12a
0653
(K12a
0653
)
A knot diagram
1
Linearized knot diagam
3 7 10 12 8 2 6 11 4 1 5 9
Solving Sequence
2,6
7 3
8,11
9 1 5 12 4 10
c
6
c
2
c
7
c
8
c
1
c
5
c
11
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h23u
32
− 20u
31
+ ··· + 2b + 192, −83u
32
+ 367u
31
+ ··· + 2a + 53, u
33
− 6u
32
+ ··· + 2u + 4i
I
u
2
= h3369103813u
13
a
3
+ 32822425576u
13
a
2
+ ··· + 472218636585a + 522982296989,
u
13
a
3
+ 8u
13
a
2
+ ··· + 22a + 15,
u
14
+ u
13
− u
12
− 2u
11
+ 4u
10
+ 5u
9
− 3u
8
− 6u
7
+ 4u
6
+ 6u
5
− 2u
4
− 2u
3
+ 2u
2
+ u − 1i
I
u
3
= hu
16
+ u
15
+ ··· + b − 1,
u
16
+ u
15
− u
14
− 3u
13
+ 4u
12
+ 7u
11
− 2u
10
− 12u
9
+ 2u
8
+ 12u
7
+ 4u
6
− 10u
5
− 4u
4
+ 3u
3
+ 6u
2
+ a − 1,
u
17
+ u
16
− 2u
15
− 3u
14
+ 6u
13
+ 8u
12
− 8u
11
− 14u
10
+ 10u
9
+ 18u
8
− 7u
7
− 17u
6
+ 4u
5
+ 11u
4
− 4u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 106 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
= h23u
32
− 20u
31
+ · · · + 2b + 192, −83u
32
+ 367u
31
+ · · · + 2a +
53, u
33
− 6u
32
+ · · · + 2u + 4i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
83
2
u
32
−
367
2
u
31
+ ··· + 65u −
53
2
−
23
2
u
32
+ 10u
31
+ ··· −
375
2
u − 96
a
9
=
−
45
4
u
32
+ 49u
31
+ ··· −
115
4
u + 4
5
2
u
32
− 32u
30
+ ··· +
113
2
u + 29
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
u
4
− u
2
+ 1
−u
4
a
12
=
3u
32
−
19
2
u
31
+ ··· +
61
2
u +
19
2
7
2
u
32
− 20u
31
+ ··· −
59
2
u − 20
a
4
=
5
4
u
32
− 3u
31
+ ··· +
11
4
u + 2
3
2
u
32
− 12u
31
+ ··· −
29
2
u − 11
a
10
=
9
2
u
32
−
43
2
u
31
+ ··· + 3u −
13
2
−
19
2
u
32
+ 48u
31
+ ··· +
47
2
u + 26
(ii) Obstruction class = −1
(iii) Cusp Shapes = −25u
32
+ 137u
31
−250u
30
−48u
29
+ 729u
28
−349u
27
−1766u
26
+
2220u
25
+ 1732u
24
− 3935u
23
− 1941u
22
+ 6635u
21
+ 458u
20
− 6613u
19
− 1876u
18
+
8144u
17
+ 1987u
16
− 6981u
15
− 4913u
14
+ 8258u
13
+ 3726u
12
− 5186u
11
− 4612u
10
+
3551u
9
+ 3476u
8
− 959u
7
− 3182u
6
+ 648u
5
+ 1495u
4
− 98u
3
− 504u
2
+ 14u + 46
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
33
+ 8u
32
+ ··· + 220u + 16
c
2
, c
6
u
33
− 6u
32
+ ··· + 2u + 4
c
3
, c
4
, c
9
c
11
u
33
+ 15u
31
+ ··· + u + 1
c
8
, c
10
u
33
+ 3u
32
+ ··· + u + 1
c
12
u
33
+ 32u
32
+ ··· + 286720u + 16384
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
33
+ 36y
32
+ ··· + 6256y −256
c
2
, c
6
y
33
− 8y
32
+ ··· + 220y −16
c
3
, c
4
, c
9
c
11
y
33
+ 30y
32
+ ··· + 5y −1
c
8
, c
10
y
33
+ 17y
32
+ ··· + 63y −1
c
12
y
33
+ 2y
32
+ ··· + 4630511616y −268435456
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.838398 + 0.613102I
a = −0.366122 + 0.442209I
b = 0.003736 − 0.378058I
1.70782 − 2.40859I −4.73211 + 2.63884I
u = 0.838398 − 0.613102I
a = −0.366122 − 0.442209I
b = 0.003736 + 0.378058I
1.70782 + 2.40859I −4.73211 − 2.63884I
u = −0.415165 + 0.823365I
a = −0.272267 + 0.601963I
b = 0.931790 + 0.355896I
9.11306 − 7.42411I −3.38968 + 4.20871I
u = −0.415165 − 0.823365I
a = −0.272267 − 0.601963I
b = 0.931790 − 0.355896I
9.11306 + 7.42411I −3.38968 − 4.20871I
u = −0.814655 + 0.420904I
a = −0.014524 + 0.720997I
b = 0.779019 + 0.954203I
−1.41171 + 3.25911I −15.5699 − 6.2232I
u = −0.814655 − 0.420904I
a = −0.014524 − 0.720997I
b = 0.779019 − 0.954203I
−1.41171 − 3.25911I −15.5699 + 6.2232I
u = −0.277153 + 0.867734I
a = 0.509978 − 0.137733I
b = −0.389242 − 0.632865I
8.34160 + 3.38775I −0.87656 − 3.53440I
u = −0.277153 − 0.867734I
a = 0.509978 + 0.137733I
b = −0.389242 + 0.632865I
8.34160 − 3.38775I −0.87656 + 3.53440I
u = 1.100190 + 0.089830I
a = −0.481622 − 0.649769I
b = 0.0208635 − 0.1183110I
3.28828 − 5.97548I −8.94862 + 7.09482I
u = 1.100190 − 0.089830I
a = −0.481622 + 0.649769I
b = 0.0208635 + 0.1183110I
3.28828 + 5.97548I −8.94862 − 7.09482I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.863288 + 0.745766I
a = −0.337012 + 0.105923I
b = −0.139284 + 0.796748I
1.75606 + 2.81515I −5.07945 − 3.99725I
u = −0.863288 − 0.745766I
a = −0.337012 − 0.105923I
b = −0.139284 − 0.796748I
1.75606 − 2.81515I −5.07945 + 3.99725I
u = −1.021670 + 0.530532I
a = −0.224206 − 0.440345I
b = −1.110970 − 0.423583I
7.0965 + 12.3235I −7.48212 − 9.31831I
u = −1.021670 − 0.530532I
a = −0.224206 + 0.440345I
b = −1.110970 + 0.423583I
7.0965 − 12.3235I −7.48212 + 9.31831I
u = −1.125530 + 0.460328I
a = 0.246731 + 0.066023I
b = 0.636793 − 0.225287I
5.49810 + 1.42945I −1.94384 − 1.59393I
u = −1.125530 − 0.460328I
a = 0.246731 − 0.066023I
b = 0.636793 + 0.225287I
5.49810 − 1.42945I −1.94384 + 1.59393I
u = 0.755893 + 0.131338I
a = 1.56947 − 0.67478I
b = −0.271312 + 0.241644I
−2.89891 − 0.34125I −18.0890 + 12.2689I
u = 0.755893 − 0.131338I
a = 1.56947 + 0.67478I
b = −0.271312 − 0.241644I
−2.89891 + 0.34125I −18.0890 − 12.2689I
u = 0.902285 + 0.867527I
a = 1.60945 + 1.85954I
b = −2.65111 − 0.44007I
6.37334 − 0.89739I −9.49648 − 0.54814I
u = 0.902285 − 0.867527I
a = 1.60945 − 1.85954I
b = −2.65111 + 0.44007I
6.37334 + 0.89739I −9.49648 + 0.54814I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929251 + 0.857665I
a = −2.32439 − 1.06449I
b = 2.64641 − 0.85846I
6.28919 − 5.49945I −9.75207 + 5.34386I
u = 0.929251 − 0.857665I
a = −2.32439 + 1.06449I
b = 2.64641 + 0.85846I
6.28919 + 5.49945I −9.75207 − 5.34386I
u = 0.863589 + 0.938538I
a = −1.84094 − 1.56412I
b = 2.90596 + 0.30561I
17.0337 + 9.7572I −4.21655 − 3.66521I
u = 0.863589 − 0.938538I
a = −1.84094 + 1.56412I
b = 2.90596 − 0.30561I
17.0337 − 9.7572I −4.21655 + 3.66521I
u = 0.844668 + 0.965107I
a = 1.26522 + 0.67302I
b = −1.79222 + 0.12655I
15.6006 + 0.0709I −2.15054 + 0.I
u = 0.844668 − 0.965107I
a = 1.26522 − 0.67302I
b = −1.79222 − 0.12655I
15.6006 − 0.0709I −2.15054 + 0.I
u = 0.995894 + 0.870348I
a = 2.13894 + 1.52075I
b = −2.94172 + 0.68814I
16.6040 − 16.4117I −4.91951 + 8.23114I
u = 0.995894 − 0.870348I
a = 2.13894 − 1.52075I
b = −2.94172 − 0.68814I
16.6040 + 16.4117I −4.91951 − 8.23114I
u = 1.021940 + 0.872778I
a = −1.10966 − 1.08266I
b = 1.80678 − 0.21056I
15.0264 − 6.8123I −3.11021 + 4.75240I
u = 1.021940 − 0.872778I
a = −1.10966 + 1.08266I
b = 1.80678 + 0.21056I
15.0264 + 6.8123I −3.11021 − 4.75240I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.528955 + 0.335215I
a = −0.495909 − 0.541436I
b = −0.718846 − 0.034946I
−0.532718 − 0.018077I −12.61831 + 0.50033I
u = −0.528955 − 0.335215I
a = −0.495909 + 0.541436I
b = −0.718846 + 0.034946I
−0.532718 + 0.018077I −12.61831 − 0.50033I
u = −0.411375
a = −0.746268
b = −0.433287
−0.639498 −15.2500
8
II. I
u
2
= h3.37 × 10
9
a
3
u
13
+ 3.28 × 10
10
a
2
u
13
+ · · · + 4.72 × 10
11
a + 5.23 ×
10
11
, u
13
a
3
+ 8u
13
a
2
+ · · · + 22a + 15, u
14
+ u
13
+ · · · + u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
a
−0.0785503a
3
u
13
− 0.765251a
2
u
13
+ ··· − 11.0097a − 12.1933
a
9
=
0.671081a
3
u
13
+ 0.917830a
2
u
13
+ ··· + 9.54350a + 12.9228
0.0443959a
3
u
13
− 0.271283a
2
u
13
+ ··· − 2.30457a − 2.87768
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
u
4
− u
2
+ 1
−u
4
a
12
=
0.522672a
3
u
13
+ 0.630403a
2
u
13
+ ··· + 8.14923a + 7.66742
−0.200386a
3
u
13
− 1.14041a
2
u
13
+ ··· − 11.4361a − 13.0321
a
4
=
−0.269227a
3
u
13
− 0.459045a
2
u
13
+ ··· − 8.30676a − 10.3719
−0.0531131a
3
u
13
− 0.444978a
2
u
13
+ ··· − 4.30811a − 4.05445
a
10
=
−0.118312a
3
u
13
− 0.241537a
2
u
13
+ ··· + 0.756822a − 0.808713
−0.200386a
3
u
13
− 1.14041a
2
u
13
+ ··· − 11.4361a − 13.0321
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
83965078880
42891044441
u
13
a
3
+
55301996548
42891044441
u
13
a
2
+ ··· +
978297781868
42891044441
a +
571131040218
42891044441
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
(u
14
+ 3u
13
+ ··· + 5u + 1)
4
c
2
, c
6
(u
14
+ u
13
+ ··· + u − 1)
4
c
3
, c
4
, c
9
c
11
u
56
+ u
55
+ ··· + 12u + 7
c
8
, c
10
u
56
− 17u
55
+ ··· − 491562u + 37537
c
12
(u
2
− u + 1)
28
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
(y
14
+ 17y
13
+ ··· − y + 1)
4
c
2
, c
6
(y
14
− 3y
13
+ ··· − 5y + 1)
4
c
3
, c
4
, c
9
c
11
y
56
+ 51y
55
+ ··· − 4428y + 49
c
8
, c
10
y
56
+ 27y
55
+ ··· + 24860581508y + 1409026369
c
12
(y
2
+ y + 1)
28
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.919323 + 0.470231I
a = 0.794474 − 0.440671I
b = 0.940770 − 0.444497I
1.95519 − 6.91244I −9.68599 + 9.90747I
u = 0.919323 + 0.470231I
a = −0.711262 + 0.512164I
b = −0.630226 − 0.503089I
1.95519 − 2.85267I −9.68599 + 2.97927I
u = 0.919323 + 0.470231I
a = 0.322504 + 0.766589I
b = −1.39913 + 0.78875I
1.95519 − 6.91244I −9.68599 + 9.90747I
u = 0.919323 + 0.470231I
a = −0.129480 + 0.292208I
b = 0.561275 − 0.065984I
1.95519 − 2.85267I −9.68599 + 2.97927I
u = 0.919323 − 0.470231I
a = 0.794474 + 0.440671I
b = 0.940770 + 0.444497I
1.95519 + 6.91244I −9.68599 − 9.90747I
u = 0.919323 − 0.470231I
a = −0.711262 − 0.512164I
b = −0.630226 + 0.503089I
1.95519 + 2.85267I −9.68599 − 2.97927I
u = 0.919323 − 0.470231I
a = 0.322504 − 0.766589I
b = −1.39913 − 0.78875I
1.95519 + 6.91244I −9.68599 − 9.90747I
u = 0.919323 − 0.470231I
a = −0.129480 − 0.292208I
b = 0.561275 + 0.065984I
1.95519 + 2.85267I −9.68599 − 2.97927I
u = −0.924961
a = −0.857787 + 0.539464I
b = −0.200651 − 0.488104I
−0.62515 + 2.02988I −14.7052 − 3.4641I
u = −0.924961
a = −0.857787 − 0.539464I
b = −0.200651 + 0.488104I
−0.62515 − 2.02988I −14.7052 + 3.4641I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.924961
a = 0.576490 + 1.026690I
b = −0.300202 + 0.379400I
−0.62515 − 2.02988I −14.7052 + 3.4641I
u = −0.924961
a = 0.576490 − 1.026690I
b = −0.300202 − 0.379400I
−0.62515 + 2.02988I −14.7052 − 3.4641I
u = −0.726911 + 0.518054I
a = −0.421333 − 0.953785I
b = 1.31925 + 0.70924I
6.28706 + 4.01626I −2.65592 − 8.55046I
u = −0.726911 + 0.518054I
a = 1.68959 + 0.08836I
b = −1.29869 − 1.68726I
6.28706 − 0.04350I −2.65592 − 1.62226I
u = −0.726911 + 0.518054I
a = −1.36173 − 1.57262I
b = −0.264552 − 0.194385I
6.28706 − 0.04350I −2.65592 − 1.62226I
u = −0.726911 + 0.518054I
a = 1.54281 + 1.97985I
b = 1.09192 − 1.12223I
6.28706 + 4.01626I −2.65592 − 8.55046I
u = −0.726911 − 0.518054I
a = −0.421333 + 0.953785I
b = 1.31925 − 0.70924I
6.28706 − 4.01626I −2.65592 + 8.55046I
u = −0.726911 − 0.518054I
a = 1.68959 − 0.08836I
b = −1.29869 + 1.68726I
6.28706 + 0.04350I −2.65592 + 1.62226I
u = −0.726911 − 0.518054I
a = −1.36173 + 1.57262I
b = −0.264552 + 0.194385I
6.28706 + 0.04350I −2.65592 + 1.62226I
u = −0.726911 − 0.518054I
a = 1.54281 − 1.97985I
b = 1.09192 + 1.12223I
6.28706 − 4.01626I −2.65592 + 8.55046I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.879333 + 0.897049I
a = −1.63730 + 0.51654I
b = 2.04526 + 0.38724I
10.73580 + 0.51054I −5.12222 − 2.81570I
u = −0.879333 + 0.897049I
a = 1.89599 − 0.54443I
b = −1.89493 − 1.05104I
10.73580 + 0.51054I −5.12222 − 2.81570I
u = −0.879333 + 0.897049I
a = −2.18425 + 1.78081I
b = 2.87794 − 0.18250I
10.73580 − 3.54923I −5.12222 + 4.11251I
u = −0.879333 + 0.897049I
a = 2.03075 − 1.99090I
b = −3.52797 + 0.38422I
10.73580 − 3.54923I −5.12222 + 4.11251I
u = −0.879333 − 0.897049I
a = −1.63730 − 0.51654I
b = 2.04526 − 0.38724I
10.73580 − 0.51054I −5.12222 + 2.81570I
u = −0.879333 − 0.897049I
a = 1.89599 + 0.54443I
b = −1.89493 + 1.05104I
10.73580 − 0.51054I −5.12222 + 2.81570I
u = −0.879333 − 0.897049I
a = −2.18425 − 1.78081I
b = 2.87794 + 0.18250I
10.73580 + 3.54923I −5.12222 − 4.11251I
u = −0.879333 − 0.897049I
a = 2.03075 + 1.99090I
b = −3.52797 − 0.38422I
10.73580 + 3.54923I −5.12222 − 4.11251I
u = 0.405736 + 0.602281I
a = 0.297803 + 0.937793I
b = −0.032334 + 0.421230I
3.52193 − 1.17765I −5.59802 + 3.07698I
u = 0.405736 + 0.602281I
a = −0.900179 + 0.198851I
b = 0.525145 − 1.039200I
3.52193 − 1.17765I −5.59802 + 3.07698I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.405736 + 0.602281I
a = −0.50022 − 1.47105I
b = 1.121790 + 0.002550I
3.52193 + 2.88212I −5.59802 − 3.85123I
u = 0.405736 + 0.602281I
a = −0.182952 + 0.381057I
b = −0.833018 + 0.733223I
3.52193 + 2.88212I −5.59802 − 3.85123I
u = 0.405736 − 0.602281I
a = 0.297803 − 0.937793I
b = −0.032334 − 0.421230I
3.52193 + 1.17765I −5.59802 − 3.07698I
u = 0.405736 − 0.602281I
a = −0.900179 − 0.198851I
b = 0.525145 + 1.039200I
3.52193 + 1.17765I −5.59802 − 3.07698I
u = 0.405736 − 0.602281I
a = −0.50022 + 1.47105I
b = 1.121790 − 0.002550I
3.52193 − 2.88212I −5.59802 + 3.85123I
u = 0.405736 − 0.602281I
a = −0.182952 − 0.381057I
b = −0.833018 − 0.733223I
3.52193 − 2.88212I −5.59802 + 3.85123I
u = 0.924969 + 0.883501I
a = 2.14164 + 0.25075I
b = −2.30748 + 0.74757I
14.5860 − 1.2351I −1.90686 − 0.97406I
u = 0.924969 + 0.883501I
a = −0.61571 − 2.27381I
b = 2.77866 + 1.93001I
14.5860 − 5.2949I −1.90686 + 5.95414I
u = 0.924969 + 0.883501I
a = −1.17366 − 2.23783I
b = 2.13014 + 0.56110I
14.5860 − 5.2949I −1.90686 + 5.95414I
u = 0.924969 + 0.883501I
a = 2.66023 + 0.45543I
b = −2.30429 + 2.25801I
14.5860 − 1.2351I −1.90686 − 0.97406I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.924969 − 0.883501I
a = 2.14164 − 0.25075I
b = −2.30748 − 0.74757I
14.5860 + 1.2351I −1.90686 + 0.97406I
u = 0.924969 − 0.883501I
a = −0.61571 + 2.27381I
b = 2.77866 − 1.93001I
14.5860 + 5.2949I −1.90686 − 5.95414I
u = 0.924969 − 0.883501I
a = −1.17366 + 2.23783I
b = 2.13014 − 0.56110I
14.5860 + 5.2949I −1.90686 − 5.95414I
u = 0.924969 − 0.883501I
a = 2.66023 − 0.45543I
b = −2.30429 − 2.25801I
14.5860 + 1.2351I −1.90686 + 0.97406I
u = −0.961925 + 0.860252I
a = −0.91964 + 1.52544I
b = 2.11052 − 0.69676I
10.47250 + 5.98498I −5.63204 − 1.91017I
u = −0.961925 + 0.860252I
a = 1.15135 − 1.57072I
b = −1.95858 + 0.06200I
10.47250 + 5.98498I −5.63204 − 1.91017I
u = −0.961925 + 0.860252I
a = 2.43924 − 1.48967I
b = −2.95999 − 0.50087I
10.4725 + 10.0447I −5.63204 − 8.83837I
u = −0.961925 + 0.860252I
a = −2.51589 + 1.71297I
b = 3.43373 + 0.94983I
10.4725 + 10.0447I −5.63204 − 8.83837I
u = −0.961925 − 0.860252I
a = −0.91964 − 1.52544I
b = 2.11052 + 0.69676I
10.47250 − 5.98498I −5.63204 + 1.91017I
u = −0.961925 − 0.860252I
a = 1.15135 + 1.57072I
b = −1.95858 − 0.06200I
10.47250 − 5.98498I −5.63204 + 1.91017I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.961925 − 0.860252I
a = 2.43924 + 1.48967I
b = −2.95999 + 0.50087I
10.4725 − 10.0447I −5.63204 + 8.83837I
u = −0.961925 − 0.860252I
a = −2.51589 − 1.71297I
b = 3.43373 − 0.94983I
10.4725 − 10.0447I −5.63204 + 8.83837I
u = 0.561243
a = −1.400310 + 0.114435I
b = −0.14296 − 1.77734I
4.20416 − 2.02988I −12.09269 + 3.46410I
u = 0.561243
a = −1.400310 − 0.114435I
b = −0.14296 + 1.77734I
4.20416 + 2.02988I −12.09269 − 3.46410I
u = 0.561243
a = −0.53119 + 3.23102I
b = 0.618594 + 0.953525I
4.20416 − 2.02988I −12.09269 + 3.46410I
u = 0.561243
a = −0.53119 − 3.23102I
b = 0.618594 − 0.953525I
4.20416 + 2.02988I −12.09269 − 3.46410I
17
III.
I
u
3
= hu
16
+ u
15
+ · · · + b − 1, u
16
+ u
15
+ · · · + a − 1, u
17
+ u
16
+ · · · − 4u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
11
=
−u
16
− u
15
+ ··· − 6u
2
+ 1
−u
16
− u
15
+ ··· + 2u + 1
a
9
=
−u
16
+ 3u
14
− 9u
12
+ 16u
10
− 24u
8
+ 25u
6
− 21u
4
+ 10u
2
− 3
u
16
− 3u
14
+ ··· − 3u
2
− 3u
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
u
4
− u
2
+ 1
−u
4
a
12
=
−u
14
+ 2u
12
+ ··· − u + 1
−u
16
− u
15
+ ··· + 2u + 1
a
4
=
u
16
− 2u
14
+ ··· + 3u + 2
u
15
+ u
14
+ ··· + u − 1
a
10
=
−u
16
− u
15
+ ··· − u + 1
−u
15
+ 3u
13
+ ··· + 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
16
+ 2u
15
+ 5u
14
−u
13
−13u
12
+ 4u
11
+ 27u
10
+ 4u
9
−37u
8
−
9u
7
+ 40u
6
+ 18u
5
− 26u
4
− 11u
3
+ 14u
2
+ 6u − 8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
17
− 5u
16
+ ··· + 8u − 1
c
2
u
17
− u
16
+ ··· + 4u
2
− 1
c
3
, c
11
u
17
+ 10u
15
+ ··· + 7u − 1
c
4
, c
9
u
17
+ 10u
15
+ ··· + 7u + 1
c
6
u
17
+ u
16
+ ··· − 4u
2
+ 1
c
7
u
17
+ 5u
16
+ ··· + 8u + 1
c
8
, c
10
u
17
+ 3u
16
+ ··· − 3u − 1
c
12
u
17
− 3u
16
+ ··· − 3u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
17
+ 19y
16
+ ··· − 12y −1
c
2
, c
6
y
17
− 5y
16
+ ··· + 8y −1
c
3
, c
4
, c
9
c
11
y
17
+ 20y
16
+ ··· + 17y −1
c
8
, c
10
y
17
+ 3y
16
+ ··· − y −1
c
12
y
17
+ y
16
+ ··· − 3y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.945890 + 0.312417I
a = −0.537448 − 0.047998I
b = −0.893405 − 0.569214I
3.35506 − 4.10794I −7.75651 + 5.82237I
u = 0.945890 − 0.312417I
a = −0.537448 + 0.047998I
b = −0.893405 + 0.569214I
3.35506 + 4.10794I −7.75651 − 5.82237I
u = −0.972331 + 0.493803I
a = 0.890091 + 0.294111I
b = −0.103792 − 0.494835I
4.39652 + 1.28712I −9.11584 − 1.90968I
u = −0.972331 − 0.493803I
a = 0.890091 − 0.294111I
b = −0.103792 + 0.494835I
4.39652 − 1.28712I −9.11584 + 1.90968I
u = 0.848338 + 0.687599I
a = 0.265141 + 0.123673I
b = 0.061069 + 0.627082I
0.88266 − 2.63503I −15.8429 + 3.4776I
u = 0.848338 − 0.687599I
a = 0.265141 − 0.123673I
b = 0.061069 − 0.627082I
0.88266 + 2.63503I −15.8429 − 3.4776I
u = −0.593107 + 0.526314I
a = 0.73924 + 1.66755I
b = −0.219744 − 0.936804I
5.62828 + 2.80024I −5.18862 − 3.17649I
u = −0.593107 − 0.526314I
a = 0.73924 − 1.66755I
b = −0.219744 + 0.936804I
5.62828 − 2.80024I −5.18862 + 3.17649I
u = −0.869075 + 0.884383I
a = −2.41044 + 0.63240I
b = 2.57239 + 1.00697I
11.29440 − 1.32784I −3.25448 + 1.21806I
u = −0.869075 − 0.884383I
a = −2.41044 − 0.63240I
b = 2.57239 − 1.00697I
11.29440 + 1.32784I −3.25448 − 1.21806I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.962617 + 0.846172I
a = 1.27291 − 2.08611I
b = −2.59045 + 0.57217I
10.99840 + 7.74112I −3.89446 − 6.31317I
u = −0.962617 − 0.846172I
a = 1.27291 + 2.08611I
b = −2.59045 − 0.57217I
10.99840 − 7.74112I −3.89446 + 6.31317I
u = 0.928421 + 0.893331I
a = −0.256712 − 0.033992I
b = −0.167997 − 0.688887I
14.1463 − 3.2953I −3.29658 + 2.36229I
u = 0.928421 − 0.893331I
a = −0.256712 + 0.033992I
b = −0.167997 + 0.688887I
14.1463 + 3.2953I −3.29658 − 2.36229I
u = −0.709513
a = −1.69728
b = 0.349817
−2.66316 −7.14040
u = 0.529238 + 0.315991I
a = −0.61414 − 1.69532I
b = 0.66702 − 1.60227I
4.91285 + 1.45910I −3.08044 + 2.03398I
u = 0.529238 − 0.315991I
a = −0.61414 + 1.69532I
b = 0.66702 + 1.60227I
4.91285 − 1.45910I −3.08044 − 2.03398I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
((u
14
+ 3u
13
+ ··· + 5u + 1)
4
)(u
17
− 5u
16
+ ··· + 8u − 1)
· (u
33
+ 8u
32
+ ··· + 220u + 16)
c
2
((u
14
+ u
13
+ ··· + u − 1)
4
)(u
17
− u
16
+ ··· + 4u
2
− 1)
· (u
33
− 6u
32
+ ··· + 2u + 4)
c
3
, c
11
(u
17
+ 10u
15
+ ··· + 7u − 1)(u
33
+ 15u
31
+ ··· + u + 1)
· (u
56
+ u
55
+ ··· + 12u + 7)
c
4
, c
9
(u
17
+ 10u
15
+ ··· + 7u + 1)(u
33
+ 15u
31
+ ··· + u + 1)
· (u
56
+ u
55
+ ··· + 12u + 7)
c
6
((u
14
+ u
13
+ ··· + u − 1)
4
)(u
17
+ u
16
+ ··· − 4u
2
+ 1)
· (u
33
− 6u
32
+ ··· + 2u + 4)
c
7
((u
14
+ 3u
13
+ ··· + 5u + 1)
4
)(u
17
+ 5u
16
+ ··· + 8u + 1)
· (u
33
+ 8u
32
+ ··· + 220u + 16)
c
8
, c
10
(u
17
+ 3u
16
+ ··· − 3u − 1)(u
33
+ 3u
32
+ ··· + u + 1)
· (u
56
− 17u
55
+ ··· − 491562u + 37537)
c
12
((u
2
− u + 1)
28
)(u
17
− 3u
16
+ ··· − 3u + 1)
· (u
33
+ 32u
32
+ ··· + 286720u + 16384)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
((y
14
+ 17y
13
+ ··· − y + 1)
4
)(y
17
+ 19y
16
+ ··· − 12y −1)
· (y
33
+ 36y
32
+ ··· + 6256y −256)
c
2
, c
6
((y
14
− 3y
13
+ ··· − 5y + 1)
4
)(y
17
− 5y
16
+ ··· + 8y −1)
· (y
33
− 8y
32
+ ··· + 220y −16)
c
3
, c
4
, c
9
c
11
(y
17
+ 20y
16
+ ··· + 17y −1)(y
33
+ 30y
32
+ ··· + 5y −1)
· (y
56
+ 51y
55
+ ··· − 4428y + 49)
c
8
, c
10
(y
17
+ 3y
16
+ ··· − y −1)(y
33
+ 17y
32
+ ··· + 63y −1)
· (y
56
+ 27y
55
+ ··· + 24860581508y + 1409026369)
c
12
((y
2
+ y + 1)
28
)(y
17
+ y
16
+ ··· − 3y −1)
· (y
33
+ 2y
32
+ ··· + 4630511616y −268435456)
24
