12n
0623
(K12n
0623
)
A knot diagram
1
Linearized knot diagam
3 8 11 8 3 10 2 12 4 6 9 5
Solving Sequence
9,11 4,12
3 8 5 6 2 1 7 10
c
11
c
3
c
8
c
4
c
5
c
2
c
1
c
7
c
10
c
6
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.63058 × 10
46
u
50
− 6.85822 × 10
46
u
49
+ ··· + 1.47546 × 10
47
b − 4.38223 × 10
45
,
1.43564 × 10
47
u
50
+ 2.66794 × 10
47
u
49
+ ··· + 2.95092 × 10
46
a − 8.98457 × 10
47
, u
51
+ 2u
50
+ ··· − 20u − 1i
I
u
2
= h734795u
24
− 937935u
23
+ ··· + 1479559b − 7004637,
7267713u
24
− 29159355u
23
+ ··· + 10356913a + 53569336, u
25
− 3u
24
+ ··· + 13u − 7i
* 2 irreducible components of dim
C
= 0, with total 76 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
= h−2.63 × 10
46
u
50
− 6.86 × 10
46
u
49
+ · · · + 1.48 × 10
47
b − 4.38 ×
10
45
, 1.44 × 10
47
u
50
+ 2.67 × 10
47
u
49
+ · · · + 2.95 × 10
46
a − 8.98 ×
10
47
, u
51
+ 2u
50
+ · · · − 20u − 1i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
−4.86506u
50
− 9.04104u
49
+ ··· + 401.075u + 30.4466
0.178289u
50
+ 0.464818u
49
+ ··· − 1.50621u + 0.0297007
a
12
=
1
−u
2
a
3
=
−4.68677u
50
− 8.57622u
49
+ ··· + 399.569u + 30.4763
0.178289u
50
+ 0.464818u
49
+ ··· − 1.50621u + 0.0297007
a
8
=
−u
u
3
+ u
a
5
=
−4.04798u
50
− 7.68387u
49
+ ··· + 394.709u + 29.9218
0.435517u
50
+ 0.759418u
49
+ ··· + 9.58290u + 0.831538
a
6
=
−0.492075u
50
− 1.07500u
49
+ ··· + 8.84678u + 0.791857
0.448896u
50
+ 0.866909u
49
+ ··· − 28.7594u − 1.09977
a
2
=
−5.17498u
50
− 9.34209u
49
+ ··· + 407.539u + 31.1016
0.116517u
50
+ 0.462241u
49
+ ··· − 13.1991u − 0.806114
a
1
=
−1.37890u
50
− 2.73615u
49
+ ··· + 223.956u + 19.6475
0.429385u
50
+ 0.695780u
49
+ ··· + 26.4629u + 1.76995
a
7
=
−2.47371u
50
− 3.53471u
49
+ ··· + 104.745u + 3.16254
0.523695u
50
+ 1.61796u
49
+ ··· − 60.5796u − 4.48349
a
10
=
2.06937u
50
+ 4.75975u
49
+ ··· − 212.579u − 11.9991
0.00104699u
50
+ 0.319182u
49
+ ··· + 22.4132u + 2.24661
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.340250u
50
+ 1.20422u
49
+ ··· − 76.8449u − 18.3790
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
51
+ 79u
50
+ ··· + 3170864u + 157609
c
2
, c
7
u
51
− u
50
+ ··· + 5960u − 397
c
3
u
51
+ 3u
50
+ ··· + 1255u + 1525
c
4
u
51
+ 5u
50
+ ··· + 121755522u + 25773061
c
5
u
51
+ 8u
50
+ ··· + 281253u − 27881
c
6
, c
10
u
51
− 2u
50
+ ··· + 6u + 1
c
8
, c
11
u
51
+ 2u
50
+ ··· − 20u − 1
c
9
u
51
− u
50
+ ··· + 1746u + 2359
c
12
u
51
− 48u
49
+ ··· − 2629425u − 635671
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
51
− 199y
50
+ ··· − 14350346271952y −24840596881
c
2
, c
7
y
51
− 79y
50
+ ··· + 3170864y −157609
c
3
y
51
− 25y
50
+ ··· − 12525125y −2325625
c
4
y
51
− 67y
50
+ ··· + 3374348243821274y −664250673309721
c
5
y
51
− 100y
50
+ ··· + 13844981409y −777350161
c
6
, c
10
y
51
+ 48y
50
+ ··· + 156y −1
c
8
, c
11
y
51
+ 40y
50
+ ··· + 128y −1
c
9
y
51
− 23y
50
+ ··· − 93576124y −5564881
c
12
y
51
− 96y
50
+ ··· − 3893761828431y −404077620241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.994138 + 0.085954I
a = −1.353360 − 0.114217I
b = 1.269410 + 0.406751I
−5.19174 − 2.40432I −8.36352 + 1.90027I
u = −0.994138 − 0.085954I
a = −1.353360 + 0.114217I
b = 1.269410 − 0.406751I
−5.19174 + 2.40432I −8.36352 − 1.90027I
u = 0.786614 + 0.574148I
a = 0.427916 + 0.361953I
b = 0.026370 − 0.354661I
1.35251 + 1.31026I 5.81869 − 2.67401I
u = 0.786614 − 0.574148I
a = 0.427916 − 0.361953I
b = 0.026370 + 0.354661I
1.35251 − 1.31026I 5.81869 + 2.67401I
u = −1.106830 + 0.122939I
a = 1.20913 + 0.99476I
b = −1.38251 − 0.85821I
−16.0490 − 8.5925I −7.67000 + 4.03651I
u = −1.106830 − 0.122939I
a = 1.20913 − 0.99476I
b = −1.38251 + 0.85821I
−16.0490 + 8.5925I −7.67000 − 4.03651I
u = 0.852088 + 0.208570I
a = 0.207993 + 0.892841I
b = 0.149185 − 0.737393I
1.55720 + 1.17905I 3.83068 − 5.32777I
u = 0.852088 − 0.208570I
a = 0.207993 − 0.892841I
b = 0.149185 + 0.737393I
1.55720 − 1.17905I 3.83068 + 5.32777I
u = 0.026626 + 1.187680I
a = −0.614290 − 0.648940I
b = −1.093360 + 0.724987I
−3.93895 − 0.13627I −8.12420 + 0.I
u = 0.026626 − 1.187680I
a = −0.614290 + 0.648940I
b = −1.093360 − 0.724987I
−3.93895 + 0.13627I −8.12420 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.310319 + 1.178590I
a = 0.422592 + 0.832622I
b = 0.701422 − 0.894046I
−1.33059 + 2.80047I 0
u = 0.310319 − 1.178590I
a = 0.422592 − 0.832622I
b = 0.701422 + 0.894046I
−1.33059 − 2.80047I 0
u = 0.158146 + 1.210580I
a = 2.63622 − 0.93189I
b = 0.669895 − 0.455137I
−17.1653 + 1.7421I 0
u = 0.158146 − 1.210580I
a = 2.63622 + 0.93189I
b = 0.669895 + 0.455137I
−17.1653 − 1.7421I 0
u = 1.22316
a = 1.10222
b = −1.25545
−10.6865 −8.45790
u = −0.288984 + 1.202430I
a = 0.47810 − 1.51286I
b = 1.034950 + 0.604820I
−4.73867 − 6.03590I 0
u = −0.288984 − 1.202430I
a = 0.47810 + 1.51286I
b = 1.034950 − 0.604820I
−4.73867 + 6.03590I 0
u = −0.058157 + 0.755707I
a = −0.636801 − 0.138149I
b = 0.020839 + 0.840879I
−2.04460 − 0.19383I −7.78460 + 0.50141I
u = −0.058157 − 0.755707I
a = −0.636801 + 0.138149I
b = 0.020839 − 0.840879I
−2.04460 + 0.19383I −7.78460 − 0.50141I
u = −0.084630 + 1.245450I
a = −0.278589 + 0.972468I
b = −1.54630 − 1.46810I
−7.13833 − 3.92211I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.084630 − 1.245450I
a = −0.278589 − 0.972468I
b = −1.54630 + 1.46810I
−7.13833 + 3.92211I 0
u = 0.016591 + 1.259310I
a = −0.702940 + 1.065780I
b = −0.894998 + 0.074500I
−7.74070 + 2.61044I 0
u = 0.016591 − 1.259310I
a = −0.702940 − 1.065780I
b = −0.894998 − 0.074500I
−7.74070 − 2.61044I 0
u = −0.220765 + 1.247150I
a = −0.083136 − 0.648485I
b = 1.56558 + 0.49642I
−5.51008 − 0.25342I 0
u = −0.220765 − 1.247150I
a = −0.083136 + 0.648485I
b = 1.56558 − 0.49642I
−5.51008 + 0.25342I 0
u = −0.159806 + 1.260190I
a = 0.772250 + 0.695570I
b = 0.721665 − 0.654312I
−11.89480 − 2.24028I 0
u = −0.159806 − 1.260190I
a = 0.772250 − 0.695570I
b = 0.721665 + 0.654312I
−11.89480 + 2.24028I 0
u = 0.161089 + 1.307720I
a = −0.387695 − 0.725680I
b = 1.45529 + 2.33010I
−18.3648 + 2.7821I 0
u = 0.161089 − 1.307720I
a = −0.387695 + 0.725680I
b = 1.45529 − 2.33010I
−18.3648 − 2.7821I 0
u = 0.689622 + 1.168360I
a = 0.106520 + 0.152425I
b = −0.293292 − 0.510638I
−0.59495 + 4.55029I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.689622 − 1.168360I
a = 0.106520 − 0.152425I
b = −0.293292 + 0.510638I
−0.59495 − 4.55029I 0
u = −0.622814 + 0.099336I
a = 1.58845 − 0.82975I
b = −0.913841 + 0.194293I
−1.42485 + 2.61753I −2.41324 − 1.50958I
u = −0.622814 − 0.099336I
a = 1.58845 + 0.82975I
b = −0.913841 − 0.194293I
−1.42485 − 2.61753I −2.41324 + 1.50958I
u = −0.503411 + 1.302910I
a = 0.222439 + 1.271540I
b = −1.185630 − 0.129138I
−9.00099 − 2.99057I 0
u = −0.503411 − 1.302910I
a = 0.222439 − 1.271540I
b = −1.185630 + 0.129138I
−9.00099 + 2.99057I 0
u = 0.40947 + 1.36366I
a = −0.526747 − 0.671786I
b = −0.752311 + 0.792221I
−3.31584 + 5.81138I 0
u = 0.40947 − 1.36366I
a = −0.526747 + 0.671786I
b = −0.752311 − 0.792221I
−3.31584 − 5.81138I 0
u = −0.42839 + 1.36330I
a = 0.044190 + 0.982449I
b = −1.81626 − 0.80792I
−9.79831 − 7.44096I 0
u = −0.42839 − 1.36330I
a = 0.044190 − 0.982449I
b = −1.81626 + 0.80792I
−9.79831 + 7.44096I 0
u = −0.49015 + 1.41710I
a = 0.274461 − 1.344710I
b = 1.60591 + 1.08179I
18.5631 − 14.2339I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.49015 − 1.41710I
a = 0.274461 + 1.344710I
b = 1.60591 − 1.08179I
18.5631 + 14.2339I 0
u = −0.64736 + 1.35681I
a = −0.744754 − 0.575553I
b = 1.33716 − 0.48247I
19.7044 + 2.3380I 0
u = −0.64736 − 1.35681I
a = −0.744754 + 0.575553I
b = 1.33716 + 0.48247I
19.7044 − 2.3380I 0
u = 0.473371 + 0.113783I
a = −1.30948 + 3.62099I
b = −0.86213 − 1.28518I
−13.90700 + 0.51978I −6.17475 − 0.20171I
u = 0.473371 − 0.113783I
a = −1.30948 − 3.62099I
b = −0.86213 + 1.28518I
−13.90700 − 0.51978I −6.17475 + 0.20171I
u = −0.466662
a = −1.70449
b = −0.595548
−8.02552 −22.3740
u = 0.56332 + 1.45126I
a = −0.174961 + 0.929296I
b = 1.39706 − 0.38413I
−15.3202 + 6.3714I 0
u = 0.56332 − 1.45126I
a = −0.174961 − 0.929296I
b = 1.39706 + 0.38413I
−15.3202 − 6.3714I 0
u = −0.166908 + 0.082981I
a = −5.15701 − 2.31484I
b = 0.960493 − 0.750766I
−3.58169 + 2.87292I −8.22764 − 2.63355I
u = −0.166908 − 0.082981I
a = −5.15701 + 2.31484I
b = 0.960493 + 0.750766I
−3.58169 − 2.87292I −8.22764 + 2.63355I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.106308
a = 3.76128
b = 0.501782
−0.859424 −11.7400
10
II. I
u
2
= h7.35 × 10
5
u
24
− 9.38 × 10
5
u
23
+ · · · + 1.48 × 10
6
b − 7.00 × 10
6
, 7.27 ×
10
6
u
24
−2.92×10
7
u
23
+· · ·+1.04×10
7
a+5.36×10
7
, u
25
−3u
24
+· · ·+13u−7i
(i) Arc colorings
a
9
=
0
u
a
11
=
1
0
a
4
=
−0.701726u
24
+ 2.81545u
23
+ ··· + 11.8091u − 5.17233
−0.496631u
24
+ 0.633929u
23
+ ··· − 9.36066u + 4.73427
a
12
=
1
−u
2
a
3
=
−1.19836u
24
+ 3.44938u
23
+ ··· + 2.44847u − 0.438053
−0.496631u
24
+ 0.633929u
23
+ ··· − 9.36066u + 4.73427
a
8
=
−u
u
3
+ u
a
5
=
−1.87701u
24
+ 5.33929u
23
+ ··· + 1.97688u + 3.82771
−1.10959u
24
+ 2.60918u
23
+ ··· − 4.32774u + 2.74843
a
6
=
1.10695u
24
− 3.28329u
23
+ ··· − 3.85869u + 2.45136
0.349387u
24
− 0.152774u
23
+ ··· + 12.4684u − 7.59653
a
2
=
−0.677384u
24
+ 2.96821u
23
+ ··· + 16.9113u − 10.2873
0.373689u
24
− 1.86668u
23
+ ··· − 13.4076u + 7.01127
a
1
=
3.51385u
24
− 9.56743u
23
+ ··· + 5.52009u − 11.3721
0.870320u
24
− 1.50061u
23
+ ··· + 8.95310u − 3.72301
a
7
=
−1.24978u
24
+ 4.85892u
23
+ ··· + 15.5740u + 1.08065
−0.427846u
24
+ 0.336245u
23
+ ··· − 11.0557u + 5.37195
a
10
=
−1.53579u
24
+ 2.59613u
23
+ ··· − 23.5205u + 13.1392
0.791862u
24
− 2.31714u
23
+ ··· − 1.63424u − 0.947584
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1222669
1479559
u
24
−
2760822
1479559
u
23
+ ··· −
13385950
1479559
u +
10657151
1479559
11
(iv) u-Polynomials at the component
12
Crossings u-Polynomials at each crossing
c
1
u
25
− 28u
24
+ ··· + 97u − 9
c
2
u
25
− 14u
23
+ ··· + 5u + 3
c
3
u
25
− 2u
24
+ ··· + 2u − 1
c
4
u
25
− 6u
23
+ ··· − 3u + 1
c
5
u
25
+ 21u
24
+ ··· + 2014u + 271
c
6
u
25
− u
24
+ ··· + u − 1
c
7
u
25
− 14u
23
+ ··· + 5u − 3
c
8
u
25
+ 3u
24
+ ··· + 13u + 7
c
9
u
25
+ 2u
23
+ ··· + 11u − 3
c
10
u
25
+ u
24
+ ··· + u + 1
c
11
u
25
− 3u
24
+ ··· + 13u − 7
c
12
u
25
+ 3u
24
+ ··· − 6u + 1
13
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
25
− 48y
24
+ ··· − 3731y −81
c
2
, c
7
y
25
− 28y
24
+ ··· + 97y −9
c
3
y
25
− 2y
24
+ ··· + 20y −1
c
4
y
25
− 12y
24
+ ··· − 9y −1
c
5
y
25
− 33y
24
+ ··· + 697422y −73441
c
6
, c
10
y
25
+ 15y
24
+ ··· − 15y −1
c
8
, c
11
y
25
+ 19y
24
+ ··· + 29y −49
c
9
y
25
+ 4y
24
+ ··· + 73y −9
c
12
y
25
− 17y
24
+ ··· − 10y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.165879 + 1.036770I
a = 1.99622 − 0.01072I
b = 0.178538 − 1.088440I
−16.3073 − 0.6846I −10.58791 − 0.36694I
u = −0.165879 − 1.036770I
a = 1.99622 + 0.01072I
b = 0.178538 + 1.088440I
−16.3073 + 0.6846I −10.58791 + 0.36694I
u = 0.878653 + 0.614276I
a = −0.388165 − 0.018797I
b = 0.519314 − 0.020674I
0.87332 + 1.24381I −11.80207 − 0.23731I
u = 0.878653 − 0.614276I
a = −0.388165 + 0.018797I
b = 0.519314 + 0.020674I
0.87332 − 1.24381I −11.80207 + 0.23731I
u = −0.241992 + 1.085870I
a = −0.080016 − 1.368120I
b = 0.99835 + 1.05321I
−5.21178 − 4.26834I −9.53069 + 3.29154I
u = −0.241992 − 1.085870I
a = −0.080016 + 1.368120I
b = 0.99835 − 1.05321I
−5.21178 + 4.26834I −9.53069 − 3.29154I
u = −0.525469 + 0.701017I
a = 1.028560 + 0.820742I
b = −0.762718 + 0.513757I
−4.05799 + 1.29515I −9.79398 + 0.20407I
u = −0.525469 − 0.701017I
a = 1.028560 − 0.820742I
b = −0.762718 − 0.513757I
−4.05799 − 1.29515I −9.79398 − 0.20407I
u = 0.777677 + 0.135052I
a = 0.311592 + 1.346060I
b = 0.258764 − 1.085200I
0.620768 + 1.112620I −6.49974 − 2.44499I
u = 0.777677 − 0.135052I
a = 0.311592 − 1.346060I
b = 0.258764 + 1.085200I
0.620768 − 1.112620I −6.49974 + 2.44499I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.310226 + 1.219750I
a = 0.473117 + 0.758104I
b = 0.347343 − 1.317550I
−2.69003 + 2.74082I −10.35889 − 2.75940I
u = 0.310226 − 1.219750I
a = 0.473117 − 0.758104I
b = 0.347343 + 1.317550I
−2.69003 − 2.74082I −10.35889 + 2.75940I
u = −0.080358 + 1.265810I
a = −0.337318 + 0.390448I
b = −1.46431 + 0.22680I
−6.46312 + 1.42279I −11.59416 − 0.83507I
u = −0.080358 − 1.265810I
a = −0.337318 − 0.390448I
b = −1.46431 − 0.22680I
−6.46312 − 1.42279I −11.59416 + 0.83507I
u = −0.688617 + 0.067271I
a = −1.045060 + 0.756974I
b = 1.051830 − 0.523343I
−2.21685 + 3.76261I −5.20350 − 5.51009I
u = −0.688617 − 0.067271I
a = −1.045060 − 0.756974I
b = 1.051830 + 0.523343I
−2.21685 − 3.76261I −5.20350 + 5.51009I
u = −0.357165 + 1.267210I
a = −0.555297 + 1.045050I
b = −1.27741 − 0.62995I
−5.96754 − 7.70508I −10.28604 + 7.69329I
u = −0.357165 − 1.267210I
a = −0.555297 − 1.045050I
b = −1.27741 + 0.62995I
−5.96754 + 7.70508I −10.28604 − 7.69329I
u = 0.159087 + 1.319010I
a = 0.607715 − 0.734484I
b = 0.665222 + 0.443905I
−12.13970 + 2.72655I −15.2074 − 7.6255I
u = 0.159087 − 1.319010I
a = 0.607715 + 0.734484I
b = 0.665222 − 0.443905I
−12.13970 − 2.72655I −15.2074 + 7.6255I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629591
a = −1.11654
b = −0.430836
−7.69986 2.83470
u = 0.367086 + 1.360610I
a = −0.793602 − 0.650211I
b = −0.772849 + 0.983417I
−4.11796 + 5.31027I −12.29936 − 3.61405I
u = 0.367086 − 1.360610I
a = −0.793602 + 0.650211I
b = −0.772849 − 0.983417I
−4.11796 − 5.31027I −12.29936 + 3.61405I
u = 0.75195 + 1.19779I
a = 0.054806 − 0.462184I
b = −0.526659 + 0.040712I
−0.97942 + 4.93110I −10.7537 − 10.6108I
u = 0.75195 − 1.19779I
a = 0.054806 + 0.462184I
b = −0.526659 − 0.040712I
−0.97942 − 4.93110I −10.7537 + 10.6108I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
25
− 28u
24
+ ··· + 97u − 9)
· (u
51
+ 79u
50
+ ··· + 3170864u + 157609)
c
2
(u
25
− 14u
23
+ ··· + 5u + 3)(u
51
− u
50
+ ··· + 5960u − 397)
c
3
(u
25
− 2u
24
+ ··· + 2u − 1)(u
51
+ 3u
50
+ ··· + 1255u + 1525)
c
4
(u
25
− 6u
23
+ ··· − 3u + 1)
· (u
51
+ 5u
50
+ ··· + 121755522u + 25773061)
c
5
(u
25
+ 21u
24
+ ··· + 2014u + 271)
· (u
51
+ 8u
50
+ ··· + 281253u − 27881)
c
6
(u
25
− u
24
+ ··· + u − 1)(u
51
− 2u
50
+ ··· + 6u + 1)
c
7
(u
25
− 14u
23
+ ··· + 5u − 3)(u
51
− u
50
+ ··· + 5960u − 397)
c
8
(u
25
+ 3u
24
+ ··· + 13u + 7)(u
51
+ 2u
50
+ ··· − 20u − 1)
c
9
(u
25
+ 2u
23
+ ··· + 11u − 3)(u
51
− u
50
+ ··· + 1746u + 2359)
c
10
(u
25
+ u
24
+ ··· + u + 1)(u
51
− 2u
50
+ ··· + 6u + 1)
c
11
(u
25
− 3u
24
+ ··· + 13u − 7)(u
51
+ 2u
50
+ ··· − 20u − 1)
c
12
(u
25
+ 3u
24
+ ··· − 6u + 1)(u
51
− 48u
49
+ ··· − 2629425u − 635671)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
25
− 48y
24
+ ··· − 3731y −81)
· (y
51
− 199y
50
+ ··· − 14350346271952y −24840596881)
c
2
, c
7
(y
25
− 28y
24
+ ··· + 97y −9)
· (y
51
− 79y
50
+ ··· + 3170864y −157609)
c
3
(y
25
− 2y
24
+ ··· + 20y −1)
· (y
51
− 25y
50
+ ··· − 12525125y −2325625)
c
4
(y
25
− 12y
24
+ ··· − 9y −1)
· (y
51
− 67y
50
+ ··· + 3374348243821274y −664250673309721)
c
5
(y
25
− 33y
24
+ ··· + 697422y −73441)
· (y
51
− 100y
50
+ ··· + 13844981409y −777350161)
c
6
, c
10
(y
25
+ 15y
24
+ ··· − 15y −1)(y
51
+ 48y
50
+ ··· + 156y −1)
c
8
, c
11
(y
25
+ 19y
24
+ ··· + 29y −49)(y
51
+ 40y
50
+ ··· + 128y −1)
c
9
(y
25
+ 4y
24
+ ··· + 73y −9)
· (y
51
− 23y
50
+ ··· − 93576124y −5564881)
c
12
(y
25
− 17y
24
+ ··· − 10y −1)
· (y
51
− 96y
50
+ ··· − 3893761828431y −404077620241)
20
