12a
1094
(K12a
1094
)
A knot diagram
1
Linearized knot diagam
4 7 10 1 12 9 2 11 3 6 8 5
Solving Sequence
6,12
5 1 4
2,8
7 11 9 10 3
c
5
c
12
c
4
c
1
c
7
c
11
c
8
c
10
c
3
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h6.83030 × 10
106
u
89
+ 1.55405 × 10
107
u
88
+ ··· + 6.21904 × 10
106
b + 7.24350 × 10
106
,
1.29538 × 10
107
u
89
+ 3.57847 × 10
107
u
88
+ ··· + 6.21904 × 10
106
a + 6.18948 × 10
106
, u
90
+ 3u
89
+ ··· + 12u + 1i
I
u
2
= hu
22
+ 2u
21
+ ··· + b − 1, u
23
+ 2u
22
+ ··· + a − 7, u
24
+ 2u
23
+ ··· + 17u
2
+ 1i
I
u
3
= hu
2
+ b, a − 1, u
7
+ 3u
5
+ 2u
3
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 121 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
= h6.83 × 10
106
u
89
+ 1.55 × 10
107
u
88
+ · · · + 6.22 × 10
106
b + 7.24 ×
10
106
, 1.30 × 10
107
u
89
+ 3.58 × 10
107
u
88
+ · · · + 6.22 × 10
106
a + 6.19 ×
10
106
, u
90
+ 3u
89
+ · · · + 12u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
8
=
−2.08292u
89
− 5.75405u
88
+ ··· − 103.537u − 0.995248
−1.09829u
89
− 2.49885u
88
+ ··· − 36.1802u − 1.16473
a
7
=
−2.30239u
89
− 5.89176u
88
+ ··· − 92.0794u + 0.607952
−0.686489u
89
− 1.62055u
88
+ ··· − 35.8591u − 1.44130
a
11
=
−0.0309762u
89
− 0.977314u
88
+ ··· − 81.9158u − 10.9345
−1.14038u
89
− 3.23467u
88
+ ··· − 35.2548u − 4.73665
a
9
=
3.07250u
89
+ 8.58048u
88
+ ··· + 42.3487u + 8.12578
0.0736579u
89
− 0.256335u
88
+ ··· − 40.1867u − 2.49488
a
10
=
−1.17135u
89
− 4.21198u
88
+ ··· − 117.171u − 15.6711
−1.14038u
89
− 3.23467u
88
+ ··· − 35.2548u − 4.73665
a
3
=
−3.38625u
89
− 10.3318u
88
+ ··· − 155.927u − 20.4178
−1.23019u
89
− 3.17312u
88
+ ··· − 10.9793u − 2.96508
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.162569u
89
− 3.73818u
88
+ ··· − 145.744u − 28.3707
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
12
u
90
− 3u
89
+ ··· − 12u + 1
c
2
, c
7
u
90
+ u
89
+ ··· − 1472u + 37417
c
3
, c
9
u
90
− 6u
89
+ ··· − 13860u + 2776
c
6
u
90
− 5u
89
+ ··· − 305292u + 114001
c
8
, c
11
u
90
+ 5u
89
+ ··· + 7842u + 839
c
10
u
90
+ u
89
+ ··· + 13461u + 2479
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
12
y
90
+ 109y
89
+ ··· + 174y + 1
c
2
, c
7
y
90
+ 65y
89
+ ··· + 22616709052y + 1400031889
c
3
, c
9
y
90
− 58y
89
+ ··· − 11659600y + 7706176
c
6
y
90
− 45y
89
+ ··· − 374166877836y + 12996228001
c
8
, c
11
y
90
+ 53y
89
+ ··· + 29423788y + 703921
c
10
y
90
− 19y
89
+ ··· − 310592405y + 6145441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.673798 + 0.745251I
a = 0.59357 − 1.29182I
b = 0.71141 + 1.77487I
−7.3826 + 13.2885I 0
u = −0.673798 − 0.745251I
a = 0.59357 + 1.29182I
b = 0.71141 − 1.77487I
−7.3826 − 13.2885I 0
u = −0.318813 + 0.972274I
a = 0.354309 − 0.417115I
b = 1.29131 + 0.58699I
−1.92726 − 1.07654I 0
u = −0.318813 − 0.972274I
a = 0.354309 + 0.417115I
b = 1.29131 − 0.58699I
−1.92726 + 1.07654I 0
u = 0.554780 + 0.764528I
a = 0.78623 + 1.29463I
b = 0.56005 − 1.47151I
−3.13661 − 7.27639I 0
u = 0.554780 − 0.764528I
a = 0.78623 − 1.29463I
b = 0.56005 + 1.47151I
−3.13661 + 7.27639I 0
u = 0.623759 + 0.627084I
a = −0.507263 − 0.842395I
b = −0.275207 + 1.385920I
−0.99512 − 2.46332I 0
u = 0.623759 − 0.627084I
a = −0.507263 + 0.842395I
b = −0.275207 − 1.385920I
−0.99512 + 2.46332I 0
u = −0.842119 + 0.262679I
a = −0.89625 + 1.19447I
b = 0.10031 − 1.55471I
−8.85310 − 8.28939I 0
u = −0.842119 − 0.262679I
a = −0.89625 − 1.19447I
b = 0.10031 + 1.55471I
−8.85310 + 8.28939I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.333793 + 0.814040I
a = 0.333808 − 0.618859I
b = −0.397603 + 0.240312I
0.82127 − 2.96271I 0
u = 0.333793 − 0.814040I
a = 0.333808 + 0.618859I
b = −0.397603 − 0.240312I
0.82127 + 2.96271I 0
u = −0.728004 + 0.474895I
a = −0.012276 + 1.177780I
b = −0.64564 − 1.47165I
−2.24160 + 4.56943I 0
u = −0.728004 − 0.474895I
a = −0.012276 − 1.177780I
b = −0.64564 + 1.47165I
−2.24160 − 4.56943I 0
u = 0.482332 + 1.026280I
a = −0.881390 − 0.301898I
b = −0.096950 + 1.030020I
−1.64550 − 1.00721I 0
u = 0.482332 − 1.026280I
a = −0.881390 + 0.301898I
b = −0.096950 − 1.030020I
−1.64550 + 1.00721I 0
u = 0.460781 + 0.723596I
a = −0.95388 − 1.13852I
b = −0.92691 + 1.88015I
−2.60445 − 6.80426I 0
u = 0.460781 − 0.723596I
a = −0.95388 + 1.13852I
b = −0.92691 − 1.88015I
−2.60445 + 6.80426I 0
u = −0.480650 + 0.682439I
a = −0.840573 − 1.018620I
b = 0.325724 + 0.037139I
−3.54498 + 7.46328I 0
u = −0.480650 − 0.682439I
a = −0.840573 + 1.018620I
b = 0.325724 − 0.037139I
−3.54498 − 7.46328I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.606401 + 0.536748I
a = 0.633565 + 0.941223I
b = 0.759168 − 1.129370I
−1.24922 − 1.84743I 0
u = 0.606401 − 0.536748I
a = 0.633565 − 0.941223I
b = 0.759168 + 1.129370I
−1.24922 + 1.84743I 0
u = −0.435225 + 0.607327I
a = 0.92412 − 1.62359I
b = −0.049735 + 1.375830I
−7.97752 + 1.18412I 0
u = −0.435225 − 0.607327I
a = 0.92412 + 1.62359I
b = −0.049735 − 1.375830I
−7.97752 − 1.18412I 0
u = −0.023012 + 0.742460I
a = 0.522236 + 0.983323I
b = −0.261413 − 0.072232I
2.61458 − 1.00048I 4.78491 + 0.I
u = −0.023012 − 0.742460I
a = 0.522236 − 0.983323I
b = −0.261413 + 0.072232I
2.61458 + 1.00048I 4.78491 + 0.I
u = 0.719114 + 0.115823I
a = −0.71219 − 1.64056I
b = 0.248123 + 1.314870I
−5.06440 + 3.04875I −8.83314 + 0.I
u = 0.719114 − 0.115823I
a = −0.71219 + 1.64056I
b = 0.248123 − 1.314870I
−5.06440 − 3.04875I −8.83314 + 0.I
u = −0.351277 + 0.637125I
a = −1.35884 + 0.80934I
b = 0.77567 − 1.76558I
−7.28579 + 3.28442I −10.21600 − 5.71945I
u = −0.351277 − 0.637125I
a = −1.35884 − 0.80934I
b = 0.77567 + 1.76558I
−7.28579 − 3.28442I −10.21600 + 5.71945I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.322032 + 0.582986I
a = −1.10239 + 1.43621I
b = −0.74002 − 1.37048I
0.31504 + 3.55410I 1.14398 − 3.08134I
u = −0.322032 − 0.582986I
a = −1.10239 − 1.43621I
b = −0.74002 + 1.37048I
0.31504 − 3.55410I 1.14398 + 3.08134I
u = 0.297325 + 0.534718I
a = −1.36743 + 1.56487I
b = 0.130393 − 0.297413I
0.640275 − 1.076890I −9.95339 + 7.93804I
u = 0.297325 − 0.534718I
a = −1.36743 − 1.56487I
b = 0.130393 + 0.297413I
0.640275 + 1.076890I −9.95339 − 7.93804I
u = −0.443413 + 1.318820I
a = −0.822661 + 0.037051I
b = −0.491648 − 0.873884I
−3.97398 − 3.73488I 0
u = −0.443413 − 1.318820I
a = −0.822661 − 0.037051I
b = −0.491648 + 0.873884I
−3.97398 + 3.73488I 0
u = 0.567850 + 0.053435I
a = 0.81195 + 1.80477I
b = 0.03229 − 1.65600I
−4.48683 + 3.36404I −10.30131 − 3.00530I
u = 0.567850 − 0.053435I
a = 0.81195 − 1.80477I
b = 0.03229 + 1.65600I
−4.48683 − 3.36404I −10.30131 + 3.00530I
u = −0.526246 + 0.154775I
a = −1.323770 − 0.193749I
b = 0.488101 + 0.678138I
−5.02204 − 3.97750I −8.31267 + 2.01753I
u = −0.526246 − 0.154775I
a = −1.323770 + 0.193749I
b = 0.488101 − 0.678138I
−5.02204 + 3.97750I −8.31267 − 2.01753I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.402344 + 0.338151I
a = −2.36158 + 1.72500I
b = −0.187161 − 0.764440I
−8.79879 + 1.84825I −12.51899 − 6.35775I
u = −0.402344 − 0.338151I
a = −2.36158 − 1.72500I
b = −0.187161 + 0.764440I
−8.79879 − 1.84825I −12.51899 + 6.35775I
u = −0.01524 + 1.48437I
a = −0.592770 − 0.554203I
b = −0.20835 + 1.83224I
0.18449 − 3.18606I 0
u = −0.01524 − 1.48437I
a = −0.592770 + 0.554203I
b = −0.20835 − 1.83224I
0.18449 + 3.18606I 0
u = −0.06610 + 1.50441I
a = −1.169580 − 0.132340I
b = −0.820952 − 0.055008I
−2.60634 + 3.24365I 0
u = −0.06610 − 1.50441I
a = −1.169580 + 0.132340I
b = −0.820952 + 0.055008I
−2.60634 − 3.24365I 0
u = 0.00019 + 1.50839I
a = 0.581366 + 0.107821I
b = 1.44483 − 2.50624I
0.80445 + 3.49717I 0
u = 0.00019 − 1.50839I
a = 0.581366 − 0.107821I
b = 1.44483 + 2.50624I
0.80445 − 3.49717I 0
u = −0.265297 + 0.365508I
a = 2.51098 − 1.84482I
b = 1.37513 + 0.76253I
−8.21913 − 0.94003I −11.00888 − 5.54594I
u = −0.265297 − 0.365508I
a = 2.51098 + 1.84482I
b = 1.37513 − 0.76253I
−8.21913 + 0.94003I −11.00888 + 5.54594I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.24051 + 1.54504I
a = −0.583822 + 0.503825I
b = −1.48518 − 1.54173I
4.44630 + 8.10930I 0
u = −0.24051 − 1.54504I
a = −0.583822 − 0.503825I
b = −1.48518 + 1.54173I
4.44630 − 8.10930I 0
u = 0.08098 + 1.57003I
a = −0.387253 + 0.899408I
b = 0.101032 − 0.825020I
7.88603 − 2.42265I 0
u = 0.08098 − 1.57003I
a = −0.387253 − 0.899408I
b = 0.101032 + 0.825020I
7.88603 + 2.42265I 0
u = 0.16159 + 1.56673I
a = 0.718608 + 0.293346I
b = 1.56681 − 0.88922I
5.85288 − 4.55236I 0
u = 0.16159 − 1.56673I
a = 0.718608 − 0.293346I
b = 1.56681 + 0.88922I
5.85288 + 4.55236I 0
u = 0.210687 + 0.367812I
a = 0.646563 + 0.374831I
b = 0.449259 + 0.341921I
−0.368069 − 0.991598I −6.64400 + 6.37236I
u = 0.210687 − 0.367812I
a = 0.646563 − 0.374831I
b = 0.449259 − 0.341921I
−0.368069 + 0.991598I −6.64400 − 6.37236I
u = −0.12311 + 1.57609I
a = 0.667344 − 0.560210I
b = 0.16269 + 1.64359I
−0.57357 + 3.21569I 0
u = −0.12311 − 1.57609I
a = 0.667344 + 0.560210I
b = 0.16269 − 1.64359I
−0.57357 − 3.21569I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.249981 + 0.334709I
a = 1.86702 − 0.71053I
b = 0.017814 + 0.949455I
−0.345879 − 1.288130I −1.87491 + 4.22491I
u = −0.249981 − 0.334709I
a = 1.86702 + 0.71053I
b = 0.017814 − 0.949455I
−0.345879 + 1.288130I −1.87491 − 4.22491I
u = −0.08703 + 1.58029I
a = −0.773840 + 0.437793I
b = −1.35053 − 1.57805I
7.74176 + 5.01802I 0
u = −0.08703 − 1.58029I
a = −0.773840 − 0.437793I
b = −1.35053 + 1.57805I
7.74176 − 5.01802I 0
u = −0.04716 + 1.58637I
a = 0.608497 − 0.272983I
b = 1.24121 + 1.11096I
6.69652 − 0.75939I 0
u = −0.04716 − 1.58637I
a = 0.608497 + 0.272983I
b = 1.24121 − 1.11096I
6.69652 + 0.75939I 0
u = −0.15493 + 1.58734I
a = 0.394991 + 0.485905I
b = 0.0701063 − 0.0944584I
5.86795 + 2.66890I 0
u = −0.15493 − 1.58734I
a = 0.394991 − 0.485905I
b = 0.0701063 + 0.0944584I
5.86795 − 2.66890I 0
u = −0.10045 + 1.59407I
a = −0.616669 + 0.144873I
b = 0.36074 − 2.32559I
0.36466 + 4.95042I 0
u = −0.10045 − 1.59407I
a = −0.616669 − 0.144873I
b = 0.36074 + 2.32559I
0.36466 − 4.95042I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14035 + 1.59728I
a = −0.207246 − 0.795941I
b = 0.384197 + 0.588606I
4.17834 + 9.77145I 0
u = −0.14035 − 1.59728I
a = −0.207246 + 0.795941I
b = 0.384197 − 0.588606I
4.17834 − 9.77145I 0
u = 0.17472 + 1.60407I
a = −0.546797 − 0.351402I
b = −0.96998 + 1.55531I
6.60181 − 5.38064I 0
u = 0.17472 − 1.60407I
a = −0.546797 + 0.351402I
b = −0.96998 − 1.55531I
6.60181 + 5.38064I 0
u = 0.13507 + 1.61066I
a = −0.788838 − 0.343903I
b = −1.72870 + 1.86516I
5.33185 − 9.04389I 0
u = 0.13507 − 1.61066I
a = −0.788838 + 0.343903I
b = −1.72870 − 1.86516I
5.33185 + 9.04389I 0
u = −0.00140 + 1.61668I
a = 0.191641 + 0.626922I
b = −0.289391 − 0.590654I
10.77350 − 0.92330I 0
u = −0.00140 − 1.61668I
a = 0.191641 − 0.626922I
b = −0.289391 + 0.590654I
10.77350 + 0.92330I 0
u = 0.05624 + 1.62502I
a = 0.465637 − 0.370971I
b = 0.534327 + 0.634388I
7.22717 − 1.13108I 0
u = 0.05624 − 1.62502I
a = 0.465637 + 0.370971I
b = 0.534327 − 0.634388I
7.22717 + 1.13108I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16723 + 1.62344I
a = 0.766081 + 0.539659I
b = 0.91859 − 1.57853I
4.94508 − 10.01770I 0
u = 0.16723 − 1.62344I
a = 0.766081 − 0.539659I
b = 0.91859 + 1.57853I
4.94508 + 10.01770I 0
u = −0.20976 + 1.62271I
a = 0.767884 − 0.515829I
b = 1.26336 + 1.81701I
0.5584 + 16.6299I 0
u = −0.20976 − 1.62271I
a = 0.767884 + 0.515829I
b = 1.26336 − 1.81701I
0.5584 − 16.6299I 0
u = 0.07507 + 1.64495I
a = 0.032254 − 0.465580I
b = −0.479350 + 0.580447I
9.34725 − 4.44995I 0
u = 0.07507 − 1.64495I
a = 0.032254 + 0.465580I
b = −0.479350 − 0.580447I
9.34725 + 4.44995I 0
u = 0.07066 + 1.74802I
a = −0.434726 − 0.045937I
b = −0.115807 + 0.391296I
8.44677 − 3.19875I 0
u = 0.07066 − 1.74802I
a = −0.434726 + 0.045937I
b = −0.115807 − 0.391296I
8.44677 + 3.19875I 0
u = −0.0303102 + 0.1028030I
a = 5.56338 − 4.06589I
b = 0.70788 − 1.78101I
−5.11888 + 3.47075I −9.80251 + 3.71753I
u = −0.0303102 − 0.1028030I
a = 5.56338 + 4.06589I
b = 0.70788 + 1.78101I
−5.11888 − 3.47075I −9.80251 − 3.71753I
13
II.
I
u
2
= hu
22
+2u
21
+· · ·+b−1, u
23
+2u
22
+· · ·+a−7, u
24
+2u
23
+· · ·+17u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
8
=
−u
23
− 2u
22
+ ··· + u + 7
−u
22
− 2u
21
+ ··· + 2u + 1
a
7
=
−u
23
− 2u
22
+ ··· + u + 8
u
8
+ u
7
+ 6u
6
+ 5u
5
+ 11u
4
+ 7u
3
+ 6u
2
+ 2u + 1
a
11
=
−3u
23
− 6u
22
+ ··· − 37u − 4
−2u
21
− 4u
20
+ ··· − 6u + 1
a
9
=
u
23
+ 2u
22
+ ··· + 12u − 8
−u
20
− 2u
19
+ ··· − 2u − 2
a
10
=
−3u
23
− 6u
22
+ ··· − 43u − 3
−2u
21
− 4u
20
+ ··· − 6u + 1
a
3
=
5u
23
+ 11u
22
+ ··· + 60u
2
+ 49u
u
23
+ 2u
22
+ ··· + 7u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
21
+ 2u
20
+ 39u
19
+ 22u
18
+ 209u
17
+ 94u
16
+ 593u
15
+ 178u
14
+ 945u
13
+ 57u
12
+
808u
11
− 355u
10
+ 285u
9
− 621u
8
− 8u
7
− 405u
6
+ 55u
5
− 97u
4
+ 96u
3
− 4u
2
+ 24u − 4
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
24
− 2u
23
+ ··· + 17u
2
+ 1
c
2
u
24
+ 12u
22
+ ··· + 10u
2
+ 1
c
3
u
24
− 8u
22
+ ··· − 7u
2
+ 1
c
4
, c
5
u
24
+ 2u
23
+ ··· + 17u
2
+ 1
c
6
u
24
− 8u
23
+ ··· − 8u + 1
c
7
u
24
+ 12u
22
+ ··· + 10u
2
+ 1
c
8
u
24
+ 4u
23
+ ··· + 4u + 1
c
9
u
24
− 8u
22
+ ··· − 7u
2
+ 1
c
10
u
24
− 12u
21
+ ··· + 17u + 5
c
11
u
24
− 4u
23
+ ··· − 4u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
12
y
24
+ 32y
23
+ ··· + 34y + 1
c
2
, c
7
y
24
+ 24y
23
+ ··· + 20y + 1
c
3
, c
9
y
24
− 16y
23
+ ··· − 14y + 1
c
6
y
24
− 10y
23
+ ··· − 16y + 1
c
8
, c
11
y
24
+ 16y
23
+ ··· + 16y + 1
c
10
y
24
− 16y
21
+ ··· + 431y + 25
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.556124 + 0.806900I
a = 0.822523 − 0.184284I
b = 0.340365 + 0.918768I
−0.169220 + 0.554447I 0.807433 − 0.716512I
u = −0.556124 − 0.806900I
a = 0.822523 + 0.184284I
b = 0.340365 − 0.918768I
−0.169220 − 0.554447I 0.807433 + 0.716512I
u = 0.238121 + 1.132010I
a = 0.638508 + 0.005594I
b = 1.28860 − 1.32573I
−2.55299 + 1.99625I −8.04434 − 3.57329I
u = 0.238121 − 1.132010I
a = 0.638508 − 0.005594I
b = 1.28860 + 1.32573I
−2.55299 − 1.99625I −8.04434 + 3.57329I
u = −0.637603 + 0.505766I
a = −0.362804 + 1.254520I
b = −0.60332 − 1.46985I
−1.05781 + 3.70114I −4.75043 − 6.52555I
u = −0.637603 − 0.505766I
a = −0.362804 − 1.254520I
b = −0.60332 + 1.46985I
−1.05781 − 3.70114I −4.75043 + 6.52555I
u = 0.052505 + 1.200480I
a = −1.081330 − 0.101440I
b = −0.397770 − 0.393742I
−5.00318 + 1.08105I −8.07466 − 0.48442I
u = 0.052505 − 1.200480I
a = −1.081330 + 0.101440I
b = −0.397770 + 0.393742I
−5.00318 − 1.08105I −8.07466 + 0.48442I
u = −0.188719 + 0.597536I
a = 0.71388 + 1.34999I
b = 0.358333 − 0.208954I
1.102000 + 0.641161I 0.911832 + 0.772275I
u = −0.188719 − 0.597536I
a = 0.71388 − 1.34999I
b = 0.358333 + 0.208954I
1.102000 − 0.641161I 0.911832 − 0.772275I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01703 + 1.52852I
a = 0.998710 − 0.123388I
b = 1.87123 + 0.89007I
−1.53461 − 1.75524I −5.42911 + 2.64882I
u = 0.01703 − 1.52852I
a = 0.998710 + 0.123388I
b = 1.87123 − 0.89007I
−1.53461 + 1.75524I −5.42911 − 2.64882I
u = 0.269205 + 0.369321I
a = −0.87619 − 1.56230I
b = 0.60303 + 1.98366I
−5.03257 − 3.89563I −5.9842 + 13.4510I
u = 0.269205 − 0.369321I
a = −0.87619 + 1.56230I
b = 0.60303 − 1.98366I
−5.03257 + 3.89563I −5.9842 − 13.4510I
u = 0.08512 + 1.55611I
a = −0.463718 − 0.342100I
b = 0.21456 + 2.34805I
1.75526 − 5.18528I −2.04679 + 5.57462I
u = 0.08512 − 1.55611I
a = −0.463718 + 0.342100I
b = 0.21456 − 2.34805I
1.75526 + 5.18528I −2.04679 − 5.57462I
u = −0.18031 + 1.58187I
a = −0.682667 + 0.395242I
b = −1.34888 − 1.52119I
6.06933 + 6.64817I −3.40989 − 5.56122I
u = −0.18031 − 1.58187I
a = −0.682667 − 0.395242I
b = −1.34888 + 1.52119I
6.06933 − 6.64817I −3.40989 + 5.56122I
u = −0.06571 + 1.59428I
a = 0.280021 + 0.662678I
b = 0.222354 − 0.684451I
8.74120 + 1.63961I 1.117347 + 0.019665I
u = −0.06571 − 1.59428I
a = 0.280021 − 0.662678I
b = 0.222354 + 0.684451I
8.74120 − 1.63961I 1.117347 − 0.019665I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.055807 + 0.298741I
a = 4.71727 + 0.37884I
b = 0.960356 + 0.621623I
−7.97814 − 1.49651I −4.08753 + 5.14572I
u = 0.055807 − 0.298741I
a = 4.71727 − 0.37884I
b = 0.960356 − 0.621623I
−7.97814 + 1.49651I −4.08753 − 5.14572I
u = −0.08933 + 1.71019I
a = 0.295800 + 0.084001I
b = 0.491146 + 0.017403I
8.95061 + 2.87283I 2.99029 + 1.35526I
u = −0.08933 − 1.71019I
a = 0.295800 − 0.084001I
b = 0.491146 − 0.017403I
8.95061 − 2.87283I 2.99029 − 1.35526I
19
III. I
u
3
= hu
2
+ b, a − 1, u
7
+ 3u
5
+ 2u
3
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
8
=
1
−u
2
a
7
=
−u
6
− 3u
4
− 2u
2
+ 1
u
6
+ 2u
4
− u
2
+ u
a
11
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
u
3
u
3
+ u
a
3
=
−u
3
+ u
2
+ 1
−u
4
− u
3
− 2u
2
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
11
, c
12
u
7
+ 3u
5
+ 2u
3
+ u + 1
c
2
, c
7
, c
10
u
7
+ 5u
5
− 2u
4
+ 4u
3
− u + 2
c
3
, c
9
(u + 1)
7
c
6
u
7
+ 2u
6
+ u
5
− 2u
4
− 4u
3
+ 2u
2
+ 5u − 3
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
11
, c
12
y
7
+ 6y
6
+ 13y
5
+ 14y
4
+ 10y
3
+ 4y
2
+ y −1
c
2
, c
7
, c
10
y
7
+ 10y
6
+ 33y
5
+ 34y
4
+ 6y
3
+ y −4
c
3
, c
9
(y −1)
7
c
6
y
7
− 2y
6
+ y
5
− 10y
4
+ 46y
3
− 56y
2
+ 37y −9
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376499 + 0.939075I
a = 1.00000
b = 0.740110 − 0.707121I
−1.64493 −6.00000
u = 0.376499 − 0.939075I
a = 1.00000
b = 0.740110 + 0.707121I
−1.64493 −6.00000
u = −0.597941 + 0.642727I
a = 1.00000
b = 0.055565 + 0.768625I
−1.64493 −6.00000
u = −0.597941 − 0.642727I
a = 1.00000
b = 0.055565 − 0.768625I
−1.64493 −6.00000
u = 0.538551
a = 1.00000
b = −0.290037
−1.64493 −6.00000
u = −0.04783 + 1.53350I
a = 1.00000
b = 2.34934 + 0.14671I
−1.64493 −6.00000
u = −0.04783 − 1.53350I
a = 1.00000
b = 2.34934 − 0.14671I
−1.64493 −6.00000
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
7
+ 3u
5
+ 2u
3
+ u + 1)(u
24
− 2u
23
+ ··· + 17u
2
+ 1)
· (u
90
− 3u
89
+ ··· − 12u + 1)
c
2
(u
7
+ 5u
5
− 2u
4
+ 4u
3
− u + 2)(u
24
+ 12u
22
+ ··· + 10u
2
+ 1)
· (u
90
+ u
89
+ ··· − 1472u + 37417)
c
3
((u + 1)
7
)(u
24
− 8u
22
+ ··· − 7u
2
+ 1)
· (u
90
− 6u
89
+ ··· − 13860u + 2776)
c
4
, c
5
(u
7
+ 3u
5
+ 2u
3
+ u + 1)(u
24
+ 2u
23
+ ··· + 17u
2
+ 1)
· (u
90
− 3u
89
+ ··· − 12u + 1)
c
6
(u
7
+ 2u
6
+ ··· + 5u − 3)(u
24
− 8u
23
+ ··· − 8u + 1)
· (u
90
− 5u
89
+ ··· − 305292u + 114001)
c
7
(u
7
+ 5u
5
− 2u
4
+ 4u
3
− u + 2)(u
24
+ 12u
22
+ ··· + 10u
2
+ 1)
· (u
90
+ u
89
+ ··· − 1472u + 37417)
c
8
(u
7
+ 3u
5
+ 2u
3
+ u + 1)(u
24
+ 4u
23
+ ··· + 4u + 1)
· (u
90
+ 5u
89
+ ··· + 7842u + 839)
c
9
((u + 1)
7
)(u
24
− 8u
22
+ ··· − 7u
2
+ 1)
· (u
90
− 6u
89
+ ··· − 13860u + 2776)
c
10
(u
7
+ 5u
5
− 2u
4
+ 4u
3
− u + 2)(u
24
− 12u
21
+ ··· + 17u + 5)
· (u
90
+ u
89
+ ··· + 13461u + 2479)
c
11
(u
7
+ 3u
5
+ 2u
3
+ u + 1)(u
24
− 4u
23
+ ··· − 4u + 1)
· (u
90
+ 5u
89
+ ··· + 7842u + 839)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
12
(y
7
+ 6y
6
+ 13y
5
+ 14y
4
+ 10y
3
+ 4y
2
+ y −1)
· (y
24
+ 32y
23
+ ··· + 34y + 1)(y
90
+ 109y
89
+ ··· + 174y + 1)
c
2
, c
7
(y
7
+ 10y
6
+ ··· + y −4)(y
24
+ 24y
23
+ ··· + 20y + 1)
· (y
90
+ 65y
89
+ ··· + 22616709052y + 1400031889)
c
3
, c
9
((y −1)
7
)(y
24
− 16y
23
+ ··· − 14y + 1)
· (y
90
− 58y
89
+ ··· − 11659600y + 7706176)
c
6
(y
7
− 2y
6
+ y
5
− 10y
4
+ 46y
3
− 56y
2
+ 37y −9)
· (y
24
− 10y
23
+ ··· − 16y + 1)
· (y
90
− 45y
89
+ ··· − 374166877836y + 12996228001)
c
8
, c
11
(y
7
+ 6y
6
+ 13y
5
+ 14y
4
+ 10y
3
+ 4y
2
+ y −1)
· (y
24
+ 16y
23
+ ··· + 16y + 1)
· (y
90
+ 53y
89
+ ··· + 29423788y + 703921)
c
10
(y
7
+ 10y
6
+ ··· + y −4)(y
24
− 16y
21
+ ··· + 431y + 25)
· (y
90
− 19y
89
+ ··· − 310592405y + 6145441)
25
