12a
0095
(K12a
0095
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 10 11 4 1 7 12 6 9
Solving Sequence
1,8 4,9
3 2 5 7 10 12 11 6
c
8
c
3
c
1
c
4
c
7
c
9
c
12
c
10
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.10803 × 10
416
u
106
− 1.09715 × 10
417
u
105
+ ··· + 5.32892 × 10
419
b + 1.96754 × 10
419
,
3.86181 × 10
419
u
106
− 3.10040 × 10
420
u
105
+ ··· + 2.82433 × 10
421
a + 1.15704 × 10
423
,
u
107
− 8u
106
+ ··· + 3774u − 53i
I
u
2
= hb, −u
3
+ a − u + 1, u
4
+ u
2
− u + 1i
I
u
3
= hb, −u
5
− u
4
− 2u
3
− 2u
2
+ a − 2u − 2, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 117 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
= h1.11 × 10
416
u
106
− 1.10 × 10
417
u
105
+ · · · + 5.33 × 10
419
b + 1.97 ×
10
419
, 3.86 × 10
419
u
106
− 3.10 × 10
420
u
105
+ · · · + 2.82 × 10
421
a + 1.16 ×
10
423
, u
107
− 8u
106
+ · · · + 3774u − 53i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−0.0136734u
106
+ 0.109775u
105
+ ··· − 1.84820u − 40.9669
−0.000207928u
106
+ 0.00205885u
105
+ ··· − 14.7641u − 0.369218
a
9
=
1
u
2
a
3
=
−0.0138813u
106
+ 0.111834u
105
+ ··· − 16.6123u − 41.3361
−0.000207928u
106
+ 0.00205885u
105
+ ··· − 14.7641u − 0.369218
a
2
=
−0.00866897u
106
+ 0.0691354u
105
+ ··· + 28.1372u − 24.9369
−0.000596204u
106
+ 0.00486010u
105
+ ··· + 3.21655u − 0.369377
a
5
=
−0.00815307u
106
+ 0.0646793u
105
+ ··· + 32.1684u − 22.5508
−0.000596204u
106
+ 0.00486010u
105
+ ··· + 3.21655u − 0.369377
a
7
=
−0.00642410u
106
+ 0.0508524u
105
+ ··· + 49.7193u − 22.6538
−0.000545278u
106
+ 0.00430644u
105
+ ··· + 8.21892u − 0.432113
a
10
=
−0.00313420u
106
+ 0.0257724u
105
+ ··· − 48.1889u − 5.16381
−0.000447025u
106
+ 0.00376175u
105
+ ··· − 13.7999u + 0.0889698
a
12
=
u
u
3
+ u
a
11
=
−0.00309075u
106
+ 0.0255452u
105
+ ··· − 44.8549u − 5.20870
−0.000405615u
106
+ 0.00336633u
105
+ ··· − 10.9176u + 0.0504615
a
6
=
−0.00211014u
106
+ 0.0160755u
105
+ ··· + 111.322u − 21.7904
0.000434043u
106
− 0.00378194u
105
+ ··· + 20.5546u − 0.562495
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00735456u
106
+ 0.0589369u
105
+ ··· − 56.4719u − 8.55387
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
107
+ 47u
106
+ ··· − u + 1
c
2
, c
4
u
107
− 11u
106
+ ··· − 11u + 1
c
3
, c
7
u
107
+ u
106
+ ··· + 2048u + 1024
c
5
u
107
− 2u
106
+ ··· + 33648u + 4360
c
6
, c
11
u
107
+ 2u
106
+ ··· + 4u + 1
c
8
, c
12
u
107
− 8u
106
+ ··· + 3774u − 53
c
9
u
107
+ 10u
106
+ ··· + 976u + 64
c
10
u
107
− 52u
106
+ ··· + 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
107
+ 37y
106
+ ··· + 155y −1
c
2
, c
4
y
107
− 47y
106
+ ··· − y −1
c
3
, c
7
y
107
+ 63y
106
+ ··· − 30932992y −1048576
c
5
y
107
− 36y
106
+ ··· + 1065366544y −19009600
c
6
, c
11
y
107
+ 52y
106
+ ··· + 8y −1
c
8
, c
12
y
107
+ 88y
106
+ ··· + 13858296y −2809
c
9
y
107
− 4y
106
+ ··· + 53376y −4096
c
10
y
107
+ 8y
106
+ ··· + 132y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.244278 + 0.967291I
a = 0.15439 + 2.43118I
b = 0.110417 − 0.860774I
−1.63198 + 2.05257I 0
u = −0.244278 − 0.967291I
a = 0.15439 − 2.43118I
b = 0.110417 + 0.860774I
−1.63198 − 2.05257I 0
u = 0.717600 + 0.714940I
a = −0.044492 − 0.756078I
b = 0.395055 + 0.774024I
1.89343 − 6.93711I 0
u = 0.717600 − 0.714940I
a = −0.044492 + 0.756078I
b = 0.395055 − 0.774024I
1.89343 + 6.93711I 0
u = 0.558306 + 0.801140I
a = 0.377242 − 0.625630I
b = 0.138099 + 0.946607I
3.73567 + 0.13008I 0
u = 0.558306 − 0.801140I
a = 0.377242 + 0.625630I
b = 0.138099 − 0.946607I
3.73567 − 0.13008I 0
u = 0.106700 + 0.961946I
a = 0.067239 + 0.134211I
b = −0.969199 + 0.200550I
−0.0780580 + 0.0329782I 0
u = 0.106700 − 0.961946I
a = 0.067239 − 0.134211I
b = −0.969199 − 0.200550I
−0.0780580 − 0.0329782I 0
u = 0.795488 + 0.531373I
a = −0.818911 + 0.454003I
b = −0.438711 − 1.131220I
2.45043 − 4.63695I 0
u = 0.795488 − 0.531373I
a = −0.818911 − 0.454003I
b = −0.438711 + 1.131220I
2.45043 + 4.63695I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.378376 + 0.979346I
a = 0.055561 − 0.405278I
b = 0.043777 + 0.657390I
3.73900 + 0.24041I 0
u = 0.378376 − 0.979346I
a = 0.055561 + 0.405278I
b = 0.043777 − 0.657390I
3.73900 − 0.24041I 0
u = 0.843285 + 0.392565I
a = −0.538159 − 0.841495I
b = −0.767046 + 0.528555I
−1.74871 − 6.44193I 0
u = 0.843285 − 0.392565I
a = −0.538159 + 0.841495I
b = −0.767046 − 0.528555I
−1.74871 + 6.44193I 0
u = −0.619548 + 0.633428I
a = 0.069724 − 0.636140I
b = −0.339848 + 0.674275I
−0.26443 + 2.25224I 0
u = −0.619548 − 0.633428I
a = 0.069724 + 0.636140I
b = −0.339848 − 0.674275I
−0.26443 − 2.25224I 0
u = 0.824445 + 0.189026I
a = −0.75491 + 1.63349I
b = −0.534754 − 0.657037I
−2.06068 − 4.19793I 0
u = 0.824445 − 0.189026I
a = −0.75491 − 1.63349I
b = −0.534754 + 0.657037I
−2.06068 + 4.19793I 0
u = 1.029330 + 0.531564I
a = 0.121699 − 0.141240I
b = −0.206401 + 0.885382I
−0.39437 + 4.15714I 0
u = 1.029330 − 0.531564I
a = 0.121699 + 0.141240I
b = −0.206401 − 0.885382I
−0.39437 − 4.15714I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.933441 + 0.702521I
a = −0.183881 − 0.207962I
b = 0.141803 + 0.854176I
−1.52785 + 0.45819I 0
u = −0.933441 − 0.702521I
a = −0.183881 + 0.207962I
b = 0.141803 − 0.854176I
−1.52785 − 0.45819I 0
u = −0.782378 + 0.261649I
a = 0.724726 − 0.937397I
b = 0.703522 + 0.525334I
−3.66184 + 1.83985I 0
u = −0.782378 − 0.261649I
a = 0.724726 + 0.937397I
b = 0.703522 − 0.525334I
−3.66184 − 1.83985I 0
u = −1.177060 + 0.290474I
a = 0.338803 + 0.320303I
b = 0.430656 − 1.007280I
−2.48557 + 4.37342I 0
u = −1.177060 − 0.290474I
a = 0.338803 − 0.320303I
b = 0.430656 + 1.007280I
−2.48557 − 4.37342I 0
u = −0.328686 + 1.168570I
a = −0.148668 − 0.117283I
b = 1.038800 + 0.287656I
−0.35619 + 4.34573I 0
u = −0.328686 − 1.168570I
a = −0.148668 + 0.117283I
b = 1.038800 − 0.287656I
−0.35619 − 4.34573I 0
u = 1.221280 + 0.130481I
a = −0.239161 + 0.249668I
b = −0.400063 − 0.972833I
−1.027490 + 0.372205I 0
u = 1.221280 − 0.130481I
a = −0.239161 − 0.249668I
b = −0.400063 + 0.972833I
−1.027490 − 0.372205I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768164 + 0.030095I
a = 0.88462 + 1.39992I
b = 0.578075 − 0.587317I
−3.83121 − 0.30767I −13.13167 + 0.I
u = −0.768164 − 0.030095I
a = 0.88462 − 1.39992I
b = 0.578075 + 0.587317I
−3.83121 + 0.30767I −13.13167 + 0.I
u = −0.763131 + 0.968657I
a = −0.156194 − 0.327440I
b = 0.050991 + 0.764285I
−0.43303 + 2.32507I 0
u = −0.763131 − 0.968657I
a = −0.156194 + 0.327440I
b = 0.050991 − 0.764285I
−0.43303 − 2.32507I 0
u = −0.091985 + 1.240100I
a = 0.77646 + 1.78490I
b = 0.54374 − 1.36147I
8.61264 − 0.05840I 0
u = −0.091985 − 1.240100I
a = 0.77646 − 1.78490I
b = 0.54374 + 1.36147I
8.61264 + 0.05840I 0
u = 0.178080 + 1.246850I
a = −0.76240 + 1.69178I
b = −0.55134 − 1.34274I
5.90630 − 4.72731I 0
u = 0.178080 − 1.246850I
a = −0.76240 − 1.69178I
b = −0.55134 + 1.34274I
5.90630 + 4.72731I 0
u = −0.145556 + 1.253260I
a = 0.364469 + 0.147648I
b = −1.089070 + 0.127073I
1.99962 + 1.17025I 0
u = −0.145556 − 1.253260I
a = 0.364469 − 0.147648I
b = −1.089070 − 0.127073I
1.99962 − 1.17025I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.135400 + 0.570705I
a = 0.443382 + 0.526000I
b = 0.489972 − 1.055080I
−1.97155 + 6.45339I 0
u = −1.135400 − 0.570705I
a = 0.443382 − 0.526000I
b = 0.489972 + 1.055080I
−1.97155 − 6.45339I 0
u = 0.468996 + 0.530095I
a = −0.68912 + 2.39644I
b = −0.280440 − 0.684314I
−0.98884 + 1.84483I −3.82797 + 1.28640I
u = 0.468996 − 0.530095I
a = −0.68912 − 2.39644I
b = −0.280440 + 0.684314I
−0.98884 − 1.84483I −3.82797 − 1.28640I
u = 0.405837 + 0.572578I
a = −0.570749 − 0.083950I
b = −0.802591 + 0.320828I
−0.174410 − 0.127515I −5.50445 + 1.13479I
u = 0.405837 − 0.572578I
a = −0.570749 + 0.083950I
b = −0.802591 − 0.320828I
−0.174410 + 0.127515I −5.50445 − 1.13479I
u = −0.291545 + 1.287990I
a = 0.07916 + 2.30407I
b = 0.110803 − 0.993595I
0.23928 + 3.46090I 0
u = −0.291545 − 1.287990I
a = 0.07916 − 2.30407I
b = 0.110803 + 0.993595I
0.23928 − 3.46090I 0
u = 0.209184 + 1.304430I
a = −0.412576 + 0.156149I
b = 1.111000 + 0.109634I
4.56308 − 6.01047I 0
u = 0.209184 − 1.304430I
a = −0.412576 − 0.156149I
b = 1.111000 − 0.109634I
4.56308 + 6.01047I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.265083 + 1.299270I
a = 0.42759 − 1.54289I
b = 0.327691 + 1.304980I
4.98675 + 0.12143I 0
u = 0.265083 − 1.299270I
a = 0.42759 + 1.54289I
b = 0.327691 − 1.304980I
4.98675 − 0.12143I 0
u = 0.744053 + 1.104860I
a = 0.118395 − 0.327376I
b = −0.054853 + 0.717685I
1.82231 − 7.19731I 0
u = 0.744053 − 1.104860I
a = 0.118395 + 0.327376I
b = −0.054853 − 0.717685I
1.82231 + 7.19731I 0
u = 1.149480 + 0.694236I
a = −0.434365 + 0.627438I
b = −0.519863 − 1.067400I
−0.01179 − 11.33370I 0
u = 1.149480 − 0.694236I
a = −0.434365 − 0.627438I
b = −0.519863 + 1.067400I
−0.01179 + 11.33370I 0
u = 0.067332 + 1.356370I
a = −0.385316 + 0.071591I
b = 1.118240 + 0.160068I
6.21427 + 2.01067I 0
u = 0.067332 − 1.356370I
a = −0.385316 − 0.071591I
b = 1.118240 − 0.160068I
6.21427 − 2.01067I 0
u = 0.043841 + 1.358030I
a = 0.49776 − 1.75459I
b = 0.29145 + 1.39069I
7.49723 + 1.30975I 0
u = 0.043841 − 1.358030I
a = 0.49776 + 1.75459I
b = 0.29145 − 1.39069I
7.49723 − 1.30975I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.016598 + 1.368280I
a = −0.51049 − 1.80982I
b = −0.28157 + 1.41137I
10.15850 − 6.16266I 0
u = 0.016598 − 1.368280I
a = −0.51049 + 1.80982I
b = −0.28157 − 1.41137I
10.15850 + 6.16266I 0
u = 0.177576 + 1.358930I
a = −0.04241 + 2.30582I
b = −0.065693 − 1.015390I
4.51674 − 0.36965I 0
u = 0.177576 − 1.358930I
a = −0.04241 − 2.30582I
b = −0.065693 + 1.015390I
4.51674 + 0.36965I 0
u = 0.500396 + 1.282940I
a = −0.62879 + 1.39268I
b = −0.584855 − 1.274260I
3.20733 − 5.65218I 0
u = 0.500396 − 1.282940I
a = −0.62879 − 1.39268I
b = −0.584855 + 1.274260I
3.20733 + 5.65218I 0
u = −0.170784 + 1.367340I
a = 0.64277 + 1.71294I
b = 0.57737 − 1.35306I
10.04680 + 8.11877I 0
u = −0.170784 − 1.367340I
a = 0.64277 − 1.71294I
b = 0.57737 + 1.35306I
10.04680 − 8.11877I 0
u = 0.331508 + 1.355170I
a = −0.07380 + 2.28294I
b = −0.121993 − 1.020340I
2.75081 − 8.34322I 0
u = 0.331508 − 1.355170I
a = −0.07380 − 2.28294I
b = −0.121993 + 1.020340I
2.75081 + 8.34322I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.599443 + 0.047851I
a = −0.467004 − 0.519575I
b = 0.580248 + 0.294112I
0.59909 + 3.23248I −3.54970 − 2.02366I
u = 0.599443 − 0.047851I
a = −0.467004 + 0.519575I
b = 0.580248 − 0.294112I
0.59909 − 3.23248I −3.54970 + 2.02366I
u = −0.523910 + 0.283236I
a = 0.283886 − 0.479371I
b = −0.413442 + 0.397977I
−1.003830 + 0.947083I −6.72670 − 4.41292I
u = −0.523910 − 0.283236I
a = 0.283886 + 0.479371I
b = −0.413442 − 0.397977I
−1.003830 − 0.947083I −6.72670 + 4.41292I
u = −0.33909 + 1.40174I
a = −0.31003 − 1.55968I
b = −0.381510 + 1.311700I
4.72927 + 4.53808I 0
u = −0.33909 − 1.40174I
a = −0.31003 + 1.55968I
b = −0.381510 − 1.311700I
4.72927 − 4.53808I 0
u = −0.34118 + 1.40161I
a = −0.304334 − 0.170972I
b = 1.117030 + 0.295556I
1.60903 + 5.96407I 0
u = −0.34118 − 1.40161I
a = −0.304334 + 0.170972I
b = 1.117030 − 0.295556I
1.60903 − 5.96407I 0
u = −0.06354 + 1.44683I
a = −0.41932 − 1.77311I
b = −0.32247 + 1.40483I
11.73440 + 2.01740I 0
u = −0.06354 − 1.44683I
a = −0.41932 + 1.77311I
b = −0.32247 − 1.40483I
11.73440 − 2.01740I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23844 + 1.43773I
a = 0.345146 − 0.116560I
b = −1.131050 + 0.263267I
5.97945 − 2.87063I 0
u = 0.23844 − 1.43773I
a = 0.345146 + 0.116560I
b = −1.131050 − 0.263267I
5.97945 + 2.87063I 0
u = 0.36411 + 1.45966I
a = 0.335672 − 0.193945I
b = −1.135240 + 0.303887I
4.12324 − 10.89930I 0
u = 0.36411 − 1.45966I
a = 0.335672 + 0.193945I
b = −1.135240 − 0.303887I
4.12324 + 10.89930I 0
u = 0.355328 + 0.327509I
a = −0.535333 + 0.829714I
b = 0.741715 − 0.054497I
0.97038 + 3.14809I −2.61784 − 5.19860I
u = 0.355328 − 0.327509I
a = −0.535333 − 0.829714I
b = 0.741715 + 0.054497I
0.97038 − 3.14809I −2.61784 + 5.19860I
u = −0.52030 + 1.42675I
a = 0.50897 + 1.43324I
b = 0.61769 − 1.28222I
2.79707 + 10.37630I 0
u = −0.52030 − 1.42675I
a = 0.50897 − 1.43324I
b = 0.61769 + 1.28222I
2.79707 − 10.37630I 0
u = 0.385481 + 0.157711I
a = 0.57690 + 1.52323I
b = −0.191599 + 1.167350I
2.53797 + 2.54179I −2.10720 − 3.38961I
u = 0.385481 − 0.157711I
a = 0.57690 − 1.52323I
b = −0.191599 − 1.167350I
2.53797 − 2.54179I −2.10720 + 3.38961I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.26127 + 1.56618I
a = 0.25567 − 1.69472I
b = 0.40497 + 1.37995I
11.33560 − 3.17947I 0
u = 0.26127 − 1.56618I
a = 0.25567 + 1.69472I
b = 0.40497 − 1.37995I
11.33560 + 3.17947I 0
u = −0.33545 + 1.55553I
a = −0.22516 − 1.64887I
b = −0.42278 + 1.35777I
6.87012 + 6.32881I 0
u = −0.33545 − 1.55553I
a = −0.22516 + 1.64887I
b = −0.42278 − 1.35777I
6.87012 − 6.32881I 0
u = −0.191098 + 0.331866I
a = −2.48353 + 0.52436I
b = 0.110517 + 1.223940I
5.65239 + 1.11140I 2.39761 − 0.78708I
u = −0.191098 − 0.331866I
a = −2.48353 − 0.52436I
b = 0.110517 − 1.223940I
5.65239 − 1.11140I 2.39761 + 0.78708I
u = 0.37243 + 1.57605I
a = −0.44058 + 1.58113I
b = −0.63720 − 1.32574I
9.36952 − 9.23755I 0
u = 0.37243 − 1.57605I
a = −0.44058 − 1.58113I
b = −0.63720 + 1.32574I
9.36952 + 9.23755I 0
u = 0.34589 + 1.59767I
a = 0.19820 − 1.66460I
b = 0.43639 + 1.36713I
9.4139 − 11.3192I 0
u = 0.34589 − 1.59767I
a = 0.19820 + 1.66460I
b = 0.43639 − 1.36713I
9.4139 + 11.3192I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.46077 + 1.59233I
a = 0.40978 + 1.52343I
b = 0.64769 − 1.30858I
4.83717 + 12.32680I 0
u = −0.46077 − 1.59233I
a = 0.40978 − 1.52343I
b = 0.64769 + 1.30858I
4.83717 − 12.32680I 0
u = 0.45699 + 1.64231I
a = −0.37754 + 1.53751I
b = −0.65776 − 1.31344I
7.3438 − 17.3524I 0
u = 0.45699 − 1.64231I
a = −0.37754 − 1.53751I
b = −0.65776 + 1.31344I
7.3438 + 17.3524I 0
u = −0.192027 + 0.008415I
a = 0.89307 + 5.19596I
b = 0.224018 + 1.245620I
5.41652 − 6.50120I 1.62481 + 7.00024I
u = −0.192027 − 0.008415I
a = 0.89307 − 5.19596I
b = 0.224018 − 1.245620I
5.41652 + 6.50120I 1.62481 − 7.00024I
u = 0.0143062
a = −40.7428
b = −0.560782
−1.12189 −9.23230
15
II. I
u
2
= hb, −u
3
+ a − u + 1, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
u
3
+ u − 1
0
a
9
=
1
u
2
a
3
=
u
3
+ u − 1
0
a
2
=
u
3
+ u − 1
u
a
5
=
0
−u
a
7
=
1
0
a
10
=
u
2
+ 1
u
2
a
12
=
u
u
3
+ u
a
11
=
−u
3
+ u
2
+ 1
u
a
6
=
−u
3
− u
2
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
+ 4u
2
− u − 10
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
u
4
c
4
(u + 1)
4
c
5
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
6
, c
8
u
4
+ u
2
− u + 1
c
9
u
4
− 2u
3
+ 3u
2
− u + 1
c
10
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
11
, c
12
u
4
+ u
2
+ u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
y
4
− y
3
+ 2y
2
+ 7y + 4
c
6
, c
8
, c
11
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
9
, c
10
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −0.851808 + 0.911292I
b = 0
−2.62503 − 1.39709I −11.91838 + 2.95607I
u = 0.547424 − 0.585652I
a = −0.851808 − 0.911292I
b = 0
−2.62503 + 1.39709I −11.91838 − 2.95607I
u = −0.547424 + 1.120870I
a = 0.351808 + 0.720342I
b = 0
0.98010 + 7.64338I −7.58162 − 7.23121I
u = −0.547424 − 1.120870I
a = 0.351808 − 0.720342I
b = 0
0.98010 − 7.64338I −7.58162 + 7.23121I
19
III.
I
u
3
= hb, −u
5
− u
4
− 2u
3
− 2u
2
+ a − 2u − 2, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2u + 2
0
a
9
=
1
u
2
a
3
=
u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2u + 2
0
a
2
=
u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2u + 2
u
a
5
=
0
−u
a
7
=
1
0
a
10
=
u
2
+ 1
u
2
a
12
=
u
u
3
+ u
a
11
=
u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2u + 2
u
5
+ 2u
3
+ u
2
+ u + 1
a
6
=
−u
5
− 2u
3
− u
−u
5
− u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
5
+ u
4
+ 7u
3
+ 3u
2
+ 6u − 4
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
(u
3
+ u
2
− 1)
2
c
6
, c
8
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
9
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
10
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
11
, c
12
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
(y
3
− y
2
+ 2y −1)
2
c
6
, c
8
, c
11
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
9
, c
10
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −0.398606 + 0.800120I
b = 0
−1.37919 − 2.82812I −10.74483 + 3.34054I
u = 0.498832 − 1.001300I
a = −0.398606 − 0.800120I
b = 0
−1.37919 + 2.82812I −10.74483 − 3.34054I
u = −0.284920 + 1.115140I
a = 0.215080 + 0.841795I
b = 0
2.75839 −4.80521 − 0.27335I
u = −0.284920 − 1.115140I
a = 0.215080 − 0.841795I
b = 0
2.75839 −4.80521 + 0.27335I
u = −0.713912 + 0.305839I
a = 1.183530 + 0.507021I
b = 0
−1.37919 − 2.82812I −7.94996 + 3.74291I
u = −0.713912 − 0.305839I
a = 1.183530 − 0.507021I
b = 0
−1.37919 + 2.82812I −7.94996 − 3.74291I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
10
)(u
107
+ 47u
106
+ ··· − u + 1)
c
2
((u − 1)
10
)(u
107
− 11u
106
+ ··· − 11u + 1)
c
3
, c
7
u
10
(u
107
+ u
106
+ ··· + 2048u + 1024)
c
4
((u + 1)
10
)(u
107
− 11u
106
+ ··· − 11u + 1)
c
5
(u
3
+ u
2
− 1)
2
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
· (u
107
− 2u
106
+ ··· + 33648u + 4360)
c
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
107
+ 2u
106
+ ··· + 4u + 1)
c
8
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
107
− 8u
106
+ ··· + 3774u − 53)
c
9
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
107
+ 10u
106
+ ··· + 976u + 64)
c
10
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
107
− 52u
106
+ ··· + 8u + 1)
c
11
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
107
+ 2u
106
+ ··· + 4u + 1)
c
12
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
107
− 8u
106
+ ··· + 3774u − 53)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
10
)(y
107
+ 37y
106
+ ··· + 155y −1)
c
2
, c
4
((y −1)
10
)(y
107
− 47y
106
+ ··· − y −1)
c
3
, c
7
y
10
(y
107
+ 63y
106
+ ··· − 3.09330 × 10
7
y −1048576)
c
5
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
107
− 36y
106
+ ··· + 1065366544y −19009600)
c
6
, c
11
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
107
+ 52y
106
+ ··· + 8y −1)
c
8
, c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
107
+ 88y
106
+ ··· + 13858296y −2809)
c
9
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
107
− 4y
106
+ ··· + 53376y −4096)
c
10
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
107
+ 8y
106
+ ··· + 132y −1)
25
