12a
0354
(K12a
0354
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 2 10 12 11 1 5 4 7
Solving Sequence
2,5
6
3,10
7 11 1 9 8 4 12
c
5
c
2
c
6
c
10
c
1
c
9
c
8
c
4
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.96195 × 10
18
u
57
− 5.61291 × 10
19
u
56
+ ··· + 1.17422 × 10
16
b + 4.90198 × 10
20
,
− 8.24820 × 10
18
u
57
− 1.13864 × 10
20
u
56
+ ··· + 1.17422 × 10
16
a + 8.05463 × 10
20
,
u
58
+ 14u
57
+ ··· − 928u − 64i
I
u
2
= h−1.56047 × 10
15
a
5
u
18
+ 3.18174 × 10
13
a
4
u
18
+ ··· + 3.31109 × 10
14
a − 1.08507 × 10
15
,
6u
18
a
5
+ 8u
18
a
4
+ ··· + 188a − 69, u
19
− 2u
18
+ ··· − 4u + 1i
I
u
3
= h−292694585u
36
+ 1804999042u
35
+ ··· + 8736867b + 1338165752,
− 544656919u
36
+ 3321883283u
35
+ ··· + 14561445a + 2220591718, u
37
− 7u
36
+ ··· − 27u + 5i
I
u
4
= ha
5
+ a
4
− 3a
3
+ 3a
2
+ 45b − 27a − 18, a
6
− 3a
5
+ 3a
4
− 9a
2
+ 27, u + 1i
* 4 irreducible components of dim
C
= 0, with total 215 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−3.96 × 10
18
u
57
− 5.61 × 10
19
u
56
+ · · · + 1.17 × 10
16
b + 4.90 ×
10
20
, −8.25 × 10
18
u
57
− 1.14 × 10
20
u
56
+ · · · + 1.17 × 10
16
a + 8.05 ×
10
20
, u
58
+ 14u
57
+ · · · − 928u − 64i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
702.443u
57
+ 9697.03u
56
+ ··· − 921874.u − 68595.8
337.412u
57
+ 4780.13u
56
+ ··· − 554592.u − 41746.8
a
7
=
−1136.18u
57
− 15917.9u
56
+ ··· + 1.72572 × 10
6
u + 129786.
−380.595u
57
− 5825.14u
56
+ ··· + 985764.u + 75499.0
a
11
=
365.031u
57
+ 4916.90u
56
+ ··· − 367281.u − 26849.0
337.412u
57
+ 4780.13u
56
+ ··· − 554592.u − 41746.8
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
458.764u
57
+ 6042.32u
56
+ ··· − 378194.u − 27373.9
403.116u
57
+ 5707.30u
56
+ ··· − 635530.u − 47706.2
a
8
=
251.070u
57
+ 3348.63u
56
+ ··· − 236664.u − 17303.7
38.8840u
57
+ 782.156u
56
+ ··· − 231104.u − 17791.9
a
4
=
740.528u
57
+ 9337.11u
56
+ ··· − 264188.u − 16959.8
1862.40u
57
+ 24267.6u
56
+ ··· − 1.31852 × 10
6
u − 94085.5
a
12
=
707.799u
57
+ 9247.31u
56
+ ··· − 543363.u − 39191.2
469.499u
57
+ 6655.32u
56
+ ··· − 808644.u − 61298.1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
6462402672161082471
2935541202435748
u
57
−
42708315538598190931
1467770601217874
u
56
+ ··· +
1380025211473468370317
733885300608937
u +
100372439627418356722
733885300608937
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
58
+ 26u
57
+ ··· + 83456u + 4096
c
2
, c
5
u
58
+ 14u
57
+ ··· − 928u − 64
c
3
, c
10
u
58
+ 17u
56
+ ··· + 461u − 77
c
4
, c
11
u
58
− u
57
+ ··· + u + 1
c
6
, c
9
u
58
− u
57
+ ··· + 17u − 1
c
7
, c
12
u
58
+ 40u
57
+ ··· − 7340032u − 262144
c
8
u
58
+ 45u
57
+ ··· + 80u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
58
+ 18y
57
+ ··· + 5636096y + 16777216
c
2
, c
5
y
58
− 26y
57
+ ··· − 83456y + 4096
c
3
, c
10
y
58
+ 34y
57
+ ··· − 273813y + 5929
c
4
, c
11
y
58
− 5y
57
+ ··· − 9y + 1
c
6
, c
9
y
58
+ 11y
57
+ ··· − 211y + 1
c
7
, c
12
y
58
+ 38y
57
+ ··· − 1030792151040y + 68719476736
c
8
y
58
− 5y
57
+ ··· + 1760y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.876279 + 0.463278I
a = −1.56801 + 0.33201I
b = −1.060230 + 0.569569I
2.91483 − 0.87856I 0
u = −0.876279 − 0.463278I
a = −1.56801 − 0.33201I
b = −1.060230 − 0.569569I
2.91483 + 0.87856I 0
u = 0.865412 + 0.530275I
a = −1.63027 + 0.75726I
b = −0.186310 − 1.351960I
−0.95828 − 2.13226I 0
u = 0.865412 − 0.530275I
a = −1.63027 − 0.75726I
b = −0.186310 + 1.351960I
−0.95828 + 2.13226I 0
u = 0.843862 + 0.501636I
a = 1.45119 − 1.42798I
b = 0.625040 + 1.262900I
3.05531 + 0.88558I 0
u = 0.843862 − 0.501636I
a = 1.45119 + 1.42798I
b = 0.625040 − 1.262900I
3.05531 − 0.88558I 0
u = −0.852561 + 0.486055I
a = 1.17675 + 1.60777I
b = 1.11394 + 0.93016I
2.98892 + 4.78290I 0
u = −0.852561 − 0.486055I
a = 1.17675 − 1.60777I
b = 1.11394 − 0.93016I
2.98892 − 4.78290I 0
u = 1.004710 + 0.183945I
a = −1.53637 + 0.82258I
b = −0.715308 − 0.228587I
−4.19172 − 0.28235I 0
u = 1.004710 − 0.183945I
a = −1.53637 − 0.82258I
b = −0.715308 + 0.228587I
−4.19172 + 0.28235I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.935675 + 0.479904I
a = 1.47112 + 0.13642I
b = −0.178971 + 1.077070I
2.81479 − 4.88334I 0
u = 0.935675 − 0.479904I
a = 1.47112 − 0.13642I
b = −0.178971 − 1.077070I
2.81479 + 4.88334I 0
u = −0.846642 + 0.421099I
a = −0.658051 − 1.168120I
b = −0.733140 − 0.764484I
−1.52095 + 1.93652I 0
u = −0.846642 − 0.421099I
a = −0.658051 + 1.168120I
b = −0.733140 + 0.764484I
−1.52095 − 1.93652I 0
u = −0.520255 + 0.931957I
a = −0.051126 − 0.179106I
b = 0.74032 + 1.58591I
10.6313 − 14.6307I 0
u = −0.520255 − 0.931957I
a = −0.051126 + 0.179106I
b = 0.74032 − 1.58591I
10.6313 + 14.6307I 0
u = −0.621310 + 0.874512I
a = −0.242172 + 0.219845I
b = −0.463059 − 1.181600I
9.91537 − 5.61324I 0
u = −0.621310 − 0.874512I
a = −0.242172 − 0.219845I
b = −0.463059 + 1.181600I
9.91537 + 5.61324I 0
u = −0.515406 + 0.977676I
a = −0.056097 + 0.195449I
b = 0.422539 − 1.243540I
10.49930 + 9.46799I 0
u = −0.515406 − 0.977676I
a = −0.056097 − 0.195449I
b = 0.422539 + 1.243540I
10.49930 − 9.46799I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.083270 + 0.260448I
a = 1.23645 + 0.70270I
b = 0.150954 + 0.884488I
2.72054 − 5.06764I 0
u = 1.083270 − 0.260448I
a = 1.23645 − 0.70270I
b = 0.150954 − 0.884488I
2.72054 + 5.06764I 0
u = −0.539639 + 0.975725I
a = 0.063073 + 0.217815I
b = −0.514156 − 1.268230I
4.44320 − 8.50447I 0
u = −0.539639 − 0.975725I
a = 0.063073 − 0.217815I
b = −0.514156 + 1.268230I
4.44320 + 8.50447I 0
u = −0.312416 + 1.100670I
a = −0.138681 − 0.270153I
b = −0.041517 + 1.155970I
7.63163 + 0.88952I 0
u = −0.312416 − 1.100670I
a = −0.138681 + 0.270153I
b = −0.041517 − 1.155970I
7.63163 − 0.88952I 0
u = −1.15086
a = 0.463126
b = 0.544886
−1.95009 0
u = −1.043040 + 0.491767I
a = 1.102130 + 0.553147I
b = 1.031740 − 0.105359I
−2.37385 + 1.31800I 0
u = −1.043040 − 0.491767I
a = 1.102130 − 0.553147I
b = 1.031740 + 0.105359I
−2.37385 − 1.31800I 0
u = −0.999163 + 0.587264I
a = −1.54058 − 0.76351I
b = −1.088130 + 0.255041I
−1.68351 + 5.60090I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.999163 − 0.587264I
a = −1.54058 + 0.76351I
b = −1.088130 − 0.255041I
−1.68351 − 5.60090I 0
u = 0.817878
a = −1.99134
b = −0.141479
−2.85067 0
u = −0.623337 + 1.006520I
a = 0.059647 − 0.268869I
b = −0.012045 + 1.023710I
4.71528 + 2.38651I 0
u = −0.623337 − 1.006520I
a = 0.059647 + 0.268869I
b = −0.012045 − 1.023710I
4.71528 − 2.38651I 0
u = −0.585968 + 0.548112I
a = 0.630401 + 0.491093I
b = 0.822789 + 0.428793I
−0.473220 − 0.946588I 0
u = −0.585968 − 0.548112I
a = 0.630401 − 0.491093I
b = 0.822789 − 0.428793I
−0.473220 + 0.946588I 0
u = 1.207810 + 0.265869I
a = 1.029380 − 0.161558I
b = 0.761719 + 0.488211I
−3.80302 − 6.16815I 0
u = 1.207810 − 0.265869I
a = 1.029380 + 0.161558I
b = 0.761719 − 0.488211I
−3.80302 + 6.16815I 0
u = −1.057620 + 0.712836I
a = 1.82206 + 0.33484I
b = 0.585417 − 1.135420I
8.5726 + 11.4964I 0
u = −1.057620 − 0.712836I
a = 1.82206 − 0.33484I
b = 0.585417 + 1.135420I
8.5726 − 11.4964I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.294710 + 0.041752I
a = −0.99269 − 1.28098I
b = −0.79302 − 1.28423I
3.71590 − 12.29490I 0
u = 1.294710 − 0.041752I
a = −0.99269 + 1.28098I
b = −0.79302 + 1.28423I
3.71590 + 12.29490I 0
u = −0.087008 + 0.675977I
a = 0.182243 − 0.501895I
b = −0.694819 + 0.071010I
0.17299 + 2.68830I −6.00000 − 3.32279I
u = −0.087008 − 0.675977I
a = 0.182243 + 0.501895I
b = −0.694819 − 0.071010I
0.17299 − 2.68830I −6.00000 + 3.32279I
u = −1.121810 + 0.698380I
a = −2.07726 − 0.21262I
b = −0.84659 + 1.65134I
8.7845 + 20.6080I 0
u = −1.121810 − 0.698380I
a = −2.07726 + 0.21262I
b = −0.84659 − 1.65134I
8.7845 − 20.6080I 0
u = −1.075910 + 0.773792I
a = −1.165870 − 0.157077I
b = −0.158853 + 0.925484I
3.31222 + 4.03148I 0
u = −1.075910 − 0.773792I
a = −1.165870 + 0.157077I
b = −0.158853 − 0.925484I
3.31222 − 4.03148I 0
u = −1.127170 + 0.720872I
a = 1.60110 + 0.25919I
b = 0.65567 − 1.33268I
2.6225 + 14.6751I 0
u = −1.127170 − 0.720872I
a = 1.60110 − 0.25919I
b = 0.65567 + 1.33268I
2.6225 − 14.6751I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.149590 + 0.743910I
a = 0.954799 − 0.533033I
b = −0.293251 − 1.059050I
8.57491 − 3.20558I 0
u = −1.149590 − 0.743910I
a = 0.954799 + 0.533033I
b = −0.293251 + 1.059050I
8.57491 + 3.20558I 0
u = −1.24299 + 0.78078I
a = −0.849782 + 0.098559I
b = −0.138776 + 1.140370I
4.87167 + 5.85154I 0
u = −1.24299 − 0.78078I
a = −0.849782 − 0.098559I
b = −0.138776 − 1.140370I
4.87167 − 5.85154I 0
u = 1.47860 + 0.08119I
a = 0.347368 + 0.572332I
b = 0.355019 + 0.875731I
−3.28236 − 5.74811I 0
u = 1.47860 − 0.08119I
a = 0.347368 − 0.572332I
b = 0.355019 − 0.875731I
−3.28236 + 5.74811I 0
u = −0.349464 + 0.143339I
a = 1.268350 − 0.510768I
b = 0.451323 − 0.441508I
−0.846218 + 0.678005I −8.10349 − 5.25581I
u = −0.349464 − 0.143339I
a = 1.268350 + 0.510768I
b = 0.451323 + 0.441508I
−0.846218 − 0.678005I −8.10349 + 5.25581I
10
II. I
u
2
= h−1.56 × 10
15
a
5
u
18
+ 3.18 × 10
13
a
4
u
18
+ · · · + 3.31 × 10
14
a − 1.09 ×
10
15
, 6u
18
a
5
+ 8u
18
a
4
+ · · · + 188a − 69, u
19
− 2u
18
+ · · · − 4u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
a
8.53027a
5
u
18
− 0.173929a
4
u
18
+ ··· − 1.81000a + 5.93153
a
7
=
−7.22607a
5
u
18
− 2.99560a
4
u
18
+ ··· − 3.73093a + 8.39393
0.998845a
2
u
18
− 0.343520u
18
+ ··· − 0.991205a
2
+ 0.308341
a
11
=
−8.53027a
5
u
18
+ 0.173929a
4
u
18
+ ··· + 2.81000a − 5.93153
8.53027a
5
u
18
− 0.173929a
4
u
18
+ ··· − 1.81000a + 5.93153
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
8.27781a
5
u
18
− 1.49235a
4
u
18
+ ··· + 0.825771a − 1.14392
−14.1439a
5
u
18
+ 2.37228a
4
u
18
+ ··· − 1.29595a + 7.21589
a
8
=
6.94768a
5
u
18
+ 0.452478a
4
u
18
+ ··· + 2.07529a + 2.53225
−12.8138a
5
u
18
+ 0.427453a
4
u
18
+ ··· − 1.54546a + 3.53972
a
4
=
59.2197a
5
u
18
+ 26.7053a
4
u
18
+ ··· + 0.392941a − 4.15300
−93.9995a
5
u
18
− 41.5321a
4
u
18
+ ··· + 1.12628a − 3.59985
a
12
=
−21.3441a
5
u
18
− 10.6095a
4
u
18
+ ··· + 2.04327a + 1.68052
35.9712a
5
u
18
+ 18.0658a
4
u
18
+ ··· + 1.54982a − 1.86103
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
2749082792001216
182932936016351
u
18
a
5
+
16259650261624
182932936016351
u
18
a
4
+ ···−
1019524816793328
182932936016351
a +
297941330504151
182932936016351
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
19
+ 8u
18
+ ··· + 4u + 1)
6
c
2
, c
5
(u
19
− 2u
18
+ ··· − 4u + 1)
6
c
3
, c
10
u
114
− 2u
113
+ ··· − 4054780664u + 1331355377
c
4
, c
11
u
114
− 4u
113
+ ··· − 2666478u + 405443
c
6
, c
9
u
114
+ 3u
113
+ ··· + 3197956u + 281947
c
7
, c
12
(u
3
− u
2
+ 2u − 1)
38
c
8
(u
19
− 9u
18
+ ··· − u + 2)
6
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
19
+ 8y
18
+ ··· − 16y − 1)
6
c
2
, c
5
(y
19
− 8y
18
+ ··· + 4y − 1)
6
c
3
, c
10
y
114
+ 64y
113
+ ··· + 6.82 × 10
19
y + 1.77 × 10
18
c
4
, c
11
y
114
− 44y
113
+ ··· − 7420008525078y + 164384026249
c
6
, c
9
y
114
+ 49y
113
+ ··· + 72527526349296y + 79494110809
c
7
, c
12
(y
3
+ 3y
2
+ 2y − 1)
38
c
8
(y
19
− 3y
18
+ ··· + 37y − 4)
6
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.785473 + 0.623414I
a = −0.511848 + 1.282950I
b = −0.350637 − 1.049250I
7.35534 + 0.92615I 5.13397 − 1.59952I
u = −0.785473 + 0.623414I
a = −0.518209 + 0.033169I
b = 0.68395 + 1.43194I
3.21776 − 1.90197I −1.39530 + 1.37993I
u = −0.785473 + 0.623414I
a = 1.44594 − 0.81966I
b = −0.71432 − 2.33279I
7.35534 − 4.73010I 5.13397 + 4.35937I
u = −0.785473 + 0.623414I
a = 1.96666 + 0.79464I
b = 0.083353 − 0.756518I
3.21776 − 1.90197I −1.39530 + 1.37993I
u = −0.785473 + 0.623414I
a = −1.98860 − 0.81593I
b = −1.20770 + 1.02129I
7.35534 + 0.92615I 5.13397 − 1.59952I
u = −0.785473 + 0.623414I
a = −2.31273 − 1.57179I
b = 0.488890 + 0.790589I
7.35534 − 4.73010I 5.13397 + 4.35937I
u = −0.785473 − 0.623414I
a = −0.511848 − 1.282950I
b = −0.350637 + 1.049250I
7.35534 − 0.92615I 5.13397 + 1.59952I
u = −0.785473 − 0.623414I
a = −0.518209 − 0.033169I
b = 0.68395 − 1.43194I
3.21776 + 1.90197I −1.39530 − 1.37993I
u = −0.785473 − 0.623414I
a = 1.44594 + 0.81966I
b = −0.71432 + 2.33279I
7.35534 + 4.73010I 5.13397 − 4.35937I
u = −0.785473 − 0.623414I
a = 1.96666 − 0.79464I
b = 0.083353 + 0.756518I
3.21776 + 1.90197I −1.39530 − 1.37993I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.785473 − 0.623414I
a = −1.98860 + 0.81593I
b = −1.20770 − 1.02129I
7.35534 − 0.92615I 5.13397 + 1.59952I
u = −0.785473 − 0.623414I
a = −2.31273 + 1.57179I
b = 0.488890 − 0.790589I
7.35534 + 4.73010I 5.13397 − 4.35937I
u = 0.511993 + 0.911621I
a = −0.255017 + 0.352927I
b = 0.89652 − 1.94808I
8.93377 + 5.15755I 6.90979 − 5.98553I
u = 0.511993 + 0.911621I
a = −0.299289 − 0.269832I
b = 0.72070 + 1.35949I
8.93377 − 0.49870I 6.90979 − 0.02664I
u = 0.511993 + 0.911621I
a = 0.218890 − 0.113013I
b = −0.60821 + 1.30701I
4.79618 + 2.32942I 0.38053 − 3.00608I
u = 0.511993 + 0.911621I
a = −0.227565 − 0.090930I
b = 0.171922 − 1.138140I
8.93377 − 0.49870I 6.90979 − 0.02664I
u = 0.511993 + 0.911621I
a = −0.186498 + 0.108363I
b = −0.533182 + 1.103240I
8.93377 + 5.15755I 6.90979 − 5.98553I
u = 0.511993 + 0.911621I
a = 0.197663 + 0.069769I
b = 0.067943 − 1.038820I
4.79618 + 2.32942I 0.38053 − 3.00608I
u = 0.511993 − 0.911621I
a = −0.255017 − 0.352927I
b = 0.89652 + 1.94808I
8.93377 − 5.15755I 6.90979 + 5.98553I
u = 0.511993 − 0.911621I
a = −0.299289 + 0.269832I
b = 0.72070 − 1.35949I
8.93377 + 0.49870I 6.90979 + 0.02664I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.511993 − 0.911621I
a = 0.218890 + 0.113013I
b = −0.60821 − 1.30701I
4.79618 − 2.32942I 0.38053 + 3.00608I
u = 0.511993 − 0.911621I
a = −0.227565 + 0.090930I
b = 0.171922 + 1.138140I
8.93377 + 0.49870I 6.90979 + 0.02664I
u = 0.511993 − 0.911621I
a = −0.186498 − 0.108363I
b = −0.533182 − 1.103240I
8.93377 − 5.15755I 6.90979 + 5.98553I
u = 0.511993 − 0.911621I
a = 0.197663 − 0.069769I
b = 0.067943 + 1.038820I
4.79618 − 2.32942I 0.38053 + 3.00608I
u = 0.835893 + 0.695746I
a = −0.126267 − 0.911046I
b = 0.88517 − 1.23416I
7.61932 − 5.49434I 5.09594 + 6.18824I
u = 0.835893 + 0.695746I
a = 1.237340 − 0.538780I
b = 0.166261 + 0.646039I
3.48174 − 2.66622I −1.43332 + 3.20879I
u = 0.835893 + 0.695746I
a = −1.40501 + 0.63403I
b = −1.116560 − 0.839803I
7.61932 + 0.16190I 5.09594 + 0.22934I
u = 0.835893 + 0.695746I
a = 0.70613 + 1.46954I
b = −0.457930 − 0.892431I
7.61932 + 0.16190I 5.09594 + 0.22934I
u = 0.835893 + 0.695746I
a = 0.004965 − 0.216359I
b = −0.114268 + 0.888372I
3.48174 − 2.66622I −1.43332 + 3.20879I
u = 0.835893 + 0.695746I
a = −2.06286 + 0.56296I
b = 0.568450 − 0.600680I
7.61932 − 5.49434I 5.09594 + 6.18824I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.835893 − 0.695746I
a = −0.126267 + 0.911046I
b = 0.88517 + 1.23416I
7.61932 + 5.49434I 5.09594 − 6.18824I
u = 0.835893 − 0.695746I
a = 1.237340 + 0.538780I
b = 0.166261 − 0.646039I
3.48174 + 2.66622I −1.43332 − 3.20879I
u = 0.835893 − 0.695746I
a = −1.40501 − 0.63403I
b = −1.116560 + 0.839803I
7.61932 − 0.16190I 5.09594 − 0.22934I
u = 0.835893 − 0.695746I
a = 0.70613 − 1.46954I
b = −0.457930 + 0.892431I
7.61932 − 0.16190I 5.09594 − 0.22934I
u = 0.835893 − 0.695746I
a = 0.004965 + 0.216359I
b = −0.114268 − 0.888372I
3.48174 + 2.66622I −1.43332 − 3.20879I
u = 0.835893 − 0.695746I
a = −2.06286 − 0.56296I
b = 0.568450 + 0.600680I
7.61932 + 5.49434I 5.09594 − 6.18824I
u = −0.902262 + 0.616698I
a = 0.045341 + 0.965489I
b = 1.06244 + 1.38651I
6.99198 + 3.94763I 3.41736 − 5.91144I
u = −0.902262 + 0.616698I
a = −0.031199 + 0.889282I
b = −0.007497 − 0.998655I
2.85440 + 6.77576I −3.11191 − 8.89089I
u = −0.902262 + 0.616698I
a = −2.14735 − 0.80705I
b = −0.93486 + 1.41456I
2.85440 + 6.77576I −3.11191 − 8.89089I
u = −0.902262 + 0.616698I
a = −0.19218 − 2.46617I
b = −0.466864 + 0.970117I
6.99198 + 9.60388I 3.41736 − 11.87034I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.902262 + 0.616698I
a = 2.64330 + 0.22094I
b = 1.15184 − 2.38340I
6.99198 + 9.60388I 3.41736 − 11.87034I
u = −0.902262 + 0.616698I
a = 2.56805 + 1.08857I
b = 0.443301 − 0.940087I
6.99198 + 3.94763I 3.41736 − 5.91144I
u = −0.902262 − 0.616698I
a = 0.045341 − 0.965489I
b = 1.06244 − 1.38651I
6.99198 − 3.94763I 3.41736 + 5.91144I
u = −0.902262 − 0.616698I
a = −0.031199 − 0.889282I
b = −0.007497 + 0.998655I
2.85440 − 6.77576I −3.11191 + 8.89089I
u = −0.902262 − 0.616698I
a = −2.14735 + 0.80705I
b = −0.93486 − 1.41456I
2.85440 − 6.77576I −3.11191 + 8.89089I
u = −0.902262 − 0.616698I
a = −0.19218 + 2.46617I
b = −0.466864 − 0.970117I
6.99198 − 9.60388I 3.41736 + 11.87034I
u = −0.902262 − 0.616698I
a = 2.64330 − 0.22094I
b = 1.15184 + 2.38340I
6.99198 − 9.60388I 3.41736 + 11.87034I
u = −0.902262 − 0.616698I
a = 2.56805 − 1.08857I
b = 0.443301 + 0.940087I
6.99198 − 3.94763I 3.41736 + 5.91144I
u = −1.114790 + 0.217503I
a = 1.027330 + 0.418259I
b = 0.549935 + 0.398240I
0.82629 + 2.06681I −9.98843 + 4.07433I
u = −1.114790 + 0.217503I
a = −0.607679 − 1.202920I
b = −0.473762 − 0.587754I
−3.31130 − 0.76131I −16.5177 + 7.0538I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.114790 + 0.217503I
a = 1.44360 + 0.08135I
b = 1.064160 − 0.834405I
−3.31130 − 0.76131I −16.5177 + 7.0538I
u = −1.114790 + 0.217503I
a = 0.20497 + 1.68305I
b = 0.169569 + 0.707717I
0.82629 − 3.58943I −9.9884 + 10.0332I
u = −1.114790 + 0.217503I
a = −0.89228 + 1.71023I
b = 0.16710 + 1.83738I
0.82629 + 2.06681I −9.98843 + 4.07433I
u = −1.114790 + 0.217503I
a = −2.28329 − 1.20421I
b = −2.25911 + 0.36278I
0.82629 − 3.58943I −9.9884 + 10.0332I
u = −1.114790 − 0.217503I
a = 1.027330 − 0.418259I
b = 0.549935 − 0.398240I
0.82629 − 2.06681I −9.98843 − 4.07433I
u = −1.114790 − 0.217503I
a = −0.607679 + 1.202920I
b = −0.473762 + 0.587754I
−3.31130 + 0.76131I −16.5177 − 7.0538I
u = −1.114790 − 0.217503I
a = 1.44360 − 0.08135I
b = 1.064160 + 0.834405I
−3.31130 + 0.76131I −16.5177 − 7.0538I
u = −1.114790 − 0.217503I
a = 0.20497 − 1.68305I
b = 0.169569 − 0.707717I
0.82629 + 3.58943I −9.9884 − 10.0332I
u = −1.114790 − 0.217503I
a = −0.89228 − 1.71023I
b = 0.16710 − 1.83738I
0.82629 − 2.06681I −9.98843 − 4.07433I
u = −1.114790 − 0.217503I
a = −2.28329 + 1.20421I
b = −2.25911 − 0.36278I
0.82629 + 3.58943I −9.9884 − 10.0332I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.036120 + 0.567146I
a = 1.01651 − 1.00032I
b = 1.55710 − 0.11758I
−1.05947 − 7.59815I −12.5535 + 8.9537I
u = 1.036120 + 0.567146I
a = 0.453618 − 0.242785I
b = −0.158539 + 0.631295I
3.07811 − 4.77002I −6.02421 + 5.97424I
u = 1.036120 + 0.567146I
a = 1.54095 + 0.16723I
b = 0.254730 + 1.390570I
3.07811 − 4.77002I −6.02421 + 5.97424I
u = 1.036120 + 0.567146I
a = −2.04587 + 0.19150I
b = −0.747009 − 0.934186I
−1.05947 − 7.59815I −12.5535 + 8.9537I
u = 1.036120 + 0.567146I
a = 2.41243 + 0.36476I
b = 0.554917 + 0.941574I
3.07811 − 10.42630I −6.02421 + 11.93313I
u = 1.036120 + 0.567146I
a = −2.01404 + 1.59108I
b = −2.53434 − 0.51839I
3.07811 − 10.42630I −6.00000 + 11.93313I
u = 1.036120 − 0.567146I
a = 1.01651 + 1.00032I
b = 1.55710 + 0.11758I
−1.05947 + 7.59815I −12.5535 − 8.9537I
u = 1.036120 − 0.567146I
a = 0.453618 + 0.242785I
b = −0.158539 − 0.631295I
3.07811 + 4.77002I −6.02421 − 5.97424I
u = 1.036120 − 0.567146I
a = 1.54095 − 0.16723I
b = 0.254730 − 1.390570I
3.07811 + 4.77002I −6.02421 − 5.97424I
u = 1.036120 − 0.567146I
a = −2.04587 − 0.19150I
b = −0.747009 + 0.934186I
−1.05947 + 7.59815I −12.5535 − 8.9537I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.036120 − 0.567146I
a = 2.41243 − 0.36476I
b = 0.554917 − 0.941574I
3.07811 + 10.42630I −6.02421 − 11.93313I
u = 1.036120 − 0.567146I
a = −2.01404 − 1.59108I
b = −2.53434 + 0.51839I
3.07811 + 10.42630I −6.00000 − 11.93313I
u = −1.27340
a = 0.472652 + 0.998672I
b = 0.213480 + 0.705953I
2.29241 − 2.82812I 10.62384 + 2.97945I
u = −1.27340
a = 0.472652 − 0.998672I
b = 0.213480 − 0.705953I
2.29241 + 2.82812I 10.62384 − 2.97945I
u = −1.27340
a = 0.357688 + 0.621119I
b = 0.487641 + 0.545529I
−1.84518 4.09457 + 0.I
u = −1.27340
a = 0.357688 − 0.621119I
b = 0.487641 − 0.545529I
−1.84518 4.09457 + 0.I
u = −1.27340
a = −1.30418 + 1.70456I
b = −1.34711 + 1.66829I
2.29241 + 2.82812I 10.62384 − 2.97945I
u = −1.27340
a = −1.30418 − 1.70456I
b = −1.34711 − 1.66829I
2.29241 − 2.82812I 10.62384 + 2.97945I
u = 0.628447 + 0.282749I
a = 0.795222 + 0.001765I
b = 0.489252 − 1.046720I
0.62365 + 3.26203I −10.84809 − 4.58696I
u = 0.628447 + 0.282749I
a = 1.39735 − 0.50505I
b = 0.09386 + 1.41761I
4.76123 + 0.43391I −4.31882 − 1.60751I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.628447 + 0.282749I
a = −2.36179 + 0.49215I
b = −0.561481 + 1.188560I
4.76123 + 6.09015I −4.31882 − 7.56641I
u = 0.628447 + 0.282749I
a = −0.56721 + 2.47674I
b = −1.042360 + 0.546394I
0.62365 + 3.26203I −10.84809 − 4.58696I
u = 0.628447 + 0.282749I
a = 0.78323 − 2.60085I
b = 0.055365 − 0.290282I
4.76123 + 0.43391I −4.31882 − 1.60751I
u = 0.628447 + 0.282749I
a = −0.34886 − 3.14808I
b = 1.69808 − 1.15277I
4.76123 + 6.09015I −4.31882 − 7.56641I
u = 0.628447 − 0.282749I
a = 0.795222 − 0.001765I
b = 0.489252 + 1.046720I
0.62365 − 3.26203I −10.84809 + 4.58696I
u = 0.628447 − 0.282749I
a = 1.39735 + 0.50505I
b = 0.09386 − 1.41761I
4.76123 − 0.43391I −4.31882 + 1.60751I
u = 0.628447 − 0.282749I
a = −2.36179 − 0.49215I
b = −0.561481 − 1.188560I
4.76123 − 6.09015I −4.31882 + 7.56641I
u = 0.628447 − 0.282749I
a = −0.56721 − 2.47674I
b = −1.042360 − 0.546394I
0.62365 − 3.26203I −10.84809 + 4.58696I
u = 0.628447 − 0.282749I
a = 0.78323 + 2.60085I
b = 0.055365 + 0.290282I
4.76123 − 0.43391I −4.31882 + 1.60751I
u = 0.628447 − 0.282749I
a = −0.34886 + 3.14808I
b = 1.69808 + 1.15277I
4.76123 − 6.09015I −4.31882 + 7.56641I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.116220 + 0.690124I
a = −1.160590 − 0.166242I
b = −0.476263 − 1.118100I
7.09153 − 5.39210I 3.37762 + 5.59055I
u = 1.116220 + 0.690124I
a = −1.358910 − 0.144699I
b = −0.290166 − 0.979475I
2.95395 − 8.22022I −3.15165 + 8.57000I
u = 1.116220 + 0.690124I
a = 1.16484 + 0.92477I
b = −0.565243 + 1.113750I
7.09153 − 5.39210I 3.37762 + 5.59055I
u = 1.116220 + 0.690124I
a = 1.65757 − 0.11395I
b = 0.745934 + 1.053680I
7.09153 − 11.04830I 3.37762 + 11.54944I
u = 1.116220 + 0.690124I
a = 1.67874 − 0.23637I
b = 0.80907 + 1.42372I
2.95395 − 8.22022I −3.15165 + 8.57000I
u = 1.116220 + 0.690124I
a = −2.40534 + 0.24130I
b = −0.91074 − 2.08208I
7.09153 − 11.04830I 3.37762 + 11.54944I
u = 1.116220 − 0.690124I
a = −1.160590 + 0.166242I
b = −0.476263 + 1.118100I
7.09153 + 5.39210I 3.37762 − 5.59055I
u = 1.116220 − 0.690124I
a = −1.358910 + 0.144699I
b = −0.290166 + 0.979475I
2.95395 + 8.22022I −3.15165 − 8.57000I
u = 1.116220 − 0.690124I
a = 1.16484 − 0.92477I
b = −0.565243 − 1.113750I
7.09153 + 5.39210I 3.37762 − 5.59055I
u = 1.116220 − 0.690124I
a = 1.65757 + 0.11395I
b = 0.745934 − 1.053680I
7.09153 + 11.04830I 3.37762 − 11.54944I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.116220 − 0.690124I
a = 1.67874 + 0.23637I
b = 0.80907 − 1.42372I
2.95395 + 8.22022I −3.15165 − 8.57000I
u = 1.116220 − 0.690124I
a = −2.40534 − 0.24130I
b = −0.91074 + 2.08208I
7.09153 + 11.04830I 3.37762 − 11.54944I
u = 0.310562 + 0.497043I
a = 0.714476 − 1.044850I
b = −0.123456 + 1.404190I
4.77699 + 0.32096I −2.07247 − 0.81483I
u = 0.310562 + 0.497043I
a = −1.07957 + 1.00521I
b = −0.384227 + 1.149880I
4.77699 + 5.97721I −2.07247 − 6.77372I
u = 0.310562 + 0.497043I
a = 0.414948 − 0.164291I
b = 0.508974 − 0.961231I
0.63941 + 3.14909I −8.60173 − 3.79428I
u = 0.310562 + 0.497043I
a = −0.48891 − 1.57968I
b = −0.254807 + 0.067957I
4.77699 + 0.32096I −2.07247 − 0.81483I
u = 0.310562 + 0.497043I
a = 0.58626 + 1.57229I
b = −0.944697 + 0.064604I
0.63941 + 3.14909I −8.60173 − 3.79428I
u = 0.310562 + 0.497043I
a = −1.47351 − 1.65389I
b = 1.77543 − 0.53762I
4.77699 + 5.97721I −2.07247 − 6.77372I
u = 0.310562 − 0.497043I
a = 0.714476 + 1.044850I
b = −0.123456 − 1.404190I
4.77699 − 0.32096I −2.07247 + 0.81483I
u = 0.310562 − 0.497043I
a = −1.07957 − 1.00521I
b = −0.384227 − 1.149880I
4.77699 − 5.97721I −2.07247 + 6.77372I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.310562 − 0.497043I
a = 0.414948 + 0.164291I
b = 0.508974 + 0.961231I
0.63941 − 3.14909I −8.60173 + 3.79428I
u = 0.310562 − 0.497043I
a = −0.48891 + 1.57968I
b = −0.254807 − 0.067957I
4.77699 − 0.32096I −2.07247 + 0.81483I
u = 0.310562 − 0.497043I
a = 0.58626 − 1.57229I
b = −0.944697 − 0.064604I
0.63941 − 3.14909I −8.60173 + 3.79428I
u = 0.310562 − 0.497043I
a = −1.47351 + 1.65389I
b = 1.77543 + 0.53762I
4.77699 − 5.97721I −2.07247 + 6.77372I
25
III.
I
u
3
= h−2.93 × 10
8
u
36
+ 1.80 × 10
9
u
35
+ · · · + 8.74 × 10
6
b + 1.34 × 10
9
, −5.45 ×
10
8
u
36
+3.32×10
9
u
35
+· · ·+1.46×10
7
a+2.22×10
9
, u
37
−7u
36
+· · ·−27u+5i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
37.4040u
36
− 228.129u
35
+ ··· + 764.974u − 152.498
33.5011u
36
− 206.596u
35
+ ··· + 740.373u − 153.163
a
7
=
36.1521u
36
− 219.407u
35
+ ··· + 748.292u − 156.108
28.5619u
36
− 177.132u
35
+ ··· + 663.711u − 143.877
a
11
=
3.90295u
36
− 21.5330u
35
+ ··· + 24.6010u + 0.665081
33.5011u
36
− 206.596u
35
+ ··· + 740.373u − 153.163
a
1
=
u
3
u
5
− u
3
+ u
a
9
=
24.8450u
36
− 146.506u
35
+ ··· + 388.640u − 67.1933
27.9413u
36
− 177.674u
35
+ ··· + 721.848u − 156.557
a
8
=
11.7379u
36
− 65.7586u
35
+ ··· + 115.843u − 13.0139
−8.14190u
36
+ 55.4654u
35
+ ··· − 322.793u + 82.2197
a
4
=
−6.36985u
36
+ 50.3342u
35
+ ··· − 348.019u + 87.8351
8.30698u
36
− 36.5225u
35
+ ··· − 89.9891u + 38.1837
a
12
=
−35.9768u
36
+ 211.706u
35
+ ··· − 583.534u + 107.249
−21.4200u
36
+ 127.666u
35
+ ··· − 363.918u + 65.6570
(ii) Obstruction class = 1
(iii) Cusp Shapes =
87458410
8736867
u
36
−
887104937
8736867
u
35
+ ··· +
7705602655
8736867
u −
1868276791
8736867
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
37
− 19u
36
+ ··· + 79u − 25
c
2
u
37
+ 7u
36
+ ··· − 27u − 5
c
3
, c
10
u
37
+ 11u
35
+ ··· + 36u − 5
c
4
, c
11
u
37
− u
36
+ ··· + 6u − 1
c
5
u
37
− 7u
36
+ ··· − 27u + 5
c
6
, c
9
u
37
− u
36
+ ··· + 6u − 1
c
7
u
37
+ 3u
36
+ ··· − 8u − 1
c
8
u
37
+ 20u
36
+ ··· − 171u − 27
c
12
u
37
− 3u
36
+ ··· − 8u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 9y
36
+ ··· + 7691y − 625
c
2
, c
5
y
37
− 19y
36
+ ··· + 79y − 25
c
3
, c
10
y
37
+ 22y
36
+ ··· + 136y − 25
c
4
, c
11
y
37
− 17y
36
+ ··· + 36y − 1
c
6
, c
9
y
37
+ 15y
36
+ ··· − 46y − 1
c
7
, c
12
y
37
+ 35y
36
+ ··· − 48y − 1
c
8
y
37
− 2y
36
+ ··· − 26325y − 729
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.333646 + 0.939120I
a = −0.193011 + 0.172477I
b = −0.077533 − 1.147930I
7.09762 − 0.58324I 0.509552 − 0.585068I
u = 0.333646 − 0.939120I
a = −0.193011 − 0.172477I
b = −0.077533 + 1.147930I
7.09762 + 0.58324I 0.509552 + 0.585068I
u = 0.533649 + 0.867204I
a = −0.0765239 − 0.0499298I
b = −0.67640 + 1.32667I
7.99073 + 4.59338I −1.20106 − 1.22376I
u = 0.533649 − 0.867204I
a = −0.0765239 + 0.0499298I
b = −0.67640 − 1.32667I
7.99073 − 4.59338I −1.20106 + 1.22376I
u = 0.792978 + 0.640101I
a = 0.919478 − 0.731739I
b = 0.388945 − 0.532935I
6.62005 − 2.14265I 2.01818 + 2.23582I
u = 0.792978 − 0.640101I
a = 0.919478 + 0.731739I
b = 0.388945 + 0.532935I
6.62005 + 2.14265I 2.01818 − 2.23582I
u = −0.846359 + 0.590769I
a = −1.26327 − 1.40969I
b = −0.68500 + 1.46478I
6.24914 + 8.49563I −1.47230 − 6.14964I
u = −0.846359 − 0.590769I
a = −1.26327 + 1.40969I
b = −0.68500 − 1.46478I
6.24914 − 8.49563I −1.47230 + 6.14964I
u = 0.976057 + 0.444673I
a = 1.75420 + 0.64768I
b = 1.09532 + 1.06092I
4.66818 − 8.69558I −2.35287 + 8.33858I
u = 0.976057 − 0.444673I
a = 1.75420 − 0.64768I
b = 1.09532 − 1.06092I
4.66818 + 8.69558I −2.35287 − 8.33858I
29
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.924863
a = −1.59939
b = −0.343954
−3.12809 −16.5560
u = −0.876737 + 0.629562I
a = −1.42305 + 0.01677I
b = 0.511199 + 1.259150I
6.14382 − 3.70973I −1.48512 + 0.82345I
u = −0.876737 − 0.629562I
a = −1.42305 − 0.01677I
b = 0.511199 − 1.259150I
6.14382 + 3.70973I −1.48512 − 0.82345I
u = 0.794699 + 0.434990I
a = −1.00134 + 1.93012I
b = −1.09272 + 1.33698I
5.31149 + 5.06761I −0.913647 − 0.036371I
u = 0.794699 − 0.434990I
a = −1.00134 − 1.93012I
b = −1.09272 − 1.33698I
5.31149 − 5.06761I −0.913647 + 0.036371I
u = 0.895946 + 0.681544I
a = −1.091620 − 0.248953I
b = −0.241094 − 0.184490I
6.29186 − 2.99378I 1.92058 + 3.39875I
u = 0.895946 − 0.681544I
a = −1.091620 + 0.248953I
b = −0.241094 + 0.184490I
6.29186 + 2.99378I 1.92058 − 3.39875I
u = −0.664550 + 0.523833I
a = 0.99217 + 1.45300I
b = 0.194593 − 1.101430I
5.75436 + 0.06331I 3.31684 − 1.50030I
u = −0.664550 − 0.523833I
a = 0.99217 − 1.45300I
b = 0.194593 + 1.101430I
5.75436 − 0.06331I 3.31684 + 1.50030I
u = 1.027800 + 0.577230I
a = −1.68851 + 0.31959I
b = −1.057550 − 0.628416I
0.09678 − 7.56844I −3.66485 + 8.77182I
30
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.027800 − 0.577230I
a = −1.68851 − 0.31959I
b = −1.057550 + 0.628416I
0.09678 + 7.56844I −3.66485 − 8.77182I
u = −1.182280 + 0.004770I
a = 1.01586 − 1.23420I
b = 0.675453 − 0.845846I
1.69419 + 2.82666I −6.95917 − 2.95818I
u = −1.182280 − 0.004770I
a = 1.01586 + 1.23420I
b = 0.675453 + 0.845846I
1.69419 − 2.82666I −6.95917 + 2.95818I
u = −1.199150 + 0.208838I
a = −0.563970 − 0.686176I
b = −0.680833 − 0.201738I
−2.29418 − 0.52722I −6.96195 + 8.29555I
u = −1.199150 − 0.208838I
a = −0.563970 + 0.686176I
b = −0.680833 + 0.201738I
−2.29418 + 0.52722I −6.96195 − 8.29555I
u = 0.609931 + 0.471460I
a = 0.597543 − 1.084170I
b = 0.811091 − 0.876518I
1.49381 + 3.08924I 0.17374 − 3.08731I
u = 0.609931 − 0.471460I
a = 0.597543 + 1.084170I
b = 0.811091 + 0.876518I
1.49381 − 3.08924I 0.17374 + 3.08731I
u = −1.018500 + 0.695071I
a = 0.923604 + 0.232404I
b = 0.087588 − 1.181260I
4.42866 + 4.86200I 2.55162 − 5.76187I
u = −1.018500 − 0.695071I
a = 0.923604 − 0.232404I
b = 0.087588 + 1.181260I
4.42866 − 4.86200I 2.55162 + 5.76187I
u = 1.094260 + 0.679352I
a = 1.98156 − 0.24227I
b = 0.84829 + 1.35968I
6.28716 − 10.33440I −6.00000 + 5.49342I
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.094260 − 0.679352I
a = 1.98156 + 0.24227I
b = 0.84829 − 1.35968I
6.28716 + 10.33440I −6.00000 − 5.49342I
u = 1.205990 + 0.732966I
a = −0.961555 − 0.187301I
b = −0.145823 − 1.137790I
4.49469 − 5.60603I 0
u = 1.205990 − 0.732966I
a = −0.961555 + 0.187301I
b = −0.145823 + 1.137790I
4.49469 + 5.60603I 0
u = 1.43625 + 0.16212I
a = −0.280153 − 0.406304I
b = −0.316656 − 0.764632I
−3.34090 − 5.49283I 0
u = 1.43625 − 0.16212I
a = −0.280153 + 0.406304I
b = −0.316656 + 0.764632I
−3.34090 + 5.49283I 0
u = 0.048816 + 0.512315I
a = −1.041720 − 0.364275I
b = 0.533101 − 0.653832I
1.66380 + 3.38344I 1.32925 − 5.64517I
u = 0.048816 − 0.512315I
a = −1.041720 + 0.364275I
b = 0.533101 + 0.653832I
1.66380 − 3.38344I 1.32925 + 5.64517I
32
IV.
I
u
4
= ha
5
+ a
4
− 3a
3
+ 3a
2
+ 45b − 27a − 18, a
6
− 3a
5
+ 3a
4
− 9a
2
+ 27, u + 1i
(i) Arc colorings
a
2
=
0
−1
a
5
=
1
0
a
6
=
1
1
a
3
=
1
0
a
10
=
a
−
1
45
a
5
−
1
45
a
4
+ ··· +
3
5
a +
2
5
a
7
=
−
4
45
a
5
+
2
15
a
4
+ ··· +
2
5
a +
8
5
−
1
3
a
2
+ 1
a
11
=
1
45
a
5
+
1
45
a
4
+ ··· +
2
5
a −
2
5
−
1
45
a
5
−
1
45
a
4
+ ··· +
3
5
a +
2
5
a
1
=
−1
−1
a
9
=
−
1
45
a
5
−
1
45
a
4
+ ··· +
3
5
a +
2
5
−
2
45
a
5
−
2
45
a
4
+ ··· +
1
5
a +
4
5
a
8
=
−
1
45
a
5
−
1
45
a
4
+ ··· +
3
5
a +
2
5
−
2
45
a
5
−
2
45
a
4
+ ··· +
1
5
a +
4
5
a
4
=
−
4
45
a
5
+
2
15
a
4
+ ··· +
2
5
a +
8
5
−
1
3
a
2
a
12
=
−
2
45
a
5
+
1
15
a
4
+ ··· +
6
5
a +
4
5
1
45
a
5
−
4
45
a
4
+ ··· +
2
5
a −
2
5
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4
45
a
5
+
4
45
a
4
−
4
15
a
3
+
4
15
a
2
+
8
5
a −
53
5
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
4
, c
10
c
11
u
6
+ u
5
+ u
4
+ 2u
3
+ u
2
+ 1
c
5
(u + 1)
6
c
6
, c
9
(u
3
+ u
2
− 1)
2
c
7
(u
3
− u
2
+ 2u − 1)
2
c
8
u
6
c
12
(u
3
+ u
2
+ 2u + 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
6
c
3
, c
4
, c
10
c
11
y
6
+ y
5
− y
4
+ 3y
2
+ 2y + 1
c
6
, c
9
(y
3
− y
2
+ 2y − 1)
2
c
7
, c
12
(y
3
+ 3y
2
+ 2y − 1)
2
c
8
y
6
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.132320 + 0.653743I
b = −0.377439 + 0.653743I
−2.75839 −12.01951 + 0.I
u = −1.00000
a = −1.132320 − 0.653743I
b = −0.377439 − 0.653743I
−2.75839 −12.01951 + 0.I
u = −1.00000
a = 1.96123 + 0.35741I
b = 1.083790 − 0.387453I
1.37919 − 2.82812I −5.49024 + 2.97945I
u = −1.00000
a = 1.96123 − 0.35741I
b = 1.083790 + 0.387453I
1.37919 + 2.82812I −5.49024 − 2.97945I
u = −1.00000
a = 0.67109 + 1.87718I
b = −0.206350 + 1.132320I
1.37919 − 2.82812I −5.49024 + 2.97945I
u = −1.00000
a = 0.67109 − 1.87718I
b = −0.206350 − 1.132320I
1.37919 + 2.82812I −5.49024 − 2.97945I
36
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
19
+ 8u
18
+ ··· + 4u + 1)
6
(u
37
− 19u
36
+ ··· + 79u − 25)
· (u
58
+ 26u
57
+ ··· + 83456u + 4096)
c
2
((u − 1)
6
)(u
19
− 2u
18
+ ··· − 4u + 1)
6
(u
37
+ 7u
36
+ ··· − 27u − 5)
· (u
58
+ 14u
57
+ ··· − 928u − 64)
c
3
, c
10
(u
6
+ u
5
+ u
4
+ 2u
3
+ u
2
+ 1)(u
37
+ 11u
35
+ ··· + 36u − 5)
· (u
58
+ 17u
56
+ ··· + 461u − 77)
· (u
114
− 2u
113
+ ··· − 4054780664u + 1331355377)
c
4
, c
11
(u
6
+ u
5
+ u
4
+ 2u
3
+ u
2
+ 1)(u
37
− u
36
+ ··· + 6u − 1)
· (u
58
− u
57
+ ··· + u + 1)(u
114
− 4u
113
+ ··· − 2666478u + 405443)
c
5
((u + 1)
6
)(u
19
− 2u
18
+ ··· − 4u + 1)
6
(u
37
− 7u
36
+ ··· − 27u + 5)
· (u
58
+ 14u
57
+ ··· − 928u − 64)
c
6
, c
9
((u
3
+ u
2
− 1)
2
)(u
37
− u
36
+ ··· + 6u − 1)(u
58
− u
57
+ ··· + 17u − 1)
· (u
114
+ 3u
113
+ ··· + 3197956u + 281947)
c
7
((u
3
− u
2
+ 2u − 1)
40
)(u
37
+ 3u
36
+ ··· − 8u − 1)
· (u
58
+ 40u
57
+ ··· − 7340032u − 262144)
c
8
u
6
(u
19
− 9u
18
+ ··· − u + 2)
6
(u
37
+ 20u
36
+ ··· − 171u − 27)
· (u
58
+ 45u
57
+ ··· + 80u + 8)
c
12
((u
3
− u
2
+ 2u − 1)
38
)(u
3
+ u
2
+ 2u + 1)
2
(u
37
− 3u
36
+ ··· − 8u + 1)
· (u
58
+ 40u
57
+ ··· − 7340032u − 262144)
37
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
19
+ 8y
18
+ ··· − 16y − 1)
6
· (y
37
+ 9y
36
+ ··· + 7691y − 625)
· (y
58
+ 18y
57
+ ··· + 5636096y + 16777216)
c
2
, c
5
((y − 1)
6
)(y
19
− 8y
18
+ ··· + 4y − 1)
6
(y
37
− 19y
36
+ ··· + 79y − 25)
· (y
58
− 26y
57
+ ··· − 83456y + 4096)
c
3
, c
10
(y
6
+ y
5
− y
4
+ 3y
2
+ 2y + 1)(y
37
+ 22y
36
+ ··· + 136y − 25)
· (y
58
+ 34y
57
+ ··· − 273813y + 5929)
· (y
114
+ 64y
113
+ ··· + 6.82 × 10
19
y + 1.77 × 10
18
)
c
4
, c
11
(y
6
+ y
5
− y
4
+ 3y
2
+ 2y + 1)(y
37
− 17y
36
+ ··· + 36y − 1)
· (y
58
− 5y
57
+ ··· − 9y + 1)
· (y
114
− 44y
113
+ ··· − 7420008525078y + 164384026249)
c
6
, c
9
((y
3
− y
2
+ 2y − 1)
2
)(y
37
+ 15y
36
+ ··· − 46y − 1)
· (y
58
+ 11y
57
+ ··· − 211y + 1)
· (y
114
+ 49y
113
+ ··· + 72527526349296y + 79494110809)
c
7
, c
12
((y
3
+ 3y
2
+ 2y − 1)
40
)(y
37
+ 35y
36
+ ··· − 48y − 1)
· (y
58
+ 38y
57
+ ··· − 1030792151040y + 68719476736)
c
8
y
6
(y
19
− 3y
18
+ ··· + 37y − 4)
6
(y
37
− 2y
36
+ ··· − 26325y − 729)
· (y
58
− 5y
57
+ ··· + 1760y + 64)
38
