12n
0001
(K12n
0001
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 10 5 6 12 7 9 11
Solving Sequence
5,7 8,10
11 4 6 9 12 3 2 1
c
7
c
10
c
4
c
6
c
8
c
11
c
3
c
2
c
1
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.37455 × 10
135
u
43
− 1.12079 × 10
136
u
42
+ ··· + 3.29429 × 10
139
b + 3.17022 × 10
139
,
5.94999 × 10
134
u
43
− 5.65113 × 10
136
u
42
+ ··· + 1.31772 × 10
140
a − 1.01004 × 10
141
,
u
44
− 2u
43
+ ··· + 18432u
2
+ 4096i
I
u
2
= hb, 2u
3
+ u
2
+ a + 5u + 1, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
v
1
= ha, −623v
11
+ 133v
10
+ ··· + 263b + 608,
v
12
− v
11
− v
10
+ 6v
9
− 5v
8
− v
7
+ 5v
6
− 9v
5
+ 11v
4
− 7v
3
+ 4v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 60 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h4.37 × 10
135
u
43
− 1.12 × 10
136
u
42
+ · · · + 3.29 × 10
139
b + 3.17 ×
10
139
, 5.95 × 10
134
u
43
− 5.65 × 10
136
u
42
+ · · · + 1.32 × 10
140
a − 1.01 ×
10
141
, u
44
− 2u
43
+ · · · + 18432u
2
+ 4096i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
−4.51538 × 10
−6
u
43
+ 0.000428858u
42
+ ··· + 11.6690u + 7.66506
−0.000132792u
43
+ 0.000340222u
42
+ ··· − 0.117088u − 0.962337
a
11
=
−0.000137307u
43
+ 0.000769080u
42
+ ··· + 11.5519u + 6.70273
−0.000132792u
43
+ 0.000340222u
42
+ ··· − 0.117088u − 0.962337
a
4
=
u
u
3
+ u
a
6
=
0.0000465812u
43
− 0.0000760961u
42
+ ··· − 2.91296u − 1.00498
−0.000146319u
43
+ 0.000385840u
42
+ ··· − 0.577119u − 0.161513
a
9
=
−0.0000233627u
43
+ 0.0000758354u
42
+ ··· + 0.973632u + 0.112523
−0.0000848623u
43
+ 0.000160319u
42
+ ··· + 0.425724u − 0.685913
a
12
=
−0.000153153u
43
+ 0.000767618u
42
+ ··· + 10.5379u + 6.59579
−0.0000848623u
43
+ 0.000160319u
42
+ ··· + 0.425724u − 0.685913
a
3
=
0.000294989u
43
− 0.000566017u
42
+ ··· + 5.23132u + 1.61723
0.0000291099u
43
− 0.0000723952u
42
+ ··· + 0.112523u + 0.0956936
a
2
=
0.000294989u
43
− 0.000566017u
42
+ ··· + 5.23132u + 1.61723
0.0000637808u
43
− 0.000165274u
42
+ ··· − 1.09575u − 0.00245309
a
1
=
−0.0000848166u
43
+ 0.000176172u
42
+ ··· + 2.52664u + 0.913367
−0.0000382354u
43
+ 0.000100076u
42
+ ··· − 0.386322u − 0.0916094
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00275050u
43
− 0.00388332u
42
+ ··· + 65.4192u + 6.54832
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 8u
43
+ ··· + 22u + 1
c
2
, c
5
u
44
+ 8u
43
+ ··· + 6u + 1
c
3
u
44
− 8u
43
+ ··· + 577140u + 41508
c
4
, c
7
u
44
− 2u
43
+ ··· + 18432u
2
+ 4096
c
6
, c
10
u
44
− 3u
43
+ ··· − 120u + 16
c
8
u
44
+ 4u
43
+ ··· + 2u + 1
c
9
, c
11
u
44
− 7u
43
+ ··· + 8u + 1
c
12
u
44
+ 17u
43
+ ··· + 48u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
+ 64y
43
+ ··· + 22y + 1
c
2
, c
5
y
44
+ 8y
43
+ ··· + 22y + 1
c
3
y
44
+ 120y
43
+ ··· + 42862402296y + 1722914064
c
4
, c
7
y
44
+ 70y
43
+ ··· + 150994944y + 16777216
c
6
, c
10
y
44
− 33y
43
+ ··· − 576y + 256
c
8
y
44
− 80y
43
+ ··· + 14y + 1
c
9
, c
11
y
44
− 17y
43
+ ··· − 48y + 1
c
12
y
44
+ 27y
43
+ ··· − 48y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.587750 + 0.727199I
a = 0.306966 − 0.640744I
b = −1.002580 + 0.067245I
0.0012605 + 0.0509035I −2.15533 + 0.17848I
u = −0.587750 − 0.727199I
a = 0.306966 + 0.640744I
b = −1.002580 − 0.067245I
0.0012605 − 0.0509035I −2.15533 − 0.17848I
u = 0.730847 + 0.390041I
a = 0.437616 − 0.402493I
b = −1.132220 − 0.401644I
2.44756 + 1.58887I 2.11619 + 0.16814I
u = 0.730847 − 0.390041I
a = 0.437616 + 0.402493I
b = −1.132220 + 0.401644I
2.44756 − 1.58887I 2.11619 − 0.16814I
u = −0.611739 + 0.487067I
a = −0.156519 + 0.760305I
b = 1.033990 + 0.442395I
−0.96246 + 4.43252I −5.23001 − 6.92056I
u = −0.611739 − 0.487067I
a = −0.156519 − 0.760305I
b = 1.033990 − 0.442395I
−0.96246 − 4.43252I −5.23001 + 6.92056I
u = −0.496705 + 0.586520I
a = 0.803429 − 0.614772I
b = −0.139559 − 0.567313I
0.003759 + 1.358260I 0.43877 − 4.70156I
u = −0.496705 − 0.586520I
a = 0.803429 + 0.614772I
b = −0.139559 + 0.567313I
0.003759 − 1.358260I 0.43877 + 4.70156I
u = 0.579885 + 0.494350I
a = −0.225969 + 0.616510I
b = 1.124200 + 0.621018I
0.29937 + 6.78003I −1.02805 − 2.83496I
u = 0.579885 − 0.494350I
a = −0.225969 − 0.616510I
b = 1.124200 − 0.621018I
0.29937 − 6.78003I −1.02805 + 2.83496I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.511627 + 0.444892I
a = 1.093280 − 0.445499I
b = 0.072410 − 0.459091I
−0.021919 + 1.380100I −0.83838 − 4.05172I
u = −0.511627 − 0.444892I
a = 1.093280 + 0.445499I
b = 0.072410 + 0.459091I
−0.021919 − 1.380100I −0.83838 + 4.05172I
u = 0.299193 + 0.591308I
a = 2.27653 − 0.10382I
b = −0.095849 + 0.693490I
−1.10964 + 2.86683I −0.194269 − 1.150607I
u = 0.299193 − 0.591308I
a = 2.27653 + 0.10382I
b = −0.095849 − 0.693490I
−1.10964 − 2.86683I −0.194269 + 1.150607I
u = −0.524212 + 0.325358I
a = −0.254256 + 1.159040I
b = 0.408649 + 0.820268I
−1.87563 − 1.38329I −4.88472 + 0.88974I
u = −0.524212 − 0.325358I
a = −0.254256 − 1.159040I
b = 0.408649 − 0.820268I
−1.87563 + 1.38329I −4.88472 − 0.88974I
u = 0.418662 + 0.429381I
a = −1.12716 + 1.24862I
b = 0.573000 + 0.460129I
−2.37055 − 0.63845I −5.51576 − 1.51985I
u = 0.418662 − 0.429381I
a = −1.12716 − 1.24862I
b = 0.573000 − 0.460129I
−2.37055 + 0.63845I −5.51576 + 1.51985I
u = −0.89693 + 1.10743I
a = −0.995115 + 0.841611I
b = 1.367840 + 0.047642I
3.71063 − 1.12943I 0
u = −0.89693 − 1.10743I
a = −0.995115 − 0.841611I
b = 1.367840 − 0.047642I
3.71063 + 1.12943I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11702 + 1.45676I
a = −0.0541211 − 0.0270150I
b = −0.525995 + 0.033075I
5.55211 + 3.08791I 0
u = −0.11702 − 1.45676I
a = −0.0541211 + 0.0270150I
b = −0.525995 − 0.033075I
5.55211 − 3.08791I 0
u = −0.50581 + 1.37651I
a = 1.240180 − 0.406596I
b = −1.36837 + 0.37289I
3.06981 − 7.05974I 0
u = −0.50581 − 1.37651I
a = 1.240180 + 0.406596I
b = −1.36837 − 0.37289I
3.06981 + 7.05974I 0
u = 0.175618 + 0.424295I
a = 6.42637 + 3.07840I
b = −0.342417 + 0.239754I
−1.92351 − 1.76678I 8.1243 + 28.0957I
u = 0.175618 − 0.424295I
a = 6.42637 − 3.07840I
b = −0.342417 − 0.239754I
−1.92351 + 1.76678I 8.1243 − 28.0957I
u = 1.11832 + 1.28481I
a = 0.800873 + 0.371072I
b = −1.46830 − 0.16447I
5.66847 + 1.40169I 0
u = 1.11832 − 1.28481I
a = 0.800873 − 0.371072I
b = −1.46830 + 0.16447I
5.66847 − 1.40169I 0
u = 1.44144 + 0.90992I
a = −0.651114 − 0.640799I
b = 1.46122 − 0.25816I
5.49304 − 4.87559I 0
u = 1.44144 − 0.90992I
a = −0.651114 + 0.640799I
b = 1.46122 + 0.25816I
5.49304 + 4.87559I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19127 + 2.08900I
a = 1.45451 + 0.12813I
b = −1.301920 + 0.064317I
8.56289 − 3.55763I 0
u = 0.19127 − 2.08900I
a = 1.45451 − 0.12813I
b = −1.301920 − 0.064317I
8.56289 + 3.55763I 0
u = −0.36840 + 2.10955I
a = −0.0581272 + 0.0787356I
b = −0.280354 + 1.371580I
10.23040 + 6.56728I 0
u = −0.36840 − 2.10955I
a = −0.0581272 − 0.0787356I
b = −0.280354 − 1.371580I
10.23040 − 6.56728I 0
u = 0.76685 + 2.01630I
a = 1.004910 + 0.650911I
b = −1.42673 + 0.75889I
13.8428 − 14.0825I 0
u = 0.76685 − 2.01630I
a = 1.004910 − 0.650911I
b = −1.42673 − 0.75889I
13.8428 + 14.0825I 0
u = −0.01900 + 2.17067I
a = 0.0496534 − 0.0826517I
b = −0.160771 − 1.385870I
10.46560 + 0.62164I 0
u = −0.01900 − 2.17067I
a = 0.0496534 + 0.0826517I
b = −0.160771 + 1.385870I
10.46560 − 0.62164I 0
u = 0.61800 + 2.21033I
a = −1.060520 − 0.447387I
b = 1.56771 − 0.52759I
16.1314 − 7.4218I 0
u = 0.61800 − 2.21033I
a = −1.060520 + 0.447387I
b = 1.56771 + 0.52759I
16.1314 + 7.4218I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.48180 + 2.24551I
a = 0.994426 − 0.463135I
b = −1.49947 − 0.71295I
14.6778 + 6.8524I 0
u = −0.48180 − 2.24551I
a = 0.994426 + 0.463135I
b = −1.49947 + 0.71295I
14.6778 − 6.8524I 0
u = −0.21908 + 2.39343I
a = −1.055840 + 0.248840I
b = 1.63553 + 0.43161I
16.6724 + 0.0015I 0
u = −0.21908 − 2.39343I
a = −1.055840 − 0.248840I
b = 1.63553 − 0.43161I
16.6724 − 0.0015I 0
9
II. I
u
2
= hb, 2u
3
+ u
2
+ a + 5u + 1, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
−2u
3
− u
2
− 5u − 1
0
a
11
=
−2u
3
− u
2
− 5u − 1
0
a
4
=
u
u
3
+ u
a
6
=
1
0
a
9
=
u
2
+ 1
u
2
a
12
=
−2u
3
− 2u
2
− 5u − 2
−u
2
a
3
=
u
3
+ 2u
u
3
+ u
a
2
=
u
3
+ 2u
u
3
+ u
2
+ 2u + 1
a
1
=
−u
2
− 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
2
− 2u − 1
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
u
4
+ u
3
+ 5u
2
− u + 2
c
5
u
4
+ u
3
+ u
2
+ 1
c
6
, c
10
u
4
c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
u
4
− 5u
3
+ 7u
2
− 2u + 1
c
9
(u − 1)
4
c
11
, c
12
(u + 1)
4
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
6
, c
10
y
4
c
8
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
9
, c
11
, c
12
(y −1)
4
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 0.59074 − 2.34806I
b = 0
−1.85594 + 1.41510I −0.51206 − 2.21528I
u = −0.395123 − 0.506844I
a = 0.59074 + 2.34806I
b = 0
−1.85594 − 1.41510I −0.51206 + 2.21528I
u = −0.10488 + 1.55249I
a = 0.409261 − 0.055548I
b = 0
5.14581 + 3.16396I −7.98794 − 4.08190I
u = −0.10488 − 1.55249I
a = 0.409261 + 0.055548I
b = 0
5.14581 − 3.16396I −7.98794 + 4.08190I
13
III. I
v
1
= ha, −623v
11
+ 133v
10
+ · · · + 263b + 608, v
12
− v
11
+ · · · − 3v + 1i
(i) Arc colorings
a
5
=
v
0
a
7
=
1
0
a
8
=
1
0
a
10
=
0
2.36882v
11
− 0.505703v
10
+ ··· + 5.05323v −2.31179
a
11
=
2.36882v
11
− 0.505703v
10
+ ··· + 5.05323v −2.31179
2.36882v
11
− 0.505703v
10
+ ··· + 5.05323v −2.31179
a
4
=
v
0
a
6
=
1
6.30038v
11
− 2.03042v
10
+ ··· + 12.9506v −7.99620
a
9
=
−6.30038v
11
+ 2.03042v
10
+ ··· − 12.9506v + 8.99620
−10.9962v
11
+ 3.69582v
10
+ ··· − 22.4943v + 16.0380
a
12
=
−4.69582v
11
+ 1.66540v
10
+ ··· − 9.54373v + 7.04183
−10.9962v
11
+ 3.69582v
10
+ ··· − 22.4943v + 16.0380
a
3
=
−4.26996v
11
+ 1.59696v
10
+ ··· − 9.90494v + 6.30038
−7.30038v
11
+ 3.03042v
10
+ ··· − 16.9506v + 10.9962
a
2
=
−1.59696v
11
+ 0.756654v
10
+ ··· − 4.39544v + 2.03042
−7.30038v
11
+ 3.03042v
10
+ ··· − 16.9506v + 10.9962
a
1
=
−1
−6.30038v
11
+ 2.03042v
10
+ ··· − 12.9506v + 7.99620
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
3729
263
v
11
+
1130
263
v
10
+
4668
263
v
9
−
19527
263
v
8
+
5107
263
v
7
+
8452
263
v
6
−
14914
263
v
5
+
24322
263
v
4
−
22832
263
v
3
+
7241
263
v
2
−
5199
263
v +
4001
263
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
7
u
12
c
6
, c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
8
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
9
, c
10
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
12
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
7
y
12
c
6
, c
9
, c
10
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
8
, c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.815127 + 0.417821I
a = 0
b = −1.002190 − 0.295542I
1.89061 − 1.10558I 2.90246 + 2.38339I
v = 0.815127 − 0.417821I
a = 0
b = −1.002190 + 0.295542I
1.89061 + 1.10558I 2.90246 − 2.38339I
v = −0.045720 + 0.914831I
a = 0
b = −1.002190 + 0.295542I
1.89061 − 2.95419I −0.30406 + 4.29351I
v = −0.045720 − 0.914831I
a = 0
b = −1.002190 − 0.295542I
1.89061 + 2.95419I −0.30406 − 4.29351I
v = 0.679704 + 0.059778I
a = 0
b = 1.073950 + 0.558752I
3.66314I 0.57335 − 2.34011I
v = 0.679704 − 0.059778I
a = 0
b = 1.073950 − 0.558752I
− 3.66314I 0.57335 + 2.34011I
v = −0.288082 + 0.618530I
a = 0
b = 1.073950 − 0.558752I
− 7.72290I −3.68173 + 10.26242I
v = −0.288082 − 0.618530I
a = 0
b = 1.073950 + 0.558752I
7.72290I −3.68173 − 10.26242I
v = 0.93136 + 1.30101I
a = 0
b = 0.428243 − 0.664531I
−1.89061 + 2.95419I −6.66783 − 2.20469I
v = 0.93136 − 1.30101I
a = 0
b = 0.428243 + 0.664531I
−1.89061 − 2.95419I −6.66783 + 2.20469I
17
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.59239 + 0.15607I
a = 0
b = 0.428243 − 0.664531I
−1.89061 − 1.10558I −2.82220 + 2.24866I
v = −1.59239 − 0.15607I
a = 0
b = 0.428243 + 0.664531I
−1.89061 + 1.10558I −2.82220 − 2.24866I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
44
+ 8u
43
+ ··· + 22u + 1)
c
2
((u
2
+ u + 1)
6
)(u
4
− u
3
+ u
2
+ 1)(u
44
+ 8u
43
+ ··· + 6u + 1)
c
3
(u
2
− u + 1)
6
(u
4
+ u
3
+ 5u
2
− u + 2)
· (u
44
− 8u
43
+ ··· + 577140u + 41508)
c
4
u
12
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
44
− 2u
43
+ ··· + 18432u
2
+ 4096)
c
5
((u
2
− u + 1)
6
)(u
4
+ u
3
+ u
2
+ 1)(u
44
+ 8u
43
+ ··· + 6u + 1)
c
6
u
4
(u
6
− u
5
+ ··· − u + 1)
2
(u
44
− 3u
43
+ ··· − 120u + 16)
c
7
u
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
44
− 2u
43
+ ··· + 18432u
2
+ 4096)
c
8
(u
4
− 5u
3
+ 7u
2
− 2u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
44
+ 4u
43
+ ··· + 2u + 1)
c
9
((u − 1)
4
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
44
− 7u
43
+ ··· + 8u + 1)
c
10
u
4
(u
6
+ u
5
+ ··· + u + 1)
2
(u
44
− 3u
43
+ ··· − 120u + 16)
c
11
((u + 1)
4
)(u
6
− u
5
+ ··· − u + 1)
2
(u
44
− 7u
43
+ ··· + 8u + 1)
c
12
(u + 1)
4
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
· (u
44
+ 17u
43
+ ··· + 48u + 1)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
44
+ 64y
43
+ ··· + 22y + 1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
44
+ 8y
43
+ ··· + 22y + 1)
c
3
(y
2
+ y + 1)
6
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
· (y
44
+ 120y
43
+ ··· + 42862402296y + 1722914064)
c
4
, c
7
y
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
44
+ 70y
43
+ ··· + 150994944y + 16777216)
c
6
, c
10
y
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
44
− 33y
43
+ ··· − 576y + 256)
c
8
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
44
− 80y
43
+ ··· + 14y + 1)
c
9
, c
11
(y −1)
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
44
− 17y
43
+ ··· − 48y + 1)
c
12
((y −1)
4
)(y
6
+ y
5
+ ··· + 3y + 1)
2
(y
44
+ 27y
43
+ ··· − 48y + 1)
20
