12a
0974
(K12a
0974
)
A knot diagram
1
Linearized knot diagam
4 6 11 7 3 10 1 12 5 2 9 8
Solving Sequence
8,12
9
1,4
2 7 5 11 3 10 6
c
8
c
12
c
1
c
7
c
4
c
11
c
3
c
10
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h164445056849340u
52
+ 1528500349483699u
51
+ ··· + 224970979095817b − 3074775125088731,
− 1.18394 × 10
14
u
52
− 1.52783 × 10
15
u
51
+ ··· + 2.24971 × 10
15
a + 4.96511 × 10
16
,
u
53
+ 8u
52
+ ··· − 90u − 10i
I
u
2
= hu
27
a − u
28
+ ··· + b − a, 2u
28
− 9u
27
+ ··· − a − 3, u
29
− 5u
28
+ ··· + 3u − 1i
I
u
3
= h−u
22
+ 4u
21
+ ··· + b + 3, 3u
22
− 15u
21
+ ··· + 2a + 13, u
23
− 5u
22
+ ··· + 15u − 2i
* 3 irreducible components of dim
C
= 0, with total 134 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
= h1.64 × 10
14
u
52
+ 1.53 × 10
15
u
51
+ · · · + 2.25 × 10
14
b − 3.07 ×
10
15
, −1.18 × 10
14
u
52
− 1.53 × 10
15
u
51
+ · · · + 2.25 × 10
15
a + 4.97 ×
10
16
, u
53
+ 8u
52
+ · · · − 90u − 10i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
0.0526262u
52
+ 0.679123u
51
+ ··· − 152.718u − 22.0700
−0.730961u
52
− 6.79421u
51
+ ··· + 138.193u + 13.6674
a
2
=
0.951306u
52
+ 5.67430u
51
+ ··· + 62.4823u + 6.08672
0.0348007u
52
+ 1.25907u
51
+ ··· − 17.3975u − 0.306208
a
7
=
u
2
+ 1
−u
2
a
5
=
−1.10863u
52
− 7.59814u
51
+ ··· − 101.312u − 14.6597
−0.258114u
52
− 2.60484u
51
+ ··· + 17.3337u − 0.526262
a
11
=
u
u
3
+ u
a
3
=
0.607936u
52
+ 5.21530u
51
+ ··· − 182.592u − 23.9187
−0.681469u
52
− 6.43444u
51
+ ··· + 122.305u + 12.7557
a
10
=
0.136819u
52
+ 0.281235u
51
+ ··· − 6.32329u − 1.45857
0.651638u
52
+ 6.44090u
51
+ ··· − 60.8623u − 7.32736
a
6
=
−0.202862u
52
− 1.47817u
51
+ ··· − 33.2032u − 1.30412
−0.528097u
52
− 4.04273u
51
+ ··· − 8.57804u − 2.01689
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
1416175396984759
224970979095817
u
52
−
11695896348510825
224970979095817
u
51
+ ···+
110459786772108940
224970979095817
u +
4937112965853666
224970979095817
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
53
− u
52
+ ··· + 11u + 1
c
2
, c
5
u
53
− 14u
52
+ ··· − 604u + 58
c
3
, c
9
u
53
− u
52
+ ··· + 76u + 79
c
6
, c
10
u
53
+ u
52
+ ··· + 5u + 1
c
7
, c
8
, c
11
c
12
u
53
− 8u
52
+ ··· − 90u + 10
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
53
+ 37y
52
+ ··· − 71y −1
c
2
, c
5
y
53
+ 30y
52
+ ··· + 4636y −3364
c
3
, c
9
y
53
+ 9y
52
+ ··· − 51894y −6241
c
6
, c
10
y
53
+ 31y
52
+ ··· − 87y −1
c
7
, c
8
, c
11
c
12
y
53
+ 64y
52
+ ··· − 1080y −100
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.571488 + 0.854314I
a = 0.032566 − 0.185130I
b = 1.47379 + 0.14025I
6.0412 + 14.8317I 0
u = −0.571488 − 0.854314I
a = 0.032566 + 0.185130I
b = 1.47379 − 0.14025I
6.0412 − 14.8317I 0
u = −0.333373 + 0.893716I
a = 0.122196 + 0.270454I
b = 0.752660 − 0.742316I
3.25780 − 1.48286I 0
u = −0.333373 − 0.893716I
a = 0.122196 − 0.270454I
b = 0.752660 + 0.742316I
3.25780 + 1.48286I 0
u = −0.514882 + 0.797117I
a = −0.190321 + 0.041120I
b = −1.47025 − 0.02613I
2.18355 + 8.95648I 0
u = −0.514882 − 0.797117I
a = −0.190321 − 0.041120I
b = −1.47025 + 0.02613I
2.18355 − 8.95648I 0
u = −0.361910 + 0.832045I
a = 0.048979 + 0.404557I
b = 1.59883 − 0.06719I
7.41008 + 3.50903I 0
u = −0.361910 − 0.832045I
a = 0.048979 − 0.404557I
b = 1.59883 + 0.06719I
7.41008 − 3.50903I 0
u = −0.533035 + 0.701728I
a = −0.185867 + 0.304202I
b = −0.714550 + 0.710437I
6.11438 + 3.16811I 0
u = −0.533035 − 0.701728I
a = −0.185867 − 0.304202I
b = −0.714550 − 0.710437I
6.11438 − 3.16811I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.508757 + 1.013150I
a = 0.189315 − 0.149873I
b = −0.836774 + 0.733674I
6.93290 − 5.87882I 0
u = −0.508757 − 1.013150I
a = 0.189315 + 0.149873I
b = −0.836774 − 0.733674I
6.93290 + 5.87882I 0
u = −0.792218 + 0.065716I
a = 0.613499 + 1.156200I
b = 0.058973 + 0.266092I
3.65102 − 10.30440I −8.91398 + 7.10436I
u = −0.792218 − 0.065716I
a = 0.613499 − 1.156200I
b = 0.058973 − 0.266092I
3.65102 + 10.30440I −8.91398 − 7.10436I
u = 0.146692 + 1.220860I
a = 0.051603 + 0.425034I
b = 0.200402 − 0.509149I
2.65741 − 1.99035I 0
u = 0.146692 − 1.220860I
a = 0.051603 − 0.425034I
b = 0.200402 + 0.509149I
2.65741 + 1.99035I 0
u = 0.362018 + 0.677893I
a = −0.245195 + 0.777289I
b = 0.514294 − 0.329515I
1.50207 − 2.55064I −9.75941 + 4.81296I
u = 0.362018 − 0.677893I
a = −0.245195 − 0.777289I
b = 0.514294 + 0.329515I
1.50207 + 2.55064I −9.75941 − 4.81296I
u = 0.690789 + 0.151095I
a = 0.180428 − 0.506714I
b = −0.137160 + 0.263242I
−0.340350 − 0.823156I −15.6364 + 2.5706I
u = 0.690789 − 0.151095I
a = 0.180428 + 0.506714I
b = −0.137160 − 0.263242I
−0.340350 + 0.823156I −15.6364 − 2.5706I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.084709 + 0.684083I
a = −0.34764 − 1.68310I
b = −1.17130 + 0.93302I
4.62340 − 0.33572I −1.95908 − 0.70589I
u = 0.084709 − 0.684083I
a = −0.34764 + 1.68310I
b = −1.17130 − 0.93302I
4.62340 + 0.33572I −1.95908 + 0.70589I
u = −0.679848 + 0.096270I
a = −0.595374 − 1.265890I
b = −0.100020 − 0.402728I
0.07833 − 4.93869I −12.17317 + 4.95425I
u = −0.679848 − 0.096270I
a = −0.595374 + 1.265890I
b = −0.100020 + 0.402728I
0.07833 + 4.93869I −12.17317 − 4.95425I
u = 0.331739 + 1.322100I
a = 0.345446 − 0.293824I
b = −0.497956 + 0.157982I
4.28652 − 4.55905I 0
u = 0.331739 − 1.322100I
a = 0.345446 + 0.293824I
b = −0.497956 − 0.157982I
4.28652 + 4.55905I 0
u = −0.548171 + 0.130924I
a = 0.97680 − 1.21375I
b = 0.379782 − 0.413933I
4.58827 + 0.51390I −6.27299 − 1.69527I
u = −0.548171 − 0.130924I
a = 0.97680 + 1.21375I
b = 0.379782 + 0.413933I
4.58827 − 0.51390I −6.27299 + 1.69527I
u = −0.193987 + 0.484551I
a = −0.23294 − 1.53315I
b = −1.067610 − 0.351475I
−1.41579 + 0.84257I −19.4951 − 7.3381I
u = −0.193987 − 0.484551I
a = −0.23294 + 1.53315I
b = −1.067610 + 0.351475I
−1.41579 − 0.84257I −19.4951 + 7.3381I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.014741 + 0.472127I
a = 1.57493 + 1.38924I
b = 0.746773 − 0.962501I
3.83390 − 0.06012I −2.56930 − 0.12602I
u = −0.014741 − 0.472127I
a = 1.57493 − 1.38924I
b = 0.746773 + 0.962501I
3.83390 + 0.06012I −2.56930 + 0.12602I
u = −0.02782 + 1.57717I
a = 1.95052 + 0.55742I
b = −2.42122 − 1.38838I
5.78164 + 1.46731I 0
u = −0.02782 − 1.57717I
a = 1.95052 − 0.55742I
b = −2.42122 + 1.38838I
5.78164 − 1.46731I 0
u = −0.01993 + 1.59734I
a = −1.79395 + 0.64309I
b = 2.58325 − 0.28191I
11.20290 + 0.20541I 0
u = −0.01993 − 1.59734I
a = −1.79395 − 0.64309I
b = 2.58325 + 0.28191I
11.20290 − 0.20541I 0
u = 0.07759 + 1.59910I
a = −1.243800 − 0.046636I
b = 1.55661 + 0.47044I
9.25697 − 4.06418I 0
u = 0.07759 − 1.59910I
a = −1.243800 + 0.046636I
b = 1.55661 − 0.47044I
9.25697 + 4.06418I 0
u = −0.16941 + 1.61795I
a = 1.35369 − 0.99049I
b = −2.16566 + 1.05980I
13.9905 + 5.8535I 0
u = −0.16941 − 1.61795I
a = 1.35369 + 0.99049I
b = −2.16566 − 1.05980I
13.9905 − 5.8535I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02664 + 1.62849I
a = 2.05682 − 0.56120I
b = −2.82798 + 0.09247I
12.75440 − 0.77114I 0
u = 0.02664 − 1.62849I
a = 2.05682 + 0.56120I
b = −2.82798 − 0.09247I
12.75440 + 0.77114I 0
u = −0.09741 + 1.63542I
a = −1.54132 + 0.75143I
b = 2.30697 − 0.60574I
11.84370 + 0.11908I 0
u = −0.09741 − 1.63542I
a = −1.54132 − 0.75143I
b = 2.30697 + 0.60574I
11.84370 − 0.11908I 0
u = −0.14856 + 1.64246I
a = 2.41249 − 0.23895I
b = −3.41599 − 0.26515I
10.5226 + 11.4856I 0
u = −0.14856 − 1.64246I
a = 2.41249 + 0.23895I
b = −3.41599 + 0.26515I
10.5226 − 11.4856I 0
u = −0.10034 + 1.64902I
a = −2.48542 + 0.14164I
b = 3.42004 + 0.46088I
15.9769 + 5.2810I 0
u = −0.10034 − 1.64902I
a = −2.48542 − 0.14164I
b = 3.42004 − 0.46088I
15.9769 − 5.2810I 0
u = 0.329619
a = 0.926533
b = −0.282332
−0.644263 −15.7010
u = −0.16800 + 1.66325I
a = −2.36636 + 0.17556I
b = 3.33573 + 0.29398I
14.6437 + 17.6986I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16800 − 1.66325I
a = −2.36636 − 0.17556I
b = 3.33573 − 0.29398I
14.6437 − 17.6986I 0
u = −0.10112 + 1.71662I
a = 1.35564 − 0.64503I
b = −1.96049 + 0.55509I
16.5969 − 3.5463I 0
u = −0.10112 − 1.71662I
a = 1.35564 + 0.64503I
b = −1.96049 − 0.55509I
16.5969 + 3.5463I 0
10
II.
I
u
2
= hu
27
a−u
28
+· · ·+b−a, 2u
28
−9u
27
+· · ·−a−3, u
29
−5u
28
+· · ·+3u−1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
a
−u
27
a + u
28
+ ··· + a − 2u
a
2
=
u
28
a − 5u
27
a + ··· − 8u + 2
u
26
a + u
27
+ ··· − au + 3u
a
7
=
u
2
+ 1
−u
2
a
5
=
u
28
a − 5u
27
a + ··· − 4au + 2a
−u
27
+ 6u
26
+ ··· + au − u
a
11
=
u
u
3
+ u
a
3
=
−u
28
a + 5u
27
a + ··· + 3au + u
−u
27
+ 6u
26
+ ··· + au − u
a
10
=
u
28
a − 5u
27
a + ··· + 2a − 2
u
27
− 4u
26
+ ··· − au + 3u
a
6
=
u
28
a − 5u
27
a + ··· + 2a + 1
u
27
− 6u
26
+ ··· + au − 7u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
27
+ 20u
26
− 116u
25
+ 400u
24
− 1332u
23
+ 3464u
22
−
8320u
21
+ 17056u
20
− 31872u
19
+ 52660u
18
− 78908u
17
+ 105992u
16
− 128548u
15
+
140200u
14
− 137200u
13
+ 120424u
12
− 94128u
11
+ 65704u
10
− 40668u
9
+ 22460u
8
−
11040u
7
+ 4780u
6
− 1836u
5
+ 588u
4
− 192u
3
+ 60u
2
− 16u − 10
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
58
− 9u
57
+ ··· − 630u + 229
c
2
, c
5
(u
29
+ 9u
28
+ ··· + 5u + 1)
2
c
3
, c
9
u
58
− u
57
+ ··· + 1134u + 197
c
6
, c
10
u
58
+ 5u
57
+ ··· + 4u + 1
c
7
, c
8
, c
11
c
12
(u
29
+ 5u
28
+ ··· + 3u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
58
− 5y
57
+ ··· + 1349912y + 52441
c
2
, c
5
(y
29
+ 19y
28
+ ··· − 13y −1)
2
c
3
, c
9
y
58
+ 19y
57
+ ··· − 508200y + 38809
c
6
, c
10
y
58
− 9y
57
+ ··· − 12y + 1
c
7
, c
8
, c
11
c
12
(y
29
+ 35y
28
+ ··· − 13y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.195688 + 0.954423I
a = −0.972128 − 0.906034I
b = 1.76849 + 0.94660I
6.38732 − 5.06785I 0.07562 + 6.89681I
u = 0.195688 + 0.954423I
a = −0.369914 + 0.336353I
b = −1.063590 + 0.478683I
6.38732 − 5.06785I 0.07562 + 6.89681I
u = 0.195688 − 0.954423I
a = −0.972128 + 0.906034I
b = 1.76849 − 0.94660I
6.38732 + 5.06785I 0.07562 − 6.89681I
u = 0.195688 − 0.954423I
a = −0.369914 − 0.336353I
b = −1.063590 − 0.478683I
6.38732 + 5.06785I 0.07562 − 6.89681I
u = 0.501023 + 0.778198I
a = 0.130975 + 0.416319I
b = 1.072090 − 0.191134I
1.64148 − 3.39274I −11.48736 + 3.20502I
u = 0.501023 + 0.778198I
a = −0.169674 + 0.385781I
b = −0.711264 − 0.349089I
1.64148 − 3.39274I −11.48736 + 3.20502I
u = 0.501023 − 0.778198I
a = 0.130975 − 0.416319I
b = 1.072090 + 0.191134I
1.64148 + 3.39274I −11.48736 − 3.20502I
u = 0.501023 − 0.778198I
a = −0.169674 − 0.385781I
b = −0.711264 + 0.349089I
1.64148 + 3.39274I −11.48736 − 3.20502I
u = 0.566469 + 0.934578I
a = 0.467515 − 0.263005I
b = −1.364860 + 0.113870I
2.84920 − 5.41618I −8.6789 + 12.8683I
u = 0.566469 + 0.934578I
a = 0.256548 − 0.030398I
b = 0.670641 − 0.168517I
2.84920 − 5.41618I −8.6789 + 12.8683I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.566469 − 0.934578I
a = 0.467515 + 0.263005I
b = −1.364860 − 0.113870I
2.84920 + 5.41618I −8.6789 − 12.8683I
u = 0.566469 − 0.934578I
a = 0.256548 + 0.030398I
b = 0.670641 + 0.168517I
2.84920 + 5.41618I −8.6789 − 12.8683I
u = 0.786511 + 0.103322I
a = 0.075590 − 0.942723I
b = −0.203314 + 0.156273I
−0.273694 − 0.889339I −18.0678 + 6.3049I
u = 0.786511 + 0.103322I
a = 0.313505 + 0.056568I
b = −0.065851 + 0.346476I
−0.273694 − 0.889339I −18.0678 + 6.3049I
u = 0.786511 − 0.103322I
a = 0.075590 + 0.942723I
b = −0.203314 − 0.156273I
−0.273694 + 0.889339I −18.0678 − 6.3049I
u = 0.786511 − 0.103322I
a = 0.313505 − 0.056568I
b = −0.065851 − 0.346476I
−0.273694 + 0.889339I −18.0678 − 6.3049I
u = 0.494082 + 0.587228I
a = 0.302521 + 0.875921I
b = 0.983777 − 0.141714I
1.43997 − 3.32019I −12.1625 + 7.9197I
u = 0.494082 + 0.587228I
a = −0.583892 + 0.586111I
b = −0.304504 − 0.604439I
1.43997 − 3.32019I −12.1625 + 7.9197I
u = 0.494082 − 0.587228I
a = 0.302521 − 0.875921I
b = 0.983777 + 0.141714I
1.43997 + 3.32019I −12.1625 − 7.9197I
u = 0.494082 − 0.587228I
a = −0.583892 − 0.586111I
b = −0.304504 + 0.604439I
1.43997 + 3.32019I −12.1625 − 7.9197I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.216772 + 0.623278I
a = −1.076190 − 0.337838I
b = 2.01966 + 0.88632I
3.13189 + 6.56560I −7.1171 − 12.8291I
u = −0.216772 + 0.623278I
a = 0.41367 + 2.27782I
b = −0.130503 + 0.584963I
3.13189 + 6.56560I −7.1171 − 12.8291I
u = −0.216772 − 0.623278I
a = −1.076190 + 0.337838I
b = 2.01966 − 0.88632I
3.13189 − 6.56560I −7.1171 + 12.8291I
u = −0.216772 − 0.623278I
a = 0.41367 − 2.27782I
b = −0.130503 − 0.584963I
3.13189 − 6.56560I −7.1171 + 12.8291I
u = −0.188616 + 0.478965I
a = 0.044120 − 1.082270I
b = −1.256420 − 0.410029I
−1.41975 + 0.83016I −16.3280 − 7.8903I
u = −0.188616 + 0.478965I
a = −0.34963 − 1.92596I
b = −0.746967 − 0.337731I
−1.41975 + 0.83016I −16.3280 − 7.8903I
u = −0.188616 − 0.478965I
a = 0.044120 + 1.082270I
b = −1.256420 + 0.410029I
−1.41975 − 0.83016I −16.3280 + 7.8903I
u = −0.188616 − 0.478965I
a = −0.34963 + 1.92596I
b = −0.746967 + 0.337731I
−1.41975 − 0.83016I −16.3280 + 7.8903I
u = 0.505604
a = 0.870038 + 0.975031I
b = −0.376046 + 0.324956I
−0.296707 −14.3160
u = 0.505604
a = 0.870038 − 0.975031I
b = −0.376046 − 0.324956I
−0.296707 −14.3160
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04467 + 1.55722I
a = 0.023319 + 0.830907I
b = −0.295170 − 0.221687I
8.27486 − 4.88057I −12.00000 + 5.42301I
u = 0.04467 + 1.55722I
a = −2.56750 − 0.54184I
b = 3.67601 + 0.75264I
8.27486 − 4.88057I −12.00000 + 5.42301I
u = 0.04467 − 1.55722I
a = 0.023319 − 0.830907I
b = −0.295170 + 0.221687I
8.27486 + 4.88057I −12.00000 − 5.42301I
u = 0.04467 − 1.55722I
a = −2.56750 + 0.54184I
b = 3.67601 − 0.75264I
8.27486 + 4.88057I −12.00000 − 5.42301I
u = −0.02297 + 1.57694I
a = 1.031300 + 0.891923I
b = −1.27596 − 1.98763I
5.75764 + 1.39775I −12.00000 + 0.I
u = −0.02297 + 1.57694I
a = 2.42065 + 0.36806I
b = −2.90576 − 0.83473I
5.75764 + 1.39775I −12.00000 + 0.I
u = −0.02297 − 1.57694I
a = 1.031300 − 0.891923I
b = −1.27596 + 1.98763I
5.75764 − 1.39775I −12.00000 + 0.I
u = −0.02297 − 1.57694I
a = 2.42065 − 0.36806I
b = −2.90576 + 0.83473I
5.75764 − 1.39775I −12.00000 + 0.I
u = −0.04870 + 1.60940I
a = 0.30754 − 1.70729I
b = −0.53659 + 3.24918I
10.92340 + 7.47108I −12.00000 + 0.I
u = −0.04870 + 1.60940I
a = −3.14722 − 0.78581I
b = 3.59046 + 0.95749I
10.92340 + 7.47108I −12.00000 + 0.I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04870 − 1.60940I
a = 0.30754 + 1.70729I
b = −0.53659 − 3.24918I
10.92340 − 7.47108I −12.00000 + 0.I
u = −0.04870 − 1.60940I
a = −3.14722 + 0.78581I
b = 3.59046 − 0.95749I
10.92340 − 7.47108I −12.00000 + 0.I
u = −0.243173 + 0.281252I
a = 2.16112 − 0.32713I
b = 0.955798 + 0.909043I
2.20930 − 4.73918I −12.69833 + 0.12567I
u = −0.243173 + 0.281252I
a = 0.20097 + 3.38461I
b = 0.552481 − 0.575987I
2.20930 − 4.73918I −12.69833 + 0.12567I
u = −0.243173 − 0.281252I
a = 2.16112 + 0.32713I
b = 0.955798 − 0.909043I
2.20930 + 4.73918I −12.69833 − 0.12567I
u = −0.243173 − 0.281252I
a = 0.20097 − 3.38461I
b = 0.552481 + 0.575987I
2.20930 + 4.73918I −12.69833 − 0.12567I
u = 0.14130 + 1.64406I
a = 1.39862 + 0.38362I
b = −2.00910 + 0.04697I
9.97047 − 5.82183I 0
u = 0.14130 + 1.64406I
a = −2.13183 − 0.07965I
b = 3.00192 − 0.19303I
9.97047 − 5.82183I 0
u = 0.14130 − 1.64406I
a = 1.39862 − 0.38362I
b = −2.00910 − 0.04697I
9.97047 + 5.82183I 0
u = 0.14130 − 1.64406I
a = −2.13183 + 0.07965I
b = 3.00192 + 0.19303I
9.97047 + 5.82183I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06820 + 1.67990I
a = 2.22054 − 0.61828I
b = −3.29320 + 1.26808I
15.5849 − 6.2095I 0
u = 0.06820 + 1.67990I
a = −2.00367 − 1.22703I
b = 2.49427 + 0.99693I
15.5849 − 6.2095I 0
u = 0.06820 − 1.67990I
a = 2.22054 + 0.61828I
b = −3.29320 − 1.26808I
15.5849 + 6.2095I 0
u = 0.06820 − 1.67990I
a = −2.00367 + 1.22703I
b = 2.49427 − 0.99693I
15.5849 + 6.2095I 0
u = 0.16948 + 1.68267I
a = −1.44232 + 0.16410I
b = 2.14852 − 0.68418I
11.8057 − 8.3466I 0
u = 0.16948 + 1.68267I
a = 2.17542 + 0.32124I
b = −2.89502 − 0.11683I
11.8057 − 8.3466I 0
u = 0.16948 − 1.68267I
a = −1.44232 − 0.16410I
b = 2.14852 + 0.68418I
11.8057 + 8.3466I 0
u = 0.16948 − 1.68267I
a = 2.17542 − 0.32124I
b = −2.89502 + 0.11683I
11.8057 + 8.3466I 0
19
III. I
u
3
=
h−u
22
+4u
21
+· · ·+b+3, 3u
22
−15u
21
+· · ·+2a+13, u
23
−5u
22
+· · ·+15u−2i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
u
a
4
=
−
3
2
u
22
+
15
2
u
21
+ ··· + 42u −
13
2
u
22
− 4u
21
+ ··· + 14u − 3
a
2
=
−
1
2
u
22
+
5
2
u
21
+ ··· + 32u −
13
2
u
22
− 4u
21
+ ··· + 13u
2
− 1
a
7
=
u
2
+ 1
−u
2
a
5
=
−
3
2
u
22
+
15
2
u
21
+ ··· + 42u −
11
2
u
21
− 4u
20
+ ··· + 16u − 3
a
11
=
u
u
3
+ u
a
3
=
−
3
2
u
22
+
15
2
u
21
+ ··· + 45u −
13
2
u
21
− 4u
20
+ ··· + 17u − 3
a
10
=
1
2
u
22
−
5
2
u
21
+ ··· − 28u +
9
2
−u
5
+ 2u
4
− 4u
3
+ 5u
2
− 3u + 1
a
6
=
−
1
2
u
22
+
5
2
u
21
+ ··· + 19u −
3
2
u
9
− 3u
8
+ 9u
7
− 17u
6
+ 25u
5
− 29u
4
+ 24u
3
− 15u
2
+ 5u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14u
22
+ 63u
21
− 337u
20
+ 1047u
19
− 3171u
18
+ 7386u
17
−
15902u
16
+ 28885u
15
− 47567u
14
+ 68545u
13
− 88589u
12
+ 101470u
11
− 103114u
10
+
92788u
9
−72959u
8
+ 50192u
7
−29523u
6
+ 14773u
5
−6201u
4
+ 2045u
3
−605u
2
+ 98u −20
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
23
− u
22
+ ··· + u − 1
c
2
u
23
− 11u
22
+ ··· + 95u − 12
c
3
, c
9
u
23
+ u
22
+ ··· + u
2
+ 1
c
5
u
23
+ 11u
22
+ ··· + 95u + 12
c
6
, c
10
u
23
+ u
22
+ ··· + u − 1
c
7
, c
8
u
23
− 5u
22
+ ··· + 15u − 2
c
11
, c
12
u
23
+ 5u
22
+ ··· + 15u + 2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
23
− 9y
22
+ ··· + 5y −1
c
2
, c
5
y
23
+ 11y
22
+ ··· − 1079y −144
c
3
, c
9
y
23
+ 11y
22
+ ··· − 2y −1
c
6
, c
10
y
23
− 7y
22
+ ··· − 7y −1
c
7
, c
8
, c
11
c
12
y
23
+ 29y
22
+ ··· − 47y −4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.055098 + 0.963623I
a = −0.659715 − 0.383311I
b = 1.089160 − 0.395794I
4.65113 − 5.19324I −6.36369 + 6.25683I
u = 0.055098 − 0.963623I
a = −0.659715 + 0.383311I
b = 1.089160 + 0.395794I
4.65113 + 5.19324I −6.36369 − 6.25683I
u = 0.595550 + 0.857992I
a = 0.008760 − 0.154425I
b = −0.925111 − 0.027434I
2.53184 − 4.13729I −5.48066 + 6.37467I
u = 0.595550 − 0.857992I
a = 0.008760 + 0.154425I
b = −0.925111 + 0.027434I
2.53184 + 4.13729I −5.48066 − 6.37467I
u = 0.846406 + 0.134230I
a = −0.034807 + 0.689285I
b = 0.0817028 + 0.1146360I
0.271559 − 0.666279I −2.13311 − 0.86043I
u = 0.846406 − 0.134230I
a = −0.034807 − 0.689285I
b = 0.0817028 − 0.1146360I
0.271559 + 0.666279I −2.13311 + 0.86043I
u = 0.368780 + 1.190300I
a = −0.362792 − 0.067037I
b = 0.856694 − 0.067276I
4.39247 − 5.06548I −3.80725 + 10.44286I
u = 0.368780 − 1.190300I
a = −0.362792 + 0.067037I
b = 0.856694 + 0.067276I
4.39247 + 5.06548I −3.80725 − 10.44286I
u = 0.130274 + 1.326600I
a = 0.361916 − 0.408395I
b = −0.312860 + 0.821004I
2.21466 − 1.65415I −14.0246 − 2.2364I
u = 0.130274 − 1.326600I
a = 0.361916 + 0.408395I
b = −0.312860 − 0.821004I
2.21466 + 1.65415I −14.0246 + 2.2364I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.172894 + 0.521546I
a = −0.02050 + 1.68866I
b = −1.261940 + 0.449992I
−1.163930 − 0.723592I 6.96325 − 4.99921I
u = 0.172894 − 0.521546I
a = −0.02050 − 1.68866I
b = −1.261940 − 0.449992I
−1.163930 + 0.723592I 6.96325 + 4.99921I
u = −0.084481 + 0.431444I
a = −1.32681 − 2.09175I
b = 1.190500 − 0.294292I
2.87183 + 5.49525I −5.86092 − 5.26519I
u = −0.084481 − 0.431444I
a = −1.32681 + 2.09175I
b = 1.190500 + 0.294292I
2.87183 − 5.49525I −5.86092 + 5.26519I
u = −0.03280 + 1.57202I
a = −1.68788 + 0.65851I
b = 1.95942 − 1.43311I
9.94959 + 5.95892I −5.64533 − 5.36115I
u = −0.03280 − 1.57202I
a = −1.68788 − 0.65851I
b = 1.95942 + 1.43311I
9.94959 − 5.95892I −5.64533 + 5.36115I
u = 0.03283 + 1.58195I
a = 2.07621 − 0.78435I
b = −2.52263 + 1.72561I
6.17515 − 1.37592I 3.79659 − 2.06448I
u = 0.03283 − 1.58195I
a = 2.07621 + 0.78435I
b = −2.52263 − 1.72561I
6.17515 + 1.37592I 3.79659 + 2.06448I
u = 0.342716
a = −1.76801
b = −0.514065
−2.03702 −20.3640
u = 0.16963 + 1.66277I
a = 1.70693 + 0.26846I
b = −2.44017 + 0.01339I
11.13330 − 7.07448I −5.11624 + 4.28864I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16963 − 1.66277I
a = 1.70693 − 0.26846I
b = −2.44017 − 0.01339I
11.13330 + 7.07448I −5.11624 − 4.28864I
u = 0.07445 + 1.67426I
a = −1.92731 + 0.14325I
b = 2.54227 − 0.68786I
13.9187 − 6.2443I −4.64599 + 5.22587I
u = 0.07445 − 1.67426I
a = −1.92731 − 0.14325I
b = 2.54227 + 0.68786I
13.9187 + 6.2443I −4.64599 − 5.22587I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
23
− u
22
+ ··· + u − 1)(u
53
− u
52
+ ··· + 11u + 1)
· (u
58
− 9u
57
+ ··· − 630u + 229)
c
2
(u
23
− 11u
22
+ ··· + 95u − 12)(u
29
+ 9u
28
+ ··· + 5u + 1)
2
· (u
53
− 14u
52
+ ··· − 604u + 58)
c
3
, c
9
(u
23
+ u
22
+ ··· + u
2
+ 1)(u
53
− u
52
+ ··· + 76u + 79)
· (u
58
− u
57
+ ··· + 1134u + 197)
c
5
(u
23
+ 11u
22
+ ··· + 95u + 12)(u
29
+ 9u
28
+ ··· + 5u + 1)
2
· (u
53
− 14u
52
+ ··· − 604u + 58)
c
6
, c
10
(u
23
+ u
22
+ ··· + u − 1)(u
53
+ u
52
+ ··· + 5u + 1)
· (u
58
+ 5u
57
+ ··· + 4u + 1)
c
7
, c
8
(u
23
− 5u
22
+ ··· + 15u − 2)(u
29
+ 5u
28
+ ··· + 3u + 1)
2
· (u
53
− 8u
52
+ ··· − 90u + 10)
c
11
, c
12
(u
23
+ 5u
22
+ ··· + 15u + 2)(u
29
+ 5u
28
+ ··· + 3u + 1)
2
· (u
53
− 8u
52
+ ··· − 90u + 10)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
23
− 9y
22
+ ··· + 5y −1)(y
53
+ 37y
52
+ ··· − 71y −1)
· (y
58
− 5y
57
+ ··· + 1349912y + 52441)
c
2
, c
5
(y
23
+ 11y
22
+ ··· − 1079y −144)(y
29
+ 19y
28
+ ··· − 13y −1)
2
· (y
53
+ 30y
52
+ ··· + 4636y −3364)
c
3
, c
9
(y
23
+ 11y
22
+ ··· − 2y −1)(y
53
+ 9y
52
+ ··· − 51894y −6241)
· (y
58
+ 19y
57
+ ··· − 508200y + 38809)
c
6
, c
10
(y
23
− 7y
22
+ ··· − 7y −1)(y
53
+ 31y
52
+ ··· − 87y −1)
· (y
58
− 9y
57
+ ··· − 12y + 1)
c
7
, c
8
, c
11
c
12
(y
23
+ 29y
22
+ ··· − 47y −4)(y
29
+ 35y
28
+ ··· − 13y −1)
2
· (y
53
+ 64y
52
+ ··· − 1080y −100)
27
