11a
2
(K11a
2
)
1
Arc Sequences
5 1 7 2 3 9 4 11 6 8 10
Solving Sequence
8,11 4,9
7 3 6 5 10 1 2
c
8
c
7
c
3
c
6
c
5
c
10
c
11
c
2
c
1
, c
4
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
\
I
v
1
I
u
1
= hu
5
+ u
4
2u
3
u
2
+ u 1, u
4
+ u
3
2u
2
+ b + 1, u
4
+ u
3
2u
2
+ a u + 1i
I
u
2
= hu
79
2u
78
+ ··· + 224u 64,
8.43927 × 10
171
u
78
+ 2.64783 × 10
171
u
77
+ ··· + 7.93337 × 10
172
b 3.91116 × 10
172
,
1.84133 × 10
172
u
78
2.17887 × 10
172
u
77
+ ··· + 1.58667 × 10
173
a + 2.00553 × 10
174
i
I
v
1
= hb
6
+ 3b
5
+ 7b
4
+ 4b
3
+ b
2
+ 2b + 1, 19b
5
45b
4
105b
3
11b
2
15b + v 30, ai
There are 3 irreducible components with 90 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
5
+u
4
2u
3
u
2
+u1, u
4
+u
3
2u
2
+b+1, u
4
+u
3
2u
2
+au+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
u
4
u
3
+ 2u
2
+ u 1
u
4
u
3
+ 2u
2
1
a
4
=
1
0
a
9
=
u
4
u
3
+ 2u
2
+ u 1
u
4
u
3
+ 2u
2
+ u 1
a
7
=
u
u
a
3
=
u
2
+ 1
u
2
a
6
=
u
u
a
5
=
u
3
+ 2u
u
3
+ u
a
10
=
u
4
u
3
+ 2u
2
+ u 1
u
4
u
3
+ 2u
2
+ u 1
a
1
=
0
u
a
2
=
u
2
+ 1
u
4
2u
2
a
2
=
u
2
+ 1
u
4
2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
4
7u
3
+ 7u
2
+ 13u 18
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.41878 0.21917I
a = 0.688402 0.106340I
b = 2.10719 + 0.11282I
7.51750 4.40083I 11.07763 + 5.80708I
u = 1.41878 + 0.21917I
a = 0.688402 + 0.106340I
b = 2.10719 0.11282I
7.51750 + 4.40083I 11.07763 5.80708I
u = 0.309916 0.549911I
a = 0.77780 1.38013I
b = 1.087720 0.830216I
1.97403 + 1.53058I 13.5086 9.8710I
u = 0.309916 + 0.549911I
a = 0.77780 + 1.38013I
b = 1.087720 + 0.830216I
1.97403 1.53058I 13.5086 + 9.8710I
u = 1.21774
a = 0.821196
b = 2.03893
4.04602 8.82744
3
II. I
u
2
= hu
79
2u
78
+ · · · + 224u 64, 8.44 × 10
171
u
78
+ 2.65 ×
10
171
u
77
+ · · · + 7.93 × 10
172
b 3.91 × 10
172
, 1.84 × 10
172
u
78
2.18 ×
10
172
u
77
+ · · · + 1.59 × 10
173
a + 2.01 × 10
174
i
(i) Arc colorings
a
8
=
0
u
a
11
=
0.116050u
78
+ 0.137323u
77
+ ··· + 16.3774u 12.6398
0.106377u
78
0.0333758u
77
+ ··· 13.4505u + 0.493002
a
4
=
1
0
a
9
=
0.297582u
78
0.224335u
77
+ ··· 42.5264u + 8.27904
0.116482u
78
0.0664093u
77
+ ··· 15.4362u + 3.29792
a
7
=
u
u
a
3
=
u
2
+ 1
u
2
a
6
=
0.0639269u
78
0.137592u
77
+ ··· 19.1719u + 15.3200
0.00882792u
78
+ 0.0326580u
77
+ ··· + 0.490610u 2.76833
a
5
=
0.0620635u
78
+ 0.0175727u
77
+ ··· + 2.17576u + 8.91653
0.0451651u
78
+ 0.0470808u
77
+ ··· + 4.36971u 2.56012
a
10
=
0.116050u
78
+ 0.137323u
77
+ ··· + 16.3774u 12.6398
0.213093u
78
0.119947u
77
+ ··· 27.2532u + 6.55867
a
1
=
0.0550990u
78
+ 0.170250u
77
+ ··· + 19.6625u 18.0883
0.0719973u
78
+ 0.140741u
77
+ ··· + 17.4685u 6.61163
a
2
=
0.388594u
78
+ 0.461693u
77
+ ··· + 69.1127u 21.9844
0.0383085u
78
0.113726u
77
+ ··· 15.8618u + 8.96884
a
2
=
0.388594u
78
+ 0.461693u
77
+ ··· + 69.1127u 21.9844
0.0383085u
78
0.113726u
77
+ ··· 15.8618u + 8.96884
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.0683647u
78
0.114454u
77
+ ··· + 17.3139u 1.86024
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.51845 0.02075I
a = 0.691436 + 0.234583I
b = 2.41269 + 0.11398I
8.17783 + 5.50134I 13.0406 8.3885I
u = 1.51845 + 0.02075I
a = 0.691436 0.234583I
b = 2.41269 0.11398I
8.17783 5.50134I 13.0406 + 8.3885I
u = 1.49958 0.33987I
a = 0.569907 + 0.299347I
b = 2.18671 0.02310I
7.50417 3.65998I 10.01456 4.03431I
u = 1.49958 + 0.33987I
a = 0.569907 0.299347I
b = 2.18671 + 0.02310I
7.50417 + 3.65998I 10.01456 + 4.03431I
u = 1.218664 0.679170I
a = 0.951769 + 0.018317I
b = 2.75391 0.03013I
0.31155 11.22024I 6.70594 + 6.91214I
u = 1.218664 + 0.679170I
a = 0.951769 0.018317I
b = 2.75391 + 0.03013I
0.31155 + 11.22024I 6.70594 6.91214I
u = 1.208388 0.353192I
a = 0.965910 + 0.132672I
b = 2.19860 0.73537I
7.01716 1.79468I 14.2576 + 1.1537I
u = 1.208388 + 0.353192I
a = 0.965910 0.132672I
b = 2.19860 + 0.73537I
7.01716 + 1.79468I 14.2576 1.1537I
u = 1.192527 0.590288I
a = 0.909137 + 0.049809I
b = 2.13189 0.77257I
5.05086 9.82294I 11.04349 + 7.66234I
u = 1.192527 + 0.590288I
a = 0.909137 0.049809I
b = 2.13189 + 0.77257I
5.05086 + 9.82294I 11.04349 7.66234I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.136342 0.085967I
a = 0.195566 0.628494I
b = 0.324737 + 0.076268I
4.51217 + 2.77386I 11.59447 4.04086I
u = 1.136342 + 0.085967I
a = 0.195566 + 0.628494I
b = 0.324737 0.076268I
4.51217 2.77386I 11.59447 + 4.04086I
u = 1.104971 0.414939I
a = 0.205520 0.713739I
b = 0.426233 + 0.181669I
3.45530 4.80167I 10.06922 + 3.52658I
u = 1.104971 + 0.414939I
a = 0.205520 + 0.713739I
b = 0.426233 0.181669I
3.45530 + 4.80167I 10.06922 3.52658I
u = 1.098622 0.654049I
a = 0.128401 + 0.751267I
b = 0.091849 + 0.495135I
2.17633 5.60365I 3.63487 + 3.38656I
u = 1.098622 + 0.654049I
a = 0.128401 0.751267I
b = 0.091849 0.495135I
2.17633 + 5.60365I 3.63487 3.38656I
u = 1.074319 0.446434I
a = 1.052823 0.121601I
b = 2.85558 0.20174I
1.85989 8.01595I 6.53864 + 8.31085I
u = 1.074319 + 0.446434I
a = 1.052823 + 0.121601I
b = 2.85558 + 0.20174I
1.85989 + 8.01595I 6.53864 8.31085I
u = 1.067751 0.420888I
a = 0.983397 0.564861I
b = 2.15062 + 0.42118I
3.40761 2.20375I 7.83498 + 3.34864I
u = 1.067751 + 0.420888I
a = 0.983397 + 0.564861I
b = 2.15062 0.42118I
3.40761 + 2.20375I 7.83498 3.34864I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.913716 0.570561I
a = 0.007077 + 0.822092I
b = 0.212863 + 0.802242I
3.68282 2.87436I 2.70760 + 3.79640I
u = 0.913716 + 0.570561I
a = 0.007077 0.822092I
b = 0.212863 0.802242I
3.68282 + 2.87436I 2.70760 3.79640I
u = 0.653865 0.591272I
a = 1.218034 0.159214I
b = 0.621978 0.030654I
4.46313 1.71758I 1.99294 + 3.91162I
u = 0.653865 + 0.591272I
a = 1.218034 + 0.159214I
b = 0.621978 + 0.030654I
4.46313 + 1.71758I 1.99294 3.91162I
u = 0.567410 0.878865I
a = 0.856749 + 0.015799I
b = 0.805642 0.221778I
3.87103 0.09665I 1.28070 + 1.54941I
u = 0.567410 + 0.878865I
a = 0.856749 0.015799I
b = 0.805642 + 0.221778I
3.87103 + 0.09665I 1.28070 1.54941I
u = 0.516322 0.514627I
a = 0.23299 + 1.66774I
b = 0.111050 0.456570I
3.64506 + 4.10175I 3.50068 + 0.16550I
u = 0.516322 + 0.514627I
a = 0.23299 1.66774I
b = 0.111050 + 0.456570I
3.64506 4.10175I 3.50068 0.16550I
u = 0.491993 0.193491I
a = 1.67997 0.26421I
b = 3.03909 1.23311I
1.20246 + 1.70054I 18.7053 + 3.5277I
u = 0.491993 + 0.193491I
a = 1.67997 + 0.26421I
b = 3.03909 + 1.23311I
1.20246 1.70054I 18.7053 3.5277I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.453727 0.479176I
a = 1.18000 1.23073I
b = 2.10762 0.28643I
1.61075 1.37550I 1.06828 + 3.88421I
u = 0.453727 + 0.479176I
a = 1.18000 + 1.23073I
b = 2.10762 + 0.28643I
1.61075 + 1.37550I 1.06828 3.88421I
u = 0.404716 1.023830I
a = 0.158547 + 1.092025I
b = 0.058892 0.715461I
2.22736 + 5.03014I 4.21808 4.05748I
u = 0.404716 + 1.023830I
a = 0.158547 1.092025I
b = 0.058892 + 0.715461I
2.22736 5.03014I 4.21808 + 4.05748I
u = 0.320495 0.912395I
a = 0.049007 1.122260I
b = 0.937426 + 0.073421I
2.34704 + 4.31468I 10.21762 4.57210I
u = 0.320495 + 0.912395I
a = 0.049007 + 1.122260I
b = 0.937426 0.073421I
2.34704 4.31468I 10.21762 + 4.57210I
u = 0.125465 0.835214I
a = 0.446998 1.279444I
b = 1.341251 0.112364I
2.81805 2.16506I 9.87540 + 5.61737I
u = 0.125465 + 0.835214I
a = 0.446998 + 1.279444I
b = 1.341251 + 0.112364I
2.81805 + 2.16506I 9.87540 5.61737I
u = 0.170048 1.184850I
a = 0.293008 + 0.905851I
b = 0.223332 0.790801I
1.69051 1.86503I 9.69807 + 2.55941I
u = 0.170048 + 1.184850I
a = 0.293008 0.905851I
b = 0.223332 + 0.790801I
1.69051 + 1.86503I 9.69807 2.55941I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.195618 0.552066I
a = 0.184894 0.062373I
b = 0.436250 0.577778I
0.36323 + 1.66196I 2.66065 3.49504I
u = 0.195618 + 0.552066I
a = 0.184894 + 0.062373I
b = 0.436250 + 0.577778I
0.36323 1.66196I 2.66065 + 3.49504I
u = 0.384773
a = 1.60078
b = 0.383322
0.986513 9.91204
u = 0.440363 0.912546I
a = 0.650010 + 0.341713I
b = 0.728978 0.462953I
0.27585 + 2.15811I 6.86313 4.29711I
u = 0.440363 + 0.912546I
a = 0.650010 0.341713I
b = 0.728978 + 0.462953I
0.27585 2.15811I 6.86313 + 4.29711I
u = 0.441408 0.647966I
a = 0.219536 1.160933I
b = 0.730862 0.017852I
0.501227 0.231040I 6.51195 + 0.36059I
u = 0.441408 + 0.647966I
a = 0.219536 + 1.160933I
b = 0.730862 + 0.017852I
0.501227 + 0.231040I 6.51195 0.36059I
u = 0.484551 1.171975I
a = 0.091088 + 0.985706I
b = 0.030468 0.808721I
0.30685 9.73004I 8.37978 + 7.87966I
u = 0.484551 + 1.171975I
a = 0.091088 0.985706I
b = 0.030468 + 0.808721I
0.30685 + 9.73004I 8.37978 7.87966I
u = 0.543636 0.978739I
a = 0.756890 0.030922I
b = 0.905676 0.260182I
1.84084 4.64712I 4.66771 + 3.52711I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.543636 + 0.978739I
a = 0.756890 + 0.030922I
b = 0.905676 + 0.260182I
1.84084 + 4.64712I 4.66771 3.52711I
u = 0.725121 0.392006I
a = 1.179478 0.121443I
b = 2.35002 1.04466I
0.64046 + 2.98061I 8.98738 7.04047I
u = 0.725121 + 0.392006I
a = 1.179478 + 0.121443I
b = 2.35002 + 1.04466I
0.64046 2.98061I 8.98738 + 7.04047I
u = 0.743273 0.192362I
a = 0.92061 + 1.35743I
b = 0.319989 0.366693I
2.43852 0.18703I 11.37446 3.74898I
u = 0.743273 + 0.192362I
a = 0.92061 1.35743I
b = 0.319989 + 0.366693I
2.43852 + 0.18703I 11.37446 + 3.74898I
u = 0.809973 0.391729I
a = 1.215869 0.511528I
b = 0.582088 + 0.138055I
2.91495 + 6.10945I 7.82272 8.97445I
u = 0.809973 + 0.391729I
a = 1.215869 + 0.511528I
b = 0.582088 0.138055I
2.91495 6.10945I 7.82272 + 8.97445I
u = 0.853592 0.508882I
a = 0.114535 + 0.855414I
b = 0.505531 + 0.956227I
2.66697 2.36282I 4.65001 + 1.65972I
u = 0.853592 + 0.508882I
a = 0.114535 0.855414I
b = 0.505531 0.956227I
2.66697 + 2.36282I 4.65001 1.65972I
u = 0.890520 0.328701I
a = 0.301645 0.712109I
b = 0.463992 + 0.093193I
1.024933 + 0.378054I 6.69847 + 0.35322I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.890520 + 0.328701I
a = 0.301645 + 0.712109I
b = 0.463992 0.093193I
1.024933 0.378054I 6.69847 0.35322I
u = 1.045419 0.303052I
a = 1.056540 0.243963I
b = 2.82773 0.36509I
1.18747 + 2.48169I 7.98413 3.19776I
u = 1.045419 + 0.303052I
a = 1.056540 + 0.243963I
b = 2.82773 + 0.36509I
1.18747 2.48169I 7.98413 + 3.19776I
u = 1.101139 0.524739I
a = 0.955623 + 0.039759I
b = 2.16178 0.80099I
2.56199 + 4.84000I 8.25132 4.21664I
u = 1.101139 + 0.524739I
a = 0.955623 0.039759I
b = 2.16178 + 0.80099I
2.56199 4.84000I 8.25132 + 4.21664I
u = 1.148700 0.510777I
a = 0.106998 + 0.695028I
b = 0.057422 + 0.331697I
2.69356 + 2.85282I 9.72728 2.04655I
u = 1.148700 + 0.510777I
a = 0.106998 0.695028I
b = 0.057422 0.331697I
2.69356 2.85282I 9.72728 + 2.04655I
u = 1.160928 0.693518I
a = 0.153650 + 0.738362I
b = 0.171940 + 0.425247I
0.15331 + 10.78920I 6.70310 7.12590I
u = 1.160928 + 0.693518I
a = 0.153650 0.738362I
b = 0.171940 0.425247I
0.15331 10.78920I 6.70310 + 7.12590I
u = 1.187715 0.505810I
a = 0.901438 0.549355I
b = 2.08930 + 0.46477I
5.97333 + 6.98094I 10.91087 6.44808I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.187715 + 0.505810I
a = 0.901438 + 0.549355I
b = 2.08930 0.46477I
5.97333 6.98094I 10.91087 + 6.44808I
u = 1.214390 0.237157I
a = 0.972916 0.428041I
b = 2.18543 + 0.53298I
7.51790 0.99407I 14.02940 + 0.20317I
u = 1.214390 + 0.237157I
a = 0.972916 + 0.428041I
b = 2.18543 0.53298I
7.51790 + 0.99407I 14.02940 0.20317I
u = 1.25392 0.74743I
a = 0.927599 + 0.046899I
b = 2.72842 0.00275I
2.7949 + 16.5881I 9.42605 10.34760I
u = 1.25392 + 0.74743I
a = 0.927599 0.046899I
b = 2.72842 + 0.00275I
2.7949 16.5881I 9.42605 + 10.34760I
u = 1.32645 0.58089I
a = 0.902959 0.034437I
b = 2.70344 0.07895I
5.48277 + 8.06356I 12.43638 5.40136I
u = 1.32645 + 0.58089I
a = 0.902959 + 0.034437I
b = 2.70344 + 0.07895I
5.48277 8.06356I 12.43638 + 5.40136I
u = 1.387237 0.184587I
a = 0.652050 + 0.327969I
b = 2.24174 + 0.16120I
4.07832 1.19726I 7.59680 + 5.55973I
u = 1.387237 + 0.184587I
a = 0.652050 0.327969I
b = 2.24174 0.16120I
4.07832 + 1.19726I 7.59680 5.55973I
12
III. I
v
1
= hb
6
+ 3b
5
+ 7b
4
+ 4b
3
+ b
2
+ 2b + 1, 19b
5
+ v + · · · 15b 30, ai
(i) Arc colorings
a
8
=
19b
5
+ 45b
4
+ 105b
3
+ 11b
2
+ 15b + 30
0
a
11
=
0
b
a
4
=
1
0
a
9
=
19b
5
+ 45b
4
+ 105b
3
+ 11b
2
+ 15b + 30
8b
5
+ 19b
4
+ 44b
3
+ 4b
2
+ 5b + 12
a
7
=
19b
5
+ 45b
4
+ 105b
3
+ 11b
2
+ 15b + 30
0
a
3
=
1
0
a
6
=
12b
5
27b
4
63b
3
+ b
2
9b 18
14b
5
33b
4
77b
3
7b
2
11b 21
a
5
=
26b
5
60b
4
140b
3
6b
2
20b 39
14b
5
33b
4
77b
3
7b
2
11b 21
a
10
=
32b
5
75b
4
175b
3
14b
2
25b 50
b
a
1
=
12b
5
+ 27b
4
+ 63b
3
b
2
+ 9b + 18
14b
5
+ 33b
4
+ 77b
3
+ 7b
2
+ 11b + 21
a
2
=
42b
5
+ 98b
4
+ 228b
3
+ 14b
2
+ 28b + 64
14b
5
+ 33b
4
+ 77b
3
+ 7b
2
+ 11b + 22
a
2
=
42b
5
+ 98b
4
+ 228b
3
+ 14b
2
+ 28b + 64
14b
5
+ 33b
4
+ 77b
3
+ 7b
2
+ 11b + 22
(ii) Obstruction class = 1
(iii) Cusp Shapes = 37b
5
+ 86b
4
+ 199b
3
+ 11b
2
+ 20b + 49
13
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 0.162359 + 0.281214I
a = 0
b = 1.16236 2.01326I
1.11345 2.02988I 15.8142 + 11.5861I
v = 0.162359 0.281214I
a = 0
b = 1.16236 + 2.01326I
1.11345 + 2.02988I 15.8142 11.5861I
v = 1.31813 1.15851I
a = 0
b = 0.655769 0.011266I
3.02413 + 0.79824I 4.05323 2.24743I
v = 1.31813 + 1.15851I
a = 0
b = 0.655769 + 0.011266I
3.02413 0.79824I 4.05323 + 2.24743I
v = 0.34423 1.72078I
a = 0
b = 0.318128 0.573545I
3.02413 4.85801I 7.63258 + 5.38377I
v = 0.34423 + 1.72078I
a = 0
b = 0.318128 + 0.573545I
3.02413 + 4.85801I 7.63258 5.38377I
14
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
2
+ u + 1)
3
(u
5
u
4
+ ··· + u 1)(u
79
+ 5u
78
+ ··· + 12u + 1)
c
2
(u
2
+ u + 1)
3
(u
5
+ 3u
4
+ ··· u 1)(u
79
+ 39u
78
+ ··· + 42u 1)
c
3
u
6
(u
5
+ u
4
+ ··· + u 1)(u
79
+ 2u
78
+ ··· + 224u + 64)
c
4
(u
2
u + 1)
3
(u
5
+ u
4
+ ··· + u + 1)(u
79
+ 5u
78
+ ··· + 12u + 1)
c
5
(u
2
+ u + 1)
3
(u
5
u
4
2u
3
+ u
2
+ u + 1)
(u
79
+ 5u
78
+ ··· + 14176u 3137)
c
6
u
5
(1 + 2u u
2
+ u
3
)
2
(u
79
+ 3u
78
+ ··· 192u 32)
c
7
u
6
(u
5
u
4
+ ··· + u + 1)(u
79
+ 2u
78
+ ··· + 224u + 64)
c
8
(u 1)
5
(u
3
+ u
2
1)
2
(u
79
+ 8u
78
+ ··· 5u 1)
c
9
u
5
(1 + 2u + u
2
+ u
3
)
2
(u
79
+ 3u
78
+ ··· 192u 32)
c
10
(u + 1)
5
(u
3
u
2
+ 1)
2
(u
79
+ 8u
78
+ ··· 5u 1)
c
11
(u + 1)
5
(1 + 2u + u
2
+ u
3
)
2
(u
79
+ 38u
78
+ ··· 137u + 1)
15
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y
2
+ y + 1)
3
(y
5
+ 3y
4
+ ··· y 1)(y
79
+ 39y
78
+ ··· + 42y 1)
c
2
(y
2
+ y + 1)
3
(y
5
y
4
+ 8y
3
3y
2
+ 3y 1)
(y
79
+ 7y
78
+ ··· + 2238y 1)
c
3
, c
7
y
6
(y
5
5y
4
+ ··· y 1)(y
79
40y
78
+ ··· + 91136y 4096)
c
5
(y
2
+ y + 1)
3
(y
5
5y
4
+ 8y
3
3y
2
y 1)
(y
79
25y
78
+ ··· + 636907866y 9840769)
c
6
, c
9
y
5
(1 + 2y + 3y
2
+ y
3
)
2
(y
79
+ 39y
78
+ ··· 15872y 1024)
c
8
, c
10
(y 1)
5
(1 + 2y y
2
+ y
3
)
2
(y
79
38y
78
+ ··· 137y 1)
c
11
(y 1)
5
(1 + 2y + 3y
2
+ y
3
)
2
(y
79
+ 14y
78
+ ··· + 11687y 1)
16