u + 2.87141
0.0627575u
49
+ 0.0177158u
48
+ ··· + 6.02426u − 0.256911
a
3
=
−0.269929u
49
+ 0.335316u
48
+ ··· + 2.98112u − 9.82945
0.884089u
49
− 0.664841u
48
+ ··· − 6.59794u + 3.47371
a
2
=
−1.13386u
49
+ 1.13404u
48
+ ··· + 2.55589u − 12.9459
0.626077u
49
− 0.347864u
48
+ ··· − 5.91190u + 2.87366
a
6
=
−1.07851u
49
+ 1.75858u
48
+ ··· + 67.4506u − 7.31372
−0.837429u
49
+ 0.432036u
48
+ ··· − 0.0882456u − 3.75890
a
10
=
1.44758u
49
− 1.29391u
48
+ ··· + 7.34620u − 2.10940
0.579155u
49
− 0.441145u
48
+ ··· − 5.55360u + 1.01483
a
1
=
−0.00688015u
49
+ 1.00008u
48
+ ··· + 22.7865u + 12.1643
1.25272u
49
− 0.864448u
48
+ ··· + 16.6689u + 2.78210
a
9
=
1.91394u
49
− 1.77626u
48
+ ··· + 6.20475u − 1.13893
0.783142u
49
− 0.639256u
48
+ ··· − 4.34819u + 1.84583
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.34948u
49
− 0.608726u
48
+ ··· − 1.48538u − 1.03264
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
+ 75u
49
+ ··· − 199u + 1
c
2
, c
5
u
50
+ u
49
+ ··· + 37u − 1
c
3
u
50
+ 3u
49
+ ··· − 622u + 257
c
4
, c
11
u
50
+ 2u
49
+ ··· − 4u − 4
c
6
u
50
+ 47u
48
+ ··· − 87532u − 28244
c
7
, c
10
u
50
+ 6u
49
+ ··· − 82u − 4
c
8
u
50
− u
49
+ ··· + 3878700u + 630961
c
9
u
50
− 2u
49
+ ··· − 9207u + 307
c
12
u
50
− 11u
49
+ ··· − 1988004u + 270187
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
− 189y
49
+ ··· − 22527y + 1
c
2
, c
5
y
50
+ 75y
49
+ ··· − 199y + 1
c
3
y
50
− 23y
49
+ ··· − 130398y + 66049
c
4
, c
11
y
50
− 42y
49
+ ··· + 736y + 16
c
6
y
50
+ 94y
49
+ ··· − 6283430848y + 797723536
c
7
, c
10
y
50
+ 44y
49
+ ··· − 1100y + 16
c
8
y
50
− 51y
49
+ ··· − 6506346297832y + 398111783521
c
9
y
50
+ 84y
49
+ ··· − 193343697y + 94249
c
12
y
50
− 67y
49
+ ··· + 7872728157574y + 73001014969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07906
a = 0.456631
b = −0.343403
−1.80303 −5.94880
u = 0.648336 + 0.609293I
a = 0.128763 − 0.334259I
b = 0.106776 − 0.597923I
−1.18171 − 1.55259I −6.05321 + 2.36458I
u = 0.648336 − 0.609293I
a = 0.128763 + 0.334259I
b = 0.106776 + 0.597923I
−1.18171 + 1.55259I −6.05321 − 2.36458I
u = 0.811486 + 0.321287I
a = 0.70261 + 1.71571I
b = 0.205601 + 0.738871I
−1.33799 − 1.34735I −5.76164 + 1.69141I
u = 0.811486 − 0.321287I
a = 0.70261 − 1.71571I
b = 0.205601 − 0.738871I
−1.33799 + 1.34735I −5.76164 − 1.69141I
u = −0.104502 + 0.839206I
a = 0.218390 + 0.701022I
b = −0.927719 − 0.160877I
−9.87904 + 3.10011I −1.02029 − 2.56068I
u = −0.104502 − 0.839206I
a = 0.218390 − 0.701022I
b = −0.927719 + 0.160877I
−9.87904 − 3.10011I −1.02029 + 2.56068I
u = −1.16764
a = 0.705198
b = 1.36379
−0.594673 −14.5600
u = 0.066997 + 0.819280I
a = 0.063502 − 0.153656I
b = 0.279335 − 1.126760I
−1.19165 − 2.46840I 1.22355 + 1.33250I
u = 0.066997 − 0.819280I
a = 0.063502 + 0.153656I
b = 0.279335 + 1.126760I
−1.19165 + 2.46840I 1.22355 − 1.33250I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.210460 + 0.134918I
a = 0.158769 + 0.327791I
b = 0.880017 − 0.080173I
−3.08696 − 0.57146I 0
u = 1.210460 − 0.134918I
a = 0.158769 − 0.327791I
b = 0.880017 + 0.080173I
−3.08696 + 0.57146I 0
u = 0.129091 + 1.253480I
a = 0.291397 + 0.571233I
b = −0.021403 + 1.308110I
−3.97379 − 2.11896I 0
u = 0.129091 − 1.253480I
a = 0.291397 − 0.571233I
b = −0.021403 − 1.308110I
−3.97379 + 2.11896I 0
u = 1.277370 + 0.120815I
a = −1.23731 − 2.34133I
b = 0.263155 − 1.360410I
−7.52184 − 3.28981I 0
u = 1.277370 − 0.120815I
a = −1.23731 + 2.34133I
b = 0.263155 + 1.360410I
−7.52184 + 3.28981I 0
u = −0.270413 + 1.257420I
a = 0.228850 − 0.640041I
b = −0.36396 − 1.41166I
−14.9314 + 7.6930I 0
u = −0.270413 − 1.257420I
a = 0.228850 + 0.640041I
b = −0.36396 + 1.41166I
−14.9314 − 7.6930I 0
u = −1.309520 + 0.061210I
a = −1.00267 − 3.07061I
b = −0.114281 − 1.322420I
−17.4959 + 3.0650I 0
u = −1.309520 − 0.061210I
a = −1.00267 + 3.07061I
b = −0.114281 + 1.322420I
−17.4959 − 3.0650I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.287640 + 0.262760I
a = 0.161981 − 0.227519I
b = −0.707113 − 0.093466I
−4.36735 + 4.61413I 0
u = −1.287640 − 0.262760I
a = 0.161981 + 0.227519I
b = −0.707113 + 0.093466I
−4.36735 − 4.61413I 0
u = −1.328400 + 0.072360I
a = 0.44568 − 1.71849I
b = −0.32965 − 1.40593I
−8.55310 − 0.56867I 0
u = −1.328400 − 0.072360I
a = 0.44568 + 1.71849I
b = −0.32965 + 1.40593I
−8.55310 + 0.56867I 0
u = 1.311730 + 0.308998I
a = 1.04568 + 1.62480I
b = −0.112849 + 1.208320I
−5.28912 − 1.66036I 0
u = 1.311730 − 0.308998I
a = 1.04568 − 1.62480I
b = −0.112849 − 1.208320I
−5.28912 + 1.66036I 0
u = 1.346080 + 0.075442I
a = −0.20642 − 1.73825I
b = −0.88688 − 1.61634I
−18.0336 + 1.1028I 0
u = 1.346080 − 0.075442I
a = −0.20642 + 1.73825I
b = −0.88688 + 1.61634I
−18.0336 − 1.1028I 0
u = −1.279240 + 0.427359I
a = −0.775969 − 0.823176I
b = −0.321757 + 0.101254I
−13.45950 + 1.53340I 0
u = −1.279240 − 0.427359I
a = −0.775969 + 0.823176I
b = −0.321757 − 0.101254I
−13.45950 − 1.53340I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.331940 + 0.309177I
a = −0.48326 + 1.82025I
b = 0.50826 + 1.45369I
−5.66081 + 6.42848I 0
u = −1.331940 − 0.309177I
a = −0.48326 − 1.82025I
b = 0.50826 − 1.45369I
−5.66081 − 6.42848I 0
u = 1.349410 + 0.336328I
a = −0.525442 + 0.560601I
b = −1.37321 + 0.35227I
−14.4886 − 7.2876I 0
u = 1.349410 − 0.336328I
a = −0.525442 − 0.560601I
b = −1.37321 − 0.35227I
−14.4886 + 7.2876I 0
u = 0.082394 + 0.547321I
a = 0.986098 − 0.631149I
b = −0.170671 − 0.044166I
−0.14617 − 1.49325I −0.46873 + 5.87257I
u = 0.082394 − 0.547321I
a = 0.986098 + 0.631149I
b = −0.170671 + 0.044166I
−0.14617 + 1.49325I −0.46873 − 5.87257I
u = −0.414715 + 0.288195I
a = 0.101777 + 1.365910I
b = 0.631123 + 0.377678I
1.14736 + 1.01845I 7.01184 − 3.19514I
u = −0.414715 − 0.288195I
a = 0.101777 − 1.365910I
b = 0.631123 − 0.377678I
1.14736 − 1.01845I 7.01184 + 3.19514I
u = −1.43825 + 0.45806I
a = 0.93844 − 1.62626I
b = −0.247398 − 1.377560I
−9.15198 + 7.96076I 0
u = −1.43825 − 0.45806I
a = 0.93844 + 1.62626I
b = −0.247398 + 1.377560I
−9.15198 − 7.96076I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50629 + 0.48152I
a = 0.63158 + 1.81709I
b = −0.49334 + 1.56307I
18.8663 − 13.7470I 0
u = 1.50629 − 0.48152I
a = 0.63158 − 1.81709I
b = −0.49334 − 1.56307I
18.8663 + 13.7470I 0
u = 1.50100 + 0.52835I
a = −0.44313 − 1.51722I
b = 0.24879 − 1.45359I
−8.62936 − 4.54432I 0
u = 1.50100 − 0.52835I
a = −0.44313 + 1.51722I
b = 0.24879 + 1.45359I
−8.62936 + 4.54432I 0
u = 0.121767 + 0.292619I
a = −0.22430 − 2.50528I
b = 0.063783 + 1.250300I
−3.84376 + 1.74410I −5.80851 − 2.56777I
u = 0.121767 − 0.292619I
a = −0.22430 + 2.50528I
b = 0.063783 − 1.250300I
−3.84376 − 1.74410I −5.80851 + 2.56777I
u = −1.49544 + 0.79557I
a = −0.698551 + 1.169030I
b = −0.131534 + 1.396950I
−18.4852 − 0.1786I 0
u = −1.49544 − 0.79557I
a = −0.698551 − 1.169030I
b = −0.131534 − 1.396950I
−18.4852 + 0.1786I 0
u = −0.058061 + 0.206058I
a = 4.91262 + 4.09459I
b = −0.49528 + 1.32653I
−13.42200 − 2.14669I −3.56304 + 0.04666I
u = −0.058061 − 0.206058I
a = 4.91262 − 4.09459I
b = −0.49528 − 1.32653I
−13.42200 + 2.14669I −3.56304 − 0.04666I
9
II. I
u
2
= h38499u
20
− 7436u
19
+ · · · + 35558b − 156754, 37681u
20
+ 484u
19
+
· · · + 35558a − 142970, u
21
+ u
20
+ · · · − 4u − 4i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
8
=
−1.05971u
20
− 0.0136116u
19
+ ··· + 4.51401u + 4.02075
−1.08271u
20
+ 0.209123u
19
+ ··· + 1.96665u + 4.40840
a
7
=
0.0230047u
20
− 0.222735u
19
+ ··· + 2.54736u − 0.387648
−1.08271u
20
+ 0.209123u
19
+ ··· + 1.96665u + 4.40840
a
3
=
0.723649u
20
− 0.307821u
19
+ ··· − 1.97356u − 1.22588
0.0756229u
20
− 0.244418u
19
+ ··· − 0.692727u + 0.527645
a
2
=
0.714902u
20
+ 0.122827u
19
+ ··· − 0.881546u − 2.17386
−1.16677u
20
+ 0.221047u
19
+ ··· − 0.0621520u + 3.23320
a
6
=
−0.340767u
20
+ 0.344592u
19
+ ··· + 2.83759u + 0.174982
−0.372968u
20
+ 0.0989088u
19
+ ··· + 0.383767u + 2.08679
a
10
=
−0.690885u
20
+ 0.802337u
19
+ ··· + 3.67549u + 2.22392
−0.822797u
20
+ 0.594803u
19
+ ··· + 2.71444u + 3.44429
a
1
=
−0.372659u
20
+ 0.935767u
19
+ ··· + 0.0702233u + 0.387198
−0.877608u
20
+ 1.04604u
19
+ ··· + 1.58693u + 0.580629
a
9
=
−0.950799u
20
+ 0.416657u
19
+ ··· + 2.92770u + 2.18803
−0.476152u
20
+ 0.150515u
19
+ ··· + 1.91951u + 2.97711
(ii) Obstruction class = 1
(iii) Cusp Shapes =
19570
17779
u
20
+
17174
17779
u
19
+ ··· +
45070
17779
u −
25746
17779
10
(iv) u-Polynomials at the component
11
Crossings u-Polynomials at each crossing
c
1
u
21
− 24u
20
+ ··· + 16u + 1
c
2
u
21
+ 12u
19
+ ··· − 4u − 1
c
3
u
21
+ 2u
20
+ ··· + u − 7
c
4
u
21
− u
20
+ ··· − 4u + 4
c
5
u
21
+ 12u
19
+ ··· − 4u + 1
c
6
u
21
− u
20
+ ··· + 20u + 4
c
7
u
21
+ 5u
20
+ ··· + 34u + 4
c
8
u
21
− 3u
19
+ ··· + 5u + 1
c
9
u
21
+ u
20
+ ··· + 2u − 1
c
10
u
21
− 5u
20
+ ··· + 34u − 4
c
11
u
21
+ u
20
+ ··· − 4u − 4
c
12
u
21
− 2u
20
+ ··· + 47u + 7
12
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 44y
20
+ ··· + 232y −1
c
2
, c
5
y
21
+ 24y
20
+ ··· + 16y −1
c
3
y
21
− 6y
20
+ ··· + 239y −49
c
4
, c
11
y
21
− 17y
20
+ ··· − 32y −16
c
6
y
21
+ 19y
20
+ ··· + 352y −16
c
7
, c
10
y
21
+ 17y
20
+ ··· + 12y −16
c
8
y
21
− 6y
20
+ ··· + 29y −1
c
9
y
21
+ 13y
20
+ ··· + 6y −1
c
12
y
21
− 14y
20
+ ··· + 67y −49
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.053654 + 0.994034I
a = −0.118262 − 0.157903I
b = 0.261258 − 1.096940I
−1.82196 − 3.31723I −3.56279 + 6.27419I
u = 0.053654 − 0.994034I
a = −0.118262 + 0.157903I
b = 0.261258 + 1.096940I
−1.82196 + 3.31723I −3.56279 − 6.27419I
u = −1.006310 + 0.386972I
a = −0.001299 − 0.196953I
b = −0.510619 − 1.094680I
−14.5544 + 3.5199I −7.00930 − 3.34595I
u = −1.006310 − 0.386972I
a = −0.001299 + 0.196953I
b = −0.510619 + 1.094680I
−14.5544 − 3.5199I −7.00930 + 3.34595I
u = 1.07842
a = 0.535095
b = 1.10310
−0.187749 6.00000
u = 0.727444 + 0.493982I
a = −0.187671 − 0.933435I
b = 0.329896 − 0.180152I
−0.14218 − 1.80240I 2.07850 + 4.52264I
u = 0.727444 − 0.493982I
a = −0.187671 + 0.933435I
b = 0.329896 + 0.180152I
−0.14218 + 1.80240I 2.07850 − 4.52264I
u = 0.712915 + 0.901061I
a = 0.383343 + 0.651191I
b = 0.098075 + 1.273330I
−3.65276 − 0.25703I −6.52769 − 0.27177I
u = 0.712915 − 0.901061I
a = 0.383343 − 0.651191I
b = 0.098075 − 1.273330I
−3.65276 + 0.25703I −6.52769 + 0.27177I
u = 1.239990 + 0.303227I
a = −0.83651 − 2.17539I
b = 0.22167 − 1.41775I
−5.86381 − 4.09879I −5.03465 + 3.45560I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.239990 − 0.303227I
a = −0.83651 + 2.17539I
b = 0.22167 + 1.41775I
−5.86381 + 4.09879I −5.03465 − 3.45560I
u = −1.261550 + 0.269071I
a = −0.62409 + 2.26542I
b = −0.366033 + 1.347970I
−15.6653 − 0.5794I −6.15872 − 0.08532I
u = −1.261550 − 0.269071I
a = −0.62409 − 2.26542I
b = −0.366033 − 1.347970I
−15.6653 + 0.5794I −6.15872 + 0.08532I
u = −1.279400 + 0.192903I
a = 0.332530 − 0.511316I
b = 1.066330 − 0.560224I
−3.93246 + 2.61822I −7.09974 − 2.69906I
u = −1.279400 − 0.192903I
a = 0.332530 + 0.511316I
b = 1.066330 + 0.560224I
−3.93246 − 2.61822I −7.09974 + 2.69906I
u = 1.348700 + 0.186645I
a = 1.03417 + 1.35712I
b = −0.146518 + 1.073210I
−6.54748 − 0.69924I −7.57202 − 0.34785I
u = 1.348700 − 0.186645I
a = 1.03417 − 1.35712I
b = −0.146518 − 1.073210I
−6.54748 + 0.69924I −7.57202 + 0.34785I
u = −1.41010 + 0.39622I
a = −0.58101 + 1.57427I
b = 0.498672 + 1.276340I
−6.71074 + 8.26508I −4.78242 − 6.51636I
u = −1.41010 − 0.39622I
a = −0.58101 − 1.57427I
b = 0.498672 − 1.276340I
−6.71074 − 8.26508I −4.78242 + 6.51636I
u = −0.164557 + 0.384273I
a = −0.66874 + 2.46746I
b = 0.495722 + 0.644048I
−0.232681 − 0.315786I −1.33114 − 1.22918I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.164557 − 0.384273I
a = −0.66874 − 2.46746I
b = 0.495722 − 0.644048I
−0.232681 + 0.315786I −1.33114 + 1.22918I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 24u
20
+ ··· + 16u + 1)(u
50
+ 75u
49
+ ··· − 199u + 1)
c
2
(u
21
+ 12u
19
+ ··· − 4u − 1)(u
50
+ u
49
+ ··· + 37u − 1)
c
3
(u
21
+ 2u
20
+ ··· + u − 7)(u
50
+ 3u
49
+ ··· − 622u + 257)
c
4
(u
21
− u
20
+ ··· − 4u + 4)(u
50
+ 2u
49
+ ··· − 4u − 4)
c
5
(u
21
+ 12u
19
+ ··· − 4u + 1)(u
50
+ u
49
+ ··· + 37u − 1)
c
6
(u
21
− u
20
+ ··· + 20u + 4)(u
50
+ 47u
48
+ ··· − 87532u − 28244)
c
7
(u
21
+ 5u
20
+ ··· + 34u + 4)(u
50
+ 6u
49
+ ··· − 82u − 4)
c
8
(u
21
− 3u
19
+ ··· + 5u + 1)(u
50
− u
49
+ ··· + 3878700u + 630961)
c
9
(u
21
+ u
20
+ ··· + 2u − 1)(u
50
− 2u
49
+ ··· − 9207u + 307)
c
10
(u
21
− 5u
20
+ ··· + 34u − 4)(u
50
+ 6u
49
+ ··· − 82u − 4)
c
11
(u
21
+ u
20
+ ··· − 4u − 4)(u
50
+ 2u
49
+ ··· − 4u − 4)
c
12
(u
21
− 2u
20
+ ··· + 47u + 7)(u
50
− 11u
49
+ ··· − 1988004u + 270187)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
− 44y
20
+ ··· + 232y −1)(y
50
− 189y
49
+ ··· − 22527y + 1)
c
2
, c
5
(y
21
+ 24y
20
+ ··· + 16y −1)(y
50
+ 75y
49
+ ··· − 199y + 1)
c
3
(y
21
− 6y
20
+ ··· + 239y −49)(y
50
− 23y
49
+ ··· − 130398y + 66049)
c
4
, c
11
(y
21
− 17y
20
+ ··· − 32y −16)(y
50
− 42y
49
+ ··· + 736y + 16)
c
6
(y
21
+ 19y
20
+ ··· + 352y −16)
· (y
50
+ 94y
49
+ ··· − 6283430848y + 797723536)
c
7
, c
10
(y
21
+ 17y
20
+ ··· + 12y −16)(y
50
+ 44y
49
+ ··· − 1100y + 16)
c
8
(y
21
− 6y
20
+ ··· + 29y −1)
· (y
50
− 51y
49
+ ··· − 6506346297832y + 398111783521)
c
9
(y
21
+ 13y
20
+ ··· + 6y −1)
· (y
50
+ 84y
49
+ ··· − 193343697y + 94249)
c
12
(y
21
− 14y
20
+ ··· + 67y −49)
· (y
50
− 67y
49
+ ··· + 7872728157574y + 73001014969)
19
