12n
0683
(K12n
0683
)
A knot diagram
1
Linearized knot diagam
4 5 12 9 11 4 12 1 2 5 6 8
Solving Sequence
1,4 2,8
9 5 10 12 3 7 6 11
c
1
c
8
c
4
c
9
c
12
c
3
c
7
c
6
c
11
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.19867 × 10
203
u
56
+ 5.65768 × 10
203
u
55
+ ··· + 1.13098 × 10
204
b − 3.04242 × 10
203
,
1.01630 × 10
202
u
56
− 2.54589 × 10
202
u
55
+ ··· + 4.34992 × 10
202
a − 1.92664 × 10
204
, u
57
− 2u
56
+ ··· + 99u + 1i
I
u
2
= h−190u
12
+ 1765u
11
+ ··· + 334b + 209, −1291u
12
+ 11918u
11
+ ··· + 167a − 2972,
u
13
− 9u
12
+ 40u
11
− 112u
10
+ 212u
9
− 270u
8
+ 213u
7
− 70u
6
− 43u
5
+ 56u
4
− 13u
3
− 10u
2
+ 3u + 1i
* 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−2.20 × 10
203
u
56
+ 5.66 × 10
203
u
55
+ · · · + 1.13 × 10
204
b − 3.04 ×
10
203
, 1.02 × 10
202
u
56
− 2.55 × 10
202
u
55
+ · · · + 4.35 × 10
202
a − 1.93 ×
10
204
, u
57
− 2u
56
+ · · · + 99u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
−0.233636u
56
+ 0.585272u
55
+ ··· + 376.156u + 44.2914
0.194404u
56
− 0.500246u
55
+ ··· − 3.13746u + 0.269007
a
9
=
−0.0392325u
56
+ 0.0850261u
55
+ ··· + 373.019u + 44.5604
0.194404u
56
− 0.500246u
55
+ ··· − 3.13746u + 0.269007
a
5
=
−0.709204u
56
+ 1.81312u
55
+ ··· + 1.23457u − 20.2316
0.113804u
56
− 0.292360u
55
+ ··· + 60.6616u + 0.512414
a
10
=
−0.206310u
56
+ 0.511643u
55
+ ··· + 375.546u + 44.2848
0.152217u
56
− 0.398947u
55
+ ··· − 12.1241u + 0.176546
a
12
=
−0.211474u
56
+ 0.400072u
55
+ ··· − 355.701u + 11.0408
−0.300940u
56
+ 0.738560u
55
+ ··· − 111.054u − 1.10820
a
3
=
1.16949u
56
− 2.32458u
55
+ ··· + 1535.29u + 14.9071
−0.275037u
56
+ 0.741382u
55
+ ··· + 63.4359u + 0.800985
a
7
=
1.71051u
56
− 3.73781u
55
+ ··· + 1743.01u + 54.3756
−0.170202u
56
+ 0.417387u
55
+ ··· + 3.50097u + 0.427858
a
6
=
1.71051u
56
− 3.73781u
55
+ ··· + 1743.01u + 54.3756
−0.0441047u
56
+ 0.107941u
55
+ ··· + 33.1523u + 0.744645
a
11
=
−0.0330544u
56
− 0.0970298u
55
+ ··· − 433.886u + 25.2387
−0.0307323u
56
+ 0.0397139u
55
+ ··· − 103.215u − 0.950993
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.49472u
56
− 3.47198u
55
+ ··· + 455.723u + 19.2896
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
57
+ 2u
56
+ ··· + 99u − 1
c
2
u
57
+ u
56
+ ··· − 217u + 31
c
3
u
57
+ 2u
56
+ ··· − 3u − 1
c
4
u
57
+ 2u
56
+ ··· − 23u − 19
c
5
, c
10
, c
11
u
57
− u
56
+ ··· + 2u − 1
c
6
u
57
+ 18u
55
+ ··· − 3u − 1
c
7
, c
8
, c
12
u
57
+ u
56
+ ··· − 27u − 9
c
9
u
57
− 2u
56
+ ··· − 15u − 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
57
− 8y
56
+ ··· + 6183y −1
c
2
y
57
+ 45y
56
+ ··· − 77345y −961
c
3
y
57
− 36y
56
+ ··· + 175y −1
c
4
y
57
− 20y
56
+ ··· + 7483y −361
c
5
, c
10
, c
11
y
57
− 43y
56
+ ··· − 26y −1
c
6
y
57
+ 36y
56
+ ··· − 413y −1
c
7
, c
8
, c
12
y
57
− 47y
56
+ ··· − 81y −81
c
9
y
57
− 40y
56
+ ··· + 29903y −361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.982069
a = 0.271580
b = −1.32023
5.72850 18.2470
u = 0.787849 + 0.663146I
a = 0.111327 − 0.249352I
b = −0.079251 − 0.513820I
−1.39291 − 1.49817I 0
u = 0.787849 − 0.663146I
a = 0.111327 + 0.249352I
b = −0.079251 + 0.513820I
−1.39291 + 1.49817I 0
u = 0.029607 + 1.080220I
a = −1.50186 + 0.62457I
b = 1.091320 − 0.039504I
1.80896 − 0.59182I 0
u = 0.029607 − 1.080220I
a = −1.50186 − 0.62457I
b = 1.091320 + 0.039504I
1.80896 + 0.59182I 0
u = 0.882972
a = −1.33547
b = −1.08958
8.40411 7.98810
u = 0.933561 + 0.625124I
a = 0.853667 − 0.081695I
b = −0.474635 − 0.684470I
−0.25852 − 1.69884I 0
u = 0.933561 − 0.625124I
a = 0.853667 + 0.081695I
b = −0.474635 + 0.684470I
−0.25852 + 1.69884I 0
u = 0.403090 + 0.774689I
a = −0.592456 − 0.151652I
b = 0.221654 + 0.904852I
1.91455 − 2.21031I 13.12081 + 2.10550I
u = 0.403090 − 0.774689I
a = −0.592456 + 0.151652I
b = 0.221654 − 0.904852I
1.91455 + 2.21031I 13.12081 − 2.10550I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.133930 + 0.358505I
a = 0.0031594 + 0.0941549I
b = 0.016164 − 0.679191I
−1.85634 − 1.60964I 0
u = 1.133930 − 0.358505I
a = 0.0031594 − 0.0941549I
b = 0.016164 + 0.679191I
−1.85634 + 1.60964I 0
u = −1.183600 + 0.191183I
a = 0.457183 + 0.050936I
b = 0.192168 + 0.919003I
−3.95643 − 2.45863I 0
u = −1.183600 − 0.191183I
a = 0.457183 − 0.050936I
b = 0.192168 − 0.919003I
−3.95643 + 2.45863I 0
u = −1.186880 + 0.423414I
a = −0.286902 + 0.017571I
b = −0.171028 − 1.023880I
−8.10408 + 3.62915I 0
u = −1.186880 − 0.423414I
a = −0.286902 − 0.017571I
b = −0.171028 + 1.023880I
−8.10408 − 3.62915I 0
u = −1.110700 + 0.610435I
a = 0.153762 − 0.058890I
b = 0.164353 + 1.087850I
−3.81501 + 9.61156I 0
u = −1.110700 − 0.610435I
a = 0.153762 + 0.058890I
b = 0.164353 − 1.087850I
−3.81501 − 9.61156I 0
u = −0.294530 + 0.662947I
a = 1.31292 − 1.50192I
b = −1.209010 − 0.204626I
6.60552 + 1.19209I 14.3056 − 1.0519I
u = −0.294530 − 0.662947I
a = 1.31292 + 1.50192I
b = −1.209010 + 0.204626I
6.60552 − 1.19209I 14.3056 + 1.0519I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.721188 + 0.010661I
a = −1.56524 + 0.58708I
b = 0.655013 + 0.306013I
0.254039 + 0.524135I 8.44441 − 3.12759I
u = 0.721188 − 0.010661I
a = −1.56524 − 0.58708I
b = 0.655013 − 0.306013I
0.254039 − 0.524135I 8.44441 + 3.12759I
u = 0.443363 + 1.220500I
a = 0.471429 + 0.461395I
b = −0.130344 + 0.192510I
0.83147 − 4.60750I 0
u = 0.443363 − 1.220500I
a = 0.471429 − 0.461395I
b = −0.130344 − 0.192510I
0.83147 + 4.60750I 0
u = 1.16130 + 0.85091I
a = −1.330120 − 0.083967I
b = 1.371540 − 0.229175I
2.34247 − 1.46589I 0
u = 1.16130 − 0.85091I
a = −1.330120 + 0.083967I
b = 1.371540 + 0.229175I
2.34247 + 1.46589I 0
u = 0.553554
a = 1.08209
b = −1.86480
11.0296 −7.52950
u = −0.482542 + 0.186548I
a = −3.17532 + 1.59578I
b = 1.163130 + 0.461068I
−0.97671 + 7.38058I 7.33354 − 5.78645I
u = −0.482542 − 0.186548I
a = −3.17532 − 1.59578I
b = 1.163130 − 0.461068I
−0.97671 − 7.38058I 7.33354 + 5.78645I
u = 0.76598 + 1.28507I
a = −1.58483 − 0.83064I
b = 1.260720 − 0.166493I
4.98441 − 6.28398I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.76598 − 1.28507I
a = −1.58483 + 0.83064I
b = 1.260720 + 0.166493I
4.98441 + 6.28398I 0
u = −0.481796 + 0.025652I
a = 2.48626 − 1.61462I
b = −1.162050 − 0.579686I
−5.07361 + 1.99676I 3.51787 − 1.41521I
u = −0.481796 − 0.025652I
a = 2.48626 + 1.61462I
b = −1.162050 + 0.579686I
−5.07361 − 1.99676I 3.51787 + 1.41521I
u = −1.52665
a = −0.719721
b = 1.64459
15.0211 0
u = 0.58877 + 1.42087I
a = −1.281560 − 0.148995I
b = 1.269080 − 0.517238I
5.24676 − 7.48865I 0
u = 0.58877 − 1.42087I
a = −1.281560 + 0.148995I
b = 1.269080 + 0.517238I
5.24676 + 7.48865I 0
u = −0.414150 + 0.153678I
a = −1.80595 − 1.43113I
b = 1.192780 − 0.738076I
−0.73053 + 3.35751I 5.35994 − 3.89314I
u = −0.414150 − 0.153678I
a = −1.80595 + 1.43113I
b = 1.192780 + 0.738076I
−0.73053 − 3.35751I 5.35994 + 3.89314I
u = 0.93882 + 1.32829I
a = 1.277810 + 0.317518I
b = −1.218700 + 0.340067I
1.96594 − 4.89349I 0
u = 0.93882 − 1.32829I
a = 1.277810 − 0.317518I
b = −1.218700 − 0.340067I
1.96594 + 4.89349I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.06256 + 1.30003I
a = 1.49425 + 0.25593I
b = −1.284040 + 0.299476I
2.20041 − 5.20017I 0
u = 1.06256 − 1.30003I
a = 1.49425 − 0.25593I
b = −1.284040 − 0.299476I
2.20041 + 5.20017I 0
u = −0.245067
a = −5.94703
b = −0.611130
7.03759 21.9860
u = −1.67017 + 0.65889I
a = 0.966468 − 0.185623I
b = −1.46672 − 0.42530I
1.33651 + 2.42655I 0
u = −1.67017 − 0.65889I
a = 0.966468 + 0.185623I
b = −1.46672 + 0.42530I
1.33651 − 2.42655I 0
u = 1.63108 + 0.83574I
a = −0.514592 − 0.394322I
b = 0.999285 − 0.104423I
0.85956 − 1.26664I 0
u = 1.63108 − 0.83574I
a = −0.514592 + 0.394322I
b = 0.999285 + 0.104423I
0.85956 + 1.26664I 0
u = −1.41187 + 1.18997I
a = 1.215900 − 0.316935I
b = −1.42291 − 0.49714I
1.1499 + 15.2354I 0
u = −1.41187 − 1.18997I
a = 1.215900 + 0.316935I
b = −1.42291 + 0.49714I
1.1499 − 15.2354I 0
u = −1.56697 + 1.00586I
a = −1.115510 + 0.256262I
b = 1.42807 + 0.47889I
−3.07994 + 9.01753I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56697 − 1.00586I
a = −1.115510 − 0.256262I
b = 1.42807 − 0.47889I
−3.07994 − 9.01753I 0
u = −0.0788245
a = 15.9721
b = 1.39717
6.57350 13.9620
u = 1.29095 + 1.44646I
a = 0.894273 + 0.319702I
b = −0.999227 + 0.285270I
1.26758 − 5.50057I 0
u = 1.29095 − 1.44646I
a = 0.894273 − 0.319702I
b = −0.999227 − 0.285270I
1.26758 + 5.50057I 0
u = −0.0129360
a = 39.3944
b = 0.359528
0.705153 14.5050
u = −0.38434 + 1.96202I
a = 1.196960 − 0.374494I
b = −1.165110 + 0.090048I
3.76984 − 4.85515I 0
u = −0.38434 − 1.96202I
a = 1.196960 + 0.374494I
b = −1.165110 − 0.090048I
3.76984 + 4.85515I 0
10
II. I
u
2
= h−190u
12
+ 1765u
11
+ · · · + 334b + 209, −1291u
12
+ 11918u
11
+
· · · + 167a − 2972, u
13
− 9u
12
+ · · · + 3u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
8
=
7.73054u
12
− 71.3653u
11
+ ··· − 2.63473u + 17.7964
0.568862u
12
− 5.28443u
11
+ ··· + 3.78443u − 0.625749
a
9
=
8.29940u
12
− 76.6497u
11
+ ··· + 1.14970u + 17.1707
0.568862u
12
− 5.28443u
11
+ ··· + 3.78443u − 0.625749
a
5
=
12.4760u
12
− 117.988u
11
+ ··· + 18.4880u + 42.8263
1.26946u
12
− 12.1347u
11
+ ··· + 5.63473u + 4.70359
a
10
=
9.36228u
12
− 85.9311u
11
+ ··· − 5.06886u + 19.7515
0.736527u
12
− 6.86826u
11
+ ··· + 1.86826u − 0.910180
a
12
=
−6.97305u
12
+ 64.7365u
11
+ ··· + 0.763473u − 17.1796
2.26946u
12
− 21.1347u
11
+ ··· − 5.36527u + 8.70359
a
3
=
18.1796u
12
− 170.590u
11
+ ··· + 13.0898u + 56.3024
1.97904u
12
− 18.7395u
11
+ ··· + 4.73952u + 5.97305
a
7
=
−2.52395u
12
+ 24.5120u
11
+ ··· − 11.5120u − 7.67365
3.33832u
12
− 30.9192u
11
+ ··· − 10.0808u + 12.5778
a
6
=
−2.52395u
12
+ 24.5120u
11
+ ··· − 11.5120u − 7.67365
3.10778u
12
− 28.5539u
11
+ ··· − 12.9461u + 10.7814
a
11
=
−17.8533u
12
+ 165.677u
11
+ ··· + 9.82335u − 48.3114
−7.58683u
12
+ 69.7934u
11
+ ··· + 10.7066u − 22.2545
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1829
334
u
12
−
8014
167
u
11
+
69353
334
u
10
−
187907
334
u
9
+
169690
167
u
8
−
398167
334
u
7
+
128115
167
u
6
+
5
2
u
5
−
79988
167
u
4
+
128227
334
u
3
−
10968
167
u
2
−
22549
334
u +
4313
167
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
13
− 9u
12
+ ··· + 3u + 1
c
2
u
13
+ 4u
12
+ ··· − 3u − 1
c
3
u
13
− 3u
12
+ ··· − 3u + 1
c
4
u
13
+ u
12
+ ··· + u + 1
c
5
u
13
− 8u
11
+ ··· + 6u + 1
c
6
u
13
− u
12
+ 2u
11
− 2u
9
+ 3u
8
− 4u
7
+ 3u
6
+ 4u
5
− 4u
4
+ u
3
− 3u − 1
c
7
, c
8
u
13
− 8u
11
+ ··· + 3u − 1
c
9
u
13
− u
12
+ ··· + u − 1
c
10
, c
11
u
13
− 8u
11
+ ··· + 6u − 1
c
12
u
13
− 8u
11
+ ··· + 3u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− y
12
+ ··· + 29y −1
c
2
y
13
+ 4y
12
+ ··· + y −1
c
3
y
13
− 9y
12
+ ··· + 13y −1
c
4
y
13
− 13y
12
+ ··· + 9y −1
c
5
, c
10
, c
11
y
13
− 16y
12
+ ··· + 36y −1
c
6
y
13
+ 3y
12
+ ··· + 9y −1
c
7
, c
8
, c
12
y
13
− 16y
12
+ ··· + 5y −1
c
9
y
13
− 9y
12
+ ··· + 13y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.435709 + 0.993312I
a = −0.520595 − 0.029912I
b = 0.654428 + 0.601760I
0.97353 − 3.17072I 9.28444 + 4.13212I
u = 0.435709 − 0.993312I
a = −0.520595 + 0.029912I
b = 0.654428 − 0.601760I
0.97353 + 3.17072I 9.28444 − 4.13212I
u = 1.061160 + 0.495497I
a = 0.732805 − 0.137224I
b = −0.251004 − 0.343068I
−0.770496 − 0.447544I 3.02105 − 1.83729I
u = 1.061160 − 0.495497I
a = 0.732805 + 0.137224I
b = −0.251004 + 0.343068I
−0.770496 + 0.447544I 3.02105 + 1.83729I
u = 0.617945
a = −2.31410
b = −0.498845
6.70177 −2.62380
u = −0.419309
a = 1.25732
b = 1.36971
4.85657 7.56690
u = 1.65121
a = −0.801610
b = 1.66990
14.7388 −2.01490
u = −0.347490
a = −4.66144
b = −1.19869
9.08187 20.5940
u = −0.284103
a = −0.246049
b = −1.84911
11.2546 28.4090
u = 1.58796 + 1.06438I
a = 1.076420 + 0.264698I
b = −1.342970 + 0.254848I
3.10162 − 2.88236I 11.48583 + 3.31049I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58796 − 1.06438I
a = 1.076420 − 0.264698I
b = −1.342970 − 0.254848I
3.10162 + 2.88236I 11.48583 − 3.31049I
u = 0.80605 + 1.83438I
a = −1.40570 − 0.19218I
b = 1.193070 − 0.241401I
2.98736 − 6.12170I 10.74301 + 9.13523I
u = 0.80605 − 1.83438I
a = −1.40570 + 0.19218I
b = 1.193070 + 0.241401I
2.98736 + 6.12170I 10.74301 − 9.13523I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
− 9u
12
+ ··· + 3u + 1)(u
57
+ 2u
56
+ ··· + 99u − 1)
c
2
(u
13
+ 4u
12
+ ··· − 3u − 1)(u
57
+ u
56
+ ··· − 217u + 31)
c
3
(u
13
− 3u
12
+ ··· − 3u + 1)(u
57
+ 2u
56
+ ··· − 3u − 1)
c
4
(u
13
+ u
12
+ ··· + u + 1)(u
57
+ 2u
56
+ ··· − 23u − 19)
c
5
(u
13
− 8u
11
+ ··· + 6u + 1)(u
57
− u
56
+ ··· + 2u − 1)
c
6
(u
13
− u
12
+ 2u
11
− 2u
9
+ 3u
8
− 4u
7
+ 3u
6
+ 4u
5
− 4u
4
+ u
3
− 3u − 1)
· (u
57
+ 18u
55
+ ··· − 3u − 1)
c
7
, c
8
(u
13
− 8u
11
+ ··· + 3u − 1)(u
57
+ u
56
+ ··· − 27u − 9)
c
9
(u
13
− u
12
+ ··· + u − 1)(u
57
− 2u
56
+ ··· − 15u − 19)
c
10
, c
11
(u
13
− 8u
11
+ ··· + 6u − 1)(u
57
− u
56
+ ··· + 2u − 1)
c
12
(u
13
− 8u
11
+ ··· + 3u + 1)(u
57
+ u
56
+ ··· − 27u − 9)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
13
− y
12
+ ··· + 29y −1)(y
57
− 8y
56
+ ··· + 6183y −1)
c
2
(y
13
+ 4y
12
+ ··· + y −1)(y
57
+ 45y
56
+ ··· − 77345y −961)
c
3
(y
13
− 9y
12
+ ··· + 13y −1)(y
57
− 36y
56
+ ··· + 175y −1)
c
4
(y
13
− 13y
12
+ ··· + 9y −1)(y
57
− 20y
56
+ ··· + 7483y −361)
c
5
, c
10
, c
11
(y
13
− 16y
12
+ ··· + 36y −1)(y
57
− 43y
56
+ ··· − 26y −1)
c
6
(y
13
+ 3y
12
+ ··· + 9y −1)(y
57
+ 36y
56
+ ··· − 413y −1)
c
7
, c
8
, c
12
(y
13
− 16y
12
+ ··· + 5y −1)(y
57
− 47y
56
+ ··· − 81y −81)
c
9
(y
13
− 9y
12
+ ··· + 13y −1)(y
57
− 40y
56
+ ··· + 29903y −361)
17
