12a
0658
(K12a
0658
)
A knot diagram
1
Linearized knot diagam
3 7 10 12 9 2 6 11 1 8 5 4
Solving Sequence
2,7 3,10
4 1 6 8 11 9 5 12
c
2
c
3
c
1
c
6
c
7
c
10
c
9
c
5
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.62898 × 10
65
u
82
− 9.33541 × 10
66
u
81
+ ··· + 9.04370 × 10
67
b + 3.29825 × 10
66
,
2.10524 × 10
67
u
82
+ 1.26169 × 10
67
u
81
+ ··· + 9.04370 × 10
67
a + 5.17635 × 10
66
, u
83
+ u
82
+ ··· − 3u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 83 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−2.63×10
65
u
82
−9.34×10
66
u
81
+· · ·+9.04×10
67
b+3.30×10
66
, 2.11×
10
67
u
82
+1.26×10
67
u
81
+· · ·+9.04×10
67
a+5.18×10
66
, u
83
+u
82
+· · ·−3u
2
−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
−0.232785u
82
− 0.139510u
81
+ ··· + 1.16873u − 0.0572371
0.00290698u
82
+ 0.103226u
81
+ ··· + 2.00815u − 0.0364701
a
4
=
6.38689u
82
+ 8.65090u
81
+ ··· + 6.46944u + 9.73885
0.0601500u
82
− 4.03734u
81
+ ··· + 6.62282u + 6.42267
a
1
=
−u
2
+ 1
−u
4
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
11
=
−0.162336u
82
− 0.0965383u
81
+ ··· + 1.25096u − 0.0980678
−0.00887391u
82
+ 0.104798u
81
+ ··· + 0.973680u + 0.0160412
a
9
=
−0.237869u
82
− 0.170081u
81
+ ··· − 0.811372u + 0.00168075
0.0182886u
82
+ 0.0928221u
81
+ ··· + 1.99990u − 0.0425818
a
5
=
−6.26650u
82
− 6.25201u
81
+ ··· + 4.47085u − 6.68810
−2.39740u
82
+ 4.01692u
81
+ ··· − 7.66722u − 6.36765
a
12
=
6.70384u
82
+ 19.4884u
81
+ ··· − 5.38905u + 1.94050
12.8932u
82
+ 25.5557u
81
+ ··· + 1.05907u + 6.64542
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.54849u
82
+ 10.1599u
81
+ ··· − 0.291458u + 0.179307
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
83
+ 25u
82
+ ··· − 6u + 1
c
2
, c
6
u
83
− u
82
+ ··· + 3u
2
+ 1
c
3
u
83
− 63u
82
+ ··· + 2026u − 173
c
4
, c
11
, c
12
u
83
+ 3u
82
+ ··· − 2u − 1
c
5
u
83
+ 57u
82
+ ··· + 4370580u − 516739
c
8
, c
10
u
83
− u
82
+ ··· + 62u + 1
c
9
u
83
− 7u
82
+ ··· + 8u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
83
+ 67y
82
+ ··· − 278y −1
c
2
, c
6
y
83
− 25y
82
+ ··· − 6y −1
c
3
y
83
− 1525y
82
+ ··· − 812330y −29929
c
4
, c
11
, c
12
y
83
+ 87y
82
+ ··· − 6y −1
c
5
y
83
− 1549y
82
+ ··· − 1262101601146y −267019194121
c
8
, c
10
y
83
− 57y
82
+ ··· + 1394y −1
c
9
y
83
+ 3y
82
+ ··· − 254y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.755268 + 0.689868I
a = 1.39106 − 0.73110I
b = −0.85372 − 1.59878I
−6.36702 − 1.67327I 0
u = −0.755268 − 0.689868I
a = 1.39106 + 0.73110I
b = −0.85372 + 1.59878I
−6.36702 + 1.67327I 0
u = 0.955926 + 0.196493I
a = −0.22750 − 2.08453I
b = −0.156061 − 1.022080I
−7.37611 − 5.46942I 0
u = 0.955926 − 0.196493I
a = −0.22750 + 2.08453I
b = −0.156061 + 1.022080I
−7.37611 + 5.46942I 0
u = 0.956828 + 0.058122I
a = −2.00868 − 1.22339I
b = −1.63195 − 0.51030I
−11.35230 − 2.20989I −15.1094 + 3.1648I
u = 0.956828 − 0.058122I
a = −2.00868 + 1.22339I
b = −1.63195 + 0.51030I
−11.35230 + 2.20989I −15.1094 − 3.1648I
u = 0.687528 + 0.643247I
a = 0.926393 − 0.698284I
b = 1.132660 + 0.246219I
−1.83104 − 2.29304I 0
u = 0.687528 − 0.643247I
a = 0.926393 + 0.698284I
b = 1.132660 − 0.246219I
−1.83104 + 2.29304I 0
u = 0.792394 + 0.712520I
a = −1.54071 − 0.89895I
b = 0.35084 − 1.82511I
0.299391 + 0.398880I 0
u = 0.792394 − 0.712520I
a = −1.54071 + 0.89895I
b = 0.35084 + 1.82511I
0.299391 − 0.398880I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904497 + 0.220913I
a = 0.17765 − 1.52628I
b = −0.029075 − 0.629089I
−1.20857 + 3.31837I −4.51564 − 9.28081I
u = −0.904497 − 0.220913I
a = 0.17765 + 1.52628I
b = −0.029075 + 0.629089I
−1.20857 − 3.31837I −4.51564 + 9.28081I
u = −0.910106 + 0.059437I
a = 1.27235 − 0.99553I
b = 1.354240 − 0.173525I
−4.57106 + 1.49550I −13.9394 − 4.6490I
u = −0.910106 − 0.059437I
a = 1.27235 + 0.99553I
b = 1.354240 + 0.173525I
−4.57106 − 1.49550I −13.9394 + 4.6490I
u = −0.887492 + 0.636493I
a = 0.683971 − 0.824958I
b = −0.671063 + 0.175785I
−8.30238 + 2.46513I 0
u = −0.887492 − 0.636493I
a = 0.683971 + 0.824958I
b = −0.671063 − 0.175785I
−8.30238 − 2.46513I 0
u = 0.875962 + 0.673460I
a = −0.806933 + 0.072405I
b = −0.225907 + 0.407373I
−1.37629 − 2.60149I 0
u = 0.875962 − 0.673460I
a = −0.806933 − 0.072405I
b = −0.225907 − 0.407373I
−1.37629 + 2.60149I 0
u = −0.661827 + 0.885032I
a = −0.964523 + 0.509781I
b = 0.022493 + 1.391210I
2.87924 − 1.90637I 0
u = −0.661827 − 0.885032I
a = −0.964523 − 0.509781I
b = 0.022493 − 1.391210I
2.87924 + 1.90637I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.835653 + 0.725148I
a = 2.60784 − 1.24490I
b = 0.75247 − 2.72826I
1.27283 + 1.90992I 0
u = −0.835653 − 0.725148I
a = 2.60784 + 1.24490I
b = 0.75247 + 2.72826I
1.27283 − 1.90992I 0
u = −0.759362 + 0.807841I
a = 1.143780 − 0.638739I
b = 0.10158 − 2.38329I
−0.92315 − 4.32848I 0
u = −0.759362 − 0.807841I
a = 1.143780 + 0.638739I
b = 0.10158 + 2.38329I
−0.92315 + 4.32848I 0
u = 0.146295 + 0.862891I
a = 0.502919 − 0.599119I
b = 0.318232 + 0.048877I
−1.16072 − 3.54724I −1.48488 + 10.43399I
u = 0.146295 − 0.862891I
a = 0.502919 + 0.599119I
b = 0.318232 − 0.048877I
−1.16072 + 3.54724I −1.48488 − 10.43399I
u = 0.781550 + 0.815567I
a = −0.931448 − 0.568907I
b = −0.16327 − 1.94279I
5.31516 + 1.68799I 0
u = 0.781550 − 0.815567I
a = −0.931448 + 0.568907I
b = −0.16327 + 1.94279I
5.31516 − 1.68799I 0
u = 0.700806 + 0.886878I
a = 1.07343 + 0.97806I
b = −0.40330 + 1.95285I
2.12600 + 7.17684I 0
u = 0.700806 − 0.886878I
a = 1.07343 − 0.97806I
b = −0.40330 − 1.95285I
2.12600 − 7.17684I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.835930 + 0.195360I
a = 1.46241 − 0.35911I
b = −0.380020 + 0.200495I
−6.95212 − 0.78250I −9.57348 − 2.76568I
u = −0.835930 − 0.195360I
a = 1.46241 + 0.35911I
b = −0.380020 − 0.200495I
−6.95212 + 0.78250I −9.57348 + 2.76568I
u = −0.715123 + 0.890294I
a = −1.04148 + 1.30724I
b = 0.78013 + 2.24858I
−5.16586 − 10.89950I 0
u = −0.715123 − 0.890294I
a = −1.04148 − 1.30724I
b = 0.78013 − 2.24858I
−5.16586 + 10.89950I 0
u = 1.115590 + 0.254027I
a = 0.455845 + 0.985086I
b = 0.752013 + 0.094668I
−12.8738 − 10.9955I 0
u = 1.115590 − 0.254027I
a = 0.455845 − 0.985086I
b = 0.752013 − 0.094668I
−12.8738 + 10.9955I 0
u = 0.873414 + 0.747229I
a = −18.3435 − 31.1898I
b = 7.4711 − 40.6923I
−3.55022 − 2.83360I 0
u = 0.873414 − 0.747229I
a = −18.3435 + 31.1898I
b = 7.4711 + 40.6923I
−3.55022 + 2.83360I 0
u = −0.904821 + 0.717976I
a = −1.83061 + 1.76546I
b = −0.38042 + 3.47812I
1.05940 + 3.60208I 0
u = −0.904821 − 0.717976I
a = −1.83061 − 1.76546I
b = −0.38042 − 3.47812I
1.05940 − 3.60208I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.893817 + 0.740208I
a = 1.00833 − 1.34709I
b = 1.86663 − 0.41544I
−1.93473 − 2.81075I 0
u = 0.893817 − 0.740208I
a = 1.00833 + 1.34709I
b = 1.86663 + 0.41544I
−1.93473 + 2.81075I 0
u = −1.137010 + 0.238482I
a = −0.311301 + 0.663025I
b = −0.670008 + 0.007941I
−5.49259 + 7.04236I 0
u = −1.137010 − 0.238482I
a = −0.311301 − 0.663025I
b = −0.670008 − 0.007941I
−5.49259 − 7.04236I 0
u = −0.816117 + 0.827408I
a = 0.526716 − 0.470929I
b = 0.079622 − 1.300680I
4.85499 + 2.01628I 0
u = −0.816117 − 0.827408I
a = 0.526716 + 0.470929I
b = 0.079622 + 1.300680I
4.85499 − 2.01628I 0
u = 0.830299
a = 0.547895
b = −2.11831
−3.06730 24.2670
u = 0.933394 + 0.705292I
a = 1.70582 + 0.14953I
b = 1.11542 + 2.14592I
−0.13209 − 5.84066I 0
u = 0.933394 − 0.705292I
a = 1.70582 − 0.14953I
b = 1.11542 − 2.14592I
−0.13209 + 5.84066I 0
u = −1.126850 + 0.320440I
a = −0.982231 − 0.060209I
b = −0.846664 − 0.369957I
−12.47050 − 3.50305I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.126850 − 0.320440I
a = −0.982231 + 0.060209I
b = −0.846664 + 0.369957I
−12.47050 + 3.50305I 0
u = −0.949439 + 0.690480I
a = −1.78958 − 0.48224I
b = −1.41736 + 1.90620I
−6.95269 + 7.01395I 0
u = −0.949439 − 0.690480I
a = −1.78958 + 0.48224I
b = −1.41736 − 1.90620I
−6.95269 − 7.01395I 0
u = 0.803038 + 0.172342I
a = −0.518092 − 0.756682I
b = 0.179057 − 0.068091I
−1.39137 − 0.61321I −5.51396 − 0.21738I
u = 0.803038 − 0.172342I
a = −0.518092 + 0.756682I
b = 0.179057 + 0.068091I
−1.39137 + 0.61321I −5.51396 + 0.21738I
u = −0.059613 + 0.818292I
a = −0.575775 − 1.028540I
b = −0.428264 − 0.253862I
−8.89496 + 7.47739I −5.21237 − 5.39640I
u = −0.059613 − 0.818292I
a = −0.575775 + 1.028540I
b = −0.428264 + 0.253862I
−8.89496 − 7.47739I −5.21237 + 5.39640I
u = −0.950078 + 0.777082I
a = −1.238970 + 0.334127I
b = −0.496426 + 1.145190I
4.43453 + 3.98266I 0
u = −0.950078 − 0.777082I
a = −1.238970 − 0.334127I
b = −0.496426 − 1.145190I
4.43453 − 3.98266I 0
u = 0.967952 + 0.758860I
a = 1.72181 + 0.71910I
b = 0.43237 + 1.88463I
4.73983 − 7.59390I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.967952 − 0.758860I
a = 1.72181 − 0.71910I
b = 0.43237 − 1.88463I
4.73983 + 7.59390I 0
u = −0.977354 + 0.747017I
a = −2.13319 + 0.86878I
b = −0.50320 + 2.36095I
−1.59108 + 10.17270I 0
u = −0.977354 − 0.747017I
a = −2.13319 − 0.86878I
b = −0.50320 − 2.36095I
−1.59108 − 10.17270I 0
u = 1.214100 + 0.292688I
a = 0.387971 + 0.106501I
b = 0.584747 − 0.216212I
−4.94592 − 1.05019I 0
u = 1.214100 − 0.292688I
a = 0.387971 − 0.106501I
b = 0.584747 + 0.216212I
−4.94592 + 1.05019I 0
u = 0.812519 + 0.989271I
a = −0.056345 + 0.335138I
b = −0.677629 + 0.060020I
−3.56075 − 3.87886I 0
u = 0.812519 − 0.989271I
a = −0.056345 − 0.335138I
b = −0.677629 − 0.060020I
−3.56075 + 3.87886I 0
u = 1.037630 + 0.760789I
a = −1.89193 − 0.59324I
b = −1.15940 − 2.23054I
1.08407 − 13.28350I 0
u = 1.037630 − 0.760789I
a = −1.89193 + 0.59324I
b = −1.15940 + 2.23054I
1.08407 + 13.28350I 0
u = −1.033520 + 0.767579I
a = 2.27501 − 0.43958I
b = 1.58296 − 2.40705I
−6.1557 + 17.0416I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.033520 − 0.767579I
a = 2.27501 + 0.43958I
b = 1.58296 + 2.40705I
−6.1557 − 17.0416I 0
u = −1.051130 + 0.750004I
a = 1.34289 − 0.60568I
b = 0.71268 − 1.80857I
1.69398 + 7.96545I 0
u = −1.051130 − 0.750004I
a = 1.34289 + 0.60568I
b = 0.71268 + 1.80857I
1.69398 − 7.96545I 0
u = 1.110610 + 0.807171I
a = −0.563340 + 0.047867I
b = −0.614033 − 0.652470I
−4.61076 − 2.95718I 0
u = 1.110610 − 0.807171I
a = −0.563340 − 0.047867I
b = −0.614033 + 0.652470I
−4.61076 + 2.95718I 0
u = 0.002893 + 0.524651I
a = 1.37326 + 0.34097I
b = 0.498150 + 0.732993I
−4.47756 + 3.05000I −1.23985 − 2.98660I
u = 0.002893 − 0.524651I
a = 1.37326 − 0.34097I
b = 0.498150 − 0.732993I
−4.47756 − 3.05000I −1.23985 + 2.98660I
u = −0.158256 + 0.499482I
a = −0.848821 + 0.049190I
b = −0.450699 + 0.399594I
1.094660 − 0.749184I 5.57918 + 2.32776I
u = −0.158256 − 0.499482I
a = −0.848821 − 0.049190I
b = −0.450699 − 0.399594I
1.094660 + 0.749184I 5.57918 − 2.32776I
u = −0.297722 + 0.336751I
a = 2.38324 + 1.06586I
b = −0.651932 + 0.763398I
−7.89690 + 1.23833I −3.73303 − 1.37380I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.297722 − 0.336751I
a = 2.38324 − 1.06586I
b = −0.651932 − 0.763398I
−7.89690 − 1.23833I −3.73303 + 1.37380I
u = 0.149787 + 0.224828I
a = −2.59164 + 2.46924I
b = 0.282178 + 0.465935I
−1.77014 − 0.63400I −5.01585 − 1.19253I
u = 0.149787 − 0.224828I
a = −2.59164 − 2.46924I
b = 0.282178 − 0.465935I
−1.77014 + 0.63400I −5.01585 + 1.19253I
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
83
+ 25u
82
+ ··· − 6u + 1
c
2
, c
6
u
83
− u
82
+ ··· + 3u
2
+ 1
c
3
u
83
− 63u
82
+ ··· + 2026u − 173
c
4
, c
11
, c
12
u
83
+ 3u
82
+ ··· − 2u − 1
c
5
u
83
+ 57u
82
+ ··· + 4370580u − 516739
c
8
, c
10
u
83
− u
82
+ ··· + 62u + 1
c
9
u
83
− 7u
82
+ ··· + 8u − 1
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
83
+ 67y
82
+ ··· − 278y −1
c
2
, c
6
y
83
− 25y
82
+ ··· − 6y −1
c
3
y
83
− 1525y
82
+ ··· − 812330y −29929
c
4
, c
11
, c
12
y
83
+ 87y
82
+ ··· − 6y −1
c
5
y
83
− 1549y
82
+ ··· − 1262101601146y −267019194121
c
8
, c
10
y
83
− 57y
82
+ ··· + 1394y −1
c
9
y
83
+ 3y
82
+ ··· − 254y −1
15
