12n
0551
(K12n
0551
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 1 11 2 1 6 4 6 10
Solving Sequence
2,8
7 3 4 1
9,11
6 5 10 12
c
7
c
2
c
3
c
1
c
8
c
6
c
5
c
10
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
30
− 13u
29
+ ··· + 2b − 2, −7u
30
+ 37u
29
+ ··· + 4a − 40, u
31
− 5u
30
+ ··· + 26u − 4i
I
u
2
= hu
18
− u
17
+ ··· + b − 2, u
18
+ 2u
17
+ ··· + a + 1,
u
19
+ 5u
17
+ 13u
15
+ 20u
13
+ 20u
11
+ 13u
9
+ u
8
+ 7u
7
+ 2u
6
+ 4u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ 1i
I
u
3
= h758a
3
u
3
− 3539u
3
a
2
+ ··· + 1193a − 9295,
a
3
u
3
+ a
3
u
2
− 2u
3
a
2
+ a
4
+ a
3
u − a
2
u
2
− a
3
+ a
2
u − 2u
2
a + u
3
− a
2
+ 3au + 9u
2
+ 3a − 7u + 2,
u
4
+ u
2
− u + 1i
I
u
4
= h−18352u
5
a
3
+ 13327u
5
a
2
+ ··· + 704a − 29929, u
5
a
2
+ u
5
a + ··· + a
4
+ a
3
,
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 90 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
= h3u
30
− 13u
29
+ · · · + 2b − 2, −7u
30
+ 37u
29
+ · · · + 4a − 40, u
31
−
5u
30
+ · · · + 26u − 4i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
11
=
7
4
u
30
−
37
4
u
29
+ ··· −
223
4
u + 10
−
3
2
u
30
+
13
2
u
29
+ ··· +
9
2
u + 1
a
6
=
−
1
2
u
30
+
1
2
u
28
+ ··· − 22u +
9
2
−
5
2
u
30
+
25
2
u
29
+ ··· +
139
2
u − 12
a
5
=
3
2
u
30
− 8u
29
+ ··· − 48u +
17
2
−
1
2
u
30
+
5
2
u
29
+ ··· +
21
2
u − 2
a
10
=
11
4
u
30
−
49
4
u
29
+ ··· −
223
4
u + 10
−
5
2
u
30
+
19
2
u
29
+ ··· +
29
2
u − 1
a
12
=
1
2
u
30
− 5u
29
+ ··· − 48u +
17
2
−
1
2
u
30
+
7
2
u
29
+ ··· −
3
2
u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
30
+11u
29
−40u
28
+89u
27
−194u
26
+336u
25
−572u
24
+853u
23
−1224u
22
+1607u
21
−
2012u
20
+2378u
19
−2693u
18
+2898u
17
−3000u
16
+2942u
15
−2813u
14
+2557u
13
−2256u
12
+
1890u
11
−1511u
10
+1161u
9
−859u
8
+595u
7
−400u
6
+233u
5
−122u
4
+58u
3
−13u
2
+6u−14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 15u
30
+ ··· + 12u − 16
c
2
, c
7
u
31
+ 5u
30
+ ··· + 26u + 4
c
3
u
31
− 5u
30
+ ··· − 240u + 32
c
4
, c
6
, c
10
c
11
u
31
+ 7u
29
+ ··· + 3u + 1
c
5
, c
9
u
31
+ u
30
+ ··· + 4u + 1
c
8
u
31
+ 25u
30
+ ··· + 101226u + 9028
c
12
u
31
− 24u
30
+ ··· − 9728u + 1024
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 3y
30
+ ··· + 5360y −256
c
2
, c
7
y
31
+ 15y
30
+ ··· + 12y −16
c
3
y
31
− 9y
30
+ ··· + 29696y −1024
c
4
, c
6
, c
10
c
11
y
31
+ 14y
30
+ ··· − 11y −1
c
5
, c
9
y
31
− 49y
30
+ ··· + 50y −1
c
8
y
31
+ 3y
30
+ ··· − 146312468y −81504784
c
12
y
31
− 18y
30
+ ··· + 4980736y −1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.721636 + 0.688504I
a = 0.652136 − 0.856774I
b = −0.153998 + 0.558335I
0.12057 − 7.84511I −4.92980 + 6.31603I
u = −0.721636 − 0.688504I
a = 0.652136 + 0.856774I
b = −0.153998 − 0.558335I
0.12057 + 7.84511I −4.92980 − 6.31603I
u = 0.107386 + 1.053710I
a = 1.161140 + 0.418626I
b = −0.848962 + 0.418880I
−1.06007 − 1.48672I −11.73110 + 4.30166I
u = 0.107386 − 1.053710I
a = 1.161140 − 0.418626I
b = −0.848962 − 0.418880I
−1.06007 + 1.48672I −11.73110 − 4.30166I
u = −0.747524 + 0.519989I
a = −0.367732 + 0.710748I
b = 0.063240 − 0.394635I
4.39870 − 0.57100I −5.18268 + 2.58205I
u = −0.747524 − 0.519989I
a = −0.367732 − 0.710748I
b = 0.063240 + 0.394635I
4.39870 + 0.57100I −5.18268 − 2.58205I
u = −0.228069 + 0.871292I
a = 0.493234 − 0.013294I
b = −0.220969 + 0.195636I
−0.647219 − 1.174890I −7.74715 + 5.33716I
u = −0.228069 − 0.871292I
a = 0.493234 + 0.013294I
b = −0.220969 − 0.195636I
−0.647219 + 1.174890I −7.74715 − 5.33716I
u = 0.826592 + 0.330880I
a = 0.611177 − 0.577058I
b = 1.51649 + 1.30911I
−1.86480 − 10.61960I −6.01076 + 5.40369I
u = 0.826592 − 0.330880I
a = 0.611177 + 0.577058I
b = 1.51649 − 1.30911I
−1.86480 + 10.61960I −6.01076 − 5.40369I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.771083 + 0.435830I
a = −0.445507 + 0.696759I
b = −1.22832 − 0.83980I
3.95523 − 3.38934I −6.35399 + 4.30144I
u = 0.771083 − 0.435830I
a = −0.445507 − 0.696759I
b = −1.22832 + 0.83980I
3.95523 + 3.38934I −6.35399 − 4.30144I
u = −0.659178 + 0.906469I
a = 0.847117 + 0.308890I
b = −0.532248 + 0.049305I
−0.52577 + 2.60216I −5.79015 − 0.92756I
u = −0.659178 − 0.906469I
a = 0.847117 − 0.308890I
b = −0.532248 − 0.049305I
−0.52577 − 2.60216I −5.79015 + 0.92756I
u = 0.431568 + 1.070840I
a = −1.72983 − 0.61820I
b = 1.51123 − 0.88116I
−3.48253 + 3.49821I −13.1203 − 5.5567I
u = 0.431568 − 1.070840I
a = −1.72983 + 0.61820I
b = 1.51123 + 0.88116I
−3.48253 − 3.49821I −13.1203 + 5.5567I
u = 0.831503 + 0.123089I
a = 0.072492 + 0.269764I
b = −0.554560 + 0.979079I
−4.92001 + 1.57506I −6.24630 − 4.36146I
u = 0.831503 − 0.123089I
a = 0.072492 − 0.269764I
b = −0.554560 − 0.979079I
−4.92001 − 1.57506I −6.24630 + 4.36146I
u = 0.210275 + 1.194020I
a = −1.29566 − 1.42704I
b = 1.62781 + 0.12223I
−6.84341 − 7.58988I −11.74966 + 3.94255I
u = 0.210275 − 1.194020I
a = −1.29566 + 1.42704I
b = 1.62781 − 0.12223I
−6.84341 + 7.58988I −11.74966 − 3.94255I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618523 + 1.046160I
a = −0.569195 − 0.233428I
b = 0.386901 − 0.028623I
2.83735 − 4.61812I −7.27766 + 3.11789I
u = −0.618523 − 1.046160I
a = −0.569195 + 0.233428I
b = 0.386901 + 0.028623I
2.83735 + 4.61812I −7.27766 − 3.11789I
u = 0.601498 + 1.094000I
a = 1.80478 + 0.82107I
b = −1.93685 + 0.87675I
2.00079 + 8.57439I −9.56481 − 9.13529I
u = 0.601498 − 1.094000I
a = 1.80478 − 0.82107I
b = −1.93685 − 0.87675I
2.00079 − 8.57439I −9.56481 + 9.13529I
u = 0.372959 + 1.216560I
a = 1.28688 − 0.66870I
b = −0.421817 + 1.280630I
−9.03283 + 5.64879I −11.83814 − 7.15330I
u = 0.372959 − 1.216560I
a = 1.28688 + 0.66870I
b = −0.421817 − 1.280630I
−9.03283 − 5.64879I −11.83814 + 7.15330I
u = 0.587276 + 1.148200I
a = −2.51290 − 0.46864I
b = 2.17768 − 1.59943I
−4.3002 + 15.8732I −8.95437 − 9.00468I
u = 0.587276 − 1.148200I
a = −2.51290 + 0.46864I
b = 2.17768 + 1.59943I
−4.3002 − 15.8732I −8.95437 + 9.00468I
u = 0.501811 + 1.205770I
a = −0.157189 + 1.192800I
b = −0.733813 − 0.955023I
−8.15901 + 3.28278I −8.89616 + 2.41825I
u = 0.501811 − 1.205770I
a = −0.157189 − 1.192800I
b = −0.733813 + 0.955023I
−8.15901 − 3.28278I −8.89616 − 2.41825I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.465958
a = 0.798102
b = 0.696353
−0.881419 −11.2140
8
II.
I
u
2
= hu
18
−u
17
+· · ·+ b − 2, u
18
+2u
17
+· · ·+ a + 1, u
19
+5u
17
+· · ·+ 2u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
11
=
−u
18
− 2u
17
+ ··· − 3u − 1
−u
18
+ u
17
+ ··· + u + 2
a
6
=
u
17
+ 5u
15
+ ··· + u + 2
u
18
+ 5u
16
+ ··· + u
3
− 1
a
5
=
2u
17
+ 9u
15
+ ··· + u + 2
u
18
+ 5u
16
+ ··· + u − 1
a
10
=
−2u
17
− u
16
+ ··· − 2u − 1
−u
18
+ u
17
+ ··· + 2u
2
+ 2
a
12
=
−3u
18
− 2u
17
+ ··· − 6u − 2
−u
18
+ u
17
+ ··· + 2u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
17
− 10u
15
+ 4u
14
− 24u
13
+ 12u
12
− 34u
11
+ 17u
10
− 30u
9
+
6u
8
− 18u
7
− 7u
6
− 7u
5
− 6u
4
+ u
3
+ u
2
+ u − 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 10u
18
+ ··· − 4u + 1
c
2
u
19
+ 5u
17
+ ··· − 2u
2
− 1
c
3
u
19
− 3u
17
+ ··· + 3u − 2
c
4
, c
11
u
19
+ 6u
17
+ ··· − u + 1
c
5
, c
9
u
19
− u
18
+ ··· + 6u
2
+ 1
c
6
, c
10
u
19
+ 6u
17
+ ··· − u − 1
c
7
u
19
+ 5u
17
+ ··· + 2u
2
+ 1
c
8
u
19
+ u
17
+ ··· + 3u
2
+ 1
c
12
u
19
+ 7u
18
+ ··· + 3u + 2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 2y
18
+ ··· − 4y −1
c
2
, c
7
y
19
+ 10y
18
+ ··· − 4y −1
c
3
y
19
− 6y
18
+ ··· + 5y −4
c
4
, c
6
, c
10
c
11
y
19
+ 12y
18
+ ··· + 7y −1
c
5
, c
9
y
19
− 7y
18
+ ··· − 12y −1
c
8
y
19
+ 2y
18
+ ··· − 6y −1
c
12
y
19
− 15y
18
+ ··· − 35y −4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.342966 + 0.928812I
a = 1.348510 + 0.263101I
b = −0.760930 + 0.339185I
2.81022 − 1.37153I −9.77927 + 0.03000I
u = −0.342966 − 0.928812I
a = 1.348510 − 0.263101I
b = −0.760930 − 0.339185I
2.81022 + 1.37153I −9.77927 − 0.03000I
u = 0.462820 + 1.013630I
a = −2.71881 − 1.75930I
b = 2.96409 − 1.05294I
−5.17143 + 3.04865I −17.3001 − 5.4133I
u = 0.462820 − 1.013630I
a = −2.71881 + 1.75930I
b = 2.96409 + 1.05294I
−5.17143 − 3.04865I −17.3001 + 5.4133I
u = 0.233225 + 1.122880I
a = 0.57215 + 1.46143I
b = −1.222460 − 0.507809I
0.773516 − 0.146851I −4.77195 + 0.70902I
u = 0.233225 − 1.122880I
a = 0.57215 − 1.46143I
b = −1.222460 + 0.507809I
0.773516 + 0.146851I −4.77195 − 0.70902I
u = −0.666278 + 0.525489I
a = −0.803308 + 0.905672I
b = 0.208916 − 0.549594I
6.17150 − 0.46362I 0.865849 + 0.093263I
u = −0.666278 − 0.525489I
a = −0.803308 − 0.905672I
b = 0.208916 + 0.549594I
6.17150 + 0.46362I 0.865849 − 0.093263I
u = 0.755679 + 0.375560I
a = −0.759994 + 0.411460I
b = −0.93480 − 1.33254I
5.35455 − 2.68854I 0.27590 + 1.63116I
u = 0.755679 − 0.375560I
a = −0.759994 − 0.411460I
b = −0.93480 + 1.33254I
5.35455 + 2.68854I 0.27590 − 1.63116I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572364 + 1.036080I
a = −0.875217 − 0.298710I
b = 0.574390 − 0.089490I
4.65158 − 4.35826I −3.03168 + 5.37971I
u = −0.572364 − 1.036080I
a = −0.875217 + 0.298710I
b = 0.574390 + 0.089490I
4.65158 + 4.35826I −3.03168 − 5.37971I
u = 0.583300 + 1.114080I
a = 2.02438 + 0.07803I
b = −1.48959 + 1.53903I
3.18311 + 7.76425I −3.26242 − 5.87229I
u = 0.583300 − 1.114080I
a = 2.02438 − 0.07803I
b = −1.48959 − 1.53903I
3.18311 − 7.76425I −3.26242 + 5.87229I
u = −0.458473 + 1.178850I
a = −0.111178 + 0.351572I
b = −0.052777 − 0.243038I
−8.21489 − 4.24741I −10.19096 + 5.10189I
u = −0.458473 − 1.178850I
a = −0.111178 − 0.351572I
b = −0.052777 + 0.243038I
−8.21489 + 4.24741I −10.19096 − 5.10189I
u = 0.351995 + 0.609402I
a = 0.67301 − 2.19679I
b = 1.56998 + 0.91609I
−3.79826 + 0.59510I −11.16480 + 2.33336I
u = 0.351995 − 0.609402I
a = 0.67301 + 2.19679I
b = 1.56998 − 0.91609I
−3.79826 − 0.59510I −11.16480 − 2.33336I
u = −0.693876
a = −0.699080
b = 0.286370
−4.94005 −7.28110
13
III. I
u
3
= h758a
3
u
3
− 3539u
3
a
2
+ · · · + 1193a − 9295, a
3
u
3
− 2u
3
a
2
+ · · · +
3a + 2, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
2
a
9
=
−u
3
+ u
2
− u + 1
−u
2
+ u − 1
a
11
=
a
−0.0877721a
3
u
3
+ 0.409796a
2
u
3
+ ··· − 0.138143a + 1.07631
a
6
=
−0.0211904a
3
u
3
+ 0.0128532a
2
u
3
+ ··· + 0.183997a − 0.0683187
0.0507179a
3
u
3
− 0.325845a
2
u
3
+ ··· − 0.178092a − 0.754516
a
5
=
−0.0620658a
3
u
3
+ 0.234368a
2
u
3
+ ··· + 0.364057a − 0.254748
0.189787a
3
u
3
− 0.0823298a
2
u
3
+ ··· − 0.232631a − 1.50834
a
10
=
−0.100741a
3
u
3
− 0.123321a
2
u
3
+ ··· + 0.788675a + 0.351436
−0.0507179a
3
u
3
+ 0.575845a
2
u
3
+ ··· + 0.428092a + 1.50452
a
12
=
−0.0211904a
3
u
3
+ 0.0128532a
2
u
3
+ ··· + 0.183997a − 0.0683187
0.0100741a
3
u
3
+ 0.387332a
2
u
3
+ ··· − 0.103868a + 2.58986
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 6
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
4
c
2
, c
7
(u
4
+ u
2
+ u + 1)
4
c
3
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
4
c
4
, c
6
, c
10
c
11
u
16
+ 3u
14
+ ··· + 4u + 19
c
5
, c
9
u
16
− 5u
14
+ ··· − 26u + 31
c
8
(u
4
− 2u
3
+ 3u
2
− u + 1)
4
c
12
(u
2
+ u − 1)
8
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
4
c
2
, c
7
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
4
c
3
(y
4
− y
3
+ 2y
2
+ 7y + 4)
4
c
4
, c
6
, c
10
c
11
y
16
+ 6y
15
+ ··· + 1428y + 361
c
5
, c
9
y
16
− 10y
15
+ ··· − 5760y + 961
c
12
(y
2
− 3y + 1)
8
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = 0.499523 − 0.414695I
b = 1.49449 + 0.67486I
−2.96775 + 1.39709I −4.22981 − 3.86736I
u = 0.547424 + 0.585652I
a = −1.41065 − 0.30491I
b = −0.139658 + 0.204609I
4.92794 + 1.39709I −4.22981 − 3.86736I
u = 0.547424 + 0.585652I
a = 0.85743 + 1.26440I
b = −0.789932 − 0.962845I
4.92794 + 1.39709I −4.22981 − 3.86736I
u = 0.547424 + 0.585652I
a = 0.94882 − 2.09729I
b = 0.93920 + 1.31022I
−2.96775 + 1.39709I −4.22981 − 3.86736I
u = 0.547424 − 0.585652I
a = 0.499523 + 0.414695I
b = 1.49449 − 0.67486I
−2.96775 − 1.39709I −4.22981 + 3.86736I
u = 0.547424 − 0.585652I
a = −1.41065 + 0.30491I
b = −0.139658 − 0.204609I
4.92794 − 1.39709I −4.22981 + 3.86736I
u = 0.547424 − 0.585652I
a = 0.85743 − 1.26440I
b = −0.789932 + 0.962845I
4.92794 − 1.39709I −4.22981 + 3.86736I
u = 0.547424 − 0.585652I
a = 0.94882 + 2.09729I
b = 0.93920 − 1.31022I
−2.96775 − 1.39709I −4.22981 + 3.86736I
u = −0.547424 + 1.120870I
a = 1.98981 − 0.07512I
b = −1.28422 − 1.69317I
1.32281 − 7.64338I −9.77019 + 6.51087I
u = −0.547424 + 1.120870I
a = −0.79640 + 1.83226I
b = 1.57066 − 0.08141I
−6.57287 − 7.64338I −9.77019 + 6.51087I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 1.120870I
a = 1.77511 − 1.01217I
b = −2.38632 − 0.09060I
−6.57287 − 7.64338I −9.77019 + 6.51087I
u = −0.547424 + 1.120870I
a = −2.36364 − 0.23813I
b = 1.59578 + 1.75888I
1.32281 − 7.64338I −9.77019 + 6.51087I
u = −0.547424 − 1.120870I
a = 1.98981 + 0.07512I
b = −1.28422 + 1.69317I
1.32281 + 7.64338I −9.77019 − 6.51087I
u = −0.547424 − 1.120870I
a = −0.79640 − 1.83226I
b = 1.57066 + 0.08141I
−6.57287 + 7.64338I −9.77019 − 6.51087I
u = −0.547424 − 1.120870I
a = 1.77511 + 1.01217I
b = −2.38632 + 0.09060I
−6.57287 + 7.64338I −9.77019 − 6.51087I
u = −0.547424 − 1.120870I
a = −2.36364 + 0.23813I
b = 1.59578 − 1.75888I
1.32281 + 7.64338I −9.77019 − 6.51087I
18
IV. I
u
4
= h−18352u
5
a
3
+ 13327u
5
a
2
+ · · · + 704a − 29929, u
5
a
2
+ u
5
a + · · · +
a
4
+ a
3
, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
u
4
+ u
2
+ u + 1
−2u
5
− u
4
− 3u
3
− 2u
2
− 3u − 2
a
11
=
a
1.15472a
3
u
5
− 0.838545a
2
u
5
+ ··· − 0.0442962a + 1.88316
a
6
=
0.0661297a
3
u
5
+ 0.889259a
2
u
5
+ ··· + 0.219782a + 0.555591
−1.41358a
3
u
5
+ 0.949475a
2
u
5
+ ··· − 0.855974a − 1.68401
a
5
=
−0.0667590a
3
u
5
+ 0.480966a
2
u
5
+ ··· + 0.115900a + 1.06424
−1.27723a
3
u
5
+ 0.321525a
2
u
5
+ ··· − 1.09835a − 1.10174
a
10
=
0.0751903a
3
u
5
+ 0.758007a
2
u
5
+ ··· + 0.385956a − 0.569999
0.960423a
3
u
5
− 1.91279a
2
u
5
+ ··· + 1.61442a + 2.68747
a
12
=
0.0661297a
3
u
5
+ 0.889259a
2
u
5
+ ··· + 0.219782a − 1.44441
1.21972a
3
u
5
− 0.682879a
2
u
5
+ ··· + 0.779714a + 3.95445
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u − 10
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
4
c
2
, c
7
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
4
c
3
(u
3
− u
2
+ 1)
8
c
4
, c
6
, c
10
c
11
u
24
− u
23
+ ··· + 16u + 11
c
5
, c
9
u
24
+ u
23
+ ··· + 186u + 79
c
8
(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
4
c
12
(u
2
+ u − 1)
12
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
4
c
2
, c
7
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
4
c
3
(y
3
− y
2
+ 2y −1)
8
c
4
, c
6
, c
10
c
11
y
24
+ 9y
23
+ ··· + 1856y + 121
c
5
, c
9
y
24
− 15y
23
+ ··· − 45972y + 6241
c
12
(y
2
− 3y + 1)
12
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −0.211070 + 0.743684I
b = −0.224034 + 0.553154I
3.68210 + 2.82812I −6.49024 − 2.97945I
u = 0.498832 + 1.001300I
a = 1.86886 + 0.18851I
b = −1.51557 + 0.21123I
3.68210 + 2.82812I −6.49024 − 2.97945I
u = 0.498832 + 1.001300I
a = −2.16524 − 0.68774I
b = 2.43868 − 1.28895I
−4.21358 + 2.82812I −6.49024 − 2.97945I
u = 0.498832 + 1.001300I
a = −2.17491 − 1.75278I
b = 2.11567 − 0.71224I
−4.21358 + 2.82812I −6.49024 − 2.97945I
u = 0.498832 − 1.001300I
a = −0.211070 − 0.743684I
b = −0.224034 − 0.553154I
3.68210 − 2.82812I −6.49024 + 2.97945I
u = 0.498832 − 1.001300I
a = 1.86886 − 0.18851I
b = −1.51557 − 0.21123I
3.68210 − 2.82812I −6.49024 + 2.97945I
u = 0.498832 − 1.001300I
a = −2.16524 + 0.68774I
b = 2.43868 + 1.28895I
−4.21358 − 2.82812I −6.49024 + 2.97945I
u = 0.498832 − 1.001300I
a = −2.17491 + 1.75278I
b = 2.11567 + 0.71224I
−4.21358 − 2.82812I −6.49024 + 2.97945I
u = −0.284920 + 1.115140I
a = 1.029620 − 0.410831I
b = −0.672823 − 1.187000I
−8.35116 −13.01951 + 0.I
u = −0.284920 + 1.115140I
a = −0.32107 + 1.53891I
b = 1.092390 − 0.411344I
−0.455481 −13.01951 + 0.I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.284920 + 1.115140I
a = 0.89594 − 1.36997I
b = −1.47716 + 0.53887I
−0.455481 −13.01951 + 0.I
u = −0.284920 + 1.115140I
a = −2.53465 − 0.03145I
b = 1.68015 + 0.85313I
−8.35116 −13.01951 + 0.I
u = −0.284920 − 1.115140I
a = 1.029620 + 0.410831I
b = −0.672823 + 1.187000I
−8.35116 −13.01951 + 0.I
u = −0.284920 − 1.115140I
a = −0.32107 − 1.53891I
b = 1.092390 + 0.411344I
−0.455481 −13.01951 + 0.I
u = −0.284920 − 1.115140I
a = 0.89594 + 1.36997I
b = −1.47716 − 0.53887I
−0.455481 −13.01951 + 0.I
u = −0.284920 − 1.115140I
a = −2.53465 + 0.03145I
b = 1.68015 − 0.85313I
−8.35116 −13.01951 + 0.I
u = −0.713912 + 0.305839I
a = 0.805409 + 0.530294I
b = 0.83973 − 1.49814I
3.68210 + 2.82812I −6.49024 − 2.97945I
u = −0.713912 + 0.305839I
a = −0.874949 + 0.153226I
b = −0.87848 + 1.19410I
3.68210 + 2.82812I −6.49024 − 2.97945I
u = −0.713912 + 0.305839I
a = −0.16062 − 1.58358I
b = −1.309340 + 0.402018I
−4.21358 + 2.82812I −6.49024 − 2.97945I
u = −0.713912 + 0.305839I
a = 0.342678 − 0.205899I
b = 1.41079 + 0.39396I
−4.21358 + 2.82812I −6.49024 − 2.97945I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.713912 − 0.305839I
a = 0.805409 − 0.530294I
b = 0.83973 + 1.49814I
3.68210 − 2.82812I −6.49024 + 2.97945I
u = −0.713912 − 0.305839I
a = −0.874949 − 0.153226I
b = −0.87848 − 1.19410I
3.68210 − 2.82812I −6.49024 + 2.97945I
u = −0.713912 − 0.305839I
a = −0.16062 + 1.58358I
b = −1.309340 − 0.402018I
−4.21358 − 2.82812I −6.49024 + 2.97945I
u = −0.713912 − 0.305839I
a = 0.342678 + 0.205899I
b = 1.41079 − 0.39396I
−4.21358 − 2.82812I −6.49024 + 2.97945I
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
4
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
4
· (u
19
− 10u
18
+ ··· − 4u + 1)(u
31
+ 15u
30
+ ··· + 12u − 16)
c
2
(u
4
+ u
2
+ u + 1)
4
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
4
· (u
19
+ 5u
17
+ ··· − 2u
2
− 1)(u
31
+ 5u
30
+ ··· + 26u + 4)
c
3
((u
3
− u
2
+ 1)
8
)(u
4
+ 3u
3
+ ··· + 3u + 2)
4
(u
19
− 3u
17
+ ··· + 3u − 2)
· (u
31
− 5u
30
+ ··· − 240u + 32)
c
4
, c
11
(u
16
+ 3u
14
+ ··· + 4u + 19)(u
19
+ 6u
17
+ ··· − u + 1)
· (u
24
− u
23
+ ··· + 16u + 11)(u
31
+ 7u
29
+ ··· + 3u + 1)
c
5
, c
9
(u
16
− 5u
14
+ ··· − 26u + 31)(u
19
− u
18
+ ··· + 6u
2
+ 1)
· (u
24
+ u
23
+ ··· + 186u + 79)(u
31
+ u
30
+ ··· + 4u + 1)
c
6
, c
10
(u
16
+ 3u
14
+ ··· + 4u + 19)(u
19
+ 6u
17
+ ··· − u − 1)
· (u
24
− u
23
+ ··· + 16u + 11)(u
31
+ 7u
29
+ ··· + 3u + 1)
c
7
(u
4
+ u
2
+ u + 1)
4
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
4
· (u
19
+ 5u
17
+ ··· + 2u
2
+ 1)(u
31
+ 5u
30
+ ··· + 26u + 4)
c
8
(u
4
− 2u
3
+ 3u
2
− u + 1)
4
(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
4
· (u
19
+ u
17
+ ··· + 3u
2
+ 1)(u
31
+ 25u
30
+ ··· + 101226u + 9028)
c
12
((u
2
+ u − 1)
20
)(u
19
+ 7u
18
+ ··· + 3u + 2)
· (u
31
− 24u
30
+ ··· − 9728u + 1024)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
4
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
4
· (y
19
+ 2y
18
+ ··· − 4y −1)(y
31
+ 3y
30
+ ··· + 5360y −256)
c
2
, c
7
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
4
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
4
· (y
19
+ 10y
18
+ ··· − 4y −1)(y
31
+ 15y
30
+ ··· + 12y −16)
c
3
(y
3
− y
2
+ 2y −1)
8
(y
4
− y
3
+ 2y
2
+ 7y + 4)
4
· (y
19
− 6y
18
+ ··· + 5y −4)(y
31
− 9y
30
+ ··· + 29696y −1024)
c
4
, c
6
, c
10
c
11
(y
16
+ 6y
15
+ ··· + 1428y + 361)(y
19
+ 12y
18
+ ··· + 7y −1)
· (y
24
+ 9y
23
+ ··· + 1856y + 121)(y
31
+ 14y
30
+ ··· − 11y −1)
c
5
, c
9
(y
16
− 10y
15
+ ··· − 5760y + 961)(y
19
− 7y
18
+ ··· − 12y −1)
· (y
24
− 15y
23
+ ··· − 45972y + 6241)(y
31
− 49y
30
+ ··· + 50y −1)
c
8
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
4
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
4
· (y
19
+ 2y
18
+ ··· − 6y −1)
· (y
31
+ 3y
30
+ ··· − 146312468y −81504784)
c
12
((y
2
− 3y + 1)
20
)(y
19
− 15y
18
+ ··· − 35y −4)
· (y
31
− 18y
30
+ ··· + 4980736y −1048576)
26
