12n
0545
(K12n
0545
)
A knot diagram
1
Linearized knot diagam
3 6 12 8 2 11 5 11 1 6 4 9
Solving Sequence
4,8 5,11
9 12 1 3 7 6 2 10
c
4
c
8
c
11
c
12
c
3
c
7
c
6
c
2
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h4.07415 × 10
97
u
57
− 1.87667 × 10
98
u
56
+ ··· + 6.83675 × 10
98
b − 3.94295 × 10
98
,
− 8.87267 × 10
97
u
57
+ 3.53450 × 10
98
u
56
+ ··· + 6.83675 × 10
98
a + 9.76518 × 10
98
, u
58
− 4u
57
+ ··· + 6u + 4i
I
u
2
= h−2u
15
+ 6u
14
+ ··· + b + 1,
− u
13
+ 3u
12
− 10u
11
+ 17u
10
− 29u
9
+ 31u
8
− 36u
7
+ 27u
6
− 29u
5
+ 18u
4
− 17u
3
+ 6u
2
+ a − 3u,
u
16
− 3u
15
+ ··· − 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
= h4.07×10
97
u
57
−1.88×10
98
u
56
+· · ·+6.84×10
98
b−3.94×10
98
, −8.87×
10
97
u
57
+3.53×10
98
u
56
+· · ·+6.84×10
98
a+9.77×10
98
, u
58
−4u
57
+· · ·+6u+4i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
0.129779u
57
− 0.516986u
56
+ ··· + 5.18894u − 1.42834
−0.0595919u
57
+ 0.274498u
56
+ ··· + 1.46859u + 0.576728
a
9
=
−0.00288585u
57
+ 0.0503023u
56
+ ··· − 2.22480u − 1.52939
−0.0906534u
57
+ 0.405030u
56
+ ··· + 1.10469u + 0.502037
a
12
=
0.189371u
57
− 0.791484u
56
+ ··· + 3.72034u − 2.00506
−0.0595919u
57
+ 0.274498u
56
+ ··· + 1.46859u + 0.576728
a
1
=
0.0387990u
57
− 0.162896u
56
+ ··· − 3.18685u − 1.73013
−0.192685u
57
+ 0.853552u
56
+ ··· + 0.855020u + 1.27477
a
3
=
−0.296992u
57
+ 0.998359u
56
+ ··· − 10.6074u − 1.68008
0.171483u
57
− 0.586975u
56
+ ··· + 8.98917u + 2.03171
a
7
=
u
u
3
+ u
a
6
=
0.0524169u
57
− 0.224873u
56
+ ··· − 1.55050u − 2.18646
−0.174759u
57
+ 0.745226u
56
+ ··· + 0.209991u + 1.01830
a
2
=
−0.342530u
57
+ 1.40424u
56
+ ··· − 3.12486u + 1.77424
0.141129u
57
− 0.526127u
56
+ ··· + 5.69791u + 0.00196869
a
10
=
−0.103749u
57
+ 0.491535u
56
+ ··· + 8.67337u + 0.492109
0.137791u
57
− 0.597731u
56
+ ··· + 2.06345u − 1.32119
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.123076u
57
− 0.812943u
56
+ ··· − 17.7171u − 16.8383
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
58
+ 41u
57
+ ··· − 191u + 169
c
2
, c
5
u
58
+ u
57
+ ··· − 37u − 13
c
3
, c
11
u
58
− 3u
57
+ ··· − u − 17
c
4
, c
7
u
58
− 4u
57
+ ··· + 6u + 4
c
6
, c
10
u
58
+ 3u
57
+ ··· − 16568u + 2143
c
8
u
58
+ u
57
+ ··· + 202u + 3
c
9
, c
12
u
58
+ 3u
57
+ ··· + 7097u + 431
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
58
− 37y
57
+ ··· − 1807601y + 28561
c
2
, c
5
y
58
− 41y
57
+ ··· + 191y + 169
c
3
, c
11
y
58
+ 47y
57
+ ··· − 171y + 289
c
4
, c
7
y
58
+ 18y
57
+ ··· + 356y + 16
c
6
, c
10
y
58
+ 65y
57
+ ··· − 280143286y + 4592449
c
8
y
58
− 15y
57
+ ··· − 60898y + 9
c
9
, c
12
y
58
− 49y
57
+ ··· − 11167097y + 185761
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.633756 + 0.791145I
a = −0.887765 + 0.616824I
b = −0.553388 + 0.628935I
−3.87656 − 0.61696I −11.92005 − 0.88689I
u = 0.633756 − 0.791145I
a = −0.887765 − 0.616824I
b = −0.553388 − 0.628935I
−3.87656 + 0.61696I −11.92005 + 0.88689I
u = 0.747067 + 0.601176I
a = −1.51970 − 0.38331I
b = −0.401468 − 0.201550I
−4.20974 − 3.93817I −13.2121 + 6.9659I
u = 0.747067 − 0.601176I
a = −1.51970 + 0.38331I
b = −0.401468 + 0.201550I
−4.20974 + 3.93817I −13.2121 − 6.9659I
u = 0.480297 + 0.959333I
a = −1.99240 + 0.86576I
b = −0.172651 − 0.899004I
−3.54839 − 3.84914I −10.22465 + 4.74982I
u = 0.480297 − 0.959333I
a = −1.99240 − 0.86576I
b = −0.172651 + 0.899004I
−3.54839 + 3.84914I −10.22465 − 4.74982I
u = −0.521709 + 0.983940I
a = 1.54639 − 0.06752I
b = 0.506281 − 1.185660I
0.09858 + 7.47040I −8.00000 − 8.36343I
u = −0.521709 − 0.983940I
a = 1.54639 + 0.06752I
b = 0.506281 + 1.185660I
0.09858 − 7.47040I −8.00000 + 8.36343I
u = 0.503661 + 0.728248I
a = −1.66274 − 0.02895I
b = −0.391966 − 1.295650I
2.85966 − 4.49859I −1.23708 + 2.46876I
u = 0.503661 − 0.728248I
a = −1.66274 + 0.02895I
b = −0.391966 + 1.295650I
2.85966 + 4.49859I −1.23708 − 2.46876I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.594982 + 0.640753I
a = 0.969927 − 0.024407I
b = 0.339779 + 0.189097I
−0.55040 + 1.69114I −3.72847 − 5.08829I
u = −0.594982 − 0.640753I
a = 0.969927 + 0.024407I
b = 0.339779 − 0.189097I
−0.55040 − 1.69114I −3.72847 + 5.08829I
u = −0.730255 + 0.859792I
a = −0.481459 + 0.177345I
b = −0.202364 + 1.025230I
1.91016 + 2.82560I −8.00000 + 0.I
u = −0.730255 − 0.859792I
a = −0.481459 − 0.177345I
b = −0.202364 − 1.025230I
1.91016 − 2.82560I −8.00000 + 0.I
u = −0.219621 + 0.839350I
a = 1.130710 + 0.505098I
b = 0.843328 + 0.336352I
−2.59431 + 2.44159I −7.94322 − 3.82016I
u = −0.219621 − 0.839350I
a = 1.130710 − 0.505098I
b = 0.843328 − 0.336352I
−2.59431 − 2.44159I −7.94322 + 3.82016I
u = 0.898691 + 0.720344I
a = 0.437549 − 0.200217I
b = 0.662131 − 1.245830I
−7.44986 − 3.49551I 0
u = 0.898691 − 0.720344I
a = 0.437549 + 0.200217I
b = 0.662131 + 1.245830I
−7.44986 + 3.49551I 0
u = 0.367889 + 0.761915I
a = 1.191700 + 0.232164I
b = 0.002717 + 1.140600I
3.25433 + 1.08651I −2.33651 − 2.83520I
u = 0.367889 − 0.761915I
a = 1.191700 − 0.232164I
b = 0.002717 − 1.140600I
3.25433 − 1.08651I −2.33651 + 2.83520I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.808356
a = 1.77037
b = 0.734307
−5.93820 −16.7950
u = −0.119623 + 1.194280I
a = −0.126368 − 1.332700I
b = −0.08348 + 1.49201I
8.29523 + 3.26345I 0
u = −0.119623 − 1.194280I
a = −0.126368 + 1.332700I
b = −0.08348 − 1.49201I
8.29523 − 3.26345I 0
u = −0.317704 + 1.163150I
a = 0.017678 − 0.187020I
b = −0.082658 + 0.494670I
1.81717 + 2.37754I 0
u = −0.317704 − 1.163150I
a = 0.017678 + 0.187020I
b = −0.082658 − 0.494670I
1.81717 − 2.37754I 0
u = −1.087360 + 0.583319I
a = −0.335602 − 0.201290I
b = −0.581501 − 1.162890I
−3.42807 − 1.99613I 0
u = −1.087360 − 0.583319I
a = −0.335602 + 0.201290I
b = −0.581501 + 1.162890I
−3.42807 + 1.99613I 0
u = 0.187149 + 1.276260I
a = 0.277466 − 0.128726I
b = 0.064672 + 1.355790I
3.33606 − 0.14941I 0
u = 0.187149 − 1.276260I
a = 0.277466 + 0.128726I
b = 0.064672 − 1.355790I
3.33606 + 0.14941I 0
u = −0.697744 + 0.126410I
a = 1.99664 − 1.33804I
b = 0.277967 − 1.258560I
−2.06001 + 3.68426I −11.27363 − 1.69816I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.697744 − 0.126410I
a = 1.99664 + 1.33804I
b = 0.277967 + 1.258560I
−2.06001 − 3.68426I −11.27363 + 1.69816I
u = 0.759635 + 1.129180I
a = 1.29689 − 0.78536I
b = 0.43433 + 1.40722I
−6.14642 − 2.75220I 0
u = 0.759635 − 1.129180I
a = 1.29689 + 0.78536I
b = 0.43433 − 1.40722I
−6.14642 + 2.75220I 0
u = −1.001480 + 0.973107I
a = −0.832664 − 0.380632I
b = −1.023700 + 0.164160I
−6.48849 + 3.63570I 0
u = −1.001480 − 0.973107I
a = −0.832664 + 0.380632I
b = −1.023700 − 0.164160I
−6.48849 − 3.63570I 0
u = −0.859580 + 1.106170I
a = 1.096860 + 0.046929I
b = 0.198273 − 1.156390I
2.21851 + 3.93693I 0
u = −0.859580 − 1.106170I
a = 1.096860 − 0.046929I
b = 0.198273 + 1.156390I
2.21851 − 3.93693I 0
u = 0.974228 + 1.008910I
a = 0.926636 − 0.331530I
b = 1.073470 + 0.135176I
−10.8043 − 9.5417I 0
u = 0.974228 − 1.008910I
a = 0.926636 + 0.331530I
b = 1.073470 − 0.135176I
−10.8043 + 9.5417I 0
u = 1.03423 + 0.96722I
a = 0.813755 − 0.507387I
b = 0.952238 + 0.123695I
−10.98340 + 2.23509I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.03423 − 0.96722I
a = 0.813755 + 0.507387I
b = 0.952238 − 0.123695I
−10.98340 − 2.23509I 0
u = 1.16247 + 0.82462I
a = −1.067170 − 0.448360I
b = −0.221458 − 1.288520I
0.24583 − 6.42034I 0
u = 1.16247 − 0.82462I
a = −1.067170 + 0.448360I
b = −0.221458 + 1.288520I
0.24583 + 6.42034I 0
u = 1.27692 + 0.71765I
a = 0.292225 − 0.279237I
b = 0.494403 − 1.216990I
−7.61679 + 7.37751I 0
u = 1.27692 − 0.71765I
a = 0.292225 + 0.279237I
b = 0.494403 + 1.216990I
−7.61679 − 7.37751I 0
u = −0.84042 + 1.21729I
a = −1.183540 − 0.496027I
b = −0.47727 + 1.42425I
−1.49972 + 9.01325I 0
u = −0.84042 − 1.21729I
a = −1.183540 + 0.496027I
b = −0.47727 − 1.42425I
−1.49972 − 9.01325I 0
u = −0.266410 + 0.401142I
a = −2.92496 + 3.15692I
b = 0.112223 + 1.152450I
−1.72433 − 3.71273I −7.24791 + 1.15995I
u = −0.266410 − 0.401142I
a = −2.92496 − 3.15692I
b = 0.112223 − 1.152450I
−1.72433 + 3.71273I −7.24791 − 1.15995I
u = 0.91423 + 1.22132I
a = 1.259520 − 0.318765I
b = 0.49545 + 1.41482I
−5.9451 − 15.1173I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.91423 − 1.22132I
a = 1.259520 + 0.318765I
b = 0.49545 − 1.41482I
−5.9451 + 15.1173I 0
u = 0.058858 + 0.410475I
a = −0.92100 + 1.87652I
b = −0.14583 − 1.62296I
5.20134 − 2.93181I −11.08507 + 6.44707I
u = 0.058858 − 0.410475I
a = −0.92100 − 1.87652I
b = −0.14583 + 1.62296I
5.20134 + 2.93181I −11.08507 − 6.44707I
u = 0.145156 + 0.296103I
a = −1.54845 + 1.00675I
b = −0.777584 + 0.065221I
−1.097500 − 0.167840I −6.15459 − 2.52205I
u = 0.145156 − 0.296103I
a = −1.54845 − 1.00675I
b = −0.777584 − 0.065221I
−1.097500 + 0.167840I −6.15459 + 2.52205I
u = −0.329275
a = 0.0370472
b = −0.490183
−0.882045 −11.0120
u = −0.31854 + 1.65683I
a = 0.326154 + 0.658457I
b = 0.035991 − 1.065230I
3.20371 + 2.59445I 0
u = −0.31854 − 1.65683I
a = 0.326154 − 0.658457I
b = 0.035991 + 1.065230I
3.20371 − 2.59445I 0
10
II.
I
u
2
= h−2u
15
+6u
14
+· · ·+b+1, −u
13
+3u
12
+· · ·+a−3u, u
16
−3u
15
+· · ·−u+1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
11
=
u
13
− 3u
12
+ ··· − 6u
2
+ 3u
2u
15
− 6u
14
+ ··· + 6u − 1
a
9
=
2u
15
− 5u
14
+ ··· + 2u + 2
−u
14
+ 3u
13
+ ··· + 3u − 1
a
12
=
−2u
15
+ 6u
14
+ ··· − 3u + 1
2u
15
− 6u
14
+ ··· + 6u − 1
a
1
=
−5u
15
+ 16u
14
+ ··· − u − 2
2u
15
− 6u
14
+ ··· + 5u − 1
a
3
=
u
15
− 5u
14
+ ··· − 12u
2
− 3
2u
14
− 5u
13
+ ··· − 2u + 5
a
7
=
u
u
3
+ u
a
6
=
2u
15
− 5u
14
+ ··· + 6u
2
+ 2
−2u
15
+ 5u
14
+ ··· − u
2
− 3u
a
2
=
−2u
14
+ 5u
13
+ ··· + 6u − 5
−2u
15
+ 8u
14
+ ··· − 6u + 4
a
10
=
4u
15
− 13u
14
+ ··· + 12u − 1
−2u
15
+ 6u
14
+ ··· − 3u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
15
+ 21u
14
− 66u
13
+ 162u
12
− 280u
11
+ 433u
10
− 498u
9
+
559u
8
− 469u
7
+ 452u
6
− 292u
5
+ 262u
4
− 114u
3
+ 85u
2
− 16u + 9
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
16
− 10u
15
+ ··· − 14u + 1
c
2
u
16
− 5u
14
+ ··· − 7u
2
+ 1
c
3
u
16
+ 2u
15
+ ··· + 4u + 1
c
4
u
16
− 3u
15
+ ··· − u + 1
c
5
u
16
− 5u
14
+ ··· − 7u
2
+ 1
c
6
u
16
+ 4u
15
+ ··· + 9u + 1
c
7
u
16
+ 3u
15
+ ··· + u + 1
c
8
u
16
− 12u
15
+ ··· + 3u + 1
c
9
u
16
+ 4u
15
+ ··· + 2u + 1
c
10
u
16
− 4u
15
+ ··· − 9u + 1
c
11
u
16
− 2u
15
+ ··· − 4u + 1
c
12
u
16
− 4u
15
+ ··· − 2u + 1
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 2y
15
+ ··· − 14y + 1
c
2
, c
5
y
16
− 10y
15
+ ··· − 14y + 1
c
3
, c
11
y
16
+ 18y
15
+ ··· + 12y + 1
c
4
, c
7
y
16
+ 13y
15
+ ··· + 11y + 1
c
6
, c
10
y
16
+ 4y
15
+ ··· − 15y + 1
c
8
y
16
− 4y
15
+ ··· − 31y + 1
c
9
, c
12
y
16
− 10y
15
+ ··· − 14y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.522632 + 0.681729I
a = 3.01304 + 0.08828I
b = 0.193850 − 1.240090I
−1.67890 + 4.79509I −7.33702 − 7.63468I
u = −0.522632 − 0.681729I
a = 3.01304 − 0.08828I
b = 0.193850 + 1.240090I
−1.67890 − 4.79509I −7.33702 + 7.63468I
u = 0.505824 + 0.614300I
a = −1.018070 + 0.161240I
b = −0.775312 + 0.317843I
−1.40771 − 0.97837I −9.52942 + 3.04465I
u = 0.505824 − 0.614300I
a = −1.018070 − 0.161240I
b = −0.775312 − 0.317843I
−1.40771 + 0.97837I −9.52942 − 3.04465I
u = 0.133841 + 1.204570I
a = −0.35849 + 1.55300I
b = −0.07812 − 1.52109I
7.65003 − 3.66078I −7.24903 + 5.37880I
u = 0.133841 − 1.204570I
a = −0.35849 − 1.55300I
b = −0.07812 + 1.52109I
7.65003 + 3.66078I −7.24903 − 5.37880I
u = 0.895544 + 0.875535I
a = −1.117880 − 0.176389I
b = −0.333939 − 1.201080I
1.48311 − 4.99831I −7.51711 + 5.80874I
u = 0.895544 − 0.875535I
a = −1.117880 + 0.176389I
b = −0.333939 + 1.201080I
1.48311 + 4.99831I −7.51711 − 5.80874I
u = 0.122314 + 0.707690I
a = 0.010586 − 0.499972I
b = −0.15573 + 1.61681I
5.66385 + 2.53909I −0.82857 + 1.24715I
u = 0.122314 − 0.707690I
a = 0.010586 + 0.499972I
b = −0.15573 − 1.61681I
5.66385 − 2.53909I −0.82857 − 1.24715I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269294 + 1.323520I
a = −0.201461 + 0.527298I
b = −0.185206 − 0.303507I
1.27597 − 2.61649I −13.2971 + 5.8003I
u = 0.269294 − 1.323520I
a = −0.201461 − 0.527298I
b = −0.185206 + 0.303507I
1.27597 + 2.61649I −13.2971 − 5.8003I
u = −0.283411 + 0.533145I
a = 2.59418 + 0.46203I
b = 0.388010 + 0.584237I
−4.14032 + 2.65100I −12.96730 − 1.15952I
u = −0.283411 − 0.533145I
a = 2.59418 − 0.46203I
b = 0.388010 − 0.584237I
−4.14032 − 2.65100I −12.96730 + 1.15952I
u = 0.37923 + 1.60128I
a = 0.078082 − 0.226823I
b = −0.053550 + 1.235140I
4.31342 − 1.80529I −1.27447 + 2.27954I
u = 0.37923 − 1.60128I
a = 0.078082 + 0.226823I
b = −0.053550 − 1.235140I
4.31342 + 1.80529I −1.27447 − 2.27954I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 10u
15
+ ··· − 14u + 1)(u
58
+ 41u
57
+ ··· − 191u + 169)
c
2
(u
16
− 5u
14
+ ··· − 7u
2
+ 1)(u
58
+ u
57
+ ··· − 37u − 13)
c
3
(u
16
+ 2u
15
+ ··· + 4u + 1)(u
58
− 3u
57
+ ··· − u − 17)
c
4
(u
16
− 3u
15
+ ··· − u + 1)(u
58
− 4u
57
+ ··· + 6u + 4)
c
5
(u
16
− 5u
14
+ ··· − 7u
2
+ 1)(u
58
+ u
57
+ ··· − 37u − 13)
c
6
(u
16
+ 4u
15
+ ··· + 9u + 1)(u
58
+ 3u
57
+ ··· − 16568u + 2143)
c
7
(u
16
+ 3u
15
+ ··· + u + 1)(u
58
− 4u
57
+ ··· + 6u + 4)
c
8
(u
16
− 12u
15
+ ··· + 3u + 1)(u
58
+ u
57
+ ··· + 202u + 3)
c
9
(u
16
+ 4u
15
+ ··· + 2u + 1)(u
58
+ 3u
57
+ ··· + 7097u + 431)
c
10
(u
16
− 4u
15
+ ··· − 9u + 1)(u
58
+ 3u
57
+ ··· − 16568u + 2143)
c
11
(u
16
− 2u
15
+ ··· − 4u + 1)(u
58
− 3u
57
+ ··· − u − 17)
c
12
(u
16
− 4u
15
+ ··· − 2u + 1)(u
58
+ 3u
57
+ ··· + 7097u + 431)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
+ 2y
15
+ ··· − 14y + 1)(y
58
− 37y
57
+ ··· − 1807601y + 28561)
c
2
, c
5
(y
16
− 10y
15
+ ··· − 14y + 1)(y
58
− 41y
57
+ ··· + 191y + 169)
c
3
, c
11
(y
16
+ 18y
15
+ ··· + 12y + 1)(y
58
+ 47y
57
+ ··· − 171y + 289)
c
4
, c
7
(y
16
+ 13y
15
+ ··· + 11y + 1)(y
58
+ 18y
57
+ ··· + 356y + 16)
c
6
, c
10
(y
16
+ 4y
15
+ ··· − 15y + 1)
· (y
58
+ 65y
57
+ ··· − 280143286y + 4592449)
c
8
(y
16
− 4y
15
+ ··· − 31y + 1)(y
58
− 15y
57
+ ··· − 60898y + 9)
c
9
, c
12
(y
16
− 10y
15
+ ··· − 14y + 1)
· (y
58
− 49y
57
+ ··· − 11167097y + 185761)
19
