12a
0264
(K12a
0264
)
A knot diagram
1
Linearized knot diagam
3 6 7 12 11 2 10 5 4 1 9 8
Solving Sequence
3,6
2 7
4,10
8 1 11 5 9 12
c
2
c
6
c
3
c
7
c
1
c
10
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−71842065294u
61
+ 662395268252u
60
+ ··· + 947973767b + 56178798404,
− 56178798404u
61
+ 433767120342u
60
+ ··· + 947973767a − 15382227914,
u
62
− 9u
61
+ ··· − 9u + 1i
I
u
2
= h−1.15142 × 10
23
a
3
u
30
+ 3.05276 × 10
22
a
2
u
30
+ ··· + 4.65181 × 10
23
a − 9.65820 × 10
21
,
3u
30
a
3
− u
30
a
2
+ ··· − 18a + 10, u
31
+ 2u
30
+ ··· + 2u + 1i
I
u
3
= h44u
32
− 157u
31
+ ··· + 13b + 41, 41u
32
− 120u
31
+ ··· + 13a − 46, u
33
− 4u
32
+ ··· + 4u − 1i
I
u
4
= hau + b + u, a
2
+ a + u + 1, u
2
+ u + 1i
I
u
5
= hau + b + 1, a
2
− au − a − 1, u
2
+ u + 1i
I
v
1
= ha, b
2
+ b + 1, v + 1i
* 6 irreducible components of dim
C
= 0, with total 229 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
= h−7.18×10
10
u
61
+6.62×10
11
u
60
+· · ·+9.48×10
8
b+5.62×10
10
, −5.62×
10
10
u
61
+4.34×10
11
u
60
+· · ·+9.48×10
8
a−1.54×10
10
, u
62
−9u
61
+· · ·−9u+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
59.2620u
61
− 457.573u
60
+ ··· − 124.491u + 16.2264
75.7849u
61
− 698.749u
60
+ ··· + 549.584u − 59.2620
a
8
=
26.0492u
61
− 110.514u
60
+ ··· − 664.765u + 81.5999
123.929u
61
− 1041.10u
60
+ ··· + 317.043u − 26.0492
a
1
=
u
2
+ 1
u
2
a
11
=
21.8645u
61
− 173.195u
60
+ ··· − 70.1773u + 7.31002
12.1565u
61
− 154.001u
60
+ ··· + 304.732u − 34.9708
a
5
=
−33.7261u
61
+ 221.896u
60
+ ··· + 215.277u − 30.0257
−86.1071u
61
+ 778.556u
60
+ ··· − 566.052u + 61.5872
a
9
=
25.5468u
61
− 184.840u
60
+ ··· − 106.937u + 11.1098
45.3238u
61
− 418.805u
60
+ ··· + 361.540u − 39.5968
a
12
=
27.2394u
61
− 187.426u
60
+ ··· − 205.689u + 23.8141
59.1448u
61
− 545.854u
60
+ ··· + 444.357u − 48.0120
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
219232172873
947973767
u
61
−
1832051343164
947973767
u
60
+ ··· +
602326693966
947973767
u −
55701717280
947973767
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
+ 33u
61
+ ··· + 25u + 1
c
2
, c
6
u
62
− 9u
61
+ ··· − 9u + 1
c
3
u
62
+ 9u
61
+ ··· + 7773u + 1609
c
4
, c
8
u
62
+ 6u
60
+ ··· − u + 1
c
5
, c
9
u
62
− u
61
+ ··· + 187u + 73
c
7
, c
10
u
62
+ u
61
+ ··· + 5u + 1
c
11
u
62
− 47u
61
+ ··· − u + 1
c
12
u
62
− 59u
61
+ ··· − 16642998272u + 536870912
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
+ y
61
+ ··· + 65y + 1
c
2
, c
6
y
62
+ 33y
61
+ ··· + 25y + 1
c
3
y
62
− 25y
61
+ ··· + 73803251y + 2588881
c
4
, c
8
y
62
+ 12y
61
+ ··· + 11y + 1
c
5
, c
9
y
62
+ 31y
61
+ ··· + 117455y + 5329
c
7
, c
10
y
62
− y
61
+ ··· + 19y + 1
c
11
y
62
− 17y
61
+ ··· + 51y + 1
c
12
y
62
− 7y
61
+ ··· + 2449958197289549824y + 288230376151711744
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.525310 + 0.867009I
a = −0.600768 + 0.046229I
b = 0.275509 − 0.545156I
−0.65471 − 6.07228I 0
u = −0.525310 − 0.867009I
a = −0.600768 − 0.046229I
b = 0.275509 + 0.545156I
−0.65471 + 6.07228I 0
u = 0.926844 + 0.250739I
a = 0.830188 − 0.409540I
b = 0.872143 − 0.171419I
−4.43605 + 4.89104I 0
u = 0.926844 − 0.250739I
a = 0.830188 + 0.409540I
b = 0.872143 + 0.171419I
−4.43605 − 4.89104I 0
u = −0.743064 + 0.765206I
a = −0.217081 − 0.304286I
b = 0.394147 + 0.059992I
−1.25651 + 8.15591I 0
u = −0.743064 − 0.765206I
a = −0.217081 + 0.304286I
b = 0.394147 − 0.059992I
−1.25651 − 8.15591I 0
u = 0.905499 + 0.201824I
a = −1.164320 − 0.612671I
b = −0.930636 − 0.789761I
−1.16212 − 6.88778I 0
u = 0.905499 − 0.201824I
a = −1.164320 + 0.612671I
b = −0.930636 + 0.789761I
−1.16212 + 6.88778I 0
u = −0.588989 + 0.909257I
a = −0.357883 − 0.232559I
b = 0.422245 − 0.188433I
3.61259 − 5.49425I 0
u = −0.588989 − 0.909257I
a = −0.357883 + 0.232559I
b = 0.422245 + 0.188433I
3.61259 + 5.49425I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704169 + 0.833864I
a = 0.375620 − 0.256229I
b = −0.050840 + 0.493644I
−1.47564 − 13.57830I 0
u = −0.704169 − 0.833864I
a = 0.375620 + 0.256229I
b = −0.050840 − 0.493644I
−1.47564 + 13.57830I 0
u = 0.363326 + 1.041380I
a = −0.006840 + 1.261370I
b = −1.316050 + 0.451165I
−0.62412 + 1.89501I 0
u = 0.363326 − 1.041380I
a = −0.006840 − 1.261370I
b = −1.316050 − 0.451165I
−0.62412 − 1.89501I 0
u = 0.859506 + 0.242025I
a = 2.19391 + 0.43936I
b = 1.77934 + 0.90861I
−4.9023 − 15.9432I 0
u = 0.859506 − 0.242025I
a = 2.19391 − 0.43936I
b = 1.77934 − 0.90861I
−4.9023 + 15.9432I 0
u = −0.611207 + 0.637669I
a = 0.531727 − 0.177328I
b = −0.211918 + 0.447450I
4.39375 + 0.78474I 0
u = −0.611207 − 0.637669I
a = 0.531727 + 0.177328I
b = −0.211918 − 0.447450I
4.39375 − 0.78474I 0
u = −0.079319 + 1.136990I
a = −0.480569 + 0.187083I
b = −0.174592 − 0.561239I
−4.25152 + 0.98540I 0
u = −0.079319 − 1.136990I
a = −0.480569 − 0.187083I
b = −0.174592 + 0.561239I
−4.25152 − 0.98540I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.322729 + 0.794916I
a = −0.159263 + 0.827046I
b = −0.708831 + 0.140311I
−0.36795 + 1.81592I 0
u = 0.322729 − 0.794916I
a = −0.159263 − 0.827046I
b = −0.708831 − 0.140311I
−0.36795 − 1.81592I 0
u = 0.822129 + 0.164447I
a = −2.15991 − 0.84806I
b = −1.63626 − 1.05240I
−4.15394 − 6.65764I 0
u = 0.822129 − 0.164447I
a = −2.15991 + 0.84806I
b = −1.63626 + 1.05240I
−4.15394 + 6.65764I 0
u = 0.467496 + 1.073050I
a = 0.99436 − 1.41095I
b = 1.97888 + 0.40739I
−2.20413 + 1.48132I 0
u = 0.467496 − 1.073050I
a = 0.99436 + 1.41095I
b = 1.97888 − 0.40739I
−2.20413 − 1.48132I 0
u = 0.447709 + 1.086620I
a = −1.01373 − 2.04574I
b = 1.76907 − 2.01743I
−2.32380 + 5.58924I 0
u = 0.447709 − 1.086620I
a = −1.01373 + 2.04574I
b = 1.76907 + 2.01743I
−2.32380 − 5.58924I 0
u = −0.447214 + 1.106010I
a = 0.151688 + 0.548614I
b = −0.674609 − 0.077580I
−2.58526 − 1.53767I 0
u = −0.447214 − 1.106010I
a = 0.151688 − 0.548614I
b = −0.674609 + 0.077580I
−2.58526 + 1.53767I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.465829 + 1.109780I
a = −0.305120 − 0.386147I
b = 0.570673 − 0.158738I
−2.44735 − 5.91573I 0
u = −0.465829 − 1.109780I
a = −0.305120 + 0.386147I
b = 0.570673 + 0.158738I
−2.44735 + 5.91573I 0
u = 0.524715 + 1.119440I
a = 0.30721 + 1.72675I
b = −1.77180 + 1.24996I
0.65537 + 5.40224I 0
u = 0.524715 − 1.119440I
a = 0.30721 − 1.72675I
b = −1.77180 − 1.24996I
0.65537 − 5.40224I 0
u = 0.684789 + 0.295063I
a = 1.77135 + 0.60140I
b = 1.035550 + 0.934494I
3.04799 − 0.75044I 4.58779 + 0.I
u = 0.684789 − 0.295063I
a = 1.77135 − 0.60140I
b = 1.035550 − 0.934494I
3.04799 + 0.75044I 4.58779 + 0.I
u = 0.285665 + 1.242200I
a = −0.25269 + 1.39333I
b = −1.80297 + 0.08414I
−9.6661 − 12.2478I 0
u = 0.285665 − 1.242200I
a = −0.25269 − 1.39333I
b = −1.80297 − 0.08414I
−9.6661 + 12.2478I 0
u = 0.355011 + 1.228510I
a = 0.60399 − 1.37956I
b = 1.90923 + 0.25225I
−8.41459 − 2.70649I 0
u = 0.355011 − 1.228510I
a = 0.60399 + 1.37956I
b = 1.90923 − 0.25225I
−8.41459 + 2.70649I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.426262 + 0.581117I
a = 1.029220 + 0.592225I
b = 0.094565 + 0.850540I
0.53461 + 1.44743I 2.35332 − 4.97569I
u = 0.426262 − 0.581117I
a = 1.029220 − 0.592225I
b = 0.094565 − 0.850540I
0.53461 − 1.44743I 2.35332 + 4.97569I
u = −0.914984 + 0.919264I
a = −0.0316931 + 0.0671937I
b = −0.0327701 − 0.0906155I
4.13536 − 3.34743I 0
u = −0.914984 − 0.919264I
a = −0.0316931 − 0.0671937I
b = −0.0327701 + 0.0906155I
4.13536 + 3.34743I 0
u = 0.276810 + 1.269650I
a = 0.405750 + 0.751740I
b = −0.842133 + 0.723251I
−9.47922 + 8.77165I 0
u = 0.276810 − 1.269650I
a = 0.405750 − 0.751740I
b = −0.842133 − 0.723251I
−9.47922 − 8.77165I 0
u = −0.386760 + 0.580436I
a = 0.762720 + 0.409085I
b = −0.532437 + 0.284493I
0.08971 + 1.99827I 0. − 5.14014I
u = −0.386760 − 0.580436I
a = 0.762720 − 0.409085I
b = −0.532437 − 0.284493I
0.08971 − 1.99827I 0. + 5.14014I
u = 0.527206 + 1.191840I
a = −0.36417 − 1.97114I
b = 2.15730 − 1.47324I
−7.19182 + 11.60850I 0
u = 0.527206 − 1.191840I
a = −0.36417 + 1.97114I
b = 2.15730 + 1.47324I
−7.19182 − 11.60850I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.563841 + 1.186620I
a = 0.03603 + 2.02308I
b = −2.38032 + 1.18345I
−7.7309 + 21.1689I 0
u = 0.563841 − 1.186620I
a = 0.03603 − 2.02308I
b = −2.38032 − 1.18345I
−7.7309 − 21.1689I 0
u = 0.306314 + 1.296820I
a = 0.256862 − 0.683661I
b = 0.965266 + 0.123689I
−6.02592 − 2.76578I 0
u = 0.306314 − 1.296820I
a = 0.256862 + 0.683661I
b = 0.965266 − 0.123689I
−6.02592 + 2.76578I 0
u = 0.561587 + 1.211320I
a = −0.292964 − 1.250370I
b = 1.35008 − 1.05707I
−4.20911 + 12.20800I 0
u = 0.561587 − 1.211320I
a = −0.292964 + 1.250370I
b = 1.35008 + 1.05707I
−4.20911 − 12.20800I 0
u = 0.572365 + 1.220510I
a = −0.301969 + 0.816851I
b = −1.169810 + 0.098980I
−7.42381 + 0.58624I 0
u = 0.572365 − 1.220510I
a = −0.301969 − 0.816851I
b = −1.169810 − 0.098980I
−7.42381 − 0.58624I 0
u = −0.340885 + 0.253081I
a = 1.47965 − 0.49678I
b = −0.378665 + 0.543817I
0.02739 + 2.02423I 0.22056 − 4.25353I
u = −0.340885 − 0.253081I
a = 1.47965 + 0.49678I
b = −0.378665 − 0.543817I
0.02739 − 2.02423I 0.22056 + 4.25353I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.107927 + 0.259314I
a = −4.52132 − 0.11032I
b = −0.459364 − 1.184350I
0.00080 − 2.02201I −0.23371 + 3.69190I
u = 0.107927 − 0.259314I
a = −4.52132 + 0.11032I
b = −0.459364 + 1.184350I
0.00080 + 2.02201I −0.23371 − 3.69190I
11
II. I
u
2
= h−1.15 × 10
23
a
3
u
30
+ 3.05 × 10
22
a
2
u
30
+ · · · + 4.65 × 10
23
a − 9.66 ×
10
21
, 3u
30
a
3
− u
30
a
2
+ · · · − 18a + 10, u
31
+ 2u
30
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
a
0.451411a
3
u
30
− 0.119683a
2
u
30
+ ··· − 1.82373a + 0.0378647
a
8
=
−0.373853a
3
u
30
+ 0.531329a
2
u
30
+ ··· + 0.699566a + 0.411044
−0.0166007a
3
u
30
− 0.209233a
2
u
30
+ ··· − 1.71928a + 1.22047
a
1
=
u
2
+ 1
u
2
a
11
=
0.119608a
3
u
30
+ 0.0998373a
2
u
30
+ ··· + 0.965753a + 0.360922
0.696660a
3
u
30
+ 0.0996759a
2
u
30
+ ··· − 2.18360a + 0.496833
a
5
=
0.251392a
3
u
30
− 0.224937a
2
u
30
+ ··· − 0.101854a + 0.472548
0.593381a
3
u
30
− 0.540369a
2
u
30
+ ··· − 1.15752a − 1.74635
a
9
=
−0.141193a
3
u
30
+ 0.628129a
2
u
30
+ ··· + 1.85936a − 0.310951
0.399349a
3
u
30
+ 0.335752a
2
u
30
+ ··· − 2.04734a − 0.151275
a
12
=
0.110556a
3
u
30
− 0.680306a
2
u
30
+ ··· + 0.0928968a + 2.38372
0.658693a
3
u
30
− 0.0994206a
2
u
30
+ ··· − 2.94567a − 3.78264
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
178962807232966314637740
255071284517025297511259
u
30
a
3
+
185226203499956905397152
255071284517025297511259
u
30
a
2
+
··· +
1121798392287197993176964
255071284517025297511259
a −
1126780589381091404557979
255071284517025297511259
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
31
+ 16u
30
+ ··· − 2u − 1)
4
c
2
, c
6
(u
31
+ 2u
30
+ ··· + 2u + 1)
4
c
3
(u
31
− 2u
30
+ ··· − 26u + 5)
4
c
4
, c
8
u
124
− 21u
122
+ ··· − u + 1
c
5
, c
9
u
124
+ 29u
122
+ ··· + 14899434913u + 3986390929
c
7
, c
10
u
124
+ 5u
123
+ ··· − 2429506u + 230137
c
11
(u
31
+ 15u
30
+ ··· + 6u + 4)
4
c
12
(u
2
+ u + 1)
62
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
31
+ 32y
29
+ ··· + 14y − 1)
4
c
2
, c
6
(y
31
+ 16y
30
+ ··· − 2y − 1)
4
c
3
(y
31
− 16y
30
+ ··· − 534y − 25)
4
c
4
, c
8
y
124
− 42y
123
+ ··· − 289y + 1
c
5
, c
9
y
124
+ 58y
123
+ ··· + 5.62 × 10
20
y + 1.59 × 10
19
c
7
, c
10
y
124
− 53y
123
+ ··· − 2641994793520y + 52963038769
c
11
(y
31
− 5y
30
+ ··· + 236y − 16)
4
c
12
(y
2
+ y + 1)
62
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.700328 + 0.800493I
a = 0.664259 + 0.251566I
b = 0.314563 − 0.171232I
−0.98466 + 4.68217I −15.4216 − 9.2051I
u = 0.700328 + 0.800493I
a = −0.260578 + 0.651220I
b = −0.0501855 − 0.0149205I
−0.984660 + 0.622402I −15.4216 − 2.2769I
u = 0.700328 + 0.800493I
a = 0.073571 − 0.328596I
b = 0.263822 + 0.707914I
−0.98466 + 4.68217I −15.4216 − 9.2051I
u = 0.700328 + 0.800493I
a = −0.0416266 + 0.0262754I
b = −0.703787 + 0.247476I
−0.984660 + 0.622402I −15.4216 − 2.2769I
u = 0.700328 − 0.800493I
a = 0.664259 − 0.251566I
b = 0.314563 + 0.171232I
−0.98466 − 4.68217I −15.4216 + 9.2051I
u = 0.700328 − 0.800493I
a = −0.260578 − 0.651220I
b = −0.0501855 + 0.0149205I
−0.984660 − 0.622402I −15.4216 + 2.2769I
u = 0.700328 − 0.800493I
a = 0.073571 + 0.328596I
b = 0.263822 − 0.707914I
−0.98466 − 4.68217I −15.4216 + 9.2051I
u = 0.700328 − 0.800493I
a = −0.0416266 − 0.0262754I
b = −0.703787 − 0.247476I
−0.984660 − 0.622402I −15.4216 + 2.2769I
u = 0.576719 + 0.939494I
a = 1.059950 + 0.394036I
b = −0.162297 + 0.738120I
0.15499 + 3.45295I −0.03280 + 3.60229I
u = 0.576719 + 0.939494I
a = −0.928139 + 0.888938I
b = −0.367406 − 0.553035I
0.154987 − 0.606820I −0.03280 + 10.53049I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.576719 + 0.939494I
a = 0.493608 + 0.475757I
b = 0.241098 + 1.223060I
0.15499 + 3.45295I −0.03280 + 3.60229I
u = 0.576719 + 0.939494I
a = −0.601901 + 0.021584I
b = −1.37043 − 0.35931I
0.154987 − 0.606820I −0.03280 + 10.53049I
u = 0.576719 − 0.939494I
a = 1.059950 − 0.394036I
b = −0.162297 − 0.738120I
0.15499 − 3.45295I −0.03280 − 3.60229I
u = 0.576719 − 0.939494I
a = −0.928139 − 0.888938I
b = −0.367406 + 0.553035I
0.154987 + 0.606820I −0.03280 − 10.53049I
u = 0.576719 − 0.939494I
a = 0.493608 − 0.475757I
b = 0.241098 − 1.223060I
0.15499 − 3.45295I −0.03280 − 3.60229I
u = 0.576719 − 0.939494I
a = −0.601901 − 0.021584I
b = −1.37043 + 0.35931I
0.154987 + 0.606820I −0.03280 − 10.53049I
u = −0.847519 + 0.248601I
a = −1.246040 − 0.305531I
b = −1.274570 − 0.076430I
−4.12908 + 2.96247I −9.07968 − 2.45371I
u = −0.847519 + 0.248601I
a = 1.36039 + 0.48922I
b = 1.132000 − 0.050822I
−4.12908 + 2.96247I −9.07968 − 2.45371I
u = −0.847519 + 0.248601I
a = −2.01636 + 0.13113I
b = −1.71522 + 0.79951I
−4.12908 + 7.02224I −9.07968 − 9.38191I
u = −0.847519 + 0.248601I
a = 2.11826 − 0.32201I
b = 1.67630 − 0.61241I
−4.12908 + 7.02224I −9.07968 − 9.38191I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.847519 − 0.248601I
a = −1.246040 + 0.305531I
b = −1.274570 + 0.076430I
−4.12908 − 2.96247I −9.07968 + 2.45371I
u = −0.847519 − 0.248601I
a = 1.36039 − 0.48922I
b = 1.132000 + 0.050822I
−4.12908 − 2.96247I −9.07968 + 2.45371I
u = −0.847519 − 0.248601I
a = −2.01636 − 0.13113I
b = −1.71522 − 0.79951I
−4.12908 − 7.02224I −9.07968 + 9.38191I
u = −0.847519 − 0.248601I
a = 2.11826 + 0.32201I
b = 1.67630 + 0.61241I
−4.12908 − 7.02224I −9.07968 + 9.38191I
u = 0.613097 + 0.623277I
a = 0.929351 − 0.319011I
b = 0.783857 − 0.797190I
1.06858 + 5.29669I 3.13719 − 12.06996I
u = 0.613097 + 0.623277I
a = 0.770806 + 0.783171I
b = −0.402554 + 0.590660I
1.06858 + 1.23693I 3.13719 − 5.14176I
u = 0.613097 + 0.623277I
a = 0.158747 + 0.802021I
b = −0.015554 + 0.960586I
1.06858 + 1.23693I 3.13719 − 5.14176I
u = 0.613097 + 0.623277I
a = −0.021312 − 1.278600I
b = 0.768615 + 0.383659I
1.06858 + 5.29669I 3.13719 − 12.06996I
u = 0.613097 − 0.623277I
a = 0.929351 + 0.319011I
b = 0.783857 + 0.797190I
1.06858 − 5.29669I 3.13719 + 12.06996I
u = 0.613097 − 0.623277I
a = 0.770806 − 0.783171I
b = −0.402554 − 0.590660I
1.06858 − 1.23693I 3.13719 + 5.14176I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.613097 − 0.623277I
a = 0.158747 − 0.802021I
b = −0.015554 − 0.960586I
1.06858 − 1.23693I 3.13719 + 5.14176I
u = 0.613097 − 0.623277I
a = −0.021312 + 1.278600I
b = 0.768615 − 0.383659I
1.06858 − 5.29669I 3.13719 + 12.06996I
u = −0.358609 + 1.074610I
a = 0.228824 − 0.595956I
b = −1.38323 − 0.88688I
−3.94298 − 0.01595I −5.20942 − 0.29784I
u = −0.358609 + 1.074610I
a = −0.35610 + 1.40602I
b = 0.558364 + 0.459613I
−3.94298 − 0.01595I −5.20942 − 0.29784I
u = −0.358609 + 1.074610I
a = 0.26809 + 2.06495I
b = 2.35757 + 1.38040I
−3.94298 + 4.04382I −5.20942 − 7.22605I
u = −0.358609 + 1.074610I
a = 0.49708 − 2.35976I
b = −2.31516 − 0.45241I
−3.94298 + 4.04382I −5.20942 − 7.22605I
u = −0.358609 − 1.074610I
a = 0.228824 + 0.595956I
b = −1.38323 + 0.88688I
−3.94298 + 0.01595I −5.20942 + 0.29784I
u = −0.358609 − 1.074610I
a = −0.35610 − 1.40602I
b = 0.558364 − 0.459613I
−3.94298 + 0.01595I −5.20942 + 0.29784I
u = −0.358609 − 1.074610I
a = 0.26809 − 2.06495I
b = 2.35757 − 1.38040I
−3.94298 − 4.04382I −5.20942 + 7.22605I
u = −0.358609 − 1.074610I
a = 0.49708 + 2.35976I
b = −2.31516 + 0.45241I
−3.94298 − 4.04382I −5.20942 + 7.22605I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.066980 + 0.843210I
a = 0.016270 + 0.584419I
b = −0.446554 − 1.324890I
−3.47334 + 0.60290I −10.56232 + 2.65852I
u = −0.066980 + 0.843210I
a = −0.11619 + 1.41223I
b = 0.48383 + 1.68216I
−3.47334 + 4.66267I −10.56232 − 4.26969I
u = −0.066980 + 0.843210I
a = −1.51959 + 0.65030I
b = −0.493877 − 0.025426I
−3.47334 + 0.60290I −10.56232 + 2.65852I
u = −0.066980 + 0.843210I
a = 1.93715 − 0.72768I
b = −1.183030 − 0.192565I
−3.47334 + 4.66267I −10.56232 − 4.26969I
u = −0.066980 − 0.843210I
a = 0.016270 − 0.584419I
b = −0.446554 + 1.324890I
−3.47334 − 0.60290I −10.56232 − 2.65852I
u = −0.066980 − 0.843210I
a = −0.11619 − 1.41223I
b = 0.48383 − 1.68216I
−3.47334 − 4.66267I −10.56232 + 4.26969I
u = −0.066980 − 0.843210I
a = −1.51959 − 0.65030I
b = −0.493877 + 0.025426I
−3.47334 − 0.60290I −10.56232 − 2.65852I
u = −0.066980 − 0.843210I
a = 1.93715 + 0.72768I
b = −1.183030 + 0.192565I
−3.47334 − 4.66267I −10.56232 + 4.26969I
u = 0.423601 + 1.144370I
a = 0.65472 − 1.44085I
b = 2.71106 − 0.05324I
−6.95850 + 1.60558I −12.76845 − 2.57313I
u = 0.423601 + 1.144370I
a = 1.51311 + 1.07231I
b = −1.80665 + 1.78737I
−6.95850 − 2.45419I −12.76845 + 4.35507I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.423601 + 1.144370I
a = 0.85970 + 1.89697I
b = −0.58615 + 2.18578I
−6.95850 − 2.45419I −12.76845 + 4.35507I
u = 0.423601 + 1.144370I
a = 0.73033 − 2.09871I
b = 1.92620 + 0.13890I
−6.95850 + 1.60558I −12.76845 − 2.57313I
u = 0.423601 − 1.144370I
a = 0.65472 + 1.44085I
b = 2.71106 + 0.05324I
−6.95850 − 1.60558I −12.76845 + 2.57313I
u = 0.423601 − 1.144370I
a = 1.51311 − 1.07231I
b = −1.80665 − 1.78737I
−6.95850 + 2.45419I −12.76845 − 4.35507I
u = 0.423601 − 1.144370I
a = 0.85970 − 1.89697I
b = −0.58615 − 2.18578I
−6.95850 + 2.45419I −12.76845 − 4.35507I
u = 0.423601 − 1.144370I
a = 0.73033 + 2.09871I
b = 1.92620 − 0.13890I
−6.95850 − 1.60558I −12.76845 + 2.57313I
u = 0.470485 + 1.145180I
a = −1.46047 + 0.81577I
b = −2.80957 − 0.91703I
−6.62488 + 10.46240I −11.4154 − 12.6305I
u = 0.470485 + 1.145180I
a = −0.55916 − 1.69926I
b = 2.44278 − 1.29459I
−6.62488 + 6.40260I −11.41543 − 5.70235I
u = 0.470485 + 1.145180I
a = −0.21742 − 2.22241I
b = 1.68289 − 1.43982I
−6.62488 + 6.40260I −11.41543 − 5.70235I
u = 0.470485 + 1.145180I
a = −1.54751 + 1.81760I
b = −1.62134 − 1.28870I
−6.62488 + 10.46240I −11.4154 − 12.6305I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.470485 − 1.145180I
a = −1.46047 − 0.81577I
b = −2.80957 + 0.91703I
−6.62488 − 10.46240I −11.4154 + 12.6305I
u = 0.470485 − 1.145180I
a = −0.55916 + 1.69926I
b = 2.44278 + 1.29459I
−6.62488 − 6.40260I −11.41543 + 5.70235I
u = 0.470485 − 1.145180I
a = −0.21742 + 2.22241I
b = 1.68289 + 1.43982I
−6.62488 − 6.40260I −11.41543 + 5.70235I
u = 0.470485 − 1.145180I
a = −1.54751 − 1.81760I
b = −1.62134 + 1.28870I
−6.62488 − 10.46240I −11.4154 + 12.6305I
u = −0.526321 + 1.124110I
a = −0.266485 + 1.038710I
b = 1.52572 + 0.52112I
−2.67637 − 7.44811I −2.45568 + 6.41849I
u = −0.526321 + 1.124110I
a = −0.140992 − 1.291250I
b = −1.027370 − 0.846255I
−2.67637 − 7.44811I −2.45568 + 6.41849I
u = −0.526321 + 1.124110I
a = 0.20472 + 2.27955I
b = 2.70261 + 1.56380I
−2.67637 − 11.50790I −2.45568 + 13.34669I
u = −0.526321 + 1.124110I
a = 0.21773 − 2.50616I
b = −2.67022 − 0.96965I
−2.67637 − 11.50790I −2.45568 + 13.34669I
u = −0.526321 − 1.124110I
a = −0.266485 − 1.038710I
b = 1.52572 − 0.52112I
−2.67637 + 7.44811I −2.45568 − 6.41849I
u = −0.526321 − 1.124110I
a = −0.140992 + 1.291250I
b = −1.027370 + 0.846255I
−2.67637 + 7.44811I −2.45568 − 6.41849I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.526321 − 1.124110I
a = 0.20472 − 2.27955I
b = 2.70261 − 1.56380I
−2.67637 + 11.50790I −2.45568 − 13.34669I
u = −0.526321 − 1.124110I
a = 0.21773 + 2.50616I
b = −2.67022 + 0.96965I
−2.67637 + 11.50790I −2.45568 − 13.34669I
u = −0.442008 + 1.171670I
a = −0.866279 − 1.066100I
b = −2.24665 + 0.12196I
−7.34243 − 2.16784I −12.88583 + 0.23702I
u = −0.442008 + 1.171670I
a = −0.97809 + 1.33461I
b = 1.80402 + 1.41454I
−7.34243 − 6.22761I −12.8858 + 7.1652I
u = −0.442008 + 1.171670I
a = 0.72436 + 1.64421I
b = 1.63202 − 0.54377I
−7.34243 − 2.16784I −12.88583 + 0.23702I
u = −0.442008 + 1.171670I
a = 0.54839 − 1.74657I
b = −1.13140 − 1.73591I
−7.34243 − 6.22761I −12.8858 + 7.1652I
u = −0.442008 − 1.171670I
a = −0.866279 + 1.066100I
b = −2.24665 − 0.12196I
−7.34243 + 2.16784I −12.88583 − 0.23702I
u = −0.442008 − 1.171670I
a = −0.97809 − 1.33461I
b = 1.80402 − 1.41454I
−7.34243 + 6.22761I −12.8858 − 7.1652I
u = −0.442008 − 1.171670I
a = 0.72436 − 1.64421I
b = 1.63202 + 0.54377I
−7.34243 + 2.16784I −12.88583 − 0.23702I
u = −0.442008 − 1.171670I
a = 0.54839 + 1.74657I
b = −1.13140 + 1.73591I
−7.34243 + 6.22761I −12.8858 − 7.1652I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688548 + 0.289520I
a = −0.714895 + 0.059146I
b = −0.872929 + 0.636144I
−0.25228 + 2.77775I 1.37986 − 3.06700I
u = −0.688548 + 0.289520I
a = 1.40742 − 0.33210I
b = 0.475116 − 0.247702I
−0.25228 + 2.77775I 1.37986 − 3.06700I
u = −0.688548 + 0.289520I
a = 2.29627 − 0.40579I
b = 1.99892 − 0.79393I
−0.25228 + 6.83751I 1.37986 − 9.99520I
u = −0.688548 + 0.289520I
a = −2.87892 − 0.05748I
b = −1.46361 + 0.94422I
−0.25228 + 6.83751I 1.37986 − 9.99520I
u = −0.688548 − 0.289520I
a = −0.714895 − 0.059146I
b = −0.872929 − 0.636144I
−0.25228 − 2.77775I 1.37986 + 3.06700I
u = −0.688548 − 0.289520I
a = 1.40742 + 0.33210I
b = 0.475116 + 0.247702I
−0.25228 − 2.77775I 1.37986 + 3.06700I
u = −0.688548 − 0.289520I
a = 2.29627 + 0.40579I
b = 1.99892 + 0.79393I
−0.25228 − 6.83751I 1.37986 + 9.99520I
u = −0.688548 − 0.289520I
a = −2.87892 + 0.05748I
b = −1.46361 − 0.94422I
−0.25228 − 6.83751I 1.37986 + 9.99520I
u = −0.282165 + 1.228290I
a = −0.498515 + 0.928241I
b = 1.191030 + 0.667601I
−8.85098 − 0.63724I −14.1587 + 1.3834I
u = −0.282165 + 1.228290I
a = 0.304688 − 1.039660I
b = −0.999487 − 0.874238I
−8.85098 − 0.63724I −14.1587 + 1.3834I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.282165 + 1.228290I
a = −0.084827 − 1.247050I
b = −1.83040 − 0.31025I
−8.85098 + 3.42253I −14.1587 − 5.5448I
u = −0.282165 + 1.228290I
a = 0.08525 + 1.47062I
b = 1.55567 + 0.24768I
−8.85098 + 3.42253I −14.1587 − 5.5448I
u = −0.282165 − 1.228290I
a = −0.498515 − 0.928241I
b = 1.191030 − 0.667601I
−8.85098 + 0.63724I −14.1587 − 1.3834I
u = −0.282165 − 1.228290I
a = 0.304688 + 1.039660I
b = −0.999487 + 0.874238I
−8.85098 + 0.63724I −14.1587 − 1.3834I
u = −0.282165 − 1.228290I
a = −0.084827 + 1.247050I
b = −1.83040 + 0.31025I
−8.85098 − 3.42253I −14.1587 + 5.5448I
u = −0.282165 − 1.228290I
a = 0.08525 − 1.47062I
b = 1.55567 − 0.24768I
−8.85098 − 3.42253I −14.1587 + 5.5448I
u = −0.729174
a = −1.50657 + 0.71407I
b = −1.38557 + 1.01783I
−3.98778 + 2.02988I −9.47960 − 3.46410I
u = −0.729174
a = −1.50657 − 0.71407I
b = −1.38557 − 1.01783I
−3.98778 − 2.02988I −9.47960 + 3.46410I
u = −0.729174
a = 1.90020 + 1.39586I
b = 1.098550 + 0.520685I
−3.98778 − 2.02988I −9.47960 + 3.46410I
u = −0.729174
a = 1.90020 − 1.39586I
b = 1.098550 − 0.520685I
−3.98778 + 2.02988I −9.47960 − 3.46410I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.280769 + 0.672881I
a = 0.220942 + 0.003201I
b = −0.06271 − 1.71546I
−2.59857 − 2.66219I −5.29896 + 7.91147I
u = −0.280769 + 0.672881I
a = −2.13825 + 0.98541I
b = −0.064187 + 0.147769I
−2.59857 − 2.66219I −5.29896 + 7.91147I
u = −0.280769 + 0.672881I
a = 2.42403 − 0.96197I
b = 1.45441 − 1.22723I
−2.59857 − 6.72196I −5.2990 + 14.8397I
u = −0.280769 + 0.672881I
a = −2.32154 − 1.19278I
b = −0.03330 + 1.90118I
−2.59857 − 6.72196I −5.2990 + 14.8397I
u = −0.280769 − 0.672881I
a = 0.220942 − 0.003201I
b = −0.06271 + 1.71546I
−2.59857 + 2.66219I −5.29896 − 7.91147I
u = −0.280769 − 0.672881I
a = −2.13825 − 0.98541I
b = −0.064187 − 0.147769I
−2.59857 + 2.66219I −5.29896 − 7.91147I
u = −0.280769 − 0.672881I
a = 2.42403 + 0.96197I
b = 1.45441 + 1.22723I
−2.59857 + 6.72196I −5.2990 − 14.8397I
u = −0.280769 − 0.672881I
a = −2.32154 + 1.19278I
b = −0.03330 − 1.90118I
−2.59857 + 6.72196I −5.2990 − 14.8397I
u = −0.562423 + 1.180730I
a = −0.482522 − 1.144740I
b = −1.74339 − 0.25581I
−6.91463 − 8.15357I −10.99915 + 5.78993I
u = −0.562423 + 1.180730I
a = 0.396671 + 1.287600I
b = 1.62301 + 0.07410I
−6.91463 − 8.15357I −10.99915 + 5.78993I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.562423 + 1.180730I
a = 0.05322 + 1.82079I
b = 2.39734 + 0.94781I
−6.91463 − 12.21330I −10.9991 + 12.7181I
u = −0.562423 + 1.180730I
a = −0.13401 − 1.96656I
b = −2.17978 − 0.96122I
−6.91463 − 12.21330I −10.9991 + 12.7181I
u = −0.562423 − 1.180730I
a = −0.482522 + 1.144740I
b = −1.74339 + 0.25581I
−6.91463 + 8.15357I −10.99915 − 5.78993I
u = −0.562423 − 1.180730I
a = 0.396671 − 1.287600I
b = 1.62301 − 0.07410I
−6.91463 + 8.15357I −10.99915 − 5.78993I
u = −0.562423 − 1.180730I
a = 0.05322 − 1.82079I
b = 2.39734 − 0.94781I
−6.91463 + 12.21330I −10.9991 − 12.7181I
u = −0.562423 − 1.180730I
a = −0.13401 + 1.96656I
b = −2.17978 + 0.96122I
−6.91463 + 12.21330I −10.9991 − 12.7181I
u = 0.635699 + 0.077135I
a = 1.73187 − 0.93607I
b = 1.49174 − 1.51912I
−3.69862 − 6.25262I −8.98921 + 9.37331I
u = 0.635699 + 0.077135I
a = −2.30894 − 0.24953I
b = −1.59915 − 0.98084I
−3.69862 − 2.19285I −8.98921 + 2.44511I
u = 0.635699 + 0.077135I
a = −2.66357 − 1.21974I
b = −1.44854 − 0.33672I
−3.69862 − 2.19285I −8.98921 + 2.44511I
u = 0.635699 + 0.077135I
a = 2.02681 − 2.63561I
b = 1.173150 − 0.461472I
−3.69862 − 6.25262I −8.98921 + 9.37331I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.635699 − 0.077135I
a = 1.73187 + 0.93607I
b = 1.49174 + 1.51912I
−3.69862 + 6.25262I −8.98921 − 9.37331I
u = 0.635699 − 0.077135I
a = −2.30894 + 0.24953I
b = −1.59915 + 0.98084I
−3.69862 + 2.19285I −8.98921 − 2.44511I
u = 0.635699 − 0.077135I
a = −2.66357 + 1.21974I
b = −1.44854 + 0.33672I
−3.69862 + 2.19285I −8.98921 − 2.44511I
u = 0.635699 − 0.077135I
a = 2.02681 + 2.63561I
b = 1.173150 + 0.461472I
−3.69862 + 6.25262I −8.98921 − 9.37331I
27
III. I
u
3
= h44u
32
− 157u
31
+ · · · + 13b + 41, 41u
32
− 120u
31
+ · · · + 13a −
46, u
33
− 4u
32
+ · · · + 4u − 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
4
=
u
4
+ u
2
+ 1
u
6
+ 2u
4
+ u
2
a
10
=
−3.15385u
32
+ 9.23077u
31
+ ··· − 1.53846u + 3.53846
−3.38462u
32
+ 12.0769u
31
+ ··· + 16.1538u − 3.15385
a
8
=
−0.153846u
32
− 1.76923u
31
+ ··· − 12.5385u + 1.53846
−2.38462u
32
+ 10.0769u
31
+ ··· + 3.15385u − 0.153846
a
1
=
u
2
+ 1
u
2
a
11
=
−1.84615u
32
+ 5.76923u
31
+ ··· − 4.46154u + 3.46154
−2.15385u
32
+ 10.2308u
31
+ ··· + 21.4615u − 4.46154
a
5
=
9.23077u
32
− 34.8462u
31
+ ··· − 36.6923u + 6.69231
0.769231u
32
− 10.1538u
31
+ ··· − 31.3077u + 10.3077
a
9
=
−3.15385u
32
+ 9.23077u
31
+ ··· − 7.53846u + 4.53846
−3.84615u
32
+ 14.7692u
31
+ ··· + 21.5385u − 4.53846
a
12
=
0.153846u
32
+ 3.76923u
31
+ ··· + 28.5385u − 7.53846
4.84615u
32
− 18.7692u
31
+ ··· − 10.5385u + 0.538462
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4
13
u
32
−
188
13
u
31
+ ··· −
857
13
u +
194
13
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
33
− 18u
32
+ ··· − 8u + 1
c
2
u
33
− 4u
32
+ ··· + 4u − 1
c
3
u
33
+ 4u
32
+ ··· + 6u − 1
c
4
, c
8
u
33
− u
32
+ ··· − 2u + 1
c
5
, c
9
u
33
+ 8u
31
+ ··· + 9u
2
− 1
c
6
u
33
+ 4u
32
+ ··· + 4u + 1
c
7
, c
10
u
33
− 8u
32
+ ··· + 14u − 1
c
11
u
33
+ 22u
32
+ ··· + 1638u + 169
c
12
u
33
+ 11u
32
+ ··· + 19u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
33
+ 2y
32
+ ··· + 16y − 1
c
2
, c
6
y
33
+ 18y
32
+ ··· − 8y − 1
c
3
y
33
− 8y
32
+ ··· − 2y − 1
c
4
, c
8
y
33
− 11y
32
+ ··· + 18y − 1
c
5
, c
9
y
33
+ 16y
32
+ ··· + 18y − 1
c
7
, c
10
y
33
− 16y
32
+ ··· + 62y − 1
c
11
y
33
− 12y
32
+ ··· − 205166y − 28561
c
12
y
33
− 7y
32
+ ··· + 53y − 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.624701 + 0.783289I
a = −0.402434 + 0.260106I
b = 0.047662 − 0.477710I
−0.24436 − 4.51186I −1.39084 + 6.52044I
u = −0.624701 − 0.783289I
a = −0.402434 − 0.260106I
b = 0.047662 + 0.477710I
−0.24436 + 4.51186I −1.39084 − 6.52044I
u = −0.616920 + 0.819893I
a = 0.159793 + 0.333234I
b = −0.371795 − 0.074566I
−0.334625 − 0.327489I −1.91642 − 2.33968I
u = −0.616920 − 0.819893I
a = 0.159793 − 0.333234I
b = −0.371795 + 0.074566I
−0.334625 + 0.327489I −1.91642 + 2.33968I
u = −0.094611 + 1.064520I
a = −0.610207 + 0.316676I
b = −0.279375 − 0.679538I
−4.53724 + 0.98979I −24.3179 − 4.9151I
u = −0.094611 − 1.064520I
a = −0.610207 − 0.316676I
b = −0.279375 + 0.679538I
−4.53724 − 0.98979I −24.3179 + 4.9151I
u = 0.825311 + 0.216879I
a = −2.04456 − 0.42568I
b = −1.59508 − 0.79474I
−3.26501 − 6.10201I −2.66167 + 3.54169I
u = 0.825311 − 0.216879I
a = −2.04456 + 0.42568I
b = −1.59508 + 0.79474I
−3.26501 + 6.10201I −2.66167 − 3.54169I
u = 0.409481 + 1.075810I
a = 0.95565 + 2.32259I
b = −2.10735 + 1.97916I
−4.69247 − 2.96530I −9.07068 + 0.57735I
u = 0.409481 − 1.075810I
a = 0.95565 − 2.32259I
b = −2.10735 − 1.97916I
−4.69247 + 2.96530I −9.07068 − 0.57735I
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.513867 + 1.089260I
a = −1.05738 + 1.71820I
b = −2.41490 − 0.26883I
−3.92239 + 10.03720I −7.05193 − 9.50792I
u = 0.513867 − 1.089260I
a = −1.05738 − 1.71820I
b = −2.41490 + 0.26883I
−3.92239 − 10.03720I −7.05193 + 9.50792I
u = −0.089152 + 0.776504I
a = −1.336450 + 0.049295I
b = 0.080870 − 1.042160I
−3.33632 − 1.97963I −13.24495 + 3.27568I
u = −0.089152 − 0.776504I
a = −1.336450 − 0.049295I
b = 0.080870 + 1.042160I
−3.33632 + 1.97963I −13.24495 − 3.27568I
u = −0.449810 + 1.152880I
a = −0.025864 − 0.429678I
b = 0.507002 + 0.163455I
−6.18796 − 9.08570I −8.45367 + 7.16094I
u = −0.449810 − 1.152880I
a = −0.025864 + 0.429678I
b = 0.507002 − 0.163455I
−6.18796 + 9.08570I −8.45367 − 7.16094I
u = 0.442886 + 1.166860I
a = 0.02512 − 1.82358I
b = 2.13897 − 0.77832I
−7.28553 + 4.16568I −13.00961 − 3.76204I
u = 0.442886 − 1.166860I
a = 0.02512 + 1.82358I
b = 2.13897 + 0.77832I
−7.28553 − 4.16568I −13.00961 + 3.76204I
u = −0.436048 + 1.179340I
a = 0.152591 + 0.284968I
b = −0.402611 + 0.055697I
−6.23886 + 0.79398I −8.97582 − 1.52794I
u = −0.436048 − 1.179340I
a = 0.152591 − 0.284968I
b = −0.402611 − 0.055697I
−6.23886 − 0.79398I −8.97582 + 1.52794I
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.320239 + 1.222920I
a = 0.288602 − 1.331550I
b = 1.72080 − 0.07348I
−7.72797 − 2.38604I −7.36564 + 0.94630I
u = 0.320239 − 1.222920I
a = 0.288602 + 1.331550I
b = 1.72080 + 0.07348I
−7.72797 + 2.38604I −7.36564 − 0.94630I
u = 0.718329
a = −2.09595
b = −1.50558
−3.96826 −9.55110
u = 0.899316 + 0.922061I
a = 0.153573 + 0.101917I
b = 0.044137 + 0.233259I
4.19248 + 3.30525I 42.0821 + 30.3850I
u = 0.899316 − 0.922061I
a = 0.153573 − 0.101917I
b = 0.044137 − 0.233259I
4.19248 − 3.30525I 42.0821 − 30.3850I
u = 0.547434 + 1.181830I
a = −0.06374 − 1.85461I
b = 2.15694 − 1.09061I
−6.12590 + 11.16710I −5.65453 − 6.80113I
u = 0.547434 − 1.181830I
a = −0.06374 + 1.85461I
b = 2.15694 + 1.09061I
−6.12590 − 11.16710I −5.65453 + 6.80113I
u = −0.693444 + 0.060916I
a = −0.329512 + 0.418469I
b = 0.203006 − 0.310257I
−2.94763 − 5.05460I −3.66921 + 4.28026I
u = −0.693444 − 0.060916I
a = −0.329512 − 0.418469I
b = 0.203006 + 0.310257I
−2.94763 + 5.05460I −3.66921 − 4.28026I
u = 0.534172 + 0.413595I
a = 1.29582 − 1.77161I
b = 1.42492 − 0.41040I
−1.89031 − 5.68794I −3.45615 + 5.59146I
33
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.534172 − 0.413595I
a = 1.29582 + 1.77161I
b = 1.42492 + 0.41040I
−1.89031 + 5.68794I −3.45615 − 5.59146I
u = 0.152814 + 0.579850I
a = 2.88698 − 0.27320I
b = 0.59959 + 1.63227I
−2.68939 + 5.96377I −6.06757 − 2.79841I
u = 0.152814 − 0.579850I
a = 2.88698 + 0.27320I
b = 0.59959 − 1.63227I
−2.68939 − 5.96377I −6.06757 + 2.79841I
34
IV. I
u
4
= hau + b + u, a
2
+ a + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u − 1
a
7
=
u
u + 1
a
4
=
0
u
a
10
=
a
−au − u
a
8
=
au + a + u
a + u + 2
a
1
=
−u
−u − 1
a
11
=
a + 1
−au − 2u
a
5
=
−au − u − 1
−2au − 2a − 2
a
9
=
a
−2au − a − u
a
12
=
a + 1
−au − 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 11u + 3
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
12
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
4
, c
5
, c
8
c
9
u
4
− u
3
+ 2u
2
− 2u + 1
c
11
u
4
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
8
c
9
y
4
+ 3y
3
+ 2y
2
+ 1
c
11
y
4
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.070696 − 0.758745I
b = −0.121744 − 1.306620I
− 4.05977I −2.50000 + 9.52628I
u = −0.500000 + 0.866025I
a = −1.070700 + 0.758745I
b = 0.621744 + 0.440597I
− 4.05977I −2.50000 + 9.52628I
u = −0.500000 − 0.866025I
a = 0.070696 + 0.758745I
b = −0.121744 + 1.306620I
4.05977I −2.50000 − 9.52628I
u = −0.500000 − 0.866025I
a = −1.070700 − 0.758745I
b = 0.621744 − 0.440597I
4.05977I −2.50000 − 9.52628I
38
V. I
u
5
= hau + b + 1, a
2
− au − a − 1, u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u − 1
a
7
=
u
u + 1
a
4
=
0
u
a
10
=
a
−au − 1
a
8
=
−au + u
−au − a + 2u + 1
a
1
=
−u
−u − 1
a
11
=
a − u − 1
−au − 2
a
5
=
−a + 1
2au + 1
a
9
=
a
−2au − a − 1
a
12
=
a − u − 1
−au − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u − 1
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
c
7
, c
10
, c
12
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
4
, c
5
, c
8
c
9
u
4
+ 2u
3
+ 2u
2
+ u + 1
c
11
u
4
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
7
, c
10
c
12
(y
2
+ y + 1)
2
c
4
, c
5
, c
8
c
9
y
4
+ 2y
2
+ 3y + 1
c
11
y
4
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.692440 + 0.318148I
b = −1.070700 + 0.758745I
0 −2.50000 + 2.59808I
u = −0.500000 + 0.866025I
a = 1.192440 + 0.547877I
b = 0.070696 − 0.758745I
0 −2.50000 + 2.59808I
u = −0.500000 − 0.866025I
a = −0.692440 − 0.318148I
b = −1.070700 − 0.758745I
0 −2.50000 − 2.59808I
u = −0.500000 − 0.866025I
a = 1.192440 − 0.547877I
b = 0.070696 + 0.758745I
0 −2.50000 − 2.59808I
42
VI. I
v
1
= ha, b
2
+ b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
−1
0
a
2
=
1
0
a
7
=
−1
0
a
4
=
1
0
a
10
=
0
b
a
8
=
−1
b + 1
a
1
=
1
0
a
11
=
−b
b
a
5
=
−b − 2
b + 1
a
9
=
−b
b
a
12
=
−b
b
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b − 2
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
11
u
2
c
4
, c
5
, c
7
c
8
, c
9
, c
10
u
2
+ u + 1
c
12
u
2
− u + 1
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
, c
11
y
2
c
4
, c
5
, c
7
c
8
, c
9
, c
10
c
12
y
2
+ y + 1
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −0.500000 + 0.866025I
2.02988I 0. − 3.46410I
v = −1.00000
a = 0
b = −0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
46
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u
2
− u + 1)
4
(u
31
+ 16u
30
+ ··· − 2u − 1)
4
· (u
33
− 18u
32
+ ··· − 8u + 1)(u
62
+ 33u
61
+ ··· + 25u + 1)
c
2
u
2
(u
2
+ u + 1)
4
(u
31
+ 2u
30
+ ··· + 2u + 1)
4
(u
33
− 4u
32
+ ··· + 4u − 1)
· (u
62
− 9u
61
+ ··· − 9u + 1)
c
3
u
2
(u
2
− u + 1)
4
(u
31
− 2u
30
+ ··· − 26u + 5)
4
· (u
33
+ 4u
32
+ ··· + 6u − 1)(u
62
+ 9u
61
+ ··· + 7773u + 1609)
c
4
, c
8
(u
2
+ u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
4
+ 2u
3
+ 2u
2
+ u + 1)
· (u
33
− u
32
+ ··· − 2u + 1)(u
62
+ 6u
60
+ ··· − u + 1)
· (u
124
− 21u
122
+ ··· − u + 1)
c
5
, c
9
(u
2
+ u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)(u
4
+ 2u
3
+ 2u
2
+ u + 1)
· (u
33
+ 8u
31
+ ··· + 9u
2
− 1)(u
62
− u
61
+ ··· + 187u + 73)
· (u
124
+ 29u
122
+ ··· + 14899434913u + 3986390929)
c
6
u
2
(u
2
− u + 1)
4
(u
31
+ 2u
30
+ ··· + 2u + 1)
4
(u
33
+ 4u
32
+ ··· + 4u + 1)
· (u
62
− 9u
61
+ ··· − 9u + 1)
c
7
, c
10
((u
2
− u + 1)
4
)(u
2
+ u + 1)(u
33
− 8u
32
+ ··· + 14u − 1)
· (u
62
+ u
61
+ ··· + 5u + 1)(u
124
+ 5u
123
+ ··· − 2429506u + 230137)
c
11
u
10
(u
31
+ 15u
30
+ ··· + 6u + 4)
4
(u
33
+ 22u
32
+ ··· + 1638u + 169)
· (u
62
− 47u
61
+ ··· − u + 1)
c
12
((u
2
− u + 1)
5
)(u
2
+ u + 1)
62
(u
33
+ 11u
32
+ ··· + 19u + 1)
· (u
62
− 59u
61
+ ··· − 16642998272u + 536870912)
47
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y
2
+ y + 1)
4
(y
31
+ 32y
29
+ ··· + 14y − 1)
4
· (y
33
+ 2y
32
+ ··· + 16y − 1)(y
62
+ y
61
+ ··· + 65y + 1)
c
2
, c
6
y
2
(y
2
+ y + 1)
4
(y
31
+ 16y
30
+ ··· − 2y − 1)
4
· (y
33
+ 18y
32
+ ··· − 8y − 1)(y
62
+ 33y
61
+ ··· + 25y + 1)
c
3
y
2
(y
2
+ y + 1)
4
(y
31
− 16y
30
+ ··· − 534y − 25)
4
· (y
33
− 8y
32
+ ··· − 2y − 1)
· (y
62
− 25y
61
+ ··· + 73803251y + 2588881)
c
4
, c
8
(y
2
+ y + 1)(y
4
+ 2y
2
+ 3y + 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
33
− 11y
32
+ ··· + 18y − 1)(y
62
+ 12y
61
+ ··· + 11y + 1)
· (y
124
− 42y
123
+ ··· − 289y + 1)
c
5
, c
9
(y
2
+ y + 1)(y
4
+ 2y
2
+ 3y + 1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
33
+ 16y
32
+ ··· + 18y − 1)(y
62
+ 31y
61
+ ··· + 117455y + 5329)
· (y
124
+ 58y
123
+ ··· + 5.62 × 10
20
y + 1.59 × 10
19
)
c
7
, c
10
((y
2
+ y + 1)
5
)(y
33
− 16y
32
+ ··· + 62y − 1)(y
62
− y
61
+ ··· + 19y + 1)
· (y
124
− 53y
123
+ ··· − 2641994793520y + 52963038769)
c
11
y
10
(y
31
− 5y
30
+ ··· + 236y − 16)
4
· (y
33
− 12y
32
+ ··· − 205166y − 28561)(y
62
− 17y
61
+ ··· + 51y + 1)
c
12
((y
2
+ y + 1)
67
)(y
33
− 7y
32
+ ··· + 53y − 1)
· (y
62
− 7y
61
+ ··· + 2449958197289549824y + 288230376151711744)
48
