12a
0156
(K12a
0156
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 11 10 12 4 1 6 8 7
Solving Sequence
5,11 3,6
2 1 4 10 7 9 8 12
c
5
c
2
c
1
c
4
c
10
c
6
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
38
− 51u
37
+ ··· + 256b − 85, −121u
38
+ 133u
37
+ ··· + 512a − 61, u
39
+ 25u
37
+ ··· + u + 1i
I
u
2
= h2.94986 × 10
44
u
49
+ 3.65735 × 10
44
u
48
+ ··· + 2.95826 × 10
45
b − 1.68829 × 10
45
,
2.14090 × 10
45
u
49
+ 1.60923 × 10
45
u
48
+ ··· + 8.87477 × 10
45
a − 4.58714 × 10
45
, u
50
+ 2u
49
+ ··· − 18u + 9i
I
u
3
= h−54276a
5
u + 156246a
4
u + ··· + 839054a − 188617,
a
6
+ 2a
5
u − 4a
4
u − a
4
+ 4a
3
u + 6a
3
+ a
2
u + 4a
2
+ 10au + a + 4u − 1, u
2
+ 1i
I
u
4
= hb + 1, u
2
+ 2a + u + 3, u
3
+ 2u − 1i
I
u
5
= hb + 1, u
3
+ u
2
+ a + u + 2, u
4
+ u
3
+ 2u
2
+ 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 108 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
38
− 51u
37
+ · · · + 256b − 85, −121u
38
+ 133u
37
+ · · · + 512a −
61, u
39
+ 25u
37
+ · · · + u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
0.236328u
38
− 0.259766u
37
+ ··· − 0.976563u + 0.119141
−0.0117188u
38
+ 0.199219u
37
+ ··· + 1.71875u + 0.332031
a
6
=
1
u
2
a
2
=
0.224609u
38
− 0.0605469u
37
+ ··· + 0.742188u + 0.451172
−0.0117188u
38
+ 0.199219u
37
+ ··· + 1.71875u + 0.332031
a
1
=
−u
3
− 2u
1
64
u
38
+
3
8
u
36
+ ··· +
1
64
u
2
+
65
64
u
a
4
=
0.0878906u
38
− 0.0644531u
37
+ ··· + 1.07031u + 1.04883
−0.199219u
38
− 0.207031u
37
+ ··· − 1.50000u − 0.761719
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−0.0156250u
38
− 0.375000u
36
+ ··· − 0.0156250u
2
+ 0.984375u
0.0312500u
38
+ 0.0312500u
37
+ ··· + 1.09375u + 0.0312500
a
8
=
−1
1
64
u
37
+
3
8
u
35
+ ··· +
1
64
u +
1
64
a
12
=
−u
1
64
u
38
+
3
8
u
36
+ ··· +
1
64
u
2
+
65
64
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2567
1024
u
38
+
507
1024
u
37
+ ··· +
2683
256
u −
8131
1024
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
+ 18u
38
+ ··· + 817u + 16
c
2
, c
4
u
39
− 4u
38
+ ··· + 13u + 4
c
3
, c
8
u
39
− 3u
38
+ ··· − 8u + 32
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
39
+ 25u
37
+ ··· + u + 1
c
9
u
39
+ 24u
38
+ ··· + 132148u + 10276
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
+ 10y
38
+ ··· + 507201y −256
c
2
, c
4
y
39
− 18y
38
+ ··· + 817y −16
c
3
, c
8
y
39
+ 21y
38
+ ··· − 3776y −1024
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
39
+ 50y
38
+ ··· − 3y −1
c
9
y
39
+ 18y
38
+ ··· − 277125320y −105596176
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.606138 + 0.433746I
a = 1.10839 − 1.72999I
b = 1.096070 + 0.636892I
1.24768 − 8.38959I −11.7192 + 9.4891I
u = 0.606138 − 0.433746I
a = 1.10839 + 1.72999I
b = 1.096070 − 0.636892I
1.24768 + 8.38959I −11.7192 − 9.4891I
u = −0.686742 + 0.093387I
a = 1.124820 + 0.357401I
b = 0.888553 + 0.474189I
−1.46543 − 1.90675I −13.8759 + 2.9903I
u = −0.686742 − 0.093387I
a = 1.124820 − 0.357401I
b = 0.888553 − 0.474189I
−1.46543 + 1.90675I −13.8759 − 2.9903I
u = 0.512624 + 0.450918I
a = −0.817372 + 0.180228I
b = 0.464938 − 0.809663I
3.12365 − 2.96834I −8.53439 + 5.45411I
u = 0.512624 − 0.450918I
a = −0.817372 − 0.180228I
b = 0.464938 + 0.809663I
3.12365 + 2.96834I −8.53439 − 5.45411I
u = 0.097297 + 1.396560I
a = 0.600483 − 0.695228I
b = 1.132180 + 0.452280I
5.93701 − 6.97505I 0
u = 0.097297 − 1.396560I
a = 0.600483 + 0.695228I
b = 1.132180 − 0.452280I
5.93701 + 6.97505I 0
u = −0.485730 + 0.337100I
a = −0.58443 − 2.43918I
b = −0.928433 + 0.452438I
−1.46092 + 2.88558I −14.3616 − 7.5955I
u = −0.485730 − 0.337100I
a = −0.58443 + 2.43918I
b = −0.928433 − 0.452438I
−1.46092 − 2.88558I −14.3616 + 7.5955I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.160047 + 0.560104I
a = −0.472825 + 0.884195I
b = 1.058660 − 0.598292I
1.75331 + 5.17154I −10.85539 − 2.38918I
u = 0.160047 − 0.560104I
a = −0.472825 − 0.884195I
b = 1.058660 + 0.598292I
1.75331 − 5.17154I −10.85539 + 2.38918I
u = 0.255669 + 0.512819I
a = 0.095335 − 1.276560I
b = 0.500188 + 0.744588I
3.42355 + 0.06447I −7.35584 + 3.68014I
u = 0.255669 − 0.512819I
a = 0.095335 + 1.276560I
b = 0.500188 − 0.744588I
3.42355 − 0.06447I −7.35584 − 3.68014I
u = 0.24730 + 1.43914I
a = 0.342403 − 0.242192I
b = 0.835724 − 0.187359I
8.20195 − 4.67633I 0
u = 0.24730 − 1.43914I
a = 0.342403 + 0.242192I
b = 0.835724 + 0.187359I
8.20195 + 4.67633I 0
u = −0.01911 + 1.46623I
a = −0.513457 − 0.986167I
b = −1.218970 + 0.402466I
5.58893 + 1.41780I 0
u = −0.01911 − 1.46623I
a = −0.513457 + 0.986167I
b = −1.218970 − 0.402466I
5.58893 − 1.41780I 0
u = 0.07057 + 1.49185I
a = 0.206418 + 0.688633I
b = −0.036484 − 0.767123I
9.22311 − 2.89697I 0
u = 0.07057 − 1.49185I
a = 0.206418 − 0.688633I
b = −0.036484 + 0.767123I
9.22311 + 2.89697I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.435690 + 0.236154I
a = −1.49896 + 0.88737I
b = −1.166600 + 0.114063I
−2.34640 − 0.81341I −13.1026 + 8.4479I
u = 0.435690 − 0.236154I
a = −1.49896 − 0.88737I
b = −1.166600 − 0.114063I
−2.34640 + 0.81341I −13.1026 − 8.4479I
u = −0.27417 + 1.55715I
a = −0.099646 − 0.449882I
b = −1.372790 − 0.112918I
10.02810 + 6.61870I 0
u = −0.27417 − 1.55715I
a = −0.099646 + 0.449882I
b = −1.372790 + 0.112918I
10.02810 − 6.61870I 0
u = 0.30186 + 1.56039I
a = 0.02339 + 2.01745I
b = −0.977777 − 0.644002I
11.2737 − 9.4013I 0
u = 0.30186 − 1.56039I
a = 0.02339 − 2.01745I
b = −0.977777 + 0.644002I
11.2737 + 9.4013I 0
u = −0.35789 + 1.55459I
a = 0.37718 + 1.87847I
b = 1.184010 − 0.683858I
14.1914 + 16.2242I 0
u = −0.35789 − 1.55459I
a = 0.37718 − 1.87847I
b = 1.184010 + 0.683858I
14.1914 − 16.2242I 0
u = 0.24560 + 1.57817I
a = 0.94180 − 1.09265I
b = −0.684865 + 0.701681I
12.16600 − 4.21253I 0
u = 0.24560 − 1.57817I
a = 0.94180 + 1.09265I
b = −0.684865 − 0.701681I
12.16600 + 4.21253I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198432 + 0.335342I
a = 1.51348 + 1.09795I
b = −0.837871 − 0.313169I
−0.884650 − 0.467058I −11.90822 − 2.02853I
u = −0.198432 − 0.335342I
a = 1.51348 − 1.09795I
b = −0.837871 + 0.313169I
−0.884650 + 0.467058I −11.90822 + 2.02853I
u = −0.33367 + 1.57837I
a = −0.848602 − 0.806276I
b = 0.422675 + 0.993588I
16.5334 + 10.1404I 0
u = −0.33367 − 1.57837I
a = −0.848602 + 0.806276I
b = 0.422675 − 0.993588I
16.5334 − 10.1404I 0
u = −0.22952 + 1.64191I
a = −0.17339 + 1.41527I
b = 0.671373 − 0.949740I
18.2436 + 4.6595I 0
u = −0.22952 − 1.64191I
a = −0.17339 − 1.41527I
b = 0.671373 + 0.949740I
18.2436 − 4.6595I 0
u = −0.340813
a = 0.891121
b = −0.149888
−0.576114 −17.1030
u = −0.17712 + 1.65299I
a = −0.520565 − 1.116590I
b = 1.044360 + 0.795151I
17.1048 − 1.6856I 0
u = −0.17712 − 1.65299I
a = −0.520565 + 1.116590I
b = 1.044360 − 0.795151I
17.1048 + 1.6856I 0
8
II. I
u
2
=
h2.95×10
44
u
49
+3.66×10
44
u
48
+· · ·+2.96×10
45
b−1.69×10
45
, 2.14×10
45
u
49
+
1.61 × 10
45
u
48
+ · · · + 8.87 × 10
45
a − 4.59 × 10
45
, u
50
+ 2u
49
+ · · · − 18u + 9i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−0.241234u
49
− 0.181326u
48
+ ··· + 0.375683u + 0.516874
−0.0997162u
49
− 0.123632u
48
+ ··· + 0.184639u + 0.570706
a
6
=
1
u
2
a
2
=
−0.340950u
49
− 0.304958u
48
+ ··· + 0.560322u + 1.08758
−0.0997162u
49
− 0.123632u
48
+ ··· + 0.184639u + 0.570706
a
1
=
−0.196743u
49
− 0.293319u
48
+ ··· − 13.0617u + 2.90182
−0.0474075u
49
− 0.0235454u
48
+ ··· − 3.48640u + 0.424677
a
4
=
−0.0231020u
49
+ 0.328429u
48
+ ··· + 9.25365u − 3.09937
0.0273358u
49
+ 0.145463u
48
+ ··· + 1.17016u − 1.26078
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−0.137409u
49
− 0.303786u
48
+ ··· − 5.99590u + 2.47777
−0.0865588u
49
− 0.101282u
48
+ ··· − 1.77113u + 0.685381
a
8
=
0.0471513u
49
+ 0.147673u
48
+ ··· − 7.45718u + 4.92740
−0.100202u
49
− 0.286035u
48
+ ··· + 0.536308u + 0.519665
a
12
=
−0.164482u
49
− 0.228762u
48
+ ··· − 16.5539u + 2.42436
0.0322612u
49
+ 0.0645573u
48
+ ··· − 1.49216u − 0.477454
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.817749u
49
− 1.70803u
48
+ ··· − 1.83623u − 9.61323
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
25
+ 11u
24
+ ··· − 2u + 1)
2
c
2
, c
4
(u
25
− 3u
24
+ ··· − 4u + 1)
2
c
3
, c
8
(u
25
+ u
24
+ ··· + 4u − 4)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
u
50
+ 2u
49
+ ··· − 18u + 9
c
9
(u
25
− 8u
24
+ ··· + 11u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
25
+ 9y
24
+ ··· − 2y −1)
2
c
2
, c
4
(y
25
− 11y
24
+ ··· − 2y −1)
2
c
3
, c
8
(y
25
+ 15y
24
+ ··· − 88y −16)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
y
50
+ 42y
49
+ ··· + 1584y + 81
c
9
(y
25
+ 20y
24
+ ··· + 251y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.863192 + 0.531967I
a = −0.56076 + 1.52524I
b = −0.903290 − 0.591334I
4.43073 − 5.11531I −8.18255 + 5.48464I
u = 0.863192 − 0.531967I
a = −0.56076 − 1.52524I
b = −0.903290 + 0.591334I
4.43073 + 5.11531I −8.18255 − 5.48464I
u = 0.790213 + 0.646113I
a = 0.322984 − 0.681750I
b = −0.781818 + 0.585895I
4.81480 − 0.43356I −7.08804 + 0.I
u = 0.790213 − 0.646113I
a = 0.322984 + 0.681750I
b = −0.781818 − 0.585895I
4.81480 + 0.43356I −7.08804 + 0.I
u = −0.800123 + 0.560428I
a = −1.41196 − 0.56327I
b = −1.306760 − 0.052319I
3.08820 + 2.66172I −6.71477 − 3.57661I
u = −0.800123 − 0.560428I
a = −1.41196 + 0.56327I
b = −1.306760 + 0.052319I
3.08820 − 2.66172I −6.71477 + 3.57661I
u = −0.125962 + 1.023520I
a = 2.16186 − 3.13157I
b = −0.819709
2.09579 −12.44382 + 0.I
u = −0.125962 − 1.023520I
a = 2.16186 + 3.13157I
b = −0.819709
2.09579 −12.44382 + 0.I
u = −0.237534 + 1.042900I
a = 0.602799 + 1.091330I
b = 1.012760 − 0.537221I
1.37392 + 5.41987I −11.35697 − 6.54919I
u = −0.237534 − 1.042900I
a = 0.602799 − 1.091330I
b = 1.012760 + 0.537221I
1.37392 − 5.41987I −11.35697 + 6.54919I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.963620 + 0.475288I
a = 1.14015 + 1.21785I
b = 1.139240 − 0.687767I
7.62261 + 11.39030I −7.28983 − 7.76664I
u = −0.963620 − 0.475288I
a = 1.14015 − 1.21785I
b = 1.139240 + 0.687767I
7.62261 − 11.39030I −7.28983 + 7.76664I
u = −0.942522 + 0.536594I
a = −0.427504 − 0.100379I
b = 0.479273 + 0.936834I
9.63785 + 5.44271I −4.49829 − 3.51350I
u = −0.942522 − 0.536594I
a = −0.427504 + 0.100379I
b = 0.479273 − 0.936834I
9.63785 − 5.44271I −4.49829 + 3.51350I
u = 0.035416 + 1.096400I
a = −0.51282 + 1.51762I
b = −1.073950 − 0.294320I
−0.175498 − 1.059220I −15.3940 + 0.I
u = 0.035416 − 1.096400I
a = −0.51282 − 1.51762I
b = −1.073950 + 0.294320I
−0.175498 + 1.059220I −15.3940 + 0.I
u = −0.863688 + 0.730509I
a = 0.349454 + 0.701314I
b = 0.563663 − 0.911236I
10.21860 + 0.59688I −3.53242 + 0.I
u = −0.863688 − 0.730509I
a = 0.349454 − 0.701314I
b = 0.563663 + 0.911236I
10.21860 − 0.59688I −3.53242 + 0.I
u = −0.828010 + 0.806350I
a = 0.246724 − 0.383981I
b = 1.089150 + 0.711472I
8.61369 − 5.36637I −5.53322 + 0.I
u = −0.828010 − 0.806350I
a = 0.246724 + 0.383981I
b = 1.089150 − 0.711472I
8.61369 + 5.36637I −5.53322 + 0.I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.416306 + 1.118060I
a = 0.86554 − 1.47471I
b = 0.840318 + 0.621070I
5.39169 − 2.44039I 0
u = 0.416306 − 1.118060I
a = 0.86554 + 1.47471I
b = 0.840318 − 0.621070I
5.39169 + 2.44039I 0
u = −0.080139 + 1.205770I
a = 0.372713 − 0.398049I
b = 0.144497 + 0.357570I
2.95409 + 1.50728I 0
u = −0.080139 − 1.205770I
a = 0.372713 + 0.398049I
b = 0.144497 − 0.357570I
2.95409 − 1.50728I 0
u = −0.219956 + 1.253270I
a = −0.0219369 + 0.1367750I
b = 0.706780 + 0.369020I
2.66645 + 1.39976I 0
u = −0.219956 − 1.253270I
a = −0.0219369 − 0.1367750I
b = 0.706780 − 0.369020I
2.66645 − 1.39976I 0
u = 0.307492 + 1.236030I
a = −0.815496 + 0.040530I
b = 0.840318 − 0.621070I
5.39169 + 2.44039I 0
u = 0.307492 − 1.236030I
a = −0.815496 − 0.040530I
b = 0.840318 + 0.621070I
5.39169 − 2.44039I 0
u = 0.647951 + 0.242324I
a = 1.40449 − 0.16649I
b = 0.706780 − 0.369020I
2.66645 − 1.39976I −7.04278 + 0.06062I
u = 0.647951 − 0.242324I
a = 1.40449 + 0.16649I
b = 0.706780 + 0.369020I
2.66645 + 1.39976I −7.04278 − 0.06062I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.396390 + 0.399496I
a = 0.963949 − 0.525295I
b = 0.144497 − 0.357570I
2.95409 − 1.50728I −6.97928 + 4.31266I
u = 0.396390 − 0.399496I
a = 0.963949 + 0.525295I
b = 0.144497 + 0.357570I
2.95409 + 1.50728I −6.97928 − 4.31266I
u = 0.10841 + 1.43332I
a = 0.410688 + 0.375917I
b = −1.306760 + 0.052319I
3.08820 − 2.66172I 0
u = 0.10841 − 1.43332I
a = 0.410688 − 0.375917I
b = −1.306760 − 0.052319I
3.08820 + 2.66172I 0
u = −0.05540 + 1.45028I
a = 1.23305 + 1.70385I
b = −0.781818 − 0.585895I
4.81480 + 0.43356I 0
u = −0.05540 − 1.45028I
a = 1.23305 − 1.70385I
b = −0.781818 + 0.585895I
4.81480 − 0.43356I 0
u = −0.14356 + 1.46162I
a = 0.59905 − 2.26807I
b = −0.903290 + 0.591334I
4.43073 + 5.11531I 0
u = −0.14356 − 1.46162I
a = 0.59905 + 2.26807I
b = −0.903290 − 0.591334I
4.43073 − 5.11531I 0
u = −0.03744 + 1.51239I
a = −0.60761 + 1.77442I
b = 1.089150 − 0.711472I
8.61369 + 5.36637I 0
u = −0.03744 − 1.51239I
a = −0.60761 − 1.77442I
b = 1.089150 + 0.711472I
8.61369 − 5.36637I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21031 + 1.50284I
a = −0.05347 − 2.08186I
b = 1.139240 + 0.687767I
7.62261 − 11.39030I 0
u = 0.21031 − 1.50284I
a = −0.05347 + 2.08186I
b = 1.139240 − 0.687767I
7.62261 + 11.39030I 0
u = 0.02120 + 1.51758I
a = −0.64643 − 1.54897I
b = 0.563663 + 0.911236I
10.21860 − 0.59688I 0
u = 0.02120 − 1.51758I
a = −0.64643 + 1.54897I
b = 0.563663 − 0.911236I
10.21860 + 0.59688I 0
u = 0.16595 + 1.51068I
a = −0.96384 + 1.16614I
b = 0.479273 − 0.936834I
9.63785 − 5.44271I 0
u = 0.16595 − 1.51068I
a = −0.96384 − 1.16614I
b = 0.479273 + 0.936834I
9.63785 + 5.44271I 0
u = 0.441747 + 0.053796I
a = 0.48121 − 1.49645I
b = 1.012760 − 0.537221I
1.37392 + 5.41987I −11.35697 − 6.54919I
u = 0.441747 − 0.053796I
a = 0.48121 + 1.49645I
b = 1.012760 + 0.537221I
1.37392 − 5.41987I −11.35697 + 6.54919I
u = −0.106624 + 0.220666I
a = −5.79950 + 1.80662I
b = −1.073950 + 0.294320I
−0.175498 + 1.059220I −15.3940 − 0.3706I
u = −0.106624 − 0.220666I
a = −5.79950 − 1.80662I
b = −1.073950 − 0.294320I
−0.175498 − 1.059220I −15.3940 + 0.3706I
16
III. I
u
3
= h−5.43 × 10
4
a
5
u + 1.56 × 10
5
a
4
u + · · · + 8.39 × 10
5
a − 1.89 ×
10
5
, 2a
5
u − 4a
4
u + · · · + a − 1, u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
a
0.0510511a
5
u − 0.146963a
4
u + ··· − 0.789201a + 0.177410
a
6
=
1
−1
a
2
=
0.0510511a
5
u − 0.146963a
4
u + ··· + 0.210799a + 0.177410
0.0510511a
5
u − 0.146963a
4
u + ··· − 0.789201a + 0.177410
a
1
=
−u
0.0269872a
5
u − 0.143796a
4
u + ··· + 0.311302a + 1.03365
a
4
=
−0.115515a
5
u + 0.102601a
4
u + ··· + 0.261687a + 1.46186
−0.0683729a
5
u + 0.141112a
4
u + ··· + 1.04666a + 0.569012
a
10
=
u
0
a
7
=
0
−1
a
9
=
−0.0269872a
5
u + 0.143796a
4
u + ··· − 0.311302a − 1.03365
0.0989937a
5
u − 0.242195a
4
u + ··· + 0.477577a − 0.543207
a
8
=
−1
0.0862375a
5
u − 0.0931583a
4
u + ··· + 0.214093a − 0.322042
a
12
=
−u
0.0269872a
5
u − 0.143796a
4
u + ··· + 0.311302a + 1.03365
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
288672
1063169
a
5
u +
504748
1063169
a
4
u + ··· −
1898092
1063169
a −
3575656
1063169
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
8
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(u
2
+ 1)
6
c
9
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
3
, c
8
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(y + 1)
12
c
9
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.477727 + 0.831626I
b = 1.073950 − 0.558752I
3.28987 + 5.69302I −6.00000 − 5.51057I
u = 1.000000I
a = 0.214242 − 1.226020I
b = 0.428243 + 0.664531I
5.18047 + 0.92430I −2.28328 − 0.79423I
u = 1.000000I
a = 1.16005 − 1.04838I
b = 1.073950 + 0.558752I
3.28987 − 5.69302I −6.00000 + 5.51057I
u = 1.000000I
a = −0.382665 − 0.093522I
b = 0.428243 − 0.664531I
5.18047 − 0.92430I −2.28328 + 0.79423I
u = 1.000000I
a = 1.39869 + 1.49594I
b = −1.002190 − 0.295542I
1.39926 − 0.92430I −9.71672 + 0.79423I
u = 1.000000I
a = −1.91259 − 1.95964I
b = −1.002190 + 0.295542I
1.39926 + 0.92430I −9.71672 − 0.79423I
u = − 1.000000I
a = −0.477727 − 0.831626I
b = 1.073950 + 0.558752I
3.28987 − 5.69302I −6.00000 + 5.51057I
u = − 1.000000I
a = 0.214242 + 1.226020I
b = 0.428243 − 0.664531I
5.18047 − 0.92430I −2.28328 + 0.79423I
u = − 1.000000I
a = 1.16005 + 1.04838I
b = 1.073950 − 0.558752I
3.28987 + 5.69302I −6.00000 − 5.51057I
u = − 1.000000I
a = −0.382665 + 0.093522I
b = 0.428243 + 0.664531I
5.18047 + 0.92430I −2.28328 − 0.79423I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 1.39869 − 1.49594I
b = −1.002190 + 0.295542I
1.39926 + 0.92430I −9.71672 − 0.79423I
u = − 1.000000I
a = −1.91259 + 1.95964I
b = −1.002190 − 0.295542I
1.39926 − 0.92430I −9.71672 + 0.79423I
21
IV. I
u
4
= hb + 1, u
2
+ 2a + u + 3, u
3
+ 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−
1
2
u
2
−
1
2
u −
3
2
−1
a
6
=
1
u
2
a
2
=
−
1
2
u
2
−
1
2
u −
5
2
−1
a
1
=
−1
0
a
4
=
−
1
2
u
2
−
1
2
u −
3
2
−1
a
10
=
u
−u + 1
a
7
=
u
2
+ 1
u
a
9
=
1
−u + 1
a
8
=
1
−u + 1
a
12
=
−u
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
7
4
u
2
−
21
4
u −
57
4
22
(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
23
(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
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = −0.335258 − 0.401127I
b = −1.00000
7.79580 + 5.13794I −9.37996 − 6.54094I
u = −0.22670 − 1.46771I
a = −0.335258 + 0.401127I
b = −1.00000
7.79580 − 5.13794I −9.37996 + 6.54094I
u = 0.453398
a = −1.82948
b = −1.00000
−2.43213 −16.9900
25
V. I
u
5
= hb + 1, u
3
+ u
2
+ a + u + 2, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
3
=
−u
3
− u
2
− u − 2
−1
a
6
=
1
u
2
a
2
=
−u
3
− u
2
− u − 3
−1
a
1
=
−1
0
a
4
=
−u
3
− u
2
− u − 2
−1
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
−u
3
− 2u − 1
a
9
=
u
3
+ 2u
u
3
+ u
a
8
=
u
3
+ 2u
u
3
+ u
a
12
=
−2u
3
− u
2
− 3u − 3
−u
3
− u
2
− u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
3
− 4u − 15
26
(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
27
(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
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = −1.69244 − 0.31815I
b = −1.00000
1.64493 + 2.02988I −13.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = −1.69244 + 0.31815I
b = −1.00000
1.64493 − 2.02988I −13.00000 + 3.46410I
u = 0.121744 + 1.306620I
a = 0.192440 + 0.547877I
b = −1.00000
1.64493 − 2.02988I −13.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = 0.192440 − 0.547877I
b = −1.00000
1.64493 + 2.02988I −13.00000 − 3.46410I
29
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
7
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· ((u
25
+ 11u
24
+ ··· − 2u + 1)
2
)(u
39
+ 18u
38
+ ··· + 817u + 16)
c
2
((u − 1)
7
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
25
− 3u
24
+ ··· − 4u + 1)
2
· (u
39
− 4u
38
+ ··· + 13u + 4)
c
3
, c
8
u
7
(u
12
+ 3u
10
+ ··· + u
2
+ 1)(u
25
+ u
24
+ ··· + 4u − 4)
2
· (u
39
− 3u
38
+ ··· − 8u + 32)
c
4
((u + 1)
7
)(u
6
− u
5
+ ··· − u + 1)
2
(u
25
− 3u
24
+ ··· − 4u + 1)
2
· (u
39
− 4u
38
+ ··· + 13u + 4)
c
5
, c
6
, c
7
((u
2
+ 1)
6
)(u
3
+ 2u − 1)(u
4
+ u
3
+ ··· + 2u + 1)(u
39
+ 25u
37
+ ··· + u + 1)
· (u
50
+ 2u
49
+ ··· − 18u + 9)
c
9
(u
2
+ u + 1)
2
(u
3
− 3u
2
+ 5u − 2)(u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1)
· ((u
25
− 8u
24
+ ··· + 11u + 1)
2
)(u
39
+ 24u
38
+ ··· + 132148u + 10276)
c
10
, c
11
, c
12
((u
2
+ 1)
6
)(u
3
+ 2u + 1)(u
4
− u
3
+ ··· − 2u + 1)(u
39
+ 25u
37
+ ··· + u + 1)
· (u
50
+ 2u
49
+ ··· − 18u + 9)
30
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
7
)(y
6
+ y
5
+ ··· + 3y + 1)
2
(y
25
+ 9y
24
+ ··· − 2y − 1)
2
· (y
39
+ 10y
38
+ ··· + 507201y − 256)
c
2
, c
4
(y − 1)
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· ((y
25
− 11y
24
+ ··· − 2y − 1)
2
)(y
39
− 18y
38
+ ··· + 817y − 16)
c
3
, c
8
y
7
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
· ((y
25
+ 15y
24
+ ··· − 88y − 16)
2
)(y
39
+ 21y
38
+ ··· − 3776y − 1024)
c
5
, c
6
, c
7
c
10
, c
11
, c
12
(y + 1)
12
(y
3
+ 4y
2
+ 4y − 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
39
+ 50y
38
+ ··· − 3y − 1)(y
50
+ 42y
49
+ ··· + 1584y + 81)
c
9
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y − 4)(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
· (y
25
+ 20y
24
+ ··· + 251y − 1)
2
· (y
39
+ 18y
38
+ ··· − 277125320y − 105596176)
31
