12a
0097
(K12a
0097
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 4 1 12 7 6 9
Solving Sequence
1,8 4,9
3 2 5 7 12 10 11 6
c
8
c
3
c
1
c
4
c
7
c
12
c
9
c
10
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.27877 × 10
118
u
70
− 1.71790 × 10
119
u
69
+ ··· + 6.29616 × 10
119
b − 2.88028 × 10
119
,
− 1.11155 × 10
119
u
70
+ 7.86535 × 10
119
u
69
+ ··· + 4.40732 × 10
120
a + 1.25108 × 10
121
,
u
71
− 8u
70
+ ··· − 336u + 49i
I
u
2
= hb, u
2
+ a + 2, u
3
+ 2u − 1i
I
u
3
= hb, −u
3
− u
2
+ a − 2u − 2, u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 78 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
= h2.28 × 10
118
u
70
− 1.72 × 10
119
u
69
+ · · · + 6.30 × 10
119
b − 2.88 ×
10
119
, −1.11 × 10
119
u
70
+ 7.87 × 10
119
u
69
+ · · · + 4.41 × 10
120
a + 1.25 ×
10
121
, u
71
− 8u
70
+ · · · − 336u + 49i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
0.0252206u
70
− 0.178461u
69
+ ··· + 12.8042u − 2.83865
−0.0361930u
70
+ 0.272848u
69
+ ··· − 10.0915u + 0.457467
a
9
=
1
u
2
a
3
=
−0.0109724u
70
+ 0.0943870u
69
+ ··· + 2.71273u − 2.38119
−0.0361930u
70
+ 0.272848u
69
+ ··· − 10.0915u + 0.457467
a
2
=
−0.0289170u
70
+ 0.232103u
69
+ ··· − 11.9842u − 0.213372
−0.00325428u
70
+ 0.0204184u
69
+ ··· + 4.10649u − 1.07519
a
5
=
0.0327771u
70
− 0.219346u
69
+ ··· + 20.2771u − 2.78303
−0.00325428u
70
+ 0.0204184u
69
+ ··· + 4.10649u − 1.07519
a
7
=
−0.0209275u
70
+ 0.142661u
69
+ ··· + 14.5291u − 1.66013
0.0428700u
70
− 0.321456u
69
+ ··· + 8.23006u − 1.60608
a
12
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
−0.0175926u
70
+ 0.136899u
69
+ ··· + 12.9847u − 2.05681
0.0348688u
70
− 0.279866u
69
+ ··· + 1.94984u + 0.536966
a
6
=
0.0410166u
70
− 0.324779u
69
+ ··· + 25.3736u − 3.63534
−0.0478328u
70
+ 0.393772u
69
+ ··· − 12.0234u + 1.27819
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0549660u
70
+ 0.494164u
69
+ ··· − 79.5880u + 1.61216
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 30u
70
+ ··· + 63u + 1
c
2
, c
4
u
71
− 8u
70
+ ··· − u + 1
c
3
, c
7
u
71
+ u
70
+ ··· + 320u + 128
c
5
u
71
− 2u
70
+ ··· − 784u + 4360
c
6
, c
10
, c
11
u
71
+ 2u
70
+ ··· + 4u + 1
c
8
, c
9
, c
12
u
71
− 8u
70
+ ··· − 336u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 30y
70
+ ··· + 3271y −1
c
2
, c
4
y
71
− 30y
70
+ ··· + 63y −1
c
3
, c
7
y
71
+ 45y
70
+ ··· − 233472y −16384
c
5
y
71
+ 36y
70
+ ··· − 370918384y −19009600
c
6
, c
10
, c
11
y
71
+ 68y
70
+ ··· + 12y −1
c
8
, c
9
, c
12
y
71
+ 80y
70
+ ··· − 77420y −2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.965089 + 0.222646I
a = −0.463055 + 0.146640I
b = −0.383523 − 1.048760I
2.17116 − 4.96264I 0
u = 0.965089 − 0.222646I
a = −0.463055 − 0.146640I
b = −0.383523 + 1.048760I
2.17116 + 4.96264I 0
u = 0.555630 + 0.843517I
a = −0.179841 − 0.287942I
b = −0.921031 + 0.373991I
3.18386 − 5.21037I 0
u = 0.555630 − 0.843517I
a = −0.179841 + 0.287942I
b = −0.921031 − 0.373991I
3.18386 + 5.21037I 0
u = −0.497939 + 0.886784I
a = −0.460887 − 0.886344I
b = −0.213854 + 1.051720I
2.29580 + 2.43328I 0
u = −0.497939 − 0.886784I
a = −0.460887 + 0.886344I
b = −0.213854 − 1.051720I
2.29580 − 2.43328I 0
u = 0.901281 + 0.483012I
a = 0.174621 − 0.074659I
b = −0.183485 + 0.929838I
2.82109 − 0.79303I 0
u = 0.901281 − 0.483012I
a = 0.174621 + 0.074659I
b = −0.183485 − 0.929838I
2.82109 + 0.79303I 0
u = −0.737991 + 0.797805I
a = 0.817472 + 0.829674I
b = 0.496722 − 1.174470I
0.78928 + 7.49831I 0
u = −0.737991 − 0.797805I
a = 0.817472 − 0.829674I
b = 0.496722 + 1.174470I
0.78928 − 7.49831I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.898468 + 0.151332I
a = 0.0921622 + 0.0914888I
b = 0.274475 + 1.005400I
−1.11803 − 2.10911I 0
u = −0.898468 − 0.151332I
a = 0.0921622 − 0.0914888I
b = 0.274475 − 1.005400I
−1.11803 + 2.10911I 0
u = 0.519063 + 0.701175I
a = −0.45976 + 2.32557I
b = −0.267550 − 0.775200I
2.27830 − 2.99192I 0
u = 0.519063 − 0.701175I
a = −0.45976 − 2.32557I
b = −0.267550 + 0.775200I
2.27830 + 2.99192I 0
u = 0.542453 + 1.060010I
a = 0.312954 − 1.139310I
b = 0.336812 + 1.112900I
7.64845 − 5.36975I 0
u = 0.542453 − 1.060010I
a = 0.312954 + 1.139310I
b = 0.336812 − 1.112900I
7.64845 + 5.36975I 0
u = −0.170069 + 1.204310I
a = −0.021614 − 0.362936I
b = −0.002806 + 0.626003I
2.50967 + 1.94105I 0
u = −0.170069 − 1.204310I
a = −0.021614 + 0.362936I
b = −0.002806 − 0.626003I
2.50967 − 1.94105I 0
u = 0.345350 + 0.682566I
a = 1.018120 − 0.634027I
b = 0.044806 + 1.135950I
3.18971 + 0.88617I −5.37424 − 3.34259I
u = 0.345350 − 0.682566I
a = 1.018120 + 0.634027I
b = 0.044806 − 1.135950I
3.18971 − 0.88617I −5.37424 + 3.34259I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.478584 + 0.568662I
a = 0.568000 − 0.216623I
b = 0.803895 + 0.353915I
−1.82493 + 2.59268I −15.3769 − 7.2742I
u = −0.478584 − 0.568662I
a = 0.568000 + 0.216623I
b = 0.803895 − 0.353915I
−1.82493 − 2.59268I −15.3769 + 7.2742I
u = 0.738278 + 1.040830I
a = −0.667814 + 1.062280I
b = −0.552812 − 1.199040I
5.84593 − 10.65120I 0
u = 0.738278 − 1.040830I
a = −0.667814 − 1.062280I
b = −0.552812 + 1.199040I
5.84593 + 10.65120I 0
u = 0.551600 + 0.463905I
a = −1.304920 + 0.339654I
b = −0.394465 − 1.185760I
2.25258 − 4.24592I −7.24520 + 3.14949I
u = 0.551600 − 0.463905I
a = −1.304920 − 0.339654I
b = −0.394465 + 1.185760I
2.25258 + 4.24592I −7.24520 − 3.14949I
u = 0.700493 + 0.073725I
a = −0.99238 − 1.19225I
b = −0.604080 + 0.530248I
0.487722 − 1.022320I −13.68239 − 0.22891I
u = 0.700493 − 0.073725I
a = −0.99238 + 1.19225I
b = −0.604080 − 0.530248I
0.487722 + 1.022320I −13.68239 + 0.22891I
u = −0.016841 + 0.702643I
a = −1.54871 − 1.43918I
b = −0.040877 + 1.295280I
9.32963 − 2.62843I −1.88831 + 2.84842I
u = −0.016841 − 0.702643I
a = −1.54871 + 1.43918I
b = −0.040877 − 1.295280I
9.32963 + 2.62843I −1.88831 − 2.84842I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.332568 + 0.605833I
a = −0.301092 + 0.636346I
b = 0.862872 − 0.007307I
4.21028 − 1.36691I −5.92252 + 0.19732I
u = 0.332568 − 0.605833I
a = −0.301092 − 0.636346I
b = 0.862872 + 0.007307I
4.21028 + 1.36691I −5.92252 − 0.19732I
u = 0.558598 + 0.272901I
a = −0.299568 − 0.501299I
b = 0.440934 + 0.406344I
3.36702 − 1.57403I −6.09432 + 4.24770I
u = 0.558598 − 0.272901I
a = −0.299568 + 0.501299I
b = 0.440934 − 0.406344I
3.36702 + 1.57403I −6.09432 − 4.24770I
u = −0.435436 + 0.347884I
a = 1.09728 + 2.39333I
b = 0.316131 − 0.580635I
−2.50844 + 0.67754I −14.4694 − 9.3694I
u = −0.435436 − 0.347884I
a = 1.09728 − 2.39333I
b = 0.316131 + 0.580635I
−2.50844 − 0.67754I −14.4694 + 9.3694I
u = 0.27752 + 1.42324I
a = 0.031422 − 0.333514I
b = −0.015427 + 0.624053I
8.54375 − 5.00674I 0
u = 0.27752 − 1.42324I
a = 0.031422 + 0.333514I
b = −0.015427 − 0.624053I
8.54375 + 5.00674I 0
u = −0.097939 + 0.485793I
a = 2.58622 + 1.57725I
b = 0.361070 − 1.308120I
8.54074 + 3.06263I −3.03957 − 2.89556I
u = −0.097939 − 0.485793I
a = 2.58622 − 1.57725I
b = 0.361070 + 1.308120I
8.54074 − 3.06263I −3.03957 + 2.89556I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06886 + 1.50531I
a = 0.01135 + 2.28493I
b = 0.024006 − 1.065750I
3.67289 + 2.17680I 0
u = −0.06886 − 1.50531I
a = 0.01135 − 2.28493I
b = 0.024006 + 1.065750I
3.67289 − 2.17680I 0
u = 0.00316 + 1.51912I
a = 0.444013 − 0.011181I
b = −1.166440 + 0.191892I
5.33599 − 0.33795I 0
u = 0.00316 − 1.51912I
a = 0.444013 + 0.011181I
b = −1.166440 − 0.191892I
5.33599 + 0.33795I 0
u = −0.12329 + 1.54920I
a = −0.430159 − 0.078037I
b = 1.170270 + 0.230752I
5.25008 + 4.73327I 0
u = −0.12329 − 1.54920I
a = −0.430159 + 0.078037I
b = 1.170270 − 0.230752I
5.25008 − 4.73327I 0
u = 0.15624 + 1.55244I
a = −0.48688 + 1.73940I
b = −0.61601 − 1.36943I
9.10594 − 6.74702I 0
u = 0.15624 − 1.55244I
a = −0.48688 − 1.73940I
b = −0.61601 + 1.36943I
9.10594 + 6.74702I 0
u = −0.04061 + 1.56679I
a = 0.47782 + 1.82859I
b = 0.61104 − 1.39480I
15.6993 + 3.6198I 0
u = −0.04061 − 1.56679I
a = 0.47782 − 1.82859I
b = 0.61104 + 1.39480I
15.6993 − 3.6198I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08851 + 1.58806I
a = −0.499554 + 0.013294I
b = 1.192900 + 0.167411I
11.75780 − 2.86927I 0
u = 0.08851 − 1.58806I
a = −0.499554 − 0.013294I
b = 1.192900 − 0.167411I
11.75780 + 2.86927I 0
u = 0.07767 + 1.59080I
a = 0.31543 − 1.81519I
b = 0.36546 + 1.43425I
10.92660 − 0.53406I 0
u = 0.07767 − 1.59080I
a = 0.31543 + 1.81519I
b = 0.36546 − 1.43425I
10.92660 + 0.53406I 0
u = 0.14393 + 1.59724I
a = −0.01779 + 2.26870I
b = −0.048367 − 1.098220I
10.02040 − 5.42403I 0
u = 0.14393 − 1.59724I
a = −0.01779 − 2.26870I
b = −0.048367 + 1.098220I
10.02040 + 5.42403I 0
u = 0.00999 + 1.62086I
a = −0.32346 − 1.87968I
b = −0.35353 + 1.46380I
17.4703 − 2.6861I 0
u = 0.00999 − 1.62086I
a = −0.32346 + 1.87968I
b = −0.35353 − 1.46380I
17.4703 + 2.6861I 0
u = −0.15869 + 1.63585I
a = −0.25913 − 1.78272I
b = −0.39647 + 1.42419I
10.77460 + 5.03788I 0
u = −0.15869 − 1.63585I
a = −0.25913 + 1.78272I
b = −0.39647 − 1.42419I
10.77460 − 5.03788I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23701 + 1.62979I
a = 0.42275 + 1.68597I
b = 0.63809 − 1.35812I
8.8506 + 11.2317I 0
u = −0.23701 − 1.62979I
a = 0.42275 − 1.68597I
b = 0.63809 + 1.35812I
8.8506 − 11.2317I 0
u = 0.17330 + 1.64014I
a = 0.465694 − 0.121420I
b = −1.196240 + 0.249549I
11.58050 − 8.05691I 0
u = 0.17330 − 1.64014I
a = 0.465694 + 0.121420I
b = −1.196240 − 0.249549I
11.58050 + 8.05691I 0
u = −0.313436
a = 0.420211
b = −0.362858
−0.621610 −15.9200
u = 0.050078 + 0.277688I
a = −0.89153 + 1.57529I
b = −0.664853 + 0.126557I
−0.930568 − 0.261352I −10.83012 − 1.62800I
u = 0.050078 − 0.277688I
a = −0.89153 − 1.57529I
b = −0.664853 − 0.126557I
−0.930568 + 0.261352I −10.83012 + 1.62800I
u = 0.18363 + 1.71053I
a = 0.20893 − 1.79674I
b = 0.42095 + 1.43650I
17.1323 − 8.4610I 0
u = 0.18363 − 1.71053I
a = 0.20893 + 1.79674I
b = 0.42095 − 1.43650I
17.1323 + 8.4610I 0
u = 0.24399 + 1.71973I
a = −0.36048 + 1.69027I
b = −0.65719 − 1.36333I
15.1368 − 14.7023I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24399 − 1.71973I
a = −0.36048 − 1.69027I
b = −0.65719 + 1.36333I
15.1368 + 14.7023I 0
12
II. I
u
2
= hb, u
2
+ a + 2, u
3
+ 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−u
2
− 2
0
a
9
=
1
u
2
a
3
=
−u
2
− 2
0
a
2
=
−u
2
− 2
u
a
5
=
0
−u
a
7
=
1
0
a
12
=
u
−u + 1
a
10
=
u
2
+ 1
u
a
11
=
u
2
− u + 1
u
a
6
=
u
2
+ u
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
− 3u − 14
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
u
3
− 3u
2
+ 5u − 2
c
6
, c
8
, c
9
u
3
+ 2u − 1
c
10
, c
11
, c
12
u
3
+ 2u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
7
y
3
c
5
y
3
+ y
2
+ 13y −4
c
6
, c
8
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = 0.102785 + 0.665457I
b = 0
7.79580 + 5.13794I −11.21712 − 3.73768I
u = −0.22670 − 1.46771I
a = 0.102785 − 0.665457I
b = 0
7.79580 − 5.13794I −11.21712 + 3.73768I
u = 0.453398
a = −2.20557
b = 0
−2.43213 −15.5660
16
III. I
u
3
= hb, −u
3
− u
2
+ a − 2u − 2, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
u
3
+ u
2
+ 2u + 2
0
a
9
=
1
u
2
a
3
=
u
3
+ u
2
+ 2u + 2
0
a
2
=
u
3
+ u
2
+ 2u + 2
u
a
5
=
0
−u
a
7
=
1
0
a
12
=
u
u
3
+ u
a
10
=
u
2
+ 1
−u
3
− 2u − 1
a
11
=
u
3
+ u
2
+ 2u + 2
−u
3
− 2u − 1
a
6
=
u
3
+ 2u + 1
u
3
+ u
2
+ u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
3
+ 2u
2
− u − 12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
(u
2
+ u + 1)
2
c
6
, c
8
, c
9
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
10
, c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
(y
2
+ y + 1)
2
c
6
, c
8
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = 1.070700 + 0.758745I
b = 0
1.64493 + 2.02988I −11.23686 − 2.38721I
u = −0.621744 − 0.440597I
a = 1.070700 − 0.758745I
b = 0
1.64493 − 2.02988I −11.23686 + 2.38721I
u = 0.121744 + 1.306620I
a = −0.070696 + 0.758745I
b = 0
1.64493 − 2.02988I −14.2631 + 3.6750I
u = 0.121744 − 1.306620I
a = −0.070696 − 0.758745I
b = 0
1.64493 + 2.02988I −14.2631 − 3.6750I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
7
)(u
71
+ 30u
70
+ ··· + 63u + 1)
c
2
((u − 1)
7
)(u
71
− 8u
70
+ ··· − u + 1)
c
3
, c
7
u
7
(u
71
+ u
70
+ ··· + 320u + 128)
c
4
((u + 1)
7
)(u
71
− 8u
70
+ ··· − u + 1)
c
5
((u
2
+ u + 1)
2
)(u
3
− 3u
2
+ 5u − 2)(u
71
− 2u
70
+ ··· − 784u + 4360)
c
6
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
71
+ 2u
70
+ ··· + 4u + 1)
c
8
, c
9
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)(u
71
− 8u
70
+ ··· − 336u + 49)
c
10
, c
11
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
71
+ 2u
70
+ ··· + 4u + 1)
c
12
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
71
− 8u
70
+ ··· − 336u + 49)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
7
)(y
71
+ 30y
70
+ ··· + 3271y −1)
c
2
, c
4
((y −1)
7
)(y
71
− 30y
70
+ ··· + 63y −1)
c
3
, c
7
y
7
(y
71
+ 45y
70
+ ··· − 233472y −16384)
c
5
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y −4)
· (y
71
+ 36y
70
+ ··· − 370918384y −19009600)
c
6
, c
10
, c
11
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)(y
71
+ 68y
70
+ ··· + 12y −1)
c
8
, c
9
, c
12
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
71
+ 80y
70
+ ··· − 77420y −2401)
22
