11a
273
(K11a
273
)
1
Arc Sequences
8 6 1 11 2 10 3 4 7 5 9
Solving Sequence
6,10 3,7
8 2 1 5 11 4 9
c
6
c
7
c
2
c
1
c
5
c
10
c
4
c
9
c
3
, c
8
, c
11
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= h2b
2
b + 1, a + 1, u + 1i
I
u
2
= hu
20
4u
19
+ ··· 6u + 1, 7246464u
19
26199033u
18
+ ··· + 1332607b 14518963,
38612166u
19
138565656u
18
+ ··· + 1332607a 92519179i
I
u
3
= hu
101
u
100
+ ··· 8u + 21,
9.73666 × 10
318
u
100
+ 1.85069 × 10
319
u
99
+ ··· + 1.92786 × 10
320
b 6.81614 × 10
320
,
4.16542 × 10
319
u
100
+ 6.90912 × 10
319
u
99
+ ··· + 2.89179 × 10
320
a 1.40664 × 10
321
i
There are 3 irreducible components with 123 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
= h2b
2
b + 1, a + 1, u + 1i
(i) Arc colorings
a
6
=
0
1
a
10
=
1
b
a
3
=
1
0
a
7
=
1
b 1
a
8
=
b 2
b 1
a
2
=
1
1
a
1
=
b 1
b
a
5
=
1
0
a
11
=
b 1
b
a
4
=
1
2
b +
1
2
1
2
b
1
2
a
9
=
2
2b 1
a
9
=
2
2b 1
(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 = 1.00000
a = 1.00000
b = 0.250000 0.661438I
3.28987 10.53125 3.72059I
u = 1.00000
a = 1.00000
b = 0.250000 + 0.661438I
3.28987 10.53125 + 3.72059I
3
II.
I
u
2
= hu
20
4u
19
+ · · · 6u + 1, 7.25 × 10
6
u
19
2.62 × 10
7
u
18
+ · · · + 1.33 ×
10
6
b 1.45 ×10
7
, 3.86× 10
7
u
19
1.39× 10
8
u
18
+· · ·+ 1.33 ×10
6
a 9.25 ×10
7
i
(i) Arc colorings
a
6
=
0
u
a
10
=
28.9749u
19
+ 103.981u
18
+ ··· 253.849u + 69.4272
5.43781u
19
+ 19.6600u
18
+ ··· 40.7300u + 10.8952
a
3
=
1
0
a
7
=
0.860935u
19
0.266479u
18
+ ··· + 14.2497u 16.0693
7.22770u
19
+ 25.6947u
18
+ ··· 55.6062u + 15.1348
a
8
=
8.08863u
19
+ 25.4283u
18
+ ··· 41.3565u 0.934551
7.22770u
19
+ 25.6947u
18
+ ··· 55.6062u + 15.1348
a
2
=
1
u
2
a
1
=
24.5231u
19
90.1889u
18
+ ··· + 235.264u 73.7335
4.40164u
19
+ 16.2681u
18
+ ··· 40.5082u + 10.6198
a
5
=
u
u
3
+ u
a
11
=
33.3765u
19
+ 120.249u
18
+ ··· 294.357u + 81.0470
1.36215u
19
+ 4.54756u
18
+ ··· 3.85091u + 0.613833
a
4
=
8.18906u
19
26.8766u
18
+ ··· + 45.6742u 1.57337
7.13884u
19
26.3527u
18
+ ··· + 61.5972u 16.4995
a
9
=
57.0369u
19
204.840u
18
+ ··· + 497.439u 133.735
3.34366u
19
+ 11.3876u
18
+ ··· 21.0620u + 2.58247
a
9
=
57.0369u
19
204.840u
18
+ ··· + 497.439u 133.735
3.34366u
19
+ 11.3876u
18
+ ··· 21.0620u + 2.58247
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.172421 0.245057I
a = 0.364217 + 0.625295I
b = 0.225809 0.140096I
2.56410 0.84466I 9.03889 + 5.09380I
u = 1.172421 + 0.245057I
a = 0.364217 0.625295I
b = 0.225809 + 0.140096I
2.56410 + 0.84466I 9.03889 5.09380I
u = 0.837562 0.477147I
a = 1.138558 0.637661I
b = 1.31483 1.01127I
1.12249 + 4.07831I 8.09612 4.25313I
u = 0.837562 + 0.477147I
a = 1.138558 + 0.637661I
b = 1.31483 + 1.01127I
1.12249 4.07831I 8.09612 + 4.25313I
u = 0.836889 0.176338I
a = 0.366456 + 1.092928I
b = 3.11922 + 0.23868I
2.03342 + 0.46303I 9.6886 + 23.5396I
u = 0.836889 + 0.176338I
a = 0.366456 1.092928I
b = 3.11922 0.23868I
2.03342 0.46303I 9.6886 23.5396I
u = 0.105746 1.231280I
a = 0.590489 + 0.142713I
b = 2.23908 0.01689I
4.80980 + 0.48058I 2.92255 + 5.81288I
u = 0.105746 + 1.231280I
a = 0.590489 0.142713I
b = 2.23908 + 0.01689I
4.80980 0.48058I 2.92255 5.81288I
u = 0.221031 1.292420I
a = 0.840043 + 0.317328I
b = 1.43028 0.03404I
6.55589 + 1.90355I 0.93873 1.80301I
u = 0.221031 + 1.292420I
a = 0.840043 0.317328I
b = 1.43028 + 0.03404I
6.55589 1.90355I 0.93873 + 1.80301I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.414622 0.063326I
a = 0.62257 + 3.97162I
b = 0.594722 + 0.429876I
7.55275 + 4.43078I 7.56186 0.93053I
u = 0.414622 + 0.063326I
a = 0.62257 3.97162I
b = 0.594722 0.429876I
7.55275 4.43078I 7.56186 + 0.93053I
u = 0.559985 0.361635I
a = 0.985080 + 0.253796I
b = 2.38060 0.60521I
2.09736 7.25746I 5.4336 + 16.3698I
u = 0.559985 + 0.361635I
a = 0.985080 0.253796I
b = 2.38060 + 0.60521I
2.09736 + 7.25746I 5.4336 16.3698I
u = 0.920937 0.381458I
a = 1.26656 + 0.86155I
b = 0.362291 0.100203I
1.29205 1.53764I 1.05852 + 6.01902I
u = 0.920937 + 0.381458I
a = 1.26656 0.86155I
b = 0.362291 + 0.100203I
1.29205 + 1.53764I 1.05852 6.01902I
u = 1.28664 0.65541I
a = 0.780399 0.656824I
b = 1.54140 0.84346I
2.81189 8.50342I 2.16622 + 7.62575I
u = 1.28664 + 0.65541I
a = 0.780399 + 0.656824I
b = 1.54140 + 0.84346I
2.81189 + 8.50342I 2.16622 7.62575I
u = 1.54941 0.10551I
a = 0.053437 + 0.258079I
b = 0.232634 + 0.881750I
2.78821 5.63151I 8.69462 + 3.84058I
u = 1.54941 + 0.10551I
a = 0.053437 0.258079I
b = 0.232634 0.881750I
2.78821 + 5.63151I 8.69462 3.84058I
6
III. I
u
3
= hu
101
u
100
+ · · · 8u + 21, 9.74 × 10
318
u
100
+ 1.85 ×
10
319
u
99
+ · · · + 1.93 × 10
320
b 6.82 × 10
320
, 4.17 × 10
319
u
100
+ 6.91 ×
10
319
u
99
+ · · · + 2.89 × 10
320
a 1.41 × 10
321
i
(i) Arc colorings
a
6
=
0
u
a
10
=
0.144043u
100
0.238922u
99
+ ··· 8.25773u + 4.86425
0.0505049u
100
0.0959970u
99
+ ··· + 0.331053u + 3.53560
a
3
=
1
0
a
7
=
0.0818995u
100
+ 0.131157u
99
+ ··· + 2.64390u 1.55314
0.131208u
100
0.198713u
99
+ ··· 6.47167u + 4.67340
a
8
=
0.0493081u
100
0.0675557u
99
+ ··· 3.82777u + 3.12026
0.131208u
100
0.198713u
99
+ ··· 6.47167u + 4.67340
a
2
=
1
u
2
a
1
=
0.241696u
100
0.361217u
99
+ ··· 15.3423u + 8.20929
0.0863851u
100
0.124875u
99
+ ··· 3.00954u + 1.30021
a
5
=
u
u
3
+ u
a
11
=
0.210967u
100
0.344136u
99
+ ··· 11.9562u + 7.04927
0.00504266u
100
0.0215908u
99
+ ··· + 2.31782u + 2.15468
a
4
=
0.152032u
100
+ 0.211868u
99
+ ··· + 12.9626u 6.91916
0.152299u
100
+ 0.217869u
99
+ ··· + 7.66986u 5.91661
a
9
=
0.0303781u
100
0.0492432u
99
+ ··· + 1.01729u + 1.14772
0.0379441u
100
+ 0.0473087u
99
+ ··· + 5.97255u + 0.135355
a
9
=
0.0303781u
100
0.0492432u
99
+ ··· + 1.01729u + 1.14772
0.0379441u
100
+ 0.0473087u
99
+ ··· + 5.97255u + 0.135355
(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 = 1.361172 0.133199I
a = 0.078067 0.570277I
b = 0.512011 + 0.109339I
1.71389 0.48354I 0.074684 + 0.673574I
u = 1.361172 + 0.133199I
a = 0.078067 + 0.570277I
b = 0.512011 0.109339I
1.71389 + 0.48354I 0.074684 0.673574I
u = 1.333447 0.274691I
a = 0.333278 + 0.615902I
b = 0.005963 + 0.528650I
3.20074 2.34746I 7.10926 + 6.82461I
u = 1.333447 + 0.274691I
a = 0.333278 0.615902I
b = 0.005963 0.528650I
3.20074 + 2.34746I 7.10926 6.82461I
u = 1.33076 0.84351I
a = 0.719794 + 0.513172I
b = 1.64575 + 1.10210I
3.83195 + 8.38721I 4.59719 8.67477I
u = 1.33076 + 0.84351I
a = 0.719794 0.513172I
b = 1.64575 1.10210I
3.83195 8.38721I 4.59719 + 8.67477I
u = 1.31453 0.55652I
a = 0.820759 + 0.679621I
b = 1.21887 + 0.72971I
1.84072 + 8.55312I 10.2259 9.9993I
u = 1.31453 + 0.55652I
a = 0.820759 0.679621I
b = 1.21887 0.72971I
1.84072 8.55312I 10.2259 + 9.9993I
u = 1.26307 0.75138I
a = 0.877319 0.553150I
b = 1.88398 1.00126I
3.9285 + 18.4008I 3.05565 9.73700I
u = 1.26307 + 0.75138I
a = 0.877319 + 0.553150I
b = 1.88398 + 1.00126I
3.9285 18.4008I 3.05565 + 9.73700I
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.168869 0.454140I
a = 0.612471 0.252497I
b = 0.035449 0.331779I
0.00702 + 3.32914I 6.84099 4.86309I
u = 1.168869 + 0.454140I
a = 0.612471 + 0.252497I
b = 0.035449 + 0.331779I
0.00702 3.32914I 6.84099 + 4.86309I
u = 1.164454 0.593434I
a = 0.655954 0.422201I
b = 1.44335 0.86354I
2.72612 + 2.16280I 9.45697 0.57028I
u = 1.164454 + 0.593434I
a = 0.655954 + 0.422201I
b = 1.44335 + 0.86354I
2.72612 2.16280I 9.45697 + 0.57028I
u = 1.14364
a = 0.100251
b = 0.547588
1.94160 2.90121
u = 1.094723 0.541791I
a = 0.878021 + 0.680182I
b = 0.092673 0.221133I
0.40633 + 11.38169I 5.18682 8.13192I
u = 1.094723 + 0.541791I
a = 0.878021 0.680182I
b = 0.092673 + 0.221133I
0.40633 11.38169I 5.18682 + 8.13192I
u = 1.081338 0.153780I
a = 0.815760 0.421824I
b = 0.003411 + 0.779985I
3.61554 0.53392I 18.1773 + 6.5335I
u = 1.081338 + 0.153780I
a = 0.815760 + 0.421824I
b = 0.003411 0.779985I
3.61554 + 0.53392I 18.1773 6.5335I
u = 1.051071 0.490677I
a = 0.898180 0.872397I
b = 1.45747 + 0.08616I
6.12272 1.23674I 0.626481 + 1.047357I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.051071 + 0.490677I
a = 0.898180 + 0.872397I
b = 1.45747 0.08616I
6.12272 + 1.23674I 0.626481 1.047357I
u = 1.030082 0.379499I
a = 0.532850 0.907751I
b = 1.87787 1.33471I
0.75196 + 1.66188I 3.50012 + 2.55507I
u = 1.030082 + 0.379499I
a = 0.532850 + 0.907751I
b = 1.87787 + 1.33471I
0.75196 1.66188I 3.50012 2.55507I
u = 0.946347 0.283313I
a = 1.32658 0.79713I
b = 0.357049 0.264722I
1.62429 + 1.14001I 13.19922 + 4.57286I
u = 0.946347 + 0.283313I
a = 1.32658 + 0.79713I
b = 0.357049 + 0.264722I
1.62429 1.14001I 13.19922 4.57286I
u = 0.916650 0.501453I
a = 1.043097 + 0.804117I
b = 1.63669 + 1.35000I
0.50891 + 4.92178I 4.79399 10.08944I
u = 0.916650 + 0.501453I
a = 1.043097 0.804117I
b = 1.63669 1.35000I
0.50891 4.92178I 4.79399 + 10.08944I
u = 0.898621 0.192907I
a = 0.334552 + 0.978954I
b = 3.24842 0.62252I
1.92376 + 0.50897I 47.5709 + 5.6468I
u = 0.898621 + 0.192907I
a = 0.334552 0.978954I
b = 3.24842 + 0.62252I
1.92376 0.50897I 47.5709 5.6468I
u = 0.849844 0.576194I
a = 0.730973 + 0.423233I
b = 1.01460 + 1.23549I
1.30478 + 2.43791I 7.78536 3.01979I
10
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.849844 + 0.576194I
a = 0.730973 0.423233I
b = 1.01460 1.23549I
1.30478 2.43791I 7.78536 + 3.01979I
u = 0.729051 0.494950I
a = 0.377452 1.008227I
b = 1.65150 0.11419I
0.051694 0.795294I 5.51068 + 2.54673I
u = 0.729051 + 0.494950I
a = 0.377452 + 1.008227I
b = 1.65150 + 0.11419I
0.051694 + 0.795294I 5.51068 2.54673I
u = 0.613912 0.069626I
a = 0.34440 1.59384I
b = 1.48386 1.13833I
2.80969 0.46563I 4.32235 1.19351I
u = 0.613912 + 0.069626I
a = 0.34440 + 1.59384I
b = 1.48386 + 1.13833I
2.80969 + 0.46563I 4.32235 + 1.19351I
u = 0.583047 0.341702I
a = 1.12346 + 2.37459I
b = 0.618051 + 0.484478I
7.77259 + 4.99480I 1.36077 11.66122I
u = 0.583047 + 0.341702I
a = 1.12346 2.37459I
b = 0.618051 0.484478I
7.77259 4.99480I 1.36077 + 11.66122I
u = 0.46375 1.48673I
a = 0.651700 0.362170I
b = 1.73737 0.05493I
6.73436 0.42071I 3.32320 0.50940I
u = 0.46375 + 1.48673I
a = 0.651700 + 0.362170I
b = 1.73737 + 0.05493I
6.73436 + 0.42071I 3.32320 + 0.50940I
u = 0.454110 1.241827I
a = 0.775477 + 0.655506I
b = 1.66585 + 0.00822I
6.55585 11.40725I 0.73029 + 7.08213I
11
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.454110 + 1.241827I
a = 0.775477 0.655506I
b = 1.66585 0.00822I
6.55585 + 11.40725I 0.73029 7.08213I
u = 0.345087 0.548844I
a = 0.451674 + 1.242646I
b = 1.218296 0.284005I
2.53838 6.84507I 2.77683 + 3.78330I
u = 0.345087 + 0.548844I
a = 0.451674 1.242646I
b = 1.218296 + 0.284005I
2.53838 + 6.84507I 2.77683 3.78330I
u = 0.315729 0.254943I
a = 1.001382 0.220287I
b = 0.437899 + 0.452467I
0.846080 + 0.799596I 7.63536 5.31715I
u = 0.315729 + 0.254943I
a = 1.001382 + 0.220287I
b = 0.437899 0.452467I
0.846080 0.799596I 7.63536 + 5.31715I
u = 0.158223 0.759419I
a = 0.284192 + 0.748126I
b = 0.561727 0.132405I
0.18427 + 2.75704I 5.69129 3.15816I
u = 0.158223 + 0.759419I
a = 0.284192 0.748126I
b = 0.561727 + 0.132405I
0.18427 2.75704I 5.69129 + 3.15816I
u = 0.092103 1.292002I
a = 0.550823 0.043635I
b = 2.07761 + 0.20904I
4.69490 + 0.90727I 2.61899 10.38125I
u = 0.092103 + 1.292002I
a = 0.550823 + 0.043635I
b = 2.07761 0.20904I
4.69490 0.90727I 2.61899 + 10.38125I
u = 0.100348 0.818854I
a = 1.088305 + 0.691451I
b = 1.77202 + 0.06110I
1.49835 + 6.68804I 1.72474 6.98621I
12
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.100348 + 0.818854I
a = 1.088305 0.691451I
b = 1.77202 0.06110I
1.49835 6.68804I 1.72474 + 6.98621I
u = 0.165088 0.329292I
a = 1.08471 2.03866I
b = 0.509979 + 0.455873I
0.18393 + 2.19511I 5.16572 4.08072I
u = 0.165088 + 0.329292I
a = 1.08471 + 2.03866I
b = 0.509979 0.455873I
0.18393 2.19511I 5.16572 + 4.08072I
u = 0.245911 1.026020I
a = 1.207172 + 0.103115I
b = 1.168548 + 0.705543I
6.36070 3.12946I 1.98397 + 7.58733I
u = 0.245911 + 1.026020I
a = 1.207172 0.103115I
b = 1.168548 0.705543I
6.36070 + 3.12946I 1.98397 7.58733I
u = 0.265912 0.216702I
a = 1.167255 0.414893I
b = 1.94967 0.91165I
2.27749 6.83721I 1.32361 + 0.76248I
u = 0.265912 + 0.216702I
a = 1.167255 + 0.414893I
b = 1.94967 + 0.91165I
2.27749 + 6.83721I 1.32361 0.76248I
u = 0.285861 0.588825I
a = 1.48337 0.48993I
b = 1.57311 + 0.27137I
3.64603 + 1.09291I 2.86206 2.09431I
u = 0.285861 + 0.588825I
a = 1.48337 + 0.48993I
b = 1.57311 0.27137I
3.64603 1.09291I 2.86206 + 2.09431I
u = 0.377834 0.906188I
a = 1.13471 0.91965I
b = 1.45597 + 0.10180I
4.23278 + 3.89315I 2.97786 5.50198I
13
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.377834 + 0.906188I
a = 1.13471 + 0.91965I
b = 1.45597 0.10180I
4.23278 3.89315I 2.97786 + 5.50198I
u = 0.392606 0.625339I
a = 0.004498 + 0.732882I
b = 0.723655 + 0.156233I
3.80282 + 0.02260I 0.528964 0.458699I
u = 0.392606 + 0.625339I
a = 0.004498 0.732882I
b = 0.723655 0.156233I
3.80282 0.02260I 0.528964 + 0.458699I
u = 0.443677 0.469538I
a = 1.63372 1.79428I
b = 0.958282 0.859125I
8.17127 + 4.22535I 4.33881 + 0.83044I
u = 0.443677 + 0.469538I
a = 1.63372 + 1.79428I
b = 0.958282 + 0.859125I
8.17127 4.22535I 4.33881 0.83044I
u = 0.561094 1.263435I
a = 0.657194 + 0.555042I
b = 1.57378 + 0.39724I
7.34821 + 2.77790I 3.91645 6.77366I
u = 0.561094 + 1.263435I
a = 0.657194 0.555042I
b = 1.57378 0.39724I
7.34821 2.77790I 3.91645 + 6.77366I
u = 0.629150 0.715151I
a = 0.715185 + 1.188980I
b = 0.621645 + 0.413985I
6.20705 0.67372I 1.44384 + 3.03787I
u = 0.629150 + 0.715151I
a = 0.715185 1.188980I
b = 0.621645 0.413985I
6.20705 + 0.67372I 1.44384 3.03787I
u = 0.877763 0.436514I
a = 1.23168 0.95729I
b = 0.453667 + 0.444178I
2.09103 1.79734I 11.98843 + 5.51665I
14
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.877763 + 0.436514I
a = 1.23168 + 0.95729I
b = 0.453667 0.444178I
2.09103 + 1.79734I 11.98843 5.51665I
u = 0.902489 0.756069I
a = 1.009086 + 0.061357I
b = 1.62187 + 0.82163I
0.02059 5.96503I 7.49624 + 7.45250I
u = 0.902489 + 0.756069I
a = 1.009086 0.061357I
b = 1.62187 0.82163I
0.02059 + 5.96503I 7.49624 7.45250I
u = 0.915965 0.599718I
a = 0.369737 1.091364I
b = 0.441158 + 0.142319I
0.156931 + 0.687508I 5.34460 3.08579I
u = 0.915965 + 0.599718I
a = 0.369737 + 1.091364I
b = 0.441158 0.142319I
0.156931 0.687508I 5.34460 + 3.08579I
u = 0.983392 0.618220I
a = 0.967390 0.429807I
b = 1.52767 0.04858I
5.13070 4.43406I 0.37002 + 4.96767I
u = 0.983392 + 0.618220I
a = 0.967390 + 0.429807I
b = 1.52767 + 0.04858I
5.13070 + 4.43406I 0.37002 4.96767I
u = 1.031922 0.315360I
a = 0.927247 + 0.843561I
b = 1.20456 + 0.78320I
2.28947 4.75466I 12.3895 + 7.4083I
u = 1.031922 + 0.315360I
a = 0.927247 0.843561I
b = 1.20456 0.78320I
2.28947 + 4.75466I 12.3895 7.4083I
u = 1.062013 0.544856I
a = 0.555092 + 0.500242I
b = 0.360118 + 0.105253I
1.91279 4.66251I 2.68730 + 5.27410I
15
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.062013 + 0.544856I
a = 0.555092 0.500242I
b = 0.360118 0.105253I
1.91279 + 4.66251I 2.68730 5.27410I
u = 1.099837 0.497352I
a = 0.658065 + 0.857069I
b = 1.90449 0.17262I
6.12003 8.35828I 0.40464 + 8.00095I
u = 1.099837 + 0.497352I
a = 0.658065 0.857069I
b = 1.90449 + 0.17262I
6.12003 + 8.35828I 0.40464 8.00095I
u = 1.117407 0.041834I
a = 0.973283 + 0.290540I
b = 0.264344 + 0.035785I
4.76348 1.49515I 16.4972 + 4.3512I
u = 1.117407 + 0.041834I
a = 0.973283 0.290540I
b = 0.264344 0.035785I
4.76348 + 1.49515I 16.4972 4.3512I
u = 1.117635 0.747660I
a = 0.419014 0.476873I
b = 1.65245 + 0.11493I
3.94300 3.16462I 1.25002 + 4.22395I
u = 1.117635 + 0.747660I
a = 0.419014 + 0.476873I
b = 1.65245 0.11493I
3.94300 + 3.16462I 1.25002 4.22395I
u = 1.126051 0.553731I
a = 0.661207 + 0.841331I
b = 1.24571 + 1.17879I
1.20250 5.71658I 2.72295 + 7.82087I
u = 1.126051 + 0.553731I
a = 0.661207 0.841331I
b = 1.24571 1.17879I
1.20250 + 5.71658I 2.72295 7.82087I
u = 1.134994 0.247699I
a = 0.495815 0.692962I
b = 0.70431 1.40706I
1.31820 + 3.86141I 5.84928 2.48248I
16
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.134994 + 0.247699I
a = 0.495815 + 0.692962I
b = 0.70431 + 1.40706I
1.31820 3.86141I 5.84928 + 2.48248I
u = 1.154093 0.639825I
a = 1.009557 + 0.701105I
b = 1.83334 + 0.82663I
1.90244 9.55301I 7.03928 + 11.89534I
u = 1.154093 + 0.639825I
a = 1.009557 0.701105I
b = 1.83334 0.82663I
1.90244 + 9.55301I 7.03928 11.89534I
u = 1.172909 0.542644I
a = 0.758411 0.698694I
b = 1.89532 1.31112I
1.48534 11.59499I 5.83853 + 9.65722I
u = 1.172909 + 0.542644I
a = 0.758411 + 0.698694I
b = 1.89532 + 1.31112I
1.48534 + 11.59499I 5.83853 9.65722I
u = 1.26083 0.76249I
a = 0.752543 0.510669I
b = 1.89741 0.80900I
4.91117 9.93167I 0.81661 + 8.53464I
u = 1.26083 + 0.76249I
a = 0.752543 + 0.510669I
b = 1.89741 + 0.80900I
4.91117 + 9.93167I 0.81661 8.53464I
u = 1.273989 0.318647I
a = 0.562561 + 0.324337I
b = 0.133596 0.333612I
4.60191 6.62398I 10.83270 + 5.35463I
u = 1.273989 + 0.318647I
a = 0.562561 0.324337I
b = 0.133596 + 0.333612I
4.60191 + 6.62398I 10.83270 5.35463I
u = 1.74884 0.04976I
a = 0.094780 0.491894I
b = 0.055440 0.420225I
2.00350 6.10245I 1.02242 + 7.34433I
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.74884 + 0.04976I
a = 0.094780 + 0.491894I
b = 0.055440 + 0.420225I
2.00350 + 6.10245I 1.02242 7.34433I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)
2
(u
20
+ 2u
19
+ ··· 10u
2
+ 1)(u
101
+ 3u
100
+ ··· + 4162u 679)
c
2
(u + 1)
2
(u
20
4u
19
+ ··· 6u + 1)(u
101
+ u
100
+ ··· 8u 21)
c
3
(2u
2
u + 1)(u
20
+ 8u
19
+ ··· + 2u
2
+ 1)(2u
101
+ 3u
100
+ ··· + 35u + 7)
c
4
(2u
2
u + 1)(u
20
+ 4u
19
+ ··· 8u + 1)
(2u
101
+ 5u
100
+ ··· 157973u 15557)
c
5
(u 1)
2
(u
20
+ 4u
19
+ ··· + 6u + 1)(u
101
+ u
100
+ ··· 8u 21)
c
6
(u + 1)
2
(u
20
+ 6u
19
+ ··· + 2u + 1)(u
101
+ 5u
100
+ ··· + 2016u 189)
c
7
(2u
2
3u + 2)(u
20
+ 6u
18
+ ··· + 7u + 5)
(2u
101
+ u
100
+ ··· 16872u + 3626)
c
8
(u
2
u + 2)(u
20
2u
18
+ ··· u
3
+ 1)(u
101
+ 2u
100
+ ··· + 4109u + 922)
c
9
(u 1)
2
(u
20
6u
19
+ ··· 2u + 1)(u
101
+ 5u
100
+ ··· + 2016u 189)
c
10
(2u
2
+ u + 1)(u
20
4u
19
+ ··· + 8u + 1)
(2u
101
+ 5u
100
+ ··· 157973u 15557)
c
11
u
2
(u
20
+ 4u
19
+ ··· + 71u + 7)(u
101
+ 7u
100
+ ··· + 278u + 48)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y 1)
2
(y
20
12y
19
+ ··· 20y + 1)
(y
101
3y
100
+ ··· 13847930y 461041)
c
2
, c
5
(y 1)
2
(y
20
8y
19
+ ··· 18y + 1)
(y
101
47y
100
+ ··· + 6868y 441)
c
3
(4y
2
+ 3y + 1)(y
20
14y
19
+ ··· + 4y + 1)
(4y
101
25y
100
+ ··· 1127y 49)
c
4
(4y
2
+ 3y + 1)(y
20
+ 6y
19
+ ··· 10y + 1)
(12y
101
+ 789y
100
+ ··· 7603957731y 726060747)
c
6
(y 1)
2
(y
20
+ 12y
19
+ ··· + 20y + 1)
(y
101
+ 57y
100
+ ··· + 1976562y 35721)
c
7
(4y
2
y + 4)(y
20
+ 12y
19
+ ··· + 11y + 25)
(4y
101
+ 11y
100
+ ··· + 641716604y 13147876)
c
8
(y
2
+ 3y + 4)(y
20
4y
19
+ ··· 12y
2
+ 1)
(y
101
18y
100
+ ··· + 29207333y 850084)
c
9
(y 1)
2
(y
20
+ 12y
19
+ ··· + 20y + 1)
(y
101
+ 57y
100
+ ··· + 1976562y 35721)
c
10
(4y
2
+ 3y + 1)(y
20
+ 6y
19
+ ··· 10y + 1)
(12y
101
+ 789y
100
+ ··· 7603957731y 726060747)
c
11
y
2
(y
20
18y
19
+ ··· 435y + 49)
(y
101
27y
100
+ ··· + 20068y 2304)
19