11a
248
(K11a
248
)
1
Arc Sequences
9 8 1 2 3 11 10 5 4 6 7
Solving Sequence
2,9 1,5
4 10 8 3 6 7 11
c
1
c
4
c
9
c
8
c
2
c
5
c
7
c
11
c
3
, c
6
, c
10
Representation Ideals
I =
3
\
i=1
I
u
i
\
I
v
1
I
u
1
= hu
13
+ 9u
12
+ ··· + 22u + 3, 2u
12
+ 17u
11
+ ··· + b + 10, 10u
12
84u
11
+ ··· + 3a 19i
I
u
2
= hb
54
4b
53
+ ··· b + 1, 8.74246 × 10
110
u 4.75301 × 10
110
b
53
+ ··· + 5.71834 × 10
110
b + 1.60015 × 10
111
,
3.30959 × 10
111
b
53
+ 1.20935 × 10
112
b
52
+ ··· + 5.24548 × 10
111
a + 3.83800 × 10
111
i
I
u
3
= hu
40
22u
39
+ ··· 9u + 2,
1.14224 × 10
33
u
39
+ 2.52168 × 10
34
u
38
+ ··· + 1.33995 × 10
33
b 7.70776 × 10
32
,
7.70776 × 10
32
u
39
+ 1.92415 × 10
34
u
38
+ ··· + 2.67990 × 10
33
a + 2.40397 × 10
34
i
I
v
1
= h−b + v, b
2
b + 1, ai
There are 4 irreducible components with 109 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
13
+ 9u
12
+ · · · + 22u + 3, 2u
12
+ 17u
11
+ · · · + b + 10, 10u
12
84u
11
+ · · · + 3a 19i
(i) Arc colorings
a
2
=
1
0
a
9
=
10
3
u
12
+ 28u
11
+ ··· + 60u +
19
3
2u
12
17u
11
+ ··· 67u 10
a
1
=
4
3
u
12
11u
11
+ ··· 47u
31
3
u
12
+ 8u
11
+ ··· + 18u + 4
a
5
=
0
u
a
4
=
u
u
a
10
=
10
3
u
12
+ 28u
11
+ ··· + 42u +
10
3
2u
12
17u
11
+ ··· 49u 7
a
8
=
10
3
u
12
+ 28u
11
+ ··· + 60u +
19
3
u
12
9u
11
+ ··· 33u 4
a
3
=
1
3
u
12
3u
11
+ ··· 29u
19
3
u + 1
a
6
=
1
3
u
12
+ 3u
11
+ ··· + 28u +
16
3
u
2
u 1
a
7
=
8
3
u
12
23u
11
+ ··· 112u
59
3
2u
12
+ 16u
11
+ ··· + 57u + 11
a
11
=
2u
12
+ 16u
11
+ ··· 6u 4
3u
12
25u
11
+ ··· 66u 9
a
11
=
2u
12
+ 16u
11
+ ··· 6u 4
3u
12
25u
11
+ ··· 66u 9
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.38849 0.89874I
a = 0.559166 + 0.246323I
b = 0.555017 0.844564I
5.16744 + 5.48401I 6.26872 7.46655I
u = 1.38849 + 0.89874I
a = 0.559166 0.246323I
b = 0.555017 + 0.844564I
5.16744 5.48401I 6.26872 + 7.46655I
u = 1.10450 1.08678I
a = 0.616668 0.034583I
b = 0.643528 + 0.708378I
0.51888 + 3.68063I 0.09698 6.26701I
u = 1.10450 + 1.08678I
a = 0.616668 + 0.034583I
b = 0.643528 0.708378I
0.51888 3.68063I 0.09698 + 6.26701I
u = 0.98054 1.39948I
a = 0.486559 0.089136I
b = 0.601837 0.593528I
4.89774 + 1.83075I 8.30741 4.84620I
u = 0.98054 + 1.39948I
a = 0.486559 + 0.089136I
b = 0.601837 + 0.593528I
4.89774 1.83075I 8.30741 + 4.84620I
u = 0.730232
a = 2.63660
b = 1.92533
9.93750 69.0383
u = 0.292896 0.381557I
a = 1.81980 + 1.43787I
b = 1.081638 + 0.273210I
0.418219 + 0.647136I 0.16669 3.99472I
u = 0.292896 + 0.381557I
a = 1.81980 1.43787I
b = 1.081638 0.273210I
0.418219 0.647136I 0.16669 + 3.99472I
u = 0.206085 0.822636I
a = 0.664815 0.879901I
b = 0.860847 0.365566I
2.18684 + 4.76062I 0.16967 6.96566I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.206085 + 0.822636I
a = 0.664815 + 0.879901I
b = 0.860847 + 0.365566I
2.18684 4.76062I 0.16967 + 6.96566I
u = 0.162361 1.122884I
a = 0.425709 + 0.610998I
b = 0.755199 + 0.378820I
2.66514 + 8.52224I 6.00968 8.13315I
u = 0.162361 + 1.122884I
a = 0.425709 0.610998I
b = 0.755199 0.378820I
2.66514 8.52224I 6.00968 + 8.13315I
4
II.
I
u
2
= hb
54
4b
53
+· · ·b+1, 8.74×10
110
u4.75×10
110
b
53
+· · ·+5.72×10
110
b+
1.60×10
111
, 3.31×10
111
b
53
+1.21 ×10
112
b
52
+· · ·+5.25×10
111
a+ 3.84×10
111
i
(i) Arc colorings
a
2
=
1
0
a
9
=
0.630942b
53
2.30552b
52
+ ··· 6.52827b 0.731678
b
a
1
=
0.218249b
53
0.962033b
52
+ ··· 0.100737b + 0.369058
b
2
a
5
=
0
0.543670b
53
1.85292b
52
+ ··· 0.654088b 1.83032
a
4
=
0.543670b
53
+ 1.85292b
52
+ ··· + 0.654088b + 1.83032
0.543670b
53
1.85292b
52
+ ··· 0.654088b 1.83032
a
10
=
0.113160b
53
0.462377b
52
+ ··· 1.60081b + 0.749878
0.517782b
53
1.84314b
52
+ ··· 3.92747b 1.48156
a
8
=
0.630942b
53
2.30552b
52
+ ··· 6.52827b 0.731678
0.974006b
53
3.45667b
52
+ ··· 5.74877b 2.46458
a
3
=
0.761919b
53
+ 2.81496b
52
+ ··· + 0.754825b + 1.46126
0.639614b
53
2.20164b
52
+ ··· 0.720343b 1.99030
a
6
=
0.0945803b
53
0.343629b
52
+ ··· + 1.69952b + 0.0305248
1.28218b
53
4.67874b
52
+ ··· 4.14435b 3.78417
a
7
=
0.483390b
53
1.58414b
52
+ ··· 2.14276b 0.0173628
0.697493b
53
2.60813b
52
+ ··· 5.36794b 1.97320
a
11
=
0.602977b
53
2.17624b
52
+ ··· 1.14987b + 0.0722525
1.24029b
53
+ 4.47041b
52
+ ··· + 4.88581b + 3.17812
a
11
=
0.602977b
53
2.17624b
52
+ ··· 1.14987b + 0.0722525
1.24029b
53
+ 4.47041b
52
+ ··· + 4.88581b + 3.17812
(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 = 0.582752 0.241692I
a = 1.44279 0.26226I
b = 1.57921 0.70794I
0.86178 5.25397I 6.46955 + 10.01314I
u = 0.582752 + 0.241692I
a = 1.44279 + 0.26226I
b = 1.57921 + 0.70794I
0.86178 + 5.25397I 6.46955 10.01314I
u = 0.686813
a = 1.72258 0.78016I
b = 1.183091 0.535826I
9.10414 14.2145
u = 0.686813
a = 1.72258 + 0.78016I
b = 1.183091 + 0.535826I
9.10414 14.2145
u = 0.379508 0.888364I
a = 0.673448 + 0.154047I
b = 1.14449 1.15173I
3.79952 + 4.67674I 5.91242 7.08419I
u = 0.379508 + 0.888364I
a = 0.673448 0.154047I
b = 1.14449 + 1.15173I
3.79952 4.67674I 5.91242 + 7.08419I
u = 0.88150 1.15459I
a = 0.634220 + 0.075664I
b = 1.006660 0.742648I
3.61252 + 2.75180I 4.02480 5.63147I
u = 0.88150 + 1.15459I
a = 0.634220 0.075664I
b = 1.006660 + 0.742648I
3.61252 2.75180I 4.02480 + 5.63147I
u = 1.15096 1.18150I
a = 0.639090 + 0.117549I
b = 0.994125 0.496662I
5.17654 + 7.89313I 8.62044 9.21586I
u = 1.15096 + 1.18150I
a = 0.639090 0.117549I
b = 0.994125 + 0.496662I
5.17654 7.89313I 8.62044 + 9.21586I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.582752 + 0.241692I
a = 1.88231 1.99550I
b = 0.777403 0.501546I
0.86178 + 5.25397I 6.46955 10.01314I
u = 0.582752 0.241692I
a = 1.88231 + 1.99550I
b = 0.777403 + 0.501546I
0.86178 5.25397I 6.46955 + 10.01314I
u = 1.09220 0.92053I
a = 0.754637 + 0.151460I
b = 0.707269 0.455921I
0.97705 + 2.90650I 6.25021 + 1.54831I
u = 1.09220 + 0.92053I
a = 0.754637 0.151460I
b = 0.707269 + 0.455921I
0.97705 2.90650I 6.25021 1.54831I
u = 1.26298 0.93908I
a = 0.543119 0.148230I
b = 0.662541 0.878869I
5.91990 + 0.72025I 11.02491 0.63973I
u = 1.26298 + 0.93908I
a = 0.543119 + 0.148230I
b = 0.662541 + 0.878869I
5.91990 0.72025I 11.02491 + 0.63973I
u = 1.06458 1.13255I
a = 0.684231 0.188755I
b = 0.584058 0.846227I
0.32804 + 4.95240I 2.66900 10.41191I
u = 1.06458 + 1.13255I
a = 0.684231 + 0.188755I
b = 0.584058 + 0.846227I
0.32804 4.95240I 2.66900 + 10.41191I
u = 1.199924 0.315775I
a = 0.298585 0.104074I
b = 0.445254 0.842141I
6.04501 + 4.08549I 10.80221 3.62417I
u = 1.199924 + 0.315775I
a = 0.298585 + 0.104074I
b = 0.445254 + 0.842141I
6.04501 4.08549I 10.80221 + 3.62417I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.408173 1.017870I
a = 1.29570 0.62828I
b = 0.156352 0.729009I
0.87383 + 8.44603I 0.29895 8.39876I
u = 0.408173 + 1.017870I
a = 1.29570 + 0.62828I
b = 0.156352 + 0.729009I
0.87383 8.44603I 0.29895 + 8.39876I
u = 0.825177 0.235104I
a = 0.76761 + 1.27328I
b = 0.141980 0.180524I
0.44505 + 1.73895I 7.45580 5.77840I
u = 0.825177 + 0.235104I
a = 0.76761 1.27328I
b = 0.141980 + 0.180524I
0.44505 1.73895I 7.45580 + 5.77840I
u = 0.331798 0.679493I
a = 2.24053 0.55468I
b = 0.052795 0.543453I
0.896800 + 0.835412I 3.62755 4.72274I
u = 0.331798 + 0.679493I
a = 2.24053 + 0.55468I
b = 0.052795 + 0.543453I
0.896800 0.835412I 3.62755 + 4.72274I
u = 0.379508 + 0.888364I
a = 1.56180 0.62111I
b = 0.118729 0.656729I
3.79952 4.67674I 5.91242 + 7.08419I
u = 0.379508 0.888364I
a = 1.56180 + 0.62111I
b = 0.118729 + 0.656729I
3.79952 + 4.67674I 5.91242 7.08419I
u = 0.825177 + 0.235104I
a = 0.216793 + 0.157003I
b = 0.334056 1.231150I
0.44505 1.73895I 7.45580 + 5.77840I
u = 0.825177 0.235104I
a = 0.216793 0.157003I
b = 0.334056 + 1.231150I
0.44505 + 1.73895I 7.45580 5.77840I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.199924 0.315775I
a = 0.519767 0.565045I
b = 0.391144 0.030595I
6.04501 + 4.08549I 10.80221 3.62417I
u = 1.199924 + 0.315775I
a = 0.519767 + 0.565045I
b = 0.391144 + 0.030595I
6.04501 4.08549I 10.80221 + 3.62417I
u = 0.88150 + 1.15459I
a = 0.826884 0.240574I
b = 0.471702 0.798962I
3.61252 2.75180I 4.02480 + 5.63147I
u = 0.88150 1.15459I
a = 0.826884 + 0.240574I
b = 0.471702 + 0.798962I
3.61252 + 2.75180I 4.02480 5.63147I
u = 1.15096 + 1.18150I
a = 0.636246 0.221608I
b = 0.596685 0.890379I
5.17654 7.89313I 8.62044 + 9.21586I
u = 1.15096 1.18150I
a = 0.636246 + 0.221608I
b = 0.596685 + 0.890379I
5.17654 + 7.89313I 8.62044 9.21586I
u = 1.09220 + 0.92053I
a = 0.584319 0.075040I
b = 0.684793 0.860087I
0.97705 2.90650I 6.25021 1.54831I
u = 1.09220 0.92053I
a = 0.584319 + 0.075040I
b = 0.684793 + 0.860087I
0.97705 + 2.90650I 6.25021 + 1.54831I
u = 0.651037 0.273406I
a = 1.54241 1.82712I
b = 0.797266 0.588915I
4.46105 9.38162I 9.06666 + 9.66600I
u = 0.651037 + 0.273406I
a = 1.54241 + 1.82712I
b = 0.797266 + 0.588915I
4.46105 + 9.38162I 9.06666 9.66600I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.519603 0.133499I
a = 2.76735 1.63400I
b = 0.825059 0.319549I
1.130917 0.684553I 13.8481 + 5.2893I
u = 0.519603 + 0.133499I
a = 2.76735 + 1.63400I
b = 0.825059 + 0.319549I
1.130917 + 0.684553I 13.8481 5.2893I
u = 1.26298 + 0.93908I
a = 0.671019 + 0.196940I
b = 0.825147 0.322819I
5.91990 0.72025I 11.02491 + 0.63973I
u = 1.26298 0.93908I
a = 0.671019 0.196940I
b = 0.825147 + 0.322819I
5.91990 + 0.72025I 11.02491 0.63973I
u = 1.06458 + 1.13255I
a = 0.654045 + 0.099092I
b = 0.942193 0.573978I
0.32804 4.95240I 2.66900 + 10.41191I
u = 1.06458 1.13255I
a = 0.654045 0.099092I
b = 0.942193 + 0.573978I
0.32804 + 4.95240I 2.66900 10.41191I
u = 0.331798 + 0.679493I
a = 0.676442 + 0.252611I
b = 1.12030 1.33838I
0.896800 0.835412I 3.62755 + 4.72274I
u = 0.331798 0.679493I
a = 0.676442 0.252611I
b = 1.12030 + 1.33838I
0.896800 + 0.835412I 3.62755 4.72274I
u = 0.408173 + 1.017870I
a = 0.670058 + 0.115091I
b = 1.16838 1.06241I
0.87383 8.44603I 0.29895 + 8.39876I
u = 0.408173 1.017870I
a = 0.670058 0.115091I
b = 1.16838 + 1.06241I
0.87383 + 8.44603I 0.29895 8.39876I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.651037 + 0.273406I
a = 1.363945 0.331785I
b = 1.50371 0.76781I
4.46105 + 9.38162I 9.06666 9.66600I
u = 0.651037 0.273406I
a = 1.363945 + 0.331785I
b = 1.50371 + 0.76781I
4.46105 9.38162I 9.06666 + 9.66600I
u = 0.519603 + 0.133499I
a = 1.63776 0.19421I
b = 1.65606 0.47960I
1.130917 + 0.684553I 13.8481 5.2893I
u = 0.519603 0.133499I
a = 1.63776 + 0.19421I
b = 1.65606 + 0.47960I
1.130917 0.684553I 13.8481 + 5.2893I
11
III. I
u
3
=
hu
40
22u
39
+· · ·9u+2, 1.14×10
33
u
39
+2.52×10
34
u
38
+· · ·+1.34×10
33
b
7.71× 10
32
, 7.71× 10
32
u
39
+1.92 ×10
34
u
38
+· · · +2.68 ×10
33
a + 2.40× 10
34
i
(i) Arc colorings
a
2
=
1
0
a
9
=
0.287614u
39
7.17995u
38
+ ··· + 18.5757u 8.97038
0.852449u
39
18.8192u
38
+ ··· + 6.38186u + 0.575227
a
1
=
1.32096u
39
+ 27.8117u
38
+ ··· 15.2340u + 2.43388
1.24936u
39
26.1933u
38
+ ··· + 10.4547u 2.64192
a
5
=
0
u
a
4
=
u
u
a
10
=
2.42973u
39
52.4094u
38
+ ··· + 29.1161u 10.8060
1.28966u
39
+ 26.4102u
38
+ ··· 4.15858u + 2.41085
a
8
=
0.287614u
39
7.17995u
38
+ ··· + 18.5757u 8.97038
0.917813u
39
18.0498u
38
+ ··· 1.86541u + 2.28013
a
3
=
0.0715990u
39
+ 1.61843u
38
+ ··· 4.77928u 0.208039
0.0768976u
39
+ 1.80500u
38
+ ··· + 2.38493u 0.229710
a
6
=
0.148497u
39
3.42344u
38
+ ··· + 2.39434u + 0.437749
0.0617970u
39
1.13756u
38
+ ··· 3.40163u + 0.763817
a
7
=
2.45327u
39
+ 51.6048u
38
+ ··· 12.7446u + 1.47342
4.87100u
39
102.661u
38
+ ··· + 31.8387u 7.69421
a
11
=
3.66160u
39
78.4540u
38
+ ··· + 28.5661u 11.4331
4.01584u
39
+ 85.6559u
38
+ ··· 30.7743u + 9.99907
a
11
=
3.66160u
39
78.4540u
38
+ ··· + 28.5661u 11.4331
4.01584u
39
+ 85.6559u
38
+ ··· 30.7743u + 9.99907
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.114946 0.470857I
a = 0.161219 0.354790I
b = 0.012695 0.471483I
5.90256 + 4.07376I 10.21690 2.73024I
u = 1.114946 + 0.470857I
a = 0.161219 + 0.354790I
b = 0.012695 + 0.471483I
5.90256 4.07376I 10.21690 + 2.73024I
u = 0.689340 0.344916I
a = 0.270895 + 0.559835I
b = 0.006357 + 0.479352I
0.54657 + 1.42879I 5.31935 4.51277I
u = 0.689340 + 0.344916I
a = 0.270895 0.559835I
b = 0.006357 0.479352I
0.54657 1.42879I 5.31935 + 4.51277I
u = 0.285753 0.168200I
a = 1.52463 + 3.16431I
b = 0.096572 + 1.160654I
1.43716 + 2.94730I 1.64080 2.63102I
u = 0.285753 + 0.168200I
a = 1.52463 3.16431I
b = 0.096572 1.160654I
1.43716 2.94730I 1.64080 + 2.63102I
u = 0.149250 0.237457I
a = 2.98531 2.47234I
b = 0.141518 1.077881I
2.81557 + 0.07740I 5.03252 + 0.22412I
u = 0.149250 + 0.237457I
a = 2.98531 + 2.47234I
b = 0.141518 + 1.077881I
2.81557 0.07740I 5.03252 0.22412I
u = 0.092104 0.401043I
a = 2.32462 + 1.19405I
b = 0.264758 + 1.042249I
1.12425 2.76728I 1.36010 + 3.97586I
u = 0.092104 + 0.401043I
a = 2.32462 1.19405I
b = 0.264758 1.042249I
1.12425 + 2.76728I 1.36010 3.97586I
13
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.009303 1.368789I
a = 0.420505 + 0.076247I
b = 0.100453 0.576293I
4.00380 + 0.89695I 3.64361 2.11192I
u = 0.009303 + 1.368789I
a = 0.420505 0.076247I
b = 0.100453 + 0.576293I
4.00380 0.89695I 3.64361 + 2.11192I
u = 0.335712
a = 2.37528
b = 0.797411
1.36099 8.46395
u = 0.583704 0.644503I
a = 1.56979 0.02991I
b = 0.935574 0.994277I
0.125718 + 0.859000I 0.712528 + 0.043707I
u = 0.583704 + 0.644503I
a = 1.56979 + 0.02991I
b = 0.935574 + 0.994277I
0.125718 0.859000I 0.712528 0.043707I
u = 0.712713 0.988658I
a = 0.403157 0.445940I
b = 0.153547 + 0.716412I
1.67832 + 1.69625I 1.45396 4.31564I
u = 0.712713 + 0.988658I
a = 0.403157 + 0.445940I
b = 0.153547 0.716412I
1.67832 1.69625I 1.45396 + 4.31564I
u = 0.748649
a = 2.52136
b = 1.88761
9.99305 75.1058
u = 0.755704 0.741495I
a = 1.391429 0.095553I
b = 0.98066 + 1.10395I
4.35513 3.45950I 3.88332 + 4.09172I
u = 0.755704 + 0.741495I
a = 1.391429 + 0.095553I
b = 0.98066 1.10395I
4.35513 + 3.45950I 3.88332 4.09172I
14
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.79480 1.74139I
a = 0.235020 0.234485I
b = 0.221536 + 0.595631I
1.50108 + 8.69698I 1.44576 9.16757I
u = 0.79480 + 1.74139I
a = 0.235020 + 0.234485I
b = 0.221536 0.595631I
1.50108 8.69698I 1.44576 + 9.16757I
u = 0.83868 1.53240I
a = 0.255350 + 0.282351I
b = 0.218516 0.628100I
3.63204 + 5.12135I 5.87713 8.64312I
u = 0.83868 + 1.53240I
a = 0.255350 0.282351I
b = 0.218516 + 0.628100I
3.63204 5.12135I 5.87713 + 8.64312I
u = 0.914030 0.829381I
a = 1.228078 + 0.165083I
b = 0.98558 1.16944I
1.51874 7.98713I 1.00079 + 8.43785I
u = 0.914030 + 0.829381I
a = 1.228078 0.165083I
b = 0.98558 + 1.16944I
1.51874 + 7.98713I 1.00079 8.43785I
u = 0.927542 1.036442I
a = 0.291220 0.457693I
b = 0.204254 + 0.726362I
1.64126 + 1.68382I 2.62360 4.24820I
u = 0.927542 + 1.036442I
a = 0.291220 + 0.457693I
b = 0.204254 0.726362I
1.64126 1.68382I 2.62360 + 4.24820I
u = 1.12354 0.94973I
a = 1.036682 + 0.196022I
b = 0.97858 1.20481I
0.67356 9.11808I 3.09330 + 5.04292I
u = 1.12354 + 0.94973I
a = 1.036682 0.196022I
b = 0.97858 + 1.20481I
0.67356 + 9.11808I 3.09330 5.04292I
15
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.153818 0.387735I
a = 0.091502 + 0.789150I
b = 0.200405 0.946014I
3.25229 1.41438I 4.70580 + 2.22096I
u = 1.153818 + 0.387735I
a = 0.091502 0.789150I
b = 0.200405 + 0.946014I
3.25229 + 1.41438I 4.70580 2.22096I
u = 1.17887 1.02242I
a = 0.980496 0.174090I
b = 0.97788 + 1.20771I
2.45998 13.64270I 1.03420 + 9.07195I
u = 1.17887 + 1.02242I
a = 0.980496 + 0.174090I
b = 0.97788 1.20771I
2.45998 + 13.64270I 1.03420 9.07195I
u = 1.21778 0.78831I
a = 1.024643 0.337678I
b = 0.98160 + 1.21895I
7.13383 7.90887I 8.08809 + 7.04843I
u = 1.21778 + 0.78831I
a = 1.024643 + 0.337678I
b = 0.98160 1.21895I
7.13383 + 7.90887I 8.08809 7.04843I
u = 1.23014 1.04879I
a = 0.945860 + 0.175380I
b = 0.97960 1.20775I
2.9545 17.7145I 5.23691 + 9.74637I
u = 1.23014 + 1.04879I
a = 0.945860 0.175380I
b = 0.97960 + 1.20775I
2.9545 + 17.7145I 5.23691 9.74637I
u = 1.348586 0.228178I
a = 0.074845 0.805781I
b = 0.284797 + 1.069588I
2.31251 4.79347I 0.81568 + 3.51271I
u = 1.348586 + 0.228178I
a = 0.074845 + 0.805781I
b = 0.284797 1.069588I
2.31251 + 4.79347I 0.81568 3.51271I
16
IV. I
v
1
= h−b + v, b
2
b + 1, ai
(i) Arc colorings
a
2
=
1
0
a
9
=
0
b
a
1
=
1
b 1
a
5
=
b
0
a
4
=
b
0
a
10
=
1
b
a
8
=
1
b
a
3
=
b + 1
b 1
a
6
=
1
b + 1
a
7
=
1
b
a
11
=
2
2b 1
a
11
=
2
2b 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
17
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 0.500000 0.866025I
a = 0
b = 0.500000 0.866025I
0 3.00000
v = 0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
0 3.00000
18
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
8
(u
2
u + 1)(u
13
+ u
12
+ ··· 2u
2
+ 1)(u
40
+ u
39
+ ··· 2u 1)
(u
54
+ 4u
53
+ ··· + u + 1)
c
2
(u
2
u + 1)(u
13
2u
11
+ ··· + u + 1)(u
40
+ 2u
38
+ ··· + u 1)
(u
54
+ 2u
53
+ ··· + 109u + 37)
c
3
(u + 1)
2
(u
13
+ 4u
12
+ ··· + 7u + 1)(u
40
+ 6u
39
+ ··· 23u + 1)
(u
54
3u
53
+ ··· + 18u + 27)
c
4
u
2
(u
13
9u
12
+ ··· + 22u 3)
(2 u + 13u
2
+ 23u
3
26u
4
125u
5
85u
6
+ 248u
7
+ 540u
8
+ 126u
9
962u
10
1454u
11
180u
12
+ 2028u
13
+ 2732u
14
+ 696u
15
2386u
16
3625u
17
2007u
18
+ 867u
19
+ 2782u
20
+ 2929u
21
+ 1989u
22
+ 964u
23
+ 338u
24
+ 83u
25
+ 13u
26
+ u
27
)
2
(u
40
22u
39
+ ··· 9u + 2)
c
5
(u + 1)
2
(u
13
+ 4u
12
+ ··· + 7u + 1)(u
40
+ 6u
39
+ ··· 23u + 1)
(u
54
3u
53
+ ··· + 18u + 27)
c
6
(u + 1)
2
(u
13
2u
12
+ ··· 7u
2
1)
(1 4u
2
7u
3
13u
4
6u
5
u
6
+ 20u
7
+ 66u
8
+ 62u
9
134u
11
220u
12
+ 6u
13
+ 288u
14
+ 222u
15
89u
16
318u
17
120u
18
+ 249u
19
+ 149u
20
130u
21
75u
22
+ 46u
23
+ 19u
24
10u
25
2u
26
+ u
27
)
2
(u
40
+ 5u
39
+ ··· + 9u 4)
c
7
u
2
(u
13
+ 6u
12
+ ··· + 8u + 3)
(8 + 37u + 109u
2
+ 289u
3
+ 734u
4
+ 1663u
5
+ 3317u
6
+ 5808u
7
+ 9000u
8
+ 1.24 × 10
4
u
9
+ 1.54 × 10
4
u
10
+ 1.72 × 10
4
u
11
+ 1.71 × 10
4
u
12
+ 1.55 × 10
4
u
13
+ 1.32 × 10
4
u
14
+ 1.09 × 10
4
u
15
+ 8778u
16
+ 6743u
17
+ 4765u
18
+ 3083u
19
+ 1890u
20
+ 1133u
21
+ 651u
22
+ 332u
23
+ 138u
24
+ 43u
25
+ 9u
26
+ u
27
)
2
(u
40
15u
39
+ ··· 89u + 4)
c
9
(u
2
u + 1)(u
13
2u
11
+ ··· + u + 1)(u
40
+ 2u
38
+ ··· + u 1)
(u
54
+ 2u
53
+ ··· + 109u + 37)
c
10
, c
11
(u 1)
2
(u
13
+ 2u
12
+ ··· + 7u
2
+ 1)
(1 4u
2
7u
3
13u
4
6u
5
u
6
+ 20u
7
+ 66u
8
+ 62u
9
134u
11
220u
12
+ 6u
13
+ 288u
14
+ 222u
15
89u
16
318u
17
120u
18
+ 249u
19
+ 149u
20
130u
21
75u
22
+ 46u
23
+ 19u
24
10u
25
2u
26
+ u
27
)
2
(u
40
+ 5u
39
+ ··· + 9u 4)
19
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
2
+ y + 1)(y
13
7y
12
+ ··· + 4y 1)(y
40
+ 17y
39
+ ··· + 44y + 1)
(y
54
12y
53
+ ··· + 5y + 1)
c
2
(y
2
+ y + 1)(y
13
4y
12
+ ··· + 7y 1)(y
40
+ 4y
39
+ ··· 23y + 1)
(y
54
+ 50y
52
+ ··· + 67373y + 1369)
c
3
(y 1)
2
(y
13
+ 8y
12
+ ··· + 11y 1)(y
40
24y
39
+ ··· 199y + 1)
(y
54
+ 13y
53
+ ··· 6318y + 729)
c
4
y
2
(y
13
+ 3y
12
+ ··· 38y 9)
(4 + 53y 319y
2
+ 1115y
3
2552y
4
+ 4473y
5
8149y
6
+ 1.64 × 10
4
y
7
2.72 × 10
4
y
8
+ 3.14 × 10
4
y
9
3.04 × 10
4
y
10
+ 3.94 × 10
4
y
11
5.00 × 10
4
y
12
+ 4.53 × 10
4
y
13
3.49 × 10
4
y
14
+ 3.29 × 10
4
y
15
2.44 × 10
4
y
16
+ 1.97 × 10
4
y
17
1.33 × 10
4
y
18
+ 8371y
19
4296y
20
+ 2231y
21
787y
22
+ 348y
23
76y
24
+ 29y
25
3y
26
+ y
27
)
2
(y
40
+ 28y
38
+ ··· 5y + 4)
c
5
(y 1)
2
(y
13
+ 8y
12
+ ··· + 11y 1)(y
40
24y
39
+ ··· 199y + 1)
(y
54
+ 13y
53
+ ··· 6318y + 729)
c
6
(y 1)
2
(y
13
14y
12
+ ··· 14y 1)(y
40
37y
39
+ ··· 9y + 16)
(y
54
48y
53
+ ··· + 16y + 1)
c
7
y
2
(y
13
6y
12
+ ··· 122y 9)(y
40
y
39
+ ··· 937y + 16)
(y
54
+ 10y
53
+ ··· + 48000y + 4096)
c
8
(y
2
+ y + 1)(y
13
7y
12
+ ··· + 4y 1)(y
40
+ 17y
39
+ ··· + 44y + 1)
(y
54
12y
53
+ ··· + 5y + 1)
c
9
(y
2
+ y + 1)(y
13
4y
12
+ ··· + 7y 1)(y
40
+ 4y
39
+ ··· 23y + 1)
(y
54
+ 50y
52
+ ··· + 67373y + 1369)
c
10
(y 1)
2
(y
13
14y
12
+ ··· 14y 1)(y
40
37y
39
+ ··· 9y + 16)
(y
54
48y
53
+ ··· + 16y + 1)
c
11
(y 1)
2
(y
13
14y
12
+ ··· 14y 1)(y
40
37y
39
+ ··· 9y + 16)
(y
54
48y
53
+ ··· + 16y + 1)
20