12n
0174
(K12n
0174
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 9 3 11 12 1 7 6
Solving Sequence
3,7 8,11
9 12 10 6 1 5 2 4
c
7
c
8
c
11
c
9
c
6
c
12
c
5
c
2
c
4
c
1
, c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.42510 × 10
95
u
48
− 1.67612 × 10
96
u
47
+ ··· + 3.37850 × 10
95
b + 3.34034 × 10
97
,
3.85868 × 10
98
u
48
+ 1.60673 × 10
99
u
47
+ ··· + 4.32448 × 10
97
a − 1.18824 × 10
101
,
u
49
+ 5u
48
+ ··· − 2656u − 256i
I
u
2
= h3.65067 × 10
30
au
29
+ 6.18961 × 10
29
u
29
+ ··· − 4.67430 × 10
31
a + 3.01744 × 10
30
,
4.65337 × 10
30
au
29
+ 5.16674 × 10
30
u
29
+ ··· − 1.73780 × 10
31
a − 4.22817 × 10
31
, u
30
− 3u
29
+ ··· − 36u + 8i
I
u
3
= h62854845u
16
+ 90595385u
15
+ ··· + 103426241b − 86148102,
825367762u
16
+ 1637559900u
15
+ ··· + 103426241a − 116862060, u
17
+ 2u
16
+ ··· + u + 1i
I
v
1
= ha, 16v
3
− 48v
2
+ b + 51v −13, 4v
4
− 13v
3
+ 16v
2
− 7v + 1i
I
v
2
= ha, b
2
− bv + v
2
− b + 2v + 2, v
3
+ 2v
2
+ 3v + 1i
* 5 irreducible components of dim
C
= 0, with total 136 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−4.43 × 10
95
u
48
− 1.68 × 10
96
u
47
+ · · · + 3.38 × 10
95
b + 3.34 ×
10
97
, 3.86 × 10
98
u
48
+ 1.61 × 10
99
u
47
+ · · · + 4.32 × 10
97
a − 1.19 ×
10
101
, u
49
+ 5u
48
+ · · · − 2656u − 256i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
−8.92288u
48
− 37.1542u
47
+ ··· + 25170.8u + 2747.71
1.30978u
48
+ 4.96113u
47
+ ··· − 1531.46u − 98.8705
a
9
=
−17.4967u
48
− 72.9082u
47
+ ··· + 49242.2u + 5362.98
5.84693u
48
+ 24.9569u
47
+ ··· − 19011.2u − 2144.77
a
12
=
−7.61310u
48
− 32.1931u
47
+ ··· + 23639.3u + 2648.84
1.30978u
48
+ 4.96113u
47
+ ··· − 1531.46u − 98.8705
a
10
=
0.226092u
48
+ 1.59877u
47
+ ··· − 3637.18u − 493.367
2.11651u
48
+ 9.72772u
47
+ ··· − 10201.7u − 1249.45
a
6
=
−0.0565490u
48
− 0.741312u
47
+ ··· + 2683.08u + 377.332
−1.10782u
48
− 5.50733u
47
+ ··· + 7171.36u + 910.721
a
1
=
−0.489227u
48
− 1.92395u
47
+ ··· + 911.166u + 83.6824
0.386968u
48
+ 1.50533u
47
+ ··· − 983.961u − 119.278
a
5
=
−0.370890u
48
− 1.37191u
47
+ ··· + 633.455u + 69.2818
0.118336u
48
+ 0.552043u
47
+ ··· − 277.710u − 14.4006
a
2
=
−0.489227u
48
− 1.92395u
47
+ ··· + 911.166u + 83.6824
−0.118336u
48
− 0.552043u
47
+ ··· + 277.710u + 14.4006
a
4
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −20.8192u
48
− 85.4422u
47
+ ··· + 52215.1u + 5489.55
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
49
+ 23u
48
+ ··· − 1887u + 256
c
2
, c
4
u
49
− 7u
48
+ ··· − 97u + 16
c
3
, c
7
u
49
− 5u
48
+ ··· − 2656u + 256
c
5
, c
11
u
49
− u
47
+ ··· − 45u − 9
c
6
, c
12
u
49
− u
48
+ ··· + 2u − 1
c
8
, c
10
u
49
− 6u
48
+ ··· + 27u + 1
c
9
u
49
− 29u
48
+ ··· + 32u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
49
+ 13y
48
+ ··· − 6281407y −65536
c
2
, c
4
y
49
− 23y
48
+ ··· − 1887y −256
c
3
, c
7
y
49
− 27y
48
+ ··· + 881664y −65536
c
5
, c
11
y
49
− 2y
48
+ ··· + 1629y −81
c
6
, c
12
y
49
+ 21y
48
+ ··· − 52y −1
c
8
, c
10
y
49
− 38y
48
+ ··· + 129y −1
c
9
y
49
− y
48
+ ··· − 968y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.302575 + 0.946892I
a = 0.487795 − 0.470190I
b = −0.537829 + 0.119509I
1.55793 + 0.36410I 4.91876 + 0.I
u = −0.302575 − 0.946892I
a = 0.487795 + 0.470190I
b = −0.537829 − 0.119509I
1.55793 − 0.36410I 4.91876 + 0.I
u = 0.974131
a = 0.688714
b = −0.548762
−2.79592 −4.65070
u = −0.219277 + 1.022680I
a = 0.539257 + 0.197168I
b = −0.834449 − 0.356396I
1.68790 + 3.84694I 5.34787 − 7.53538I
u = −0.219277 − 1.022680I
a = 0.539257 − 0.197168I
b = −0.834449 + 0.356396I
1.68790 − 3.84694I 5.34787 + 7.53538I
u = −0.293680 + 1.027110I
a = 0.358766 − 0.282615I
b = 0.665231 + 0.062646I
−0.67993 − 2.04702I 0
u = −0.293680 − 1.027110I
a = 0.358766 + 0.282615I
b = 0.665231 − 0.062646I
−0.67993 + 2.04702I 0
u = −0.923443 + 0.075172I
a = 0.691906 − 0.132695I
b = −0.595517 − 0.867911I
0.783168 + 0.637600I 3.87822 + 1.68066I
u = −0.923443 − 0.075172I
a = 0.691906 + 0.132695I
b = −0.595517 + 0.867911I
0.783168 − 0.637600I 3.87822 − 1.68066I
u = 1.073330 + 0.417383I
a = 0.707312 − 0.335231I
b = −0.346407 − 1.053070I
−0.18835 + 5.00375I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073330 − 0.417383I
a = 0.707312 + 0.335231I
b = −0.346407 + 1.053070I
−0.18835 − 5.00375I 0
u = −0.819012 + 0.013094I
a = −2.62948 + 1.26317I
b = 0.659606 − 0.349888I
0.26853 − 1.69713I 7.44745 + 4.57395I
u = −0.819012 − 0.013094I
a = −2.62948 − 1.26317I
b = 0.659606 + 0.349888I
0.26853 + 1.69713I 7.44745 − 4.57395I
u = 0.459292 + 0.602444I
a = 1.39544 − 0.40680I
b = 0.147252 − 0.682059I
−2.10843 − 0.93637I −6.13827 − 0.19831I
u = 0.459292 − 0.602444I
a = 1.39544 + 0.40680I
b = 0.147252 + 0.682059I
−2.10843 + 0.93637I −6.13827 + 0.19831I
u = −1.305630 + 0.150067I
a = −0.987363 − 0.519908I
b = 0.79108 + 1.31437I
4.85770 − 2.55718I 0
u = −1.305630 − 0.150067I
a = −0.987363 + 0.519908I
b = 0.79108 − 1.31437I
4.85770 + 2.55718I 0
u = −1.302310 + 0.206487I
a = 1.49257 − 0.44915I
b = −1.07120 + 0.96030I
−0.45845 − 8.65599I 0
u = −1.302310 − 0.206487I
a = 1.49257 + 0.44915I
b = −1.07120 − 0.96030I
−0.45845 + 8.65599I 0
u = 1.294620 + 0.259705I
a = −1.253650 − 0.048468I
b = 0.55442 + 1.55115I
4.63789 + 3.07349I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.294620 − 0.259705I
a = −1.253650 + 0.048468I
b = 0.55442 − 1.55115I
4.63789 − 3.07349I 0
u = 1.263480 + 0.434859I
a = −1.041090 + 0.700204I
b = 0.702629 + 0.155346I
6.38898 + 0.61653I 0
u = 1.263480 − 0.434859I
a = −1.041090 − 0.700204I
b = 0.702629 − 0.155346I
6.38898 − 0.61653I 0
u = 0.354370 + 1.295710I
a = 0.105629 + 0.157331I
b = 0.543974 + 0.270866I
−7.18670 + 5.04005I 0
u = 0.354370 − 1.295710I
a = 0.105629 − 0.157331I
b = 0.543974 − 0.270866I
−7.18670 − 5.04005I 0
u = 1.341470 + 0.323853I
a = −1.56393 + 0.05107I
b = 1.032020 + 0.307473I
6.88817 + 3.81636I 0
u = 1.341470 − 0.323853I
a = −1.56393 − 0.05107I
b = 1.032020 − 0.307473I
6.88817 − 3.81636I 0
u = 0.026734 + 1.387210I
a = 0.022345 − 0.231742I
b = 1.119070 − 0.793463I
1.76109 − 5.81272I 0
u = 0.026734 − 1.387210I
a = 0.022345 + 0.231742I
b = 1.119070 + 0.793463I
1.76109 + 5.81272I 0
u = −0.380557 + 1.343750I
a = 0.016368 + 0.214106I
b = 1.11855 + 1.08866I
0.98269 + 11.73260I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.380557 − 1.343750I
a = 0.016368 − 0.214106I
b = 1.11855 − 1.08866I
0.98269 − 11.73260I 0
u = −1.226540 + 0.689864I
a = −0.817481 − 0.645518I
b = 0.556910 − 0.381512I
4.16675 − 6.30819I 0
u = −1.226540 − 0.689864I
a = −0.817481 + 0.645518I
b = 0.556910 + 0.381512I
4.16675 + 6.30819I 0
u = 0.007957 + 0.579842I
a = 2.22180 + 3.71913I
b = −0.229643 + 1.056670I
0.553056 − 0.011412I −0.409957 − 0.498269I
u = 0.007957 − 0.579842I
a = 2.22180 − 3.71913I
b = −0.229643 − 1.056670I
0.553056 + 0.011412I −0.409957 + 0.498269I
u = −1.30886 + 0.58519I
a = −1.49711 − 0.39372I
b = 1.085290 − 0.452742I
5.14203 − 9.72658I 0
u = −1.30886 − 0.58519I
a = −1.49711 + 0.39372I
b = 1.085290 + 0.452742I
5.14203 + 9.72658I 0
u = −0.438088 + 0.264005I
a = 0.951300 + 0.031983I
b = −0.452918 + 0.612196I
0.805812 − 1.108410I 4.74408 + 4.07736I
u = −0.438088 − 0.264005I
a = 0.951300 − 0.031983I
b = −0.452918 − 0.612196I
0.805812 + 1.108410I 4.74408 − 4.07736I
u = −0.486204 + 0.026452I
a = 0.037081 + 0.205362I
b = 0.509879 + 1.181350I
−3.95139 + 7.58730I 10.40617 − 4.11305I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.486204 − 0.026452I
a = 0.037081 − 0.205362I
b = 0.509879 − 1.181350I
−3.95139 − 7.58730I 10.40617 + 4.11305I
u = −1.37791 + 0.76656I
a = 1.39934 + 0.40752I
b = −1.14396 + 1.35722I
4.1900 − 19.1789I 0
u = −1.37791 − 0.76656I
a = 1.39934 − 0.40752I
b = −1.14396 − 1.35722I
4.1900 + 19.1789I 0
u = 1.49189 + 0.57453I
a = 1.347660 − 0.139984I
b = −1.22860 − 1.22772I
6.6161 + 12.7102I 0
u = 1.49189 − 0.57453I
a = 1.347660 + 0.139984I
b = −1.22860 + 1.22772I
6.6161 − 12.7102I 0
u = −1.56868 + 0.48166I
a = 0.749006 + 0.413054I
b = −1.377520 − 0.236905I
7.24686 − 1.08754I 0
u = −1.56868 − 0.48166I
a = 0.749006 − 0.413054I
b = −1.377520 + 0.236905I
7.24686 + 1.08754I 0
u = 1.65256 + 0.20506I
a = 0.875290 − 0.376854I
b = −1.39348 + 0.55816I
8.42952 − 5.77862I 0
u = 1.65256 − 0.20506I
a = 0.875290 + 0.376854I
b = −1.39348 − 0.55816I
8.42952 + 5.77862I 0
9
II. I
u
2
= h3.65 × 10
30
au
29
+ 6.19 × 10
29
u
29
+ · · · − 4.67 × 10
31
a + 3.02 ×
10
30
, 4.65 × 10
30
au
29
+ 5.17 × 10
30
u
29
+ · · · − 1.74 × 10
31
a − 4.23 ×
10
31
, u
30
− 3u
29
+ · · · − 36u + 8i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
a
−3.99021au
29
− 0.676528u
29
+ ··· + 51.0904a − 3.29808
a
9
=
1.53809au
29
+ 1.15252u
29
+ ··· − 16.4838a − 3.16714
0.913366au
29
− 0.111232u
29
+ ··· − 19.3324a + 4.63278
a
12
=
−3.99021au
29
− 0.676528u
29
+ ··· + 52.0904a − 3.29808
−3.99021au
29
− 0.676528u
29
+ ··· + 51.0904a − 3.29808
a
10
=
3.08004au
29
− 1.92711u
29
+ ··· − 47.2217a + 20.8523
3.19127au
29
− 3.19087u
29
+ ··· − 51.8545a + 28.6522
a
6
=
−1.83781au
29
+ 0.343590u
29
+ ··· + 35.2484a − 7.86223
−3.42270au
29
+ 1.58488u
29
+ ··· + 52.6114a − 17.3631
a
1
=
0.551238u
29
− 0.841026u
28
+ ··· + 9.99428u − 2.03557
−0.111232u
29
+ 0.428317u
28
+ ··· − 7.59237u + 3.63278
a
5
=
−0.358930u
29
+ 0.546787u
28
+ ··· − 7.26027u + 0.833169
−0.910168u
29
+ 1.38781u
28
+ ··· − 17.2545u + 2.86874
a
2
=
0.551238u
29
− 0.841026u
28
+ ··· + 9.99428u − 2.03557
0.910168u
29
− 1.38781u
28
+ ··· + 17.2545u − 2.86874
a
4
=
−u
−u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.90078u
29
+ 7.21462u
28
+ ··· − 79.1331u + 24.9566
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
30
+ 12u
29
+ ··· − 31u + 1)
2
c
2
, c
4
(u
30
− 4u
29
+ ··· + 5u − 1)
2
c
3
, c
7
(u
30
+ 3u
29
+ ··· + 36u + 8)
2
c
5
, c
11
u
60
− 2u
59
+ ··· − 270u − 81
c
6
, c
12
u
60
− 6u
59
+ ··· − 48u + 9
c
8
, c
10
u
60
+ 2u
59
+ ··· − 15444u − 13239
c
9
(u
30
+ 14u
29
+ ··· − 8u
2
+ 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
30
+ 16y
29
+ ··· − 433y + 1)
2
c
2
, c
4
(y
30
− 12y
29
+ ··· + 31y + 1)
2
c
3
, c
7
(y
30
− 21y
29
+ ··· − 464y + 64)
2
c
5
, c
11
y
60
− 6y
59
+ ··· − 1175148y + 6561
c
6
, c
12
y
60
− 14y
59
+ ··· + 2088y + 81
c
8
, c
10
y
60
+ 6y
59
+ ··· − 3061177848y + 175271121
c
9
(y
30
− 2y
29
+ ··· − 16y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830725 + 0.628367I
a = 0.688019 + 0.947099I
b = 0.160329 − 0.753919I
−1.64380 − 1.34107I −7.65064 + 5.35088I
u = 0.830725 + 0.628367I
a = 1.56582 − 0.84528I
b = −0.39356 − 1.37701I
−1.64380 − 1.34107I −7.65064 + 5.35088I
u = 0.830725 − 0.628367I
a = 0.688019 − 0.947099I
b = 0.160329 + 0.753919I
−1.64380 + 1.34107I −7.65064 − 5.35088I
u = 0.830725 − 0.628367I
a = 1.56582 + 0.84528I
b = −0.39356 + 1.37701I
−1.64380 + 1.34107I −7.65064 − 5.35088I
u = −0.168778 + 1.072190I
a = 0.650690 + 0.898653I
b = 1.26293 + 1.13876I
1.03788 − 3.22048I 5.62712 + 10.05807I
u = −0.168778 + 1.072190I
a = 0.467167 − 0.068877I
b = −0.502223 + 0.689712I
1.03788 − 3.22048I 5.62712 + 10.05807I
u = −0.168778 − 1.072190I
a = 0.650690 − 0.898653I
b = 1.26293 − 1.13876I
1.03788 + 3.22048I 5.62712 − 10.05807I
u = −0.168778 − 1.072190I
a = 0.467167 + 0.068877I
b = −0.502223 − 0.689712I
1.03788 + 3.22048I 5.62712 − 10.05807I
u = 1.060350 + 0.303256I
a = 1.294080 − 0.561022I
b = −0.211404 − 0.480074I
−0.55296 + 4.80222I −2.95250 − 5.41049I
u = 1.060350 + 0.303256I
a = 0.304725 + 0.037696I
b = −0.229158 − 1.394020I
−0.55296 + 4.80222I −2.95250 − 5.41049I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.060350 − 0.303256I
a = 1.294080 + 0.561022I
b = −0.211404 + 0.480074I
−0.55296 − 4.80222I −2.95250 + 5.41049I
u = 1.060350 − 0.303256I
a = 0.304725 − 0.037696I
b = −0.229158 + 1.394020I
−0.55296 − 4.80222I −2.95250 + 5.41049I
u = −1.077790 + 0.240862I
a = 1.65758 − 0.11424I
b = −0.239330 + 0.061735I
−0.435749 + 0.269407I −2.76265 + 1.35969I
u = −1.077790 + 0.240862I
a = 0.094420 + 0.237347I
b = −0.61150 − 1.52674I
−0.435749 + 0.269407I −2.76265 + 1.35969I
u = −1.077790 − 0.240862I
a = 1.65758 + 0.11424I
b = −0.239330 − 0.061735I
−0.435749 − 0.269407I −2.76265 − 1.35969I
u = −1.077790 − 0.240862I
a = 0.094420 − 0.237347I
b = −0.61150 + 1.52674I
−0.435749 − 0.269407I −2.76265 − 1.35969I
u = 1.192960 + 0.010682I
a = 0.183774 + 0.819595I
b = −0.276666 + 1.102260I
1.73972 − 3.17328I 2.25970 + 4.53501I
u = 1.192960 + 0.010682I
a = −1.63092 + 0.75681I
b = 1.70671 − 0.84801I
1.73972 − 3.17328I 2.25970 + 4.53501I
u = 1.192960 − 0.010682I
a = 0.183774 − 0.819595I
b = −0.276666 − 1.102260I
1.73972 + 3.17328I 2.25970 − 4.53501I
u = 1.192960 − 0.010682I
a = −1.63092 − 0.75681I
b = 1.70671 + 0.84801I
1.73972 + 3.17328I 2.25970 − 4.53501I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.233140 + 0.387255I
a = −0.168429 + 0.838831I
b = −0.047811 + 1.029580I
0.93505 − 8.49512I −0.70544 + 9.78968I
u = −1.233140 + 0.387255I
a = −1.80216 − 0.00827I
b = 1.59192 − 1.20968I
0.93505 − 8.49512I −0.70544 + 9.78968I
u = −1.233140 − 0.387255I
a = −0.168429 − 0.838831I
b = −0.047811 − 1.029580I
0.93505 + 8.49512I −0.70544 − 9.78968I
u = −1.233140 − 0.387255I
a = −1.80216 + 0.00827I
b = 1.59192 + 1.20968I
0.93505 + 8.49512I −0.70544 − 9.78968I
u = −0.210876 + 0.639148I
a = −1.58258 + 0.71331I
b = −1.106760 − 0.872397I
−2.28826 + 4.44786I −7.27742 − 9.17246I
u = −0.210876 + 0.639148I
a = 3.14040 + 3.89458I
b = 0.357221 + 0.755095I
−2.28826 + 4.44786I −7.27742 − 9.17246I
u = −0.210876 − 0.639148I
a = −1.58258 − 0.71331I
b = −1.106760 + 0.872397I
−2.28826 − 4.44786I −7.27742 + 9.17246I
u = −0.210876 − 0.639148I
a = 3.14040 − 3.89458I
b = 0.357221 − 0.755095I
−2.28826 − 4.44786I −7.27742 + 9.17246I
u = 1.40234
a = 1.20292
b = −1.60235
−2.47862 −20.4370
u = 1.40234
a = −0.335009
b = 0.0789471
−2.47862 −20.4370
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.328237 + 0.429693I
a = −2.85890 + 2.68232I
b = −0.453308 + 0.394776I
−2.64797 − 3.16007I −9.92848 + 8.55630I
u = −0.328237 + 0.429693I
a = −5.69041 − 5.45788I
b = 0.773105 − 1.012340I
−2.64797 − 3.16007I −9.92848 + 8.55630I
u = −0.328237 − 0.429693I
a = −2.85890 − 2.68232I
b = −0.453308 − 0.394776I
−2.64797 + 3.16007I −9.92848 − 8.55630I
u = −0.328237 − 0.429693I
a = −5.69041 + 5.45788I
b = 0.773105 + 1.012340I
−2.64797 + 3.16007I −9.92848 − 8.55630I
u = 0.539988
a = 0.257913 + 0.081587I
b = 0.238979 + 1.220830I
−5.60678 4.51860
u = 0.539988
a = 0.257913 − 0.081587I
b = 0.238979 − 1.220830I
−5.60678 4.51860
u = 0.30931 + 1.43313I
a = 0.414697 − 0.125231I
b = 1.62538 − 0.86203I
−0.72901 − 3.16597I −11.1224 + 14.5296I
u = 0.30931 + 1.43313I
a = 0.250658 + 0.025237I
b = −0.253505 + 0.236793I
−0.72901 − 3.16597I −11.1224 + 14.5296I
u = 0.30931 − 1.43313I
a = 0.414697 + 0.125231I
b = 1.62538 + 0.86203I
−0.72901 + 3.16597I −11.1224 − 14.5296I
u = 0.30931 − 1.43313I
a = 0.250658 − 0.025237I
b = −0.253505 − 0.236793I
−0.72901 + 3.16597I −11.1224 − 14.5296I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44530 + 0.50503I
a = 0.873903 − 0.794655I
b = −2.05881 + 0.78042I
6.03993 + 9.01155I 6.36928 − 7.51699I
u = 1.44530 + 0.50503I
a = −1.42172 + 0.03163I
b = 0.890576 + 0.847975I
6.03993 + 9.01155I 6.36928 − 7.51699I
u = 1.44530 − 0.50503I
a = 0.873903 + 0.794655I
b = −2.05881 − 0.78042I
6.03993 − 9.01155I 6.36928 + 7.51699I
u = 1.44530 − 0.50503I
a = −1.42172 − 0.03163I
b = 0.890576 − 0.847975I
6.03993 − 9.01155I 6.36928 + 7.51699I
u = 0.374069 + 0.272103I
a = 1.009080 − 0.139327I
b = −0.561974 + 0.976950I
−0.25810 − 3.13859I 5.54807 + 1.96798I
u = 0.374069 + 0.272103I
a = 1.13211 + 2.46814I
b = 0.889012 + 0.000796I
−0.25810 − 3.13859I 5.54807 + 1.96798I
u = 0.374069 − 0.272103I
a = 1.009080 + 0.139327I
b = −0.561974 − 0.976950I
−0.25810 + 3.13859I 5.54807 − 1.96798I
u = 0.374069 − 0.272103I
a = 1.13211 − 2.46814I
b = 0.889012 − 0.000796I
−0.25810 + 3.13859I 5.54807 − 1.96798I
u = −1.53404 + 0.18591I
a = −1.192930 + 0.300657I
b = 0.861605 − 0.648597I
7.29465 − 2.57518I 9.44800 + 2.42621I
u = −1.53404 + 0.18591I
a = 1.106650 + 0.543891I
b = −1.93911 − 1.08341I
7.29465 − 2.57518I 9.44800 + 2.42621I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53404 − 0.18591I
a = −1.192930 − 0.300657I
b = 0.861605 + 0.648597I
7.29465 + 2.57518I 9.44800 − 2.42621I
u = −1.53404 − 0.18591I
a = 1.106650 − 0.543891I
b = −1.93911 + 1.08341I
7.29465 + 2.57518I 9.44800 − 2.42621I
u = 1.40724 + 0.75831I
a = −0.908110 + 0.140923I
b = 0.584406 + 0.635478I
2.76218 + 10.76250I 0. − 10.69821I
u = 1.40724 + 0.75831I
a = 1.262290 − 0.375449I
b = −1.30126 − 1.53580I
2.76218 + 10.76250I 0. − 10.69821I
u = 1.40724 − 0.75831I
a = −0.908110 − 0.140923I
b = 0.584406 − 0.635478I
2.76218 − 10.76250I 0. + 10.69821I
u = 1.40724 − 0.75831I
a = 1.262290 + 0.375449I
b = −1.30126 + 1.53580I
2.76218 − 10.76250I 0. + 10.69821I
u = −1.53824 + 0.56889I
a = 1.221720 + 0.179869I
b = −1.57421 + 1.41354I
5.12616 − 4.17577I 0. + 10.28228I
u = −1.53824 + 0.56889I
a = −0.753482 − 0.099863I
b = 0.580107 − 0.368498I
5.12616 − 4.17577I 0. + 10.28228I
u = −1.53824 − 0.56889I
a = 1.221720 − 0.179869I
b = −1.57421 − 1.41354I
5.12616 + 4.17577I 0. − 10.28228I
u = −1.53824 − 0.56889I
a = −0.753482 + 0.099863I
b = 0.580107 + 0.368498I
5.12616 + 4.17577I 0. − 10.28228I
18
III.
I
u
3
= h6.29 × 10
7
u
16
+ 9.06 × 10
7
u
15
+ · · · + 1.03 × 10
8
b − 8.61 × 10
7
, 8.25 ×
10
8
u
16
+ 1.64 × 10
9
u
15
+ · · · + 1.03 × 10
8
a − 1.17 × 10
8
, u
17
+ 2u
16
+ · · · + u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
−7.98025u
16
− 15.8331u
15
+ ··· − 58.7686u + 1.12991
−0.607726u
16
− 0.875942u
15
+ ··· − 2.58963u + 0.832942
a
9
=
0.812543u
16
− 1.15789u
15
+ ··· − 20.2157u − 19.9470
−0.0211113u
16
− 0.134382u
15
+ ··· − 2.23865u − 1.44347
a
12
=
−8.58798u
16
− 16.7091u
15
+ ··· − 61.3582u + 1.96285
−0.607726u
16
− 0.875942u
15
+ ··· − 2.58963u + 0.832942
a
10
=
−8.56687u
16
− 16.5747u
15
+ ··· − 59.1196u + 4.40632
−0.607726u
16
− 0.875942u
15
+ ··· − 2.58963u + 0.832942
a
6
=
−5.33175u
16
− 12.7204u
15
+ ··· − 56.8680u − 13.8299
−0.630211u
16
− 1.49278u
15
+ ··· − 5.14996u − 0.613392
a
1
=
−1.25905u
16
− 2.50310u
15
+ ··· − 9.97824u − 1.22392
−0.198592u
16
− 0.408701u
15
+ ··· − 0.862568u − 0.232357
a
5
=
0.995664u
16
+ 2.18008u
15
+ ··· + 10.3597u + 0.976565
−0.263385u
16
− 0.323020u
15
+ ··· + 0.381486u − 0.247351
a
2
=
−1.25905u
16
− 2.50310u
15
+ ··· − 9.97824u − 1.22392
−0.263385u
16
− 0.323020u
15
+ ··· + 0.381486u − 0.247351
a
4
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
821304331
103426241
u
16
+
1347785326
103426241
u
15
+ ··· +
2768366202
103426241
u −
3171807864
103426241
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 10u
16
+ ··· + 21u − 1
c
2
u
17
+ 4u
16
+ ··· + 3u − 1
c
3
u
17
− 2u
16
+ ··· + u − 1
c
4
u
17
− 4u
16
+ ··· + 3u + 1
c
5
, c
11
u
17
− 3u
15
+ ··· − 3u + 1
c
6
, c
12
u
17
− 3u
16
+ ··· − 3u
2
+ 1
c
7
u
17
+ 2u
16
+ ··· + u + 1
c
8
, c
10
u
17
+ 6u
16
+ ··· + 7u + 1
c
9
u
17
− 11u
16
+ ··· + 11u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 2y
16
+ ··· + 121y −1
c
2
, c
4
y
17
− 10y
16
+ ··· + 21y −1
c
3
, c
7
y
17
− 6y
16
+ ··· − 19y −1
c
5
, c
11
y
17
− 6y
16
+ ··· + 7y −1
c
6
, c
12
y
17
− 7y
16
+ ··· + 6y −1
c
8
, c
10
y
17
+ 6y
16
+ ··· − 17y −1
c
9
y
17
+ y
16
+ ··· + 5y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.043200 + 0.168287I
a = 1.038300 − 0.182643I
b = −0.798280 − 0.935617I
0.36692 + 1.60299I 0.36498 − 4.08341I
u = −1.043200 − 0.168287I
a = 1.038300 + 0.182643I
b = −0.798280 + 0.935617I
0.36692 − 1.60299I 0.36498 + 4.08341I
u = 1.022030 + 0.288227I
a = 0.783907 − 0.680893I
b = −0.600785 − 0.956560I
0.09494 + 6.05613I 1.62217 − 10.70941I
u = 1.022030 − 0.288227I
a = 0.783907 + 0.680893I
b = −0.600785 + 0.956560I
0.09494 − 6.05613I 1.62217 + 10.70941I
u = −0.345041 + 1.234750I
a = −0.175656 + 0.124962I
b = −0.459926 + 0.324004I
−7.30928 − 5.03230I −35.8098 + 2.0999I
u = −0.345041 − 1.234750I
a = −0.175656 − 0.124962I
b = −0.459926 − 0.324004I
−7.30928 + 5.03230I −35.8098 − 2.0999I
u = −0.087423 + 1.326950I
a = −0.0462067 + 0.0871223I
b = −0.920987 − 0.168672I
−0.16476 + 2.91810I 3.50192 − 5.82402I
u = −0.087423 − 1.326950I
a = −0.0462067 − 0.0871223I
b = −0.920987 + 0.168672I
−0.16476 − 2.91810I 3.50192 + 5.82402I
u = −1.34164
a = −0.890647
b = 0.861305
−2.08721 6.80050
u = 0.021367 + 0.554259I
a = −2.01866 + 0.67494I
b = −0.702902 − 0.628013I
−1.26702 + 3.69006I −2.09916 − 5.66136I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.021367 − 0.554259I
a = −2.01866 − 0.67494I
b = −0.702902 + 0.628013I
−1.26702 − 3.69006I −2.09916 + 5.66136I
u = −1.38456 + 0.57144I
a = −1.243860 − 0.238832I
b = 1.182010 − 0.472177I
4.17706 − 9.34432I −0.13250 + 7.24088I
u = −1.38456 − 0.57144I
a = −1.243860 + 0.238832I
b = 1.182010 + 0.472177I
4.17706 + 9.34432I −0.13250 − 7.24088I
u = 1.47952 + 0.32711I
a = −1.140820 + 0.059425I
b = 1.164170 + 0.294594I
5.82050 + 3.06022I 3.26385 − 2.28981I
u = 1.47952 − 0.32711I
a = −1.140820 − 0.059425I
b = 1.164170 − 0.294594I
5.82050 − 3.06022I 3.26385 + 2.28981I
u = 0.008126 + 0.358392I
a = 5.7483 − 13.6218I
b = 0.706047 − 0.738870I
−2.31969 − 3.66781I −26.6116 + 4.6726I
u = 0.008126 − 0.358392I
a = 5.7483 + 13.6218I
b = 0.706047 + 0.738870I
−2.31969 + 3.66781I −26.6116 − 4.6726I
23
IV. I
v
1
= ha, 16v
3
− 48v
2
+ b + 51v − 13, 4v
4
− 13v
3
+ 16v
2
− 7v + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−16v
3
+ 48v
2
− 51v + 13
a
9
=
1
20v
3
− 57v
2
+ 58v − 13
a
12
=
−16v
3
+ 48v
2
− 51v + 13
−16v
3
+ 48v
2
− 51v + 13
a
10
=
16v
3
− 48v
2
+ 51v − 13
36v
3
− 105v
2
+ 109v − 27
a
6
=
−20v
3
+ 57v
2
− 58v + 14
−36v
3
+ 105v
2
− 109v + 27
a
1
=
−1
4v
3
− 13v
2
+ 16v − 7
a
5
=
1
−4v
3
+ 13v
2
− 16v + 7
a
2
=
v − 1
4v
3
− 13v
2
+ 16v − 7
a
4
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 124v
3
− 368v
2
+ 395v − 111
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
, c
8
, c
10
u
4
+ u
2
+ u + 1
c
6
u
4
− 2u
3
+ 3u
2
− u + 1
c
9
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
11
u
4
+ u
2
− u + 1
c
12
u
4
+ 2u
3
+ 3u
2
+ u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
y
4
c
5
, c
8
, c
10
c
11
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
6
, c
12
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
9
y
4
− y
3
+ 2y
2
+ 7y + 4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.28654 + 0.69736I
a = 0
b = −0.547424 + 0.585652I
−0.66484 − 1.39709I −1.65357 + 2.46427I
v = 1.28654 − 0.69736I
a = 0
b = −0.547424 − 0.585652I
−0.66484 + 1.39709I −1.65357 − 2.46427I
v = 0.338459 + 0.046758I
a = 0
b = 0.547424 − 1.120870I
−4.26996 − 7.64338I −14.1277 + 8.8017I
v = 0.338459 − 0.046758I
a = 0
b = 0.547424 + 1.120870I
−4.26996 + 7.64338I −14.1277 − 8.8017I
27
V. I
v
2
= ha, b
2
− bv + v
2
− b + 2v + 2, v
3
+ 2v
2
+ 3v + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
b
a
9
=
1
−bv + v
2
− b + 2v + 2
a
12
=
b
b
a
10
=
−v
2
b − bv − b + 1
−v
2
b − 2bv + v
2
− 2b + 2v + 2
a
6
=
bv − v
2
+ b − 2v − 1
v
2
b + 2bv − v
2
+ 2b − 2v − 2
a
1
=
−bv + v
2
+ v + 1
v
2
+ 2v + 3
a
5
=
bv − v
2
− v − 1
−v
2
− 2v − 3
a
2
=
−bv + v
2
+ 2v + 1
v
2
+ 2v + 3
a
4
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8v
2
− 9v − 17
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
8
, c
10
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
6
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
9
(u
3
− u
2
+ 1)
2
c
11
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
12
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
6
c
3
, c
7
y
6
c
5
, c
8
, c
10
c
11
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
6
, c
12
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
9
(y
3
− y
2
+ 2y − 1)
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.78492 + 1.30714I
a = 0
b = −0.498832 + 1.001300I
−1.91067 − 2.82812I −1.19557 + 4.65175I
v = −0.78492 + 1.30714I
a = 0
b = 0.713912 + 0.305839I
−1.91067 − 2.82812I −1.19557 + 4.65175I
v = −0.78492 − 1.30714I
a = 0
b = −0.498832 − 1.001300I
−1.91067 + 2.82812I −1.19557 − 4.65175I
v = −0.78492 − 1.30714I
a = 0
b = 0.713912 − 0.305839I
−1.91067 + 2.82812I −1.19557 − 4.65175I
v = −0.430160
a = 0
b = 0.284920 + 1.115140I
−6.04826 −14.6090
v = −0.430160
a = 0
b = 0.284920 − 1.115140I
−6.04826 −14.6090
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
17
− 10u
16
+ ··· + 21u − 1)(u
30
+ 12u
29
+ ··· − 31u + 1)
2
· (u
49
+ 23u
48
+ ··· − 1887u + 256)
c
2
((u − 1)
10
)(u
17
+ 4u
16
+ ··· + 3u − 1)(u
30
− 4u
29
+ ··· + 5u − 1)
2
· (u
49
− 7u
48
+ ··· − 97u + 16)
c
3
u
10
(u
17
− 2u
16
+ ··· + u − 1)(u
30
+ 3u
29
+ ··· + 36u + 8)
2
· (u
49
− 5u
48
+ ··· − 2656u + 256)
c
4
((u + 1)
10
)(u
17
− 4u
16
+ ··· + 3u + 1)(u
30
− 4u
29
+ ··· + 5u − 1)
2
· (u
49
− 7u
48
+ ··· − 97u + 16)
c
5
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
17
− 3u
15
+ ··· − 3u + 1)(u
49
− u
47
+ ··· − 45u − 9)
· (u
60
− 2u
59
+ ··· − 270u − 81)
c
6
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
17
− 3u
16
+ ··· − 3u
2
+ 1)(u
49
− u
48
+ ··· + 2u − 1)
· (u
60
− 6u
59
+ ··· − 48u + 9)
c
7
u
10
(u
17
+ 2u
16
+ ··· + u + 1)(u
30
+ 3u
29
+ ··· + 36u + 8)
2
· (u
49
− 5u
48
+ ··· − 2656u + 256)
c
8
, c
10
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
17
+ 6u
16
+ ··· + 7u + 1)(u
49
− 6u
48
+ ··· + 27u + 1)
· (u
60
+ 2u
59
+ ··· − 15444u − 13239)
c
9
((u
3
− u
2
+ 1)
2
)(u
4
+ 3u
3
+ ··· + 3u + 2)(u
17
− 11u
16
+ ··· + 11u − 1)
· ((u
30
+ 14u
29
+ ··· − 8u
2
+ 1)
2
)(u
49
− 29u
48
+ ··· + 32u − 4)
c
11
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
17
− 3u
15
+ ··· − 3u + 1)(u
49
− u
47
+ ··· − 45u − 9)
· (u
60
− 2u
59
+ ··· − 270u − 81)
c
12
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
17
− 3u
16
+ ··· − 3u
2
+ 1)(u
49
− u
48
+ ··· + 2u − 1)
· (u
60
− 6u
59
+ ··· − 48u + 9)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
17
− 2y
16
+ ··· + 121y − 1)
· (y
30
+ 16y
29
+ ··· − 433y + 1)
2
· (y
49
+ 13y
48
+ ··· − 6281407y − 65536)
c
2
, c
4
((y − 1)
10
)(y
17
− 10y
16
+ ··· + 21y − 1)(y
30
− 12y
29
+ ··· + 31y + 1)
2
· (y
49
− 23y
48
+ ··· − 1887y − 256)
c
3
, c
7
y
10
(y
17
− 6y
16
+ ··· − 19y − 1)(y
30
− 21y
29
+ ··· − 464y + 64)
2
· (y
49
− 27y
48
+ ··· + 881664y − 65536)
c
5
, c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
17
− 6y
16
+ ··· + 7y − 1)(y
49
− 2y
48
+ ··· + 1629y − 81)
· (y
60
− 6y
59
+ ··· − 1175148y + 6561)
c
6
, c
12
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
17
− 7y
16
+ ··· + 6y − 1)(y
49
+ 21y
48
+ ··· − 52y − 1)
· (y
60
− 14y
59
+ ··· + 2088y + 81)
c
8
, c
10
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
17
+ 6y
16
+ ··· − 17y − 1)(y
49
− 38y
48
+ ··· + 129y − 1)
· (y
60
+ 6y
59
+ ··· − 3061177848y + 175271121)
c
9
((y
3
− y
2
+ 2y − 1)
2
)(y
4
− y
3
+ 2y
2
+ 7y + 4)(y
17
+ y
16
+ ··· + 5y − 1)
· ((y
30
− 2y
29
+ ··· − 16y + 1)
2
)(y
49
− y
48
+ ··· − 968y − 16)
33
