12a
1119
(K12a
1119
)
A knot diagram
1
Linearized knot diagam
4 7 12 1 9 10 11 3 6 2 8 5
Solving Sequence
5,9
6 10
1,7
4 2 12 3 8 11
c
5
c
9
c
6
c
4
c
1
c
12
c
3
c
8
c
11
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.43683 × 10
139
u
83
+ 3.15689 × 10
140
u
82
+ ··· + 5.45656 × 10
140
b − 2.22182 × 10
139
,
2.34091 × 10
140
u
83
− 1.44662 × 10
141
u
82
+ ··· + 5.45656 × 10
140
a − 5.49196 × 10
140
, u
84
− 7u
83
+ ··· + 7u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 84 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−2.44 × 10
139
u
83
+ 3.16 × 10
140
u
82
+ · · · + 5.46 × 10
140
b − 2.22 ×
10
139
, 2.34 × 10
140
u
83
− 1.45 × 10
141
u
82
+ · · · + 5.46 × 10
140
a − 5.49 ×
10
140
, u
84
− 7u
83
+ · · · + 7u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
−u
2
a
10
=
u
−u
3
+ u
a
1
=
−0.429009u
83
+ 2.65116u
82
+ ··· + 6.73479u + 1.00649
0.0446588u
83
− 0.578550u
82
+ ··· + 0.0135038u + 0.0407184
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
0.334513u
83
− 2.87235u
82
+ ··· + 1.44740u + 2.70338
−0.162239u
83
+ 0.872984u
82
+ ··· + 1.58318u − 0.361124
a
2
=
−0.133440u
83
− 0.707253u
82
+ ··· + 11.9226u + 0.535960
−0.167963u
83
+ 1.28402u
82
+ ··· + 1.04242u − 1.33717
a
12
=
−0.384350u
83
+ 2.07261u
82
+ ··· + 6.74830u + 1.04721
0.0446588u
83
− 0.578550u
82
+ ··· + 0.0135038u + 0.0407184
a
3
=
−0.288339u
83
+ 0.698691u
82
+ ··· + 11.0956u + 0.146923
−0.197313u
83
+ 1.54442u
82
+ ··· + 0.418755u − 1.18254
a
8
=
0.911994u
83
− 5.64628u
82
+ ··· − 10.3785u − 5.24643
0.158497u
83
− 0.788027u
82
+ ··· + 2.54815u + 0.342618
a
11
=
1.62663u
83
− 11.7707u
82
+ ··· − 6.84432u − 3.89169
0.694473u
83
− 4.03384u
82
+ ··· + 1.64447u − 0.0378106
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6.53695u
83
+ 39.5178u
82
+ ··· + 24.3239u − 1.59872
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
84
− u
83
+ ··· − 14u + 1
c
2
u
84
+ 3u
83
+ ··· + 4u + 1
c
3
u
84
+ u
83
+ ··· − 43278u + 4801
c
5
, c
6
, c
9
u
84
− 7u
83
+ ··· + 7u
2
+ 1
c
7
, c
11
u
84
+ u
83
+ ··· + 7u
2
+ 1
c
8
u
84
− u
83
+ ··· − 6188u + 3431
c
10
u
84
+ 5u
83
+ ··· − 46u + 13
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
84
+ 73y
83
+ ··· − 102y + 1
c
2
y
84
− 7y
83
+ ··· − 78y + 1
c
3
y
84
− 19y
83
+ ··· − 2061501350y + 23049601
c
5
, c
6
, c
9
y
84
− 83y
83
+ ··· + 14y + 1
c
7
, c
11
y
84
− 59y
83
+ ··· + 14y + 1
c
8
y
84
− 211y
83
+ ··· + 403051910y + 11771761
c
10
y
84
− 259y
83
+ ··· + 32802y + 169
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.558103 + 0.837786I
a = 1.52550 − 1.04449I
b = 0.32653 + 1.38845I
−0.28320 − 12.83660I 0
u = −0.558103 − 0.837786I
a = 1.52550 + 1.04449I
b = 0.32653 − 1.38845I
−0.28320 + 12.83660I 0
u = −0.639681 + 0.783616I
a = 0.411406 − 0.299400I
b = 0.711341 − 0.142714I
−4.95491 + 3.53314I 0
u = −0.639681 − 0.783616I
a = 0.411406 + 0.299400I
b = 0.711341 + 0.142714I
−4.95491 − 3.53314I 0
u = −0.747659 + 0.597758I
a = 1.51169 − 1.14560I
b = 0.227897 + 1.113580I
−2.10479 + 0.01557I 0
u = −0.747659 − 0.597758I
a = 1.51169 + 1.14560I
b = 0.227897 − 1.113580I
−2.10479 − 0.01557I 0
u = −0.490660 + 0.800323I
a = 0.681388 − 0.567665I
b = 0.792584 + 0.213001I
−5.35864 − 8.79455I 0
u = −0.490660 − 0.800323I
a = 0.681388 + 0.567665I
b = 0.792584 − 0.213001I
−5.35864 + 8.79455I 0
u = 0.401609 + 0.848172I
a = 0.805169 + 0.380180I
b = 0.613779 − 0.176501I
−0.43669 + 3.36220I 0
u = 0.401609 − 0.848172I
a = 0.805169 − 0.380180I
b = 0.613779 + 0.176501I
−0.43669 − 3.36220I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.593656 + 0.901541I
a = 0.177974 + 0.754728I
b = 0.288082 − 1.348880I
−0.24649 + 7.15365I 0
u = −0.593656 − 0.901541I
a = 0.177974 − 0.754728I
b = 0.288082 + 1.348880I
−0.24649 − 7.15365I 0
u = 1.088040 + 0.044118I
a = 1.15502 + 1.02120I
b = −0.028874 − 1.253000I
5.55571 + 0.01357I 0
u = 1.088040 − 0.044118I
a = 1.15502 − 1.02120I
b = −0.028874 + 1.253000I
5.55571 − 0.01357I 0
u = 0.523355 + 0.968000I
a = 1.40292 + 0.93077I
b = 0.248772 − 1.359780I
4.42501 + 6.53157I 0
u = 0.523355 − 0.968000I
a = 1.40292 − 0.93077I
b = 0.248772 + 1.359780I
4.42501 − 6.53157I 0
u = 0.985199 + 0.608775I
a = 0.194220 − 1.206160I
b = 0.134578 + 1.326750I
5.97791 − 0.32219I 0
u = 0.985199 − 0.608775I
a = 0.194220 + 1.206160I
b = 0.134578 − 1.326750I
5.97791 + 0.32219I 0
u = −0.014818 + 0.841024I
a = 1.022770 − 0.141577I
b = 0.101645 + 1.273120I
2.45064 + 1.09496I 0. − 4.87467I
u = −0.014818 − 0.841024I
a = 1.022770 + 0.141577I
b = 0.101645 − 1.273120I
2.45064 − 1.09496I 0. + 4.87467I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.403808 + 0.710608I
a = 0.183228 + 0.122343I
b = 0.390587 − 0.945271I
−3.07733 − 4.49445I 0. + 4.03751I
u = −0.403808 − 0.710608I
a = 0.183228 − 0.122343I
b = 0.390587 + 0.945271I
−3.07733 + 4.49445I 0. − 4.03751I
u = −0.609196 + 0.406672I
a = −0.28476 + 1.62479I
b = −0.04981 − 1.43688I
4.61918 − 4.68420I 2.69222 + 7.52303I
u = −0.609196 − 0.406672I
a = −0.28476 − 1.62479I
b = −0.04981 + 1.43688I
4.61918 + 4.68420I 2.69222 − 7.52303I
u = 1.31401
a = 0.437229
b = −1.04347
−1.24406 0
u = −1.330080 + 0.068788I
a = 0.429993 + 0.933227I
b = −0.903437 − 0.502221I
−0.39209 − 2.89833I 0
u = −1.330080 − 0.068788I
a = 0.429993 − 0.933227I
b = −0.903437 + 0.502221I
−0.39209 + 2.89833I 0
u = −1.346290 + 0.084631I
a = −0.465672 + 0.572476I
b = −0.270534 − 1.164230I
6.20610 − 3.71389I 0
u = −1.346290 − 0.084631I
a = −0.465672 − 0.572476I
b = −0.270534 + 1.164230I
6.20610 + 3.71389I 0
u = 0.470607 + 0.437247I
a = 0.379162 − 0.111252I
b = 0.167310 + 0.380669I
1.018620 + 0.865781I 4.46908 − 2.51048I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.470607 − 0.437247I
a = 0.379162 + 0.111252I
b = 0.167310 − 0.380669I
1.018620 − 0.865781I 4.46908 + 2.51048I
u = 1.357310 + 0.113910I
a = −0.08709 − 1.41361I
b = −0.595285 + 1.116090I
2.14730 + 5.65478I 0
u = 1.357310 − 0.113910I
a = −0.08709 + 1.41361I
b = −0.595285 − 1.116090I
2.14730 − 5.65478I 0
u = −1.36225
a = −0.619840
b = −0.737594
2.64928 0
u = 1.372000 + 0.056138I
a = 0.166578 − 1.098660I
b = −0.589738 + 0.319680I
3.44980 + 1.64919I 0
u = 1.372000 − 0.056138I
a = 0.166578 + 1.098660I
b = −0.589738 − 0.319680I
3.44980 − 1.64919I 0
u = −1.40478
a = −9.12724
b = −0.576785
2.15827 0
u = −1.414000 + 0.020024I
a = −10.33470 + 3.36484I
b = −0.218790 − 1.310170I
6.31232 − 2.86771I 0
u = −1.414000 − 0.020024I
a = −10.33470 − 3.36484I
b = −0.218790 + 1.310170I
6.31232 + 2.86771I 0
u = −1.41705 + 0.12490I
a = −0.72952 + 2.35259I
b = −0.36926 − 1.49647I
5.91677 − 7.57306I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41705 − 0.12490I
a = −0.72952 − 2.35259I
b = −0.36926 + 1.49647I
5.91677 + 7.57306I 0
u = 1.43896 + 0.09315I
a = −1.15853 − 2.79825I
b = −0.24915 + 1.42600I
9.04553 + 4.79524I 0
u = 1.43896 − 0.09315I
a = −1.15853 + 2.79825I
b = −0.24915 − 1.42600I
9.04553 − 4.79524I 0
u = 1.42046 + 0.37578I
a = 0.456228 + 0.488501I
b = 0.548985 − 0.149764I
2.49026 + 1.60685I 0
u = 1.42046 − 0.37578I
a = 0.456228 − 0.488501I
b = 0.548985 + 0.149764I
2.49026 − 1.60685I 0
u = −0.204867 + 0.486225I
a = −0.343437 + 0.220412I
b = −0.482066 − 0.851406I
−2.67638 − 3.53656I −7.87807 + 8.61174I
u = −0.204867 − 0.486225I
a = −0.343437 − 0.220412I
b = −0.482066 + 0.851406I
−2.67638 + 3.53656I −7.87807 − 8.61174I
u = 1.47597
a = 0.594054
b = 0.100712
3.39757 0
u = 0.287913 + 0.434694I
a = −1.36655 − 0.68485I
b = −0.35900 + 1.38494I
0.44827 + 5.59393I −4.07425 − 9.66974I
u = 0.287913 − 0.434694I
a = −1.36655 + 0.68485I
b = −0.35900 − 1.38494I
0.44827 − 5.59393I −4.07425 + 9.66974I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47315 + 0.20651I
a = −0.143376 + 0.617668I
b = 0.401164 − 0.693355I
7.23640 − 3.44789I 0
u = −1.47315 − 0.20651I
a = −0.143376 − 0.617668I
b = 0.401164 + 0.693355I
7.23640 + 3.44789I 0
u = 1.47977 + 0.24770I
a = −0.358315 − 0.779942I
b = 0.534813 + 0.884353I
3.04368 + 7.95765I 0
u = 1.47977 − 0.24770I
a = −0.358315 + 0.779942I
b = 0.534813 − 0.884353I
3.04368 − 7.95765I 0
u = −0.344988 + 0.334848I
a = 1.92138 + 0.14934I
b = −0.197517 + 0.346890I
−1.92460 + 0.99564I −1.96608 + 2.11328I
u = −0.344988 − 0.334848I
a = 1.92138 − 0.14934I
b = −0.197517 − 0.346890I
−1.92460 − 0.99564I −1.96608 − 2.11328I
u = 1.51666 + 0.14625I
a = −0.29716 − 2.66877I
b = −0.00970 + 1.54752I
11.56010 + 6.78696I 0
u = 1.51666 − 0.14625I
a = −0.29716 + 2.66877I
b = −0.00970 − 1.54752I
11.56010 − 6.78696I 0
u = −1.49761 + 0.29399I
a = 0.233342 − 0.820168I
b = 0.726980 + 0.278450I
5.75269 − 7.44281I 0
u = −1.49761 − 0.29399I
a = 0.233342 + 0.820168I
b = 0.726980 − 0.278450I
5.75269 + 7.44281I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51599 + 0.28498I
a = 0.058636 + 0.886807I
b = 0.835240 − 0.276491I
1.14844 + 12.74900I 0
u = 1.51599 − 0.28498I
a = 0.058636 − 0.886807I
b = 0.835240 + 0.276491I
1.14844 − 12.74900I 0
u = −0.012086 + 0.442740I
a = 0.89158 + 2.28803I
b = −0.162190 + 1.277820I
2.28626 + 2.04027I −3.92912 − 5.24188I
u = −0.012086 − 0.442740I
a = 0.89158 − 2.28803I
b = −0.162190 − 1.277820I
2.28626 − 2.04027I −3.92912 + 5.24188I
u = 0.076173 + 0.427342I
a = −0.694821 − 0.381532I
b = −0.857353 + 0.238672I
−4.65098 + 1.20835I −15.0329 − 4.8481I
u = 0.076173 − 0.427342I
a = −0.694821 + 0.381532I
b = −0.857353 − 0.238672I
−4.65098 − 1.20835I −15.0329 + 4.8481I
u = −1.56700 + 0.14380I
a = −0.02967 + 2.52214I
b = 0.07633 − 1.46544I
14.1292 − 2.0376I 0
u = −1.56700 − 0.14380I
a = −0.02967 − 2.52214I
b = 0.07633 + 1.46544I
14.1292 + 2.0376I 0
u = 1.54885 + 0.29519I
a = 1.34400 + 2.12210I
b = 0.33964 − 1.42580I
6.5668 + 16.9923I 0
u = 1.54885 − 0.29519I
a = 1.34400 − 2.12210I
b = 0.33964 + 1.42580I
6.5668 − 16.9923I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.54618 + 0.32454I
a = 1.38269 − 2.01148I
b = 0.29004 + 1.41078I
11.1318 − 11.1393I 0
u = −1.54618 − 0.32454I
a = 1.38269 + 2.01148I
b = 0.29004 − 1.41078I
11.1318 + 11.1393I 0
u = 0.345350 + 0.231832I
a = 4.98640 + 1.68201I
b = −0.262208 − 1.299920I
0.91964 − 3.32129I 6.11652 − 8.60509I
u = 0.345350 − 0.231832I
a = 4.98640 − 1.68201I
b = −0.262208 + 1.299920I
0.91964 + 3.32129I 6.11652 + 8.60509I
u = −0.300231 + 0.276423I
a = −2.82551 + 2.03371I
b = −0.229473 − 1.345730I
3.36187 − 3.41278I −0.247336 + 1.025326I
u = −0.300231 − 0.276423I
a = −2.82551 − 2.03371I
b = −0.229473 + 1.345730I
3.36187 + 3.41278I −0.247336 − 1.025326I
u = 1.61987
a = 0.207346
b = 0.397949
3.31098 0
u = 1.56407 + 0.45989I
a = 1.32437 + 1.73919I
b = 0.223403 − 1.352190I
7.25184 + 4.47084I 0
u = 1.56407 − 0.45989I
a = 1.32437 − 1.73919I
b = 0.223403 + 1.352190I
7.25184 − 4.47084I 0
u = 0.316396
a = 4.76803
b = −0.657423
−3.17231 16.2440
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.116009 + 0.290071I
a = −1.05692 + 1.73060I
b = −0.574135 − 0.102366I
−1.248270 − 0.474713I −7.55961 + 0.17216I
u = −0.116009 − 0.290071I
a = −1.05692 − 1.73060I
b = −0.574135 + 0.102366I
−1.248270 + 0.474713I −7.55961 − 0.17216I
u = 1.75518 + 0.17068I
a = 0.40063 − 1.98817I
b = 0.187126 + 1.339880I
7.78775 − 2.29126I 0
u = 1.75518 − 0.17068I
a = 0.40063 + 1.98817I
b = 0.187126 − 1.339880I
7.78775 + 2.29126I 0
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
84
− u
83
+ ··· − 14u + 1
c
2
u
84
+ 3u
83
+ ··· + 4u + 1
c
3
u
84
+ u
83
+ ··· − 43278u + 4801
c
5
, c
6
, c
9
u
84
− 7u
83
+ ··· + 7u
2
+ 1
c
7
, c
11
u
84
+ u
83
+ ··· + 7u
2
+ 1
c
8
u
84
− u
83
+ ··· − 6188u + 3431
c
10
u
84
+ 5u
83
+ ··· − 46u + 13
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
84
+ 73y
83
+ ··· − 102y + 1
c
2
y
84
− 7y
83
+ ··· − 78y + 1
c
3
y
84
− 19y
83
+ ··· − 2061501350y + 23049601
c
5
, c
6
, c
9
y
84
− 83y
83
+ ··· + 14y + 1
c
7
, c
11
y
84
− 59y
83
+ ··· + 14y + 1
c
8
y
84
− 211y
83
+ ··· + 403051910y + 11771761
c
10
y
84
− 259y
83
+ ··· + 32802y + 169
15
