12n
0421
(K12n
0421
)
A knot diagram
1
Linearized knot diagam
3 5 7 12 2 8 3 11 5 4 9 10
Solving Sequence
3,5
2
1,10
9 12 4 11 8 7 6
c
2
c
1
c
9
c
12
c
4
c
11
c
8
c
7
c
6
c
3
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h6.94451 × 10
73
u
53
− 1.34116 × 10
74
u
52
+ ··· + 3.81141 × 10
75
b − 1.25088 × 10
75
,
− 3.43142 × 10
75
u
53
+ 7.05210 × 10
75
u
52
+ ··· + 3.23970 × 10
76
a + 1.89860 × 10
77
,
u
54
− 2u
53
+ ··· − 112u + 17i
I
u
2
= h−44u
17
+ 4u
16
+ ··· + 69b + 127u, −44u
17
− 264u
15
+ ··· + 69a − 224, u
18
+ 6u
16
+ ··· + 3u + 1i
I
u
3
= ha
4
− a
3
u + 2a
2
− au + b − u + 2, a
5
− a
4
+ 2a
3
− a
2
+ a − 1, u
2
+ 1i
I
u
4
= h−3u
3
+ 6u
2
+ 4b − 5u + 1, u
3
+ 2a − 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
= h6.94 × 10
73
u
53
− 1.34 × 10
74
u
52
+ · · · + 3.81 × 10
75
b − 1.25 ×
10
75
, −3.43 × 10
75
u
53
+ 7.05 × 10
75
u
52
+ · · · + 3.24 × 10
76
a + 1.90 ×
10
77
, u
54
− 2u
53
+ · · · − 112u + 17i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
10
=
0.105918u
53
− 0.217677u
52
+ ··· + 63.2432u − 5.86042
−0.0182203u
53
+ 0.0351879u
52
+ ··· − 10.1732u + 0.328192
a
9
=
0.105918u
53
− 0.217677u
52
+ ··· + 63.2432u − 5.86042
−0.0293505u
53
+ 0.0578164u
52
+ ··· − 12.6281u + 0.427504
a
12
=
−0.0377580u
53
+ 0.0561954u
52
+ ··· + 17.7971u − 6.35371
−0.0210496u
53
+ 0.0288416u
52
+ ··· − 9.16703u + 1.99686
a
4
=
0.0736388u
53
− 0.109834u
52
+ ··· + 5.97498u + 3.87914
−0.00164042u
53
+ 0.00683312u
52
+ ··· − 1.67223u − 0.577146
a
11
=
0.0157800u
53
− 0.0231466u
52
+ ··· + 29.3692u − 3.16089
−0.0328608u
53
+ 0.0646084u
52
+ ··· − 11.4634u + 0.980987
a
8
=
0.0000582809u
53
+ 0.00965479u
52
+ ··· + 26.4948u − 4.19485
−0.0248738u
53
+ 0.0481071u
52
+ ··· − 11.7942u + 1.11363
a
7
=
−0.0248155u
53
+ 0.0577619u
52
+ ··· + 14.7006u − 3.08122
−0.0248738u
53
+ 0.0481071u
52
+ ··· − 11.7942u + 1.11363
a
6
=
−u
−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
+ 60u
53
+ ··· + 17614u + 289
c
2
, c
5
u
54
+ 2u
53
+ ··· + 112u + 17
c
3
, c
7
u
54
+ 2u
53
+ ··· + 20u + 17
c
4
u
54
− 7u
53
+ ··· − 8u + 4
c
6
u
54
− 20u
53
+ ··· − 15886u + 289
c
8
, c
11
u
54
+ 4u
53
+ ··· + 481u + 16
c
9
2(2u
54
+ 11u
53
+ ··· + 27633u + 3982)
c
10
2(2u
54
+ 3u
53
+ ··· − 26787u + 17894)
c
12
u
54
− 8u
53
+ ··· − 2976u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
− 120y
53
+ ··· − 34842354y + 83521
c
2
, c
5
y
54
+ 60y
53
+ ··· + 17614y + 289
c
3
, c
7
y
54
+ 20y
53
+ ··· + 15886y + 289
c
4
y
54
+ 17y
53
+ ··· + 152y + 16
c
6
y
54
+ 40y
53
+ ··· − 35600546y + 83521
c
8
, c
11
y
54
− 32y
53
+ ··· − 95457y + 256
c
9
4(4y
54
− 173y
53
+ ··· + 1.70212 × 10
8
y + 1.58563 × 10
7
)
c
10
4(4y
54
− 205y
53
+ ··· + 5.53025 × 10
9
y + 3.20195 × 10
8
)
c
12
y
54
− 12y
53
+ ··· − 1545216y + 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957433 + 0.281564I
a = −0.366782 + 0.368685I
b = −0.536027 − 0.041780I
0.08167 − 4.27758I 0. + 6.47467I
u = −0.957433 − 0.281564I
a = −0.366782 − 0.368685I
b = −0.536027 + 0.041780I
0.08167 + 4.27758I 0. − 6.47467I
u = 0.793853 + 0.517771I
a = −0.989605 − 0.419229I
b = −0.745351 + 0.352281I
−1.69843 + 5.87991I −0.83203 − 7.69197I
u = 0.793853 − 0.517771I
a = −0.989605 + 0.419229I
b = −0.745351 − 0.352281I
−1.69843 − 5.87991I −0.83203 + 7.69197I
u = 1.013690 + 0.409819I
a = 1.40509 + 0.61654I
b = 1.023680 − 0.012588I
1.51017 + 11.89510I 0. − 8.55352I
u = 1.013690 − 0.409819I
a = 1.40509 − 0.61654I
b = 1.023680 + 0.012588I
1.51017 − 11.89510I 0. + 8.55352I
u = 0.037687 + 0.876774I
a = −0.411613 − 0.841558I
b = −0.730721 − 0.454623I
−1.21558 − 1.50306I −6.28567 + 3.87694I
u = 0.037687 − 0.876774I
a = −0.411613 + 0.841558I
b = −0.730721 + 0.454623I
−1.21558 + 1.50306I −6.28567 − 3.87694I
u = 0.001197 + 1.155080I
a = 0.344466 + 1.134660I
b = 0.086158 + 0.503268I
4.74660 − 4.32144I 0
u = 0.001197 − 1.155080I
a = 0.344466 − 1.134660I
b = 0.086158 − 0.503268I
4.74660 + 4.32144I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904014 + 0.749313I
a = 0.409227 − 0.949421I
b = 0.254579 − 0.478630I
−0.351082 − 0.581835I 0
u = −0.904014 − 0.749313I
a = 0.409227 + 0.949421I
b = 0.254579 + 0.478630I
−0.351082 + 0.581835I 0
u = −0.409754 + 0.654267I
a = 0.670688 − 0.470147I
b = 0.024664 − 0.332222I
−0.11724 − 1.46636I −1.51920 + 4.74355I
u = −0.409754 − 0.654267I
a = 0.670688 + 0.470147I
b = 0.024664 + 0.332222I
−0.11724 + 1.46636I −1.51920 − 4.74355I
u = 0.897207 + 0.878746I
a = 0.412964 + 0.196074I
b = 0.230506 + 0.127637I
8.36051 + 3.29219I 0
u = 0.897207 − 0.878746I
a = 0.412964 − 0.196074I
b = 0.230506 − 0.127637I
8.36051 − 3.29219I 0
u = 0.611149 + 0.347151I
a = 1.350850 − 0.353105I
b = 1.28376 + 1.02238I
3.32384 + 4.22762I 7.57484 − 8.95989I
u = 0.611149 − 0.347151I
a = 1.350850 + 0.353105I
b = 1.28376 − 1.02238I
3.32384 − 4.22762I 7.57484 + 8.95989I
u = −0.483135 + 0.456682I
a = −2.56114 − 3.18734I
b = −1.88415 + 0.56985I
1.86209 − 1.74879I 7.3853 − 15.6719I
u = −0.483135 − 0.456682I
a = −2.56114 + 3.18734I
b = −1.88415 − 0.56985I
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 = 2.52817 + 2.38441I
b = 0.71366 − 1.77517I
1.60277 − 1.13073I 16.4890 + 3.6045I
u = −0.246711 − 0.521269I
a = 2.52817 − 2.38441I
b = 0.71366 + 1.77517I
1.60277 + 1.13073I 16.4890 − 3.6045I
u = 0.10747 + 1.43757I
a = −0.231658 + 0.116000I
b = −2.40283 − 0.09567I
−1.12918 + 2.68232I 0
u = 0.10747 − 1.43757I
a = −0.231658 − 0.116000I
b = −2.40283 + 0.09567I
−1.12918 − 2.68232I 0
u = −0.00780 + 1.45535I
a = −0.234240 − 0.821894I
b = −0.634589 + 0.224881I
−3.51163 − 1.45830I 0
u = −0.00780 − 1.45535I
a = −0.234240 + 0.821894I
b = −0.634589 − 0.224881I
−3.51163 + 1.45830I 0
u = 0.19633 + 1.47266I
a = −0.180761 + 0.764063I
b = −0.450752 − 0.458790I
−2.64331 + 7.12189I 0
u = 0.19633 − 1.47266I
a = −0.180761 − 0.764063I
b = −0.450752 + 0.458790I
−2.64331 − 7.12189I 0
u = −0.04819 + 1.51041I
a = 0.39189 − 1.67295I
b = 0.87803 − 2.40931I
−5.05765 − 2.00436I 0
u = −0.04819 − 1.51041I
a = 0.39189 + 1.67295I
b = 0.87803 + 2.40931I
−5.05765 + 2.00436I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14469 + 1.50993I
a = 0.47360 + 1.91984I
b = 1.53856 + 2.59401I
−4.66611 − 3.99543I 0
u = −0.14469 − 1.50993I
a = 0.47360 − 1.91984I
b = 1.53856 − 2.59401I
−4.66611 + 3.99543I 0
u = 0.416507 + 0.239610I
a = 0.373760 − 0.682809I
b = 1.212780 − 0.597298I
4.35238 + 0.88122I 11.36984 − 2.33709I
u = 0.416507 − 0.239610I
a = 0.373760 + 0.682809I
b = 1.212780 + 0.597298I
4.35238 − 0.88122I 11.36984 + 2.33709I
u = 0.076348 + 0.449359I
a = 1.54451 − 2.17798I
b = 0.371098 − 0.688121I
7.12845 + 4.50045I 11.43251 − 4.54345I
u = 0.076348 − 0.449359I
a = 1.54451 + 2.17798I
b = 0.371098 + 0.688121I
7.12845 − 4.50045I 11.43251 + 4.54345I
u = −0.40434 + 1.49345I
a = 0.473577 + 0.252036I
b = 1.54220 − 0.04301I
−5.61605 − 9.26553I 0
u = −0.40434 − 1.49345I
a = 0.473577 − 0.252036I
b = 1.54220 + 0.04301I
−5.61605 + 9.26553I 0
u = 0.30238 + 1.53005I
a = 0.508036 − 0.093774I
b = 1.60740 + 0.32922I
−8.31392 + 2.90879I 0
u = 0.30238 − 1.53005I
a = 0.508036 + 0.093774I
b = 1.60740 − 0.32922I
−8.31392 − 2.90879I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27909 + 1.54859I
a = 0.761075 − 0.328934I
b = 2.56556 − 0.27826I
−8.47521 + 9.84153I 0
u = 0.27909 − 1.54859I
a = 0.761075 + 0.328934I
b = 2.56556 + 0.27826I
−8.47521 − 9.84153I 0
u = 0.39619 + 1.53466I
a = −0.989911 + 0.661170I
b = −2.69175 + 0.38369I
−4.7262 + 17.0140I 0
u = 0.39619 − 1.53466I
a = −0.989911 − 0.661170I
b = −2.69175 − 0.38369I
−4.7262 − 17.0140I 0
u = −0.13238 + 1.58588I
a = 0.710747 + 0.251585I
b = 2.39257 + 0.46175I
−10.02230 − 3.29278I 0
u = −0.13238 − 1.58588I
a = 0.710747 − 0.251585I
b = 2.39257 − 0.46175I
−10.02230 + 3.29278I 0
u = −0.23845 + 1.60519I
a = −1.019030 − 0.001725I
b = −2.17248 + 0.26878I
−8.27340 − 4.54754I 0
u = −0.23845 − 1.60519I
a = −1.019030 + 0.001725I
b = −2.17248 − 0.26878I
−8.27340 + 4.54754I 0
u = −0.30330 + 1.60247I
a = −0.977488 − 0.584250I
b = −2.55816 − 0.50781I
−7.29392 − 10.27410I 0
u = −0.30330 − 1.60247I
a = −0.977488 + 0.584250I
b = −2.55816 + 0.50781I
−7.29392 + 10.27410I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.09043 + 1.66784I
a = −0.977056 − 0.182021I
b = −2.14804 − 0.39830I
−9.44818 − 2.46020I 0
u = 0.09043 − 1.66784I
a = −0.977056 + 0.182021I
b = −2.14804 + 0.39830I
−9.44818 + 2.46020I 0
u = 0.060670 + 0.183744I
a = 0.36004 + 5.05217I
b = −0.395346 − 1.125760I
1.88776 − 1.50114I 7.21238 + 4.30156I
u = 0.060670 − 0.183744I
a = 0.36004 − 5.05217I
b = −0.395346 + 1.125760I
1.88776 + 1.50114I 7.21238 − 4.30156I
10
II. I
u
2
= h−44u
17
+ 4u
16
+ · · · + 69b + 127u, −44u
17
− 264u
15
+ · · · + 69a −
224, u
18
+ 6u
16
+ · · · + 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
10
=
0.637681u
17
+ 3.82609u
15
+ ··· + 2.66667u + 3.24638
0.637681u
17
− 0.0579710u
16
+ ··· + 3.91304u
2
− 1.84058u
a
9
=
0.637681u
17
+ 3.82609u
15
+ ··· + 2.66667u + 3.24638
0.637681u
17
+ 0.173913u
16
+ ··· + 5.24638u
2
− 2.47826u
a
12
=
0.594203u
17
+ 3.56522u
15
+ ··· + 3.66667u + 0.115942
0.594203u
17
− 0.594203u
16
+ ··· − 3.55072u
2
− 0.115942u
a
4
=
u
2
+ 1
u
2
a
11
=
0.840580u
17
+ 5.04348u
15
+ ··· + 4.33333u + 3.18841
0.840580u
17
− 0.0579710u
16
+ ··· + 3.85507u
2
− 1.84058u
a
8
=
0
−u
a
7
=
−u
−u
a
6
=
−u
−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
5
c
7
u
18
+ 6u
16
+ ··· − 3u + 1
c
4
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
c
6
u
18
− 12u
17
+ ··· − 3u + 1
c
8
, c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
3
c
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
3
c
10
, c
12
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
3
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
18
− 12y
17
+ ··· + 95y + 1
c
2
, c
3
, c
5
c
7
y
18
+ 12y
17
+ ··· + 3y + 1
c
4
, c
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
c
8
, c
10
, c
11
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 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 = −0.598036 + 0.102351I
b = −0.488236 − 0.375359I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = −0.577722 − 0.852843I
a = −0.598036 − 0.102351I
b = −0.488236 + 0.375359I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = 0.196160 + 0.885066I
a = 0.419078 + 1.129010I
b = −2.92263 − 1.35280I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 0.196160 − 0.885066I
a = 0.419078 − 1.129010I
b = −2.92263 + 1.35280I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = −0.945163 + 0.610473I
a = 1.206700 − 0.490377I
b = 0.819070 − 0.094621I
− 5.69302I 0. + 5.51057I
u = −0.945163 − 0.610473I
a = 1.206700 + 0.490377I
b = 0.819070 + 0.094621I
5.69302I 0. − 5.51057I
u = 0.090472 + 1.133120I
a = −0.583686 + 0.762709I
b = −3.11733 − 0.76503I
1.89061 + 0.92430I 3.71672 − 0.79423I
u = 0.090472 − 1.133120I
a = −0.583686 − 0.762709I
b = −3.11733 + 0.76503I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = 0.686633 + 0.502578I
a = −0.150201 − 0.718978I
b = −0.530542 − 0.156218I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = 0.686633 − 0.502578I
a = −0.150201 + 0.718978I
b = −0.530542 + 0.156218I
−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 = 0.271648 + 1.151080I
b = 0.190767 + 0.581448I
− 5.69302I 0. + 5.51057I
u = 0.824262 − 0.925280I
a = 0.271648 − 1.151080I
b = 0.190767 − 0.581448I
5.69302I 0. − 5.51057I
u = −0.108911 + 1.355420I
a = 0.402013 − 0.222804I
b = 1.71123 − 1.31922I
−1.89061 + 0.92430I −3.71672 − 0.79423I
u = −0.108911 − 1.355420I
a = 0.402013 + 0.222804I
b = 1.71123 + 1.31922I
−1.89061 − 0.92430I −3.71672 + 0.79423I
u = 0.12090 + 1.53575I
a = −0.819509 + 0.483205I
b = −2.32751 + 0.84183I
5.69302I 0. − 5.51057I
u = 0.12090 − 1.53575I
a = −0.819509 − 0.483205I
b = −2.32751 − 0.84183I
− 5.69302I 0. + 5.51057I
u = −0.286632 + 0.248050I
a = 2.85200 + 0.40141I
b = 0.665192 − 0.947661I
1.89061 − 0.92430I 3.71672 + 0.79423I
u = −0.286632 − 0.248050I
a = 2.85200 − 0.40141I
b = 0.665192 + 0.947661I
1.89061 + 0.92430I 3.71672 − 0.79423I
15
III. I
u
3
= ha
4
− a
3
u + 2a
2
− au + b − u + 2, a
5
− a
4
+ 2a
3
− a
2
+ a − 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
−1
a
1
=
0
−1
a
10
=
a
−a
4
+ a
3
u − 2a
2
+ au + u − 2
a
9
=
a
−a
4
+ a
3
u − 2a
2
+ au − a + u − 2
a
12
=
−a
2
−a
4
u + a
4
− a
2
u + a
2
− au + a
a
4
=
a
4
u
−1
a
11
=
a
4
−a
4
− 2a
2
+ u − 2
a
8
=
a
4
u
a
7
=
a
4
+ u
u
a
6
=
u
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
3
+ 4a
2
− 4a + 4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
c
2
, c
3
, c
5
c
7
(u
2
+ 1)
5
c
4
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
c
6
(u + 1)
10
c
8
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
9
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
10
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
12
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y −1)
10
c
2
, c
3
, c
5
c
7
(y + 1)
10
c
4
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
c
8
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
9
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
10
(y
5
+ 5y
4
+ 8y
3
+ 3y
2
− y + 1)
2
c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.339110 + 0.822375I
b = −1.43128 + 1.79928I
0.32910 + 1.53058I 0.51511 − 4.43065I
u = 1.000000I
a = −0.339110 − 0.822375I
b = −0.331455 + 0.820551I
0.32910 − 1.53058I 0.51511 + 4.43065I
u = 1.000000I
a = 0.766826
b = −3.52181 + 2.21774I
2.40108 1.48110
u = 1.000000I
a = 0.455697 + 1.200150I
b = −0.0768928 + 0.0902877I
5.87256 − 4.40083I 4.74431 + 3.49859I
u = 1.000000I
a = 0.455697 − 1.200150I
b = 0.361438 − 0.927855I
5.87256 + 4.40083I 4.74431 − 3.49859I
u = − 1.000000I
a = −0.339110 + 0.822375I
b = −0.331455 − 0.820551I
0.32910 + 1.53058I 0.51511 − 4.43065I
u = − 1.000000I
a = −0.339110 − 0.822375I
b = −1.43128 − 1.79928I
0.32910 − 1.53058I 0.51511 + 4.43065I
u = − 1.000000I
a = 0.766826
b = −3.52181 − 2.21774I
2.40108 1.48110
u = − 1.000000I
a = 0.455697 + 1.200150I
b = 0.361438 + 0.927855I
5.87256 − 4.40083I 4.74431 + 3.49859I
u = − 1.000000I
a = 0.455697 − 1.200150I
b = −0.0768928 − 0.0902877I
5.87256 + 4.40083I 4.74431 − 3.49859I
19
IV. I
u
4
= h−3u
3
+ 6u
2
+ 4b − 5u + 1, u
3
+ 2a − u + 3, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
10
=
−
1
2
u
3
+
1
2
u −
3
2
3
4
u
3
−
3
2
u
2
+
5
4
u −
1
4
a
9
=
−
1
2
u
3
+
1
2
u −
3
2
5
4
u
3
−
5
2
u
2
+
7
4
u +
1
4
a
12
=
u
2
+ 1
u
2
a
4
=
2u
3
− u
2
− 1
u
3
− u
2
− 1
a
11
=
−
1
2
u
3
+ u
2
+
1
2
u −
1
2
5
4
u
3
−
3
2
u
2
+
7
4
u +
1
4
a
8
=
−u
2
− 1
−u
2
a
7
=
−2u
2
− 1
−u
2
a
6
=
u
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
, c
3
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
4
u
4
− u
3
+ 5u
2
+ u + 2
c
5
u
4
+ u
3
+ u
2
+ 1
c
6
u
4
+ 5u
3
+ 7u
2
+ 2u + 1
c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
(u + 1)
4
c
9
, c
10
2(2u
4
− u
3
+ 5u
2
+ u + 1)
c
11
(u − 1)
4
c
12
u
4
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
4
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
6
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
8
, c
11
(y −1)
4
c
9
, c
10
4(4y
4
+ 19y
3
+ 31y
2
+ 9y + 1)
c
12
y
4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351808 + 0.720342I
a = −1.92796 + 0.41333I
b = 0.28101 + 1.58096I
1.43393 − 1.41510I 5.77964 + 9.93490I
u = −0.351808 − 0.720342I
a = −1.92796 − 0.41333I
b = 0.28101 − 1.58096I
1.43393 + 1.41510I 5.77964 − 9.93490I
u = 0.851808 + 0.911292I
a = −0.322042 − 0.157780I
b = −0.156006 − 0.269484I
8.43568 + 3.16396I 15.2516 + 20.5289I
u = 0.851808 − 0.911292I
a = −0.322042 + 0.157780I
b = −0.156006 + 0.269484I
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
− u
3
+ 3u
2
− 2u + 1)(u
18
+ 12u
17
+ ··· + 3u + 1)
· (u
54
+ 60u
53
+ ··· + 17614u + 289)
c
2
((u
2
+ 1)
5
)(u
4
− u
3
+ u
2
+ 1)(u
18
+ 6u
16
+ ··· − 3u + 1)
· (u
54
+ 2u
53
+ ··· + 112u + 17)
c
3
((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
4
(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)
c
5
((u
2
+ 1)
5
)(u
4
+ u
3
+ u
2
+ 1)(u
18
+ 6u
16
+ ··· − 3u + 1)
· (u
54
+ 2u
53
+ ··· + 112u + 17)
c
6
((u + 1)
10
)(u
4
+ 5u
3
+ ··· + 2u + 1)(u
18
− 12u
17
+ ··· − 3u + 1)
· (u
54
− 20u
53
+ ··· − 15886u + 289)
c
7
((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
8
(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
9
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
10
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
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
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)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
18
− 12y
17
+ ··· + 95y + 1)
· (y
54
− 120y
53
+ ··· − 34842354y + 83521)
c
2
, c
5
((y + 1)
10
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
18
+ 12y
17
+ ··· + 3y + 1)
· (y
54
+ 60y
53
+ ··· + 17614y + 289)
c
3
, c
7
((y + 1)
10
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
18
+ 12y
17
+ ··· + 3y + 1)
· (y
54
+ 20y
53
+ ··· + 15886y + 289)
c
4
(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)
c
6
((y −1)
10
)(y
4
− 11y
3
+ ··· + 10y + 1)(y
18
− 12y
17
+ ··· + 95y + 1)
· (y
54
+ 40y
53
+ ··· − 35600546y + 83521)
c
8
, 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
9
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
10
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
12
y
4
(y
5
+ 3y
4
+ ··· − y −1)
2
(y
6
− 3y
5
+ ··· − y + 1)
3
· (y
54
− 12y
53
+ ··· − 1545216y + 65536)
25
