12a
0613
(K12a
0613
)
A knot diagram
1
Linearized knot diagam
3 7 9 12 11 2 10 1 6 8 5 4
Solving Sequence
4,12
5
1,9
3 2 8 11 6 10 7
c
4
c
12
c
3
c
1
c
8
c
11
c
5
c
10
c
7
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.03882 × 10
79
u
78
+ 2.23239 × 10
79
u
77
+ ··· + 2.55472 × 10
80
b − 1.96227 × 10
79
,
− 8.18368 × 10
80
u
78
+ 6.97572 × 10
80
u
77
+ ··· + 1.02189 × 10
81
a − 2.19255 × 10
81
, u
79
− 2u
78
+ ··· − u
2
+ 1i
I
u
2
= hb, 2a − 1, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 81 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−2.04×10
79
u
78
+2.23×10
79
u
77
+· · ·+2.55×10
80
b−1.96×10
79
, −8.18×
10
80
u
78
+6.98×10
80
u
77
+· · ·+1.02 ×10
81
a−2.19×10
81
, u
79
−2u
78
+· · ·−u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
−u
2
a
1
=
u
u
a
9
=
0.800839u
78
− 0.682630u
77
+ ··· + 3.30143u + 2.14559
0.0798060u
78
− 0.0873829u
77
+ ··· + 1.62926u + 0.0768097
a
3
=
0.00402796u
78
− 0.254054u
77
+ ··· − 0.699999u − 0.768387
0.181867u
78
− 0.302615u
77
+ ··· − 0.399516u − 0.657378
a
2
=
0.867844u
78
− 1.44502u
77
+ ··· − 1.58649u − 0.804996
0.630533u
78
− 0.911235u
77
+ ··· + 1.37596u − 0.234189
a
8
=
0.747578u
78
− 1.04412u
77
+ ··· + 2.58040u + 1.29877
0.0265456u
78
− 0.448872u
77
+ ··· + 0.908223u − 0.770009
a
11
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
0.885426u
78
− 1.25091u
77
+ ··· + 3.14176u + 1.13115
0.101593u
78
− 0.552926u
77
+ ··· + 1.81848u − 0.679272
a
7
=
−0.411380u
78
+ 0.671759u
77
+ ··· − 1.60537u + 0.403544
−0.193891u
78
+ 0.272615u
77
+ ··· − 1.17977u − 0.155029
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.00132u
78
− 2.47157u
77
+ ··· − 17.5561u − 2.90148
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
79
+ 28u
78
+ ··· + 2u + 1
c
2
, c
6
u
79
− 2u
78
+ ··· + 4u − 1
c
3
u
79
− u
78
+ ··· + 224u − 64
c
4
, c
5
, c
11
c
12
u
79
+ 2u
78
+ ··· + u
2
− 1
c
7
, c
10
u
79
+ 3u
78
+ ··· + 8u − 16
c
8
4(4u
79
+ 62u
78
+ ··· − 19u − 983)
c
9
4(4u
79
+ 70u
78
+ ··· + 5805u − 1399)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
79
+ 40y
78
+ ··· − 82y −1
c
2
, c
6
y
79
− 28y
78
+ ··· + 2y −1
c
3
y
79
+ 15y
78
+ ··· − 1536y −4096
c
4
, c
5
, c
11
c
12
y
79
+ 92y
78
+ ··· + 2y −1
c
7
, c
10
y
79
− 47y
78
+ ··· + 10272y −256
c
8
16(16y
79
+ 916y
78
+ ··· − 1527221y −966289)
c
9
16(16y
79
− 828y
78
+ ··· + 2.53292 × 10
7
y −1957201)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.562843 + 0.832702I
a = −0.56281 + 1.45509I
b = 0.98702 + 1.13654I
1.52292 + 13.66740I 0
u = 0.562843 − 0.832702I
a = −0.56281 − 1.45509I
b = 0.98702 − 1.13654I
1.52292 − 13.66740I 0
u = −0.741395 + 0.678986I
a = 0.310828 + 0.208855I
b = −0.225354 + 0.507570I
1.56279 − 2.63526I 0
u = −0.741395 − 0.678986I
a = 0.310828 − 0.208855I
b = −0.225354 − 0.507570I
1.56279 + 2.63526I 0
u = −0.579273 + 0.830831I
a = 0.417162 + 1.259300I
b = −0.933225 + 0.954782I
3.15768 − 7.68910I 0
u = −0.579273 − 0.830831I
a = 0.417162 − 1.259300I
b = −0.933225 − 0.954782I
3.15768 + 7.68910I 0
u = 0.568605 + 0.766638I
a = −0.846313 + 0.755150I
b = 0.443486 + 1.011560I
−3.94285 + 6.03723I 0
u = 0.568605 − 0.766638I
a = −0.846313 − 0.755150I
b = 0.443486 − 1.011560I
−3.94285 − 6.03723I 0
u = 0.338960 + 0.869847I
a = 0.612024 − 1.143240I
b = −0.336341 − 1.122390I
−5.58907 + 1.26010I 0
u = 0.338960 − 0.869847I
a = 0.612024 + 1.143240I
b = −0.336341 + 1.122390I
−5.58907 − 1.26010I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.370841 + 0.777492I
a = 0.33367 − 1.64645I
b = −1.06752 − 1.25567I
−2.35487 + 7.66759I 0
u = 0.370841 − 0.777492I
a = 0.33367 + 1.64645I
b = −1.06752 + 1.25567I
−2.35487 − 7.66759I 0
u = 0.501863 + 1.023240I
a = 0.790922 − 0.128653I
b = 0.562719 − 0.703503I
0.48015 − 4.91507I 0
u = 0.501863 − 1.023240I
a = 0.790922 + 0.128653I
b = 0.562719 + 0.703503I
0.48015 + 4.91507I 0
u = −0.331748 + 0.759592I
a = −0.17186 − 1.41166I
b = 1.020660 − 0.871256I
−0.93419 − 2.69523I 0
u = −0.331748 − 0.759592I
a = −0.17186 + 1.41166I
b = 1.020660 + 0.871256I
−0.93419 + 2.69523I 0
u = −0.801592 + 0.090466I
a = −0.152170 − 0.181666I
b = 0.785054 + 0.668987I
5.40107 + 3.12470I 10.83520 − 3.71526I
u = −0.801592 − 0.090466I
a = −0.152170 + 0.181666I
b = 0.785054 − 0.668987I
5.40107 − 3.12470I 10.83520 + 3.71526I
u = 0.771291 + 0.077638I
a = 0.207850 − 0.230451I
b = −0.869715 + 0.901562I
3.80470 − 9.23717I 8.33412 + 6.93035I
u = 0.771291 − 0.077638I
a = 0.207850 + 0.230451I
b = −0.869715 − 0.901562I
3.80470 + 9.23717I 8.33412 − 6.93035I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.553421 + 1.128580I
a = −0.458687 − 0.080550I
b = −0.373011 − 0.438940I
1.82683 − 1.50251I 0
u = −0.553421 − 1.128580I
a = −0.458687 + 0.080550I
b = −0.373011 + 0.438940I
1.82683 + 1.50251I 0
u = −0.231967 + 0.666632I
a = −0.366445 − 0.960576I
b = 0.783116 − 0.050253I
−0.79258 − 1.89815I 1.36018 + 5.78831I
u = −0.231967 − 0.666632I
a = −0.366445 + 0.960576I
b = 0.783116 + 0.050253I
−0.79258 + 1.89815I 1.36018 − 5.78831I
u = −0.182894 + 0.674305I
a = −0.009457 − 1.377310I
b = 0.480502 − 0.004250I
−0.67916 − 1.82123I 2.42742 + 5.42469I
u = −0.182894 − 0.674305I
a = −0.009457 + 1.377310I
b = 0.480502 + 0.004250I
−0.67916 + 1.82123I 2.42742 − 5.42469I
u = 0.391868 + 0.577092I
a = −0.872126 − 0.595448I
b = −0.209144 + 0.629764I
−1.69314 − 1.96298I −0.140339 − 0.849160I
u = 0.391868 − 0.577092I
a = −0.872126 + 0.595448I
b = −0.209144 − 0.629764I
−1.69314 + 1.96298I −0.140339 + 0.849160I
u = 0.654803 + 0.208319I
a = −0.109482 − 0.416917I
b = −0.076780 + 0.829628I
−2.27524 − 1.80401I 0.55826 + 3.15083I
u = 0.654803 − 0.208319I
a = −0.109482 + 0.416917I
b = −0.076780 − 0.829628I
−2.27524 + 1.80401I 0.55826 − 3.15083I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.049356 + 0.679141I
a = −4.06707 − 7.37445I
b = 0.211661 − 0.213403I
0.65806 + 2.13491I −3.7911 + 41.5128I
u = −0.049356 − 0.679141I
a = −4.06707 + 7.37445I
b = 0.211661 + 0.213403I
0.65806 − 2.13491I −3.7911 − 41.5128I
u = −0.345401 + 0.562828I
a = 1.079840 − 0.026704I
b = 1.43886 + 0.80805I
2.60435 − 5.50536I 8.17810 + 10.12100I
u = −0.345401 − 0.562828I
a = 1.079840 + 0.026704I
b = 1.43886 − 0.80805I
2.60435 + 5.50536I 8.17810 − 10.12100I
u = 0.331681 + 0.523775I
a = −1.065230 + 0.540959I
b = −1.11153 + 1.03548I
3.09371 + 0.52538I 9.90827 − 3.67207I
u = 0.331681 − 0.523775I
a = −1.065230 − 0.540959I
b = −1.11153 − 1.03548I
3.09371 − 0.52538I 9.90827 + 3.67207I
u = 0.170277 + 0.493014I
a = 0.73593 + 1.99770I
b = −0.348401 + 0.520479I
1.35750 + 0.77449I 3.79816 + 1.46964I
u = 0.170277 − 0.493014I
a = 0.73593 − 1.99770I
b = −0.348401 − 0.520479I
1.35750 − 0.77449I 3.79816 − 1.46964I
u = 0.485463 + 0.020121I
a = −0.398789 − 1.077720I
b = 0.850535 + 0.743850I
−0.04571 + 4.74027I 6.49908 − 5.57095I
u = 0.485463 − 0.020121I
a = −0.398789 + 1.077720I
b = 0.850535 − 0.743850I
−0.04571 − 4.74027I 6.49908 + 5.57095I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.334435 + 0.319559I
a = −1.47425 + 2.33133I
b = 0.404340 + 1.278840I
3.64262 + 2.01368I 11.35214 − 6.18075I
u = 0.334435 − 0.319559I
a = −1.47425 − 2.33133I
b = 0.404340 − 1.278840I
3.64262 − 2.01368I 11.35214 + 6.18075I
u = 0.00649 + 1.54238I
a = 0.21865 − 2.91487I
b = 0.21929 − 2.08709I
−2.64074 + 2.57318I 0
u = 0.00649 − 1.54238I
a = 0.21865 + 2.91487I
b = 0.21929 + 2.08709I
−2.64074 − 2.57318I 0
u = −0.351711 + 0.263028I
a = 1.52295 + 2.40752I
b = −0.773586 + 1.088950I
3.41440 + 2.89559I 11.29503 − 0.80048I
u = −0.351711 − 0.263028I
a = 1.52295 − 2.40752I
b = −0.773586 − 1.088950I
3.41440 − 2.89559I 11.29503 + 0.80048I
u = 0.05749 + 1.56794I
a = 1.60542 − 1.04355I
b = 1.76518 − 0.94006I
−4.04246 + 1.74152I 0
u = 0.05749 − 1.56794I
a = 1.60542 + 1.04355I
b = 1.76518 + 0.94006I
−4.04246 − 1.74152I 0
u = −0.06787 + 1.57326I
a = −1.88218 − 0.50014I
b = −2.03284 − 0.61356I
−4.67331 − 6.86430I 0
u = −0.06787 − 1.57326I
a = −1.88218 + 0.50014I
b = −2.03284 + 0.61356I
−4.67331 + 6.86430I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02636 + 1.58296I
a = −0.03578 − 1.50159I
b = 0.705909 − 0.781446I
−5.92590 + 1.33377I 0
u = 0.02636 − 1.58296I
a = −0.03578 + 1.50159I
b = 0.705909 + 0.781446I
−5.92590 − 1.33377I 0
u = 0.18347 + 1.58484I
a = 0.360763 − 0.757569I
b = −0.261769 − 0.839182I
−8.84874 + 0.48741I 0
u = 0.18347 − 1.58484I
a = 0.360763 + 0.757569I
b = −0.261769 + 0.839182I
−8.84874 − 0.48741I 0
u = −0.398279 + 0.013530I
a = 0.938259 + 1.052560I
b = −0.839928 − 0.266112I
1.200820 + 0.135633I 10.41521 − 0.49094I
u = −0.398279 − 0.013530I
a = 0.938259 − 1.052560I
b = −0.839928 + 0.266112I
1.200820 − 0.135633I 10.41521 + 0.49094I
u = −0.04900 + 1.60834I
a = −0.163063 + 0.427641I
b = −0.996770 + 0.017416I
−8.65958 − 2.85508I 0
u = −0.04900 − 1.60834I
a = −0.163063 − 0.427641I
b = −0.996770 − 0.017416I
−8.65958 + 2.85508I 0
u = −0.01243 + 1.61005I
a = 4.20907 − 1.82134I
b = −0.282683 − 0.182370I
−7.26471 + 1.91119I 0
u = −0.01243 − 1.61005I
a = 4.20907 + 1.82134I
b = −0.282683 + 0.182370I
−7.26471 − 1.91119I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.09234 + 1.63211I
a = −0.52019 + 1.88202I
b = −1.13740 + 1.31093I
−9.19819 − 4.29526I 0
u = −0.09234 − 1.63211I
a = −0.52019 − 1.88202I
b = −1.13740 − 1.31093I
−9.19819 + 4.29526I 0
u = 0.10241 + 1.63406I
a = 0.44688 + 2.25253I
b = 1.13698 + 1.65533I
−10.6594 + 9.4536I 0
u = 0.10241 − 1.63406I
a = 0.44688 − 2.25253I
b = 1.13698 − 1.65533I
−10.6594 − 9.4536I 0
u = −0.19581 + 1.62772I
a = −0.028644 − 1.044970I
b = 0.575863 − 0.832632I
−6.29500 − 6.01229I 0
u = −0.19581 − 1.62772I
a = −0.028644 + 1.044970I
b = 0.575863 + 0.832632I
−6.29500 + 6.01229I 0
u = 0.16718 + 1.63714I
a = 0.27278 − 1.56528I
b = −0.651768 − 1.223680I
−12.1301 + 8.8302I 0
u = 0.16718 − 1.63714I
a = 0.27278 + 1.56528I
b = −0.651768 + 1.223680I
−12.1301 − 8.8302I 0
u = −0.04375 + 1.64757I
a = −0.028083 + 1.158780I
b = −0.425950 + 0.521893I
−8.90382 − 2.51455I 0
u = −0.04375 − 1.64757I
a = −0.028083 − 1.158780I
b = −0.425950 − 0.521893I
−8.90382 + 2.51455I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.09434 + 1.65580I
a = −0.15890 + 1.82134I
b = 0.48529 + 1.40625I
−14.3142 + 2.9381I 0
u = 0.09434 − 1.65580I
a = −0.15890 − 1.82134I
b = 0.48529 − 1.40625I
−14.3142 − 2.9381I 0
u = −0.17049 + 1.65268I
a = 0.18613 − 1.81679I
b = 1.00691 − 1.19883I
−5.29842 − 10.57260I 0
u = −0.17049 − 1.65268I
a = 0.18613 + 1.81679I
b = 1.00691 + 1.19883I
−5.29842 + 10.57260I 0
u = 0.16564 + 1.65397I
a = −0.12615 − 2.02494I
b = −1.04487 − 1.34226I
−6.9597 + 16.4745I 0
u = 0.16564 − 1.65397I
a = −0.12615 + 2.02494I
b = −1.04487 + 1.34226I
−6.9597 − 16.4745I 0
u = −0.295195
a = 2.10631
b = −0.614585
0.931731 11.9810
u = 0.06001 + 1.71584I
a = −0.304602 + 0.966268I
b = −0.057490 + 0.749405I
−9.46041 − 2.81380I 0
u = 0.06001 − 1.71584I
a = −0.304602 − 0.966268I
b = −0.057490 − 0.749405I
−9.46041 + 2.81380I 0
12
II. I
u
2
= hb, 2a − 1, u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
−u + 1
a
1
=
u
u
a
9
=
0.5
0
a
3
=
1
0
a
2
=
0
u
a
8
=
1
2
u
1
2
u −
1
2
a
11
=
−u
u − 1
a
6
=
u
−u + 2
a
10
=
−
1
2
u
3
2
u −
3
2
a
7
=
u
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u +
23
4
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
11
c
12
u
2
+ u + 1
c
2
, c
4
, c
5
u
2
− u + 1
c
3
u
2
c
7
(u + 1)
2
c
8
4(4u
2
− 2u + 1)
c
9
4(4u
2
− 6u + 3)
c
10
(u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
11
c
12
y
2
+ y + 1
c
3
y
2
c
7
, c
10
(y −1)
2
c
8
16(16y
2
+ 4y + 1)
c
9
16(16y
2
− 12y + 9)
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000
b = 0
1.64493 + 2.02988I 3.75000 − 3.46410I
u = 0.500000 − 0.866025I
a = 0.500000
b = 0
1.64493 − 2.02988I 3.75000 + 3.46410I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
79
+ 28u
78
+ ··· + 2u + 1)
c
2
(u
2
− u + 1)(u
79
− 2u
78
+ ··· + 4u − 1)
c
3
u
2
(u
79
− u
78
+ ··· + 224u − 64)
c
4
, c
5
(u
2
− u + 1)(u
79
+ 2u
78
+ ··· + u
2
− 1)
c
6
(u
2
+ u + 1)(u
79
− 2u
78
+ ··· + 4u − 1)
c
7
((u + 1)
2
)(u
79
+ 3u
78
+ ··· + 8u − 16)
c
8
16(4u
2
− 2u + 1)(4u
79
+ 62u
78
+ ··· − 19u − 983)
c
9
16(4u
2
− 6u + 3)(4u
79
+ 70u
78
+ ··· + 5805u − 1399)
c
10
((u − 1)
2
)(u
79
+ 3u
78
+ ··· + 8u − 16)
c
11
, c
12
(u
2
+ u + 1)(u
79
+ 2u
78
+ ··· + u
2
− 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
79
+ 40y
78
+ ··· − 82y −1)
c
2
, c
6
(y
2
+ y + 1)(y
79
− 28y
78
+ ··· + 2y −1)
c
3
y
2
(y
79
+ 15y
78
+ ··· − 1536y −4096)
c
4
, c
5
, c
11
c
12
(y
2
+ y + 1)(y
79
+ 92y
78
+ ··· + 2y −1)
c
7
, c
10
((y −1)
2
)(y
79
− 47y
78
+ ··· + 10272y −256)
c
8
256(16y
2
+ 4y + 1)(16y
79
+ 916y
78
+ ··· − 1527221y −966289)
c
9
256(16y
2
− 12y + 9)(16y
79
− 828y
78
+ ··· + 2.53292 × 10
7
y −1957201)
18
