12n
0317
(K12n
0317
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 2 10 11 3 12 5 9 10
Solving Sequence
6,10 3,7
2 1 5 11 4 12 9 8
c
6
c
2
c
1
c
5
c
10
c
4
c
12
c
9
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.91786 × 10
186
u
49
− 4.41920 × 10
186
u
48
+ ··· + 3.02291 × 10
188
b − 8.34981 × 10
189
,
− 8.33281 × 10
189
u
49
+ 2.07014 × 10
190
u
48
+ ··· + 7.45751 × 10
191
a + 3.95262 × 10
193
,
u
50
− 3u
49
+ ··· − 20763u + 2467i
I
u
2
= h−215u
7
+ 940u
6
− 132u
5
− 2470u
4
− 1050u
3
− 1010u
2
+ 714b − 1325u + 456,
33u
7
− 457u
6
+ 1280u
5
+ 678u
4
− 3752u
3
− 2070u
2
+ 714a − 1363u − 3697,
u
8
− 4u
7
− u
6
+ 12u
5
+ 8u
4
+ 6u
3
+ 11u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 58 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
= h1.92 × 10
186
u
49
− 4.42 × 10
186
u
48
+ · · · + 3.02 × 10
188
b − 8.35 ×
10
189
, −8.33 × 10
189
u
49
+ 2.07 × 10
190
u
48
+ · · · + 7.46 × 10
191
a + 3.95 ×
10
193
, u
50
− 3u
49
+ · · · − 20763u + 2467i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
0.0111737u
49
− 0.0277592u
48
+ ··· + 350.989u − 53.0019
−0.00634441u
49
+ 0.0146190u
48
+ ··· − 179.609u + 27.6218
a
7
=
1
u
2
a
2
=
0.00482931u
49
− 0.0131401u
48
+ ··· + 171.380u − 25.3800
−0.00634441u
49
+ 0.0146190u
48
+ ··· − 179.609u + 27.6218
a
1
=
−0.00125206u
49
+ 0.00578813u
48
+ ··· − 123.642u + 25.1827
−0.00103824u
49
+ 0.00521397u
48
+ ··· − 175.306u + 29.1803
a
5
=
0.00963656u
49
− 0.0235349u
48
+ ··· + 264.866u − 35.0739
0.00325201u
49
− 0.00880623u
48
+ ··· + 84.8902u − 6.25925
a
11
=
−0.0121639u
49
+ 0.0321646u
48
+ ··· − 424.122u + 61.3195
−0.000528690u
49
+ 0.00275946u
48
+ ··· − 54.2826u + 5.53435
a
4
=
0.00923043u
49
− 0.0215045u
48
+ ··· + 267.799u − 42.0742
0.00540308u
49
− 0.0125904u
48
+ ··· + 102.752u − 8.26248
a
12
=
−0.00125206u
49
+ 0.00578813u
48
+ ··· − 123.642u + 25.1827
0.00199645u
49
− 0.000875897u
48
+ ··· − 130.028u + 24.1675
a
9
=
0.00315773u
49
− 0.00845015u
48
+ ··· + 155.251u − 29.5459
0.00922550u
49
− 0.0248174u
48
+ ··· + 380.914u − 56.7451
a
8
=
0.00526362u
49
− 0.00912528u
48
+ ··· + 65.8379u − 6.54803
0.00917621u
49
− 0.0232077u
48
+ ··· + 309.861u − 48.3200
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0301306u
49
− 0.0796043u
48
+ ··· + 1263.65u − 235.993
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
+ 27u
49
+ ··· + 279u + 81
c
2
, c
5
u
50
+ 3u
49
+ ··· + 27u + 9
c
3
u
50
− 9u
49
+ ··· + 6491u + 1543
c
4
, c
8
u
50
+ 3u
49
+ ··· − 72u + 36
c
6
u
50
+ 3u
49
+ ··· + 20763u + 2467
c
7
u
50
− 3u
49
+ ··· − 1360u + 64
c
9
, c
11
, c
12
u
50
+ 5u
49
+ ··· + 11u + 1
c
10
u
50
− u
49
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
− 3y
49
+ ··· − 40743y + 6561
c
2
, c
5
y
50
− 27y
49
+ ··· − 279y + 81
c
3
y
50
− 137y
49
+ ··· + 71302107y + 2380849
c
4
, c
8
y
50
+ 53y
49
+ ··· + 2232y + 1296
c
6
y
50
+ 43y
49
+ ··· − 163462273y + 6086089
c
7
y
50
+ 143y
49
+ ··· + 1959168y + 4096
c
9
, c
11
, c
12
y
50
− 39y
49
+ ··· − 35y + 1
c
10
y
50
+ 9y
49
+ ··· − 35y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663546 + 0.807023I
a = −0.149925 − 1.093180I
b = 0.227624 + 0.962311I
3.78569 + 3.81617I 5.99930 − 6.58404I
u = −0.663546 − 0.807023I
a = −0.149925 + 1.093180I
b = 0.227624 − 0.962311I
3.78569 − 3.81617I 5.99930 + 6.58404I
u = 0.989845 + 0.334652I
a = −0.852002 − 0.574478I
b = 0.075144 + 0.777118I
−2.75103 + 1.66476I 0
u = 0.989845 − 0.334652I
a = −0.852002 + 0.574478I
b = 0.075144 − 0.777118I
−2.75103 − 1.66476I 0
u = −1.038610 + 0.115738I
a = 0.07663 + 1.46376I
b = 1.283560 − 0.355028I
−11.43970 + 0.61215I −5.56930 − 0.95685I
u = −1.038610 − 0.115738I
a = 0.07663 − 1.46376I
b = 1.283560 + 0.355028I
−11.43970 − 0.61215I −5.56930 + 0.95685I
u = −0.976418 + 0.409184I
a = −0.117550 − 1.213630I
b = −0.889554 − 0.262388I
6.22845 − 1.17042I −3.22256 + 0.I
u = −0.976418 − 0.409184I
a = −0.117550 + 1.213630I
b = −0.889554 + 0.262388I
6.22845 + 1.17042I −3.22256 + 0.I
u = 0.856388 + 0.349802I
a = −0.217606 − 1.026260I
b = −0.931404 + 0.588464I
−1.84212 + 2.10652I −6.74335 − 2.91333I
u = 0.856388 − 0.349802I
a = −0.217606 + 1.026260I
b = −0.931404 − 0.588464I
−1.84212 − 2.10652I −6.74335 + 2.91333I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666952 + 0.913096I
a = −0.008649 − 0.157261I
b = 0.697921 + 0.367007I
1.14279 − 1.51204I 0
u = −0.666952 − 0.913096I
a = −0.008649 + 0.157261I
b = 0.697921 − 0.367007I
1.14279 + 1.51204I 0
u = 0.553985 + 0.646141I
a = 0.195853 + 0.760473I
b = 0.095352 − 0.510935I
0.078263 − 1.314770I 0.82809 + 5.18119I
u = 0.553985 − 0.646141I
a = 0.195853 − 0.760473I
b = 0.095352 + 0.510935I
0.078263 + 1.314770I 0.82809 − 5.18119I
u = 0.772929 + 0.314148I
a = −0.24097 − 2.31460I
b = 1.197270 + 0.484749I
−6.02259 − 6.28550I −2.35130 + 4.21184I
u = 0.772929 − 0.314148I
a = −0.24097 + 2.31460I
b = 1.197270 − 0.484749I
−6.02259 + 6.28550I −2.35130 − 4.21184I
u = 1.232170 + 0.182436I
a = 0.142577 + 0.722468I
b = 1.327810 − 0.185520I
−8.47541 − 5.36250I 0
u = 1.232170 − 0.182436I
a = 0.142577 − 0.722468I
b = 1.327810 + 0.185520I
−8.47541 + 5.36250I 0
u = −0.665058 + 0.099931I
a = −0.450338 − 0.389982I
b = −1.190510 + 0.112073I
−1.93432 + 0.03774I −6.75026 + 1.46726I
u = −0.665058 − 0.099931I
a = −0.450338 + 0.389982I
b = −1.190510 − 0.112073I
−1.93432 − 0.03774I −6.75026 − 1.46726I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.219730 + 0.587243I
a = −0.224495 + 0.844921I
b = −0.158932 − 0.906350I
−6.85044 + 3.69371I 0
u = −1.219730 − 0.587243I
a = −0.224495 − 0.844921I
b = −0.158932 + 0.906350I
−6.85044 − 3.69371I 0
u = 0.572239 + 0.270156I
a = 0.04237 + 1.45670I
b = −1.203320 − 0.645182I
−1.68209 − 2.49103I −8.75436 + 6.26567I
u = 0.572239 − 0.270156I
a = 0.04237 − 1.45670I
b = −1.203320 + 0.645182I
−1.68209 + 2.49103I −8.75436 − 6.26567I
u = −0.504003 + 0.379964I
a = 1.17363 + 1.99927I
b = −0.391480 − 0.395210I
2.40372 + 0.20646I 4.09834 + 1.60523I
u = −0.504003 − 0.379964I
a = 1.17363 − 1.99927I
b = −0.391480 + 0.395210I
2.40372 − 0.20646I 4.09834 − 1.60523I
u = 0.988631 + 0.981714I
a = 0.270126 + 0.926267I
b = −0.867195 − 0.191758I
−1.69134 − 0.97922I 0
u = 0.988631 − 0.981714I
a = 0.270126 − 0.926267I
b = −0.867195 + 0.191758I
−1.69134 + 0.97922I 0
u = −0.74624 + 1.31133I
a = 0.534856 − 1.257750I
b = −1.029620 + 0.449989I
0.61177 + 3.94770I 0
u = −0.74624 − 1.31133I
a = 0.534856 + 1.257750I
b = −1.029620 − 0.449989I
0.61177 − 3.94770I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.08135 + 1.05259I
a = −0.017301 + 1.142600I
b = 1.215370 − 0.580128I
0.77226 + 9.34517I 0
u = −1.08135 − 1.05259I
a = −0.017301 − 1.142600I
b = 1.215370 + 0.580128I
0.77226 − 9.34517I 0
u = 0.345794 + 0.327250I
a = −0.38006 − 1.82618I
b = 0.824382 − 0.600279I
8.49427 + 2.35863I 9.67846 − 4.20278I
u = 0.345794 − 0.327250I
a = −0.38006 + 1.82618I
b = 0.824382 + 0.600279I
8.49427 − 2.35863I 9.67846 + 4.20278I
u = 1.29112 + 0.85257I
a = 0.129364 − 0.986571I
b = −0.333303 + 0.969379I
−2.65959 − 9.10689I 0
u = 1.29112 − 0.85257I
a = 0.129364 + 0.986571I
b = −0.333303 − 0.969379I
−2.65959 + 9.10689I 0
u = 1.27077 + 0.89539I
a = 0.166830 − 0.847725I
b = 1.141690 + 0.428927I
−2.80920 − 5.12014I 0
u = 1.27077 − 0.89539I
a = 0.166830 + 0.847725I
b = 1.141690 − 0.428927I
−2.80920 + 5.12014I 0
u = 0.353111 + 0.190645I
a = 1.170400 + 0.676061I
b = −0.715685 − 0.985730I
0.02992 − 4.02059I −0.43876 + 11.60977I
u = 0.353111 − 0.190645I
a = 1.170400 − 0.676061I
b = −0.715685 + 0.985730I
0.02992 + 4.02059I −0.43876 − 11.60977I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.68410 + 0.25011I
a = −0.209855 + 0.322284I
b = −1.203160 − 0.421900I
−6.47293 − 2.51617I 0
u = 1.68410 − 0.25011I
a = −0.209855 − 0.322284I
b = −1.203160 + 0.421900I
−6.47293 + 2.51617I 0
u = −1.75503 + 0.68133I
a = −0.093305 − 0.780362I
b = −1.229330 + 0.542511I
−10.09350 + 8.94227I 0
u = −1.75503 − 0.68133I
a = −0.093305 + 0.780362I
b = −1.229330 − 0.542511I
−10.09350 − 8.94227I 0
u = 1.64933 + 1.01561I
a = −0.043620 + 1.103240I
b = −1.205270 − 0.631705I
−5.3380 − 14.9199I 0
u = 1.64933 − 1.01561I
a = −0.043620 − 1.103240I
b = −1.205270 + 0.631705I
−5.3380 + 14.9199I 0
u = −2.11053 + 0.20467I
a = 0.206325 + 0.667266I
b = 0.947425 − 0.426776I
0.37870 + 1.85992I 0
u = −2.11053 − 0.20467I
a = 0.206325 − 0.667266I
b = 0.947425 + 0.426776I
0.37870 − 1.85992I 0
u = 0.36706 + 6.35882I
a = 0.047914 + 1.066360I
b = 0.815200 − 0.491841I
0.07826 + 2.04862I 0
u = 0.36706 − 6.35882I
a = 0.047914 − 1.066360I
b = 0.815200 + 0.491841I
0.07826 − 2.04862I 0
9
II. I
u
2
= h−215u
7
+ 940u
6
+ · · · + 714b + 456, 33u
7
− 457u
6
+ · · · + 714a −
3697, u
8
− 4u
7
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
3
=
−0.0462185u
7
+ 0.640056u
6
+ ··· + 1.90896u + 5.17787
0.301120u
7
− 1.31653u
6
+ ··· + 1.85574u − 0.638655
a
7
=
1
u
2
a
2
=
0.254902u
7
− 0.676471u
6
+ ··· + 3.76471u + 4.53922
0.301120u
7
− 1.31653u
6
+ ··· + 1.85574u − 0.638655
a
1
=
1.79552u
7
− 7.23389u
6
+ ··· + 17.5770u + 3.05462
−0.151261u
7
+ 0.564426u
6
+ ··· − 1.69188u − 0.948179
a
5
=
−0.610644u
7
+ 3.00700u
6
+ ··· − 3.87955u + 4.56723
0.343137u
7
− 1.35294u
6
+ ··· + 3.02941u − 0.254902
a
11
=
−2.79552u
7
+ 11.2339u
6
+ ··· − 28.5770u − 5.05462
0.203081u
7
− 0.620448u
6
+ ··· + 4.22829u + 1.74370
a
4
=
−1.06303u
7
+ 4.88796u
6
+ ··· − 7.42717u + 4.25770
0.366947u
7
− 1.32913u
6
+ ··· + 3.33894u − 0.326331
a
12
=
1.79552u
7
− 7.23389u
6
+ ··· + 17.5770u + 3.05462
−0.302521u
7
+ 1.12885u
6
+ ··· − 3.38375u − 0.896359
a
9
=
2.79552u
7
− 11.2339u
6
+ ··· + 28.5770u + 5.05462
−0.354342u
7
+ 1.18487u
6
+ ··· − 4.92017u − 1.69188
a
8
=
4.53922u
7
− 18.4118u
6
+ ··· + 45.6176u + 6.31373
−0.697479u
7
+ 2.53782u
6
+ ··· − 7.94958u − 2.43697
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
70
51
u
7
+
92
17
u
6
+
112
51
u
5
−
956
51
u
4
−
568
51
u
3
−
196
51
u
2
−
206
17
u +
52
51
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
4
c
2
, c
5
(u
4
− u
2
+ 1)
2
c
3
u
8
+ 2u
7
+ 11u
6
+ 6u
5
+ 8u
4
+ 12u
3
− u
2
− 4u + 1
c
4
, c
8
(u
2
+ 1)
4
c
6
u
8
− 4u
7
− u
6
+ 12u
5
+ 8u
4
+ 6u
3
+ 11u
2
+ 2u + 1
c
7
u
8
− 8u
7
+ 25u
6
− 38u
5
+ 33u
4
− 28u
3
+ 28u
2
− 16u + 4
c
9
(u
2
− u − 1)
4
c
10
(u
4
+ 3u
2
+ 1)
2
c
11
, c
12
(u
2
+ u − 1)
4
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
4
c
2
, c
5
(y
2
− y + 1)
4
c
3
y
8
+ 18y
7
+ 113y
6
+ 90y
5
− 84y
4
− 90y
3
+ 113y
2
− 18y + 1
c
4
, c
8
(y + 1)
8
c
6
y
8
− 18y
7
+ 113y
6
− 90y
5
− 84y
4
+ 90y
3
+ 113y
2
+ 18y + 1
c
7
y
8
− 14y
7
+ 83y
6
− 186y
5
+ 113y
4
+ 48y
3
+ 152y
2
− 32y + 16
c
9
, c
11
, c
12
(y
2
− 3y + 1)
4
c
10
(y
2
+ 3y + 1)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.216775 + 0.809017I
a = 0.712758 + 0.809017I
b = −0.866025 − 0.500000I
−0.65797 − 2.02988I 2.00000 + 3.46410I
u = 0.216775 − 0.809017I
a = 0.712758 − 0.809017I
b = −0.866025 + 0.500000I
−0.65797 + 2.02988I 2.00000 − 3.46410I
u = −1.153270 + 0.309017I
a = 0.350750 + 0.309017I
b = 0.866025 + 0.500000I
7.23771 − 2.02988I 2.00000 + 3.46410I
u = −1.153270 − 0.309017I
a = 0.350750 − 0.309017I
b = 0.866025 − 0.500000I
7.23771 + 2.02988I 2.00000 − 3.46410I
u = −0.082801 + 0.309017I
a = 4.88532 + 0.30902I
b = −0.866025 + 0.500000I
7.23771 + 2.02988I 2.00000 − 3.46410I
u = −0.082801 − 0.309017I
a = 4.88532 − 0.30902I
b = −0.866025 − 0.500000I
7.23771 − 2.02988I 2.00000 + 3.46410I
u = 3.01929 + 0.80902I
a = 0.051174 + 0.809017I
b = 0.866025 − 0.500000I
−0.65797 + 2.02988I 2.00000 − 3.46410I
u = 3.01929 − 0.80902I
a = 0.051174 − 0.809017I
b = 0.866025 + 0.500000I
−0.65797 − 2.02988I 2.00000 + 3.46410I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
50
+ 27u
49
+ ··· + 279u + 81)
c
2
, c
5
((u
4
− u
2
+ 1)
2
)(u
50
+ 3u
49
+ ··· + 27u + 9)
c
3
(u
8
+ 2u
7
+ 11u
6
+ 6u
5
+ 8u
4
+ 12u
3
− u
2
− 4u + 1)
· (u
50
− 9u
49
+ ··· + 6491u + 1543)
c
4
, c
8
((u
2
+ 1)
4
)(u
50
+ 3u
49
+ ··· − 72u + 36)
c
6
(u
8
− 4u
7
− u
6
+ 12u
5
+ 8u
4
+ 6u
3
+ 11u
2
+ 2u + 1)
· (u
50
+ 3u
49
+ ··· + 20763u + 2467)
c
7
(u
8
− 8u
7
+ 25u
6
− 38u
5
+ 33u
4
− 28u
3
+ 28u
2
− 16u + 4)
· (u
50
− 3u
49
+ ··· − 1360u + 64)
c
9
((u
2
− u − 1)
4
)(u
50
+ 5u
49
+ ··· + 11u + 1)
c
10
((u
4
+ 3u
2
+ 1)
2
)(u
50
− u
49
+ ··· + 3u + 1)
c
11
, c
12
((u
2
+ u − 1)
4
)(u
50
+ 5u
49
+ ··· + 11u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
50
− 3y
49
+ ··· − 40743y + 6561)
c
2
, c
5
((y
2
− y + 1)
4
)(y
50
− 27y
49
+ ··· − 279y + 81)
c
3
(y
8
+ 18y
7
+ 113y
6
+ 90y
5
− 84y
4
− 90y
3
+ 113y
2
− 18y + 1)
· (y
50
− 137y
49
+ ··· + 71302107y + 2380849)
c
4
, c
8
((y + 1)
8
)(y
50
+ 53y
49
+ ··· + 2232y + 1296)
c
6
(y
8
− 18y
7
+ 113y
6
− 90y
5
− 84y
4
+ 90y
3
+ 113y
2
+ 18y + 1)
· (y
50
+ 43y
49
+ ··· − 163462273y + 6086089)
c
7
(y
8
− 14y
7
+ 83y
6
− 186y
5
+ 113y
4
+ 48y
3
+ 152y
2
− 32y + 16)
· (y
50
+ 143y
49
+ ··· + 1959168y + 4096)
c
9
, c
11
, c
12
((y
2
− 3y + 1)
4
)(y
50
− 39y
49
+ ··· − 35y + 1)
c
10
((y
2
+ 3y + 1)
4
)(y
50
+ 9y
49
+ ··· − 35y + 1)
15
