11a
278
(K11a
278
)
1
Arc Sequences
9 5 1 10 2 4 11 3 6 8 7
Solving Sequence
2,6
5
3,10
4 7 9 1 8 11
c
5
c
2
c
4
c
6
c
9
c
1
c
8
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= hu
17
8u
16
+ ··· + 29u 5, 2u
16
+ 17u
15
+ ··· + b 8, 8u
16
+ 64u
15
+ ··· + 5a + 3i
I
u
2
= ha
46
2a
44
+ ··· + a + 1, 1.52610 × 10
110
u + 1.46097 × 10
110
a
45
+ ··· + 2.02303 × 10
110
a 2.30734 × 10
110
,
1.52610 × 10
110
b + 3.95463 × 10
110
a
45
+ ··· + 3.38990 × 10
110
a 8.67389 × 10
110
i
I
u
3
= hu
41
+ 11u
40
+ ··· 239u 24,
5.24422 × 10
17
u
40
7.01694 × 10
18
u
39
+ ··· + 1.66044 × 10
18
b + 4.68165 × 10
19
,
1.81027 × 10
19
u
40
2.27843 × 10
20
u
39
+ ··· + 3.98505 × 10
19
a + 1.63232 × 10
21
i
There are 3 irreducible components with 104 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
17
8u
16
+· · ·+29u5, 2u
16
+17u
15
+· · ·+b8, 8u
16
+64u
15
+· · ·+5a+3i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
5
=
u
u
a
3
=
u
2
+ 1
u
2
a
10
=
8
5
u
16
64
5
u
15
+ ··· 3u
3
5
2u
16
17u
15
+ ··· 55u + 8
a
4
=
1
5
u
16
8
5
u
15
+ ··· 19u +
24
5
u
2
u + 1
a
7
=
1
5
u
16
+
8
5
u
15
+ ··· + 17u
19
5
u
4
+ 2u
3
3u
2
+ 3u 1
a
9
=
8
5
u
16
64
5
u
15
+ ··· 3u
3
5
2u
15
+ 15u
14
+ ··· 47u + 8
a
1
=
4
5
u
16
32
5
u
15
+ ··· 8u +
1
5
u
15
+ 7u
14
+ ··· 24u + 4
a
8
=
8
5
u
16
64
5
u
15
+ ··· 11u +
7
5
u
16
10u
15
+ ··· 52u + 8
a
11
=
2
5
u
16
16
5
u
15
+ ··· + 18u
22
5
u
16
8u
15
+ ··· 20u + 2
a
11
=
2
5
u
16
16
5
u
15
+ ··· + 18u
22
5
u
16
8u
15
+ ··· 20u + 2
(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 = 0.187789 0.804462I
a = 1.297904 + 0.024002I
b = 0.52389 + 1.44644I
7.01302 6.58132I 2.73271 + 4.66890I
u = 0.187789 + 0.804462I
a = 1.297904 0.024002I
b = 0.52389 1.44644I
7.01302 + 6.58132I 2.73271 4.66890I
u = 0.049862 0.811132I
a = 1.47990 0.46053I
b = 0.70749 1.40551I
0.38103 2.23066I 3.27072 + 6.66488I
u = 0.049862 + 0.811132I
a = 1.47990 + 0.46053I
b = 0.70749 + 1.40551I
0.38103 + 2.23066I 3.27072 6.66488I
u = 0.159792 1.337935I
a = 0.573080 0.585069I
b = 0.57018 1.64757I
9.78949 + 6.03317I 3.31072 5.48564I
u = 0.159792 + 1.337935I
a = 0.573080 + 0.585069I
b = 0.57018 + 1.64757I
9.78949 6.03317I 3.31072 + 5.48564I
u = 0.212883 0.989804I
a = 1.13211 + 0.90529I
b = 0.78429 + 1.68209I
1.43397 + 3.72395I 9.02521 8.71756I
u = 0.212883 + 0.989804I
a = 1.13211 0.90529I
b = 0.78429 1.68209I
1.43397 3.72395I 9.02521 + 8.71756I
u = 0.459989 1.288471I
a = 0.267482 + 0.862976I
b = 0.42153 + 1.67462I
2.67441 + 5.22342I 1.79503 5.33597I
u = 0.459989 + 1.288471I
a = 0.267482 0.862976I
b = 0.42153 1.67462I
2.67441 5.22342I 1.79503 + 5.33597I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.623402 0.351291I
a = 1.017724 0.719190I
b = 0.426879 0.169361I
0.81423 1.18978I 7.16259 + 1.41463I
u = 0.623402 + 0.351291I
a = 1.017724 + 0.719190I
b = 0.426879 + 0.169361I
0.81423 + 1.18978I 7.16259 1.41463I
u = 0.63999 1.39192I
a = 0.047114 0.703808I
b = 0.37642 1.50738I
6.14483 + 5.85758I 2.31283 5.33514I
u = 0.63999 + 1.39192I
a = 0.047114 + 0.703808I
b = 0.37642 + 1.50738I
6.14483 5.85758I 2.31283 + 5.33514I
u = 1.26194
a = 0.351598
b = 0.116222
1.98855 20.3119
u = 1.41090 0.33080I
a = 0.396122 0.034106I
b = 0.206855 0.222682I
2.33565 + 1.27004I 12.05941 + 2.53511I
u = 1.41090 + 0.33080I
a = 0.396122 + 0.034106I
b = 0.206855 + 0.222682I
2.33565 1.27004I 12.05941 2.53511I
4
II.
I
u
2
= ha
46
2a
44
+· · ·+a+1, 1.53×10
110
u+1.46×10
110
a
45
+· · ·+2.02×10
110
a
2.31×10
110
, 1.53×10
110
b+3.95× 10
110
a
45
+· · ·+3.39× 10
110
a8.67× 10
110
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
0.957324a
45
0.383445a
44
+ ··· 1.32562a + 1.51192
a
5
=
0.957324a
45
0.383445a
44
+ ··· 1.32562a + 1.51192
0.957324a
45
0.383445a
44
+ ··· 1.32562a + 1.51192
a
3
=
1.46700a
45
+ 0.999285a
44
+ ··· + 8.44280a + 7.57757
1.46700a
45
+ 0.999285a
44
+ ··· + 8.44280a + 6.57757
a
10
=
a
2.59133a
45
+ 1.93310a
44
+ ··· 2.22128a + 5.68370
a
4
=
1.54484a
45
+ 0.397211a
44
+ ··· + 5.75585a + 3.16488
2.40991a
45
+ 0.272951a
44
+ ··· 2.98102a 2.01086
a
7
=
1.43573a
45
0.869536a
44
+ ··· 7.51485a 6.67814
1.82366a
45
+ 1.44800a
44
+ ··· + 15.0421a + 2.67972
a
9
=
a
1.59204a
45
+ 1.63823a
44
+ ··· + 2.88929a + 4.21670
a
1
=
1.63823a
45
+ 0.568060a
44
+ ··· + 5.80874a + 2.59204
2.98215a
45
+ 2.03765a
44
+ ··· + 7.35905a + 2.13238
a
8
=
0.646576a
45
1.98885a
44
+ ··· 12.7444a 10.3648
0.235703a
45
0.841836a
44
+ ··· 1.40771a 5.16715
a
11
=
4.21332a
45
1.39340a
44
+ ··· + 26.4455a 4.42054
0.964043a
45
+ 1.14515a
44
+ ··· + 9.91606a + 6.29299
a
11
=
4.21332a
45
1.39340a
44
+ ··· + 26.4455a 4.42054
0.964043a
45
+ 1.14515a
44
+ ··· + 9.91606a + 6.29299
(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 = 0.300297 0.396341I
a = 2.29108 0.26263I
b = 0.659064 0.272120I
5.91614 + 5.40360I 0.73363 1.75125I
u = 0.300297 + 0.396341I
a = 2.29108 + 0.26263I
b = 0.659064 + 0.272120I
5.91614 5.40360I 0.73363 + 1.75125I
u = 0.186753 0.913593I
a = 2.12924 0.45864I
b = 1.41577 0.22926I
0.48240 3.68961I 4.31455 + 10.86650I
u = 0.186753 + 0.913593I
a = 2.12924 + 0.45864I
b = 1.41577 + 0.22926I
0.48240 + 3.68961I 4.31455 10.86650I
u = 0.184645 + 1.327796I
a = 0.76864 1.22003I
b = 1.16196 1.98582I
11.44284 6.01561I 9.34351 + 5.45649I
u = 0.184645 1.327796I
a = 0.76864 + 1.22003I
b = 1.16196 + 1.98582I
11.44284 + 6.01561I 9.34351 5.45649I
u = 0.186753 0.913593I
a = 0.523578 0.592634I
b = 0.59960 2.32622I
0.48240 3.68961I 4.31455 + 10.86650I
u = 0.186753 + 0.913593I
a = 0.523578 + 0.592634I
b = 0.59960 + 2.32622I
0.48240 + 3.68961I 4.31455 10.86650I
u = 0.55226 + 1.43648I
a = 0.394595 0.763047I
b = 0.86738 1.18435I
6.99739 7.32012I 2.83321 + 9.36955I
u = 0.55226 1.43648I
a = 0.394595 + 0.763047I
b = 0.86738 + 1.18435I
6.99739 + 7.32012I 2.83321 9.36955I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.126296 0.206470I
a = 0.325064 0.295967I
b = 0.532160 0.269149I
1.93766 + 1.32101I 4.99704 4.34736I
u = 1.126296 + 0.206470I
a = 0.325064 + 0.295967I
b = 0.532160 + 0.269149I
1.93766 1.32101I 4.99704 + 4.34736I
u = 0.616588 + 1.034050I
a = 0.280768 0.666044I
b = 0.175511 0.450071I
4.52825 4.72419I 0.87243 + 5.66443I
u = 0.616588 1.034050I
a = 0.280768 + 0.666044I
b = 0.175511 + 0.450071I
4.52825 + 4.72419I 0.87243 5.66443I
u = 0.616588 1.034050I
a = 0.269180 1.017674I
b = 0.59661 1.74551I
4.52825 + 4.72419I 0.87243 5.66443I
u = 0.616588 + 1.034050I
a = 0.269180 + 1.017674I
b = 0.59661 + 1.74551I
4.52825 4.72419I 0.87243 + 5.66443I
u = 0.300297 0.396341I
a = 0.21968 2.37381I
b = 1.16367 1.09345I
5.91614 + 5.40360I 0.73363 1.75125I
u = 0.300297 + 0.396341I
a = 0.21968 + 2.37381I
b = 1.16367 + 1.09345I
5.91614 5.40360I 0.73363 + 1.75125I
u = 0.356806 + 1.198902I
a = 0.208082 0.624477I
b = 0.66825 1.38472I
4.04810 4.55921I 5.41713 + 6.09867I
u = 0.356806 1.198902I
a = 0.208082 + 0.624477I
b = 0.66825 + 1.38472I
4.04810 + 4.55921I 5.41713 6.09867I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.126296 + 0.206470I
a = 0.072281 0.413630I
b = 0.323461 + 0.274461I
1.93766 1.32101I 4.99704 + 4.34736I
u = 1.126296 0.206470I
a = 0.072281 + 0.413630I
b = 0.323461 0.274461I
1.93766 + 1.32101I 4.99704 4.34736I
u = 0.54822 + 1.33148I
a = 0.071226 0.829845I
b = 0.47263 1.93178I
1.92714 5.73570I 6.54258 + 11.45569I
u = 0.54822 1.33148I
a = 0.071226 + 0.829845I
b = 0.47263 + 1.93178I
1.92714 + 5.73570I 6.54258 11.45569I
u = 0.55226 1.43648I
a = 0.042372 0.738312I
b = 0.36774 2.21932I
6.99739 + 7.32012I 2.83321 9.36955I
u = 0.55226 + 1.43648I
a = 0.042372 + 0.738312I
b = 0.36774 + 2.21932I
6.99739 7.32012I 2.83321 + 9.36955I
u = 0.184645 1.327796I
a = 0.108563 0.591394I
b = 1.00034 2.21512I
11.44284 + 6.01561I 9.34351 5.45649I
u = 0.184645 + 1.327796I
a = 0.108563 + 0.591394I
b = 1.00034 + 2.21512I
11.44284 6.01561I 9.34351 + 5.45649I
u = 1.07372
a = 0.124252 0.220240I
b = 0.276659 + 0.017433I
2.18491 16.7310
u = 1.07372
a = 0.124252 + 0.220240I
b = 0.276659 0.017433I
2.18491 16.7310
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.388479 0.400318I
a = 0.225563 1.314025I
b = 0.508689 + 0.404794I
0.02603 + 1.77955I 5.09313 4.79070I
u = 0.388479 + 0.400318I
a = 0.225563 + 1.314025I
b = 0.508689 0.404794I
0.02603 1.77955I 5.09313 + 4.79070I
u = 0.356806 1.198902I
a = 0.234189 1.300088I
b = 0.74465 1.97512I
4.04810 + 4.55921I 5.41713 6.09867I
u = 0.356806 + 1.198902I
a = 0.234189 + 1.300088I
b = 0.74465 + 1.97512I
4.04810 4.55921I 5.41713 + 6.09867I
u = 0.233567 + 1.031348I
a = 0.252571 0.635915I
b = 1.16183 2.65957I
7.62895 + 7.86344I 3.61806 10.44591I
u = 0.233567 1.031348I
a = 0.252571 + 0.635915I
b = 1.16183 + 2.65957I
7.62895 7.86344I 3.61806 + 10.44591I
u = 0.54822 1.33148I
a = 0.299644 0.757047I
b = 0.480499 1.226914I
1.92714 + 5.73570I 6.54258 11.45569I
u = 0.54822 + 1.33148I
a = 0.299644 + 0.757047I
b = 0.480499 + 1.226914I
1.92714 5.73570I 6.54258 + 11.45569I
u = 0.089537 + 0.682903I
a = 1.25817 1.62197I
b = 0.97421 1.47696I
0.19963 1.69919I 7.29306 + 0.59779I
u = 0.089537 0.682903I
a = 1.25817 + 1.62197I
b = 0.97421 + 1.47696I
0.19963 + 1.69919I 7.29306 0.59779I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.089537 0.682903I
a = 1.315106 0.119247I
b = 0.406813 + 0.788955I
0.19963 + 1.69919I 7.29306 0.59779I
u = 0.089537 + 0.682903I
a = 1.315106 + 0.119247I
b = 0.406813 0.788955I
0.19963 1.69919I 7.29306 + 0.59779I
u = 0.388479 + 0.400318I
a = 1.59424 0.74983I
b = 0.220071 1.103626I
0.02603 1.77955I 5.09313 + 4.79070I
u = 0.388479 0.400318I
a = 1.59424 + 0.74983I
b = 0.220071 + 1.103626I
0.02603 + 1.77955I 5.09313 4.79070I
u = 0.233567 1.031348I
a = 2.09874 0.10703I
b = 1.46947 0.71011I
7.62895 7.86344I 3.61806 + 10.44591I
u = 0.233567 + 1.031348I
a = 2.09874 + 0.10703I
b = 1.46947 + 0.71011I
7.62895 + 7.86344I 3.61806 10.44591I
10
III. I
u
3
= hu
41
+ 11u
40
+ · · · 239u 24, 5.24 × 10
17
u
40
7.02 ×
10
18
u
39
+ · · · + 1.66 × 10
18
b + 4.68 × 10
19
, 1.81 × 10
19
u
40
2.28 ×
10
20
u
39
+ · · · + 3.99 × 10
19
a + 1.63 × 10
21
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
5
=
u
u
a
3
=
u
2
+ 1
u
2
a
10
=
0.454264u
40
+ 5.71745u
39
+ ··· 387.153u 40.9611
0.315834u
40
+ 4.22596u
39
+ ··· 250.719u 28.1953
a
4
=
0.406963u
40
5.21537u
39
+ ··· + 74.2686u + 3.95900
0.784851u
40
9.15906u
39
+ ··· + 280.640u + 27.4978
a
7
=
1.35883u
40
14.0083u
39
+ ··· + 46.7401u + 2.26122
1.44090u
40
15.2553u
39
+ ··· + 173.604u + 15.1956
a
9
=
0.454264u
40
+ 5.71745u
39
+ ··· 387.153u 40.9611
0.720540u
40
6.88956u
39
+ ··· 67.6080u 10.9023
a
1
=
1.28278u
40
+ 13.4475u
39
+ ··· 94.7279u 9.91551
0.663004u
40
+ 8.31978u
39
+ ··· 295.668u 30.7866
a
8
=
0.283426u
40
2.58335u
39
+ ··· 192.778u 20.0851
1.42698u
40
15.5781u
39
+ ··· + 106.447u + 6.65133
a
11
=
0.828643u
40
+ 9.45479u
39
+ ··· 243.403u 24.0844
0.638552u
40
+ 8.31334u
39
+ ··· 521.048u 55.1077
a
11
=
0.828643u
40
+ 9.45479u
39
+ ··· 243.403u 24.0844
0.638552u
40
+ 8.31334u
39
+ ··· 521.048u 55.1077
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.182594 0.075770I
a = 0.861334 + 0.534048I
b = 0.125805 0.201350I
6.46948 + 11.04653I 1.00030 7.47384I
u = 1.182594 + 0.075770I
a = 0.861334 0.534048I
b = 0.125805 + 0.201350I
6.46948 11.04653I 1.00030 + 7.47384I
u = 1.052801 0.131390I
a = 0.989565 0.532958I
b = 0.039494 + 0.164175I
0.26528 + 7.29842I 2.61009 7.62825I
u = 1.052801 + 0.131390I
a = 0.989565 + 0.532958I
b = 0.039494 0.164175I
0.26528 7.29842I 2.61009 + 7.62825I
u = 0.821173 0.119690I
a = 1.231442 + 0.646031I
b = 0.248144 + 0.009447I
0.99974 + 2.62993I 0.91222 3.18628I
u = 0.821173 + 0.119690I
a = 1.231442 0.646031I
b = 0.248144 0.009447I
0.99974 2.62993I 0.91222 + 3.18628I
u = 0.717608 0.311811I
a = 0.92139 + 1.18966I
b = 0.114856 + 0.481785I
7.82283 0.16471I 3.38955 + 1.65431I
u = 0.717608 + 0.311811I
a = 0.92139 1.18966I
b = 0.114856 0.481785I
7.82283 + 0.16471I 3.38955 1.65431I
u = 0.684336 1.194054I
a = 0.491630 + 0.663349I
b = 0.515135 + 1.305498I
10.00544 5.34593I 6.97622 + 3.91982I
u = 0.684336 + 1.194054I
a = 0.491630 0.663349I
b = 0.515135 1.305498I
10.00544 + 5.34593I 6.97622 3.91982I
12
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.58068 1.35810I
a = 0.213713 1.113859I
b = 0.69031 2.27881I
10.5240 17.2112I 2.94234 + 8.67373I
u = 0.58068 + 1.35810I
a = 0.213713 + 1.113859I
b = 0.69031 + 2.27881I
10.5240 + 17.2112I 2.94234 8.67373I
u = 0.558892 1.297927I
a = 0.223473 + 1.175296I
b = 0.61123 + 2.23550I
3.92238 13.02368I 0.07893 + 9.11009I
u = 0.558892 + 1.297927I
a = 0.223473 1.175296I
b = 0.61123 2.23550I
3.92238 + 13.02368I 0.07893 9.11009I
u = 0.495810 1.155838I
a = 0.309610 0.841076I
b = 0.49917 1.33090I
4.52174 1.46436I 3.61202 + 2.25685I
u = 0.495810 + 1.155838I
a = 0.309610 + 0.841076I
b = 0.49917 + 1.33090I
4.52174 + 1.46436I 3.61202 2.25685I
u = 0.490892 1.239605I
a = 0.300435 1.251025I
b = 0.50849 2.24179I
4.41136 7.49164I 2.21822 + 5.79104I
u = 0.490892 + 1.239605I
a = 0.300435 + 1.251025I
b = 0.50849 + 2.24179I
4.41136 + 7.49164I 2.21822 5.79104I
u = 0.38362 1.54611I
a = 0.124908 0.520175I
b = 0.51532 1.32151I
11.91805 + 4.98494I 7.36557 3.29856I
u = 0.38362 + 1.54611I
a = 0.124908 + 0.520175I
b = 0.51532 + 1.32151I
11.91805 4.98494I 7.36557 + 3.29856I
13
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.347665 1.264829I
a = 0.459099 + 1.166379I
b = 0.38911 + 2.30741I
12.33802 3.83464I 6.62030 + 3.17897I
u = 0.347665 + 1.264829I
a = 0.459099 1.166379I
b = 0.38911 2.30741I
12.33802 + 3.83464I 6.62030 3.17897I
u = 0.325776 1.364772I
a = 0.090435 + 0.652622I
b = 0.498665 + 1.315915I
5.42164 + 2.35534I 4.38781 4.47001I
u = 0.325776 + 1.364772I
a = 0.090435 0.652622I
b = 0.498665 1.315915I
5.42164 2.35534I 4.38781 + 4.47001I
u = 0.212627 0.952062I
a = 1.03120 1.05086I
b = 0.53232 1.69272I
1.10287 3.44596I 5.05254 2.71451I
u = 0.212627 + 0.952062I
a = 1.03120 + 1.05086I
b = 0.53232 + 1.69272I
1.10287 + 3.44596I 5.05254 + 2.71451I
u = 0.113639 0.464794I
a = 1.57765 + 0.07476I
b = 0.472884 + 0.590304I
0.006980 + 1.308314I 1.77615 2.91870I
u = 0.113639 + 0.464794I
a = 1.57765 0.07476I
b = 0.472884 0.590304I
0.006980 1.308314I 1.77615 + 2.91870I
u = 0.038850 0.715738I
a = 0.39907 + 1.63492I
b = 0.85992 + 1.16202I
7.32305 + 0.14265I 5.03936 + 0.27284I
u = 0.038850 + 0.715738I
a = 0.39907 1.63492I
b = 0.85992 1.16202I
7.32305 0.14265I 5.03936 0.27284I
14
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.029022 1.006329I
a = 0.503900 1.096770I
b = 0.67253 1.61446I
3.33397 + 0.06687I 6.02301 + 0.24252I
u = 0.029022 + 1.006329I
a = 0.503900 + 1.096770I
b = 0.67253 + 1.61446I
3.33397 0.06687I 6.02301 0.24252I
u = 0.125412 1.084045I
a = 0.628323 + 1.038113I
b = 0.75793 + 1.92540I
8.77240 + 0.69151I 5.83897 + 1.00152I
u = 0.125412 + 1.084045I
a = 0.628323 1.038113I
b = 0.75793 1.92540I
8.77240 0.69151I 5.83897 1.00152I
u = 0.185808 0.685986I
a = 0.869279 + 0.128351I
b = 0.096765 + 0.850031I
0.087291 + 1.322904I 3.26673 3.24423I
u = 0.185808 + 0.685986I
a = 0.869279 0.128351I
b = 0.096765 0.850031I
0.087291 1.322904I 3.26673 + 3.24423I
u = 0.388375 1.153132I
a = 0.376979 0.314906I
b = 0.347184 1.021300I
5.35338 + 3.81903I 0.34343 3.03057I
u = 0.388375 + 1.153132I
a = 0.376979 + 0.314906I
b = 0.347184 + 1.021300I
5.35338 3.81903I 0.34343 + 3.03057I
u = 1.12668
a = 0.115460
b = 0.276655
2.19078 19.8799
u = 1.215004 0.331445I
a = 0.176835 + 0.024248I
b = 0.428913 0.263631I
1.95983 + 1.37588I 8.33065 3.10614I
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.215004 + 0.331445I
a = 0.176835 0.024248I
b = 0.428913 + 0.263631I
1.95983 1.37588I 8.33065 + 3.10614I
15
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
17
+ 3u
15
+ ··· u 1)(u
41
12u
39
+ ··· 2u 1)
(u
46
+ u
45
+ ··· + 8u
2
+ 1)
c
2
(u
17
8u
16
+ ··· + 29u 5)
(1 + 4u + 14u
2
+ 38u
3
+ 99u
4
+ 222u
5
+ 461u
6
+ 857u
7
+ 1431u
8
+ 2150u
9
+ 2896u
10
+ 3514u
11
+ 3832u
12
+ 3758u
13
+ 3308u
14
+ 2602u
15
+ 1821u
16
+ 1122u
17
+ 602u
18
+ 276u
19
+ 105u
20
+ 32u
21
+ 7u
22
+ u
23
)
2
(u
41
11u
40
+ ··· 239u + 24)
c
3
(u
17
+ u
16
+ ··· + u + 1)(u
41
+ u
40
+ ··· + 6u 1)
(u
46
+ 7u
45
+ ··· + 188u + 37)
c
4
(u
17
4u
15
+ ··· 2u
2
+ 1)(u
41
3u
39
+ ··· + 39u + 19)
(u
46
+ u
45
+ ··· + 36u + 11)
c
5
(u
17
+ 8u
16
+ ··· + 29u + 5)
(1 + 4u + 14u
2
+ 38u
3
+ 99u
4
+ 222u
5
+ 461u
6
+ 857u
7
+ 1431u
8
+ 2150u
9
+ 2896u
10
+ 3514u
11
+ 3832u
12
+ 3758u
13
+ 3308u
14
+ 2602u
15
+ 1821u
16
+ 1122u
17
+ 602u
18
+ 276u
19
+ 105u
20
+ 32u
21
+ 7u
22
+ u
23
)
2
(u
41
11u
40
+ ··· 239u + 24)
c
6
(u
17
+ u
16
+ ··· + u + 1)(u
41
+ u
40
+ ··· + 6u 1)
(u
46
+ 7u
45
+ ··· + 188u + 37)
c
7
(u
17
5u
16
+ ··· + 6u 1)(u
41
8u
40
+ ··· + 9u 2)
(u
46
+ 10u
45
+ ··· 12u
2
+ 1)
c
8
(u
17
4u
15
+ ··· 2u
2
+ 1)(u
41
3u
39
+ ··· + 39u + 19)
(u
46
+ u
45
+ ··· + 36u + 11)
c
9
(u
17
+ 3u
15
+ ··· u 1)(u
41
12u
39
+ ··· 2u 1)
(u
46
+ u
45
+ ··· + 8u
2
+ 1)
c
10
(u
17
+ 5u
16
+ ··· + 6u + 1)
(1 + 6u
2
+ 12u
3
3u
4
52u
5
105u
6
29u
7
+ 317u
8
+ 1008u
9
+ 1928u
10
+ 2824u
11
+ 3380u
12
+ 3448u
13
+ 3028u
14
+ 2328u
15
+ 1559u
16
+ 920u
17
+ 466u
18
+ 208u
19
+ 75u
20
+ 24u
21
+ 5u
22
+ u
23
)
2
(u
41
8u
40
+ ··· + 9u 2)
c
11
(u
17
+ 5u
16
+ ··· + 6u + 1)(u
41
8u
40
+ ··· + 9u 2)
(u
46
+ 10u
45
+ ··· 12u
2
+ 1)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
17
+ 6y
16
+ ··· + 7y 1)(y
41
24y
40
+ ··· + 96y 1)
(y
46
+ 7y
45
+ ··· + 16y + 1)
c
2
, c
5
(y
17
+ 8y
16
+ ··· 159y 25)
(1 12y 90y
2
474y
3
1843y
4
5522y
5
1.26 × 10
4
y
6
2.05 × 10
4
y
7
2.11 × 10
4
y
8
7856y
9
+ 1.26 × 10
4
y
10
+ 2.33 × 10
4
y
11
+ 1.60 × 10
4
y
12
+ 504y
13
8616y
14
7260y
15
1637y
16
+ 1916y
17
+ 2262y
18
+ 1274y
19
+ 455y
20
+ 106y
21
+ 15y
22
+ y
23
)
2
(y
41
+ 23y
40
+ ··· 10223y 576)
c
3
(y
17
7y
16
+ ··· + y 1)(y
41
+ 27y
40
+ ··· 82y 1)
(y
46
5y
45
+ ··· + 23412y + 1369)
c
4
(y
17
8y
16
+ ··· + 4y 1)(y
41
6y
40
+ ··· + 4637y 361)
(y
46
13y
45
+ ··· + 4820y + 121)
c
6
(y
17
7y
16
+ ··· + y 1)(y
41
+ 27y
40
+ ··· 82y 1)
(y
46
5y
45
+ ··· + 23412y + 1369)
c
7
, c
11
(y
17
+ 17y
16
+ ··· 8y 1)(y
41
+ 40y
40
+ ··· 87y 4)
(y
46
+ 46y
45
+ ··· 24y + 1)
c
8
(y
17
8y
16
+ ··· + 4y 1)(y
41
6y
40
+ ··· + 4637y 361)
(y
46
13y
45
+ ··· + 4820y + 121)
c
9
(y
17
+ 6y
16
+ ··· + 7y 1)(y
41
24y
40
+ ··· + 96y 1)
(y
46
+ 7y
45
+ ··· + 16y + 1)
c
10
(y
17
+ 17y
16
+ ··· 8y 1)(y
41
+ 40y
40
+ ··· 87y 4)
(y
46
+ 46y
45
+ ··· 24y + 1)
17