12a
0081
(K12a
0081
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 9 11 4 7 1 12 6 10
Solving Sequence
4,7
8
1,9
10 3 2 5 12 11 6
c
7
c
8
c
9
c
3
c
1
c
4
c
12
c
10
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.57817 × 10
68
u
82
− 4.41680 × 10
68
u
81
+ ··· + 1.40607 × 10
69
b − 1.45069 × 10
70
,
− 8.02816 × 10
70
u
82
− 7.69195 × 10
70
u
81
+ ··· + 1.71541 × 10
71
a − 8.36164 × 10
71
,
u
83
+ u
82
+ ··· + 24u + 16i
I
v
1
= ha, −v
3
+ 2v
2
+ b − 3v + 1, v
4
− 2v
3
+ 3v
2
− v + 1i
* 2 irreducible components of dim
C
= 0, with total 87 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−4.58 × 10
68
u
82
− 4.42 × 10
68
u
81
+ · · · + 1.41 × 10
69
b − 1.45 ×
10
70
, −8.03 × 10
70
u
82
− 7.69 × 10
70
u
81
+ · · · + 1.72 × 10
71
a − 8.36 ×
10
71
, u
83
+ u
82
+ · · · + 24u + 16i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
1
=
0.468003u
82
+ 0.448403u
81
+ ··· + 25.8370u + 4.87443
0.325600u
82
+ 0.314123u
81
+ ··· + 27.3694u + 10.3173
a
9
=
u
2
+ 1
u
2
a
10
=
−0.300402u
82
− 0.851248u
81
+ ··· − 25.8721u − 4.83081
−0.617837u
82
− 0.388150u
81
+ ··· − 21.4249u + 11.7726
a
3
=
u
u
3
+ u
a
2
=
0.518352u
82
+ 0.412444u
81
+ ··· + 28.9820u + 7.48317
0.507921u
82
+ 0.442205u
81
+ ··· + 31.7802u + 14.3070
a
5
=
−0.0480076u
82
+ 0.115039u
81
+ ··· + 8.55001u + 5.12927
0.419995u
82
+ 0.563442u
81
+ ··· + 34.3871u + 10.0037
a
12
=
−0.535339u
82
− 0.604770u
81
+ ··· − 41.7844u − 16.0490
0.173440u
82
− 0.441183u
81
+ ··· − 33.7669u − 28.0780
a
11
=
1.16268u
82
+ 0.674679u
81
+ ··· + 49.5790u − 5.78307
0.545400u
82
+ 0.632005u
81
+ ··· + 36.8130u + 12.6970
a
6
=
0.340652u
82
+ 0.495917u
81
+ ··· + 30.9853u + 15.6302
0.483055u
82
+ 0.630197u
81
+ ··· + 29.4529u + 10.1873
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.97759u
82
− 1.33141u
81
+ ··· − 38.4761u + 8.31564
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
83
+ 45u
82
+ ··· + 4u + 1
c
2
, c
4
u
83
− 5u
82
+ ··· − 6u + 1
c
3
, c
7
u
83
+ u
82
+ ··· + 24u + 16
c
5
u
83
+ 2u
82
+ ··· + 15190u + 7769
c
6
, c
11
u
83
+ 2u
82
+ ··· + 2u + 1
c
8
u
83
− 27u
82
+ ··· − 5056u + 256
c
9
, c
10
, c
12
u
83
− 20u
82
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
83
− 9y
82
+ ··· + 44y −1
c
2
, c
4
y
83
− 45y
82
+ ··· + 4y −1
c
3
, c
7
y
83
+ 27y
82
+ ··· − 5056y −256
c
5
y
83
+ 28y
82
+ ··· + 953082182y −60357361
c
6
, c
11
y
83
+ 20y
82
+ ··· + 6y −1
c
8
y
83
+ 51y
82
+ ··· + 1724416y −65536
c
9
, c
10
, c
12
y
83
+ 88y
82
+ ··· + 190y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.625725 + 0.803794I
a = 0.95593 − 1.78325I
b = −0.809211 − 0.773750I
−2.81993 + 3.24237I 0
u = −0.625725 − 0.803794I
a = 0.95593 + 1.78325I
b = −0.809211 + 0.773750I
−2.81993 − 3.24237I 0
u = 0.823326 + 0.601133I
a = 0.994172 + 0.602548I
b = 0.97443 + 1.36618I
−7.35489 + 5.05736I 0
u = 0.823326 − 0.601133I
a = 0.994172 − 0.602548I
b = 0.97443 − 1.36618I
−7.35489 − 5.05736I 0
u = −0.811916 + 0.631020I
a = −0.985111 + 0.659411I
b = −0.84786 + 1.43938I
−7.63827 + 1.26608I 0
u = −0.811916 − 0.631020I
a = −0.985111 − 0.659411I
b = −0.84786 − 1.43938I
−7.63827 − 1.26608I 0
u = −0.133744 + 1.033610I
a = −0.235231 + 0.258306I
b = 0.952290 + 0.214525I
2.24045 + 2.24996I 0
u = −0.133744 − 1.033610I
a = −0.235231 − 0.258306I
b = 0.952290 − 0.214525I
2.24045 − 2.24996I 0
u = 0.718219 + 0.755764I
a = −1.01018 − 1.43608I
b = 0.328670 − 1.008960I
−4.52117 + 0.45961I 0
u = 0.718219 − 0.755764I
a = −1.01018 + 1.43608I
b = 0.328670 + 1.008960I
−4.52117 − 0.45961I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.583379 + 0.744333I
a = −0.599499 + 0.857080I
b = −0.084857 + 0.949548I
−1.06506 + 1.56831I −4.77521 − 3.38157I
u = −0.583379 − 0.744333I
a = −0.599499 − 0.857080I
b = −0.084857 − 0.949548I
−1.06506 − 1.56831I −4.77521 + 3.38157I
u = −0.699113 + 0.817903I
a = 1.03783 − 1.03599I
b = 1.03036 − 1.77245I
−10.88710 − 1.33695I 0
u = −0.699113 − 0.817903I
a = 1.03783 + 1.03599I
b = 1.03036 + 1.77245I
−10.88710 + 1.33695I 0
u = −0.761911 + 0.520219I
a = 0.419807 − 0.889805I
b = 0.245481 − 0.220375I
−0.709170 − 1.043470I − 60.10 + 0.525052I
u = −0.761911 − 0.520219I
a = 0.419807 + 0.889805I
b = 0.245481 + 0.220375I
−0.709170 + 1.043470I − 60.10 − 0.525052I
u = 0.843982 + 0.682431I
a = −1.033390 − 0.928808I
b = −0.476474 − 1.005040I
−4.36263 + 2.17365I 0
u = 0.843982 − 0.682431I
a = −1.033390 + 0.928808I
b = −0.476474 + 1.005040I
−4.36263 − 2.17365I 0
u = −0.894299 + 0.161895I
a = −0.276725 − 0.077384I
b = −0.201389 + 0.785138I
−5.54438 + 1.11456I −5.40813 + 0.61307I
u = −0.894299 − 0.161895I
a = −0.276725 + 0.077384I
b = −0.201389 − 0.785138I
−5.54438 − 1.11456I −5.40813 − 0.61307I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.899076 + 0.117669I
a = 0.356440 − 0.034756I
b = 0.361343 + 0.806350I
−5.43027 + 4.95461I −4.96710 − 6.01399I
u = 0.899076 − 0.117669I
a = 0.356440 + 0.034756I
b = 0.361343 − 0.806350I
−5.43027 − 4.95461I −4.96710 + 6.01399I
u = 0.482182 + 0.982828I
a = 0.288985 + 1.186530I
b = −0.515329 + 0.386646I
3.22997 − 1.59915I 0
u = 0.482182 − 0.982828I
a = 0.288985 − 1.186530I
b = −0.515329 − 0.386646I
3.22997 + 1.59915I 0
u = 0.711300 + 0.832616I
a = −1.01619 − 1.09996I
b = −0.88624 − 1.84707I
−11.15090 − 5.10243I 0
u = 0.711300 − 0.832616I
a = −1.01619 + 1.09996I
b = −0.88624 + 1.84707I
−11.15090 + 5.10243I 0
u = −0.615819 + 0.910490I
a = 0.610401 − 0.943583I
b = 0.554605 − 0.956704I
−2.48058 + 1.63613I 0
u = −0.615819 − 0.910490I
a = 0.610401 + 0.943583I
b = 0.554605 + 0.956704I
−2.48058 − 1.63613I 0
u = 0.177547 + 1.086860I
a = −0.252176 + 0.904141I
b = 0.383665 − 0.271787I
−1.02878 + 1.71356I 0
u = 0.177547 − 1.086860I
a = −0.252176 − 0.904141I
b = 0.383665 + 0.271787I
−1.02878 − 1.71356I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.907958 + 0.636974I
a = 1.005050 − 0.653160I
b = 0.911110 − 0.798415I
−2.46547 − 5.87569I 0
u = −0.907958 − 0.636974I
a = 1.005050 + 0.653160I
b = 0.911110 + 0.798415I
−2.46547 + 5.87569I 0
u = 0.042401 + 1.116900I
a = 0.433979 + 0.466369I
b = −0.986304 − 0.010974I
5.17570 + 0.24359I 0
u = 0.042401 − 1.116900I
a = 0.433979 − 0.466369I
b = −0.986304 + 0.010974I
5.17570 − 0.24359I 0
u = −0.612006 + 0.947681I
a = −0.555624 + 1.230060I
b = 0.671376 + 0.949859I
−0.42036 + 3.20206I 0
u = −0.612006 − 0.947681I
a = −0.555624 − 1.230060I
b = 0.671376 − 0.949859I
−0.42036 − 3.20206I 0
u = −0.688688 + 0.902295I
a = 1.35307 − 1.82858I
b = −1.17653 − 1.38858I
−10.62590 + 6.67086I 0
u = −0.688688 − 0.902295I
a = 1.35307 + 1.82858I
b = −1.17653 + 1.38858I
−10.62590 − 6.67086I 0
u = −0.130223 + 1.128200I
a = 0.371504 + 0.849128I
b = −0.586964 − 0.357707I
−0.78024 + 4.16353I 0
u = −0.130223 − 1.128200I
a = 0.371504 − 0.849128I
b = −0.586964 + 0.357707I
−0.78024 − 4.16353I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.705533 + 0.893072I
a = −1.36631 − 1.76146I
b = 1.05906 − 1.46524I
−10.96570 − 0.32078I 0
u = 0.705533 − 0.893072I
a = −1.36631 + 1.76146I
b = 1.05906 + 1.46524I
−10.96570 + 0.32078I 0
u = 0.178051 + 1.133310I
a = 0.475422 + 0.121754I
b = −1.104570 + 0.260893I
4.88279 − 5.16978I 0
u = 0.178051 − 1.133310I
a = 0.475422 − 0.121754I
b = −1.104570 − 0.260893I
4.88279 + 5.16978I 0
u = 0.682445 + 0.946950I
a = −0.606629 − 1.215410I
b = −0.077100 − 1.272730I
−3.93501 − 5.83096I 0
u = 0.682445 − 0.946950I
a = −0.606629 + 1.215410I
b = −0.077100 + 1.272730I
−3.93501 + 5.83096I 0
u = −0.328722 + 1.121940I
a = −0.378755 − 0.308254I
b = 0.871825 + 0.461176I
−2.09689 + 3.19207I 0
u = −0.328722 − 1.121940I
a = −0.378755 + 0.308254I
b = 0.871825 − 0.461176I
−2.09689 − 3.19207I 0
u = −0.024967 + 0.807121I
a = 0.02719 − 2.76173I
b = −0.077777 + 0.925635I
−6.94496 − 3.05666I −3.34321 + 2.43833I
u = −0.024967 − 0.807121I
a = 0.02719 + 2.76173I
b = −0.077777 − 0.925635I
−6.94496 + 3.05666I −3.34321 − 2.43833I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.953754 + 0.717155I
a = −1.34040 − 0.64551I
b = −1.17536 − 1.41586I
−10.65320 + 3.17121I 0
u = 0.953754 − 0.717155I
a = −1.34040 + 0.64551I
b = −1.17536 + 1.41586I
−10.65320 − 3.17121I 0
u = 0.612206 + 1.024920I
a = 0.49614 + 1.38727I
b = −1.042550 + 0.782141I
1.70143 − 6.86053I 0
u = 0.612206 − 1.024920I
a = 0.49614 − 1.38727I
b = −1.042550 − 0.782141I
1.70143 + 6.86053I 0
u = −0.965499 + 0.705935I
a = 1.32437 − 0.58698I
b = 1.28457 − 1.33784I
−10.27720 − 9.51955I 0
u = −0.965499 − 0.705935I
a = 1.32437 + 0.58698I
b = 1.28457 + 1.33784I
−10.27720 + 9.51955I 0
u = 0.308366 + 1.156900I
a = 0.497714 − 0.266067I
b = −0.962809 + 0.528516I
−1.69711 − 9.21658I 0
u = 0.308366 − 1.156900I
a = 0.497714 + 0.266067I
b = −0.962809 − 0.528516I
−1.69711 + 9.21658I 0
u = −0.658528 + 1.040780I
a = 0.255350 − 1.290700I
b = −0.415674 − 0.643365I
0.75318 + 6.40214I 0
u = −0.658528 − 1.040780I
a = 0.255350 + 1.290700I
b = −0.415674 + 0.643365I
0.75318 − 6.40214I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.620582 + 0.449791I
a = 0.654422 + 0.442608I
b = 0.668686 + 0.618299I
0.19658 + 1.98439I −0.35883 − 3.65260I
u = 0.620582 − 0.449791I
a = 0.654422 − 0.442608I
b = 0.668686 − 0.618299I
0.19658 − 1.98439I −0.35883 + 3.65260I
u = −0.702934 + 1.028920I
a = −0.69461 + 1.46829I
b = 1.29225 + 1.30098I
−6.45103 + 4.41679I 0
u = −0.702934 − 1.028920I
a = −0.69461 − 1.46829I
b = 1.29225 − 1.30098I
−6.45103 − 4.41679I 0
u = 0.697502 + 1.045330I
a = 0.66970 + 1.50286I
b = −1.38883 + 1.22662I
−6.03150 − 10.74760I 0
u = 0.697502 − 1.045330I
a = 0.66970 − 1.50286I
b = −1.38883 − 1.22662I
−6.03150 + 10.74760I 0
u = 0.725825 + 1.027170I
a = −0.41366 − 1.49953I
b = 0.739147 − 1.174460I
−3.29687 − 8.03651I 0
u = 0.725825 − 1.027170I
a = −0.41366 + 1.49953I
b = 0.739147 + 1.174460I
−3.29687 + 8.03651I 0
u = 0.734057 + 0.024032I
a = 0.624319 + 0.126422I
b = 0.622005 − 0.237528I
0.75127 − 2.02484I 1.59693 + 6.45609I
u = 0.734057 − 0.024032I
a = 0.624319 − 0.126422I
b = 0.622005 + 0.237528I
0.75127 + 2.02484I 1.59693 − 6.45609I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.731167 + 1.068540I
a = 0.27765 − 1.58986I
b = −1.08074 − 0.92958I
−1.11740 + 11.92050I 0
u = −0.731167 − 1.068540I
a = 0.27765 + 1.58986I
b = −1.08074 + 0.92958I
−1.11740 − 11.92050I 0
u = 0.032183 + 0.683518I
a = 0.122279 + 0.645170I
b = 0.378758 + 0.708726I
−0.18526 + 1.83671I −0.17945 − 5.42341I
u = 0.032183 − 0.683518I
a = 0.122279 − 0.645170I
b = 0.378758 − 0.708726I
−0.18526 − 1.83671I −0.17945 + 5.42341I
u = 0.786417 + 1.062400I
a = −0.39849 − 1.77701I
b = 1.45355 − 1.41705I
−9.54622 − 9.55900I 0
u = 0.786417 − 1.062400I
a = −0.39849 + 1.77701I
b = 1.45355 + 1.41705I
−9.54622 + 9.55900I 0
u = −0.785674 + 1.073250I
a = 0.35783 − 1.79447I
b = −1.54191 − 1.32398I
−9.0989 + 15.9376I 0
u = −0.785674 − 1.073250I
a = 0.35783 + 1.79447I
b = −1.54191 + 1.32398I
−9.0989 − 15.9376I 0
u = −0.285370 + 0.536051I
a = −0.20738 − 2.27538I
b = −0.292337 + 0.215670I
−1.090240 − 0.878173I 1.75140 − 2.55924I
u = −0.285370 − 0.536051I
a = −0.20738 + 2.27538I
b = −0.292337 − 0.215670I
−1.090240 + 0.878173I 1.75140 + 2.55924I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.009997 + 0.555746I
a = 0.044009 + 1.061120I
b = 0.10010 + 1.81655I
−7.85138 + 3.20272I 2.27436 − 3.02667I
u = −0.009997 − 0.555746I
a = 0.044009 − 1.061120I
b = 0.10010 − 1.81655I
−7.85138 − 3.20272I 2.27436 + 3.02667I
u = −0.554632
a = −1.06641
b = −0.304951
−1.12795 −9.38540
13
II. I
v
1
= ha, −v
3
+ 2v
2
+ b − 3v + 1, v
4
− 2v
3
+ 3v
2
− v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
1
=
0
v
3
− 2v
2
+ 3v − 1
a
9
=
1
0
a
10
=
1
v
3
− v
2
+ v + 2
a
3
=
v
0
a
2
=
v
v
3
− 2v
2
+ 3v − 1
a
5
=
0
−v
3
+ 2v
2
− 3v + 1
a
12
=
−v
3
+ 2v
2
− 3v + 1
−v
3
+ 3v
2
− 4v + 2
a
11
=
−v
3
+ v
2
− v − 1
−v
3
+ 2v
2
− 2v
a
6
=
−v
3
+ 2v
2
− 3v + 1
−v
3
+ 2v
2
− 3v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −v
3
+ 2v
2
+ 3v − 12
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
9
, c
10
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
6
u
4
+ u
3
+ u
2
+ 1
c
11
u
4
− u
3
+ u
2
+ 1
c
12
u
4
− u
3
+ 3u
2
− 2u + 1
15
(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
, c
8
y
4
c
5
, c
9
, c
10
c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
6
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.043315 + 0.641200I
a = 0
b = −0.10488 + 1.55249I
−8.43568 − 3.16396I −12.63523 + 2.29471I
v = 0.043315 − 0.641200I
a = 0
b = −0.10488 − 1.55249I
−8.43568 + 3.16396I −12.63523 − 2.29471I
v = 0.95668 + 1.22719I
a = 0
b = −0.395123 + 0.506844I
−1.43393 − 1.41510I −6.86477 + 6.85627I
v = 0.95668 − 1.22719I
a = 0
b = −0.395123 − 0.506844I
−1.43393 + 1.41510I −6.86477 − 6.85627I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
83
+ 45u
82
+ ··· + 4u + 1)
c
2
((u − 1)
4
)(u
83
− 5u
82
+ ··· − 6u + 1)
c
3
, c
7
u
4
(u
83
+ u
82
+ ··· + 24u + 16)
c
4
((u + 1)
4
)(u
83
− 5u
82
+ ··· − 6u + 1)
c
5
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
83
+ 2u
82
+ ··· + 15190u + 7769)
c
6
(u
4
+ u
3
+ u
2
+ 1)(u
83
+ 2u
82
+ ··· + 2u + 1)
c
8
u
4
(u
83
− 27u
82
+ ··· − 5056u + 256)
c
9
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
83
− 20u
82
+ ··· + 6u + 1)
c
11
(u
4
− u
3
+ u
2
+ 1)(u
83
+ 2u
82
+ ··· + 2u + 1)
c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
83
− 20u
82
+ ··· + 6u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
4
)(y
83
− 9y
82
+ ··· + 44y − 1)
c
2
, c
4
((y − 1)
4
)(y
83
− 45y
82
+ ··· + 4y − 1)
c
3
, c
7
y
4
(y
83
+ 27y
82
+ ··· − 5056y − 256)
c
5
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
83
+ 28y
82
+ ··· + 953082182y − 60357361)
c
6
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
83
+ 20y
82
+ ··· + 6y − 1)
c
8
y
4
(y
83
+ 51y
82
+ ··· + 1724416y − 65536)
c
9
, c
10
, c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
83
+ 88y
82
+ ··· + 190y − 1)
19
