12a
0260
(K12a
0260
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 1 2 11 5 12 8 4 9
Solving Sequence
2,6
3 7
4,11
8 12 1 5 10 9
c
2
c
6
c
3
c
7
c
11
c
1
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.75234 × 10
17
u
39
+ 5.61074 × 10
17
u
38
+ ··· + 1.58801 × 10
18
b − 1.77103 × 10
18
,
− 9.73786 × 10
17
u
39
− 2.24750 × 10
17
u
38
+ ··· + 3.17601 × 10
18
a + 6.50880 × 10
18
,
u
40
+ 2u
39
+ ··· − 15u − 4i
I
u
2
= h142u
29
a + u
29
+ ··· − 811a + 77, 4u
28
a + u
29
+ ··· − 5a + 16, u
30
+ u
29
+ ··· + u − 1i
I
u
3
= h2u
4
− 2u
3
+ 2u
2
+ 2b − u, −2u
2
+ 2a + u − 2, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
u
4
= h−au + b − 2a + u + 1, a
2
− 2a + 2, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 109 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−1.75 × 10
17
u
39
+ 5.61 × 10
17
u
38
+ · · · + 1.59 × 10
18
b − 1.77 ×
10
18
, −9.74 × 10
17
u
39
− 2.25 × 10
17
u
38
+ · · · + 3.18 × 10
18
a + 6.51 ×
10
18
, u
40
+ 2u
39
+ · · · − 15u − 4i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
11
=
0.306607u
39
+ 0.0707647u
38
+ ··· − 2.18335u − 2.04936
0.110349u
39
− 0.353320u
38
+ ··· + 4.43538u + 1.11525
a
8
=
0.330016u
39
+ 0.209936u
38
+ ··· − 2.54790u − 1.41013
0.167912u
39
− 0.146809u
38
+ ··· + 3.63862u + 0.864836
a
12
=
0.233887u
39
+ 0.0964315u
38
+ ··· − 2.14298u − 1.71555
0.223896u
39
+ 0.0820644u
38
+ ··· + 1.09448u + 0.165309
a
1
=
u
2
+ 1
−u
4
a
5
=
u
5
+ 2u
3
+ u
−u
7
− u
5
+ u
a
10
=
0.606364u
39
+ 0.274704u
38
+ ··· − 4.91727u − 2.84677
0.385943u
39
− 0.202353u
38
+ ··· + 5.39621u + 1.32664
a
9
=
0.263635u
39
+ 0.0269093u
38
+ ··· − 1.67340u − 1.47960
0.148444u
39
− 0.225204u
38
+ ··· + 3.90113u + 0.775015
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1027807058031671441
794003375424954487
u
39
−
7796249979768242351
3176013501699817948
u
38
+ ··· −
1978648037828171537
794003375424954487
u +
67049658634384246
794003375424954487
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
+ 22u
39
+ ··· − u + 16
c
2
, c
6
u
40
− 2u
39
+ ··· + 15u − 4
c
3
, c
5
u
40
+ 2u
39
+ ··· + 871u − 676
c
4
u
40
− 3u
39
+ ··· + 512u + 2048
c
7
, c
9
, c
10
c
12
u
40
− 5u
39
+ ··· − 3u − 1
c
8
, c
11
32(32u
40
+ 48u
39
+ ··· + 8u + 4)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
− 6y
39
+ ··· − 3905y + 256
c
2
, c
6
y
40
+ 22y
39
+ ··· − y + 16
c
3
, c
5
y
40
− 34y
39
+ ··· + 2269839y + 456976
c
4
y
40
− 13y
39
+ ··· − 63176704y + 4194304
c
7
, c
9
, c
10
c
12
y
40
+ 27y
39
+ ··· + 25y + 1
c
8
, c
11
1024(1024y
40
− 27904y
39
+ ··· + 16y + 16)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.748783 + 0.635787I
a = 0.497441 − 0.487921I
b = −0.443502 + 0.321931I
−3.86456 − 4.42335I −6.59807 + 7.34601I
u = −0.748783 − 0.635787I
a = 0.497441 + 0.487921I
b = −0.443502 − 0.321931I
−3.86456 + 4.42335I −6.59807 − 7.34601I
u = 0.370444 + 0.884043I
a = −0.741241 − 0.879542I
b = −0.990076 + 0.305719I
1.27740 + 1.88898I −6.0015 − 15.6995I
u = 0.370444 − 0.884043I
a = −0.741241 + 0.879542I
b = −0.990076 − 0.305719I
1.27740 − 1.88898I −6.0015 + 15.6995I
u = 0.936692 + 0.132944I
a = −0.36069 − 2.07229I
b = −0.283700 − 0.679214I
−10.28620 − 2.94658I −8.50665 + 2.50672I
u = 0.936692 − 0.132944I
a = −0.36069 + 2.07229I
b = −0.283700 + 0.679214I
−10.28620 + 2.94658I −8.50665 − 2.50672I
u = −0.893287 + 0.111704I
a = −0.24516 + 2.54481I
b = −0.611222 + 0.896510I
−11.6323 + 12.6478I −5.02011 − 6.24043I
u = −0.893287 − 0.111704I
a = −0.24516 − 2.54481I
b = −0.611222 − 0.896510I
−11.6323 − 12.6478I −5.02011 + 6.24043I
u = −0.433282 + 1.016950I
a = −0.826445 + 0.289312I
b = −1.227630 + 0.661551I
−1.48385 − 1.77946I −1.213579 + 0.177328I
u = −0.433282 − 1.016950I
a = −0.826445 − 0.289312I
b = −1.227630 − 0.661551I
−1.48385 + 1.77946I −1.213579 − 0.177328I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.735196 + 0.474957I
a = 0.73676 + 1.52515I
b = 0.299735 + 0.089122I
−4.66772 − 7.25009I −3.73082 + 5.45853I
u = 0.735196 − 0.474957I
a = 0.73676 − 1.52515I
b = 0.299735 − 0.089122I
−4.66772 + 7.25009I −3.73082 − 5.45853I
u = 0.590773 + 1.005950I
a = 0.968619 + 0.798321I
b = 2.11021 + 1.04129I
−6.21633 + 12.24890I −5.37332 − 9.94766I
u = 0.590773 − 1.005950I
a = 0.968619 − 0.798321I
b = 2.11021 − 1.04129I
−6.21633 − 12.24890I −5.37332 + 9.94766I
u = −0.691554 + 0.944218I
a = 0.219338 − 0.024885I
b = 0.996837 − 0.702945I
−4.74262 − 0.98558I −10.53556 − 1.39688I
u = −0.691554 − 0.944218I
a = 0.219338 + 0.024885I
b = 0.996837 + 0.702945I
−4.74262 + 0.98558I −10.53556 + 1.39688I
u = −0.429290 + 1.094810I
a = 1.52361 + 0.07658I
b = 2.25201 + 0.30626I
−1.51361 − 4.99339I −1.46170 + 7.63475I
u = −0.429290 − 1.094810I
a = 1.52361 − 0.07658I
b = 2.25201 − 0.30626I
−1.51361 + 4.99339I −1.46170 − 7.63475I
u = −0.810513
a = −1.68768
b = 0.0637912
−1.48600 −8.82010
u = −0.298599 + 0.749021I
a = −0.230770 + 0.654861I
b = −0.010961 + 0.514630I
−0.340785 − 1.228130I −3.72246 + 5.05532I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.298599 − 0.749021I
a = −0.230770 − 0.654861I
b = −0.010961 − 0.514630I
−0.340785 + 1.228130I −3.72246 − 5.05532I
u = 0.043335 + 1.221830I
a = −1.41988 + 0.07791I
b = −2.52419 − 0.17469I
−10.36550 − 5.41067I −11.07269 + 4.06686I
u = 0.043335 − 1.221830I
a = −1.41988 − 0.07791I
b = −2.52419 + 0.17469I
−10.36550 + 5.41067I −11.07269 − 4.06686I
u = 0.340574 + 0.682840I
a = −0.201912 − 1.203320I
b = −1.136840 − 0.348081I
1.86966 + 1.36297I 7.37182 + 2.84076I
u = 0.340574 − 0.682840I
a = −0.201912 + 1.203320I
b = −1.136840 + 0.348081I
1.86966 − 1.36297I 7.37182 − 2.84076I
u = 0.732733
a = 0.0215748
b = 0.419703
−1.91322 −6.72230
u = 0.455122 + 1.187290I
a = 0.297888 + 0.394001I
b = 0.358967 + 0.124690I
−5.28776 + 4.30879I −10.28965 − 3.19866I
u = 0.455122 − 1.187290I
a = 0.297888 − 0.394001I
b = 0.358967 − 0.124690I
−5.28776 − 4.30879I −10.28965 + 3.19866I
u = −0.459206 + 1.219680I
a = 0.496160 + 0.913959I
b = 0.85669 + 1.97796I
−5.08353 − 4.54254I −11.30086 + 4.03212I
u = −0.459206 − 1.219680I
a = 0.496160 − 0.913959I
b = 0.85669 − 1.97796I
−5.08353 + 4.54254I −11.30086 − 4.03212I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395526 + 1.274220I
a = 1.88050 + 0.61513I
b = 2.81622 − 0.05833I
−15.9475 + 8.1867I −9.06394 − 3.34621I
u = −0.395526 − 1.274220I
a = 1.88050 − 0.61513I
b = 2.81622 + 0.05833I
−15.9475 − 8.1867I −9.06394 + 3.34621I
u = −0.521628 + 1.236120I
a = −2.58052 + 0.56454I
b = −3.72507 + 0.61373I
−15.0274 − 17.7587I −7.82233 + 9.25326I
u = −0.521628 − 1.236120I
a = −2.58052 − 0.56454I
b = −3.72507 − 0.61373I
−15.0274 + 17.7587I −7.82233 − 9.25326I
u = 0.380735 + 1.301160I
a = 1.75721 − 0.48165I
b = 2.71281 − 0.14779I
−14.8538 + 1.6038I −12.02430 − 0.97260I
u = 0.380735 − 1.301160I
a = 1.75721 + 0.48165I
b = 2.71281 + 0.14779I
−14.8538 − 1.6038I −12.02430 + 0.97260I
u = 0.538772 + 1.252000I
a = −1.97956 − 0.36072I
b = −2.92363 − 0.63492I
−13.7050 + 8.2667I −10.58240 − 5.91047I
u = 0.538772 − 1.252000I
a = −1.97956 + 0.36072I
b = −2.92363 + 0.63492I
−13.7050 − 8.2667I −10.58240 + 5.91047I
u = −0.481597 + 0.152677I
a = −0.83330 − 1.69163I
b = −0.018409 − 0.472499I
1.02330 + 1.25064I 5.09440 − 3.99293I
u = −0.481597 − 0.152677I
a = −0.83330 + 1.69163I
b = −0.018409 + 0.472499I
1.02330 − 1.25064I 5.09440 + 3.99293I
8
II. I
u
2
=
h142u
29
a+u
29
+· · ·−811a+77, 4u
28
a+u
29
+· · ·−5a +16, u
30
+u
29
+· · ·+u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
11
=
a
−0.181354au
29
− 0.00127714u
29
+ ··· + 1.03576a − 0.0983397
a
8
=
1.07791au
29
− 1.96424u
29
+ ··· − 0.00127714a + 2.75351
1.96424au
29
− 1.90166u
29
+ ··· + 0.246488a + 3.57216
a
12
=
0.494253au
29
− 0.609195u
29
+ ··· + 0.0574713a + 0.0919540
0.132822au
29
− 0.365262u
29
+ ··· + 0.227331a + 0.874840
a
1
=
u
2
+ 1
−u
4
a
5
=
u
5
+ 2u
3
+ u
−u
7
− u
5
+ u
a
10
=
u
29
+ 8u
27
+ ··· + 4u
3
+ u
u
29
+ 7u
27
+ ··· − u
3
− u
a
9
=
1.03576au
29
− 2.09834u
29
+ ··· − 0.246488a + 1.42784
0.937420au
29
+ 0.922095u
29
+ ··· + 0.181354a + 2.00128
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
29
− 4u
28
− 32u
27
− 28u
26
− 120u
25
− 96u
24
− 260u
23
−
196u
22
−332u
21
−256u
20
−196u
19
−204u
18
+ 76u
17
−72u
16
+ 224u
15
+ 52u
14
+ 136u
13
+
108u
12
−12u
11
+ 100u
10
−60u
9
+ 44u
8
−32u
7
−12u
6
−8u
5
−24u
4
+ 8u
3
−12u
2
+ 8u −6
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
30
+ 17u
29
+ ··· − u + 1)
2
c
2
, c
6
(u
30
− u
29
+ ··· − u − 1)
2
c
3
, c
5
(u
30
+ u
29
+ ··· + 7u − 1)
2
c
4
(u
30
+ u
29
+ ··· + u − 1)
2
c
7
, c
9
, c
10
c
12
u
60
+ 11u
59
+ ··· + 20u + 1
c
8
, c
11
u
60
+ 5u
59
+ ··· − 23472726u + 8156149
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
30
− 7y
29
+ ··· − 25y + 1)
2
c
2
, c
6
(y
30
+ 17y
29
+ ··· − y + 1)
2
c
3
, c
5
(y
30
− 31y
29
+ ··· − 49y + 1)
2
c
4
(y
30
− 11y
29
+ ··· − y + 1)
2
c
7
, c
9
, c
10
c
12
y
60
+ 43y
59
+ ··· + 64y + 1
c
8
, c
11
y
60
− 37y
59
+ ··· − 1403816325059308y + 66522766510201
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.095027 + 1.028250I
a = 1.034680 + 0.226441I
b = 2.30549 + 0.52767I
−5.04140 − 2.04857I −7.94351 + 2.92796I
u = 0.095027 + 1.028250I
a = 0.716670 + 0.339240I
b = 0.426153 − 0.394651I
−5.04140 − 2.04857I −7.94351 + 2.92796I
u = 0.095027 − 1.028250I
a = 1.034680 − 0.226441I
b = 2.30549 − 0.52767I
−5.04140 + 2.04857I −7.94351 − 2.92796I
u = 0.095027 − 1.028250I
a = 0.716670 − 0.339240I
b = 0.426153 + 0.394651I
−5.04140 + 2.04857I −7.94351 − 2.92796I
u = −0.486868 + 0.916512I
a = −0.940915 − 0.299954I
b = −1.039270 − 0.311684I
−1.61342 − 2.06909I −0.15841 + 3.38718I
u = −0.486868 + 0.916512I
a = −0.447231 + 0.917418I
b = −1.24616 + 1.37787I
−1.61342 − 2.06909I −0.15841 + 3.38718I
u = −0.486868 − 0.916512I
a = −0.940915 + 0.299954I
b = −1.039270 + 0.311684I
−1.61342 + 2.06909I −0.15841 − 3.38718I
u = −0.486868 − 0.916512I
a = −0.447231 − 0.917418I
b = −1.24616 − 1.37787I
−1.61342 + 2.06909I −0.15841 − 3.38718I
u = 0.336716 + 1.031390I
a = −0.398995 + 0.561283I
b = −1.50734 − 0.06821I
−6.92657 + 2.97945I −9.92079 − 5.34085I
u = 0.336716 + 1.031390I
a = 0.64157 + 1.48251I
b = 1.74824 + 1.30378I
−6.92657 + 2.97945I −9.92079 − 5.34085I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.336716 − 1.031390I
a = −0.398995 − 0.561283I
b = −1.50734 + 0.06821I
−6.92657 − 2.97945I −9.92079 + 5.34085I
u = 0.336716 − 1.031390I
a = 0.64157 − 1.48251I
b = 1.74824 − 1.30378I
−6.92657 − 2.97945I −9.92079 + 5.34085I
u = 0.500817 + 0.966472I
a = 0.522463 + 0.779303I
b = 0.877769 + 0.011516I
−2.27531 + 7.42449I −2.02063 − 8.82247I
u = 0.500817 + 0.966472I
a = −0.759314 − 1.014940I
b = −1.98900 − 1.15324I
−2.27531 + 7.42449I −2.02063 − 8.82247I
u = 0.500817 − 0.966472I
a = 0.522463 − 0.779303I
b = 0.877769 − 0.011516I
−2.27531 − 7.42449I −2.02063 + 8.82247I
u = 0.500817 − 0.966472I
a = −0.759314 + 1.014940I
b = −1.98900 + 1.15324I
−2.27531 − 7.42449I −2.02063 + 8.82247I
u = −0.272716 + 0.834978I
a = 4.75539 + 1.58121I
b = 5.93533 + 1.26168I
−3.79299 − 1.32269I −1.12281 + 4.79072I
u = −0.272716 + 0.834978I
a = 2.73856 − 4.77786I
b = 1.76585 − 4.35750I
−3.79299 − 1.32269I −1.12281 + 4.79072I
u = −0.272716 − 0.834978I
a = 4.75539 − 1.58121I
b = 5.93533 − 1.26168I
−3.79299 + 1.32269I −1.12281 − 4.79072I
u = −0.272716 − 0.834978I
a = 2.73856 + 4.77786I
b = 1.76585 + 4.35750I
−3.79299 + 1.32269I −1.12281 − 4.79072I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.856648
a = 0.36456 + 2.45841I
b = −0.369614 + 0.732227I
−10.8641 −7.49220
u = −0.856648
a = 0.36456 − 2.45841I
b = −0.369614 − 0.732227I
−10.8641 −7.49220
u = −0.851057 + 0.073998I
a = 1.134850 + 0.440270I
b = −0.235397 + 0.177357I
−6.70542 + 6.72016I −3.40084 − 4.93754I
u = −0.851057 + 0.073998I
a = 0.02043 − 2.70525I
b = 0.471768 − 0.912252I
−6.70542 + 6.72016I −3.40084 − 4.93754I
u = −0.851057 − 0.073998I
a = 1.134850 − 0.440270I
b = −0.235397 − 0.177357I
−6.70542 − 6.72016I −3.40084 + 4.93754I
u = −0.851057 − 0.073998I
a = 0.02043 + 2.70525I
b = 0.471768 + 0.912252I
−6.70542 − 6.72016I −3.40084 + 4.93754I
u = 0.814472 + 0.061657I
a = −0.211672 − 0.026337I
b = −0.622855 + 0.448979I
−5.23568 − 1.35458I −1.234126 + 0.230757I
u = 0.814472 + 0.061657I
a = 0.71424 + 2.65174I
b = 0.706924 + 1.195690I
−5.23568 − 1.35458I −1.234126 + 0.230757I
u = 0.814472 − 0.061657I
a = −0.211672 + 0.026337I
b = −0.622855 − 0.448979I
−5.23568 + 1.35458I −1.234126 − 0.230757I
u = 0.814472 − 0.061657I
a = 0.71424 − 2.65174I
b = 0.706924 − 1.195690I
−5.23568 + 1.35458I −1.234126 − 0.230757I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.517153 + 0.543315I
a = 0.374179 + 1.229410I
b = 0.087079 + 0.755551I
−0.57483 − 2.05267I 2.41797 + 3.48780I
u = −0.517153 + 0.543315I
a = −1.328260 + 0.442484I
b = −0.139959 − 0.267825I
−0.57483 − 2.05267I 2.41797 + 3.48780I
u = −0.517153 − 0.543315I
a = 0.374179 − 1.229410I
b = 0.087079 − 0.755551I
−0.57483 + 2.05267I 2.41797 − 3.48780I
u = −0.517153 − 0.543315I
a = −1.328260 − 0.442484I
b = −0.139959 + 0.267825I
−0.57483 + 2.05267I 2.41797 − 3.48780I
u = 0.552271 + 0.456360I
a = 0.048193 + 0.721700I
b = 0.879122 + 0.103276I
−0.86006 − 3.18388I 1.51706 + 3.33039I
u = 0.552271 + 0.456360I
a = −1.00716 − 1.45803I
b = −0.385363 + 0.145063I
−0.86006 − 3.18388I 1.51706 + 3.33039I
u = 0.552271 − 0.456360I
a = 0.048193 − 0.721700I
b = 0.879122 − 0.103276I
−0.86006 + 3.18388I 1.51706 − 3.33039I
u = 0.552271 − 0.456360I
a = −1.00716 + 1.45803I
b = −0.385363 − 0.145063I
−0.86006 + 3.18388I 1.51706 − 3.33039I
u = 0.429988 + 1.221650I
a = −0.770876 − 0.449946I
b = −0.527325 − 0.034027I
−9.03965 + 2.99724I −4.94829 − 3.11480I
u = 0.429988 + 1.221650I
a = −2.43427 + 1.26220I
b = −3.31200 + 0.90775I
−9.03965 + 2.99724I −4.94829 − 3.11480I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.429988 − 1.221650I
a = −0.770876 + 0.449946I
b = −0.527325 + 0.034027I
−9.03965 − 2.99724I −4.94829 + 3.11480I
u = 0.429988 − 1.221650I
a = −2.43427 − 1.26220I
b = −3.31200 − 0.90775I
−9.03965 − 2.99724I −4.94829 + 3.11480I
u = 0.484811 + 1.215220I
a = −0.098795 − 0.799736I
b = −0.458370 − 0.566062I
−8.64541 + 6.07028I −4.34155 − 3.40396I
u = 0.484811 + 1.215220I
a = 2.83314 + 0.69066I
b = 3.72402 + 0.94519I
−8.64541 + 6.07028I −4.34155 − 3.40396I
u = 0.484811 − 1.215220I
a = −0.098795 + 0.799736I
b = −0.458370 + 0.566062I
−8.64541 − 6.07028I −4.34155 + 3.40396I
u = 0.484811 − 1.215220I
a = 2.83314 − 0.69066I
b = 3.72402 − 0.94519I
−8.64541 − 6.07028I −4.34155 + 3.40396I
u = −0.420533 + 1.243280I
a = −0.106443 − 0.515997I
b = −0.26568 − 1.43136I
−10.69750 + 2.28828I −7.38974 − 1.78470I
u = −0.420533 + 1.243280I
a = −2.05833 − 0.35082I
b = −3.04741 + 0.37403I
−10.69750 + 2.28828I −7.38974 − 1.78470I
u = −0.420533 − 1.243280I
a = −0.106443 + 0.515997I
b = −0.26568 + 1.43136I
−10.69750 − 2.28828I −7.38974 + 1.78470I
u = −0.420533 − 1.243280I
a = −2.05833 + 0.35082I
b = −3.04741 − 0.37403I
−10.69750 − 2.28828I −7.38974 + 1.78470I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.496075 + 1.226990I
a = −0.788632 − 0.515998I
b = −1.20409 − 1.35223I
−10.1523 − 11.5895I −6.39391 + 7.89908I
u = −0.496075 + 1.226990I
a = 2.65406 − 0.36532I
b = 3.86845 − 0.40313I
−10.1523 − 11.5895I −6.39391 + 7.89908I
u = −0.496075 − 1.226990I
a = −0.788632 + 0.515998I
b = −1.20409 + 1.35223I
−10.1523 + 11.5895I −6.39391 − 7.89908I
u = −0.496075 − 1.226990I
a = 2.65406 + 0.36532I
b = 3.86845 + 0.40313I
−10.1523 + 11.5895I −6.39391 − 7.89908I
u = −0.462371 + 1.241170I
a = 1.76758 − 0.00509I
b = 2.68786 − 0.84395I
−14.5974 − 4.6970I −10.66421 + 3.29760I
u = −0.462371 + 1.241170I
a = −2.42951 + 0.13001I
b = −3.65543 + 0.03686I
−14.5974 − 4.6970I −10.66421 + 3.29760I
u = −0.462371 − 1.241170I
a = 1.76758 + 0.00509I
b = 2.68786 + 0.84395I
−14.5974 + 4.6970I −10.66421 − 3.29760I
u = −0.462371 − 1.241170I
a = −2.42951 − 0.13001I
b = −3.65543 − 0.03686I
−14.5974 + 4.6970I −10.66421 − 3.29760I
u = 0.441992
a = 0.45986 + 1.89002I
b = 1.021210 − 0.572546I
−4.34249 −5.30020
u = 0.441992
a = 0.45986 − 1.89002I
b = 1.021210 + 0.572546I
−4.34249 −5.30020
17
III.
I
u
3
= h2u
4
− 2u
3
+ 2u
2
+ 2b − u, −2u
2
+ 2a + u − 2, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
11
=
u
2
−
1
2
u + 1
−u
4
+ u
3
− u
2
+
1
2
u
a
8
=
u
2
+
1
2
u + 1
−u
4
+ u
3
− u
2
+
3
2
u
a
12
=
3
2
u
2
+
3
2
−
3
2
u
4
+ u
3
− u
2
+ u
a
1
=
u
2
+ 1
−u
4
a
5
=
u
4
+ u
2
+ 1
u
4
a
10
=
2u
2
+ 2
−2u
4
+ 2u
3
− 2u
2
+ 2u
a
9
=
1
2
u
2
+
1
2
−
1
2
u
4
+ u
3
− u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17
4
u
4
−
17
4
u
3
+
33
4
u
2
− 4u +
9
4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
4
u
5
c
5
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
, c
9
(u + 1)
5
c
8
32(32u
5
− 16u
4
− 16u
3
+ 4u
2
+ 2u + 1)
c
10
, c
12
(u − 1)
5
c
11
32(32u
5
+ 16u
4
− 16u
3
− 4u
2
+ 2u − 1)
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
6
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
, c
5
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
4
y
5
c
7
, c
9
, c
10
c
12
(y −1)
5
c
8
, c
11
1024(1024y
5
− 1280y
4
+ 512y
3
− 48y
2
− 4y −1)
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.608249 − 0.968939I
b = 1.036800 + 0.070336I
1.31583 − 1.53058I −3.76579 − 4.07189I
u = −0.339110 − 0.822375I
a = 0.608249 + 0.968939I
b = 1.036800 − 0.070336I
1.31583 + 1.53058I −3.76579 + 4.07189I
u = 0.766826
a = 1.20461
b = −0.0994683
−0.756147 3.58700
u = 0.455697 + 1.200150I
a = −0.460554 + 0.493736I
b = −0.73706 + 1.22197I
−4.22763 + 4.40083I −0.40273 − 3.06842I
u = 0.455697 − 1.200150I
a = −0.460554 − 0.493736I
b = −0.73706 − 1.22197I
−4.22763 − 4.40083I −0.40273 + 3.06842I
21
IV. I
u
4
= h−au + b − 2a + u + 1, a
2
− 2a + 2, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u + 1
a
7
=
u
u
a
4
=
0
u
a
11
=
a
au + 2a − u − 1
a
8
=
a + u − 2
a − 3
a
12
=
a
a − u − 1
a
1
=
−u
−u
a
5
=
1
u + 1
a
10
=
au − u
au − u
a
9
=
au + a − u − 2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u − 4
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
6
(u
2
− u + 1)
2
c
2
, c
5
(u
2
+ u + 1)
2
c
4
u
4
− u
2
+ 1
c
7
, c
9
, c
10
c
12
(u
2
+ 1)
2
c
8
u
4
− 2u
3
+ 2u
2
− 4u + 4
c
11
u
4
+ 2u
3
+ 2u
2
+ 4u + 4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
(y
2
+ y + 1)
2
c
4
(y
2
− y + 1)
2
c
7
, c
9
, c
10
c
12
(y + 1)
4
c
8
, c
11
y
4
− 4y
2
+ 16
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.00000 + 1.00000I
b = 0.13397 + 1.50000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 1.00000 − 1.00000I
b = 1.86603 − 1.50000I
−3.28987 − 2.02988I −6.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 1.00000 + 1.00000I
b = 1.86603 + 1.50000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 1.00000 − 1.00000I
b = 0.13397 − 1.50000I
−3.28987 + 2.02988I −6.00000 − 3.46410I
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
5
− 3u
4
+ ··· − u + 1)(u
30
+ 17u
29
+ ··· − u + 1)
2
· (u
40
+ 22u
39
+ ··· − u + 16)
c
2
((u
2
+ u + 1)
2
)(u
5
− u
4
+ ··· + u − 1)(u
30
− u
29
+ ··· − u − 1)
2
· (u
40
− 2u
39
+ ··· + 15u − 4)
c
3
((u
2
− u + 1)
2
)(u
5
+ u
4
+ ··· + u − 1)(u
30
+ u
29
+ ··· + 7u − 1)
2
· (u
40
+ 2u
39
+ ··· + 871u − 676)
c
4
u
5
(u
4
− u
2
+ 1)(u
30
+ u
29
+ ··· + u − 1)
2
· (u
40
− 3u
39
+ ··· + 512u + 2048)
c
5
((u
2
+ u + 1)
2
)(u
5
− u
4
+ ··· + u + 1)(u
30
+ u
29
+ ··· + 7u − 1)
2
· (u
40
+ 2u
39
+ ··· + 871u − 676)
c
6
((u
2
− u + 1)
2
)(u
5
+ u
4
+ ··· + u + 1)(u
30
− u
29
+ ··· − u − 1)
2
· (u
40
− 2u
39
+ ··· + 15u − 4)
c
7
, c
9
((u + 1)
5
)(u
2
+ 1)
2
(u
40
− 5u
39
+ ··· − 3u − 1)
· (u
60
+ 11u
59
+ ··· + 20u + 1)
c
8
1024(u
4
− 2u
3
+ ··· − 4u + 4)(32u
5
− 16u
4
+ ··· + 2u + 1)
· (32u
40
+ 48u
39
+ ··· + 8u + 4)
· (u
60
+ 5u
59
+ ··· − 23472726u + 8156149)
c
10
, c
12
((u − 1)
5
)(u
2
+ 1)
2
(u
40
− 5u
39
+ ··· − 3u − 1)
· (u
60
+ 11u
59
+ ··· + 20u + 1)
c
11
1024(u
4
+ 2u
3
+ ··· + 4u + 4)(32u
5
+ 16u
4
+ ··· + 2u − 1)
· (32u
40
+ 48u
39
+ ··· + 8u + 4)
· (u
60
+ 5u
59
+ ··· − 23472726u + 8156149)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)
2
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· ((y
30
− 7y
29
+ ··· − 25y + 1)
2
)(y
40
− 6y
39
+ ··· − 3905y + 256)
c
2
, c
6
((y
2
+ y + 1)
2
)(y
5
+ 3y
4
+ ··· − y −1)(y
30
+ 17y
29
+ ··· − y + 1)
2
· (y
40
+ 22y
39
+ ··· − y + 16)
c
3
, c
5
(y
2
+ y + 1)
2
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
· (y
30
− 31y
29
+ ··· − 49y + 1)
2
· (y
40
− 34y
39
+ ··· + 2269839y + 456976)
c
4
y
5
(y
2
− y + 1)
2
(y
30
− 11y
29
+ ··· − y + 1)
2
· (y
40
− 13y
39
+ ··· − 63176704y + 4194304)
c
7
, c
9
, c
10
c
12
((y −1)
5
)(y + 1)
4
(y
40
+ 27y
39
+ ··· + 25y + 1)
· (y
60
+ 43y
59
+ ··· + 64y + 1)
c
8
, c
11
1048576(y
4
− 4y
2
+ 16)(1024y
5
− 1280y
4
+ ··· − 4y −1)
· (1024y
40
− 27904y
39
+ ··· + 16y + 16)
· (y
60
− 37y
59
+ ··· − 1403816325059308y + 66522766510201)
27
