12a
0123
(K12a
0123
)
A knot diagram
1
Linearized knot diagam
3 5 8 6 2 9 11 4 12 1 7 10
Solving Sequence
7,12
11
4,8
9 10 1 3 6 5 2
c
11
c
7
c
8
c
9
c
12
c
3
c
6
c
4
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.51942 × 10
285
u
92
+ 8.00642 × 10
285
u
91
+ ··· + 4.40333 × 10
288
b − 5.99526 × 10
288
,
3.85027 × 10
286
u
92
+ 1.46536 × 10
287
u
91
+ ··· + 8.80666 × 10
288
a − 6.43241 × 10
289
,
u
93
+ 3u
92
+ ··· − 1024u + 512i
I
u
2
= hu
2
a + b + a, −u
4
a + u
3
a + u
4
− 2u
2
a + a
2
+ au + u
2
− a + u, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
v
1
= ha, v
8
+ 4v
7
+ 7v
6
+ 4v
5
− 3v
4
− 6v
3
− 2v
2
+ b + 1, v
9
+ 5v
8
+ 12v
7
+ 15v
6
+ 9v
5
− v
4
− 4v
3
− 2v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 112 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
= h2.52 × 10
285
u
92
+ 8.01 × 10
285
u
91
+ · · · + 4.40 × 10
288
b − 6.00 ×
10
288
, 3.85 × 10
286
u
92
+ 1.47 × 10
287
u
91
+ · · · + 8.81 × 10
288
a − 6.43 ×
10
289
, u
93
+ 3u
92
+ · · · − 1024u + 512i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
11
=
1
−u
2
a
4
=
−0.00437199u
92
− 0.0166393u
91
+ ··· + 5.57776u + 7.30402
−0.000572162u
92
− 0.00181826u
91
+ ··· − 0.396111u + 1.36153
a
8
=
−u
u
3
+ u
a
9
=
−0.0121780u
92
− 0.0398559u
91
+ ··· − 3.82371u + 10.7352
0.00336113u
92
+ 0.0126239u
91
+ ··· − 0.559837u − 5.16081
a
10
=
−0.00881684u
92
− 0.0272320u
91
+ ··· − 4.38355u + 5.57440
0.00336113u
92
+ 0.0126239u
91
+ ··· − 0.559837u − 5.16081
a
1
=
−0.00881684u
92
− 0.0272320u
91
+ ··· − 4.38355u + 5.57440
−0.00804363u
92
− 0.0257825u
91
+ ··· − 3.15420u + 4.76072
a
3
=
−0.000573324u
92
− 0.00638541u
91
+ ··· + 8.37452u + 3.38703
−0.00392517u
92
− 0.0143906u
91
+ ··· − 0.0783778u + 4.69374
a
6
=
0.00770029u
92
+ 0.0301959u
91
+ ··· − 2.38268u − 3.55915
0.000870195u
92
+ 0.00510555u
91
+ ··· + 0.0219210u + 0.395882
a
5
=
−0.00441454u
92
− 0.0207171u
91
+ ··· + 8.92302u + 2.84951
−0.00237340u
92
− 0.00983384u
91
+ ··· − 1.33682u + 1.89139
a
2
=
−0.00236713u
92
− 0.00962072u
91
+ ··· + 4.13460u − 0.151447
−0.00720868u
92
− 0.0248131u
91
+ ··· − 3.72884u + 5.65750
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0147962u
92
− 0.0552504u
91
+ ··· + 35.4620u + 14.3294
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
93
+ 29u
92
+ ··· + 3u − 1
c
2
, c
5
u
93
+ 7u
92
+ ··· + 3u − 1
c
3
, c
8
u
93
− 2u
92
+ ··· − 4096u + 1024
c
6
u
93
+ 4u
92
+ ··· + 7544u + 1681
c
7
, c
11
u
93
+ 3u
92
+ ··· − 1024u + 512
c
9
, c
10
, c
12
u
93
+ 12u
92
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
93
+ 77y
92
+ ··· + 1907y −1
c
2
, c
5
y
93
+ 29y
92
+ ··· + 3y −1
c
3
, c
8
y
93
− 60y
92
+ ··· + 10485760y −1048576
c
6
y
93
− 62y
92
+ ··· − 79232254y −2825761
c
7
, c
11
y
93
+ 63y
92
+ ··· + 1048576y −262144
c
9
, c
10
, c
12
y
93
− 94y
92
+ ··· + 46y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.716646 + 0.701981I
a = 0.105914 + 0.387753I
b = 0.124940 + 0.652647I
2.16512 + 5.38944I 0
u = −0.716646 − 0.701981I
a = 0.105914 − 0.387753I
b = 0.124940 − 0.652647I
2.16512 − 5.38944I 0
u = 0.326973 + 0.954295I
a = 0.619905 + 0.869125I
b = 0.546397 + 0.505887I
6.00254 − 8.25583I 0
u = 0.326973 − 0.954295I
a = 0.619905 − 0.869125I
b = 0.546397 − 0.505887I
6.00254 + 8.25583I 0
u = −0.684870 + 0.783633I
a = −0.099146 − 0.337681I
b = −0.207481 − 0.628643I
2.41502 − 0.18063I 0
u = −0.684870 − 0.783633I
a = −0.099146 + 0.337681I
b = −0.207481 + 0.628643I
2.41502 + 0.18063I 0
u = 0.920090 + 0.240027I
a = 0.041844 − 0.175746I
b = −0.504669 + 0.954860I
1.78871 + 0.48442I 0
u = 0.920090 − 0.240027I
a = 0.041844 + 0.175746I
b = −0.504669 − 0.954860I
1.78871 − 0.48442I 0
u = −0.416522 + 0.984253I
a = −0.108854 − 0.193496I
b = −0.494465 − 0.255957I
−0.72672 + 2.38399I 0
u = −0.416522 − 0.984253I
a = −0.108854 + 0.193496I
b = −0.494465 + 0.255957I
−0.72672 − 2.38399I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.106666 + 1.072270I
a = 1.262650 + 0.357117I
b = 0.857579 + 0.565640I
1.77787 − 2.72179I 0
u = 0.106666 − 1.072270I
a = 1.262650 − 0.357117I
b = 0.857579 − 0.565640I
1.77787 + 2.72179I 0
u = 0.705042 + 0.824626I
a = 0.028648 + 0.267284I
b = 1.12864 − 1.02229I
5.76366 + 4.24931I 0
u = 0.705042 − 0.824626I
a = 0.028648 − 0.267284I
b = 1.12864 + 1.02229I
5.76366 − 4.24931I 0
u = 0.781820 + 0.757204I
a = −0.012561 − 0.256334I
b = −1.07841 + 1.07714I
5.87081 − 1.54110I 0
u = 0.781820 − 0.757204I
a = −0.012561 + 0.256334I
b = −1.07841 − 1.07714I
5.87081 + 1.54110I 0
u = 0.417115 + 1.028530I
a = −0.329817 − 0.655686I
b = −0.444154 − 0.451529I
6.69196 − 2.98020I 0
u = 0.417115 − 1.028530I
a = −0.329817 + 0.655686I
b = −0.444154 + 0.451529I
6.69196 + 2.98020I 0
u = 0.118297 + 1.105340I
a = 0.33533 + 1.91548I
b = 0.804701 − 0.588763I
1.72008 + 1.14890I 0
u = 0.118297 − 1.105340I
a = 0.33533 − 1.91548I
b = 0.804701 + 0.588763I
1.72008 − 1.14890I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.188180 + 0.116830I
a = 1.95026 + 0.30013I
b = −3.83727 − 0.30619I
3.58259 − 3.65771I 0
u = −1.188180 − 0.116830I
a = 1.95026 − 0.30013I
b = −3.83727 + 0.30619I
3.58259 + 3.65771I 0
u = −0.181784 + 1.192720I
a = 0.155333 + 0.205316I
b = 0.955229 + 0.002377I
4.35591 − 0.27954I 0
u = −0.181784 − 1.192720I
a = 0.155333 − 0.205316I
b = 0.955229 − 0.002377I
4.35591 + 0.27954I 0
u = 0.328044 + 1.167600I
a = −0.27690 + 1.96117I
b = 1.39765 − 0.23420I
1.21815 − 6.10394I 0
u = 0.328044 − 1.167600I
a = −0.27690 − 1.96117I
b = 1.39765 + 0.23420I
1.21815 + 6.10394I 0
u = −0.215840 + 0.754790I
a = 0.294553 + 0.012206I
b = 0.255474 − 0.390927I
0.429600 + 1.174350I 4.96827 − 5.78542I
u = −0.215840 − 0.754790I
a = 0.294553 − 0.012206I
b = 0.255474 + 0.390927I
0.429600 − 1.174350I 4.96827 + 5.78542I
u = −0.080295 + 1.215380I
a = 1.59238 − 0.35167I
b = 1.47149 + 0.74346I
5.35775 + 3.59410I 0
u = −0.080295 − 1.215380I
a = 1.59238 + 0.35167I
b = 1.47149 − 0.74346I
5.35775 − 3.59410I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.254594 + 1.203760I
a = −0.151299 − 0.203013I
b = −0.925300 − 0.111558I
4.19460 + 5.47852I 0
u = −0.254594 − 1.203760I
a = −0.151299 + 0.203013I
b = −0.925300 + 0.111558I
4.19460 − 5.47852I 0
u = 0.215406 + 1.216710I
a = 0.00099 − 1.80977I
b = −1.052840 + 0.222334I
5.09762 − 2.63896I 0
u = 0.215406 − 1.216710I
a = 0.00099 + 1.80977I
b = −1.052840 − 0.222334I
5.09762 + 2.63896I 0
u = 1.248400 + 0.039111I
a = 0.001301 − 0.176183I
b = −0.06146 + 1.43162I
6.41890 + 2.89431I 0
u = 1.248400 − 0.039111I
a = 0.001301 + 0.176183I
b = −0.06146 − 1.43162I
6.41890 − 2.89431I 0
u = −1.26787
a = −1.82174
b = 3.74933
7.24874 0
u = 0.023239 + 1.281130I
a = −1.208500 + 0.307783I
b = −1.37475 − 0.35528I
6.92419 − 1.52206I 0
u = 0.023239 − 1.281130I
a = −1.208500 − 0.307783I
b = −1.37475 + 0.35528I
6.92419 + 1.52206I 0
u = 0.697459 + 0.106150I
a = −2.05513 − 0.08168I
b = 1.150630 − 0.024496I
4.30707 + 7.71222I 3.50170 − 6.75559I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697459 − 0.106150I
a = −2.05513 + 0.08168I
b = 1.150630 + 0.024496I
4.30707 − 7.71222I 3.50170 + 6.75559I
u = −0.052453 + 1.296170I
a = 0.30713 + 1.48441I
b = 0.367207 − 0.064350I
8.99975 + 6.38792I 0
u = −0.052453 − 1.296170I
a = 0.30713 − 1.48441I
b = 0.367207 + 0.064350I
8.99975 − 6.38792I 0
u = 0.339408 + 1.257430I
a = −0.542089 + 0.027267I
b = −0.650667 + 0.054172I
6.36795 − 3.44151I 0
u = 0.339408 − 1.257430I
a = −0.542089 − 0.027267I
b = −0.650667 − 0.054172I
6.36795 + 3.44151I 0
u = 0.167910 + 0.674065I
a = 0.192935 + 0.477941I
b = 0.805837 − 0.947893I
0.66358 + 1.44577I 8.36312 − 2.48349I
u = 0.167910 − 0.674065I
a = 0.192935 − 0.477941I
b = 0.805837 + 0.947893I
0.66358 − 1.44577I 8.36312 + 2.48349I
u = −0.526782 + 0.452563I
a = −0.096556 + 0.612229I
b = −0.013650 + 0.517969I
−2.29291 + 1.46330I −3.12922 − 3.73940I
u = −0.526782 − 0.452563I
a = −0.096556 − 0.612229I
b = −0.013650 − 0.517969I
−2.29291 − 1.46330I −3.12922 + 3.73940I
u = 0.001100 + 1.307870I
a = −0.24813 − 1.51407I
b = −0.493959 + 0.042171I
9.74889 + 0.18700I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.001100 − 1.307870I
a = −0.24813 + 1.51407I
b = −0.493959 − 0.042171I
9.74889 − 0.18700I 0
u = 0.663828 + 0.079069I
a = 2.13002 + 0.09244I
b = −1.098470 + 0.018862I
5.08023 + 1.81268I 4.74416 − 1.60295I
u = 0.663828 − 0.079069I
a = 2.13002 − 0.09244I
b = −1.098470 − 0.018862I
5.08023 − 1.81268I 4.74416 + 1.60295I
u = 0.380156 + 1.303240I
a = 0.33177 − 1.62783I
b = −1.350340 − 0.110866I
8.99022 − 5.87602I 0
u = 0.380156 − 1.303240I
a = 0.33177 + 1.62783I
b = −1.350340 + 0.110866I
8.99022 + 5.87602I 0
u = 0.419100 + 1.292060I
a = −0.40732 + 1.62182I
b = 1.42991 + 0.12717I
8.0548 − 12.0517I 0
u = 0.419100 − 1.292060I
a = −0.40732 − 1.62182I
b = 1.42991 − 0.12717I
8.0548 + 12.0517I 0
u = 0.536124 + 1.253660I
a = 0.245774 − 0.324193I
b = 0.170908 − 0.518899I
5.01510 − 5.87964I 0
u = 0.536124 − 1.253660I
a = 0.245774 + 0.324193I
b = 0.170908 + 0.518899I
5.01510 + 5.87964I 0
u = −1.346770 + 0.245568I
a = 1.56067 + 0.37615I
b = −3.44942 − 0.23902I
10.7002 − 9.3495I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.346770 − 0.245568I
a = 1.56067 − 0.37615I
b = −3.44942 + 0.23902I
10.7002 + 9.3495I 0
u = −1.359400 + 0.198057I
a = −1.57991 − 0.30459I
b = 3.49858 + 0.19464I
11.55180 − 3.13531I 0
u = −1.359400 − 0.198057I
a = −1.57991 + 0.30459I
b = 3.49858 − 0.19464I
11.55180 + 3.13531I 0
u = 0.013634 + 0.620332I
a = 1.024120 + 0.659773I
b = 0.081044 − 1.114670I
0.80001 + 1.38974I 9.06195 − 5.30423I
u = 0.013634 − 0.620332I
a = 1.024120 − 0.659773I
b = 0.081044 + 1.114670I
0.80001 − 1.38974I 9.06195 + 5.30423I
u = 0.539158 + 0.220242I
a = −2.16591 + 0.12543I
b = 1.083310 + 0.212051I
−1.64742 + 2.59719I −1.56655 − 4.74635I
u = 0.539158 − 0.220242I
a = −2.16591 − 0.12543I
b = 1.083310 − 0.212051I
−1.64742 − 2.59719I −1.56655 + 4.74635I
u = 0.224026 + 0.525069I
a = −2.12240 − 0.17767I
b = 0.653616 + 1.040690I
0.07245 − 2.77451I 3.04583 − 0.54563I
u = 0.224026 − 0.525069I
a = −2.12240 + 0.17767I
b = 0.653616 − 1.040690I
0.07245 + 2.77451I 3.04583 + 0.54563I
u = 0.530631
a = 0.296252
b = −1.11874
2.15469 2.08140
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500625
a = 2.26750
b = −0.949182
1.53592 5.87220
u = −0.47269 + 1.43484I
a = −0.41240 + 1.96747I
b = −3.24772 + 0.33128I
8.66015 + 2.14339I 0
u = −0.47269 − 1.43484I
a = −0.41240 − 1.96747I
b = −3.24772 − 0.33128I
8.66015 − 2.14339I 0
u = −0.475892 + 0.063884I
a = −0.026871 + 1.187250I
b = −0.017488 + 0.392777I
0.87050 − 2.57947I 1.01592 + 3.11295I
u = −0.475892 − 0.063884I
a = −0.026871 − 1.187250I
b = −0.017488 − 0.392777I
0.87050 + 2.57947I 1.01592 − 3.11295I
u = −0.59655 + 1.40349I
a = 0.24650 + 1.98611I
b = −3.22566 + 0.79330I
7.69431 + 10.06070I 0
u = −0.59655 − 1.40349I
a = 0.24650 − 1.98611I
b = −3.22566 − 0.79330I
7.69431 − 10.06070I 0
u = 0.56984 + 1.44902I
a = 0.416518 − 0.388950I
b = 0.539327 − 0.858010I
10.9765 − 9.3795I 0
u = 0.56984 − 1.44902I
a = 0.416518 + 0.388950I
b = 0.539327 + 0.858010I
10.9765 + 9.3795I 0
u = 0.52288 + 1.46731I
a = −0.439913 + 0.377803I
b = −0.641224 + 0.806368I
11.34270 − 3.40968I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.52288 − 1.46731I
a = −0.439913 − 0.377803I
b = −0.641224 − 0.806368I
11.34270 + 3.40968I 0
u = −0.55003 + 1.47001I
a = 0.06072 − 1.79945I
b = 3.13549 − 0.58444I
12.03550 + 6.48389I 0
u = −0.55003 − 1.47001I
a = 0.06072 + 1.79945I
b = 3.13549 + 0.58444I
12.03550 − 6.48389I 0
u = −0.70078 + 1.42632I
a = 0.47338 + 1.62875I
b = −2.98031 + 0.84391I
14.4974 + 16.5945I 0
u = −0.70078 − 1.42632I
a = 0.47338 − 1.62875I
b = −2.98031 − 0.84391I
14.4974 − 16.5945I 0
u = −0.68210 + 1.45122I
a = −0.37508 − 1.62489I
b = 3.00283 − 0.79833I
15.5835 + 10.3685I 0
u = −0.68210 − 1.45122I
a = −0.37508 + 1.62489I
b = 3.00283 + 0.79833I
15.5835 − 10.3685I 0
u = −0.375100 + 0.126927I
a = 0.24476 + 2.34220I
b = −0.24576 − 3.61476I
1.95064 − 2.18031I −23.8772 − 10.0587I
u = −0.375100 − 0.126927I
a = 0.24476 − 2.34220I
b = −0.24576 + 3.61476I
1.95064 + 2.18031I −23.8772 + 10.0587I
u = −0.36012 + 1.61251I
a = −0.507192 + 1.263010I
b = −2.67480 + 0.39946I
17.1546 − 3.0296I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.36012 − 1.61251I
a = −0.507192 − 1.263010I
b = −2.67480 − 0.39946I
17.1546 + 3.0296I 0
u = −0.41001 + 1.60645I
a = 0.421539 − 1.334630I
b = 2.76878 − 0.43730I
17.7186 + 3.3774I 0
u = −0.41001 − 1.60645I
a = 0.421539 + 1.334630I
b = 2.76878 + 0.43730I
17.7186 − 3.3774I 0
14
II. I
u
2
= hu
2
a + b + a, −u
4
a + u
4
+ · · · + a
2
− a, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
7
=
0
u
a
12
=
1
0
a
11
=
1
−u
2
a
4
=
a
−u
2
a − a
a
8
=
−u
u
3
+ u
a
9
=
−u
u
3
+ u
a
10
=
u
3
u
3
+ u
a
1
=
u
3
−u
4
+ u
3
− u
2
− 1
a
3
=
a
−u
2
a − a
a
6
=
−u
3
u
4
− u
3
+ u
2
+ 1
a
5
=
−u
4
a + a
−u
3
a
a
2
=
−u
4
+ 2u
3
− 2u
2
+ a + u − 1
−u
2
a + u
2
− a
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
4
a − 3u
3
a + u
4
+ u
2
a − 5u
3
+ 2au + 7u
2
− 5u + 8
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
3
, c
8
u
10
c
6
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
7
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
9
, c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
5
c
3
, c
8
y
10
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
c
7
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
c
9
, c
10
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −1.114310 − 0.148503I
b = 0.571671 − 0.556363I
0.329100 − 0.499304I 2.59686 − 1.45733I
u = −0.339110 + 0.822375I
a = 0.685764 − 0.890773I
b = 0.195989 + 0.773263I
0.32910 + 3.56046I 6.44749 − 8.37485I
u = −0.339110 − 0.822375I
a = −1.114310 + 0.148503I
b = 0.571671 + 0.556363I
0.329100 + 0.499304I 2.59686 + 1.45733I
u = −0.339110 − 0.822375I
a = 0.685764 + 0.890773I
b = 0.195989 − 0.773263I
0.32910 − 3.56046I 6.44749 + 8.37485I
u = 0.766826
a = 0.652039 + 1.129360I
b = −1.03545 − 1.79345I
2.40108 − 2.02988I 7.10008 + 1.25892I
u = 0.766826
a = 0.652039 − 1.129360I
b = −1.03545 + 1.79345I
2.40108 + 2.02988I 7.10008 − 1.25892I
u = 0.455697 + 1.200150I
a = −0.492416 − 0.603584I
b = −0.774795 + 0.398153I
5.87256 − 6.43072I 11.57979 + 6.03904I
u = 0.455697 + 1.200150I
a = 0.768927 − 0.124653I
b = 0.042587 − 0.870069I
5.87256 − 2.37095I 6.27578 − 1.37298I
u = 0.455697 − 1.200150I
a = −0.492416 + 0.603584I
b = −0.774795 − 0.398153I
5.87256 + 6.43072I 11.57979 − 6.03904I
u = 0.455697 − 1.200150I
a = 0.768927 + 0.124653I
b = 0.042587 + 0.870069I
5.87256 + 2.37095I 6.27578 + 1.37298I
18
III. I
v
1
= ha, v
8
+ 4v
7
+ · · · + b + 1, v
9
+ 5v
8
+ · · · + v + 1i
(i) Arc colorings
a
7
=
v
0
a
12
=
1
0
a
11
=
1
0
a
4
=
0
−v
8
− 4v
7
− 7v
6
− 4v
5
+ 3v
4
+ 6v
3
+ 2v
2
− 1
a
8
=
v
0
a
9
=
v
1
a
10
=
v + 1
1
a
1
=
−v
−1
a
3
=
v
7
+ 3v
6
+ 4v
5
+ v
4
− 2v
3
− 2v
2
+ 1
−v
8
− 4v
7
− 7v
6
− 4v
5
+ 3v
4
+ 6v
3
+ 2v
2
− 1
a
6
=
v
2
+ v
v
a
5
=
−v
7
− 3v
6
− 5v
5
− 4v
4
− 2v
3
+ v
2
+ v
v
5
+ 2v
4
+ 2v
3
+ v
a
2
=
−v
3
− v
2
− v
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5v
8
+ 24v
7
+ 51v
6
+ 47v
5
+ 2v
4
− 34v
3
− 18v
2
+ 2v + 17
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
2
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
3
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
6
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
7
, c
11
u
9
c
8
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
9
, c
10
(u + 1)
9
c
12
(u − 1)
9
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1
c
2
, c
5
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1
c
3
, c
8
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
c
6
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1
c
7
, c
11
y
9
c
9
, c
10
, c
12
(y − 1)
9
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.336947 + 0.788921I
a = 0
b = 0.900982 + 0.594909I
−0.13850 − 2.09337I 2.03658 + 4.61282I
v = −0.336947 − 0.788921I
a = 0
b = 0.900982 − 0.594909I
−0.13850 + 2.09337I 2.03658 − 4.61282I
v = −0.682165
a = 0
b = −1.21075
2.84338 15.2670
v = 0.527091 + 0.209303I
a = 0
b = 0.249476 + 1.304240I
2.26187 + 2.45442I 8.82413 − 4.82524I
v = 0.527091 − 0.209303I
a = 0
b = 0.249476 − 1.304240I
2.26187 − 2.45442I 8.82413 + 4.82524I
v = −1.22475 + 0.91930I
a = 0
b = −0.766570 − 0.255687I
6.01628 − 1.33617I 12.05808 − 1.14063I
v = −1.22475 − 0.91930I
a = 0
b = −0.766570 + 0.255687I
6.01628 + 1.33617I 12.05808 + 1.14063I
v = −1.12431 + 1.17337I
a = 0
b = 0.721488 + 0.307914I
5.24306 − 7.08493I 9.44791 + 3.65320I
v = −1.12431 − 1.17337I
a = 0
b = 0.721488 − 0.307914I
5.24306 + 7.08493I 9.44791 − 3.65320I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
2
− u + 1)
5
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
93
+ 29u
92
+ ··· + 3u − 1)
c
2
(u
2
+ u + 1)
5
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
93
+ 7u
92
+ ··· + 3u − 1)
c
3
u
10
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
93
− 2u
92
+ ··· − 4096u + 1024)
c
5
(u
2
− u + 1)
5
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
93
+ 7u
92
+ ··· + 3u − 1)
c
6
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
93
+ 4u
92
+ ··· + 7544u + 1681)
c
7
u
9
(u
5
+ u
4
+ ··· + u + 1)
2
(u
93
+ 3u
92
+ ··· − 1024u + 512)
c
8
u
10
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
93
− 2u
92
+ ··· − 4096u + 1024)
c
9
, c
10
((u + 1)
9
)(u
5
− u
4
+ ··· + u + 1)
2
(u
93
+ 12u
92
+ ··· + 6u + 1)
c
11
u
9
(u
5
− u
4
+ ··· + u − 1)
2
(u
93
+ 3u
92
+ ··· − 1024u + 512)
c
12
((u − 1)
9
)(u
5
+ u
4
+ ··· + u − 1)
2
(u
93
+ 12u
92
+ ··· + 6u + 1)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
5
)(y
9
+ 7y
8
+ ··· + 13y − 1)
· (y
93
+ 77y
92
+ ··· + 1907y − 1)
c
2
, c
5
(y
2
+ y + 1)
5
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
93
+ 29y
92
+ ··· + 3y − 1)
c
3
, c
8
y
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
93
− 60y
92
+ ··· + 10485760y − 1048576)
c
6
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
93
− 62y
92
+ ··· − 79232254y − 2825761)
c
7
, c
11
y
9
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
2
· (y
93
+ 63y
92
+ ··· + 1048576y − 262144)
c
9
, c
10
, c
12
((y − 1)
9
)(y
5
− 5y
4
+ ··· − y − 1)
2
(y
93
− 94y
92
+ ··· + 46y − 1)
24
