12a
0265
(K12a
0265
)
A knot diagram
1
Linearized knot diagam
3 6 7 12 11 2 1 5 4 8 9 10
Solving Sequence
4,12 5,10
1 9 8 7 3 11 6 2
c
4
c
12
c
9
c
8
c
7
c
3
c
11
c
5
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.30744 × 10
71
u
76
+ 3.22892 × 10
71
u
75
+ ··· + 3.31124 × 10
66
b + 7.87073 × 10
71
,
− 2.93126 × 10
71
u
76
− 5.90588 × 10
71
u
75
+ ··· + 1.65562 × 10
66
a − 1.20168 × 10
72
, u
77
+ u
76
+ ··· + 2u + 1i
I
u
2
= h−6.34090 × 10
421
u
101
− 2.36894 × 10
422
u
100
+ ··· + 1.13936 × 10
422
b − 4.46492 × 10
422
,
5.97619 × 10
421
u
101
+ 2.38844 × 10
422
u
100
+ ··· + 1.13936 × 10
422
a + 8.88412 × 10
422
,
u
102
+ 4u
101
+ ··· + 15u + 2i
I
u
3
= h−u
26
+ u
25
+ ··· + b + 4u, −4u
26
+ 4u
25
+ ··· + a − 1, u
27
− u
26
+ ··· − 4u
2
+ 1i
I
u
4
= h−u
3
− u
2
+ b − 3u − 1, −u
3
− u
2
+ a − 3u − 1, u
4
+ u
3
+ 3u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 210 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
= h1.31×10
71
u
76
+3.23×10
71
u
75
+· · ·+3.31×10
66
b+7.87×10
71
, −2.93×
10
71
u
76
−5.91×10
71
u
75
+· · ·+1.66×10
66
a−1.20×10
72
, u
77
+u
76
+· · ·+2u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
10
=
177049.u
76
+ 356717.u
75
+ ··· + 2.31166 × 10
6
u + 725817.
−39484.9u
76
− 97513.7u
75
+ ··· − 691926.u − 237697.
a
1
=
213753.u
76
+ 298403.u
75
+ ··· + 1.52213 × 10
6
u + 328591.
−109347.u
76
− 197571.u
75
+ ··· − 1.20523 × 10
6
u − 352541.
a
9
=
216534.u
76
+ 454230.u
75
+ ··· + 3.00359 × 10
6
u + 963514.
−39484.9u
76
− 97513.7u
75
+ ··· − 691926.u − 237697.
a
8
=
216534.u
76
+ 454230.u
75
+ ··· + 3.00359 × 10
6
u + 963514.
−39484.9u
76
− 97513.7u
75
+ ··· − 691926.u − 237697.
a
7
=
174969.u
76
+ 449646.u
75
+ ··· + 3.26129 × 10
6
u + 1.11170 × 10
6
199191.u
76
+ 247170.u
75
+ ··· + 1.13303 × 10
6
u + 186587.
a
3
=
−228577.u
76
− 539101.u
75
+ ··· − 3.65918 × 10
6
u − 1.25213 × 10
6
−289691.u
76
+ 11209.4u
75
+ ··· + 1.42905 × 10
6
u + 1.31972 × 10
6
a
11
=
466449.u
76
+ 774901.u
75
+ ··· + 4.50264 × 10
6
u + 1.22728 × 10
6
−143349.u
76
− 278927.u
75
+ ··· − 1.77528 × 10
6
u − 546149.
a
6
=
−508259.u
76
− 260806.u
75
+ ··· + 67914.3u + 1.04200 × 10
6
322346.u
76
+ 230196.u
75
+ ··· + 431531.u − 430287.
a
2
=
−2.09543 × 10
6
u
76
− 2.05278 × 10
6
u
75
+ ··· − 8.27941 × 10
6
u + 429977.
728151.u
76
+ 1.13395 × 10
6
u
75
+ ··· + 6.79368 × 10
6
u + 1.68063 × 10
6
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 928131.u
76
− 1.10298 × 10
6
u
75
+ ··· − 1.45398 × 10
7
u − 8.87559 × 10
6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 37u
76
+ ··· − 7u − 16
c
2
, c
6
u
77
− 5u
76
+ ··· − 33u + 4
c
3
u
77
+ 5u
76
+ ··· + 17874u + 1768
c
4
, c
8
u
77
+ u
76
+ ··· + 2u + 1
c
5
, c
9
u
77
+ 3u
75
+ ··· − 9u + 2
c
7
u
77
− 25u
76
+ ··· − 818285u + 37300
c
10
, c
12
u
77
− 12u
76
+ ··· + 17u + 1
c
11
u
77
− 42u
76
+ ··· + 11u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
+ 9y
76
+ ··· + 401y −256
c
2
, c
6
y
77
+ 37y
76
+ ··· − 7y −16
c
3
y
77
− 19y
76
+ ··· + 74410324y −3125824
c
4
, c
8
y
77
+ 33y
76
+ ··· − 86y −1
c
5
, c
9
y
77
+ 6y
76
+ ··· + 145y −4
c
7
y
77
+ 17y
76
+ ··· − 27321142975y −1391290000
c
10
, c
12
y
77
− 50y
76
+ ··· + 83y −1
c
11
y
77
+ 60y
75
+ ··· − 39y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.267790 + 0.992695I
a = −0.431267 + 1.100390I
b = −0.420752 − 0.212748I
3.46656 + 2.98634I 0
u = 0.267790 − 0.992695I
a = −0.431267 − 1.100390I
b = −0.420752 + 0.212748I
3.46656 − 2.98634I 0
u = 0.237290 + 0.931626I
a = 0.199446 + 0.750390I
b = 0.577247 + 0.825765I
−0.063419 + 0.815170I 0
u = 0.237290 − 0.931626I
a = 0.199446 − 0.750390I
b = 0.577247 − 0.825765I
−0.063419 − 0.815170I 0
u = −0.300216 + 1.022690I
a = 0.507425 + 1.023370I
b = 0.414276 − 0.285176I
1.11208 − 7.98543I 0
u = −0.300216 − 1.022690I
a = 0.507425 − 1.023370I
b = 0.414276 + 0.285176I
1.11208 + 7.98543I 0
u = −0.188410 + 1.058390I
a = 0.270943 + 0.956122I
b = 0.259606 − 0.198061I
−0.984111 − 0.167610I 0
u = −0.188410 − 1.058390I
a = 0.270943 − 0.956122I
b = 0.259606 + 0.198061I
−0.984111 + 0.167610I 0
u = 0.242342 + 0.878864I
a = −0.29452 + 1.39873I
b = −0.551628 − 0.034407I
4.85147 + 0.97941I 0
u = 0.242342 − 0.878864I
a = −0.29452 − 1.39873I
b = −0.551628 + 0.034407I
4.85147 − 0.97941I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.199438 + 1.083720I
a = −0.317566 + 0.995974I
b = −0.580208 + 1.187420I
3.66736 + 0.81055I 0
u = −0.199438 − 1.083720I
a = −0.317566 − 0.995974I
b = −0.580208 − 1.187420I
3.66736 − 0.81055I 0
u = 0.239909 + 1.079520I
a = 0.376611 + 0.943149I
b = 0.681597 + 1.143600I
1.84653 − 5.56859I 0
u = 0.239909 − 1.079520I
a = 0.376611 − 0.943149I
b = 0.681597 − 1.143600I
1.84653 + 5.56859I 0
u = 0.055475 + 1.130470I
a = 0.102708 + 1.179470I
b = 0.177608 + 1.391890I
−0.297314 − 0.869794I 0
u = 0.055475 − 1.130470I
a = 0.102708 − 1.179470I
b = 0.177608 − 1.391890I
−0.297314 + 0.869794I 0
u = −0.136518 + 1.129770I
a = −0.252093 + 1.133130I
b = −0.43003 + 1.35913I
3.55022 − 1.05637I 0
u = −0.136518 − 1.129770I
a = −0.252093 − 1.133130I
b = −0.43003 − 1.35913I
3.55022 + 1.05637I 0
u = −0.244151 + 0.819410I
a = 0.20371 + 1.60022I
b = 0.649592 + 0.048331I
3.79661 + 3.71278I 0
u = −0.244151 − 0.819410I
a = 0.20371 − 1.60022I
b = 0.649592 − 0.048331I
3.79661 − 3.71278I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.123768 + 1.156590I
a = 0.247722 + 1.193980I
b = 0.40510 + 1.44972I
1.61740 + 5.84088I 0
u = 0.123768 − 1.156590I
a = 0.247722 − 1.193980I
b = 0.40510 − 1.44972I
1.61740 − 5.84088I 0
u = −0.471665 + 0.554278I
a = −0.100726 + 0.197032I
b = −0.574410 + 0.316752I
−0.31083 + 1.94641I 0
u = −0.471665 − 0.554278I
a = −0.100726 − 0.197032I
b = −0.574410 − 0.316752I
−0.31083 − 1.94641I 0
u = −0.240699 + 0.670164I
a = −0.38161 + 2.29089I
b = 0.900486 + 0.308186I
4.01950 − 0.35456I 0
u = −0.240699 − 0.670164I
a = −0.38161 − 2.29089I
b = 0.900486 − 0.308186I
4.01950 + 0.35456I 0
u = 0.234998 + 0.645618I
a = 0.58520 + 2.40806I
b = −0.932639 + 0.368794I
5.19817 − 4.45515I 0
u = 0.234998 − 0.645618I
a = 0.58520 − 2.40806I
b = −0.932639 − 0.368794I
5.19817 + 4.45515I 0
u = −0.083179 + 0.652582I
a = −0.87829 + 1.18464I
b = 0.609255 + 0.546894I
1.03201 + 1.52201I 0
u = −0.083179 − 0.652582I
a = −0.87829 − 1.18464I
b = 0.609255 − 0.546894I
1.03201 − 1.52201I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.229679 + 0.611677I
a = 0.91232 + 2.60024I
b = −0.982166 + 0.454289I
4.09903 − 6.69028I 0
u = 0.229679 − 0.611677I
a = 0.91232 − 2.60024I
b = −0.982166 − 0.454289I
4.09903 + 6.69028I 0
u = −0.231062 + 0.601022I
a = −1.00848 + 2.69638I
b = 1.005210 + 0.477155I
1.89130 + 11.72090I 0
u = −0.231062 − 0.601022I
a = −1.00848 − 2.69638I
b = 1.005210 − 0.477155I
1.89130 − 11.72090I 0
u = −0.205361 + 0.608972I
a = −1.10138 + 2.36975I
b = 0.928718 + 0.503276I
−0.48681 + 4.19549I 0
u = −0.205361 − 0.608972I
a = −1.10138 − 2.36975I
b = 0.928718 − 0.503276I
−0.48681 − 4.19549I 0
u = 0.125484 + 0.599783I
a = 1.40360 + 1.48105I
b = −0.740111 + 0.629556I
−2.06907 − 4.76842I 0
u = 0.125484 − 0.599783I
a = 1.40360 − 1.48105I
b = −0.740111 − 0.629556I
−2.06907 + 4.76842I 0
u = −0.916730 + 1.049410I
a = −0.459450 − 0.271004I
b = −1.137030 − 0.248373I
3.36045 − 3.51281I 0
u = −0.916730 − 1.049410I
a = −0.459450 + 0.271004I
b = −1.137030 + 0.248373I
3.36045 + 3.51281I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.066908 + 0.574195I
a = 1.44105 + 0.75476I
b = −0.599404 + 0.719514I
−1.31483 + 2.41918I 0
u = 0.066908 − 0.574195I
a = 1.44105 − 0.75476I
b = −0.599404 − 0.719514I
−1.31483 − 2.41918I 0
u = 0.94070 + 1.07555I
a = 0.430643 − 0.337969I
b = 1.129410 − 0.338602I
5.32767 − 1.72237I 0
u = 0.94070 − 1.07555I
a = 0.430643 + 0.337969I
b = 1.129410 + 0.338602I
5.32767 + 1.72237I 0
u = 0.028351 + 0.525345I
a = −0.721133 − 0.031678I
b = 0.342687 + 0.693104I
0.54233 + 1.43169I 0
u = 0.028351 − 0.525345I
a = −0.721133 + 0.031678I
b = 0.342687 − 0.693104I
0.54233 − 1.43169I 0
u = 0.96061 + 1.13614I
a = 0.391292 − 0.507155I
b = 1.155580 − 0.546700I
6.01308 − 4.66397I 0
u = 0.96061 − 1.13614I
a = 0.391292 + 0.507155I
b = 1.155580 + 0.546700I
6.01308 + 4.66397I 0
u = −1.02412 + 1.08661I
a = −0.264678 − 0.351646I
b = −0.941090 − 0.429042I
0.04793 + 3.81894I 0
u = −1.02412 − 1.08661I
a = −0.264678 + 0.351646I
b = −0.941090 + 0.429042I
0.04793 − 3.81894I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.96343 + 1.15675I
a = −0.372594 − 0.586734I
b = −1.169160 − 0.640918I
4.66198 + 9.87576I 0
u = −0.96343 − 1.15675I
a = −0.372594 + 0.586734I
b = −1.169160 + 0.640918I
4.66198 − 9.87576I 0
u = −0.009239 + 0.482143I
a = −0.895002 − 0.903005I
b = 0.237807 + 0.914606I
−0.46807 + 2.55260I 0
u = −0.009239 − 0.482143I
a = −0.895002 + 0.903005I
b = 0.237807 − 0.914606I
−0.46807 − 2.55260I 0
u = −1.52052
a = −0.104427
b = −0.531994
−3.29769 0
u = 0.015503 + 0.476991I
a = 1.03707 − 1.14519I
b = −0.244321 + 0.978648I
−2.75638 − 7.27121I 0
u = 0.015503 − 0.476991I
a = 1.03707 + 1.14519I
b = −0.244321 − 0.978648I
−2.75638 + 7.27121I 0
u = 0.005166 + 0.470849I
a = 0.507758 − 1.215430I
b = −0.124407 + 0.955062I
−4.44293 + 0.17554I 0
u = 0.005166 − 0.470849I
a = 0.507758 + 1.215430I
b = −0.124407 − 0.955062I
−4.44293 − 0.17554I 0
u = −0.97518 + 1.20606I
a = −0.165001 − 0.972043I
b = −1.12107 − 1.11471I
3.46864 + 7.75820I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.97518 − 1.20606I
a = −0.165001 + 0.972043I
b = −1.12107 + 1.11471I
3.46864 − 7.75820I 0
u = 0.97636 + 1.20780I
a = 0.133635 − 1.024500I
b = 1.11204 − 1.17668I
4.41037 − 12.87510I 0
u = 0.97636 − 1.20780I
a = 0.133635 + 1.024500I
b = 1.11204 + 1.17668I
4.41037 + 12.87510I 0
u = −0.97855 + 1.20740I
a = −0.021538 − 1.054220I
b = −1.01964 − 1.24813I
−1.99941 + 12.83550I 0
u = −0.97855 − 1.20740I
a = −0.021538 + 1.054220I
b = −1.01964 + 1.24813I
−1.99941 − 12.83550I 0
u = 0.97871 + 1.20856I
a = 0.068337 − 1.097820I
b = 1.07950 − 1.27011I
2.9307 − 15.5594I 0
u = 0.97871 − 1.20856I
a = 0.068337 + 1.097820I
b = 1.07950 + 1.27011I
2.9307 + 15.5594I 0
u = −0.97948 + 1.20857I
a = −0.051848 − 1.123910I
b = −1.07421 − 1.30036I
0.6392 + 20.7593I 0
u = −0.97948 − 1.20857I
a = −0.051848 + 1.123910I
b = −1.07421 + 1.30036I
0.6392 − 20.7593I 0
u = 0.98077 + 1.21178I
a = −0.079041 − 0.823030I
b = 0.830388 − 1.080080I
−4.60835 − 12.16330I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.98077 − 1.21178I
a = −0.079041 + 0.823030I
b = 0.830388 + 1.080080I
−4.60835 + 12.16330I 0
u = −0.98735 + 1.20932I
a = 0.009211 − 0.754065I
b = −0.862376 − 0.984364I
−1.04934 + 8.15459I 0
u = −0.98735 − 1.20932I
a = 0.009211 + 0.754065I
b = −0.862376 + 0.984364I
−1.04934 − 8.15459I 0
u = 0.99244 + 1.21885I
a = −0.071700 − 0.678304I
b = 0.767518 − 0.944950I
−4.32252 − 3.84533I 0
u = 0.99244 − 1.21885I
a = −0.071700 + 0.678304I
b = 0.767518 + 0.944950I
−4.32252 + 3.84533I 0
u = 1.69278 + 0.20454I
a = 0.0914533 − 0.0154027I
b = 0.507034 − 0.033144I
−6.89489 − 4.51892I 0
u = 1.69278 − 0.20454I
a = 0.0914533 + 0.0154027I
b = 0.507034 + 0.033144I
−6.89489 + 4.51892I 0
12
II. I
u
2
= h−6.34 × 10
421
u
101
− 2.37 × 10
422
u
100
+ · · · + 1.14 × 10
422
b − 4.46 ×
10
422
, 5.98 × 10
421
u
101
+ 2.39 × 10
422
u
100
+ · · · + 1.14 × 10
422
a + 8.88 ×
10
422
, u
102
+ 4u
101
+ · · · + 15u + 2i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
10
=
−0.524521u
101
− 2.09630u
100
+ ··· − 21.0688u − 7.79745
0.556531u
101
+ 2.07918u
100
+ ··· + 11.3560u + 3.91879
a
1
=
−0.547866u
101
− 2.18899u
100
+ ··· − 21.1140u − 8.10568
0.585402u
101
+ 2.18997u
100
+ ··· + 13.3496u + 4.20758
a
9
=
−1.08105u
101
− 4.17548u
100
+ ··· − 32.4248u − 11.7162
0.556531u
101
+ 2.07918u
100
+ ··· + 11.3560u + 3.91879
a
8
=
−
1
2
u
101
− 2u
100
+ ··· − 21u −
15
2
0.581051u
101
+ 2.17548u
100
+ ··· + 12.4248u + 4.21624
a
7
=
1.39908u
101
+ 5.28370u
100
+ ··· + 33.0663u + 11.4758
0.0145918u
101
+ 0.0567883u
100
+ ··· − 3.53157u + 0.00354395
a
3
=
−0.924593u
101
− 3.62496u
100
+ ··· − 30.3174u − 7.66250
0.0408050u
101
+ 0.111099u
100
+ ··· − 0.964190u − 0.142013
a
11
=
−1.71951u
101
− 6.57952u
100
+ ··· − 48.3027u − 16.8410
0.586241u
101
+ 2.20056u
100
+ ··· + 15.8391u + 4.52771
a
6
=
2.71136u
101
+ 10.1758u
100
+ ··· + 82.6432u + 21.9005
0.304172u
101
+ 1.16670u
100
+ ··· + 9.11683u + 3.50125
a
2
=
−1.34710u
101
− 5.30690u
100
+ ··· − 37.6711u − 15.6054
1.07319u
101
+ 3.96909u
100
+ ··· + 28.8646u + 7.58637
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0351821u
101
+ 0.0568820u
100
+ ··· + 29.4565u − 5.38180
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
51
+ 24u
50
+ ··· − 4u − 1)
2
c
2
, c
6
(u
51
+ 2u
50
+ ··· + 4u + 1)
2
c
3
(u
51
− 2u
50
+ ··· − 139u + 26)
2
c
4
, c
8
u
102
+ 4u
101
+ ··· + 15u + 2
c
5
, c
9
u
102
+ 2u
101
+ ··· + 2916u + 376
c
7
(u
51
+ 15u
50
+ ··· + 1000u + 64)
2
c
10
, c
12
u
102
+ 5u
101
+ ··· + 10593u + 956
c
11
(u
51
+ 25u
50
+ ··· − 10u − 4)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
51
+ 8y
50
+ ··· − 32y −1)
2
c
2
, c
6
(y
51
+ 24y
50
+ ··· − 4y −1)
2
c
3
(y
51
− 8y
50
+ ··· + 15733y −676)
2
c
4
, c
8
y
102
− 20y
101
+ ··· − 57y + 4
c
5
, c
9
y
102
+ 96y
100
+ ··· + 16598704y + 141376
c
7
(y
51
+ 19y
50
+ ··· − 5184y −4096)
2
c
10
, c
12
y
102
+ 23y
101
+ ··· + 48008215y + 913936
c
11
(y
51
− 5y
50
+ ··· + 428y −16)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.543911 + 0.836758I
a = 0.117663 + 0.631387I
b = −1.40715 + 0.83802I
0.71471 − 4.40922I 0
u = 0.543911 − 0.836758I
a = 0.117663 − 0.631387I
b = −1.40715 − 0.83802I
0.71471 + 4.40922I 0
u = 0.508128 + 0.885564I
a = 0.718931 + 0.401841I
b = −0.205409 + 1.199330I
−2.99458 − 7.31406I 0
u = 0.508128 − 0.885564I
a = 0.718931 − 0.401841I
b = −0.205409 − 1.199330I
−2.99458 + 7.31406I 0
u = −0.819608 + 0.534290I
a = −0.468530 − 1.081200I
b = −1.13192 − 1.23128I
−3.57874 + 4.50800I 0
u = −0.819608 − 0.534290I
a = −0.468530 + 1.081200I
b = −1.13192 + 1.23128I
−3.57874 − 4.50800I 0
u = −0.504708 + 0.828571I
a = −0.033334 + 0.495798I
b = 1.51079 + 0.69174I
−0.933655 − 0.114205I 0
u = −0.504708 − 0.828571I
a = −0.033334 − 0.495798I
b = 1.51079 − 0.69174I
−0.933655 + 0.114205I 0
u = −0.767514 + 0.585787I
a = −0.509453 − 1.224380I
b = −1.21496 − 1.38047I
−0.86229 + 12.39040I 0
u = −0.767514 − 0.585787I
a = −0.509453 + 1.224380I
b = −1.21496 + 1.38047I
−0.86229 − 12.39040I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578997 + 0.874717I
a = 0.128315 + 0.847207I
b = −1.38670 + 1.09740I
0.11206 − 6.09970I 0
u = 0.578997 − 0.874717I
a = 0.128315 − 0.847207I
b = −1.38670 − 1.09740I
0.11206 + 6.09970I 0
u = 0.759999 + 0.558112I
a = 0.549826 − 1.183120I
b = 1.24852 − 1.32345I
1.40035 − 7.17372I 0. + 9.10187I
u = 0.759999 − 0.558112I
a = 0.549826 + 1.183120I
b = 1.24852 + 1.32345I
1.40035 + 7.17372I 0. − 9.10187I
u = 0.308294 + 0.889111I
a = 0.506569 + 0.044497I
b = −0.085886 + 1.085100I
−4.48802 + 0.11163I −8.96076 + 0.I
u = 0.308294 − 0.889111I
a = 0.506569 − 0.044497I
b = −0.085886 − 1.085100I
−4.48802 − 0.11163I −8.96076 + 0.I
u = −0.583693 + 0.888913I
a = −0.106865 + 0.912865I
b = 1.41554 + 1.17786I
−2.00550 + 10.91820I 0
u = −0.583693 − 0.888913I
a = −0.106865 − 0.912865I
b = 1.41554 − 1.17786I
−2.00550 − 10.91820I 0
u = 0.944534 + 0.491700I
a = 1.36305 + 1.19440I
b = −0.081185 + 0.753822I
−3.97661 − 3.74895I 0
u = 0.944534 − 0.491700I
a = 1.36305 − 1.19440I
b = −0.081185 − 0.753822I
−3.97661 + 3.74895I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.611253 + 0.874206I
a = −0.254015 + 0.923303I
b = 1.22771 + 1.19989I
−3.97661 + 3.74895I 0
u = −0.611253 − 0.874206I
a = −0.254015 − 0.923303I
b = 1.22771 − 1.19989I
−3.97661 − 3.74895I 0
u = −0.838110 + 0.385745I
a = −1.62040 + 0.84063I
b = 0.019928 + 0.419465I
−4.41316 + 4.70182I −9.28883 − 5.08326I
u = −0.838110 − 0.385745I
a = −1.62040 − 0.84063I
b = 0.019928 − 0.419465I
−4.41316 − 4.70182I −9.28883 + 5.08326I
u = 0.655738 + 0.874329I
a = 0.482098 + 0.974345I
b = −0.90500 + 1.32060I
−4.41316 − 4.70182I 0
u = 0.655738 − 0.874329I
a = 0.482098 − 0.974345I
b = −0.90500 − 1.32060I
−4.41316 + 4.70182I 0
u = 0.664362 + 0.877603I
a = 0.603363 + 0.968185I
b = −0.72887 + 1.39102I
−2.94615 + 2.41292I 0
u = 0.664362 − 0.877603I
a = 0.603363 − 0.968185I
b = −0.72887 − 1.39102I
−2.94615 − 2.41292I 0
u = −0.667775 + 0.877732I
a = −0.575722 + 0.905547I
b = 0.70769 + 1.28360I
−0.80279 + 2.13782I 0
u = −0.667775 − 0.877732I
a = −0.575722 − 0.905547I
b = 0.70769 − 1.28360I
−0.80279 − 2.13782I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.503184 + 0.998319I
a = −0.497086 + 0.435606I
b = 0.251845 + 1.083850I
−0.68241 + 2.75592I 0
u = −0.503184 − 0.998319I
a = −0.497086 − 0.435606I
b = 0.251845 − 1.083850I
−0.68241 − 2.75592I 0
u = −0.988830 + 0.544741I
a = −1.21665 + 1.33681I
b = 0.138189 + 0.889503I
0.11206 + 6.09970I 0
u = −0.988830 − 0.544741I
a = −1.21665 − 1.33681I
b = 0.138189 − 0.889503I
0.11206 − 6.09970I 0
u = 1.006250 + 0.521050I
a = 1.29034 + 1.38606I
b = −0.077021 + 0.902938I
−2.00550 − 10.91820I 0
u = 1.006250 − 0.521050I
a = 1.29034 − 1.38606I
b = −0.077021 − 0.902938I
−2.00550 + 10.91820I 0
u = 0.713392 + 0.461416I
a = 0.731803 − 1.062980I
b = 1.41295 − 1.14632I
2.79995 − 4.40530I −1.85664 + 11.89899I
u = 0.713392 − 0.461416I
a = 0.731803 + 1.062980I
b = 1.41295 + 1.14632I
2.79995 + 4.40530I −1.85664 − 11.89899I
u = −0.440268 + 0.724211I
a = −0.205437 + 0.057724I
b = 1.373050 + 0.237187I
−1.98882 + 6.12259I 0.32445 − 9.83526I
u = −0.440268 − 0.724211I
a = −0.205437 − 0.057724I
b = 1.373050 − 0.237187I
−1.98882 − 6.12259I 0.32445 + 9.83526I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.783884 + 0.301519I
a = −1.82815 + 0.64760I
b = −0.052502 + 0.197445I
−2.94615 − 2.41292I −5.85975 + 2.81162I
u = −0.783884 − 0.301519I
a = −1.82815 − 0.64760I
b = −0.052502 − 0.197445I
−2.94615 + 2.41292I −5.85975 − 2.81162I
u = −0.978723 + 0.633481I
a = −0.96396 + 1.30760I
b = 0.300031 + 0.936915I
0.71471 + 4.40922I 0
u = −0.978723 − 0.633481I
a = −0.96396 − 1.30760I
b = 0.300031 − 0.936915I
0.71471 − 4.40922I 0
u = −0.750448 + 0.912373I
a = −0.490257 + 0.851972I
b = 0.574944 + 1.026750I
−0.37303 + 2.91970I 0
u = −0.750448 − 0.912373I
a = −0.490257 − 0.851972I
b = 0.574944 − 1.026750I
−0.37303 − 2.91970I 0
u = 0.734411 + 0.343567I
a = 1.68997 + 0.52774I
b = −0.094953 + 0.172627I
−0.80279 − 2.13782I −2.33645 + 0.81055I
u = 0.734411 − 0.343567I
a = 1.68997 − 0.52774I
b = −0.094953 − 0.172627I
−0.80279 + 2.13782I −2.33645 − 0.81055I
u = 1.107430 + 0.474599I
a = 0.056779 − 0.687226I
b = 0.571965 − 0.868277I
−6.50257 − 4.09181I 0
u = 1.107430 − 0.474599I
a = 0.056779 + 0.687226I
b = 0.571965 + 0.868277I
−6.50257 + 4.09181I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688713 + 0.384093I
a = −0.865622 − 0.950501I
b = −1.52542 − 1.00016I
1.79878 − 0.77129I −5.60286 − 8.41847I
u = −0.688713 − 0.384093I
a = −0.865622 + 0.950501I
b = −1.52542 + 1.00016I
1.79878 + 0.77129I −5.60286 + 8.41847I
u = 1.007920 + 0.684334I
a = 0.82037 + 1.37323I
b = −0.363432 + 1.005740I
−0.933655 + 0.114205I 0
u = 1.007920 − 0.684334I
a = 0.82037 − 1.37323I
b = −0.363432 − 1.005740I
−0.933655 − 0.114205I 0
u = 0.127528 + 0.728266I
a = −0.452419 − 0.940221I
b = −1.87592 − 0.69195I
2.50493 − 11.29680I 5.67648 + 10.43402I
u = 0.127528 − 0.728266I
a = −0.452419 + 0.940221I
b = −1.87592 + 0.69195I
2.50493 + 11.29680I 5.67648 − 10.43402I
u = −1.213180 + 0.372173I
a = −0.012938 − 0.458263I
b = −0.472745 − 0.599319I
−3.13067 0
u = −1.213180 − 0.372173I
a = −0.012938 + 0.458263I
b = −0.472745 + 0.599319I
−3.13067 0
u = 0.965571 + 0.828742I
a = 0.510970 + 1.199320I
b = −0.525646 + 0.986946I
−1.98882 − 6.12259I 0
u = 0.965571 − 0.828742I
a = 0.510970 − 1.199320I
b = −0.525646 − 0.986946I
−1.98882 + 6.12259I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.116348 + 0.703898I
a = 0.406844 − 1.021210I
b = 1.81744 − 0.75017I
4.55793 + 6.21102I 9.11454 − 6.33203I
u = −0.116348 − 0.703898I
a = 0.406844 + 1.021210I
b = 1.81744 + 0.75017I
4.55793 − 6.21102I 9.11454 + 6.33203I
u = 0.527476 + 0.478971I
a = 1.142170 − 0.040811I
b = −0.647350 − 0.009667I
−0.37303 − 2.91970I 1.95927 + 0.79655I
u = 0.527476 − 0.478971I
a = 1.142170 + 0.040811I
b = −0.647350 + 0.009667I
−0.37303 + 2.91970I 1.95927 − 0.79655I
u = 0.181333 + 0.665675I
a = −0.151869 − 0.915760I
b = −1.63089 − 0.60949I
−0.19423 − 4.09608I 2.11668 + 6.01964I
u = 0.181333 − 0.665675I
a = −0.151869 + 0.915760I
b = −1.63089 + 0.60949I
−0.19423 + 4.09608I 2.11668 − 6.01964I
u = −0.066734 + 0.644109I
a = 0.364465 − 1.283810I
b = 1.70994 − 0.95105I
5.26187 + 3.68883I 10.94093 − 6.31491I
u = −0.066734 − 0.644109I
a = 0.364465 + 1.283810I
b = 1.70994 + 0.95105I
5.26187 − 3.68883I 10.94093 + 6.31491I
u = 1.278070 + 0.507990I
a = −0.185665 − 0.545799I
b = 0.246078 − 0.751833I
−6.50257 + 4.09181I 0
u = 1.278070 − 0.507990I
a = −0.185665 + 0.545799I
b = 0.246078 + 0.751833I
−6.50257 − 4.09181I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.033793 + 0.612034I
a = −0.37729 − 1.43867I
b = −1.66901 − 1.07226I
3.85162 + 1.33085I 9.33343 + 1.20365I
u = 0.033793 − 0.612034I
a = −0.37729 + 1.43867I
b = −1.66901 + 1.07226I
3.85162 − 1.33085I 9.33343 − 1.20365I
u = −1.09807 + 1.09220I
a = 0.038512 + 1.080370I
b = 0.677631 + 0.870035I
−0.19423 + 4.09608I 0
u = −1.09807 − 1.09220I
a = 0.038512 − 1.080370I
b = 0.677631 − 0.870035I
−0.19423 − 4.09608I 0
u = −0.436888 + 0.052039I
a = −2.74913 − 0.02705I
b = 0.015896 − 0.643790I
−2.99458 + 7.31406I −5.67566 − 6.83311I
u = −0.436888 − 0.052039I
a = −2.74913 + 0.02705I
b = 0.015896 + 0.643790I
−2.99458 − 7.31406I −5.67566 + 6.83311I
u = −1.19020 + 1.08400I
a = 0.198941 + 1.170700I
b = 0.785716 + 0.860699I
2.50493 + 11.29680I 0
u = −1.19020 − 1.08400I
a = 0.198941 − 1.170700I
b = 0.785716 − 0.860699I
2.50493 − 11.29680I 0
u = 0.346330 + 0.150517I
a = 2.71989 − 0.75542I
b = −0.211981 − 0.698216I
−0.68241 − 2.75592I −1.99878 + 3.60983I
u = 0.346330 − 0.150517I
a = 2.71989 + 0.75542I
b = −0.211981 + 0.698216I
−0.68241 + 2.75592I −1.99878 − 3.60983I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.18201 + 1.11184I
a = −0.200539 + 1.108740I
b = −0.765750 + 0.827059I
4.55793 − 6.21102I 0
u = 1.18201 − 1.11184I
a = −0.200539 − 1.108740I
b = −0.765750 − 0.827059I
4.55793 + 6.21102I 0
u = −1.51963 + 0.70825I
a = 0.571398 − 0.342145I
b = 0.292414 − 0.624469I
−3.57874 − 4.50800I 0
u = −1.51963 − 0.70825I
a = 0.571398 + 0.342145I
b = 0.292414 + 0.624469I
−3.57874 + 4.50800I 0
u = 1.18633 + 1.20329I
a = −0.239816 + 0.946287I
b = −0.722036 + 0.723602I
5.26187 − 3.68883I 0
u = 1.18633 − 1.20329I
a = −0.239816 − 0.946287I
b = −0.722036 − 0.723602I
5.26187 + 3.68883I 0
u = −1.52882 + 0.78446I
a = 0.680075 − 0.313510I
b = 0.430335 − 0.633618I
−0.86229 − 12.39040I 0
u = −1.52882 − 0.78446I
a = 0.680075 + 0.313510I
b = 0.430335 + 0.633618I
−0.86229 + 12.39040I 0
u = 0.025728 + 0.280461I
a = 0.30072 − 3.39115I
b = −0.32413 − 1.65229I
1.32373 − 2.30468I −8.78048 + 10.23043I
u = 0.025728 − 0.280461I
a = 0.30072 + 3.39115I
b = −0.32413 + 1.65229I
1.32373 + 2.30468I −8.78048 − 10.23043I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.55351 + 0.76807I
a = −0.646932 − 0.283652I
b = −0.404196 − 0.586023I
1.40035 + 7.17372I 0
u = 1.55351 − 0.76807I
a = −0.646932 + 0.283652I
b = −0.404196 + 0.586023I
1.40035 − 7.17372I 0
u = −1.20178 + 1.26252I
a = 0.264973 + 0.857917I
b = 0.694318 + 0.661426I
3.85162 − 1.33085I 0
u = −1.20178 − 1.26252I
a = 0.264973 − 0.857917I
b = 0.694318 − 0.661426I
3.85162 + 1.33085I 0
u = −0.244322 + 0.036595I
a = −4.28136 − 0.60938I
b = 0.030082 + 0.879336I
−4.48802 + 0.11163I −8.96076 − 0.03392I
u = −0.244322 − 0.036595I
a = −4.28136 + 0.60938I
b = 0.030082 − 0.879336I
−4.48802 − 0.11163I −8.96076 + 0.03392I
u = 1.66945 + 0.72257I
a = −0.555069 − 0.171819I
b = −0.346168 − 0.414881I
2.79995 + 4.40530I 0
u = 1.66945 − 0.72257I
a = −0.555069 + 0.171819I
b = −0.346168 + 0.414881I
2.79995 − 4.40530I 0
u = −0.30049 + 1.79694I
a = −0.007389 + 0.403077I
b = 0.108868 + 0.663979I
1.32373 + 2.30468I 0
u = −0.30049 − 1.79694I
a = −0.007389 − 0.403077I
b = 0.108868 − 0.663979I
1.32373 − 2.30468I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.76731 + 0.66732I
a = 0.487865 − 0.115529I
b = 0.294375 − 0.312630I
1.79878 + 0.77129I 0
u = −1.76731 − 0.66732I
a = 0.487865 + 0.115529I
b = 0.294375 + 0.312630I
1.79878 − 0.77129I 0
26
III.
I
u
3
= h−u
26
+u
25
+· · ·+b+4u, −4u
26
+4u
25
+· · ·+a−1, u
27
−u
26
+· · ·−4u
2
+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
10
=
4u
26
− 4u
25
+ ··· − 4u + 1
u
26
− u
25
+ ··· + u
2
− 4u
a
1
=
−4u
26
+ 5u
25
+ ··· − 6u − 4
−4u
26
+ 4u
25
+ ··· + 5u − 1
a
9
=
3u
26
− 3u
25
+ ··· − u
2
+ 1
u
26
− u
25
+ ··· + u
2
− 4u
a
8
=
3u
26
− 3u
25
+ ··· − u + 1
u
26
− u
25
+ ··· + u
2
− 4u
a
7
=
−7u
26
+ 7u
25
+ ··· + u − 10
−3u
26
+ 23u
24
+ ··· + 5u + 1
a
3
=
−u
26
+ 4u
25
+ ··· + 4u − 25
−10u
25
+ 12u
24
+ ··· − 2u + 4
a
11
=
3u
26
− 2u
25
+ ··· − 10u − 2
−3u
26
+ 3u
25
+ ··· + u − 1
a
6
=
−2u
26
− u
25
+ ··· − 4u + 11
−u
26
+ 4u
25
+ ··· + 3u − 1
a
2
=
8u
26
− 6u
25
+ ··· + 10u − 24
3u
26
− 15u
25
+ ··· − 11u + 8
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
26
+ 16u
25
− 31u
24
− 88u
23
+ 136u
22
+ 223u
21
− 300u
20
−
406u
19
+ 587u
18
+ 565u
17
− 873u
16
− 672u
15
+ 1075u
14
+ 663u
13
− 1103u
12
− 546u
11
+
976u
10
+ 379u
9
− 718u
8
− 227u
7
+ 444u
6
+ 104u
5
− 214u
4
− 37u
3
+ 89u
2
+ 7u − 19
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
− 14u
26
+ ··· − 4u + 1
c
2
u
27
− 2u
26
+ ··· + 2u − 1
c
3
u
27
+ 2u
26
+ ··· − 4u − 1
c
4
, c
8
u
27
− u
26
+ ··· − 4u
2
+ 1
c
5
, c
9
u
27
− 4u
25
+ ··· − u + 1
c
6
u
27
+ 2u
26
+ ··· + 2u + 1
c
7
u
27
+ 10u
26
+ ··· + 82u + 21
c
10
, c
12
u
27
− 8u
26
+ ··· + 13u − 1
c
11
u
27
+ 19u
26
+ ··· + 269u + 21
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
+ 2y
26
+ ··· − 8y −1
c
2
, c
6
y
27
+ 14y
26
+ ··· − 4y −1
c
3
y
27
− 10y
26
+ ··· − 6y −1
c
4
, c
8
y
27
− 13y
26
+ ··· + 8y −1
c
5
, c
9
y
27
− 8y
26
+ ··· + 13y −1
c
7
y
27
− 2y
26
+ ··· − 4280y −441
c
10
, c
12
y
27
+ 16y
26
+ ··· + 13y −1
c
11
y
27
+ 5y
26
+ ··· − 4331y −441
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.939884 + 0.236987I
a = 0.810144 + 0.741206I
b = 1.000360 + 0.252236I
2.51856 − 1.21074I 3.94040 − 0.29577I
u = −0.939884 − 0.236987I
a = 0.810144 − 0.741206I
b = 1.000360 − 0.252236I
2.51856 + 1.21074I 3.94040 + 0.29577I
u = 0.548007 + 0.792337I
a = 1.085160 + 0.270704I
b = −0.590455 + 0.853710I
−2.27602 − 8.69889I −1.42722 + 11.13289I
u = 0.548007 − 0.792337I
a = 1.085160 − 0.270704I
b = −0.590455 − 0.853710I
−2.27602 + 8.69889I −1.42722 − 11.13289I
u = −0.589968 + 0.754758I
a = −1.038790 + 0.463379I
b = 0.642862 + 0.822425I
−0.15087 + 4.24442I 2.14665 − 7.03819I
u = −0.589968 − 0.754758I
a = −1.038790 − 0.463379I
b = 0.642862 − 0.822425I
−0.15087 − 4.24442I 2.14665 + 7.03819I
u = 0.890158 + 0.290116I
a = −0.713570 + 0.987743I
b = −1.015530 + 0.330975I
3.77214 − 3.83630I 5.06007 + 5.94321I
u = 0.890158 − 0.290116I
a = −0.713570 − 0.987743I
b = −1.015530 − 0.330975I
3.77214 + 3.83630I 5.06007 − 5.94321I
u = −0.807919 + 0.441219I
a = 0.091226 + 1.278670I
b = 0.953401 + 0.520669I
−1.87221 + 4.10431I −3.94238 − 5.87297I
u = −0.807919 − 0.441219I
a = 0.091226 − 1.278670I
b = 0.953401 − 0.520669I
−1.87221 − 4.10431I −3.94238 + 5.87297I
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.636947 + 0.872631I
a = 0.752579 + 0.250043I
b = −0.545712 + 0.747636I
−3.40751 − 1.59530I −3.92861 + 2.68860I
u = 0.636947 − 0.872631I
a = 0.752579 − 0.250043I
b = −0.545712 − 0.747636I
−3.40751 + 1.59530I −3.92861 − 2.68860I
u = −0.602822 + 0.659526I
a = −1.115350 + 0.849181I
b = 0.755067 + 0.826092I
−0.05975 + 3.16559I 1.56369 − 5.73335I
u = −0.602822 − 0.659526I
a = −1.115350 − 0.849181I
b = 0.755067 − 0.826092I
−0.05975 − 3.16559I 1.56369 + 5.73335I
u = −0.839987 + 0.722261I
a = −0.390556 + 0.623286I
b = 0.684453 + 0.588525I
−1.55294 + 3.72964I −4.26933 − 5.42150I
u = −0.839987 − 0.722261I
a = −0.390556 − 0.623286I
b = 0.684453 − 0.588525I
−1.55294 − 3.72964I −4.26933 + 5.42150I
u = 0.649962 + 0.584702I
a = 0.87800 + 1.21188I
b = −0.850371 + 0.764989I
−3.26608 − 5.58744I −5.80184 + 8.84617I
u = 0.649962 − 0.584702I
a = 0.87800 − 1.21188I
b = −0.850371 − 0.764989I
−3.26608 + 5.58744I −5.80184 − 8.84617I
u = 0.798802 + 0.345503I
a = −0.51460 + 1.42697I
b = −1.054580 + 0.456135I
2.85840 − 6.36076I 2.86410 + 6.10449I
u = 0.798802 − 0.345503I
a = −0.51460 − 1.42697I
b = −1.054580 − 0.456135I
2.85840 + 6.36076I 2.86410 − 6.10449I
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.585205 + 0.621689I
a = 1.23433 + 1.02860I
b = −0.802792 + 0.852842I
−2.06572 + 1.27631I −2.78728 + 1.66276I
u = 0.585205 − 0.621689I
a = 1.23433 − 1.02860I
b = −0.802792 − 0.852842I
−2.06572 − 1.27631I −2.78728 − 1.66276I
u = −0.767504 + 0.349092I
a = 0.47733 + 1.59851I
b = 1.079580 + 0.491037I
0.73528 + 11.44510I −0.67840 − 10.12582I
u = −0.767504 − 0.349092I
a = 0.47733 − 1.59851I
b = 1.079580 − 0.491037I
0.73528 − 11.44510I −0.67840 + 10.12582I
u = −1.60182
a = 0.243310
b = 0.624290
−3.15306 31.1530
u = 1.73991 + 0.18336I
a = −0.177547 + 0.057851I
b = −0.568429 + 0.059903I
−6.81621 − 4.56624I 37.1836 + 25.7917I
u = 1.73991 − 0.18336I
a = −0.177547 − 0.057851I
b = −0.568429 − 0.059903I
−6.81621 + 4.56624I 37.1836 − 25.7917I
32
IV.
I
u
4
= h−u
3
− u
2
+ b − 3u − 1, −u
3
− u
2
+ a − 3u − 1, u
4
+ u
3
+ 3u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
10
=
u
3
+ u
2
+ 3u + 1
u
3
+ u
2
+ 3u + 1
a
1
=
−u
3
− u
2
− 3u − 1
−u
3
− u
2
− 2u − 1
a
9
=
0
u
3
+ u
2
+ 3u + 1
a
8
=
u
3
+ u
2
+ 3u + 1
u
3
+ u
2
+ 2u + 1
a
7
=
u
3
+ u
2
+ 3u + 1
u
3
+ u
2
+ 2u + 1
a
3
=
−u
3
− 2u + 2
−u
3
− u
2
− 2u
a
11
=
0
u
a
6
=
1
0
a
2
=
u
2
+ 2
−u
3
− u
2
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
3
− u
2
− 2u + 7
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
4
, c
5
, c
8
c
9
u
4
+ u
3
+ 3u
2
+ u + 1
c
7
, c
11
u
4
c
10
, c
12
(u − 1)
4
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y
2
+ y + 1)
2
c
4
, c
5
, c
8
c
9
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
c
7
, c
11
y
4
c
10
, c
12
(y − 1)
4
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.148403 + 0.632502I
a = 0.35160 + 1.49853I
b = 0.35160 + 1.49853I
1.64493 − 2.02988I 7.50000 − 0.86603I
u = −0.148403 − 0.632502I
a = 0.35160 − 1.49853I
b = 0.35160 − 1.49853I
1.64493 + 2.02988I 7.50000 + 0.86603I
u = −0.35160 + 1.49853I
a = 0.148403 + 0.632502I
b = 0.148403 + 0.632502I
1.64493 + 2.02988I 7.50000 + 0.86603I
u = −0.35160 − 1.49853I
a = 0.148403 − 0.632502I
b = 0.148403 − 0.632502I
1.64493 − 2.02988I 7.50000 − 0.86603I
36
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
27
− 14u
26
+ ··· − 4u + 1)
· ((u
51
+ 24u
50
+ ··· − 4u − 1)
2
)(u
77
+ 37u
76
+ ··· − 7u − 16)
c
2
((u
2
+ u + 1)
2
)(u
27
− 2u
26
+ ··· + 2u − 1)(u
51
+ 2u
50
+ ··· + 4u + 1)
2
· (u
77
− 5u
76
+ ··· − 33u + 4)
c
3
((u
2
− u + 1)
2
)(u
27
+ 2u
26
+ ··· − 4u − 1)
· ((u
51
− 2u
50
+ ··· − 139u + 26)
2
)(u
77
+ 5u
76
+ ··· + 17874u + 1768)
c
4
, c
8
(u
4
+ u
3
+ 3u
2
+ u + 1)(u
27
− u
26
+ ··· − 4u
2
+ 1)(u
77
+ u
76
+ ··· + 2u + 1)
· (u
102
+ 4u
101
+ ··· + 15u + 2)
c
5
, c
9
(u
4
+ u
3
+ 3u
2
+ u + 1)(u
27
− 4u
25
+ ··· − u + 1)
· (u
77
+ 3u
75
+ ··· − 9u + 2)(u
102
+ 2u
101
+ ··· + 2916u + 376)
c
6
((u
2
− u + 1)
2
)(u
27
+ 2u
26
+ ··· + 2u + 1)(u
51
+ 2u
50
+ ··· + 4u + 1)
2
· (u
77
− 5u
76
+ ··· − 33u + 4)
c
7
u
4
(u
27
+ 10u
26
+ ··· + 82u + 21)(u
51
+ 15u
50
+ ··· + 1000u + 64)
2
· (u
77
− 25u
76
+ ··· − 818285u + 37300)
c
10
, c
12
((u − 1)
4
)(u
27
− 8u
26
+ ··· + 13u − 1)(u
77
− 12u
76
+ ··· + 17u + 1)
· (u
102
+ 5u
101
+ ··· + 10593u + 956)
c
11
u
4
(u
27
+ 19u
26
+ ··· + 269u + 21)(u
51
+ 25u
50
+ ··· − 10u − 4)
2
· (u
77
− 42u
76
+ ··· + 11u − 2)
37
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
27
+ 2y
26
+ ··· − 8y − 1)(y
51
+ 8y
50
+ ··· − 32y − 1)
2
· (y
77
+ 9y
76
+ ··· + 401y − 256)
c
2
, c
6
((y
2
+ y + 1)
2
)(y
27
+ 14y
26
+ ··· − 4y − 1)
· ((y
51
+ 24y
50
+ ··· − 4y − 1)
2
)(y
77
+ 37y
76
+ ··· − 7y − 16)
c
3
((y
2
+ y + 1)
2
)(y
27
− 10y
26
+ ··· − 6y − 1)
· (y
51
− 8y
50
+ ··· + 15733y − 676)
2
· (y
77
− 19y
76
+ ··· + 74410324y − 3125824)
c
4
, c
8
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
27
− 13y
26
+ ··· + 8y − 1)
· (y
77
+ 33y
76
+ ··· − 86y − 1)(y
102
− 20y
101
+ ··· − 57y + 4)
c
5
, c
9
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
27
− 8y
26
+ ··· + 13y − 1)
· (y
77
+ 6y
76
+ ··· + 145y − 4)
· (y
102
+ 96y
100
+ ··· + 16598704y + 141376)
c
7
y
4
(y
27
− 2y
26
+ ··· − 4280y − 441)
· (y
51
+ 19y
50
+ ··· − 5184y − 4096)
2
· (y
77
+ 17y
76
+ ··· − 27321142975y − 1391290000)
c
10
, c
12
((y − 1)
4
)(y
27
+ 16y
26
+ ··· + 13y − 1)(y
77
− 50y
76
+ ··· + 83y − 1)
· (y
102
+ 23y
101
+ ··· + 48008215y + 913936)
c
11
y
4
(y
27
+ 5y
26
+ ··· − 4331y − 441)(y
51
− 5y
50
+ ··· + 428y − 16)
2
· (y
77
+ 60y
75
+ ··· − 39y − 4)
38
