12n
0324
(K12n
0324
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 4 11 1 12 6 4 9
Solving Sequence
4,6 7,12
11 8 3 2 1 5 10 9
c
6
c
11
c
7
c
3
c
2
c
1
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.20623 × 10
189
u
50
+ 1.91950 × 10
190
u
49
+ ··· + 1.83109 × 10
190
b − 2.76698 × 10
190
,
6.53118 × 10
190
u
50
− 2.00240 × 10
191
u
49
+ ··· + 1.83109 × 10
190
a + 4.17386 × 10
191
, u
51
− 3u
50
+ ··· + 21u + 1i
I
u
2
= h−15199u
17
− 83246u
16
+ ··· + b − 28434, 13363u
17
+ 74911u
16
+ ··· + a + 32129,
u
18
+ 6u
17
+ ··· + 16u + 1i
* 2 irreducible components of dim
C
= 0, with total 69 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−6.21 × 10
189
u
50
+ 1.92 × 10
190
u
49
+ · · · + 1.83 × 10
190
b − 2.77 ×
10
190
, 6.53 × 10
190
u
50
− 2.00 × 10
191
u
49
+ · · · + 1.83 × 10
190
a + 4.17 ×
10
191
, u
51
− 3u
50
+ · · · + 21u + 1i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
12
=
−3.56682u
50
+ 10.9355u
49
+ ··· − 381.856u − 22.7943
0.338936u
50
− 1.04828u
49
+ ··· + 35.0303u + 1.51111
a
11
=
−3.56682u
50
+ 10.9355u
49
+ ··· − 381.856u − 22.7943
0.367596u
50
− 1.14233u
49
+ ··· + 33.6608u + 1.27604
a
8
=
1.31856u
50
− 4.24593u
49
+ ··· + 43.2461u − 7.28846
0.372098u
50
− 1.15390u
49
+ ··· + 41.7658u + 3.50605
a
3
=
2.56187u
50
− 8.01615u
49
+ ··· + 312.685u + 11.1314
−0.123273u
50
+ 0.394024u
49
+ ··· − 16.0948u + 0.114225
a
2
=
2.43859u
50
− 7.62212u
49
+ ··· + 296.590u + 11.2457
−0.123273u
50
+ 0.394024u
49
+ ··· − 16.0948u + 0.114225
a
1
=
−0.386563u
50
+ 1.15851u
49
+ ··· − 202.479u − 17.3283
0.237140u
50
− 0.750279u
49
+ ··· + 32.0577u + 2.33690
a
5
=
−2.62715u
50
+ 8.16557u
49
+ ··· − 395.092u − 18.3358
0.245732u
50
− 0.780842u
49
+ ··· + 33.6386u + 1.03443
a
10
=
−3.93442u
50
+ 12.0779u
49
+ ··· − 415.517u − 24.0704
0.367596u
50
− 1.14233u
49
+ ··· + 33.6608u + 1.27604
a
9
=
−1.41365u
50
+ 4.64782u
49
+ ··· + 32.0023u + 3.74234
−0.0397767u
50
+ 0.116546u
49
+ ··· − 24.0454u − 1.81099
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.64179u
50
+ 8.09527u
49
+ ··· − 400.109u − 30.6870
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
51
+ 29u
50
+ ··· − 31u + 49
c
2
, c
5
u
51
+ 3u
50
+ ··· + 33u + 7
c
3
u
51
+ u
50
+ ··· − 133u + 163
c
4
, c
11
u
51
− u
50
+ ··· − 3u + 1
c
6
u
51
− 3u
50
+ ··· + 21u + 1
c
7
u
51
− 2u
50
+ ··· + 6290u + 161
c
8
, c
9
, c
12
u
51
− 4u
50
+ ··· + 131u − 29
c
10
u
51
+ 33u
49
+ ··· + 63366u + 32041
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
51
− y
50
+ ··· + 295745y −2401
c
2
, c
5
y
51
− 29y
50
+ ··· − 31y −49
c
3
y
51
+ 19y
50
+ ··· − 159329y −26569
c
4
, c
11
y
51
+ 67y
50
+ ··· + 111y −1
c
6
y
51
− 87y
50
+ ··· − 61y −1
c
7
y
51
+ 68y
50
+ ··· + 46092006y −25921
c
8
, c
9
, c
12
y
51
+ 46y
50
+ ··· + 14783y −841
c
10
y
51
+ 66y
50
+ ··· − 134123626y −1026625681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438854 + 0.881387I
a = 0.802989 + 0.488950I
b = 1.46263 + 0.44970I
2.55303 + 5.62854I 0
u = 0.438854 − 0.881387I
a = 0.802989 − 0.488950I
b = 1.46263 − 0.44970I
2.55303 − 5.62854I 0
u = 0.786917 + 0.547490I
a = 1.231510 + 0.622312I
b = −0.561675 − 0.635936I
5.38314 + 2.25660I 0
u = 0.786917 − 0.547490I
a = 1.231510 − 0.622312I
b = −0.561675 + 0.635936I
5.38314 − 2.25660I 0
u = −0.969635 + 0.549105I
a = 0.592870 − 0.730545I
b = 1.099540 + 0.169847I
2.80334 + 0.19977I 0
u = −0.969635 − 0.549105I
a = 0.592870 + 0.730545I
b = 1.099540 − 0.169847I
2.80334 − 0.19977I 0
u = −0.258956 + 1.084080I
a = −0.0078550 + 0.1186930I
b = 0.680266 + 0.175141I
2.08270 + 2.42338I 0
u = −0.258956 − 1.084080I
a = −0.0078550 − 0.1186930I
b = 0.680266 − 0.175141I
2.08270 − 2.42338I 0
u = −0.877771 + 0.053196I
a = 1.06003 − 0.99974I
b = −0.050000 + 0.341986I
2.86052 + 0.92213I −4.00000 + 0.I
u = −0.877771 − 0.053196I
a = 1.06003 + 0.99974I
b = −0.050000 − 0.341986I
2.86052 − 0.92213I −4.00000 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.077227 + 0.787735I
a = −1.39631 + 0.29538I
b = 0.405257 − 0.172699I
−1.082690 − 0.753222I −8.27224 − 0.58913I
u = 0.077227 − 0.787735I
a = −1.39631 − 0.29538I
b = 0.405257 + 0.172699I
−1.082690 + 0.753222I −8.27224 + 0.58913I
u = −0.371822 + 0.643704I
a = −1.319030 + 0.489182I
b = −1.058190 − 0.552894I
−1.31122 + 2.27509I −10.03353 − 3.12250I
u = −0.371822 − 0.643704I
a = −1.319030 − 0.489182I
b = −1.058190 + 0.552894I
−1.31122 − 2.27509I −10.03353 + 3.12250I
u = 0.415418 + 1.187680I
a = 0.210614 + 0.007241I
b = −0.711873 − 0.851088I
7.01209 + 0.55331I 0
u = 0.415418 − 1.187680I
a = 0.210614 − 0.007241I
b = −0.711873 + 0.851088I
7.01209 − 0.55331I 0
u = −0.851182 + 0.945181I
a = 0.492401 − 0.719354I
b = −0.574356 + 0.893531I
1.61849 − 3.97257I 0
u = −0.851182 − 0.945181I
a = 0.492401 + 0.719354I
b = −0.574356 − 0.893531I
1.61849 + 3.97257I 0
u = −0.654550
a = −0.815626
b = −0.0235623
−1.51224 −6.39690
u = −0.61210 + 1.42769I
a = −0.0766712 − 0.0666805I
b = −0.855685 + 0.583788I
5.29873 + 5.39295I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.61210 − 1.42769I
a = −0.0766712 + 0.0666805I
b = −0.855685 − 0.583788I
5.29873 − 5.39295I 0
u = 0.244067 + 0.211790I
a = 3.58624 − 0.14006I
b = −0.172244 − 0.891038I
6.22807 + 3.03641I −0.15194 − 4.08278I
u = 0.244067 − 0.211790I
a = 3.58624 + 0.14006I
b = −0.172244 + 0.891038I
6.22807 − 3.03641I −0.15194 + 4.08278I
u = −0.052211 + 0.243333I
a = −1.65333 + 1.57397I
b = 0.032030 + 0.489627I
−0.123994 + 1.016060I −2.35884 − 6.62848I
u = −0.052211 − 0.243333I
a = −1.65333 − 1.57397I
b = 0.032030 − 0.489627I
−0.123994 − 1.016060I −2.35884 + 6.62848I
u = −0.153372 + 0.111375I
a = 2.84799 + 0.60731I
b = 0.517369 + 1.121390I
−1.19162 + 1.61010I −0.97639 + 4.58807I
u = −0.153372 − 0.111375I
a = 2.84799 − 0.60731I
b = 0.517369 − 1.121390I
−1.19162 − 1.61010I −0.97639 − 4.58807I
u = 0.007539 + 0.153031I
a = −5.36804 + 7.36280I
b = 0.090420 − 0.966899I
3.36883 + 8.08804I −4.16795 − 6.45391I
u = 0.007539 − 0.153031I
a = −5.36804 − 7.36280I
b = 0.090420 + 0.966899I
3.36883 − 8.08804I −4.16795 + 6.45391I
u = −0.0981206 + 0.0761409I
a = −2.13969 − 7.63551I
b = −0.180819 + 1.098890I
−2.72745 + 3.79308I −7.08139 − 6.39060I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0981206 − 0.0761409I
a = −2.13969 + 7.63551I
b = −0.180819 − 1.098890I
−2.72745 − 3.79308I −7.08139 + 6.39060I
u = 2.03972 + 0.34818I
a = −0.167321 − 0.858121I
b = 0.24093 + 2.09041I
−7.53123 − 4.56112I 0
u = 2.03972 − 0.34818I
a = −0.167321 + 0.858121I
b = 0.24093 − 2.09041I
−7.53123 + 4.56112I 0
u = 2.11807 + 0.20852I
a = 0.111419 + 0.870257I
b = 0.53451 − 1.37759I
−9.45111 − 1.99019I 0
u = 2.11807 − 0.20852I
a = 0.111419 − 0.870257I
b = 0.53451 + 1.37759I
−9.45111 + 1.99019I 0
u = 2.14783 + 0.07904I
a = 0.027350 + 0.853045I
b = −0.32027 − 1.82960I
−12.63600 − 1.06445I 0
u = 2.14783 − 0.07904I
a = 0.027350 − 0.853045I
b = −0.32027 + 1.82960I
−12.63600 + 1.06445I 0
u = 2.09075 + 0.50266I
a = −0.344685 − 0.686017I
b = 0.07196 + 1.68618I
−7.39570 + 2.33947I 0
u = 2.09075 − 0.50266I
a = −0.344685 + 0.686017I
b = 0.07196 − 1.68618I
−7.39570 − 2.33947I 0
u = −2.16315 + 0.30765I
a = −0.100617 + 0.731102I
b = −0.04164 − 2.25566I
−5.84292 + 0.77536I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.16315 − 0.30765I
a = −0.100617 − 0.731102I
b = −0.04164 + 2.25566I
−5.84292 − 0.77536I 0
u = −2.24014 + 0.35466I
a = 0.021038 − 0.775624I
b = 0.69469 + 1.78191I
−2.40989 + 7.37799I 0
u = −2.24014 − 0.35466I
a = 0.021038 + 0.775624I
b = 0.69469 − 1.78191I
−2.40989 − 7.37799I 0
u = −2.22716 + 0.44704I
a = −0.192890 + 0.625827I
b = −0.19805 − 1.86310I
−5.46694 + 1.77932I 0
u = −2.22716 − 0.44704I
a = −0.192890 − 0.625827I
b = −0.19805 + 1.86310I
−5.46694 − 1.77932I 0
u = −2.28681 + 0.02141I
a = 0.069554 + 0.723390I
b = −0.35195 − 1.92261I
−7.57553 + 3.10359I 0
u = −2.28681 − 0.02141I
a = 0.069554 − 0.723390I
b = −0.35195 + 1.92261I
−7.57553 − 3.10359I 0
u = 2.29535 + 0.30641I
a = −0.050327 + 0.786971I
b = 0.58797 − 1.96230I
−5.2040 − 14.0594I 0
u = 2.29535 − 0.30641I
a = −0.050327 − 0.786971I
b = 0.58797 + 1.96230I
−5.2040 + 14.0594I 0
u = 2.32797 + 0.06553I
a = 0.170579 + 0.730407I
b = −0.32905 − 1.92841I
−10.44840 + 8.57270I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 2.32797 − 0.06553I
a = 0.170579 − 0.730407I
b = −0.32905 + 1.92841I
−10.44840 − 8.57270I 0
10
II. I
u
2
= h−15199u
17
− 83246u
16
+ · · · + b − 28434, 13363u
17
+ 74911u
16
+
· · · + a + 32129, u
18
+ 6u
17
+ · · · + 16u + 1i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
12
=
−13363u
17
− 74911u
16
+ ··· − 440720u − 32129
15199u
17
+ 83246u
16
+ ··· + 403343u + 28434
a
11
=
−13363u
17
− 74911u
16
+ ··· − 440720u − 32129
13235u
17
+ 72159u
16
+ ··· + 332434u + 23167
a
8
=
−16u
17
− 94u
16
+ ··· − 1251u − 125
16384u
17
+ 90112u
16
+ ··· + 458752u + 32767
a
3
=
−93u
17
− 558u
16
+ ··· − 6698u − 592
−u
17
− 6u
16
+ ··· − 115u − 15
a
2
=
−94u
17
− 564u
16
+ ··· − 6813u − 607
−u
17
− 6u
16
+ ··· − 115u − 15
a
1
=
1589u
17
+ 9128u
16
+ ··· + 70803u + 5487
95u
17
+ 557u
16
+ ··· + 5933u + 515
a
5
=
−513u
17
− 2984u
16
+ ··· − 27756u − 2291
−14u
17
− 83u
16
+ ··· − 1120u − 110
a
10
=
−26598u
17
− 147070u
16
+ ··· − 773154u − 55296
13235u
17
+ 72159u
16
+ ··· + 332434u + 23167
a
9
=
−24899u
17
− 137296u
16
+ ··· − 695183u − 49170
13235u
17
+ 72171u
16
+ ··· + 333330u + 23261
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 96456u
17
+ 526448u
16
+ 968430u
15
− 43279u
14
− 4993167u
13
− 14847798u
12
−
21267959u
11
−7843139u
10
+ 43624726u
9
+ 131260980u
8
+ 221053250u
7
+ 262385524u
6
+
225728266u
5
+ 138033421u
4
+ 57916786u
3
+ 15777654u
2
+ 2510027u + 177106
11
(iv) u-Polynomials at the component
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
16
+ ··· − 6u + 1
c
4
u
18
+ 10u
16
+ ··· + 17u
2
+ 1
c
5
u
18
− 2u
17
+ ··· − 2u + 1
c
6
u
18
+ 6u
17
+ ··· + 16u + 1
c
7
u
18
− u
17
+ ··· − u + 1
c
8
, c
9
u
18
− 3u
17
+ ··· − 4u + 1
c
10
u
18
+ u
17
+ ··· + u + 1
c
11
u
18
+ 10u
16
+ ··· + 17u
2
+ 1
c
12
u
18
+ 3u
17
+ ··· + 4u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 8y
16
+ ··· − 8y + 1
c
2
, c
5
y
18
− 12y
17
+ ··· − 12y + 1
c
3
y
18
+ 12y
17
+ ··· − 6y + 1
c
4
, c
11
y
18
+ 20y
17
+ ··· + 34y + 1
c
6
y
18
− 10y
17
+ ··· − 26y + 1
c
7
y
18
+ 13y
17
+ ··· − 5y + 1
c
8
, c
9
, c
12
y
18
+ 19y
17
+ ··· + 34y + 1
c
10
y
18
+ 7y
17
+ ··· − 9y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.642965 + 1.138500I
a = −0.809556 − 0.016966I
b = −0.104175 − 0.781798I
6.64743 − 1.50205I 0
u = −0.642965 − 1.138500I
a = −0.809556 + 0.016966I
b = −0.104175 + 0.781798I
6.64743 + 1.50205I 0
u = −0.586828 + 0.199257I
a = −1.39182 + 1.34971I
b = 0.880804 − 0.592549I
6.10975 − 2.66232I 2.22310 + 5.30109I
u = −0.586828 − 0.199257I
a = −1.39182 − 1.34971I
b = 0.880804 + 0.592549I
6.10975 + 2.66232I 2.22310 − 5.30109I
u = 0.12002 + 1.43750I
a = −0.563405 + 0.344470I
b = −0.585179 + 0.241540I
5.29038 + 6.84249I 0
u = 0.12002 − 1.43750I
a = −0.563405 − 0.344470I
b = −0.585179 − 0.241540I
5.29038 − 6.84249I 0
u = −0.533613 + 0.020740I
a = 0.029715 − 0.541718I
b = −0.493263 + 0.922302I
−1.38579 − 2.18536I −5.51806 + 7.75600I
u = −0.533613 − 0.020740I
a = 0.029715 + 0.541718I
b = −0.493263 − 0.922302I
−1.38579 + 2.18536I −5.51806 − 7.75600I
u = −0.483081 + 0.122779I
a = 0.22219 − 1.99454I
b = −0.880434 + 0.479597I
−0.12655 − 1.97803I −2.99483 + 2.76111I
u = −0.483081 − 0.122779I
a = 0.22219 + 1.99454I
b = −0.880434 − 0.479597I
−0.12655 + 1.97803I −2.99483 − 2.76111I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.30885 + 1.52377I
a = 0.446642 − 0.096804I
b = 0.487692 + 0.273624I
1.24279 + 2.46392I 0
u = −0.30885 − 1.52377I
a = 0.446642 + 0.096804I
b = 0.487692 − 0.273624I
1.24279 − 2.46392I 0
u = −0.413975 + 0.113860I
a = 0.76007 + 3.22513I
b = 0.849984 − 0.349023I
3.66442 − 2.08584I −0.82702 + 3.16487I
u = −0.413975 − 0.113860I
a = 0.76007 − 3.22513I
b = 0.849984 + 0.349023I
3.66442 + 2.08584I −0.82702 − 3.16487I
u = 2.09428 + 0.29167I
a = 0.161339 + 0.853648I
b = 0.18266 − 1.56242I
−10.12730 − 0.84676I 0
u = 2.09428 − 0.29167I
a = 0.161339 − 0.853648I
b = 0.18266 + 1.56242I
−10.12730 + 0.84676I 0
u = −2.24499 + 0.38125I
a = 0.144822 − 0.657660I
b = 0.16191 + 2.21998I
−6.38032 + 1.49135I 0
u = −2.24499 − 0.38125I
a = 0.144822 + 0.657660I
b = 0.16191 − 2.21998I
−6.38032 − 1.49135I 0
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 12u
17
+ ··· − 12u + 1)(u
51
+ 29u
50
+ ··· − 31u + 49)
c
2
(u
18
+ 2u
17
+ ··· + 2u + 1)(u
51
+ 3u
50
+ ··· + 33u + 7)
c
3
(u
18
+ 6u
16
+ ··· − 6u + 1)(u
51
+ u
50
+ ··· − 133u + 163)
c
4
(u
18
+ 10u
16
+ ··· + 17u
2
+ 1)(u
51
− u
50
+ ··· − 3u + 1)
c
5
(u
18
− 2u
17
+ ··· − 2u + 1)(u
51
+ 3u
50
+ ··· + 33u + 7)
c
6
(u
18
+ 6u
17
+ ··· + 16u + 1)(u
51
− 3u
50
+ ··· + 21u + 1)
c
7
(u
18
− u
17
+ ··· − u + 1)(u
51
− 2u
50
+ ··· + 6290u + 161)
c
8
, c
9
(u
18
− 3u
17
+ ··· − 4u + 1)(u
51
− 4u
50
+ ··· + 131u − 29)
c
10
(u
18
+ u
17
+ ··· + u + 1)(u
51
+ 33u
49
+ ··· + 63366u + 32041)
c
11
(u
18
+ 10u
16
+ ··· + 17u
2
+ 1)(u
51
− u
50
+ ··· − 3u + 1)
c
12
(u
18
+ 3u
17
+ ··· + 4u + 1)(u
51
− 4u
50
+ ··· + 131u − 29)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 8y
16
+ ··· − 8y + 1)(y
51
− y
50
+ ··· + 295745y −2401)
c
2
, c
5
(y
18
− 12y
17
+ ··· − 12y + 1)(y
51
− 29y
50
+ ··· − 31y −49)
c
3
(y
18
+ 12y
17
+ ··· − 6y + 1)(y
51
+ 19y
50
+ ··· − 159329y −26569)
c
4
, c
11
(y
18
+ 20y
17
+ ··· + 34y + 1)(y
51
+ 67y
50
+ ··· + 111y −1)
c
6
(y
18
− 10y
17
+ ··· − 26y + 1)(y
51
− 87y
50
+ ··· − 61y −1)
c
7
(y
18
+ 13y
17
+ ··· − 5y + 1)(y
51
+ 68y
50
+ ··· + 4.60920 × 10
7
y −25921)
c
8
, c
9
, c
12
(y
18
+ 19y
17
+ ··· + 34y + 1)(y
51
+ 46y
50
+ ··· + 14783y −841)
c
10
(y
18
+ 7y
17
+ ··· − 9y + 1)
· (y
51
+ 66y
50
+ ··· − 134123626y −1026625681)
17
