12n
0459
(K12n
0459
)
A knot diagram
1
Linearized knot diagam
3 6 9 12 2 1 12 5 7 5 9 10
Solving Sequence
5,12 4,9
3 8 7 11 10 1 2 6
c
4
c
3
c
8
c
7
c
11
c
10
c
12
c
1
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −2.55290 × 10
42
u
36
+ 5.44795 × 10
42
u
35
+ ··· + 1.76508 × 10
43
a − 3.00825 × 10
43
,
u
37
− u
36
+ ··· + 3u − 1i
I
u
2
= hb + u, 250u
18
− 299u
17
+ ··· + 73a + 547, u
19
− u
18
+ ··· + 3u + 1i
I
u
3
= h2.39883 × 10
77
u
33
+ 4.38682 × 10
77
u
32
+ ··· + 2.11269 × 10
80
b + 4.67078 × 10
80
,
− 2.66819 × 10
80
u
33
− 6.63024 × 10
80
u
32
+ ··· + 4.21058 × 10
83
a − 5.18491 × 10
83
,
u
34
+ u
33
+ ··· + 1952u − 1993i
* 3 irreducible components of dim
C
= 0, with total 90 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
= hb − u, −2.55 × 10
42
u
36
+ 5.45 × 10
42
u
35
+ · · · + 1.77 × 10
43
a −
3.01 × 10
43
, u
37
− u
36
+ · · · + 3u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
9
=
0.144634u
36
− 0.308653u
35
+ ··· − 1.70408u + 1.70432
u
a
3
=
0.0641583u
36
− 0.204773u
35
+ ··· − 2.93838u + 1.14286
0.00595874u
36
− 0.0145660u
35
+ ··· + 0.258814u − 0.0315982
a
8
=
0.144634u
36
− 0.308653u
35
+ ··· − 0.704084u + 1.70432
u
a
7
=
0.144634u
36
− 0.308653u
35
+ ··· − 0.704084u + 1.70432
−0.0315982u
36
+ 0.0375570u
35
+ ··· + 0.363310u + 0.164019
a
11
=
−0.287497u
36
+ 0.387357u
35
+ ··· + 0.523806u + 0.805473
0.0315982u
36
− 0.0375570u
35
+ ··· + 1.63669u − 0.164019
a
10
=
−0.255898u
36
+ 0.349800u
35
+ ··· + 2.16050u + 0.641454
0.0315982u
36
− 0.0375570u
35
+ ··· + 1.63669u − 0.164019
a
1
=
−0.113036u
36
+ 0.271096u
35
+ ··· + 3.34077u − 1.86834
0.206163u
36
− 0.241526u
35
+ ··· − 0.860551u + 0.362165
a
2
=
0.121719u
36
+ 0.0603587u
35
+ ··· + 2.89319u − 1.94734
0.177072u
36
− 0.177109u
35
+ ··· − 0.860687u + 0.281992
a
6
=
−0.0205670u
36
− 0.0114078u
35
+ ··· − 1.02788u + 1.87960
−0.0935046u
36
+ 0.0800631u
35
+ ··· + 1.12160u + 0.0897229
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.05287u
36
+ 2.19238u
35
+ ··· + 12.4820u − 10.7486
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
37
+ 19u
36
+ ··· + 13u + 4
c
2
, c
5
u
37
+ 5u
36
+ ··· + 11u + 2
c
3
, c
10
u
37
− 16u
35
+ ··· + 286u + 313
c
4
, c
8
u
37
+ u
36
+ ··· + 3u + 1
c
6
u
37
+ 15u
36
+ ··· + 1057u + 142
c
7
u
37
+ 33u
36
+ ··· + 2424832u + 131072
c
9
, c
12
u
37
+ 2u
36
+ ··· − 4u + 1
c
11
u
37
− 20u
36
+ ··· + 3129u + 416
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ y
36
+ ··· + 417y −16
c
2
, c
5
y
37
− 19y
36
+ ··· + 13y −4
c
3
, c
10
y
37
− 32y
36
+ ··· + 1668y −97969
c
4
, c
8
y
37
− 53y
36
+ ··· + y −1
c
6
y
37
+ 17y
36
+ ··· + 321765y −20164
c
7
y
37
− 7y
36
+ ··· + 124554051584y −17179869184
c
9
, c
12
y
37
+ 18y
36
+ ··· + 52y −1
c
11
y
37
− 40y
36
+ ··· + 11555313y −173056
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227341 + 1.006740I
a = −0.014320 + 0.531612I
b = 0.227341 + 1.006740I
2.19421 − 2.66186I −12.2194 + 11.4876I
u = 0.227341 − 1.006740I
a = −0.014320 − 0.531612I
b = 0.227341 − 1.006740I
2.19421 + 2.66186I −12.2194 − 11.4876I
u = −0.572877 + 0.421277I
a = −0.589584 − 0.431854I
b = −0.572877 + 0.421277I
−4.23503 − 2.99580I −10.42564 + 0.99385I
u = −0.572877 − 0.421277I
a = −0.589584 + 0.431854I
b = −0.572877 − 0.421277I
−4.23503 + 2.99580I −10.42564 − 0.99385I
u = 0.443470 + 0.512589I
a = −0.93334 − 2.14850I
b = 0.443470 + 0.512589I
−2.92897 + 7.93095I −9.93339 − 5.60925I
u = 0.443470 − 0.512589I
a = −0.93334 + 2.14850I
b = 0.443470 − 0.512589I
−2.92897 − 7.93095I −9.93339 + 5.60925I
u = −0.425682 + 0.515838I
a = −0.912897 − 0.668737I
b = −0.425682 + 0.515838I
−4.36721 + 4.92237I −9.76383 − 6.76217I
u = −0.425682 − 0.515838I
a = −0.912897 + 0.668737I
b = −0.425682 − 0.515838I
−4.36721 − 4.92237I −9.76383 + 6.76217I
u = 0.640765 + 0.065448I
a = 0.06676 + 1.55654I
b = 0.640765 + 0.065448I
0.561173 + 0.639753I −5.50967 − 0.34463I
u = 0.640765 − 0.065448I
a = 0.06676 − 1.55654I
b = 0.640765 − 0.065448I
0.561173 − 0.639753I −5.50967 + 0.34463I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.276215 + 0.533554I
a = −1.16500 − 2.16159I
b = 0.276215 + 0.533554I
−3.55570 − 0.00267I −10.39254 + 2.55625I
u = 0.276215 − 0.533554I
a = −1.16500 + 2.16159I
b = 0.276215 − 0.533554I
−3.55570 + 0.00267I −10.39254 − 2.55625I
u = 0.440393 + 0.380348I
a = 0.896498 − 0.271334I
b = 0.440393 + 0.380348I
−1.26315 − 1.02773I −6.64941 + 3.71665I
u = 0.440393 − 0.380348I
a = 0.896498 + 0.271334I
b = 0.440393 − 0.380348I
−1.26315 + 1.02773I −6.64941 − 3.71665I
u = −0.388482 + 0.417207I
a = 0.91985 − 2.32255I
b = −0.388482 + 0.417207I
−0.15749 − 3.53597I −7.19576 + 1.75427I
u = −0.388482 − 0.417207I
a = 0.91985 + 2.32255I
b = −0.388482 − 0.417207I
−0.15749 + 3.53597I −7.19576 − 1.75427I
u = −0.536439 + 0.152143I
a = 0.19810 − 2.15263I
b = −0.536439 + 0.152143I
1.28152 − 3.19239I −5.87746 + 5.99544I
u = −0.536439 − 0.152143I
a = 0.19810 + 2.15263I
b = −0.536439 − 0.152143I
1.28152 + 3.19239I −5.87746 − 5.99544I
u = 0.411639
a = 0.358793
b = 0.411639
−0.908630 −11.5680
u = 0.069113 + 0.352786I
a = 2.46626 − 1.42359I
b = 0.069113 + 0.352786I
−0.90988 − 2.23770I 0.21125 + 2.16221I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.069113 − 0.352786I
a = 2.46626 + 1.42359I
b = 0.069113 − 0.352786I
−0.90988 + 2.23770I 0.21125 − 2.16221I
u = −1.79797 + 0.39975I
a = 0.791512 + 0.386512I
b = −1.79797 + 0.39975I
−10.49280 − 5.44002I 0
u = −1.79797 − 0.39975I
a = 0.791512 − 0.386512I
b = −1.79797 − 0.39975I
−10.49280 + 5.44002I 0
u = 1.84834 + 0.40321I
a = −0.787306 + 0.304002I
b = 1.84834 + 0.40321I
−7.74174 − 0.09044I 0
u = 1.84834 − 0.40321I
a = −0.787306 − 0.304002I
b = 1.84834 − 0.40321I
−7.74174 + 0.09044I 0
u = −1.86346 + 0.35746I
a = 0.898519 + 0.269725I
b = −1.86346 + 0.35746I
−12.94290 + 3.71649I 0
u = −1.86346 − 0.35746I
a = 0.898519 − 0.269725I
b = −1.86346 − 0.35746I
−12.94290 − 3.71649I 0
u = −1.87706 + 0.37684I
a = 0.894002 + 0.031082I
b = −1.87706 + 0.37684I
−5.46083 + 8.77952I 0
u = −1.87706 − 0.37684I
a = 0.894002 − 0.031082I
b = −1.87706 − 0.37684I
−5.46083 − 8.77952I 0
u = 1.88332 + 0.36296I
a = −0.835463 + 0.083202I
b = 1.88332 + 0.36296I
−5.07424 − 3.40985I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.88332 − 0.36296I
a = −0.835463 − 0.083202I
b = 1.88332 − 0.36296I
−5.07424 + 3.40985I 0
u = −1.91093 + 0.40135I
a = 1.032100 + 0.006450I
b = −1.91093 + 0.40135I
−9.1177 + 10.8968I 0
u = −1.91093 − 0.40135I
a = 1.032100 − 0.006450I
b = −1.91093 − 0.40135I
−9.1177 − 10.8968I 0
u = 1.91805 + 0.38450I
a = −1.045410 + 0.056772I
b = 1.91805 + 0.38450I
−13.7875 − 7.1044I 0
u = 1.91805 − 0.38450I
a = −1.045410 − 0.056772I
b = 1.91805 − 0.38450I
−13.7875 + 7.1044I 0
u = 1.92006 + 0.40960I
a = −1.059660 − 0.009858I
b = 1.92006 + 0.40960I
−12.0188 − 16.0848I 0
u = 1.92006 − 0.40960I
a = −1.059660 + 0.009858I
b = 1.92006 − 0.40960I
−12.0188 + 16.0848I 0
8
II. I
u
2
= hb + u, 250u
18
− 299u
17
+ · · · + 73a + 547, u
19
− u
18
+ · · · + 3u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
9
=
−3.42466u
18
+ 4.09589u
17
+ ··· − 5.61644u − 7.49315
−u
a
3
=
−0.219178u
18
+ 0.630137u
17
+ ··· − 0.479452u + 1.61644
0.219178u
18
− 0.630137u
17
+ ··· + 0.479452u + 0.383562
a
8
=
−3.42466u
18
+ 4.09589u
17
+ ··· − 6.61644u − 7.49315
−u
a
7
=
−3.42466u
18
+ 4.09589u
17
+ ··· − 6.61644u − 7.49315
0.383562u
18
− 0.602740u
17
+ ··· − 2.41096u + 0.671233
a
11
=
−2.80822u
18
+ 3.69863u
17
+ ··· − 2.20548u − 5.16438
0.383562u
18
− 0.602740u
17
+ ··· − 0.410959u + 0.671233
a
10
=
−2.42466u
18
+ 3.09589u
17
+ ··· − 2.61644u − 4.49315
0.383562u
18
− 0.602740u
17
+ ··· − 0.410959u + 0.671233
a
1
=
3.04110u
18
− 3.49315u
17
+ ··· + 6.02740u + 6.82192
0.0273973u
18
+ 0.671233u
17
+ ··· + 2.68493u − 0.452055
a
2
=
4.10959u
18
− 4.31507u
17
+ ··· + 2.73973u + 8.19178
−0.561644u
18
+ 0.739726u
17
+ ··· + 2.95890u − 0.232877
a
6
=
−3.30137u
18
+ 4.61644u
17
+ ··· − 1.53425u − 7.02740
0.0547945u
18
− 0.657534u
17
+ ··· − 0.630137u + 1.09589
(ii) Obstruction class = 1
(iii) Cusp Shapes =
128
73
u
18
−
149
73
u
17
+ ··· +
2032
73
u +
589
73
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
19
− 10u
18
+ ··· + 4u − 1
c
2
u
19
+ 2u
18
+ ··· + 2u + 1
c
3
, c
10
u
19
− 9u
17
+ ··· + 5u
2
+ 1
c
4
, c
8
u
19
− u
18
+ ··· + 3u + 1
c
5
u
19
− 2u
18
+ ··· + 2u − 1
c
6
u
19
− 6u
18
+ ··· + 2u
2
− 1
c
7
u
19
− 2u
18
+ ··· − 2u + 1
c
9
, c
12
u
19
− 2u
18
+ ··· − 2u + 1
c
11
u
19
+ 17u
18
+ ··· + 126u + 13
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
+ 2y
18
+ ··· + 8y − 1
c
2
, c
5
y
19
− 10y
18
+ ··· + 4y − 1
c
3
, c
10
y
19
− 18y
18
+ ··· − 10y − 1
c
4
, c
8
y
19
− 15y
18
+ ··· + 3y − 1
c
6
y
19
+ 6y
18
+ ··· + 4y − 1
c
7
y
19
− 6y
18
+ ··· + 4y − 1
c
9
, c
12
y
19
− 4y
18
+ ··· + 6y − 1
c
11
y
19
− 19y
18
+ ··· − 1076y − 169
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.389670 + 0.971259I
a = 0.122229 − 0.627078I
b = 0.389670 − 0.971259I
2.33089 + 2.35439I −2.65418 + 9.07433I
u = −0.389670 − 0.971259I
a = 0.122229 + 0.627078I
b = 0.389670 + 0.971259I
2.33089 − 2.35439I −2.65418 − 9.07433I
u = 0.107461 + 0.844602I
a = −0.493610 − 0.405220I
b = −0.107461 − 0.844602I
2.97743 + 2.82971I 1.23971 − 7.37257I
u = 0.107461 − 0.844602I
a = −0.493610 + 0.405220I
b = −0.107461 + 0.844602I
2.97743 − 2.82971I 1.23971 + 7.37257I
u = 0.297145 + 0.782682I
a = 1.072240 + 0.413603I
b = −0.297145 − 0.782682I
−1.69545 − 9.35446I −5.05835 + 8.47597I
u = 0.297145 − 0.782682I
a = 1.072240 − 0.413603I
b = −0.297145 + 0.782682I
−1.69545 + 9.35446I −5.05835 − 8.47597I
u = −0.219141 + 0.729049I
a = −1.127880 + 0.213922I
b = 0.219141 − 0.729049I
0.95654 + 4.52756I −1.42515 − 5.36291I
u = −0.219141 − 0.729049I
a = −1.127880 − 0.213922I
b = 0.219141 + 0.729049I
0.95654 − 4.52756I −1.42515 + 5.36291I
u = 0.347645 + 0.580389I
a = 1.49707 + 0.47525I
b = −0.347645 − 0.580389I
−3.09155 − 1.28314I −7.80963 + 3.01643I
u = 0.347645 − 0.580389I
a = 1.49707 − 0.47525I
b = −0.347645 + 0.580389I
−3.09155 + 1.28314I −7.80963 − 3.01643I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.409426 + 0.038014I
a = −1.22838 − 2.29649I
b = 0.409426 − 0.038014I
−1.45073 − 2.37737I −14.4553 + 5.2559I
u = −0.409426 − 0.038014I
a = −1.22838 + 2.29649I
b = 0.409426 + 0.038014I
−1.45073 + 2.37737I −14.4553 − 5.2559I
u = 1.63934 + 0.02428I
a = 1.081950 − 0.322533I
b = −1.63934 − 0.02428I
−8.75263 + 5.21255I −9.20929 − 3.46517I
u = 1.63934 − 0.02428I
a = 1.081950 + 0.322533I
b = −1.63934 + 0.02428I
−8.75263 − 5.21255I −9.20929 + 3.46517I
u = 1.70890 + 0.02593I
a = 1.228870 + 0.191361I
b = −1.70890 − 0.02593I
−9.57662 + 2.62847I −9.72201 − 4.27468I
u = 1.70890 − 0.02593I
a = 1.228870 − 0.191361I
b = −1.70890 + 0.02593I
−9.57662 − 2.62847I −9.72201 + 4.27468I
u = −1.71417 + 0.03393I
a = −1.039940 − 0.168963I
b = 1.71417 − 0.03393I
−6.19104 − 0.62856I −6.47218 − 0.41177I
u = −1.71417 − 0.03393I
a = −1.039940 + 0.168963I
b = 1.71417 + 0.03393I
−6.19104 + 0.62856I −6.47218 + 0.41177I
u = −1.73618
a = −1.22509
b = 1.73618
−6.94142 −2.86710
13
III. I
u
3
= h2.40 × 10
77
u
33
+ 4.39 × 10
77
u
32
+ · · · + 2.11 × 10
80
b + 4.67 ×
10
80
, −2.67 × 10
80
u
33
− 6.63 × 10
80
u
32
+ · · · + 4.21 × 10
83
a − 5.18 ×
10
83
, u
34
+ u
33
+ · · · + 1952u − 1993i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
4
=
1
−u
2
a
9
=
0.000633687u
33
+ 0.00157466u
32
+ ··· − 1.38149u + 1.23140
−0.00113544u
33
− 0.00207642u
32
+ ··· − 0.586403u − 2.21083
a
3
=
−0.00161924u
33
− 0.00401377u
32
+ ··· − 1.64818u − 2.45216
0.00145092u
33
+ 0.00405054u
32
+ ··· − 2.20190u + 1.96335
a
8
=
−0.000501756u
33
− 0.000501756u
32
+ ··· − 1.96789u − 0.979428
−0.00113544u
33
− 0.00207642u
32
+ ··· − 0.586403u − 2.21083
a
7
=
−0.000501756u
33
− 0.000501756u
32
+ ··· − 1.96789u − 0.979428
−0.00113544u
33
− 0.00207642u
32
+ ··· + 0.413597u − 2.21083
a
11
=
0.00225250u
33
+ 0.00558537u
32
+ ··· − 0.926455u + 2.18386
−0.00288618u
33
− 0.00716003u
32
+ ··· + 3.30794u − 3.41526
a
10
=
−0.000633687u
33
− 0.00157466u
32
+ ··· + 2.38149u − 1.23140
−0.00288618u
33
− 0.00716003u
32
+ ··· + 3.30794u − 3.41526
a
1
=
−0.000428587u
33
− 0.000572264u
32
+ ··· + 0.221236u − 1.56686
0.00234022u
33
+ 0.00587590u
32
+ ··· + 1.14397u + 2.65445
a
2
=
0.00298530u
33
+ 0.00738719u
32
+ ··· − 1.07544u + 3.26522
−0.00158678u
33
− 0.00381361u
32
+ ··· − 0.818276u − 3.70164
a
6
=
0.000923865u
33
+ 0.00208460u
32
+ ··· + 1.06868u + 2.80386
0.000581990u
33
+ 0.000749672u
32
+ ··· + 2.17844u + 2.36276
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00320571u
33
+ 0.00635032u
32
+ ··· + 0.739925u + 0.207764
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
17
+ 9u
16
+ ··· + u + 1)
2
c
2
, c
5
(u
17
− u
16
+ ··· + u − 1)
2
c
3
, c
10
u
34
− u
33
+ ··· + 116748u − 21241
c
4
, c
8
u
34
− u
33
+ ··· − 1952u − 1993
c
6
(u
17
− 3u
16
+ ··· + 9u − 3)
2
c
7
(u − 1)
34
c
9
, c
12
u
34
+ 15u
33
+ ··· + 284u + 23
c
11
(u
17
+ 15u
16
+ ··· − 15u + 3)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
17
− y
16
+ ··· + 9y − 1)
2
c
2
, c
5
(y
17
− 9y
16
+ ··· + y − 1)
2
c
3
, c
10
y
34
− 33y
33
+ ··· − 8863869996y + 451180081
c
4
, c
8
y
34
− 45y
33
+ ··· − 19443396y + 3972049
c
6
(y
17
+ 11y
16
+ ··· + 57y − 9)
2
c
7
(y − 1)
34
c
9
, c
12
y
34
− 5y
33
+ ··· + 580y + 529
c
11
(y
17
− 33y
16
+ ··· − 15y − 9)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.167398 + 1.144780I
a = 0.014539 + 0.424029I
b = −0.139598 + 0.431211I
2.19127 − 2.39923I −7.13400 + 3.27109I
u = 0.167398 − 1.144780I
a = 0.014539 − 0.424029I
b = −0.139598 − 0.431211I
2.19127 + 2.39923I −7.13400 − 3.27109I
u = 0.622028 + 0.358140I
a = −0.443652 − 0.412413I
b = −0.763740 + 1.107580I
−4.71195 + 0.50801I −13.57451 + 0.23246I
u = 0.622028 − 0.358140I
a = −0.443652 + 0.412413I
b = −0.763740 − 1.107580I
−4.71195 − 0.50801I −13.57451 − 0.23246I
u = −0.763740 + 1.107580I
a = −0.200081 + 0.253771I
b = 0.622028 + 0.358140I
−4.71195 + 0.50801I −13.57451 + 0.23246I
u = −0.763740 − 1.107580I
a = −0.200081 − 0.253771I
b = 0.622028 − 0.358140I
−4.71195 − 0.50801I −13.57451 − 0.23246I
u = 0.612488 + 1.252450I
a = 0.160762 + 0.357838I
b = −0.475864 + 0.286501I
−0.42874 − 3.91820I −8.40216 + 2.39256I
u = 0.612488 − 1.252450I
a = 0.160762 − 0.357838I
b = −0.475864 − 0.286501I
−0.42874 + 3.91820I −8.40216 − 2.39256I
u = −0.475864 + 0.286501I
a = 0.929876 − 0.323850I
b = 0.612488 + 1.252450I
−0.42874 − 3.91820I −8.40216 + 2.39256I
u = −0.475864 − 0.286501I
a = 0.929876 + 0.323850I
b = 0.612488 − 1.252450I
−0.42874 + 3.91820I −8.40216 − 2.39256I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.507585 + 0.207409I
a = −1.006380 − 0.653748I
b = −0.68185 + 1.34359I
−3.16740 + 8.83664I −11.62632 − 5.87120I
u = 0.507585 − 0.207409I
a = −1.006380 + 0.653748I
b = −0.68185 − 1.34359I
−3.16740 − 8.83664I −11.62632 + 5.87120I
u = 1.46214 + 0.04893I
a = 1.35960 − 0.49813I
b = −2.04276 + 0.52099I
−10.22540 + 6.09306I −15.2930 − 6.8742I
u = 1.46214 − 0.04893I
a = 1.35960 + 0.49813I
b = −2.04276 − 0.52099I
−10.22540 − 6.09306I −15.2930 + 6.8742I
u = −1.49197 + 0.07442I
a = −1.311960 − 0.394189I
b = 1.98055 + 0.42754I
−7.27776 − 1.70542I −12.10923 + 4.02096I
u = −1.49197 − 0.07442I
a = −1.311960 + 0.394189I
b = 1.98055 − 0.42754I
−7.27776 + 1.70542I −12.10923 − 4.02096I
u = −0.68185 + 1.34359I
a = −0.207231 + 0.384441I
b = 0.507585 + 0.207409I
−3.16740 + 8.83664I −11.62632 − 5.87120I
u = −0.68185 − 1.34359I
a = −0.207231 − 0.384441I
b = 0.507585 − 0.207409I
−3.16740 − 8.83664I −11.62632 + 5.87120I
u = 1.51009 + 0.03397I
a = 1.44977 − 0.35194I
b = −2.11165 + 0.36683I
−10.72210 − 2.05778I −17.0193 + 0.3782I
u = 1.51009 − 0.03397I
a = 1.44977 + 0.35194I
b = −2.11165 − 0.36683I
−10.72210 + 2.05778I −17.0193 − 0.3782I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49205 + 0.25792I
a = −0.992537 − 0.309405I
b = 1.64331 + 0.42190I
−5.45645 − 1.83062I −8.40697 + 5.22267I
u = −1.49205 − 0.25792I
a = −0.992537 + 0.309405I
b = 1.64331 − 0.42190I
−5.45645 + 1.83062I −8.40697 − 5.22267I
u = −0.139598 + 0.431211I
a = 0.512141 + 0.954274I
b = 0.167398 + 1.144780I
2.19127 − 2.39923I −7.13400 + 3.27109I
u = −0.139598 − 0.431211I
a = 0.512141 − 0.954274I
b = 0.167398 − 1.144780I
2.19127 + 2.39923I −7.13400 − 3.27109I
u = −1.59159
a = −1.35109
b = 1.97939
−7.58450 −18.8690
u = 1.64331 + 0.42190I
a = 0.921155 − 0.111350I
b = −1.49205 + 0.25792I
−5.45645 − 1.83062I −8.40697 + 5.22267I
u = 1.64331 − 0.42190I
a = 0.921155 + 0.111350I
b = −1.49205 − 0.25792I
−5.45645 + 1.83062I −8.40697 − 5.22267I
u = 1.97939
a = 1.08639
b = −1.59159
−7.58450 −18.8690
u = 1.98055 + 0.42754I
a = 1.009540 + 0.029722I
b = −1.49197 + 0.07442I
−7.27776 − 1.70542I 0
u = 1.98055 − 0.42754I
a = 1.009540 − 0.029722I
b = −1.49197 − 0.07442I
−7.27776 + 1.70542I 0
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −2.04276 + 0.52099I
a = −1.002510 + 0.068296I
b = 1.46214 + 0.04893I
−10.22540 + 6.09306I 0
u = −2.04276 − 0.52099I
a = −1.002510 − 0.068296I
b = 1.46214 − 0.04893I
−10.22540 − 6.09306I 0
u = −2.11165 + 0.36683I
a = −1.050400 + 0.045887I
b = 1.51009 + 0.03397I
−10.72210 − 2.05778I 0
u = −2.11165 − 0.36683I
a = −1.050400 − 0.045887I
b = 1.51009 − 0.03397I
−10.72210 + 2.05778I 0
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
17
+ 9u
16
+ ··· + u + 1)
2
)(u
19
− 10u
18
+ ··· + 4u − 1)
· (u
37
+ 19u
36
+ ··· + 13u + 4)
c
2
((u
17
− u
16
+ ··· + u − 1)
2
)(u
19
+ 2u
18
+ ··· + 2u + 1)
· (u
37
+ 5u
36
+ ··· + 11u + 2)
c
3
, c
10
(u
19
− 9u
17
+ ··· + 5u
2
+ 1)(u
34
− u
33
+ ··· + 116748u − 21241)
· (u
37
− 16u
35
+ ··· + 286u + 313)
c
4
, c
8
(u
19
− u
18
+ ··· + 3u + 1)(u
34
− u
33
+ ··· − 1952u − 1993)
· (u
37
+ u
36
+ ··· + 3u + 1)
c
5
((u
17
− u
16
+ ··· + u − 1)
2
)(u
19
− 2u
18
+ ··· + 2u − 1)
· (u
37
+ 5u
36
+ ··· + 11u + 2)
c
6
((u
17
− 3u
16
+ ··· + 9u − 3)
2
)(u
19
− 6u
18
+ ··· + 2u
2
− 1)
· (u
37
+ 15u
36
+ ··· + 1057u + 142)
c
7
((u − 1)
34
)(u
19
− 2u
18
+ ··· − 2u + 1)
· (u
37
+ 33u
36
+ ··· + 2424832u + 131072)
c
9
, c
12
(u
19
− 2u
18
+ ··· − 2u + 1)(u
34
+ 15u
33
+ ··· + 284u + 23)
· (u
37
+ 2u
36
+ ··· − 4u + 1)
c
11
((u
17
+ 15u
16
+ ··· − 15u + 3)
2
)(u
19
+ 17u
18
+ ··· + 126u + 13)
· (u
37
− 20u
36
+ ··· + 3129u + 416)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
17
− y
16
+ ··· + 9y − 1)
2
)(y
19
+ 2y
18
+ ··· + 8y − 1)
· (y
37
+ y
36
+ ··· + 417y − 16)
c
2
, c
5
((y
17
− 9y
16
+ ··· + y − 1)
2
)(y
19
− 10y
18
+ ··· + 4y − 1)
· (y
37
− 19y
36
+ ··· + 13y − 4)
c
3
, c
10
(y
19
− 18y
18
+ ··· − 10y − 1)
· (y
34
− 33y
33
+ ··· − 8863869996y + 451180081)
· (y
37
− 32y
36
+ ··· + 1668y − 97969)
c
4
, c
8
(y
19
− 15y
18
+ ··· + 3y − 1)
· (y
34
− 45y
33
+ ··· − 19443396y + 3972049)
· (y
37
− 53y
36
+ ··· + y − 1)
c
6
((y
17
+ 11y
16
+ ··· + 57y − 9)
2
)(y
19
+ 6y
18
+ ··· + 4y − 1)
· (y
37
+ 17y
36
+ ··· + 321765y − 20164)
c
7
((y − 1)
34
)(y
19
− 6y
18
+ ··· + 4y − 1)
· (y
37
− 7y
36
+ ··· + 124554051584y − 17179869184)
c
9
, c
12
(y
19
− 4y
18
+ ··· + 6y − 1)(y
34
− 5y
33
+ ··· + 580y + 529)
· (y
37
+ 18y
36
+ ··· + 52y − 1)
c
11
((y
17
− 33y
16
+ ··· − 15y − 9)
2
)(y
19
− 19y
18
+ ··· − 1076y − 169)
· (y
37
− 40y
36
+ ··· + 11555313y − 173056)
22
