12n
0361
(K12n
0361
)
A knot diagram
1
Linearized knot diagam
3 6 8 1 11 2 10 1 5 7 5 10
Solving Sequence
2,7
6 3
1,11
5 4 10 8 9 12
c
6
c
2
c
1
c
5
c
4
c
10
c
7
c
8
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.05168 × 10
34
u
53
+ 1.07637 × 10
35
u
52
+ ··· + 6.87463 × 10
34
b − 6.05852 × 10
33
,
1.46995 × 10
35
u
53
− 2.86110 × 10
35
u
52
+ ··· + 6.87463 × 10
34
a + 1.14483 × 10
36
, u
54
− 2u
53
+ ··· + 7u + 1i
I
u
2
= h−u
17
− 2u
16
+ ··· + b − 2, −2u
17
− u
16
+ ··· + a − 2u, u
18
+ u
17
+ ··· + u + 1i
* 2 irreducible components of dim
C
= 0, with total 72 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−8.05×10
34
u
53
+1.08×10
35
u
52
+· · ·+6.87×10
34
b−6.06×10
33
, 1.47×
10
35
u
53
−2.86×10
35
u
52
+· · ·+6.87×10
34
a+1.14×10
36
, u
54
−2u
53
+· · ·+7u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
−2.13823u
53
+ 4.16183u
52
+ ··· + 32.8959u − 16.6530
1.17122u
53
− 1.56572u
52
+ ··· − 4.86988u + 0.0881286
a
5
=
1.09873u
53
− 2.43744u
52
+ ··· − 25.3391u + 18.7511
−0.466742u
53
+ 0.548863u
52
+ ··· + 1.52955u − 0.570206
a
4
=
1.26181u
53
− 2.68085u
52
+ ··· − 26.6668u + 18.5566
−0.318054u
53
+ 0.489820u
52
+ ··· + 3.00911u − 0.691152
a
10
=
−0.967010u
53
+ 2.59611u
52
+ ··· + 28.0260u − 16.5649
1.17122u
53
− 1.56572u
52
+ ··· − 4.86988u + 0.0881286
a
8
=
−1.33496u
53
+ 2.06007u
52
+ ··· + 16.5981u − 12.0861
−0.518639u
53
+ 0.583965u
52
+ ··· + 0.382552u + 0.726746
a
9
=
−0.951780u
53
+ 1.73096u
52
+ ··· + 16.4888u − 12.1502
−0.301232u
53
+ 0.483930u
52
+ ··· + 1.35754u + 0.613972
a
12
=
−3.98736u
53
+ 8.09125u
52
+ ··· + 69.3422u − 34.0361
−0.388553u
53
+ 0.437828u
52
+ ··· + 1.16197u + 1.80831
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.52952u
53
+ 4.81017u
52
+ ··· + 32.1330u − 13.0471
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
54
+ 20u
53
+ ··· − 87u + 1
c
2
, c
6
u
54
− 2u
53
+ ··· + 7u + 1
c
3
, c
9
u
54
− u
53
+ ··· + 10u − 1
c
4
u
54
− 3u
53
+ ··· + 16u + 1
c
5
, c
11
u
54
+ u
53
+ ··· − 200u − 449
c
7
, c
10
u
54
− 5u
53
+ ··· + 436u − 41
c
8
u
54
+ 3u
53
+ ··· − 50452u − 32411
c
12
u
54
− 5u
53
+ ··· − 22095u + 889
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
+ 36y
53
+ ··· − 6711y + 1
c
2
, c
6
y
54
+ 20y
53
+ ··· − 87y + 1
c
3
, c
9
y
54
− 67y
53
+ ··· − 88y + 1
c
4
y
54
− 93y
53
+ ··· − 30y + 1
c
5
, c
11
y
54
+ 25y
53
+ ··· + 1723672y + 201601
c
7
, c
10
y
54
+ 25y
53
+ ··· − 41512y + 1681
c
8
y
54
− 65y
53
+ ··· − 8887523962y + 1050472921
c
12
y
54
− 73y
53
+ ··· − 593861y + 790321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.782221 + 0.634653I
a = −0.195755 + 0.247117I
b = −0.41123 + 1.41581I
4.48864 + 3.39067I −4.34936 − 2.94495I
u = −0.782221 − 0.634653I
a = −0.195755 − 0.247117I
b = −0.41123 − 1.41581I
4.48864 − 3.39067I −4.34936 + 2.94495I
u = −0.977318 + 0.276740I
a = −0.0878048 − 0.0221906I
b = 0.424255 + 0.996657I
−5.26391 − 2.95255I −5.80358 + 3.54585I
u = −0.977318 − 0.276740I
a = −0.0878048 + 0.0221906I
b = 0.424255 − 0.996657I
−5.26391 + 2.95255I −5.80358 − 3.54585I
u = 0.624202 + 0.755472I
a = 0.453136 + 0.731003I
b = −0.108485 + 1.364720I
3.16221 + 2.63478I −6.89633 − 3.54122I
u = 0.624202 − 0.755472I
a = 0.453136 − 0.731003I
b = −0.108485 − 1.364720I
3.16221 − 2.63478I −6.89633 + 3.54122I
u = 0.775989 + 0.663204I
a = −1.14721 − 1.07182I
b = 1.33969 − 0.51090I
−5.82772 − 0.87480I −6.95939 − 0.10046I
u = 0.775989 − 0.663204I
a = −1.14721 + 1.07182I
b = 1.33969 + 0.51090I
−5.82772 + 0.87480I −6.95939 + 0.10046I
u = −0.716852 + 0.650173I
a = 1.11464 − 1.50236I
b = 0.267394 − 0.730103I
−6.42976 + 0.18074I −5.35993 − 0.34747I
u = −0.716852 − 0.650173I
a = 1.11464 + 1.50236I
b = 0.267394 + 0.730103I
−6.42976 − 0.18074I −5.35993 + 0.34747I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.594108 + 0.867348I
a = 1.02463 − 1.10108I
b = −1.340650 + 0.132088I
−1.16353 − 2.34293I −3.59630 + 5.63955I
u = −0.594108 − 0.867348I
a = 1.02463 + 1.10108I
b = −1.340650 − 0.132088I
−1.16353 + 2.34293I −3.59630 − 5.63955I
u = 0.010981 + 1.054630I
a = 0.72169 − 1.40947I
b = −0.409945 + 1.038840I
−1.20571 + 2.80469I −12.64158 − 4.77437I
u = 0.010981 − 1.054630I
a = 0.72169 + 1.40947I
b = −0.409945 − 1.038840I
−1.20571 − 2.80469I −12.64158 + 4.77437I
u = −0.026887 + 1.056610I
a = −1.86596 + 0.02219I
b = 0.945058 − 0.845598I
−11.48580 − 0.47734I −13.44450 + 0.I
u = −0.026887 − 1.056610I
a = −1.86596 − 0.02219I
b = 0.945058 + 0.845598I
−11.48580 + 0.47734I −13.44450 + 0.I
u = 0.238163 + 1.041600I
a = −0.453012 + 1.312980I
b = −0.151747 − 0.544879I
−0.264943 + 0.782686I −8.72185 + 0.87919I
u = 0.238163 − 1.041600I
a = −0.453012 − 1.312980I
b = −0.151747 + 0.544879I
−0.264943 − 0.782686I −8.72185 − 0.87919I
u = −0.213122 + 0.886225I
a = 1.87729 − 0.42780I
b = −0.854175 − 0.507735I
−2.99097 − 1.86676I −15.5248 + 2.2145I
u = −0.213122 − 0.886225I
a = 1.87729 + 0.42780I
b = −0.854175 + 0.507735I
−2.99097 + 1.86676I −15.5248 − 2.2145I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.554630 + 0.711383I
a = 0.666586 + 0.663185I
b = −0.632614 − 1.163320I
2.75948 − 0.58527I −6.51121 − 1.30492I
u = 0.554630 − 0.711383I
a = 0.666586 − 0.663185I
b = −0.632614 + 1.163320I
2.75948 + 0.58527I −6.51121 + 1.30492I
u = 0.642108 + 0.935178I
a = −1.63379 − 0.11874I
b = 0.101662 − 1.230990I
2.59369 + 2.34772I −8.00000 + 0.I
u = 0.642108 − 0.935178I
a = −1.63379 + 0.11874I
b = 0.101662 + 1.230990I
2.59369 − 2.34772I −8.00000 + 0.I
u = 0.957330 + 0.627734I
a = −0.0824892 − 0.0033199I
b = 0.73765 + 1.30778I
−2.98894 − 8.13870I −8.00000 + 3.35962I
u = 0.957330 − 0.627734I
a = −0.0824892 + 0.0033199I
b = 0.73765 − 1.30778I
−2.98894 + 8.13870I −8.00000 − 3.35962I
u = 0.588547 + 0.982520I
a = 1.96371 − 0.17505I
b = −0.758072 + 0.897967I
1.85903 + 5.19987I −8.00000 − 5.59193I
u = 0.588547 − 0.982520I
a = 1.96371 + 0.17505I
b = −0.758072 − 0.897967I
1.85903 − 5.19987I −8.00000 + 5.59193I
u = 0.276388 + 0.802714I
a = −0.813277 − 0.007279I
b = 0.173039 + 0.072417I
−0.465364 + 1.306920I −5.27166 − 4.29457I
u = 0.276388 − 0.802714I
a = −0.813277 + 0.007279I
b = 0.173039 − 0.072417I
−0.465364 − 1.306920I −5.27166 + 4.29457I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.838110 + 0.796599I
a = −0.256450 + 0.157165I
b = 0.516019 − 1.021330I
6.91184 − 0.61269I 0
u = −0.838110 − 0.796599I
a = −0.256450 − 0.157165I
b = 0.516019 + 1.021330I
6.91184 + 0.61269I 0
u = −0.663079 + 1.010530I
a = −0.785137 + 1.170500I
b = 0.347854 + 1.011880I
−7.52025 − 5.50179I 0
u = −0.663079 − 1.010530I
a = −0.785137 − 1.170500I
b = 0.347854 − 1.011880I
−7.52025 + 5.50179I 0
u = 0.846451 + 0.872894I
a = −0.251748 − 0.075444I
b = −0.431221 − 0.973967I
3.50126 + 0.93079I 0
u = 0.846451 − 0.872894I
a = −0.251748 + 0.075444I
b = −0.431221 + 0.973967I
3.50126 − 0.93079I 0
u = 0.691798 + 1.020090I
a = −0.736000 − 1.034630I
b = 1.40572 + 0.65983I
−6.91490 + 6.44905I 0
u = 0.691798 − 1.020090I
a = −0.736000 + 1.034630I
b = 1.40572 − 0.65983I
−6.91490 − 6.44905I 0
u = −0.685621 + 1.030320I
a = 1.85848 − 0.20635I
b = −0.56316 − 1.42285I
3.29320 − 8.95161I 0
u = −0.685621 − 1.030320I
a = 1.85848 + 0.20635I
b = −0.56316 + 1.42285I
3.29320 + 8.95161I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.814791 + 0.938243I
a = 1.082890 + 0.699947I
b = −0.565715 + 0.957837I
3.28563 + 5.26424I 0
u = 0.814791 − 0.938243I
a = 1.082890 − 0.699947I
b = −0.565715 − 0.957837I
3.28563 − 5.26424I 0
u = −0.783368 + 0.973705I
a = −1.53300 + 0.36496I
b = 0.642887 + 0.900173I
6.36672 − 5.44538I 0
u = −0.783368 − 0.973705I
a = −1.53300 − 0.36496I
b = 0.642887 − 0.900173I
6.36672 + 5.44538I 0
u = −0.169579 + 1.266130I
a = −1.24464 − 0.96277I
b = 0.714749 + 0.999139I
−10.81370 − 6.61602I 0
u = −0.169579 − 1.266130I
a = −1.24464 + 0.96277I
b = 0.714749 − 0.999139I
−10.81370 + 6.61602I 0
u = 0.753233 + 1.099800I
a = −1.82443 − 0.33859I
b = 0.84183 − 1.33565I
−4.4657 + 14.4090I 0
u = 0.753233 − 1.099800I
a = −1.82443 + 0.33859I
b = 0.84183 + 1.33565I
−4.4657 − 14.4090I 0
u = −0.564814 + 1.229530I
a = 0.345121 + 0.886401I
b = 0.335671 − 0.800648I
−8.30076 − 2.64729I 0
u = −0.564814 − 1.229530I
a = 0.345121 − 0.886401I
b = 0.335671 + 0.800648I
−8.30076 + 2.64729I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.444579 + 0.121551I
a = −0.860489 + 0.135214I
b = −0.187796 + 1.115610I
2.66689 + 1.69511I −1.25940 − 4.46780I
u = 0.444579 − 0.121551I
a = −0.860489 − 0.135214I
b = −0.187796 − 1.115610I
2.66689 − 1.69511I −1.25940 + 4.46780I
u = −0.297162
a = −0.983290
b = −0.513330
−0.837204 −11.6370
u = −0.111060
a = −19.6906
b = 0.755994
−7.69304 −16.8530
10
II.
I
u
2
= h−u
17
−2u
16
+· · ·+b−2, −2u
17
−u
16
+· · ·+a−2u, u
18
+u
17
+· · ·+u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
2u
17
+ u
16
+ ··· + 7u
2
+ 2u
u
17
+ 2u
16
+ ··· + 4u + 2
a
5
=
u
16
+ u
15
+ ··· + 6u + 1
−u
17
− u
16
+ ··· − u + 2
a
4
=
u
15
+ 3u
13
+ 8u
11
+ 13u
9
+ 17u
7
− u
6
+ 16u
5
+ 11u
3
− 2u
2
+ 6u
−u
17
− u
16
+ ··· + u
2
+ 2
a
10
=
3u
17
+ 3u
16
+ ··· + 6u + 2
u
17
+ 2u
16
+ ··· + 4u + 2
a
8
=
−u
16
− u
15
+ ··· − 3u − 4
2u
17
+ 2u
16
+ ··· + 4u − 1
a
9
=
−u
16
− u
15
+ ··· − 3u − 4
2u
17
+ 2u
16
+ ··· + 6u
2
+ 4u
a
12
=
u
17
+ u
16
+ ··· − u + 5
−u
17
− u
16
+ ··· − 4u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
17
+ 2u
16
+ 4u
15
+ 7u
14
+ 11u
13
+ 19u
12
+ 22u
11
+ 31u
10
+
32u
9
+ 40u
8
+ 38u
7
+ 34u
6
+ 33u
5
+ 19u
4
+ 21u
3
+ 2u
2
+ 8u − 12
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
18
− 7u
17
+ ··· − 11u + 1
c
2
u
18
− u
17
+ ··· − u + 1
c
3
u
18
− 10u
16
+ ··· − 4u + 1
c
4
u
18
+ 4u
17
+ ··· + 10u + 1
c
5
u
18
+ 6u
16
+ ··· + 4u + 1
c
6
u
18
+ u
17
+ ··· + u + 1
c
7
u
18
− 4u
17
+ ··· + 2u + 1
c
8
u
18
+ 2u
17
+ ··· − 4u + 1
c
9
u
18
− 10u
16
+ ··· + 4u + 1
c
10
u
18
+ 4u
17
+ ··· − 2u + 1
c
11
u
18
+ 6u
16
+ ··· − 4u + 1
c
12
u
18
+ 6u
17
+ ··· + 3u + 1
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 15y
17
+ ··· − 9y + 1
c
2
, c
6
y
18
+ 7y
17
+ ··· + 11y + 1
c
3
, c
9
y
18
− 20y
17
+ ··· − 2y + 1
c
4
y
18
− 6y
17
+ ··· + 16y + 1
c
5
, c
11
y
18
+ 12y
17
+ ··· + 14y + 1
c
7
, c
10
y
18
+ 8y
17
+ ··· − 6y + 1
c
8
y
18
− 6y
17
+ ··· + 8y + 1
c
12
y
18
− 10y
17
+ ··· + 41y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.091159 + 1.006750I
a = −0.59976 + 1.69234I
b = 0.388323 − 0.837519I
−0.09795 + 2.04194I −8.19600 − 3.28582I
u = 0.091159 − 1.006750I
a = −0.59976 − 1.69234I
b = 0.388323 + 0.837519I
−0.09795 − 2.04194I −8.19600 + 3.28582I
u = 0.428224 + 0.818772I
a = −1.047530 − 0.864539I
b = 0.969311 − 0.074817I
−1.77131 + 1.77665I −11.30886 − 0.92535I
u = 0.428224 − 0.818772I
a = −1.047530 + 0.864539I
b = 0.969311 + 0.074817I
−1.77131 − 1.77665I −11.30886 + 0.92535I
u = 0.809863 + 0.775804I
a = 0.085335 − 0.361987I
b = −0.063154 − 1.130870I
5.17943 + 2.43180I −3.07617 − 3.07688I
u = 0.809863 − 0.775804I
a = 0.085335 + 0.361987I
b = −0.063154 + 1.130870I
5.17943 − 2.43180I −3.07617 + 3.07688I
u = −0.818820 + 0.829999I
a = −0.074029 + 0.382486I
b = 0.79917 − 1.22352I
6.09112 + 0.44976I −5.66829 − 1.09802I
u = −0.818820 − 0.829999I
a = −0.074029 − 0.382486I
b = 0.79917 + 1.22352I
6.09112 − 0.44976I −5.66829 + 1.09802I
u = −0.504823 + 1.105300I
a = −0.154172 + 0.197850I
b = −0.504990 + 0.129328I
−9.12920 − 3.64508I −11.43133 + 3.76283I
u = −0.504823 − 1.105300I
a = −0.154172 − 0.197850I
b = −0.504990 − 0.129328I
−9.12920 + 3.64508I −11.43133 − 3.76283I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.785279 + 0.951987I
a = −1.67084 + 0.49888I
b = 0.87993 + 1.12839I
5.71337 − 6.46460I −6.13451 + 6.89115I
u = −0.785279 − 0.951987I
a = −1.67084 − 0.49888I
b = 0.87993 − 1.12839I
5.71337 + 6.46460I −6.13451 − 6.89115I
u = −0.521000 + 0.558610I
a = 0.59336 − 2.95727I
b = −0.677831 − 0.107119I
−7.27036 − 0.63283I −11.04604 + 6.53524I
u = −0.521000 − 0.558610I
a = 0.59336 + 2.95727I
b = −0.677831 + 0.107119I
−7.27036 + 0.63283I −11.04604 − 6.53524I
u = 0.756396 + 0.998306I
a = 1.397980 + 0.092696I
b = −0.143221 + 0.991419I
4.49100 + 3.47686I −4.58711 − 2.67317I
u = 0.756396 − 0.998306I
a = 1.397980 − 0.092696I
b = −0.143221 − 0.991419I
4.49100 − 3.47686I −4.58711 + 2.67317I
u = 0.044280 + 0.568991I
a = −1.53033 + 0.05306I
b = 0.352467 + 1.264600I
1.72870 − 1.47373I −11.55167 + 1.90648I
u = 0.044280 − 0.568991I
a = −1.53033 − 0.05306I
b = 0.352467 − 1.264600I
1.72870 + 1.47373I −11.55167 − 1.90648I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 7u
17
+ ··· − 11u + 1)(u
54
+ 20u
53
+ ··· − 87u + 1)
c
2
(u
18
− u
17
+ ··· − u + 1)(u
54
− 2u
53
+ ··· + 7u + 1)
c
3
(u
18
− 10u
16
+ ··· − 4u + 1)(u
54
− u
53
+ ··· + 10u − 1)
c
4
(u
18
+ 4u
17
+ ··· + 10u + 1)(u
54
− 3u
53
+ ··· + 16u + 1)
c
5
(u
18
+ 6u
16
+ ··· + 4u + 1)(u
54
+ u
53
+ ··· − 200u − 449)
c
6
(u
18
+ u
17
+ ··· + u + 1)(u
54
− 2u
53
+ ··· + 7u + 1)
c
7
(u
18
− 4u
17
+ ··· + 2u + 1)(u
54
− 5u
53
+ ··· + 436u − 41)
c
8
(u
18
+ 2u
17
+ ··· − 4u + 1)(u
54
+ 3u
53
+ ··· − 50452u − 32411)
c
9
(u
18
− 10u
16
+ ··· + 4u + 1)(u
54
− u
53
+ ··· + 10u − 1)
c
10
(u
18
+ 4u
17
+ ··· − 2u + 1)(u
54
− 5u
53
+ ··· + 436u − 41)
c
11
(u
18
+ 6u
16
+ ··· − 4u + 1)(u
54
+ u
53
+ ··· − 200u − 449)
c
12
(u
18
+ 6u
17
+ ··· + 3u + 1)(u
54
− 5u
53
+ ··· − 22095u + 889)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
+ 15y
17
+ ··· − 9y + 1)(y
54
+ 36y
53
+ ··· − 6711y + 1)
c
2
, c
6
(y
18
+ 7y
17
+ ··· + 11y + 1)(y
54
+ 20y
53
+ ··· − 87y + 1)
c
3
, c
9
(y
18
− 20y
17
+ ··· − 2y + 1)(y
54
− 67y
53
+ ··· − 88y + 1)
c
4
(y
18
− 6y
17
+ ··· + 16y + 1)(y
54
− 93y
53
+ ··· − 30y + 1)
c
5
, c
11
(y
18
+ 12y
17
+ ··· + 14y + 1)
· (y
54
+ 25y
53
+ ··· + 1723672y + 201601)
c
7
, c
10
(y
18
+ 8y
17
+ ··· − 6y + 1)(y
54
+ 25y
53
+ ··· − 41512y + 1681)
c
8
(y
18
− 6y
17
+ ··· + 8y + 1)
· (y
54
− 65y
53
+ ··· − 8887523962y + 1050472921)
c
12
(y
18
− 10y
17
+ ··· + 41y + 1)(y
54
− 73y
53
+ ··· − 593861y + 790321)
19
