12n
0422
(K12n
0422
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 10 2 9 3 12 1 9 5
Solving Sequence
3,8 4,11
5 9 12 10 6 1 2 7
c
3
c
4
c
8
c
11
c
9
c
5
c
12
c
2
c
6
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.28749 × 10
71
u
53
− 2.33614 × 10
73
u
52
+ ··· + 3.81141 × 10
75
b + 2.99444 × 10
75
,
− 5.98664 × 10
75
u
53
+ 1.19971 × 10
76
u
52
+ ··· + 6.47940 × 10
76
a + 3.22020 × 10
76
,
u
54
− 2u
53
+ ··· − 112u + 17i
I
u
2
= h−58u
17
− 4u
16
+ ··· + 69b − 127u, 4u
16
− 58u
15
+ ··· + 69a − 220, u
18
+ 6u
16
+ ··· + 3u + 1i
I
u
3
= h−4a
4
u + 18a
3
u + 16a
3
+ 9a
2
u − 54a
2
− 52au + 5b + 19a + 13u + 16,
a
5
+ 5a
4
u − 5a
4
− 20a
3
u − 4a
3
+ 8a
2
u + 27a
2
+ 14au − 12a − 4u − 3, u
2
+ 1i
I
u
4
= h−u
3
− 2u
2
+ 4b − 3u − 3, −3u
3
− 2u
2
+ 4a − u + 3, u
4
+ u
3
+ u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 86 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−8.29 × 10
71
u
53
− 2.34 × 10
73
u
52
+ · · · + 3.81 × 10
75
b + 2.99 ×
10
75
, −5.99 × 10
75
u
53
+ 1.20 × 10
76
u
52
+ · · · + 6.48 × 10
76
a + 3.22 ×
10
76
, u
54
− 2u
53
+ · · · − 112u + 17i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
0.0923949u
53
− 0.185157u
52
+ ··· + 40.8873u − 0.496990
0.000217439u
53
+ 0.00612933u
52
+ ··· − 0.304074u − 0.785651
a
5
=
0.0305442u
53
− 0.0451577u
52
+ ··· + 24.5663u − 1.15616
−0.0138523u
53
+ 0.00619132u
52
+ ··· − 0.901321u − 0.406547
a
9
=
−u
u
a
12
=
0.0985707u
53
− 0.190389u
52
+ ··· + 41.7676u − 0.391645
−0.00595836u
53
+ 0.0113616u
52
+ ··· − 1.18445u − 0.890996
a
10
=
−0.0179807u
53
+ 0.0629584u
52
+ ··· − 19.1557u + 6.53660
0.0110158u
53
− 0.0169178u
52
+ ··· + 5.55246u − 1.06284
a
6
=
0.0249321u
53
− 0.0384523u
52
+ ··· + 38.2889u − 5.30849
−0.0248738u
53
+ 0.0481071u
52
+ ··· − 11.7942u + 1.11363
a
1
=
0.0752792u
53
− 0.116667u
52
+ ··· + 7.64721u + 4.45628
−0.00164042u
53
+ 0.00683312u
52
+ ··· − 1.67223u − 0.577146
a
2
=
0.0769197u
53
− 0.123500u
52
+ ··· + 9.31944u + 5.03343
−0.00164042u
53
+ 0.00683312u
52
+ ··· − 1.67223u − 0.577146
a
7
=
u
3
−u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0961909u
53
+ 0.214297u
52
+ ··· − 61.1959u − 0.495059
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
54
+ 20u
53
+ ··· + 15886u + 289
c
2
, c
6
u
54
− 2u
53
+ ··· − 20u + 17
c
3
, c
8
u
54
− 2u
53
+ ··· − 112u + 17
c
4
2(2u
54
− 3u
53
+ ··· + 26787u + 17894)
c
5
2(2u
54
− 11u
53
+ ··· − 27633u + 3982)
c
7
u
54
− 60u
53
+ ··· − 17614u + 289
c
9
, c
11
u
54
− 4u
53
+ ··· − 481u + 16
c
10
u
54
+ 8u
53
+ ··· + 2976u + 256
c
12
u
54
+ 7u
53
+ ··· + 8u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
+ 40y
53
+ ··· − 35600546y + 83521
c
2
, c
6
y
54
+ 20y
53
+ ··· + 15886y + 289
c
3
, c
8
y
54
+ 60y
53
+ ··· + 17614y + 289
c
4
4(4y
54
− 205y
53
+ ··· + 5.53025 × 10
9
y + 3.20195 × 10
8
)
c
5
4(4y
54
− 173y
53
+ ··· + 1.70212 × 10
8
y + 1.58563 × 10
7
)
c
7
y
54
− 120y
53
+ ··· − 34842354y + 83521
c
9
, c
11
y
54
− 32y
53
+ ··· − 95457y + 256
c
10
y
54
− 12y
53
+ ··· − 1545216y + 65536
c
12
y
54
+ 17y
53
+ ··· + 152y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957433 + 0.281564I
a = −0.006064 + 0.203861I
b = −0.977124 − 0.024450I
−0.08167 + 4.27758I 0. − 6.47467I
u = −0.957433 − 0.281564I
a = −0.006064 − 0.203861I
b = −0.977124 + 0.024450I
−0.08167 − 4.27758I 0. + 6.47467I
u = 0.793853 + 0.517771I
a = −0.306183 − 1.163520I
b = −0.116628 + 0.088009I
1.69843 − 5.87991I 0.83203 + 7.69197I
u = 0.793853 − 0.517771I
a = −0.306183 + 1.163520I
b = −0.116628 − 0.088009I
1.69843 + 5.87991I 0.83203 − 7.69197I
u = 1.013690 + 0.409819I
a = 0.220672 + 0.502762I
b = 1.064360 − 0.405958I
−1.51017 − 11.89510I 0. + 8.55352I
u = 1.013690 − 0.409819I
a = 0.220672 − 0.502762I
b = 1.064360 + 0.405958I
−1.51017 + 11.89510I 0. − 8.55352I
u = 0.037687 + 0.876774I
a = 0.136169 − 0.748261I
b = 0.550636 + 0.960686I
1.21558 + 1.50306I 6.28567 − 3.87694I
u = 0.037687 − 0.876774I
a = 0.136169 + 0.748261I
b = 0.550636 − 0.960686I
1.21558 − 1.50306I 6.28567 + 3.87694I
u = 0.001197 + 1.155080I
a = 0.039928 − 0.931322I
b = −0.218113 − 0.358208I
−4.74660 + 4.32144I 0
u = 0.001197 − 1.155080I
a = 0.039928 + 0.931322I
b = −0.218113 + 0.358208I
−4.74660 − 4.32144I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904014 + 0.749313I
a = −0.058317 − 0.639795I
b = −0.223581 − 0.049635I
0.351082 + 0.581835I 0
u = −0.904014 − 0.749313I
a = −0.058317 + 0.639795I
b = −0.223581 + 0.049635I
0.351082 − 0.581835I 0
u = −0.409754 + 0.654267I
a = 0.291468 − 0.544174I
b = −0.353183 + 0.474337I
0.11724 + 1.46636I 1.51920 − 4.74355I
u = −0.409754 − 0.654267I
a = 0.291468 + 0.544174I
b = −0.353183 − 0.474337I
0.11724 − 1.46636I 1.51920 + 4.74355I
u = 0.897207 + 0.878746I
a = 0.058361 − 0.299184I
b = 0.522375 − 0.201536I
−8.36051 − 3.29219I 0
u = 0.897207 − 0.878746I
a = 0.058361 + 0.299184I
b = 0.522375 + 0.201536I
−8.36051 + 3.29219I 0
u = 0.611149 + 0.347151I
a = −1.294480 + 0.114710I
b = −0.647792 − 0.170688I
−3.32384 − 4.22762I −7.57484 + 8.95989I
u = 0.611149 − 0.347151I
a = −1.294480 − 0.114710I
b = −0.647792 + 0.170688I
−3.32384 + 4.22762I −7.57484 − 8.95989I
u = −0.483135 + 0.456682I
a = −1.53675 + 0.04736I
b = 2.67924 + 0.85527I
−1.86209 + 1.74879I −7.3853 + 15.6719I
u = −0.483135 − 0.456682I
a = −1.53675 − 0.04736I
b = 2.67924 − 0.85527I
−1.86209 − 1.74879I −7.3853 − 15.6719I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.246711 + 0.521269I
a = 2.44870 + 1.79272I
b = −1.76240 − 0.40967I
−1.60277 + 1.13073I −16.4890 − 3.6045I
u = −0.246711 − 0.521269I
a = 2.44870 − 1.79272I
b = −1.76240 + 0.40967I
−1.60277 − 1.13073I −16.4890 + 3.6045I
u = 0.10747 + 1.43757I
a = 0.102943 + 0.232479I
b = −0.094147 + 1.058770I
1.12918 − 2.68232I 0
u = 0.10747 − 1.43757I
a = 0.102943 − 0.232479I
b = −0.094147 − 1.058770I
1.12918 + 2.68232I 0
u = −0.00780 + 1.45535I
a = −1.192260 − 0.326002I
b = 1.97371 + 1.02164I
3.51163 + 1.45830I 0
u = −0.00780 − 1.45535I
a = −1.192260 + 0.326002I
b = 1.97371 − 1.02164I
3.51163 − 1.45830I 0
u = 0.19633 + 1.47266I
a = 1.48406 − 0.07567I
b = −2.29341 + 0.86754I
2.64331 − 7.12189I 0
u = 0.19633 − 1.47266I
a = 1.48406 + 0.07567I
b = −2.29341 − 0.86754I
2.64331 + 7.12189I 0
u = −0.04819 + 1.51041I
a = 2.12814 + 0.24940I
b = −2.35877 + 0.37102I
5.05765 + 2.00436I 0
u = −0.04819 − 1.51041I
a = 2.12814 − 0.24940I
b = −2.35877 − 0.37102I
5.05765 − 2.00436I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14469 + 1.50993I
a = −2.37791 + 0.99739I
b = 2.62830 − 0.29767I
4.66611 + 3.99543I 0
u = −0.14469 − 1.50993I
a = −2.37791 − 0.99739I
b = 2.62830 + 0.29767I
4.66611 − 3.99543I 0
u = 0.416507 + 0.239610I
a = −1.55874 + 2.96139I
b = −0.873187 − 1.078590I
−4.35238 − 0.88122I −11.36984 + 2.33709I
u = 0.416507 − 0.239610I
a = −1.55874 − 2.96139I
b = −0.873187 + 1.078590I
−4.35238 + 0.88122I −11.36984 − 2.33709I
u = 0.076348 + 0.449359I
a = 0.72833 − 2.03428I
b = 0.287091 − 0.797176I
−7.12845 − 4.50045I −11.43251 + 4.54345I
u = 0.076348 − 0.449359I
a = 0.72833 + 2.03428I
b = 0.287091 + 0.797176I
−7.12845 + 4.50045I −11.43251 − 4.54345I
u = −0.40434 + 1.49345I
a = 1.322190 − 0.362322I
b = −1.84535 − 0.27981I
5.61605 + 9.26553I 0
u = −0.40434 − 1.49345I
a = 1.322190 + 0.362322I
b = −1.84535 + 0.27981I
5.61605 − 9.26553I 0
u = 0.30238 + 1.53005I
a = −1.301220 − 0.393687I
b = 1.85609 − 0.14113I
8.31392 − 2.90879I 0
u = 0.30238 − 1.53005I
a = −1.301220 + 0.393687I
b = 1.85609 + 0.14113I
8.31392 + 2.90879I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27909 + 1.54859I
a = 1.298040 + 0.169903I
b = −2.14228 − 0.45801I
8.47521 − 9.84153I 0
u = 0.27909 − 1.54859I
a = 1.298040 − 0.169903I
b = −2.14228 + 0.45801I
8.47521 + 9.84153I 0
u = 0.39619 + 1.53466I
a = −1.76073 − 0.05353I
b = 2.40677 − 0.68198I
4.7262 − 17.0140I 0
u = 0.39619 − 1.53466I
a = −1.76073 + 0.05353I
b = 2.40677 + 0.68198I
4.7262 + 17.0140I 0
u = −0.13238 + 1.58588I
a = −1.380160 − 0.026218I
b = 2.15283 − 0.30201I
10.02230 + 3.29278I 0
u = −0.13238 − 1.58588I
a = −1.380160 + 0.026218I
b = 2.15283 + 0.30201I
10.02230 − 3.29278I 0
u = −0.23845 + 1.60519I
a = −0.816814 − 0.178396I
b = 1.219210 − 0.053943I
8.27340 + 4.54754I 0
u = −0.23845 − 1.60519I
a = −0.816814 + 0.178396I
b = 1.219210 + 0.053943I
8.27340 − 4.54754I 0
u = −0.30330 + 1.60247I
a = 1.55917 + 0.09890I
b = −2.15065 − 0.77492I
7.29392 + 10.27410I 0
u = −0.30330 − 1.60247I
a = 1.55917 − 0.09890I
b = −2.15065 + 0.77492I
7.29392 − 10.27410I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.09043 + 1.66784I
a = 0.873862 + 0.020648I
b = −1.291800 − 0.398267I
9.44818 + 2.46020I 0
u = 0.09043 − 1.66784I
a = 0.873862 − 0.020648I
b = −1.291800 + 0.398267I
9.44818 − 2.46020I 0
u = 0.060670 + 0.183744I
a = 2.84612 + 3.51731I
b = −0.617177 − 0.303114I
−1.88776 + 1.50114I −7.21238 − 4.30156I
u = 0.060670 − 0.183744I
a = 2.84612 − 3.51731I
b = −0.617177 + 0.303114I
−1.88776 − 1.50114I −7.21238 + 4.30156I
10
II. I
u
2
= h−58u
17
− 4u
16
+ · · · + 69b − 127u, 4u
16
− 58u
15
+ · · · + 69a −
220, u
18
+ 6u
16
+ · · · + 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
−0.0579710u
16
+ 0.840580u
15
+ ··· + 2.49275u + 3.18841
0.840580u
17
+ 0.0579710u
16
+ ··· + 2.52174u
2
+ 1.84058u
a
5
=
0.594203u
16
− 0.173913u
15
+ ··· − 1.88406u + 2.47826
−0.173913u
17
− 0.594203u
16
+ ··· − 1.18841u
2
− 0.115942u
a
9
=
−u
u
a
12
=
0.840580u
15
+ 4.20290u
13
+ ··· + 3.33333u + 3.18841
0.840580u
17
+ 4.20290u
15
+ ··· + 3.18841u
2
+ u
a
10
=
−0.0579710u
16
+ 0.637681u
15
+ ··· + 0.826087u + 3.24638
0.637681u
17
+ 0.0579710u
16
+ ··· + 2.57971u
2
+ 1.84058u
a
6
=
u
−u
a
1
=
1
u
2
a
2
=
−u
2
+ 1
u
2
a
7
=
u
3
−u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
20
23
u
15
−
100
23
u
13
−
44
23
u
12
−
200
23
u
11
−
176
23
u
10
−
316
23
u
9
−
264
23
u
8
−
448
23
u
7
−
260
23
u
6
− 16u
5
−
212
23
u
4
−
208
23
u
3
−
84
23
u
2
− 4u −
106
23
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 12u
17
+ ··· + 3u + 1
c
2
, c
3
, c
6
c
8
u
18
+ 6u
16
+ ··· + 3u + 1
c
4
, c
10
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
3
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
c
7
u
18
− 12u
17
+ ··· − 3u + 1
c
9
, c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
c
12
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
3
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
18
− 12y
17
+ ··· + 95y + 1
c
2
, c
3
, c
6
c
8
y
18
+ 12y
17
+ ··· + 3y + 1
c
4
, c
9
, c
10
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
c
5
, c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.577722 + 0.852843I
a = 0.419544 − 0.969814I
b = −0.118598 + 0.263815I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = −0.577722 − 0.852843I
a = 0.419544 + 0.969814I
b = −0.118598 − 0.263815I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 0.196160 + 0.885066I
a = 1.60482 − 0.28185I
b = −1.52575 + 1.43171I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = 0.196160 − 0.885066I
a = 1.60482 + 0.28185I
b = −1.52575 − 1.43171I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −0.945163 + 0.610473I
a = −0.143905 + 0.192004I
b = −0.927303 − 0.292719I
5.69302I 0. − 5.51057I
u = −0.945163 − 0.610473I
a = −0.143905 − 0.192004I
b = −0.927303 + 0.292719I
− 5.69302I 0. + 5.51057I
u = 0.090472 + 1.133120I
a = 2.41289 − 3.72770I
b = −2.74223 + 4.58587I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = 0.090472 − 1.133120I
a = 2.41289 + 3.72770I
b = −2.74223 − 4.58587I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = 0.686633 + 0.502578I
a = −0.0705976 + 0.0706558I
b = 0.937976 + 0.262282I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.686633 − 0.502578I
a = −0.0705976 − 0.0706558I
b = 0.937976 − 0.262282I
1.89061 − 0.92430I 3.71672 + 0.79423I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.824262 + 0.925280I
a = 0.162842 − 0.773386I
b = 0.076951 − 0.173677I
5.69302I 0. − 5.51057I
u = 0.824262 − 0.925280I
a = 0.162842 + 0.773386I
b = 0.076951 + 0.173677I
− 5.69302I 0. + 5.51057I
u = −0.108911 + 1.355420I
a = 1.61896 − 0.60431I
b = −2.13131 + 0.32954I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = −0.108911 − 1.355420I
a = 1.61896 + 0.60431I
b = −2.13131 − 0.32954I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.12090 + 1.53575I
a = −1.264280 + 0.562374I
b = 1.68058 − 1.22890I
− 5.69302I 0. + 5.51057I
u = 0.12090 − 1.53575I
a = −1.264280 − 0.562374I
b = 1.68058 + 1.22890I
5.69302I 0. − 5.51057I
u = −0.286632 + 0.248050I
a = 2.75973 + 0.85089I
b = −0.250316 + 0.289655I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.286632 − 0.248050I
a = 2.75973 − 0.85089I
b = −0.250316 − 0.289655I
−1.89061 − 0.92430I −3.71672 + 0.79423I
15
III.
I
u
3
= h−4a
4
u + 18a
3
u + · · · + 19a + 16, 5a
4
u − 20a
3
u + · · · − 12a − 3, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−1
a
11
=
a
4
5
a
4
u −
18
5
a
3
u + ··· −
19
5
a −
16
5
a
5
=
−
2
5
a
4
u −
7
5
a
3
u + ··· − 8a +
21
5
2
5
a
4
u − a
3
u + ··· +
16
5
a
2
−
4
5
a
a
9
=
−u
u
a
12
=
4
5
a
4
u −
18
5
a
3
u + ··· −
9
5
a −
16
5
−a
a
10
=
−1.40000a
4
u + 8.40000a
3
u + ··· + 12.6000a + 4.80000
4
5
a
4
u −
26
5
a
3
u + ··· − 7a −
12
5
a
6
=
−1.60000a
3
u + 8.40000a
2
u + ··· − 4.20000a + 4.80000
u
a
1
=
−
2
5
a
4
u +
14
5
a
3
u + ··· +
52
5
a −
2
5
−1
a
2
=
−
2
5
a
4
u +
14
5
a
3
u + ··· +
52
5
a +
3
5
−1
a
7
=
u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =
12
5
a
4
+
48
5
a
3
u −
44
5
a
3
−
132
5
a
2
u −
72
5
a
2
−
48
5
au +
156
5
a +
68
5
u −
4
5
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
c
2
, c
3
, c
6
c
8
(u
2
+ 1)
5
c
4
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
5
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
7
(u + 1)
10
c
9
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
10
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
11
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
12
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y −1)
10
c
2
, c
3
, c
6
c
8
(y + 1)
10
c
4
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
5
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
9
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
12
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.881366 − 0.510635I
b = −0.331455 + 0.820551I
−0.32910 + 1.53058I −0.51511 − 4.43065I
u = 1.000000I
a = −0.142272 − 0.490929I
b = 0.361438 − 0.927855I
−5.87256 − 4.40083I −4.74431 + 3.49859I
u = 1.000000I
a = −0.14227 − 1.50907I
b = −0.0768928 + 0.0902877I
−5.87256 + 4.40083I −4.74431 − 3.49859I
u = 1.000000I
a = 0.88137 − 1.48936I
b = −1.43128 + 1.79928I
−0.32910 − 1.53058I −0.51511 + 4.43065I
u = 1.000000I
a = 3.52181 − 1.00000I
b = −3.52181 + 2.21774I
−2.40108 −1.48114 + 0.I
u = − 1.000000I
a = 0.881366 + 0.510635I
b = −0.331455 − 0.820551I
−0.32910 − 1.53058I −0.51511 + 4.43065I
u = − 1.000000I
a = −0.142272 + 0.490929I
b = 0.361438 + 0.927855I
−5.87256 + 4.40083I −4.74431 − 3.49859I
u = − 1.000000I
a = −0.14227 + 1.50907I
b = −0.0768928 − 0.0902877I
−5.87256 − 4.40083I −4.74431 + 3.49859I
u = − 1.000000I
a = 0.88137 + 1.48936I
b = −1.43128 − 1.79928I
−0.32910 + 1.53058I −0.51511 − 4.43065I
u = − 1.000000I
a = 3.52181 + 1.00000I
b = −3.52181 − 2.21774I
−2.40108 −1.48114 + 0.I
19
IV.
I
u
4
= h−u
3
− 2u
2
+ 4b − 3u − 3, −3u
3
− 2u
2
+ 4a − u + 3, u
4
+ u
3
+ u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
3
4
u
3
+
1
2
u
2
+
1
4
u −
3
4
1
4
u
3
+
1
2
u
2
+
3
4
u +
3
4
a
5
=
3
8
u
3
+
5
4
u
2
+
13
8
u +
17
8
−
7
8
u
3
−
1
4
u
2
−
9
8
u +
3
8
a
9
=
−u
u
a
12
=
3
4
u
3
+
1
2
u
2
+
5
4
u −
3
4
1
4
u
3
+
1
2
u
2
−
1
4
u +
3
4
a
10
=
3
4
u
3
+
1
2
u
2
+
1
4
u −
3
4
1
4
u
3
+
1
2
u
2
+
3
4
u +
3
4
a
6
=
1
u
2
a
1
=
−u
3
−u
3
− u
2
− 1
a
2
=
u
2
+ 1
−u
3
− u
2
− 1
a
7
=
−u
3
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
71
16
u
3
−
7
8
u
2
+
241
16
u −
147
16
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 5u
3
+ 7u
2
− 2u + 1
c
2
, c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
3
u
4
+ u
3
+ u
2
+ 1
c
4
, c
5
2(2u
4
− u
3
+ 5u
2
+ u + 1)
c
6
u
4
− u
3
+ 3u
2
− 2u + 1
c
8
u
4
− u
3
+ u
2
+ 1
c
9
(u − 1)
4
c
10
u
4
c
11
(u + 1)
4
c
12
u
4
− u
3
+ 5u
2
+ u + 2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
2
, c
6
, c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
3
, c
8
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
4
, c
5
4(4y
4
+ 19y
3
+ 31y
2
+ 9y + 1)
c
9
, c
11
(y − 1)
4
c
10
y
4
c
12
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351808 + 0.720342I
a = −1.237690 + 0.353773I
b = 0.690267 + 0.767100I
−1.43393 − 1.41510I −5.77964 + 9.93490I
u = 0.351808 − 0.720342I
a = −1.237690 − 0.353773I
b = 0.690267 − 0.767100I
−1.43393 + 1.41510I −5.77964 − 9.93490I
u = −0.851808 + 0.911292I
a = 0.112691 + 0.371716I
b = 0.434733 + 0.213936I
−8.43568 + 3.16396I −15.2516 + 20.5289I
u = −0.851808 − 0.911292I
a = 0.112691 − 0.371716I
b = 0.434733 − 0.213936I
−8.43568 − 3.16396I −15.2516 − 20.5289I
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
4
− 5u
3
+ ··· − 2u + 1)(u
18
+ 12u
17
+ ··· + 3u + 1)
· (u
54
+ 20u
53
+ ··· + 15886u + 289)
c
2
((u
2
+ 1)
5
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
18
+ 6u
16
+ ··· + 3u + 1)
· (u
54
− 2u
53
+ ··· − 20u + 17)
c
3
((u
2
+ 1)
5
)(u
4
+ u
3
+ u
2
+ 1)(u
18
+ 6u
16
+ ··· + 3u + 1)
· (u
54
− 2u
53
+ ··· − 112u + 17)
c
4
4(2u
4
− u
3
+ 5u
2
+ u + 1)(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
3
· (u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1)(2u
54
− 3u
53
+ ··· + 26787u + 17894)
c
5
4(2u
4
− u
3
+ 5u
2
+ u + 1)(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
· (u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1)(2u
54
− 11u
53
+ ··· − 27633u + 3982)
c
6
((u
2
+ 1)
5
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
18
+ 6u
16
+ ··· + 3u + 1)
· (u
54
− 2u
53
+ ··· − 20u + 17)
c
7
((u + 1)
10
)(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
18
− 12u
17
+ ··· − 3u + 1)
· (u
54
− 60u
53
+ ··· − 17614u + 289)
c
8
((u
2
+ 1)
5
)(u
4
− u
3
+ u
2
+ 1)(u
18
+ 6u
16
+ ··· + 3u + 1)
· (u
54
− 2u
53
+ ··· − 112u + 17)
c
9
(u − 1)
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
· (u
54
− 4u
53
+ ··· − 481u + 16)
c
10
u
4
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
3
· (u
54
+ 8u
53
+ ··· + 2976u + 256)
c
11
(u + 1)
4
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
· (u
54
− 4u
53
+ ··· − 481u + 16)
c
12
(u
4
− u
3
+ 5u
2
+ u + 2)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
3
· (u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1)(u
54
+ 7u
53
+ ··· + 8u + 4)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
4
− 11y
3
+ ··· + 10y + 1)(y
18
− 12y
17
+ ··· + 95y + 1)
· (y
54
+ 40y
53
+ ··· − 35600546y + 83521)
c
2
, c
6
((y + 1)
10
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
18
+ 12y
17
+ ··· + 3y + 1)
· (y
54
+ 20y
53
+ ··· + 15886y + 289)
c
3
, c
8
((y + 1)
10
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
18
+ 12y
17
+ ··· + 3y + 1)
· (y
54
+ 60y
53
+ ··· + 17614y + 289)
c
4
16(4y
4
+ 19y
3
+ 31y
2
+ 9y + 1)(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
· (y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· (4y
54
− 205y
53
+ ··· + 5530254095y + 320195236)
c
5
16(4y
4
+ 19y
3
+ 31y
2
+ 9y + 1)(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
· (y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
· (4y
54
− 173y
53
+ ··· + 170212239y + 15856324)
c
7
((y − 1)
10
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
18
− 12y
17
+ ··· + 95y + 1)
· (y
54
− 120y
53
+ ··· − 34842354y + 83521)
c
9
, c
11
(y − 1)
4
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
· (y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
3
· (y
54
− 32y
53
+ ··· − 95457y + 256)
c
10
y
4
(y
5
+ 3y
4
+ ··· − y − 1)
2
(y
6
− 3y
5
+ ··· − y + 1)
3
· (y
54
− 12y
53
+ ··· − 1545216y + 65536)
c
12
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
· ((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
)(y
54
+ 17y
53
+ ··· + 152y + 16)
25
