11a
231
(K11a
231
)
1
Arc Sequences
7 1 6 10 3 4 2 11 5 8 9
Solving Sequence
1,7 2,4
6 3
5,9
11 8 10
c
1
c
6
c
3
c
5
c
11
c
8
c
10
c
2
, c
4
, c
7
, c
9
Representation Ideals
I =
6
\
i=1
I
u
i
3
\
j=1
I
v
j
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
= hc, d + 1, b + 1, au 1i
I
u
2
= ha, c, b 1, d 1, u 1i
I
u
3
= hb, c, d 1, a + 1, u + 1i
I
u
4
= hu
8
+ 4u
7
+ 16u
6
+ 28u
5
+ 66u
4
+ 60u
3
+ 200u
2
+ 256b + 36u + 357,
u
8
+ 4u
7
+ 16u
6
+ 28u
5
+ 66u
4
+ 60u
3
+ 200u
2
+ 256d + 36u + 357,
u
10
+ 4u
9
+ 15u
8
+ 24u
7
+ 50u
6
+ 32u
5
+ 198u
4
+ 104u
3
+ 413u
2
164u + 347,
10u
9
+ 387u
8
+ ··· + 88832a + 56309, 10u
9
+ 387u
8
+ ··· + 88832c + 56309i
I
u
5
= hu
14
+ 6u
13
+ ··· + 1160u + 142, 643u
13
3077u
12
+ ··· + 145408a 640374,
7u
13
21u
12
+ ··· + 4096b + 1546, 2359u
13
+ 17065u
12
+ ··· + 290816c + 2261166,
29u
13
+ 159u
12
+ ··· + 4096d + 1026i
I
u
6
= h−u
15
5u
14
+ ··· + 1024b + 387, u
17
+ 3u
16
+ ··· + 839u 347,
4137u
16
11370u
15
+ ··· + 2842624a 2272405,
3443u
16
11370u
15
+ ··· + 2842624c + 2043581, 3u
16
+ 2u
15
+ ··· + 8192d + 4137i
I
v
1
= ha, d, c 1, v 1, b + 1i
I
v
2
= ha, v 1, d + b, c + a, d
5
d
4
2d
3
+ d
2
+ d + 1i
I
v
3
= ha, v 1, d
2
+ db + b
2
1, d
2
c + d
2
a + dba + d c b, 2d
3
b 2d
2
b + d
2
a dcb 2db d 2b,
4d
3
a + d
2
a 5dcb + dca a
2
d c
2
b + cba 4db 4da 5d 3c 6b 3a,
4d
4
4d
3
3d
2
a + 3dcb dca a
2
d + c
2
b + cba 4d
2
+ 4db + 3d c + 2b + a,
4d
2
cb + d
2
a 5dcb + dca a
2
d c
2
b + cba + 4d
2
+ 4db 4cb 5d 3c 6b 3a 4,
3d
2
ca 4d
2
c + ··· + 4b + 6, 3d
2
c
2
12d
3
+ ··· 8b 9, 2d
3
c
2
6d
3
+ ··· + 2a + 7,
24d
3
+ 8d
2
c + ··· 3a
2
15, 6c
3
d
2
102d
3
+ ··· + 39a + 96, 60d
3
c + 48d
3
+ ··· + 129a + 240,
6d
3
c 24d
3
+ ··· 6a 60, 16d
3
c 158d
3
+ ··· + 2a + 129, 56d
3
c + 648d
3
+ ··· 69a 632,
120d
3
c 10500d
3
+ ··· + 1981a + 11478, c
10
+ 7c
9
a + ··· + 104a + 347,
19122d
3
c + 30588d
3
+ ··· 36975a 80544,
70300254d
3
c 187418508d
3
+ ··· + 153731535a + 377409480,
904394418d
3
c 2795501772d
3
+ ··· + 2051846767a + 5274810244i
There are 9 irreducible components with 59 representations.
There are 1 irreducible components of dim
C
= 1 for 11a
231
2
I. I
u
1
= hc, d + 1, b + 1, au 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
a
1
a
2
=
a + 1
1
a
4
=
0
u
a
6
=
a
u 1
a
3
=
a
1
a
5
=
0
u
a
9
=
0
1
a
11
=
1
1
a
8
=
1
0
a
10
=
0
1
a
10
=
0
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 3.81383 1.18496I
4
II. I
u
2
= ha, c, b 1, d 1, u 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
1
a
2
=
1
1
a
4
=
0
1
a
6
=
0
1
a
3
=
0
1
a
5
=
0
1
a
9
=
0
1
a
11
=
1
1
a
8
=
1
0
a
10
=
0
1
a
10
=
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
= hb, c, d 1, a + 1, u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
1
0
a
2
=
1
0
a
4
=
0
1
a
6
=
1
1
a
3
=
1
0
a
5
=
0
1
a
9
=
0
1
a
11
=
1
1
a
8
=
1
0
a
10
=
0
1
a
10
=
0
1
(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 = 1.00000
b = 0
c = 0
d = 1.00000
3.28987 12.0000
8
IV. I
u
4
= hu
8
+ 4u
7
+ · · · + 256b + 357, u
8
+ 4u
7
+ · · · + 256d + 357, u
10
+
4u
9
+ · · · 164u + 347, 10u
9
+ 387u
8
+ · · · + 8.88 × 10
4
a + 5.63 ×
10
4
, 10u
9
+ 387u
8
+ · · · + 8.88 × 10
4
c + 5.63 × 10
4
i
(i) Arc colorings
a
1
=
1
0
a
7
=
0.000112572u
9
0.00435654u
8
+ ··· 0.366805u 0.633882
0.00390625u
8
0.0156250u
7
+ ··· 0.140625u 1.39453
a
2
=
0.000309573u
9
+ 0.00319142u
8
+ ··· + 0.659104u + 1.06837
0.00390625u
8
+ 0.0156250u
7
+ ··· + 0.453125u + 0.785156
a
4
=
0
u
a
6
=
0.000112572u
9
0.00435654u
8
+ ··· 0.366805u 0.633882
0.00781250u
7
0.0234375u
6
+ ··· 0.742188u 0.0390625
a
3
=
0.000309573u
9
0.000714832u
8
+ ··· + 0.205979u + 0.283214
0.00390625u
8
+ 0.0156250u
7
+ ··· + 0.453125u + 0.785156
a
5
=
0.00267921u
9
0.0107169u
8
+ ··· 0.989328u 0.396546
0.00390625u
8
0.0234375u
7
+ ··· 0.695313u + 0.425781
a
9
=
0.000112572u
9
0.00435654u
8
+ ··· 0.366805u 0.633882
0.00390625u
8
0.0156250u
7
+ ··· 0.140625u 1.39453
a
11
=
0.000309573u
9
+ 0.00319142u
8
+ ··· + 0.659104u + 1.06837
0.00390625u
8
+ 0.0156250u
7
+ ··· + 0.453125u + 0.785156
a
8
=
0.00122704u
9
+ 0.00490814u
8
+ ··· + 0.686453u + 0.494079
0.00781250u
7
+ 0.0234375u
6
+ ··· + 0.835938u 0.929688
a
10
=
0.00208821u
9
0.00639972u
8
+ ··· + 0.0750687u + 0.852232
0.00195313u
9
+ 0.00195313u
8
+ ··· 0.314453u + 1.98633
a
10
=
0.00208821u
9
0.00639972u
8
+ ··· + 0.0750687u + 0.852232
0.00195313u
9
+ 0.00195313u
8
+ ··· 0.314453u + 1.98633
(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 = 2.07090 1.68913I
a = 0.353106 + 0.288011I
b = 0.608868 + 0.334904I
c = 0.353106 + 0.288011I
d = 0.608868 + 0.334904I
2.40108 3.48114
u = 2.07090 + 1.68913I
a = 0.353106 0.288011I
b = 0.608868 0.334904I
c = 0.353106 0.288011I
d = 0.608868 0.334904I
2.40108 3.48114
u = 0.79421 1.56643I
a = 0.476620 0.664090I
b = 0.400287 0.864056I
c = 0.476620 0.664090I
d = 0.400287 0.864056I
5.87256 + 4.40083I 6.74431 3.49859I
u = 0.79421 + 1.56643I
a = 0.476620 + 0.664090I
b = 0.400287 + 0.864056I
c = 0.476620 + 0.664090I
d = 0.400287 + 0.864056I
5.87256 4.40083I 6.74431 + 3.49859I
u = 0.67021 2.51026I
a = 0.059361 0.549346I
b = 1.018496 0.644891I
c = 0.059361 0.549346I
d = 1.018496 0.644891I
5.87256 4.40083I 6.74431 + 3.49859I
u = 0.67021 + 2.51026I
a = 0.059361 + 0.549346I
b = 1.018496 + 0.644891I
c = 0.059361 + 0.549346I
d = 1.018496 + 0.644891I
5.87256 + 4.40083I 6.74431 3.49859I
10
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.395435 0.813137I
a = 0.397036 + 0.574218I
b = 0.926127 + 0.393188I
c = 0.397036 + 0.574218I
d = 0.926127 + 0.393188I
0.32910 + 1.53058I 2.51511 4.43065I
u = 0.395435 + 0.813137I
a = 0.397036 0.574218I
b = 0.926127 0.393188I
c = 0.397036 0.574218I
d = 0.926127 0.393188I
0.32910 1.53058I 2.51511 + 4.43065I
u = 1.13988 1.24694I
a = 0.364017 0.084223I
b = 1.236043 0.156723I
c = 0.364017 0.084223I
d = 1.236043 0.156723I
0.32910 1.53058I 2.51511 + 4.43065I
u = 1.13988 + 1.24694I
a = 0.364017 + 0.084223I
b = 1.236043 + 0.156723I
c = 0.364017 + 0.084223I
d = 1.236043 + 0.156723I
0.32910 + 1.53058I 2.51511 4.43065I
11
V. I
u
5
= hu
14
+ 6u
13
+ · · · + 1160u + 142, 643u
13
3077u
12
+ · · · + 1.45 ×
10
5
a 6.40 × 10
5
, 7u
13
21u
12
+ · · · + 4096b + 1546, 2359u
13
+ 1.71 ×
10
4
u
12
+ · · · + 2.91 × 10
5
c + 2.26 × 10
6
, 29u
13
+ 159u
12
+ · · · + 4096d + 1026i
(i) Arc colorings
a
1
=
1
0
a
7
=
0.00442204u
13
+ 0.0211611u
12
+ ··· 4.50607u + 4.40398
0.00170898u
13
+ 0.00512695u
12
+ ··· 7.23682u 0.377441
a
2
=
0.00251018u
13
+ 0.0145728u
12
+ ··· + 1.82907u + 3.69989
0.000976563u
12
0.00585938u
11
+ ··· + 0.289063u + 0.287109
a
4
=
0
u
a
6
=
0.00442204u
13
+ 0.0211611u
12
+ ··· 4.50607u + 4.40398
0.000244141u
13
0.00122070u
12
+ ··· 1.63428u + 0.385254
a
3
=
0.00251018u
13
+ 0.0155494u
12
+ ··· + 1.54001u + 3.41278
0.000976563u
12
0.00585938u
11
+ ··· + 0.289063u + 0.287109
a
5
=
0.000144421u
13
0.00623762u
12
+ ··· 5.57143u + 2.26314
0.00317383u
13
0.0212402u
12
+ ··· + 2.70654u + 0.776855
a
9
=
0.00811166u
13
0.0586797u
12
+ ··· 11.9727u 7.77525
0.00708008u
13
0.0388184u
12
+ ··· + 6.51123u 0.250488
a
11
=
0.00930829u
13
+ 0.0560939u
12
+ ··· + 2.55507u + 8.61647
0.000488281u
13
+ 0.00341797u
12
+ ··· + 0.211914u + 1.35645
a
8
=
0.00547081u
13
+ 0.0359987u
12
+ ··· + 4.30113u + 3.63960
0.00537109u
13
+ 0.0336914u
12
+ ··· 2.43066u 0.0205078
a
10
=
0.00514758u
13
+ 0.0286882u
12
+ ··· + 0.0274332u + 4.61719
0.00244141u
13
0.0151367u
12
+ ··· 0.586914u + 0.834961
a
10
=
0.00514758u
13
+ 0.0286882u
12
+ ··· + 0.0274332u + 4.61719
0.00244141u
13
0.0151367u
12
+ ··· 0.586914u + 0.834961
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 2.55018
a = 0.451585
b = 0.502855
c = 0.330655
d = 0.648769
2.33847 2.06079
u = 0.93059 1.80484I
a = 0.357322 0.607046I
b = 0.597306 0.773845I
c = 0.084089 + 0.362047I
d = 0.830837 + 0.693845I
7.14223 0.95540I 8.68929 + 2.37083I
u = 0.93059 + 1.80484I
a = 0.357322 + 0.607046I
b = 0.597306 + 0.773845I
c = 0.084089 0.362047I
d = 0.830837 0.693845I
7.14223 + 0.95540I 8.68929 2.37083I
u = 0.87948 2.83263I
a = 0.065820 + 0.442998I
b = 0.985336 + 0.506466I
c = 0.370918 0.609804I
d = 0.327402 0.709633I
1.19445 3.93070I 1.74059 + 4.87230I
u = 0.87948 + 2.83263I
a = 0.065820 0.442998I
b = 0.985336 0.506466I
c = 0.370918 + 0.609804I
d = 0.327402 + 0.709633I
1.19445 + 3.93070I 1.74059 4.87230I
u = 0.43400 2.57241I
a = 0.029458 0.557313I
b = 1.139458 0.630170I
c = 0.260056 + 0.784166I
d = 0.281398 + 0.947821I
3.65356 9.93065I 3.53972 + 7.33664I
13
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.43400 + 2.57241I
a = 0.029458 + 0.557313I
b = 1.139458 + 0.630170I
c = 0.260056 0.784166I
d = 0.281398 0.947821I
3.65356 + 9.93065I 3.53972 7.33664I
u = 0.126703
a = 5.12039
b = 0.502855
c = 6.65517
d = 1.15162
2.33847 2.06079
u = 0.105622 1.033608I
a = 0.745639 + 0.727627I
b = 0.597306 + 0.773845I
c = 0.524187 + 0.502918I
d = 1.42814 0.08000I
7.14223 + 0.95540I 8.68929 2.37083I
u = 0.105622 + 1.033608I
a = 0.745639 0.727627I
b = 0.597306 0.773845I
c = 0.524187 0.502918I
d = 1.42814 + 0.08000I
7.14223 0.95540I 8.68929 + 2.37083I
u = 0.338688 1.186310I
a = 0.676134 + 0.430239I
b = 1.139458 + 0.630170I
c = 0.36291 + 1.70887I
d = 1.42086 + 0.31765I
3.65356 + 9.93065I 3.53972 7.33664I
u = 0.338688 + 1.186310I
a = 0.676134 0.430239I
b = 1.139458 0.630170I
c = 0.36291 1.70887I
d = 1.42086 0.31765I
3.65356 9.93065I 3.53972 + 7.33664I
14
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.349450 0.980466I
a = 0.536593 0.525174I
b = 0.985336 0.506466I
c = 0.98425 1.77985I
d = 1.312739 0.203166I
1.19445 + 3.93070I 1.74059 4.87230I
u = 0.349450 + 0.980466I
a = 0.536593 + 0.525174I
b = 0.985336 + 0.506466I
c = 0.98425 + 1.77985I
d = 1.312739 + 0.203166I
1.19445 3.93070I 1.74059 + 4.87230I
15
VI. I
u
6
= h−u
15
5u
14
+ · · · + 1024b + 387, u
17
+ 3u
16
+ · · · + 839u
347, 4137u
16
1.14 × 10
4
u
15
+ · · · + 2.84 × 10
6
a 2.27 × 10
6
, 3443u
16
1.14×10
4
u
15
+· · ·+2.84×10
6
c+2.04×10
6
, 3u
16
+2u
15
+· · ·+8192d+4137i
(i) Arc colorings
a
1
=
1
0
a
7
=
0.00145535u
16
+ 0.00399983u
15
+ ··· 5.63391u + 0.799404
0.000976563u
15
+ 0.00488281u
14
+ ··· 0.768555u 0.377930
a
2
=
0.00104200u
16
0.00288184u
15
+ ··· + 3.59610u + 0.165805
0.000488281u
15
+ 0.00146484u
14
+ ··· + 0.803223u + 0.276855
a
4
=
0
u
a
6
=
0.00145535u
16
+ 0.00399983u
15
+ ··· 5.63391u + 0.799404
0.00134277u
16
+ 0.00463867u
15
+ ··· + 0.0437012u 0.505005
a
3
=
0.00104200u
16
0.00337013u
15
+ ··· + 2.79288u 0.111050
0.000488281u
15
+ 0.00146484u
14
+ ··· + 0.803223u + 0.276855
a
5
=
0.000726090u
16
+ 0.00315483u
15
+ ··· 3.84790u + 0.756650
0.00183105u
16
+ 0.00561523u
15
+ ··· 0.166260u 0.209595
a
9
=
0.00121120u
16
+ 0.00399983u
15
+ ··· 0.655397u 0.718907
0.000366211u
16
0.000244141u
15
+ ··· + 0.421631u 0.505005
a
11
=
0.000675784u
16
0.00214942u
15
+ ··· 0.0223054u + 1.48502
0.000244141u
16
+ 0.000488281u
15
+ ··· 0.763184u + 0.361572
a
8
=
0.000604019u
16
0.0000189965u
15
+ ··· 3.01514u + 0.673032
0.000976563u
16
0.00292969u
15
+ ··· 0.147461u 0.251953
a
10
=
0.00145183u
16
0.00569826u
15
+ ··· + 1.07920u + 1.45990
0.000976563u
16
0.00439453u
15
+ ··· 1.36768u + 0.800293
a
10
=
0.00145183u
16
0.00569826u
15
+ ··· + 1.07920u + 1.45990
0.000976563u
16
0.00439453u
15
+ ··· 1.36768u + 0.800293
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
16
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.83951 1.68304I
a = 0.414668 + 0.649824I
b = 0.506004 + 0.842901I
c = 1.51014 0.91618I
d = 1.44180 0.15237I
8.60033 + 1.91429I 8.38805 0.33236I
u = 0.83951 + 1.68304I
a = 0.414668 0.649824I
b = 0.506004 0.842901I
c = 1.51014 + 0.91618I
d = 1.44180 + 0.15237I
8.60033 1.91429I 8.38805 + 0.33236I
u = 0.64187 2.04823I
a = 0.195951 0.711872I
b = 0.862143 0.912454I
c = 1.026126 + 0.030684I
d = 1.58385 0.05558I
15.7365 3.2760I 10.07807 + 2.58290I
u = 0.64187 + 2.04823I
a = 0.195951 + 0.711872I
b = 0.862143 + 0.912454I
c = 1.026126 0.030684I
d = 1.58385 + 0.05558I
15.7365 + 3.2760I 10.07807 2.58290I
u = 0.62665 1.54737I
a = 0.512277 0.752794I
b = 0.329755 1.026106I
c = 0.98657 + 1.27093I
d = 1.48587 + 0.32095I
11.9481 + 8.6770I 9.06927 4.38269I
u = 0.62665 + 1.54737I
a = 0.512277 + 0.752794I
b = 0.329755 + 1.026106I
c = 0.98657 1.27093I
d = 1.48587 0.32095I
11.9481 8.6770I 9.06927 + 4.38269I
17
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.53450 2.51747I
a = 0.013137 + 0.567764I
b = 1.085846 + 0.657061I
c = 0.962342 + 0.981810I
d = 1.43635 + 0.27040I
6.85439 7.49245I 6.04980 + 5.00652I
u = 0.53450 + 2.51747I
a = 0.013137 0.567764I
b = 1.085846 0.657061I
c = 0.962342 0.981810I
d = 1.43635 0.27040I
6.85439 + 7.49245I 6.04980 5.00652I
u = 0.29374 2.50052I
a = 0.085494 0.592396I
b = 1.225497 0.657562I
c = 0.529768 1.079299I
d = 1.45618 0.38779I
9.1924 14.7354I 6.16899 + 8.15927I
u = 0.29374 + 2.50052I
a = 0.085494 + 0.592396I
b = 1.225497 + 0.657562I
c = 0.529768 + 1.079299I
d = 1.45618 + 0.38779I
9.1924 + 14.7354I 6.16899 8.15927I
u = 0.058528 0.403504I
a = 0.39637 + 1.43679I
b = 0.629978 + 0.234165I
c = 0.870252 + 0.151813I
d = 0.556553 0.244029I
0.88275 + 1.29794I 5.86581 6.22804I
u = 0.058528 + 0.403504I
a = 0.39637 1.43679I
b = 0.629978 0.234165I
c = 0.870252 0.151813I
d = 0.556553 + 0.244029I
0.88275 1.29794I 5.86581 + 6.22804I
18
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.391906 1.073303I
a = 0.575830 + 0.453053I
b = 1.069945 + 0.527349I
c = 0.434643 1.106746I
d = 0.260592 0.795594I
1.71782 + 5.90288I 0.75718 7.23695I
u = 0.391906 + 1.073303I
a = 0.575830 0.453053I
b = 1.069945 0.527349I
c = 0.434643 + 1.106746I
d = 0.260592 + 0.795594I
1.71782 5.90288I 0.75718 + 7.23695I
u = 0.645411
a = 0.297231
b = 0.890185
c = 0.789084
d = 0.191836
1.29941 8.68291
u = 0.663134 0.926936I
a = 0.375451 0.347862I
b = 1.080374 0.317895I
c = 0.650302 + 0.844081I
d = 0.073472 + 0.578699I
3.14388 + 1.09865I 5.52136 1.09882I
u = 0.663134 + 0.926936I
a = 0.375451 + 0.347862I
b = 1.080374 + 0.317895I
c = 0.650302 0.844081I
d = 0.073472 0.578699I
3.14388 1.09865I 5.52136 + 1.09882I
19
VII. I
v
1
= ha, d, c 1, v 1, b + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
1
a
2
=
1
1
a
4
=
1
0
a
6
=
1
1
a
3
=
0
1
a
5
=
1
0
a
9
=
1
0
a
11
=
1
0
a
8
=
1
0
a
10
=
1
0
a
10
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
20
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
c = 1.00000
d = 0
0 0
21
VIII. I
v
2
= ha, v 1, d + b, c + a, d
5
d
4
2d
3
+ d
2
+ d + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
d
a
2
=
1
d
2
a
4
=
1
0
a
6
=
d
d
a
3
=
d
2
+ 1
d
2
a
5
=
d
3
2d
d
3
+ d
a
9
=
0
d
a
11
=
1
d
2
a
8
=
d
d
3
+ d
a
10
=
d
2
+ 1
d
4
+ 2d
2
a
10
=
d
2
+ 1
d
4
+ 2d
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
22
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
2
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 1.21774
c = 0
d = 1.21774
2.40108 3.48114
v = 1.00000
a = 0
b = 0.309916 0.549911I
c = 0
d = 0.309916 0.549911I
0.32910 + 1.53058I 2.51511 4.43065I
v = 1.00000
a = 0
b = 0.309916 + 0.549911I
c = 0
d = 0.309916 + 0.549911I
0.32910 1.53058I 2.51511 + 4.43065I
v = 1.00000
a = 0
b = 1.41878 0.21917I
c = 0
d = 1.41878 0.21917I
5.87256 4.40083I 6.74431 + 3.49859I
v = 1.00000
a = 0
b = 1.41878 + 0.21917I
c = 0
d = 1.41878 + 0.21917I
5.87256 + 4.40083I 6.74431 3.49859I
23
IX.
I
v
3
= ha, v 1, d
2
+ bd + b
2
1, cd
2
+ ad
2
+ · · · c b, 2bd
3
2bd
2
+ · · · d
2b, 4ad
3
+ ad
2
+ · · · 6b 3a, 4d
4
4d
3
+ · · · + 2b + a, 4bcd
2
+ ad
2
+ · · · 3a
4, 3acd
2
4cd
2
+ · · · + 4b + 6, 12d
3
+ 3c
2
d
2
+ · · · 8b 9, 2c
2
d
3
6d
3
+ · · · +
2a + 7, 24d
3
+ 8cd
2
+ · · · 3a
2
15, 102d
3
+ 6c
3
d
2
+ · · · + 39a + 96, 60cd
3
+
48d
3
+ · · · + 129a + 240, 6cd
3
24d
3
+ · · · 6a 60, 16cd
3
158d
3
+ · · · +
2a+129, 56cd
3
+648d
3
+· · ·69a 632, 120cd
3
1.05×10
4
d
3
+· · ·+1981a +
1.15 × 10
4
, c
10
+ 7ac
9
+ · · · + 104a + 347, 1.91 × 10
4
cd
3
+ 3.06 × 10
4
d
3
+ · · ·
3.70 × 10
4
a 8.05 × 10
4
, 7.03 × 10
7
cd
3
1.87 × 10
8
d
3
+ · · · + 1.54 × 10
8
a +
3.77 × 10
8
, 9.04 × 10
8
cd
3
2.80 × 10
9
d
3
+ · · · + 2.05 × 10
9
a + 5.27 × 10
9
i
(i) Arc colorings
a
1
=
1
0
a
7
=
a
b
a
2
=
1
d
3
c 2d
2
+ dc + 1
a
4
=
1
0
a
6
=
d
2
c d + c
d
2
c + d c
a
3
=
d
3
c + 2d
2
dc
d
3
c 2d
2
+ dc + 1
a
5
=
d
3
d
2
c 2d + c
d
3
+ d
a
9
=
c
d
a
11
=
dc + 1
d
2
a
8
=
d
2
c d + c
d
3
+ d
a
10
=
d
3
c d
2
+ 2dc + 1
d
4
+ 2d
2
a
10
=
d
3
c d
2
+ 2dc + 1
d
4
+ 2d
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
24
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
3
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 0.608868 0.334904I
c = 3.78272 0.69355I
d = 1.21774
2.40108 3.48114
v = 1.00000
a = 0
b = 0.608868 + 0.334904I
c = 3.78272 + 0.69355I
d = 1.21774
2.40108 3.48114
v = 1.00000
a = 0
b = 1.018496 0.644891I
c = 1.58369 1.46191I
d = 1.41878 0.21917I
5.87256 4.40083I 6.74431 + 3.49859I
v = 1.00000
a = 0
b = 1.018496 + 0.644891I
c = 1.58369 + 1.46191I
d = 1.41878 + 0.21917I
5.87256 + 4.40083I 6.74431 3.49859I
v = 1.00000
a = 0
b = 1.236043 + 0.156723I
c = 1.033501 0.877772I
d = 0.309916 0.549911I
0.32910 + 1.53058I 2.51511 4.43065I
v = 1.00000
a = 0
b = 1.236043 0.156723I
c = 1.033501 + 0.877772I
d = 0.309916 + 0.549911I
0.32910 1.53058I 2.51511 + 4.43065I
25
Solution to I
v
3
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 0.926127 + 0.393188I
c = 0.677599 0.590322I
d = 0.309916 0.549911I
0.32910 + 1.53058I 2.51511 4.43065I
v = 1.00000
a = 0
b = 0.926127 0.393188I
c = 0.677599 + 0.590322I
d = 0.309916 + 0.549911I
0.32910 1.53058I 2.51511 + 4.43065I
v = 1.00000
a = 0
b = 0.400287 0.864056I
c = 1.84313 + 0.06530I
d = 1.41878 + 0.21917I
5.87256 + 4.40083I 6.74431 3.49859I
v = 1.00000
a = 0
b = 0.400287 + 0.864056I
c = 1.84313 0.06530I
d = 1.41878 0.21917I
5.87256 4.40083I 6.74431 + 3.49859I
26
X. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
u(u 1)(u + 1)(u
5
u
4
2u
3
+ u
2
+ u + 1)
(u
7
+ u
6
u
5
2u
4
+ u
3
+ 2u
2
+ u 1)
2
(u
10
+ u
9
2u
8
4u
7
+ 4u
5
+ 3u
4
u
3
2u
2
+ 1)
2
(u
17
+ 2u
16
+ ··· 8u 4)
c
2
u(u + 1)
2
(u
5
+ 5u
4
+ 8u
3
+ 3u
2
u + 1)
(u
7
+ 3u
6
+ 7u
5
+ 8u
4
+ 9u
3
+ 6u
2
+ 5u + 1)
2
(1 + 4u + 10u
2
+ 13u
3
+ 13u
4
+ 14u
5
+ 18u
6
+ 18u
7
+ 12u
8
+ 5u
9
+ u
10
)
2
(u
17
+ 6u
16
+ ··· + 88u + 16)
c
3
u(u 1)(u + 1)(u
5
+ u
4
2u
3
u
2
+ u 1)
3
(u
10
u
9
2u
8
+ 4u
7
4u
5
+ 3u
4
+ u
3
2u
2
+ 1)
(u
14
+ u
13
+ ··· 4u 4)(u
17
+ 2u
16
+ ··· + 3u + 1)
c
4
, c
9
u
3
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
5
(2 2u u
2
+ 5u
3
7u
4
+ 6u
5
3u
6
+ u
7
)
2
(u
17
+ 2u
16
+ ··· + 4u
2
8)
c
5
, c
6
u(u 1)
2
(u
5
+ u
4
2u
3
u
2
+ u 1)
3
(u
10
u
9
2u
8
+ 4u
7
4u
5
+ 3u
4
+ u
3
2u
2
+ 1)
(u
14
+ u
13
+ ··· 4u 4)(u
17
+ 2u
16
+ ··· + 3u + 1)
c
7
u(u 1)
2
(u
5
u
4
2u
3
+ u
2
+ u + 1)
(u
7
+ u
6
u
5
2u
4
+ u
3
+ 2u
2
+ u 1)
2
(u
10
+ u
9
2u
8
4u
7
+ 4u
5
+ 3u
4
u
3
2u
2
+ 1)
2
(u
17
+ 2u
16
+ ··· 8u 4)
c
8
, c
10
, c
11
u(u + 1)
2
(u
5
+ u
4
2u
3
u
2
+ u 1)
3
(u
10
u
9
2u
8
+ 4u
7
4u
5
+ 3u
4
+ u
3
2u
2
+ 1)
(u
14
+ u
13
+ ··· 4u 4)(u
17
+ 2u
16
+ ··· + 3u + 1)
27
XI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
7
y(y 1)
2
(y
5
5y
4
+ 8y
3
3y
2
y 1)
(y
7
3y
6
+ 7y
5
8y
4
+ 9y
3
6y
2
+ 5y 1)
2
(1 4y + 10y
2
13y
3
+ 13y
4
14y
5
+ 18y
6
18y
7
+ 12y
8
5y
9
+ y
10
)
2
(y
17
6y
16
+ ··· + 88y 16)
c
2
y(y 1)
2
(y
5
9y
4
+ 32y
3
35y
2
5y 1)
(y
7
+ 5y
6
+ 19y
5
+ 36y
4
+ 49y
3
+ 38y
2
+ 13y 1)
2
(y
10
y
9
6y
7
+ 22y
6
+ 6y
5
+ 45y
4
+ 15y
3
+ 22y
2
+ 4y + 1)
2
(y
17
+ 10y
16
+ ··· + 288y 256)
c
3
, c
5
, c
6
c
8
, c
10
, c
11
(y)(y 1)
2
(1 y 3y
2
+ 8y
3
5y
4
+ y
5
)
3
(y
10
5y
9
+ ··· 4y + 1)
(y
14
11y
13
+ ··· 40y + 16)(y
17
20y
16
+ ··· + 27y 1)
c
4
, c
9
y
3
(y
5
+ 3y
4
+ 4y
3
+ y
2
y 1)
5
(y
7
+ 3y
6
+ 4y
5
+ y
4
y
3
+ 7y
2
+ 8y 4)
2
(y
17
+ 6y
16
+ ··· + 64y 64)
28