12a
0073
(K12a
0073
)
A knot diagram
1
Linearized knot diagam
3 5 7 10 2 9 12 4 6 1 8 11
Solving Sequence
2,6
5 3
1,10
11 4 9 7 8 12
c
5
c
2
c
1
c
10
c
4
c
9
c
6
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h7.66892 × 10
214
u
104
− 5.54270 × 10
214
u
103
+ ··· + 8.78552 × 10
214
b − 2.62937 × 10
214
,
− 7.70789 × 10
214
u
104
− 9.86900 × 10
214
u
103
+ ··· + 8.78552 × 10
214
a − 3.93480 × 10
215
,
u
105
+ u
104
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 105 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
= h7.67 × 10
214
u
104
− 5.54 × 10
214
u
103
+ · · · + 8.79 × 10
214
b − 2.63 ×
10
214
, −7.71 × 10
214
u
104
− 9.87 × 10
214
u
103
+ · · · + 8.79 × 10
214
a − 3.93 ×
10
215
, u
105
+ u
104
+ · · · + 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
0.877340u
104
+ 1.12333u
103
+ ··· − 4.89904u + 4.47874
−0.872905u
104
+ 0.630891u
103
+ ··· − 2.07805u + 0.299284
a
11
=
−0.214388u
104
+ 1.49205u
103
+ ··· − 4.86698u + 4.98395
−0.608798u
104
+ 0.442648u
103
+ ··· − 2.47648u + 0.150688
a
4
=
−2.51175u
104
− 2.39463u
103
+ ··· + 10.4331u + 4.89572
−0.0579607u
104
− 0.975123u
103
+ ··· − 3.10564u − 0.356969
a
9
=
0.00443566u
104
+ 1.75422u
103
+ ··· − 6.97708u + 4.77802
−0.872905u
104
+ 0.630891u
103
+ ··· − 2.07805u + 0.299284
a
7
=
−2.21119u
104
− 1.97819u
103
+ ··· − 8.95378u − 4.10035
0.647194u
104
− 1.16684u
103
+ ··· − 0.177061u − 1.69006
a
8
=
0.0758079u
104
+ 1.33160u
103
+ ··· − 5.78845u + 6.83418
−1.04456u
104
+ 0.913641u
103
+ ··· − 3.12835u + 0.562654
a
12
=
−2.58052u
104
− 1.81430u
103
+ ··· − 14.5209u − 2.88953
0.434434u
104
− 0.542417u
103
+ ··· − 0.463397u − 1.49524
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.26566u
104
− 6.31791u
103
+ ··· + 10.2404u − 6.23126
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
105
+ 43u
104
+ ··· − 7u − 1
c
2
, c
5
u
105
+ u
104
+ ··· + 3u + 1
c
3
u
105
− 27u
104
+ ··· − 9u + 1
c
4
u
105
− 15u
104
+ ··· + 15789u + 52699
c
6
, c
9
u
105
− 5u
104
+ ··· − 3u + 1
c
7
, c
11
u
105
+ 5u
104
+ ··· − u + 1
c
8
u
105
− u
104
+ ··· − 11u + 1
c
10
, c
12
u
105
− 31u
104
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 39y
104
+ ··· − 579y −1
c
2
, c
5
y
105
+ 43y
104
+ ··· − 7y −1
c
3
y
105
+ 95y
104
+ ··· − 295y −1
c
4
y
105
− 17y
104
+ ··· + 26937541693y −2777184601
c
6
, c
9
y
105
+ 75y
104
+ ··· + 5y −1
c
7
, c
11
y
105
+ 31y
104
+ ··· + 5y −1
c
8
y
105
− 5y
104
+ ··· + 33y −1
c
10
, c
12
y
105
+ 87y
104
+ ··· − 251y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.508255 + 0.862936I
a = 7.42480 + 9.85920I
b = −0.027672 − 0.963307I
−1.35091 + 4.86008I 0
u = 0.508255 − 0.862936I
a = 7.42480 − 9.85920I
b = −0.027672 + 0.963307I
−1.35091 − 4.86008I 0
u = −0.726437 + 0.681228I
a = 0.302847 − 0.123414I
b = 0.41559 − 1.45271I
7.14004 − 0.17018I 0
u = −0.726437 − 0.681228I
a = 0.302847 + 0.123414I
b = 0.41559 + 1.45271I
7.14004 + 0.17018I 0
u = 0.670011 + 0.735882I
a = −0.398917 + 1.060470I
b = 0.218711 − 0.343183I
−1.53322 + 5.27277I 0
u = 0.670011 − 0.735882I
a = −0.398917 − 1.060470I
b = 0.218711 + 0.343183I
−1.53322 − 5.27277I 0
u = 0.498514 + 0.873517I
a = −13.15460 + 0.69616I
b = 0.039933 + 1.006260I
−1.39472 − 0.77663I 0
u = 0.498514 − 0.873517I
a = −13.15460 − 0.69616I
b = 0.039933 − 1.006260I
−1.39472 + 0.77663I 0
u = 0.416633 + 0.881483I
a = −0.697391 − 0.189517I
b = 0.218983 + 0.169046I
−0.33676 + 1.74914I 0
u = 0.416633 − 0.881483I
a = −0.697391 + 0.189517I
b = 0.218983 − 0.169046I
−0.33676 − 1.74914I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.421508 + 0.941394I
a = 0.113393 − 1.188910I
b = −0.88553 + 1.17946I
−2.90888 − 0.14378I 0
u = −0.421508 − 0.941394I
a = 0.113393 + 1.188910I
b = −0.88553 − 1.17946I
−2.90888 + 0.14378I 0
u = −0.000183 + 1.041080I
a = 0.655071 − 1.227110I
b = −0.461490 + 0.982731I
−1.37985 + 2.60061I 0
u = −0.000183 − 1.041080I
a = 0.655071 + 1.227110I
b = −0.461490 − 0.982731I
−1.37985 − 2.60061I 0
u = −0.462542 + 0.937742I
a = 2.01181 − 0.08750I
b = −0.38997 − 1.69307I
−2.72043 − 5.15393I 0
u = −0.462542 − 0.937742I
a = 2.01181 + 0.08750I
b = −0.38997 + 1.69307I
−2.72043 + 5.15393I 0
u = −0.944508 + 0.449202I
a = 0.227674 + 0.414665I
b = −0.43011 + 1.35679I
0.58537 + 6.60149I 0
u = −0.944508 − 0.449202I
a = 0.227674 − 0.414665I
b = −0.43011 − 1.35679I
0.58537 − 6.60149I 0
u = 0.673932 + 0.800679I
a = 0.449328 − 0.906610I
b = −0.236551 + 0.292446I
−1.68329 − 0.14385I 0
u = 0.673932 − 0.800679I
a = 0.449328 + 0.906610I
b = −0.236551 − 0.292446I
−1.68329 + 0.14385I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.420652 + 0.958376I
a = 1.60412 − 0.80365I
b = −1.169270 − 0.420460I
−2.94183 − 2.82687I 0
u = −0.420652 − 0.958376I
a = 1.60412 + 0.80365I
b = −1.169270 + 0.420460I
−2.94183 + 2.82687I 0
u = −0.406993 + 0.861247I
a = −1.79250 + 0.05635I
b = 0.11232 + 1.69617I
−2.32293 + 1.64088I 0
u = −0.406993 − 0.861247I
a = −1.79250 − 0.05635I
b = 0.11232 − 1.69617I
−2.32293 − 1.64088I 0
u = −0.883123 + 0.572875I
a = −0.048849 − 0.279960I
b = 0.42862 − 1.38709I
7.89421 + 6.86350I 0
u = −0.883123 − 0.572875I
a = −0.048849 + 0.279960I
b = 0.42862 + 1.38709I
7.89421 − 6.86350I 0
u = 0.604807 + 0.709411I
a = −0.06549 + 1.57847I
b = −0.034649 + 1.142580I
3.17185 + 1.49000I 0
u = 0.604807 − 0.709411I
a = −0.06549 − 1.57847I
b = −0.034649 − 1.142580I
3.17185 − 1.49000I 0
u = −0.758524 + 0.535990I
a = −0.154021 + 0.433594I
b = −0.39001 + 1.39514I
3.99639 + 3.72302I 0
u = −0.758524 − 0.535990I
a = −0.154021 − 0.433594I
b = −0.39001 − 1.39514I
3.99639 − 3.72302I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.524210 + 0.945636I
a = 0.190673 + 0.999026I
b = 0.80345 − 1.44636I
−1.36172 − 6.40994I 0
u = −0.524210 − 0.945636I
a = 0.190673 − 0.999026I
b = 0.80345 + 1.44636I
−1.36172 + 6.40994I 0
u = −0.978052 + 0.472820I
a = −0.250397 − 0.357539I
b = 0.43741 − 1.35953I
1.51311 + 12.62850I 0
u = −0.978052 − 0.472820I
a = −0.250397 + 0.357539I
b = 0.43741 + 1.35953I
1.51311 − 12.62850I 0
u = −0.786078 + 0.399159I
a = −0.422992 + 0.480443I
b = 0.929515 − 0.138087I
−3.14157 + 7.73150I 0
u = −0.786078 − 0.399159I
a = −0.422992 − 0.480443I
b = 0.929515 + 0.138087I
−3.14157 − 7.73150I 0
u = 0.101092 + 0.874217I
a = −1.52874 − 0.02687I
b = 0.509118 + 0.386326I
−1.22927 + 1.94221I 0
u = 0.101092 − 0.874217I
a = −1.52874 + 0.02687I
b = 0.509118 − 0.386326I
−1.22927 − 1.94221I 0
u = 0.572492 + 0.963051I
a = 0.618677 − 0.447757I
b = −0.289709 + 0.100685I
1.38092 + 3.06411I 0
u = 0.572492 − 0.963051I
a = 0.618677 + 0.447757I
b = −0.289709 − 0.100685I
1.38092 − 3.06411I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.577256 + 0.970351I
a = −1.24254 + 0.92560I
b = 1.265650 + 0.082613I
1.68086 − 6.53955I 0
u = −0.577256 − 0.970351I
a = −1.24254 − 0.92560I
b = 1.265650 − 0.082613I
1.68086 + 6.53955I 0
u = 1.133270 + 0.094508I
a = −0.0108772 − 0.1312870I
b = 0.008558 − 1.226130I
3.44061 − 2.55226I 0
u = 1.133270 − 0.094508I
a = −0.0108772 + 0.1312870I
b = 0.008558 + 1.226130I
3.44061 + 2.55226I 0
u = −0.443283 + 0.714059I
a = −2.00536 + 0.69393I
b = 0.845499 + 0.998451I
−0.58409 + 2.30355I 0
u = −0.443283 − 0.714059I
a = −2.00536 − 0.69393I
b = 0.845499 − 0.998451I
−0.58409 − 2.30355I 0
u = 1.062760 + 0.471860I
a = −0.118414 − 0.270868I
b = 0.044239 − 1.215040I
6.76585 + 1.83284I 0
u = 1.062760 − 0.471860I
a = −0.118414 + 0.270868I
b = 0.044239 + 1.215040I
6.76585 − 1.83284I 0
u = −0.651366 + 0.971836I
a = −1.92468 + 0.26060I
b = 0.59797 + 1.44518I
6.25598 − 5.09845I 0
u = −0.651366 − 0.971836I
a = −1.92468 − 0.26060I
b = 0.59797 − 1.44518I
6.25598 + 5.09845I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.557017 + 0.613871I
a = −0.409467 + 0.939341I
b = 0.987950 − 0.342672I
2.71513 + 1.93385I 0
u = −0.557017 − 0.613871I
a = −0.409467 − 0.939341I
b = 0.987950 + 0.342672I
2.71513 − 1.93385I 0
u = −0.747186 + 0.332399I
a = 0.332745 − 0.437546I
b = −0.896635 + 0.130466I
−4.04595 + 1.81268I 0
u = −0.747186 − 0.332399I
a = 0.332745 + 0.437546I
b = −0.896635 − 0.130466I
−4.04595 − 1.81268I 0
u = 0.622436 + 1.009490I
a = −1.69807 − 0.26278I
b = 0.139745 − 1.105790I
2.09705 + 3.42836I 0
u = 0.622436 − 1.009490I
a = −1.69807 + 0.26278I
b = 0.139745 + 1.105790I
2.09705 − 3.42836I 0
u = −0.181525 + 1.172900I
a = 1.42896 − 0.46621I
b = −0.829191 − 0.232875I
−8.82234 − 0.91544I 0
u = −0.181525 − 1.172900I
a = 1.42896 + 0.46621I
b = −0.829191 + 0.232875I
−8.82234 + 0.91544I 0
u = 0.456154 + 0.664711I
a = 0.61525 + 1.56775I
b = −0.020906 − 0.518366I
2.33820 + 1.37333I 0
u = 0.456154 − 0.664711I
a = 0.61525 − 1.56775I
b = −0.020906 + 0.518366I
2.33820 − 1.37333I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.133227 + 1.187360I
a = −1.41101 + 0.43669I
b = 0.795493 + 0.218832I
−8.34685 + 5.22128I 0
u = −0.133227 − 1.187360I
a = −1.41101 − 0.43669I
b = 0.795493 − 0.218832I
−8.34685 − 5.22128I 0
u = 0.477886 + 1.111110I
a = −0.927862 + 0.357458I
b = 0.433014 − 0.015021I
−3.85790 + 1.05487I 0
u = 0.477886 − 1.111110I
a = −0.927862 − 0.357458I
b = 0.433014 + 0.015021I
−3.85790 − 1.05487I 0
u = 0.522546 + 1.107910I
a = 0.895110 − 0.406895I
b = −0.423129 + 0.048731I
−3.53406 + 6.74367I 0
u = 0.522546 − 1.107910I
a = 0.895110 + 0.406895I
b = −0.423129 − 0.048731I
−3.53406 − 6.74367I 0
u = 0.195343 + 1.213140I
a = −0.955707 + 0.975328I
b = 0.347571 − 1.069600I
0.76843 + 5.57184I 0
u = 0.195343 − 1.213140I
a = −0.955707 − 0.975328I
b = 0.347571 + 1.069600I
0.76843 − 5.57184I 0
u = −0.635360 + 1.051860I
a = 1.91539 − 0.19142I
b = −0.53909 − 1.43926I
2.46261 − 9.01692I 0
u = −0.635360 − 1.051860I
a = 1.91539 + 0.19142I
b = −0.53909 + 1.43926I
2.46261 + 9.01692I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.573696 + 1.101490I
a = 1.27872 − 0.73078I
b = −1.113830 − 0.111897I
−6.25145 − 6.77312I 0
u = −0.573696 − 1.101490I
a = 1.27872 + 0.73078I
b = −1.113830 + 0.111897I
−6.25145 + 6.77312I 0
u = −0.607709 + 1.103640I
a = −1.24531 + 0.72570I
b = 1.113740 + 0.085690I
−5.20237 − 12.95960I 0
u = −0.607709 − 1.103640I
a = −1.24531 − 0.72570I
b = 1.113740 − 0.085690I
−5.20237 + 12.95960I 0
u = −0.695529 + 1.076720I
a = −1.86993 + 0.18482I
b = 0.54253 + 1.40519I
6.3495 − 12.6969I 0
u = −0.695529 − 1.076720I
a = −1.86993 − 0.18482I
b = 0.54253 − 1.40519I
6.3495 + 12.6969I 0
u = 0.604480 + 0.379071I
a = −0.551150 + 0.357450I
b = −0.018965 + 1.181400I
3.35286 + 1.30846I −2.29563 − 4.32140I
u = 0.604480 − 0.379071I
a = −0.551150 − 0.357450I
b = −0.018965 − 1.181400I
3.35286 − 1.30846I −2.29563 + 4.32140I
u = 1.016120 + 0.853696I
a = 0.519396 + 0.310803I
b = −0.094416 + 1.202750I
2.39877 + 1.01374I 0
u = 1.016120 − 0.853696I
a = 0.519396 − 0.310803I
b = −0.094416 − 1.202750I
2.39877 − 1.01374I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.672944 + 1.147260I
a = 1.87685 − 0.13801I
b = −0.51403 − 1.39635I
−1.55003 − 12.50060I 0
u = −0.672944 − 1.147260I
a = 1.87685 + 0.13801I
b = −0.51403 + 1.39635I
−1.55003 + 12.50060I 0
u = 1.094560 + 0.763773I
a = −0.387061 − 0.268070I
b = 0.080994 − 1.214740I
2.71739 + 6.28347I 0
u = 1.094560 − 0.763773I
a = −0.387061 + 0.268070I
b = 0.080994 + 1.214740I
2.71739 − 6.28347I 0
u = −0.016022 + 1.345400I
a = 0.689201 − 0.878906I
b = −0.426397 + 1.135310I
−6.05046 + 3.63906I 0
u = −0.016022 − 1.345400I
a = 0.689201 + 0.878906I
b = −0.426397 − 1.135310I
−6.05046 − 3.63906I 0
u = −0.692371 + 1.153980I
a = −1.86487 + 0.13570I
b = 0.51713 + 1.38967I
−0.5913 − 18.6960I 0
u = −0.692371 − 1.153980I
a = −1.86487 − 0.13570I
b = 0.51713 − 1.38967I
−0.5913 + 18.6960I 0
u = 0.023126 + 1.377250I
a = −0.719581 + 0.849284I
b = 0.409086 − 1.141730I
−5.52098 + 9.62166I 0
u = 0.023126 − 1.377250I
a = −0.719581 − 0.849284I
b = 0.409086 + 1.141730I
−5.52098 − 9.62166I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805185 + 1.119210I
a = 1.009610 + 0.085722I
b = −0.154249 + 1.170110I
4.84892 + 4.84004I 0
u = 0.805185 − 1.119210I
a = 1.009610 − 0.085722I
b = −0.154249 − 1.170110I
4.84892 − 4.84004I 0
u = 0.272901 + 0.554183I
a = −0.19275 + 2.00690I
b = 0.257419 − 0.608789I
2.30617 + 1.35689I 0.69154 − 4.56259I
u = 0.272901 − 0.554183I
a = −0.19275 − 2.00690I
b = 0.257419 + 0.608789I
2.30617 − 1.35689I 0.69154 + 4.56259I
u = 0.65848 + 1.29036I
a = −1.068220 + 0.283751I
b = 0.211206 − 1.163030I
−0.52858 + 3.53870I 0
u = 0.65848 − 1.29036I
a = −1.068220 − 0.283751I
b = 0.211206 + 1.163030I
−0.52858 − 3.53870I 0
u = 0.72220 + 1.29833I
a = 1.003820 − 0.223822I
b = −0.201729 + 1.176080I
−0.06083 + 9.13213I 0
u = 0.72220 − 1.29833I
a = 1.003820 + 0.223822I
b = −0.201729 − 1.176080I
−0.06083 − 9.13213I 0
u = 0.270706 + 0.375679I
a = 2.42139 + 1.77339I
b = −0.236524 − 0.659638I
−1.27823 − 2.63513I −5.66825 + 3.44323I
u = 0.270706 − 0.375679I
a = 2.42139 − 1.77339I
b = −0.236524 + 0.659638I
−1.27823 + 2.63513I −5.66825 − 3.44323I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.336905
a = −0.721891
b = −0.588949
−0.940602 −10.3260
u = 0.322904 + 0.028835I
a = −1.17535 − 3.20754I
b = 0.143408 + 0.600910I
−1.22625 + 2.67668I −4.97081 − 2.18693I
u = 0.322904 − 0.028835I
a = −1.17535 + 3.20754I
b = 0.143408 − 0.600910I
−1.22625 − 2.67668I −4.97081 + 2.18693I
u = −0.141033 + 0.171770I
a = 4.56827 − 2.64364I
b = −0.276321 − 0.948170I
−1.35507 − 2.65461I −5.59031 + 3.22885I
u = −0.141033 − 0.171770I
a = 4.56827 + 2.64364I
b = −0.276321 + 0.948170I
−1.35507 + 2.65461I −5.59031 − 3.22885I
15
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
105
+ 43u
104
+ ··· − 7u − 1
c
2
, c
5
u
105
+ u
104
+ ··· + 3u + 1
c
3
u
105
− 27u
104
+ ··· − 9u + 1
c
4
u
105
− 15u
104
+ ··· + 15789u + 52699
c
6
, c
9
u
105
− 5u
104
+ ··· − 3u + 1
c
7
, c
11
u
105
+ 5u
104
+ ··· − u + 1
c
8
u
105
− u
104
+ ··· − 11u + 1
c
10
, c
12
u
105
− 31u
104
+ ··· + 5u + 1
16
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 39y
104
+ ··· − 579y −1
c
2
, c
5
y
105
+ 43y
104
+ ··· − 7y −1
c
3
y
105
+ 95y
104
+ ··· − 295y −1
c
4
y
105
− 17y
104
+ ··· + 26937541693y −2777184601
c
6
, c
9
y
105
+ 75y
104
+ ··· + 5y −1
c
7
, c
11
y
105
+ 31y
104
+ ··· + 5y −1
c
8
y
105
− 5y
104
+ ··· + 33y −1
c
10
, c
12
y
105
+ 87y
104
+ ··· − 251y −1
17
