12n
0100
(K12n
0100
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 3 11 5 12 8 6 9
Solving Sequence
7,11 3,8
6 12 10 5 2 1 4 9
c
7
c
6
c
11
c
10
c
5
c
2
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h10938104279u
29
+ 17799069811u
28
+ ··· + 790454724608b + 452983966639,
3054129323185u
29
− 6949903407647u
28
+ ··· + 6323637796864a − 16733471682507,
u
30
− 2u
29
+ ··· − 6u + 1i
I
u
2
= h−1.61369 × 10
45
u
39
− 9.40408 × 10
45
u
38
+ ··· + 2.40030 × 10
46
b − 2.57635 × 10
47
,
− 2.95178 × 10
47
u
39
− 1.77493 × 10
48
u
38
+ ··· + 2.32829 × 10
48
a − 4.68541 × 10
49
,
u
40
+ 6u
39
+ ··· + 666u + 97i
I
u
3
= hb, 5u
2
+ 4a + 3u + 11, u
3
+ 2u − 1i
I
u
4
= h−12a
2
u + 91a
2
− 564au + 337b + 570a + 188u + 147, a
3
− 5a
2
u + 7a
2
+ 4au + a + 2u + 1, u
2
+ 1i
I
u
5
= hb, u
3
+ a + u, u
4
+ u
3
+ 2u
2
+ 2u + 1i
I
u
6
= h3b − 2a − 2, 4a
2
+ 2a − 11, u − 1i
* 6 irreducible components of dim
C
= 0, with total 85 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
= h1.09 × 10
10
u
29
+ 1.78 × 10
10
u
28
+ · · · + 7.90 × 10
11
b + 4.53 × 10
11
, 3.05 ×
10
12
u
29
−6.95×10
12
u
28
+· · ·+6.32×10
12
a−1.67×10
13
, u
30
−2u
29
+· · ·−6u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
−0.482970u
29
+ 1.09904u
28
+ ··· − 14.1778u + 2.64618
−0.0138377u
29
− 0.0225175u
28
+ ··· − 0.0339714u − 0.573068
a
8
=
1
u
2
a
6
=
−0.269448u
29
+ 0.688032u
28
+ ··· − 10.5362u + 2.79507
−0.306258u
29
+ 0.647053u
28
+ ··· + 0.353711u − 0.471726
a
12
=
0.000122070u
29
− 0.000366211u
28
+ ··· + 1.99915u − 0.999878
0.000244141u
29
− 0.000732422u
28
+ ··· + 1.99829u + 0.000244141
a
10
=
u
u
3
+ u
a
5
=
−0.198114u
29
+ 0.535158u
28
+ ··· − 10.9040u + 2.84822
−0.159014u
29
+ 0.310603u
28
+ ··· − 0.146693u − 0.408378
a
2
=
−0.116259u
29
+ 0.299479u
28
+ ··· − 6.99440u + 1.41903
−0.159014u
29
+ 0.310603u
28
+ ··· − 0.146693u − 0.408378
a
1
=
−0.000244141u
29
+ 0.000732422u
28
+ ··· − 1.99829u + 0.999756
−0.000488281u
29
+ 0.00146484u
28
+ ··· − 1.99658u − 0.000488281
a
4
=
−0.469133u
29
+ 1.12155u
28
+ ··· − 14.1438u + 3.21925
−0.0138377u
29
− 0.0225175u
28
+ ··· − 0.0339714u − 0.573068
a
9
=
0.000122070u
29
− 0.000366211u
28
+ ··· + 1.99915u + 0.000122070
0.000244141u
29
− 0.000732422u
28
+ ··· + 0.998291u + 0.000244141
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
5758735881521
25294551187456
u
29
−
9442271879503
25294551187456
u
28
+ ··· +
149768918108921
25294551187456
u −
343005319822011
25294551187456
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 27u
29
+ ··· + 20513u + 256
c
2
, c
4
u
30
− 5u
29
+ ··· + 161u + 16
c
3
, c
6
u
30
+ 2u
29
+ ··· − 400u − 128
c
5
u
30
− 6u
29
+ ··· + 240u − 64
c
7
, c
9
, c
10
c
12
u
30
+ 2u
29
+ ··· + 6u + 1
c
8
, c
11
4(4u
30
+ 6u
29
+ ··· + 40u − 8)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 43y
29
+ ··· − 326031937y + 65536
c
2
, c
4
y
30
− 27y
29
+ ··· − 20513y + 256
c
3
, c
6
y
30
− 12y
29
+ ··· − 181504y + 16384
c
5
y
30
+ 16y
29
+ ··· − 44800y + 4096
c
7
, c
9
, c
10
c
12
y
30
+ 12y
29
+ ··· + 20y + 1
c
8
, c
11
16(16y
30
− 220y
29
+ ··· − 2368y + 64)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.306081 + 0.971496I
a = −0.379940 − 0.267068I
b = 0.17194 + 1.49872I
6.31796 + 4.23185I −8.08189 − 9.05731I
u = −0.306081 − 0.971496I
a = −0.379940 + 0.267068I
b = 0.17194 − 1.49872I
6.31796 − 4.23185I −8.08189 + 9.05731I
u = 0.726332 + 0.717882I
a = −0.266956 + 0.595547I
b = 0.470087 − 0.986044I
−3.92620 − 2.24705I −15.5498 + 1.9306I
u = 0.726332 − 0.717882I
a = −0.266956 − 0.595547I
b = 0.470087 + 0.986044I
−3.92620 + 2.24705I −15.5498 − 1.9306I
u = 0.885171 + 0.404098I
a = 1.67056 − 0.76180I
b = 0.819942 + 0.114529I
−2.95432 + 0.04023I −20.3286 − 5.5388I
u = 0.885171 − 0.404098I
a = 1.67056 + 0.76180I
b = 0.819942 − 0.114529I
−2.95432 − 0.04023I −20.3286 + 5.5388I
u = 0.558846 + 0.895019I
a = −0.770167 + 1.055880I
b = −1.031020 − 0.715634I
−0.75719 − 4.19906I −11.33346 + 6.22509I
u = 0.558846 − 0.895019I
a = −0.770167 − 1.055880I
b = −1.031020 + 0.715634I
−0.75719 + 4.19906I −11.33346 − 6.22509I
u = −0.657049 + 0.551609I
a = 1.23906 + 0.82471I
b = 1.83855 + 0.13734I
−10.22390 + 1.23818I −12.68969 − 5.92681I
u = −0.657049 − 0.551609I
a = 1.23906 − 0.82471I
b = 1.83855 − 0.13734I
−10.22390 − 1.23818I −12.68969 + 5.92681I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.565389 + 1.005700I
a = −1.162420 − 0.720365I
b = −1.58427 + 0.36083I
0.05463 + 4.76238I −11.14668 − 5.25286I
u = −0.565389 − 1.005700I
a = −1.162420 + 0.720365I
b = −1.58427 − 0.36083I
0.05463 − 4.76238I −11.14668 + 5.25286I
u = 0.843377
a = 2.75809
b = 0.513113
−2.79129 −49.4130
u = −0.140757 + 0.828367I
a = 0.367813 + 0.583725I
b = −0.28661 − 1.50907I
5.58489 − 2.26037I −14.4927 − 3.6390I
u = −0.140757 − 0.828367I
a = 0.367813 − 0.583725I
b = −0.28661 + 1.50907I
5.58489 + 2.26037I −14.4927 + 3.6390I
u = −0.631272 + 1.097650I
a = 0.392830 − 0.018581I
b = −0.50506 − 1.57122I
−1.35975 + 8.36352I −11.27390 − 6.50510I
u = −0.631272 − 1.097650I
a = 0.392830 + 0.018581I
b = −0.50506 + 1.57122I
−1.35975 − 8.36352I −11.27390 + 6.50510I
u = 0.604075 + 1.194270I
a = 0.706087 − 0.904055I
b = 1.23790 + 0.84225I
−5.88204 − 8.98025I −12.45579 + 6.40354I
u = 0.604075 − 1.194270I
a = 0.706087 + 0.904055I
b = 1.23790 − 0.84225I
−5.88204 + 8.98025I −12.45579 − 6.40354I
u = −0.630005 + 1.198400I
a = 1.18843 + 0.82286I
b = 1.46968 − 0.61664I
1.77400 + 11.41590I −9.49161 − 8.04508I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.630005 − 1.198400I
a = 1.18843 − 0.82286I
b = 1.46968 + 0.61664I
1.77400 − 11.41590I −9.49161 + 8.04508I
u = −0.21630 + 1.42652I
a = −0.0559978 − 0.0670005I
b = −0.071308 + 0.475747I
8.04558 + 5.22550I 7.68375 − 8.68899I
u = −0.21630 − 1.42652I
a = −0.0559978 + 0.0670005I
b = −0.071308 − 0.475747I
8.04558 − 5.22550I 7.68375 + 8.68899I
u = −0.71570 + 1.32576I
a = −1.09519 − 0.90719I
b = −1.44754 + 0.87678I
−4.4797 + 16.8602I −12.0000 − 8.5659I
u = −0.71570 − 1.32576I
a = −1.09519 + 0.90719I
b = −1.44754 − 0.87678I
−4.4797 − 16.8602I −12.0000 + 8.5659I
u = 1.44106 + 0.58374I
a = −0.975310 + 0.305052I
b = −1.44083 + 0.27330I
−10.25000 + 1.95101I −14.1127 − 3.6126I
u = 1.44106 − 0.58374I
a = −0.975310 − 0.305052I
b = −1.44083 − 0.27330I
−10.25000 − 1.95101I −14.1127 + 3.6126I
u = 0.330393
a = 0.875273
b = −0.342608
−0.684602 −14.4040
u = 0.060190 + 0.268373I
a = 0.19952 − 1.89319I
b = −0.726719 + 0.048459I
−0.767693 + 0.138293I −11.78528 + 0.30985I
u = 0.060190 − 0.268373I
a = 0.19952 + 1.89319I
b = −0.726719 − 0.048459I
−0.767693 − 0.138293I −11.78528 − 0.30985I
7
II. I
u
2
= h−1.61 × 10
45
u
39
− 9.40 × 10
45
u
38
+ · · · + 2.40 × 10
46
b − 2.58 ×
10
47
, −2.95 × 10
47
u
39
− 1.77 × 10
48
u
38
+ · · · + 2.33 × 10
48
a − 4.69 ×
10
49
, u
40
+ 6u
39
+ · · · + 666u + 97i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
0.126779u
39
+ 0.762331u
38
+ ··· + 125.069u + 20.1238
0.0672286u
39
+ 0.391787u
38
+ ··· + 63.2326u + 10.7335
a
8
=
1
u
2
a
6
=
0.102593u
39
+ 0.627245u
38
+ ··· + 80.1048u + 12.8462
0.0338897u
39
+ 0.223578u
38
+ ··· + 43.4453u + 7.70229
a
12
=
−0.153021u
39
− 0.645296u
38
+ ··· + 86.5001u + 15.5286
−0.0899725u
39
− 0.492162u
38
+ ··· − 65.3776u − 10.0258
a
10
=
u
u
3
+ u
a
5
=
0.114842u
39
+ 0.690016u
38
+ ··· + 87.9315u + 13.8490
0.0721576u
39
+ 0.397847u
38
+ ··· + 57.2261u + 9.74529
a
2
=
0.0427641u
39
+ 0.258615u
38
+ ··· + 68.3523u + 12.7917
0.0721576u
39
+ 0.397847u
38
+ ··· + 57.2261u + 9.74529
a
1
=
0.0551092u
39
+ 0.267827u
38
+ ··· + 5.30009u + 0.972082
0.0961666u
39
+ 0.488952u
38
+ ··· + 41.7982u + 6.06644
a
4
=
0.0595503u
39
+ 0.370543u
38
+ ··· + 61.8366u + 9.39035
0.0672286u
39
+ 0.391787u
38
+ ··· + 63.2326u + 10.7335
a
9
=
0.196886u
39
+ 1.21771u
38
+ ··· + 77.1544u + 10.6242
−0.0343140u
39
− 0.208019u
38
+ ··· − 28.2185u − 5.36491
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0728219u
39
+ 0.430060u
38
+ ··· + 88.4314u + 10.6322
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 21u
19
+ ··· + 13u + 1)
2
c
2
, c
4
(u
20
− 3u
19
+ ··· + u − 1)
2
c
3
, c
6
(u
20
+ u
19
+ ··· − 8u − 4)
2
c
5
(u
20
+ 2u
19
+ ··· − 2u + 1)
2
c
7
, c
9
, c
10
c
12
u
40
− 6u
39
+ ··· − 666u + 97
c
8
, c
11
u
40
− 6u
39
+ ··· − 10066u + 3683
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
− 41y
19
+ ··· − 33y + 1)
2
c
2
, c
4
(y
20
− 21y
19
+ ··· − 13y + 1)
2
c
3
, c
6
(y
20
− 15y
19
+ ··· − 24y + 16)
2
c
5
(y
20
+ 6y
19
+ ··· − 2y + 1)
2
c
7
, c
9
, c
10
c
12
y
40
+ 22y
39
+ ··· + 37176y + 9409
c
8
, c
11
y
40
+ 10y
39
+ ··· − 492576812y + 13564489
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.949389 + 0.318916I
a = 1.45882 + 0.65851I
b = 1.268400 + 0.295253I
−0.89345 − 5.67427I −12.59597 + 5.66395I
u = −0.949389 − 0.318916I
a = 1.45882 − 0.65851I
b = 1.268400 − 0.295253I
−0.89345 + 5.67427I −12.59597 − 5.66395I
u = 0.055076 + 1.004540I
a = 3.54069 + 5.49904I
b = −0.610309
2.43031 −15.8646 + 0.I
u = 0.055076 − 1.004540I
a = 3.54069 − 5.49904I
b = −0.610309
2.43031 −15.8646 + 0.I
u = −0.261046 + 0.924940I
a = −2.18019 − 0.55269I
b = −0.439566 − 0.534727I
2.07115 + 0.86143I −9.55325 + 0.99952I
u = −0.261046 − 0.924940I
a = −2.18019 + 0.55269I
b = −0.439566 + 0.534727I
2.07115 − 0.86143I −9.55325 − 0.99952I
u = −0.802373 + 0.466386I
a = −1.070220 − 0.185255I
b = −0.089922 + 1.317200I
−3.24441 − 2.97363I −13.9234 + 2.6854I
u = −0.802373 − 0.466386I
a = −1.070220 + 0.185255I
b = −0.089922 − 1.317200I
−3.24441 + 2.97363I −13.9234 − 2.6854I
u = 0.507721 + 0.743875I
a = −0.915680 + 0.137961I
b = −1.256010 + 0.124886I
−1.249910 − 0.191668I −13.73570 − 0.22109I
u = 0.507721 − 0.743875I
a = −0.915680 − 0.137961I
b = −1.256010 − 0.124886I
−1.249910 + 0.191668I −13.73570 + 0.22109I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851192 + 0.285618I
a = 0.918683 − 0.525649I
b = 1.52621 − 0.50989I
−8.58220 + 3.56941I −15.7159 − 1.0074I
u = 0.851192 − 0.285618I
a = 0.918683 + 0.525649I
b = 1.52621 + 0.50989I
−8.58220 − 3.56941I −15.7159 + 1.0074I
u = 0.640368 + 0.940231I
a = 0.250357 − 0.419468I
b = −0.089922 + 1.317200I
−3.24441 − 2.97363I −13.9234 + 2.6854I
u = 0.640368 − 0.940231I
a = 0.250357 + 0.419468I
b = −0.089922 − 1.317200I
−3.24441 + 2.97363I −13.9234 − 2.6854I
u = −0.532340 + 1.015670I
a = 1.61077 + 0.30511I
b = 0.685016 − 0.443026I
4.73160 + 1.82256I −4.87459 − 5.12436I
u = −0.532340 − 1.015670I
a = 1.61077 − 0.30511I
b = 0.685016 + 0.443026I
4.73160 − 1.82256I −4.87459 + 5.12436I
u = −0.131384 + 1.153900I
a = −2.89792 − 2.19839I
b = −0.439566 + 0.534727I
2.07115 − 0.86143I −9.55325 − 0.99952I
u = −0.131384 − 1.153900I
a = −2.89792 + 2.19839I
b = −0.439566 − 0.534727I
2.07115 + 0.86143I −9.55325 + 0.99952I
u = −0.557461 + 0.561067I
a = −1.13556 − 1.31193I
b = −1.256010 + 0.124886I
−1.249910 − 0.191668I −13.73570 − 0.22109I
u = −0.557461 − 0.561067I
a = −1.13556 + 1.31193I
b = −1.256010 − 0.124886I
−1.249910 + 0.191668I −13.73570 + 0.22109I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.353190 + 1.172280I
a = −0.30264 − 1.50729I
b = 1.36144
−4.11381 −16.6683 + 0.I
u = 0.353190 − 1.172280I
a = −0.30264 + 1.50729I
b = 1.36144
−4.11381 −16.6683 + 0.I
u = −0.574260 + 1.083700I
a = 0.703109 + 1.169540I
b = 1.52621 − 0.50989I
−8.58220 + 3.56941I −15.7159 − 1.0074I
u = −0.574260 − 1.083700I
a = 0.703109 − 1.169540I
b = 1.52621 + 0.50989I
−8.58220 − 3.56941I −15.7159 + 1.0074I
u = 0.211725 + 1.229800I
a = 0.108080 + 0.199216I
b = 0.078647 − 0.574169I
2.82359 − 2.30782I −5.88733 + 3.58910I
u = 0.211725 − 1.229800I
a = 0.108080 − 0.199216I
b = 0.078647 + 0.574169I
2.82359 + 2.30782I −5.88733 − 3.58910I
u = 0.652486 + 1.117780I
a = 1.178370 − 0.534825I
b = 1.268400 + 0.295253I
−0.89345 − 5.67427I −12.00000 + 5.66395I
u = 0.652486 − 1.117780I
a = 1.178370 + 0.534825I
b = 1.268400 − 0.295253I
−0.89345 + 5.67427I −12.00000 − 5.66395I
u = −1.281360 + 0.321932I
a = −1.139100 − 0.351922I
b = −1.47182 − 0.62184I
−7.69158 − 9.88458I −14.3825 + 5.7764I
u = −1.281360 − 0.321932I
a = −1.139100 + 0.351922I
b = −1.47182 + 0.62184I
−7.69158 + 9.88458I −14.3825 − 5.7764I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.607865 + 0.225887I
a = 0.763840 + 0.694546I
b = 0.078647 + 0.574169I
2.82359 + 2.30782I −5.88733 − 3.58910I
u = −0.607865 − 0.225887I
a = 0.763840 − 0.694546I
b = 0.078647 − 0.574169I
2.82359 − 2.30782I −5.88733 + 3.58910I
u = −0.225404 + 1.332760I
a = 0.222126 + 0.306934I
b = 0.685016 + 0.443026I
4.73160 − 1.82256I −4.87459 + 5.12436I
u = −0.225404 − 1.332760I
a = 0.222126 − 0.306934I
b = 0.685016 − 0.443026I
4.73160 + 1.82256I −4.87459 − 5.12436I
u = −1.04608 + 1.04120I
a = −0.923744 − 0.369988I
b = −1.176520 + 0.244065I
−0.28251 + 3.88098I 0
u = −1.04608 − 1.04120I
a = −0.923744 + 0.369988I
b = −1.176520 − 0.244065I
−0.28251 − 3.88098I 0
u = 0.84940 + 1.32134I
a = −0.956517 + 0.698756I
b = −1.47182 − 0.62184I
−7.69158 − 9.88458I 0
u = 0.84940 − 1.32134I
a = −0.956517 − 0.698756I
b = −1.47182 + 0.62184I
−7.69158 + 9.88458I 0
u = −0.15220 + 1.73038I
a = −0.0374057 − 0.0650581I
b = −1.176520 − 0.244065I
−0.28251 − 3.88098I 0
u = −0.15220 − 1.73038I
a = −0.0374057 + 0.0650581I
b = −1.176520 + 0.244065I
−0.28251 + 3.88098I 0
14
III. I
u
3
= hb, 5u
2
+ 4a + 3u + 11, u
3
+ 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
−
5
4
u
2
−
3
4
u −
11
4
0
a
8
=
1
u
2
a
6
=
1
0
a
12
=
−u
u
a
10
=
u
−u + 1
a
5
=
u
2
− u + 1
−u
2
+ 2u − 1
a
2
=
−
9
4
u
2
+
1
4
u −
15
4
u
2
− 2u + 1
a
1
=
−u
2
+ u − 1
u
2
− 2u + 1
a
4
=
−
5
4
u
2
−
3
4
u −
11
4
0
a
9
=
u
2
+ u
−u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
69
16
u
2
+
47
16
u −
185
16
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
u
3
c
4
(u + 1)
3
c
5
u
3
− 3u
2
+ 5u − 2
c
7
, c
9
u
3
+ 2u − 1
c
8
, c
10
, c
11
c
12
u
3
+ 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
6
y
3
c
5
y
3
+ y
2
+ 13y −4
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22670 + 1.46771I
a = 0.048505 − 0.268962I
b = 0
7.79580 + 5.13794I −21.2967 + 1.4416I
u = −0.22670 − 1.46771I
a = 0.048505 + 0.268962I
b = 0
7.79580 − 5.13794I −21.2967 − 1.4416I
u = 0.453398
a = −3.34701
b = 0
−2.43213 −9.34410
18
IV. I
u
4
=
h−12a
2
u−564au+· · ·+570a +147, a
3
−5a
2
u+7a
2
+4au+a +2u +1, u
2
+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
a
0.0356083a
2
u + 1.67359au + ··· − 1.69139a − 0.436202
a
8
=
1
−1
a
6
=
−0.0741840a
2
u − 0.486647au + ··· + 0.0237389a + 0.658754
−0.00593472a
2
u + 0.721068au + ··· − 0.718101a + 1.57270
a
12
=
−0.201780a
2
u + 0.516320au + ··· − 0.415430a − 0.528190
−1
a
10
=
u
0
a
5
=
−0.0682493a
2
u − 1.20772au + ··· + 0.741840a − 0.913947
−0.00593472a
2
u + 0.721068au + ··· − 0.718101a + 1.57270
a
2
=
−0.0741840a
2
u − 0.486647au + ··· + 0.0237389a − 1.34125
−0.00593472a
2
u + 0.721068au + ··· − 0.718101a + 1.57270
a
1
=
−1
0
a
4
=
−0.0356083a
2
u − 1.67359au + ··· + 2.69139a + 0.436202
0.0356083a
2
u + 1.67359au + ··· − 1.69139a − 0.436202
a
9
=
−0.136499a
2
u − 0.415430au + ··· − 0.516320a + 0.172107
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
56
337
a
2
u +
200
337
a
2
−
1284
337
au +
1312
337
a +
428
337
u −
1336
337
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
u
6
+ 5u
4
+ 10u
2
+ 1
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
9
, c
10
c
12
(u
2
+ 1)
3
c
8
u
6
+ 4u
5
+ 8u
4
− 28u
3
+ 36u
2
− 24u + 8
c
11
u
6
− 4u
5
+ 8u
4
+ 28u
3
+ 36u
2
+ 24u + 8
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
(y
3
+ 5y
2
+ 10y + 1)
2
c
7
, c
9
, c
10
c
12
(y + 1)
6
c
8
, c
11
y
6
+ 360y
4
+ 80y
2
+ 64
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.459293 − 0.567321I
b = −0.215080 + 1.307140I
6.31400 + 2.82812I −4.49024 − 2.97945I
u = 1.000000I
a = −0.300102 + 0.163008I
b = −0.215080 − 1.307140I
6.31400 − 2.82812I −4.49024 + 2.97945I
u = 1.000000I
a = −7.15919 + 5.40431I
b = −0.569840
2.17641 −11.01951 + 0.I
u = − 1.000000I
a = 0.459293 + 0.567321I
b = −0.215080 − 1.307140I
6.31400 − 2.82812I −4.49024 + 2.97945I
u = − 1.000000I
a = −0.300102 − 0.163008I
b = −0.215080 + 1.307140I
6.31400 + 2.82812I −4.49024 − 2.97945I
u = − 1.000000I
a = −7.15919 − 5.40431I
b = −0.569840
2.17641 −11.01951 + 0.I
22
V. I
u
5
= hb, u
3
+ a + u, u
4
+ u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
−u
3
− u
0
a
8
=
1
u
2
a
6
=
1
0
a
12
=
−u
u
a
10
=
u
u
3
+ u
a
5
=
u
3
+ u
2
+ 2u + 2
u
3
+ u + 1
a
2
=
−2u
3
− u
2
− 3u − 2
−u
3
− u − 1
a
1
=
−u
3
− u
2
− 2u − 2
−u
3
− u − 1
a
4
=
−u
3
− u
0
a
9
=
u
3
+ 2u + 1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
3
− 4u − 15
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
6
u
4
c
4
(u + 1)
4
c
5
(u
2
+ u + 1)
2
c
7
, c
9
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
8
, c
10
, c
11
c
12
u
4
− u
3
+ 2u
2
− 2u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
6
y
4
c
5
(y
2
+ y + 1)
2
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.621744 + 0.440597I
a = 0.500000 − 0.866025I
b = 0
1.64493 + 2.02988I −13.00000 − 3.46410I
u = −0.621744 − 0.440597I
a = 0.500000 + 0.866025I
b = 0
1.64493 − 2.02988I −13.00000 + 3.46410I
u = 0.121744 + 1.306620I
a = 0.500000 + 0.866025I
b = 0
1.64493 − 2.02988I −13.00000 + 3.46410I
u = 0.121744 − 1.306620I
a = 0.500000 − 0.866025I
b = 0
1.64493 + 2.02988I −13.00000 − 3.46410I
26
VI. I
u
6
= h3b − 2a − 2, 4a
2
+ 2a − 11, u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
1
a
3
=
a
2
3
a +
2
3
a
8
=
1
1
a
6
=
−
1
3
a −
5
6
−
2
3
a −
5
3
a
12
=
−
1
2
a − 1
−a − 1
a
10
=
1
2
a
5
=
−
1
3
a −
5
6
−
2
3
a −
5
3
a
2
=
1
3
a −
7
6
−
2
3
a −
5
3
a
1
=
−a − 3
−2a − 4
a
4
=
1
3
a −
2
3
2
3
a +
2
3
a
9
=
1
2
a + 2
a + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
15
2
a − 5
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
− 3u + 1
c
2
, c
3
u
2
+ u − 1
c
4
, c
6
u
2
− u − 1
c
5
u
2
c
7
, c
9
(u − 1)
2
c
8
4(4u
2
+ 6u + 1)
c
10
, c
12
(u + 1)
2
c
11
4(4u
2
− 6u + 1)
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
− 7y + 1
c
2
, c
3
, c
4
c
6
y
2
− 3y + 1
c
5
y
2
c
7
, c
9
, c
10
c
12
(y −1)
2
c
8
, c
11
16(16y
2
− 28y + 1)
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.42705
b = 1.61803
−10.5276 −15.7030
u = 1.00000
a = −1.92705
b = −0.618034
−2.63189 9.45290
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
7
(u
2
− 3u + 1)(u
3
− u
2
+ 2u − 1)
2
· ((u
20
+ 21u
19
+ ··· + 13u + 1)
2
)(u
30
+ 27u
29
+ ··· + 20513u + 256)
c
2
((u − 1)
7
)(u
2
+ u − 1)(u
3
+ u
2
− 1)
2
(u
20
− 3u
19
+ ··· + u − 1)
2
· (u
30
− 5u
29
+ ··· + 161u + 16)
c
3
u
7
(u
2
+ u − 1)(u
3
− u
2
+ 2u − 1)
2
(u
20
+ u
19
+ ··· − 8u − 4)
2
· (u
30
+ 2u
29
+ ··· − 400u − 128)
c
4
((u + 1)
7
)(u
2
− u − 1)(u
3
− u
2
+ 1)
2
(u
20
− 3u
19
+ ··· + u − 1)
2
· (u
30
− 5u
29
+ ··· + 161u + 16)
c
5
u
2
(u
2
+ u + 1)
2
(u
3
− 3u
2
+ 5u − 2)(u
6
+ 5u
4
+ 10u
2
+ 1)
· ((u
20
+ 2u
19
+ ··· − 2u + 1)
2
)(u
30
− 6u
29
+ ··· + 240u − 64)
c
6
u
7
(u
2
− u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
20
+ u
19
+ ··· − 8u − 4)
2
· (u
30
+ 2u
29
+ ··· − 400u − 128)
c
7
, c
9
(u − 1)
2
(u
2
+ 1)
3
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
30
+ 2u
29
+ ··· + 6u + 1)(u
40
− 6u
39
+ ··· − 666u + 97)
c
8
16(4u
2
+ 6u + 1)(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
6
+ 4u
5
+ ··· − 24u + 8)(4u
30
+ 6u
29
+ ··· + 40u − 8)
· (u
40
− 6u
39
+ ··· − 10066u + 3683)
c
10
, c
12
(u + 1)
2
(u
2
+ 1)
3
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
30
+ 2u
29
+ ··· + 6u + 1)(u
40
− 6u
39
+ ··· − 666u + 97)
c
11
16(4u
2
− 6u + 1)(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
6
− 4u
5
+ ··· + 24u + 8)(4u
30
+ 6u
29
+ ··· + 40u − 8)
· (u
40
− 6u
39
+ ··· − 10066u + 3683)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
7
(y
2
− 7y + 1)(y
3
+ 3y
2
+ 2y −1)
2
· (y
20
− 41y
19
+ ··· − 33y + 1)
2
· (y
30
− 43y
29
+ ··· − 326031937y + 65536)
c
2
, c
4
(y −1)
7
(y
2
− 3y + 1)(y
3
− y
2
+ 2y −1)
2
· ((y
20
− 21y
19
+ ··· − 13y + 1)
2
)(y
30
− 27y
29
+ ··· − 20513y + 256)
c
3
, c
6
y
7
(y
2
− 3y + 1)(y
3
+ 3y
2
+ 2y −1)
2
(y
20
− 15y
19
+ ··· − 24y + 16)
2
· (y
30
− 12y
29
+ ··· − 181504y + 16384)
c
5
y
2
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y −4)(y
3
+ 5y
2
+ 10y + 1)
2
· ((y
20
+ 6y
19
+ ··· − 2y + 1)
2
)(y
30
+ 16y
29
+ ··· − 44800y + 4096)
c
7
, c
9
, c
10
c
12
(y −1)
2
(y + 1)
6
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
30
+ 12y
29
+ ··· + 20y + 1)(y
40
+ 22y
39
+ ··· + 37176y + 9409)
c
8
, c
11
256(16y
2
− 28y + 1)(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
6
+ 360y
4
+ 80y
2
+ 64)(16y
30
− 220y
29
+ ··· − 2368y + 64)
· (y
40
+ 10y
39
+ ··· − 492576812y + 13564489)
32
