12a
0194
(K12a
0194
)
A knot diagram
1
Linearized knot diagam
3 5 10 6 2 11 12 1 4 9 8 7
Solving Sequence
3,10 4,5
2 6 1 9 11 7 8 12
c
3
c
2
c
5
c
1
c
9
c
10
c
6
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.93196 × 10
140
u
86
+ 6.66096 × 10
139
u
85
+ ··· + 1.09402 × 10
141
b + 3.74745 × 10
141
,
1.59602 × 10
141
u
86
− 1.20857 × 10
140
u
85
+ ··· + 2.18804 × 10
141
a − 3.03570 × 10
142
, u
87
− u
86
+ ··· − 32u − 64i
I
v
1
= ha, v
4
+ v
3
+ v
2
+ b + v + 1, v
6
+ v
5
+ v
4
+ 2v
3
+ v
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 93 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−1.93 × 10
140
u
86
+ 6.66 × 10
139
u
85
+ · · · + 1.09 × 10
141
b + 3.75 ×
10
141
, 1.60 × 10
141
u
86
− 1.21 × 10
140
u
85
+ · · · + 2.19 × 10
141
a − 3.04 ×
10
142
, u
87
− u
86
+ · · · − 32u − 64i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
5
=
−0.729429u
86
+ 0.0552353u
85
+ ··· + 62.6495u + 13.8741
0.176593u
86
− 0.0608853u
85
+ ··· − 15.4584u − 3.42540
a
2
=
0.0681336u
86
− 0.709362u
85
+ ··· + 54.5898u + 49.3534
−0.134816u
86
+ 0.459791u
85
+ ··· − 32.0043u − 32.4889
a
6
=
0.0681336u
86
− 0.709362u
85
+ ··· + 54.5898u + 49.3534
−0.398582u
86
+ 0.178985u
85
+ ··· + 15.8456u − 8.54975
a
1
=
−0.0666825u
86
− 0.249571u
85
+ ··· + 22.5855u + 16.8646
−0.134816u
86
+ 0.459791u
85
+ ··· − 32.0043u − 32.4889
a
9
=
u
u
3
+ u
a
11
=
u
3
u
5
+ u
3
+ u
a
7
=
−0.368646u
86
− 0.527148u
85
+ ··· + 71.9013u + 40.4381
−0.312704u
86
+ 0.0963934u
85
+ ··· + 15.1995u − 3.76857
a
8
=
−0.439933u
86
− 0.447080u
85
+ ··· + 58.1327u + 22.1757
−0.0174712u
86
+ 0.0259493u
85
+ ··· − 0.972693u − 3.56818
a
12
=
0.774940u
86
− 1.07849u
85
+ ··· + 41.4842u + 76.3652
−0.00285224u
86
− 0.0798040u
85
+ ··· + 8.17160u + 2.44523
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00629905u
86
− 0.167117u
85
+ ··· + 11.7485u + 43.8850
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
87
+ 30u
86
+ ··· + 10u − 1
c
2
, c
5
u
87
+ 4u
86
+ ··· + 2u + 1
c
3
, c
9
u
87
− u
86
+ ··· − 32u − 64
c
6
, c
8
u
87
− 3u
86
+ ··· + 313u − 73
c
7
, c
11
, c
12
u
87
+ 3u
86
+ ··· − u − 1
c
10
u
87
− 35u
86
+ ··· − 44032u + 4096
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
87
+ 58y
86
+ ··· + 94y −1
c
2
, c
5
y
87
+ 30y
86
+ ··· + 10y −1
c
3
, c
9
y
87
+ 35y
86
+ ··· − 44032y −4096
c
6
, c
8
y
87
− 51y
86
+ ··· − 128331y −5329
c
7
, c
11
, c
12
y
87
+ 73y
86
+ ··· − 19y −1
c
10
y
87
+ 23y
86
+ ··· − 99614720y −16777216
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.611285 + 0.788569I
a = 0.917741 + 0.861333I
b = −0.082818 + 1.004170I
−3.36212 − 2.35337I 0
u = 0.611285 − 0.788569I
a = 0.917741 − 0.861333I
b = −0.082818 − 1.004170I
−3.36212 + 2.35337I 0
u = 0.443560 + 0.899987I
a = 0.644315 − 0.499952I
b = −0.526359 − 1.058500I
−2.47271 − 2.75618I 0
u = 0.443560 − 0.899987I
a = 0.644315 + 0.499952I
b = −0.526359 + 1.058500I
−2.47271 + 2.75618I 0
u = 0.767266 + 0.648567I
a = 1.04401 + 1.12977I
b = 0.055082 + 1.005560I
−6.09885 + 4.42777I 0
u = 0.767266 − 0.648567I
a = 1.04401 − 1.12977I
b = 0.055082 − 1.005560I
−6.09885 − 4.42777I 0
u = 0.277378 + 0.974111I
a = −1.10874 − 1.67118I
b = 0.716351 + 0.750458I
3.27239 + 1.34065I 0
u = 0.277378 − 0.974111I
a = −1.10874 + 1.67118I
b = 0.716351 − 0.750458I
3.27239 − 1.34065I 0
u = 0.678907 + 0.702812I
a = 0.769386 + 0.217668I
b = −0.650762 + 0.511807I
−4.66548 − 1.46210I 0. + 3.02931I
u = 0.678907 − 0.702812I
a = 0.769386 − 0.217668I
b = −0.650762 − 0.511807I
−4.66548 + 1.46210I 0. − 3.02931I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768238 + 0.688700I
a = 0.634804 + 0.441462I
b = −0.618764 + 1.016630I
−6.05440 − 3.49870I 0
u = −0.768238 − 0.688700I
a = 0.634804 − 0.441462I
b = −0.618764 − 1.016630I
−6.05440 + 3.49870I 0
u = −1.008650 + 0.241433I
a = 0.684736 − 0.311760I
b = −0.725433 − 0.765619I
0.50208 + 3.44185I 0
u = −1.008650 − 0.241433I
a = 0.684736 + 0.311760I
b = −0.725433 + 0.765619I
0.50208 − 3.44185I 0
u = 0.426093 + 0.859319I
a = −3.15793 − 0.28000I
b = 0.652013 − 0.953417I
−2.63778 − 0.82623I 4.00000 + 3.60231I
u = 0.426093 − 0.859319I
a = −3.15793 + 0.28000I
b = 0.652013 + 0.953417I
−2.63778 + 0.82623I 4.00000 − 3.60231I
u = −0.695363 + 0.644567I
a = 1.10625 − 1.01304I
b = 0.026957 − 0.964064I
−1.31652 − 0.83169I 1.65300 + 1.09851I
u = −0.695363 − 0.644567I
a = 1.10625 + 1.01304I
b = 0.026957 + 0.964064I
−1.31652 + 0.83169I 1.65300 − 1.09851I
u = 0.520735 + 0.931628I
a = 0.792847 + 0.788022I
b = −0.164125 + 1.058190I
−3.08368 − 2.00968I 0
u = 0.520735 − 0.931628I
a = 0.792847 − 0.788022I
b = −0.164125 − 1.058190I
−3.08368 + 2.00968I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.005790 + 0.366180I
a = 0.691862 + 0.291804I
b = −0.735938 + 0.721753I
3.86176 + 0.42107I 0
u = 1.005790 − 0.366180I
a = 0.691862 − 0.291804I
b = −0.735938 − 0.721753I
3.86176 − 0.42107I 0
u = 1.006180 + 0.368157I
a = 0.639735 − 0.387808I
b = −0.692514 − 0.944335I
−0.04609 + 1.98521I 0
u = 1.006180 − 0.368157I
a = 0.639735 + 0.387808I
b = −0.692514 + 0.944335I
−0.04609 − 1.98521I 0
u = −0.421885 + 0.985583I
a = −2.66540 + 0.10722I
b = 0.684806 + 0.957414I
2.63586 + 4.03889I 0
u = −0.421885 − 0.985583I
a = −2.66540 − 0.10722I
b = 0.684806 − 0.957414I
2.63586 − 4.03889I 0
u = −0.296732 + 1.041850I
a = 0.777629 − 0.073278I
b = −0.689752 − 0.183697I
0.964622 − 0.562642I 0
u = −0.296732 − 1.041850I
a = 0.777629 + 0.073278I
b = −0.689752 + 0.183697I
0.964622 + 0.562642I 0
u = −0.331769 + 0.849752I
a = 0.664057 + 0.509027I
b = −0.498045 + 1.039790I
1.93817 − 0.98719I 8.58368 − 0.93595I
u = −0.331769 − 0.849752I
a = 0.664057 − 0.509027I
b = −0.498045 − 1.039790I
1.93817 + 0.98719I 8.58368 + 0.93595I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.019790 + 0.453057I
a = 0.692708 − 0.276370I
b = −0.751523 − 0.691973I
−0.55415 − 4.35219I 0
u = −1.019790 − 0.453057I
a = 0.692708 + 0.276370I
b = −0.751523 + 0.691973I
−0.55415 + 4.35219I 0
u = 0.594895 + 0.947229I
a = −0.324433 − 1.258840I
b = 0.746602 + 0.626637I
−3.92192 − 3.46935I 0
u = 0.594895 − 0.947229I
a = −0.324433 + 1.258840I
b = 0.746602 − 0.626637I
−3.92192 + 3.46935I 0
u = 0.149465 + 0.867093I
a = 0.686866 − 0.538383I
b = −0.444261 − 1.034670I
−1.54609 + 4.58317I 5.10158 − 4.29853I
u = 0.149465 − 0.867093I
a = 0.686866 + 0.538383I
b = −0.444261 + 1.034670I
−1.54609 − 4.58317I 5.10158 + 4.29853I
u = 0.411198 + 1.044420I
a = 0.765130 + 0.098490I
b = −0.714320 + 0.248220I
4.23995 − 3.36961I 0
u = 0.411198 − 1.044420I
a = 0.765130 − 0.098490I
b = −0.714320 − 0.248220I
4.23995 + 3.36961I 0
u = −0.740949 + 0.850608I
a = 0.826055 − 0.975867I
b = −0.041288 − 1.076880I
−9.58781 + 2.79623I 0
u = −0.740949 − 0.850608I
a = 0.826055 + 0.975867I
b = −0.041288 + 1.076880I
−9.58781 − 2.79623I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.446275 + 1.037880I
a = −0.71304 + 1.33524I
b = 0.757142 − 0.696856I
2.32576 + 2.18173I 0
u = −0.446275 − 1.037880I
a = −0.71304 − 1.33524I
b = 0.757142 + 0.696856I
2.32576 − 2.18173I 0
u = −1.026800 + 0.483421I
a = 0.628167 + 0.397780I
b = −0.692708 + 0.975062I
3.09256 − 5.88380I 0
u = −1.026800 − 0.483421I
a = 0.628167 − 0.397780I
b = −0.692708 − 0.975062I
3.09256 + 5.88380I 0
u = −0.233192 + 0.805989I
a = −1.13555 + 2.48104I
b = 0.652662 − 0.757523I
−2.01462 − 4.26726I 5.97179 + 2.61130I
u = −0.233192 − 0.805989I
a = −1.13555 − 2.48104I
b = 0.652662 + 0.757523I
−2.01462 + 4.26726I 5.97179 − 2.61130I
u = −0.488848 + 1.054160I
a = 0.753394 − 0.112714I
b = −0.738176 − 0.286575I
−0.22381 + 7.35518I 0
u = −0.488848 − 1.054160I
a = 0.753394 + 0.112714I
b = −0.738176 + 0.286575I
−0.22381 − 7.35518I 0
u = −0.607515 + 0.995263I
a = 0.748024 − 0.842364I
b = −0.136497 − 1.103500I
−0.23467 + 5.86188I 0
u = −0.607515 − 0.995263I
a = 0.748024 + 0.842364I
b = −0.136497 + 1.103500I
−0.23467 − 5.86188I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.043830 + 0.551455I
a = 0.620829 − 0.402944I
b = −0.694009 − 0.993135I
−1.46195 + 9.86196I 0
u = 1.043830 − 0.551455I
a = 0.620829 + 0.402944I
b = −0.694009 + 0.993135I
−1.46195 − 9.86196I 0
u = 0.540953 + 1.061670I
a = −2.32849 − 0.37630I
b = 0.698997 − 0.991276I
1.43879 − 7.72271I 0
u = 0.540953 − 1.061670I
a = −2.32849 + 0.37630I
b = 0.698997 + 0.991276I
1.43879 + 7.72271I 0
u = −0.657070 + 0.997761I
a = −2.30139 + 0.72609I
b = 0.677860 + 1.017760I
−5.07559 + 8.90900I 0
u = −0.657070 − 0.997761I
a = −2.30139 − 0.72609I
b = 0.677860 − 1.017760I
−5.07559 − 8.90900I 0
u = 0.668410 + 0.428154I
a = 0.670160 − 0.423926I
b = −0.603421 − 0.947278I
−0.45864 + 3.05031I 0.11561 − 3.71074I
u = 0.668410 − 0.428154I
a = 0.670160 + 0.423926I
b = −0.603421 + 0.947278I
−0.45864 − 3.05031I 0.11561 + 3.71074I
u = 0.652989 + 1.019560I
a = 0.726453 + 0.866754I
b = −0.122757 + 1.123020I
−4.94082 − 9.82420I 0
u = 0.652989 − 1.019560I
a = 0.726453 − 0.866754I
b = −0.122757 − 1.123020I
−4.94082 + 9.82420I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.527998 + 0.508519I
a = 1.38834 + 0.49257I
b = 0.025988 + 0.717177I
−4.08095 − 1.96025I −2.32551 + 3.82515I
u = 0.527998 − 0.508519I
a = 1.38834 − 0.49257I
b = 0.025988 − 0.717177I
−4.08095 + 1.96025I −2.32551 − 3.82515I
u = −0.250839 + 0.646005I
a = 0.913229 − 0.095011I
b = −0.377028 − 0.231372I
0.322925 + 0.980399I 5.93960 − 6.62047I
u = −0.250839 − 0.646005I
a = 0.913229 + 0.095011I
b = −0.377028 + 0.231372I
0.322925 − 0.980399I 5.93960 + 6.62047I
u = −0.561413 + 1.185130I
a = −0.662931 + 0.987024I
b = 0.824524 − 0.680211I
3.53114 + 2.02176I 0
u = −0.561413 − 1.185130I
a = −0.662931 − 0.987024I
b = 0.824524 + 0.680211I
3.53114 − 2.02176I 0
u = 0.029916 + 1.327490I
a = −1.49885 − 0.68928I
b = 0.804293 + 0.856431I
6.54252 − 1.34989I 0
u = 0.029916 − 1.327490I
a = −1.49885 + 0.68928I
b = 0.804293 − 0.856431I
6.54252 + 1.34989I 0
u = 0.047029 + 1.330660I
a = −1.59556 + 0.59324I
b = 0.798778 − 0.877711I
10.37450 − 2.98463I 0
u = 0.047029 − 1.330660I
a = −1.59556 − 0.59324I
b = 0.798778 + 0.877711I
10.37450 + 2.98463I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.121603 + 1.328060I
a = −1.68238 − 0.49161I
b = 0.792331 + 0.897528I
6.41712 + 7.31572I 0
u = −0.121603 − 1.328060I
a = −1.68238 + 0.49161I
b = 0.792331 − 0.897528I
6.41712 − 7.31572I 0
u = 0.634374 + 1.173840I
a = −2.00540 − 0.45132I
b = 0.722792 − 1.019870I
2.49663 − 7.82179I 0
u = 0.634374 − 1.173840I
a = −2.00540 + 0.45132I
b = 0.722792 + 1.019870I
2.49663 + 7.82179I 0
u = 0.633489 + 1.184630I
a = −0.577053 − 0.930602I
b = 0.836929 + 0.657205I
6.44169 − 6.28675I 0
u = 0.633489 − 1.184630I
a = −0.577053 + 0.930602I
b = 0.836929 − 0.657205I
6.44169 + 6.28675I 0
u = −0.622610 + 0.177262I
a = 0.884623 + 0.156178I
b = 0.346087 − 0.160520I
−2.55006 − 3.29913I 1.11145 + 2.49429I
u = −0.622610 − 0.177262I
a = 0.884623 − 0.156178I
b = 0.346087 + 0.160520I
−2.55006 + 3.29913I 1.11145 − 2.49429I
u = −0.679060 + 1.174990I
a = −0.522511 + 0.901931I
b = 0.842463 − 0.641024I
1.73423 + 10.47340I 0
u = −0.679060 − 1.174990I
a = −0.522511 − 0.901931I
b = 0.842463 + 0.641024I
1.73423 − 10.47340I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.696216 + 1.175180I
a = −1.94109 + 0.54914I
b = 0.720267 + 1.035200I
5.29166 + 12.11040I 0
u = −0.696216 − 1.175180I
a = −1.94109 − 0.54914I
b = 0.720267 − 1.035200I
5.29166 − 12.11040I 0
u = 0.733904 + 1.165900I
a = −1.91300 − 0.61390I
b = 0.716303 − 1.044050I
0.5090 − 16.2964I 0
u = 0.733904 − 1.165900I
a = −1.91300 + 0.61390I
b = 0.716303 + 1.044050I
0.5090 + 16.2964I 0
u = −0.509418 + 0.232441I
a = 0.763520 − 0.371468I
b = −0.541403 − 0.775770I
0.16334 + 1.55638I −0.76791 − 2.56835I
u = −0.509418 − 0.232441I
a = 0.763520 + 0.371468I
b = −0.541403 + 0.775770I
0.16334 − 1.55638I −0.76791 + 2.56835I
u = 0.557201
a = 0.897719
b = 0.285348
1.51878 6.53030
13
II. I
v
1
= ha, v
4
+ v
3
+ v
2
+ b + v + 1, v
6
+ v
5
+ v
4
+ 2v
3
+ v
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
v
0
a
4
=
1
0
a
5
=
0
−v
4
− v
3
− v
2
− v −1
a
2
=
1
v
4
+ v
3
+ v
2
+ v
a
6
=
−v
4
− v
3
− v
2
− v −1
−v
4
− v
3
− v
2
− v
a
1
=
v
4
+ v
3
+ v
2
+ v + 1
v
4
+ v
3
+ v
2
+ v
a
9
=
v
0
a
11
=
v
0
a
7
=
−v
4
− v
−v
4
− v
3
− v
2
− v
a
8
=
0
−v
5
− v
4
− v
3
− v
2
− v
a
12
=
v
v
4
+ v
3
+ v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v
5
− 9v
4
− 9v
3
− 8v
2
− 6v + 1
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
, c
9
, c
10
u
6
c
6
, c
8
(u
3
− u
2
+ 1)
2
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
9
, c
10
y
6
c
6
, c
8
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.206350 + 1.132320I
a = 0
b = −0.500000 + 0.866025I
−3.02413 − 4.85801I −1.45566 + 6.64456I
v = 0.206350 − 1.132320I
a = 0
b = −0.500000 − 0.866025I
−3.02413 + 4.85801I −1.45566 − 6.64456I
v = −1.083790 + 0.387453I
a = 0
b = −0.500000 + 0.866025I
−3.02413 + 0.79824I 2.09851 + 0.12339I
v = −1.083790 − 0.387453I
a = 0
b = −0.500000 − 0.866025I
−3.02413 − 0.79824I 2.09851 − 0.12339I
v = 0.377439 + 0.653743I
a = 0
b = −0.500000 − 0.866025I
1.11345 + 2.02988I 5.85715 − 4.49037I
v = 0.377439 − 0.653743I
a = 0
b = −0.500000 + 0.866025I
1.11345 − 2.02988I 5.85715 + 4.49037I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
3
)(u
87
+ 30u
86
+ ··· + 10u − 1)
c
2
((u
2
+ u + 1)
3
)(u
87
+ 4u
86
+ ··· + 2u + 1)
c
3
, c
9
u
6
(u
87
− u
86
+ ··· − 32u − 64)
c
5
((u
2
− u + 1)
3
)(u
87
+ 4u
86
+ ··· + 2u + 1)
c
6
, c
8
((u
3
− u
2
+ 1)
2
)(u
87
− 3u
86
+ ··· + 313u − 73)
c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
87
+ 3u
86
+ ··· − u − 1)
c
10
u
6
(u
87
− 35u
86
+ ··· − 44032u + 4096)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
2
)(u
87
+ 3u
86
+ ··· − u − 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
87
+ 58y
86
+ ··· + 94y −1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
87
+ 30y
86
+ ··· + 10y −1)
c
3
, c
9
y
6
(y
87
+ 35y
86
+ ··· − 44032y −4096)
c
6
, c
8
((y
3
− y
2
+ 2y −1)
2
)(y
87
− 51y
86
+ ··· − 128331y −5329)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
87
+ 73y
86
+ ··· − 19y −1)
c
10
y
6
(y
87
+ 23y
86
+ ··· − 9.96147 × 10
7
y −1.67772 × 10
7
)
19
