12n
0677
(K12n
0677
)
A knot diagram
1
Linearized knot diagam
4 5 7 2 9 3 11 12 5 1 9 8
Solving Sequence
9,11
12 8 1
3,7
4 6 5 2 10
c
11
c
8
c
12
c
7
c
3
c
6
c
5
c
2
c
10
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h84729282499200u
49
+ 3758065856672058u
48
+ ··· + 6852922461300829b − 6852284696559709,
− 6.85291 × 10
15
u
49
+ 2.05586 × 10
16
u
48
+ ··· + 1.37058 × 10
16
a + 9.44180 × 10
16
,
u
50
− 3u
49
+ ··· − 14u + 1i
I
u
2
= h2au + u
2
+ b + u + 1, −u
2
a + a
2
− u
2
− a − u − 2, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 56 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
= h8.47 × 10
13
u
49
+ 3.76 × 10
15
u
48
+ · · · + 6.85 × 10
15
b − 6.85 ×
10
15
, −6.85 × 10
15
u
49
+ 2.06 × 10
16
u
48
+ · · · + 1.37 × 10
16
a + 9.44 ×
10
16
, u
50
− 3u
49
+ · · · − 14u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
0.499999u
49
− 1.49999u
48
+ ··· + 15.0256u − 6.88889
−0.0123640u
49
− 0.548389u
48
+ ··· − 3.33203u + 0.999907
a
7
=
u
3
+ 2u
u
3
+ u
a
4
=
0.666682u
49
− 2.00117u
48
+ ··· + 26.2921u − 7.92593
−0.00103128u
49
+ 0.120354u
48
+ ··· − 2.70359u + 0.833325
a
6
=
−0.333328u
49
+ 0.999541u
48
+ ··· + 1.63220u + 3.29630
−0.0354893u
49
+ 1.92137u
48
+ ··· − 2.80779u − 0.167168
a
5
=
−0.333328u
49
+ 0.999541u
48
+ ··· + 1.63220u + 3.29630
−0.00783089u
49
+ 0.919108u
48
+ ··· − 2.48066u − 0.166726
a
2
=
0.166654u
49
− 0.499067u
48
+ ··· + 15.7612u − 4.48148
0.00329781u
49
+ 0.613395u
48
+ ··· + 0.629281u + 0.333358
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
5330467839288029
6852922461300829
u
49
−
25189087260468945
13705844922601658
u
48
+ ···+
266207119693174765
13705844922601658
u −
140924841106764001
13705844922601658
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
50
− 4u
49
+ ··· + 11u + 1
c
3
, c
6
u
50
+ 4u
49
+ ··· − u + 1
c
5
, c
9
u
50
− 3u
49
+ ··· + 32u + 64
c
7
u
50
+ 3u
49
+ ··· − 12700u + 977
c
8
, c
11
, c
12
u
50
− 3u
49
+ ··· − 14u + 1
c
10
u
50
− 9u
49
+ ··· + 13688u + 209
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
50
− 40y
49
+ ··· − 19y + 1
c
3
, c
6
y
50
− 12y
49
+ ··· − 19y + 1
c
5
, c
9
y
50
− 35y
49
+ ··· − 82944y + 4096
c
7
y
50
+ 11y
49
+ ··· − 129195550y + 954529
c
8
, c
11
, c
12
y
50
+ 47y
49
+ ··· − 150y + 1
c
10
y
50
+ 31y
49
+ ··· − 210039934y + 43681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.552389 + 0.742281I
a = 0.58850 + 1.59488I
b = −0.405792 + 0.376362I
0.54313 + 5.94487I −9.08850 − 3.35912I
u = 0.552389 − 0.742281I
a = 0.58850 − 1.59488I
b = −0.405792 − 0.376362I
0.54313 − 5.94487I −9.08850 + 3.35912I
u = −0.922692
a = −1.08212
b = −0.943183
−5.06588 −21.9910
u = −0.749534 + 0.478843I
a = 0.202016 − 0.272595I
b = 0.365555 − 0.028774I
−4.15396 + 2.45065I −18.0240 − 7.7083I
u = −0.749534 − 0.478843I
a = 0.202016 + 0.272595I
b = 0.365555 + 0.028774I
−4.15396 − 2.45065I −18.0240 + 7.7083I
u = 0.790702 + 0.343009I
a = 1.63606 + 1.17395I
b = 1.55555 + 0.92027I
−0.76132 − 10.59360I −11.03214 + 7.66029I
u = 0.790702 − 0.343009I
a = 1.63606 − 1.17395I
b = 1.55555 − 0.92027I
−0.76132 + 10.59360I −11.03214 − 7.66029I
u = 0.702274 + 0.393042I
a = −1.31621 − 1.35430I
b = −1.36162 − 0.89962I
3.75899 − 5.49083I −7.01323 + 5.78466I
u = 0.702274 − 0.393042I
a = −1.31621 + 1.35430I
b = −1.36162 + 0.89962I
3.75899 + 5.49083I −7.01323 − 5.78466I
u = 0.566166 + 0.558111I
a = −0.90619 − 1.55455I
b = −0.020776 − 0.271583I
4.38215 + 1.22744I −5.15353 + 0.43980I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.566166 − 0.558111I
a = −0.90619 + 1.55455I
b = −0.020776 + 0.271583I
4.38215 − 1.22744I −5.15353 − 0.43980I
u = −0.120712 + 1.229850I
a = 1.45598 + 0.19323I
b = 0.507473 − 0.965365I
0.54799 + 1.96970I 0
u = −0.120712 − 1.229850I
a = 1.45598 − 0.19323I
b = 0.507473 + 0.965365I
0.54799 − 1.96970I 0
u = −0.457079 + 1.168010I
a = 0.722675 + 0.578522I
b = 0.755050 − 0.558234I
−1.48101 + 4.89320I 0
u = −0.457079 − 1.168010I
a = 0.722675 − 0.578522I
b = 0.755050 + 0.558234I
−1.48101 − 4.89320I 0
u = 0.623208 + 0.370284I
a = 1.11093 + 1.42613I
b = 0.450819 + 0.112665I
0.00046 − 3.40676I −9.23836 + 4.55497I
u = 0.623208 − 0.370284I
a = 1.11093 − 1.42613I
b = 0.450819 − 0.112665I
0.00046 + 3.40676I −9.23836 − 4.55497I
u = −0.024870 + 1.281810I
a = 0.558643 − 0.077771I
b = −0.47247 − 2.22216I
2.27889 + 0.01971I 0
u = −0.024870 − 1.281810I
a = 0.558643 + 0.077771I
b = −0.47247 + 2.22216I
2.27889 − 0.01971I 0
u = −0.239006 + 1.260440I
a = −0.861709 − 0.739108I
b = −1.15757 + 1.31290I
2.34625 + 3.21609I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.239006 − 1.260440I
a = −0.861709 + 0.739108I
b = −1.15757 − 1.31290I
2.34625 − 3.21609I 0
u = 0.149426 + 1.300560I
a = 0.0642609 − 0.0722773I
b = 1.63464 + 2.09669I
−5.69465 − 2.27909I 0
u = 0.149426 − 1.300560I
a = 0.0642609 + 0.0722773I
b = 1.63464 − 2.09669I
−5.69465 + 2.27909I 0
u = 0.535241 + 0.419966I
a = 0.82919 + 1.50246I
b = 1.147110 + 0.719409I
0.319873 − 0.282575I −8.47740 + 2.84929I
u = 0.535241 − 0.419966I
a = 0.82919 − 1.50246I
b = 1.147110 − 0.719409I
0.319873 + 0.282575I −8.47740 − 2.84929I
u = −0.203499 + 1.334990I
a = −2.06609 + 0.25372I
b = −0.87123 + 3.23217I
1.75099 + 3.13920I 0
u = −0.203499 − 1.334990I
a = −2.06609 − 0.25372I
b = −0.87123 − 3.23217I
1.75099 − 3.13920I 0
u = −0.646196
a = 1.77141
b = 1.30808
−1.56699 −3.89440
u = −0.16539 + 1.41406I
a = −0.381243 + 0.117701I
b = 0.345250 − 0.188328I
4.73635 + 3.24367I 0
u = −0.16539 − 1.41406I
a = −0.381243 − 0.117701I
b = 0.345250 + 0.188328I
4.73635 − 3.24367I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.545177 + 0.098559I
a = −0.20103 − 4.61567I
b = −0.12303 − 2.25640I
−2.79473 + 0.42156I −9.5718 + 13.6793I
u = −0.545177 − 0.098559I
a = −0.20103 + 4.61567I
b = −0.12303 + 2.25640I
−2.79473 − 0.42156I −9.5718 − 13.6793I
u = 0.20588 + 1.44689I
a = −0.759687 − 0.164512I
b = −1.97063 − 2.49195I
6.28981 − 3.04185I 0
u = 0.20588 − 1.44689I
a = −0.759687 + 0.164512I
b = −1.97063 + 2.49195I
6.28981 + 3.04185I 0
u = 0.23659 + 1.44426I
a = −0.896231 − 0.085608I
b = −1.88095 − 0.27769I
5.83118 − 6.56630I 0
u = 0.23659 − 1.44426I
a = −0.896231 + 0.085608I
b = −1.88095 + 0.27769I
5.83118 + 6.56630I 0
u = 0.26311 + 1.46153I
a = 1.048660 − 0.063993I
b = 2.20151 + 2.19868I
9.72958 − 9.01297I 0
u = 0.26311 − 1.46153I
a = 1.048660 + 0.063993I
b = 2.20151 − 2.19868I
9.72958 + 9.01297I 0
u = 0.30795 + 1.45297I
a = −1.163440 + 0.334790I
b = −2.26238 − 1.86908I
4.9961 − 14.5819I 0
u = 0.30795 − 1.45297I
a = −1.163440 − 0.334790I
b = −2.26238 + 1.86908I
4.9961 + 14.5819I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.17767 + 1.48810I
a = 0.910279 + 0.279030I
b = 1.58884 + 0.42973I
11.00730 − 1.41798I 0
u = 0.17767 − 1.48810I
a = 0.910279 − 0.279030I
b = 1.58884 − 0.42973I
11.00730 + 1.41798I 0
u = −0.28006 + 1.47904I
a = −0.234853 + 0.002148I
b = −0.706929 + 0.767521I
2.11187 + 6.21835I 0
u = −0.28006 − 1.47904I
a = −0.234853 − 0.002148I
b = −0.706929 − 0.767521I
2.11187 − 6.21835I 0
u = −0.424070 + 0.252385I
a = 0.469708 − 0.951492I
b = −0.347645 − 0.564793I
−0.662266 + 1.036830I −7.92072 − 6.52809I
u = −0.424070 − 0.252385I
a = 0.469708 + 0.951492I
b = −0.347645 + 0.564793I
−0.662266 − 1.036830I −7.92072 + 6.52809I
u = 0.489012
a = −0.158233
b = −1.61950
−9.76798 6.36650
u = 0.09636 + 1.51933I
a = −0.818964 − 0.431147I
b = −1.187120 − 0.592577I
8.07849 + 3.95049I 0
u = 0.09636 − 1.51933I
a = −0.818964 + 0.431147I
b = −1.187120 + 0.592577I
8.07849 − 3.95049I 0
u = 0.0847567
a = −5.51357
b = 0.687292
−1.09557 −8.51770
9
II. I
u
2
= h2au + u
2
+ b + u + 1, −u
2
a + a
2
− u
2
− a − u − 2, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
u
−u
2
− u − 1
a
1
=
u
2
+ 1
u
2
+ u + 1
a
3
=
a
−2au − u
2
− u − 1
a
7
=
−u
2
− 1
−u
2
− u − 1
a
4
=
u
2
+ 1
−au
a
6
=
0
au + 2u
2
+ 2u + 2
a
5
=
0
au + 2u
2
+ 2u + 2
a
2
=
a
2u
2
+ 2u + 2
a
10
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
2
a − 3au − 9u
2
− 7u − 28
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u
2
+ u − 1)
3
c
4
, c
6
(u
2
− u − 1)
3
c
5
, c
9
u
6
c
7
, c
10
(u
3
+ u
2
− 1)
2
c
8
(u
3
− u
2
+ 2u − 1)
2
c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
(y
2
− 3y + 1)
3
c
5
, c
9
y
6
c
7
, c
10
(y
3
− y
2
+ 2y −1)
2
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −1.071720 − 0.909787I
b = −1.96201 + 1.66556I
2.03717 + 2.82812I −11.98231 + 5.87116I
u = −0.215080 + 1.307140I
a = 0.409360 + 0.347508I
b = 1.96201 − 1.66556I
−5.85852 + 2.82812I −11.36167 − 7.89410I
u = −0.215080 − 1.307140I
a = −1.071720 + 0.909787I
b = −1.96201 − 1.66556I
2.03717 − 2.82812I −11.98231 − 5.87116I
u = −0.215080 − 1.307140I
a = 0.409360 − 0.347508I
b = 1.96201 + 1.66556I
−5.85852 − 2.82812I −11.36167 + 7.89410I
u = −0.569840
a = −0.818721
b = −1.68796
−9.99610 −29.1310
u = −0.569840
a = 2.14344
b = 1.68796
−2.10041 −21.1810
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u
2
+ u − 1)
3
)(u
50
− 4u
49
+ ··· + 11u + 1)
c
3
((u
2
+ u − 1)
3
)(u
50
+ 4u
49
+ ··· − u + 1)
c
4
((u
2
− u − 1)
3
)(u
50
− 4u
49
+ ··· + 11u + 1)
c
5
, c
9
u
6
(u
50
− 3u
49
+ ··· + 32u + 64)
c
6
((u
2
− u − 1)
3
)(u
50
+ 4u
49
+ ··· − u + 1)
c
7
((u
3
+ u
2
− 1)
2
)(u
50
+ 3u
49
+ ··· − 12700u + 977)
c
8
((u
3
− u
2
+ 2u − 1)
2
)(u
50
− 3u
49
+ ··· − 14u + 1)
c
10
((u
3
+ u
2
− 1)
2
)(u
50
− 9u
49
+ ··· + 13688u + 209)
c
11
, c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
50
− 3u
49
+ ··· − 14u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y
2
− 3y + 1)
3
)(y
50
− 40y
49
+ ··· − 19y + 1)
c
3
, c
6
((y
2
− 3y + 1)
3
)(y
50
− 12y
49
+ ··· − 19y + 1)
c
5
, c
9
y
6
(y
50
− 35y
49
+ ··· − 82944y + 4096)
c
7
((y
3
− y
2
+ 2y −1)
2
)(y
50
+ 11y
49
+ ··· − 1.29196 × 10
8
y + 954529)
c
8
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
50
+ 47y
49
+ ··· − 150y + 1)
c
10
((y
3
− y
2
+ 2y −1)
2
)(y
50
+ 31y
49
+ ··· − 2.10040 × 10
8
y + 43681)
15
