12a
1100
(K12a
1100
)
A knot diagram
1
Linearized knot diagam
4 7 11 9 12 2 10 1 6 3 8 5
Solving Sequence
5,12 6,9
10 1 4 2 7 3 8 11
c
5
c
9
c
12
c
4
c
1
c
6
c
2
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.72959 × 10
14
u
38
+ 1.09041 × 10
16
u
37
+ ··· + 2.39027 × 10
15
b + 2.06660 × 10
16
,
− 1.43733 × 10
15
u
38
− 1.83777 × 10
16
u
37
+ ··· + 4.78054 × 10
15
a − 3.39110 × 10
16
,
u
39
+ 16u
38
+ ··· + 384u + 16i
I
u
2
= h2.68281 × 10
59
au
64
+ 6.81399 × 10
65
u
64
+ ··· − 1.07313 × 10
60
a + 1.71010 × 10
66
,
− 9.81930 × 10
61
au
64
− 2.55544 × 10
62
u
64
+ ··· + 6.76295 × 10
62
a − 1.80547 × 10
63
,
u
65
− 6u
64
+ ··· − 36u + 4i
I
u
3
= h4u
19
+ 19u
18
+ ··· + 3b − 84, 40u
19
+ 265u
18
+ ··· + 9a − 252, u
20
+ 7u
19
+ ··· + 42u + 9i
I
u
4
= h−u
6
a + 3u
5
a + 3u
6
− 4u
4
a − 17u
5
+ 7u
3
a + 37u
4
− 2u
2
a − 50u
3
+ 8au + 49u
2
+ 7b − 3a − 27u + 20,
105u
6
a + 64u
6
+ ··· − 84a − 80, u
7
− 4u
6
+ 7u
5
− 11u
4
+ 9u
3
− 10u
2
+ 4u − 3i
I
v
1
= ha, b + 1, v
2
− v + 1i
I
v
2
= ha, b + v −1, v
2
− v + 1i
I
v
3
= ha, b + 1, v + 1i
* 7 irreducible components of dim
C
= 0, with total 208 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
= h5.73 × 10
14
u
38
+ 1.09 × 10
16
u
37
+ · · · + 2.39 × 10
15
b + 2.07 ×
10
16
, −1.44 × 10
15
u
38
− 1.84 × 10
16
u
37
+ · · · + 4.78 × 10
15
a − 3.39 ×
10
16
, u
39
+ 16u
38
+ · · · + 384u + 16i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
0.300662u
38
+ 3.84428u
37
+ ··· − 77.7458u + 7.09355
−0.239704u
38
− 4.56188u
37
+ ··· − 191.761u − 8.64586
a
10
=
0.428147u
38
+ 6.52414u
37
+ ··· + 96.7473u + 13.9087
0.905515u
38
+ 13.2597u
37
+ ··· + 56.0756u + 1.59569
a
1
=
u
u
a
4
=
0.239436u
38
+ 4.06041u
37
+ ··· + 114.171u − 2.79844
0.0678388u
38
+ 1.24701u
37
+ ··· − 66.9463u − 2.74556
a
2
=
−0.730365u
38
− 9.31593u
37
+ ··· + 536.715u + 28.7964
1.69641u
38
+ 27.9777u
37
+ ··· + 895.140u + 37.7430
a
7
=
−0.368631u
38
− 6.47910u
37
+ ··· − 578.385u − 26.6962
−1.09599u
38
− 18.3459u
37
+ ··· − 583.090u − 24.3794
a
3
=
−0.536809u
38
− 8.88416u
37
+ ··· − 128.853u − 1.15988
−1.23413u
38
− 19.3337u
37
+ ··· − 191.781u − 7.92257
a
8
=
−0.425949u
38
− 6.68769u
37
+ ··· + 5.65478u + 10.9288
−0.966315u
38
− 15.0939u
37
+ ··· − 108.361u − 4.81059
a
11
=
−0.152023u
38
− 2.64110u
37
+ ··· − 41.2325u + 6.25229
0.249003u
38
+ 3.45982u
37
+ ··· + 45.1427u + 1.36843
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
55786339166132
27162180570893
u
38
+
844053926444108
27162180570893
u
37
+ ··· +
4041570281227700
27162180570893
u +
344262331286382
27162180570893
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
39
− 30u
38
+ ··· − 270336u + 16384
c
2
, c
3
, c
6
c
10
u
39
− 17u
37
+ ··· + 3u − 1
c
4
, c
8
u
39
+ 7u
37
+ ··· − 10u − 1
c
5
, c
12
u
39
− 16u
38
+ ··· + 384u − 16
c
7
u
39
+ 28u
38
+ ··· − 39904u − 2512
c
9
, c
11
u
39
+ 2u
38
+ ··· − 20u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
39
+ 48y
37
+ ··· + 1677721600y −268435456
c
2
, c
3
, c
6
c
10
y
39
− 34y
38
+ ··· − 13y −1
c
4
, c
8
y
39
+ 14y
38
+ ··· + 28y −1
c
5
, c
12
y
39
+ 24y
38
+ ··· + 30592y −256
c
7
y
39
− 10y
38
+ ··· − 133816704y −6310144
c
9
, c
11
y
39
− 10y
38
+ ··· + 120y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.036584 + 1.055630I
a = −0.33336 − 2.00119I
b = 0.78963 − 1.21425I
−8.44685 − 3.59036I 0
u = 0.036584 − 1.055630I
a = −0.33336 + 2.00119I
b = 0.78963 + 1.21425I
−8.44685 + 3.59036I 0
u = −0.878996 + 0.590569I
a = −0.494056 − 0.310732I
b = 0.175406 − 1.010140I
−7.20717 + 4.28473I 0
u = −0.878996 − 0.590569I
a = −0.494056 + 0.310732I
b = 0.175406 + 1.010140I
−7.20717 − 4.28473I 0
u = −0.956553 + 0.471077I
a = 0.535712 − 0.170609I
b = 0.790827 + 0.990127I
−1.05743 + 4.09464I 0
u = −0.956553 − 0.471077I
a = 0.535712 + 0.170609I
b = 0.790827 − 0.990127I
−1.05743 − 4.09464I 0
u = 0.924956 + 0.600813I
a = 0.371281 + 0.003907I
b = 0.194948 + 0.056914I
−1.90733 − 0.89775I 0
u = 0.924956 − 0.600813I
a = 0.371281 − 0.003907I
b = 0.194948 − 0.056914I
−1.90733 + 0.89775I 0
u = 0.165288 + 0.859735I
a = 0.19991 + 1.68117I
b = −0.600415 + 0.828931I
0.894106 + 0.967260I −3.54690 + 1.12714I
u = 0.165288 − 0.859735I
a = 0.19991 − 1.68117I
b = −0.600415 − 0.828931I
0.894106 − 0.967260I −3.54690 − 1.12714I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.147020 + 0.124747I
a = 0.171216 + 0.003090I
b = 0.837941 + 0.589840I
5.13665 + 3.68306I 0
u = −1.147020 − 0.124747I
a = 0.171216 − 0.003090I
b = 0.837941 − 0.589840I
5.13665 − 3.68306I 0
u = −1.198810 + 0.091688I
a = −0.203582 − 0.083707I
b = −0.887863 − 0.820311I
−2.5570 + 14.4897I 0
u = −1.198810 − 0.091688I
a = −0.203582 + 0.083707I
b = −0.887863 + 0.820311I
−2.5570 − 14.4897I 0
u = −0.086623 + 1.203880I
a = 0.166421 − 0.717215I
b = 0.477964 − 0.342610I
−1.53805 − 1.55148I 0
u = −0.086623 − 1.203880I
a = 0.166421 + 0.717215I
b = 0.477964 + 0.342610I
−1.53805 + 1.55148I 0
u = −0.436516 + 1.163100I
a = −0.01640 − 1.55798I
b = 1.07400 − 1.04381I
−1.26442 − 4.12128I 0
u = −0.436516 − 1.163100I
a = −0.01640 + 1.55798I
b = 1.07400 + 1.04381I
−1.26442 + 4.12128I 0
u = 0.086287 + 1.258930I
a = −0.440278 − 0.963873I
b = 0.171571 − 0.785654I
−7.91630 + 2.00919I 0
u = 0.086287 − 1.258930I
a = −0.440278 + 0.963873I
b = 0.171571 + 0.785654I
−7.91630 − 2.00919I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270947 + 1.287730I
a = 0.34276 + 1.52890I
b = −0.670447 + 1.221440I
−12.67430 + 1.13506I 0
u = −0.270947 − 1.287730I
a = 0.34276 − 1.52890I
b = −0.670447 − 1.221440I
−12.67430 − 1.13506I 0
u = −0.640026 + 1.167660I
a = 0.30621 + 1.53504I
b = −0.96815 + 1.40442I
−3.29095 − 9.95463I 0
u = −0.640026 − 1.167660I
a = 0.30621 − 1.53504I
b = −0.96815 − 1.40442I
−3.29095 + 9.95463I 0
u = −0.107147 + 0.577529I
a = −1.68285 − 0.68447I
b = −0.004425 − 1.003520I
−7.10874 + 3.72846I −6.61899 − 2.67591I
u = −0.107147 − 0.577529I
a = −1.68285 + 0.68447I
b = −0.004425 + 1.003520I
−7.10874 − 3.72846I −6.61899 + 2.67591I
u = −0.505641 + 0.268154I
a = 0.229112 + 0.984301I
b = −0.963460 − 0.359880I
1.45784 + 0.14435I 8.80782 + 0.96026I
u = −0.505641 − 0.268154I
a = 0.229112 − 0.984301I
b = −0.963460 + 0.359880I
1.45784 − 0.14435I 8.80782 − 0.96026I
u = −0.72717 + 1.23001I
a = 0.146791 + 0.665989I
b = −0.394498 + 0.665266I
0.51433 − 3.59139I 0
u = −0.72717 − 1.23001I
a = 0.146791 − 0.665989I
b = −0.394498 − 0.665266I
0.51433 + 3.59139I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.58754 + 1.31220I
a = −0.03772 + 1.45994I
b = −1.04205 + 1.11551I
1.41624 − 9.73414I 0
u = −0.58754 − 1.31220I
a = −0.03772 − 1.45994I
b = −1.04205 − 1.11551I
1.41624 + 9.73414I 0
u = −0.72423 + 1.24628I
a = −0.564329 − 0.961952I
b = 0.267022 − 1.230810I
−9.2783 − 10.7010I 0
u = −0.72423 − 1.24628I
a = −0.564329 + 0.961952I
b = 0.267022 + 1.230810I
−9.2783 + 10.7010I 0
u = −0.59784 + 1.35155I
a = −0.00220 − 1.60026I
b = 1.08597 − 1.27810I
−6.5200 − 20.7521I 0
u = −0.59784 − 1.35155I
a = −0.00220 + 1.60026I
b = 1.08597 + 1.27810I
−6.5200 + 20.7521I 0
u = −0.30394 + 1.70133I
a = 0.362788 + 0.429884I
b = 0.071610 + 0.523994I
−8.37466 + 8.10029I 0
u = −0.30394 − 1.70133I
a = 0.362788 − 0.429884I
b = 0.071610 − 0.523994I
−8.37466 − 8.10029I 0
u = −0.0882066
a = 8.38515
b = −0.811176
1.27021 8.62500
8
II. I
u
2
= h2.68 × 10
59
au
64
+ 6.81 × 10
65
u
64
+ · · · − 1.07 × 10
60
a + 1.71 ×
10
66
, −9.82 × 10
61
au
64
− 2.56 × 10
62
u
64
+ · · · + 6.76 × 10
62
a − 1.81 ×
10
63
, u
65
− 6u
64
+ · · · − 36u + 4i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
a
−0.0000218403au
64
− 55.4714u
64
+ ··· + 0.0000873610a − 139.216
a
10
=
−0.0000218403au
64
− 55.4714u
64
+ ··· + 1.00009a − 139.216
−64.8523u
64
+ 284.498u
63
+ ··· + 2663.86u − 366.008
a
1
=
u
u
a
4
=
56.6979au
64
− 192.867u
64
+ ··· − 221.886a + 1724.99
56.6979au
64
− 145.418u
64
+ ··· − 221.886a + 1221.26
a
2
=
−108.979au
64
− 13.2505u
64
+ ··· + 462.409a − 733.686
−108.979au
64
− 27.1699u
64
+ ··· + 462.409a − 810.279
a
7
=
−1.31934au
64
+ 84.7625u
64
+ ··· − 112.851a + 91.0139
15.9696au
64
+ 48.2854u
64
+ ··· − 77.0154a + 364.848
a
3
=
−98.5806au
64
+ 104.912u
64
+ ··· + 119.466a − 1082.90
−89.2888au
64
+ 3.51127u
64
+ ··· + 286.401a − 884.916
a
8
=
0.0000218403au
64
− 9.38086u
64
+ ··· + 0.999913a − 226.791
−64.8523u
64
+ 284.498u
63
+ ··· + 2663.86u − 366.008
a
11
=
26.9885au
64
− 138.933u
64
+ ··· + 104.097a − 385.846
−19.1021au
64
− 165.186u
64
+ ··· + 191.672a − 947.582
(ii) Obstruction class = −1
(iii) Cusp Shapes = 408.688u
64
− 2253.95u
63
+ ··· + 4418.85u − 264.380
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
65
+ 9u
64
+ ··· − 21u − 1)
2
c
2
, c
3
u
130
− 4u
129
+ ··· + 172541u − 40873
c
4
u
130
+ 2u
129
+ ··· + 6u + 1
c
5
(u
65
+ 6u
64
+ ··· − 36u − 4)
2
c
6
, c
10
− u
130
− 4u
129
+ ··· + 172541u + 40873
c
7
(u
65
− 19u
64
+ ··· + 1083u − 127)
2
c
8
u
130
− 2u
129
+ ··· − 6u + 1
c
9
, c
11
− u
130
− u
129
+ ··· − 169602u + 2381
c
12
(u
65
− 6u
64
+ ··· − 36u + 4)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
65
+ 15y
64
+ ··· + 11y −1)
2
c
2
, c
3
, c
6
c
10
y
130
− 96y
129
+ ··· − 76191742939y + 1670602129
c
4
, c
8
y
130
+ 90y
128
+ ··· + 136y + 1
c
5
, c
12
(y
65
+ 34y
64
+ ··· − 88y −16)
2
c
7
(y
65
+ 25y
64
+ ··· − 23197y −16129)
2
c
9
, c
11
y
130
− 45y
129
+ ··· − 27142067854y + 5669161
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135273 + 0.982877I
a = −0.025609 − 0.204215I
b = −1.42958 − 0.25538I
−1.50370 − 0.71239I 0
u = −0.135273 + 0.982877I
a = −0.29876 + 2.83555I
b = −0.240212 + 1.373010I
−1.50370 − 0.71239I 0
u = −0.135273 − 0.982877I
a = −0.025609 + 0.204215I
b = −1.42958 + 0.25538I
−1.50370 + 0.71239I 0
u = −0.135273 − 0.982877I
a = −0.29876 − 2.83555I
b = −0.240212 − 1.373010I
−1.50370 + 0.71239I 0
u = 0.873657 + 0.506517I
a = 0.536307 − 0.042237I
b = 0.209134 − 0.330256I
−1.89142 − 0.85095I 0
u = 0.873657 + 0.506517I
a = 0.155081 + 0.030561I
b = 0.139950 + 0.417349I
−1.89142 − 0.85095I 0
u = 0.873657 − 0.506517I
a = 0.536307 + 0.042237I
b = 0.209134 + 0.330256I
−1.89142 + 0.85095I 0
u = 0.873657 − 0.506517I
a = 0.155081 − 0.030561I
b = 0.139950 − 0.417349I
−1.89142 + 0.85095I 0
u = 0.265755 + 0.978715I
a = 1.71172 − 0.88637I
b = 2.08366 − 1.09709I
−5.11006 + 11.01450I 0
u = 0.265755 + 0.978715I
a = −0.81065 − 2.57429I
b = −0.305076 − 0.308030I
−5.11006 + 11.01450I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.265755 − 0.978715I
a = 1.71172 + 0.88637I
b = 2.08366 + 1.09709I
−5.11006 − 11.01450I 0
u = 0.265755 − 0.978715I
a = −0.81065 + 2.57429I
b = −0.305076 + 0.308030I
−5.11006 − 11.01450I 0
u = −0.742829 + 0.638369I
a = −0.41941 − 1.37103I
b = 0.589065 − 1.223740I
−4.14188 − 7.28968I 0
u = −0.742829 + 0.638369I
a = −0.427327 + 0.021229I
b = 0.843142 − 0.534369I
−4.14188 − 7.28968I 0
u = −0.742829 − 0.638369I
a = −0.41941 + 1.37103I
b = 0.589065 + 1.223740I
−4.14188 + 7.28968I 0
u = −0.742829 − 0.638369I
a = −0.427327 − 0.021229I
b = 0.843142 + 0.534369I
−4.14188 + 7.28968I 0
u = 1.005090 + 0.203751I
a = 0.390055 + 0.569052I
b = 0.992721 + 0.453947I
−1.89869 − 1.35541I 0
u = 1.005090 + 0.203751I
a = 0.407466 + 0.234397I
b = −0.629185 − 0.007103I
−1.89869 − 1.35541I 0
u = 1.005090 − 0.203751I
a = 0.390055 − 0.569052I
b = 0.992721 − 0.453947I
−1.89869 + 1.35541I 0
u = 1.005090 − 0.203751I
a = 0.407466 − 0.234397I
b = −0.629185 + 0.007103I
−1.89869 + 1.35541I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.186491 + 1.039210I
a = −1.00664 − 1.61801I
b = −1.36270 − 1.66152I
−2.09496 − 5.20115I 0
u = −0.186491 + 1.039210I
a = −1.43259 + 1.91024I
b = −0.111619 + 0.361911I
−2.09496 − 5.20115I 0
u = −0.186491 − 1.039210I
a = −1.00664 + 1.61801I
b = −1.36270 + 1.66152I
−2.09496 + 5.20115I 0
u = −0.186491 − 1.039210I
a = −1.43259 − 1.91024I
b = −0.111619 − 0.361911I
−2.09496 + 5.20115I 0
u = −0.314803 + 1.029530I
a = −0.305597 − 0.888428I
b = 1.038740 − 0.353898I
−0.79992 − 3.22325I 0
u = −0.314803 + 1.029530I
a = 0.37703 − 2.04231I
b = 0.97352 − 1.21576I
−0.79992 − 3.22325I 0
u = −0.314803 − 1.029530I
a = −0.305597 + 0.888428I
b = 1.038740 + 0.353898I
−0.79992 + 3.22325I 0
u = −0.314803 − 1.029530I
a = 0.37703 + 2.04231I
b = 0.97352 + 1.21576I
−0.79992 + 3.22325I 0
u = 0.266219 + 1.061790I
a = −0.542806 + 1.038340I
b = 1.097150 + 0.519899I
−2.44218 + 7.00189I 0
u = 0.266219 + 1.061790I
a = −0.28263 − 2.45996I
b = −0.98707 − 1.60327I
−2.44218 + 7.00189I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.266219 − 1.061790I
a = −0.542806 − 1.038340I
b = 1.097150 − 0.519899I
−2.44218 − 7.00189I 0
u = 0.266219 − 1.061790I
a = −0.28263 + 2.45996I
b = −0.98707 + 1.60327I
−2.44218 − 7.00189I 0
u = −1.084880 + 0.199306I
a = −0.692212 − 0.049681I
b = −0.826317 − 0.566134I
−3.26895 + 0.49541I 0
u = −1.084880 + 0.199306I
a = 0.395640 + 0.106601I
b = −0.248420 − 0.533561I
−3.26895 + 0.49541I 0
u = −1.084880 − 0.199306I
a = −0.692212 + 0.049681I
b = −0.826317 + 0.566134I
−3.26895 − 0.49541I 0
u = −1.084880 − 0.199306I
a = 0.395640 − 0.106601I
b = −0.248420 + 0.533561I
−3.26895 − 0.49541I 0
u = −0.294216 + 0.815936I
a = 1.77206 + 0.07629I
b = 1.90194 + 0.33372I
0.39000 − 5.04655I 0
u = −0.294216 + 0.815936I
a = −0.13362 − 2.22352I
b = 0.248256 − 0.030235I
0.39000 − 5.04655I 0
u = −0.294216 − 0.815936I
a = 1.77206 − 0.07629I
b = 1.90194 − 0.33372I
0.39000 + 5.04655I 0
u = −0.294216 − 0.815936I
a = −0.13362 + 2.22352I
b = 0.248256 + 0.030235I
0.39000 + 5.04655I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.712127 + 0.485206I
a = −0.455027 − 0.805112I
b = −0.827312 + 0.723163I
0.09123 − 3.78957I 0
u = 0.712127 + 0.485206I
a = 0.685764 + 0.326436I
b = 1.006640 − 0.907692I
0.09123 − 3.78957I 0
u = 0.712127 − 0.485206I
a = −0.455027 + 0.805112I
b = −0.827312 − 0.723163I
0.09123 + 3.78957I 0
u = 0.712127 − 0.485206I
a = 0.685764 − 0.326436I
b = 1.006640 + 0.907692I
0.09123 + 3.78957I 0
u = 0.295334 + 0.803324I
a = −0.501851 + 0.068394I
b = −1.50597 + 0.47002I
−0.37995 + 1.40068I 0
u = 0.295334 + 0.803324I
a = 0.52748 + 2.52898I
b = 0.619190 + 0.688019I
−0.37995 + 1.40068I 0
u = 0.295334 − 0.803324I
a = −0.501851 − 0.068394I
b = −1.50597 − 0.47002I
−0.37995 − 1.40068I 0
u = 0.295334 − 0.803324I
a = 0.52748 − 2.52898I
b = 0.619190 − 0.688019I
−0.37995 − 1.40068I 0
u = 0.213974 + 0.827868I
a = −1.63285 + 1.00507I
b = −1.76177 + 0.98637I
2.00006 + 1.07708I 0
u = 0.213974 + 0.827868I
a = 0.61337 + 2.39422I
b = 0.0121104 + 0.1107320I
2.00006 + 1.07708I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.213974 − 0.827868I
a = −1.63285 − 1.00507I
b = −1.76177 − 0.98637I
2.00006 − 1.07708I 0
u = 0.213974 − 0.827868I
a = 0.61337 − 2.39422I
b = 0.0121104 − 0.1107320I
2.00006 − 1.07708I 0
u = 1.149900 + 0.043012I
a = −0.215152 + 0.193663I
b = −0.934018 + 0.781388I
2.26216 − 8.28168I 0
u = 1.149900 + 0.043012I
a = 0.0661547 + 0.0640179I
b = 0.851900 − 0.644902I
2.26216 − 8.28168I 0
u = 1.149900 − 0.043012I
a = −0.215152 − 0.193663I
b = −0.934018 − 0.781388I
2.26216 + 8.28168I 0
u = 1.149900 − 0.043012I
a = 0.0661547 − 0.0640179I
b = 0.851900 + 0.644902I
2.26216 + 8.28168I 0
u = 0.229791 + 0.789280I
a = 1.54262 + 0.35953I
b = −0.765175 − 0.004533I
2.08858 + 1.30200I 0
u = 0.229791 + 0.789280I
a = −0.02253 + 2.79732I
b = 0.24296 + 1.90515I
2.08858 + 1.30200I 0
u = 0.229791 − 0.789280I
a = 1.54262 − 0.35953I
b = −0.765175 + 0.004533I
2.08858 − 1.30200I 0
u = 0.229791 − 0.789280I
a = −0.02253 − 2.79732I
b = 0.24296 − 1.90515I
2.08858 − 1.30200I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.036195 + 0.802302I
a = −1.54847 + 0.81841I
b = 0.800767 + 0.464000I
−0.71965 + 4.02232I 0
u = 0.036195 + 0.802302I
a = 0.25272 − 2.84199I
b = −0.36938 − 1.87197I
−0.71965 + 4.02232I 0
u = 0.036195 − 0.802302I
a = −1.54847 − 0.81841I
b = 0.800767 − 0.464000I
−0.71965 − 4.02232I 0
u = 0.036195 − 0.802302I
a = 0.25272 + 2.84199I
b = −0.36938 + 1.87197I
−0.71965 − 4.02232I 0
u = −0.500846 + 0.617088I
a = 1.139970 − 0.142931I
b = −0.880059 + 0.058472I
0.85573 + 1.62074I 0
u = −0.500846 + 0.617088I
a = −0.13250 + 2.16082I
b = −0.88744 + 1.34741I
0.85573 + 1.62074I 0
u = −0.500846 − 0.617088I
a = 1.139970 + 0.142931I
b = −0.880059 − 0.058472I
0.85573 − 1.62074I 0
u = −0.500846 − 0.617088I
a = −0.13250 − 2.16082I
b = −0.88744 − 1.34741I
0.85573 − 1.62074I 0
u = −0.131700 + 0.774275I
a = 0.544011 + 0.271864I
b = 1.046830 + 0.778835I
−0.957261 − 0.737396I 0
u = −0.131700 + 0.774275I
a = 1.21286 − 1.80284I
b = 0.458757 − 0.322553I
−0.957261 − 0.737396I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.131700 − 0.774275I
a = 0.544011 − 0.271864I
b = 1.046830 − 0.778835I
−0.957261 + 0.737396I 0
u = −0.131700 − 0.774275I
a = 1.21286 + 1.80284I
b = 0.458757 + 0.322553I
−0.957261 + 0.737396I 0
u = 0.655247 + 1.028660I
a = 0.590854 − 0.492500I
b = 0.198784 − 0.635513I
−1.97604 − 1.03573I 0
u = 0.655247 + 1.028660I
a = −0.242127 + 0.079600I
b = 0.109791 + 0.497015I
−1.97604 − 1.03573I 0
u = 0.655247 − 1.028660I
a = 0.590854 + 0.492500I
b = 0.198784 + 0.635513I
−1.97604 + 1.03573I 0
u = 0.655247 − 1.028660I
a = −0.242127 − 0.079600I
b = 0.109791 − 0.497015I
−1.97604 + 1.03573I 0
u = 0.513393 + 1.159540I
a = −0.30718 + 1.49009I
b = 1.03112 + 1.15926I
−2.18244 + 8.52370I 0
u = 0.513393 + 1.159540I
a = 0.09440 − 1.75536I
b = −1.07069 − 1.38196I
−2.18244 + 8.52370I 0
u = 0.513393 − 1.159540I
a = −0.30718 − 1.49009I
b = 1.03112 − 1.15926I
−2.18244 − 8.52370I 0
u = 0.513393 − 1.159540I
a = 0.09440 + 1.75536I
b = −1.07069 + 1.38196I
−2.18244 − 8.52370I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.272051 + 1.299290I
a = −0.65792 + 1.66124I
b = −1.42240 + 1.38378I
−9.76212 − 10.19140I 0
u = −0.272051 + 1.299290I
a = 0.67141 + 1.75293I
b = −0.568486 + 0.917793I
−9.76212 − 10.19140I 0
u = −0.272051 − 1.299290I
a = −0.65792 − 1.66124I
b = −1.42240 − 1.38378I
−9.76212 + 10.19140I 0
u = −0.272051 − 1.299290I
a = 0.67141 − 1.75293I
b = −0.568486 − 0.917793I
−9.76212 + 10.19140I 0
u = 0.357802 + 1.288170I
a = −0.041853 + 0.572645I
b = 0.813564 + 0.482299I
−6.90283 + 3.01551I 0
u = 0.357802 + 1.288170I
a = 0.08800 − 1.55938I
b = −0.422451 − 1.069590I
−6.90283 + 3.01551I 0
u = 0.357802 − 1.288170I
a = −0.041853 − 0.572645I
b = 0.813564 − 0.482299I
−6.90283 − 3.01551I 0
u = 0.357802 − 1.288170I
a = 0.08800 + 1.55938I
b = −0.422451 + 1.069590I
−6.90283 − 3.01551I 0
u = 0.333862 + 1.327410I
a = 0.212267 + 0.954228I
b = 1.082160 + 0.784375I
−6.98353 + 3.11049I 0
u = 0.333862 + 1.327410I
a = 0.23271 − 1.72495I
b = −0.515887 − 1.097990I
−6.98353 + 3.11049I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.333862 − 1.327410I
a = 0.212267 − 0.954228I
b = 1.082160 − 0.784375I
−6.98353 − 3.11049I 0
u = 0.333862 − 1.327410I
a = 0.23271 + 1.72495I
b = −0.515887 + 1.097990I
−6.98353 − 3.11049I 0
u = 0.292504 + 0.547831I
a = −1.40577 − 0.57253I
b = 1.007980 − 0.333918I
−3.91622 − 8.35714I 1.35538 + 4.69267I
u = 0.292504 + 0.547831I
a = −0.28515 − 3.07714I
b = −0.57531 − 1.39212I
−3.91622 − 8.35714I 1.35538 + 4.69267I
u = 0.292504 − 0.547831I
a = −1.40577 + 0.57253I
b = 1.007980 + 0.333918I
−3.91622 + 8.35714I 1.35538 − 4.69267I
u = 0.292504 − 0.547831I
a = −0.28515 + 3.07714I
b = −0.57531 + 1.39212I
−3.91622 + 8.35714I 1.35538 − 4.69267I
u = 0.574631 + 1.274680I
a = −0.300009 + 1.087250I
b = 0.638666 + 0.586332I
−5.25277 + 7.06492I 0
u = 0.574631 + 1.274680I
a = −0.607879 − 1.152740I
b = −1.17790 − 0.90866I
−5.25277 + 7.06492I 0
u = 0.574631 − 1.274680I
a = −0.300009 − 1.087250I
b = 0.638666 − 0.586332I
−5.25277 − 7.06492I 0
u = 0.574631 − 1.274680I
a = −0.607879 + 1.152740I
b = −1.17790 + 0.90866I
−5.25277 − 7.06492I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.37185 + 1.38007I
a = 0.799555 + 0.256222I
b = −0.058801 + 0.351793I
−8.50119 − 4.52025I 0
u = −0.37185 + 1.38007I
a = 0.061072 + 1.195820I
b = −0.187287 + 1.220130I
−8.50119 − 4.52025I 0
u = −0.37185 − 1.38007I
a = 0.799555 − 0.256222I
b = −0.058801 − 0.351793I
−8.50119 + 4.52025I 0
u = −0.37185 − 1.38007I
a = 0.061072 − 1.195820I
b = −0.187287 − 1.220130I
−8.50119 + 4.52025I 0
u = 0.62626 + 1.29138I
a = 0.046418 − 1.102100I
b = −0.694372 − 1.072530I
−4.75054 + 7.12597I 0
u = 0.62626 + 1.29138I
a = −0.381384 + 1.047360I
b = 0.502119 + 0.938123I
−4.75054 + 7.12597I 0
u = 0.62626 − 1.29138I
a = 0.046418 + 1.102100I
b = −0.694372 + 1.072530I
−4.75054 − 7.12597I 0
u = 0.62626 − 1.29138I
a = −0.381384 − 1.047360I
b = 0.502119 − 0.938123I
−4.75054 − 7.12597I 0
u = −0.57994 + 1.33675I
a = −0.255760 − 1.045310I
b = 0.901436 − 0.780415I
−6.95291 − 6.59702I 0
u = −0.57994 + 1.33675I
a = 0.28765 − 1.74762I
b = 1.02520 − 1.39326I
−6.95291 − 6.59702I 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.57994 − 1.33675I
a = −0.255760 + 1.045310I
b = 0.901436 + 0.780415I
−6.95291 + 6.59702I 0
u = −0.57994 − 1.33675I
a = 0.28765 + 1.74762I
b = 1.02520 + 1.39326I
−6.95291 + 6.59702I 0
u = 0.57141 + 1.34515I
a = −0.04647 − 1.43045I
b = −1.12942 − 1.11659I
−1.7952 + 14.2981I 0
u = 0.57141 + 1.34515I
a = 0.03565 + 1.68994I
b = 1.04099 + 1.27738I
−1.7952 + 14.2981I 0
u = 0.57141 − 1.34515I
a = −0.04647 + 1.43045I
b = −1.12942 + 1.11659I
−1.7952 − 14.2981I 0
u = 0.57141 − 1.34515I
a = 0.03565 − 1.68994I
b = 1.04099 − 1.27738I
−1.7952 − 14.2981I 0
u = 0.04804 + 1.51825I
a = 0.482203 − 0.795052I
b = 0.100540 − 0.361534I
−3.59145 − 1.62787I 0
u = 0.04804 + 1.51825I
a = 0.440731 + 0.484955I
b = 0.676525 + 0.558637I
−3.59145 − 1.62787I 0
u = 0.04804 − 1.51825I
a = 0.482203 + 0.795052I
b = 0.100540 + 0.361534I
−3.59145 + 1.62787I 0
u = 0.04804 − 1.51825I
a = 0.440731 − 0.484955I
b = 0.676525 − 0.558637I
−3.59145 + 1.62787I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.451010 + 0.159443I
a = 0.241718 + 1.096620I
b = −0.973442 − 0.244762I
1.43317 + 0.17568I 8.43284 − 0.01950I
u = −0.451010 + 0.159443I
a = 0.986111 + 0.749441I
b = −0.761924 − 0.411230I
1.43317 + 0.17568I 8.43284 − 0.01950I
u = −0.451010 − 0.159443I
a = 0.241718 − 1.096620I
b = −0.973442 + 0.244762I
1.43317 − 0.17568I 8.43284 + 0.01950I
u = −0.451010 − 0.159443I
a = 0.986111 − 0.749441I
b = −0.761924 + 0.411230I
1.43317 − 0.17568I 8.43284 + 0.01950I
u = 0.322814 + 0.079473I
a = 0.52772 + 1.82244I
b = 1.041910 − 0.610442I
−0.07886 − 4.39922I 2.83973 + 4.40314I
u = 0.322814 + 0.079473I
a = 2.24485 − 1.78762I
b = −0.359334 + 0.744505I
−0.07886 − 4.39922I 2.83973 + 4.40314I
u = 0.322814 − 0.079473I
a = 0.52772 − 1.82244I
b = 1.041910 + 0.610442I
−0.07886 + 4.39922I 2.83973 − 4.40314I
u = 0.322814 − 0.079473I
a = 2.24485 + 1.78762I
b = −0.359334 − 0.744505I
−0.07886 + 4.39922I 2.83973 − 4.40314I
u = −2.55622
a = −0.440039
b = −0.506514
−3.73596 0
u = −2.55622
a = 0.0282265
b = −0.169924
−3.73596 0
24
III. I
u
3
= h4u
19
+ 19u
18
+ · · · + 3b − 84, 40u
19
+ 265u
18
+ · · · + 9a −
252, u
20
+ 7u
19
+ · · · + 42u + 9i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
−
40
9
u
19
−
265
9
u
18
+ ··· +
968
9
u + 28
−
4
3
u
19
−
19
3
u
18
+ ··· +
392
3
u + 28
a
10
=
−
7
9
u
19
−
16
9
u
18
+ ··· +
1874
9
u + 41
2
3
u
19
+
29
3
u
18
+ ··· +
743
3
u + 46
a
1
=
u
u
a
4
=
5
3
u
18
+
38
3
u
17
+ ··· +
379
3
u +
74
3
2
3
u
19
+
17
3
u
18
+ ··· +
137
3
u + 6
a
2
=
29
9
u
19
+
200
9
u
18
+ ··· −
592
9
u − 17
8
3
u
19
+
50
3
u
18
+ ··· −
151
3
u − 11
a
7
=
−
20
3
u
19
− 47u
18
+ ··· −
40
3
u +
41
3
−
13
3
u
19
−
88
3
u
18
+ ··· +
293
3
u + 33
a
3
=
−2.55556u
19
− 22.2222u
18
+ ··· − 193.889u − 32.6667
−
13
3
u
19
−
100
3
u
18
+ ··· −
415
3
u − 19
a
8
=
−
13
9
u
19
−
58
9
u
18
+ ··· +
1724
9
u + 40
5
3
u
19
+
50
3
u
18
+ ··· +
644
3
u + 40
a
11
=
−
8
3
u
19
−
58
3
u
18
+ ··· − u +
19
3
−
5
3
u
19
−
32
3
u
18
+ ··· +
313
3
u + 24
(ii) Obstruction class = 1
(iii) Cusp Shapes = −13u
19
− 93u
18
− 421u
17
− 1363u
16
− 3495u
15
− 7363u
14
−
13102u
13
− 20033u
12
− 26617u
11
− 30997u
10
− 31771u
9
− 28679u
8
− 22729u
7
−
15646u
6
− 9231u
5
− 4507u
4
− 1738u
3
− 439u
2
− 39u + 30
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 8u
19
+ ··· − 8u + 1
c
2
, c
10
u
20
+ u
19
+ ··· − u + 1
c
3
, c
6
u
20
− u
19
+ ··· + u + 1
c
4
, c
8
u
20
− u
19
+ ··· + 4u + 1
c
5
u
20
+ 7u
19
+ ··· + 42u + 9
c
7
u
20
+ 5u
19
+ ··· + 89u + 7
c
9
, c
11
u
20
− u
19
+ ··· + 2u + 1
c
12
u
20
− 7u
19
+ ··· − 42u + 9
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 16y
19
+ ··· + 16y + 1
c
2
, c
3
, c
6
c
10
y
20
− 15y
19
+ ··· − 7y + 1
c
4
, c
8
y
20
+ y
19
+ ··· + 4y + 1
c
5
, c
12
y
20
+ 15y
19
+ ··· + 738y + 81
c
7
y
20
+ 5y
19
+ ··· − 95y + 49
c
9
, c
11
y
20
− 7y
19
+ ··· − 4y + 1
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.132354 + 0.898303I
a = 0.15715 + 1.96554I
b = −0.773170 + 0.967766I
1.44598 + 0.41600I 3.49879 + 5.89775I
u = 0.132354 − 0.898303I
a = 0.15715 − 1.96554I
b = −0.773170 − 0.967766I
1.44598 − 0.41600I 3.49879 − 5.89775I
u = 0.196976 + 0.872387I
a = 0.53045 − 1.92774I
b = 1.007610 − 0.664998I
−4.98839 + 9.92530I −1.69942 − 5.27594I
u = 0.196976 − 0.872387I
a = 0.53045 + 1.92774I
b = 1.007610 + 0.664998I
−4.98839 − 9.92530I −1.69942 + 5.27594I
u = −0.763618 + 0.456574I
a = 0.588522 − 0.510428I
b = 0.943872 + 0.962545I
0.36096 + 4.68512I 5.51102 − 11.41474I
u = −0.763618 − 0.456574I
a = 0.588522 + 0.510428I
b = 0.943872 − 0.962545I
0.36096 − 4.68512I 5.51102 + 11.41474I
u = 0.258613 + 0.846747I
a = 0.263583 + 1.364150I
b = −0.382563 + 0.715000I
1.14834 + 1.50481I 2.91202 − 9.16284I
u = 0.258613 − 0.846747I
a = 0.263583 − 1.364150I
b = −0.382563 − 0.715000I
1.14834 − 1.50481I 2.91202 + 9.16284I
u = −0.298366 + 0.813116I
a = −0.35523 − 1.63918I
b = 1.016380 − 0.892498I
−1.37181 − 5.75633I 1.47939 + 6.24502I
u = −0.298366 − 0.813116I
a = −0.35523 + 1.63918I
b = 1.016380 + 0.892498I
−1.37181 + 5.75633I 1.47939 − 6.24502I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.181400 + 0.267071I
a = −0.059306 + 0.160162I
b = −0.572894 + 0.286937I
−1.43260 + 0.73706I 5.63800 + 6.58777I
u = −1.181400 − 0.267071I
a = −0.059306 − 0.160162I
b = −0.572894 − 0.286937I
−1.43260 − 0.73706I 5.63800 − 6.58777I
u = −0.570897 + 1.173290I
a = 0.24797 + 1.62734I
b = −1.04356 + 1.36634I
−1.96294 − 9.84242I 2.62456 + 11.26073I
u = −0.570897 − 1.173290I
a = 0.24797 − 1.62734I
b = −1.04356 − 1.36634I
−1.96294 + 9.84242I 2.62456 − 11.26073I
u = −0.52244 + 1.37539I
a = 0.110941 − 1.252670I
b = 0.898732 − 0.898470I
−6.24410 − 5.00718I −3.03575 + 3.84902I
u = −0.52244 − 1.37539I
a = 0.110941 + 1.252670I
b = 0.898732 + 0.898470I
−6.24410 + 5.00718I −3.03575 − 3.84902I
u = −0.64850 + 1.37043I
a = −0.323700 − 0.338117I
b = −0.035363 − 0.500365I
−2.34740 + 1.34900I −17.2853 − 3.1865I
u = −0.64850 − 1.37043I
a = −0.323700 + 0.338117I
b = −0.035363 + 0.500365I
−2.34740 − 1.34900I −17.2853 + 3.1865I
u = −0.10273 + 1.53255I
a = −0.327046 + 0.668911I
b = −0.559048 + 0.319678I
−7.63713 − 8.31054I −1.64333 + 9.35402I
u = −0.10273 − 1.53255I
a = −0.327046 − 0.668911I
b = −0.559048 − 0.319678I
−7.63713 + 8.31054I −1.64333 − 9.35402I
29
IV. I
u
4
= h−u
6
a + 3u
6
+ · · · − 3a + 20, 105u
6
a + 64u
6
+ · · · − 84a − 80, u
7
−
4u
6
+ 7u
5
− 11u
4
+ 9u
3
− 10u
2
+ 4u − 3i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
9
=
a
1
7
u
6
a −
3
7
u
6
+ ··· +
3
7
a −
20
7
a
10
=
1
7
u
6
a −
3
7
u
6
+ ··· +
10
7
a −
20
7
−u
6
− u
4
a + 5u
5
− 10u
4
− u
2
a + 14u
3
− au − 13u
2
+ 8u − 5
a
1
=
u
u
a
4
=
−
5
7
u
6
a −
2
21
u
6
+ ··· +
9
7
a +
79
21
−
5
7
u
6
a +
2
7
u
6
+ ··· +
9
7
a +
30
7
a
2
=
−0.571429au
6
− 0.333333u
6
+ ··· + 0.619048u + 1.95238
−
4
7
u
6
a −
1
7
u
6
+ ··· +
2
7
u +
12
7
a
7
=
4
7
u
5
a −
1
7
u
6
+ ··· −
16
7
a +
1
7
−
2
7
u
6
a +
10
7
u
5
a + ··· −
15
7
a − 1
a
3
=
−
4
7
u
6
a −
2
3
u
6
+ ··· +
4
7
a +
46
21
−
4
7
u
6
a −
5
7
u
6
+ ··· +
6
7
a +
16
7
a
8
=
−
1
7
u
6
a −
4
7
u
6
+ ··· +
4
7
a −
15
7
−u
6
+ 5u
5
− 10u
4
+ 14u
3
− au − 13u
2
+ 8u − 5
a
11
=
2
7
u
6
a +
4
21
u
6
+ ··· +
11
7
a −
17
21
3
7
u
6
a −
10
7
u
5
a + ··· +
6
7
a −
13
7
(ii) Obstruction class = 1
(iii) Cusp Shapes =
48
7
u
6
−
142
7
u
5
+
282
7
u
4
−
278
7
u
3
+
220
7
u
2
− 19u +
66
7
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 2u
6
− 2u
5
− u
4
+ 2u
3
− 2u + 1)
2
c
2
, c
10
u
14
+ 2u
13
+ ··· − 2u − 1
c
3
, c
6
u
14
− 2u
13
+ ··· + 2u − 1
c
4
, c
8
u
14
+ u
12
+ ··· − u − 1
c
5
(u
7
− 4u
6
+ 7u
5
− 11u
4
+ 9u
3
− 10u
2
+ 4u − 3)
2
c
7
(u
7
+ 2u
6
− 2u
4
− u
3
+ 2u
2
+ 2u − 1)
2
c
9
, c
11
u
14
+ 5u
13
+ ··· + 19u − 1
c
12
(u
7
+ 4u
6
+ 7u
5
+ 11u
4
+ 9u
3
+ 10u
2
+ 4u + 3)
2
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
7
− 8y
6
+ 12y
5
− 13y
4
+ 8y
3
− 6y
2
+ 4y − 1)
2
c
2
, c
3
, c
6
c
10
y
14
− 22y
13
+ ··· − 6y + 1
c
4
, c
8
y
14
+ 2y
13
+ ··· − 39y + 1
c
5
, c
12
(y
7
− 2y
6
− 21y
5
− 67y
4
− 107y
3
− 94y
2
− 44y − 9)
2
c
7
(y
7
− 4y
6
+ 6y
5
− 8y
4
+ 13y
3
− 12y
2
+ 8y − 1)
2
c
9
, c
11
y
14
− 23y
13
+ ··· − 253y + 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.192587 + 0.916625I
a = −0.831182 + 0.178282I
b = 0.954520 − 0.175020I
−1.06765 − 4.78787I 0.89921 + 9.02652I
u = −0.192587 + 0.916625I
a = −0.37235 − 2.66376I
b = 0.02006 − 1.70486I
−1.06765 − 4.78787I 0.89921 + 9.02652I
u = −0.192587 − 0.916625I
a = −0.831182 − 0.178282I
b = 0.954520 + 0.175020I
−1.06765 + 4.78787I 0.89921 − 9.02652I
u = −0.192587 − 0.916625I
a = −0.37235 + 2.66376I
b = 0.02006 + 1.70486I
−1.06765 + 4.78787I 0.89921 − 9.02652I
u = 0.248771 + 0.802486I
a = −0.419648 − 0.132335I
b = −1.361380 + 0.281050I
0.79884 + 1.27057I 4.19539 − 5.04627I
u = 0.248771 + 0.802486I
a = 0.40574 + 2.29966I
b = 0.566012 + 0.652891I
0.79884 + 1.27057I 4.19539 − 5.04627I
u = 0.248771 − 0.802486I
a = −0.419648 + 0.132335I
b = −1.361380 − 0.281050I
0.79884 − 1.27057I 4.19539 + 5.04627I
u = 0.248771 − 0.802486I
a = 0.40574 − 2.29966I
b = 0.566012 − 0.652891I
0.79884 − 1.27057I 4.19539 + 5.04627I
u = 0.634150 + 1.203070I
a = −0.527419 + 0.961767I
b = 0.693861 + 0.745868I
−6.08989 + 7.46557I −5.74304 − 10.76826I
u = 0.634150 + 1.203070I
a = −0.31114 − 1.52798I
b = −1.03422 − 1.33238I
−6.08989 + 7.46557I −5.74304 − 10.76826I
33
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.634150 − 1.203070I
a = −0.527419 − 0.961767I
b = 0.693861 − 0.745868I
−6.08989 − 7.46557I −5.74304 + 10.76826I
u = 0.634150 − 1.203070I
a = −0.31114 + 1.52798I
b = −1.03422 + 1.33238I
−6.08989 − 7.46557I −5.74304 + 10.76826I
u = 2.61933
a = 0.429320
b = 0.495409
−3.73195 1071.30
u = 2.61933
a = 0.0160275
b = −0.173108
−3.73195 1071.30
34
V. I
v
1
= ha, b + 1, v
2
− v + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
v
0
a
6
=
1
0
a
9
=
0
−1
a
10
=
−1
−1
a
1
=
v
0
a
4
=
1
1
a
2
=
2v
v
a
7
=
2v − 1
v − 1
a
3
=
v + 2
v + 1
a
8
=
v − 1
−1
a
11
=
v + 1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
2
− u + 1
c
2
, c
7
, c
11
u
2
+ u + 1
c
3
, c
4
(u + 1)
2
c
5
, c
12
u
2
c
9
, c
10
(u − 1)
2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
11
y
2
+ y + 1
c
3
, c
4
, c
9
c
10
(y − 1)
2
c
5
, c
12
y
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −1.00000
0 3.00000
v = 0.500000 − 0.866025I
a = 0
b = −1.00000
0 3.00000
38
VI. I
v
2
= ha, b + v − 1, v
2
− v + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
v
0
a
6
=
1
0
a
9
=
0
−v + 1
a
10
=
−v + 1
−v + 1
a
1
=
v
0
a
4
=
1
−v
a
2
=
1
−1
a
7
=
0
1
a
3
=
1
0
a
8
=
−v
−v + 1
a
11
=
0
−v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
2
− u + 1
c
2
, c
11
(u − 1)
2
c
5
, c
12
u
2
c
6
, c
8
(u + 1)
2
c
7
, c
9
, c
10
u
2
+ u + 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
, c
9
, c
10
y
2
+ y + 1
c
2
, c
6
, c
8
c
11
(y − 1)
2
c
5
, c
12
y
2
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
0 3.00000
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
0 3.00000
42
VII. I
v
3
= ha, b + 1, v + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
−1
0
a
6
=
1
0
a
9
=
0
−1
a
10
=
−1
−1
a
1
=
−1
0
a
4
=
1
1
a
2
=
−2
−1
a
7
=
3
1
a
3
=
1
0
a
8
=
1
−1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
43
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
6
, c
8
u + 1
c
2
, c
9
, c
10
c
11
u − 1
c
5
, c
12
u
c
7
u + 2
44
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
8
c
9
, c
10
, c
11
y − 1
c
5
, c
12
y
c
7
y − 4
45
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
0 0
46
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
2
− u + 1)
2
(u
7
+ 2u
6
− 2u
5
− u
4
+ 2u
3
− 2u + 1)
2
· (u
20
− 8u
19
+ ··· − 8u + 1)(u
39
− 30u
38
+ ··· − 270336u + 16384)
c
2
, c
10
((u − 1)
3
)(u
2
+ u + 1)(u
14
+ 2u
13
+ ··· − 2u − 1)(u
20
+ u
19
+ ··· − u + 1)
· (u
39
− 17u
37
+ ··· + 3u − 1)
c
3
, c
6
((u + 1)
3
)(u
2
− u + 1)(u
14
− 2u
13
+ ··· + 2u − 1)(u
20
− u
19
+ ··· + u + 1)
· (u
39
− 17u
37
+ ··· + 3u − 1)
c
4
, c
8
((u + 1)
3
)(u
2
− u + 1)(u
14
+ u
12
+ ··· − u − 1)(u
20
− u
19
+ ··· + 4u + 1)
· (u
39
+ 7u
37
+ ··· − 10u − 1)
c
5
u
5
(u
7
− 4u
6
+ 7u
5
− 11u
4
+ 9u
3
− 10u
2
+ 4u − 3)
2
· (u
20
+ 7u
19
+ ··· + 42u + 9)(u
39
− 16u
38
+ ··· + 384u − 16)
c
7
(u + 2)(u
2
+ u + 1)
2
(u
7
+ 2u
6
− 2u
4
− u
3
+ 2u
2
+ 2u − 1)
2
· (u
20
+ 5u
19
+ ··· + 89u + 7)(u
39
+ 28u
38
+ ··· − 39904u − 2512)
c
9
, c
11
((u − 1)
3
)(u
2
+ u + 1)(u
14
+ 5u
13
+ ··· + 19u − 1)
· (u
20
− u
19
+ ··· + 2u + 1)(u
39
+ 2u
38
+ ··· − 20u − 7)
c
12
u
5
(u
7
+ 4u
6
+ 7u
5
+ 11u
4
+ 9u
3
+ 10u
2
+ 4u + 3)
2
· (u
20
− 7u
19
+ ··· − 42u + 9)(u
39
− 16u
38
+ ··· + 384u − 16)
47
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)(y
2
+ y + 1)
2
(y
7
− 8y
6
+ ··· + 4y − 1)
2
· (y
20
+ 16y
19
+ ··· + 16y + 1)
· (y
39
+ 48y
37
+ ··· + 1677721600y − 268435456)
c
2
, c
3
, c
6
c
10
((y − 1)
3
)(y
2
+ y + 1)(y
14
− 22y
13
+ ··· − 6y + 1)
· (y
20
− 15y
19
+ ··· − 7y + 1)(y
39
− 34y
38
+ ··· − 13y − 1)
c
4
, c
8
((y − 1)
3
)(y
2
+ y + 1)(y
14
+ 2y
13
+ ··· − 39y + 1)
· (y
20
+ y
19
+ ··· + 4y + 1)(y
39
+ 14y
38
+ ··· + 28y − 1)
c
5
, c
12
y
5
(y
7
− 2y
6
− 21y
5
− 67y
4
− 107y
3
− 94y
2
− 44y − 9)
2
· (y
20
+ 15y
19
+ ··· + 738y + 81)(y
39
+ 24y
38
+ ··· + 30592y − 256)
c
7
(y − 4)(y
2
+ y + 1)
2
(y
7
− 4y
6
+ ··· + 8y − 1)
2
· (y
20
+ 5y
19
+ ··· − 95y + 49)
· (y
39
− 10y
38
+ ··· − 133816704y − 6310144)
c
9
, c
11
((y − 1)
3
)(y
2
+ y + 1)(y
14
− 23y
13
+ ··· − 253y + 1)
· (y
20
− 7y
19
+ ··· − 4y + 1)(y
39
− 10y
38
+ ··· + 120y − 49)
48
