11a
326
(K11a
326
)
1
Arc Sequences
10 6 1 8 9 2 4 11 3 7 5
Solving Sequence
3,6
2
7,10
11 1 4 9 5 8
c
2
c
6
c
10
c
1
c
3
c
9
c
5
c
8
c
4
, c
7
, c
11
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
22
+ 6u
20
+ ··· + 3u 1, 311058123u
21
50616715u
20
+ ··· + 462381937b 8437483,
616215260u
21
+ 9916634u
20
+ ··· + 462381937a + 572933757i
I
u
2
= hu
106
+ 3u
105
+ ··· + 19u 1,
1.39236 × 10
318
u
105
4.25978 × 10
318
u
104
+ ··· + 4.43640 × 10
318
b 1.00560 × 10
319
,
7.92637 × 10
317
u
105
2.62180 × 10
318
u
104
+ ··· + 3.41262 × 10
317
a 1.84851 × 10
318
i
There are 2 irreducible components with 128 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
22
+ 6u
20
+ · · · + 3u 1, 3.11 × 10
8
u
21
5.06 × 10
7
u
20
+ · · · + 4.62 ×
10
8
b 8.44 ×10
6
, 6.16×10
8
u
21
+9.92× 10
6
u
20
+· · ·+ 4.62 ×10
8
a +5.73 ×10
8
i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
10
=
1.33270u
21
0.0214468u
20
+ ··· + 16.3655u 1.23909
0.672730u
21
+ 0.109469u
20
+ ··· + 4.81158u + 0.0182479
a
11
=
0.696047u
21
0.161894u
20
+ ··· + 14.7684u 1.34848
0.715551u
21
+ 0.0211544u
20
+ ··· + 5.35065u + 0.268079
a
1
=
0.144867u
21
+ 0.978270u
20
+ ··· + 8.34464u 3.62987
0.0360791u
21
0.0309779u
20
+ ··· + 3.21453u 1.09114
a
4
=
1.70592u
21
0.186649u
20
+ ··· 13.7543u + 2.74226
0.421055u
21
0.0663724u
20
+ ··· 4.73592u + 0.397875
a
9
=
0.659968u
21
0.130916u
20
+ ··· + 11.5539u 1.25734
0.672730u
21
+ 0.109469u
20
+ ··· + 4.81158u + 0.0182479
a
5
=
0.260687u
21
0.718677u
20
+ ··· + 5.80976u + 1.01397
0.711817u
21
0.495571u
20
+ ··· + 2.41133u + 1.03330
a
8
=
1.53126u
21
0.483339u
20
+ ··· + 15.6276u 2.33995
0.416122u
21
+ 0.251675u
20
+ ··· + 6.97099u 0.324031
a
8
=
1.53126u
21
0.483339u
20
+ ··· + 15.6276u 2.33995
0.416122u
21
+ 0.251675u
20
+ ··· + 6.97099u 0.324031
(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 = 1.98925
a = 0.116796
b = 0.270895
5.42454 52.7847
u = 0.685709 0.044403I
a = 0.022521 + 0.524665I
b = 0.898671 + 0.630847I
0.20007 + 3.13940I 5.66733 4.39177I
u = 0.685709 + 0.044403I
a = 0.022521 0.524665I
b = 0.898671 0.630847I
0.20007 3.13940I 5.66733 + 4.39177I
u = 0.41396 1.41951I
a = 1.47000 + 0.10658I
b = 1.28210 + 0.79536I
4.93626 7.53570I 0.99061 + 3.53310I
u = 0.41396 + 1.41951I
a = 1.47000 0.10658I
b = 1.28210 0.79536I
4.93626 + 7.53570I 0.99061 3.53310I
u = 0.246048 0.886009I
a = 1.25931 + 1.49417I
b = 0.878783 0.282838I
3.59823 3.07145I 4.51954 + 4.54839I
u = 0.246048 + 0.886009I
a = 1.25931 1.49417I
b = 0.878783 + 0.282838I
3.59823 + 3.07145I 4.51954 4.54839I
u = 0.032705 1.338776I
a = 0.150619 0.181179I
b = 0.143457 1.012656I
2.36180 6.75752I 2.14760 + 5.66405I
u = 0.032705 + 1.338776I
a = 0.150619 + 0.181179I
b = 0.143457 + 1.012656I
2.36180 + 6.75752I 2.14760 5.66405I
u = 0.020675 1.210052I
a = 0.916160 0.468193I
b = 0.742004 + 0.587064I
5.49012 + 1.99940I 7.14235 2.66277I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.020675 + 1.210052I
a = 0.916160 + 0.468193I
b = 0.742004 0.587064I
5.49012 1.99940I 7.14235 + 2.66277I
u = 0.060765 1.259520I
a = 1.66722 0.24295I
b = 1.116408 + 0.119930I
5.20735 + 2.19424I 7.08492 2.83841I
u = 0.060765 + 1.259520I
a = 1.66722 + 0.24295I
b = 1.116408 0.119930I
5.20735 2.19424I 7.08492 + 2.83841I
u = 0.131904 0.260531I
a = 0.76146 3.92106I
b = 0.615723 1.055177I
2.91039 2.89939I 7.87662 + 2.74117I
u = 0.131904 + 0.260531I
a = 0.76146 + 3.92106I
b = 0.615723 + 1.055177I
2.91039 + 2.89939I 7.87662 2.74117I
u = 0.222746 0.907894I
a = 2.03946 1.59282I
b = 1.266432 0.461280I
0.36060 + 8.25334I 2.83947 7.63102I
u = 0.222746 + 0.907894I
a = 2.03946 + 1.59282I
b = 1.266432 + 0.461280I
0.36060 8.25334I 2.83947 + 7.63102I
u = 0.47367 1.40435I
a = 1.280778 + 0.175095I
b = 1.55280 0.85270I
2.55491 + 6.09609I 7.79395 10.16302I
u = 0.47367 + 1.40435I
a = 1.280778 0.175095I
b = 1.55280 + 0.85270I
2.55491 6.09609I 7.79395 + 10.16302I
u = 0.784102 0.072947I
a = 0.678691 + 0.020479I
b = 0.280288 + 0.262690I
0.275443 + 0.077477I 0.515061 + 1.191364I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.784102 + 0.072947I
a = 0.678691 0.020479I
b = 0.280288 0.262690I
0.275443 0.077477I 0.515061 1.191364I
u = 1.35835
a = 0.272613
b = 1.06465
2.53570 47.8658
4
II. I
u
2
= hu
106
+ 3u
105
+ · · · + 19u 1, 1.39 × 10
318
u
105
4.26 ×
10
318
u
104
+ · · · + 4.44 × 10
318
b 1.01 × 10
319
, 7.93 × 10
317
u
105
2.62 ×
10
318
u
104
+ · · · + 3.41 × 10
317
a 1.85 × 10
318
i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
7
=
u
u
3
+ u
a
10
=
2.32267u
105
+ 7.68268u
104
+ ··· 77.0561u + 5.41671
0.313848u
105
+ 0.960189u
104
+ ··· 28.1503u + 2.26670
a
11
=
1.94720u
105
+ 6.49173u
104
+ ··· 80.8911u + 5.76853
0.0903806u
105
+ 0.134570u
104
+ ··· 25.1663u + 1.97942
a
1
=
0.536095u
105
+ 0.763638u
104
+ ··· 218.875u + 17.7105
0.0757890u
105
+ 0.130522u
104
+ ··· 27.0376u + 2.47019
a
4
=
1.74444u
105
+ 5.31471u
104
+ ··· 231.801u + 15.2966
0.636229u
105
+ 2.00879u
104
+ ··· 43.7176u + 2.69763
a
9
=
2.00882u
105
+ 6.72249u
104
+ ··· 48.9057u + 3.15001
0.313848u
105
+ 0.960189u
104
+ ··· 28.1503u + 2.26670
a
5
=
1.45668u
105
4.17549u
104
+ ··· + 45.8949u 8.57048
0.300360u
105
1.16893u
104
+ ··· 4.12988u 0.387022
a
8
=
0.131397u
105
+ 0.259568u
104
+ ··· + 251.587u 13.5190
0.400537u
105
1.31079u
104
+ ··· + 39.8917u 2.14966
a
8
=
0.131397u
105
+ 0.259568u
104
+ ··· + 251.587u 13.5190
0.400537u
105
1.31079u
104
+ ··· + 39.8917u 2.14966
(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 = 1.32729
a = 0.326095
b = 1.12870
2.61066 60.1001
u = 1.216419 0.068761I
a = 0.122226 0.112703I
b = 0.768405 0.177790I
1.244554 0.367853I 7.95101 0.06945I
u = 1.216419 + 0.068761I
a = 0.122226 + 0.112703I
b = 0.768405 + 0.177790I
1.244554 + 0.367853I 7.95101 + 0.06945I
u = 1.190850 0.079603I
a = 0.0103139 + 0.0381641I
b = 0.959119 + 0.684372I
0.49934 12.68122I 1.17808 + 8.95575I
u = 1.190850 + 0.079603I
a = 0.0103139 0.0381641I
b = 0.959119 0.684372I
0.49934 + 12.68122I 1.17808 8.95575I
u = 0.988852 0.225632I
a = 0.526268 0.083150I
b = 0.571986 + 0.392628I
2.95995 0.48399I 7.58132 1.74898I
u = 0.988852 + 0.225632I
a = 0.526268 + 0.083150I
b = 0.571986 0.392628I
2.95995 + 0.48399I 7.58132 + 1.74898I
u = 0.799379 0.132865I
a = 0.308761 + 0.530180I
b = 0.757517 0.598819I
1.149224 0.819705I 5.79346 + 6.19362I
u = 0.799379 + 0.132865I
a = 0.308761 0.530180I
b = 0.757517 + 0.598819I
1.149224 + 0.819705I 5.79346 6.19362I
u = 0.701103 0.525072I
a = 0.191668 + 1.088294I
b = 1.120553 + 0.725615I
2.25902 + 4.46440I 3.75032 6.93016I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.701103 + 0.525072I
a = 0.191668 1.088294I
b = 1.120553 0.725615I
2.25902 4.46440I 3.75032 + 6.93016I
u = 0.692760 0.496513I
a = 0.078806 0.123174I
b = 0.509835 0.878093I
1.04735 4.26740I 3.86831 + 9.88506I
u = 0.692760 + 0.496513I
a = 0.078806 + 0.123174I
b = 0.509835 + 0.878093I
1.04735 + 4.26740I 3.86831 9.88506I
u = 0.631262 0.289324I
a = 0.428728 + 0.158961I
b = 0.306482 0.572159I
1.208000 0.625059I 7.37009 + 3.11596I
u = 0.631262 + 0.289324I
a = 0.428728 0.158961I
b = 0.306482 + 0.572159I
1.208000 + 0.625059I 7.37009 3.11596I
u = 0.600947 0.531433I
a = 0.932449 0.440471I
b = 0.115276 0.584261I
1.178379 + 0.043868I 5.59483 0.89889I
u = 0.600947 + 0.531433I
a = 0.932449 + 0.440471I
b = 0.115276 + 0.584261I
1.178379 0.043868I 5.59483 + 0.89889I
u = 0.57324 1.56752I
a = 0.543694 + 0.357317I
b = 0.882594 0.153067I
4.02884 + 5.89856I 6.07198 3.74399I
u = 0.57324 + 1.56752I
a = 0.543694 0.357317I
b = 0.882594 + 0.153067I
4.02884 5.89856I 6.07198 + 3.74399I
u = 0.53778 1.43935I
a = 0.974047 0.276594I
b = 0.931840 + 0.520260I
5.80499 6.00260I 5.72530 + 6.45441I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.53778 + 1.43935I
a = 0.974047 + 0.276594I
b = 0.931840 0.520260I
5.80499 + 6.00260I 5.72530 6.45441I
u = 0.53305 1.41069I
a = 1.52613 + 0.08254I
b = 1.39554 1.05056I
4.1975 18.6893I 0.90155 + 9.61946I
u = 0.53305 + 1.41069I
a = 1.52613 0.08254I
b = 1.39554 + 1.05056I
4.1975 + 18.6893I 0.90155 9.61946I
u = 0.51635 1.40331I
a = 1.332899 + 0.183815I
b = 1.52570 1.11882I
2.22217 6.15586I 14.2393 + 15.8648I
u = 0.51635 + 1.40331I
a = 1.332899 0.183815I
b = 1.52570 + 1.11882I
2.22217 + 6.15586I 14.2393 15.8648I
u = 0.50858 1.42395I
a = 1.284313 0.199332I
b = 1.189530 + 0.588679I
6.08341 6.36617I 5.95100 + 2.75865I
u = 0.50858 + 1.42395I
a = 1.284313 + 0.199332I
b = 1.189530 0.588679I
6.08341 + 6.36617I 5.95100 2.75865I
u = 0.493513 1.087523I
a = 0.696366 0.086215I
b = 0.105701 0.295084I
0.32843 4.85662I 3.64745 + 4.90866I
u = 0.493513 + 1.087523I
a = 0.696366 + 0.086215I
b = 0.105701 + 0.295084I
0.32843 + 4.85662I 3.64745 4.90866I
u = 0.470101 1.319378I
a = 1.091906 + 0.574427I
b = 1.60385 0.08129I
3.09477 5.46170I 9.11752 + 5.59449I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.470101 + 1.319378I
a = 1.091906 0.574427I
b = 1.60385 + 0.08129I
3.09477 + 5.46170I 9.11752 5.59449I
u = 0.406727 1.097531I
a = 1.71248 + 0.36450I
b = 0.625733 0.824713I
1.61482 3.62256I 4.03032 + 6.19652I
u = 0.406727 + 1.097531I
a = 1.71248 0.36450I
b = 0.625733 + 0.824713I
1.61482 + 3.62256I 4.03032 6.19652I
u = 0.374861 0.992057I
a = 2.21826 0.55212I
b = 1.99480 + 0.51836I
0.83829 8.68306I 4.09342 + 11.16799I
u = 0.374861 + 0.992057I
a = 2.21826 + 0.55212I
b = 1.99480 0.51836I
0.83829 + 8.68306I 4.09342 11.16799I
u = 0.35962 1.47520I
a = 1.40447 + 0.34708I
b = 1.23059 + 1.05452I
5.16254 8.34567I 4.74374 + 13.15510I
u = 0.35962 + 1.47520I
a = 1.40447 0.34708I
b = 1.23059 1.05452I
5.16254 + 8.34567I 4.74374 13.15510I
u = 0.316207 1.138555I
a = 1.259313 + 0.221509I
b = 0.882260 0.766558I
1.44043 2.95357I 2.89476 + 3.29252I
u = 0.316207 + 1.138555I
a = 1.259313 0.221509I
b = 0.882260 + 0.766558I
1.44043 + 2.95357I 2.89476 3.29252I
u = 0.113729 1.219746I
a = 1.40995 + 1.15814I
b = 0.726644 0.472380I
3.22712 8.49581I 5.57013 + 9.61676I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.113729 + 1.219746I
a = 1.40995 1.15814I
b = 0.726644 + 0.472380I
3.22712 + 8.49581I 5.57013 9.61676I
u = 0.102743 1.170900I
a = 1.92213 + 0.58353I
b = 1.151571 0.157014I
3.99548 3.56708I 3.32826 + 4.09486I
u = 0.102743 + 1.170900I
a = 1.92213 0.58353I
b = 1.151571 + 0.157014I
3.99548 + 3.56708I 3.32826 4.09486I
u = 0.054207 1.343778I
a = 1.199353 0.512320I
b = 1.36559 1.06037I
3.20451 4.04224I 4.87146 + 5.28209I
u = 0.054207 + 1.343778I
a = 1.199353 + 0.512320I
b = 1.36559 + 1.06037I
3.20451 + 4.04224I 4.87146 5.28209I
u = 0.031541 1.224943I
a = 1.57808 + 1.10464I
b = 1.83161 + 1.76546I
6.73950 2.12275I 14.7675 + 3.1818I
u = 0.031541 + 1.224943I
a = 1.57808 1.10464I
b = 1.83161 1.76546I
6.73950 + 2.12275I 14.7675 3.1818I
u = 0.023574 1.153232I
a = 1.40824 + 0.41746I
b = 0.90634 + 1.37571I
4.45667 + 0.16513I 5.03131 2.33793I
u = 0.023574 + 1.153232I
a = 1.40824 0.41746I
b = 0.90634 1.37571I
4.45667 0.16513I 5.03131 + 2.33793I
u = 0.0204907 0.1082278I
a = 6.53654 11.18411I
b = 0.967717 0.480107I
0.61540 7.55088I 2.60197 + 3.80824I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.0204907 + 0.1082278I
a = 6.53654 + 11.18411I
b = 0.967717 + 0.480107I
0.61540 + 7.55088I 2.60197 3.80824I
u = 0.004504 0.988733I
a = 0.315079 0.330456I
b = 0.50078 1.51754I
1.37131 2.82623I 1.44799 + 2.97770I
u = 0.004504 + 0.988733I
a = 0.315079 + 0.330456I
b = 0.50078 + 1.51754I
1.37131 + 2.82623I 1.44799 2.97770I
u = 0.016823 0.887495I
a = 1.97243 1.45010I
b = 0.975184 0.646919I
1.63192 + 3.20943I 0.38444 3.90703I
u = 0.016823 + 0.887495I
a = 1.97243 + 1.45010I
b = 0.975184 + 0.646919I
1.63192 3.20943I 0.38444 + 3.90703I
u = 0.065415 1.325978I
a = 1.27538 0.63900I
b = 0.665910 + 0.084742I
4.68399 + 3.43734I 3.40358 6.64123I
u = 0.065415 + 1.325978I
a = 1.27538 + 0.63900I
b = 0.665910 0.084742I
4.68399 3.43734I 3.40358 + 6.64123I
u = 0.068377 1.247174I
a = 1.37853 + 0.87229I
b = 0.771379 0.041317I
5.32826 0.34844I 6.51329 2.36514I
u = 0.068377 + 1.247174I
a = 1.37853 0.87229I
b = 0.771379 + 0.041317I
5.32826 + 0.34844I 6.51329 + 2.36514I
u = 0.077677 1.206178I
a = 1.68619 0.30262I
b = 0.977064 + 0.485797I
5.06946 + 0.97532I 4.14734 + 4.60251I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.077677 + 1.206178I
a = 1.68619 + 0.30262I
b = 0.977064 0.485797I
5.06946 0.97532I 4.14734 4.60251I
u = 0.095837 1.144677I
a = 0.86253 1.42437I
b = 0.510950 + 0.540666I
5.27080 + 3.32416I 7.75997 7.08041I
u = 0.095837 + 1.144677I
a = 0.86253 + 1.42437I
b = 0.510950 0.540666I
5.27080 3.32416I 7.75997 + 7.08041I
u = 0.101593 1.167758I
a = 1.24334 1.44830I
b = 1.44794 2.20911I
2.35723 + 8.34056I 4.82399 10.89303I
u = 0.101593 + 1.167758I
a = 1.24334 + 1.44830I
b = 1.44794 + 2.20911I
2.35723 8.34056I 4.82399 + 10.89303I
u = 0.145461 0.038298I
a = 4.87152 + 1.53021I
b = 0.686731 + 0.192242I
1.53431 + 0.08305I 7.93818 + 0.76201I
u = 0.145461 + 0.038298I
a = 4.87152 1.53021I
b = 0.686731 0.192242I
1.53431 0.08305I 7.93818 0.76201I
u = 0.147042 0.180501I
a = 5.11515 + 1.84087I
b = 0.702411 0.384809I
2.64028 2.19448I 0.848936 + 0.928898I
u = 0.147042 + 0.180501I
a = 5.11515 1.84087I
b = 0.702411 + 0.384809I
2.64028 + 2.19448I 0.848936 0.928898I
u = 0.156701 0.151110I
a = 1.21241 2.18071I
b = 0.934257 + 0.691915I
1.02581 + 2.96908I 6.06244 5.34743I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.156701 + 0.151110I
a = 1.21241 + 2.18071I
b = 0.934257 0.691915I
1.02581 2.96908I 6.06244 + 5.34743I
u = 0.175510 0.953433I
a = 1.51425 + 0.81029I
b = 0.389599 + 0.483666I
2.89668 + 0.78297I 2.75820 + 0.48427I
u = 0.175510 + 0.953433I
a = 1.51425 0.81029I
b = 0.389599 0.483666I
2.89668 0.78297I 2.75820 0.48427I
u = 0.186634 1.167288I
a = 2.13192 0.37046I
b = 1.77762 1.27346I
4.63424 + 5.02298I 7.93392 7.51170I
u = 0.186634 + 1.167288I
a = 2.13192 + 0.37046I
b = 1.77762 + 1.27346I
4.63424 5.02298I 7.93392 + 7.51170I
u = 0.311116 1.361004I
a = 1.69918 0.22324I
b = 1.46602 0.99946I
5.69514 + 5.75539I 6.61993 2.63042I
u = 0.311116 + 1.361004I
a = 1.69918 + 0.22324I
b = 1.46602 + 0.99946I
5.69514 5.75539I 6.61993 + 2.63042I
u = 0.357793 1.097088I
a = 2.14597 0.07710I
b = 0.567709 + 0.622795I
0.75293 + 9.92335I 1.55457 10.93864I
u = 0.357793 + 1.097088I
a = 2.14597 + 0.07710I
b = 0.567709 0.622795I
0.75293 9.92335I 1.55457 + 10.93864I
u = 0.398783 1.042842I
a = 1.58801 + 0.16903I
b = 0.659942 + 0.624132I
3.88026 + 0.66373I 5.26047 1.99477I
13
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.398783 + 1.042842I
a = 1.58801 0.16903I
b = 0.659942 0.624132I
3.88026 0.66373I 5.26047 + 1.99477I
u = 0.432345 0.999010I
a = 0.865851 0.039909I
b = 0.902968 + 1.032281I
0.74617 + 3.75338I 1.79947 4.15298I
u = 0.432345 + 0.999010I
a = 0.865851 + 0.039909I
b = 0.902968 1.032281I
0.74617 3.75338I 1.79947 + 4.15298I
u = 0.52181 1.39852I
a = 1.49604 0.13659I
b = 1.37408 + 1.06314I
8.0314 + 12.5109I 4.10688 8.00160I
u = 0.52181 + 1.39852I
a = 1.49604 + 0.13659I
b = 1.37408 1.06314I
8.0314 12.5109I 4.10688 + 8.00160I
u = 0.52411 1.59798I
a = 0.733847 0.202700I
b = 0.700537 0.864249I
1.17695 + 8.45492I 2.54896 11.80872I
u = 0.52411 + 1.59798I
a = 0.733847 + 0.202700I
b = 0.700537 + 0.864249I
1.17695 8.45492I 2.54896 + 11.80872I
u = 0.529524 1.272819I
a = 0.731030 + 0.686544I
b = 0.750585 0.301375I
5.06870 + 1.53215I 6.64698 + 0.06326I
u = 0.529524 + 1.272819I
a = 0.731030 0.686544I
b = 0.750585 + 0.301375I
5.06870 1.53215I 6.64698 0.06326I
u = 0.53425 1.33824I
a = 1.53258 + 0.24376I
b = 1.43103 0.58261I
4.86742 + 9.03960I 2.67654 11.09888I
14
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.53425 + 1.33824I
a = 1.53258 0.24376I
b = 1.43103 + 0.58261I
4.86742 9.03960I 2.67654 + 11.09888I
u = 0.53504 1.47340I
a = 0.726951 0.400186I
b = 1.097412 + 0.168495I
7.90856 0.24319I 8.57392 + 0.12237I
u = 0.53504 + 1.47340I
a = 0.726951 + 0.400186I
b = 1.097412 0.168495I
7.90856 + 0.24319I 8.57392 0.12237I
u = 0.568944 0.000711I
a = 0.504225 + 0.369748I
b = 0.845681 + 0.675804I
1.13963 + 2.56882I 0.16888 2.12016I
u = 0.568944 + 0.000711I
a = 0.504225 0.369748I
b = 0.845681 0.675804I
1.13963 2.56882I 0.16888 + 2.12016I
u = 0.704455 0.335430I
a = 0.230257 0.755369I
b = 0.496140 + 1.015630I
3.06693 5.91340I 5.33910 + 6.29314I
u = 0.704455 + 0.335430I
a = 0.230257 + 0.755369I
b = 0.496140 1.015630I
3.06693 + 5.91340I 5.33910 6.29314I
u = 0.758523 0.371148I
a = 0.1018867 0.0081553I
b = 0.199249 + 0.990047I
5.96051 + 3.62479I 8.74625 4.70123I
u = 0.758523 + 0.371148I
a = 0.1018867 + 0.0081553I
b = 0.199249 0.990047I
5.96051 3.62479I 8.74625 + 4.70123I
u = 0.801015 0.368704I
a = 0.809671 + 0.532522I
b = 0.097040 + 0.678675I
1.18628 + 0.97362I 4.69177 + 0.11830I
15
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.801015 + 0.368704I
a = 0.809671 0.532522I
b = 0.097040 0.678675I
1.18628 0.97362I 4.69177 0.11830I
u = 1.009822 0.111821I
a = 0.138217 0.405761I
b = 0.954539 0.430058I
0.96920 3.40112I 6.48267 + 7.68033I
u = 1.009822 + 0.111821I
a = 0.138217 + 0.405761I
b = 0.954539 + 0.430058I
0.96920 + 3.40112I 6.48267 7.68033I
u = 1.163591 0.066017I
a = 0.0598488 + 0.0640823I
b = 0.987786 0.628731I
3.40089 + 6.62997I 2.99121 7.64062I
u = 1.163591 + 0.066017I
a = 0.0598488 0.0640823I
b = 0.987786 + 0.628731I
3.40089 6.62997I 2.99121 + 7.64062I
u = 2.05765
a = 0.0115115
b = 0.377018
5.34489 47.9581
16
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
22
9u
21
+ ··· 11u + 1)(u
106
+ 8u
105
+ ··· 8867u 3445)
c
2
(u
22
+ 6u
20
+ ··· + 3u 1)(u
106
+ 3u
105
+ ··· + 19u 1)
c
3
(u
22
+ 3u
21
+ ··· + 2u + 1)(u
106
+ 10u
105
+ ··· + 35874u + 5203)
c
4
(u
22
+ u
21
+ ··· + u 1)(u
106
36u
104
+ ··· 191u 11)
c
5
(u
22
u
21
+ ··· + 2u + 1)(u
106
+ 4u
105
+ ··· + 9831064u + 2445611)
c
6
(u
22
+ 6u
20
+ ··· 3u 1)(u
106
+ 3u
105
+ ··· + 19u 1)
c
7
(u
22
u
21
+ ··· u 1)(u
106
36u
104
+ ··· 191u 11)
c
8
(u
22
+ 9u
21
+ ··· + 3u 1)(u
106
+ 4u
105
+ ··· + 31u 1)
c
9
(u
22
u
21
+ ··· u 1)(u
106
19u
104
+ ··· 97525u 19379)
c
10
(u
22
+ 3u
21
+ ··· + 21u 5)(u
106
22u
104
+ ··· + 40099u + 4897)
c
11
(u
22
+ u
21
+ ··· + 3u + 1)(u
106
+ 2u
105
+ ··· 5u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
22
3y
21
+ ··· 33y + 1)
(y
106
26y
105
+ ··· 349655619y + 11868025)
c
2
, c
6
(y
22
+ 12y
21
+ ··· + 15y + 1)(y
106
+ 73y
105
+ ··· + 93y + 1)
c
3
(y
22
13y
21
+ ··· + 8y + 1)
(y
106
+ 12y
105
+ ··· + 307328166y + 27071209)
c
4
(y
22
21y
21
+ ··· 9y + 1)(y
106
72y
105
+ ··· 20795y + 121)
c
5
(y
22
19y
21
+ ··· 16y + 1)
(y
106
62y
105
+ ··· 243034883661070y + 5981013163321)
c
7
(y
22
21y
21
+ ··· 9y + 1)(y
106
72y
105
+ ··· 20795y + 121)
c
8
(y
22
9y
21
+ ··· 19y + 1)(y
106
8y
105
+ ··· 345y + 1)
c
9
(y
22
11y
21
+ ··· 19y + 1)
(y
106
38y
105
+ ··· 3790134761y + 375545641)
c
10
(y
22
9y
21
+ ··· 371y + 25)
(y
106
44y
105
+ ··· 2051676353y + 23980609)
c
11
(y
22
+ 3y
21
+ ··· y + 1)(y
106
+ 84y
104
+ ··· 7y + 1)
18