11a
266
(K11a
266
)
A knot diagram
1
Linearized knot diagam
10 9 1 11 2 3 4 5 6 8 7
Solving Sequence
2,9 3,6
7 10 1 4 5 8 11
c
2
c
6
c
9
c
1
c
3
c
5
c
8
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.09838 × 10
20
u
29
+ 6.55534 × 10
21
u
28
+ ··· + 1.72668 × 10
21
b + 1.91679 × 10
23
,
7.48748 × 10
20
u
29
+ 2.12940 × 10
22
u
28
+ ··· + 3.45337 × 10
21
a + 2.83237 × 10
23
,
u
30
+ 29u
29
+ ··· + 5632u + 512i
I
u
2
= h222790111u
46
− 4153864769u
45
+ ··· + 2281728b + 6714872532,
− 2238290844u
46
a − 21314380402u
46
+ ··· − 16228635188a − 83493140173,
u
47
− 14u
46
+ ··· + 30u − 3i
I
u
3
= h−1345u
15
+ 7729u
14
+ ··· + 3655b + 38, −38u
15
− 1117u
14
+ ··· + 3655a + 12877,
u
16
− 6u
15
+ ··· + u + 1i
I
u
4
= h3au + 3b + 2u + 3, 3a
2
− au − a + 1, u
2
+ 3u + 3i
* 4 irreducible components of dim
C
= 0, with total 144 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
=
h2.10×10
20
u
29
+6.56×10
21
u
28
+· · ·+1.73×10
21
b+1.92×10
23
, 7.49×10
20
u
29
+
2.13×10
22
u
28
+· · ·+3.45×10
21
a+2.83×10
23
, u
30
+29u
29
+· · ·+5632u+512i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
6
=
−0.216817u
29
− 6.16616u
28
+ ··· − 843.133u − 82.0175
−0.121527u
29
− 3.79649u
28
+ ··· − 1139.09u − 111.010
a
7
=
0.176923u
29
+ 4.51009u
28
+ ··· − 277.468u − 33.2290
0.726411u
29
+ 20.5852u
28
+ ··· + 2839.46u + 269.003
a
10
=
0.0737630u
29
+ 2.11244u
28
+ ··· + 454.512u + 44.0773
0.0266890u
29
+ 0.858935u
28
+ ··· + 372.356u + 37.7667
a
1
=
−0.181935u
29
− 4.87001u
28
+ ··· − 131.180u − 9.97749
−0.321147u
29
− 9.00243u
28
+ ··· − 1126.22u − 106.815
a
4
=
−0.344913u
29
− 9.38133u
28
+ ··· − 491.954u − 39.3302
−0.241720u
29
− 7.27828u
28
+ ··· − 1882.54u − 183.233
a
5
=
−0.0952900u
29
− 2.36967u
28
+ ··· + 295.961u + 28.9927
−0.121527u
29
− 3.79649u
28
+ ··· − 1139.09u − 111.010
a
8
=
−0.0645692u
29
− 1.79489u
28
+ ··· − 175.655u − 17.7913
0.111643u
29
+ 3.04839u
28
+ ··· + 259.810u + 24.1019
a
11
=
−0.293270u
29
− 8.33770u
28
+ ··· − 1123.71u − 104.995
0.527885u
29
+ 14.3259u
28
+ ··· + 755.639u + 64.5890
a
11
=
−0.293270u
29
− 8.33770u
28
+ ··· − 1123.71u − 104.995
0.527885u
29
+ 14.3259u
28
+ ··· + 755.639u + 64.5890
(ii) Obstruction class = −1
(iii) Cusp Shapes =
190232019886448235663
431670906353547523808
u
29
+
1299412671514678966295
107917726588386880952
u
28
+ ··· +
3145923075548619685658
13489715823548360119
u +
100943563341881674894
13489715823548360119
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 26u
29
+ ··· + 12288u + 1024
c
2
u
30
+ 29u
29
+ ··· + 5632u + 512
c
3
, c
10
u
30
− u
28
+ ··· − 6u + 1
c
4
, c
11
u
30
+ 8u
28
+ ··· + 3u + 1
c
5
, c
9
u
30
− u
29
+ ··· − 2u + 1
c
6
, c
8
u
30
− u
29
+ ··· + 46u + 27
c
7
u
30
− 19u
29
+ ··· − 288u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 2y
29
+ ··· + 12976128y + 1048576
c
2
y
30
− 11y
29
+ ··· + 11665408y + 262144
c
3
, c
10
y
30
− 2y
29
+ ··· − 10y + 1
c
4
, c
11
y
30
+ 16y
29
+ ··· + 33y + 1
c
5
, c
9
y
30
+ 3y
29
+ ··· + 6y + 1
c
6
, c
8
y
30
− 13y
29
+ ··· − 5896y + 729
c
7
y
30
+ y
29
+ ··· + 11776y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.294179 + 0.829081I
a = 0.118653 − 1.232520I
b = −0.986950 − 0.460952I
3.99955 − 4.35128I 6.59095 + 3.41349I
u = −0.294179 − 0.829081I
a = 0.118653 + 1.232520I
b = −0.986950 + 0.460952I
3.99955 + 4.35128I 6.59095 − 3.41349I
u = −0.620636 + 0.594308I
a = −0.605489 + 0.728544I
b = 0.057191 + 0.812008I
−0.89506 + 1.64854I −1.59568 − 3.27710I
u = −0.620636 − 0.594308I
a = −0.605489 − 0.728544I
b = 0.057191 − 0.812008I
−0.89506 − 1.64854I −1.59568 + 3.27710I
u = 0.240502 + 0.822969I
a = −0.329651 + 0.513210I
b = 0.501638 + 0.147864I
1.54778 + 0.98121I 6.08132 − 1.87254I
u = 0.240502 − 0.822969I
a = −0.329651 − 0.513210I
b = 0.501638 − 0.147864I
1.54778 − 0.98121I 6.08132 + 1.87254I
u = −0.593121 + 1.014040I
a = −0.296194 + 1.000500I
b = 0.838868 + 0.893772I
0.40807 + 2.90881I 0
u = −0.593121 − 1.014040I
a = −0.296194 − 1.000500I
b = 0.838868 − 0.893772I
0.40807 − 2.90881I 0
u = −1.218960 + 0.602440I
a = 0.242601 + 1.087790I
b = 0.95105 + 1.17983I
−5.97727 + 1.40898I 0
u = −1.218960 − 0.602440I
a = 0.242601 − 1.087790I
b = 0.95105 − 1.17983I
−5.97727 − 1.40898I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.062633 + 0.568284I
a = −0.89194 + 1.92406I
b = 1.037550 + 0.627385I
2.49609 + 5.04306I 4.14627 − 10.34955I
u = −0.062633 − 0.568284I
a = −0.89194 − 1.92406I
b = 1.037550 − 0.627385I
2.49609 − 5.04306I 4.14627 + 10.34955I
u = −1.26166 + 0.95513I
a = 0.035716 − 0.830069I
b = −0.747763 − 1.081370I
−5.36512 + 5.09529I 0
u = −1.26166 − 0.95513I
a = 0.035716 + 0.830069I
b = −0.747763 + 1.081370I
−5.36512 − 5.09529I 0
u = −1.45922 + 0.74935I
a = −0.234481 − 0.798219I
b = −0.940309 − 0.989071I
−5.17774 + 5.90499I 0
u = −1.45922 − 0.74935I
a = −0.234481 + 0.798219I
b = −0.940309 + 0.989071I
−5.17774 − 5.90499I 0
u = −1.27724 + 1.06097I
a = 0.038188 + 0.956845I
b = 1.06395 + 1.18161I
−4.2629 + 20.2286I 0
u = −1.27724 − 1.06097I
a = 0.038188 − 0.956845I
b = 1.06395 − 1.18161I
−4.2629 − 20.2286I 0
u = −1.24188 + 1.13304I
a = 0.028366 − 0.909730I
b = −0.99553 − 1.16192I
−5.60137 + 11.70800I 0
u = −1.24188 − 1.13304I
a = 0.028366 + 0.909730I
b = −0.99553 + 1.16192I
−5.60137 − 11.70800I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.003667 + 0.237046I
a = −2.94819 − 2.24065I
b = −0.520327 + 0.707073I
−1.89594 + 2.12626I −1.09090 − 3.98101I
u = 0.003667 − 0.237046I
a = −2.94819 + 2.24065I
b = −0.520327 − 0.707073I
−1.89594 − 2.12626I −1.09090 + 3.98101I
u = −1.43708 + 1.34143I
a = 0.060155 − 0.374617I
b = −0.416075 − 0.619050I
−4.05984 + 4.16834I 0
u = −1.43708 − 1.34143I
a = 0.060155 + 0.374617I
b = −0.416075 + 0.619050I
−4.05984 − 4.16834I 0
u = −1.73010 + 1.21293I
a = 0.178166 − 0.282307I
b = −0.034172 − 0.704524I
−5.55355 − 1.97987I 0
u = −1.73010 − 1.21293I
a = 0.178166 + 0.282307I
b = −0.034172 + 0.704524I
−5.55355 + 1.97987I 0
u = −1.93940 + 0.86304I
a = 0.299482 + 0.276653I
b = 0.819579 + 0.278076I
−1.09814 + 9.90729I 0
u = −1.93940 − 0.86304I
a = 0.299482 − 0.276653I
b = 0.819579 − 0.278076I
−1.09814 − 9.90729I 0
u = −1.60805 + 1.94539I
a = −0.195384 + 0.095348I
b = −0.128699 + 0.533421I
−3.10815 − 10.44340I 0
u = −1.60805 − 1.94539I
a = −0.195384 − 0.095348I
b = −0.128699 − 0.533421I
−3.10815 + 10.44340I 0
7
II. I
u
2
=
h2.23×10
8
u
46
−4.15×10
9
u
45
+· · ·+2.28×10
6
b+6.71×10
9
, −2.24×10
9
au
46
−
2.13 × 10
10
u
46
+ · · · − 1.62 × 10
10
a − 8.35 × 10
10
, u
47
− 14u
46
+ · · · + 30u − 3i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
6
=
a
−97.6410u
46
+ 1820.49u
45
+ ··· + 22316.5u − 2942.89
a
7
=
97.6410u
46
− 1820.49u
45
+ ··· + a + 2942.89
−875.274u
46
+ 11767.0u
45
+ ··· + 36214.9u − 4303.44
a
10
=
97.6410au
46
+ 6581.46u
46
+ ··· + 2942.89a + 28024.0
4213.21u
46
− 56627.3u
45
+ ··· − 169419.u + 19744.4
a
1
=
−3947.68au
46
− 9825.94u
46
+ ··· − 16530.6a − 44744.7
−3404.42u
46
+ 45900.4u
45
+ ··· + 143381.u − 16838.2
a
4
=
20.4112au
46
− 4497.13u
46
+ ··· − 75.8750a − 19073.6
121.715au
46
+ 2423.70u
46
+ ··· − 32.4492a + 11974.6
a
5
=
97.6410u
46
− 1820.49u
45
+ ··· + a + 2942.89
−97.6410u
46
+ 1820.49u
45
+ ··· + 22316.5u − 2942.89
a
8
=
875.274au
46
+ 5244.35u
46
+ ··· + 4303.44a + 22464.4
−777.633au
46
− 2876.10u
46
+ ··· − 1360.55a − 14184.8
a
11
=
2411.09au
46
+ 5244.06u
46
+ ··· + 5482.49a + 8858.44
−123.596au
46
+ 924.784u
46
+ ··· + 518.225a − 1814.05
a
11
=
2411.09au
46
+ 5244.06u
46
+ ··· + 5482.49a + 8858.44
−123.596au
46
+ 924.784u
46
+ ··· + 518.225a − 1814.05
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1922246023
142608
u
46
−
103339844495
570432
u
45
+ ··· −
317627554903
570432
u +
12453313365
190144
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
47
− 13u
46
+ ··· + 193u − 27)
2
c
2
(u
47
− 14u
46
+ ··· + 30u − 3)
2
c
3
, c
10
3(3u
94
+ 24u
93
+ ··· + 45u − 1)
c
4
, c
11
3(3u
94
+ 15u
93
+ ··· − 14505u − 1083)
c
5
, c
9
3(3u
94
+ 3u
93
+ ··· − 93u − 3)
c
6
, c
8
3(3u
94
+ 6u
93
+ ··· + 9495938u − 2259497)
c
7
(u
47
+ 10u
46
+ ··· + 18u + 3)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
47
+ 9y
46
+ ··· − 11945y −729)
2
c
2
(y
47
− 12y
46
+ ··· + 138y −9)
2
c
3
, c
10
9(9y
94
− 156y
93
+ ··· − 451y + 1)
c
4
, c
11
9(9y
94
− 165y
93
+ ··· + 1.44834 × 10
7
y + 1172889)
c
5
, c
9
9(9y
94
+ 195y
93
+ ··· − 885y + 9)
c
6
, c
8
9(9y
94
− 318y
93
+ ··· − 1.81298 × 10
14
y + 5.10533 × 10
12
)
c
7
(y
47
− 8y
46
+ ··· + 120y −9)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.975919 + 0.025887I
a = −0.095171 − 0.809640I
b = −1.04838 − 1.34279I
−5.74704 − 2.00651I 0
u = −0.975919 + 0.025887I
a = −1.03702 − 1.40343I
b = −0.113839 − 0.787679I
−5.74704 − 2.00651I 0
u = −0.975919 − 0.025887I
a = −0.095171 + 0.809640I
b = −1.04838 + 1.34279I
−5.74704 + 2.00651I 0
u = −0.975919 − 0.025887I
a = −1.03702 + 1.40343I
b = −0.113839 + 0.787679I
−5.74704 + 2.00651I 0
u = 0.659230 + 0.697787I
a = −0.690219 + 0.639282I
b = −0.142130 − 0.073719I
1.93536 + 0.83864I 0
u = 0.659230 + 0.697787I
a = 0.157502 − 0.054887I
b = 0.901096 + 0.060192I
1.93536 + 0.83864I 0
u = 0.659230 − 0.697787I
a = −0.690219 − 0.639282I
b = −0.142130 + 0.073719I
1.93536 − 0.83864I 0
u = 0.659230 − 0.697787I
a = 0.157502 + 0.054887I
b = 0.901096 − 0.060192I
1.93536 − 0.83864I 0
u = 0.791795 + 0.721190I
a = −0.345700 + 1.037280I
b = −0.800003 + 0.474165I
3.87155 − 2.62212I 0
u = 0.791795 + 0.721190I
a = 0.254108 − 0.830297I
b = 1.021800 − 0.572001I
3.87155 − 2.62212I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.791795 − 0.721190I
a = −0.345700 − 1.037280I
b = −0.800003 − 0.474165I
3.87155 + 2.62212I 0
u = 0.791795 − 0.721190I
a = 0.254108 + 0.830297I
b = 1.021800 + 0.572001I
3.87155 + 2.62212I 0
u = 0.716995 + 0.585257I
a = 0.211947 − 0.998129I
b = 1.08043 − 1.20236I
1.44210 − 5.12633I 0
u = 0.716995 + 0.585257I
a = −0.08286 + 1.74458I
b = −0.736127 + 0.591610I
1.44210 − 5.12633I 0
u = 0.716995 − 0.585257I
a = 0.211947 + 0.998129I
b = 1.08043 + 1.20236I
1.44210 + 5.12633I 0
u = 0.716995 − 0.585257I
a = −0.08286 − 1.74458I
b = −0.736127 − 0.591610I
1.44210 + 5.12633I 0
u = 0.548341 + 0.960440I
a = −0.089172 + 0.923171I
b = −0.38411 + 1.47635I
−0.215372 − 0.545445I 0
u = 0.548341 + 0.960440I
a = −0.987086 − 0.963483I
b = 0.935547 − 0.420568I
−0.215372 − 0.545445I 0
u = 0.548341 − 0.960440I
a = −0.089172 − 0.923171I
b = −0.38411 − 1.47635I
−0.215372 + 0.545445I 0
u = 0.548341 − 0.960440I
a = −0.987086 + 0.963483I
b = 0.935547 + 0.420568I
−0.215372 + 0.545445I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.643393 + 1.000610I
a = 0.015163 − 0.916515I
b = −0.96718 − 1.40104I
0.77111 + 11.39920I 0
u = −0.643393 + 1.000610I
a = 0.55090 − 1.32082I
b = −0.907319 − 0.604852I
0.77111 + 11.39920I 0
u = −0.643393 − 1.000610I
a = 0.015163 + 0.916515I
b = −0.96718 + 1.40104I
0.77111 − 11.39920I 0
u = −0.643393 − 1.000610I
a = 0.55090 + 1.32082I
b = −0.907319 + 0.604852I
0.77111 − 11.39920I 0
u = 0.743194 + 0.234677I
a = 0.126137 − 0.765467I
b = −1.42530 − 1.15084I
−4.71436 − 3.28575I −12.0478 + 10.0322I
u = 0.743194 + 0.234677I
a = 2.18855 + 0.85743I
b = −0.273382 + 0.539289I
−4.71436 − 3.28575I −12.0478 + 10.0322I
u = 0.743194 − 0.234677I
a = 0.126137 + 0.765467I
b = −1.42530 + 1.15084I
−4.71436 + 3.28575I −12.0478 − 10.0322I
u = 0.743194 − 0.234677I
a = 2.18855 − 0.85743I
b = −0.273382 − 0.539289I
−4.71436 + 3.28575I −12.0478 − 10.0322I
u = 0.563178 + 1.087130I
a = −0.528826 + 0.308180I
b = −0.320532 − 0.491610I
−0.26046 + 4.20130I 0
u = 0.563178 + 1.087130I
a = 0.476952 − 0.047762I
b = 0.632856 + 0.401342I
−0.26046 + 4.20130I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.563178 − 1.087130I
a = −0.528826 − 0.308180I
b = −0.320532 + 0.491610I
−0.26046 − 4.20130I 0
u = 0.563178 − 1.087130I
a = 0.476952 + 0.047762I
b = 0.632856 − 0.401342I
−0.26046 − 4.20130I 0
u = 0.716855 + 0.240599I
a = −0.311842 − 1.295060I
b = 1.25725 − 1.15394I
−5.08486 − 6.93394I −6.67195 + 7.26599I
u = 0.716855 + 0.240599I
a = −1.09070 + 1.97580I
b = −0.088046 + 1.003400I
−5.08486 − 6.93394I −6.67195 + 7.26599I
u = 0.716855 − 0.240599I
a = −0.311842 + 1.295060I
b = 1.25725 + 1.15394I
−5.08486 + 6.93394I −6.67195 − 7.26599I
u = 0.716855 − 0.240599I
a = −1.09070 − 1.97580I
b = −0.088046 − 1.003400I
−5.08486 + 6.93394I −6.67195 − 7.26599I
u = 0.722078 + 0.185952I
a = −0.156126 + 1.004530I
b = 1.42280 + 1.34318I
−3.74054 − 11.30760I −5.50352 + 11.29218I
u = 0.722078 + 0.185952I
a = −2.29711 − 1.26859I
b = 0.299530 − 0.696319I
−3.74054 − 11.30760I −5.50352 + 11.29218I
u = 0.722078 − 0.185952I
a = −0.156126 − 1.004530I
b = 1.42280 − 1.34318I
−3.74054 + 11.30760I −5.50352 − 11.29218I
u = 0.722078 − 0.185952I
a = −2.29711 + 1.26859I
b = 0.299530 + 0.696319I
−3.74054 + 11.30760I −5.50352 − 11.29218I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.502161 + 0.502278I
a = −0.811589 + 0.399482I
b = 0.507340 + 1.250810I
−1.33437 + 1.73522I 1.00000 + 1.18204I
u = −0.502161 + 0.502278I
a = −0.74039 + 1.75030I
b = −0.206898 + 0.608248I
−1.33437 + 1.73522I 1.00000 + 1.18204I
u = −0.502161 − 0.502278I
a = −0.811589 − 0.399482I
b = 0.507340 − 1.250810I
−1.33437 − 1.73522I 1.00000 − 1.18204I
u = −0.502161 − 0.502278I
a = −0.74039 − 1.75030I
b = −0.206898 − 0.608248I
−1.33437 − 1.73522I 1.00000 − 1.18204I
u = 0.683669 + 0.161155I
a = 0.691014 + 0.943770I
b = −1.26363 + 0.80256I
−4.37399 − 1.07626I −9.22616 − 2.29912I
u = 0.683669 + 0.161155I
a = 1.48887 − 1.52485I
b = −0.320332 − 0.756587I
−4.37399 − 1.07626I −9.22616 − 2.29912I
u = 0.683669 − 0.161155I
a = 0.691014 − 0.943770I
b = −1.26363 − 0.80256I
−4.37399 + 1.07626I −9.22616 + 2.29912I
u = 0.683669 − 0.161155I
a = 1.48887 + 1.52485I
b = −0.320332 + 0.756587I
−4.37399 + 1.07626I −9.22616 + 2.29912I
u = −0.786407 + 1.095290I
a = −0.182272 + 1.111210I
b = 0.654941 + 0.857680I
0.65352 + 2.88892I 0
u = −0.786407 + 1.095290I
a = −0.233409 + 0.765544I
b = 1.07376 + 1.07351I
0.65352 + 2.88892I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.786407 − 1.095290I
a = −0.182272 − 1.111210I
b = 0.654941 − 0.857680I
0.65352 − 2.88892I 0
u = −0.786407 − 1.095290I
a = −0.233409 − 0.765544I
b = 1.07376 − 1.07351I
0.65352 − 2.88892I 0
u = −0.608189 + 0.167810I
a = −0.18394 + 1.42724I
b = −1.03173 + 1.22867I
−1.98777 + 3.16700I −4.3128 − 13.8397I
u = −0.608189 + 0.167810I
a = −2.09437 + 1.44234I
b = 0.127634 + 0.898898I
−1.98777 + 3.16700I −4.3128 − 13.8397I
u = −0.608189 − 0.167810I
a = −0.18394 − 1.42724I
b = −1.03173 − 1.22867I
−1.98777 − 3.16700I −4.3128 + 13.8397I
u = −0.608189 − 0.167810I
a = −2.09437 − 1.44234I
b = 0.127634 − 0.898898I
−1.98777 − 3.16700I −4.3128 + 13.8397I
u = 1.16636 + 0.87110I
a = 0.122373 − 1.028040I
b = 1.07792 − 1.22753I
−2.00176 − 11.29870I 0
u = 1.16636 + 0.87110I
a = −0.088680 + 1.118680I
b = −1.03826 + 1.09246I
−2.00176 − 11.29870I 0
u = 1.16636 − 0.87110I
a = 0.122373 + 1.028040I
b = 1.07792 + 1.22753I
−2.00176 + 11.29870I 0
u = 1.16636 − 0.87110I
a = −0.088680 − 1.118680I
b = −1.03826 − 1.09246I
−2.00176 + 11.29870I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21053 + 0.81525I
a = 0.542590 + 0.756883I
b = −0.322362 + 0.629048I
−2.23455 − 6.04607I 0
u = 1.21053 + 0.81525I
a = −0.057558 − 0.480884I
b = −0.039775 − 1.358570I
−2.23455 − 6.04607I 0
u = 1.21053 − 0.81525I
a = 0.542590 − 0.756883I
b = −0.322362 − 0.629048I
−2.23455 + 6.04607I 0
u = 1.21053 − 0.81525I
a = −0.057558 + 0.480884I
b = −0.039775 + 1.358570I
−2.23455 + 6.04607I 0
u = −0.470296 + 0.186708I
a = −0.295873 + 1.159110I
b = 1.40842 + 1.93656I
−1.52745 − 1.61554I −1.60105 − 0.11717I
u = −0.470296 + 0.186708I
a = 1.17484 + 4.58415I
b = 0.077266 + 0.600364I
−1.52745 − 1.61554I −1.60105 − 0.11717I
u = −0.470296 − 0.186708I
a = −0.295873 − 1.159110I
b = 1.40842 − 1.93656I
−1.52745 + 1.61554I −1.60105 + 0.11717I
u = −0.470296 − 0.186708I
a = 1.17484 − 4.58415I
b = 0.077266 − 0.600364I
−1.52745 + 1.61554I −1.60105 + 0.11717I
u = 1.18764 + 0.95978I
a = 0.082132 − 1.031720I
b = 0.78545 − 1.22589I
−5.61718 − 10.70300I 0
u = 1.18764 + 0.95978I
a = 0.104538 + 0.947719I
b = −1.08778 + 1.14649I
−5.61718 − 10.70300I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.18764 − 0.95978I
a = 0.082132 + 1.031720I
b = 0.78545 + 1.22589I
−5.61718 + 10.70300I 0
u = 1.18764 − 0.95978I
a = 0.104538 − 0.947719I
b = −1.08778 − 1.14649I
−5.61718 + 10.70300I 0
u = −0.77762 + 1.35805I
a = 0.032014 − 0.538519I
b = −0.1212740 + 0.0325207I
−0.08320 + 5.80714I 0
u = −0.77762 + 1.35805I
a = −0.0565417 − 0.0569243I
b = −0.706440 − 0.462240I
−0.08320 + 5.80714I 0
u = −0.77762 − 1.35805I
a = 0.032014 + 0.538519I
b = −0.1212740 − 0.0325207I
−0.08320 − 5.80714I 0
u = −0.77762 − 1.35805I
a = −0.0565417 + 0.0569243I
b = −0.706440 + 0.462240I
−0.08320 − 5.80714I 0
u = −1.58144 + 0.09381I
a = 0.463468 − 0.619520I
b = 0.088917 − 0.687357I
−2.60428 − 5.02841I 0
u = −1.58144 + 0.09381I
a = 0.081721 − 0.429793I
b = 0.674827 − 1.023210I
−2.60428 − 5.02841I 0
u = −1.58144 − 0.09381I
a = 0.463468 + 0.619520I
b = 0.088917 + 0.687357I
−2.60428 + 5.02841I 0
u = −1.58144 − 0.09381I
a = 0.081721 + 0.429793I
b = 0.674827 + 1.023210I
−2.60428 + 5.02841I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.166825 + 0.327662I
a = −0.573099 − 0.554415I
b = −1.66992 + 1.58351I
−1.67841 + 1.93955I 15.1921 − 13.7852I
u = 0.166825 + 0.327662I
a = −1.77725 − 6.00135I
b = −0.086053 + 0.280273I
−1.67841 + 1.93955I 15.1921 − 13.7852I
u = 0.166825 − 0.327662I
a = −0.573099 + 0.554415I
b = −1.66992 − 1.58351I
−1.67841 − 1.93955I 15.1921 + 13.7852I
u = 0.166825 − 0.327662I
a = −1.77725 + 6.00135I
b = −0.086053 − 0.280273I
−1.67841 − 1.93955I 15.1921 + 13.7852I
u = 1.64271
a = −0.742401
b = −1.13646
3.08221 0
u = 1.64271
a = 0.691818
b = 1.21955
3.08221 0
u = 1.50030 + 0.91446I
a = −0.108637 + 0.809699I
b = −0.602944 + 0.780086I
−1.20562 − 5.42950I 0
u = 1.50030 + 0.91446I
a = 0.061948 − 0.557711I
b = 0.90342 − 1.11545I
−1.20562 − 5.42950I 0
u = 1.50030 − 0.91446I
a = −0.108637 − 0.809699I
b = −0.602944 − 0.780086I
−1.20562 + 5.42950I 0
u = 1.50030 − 0.91446I
a = 0.061948 + 0.557711I
b = 0.90342 + 1.11545I
−1.20562 + 5.42950I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.14708 + 1.44106I
a = −0.396893 − 0.220062I
b = 0.092839 − 0.491834I
−4.45949 + 2.25311I 0
u = 1.14708 + 1.44106I
a = 0.177533 + 0.205739I
b = 0.138145 + 0.824376I
−4.45949 + 2.25311I 0
u = 1.14708 − 1.44106I
a = −0.396893 + 0.220062I
b = 0.092839 + 0.491834I
−4.45949 − 2.25311I 0
u = 1.14708 − 1.44106I
a = 0.177533 − 0.205739I
b = 0.138145 − 0.824376I
−4.45949 − 2.25311I 0
20
III. I
u
3
= h−1345u
15
+ 7729u
14
+ · · · + 3655b + 38, −38u
15
− 1117u
14
+ · · · +
3655a + 12877, u
16
− 6u
15
+ · · · + u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
6
=
0.0103967u
15
+ 0.305609u
14
+ ··· + 0.0399453u − 3.52312
0.367989u
15
− 2.11464u
14
+ ··· − 3.53352u − 0.0103967
a
7
=
−0.264295u
15
+ 1.90479u
14
+ ··· + 3.19508u − 3.88071
0.671409u
15
− 3.59042u
14
+ ··· − 3.20985u + 0.0385773
a
10
=
−1.59726u
15
+ 9.25937u
14
+ ··· + 4.17893u − 1.00082
−0.324213u
15
+ 1.66457u
14
+ ··· + 1.59644u + 1.59726
a
1
=
−1.48892u
15
+ 8.37045u
14
+ ··· − 2.61532u + 0.926676
−0.843776u
15
+ 3.85007u
14
+ ··· + 3.33707u + 1.81313
a
4
=
1.84268u
15
− 11.7138u
14
+ ··· − 8.28865u + 3.94720
−1.07250u
15
+ 5.32668u
14
+ ··· + 0.458276u − 1.27825
a
5
=
−0.357592u
15
+ 2.42025u
14
+ ··· + 3.57346u − 3.51272
0.367989u
15
− 2.11464u
14
+ ··· − 3.53352u − 0.0103967
a
8
=
−1.22955u
15
+ 7.27880u
14
+ ··· + 4.90752u − 3.87114
−0.0435021u
15
+ 0.316005u
14
+ ··· − 0.325034u + 1.27305
a
11
=
−2.21423u
15
+ 13.9713u
14
+ ··· − 6.77045u − 0.315732
−0.0943912u
15
− 0.148290u
14
+ ··· + 3.42681u + 1.52832
a
11
=
−2.21423u
15
+ 13.9713u
14
+ ··· − 6.77045u − 0.315732
−0.0943912u
15
− 0.148290u
14
+ ··· + 3.42681u + 1.52832
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
12541
3655
u
15
+
63901
3655
u
14
+ ··· +
29533
3655
u −
10346
3655
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
− 9u
15
+ ··· − 33u + 9
c
2
u
16
− 6u
15
+ ··· + u + 1
c
3
, c
10
u
16
+ 4u
15
+ ··· + 2u − 1
c
4
, c
11
u
16
− u
14
+ ··· + 3u − 1
c
5
, c
9
u
16
+ u
15
+ ··· + u
2
− 1
c
6
, c
8
u
16
+ u
15
+ ··· + 2u − 1
c
7
u
16
+ 8u
15
+ ··· − 3u
2
+ 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 13y
15
+ ··· − 27y + 81
c
2
y
16
− 10y
15
+ ··· − 15y + 1
c
3
, c
10
y
16
+ 2y
14
+ ··· − 26y + 1
c
4
, c
11
y
16
− 2y
15
+ ··· + 13y + 1
c
5
, c
9
y
16
− 3y
15
+ ··· − 2y + 1
c
6
, c
8
y
16
− 7y
15
+ ··· + 8y
2
+ 1
c
7
y
16
+ 2y
15
+ ··· − 6y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.843774 + 0.020472I
a = −0.814747 + 0.307970I
b = 0.681158 − 0.276536I
−4.17810 + 2.37838I −5.85782 − 3.30047I
u = −0.843774 − 0.020472I
a = −0.814747 − 0.307970I
b = 0.681158 + 0.276536I
−4.17810 − 2.37838I −5.85782 + 3.30047I
u = 0.650319 + 1.149000I
a = 0.299647 + 0.918726I
b = −0.860745 + 0.941758I
0.40659 − 2.51099I −3.33911 − 9.63855I
u = 0.650319 − 1.149000I
a = 0.299647 − 0.918726I
b = −0.860745 − 0.941758I
0.40659 + 2.51099I −3.33911 + 9.63855I
u = −1.028220 + 0.857975I
a = −0.029407 + 0.419644I
b = −0.329808 − 0.456715I
−2.63766 − 10.07530I 0.70439 + 5.81996I
u = −1.028220 − 0.857975I
a = −0.029407 − 0.419644I
b = −0.329808 + 0.456715I
−2.63766 + 10.07530I 0.70439 − 5.81996I
u = 1.357830 + 0.318055I
a = −0.263706 − 0.623927I
b = −0.159624 − 0.931056I
−3.99183 + 4.14407I −8.04295 − 6.13289I
u = 1.357830 − 0.318055I
a = −0.263706 + 0.623927I
b = −0.159624 + 0.931056I
−3.99183 − 4.14407I −8.04295 + 6.13289I
u = 0.494805 + 0.313135I
a = −0.76630 + 1.72817I
b = −0.920318 + 0.615155I
2.37780 − 3.65031I 5.77914 + 4.75975I
u = 0.494805 − 0.313135I
a = −0.76630 − 1.72817I
b = −0.920318 − 0.615155I
2.37780 + 3.65031I 5.77914 − 4.75975I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.09063 + 0.91474I
a = 0.001019 − 1.085380I
b = 0.99396 − 1.18281I
−3.41791 − 10.94270I −2.27266 + 9.01140I
u = 1.09063 − 0.91474I
a = 0.001019 + 1.085380I
b = 0.99396 + 1.18281I
−3.41791 + 10.94270I −2.27266 − 9.01140I
u = 1.51464
a = −0.673129
b = −1.01955
3.85452 16.3090
u = −0.317141 + 0.174078I
a = −1.95569 − 2.13567I
b = 0.992001 + 0.336866I
−1.67458 + 2.27154I −1.49720 − 3.30379I
u = −0.317141 − 0.174078I
a = −1.95569 + 2.13567I
b = 0.992001 − 0.336866I
−1.67458 − 2.27154I −1.49720 + 3.30379I
u = 1.67647
a = 0.731484
b = 1.22631
2.63767 −12.2560
25
IV. I
u
4
= h3au + 3b + 2u + 3, 3a
2
− au − a + 1, u
2
+ 3u + 3i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
−3u − 3
a
6
=
a
−au −
2
3
u − 1
a
7
=
−2au − 2a +
2
3
u + 1
−4au − 9a +
1
3
u + 2
a
10
=
−
2
3
au − a −
1
3
u
−1
a
1
=
2
3
au + a +
1
3
u + 1
1
a
4
=
−au −
7
3
a +
2
3
u +
4
3
−au − 3a − 2u − 2
a
5
=
au + a +
2
3
u + 1
−au −
2
3
u − 1
a
8
=
1
3
au + 2a −
2
3
u − 1
−au − 3a +
7
3
u + 2
a
11
=
−
1
3
au − a − u −
4
3
au − a −
5
3
a
11
=
−
1
3
au − a − u −
4
3
au − a −
5
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
145
9
u −
65
3
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u + 1)
4
c
2
(u
2
+ 3u + 3)
2
c
3
, c
10
3(3u
4
+ 3u
3
+ 7u
2
− 5u + 1)
c
4
, c
5
, c
9
c
11
3(3u
4
+ 4u
2
+ 3u + 3)
c
6
, c
8
3(3u
4
− 3u
3
− 2u
2
+ 2u + 7)
c
7
(u
2
− 3u + 3)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
4
c
2
, c
7
(y
2
− 3y + 9)
2
c
3
, c
10
9(9y
4
+ 33y
3
+ 85y
2
− 11y + 1)
c
4
, c
5
, c
9
c
11
9(9y
4
+ 24y
3
+ 34y
2
+ 15y + 9)
c
6
, c
8
9(9y
4
− 21y
3
+ 58y
2
− 32y + 49)
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.50000 + 0.86603I
a = −0.103734 + 0.733946I
b = 0.480016 + 0.613405I
−1.64493 + 6.08965I 2.5000 − 13.9526I
u = −1.50000 + 0.86603I
a = −0.062933 − 0.445271I
b = −0.480016 − 1.190760I
−1.64493 + 6.08965I 2.5000 − 13.9526I
u = −1.50000 − 0.86603I
a = −0.103734 − 0.733946I
b = 0.480016 − 0.613405I
−1.64493 − 6.08965I 2.5000 + 13.9526I
u = −1.50000 − 0.86603I
a = −0.062933 + 0.445271I
b = −0.480016 + 1.190760I
−1.64493 − 6.08965I 2.5000 + 13.9526I
29
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u + 1)
4
)(u
16
− 9u
15
+ ··· − 33u + 9)
· (u
30
+ 26u
29
+ ··· + 12288u + 1024)
· (u
47
− 13u
46
+ ··· + 193u − 27)
2
c
2
((u
2
+ 3u + 3)
2
)(u
16
− 6u
15
+ ··· + u + 1)
· (u
30
+ 29u
29
+ ··· + 5632u + 512)(u
47
− 14u
46
+ ··· + 30u − 3)
2
c
3
, c
10
9(3u
4
+ 3u
3
+ ··· − 5u + 1)(u
16
+ 4u
15
+ ··· + 2u − 1)
· (u
30
− u
28
+ ··· − 6u + 1)(3u
94
+ 24u
93
+ ··· + 45u − 1)
c
4
, c
11
9(3u
4
+ 4u
2
+ 3u + 3)(u
16
− u
14
+ ··· + 3u − 1)
· (u
30
+ 8u
28
+ ··· + 3u + 1)(3u
94
+ 15u
93
+ ··· − 14505u − 1083)
c
5
, c
9
9(3u
4
+ 4u
2
+ 3u + 3)(u
16
+ u
15
+ ··· + u
2
− 1)(u
30
− u
29
+ ··· − 2u + 1)
· (3u
94
+ 3u
93
+ ··· − 93u − 3)
c
6
, c
8
9(3u
4
− 3u
3
+ ··· + 2u + 7)(u
16
+ u
15
+ ··· + 2u − 1)
· (u
30
− u
29
+ ··· + 46u + 27)
· (3u
94
+ 6u
93
+ ··· + 9495938u − 2259497)
c
7
((u
2
− 3u + 3)
2
)(u
16
+ 8u
15
+ ··· − 3u
2
+ 1)
· (u
30
− 19u
29
+ ··· − 288u + 32)(u
47
+ 10u
46
+ ··· + 18u + 3)
2
30
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
4
)(y
16
− 13y
15
+ ··· − 27y + 81)
· (y
30
− 2y
29
+ ··· + 12976128y + 1048576)
· (y
47
+ 9y
46
+ ··· − 11945y − 729)
2
c
2
((y
2
− 3y + 9)
2
)(y
16
− 10y
15
+ ··· − 15y + 1)
· (y
30
− 11y
29
+ ··· + 11665408y + 262144)
· (y
47
− 12y
46
+ ··· + 138y − 9)
2
c
3
, c
10
81(9y
4
+ 33y
3
+ ··· − 11y + 1)(y
16
+ 2y
14
+ ··· − 26y + 1)
· (y
30
− 2y
29
+ ··· − 10y + 1)(9y
94
− 156y
93
+ ··· − 451y + 1)
c
4
, c
11
81(9y
4
+ 24y
3
+ ··· + 15y + 9)(y
16
− 2y
15
+ ··· + 13y + 1)
· (y
30
+ 16y
29
+ ··· + 33y + 1)
· (9y
94
− 165y
93
+ ··· + 14483427y + 1172889)
c
5
, c
9
81(9y
4
+ 24y
3
+ ··· + 15y + 9)(y
16
− 3y
15
+ ··· − 2y + 1)
· (y
30
+ 3y
29
+ ··· + 6y + 1)(9y
94
+ 195y
93
+ ··· − 885y + 9)
c
6
, c
8
81(9y
4
− 21y
3
+ ··· − 32y + 49)(y
16
− 7y
15
+ ··· + 8y
2
+ 1)
· (y
30
− 13y
29
+ ··· − 5896y + 729)
· (9y
94
− 318y
93
+ ··· − 181297638508792y + 5105326693009)
c
7
((y
2
− 3y + 9)
2
)(y
16
+ 2y
15
+ ··· − 6y + 1)
· (y
30
+ y
29
+ ··· + 11776y + 1024)(y
47
− 8y
46
+ ··· + 120y − 9)
2
31
