11n
173
(K11n
173
)
A knot diagram
1
Linearized knot diagam
5 8 1 10 1 4 11 3 7 5 9
Solving Sequence
7,9 5,10
11 1 2 4 3 6 8
c
9
c
10
c
11
c
1
c
4
c
3
c
6
c
8
c
2
, c
5
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h616u
12
+ 178u
11
+ ··· + 1367b + 80, 654u
12
− 388u
11
+ ··· + 1367a + 1807,
u
13
+ 3u
11
− 5u
10
+ 10u
9
− 14u
8
+ 22u
7
− 29u
6
+ 36u
5
− 32u
4
+ 24u
3
− 11u
2
+ 4u + 1i
I
u
2
= h−u
4
+ u
2
+ b − 1, a + u − 1, u
5
− u
3
− u
2
+ u + 1i
I
u
3
= h−7.93323 × 10
30
u
27
− 2.30191 × 10
31
u
26
+ ··· + 1.77551 × 10
32
b − 1.02298 × 10
33
,
5.27149 × 10
33
u
27
+ 4.23845 × 10
33
u
26
+ ··· + 4.70510 × 10
34
a − 4.74518 × 10
34
, u
28
+ 2u
27
+ ··· + 16u + 53i
I
u
4
= h−89u
13
+ 200u
12
+ ··· + 113b − 381, 134u
13
− 503u
12
+ ··· + 113a − 178,
u
14
− 3u
13
+ 4u
12
− 4u
11
− u
10
+ 2u
9
− 2u
8
+ u
7
+ 13u
6
− 7u
5
+ 22u
4
− u
3
+ 8u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 60 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
= h616u
12
+ 178u
11
+ · · · + 1367b + 80, 654u
12
− 388u
11
+ · · · +
1367a + 1807, u
13
+ 3u
11
+ · · · + 4u + 1i
(i) Arc colorings
a
7
=
0
u
a
9
=
1
0
a
5
=
−0.478420u
12
+ 0.283833u
11
+ ··· + 4.18288u − 1.32187
−0.450622u
12
− 0.130212u
11
+ ··· + 1.21507u − 0.0585223
a
10
=
1
−u
2
a
11
=
−0.384784u
12
− 0.637162u
11
+ ··· − 4.49817u + 1.19678
−u
a
1
=
−0.384784u
12
− 0.637162u
11
+ ··· − 5.49817u + 1.19678
−u
a
2
=
−0.513533u
12
− 1.24579u
11
+ ··· − 9.43672u + 1.60863
0.319678u
12
+ 0.238478u
11
+ ··· − 1.62985u + 0.0285296
a
4
=
−0.314557u
12
+ 0.422092u
11
+ ··· + 4.74104u − 1.66423
−0.286028u
12
+ 0.102414u
11
+ ··· + 1.93197u + 0.0797366
a
3
=
−0.228237u
12
− 0.442575u
11
+ ··· + 2.47257u − 2.95172
0.163862u
12
+ 0.138259u
11
+ ··· + 0.558157u − 0.342356
a
6
=
−1.17776u
12
− 0.931236u
11
+ ··· + 0.425750u − 0.789320
−0.514996u
12
− 0.434528u
11
+ ··· − 0.754206u − 0.352597
a
8
=
−0.259693u
12
− 1.50037u
11
+ ··· − 5.35333u − 1.61814
0.193855u
12
+ 0.00731529u
11
+ ··· − 1.93343u − 0.637162
a
8
=
−0.259693u
12
− 1.50037u
11
+ ··· − 5.35333u − 1.61814
0.193855u
12
+ 0.00731529u
11
+ ··· − 1.93343u − 0.637162
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
2267
1367
u
12
−
1272
1367
u
11
−
8216
1367
u
10
+
5428
1367
u
9
−
22362
1367
u
8
+
19107
1367
u
7
−
40203
1367
u
6
+
45449
1367
u
5
−
57148
1367
u
4
+
42609
1367
u
3
−
31315
1367
u
2
+
5649
1367
u −
15793
1367
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
13
+ 8u
12
+ ··· − 10u + 4
c
2
, c
4
, c
8
c
10
u
13
− 8u
11
+ ··· − 2u + 2
c
3
, c
6
u
13
− 2u
12
+ ··· − 3u + 1
c
7
u
13
− 10u
12
+ ··· − 40u + 20
c
9
, c
11
u
13
+ 3u
11
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
13
− 16y
12
+ ··· + 284y −16
c
2
, c
4
, c
8
c
10
y
13
− 16y
12
+ ··· + 12y −4
c
3
, c
6
y
13
− 24y
12
+ ··· − 7y −1
c
7
y
13
− 2y
12
+ ··· + 4440y −400
c
9
, c
11
y
13
+ 6y
12
+ ··· + 38y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.949645 + 0.417400I
a = −0.333458 − 0.234834I
b = 0.346830 + 0.825972I
1.81165 + 1.04217I 4.67201 − 2.86908I
u = 0.949645 − 0.417400I
a = −0.333458 + 0.234834I
b = 0.346830 − 0.825972I
1.81165 − 1.04217I 4.67201 + 2.86908I
u = 0.654297 + 0.696942I
a = 0.22522 + 2.10852I
b = 0.476213 − 0.178047I
−13.48820 + 1.07762I −12.25276 − 5.21840I
u = 0.654297 − 0.696942I
a = 0.22522 − 2.10852I
b = 0.476213 + 0.178047I
−13.48820 − 1.07762I −12.25276 + 5.21840I
u = 0.326551 + 0.994649I
a = 0.241683 − 0.736746I
b = −0.03079 − 1.57197I
−4.25079 + 1.54146I −6.85137 − 4.44536I
u = 0.326551 − 0.994649I
a = 0.241683 + 0.736746I
b = −0.03079 + 1.57197I
−4.25079 − 1.54146I −6.85137 + 4.44536I
u = −0.003594 + 0.899426I
a = −1.89385 − 0.60583I
b = −0.370370 − 0.914227I
−5.78882 + 3.81724I −10.21345 − 4.30874I
u = −0.003594 − 0.899426I
a = −1.89385 + 0.60583I
b = −0.370370 + 0.914227I
−5.78882 − 3.81724I −10.21345 + 4.30874I
u = −0.80574 + 1.33514I
a = 1.031480 − 0.243645I
b = 0.01943 + 2.08470I
−7.16558 − 2.61229I −10.71663 + 1.92921I
u = −0.80574 − 1.33514I
a = 1.031480 + 0.243645I
b = 0.01943 − 2.08470I
−7.16558 + 2.61229I −10.71663 − 1.92921I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04344 + 1.39492I
a = −1.146970 + 0.493456I
b = −0.74257 − 2.29110I
−16.7932 − 13.5804I −9.69096 + 5.75208I
u = −1.04344 − 1.39492I
a = −1.146970 − 0.493456I
b = −0.74257 + 2.29110I
−16.7932 + 13.5804I −9.69096 − 5.75208I
u = −0.155431
a = −2.24820
b = −0.397493
−0.766508 −12.8940
6
II. I
u
2
= h−u
4
+ u
2
+ b − 1, a + u − 1, u
5
− u
3
− u
2
+ u + 1i
(i) Arc colorings
a
7
=
0
u
a
9
=
1
0
a
5
=
−u + 1
u
4
− u
2
+ 1
a
10
=
1
−u
2
a
11
=
2u
4
− 2u
3
− u
2
+ 3
−u
a
1
=
2u
4
− 2u
3
− u
2
− u + 3
−u
a
2
=
4u
4
− 3u
3
− 3u
2
− 2u + 6
u
4
− u
3
− u + 1
a
4
=
u
4
− u
3
− u + 2
0
a
3
=
−4u
4
+ 2u
3
+ 3u
2
+ 2u − 5
−u
4
+ u
3
− 1
a
6
=
−4u
4
+ 3u
3
+ 2u
2
+ 2u − 5
u
a
8
=
−4u
4
+ 3u
3
+ u
2
+ 4u − 5
−u
4
+ u
2
+ u − 2
a
8
=
−4u
4
+ 3u
3
+ u
2
+ 4u − 5
−u
4
+ u
2
+ u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
− 3u
2
+ u − 10
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 3u
3
− 3u
2
+ 2u − 1
c
2
, c
10
u
5
− 3u
3
+ 2u − 1
c
3
, c
6
u
5
− 2u
3
− 5u
2
− 4u − 1
c
4
, c
8
u
5
− 3u
3
+ 2u + 1
c
5
u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ 2u + 1
c
7
u
5
+ u
4
− 2u
3
− 9u
2
− 17u − 11
c
9
, c
11
u
5
− u
3
− u
2
+ u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
5
− 3y
4
− 5y
3
− 3y
2
− 2y −1
c
2
, c
4
, c
8
c
10
y
5
− 6y
4
+ 13y
3
− 12y
2
+ 4y −1
c
3
, c
6
y
5
− 4y
4
− 4y
3
− 9y
2
+ 6y −1
c
7
y
5
− 5y
4
− 12y
3
+ 9y
2
+ 91y −121
c
9
, c
11
y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.699311 + 0.811268I
a = 1.69931 − 0.81127I
b = −0.08973 + 1.51845I
−4.27168 − 5.69445I −7.07561 + 6.18407I
u = −0.699311 − 0.811268I
a = 1.69931 + 0.81127I
b = −0.08973 − 1.51845I
−4.27168 + 5.69445I −7.07561 − 6.18407I
u = 1.045750 + 0.405588I
a = −0.045747 − 0.405588I
b = 0.214528 + 0.727972I
1.28936 + 0.85728I −9.85891 + 1.65248I
u = 1.045750 − 0.405588I
a = −0.045747 + 0.405588I
b = 0.214528 − 0.727972I
1.28936 − 0.85728I −9.85891 − 1.65248I
u = −0.692872
a = 1.69287
b = 0.750397
−13.7746 −13.1310
10
III. I
u
3
= h−7.93 × 10
30
u
27
− 2.30 × 10
31
u
26
+ · · · + 1.78 × 10
32
b − 1.02 ×
10
33
, 5.27 × 10
33
u
27
+ 4.24 × 10
33
u
26
+ · · · + 4.71 × 10
34
a − 4.75 ×
10
34
, u
28
+ 2u
27
+ · · · + 16u + 53i
(i) Arc colorings
a
7
=
0
u
a
9
=
1
0
a
5
=
−0.112038u
27
− 0.0900820u
26
+ ··· − 11.0154u + 1.00852
0.0446814u
27
+ 0.129648u
26
+ ··· − 2.93741u + 5.76160
a
10
=
1
−u
2
a
11
=
0.0412335u
27
+ 0.151288u
26
+ ··· + 0.947304u + 6.52946
0.0570546u
27
+ 0.0640613u
26
+ ··· + 2.64220u − 0.694529
a
1
=
0.0982881u
27
+ 0.215349u
26
+ ··· + 3.58950u + 5.83493
0.0570546u
27
+ 0.0640613u
26
+ ··· + 2.64220u − 0.694529
a
2
=
−0.139493u
27
− 0.00902673u
26
+ ··· − 14.8255u + 7.85460
0.0820733u
27
+ 0.170760u
26
+ ··· − 2.23022u + 6.62107
a
4
=
−0.112897u
27
− 0.126972u
26
+ ··· − 10.1587u − 0.331526
0.0120291u
27
+ 0.0408066u
26
+ ··· − 3.54568u + 3.89750
a
3
=
0.147589u
27
+ 0.261948u
26
+ ··· + 0.542279u + 10.1056
0.137753u
27
+ 0.229592u
26
+ ··· + 5.02332u + 5.68909
a
6
=
−0.318579u
27
− 0.451498u
26
+ ··· − 21.0133u − 6.91766
−0.0305242u
27
+ 0.0725772u
26
+ ··· − 12.1016u + 8.59819
a
8
=
−0.00984630u
27
− 0.0983526u
26
+ ··· + 6.93307u − 6.10852
0.00262412u
27
− 0.0638304u
26
+ ··· + 3.31657u − 6.12608
a
8
=
−0.00984630u
27
− 0.0983526u
26
+ ··· + 6.93307u − 6.10852
0.00262412u
27
− 0.0638304u
26
+ ··· + 3.31657u − 6.12608
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0687616u
27
− 0.161087u
26
+ ··· + 10.9847u − 14.9327
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
14
− 3u
13
+ ··· − 9u + 43)
2
c
2
, c
4
, c
8
c
10
u
28
− u
27
+ ··· − 10u + 5
c
3
, c
6
u
28
− 3u
27
+ ··· + 67u + 71
c
7
(u
14
+ 4u
13
+ ··· + 10u + 25)
2
c
9
, c
11
u
28
+ 2u
27
+ ··· + 16u + 53
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
14
− 23y
13
+ ··· + 7573y + 1849)
2
c
2
, c
4
, c
8
c
10
y
28
− 23y
27
+ ··· + 790y + 25
c
3
, c
6
y
28
− 39y
27
+ ··· − 40699y + 5041
c
7
(y
14
+ 12y
13
+ ··· − 900y + 625)
2
c
9
, c
11
y
28
+ 4y
27
+ ··· + 5998y + 2809
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584190 + 0.830454I
a = −0.230171 + 0.016365I
b = −0.120673 + 0.549343I
−2.45167 − 0.19028I −7.59069 − 0.07427I
u = −0.584190 − 0.830454I
a = −0.230171 − 0.016365I
b = −0.120673 − 0.549343I
−2.45167 + 0.19028I −7.59069 + 0.07427I
u = −0.189224 + 0.962916I
a = −1.81744 − 0.19971I
b = 0.015564 − 0.852076I
−6.04992 − 4.80511I −11.59839 + 3.59136I
u = −0.189224 − 0.962916I
a = −1.81744 + 0.19971I
b = 0.015564 + 0.852076I
−6.04992 + 4.80511I −11.59839 − 3.59136I
u = −0.579209 + 0.947954I
a = −0.979797 + 0.974887I
b = −0.149625 − 0.259516I
−8.72421 − 2.38151I −11.54622 − 4.13808I
u = −0.579209 − 0.947954I
a = −0.979797 − 0.974887I
b = −0.149625 + 0.259516I
−8.72421 + 2.38151I −11.54622 + 4.13808I
u = 0.069986 + 0.864215I
a = 1.70791 − 0.59133I
b = 0.019429 − 0.811599I
−2.45167 + 0.19028I −7.59069 + 0.07427I
u = 0.069986 − 0.864215I
a = 1.70791 + 0.59133I
b = 0.019429 + 0.811599I
−2.45167 − 0.19028I −7.59069 − 0.07427I
u = −0.998105 + 0.539137I
a = 0.556120 − 0.028718I
b = −0.270263 + 0.404856I
−0.77359 − 4.74950I −0.89732 + 5.36294I
u = −0.998105 − 0.539137I
a = 0.556120 + 0.028718I
b = −0.270263 − 0.404856I
−0.77359 + 4.74950I −0.89732 − 5.36294I
14
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.358359 + 1.130590I
a = 0.132188 + 0.113341I
b = −0.21610 − 1.47756I
−10.59290 − 5.53516I −10.41956 + 3.78484I
u = −0.358359 − 1.130590I
a = 0.132188 − 0.113341I
b = −0.21610 + 1.47756I
−10.59290 + 5.53516I −10.41956 − 3.78484I
u = −0.412188 + 0.675927I
a = −1.94357 − 2.32635I
b = 0.57652 − 1.49217I
−8.72421 + 2.38151I −11.54622 + 4.13808I
u = −0.412188 − 0.675927I
a = −1.94357 + 2.32635I
b = 0.57652 + 1.49217I
−8.72421 − 2.38151I −11.54622 − 4.13808I
u = 0.570770 + 1.172340I
a = 1.060560 + 0.334570I
b = −0.224953 − 0.214426I
−15.2043 + 3.9716I −10.71811 − 2.64104I
u = 0.570770 − 1.172340I
a = 1.060560 − 0.334570I
b = −0.224953 + 0.214426I
−15.2043 − 3.9716I −10.71811 + 2.64104I
u = −0.905713 + 0.967441I
a = 1.44298 − 1.00864I
b = 0.70117 + 1.92457I
−6.04992 − 4.80511I −11.59839 + 3.59136I
u = −0.905713 − 0.967441I
a = 1.44298 + 1.00864I
b = 0.70117 − 1.92457I
−6.04992 + 4.80511I −11.59839 − 3.59136I
u = 0.643586 + 1.170970I
a = −1.45530 − 0.21856I
b = −0.55150 + 1.53777I
−0.77359 + 4.74950I −0.89732 − 5.36294I
u = 0.643586 − 1.170970I
a = −1.45530 + 0.21856I
b = −0.55150 − 1.53777I
−0.77359 − 4.74950I −0.89732 + 5.36294I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.412432 + 0.193729I
a = −0.741642 − 0.146832I
b = 0.093330 + 1.298980I
2.67330 + 1.05149I 1.77030 − 7.85829I
u = 0.412432 − 0.193729I
a = −0.741642 + 0.146832I
b = 0.093330 − 1.298980I
2.67330 − 1.05149I 1.77030 + 7.85829I
u = 1.63897 + 0.02744I
a = −0.646267 − 0.284696I
b = 2.54792 + 0.58842I
2.67330 + 1.05149I 1.77030 − 7.85829I
u = 1.63897 − 0.02744I
a = −0.646267 + 0.284696I
b = 2.54792 − 0.58842I
2.67330 − 1.05149I 1.77030 + 7.85829I
u = −1.63324 + 1.14769I
a = −0.616837 + 0.451371I
b = 0.72750 − 3.04503I
−15.2043 + 3.9716I −10.71811 − 2.64104I
u = −1.63324 − 1.14769I
a = −0.616837 − 0.451371I
b = 0.72750 + 3.04503I
−15.2043 − 3.9716I −10.71811 + 2.64104I
u = 1.32448 + 1.58910I
a = 0.908615 + 0.412051I
b = 0.85169 − 3.21610I
−10.59290 + 5.53516I −10.41956 − 3.78484I
u = 1.32448 − 1.58910I
a = 0.908615 − 0.412051I
b = 0.85169 + 3.21610I
−10.59290 − 5.53516I −10.41956 + 3.78484I
16
IV. I
u
4
= h−89u
13
+ 200u
12
+ · · · + 113b − 381, 134u
13
− 503u
12
+ · · · +
113a − 178, u
14
− 3u
13
+ · · · + 8u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
9
=
1
0
a
5
=
−1.18584u
13
+ 4.45133u
12
+ ··· − 8.74336u + 1.57522
0.787611u
13
− 1.76991u
12
+ ··· + 2.15044u + 3.37168
a
10
=
1
−u
2
a
11
=
−2.44248u
13
+ 7.64602u
12
+ ··· − 9.76991u − 0.725664
0.840708u
13
− 2.32743u
12
+ ··· + 1.36283u − 0.221239
a
1
=
−1.60177u
13
+ 5.31858u
12
+ ··· − 8.40708u − 0.946903
0.840708u
13
− 2.32743u
12
+ ··· + 1.36283u − 0.221239
a
2
=
1.02655u
13
− 3.77876u
12
+ ··· + 8.10619u − 4.79646
−1.26549u
13
+ 2.78761u
12
+ ··· − 0.0619469u − 1.03540
a
4
=
−0.601770u
13
+ 3.31858u
12
+ ··· − 5.40708u + 4.05310
0.433628u
13
− 1.05310u
12
+ ··· + 2.73451u + 3.99115
a
3
=
1.22124u
13
− 2.82301u
12
+ ··· + 0.884956u + 3.36283
1.00885u
13
− 3.59292u
12
+ ··· + 4.03540u − 0.265487
a
6
=
−4.58407u
13
+ 16.1327u
12
+ ··· − 24.3363u + 3.52212
−0.212389u
13
+ 1.23009u
12
+ ··· − 5.84956u + 3.37168
a
8
=
−1.70796u
13
+ 4.43363u
12
+ ··· + 0.168142u − 3.76106
−0.823009u
13
+ 2.14159u
12
+ ··· − 2.29204u − 2.30973
a
8
=
−1.70796u
13
+ 4.43363u
12
+ ··· + 0.168142u − 3.76106
−0.823009u
13
+ 2.14159u
12
+ ··· − 2.29204u − 2.30973
(ii) Obstruction class = 1
(iii) Cusp Shapes =
42
113
u
13
−
102
113
u
12
−
84
113
u
11
+
236
113
u
10
−
569
113
u
9
+
340
113
u
8
+
417
113
u
7
+
22
113
u
6
+
1511
113
u
5
+
1086
113
u
4
+
350
113
u
3
+
2192
113
u
2
−
849
113
u −
1034
113
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
7
+ 2u
6
+ u
5
+ 2u
4
+ u
3
− 2u
2
− 1)
2
c
2
, c
10
u
14
− 3u
12
+ ··· + 2u + 2
c
3
, c
6
u
14
+ 8u
13
+ ··· + 23u + 17
c
4
, c
8
u
14
− 3u
12
+ ··· − 2u + 2
c
5
(u
7
− 2u
6
+ u
5
− 2u
4
+ u
3
+ 2u
2
+ 1)
2
c
7
(u
7
− u
6
+ u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
2
c
9
, c
11
u
14
− 3u
13
+ ··· + 8u
2
+ 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
7
− 2y
6
− 5y
5
+ 6y
4
+ 13y
3
− 4y −1)
2
c
2
, c
4
, c
8
c
10
y
14
− 6y
13
+ ··· − 32y + 4
c
3
, c
6
y
14
− 16y
13
+ ··· − 1889y + 289
c
7
(y
7
+ y
6
− y
5
+ y
4
+ 16y
3
− 6y
2
+ 5y −1)
2
c
9
, c
11
y
14
− y
13
+ ··· + 16y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.222980 + 1.103480I
a = 0.714846 − 1.000800I
b = 0.621624 − 1.229020I
−5.45029 −12.49575 + 0.I
u = −0.222980 − 1.103480I
a = 0.714846 + 1.000800I
b = 0.621624 + 1.229020I
−5.45029 −12.49575 + 0.I
u = −1.119060 + 0.443308I
a = −0.158358 + 0.073033I
b = −0.636639 − 0.251429I
−1.53052 − 4.84436I −11.44020 + 5.79651I
u = −1.119060 − 0.443308I
a = −0.158358 − 0.073033I
b = −0.636639 + 0.251429I
−1.53052 + 4.84436I −11.44020 − 5.79651I
u = 0.525099 + 1.185640I
a = 1.165850 + 0.707967I
b = 0.736311 − 0.401224I
−8.72501 + 3.10373I −11.79285 − 6.01633I
u = 0.525099 − 1.185640I
a = 1.165850 − 0.707967I
b = 0.736311 + 0.401224I
−8.72501 − 3.10373I −11.79285 + 6.01633I
u = 0.594473 + 1.187010I
a = −1.44607 − 0.16012I
b = −0.58093 + 1.29906I
−1.53052 + 4.84436I −11.44020 − 5.79651I
u = 0.594473 − 1.187010I
a = −1.44607 + 0.16012I
b = −0.58093 − 1.29906I
−1.53052 − 4.84436I −11.44020 + 5.79651I
u = −0.153533 + 0.473920I
a = −3.47416 − 2.94650I
b = 0.38762 − 1.68131I
−8.72501 + 3.10373I −11.79285 − 6.01633I
u = −0.153533 − 0.473920I
a = −3.47416 + 2.94650I
b = 0.38762 + 1.68131I
−8.72501 − 3.10373I −11.79285 + 6.01633I
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.082843 + 0.472693I
a = −0.662827 − 0.167108I
b = −0.05161 + 1.42362I
2.28861 − 0.77726I −13.51907 − 2.44765I
u = 0.082843 − 0.472693I
a = −0.662827 + 0.167108I
b = −0.05161 − 1.42362I
2.28861 + 0.77726I −13.51907 + 2.44765I
u = 1.79315 + 0.00147I
a = −0.639276 + 0.400787I
b = 3.02363 − 1.09128I
2.28861 − 0.77726I −13.51907 − 2.44765I
u = 1.79315 − 0.00147I
a = −0.639276 − 0.400787I
b = 3.02363 + 1.09128I
2.28861 + 0.77726I −13.51907 + 2.44765I
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 3u
3
− 3u
2
+ 2u − 1)(u
7
+ 2u
6
+ u
5
+ 2u
4
+ u
3
− 2u
2
− 1)
2
· (u
13
+ 8u
12
+ ··· − 10u + 4)(u
14
− 3u
13
+ ··· − 9u + 43)
2
c
2
, c
10
(u
5
− 3u
3
+ 2u − 1)(u
13
− 8u
11
+ ··· − 2u + 2)(u
14
− 3u
12
+ ··· + 2u + 2)
· (u
28
− u
27
+ ··· − 10u + 5)
c
3
, c
6
(u
5
− 2u
3
− 5u
2
− 4u − 1)(u
13
− 2u
12
+ ··· − 3u + 1)
· (u
14
+ 8u
13
+ ··· + 23u + 17)(u
28
− 3u
27
+ ··· + 67u + 71)
c
4
, c
8
(u
5
− 3u
3
+ 2u + 1)(u
13
− 8u
11
+ ··· − 2u + 2)(u
14
− 3u
12
+ ··· − 2u + 2)
· (u
28
− u
27
+ ··· − 10u + 5)
c
5
(u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ 2u + 1)(u
7
− 2u
6
+ u
5
− 2u
4
+ u
3
+ 2u
2
+ 1)
2
· (u
13
+ 8u
12
+ ··· − 10u + 4)(u
14
− 3u
13
+ ··· − 9u + 43)
2
c
7
(u
5
+ u
4
− 2u
3
− 9u
2
− 17u − 11)
· (u
7
− u
6
+ u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
2
· (u
13
− 10u
12
+ ··· − 40u + 20)(u
14
+ 4u
13
+ ··· + 10u + 25)
2
c
9
, c
11
(u
5
− u
3
− u
2
+ u + 1)(u
13
+ 3u
11
+ ··· + 4u + 1)
· (u
14
− 3u
13
+ ··· + 8u
2
+ 1)(u
28
+ 2u
27
+ ··· + 16u + 53)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
5
− 3y
4
− 5y
3
− 3y
2
− 2y −1)
· (y
7
− 2y
6
− 5y
5
+ 6y
4
+ 13y
3
− 4y −1)
2
· (y
13
− 16y
12
+ ··· + 284y −16)(y
14
− 23y
13
+ ··· + 7573y + 1849)
2
c
2
, c
4
, c
8
c
10
(y
5
− 6y
4
+ 13y
3
− 12y
2
+ 4y −1)(y
13
− 16y
12
+ ··· + 12y −4)
· (y
14
− 6y
13
+ ··· − 32y + 4)(y
28
− 23y
27
+ ··· + 790y + 25)
c
3
, c
6
(y
5
− 4y
4
− 4y
3
− 9y
2
+ 6y −1)(y
13
− 24y
12
+ ··· − 7y −1)
· (y
14
− 16y
13
+ ··· − 1889y + 289)
· (y
28
− 39y
27
+ ··· − 40699y + 5041)
c
7
(y
5
− 5y
4
− 12y
3
+ 9y
2
+ 91y −121)
· (y
7
+ y
6
− y
5
+ y
4
+ 16y
3
− 6y
2
+ 5y −1)
2
· (y
13
− 2y
12
+ ··· + 4440y −400)(y
14
+ 12y
13
+ ··· − 900y + 625)
2
c
9
, c
11
(y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1)(y
13
+ 6y
12
+ ··· + 38y −1)
· (y
14
− y
13
+ ··· + 16y + 1)(y
28
+ 4y
27
+ ··· + 5998y + 2809)
23
