12n
0651
(K12n
0651
)
A knot diagram
1
Linearized knot diagam
3 8 10 11 12 4 2 12 7 6 9 6
Solving Sequence
6,12
1
5,9
8 11 4 7 10 3 2
c
12
c
5
c
8
c
11
c
4
c
6
c
10
c
3
c
2
c
1
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.87738 × 10
79
u
37
− 4.81123 × 10
79
u
36
+ ··· + 1.09631 × 10
80
b + 6.40170 × 10
79
,
− 5.87738 × 10
79
u
37
− 4.81123 × 10
79
u
36
+ ··· + 1.09631 × 10
80
a − 4.56137 × 10
79
, u
38
+ u
37
+ ··· − 2u + 1i
I
u
2
= h−1.04653 × 10
27
u
29
+ 6.40175 × 10
26
u
28
+ ··· + 7.20755 × 10
25
b − 2.20858 × 10
27
,
− 1.04653 × 10
27
u
29
+ 6.40175 × 10
26
u
28
+ ··· + 7.20755 × 10
25
a − 2.13651 × 10
27
, u
30
+ u
28
+ ··· + 2u + 1i
I
u
3
= h−8.10037 × 10
37
u
23
− 8.29349 × 10
37
u
22
+ ··· + 3.72935 × 10
40
b + 3.34631 × 10
39
,
− 4.67951 × 10
43
u
23
− 5.81164 × 10
43
u
22
+ ··· + 3.64130 × 10
45
a + 6.70319 × 10
45
,
u
24
+ u
23
+ ··· − 72u + 389i
I
u
4
= h−7.05840 × 10
36
u
23
+ 1.01927 × 10
37
u
22
+ ··· + 1.33403 × 10
40
b − 9.50718 × 10
39
,
− 4.57492 × 10
42
u
23
+ 4.23759 × 10
42
u
22
+ ··· + 2.64466 × 10
45
a − 1.17455 × 10
45
,
u
24
+ 12u
22
+ ··· + 1224u + 631i
I
u
5
= hb, a − 1, u
3
− u
2
+ 2u − 1i
* 5 irreducible components of dim
C
= 0, with total 119 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−5.88×10
79
u
37
−4.81×10
79
u
36
+· · ·+1.10×10
80
b+6.40×10
79
, −5.88×
10
79
u
37
−4.81×10
79
u
36
+· · ·+1.10×10
80
a−4.56×10
79
, u
38
+u
37
+· · ·−2u+1i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
u
u
a
9
=
0.536107u
37
+ 0.438858u
36
+ ··· + 5.20206u + 0.416067
0.536107u
37
+ 0.438858u
36
+ ··· + 5.20206u − 0.583933
a
8
=
1
0.536107u
37
+ 0.438858u
36
+ ··· + 5.20206u − 0.583933
a
11
=
0.551933u
37
+ 0.184165u
36
+ ··· + 5.75746u − 1.74427
0.0158259u
37
− 0.254694u
36
+ ··· + 0.555407u − 2.16033
a
4
=
0.880326u
37
+ 1.05073u
36
+ ··· + 6.21709u − 0.512405
0.415309u
37
+ 0.344712u
36
+ ··· + 6.06497u − 1.60045
a
7
=
0.370131u
37
+ 0.566178u
36
+ ··· + 2.00968u + 1.02387
0.484697u
37
+ 0.579181u
36
+ ··· + 5.16811u − 0.0626616
a
10
=
0.551933u
37
+ 0.184165u
36
+ ··· + 5.75746u − 1.74427
−0.138322u
37
− 0.383483u
36
+ ··· − 0.732063u − 1.79256
a
3
=
−0.603900u
37
− 0.605524u
36
+ ··· − 4.99750u + 1.42841
−0.121286u
37
+ 0.101025u
36
+ ··· − 2.38717u + 2.45390
a
2
=
−0.624236u
37
− 0.742981u
36
+ ··· − 4.51871u − 0.410519
−0.794152u
37
− 0.640181u
36
+ ··· − 8.11717u + 1.88051
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.67858u
37
− 0.851719u
36
+ ··· − 22.0981u + 8.20713
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
38
+ 20u
37
+ ··· + 65536u + 65536
c
2
, c
7
u
38
− 16u
37
+ ··· − 2560u + 256
c
3
, c
9
u
38
− 2u
37
+ ··· − 8u + 1
c
4
u
38
− 22u
36
+ ··· − 1528u + 1456
c
5
, c
12
u
38
− u
37
+ ··· + 2u + 1
c
6
u
38
− 19u
37
+ ··· − 3108u + 245
c
8
, c
11
u
38
+ 12u
37
+ ··· + 1309u + 245
c
10
u
38
− u
37
+ ··· − 189u + 61
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
38
− 4y
37
+ ··· − 15032385536y + 4294967296
c
2
, c
7
y
38
− 20y
37
+ ··· − 65536y + 65536
c
3
, c
9
y
38
+ 20y
37
+ ··· + 38y + 1
c
4
y
38
− 44y
37
+ ··· − 18656544y + 2119936
c
5
, c
12
y
38
+ 51y
37
+ ··· + 14y + 1
c
6
y
38
− 9y
37
+ ··· + 500486y + 60025
c
8
, c
11
y
38
+ 12y
37
+ ··· + 698299y + 60025
c
10
y
38
− 27y
37
+ ··· − 45603y + 3721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.769678 + 0.293616I
a = 0.990107 + 0.482059I
b = −0.009893 + 0.482059I
−1.363000 − 0.273225I −9.42966 + 1.77588I
u = 0.769678 − 0.293616I
a = 0.990107 − 0.482059I
b = −0.009893 − 0.482059I
−1.363000 + 0.273225I −9.42966 − 1.77588I
u = 0.145322 + 0.514446I
a = 0.88401 + 1.27389I
b = −0.115995 + 1.273890I
−5.36598 − 0.46970I −5.55031 + 3.34064I
u = 0.145322 − 0.514446I
a = 0.88401 − 1.27389I
b = −0.115995 − 1.273890I
−5.36598 + 0.46970I −5.55031 − 3.34064I
u = −0.471950 + 0.049779I
a = 1.55201 − 0.71853I
b = 0.552008 − 0.718532I
0.91968 − 1.81363I −0.50505 + 3.48218I
u = −0.471950 − 0.049779I
a = 1.55201 + 0.71853I
b = 0.552008 + 0.718532I
0.91968 + 1.81363I −0.50505 − 3.48218I
u = 0.451414 + 0.116571I
a = 1.47086 − 1.11033I
b = 0.470864 − 1.110330I
−1.87643 − 5.76844I −7.26109 + 7.17876I
u = 0.451414 − 0.116571I
a = 1.47086 + 1.11033I
b = 0.470864 + 1.110330I
−1.87643 + 5.76844I −7.26109 − 7.17876I
u = −1.52338 + 0.33853I
a = 0.660164 − 0.721621I
b = −0.339836 − 0.721621I
−9.11191 + 1.39764I 0
u = −1.52338 − 0.33853I
a = 0.660164 + 0.721621I
b = −0.339836 + 0.721621I
−9.11191 − 1.39764I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.41128 + 1.51296I
a = 0.046743 + 0.690253I
b = −0.953257 + 0.690253I
1.47310 + 1.34582I 0
u = 0.41128 − 1.51296I
a = 0.046743 − 0.690253I
b = −0.953257 − 0.690253I
1.47310 − 1.34582I 0
u = −0.016686 + 0.398344I
a = 1.31541 − 1.24871I
b = 0.315412 − 1.248710I
−1.19389 − 3.34823I 1.04129 + 3.46922I
u = −0.016686 − 0.398344I
a = 1.31541 + 1.24871I
b = 0.315412 + 1.248710I
−1.19389 + 3.34823I 1.04129 − 3.46922I
u = −0.310405 + 0.170863I
a = 1.95426 − 0.20841I
b = 0.954255 − 0.208414I
2.29409 − 1.35414I 2.68942 + 3.98636I
u = −0.310405 − 0.170863I
a = 1.95426 + 0.20841I
b = 0.954255 + 0.208414I
2.29409 + 1.35414I 2.68942 − 3.98636I
u = −0.19463 + 1.64159I
a = 0.195587 − 1.105580I
b = −0.804413 − 1.105580I
0.19003 + 7.83950I 0
u = −0.19463 − 1.64159I
a = 0.195587 + 1.105580I
b = −0.804413 + 1.105580I
0.19003 − 7.83950I 0
u = 0.230980 + 0.257221I
a = 1.92353 − 0.29790I
b = 0.923530 − 0.297905I
1.90925 − 2.85593I −1.44584 + 3.55066I
u = 0.230980 − 0.257221I
a = 1.92353 + 0.29790I
b = 0.923530 + 0.297905I
1.90925 + 2.85593I −1.44584 − 3.55066I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.063281 + 0.328463I
a = 1.38439 + 1.55227I
b = 0.38439 + 1.55227I
−4.17774 + 8.19316I 2.57658 − 7.35106I
u = 0.063281 − 0.328463I
a = 1.38439 − 1.55227I
b = 0.38439 − 1.55227I
−4.17774 − 8.19316I 2.57658 + 7.35106I
u = −0.29571 + 1.65878I
a = −0.115023 + 0.852244I
b = −1.115020 + 0.852244I
7.44352 + 10.43800I 0
u = −0.29571 − 1.65878I
a = −0.115023 − 0.852244I
b = −1.115020 − 0.852244I
7.44352 − 10.43800I 0
u = 0.33699 + 1.67811I
a = 0.190397 − 0.903287I
b = −0.809603 − 0.903287I
6.17744 − 3.28622I 0
u = 0.33699 − 1.67811I
a = 0.190397 + 0.903287I
b = −0.809603 + 0.903287I
6.17744 + 3.28622I 0
u = 0.08401 + 1.79386I
a = −0.064653 − 0.833573I
b = −1.064650 − 0.833573I
9.31632 − 4.00848I 0
u = 0.08401 − 1.79386I
a = −0.064653 + 0.833573I
b = −1.064650 + 0.833573I
9.31632 + 4.00848I 0
u = −0.14610 + 1.84614I
a = 0.181975 + 0.975853I
b = −0.818025 + 0.975853I
8.09306 − 3.65630I 0
u = −0.14610 − 1.84614I
a = 0.181975 − 0.975853I
b = −0.818025 − 0.975853I
8.09306 + 3.65630I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.83573 + 1.82057I
a = 0.065993 − 1.107020I
b = −0.93401 − 1.10702I
6.5788 + 17.8341I 0
u = −0.83573 − 1.82057I
a = 0.065993 + 1.107020I
b = −0.93401 + 1.10702I
6.5788 − 17.8341I 0
u = −0.69403 + 1.88222I
a = 0.117388 − 0.861621I
b = −0.882612 − 0.861621I
8.47233 + 2.68142I 0
u = −0.69403 − 1.88222I
a = 0.117388 + 0.861621I
b = −0.882612 + 0.861621I
8.47233 − 2.68142I 0
u = 0.61560 + 1.91074I
a = 0.092836 + 1.092150I
b = −0.90716 + 1.09215I
8.46080 − 11.17390I 0
u = 0.61560 − 1.91074I
a = 0.092836 − 1.092150I
b = −0.90716 − 1.09215I
8.46080 + 11.17390I 0
u = 0.88007 + 1.80431I
a = 0.154018 + 0.915742I
b = −0.845982 + 0.915742I
6.17371 − 9.49223I 0
u = 0.88007 − 1.80431I
a = 0.154018 − 0.915742I
b = −0.845982 − 0.915742I
6.17371 + 9.49223I 0
8
II.
I
u
2
= h−1.05×10
27
u
29
+6.40×10
26
u
28
+· · ·+7.21×10
25
b−2.21×10
27
, −1.05×
10
27
u
29
+6.40×10
26
u
28
+· · ·+7.21×10
25
a−2.14×10
27
, u
30
+u
28
+· · ·+2u+1i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
u
u
a
9
=
14.5199u
29
− 8.88201u
28
+ ··· + 8.39444u + 29.6427
14.5199u
29
− 8.88201u
28
+ ··· + 8.39444u + 30.6427
a
8
=
−1
14.5199u
29
− 8.88201u
28
+ ··· + 8.39444u + 30.6427
a
11
=
−4.06825u
29
+ 4.09990u
28
+ ··· − 9.54483u − 14.8631
10.4516u
29
− 4.78211u
28
+ ··· − 1.15039u + 14.7796
a
4
=
7.78523u
29
− 6.01099u
28
+ ··· + 15.7391u + 19.5443
20.7671u
29
− 10.4401u
28
+ ··· + 7.40959u + 38.1324
a
7
=
−11.5035u
29
+ 9.71998u
28
+ ··· − 22.2318u − 32.1347
−17.0902u
29
+ 9.54834u
28
+ ··· − 10.8920u − 36.3401
a
10
=
−4.06825u
29
+ 4.09990u
28
+ ··· − 9.54483u − 14.8631
9.84035u
29
− 3.57850u
28
+ ··· − 5.28194u + 10.6797
a
3
=
−0.746741u
29
− 2.39409u
28
+ ··· + 16.9625u + 9.48042
−13.0525u
29
+ 6.82801u
28
+ ··· + 0.265643u − 20.2601
a
2
=
−5.91549u
29
− 0.395824u
28
+ ··· + 17.1709u + 0.984383
−29.7670u
29
+ 14.4764u
28
+ ··· + 2.95769u − 47.2696
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
5442943404112663257393818411
72075479222065155542383621
u
29
+
2290494485521047290127820068
72075479222065155542383621
u
28
+
··· +
2199058764523746184678942173
72075479222065155542383621
u −
9035792265526014806594255672
72075479222065155542383621
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
− 20u
29
+ ··· − 157u + 9
c
2
u
30
− 10u
28
+ ··· − u + 3
c
3
, c
9
u
30
+ u
29
+ ··· − 4u + 1
c
4
u
30
− u
29
+ ··· + 32u + 52
c
5
u
30
+ u
28
+ ··· − 2u + 1
c
6
u
30
+ 18u
29
+ ··· − u
2
+ 1
c
7
u
30
− 10u
28
+ ··· + u + 3
c
8
u
30
+ 11u
29
+ ··· + 5u + 1
c
10
u
30
− 4u
28
+ ··· + 5u + 3
c
11
u
30
− 11u
29
+ ··· − 5u + 1
c
12
u
30
+ u
28
+ ··· + 2u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 4y
29
+ ··· − 817y + 81
c
2
, c
7
y
30
− 20y
29
+ ··· − 157y + 9
c
3
, c
9
y
30
− 9y
29
+ ··· + 10y + 1
c
4
y
30
− 9y
29
+ ··· + 952y + 2704
c
5
, c
12
y
30
+ 2y
29
+ ··· − 14y + 1
c
6
y
30
− 10y
29
+ ··· − 2y + 1
c
8
, c
11
y
30
+ 11y
29
+ ··· + 27y + 1
c
10
y
30
− 8y
29
+ ··· − 43y + 9
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.192553 + 1.043410I
a = −0.186549 + 1.226810I
b = 0.81345 + 1.22681I
−0.33621 + 6.09015I −3.88862 − 7.39365I
u = −0.192553 − 1.043410I
a = −0.186549 − 1.226810I
b = 0.81345 − 1.22681I
−0.33621 − 6.09015I −3.88862 + 7.39365I
u = −0.275781 + 0.879549I
a = 0.223505 + 0.732747I
b = 1.22350 + 0.73275I
2.85792 + 3.57779I 4.92513 − 8.66685I
u = −0.275781 − 0.879549I
a = 0.223505 − 0.732747I
b = 1.22350 − 0.73275I
2.85792 − 3.57779I 4.92513 + 8.66685I
u = 0.499454 + 0.690994I
a = −1.210630 − 0.663508I
b = −0.210632 − 0.663508I
−3.77754 − 2.97804I −4.88613 + 5.33573I
u = 0.499454 − 0.690994I
a = −1.210630 + 0.663508I
b = −0.210632 + 0.663508I
−3.77754 + 2.97804I −4.88613 − 5.33573I
u = 0.617119 + 0.976797I
a = −0.011660 − 1.138620I
b = 0.98834 − 1.13862I
1.65191 − 4.24761I 3.36736 + 1.91762I
u = 0.617119 − 0.976797I
a = −0.011660 + 1.138620I
b = 0.98834 + 1.13862I
1.65191 + 4.24761I 3.36736 − 1.91762I
u = 0.755859 + 0.951225I
a = −0.088028 − 0.491277I
b = 0.911972 − 0.491277I
1.88263 − 0.42999I 0.216000 + 0.636863I
u = 0.755859 − 0.951225I
a = −0.088028 + 0.491277I
b = 0.911972 + 0.491277I
1.88263 + 0.42999I 0.216000 − 0.636863I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.605699 + 0.450661I
a = −1.57115 + 0.40450I
b = −0.571149 + 0.404502I
−2.94832 − 4.03310I −3.08569 − 0.46145I
u = −0.605699 − 0.450661I
a = −1.57115 − 0.40450I
b = −0.571149 − 0.404502I
−2.94832 + 4.03310I −3.08569 + 0.46145I
u = 0.738105 + 0.100363I
a = −0.685141 − 1.115870I
b = 0.314859 − 1.115870I
−2.11126 − 3.24044I −8.53743 + 3.11023I
u = 0.738105 − 0.100363I
a = −0.685141 + 1.115870I
b = 0.314859 + 1.115870I
−2.11126 + 3.24044I −8.53743 − 3.11023I
u = 1.335800 + 0.011955I
a = −0.802388 − 0.480325I
b = 0.197612 − 0.480325I
0.403793 + 0.548900I −2.92133 − 2.10151I
u = 1.335800 − 0.011955I
a = −0.802388 + 0.480325I
b = 0.197612 + 0.480325I
0.403793 − 0.548900I −2.92133 + 2.10151I
u = 0.642239 + 0.139313I
a = −1.51104 − 0.81141I
b = −0.511044 − 0.811406I
−4.13100 + 6.13004I −10.9996 − 9.9739I
u = 0.642239 − 0.139313I
a = −1.51104 + 0.81141I
b = −0.511044 + 0.811406I
−4.13100 − 6.13004I −10.9996 + 9.9739I
u = −1.372170 + 0.319453I
a = −1.011380 + 0.367883I
b = −0.011383 + 0.367883I
0.40035 − 6.49171I −5.66132 + 6.20888I
u = −1.372170 − 0.319453I
a = −1.011380 − 0.367883I
b = −0.011383 − 0.367883I
0.40035 + 6.49171I −5.66132 − 6.20888I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.538379 + 0.006202I
a = −0.66784 + 1.45649I
b = 0.33216 + 1.45649I
−4.63983 + 8.15895I −14.9285 − 6.3499I
u = −0.538379 − 0.006202I
a = −0.66784 − 1.45649I
b = 0.33216 − 1.45649I
−4.63983 − 8.15895I −14.9285 + 6.3499I
u = −0.410661 + 0.302060I
a = −1.29493 + 1.22348I
b = −0.294926 + 1.223480I
−5.87855 + 0.33581I −10.20797 − 1.77628I
u = −0.410661 − 0.302060I
a = −1.29493 − 1.22348I
b = −0.294926 − 1.223480I
−5.87855 − 0.33581I −10.20797 + 1.77628I
u = −1.51392 + 0.29861I
a = −0.650786 + 0.746403I
b = 0.349214 + 0.746403I
−9.10945 + 1.47002I −4.0000 − 56.0927I
u = −1.51392 − 0.29861I
a = −0.650786 − 0.746403I
b = 0.349214 − 0.746403I
−9.10945 − 1.47002I −4.0000 + 56.0927I
u = −0.14376 + 1.63552I
a = 0.001371 + 0.952810I
b = 1.001370 + 0.952810I
5.51706 + 0.72621I 0
u = −0.14376 − 1.63552I
a = 0.001371 − 0.952810I
b = 1.001370 − 0.952810I
5.51706 − 0.72621I 0
u = 0.46435 + 1.70410I
a = −0.033350 − 0.978342I
b = 0.966650 − 0.978342I
5.41410 − 6.42832I 0
u = 0.46435 − 1.70410I
a = −0.033350 + 0.978342I
b = 0.966650 + 0.978342I
5.41410 + 6.42832I 0
14
III. I
u
3
= h−8.10 × 10
37
u
23
− 8.29 × 10
37
u
22
+ · · · + 3.73 × 10
40
b + 3.35 ×
10
39
, −4.68 × 10
43
u
23
− 5.81 × 10
43
u
22
+ · · · + 3.64 × 10
45
a + 6.70 ×
10
45
, u
24
+ u
23
+ · · · − 72u + 389i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
u
u
a
9
=
0.0128512u
23
+ 0.0159603u
22
+ ··· − 14.5752u − 1.84088
0.00217206u
23
+ 0.00222384u
22
+ ··· − 2.33706u − 0.0897290
a
8
=
0.0106791u
23
+ 0.0137365u
22
+ ··· − 12.2382u − 1.75115
0.00217206u
23
+ 0.00222384u
22
+ ··· − 2.33706u − 0.0897290
a
11
=
−0.00298677u
23
− 0.00907284u
22
+ ··· − 0.491641u + 4.86694
−0.00167288u
23
− 0.00194185u
22
+ ··· + 2.00850u − 0.281410
a
4
=
−0.00374148u
23
+ 0.000694410u
22
+ ··· + 9.49017u − 4.64825
0.0000211845u
23
+ 0.000246509u
22
+ ··· + 0.539375u + 0.850723
a
7
=
0.00166354u
23
− 0.00661729u
22
+ ··· − 7.23299u + 9.14342
−0.00359698u
23
− 0.00568733u
22
+ ··· + 2.35046u + 0.996357
a
10
=
−0.00298677u
23
− 0.00907284u
22
+ ··· − 0.491641u + 4.86694
−0.00346718u
23
− 0.00578265u
22
+ ··· + 2.73215u + 2.08607
a
3
=
0.00195405u
23
+ 0.00977649u
22
+ ··· + 3.63919u − 6.91853
0.00531328u
23
+ 0.00782872u
22
+ ··· − 3.79070u − 0.818042
a
2
=
0.0102467u
23
+ 0.0128559u
22
+ ··· − 10.6412u + 1.34843
0.00311597u
23
+ 0.00391760u
22
+ ··· − 2.20109u + 0.0846023
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0560152u
23
+ 0.0569676u
22
+ ··· − 65.8499u − 1.78467
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
+ 2u + 1)
8
c
2
, c
7
(u
3
+ u
2
− 1)
8
c
3
, c
9
u
24
+ u
23
+ ··· + 264u + 59
c
4
u
24
− 2u
23
+ ··· + 17490u + 21275
c
5
, c
12
u
24
− u
23
+ ··· + 72u + 389
c
6
(u
4
+ u
3
+ u
2
− u + 1)
6
c
8
, c
11
(u
4
− u
3
+ u
2
+ u + 1)
6
c
10
u
24
+ 2u
23
+ ··· + 1360u + 2423
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
8
c
2
, c
7
(y
3
− y
2
+ 2y −1)
8
c
3
, c
9
y
24
− 9y
23
+ ··· − 26862y + 3481
c
4
y
24
− 36y
23
+ ··· − 770163150y + 452625625
c
5
, c
12
y
24
+ 3y
23
+ ··· − 1491942y + 151321
c
6
, c
8
, c
11
(y
4
+ y
3
+ 5y
2
+ y + 1)
6
c
10
y
24
− 12y
23
+ ··· − 19290354y + 5870929
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.600947 + 0.848047I
a = −0.242385 + 1.316620I
b = 0.93338 + 1.13249I
1.12763 + 4.68603I −7.72892 − 10.27938I
u = −0.600947 − 0.848047I
a = −0.242385 − 1.316620I
b = 0.93338 − 1.13249I
1.12763 − 4.68603I −7.72892 + 10.27938I
u = 0.742465 + 0.295225I
a = 2.13643 + 0.44294I
b = −0.433380 + 0.525827I
0.78305 − 1.85791I −3.78084 + 7.29993I
u = 0.742465 − 0.295225I
a = 2.13643 − 0.44294I
b = −0.433380 − 0.525827I
0.78305 + 1.85791I −3.78084 − 7.29993I
u = 0.550416 + 1.107760I
a = 0.103231 − 1.002480I
b = 0.93338 − 1.13249I
1.12763 − 4.68603I −7.72892 + 10.27938I
u = 0.550416 − 1.107760I
a = 0.103231 + 1.002480I
b = 0.93338 + 1.13249I
1.12763 + 4.68603I −7.72892 − 10.27938I
u = 0.654636 + 0.170247I
a = −1.32048 + 2.33671I
b = −0.433380 + 0.525827I
−3.35454 − 4.68603I −10.3101 + 10.2794I
u = 0.654636 − 0.170247I
a = −1.32048 − 2.33671I
b = −0.433380 − 0.525827I
−3.35454 + 4.68603I −10.3101 − 10.2794I
u = −0.889025 + 1.034440I
a = −0.651543 + 0.080481I
b = −0.433380 + 0.525827I
−3.35454 − 4.68603I −10.3101 + 10.2794I
u = −0.889025 − 1.034440I
a = −0.651543 − 0.080481I
b = −0.433380 − 0.525827I
−3.35454 + 4.68603I −10.3101 − 10.2794I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.525945 + 0.044493I
a = 3.93720 + 1.13790I
b = −0.433380 + 0.525827I
0.78305 − 7.51416I −3.78084 + 13.25883I
u = −0.525945 − 0.044493I
a = 3.93720 − 1.13790I
b = −0.433380 − 0.525827I
0.78305 + 7.51416I −3.78084 − 13.25883I
u = 0.09099 + 1.49396I
a = −0.185870 + 0.739217I
b = 0.93338 + 1.13249I
5.26521 + 1.85791I −1.19965 − 7.29993I
u = 0.09099 − 1.49396I
a = −0.185870 − 0.739217I
b = 0.93338 − 1.13249I
5.26521 − 1.85791I −1.19965 + 7.29993I
u = 0.20404 + 1.65325I
a = −0.122484 − 0.767493I
b = 0.93338 − 1.13249I
5.26521 − 7.51416I −1.19965 + 13.25883I
u = 0.20404 − 1.65325I
a = −0.122484 + 0.767493I
b = 0.93338 + 1.13249I
5.26521 + 7.51416I −1.19965 − 13.25883I
u = 0.48569 + 1.70790I
a = 0.13811 − 1.41192I
b = 0.93338 − 1.13249I
5.26521 − 1.85791I −1.19965 + 7.29993I
u = 0.48569 − 1.70790I
a = 0.13811 + 1.41192I
b = 0.93338 + 1.13249I
5.26521 + 1.85791I −1.19965 − 7.29993I
u = −0.81886 + 1.67114I
a = 0.08738 + 1.42493I
b = 0.93338 + 1.13249I
5.26521 + 7.51416I −1.19965 − 13.25883I
u = −0.81886 − 1.67114I
a = 0.08738 − 1.42493I
b = 0.93338 − 1.13249I
5.26521 − 7.51416I −1.19965 + 13.25883I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.93247 + 0.69713I
a = −0.044651 + 0.538366I
b = −0.433380 + 0.525827I
0.78305 − 1.85791I −3.78084 + 7.29993I
u = 1.93247 − 0.69713I
a = −0.044651 − 0.538366I
b = −0.433380 − 0.525827I
0.78305 + 1.85791I −3.78084 − 7.29993I
u = −2.32592 + 0.12746I
a = −0.208979 − 0.494401I
b = −0.433380 − 0.525827I
0.78305 + 7.51416I −4.00000 − 13.25883I
u = −2.32592 − 0.12746I
a = −0.208979 + 0.494401I
b = −0.433380 + 0.525827I
0.78305 − 7.51416I −4.00000 + 13.25883I
20
IV. I
u
4
= h−7.06 × 10
36
u
23
+ 1.02 × 10
37
u
22
+ · · · + 1.33 × 10
40
b − 9.51 ×
10
39
, −4.57 × 10
42
u
23
+ 4.24 × 10
42
u
22
+ · · · + 2.64 × 10
45
a − 1.17 ×
10
45
, u
24
+ 12u
22
+ · · · + 1224u + 631i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
u
u
a
9
=
0.00172987u
23
− 0.00160232u
22
+ ··· + 1.02017u + 0.444120
0.000529102u
23
− 0.000764052u
22
+ ··· − 0.0148259u + 0.712663
a
8
=
0.00120077u
23
− 0.000838266u
22
+ ··· + 1.03499u − 0.268543
0.000529102u
23
− 0.000764052u
22
+ ··· − 0.0148259u + 0.712663
a
11
=
−0.00206826u
23
+ 0.000834451u
22
+ ··· − 1.24002u − 2.01979
−0.000338403u
23
− 0.000759834u
22
+ ··· − 1.08992u − 0.895038
a
4
=
−0.000455367u
23
− 0.000529102u
22
+ ··· + 0.871751u − 0.542543
0.000129944u
23
− 0.00137802u
22
+ ··· − 0.661740u − 0.202850
a
7
=
−0.00209250u
23
+ 0.00139661u
22
+ ··· − 2.38274u − 1.50095
−0.00103460u
23
+ 0.00104292u
22
+ ··· − 0.196129u − 1.35059
a
10
=
−0.00206826u
23
+ 0.000834451u
22
+ ··· − 1.24002u − 2.01979
−0.00103287u
23
+ 0.000438081u
22
+ ··· − 0.806214u − 1.42158
a
3
=
0.00235883u
23
− 0.00154095u
22
+ ··· + 2.18979u + 1.97028
0.000806262u
23
− 0.000712088u
22
+ ··· + 0.204750u + 1.44167
a
2
=
0.00128858u
23
− 0.00116685u
22
+ ··· + 0.751812u + 1.91517
0.000810721u
23
+ 0.000179541u
22
+ ··· + 0.331946u + 0.919998
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00703358u
23
+ 0.00486786u
22
+ ··· + 3.00965u − 13.0147
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
+ 2u + 1)
8
c
2
, c
7
(u
3
+ u
2
− 1)
8
c
3
, c
9
u
24
− 7u
21
+ ··· − 30u + 19
c
4
u
24
+ u
23
+ ··· + 70u + 7
c
5
, c
12
u
24
+ 12u
22
+ ··· − 1224u + 631
c
6
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
6
c
8
, c
11
(u
4
− 2u
3
+ 2u
2
− u + 1)
6
c
10
u
24
− u
23
+ ··· + 606u + 157
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
3
+ 3y
2
+ 2y −1)
8
c
2
, c
7
(y
3
− y
2
+ 2y −1)
8
c
3
, c
9
y
24
+ 46y
22
+ ··· + 2862y + 361
c
4
y
24
+ 3y
23
+ ··· + 1722y + 49
c
5
, c
12
y
24
+ 24y
23
+ ··· − 585750y + 398161
c
6
, c
8
, c
11
(y
4
+ 2y
2
+ 3y + 1)
6
c
10
y
24
− 9y
23
+ ··· − 34710y + 24649
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.928233 + 0.439911I
a = 0.74033 − 2.04422I
b = −0.070696 − 0.758745I
−0.367792 + 0.232734I −10.02977 − 2.06053I
u = 0.928233 − 0.439911I
a = 0.74033 + 2.04422I
b = −0.070696 + 0.758745I
−0.367792 − 0.232734I −10.02977 + 2.06053I
u = 0.245486 + 0.911245I
a = −0.081489 − 0.442862I
b = 1.070700 − 0.758745I
2.27847 − 2.59539I −1.47999 + 0.91892I
u = 0.245486 − 0.911245I
a = −0.081489 + 0.442862I
b = 1.070700 + 0.758745I
2.27847 + 2.59539I −1.47999 − 0.91892I
u = −0.570691 + 0.972378I
a = 0.263455 + 0.980058I
b = 1.070700 + 0.758745I
2.27847 + 2.59539I −1.47999 − 0.91892I
u = −0.570691 − 0.972378I
a = 0.263455 − 0.980058I
b = 1.070700 − 0.758745I
2.27847 − 2.59539I −1.47999 + 0.91892I
u = −1.118820 + 0.403382I
a = 0.19970 + 2.19588I
b = −0.070696 + 0.758745I
−0.36779 + 5.42351I −10.02977 − 3.89837I
u = −1.118820 − 0.403382I
a = 0.19970 − 2.19588I
b = −0.070696 − 0.758745I
−0.36779 − 5.42351I −10.02977 + 3.89837I
u = −0.161538 + 1.325950I
a = −0.442722 + 1.019620I
b = 1.070700 + 0.758745I
6.41605 − 0.23273I 5.04928 + 2.06053I
u = −0.161538 − 1.325950I
a = −0.442722 − 1.019620I
b = 1.070700 − 0.758745I
6.41605 + 0.23273I 5.04928 − 2.06053I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.592456 + 0.139203I
a = −1.93886 + 2.11751I
b = −0.070696 + 0.758745I
−4.50538 + 2.59539I −16.5590 − 0.9189I
u = −0.592456 − 0.139203I
a = −1.93886 − 2.11751I
b = −0.070696 − 0.758745I
−4.50538 − 2.59539I −16.5590 + 0.9189I
u = 0.917662 + 1.065060I
a = −0.420784 − 0.504118I
b = −0.070696 − 0.758745I
−4.50538 − 2.59539I −16.5590 + 0.9189I
u = 0.917662 − 1.065060I
a = −0.420784 + 0.504118I
b = −0.070696 + 0.758745I
−4.50538 + 2.59539I −16.5590 − 0.9189I
u = 0.386661 + 1.354340I
a = −0.450944 − 0.920583I
b = 1.070700 − 0.758745I
6.41605 − 5.42351I 5.04928 + 3.89837I
u = 0.386661 − 1.354340I
a = −0.450944 + 0.920583I
b = 1.070700 + 0.758745I
6.41605 + 5.42351I 5.04928 − 3.89837I
u = 1.31832 + 0.83644I
a = 0.280368 + 0.202313I
b = −0.070696 + 0.758745I
−0.367792 − 0.232734I −10.02977 + 2.06053I
u = 1.31832 − 0.83644I
a = 0.280368 − 0.202313I
b = −0.070696 − 0.758745I
−0.367792 + 0.232734I −10.02977 − 2.06053I
u = −0.88224 + 1.49882I
a = 0.0557491 − 0.0867063I
b = −0.070696 − 0.758745I
−0.36779 − 5.42351I −10.02977 + 3.89837I
u = −0.88224 − 1.49882I
a = 0.0557491 + 0.0867063I
b = −0.070696 + 0.758745I
−0.36779 + 5.42351I −10.02977 − 3.89837I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10144 + 2.04885I
a = 0.429007 − 0.648132I
b = 1.070700 − 0.758745I
6.41605 + 0.23273I 5.04928 − 2.06053I
u = −0.10144 − 2.04885I
a = 0.429007 + 0.648132I
b = 1.070700 + 0.758745I
6.41605 − 0.23273I 5.04928 + 2.06053I
u = −0.36918 + 2.12340I
a = 0.420861 + 0.689630I
b = 1.070700 + 0.758745I
6.41605 + 5.42351I 5.04928 − 3.89837I
u = −0.36918 − 2.12340I
a = 0.420861 − 0.689630I
b = 1.070700 − 0.758745I
6.41605 − 5.42351I 5.04928 + 3.89837I
26
V. I
u
5
= hb, a − 1, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
u
u
a
9
=
1
0
a
8
=
1
0
a
11
=
1
0
a
4
=
0
u
a
7
=
0
u
a
10
=
1
u
2
a
3
=
u
u
2
− u + 1
a
2
=
u
2
+ 1
u
2
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
+ 4u − 10
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
c
12
u
3
+ u
2
+ 2u + 1
c
2
, c
7
u
3
− u
2
+ 1
c
6
, c
8
, c
11
u
3
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
9
, c
10
c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
7
y
3
− y
2
+ 2y −1
c
6
, c
8
, c
11
y
3
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 1.00000
b = 0
3.02413 − 2.82812I −2.49024 + 2.97945I
u = 0.215080 − 1.307140I
a = 1.00000
b = 0
3.02413 + 2.82812I −2.49024 − 2.97945I
u = 0.569840
a = 1.00000
b = 0
−1.11345 −9.01950
30
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
+ u
2
+ 2u + 1)
17
)(u
30
− 20u
29
+ ··· − 157u + 9)
· (u
38
+ 20u
37
+ ··· + 65536u + 65536)
c
2
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
16
(u
30
− 10u
28
+ ··· − u + 3)
· (u
38
− 16u
37
+ ··· − 2560u + 256)
c
3
, c
9
(u
3
+ u
2
+ 2u + 1)(u
24
− 7u
21
+ ··· − 30u + 19)
· (u
24
+ u
23
+ ··· + 264u + 59)(u
30
+ u
29
+ ··· − 4u + 1)
· (u
38
− 2u
37
+ ··· − 8u + 1)
c
4
(u
3
+ u
2
+ 2u + 1)(u
24
− 2u
23
+ ··· + 17490u + 21275)
· (u
24
+ u
23
+ ··· + 70u + 7)(u
30
− u
29
+ ··· + 32u + 52)
· (u
38
− 22u
36
+ ··· − 1528u + 1456)
c
5
(u
3
+ u
2
+ 2u + 1)(u
24
+ 12u
22
+ ··· − 1224u + 631)
· (u
24
− u
23
+ ··· + 72u + 389)(u
30
+ u
28
+ ··· − 2u + 1)
· (u
38
− u
37
+ ··· + 2u + 1)
c
6
u
3
(u
4
+ u
3
+ u
2
− u + 1)
6
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
6
· (u
30
+ 18u
29
+ ··· − u
2
+ 1)(u
38
− 19u
37
+ ··· − 3108u + 245)
c
7
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
16
(u
30
− 10u
28
+ ··· + u + 3)
· (u
38
− 16u
37
+ ··· − 2560u + 256)
c
8
u
3
(u
4
− 2u
3
+ 2u
2
− u + 1)
6
(u
4
− u
3
+ u
2
+ u + 1)
6
· (u
30
+ 11u
29
+ ··· + 5u + 1)(u
38
+ 12u
37
+ ··· + 1309u + 245)
c
10
(u
3
+ u
2
+ 2u + 1)(u
24
− u
23
+ ··· + 606u + 157)
· (u
24
+ 2u
23
+ ··· + 1360u + 2423)(u
30
− 4u
28
+ ··· + 5u + 3)
· (u
38
− u
37
+ ··· − 189u + 61)
c
11
u
3
(u
4
− 2u
3
+ 2u
2
− u + 1)
6
(u
4
− u
3
+ u
2
+ u + 1)
6
· (u
30
− 11u
29
+ ··· − 5u + 1)(u
38
+ 12u
37
+ ··· + 1309u + 245)
c
12
(u
3
+ u
2
+ 2u + 1)(u
24
+ 12u
22
+ ··· − 1224u + 631)
· (u
24
− u
23
+ ··· + 72u + 389)(u
30
+ u
28
+ ··· + 2u + 1)
· (u
38
− u
37
+ ··· + 2u + 1)
31
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y −1)
17
)(y
30
− 4y
29
+ ··· − 817y + 81)
· (y
38
− 4y
37
+ ··· − 15032385536y + 4294967296)
c
2
, c
7
((y
3
− y
2
+ 2y −1)
17
)(y
30
− 20y
29
+ ··· − 157y + 9)
· (y
38
− 20y
37
+ ··· − 65536y + 65536)
c
3
, c
9
(y
3
+ 3y
2
+ 2y −1)(y
24
+ 46y
22
+ ··· + 2862y + 361)
· (y
24
− 9y
23
+ ··· − 26862y + 3481)(y
30
− 9y
29
+ ··· + 10y + 1)
· (y
38
+ 20y
37
+ ··· + 38y + 1)
c
4
(y
3
+ 3y
2
+ 2y −1)(y
24
− 36y
23
+ ··· − 7.70163 × 10
8
y + 4.52626 × 10
8
)
· (y
24
+ 3y
23
+ ··· + 1722y + 49)(y
30
− 9y
29
+ ··· + 952y + 2704)
· (y
38
− 44y
37
+ ··· − 18656544y + 2119936)
c
5
, c
12
(y
3
+ 3y
2
+ 2y −1)(y
24
+ 3y
23
+ ··· − 1491942y + 151321)
· (y
24
+ 24y
23
+ ··· − 585750y + 398161)(y
30
+ 2y
29
+ ··· − 14y + 1)
· (y
38
+ 51y
37
+ ··· + 14y + 1)
c
6
y
3
(y
4
+ 2y
2
+ 3y + 1)
6
(y
4
+ y
3
+ 5y
2
+ y + 1)
6
· (y
30
− 10y
29
+ ··· − 2y + 1)(y
38
− 9y
37
+ ··· + 500486y + 60025)
c
8
, c
11
y
3
(y
4
+ 2y
2
+ 3y + 1)
6
(y
4
+ y
3
+ 5y
2
+ y + 1)
6
· (y
30
+ 11y
29
+ ··· + 27y + 1)(y
38
+ 12y
37
+ ··· + 698299y + 60025)
c
10
(y
3
+ 3y
2
+ 2y −1)(y
24
− 12y
23
+ ··· − 1.92904 × 10
7
y + 5870929)
· (y
24
− 9y
23
+ ··· − 34710y + 24649)(y
30
− 8y
29
+ ··· − 43y + 9)
· (y
38
− 27y
37
+ ··· − 45603y + 3721)
32
