12a
0845
(K12a
0845
)
A knot diagram
1
Linearized knot diagam
4 5 9 2 11 10 12 3 1 6 8 7
Solving Sequence
5,11 2,6
4 1 10 7 9 3 12 8
c
5
c
4
c
1
c
10
c
6
c
9
c
3
c
12
c
7
c
2
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h27u
31
− 17u
30
+ ··· + 128b + 71, 95u
31
− 45u
30
+ ··· + 256a − 341, u
32
+ 21u
30
+ ··· − 4u − 1i
I
u
2
= h2.51515 × 10
30
u
39
− 4.97836 × 10
30
u
38
+ ··· + 2.65897 × 10
31
b + 5.38153 × 10
30
,
5.98427 × 10
30
u
39
+ 1.37483 × 10
32
u
38
+ ··· + 4.52025 × 10
32
a + 1.58918 × 10
33
, u
40
− 2u
39
+ ··· + 70u + 17i
I
u
3
= hb + 1, −u
2
+ 2a + u − 1, u
3
+ 2u + 1i
I
u
4
= h1700a
4
u + 1422a
3
u + ··· − 9124a + 3991,
a
5
+ 2a
4
u − 4a
3
u − 3a
3
+ 8a
2
u + 2a
2
− 11au − 3a + 4u − 1, u
2
+ 1i
I
u
5
= hb + 1, u
3
− u
2
+ a + u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 89 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
= h27u
31
− 17u
30
+ · · · + 128b + 71, 95u
31
− 45u
30
+ · · · + 256a −
341, u
32
+ 21u
30
+ · · · − 4u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−0.371094u
31
+ 0.175781u
30
+ ··· − 1.19922u + 1.33203
−0.210938u
31
+ 0.132813u
30
+ ··· + 1.32031u − 0.554688
a
6
=
1
−u
2
a
4
=
−0.175781u
31
− 0.160156u
30
+ ··· − 0.847656u + 2.62109
−0.0234375u
31
− 0.242188u
30
+ ··· + 2.13281u + 0.132813
a
1
=
u
3
+ 2u
−
1
32
u
30
−
5
8
u
28
+ ··· +
9
8
u +
1
32
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−
1
32
u
30
−
5
8
u
28
+ ··· −
7
8
u +
1
32
−0.0625000u
31
− 0.0312500u
30
+ ··· + 1.43750u + 0.0937500
a
3
=
−0.160156u
31
+ 0.0429688u
30
+ ··· − 2.51953u + 1.88672
−0.210938u
31
+ 0.132813u
30
+ ··· + 1.32031u − 0.554688
a
12
=
u
−
1
32
u
30
−
5
8
u
28
+ ··· +
9
8
u +
1
32
a
8
=
1
1
32
u
31
+
5
8
u
29
+ ··· −
25
8
u
2
−
1
32
u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1101
512
u
31
−
87
512
u
30
+ ··· +
3849
512
u −
4159
512
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
32
− 4u
31
+ ··· + 7u − 4
c
3
, c
8
u
32
+ 3u
31
+ ··· + 104u + 32
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
32
+ 21u
30
+ ··· − 4u − 1
c
9
u
32
− 18u
31
+ ··· − 14736u + 916
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
32
− 32y
31
+ ··· + 319y + 16
c
3
, c
8
y
32
− 21y
31
+ ··· − 7488y + 1024
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
32
+ 42y
31
+ ··· − 14y + 1
c
9
y
32
+ 20y
31
+ ··· − 30763848y + 839056
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.596205 + 0.498969I
a = 1.06549 − 1.64640I
b = 1.49564 + 0.24366I
−7.50818 − 6.89795I −2.71124 + 7.50017I
u = −0.596205 − 0.498969I
a = 1.06549 + 1.64640I
b = 1.49564 − 0.24366I
−7.50818 + 6.89795I −2.71124 − 7.50017I
u = 0.754755
a = −0.570917
b = 1.39668
−3.40793 −0.829000
u = −0.211830 + 0.599469I
a = 1.65626 − 0.21759I
b = 1.46116 − 0.21545I
−7.75015 + 3.68745I −3.07982 + 0.49088I
u = −0.211830 − 0.599469I
a = 1.65626 + 0.21759I
b = 1.46116 + 0.21545I
−7.75015 − 3.68745I −3.07982 − 0.49088I
u = −0.479084 + 0.400920I
a = −0.765594 + 0.958623I
b = −0.444406 − 0.698143I
−1.18593 − 3.45933I 0.36714 + 8.58181I
u = −0.479084 − 0.400920I
a = −0.765594 − 0.958623I
b = −0.444406 + 0.698143I
−1.18593 + 3.45933I 0.36714 − 8.58181I
u = −0.160222 + 1.392530I
a = 0.650299 − 0.572723I
b = 1.266450 + 0.201760I
−11.40110 − 6.30632I −9.82325 + 7.00988I
u = −0.160222 − 1.392530I
a = 0.650299 + 0.572723I
b = 1.266450 − 0.201760I
−11.40110 + 6.30632I −9.82325 − 7.00988I
u = 0.382126 + 0.419731I
a = −2.30352 − 1.43026I
b = −1.338740 + 0.035203I
−3.40611 + 1.30629I −1.33758 − 5.13961I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.382126 − 0.419731I
a = −2.30352 + 1.43026I
b = −1.338740 − 0.035203I
−3.40611 − 1.30629I −1.33758 + 5.13961I
u = −0.06475 + 1.47499I
a = 0.180600 + 0.329919I
b = 0.011515 − 0.768259I
−7.68442 − 2.87580I −3.53748 + 2.84926I
u = −0.06475 − 1.47499I
a = 0.180600 − 0.329919I
b = 0.011515 + 0.768259I
−7.68442 + 2.87580I −3.53748 − 2.84926I
u = −0.254205 + 0.420009I
a = 0.174493 + 0.167283I
b = −0.487143 + 0.568904I
−1.54825 + 0.79595I −1.86394 + 0.64403I
u = −0.254205 − 0.420009I
a = 0.174493 − 0.167283I
b = −0.487143 − 0.568904I
−1.54825 − 0.79595I −1.86394 − 0.64403I
u = 0.468066 + 0.127863I
a = 0.912830 + 0.528691I
b = 0.066081 − 0.253115I
0.944780 + 0.326097I 9.67071 − 2.04247I
u = 0.468066 − 0.127863I
a = 0.912830 − 0.528691I
b = 0.066081 + 0.253115I
0.944780 − 0.326097I 9.67071 + 2.04247I
u = −0.23451 + 1.51253I
a = 0.846875 − 0.269710I
b = 0.523812 + 0.289998I
−10.33180 − 5.71165I 0
u = −0.23451 − 1.51253I
a = 0.846875 + 0.269710I
b = 0.523812 − 0.289998I
−10.33180 + 5.71165I 0
u = 0.02829 + 1.53350I
a = −1.102420 − 0.698559I
b = −1.221070 + 0.439429I
−11.45660 + 1.47285I −7.62357 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02829 − 1.53350I
a = −1.102420 + 0.698559I
b = −1.221070 − 0.439429I
−11.45660 − 1.47285I −7.62357 + 0.I
u = 0.31678 + 1.58141I
a = −0.893014 − 0.277667I
b = −0.473160 + 0.942126I
−14.4681 + 10.1956I 0
u = 0.31678 − 1.58141I
a = −0.893014 + 0.277667I
b = −0.473160 − 0.942126I
−14.4681 − 10.1956I 0
u = 0.37112 + 1.57673I
a = 1.69318 + 1.26301I
b = 1.54683 − 0.35117I
18.4767 + 14.9244I 0
u = 0.37112 − 1.57673I
a = 1.69318 − 1.26301I
b = 1.54683 + 0.35117I
18.4767 − 14.9244I 0
u = 0.26017 + 1.60825I
a = −0.360654 − 0.247692I
b = −0.783401 − 0.817291I
−15.3979 + 4.2870I 0
u = 0.26017 − 1.60825I
a = −0.360654 + 0.247692I
b = −0.783401 + 0.817291I
−15.3979 − 4.2870I 0
u = −0.29422 + 1.60301I
a = −2.19215 + 0.90406I
b = −1.52077 − 0.11946I
−17.1436 − 7.3763I 0
u = −0.29422 − 1.60301I
a = −2.19215 − 0.90406I
b = −1.52077 + 0.11946I
−17.1436 + 7.3763I 0
u = 0.20651 + 1.69012I
a = 1.84144 + 0.18045I
b = 1.64925 + 0.18271I
15.7187 + 0.6038I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.20651 − 1.69012I
a = 1.84144 − 0.18045I
b = 1.64925 − 0.18271I
15.7187 − 0.6038I 0
u = −0.230813
a = 2.26267
b = −0.900755
−1.28704 −11.6950
8
II. I
u
2
=
h2.52×10
30
u
39
−4.98×10
30
u
38
+· · ·+2.66×10
31
b+5.38×10
30
, 5.98×10
30
u
39
+
1.37 × 10
32
u
38
+ · · · + 4.52 × 10
32
a + 1.59 × 10
33
, u
40
− 2u
39
+ · · · + 70u + 17i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−0.0132388u
39
− 0.304149u
38
+ ··· − 19.0490u − 3.51569
−0.0945910u
39
+ 0.187229u
38
+ ··· − 1.05104u − 0.202391
a
6
=
1
−u
2
a
4
=
0.0200117u
39
− 0.351489u
38
+ ··· − 16.4010u − 2.88540
−0.111153u
39
+ 0.190940u
38
+ ··· − 1.07291u + 0.135035
a
1
=
0.0353564u
39
− 0.163030u
38
+ ··· + 6.81251u + 3.38142
0.0225725u
39
− 0.0296256u
38
+ ··· + 0.156751u − 0.0137151
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
0.107258u
39
− 0.235738u
38
+ ··· + 10.0225u + 5.03405
−0.0000152608u
39
+ 0.0654597u
38
+ ··· + 1.49458u − 0.374494
a
3
=
0.0813522u
39
− 0.491378u
38
+ ··· − 17.9980u − 3.31330
−0.0945910u
39
+ 0.187229u
38
+ ··· − 1.05104u − 0.202391
a
12
=
0.0115865u
39
− 0.0664804u
38
+ ··· + 9.46368u + 3.29819
0.0237699u
39
− 0.0965499u
38
+ ··· − 0.651167u + 0.0832334
a
8
=
−0.0482035u
39
+ 0.143644u
38
+ ··· + 3.33815u − 2.19086
−0.0433074u
39
+ 0.110082u
38
+ ··· + 2.48713u + 1.80303
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.224463u
39
+ 0.00102049u
38
+ ··· − 18.8412u − 3.74724
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
20
− 3u
19
+ ··· + u − 1)
2
c
3
, c
8
(u
20
− u
19
+ ··· + 8u − 4)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
40
− 2u
39
+ ··· + 70u + 17
c
9
(u
20
+ 6u
19
+ ··· − 2u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
20
− 21y
19
+ ··· − 13y + 1)
2
c
3
, c
8
(y
20
− 15y
19
+ ··· − 24y + 16)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
40
+ 34y
39
+ ··· + 1832y + 289
c
9
(y
20
+ 18y
19
+ ··· − 86y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.165946 + 1.040490I
a = 0.81855 + 1.38502I
b = −0.490452
−4.14943 −7.86459 + 0.I
u = −0.165946 − 1.040490I
a = 0.81855 − 1.38502I
b = −0.490452
−4.14943 −7.86459 + 0.I
u = 0.907483 + 0.556580I
a = −0.439591 − 0.994091I
b = −0.528240 + 0.848460I
−7.47319 + 5.67427I −4.59597 − 5.66395I
u = 0.907483 − 0.556580I
a = −0.439591 + 0.994091I
b = −0.528240 − 0.848460I
−7.47319 − 5.67427I −4.59597 + 5.66395I
u = 0.849096 + 0.668982I
a = 0.274937 + 0.407232I
b = −0.637670 − 0.786578I
−7.82964 + 0.19167I −5.73570 + 0.22109I
u = 0.849096 − 0.668982I
a = 0.274937 − 0.407232I
b = −0.637670 + 0.786578I
−7.82964 − 0.19167I −5.73570 − 0.22109I
u = −0.893068 + 0.616859I
a = −1.19973 + 0.80164I
b = −1.47518 − 0.04286I
−9.82414 − 2.97363I −5.92336 + 2.68538I
u = −0.893068 − 0.616859I
a = −1.19973 − 0.80164I
b = −1.47518 + 0.04286I
−9.82414 + 2.97363I −5.92336 − 2.68538I
u = 1.002000 + 0.504102I
a = 0.578230 + 1.285260I
b = 1.55303 − 0.29778I
−14.2713 + 9.8846I −6.38252 − 5.77638I
u = 1.002000 − 0.504102I
a = 0.578230 − 1.285260I
b = 1.55303 + 0.29778I
−14.2713 − 9.8846I −6.38252 + 5.77638I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.085676 + 1.124200I
a = 0.250275 − 0.440703I
b = −0.155247 + 0.510694I
−1.84814 + 1.82256I 3.12541 − 5.12436I
u = 0.085676 − 1.124200I
a = 0.250275 + 0.440703I
b = −0.155247 − 0.510694I
−1.84814 − 1.82256I 3.12541 + 5.12436I
u = −0.696648 + 0.501396I
a = 0.450944 − 0.346330I
b = 0.345319 + 0.136644I
−3.75614 − 2.30782I 2.11267 + 3.58910I
u = −0.696648 − 0.501396I
a = 0.450944 + 0.346330I
b = 0.345319 − 0.136644I
−3.75614 + 2.30782I 2.11267 − 3.58910I
u = 0.309526 + 1.128320I
a = 0.941074 + 0.963953I
b = 1.407720 − 0.116456I
−6.86225 + 3.88098I −4.06498 − 4.02252I
u = 0.309526 − 1.128320I
a = 0.941074 − 0.963953I
b = 1.407720 + 0.116456I
−6.86225 − 3.88098I −4.06498 + 4.02252I
u = −0.013501 + 1.171490I
a = −1.93036 + 1.33290I
b = −1.090200 − 0.185729I
−4.50859 − 0.86143I −1.55325 − 0.99952I
u = −0.013501 − 1.171490I
a = −1.93036 − 1.33290I
b = −1.090200 + 0.185729I
−4.50859 + 0.86143I −1.55325 + 0.99952I
u = 0.891957 + 0.807557I
a = 0.655723 + 0.126089I
b = 1.57757 + 0.24291I
−15.1619 − 3.5694I −7.71587 + 1.00735I
u = 0.891957 − 0.807557I
a = 0.655723 − 0.126089I
b = 1.57757 − 0.24291I
−15.1619 + 3.5694I −7.71587 − 1.00735I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.420232 + 1.236850I
a = 1.24867 − 1.29040I
b = 1.49625
−10.6935 −8.66827 + 0.I
u = −0.420232 − 1.236850I
a = 1.24867 + 1.29040I
b = 1.49625
−10.6935 −8.66827 + 0.I
u = 0.112225 + 1.360290I
a = 1.031720 + 0.131109I
b = 0.345319 − 0.136644I
−3.75614 + 2.30782I 2.00000 − 3.58910I
u = 0.112225 − 1.360290I
a = 1.031720 − 0.131109I
b = 0.345319 + 0.136644I
−3.75614 − 2.30782I 2.00000 + 3.58910I
u = −0.612885 + 0.007595I
a = −0.720052 − 0.811944I
b = 1.407720 − 0.116456I
−6.86225 + 3.88098I −4.06498 − 4.02252I
u = −0.612885 − 0.007595I
a = −0.720052 + 0.811944I
b = 1.407720 + 0.116456I
−6.86225 − 3.88098I −4.06498 + 4.02252I
u = 0.189437 + 0.520813I
a = 2.29770 − 2.15386I
b = −1.090200 + 0.185729I
−4.50859 + 0.86143I −1.55325 + 0.99952I
u = 0.189437 − 0.520813I
a = 2.29770 + 2.15386I
b = −1.090200 − 0.185729I
−4.50859 − 0.86143I −1.55325 − 0.99952I
u = −0.05659 + 1.49228I
a = −0.735047 + 0.389310I
b = −0.637670 + 0.786578I
−7.82964 − 0.19167I −5.73570 + 0.I
u = −0.05659 − 1.49228I
a = −0.735047 − 0.389310I
b = −0.637670 − 0.786578I
−7.82964 + 0.19167I −5.73570 + 0.I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14258 + 1.49572I
a = −1.026510 − 0.040293I
b = −0.528240 − 0.848460I
−7.47319 − 5.67427I 0
u = −0.14258 − 1.49572I
a = −1.026510 + 0.040293I
b = −0.528240 + 0.848460I
−7.47319 + 5.67427I 0
u = 0.10126 + 1.50509I
a = −2.95162 − 0.51566I
b = −1.47518 + 0.04286I
−9.82414 + 2.97363I −5.92336 + 0.I
u = 0.10126 − 1.50509I
a = −2.95162 + 0.51566I
b = −1.47518 − 0.04286I
−9.82414 − 2.97363I −5.92336 + 0.I
u = −0.20603 + 1.53635I
a = 2.21586 − 1.04966I
b = 1.55303 + 0.29778I
−14.2713 − 9.8846I 0
u = −0.20603 − 1.53635I
a = 2.21586 + 1.04966I
b = 1.55303 − 0.29778I
−14.2713 + 9.8846I 0
u = 0.02291 + 1.55592I
a = 2.40886 + 0.34865I
b = 1.57757 − 0.24291I
−15.1619 + 3.5694I −7.71587 + 0.I
u = 0.02291 − 1.55592I
a = 2.40886 − 0.34865I
b = 1.57757 + 0.24291I
−15.1619 − 3.5694I −7.71587 + 0.I
u = −0.264100 + 0.235618I
a = 1.68330 + 1.93764I
b = −0.155247 − 0.510694I
−1.84814 − 1.82256I 3.12541 + 5.12436I
u = −0.264100 − 0.235618I
a = 1.68330 − 1.93764I
b = −0.155247 + 0.510694I
−1.84814 + 1.82256I 3.12541 − 5.12436I
15
III. I
u
3
= hb + 1, −u
2
+ 2a + u − 1, u
3
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
1
2
u
2
−
1
2
u +
1
2
−1
a
6
=
1
−u
2
a
4
=
1
2
u
2
−
1
2
u +
3
2
−1
a
1
=
−1
0
a
10
=
−u
−u − 1
a
7
=
u
2
+ 1
u
a
9
=
1
−u − 1
a
3
=
1
2
u
2
−
1
2
u +
3
2
−1
a
12
=
u
−u
2
a
8
=
1
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
25
4
u
2
−
11
4
u +
23
4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
8
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
7
u
3
+ 2u + 1
c
9
u
3
+ 3u
2
+ 5u + 2
c
10
, c
11
, c
12
u
3
+ 2u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
8
y
3
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
c
9
y
3
+ y
2
+ 13y −4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22670 + 1.46771I
a = −0.664742 − 0.401127I
b = −1.00000
−11.08570 + 5.13794I −8.01583 + 0.12290I
u = 0.22670 − 1.46771I
a = −0.664742 + 0.401127I
b = −1.00000
−11.08570 − 5.13794I −8.01583 − 0.12290I
u = −0.453398
a = 0.829484
b = −1.00000
−0.857735 8.28170
19
IV.
I
u
4
= h1700a
4
u+1422a
3
u+· · ·−9124a+3991, 2a
4
u−4a
3
u+· · ·−3a−1, u
2
+1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
a
−0.165225a
4
u − 0.138206a
3
u + ··· + 0.886772a − 0.387890
a
6
=
1
1
a
4
=
0.194382a
4
u − 0.0726990a
3
u + ··· − 1.51385a + 1.63281
0.140441a
4
u − 0.182525a
3
u + ··· − 1.15376a + 0.179706
a
1
=
u
0.0432501a
4
u − 0.146176a
3
u + ··· − 0.396832a − 0.636699
a
10
=
−u
0
a
7
=
0
1
a
9
=
0.0432501a
4
u − 0.146176a
3
u + ··· − 0.396832a − 0.636699
−0.217514a
4
u − 0.226650a
3
u + ··· + 1.39800a − 1.02712
a
3
=
0.165225a
4
u + 0.138206a
3
u + ··· + 0.113228a + 0.387890
−0.165225a
4
u − 0.138206a
3
u + ··· + 0.886772a − 0.387890
a
12
=
u
0.0432501a
4
u − 0.146176a
3
u + ··· − 0.396832a − 0.636699
a
8
=
−1
−0.157353a
4
u − 0.0951502a
3
u + ··· + 1.07746a − 0.921761
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5020
10289
a
4
u +
5320
10289
a
4
+
11704
10289
a
3
u −
11044
10289
a
3
−
46780
10289
a
2
u −
6452
10289
a
2
+
26616
10289
au −
20164
10289
a −
44688
10289
u −
40144
10289
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
3
, c
8
u
10
− 3u
8
+ 4u
6
− u
4
− u
2
+ 1
c
4
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(u
2
+ 1)
5
c
9
u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
3
, c
8
(y
5
− 3y
4
+ 4y
3
− y
2
− y + 1)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(y + 1)
10
c
9
(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.098266 + 1.257020I
b = −0.309916 − 0.549911I
−3.61897 − 1.53058I −4.51511 + 4.43065I
u = 1.000000I
a = 0.670357 − 1.241280I
b = 1.41878 + 0.21917I
−9.16243 − 4.40083I −8.74431 + 3.49859I
u = 1.000000I
a = 0.335534 + 0.278295I
b = −0.309916 + 0.549911I
−3.61897 + 1.53058I −4.51511 − 4.43065I
u = 1.000000I
a = 1.61419 − 0.22314I
b = 1.41878 − 0.21917I
−9.16243 + 4.40083I −8.74431 − 3.49859I
u = 1.000000I
a = −2.52181 − 2.07090I
b = −1.21774
−5.69095 −5.48114 + 0.I
u = − 1.000000I
a = −0.098266 − 1.257020I
b = −0.309916 + 0.549911I
−3.61897 + 1.53058I −4.51511 − 4.43065I
u = − 1.000000I
a = 0.670357 + 1.241280I
b = 1.41878 − 0.21917I
−9.16243 + 4.40083I −8.74431 − 3.49859I
u = − 1.000000I
a = 0.335534 − 0.278295I
b = −0.309916 − 0.549911I
−3.61897 − 1.53058I −4.51511 + 4.43065I
u = − 1.000000I
a = 1.61419 + 0.22314I
b = 1.41878 + 0.21917I
−9.16243 − 4.40083I −8.74431 + 3.49859I
u = − 1.000000I
a = −2.52181 + 2.07090I
b = −1.21774
−5.69095 −5.48114 + 0.I
23
V. I
u
5
= hb + 1, u
3
− u
2
+ a + u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−u
3
+ u
2
− u + 1
−1
a
6
=
1
−u
2
a
4
=
−u
3
+ u
2
− u + 2
−1
a
1
=
−1
0
a
10
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
3
− 2u + 1
a
9
=
−u
3
− 2u
u
3
+ u
a
3
=
−u
3
+ u
2
− u + 2
−1
a
12
=
2u
3
− u
2
+ 3u − 3
−u
3
+ u
2
− u + 2
a
8
=
−u
3
− 2u
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
3
− 4u − 3
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
6
, c
7
u
4
− u
3
+ 2u
2
− 2u + 1
c
9
(u
2
− u + 1)
2
c
10
, c
11
, c
12
u
4
+ u
3
+ 2u
2
+ 2u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
8
y
4
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
c
9
(y
2
+ y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = 0.692440 − 0.318148I
b = −1.00000
−4.93480 + 2.02988I −5.00000 − 3.46410I
u = 0.621744 − 0.440597I
a = 0.692440 + 0.318148I
b = −1.00000
−4.93480 − 2.02988I −5.00000 + 3.46410I
u = −0.121744 + 1.306620I
a = −1.192440 + 0.547877I
b = −1.00000
−4.93480 − 2.02988I −5.00000 + 3.46410I
u = −0.121744 − 1.306620I
a = −1.192440 − 0.547877I
b = −1.00000
−4.93480 + 2.02988I −5.00000 − 3.46410I
27
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
7
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
20
− 3u
19
+ ··· + u − 1)
2
· (u
32
− 4u
31
+ ··· + 7u − 4)
c
3
, c
8
u
7
(u
10
− 3u
8
+ ··· − u
2
+ 1)(u
20
− u
19
+ ··· + 8u − 4)
2
· (u
32
+ 3u
31
+ ··· + 104u + 32)
c
4
((u + 1)
7
)(u
5
− u
4
+ ··· + u + 1)
2
(u
20
− 3u
19
+ ··· + u − 1)
2
· (u
32
− 4u
31
+ ··· + 7u − 4)
c
5
, c
6
, c
7
(u
2
+ 1)
5
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
32
+ 21u
30
+ ··· − 4u − 1)(u
40
− 2u
39
+ ··· + 70u + 17)
c
9
(u
2
− u + 1)
2
(u
3
+ 3u
2
+ 5u + 2)(u
10
+ u
8
+ 8u
6
+ 3u
4
+ 3u
2
+ 1)
· ((u
20
+ 6u
19
+ ··· − 2u + 1)
2
)(u
32
− 18u
31
+ ··· − 14736u + 916)
c
10
, c
11
, c
12
(u
2
+ 1)
5
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
32
+ 21u
30
+ ··· − 4u − 1)(u
40
− 2u
39
+ ··· + 70u + 17)
28
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
· ((y
20
− 21y
19
+ ··· − 13y + 1)
2
)(y
32
− 32y
31
+ ··· + 319y + 16)
c
3
, c
8
y
7
(y
5
− 3y
4
+ ··· − y + 1)
2
(y
20
− 15y
19
+ ··· − 24y + 16)
2
· (y
32
− 21y
31
+ ··· − 7488y + 1024)
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(y + 1)
10
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
32
+ 42y
31
+ ··· − 14y + 1)(y
40
+ 34y
39
+ ··· + 1832y + 289)
c
9
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y −4)(y
5
+ y
4
+ 8y
3
+ 3y
2
+ 3y + 1)
2
· (y
20
+ 18y
19
+ ··· − 86y + 1)
2
· (y
32
+ 20y
31
+ ··· − 30763848y + 839056)
29
