12a
1012
(K12a
1012
)
A knot diagram
1
Linearized knot diagam
4 6 1 9 10 11 12 2 5 3 8 7
Solving Sequence
8,11
12 7
1,3
4 6 2 10 5 9
c
11
c
7
c
12
c
3
c
6
c
2
c
10
c
5
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.05532 × 10
66
u
82
+ 2.51093 × 10
66
u
81
+ ··· + 1.60291 × 10
67
b − 6.72720 × 10
65
,
1.11417 × 10
67
u
82
− 1.22744 × 10
67
u
81
+ ··· + 1.60291 × 10
67
a − 2.52964 × 10
67
, u
83
− 2u
82
+ ··· − 2u + 1i
I
u
2
= h7b − 2u − 1, 7a + u + 4, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 85 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−2.06×10
66
u
82
+2.51×10
66
u
81
+· · ·+1.60×10
67
b−6.73×10
65
, 1.11×
10
67
u
82
−1.23×10
67
u
81
+· · ·+1.60×10
67
a−2.53×10
67
, u
83
−2u
82
+· · ·−2u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
3
=
−0.695089u
82
+ 0.765754u
81
+ ··· − 0.805908u + 1.57815
0.128224u
82
− 0.156648u
81
+ ··· − 0.183076u + 0.0419686
a
4
=
−0.506927u
82
+ 0.383641u
81
+ ··· + 0.301338u + 0.370054
0.187208u
82
− 0.231332u
81
+ ··· + 0.176599u + 0.0714091
a
6
=
−u
3
− 2u
u
3
+ u
a
2
=
−0.771316u
82
+ 0.876988u
81
+ ··· − 1.09248u + 1.44647
0.168393u
82
− 0.226519u
81
+ ··· − 0.0270658u + 0.0924313
a
10
=
2.08991u
82
− 3.13988u
81
+ ··· − 3.52603u − 2.11892
−1.17284u
82
+ 1.89402u
81
+ ··· + 3.09591u + 0.772956
a
5
=
1.18628u
82
− 3.04794u
81
+ ··· − 5.78944u + 1.01993
−0.959505u
82
+ 1.55012u
81
+ ··· + 4.15771u − 0.726348
a
9
=
1.32283u
82
− 1.63143u
81
+ ··· + 2.70703u − 4.79684
−1.24263u
82
+ 0.911270u
81
+ ··· − 0.275552u + 2.26730
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.167112u
82
+ 1.45471u
81
+ ··· − 2.64274u + 0.360927
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
83
− 3u
82
+ ··· + 285u + 49
c
2
u
83
− 7u
82
+ ··· + 1260u − 196
c
4
, c
5
, c
9
u
83
− 2u
82
+ ··· + 2u
2
− 1
c
6
u
83
+ 2u
82
+ ··· + 762u + 65
c
7
, c
11
, c
12
u
83
− 2u
82
+ ··· − 2u + 1
c
8
7(7u
83
+ 28u
82
+ ··· + 4430074u + 1636183)
c
10
7(7u
83
− 49u
82
+ ··· + 141221u − 21311)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
83
− 63y
82
+ ··· − 5505y −2401
c
2
y
83
+ 15y
82
+ ··· − 873768y −38416
c
4
, c
5
, c
9
y
83
− 84y
82
+ ··· + 4y −1
c
6
y
83
− 12y
82
+ ··· + 353924y −4225
c
7
, c
11
, c
12
y
83
+ 72y
82
+ ··· + 4y −1
c
8
49
· (49y
83
+ 2716y
82
+ ··· − 90553024520728y −2677094809489)
c
10
49(49y
83
− 371y
82
+ ··· + 1.72569 × 10
10
y −4.54159 × 10
8
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.475006 + 0.859601I
a = 1.067640 − 0.053405I
b = −1.19843 − 0.84086I
−10.20070 − 8.08224I 0
u = 0.475006 − 0.859601I
a = 1.067640 + 0.053405I
b = −1.19843 + 0.84086I
−10.20070 + 8.08224I 0
u = 0.064627 + 1.021110I
a = −0.097879 − 0.830642I
b = 0.816969 + 0.914245I
−5.67104 − 3.00245I 0
u = 0.064627 − 1.021110I
a = −0.097879 + 0.830642I
b = 0.816969 − 0.914245I
−5.67104 + 3.00245I 0
u = −0.514621 + 0.829465I
a = 0.878968 − 0.069917I
b = −0.828395 + 0.694970I
−2.74113 + 4.19441I 0
u = −0.514621 − 0.829465I
a = 0.878968 + 0.069917I
b = −0.828395 − 0.694970I
−2.74113 − 4.19441I 0
u = −0.887144 + 0.240007I
a = −0.903715 − 0.450278I
b = 0.644498 − 0.077979I
−7.32946 + 1.81939I −9.08409 − 3.25302I
u = −0.887144 − 0.240007I
a = −0.903715 + 0.450278I
b = 0.644498 + 0.077979I
−7.32946 − 1.81939I −9.08409 + 3.25302I
u = −0.196848 + 1.067180I
a = −0.135156 + 0.515710I
b = 0.433799 − 0.853225I
0.117492 + 0.387913I 0
u = −0.196848 − 1.067180I
a = −0.135156 − 0.515710I
b = 0.433799 + 0.853225I
0.117492 − 0.387913I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.485786 + 0.988027I
a = 0.446200 + 0.372854I
b = −0.791315 − 0.421140I
−9.68489 − 6.70543I 0
u = −0.485786 − 0.988027I
a = 0.446200 − 0.372854I
b = −0.791315 + 0.421140I
−9.68489 + 6.70543I 0
u = 0.831753 + 0.330980I
a = −0.300588 + 1.183040I
b = 0.605846 − 0.630936I
−0.32503 + 3.27303I −2.53912 − 7.98791I
u = 0.831753 − 0.330980I
a = −0.300588 − 1.183040I
b = 0.605846 + 0.630936I
−0.32503 − 3.27303I −2.53912 + 7.98791I
u = 0.648808 + 0.920395I
a = 0.494724 + 0.001353I
b = −0.506519 − 0.199456I
−1.94282 + 1.87194I 0
u = 0.648808 − 0.920395I
a = 0.494724 − 0.001353I
b = −0.506519 + 0.199456I
−1.94282 − 1.87194I 0
u = −0.804514 + 0.287110I
a = −0.53594 − 1.81584I
b = 1.012310 + 0.946985I
−1.01980 − 8.80520I −1.34312 + 8.67899I
u = −0.804514 − 0.287110I
a = −0.53594 + 1.81584I
b = 1.012310 − 0.946985I
−1.01980 + 8.80520I −1.34312 − 8.67899I
u = 0.805730 + 0.269407I
a = −0.86968 + 2.12116I
b = 1.36813 − 1.02151I
−8.3267 + 12.6232I −3.82071 − 7.57574I
u = 0.805730 − 0.269407I
a = −0.86968 − 2.12116I
b = 1.36813 + 1.02151I
−8.3267 − 12.6232I −3.82071 + 7.57574I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.315485 + 1.137810I
a = 0.011028 − 0.251257I
b = 0.149783 + 0.594962I
−0.96189 + 3.32369I 0
u = 0.315485 − 1.137810I
a = 0.011028 + 0.251257I
b = 0.149783 − 0.594962I
−0.96189 − 3.32369I 0
u = 0.721078 + 0.104434I
a = 0.192013 − 0.856291I
b = −0.541096 + 0.418060I
2.18731 + 0.45631I 4.25707 + 1.46675I
u = 0.721078 − 0.104434I
a = 0.192013 + 0.856291I
b = −0.541096 − 0.418060I
2.18731 − 0.45631I 4.25707 − 1.46675I
u = 0.697920 + 0.208237I
a = −0.06509 − 2.19317I
b = −1.001020 + 0.864477I
−3.51395 + 6.33078I −1.40613 − 6.95376I
u = 0.697920 − 0.208237I
a = −0.06509 + 2.19317I
b = −1.001020 − 0.864477I
−3.51395 − 6.33078I −1.40613 + 6.95376I
u = −0.705904 + 0.173366I
a = −0.00653 + 1.68655I
b = −0.751506 − 0.750263I
2.69458 − 3.85814I 3.94212 + 7.39409I
u = −0.705904 − 0.173366I
a = −0.00653 − 1.68655I
b = −0.751506 + 0.750263I
2.69458 + 3.85814I 3.94212 − 7.39409I
u = −0.201198 + 1.284730I
a = −5.05419 + 0.23869I
b = 0.47343 − 6.07002I
−9.49174 − 2.91911I 0
u = −0.201198 − 1.284730I
a = −5.05419 − 0.23869I
b = 0.47343 + 6.07002I
−9.49174 + 2.91911I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.153067 + 1.295210I
a = −1.46523 − 0.72615I
b = −0.708458 + 1.122390I
−4.25517 + 1.80505I 0
u = 0.153067 − 1.295210I
a = −1.46523 + 0.72615I
b = −0.708458 − 1.122390I
−4.25517 − 1.80505I 0
u = −0.103113 + 1.315490I
a = −1.137520 + 0.803248I
b = −0.446110 − 0.029511I
−4.75098 + 0.70977I 0
u = −0.103113 − 1.315490I
a = −1.137520 − 0.803248I
b = −0.446110 + 0.029511I
−4.75098 − 0.70977I 0
u = −0.246151 + 1.332300I
a = −0.65866 − 1.28463I
b = 1.63452 − 0.64490I
−8.26726 − 2.71936I 0
u = −0.246151 − 1.332300I
a = −0.65866 + 1.28463I
b = 1.63452 + 0.64490I
−8.26726 + 2.71936I 0
u = 0.214045 + 1.342100I
a = 1.45885 + 0.68329I
b = −0.32165 − 2.41633I
−5.15605 + 3.28846I 0
u = 0.214045 − 1.342100I
a = 1.45885 − 0.68329I
b = −0.32165 + 2.41633I
−5.15605 − 3.28846I 0
u = 0.088800 + 1.356500I
a = −1.27024 − 0.97335I
b = −0.624479 − 0.521635I
−11.14690 − 2.43409I 0
u = 0.088800 − 1.356500I
a = −1.27024 + 0.97335I
b = −0.624479 + 0.521635I
−11.14690 + 2.43409I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.283140 + 1.336130I
a = 0.505201 + 0.841714I
b = 0.890946 − 0.298623I
−2.35239 + 4.06574I 0
u = 0.283140 − 1.336130I
a = 0.505201 − 0.841714I
b = 0.890946 + 0.298623I
−2.35239 − 4.06574I 0
u = −0.176964 + 1.360150I
a = −0.590958 + 0.069979I
b = −1.215720 + 0.395720I
−7.28744 − 1.94916I 0
u = −0.176964 − 1.360150I
a = −0.590958 − 0.069979I
b = −1.215720 − 0.395720I
−7.28744 + 1.94916I 0
u = 0.562967 + 0.258206I
a = 0.91272 − 2.17851I
b = −0.502187 − 0.190942I
−8.27455 + 3.42400I −6.60317 − 6.41709I
u = 0.562967 − 0.258206I
a = 0.91272 + 2.17851I
b = −0.502187 + 0.190942I
−8.27455 − 3.42400I −6.60317 + 6.41709I
u = −0.593523 + 0.159631I
a = 2.10426 − 0.35004I
b = −1.068470 + 0.631484I
−3.63121 + 0.36859I 0.14544 + 2.24269I
u = −0.593523 − 0.159631I
a = 2.10426 + 0.35004I
b = −1.068470 − 0.631484I
−3.63121 − 0.36859I 0.14544 − 2.24269I
u = −0.227049 + 1.369170I
a = 0.45671 − 1.47672I
b = 0.458092 + 0.749861I
−6.58085 − 5.34361I 0
u = −0.227049 − 1.369170I
a = 0.45671 + 1.47672I
b = 0.458092 − 0.749861I
−6.58085 + 5.34361I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.612038
a = 13.8516
b = −8.20930
−5.55052 56.4320
u = 0.024059 + 0.608715I
a = 0.522848 − 0.442561I
b = 0.816972 + 0.871424I
−5.56598 − 3.04650I −5.26168 + 2.94884I
u = 0.024059 − 0.608715I
a = 0.522848 + 0.442561I
b = 0.816972 − 0.871424I
−5.56598 + 3.04650I −5.26168 − 2.94884I
u = −0.284196 + 1.364560I
a = 1.05657 − 1.05386I
b = 0.944479 + 0.673054I
−2.17553 − 7.44915I 0
u = −0.284196 − 1.364560I
a = 1.05657 + 1.05386I
b = 0.944479 − 0.673054I
−2.17553 + 7.44915I 0
u = 0.171165 + 1.383490I
a = −1.236300 + 0.358353I
b = −1.122770 − 0.073322I
−14.2618 + 1.5244I 0
u = 0.171165 − 1.383490I
a = −1.236300 − 0.358353I
b = −1.122770 + 0.073322I
−14.2618 − 1.5244I 0
u = 0.226585 + 1.387380I
a = 0.14113 + 1.87100I
b = 0.487387 − 0.142506I
−13.4949 + 6.3486I 0
u = 0.226585 − 1.387380I
a = 0.14113 − 1.87100I
b = 0.487387 + 0.142506I
−13.4949 − 6.3486I 0
u = 0.280416 + 1.379490I
a = 1.37093 + 1.32206I
b = 1.109010 − 0.804345I
−8.55319 + 9.88755I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.280416 − 1.379490I
a = 1.37093 − 1.32206I
b = 1.109010 + 0.804345I
−8.55319 − 9.88755I 0
u = −0.556007 + 0.198624I
a = 0.64889 + 2.30970I
b = −0.361053 − 0.390068I
−1.60606 − 2.43462I −4.11520 + 8.58615I
u = −0.556007 − 0.198624I
a = 0.64889 − 2.30970I
b = −0.361053 + 0.390068I
−1.60606 + 2.43462I −4.11520 − 8.58615I
u = 0.540026 + 0.095845I
a = −0.08882 − 4.08497I
b = 0.11563 + 1.93050I
−0.576070 + 0.516826I 3.2266 + 14.4230I
u = 0.540026 − 0.095845I
a = −0.08882 + 4.08497I
b = 0.11563 − 1.93050I
−0.576070 − 0.516826I 3.2266 − 14.4230I
u = 0.32617 + 1.41892I
a = −0.77942 − 1.59755I
b = −1.52531 + 1.07291I
−13.7023 + 16.7170I 0
u = 0.32617 − 1.41892I
a = −0.77942 + 1.59755I
b = −1.52531 − 1.07291I
−13.7023 − 16.7170I 0
u = −0.32343 + 1.42557I
a = −0.73068 + 1.30369I
b = −1.19487 − 1.02795I
−6.4767 − 12.8862I 0
u = −0.32343 − 1.42557I
a = −0.73068 − 1.30369I
b = −1.19487 + 1.02795I
−6.4767 + 12.8862I 0
u = 0.32635 + 1.44037I
a = −0.511432 − 0.981821I
b = −0.839069 + 0.790583I
−5.96457 + 7.44234I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.32635 − 1.44037I
a = −0.511432 + 0.981821I
b = −0.839069 − 0.790583I
−5.96457 − 7.44234I 0
u = −0.35997 + 1.43695I
a = 0.040198 + 0.863532I
b = −0.714170 − 0.214535I
−12.69990 − 2.69645I 0
u = −0.35997 − 1.43695I
a = 0.040198 − 0.863532I
b = −0.714170 + 0.214535I
−12.69990 + 2.69645I 0
u = 0.363932 + 0.344823I
a = 0.666144 − 0.751661I
b = 1.099950 − 0.265568I
−8.91963 − 0.57767I −8.53729 − 2.31769I
u = 0.363932 − 0.344823I
a = 0.666144 + 0.751661I
b = 1.099950 + 0.265568I
−8.91963 + 0.57767I −8.53729 + 2.31769I
u = 0.01649 + 1.50014I
a = 0.405278 + 0.345940I
b = 1.39329 + 0.42487I
−18.0876 − 7.1086I 0
u = 0.01649 − 1.50014I
a = 0.405278 − 0.345940I
b = 1.39329 − 0.42487I
−18.0876 + 7.1086I 0
u = −0.01547 + 1.51995I
a = 0.229511 − 0.148482I
b = 1.151530 − 0.202710I
−10.80190 + 2.92909I 0
u = −0.01547 − 1.51995I
a = 0.229511 + 0.148482I
b = 1.151530 + 0.202710I
−10.80190 − 2.92909I 0
u = 0.146993 + 0.405037I
a = 0.805858 + 0.297081I
b = 0.282795 − 0.494464I
0.039086 + 0.986146I 0.86398 − 6.49458I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.146993 − 0.405037I
a = 0.805858 − 0.297081I
b = 0.282795 + 0.494464I
0.039086 − 0.986146I 0.86398 + 6.49458I
u = −0.296698 + 0.219856I
a = 0.096577 + 0.687464I
b = 0.977900 − 0.039618I
−2.38293 + 0.13615I −6.35328 + 3.24648I
u = −0.296698 − 0.219856I
a = 0.096577 − 0.687464I
b = 0.977900 + 0.039618I
−2.38293 − 0.13615I −6.35328 − 3.24648I
13
II. I
u
2
= h7b − 2u − 1, 7a + u + 4, u
2
− u + 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u + 1
a
7
=
−u
u − 1
a
1
=
u
−u + 2
a
3
=
−
1
7
u −
4
7
2
7
u +
1
7
a
4
=
−
8
7
u −
4
7
9
7
u −
13
7
a
6
=
−2u + 1
u − 1
a
2
=
−
1
7
u −
4
7
2
7
u +
1
7
a
10
=
11
49
u +
51
49
−
8
49
u +
3
49
a
5
=
−
47
49
u −
13
49
52
49
u −
44
49
a
9
=
24
49
u −
9
49
36
49
u +
11
49
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
340
49
u +
299
49
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
u
2
c
3
(u + 1)
2
c
4
, c
5
, c
6
c
11
, c
12
u
2
− u + 1
c
7
, c
9
u
2
+ u + 1
c
8
7(7u
2
− 3u + 3)
c
10
7(7u
2
− 4u + 1)
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
2
c
2
y
2
c
4
, c
5
, c
6
c
7
, c
9
, c
11
c
12
y
2
+ y + 1
c
8
49(49y
2
+ 33y + 9)
c
10
49(49y
2
− 2y + 1)
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.642857 − 0.123718I
b = 0.285714 + 0.247436I
−1.64493 + 2.02988I 2.63265 − 6.00916I
u = 0.500000 − 0.866025I
a = −0.642857 + 0.123718I
b = 0.285714 − 0.247436I
−1.64493 − 2.02988I 2.63265 + 6.00916I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
83
− 3u
82
+ ··· + 285u + 49)
c
2
u
2
(u
83
− 7u
82
+ ··· + 1260u − 196)
c
3
((u + 1)
2
)(u
83
− 3u
82
+ ··· + 285u + 49)
c
4
, c
5
(u
2
− u + 1)(u
83
− 2u
82
+ ··· + 2u
2
− 1)
c
6
(u
2
− u + 1)(u
83
+ 2u
82
+ ··· + 762u + 65)
c
7
(u
2
+ u + 1)(u
83
− 2u
82
+ ··· − 2u + 1)
c
8
49(7u
2
− 3u + 3)(7u
83
+ 28u
82
+ ··· + 4430074u + 1636183)
c
9
(u
2
+ u + 1)(u
83
− 2u
82
+ ··· + 2u
2
− 1)
c
10
49(7u
2
− 4u + 1)(7u
83
− 49u
82
+ ··· + 141221u − 21311)
c
11
, c
12
(u
2
− u + 1)(u
83
− 2u
82
+ ··· − 2u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y −1)
2
)(y
83
− 63y
82
+ ··· − 5505y −2401)
c
2
y
2
(y
83
+ 15y
82
+ ··· − 873768y −38416)
c
4
, c
5
, c
9
(y
2
+ y + 1)(y
83
− 84y
82
+ ··· + 4y −1)
c
6
(y
2
+ y + 1)(y
83
− 12y
82
+ ··· + 353924y −4225)
c
7
, c
11
, c
12
(y
2
+ y + 1)(y
83
+ 72y
82
+ ··· + 4y −1)
c
8
2401(49y
2
+ 33y + 9)
· (49y
83
+ 2716y
82
+ ··· − 90553024520728y −2677094809489)
c
10
2401(49y
2
− 2y + 1)
· (49y
83
− 371y
82
+ ··· + 17256948803y −454158721)
19
