12a
1035
(K12a
1035
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 12 2 3 11 5 1 6 9
Solving Sequence
2,7
3 8
4,11
9 1 6 12 5 10
c
2
c
7
c
3
c
8
c
1
c
6
c
11
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−181u
30
− 802u
29
+ ··· + 2b + 456, −133u
30
− 587u
29
+ ··· + 2a + 329, u
31
+ 6u
30
+ ··· + 14u − 4i
I
u
2
= h22271u
14
a
3
− 122677u
14
a
2
+ ··· + 165657a − 109901, −u
14
a
2
+ 7u
14
a + ··· − 30a + 28,
u
15
− u
14
− 8u
13
+ 7u
12
+ 24u
11
− 16u
10
− 34u
9
+ 11u
8
+ 26u
7
+ 2u
6
− 14u
5
+ 4u
3
+ 2u
2
− 2u − 1i
I
u
3
= h−u
13
+ 7u
11
+ u
10
− 17u
9
− 4u
8
+ 16u
7
+ 2u
6
− 7u
5
+ 5u
4
+ 7u
3
− u
2
+ b,
− u
12
+ 8u
10
− 22u
8
+ 24u
6
− 2u
5
− 11u
4
+ 6u
3
+ 7u
2
+ a − 3u,
u
14
− u
13
− 8u
12
+ 7u
11
+ 24u
10
− 17u
9
− 33u
8
+ 17u
7
+ 21u
6
− 10u
5
− 7u
4
+ 9u
3
+ 2u
2
− u − 1i
* 3 irreducible components of dim
C
= 0, with total 105 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−181u
30
− 802u
29
+ · · · + 2b + 456, −133u
30
− 587u
29
+ · · · + 2a +
329, u
31
+ 6u
30
+ · · · + 14u − 4i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
8
=
−u
−u
3
+ u
a
4
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
133
2
u
30
+
587
2
u
29
+ ··· + 686u −
329
2
181
2
u
30
+ 401u
29
+ ··· +
1881
2
u − 228
a
9
=
−
79
4
u
30
− 89u
29
+ ··· −
885
4
u + 52
−
59
2
u
30
− 132u
29
+ ··· −
639
2
u + 77
a
1
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
6
=
u
u
a
12
=
21
2
u
30
+
83
2
u
29
+ ··· + 79u −
37
2
69
2
u
30
+ 149u
29
+ ··· +
667
2
u − 82
a
5
=
−
49
4
u
30
− 54u
29
+ ··· −
479
4
u + 30
−
21
2
u
30
− 48u
29
+ ··· −
241
2
u + 29
a
10
=
−u
30
+
1
2
u
29
+ ··· +
57
2
u −
9
2
7
2
u
30
+ 20u
29
+ ··· +
141
2
u − 16
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −81u
30
− 353u
29
+ 499u
28
+ 3872u
27
− 74u
26
− 17898u
25
− 4528u
24
+ 48948u
23
+
3960u
22
− 97075u
21
+ 31813u
20
+ 144406u
19
− 112024u
18
− 128297u
17
+ 202242u
16
+
19409u
15
− 222196u
14
+ 102946u
13
+ 118470u
12
− 155647u
11
− 3449u
10
+ 92237u
9
−
51860u
8
− 22781u
7
+ 31120u
6
− 7025u
5
− 7682u
4
+ 4279u
3
− 14u
2
− 756u + 170
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
− 6u
30
+ ··· + 17032u + 3008
c
2
, c
3
, c
6
c
7
u
31
− 6u
30
+ ··· + 14u + 4
c
4
, c
5
, c
9
c
11
u
31
+ 12u
29
+ ··· + 2u + 1
c
8
, c
10
u
31
+ 2u
30
+ ··· + 11u + 1
c
12
u
31
+ 33u
30
+ ··· + 655360u + 32768
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 14y
30
+ ··· + 194260160y −9048064
c
2
, c
3
, c
6
c
7
y
31
− 34y
30
+ ··· + 268y −16
c
4
, c
5
, c
9
c
11
y
31
+ 24y
30
+ ··· + 12y −1
c
8
, c
10
y
31
+ 2y
30
+ ··· + 29y −1
c
12
y
31
+ 3y
30
+ ··· + 20401094656y −1073741824
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.689568 + 0.711824I
a = 0.130088 − 0.331811I
b = 1.002630 + 0.498746I
5.82989 − 3.44362I −5.04834 + 9.30785I
u = 0.689568 − 0.711824I
a = 0.130088 + 0.331811I
b = 1.002630 − 0.498746I
5.82989 + 3.44362I −5.04834 − 9.30785I
u = 0.644371 + 0.613769I
a = −0.242643 + 0.183681I
b = −1.78223 − 0.62081I
8.1222 − 13.5080I −8.59420 + 9.11815I
u = 0.644371 − 0.613769I
a = −0.242643 − 0.183681I
b = −1.78223 + 0.62081I
8.1222 + 13.5080I −8.59420 − 9.11815I
u = −1.052860 + 0.374486I
a = 0.147933 + 0.319672I
b = 0.749156 − 0.604636I
2.99598 + 5.86638I −8.62905 − 10.38587I
u = −1.052860 − 0.374486I
a = 0.147933 − 0.319672I
b = 0.749156 + 0.604636I
2.99598 − 5.86638I −8.62905 + 10.38587I
u = 0.246593 + 0.835945I
a = −0.706404 − 0.362266I
b = 0.645159 − 0.082571I
7.12015 − 1.65223I 4.05704 + 1.14509I
u = 0.246593 − 0.835945I
a = −0.706404 + 0.362266I
b = 0.645159 + 0.082571I
7.12015 + 1.65223I 4.05704 − 1.14509I
u = 0.326413 + 0.688470I
a = 0.76255 + 1.47066I
b = −0.692232 + 0.121974I
9.06712 + 9.13286I −6.46930 − 3.89273I
u = 0.326413 − 0.688470I
a = 0.76255 − 1.47066I
b = −0.692232 − 0.121974I
9.06712 − 9.13286I −6.46930 + 3.89273I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.561340 + 0.467670I
a = 0.213153 + 0.590915I
b = 0.929737 − 0.172994I
−0.79381 − 3.44032I −15.0997 + 6.5409I
u = 0.561340 − 0.467670I
a = 0.213153 − 0.590915I
b = 0.929737 + 0.172994I
−0.79381 + 3.44032I −15.0997 − 6.5409I
u = −1.322110 + 0.192020I
a = −0.001468 − 0.451220I
b = 0.130828 + 0.618327I
3.87543 − 5.94393I −9.66825 + 3.93876I
u = −1.322110 − 0.192020I
a = −0.001468 + 0.451220I
b = 0.130828 − 0.618327I
3.87543 + 5.94393I −9.66825 − 3.93876I
u = −0.590937 + 0.161479I
a = −0.626188 − 0.664332I
b = −1.351820 − 0.247148I
−2.73754 + 0.38412I −17.5394 − 12.3371I
u = −0.590937 − 0.161479I
a = −0.626188 + 0.664332I
b = −1.351820 + 0.247148I
−2.73754 − 0.38412I −17.5394 + 12.3371I
u = 0.380886 + 0.410622I
a = 0.376186 − 0.990063I
b = −0.338423 − 0.093255I
−0.260092 + 0.248902I −13.42836 + 0.35598I
u = 0.380886 − 0.410622I
a = 0.376186 + 0.990063I
b = −0.338423 + 0.093255I
−0.260092 − 0.248902I −13.42836 − 0.35598I
u = −1.54304 + 0.09101I
a = −1.153730 − 0.253473I
b = −1.60000 − 0.46649I
−6.90265 + 1.26668I 0
u = −1.54304 − 0.09101I
a = −1.153730 + 0.253473I
b = −1.60000 + 0.46649I
−6.90265 − 1.26668I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55633 + 0.13225I
a = 1.87141 + 0.87299I
b = 2.39850 + 1.02474I
−7.92003 + 5.59839I 0
u = −1.55633 − 0.13225I
a = 1.87141 − 0.87299I
b = 2.39850 − 1.02474I
−7.92003 − 5.59839I 0
u = 1.57004 + 0.04724I
a = −2.37428 + 0.51267I
b = −2.70859 + 0.17576I
−10.13910 − 1.16704I 0
u = 1.57004 − 0.04724I
a = −2.37428 − 0.51267I
b = −2.70859 − 0.17576I
−10.13910 + 1.16704I 0
u = −1.58052 + 0.19018I
a = −2.71394 − 0.04037I
b = −3.15957 + 0.84008I
0.6908 + 16.4865I 0
u = −1.58052 − 0.19018I
a = −2.71394 + 0.04037I
b = −3.15957 − 0.84008I
0.6908 − 16.4865I 0
u = −1.58443 + 0.22713I
a = 1.47735 + 0.07070I
b = 1.64032 − 0.65576I
−1.67379 + 6.94665I 0
u = −1.58443 − 0.22713I
a = 1.47735 − 0.07070I
b = 1.64032 + 0.65576I
−1.67379 − 6.94665I 0
u = 1.64692 + 0.06572I
a = 1.42991 + 0.89247I
b = 1.75616 + 1.56825I
−6.18258 − 7.30230I 0
u = 1.64692 − 0.06572I
a = 1.42991 − 0.89247I
b = 1.75616 − 1.56825I
−6.18258 + 7.30230I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.328219
a = 0.820145
b = −0.239259
−0.539109 −18.1900
8
II. I
u
2
= h2.23 × 10
4
a
3
u
14
− 1.23 × 10
5
a
2
u
14
+ · · · + 1.66 × 10
5
a − 1.10 ×
10
5
, −u
14
a
2
+ 7u
14
a + · · · − 30a + 28, u
15
− u
14
+ · · · − 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
8
=
−u
−u
3
+ u
a
4
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
a
−0.545443a
3
u
14
+ 3.00451a
2
u
14
+ ··· − 4.05714a + 2.69161
a
9
=
0.172687a
3
u
14
− 0.897529a
2
u
14
+ ··· + 1.26455a − 0.490853
0.172687a
3
u
14
+ 0.264872a
2
u
14
+ ··· + 1.26455a − 1.43082
a
1
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
6
=
u
u
a
12
=
0.292743a
3
u
14
− 0.897529a
2
u
14
+ ··· + 4.26595a − 2.49085
−0.252700a
3
u
14
+ 2.10698a
2
u
14
+ ··· − 0.791188a + 0.200754
a
5
=
0.610247a
3
u
14
− 0.567779a
2
u
14
+ ··· + 0.0456516a + 0.594989
0.772893a
3
u
14
+ 2.14653a
2
u
14
+ ··· + 0.848644a − 2.81041
a
10
=
−1.24011a
3
u
14
+ 0.00279200a
2
u
14
+ ··· + 0.997208a + 1.06980
−1.85256a
3
u
14
− 0.317504a
2
u
14
+ ··· − 1.73513a + 2.64135
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
293736
40831
u
14
a
3
+
28204
40831
u
14
a
2
+ ··· −
79780
40831
a −
605790
40831
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
15
− 3u
14
+ ··· + 4u
2
− 1)
4
c
2
, c
3
, c
6
c
7
(u
15
+ u
14
+ ··· − 2u + 1)
4
c
4
, c
5
, c
9
c
11
u
60
− u
59
+ ··· − 4u + 7
c
8
, c
10
u
60
− 17u
59
+ ··· − 42774u + 2977
c
12
(u
2
− u + 1)
30
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
15
+ 7y
14
+ ··· + 8y − 1)
4
c
2
, c
3
, c
6
c
7
(y
15
− 17y
14
+ ··· + 8y − 1)
4
c
4
, c
5
, c
9
c
11
y
60
+ 51y
59
+ ··· + 4212y + 49
c
8
, c
10
y
60
+ 19y
59
+ ··· + 124785424y + 8862529
c
12
(y
2
+ y + 1)
30
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.837202
a = 0.093012 + 0.540038I
b = −0.884228 + 0.470380I
−0.59068 + 2.02988I −15.0394 − 3.4641I
u = 0.837202
a = 0.093012 − 0.540038I
b = −0.884228 − 0.470380I
−0.59068 − 2.02988I −15.0394 + 3.4641I
u = 0.837202
a = 0.367613 + 0.257786I
b = 0.566476 − 1.020740I
−0.59068 + 2.02988I −15.0394 − 3.4641I
u = 0.837202
a = 0.367613 − 0.257786I
b = 0.566476 + 1.020740I
−0.59068 − 2.02988I −15.0394 + 3.4641I
u = −0.616241 + 0.538656I
a = −0.019747 + 0.571805I
b = 0.120120 + 0.478574I
2.75151 + 3.42335I −9.99532 − 2.88720I
u = −0.616241 + 0.538656I
a = −0.234673 − 0.495636I
b = 1.121840 + 0.294991I
2.75151 + 7.48312I −9.99532 − 9.81541I
u = −0.616241 + 0.538656I
a = −0.486462 + 0.014976I
b = −1.79976 + 0.86947I
2.75151 + 7.48312I −9.99532 − 9.81541I
u = −0.616241 + 0.538656I
a = −0.035949 + 0.293046I
b = 1.227290 − 0.473717I
2.75151 + 3.42335I −9.99532 − 2.88720I
u = −0.616241 − 0.538656I
a = −0.019747 − 0.571805I
b = 0.120120 − 0.478574I
2.75151 − 3.42335I −9.99532 + 2.88720I
u = −0.616241 − 0.538656I
a = −0.234673 + 0.495636I
b = 1.121840 − 0.294991I
2.75151 − 7.48312I −9.99532 + 9.81541I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.616241 − 0.538656I
a = −0.486462 − 0.014976I
b = −1.79976 − 0.86947I
2.75151 − 7.48312I −9.99532 + 9.81541I
u = −0.616241 − 0.538656I
a = −0.035949 − 0.293046I
b = 1.227290 + 0.473717I
2.75151 − 3.42335I −9.99532 + 2.88720I
u = 0.486836 + 0.521522I
a = −0.946967 + 0.660142I
b = −2.18118 − 0.52953I
7.10906 + 0.21740I −4.14381 + 0.87503I
u = 0.486836 + 0.521522I
a = −0.467835 − 0.365440I
b = 1.81439 + 0.42746I
7.10906 − 3.84236I −4.14381 + 7.80323I
u = 0.486836 + 0.521522I
a = −0.40009 − 1.79957I
b = 0.712411 + 0.380582I
7.10906 + 0.21740I −4.14381 + 0.87503I
u = 0.486836 + 0.521522I
a = 0.15459 + 2.10173I
b = −1.20900 + 0.91901I
7.10906 − 3.84236I −4.14381 + 7.80323I
u = 0.486836 − 0.521522I
a = −0.946967 − 0.660142I
b = −2.18118 + 0.52953I
7.10906 − 0.21740I −4.14381 − 0.87503I
u = 0.486836 − 0.521522I
a = −0.467835 + 0.365440I
b = 1.81439 − 0.42746I
7.10906 + 3.84236I −4.14381 − 7.80323I
u = 0.486836 − 0.521522I
a = −0.40009 + 1.79957I
b = 0.712411 − 0.380582I
7.10906 − 0.21740I −4.14381 − 0.87503I
u = 0.486836 − 0.521522I
a = 0.15459 − 2.10173I
b = −1.20900 − 0.91901I
7.10906 + 3.84236I −4.14381 − 7.80323I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.309525 + 0.567792I
a = 0.698451 + 0.145972I
b = 0.514606 − 0.126396I
3.63586 + 0.38063I −7.60633 − 3.29888I
u = −0.309525 + 0.567792I
a = 0.128105 + 1.336890I
b = −0.279055 − 0.409922I
3.63586 − 3.67914I −7.60633 + 3.62932I
u = −0.309525 + 0.567792I
a = −0.93586 + 1.08283I
b = 0.565939 − 0.059075I
3.63586 + 0.38063I −7.60633 − 3.29888I
u = −0.309525 + 0.567792I
a = 1.05477 − 1.74569I
b = −0.421840 − 0.433122I
3.63586 − 3.67914I −7.60633 + 3.62932I
u = −0.309525 − 0.567792I
a = 0.698451 − 0.145972I
b = 0.514606 + 0.126396I
3.63586 − 0.38063I −7.60633 + 3.29888I
u = −0.309525 − 0.567792I
a = 0.128105 − 1.336890I
b = −0.279055 + 0.409922I
3.63586 + 3.67914I −7.60633 − 3.62932I
u = −0.309525 − 0.567792I
a = −0.93586 − 1.08283I
b = 0.565939 + 0.059075I
3.63586 − 0.38063I −7.60633 + 3.29888I
u = −0.309525 − 0.567792I
a = 1.05477 + 1.74569I
b = −0.421840 + 0.433122I
3.63586 + 3.67914I −7.60633 − 3.62932I
u = 1.48203 + 0.05428I
a = 0.958296 + 0.658858I
b = 1.068010 − 0.257137I
−1.82904 + 1.87081I −11.79403 − 4.31605I
u = 1.48203 + 0.05428I
a = 0.653190 + 0.048914I
b = 0.708901 + 1.031320I
−1.82904 − 2.18896I −11.79403 + 2.61216I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48203 + 0.05428I
a = −0.66166 + 1.71009I
b = −1.25751 + 2.21680I
−1.82904 + 1.87081I −11.79403 − 4.31605I
u = 1.48203 + 0.05428I
a = 1.25006 − 1.49028I
b = 1.08297 − 1.84703I
−1.82904 − 2.18896I −11.79403 + 2.61216I
u = 1.48203 − 0.05428I
a = 0.958296 − 0.658858I
b = 1.068010 + 0.257137I
−1.82904 − 1.87081I −11.79403 + 4.31605I
u = 1.48203 − 0.05428I
a = 0.653190 − 0.048914I
b = 0.708901 − 1.031320I
−1.82904 + 2.18896I −11.79403 − 2.61216I
u = 1.48203 − 0.05428I
a = −0.66166 − 1.71009I
b = −1.25751 − 2.21680I
−1.82904 − 1.87081I −11.79403 + 4.31605I
u = 1.48203 − 0.05428I
a = 1.25006 + 1.49028I
b = 1.08297 + 1.84703I
−1.82904 + 2.18896I −11.79403 − 2.61216I
u = −1.52656 + 0.13829I
a = 0.546171 − 0.537531I
b = 0.30609 − 1.68944I
0.41207 + 2.08737I −8.59688 − 0.25519I
u = −1.52656 + 0.13829I
a = −0.53041 − 1.95768I
b = −0.643723 − 1.088220I
0.41207 + 6.14713I −8.59688 − 7.18339I
u = −1.52656 + 0.13829I
a = 3.09108 + 0.04871I
b = 3.70952 − 0.90997I
0.41207 + 6.14713I −8.59688 − 7.18339I
u = −1.52656 + 0.13829I
a = −3.47972 − 0.72559I
b = −3.56947 + 0.03348I
0.41207 + 2.08737I −8.59688 − 0.25519I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52656 − 0.13829I
a = 0.546171 + 0.537531I
b = 0.30609 + 1.68944I
0.41207 − 2.08737I −8.59688 + 0.25519I
u = −1.52656 − 0.13829I
a = −0.53041 + 1.95768I
b = −0.643723 + 1.088220I
0.41207 − 6.14713I −8.59688 + 7.18339I
u = −1.52656 − 0.13829I
a = 3.09108 − 0.04871I
b = 3.70952 + 0.90997I
0.41207 − 6.14713I −8.59688 + 7.18339I
u = −1.52656 − 0.13829I
a = −3.47972 + 0.72559I
b = −3.56947 − 0.03348I
0.41207 − 2.08737I −8.59688 + 0.25519I
u = 1.57098 + 0.16034I
a = −0.474753 − 0.384814I
b = −0.525989 − 0.241777I
−4.58415 − 5.98693I −13.04132 + 1.43269I
u = 1.57098 + 0.16034I
a = 2.00920 + 0.00458I
b = 2.40901 + 0.68627I
−4.58415 − 5.98693I −13.04132 + 1.43269I
u = 1.57098 + 0.16034I
a = 1.97730 − 0.92306I
b = 2.84371 − 0.89022I
−4.58415 − 10.04670I −13.0413 + 8.3609I
u = 1.57098 + 0.16034I
a = −3.07382 − 0.21569I
b = −3.40028 − 0.96277I
−4.58415 − 10.04670I −13.0413 + 8.3609I
u = 1.57098 − 0.16034I
a = −0.474753 + 0.384814I
b = −0.525989 + 0.241777I
−4.58415 + 5.98693I −13.04132 − 1.43269I
u = 1.57098 − 0.16034I
a = 2.00920 − 0.00458I
b = 2.40901 − 0.68627I
−4.58415 + 5.98693I −13.04132 − 1.43269I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.57098 − 0.16034I
a = 1.97730 + 0.92306I
b = 2.84371 + 0.89022I
−4.58415 + 10.04670I −13.0413 − 8.3609I
u = 1.57098 − 0.16034I
a = −3.07382 + 0.21569I
b = −3.40028 + 0.96277I
−4.58415 + 10.04670I −13.0413 − 8.3609I
u = −0.404272
a = 1.36497 + 0.92368I
b = 0.31033 − 1.75866I
4.33687 − 2.02988I −14.6282 + 3.4641I
u = −0.404272
a = 1.36497 − 0.92368I
b = 0.31033 + 1.75866I
4.33687 + 2.02988I −14.6282 − 3.4641I
u = −0.404272
a = 0.13282 + 3.51793I
b = 0.767965 + 0.109009I
4.33687 + 2.02988I −14.6282 − 3.4641I
u = −0.404272
a = 0.13282 − 3.51793I
b = 0.767965 − 0.109009I
4.33687 − 2.02988I −14.6282 + 3.4641I
u = −1.60797
a = 1.28440 + 1.48571I
b = 1.45852 + 2.07683I
−8.86719 − 2.02988I −15.9771 + 3.4641I
u = −1.60797
a = 1.28440 − 1.48571I
b = 1.45852 − 2.07683I
−8.86719 + 2.02988I −15.9771 − 3.4641I
u = −1.60797
a = −2.01610 + 0.21838I
b = −2.63607 + 0.03726I
−8.86719 + 2.02988I −15.9771 − 3.4641I
u = −1.60797
a = −2.01610 − 0.21838I
b = −2.63607 − 0.03726I
−8.86719 − 2.02988I −15.9771 + 3.4641I
17
III.
I
u
3
= h−u
13
+7u
11
+· · ·−u
2
+b, −u
12
+8u
10
+· · ·+a−3u, u
14
−u
13
+· · ·−u−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
8
=
−u
−u
3
+ u
a
4
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
u
12
− 8u
10
+ 22u
8
− 24u
6
+ 2u
5
+ 11u
4
− 6u
3
− 7u
2
+ 3u
u
13
− 7u
11
− u
10
+ 17u
9
+ 4u
8
− 16u
7
− 2u
6
+ 7u
5
− 5u
4
− 7u
3
+ u
2
a
9
=
u
13
− u
12
+ ··· − 2u − 2
u
11
− 6u
9
+ 12u
7
− 9u
5
+ u
4
+ 3u
3
− 2u
2
− u
a
1
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
6
=
u
u
a
12
=
−u
13
+ u
12
+ ··· − 8u
2
+ 2u
−u
8
+ 4u
6
+ u
5
− 4u
4
− 2u
3
− u
a
5
=
u
11
− u
10
− 6u
9
+ 5u
8
+ 13u
7
− 8u
6
− 13u
5
+ 6u
4
+ 7u
3
− 5u
2
− 2u + 2
u
13
− 7u
11
− u
10
+ 18u
9
+ 5u
8
− 21u
7
− 7u
6
+ 13u
5
+ 2u
4
− 7u
3
+ 2u
a
10
=
u
12
− 7u
10
+ 17u
8
− 17u
6
+ 2u
5
+ 9u
4
− 5u
3
− 6u
2
+ u
u
13
− 7u
11
+ 17u
9
− u
8
− 16u
7
+ 5u
6
+ 7u
5
− 7u
4
− 7u
3
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
13
−2u
12
+10u
11
+13u
10
−35u
9
−29u
8
+53u
7
+25u
6
−36u
5
−8u
4
+17u
3
+2u
2
−8u−7
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
+ 3u
13
+ ··· − u − 1
c
2
, c
3
u
14
− u
13
+ ··· − u − 1
c
4
, c
11
u
14
+ 8u
12
+ ··· + 3u − 1
c
5
, c
9
u
14
+ 8u
12
+ ··· − 3u − 1
c
6
, c
7
u
14
+ u
13
+ ··· + u − 1
c
8
, c
10
u
14
+ 2u
13
+ ··· + 2u + 1
c
12
u
14
− 2u
13
+ ··· − 2u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
+ 7y
13
+ ··· + 11y + 1
c
2
, c
3
, c
6
c
7
y
14
− 17y
13
+ ··· − 5y + 1
c
4
, c
5
, c
9
c
11
y
14
+ 16y
13
+ ··· − 33y + 1
c
8
, c
10
y
14
+ 2y
13
+ ··· + 2y + 1
c
12
y
14
+ 2y
13
+ ··· + 2y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.718088 + 0.503923I
a = −0.205716 + 0.112452I
b = 0.818488 − 0.600589I
3.57950 + 4.67648I −6.79955 − 7.09639I
u = −0.718088 − 0.503923I
a = −0.205716 − 0.112452I
b = 0.818488 + 0.600589I
3.57950 − 4.67648I −6.79955 + 7.09639I
u = 0.426851 + 0.612202I
a = −0.355495 − 0.949467I
b = 1.170670 − 0.055723I
6.26107 − 2.12457I −6.16651 + 3.75177I
u = 0.426851 − 0.612202I
a = −0.355495 + 0.949467I
b = 1.170670 + 0.055723I
6.26107 + 2.12457I −6.16651 − 3.75177I
u = 0.557327
a = −0.908845
b = −1.22260
−2.52431 −9.36780
u = −1.50662 + 0.13345I
a = 1.78609 + 0.99935I
b = 2.01136 + 0.06834I
−0.03745 + 4.54103I −10.18751 − 2.61697I
u = −1.50662 − 0.13345I
a = 1.78609 − 0.99935I
b = 2.01136 − 0.06834I
−0.03745 − 4.54103I −10.18751 + 2.61697I
u = 1.51391 + 0.07655I
a = −1.20822 + 1.22102I
b = −1.47982 + 2.09790I
−1.196780 + 0.352553I −9.60347 + 0.25501I
u = 1.51391 − 0.07655I
a = −1.20822 − 1.22102I
b = −1.47982 − 2.09790I
−1.196780 − 0.352553I −9.60347 − 0.25501I
u = −0.301894 + 0.325169I
a = −1.62327 + 1.87128I
b = −0.189143 − 0.685382I
5.09564 − 1.64107I −3.64136 − 1.51727I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.301894 − 0.325169I
a = −1.62327 − 1.87128I
b = −0.189143 + 0.685382I
5.09564 + 1.64107I −3.64136 + 1.51727I
u = −1.57402
a = −2.05566
b = −2.30452
−9.91641 −16.7860
u = 1.59419 + 0.16791I
a = 1.58886 + 0.31397I
b = 1.93200 + 0.84118I
−4.19176 − 7.28281I −11.02487 + 7.66069I
u = 1.59419 − 0.16791I
a = 1.58886 − 0.31397I
b = 1.93200 − 0.84118I
−4.19176 + 7.28281I −11.02487 − 7.66069I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
+ 3u
13
+ ··· − u − 1)(u
15
− 3u
14
+ ··· + 4u
2
− 1)
4
· (u
31
− 6u
30
+ ··· + 17032u + 3008)
c
2
, c
3
(u
14
− u
13
+ ··· − u − 1)(u
15
+ u
14
+ ··· − 2u + 1)
4
· (u
31
− 6u
30
+ ··· + 14u + 4)
c
4
, c
11
(u
14
+ 8u
12
+ ··· + 3u − 1)(u
31
+ 12u
29
+ ··· + 2u + 1)
· (u
60
− u
59
+ ··· − 4u + 7)
c
5
, c
9
(u
14
+ 8u
12
+ ··· − 3u − 1)(u
31
+ 12u
29
+ ··· + 2u + 1)
· (u
60
− u
59
+ ··· − 4u + 7)
c
6
, c
7
(u
14
+ u
13
+ ··· + u − 1)(u
15
+ u
14
+ ··· − 2u + 1)
4
· (u
31
− 6u
30
+ ··· + 14u + 4)
c
8
, c
10
(u
14
+ 2u
13
+ ··· + 2u + 1)(u
31
+ 2u
30
+ ··· + 11u + 1)
· (u
60
− 17u
59
+ ··· − 42774u + 2977)
c
12
((u
2
− u + 1)
30
)(u
14
− 2u
13
+ ··· − 2u + 1)
· (u
31
+ 33u
30
+ ··· + 655360u + 32768)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
14
+ 7y
13
+ ··· + 11y + 1)(y
15
+ 7y
14
+ ··· + 8y − 1)
4
· (y
31
+ 14y
30
+ ··· + 194260160y − 9048064)
c
2
, c
3
, c
6
c
7
(y
14
− 17y
13
+ ··· − 5y + 1)(y
15
− 17y
14
+ ··· + 8y − 1)
4
· (y
31
− 34y
30
+ ··· + 268y − 16)
c
4
, c
5
, c
9
c
11
(y
14
+ 16y
13
+ ··· − 33y + 1)(y
31
+ 24y
30
+ ··· + 12y − 1)
· (y
60
+ 51y
59
+ ··· + 4212y + 49)
c
8
, c
10
(y
14
+ 2y
13
+ ··· + 2y + 1)(y
31
+ 2y
30
+ ··· + 29y − 1)
· (y
60
+ 19y
59
+ ··· + 124785424y + 8862529)
c
12
((y
2
+ y + 1)
30
)(y
14
+ 2y
13
+ ··· + 2y + 1)
· (y
31
+ 3y
30
+ ··· + 20401094656y − 1073741824)
24
