11n
179
(K11n
179
)
1
Arc Sequences
6 11 1 7 1 10 4 11 7 2 8
Solving Sequence
1,4 3,8
7 5 6 11 9 2 10
c
3
c
7
c
4
c
5
c
11
c
8
c
2
c
10
c
1
, c
6
, c
9
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= ha
6
+ 4a
5
+ 8a
4
+ 6a
3
+ 3a
2
+ 1, a
4
+ 3a
3
+ 5a
2
+ 2a + 2u + 3, a
5
4a
4
8a
3
7a
2
+ 2b 5a 1i
I
u
2
= hu
7
3u
6
+ 7u
5
13u
4
+ 18u
3
10u
2
+ 2u + 1,
u
6
+ 55u
5
142u
4
+ 312u
3
546u
2
+ 109a + 716u 174,
52u
6
135u
5
+ 299u
4
528u
3
+ 706u
2
+ 109b 172u + 1i
I
u
3
= hu
15
+ 14u
14
+ ··· + 464u + 32, 991u
14
+ 44316u
13
+ ··· + 44456a + 908664,
30442u
14
342325u
13
+ ··· + 44456b + 31712i
I
u
4
= hb
36
2b
35
+ ··· 151b + 47,
9.61987 × 10
32
b
35
7.90636 × 10
33
b
34
+ ··· + 2.38862 × 10
34
a 3.32637 × 10
35
,
2.38862 × 10
34
u + 7.83496 × 10
33
b
35
+ ··· + 2.38324 × 10
35
b + 1.27422 × 10
35
i
There are 4 irreducible components with 64 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
= ha
6
+ 4a
5
+ 8a
4
+ 6a
3
+ 3a
2
+ 1, a
4
+ 3a
3
+ 5a
2
+ 2a + 2u +
3, a
5
4a
4
8a
3
7a
2
+ 2b 5a 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
2
a
4
3
2
a
3
5
2
a
2
a
3
2
a
3
=
1
2
a
4
3
2
a
3
5
2
a
2
a
3
2
1
2
a
4
3
2
a
3
5
2
a
2
a
3
2
a
8
=
a
1
2
a
5
+ 2a
4
+ ··· +
5
2
a +
1
2
a
7
=
a
1
2
a
5
3
2
a
4
2a
3
+ a
2
+ a +
1
2
a
5
=
1
2
a
5
3
2
a
4
2a
3
1
2
1
2
a
5
+ 2a
4
+
7
2
a
3
+
3
2
a
2
a 1
a
6
=
1
2
a
4
+
3
2
a
3
+
3
2
a
2
a
3
2
1
2
a
5
+ 2a
4
+
7
2
a
3
+
3
2
a
2
a 1
a
11
=
1
2
a
3
a
2
1
2
a +
3
2
1
2
a
5
2a
4
+ ···
1
2
a +
3
2
a
9
=
1
2
a
5
2a
4
9
2
a
3
9
2
a
2
3a 1
1
2
a
4
2a
3
7
2
a
2
5
2
a 1
a
2
=
a
5
+
7
2
a
4
+ ··· 2a
3
2
1
2
a
5
+
3
2
a
4
+ 2a
3
a
2
2a
5
2
a
10
=
a
5
4a
4
8a
3
6a
2
3a 1
1
2
a
5
2a
4
9
2
a
3
9
2
a
2
4a
a
10
=
a
5
4a
4
8a
3
6a
2
3a 1
1
2
a
5
2a
4
9
2
a
3
9
2
a
2
4a
(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 = 0.465571
a = 1.57395 1.46156I
b = 0.732786 + 0.680460I
1.13287 2.66045
u = 0.465571
a = 1.57395 + 1.46156I
b = 0.732786 0.680460I
1.13287 2.66045
u = 1.23279 0.79255I
a = 0.632657 0.782837I
b = 0.073295 0.673932I
8.79110 + 1.58317I 4.83023 3.06106I
u = 1.23279 + 0.79255I
a = 0.632657 + 0.782837I
b = 0.073295 + 0.673932I
8.79110 1.58317I 4.83023 + 3.06106I
u = 1.23279 + 0.79255I
a = 0.206606 0.413848I
b = 0.15949 1.46648I
8.79110 1.58317I 4.83023 + 3.06106I
u = 1.23279 0.79255I
a = 0.206606 + 0.413848I
b = 0.15949 + 1.46648I
8.79110 + 1.58317I 4.83023 3.06106I
3
II. I
u
2
= hu
7
3u
6
+ 7u
5
13u
4
+ 18u
3
10u
2
+ 2u + 1, u
6
+ 55u
5
+ · · · +
109a 174, 52u
6
135u
5
+ · · · + 109b + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
8
=
0.00917431u
6
0.504587u
5
+ ··· 6.56881u + 1.59633
0.477064u
6
+ 1.23853u
5
+ ··· + 1.57798u 0.00917431
a
7
=
0.00917431u
6
0.504587u
5
+ ··· 6.56881u + 1.59633
0.284404u
6
+ 0.642202u
5
+ ··· + 0.633028u 0.486239
a
5
=
0.440367u
6
+ 1.22018u
5
+ ··· + 0.302752u + 2.37615
0.348624u
6
+ 1.17431u
5
+ ··· + 3.61468u + 0.339450
a
6
=
0.788991u
6
+ 2.39450u
5
+ ··· + 3.91743u + 2.71560
0.348624u
6
+ 1.17431u
5
+ ··· + 3.61468u + 0.339450
a
11
=
0.440367u
6
+ 1.22018u
5
+ ··· + 0.302752u + 3.37615
0.100917u
6
+ 0.550459u
5
+ ··· + 3.25688u + 0.440367
a
9
=
1.37615u
6
3.68807u
5
+ ··· 8.32110u + 2.44954
0.247706u
6
0.623853u
5
+ ··· + 0.642202u 0.899083
a
2
=
1.68807u
6
4.84404u
5
+ ··· 9.66055u 1.27523
0.348624u
6
1.17431u
5
+ ··· 2.61468u 1.33945
a
10
=
1.71560u
6
4.35780u
5
+ ··· 5.36697u 0.486239
0.724771u
6
1.86239u
5
+ ··· 1.93578u 0.889908
a
10
=
1.71560u
6
4.35780u
5
+ ··· 5.36697u 0.486239
0.724771u
6
1.86239u
5
+ ··· 1.93578u 0.889908
(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 = 0.26392 1.89105I
a = 0.317866 + 0.254422I
b = 0.397234 0.668248I
5.40832 + 4.21557I 0.78856 7.31442I
u = 0.26392 + 1.89105I
a = 0.317866 0.254422I
b = 0.397234 + 0.668248I
5.40832 4.21557I 0.78856 + 7.31442I
u = 0.203752
a = 3.16933
b = 0.645755
0.607992 3.49113
u = 0.508137 0.486029I
a = 1.22583 + 1.38607I
b = 0.050784 + 1.300105I
11.34657 + 1.05141I 8.13453 0.52743I
u = 0.508137 + 0.486029I
a = 1.22583 1.38607I
b = 0.050784 1.300105I
11.34657 1.05141I 8.13453 + 0.52743I
u = 1.35766 0.93784I
a = 0.676700 + 0.313046I
b = 0.625140 + 1.059644I
0.00156 + 5.16496I 0.90846 5.47109I
u = 1.35766 + 0.93784I
a = 0.676700 0.313046I
b = 0.625140 1.059644I
0.00156 5.16496I 0.90846 + 5.47109I
5
III. I
u
3
= hu
15
+ 14u
14
+ · · · + 464u + 32, 991u
14
+ 44316u
13
+ · · · + 44456a +
908664, 3.04 × 10
4
u
14
3.42 × 10
5
u
13
+ · · · + 4.45 × 10
4
b + 3.17 × 10
4
i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
3
=
u
u
a
8
=
0.0222917u
14
0.996851u
13
+ ··· 194.288u 20.4396
0.684767u
14
+ 7.70031u
13
+ ··· + 10.0963u 0.713335
a
7
=
0.0222917u
14
0.996851u
13
+ ··· 194.288u 20.4396
1.20166u
14
14.9293u
13
+ ··· 308.349u 22.6259
a
5
=
0.396459u
14
5.03367u
13
+ ··· 94.8459u 3.24915
0.0268580u
14
+ 0.551579u
13
+ ··· + 47.3811u + 3.84956
a
6
=
0.369601u
14
4.48209u
13
+ ··· 47.4649u + 0.600414
0.0268580u
14
+ 0.551579u
13
+ ··· + 47.3811u + 3.84956
a
11
=
0.396459u
14
+ 5.03367u
13
+ ··· + 94.8459u + 4.24915
0.516758u
14
+ 6.69100u
13
+ ··· + 180.708u + 12.6867
a
9
=
1.67223u
14
+ 21.5389u
13
+ ··· + 540.283u + 31.9909
3.75867u
14
+ 47.0944u
13
+ ··· + 1062.37u + 75.4238
a
2
=
0.469250u
14
5.83343u
13
+ ··· 122.999u 8.50306
0.911643u
14
11.1153u
13
+ ··· 199.617u 14.1566
a
10
=
1.33223u
14
+ 16.8035u
13
+ ··· + 380.108u + 24.9858
3.09752u
14
+ 38.9099u
13
+ ··· + 912.081u + 65.3264
a
10
=
1.33223u
14
+ 16.8035u
13
+ ··· + 380.108u + 24.9858
3.09752u
14
+ 38.9099u
13
+ ··· + 912.081u + 65.3264
(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 = 1.41089 1.28897I
a = 0.730743 + 0.221034I
b = 0.74609 + 1.25376I
4.8601 14.7989I 2.41187 + 8.28326I
u = 1.41089 + 1.28897I
a = 0.730743 0.221034I
b = 0.74609 1.25376I
4.8601 + 14.7989I 2.41187 8.28326I
u = 1.38613 0.32674I
a = 0.553085 0.614738I
b = 0.565792 1.032821I
0.37742 3.22470I 1.69059 + 1.81692I
u = 1.38613 + 0.32674I
a = 0.553085 + 0.614738I
b = 0.565792 + 1.032821I
0.37742 + 3.22470I 1.69059 1.81692I
u = 1.360540 0.261249I
a = 0.645886 + 0.354688I
b = 0.786092 + 0.651305I
1.20190 + 2.43151I 0.902369 0.814710I
u = 1.360540 + 0.261249I
a = 0.645886 0.354688I
b = 0.786092 0.651305I
1.20190 2.43151I 0.902369 + 0.814710I
u = 1.07386 2.16285I
a = 0.293966 0.146746I
b = 0.001713 0.793388I
6.23698 + 3.49716I 6.18530 1.96585I
u = 1.07386 + 2.16285I
a = 0.293966 + 0.146746I
b = 0.001713 + 0.793388I
6.23698 3.49716I 6.18530 + 1.96585I
u = 1.03444 1.15733I
a = 0.878543 0.103476I
b = 0.789042 1.123807I
0.98276 7.96105I 1.19655 + 6.90467I
u = 1.03444 + 1.15733I
a = 0.878543 + 0.103476I
b = 0.789042 + 1.123807I
0.98276 + 7.96105I 1.19655 6.90467I
7
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.441017 0.682615I
a = 0.626506 + 0.383690I
b = 0.014387 + 0.596876I
1.16432 + 1.11480I 3.42758 4.27035I
u = 0.441017 + 0.682615I
a = 0.626506 0.383690I
b = 0.014387 0.596876I
1.16432 1.11480I 3.42758 + 4.27035I
u = 0.231740 1.386456I
a = 0.727304 0.321329I
b = 0.614054 + 0.933909I
7.18561 1.74581I 4.31703 + 3.15532I
u = 0.231740 + 1.386456I
a = 0.727304 + 0.321329I
b = 0.614054 0.933909I
7.18561 + 1.74581I 4.31703 3.15532I
u = 0.122764
a = 5.00969
b = 0.615011
1.24987 10.6531
8
IV.
I
u
4
= hb
36
2b
35
+ · · · 151b + 47, 9.62 × 10
32
b
35
7.91 × 10
33
b
34
+ · · · + 2.39 ×
10
34
a3.33×10
35
, 2.39×10
34
u+7.83×10
33
b
35
+· · ·+2.38×10
35
b+1.27×10
35
i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
0.328012b
35
+ 0.385558b
34
+ ··· 9.97748b 5.33455
a
3
=
0.328012b
35
+ 0.385558b
34
+ ··· 9.97748b 5.33455
0.328012b
35
+ 0.385558b
34
+ ··· 9.97748b 5.33455
a
8
=
0.0402737b
35
+ 0.331001b
34
+ ··· 38.7844b + 13.9259
b
a
7
=
0.0402737b
35
+ 0.331001b
34
+ ··· 38.7844b + 13.9259
0.00828442b
35
+ 0.222719b
34
+ ··· 36.3623b + 14.0111
a
5
=
0.887148b
35
+ 1.45532b
34
+ ··· 62.8575b + 2.90056
0.0114837b
35
0.0694659b
34
+ ··· + 8.68076b + 0.0974858
a
6
=
0.875664b
35
+ 1.38585b
34
+ ··· 54.1767b + 2.99805
0.0114837b
35
0.0694659b
34
+ ··· + 8.68076b + 0.0974858
a
11
=
0.250453b
35
+ 0.340002b
34
+ ··· 7.84455b 0.892865
b
2
a
9
=
0.120631b
35
0.154805b
34
+ ··· 0.0730998b + 2.15457
b
3
+ b
a
2
=
0.899901b
35
1.17955b
34
+ ··· + 24.5791b + 12.5140
0.206127b
35
+ 0.384466b
34
+ ··· 34.6868b + 9.39768
a
10
=
0.382428b
35
0.386063b
34
+ ··· 15.2423b + 11.3695
0.203833b
35
0.330403b
34
+ ··· + 23.6744b 1.69295
a
10
=
0.382428b
35
0.386063b
34
+ ··· 15.2423b + 11.3695
0.203833b
35
0.330403b
34
+ ··· + 23.6744b 1.69295
(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 = 0.550574 + 0.534542I
a = 1.151547 + 0.184083I
b = 1.137441 0.607496I
0.695457 + 1.211150I 2.01684 5.97065I
u = 0.550574 0.534542I
a = 1.151547 0.184083I
b = 1.137441 + 0.607496I
0.695457 1.211150I 2.01684 + 5.97065I
u = 0.559442 + 0.038809I
a = 0.97669 + 1.89819I
b = 0.848848 0.737023I
0.388234 + 1.127972I 1.85464 1.58148I
u = 0.559442 0.038809I
a = 0.97669 1.89819I
b = 0.848848 + 0.737023I
0.388234 1.127972I 1.85464 + 1.58148I
u = 0.950537 + 0.162221I
a = 0.697241 + 0.431990I
b = 0.832013 0.692310I
1.79766 2.11512I 3.46832 + 4.22083I
u = 0.950537 0.162221I
a = 0.697241 0.431990I
b = 0.832013 + 0.692310I
1.79766 + 2.11512I 3.46832 4.22083I
u = 1.59445 + 1.02172I
a = 0.595268 0.396932I
b = 0.754617 0.978635I
1.11892 7.08645I 2.27907 + 7.07165I
u = 1.59445 1.02172I
a = 0.595268 + 0.396932I
b = 0.754617 + 0.978635I
1.11892 + 7.08645I 2.27907 7.07165I
u = 1.20149 + 0.95062I
a = 0.601110 0.138403I
b = 0.700489 1.075933I
0.58133 3.63224I 1.22357 + 0.72654I
u = 1.20149 0.95062I
a = 0.601110 + 0.138403I
b = 0.700489 + 1.075933I
0.58133 + 3.63224I 1.22357 0.72654I
10
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.550574 0.534542I
a = 0.51202 + 1.60050I
b = 0.535612 0.716902I
0.695457 1.211150I 2.01684 + 5.97065I
u = 0.550574 + 0.534542I
a = 0.51202 1.60050I
b = 0.535612 + 0.716902I
0.695457 + 1.211150I 2.01684 5.97065I
u = 1.57847 + 0.07406I
a = 0.182614 0.464051I
b = 0.01910 1.49587I
8.78344 0.53962I 4.04425 2.43806I
u = 1.57847 0.07406I
a = 0.182614 + 0.464051I
b = 0.01910 + 1.49587I
8.78344 + 0.53962I 4.04425 + 2.43806I
u = 0.08820 + 1.71388I
a = 0.440400 + 0.416925I
b = 0.047819 0.888995I
6.66136 3.28569I 5.54170 + 2.88739I
u = 0.08820 1.71388I
a = 0.440400 0.416925I
b = 0.047819 + 0.888995I
6.66136 + 3.28569I 5.54170 2.88739I
u = 0.305821 0.029607I
a = 0.52691 2.98749I
b = 0.20657 1.64071I
9.40827 2.73362I 5.19032 + 6.28765I
u = 0.305821 + 0.029607I
a = 0.52691 + 2.98749I
b = 0.20657 + 1.64071I
9.40827 + 2.73362I 5.19032 6.28765I
u = 0.305821 + 0.029607I
a = 1.18377 5.25035I
b = 0.249590 0.898036I
9.40827 + 2.73362I 5.19032 6.28765I
u = 0.305821 0.029607I
a = 1.18377 + 5.25035I
b = 0.249590 + 0.898036I
9.40827 2.73362I 5.19032 + 6.28765I
11
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.57847 + 0.07406I
a = 0.056442 0.945021I
b = 0.253884 0.746014I
8.78344 0.53962I 4.04425 2.43806I
u = 1.57847 0.07406I
a = 0.056442 + 0.945021I
b = 0.253884 + 0.746014I
8.78344 + 0.53962I 4.04425 + 2.43806I
u = 1.59445 1.02172I
a = 0.614327 0.220117I
b = 0.543574 1.241085I
1.11892 + 7.08645I 2.27907 7.07165I
u = 1.59445 + 1.02172I
a = 0.614327 + 0.220117I
b = 0.543574 + 1.241085I
1.11892 7.08645I 2.27907 + 7.07165I
u = 1.20149 0.95062I
a = 0.794303 0.267048I
b = 0.590660 0.737715I
0.58133 + 3.63224I 1.22357 0.72654I
u = 1.20149 + 0.95062I
a = 0.794303 + 0.267048I
b = 0.590660 + 0.737715I
0.58133 3.63224I 1.22357 + 0.72654I
u = 0.559442 + 0.038809I
a = 1.60100 + 1.20636I
b = 0.620068 1.024026I
0.388234 + 1.127972I 1.85464 1.58148I
u = 0.559442 0.038809I
a = 1.60100 1.20636I
b = 0.620068 + 1.024026I
0.388234 1.127972I 1.85464 + 1.58148I
u = 0.08820 1.71388I
a = 0.518764 0.001204I
b = 0.675718 0.791567I
6.66136 + 3.28569I 5.54170 2.88739I
u = 0.08820 + 1.71388I
a = 0.518764 + 0.001204I
b = 0.675718 + 0.791567I
6.66136 3.28569I 5.54170 + 2.88739I
12
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.894501 + 0.439989I
a = 0.877218 + 0.880723I
b = 0.697017 0.997253I
2.21070 + 8.01702I 0.26506 6.04046I
u = 0.894501 0.439989I
a = 0.877218 0.880723I
b = 0.697017 + 0.997253I
2.21070 8.01702I 0.26506 + 6.04046I
u = 0.950537 + 0.162221I
a = 0.971317 + 0.562568I
b = 0.732831 0.297516I
1.79766 2.11512I 3.46832 + 4.22083I
u = 0.950537 0.162221I
a = 0.971317 0.562568I
b = 0.732831 + 0.297516I
1.79766 + 2.11512I 3.46832 4.22083I
u = 0.894501 0.439989I
a = 1.068973 + 0.589062I
b = 1.172181 0.401841I
2.21070 8.01702I 0.26506 + 6.04046I
u = 0.894501 + 0.439989I
a = 1.068973 0.589062I
b = 1.172181 + 0.401841I
2.21070 + 8.01702I 0.26506 6.04046I
13
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
10
(u
6
+ 3u
5
+ ··· + u + 1)(u
7
2u
5
+ ··· + 2u + 1)
(u
15
5u
13
+ ··· + 3u + 1)(u
36
10u
34
+ ··· + 503u + 161)
c
2
, c
5
(u
6
3u
5
+ ··· u + 1)(u
7
2u
5
+ ··· + 2u 1)
(u
15
5u
13
+ ··· + 3u + 1)(u
36
10u
34
+ ··· + 503u + 161)
c
3
(u
3
2u
2
+ u + 1)
2
(u
7
+ 3u
6
+ 7u
5
+ 13u
4
+ 18u
3
+ 10u
2
+ 2u 1)
(u
15
+ 14u
14
+ ··· + 464u + 32)
(1 9u + 25u
2
9u
3
47u
4
u
5
+ 129u
6
36u
7
139u
8
+ 51u
9
+ 91u
10
65u
11
+ 18u
13
16u
14
+ 9u
15
+ u
16
3u
17
+ u
18
)
2
c
4
, c
8
(u
6
u
5
+ 3u
4
3u
3
+ 3u
2
u + 1)
(u
7
u
6
+ ··· + u 1)(u
15
+ u
14
+ ··· 4u
2
1)
(u
36
+ 2u
35
+ ··· + 151u + 47)
c
6
(u
3
+ u 1)
2
(u
7
u
6
+ 3u
5
2u
4
+ u
3
u
2
u 1)
(u
15
+ 8u
14
+ ··· 56u 8)
(5 4u + 19u
2
16u
3
+ 47u
4
53u
5
+ 97u
6
110u
7
+ 139u
8
140u
9
+ 135u
10
115u
11
+ 89u
12
61u
13
+ 39u
14
20u
15
+ 10u
16
3u
17
+ u
18
)
2
c
7
, c
11
(u
6
+ u
5
+ 3u
4
+ 3u
3
+ 3u
2
+ u + 1)
(u
7
+ u
6
+ ··· + u + 1)(u
15
+ u
14
+ ··· 4u
2
1)
(u
36
+ 2u
35
+ ··· + 151u + 47)
c
9
(u
3
+ u + 1)
2
(u
7
+ u
6
+ 3u
5
+ 2u
4
+ u
3
+ u
2
u + 1)
(u
15
+ 8u
14
+ ··· 56u 8)
(5 4u + 19u
2
16u
3
+ 47u
4
53u
5
+ 97u
6
110u
7
+ 139u
8
140u
9
+ 135u
10
115u
11
+ 89u
12
61u
13
+ 39u
14
20u
15
+ 10u
16
3u
17
+ u
18
)
2
14
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
5
c
10
(y
6
7y
5
+ 17y
4
15y
3
+ 9y
2
3y + 1)
(y
7
4y
6
+ ··· + 4y
2
1)(y
15
10y
14
+ ··· + 29y 1)
(y
36
20y
35
+ ··· 295835y + 25921)
c
3
(y
3
2y
2
+ 5y 1)
2
(y
7
+ 5y
6
+ ··· + 24y 1)
(y
15
+ 4y
14
+ ··· + 67328y 1024)
(1 31y + 369y
2
2191y
3
+ 7715y
4
1.86 × 10
4
y
5
+ 3.39 × 10
4
y
6
4.65 × 10
4
y
7
+ 4.60 × 10
4
y
8
3.09 × 10
4
y
9
+ 1.20 × 10
4
y
10
807y
11
1726y
12
+ 1056y
13
276y
14
5y
15
+ 23y
16
7y
17
+ y
18
)
2
c
4
, c
7
, c
8
c
11
(y
6
+ 5y
5
+ 9y
4
+ 9y
3
+ 9y
2
+ 5y + 1)
(y
7
+ 5y
6
+ ··· y 1)(y
15
+ 7y
14
+ ··· 8y 1)
(y
36
+ 16y
35
+ ··· + 18277y + 2209)
c
6
, c
9
(y
3
+ 2y
2
+ y 1)
2
(y
7
+ 5y
6
+ 7y
5
2y
4
11y
3
7y
2
y 1)
(y
15
+ 8y
14
+ ··· + 224y 64)
(25 + 174y + 703y
2
+ 2076y
3
+ 4709y
4
+ 8301y
5
+ 1.14 × 10
4
y
6
+ 1.23 × 10
4
y
7
+ 1.04 × 10
4
y
8
+ 6822y
9
+ 3675y
10
+ 1883y
11
+ 1135y
12
+ 759y
13
+ 441y
14
+ 192y
15
+ 58y
16
+ 11y
17
+ y
18
)
2
15