12n
0663
(K12n
0663
)
A knot diagram
1
Linearized knot diagam
3 8 6 8 11 10 2 12 4 3 9 5
Solving Sequence
5,12 1,9
8 4 11 6 3 2 7 10
c
12
c
8
c
4
c
11
c
5
c
3
c
2
c
7
c
10
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.19807 × 10
112
u
43
− 4.22174 × 10
112
u
42
+ ··· + 2.66093 × 10
114
b − 1.56181 × 10
114
,
− 8.19807 × 10
112
u
43
− 4.22174 × 10
112
u
42
+ ··· + 2.66093 × 10
114
a − 4.22274 × 10
114
,
u
44
− 18u
42
+ ··· + 2u + 1i
I
u
2
= h−4.22056 × 10
31
u
30
+ 2.20340 × 10
32
u
29
+ ··· + 1.00720 × 10
32
b + 8.09762 × 10
32
,
− 4.22056 × 10
31
u
30
+ 2.20340 × 10
32
u
29
+ ··· + 1.00720 × 10
32
a + 9.10482 × 10
32
, u
31
+ 8u
29
+ ··· − 3u + 1i
I
u
3
= h5.43266 × 10
151
u
43
− 8.90811 × 10
150
u
42
+ ··· + 2.96118 × 10
156
b − 3.66107 × 10
156
,
4.95705 × 10
158
u
43
− 6.16258 × 10
158
u
42
+ ··· + 2.92136 × 10
162
a − 1.06601 × 10
163
,
u
44
− u
43
+ ··· − 44412u − 15101i
* 3 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−8.20 × 10
112
u
43
− 4.22 × 10
112
u
42
+ · · · + 2.66 × 10
114
b − 1.56 ×
10
114
, −8.20 × 10
112
u
43
− 4.22 × 10
112
u
42
+ · · · + 2.66 × 10
114
a − 4.22 ×
10
114
, u
44
− 18u
42
+ · · · + 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
9
=
0.0308091u
43
+ 0.0158657u
42
+ ··· − 3.90450u + 1.58694
0.0308091u
43
+ 0.0158657u
42
+ ··· − 3.90450u + 0.586943
a
8
=
1
0.0308091u
43
+ 0.0158657u
42
+ ··· − 3.90450u + 0.586943
a
4
=
u
0.0158657u
43
+ 0.0189392u
42
+ ··· + 1.52533u − 0.0308091
a
11
=
0.0530718u
43
− 0.0187857u
42
+ ··· − 11.2966u + 1.08380
0.0222628u
43
− 0.0346514u
42
+ ··· − 7.39214u − 0.503148
a
6
=
0.357406u
43
+ 0.0114222u
42
+ ··· + 6.14355u + 0.578976
0.220586u
43
+ 0.0415889u
42
+ ··· + 6.14139u + 0.390597
a
3
=
0.102339u
43
− 0.0535366u
42
+ ··· + 6.75934u + 0.686328
−0.0123699u
43
− 0.00873329u
42
+ ··· + 6.69838u + 0.626720
a
2
=
0.0591298u
43
− 0.0619282u
42
+ ··· + 3.09120u − 0.165265
0.0273984u
43
− 0.0288691u
42
+ ··· + 6.49347u + 0.00931667
a
7
=
0.0896482u
43
− 0.0548409u
42
+ ··· + 0.0656990u + 0.113144
0.0883392u
43
− 0.0530903u
42
+ ··· − 0.256176u + 0.163412
a
10
=
0.0552606u
43
+ 0.0222813u
42
+ ··· − 3.92001u + 1.60573
0.0609758u
43
+ 0.0207299u
42
+ ··· − 3.81924u + 0.723763
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.04104u
43
+ 0.0210798u
42
+ ··· + 86.9727u − 5.18413
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 35u
43
+ ··· + 17825792u + 4194304
c
2
, c
7
u
44
− 23u
43
+ ··· − 15360u + 2048
c
3
u
44
+ 14u
43
+ ··· + 38u + 4
c
4
, c
12
u
44
− 18u
42
+ ··· − 2u + 1
c
5
, c
9
u
44
− 7u
42
+ ··· + 89u + 21
c
6
, c
10
u
44
− u
43
+ ··· − u + 1
c
8
, c
11
u
44
+ 9u
43
+ ··· + 172u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
− 51y
43
+ ··· + 3298534883328y + 17592186044416
c
2
, c
7
y
44
− 35y
43
+ ··· − 17825792y + 4194304
c
3
y
44
− 14y
43
+ ··· + 612y + 16
c
4
, c
12
y
44
− 36y
43
+ ··· + 28y + 1
c
5
, c
9
y
44
− 14y
43
+ ··· − 9727y + 441
c
6
, c
10
y
44
+ 31y
43
+ ··· + 3y + 1
c
8
, c
11
y
44
+ 25y
43
+ ··· + 2896y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.876522 + 0.528391I
a = 1.09112 + 0.98148I
b = 0.091117 + 0.981484I
−2.64902 + 0.33804I −9.24425 + 1.00857I
u = 0.876522 − 0.528391I
a = 1.09112 − 0.98148I
b = 0.091117 − 0.981484I
−2.64902 − 0.33804I −9.24425 − 1.00857I
u = 1.079670 + 0.134336I
a = 0.239829 + 0.233289I
b = −0.760171 + 0.233289I
−1.52443 − 0.21103I −4.97310 + 0.I
u = 1.079670 − 0.134336I
a = 0.239829 − 0.233289I
b = −0.760171 − 0.233289I
−1.52443 + 0.21103I −4.97310 + 0.I
u = −1.189010 + 0.306258I
a = 0.67617 − 1.33662I
b = −0.323832 − 1.336620I
−6.03434 − 1.69757I 0
u = −1.189010 − 0.306258I
a = 0.67617 + 1.33662I
b = −0.323832 + 1.336620I
−6.03434 + 1.69757I 0
u = −1.207620 + 0.405136I
a = −0.011672 + 0.201487I
b = −1.011670 + 0.201487I
−0.85999 + 6.23657I 0
u = −1.207620 − 0.405136I
a = −0.011672 − 0.201487I
b = −1.011670 − 0.201487I
−0.85999 − 6.23657I 0
u = 1.253320 + 0.360663I
a = 0.58221 − 1.41088I
b = −0.41779 − 1.41088I
−13.0195 − 6.3051I 0
u = 1.253320 − 0.360663I
a = 0.58221 + 1.41088I
b = −0.41779 + 1.41088I
−13.0195 + 6.3051I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609637 + 0.085004I
a = 0.800710 + 0.311107I
b = −0.199290 + 0.311107I
−1.232890 − 0.407507I −8.23914 + 1.51919I
u = 0.609637 − 0.085004I
a = 0.800710 − 0.311107I
b = −0.199290 − 0.311107I
−1.232890 + 0.407507I −8.23914 − 1.51919I
u = −0.15451 + 1.43462I
a = 0.738629 − 0.751056I
b = −0.261371 − 0.751056I
2.74125 − 1.62157I 0
u = −0.15451 − 1.43462I
a = 0.738629 + 0.751056I
b = −0.261371 + 0.751056I
2.74125 + 1.62157I 0
u = −0.399143 + 0.330546I
a = 1.40923 − 0.92070I
b = 0.409229 − 0.920695I
0.05653 − 2.19737I 0.00628 + 3.06449I
u = −0.399143 − 0.330546I
a = 1.40923 + 0.92070I
b = 0.409229 + 0.920695I
0.05653 + 2.19737I 0.00628 − 3.06449I
u = −1.50977 + 0.31090I
a = 0.560340 + 1.196140I
b = −0.439660 + 1.196140I
−12.57110 + 0.21179I 0
u = −1.50977 − 0.31090I
a = 0.560340 − 1.196140I
b = −0.439660 − 1.196140I
−12.57110 − 0.21179I 0
u = 0.414615 + 0.126074I
a = 1.46142 + 1.21039I
b = 0.461422 + 1.210400I
−2.58939 + 6.06896I −6.96240 − 5.29777I
u = 0.414615 − 0.126074I
a = 1.46142 − 1.21039I
b = 0.461422 − 1.210400I
−2.58939 − 6.06896I −6.96240 + 5.29777I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54962 + 0.23074I
a = 0.439073 + 1.200720I
b = −0.560927 + 1.200720I
−4.34261 − 4.88782I 0
u = 1.54962 − 0.23074I
a = 0.439073 − 1.200720I
b = −0.560927 − 1.200720I
−4.34261 + 4.88782I 0
u = −1.33716 + 0.82047I
a = 0.163799 + 0.042605I
b = −0.836201 + 0.042605I
−8.84801 + 4.59946I 0
u = −1.33716 − 0.82047I
a = 0.163799 − 0.042605I
b = −0.836201 − 0.042605I
−8.84801 − 4.59946I 0
u = 0.53152 + 1.54489I
a = 0.728029 + 0.866444I
b = −0.271971 + 0.866444I
2.40594 − 4.26197I 0
u = 0.53152 − 1.54489I
a = 0.728029 − 0.866444I
b = −0.271971 − 0.866444I
2.40594 + 4.26197I 0
u = −0.071957 + 0.347959I
a = 1.68636 − 0.27524I
b = 0.686363 − 0.275238I
1.56185 − 1.94947I 2.03078 + 4.77946I
u = −0.071957 − 0.347959I
a = 1.68636 + 0.27524I
b = 0.686363 + 0.275238I
1.56185 + 1.94947I 2.03078 − 4.77946I
u = 1.37910 + 0.91921I
a = −0.0534857 − 0.1038620I
b = −1.053490 − 0.103862I
−8.1171 − 11.6018I 0
u = 1.37910 − 0.91921I
a = −0.0534857 + 0.1038620I
b = −1.053490 + 0.103862I
−8.1171 + 11.6018I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.64285 + 0.31556I
a = 1.00976 − 1.01253I
b = 0.009762 − 1.012530I
−10.55820 − 0.01477I 0
u = −1.64285 − 0.31556I
a = 1.00976 + 1.01253I
b = 0.009762 + 1.012530I
−10.55820 + 0.01477I 0
u = 1.44509 + 0.84306I
a = 0.610238 + 1.224140I
b = −0.389762 + 1.224140I
−5.59770 − 4.07714I 0
u = 1.44509 − 0.84306I
a = 0.610238 − 1.224140I
b = −0.389762 − 1.224140I
−5.59770 + 4.07714I 0
u = −1.59950 + 0.65744I
a = 0.417136 − 1.269310I
b = −0.582864 − 1.269310I
−4.18114 + 11.97330I 0
u = −1.59950 − 0.65744I
a = 0.417136 + 1.269310I
b = −0.582864 + 1.269310I
−4.18114 − 11.97330I 0
u = −0.142365 + 0.099749I
a = 2.04560 + 0.61037I
b = 1.045600 + 0.610374I
2.62916 + 1.12288I −7.07882 + 9.08866I
u = −0.142365 − 0.099749I
a = 2.04560 − 0.61037I
b = 1.045600 − 0.610374I
2.62916 − 1.12288I −7.07882 − 9.08866I
u = 0.044194 + 0.164660I
a = 1.93626 − 1.21271I
b = 0.93626 − 1.21271I
0.80464 − 6.11087I −11.6087 + 22.8648I
u = 0.044194 − 0.164660I
a = 1.93626 + 1.21271I
b = 0.93626 + 1.21271I
0.80464 + 6.11087I −11.6087 − 22.8648I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.67061 + 1.16694I
a = 0.531277 − 1.236650I
b = −0.468723 − 1.236650I
−12.4436 + 9.3189I 0
u = −1.67061 − 1.16694I
a = 0.531277 + 1.236650I
b = −0.468723 + 1.236650I
−12.4436 − 9.3189I 0
u = 1.74121 + 1.12234I
a = 0.437976 + 1.307160I
b = −0.56202 + 1.30716I
−11.8590 − 17.3430I 0
u = 1.74121 − 1.12234I
a = 0.437976 − 1.307160I
b = −0.56202 − 1.30716I
−11.8590 + 17.3430I 0
9
II.
I
u
2
= h−4.22×10
31
u
30
+2.20×10
32
u
29
+· · ·+1.01×10
32
b+8.10×10
32
, −4.22×
10
31
u
30
+2.20×10
32
u
29
+· · ·+1.01×10
32
a+9.10×10
32
, u
31
+8u
29
+· · ·−3u+1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
9
=
0.419039u
30
− 2.18765u
29
+ ··· + 14.5202u − 9.03974
0.419039u
30
− 2.18765u
29
+ ··· + 14.5202u − 8.03974
a
8
=
−1
0.419039u
30
− 2.18765u
29
+ ··· + 14.5202u − 8.03974
a
4
=
u
2.18765u
30
+ 1.08094u
29
+ ··· + 7.78263u + 0.419039
a
11
=
−0.500932u
30
− 1.84733u
29
+ ··· + 5.71896u − 7.55669
−0.0818935u
30
− 4.03498u
29
+ ··· + 20.2391u − 16.5964
a
6
=
−0.134161u
30
+ 0.273690u
29
+ ··· + 1.51196u − 0.199830
1.24808u
30
+ 0.183025u
29
+ ··· + 10.7167u − 3.11982
a
3
=
1.57804u
30
+ 0.544822u
29
+ ··· + 4.95031u − 0.596126
2.25205u
30
+ 0.921857u
29
+ ··· + 5.25234u + 1.41922
a
2
=
2.13048u
30
+ 0.190785u
29
+ ··· + 9.66763u − 1.11457
−2.66458u
30
+ 1.29047u
29
+ ··· − 27.0753u + 10.7100
a
7
=
0.914126u
30
+ 0.818689u
29
+ ··· + 0.245607u + 2.56016
−5.70362u
30
− 1.64130u
29
+ ··· − 27.9449u + 3.71554
a
10
=
1.18661u
30
− 2.18060u
29
+ ··· + 19.5612u − 10.8871
0.509703u
30
− 1.77620u
29
+ ··· + 13.2934u − 6.65750
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5.23434u
30
− 0.611283u
29
+ ··· + 1.07019u + 13.5933
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
− 32u
30
+ ··· + 18u − 1
c
2
u
31
− 16u
29
+ ··· − 6u + 1
c
3
u
31
+ 19u
30
+ ··· + 13u + 1
c
4
, c
12
u
31
+ 8u
29
+ ··· − 3u + 1
c
5
, c
9
u
31
− u
29
+ ··· + 7u
2
− 1
c
6
, c
10
u
31
− u
30
+ ··· − 9u
3
− 1
c
7
u
31
− 16u
29
+ ··· − 6u − 1
c
8
u
31
+ 10u
30
+ ··· + 11u + 5
c
11
u
31
− 10u
30
+ ··· + 11u − 5
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 44y
30
+ ··· − 1382y −1
c
2
, c
7
y
31
− 32y
30
+ ··· + 18y −1
c
3
y
31
− 13y
30
+ ··· + 11y −1
c
4
, c
12
y
31
+ 16y
30
+ ··· − 9y −1
c
5
, c
9
y
31
− 2y
30
+ ··· + 14y −1
c
6
, c
10
y
31
− 13y
30
+ ··· + 6y
2
− 1
c
8
, c
11
y
31
+ 18y
30
+ ··· − 169y −25
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.452905 + 0.853811I
a = −0.41115 + 1.40701I
b = 0.58885 + 1.40701I
−1.88667 + 7.24502I −3.56693 − 12.29348I
u = −0.452905 − 0.853811I
a = −0.41115 − 1.40701I
b = 0.58885 − 1.40701I
−1.88667 − 7.24502I −3.56693 + 12.29348I
u = −0.537908 + 0.776764I
a = −1.25638 + 0.81390I
b = −0.256377 + 0.813898I
1.05321 − 4.42170I 1.63233 + 2.08309I
u = −0.537908 − 0.776764I
a = −1.25638 − 0.81390I
b = −0.256377 − 0.813898I
1.05321 + 4.42170I 1.63233 − 2.08309I
u = 0.186959 + 0.922387I
a = 0.136989 + 0.093867I
b = 1.136990 + 0.093867I
2.74478 + 1.10405I 4.27026 − 4.94566I
u = 0.186959 − 0.922387I
a = 0.136989 − 0.093867I
b = 1.136990 − 0.093867I
2.74478 − 1.10405I 4.27026 + 4.94566I
u = 0.785470 + 0.888097I
a = −0.68298 − 1.26508I
b = 0.317017 − 1.265080I
−2.98382 − 5.05597I −1.85048 + 6.61092I
u = 0.785470 − 0.888097I
a = −0.68298 + 1.26508I
b = 0.317017 + 1.265080I
−2.98382 + 5.05597I −1.85048 − 6.61092I
u = 0.716103 + 0.268510I
a = −1.33254 − 1.08651I
b = −0.332542 − 1.086510I
−0.64391 + 6.63799I −4.09253 − 8.74235I
u = 0.716103 − 0.268510I
a = −1.33254 + 1.08651I
b = −0.332542 + 1.086510I
−0.64391 − 6.63799I −4.09253 + 8.74235I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.870665 + 0.895756I
a = −0.413460 − 1.291070I
b = 0.58654 − 1.29107I
−0.92154 − 4.91630I −0.630490 + 1.059159I
u = 0.870665 − 0.895756I
a = −0.413460 + 1.291070I
b = 0.58654 + 1.29107I
−0.92154 + 4.91630I −0.630490 − 1.059159I
u = −1.28812
a = 0.0316573
b = 1.03166
−5.54014 −6.97090
u = 0.337074 + 0.547150I
a = −1.333870 − 0.200623I
b = −0.333874 − 0.200623I
1.82880 − 3.66778I 3.40426 + 8.66722I
u = 0.337074 − 0.547150I
a = −1.333870 + 0.200623I
b = −0.333874 + 0.200623I
1.82880 + 3.66778I 3.40426 − 8.66722I
u = −0.550474 + 0.090472I
a = −1.48951 + 0.83661I
b = −0.489508 + 0.836612I
0.747383 + 1.132650I −2.64987 + 1.35406I
u = −0.550474 − 0.090472I
a = −1.48951 − 0.83661I
b = −0.489508 − 0.836612I
0.747383 − 1.132650I −2.64987 − 1.35406I
u = 0.275688 + 0.445827I
a = 0.090985 − 0.553978I
b = 1.090990 − 0.553978I
2.79142 − 1.37520I 7.9988 + 12.6336I
u = 0.275688 − 0.445827I
a = 0.090985 + 0.553978I
b = 1.090990 + 0.553978I
2.79142 + 1.37520I 7.9988 − 12.6336I
u = −0.03863 + 1.48036I
a = −0.685298 + 0.806812I
b = 0.314702 + 0.806812I
2.64360 − 1.37646I −7.6626 − 13.0384I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03863 − 1.48036I
a = −0.685298 − 0.806812I
b = 0.314702 − 0.806812I
2.64360 + 1.37646I −7.6626 + 13.0384I
u = 0.56127 + 1.43073I
a = −0.718872 − 0.806067I
b = 0.281128 − 0.806067I
2.65382 − 4.19990I 12.92958 + 1.02953I
u = 0.56127 − 1.43073I
a = −0.718872 + 0.806067I
b = 0.281128 + 0.806067I
2.65382 + 4.19990I 12.92958 − 1.02953I
u = 0.181284 + 0.425324I
a = −0.071576 + 1.199900I
b = 0.92842 + 1.19990I
0.90637 + 5.93162I 7.27226 + 10.53139I
u = 0.181284 − 0.425324I
a = −0.071576 − 1.199900I
b = 0.92842 − 1.19990I
0.90637 − 5.93162I 7.27226 − 10.53139I
u = −1.49593 + 0.44328I
a = −0.52089 + 1.33114I
b = 0.47911 + 1.33114I
−9.78380 + 5.35394I −8.97149 − 3.53143I
u = −1.49593 − 0.44328I
a = −0.52089 − 1.33114I
b = 0.47911 − 1.33114I
−9.78380 − 5.35394I −8.97149 + 3.53143I
u = −0.44448 + 1.60114I
a = −0.874742 + 1.099660I
b = 0.125258 + 1.099660I
−8.55901 + 4.17105I −9.11820 + 0.I
u = −0.44448 − 1.60114I
a = −0.874742 − 1.099660I
b = 0.125258 − 1.099660I
−8.55901 − 4.17105I −9.11820 + 0.I
u = 0.24987 + 1.74772I
a = −0.952529 − 0.868304I
b = 0.047471 − 0.868304I
−7.55978 + 3.46072I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24987 − 1.74772I
a = −0.952529 + 0.868304I
b = 0.047471 + 0.868304I
−7.55978 − 3.46072I 0
16
III. I
u
3
= h5.43 × 10
151
u
43
− 8.91 × 10
150
u
42
+ · · · + 2.96 × 10
156
b − 3.66 ×
10
156
, 4.96 × 10
158
u
43
− 6.16 × 10
158
u
42
+ · · · + 2.92 × 10
162
a − 1.07 ×
10
163
, u
44
− u
43
+ · · · − 44412u − 15101i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
9
=
−0.000169683u
43
+ 0.000210949u
42
+ ··· + 5.78299u + 3.64903
−0.0000183462u
43
+ 3.00829 × 10
−6
u
42
+ ··· + 0.211471u + 1.23635
a
8
=
−0.000151336u
43
+ 0.000207940u
42
+ ··· + 5.57152u + 2.41268
−0.0000183462u
43
+ 3.00829 × 10
−6
u
42
+ ··· + 0.211471u + 1.23635
a
4
=
−0.0000756392u
43
+ 0.0000596207u
42
+ ··· + 5.24244u + 3.86675
0.0000561723u
43
− 0.0000698589u
42
+ ··· − 2.23717u − 0.996626
a
11
=
−0.0000850891u
43
+ 0.000117555u
42
+ ··· + 3.71467u + 1.98036
−0.0000190918u
43
− 4.61504 × 10
−6
u
42
+ ··· + 1.55518u + 1.28646
a
6
=
0.0000606296u
43
− 0.0000562866u
42
+ ··· − 1.42364u − 1.02194
−0.0000643844u
43
+ 0.000160536u
42
+ ··· + 2.39137u − 0.0933425
a
3
=
−0.000156271u
43
+ 0.000208628u
42
+ ··· + 5.58861u + 4.03110
−0.0000100454u
43
− 0.0000181491u
42
+ ··· − 0.0516493u + 1.17222
a
2
=
−0.0000549133u
43
+ 0.0000701005u
42
+ ··· + 1.66912u + 2.45455
2.89573 × 10
−6
u
43
− 0.0000135692u
42
+ ··· − 0.206033u + 0.374072
a
7
=
−0.000202715u
43
+ 0.000277055u
42
+ ··· + 7.83899u + 4.15309
−0.0000258823u
43
− 9.15989 × 10
−6
u
42
+ ··· + 0.308767u + 1.59630
a
10
=
−0.000217536u
43
+ 0.000305300u
42
+ ··· + 9.06131u + 5.15377
−0.0000433575u
43
− 4.00488 × 10
−6
u
42
+ ··· + 2.70727u + 2.71279
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000482548u
43
− 0.000947210u
42
+ ··· − 25.8562u − 10.1385
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
2
+ 3u + 1)
22
c
2
, c
7
(u
2
+ u − 1)
22
c
3
(u
11
− 5u
10
+ 12u
9
− 15u
8
+ 8u
7
+ 4u
6
− 8u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1)
4
c
4
, c
12
u
44
+ u
43
+ ··· + 44412u − 15101
c
5
, c
9
u
44
− u
43
+ ··· + 13386u − 3929
c
6
, c
10
u
44
− 3u
43
+ ··· + 4314u + 5531
c
8
, c
11
(u
11
− 3u
10
+ ··· + 2u − 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
2
− 7y + 1)
22
c
2
, c
7
(y
2
− 3y + 1)
22
c
3
(y
11
− y
10
+ ··· + 6y −1)
4
c
4
, c
12
y
44
+ 3y
43
+ ··· − 694095892y + 228040201
c
5
, c
9
y
44
− 17y
43
+ ··· + 89464308y + 15437041
c
6
, c
10
y
44
− 5y
43
+ ··· − 38477948y + 30591961
c
8
, c
11
(y
11
+ 7y
10
+ ··· − 6y −1)
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.996280
a = −0.412904
b = 1.10821
−4.85895 8.26130
u = −0.266771 + 0.948488I
a = 2.77905 − 1.65654I
b = −0.253759 − 0.946686I
−7.37536 + 5.21629I −3.56397 − 9.01278I
u = −0.266771 − 0.948488I
a = 2.77905 + 1.65654I
b = −0.253759 + 0.946686I
−7.37536 − 5.21629I −3.56397 + 9.01278I
u = 0.482860 + 0.928813I
a = −0.363105 + 0.172184I
b = −0.234018 − 0.605151I
1.46087 − 2.70441I −0.532381 − 0.083327I
u = 0.482860 − 0.928813I
a = −0.363105 − 0.172184I
b = −0.234018 + 0.605151I
1.46087 + 2.70441I −0.532381 + 0.083327I
u = 1.066300 + 0.071698I
a = −1.87842 − 2.10327I
b = 0.290349 − 1.272230I
−11.86840 − 5.00074I −11.84059 + 6.22751I
u = 1.066300 − 0.071698I
a = −1.87842 + 2.10327I
b = 0.290349 + 1.272230I
−11.86840 + 5.00074I −11.84059 − 6.22751I
u = −0.923334 + 0.570347I
a = −0.611529 − 0.812570I
b = 0.572881 + 0.536287I
−6.81371 + 2.24779I −0.36418 − 5.06360I
u = −0.923334 − 0.570347I
a = −0.611529 + 0.812570I
b = 0.572881 − 0.536287I
−6.81371 − 2.24779I −0.36418 + 5.06360I
u = −0.630454 + 0.605922I
a = −1.37698 + 1.21851I
b = 0.290349 + 1.272230I
−3.97275 + 5.00074I −11.84059 − 6.22751I
20
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.630454 − 0.605922I
a = −1.37698 − 1.21851I
b = 0.290349 − 1.272230I
−3.97275 − 5.00074I −11.84059 + 6.22751I
u = −0.835914 + 0.774383I
a = −0.44948 + 1.56622I
b = 0.57044 + 1.34258I
−1.10226 + 5.92443I −0.82955 − 10.02355I
u = −0.835914 − 0.774383I
a = −0.44948 − 1.56622I
b = 0.57044 − 1.34258I
−1.10226 − 5.92443I −0.82955 + 10.02355I
u = −0.099154 + 0.846413I
a = 0.135288 + 0.231121I
b = 1.10821
3.03673 8.26134 + 0.I
u = −0.099154 − 0.846413I
a = 0.135288 − 0.231121I
b = 1.10821
3.03673 8.26134 + 0.I
u = 0.205413 + 0.812965I
a = −0.0283734 + 0.0059244I
b = 0.572881 − 0.536287I
1.08197 − 2.24779I −0.36418 + 5.06360I
u = 0.205413 − 0.812965I
a = −0.0283734 − 0.0059244I
b = 0.572881 + 0.536287I
1.08197 + 2.24779I −0.36418 − 5.06360I
u = −0.784330 + 0.255447I
a = −0.44192 − 1.85707I
b = −0.234018 − 0.605151I
1.46087 − 2.70441I −0.532381 − 0.083327I
u = −0.784330 − 0.255447I
a = −0.44192 + 1.85707I
b = −0.234018 + 0.605151I
1.46087 + 2.70441I −0.532381 + 0.083327I
u = 0.679381 + 0.976751I
a = −0.365051 − 1.137450I
b = 0.57044 − 1.34258I
−1.10226 − 5.92443I −0.82955 + 10.02355I
21
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679381 − 0.976751I
a = −0.365051 + 1.137450I
b = 0.57044 + 1.34258I
−1.10226 + 5.92443I −0.82955 − 10.02355I
u = 0.741850 + 0.143502I
a = −0.66856 + 2.90045I
b = −0.253759 + 0.946686I
0.52032 − 5.21629I −3.56397 + 9.01278I
u = 0.741850 − 0.143502I
a = −0.66856 − 2.90045I
b = −0.253759 − 0.946686I
0.52032 + 5.21629I −3.56397 − 9.01278I
u = −0.462531 + 1.189510I
a = 0.806013 − 0.851616I
b = −0.234018 + 0.605151I
−6.43481 + 2.70441I −0.532381 + 0.083327I
u = −0.462531 − 1.189510I
a = 0.806013 + 0.851616I
b = −0.234018 − 0.605151I
−6.43481 − 2.70441I −0.532381 − 0.083327I
u = −0.564304 + 0.377422I
a = −0.344364 + 1.363460I
b = 0.572881 + 0.536287I
1.08197 + 2.24779I −0.36418 − 5.06360I
u = −0.564304 − 0.377422I
a = −0.344364 − 1.363460I
b = 0.572881 − 0.536287I
1.08197 − 2.24779I −0.36418 + 5.06360I
u = −1.27598 + 0.68156I
a = −0.506884 + 0.886061I
b = 0.57044 + 1.34258I
−8.99794 + 5.92443I −0.82955 − 10.02355I
u = −1.27598 − 0.68156I
a = −0.506884 − 0.886061I
b = 0.57044 − 1.34258I
−8.99794 − 5.92443I −0.82955 + 10.02355I
u = 1.08373 + 0.97640I
a = −0.308790 − 1.291540I
b = 0.290349 − 1.272230I
−3.97275 − 5.00074I −11.84059 + 6.22751I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.08373 − 0.97640I
a = −0.308790 + 1.291540I
b = 0.290349 + 1.272230I
−3.97275 + 5.00074I −11.84059 − 6.22751I
u = −0.58809 + 1.38988I
a = −0.357739 + 0.456930I
b = −0.253759 + 0.946686I
0.52032 − 5.21629I −3.56397 + 9.01278I
u = −0.58809 − 1.38988I
a = −0.357739 − 0.456930I
b = −0.253759 − 0.946686I
0.52032 + 5.21629I −3.56397 − 9.01278I
u = 1.51546
a = 0.450801
b = 1.10821
−4.85895 8.26130
u = 1.68578 + 0.15175I
a = −0.21648 − 1.67604I
b = 0.57044 − 1.34258I
−8.99794 − 5.92443I 0. + 10.02355I
u = 1.68578 − 0.15175I
a = −0.21648 + 1.67604I
b = 0.57044 + 1.34258I
−8.99794 + 5.92443I 0. − 10.02355I
u = 1.86292 + 0.56992I
a = 0.205308 + 0.954895I
b = 0.572881 + 0.536287I
−6.81371 + 2.24779I 0
u = 1.86292 − 0.56992I
a = 0.205308 − 0.954895I
b = 0.572881 − 0.536287I
−6.81371 − 2.24779I 0
u = 1.25179 + 1.91093I
a = 0.090602 + 1.059850I
b = −0.234018 + 0.605151I
−6.43481 + 2.70441I 0
u = 1.25179 − 1.91093I
a = 0.090602 − 1.059850I
b = −0.234018 − 0.605151I
−6.43481 − 2.70441I 0
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −2.25299 + 1.04163I
a = −0.111708 + 1.118170I
b = 0.290349 + 1.272230I
−11.86840 + 5.00074I 0
u = −2.25299 − 1.04163I
a = −0.111708 − 1.118170I
b = 0.290349 − 1.272230I
−11.86840 − 5.00074I 0
u = −0.13577 + 3.06595I
a = 0.058843 − 0.873519I
b = −0.253759 − 0.946686I
−7.37536 + 5.21629I 0
u = −0.13577 − 3.06595I
a = 0.058843 + 0.873519I
b = −0.253759 + 0.946686I
−7.37536 − 5.21629I 0
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ 3u + 1)
22
)(u
31
− 32u
30
+ ··· + 18u − 1)
· (u
44
+ 35u
43
+ ··· + 17825792u + 4194304)
c
2
((u
2
+ u − 1)
22
)(u
31
− 16u
29
+ ··· − 6u + 1)
· (u
44
− 23u
43
+ ··· − 15360u + 2048)
c
3
(u
11
− 5u
10
+ 12u
9
− 15u
8
+ 8u
7
+ 4u
6
− 8u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1)
4
· (u
31
+ 19u
30
+ ··· + 13u + 1)(u
44
+ 14u
43
+ ··· + 38u + 4)
c
4
, c
12
(u
31
+ 8u
29
+ ··· − 3u + 1)(u
44
− 18u
42
+ ··· − 2u + 1)
· (u
44
+ u
43
+ ··· + 44412u − 15101)
c
5
, c
9
(u
31
− u
29
+ ··· + 7u
2
− 1)(u
44
− 7u
42
+ ··· + 89u + 21)
· (u
44
− u
43
+ ··· + 13386u − 3929)
c
6
, c
10
(u
31
− u
30
+ ··· − 9u
3
− 1)(u
44
− 3u
43
+ ··· + 4314u + 5531)
· (u
44
− u
43
+ ··· − u + 1)
c
7
((u
2
+ u − 1)
22
)(u
31
− 16u
29
+ ··· − 6u − 1)
· (u
44
− 23u
43
+ ··· − 15360u + 2048)
c
8
((u
11
− 3u
10
+ ··· + 2u − 1)
4
)(u
31
+ 10u
30
+ ··· + 11u + 5)
· (u
44
+ 9u
43
+ ··· + 172u + 16)
c
11
((u
11
− 3u
10
+ ··· + 2u − 1)
4
)(u
31
− 10u
30
+ ··· + 11u − 5)
· (u
44
+ 9u
43
+ ··· + 172u + 16)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
− 7y + 1)
22
)(y
31
− 44y
30
+ ··· − 1382y −1)
· (y
44
− 51y
43
+ ··· + 3298534883328y + 17592186044416)
c
2
, c
7
((y
2
− 3y + 1)
22
)(y
31
− 32y
30
+ ··· + 18y −1)
· (y
44
− 35y
43
+ ··· − 17825792y + 4194304)
c
3
((y
11
− y
10
+ ··· + 6y −1)
4
)(y
31
− 13y
30
+ ··· + 11y −1)
· (y
44
− 14y
43
+ ··· + 612y + 16)
c
4
, c
12
(y
31
+ 16y
30
+ ··· − 9y −1)(y
44
− 36y
43
+ ··· + 28y + 1)
· (y
44
+ 3y
43
+ ··· − 694095892y + 228040201)
c
5
, c
9
(y
31
− 2y
30
+ ··· + 14y −1)
· (y
44
− 17y
43
+ ··· + 89464308y + 15437041)
· (y
44
− 14y
43
+ ··· − 9727y + 441)
c
6
, c
10
(y
31
− 13y
30
+ ··· + 6y
2
− 1)
· (y
44
− 5y
43
+ ··· − 38477948y + 30591961)
· (y
44
+ 31y
43
+ ··· + 3y + 1)
c
8
, c
11
((y
11
+ 7y
10
+ ··· − 6y −1)
4
)(y
31
+ 18y
30
+ ··· − 169y −25)
· (y
44
+ 25y
43
+ ··· + 2896y + 256)
26
