12a
0598
(K12a
0598
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 12 2 10 6 1 8 5 4
Solving Sequence
6,12 5,9
8 11 4 1 3 2 10 7
c
5
c
8
c
11
c
4
c
12
c
3
c
1
c
10
c
7
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.88484 × 10
108
u
104
− 5.09336 × 10
110
u
103
+ ··· + 8.35512 × 10
110
b − 2.14019 × 10
110
,
6.52267 × 10
110
u
104
+ 1.42528 × 10
111
u
103
+ ··· + 8.35512 × 10
110
a − 2.67566 × 10
111
, u
105
+ 3u
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
= h−2.88 × 10
108
u
104
− 5.09 × 10
110
u
103
+ · · · + 8.36 × 10
110
b − 2.14 ×
10
110
, 6.52 × 10
110
u
104
+ 1.43 × 10
111
u
103
+ · · · + 8.36 × 10
110
a − 2.68 ×
10
111
, u
105
+ 3u
104
+ · · · + 3u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
9
=
−0.780679u
104
− 1.70588u
103
+ ··· − 4.20124u + 3.20242
0.00345278u
104
+ 0.609609u
103
+ ··· + 0.427791u + 0.256153
a
8
=
−0.777226u
104
− 1.09627u
103
+ ··· − 3.77344u + 3.45857
0.00345278u
104
+ 0.609609u
103
+ ··· + 0.427791u + 0.256153
a
11
=
−u
−u
3
+ u
a
4
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
3
=
0.00955622u
104
− 0.543671u
103
+ ··· + 1.65157u − 0.986304
0.0176604u
104
+ 0.542716u
103
+ ··· − 0.341063u − 0.0571853
a
2
=
0.455592u
104
+ 1.26266u
103
+ ··· − 2.33857u + 0.208499
−0.376670u
104
− 1.24789u
103
+ ··· + 2.98305u − 0.410701
a
10
=
−0.591260u
104
− 0.829214u
103
+ ··· − 5.61982u + 3.23227
0.261471u
104
+ 1.08908u
103
+ ··· + 1.38898u + 0.232872
a
7
=
−0.362637u
104
− 0.610684u
103
+ ··· + 3.25250u + 0.271811
−0.447610u
104
− 0.767496u
103
+ ··· − 1.00923u + 0.0171223
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7.93747u
104
− 23.0087u
103
+ ··· + 20.0215u − 13.3715
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
105
+ 45u
104
+ ··· + 13u + 1
c
2
, c
6
u
105
− 3u
104
+ ··· + u + 1
c
3
u
105
− u
104
+ ··· − 23u + 1
c
4
, c
5
, c
11
u
105
− 3u
104
+ ··· + 3u + 1
c
7
, c
10
u
105
− u
104
+ ··· − u + 1
c
8
u
105
− 3u
104
+ ··· − 119583u + 5771
c
9
u
105
+ 47u
104
+ ··· + 6197u + 361
c
12
u
105
+ 9u
104
+ ··· + 4875u + 725
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 31y
104
+ ··· + 29y −1
c
2
, c
6
y
105
− 45y
104
+ ··· + 13y −1
c
3
y
105
+ 3y
104
+ ··· + 65y −1
c
4
, c
5
, c
11
y
105
− 89y
104
+ ··· + 13y −1
c
7
, c
10
y
105
− 69y
104
+ ··· − 303y −1
c
8
y
105
+ 603y
104
+ ··· − 4958310211y −33304441
c
9
y
105
− 601y
104
+ ··· + 13093821y −130321
c
12
y
105
+ 43y
104
+ ··· + 17234825y −525625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.835184 + 0.520025I
a = 0.360506 − 0.068147I
b = −0.829850 + 0.345460I
−2.42444 + 8.41666I 0
u = 0.835184 − 0.520025I
a = 0.360506 + 0.068147I
b = −0.829850 − 0.345460I
−2.42444 − 8.41666I 0
u = −0.746918 + 0.607750I
a = −0.0897859 − 0.0066868I
b = 0.511139 + 0.226833I
0.21664 − 2.52485I 0
u = −0.746918 − 0.607750I
a = −0.0897859 + 0.0066868I
b = 0.511139 − 0.226833I
0.21664 + 2.52485I 0
u = 0.968336 + 0.444170I
a = 0.292688 + 1.045270I
b = −1.28872 − 0.80671I
−3.01132 − 9.72877I 0
u = 0.968336 − 0.444170I
a = 0.292688 − 1.045270I
b = −1.28872 + 0.80671I
−3.01132 + 9.72877I 0
u = −0.148343 + 0.916907I
a = −0.703771 − 0.605834I
b = 0.468690 + 0.795685I
−1.84431 − 3.57958I 0
u = −0.148343 − 0.916907I
a = −0.703771 + 0.605834I
b = 0.468690 − 0.795685I
−1.84431 + 3.57958I 0
u = 0.344765 + 0.860619I
a = 0.345825 + 0.509616I
b = −0.561964 + 0.031104I
−4.04123 − 3.56458I 0
u = 0.344765 − 0.860619I
a = 0.345825 − 0.509616I
b = −0.561964 − 0.031104I
−4.04123 + 3.56458I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.988248 + 0.449527I
a = −0.165508 + 0.933742I
b = 1.128390 − 0.776285I
−0.78839 + 3.94193I 0
u = −0.988248 − 0.449527I
a = −0.165508 − 0.933742I
b = 1.128390 + 0.776285I
−0.78839 − 3.94193I 0
u = 0.968154 + 0.501536I
a = 0.326075 + 0.599872I
b = −1.091240 − 0.399010I
−7.13633 − 0.95829I 0
u = 0.968154 − 0.501536I
a = 0.326075 − 0.599872I
b = −1.091240 + 0.399010I
−7.13633 + 0.95829I 0
u = 1.116150 + 0.109673I
a = −1.11913 − 0.94024I
b = 0.292739 + 0.554032I
1.62943 − 4.65679I 0
u = 1.116150 − 0.109673I
a = −1.11913 + 0.94024I
b = 0.292739 − 0.554032I
1.62943 + 4.65679I 0
u = 0.222756 + 0.849694I
a = 1.70609 − 0.03313I
b = −1.181070 + 0.684267I
−9.44311 + 5.72371I 0
u = 0.222756 − 0.849694I
a = 1.70609 + 0.03313I
b = −1.181070 − 0.684267I
−9.44311 − 5.72371I 0
u = −0.209090 + 0.831888I
a = −2.05677 − 0.51541I
b = 1.26739 + 1.03687I
−3.19164 − 8.52606I 0
u = −0.209090 − 0.831888I
a = −2.05677 + 0.51541I
b = 1.26739 − 1.03687I
−3.19164 + 8.52606I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215836 + 0.826794I
a = 2.31098 − 0.41965I
b = −1.43199 + 1.04167I
−5.3447 + 14.2818I 0
u = 0.215836 − 0.826794I
a = 2.31098 + 0.41965I
b = −1.43199 − 1.04167I
−5.3447 − 14.2818I 0
u = −1.199490 + 0.084134I
a = 1.012850 − 0.779084I
b = −0.0268957 + 0.0957309I
3.03034 + 0.03937I 0
u = −1.199490 − 0.084134I
a = 1.012850 + 0.779084I
b = −0.0268957 − 0.0957309I
3.03034 − 0.03937I 0
u = 1.192380 + 0.197269I
a = −1.32061 − 0.70014I
b = 0.970216 + 0.130709I
−0.625381 + 1.141580I 0
u = 1.192380 − 0.197269I
a = −1.32061 + 0.70014I
b = 0.970216 − 0.130709I
−0.625381 − 1.141580I 0
u = −1.216840 + 0.260512I
a = 1.290360 − 0.063225I
b = −1.187130 + 0.224619I
−2.21717 + 1.68335I 0
u = −1.216840 − 0.260512I
a = 1.290360 + 0.063225I
b = −1.187130 − 0.224619I
−2.21717 − 1.68335I 0
u = 0.174068 + 0.720095I
a = −2.36969 + 0.62007I
b = 0.768527 − 0.706573I
−0.86914 + 8.02608I −6.61004 − 8.90556I
u = 0.174068 − 0.720095I
a = −2.36969 − 0.62007I
b = 0.768527 + 0.706573I
−0.86914 − 8.02608I −6.61004 + 8.90556I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.243810 + 0.242530I
a = −0.697347 − 0.382319I
b = 1.333690 + 0.464789I
−0.14479 + 1.90230I 0
u = 1.243810 − 0.242530I
a = −0.697347 + 0.382319I
b = 1.333690 − 0.464789I
−0.14479 − 1.90230I 0
u = −0.188704 + 0.703575I
a = 1.98396 + 0.53674I
b = −0.614347 − 0.569283I
0.65316 − 3.05675I −3.14752 + 3.85942I
u = −0.188704 − 0.703575I
a = 1.98396 − 0.53674I
b = −0.614347 + 0.569283I
0.65316 + 3.05675I −3.14752 − 3.85942I
u = −1.247660 + 0.276327I
a = 0.708973 + 0.575189I
b = −0.792583 + 0.299699I
−2.76146 − 4.65754I 0
u = −1.247660 − 0.276327I
a = 0.708973 − 0.575189I
b = −0.792583 − 0.299699I
−2.76146 + 4.65754I 0
u = −0.064599 + 0.718534I
a = 2.19264 − 0.94433I
b = −0.999918 − 0.304231I
−5.70573 − 5.23809I −13.0177 + 7.3510I
u = −0.064599 − 0.718534I
a = 2.19264 + 0.94433I
b = −0.999918 + 0.304231I
−5.70573 + 5.23809I −13.0177 − 7.3510I
u = −0.025247 + 0.714909I
a = 0.979468 − 1.000930I
b = −0.464191 − 0.337560I
−6.51755 + 1.07168I −15.0012 − 1.4774I
u = −0.025247 − 0.714909I
a = 0.979468 + 1.000930I
b = −0.464191 + 0.337560I
−6.51755 − 1.07168I −15.0012 + 1.4774I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.280720 + 0.160056I
a = −1.91585 + 0.43839I
b = −0.25113 − 1.97638I
2.19634 + 4.89955I 0
u = 1.280720 − 0.160056I
a = −1.91585 − 0.43839I
b = −0.25113 + 1.97638I
2.19634 − 4.89955I 0
u = −1.284100 + 0.142479I
a = 0.936347 − 0.126373I
b = 0.151272 − 0.793687I
3.05697 − 0.67088I 0
u = −1.284100 − 0.142479I
a = 0.936347 + 0.126373I
b = 0.151272 + 0.793687I
3.05697 + 0.67088I 0
u = 0.124439 + 0.686536I
a = −2.42949 − 0.26927I
b = 1.068160 − 0.363696I
−3.72572 + 2.08696I −11.68404 − 4.11975I
u = 0.124439 − 0.686536I
a = −2.42949 + 0.26927I
b = 1.068160 + 0.363696I
−3.72572 − 2.08696I −11.68404 + 4.11975I
u = 0.059230 + 0.685011I
a = −2.07970 − 0.22376I
b = 1.043660 − 0.624783I
−3.74935 + 1.43161I −8.78007 − 1.80708I
u = 0.059230 − 0.685011I
a = −2.07970 + 0.22376I
b = 1.043660 + 0.624783I
−3.74935 − 1.43161I −8.78007 + 1.80708I
u = 1.282390 + 0.288191I
a = 0.246542 + 1.355230I
b = −0.159362 + 0.450798I
−2.45187 + 2.55549I 0
u = 1.282390 − 0.288191I
a = 0.246542 − 1.355230I
b = −0.159362 − 0.450798I
−2.45187 − 2.55549I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307120 + 0.221613I
a = 14.9638 + 2.8384I
b = −6.5950 + 19.3509I
1.38267 + 0.81012I 0
u = 1.307120 − 0.221613I
a = 14.9638 − 2.8384I
b = −6.5950 − 19.3509I
1.38267 − 0.81012I 0
u = −1.322190 + 0.180225I
a = 0.484520 + 0.288492I
b = 0.513117 − 0.734299I
3.02345 − 0.73209I 0
u = −1.322190 − 0.180225I
a = 0.484520 − 0.288492I
b = 0.513117 + 0.734299I
3.02345 + 0.73209I 0
u = −1.307090 + 0.279876I
a = −0.91965 + 1.40946I
b = 0.835275 + 0.807534I
0.53283 − 4.93427I 0
u = −1.307090 − 0.279876I
a = −0.91965 − 1.40946I
b = 0.835275 − 0.807534I
0.53283 + 4.93427I 0
u = 1.305150 + 0.296875I
a = 0.82634 + 1.73784I
b = −0.819605 + 0.406710I
−1.42154 + 8.91528I 0
u = 1.305150 − 0.296875I
a = 0.82634 − 1.73784I
b = −0.819605 − 0.406710I
−1.42154 − 8.91528I 0
u = −1.317280 + 0.243026I
a = −1.87149 + 2.53415I
b = 3.21287 + 2.05643I
1.68720 − 5.00295I 0
u = −1.317280 − 0.243026I
a = −1.87149 − 2.53415I
b = 3.21287 − 2.05643I
1.68720 + 5.00295I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.627395 + 0.186667I
a = 0.559848 − 0.394352I
b = −0.165072 + 0.762467I
2.62216 − 0.25104I 2.09657 + 1.88540I
u = −0.627395 − 0.186667I
a = 0.559848 + 0.394352I
b = −0.165072 − 0.762467I
2.62216 + 0.25104I 2.09657 − 1.88540I
u = 0.645443 + 0.056887I
a = −0.881994 − 0.365556I
b = 0.380798 + 0.911069I
1.42997 − 4.72445I −0.79602 + 4.87256I
u = 0.645443 − 0.056887I
a = −0.881994 + 0.365556I
b = 0.380798 − 0.911069I
1.42997 + 4.72445I −0.79602 − 4.87256I
u = 0.073319 + 0.633206I
a = −0.50166 − 1.92461I
b = 0.404234 + 1.091190I
−1.20660 − 2.20475I −6.51094 + 1.95613I
u = 0.073319 − 0.633206I
a = −0.50166 + 1.92461I
b = 0.404234 − 1.091190I
−1.20660 + 2.20475I −6.51094 − 1.95613I
u = −0.228583 + 0.589038I
a = 0.963508 − 0.155080I
b = −0.304870 + 0.051156I
−0.05987 − 1.41751I −0.79609 + 4.17596I
u = −0.228583 − 0.589038I
a = 0.963508 + 0.155080I
b = −0.304870 − 0.051156I
−0.05987 + 1.41751I −0.79609 − 4.17596I
u = −1.342080 + 0.282456I
a = −1.15220 + 1.18524I
b = 1.125300 + 0.539725I
0.90242 − 5.61216I 0
u = −1.342080 − 0.282456I
a = −1.15220 − 1.18524I
b = 1.125300 − 0.539725I
0.90242 + 5.61216I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.362960 + 0.299930I
a = −1.65438 + 0.70144I
b = 0.941583 + 0.796227I
3.98792 − 11.73540I 0
u = −1.362960 − 0.299930I
a = −1.65438 − 0.70144I
b = 0.941583 − 0.796227I
3.98792 + 11.73540I 0
u = −1.396400 + 0.031652I
a = −0.081863 − 0.742104I
b = 0.521230 − 1.219980I
7.54219 + 4.35004I 0
u = −1.396400 − 0.031652I
a = −0.081863 + 0.742104I
b = 0.521230 + 1.219980I
7.54219 − 4.35004I 0
u = 1.368000 + 0.292512I
a = 1.42774 + 0.56726I
b = −0.824571 + 0.694299I
5.57568 + 6.68804I 0
u = 1.368000 − 0.292512I
a = 1.42774 − 0.56726I
b = −0.824571 − 0.694299I
5.57568 − 6.68804I 0
u = 1.382570 + 0.259777I
a = 0.700195 + 0.360891I
b = −0.596425 + 0.200992I
5.06235 + 4.61386I 0
u = 1.382570 − 0.259777I
a = 0.700195 − 0.360891I
b = −0.596425 − 0.200992I
5.06235 − 4.61386I 0
u = 1.410960 + 0.044569I
a = 0.138486 − 0.611363I
b = −0.277739 − 1.192300I
8.87302 + 0.97005I 0
u = 1.410960 − 0.044569I
a = 0.138486 + 0.611363I
b = −0.277739 + 1.192300I
8.87302 − 0.97005I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.062381 + 0.572402I
a = −7.35463 − 3.71461I
b = 4.35720 + 1.32650I
−2.67647 + 1.95883I −34.9750 − 16.4884I
u = 0.062381 − 0.572402I
a = −7.35463 + 3.71461I
b = 4.35720 − 1.32650I
−2.67647 − 1.95883I −34.9750 + 16.4884I
u = 1.37588 + 0.37618I
a = −0.977282 − 0.375034I
b = 0.577111 − 1.088540I
2.98433 + 8.15931I 0
u = 1.37588 − 0.37618I
a = −0.977282 + 0.375034I
b = 0.577111 + 1.088540I
2.98433 − 8.15931I 0
u = −1.35139 + 0.45843I
a = 0.535397 − 0.020160I
b = −0.087891 − 0.759036I
1.82692 − 1.70057I 0
u = −1.35139 − 0.45843I
a = 0.535397 + 0.020160I
b = −0.087891 + 0.759036I
1.82692 + 1.70057I 0
u = 1.39291 + 0.34836I
a = −1.34684 − 0.95917I
b = 1.28758 − 1.23528I
1.88242 + 12.78090I 0
u = 1.39291 − 0.34836I
a = −1.34684 + 0.95917I
b = 1.28758 + 1.23528I
1.88242 − 12.78090I 0
u = −1.39567 + 0.34536I
a = 1.40205 − 1.11216I
b = −1.45944 − 1.22615I
−0.2378 − 18.5105I 0
u = −1.39567 − 0.34536I
a = 1.40205 + 1.11216I
b = −1.45944 + 1.22615I
−0.2378 + 18.5105I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40033 + 0.35615I
a = 0.989256 − 0.979951I
b = −1.16632 − 0.88268I
−4.30287 − 10.06720I 0
u = −1.40033 − 0.35615I
a = 0.989256 + 0.979951I
b = −1.16632 + 0.88268I
−4.30287 + 10.06720I 0
u = 1.46723 + 0.05906I
a = 0.308718 − 0.332777I
b = 0.375517 − 0.954523I
7.54231 + 4.16958I 0
u = 1.46723 − 0.05906I
a = 0.308718 + 0.332777I
b = 0.375517 + 0.954523I
7.54231 − 4.16958I 0
u = −1.48071 + 0.04467I
a = −0.388108 − 0.290070I
b = −0.645679 − 0.954511I
5.22152 − 9.69735I 0
u = −1.48071 − 0.04467I
a = −0.388108 + 0.290070I
b = −0.645679 + 0.954511I
5.22152 + 9.69735I 0
u = −1.53736 + 0.19627I
a = −0.191091 − 0.176358I
b = −0.183673 − 0.239316I
2.37909 − 0.66156I 0
u = −1.53736 − 0.19627I
a = −0.191091 + 0.176358I
b = −0.183673 + 0.239316I
2.37909 + 0.66156I 0
u = −0.301039 + 0.221101I
a = 0.67534 − 3.04513I
b = −1.43869 + 0.29683I
−2.21959 − 3.56667I −4.12086 + 5.07705I
u = −0.301039 − 0.221101I
a = 0.67534 + 3.04513I
b = −1.43869 − 0.29683I
−2.21959 + 3.56667I −4.12086 − 5.07705I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.358709 + 0.083611I
a = −0.138357 − 1.105560I
b = 0.983350 − 0.152205I
−1.191440 − 0.128880I −4.12618 − 0.27432I
u = 0.358709 − 0.083611I
a = −0.138357 + 1.105560I
b = 0.983350 + 0.152205I
−1.191440 + 0.128880I −4.12618 + 0.27432I
u = −0.125009 + 0.320483I
a = 0.54385 − 5.72141I
b = −0.98049 + 1.47982I
−2.74673 + 1.70679I 2.25344 − 2.71408I
u = −0.125009 − 0.320483I
a = 0.54385 + 5.72141I
b = −0.98049 − 1.47982I
−2.74673 − 1.70679I 2.25344 + 2.71408I
u = 0.273678
a = 1.38975
b = 0.813615
−1.17395 −7.50700
15
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
105
+ 45u
104
+ ··· + 13u + 1
c
2
, c
6
u
105
− 3u
104
+ ··· + u + 1
c
3
u
105
− u
104
+ ··· − 23u + 1
c
4
, c
5
, c
11
u
105
− 3u
104
+ ··· + 3u + 1
c
7
, c
10
u
105
− u
104
+ ··· − u + 1
c
8
u
105
− 3u
104
+ ··· − 119583u + 5771
c
9
u
105
+ 47u
104
+ ··· + 6197u + 361
c
12
u
105
+ 9u
104
+ ··· + 4875u + 725
16
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
105
+ 31y
104
+ ··· + 29y −1
c
2
, c
6
y
105
− 45y
104
+ ··· + 13y −1
c
3
y
105
+ 3y
104
+ ··· + 65y −1
c
4
, c
5
, c
11
y
105
− 89y
104
+ ··· + 13y −1
c
7
, c
10
y
105
− 69y
104
+ ··· − 303y −1
c
8
y
105
+ 603y
104
+ ··· − 4958310211y −33304441
c
9
y
105
− 601y
104
+ ··· + 13093821y −130321
c
12
y
105
+ 43y
104
+ ··· + 17234825y −525625
17
