12n
0141
(K12n
0141
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 10 4 11 6 12 8 5 9
Solving Sequence
7,11 4,8
6 3 10 5 12 2 1 9
c
7
c
6
c
3
c
10
c
5
c
11
c
2
c
1
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−6686875043u
25
− 624104415u
24
+ ··· + 13435529728b + 3806288503,
79755561391u
25
+ 46013804251u
24
+ ··· + 214968475648a − 231933695795,
u
26
+ 2u
24
+ ··· − u + 1i
I
u
2
= h−6.09745 × 10
15
u
23
+ 2.23561 × 10
15
u
22
+ ··· + 4.70830 × 10
16
b − 9.49470 × 10
16
,
3.77245 × 10
16
u
23
− 4.36637 × 10
15
u
22
+ ··· + 1.14344 × 10
17
a + 1.28843 × 10
18
, u
24
− 2u
23
+ ··· + 20u + 17i
I
u
3
= hb, −u
3
− u
2
+ 4a + 2u − 3, u
4
+ u
2
+ u + 1i
I
u
4
= h13362a
5
u − 25075a
4
u + ··· + 39143a + 74777,
a
6
− 5a
5
u − 5a
5
+ 14a
4
u + 2a
3
u + 9a
3
− 14a
2
u + 10a
2
− 5au − 13a + 3u, u
2
+ 1i
I
u
5
= hb, −u
3
+ a − u + 1, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
* 5 irreducible components of dim
C
= 0, with total 72 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−6.69 × 10
9
u
25
− 6.24 × 10
8
u
24
+ · · · + 1.34 × 10
10
b + 3.81 × 10
9
, 7.98 ×
10
10
u
25
+4.60×10
10
u
24
+· · ·+2.15×10
11
a−2.32×10
11
, u
26
+2u
24
+· · ·−u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−0.371010u
25
− 0.214049u
24
+ ··· − 2.37389u + 1.07892
0.497701u
25
+ 0.0464518u
24
+ ··· − 0.303652u − 0.283300
a
8
=
1
−u
2
a
6
=
0.786727u
25
+ 0.355240u
24
+ ··· + 0.268947u + 0.181402
−0.281655u
25
+ 0.162782u
24
+ ··· − 0.150036u + 1.19156
a
3
=
−0.0563150u
25
− 0.379621u
24
+ ··· − 1.27287u − 1.11514
0.478616u
25
− 0.0163741u
24
+ ··· + 1.75358u − 0.0264586
a
10
=
−u
u
3
+ u
a
5
=
0.836319u
25
+ 0.321913u
24
+ ··· + 0.240330u − 0.254796
−0.290547u
25
+ 0.204134u
24
+ ··· − 0.0385003u + 1.59443
a
12
=
−0.00390625u
25
− 0.00390625u
24
+ ··· − 2u − 0.996094
0.00781250u
25
+ 0.00781250u
24
+ ··· + 2u − 0.00781250
a
2
=
−0.977915u
25
− 0.402299u
24
+ ··· − 2.88010u + 0.873808
0.278382u
25
− 0.0788085u
24
+ ··· − 1.17498u − 1.03877
a
1
=
0.00781250u
25
+ 0.00781250u
24
+ ··· + 2u + 0.992188
−
1
64
u
25
−
1
64
u
24
+ ··· − 2u +
1
64
a
9
=
−0.00390625u
25
− 0.00390625u
24
+ ··· − 2u + 0.00390625
1
128
u
25
+
1
128
u
24
+ ··· + u −
1
128
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
2427750693445
859873902592
u
25
−
360782953559
859873902592
u
24
+ ··· +
1801599863713
214968475648
u −
3455303354737
859873902592
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
+ 7u
25
+ ··· + 801u + 256
c
2
, c
4
u
26
− 5u
25
+ ··· − 97u + 16
c
3
, c
6
u
26
+ 3u
25
+ ··· − 288u + 256
c
5
u
26
+ 6u
25
+ ··· + 12u + 4
c
7
, c
9
, c
10
c
12
u
26
+ 2u
24
+ ··· + u + 1
c
8
, c
11
u
26
− 4u
25
+ ··· + 64u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 29y
25
+ ··· − 2714689y + 65536
c
2
, c
4
y
26
− 7y
25
+ ··· − 801y + 256
c
3
, c
6
y
26
− 27y
25
+ ··· − 709632y + 65536
c
5
y
26
− 4y
25
+ ··· + 8y + 16
c
7
, c
9
, c
10
c
12
y
26
+ 4y
25
+ ··· + 11y + 1
c
8
, c
11
y
26
+ 40y
25
+ ··· + 114688y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.667716 + 0.516448I
a = 0.351921 − 0.458400I
b = −1.12559 + 1.18769I
−2.22323 + 3.06268I −3.92422 − 7.01336I
u = 0.667716 − 0.516448I
a = 0.351921 + 0.458400I
b = −1.12559 − 1.18769I
−2.22323 − 3.06268I −3.92422 + 7.01336I
u = −0.801593 + 0.232094I
a = −1.51203 + 1.55558I
b = 0.422167 + 0.399037I
−0.278324 − 0.685873I 9.0494 − 11.0486I
u = −0.801593 − 0.232094I
a = −1.51203 − 1.55558I
b = 0.422167 − 0.399037I
−0.278324 + 0.685873I 9.0494 + 11.0486I
u = 0.469402 + 1.100720I
a = −0.043572 − 0.410845I
b = −0.655893 − 0.316475I
−4.13271 + 8.27529I −1.38622 − 13.75239I
u = 0.469402 − 1.100720I
a = −0.043572 + 0.410845I
b = −0.655893 + 0.316475I
−4.13271 − 8.27529I −1.38622 + 13.75239I
u = 0.923141 + 0.764696I
a = −0.958376 + 0.099240I
b = 0.77338 + 1.80053I
1.82654 + 6.11440I 0.00845 − 7.81451I
u = 0.923141 − 0.764696I
a = −0.958376 − 0.099240I
b = 0.77338 − 1.80053I
1.82654 − 6.11440I 0.00845 + 7.81451I
u = −1.080690 + 0.597719I
a = 0.810296 + 0.338780I
b = −0.479644 + 0.933985I
2.44292 − 1.70853I 2.53010 − 0.44010I
u = −1.080690 − 0.597719I
a = 0.810296 − 0.338780I
b = −0.479644 − 0.933985I
2.44292 + 1.70853I 2.53010 + 0.44010I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.357275 + 0.656602I
a = 0.625898 − 0.297698I
b = 0.617127 − 0.011460I
0.43304 − 1.45422I 6.37162 + 4.53869I
u = −0.357275 − 0.656602I
a = 0.625898 + 0.297698I
b = 0.617127 + 0.011460I
0.43304 + 1.45422I 6.37162 − 4.53869I
u = 0.064603 + 0.724531I
a = −0.732028 + 0.504908I
b = −0.988101 + 0.632950I
−2.19370 − 5.44910I 2.44328 + 3.74912I
u = 0.064603 − 0.724531I
a = −0.732028 − 0.504908I
b = −0.988101 − 0.632950I
−2.19370 + 5.44910I 2.44328 − 3.74912I
u = −0.122998 + 0.488840I
a = 0.938808 − 0.475125I
b = 0.643196 − 0.415198I
0.295014 − 1.313020I 3.29344 + 4.27536I
u = −0.122998 − 0.488840I
a = 0.938808 + 0.475125I
b = 0.643196 + 0.415198I
0.295014 + 1.313020I 3.29344 − 4.27536I
u = 0.308360 + 0.340398I
a = 2.08611 − 1.44710I
b = −0.946580 − 0.566353I
−2.70538 − 0.26841I −4.73409 − 2.48832I
u = 0.308360 − 0.340398I
a = 2.08611 + 1.44710I
b = −0.946580 + 0.566353I
−2.70538 + 0.26841I −4.73409 + 2.48832I
u = −0.89844 + 1.25514I
a = −0.795341 − 1.127880I
b = 1.75386 − 0.65984I
9.35192 − 8.60133I −0.45347 + 4.28581I
u = −0.89844 − 1.25514I
a = −0.795341 + 1.127880I
b = 1.75386 + 0.65984I
9.35192 + 8.60133I −0.45347 − 4.28581I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07814 + 1.14400I
a = −0.949321 + 0.843430I
b = 2.35374 + 0.29535I
10.68100 + 7.33921I 0.71166 − 4.65613I
u = 1.07814 − 1.14400I
a = −0.949321 − 0.843430I
b = 2.35374 − 0.29535I
10.68100 − 7.33921I 0.71166 + 4.65613I
u = 0.91358 + 1.30265I
a = 1.01202 − 1.05301I
b = −1.86071 − 0.87913I
8.8427 + 15.8962I −1.12202 − 7.88761I
u = 0.91358 − 1.30265I
a = 1.01202 + 1.05301I
b = −1.86071 + 0.87913I
8.8427 − 15.8962I −1.12202 + 7.88761I
u = −1.16396 + 1.16780I
a = 0.790615 + 0.787753I
b = −2.00696 + 0.05529I
10.55890 − 0.78971I 0.743315 − 0.651860I
u = −1.16396 − 1.16780I
a = 0.790615 − 0.787753I
b = −2.00696 − 0.05529I
10.55890 + 0.78971I 0.743315 + 0.651860I
7
II. I
u
2
= h−6.10 × 10
15
u
23
+ 2.24 × 10
15
u
22
+ · · · + 4.71 × 10
16
b − 9.49 ×
10
16
, 3.77 × 10
16
u
23
− 4.37 × 10
15
u
22
+ · · · + 1.14 × 10
17
a + 1.29 ×
10
18
, u
24
− 2u
23
+ · · · + 20u + 17i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−0.329920u
23
+ 0.0381861u
22
+ ··· − 16.1056u − 11.2680
0.129504u
23
− 0.0474822u
22
+ ··· + 6.03349u + 2.01659
a
8
=
1
−u
2
a
6
=
0.134080u
23
+ 0.273604u
22
+ ··· + 18.4960u + 7.55474
−0.0652274u
23
+ 0.230684u
22
+ ··· + 2.08553u − 0.246283
a
3
=
−0.525803u
23
+ 0.373005u
22
+ ··· − 21.1910u − 9.77304
0.290659u
23
− 0.568556u
22
+ ··· + 0.961671u + 1.16554
a
10
=
−u
u
3
+ u
a
5
=
0.0378807u
23
+ 0.376737u
22
+ ··· + 15.4253u + 5.78825
0.0130146u
23
+ 0.0806472u
22
+ ··· + 1.73550u + 0.00270381
a
12
=
0.381461u
23
+ 0.0579674u
22
+ ··· + 17.8645u + 15.5499
−0.233501u
23
+ 0.551364u
22
+ ··· + 3.42307u + 2.97882
a
2
=
−0.372396u
23
− 0.256379u
22
+ ··· − 28.9922u − 15.0699
0.158126u
23
− 0.156008u
22
+ ··· + 5.53212u + 2.08728
a
1
=
−0.171014u
23
+ 0.00109401u
22
+ ··· − 7.41524u − 4.78310
0.217158u
23
− 0.502812u
22
+ ··· − 2.31071u − 0.0127898
a
9
=
−0.561081u
23
+ 1.28719u
22
+ ··· − 10.6082u + 5.36892
−0.125093u
23
+ 0.0910163u
22
+ ··· + 0.476538u − 4.41213
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−
8343946159698214
47083027591501867
u
23
−
14877793040005974
47083027591501867
u
22
+···−
1332066838354670501
47083027591501867
u−
405177085834515952
47083027591501867
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
12
+ 14u
10
+ ··· + 12u + 1)
2
c
2
, c
4
(u
12
− 4u
11
+ 8u
10
− 5u
9
− 5u
8
+ 15u
7
− 9u
6
+ 8u
4
− 2u
3
− 2u
2
+ 4u − 1)
2
c
3
, c
6
(u
12
+ u
11
+ ··· + 36u + 8)
2
c
5
(u
12
− 2u
11
+ u
10
+ 2u
9
+ u
8
− 6u
7
+ 4u
6
+ 3u
5
− 6u
3
+ 3u
2
+ u − 1)
2
c
7
, c
9
, c
10
c
12
u
24
+ 2u
23
+ ··· − 20u + 17
c
8
, c
11
u
24
− 4u
23
+ ··· + 206508u + 103417
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
12
+ 28y
11
+ ··· − 136y + 1)
2
c
2
, c
4
(y
12
+ 14y
10
+ ··· − 12y + 1)
2
c
3
, c
6
(y
12
− 21y
11
+ ··· − 464y + 64)
2
c
5
(y
12
− 2y
11
+ ··· − 7y + 1)
2
c
7
, c
9
, c
10
c
12
y
24
+ 6y
23
+ ··· − 672y + 289
c
8
, c
11
y
24
+ 10y
23
+ ··· − 21593989544y + 10695075889
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.969635 + 0.106868I
a = 1.001160 + 0.317590I
b = −1.109170 + 0.168712I
−0.62669 + 4.39533I 1.05572 − 5.22312I
u = 0.969635 − 0.106868I
a = 1.001160 − 0.317590I
b = −1.109170 − 0.168712I
−0.62669 − 4.39533I 1.05572 + 5.22312I
u = 0.123724 + 1.022700I
a = 5.28074 − 2.03927I
b = −0.523623
−5.52228 4.00782 + 0.I
u = 0.123724 − 1.022700I
a = 5.28074 + 2.03927I
b = −0.523623
−5.52228 4.00782 + 0.I
u = 0.238605 + 1.047760I
a = 0.655906 + 0.223543I
b = 1.121780 − 0.617797I
0.439990 − 1.030190I 2.72057 + 1.44119I
u = 0.238605 − 1.047760I
a = 0.655906 − 0.223543I
b = 1.121780 + 0.617797I
0.439990 + 1.030190I 2.72057 − 1.44119I
u = 0.020698 + 1.152910I
a = 1.61672 − 1.91219I
b = −0.080299 − 0.791847I
−4.16359 − 1.32529I −2.28742 + 4.78445I
u = 0.020698 − 1.152910I
a = 1.61672 + 1.91219I
b = −0.080299 + 0.791847I
−4.16359 + 1.32529I −2.28742 − 4.78445I
u = 0.364095 + 1.182240I
a = 0.285055 − 0.547656I
b = −0.516192
−4.70703 −2.22072 + 0.I
u = 0.364095 − 1.182240I
a = 0.285055 + 0.547656I
b = −0.516192
−4.70703 −2.22072 + 0.I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.117212 + 0.716758I
a = 1.17962 − 1.95274I
b = −0.080299 + 0.791847I
−4.16359 + 1.32529I −2.28742 − 4.78445I
u = 0.117212 − 0.716758I
a = 1.17962 + 1.95274I
b = −0.080299 − 0.791847I
−4.16359 − 1.32529I −2.28742 + 4.78445I
u = −0.42521 + 1.35732I
a = −0.082612 + 0.195129I
b = −1.109170 − 0.168712I
−0.62669 − 4.39533I 1.05572 + 5.22312I
u = −0.42521 − 1.35732I
a = −0.082612 − 0.195129I
b = −1.109170 + 0.168712I
−0.62669 + 4.39533I 1.05572 − 5.22312I
u = −1.26329 + 0.77255I
a = −0.983614 − 0.427684I
b = 2.18164 + 0.33163I
11.04720 + 0.80453I 1.287091 + 0.160859I
u = −1.26329 − 0.77255I
a = −0.983614 + 0.427684I
b = 2.18164 − 0.33163I
11.04720 − 0.80453I 1.287091 − 0.160859I
u = 1.14727 + 1.03329I
a = −0.996717 + 0.865474I
b = 2.18164 + 0.33163I
11.04720 + 0.80453I 1.287091 + 0.160859I
u = 1.14727 − 1.03329I
a = −0.996717 − 0.865474I
b = 2.18164 − 0.33163I
11.04720 − 0.80453I 1.287091 − 0.160859I
u = 1.34944 + 0.76245I
a = 0.973078 − 0.515965I
b = −2.09405 + 0.51270I
10.75480 − 7.79830I 0.83048 + 4.22102I
u = 1.34944 − 0.76245I
a = 0.973078 + 0.515965I
b = −2.09405 − 0.51270I
10.75480 + 7.79830I 0.83048 − 4.22102I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.447244 + 0.047871I
a = −1.70744 − 1.42312I
b = 1.121780 − 0.617797I
0.439990 − 1.030190I 2.72057 + 1.44119I
u = −0.447244 − 0.047871I
a = −1.70744 + 1.42312I
b = 1.121780 + 0.617797I
0.439990 + 1.030190I 2.72057 − 1.44119I
u = −1.19493 + 1.10213I
a = 1.042810 + 0.655912I
b = −2.09405 + 0.51270I
10.75480 − 7.79830I 0.83048 + 4.22102I
u = −1.19493 − 1.10213I
a = 1.042810 − 0.655912I
b = −2.09405 − 0.51270I
10.75480 + 7.79830I 0.83048 − 4.22102I
13
III. I
u
3
= hb, −u
3
− u
2
+ 4a + 2u − 3, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
1
4
u
3
+
1
4
u
2
−
1
2
u +
3
4
0
a
8
=
1
−u
2
a
6
=
1
0
a
3
=
1
4
u
3
+
1
4
u
2
−
1
2
u +
3
4
0
a
10
=
−u
u
3
+ u
a
5
=
−u
u
3
+ u
2
+ u + 1
a
12
=
−u
3
−u
2
− u − 1
a
2
=
1
4
u
3
+
1
4
u
2
+
1
2
u +
3
4
−u
3
− u
2
− u − 1
a
1
=
u
−u
3
− u
2
− u − 1
a
9
=
u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
49
16
u
3
−
43
16
u
2
+
21
8
u −
29
16
14
(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
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
7
, c
9
u
4
+ u
2
+ u + 1
c
8
, c
11
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
10
, c
12
u
4
+ u
2
− u + 1
15
(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
4
− y
3
+ 2y
2
+ 7y + 4
c
7
, c
9
, c
10
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
8
, c
11
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = 1.112690 − 0.371716I
b = 0
−0.66484 − 1.39709I −1.91043 + 4.25783I
u = −0.547424 − 0.585652I
a = 1.112690 + 0.371716I
b = 0
−0.66484 + 1.39709I −1.91043 − 4.25783I
u = 0.547424 + 1.120870I
a = −0.237691 − 0.353773I
b = 0
−4.26996 + 7.64338I −3.62082 − 1.58240I
u = 0.547424 − 1.120870I
a = −0.237691 + 0.353773I
b = 0
−4.26996 − 7.64338I −3.62082 + 1.58240I
17
IV. I
u
4
= h13362a
5
u − 25075a
4
u + · · · + 39143a + 74777, −5a
5
u + 14a
4
u +
· · · + 10a
2
− 13a, u
2
+ 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
a
−0.500206a
5
u + 0.938682a
4
u + ··· − 1.46532a − 2.79927
a
8
=
1
1
a
6
=
−0.0900311a
5
u − 1.26744a
4
u + ··· + 3.52978a − 0.500618
0.0680942a
5
u − 1.17486a
4
u + ··· + 2.89286a + 0.341631
a
3
=
0.542657a
5
u − 0.659567a
4
u + ··· + 0.405121a + 2.59499
0.125332a
5
u − 2.12833a
4
u + ··· + 5.25085a − 2.46026
a
10
=
−u
0
a
5
=
−0.158125a
5
u − 0.0925766a
4
u + ··· + 0.636918a − 0.842249
0.0680942a
5
u − 1.17486a
4
u + ··· + 2.89286a + 0.341631
a
12
=
−0.138884a
5
u + 1.72882a
4
u + ··· − 1.87714a − 1.14648
1
a
2
=
0.202635a
5
u − 0.0151237a
4
u + ··· − 1.04395a + 0.630704
0.339086a
5
u − 2.83225a
4
u + ··· + 6.33399a + 0.331224
a
1
=
−1
0
a
9
=
0.280163a
5
u − 0.0168457a
4
u + ··· − 2.83113a + 1.59361
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
45304
26713
a
5
u +
242984
26713
a
4
u + ··· −
450232
26713
a −
205440
26713
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
7
, c
9
, c
10
c
12
(u
2
+ 1)
6
c
8
u
12
+ 2u
11
+ ··· + 192u + 64
c
11
u
12
− 2u
11
+ ··· − 192u + 64
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
3
, c
4
c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
5
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
7
, c
9
, c
10
c
12
(y + 1)
12
c
8
, c
11
y
12
− 12y
10
+ 736y
8
− 3584y
6
+ 9472y
4
− 9216y
2
+ 4096
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.973865 − 0.455201I
b = −1.073950 − 0.558752I
−3.28987 + 5.69302I −6.00000 − 5.51057I
u = 1.000000I
a = −0.008563 + 0.670038I
b = 1.002190 − 0.295542I
−1.39926 − 0.92430I −2.28328 + 0.79423I
u = 1.000000I
a = 1.320500 + 0.473476I
b = 1.002190 + 0.295542I
−1.39926 + 0.92430I −2.28328 − 0.79423I
u = 1.000000I
a = 0.143638 + 0.307302I
b = −1.073950 + 0.558752I
−3.28987 − 5.69302I −6.00000 + 5.51057I
u = 1.000000I
a = 1.96360 + 0.56994I
b = −0.428243 − 0.664531I
−5.18047 − 0.92430I −9.71672 + 0.79423I
u = 1.000000I
a = 2.55469 + 3.43444I
b = −0.428243 + 0.664531I
−5.18047 + 0.92430I −9.71672 − 0.79423I
u = − 1.000000I
a = −0.973865 + 0.455201I
b = −1.073950 + 0.558752I
−3.28987 − 5.69302I −6.00000 + 5.51057I
u = − 1.000000I
a = −0.008563 − 0.670038I
b = 1.002190 + 0.295542I
−1.39926 + 0.92430I −2.28328 − 0.79423I
u = − 1.000000I
a = 1.320500 − 0.473476I
b = 1.002190 − 0.295542I
−1.39926 − 0.92430I −2.28328 + 0.79423I
u = − 1.000000I
a = 0.143638 − 0.307302I
b = −1.073950 − 0.558752I
−3.28987 + 5.69302I −6.00000 − 5.51057I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = 1.96360 − 0.56994I
b = −0.428243 + 0.664531I
−5.18047 + 0.92430I −9.71672 − 0.79423I
u = − 1.000000I
a = 2.55469 − 3.43444I
b = −0.428243 − 0.664531I
−5.18047 − 0.92430I −9.71672 + 0.79423I
22
V. I
u
5
= hb, −u
3
+ a − u + 1, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
u
3
+ u − 1
0
a
8
=
1
−u
2
a
6
=
1
0
a
3
=
u
3
+ u − 1
0
a
10
=
−u
u
3
+ u
a
5
=
u
4
+ u
2
+ 1
−u
5
− 2u
3
+ u
2
− 2u + 1
a
12
=
−2u
5
− 3u
3
+ u
2
− 2u + 1
2u
5
− u
4
+ 3u
3
− 2u
2
+ 3u − 2
a
2
=
−u
4
+ u
3
− u
2
+ u − 2
u
5
+ 2u
3
− u
2
+ 2u − 1
a
1
=
−u
4
− u
2
− 1
u
5
+ 2u
3
− u
2
+ 2u − 1
a
9
=
u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
5
+ 3u
3
+ 2u
2
+ 3u − 4
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
u
6
c
4
(u + 1)
6
c
5
(u
3
− u
2
+ 1)
2
c
7
, c
9
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
8
, c
11
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
10
, c
12
u
6
+ u
5
+ 2u
4
+ 2u
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)
6
c
3
, c
6
y
6
c
5
(y
3
− y
2
+ 2y − 1)
2
c
7
, c
9
, c
10
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
8
, c
11
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = −0.122561 + 0.744862I
b = 0
−1.91067 − 2.82812I −0.28809 + 2.59975I
u = −0.498832 − 1.001300I
a = −0.122561 − 0.744862I
b = 0
−1.91067 + 2.82812I −0.28809 − 2.59975I
u = 0.284920 + 1.115140I
a = −1.75488
b = 0
−6.04826 −12.42382 + 0.I
u = 0.284920 − 1.115140I
a = −1.75488
b = 0
−6.04826 −12.42382 + 0.I
u = 0.713912 + 0.305839I
a = −0.122561 + 0.744862I
b = 0
−1.91067 − 2.82812I −0.28809 + 2.59975I
u = 0.713912 − 0.305839I
a = −0.122561 − 0.744862I
b = 0
−1.91067 + 2.82812I −0.28809 − 2.59975I
26
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
10
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· ((u
12
+ 14u
10
+ ··· + 12u + 1)
2
)(u
26
+ 7u
25
+ ··· + 801u + 256)
c
2
(u − 1)
10
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
· (u
12
− 4u
11
+ 8u
10
− 5u
9
− 5u
8
+ 15u
7
− 9u
6
+ 8u
4
− 2u
3
− 2u
2
+ 4u − 1)
2
· (u
26
− 5u
25
+ ··· − 97u + 16)
c
3
u
10
(u
6
− u
5
+ ··· − u + 1)
2
(u
12
+ u
11
+ ··· + 36u + 8)
2
· (u
26
+ 3u
25
+ ··· − 288u + 256)
c
4
(u + 1)
10
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
12
− 4u
11
+ 8u
10
− 5u
9
− 5u
8
+ 15u
7
− 9u
6
+ 8u
4
− 2u
3
− 2u
2
+ 4u − 1)
2
· (u
26
− 5u
25
+ ··· − 97u + 16)
c
5
((u
3
− u
2
+ 1)
2
)(u
4
+ 3u
3
+ ··· + 3u + 2)(u
12
− u
10
+ ··· − 3u
2
+ 1)
· (u
12
− 2u
11
+ u
10
+ 2u
9
+ u
8
− 6u
7
+ 4u
6
+ 3u
5
− 6u
3
+ 3u
2
+ u − 1)
2
· (u
26
+ 6u
25
+ ··· + 12u + 4)
c
6
u
10
(u
6
+ u
5
+ ··· + u + 1)
2
(u
12
+ u
11
+ ··· + 36u + 8)
2
· (u
26
+ 3u
25
+ ··· − 288u + 256)
c
7
, c
9
(u
2
+ 1)
6
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
24
+ 2u
23
+ ··· − 20u + 17)(u
26
+ 2u
24
+ ··· + u + 1)
c
8
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
12
+ 2u
11
+ ··· + 192u + 64)(u
24
− 4u
23
+ ··· + 206508u + 103417)
· (u
26
− 4u
25
+ ··· + 64u + 64)
c
10
, c
12
(u
2
+ 1)
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
24
+ 2u
23
+ ··· − 20u + 17)(u
26
+ 2u
24
+ ··· + u + 1)
c
11
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
12
− 2u
11
+ ··· − 192u + 64)(u
24
− 4u
23
+ ··· + 206508u + 103417)
· (u
26
− 4u
25
+ ··· + 64u + 64)
27
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
10
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
12
+ 28y
11
+ ··· − 136y + 1)
2
· (y
26
+ 29y
25
+ ··· − 2714689y + 65536)
c
2
, c
4
(y − 1)
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· ((y
12
+ 14y
10
+ ··· − 12y + 1)
2
)(y
26
− 7y
25
+ ··· − 801y + 256)
c
3
, c
6
y
10
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
12
− 21y
11
+ ··· − 464y + 64)
2
· (y
26
− 27y
25
+ ··· − 709632y + 65536)
c
5
(y
3
− y
2
+ 2y − 1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· ((y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
)(y
12
− 2y
11
+ ··· − 7y + 1)
2
· (y
26
− 4y
25
+ ··· + 8y + 16)
c
7
, c
9
, c
10
c
12
(y + 1)
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
24
+ 6y
23
+ ··· − 672y + 289)(y
26
+ 4y
25
+ ··· + 11y + 1)
c
8
, c
11
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
12
− 12y
10
+ 736y
8
− 3584y
6
+ 9472y
4
− 9216y
2
+ 4096)
· (y
24
+ 10y
23
+ ··· − 21593989544y + 10695075889)
· (y
26
+ 40y
25
+ ··· + 114688y + 4096)
28
