12n
0505
(K12n
0505
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 7 2 10 11 5 1 5 8
Solving Sequence
2,6
3
7,10
8 1 11 5 4 9 12
c
2
c
6
c
7
c
1
c
10
c
5
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−19u
31
+ 110u
30
+ ··· + b + 35, −27u
31
+ 170u
30
+ ··· + 2a + 74, u
32
− 6u
31
+ ··· + 2u + 2i
I
u
2
= h2u
14
+ 4u
12
− u
11
+ 9u
10
+ 2u
9
+ 8u
8
+ 2u
7
+ 5u
6
+ 7u
5
+ 2u
4
+ 3u
3
− 2u
2
+ b + u − 1,
3u
14
− u
13
+ 5u
12
− 4u
11
+ 11u
10
− 3u
9
+ 6u
8
− 6u
7
− u
6
− 5u
4
− 4u
3
− 11u
2
+ 2a − 3u − 4,
u
15
− u
14
+ 3u
13
− 2u
12
+ 7u
11
− 3u
10
+ 8u
9
+ 7u
7
+ 4u
6
+ 3u
5
+ 6u
4
+ u
3
+ 5u
2
+ 2i
I
u
3
= h−u
15
− u
14
− 2u
13
− u
12
− 4u
11
− 2u
10
− 4u
9
− u
8
− 4u
7
− 2u
5
+ u
2
a − 2u
3
+ au + b + 1,
u
15
a − 5u
15
+ ··· − 2a + 8,
u
16
+ u
15
+ 3u
14
+ 2u
13
+ 7u
12
+ 4u
11
+ 10u
10
+ 4u
9
+ 11u
8
+ 2u
7
+ 8u
6
+ 4u
4
− 2u
3
− 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 79 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−19u
31
+ 110u
30
+ · · · + b + 35, −27u
31
+ 170u
30
+ · · · + 2a +
74, u
32
− 6u
31
+ · · · + 2u + 2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
27
2
u
31
− 85u
30
+ ··· − 58u − 37
19u
31
− 110u
30
+ ··· − 45u − 35
a
8
=
5
2
u
31
− 15u
30
+ ··· − 9u − 6
2u
31
− 13u
30
+ ··· − 5u − 5
a
1
=
u
2
+ 1
−u
4
a
11
=
17
2
u
31
− 50u
30
+ ··· − 23u − 16
10u
31
− 55u
30
+ ··· − 19u − 15
a
5
=
u
3
u
3
+ u
a
4
=
−
7
2
u
31
+ 16u
30
+ ··· − u + 1
−u
31
+ 4u
29
+ ··· − 11u − 5
a
9
=
7
2
u
31
− 16u
30
+ ··· + 4u − 1
−4u
31
+ 19u
30
+ ··· + 2u + 3
a
12
=
21
2
u
31
− 65u
30
+ ··· − 41u − 26
16u
31
− 89u
30
+ ··· − 30u − 25
(ii) Obstruction class = −1
(iii) Cusp Shapes = −16u
31
+ 83u
30
− 289u
29
+ 706u
28
− 1480u
27
+ 2622u
26
−
4235u
25
+ 6012u
24
− 7923u
23
+ 9315u
22
− 10193u
21
+ 9679u
20
− 8295u
19
+ 5507u
18
−
2564u
17
− 852u
16
+ 3101u
15
− 4711u
14
+ 4654u
13
− 4018u
12
+ 2292u
11
− 761u
10
−
695u
9
+ 1289u
8
− 1440u
7
+ 990u
6
− 534u
5
+ 157u
4
− 23u
3
− 26u
2
+ 2u + 16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
32
+ 10u
31
+ ··· − 12u + 4
c
2
, c
6
u
32
− 6u
31
+ ··· + 2u + 2
c
3
, c
4
, c
11
u
32
+ u
31
+ ··· − 2u + 1
c
7
, c
10
u
32
+ 3u
31
+ ··· − 4u + 1
c
8
u
32
− 15u
31
+ ··· + 330u + 50
c
9
u
32
− u
31
+ ··· + 7u + 4
c
12
u
32
+ 30u
31
+ ··· + 983040u + 65536
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
32
+ 26y
31
+ ··· + 336y + 16
c
2
, c
6
y
32
+ 10y
31
+ ··· − 12y + 4
c
3
, c
4
, c
11
y
32
+ 45y
31
+ ··· + 10y + 1
c
7
, c
10
y
32
+ 5y
31
+ ··· − 12y + 1
c
8
y
32
− 23y
31
+ ··· − 127900y + 2500
c
9
y
32
+ 9y
31
+ ··· + 151y + 16
c
12
y
32
− 24y
30
+ ··· + 4294967296y + 4294967296
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.683755 + 0.852208I
a = 0.487406 + 0.002344I
b = −0.211885 + 0.982398I
1.307790 − 0.204998I 8.20443 + 1.69179I
u = −0.683755 − 0.852208I
a = 0.487406 − 0.002344I
b = −0.211885 − 0.982398I
1.307790 + 0.204998I 8.20443 − 1.69179I
u = 0.779459 + 0.786382I
a = −1.93860 − 1.52370I
b = −2.20178 − 0.35212I
4.25545 − 1.80010I 6.28414 + 0.97881I
u = 0.779459 − 0.786382I
a = −1.93860 + 1.52370I
b = −2.20178 + 0.35212I
4.25545 + 1.80010I 6.28414 − 0.97881I
u = −0.015119 + 0.891995I
a = 0.067954 + 0.845861I
b = −0.724294 + 0.722479I
−2.42371 + 1.04680I −1.12616 − 4.02159I
u = −0.015119 − 0.891995I
a = 0.067954 − 0.845861I
b = −0.724294 − 0.722479I
−2.42371 − 1.04680I −1.12616 + 4.02159I
u = −0.127331 + 0.878306I
a = 0.247595 − 1.216250I
b = 1.49574 − 0.49081I
−1.46153 − 3.39079I −2.40633 + 1.52334I
u = −0.127331 − 0.878306I
a = 0.247595 + 1.216250I
b = 1.49574 + 0.49081I
−1.46153 + 3.39079I −2.40633 − 1.52334I
u = 0.755098 + 0.457354I
a = 0.394809 − 0.506304I
b = 0.037452 − 0.291658I
1.48779 + 0.53337I 11.99767 − 5.02878I
u = 0.755098 − 0.457354I
a = 0.394809 + 0.506304I
b = 0.037452 + 0.291658I
1.48779 − 0.53337I 11.99767 + 5.02878I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.686701 + 0.891793I
a = −0.391138 − 0.204261I
b = 0.574304 − 0.753738I
1.18083 − 5.07845I 7.57041 + 6.17791I
u = −0.686701 − 0.891793I
a = −0.391138 + 0.204261I
b = 0.574304 + 0.753738I
1.18083 + 5.07845I 7.57041 − 6.17791I
u = 0.884596 + 0.702295I
a = 1.55531 + 1.46424I
b = 1.71686 + 0.03149I
−2.61872 − 9.73264I 5.09358 + 3.95758I
u = 0.884596 − 0.702295I
a = 1.55531 − 1.46424I
b = 1.71686 − 0.03149I
−2.61872 + 9.73264I 5.09358 − 3.95758I
u = 0.719909 + 0.881933I
a = 0.89512 + 1.20915I
b = 1.34574 + 0.83709I
1.47719 + 2.75279I 4.12705 − 2.54789I
u = 0.719909 − 0.881933I
a = 0.89512 − 1.20915I
b = 1.34574 − 0.83709I
1.47719 − 2.75279I 4.12705 + 2.54789I
u = −0.232859 + 1.122020I
a = −0.327320 + 0.701313I
b = −1.47146 + 0.14327I
−10.17100 − 9.66976I −1.12021 + 6.59590I
u = −0.232859 − 1.122020I
a = −0.327320 − 0.701313I
b = −1.47146 − 0.14327I
−10.17100 + 9.66976I −1.12021 − 6.59590I
u = −0.815946 + 0.102282I
a = 0.523040 − 0.339256I
b = −0.678199 + 0.639931I
−6.02453 − 6.28492I 4.69674 + 5.01750I
u = −0.815946 − 0.102282I
a = 0.523040 + 0.339256I
b = −0.678199 − 0.639931I
−6.02453 + 6.28492I 4.69674 − 5.01750I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.359796 + 1.131210I
a = −0.396826 − 0.243138I
b = 0.159308 − 0.964091I
−9.40796 + 2.11722I −1.44983 − 2.28702I
u = −0.359796 − 1.131210I
a = −0.396826 + 0.243138I
b = 0.159308 + 0.964091I
−9.40796 − 2.11722I −1.44983 + 2.28702I
u = 0.738924 + 0.951964I
a = −1.23531 − 2.20933I
b = −2.36280 − 1.86645I
3.74678 + 7.53753I 5.07954 − 6.16050I
u = 0.738924 − 0.951964I
a = −1.23531 + 2.20933I
b = −2.36280 + 1.86645I
3.74678 − 7.53753I 5.07954 + 6.16050I
u = 0.908160 + 0.896082I
a = 0.386593 + 0.792958I
b = 0.922704 + 0.420064I
0.14826 + 3.30667I 11.82122 − 5.07419I
u = 0.908160 − 0.896082I
a = 0.386593 − 0.792958I
b = 0.922704 − 0.420064I
0.14826 − 3.30667I 11.82122 + 5.07419I
u = 0.759511 + 1.036240I
a = 1.17713 + 1.86108I
b = 2.47993 + 1.70524I
−3.6530 + 15.8290I 3.56651 − 8.43512I
u = 0.759511 − 1.036240I
a = 1.17713 − 1.86108I
b = 2.47993 − 1.70524I
−3.6530 − 15.8290I 3.56651 + 8.43512I
u = 0.722062 + 1.151000I
a = −0.296051 − 0.228149I
b = −0.568245 − 0.196699I
−0.61804 + 5.20487I 14.5642 − 21.0319I
u = 0.722062 − 1.151000I
a = −0.296051 + 0.228149I
b = −0.568245 + 0.196699I
−0.61804 − 5.20487I 14.5642 + 21.0319I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.346211 + 0.168211I
a = −0.14971 − 1.47915I
b = 0.486627 + 0.604920I
0.56782 + 1.66520I 4.09705 − 5.80076I
u = −0.346211 − 0.168211I
a = −0.14971 + 1.47915I
b = 0.486627 − 0.604920I
0.56782 − 1.66520I 4.09705 + 5.80076I
8
II.
I
u
2
= h2u
14
+4u
12
+· · ·+b−1, 3u
14
−u
13
+· · ·+2a−4, u
15
−u
14
+· · ·+5u
2
+2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
−
3
2
u
14
+
1
2
u
13
+ ··· +
3
2
u + 2
−2u
14
− 4u
12
+ ··· − u + 1
a
8
=
1
2
u
14
+
1
2
u
13
+ ··· −
1
2
u − 1
u
14
+ u
13
+ ··· + u + 1
a
1
=
u
2
+ 1
−u
4
a
11
=
−
1
2
u
14
−
1
2
u
13
+ ··· +
1
2
u − 1
−u
14
− 2u
12
+ ··· − u − 1
a
5
=
u
3
u
3
+ u
a
4
=
−
1
2
u
14
−
3
2
u
13
+ ··· −
11
2
u − 4
−u
14
− 2u
12
+ ··· − 3u − 1
a
9
=
1
2
u
14
−
3
2
u
13
+ ··· +
3
2
u − 2
−u
9
− u
7
− 2u
5
− u
4
− u
2
− 1
a
12
=
−
3
2
u
14
+
1
2
u
13
+ ··· +
1
2
u + 1
−2u
14
− 4u
12
+ ··· − 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
14
−6u
13
+12u
12
−12u
11
+24u
10
−24u
9
+22u
8
−14u
7
+8u
6
−8u
5
−8u
4
−u
3
−12u
2
+2u−4
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
15
− 5u
14
+ ··· − 20u + 4
c
2
u
15
− u
14
+ ··· + 5u
2
+ 2
c
3
, c
11
u
15
− u
14
+ ··· − 3u + 1
c
4
u
15
+ u
14
+ ··· − 3u − 1
c
6
u
15
+ u
14
+ ··· − 5u
2
− 2
c
7
, c
10
u
15
+ 3u
14
+ ··· + 3u + 1
c
8
u
15
− 12u
14
+ ··· + 12u − 2
c
9
u
15
+ u
14
+ ··· + u − 1
c
12
u
15
+ 3u
14
+ ··· + 3u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
15
+ 13y
14
+ ··· + 8y −16
c
2
, c
6
y
15
+ 5y
14
+ ··· − 20y −4
c
3
, c
4
, c
11
y
15
+ 9y
14
+ ··· + y −1
c
7
, c
10
y
15
− 7y
14
+ ··· − y −1
c
8
y
15
− 16y
14
+ ··· − 12y −4
c
9
y
15
+ 13y
14
+ ··· + 9y −1
c
12
y
15
+ y
14
+ ··· + 7y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.280327 + 0.923287I
a = 0.052905 − 0.728078I
b = 1.075220 − 0.283109I
−0.70220 − 4.00075I 5.18084 + 7.73675I
u = −0.280327 − 0.923287I
a = 0.052905 + 0.728078I
b = 1.075220 + 0.283109I
−0.70220 + 4.00075I 5.18084 − 7.73675I
u = −0.571277 + 0.761420I
a = 0.483935 − 0.067367I
b = −0.043929 + 0.810898I
0.370462 + 0.285171I 1.32756 − 0.80118I
u = −0.571277 − 0.761420I
a = 0.483935 + 0.067367I
b = −0.043929 − 0.810898I
0.370462 − 0.285171I 1.32756 + 0.80118I
u = 0.692893 + 0.869031I
a = 2.38866 + 2.52848I
b = 3.15994 + 1.64676I
−4.59955 + 2.66562I 7.43536 − 3.52497I
u = 0.692893 − 0.869031I
a = 2.38866 − 2.52848I
b = 3.15994 − 1.64676I
−4.59955 − 2.66562I 7.43536 + 3.52497I
u = −0.877263
a = −0.247126
b = 0.406981
1.99799 22.9980
u = 0.852657 + 0.760960I
a = −1.19418 − 1.44954I
b = −1.61952 − 0.38054I
6.57862 − 2.60076I 11.64016 + 2.05519I
u = 0.852657 − 0.760960I
a = −1.19418 + 1.44954I
b = −1.61952 + 0.38054I
6.57862 + 2.60076I 11.64016 − 2.05519I
u = 0.142705 + 0.800687I
a = −1.76224 + 0.77168I
b = −1.78689 − 0.41916I
−7.67025 + 0.63840I −0.866787 + 0.877859I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.142705 − 0.800687I
a = −1.76224 − 0.77168I
b = −1.78689 + 0.41916I
−7.67025 − 0.63840I −0.866787 − 0.877859I
u = 0.769086 + 0.992896I
a = −1.22437 − 1.54363I
b = −2.24931 − 1.14168I
5.85838 + 8.64297I 10.04873 − 7.11633I
u = 0.769086 − 0.992896I
a = −1.22437 + 1.54363I
b = −2.24931 + 1.14168I
5.85838 − 8.64297I 10.04873 + 7.11633I
u = −0.667106 + 1.077180I
a = −0.121148 − 0.106125I
b = 0.261000 − 0.309723I
−0.83445 − 4.97703I −3.26494 + 1.29068I
u = −0.667106 − 1.077180I
a = −0.121148 + 0.106125I
b = 0.261000 + 0.309723I
−0.83445 + 4.97703I −3.26494 − 1.29068I
13
III.
I
u
3
= h−u
15
−u
14
+· · ·+b+1, u
15
a−5u
15
+· · ·−2a+8, u
16
+u
15
+· · ·−2u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
10
=
a
u
15
+ u
14
+ ··· − au − 1
a
8
=
u
15
+ u
14
+ ··· − a + 2
−u
13
a + 2u
13
+ ··· + au + 1
a
1
=
u
2
+ 1
−u
4
a
11
=
−u
15
− u
14
+ ··· + a − 1
−2u
13
− 2u
12
+ ··· + u − 1
a
5
=
u
3
u
3
+ u
a
4
=
3u
15
+ u
14
+ ··· + a − 5
u
15
+ u
14
+ ··· + au − 1
a
9
=
−u
15
− u
14
+ ··· + u
3
+ a
−2u
13
− 2u
12
+ ··· + u − 1
a
12
=
−u
15
− u
14
+ ··· + a − 1
u
13
a − 2u
13
+ ··· − au − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−4u
15
−8u
13
+4u
12
−20u
11
+8u
10
−24u
9
+16u
8
−28u
7
+20u
6
−20u
5
+16u
4
−12u
3
+12u
2
+2
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
16
+ 5u
15
+ ··· − 4u + 1)
2
c
2
, c
6
(u
16
+ u
15
+ ··· − 2u − 1)
2
c
3
, c
4
, c
11
u
32
+ u
31
+ ··· − 27u + 286
c
7
, c
10
u
32
+ 13u
31
+ ··· − 41u − 2
c
8
(u
16
+ 13u
15
+ ··· + 44u − 7)
2
c
9
u
32
− u
31
+ ··· − 5662u − 169
c
12
(u − 1)
32
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
16
+ 13y
15
+ ··· − 48y + 1)
2
c
2
, c
6
(y
16
+ 5y
15
+ ··· − 4y + 1)
2
c
3
, c
4
, c
11
y
32
+ 39y
31
+ ··· + 1346331y + 81796
c
7
, c
10
y
32
− 9y
31
+ ··· − 53y + 4
c
8
(y
16
− 31y
15
+ ··· − 704y + 49)
2
c
9
y
32
+ 19y
31
+ ··· − 25101866y + 28561
c
12
(y −1)
32
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.254861 + 1.023380I
a = 0.166841 + 0.823281I
b = 0.776440 + 0.691048I
−1.88017 + 3.12434I −2.05940 − 3.66013I
u = 0.254861 + 1.023380I
a = 0.013723 − 0.175484I
b = −0.878070 + 0.201017I
−1.88017 + 3.12434I −2.05940 − 3.66013I
u = 0.254861 − 1.023380I
a = 0.166841 − 0.823281I
b = 0.776440 − 0.691048I
−1.88017 − 3.12434I −2.05940 + 3.66013I
u = 0.254861 − 1.023380I
a = 0.013723 + 0.175484I
b = −0.878070 − 0.201017I
−1.88017 − 3.12434I −2.05940 + 3.66013I
u = 0.750689 + 0.759364I
a = 0.24992 + 1.51155I
b = −0.196588 + 0.591384I
−2.97876 − 0.48968I 2.35607 + 1.43137I
u = 0.750689 + 0.759364I
a = −0.69577 + 1.84479I
b = 1.13391 + 2.14189I
−2.97876 − 0.48968I 2.35607 + 1.43137I
u = 0.750689 − 0.759364I
a = 0.24992 − 1.51155I
b = −0.196588 − 0.591384I
−2.97876 + 0.48968I 2.35607 − 1.43137I
u = 0.750689 − 0.759364I
a = −0.69577 − 1.84479I
b = 1.13391 − 2.14189I
−2.97876 + 0.48968I 2.35607 − 1.43137I
u = −0.099165 + 0.920214I
a = 0.057858 + 1.349270I
b = 0.976760 − 0.554322I
−8.46679 − 1.52971I −6.72737 + 5.08772I
u = −0.099165 + 0.920214I
a = −1.95590 − 1.06565I
b = −2.68988 − 1.32943I
−8.46679 − 1.52971I −6.72737 + 5.08772I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.099165 − 0.920214I
a = 0.057858 − 1.349270I
b = 0.976760 + 0.554322I
−8.46679 + 1.52971I −6.72737 − 5.08772I
u = −0.099165 − 0.920214I
a = −1.95590 + 1.06565I
b = −2.68988 + 1.32943I
−8.46679 + 1.52971I −6.72737 − 5.08772I
u = −0.665350 + 0.873267I
a = 2.10683 − 2.08817I
b = 2.12567 − 2.22461I
−5.56244 − 2.57669I −3.30756 + 2.71681I
u = −0.665350 + 0.873267I
a = −2.36347 + 2.91711I
b = −3.72419 + 1.41589I
−5.56244 − 2.57669I −3.30756 + 2.71681I
u = −0.665350 − 0.873267I
a = 2.10683 + 2.08817I
b = 2.12567 + 2.22461I
−5.56244 + 2.57669I −3.30756 − 2.71681I
u = −0.665350 − 0.873267I
a = −2.36347 − 2.91711I
b = −3.72419 − 1.41589I
−5.56244 + 2.57669I −3.30756 − 2.71681I
u = −0.847960 + 0.745397I
a = −1.07862 + 1.20524I
b = −1.287070 + 0.510746I
5.32084 + 2.28357I 3.92472 − 0.30826I
u = −0.847960 + 0.745397I
a = 1.17114 − 1.41311I
b = 1.61121 − 0.11458I
5.32084 + 2.28357I 3.92472 − 0.30826I
u = −0.847960 − 0.745397I
a = −1.07862 − 1.20524I
b = −1.287070 − 0.510746I
5.32084 − 2.28357I 3.92472 + 0.30826I
u = −0.847960 − 0.745397I
a = 1.17114 + 1.41311I
b = 1.61121 + 0.11458I
5.32084 − 2.28357I 3.92472 + 0.30826I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.716556 + 0.957138I
a = 1.273310 − 0.043889I
b = 2.08123 + 0.26719I
−3.57736 + 6.07197I 0.61575 − 7.02814I
u = 0.716556 + 0.957138I
a = 2.17649 − 0.07224I
b = 1.73170 − 1.82727I
−3.57736 + 6.07197I 0.61575 − 7.02814I
u = 0.716556 − 0.957138I
a = 1.273310 + 0.043889I
b = 2.08123 − 0.26719I
−3.57736 − 6.07197I 0.61575 + 7.02814I
u = 0.716556 − 0.957138I
a = 2.17649 + 0.07224I
b = 1.73170 + 1.82727I
−3.57736 − 6.07197I 0.61575 + 7.02814I
u = −0.761782 + 1.000110I
a = −1.07483 + 1.36444I
b = −1.75138 + 1.17047I
4.53468 − 8.28859I 2.57708 + 5.27135I
u = −0.761782 + 1.000110I
a = 1.03895 − 1.57028I
b = 2.28316 − 1.19066I
4.53468 − 8.28859I 2.57708 + 5.27135I
u = −0.761782 − 1.000110I
a = −1.07483 − 1.36444I
b = −1.75138 − 1.17047I
4.53468 + 8.28859I 2.57708 − 5.27135I
u = −0.761782 − 1.000110I
a = 1.03895 + 1.57028I
b = 2.28316 + 1.19066I
4.53468 + 8.28859I 2.57708 − 5.27135I
u = 0.689113
a = 0.757498
b = −0.278882
1.42684 4.14780
u = 0.689113
a = 0.117305
b = 0.466296
1.42684 4.14780
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.384812
a = 1.47613 + 2.83234I
b = −0.786617 + 0.670506I
−5.81564 5.09360
u = −0.384812
a = 1.47613 − 2.83234I
b = −0.786617 − 0.670506I
−5.81564 5.09360
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
15
− 5u
14
+ ··· − 20u + 4)(u
16
+ 5u
15
+ ··· − 4u + 1)
2
· (u
32
+ 10u
31
+ ··· − 12u + 4)
c
2
(u
15
− u
14
+ ··· + 5u
2
+ 2)(u
16
+ u
15
+ ··· − 2u − 1)
2
· (u
32
− 6u
31
+ ··· + 2u + 2)
c
3
, c
11
(u
15
− u
14
+ ··· − 3u + 1)(u
32
+ u
31
+ ··· − 27u + 286)
· (u
32
+ u
31
+ ··· − 2u + 1)
c
4
(u
15
+ u
14
+ ··· − 3u − 1)(u
32
+ u
31
+ ··· − 27u + 286)
· (u
32
+ u
31
+ ··· − 2u + 1)
c
6
(u
15
+ u
14
+ ··· − 5u
2
− 2)(u
16
+ u
15
+ ··· − 2u − 1)
2
· (u
32
− 6u
31
+ ··· + 2u + 2)
c
7
, c
10
(u
15
+ 3u
14
+ ··· + 3u + 1)(u
32
+ 3u
31
+ ··· − 4u + 1)
· (u
32
+ 13u
31
+ ··· − 41u − 2)
c
8
(u
15
− 12u
14
+ ··· + 12u − 2)(u
16
+ 13u
15
+ ··· + 44u − 7)
2
· (u
32
− 15u
31
+ ··· + 330u + 50)
c
9
(u
15
+ u
14
+ ··· + u − 1)(u
32
− u
31
+ ··· + 7u + 4)
· (u
32
− u
31
+ ··· − 5662u − 169)
c
12
((u − 1)
32
)(u
15
+ 3u
14
+ ··· + 3u + 1)
· (u
32
+ 30u
31
+ ··· + 983040u + 65536)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
15
+ 13y
14
+ ··· + 8y −16)(y
16
+ 13y
15
+ ··· − 48y + 1)
2
· (y
32
+ 26y
31
+ ··· + 336y + 16)
c
2
, c
6
(y
15
+ 5y
14
+ ··· − 20y −4)(y
16
+ 5y
15
+ ··· − 4y + 1)
2
· (y
32
+ 10y
31
+ ··· − 12y + 4)
c
3
, c
4
, c
11
(y
15
+ 9y
14
+ ··· + y −1)(y
32
+ 39y
31
+ ··· + 1346331y + 81796)
· (y
32
+ 45y
31
+ ··· + 10y + 1)
c
7
, c
10
(y
15
− 7y
14
+ ··· − y −1)(y
32
− 9y
31
+ ··· − 53y + 4)
· (y
32
+ 5y
31
+ ··· − 12y + 1)
c
8
(y
15
− 16y
14
+ ··· − 12y −4)(y
16
− 31y
15
+ ··· − 704y + 49)
2
· (y
32
− 23y
31
+ ··· − 127900y + 2500)
c
9
(y
15
+ 13y
14
+ ··· + 9y −1)(y
32
+ 9y
31
+ ··· + 151y + 16)
· (y
32
+ 19y
31
+ ··· − 25101866y + 28561)
c
12
((y −1)
32
)(y
15
+ y
14
+ ··· + 7y −1)
· (y
32
− 24y
30
+ ··· + 4294967296y + 4294967296)
22
