12n
0804
(K12n
0804
)
A knot diagram
1
Linearized knot diagam
4 7 10 1 11 3 1 12 6 4 8 9
Solving Sequence
9,12 1,4
2 5 8 7 11 6 10 3
c
12
c
1
c
4
c
8
c
7
c
11
c
5
c
10
c
3
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−15u
27
− 74u
26
+ ··· + 2b + 46, 7u
27
+ 28u
26
+ ··· + 4a − 16, u
28
+ 6u
27
+ ··· − 2u − 4i
I
u
2
= h−26336u
8
a
3
− 36861u
8
a
2
+ ··· − 5783a + 173926, −4u
8
a
2
− 11u
8
a + ··· − 3a + 11,
u
9
− u
8
− 4u
7
+ 3u
6
+ 5u
5
− u
4
− 2u
3
− 2u
2
+ u − 1i
I
u
3
= hu
15
− u
14
− 7u
13
+ 5u
12
+ 20u
11
− 7u
10
− 27u
9
− 4u
8
+ 12u
7
+ 15u
6
+ 8u
5
− 3u
4
− 7u
3
− 8u
2
+ b − u,
− u
16
+ u
15
+ ··· + a − 1, u
17
− u
16
+ ··· − u + 1i
* 3 irreducible components of dim
C
= 0, with total 81 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−15u
27
− 74u
26
+ · · · + 2b + 46, 7u
27
+ 28u
26
+ · · · + 4a − 16, u
28
+
6u
27
+ · · · − 2u − 4i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
−
7
4
u
27
− 7u
26
+ ··· −
5
4
u + 4
15
2
u
27
+ 37u
26
+ ··· +
11
2
u − 23
a
2
=
−6u
27
−
61
2
u
26
+ ··· − 6u +
45
2
−
27
2
u
27
− 66u
26
+ ··· −
25
2
u + 46
a
5
=
−
65
4
u
27
− 72u
26
+ ··· −
27
4
u + 41
−
51
2
u
27
− 113u
26
+ ··· −
17
2
u + 65
a
8
=
u
u
a
7
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
11
=
−u
2
+ 1
−u
2
a
6
=
−
23
4
u
27
− 29u
26
+ ··· −
29
4
u + 20
−
23
2
u
27
− 56u
26
+ ··· −
17
2
u + 37
a
10
=
2u
27
+
17
2
u
26
+ ··· − u
2
−
7
2
7
2
u
27
+ 14u
26
+ ··· −
1
2
u − 6
a
3
=
−2u
27
−
19
2
u
26
+ ··· − 2u +
13
2
13
2
u
27
+ 31u
26
+ ··· +
13
2
u − 20
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −25u
27
−119u
26
+ 24u
25
+ 825u
24
+ 445u
23
−2632u
22
−1414u
21
+ 5532u
20
+ 700u
19
−
8560u
18
+ 4311u
17
+ 8407u
16
− 10994u
15
− 1234u
14
+ 11725u
13
− 8592u
12
− 3652u
11
+
9729u
10
−5400u
9
−2649u
8
+5362u
7
−2247u
6
−727u
5
+1376u
4
−434u
3
+57u
2
−28u +74
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
28
− 2u
27
+ ··· + 13u − 1
c
2
, c
6
u
28
+ 20u
27
+ ··· − 5888u − 512
c
3
, c
9
, c
10
u
28
− u
27
+ ··· + u + 1
c
5
u
28
+ 16u
26
+ ··· − 4u − 11
c
7
u
28
− 18u
27
+ ··· − 990u + 52
c
8
, c
11
, c
12
u
28
+ 6u
27
+ ··· − 2u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
28
− 38y
27
+ ··· − 43y + 1
c
2
, c
6
y
28
+ 10y
27
+ ··· − 65536y + 262144
c
3
, c
9
, c
10
y
28
− 15y
27
+ ··· − 7y + 1
c
5
y
28
+ 32y
27
+ ··· + 2096y + 121
c
7
y
28
− 2y
27
+ ··· − 384700y + 2704
c
8
, c
11
, c
12
y
28
− 26y
27
+ ··· + 4y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.953650
a = 0.557977
b = 1.71191
−2.95076 1.04180
u = 0.658308 + 0.612846I
a = −1.282020 − 0.481173I
b = −1.120110 − 0.609967I
0.15275 + 6.58351I −2.72995 − 3.03083I
u = 0.658308 − 0.612846I
a = −1.282020 + 0.481173I
b = −1.120110 + 0.609967I
0.15275 − 6.58351I −2.72995 + 3.03083I
u = 0.402654 + 0.774191I
a = −1.05898 − 1.82975I
b = 0.061414 − 0.574417I
1.01000 − 11.30550I −1.14807 + 7.82851I
u = 0.402654 − 0.774191I
a = −1.05898 + 1.82975I
b = 0.061414 + 0.574417I
1.01000 + 11.30550I −1.14807 − 7.82851I
u = 0.046469 + 0.849926I
a = −0.926104 − 0.236908I
b = 0.122562 + 0.203546I
6.61374 + 1.82301I −2.15341 − 3.95044I
u = 0.046469 − 0.849926I
a = −0.926104 + 0.236908I
b = 0.122562 − 0.203546I
6.61374 − 1.82301I −2.15341 + 3.95044I
u = −1.19440
a = 0.501244
b = 0.563490
−2.49793 −0.727600
u = 0.323728 + 0.735663I
a = 1.50512 + 1.36499I
b = 0.190601 + 0.251246I
−1.82680 − 3.57508I −0.50281 + 5.56081I
u = 0.323728 − 0.735663I
a = 1.50512 − 1.36499I
b = 0.190601 − 0.251246I
−1.82680 + 3.57508I −0.50281 − 5.56081I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.199900 + 0.405002I
a = −0.456093 − 0.265236I
b = −1.03504 − 0.98880I
3.05496 − 6.32046I −4.20827 + 7.87588I
u = 1.199900 − 0.405002I
a = −0.456093 + 0.265236I
b = −1.03504 + 0.98880I
3.05496 + 6.32046I −4.20827 − 7.87588I
u = 0.559106 + 0.438994I
a = 0.554411 + 1.068500I
b = 0.939165 + 0.581582I
−2.96704 − 0.44419I −3.65164 − 1.30956I
u = 0.559106 − 0.438994I
a = 0.554411 − 1.068500I
b = 0.939165 − 0.581582I
−2.96704 + 0.44419I −3.65164 + 1.30956I
u = −1.291540 + 0.383259I
a = −0.271704 + 0.642178I
b = −0.236794 + 1.202110I
2.45039 + 2.60036I −6.92230 − 0.38709I
u = −1.291540 − 0.383259I
a = −0.271704 − 0.642178I
b = −0.236794 − 1.202110I
2.45039 − 2.60036I −6.92230 + 0.38709I
u = 1.393630 + 0.056371I
a = 0.117598 + 0.610861I
b = 0.32341 + 2.06894I
−5.35082 − 2.09473I −9.32900 + 3.91976I
u = 1.393630 − 0.056371I
a = 0.117598 − 0.610861I
b = 0.32341 − 2.06894I
−5.35082 + 2.09473I −9.32900 − 3.91976I
u = −1.44514 + 0.28991I
a = −0.09541 − 1.48867I
b = 0.20048 − 3.17159I
−7.50725 + 7.32315I −4.57096 − 5.41383I
u = −1.44514 − 0.28991I
a = −0.09541 + 1.48867I
b = 0.20048 + 3.17159I
−7.50725 − 7.32315I −4.57096 + 5.41383I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.47470 + 0.16414I
a = −0.609161 − 0.895856I
b = −0.02962 − 2.05701I
−9.43653 + 2.71269I −7.85713 + 0.I
u = −1.47470 − 0.16414I
a = −0.609161 + 0.895856I
b = −0.02962 + 2.05701I
−9.43653 − 2.71269I −7.85713 + 0.I
u = −1.47870 + 0.29110I
a = 0.46176 + 1.47662I
b = 0.52784 + 3.55403I
−5.0564 + 15.1855I −4.66281 − 7.85224I
u = −1.47870 − 0.29110I
a = 0.46176 − 1.47662I
b = 0.52784 − 3.55403I
−5.0564 − 15.1855I −4.66281 + 7.85224I
u = −1.52541 + 0.15808I
a = 0.112693 + 0.750612I
b = −0.99764 + 1.57771I
−7.05591 − 3.93502I −6.54817 + 3.13330I
u = −1.52541 − 0.15808I
a = 0.112693 − 0.750612I
b = −0.99764 − 1.57771I
−7.05591 + 3.93502I −6.54817 − 3.13330I
u = −0.247934 + 0.324230I
a = 0.668275 − 0.831350I
b = −0.083982 − 0.333429I
−0.143060 + 0.866290I −3.37260 − 7.97095I
u = −0.247934 − 0.324230I
a = 0.668275 + 0.831350I
b = −0.083982 + 0.333429I
−0.143060 − 0.866290I −3.37260 + 7.97095I
7
II. I
u
2
= h−2.63 × 10
4
a
3
u
8
− 3.69 × 10
4
a
2
u
8
+ · · · − 5783a + 1.74 ×
10
5
, −4u
8
a
2
− 11u
8
a + · · · − 3a + 11, u
9
− u
8
+ · · · + u − 1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
a
0.217680a
3
u
8
+ 0.304674a
2
u
8
+ ··· + 0.0477993a − 1.43758
a
2
=
−0.0388230a
3
u
8
+ 0.221854a
2
u
8
+ ··· + 0.325520a + 1.11376
−0.487796a
3
u
8
− 0.886325a
2
u
8
+ ··· + 0.0427656a + 1.01842
a
5
=
−0.217680a
3
u
8
− 0.304674a
2
u
8
+ ··· + 0.952201a + 1.43758
−0.204720a
3
u
8
− 0.196619a
2
u
8
+ ··· + 0.127586a − 0.334521
a
8
=
u
u
a
7
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
11
=
−u
2
+ 1
−u
2
a
6
=
−0.00223995a
3
u
8
− 0.310129a
2
u
8
+ ··· + 0.227979a − 0.929694
0.579593a
3
u
8
+ 0.0401868a
2
u
8
+ ··· + 0.201769a − 2.52773
a
10
=
0.199330a
3
u
8
+ 0.0246477a
2
u
8
+ ··· + 0.744894a + 2.28670
0.991354a
3
u
8
+ 1.06644a
2
u
8
+ ··· + 1.13530a + 0.724503
a
3
=
0.0717692a
3
u
8
+ 0.0393107a
2
u
8
+ ··· + 0.243030a + 1.08904
0.482366a
3
u
8
− 2.04709a
2
u
8
+ ··· + 0.821375a + 0.907005
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
13960
24197
u
8
a
3
+
55088
24197
u
8
a
2
+ ··· −
10276
24197
a +
14766
24197
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
36
− 7u
35
+ ··· − 5076u + 409
c
2
, c
6
(u
2
− u + 1)
18
c
3
, c
9
, c
10
u
36
+ u
35
+ ··· − 1924u + 1369
c
5
u
36
+ u
35
+ ··· + 270248u + 42439
c
7
(u
9
+ 3u
8
+ 2u
7
− 5u
6
− u
5
+ 13u
4
+ 10u
3
− 2u
2
+ u + 3)
4
c
8
, c
11
, c
12
(u
9
− u
8
− 4u
7
+ 3u
6
+ 5u
5
− u
4
− 2u
3
− 2u
2
+ u − 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
36
− 13y
35
+ ··· + 722700y + 167281
c
2
, c
6
(y
2
+ y + 1)
18
c
3
, c
9
, c
10
y
36
− 21y
35
+ ··· − 24937704y + 1874161
c
5
y
36
+ 3y
35
+ ··· − 30558823476y + 1801068721
c
7
(y
9
− 5y
8
+ 32y
7
− 87y
6
+ 185y
5
− 223y
4
+ 180y
3
− 62y
2
+ 13y − 9)
4
c
8
, c
11
, c
12
(y
9
− 9y
8
+ 32y
7
− 55y
6
+ 45y
5
− 19y
4
+ 16y
3
− 10y
2
− 3y − 1)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482242 + 0.666986I
a = −1.051030 + 0.210171I
b = −0.827471 + 0.256935I
−2.12882 + 0.18400I −2.24115 + 0.41812I
u = −0.482242 + 0.666986I
a = 1.20765 − 1.03644I
b = 0.590198 − 0.907501I
−2.12882 + 4.24376I −2.24115 − 6.51008I
u = −0.482242 + 0.666986I
a = −0.32978 + 1.74923I
b = 0.047751 + 0.476433I
−2.12882 + 4.24376I −2.24115 − 6.51008I
u = −0.482242 + 0.666986I
a = 1.22939 − 1.32682I
b = 0.135181 − 0.593881I
−2.12882 + 0.18400I −2.24115 + 0.41812I
u = −0.482242 − 0.666986I
a = −1.051030 − 0.210171I
b = −0.827471 − 0.256935I
−2.12882 − 0.18400I −2.24115 − 0.41812I
u = −0.482242 − 0.666986I
a = 1.20765 + 1.03644I
b = 0.590198 + 0.907501I
−2.12882 − 4.24376I −2.24115 + 6.51008I
u = −0.482242 − 0.666986I
a = −0.32978 − 1.74923I
b = 0.047751 − 0.476433I
−2.12882 − 4.24376I −2.24115 + 6.51008I
u = −0.482242 − 0.666986I
a = 1.22939 + 1.32682I
b = 0.135181 + 0.593881I
−2.12882 − 0.18400I −2.24115 − 0.41812I
u = 1.28056
a = 1.073610 + 0.310999I
b = 0.35482 + 1.72769I
2.09801 − 2.02988I 0.33330 + 3.46410I
u = 1.28056
a = 1.073610 − 0.310999I
b = 0.35482 − 1.72769I
2.09801 + 2.02988I 0.33330 − 3.46410I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28056
a = −1.84588 + 1.02661I
b = −2.79563 + 2.49991I
2.09801 − 2.02988I 0.33330 + 3.46410I
u = 1.28056
a = −1.84588 − 1.02661I
b = −2.79563 − 2.49991I
2.09801 + 2.02988I 0.33330 − 3.46410I
u = −1.380230 + 0.162431I
a = −0.765740 − 0.299051I
b = −1.69716 − 2.22480I
−0.22800 + 5.44061I −3.88238 − 7.86053I
u = −1.380230 + 0.162431I
a = −0.59954 + 1.33085I
b = −0.60116 + 3.08351I
−0.22800 + 5.44061I −3.88238 − 7.86053I
u = −1.380230 + 0.162431I
a = 1.22002 + 0.90366I
b = 2.56008 + 2.51241I
−0.227995 + 1.380850I −3.88238 − 0.93232I
u = −1.380230 + 0.162431I
a = 0.356182 − 0.237194I
b = −0.667250 − 0.951369I
−0.227995 + 1.380850I −3.88238 − 0.93232I
u = −1.380230 − 0.162431I
a = −0.765740 + 0.299051I
b = −1.69716 + 2.22480I
−0.22800 − 5.44061I −3.88238 + 7.86053I
u = −1.380230 − 0.162431I
a = −0.59954 − 1.33085I
b = −0.60116 − 3.08351I
−0.22800 − 5.44061I −3.88238 + 7.86053I
u = −1.380230 − 0.162431I
a = 1.22002 − 0.90366I
b = 2.56008 − 2.51241I
−0.227995 − 1.380850I −3.88238 + 0.93232I
u = −1.380230 − 0.162431I
a = 0.356182 + 0.237194I
b = −0.667250 + 0.951369I
−0.227995 − 1.380850I −3.88238 + 0.93232I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.230908 + 0.456719I
a = −0.131464 + 0.571431I
b = −1.154890 − 0.321257I
4.89942 + 0.92019I 1.44626 + 2.77537I
u = 0.230908 + 0.456719I
a = −1.11828 + 2.44778I
b = −0.822161 + 0.979129I
4.89942 − 3.13958I 1.44626 + 9.70357I
u = 0.230908 + 0.456719I
a = −2.02069 − 2.00197I
b = 0.537114 + 0.030275I
4.89942 − 3.13958I 1.44626 + 9.70357I
u = 0.230908 + 0.456719I
a = 1.31486 − 3.51276I
b = 0.423243 − 0.430303I
4.89942 + 0.92019I 1.44626 + 2.77537I
u = 0.230908 − 0.456719I
a = −0.131464 − 0.571431I
b = −1.154890 + 0.321257I
4.89942 − 0.92019I 1.44626 − 2.77537I
u = 0.230908 − 0.456719I
a = −1.11828 − 2.44778I
b = −0.822161 − 0.979129I
4.89942 + 3.13958I 1.44626 − 9.70357I
u = 0.230908 − 0.456719I
a = −2.02069 + 2.00197I
b = 0.537114 − 0.030275I
4.89942 + 3.13958I 1.44626 − 9.70357I
u = 0.230908 − 0.456719I
a = 1.31486 + 3.51276I
b = 0.423243 + 0.430303I
4.89942 − 0.92019I 1.44626 − 2.77537I
u = 1.49128 + 0.23430I
a = −0.186213 + 0.985787I
b = 0.84640 + 2.46596I
−8.52641 − 7.53037I −5.48937 + 6.43708I
u = 1.49128 + 0.23430I
a = −0.145881 + 1.246310I
b = 0.20347 + 3.14266I
−8.52641 − 3.47060I −5.48937 − 0.49112I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49128 + 0.23430I
a = 0.083099 − 0.678110I
b = −0.753793 − 1.188340I
−8.52641 − 3.47060I −5.48937 − 0.49112I
u = 1.49128 + 0.23430I
a = 0.709680 − 1.215520I
b = 1.12126 − 2.96653I
−8.52641 − 7.53037I −5.48937 + 6.43708I
u = 1.49128 − 0.23430I
a = −0.186213 − 0.985787I
b = 0.84640 − 2.46596I
−8.52641 + 7.53037I −5.48937 − 6.43708I
u = 1.49128 − 0.23430I
a = −0.145881 − 1.246310I
b = 0.20347 − 3.14266I
−8.52641 + 3.47060I −5.48937 + 0.49112I
u = 1.49128 − 0.23430I
a = 0.083099 + 0.678110I
b = −0.753793 + 1.188340I
−8.52641 + 3.47060I −5.48937 + 0.49112I
u = 1.49128 − 0.23430I
a = 0.709680 + 1.215520I
b = 1.12126 + 2.96653I
−8.52641 + 7.53037I −5.48937 − 6.43708I
14
III.
I
u
3
= hu
15
− u
14
+ · · · + b − u, −u
16
+ u
15
+ · · · + a − 1, u
17
− u
16
+ · · · − u + 1i
(i) Arc colorings
a
9
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
16
− u
15
+ ··· + 10u + 1
−u
15
+ u
14
+ ··· + 8u
2
+ u
a
2
=
−u
16
− u
15
+ ··· − 5u − 2
−u
16
− u
15
+ ··· − 4u + 1
a
5
=
u
16
− 8u
14
+ ··· + 8u + 1
u
16
− 7u
14
+ 19u
12
− 23u
10
+ 9u
8
+ u
7
+ 3u
6
− 2u
5
− u
4
+ u
2
+ 2u − 1
a
8
=
u
u
a
7
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
11
=
−u
2
+ 1
−u
2
a
6
=
u
16
− u
15
+ ··· + 9u
2
+ 10u
u
16
− u
15
+ ··· + 2u − 1
a
10
=
−u
16
+ u
15
+ ··· − 13u − 1
u
14
− u
13
+ ··· − 3u + 1
a
3
=
−u
16
+ 8u
14
+ ··· − 6u − 2
−u
16
+ 8u
14
+ ··· − 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
16
+ 3u
15
+ 4u
14
− 21u
13
+ u
12
+ 57u
11
− 24u
10
− 70u
9
+
29u
8
+ 28u
7
+ 8u
6
+ 13u
5
− 14u
4
− 12u
3
− 16u
2
+ 6u + 3
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
− 2u
16
+ ··· − u − 1
c
2
u
17
+ u
16
+ ··· + 2u − 1
c
3
, c
9
u
17
+ u
16
+ ··· + 3u + 1
c
4
u
17
+ 2u
16
+ ··· − u + 1
c
5
u
17
− 2u
15
+ ··· + 84u − 41
c
6
u
17
− u
16
+ ··· + 2u + 1
c
7
u
17
− 3u
16
+ ··· + 3u + 1
c
8
u
17
+ u
16
+ ··· − u − 1
c
10
u
17
− u
16
+ ··· + 3u − 1
c
11
, c
12
u
17
− u
16
+ ··· − u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
17
− 2y
16
+ ··· − 9y − 1
c
2
, c
6
y
17
+ 9y
16
+ ··· + 2y − 1
c
3
, c
9
, c
10
y
17
− 15y
16
+ ··· + 11y − 1
c
5
y
17
− 4y
16
+ ··· − 488y − 1681
c
7
y
17
+ 3y
16
+ ··· + 5y − 1
c
8
, c
11
, c
12
y
17
− 17y
16
+ ··· − 13y − 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10763
a = 0.523883
b = 1.55918
−3.57905 −12.6170
u = −0.425905 + 0.642898I
a = 0.97515 − 1.20944I
b = 0.403007 − 0.429698I
−2.71770 + 2.02657I −3.63087 − 3.52897I
u = −0.425905 − 0.642898I
a = 0.97515 + 1.20944I
b = 0.403007 + 0.429698I
−2.71770 − 2.02657I −3.63087 + 3.52897I
u = 0.042131 + 0.757767I
a = −0.815059 − 1.037950I
b = 0.377107 − 0.136334I
7.62816 + 1.34697I 6.00457 − 0.36396I
u = 0.042131 − 0.757767I
a = −0.815059 + 1.037950I
b = 0.377107 + 0.136334I
7.62816 − 1.34697I 6.00457 + 0.36396I
u = 1.254420 + 0.313440I
a = −1.064240 − 0.333124I
b = −1.56387 − 0.74311I
3.88217 − 5.20142I −0.01102 + 3.47502I
u = 1.254420 − 0.313440I
a = −1.064240 + 0.333124I
b = −1.56387 + 0.74311I
3.88217 + 5.20142I −0.01102 − 3.47502I
u = 1.299980 + 0.091388I
a = 1.56649 + 0.19813I
b = 1.82630 + 0.03282I
1.28803 + 0.77615I −3.30157 + 0.81536I
u = 1.299980 − 0.091388I
a = 1.56649 − 0.19813I
b = 1.82630 − 0.03282I
1.28803 − 0.77615I −3.30157 − 0.81536I
u = −1.309310 + 0.331733I
a = 0.075882 + 0.519832I
b = 0.55535 + 1.50065I
3.38854 + 2.59091I 2.12182 − 1.26130I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.309310 − 0.331733I
a = 0.075882 − 0.519832I
b = 0.55535 − 1.50065I
3.38854 − 2.59091I 2.12182 + 1.26130I
u = −1.384890 + 0.123590I
a = −0.394901 − 0.892836I
b = −1.54132 − 2.86492I
0.25538 + 3.89922I −2.28228 − 2.97017I
u = −1.384890 − 0.123590I
a = −0.394901 + 0.892836I
b = −1.54132 + 2.86492I
0.25538 − 3.89922I −2.28228 + 2.97017I
u = 1.47712 + 0.23945I
a = −0.303394 + 1.097550I
b = 0.08342 + 2.50104I
−8.88015 − 5.28838I −6.60018 + 3.61585I
u = 1.47712 − 0.23945I
a = −0.303394 − 1.097550I
b = 0.08342 − 2.50104I
−8.88015 + 5.28838I −6.60018 − 3.61585I
u = 0.100269 + 0.327858I
a = 0.69814 + 4.13737I
b = −0.919590 + 0.605338I
5.16976 − 2.21853I 5.50802 + 1.42500I
u = 0.100269 − 0.327858I
a = 0.69814 − 4.13737I
b = −0.919590 − 0.605338I
5.16976 + 2.21853I 5.50802 − 1.42500I
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
17
− 2u
16
+ ··· − u − 1)(u
28
− 2u
27
+ ··· + 13u − 1)
· (u
36
− 7u
35
+ ··· − 5076u + 409)
c
2
((u
2
− u + 1)
18
)(u
17
+ u
16
+ ··· + 2u − 1)
· (u
28
+ 20u
27
+ ··· − 5888u − 512)
c
3
, c
9
(u
17
+ u
16
+ ··· + 3u + 1)(u
28
− u
27
+ ··· + u + 1)
· (u
36
+ u
35
+ ··· − 1924u + 1369)
c
4
(u
17
+ 2u
16
+ ··· − u + 1)(u
28
− 2u
27
+ ··· + 13u − 1)
· (u
36
− 7u
35
+ ··· − 5076u + 409)
c
5
(u
17
− 2u
15
+ ··· + 84u − 41)(u
28
+ 16u
26
+ ··· − 4u − 11)
· (u
36
+ u
35
+ ··· + 270248u + 42439)
c
6
((u
2
− u + 1)
18
)(u
17
− u
16
+ ··· + 2u + 1)
· (u
28
+ 20u
27
+ ··· − 5888u − 512)
c
7
(u
9
+ 3u
8
+ 2u
7
− 5u
6
− u
5
+ 13u
4
+ 10u
3
− 2u
2
+ u + 3)
4
· (u
17
− 3u
16
+ ··· + 3u + 1)(u
28
− 18u
27
+ ··· − 990u + 52)
c
8
(u
9
− u
8
− 4u
7
+ 3u
6
+ 5u
5
− u
4
− 2u
3
− 2u
2
+ u − 1)
4
· (u
17
+ u
16
+ ··· − u − 1)(u
28
+ 6u
27
+ ··· − 2u − 4)
c
10
(u
17
− u
16
+ ··· + 3u − 1)(u
28
− u
27
+ ··· + u + 1)
· (u
36
+ u
35
+ ··· − 1924u + 1369)
c
11
, c
12
(u
9
− u
8
− 4u
7
+ 3u
6
+ 5u
5
− u
4
− 2u
3
− 2u
2
+ u − 1)
4
· (u
17
− u
16
+ ··· − u + 1)(u
28
+ 6u
27
+ ··· − 2u − 4)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
17
− 2y
16
+ ··· − 9y − 1)(y
28
− 38y
27
+ ··· − 43y + 1)
· (y
36
− 13y
35
+ ··· + 722700y + 167281)
c
2
, c
6
((y
2
+ y + 1)
18
)(y
17
+ 9y
16
+ ··· + 2y − 1)
· (y
28
+ 10y
27
+ ··· − 65536y + 262144)
c
3
, c
9
, c
10
(y
17
− 15y
16
+ ··· + 11y − 1)(y
28
− 15y
27
+ ··· − 7y + 1)
· (y
36
− 21y
35
+ ··· − 24937704y + 1874161)
c
5
(y
17
− 4y
16
+ ··· − 488y − 1681)(y
28
+ 32y
27
+ ··· + 2096y + 121)
· (y
36
+ 3y
35
+ ··· − 30558823476y + 1801068721)
c
7
(y
9
− 5y
8
+ 32y
7
− 87y
6
+ 185y
5
− 223y
4
+ 180y
3
− 62y
2
+ 13y − 9)
4
· (y
17
+ 3y
16
+ ··· + 5y − 1)(y
28
− 2y
27
+ ··· − 384700y + 2704)
c
8
, c
11
, c
12
(y
9
− 9y
8
+ 32y
7
− 55y
6
+ 45y
5
− 19y
4
+ 16y
3
− 10y
2
− 3y − 1)
4
· (y
17
− 17y
16
+ ··· − 13y − 1)(y
28
− 26y
27
+ ··· + 4y + 16)
21
