12a
0176
(K12a
0176
)
A knot diagram
1
Linearized knot diagam
3 5 9 6 2 10 12 11 4 1 8 7
Solving Sequence
2,5
3
6,10
7 1 11 4 9 8 12
c
2
c
5
c
6
c
1
c
10
c
4
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h93u
72
− 418u
71
+ ··· + 8b − 68, −11u
72
+ 5u
71
+ ··· + 8a − 35, u
73
− 5u
72
+ ··· − 7u + 1i
I
u
2
= h−au + b − a, a
4
− a
3
u − a
2
u − a
2
+ u, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 81 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
= h93u
72
− 418u
71
+ · · · + 8b − 68, −11u
72
+ 5u
71
+ · · · + 8a −
35, u
73
− 5u
72
+ · · · − 7u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
−u
2
a
6
=
u
u
a
10
=
11
8
u
72
−
5
8
u
71
+ ··· −
269
8
u +
35
8
−11.6250u
72
+ 52.2500u
71
+ ··· − 60.3750u + 8.50000
a
7
=
−
1
8
u
72
+
1
2
u
71
+ ··· −
1
8
u − 1
−
1
8
u
71
+
1
2
u
70
+ ··· +
11
4
u −
1
8
a
1
=
u
2
+ 1
−u
4
a
11
=
11
2
u
72
+ 4u
71
+ ··· −
229
2
u +
37
2
−26.5000u
72
+ 137.875u
71
+ ··· − 219.250u + 33.6250
a
4
=
u
3
u
3
+ u
a
9
=
3.37500u
72
+ 8.12500u
71
+ ··· − 101.625u + 16.1250
−23.8750u
72
+ 120.500u
71
+ ··· − 179.625u + 27.2500
a
8
=
−1.37500u
72
+ 16.1250u
71
+ ··· − 58.8750u + 8.62500
−
101
8
u
72
+
243
4
u
71
+ ··· −
677
8
u + 13
a
12
=
7
4
u
72
−
37
4
u
71
+ ··· +
37
2
u −
3
2
21
8
u
72
−
89
8
u
71
+ ··· +
63
8
u −
7
8
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
139
8
u
72
+
339
4
u
71
+ ··· −
861
8
u +
73
4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
73
+ 23u
72
+ ··· − 7u − 1
c
2
, c
5
u
73
+ 5u
72
+ ··· − 7u − 1
c
3
, c
9
u
73
+ u
72
+ ··· − 384u − 256
c
6
u
73
− 3u
72
+ ··· + 1455u − 1009
c
7
, c
8
, c
11
c
12
u
73
− 3u
72
+ ··· + 5u − 1
c
10
u
73
+ 21u
72
+ ··· + 34585u + 3971
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
73
+ 59y
72
+ ··· − 779y −1
c
2
, c
5
y
73
+ 23y
72
+ ··· − 7y −1
c
3
, c
9
y
73
− 45y
72
+ ··· + 638976y −65536
c
6
y
73
− 39y
72
+ ··· − 96349267y −1018081
c
7
, c
8
, c
11
c
12
y
73
+ 85y
72
+ ··· − 11y −1
c
10
y
73
− 19y
72
+ ··· + 205103581y −15768841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.061031 + 0.988224I
a = 0.443695 − 0.459047I
b = −0.724621 − 0.580258I
3.27771 − 2.37789I 0
u = −0.061031 − 0.988224I
a = 0.443695 + 0.459047I
b = −0.724621 + 0.580258I
3.27771 + 2.37789I 0
u = −0.225938 + 1.037910I
a = 0.166934 − 0.176912I
b = 0.821680 + 0.445687I
−1.40695 − 2.98844I 0
u = −0.225938 − 1.037910I
a = 0.166934 + 0.176912I
b = 0.821680 − 0.445687I
−1.40695 + 2.98844I 0
u = −0.518783 + 0.940844I
a = 0.323471 + 0.705744I
b = 0.015920 + 0.894645I
−0.10046 − 2.66980I 0
u = −0.518783 − 0.940844I
a = 0.323471 − 0.705744I
b = 0.015920 − 0.894645I
−0.10046 + 2.66980I 0
u = 0.715152 + 0.803648I
a = 1.139520 + 0.387119I
b = 0.640803 − 1.009380I
8.18684 − 1.63882I 0
u = 0.715152 − 0.803648I
a = 1.139520 − 0.387119I
b = 0.640803 + 1.009380I
8.18684 + 1.63882I 0
u = −0.373664 + 1.042010I
a = −0.819992 − 0.035159I
b = −0.890346 − 0.754074I
1.042010 − 0.690934I 0
u = −0.373664 − 1.042010I
a = −0.819992 + 0.035159I
b = −0.890346 + 0.754074I
1.042010 + 0.690934I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.717261 + 0.854752I
a = −0.819762 + 0.064738I
b = −0.019915 + 1.100780I
1.69272 + 0.80380I 0
u = 0.717261 − 0.854752I
a = −0.819762 − 0.064738I
b = −0.019915 − 1.100780I
1.69272 − 0.80380I 0
u = −0.751631 + 0.827950I
a = 1.75700 − 1.36118I
b = 2.26394 − 0.53802I
3.44600 + 0.21774I 0
u = −0.751631 − 0.827950I
a = 1.75700 + 1.36118I
b = 2.26394 + 0.53802I
3.44600 − 0.21774I 0
u = −0.703331 + 0.876144I
a = −1.12934 + 1.54579I
b = −1.74415 + 1.00598I
1.23434 − 2.69793I 0
u = −0.703331 − 0.876144I
a = −1.12934 − 1.54579I
b = −1.74415 − 1.00598I
1.23434 + 2.69793I 0
u = −0.231481 + 1.101900I
a = −0.179153 + 0.561689I
b = −0.892539 − 0.338296I
0.16539 − 6.33155I 0
u = −0.231481 − 1.101900I
a = −0.179153 − 0.561689I
b = −0.892539 + 0.338296I
0.16539 + 6.33155I 0
u = 0.854843 + 0.737463I
a = −0.97759 − 1.56121I
b = −1.53845 − 0.36332I
5.77476 − 2.35899I 0
u = 0.854843 − 0.737463I
a = −0.97759 + 1.56121I
b = −1.53845 + 0.36332I
5.77476 + 2.35899I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877139 + 0.718077I
a = 1.13328 + 1.73513I
b = 1.86444 + 0.47628I
7.65392 − 6.17000I 0
u = 0.877139 − 0.718077I
a = 1.13328 − 1.73513I
b = 1.86444 − 0.47628I
7.65392 + 6.17000I 0
u = −0.011705 + 0.860688I
a = −0.052223 + 0.967136I
b = 0.932645 + 0.558548I
−2.42316 − 0.99351I −5.92732 + 3.87741I
u = −0.011705 − 0.860688I
a = −0.052223 − 0.967136I
b = 0.932645 − 0.558548I
−2.42316 + 0.99351I −5.92732 − 3.87741I
u = −0.789311 + 0.824660I
a = −2.12466 + 1.44766I
b = −2.66983 + 0.45270I
11.52080 + 2.07129I 0
u = −0.789311 − 0.824660I
a = −2.12466 − 1.44766I
b = −2.66983 − 0.45270I
11.52080 − 2.07129I 0
u = 0.897183 + 0.709153I
a = −1.23173 − 1.88439I
b = −2.09388 − 0.61056I
15.7401 − 8.6060I 0
u = 0.897183 − 0.709153I
a = −1.23173 + 1.88439I
b = −2.09388 + 0.61056I
15.7401 + 8.6060I 0
u = 0.715229 + 0.893228I
a = 0.536474 − 0.487123I
b = −0.499667 − 1.216460I
1.57244 + 4.67543I 0
u = 0.715229 − 0.893228I
a = 0.536474 + 0.487123I
b = −0.499667 + 1.216460I
1.57244 − 4.67543I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.858736 + 0.779751I
a = 0.60446 + 1.54193I
b = 1.076970 + 0.610092I
8.88013 + 0.82331I 0
u = 0.858736 − 0.779751I
a = 0.60446 − 1.54193I
b = 1.076970 − 0.610092I
8.88013 − 0.82331I 0
u = −0.587723 + 1.000390I
a = −0.51702 − 1.42783I
b = 0.17444 − 1.64638I
6.38689 − 3.34175I 0
u = −0.587723 − 1.000390I
a = −0.51702 + 1.42783I
b = 0.17444 + 1.64638I
6.38689 + 3.34175I 0
u = −0.236324 + 1.136820I
a = 0.216812 − 0.826663I
b = 0.952968 + 0.243595I
8.01784 − 8.50189I 0
u = −0.236324 − 1.136820I
a = 0.216812 + 0.826663I
b = 0.952968 − 0.243595I
8.01784 + 8.50189I 0
u = −0.642269 + 0.533189I
a = 1.44113 + 0.31196I
b = 0.909868 + 0.853465I
7.73992 − 1.45409I 7.03228 + 2.97950I
u = −0.642269 − 0.533189I
a = 1.44113 − 0.31196I
b = 0.909868 − 0.853465I
7.73992 + 1.45409I 7.03228 − 2.97950I
u = −0.386720 + 1.102060I
a = 1.151370 − 0.153712I
b = 1.145290 + 0.823796I
8.94434 + 0.93346I 0
u = −0.386720 − 1.102060I
a = 1.151370 + 0.153712I
b = 1.145290 − 0.823796I
8.94434 − 0.93346I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.161589 + 0.815556I
a = 0.08027 + 1.73701I
b = 1.38565 + 0.62057I
5.75319 + 4.41448I 0.071981 − 1.204152I
u = 0.161589 − 0.815556I
a = 0.08027 − 1.73701I
b = 1.38565 − 0.62057I
5.75319 − 4.41448I 0.071981 + 1.204152I
u = 0.709045 + 0.936655I
a = −0.200425 + 1.044420I
b = 1.10352 + 1.40660I
7.77191 + 7.10200I 0
u = 0.709045 − 0.936655I
a = −0.200425 − 1.044420I
b = 1.10352 − 1.40660I
7.77191 − 7.10200I 0
u = 0.085563 + 0.820766I
a = −0.030152 − 1.397210I
b = −1.154110 − 0.576548I
−1.57706 + 2.30309I −2.80955 − 3.48929I
u = 0.085563 − 0.820766I
a = −0.030152 + 1.397210I
b = −1.154110 + 0.576548I
−1.57706 − 2.30309I −2.80955 + 3.48929I
u = −0.736971 + 0.917281I
a = 1.16448 − 2.10961I
b = 2.02664 − 1.52743I
3.17218 − 5.86940I 0
u = −0.736971 − 0.917281I
a = 1.16448 + 2.10961I
b = 2.02664 + 1.52743I
3.17218 + 5.86940I 0
u = −0.810712 + 0.097990I
a = −0.550183 − 0.371106I
b = 1.117360 − 0.604474I
12.19710 − 5.07416I 9.95336 + 3.32776I
u = −0.810712 − 0.097990I
a = −0.550183 + 0.371106I
b = 1.117360 + 0.604474I
12.19710 + 5.07416I 9.95336 − 3.32776I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.885484 + 0.802555I
a = −0.31616 − 1.77942I
b = −0.904553 − 1.071020I
17.5514 + 2.3531I 0
u = 0.885484 − 0.802555I
a = −0.31616 + 1.77942I
b = −0.904553 + 1.071020I
17.5514 − 2.3531I 0
u = −0.440972 + 0.666613I
a = −0.915006 − 0.235271I
b = −0.765196 − 0.346372I
0.70719 − 1.37392I 6.54862 + 4.55339I
u = −0.440972 − 0.666613I
a = −0.915006 + 0.235271I
b = −0.765196 + 0.346372I
0.70719 + 1.37392I 6.54862 − 4.55339I
u = −0.760835 + 0.932568I
a = −1.29393 + 2.43000I
b = −2.28636 + 1.77924I
11.18770 − 7.91039I 0
u = −0.760835 − 0.932568I
a = −1.29393 − 2.43000I
b = −2.28636 − 1.77924I
11.18770 + 7.91039I 0
u = −0.753565 + 0.082487I
a = 0.721227 + 0.258241I
b = −0.834537 + 0.418462I
4.10320 − 3.11301I 8.46380 + 5.00455I
u = −0.753565 − 0.082487I
a = 0.721227 − 0.258241I
b = −0.834537 − 0.418462I
4.10320 + 3.11301I 8.46380 − 5.00455I
u = 0.782341 + 0.985456I
a = 1.20777 + 0.80647I
b = 2.05755 + 0.44861I
8.23968 + 5.28180I 0
u = 0.782341 − 0.985456I
a = 1.20777 − 0.80647I
b = 2.05755 − 0.44861I
8.23968 − 5.28180I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.761516 + 1.008750I
a = −1.23045 − 1.35600I
b = −2.34331 − 0.87664I
4.93630 + 8.38429I 0
u = 0.761516 − 1.008750I
a = −1.23045 + 1.35600I
b = −2.34331 + 0.87664I
4.93630 − 8.38429I 0
u = 0.811502 + 0.986113I
a = −1.56384 − 0.43043I
b = −2.16930 + 0.04197I
16.9773 + 3.9268I 0
u = 0.811502 − 0.986113I
a = −1.56384 + 0.43043I
b = −2.16930 − 0.04197I
16.9773 − 3.9268I 0
u = 0.764032 + 1.027340I
a = 1.48760 + 1.57665I
b = 2.64607 + 0.93109I
6.69651 + 12.26470I 0
u = 0.764032 − 1.027340I
a = 1.48760 − 1.57665I
b = 2.64607 − 0.93109I
6.69651 − 12.26470I 0
u = 0.768706 + 1.040500I
a = −1.71369 − 1.70604I
b = −2.88056 − 0.93363I
14.7102 + 14.7725I 0
u = 0.768706 − 1.040500I
a = −1.71369 + 1.70604I
b = −2.88056 + 0.93363I
14.7102 − 14.7725I 0
u = −0.677649
a = −0.901471
b = 0.554098
1.96978 4.04310
u = 0.324856 + 0.303719I
a = 0.84450 + 1.41509I
b = 0.866089 − 0.815927I
7.15764 − 2.51422I 4.29524 + 3.51135I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.324856 − 0.303719I
a = 0.84450 − 1.41509I
b = 0.866089 + 0.815927I
7.15764 + 2.51422I 4.29524 − 3.51135I
u = 0.171616 + 0.146966I
a = −0.80395 − 1.95618I
b = −0.367565 + 0.544328I
0.038818 − 1.169610I 0.66472 + 6.00737I
u = 0.171616 − 0.146966I
a = −0.80395 + 1.95618I
b = −0.367565 − 0.544328I
0.038818 + 1.169610I 0.66472 − 6.00737I
12
II. I
u
2
= h−au + b − a, a
4
− a
3
u − a
2
u − a
2
+ u, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u + 1
a
6
=
u
u
a
10
=
a
au + a
a
7
=
a
2
u + a
2
+ u
a
2
u + u
a
1
=
−u
−u
a
11
=
2a
au + 2a
a
4
=
1
u + 1
a
9
=
a
au + a
a
8
=
2a
3
u + a
a
3
u − a
3
+ au + a
a
12
=
a
3
u + 2a
2
u + 2a
2
− 2u
−a
3
+ 2a
2
u + a
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5a
2
u − 2a
2
− 4au − 5a + 5u + 2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
3
, c
9
u
8
c
6
, c
10
(u
4
− u
3
+ u
2
+ 1)
2
c
7
, c
8
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
11
, c
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
4
c
3
, c
9
y
8
c
6
, c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
7
, c
8
, c
11
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.447930 − 0.664845I
b = 0.351808 − 0.720342I
−0.21101 − 3.44499I 0.99907 + 9.21934I
u = −0.500000 + 0.866025I
a = 0.799738 + 0.055496I
b = 0.351808 + 0.720342I
−0.211005 − 0.614778I −2.00436 − 1.31849I
u = −0.500000 + 0.866025I
a = 0.363298 + 1.193330I
b = −0.851808 + 0.911292I
6.79074 − 5.19385I 5.65243 + 5.51994I
u = −0.500000 + 0.866025I
a = −1.215110 + 0.282041I
b = −0.851808 − 0.911292I
6.79074 + 1.13408I 1.85285 + 1.30164I
u = −0.500000 − 0.866025I
a = −0.447930 + 0.664845I
b = 0.351808 + 0.720342I
−0.21101 + 3.44499I 0.99907 − 9.21934I
u = −0.500000 − 0.866025I
a = 0.799738 − 0.055496I
b = 0.351808 − 0.720342I
−0.211005 + 0.614778I −2.00436 + 1.31849I
u = −0.500000 − 0.866025I
a = 0.363298 − 1.193330I
b = −0.851808 − 0.911292I
6.79074 + 5.19385I 5.65243 − 5.51994I
u = −0.500000 − 0.866025I
a = −1.215110 − 0.282041I
b = −0.851808 + 0.911292I
6.79074 − 1.13408I 1.85285 − 1.30164I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
((u
2
− u + 1)
4
)(u
73
+ 23u
72
+ ··· − 7u − 1)
c
2
((u
2
+ u + 1)
4
)(u
73
+ 5u
72
+ ··· − 7u − 1)
c
3
, c
9
u
8
(u
73
+ u
72
+ ··· − 384u − 256)
c
5
((u
2
− u + 1)
4
)(u
73
+ 5u
72
+ ··· − 7u − 1)
c
6
((u
4
− u
3
+ u
2
+ 1)
2
)(u
73
− 3u
72
+ ··· + 1455u − 1009)
c
7
, c
8
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
73
− 3u
72
+ ··· + 5u − 1)
c
10
((u
4
− u
3
+ u
2
+ 1)
2
)(u
73
+ 21u
72
+ ··· + 34585u + 3971)
c
11
, c
12
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
)(u
73
− 3u
72
+ ··· + 5u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
4
)(y
73
+ 59y
72
+ ··· − 779y −1)
c
2
, c
5
((y
2
+ y + 1)
4
)(y
73
+ 23y
72
+ ··· − 7y −1)
c
3
, c
9
y
8
(y
73
− 45y
72
+ ··· + 638976y −65536)
c
6
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
· (y
73
− 39y
72
+ ··· − 96349267y −1018081)
c
7
, c
8
, c
11
c
12
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
73
+ 85y
72
+ ··· − 11y −1)
c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
· (y
73
− 19y
72
+ ··· + 205103581y −15768841)
18
