11a
47
(K11a
47
)
1
Arc Sequences
4 1 8 2 11 9 3 10 7 5 6
Solving Sequence
2,4 5,10
11 6
1,8
3 7 9
c
4
c
10
c
5
c
1
c
3
c
7
c
9
c
2
, c
6
, c
8
, c
11
Representation Ideals
I =
8
\
i=1
I
u
i
\
I
v
1
1
The knot diagram image is adapter from “C. Livingston and A. H. Mo ore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I
u
1
= ha, u 1, d + c 1, cb + 1i
I
u
2
= ha, c, b 1, d 1, u 1i
I
u
3
= ha, c 1, u 1, d + 1, b + 1i
I
u
4
= hu
4
+ b, u
2
+ d, u
2
+ c 1, u
4
+ u
2
+ a 1, u
6
+ u
5
u
4
2u
3
+ u + 1i
I
u
5
= hc
12
+ 7c
11
+ 37c
10
+ 125c
9
+ 301c
8
+ 563c
7
+ 855c
6
+ 1020c
5
+ 986c
4
+ 748c
3
+ 504c
2
+ 277c + 137,
360449610467c
11
2239492377762c
10
+ ··· + 16501719305943a 35208293717353,
56083107757c
11
+ 408621304548c
10
+ ··· + 5500573101981b + 9355307354771,
137214226835c
11
+ 16501719305943d + ··· + 23477181903284c + 13375366451981,
92559389066c
11
+ 16501719305943u + ··· + 14724871632887c + 15975316836953i
I
u
6
= h−u
2
+ d, u
2
+ c 1, u
7
2u
5
u
4
+ u
2
+ a + 2u + 1, u
9
+ u
7
+ 2u
6
+ u
5
u
4
2u
3
2u
2
+ b u,
u
12
u
11
4u
10
+ 2u
9
+ 7u
8
+ u
7
5u
6
5u
5
u
4
+ 3u
3
+ 2u
2
+ 1i
I
u
7
= hu
16
+ u
15
3u
14
5u
13
+ 3u
12
+ 9u
11
+ 2u
10
8u
9
6u
8
+ 2u
7
+ 5u
6
+ u
5
u
4
+ 2u
3
+ 3u
2
4u 4,
271u
15
165u
14
+ ··· + 2360a + 162, 581u
15
+ 93u
14
+ ··· + 1180b + 3350,
99u
15
197u
14
+ ··· + 2360c 34, 173u
15
+ 57u
14
+ ··· + 590d 204i
I
u
8
= hu
17
3u
15
2u
14
+ 4u
13
+ 4u
12
+ u
11
4u
10
5u
9
2u
8
+ 5u
7
+ 4u
6
+ u
5
u
4
u
3
+ 4u
2
+ 4d + u 3,
u
18
+ u
17
+ ··· + 2b 1, u
19
+ 2u
18
+ ··· + 3u + 1, 2u
18
3u
17
+ ··· + 2a 4,
u
18
2u
17
+ ··· + 2c 5i
I
v
1
= hb, c, d 1, v 1, a 1i
There are 9 irreducible components with 68 representations.
There are 1 irreducible components of dim
C
= 1 for 11a
47
2
I. I
u
1
= ha, u 1, d + c 1, cb + 1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
1
a
5
=
1
1
a
10
=
c
c + 1
a
11
=
c + 1
c
a
6
=
c
c + 1
a
1
=
1
1
a
8
=
0
b
a
3
=
0
1
a
7
=
0
b
a
9
=
c
c + b + 1
a
9
=
c
c + b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
3
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
1.64493 1.106145 + 0.511900I
4
II. I
u
2
= ha, c, b 1, d 1, u 1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
1
a
5
=
1
1
a
10
=
0
1
a
11
=
1
0
a
6
=
0
1
a
1
=
1
1
a
8
=
0
1
a
3
=
0
1
a
7
=
0
1
a
9
=
0
1
a
9
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
c = 0
d = 1.00000
0 0
6
III. I
u
3
= ha, c 1, u 1, d + 1, b + 1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
1
a
5
=
1
1
a
10
=
1
1
a
11
=
1
1
a
6
=
1
1
a
1
=
1
1
a
8
=
0
1
a
3
=
0
1
a
7
=
0
1
a
9
=
1
2
a
9
=
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
c = 1.00000
d = 1.00000
3.28987 12.0000
8
IV.
I
u
4
= hu
4
+ b, u
2
+ d, u
2
+ c 1, u
4
+ u
2
+ a 1, u
6
+ u
5
u
4
2u
3
+ u +1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
5
=
u
u
a
10
=
u
2
+ 1
u
2
a
11
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
8
=
u
4
u
2
+ 1
u
4
a
3
=
u
2
+ 1
u
4
a
7
=
u
u
a
9
=
1
0
a
9
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.073950 0.558752I
a = 0.573950 + 0.818891I
b = 0.73279 2.01903I
c = 0.158836 1.200143I
d = 0.84116 + 1.20014I
5.69302I 5.51057I
u = 1.073950 + 0.558752I
a = 0.573950 0.818891I
b = 0.73279 + 2.01903I
c = 0.158836 + 1.200143I
d = 0.84116 1.20014I
5.69302I 5.51057I
u = 0.428243 0.664531I
a = 1.000936 0.863088I
b = 0.257273 + 0.293926I
c = 1.258209 0.569162I
d = 0.258209 + 0.569162I
1.89061 + 0.92430I 3.71672 0.79423I
u = 0.428243 + 0.664531I
a = 1.000936 + 0.863088I
b = 0.257273 0.293926I
c = 1.258209 + 0.569162I
d = 0.258209 0.569162I
1.89061 0.92430I 3.71672 + 0.79423I
u = 1.002193 0.295542I
a = 0.573013 0.494098I
b = 0.490059 + 1.086478I
c = 0.082955 + 0.592379I
d = 0.917045 0.592379I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.002193 + 0.295542I
a = 0.573013 + 0.494098I
b = 0.490059 1.086478I
c = 0.082955 0.592379I
d = 0.917045 + 0.592379I
1.89061 0.92430I 3.71672 + 0.79423I
10
V. I
u
5
= hc
12
+ 7c
11
+ · · · + 277c + 137, 3.60 × 10
11
c
11
2.24 × 10
12
c
10
+
· · · + 1.65 × 10
13
a 3.52 × 10
13
, 5.61 × 10
10
c
11
+ 4.09 × 10
11
c
10
+ · · · + 5.50 ×
10
12
b + 9.36 × 10
12
, 1.65 × 10
13
d 1.37 × 10
11
c
11
+ · · · + 2.35 × 10
13
c +
1.34 × 10
13
, 1.65 × 10
13
u 9.26 × 10
10
c
11
+ · · · + 1.47 × 10
13
c + 1.60 × 10
13
i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
0.00560908c
11
+ 0.0192675c
10
+ ··· 0.892323c 0.968100
a
5
=
0.00560908c
11
0.0192675c
10
+ ··· + 0.892323c + 0.968100
0.00560908c
11
+ 0.0192675c
10
+ ··· 0.892323c 0.968100
a
10
=
c
0.00831515c
11
+ 0.0396045c
10
+ ··· 1.42271c 0.810544
a
11
=
0.00184239c
11
0.00931661c
10
+ ··· + 0.279479c + 0.285527
0.0101575c
11
+ 0.0489212c
10
+ ··· 0.702190c 1.09607
a
6
=
0.000872373c
11
+ 0.0198965c
10
+ ··· + 2.00425c + 1.76513
0.00700307c
11
0.0495165c
10
+ ··· 1.93598c 0.956306
a
1
=
1
0.0116473c
11
+ 0.0614256c
10
+ ··· + 0.422287c 0.567174
a
8
=
0.0218432c
11
+ 0.135713c
10
+ ··· + 3.86882c + 2.13361
0.0101959c
11
0.0742870c
10
+ ··· 3.44653c 1.70079
a
3
=
0.0116473c
11
+ 0.0614256c
10
+ ··· + 0.422287c + 0.432826
0.0101959c
11
+ 0.0742870c
10
+ ··· + 3.44653c + 1.70079
a
7
=
0.00560908c
11
+ 0.0192675c
10
+ ··· 0.892323c 0.968100
0.00560908c
11
0.0192675c
10
+ ··· + 0.892323c + 0.968100
a
9
=
0.00184239c
11
0.00931661c
10
+ ··· + 0.279479c + 0.285527
0.0101575c
11
+ 0.0489212c
10
+ ··· 0.702190c 1.09607
a
9
=
0.00184239c
11
0.00931661c
10
+ ··· + 0.279479c + 0.285527
0.0101575c
11
+ 0.0489212c
10
+ ··· 0.702190c 1.09607
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.428243 + 0.664531I
a = 1.000936 + 0.863088I
b = 0.257273 0.293926I
c = 1.64624 0.72836I
d = 0.590678 0.583006I
1.89061 0.92430I 3.71672 + 0.79423I
u = 0.428243 0.664531I
a = 1.000936 0.863088I
b = 0.257273 + 0.293926I
c = 1.64624 + 0.72836I
d = 0.590678 + 0.583006I
1.89061 + 0.92430I 3.71672 0.79423I
u = 0.428243 0.664531I
a = 1.000936 0.863088I
b = 0.257273 + 0.293926I
c = 0.931516 0.756104I
d = 0.987076 0.555260I
1.89061 + 0.92430I 3.71672 0.79423I
u = 0.428243 + 0.664531I
a = 1.000936 + 0.863088I
b = 0.257273 0.293926I
c = 0.931516 + 0.756104I
d = 0.987076 + 0.555260I
1.89061 0.92430I 3.71672 + 0.79423I
u = 1.002193 + 0.295542I
a = 0.573013 + 0.494098I
b = 0.490059 1.086478I
c = 0.86373 3.45204I
d = 0.14460 + 3.94091I
1.89061 0.92430I 3.71672 + 0.79423I
u = 1.002193 0.295542I
a = 0.573013 0.494098I
b = 0.490059 + 1.086478I
c = 0.86373 + 3.45204I
d = 0.14460 3.94091I
1.89061 + 0.92430I 3.71672 0.79423I
12
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.073950 + 0.558752I
a = 0.573950 0.818891I
b = 0.73279 + 2.01903I
c = 0.509721 1.113504I
d = 0.40051 + 1.82841I
5.69302I 5.51057I
u = 1.073950 0.558752I
a = 0.573950 + 0.818891I
b = 0.73279 2.01903I
c = 0.509721 + 1.113504I
d = 0.40051 1.82841I
5.69302I 5.51057I
u = 1.073950 0.558752I
a = 0.573950 + 0.818891I
b = 0.73279 2.01903I
c = 0.13413 1.55114I
d = 1.02492 + 2.26605I
5.69302I 5.51057I
u = 1.073950 + 0.558752I
a = 0.573950 0.818891I
b = 0.73279 + 2.01903I
c = 0.13413 + 1.55114I
d = 1.02492 2.26605I
5.69302I 5.51057I
u = 1.002193 0.295542I
a = 0.573013 0.494098I
b = 0.490059 + 1.086478I
c = 0.317076 0.733138I
d = 0.308747 + 1.222005I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.002193 + 0.295542I
a = 0.573013 + 0.494098I
b = 0.490059 1.086478I
c = 0.317076 + 0.733138I
d = 0.308747 1.222005I
1.89061 0.92430I 3.71672 + 0.79423I
13
VI. I
u
6
= h−u
2
+ d, u
2
+ c 1, u
7
2u
5
+ · · · + a + 1, u
9
+ u
7
+ · · · + b
u, u
12
u
11
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
5
=
u
u
a
10
=
u
2
+ 1
u
2
a
11
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
8
=
u
7
+ 2u
5
+ u
4
u
2
2u 1
u
9
u
7
2u
6
u
5
+ u
4
+ 2u
3
+ 2u
2
+ u
a
3
=
u
2
+ 1
u
4
a
7
=
u
10
3u
8
2u
7
+ 2u
6
+ 4u
5
+ 3u
4
3u
2
3u 1
u
11
2u
10
+ 4u
9
+ 7u
8
u
7
9u
6
7u
5
+ 5u
3
+ 4u
2
+ u + 1
a
9
=
u
11
+ 4u
9
+ 2u
8
6u
7
6u
6
+ 2u
5
+ 6u
4
+ 3u
3
2u
2
2u
2u
11
6u
9
4u
8
+ 6u
7
+ 8u
6
+ 2u
5
4u
4
4u
3
1
a
9
=
u
11
+ 4u
9
+ 2u
8
6u
7
6u
6
+ 2u
5
+ 6u
4
+ 3u
3
2u
2
2u
2u
11
6u
9
4u
8
+ 6u
7
+ 8u
6
+ 2u
5
4u
4
4u
3
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.155020 0.191936I
a = 0.267765 + 0.619837I
b = 0.38259 3.72805I
c = 0.297233 0.443379I
d = 1.297233 + 0.443379I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.155020 + 0.191936I
a = 0.267765 0.619837I
b = 0.38259 + 3.72805I
c = 0.297233 + 0.443379I
d = 1.297233 0.443379I
1.89061 0.92430I 3.71672 + 0.79423I
u = 0.895235 0.524661I
a = 0.689262 0.734076I
b = 0.14376 + 1.46753I
c = 0.473823 0.939391I
d = 0.526177 + 0.939391I
1.89061 0.92430I 3.71672 + 0.79423I
u = 0.895235 + 0.524661I
a = 0.689262 + 0.734076I
b = 0.14376 1.46753I
c = 0.473823 + 0.939391I
d = 0.526177 0.939391I
1.89061 + 0.92430I 3.71672 0.79423I
u = 0.282166 0.828798I
a = 0.999480 + 0.955518I
b = 0.416114 0.026273I
c = 1.60729 0.46772I
d = 0.607288 + 0.467717I
5.69302I 5.51057I
u = 0.282166 + 0.828798I
a = 0.999480 0.955518I
b = 0.416114 + 0.026273I
c = 1.60729 + 0.46772I
d = 0.607288 0.467717I
5.69302I 5.51057I
15
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.152828 0.487477I
a = 0.99044 + 1.18900I
b = 0.497742 0.515052I
c = 1.214278 + 0.149000I
d = 0.214278 0.149000I
1.89061 0.92430I 3.71672 + 0.79423I
u = 0.152828 + 0.487477I
a = 0.99044 1.18900I
b = 0.497742 + 0.515052I
c = 1.214278 0.149000I
d = 0.214278 + 0.149000I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.323479 0.139870I
a = 0.772216 + 0.141696I
b = 1.72245 0.63219I
c = 0.732032 + 0.370229I
d = 1.73203 0.37023I
1.89061 0.92430I 3.71672 + 0.79423I
u = 1.323479 + 0.139870I
a = 0.772216 0.141696I
b = 1.72245 + 0.63219I
c = 0.732032 0.370229I
d = 1.73203 + 0.37023I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.356115 0.270046I
a = 0.840643 0.244625I
b = 1.78224 + 1.23026I
c = 0.766124 + 0.732426I
d = 1.76612 0.73243I
5.69302I 5.51057I
u = 1.356115 + 0.270046I
a = 0.840643 + 0.244625I
b = 1.78224 1.23026I
c = 0.766124 0.732426I
d = 1.76612 + 0.73243I
5.69302I 5.51057I
16
VII. I
u
7
= hu
16
+ u
15
+ · · · 4u 4, 271u
15
165u
14
+ · · · + 2360a +
162, 581u
15
+ 93u
14
+ · · · + 1180b + 3350, 99u
15
197u
14
+ · · · +
2360c 34, 173u
15
+ 57u
14
+ · · · + 590d 204i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
5
=
u
u
a
10
=
0.0419492u
15
+ 0.0834746u
14
+ ··· + 0.210593u + 0.0144068
0.293220u
15
0.0966102u
14
+ ··· 0.245763u + 0.345763
a
11
=
0.102119u
15
+ 0.0614407u
14
+ ··· + 0.158051u + 0.966949
0.149153u
15
0.0745763u
14
+ ··· 0.193220u 0.606780
a
6
=
0.151695u
15
0.300847u
14
+ ··· 0.163559u + 0.413559
0.163559u
15
+ 0.456780u
14
+ ··· + 0.558475u 0.408475
a
1
=
1
u
2
a
8
=
0.114831u
15
+ 0.0699153u
14
+ ··· + 0.693644u 0.0686441
0.492373u
15
0.0788136u
14
+ ··· 0.211017u 2.83898
a
3
=
u
2
+ 1
u
4
a
7
=
0.0936441u
15
0.115678u
14
+ ··· + 0.674153u 0.199153
0.336441u
15
+ 0.0432203u
14
+ ··· + 0.941525u 1.59153
a
9
=
0.146610u
15
+ 0.0483051u
14
+ ··· + 0.622881u 0.172881
0.353390u
15
0.0483051u
14
+ ··· 0.122881u 2.32712
a
9
=
0.146610u
15
+ 0.0483051u
14
+ ··· + 0.622881u 0.172881
0.353390u
15
0.0483051u
14
+ ··· 0.122881u 2.32712
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
17
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.157569 0.635502I
a = 0.557421 0.896927I
b = 1.27411 + 2.07243I
c = 0.63638 1.29602I
d = 1.46293 + 2.03683I
5.44991 9.88301I 3.28252 + 6.06963I
u = 1.157569 + 0.635502I
a = 0.557421 + 0.896927I
b = 1.27411 2.07243I
c = 0.63638 + 1.29602I
d = 1.46293 2.03683I
5.44991 + 9.88301I 3.28252 6.06963I
u = 1.076279 0.402850I
a = 0.496617 0.712709I
b = 0.12673 + 2.50547I
c = 0.018628 + 1.062865I
d = 0.10060 1.65754I
4.77492 2.26376I 6.05872 + 4.53378I
u = 1.076279 + 0.402850I
a = 0.496617 + 0.712709I
b = 0.12673 2.50547I
c = 0.018628 1.062865I
d = 0.10060 + 1.65754I
4.77492 + 2.26376I 6.05872 4.53378I
u = 0.783583
a = 0.701860
b = 2.11028
c = 0.560255
d = 0.122887
2.57083 2.16015
u = 0.754559 0.841472I
a = 0.820135 + 0.914602I
b = 0.604123 0.352309I
c = 0.535511 + 0.275794I
d = 0.355898 + 0.718293I
10.1546 6.33746
18
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 0.754559 + 0.841472I
a = 0.820135 0.914602I
b = 0.604123 + 0.352309I
c = 0.535511 0.275794I
d = 0.355898 0.718293I
10.1546 6.33746
u = 0.270006 0.967768I
a = 0.980795 0.982086I
b = 0.487066 0.220623I
c = 1.28957 + 1.26937I
d = 0.589201 + 0.010347I
5.44991 + 9.88301I 3.28252 6.06963I
u = 0.270006 + 0.967768I
a = 0.980795 + 0.982086I
b = 0.487066 + 0.220623I
c = 1.28957 1.26937I
d = 0.589201 0.010347I
5.44991 9.88301I 3.28252 + 6.06963I
u = 0.365525 0.776365I
a = 0.923174 0.991527I
b = 0.895563 + 0.792065I
c = 1.43774 0.96789I
d = 0.544344 0.362514I
2.93531 3.55755I 2.52739 + 2.62489I
u = 0.365525 + 0.776365I
a = 0.923174 + 0.991527I
b = 0.895563 0.792065I
c = 1.43774 + 0.96789I
d = 0.544344 + 0.362514I
2.93531 + 3.55755I 2.52739 2.62489I
u = 0.993914 0.569061I
a = 0.795774 + 0.630139I
b = 0.15894 1.76185I
c = 0.257812 + 1.346396I
d = 0.68234 2.09325I
2.93531 + 3.55755I 2.52739 2.62489I
19
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 0.993914 + 0.569061I
a = 0.795774 0.630139I
b = 0.15894 + 1.76185I
c = 0.257812 1.346396I
d = 0.68234 + 2.09325I
2.93531 3.55755I 2.52739 + 2.62489I
u = 1.12630
a = 0.488295
b = 0.878073
c = 1.95645
d = 2.26074
2.57083 2.16015
u = 1.227616 0.270214I
a = 0.735315 + 0.300028I
b = 1.24932 1.12484I
c = 0.60727 1.55946I
d = 0.83996 + 2.05652I
4.77492 2.26376I 6.05872 + 4.53378I
u = 1.227616 + 0.270214I
a = 0.735315 0.300028I
b = 1.24932 + 1.12484I
c = 0.60727 + 1.55946I
d = 0.83996 2.05652I
4.77492 + 2.26376I 6.05872 4.53378I
20
VIII. I
u
8
= hu
17
3u
15
+ · · · + 4d 3, u
18
+ u
17
+ · · · + 2b 1, u
19
+ 2u
18
+
· · · + 3u + 1, 2u
18
3u
17
+ · · · + 2a 4, u
18
2u
17
+ · · · + 2c 5i
(i) Arc colorings
a
2
=
1
0
a
4
=
0
u
a
5
=
u
u
a
10
=
1
2
u
18
+ u
17
+ ··· u +
5
2
1
4
u
17
+
3
4
u
15
+ ···
1
4
u +
3
4
a
11
=
1
2
u
18
+
3
4
u
17
+ ···
3
4
u +
11
4
1
2
u
15
+ 2u
13
+ ···
1
2
u +
1
2
a
6
=
1
2
u
18
u
17
+ ··· + u 2
1
4
u
18
1
2
u
17
+ ··· +
5
4
u
1
2
a
1
=
1
u
2
a
8
=
u
18
+
3
2
u
17
+ ···
1
2
u + 2
1
2
u
18
1
2
u
17
+ ···
1
2
u +
1
2
a
3
=
u
2
+ 1
u
4
a
7
=
1
2
u
18
+ u
17
+ ···
1
2
u +
3
2
1
2
u
15
+ u
13
+ ···
1
2
u +
1
2
a
9
=
1
2
u
18
+ u
17
+ ··· u + 2
1
4
u
17
1
2
u
16
+ ··· +
1
4
u +
3
4
a
9
=
1
2
u
18
+ u
17
+ ··· u + 2
1
4
u
17
1
2
u
16
+ ··· +
1
4
u +
3
4
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
21
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 1.219915 0.612443I
a = 0.516047 + 0.911869I
b = 1.40218 2.37571I
c = 0.88613 1.46384I
d = 1.68494 + 2.18403I
2.5538 15.5977I 0.09598 + 9.40344I
u = 1.219915 + 0.612443I
a = 0.516047 0.911869I
b = 1.40218 + 2.37571I
c = 0.88613 + 1.46384I
d = 1.68494 2.18403I
2.5538 + 15.5977I 0.09598 9.40344I
u = 1.163712 0.575900I
a = 0.528681 0.867726I
b = 1.07974 + 2.29207I
c = 0.55106 + 1.42435I
d = 0.38413 2.13228I
2.61225 10.89709I 3.23641 + 8.50579I
u = 1.163712 + 0.575900I
a = 0.528681 + 0.867726I
b = 1.07974 2.29207I
c = 0.55106 1.42435I
d = 0.38413 + 2.13228I
2.61225 + 10.89709I 3.23641 8.50579I
u = 0.892218 0.798617I
a = 0.745739 0.908893I
b = 0.917511 + 0.756234I
c = 0.171773 0.152659I
d = 0.711062 + 1.057967I
9.74824 5.99256I 5.35093 + 5.49640I
u = 0.892218 + 0.798617I
a = 0.745739 + 0.908893I
b = 0.917511 0.756234I
c = 0.171773 + 0.152659I
d = 0.711062 1.057967I
9.74824 + 5.99256I 5.35093 5.49640I
22
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.713652 0.621261I
a = 0.837060 + 0.785608I
b = 0.081748 0.770811I
c = 0.755312 + 0.014797I
d = 0.830029 0.977305I
2.40223 3.63220I 3.52732 + 6.81616I
u = 0.713652 + 0.621261I
a = 0.837060 0.785608I
b = 0.081748 + 0.770811I
c = 0.755312 0.014797I
d = 0.830029 + 0.977305I
2.40223 + 3.63220I 3.52732 6.81616I
u = 0.379493 0.913957I
a = 0.963127 + 0.958960I
b = 0.245388 + 0.138357I
c = 1.20852 + 1.09732I
d = 0.418501 + 0.149638I
7.80660 + 4.21764I 6.24313 1.77538I
u = 0.379493 + 0.913957I
a = 0.963127 0.958960I
b = 0.245388 0.138357I
c = 1.20852 1.09732I
d = 0.418501 0.149638I
7.80660 4.21764I 6.24313 + 1.77538I
u = 0.266152
a = 1.86845
b = 0.545293
c = 2.41374
d = 0.742345
1.20822 9.19790
u = 0.587370 0.660248I
a = 0.821562 + 0.916371I
b = 0.609822 1.161649I
c = 1.43138 0.24528I
d = 0.357611 0.863012I
4.14406 + 1.22871I 4.10945 3.37998I
23
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.587370 + 0.660248I
a = 0.821562 0.916371I
b = 0.609822 + 1.161649I
c = 1.43138 + 0.24528I
d = 0.357611 + 0.863012I
4.14406 1.22871I 4.10945 + 3.37998I
u = 0.710407 0.203370I
a = 0.342230 0.841271I
b = 0.002742 + 0.868397I
c = 0.339488 + 0.027126I
d = 0.176169 + 0.449965I
1.32552 + 1.22673I 3.58366 5.47914I
u = 0.710407 + 0.203370I
a = 0.342230 + 0.841271I
b = 0.002742 0.868397I
c = 0.339488 0.027126I
d = 0.176169 0.449965I
1.32552 1.22673I 3.58366 + 5.47914I
u = 1.085303 0.470880I
a = 0.766359 + 0.526722I
b = 0.55681 1.65227I
c = 0.209548 1.125546I
d = 0.11074 + 1.77582I
4.29720 + 4.85510I 5.63265 5.33490I
u = 1.085303 + 0.470880I
a = 0.766359 0.526722I
b = 0.55681 + 1.65227I
c = 0.209548 + 1.125546I
d = 0.11074 1.77582I
4.29720 4.85510I 5.63265 + 5.33490I
u = 1.118985 0.584861I
a = 0.853281 0.557689I
b = 0.45818 + 2.04080I
c = 0.39510 + 1.48312I
d = 1.25236 2.20391I
0.71510 + 8.68076I 0.47305 6.48182I
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 1.118985 + 0.584861I
a = 0.853281 + 0.557689I
b = 0.45818 2.04080I
c = 0.39510 1.48312I
d = 1.25236 + 2.20391I
0.71510 8.68076I 0.47305 + 6.48182I
24
IX. I
v
1
= hb, c, d 1, v 1, a 1i
(i) Arc colorings
a
2
=
1
0
a
4
=
1
0
a
5
=
1
0
a
10
=
0
1
a
11
=
1
1
a
6
=
0
1
a
1
=
1
0
a
8
=
1
0
a
3
=
1
0
a
7
=
1
0
a
9
=
1
1
a
9
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
25
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 1.00000
b = 0
c = 0
d = 1.00000
0 0
26
X. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
4
u(u 1)
3
(u
6
+ u
5
u
4
2u
3
+ u + 1)
3
(u
12
u
11
4u
10
+ 2u
9
+ 7u
8
+ u
7
5u
6
5u
5
u
4
+ 3u
3
+ 2u
2
+ 1)
(u
16
+ u
15
+ ··· 4u 4)(u
19
+ 2u
18
+ ··· + 3u + 1)
c
2
u(u + 1)
3
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
(u
12
+ 9u
11
+ ··· 4u + 1)(u
16
+ 7u
15
+ ··· + 40u + 16)
(u
19
+ 8u
18
+ ··· + 19u + 1)
c
3
, c
7
u
4
(u
6
+ u
5
u
4
2u
3
+ u + 1)
5
(u
8
3u
7
+ 3u
6
+ 2u
5
8u
4
+ 9u
3
3u
2
2u + 2)
2
(u
19
+ 2u
18
+ ··· + 4u
2
8)
c
5
u(u 1)(u + 1)
2
(u
6
u
5
u
4
+ 2u
3
u + 1)
(u
8
+ u
7
4u
6
3u
5
+ 5u
4
+ u
3
u
2
+ 3u 1)
2
(u
12
+ u
11
4u
10
2u
9
+ 7u
8
u
7
5u
6
+ 5u
5
u
4
3u
3
+ 2u
2
+ 1)
2
(u
19
+ 2u
18
+ ··· 8u 4)
c
6
, c
9
u(u 1)
2
(u + 1)(u
6
+ u
5
u
4
2u
3
+ u + 1)
3
(u
12
u
11
4u
10
+ 2u
9
+ 7u
8
+ u
7
5u
6
5u
5
u
4
+ 3u
3
+ 2u
2
+ 1)
(u
16
+ u
15
+ ··· 4u 4)(u
19
+ 2u
18
+ ··· + 3u + 1)
c
8
u(u 1)(u + 1)
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
3
(u
12
+ 9u
11
+ ··· 4u + 1)(u
16
+ 7u
15
+ ··· + 40u + 16)
(u
19
+ 8u
18
+ ··· + 19u + 1)
c
10
, c
11
u(u + 1)
3
(u
6
u
5
u
4
+ 2u
3
u + 1)
(u
8
+ u
7
4u
6
3u
5
+ 5u
4
+ u
3
u
2
+ 3u 1)
2
(u
12
+ u
11
4u
10
2u
9
+ 7u
8
u
7
5u
6
+ 5u
5
u
4
3u
3
+ 2u
2
+ 1)
2
(u
19
+ 2u
18
+ ··· 8u 4)
27
XI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
, c
6
c
9
y(y 1)
3
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
3
(y
12
9y
11
+ ··· + 4y + 1)(y
16
7y
15
+ ··· 40y + 16)
(y
19
8y
18
+ ··· + 19y 1)
c
2
, c
8
y(y 1)
3
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
3
(y
12
13y
11
+ ··· 12y + 1)(y
16
+ y
15
+ ··· 544y + 256)
(y
19
+ 12y
18
+ ··· + 195y 1)
c
3
, c
7
y
4
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
5
(y
8
3y
7
+ 5y
6
4y
5
+ 2y
4
13y
3
+ 13y
2
16y + 4)
2
(y
19
6y
18
+ ··· + 64y 64)
c
5
, c
10
, c
11
y(y 1)
3
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
(y
8
9y
7
+ 32y
6
53y
5
+ 31y
4
+ 15y
3
15y
2
7y + 1)
2
(1 + 4y + 2y
2
23y
3
+ 25y
4
y
5
5y
6
33y
7
+ 73y
8
68y
9
+ 34y
10
9y
11
+ y
12
)
2
(y
19
18y
18
+ ··· + 88y 16)
28