12n
0637
(K12n
0637
)
A knot diagram
1
Linearized knot diagam
3 8 9 11 10 9 5 2 12 8 7 6
Solving Sequence
8,10 5,11
4 7 12 9 3 2 1 6
c
10
c
4
c
7
c
11
c
9
c
3
c
2
c
1
c
6
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
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).
1
I
u
1
= h−35223725986u
21
+ 30523664755u
20
+ ··· + 210473051795b + 25821213245,
740868672496u
21
− 766689885741u
20
+ ··· + 210473051795a − 869880690251,
u
22
− u
21
+ ··· − u + 1i
I
u
2
= h3.78529 × 10
20
u
19
− 4.63105 × 10
20
u
18
+ ··· + 8.62031 × 10
21
b − 2.24738 × 10
21
,
2.73069 × 10
22
u
19
− 2.50595 × 10
22
u
18
+ ··· + 8.62031 × 10
21
a − 1.80097 × 10
23
, u
20
− u
19
+ ··· − 7u + 1i
I
u
3
= h−3.35706 × 10
35
u
33
− 7.63609 × 10
35
u
32
+ ··· + 5.24183 × 10
36
b − 4.09915 × 10
36
,
1.95717 × 10
37
u
33
+ 4.09915 × 10
36
u
32
+ ··· + 5.24183 × 10
36
a − 6.08409 × 10
37
, u
34
− 9u
32
+ ··· − 5u + 1i
I
u
4
= h16685766983482u
15
+ 6555188230121u
14
+ ··· + 453436720809281b + 250672039562051,
− 35828884147u
15
− 26710704549u
14
+ ··· + 766837175819a + 930772601969,
u
16
− u
15
+ ··· − 20u + 13i
I
u
5
= h3.61106 × 10
67
u
31
+ 1.33112 × 10
67
u
30
+ ··· + 5.05264 × 10
70
b − 7.80220 × 10
69
,
− 2.81341 × 10
59
u
31
− 1.32370 × 10
59
u
30
+ ··· + 1.01984 × 10
63
a + 2.59788 × 10
62
,
u
32
+ u
31
+ ··· − 1290u + 1501i
I
u
6
= hb − u, a, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
7
= h11u
7
+ 19u
6
+ 58u
5
+ 65u
4
− 6u
3
− 34u
2
+ 2b + 9u − 28, u
7
+ u
6
+ 4u
5
+ 2u
4
− 5u
3
− 3u
2
+ 2a + 3u − 3,
u
8
+ u
7
+ 4u
6
+ 2u
5
− 5u
4
− 3u
3
+ 3u
2
− 3u + 2i
I
u
8
= hb, a + 1, u + 1i
* 8 irreducible components of dim
C
= 0, with total 137 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I.
I
u
1
= h−3.52×10
10
u
21
+3.05×10
10
u
20
+· · ·+2.10×10
11
b+2.58×10
10
, 7.41×
10
11
u
21
−7.67×10
11
u
20
+· · ·+2.10×10
11
a−8.70×10
11
, u
22
−u
21
+· · ·−u+1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
−3.52002u
21
+ 3.64270u
20
+ ··· − 40.0291u + 4.13298
0.167355u
21
− 0.145024u
20
+ ··· + 4.64270u − 0.122682
a
11
=
1
u
2
a
4
=
−3.52002u
21
+ 3.64270u
20
+ ··· − 39.0291u + 4.13298
0.167355u
21
− 0.145024u
20
+ ··· + 4.64270u − 0.122682
a
7
=
−7.95997u
21
+ 8.71460u
20
+ ··· − 67.9417u + 11.7340
0.832645u
21
− 0.854976u
20
+ ··· + 13.3573u − 0.877318
a
12
=
−3.13298u
21
+ 0.612962u
20
+ ··· − 16.2045u − 19.8962
0.122682u
21
+ 0.0446732u
20
+ ··· + 0.612962u + 3.52002
a
9
=
7.72374u
21
− 3.11644u
20
+ ··· + 40.9995u + 24.8315
−0.754636u
21
+ 0.0893465u
20
+ ··· − 3.77408u − 7.95997
a
3
=
2.10661u
21
+ 3.86613u
20
+ ··· + 4.19416u + 30.2779
4.12150u
21
− 5.66719u
20
+ ··· + 21.5571u − 12.2542
a
2
=
2.10661u
21
+ 3.86613u
20
+ ··· + 4.19416u + 30.2779
4.99760u
21
− 7.47535u
20
+ ··· + 25.4233u − 18.2269
a
1
=
2.98797u
21
− 0.624862u
20
+ ··· + 15.5468u + 16.5435
−0.145013u
21
− 0.0118996u
20
+ ··· − 0.657635u − 3.35266
a
6
=
−3.35266u
21
+ 3.49767u
20
+ ··· − 35.3864u + 4.01030
0.167355u
21
− 0.145024u
20
+ ··· + 4.64270u − 0.122682
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
1913935713454
210473051795
u
21
−
1492818570442
210473051795
u
20
+ ··· −
6526154909884
210473051795
u −
14593217553892
210473051795
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
+ 8u
21
+ ··· + 160u + 64
c
2
, c
8
u
22
+ 6u
21
+ ··· + 32u + 8
c
3
u
22
− 6u
21
+ ··· − 5072u + 3880
c
4
, c
6
, c
10
c
12
u
22
− u
21
+ ··· − u + 1
c
5
, c
11
u
22
− u
21
+ ··· − 16u + 10
c
7
, c
9
u
22
− 9u
21
+ ··· − 15u + 19
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 12y
21
+ ··· + 28160y + 4096
c
2
, c
8
y
22
+ 8y
21
+ ··· + 160y + 64
c
3
y
22
+ 16y
21
+ ··· + 18242976y + 15054400
c
4
, c
6
, c
10
c
12
y
22
+ 21y
21
+ ··· + 35y + 1
c
5
, c
11
y
22
+ y
21
+ ··· + 624y + 100
c
7
, c
9
y
22
− 9y
21
+ ··· − 187y + 361
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.251396 + 1.197270I
a = −0.727101 + 0.853670I
b = 0.733815 − 0.410169I
−1.69375 − 1.58224I −2.92761 + 2.99168I
u = 0.251396 − 1.197270I
a = −0.727101 − 0.853670I
b = 0.733815 + 0.410169I
−1.69375 + 1.58224I −2.92761 − 2.99168I
u = −0.439138 + 1.208940I
a = −0.366754 + 0.753125I
b = 0.825819 + 0.642867I
7.22176 + 4.64537I −1.48411 − 2.36378I
u = −0.439138 − 1.208940I
a = −0.366754 − 0.753125I
b = 0.825819 − 0.642867I
7.22176 − 4.64537I −1.48411 + 2.36378I
u = −0.100425 + 0.610392I
a = −0.598286 − 0.326486I
b = 0.076424 + 0.802089I
−0.049452 + 1.407930I −0.88049 − 5.93296I
u = −0.100425 − 0.610392I
a = −0.598286 + 0.326486I
b = 0.076424 − 0.802089I
−0.049452 − 1.407930I −0.88049 + 5.93296I
u = 0.311341 + 1.349370I
a = 0.386640 + 0.716640I
b = −0.957311 + 0.438847I
8.03816 + 1.82472I −0.36555 − 2.90365I
u = 0.311341 − 1.349370I
a = 0.386640 − 0.716640I
b = −0.957311 − 0.438847I
8.03816 − 1.82472I −0.36555 + 2.90365I
u = 0.70785 + 1.27677I
a = −0.942108 + 0.435063I
b = 0.985198 − 0.917340I
−2.15736 − 11.05600I −5.86304 + 8.74726I
u = 0.70785 − 1.27677I
a = −0.942108 − 0.435063I
b = 0.985198 + 0.917340I
−2.15736 + 11.05600I −5.86304 − 8.74726I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.43272 + 1.42172I
a = 0.745026 + 0.586778I
b = −1.077150 − 0.571146I
2.42448 + 6.49307I −0.75771 − 5.60630I
u = −0.43272 − 1.42172I
a = 0.745026 − 0.586778I
b = −1.077150 + 0.571146I
2.42448 − 6.49307I −0.75771 + 5.60630I
u = −0.131155 + 0.475245I
a = −1.59000 − 1.04889I
b = 0.069853 + 0.892314I
−0.69331 + 1.97766I −2.32963 − 3.06093I
u = −0.131155 − 0.475245I
a = −1.59000 + 1.04889I
b = 0.069853 − 0.892314I
−0.69331 − 1.97766I −2.32963 + 3.06093I
u = 0.145985 + 0.422253I
a = 2.38098 − 1.30459I
b = −0.066959 + 0.920596I
−2.79098 − 6.48658I −4.59769 + 4.99587I
u = 0.145985 − 0.422253I
a = 2.38098 + 1.30459I
b = −0.066959 − 0.920596I
−2.79098 + 6.48658I −4.59769 − 4.99587I
u = 0.062233 + 0.424223I
a = 1.23180 − 2.37884I
b = −0.029071 + 0.908159I
−4.30511 + 0.52403I −12.36500 − 2.34222I
u = 0.062233 − 0.424223I
a = 1.23180 + 2.37884I
b = −0.029071 − 0.908159I
−4.30511 − 0.52403I −12.36500 + 2.34222I
u = −1.05080 + 1.58014I
a = 0.749692 + 0.219224I
b = −1.36686 − 1.21476I
7.00864 + 11.78040I −2.49367 − 5.42252I
u = −1.05080 − 1.58014I
a = 0.749692 − 0.219224I
b = −1.36686 + 1.21476I
7.00864 − 11.78040I −2.49367 + 5.42252I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.17544 + 1.50294I
a = −0.769890 + 0.154115I
b = 1.30624 − 1.35244I
5.9137 − 18.4120I −4.00000 + 9.61591I
u = 1.17544 − 1.50294I
a = −0.769890 − 0.154115I
b = 1.30624 + 1.35244I
5.9137 + 18.4120I −4.00000 − 9.61591I
8
II.
I
u
2
= h3.79 × 10
20
u
19
− 4.63 × 10
20
u
18
+ · · · + 8.62 × 10
21
b − 2.25 × 10
21
, 2.73 ×
10
22
u
19
−2.51×10
22
u
18
+· · ·+8.62×10
21
a−1.80×10
23
, u
20
−u
19
+· · ·−7u+1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
−3.16774u
19
+ 2.90704u
18
+ ··· + 10.9832u + 20.8921
−0.0439113u
19
+ 0.0537225u
18
+ ··· + 2.34279u + 0.260708
a
11
=
1
u
2
a
4
=
−3.16774u
19
+ 2.90704u
18
+ ··· + 11.9832u + 20.8921
−0.0439113u
19
+ 0.0537225u
18
+ ··· + 2.34279u + 0.260708
a
7
=
−8.81122u
19
+ 7.79546u
18
+ ··· − 18.5918u + 54.1639
−0.175015u
19
+ 0.186912u
18
+ ··· + 4.04373u + 1.27646
a
12
=
3.92566u
19
− 3.36351u
18
+ ··· + 33.8425u − 29.7066
0.0217085u
19
− 0.0143026u
18
+ ··· + 0.00468521u − 0.781074
a
9
=
2.88820u
19
− 2.46456u
18
+ ··· + 26.3232u − 20.1143
0.0364007u
19
− 0.0247875u
18
+ ··· + 0.0259089u − 0.598653
a
3
=
1.64440u
19
− 1.25672u
18
+ ··· + 38.9478u − 7.71164
0.0771122u
19
− 0.0734388u
18
+ ··· + 0.753454u − 0.595866
a
2
=
1.64440u
19
− 1.25672u
18
+ ··· + 38.9478u − 7.71164
0.122553u
19
− 0.0983998u
18
+ ··· + 1.82280u − 0.983543
a
1
=
1.28627u
19
− 1.10467u
18
+ ··· + 8.75002u − 13.9350
−0.0118974u
19
+ 0.0110797u
18
+ ··· − 0.0513570u − 0.175015
a
6
=
−3.21165u
19
+ 2.96076u
18
+ ··· + 13.3259u + 21.1528
−0.0439113u
19
+ 0.0537225u
18
+ ··· + 2.34279u + 0.260708
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
97906072790078772930140
8620310934921930687151
u
19
+
81524634991414853459581
8620310934921930687151
u
18
+ ··· −
1059865978912088574268036
8620310934921930687151
u +
616271317183349139490199
8620310934921930687151
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 4u
9
+ ··· − 12u + 16)
2
c
2
, c
8
(u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 15u
5
+ 6u
4
− 5u
3
− 11u
2
− 10u − 4)
2
c
3
(u
10
− 4u
9
+ ··· − 66u − 52)
2
c
4
, c
6
, c
10
c
12
u
20
− u
19
+ ··· − 7u + 1
c
5
, c
11
(u
10
− 4u
8
− u
7
+ 10u
6
+ 3u
5
− 12u
4
− 4u
3
+ 6u
2
+ u − 1)
2
c
7
, c
9
u
20
− 7u
19
+ ··· + 710u − 71
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ 4y
9
+ ··· − 1008y + 256)
2
c
2
, c
8
(y
10
+ 4y
9
+ ··· − 12y + 16)
2
c
3
(y
10
+ 4y
9
+ ··· − 14028y + 2704)
2
c
4
, c
6
, c
10
c
12
y
20
+ 3y
19
+ ··· − 77y + 1
c
5
, c
11
(y
10
− 8y
9
+ ··· − 13y + 1)
2
c
7
, c
9
y
20
− 7y
19
+ ··· − 29394y + 5041
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.606294 + 1.022320I
a = 0.506435 + 1.185730I
b = −1.20672 + 0.84674I
6.80818 − 10.55520I −2.80651 + 7.76192I
u = 0.606294 − 1.022320I
a = 0.506435 − 1.185730I
b = −1.20672 − 0.84674I
6.80818 + 10.55520I −2.80651 − 7.76192I
u = 0.410689 + 1.146110I
a = −0.911522 + 0.251562I
b = 1.21747
3.96203 1.71627 + 0.I
u = 0.410689 − 1.146110I
a = −0.911522 − 0.251562I
b = 1.21747
3.96203 1.71627 + 0.I
u = −0.447983 + 1.156950I
a = −0.650705 + 0.989358I
b = 1.31797 + 0.70573I
7.99409 + 4.11330I −0.72706 − 2.84018I
u = −0.447983 − 1.156950I
a = −0.650705 − 0.989358I
b = 1.31797 − 0.70573I
7.99409 − 4.11330I −0.72706 + 2.84018I
u = −0.050609 + 0.749544I
a = 1.71190 + 0.54431I
b = −0.966704 + 0.315261I
−0.07213 − 3.52780I −2.13233 + 4.34006I
u = −0.050609 − 0.749544I
a = 1.71190 − 0.54431I
b = −0.966704 − 0.315261I
−0.07213 + 3.52780I −2.13233 − 4.34006I
u = −0.884394 + 1.054470I
a = 0.719695 + 0.083108I
b = −0.966704 − 0.315261I
−0.07213 + 3.52780I −2.13233 − 4.34006I
u = −0.884394 − 1.054470I
a = 0.719695 − 0.083108I
b = −0.966704 + 0.315261I
−0.07213 − 3.52780I −2.13233 + 4.34006I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53443
a = 0.408700
b = −0.572155
−3.24417 9.61450
u = 1.70396 + 0.20280I
a = −0.406335 + 0.011690I
b = 0.532805 − 0.044567I
−6.86440 − 4.53571I 10.5005 + 34.9465I
u = 1.70396 − 0.20280I
a = −0.406335 − 0.011690I
b = 0.532805 + 0.044567I
−6.86440 + 4.53571I 10.5005 − 34.9465I
u = −0.213343
a = −7.88331
b = −0.572155
−3.24417 9.61450
u = 1.03765 + 1.47270I
a = −0.661123 + 0.144524I
b = 1.31797 − 0.70573I
7.99409 − 4.11330I −0.72706 + 2.84018I
u = 1.03765 − 1.47270I
a = −0.661123 − 0.144524I
b = 1.31797 + 0.70573I
7.99409 + 4.11330I −0.72706 − 2.84018I
u = −1.16158 + 1.41196I
a = 0.665605 + 0.116987I
b = −1.20672 − 0.84674I
6.80818 + 10.55520I −2.80651 − 7.76192I
u = −1.16158 − 1.41196I
a = 0.665605 − 0.116987I
b = −1.20672 + 0.84674I
6.80818 − 10.55520I −2.80651 + 7.76192I
u = 0.159854 + 0.046896I
a = 11.26340 − 7.33066I
b = 0.532805 + 0.044567I
−6.86440 + 4.53571I 10.5005 − 34.9465I
u = 0.159854 − 0.046896I
a = 11.26340 + 7.33066I
b = 0.532805 − 0.044567I
−6.86440 − 4.53571I 10.5005 + 34.9465I
13
III.
I
u
3
= h−3.36×10
35
u
33
−7.64×10
35
u
32
+· · ·+5.24×10
36
b−4.10×10
36
, 1.96×
10
37
u
33
+4.10×10
36
u
32
+· · ·+5.24×10
36
a−6.08×10
37
, u
34
−9u
32
+· · ·−5u+1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
−3.73375u
33
− 0.782006u
32
+ ··· − 25.6210u + 11.6068
0.0640435u
33
+ 0.145676u
32
+ ··· − 1.17628u + 0.782006
a
11
=
1
u
2
a
4
=
−3.73375u
33
− 0.782006u
32
+ ··· − 26.6210u + 11.6068
0.0640435u
33
+ 0.145676u
32
+ ··· − 1.17628u + 0.782006
a
7
=
−8.90770u
33
− 2.14572u
32
+ ··· − 71.2828u + 27.4824
−0.376603u
33
+ 0.0354177u
32
+ ··· − 0.644601u + 1.36371
a
12
=
−4.42221u
33
− 0.993348u
32
+ ··· − 37.1005u + 14.3537
−0.0610815u
33
− 0.112187u
32
+ ··· + 1.07701u + 0.552701
a
9
=
3.06716u
33
+ 0.825714u
32
+ ··· + 27.3561u − 9.54342
0.232957u
33
+ 0.180886u
32
+ ··· − 1.92567u − 0.0777394
a
3
=
1.55716u
33
+ 0.844911u
32
+ ··· + 11.9349u − 1.31495
−0.0686076u
33
− 0.182006u
32
+ ··· + 3.42735u − 1.07782
a
2
=
1.55716u
33
+ 0.844911u
32
+ ··· + 11.9349u − 1.31495
0.202905u
33
− 0.0632946u
32
+ ··· + 6.09474u − 1.92273
a
1
=
2.08828u
33
+ 0.392969u
32
+ ··· + 13.8037u − 7.12091
0.0856981u
33
− 0.102474u
32
+ ··· + 2.98707u − 0.747975
a
6
=
−3.66970u
33
− 0.636330u
32
+ ··· − 26.7973u + 12.3888
0.0640435u
33
+ 0.145676u
32
+ ··· − 1.17628u + 0.782006
(ii) Obstruction class = 1
(iii) Cusp Shapes = 20.8441u
33
+ 4.37870u
32
+ ··· + 173.006u − 75.6418
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
17
− 8u
16
+ ··· − 11u + 2)
2
c
2
, c
8
u
34
+ 8u
32
+ ··· − 11u
2
− 2
c
3
u
34
+ 12u
32
+ ··· − 99u
2
− 2
c
4
, c
10
u
34
− 9u
32
+ ··· − 5u + 1
c
5
, c
11
u
34
+ 3u
32
+ ··· + 31u
2
− 2
c
6
, c
12
u
34
− 9u
32
+ ··· + 5u + 1
c
7
u
34
+ 18u
33
+ ··· + 10u + 1
c
9
u
34
− 18u
33
+ ··· − 10u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
17
+ 10y
16
+ ··· − 11y −4)
2
c
2
, c
8
(y
17
+ 8y
16
+ ··· − 11y −2)
2
c
3
(y
17
+ 12y
16
+ ··· − 99y −2)
2
c
4
, c
6
, c
10
c
12
y
34
− 18y
33
+ ··· − 5y + 1
c
5
, c
11
(y
17
+ 3y
16
+ ··· + 31y −2)
2
c
7
, c
9
y
34
− 14y
33
+ ··· − 4y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.948002 + 0.313646I
a = 1.49270 + 0.75341I
b = −0.201379 + 1.177010I
−3.90984 − 7.35529I −10.7026 + 11.0707I
u = 0.948002 − 0.313646I
a = 1.49270 − 0.75341I
b = −0.201379 − 1.177010I
−3.90984 + 7.35529I −10.7026 − 11.0707I
u = 0.956410 + 0.604090I
a = 1.388120 + 0.148389I
b = −0.364697 + 1.081480I
−4.51641 − 1.30867I −12.27157 + 0.31860I
u = 0.956410 − 0.604090I
a = 1.388120 − 0.148389I
b = −0.364697 − 1.081480I
−4.51641 + 1.30867I −12.27157 − 0.31860I
u = 0.301826 + 0.794742I
a = −0.242452 + 0.645424I
b = −0.480417 − 1.259920I
−3.12305 + 4.90974I −4.98224 − 0.13853I
u = 0.301826 − 0.794742I
a = −0.242452 − 0.645424I
b = −0.480417 + 1.259920I
−3.12305 − 4.90974I −4.98224 + 0.13853I
u = −1.127990 + 0.273851I
a = −1.138540 + 0.718861I
b = 0.208856 + 1.290280I
−2.73299 + 3.07671I −3.59376 − 6.57908I
u = −1.127990 − 0.273851I
a = −1.138540 − 0.718861I
b = 0.208856 − 1.290280I
−2.73299 − 3.07671I −3.59376 + 6.57908I
u = −0.070405 + 0.815044I
a = 0.532860 + 0.628017I
b = −0.208856 − 1.290280I
−2.73299 + 3.07671I −3.59376 − 6.57908I
u = −0.070405 − 0.815044I
a = 0.532860 − 0.628017I
b = −0.208856 + 1.290280I
−2.73299 − 3.07671I −3.59376 + 6.57908I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.251748 + 1.192390I
a = 1.025750 − 0.598178I
b = −1.286020 + 0.236008I
4.34137 − 0.62662I 0.702844 + 0.664865I
u = 0.251748 − 1.192390I
a = 1.025750 + 0.598178I
b = −1.286020 − 0.236008I
4.34137 + 0.62662I 0.702844 − 0.664865I
u = −1.044090 + 0.683860I
a = −0.761913 + 0.166704I
b = 0.807885 + 0.507938I
−1.39035 + 4.13256I −8.96641 − 7.21181I
u = −1.044090 − 0.683860I
a = −0.761913 − 0.166704I
b = 0.807885 − 0.507938I
−1.39035 − 4.13256I −8.96641 + 7.21181I
u = 0.647873 + 0.299417I
a = 1.00359 + 1.26631I
b = −0.807885 + 0.507938I
−1.39035 − 4.13256I −8.96641 + 7.21181I
u = 0.647873 − 0.299417I
a = 1.00359 − 1.26631I
b = −0.807885 − 0.507938I
−1.39035 + 4.13256I −8.96641 − 7.21181I
u = −1.199710 + 0.613641I
a = −1.068440 + 0.282667I
b = 0.480417 + 1.259920I
−3.12305 + 4.90974I −4.98224 + 0.I
u = −1.199710 − 0.613641I
a = −1.068440 − 0.282667I
b = 0.480417 − 1.259920I
−3.12305 − 4.90974I −4.98224 + 0.I
u = 0.067240 + 0.640701I
a = −0.90142 + 1.12971I
b = 0.201379 − 1.177010I
−3.90984 − 7.35529I −10.7026 + 11.0707I
u = 0.067240 − 0.640701I
a = −0.90142 − 1.12971I
b = 0.201379 + 1.177010I
−3.90984 + 7.35529I −10.7026 − 11.0707I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.504150 + 1.265790I
a = −0.961784 − 0.364583I
b = 1.335370 + 0.453210I
4.40017 + 6.90997I 0. − 5.88125I
u = −0.504150 − 1.265790I
a = −0.961784 + 0.364583I
b = 1.335370 − 0.453210I
4.40017 − 6.90997I 0. + 5.88125I
u = −0.604342
a = −2.59153
b = −0.342161
−3.55226 −16.8940
u = −1.39868
a = −0.540058
b = 0.342161
−3.55226 −16.8940
u = −0.179282 + 0.553299I
a = 0.47174 + 1.58611I
b = 0.364697 − 1.081480I
−4.51641 − 1.30867I −12.27157 + 0.31860I
u = −0.179282 − 0.553299I
a = 0.47174 − 1.58611I
b = 0.364697 + 1.081480I
−4.51641 + 1.30867I −12.27157 − 0.31860I
u = 1.56336 + 0.01828I
a = 0.097753 + 0.190650I
b = −1.335370 + 0.453210I
4.40017 − 6.90997I 0. + 5.88125I
u = 1.56336 − 0.01828I
a = 0.097753 − 0.190650I
b = −1.335370 − 0.453210I
4.40017 + 6.90997I 0. − 5.88125I
u = 0.329313 + 0.165692I
a = 4.37347 − 4.17301I
b = 0.480307 − 0.026404I
−6.91964 + 4.44078I −26.1531 + 27.7299I
u = 0.329313 − 0.165692I
a = 4.37347 + 4.17301I
b = 0.480307 + 0.026404I
−6.91964 − 4.44078I −26.1531 − 27.7299I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61858 + 0.22328I
a = −0.166497 + 0.131888I
b = 1.286020 + 0.236008I
4.34137 + 0.62662I 0
u = −1.61858 − 0.22328I
a = −0.166497 − 0.131888I
b = 1.286020 − 0.236008I
4.34137 − 0.62662I 0
u = 1.67995 + 0.23279I
a = 0.420857 − 0.044359I
b = −0.480307 − 0.026404I
−6.91964 − 4.44078I 0
u = 1.67995 − 0.23279I
a = 0.420857 + 0.044359I
b = −0.480307 + 0.026404I
−6.91964 + 4.44078I 0
20
IV. I
u
4
= h1.67 × 10
13
u
15
+ 6.56 × 10
12
u
14
+ · · · + 4.53 × 10
14
b + 2.51 ×
10
14
, −3.58 × 10
10
u
15
− 2.67 × 10
10
u
14
+ · · · + 7.67 × 10
11
a + 9.31 ×
10
11
, u
16
− u
15
+ · · · − 20u + 13i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
0.0467229u
15
+ 0.0348323u
14
+ ··· + 0.00279962u − 1.21378
−0.0367984u
15
− 0.0144567u
14
+ ··· − 0.0545409u − 0.552827
a
11
=
1
u
2
a
4
=
−0.00998312u
15
+ 0.0408553u
14
+ ··· − 1.07545u − 0.706390
−0.00626482u
15
− 0.0388182u
14
+ ··· − 0.331023u + 0.106053
a
7
=
0.123646u
15
− 0.0420908u
14
+ ··· + 0.00279962u − 2.75224
−0.0640970u
15
+ 0.0544416u
14
+ ··· − 0.865462u + 1.19024
a
12
=
−0.120585u
15
+ 0.0439717u
14
+ ··· + 0.747958u + 2.30975
0.0815552u
15
− 0.0616476u
14
+ ··· − 0.279323u − 0.607398
a
9
=
0.0915566u
15
− 0.0274596u
14
+ ··· − 1.75803u − 0.965670
−0.0815552u
15
+ 0.0616476u
14
+ ··· + 0.279323u + 1.60740
a
3
=
0.114902u
15
− 0.0966243u
14
+ ··· + 0.137579u − 0.901552
0.0610974u
15
− 0.133458u
14
+ ··· − 0.754389u + 1.02422
a
2
=
0.114902u
15
− 0.0966243u
14
+ ··· + 0.137579u − 0.901552
0.0568444u
15
− 0.0636001u
14
+ ··· − 1.88256u + 0.786613
a
1
=
0.0902852u
15
− 0.105232u
14
+ ··· + 0.820160u − 2.18073
−0.0303001u
15
− 0.0612608u
14
+ ··· + 1.56812u + 0.129018
a
6
=
0.00992449u
15
+ 0.0203756u
14
+ ··· − 0.0517413u − 1.76661
−0.0367984u
15
− 0.0144567u
14
+ ··· − 0.0545409u − 0.552827
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
146434412728192
453436720809281
u
15
−
84018496727016
453436720809281
u
14
+ ··· −
5115840542393260
453436720809281
u −
55929004883582
453436720809281
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
4
c
2
, c
8
(u
4
− u
3
+ u
2
+ 1)
4
c
3
(u
4
+ u
3
+ 5u
2
− u + 2)
4
c
4
, c
6
, c
10
c
12
u
16
− u
15
+ ··· − 20u + 13
c
5
, c
11
u
16
− 3u
15
+ ··· + 198u + 97
c
7
, c
9
(u
2
+ u + 1)
8
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
4
c
2
, c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
4
c
3
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
4
c
4
, c
6
, c
10
c
12
y
16
+ 7y
15
+ ··· − 400y + 169
c
5
, c
11
y
16
− 13y
15
+ ··· − 37264y + 9409
c
7
, c
9
(y
2
+ y + 1)
8
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.092007 + 1.034470I
a = −0.787948 − 0.553421I
b = 2.24681 − 1.28233I
6.79074 + 7.22373I 1.82674 − 9.49300I
u = 0.092007 − 1.034470I
a = −0.787948 + 0.553421I
b = 2.24681 + 1.28233I
6.79074 − 7.22373I 1.82674 + 9.49300I
u = −0.239797 + 0.921033I
a = 0.748218 − 0.737673I
b = −1.96980 − 1.53526I
6.79074 − 0.89580I 1.82674 + 4.36340I
u = −0.239797 − 0.921033I
a = 0.748218 + 0.737673I
b = −1.96980 + 1.53526I
6.79074 + 0.89580I 1.82674 − 4.36340I
u = −0.639205 + 0.691048I
a = −1.036040 + 0.234778I
b = 1.55457 + 0.29681I
−0.21101 + 5.47487I −1.82674 − 11.83695I
u = −0.639205 − 0.691048I
a = −1.036040 − 0.234778I
b = 1.55457 − 0.29681I
−0.21101 − 5.47487I −1.82674 + 11.83695I
u = −0.811044 + 0.687008I
a = −0.885567 + 0.317657I
b = 0.759110 + 0.954489I
−0.21101 + 2.64466I −1.82674 − 2.01946I
u = −0.811044 − 0.687008I
a = −0.885567 − 0.317657I
b = 0.759110 − 0.954489I
−0.21101 − 2.64466I −1.82674 + 2.01946I
u = 1.275710 + 0.602283I
a = 0.582586 + 0.403811I
b = −0.522944 + 0.714888I
−0.21101 − 5.47487I −1.82674 + 11.83695I
u = 1.275710 − 0.602283I
a = 0.582586 − 0.403811I
b = −0.522944 − 0.714888I
−0.21101 + 5.47487I −1.82674 − 11.83695I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569666 + 0.091399I
a = 1.09347 + 1.34479I
b = −0.605365 − 0.147963I
−0.21101 − 2.64466I −1.82674 + 2.01946I
u = 0.569666 − 0.091399I
a = 1.09347 − 1.34479I
b = −0.605365 + 0.147963I
−0.21101 + 2.64466I −1.82674 − 2.01946I
u = −1.05226 + 1.78810I
a = −0.481970 + 0.004004I
b = 0.782616 + 0.884305I
6.79074 + 0.89580I 1.82674 − 4.36340I
u = −1.05226 − 1.78810I
a = −0.481970 − 0.004004I
b = 0.782616 − 0.884305I
6.79074 − 0.89580I 1.82674 + 4.36340I
u = 1.30493 + 1.71989I
a = 0.459558 + 0.057963I
b = −0.744996 + 0.955578I
6.79074 − 7.22373I 1.82674 + 9.49300I
u = 1.30493 − 1.71989I
a = 0.459558 − 0.057963I
b = −0.744996 − 0.955578I
6.79074 + 7.22373I 1.82674 − 9.49300I
25
V. I
u
5
= h3.61 × 10
67
u
31
+ 1.33 × 10
67
u
30
+ · · · + 5.05 × 10
70
b − 7.80 ×
10
69
, −2.81 × 10
59
u
31
− 1.32 × 10
59
u
30
+ · · · + 1.02 × 10
63
a + 2.60 ×
10
62
, u
32
+ u
31
+ · · · − 1290u + 1501i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
0.000275867u
31
+ 0.000129795u
30
+ ··· − 1.94837u − 0.254733
−0.000714688u
31
− 0.000263450u
30
+ ··· + 1.30103u + 0.154418
a
11
=
1
u
2
a
4
=
−0.000372259u
31
− 0.000239040u
30
+ ··· − 0.0448239u − 0.319569
−0.000812029u
31
− 0.000379010u
30
+ ··· + 2.63416u − 0.264798
a
7
=
−0.000214542u
31
+ 0.000103732u
30
+ ··· + 1.76603u + 0.160004
0.000541250u
31
+ 0.000557760u
30
+ ··· + 0.234939u − 0.714606
a
12
=
0.000104855u
31
+ 0.000223448u
30
+ ··· + 0.402197u + 1.00171
0.000587979u
31
+ 0.000584757u
30
+ ··· − 0.413622u + 0.911091
a
9
=
0.0000192851u
31
+ 0.000101444u
30
+ ··· − 1.67116u − 0.632751
−0.00100745u
31
− 0.000782374u
30
+ ··· + 0.820704u − 0.169014
a
3
=
−0.000684276u
31
− 0.000635526u
30
+ ··· − 0.323358u + 0.130143
−0.000925024u
31
− 0.000629723u
30
+ ··· + 4.84174u + 0.562738
a
2
=
−0.000684276u
31
− 0.000635526u
30
+ ··· − 0.323358u + 0.130143
−0.00111240u
31
− 0.000654767u
30
+ ··· + 5.93173u + 0.489565
a
1
=
−0.000409598u
31
− 0.000309788u
30
+ ··· − 1.27330u − 0.416102
−0.00130652u
31
− 0.000909626u
30
+ ··· + 2.57060u + 0.0601876
a
6
=
−0.000438821u
31
− 0.000133655u
30
+ ··· − 0.647334u − 0.100315
−0.000714688u
31
− 0.000263450u
30
+ ··· + 1.30103u + 0.154418
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00301162u
31
+ 0.00331224u
30
+ ··· + 2.94189u − 18.0165
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
8
c
2
, c
8
(u
4
− u
3
+ u
2
+ 1)
8
c
3
(u
4
+ u
3
+ 5u
2
− u + 2)
8
c
4
, c
6
, c
10
c
12
u
32
+ u
31
+ ··· − 1290u + 1501
c
5
, c
11
(u
16
+ u
15
+ ··· + 2u + 19)
2
c
7
, c
9
(u
4
+ u
3
− 2u + 1)
8
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
8
c
2
, c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
8
c
3
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
8
c
4
, c
6
, c
10
c
12
y
32
− 23y
31
+ ··· − 13272834y + 2253001
c
5
, c
11
(y
16
− y
15
+ ··· − 2512y + 361)
2
c
7
, c
9
(y
4
− y
3
+ 6y
2
− 4y + 1)
8
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.933125 + 0.345373I
a = 1.42512 + 0.60180I
b = −0.507415 + 1.111340I
−3.50087 − 2.64466I −13.82674 + 2.01946I
u = 0.933125 − 0.345373I
a = 1.42512 − 0.60180I
b = −0.507415 − 1.111340I
−3.50087 + 2.64466I −13.82674 − 2.01946I
u = −0.465677 + 0.912383I
a = −1.41419 − 0.50791I
b = 0.505216 + 0.080628I
3.50087 + 0.89580I −10.17326 − 4.36340I
u = −0.465677 − 0.912383I
a = −1.41419 + 0.50791I
b = 0.505216 − 0.080628I
3.50087 − 0.89580I −10.17326 + 4.36340I
u = 1.105300 + 0.270519I
a = −0.570130 − 0.030308I
b = 1.91342 − 1.12465I
3.50087 − 7.22373I −10.17326 + 9.49300I
u = 1.105300 − 0.270519I
a = −0.570130 + 0.030308I
b = 1.91342 + 1.12465I
3.50087 + 7.22373I −10.17326 − 9.49300I
u = 0.672655 + 0.976570I
a = 1.268540 − 0.275121I
b = −0.621358 + 0.257578I
3.50087 − 7.22373I −10.17326 + 9.49300I
u = 0.672655 − 0.976570I
a = 1.268540 + 0.275121I
b = −0.621358 − 0.257578I
3.50087 + 7.22373I −10.17326 − 9.49300I
u = −1.140760 + 0.351108I
a = 0.544306 + 0.002963I
b = −1.90215 − 0.76605I
3.50087 + 0.89580I −10.17326 − 4.36340I
u = −1.140760 − 0.351108I
a = 0.544306 − 0.002963I
b = −1.90215 + 0.76605I
3.50087 − 0.89580I −10.17326 + 4.36340I
29
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.190410 + 0.259439I
a = −1.083940 + 0.648970I
b = −0.129086 + 1.200110I
−3.50087 + 2.64466I −13.82674 − 2.01946I
u = −1.190410 − 0.259439I
a = −1.083940 − 0.648970I
b = −0.129086 − 1.200110I
−3.50087 − 2.64466I −13.82674 + 2.01946I
u = 1.166990 + 0.483595I
a = 1.139860 + 0.430615I
b = −0.387825 + 1.018230I
−3.50087 − 5.47487I −13.8267 + 11.8369I
u = 1.166990 − 0.483595I
a = 1.139860 − 0.430615I
b = −0.387825 − 1.018230I
−3.50087 + 5.47487I −13.8267 − 11.8369I
u = −0.662252 + 0.286911I
a = 0.687346 + 0.581256I
b = −0.129086 − 1.200110I
−3.50087 − 2.64466I −13.82674 + 2.01946I
u = −0.662252 − 0.286911I
a = 0.687346 − 0.581256I
b = −0.129086 + 1.200110I
−3.50087 + 2.64466I −13.82674 − 2.01946I
u = −0.594845 + 1.145980I
a = 0.350970 + 0.360556I
b = −0.507415 − 1.111340I
−3.50087 + 2.64466I −13.82674 − 2.01946I
u = −0.594845 − 1.145980I
a = 0.350970 − 0.360556I
b = −0.507415 + 1.111340I
−3.50087 − 2.64466I −13.82674 + 2.01946I
u = −1.187550 + 0.754071I
a = −1.074840 + 0.204836I
b = 0.62920 + 1.61384I
−3.50087 + 5.47487I −13.8267 − 11.8369I
u = −1.187550 − 0.754071I
a = −1.074840 − 0.204836I
b = 0.62920 − 1.61384I
−3.50087 − 5.47487I −13.8267 + 11.8369I
30
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06626 + 1.43374I
a = 0.769490 − 0.746980I
b = −1.90215 + 0.76605I
3.50087 − 0.89580I −10.17326 + 4.36340I
u = 0.06626 − 1.43374I
a = 0.769490 + 0.746980I
b = −1.90215 − 0.76605I
3.50087 + 0.89580I −10.17326 − 4.36340I
u = 0.353208 + 0.331710I
a = −1.200900 + 0.596300I
b = 0.62920 − 1.61384I
−3.50087 − 5.47487I −13.8267 + 11.8369I
u = 0.353208 − 0.331710I
a = −1.200900 − 0.596300I
b = 0.62920 + 1.61384I
−3.50087 + 5.47487I −13.8267 − 11.8369I
u = 0.78661 + 1.34122I
a = −0.098220 + 0.406126I
b = −0.387825 − 1.018230I
−3.50087 + 5.47487I −13.8267 − 11.8369I
u = 0.78661 − 1.34122I
a = −0.098220 − 0.406126I
b = −0.387825 + 1.018230I
−3.50087 − 5.47487I −13.8267 + 11.8369I
u = −0.34699 + 1.54691I
a = −0.803463 − 0.545068I
b = 1.91342 + 1.12465I
3.50087 + 7.22373I −10.17326 − 9.49300I
u = −0.34699 − 1.54691I
a = −0.803463 + 0.545068I
b = 1.91342 − 1.12465I
3.50087 − 7.22373I −10.17326 + 9.49300I
u = −2.54575 + 0.33352I
a = 0.230694 + 0.103966I
b = 0.505216 − 0.080628I
3.50087 − 0.89580I 0
u = −2.54575 − 0.33352I
a = 0.230694 − 0.103966I
b = 0.505216 + 0.080628I
3.50087 + 0.89580I 0
31
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 2.55009 + 0.74890I
a = −0.204631 + 0.133712I
b = −0.621358 − 0.257578I
3.50087 + 7.22373I 0
u = 2.55009 − 0.74890I
a = −0.204631 − 0.133712I
b = −0.621358 + 0.257578I
3.50087 − 7.22373I 0
32
VI. I
u
6
= hb − u, a, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
0
u
a
11
=
1
u
2
a
4
=
u
u
3
+ u
a
7
=
0
u
a
12
=
1
0
a
9
=
1
0
a
3
=
u
3
+ 2u
u
3
+ u
a
2
=
u
3
+ 2u
u
3
+ u
2
+ 2u + 1
a
1
=
−u
2
− 1
−u
2
a
6
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 12u − 6
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
10
, c
11
c
12
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
2
, c
8
u
4
+ u
3
+ u
2
+ 1
c
3
u
4
− u
3
+ 5u
2
+ u + 2
c
7
, c
9
u
4
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
10
, c
11
c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
8
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
7
, c
9
y
4
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 0
b = −0.395123 + 0.506844I
−0.21101 + 1.41510I −1.82674 − 4.90874I
u = −0.395123 − 0.506844I
a = 0
b = −0.395123 − 0.506844I
−0.21101 − 1.41510I −1.82674 + 4.90874I
u = −0.10488 + 1.55249I
a = 0
b = −0.10488 + 1.55249I
6.79074 + 3.16396I 1.82674 − 2.56480I
u = −0.10488 − 1.55249I
a = 0
b = −0.10488 − 1.55249I
6.79074 − 3.16396I 1.82674 + 2.56480I
36
VII. I
u
7
= h11u
7
+ 19u
6
+ · · · + 2b − 28, u
7
+ u
6
+ 4u
5
+ 2u
4
− 5u
3
− 3u
2
+
2a + 3u − 3, u
8
+ u
7
+ · · · − 3u + 2i
(i) Arc colorings
a
8
=
0
u
a
10
=
1
0
a
5
=
−
1
2
u
7
−
1
2
u
6
+ ··· −
3
2
u +
3
2
−
11
2
u
7
−
19
2
u
6
+ ··· −
9
2
u + 14
a
11
=
1
u
2
a
4
=
−6u
7
− 10u
6
+ ··· − 7u +
31
2
−
17
2
u
7
− 15u
6
+ ··· −
11
2
u + 22
a
7
=
−
1
2
u
7
−
1
2
u
6
+ ··· −
3
2
u +
3
2
−
11
2
u
7
−
19
2
u
6
+ ··· −
7
2
u + 14
a
12
=
7u
7
+
25
2
u
6
+ ··· + 4u −
31
2
1
a
9
=
−7u
7
−
25
2
u
6
+ ··· − 4u +
33
2
−1
a
3
=
−
19
2
u
7
− 17u
6
+ ··· −
7
2
u +
51
2
−
29
2
u
7
− 26u
6
+ ··· −
13
2
u + 38
a
2
=
−
19
2
u
7
− 17u
6
+ ··· −
7
2
u +
51
2
−
41
2
u
7
−
73
2
u
6
+ ··· − 10u + 53
a
1
=
−8u
7
− 14u
6
− 43u
5
− 49u
4
+ u
3
+ 23u
2
− 5u + 23
−8u
7
− 14u
6
− 43u
5
− 49u
4
+ u
3
+ 23u
2
− 5u + 22
a
6
=
−6u
7
− 10u
6
+ ··· − 6u +
31
2
−
11
2
u
7
−
19
2
u
6
+ ··· −
9
2
u + 14
(ii) Obstruction class = −1
(iii) Cusp Shapes = 52u
7
+ 92u
6
+ 278u
5
+ 318u
4
− 18u
3
− 168u
2
+ 30u − 146
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
11
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
2
, c
8
(u
4
− u
3
+ u
2
+ 1)
2
c
3
(u
4
+ u
3
+ 5u
2
− u + 2)
2
c
4
, c
6
, c
10
c
12
u
8
+ u
7
+ 4u
6
+ 2u
5
− 5u
4
− 3u
3
+ 3u
2
− 3u + 2
c
7
, c
9
(u + 1)
8
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
2
, c
8
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
c
3
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
2
c
4
, c
6
, c
10
c
12
y
8
+ 7y
7
+ 2y
6
− 32y
5
+ 71y
4
− 11y
3
− 29y
2
+ 3y + 4
c
7
, c
9
(y −1)
8
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772314 + 0.004686I
a = 1.294760 − 0.007855I
b = −0.395123 − 0.506844I
−3.50087 − 1.41510I −13.8267 + 4.9087I
u = 0.772314 − 0.004686I
a = 1.294760 + 0.007855I
b = −0.395123 + 0.506844I
−3.50087 + 1.41510I −13.8267 − 4.9087I
u = −1.167440 + 0.511530I
a = −0.718612 − 0.314870I
b = −0.395123 + 0.506844I
−3.50087 + 1.41510I −13.8267 − 4.9087I
u = −1.167440 − 0.511530I
a = −0.718612 + 0.314870I
b = −0.395123 − 0.506844I
−3.50087 − 1.41510I −13.8267 + 4.9087I
u = 0.090777 + 0.644863I
a = 0.21405 − 1.52058I
b = −0.10488 − 1.55249I
3.50087 − 3.16396I −10.17326 + 2.56480I
u = 0.090777 − 0.644863I
a = 0.21405 + 1.52058I
b = −0.10488 + 1.55249I
3.50087 + 3.16396I −10.17326 − 2.56480I
u = −0.19565 + 2.19735I
a = −0.040203 − 0.451513I
b = −0.10488 + 1.55249I
3.50087 + 3.16396I −10.17326 − 2.56480I
u = −0.19565 − 2.19735I
a = −0.040203 + 0.451513I
b = −0.10488 − 1.55249I
3.50087 − 3.16396I −10.17326 + 2.56480I
40
VIII. I
u
8
= hb, a + 1, u + 1i
(i) Arc colorings
a
8
=
0
−1
a
10
=
1
0
a
5
=
−1
0
a
11
=
1
1
a
4
=
0
1
a
7
=
−1
−1
a
12
=
1
1
a
9
=
0
−1
a
3
=
0
1
a
2
=
0
1
a
1
=
0
1
a
6
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
8
, c
11
u
c
4
, c
7
, c
10
u + 1
c
6
, c
9
, c
12
u − 1
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
8
, c
11
y
c
4
, c
6
, c
7
c
9
, c
10
, c
12
y −1
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
44
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
4
+ u
3
+ 3u
2
+ 2u + 1)
15
(u
10
+ 4u
9
+ ··· − 12u + 16)
2
· ((u
17
− 8u
16
+ ··· − 11u + 2)
2
)(u
22
+ 8u
21
+ ··· + 160u + 64)
c
2
, c
8
u(u
4
− u
3
+ u
2
+ 1)
14
(u
4
+ u
3
+ u
2
+ 1)
· (u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 15u
5
+ 6u
4
− 5u
3
− 11u
2
− 10u − 4)
2
· (u
22
+ 6u
21
+ ··· + 32u + 8)(u
34
+ 8u
32
+ ··· − 11u
2
− 2)
c
3
u(u
4
− u
3
+ 5u
2
+ u + 2)(u
4
+ u
3
+ 5u
2
− u + 2)
14
· ((u
10
− 4u
9
+ ··· − 66u − 52)
2
)(u
22
− 6u
21
+ ··· − 5072u + 3880)
· (u
34
+ 12u
32
+ ··· − 99u
2
− 2)
c
4
, c
10
(u + 1)(u
4
+ u
3
+ 3u
2
+ 2u + 1)
· (u
8
+ u
7
+ 4u
6
+ 2u
5
− 5u
4
− 3u
3
+ 3u
2
− 3u + 2)
· (u
16
− u
15
+ ··· − 20u + 13)(u
20
− u
19
+ ··· − 7u + 1)
· (u
22
− u
21
+ ··· − u + 1)(u
32
+ u
31
+ ··· − 1290u + 1501)
· (u
34
− 9u
32
+ ··· − 5u + 1)
c
5
, c
11
u(u
4
+ u
3
+ 3u
2
+ 2u + 1)
3
· (u
10
− 4u
8
− u
7
+ 10u
6
+ 3u
5
− 12u
4
− 4u
3
+ 6u
2
+ u − 1)
2
· (u
16
− 3u
15
+ ··· + 198u + 97)(u
16
+ u
15
+ ··· + 2u + 19)
2
· (u
22
− u
21
+ ··· − 16u + 10)(u
34
+ 3u
32
+ ··· + 31u
2
− 2)
c
6
, c
12
(u − 1)(u
4
+ u
3
+ 3u
2
+ 2u + 1)
· (u
8
+ u
7
+ 4u
6
+ 2u
5
− 5u
4
− 3u
3
+ 3u
2
− 3u + 2)
· (u
16
− u
15
+ ··· − 20u + 13)(u
20
− u
19
+ ··· − 7u + 1)
· (u
22
− u
21
+ ··· − u + 1)(u
32
+ u
31
+ ··· − 1290u + 1501)
· (u
34
− 9u
32
+ ··· + 5u + 1)
c
7
u
4
(u + 1)
9
(u
2
+ u + 1)
8
(u
4
+ u
3
− 2u + 1)
8
· (u
20
− 7u
19
+ ··· + 710u − 71)(u
22
− 9u
21
+ ··· − 15u + 19)
· (u
34
+ 18u
33
+ ··· + 10u + 1)
c
9
u
4
(u − 1)(u + 1)
8
(u
2
+ u + 1)
8
(u
4
+ u
3
− 2u + 1)
8
· (u
20
− 7u
19
+ ··· + 710u − 71)(u
22
− 9u
21
+ ··· − 15u + 19)
· (u
34
− 18u
33
+ ··· − 10u + 1)
45
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
4
+ 5y
3
+ ··· + 2y + 1)
15
(y
10
+ 4y
9
+ ··· − 1008y + 256)
2
· ((y
17
+ 10y
16
+ ··· − 11y −4)
2
)(y
22
+ 12y
21
+ ··· + 28160y + 4096)
c
2
, c
8
y(y
4
+ y
3
+ 3y
2
+ 2y + 1)
15
(y
10
+ 4y
9
+ ··· − 12y + 16)
2
· ((y
17
+ 8y
16
+ ··· − 11y −2)
2
)(y
22
+ 8y
21
+ ··· + 160y + 64)
c
3
y(y
4
+ 9y
3
+ ··· + 19y + 4)
15
(y
10
+ 4y
9
+ ··· − 14028y + 2704)
2
· (y
17
+ 12y
16
+ ··· − 99y −2)
2
· (y
22
+ 16y
21
+ ··· + 18242976y + 15054400)
c
4
, c
6
, c
10
c
12
(y −1)(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
8
+ 7y
7
+ 2y
6
− 32y
5
+ 71y
4
− 11y
3
− 29y
2
+ 3y + 4)
· (y
16
+ 7y
15
+ ··· − 400y + 169)(y
20
+ 3y
19
+ ··· − 77y + 1)
· (y
22
+ 21y
21
+ ··· + 35y + 1)
· (y
32
− 23y
31
+ ··· − 13272834y + 2253001)
· (y
34
− 18y
33
+ ··· − 5y + 1)
c
5
, c
11
y(y
4
+ 5y
3
+ ··· + 2y + 1)
3
(y
10
− 8y
9
+ ··· − 13y + 1)
2
· (y
16
− 13y
15
+ ··· − 37264y + 9409)
· ((y
16
− y
15
+ ··· − 2512y + 361)
2
)(y
17
+ 3y
16
+ ··· + 31y −2)
2
· (y
22
+ y
21
+ ··· + 624y + 100)
c
7
, c
9
y
4
(y −1)
9
(y
2
+ y + 1)
8
(y
4
− y
3
+ 6y
2
− 4y + 1)
8
· (y
20
− 7y
19
+ ··· − 29394y + 5041)(y
22
− 9y
21
+ ··· − 187y + 361)
· (y
34
− 14y
33
+ ··· − 4y + 1)
46
