11n
184
(K11n
184
)
1
Arc Sequences
5 7 1 10 3 9 3 11 4 7 6
Solving Sequence
4,9 7,10
11 6 1 3 5 2 8
c
9
c
10
c
6
c
11
c
3
c
5
c
1
c
8
c
2
, c
4
, c
7
Representation Ideals
I =
5
\
i=1
I
u
i
I
u
1
= hu 1, b, a + 1i
I
u
2
= hb
2
2, u 1, b + a + 1i
I
u
3
= hu
18
u
17
+ ··· 83u 23,
6.29390 × 10
28
u
17
+ 7.78891 × 10
28
u
16
+ ··· + 2.04566 × 10
30
b + 6.03173 × 10
30
,
2.66337 × 10
30
u
17
2.65139 × 10
30
u
16
+ ··· + 4.70503 × 10
31
a 1.83610 × 10
32
i
I
u
4
= hu
28
+ 3u
27
+ ··· 125u + 17,
4.79286 × 10
45
u
27
+ 1.78737 × 10
46
u
26
+ ··· + 1.41493 × 10
47
b + 2.94581 × 10
47
,
2.57383 × 10
48
u
27
7.90436 × 10
48
u
26
+ ··· + 2.40537 × 10
48
a + 1.28302 × 10
50
i
I
u
5
= hu
36
4u
35
+ ··· + 6947u 251,
1.60478 × 10
113
u
35
+ 5.79166 × 10
113
u
34
+ ··· + 3.54731 × 10
115
b 1.20162 × 10
116
,
3.26903 × 10
115
u
35
1.20817 × 10
116
u
34
+ ··· + 1.78075 × 10
117
a + 7.32432 × 10
118
i
There are 5 irreducible components with 85 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 1, b, a + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
1
0
a
7
=
0
1
a
10
=
1
0
a
11
=
1
1
a
6
=
1
1
a
1
=
1
1
a
3
=
0
1
a
5
=
1
0
a
2
=
0
1
a
8
=
0
1
a
8
=
0
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
3.28987 12.0000
3
II. I
u
2
= hb
2
2, u 1, b + a + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
b 1
b
a
7
=
0
1
a
10
=
1
b
a
11
=
1
b 1
a
6
=
2b + 3
b 1
a
1
=
1
b 1
a
3
=
b
2b 3
a
5
=
b + 1
2
a
2
=
b
b 3
a
8
=
2
3b 3
a
8
=
2
3b 3
(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 = 1.00000
a = 0.414214
b = 1.41421
3.28987 44.0000
u = 1.00000
a = 2.41421
b = 1.41421
3.28987 44.0000
5
III. I
u
3
=
hu
18
u
17
+· · ·83u23, 6.29×10
28
u
17
+7.79×10
28
u
16
+· · ·+2.05×10
30
b+
6.03 × 10
30
, 2.66 × 10
30
u
17
2.65 × 10
30
u
16
+ · · · + 4.71 × 10
31
a 1.84 × 10
32
i
(i) Arc colorings
a
4
=
1
0
a
9
=
0.0566070u
17
+ 0.0563523u
16
+ ··· 9.44672u + 3.90242
0.0307670u
17
0.0380752u
16
+ ··· + 4.32161u 2.94855
a
7
=
0
u
a
10
=
0.0258400u
17
+ 0.0182771u
16
+ ··· 5.12511u + 0.953870
0.0307670u
17
0.0380752u
16
+ ··· + 4.32161u 2.94855
a
11
=
0.0258400u
17
+ 0.0182771u
16
+ ··· 5.12511u + 0.953870
0.0270755u
17
0.0300346u
16
+ ··· + 3.09957u 3.12249
a
6
=
0.0203844u
17
0.0465566u
16
+ ··· + 8.34647u 2.28178
0.00506377u
17
+ 0.0213564u
16
+ ··· 0.784984u + 1.85838
a
1
=
0.0000370538u
17
+ 0.0218509u
16
+ ··· 3.58871u + 1.52433
0.0395595u
17
0.0476383u
16
+ ··· + 3.12669u 3.93922
a
3
=
0.0575043u
17
+ 0.0787965u
16
+ ··· 5.74565u + 8.16136
0.0806359u
17
0.0971476u
16
+ ··· + 3.85683u 7.19376
a
5
=
0.0313879u
17
+ 0.0313655u
16
+ ··· + 1.52654u + 5.36444
0.0494111u
17
0.0544972u
16
+ ··· + 1.90750u 4.12685
a
2
=
0.0575043u
17
+ 0.0787965u
16
+ ··· 5.74565u + 8.16136
0.0835851u
17
0.0956861u
16
+ ··· + 3.41218u 7.68348
a
8
=
0.0789474u
17
+ 0.0939882u
16
+ ··· 7.25354u + 7.88993
0.0455677u
17
0.0598726u
16
+ ··· + 2.33159u 4.53145
a
8
=
0.0789474u
17
+ 0.0939882u
16
+ ··· 7.25354u + 7.88993
0.0455677u
17
0.0598726u
16
+ ··· + 2.33159u 4.53145
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 2.58784 1.47981I
a = 0.078364 0.177205I
b = 0.631814 + 0.103081I
1.92430 + 3.93083I 7.6382 13.9939I
u = 2.58784 + 1.47981I
a = 0.078364 + 0.177205I
b = 0.631814 0.103081I
1.92430 3.93083I 7.6382 + 13.9939I
u = 1.53928
a = 0.611253
b = 0.845186
5.14686 3.50430
u = 0.232302 0.025656I
a = 1.81397 1.20104I
b = 0.822250 + 0.912603I
2.29959 + 1.27814I 15.7772 13.4535I
u = 0.232302 + 0.025656I
a = 1.81397 + 1.20104I
b = 0.822250 0.912603I
2.29959 1.27814I 15.7772 + 13.4535I
u = 0.237029 1.026868I
a = 0.108161 0.908040I
b = 0.996123 + 0.550603I
1.46928 6.40624I 13.4313 + 7.0584I
u = 0.237029 + 1.026868I
a = 0.108161 + 0.908040I
b = 0.996123 0.550603I
1.46928 + 6.40624I 13.4313 7.0584I
u = 0.38613 2.10322I
a = 0.593638 + 0.368176I
b = 1.38034 0.42829I
6.06294 + 4.89735I 1.40550 2.57464I
u = 0.38613 + 2.10322I
a = 0.593638 0.368176I
b = 1.38034 + 0.42829I
6.06294 4.89735I 1.40550 + 2.57464I
u = 0.386681 0.868938I
a = 1.34559 + 0.73177I
b = 0.631814 0.103081I
1.92430 + 3.93083I 7.6382 13.9939I
7
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.386681 + 0.868938I
a = 1.34559 0.73177I
b = 0.631814 + 0.103081I
1.92430 3.93083I 7.6382 + 13.9939I
u = 0.445869 0.276885I
a = 2.94638 + 0.60643I
b = 0.822250 0.912603I
2.29959 + 1.27814I 15.7772 13.4535I
u = 0.445869 + 0.276885I
a = 2.94638 0.60643I
b = 0.822250 + 0.912603I
2.29959 1.27814I 15.7772 + 13.4535I
u = 0.700962 1.201847I
a = 0.301589 + 0.122856I
b = 1.38034 + 0.42829I
6.06294 + 4.89735I 1.40550 2.57464I
u = 0.700962 + 1.201847I
a = 0.301589 0.122856I
b = 1.38034 0.42829I
6.06294 4.89735I 1.40550 + 2.57464I
u = 0.77412 2.19584I
a = 0.644810 0.243274I
b = 0.996123 + 0.550603I
1.46928 + 6.40624I 13.4313 7.0584I
u = 0.77412 + 2.19584I
a = 0.644810 + 0.243274I
b = 0.996123 0.550603I
1.46928 6.40624I 13.4313 + 7.0584I
u = 2.31799
a = 0.917422
b = 0.845186
5.14686 3.50430
8
IV. I
u
4
=
hu
28
+3u
27
+· · ·125u+17, 4.79×10
45
u
27
+1.79×10
46
u
26
+· · ·+1.41×10
47
b+
2.95× 10
47
, 2.57 × 10
48
u
27
7.90 ×10
48
u
26
+· · · +2.41 ×10
48
a + 1.28× 10
50
i
(i) Arc colorings
a
4
=
1
0
a
9
=
1.07003u
27
+ 3.28612u
26
+ ··· + 337.294u 53.3398
0.0338736u
27
0.126322u
26
+ ··· + 2.66788u 2.08195
a
7
=
0
u
a
10
=
1.03616u
27
+ 3.15980u
26
+ ··· + 339.962u 55.4218
0.0338736u
27
0.126322u
26
+ ··· + 2.66788u 2.08195
a
11
=
1.03616u
27
+ 3.15980u
26
+ ··· + 339.962u 55.4218
0.153416u
27
0.550842u
26
+ ··· 8.53128u 2.95447
a
6
=
0.575962u
27
+ 1.63101u
26
+ ··· + 253.342u 47.9590
0.593887u
27
1.97693u
26
+ ··· 115.735u + 12.0035
a
1
=
0.646484u
27
2.07816u
26
+ ··· 159.429u + 18.8095
0.0760259u
27
0.111273u
26
+ ··· 80.4143u + 18.1906
a
3
=
0.969330u
27
2.81311u
26
+ ··· 384.472u + 69.1116
0.0968707u
27
+ 0.406344u
26
+ ··· 24.0363u + 9.79135
a
5
=
0.837132u
27
+ 3.09284u
26
+ ··· + 19.6620u + 21.6994
0.131042u
27
+ 0.380680u
26
+ ··· + 50.9563u 7.77398
a
2
=
0.969330u
27
+ 2.81311u
26
+ ··· + 384.472u 69.1116
0.0844514u
27
+ 0.211743u
26
+ ··· + 52.3746u 11.4043
a
8
=
0.963788u
27
+ 3.43540u
26
+ ··· + 75.0046u + 11.8074
0.757135u
27
+ 2.39383u
26
+ ··· + 209.166u 30.1609
a
8
=
0.963788u
27
+ 3.43540u
26
+ ··· + 75.0046u + 11.8074
0.757135u
27
+ 2.39383u
26
+ ··· + 209.166u 30.1609
(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 = 0.731240 0.064447I
a = 0.823313 0.952322I
b = 0.097920 0.715313I
4.52132 1.28199I 1.48628 + 3.62447I
u = 0.731240 + 0.064447I
a = 0.823313 + 0.952322I
b = 0.097920 + 0.715313I
4.52132 + 1.28199I 1.48628 3.62447I
u = 0.63877 2.06429I
a = 0.585474 0.449236I
b = 1.299883 + 0.322120I
2.44490 7.44961I 1.45384 + 5.70278I
u = 0.63877 + 2.06429I
a = 0.585474 + 0.449236I
b = 1.299883 0.322120I
2.44490 + 7.44961I 1.45384 5.70278I
u = 0.62953 2.23645I
a = 0.579647 + 0.369147I
b = 1.42770 0.62293I
8.0703 16.3840I 2.82061 + 8.06423I
u = 0.62953 + 2.23645I
a = 0.579647 0.369147I
b = 1.42770 + 0.62293I
8.0703 + 16.3840I 2.82061 8.06423I
u = 0.58519 1.57794I
a = 0.210407 0.074791I
b = 1.099022 + 0.606761I
7.22801 + 2.43402I 1.57040 0.59342I
u = 0.58519 + 1.57794I
a = 0.210407 + 0.074791I
b = 1.099022 0.606761I
7.22801 2.43402I 1.57040 + 0.59342I
u = 0.44223 1.70839I
a = 0.525393 + 0.471037I
b = 1.216128 + 0.158248I
8.36654 + 1.60580I 0.541797 0.240729I
u = 0.44223 + 1.70839I
a = 0.525393 0.471037I
b = 1.216128 0.158248I
8.36654 1.60580I 0.541797 + 0.240729I
10
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.377717 0.710971I
a = 0.17452 1.46846I
b = 0.014763 + 0.486702I
1.69684 + 4.08256I 6.58477 6.33725I
u = 0.377717 + 0.710971I
a = 0.17452 + 1.46846I
b = 0.014763 0.486702I
1.69684 4.08256I 6.58477 + 6.33725I
u = 0.244035 0.890628I
a = 0.228727 + 0.651636I
b = 0.892804 0.444060I
1.26054 + 1.72230I 0.40850 1.70276I
u = 0.244035 + 0.890628I
a = 0.228727 0.651636I
b = 0.892804 + 0.444060I
1.26054 1.72230I 0.40850 + 1.70276I
u = 0.05973 1.53422I
a = 0.473924 0.658984I
b = 0.802643 + 0.305370I
1.15395 + 4.47162I 7.14862 4.64379I
u = 0.05973 + 1.53422I
a = 0.473924 + 0.658984I
b = 0.802643 0.305370I
1.15395 4.47162I 7.14862 + 4.64379I
u = 0.238216 0.285105I
a = 3.55235 + 0.24485I
b = 0.062707 1.338023I
3.71060 + 9.58638I 3.92148 6.82839I
u = 0.238216 + 0.285105I
a = 3.55235 0.24485I
b = 0.062707 + 1.338023I
3.71060 9.58638I 3.92148 + 6.82839I
u = 0.251849 0.286150I
a = 1.59320 + 0.43835I
b = 0.218854 1.012420I
1.38872 + 0.92374I 4.94776 7.36786I
u = 0.251849 + 0.286150I
a = 1.59320 0.43835I
b = 0.218854 + 1.012420I
1.38872 0.92374I 4.94776 + 7.36786I
11
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.354448 1.303945I
a = 0.907226 + 0.089268I
b = 1.68545 + 0.44537I
9.49594 + 2.56707I 1.74205 3.34695I
u = 0.354448 + 1.303945I
a = 0.907226 0.089268I
b = 1.68545 0.44537I
9.49594 2.56707I 1.74205 + 3.34695I
u = 0.376402 0.040088I
a = 1.89008 + 1.03511I
b = 0.584905 0.590380I
1.36729 + 0.61050I 5.48708 0.91172I
u = 0.376402 + 0.040088I
a = 1.89008 1.03511I
b = 0.584905 + 0.590380I
1.36729 0.61050I 5.48708 + 0.91172I
u = 0.39643 2.55523I
a = 0.374449 + 0.114776I
b = 1.193668 0.454674I
7.75458 + 5.65256I 3.62489 8.19789I
u = 0.39643 + 2.55523I
a = 0.374449 0.114776I
b = 1.193668 + 0.454674I
7.75458 5.65256I 3.62489 + 8.19789I
u = 0.59110 1.65967I
a = 0.642460 0.003573I
b = 1.243004 + 0.278668I
2.92454 + 5.00287I 4.13660 6.40651I
u = 0.59110 + 1.65967I
a = 0.642460 + 0.003573I
b = 1.243004 0.278668I
2.92454 5.00287I 4.13660 + 6.40651I
12
V. I
u
5
= hu
36
4u
35
+ · · · + 6947u 251, 1.60 × 10
113
u
35
+ 5.79 ×
10
113
u
34
+ · · · + 3.55 × 10
115
b 1.20 × 10
116
, 3.27 × 10
115
u
35
1.21 ×
10
116
u
34
+ · · · + 1.78 × 10
117
a + 7.32 × 10
118
i
(i) Arc colorings
a
4
=
1
0
a
9
=
0.0183576u
35
+ 0.0678462u
34
+ ··· + 476.120u 41.1305
0.00452393u
35
0.0163269u
34
+ ··· 65.7623u + 3.38741
a
7
=
0
u
a
10
=
0.0138337u
35
+ 0.0515193u
34
+ ··· + 410.358u 37.7431
0.00452393u
35
0.0163269u
34
+ ··· 65.7623u + 3.38741
a
11
=
0.0138337u
35
+ 0.0515193u
34
+ ··· + 410.358u 37.7431
0.00342044u
35
0.0119163u
34
+ ··· 42.7286u + 2.42973
a
6
=
0.0212397u
35
0.0808632u
34
+ ··· 646.439u + 53.6809
0.00155932u
35
+ 0.00692705u
34
+ ··· + 67.5224u 3.77705
a
1
=
0.00497737u
35
+ 0.0218875u
34
+ ··· + 328.554u 28.7881
0.00146486u
35
0.00509672u
34
+ ··· 29.0936u + 1.76728
a
3
=
0.00361538u
35
0.0131803u
34
+ ··· 146.842u + 15.6730
0.00152183u
35
0.00499712u
34
+ ··· 5.99081u 0.140753
a
5
=
0.0124398u
35
0.0481132u
34
+ ··· 402.350u + 35.2077
0.00260825u
35
+ 0.0105195u
34
+ ··· + 76.3882u 3.80851
a
2
=
0.00361538u
35
+ 0.0131803u
34
+ ··· + 146.842u 15.6730
0.000438594u
35
+ 0.00141548u
34
+ ··· 2.00255u + 0.462346
a
8
=
0.00995392u
35
+ 0.0348670u
34
+ ··· + 169.876u 12.0464
0.00271014u
35
+ 0.00975590u
34
+ ··· + 35.9719u 1.16357
a
8
=
0.00995392u
35
+ 0.0348670u
34
+ ··· + 169.876u 12.0464
0.00271014u
35
+ 0.00975590u
34
+ ··· + 35.9719u 1.16357
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
13
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 2.55937 1.36105I
a = 0.0143120 0.0886356I
b = 0.629486 + 0.021587I
2.02553 + 3.59036I 0.89678 + 6.78897I
u = 2.55937 + 1.36105I
a = 0.0143120 + 0.0886356I
b = 0.629486 0.021587I
2.02553 3.59036I 0.89678 6.78897I
u = 1.08331
a = 0.318983
b = 1.35768
3.16853 23.1983
u = 0.79823 2.05730I
a = 0.520364 + 0.220406I
b = 1.42125 0.38509I
8.94298 7.76278I 0.81388 + 5.96589I
u = 0.79823 + 2.05730I
a = 0.520364 0.220406I
b = 1.42125 + 0.38509I
8.94298 + 7.76278I 0.81388 5.96589I
u = 0.67006 1.75253I
a = 0.651911 0.052080I
b = 1.32619
4.77670 0.191180
u = 0.67006 + 1.75253I
a = 0.651911 + 0.052080I
b = 1.32619
4.77670 0.191180
u = 0.605069 0.943581I
a = 0.556517 0.126671I
b = 1.60799 + 0.59422I
5.93656 5.69637I 3.56158 + 12.64720I
u = 0.605069 + 0.943581I
a = 0.556517 + 0.126671I
b = 1.60799 0.59422I
5.93656 + 5.69637I 3.56158 12.64720I
u = 0.59070 1.58922I
a = 0.979929 + 0.260708I
b = 1.42125 + 0.38509I
8.94298 + 7.76278I 0.81388 5.96589I
14
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.59070 + 1.58922I
a = 0.979929 0.260708I
b = 1.42125 0.38509I
8.94298 7.76278I 0.81388 + 5.96589I
u = 0.422925 1.232861I
a = 0.659000 + 0.587089I
b = 0.517954 0.930078I
3.10062 + 3.22877I 6.92519 4.57894I
u = 0.422925 + 1.232861I
a = 0.659000 0.587089I
b = 0.517954 + 0.930078I
3.10062 3.22877I 6.92519 + 4.57894I
u = 0.010873 0.481141I
a = 0.107938 + 0.595624I
b = 0.695159 0.848524I
2.09116 + 0.97054I 2.23750 + 5.32372I
u = 0.010873 + 0.481141I
a = 0.107938 0.595624I
b = 0.695159 + 0.848524I
2.09116 0.97054I 2.23750 5.32372I
u = 0.0598707
a = 21.0125
b = 0.853350
1.86607 5.91386
u = 0.285810 0.253999I
a = 3.60193 0.14308I
b = 0.695159 0.848524I
2.09116 + 0.97054I 2.23750 + 5.32372I
u = 0.285810 + 0.253999I
a = 3.60193 + 0.14308I
b = 0.695159 + 0.848524I
2.09116 0.97054I 2.23750 5.32372I
u = 0.32385 1.93426I
a = 0.705179 + 0.633171I
b = 1.60799 0.59422I
5.93656 + 5.69637I 3.56158 12.64720I
u = 0.32385 + 1.93426I
a = 0.705179 0.633171I
b = 1.60799 + 0.59422I
5.93656 5.69637I 3.56158 + 12.64720I
15
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.372405 0.956805I
a = 0.042108 + 0.763185I
b = 0.992764 0.622226I
0.99172 6.40330I 3.42158 + 6.30629I
u = 0.372405 + 0.956805I
a = 0.042108 0.763185I
b = 0.992764 + 0.622226I
0.99172 + 6.40330I 3.42158 6.30629I
u = 0.378089 0.480177I
a = 2.19832 + 0.70237I
b = 0.629486 + 0.021587I
2.02553 + 3.59036I 0.89678 + 6.78897I
u = 0.378089 + 0.480177I
a = 2.19832 0.70237I
b = 0.629486 0.021587I
2.02553 3.59036I 0.89678 6.78897I
u = 0.515425 0.175411I
a = 1.75121 0.23244I
b = 0.517954 0.930078I
3.10062 + 3.22877I 6.92519 4.57894I
u = 0.515425 + 0.175411I
a = 1.75121 + 0.23244I
b = 0.517954 + 0.930078I
3.10062 3.22877I 6.92519 + 4.57894I
u = 0.75620 2.15496I
a = 0.635527 0.225345I
b = 0.992764 + 0.622226I
0.99172 + 6.40330I 3.42158 6.30629I
u = 0.75620 + 2.15496I
a = 0.635527 + 0.225345I
b = 0.992764 0.622226I
0.99172 6.40330I 3.42158 + 6.30629I
u = 1.00473
a = 0.562627
b = 0.853350
1.86607 5.91386
u = 1.03221 2.16455I
a = 0.672914 + 0.205500I
b = 1.153562 0.127277I
4.01524 + 4.53987I 4.29652 4.59405I
16
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.03221 + 2.16455I
a = 0.672914 0.205500I
b = 1.153562 + 0.127277I
4.01524 4.53987I 4.29652 + 4.59405I
u = 1.09336
a = 2.15786
b = 1.35768
3.16853 23.1983
u = 1.47647
a = 0.631554
b = 0.714803
5.42967 25.4735
u = 1.64861 0.22586I
a = 0.523780 0.153130I
b = 1.153562 + 0.127277I
4.01524 4.53987I 4.29652 + 4.59405I
u = 1.64861 + 0.22586I
a = 0.523780 + 0.153130I
b = 1.153562 0.127277I
4.01524 + 4.53987I 4.29652 4.59405I
u = 2.13817
a = 0.969448
b = 0.714803
5.42967 25.4735
17
VI. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)
2
(u + 1)(u
18
6u
16
+ ··· + 13u 1)(u
28
u
27
+ ··· 303u + 49)
(u
36
+ u
35
+ ··· + 2025u + 675)
c
2
, c
7
(u)(u
2
2)(u
18
+ 4u
16
+ ··· + 9u
2
2)
(1 + 9u + 52u
2
+ 161u
3
+ 250u
4
+ 165u
5
+ 56u
6
38u
7
191u
8
49u
9
118u
10
+ 7u
11
u
12
+ 8u
13
+ 21u
14
+ u
15
+ 8u
16
+ u
18
)
2
(u
28
+ 3u
27
+ ··· 120u + 26)
c
3
(u + 1)(u
2
+ 2u 1)(u
18
+ 5u
17
+ ··· 8u 1)(u
28
+ u
27
+ ··· + u + 1)
(u
36
+ 4u
35
+ ··· + 8u + 1)
c
4
, c
9
u(u
2
2)
(7 + 3u + 40u
2
7u
3
88u
4
u
5
+ 102u
6
89u
8
+ 19u
9
+ 78u
10
21u
11
59u
12
+ 8u
13
+ 29u
14
u
15
8u
16
+ u
18
)
2
(u
18
6u
16
+ 19u
14
40u
12
+ 66u
10
82u
8
+ 76u
6
46u
4
+ 15u
2
2)
(u
28
+ 3u
27
+ ··· + 40u + 10)
c
5
(u 1)(u
2
2u 1)(u
18
u
15
+ ··· + 2u
2
1)(u
28
+ u
27
+ ··· 21u + 5)
(u
36
+ 7u
35
+ ··· 512u + 139)
c
6
(u 1)(u
2
2u 1)(u
18
5u
17
+ ··· + 8u 1)(u
28
+ u
27
+ ··· + u + 1)
(u
36
+ 4u
35
+ ··· + 8u + 1)
c
8
(u 1)(u
2
+ 2u 1)(u
18
+ u
15
+ ··· + 2u
2
1)(u
28
+ u
27
+ ··· 21u + 5)
(u
36
+ 7u
35
+ ··· 512u + 139)
c
10
(u + 1)
3
(u
18
6u
16
+ ··· 13u 1)(u
28
+ u
27
+ ··· + 303u + 49)
(u
36
u
35
+ ··· 2025u + 675)
c
11
u
3
(1 + 10u + 32u
2
+ 30u
3
30u
4
83u
5
74u
6
2u
7
+ 41u
8
66u
9
16u
10
+ 66u
11
+ 11u
12
19u
13
+ 15u
14
+ 7u
15
3u
16
+ u
18
)
2
(u
18
2u
16
+ 21u
14
+ 27u
10
174u
8
+ 205u
6
+ 30u
4
53u
2
32)
(u
28
+ 3u
27
+ ··· + 56u + 8)
18
VII. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
10
(y 1)
3
(y
18
12y
17
+ ··· 71y + 1)
(y
28
+ 29y
27
+ ··· 8019y + 2401)
(y
36
9y
35
+ ··· 2634525y + 455625)
c
2
, c
7
y(y 2)
2
(y
9
+ 4y
8
2y
7
22y
6
13y
5
+ 16y
4
3y
3
11y
2
+ 9y 2)
2
(1 + 23y + 306y
2
2779y
3
+ 1.55 × 10
4
y
4
6207y
5
7.64 × 10
4
y
6
6.81 × 10
4
y
7
+ 1.63 × 10
4
y
8
+ 5.15 × 10
4
y
9
+ 2.17 × 10
4
y
10
5579y
11
7913y
12
2390y
13
+ 173y
14
+ 333y
15
+ 106y
16
+ 16y
17
+ y
18
)
2
(y
28
+ 23y
27
+ ··· 1816y + 676)
c
3
, c
6
(y 1)(y
2
6y + 1)(y
18
7y
17
+ ··· 8y
2
+ 1)(y
28
+ y
27
+ ··· + 17y + 1)
(y
36
16y
35
+ ··· 18y + 1)
c
4
, c
9
y(y 2)
2
(y
9
6y
8
+ 19y
7
40y
6
+ 66y
5
82y
4
+ 76y
3
46y
2
+ 15y 2)
2
(49 569y + 2874y
2
8511y
3
+ 1.71 × 10
4
y
4
2.63 × 10
4
y
5
+ 3.35 × 10
4
y
6
3.73 × 10
4
y
7
+ 3.67 × 10
4
y
8
3.20 × 10
4
y
9
+ 2.48 × 10
4
y
10
1.69 × 10
4
y
11
+ 1.00 × 10
4
y
12
4954y
13
+ 1957y
14
583y
15
+ 122y
16
16y
17
+ y
18
)
2
(y
28
17y
27
+ ··· + 560y + 100)
c
5
, c
8
(y 1)(y
2
6y + 1)(y
18
8y
16
+ ··· 4y + 1)
(y
28
+ 19y
27
+ ··· + 379y + 25)(y
36
3y
35
+ ··· 372232y + 19321)
c
11
y
3
(y
9
2y
8
+ 21y
7
+ 27y
5
174y
4
+ 205y
3
+ 30y
2
53y 32)
2
(1 36y + 364y
2
1308y
3
+ 1266y
4
+ 1583y
5
+ 4322y
6
1.89 × 10
4
y
7
+ 1.60 × 10
4
y
8
1.17 × 10
4
y
9
+ 8980y
10
5574y
11
+ 2679y
12
777y
13
+ 393y
14
117y
15
+ 39y
16
6y
17
+ y
18
)
2
(y
28
y
27
+ ··· + 640y + 64)
19