12a
0450
(K12a
0450
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 8 2 11 1 4 12 7 5
Solving Sequence
2,7
6 3
1,12
11 8 9 5 4 10
c
6
c
2
c
1
c
11
c
7
c
8
c
5
c
4
c
10
c
3
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, −11204011u
28
+ 11782800u
27
+ ··· + 11150225a + 3596564, u
29
− u
28
+ ··· + u − 1i
I
u
2
= h−1.58760 × 10
230
u
101
− 4.36695 × 10
230
u
100
+ ··· + 1.89430 × 10
230
b + 1.72802 × 10
231
,
1.44256 × 10
231
u
101
+ 3.32780 × 10
231
u
100
+ ··· + 7.00892 × 10
231
a + 5.69101 × 10
232
,
u
102
+ 2u
101
+ ··· + 355u + 37i
I
u
3
= hb + u,
4u
13
+ 5u
12
+ 15u
11
+ 14u
10
+ 31u
9
+ 27u
8
+ 41u
7
+ 30u
6
+ 36u
5
+ 25u
4
+ 25u
3
+ 13u
2
+ a + 9u + 5,
u
14
+ u
13
+ 4u
12
+ 3u
11
+ 9u
10
+ 6u
9
+ 13u
8
+ 7u
7
+ 13u
6
+ 6u
5
+ 10u
4
+ 3u
3
+ 5u
2
+ u + 1i
I
u
4
= h−u
13
− u
12
− 4u
11
− 3u
10
− 9u
9
− 6u
8
− 14u
7
− 7u
6
− 14u
5
− 6u
4
− 9u
3
− 3u
2
+ b − 4u − 1,
3u
13
+ 4u
12
+ 11u
11
+ 11u
10
+ 22u
9
+ 21u
8
+ 31u
7
+ 24u
6
+ 24u
5
+ 20u
4
+ 10u
3
+ 9u
2
+ a + 4u + 3,
u
14
+ u
13
+ 4u
12
+ 3u
11
+ 9u
10
+ 6u
9
+ 14u
8
+ 7u
7
+ 14u
6
+ 6u
5
+ 9u
4
+ 3u
3
+ 4u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 159 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
= hb − u, −1.12 × 10
7
u
28
+ 1.18 × 10
7
u
27
+ · · · + 1.12 × 10
7
a + 3.60 ×
10
6
, u
29
− u
28
+ · · · + u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
1.00482u
28
− 1.05673u
27
+ ··· − 1.71703u − 0.322555
u
a
11
=
1.00482u
28
− 1.05673u
27
+ ··· − 2.71703u − 0.322555
u
a
8
=
0.0519083u
28
− 0.150688u
27
+ ··· + 1.32738u − 0.00482376
−u
2
a
9
=
−0.189436u
28
+ 0.263701u
27
+ ··· + 1.76119u − 0.259466
0.108962u
28
− 0.0707161u
27
+ ··· − 0.422843u + 0.0385933
a
5
=
0.354849u
28
− 0.895361u
27
+ ··· + 0.459547u + 0.601333
−0.147097u
28
+ 0.813257u
27
+ ··· + 0.521680u − 0.644748
a
4
=
0.00618741u
28
+ 0.549901u
27
+ ··· + 0.308783u + 0.152467
−0.113039u
28
+ 0.353098u
27
+ ··· + 1.44615u − 0.413071
a
10
=
1.10360u
28
− 1.27858u
27
+ ··· − 1.66030u − 0.374464
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
32073842
11150225
u
28
−
607928
446009
u
27
+ ··· +
2213155
446009
u +
88659642
11150225
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
29
+ 15u
28
+ ··· + 7u − 1
c
2
, c
6
, c
7
c
11
u
29
− u
28
+ ··· + u − 1
c
3
, c
4
, c
9
u
29
− 11u
28
+ ··· + 344u − 32
c
5
u
29
− 25u
28
+ ··· + 30720u − 2048
c
8
, c
12
u
29
+ 7u
27
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
29
+ 7y
28
+ ··· + 111y −1
c
2
, c
6
, c
7
c
11
y
29
+ 15y
28
+ ··· + 7y −1
c
3
, c
4
, c
9
y
29
+ 25y
28
+ ··· − 1728y −1024
c
5
y
29
− 3y
28
+ ··· + 85983232y −4194304
c
8
, c
12
y
29
+ 14y
28
+ ··· − 30y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.823702 + 0.553499I
a = −1.386270 + 0.264015I
b = −0.823702 + 0.553499I
4.15742 + 2.94610I 10.44832 − 2.08399I
u = −0.823702 − 0.553499I
a = −1.386270 − 0.264015I
b = −0.823702 − 0.553499I
4.15742 − 2.94610I 10.44832 + 2.08399I
u = 0.909923 + 0.492711I
a = 1.55550 + 0.08106I
b = 0.909923 + 0.492711I
−1.63366 − 6.77137I 6.32659 + 2.86609I
u = 0.909923 − 0.492711I
a = 1.55550 − 0.08106I
b = 0.909923 − 0.492711I
−1.63366 + 6.77137I 6.32659 − 2.86609I
u = −0.139705 + 1.052750I
a = −0.94818 − 1.53693I
b = −0.139705 + 1.052750I
−5.81423 + 0.14287I −5.03844 − 0.22076I
u = −0.139705 − 1.052750I
a = −0.94818 + 1.53693I
b = −0.139705 − 1.052750I
−5.81423 − 0.14287I −5.03844 + 0.22076I
u = 0.501294 + 0.940692I
a = 3.02556 − 0.44481I
b = 0.501294 + 0.940692I
−1.91483 + 3.97058I 1.30591 − 5.30743I
u = 0.501294 − 0.940692I
a = 3.02556 + 0.44481I
b = 0.501294 − 0.940692I
−1.91483 − 3.97058I 1.30591 + 5.30743I
u = 0.688832 + 0.611331I
a = 1.036710 + 0.591577I
b = 0.688832 + 0.611331I
2.69727 + 1.72831I 8.88157 − 2.20446I
u = 0.688832 − 0.611331I
a = 1.036710 − 0.591577I
b = 0.688832 − 0.611331I
2.69727 − 1.72831I 8.88157 + 2.20446I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.381004 + 0.827261I
a = −3.27823 − 1.66424I
b = −0.381004 + 0.827261I
−5.43501 + 1.14701I −0.01474 + 3.75777I
u = −0.381004 − 0.827261I
a = −3.27823 + 1.66424I
b = −0.381004 − 0.827261I
−5.43501 − 1.14701I −0.01474 − 3.75777I
u = 0.200189 + 0.870048I
a = −0.372681 − 0.947305I
b = 0.200189 + 0.870048I
−1.79658 + 2.03837I 4.94429 − 3.28871I
u = 0.200189 − 0.870048I
a = −0.372681 + 0.947305I
b = 0.200189 − 0.870048I
−1.79658 − 2.03837I 4.94429 + 3.28871I
u = −0.578952 + 1.009070I
a = −2.51075 + 0.14445I
b = −0.578952 + 1.009070I
−7.21490 − 9.32769I −0.02899 + 8.70521I
u = −0.578952 − 1.009070I
a = −2.51075 − 0.14445I
b = −0.578952 − 1.009070I
−7.21490 + 9.32769I −0.02899 − 8.70521I
u = −0.366567 + 1.150180I
a = −0.599376 − 1.180700I
b = −0.366567 + 1.150180I
−10.01000 − 4.88118I −3.58337 + 4.01368I
u = −0.366567 − 1.150180I
a = −0.599376 + 1.180700I
b = −0.366567 − 1.150180I
−10.01000 + 4.88118I −3.58337 − 4.01368I
u = 0.571321 + 1.081410I
a = 1.82115 − 1.33171I
b = 0.571321 + 1.081410I
−0.35835 + 8.16861I 2.21656 − 9.01555I
u = 0.571321 − 1.081410I
a = 1.82115 + 1.33171I
b = 0.571321 − 1.081410I
−0.35835 − 8.16861I 2.21656 + 9.01555I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.243891 + 1.224920I
a = 1.121270 − 0.632499I
b = 0.243891 + 1.224920I
−12.57930 − 1.15698I −3.98720 + 0.28766I
u = 0.243891 − 1.224920I
a = 1.121270 + 0.632499I
b = 0.243891 − 1.224920I
−12.57930 + 1.15698I −3.98720 − 0.28766I
u = −0.654621 + 1.124150I
a = −1.94822 − 0.83430I
b = −0.654621 + 1.124150I
0.6028 − 14.1894I 4.78129 + 10.53310I
u = −0.654621 − 1.124150I
a = −1.94822 + 0.83430I
b = −0.654621 − 1.124150I
0.6028 + 14.1894I 4.78129 − 10.53310I
u = 0.693321 + 1.177040I
a = 1.87545 − 0.58432I
b = 0.693321 + 1.177040I
−5.8236 + 18.7593I 1.79263 − 10.16559I
u = 0.693321 − 1.177040I
a = 1.87545 + 0.58432I
b = 0.693321 − 1.177040I
−5.8236 − 18.7593I 1.79263 + 10.16559I
u = −0.523955 + 0.098439I
a = −0.110227 − 1.340260I
b = −0.523955 + 0.098439I
−3.75088 − 2.12272I 6.69106 + 3.68056I
u = −0.523955 − 0.098439I
a = −0.110227 + 1.340260I
b = −0.523955 − 0.098439I
−3.75088 + 2.12272I 6.69106 − 3.68056I
u = 0.319467
a = −0.563407
b = 0.319467
0.696514 14.5290
7
II. I
u
2
= h−1.59 × 10
230
u
101
− 4.37 × 10
230
u
100
+ · · · + 1.89 × 10
230
b + 1.73 ×
10
231
, 1.44 × 10
231
u
101
+ 3.33 × 10
231
u
100
+ · · · + 7.01 × 10
231
a + 5.69 ×
10
232
, u
102
+ 2u
101
+ · · · + 355u + 37i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−0.205818u
101
− 0.474795u
100
+ ··· − 64.7467u − 8.11967
0.838092u
101
+ 2.30531u
100
+ ··· − 43.9751u − 9.12218
a
11
=
−1.04391u
101
− 2.78011u
100
+ ··· − 20.7715u + 1.00251
0.838092u
101
+ 2.30531u
100
+ ··· − 43.9751u − 9.12218
a
8
=
−0.984141u
101
− 1.37621u
100
+ ··· + 694.233u + 78.9684
1.36924u
101
+ 3.70181u
100
+ ··· + 5.91034u − 0.0524316
a
9
=
0.285754u
101
+ 1.91382u
100
+ ··· + 609.940u + 66.2871
1.03471u
101
+ 2.90092u
100
+ ··· + 57.2355u + 5.57705
a
5
=
−0.939420u
101
− 2.38631u
100
+ ··· + 19.5952u + 6.62970
−0.188605u
101
+ 0.204315u
100
+ ··· + 279.590u + 26.3027
a
4
=
−2.63329u
101
− 5.95720u
100
+ ··· + 491.628u + 57.3639
−0.991232u
101
− 0.713435u
100
+ ··· + 811.851u + 80.0452
a
10
=
0.270960u
101
+ 2.58308u
100
+ ··· + 579.670u + 39.5655
1.65331u
101
+ 4.81448u
100
+ ··· + 19.6099u − 9.60995
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.51275u
101
+ 5.29401u
100
+ ··· + 609.190u + 70.3877
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
102
+ 42u
101
+ ··· − 35449u + 1369
c
2
, c
6
, c
7
c
11
u
102
+ 2u
101
+ ··· + 355u + 37
c
3
, c
4
, c
9
(u
51
+ 5u
50
+ ··· + 4u + 1)
2
c
5
(u
51
+ 10u
50
+ ··· + 14u + 1)
2
c
8
, c
12
u
102
− 5u
101
+ ··· + 1274u + 283
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
102
+ 42y
101
+ ··· − 2105827777y + 1874161
c
2
, c
6
, c
7
c
11
y
102
+ 42y
101
+ ··· − 35449y + 1369
c
3
, c
4
, c
9
(y
51
+ 51y
50
+ ··· + 34y −1)
2
c
5
(y
51
+ 10y
50
+ ··· + 6y −1)
2
c
8
, c
12
y
102
+ 13y
101
+ ··· + 4966862y + 80089
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.883326 + 0.463294I
a = −1.231930 − 0.443970I
b = −0.664065 − 1.064720I
2.61076 + 8.50985I 0
u = −0.883326 − 0.463294I
a = −1.231930 + 0.443970I
b = −0.664065 + 1.064720I
2.61076 − 8.50985I 0
u = −0.289966 + 0.954333I
a = −0.582972 + 0.991317I
b = −0.497422 − 1.198620I
−9.16350 + 3.64097I 0
u = −0.289966 − 0.954333I
a = −0.582972 − 0.991317I
b = −0.497422 + 1.198620I
−9.16350 − 3.64097I 0
u = 0.927953 + 0.394599I
a = −1.171310 + 0.410044I
b = −0.626513 + 0.835531I
3.12347 − 0.88237I 0
u = 0.927953 − 0.394599I
a = −1.171310 − 0.410044I
b = −0.626513 − 0.835531I
3.12347 + 0.88237I 0
u = 0.437910 + 0.886426I
a = −0.786248 + 0.965153I
b = −0.956072 + 0.995678I
−2.53266 − 1.33076I 0
u = 0.437910 − 0.886426I
a = −0.786248 − 0.965153I
b = −0.956072 − 0.995678I
−2.53266 + 1.33076I 0
u = 0.433026 + 0.928647I
a = −0.36931 + 1.49334I
b = 0.285145 − 1.082800I
−2.34731 + 1.07784I 0
u = 0.433026 − 0.928647I
a = −0.36931 − 1.49334I
b = 0.285145 + 1.082800I
−2.34731 − 1.07784I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.404366 + 0.884641I
a = −2.07074 + 1.38245I
b = −0.767699 − 1.008430I
−2.47454 + 4.82487I 0
u = 0.404366 − 0.884641I
a = −2.07074 − 1.38245I
b = −0.767699 + 1.008430I
−2.47454 − 4.82487I 0
u = 0.755781 + 0.710365I
a = −0.534011 + 0.998595I
b = −0.677343 + 1.207820I
−3.02328 − 3.40270I 0
u = 0.755781 − 0.710365I
a = −0.534011 − 0.998595I
b = −0.677343 − 1.207820I
−3.02328 + 3.40270I 0
u = 0.277630 + 1.001670I
a = −0.178779 − 0.751026I
b = −0.057194 + 0.740808I
−1.81087 + 1.95780I 0
u = 0.277630 − 1.001670I
a = −0.178779 + 0.751026I
b = −0.057194 − 0.740808I
−1.81087 − 1.95780I 0
u = −0.626513 + 0.835531I
a = 0.654741 + 1.003570I
b = 0.927953 + 0.394599I
3.12347 − 0.88237I 0
u = −0.626513 − 0.835531I
a = 0.654741 − 1.003570I
b = 0.927953 − 0.394599I
3.12347 + 0.88237I 0
u = −0.634342 + 0.842559I
a = 1.45930 + 0.26477I
b = 0.935236 − 0.574503I
3.10678 − 4.05702I 0
u = −0.634342 − 0.842559I
a = 1.45930 − 0.26477I
b = 0.935236 + 0.574503I
3.10678 + 4.05702I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.450001 + 0.954825I
a = −1.37840 − 1.44259I
b = −0.615703 − 0.610926I
−5.99173 − 4.58565I 0
u = −0.450001 − 0.954825I
a = −1.37840 + 1.44259I
b = −0.615703 + 0.610926I
−5.99173 + 4.58565I 0
u = 0.087230 + 1.060010I
a = −0.219547 − 0.428028I
b = −0.454749 + 0.396373I
−1.98416 + 1.90385I 0
u = 0.087230 − 1.060010I
a = −0.219547 + 0.428028I
b = −0.454749 − 0.396373I
−1.98416 − 1.90385I 0
u = 0.536643 + 0.765315I
a = −0.186999 + 1.349050I
b = −1.008530 + 0.628210I
−1.34733 − 1.57036I 0
u = 0.536643 − 0.765315I
a = −0.186999 − 1.349050I
b = −1.008530 − 0.628210I
−1.34733 + 1.57036I 0
u = 0.535064 + 0.922653I
a = −1.60320 + 0.23068I
b = −1.093070 − 0.770145I
−1.85244 + 5.89606I 0
u = 0.535064 − 0.922653I
a = −1.60320 − 0.23068I
b = −1.093070 + 0.770145I
−1.85244 − 5.89606I 0
u = −1.070460 + 0.069288I
a = 1.47183 − 0.43431I
b = 0.707727 − 0.854284I
0.14618 − 2.70697I 0
u = −1.070460 − 0.069288I
a = 1.47183 + 0.43431I
b = 0.707727 + 0.854284I
0.14618 + 2.70697I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.410743 + 0.992038I
a = −0.360677 − 0.010930I
b = −0.808634 + 0.158889I
−6.02820 − 1.17456I 0
u = −0.410743 − 0.992038I
a = −0.360677 + 0.010930I
b = −0.808634 − 0.158889I
−6.02820 + 1.17456I 0
u = 0.935236 + 0.574503I
a = −1.39806 − 0.27630I
b = −0.634342 − 0.842559I
3.10678 + 4.05702I 0
u = 0.935236 − 0.574503I
a = −1.39806 + 0.27630I
b = −0.634342 + 0.842559I
3.10678 − 4.05702I 0
u = 1.011940 + 0.447765I
a = 1.143230 − 0.616579I
b = 0.674922 − 1.122140I
−3.56054 − 12.59790I 0
u = 1.011940 − 0.447765I
a = 1.143230 + 0.616579I
b = 0.674922 + 1.122140I
−3.56054 + 12.59790I 0
u = −0.571975 + 0.684267I
a = 0.732205 + 0.954750I
b = 0.769505 + 1.032950I
1.73965 + 2.15384I 0
u = −0.571975 − 0.684267I
a = 0.732205 − 0.954750I
b = 0.769505 − 1.032950I
1.73965 − 2.15384I 0
u = 0.707727 + 0.854284I
a = −1.28225 + 0.74677I
b = −1.070460 − 0.069288I
0.14618 + 2.70697I 0
u = 0.707727 − 0.854284I
a = −1.28225 − 0.74677I
b = −1.070460 + 0.069288I
0.14618 − 2.70697I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455083 + 0.761511I
a = 1.24999 − 2.09166I
b = 0.455083 − 0.761511I
−1.28248 0
u = 0.455083 − 0.761511I
a = 1.24999 + 2.09166I
b = 0.455083 + 0.761511I
−1.28248 0
u = 0.685999 + 0.880355I
a = −0.640843 + 0.203641I
b = −0.199272 − 0.020479I
1.10860 + 2.64346I 0
u = 0.685999 − 0.880355I
a = −0.640843 − 0.203641I
b = −0.199272 + 0.020479I
1.10860 − 2.64346I 0
u = 0.285145 + 1.082800I
a = −0.614055 + 1.266720I
b = 0.433026 − 0.928647I
−2.34731 − 1.07784I 0
u = 0.285145 − 1.082800I
a = −0.614055 − 1.266720I
b = 0.433026 + 0.928647I
−2.34731 + 1.07784I 0
u = −0.615703 + 0.610926I
a = −1.09332 − 2.16809I
b = −0.450001 − 0.954825I
−5.99173 + 4.58565I 0
u = −0.615703 − 0.610926I
a = −1.09332 + 2.16809I
b = −0.450001 + 0.954825I
−5.99173 − 4.58565I 0
u = −0.592827 + 0.968328I
a = 2.02629 + 0.65635I
b = 0.697752 − 1.156900I
0.84909 − 6.84814I 0
u = −0.592827 − 0.968328I
a = 2.02629 − 0.65635I
b = 0.697752 + 1.156900I
0.84909 + 6.84814I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.542428 + 1.004560I
a = 0.907869 + 0.798248I
b = −0.032353 − 1.204750I
−3.49032 − 6.17948I 0
u = −0.542428 − 1.004560I
a = 0.907869 − 0.798248I
b = −0.032353 + 1.204750I
−3.49032 + 6.17948I 0
u = −0.808634 + 0.158889I
a = −0.271966 + 0.383490I
b = −0.410743 + 0.992038I
−6.02820 − 1.17456I 0
u = −0.808634 − 0.158889I
a = −0.271966 − 0.383490I
b = −0.410743 − 0.992038I
−6.02820 + 1.17456I 0
u = 0.626135 + 0.999013I
a = −0.051918 − 0.861877I
b = 0.645864 − 0.429108I
1.54195 + 3.35933I 0
u = 0.626135 − 0.999013I
a = −0.051918 + 0.861877I
b = 0.645864 + 0.429108I
1.54195 − 3.35933I 0
u = −1.008530 + 0.628210I
a = 1.067700 + 0.089134I
b = 0.536643 + 0.765315I
−1.34733 − 1.57036I 0
u = −1.008530 − 0.628210I
a = 1.067700 − 0.089134I
b = 0.536643 − 0.765315I
−1.34733 + 1.57036I 0
u = 0.686733 + 0.970497I
a = −2.02739 + 0.27982I
b = −0.66825 − 1.31639I
−3.81313 + 8.88150I 0
u = 0.686733 − 0.970497I
a = −2.02739 − 0.27982I
b = −0.66825 + 1.31639I
−3.81313 − 8.88150I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.032353 + 1.204750I
a = −0.368491 + 1.084260I
b = −0.542428 − 1.004560I
−3.49032 + 6.17948I 0
u = −0.032353 − 1.204750I
a = −0.368491 − 1.084260I
b = −0.542428 + 1.004560I
−3.49032 − 6.17948I 0
u = 0.645864 + 0.429108I
a = 1.312110 + 0.044101I
b = 0.626135 − 0.999013I
1.54195 − 3.35933I 6.00000 + 3.99088I
u = 0.645864 − 0.429108I
a = 1.312110 − 0.044101I
b = 0.626135 + 0.999013I
1.54195 + 3.35933I 6.00000 − 3.99088I
u = −0.023255 + 1.228140I
a = 0.676336 − 0.446835I
b = 0.692834 + 0.181713I
−8.18698 − 4.53726I 0
u = −0.023255 − 1.228140I
a = 0.676336 + 0.446835I
b = 0.692834 − 0.181713I
−8.18698 + 4.53726I 0
u = 0.547155 + 1.099940I
a = −0.772638 + 0.327884I
b = 0.02015 − 1.42437I
−10.59120 + 9.14688I 0
u = 0.547155 − 1.099940I
a = −0.772638 − 0.327884I
b = 0.02015 + 1.42437I
−10.59120 − 9.14688I 0
u = −0.664065 + 1.064720I
a = −0.424925 − 0.950207I
b = −0.883326 − 0.463294I
2.61076 − 8.50985I 0
u = −0.664065 − 1.064720I
a = −0.424925 + 0.950207I
b = −0.883326 + 0.463294I
2.61076 + 8.50985I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.057194 + 0.740808I
a = −0.592886 − 0.902712I
b = 0.277630 + 1.001670I
−1.81087 + 1.95780I 3.49223 − 4.81893I
u = −0.057194 − 0.740808I
a = −0.592886 + 0.902712I
b = 0.277630 − 1.001670I
−1.81087 − 1.95780I 3.49223 + 4.81893I
u = −0.767699 + 1.008430I
a = 1.78379 + 0.68512I
b = 0.404366 − 0.884641I
−2.47454 − 4.82487I 0
u = −0.767699 − 1.008430I
a = 1.78379 − 0.68512I
b = 0.404366 + 0.884641I
−2.47454 + 4.82487I 0
u = 0.692834 + 0.181713I
a = 1.017740 + 0.946966I
b = −0.023255 + 1.228140I
−8.18698 − 4.53726I 0.39761 + 4.02058I
u = 0.692834 − 0.181713I
a = 1.017740 − 0.946966I
b = −0.023255 − 1.228140I
−8.18698 + 4.53726I 0.39761 − 4.02058I
u = 0.769505 + 1.032950I
a = −0.525306 + 0.646577I
b = −0.571975 + 0.684267I
1.73965 + 2.15384I 0
u = 0.769505 − 1.032950I
a = −0.525306 − 0.646577I
b = −0.571975 − 0.684267I
1.73965 − 2.15384I 0
u = −0.497422 + 1.198620I
a = 0.830046 + 0.303784I
b = −0.289966 − 0.954333I
−9.16350 − 3.64097I 0
u = −0.497422 − 1.198620I
a = 0.830046 − 0.303784I
b = −0.289966 + 0.954333I
−9.16350 + 3.64097I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.674922 + 1.122140I
a = 0.637340 − 0.893652I
b = 1.011940 − 0.447765I
−3.56054 + 12.59790I 0
u = 0.674922 − 1.122140I
a = 0.637340 + 0.893652I
b = 1.011940 + 0.447765I
−3.56054 − 12.59790I 0
u = −0.330282 + 1.293050I
a = 0.290390 − 0.963127I
b = 0.088687 + 0.632851I
−7.89454 − 5.07882I 0
u = −0.330282 − 1.293050I
a = 0.290390 + 0.963127I
b = 0.088687 − 0.632851I
−7.89454 + 5.07882I 0
u = −1.093070 + 0.770145I
a = 1.238560 − 0.367686I
b = 0.535064 − 0.922653I
−1.85244 − 5.89606I 0
u = −1.093070 − 0.770145I
a = 1.238560 + 0.367686I
b = 0.535064 + 0.922653I
−1.85244 + 5.89606I 0
u = 0.697752 + 1.156900I
a = −1.69916 + 0.56289I
b = −0.592827 − 0.968328I
0.84909 + 6.84814I 0
u = 0.697752 − 1.156900I
a = −1.69916 − 0.56289I
b = −0.592827 + 0.968328I
0.84909 − 6.84814I 0
u = 0.088687 + 0.632851I
a = 1.32451 − 1.63071I
b = −0.330282 + 1.293050I
−7.89454 − 5.07882I 0.44303 + 9.15635I
u = 0.088687 − 0.632851I
a = 1.32451 + 1.63071I
b = −0.330282 − 1.293050I
−7.89454 + 5.07882I 0.44303 − 9.15635I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.956072 + 0.995678I
a = 0.458696 + 0.764601I
b = 0.437910 + 0.886426I
−2.53266 − 1.33076I 0
u = −0.956072 − 0.995678I
a = 0.458696 − 0.764601I
b = 0.437910 − 0.886426I
−2.53266 + 1.33076I 0
u = −0.677343 + 1.207820I
a = 0.629553 + 0.568412I
b = 0.755781 + 0.710365I
−3.02328 − 3.40270I 0
u = −0.677343 − 1.207820I
a = 0.629553 − 0.568412I
b = 0.755781 − 0.710365I
−3.02328 + 3.40270I 0
u = −0.454749 + 0.396373I
a = −0.837192 − 0.135858I
b = 0.087230 + 1.060010I
−1.98416 + 1.90385I 3.55438 − 4.24551I
u = −0.454749 − 0.396373I
a = −0.837192 + 0.135858I
b = 0.087230 − 1.060010I
−1.98416 − 1.90385I 3.55438 + 4.24551I
u = 0.02015 + 1.42437I
a = 0.462827 + 0.556548I
b = 0.547155 − 1.099940I
−10.59120 − 9.14688I 0
u = 0.02015 − 1.42437I
a = 0.462827 − 0.556548I
b = 0.547155 + 1.099940I
−10.59120 + 9.14688I 0
u = −0.66825 + 1.31639I
a = 1.58251 + 0.46059I
b = 0.686733 − 0.970497I
−3.81313 − 8.88150I 0
u = −0.66825 − 1.31639I
a = 1.58251 − 0.46059I
b = 0.686733 + 0.970497I
−3.81313 + 8.88150I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.199272 + 0.020479I
a = 3.28994 − 1.79201I
b = 0.685999 − 0.880355I
1.10860 − 2.64346I 2.48196 + 4.19857I
u = −0.199272 − 0.020479I
a = 3.28994 + 1.79201I
b = 0.685999 + 0.880355I
1.10860 + 2.64346I 2.48196 − 4.19857I
21
III. I
u
3
= hb + u, 4u
13
+ 5u
12
+ · · · + a + 5, u
14
+ u
13
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−4u
13
− 5u
12
+ ··· − 9u − 5
−u
a
11
=
−4u
13
− 5u
12
+ ··· − 8u − 5
−u
a
8
=
−u
13
+ u
12
+ ··· − u + 5
−u
2
a
9
=
−u
13
+ u
12
+ ··· − u + 5
u
8
+ 2u
6
+ 3u
4
+ u
2
+ 1
a
5
=
u
13
− 2u
12
+ ··· − 17u
2
− 6
u
12
+ u
11
+ 3u
10
+ 2u
9
+ 5u
8
+ 3u
7
+ 5u
6
+ 2u
5
+ 3u
4
+ u
3
+ 3u
2
a
4
=
4u
13
+ 3u
12
+ ··· + 22u
3
+ 10u
−u
8
− 2u
6
− 3u
4
+ u
3
− 2u
2
+ u − 1
a
10
=
−2u
13
− 3u
12
+ ··· − 3u − 4
−u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
13
+ 6u
12
+ 2u
11
+ 17u
10
+ 3u
9
+ 31u
8
+ 8u
7
+ 31u
6
+ 2u
5
+ 20u
4
+ 10u
2
− 6u + 1
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
14
− 7u
13
+ ··· − 9u + 1
c
2
, c
7
u
14
− u
13
+ ··· − u + 1
c
3
, c
4
u
14
− 2u
13
+ ··· + 6u
2
+ 1
c
5
u
14
− 4u
13
+ ··· + 2u
3
+ 1
c
6
, c
11
u
14
+ u
13
+ ··· + u + 1
c
8
, c
12
u
14
+ u
12
+ u
11
+ 4u
10
+ 4u
8
+ u
7
+ 4u
6
− 3u
5
− 2u
3
+ u
2
+ 1
c
9
u
14
+ 2u
13
+ ··· + 6u
2
+ 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 7y
13
+ ··· − 3y + 1
c
2
, c
6
, c
7
c
11
y
14
+ 7y
13
+ ··· + 9y + 1
c
3
, c
4
, c
9
y
14
+ 14y
13
+ ··· + 12y + 1
c
5
y
14
− 4y
13
+ ··· − 4y
2
+ 1
c
8
, c
12
y
14
+ 2y
13
+ ··· + 2y + 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671182 + 0.725901I
a = −1.292460 − 0.243143I
b = −0.671182 − 0.725901I
2.06538 + 3.67080I 5.64541 − 6.66163I
u = 0.671182 − 0.725901I
a = −1.292460 + 0.243143I
b = −0.671182 + 0.725901I
2.06538 − 3.67080I 5.64541 + 6.66163I
u = −0.793038 + 0.664651I
a = 1.71383 + 0.30923I
b = 0.793038 − 0.664651I
−0.88145 − 3.69626I 6.44058 + 5.14741I
u = −0.793038 − 0.664651I
a = 1.71383 − 0.30923I
b = 0.793038 + 0.664651I
−0.88145 + 3.69626I 6.44058 − 5.14741I
u = 0.224536 + 0.872130I
a = 0.971389 + 0.173451I
b = −0.224536 − 0.872130I
−2.52555 + 2.12926I −5.96582 − 3.57240I
u = 0.224536 − 0.872130I
a = 0.971389 − 0.173451I
b = −0.224536 + 0.872130I
−2.52555 − 2.12926I −5.96582 + 3.57240I
u = −0.302417 + 1.114430I
a = 0.186586 + 0.619048I
b = 0.302417 − 1.114430I
−9.50477 − 6.59501I −1.80372 + 7.43625I
u = −0.302417 − 1.114430I
a = 0.186586 − 0.619048I
b = 0.302417 + 1.114430I
−9.50477 + 6.59501I −1.80372 − 7.43625I
u = 0.579917 + 1.045350I
a = −1.83805 + 0.88797I
b = −0.579917 − 1.045350I
−0.05133 + 6.16066I 2.99536 − 5.28102I
u = 0.579917 − 1.045350I
a = −1.83805 − 0.88797I
b = −0.579917 + 1.045350I
−0.05133 − 6.16066I 2.99536 + 5.28102I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.701928 + 1.086370I
a = 1.81639 + 0.26973I
b = 0.701928 − 1.086370I
−3.52038 − 7.74611I 3.61719 + 4.78597I
u = −0.701928 − 1.086370I
a = 1.81639 − 0.26973I
b = 0.701928 + 1.086370I
−3.52038 + 7.74611I 3.61719 − 4.78597I
u = −0.178252 + 0.581238I
a = −3.05769 − 1.63827I
b = 0.178252 − 0.581238I
−5.32110 + 2.03598I 0.07099 − 4.06570I
u = −0.178252 − 0.581238I
a = −3.05769 + 1.63827I
b = 0.178252 + 0.581238I
−5.32110 − 2.03598I 0.07099 + 4.06570I
26
IV.
I
u
4
= h−u
13
−u
12
+· · · +b − 1, 3u
13
+4u
12
+· · · +a + 3, u
14
+u
13
+· · · +u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
12
=
−3u
13
− 4u
12
+ ··· − 4u − 3
u
13
+ u
12
+ ··· + 4u + 1
a
11
=
−4u
13
− 5u
12
+ ··· − 8u − 4
u
13
+ u
12
+ ··· + 4u + 1
a
8
=
4u
13
+ 11u
11
+ ··· + 4u − 3
−u
13
− 3u
11
+ ··· − u + 3
a
9
=
4u
13
+ 11u
11
+ ··· + 4u − 2
u
6
+ 2u
4
+ 3u
2
+ 2
a
5
=
u
13
− 2u
12
+ ··· − u − 5
u
12
+ u
11
+ 3u
10
+ 2u
9
+ 5u
8
+ 3u
7
+ 6u
6
+ 2u
5
+ 3u
4
+ u
3
+ u
2
+ 1
a
4
=
2u
13
+ 2u
12
+ ··· − 3u
2
+ 6u
−u
13
− 2u
12
+ ··· − u − 2
a
10
=
−3u
13
− u
12
+ ··· − 2u
2
− 5u
−2u
13
− 3u
12
+ ··· − 2u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 7u
13
+ 3u
12
+ 23u
11
+ 5u
10
+ 46u
9
+ 7u
8
+ 62u
7
−4u
6
+ 50u
5
−8u
4
+ 18u
3
−4u
2
+ 3u −1
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
14
− 7u
13
+ ··· − 7u + 1
c
2
, c
7
u
14
− u
13
+ ··· − u + 1
c
3
, c
4
(u
7
+ u
6
+ 4u
5
+ 3u
4
+ 4u
3
+ 3u
2
+ 1)
2
c
5
(u
7
+ u
6
+ 2u
4
+ 2u
3
+ 1)
2
c
6
, c
11
u
14
+ u
13
+ ··· + u + 1
c
8
, c
12
u
14
+ 3u
12
+ ··· + u
2
+ 1
c
9
(u
7
− u
6
+ 4u
5
− 3u
4
+ 4u
3
− 3u
2
− 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
14
+ 7y
13
+ ··· + 7y + 1
c
2
, c
6
, c
7
c
11
y
14
+ 7y
13
+ ··· + 7y + 1
c
3
, c
4
, c
9
(y
7
+ 7y
6
+ 18y
5
+ 17y
4
− 4y
3
− 15y
2
− 6y −1)
2
c
5
(y
7
− y
6
− 4y
4
+ 2y
3
− 4y
2
− 1)
2
c
8
, c
12
y
14
+ 6y
13
+ ··· + 2y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.271185 + 0.962527I
a = 0.57562 − 2.04306I
b = −0.271185 + 0.962527I
−2.92298 −2.67806 + 0.I
u = 0.271185 − 0.962527I
a = 0.57562 + 2.04306I
b = −0.271185 − 0.962527I
−2.92298 −2.67806 + 0.I
u = 0.495942 + 0.666193I
a = −1.018620 + 0.675189I
b = −0.718995 + 0.965817I
1.30150 − 1.74054I 3.15536 − 3.74217I
u = 0.495942 − 0.666193I
a = −1.018620 − 0.675189I
b = −0.718995 − 0.965817I
1.30150 + 1.74054I 3.15536 + 3.74217I
u = 0.718995 + 0.965817I
a = −0.244617 + 0.806678I
b = −0.495942 + 0.666193I
1.30150 + 1.74054I 3.15536 + 3.74217I
u = 0.718995 − 0.965817I
a = −0.244617 − 0.806678I
b = −0.495942 − 0.666193I
1.30150 − 1.74054I 3.15536 − 3.74217I
u = −0.216324 + 0.753207I
a = −0.66599 − 2.09077I
b = 0.352252 + 1.226490I
−8.02266 + 4.40574I −1.79398 + 0.51667I
u = −0.216324 − 0.753207I
a = −0.66599 + 2.09077I
b = 0.352252 − 1.226490I
−8.02266 − 4.40574I −1.79398 − 0.51667I
u = −0.531010 + 0.563027I
a = 0.70050 + 1.69298I
b = 0.886537 + 0.939991I
−1.68696 + 2.64701I 5.97765 − 4.71404I
u = −0.531010 − 0.563027I
a = 0.70050 − 1.69298I
b = 0.886537 − 0.939991I
−1.68696 − 2.64701I 5.97765 + 4.71404I
30
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.352252 + 1.226490I
a = −0.334661 − 1.305320I
b = 0.216324 + 0.753207I
−8.02266 − 4.40574I −1.79398 − 0.51667I
u = −0.352252 − 1.226490I
a = −0.334661 + 1.305320I
b = 0.216324 − 0.753207I
−8.02266 + 4.40574I −1.79398 + 0.51667I
u = −0.886537 + 0.939991I
a = 0.987774 + 0.478161I
b = 0.531010 + 0.563027I
−1.68696 − 2.64701I 5.97765 + 4.71404I
u = −0.886537 − 0.939991I
a = 0.987774 − 0.478161I
b = 0.531010 − 0.563027I
−1.68696 + 2.64701I 5.97765 − 4.71404I
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
14
− 7u
13
+ ··· − 7u + 1)(u
14
− 7u
13
+ ··· − 9u + 1)
· (u
29
+ 15u
28
+ ··· + 7u − 1)(u
102
+ 42u
101
+ ··· − 35449u + 1369)
c
2
, c
7
(u
14
− u
13
+ ··· − u + 1)(u
14
− u
13
+ ··· − u + 1)(u
29
− u
28
+ ··· + u − 1)
· (u
102
+ 2u
101
+ ··· + 355u + 37)
c
3
, c
4
((u
7
+ u
6
+ ··· + 3u
2
+ 1)
2
)(u
14
− 2u
13
+ ··· + 6u
2
+ 1)
· (u
29
− 11u
28
+ ··· + 344u − 32)(u
51
+ 5u
50
+ ··· + 4u + 1)
2
c
5
((u
7
+ u
6
+ 2u
4
+ 2u
3
+ 1)
2
)(u
14
− 4u
13
+ ··· + 2u
3
+ 1)
· (u
29
− 25u
28
+ ··· + 30720u − 2048)(u
51
+ 10u
50
+ ··· + 14u + 1)
2
c
6
, c
11
(u
14
+ u
13
+ ··· + u + 1)(u
14
+ u
13
+ ··· + u + 1)(u
29
− u
28
+ ··· + u − 1)
· (u
102
+ 2u
101
+ ··· + 355u + 37)
c
8
, c
12
(u
14
+ u
12
+ u
11
+ 4u
10
+ 4u
8
+ u
7
+ 4u
6
− 3u
5
− 2u
3
+ u
2
+ 1)
· (u
14
+ 3u
12
+ ··· + u
2
+ 1)(u
29
+ 7u
27
+ ··· − 2u − 1)
· (u
102
− 5u
101
+ ··· + 1274u + 283)
c
9
((u
7
− u
6
+ ··· − 3u
2
− 1)
2
)(u
14
+ 2u
13
+ ··· + 6u
2
+ 1)
· (u
29
− 11u
28
+ ··· + 344u − 32)(u
51
+ 5u
50
+ ··· + 4u + 1)
2
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
14
+ 7y
13
+ ··· + 7y + 1)(y
14
+ 7y
13
+ ··· − 3y + 1)
· (y
29
+ 7y
28
+ ··· + 111y −1)
· (y
102
+ 42y
101
+ ··· − 2105827777y + 1874161)
c
2
, c
6
, c
7
c
11
(y
14
+ 7y
13
+ ··· + 9y + 1)(y
14
+ 7y
13
+ ··· + 7y + 1)
· (y
29
+ 15y
28
+ ··· + 7y −1)(y
102
+ 42y
101
+ ··· − 35449y + 1369)
c
3
, c
4
, c
9
(y
7
+ 7y
6
+ 18y
5
+ 17y
4
− 4y
3
− 15y
2
− 6y −1)
2
· (y
14
+ 14y
13
+ ··· + 12y + 1)(y
29
+ 25y
28
+ ··· − 1728y −1024)
· (y
51
+ 51y
50
+ ··· + 34y −1)
2
c
5
((y
7
− y
6
− 4y
4
+ 2y
3
− 4y
2
− 1)
2
)(y
14
− 4y
13
+ ··· − 4y
2
+ 1)
· (y
29
− 3y
28
+ ··· + 85983232y −4194304)
· (y
51
+ 10y
50
+ ··· + 6y −1)
2
c
8
, c
12
(y
14
+ 2y
13
+ ··· + 2y + 1)(y
14
+ 6y
13
+ ··· + 2y + 1)
· (y
29
+ 14y
28
+ ··· − 30y −1)
· (y
102
+ 13y
101
+ ··· + 4966862y + 80089)
33
