12n
0277
(K12n
0277
)
A knot diagram
1
Linearized knot diagam
3 4 9 2 10 4 12 11 6 3 7 8
Solving Sequence
3,9 4,6
7 10 11 2 1 5 8 12
c
3
c
6
c
9
c
10
c
2
c
1
c
5
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.31866 × 10
31
u
44
− 1.02208 × 10
31
u
43
+ ··· + 1.69549 × 10
31
b + 1.38177 × 10
31
,
5.31714 × 10
31
u
44
+ 5.34083 × 10
31
u
43
+ ··· + 4.23874 × 10
31
a − 8.50686 × 10
31
, u
45
+ u
44
+ ··· − 3u + 5i
I
u
2
= hu
3
b
2
+ 6b
2
u
2
− 2u
3
b + b
3
− b
2
u − 4u
3
− 3b
2
− 2bu − 6u
2
− 9b + 3u + 3, −u
2
+ a, u
4
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 57 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−1.32×10
31
u
44
−1.02×10
31
u
43
+· · ·+1.70×10
31
b+1.38×10
31
, 5.32×
10
31
u
44
+5.34×10
31
u
43
+· · ·+4.24×10
31
a−8.51×10
31
, u
45
+u
44
+· · ·−3u+5i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
−1.25442u
44
− 1.26001u
43
+ ··· + 17.1020u + 2.00693
0.777745u
44
+ 0.602821u
43
+ ··· − 13.4579u − 0.814966
a
7
=
−0.857487u
44
− 0.977954u
43
+ ··· + 9.89939u + 1.21992
0.622066u
44
+ 0.528291u
43
+ ··· − 11.1287u − 1.38935
a
10
=
−0.251178u
44
− 0.450479u
43
+ ··· + 8.17819u + 4.56451
−0.0401479u
44
− 0.367454u
43
+ ··· − 2.48738u + 6.40126
a
11
=
−0.291326u
44
− 0.817933u
43
+ ··· + 5.69081u + 10.9658
−0.0401479u
44
− 0.367454u
43
+ ··· − 2.48738u + 6.40126
a
2
=
−u
2
+ 1
u
4
a
1
=
u
4
− u
2
+ 1
u
4
a
5
=
u
4
− u
2
+ 1
−u
6
− u
2
a
8
=
−0.701040u
44
− 1.41736u
43
+ ··· + 4.97925u + 12.1312
−0.302362u
44
− 0.273729u
43
+ ··· + 1.07283u − 1.67880
a
12
=
−1.08462u
44
− 1.85577u
43
+ ··· + 9.70163u + 13.7283
0.284549u
44
+ 0.197516u
43
+ ··· − 7.73043u − 0.550539
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.476359u
44
− 0.619053u
43
+ ··· + 0.718999u + 7.19239
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 53u
44
+ ··· + 16971u − 625
c
2
, c
4
u
45
− 11u
44
+ ··· + 439u − 25
c
3
u
45
+ u
44
+ ··· − 3u + 5
c
5
, c
9
u
45
+ u
44
+ ··· − 7u + 1
c
6
u
45
+ 5u
44
+ ··· + 75641u − 14459
c
7
, c
11
, c
12
u
45
+ u
44
+ ··· − 7u + 1
c
8
u
45
− 3u
44
+ ··· + 5891u − 783
c
10
u
45
− 3u
44
+ ··· + 1507645u + 1600703
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 115y
44
+ ··· + 26596091y −390625
c
2
, c
4
y
45
+ 53y
44
+ ··· + 16971y −625
c
3
y
45
− 11y
44
+ ··· + 439y −25
c
5
, c
9
y
45
+ 11y
44
+ ··· + 21y −1
c
6
y
45
+ 39y
44
+ ··· + 4268922987y −209062681
c
7
, c
11
, c
12
y
45
− 45y
44
+ ··· + 9y −1
c
8
y
45
− 25y
44
+ ··· + 15213445y −613089
c
10
y
45
+ 51y
44
+ ··· − 58950999031545y −2562250094209
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618448 + 0.778257I
a = 0.843482 − 1.073790I
b = 0.67091 + 1.41701I
−3.92090 − 3.01938I −6.65827 + 3.07965I
u = −0.618448 − 0.778257I
a = 0.843482 + 1.073790I
b = 0.67091 − 1.41701I
−3.92090 + 3.01938I −6.65827 − 3.07965I
u = −0.759629 + 0.693608I
a = 0.128652 + 0.688884I
b = 0.655655 − 0.423799I
−3.53574 − 5.66792I −6.96528 + 6.84523I
u = −0.759629 − 0.693608I
a = 0.128652 − 0.688884I
b = 0.655655 + 0.423799I
−3.53574 + 5.66792I −6.96528 − 6.84523I
u = 0.944274 + 0.424458I
a = 0.238661 + 0.516045I
b = 0.06927 − 1.44724I
1.42274 + 1.68081I −1.366109 + 0.313836I
u = 0.944274 − 0.424458I
a = 0.238661 − 0.516045I
b = 0.06927 + 1.44724I
1.42274 − 1.68081I −1.366109 − 0.313836I
u = −0.889096 + 0.544606I
a = −0.185199 + 0.005412I
b = 0.646513 + 0.958649I
−3.03850 + 0.83965I −7.40372 + 0.18436I
u = −0.889096 − 0.544606I
a = −0.185199 − 0.005412I
b = 0.646513 − 0.958649I
−3.03850 − 0.83965I −7.40372 − 0.18436I
u = −0.948668
a = 0.655960
b = −0.748646
−2.56039 −4.14140
u = 0.775946 + 0.528064I
a = 0.568356 + 1.013240I
b = 0.08102 − 1.65679I
1.51011 + 2.10810I −4.11821 − 4.61603I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.775946 − 0.528064I
a = 0.568356 − 1.013240I
b = 0.08102 + 1.65679I
1.51011 − 2.10810I −4.11821 + 4.61603I
u = 0.257571 + 0.891870I
a = 0.711919 − 0.919092I
b = 0.235209 − 0.154714I
−7.44321 − 2.20730I −9.27201 + 1.65458I
u = 0.257571 − 0.891870I
a = 0.711919 + 0.919092I
b = 0.235209 + 0.154714I
−7.44321 + 2.20730I −9.27201 − 1.65458I
u = 0.702892 + 0.579313I
a = 0.237201 − 0.451530I
b = 0.500813 − 0.118824I
0.77346 + 2.06694I −2.46311 − 4.64250I
u = 0.702892 − 0.579313I
a = 0.237201 + 0.451530I
b = 0.500813 + 0.118824I
0.77346 − 2.06694I −2.46311 + 4.64250I
u = −1.056350 + 0.360065I
a = −0.229265 − 0.766380I
b = 0.63174 + 2.00415I
1.51977 − 4.35751I 0. + 8.87124I
u = −1.056350 − 0.360065I
a = −0.229265 + 0.766380I
b = 0.63174 − 2.00415I
1.51977 + 4.35751I 0. − 8.87124I
u = 0.857894 + 0.110360I
a = −0.177987 + 1.247320I
b = −0.56576 − 2.29673I
0.48114 + 3.04926I 2.28179 − 3.92639I
u = 0.857894 − 0.110360I
a = −0.177987 − 1.247320I
b = −0.56576 + 2.29673I
0.48114 − 3.04926I 2.28179 + 3.92639I
u = −1.036040 + 0.598318I
a = 0.757783 − 0.678172I
b = −0.25466 + 2.13165I
−2.51811 − 2.22489I −4.30685 + 1.76102I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.036040 − 0.598318I
a = 0.757783 + 0.678172I
b = −0.25466 − 2.13165I
−2.51811 + 2.22489I −4.30685 − 1.76102I
u = 1.158630 + 0.404439I
a = −0.410963 + 0.740323I
b = 1.15725 − 2.04071I
−4.29007 + 6.94511I −4.75487 − 6.62606I
u = 1.158630 − 0.404439I
a = −0.410963 − 0.740323I
b = 1.15725 + 2.04071I
−4.29007 − 6.94511I −4.75487 + 6.62606I
u = 0.837424 + 0.951363I
a = −1.128450 + 0.074712I
b = −0.064368 + 0.566620I
−7.63574 − 2.82737I −3.82687 + 2.49371I
u = 0.837424 − 0.951363I
a = −1.128450 − 0.074712I
b = −0.064368 − 0.566620I
−7.63574 + 2.82737I −3.82687 − 2.49371I
u = −0.801777 + 1.006980I
a = −1.201550 − 0.076316I
b = −0.276801 − 0.814787I
−14.1872 + 6.6052I −6.86353 − 2.64020I
u = −0.801777 − 1.006980I
a = −1.201550 + 0.076316I
b = −0.276801 + 0.814787I
−14.1872 − 6.6052I −6.86353 + 2.64020I
u = −0.903629 + 0.926208I
a = −1.064140 − 0.131199I
b = 0.289994 − 0.475837I
−7.87444 − 2.11161I −4.26706 + 2.79875I
u = −0.903629 − 0.926208I
a = −1.064140 + 0.131199I
b = 0.289994 + 0.475837I
−7.87444 + 2.11161I −4.26706 − 2.79875I
u = −0.972656 + 0.889052I
a = 0.051088 + 1.077000I
b = −0.66690 − 1.87327I
−7.64726 − 4.57879I −3.97932 + 1.83960I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.972656 − 0.889052I
a = 0.051088 − 1.077000I
b = −0.66690 + 1.87327I
−7.64726 + 4.57879I −3.97932 − 1.83960I
u = 1.023050 + 0.858993I
a = −0.002769 − 1.094260I
b = −0.66351 + 2.30984I
−7.03534 + 9.49120I −2.00000 − 6.96236I
u = 1.023050 − 0.858993I
a = −0.002769 + 1.094260I
b = −0.66351 − 2.30984I
−7.03534 − 9.49120I −2.00000 + 6.96236I
u = 0.954554 + 0.963302I
a = 0.111126 − 1.116440I
b = −1.04228 + 1.51734I
−14.8390 + 1.4214I −7.29509 − 1.55685I
u = 0.954554 − 0.963302I
a = 0.111126 + 1.116440I
b = −1.04228 − 1.51734I
−14.8390 − 1.4214I −7.29509 + 1.55685I
u = −0.268767 + 0.584540I
a = 0.816355 + 0.624887I
b = 0.153086 − 0.014362I
−1.033970 + 0.656542I −7.43314 − 3.12832I
u = −0.268767 − 0.584540I
a = 0.816355 − 0.624887I
b = 0.153086 + 0.014362I
−1.033970 − 0.656542I −7.43314 + 3.12832I
u = 0.972776 + 0.950767I
a = −1.063580 + 0.218802I
b = 0.643513 + 0.647443I
−14.7763 + 5.5885I −7.26736 − 2.90698I
u = 0.972776 − 0.950767I
a = −1.063580 − 0.218802I
b = 0.643513 − 0.647443I
−14.7763 − 5.5885I −7.26736 + 2.90698I
u = −1.069130 + 0.858613I
a = −0.028711 + 1.127660I
b = −0.86002 − 2.60268I
−13.3108 − 13.4287I −5.61656 + 7.05289I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.069130 − 0.858613I
a = −0.028711 − 1.127660I
b = −0.86002 + 2.60268I
−13.3108 + 13.4287I −5.61656 − 7.05289I
u = −0.618743 + 0.061116I
a = −0.16921 − 1.71012I
b = −1.01368 + 1.54051I
3.56768 − 0.22451I 5.93213 − 0.90945I
u = −0.618743 − 0.061116I
a = −0.16921 + 1.71012I
b = −1.01368 − 1.54051I
3.56768 + 0.22451I 5.93213 + 0.90945I
u = 0.483587 + 0.089423I
a = −0.73078 − 2.06551I
b = −1.45266 + 1.03026I
−1.00640 + 2.97190I −0.65660 − 1.82986I
u = 0.483587 − 0.089423I
a = −0.73078 + 2.06551I
b = −1.45266 − 1.03026I
−1.00640 − 2.97190I −0.65660 + 1.82986I
9
II. I
u
2
= hu
3
b
2
− 2u
3
b + · · · − 9b + 3, −u
2
+ a, u
4
− u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
6
=
u
2
b
a
7
=
2u
2
+ b − 1
−u
2
b + b + 1
a
10
=
−u
3
+ u
−u
3
b + u
a
11
=
−u
3
b − u
3
+ 2u
−u
3
b + u
a
2
=
−u
2
+ 1
u
2
− 1
a
1
=
0
u
2
− 1
a
5
=
0
−u
2
+ 1
a
8
=
−4u
3
b − b
2
u + 2bu + 3u
−3u
3
b − b
2
u + u
3
+ 2bu + 2u
a
12
=
b
2
u
2
− u
3
b − 2u
2
b − u
3
− b
2
− 4u
2
− 2b + 2u + 3
b
2
u
2
+ 3u
3
b + b
2
u + 2u
2
b − 2bu − 3u
2
− 4b − 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
3
− 4bu − 4u
2
+ 4u + 4
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
3
(u
4
− u
2
+ 1)
3
c
5
, c
9
(u
2
+ 1)
6
c
6
u
12
− 6u
11
+ ··· − 70u + 25
c
7
, c
11
, c
12
(u
6
− 3u
4
+ 2u
2
+ 1)
2
c
8
(u
6
+ u
4
+ 2u
2
+ 1)
2
c
10
u
12
− 2u
11
+ ··· − 40u + 25
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
2
+ y + 1)
6
c
3
(y
2
− y + 1)
6
c
5
, c
9
(y + 1)
12
c
6
y
12
+ 4y
11
+ ··· − 850y + 625
c
7
, c
11
, c
12
(y
3
− 3y
2
+ 2y + 1)
4
c
8
(y
3
+ y
2
+ 2y + 1)
4
c
10
y
12
− 4y
11
+ ··· + 850y + 625
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.500000 + 0.866025I
b = −0.65374 − 1.35461I
2.75839 + 2.02988I 5.01951 − 3.46410I
u = 0.866025 + 0.500000I
a = 0.500000 + 0.866025I
b = 1.13232 − 1.52570I
−1.37919 + 4.85801I −1.50976 − 6.44355I
u = 0.866025 + 0.500000I
a = 0.500000 + 0.866025I
b = 0.38745 − 2.81584I
−1.37919 − 0.79824I −1.50976 − 0.48465I
u = 0.866025 − 0.500000I
a = 0.500000 − 0.866025I
b = −0.65374 + 1.35461I
2.75839 − 2.02988I 5.01951 + 3.46410I
u = 0.866025 − 0.500000I
a = 0.500000 − 0.866025I
b = 1.13232 + 1.52570I
−1.37919 − 4.85801I −1.50976 + 6.44355I
u = 0.866025 − 0.500000I
a = 0.500000 − 0.866025I
b = 0.38745 + 2.81584I
−1.37919 + 0.79824I −1.50976 + 0.48465I
u = −0.866025 + 0.500000I
a = 0.500000 − 0.866025I
b = −0.387453 + 0.648262I
−1.37919 + 0.79824I −1.50976 + 0.48465I
u = −0.866025 + 0.500000I
a = 0.500000 − 0.866025I
b = 0.65374 + 2.10949I
2.75839 − 2.02988I 5.01951 + 3.46410I
u = −0.866025 + 0.500000I
a = 0.500000 − 0.866025I
b = −1.13232 + 1.93840I
−1.37919 − 4.85801I −1.50976 + 6.44355I
u = −0.866025 − 0.500000I
a = 0.500000 + 0.866025I
b = −0.387453 − 0.648262I
−1.37919 − 0.79824I −1.50976 − 0.48465I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866025 − 0.500000I
a = 0.500000 + 0.866025I
b = 0.65374 − 2.10949I
2.75839 + 2.02988I 5.01951 − 3.46410I
u = −0.866025 − 0.500000I
a = 0.500000 + 0.866025I
b = −1.13232 − 1.93840I
−1.37919 + 4.85801I −1.50976 − 6.44355I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
45
+ 53u
44
+ ··· + 16971u − 625)
c
2
((u
2
+ u + 1)
6
)(u
45
− 11u
44
+ ··· + 439u − 25)
c
3
((u
4
− u
2
+ 1)
3
)(u
45
+ u
44
+ ··· − 3u + 5)
c
4
((u
2
− u + 1)
6
)(u
45
− 11u
44
+ ··· + 439u − 25)
c
5
, c
9
((u
2
+ 1)
6
)(u
45
+ u
44
+ ··· − 7u + 1)
c
6
(u
12
− 6u
11
+ ··· − 70u + 25)(u
45
+ 5u
44
+ ··· + 75641u − 14459)
c
7
, c
11
, c
12
((u
6
− 3u
4
+ 2u
2
+ 1)
2
)(u
45
+ u
44
+ ··· − 7u + 1)
c
8
((u
6
+ u
4
+ 2u
2
+ 1)
2
)(u
45
− 3u
44
+ ··· + 5891u − 783)
c
10
(u
12
− 2u
11
+ ··· − 40u + 25)
· (u
45
− 3u
44
+ ··· + 1507645u + 1600703)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
45
− 115y
44
+ ··· + 2.65961 × 10
7
y − 390625)
c
2
, c
4
((y
2
+ y + 1)
6
)(y
45
+ 53y
44
+ ··· + 16971y − 625)
c
3
((y
2
− y + 1)
6
)(y
45
− 11y
44
+ ··· + 439y − 25)
c
5
, c
9
((y + 1)
12
)(y
45
+ 11y
44
+ ··· + 21y − 1)
c
6
(y
12
+ 4y
11
+ ··· − 850y + 625)
· (y
45
+ 39y
44
+ ··· + 4268922987y − 209062681)
c
7
, c
11
, c
12
((y
3
− 3y
2
+ 2y + 1)
4
)(y
45
− 45y
44
+ ··· + 9y − 1)
c
8
((y
3
+ y
2
+ 2y + 1)
4
)(y
45
− 25y
44
+ ··· + 1.52134 × 10
7
y − 613089)
c
10
(y
12
− 4y
11
+ ··· + 850y + 625)
· (y
45
+ 51y
44
+ ··· − 58950999031545y − 2562250094209)
16
