12n
0359
(K12n
0359
)
A knot diagram
1
Linearized knot diagam
3 6 12 9 11 2 10 3 12 7 5 9
Solving Sequence
3,12 4,10
9 5 1 8 7 11 6 2
c
3
c
9
c
4
c
12
c
8
c
7
c
11
c
5
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.47058 × 10
201
u
51
+ 5.71881 × 10
201
u
50
+ ··· + 6.09460 × 10
202
b + 1.54791 × 10
203
,
− 1.76593 × 10
202
u
51
+ 1.24322 × 10
204
u
50
+ ··· + 2.49879 × 10
204
a + 8.25019 × 10
206
,
u
52
− 3u
51
+ ··· + 774u + 41i
I
u
2
= h−352794218079u
17
− 1984503379263u
16
+ ··· + 27696360721b − 8429306818513,
− 9258892608982u
17
− 56236696433763u
16
+ ··· + 470838132257a − 283519838364447,
u
18
+ 6u
17
+ ··· + 137u + 17i
* 2 irreducible components of dim
C
= 0, with total 70 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−1.47 × 10
201
u
51
+ 5.72 × 10
201
u
50
+ · · · + 6.09 × 10
202
b + 1.55 ×
10
203
, −1.77 × 10
202
u
51
+ 1.24 × 10
204
u
50
+ · · · + 2.50 × 10
204
a + 8.25 ×
10
206
, u
52
− 3u
51
+ · · · + 774u + 41i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
10
=
0.00706714u
51
− 0.497531u
50
+ ··· − 4176.94u − 330.168
0.0241292u
51
− 0.0938340u
50
+ ··· − 43.0144u − 2.53980
a
9
=
0.00706714u
51
− 0.497531u
50
+ ··· − 4176.94u − 330.168
0.197950u
51
− 0.650977u
50
+ ··· + 325.375u + 16.9897
a
5
=
3.73750u
51
− 11.7980u
50
+ ··· + 9454.68u + 541.305
0.193063u
51
− 0.579335u
50
+ ··· + 677.585u + 43.3523
a
1
=
−2.42736u
51
+ 7.50252u
50
+ ··· − 7583.02u − 470.483
0.650781u
51
− 1.98369u
50
+ ··· + 2282.43u + 144.200
a
8
=
−0.190883u
51
+ 0.153446u
50
+ ··· − 4502.31u − 347.158
0.197950u
51
− 0.650977u
50
+ ··· + 325.375u + 16.9897
a
7
=
−3.76231u
51
+ 12.0301u
50
+ ··· − 8407.16u − 464.145
0.726083u
51
− 2.30029u
50
+ ··· + 1789.52u + 100.639
a
11
=
2.24745u
51
− 6.98939u
50
+ ··· + 6618.23u + 408.458
−0.635359u
51
+ 1.80797u
50
+ ··· − 3338.50u − 227.183
a
6
=
−0.815911u
51
+ 2.78119u
50
+ ··· − 191.619u + 36.3758
−0.365167u
51
+ 1.04144u
50
+ ··· − 1859.62u − 126.481
a
2
=
−3.07815u
51
+ 9.48621u
50
+ ··· − 9865.45u − 614.683
0.650781u
51
− 1.98369u
50
+ ··· + 2282.43u + 144.200
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.01660u
51
+ 5.78735u
50
+ ··· − 10137.6u − 684.151
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
52
+ 29u
51
+ ··· + 1305u + 49
c
2
, c
6
u
52
− 3u
51
+ ··· − 33u + 7
c
3
u
52
− 3u
51
+ ··· + 774u + 41
c
4
u
52
+ u
51
+ ··· − 6854u + 3421
c
5
, c
11
u
52
+ u
51
+ ··· + 67u + 173
c
7
, c
10
u
52
− 5u
51
+ ··· − 175u + 43
c
8
u
52
− u
51
+ ··· + 35897u + 98677
c
9
, c
12
u
52
+ u
51
+ ··· − 164u + 14
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
52
+ y
51
+ ··· − 11839y + 2401
c
2
, c
6
y
52
+ 29y
51
+ ··· + 1305y + 49
c
3
y
52
− 91y
51
+ ··· − 17778y + 1681
c
4
y
52
+ 65y
51
+ ··· + 435342632y + 11703241
c
5
, c
11
y
52
+ 47y
51
+ ··· + 156055y + 29929
c
7
, c
10
y
52
+ 21y
51
+ ··· + 50043y + 1849
c
8
y
52
+ 71y
51
+ ··· + 159369402631y + 9737150329
c
9
, c
12
y
52
+ 65y
51
+ ··· + 1188y + 196
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.847196 + 0.544439I
a = 0.821121 − 1.049870I
b = 1.283350 + 0.463702I
2.14411 + 0.25670I 0
u = −0.847196 − 0.544439I
a = 0.821121 + 1.049870I
b = 1.283350 − 0.463702I
2.14411 − 0.25670I 0
u = −0.633779 + 0.695586I
a = −0.465169 + 0.186673I
b = −0.777699 + 0.134617I
0.20861 + 2.21635I 0
u = −0.633779 − 0.695586I
a = −0.465169 − 0.186673I
b = −0.777699 − 0.134617I
0.20861 − 2.21635I 0
u = −1.050210 + 0.243025I
a = −1.018580 + 0.716714I
b = −0.003518 − 0.905590I
1.62405 + 1.56252I 0
u = −1.050210 − 0.243025I
a = −1.018580 − 0.716714I
b = −0.003518 + 0.905590I
1.62405 − 1.56252I 0
u = 0.244644 + 0.877276I
a = −1.323870 − 0.306984I
b = −1.55896 − 0.12562I
1.74102 + 5.91393I 0
u = 0.244644 − 0.877276I
a = −1.323870 + 0.306984I
b = −1.55896 + 0.12562I
1.74102 − 5.91393I 0
u = 0.025679 + 0.905219I
a = 0.551984 + 0.188120I
b = 0.917186 + 0.799077I
0.33243 + 2.42561I 0
u = 0.025679 − 0.905219I
a = 0.551984 − 0.188120I
b = 0.917186 − 0.799077I
0.33243 − 2.42561I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.765182 + 1.001930I
a = 0.914709 + 0.294749I
b = −0.309410 − 0.681136I
5.54999 + 1.24202I 0
u = 0.765182 − 1.001930I
a = 0.914709 − 0.294749I
b = −0.309410 + 0.681136I
5.54999 − 1.24202I 0
u = 0.248997 + 1.272460I
a = 0.245962 + 0.003913I
b = −0.696361 − 0.656099I
7.59032 + 0.63287I 0
u = 0.248997 − 1.272460I
a = 0.245962 − 0.003913I
b = −0.696361 + 0.656099I
7.59032 − 0.63287I 0
u = −0.638428 + 1.232980I
a = −0.642920 + 0.541264I
b = 0.385485 − 0.613568I
2.65578 − 3.46508I 0
u = −0.638428 − 1.232980I
a = −0.642920 − 0.541264I
b = 0.385485 + 0.613568I
2.65578 + 3.46508I 0
u = −0.38784 + 1.46878I
a = −0.0152670 + 0.1382970I
b = 0.831341 − 0.322019I
6.10025 + 5.08562I 0
u = −0.38784 − 1.46878I
a = −0.0152670 − 0.1382970I
b = 0.831341 + 0.322019I
6.10025 − 5.08562I 0
u = 0.375483 + 0.228163I
a = 2.56228 + 0.24619I
b = −0.215892 − 1.055770I
5.75363 + 3.02665I 4.71645 − 3.29713I
u = 0.375483 − 0.228163I
a = 2.56228 − 0.24619I
b = −0.215892 + 1.055770I
5.75363 − 3.02665I 4.71645 + 3.29713I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.298437 + 0.284498I
a = 0.72312 − 1.93166I
b = −0.388212 + 0.879733I
−3.46306 − 1.08201I −6.90118 + 2.33671I
u = −0.298437 − 0.284498I
a = 0.72312 + 1.93166I
b = −0.388212 − 0.879733I
−3.46306 + 1.08201I −6.90118 − 2.33671I
u = 0.232288 + 0.339454I
a = −2.95102 + 0.30891I
b = 0.161718 − 0.404964I
−0.84133 + 4.24331I −4.56382 − 3.75528I
u = 0.232288 − 0.339454I
a = −2.95102 − 0.30891I
b = 0.161718 + 0.404964I
−0.84133 − 4.24331I −4.56382 + 3.75528I
u = −0.163777 + 0.328240I
a = −0.339926 + 1.248850I
b = 0.092253 + 0.440028I
0.150148 + 0.981907I 2.74729 − 6.88100I
u = −0.163777 − 0.328240I
a = −0.339926 − 1.248850I
b = 0.092253 − 0.440028I
0.150148 − 0.981907I 2.74729 + 6.88100I
u = −0.334264 + 0.127751I
a = 1.07054 + 1.94531I
b = 0.081971 + 0.413525I
0.311391 + 0.999972I 0.90930 − 4.81258I
u = −0.334264 − 0.127751I
a = 1.07054 − 1.94531I
b = 0.081971 − 0.413525I
0.311391 − 0.999972I 0.90930 + 4.81258I
u = −0.183867 + 0.172355I
a = 2.54602 + 1.33773I
b = 0.17080 + 1.43660I
−0.98629 − 1.61388I 2.28734 + 4.84078I
u = −0.183867 − 0.172355I
a = 2.54602 − 1.33773I
b = 0.17080 − 1.43660I
−0.98629 + 1.61388I 2.28734 − 4.84078I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.185720 + 0.154950I
a = −1.93380 − 4.94041I
b = 0.136329 + 1.191260I
2.68654 + 8.47879I 1.23045 − 6.70789I
u = −0.185720 − 0.154950I
a = −1.93380 + 4.94041I
b = 0.136329 − 1.191260I
2.68654 − 8.47879I 1.23045 + 6.70789I
u = 2.00082 + 0.40115I
a = −0.214150 − 0.799893I
b = 0.41792 + 1.72055I
−7.56845 − 0.87082I 0
u = 2.00082 − 0.40115I
a = −0.214150 + 0.799893I
b = 0.41792 − 1.72055I
−7.56845 + 0.87082I 0
u = −2.09373 + 0.02995I
a = 0.059316 − 0.721313I
b = −0.49890 + 1.90563I
−5.68259 − 2.55465I 0
u = −2.09373 − 0.02995I
a = 0.059316 + 0.721313I
b = −0.49890 − 1.90563I
−5.68259 + 2.55465I 0
u = 2.10852 + 0.00032I
a = 0.028769 + 0.877656I
b = −0.61366 − 1.33060I
−9.43352 + 2.31093I 0
u = 2.10852 − 0.00032I
a = 0.028769 − 0.877656I
b = −0.61366 + 1.33060I
−9.43352 − 2.31093I 0
u = −2.28057 + 0.24594I
a = −0.054836 + 0.719976I
b = −0.23588 − 1.93061I
−7.58635 + 2.76111I 0
u = −2.28057 − 0.24594I
a = −0.054836 − 0.719976I
b = −0.23588 + 1.93061I
−7.58635 − 2.76111I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.27534 + 0.29106I
a = 0.028049 + 0.773187I
b = 0.12810 − 1.98850I
−10.56000 − 8.01521I 0
u = 2.27534 − 0.29106I
a = 0.028049 − 0.773187I
b = 0.12810 + 1.98850I
−10.56000 + 8.01521I 0
u = 2.29164 + 0.20640I
a = 0.140048 + 0.750160I
b = 0.14771 − 1.74394I
−12.40010 + 1.52484I 0
u = 2.29164 − 0.20640I
a = 0.140048 − 0.750160I
b = 0.14771 + 1.74394I
−12.40010 − 1.52484I 0
u = −2.31506 + 0.25454I
a = −0.037212 − 0.734956I
b = 0.71969 + 1.72452I
−2.28298 + 7.52055I 0
u = −2.31506 − 0.25454I
a = −0.037212 + 0.734956I
b = 0.71969 − 1.72452I
−2.28298 − 7.52055I 0
u = 2.37101 + 0.45768I
a = −0.270747 − 0.604903I
b = 0.22193 + 1.81314I
−6.89637 + 5.83330I 0
u = 2.37101 − 0.45768I
a = −0.270747 + 0.604903I
b = 0.22193 − 1.81314I
−6.89637 − 5.83330I 0
u = 2.43147 + 0.21360I
a = 0.094716 − 0.708934I
b = −0.59712 + 1.86521I
−4.9756 − 14.1776I 0
u = 2.43147 − 0.21360I
a = 0.094716 + 0.708934I
b = −0.59712 − 1.86521I
−4.9756 + 14.1776I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.45820 + 0.23118I
a = 0.151599 − 0.573246I
b = −0.30016 + 1.95716I
−5.29494 − 1.56622I 0
u = −2.45820 − 0.23118I
a = 0.151599 + 0.573246I
b = −0.30016 − 1.95716I
−5.29494 + 1.56622I 0
10
II. I
u
2
= h−3.53 × 10
11
u
17
− 1.98 × 10
12
u
16
+ · · · + 2.77 × 10
10
b − 8.43 ×
10
12
, −9.26 × 10
12
u
17
− 5.62 × 10
13
u
16
+ · · · + 4.71 × 10
11
a − 2.84 ×
10
14
, u
18
+ 6u
17
+ · · · + 137u + 17i
(i) Arc colorings
a
3
=
1
0
a
12
=
0
u
a
4
=
1
u
2
a
10
=
19.6647u
17
+ 119.440u
16
+ ··· + 4444.89u + 602.160
12.7379u
17
+ 71.6521u
16
+ ··· + 2254.63u + 304.347
a
9
=
19.6647u
17
+ 119.440u
16
+ ··· + 4444.89u + 602.160
0.110913u
17
+ 7.21160u
16
+ ··· + 1721.50u + 279.675
a
5
=
13.7009u
17
+ 72.2945u
16
+ ··· + 1271.37u + 134.143
−11.8163u
17
− 47.6476u
16
+ ··· + 2065.95u + 402.732
a
1
=
5.11275u
17
+ 16.1679u
16
+ ··· − 2105.02u − 377.911
20.5194u
17
+ 116.891u
16
+ ··· + 3645.65u + 479.562
a
8
=
19.5538u
17
+ 112.228u
16
+ ··· + 2723.39u + 322.485
0.110913u
17
+ 7.21160u
16
+ ··· + 1721.50u + 279.675
a
7
=
7.98918u
17
+ 34.4198u
16
+ ··· − 1811.82u − 363.145
−4.57845u
17
− 13.0076u
16
+ ··· + 2114.17u + 369.442
a
11
=
−11.5058u
17
− 77.4552u
16
+ ··· − 4500.68u − 677.571
41.3674u
17
+ 233.328u
16
+ ··· + 6729.08u + 868.915
a
6
=
−31.6037u
17
− 166.973u
16
+ ··· − 3107.94u − 332.195
3.73112u
17
+ 15.7034u
16
+ ··· − 506.045u − 106.831
a
2
=
−15.4066u
17
− 100.723u
16
+ ··· − 5750.66u − 857.473
20.5194u
17
+ 116.891u
16
+ ··· + 3645.65u + 479.562
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
1031347589724
27696360721
u
17
−
7091677654231
27696360721
u
16
+ ··· −
428423029545491
27696360721
u −
64866752095286
27696360721
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
18
− 12u
17
+ ··· − 12u + 1
c
2
u
18
− 2u
17
+ ··· − 2u + 1
c
3
u
18
+ 6u
17
+ ··· + 137u + 17
c
4
u
18
+ 6u
16
+ ··· − u + 1
c
5
u
18
+ 11u
16
+ ··· + 2u + 1
c
6
u
18
+ 2u
17
+ ··· + 2u + 1
c
7
u
18
− 4u
17
+ ··· + 2u + 1
c
8
u
18
+ 3u
16
+ ··· + 2u + 1
c
9
u
18
+ 10u
16
+ ··· + 5u + 2
c
10
u
18
+ 4u
17
+ ··· − 2u + 1
c
11
u
18
+ 11u
16
+ ··· − 2u + 1
c
12
u
18
+ 10u
16
+ ··· − 5u + 2
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 8y
16
+ ··· − 8y + 1
c
2
, c
6
y
18
+ 12y
17
+ ··· + 12y + 1
c
3
y
18
− 8y
17
+ ··· + 1189y + 289
c
4
y
18
+ 12y
17
+ ··· − 5y + 1
c
5
, c
11
y
18
+ 22y
17
+ ··· − 6y + 1
c
7
, c
10
y
18
+ 8y
17
+ ··· − 6y + 1
c
8
y
18
+ 6y
17
+ ··· + 10y + 1
c
9
, c
12
y
18
+ 20y
17
+ ··· + 39y + 4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.658686 + 0.580480I
a = 1.183330 − 0.453838I
b = 0.641287 + 0.684543I
−0.049129 + 0.479336I −2.63779 + 0.48041I
u = −0.658686 − 0.580480I
a = 1.183330 + 0.453838I
b = 0.641287 − 0.684543I
−0.049129 − 0.479336I −2.63779 − 0.48041I
u = −0.563352 + 0.585475I
a = −1.224900 + 0.583463I
b = 0.725527 − 0.651658I
6.30490 − 1.95106I 4.05302 + 5.53919I
u = −0.563352 − 0.585475I
a = −1.224900 − 0.583463I
b = 0.725527 + 0.651658I
6.30490 + 1.95106I 4.05302 − 5.53919I
u = −0.129010 + 0.740804I
a = −1.064850 + 0.763925I
b = −0.832283 − 0.109973I
0.36326 + 4.10768I 1.77356 − 5.10612I
u = −0.129010 − 0.740804I
a = −1.064850 − 0.763925I
b = −0.832283 + 0.109973I
0.36326 − 4.10768I 1.77356 + 5.10612I
u = −0.487501 + 0.501661I
a = 0.593618 − 0.000224I
b = 0.006490 + 1.141070I
−1.68671 + 0.57803I −2.61647 + 0.05282I
u = −0.487501 − 0.501661I
a = 0.593618 + 0.000224I
b = 0.006490 − 1.141070I
−1.68671 − 0.57803I −2.61647 − 0.05282I
u = −0.451462 + 0.525720I
a = 0.86844 − 1.65712I
b = −0.819153 + 0.224312I
3.90707 − 2.76377I 4.16735 + 1.82045I
u = −0.451462 − 0.525720I
a = 0.86844 + 1.65712I
b = −0.819153 − 0.224312I
3.90707 + 2.76377I 4.16735 − 1.82045I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.66448 + 1.54686I
a = −0.573045 + 0.032453I
b = −0.232872 − 0.694995I
6.81177 − 0.72306I 3.17550 − 0.34252I
u = −0.66448 − 1.54686I
a = −0.573045 − 0.032453I
b = −0.232872 + 0.694995I
6.81177 + 0.72306I 3.17550 + 0.34252I
u = 0.14544 + 1.87487I
a = 0.431442 − 0.149048I
b = 0.575402 − 0.102615I
5.46183 + 5.97318I 0.92827 − 6.61935I
u = 0.14544 − 1.87487I
a = 0.431442 + 0.149048I
b = 0.575402 + 0.102615I
5.46183 − 5.97318I 0.92827 + 6.61935I
u = 2.14106 + 0.15296I
a = −0.118697 − 0.824657I
b = 0.38314 + 1.44742I
−10.00120 + 1.52667I −2.95677 + 1.29262I
u = 2.14106 − 0.15296I
a = −0.118697 + 0.824657I
b = 0.38314 − 1.44742I
−10.00120 − 1.52667I −2.95677 − 1.29262I
u = −2.33202 + 0.08143I
a = 0.081135 − 0.622597I
b = −0.44753 + 2.04634I
−6.17694 − 2.22783I −8.88668 + 0.I
u = −2.33202 − 0.08143I
a = 0.081135 + 0.622597I
b = −0.44753 − 2.04634I
−6.17694 + 2.22783I −8.88668 + 0.I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 12u
17
+ ··· − 12u + 1)(u
52
+ 29u
51
+ ··· + 1305u + 49)
c
2
(u
18
− 2u
17
+ ··· − 2u + 1)(u
52
− 3u
51
+ ··· − 33u + 7)
c
3
(u
18
+ 6u
17
+ ··· + 137u + 17)(u
52
− 3u
51
+ ··· + 774u + 41)
c
4
(u
18
+ 6u
16
+ ··· − u + 1)(u
52
+ u
51
+ ··· − 6854u + 3421)
c
5
(u
18
+ 11u
16
+ ··· + 2u + 1)(u
52
+ u
51
+ ··· + 67u + 173)
c
6
(u
18
+ 2u
17
+ ··· + 2u + 1)(u
52
− 3u
51
+ ··· − 33u + 7)
c
7
(u
18
− 4u
17
+ ··· + 2u + 1)(u
52
− 5u
51
+ ··· − 175u + 43)
c
8
(u
18
+ 3u
16
+ ··· + 2u + 1)(u
52
− u
51
+ ··· + 35897u + 98677)
c
9
(u
18
+ 10u
16
+ ··· + 5u + 2)(u
52
+ u
51
+ ··· − 164u + 14)
c
10
(u
18
+ 4u
17
+ ··· − 2u + 1)(u
52
− 5u
51
+ ··· − 175u + 43)
c
11
(u
18
+ 11u
16
+ ··· − 2u + 1)(u
52
+ u
51
+ ··· + 67u + 173)
c
12
(u
18
+ 10u
16
+ ··· − 5u + 2)(u
52
+ u
51
+ ··· − 164u + 14)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 8y
16
+ ··· − 8y + 1)(y
52
+ y
51
+ ··· − 11839y + 2401)
c
2
, c
6
(y
18
+ 12y
17
+ ··· + 12y + 1)(y
52
+ 29y
51
+ ··· + 1305y + 49)
c
3
(y
18
− 8y
17
+ ··· + 1189y + 289)(y
52
− 91y
51
+ ··· − 17778y + 1681)
c
4
(y
18
+ 12y
17
+ ··· − 5y + 1)
· (y
52
+ 65y
51
+ ··· + 435342632y + 11703241)
c
5
, c
11
(y
18
+ 22y
17
+ ··· − 6y + 1)(y
52
+ 47y
51
+ ··· + 156055y + 29929)
c
7
, c
10
(y
18
+ 8y
17
+ ··· − 6y + 1)(y
52
+ 21y
51
+ ··· + 50043y + 1849)
c
8
(y
18
+ 6y
17
+ ··· + 10y + 1)
· (y
52
+ 71y
51
+ ··· + 159369402631y + 9737150329)
c
9
, c
12
(y
18
+ 20y
17
+ ··· + 39y + 4)(y
52
+ 65y
51
+ ··· + 1188y + 196)
19
