11a
239
(K11a
239
)
1
Arc Sequences
7 1 6 8 9 10 2 11 3 4 5
Solving Sequence
1,7
2 3
8,10
6 4 9 5 11
c
1
c
2
c
7
c
6
c
3
c
9
c
5
c
11
c
4
, c
8
, c
10
Representation Ideals
I =
7
\
i=1
I
u
i
\
I
v
1
I
u
1
= hu
6
+ u
5
u
4
2u
3
+ u + 1, u
4
+ u
2
+ a 1, u
5
+ u
4
2u
3
u
2
+ b + u + 1i
I
u
2
= h16a
14
16a
13
+ 16a
12
2a
11
+ 13a
10
+ 36a
9
+ 21a
8
+ 33a
7
+ 58a
6
5a
5
a
3
3a
2
+ 1,
111056254080a
13
+ 51186652385b + ··· + 34382042909a 2969154763,
272907035504a
13
+ 51186652385u + ··· 93468003245a 2736151556i
I
u
3
= hu
22
8u
20
+ 29u
18
65u
16
+ 96u
14
95u
12
+ 59u
10
20u
8
+ 5u
6
8u
4
+ 8u
2
3,
9u
21
14u
20
+ ··· + 2b 22, 5u
21
+ 15u
20
+ ··· + 6a + 69i
I
u
4
= hu
17
+ 6u
16
+ ··· + 28u + 8, u
16
+ 8u
15
+ ··· + 4b + 44, 9u
16
+ 48u
15
+ ··· + 8a + 44i
I
u
5
= ha
12
2a
11
+ 3a
10
4a
9
+ 8a
8
5a
7
+ 3a
6
+ 6a
5
+ 11a
4
+ 12a
3
+ 6a
2
+ 3a + 1,
3121a
11
+ 12489b + ··· + 55324a + 4586, 9314a
11
+ 12489u + ··· + 46688a + 12855i
I
u
6
= ha
24
+ 2a
23
+ ··· 2a + 1, 2.06281 × 10
16
u 8.35767 × 10
15
a
23
+ ··· 5.12296 × 10
16
a 8.38945 × 10
15
,
5.98216 × 10
17
b + 3.76658 × 10
17
a
23
+ ··· + 4.17677 × 10
18
a 7.43326 × 10
17
i
I
u
7
= ha
48
2a
47
+ ··· + 327a + 67,
3.26339 × 10
136
u + 6.79974 × 10
134
a
47
+ ··· + 5.51841 × 10
137
a + 6.53319 × 10
136
,
1.43970 × 10
154
b 5.82238 × 10
151
a
47
+ ··· 1.84697 × 10
155
a 9.03893 × 10
154
i
I
v
1
= hv + 1, b
2
b + 1, ai
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
There are 8 irreducible components with 145 representations.
2
I.
I
u
1
= hu
6
+u
5
u
4
2u
3
+u+1, u
4
+u
2
+a1, u
5
+u
4
2u
3
u
2
+b+u+1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
8
=
u
u
3
+ u
a
10
=
u
4
u
2
+ 1
u
5
u
4
+ 2u
3
+ u
2
u 1
a
6
=
u
2
+ 1
u
2
a
4
=
u
2
+ 1
u
2
a
9
=
u
u
3
u
a
5
=
u
5
+ 2u
3
u
u
5
u
3
+ u
a
11
=
u
u
3
u
a
11
=
u
u
3
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
3
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.073950 0.558752I
a = 0.573950 + 0.818891I
b = 0.73279 2.01903I
5.69302I 5.51057I
u = 1.073950 + 0.558752I
a = 0.573950 0.818891I
b = 0.73279 + 2.01903I
5.69302I 5.51057I
u = 0.428243 0.664531I
a = 1.000936 0.863088I
b = 0.490059 + 1.086478I
1.89061 + 0.92430I 3.71672 0.79423I
u = 0.428243 + 0.664531I
a = 1.000936 + 0.863088I
b = 0.490059 1.086478I
1.89061 0.92430I 3.71672 + 0.79423I
u = 1.002193 0.295542I
a = 0.573013 0.494098I
b = 0.257273 + 0.293926I
1.89061 + 0.92430I 3.71672 0.79423I
u = 1.002193 + 0.295542I
a = 0.573013 + 0.494098I
b = 0.257273 0.293926I
1.89061 0.92430I 3.71672 + 0.79423I
4
II.
I
u
2
= h16a
14
16a
13
+ · · · 3a
2
+ 1, 5.12× 10
10
b + 1.11 × 10
11
a
13
+ · · · + 3.44 ×
10
10
a2.97×10
9
, 5.12×10
10
u+2.73×10
11
a
13
+· · ·9.35×10
10
a2.74×10
9
i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
5.33161a
13
+ 5.06330a
12
+ ··· + 1.82602a + 0.0534544
a
2
=
1
9.58396a
13
+ 8.76707a
12
+ ··· + 2.71989a + 0.820762
a
3
=
9.58396a
13
8.76707a
12
+ ··· 2.71989a + 0.179238
9.58396a
13
+ 8.76707a
12
+ ··· + 2.71989a + 0.820762
a
8
=
5.33161a
13
5.06330a
12
+ ··· 1.82602a 0.0534544
6.47816a
13
+ 10.5372a
12
+ ··· 1.96238a 1.87038
a
10
=
a
2.16963a
13
+ 3.30315a
12
+ ··· 0.671699a + 0.0580064
a
6
=
1.38920a
13
2.08925a
12
+ ··· 0.333225a 0.0167692
5.58729a
13
+ 6.36284a
12
+ ··· + 2.21725a + 0.205826
a
4
=
7.85742a
13
5.07608a
12
+ ··· 2.07881a + 0.367319
0.174899a
13
+ 0.764710a
12
+ ··· + 0.623888a 0.375587
a
9
=
4.05899a
13
4.45378a
12
+ ··· 0.870376a + 0.404885
6.49693a
13
+ 6.63603a
12
+ ··· + 1.25213a 0.0136534
a
5
=
5.24891a
13
8.04288a
12
+ ··· 0.476923a + 0.294903
5.64656a
13
+ 8.72584a
12
+ ··· + 2.14223a 0.148622
a
11
=
7.60960a
13
+ 7.65058a
12
+ ··· + 0.435251a 0.147555
10.6160a
13
15.7295a
12
+ ··· + 1.43580a + 0.656289
a
11
=
7.60960a
13
+ 7.65058a
12
+ ··· + 0.435251a 0.147555
10.6160a
13
15.7295a
12
+ ··· + 1.43580a + 0.656289
(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 = 0.814935 + 0.691474I
a = 0.898271 0.366083I
b = 0.07979 + 1.44609I
4.60437 + 2.63118I 2.98391 3.36378I
u = 0.814935 0.691474I
a = 0.898271 + 0.366083I
b = 0.07979 1.44609I
4.60437 2.63118I 2.98391 + 3.36378I
u = 0.244291 + 1.049541I
a = 0.438032 0.210537I
b = 0.108018 + 0.390271I
0.04250 5.03576I 2.7810 + 16.4347I
u = 0.244291 1.049541I
a = 0.438032 + 0.210537I
b = 0.108018 0.390271I
0.04250 + 5.03576I 2.7810 16.4347I
u = 1.229509 + 0.632474I
a = 0.314061 1.142756I
b = 1.12328 + 2.16089I
2.94764 + 10.98552I 7.63392 11.66372I
u = 1.229509 0.632474I
a = 0.314061 + 1.142756I
b = 1.12328 2.16089I
2.94764 10.98552I 7.63392 + 11.66372I
u = 1.229509 0.632474I
a = 0.034949 0.573770I
b = 0.748959 + 0.913488I
2.94764 10.98552I 7.63392 + 11.66372I
u = 1.229509 + 0.632474I
a = 0.034949 + 0.573770I
b = 0.748959 0.913488I
2.94764 + 10.98552I 7.63392 11.66372I
u = 0.814935 0.691474I
a = 0.414372 1.049008I
b = 1.15095 + 1.22933I
4.60437 2.63118I 2.98391 + 3.36378I
u = 0.814935 + 0.691474I
a = 0.414372 + 1.049008I
b = 1.15095 1.22933I
4.60437 + 2.63118I 2.98391 3.36378I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.57747
a = 0.434584 0.157823I
b = 0.265975 + 0.096591I
6.68831 6.86200
u = 1.57747
a = 0.434584 + 0.157823I
b = 0.265975 0.096591I
6.68831 6.86200
u = 0.244291 1.049541I
a = 1.26646 0.79015I
b = 0.198461 + 1.227831I
0.04250 + 5.03576I 2.7810 16.4347I
u = 0.244291 + 1.049541I
a = 1.26646 + 0.79015I
b = 0.198461 1.227831I
0.04250 5.03576I 2.7810 + 16.4347I
7
III. I
u
3
= hu
22
8u
20
+ · · · + 8u
2
3, 9u
21
14u
20
+ · · · + 2b 22, 5u
21
+
15u
20
+ · · · + 6a + 69i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
8
=
u
u
3
+ u
a
10
=
5
6
u
21
5
2
u
20
+ ···
8
3
u
23
2
9
2
u
21
+ 7u
20
+ ···
1
2
u + 11
a
6
=
4
3
u
21
+ 3u
20
+ ···
2
3
u +
5
2
3u
21
22u
19
+ ··· +
17
2
u + 5
a
4
=
25
6
u
21
+ 5u
20
+ ··· +
2
3
u + 7
2u
21
3
2
u
20
+ ···
21
2
u
7
2
a
9
=
7
6
u
21
2u
20
+ ··· +
4
3
u
21
2
5u
21
+ 7u
20
+ ··· + 7u +
25
2
a
5
=
11
3
u
21
+
9
2
u
20
+ ··· +
19
6
u
1
2
5
2
u
21
+
1
2
u
20
+ ···
23
2
u +
5
2
a
11
=
5
3
u
21
+ 3u
20
+ ···
41
6
u +
17
2
3u
21
+ 2u
20
+ ··· +
5
2
u + 4
a
11
=
5
3
u
21
+ 3u
20
+ ···
41
6
u +
17
2
3u
21
+ 2u
20
+ ··· +
5
2
u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.67677
a = 0.721084
b = 0.451698
6.81120 59.5783
u = 1.091462 0.565363I
a = 0.681059 0.467930I
b = 0.321235 + 0.341464I
2.38202 9.18219I 3.93831 + 7.03572I
u = 1.091462 + 0.565363I
a = 0.681059 + 0.467930I
b = 0.321235 0.341464I
2.38202 + 9.18219I 3.93831 7.03572I
u = 0.960008 0.311265I
a = 0.94876 + 1.07476I
b = 0.391671 0.614884I
4.63619 + 2.72788I 3.55265 + 2.90330I
u = 0.960008 + 0.311265I
a = 0.94876 1.07476I
b = 0.391671 + 0.614884I
4.63619 2.72788I 3.55265 2.90330I
u = 0.958173 0.586442I
a = 0.839662 + 0.903821I
b = 0.319304 0.598097I
3.10505 2.43732I 10.07137 + 9.32376I
u = 0.958173 + 0.586442I
a = 0.839662 0.903821I
b = 0.319304 + 0.598097I
3.10505 + 2.43732I 10.07137 9.32376I
u = 0.917066 0.263679I
a = 0.061411 + 1.313464I
b = 0.062515 0.645366I
4.39205 5.08643I 2.94559 + 9.60994I
u = 0.917066 + 0.263679I
a = 0.061411 1.313464I
b = 0.062515 + 0.645366I
4.39205 + 5.08643I 2.94559 9.60994I
u = 0.261071 0.718323I
a = 0.853327 0.345240I
b = 0.224686 + 0.429555I
0.17337 + 4.31510I 2.70293 4.01489I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.261071 + 0.718323I
a = 0.853327 + 0.345240I
b = 0.224686 0.429555I
0.17337 4.31510I 2.70293 + 4.01489I
u = 0.261071 0.718323I
a = 1.60659 + 0.62123I
b = 0.068551 1.275657I
0.17337 4.31510I 2.70293 + 4.01489I
u = 0.261071 + 0.718323I
a = 1.60659 0.62123I
b = 0.068551 + 1.275657I
0.17337 + 4.31510I 2.70293 4.01489I
u = 0.917066 0.263679I
a = 0.901054 0.299141I
b = 1.10936 + 3.08405I
4.39205 + 5.08643I 2.94559 9.60994I
u = 0.917066 + 0.263679I
a = 0.901054 + 0.299141I
b = 1.10936 3.08405I
4.39205 5.08643I 2.94559 + 9.60994I
u = 0.958173 0.586442I
a = 0.084104 0.611100I
b = 1.110701 + 0.394467I
3.10505 + 2.43732I 10.07137 9.32376I
u = 0.958173 + 0.586442I
a = 0.084104 + 0.611100I
b = 1.110701 0.394467I
3.10505 2.43732I 10.07137 + 9.32376I
u = 0.960008 0.311265I
a = 0.807868 + 0.572072I
b = 1.32823 2.89305I
4.63619 2.72788I 3.55265 2.90330I
u = 0.960008 + 0.311265I
a = 0.807868 0.572072I
b = 1.32823 + 2.89305I
4.63619 + 2.72788I 3.55265 + 2.90330I
u = 1.091462 0.565363I
a = 0.324530 1.160211I
b = 1.58479 + 2.04311I
2.38202 + 9.18219I 3.93831 7.03572I
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.091462 + 0.565363I
a = 0.324530 + 1.160211I
b = 1.58479 2.04311I
2.38202 9.18219I 3.93831 + 7.03572I
u = 1.67677
a = 0.102071
b = 0.252892
6.81120 59.5783
10
IV. I
u
4
=
hu
17
+6u
16
+· · ·+28u+8, u
16
+8u
15
+· · ·+4b+44, 9u
16
+48u
15
+· · ·+8a+44i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
8
=
u
u
3
+ u
a
10
=
9
8
u
16
6u
15
+ ···
45
2
u
11
2
1
4
u
16
2u
15
+ ··· 22u 11
a
6
=
7
8
u
16
+
13
4
u
15
+ ··· + 2u +
1
2
2u
15
+
15
2
u
14
+ ··· + 18u + 7
a
4
=
1.37500u
16
7.50000u
15
+ ··· 32.5000u 10.5000
3
4
u
16
+ 2u
15
+ ··· + 5u
2
1
a
9
=
1
8
u
16
+
3
2
u
15
+ ··· +
19
2
u +
7
2
3
4
u
16
5u
15
+ ··· 28u 11
a
5
=
11
8
u
16
8u
15
+ ···
89
2
u
33
2
3
4
u
16
+
9
2
u
15
+ ··· + 26u + 9
a
11
=
7
8
u
16
21
4
u
15
+ ··· 19u
13
2
2u
16
+
19
2
u
15
+ ··· + 24u + 7
a
11
=
7
8
u
16
21
4
u
15
+ ··· 19u
13
2
2u
16
+
19
2
u
15
+ ··· + 24u + 7
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.46179
a = 0.231801
b = 0.733765
7.70589 19.1409
u = 1.187761 0.627012I
a = 0.314160 1.210751I
b = 1.32023 + 2.20122I
3.7013 19.5737I 5.36728 + 10.75666I
u = 1.187761 + 0.627012I
a = 0.314160 + 1.210751I
b = 1.32023 2.20122I
3.7013 + 19.5737I 5.36728 10.75666I
u = 1.164701 0.502631I
a = 0.357657 + 0.484156I
b = 0.30163 1.41176I
0.77068 5.56913I 2.33811 + 7.26294I
u = 1.164701 + 0.502631I
a = 0.357657 0.484156I
b = 0.30163 + 1.41176I
0.77068 + 5.56913I 2.33811 7.26294I
u = 0.857122 0.870195I
a = 0.290914 + 0.961856I
b = 0.838854 1.110667I
2.21297 9.35015I 0.11785 + 9.82632I
u = 0.857122 + 0.870195I
a = 0.290914 0.961856I
b = 0.838854 + 1.110667I
2.21297 + 9.35015I 0.11785 9.82632I
u = 0.788176 0.924452I
a = 0.739726 0.468660I
b = 0.083853 + 1.118555I
2.41973 + 2.94950I 2.91048 5.30771I
u = 0.788176 + 0.924452I
a = 0.739726 + 0.468660I
b = 0.083853 1.118555I
2.41973 2.94950I 2.91048 + 5.30771I
u = 0.337237 0.670381I
a = 0.679803 0.801795I
b = 0.432039 + 0.716641I
1.74054 + 0.98669I 3.14210 1.82725I
12
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.337237 + 0.670381I
a = 0.679803 + 0.801795I
b = 0.432039 0.716641I
1.74054 0.98669I 3.14210 + 1.82725I
u = 0.334231 0.945289I
a = 1.42147 + 0.67749I
b = 0.234478 1.345228I
1.10093 + 13.85923I 2.71296 7.57439I
u = 0.334231 + 0.945289I
a = 1.42147 0.67749I
b = 0.234478 + 1.345228I
1.10093 13.85923I 2.71296 + 7.57439I
u = 0.515829
a = 1.00580
b = 0.342267
1.37384 7.65926
u = 1.340968 0.177838I
a = 0.750351 + 0.678095I
b = 0.409781 0.414303I
6.89672 10.17426I 7.93890 + 7.26215I
u = 1.340968 + 0.177838I
a = 0.750351 0.678095I
b = 0.409781 + 0.414303I
6.89672 + 10.17426I 7.93890 7.26215I
u = 1.60248
a = 0.435805
b = 0.268348
6.69142 13.6452
13
V. I
u
5
= ha
12
2a
11
+ · · · + 3a + 1, 3121a
11
+ 12489b + · · · + 55324a +
4586, 9314a
11
+ 12489u + · · · + 46688a + 12855i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
0.745776a
11
+ 1.45192a
10
+ ··· 3.73833a 1.02931
a
2
=
1
0.826567a
11
+ 1.82977a
10
+ ··· 4.18905a 1.42293
a
3
=
0.826567a
11
1.82977a
10
+ ··· + 4.18905a + 2.42293
0.826567a
11
+ 1.82977a
10
+ ··· 4.18905a 1.42293
a
8
=
0.745776a
11
1.45192a
10
+ ··· + 3.73833a + 1.02931
0.582753a
11
+ 1.56922a
10
+ ··· + 0.773721a + 0.736888
a
10
=
a
0.249900a
11
0.166226a
10
+ ··· 4.42982a 0.367203
a
6
=
0.0796701a
11
0.0172151a
10
+ ··· 0.864681a 0.0396349
0.0504444a
11
0.111378a
10
+ ··· 1.62839a 0.403715
a
4
=
0.746897a
11
1.84699a
10
+ ··· + 3.32437a + 2.38330
0.776123a
11
+ 1.71839a
10
+ ··· 5.81744a 1.82665
a
9
=
0.0797502a
11
0.417567a
10
+ ··· 4.12083a 0.279206
0.446553a
11
1.23517a
10
+ ··· 0.477060a 0.913524
a
5
=
0.483786a
11
0.738009a
10
+ ··· + 2.63055a + 0.820242
0.0396349a
11
+ 0.158940a
10
+ ··· + 1.20802a + 0.745776
a
11
=
0.666026a
11
1.86949a
10
+ ··· 0.382497a + 0.750100
0.136200a
11
+ 0.334054a
10
+ ··· + 0.296661a 0.176635
a
11
=
0.666026a
11
1.86949a
10
+ ··· 0.382497a + 0.750100
0.136200a
11
+ 0.334054a
10
+ ··· + 0.296661a 0.176635
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.073950 0.558752I
a = 0.60802 1.36921I
b = 1.08479 + 1.93849I
3.28987 + 5.69302I 12.00000 5.51057I
u = 1.073950 + 0.558752I
a = 0.60802 + 1.36921I
b = 1.08479 1.93849I
3.28987 5.69302I 12.00000 + 5.51057I
u = 0.428243 + 0.664531I
a = 0.545929 0.095794I
b = 0.350413 0.941641I
1.39926 + 0.92430I 8.28328 0.79423I
u = 0.428243 0.664531I
a = 0.545929 + 0.095794I
b = 0.350413 + 0.941641I
1.39926 0.92430I 8.28328 + 0.79423I
u = 1.002193 0.295542I
a = 0.309985 0.762874I
b = 0.89751 + 1.27543I
5.18047 0.92430I 15.7167 + 0.7942I
u = 1.002193 + 0.295542I
a = 0.309985 + 0.762874I
b = 0.89751 1.27543I
5.18047 + 0.92430I 15.7167 0.7942I
u = 1.073950 + 0.558752I
a = 0.034069 0.550318I
b = 1.49990 + 1.55724I
3.28987 5.69302I 12.00000 + 5.51057I
u = 1.073950 0.558752I
a = 0.034069 + 0.550318I
b = 1.49990 1.55724I
3.28987 + 5.69302I 12.00000 5.51057I
u = 1.002193 + 0.295542I
a = 0.88300 1.25697I
b = 1.361630 0.156816I
5.18047 + 0.92430I 15.7167 0.7942I
u = 1.002193 0.295542I
a = 0.88300 + 1.25697I
b = 1.361630 + 0.156816I
5.18047 0.92430I 15.7167 + 0.7942I
15
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.428243 + 0.664531I
a = 1.54687 0.76729I
b = 0.305555 + 1.039922I
1.39926 + 0.92430I 8.28328 0.79423I
u = 0.428243 0.664531I
a = 1.54687 + 0.76729I
b = 0.305555 1.039922I
1.39926 0.92430I 8.28328 + 0.79423I
16
VI.
I
u
6
= ha
24
+2a
23
+· · ·2a+1, 2.06×10
16
u8.36×10
15
a
23
+· · ·5.12×10
16
a
8.39 × 10
15
, 5.98 × 10
17
b + 3.77 × 10
17
a
23
+ · · · + 4.18 × 10
18
a 7.43 × 10
17
i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
0.405159a
23
+ 0.782450a
22
+ ··· + 2.48348a + 0.406699
a
2
=
1
0.551978a
23
+ 0.945244a
22
+ ··· + 6.32589a 0.650680
a
3
=
0.551978a
23
0.945244a
22
+ ··· 6.32589a + 1.65068
0.551978a
23
+ 0.945244a
22
+ ··· + 6.32589a 0.650680
a
8
=
0.405159a
23
0.782450a
22
+ ··· 2.48348a 0.406699
0.239746a
23
0.438424a
22
+ ··· 5.42007a + 1.66428
a
10
=
a
0.629635a
23
1.10644a
22
+ ··· 6.98204a + 1.24257
a
6
=
0.108270a
23
+ 0.179375a
22
+ ··· + 0.460892a 0.0278669
0.322660a
23
+ 0.595083a
22
+ ··· + 1.57077a + 0.140104
a
4
=
0.470922a
23
0.756396a
22
+ ··· 6.43532a + 1.79455
0.695098a
23
+ 1.40269a
22
+ ··· + 5.07917a + 0.0285757
a
9
=
0.00594299a
23
+ 0.113882a
22
+ ··· 4.04918a + 0.797968
0.0700505a
23
+ 0.0141059a
22
+ ··· + 1.13850a + 0.650109
a
5
=
0.629635a
23
1.10644a
22
+ ··· 5.98204a + 1.24257
0.553641a
23
+ 1.23443a
22
+ ··· + 3.07136a + 0.205505
a
11
=
0.0475267a
23
+ 0.171755a
22
+ ··· 4.60067a + 1.49152
0.312887a
23
+ 0.886040a
22
+ ··· + 3.66406a + 1.34367
a
11
=
0.0475267a
23
+ 0.171755a
22
+ ··· 4.60067a + 1.49152
0.312887a
23
+ 0.886040a
22
+ ··· + 3.66406a + 1.34367
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
17
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.428243 0.664531I
a = 2.16332 0.20464I
b = 0.235495 + 1.179730I
1.89061 4.98407I 3.71672 + 7.72243I
u = 0.428243 + 0.664531I
a = 2.16332 + 0.20464I
b = 0.235495 1.179730I
1.89061 + 4.98407I 3.71672 7.72243I
u = 1.002193 0.295542I
a = 0.77350 1.21773I
b = 1.55547 + 1.11360I
1.89061 + 3.13546I 3.71672 6.13398I
u = 1.002193 + 0.295542I
a = 0.77350 + 1.21773I
b = 1.55547 1.11360I
1.89061 3.13546I 3.71672 + 6.13398I
u = 1.073950 0.558752I
a = 0.564698 0.689890I
b = 1.51345 + 1.75612I
9.75279I 12.4388I
u = 1.073950 + 0.558752I
a = 0.564698 + 0.689890I
b = 1.51345 1.75612I
9.75279I 12.4388I
u = 1.002193 0.295542I
a = 0.394925 0.662974I
b = 0.092938 0.930975I
1.89061 4.98407I 3.71672 + 7.72243I
u = 1.002193 + 0.295542I
a = 0.394925 + 0.662974I
b = 0.092938 + 0.930975I
1.89061 + 4.98407I 3.71672 7.72243I
u = 1.002193 + 0.295542I
a = 0.319484 0.912169I
b = 0.01785 + 1.74163I
1.89061 + 4.98407I 3.71672 7.72243I
u = 1.002193 0.295542I
a = 0.319484 + 0.912169I
b = 0.01785 1.74163I
1.89061 4.98407I 3.71672 + 7.72243I
18
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.073950 0.558752I
a = 0.017393 0.313303I
b = 0.107419 + 1.323329I
1.63325I 1.41763I
u = 1.073950 + 0.558752I
a = 0.017393 + 0.313303I
b = 0.107419 1.323329I
1.63325I 1.41763I
u = 0.428243 0.664531I
a = 0.00371 1.69646I
b = 0.751579 + 0.686728I
1.89061 + 3.13546I 3.71672 6.13398I
u = 0.428243 + 0.664531I
a = 0.00371 + 1.69646I
b = 0.751579 0.686728I
1.89061 3.13546I 3.71672 + 6.13398I
u = 1.073950 + 0.558752I
a = 0.14249 1.59639I
b = 1.63606 + 2.30625I
9.75279I 12.4388I
u = 1.073950 0.558752I
a = 0.14249 + 1.59639I
b = 1.63606 2.30625I
9.75279I 12.4388I
u = 0.428243 + 0.664531I
a = 0.250700 0.398084I
b = 0.994449 + 0.069503I
1.89061 3.13546I 3.71672 + 6.13398I
u = 0.428243 0.664531I
a = 0.250700 + 0.398084I
b = 0.994449 0.069503I
1.89061 + 3.13546I 3.71672 6.13398I
u = 1.002193 + 0.295542I
a = 0.914896 0.474441I
b = 0.814463 0.126748I
1.89061 3.13546I 3.71672 + 6.13398I
u = 1.002193 0.295542I
a = 0.914896 + 0.474441I
b = 0.814463 + 0.126748I
1.89061 + 3.13546I 3.71672 6.13398I
19
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.428243 + 0.664531I
a = 0.915397 0.639936I
b = 0.17760 + 1.69867I
1.89061 + 4.98407I 3.71672 7.72243I
u = 0.428243 0.664531I
a = 0.915397 + 0.639936I
b = 0.17760 1.69867I
1.89061 4.98407I 3.71672 + 7.72243I
u = 1.073950 + 0.558752I
a = 1.013548 0.225694I
b = 0.430311 + 1.154456I
1.63325I 1.41763I
u = 1.073950 0.558752I
a = 1.013548 + 0.225694I
b = 0.430311 1.154456I
1.63325I 1.41763I
20
VII. I
u
7
=
ha
48
2a
47
+· · ·+327a+67, 3.26×10
136
u+6.80×10
134
a
47
+· · ·+5.52×10
137
a+
6.53×10
136
, 1.44× 10
154
b5.82× 10
151
a
47
+· · ·1.85× 10
155
a9.04× 10
154
i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
0.0208364a
47
+ 0.0429378a
46
+ ··· 16.9101a 2.00196
a
2
=
1
0.00549918a
47
+ 0.00820017a
46
+ ··· 11.0867a 0.934874
a
3
=
0.00549918a
47
0.00820017a
46
+ ··· + 11.0867a + 1.93487
0.00549918a
47
+ 0.00820017a
46
+ ··· 11.0867a 0.934874
a
8
=
0.0208364a
47
0.0429378a
46
+ ··· + 16.9101a + 2.00196
0.00293004a
47
+ 0.0102806a
46
+ ··· + 4.54812a + 3.25350
a
10
=
a
0.00404416a
47
0.00307487a
46
+ ··· + 12.8289a + 6.27834
a
6
=
0.00172658a
47
+ 0.00319262a
46
+ ··· 0.982407a + 0.0847506
0.0158896a
47
+ 0.0324194a
46
+ ··· 15.3322a 3.31328
a
4
=
0.00661461a
47
0.0104366a
46
+ ··· + 11.6704a + 2.13330
0.0195624a
47
+ 0.0384848a
46
+ ··· 19.4347a + 0.809197
a
9
=
0.00530471a
47
+ 0.0138002a
46
+ ··· 2.87346a + 1.52891
0.0000157061a
47
+ 0.00432528a
46
+ ··· + 0.763682a + 2.22508
a
5
=
0.00380068a
47
+ 0.00750192a
46
+ ··· 5.83156a + 0.348954
0.00643984a
47
+ 0.0104429a
46
+ ··· 9.68986a 0.347734
a
11
=
0.00177691a
47
+ 0.00278236a
46
+ ··· 6.04414a + 0.0894034
0.00573876a
47
+ 0.0127063a
46
+ ··· 4.68235a 0.705705
a
11
=
0.00177691a
47
+ 0.00278236a
46
+ ··· 6.04414a + 0.0894034
0.00573876a
47
+ 0.0127063a
46
+ ··· 4.68235a 0.705705
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
21
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.073950 + 0.558752I
a = 1.81554 0.63947I
b = 1.51180 0.92635I
3.28987 9.75279I 12.0000 + 12.4388I
u = 1.073950 0.558752I
a = 1.81554 + 0.63947I
b = 1.51180 + 0.92635I
3.28987 + 9.75279I 12.0000 12.4388I
u = 0.428243 + 0.664531I
a = 1.51712 0.00799I
b = 0.078461 1.349724I
1.39926 + 4.98407I 8.28328 7.72243I
u = 0.428243 0.664531I
a = 1.51712 + 0.00799I
b = 0.078461 + 1.349724I
1.39926 4.98407I 8.28328 + 7.72243I
u = 1.002193 + 0.295542I
a = 1.25412 0.97520I
b = 1.47789 + 2.64672I
5.18047 + 4.98407I 15.7167 7.7224I
u = 1.002193 0.295542I
a = 1.25412 + 0.97520I
b = 1.47789 2.64672I
5.18047 4.98407I 15.7167 + 7.7224I
u = 0.428243 + 0.664531I
a = 1.017602 0.201613I
b = 0.818500 + 0.453287I
1.39926 + 4.98407I 8.28328 7.72243I
u = 0.428243 0.664531I
a = 1.017602 + 0.201613I
b = 0.818500 0.453287I
1.39926 4.98407I 8.28328 + 7.72243I
u = 0.428243 + 0.664531I
a = 0.87467 2.29324I
b = 0.95354 + 1.11237I
1.39926 + 4.98407I 8.28328 7.72243I
u = 0.428243 0.664531I
a = 0.87467 + 2.29324I
b = 0.95354 1.11237I
1.39926 4.98407I 8.28328 + 7.72243I
22
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.002193 0.295542I
a = 0.770016 1.025326I
b = 0.169276 + 1.116903I
5.18047 + 3.13546I 15.7167 6.1340I
u = 1.002193 + 0.295542I
a = 0.770016 + 1.025326I
b = 0.169276 1.116903I
5.18047 3.13546I 15.7167 + 6.1340I
u = 1.073950 0.558752I
a = 0.511946 1.275334I
b = 1.60149 + 2.05072I
3.28987 + 9.75279I 12.0000 12.4388I
u = 1.073950 + 0.558752I
a = 0.511946 + 1.275334I
b = 1.60149 2.05072I
3.28987 9.75279I 12.0000 + 12.4388I
u = 1.073950 + 0.558752I
a = 0.205948 0.596138I
b = 0.54870 + 1.85133I
3.28987 9.75279I 12.0000 + 12.4388I
u = 1.073950 0.558752I
a = 0.205948 + 0.596138I
b = 0.54870 1.85133I
3.28987 + 9.75279I 12.0000 12.4388I
u = 1.002193 0.295542I
a = 0.172247 0.208678I
b = 1.96527 + 2.61396I
5.18047 + 3.13546I 15.7167 6.1340I
u = 1.002193 + 0.295542I
a = 0.172247 + 0.208678I
b = 1.96527 2.61396I
5.18047 3.13546I 15.7167 + 6.1340I
u = 1.073950 + 0.558752I
a = 0.103437 0.284886I
b = 1.021628 + 0.323158I
3.28987 1.63325I 12.00000 1.41763I
u = 1.073950 0.558752I
a = 0.103437 + 0.284886I
b = 1.021628 0.323158I
3.28987 + 1.63325I 12.00000 + 1.41763I
23
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 0.428243 + 0.664531I
a = 0.099477 0.811373I
b = 0.640979 0.185828I
1.39926 3.13546I 8.28328 + 6.13398I
u = 0.428243 0.664531I
a = 0.099477 + 0.811373I
b = 0.640979 + 0.185828I
1.39926 + 3.13546I 8.28328 6.13398I
u = 1.002193 0.295542I
a = 0.097689 1.005698I
b = 0.576102 + 0.590876I
5.18047 4.98407I 15.7167 + 7.7224I
u = 1.002193 + 0.295542I
a = 0.097689 + 1.005698I
b = 0.576102 0.590876I
5.18047 + 4.98407I 15.7167 7.7224I
u = 1.073950 0.558752I
a = 0.092868 0.706836I
b = 0.964707 + 0.554143I
3.28987 + 1.63325I 12.00000 + 1.41763I
u = 1.073950 + 0.558752I
a = 0.092868 + 0.706836I
b = 0.964707 0.554143I
3.28987 1.63325I 12.00000 1.41763I
u = 1.073950 + 0.558752I
a = 0.118917 1.121445I
b = 1.83647 + 2.01361I
3.28987 9.75279I 12.0000 + 12.4388I
u = 1.073950 0.558752I
a = 0.118917 + 1.121445I
b = 1.83647 2.01361I
3.28987 + 9.75279I 12.0000 12.4388I
u = 1.002193 + 0.295542I
a = 0.170837 0.453042I
b = 2.24400 + 2.48260I
5.18047 + 4.98407I 15.7167 7.7224I
u = 1.002193 0.295542I
a = 0.170837 + 0.453042I
b = 2.24400 2.48260I
5.18047 4.98407I 15.7167 + 7.7224I
24
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.002193 + 0.295542I
a = 0.183775 1.313234I
b = 0.552671 + 0.614865I
5.18047 + 4.98407I 15.7167 7.7224I
u = 1.002193 0.295542I
a = 0.183775 + 1.313234I
b = 0.552671 0.614865I
5.18047 4.98407I 15.7167 + 7.7224I
u = 1.073950 0.558752I
a = 0.597368 0.727824I
b = 0.004893 + 1.082152I
3.28987 + 1.63325I 12.00000 + 1.41763I
u = 1.073950 + 0.558752I
a = 0.597368 + 0.727824I
b = 0.004893 1.082152I
3.28987 1.63325I 12.00000 1.41763I
u = 0.428243 0.664531I
a = 0.652954 0.741656I
b = 0.894566 0.067200I
1.39926 + 3.13546I 8.28328 6.13398I
u = 0.428243 + 0.664531I
a = 0.652954 + 0.741656I
b = 0.894566 + 0.067200I
1.39926 3.13546I 8.28328 + 6.13398I
u = 0.428243 0.664531I
a = 0.65936 1.47253I
b = 0.358830 + 1.235086I
1.39926 + 3.13546I 8.28328 6.13398I
u = 0.428243 + 0.664531I
a = 0.65936 + 1.47253I
b = 0.358830 1.235086I
1.39926 3.13546I 8.28328 + 6.13398I
u = 1.002193 + 0.295542I
a = 1.08687 1.06524I
b = 0.629122 + 0.085765I
5.18047 3.13546I 15.7167 + 6.1340I
u = 1.002193 0.295542I
a = 1.08687 + 1.06524I
b = 0.629122 0.085765I
5.18047 + 3.13546I 15.7167 6.1340I
25
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.073950 0.558752I
a = 1.25377 0.75084I
b = 0.844780 0.044015I
3.28987 + 1.63325I 12.00000 + 1.41763I
u = 1.073950 + 0.558752I
a = 1.25377 + 0.75084I
b = 0.844780 + 0.044015I
3.28987 1.63325I 12.00000 1.41763I
u = 1.002193 0.295542I
a = 1.42561 1.07292I
b = 1.08610 + 2.94046I
5.18047 + 3.13546I 15.7167 6.1340I
u = 1.002193 + 0.295542I
a = 1.42561 + 1.07292I
b = 1.08610 2.94046I
5.18047 3.13546I 15.7167 + 6.1340I
u = 0.428243 0.664531I
a = 1.53000 0.76615I
b = 0.029091 + 0.301400I
1.39926 + 3.13546I 8.28328 6.13398I
u = 0.428243 + 0.664531I
a = 1.53000 + 0.76615I
b = 0.029091 0.301400I
1.39926 3.13546I 8.28328 + 6.13398I
u = 0.428243 + 0.664531I
a = 1.66749 0.52921I
b = 0.28615 + 1.53746I
1.39926 + 4.98407I 8.28328 7.72243I
u = 0.428243 0.664531I
a = 1.66749 + 0.52921I
b = 0.28615 1.53746I
1.39926 4.98407I 8.28328 + 7.72243I
26
VIII. I
v
1
= hv + 1, b
2
b + 1, ai
(i) Arc colorings
a
1
=
1
0
a
7
=
1
0
a
2
=
1
0
a
3
=
1
0
a
8
=
1
0
a
10
=
0
b
a
6
=
1
b + 1
a
4
=
b
b
a
9
=
b
b
a
5
=
0
b
a
11
=
1
b 1
a
11
=
1
b 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
27
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 0.866025I
4.05977I 6.92820I
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
4.05977I 6.92820I
28
IX. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
7
u
2
(u
6
u
5
u
4
+ 2u
3
u + 1)(u
6
+ u
5
u
4
2u
3
+ u + 1)
14
(u
7
3u
6
+ 3u
5
+ 2u
4
9u
3
+ 13u
2
10u + 4)
2
(u
17
6u
16
+ ··· + 28u 8)(u
22
8u
20
+ ··· + 8u
2
3)
c
2
u
2
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
15
(u
7
+ 3u
6
+ 3u
5
7u
3
+ 5u
2
4u + 16)
2
(3 + 8u + 8u
2
+ 5u
3
+ 20u
4
+ 59u
5
+ 95u
6
+ 96u
7
+ 65u
8
+ 29u
9
+ 8u
10
+ u
11
)
2
(u
17
+ 10u
16
+ ··· + 208u + 64)
c
3
u
6
(u + 1)
12
(u
2
u + 1)(1 + u + u
2
)
12
(u
14
15u
13
+ ··· 1309u + 187)
(u
17
13u
16
+ ··· + 259u 47)(u
22
8u
21
+ ··· u 1)
(u
48
+ 12u
47
+ ··· 24u + 1)
c
4
, c
6
, c
9
(u
2
+ u + 1)(u
6
+ u
5
u
4
2u
3
+ u + 1)
(u
12
u
11
+ 2u
10
+ 2u
9
+ 3u
8
+ 3u
7
+ 17u
6
+ 9u
5
+ 19u
4
+ 5u
3
+ 6u
2
+ 1)
(u
14
+ u
13
+ ··· + 4u + 1)(u
17
u
16
+ ··· + u 1)
(u
22
2u
21
+ ··· 4u 1)(u
24
+ u
23
+ ··· + 4u + 1)
(u
48
u
47
+ ··· + 258u + 67)
c
5
, c
10
(u
2
u + 1)(1 u + 2u
3
u
4
u
5
+ u
6
)
2
(u
6
+ u
5
+ ··· + u + 1)
(u
7
u
6
+ u
5
u
4
+ u
3
+ u 1)
2
(u
11
+ u
10
3u
9
4u
8
+ 4u
7
+ 5u
6
5u
5
4u
4
+ 8u
3
+ 2u
2
u + 1)
2
(u
17
+ 2u
16
+ ··· u + 4)
(43 148u + 12u
2
+ 421u
3
+ 3u
4
1042u
5
64u
6
+ 1726u
7
+ 532u
8
2159u
9
1157u
10
+ 1905u
11
+ 1578u
12
1090u
13
1340u
14
+ 338u
15
+ 752u
16
14u
17
269u
18
21u
19
+ 64u
20
+ 7u
21
10u
22
u
23
+ u
24
)
2
(u
24
+ 3u
23
+ ··· + 114u + 31)
c
8
u
6
(u + 1)
12
(u
2
u + 1)(1 + u + u
2
)
12
(u
14
15u
13
+ ··· 1309u + 187)
(u
17
13u
16
+ ··· + 259u 47)(u
22
8u
21
+ ··· u 1)
(u
48
+ 12u
47
+ ··· 24u + 1)
c
11
(u
2
+ u + 1)(u
6
+ u
5
u
4
2u
3
+ u + 1)
(u
12
u
11
+ 2u
10
+ 2u
9
+ 3u
8
+ 3u
7
+ 17u
6
+ 9u
5
+ 19u
4
+ 5u
3
+ 6u
2
+ 1)
(u
14
+ u
13
+ ··· + 4u + 1)(u
17
u
16
+ ··· + u 1)
(u
22
2u
21
+ ··· 4u 1)(u
24
+ u
23
+ ··· + 4u + 1)
(u
48
u
47
+ ··· + 258u + 67)
29
X. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
7
y
2
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
15
(y
7
3y
6
+ 3y
5
7y
3
5y
2
4y 16)
2
(3 + 8y 8y
2
+ 5y
3
20y
4
+ 59y
5
95y
6
+ 96y
7
65y
8
+ 29y
9
8y
10
+ y
11
)
2
(y
17
10y
16
+ ··· + 208y 64)
c
2
y
2
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
15
(y
7
3y
6
5y
5
80y
4
71y
3
+ 31y
2
144y 256)
2
(9 + 16y 104y
2
+ 79y
3
184y
4
+ 17y
5
119y
6
22y
7
59y
8
7y
9
6y
10
+ y
11
)
2
(y
17
6y
16
+ ··· + 47360y 4096)
c
3
y
6
(y 1)
12
(1 + y + y
2
)
13
(y
14
3y
13
+ ··· 5797y + 34969)
(y
17
13y
16
+ ··· 7555y 2209)(y
22
16y
21
+ ··· 11y + 1)
(y
48
12y
47
+ ··· 48y + 1)
c
4
(y
2
+ y + 1)(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
(y
12
+ 3y
11
+ ··· + 12y + 1)(y
14
3y
13
+ ··· 2y + 1)
(y
17
5y
16
+ ··· + 21y 1)(y
22
+ 8y
21
+ ··· 28y + 1)
(y
24
+ 3y
23
+ ··· 8y + 1)(y
48
+ 21y
47
+ ··· + 251016y + 4489)
c
5
(y
2
+ y + 1)(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
3
(y
7
+ y
6
+ y
5
+ 3y
4
+ y
3
+ y 1)
2
(1 3y 12y
2
+ 80y
3
116y
4
+ 149y
5
151y
6
+ 110y
7
60y
8
+ 25y
9
7y
10
+ y
11
)
2
(y
17
12y
16
+ ··· + 177y 16)(y
24
+ 15y
23
+ ··· + 25444y + 961)
(y
48
42y
47
+ ··· 77184656y + 3418801)
c
6
(y
2
+ y + 1)(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
(y
12
+ 3y
11
+ ··· + 12y + 1)(y
14
3y
13
+ ··· 2y + 1)
(y
17
5y
16
+ ··· + 21y 1)(y
22
+ 8y
21
+ ··· 28y + 1)
(y
24
+ 3y
23
+ ··· 8y + 1)(y
48
+ 21y
47
+ ··· + 251016y + 4489)
c
8
y
6
(y 1)
12
(1 + y + y
2
)
13
(y
14
3y
13
+ ··· 5797y + 34969)
(y
17
13y
16
+ ··· 7555y 2209)(y
22
16y
21
+ ··· 11y + 1)
(y
48
12y
47
+ ··· 48y + 1)
c
9
(y
2
+ y + 1)(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
(y
12
+ 3y
11
+ ··· + 12y + 1)(y
14
3y
13
+ ··· 2y + 1)
(y
17
5y
16
+ ··· + 21y 1)(y
22
+ 8y
21
+ ··· 28y + 1)
(y
24
+ 3y
23
+ ··· 8y + 1)(y
48
+ 21y
47
+ ··· + 251016y + 4489)
c
10
(y
2
+ y + 1)(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
3
(y
7
+ y
6
+ y
5
+ 3y
4
+ y
3
+ y 1)
2
(1 3y 12y
2
+ 80y
3
116y
4
+ 149y
5
151y
6
+ 110y
7
60y
8
+ 25y
9
7y
10
+ y
11
)
2
(y
17
12y
16
+ ··· + 177y 16)(y
24
+ 15y
23
+ ··· + 25444y + 961)
(y
48
42y
47
+ ··· 77184656y + 3418801)
c
11
(y
2
+ y + 1)(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
(y
12
+ 3y
11
+ ··· + 12y + 1)(y
14
3y
13
+ ··· 2y + 1)
(y
17
5y
16
+ ··· + 21y 1)(y
22
+ 8y
21
+ ··· 28y + 1)
(y
24
+ 3y
23
+ ··· 8y + 1)(y
48
+ 21y
47
+ ··· + 251016y + 4489)
30