12a
0987
(K12a
0987
)
A knot diagram
1
Linearized knot diagam
4 6 11 10 8 3 12 5 1 2 7 9
Solving Sequence
2,6 3,11
4 7 12 8 1 5 10 9
c
2
c
3
c
6
c
11
c
7
c
1
c
5
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.86463 × 10
467
u
122
− 1.08545 × 10
468
u
121
+ ··· + 8.79558 × 10
470
b + 5.71526 × 10
472
,
7.73571 × 10
471
u
122
− 5.76169 × 10
472
u
121
+ ··· + 7.85533 × 10
474
a − 1.00953 × 10
477
,
u
123
− 9u
122
+ ··· − 2948798u + 321516i
I
u
2
= h5.83720 × 10
21
u
26
− 2.72828 × 10
22
u
25
+ ··· + 2.89110 × 10
21
b − 1.48508 × 10
22
,
− 2.42389 × 10
21
u
26
+ 6.65883 × 10
21
u
25
+ ··· + 2.89110 × 10
21
a − 7.96830 × 10
21
, u
27
− 5u
26
+ ··· − 6u + 1i
I
u
3
= h−3a
3
− 2a
2
+ 23b + 10a − 17, a
4
+ a
3
+ 2a
2
+ 2a + 7, u + 1i
I
u
4
= hb + 1, a + 1, u + 1i
I
u
5
= hb
5
+ 2b
4
a + b
3
a
2
− 3b
3
− 4b
2
a − a
2
b + 3b + a − 1, u + 1i
I
v
1
= ha, b
4
+ b
3
+ 1, v − 1i
I
v
2
= ha, b − 1, v − 1i
* 6 irreducible components of dim
C
= 0, with total 160 representations.
* 1 irreducible components of dim
C
= 1
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
= h1.86 × 10
467
u
122
− 1.09 × 10
468
u
121
+ · · · + 8.80 × 10
470
b + 5.72 ×
10
472
, 7.74 × 10
471
u
122
− 5.76 × 10
472
u
121
+ · · · + 7.86 × 10
474
a − 1.01 ×
10
477
, u
123
− 9u
122
+ · · · − 2948798u + 321516i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
11
=
−0.000984772u
122
+ 0.00733475u
121
+ ··· − 1234.17u + 128.515
−0.000211996u
122
+ 0.00123409u
121
+ ··· + 422.058u − 64.9788
a
4
=
−0.000241210u
122
+ 0.00133391u
121
+ ··· + 646.806u − 97.3597
0.000175060u
122
− 0.00154456u
121
+ ··· + 739.001u − 94.1782
a
7
=
u
−u
3
+ u
a
12
=
−0.00299049u
122
+ 0.0230242u
121
+ ··· − 5627.68u + 651.606
0.000450486u
122
− 0.00419159u
121
+ ··· + 2348.96u − 301.333
a
8
=
0.000631004u
122
− 0.00491033u
121
+ ··· + 1254.82u − 147.152
0.000419888u
122
− 0.00359154u
121
+ ··· + 1623.36u − 207.809
a
1
=
−0.00262832u
122
+ 0.0218172u
121
+ ··· − 8417.78u + 1051.74
−0.00182420u
122
+ 0.0147858u
121
+ ··· − 5107.11u + 627.881
a
5
=
0.00219190u
122
− 0.0176406u
121
+ ··· + 5863.43u − 716.510
0.000438168u
122
− 0.00344815u
121
+ ··· + 979.105u − 116.314
a
10
=
−0.00119677u
122
+ 0.00856883u
121
+ ··· − 812.114u + 63.5364
−0.000211996u
122
+ 0.00123409u
121
+ ··· + 422.058u − 64.9788
a
9
=
−0.00190443u
122
+ 0.0157881u
121
+ ··· − 6034.26u + 752.676
−0.00194277u
122
+ 0.0160788u
121
+ ··· − 6183.07u + 771.699
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.00105806u
122
+ 0.00697489u
121
+ ··· + 464.652u − 97.2317
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
16(16u
123
− 216u
122
+ ··· − 705357u + 15123)
c
2
, c
6
u
123
+ 9u
122
+ ··· − 2948798u − 321516
c
3
48(48u
123
+ 1409u
121
+ ··· − 1.26434 × 10
9
u + 8.64983 × 10
7
)
c
4
48(48u
123
− 96u
122
+ ··· − 1112u − 192)
c
5
, c
8
16(16u
123
+ 88u
122
+ ··· − 21054u − 1797)
c
7
, c
11
16(16u
123
− 8u
122
+ ··· + 1543440u + 242409)
c
9
, c
12
u
123
+ 12u
122
+ ··· + 413544u + 22932
c
10
16(16u
123
+ 72u
122
+ ··· − 3849u − 357)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
256(256y
123
+ 5088y
122
+ ··· + 3.00705 × 10
11
y − 2.28705 × 10
8
)
c
2
, c
6
y
123
− 73y
122
+ ··· − 2074541056628y − 103372538256
c
3
2304(2304y
123
+ 135264y
122
+ ··· − 6.88635 × 10
16
y − 7.48195 × 10
15
)
c
4
2304(2304y
123
− 96y
122
+ ··· + 1.09813 × 10
7
y − 36864)
c
5
, c
8
256(256y
123
+ 14560y
122
+ ··· + 5.22257 × 10
7
y − 3229209)
c
7
, c
11
256
· (256y
123
− 25888y
122
+ ··· + 2905429891470y − 58762123281)
c
9
, c
12
y
123
− 88y
122
+ ··· + 39388547160y − 525876624
c
10
256(256y
123
− 544y
122
+ ··· + 1.34154 × 10
7
y − 127449)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.828835 + 0.559706I
a = 0.410272 + 1.240470I
b = 0.542712 + 0.036145I
−3.93622 + 2.28082I 0
u = 0.828835 − 0.559706I
a = 0.410272 − 1.240470I
b = 0.542712 − 0.036145I
−3.93622 − 2.28082I 0
u = −0.083475 + 0.998976I
a = 0.121967 − 0.191332I
b = 0.656002 + 0.694825I
1.59978 − 3.93172I 0
u = −0.083475 − 0.998976I
a = 0.121967 + 0.191332I
b = 0.656002 − 0.694825I
1.59978 + 3.93172I 0
u = 0.976198 + 0.186088I
a = −0.700323 + 0.444307I
b = 1.59666 − 0.10866I
2.89132 + 0.96593I 0
u = 0.976198 − 0.186088I
a = −0.700323 − 0.444307I
b = 1.59666 + 0.10866I
2.89132 − 0.96593I 0
u = 0.830942 + 0.593877I
a = −1.187380 + 0.173809I
b = −0.601051 + 0.305501I
0.59992 + 6.10560I 0
u = 0.830942 − 0.593877I
a = −1.187380 − 0.173809I
b = −0.601051 − 0.305501I
0.59992 − 6.10560I 0
u = 1.024870 + 0.196236I
a = 0.928097 − 0.195465I
b = 1.037450 − 0.230394I
2.39522 + 10.37410I 0
u = 1.024870 − 0.196236I
a = 0.928097 + 0.195465I
b = 1.037450 + 0.230394I
2.39522 − 10.37410I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.390784 + 0.970261I
a = −0.309480 − 0.661325I
b = 0.470803 − 0.882112I
−0.51041 − 4.68989I 0
u = −0.390784 − 0.970261I
a = −0.309480 + 0.661325I
b = 0.470803 + 0.882112I
−0.51041 + 4.68989I 0
u = 0.013998 + 1.051830I
a = −0.440184 + 0.218061I
b = −1.017510 − 0.805771I
6.77422 − 6.54883I 0
u = 0.013998 − 1.051830I
a = −0.440184 − 0.218061I
b = −1.017510 + 0.805771I
6.77422 + 6.54883I 0
u = 1.036360 + 0.208971I
a = −0.488519 − 0.219809I
b = −1.200680 + 0.226964I
−1.47789 + 5.31372I 0
u = 1.036360 − 0.208971I
a = −0.488519 + 0.219809I
b = −1.200680 − 0.226964I
−1.47789 − 5.31372I 0
u = −1.055400 + 0.128723I
a = 0.10188 − 1.85654I
b = −0.54814 + 1.48844I
3.80056 + 1.51795I 0
u = −1.055400 − 0.128723I
a = 0.10188 + 1.85654I
b = −0.54814 − 1.48844I
3.80056 − 1.51795I 0
u = −0.034599 + 0.923850I
a = 0.123180 + 0.215194I
b = −0.354838 − 0.932334I
4.30405 − 4.99081I 0
u = −0.034599 − 0.923850I
a = 0.123180 − 0.215194I
b = −0.354838 + 0.932334I
4.30405 + 4.99081I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.024660 + 0.330349I
a = −1.159970 − 0.046719I
b = 0.387313 − 0.417488I
4.05951 + 0.77163I 0
u = −1.024660 − 0.330349I
a = −1.159970 + 0.046719I
b = 0.387313 + 0.417488I
4.05951 − 0.77163I 0
u = 0.752714 + 0.794721I
a = 0.412107 + 0.130757I
b = 0.797168 − 0.071425I
−4.37049 + 2.83892I 0
u = 0.752714 − 0.794721I
a = 0.412107 − 0.130757I
b = 0.797168 + 0.071425I
−4.37049 − 2.83892I 0
u = −1.090890 + 0.119207I
a = −0.11920 − 1.46693I
b = 1.04096 + 1.32503I
2.28408 + 1.07076I 0
u = −1.090890 − 0.119207I
a = −0.11920 + 1.46693I
b = 1.04096 − 1.32503I
2.28408 − 1.07076I 0
u = −1.010600 + 0.479528I
a = 0.48517 − 1.74911I
b = 1.358710 + 0.383974I
2.04201 − 2.12820I 0
u = −1.010600 − 0.479528I
a = 0.48517 + 1.74911I
b = 1.358710 − 0.383974I
2.04201 + 2.12820I 0
u = 0.414351 + 0.774816I
a = −0.0630441 + 0.0216587I
b = −0.874765 − 0.091336I
−3.02638 − 1.52135I 0
u = 0.414351 − 0.774816I
a = −0.0630441 − 0.0216587I
b = −0.874765 + 0.091336I
−3.02638 + 1.52135I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.462837 + 0.742107I
a = −0.141675 + 0.465436I
b = −1.21146 + 0.76832I
−4.81381 + 2.77717I 0
u = −0.462837 − 0.742107I
a = −0.141675 − 0.465436I
b = −1.21146 − 0.76832I
−4.81381 − 2.77717I 0
u = −0.229596 + 0.838615I
a = −0.661012 − 0.274328I
b = −0.679351 + 0.809644I
7.60389 − 0.56705I 0
u = −0.229596 − 0.838615I
a = −0.661012 + 0.274328I
b = −0.679351 − 0.809644I
7.60389 + 0.56705I 0
u = 0.750670 + 0.409190I
a = −0.50829 − 1.77502I
b = −0.067633 − 0.149073I
0.40590 − 1.89067I 0
u = 0.750670 − 0.409190I
a = −0.50829 + 1.77502I
b = −0.067633 + 0.149073I
0.40590 + 1.89067I 0
u = 1.034840 + 0.517031I
a = 0.079654 − 1.254180I
b = −0.819752 + 0.341032I
−1.11289 + 6.31877I 0
u = 1.034840 − 0.517031I
a = 0.079654 + 1.254180I
b = −0.819752 − 0.341032I
−1.11289 − 6.31877I 0
u = −1.16414
a = 1.10361
b = −0.570627
2.67454 0
u = 0.866156 + 0.787470I
a = 0.465476 + 0.470261I
b = 0.879857 − 0.052529I
−4.40611 + 2.95802I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866156 − 0.787470I
a = 0.465476 − 0.470261I
b = 0.879857 + 0.052529I
−4.40611 − 2.95802I 0
u = −1.112140 + 0.413385I
a = −0.01016 − 2.11297I
b = 1.23374 + 1.21001I
1.45609 − 12.69390I 0
u = −1.112140 − 0.413385I
a = −0.01016 + 2.11297I
b = 1.23374 − 1.21001I
1.45609 + 12.69390I 0
u = −1.116460 + 0.435612I
a = −0.02823 + 1.94732I
b = −1.36725 − 1.02354I
−2.67479 − 7.21218I 0
u = −1.116460 − 0.435612I
a = −0.02823 − 1.94732I
b = −1.36725 + 1.02354I
−2.67479 + 7.21218I 0
u = 1.178880 + 0.228771I
a = 0.31491 − 1.71324I
b = −0.91885 + 1.13445I
2.32646 + 4.10744I 0
u = 1.178880 − 0.228771I
a = 0.31491 + 1.71324I
b = −0.91885 − 1.13445I
2.32646 − 4.10744I 0
u = −0.088174 + 0.786377I
a = 0.0847556 + 0.0688453I
b = 0.822039 + 0.684232I
1.10331 − 4.64342I 6.00000 + 6.67055I
u = −0.088174 − 0.786377I
a = 0.0847556 − 0.0688453I
b = 0.822039 − 0.684232I
1.10331 + 4.64342I 6.00000 − 6.67055I
u = 1.015090 + 0.666490I
a = 0.998214 + 0.683939I
b = 0.068096 − 0.285870I
10.35030 + 2.66298I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.015090 − 0.666490I
a = 0.998214 − 0.683939I
b = 0.068096 + 0.285870I
10.35030 − 2.66298I 0
u = 1.220670 + 0.115449I
a = −0.45375 + 1.63628I
b = 1.21373 − 1.28394I
5.19186 − 0.08640I 0
u = 1.220670 − 0.115449I
a = −0.45375 − 1.63628I
b = 1.21373 + 1.28394I
5.19186 + 0.08640I 0
u = 0.055343 + 1.227770I
a = 0.091697 − 0.346801I
b = 0.372975 + 0.050693I
−0.27253 − 5.19214I 0
u = 0.055343 − 1.227770I
a = 0.091697 + 0.346801I
b = 0.372975 − 0.050693I
−0.27253 + 5.19214I 0
u = 0.550932 + 1.103300I
a = −0.391350 + 0.283478I
b = −0.1203470 + 0.0126864I
−0.400588 + 0.392163I 0
u = 0.550932 − 1.103300I
a = −0.391350 − 0.283478I
b = −0.1203470 − 0.0126864I
−0.400588 − 0.392163I 0
u = −0.382598 + 0.657347I
a = −0.028276 − 0.190135I
b = 1.124250 − 0.827108I
−0.81371 + 8.56442I 3.64621 − 4.29467I
u = −0.382598 − 0.657347I
a = −0.028276 + 0.190135I
b = 1.124250 + 0.827108I
−0.81371 − 8.56442I 3.64621 + 4.29467I
u = −0.150461 + 1.237080I
a = −0.328855 + 0.030863I
b = −1.03176 + 1.05367I
3.35801 + 13.25030I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.150461 − 1.237080I
a = −0.328855 − 0.030863I
b = −1.03176 − 1.05367I
3.35801 − 13.25030I 0
u = −1.228870 + 0.397700I
a = 0.08969 − 1.57447I
b = 0.570243 + 0.592233I
4.49394 − 3.40604I 0
u = −1.228870 − 0.397700I
a = 0.08969 + 1.57447I
b = 0.570243 − 0.592233I
4.49394 + 3.40604I 0
u = −1.191680 + 0.517268I
a = −0.59329 + 1.65830I
b = −0.748192 − 0.831877I
10.49870 − 4.42770I 0
u = −1.191680 − 0.517268I
a = −0.59329 − 1.65830I
b = −0.748192 + 0.831877I
10.49870 + 4.42770I 0
u = −0.700041
a = −3.46582
b = −0.845285
2.31941 0.443950
u = 1.284450 + 0.237750I
a = −0.39069 + 1.59706I
b = 0.96373 − 1.07159I
5.77783 + 8.39759I 0
u = 1.284450 − 0.237750I
a = −0.39069 − 1.59706I
b = 0.96373 + 1.07159I
5.77783 − 8.39759I 0
u = 0.472125 + 1.219030I
a = −0.570130 − 0.460024I
b = −1.34299 − 1.14829I
2.91692 + 5.27638I 0
u = 0.472125 − 1.219030I
a = −0.570130 + 0.460024I
b = −1.34299 + 1.14829I
2.91692 − 5.27638I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.614414 + 0.314551I
a = −1.71773 + 2.03546I
b = 0.301403 + 0.506143I
1.23105 − 8.16321I 8.47951 + 2.08496I
u = 0.614414 − 0.314551I
a = −1.71773 − 2.03546I
b = 0.301403 − 0.506143I
1.23105 + 8.16321I 8.47951 − 2.08496I
u = 1.322920 + 0.296994I
a = 0.702354 + 1.117660I
b = −0.74866 − 1.26079I
12.55080 + 4.40273I 0
u = 1.322920 − 0.296994I
a = 0.702354 − 1.117660I
b = −0.74866 + 1.26079I
12.55080 − 4.40273I 0
u = −0.131122 + 1.359530I
a = 0.164937 + 0.064096I
b = 0.464130 + 1.045050I
0.66521 − 3.37641I 0
u = −0.131122 − 1.359530I
a = 0.164937 − 0.064096I
b = 0.464130 − 1.045050I
0.66521 + 3.37641I 0
u = 1.301590 + 0.475831I
a = −0.34605 − 1.59012I
b = −0.574828 + 1.276480I
8.38378 + 9.99022I 0
u = 1.301590 − 0.475831I
a = −0.34605 + 1.59012I
b = −0.574828 − 1.276480I
8.38378 − 9.99022I 0
u = −1.277490 + 0.540266I
a = 0.732718 − 0.918215I
b = 0.161870 + 0.933657I
7.96462 − 0.21748I 0
u = −1.277490 − 0.540266I
a = 0.732718 + 0.918215I
b = 0.161870 − 0.933657I
7.96462 + 0.21748I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.230640 + 1.388580I
a = 0.276694 − 0.167507I
b = 0.95706 − 1.21825I
−1.28083 + 6.15014I 0
u = −0.230640 − 1.388580I
a = 0.276694 + 0.167507I
b = 0.95706 + 1.21825I
−1.28083 − 6.15014I 0
u = 0.493141 + 0.305872I
a = 1.13936 − 2.32407I
b = −0.443124 − 0.499990I
−2.98383 − 3.05850I 4.76456 − 0.20674I
u = 0.493141 − 0.305872I
a = 1.13936 + 2.32407I
b = −0.443124 + 0.499990I
−2.98383 + 3.05850I 4.76456 + 0.20674I
u = −1.39870 + 0.29010I
a = 0.419763 + 0.881174I
b = −0.303031 − 0.343268I
5.51493 − 0.47579I 0
u = −1.39870 − 0.29010I
a = 0.419763 − 0.881174I
b = −0.303031 + 0.343268I
5.51493 + 0.47579I 0
u = 1.34744 + 0.48676I
a = 0.11183 + 1.51637I
b = 0.94734 − 1.09326I
5.99766 + 9.20816I 0
u = 1.34744 − 0.48676I
a = 0.11183 − 1.51637I
b = 0.94734 + 1.09326I
5.99766 − 9.20816I 0
u = 1.33667 + 0.53031I
a = −0.14731 − 1.62753I
b = −1.24169 + 0.91014I
10.8817 + 12.1545I 0
u = 1.33667 − 0.53031I
a = −0.14731 + 1.62753I
b = −1.24169 − 0.91014I
10.8817 − 12.1545I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.29826 + 0.65300I
a = −0.254869 − 0.871205I
b = −0.404942 + 0.396327I
2.31862 + 6.14292I 0
u = 1.29826 − 0.65300I
a = −0.254869 + 0.871205I
b = −0.404942 − 0.396327I
2.31862 − 6.14292I 0
u = 0.026187 + 0.544127I
a = 0.034176 − 0.377129I
b = −0.759966 − 0.450122I
−1.17002 − 1.27546I −0.38060 + 2.73816I
u = 0.026187 − 0.544127I
a = 0.034176 + 0.377129I
b = −0.759966 + 0.450122I
−1.17002 + 1.27546I −0.38060 − 2.73816I
u = 1.38163 + 0.46898I
a = 0.06091 + 1.47779I
b = 1.02568 − 1.18214I
5.91695 + 9.19563I 0
u = 1.38163 − 0.46898I
a = 0.06091 − 1.47779I
b = 1.02568 + 1.18214I
5.91695 − 9.19563I 0
u = −1.42605 + 0.33410I
a = 0.710362 − 1.080280I
b = −0.75825 + 1.78952I
9.21281 − 10.15130I 0
u = −1.42605 − 0.33410I
a = 0.710362 + 1.080280I
b = −0.75825 − 1.78952I
9.21281 + 10.15130I 0
u = 1.35996 + 0.56161I
a = −0.020373 + 1.105490I
b = 0.700048 − 0.465428I
3.90882 + 11.31930I 0
u = 1.35996 − 0.56161I
a = −0.020373 − 1.105490I
b = 0.700048 + 0.465428I
3.90882 − 11.31930I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40029 + 0.50264I
a = 0.624070 − 0.528110I
b = −0.676798 + 0.954907I
11.18180 + 0.89647I 0
u = −1.40029 − 0.50264I
a = 0.624070 + 0.528110I
b = −0.676798 − 0.954907I
11.18180 − 0.89647I 0
u = −1.37108 + 0.62024I
a = −0.25243 + 1.51407I
b = −1.35339 − 1.10536I
7.2653 − 19.7668I 0
u = −1.37108 − 0.62024I
a = −0.25243 − 1.51407I
b = −1.35339 + 1.10536I
7.2653 + 19.7668I 0
u = −1.40683 + 0.55628I
a = −0.318649 + 0.708087I
b = −0.136711 − 0.752207I
5.45365 − 2.02375I 0
u = −1.40683 − 0.55628I
a = −0.318649 − 0.708087I
b = −0.136711 + 0.752207I
5.45365 + 2.02375I 0
u = −0.459524
a = 1.84056
b = 0.276685
0.953550 13.0960
u = 1.53752 + 0.13256I
a = −0.441501 − 1.076780I
b = 0.93797 + 1.71211I
5.98736 − 0.11783I 0
u = 1.53752 − 0.13256I
a = −0.441501 + 1.076780I
b = 0.93797 − 1.71211I
5.98736 + 0.11783I 0
u = −1.40555 + 0.65738I
a = 0.267599 − 1.360540I
b = 1.36887 + 1.12677I
2.63989 − 13.24310I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40555 − 0.65738I
a = 0.267599 + 1.360540I
b = 1.36887 − 1.12677I
2.63989 + 13.24310I 0
u = 1.55041 + 0.34359I
a = 0.521379 + 0.796876I
b = −0.60108 − 1.40728I
9.27752 − 7.27133I 0
u = 1.55041 − 0.34359I
a = 0.521379 − 0.796876I
b = −0.60108 + 1.40728I
9.27752 + 7.27133I 0
u = −1.53066 + 0.45877I
a = −0.416330 + 0.899541I
b = 0.08069 − 1.57157I
5.77201 − 3.47374I 0
u = −1.53066 − 0.45877I
a = −0.416330 − 0.899541I
b = 0.08069 + 1.57157I
5.77201 + 3.47374I 0
u = −0.168192 + 0.353066I
a = 1.71628 + 1.21552I
b = 0.633913 − 0.306029I
1.197990 − 0.022972I 8.49004 − 0.40673I
u = −0.168192 − 0.353066I
a = 1.71628 − 1.21552I
b = 0.633913 + 0.306029I
1.197990 + 0.022972I 8.49004 + 0.40673I
u = 1.54636 + 0.69953I
a = −0.301488 − 1.184520I
b = −1.65214 + 1.54026I
6.28204 + 2.48766I 0
u = 1.54636 − 0.69953I
a = −0.301488 + 1.184520I
b = −1.65214 − 1.54026I
6.28204 − 2.48766I 0
u = 0.072507 + 0.218572I
a = 2.28107 + 3.92479I
b = 0.522727 + 0.798281I
1.01513 + 2.21239I 8.96888 − 1.25136I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.072507 − 0.218572I
a = 2.28107 − 3.92479I
b = 0.522727 − 0.798281I
1.01513 − 2.21239I 8.96888 + 1.25136I
u = −1.43474 + 1.05424I
a = −0.452244 + 1.005240I
b = −2.35935 − 0.93568I
7.52546 − 4.69662I 0
u = −1.43474 − 1.05424I
a = −0.452244 − 1.005240I
b = −2.35935 + 0.93568I
7.52546 + 4.69662I 0
17
II.
I
u
2
= h5.84×10
21
u
26
−2.73×10
22
u
25
+· · ·+2.89×10
21
b−1.49×10
22
, −2.42×
10
21
u
26
+6.66×10
21
u
25
+· · ·+2.89×10
21
a−7.97×10
21
, u
27
−5u
26
+· · ·−6u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
11
=
0.838399u
26
− 2.30322u
25
+ ··· − 1.60882u + 2.75615
−2.01903u
26
+ 9.43683u
25
+ ··· − 18.9143u + 5.13672
a
4
=
0.975207u
26
− 3.24747u
25
+ ··· + 3.20862u + 4.59182
−2.20451u
26
+ 10.2192u
25
+ ··· − 19.8537u + 6.06783
a
7
=
u
−u
3
+ u
a
12
=
−0.298330u
26
+ 2.67002u
25
+ ··· − 9.84718u + 4.38121
−2.74292u
26
+ 12.6626u
25
+ ··· − 24.0269u + 6.05137
a
8
=
5.28341u
26
− 23.9244u
25
+ ··· + 46.7030u − 9.29851
−0.555857u
26
+ 2.59900u
25
+ ··· − 3.64225u + 2.27621
a
1
=
12.6767u
26
− 60.2433u
25
+ ··· + 104.111u − 31.4079
3.86936u
26
− 17.8206u
25
+ ··· + 31.7545u − 8.25753
a
5
=
−10.4420u
26
+ 48.2168u
25
+ ··· − 94.0732u + 25.3594
−3.20451u
26
+ 14.2192u
25
+ ··· − 25.8537u + 6.06783
a
10
=
−1.18063u
26
+ 7.13361u
25
+ ··· − 20.5231u + 7.89287
−2.01903u
26
+ 9.43683u
25
+ ··· − 18.9143u + 5.13672
a
9
=
12.0091u
26
− 56.9436u
25
+ ··· + 97.0409u − 29.2410
4.08051u
26
− 18.9118u
25
+ ··· + 34.4280u − 8.70409
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
54586491030429944288229
2891097935499617764769
u
26
+
252590371939791998353306
2891097935499617764769
u
25
+ ··· −
489631306821485248219363
2891097935499617764769
u +
150491225102484366518807
2891097935499617764769
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
u
27
− 8u
26
+ ··· + u + 1
c
2
u
27
− 5u
26
+ ··· − 6u + 1
c
3
u
27
− 5u
26
+ ··· + 4u + 1
c
4
u
27
+ 3u
26
+ ··· − 4u + 1
c
5
u
27
+ 7u
26
+ ··· − 4u + 1
c
6
u
27
+ 5u
26
+ ··· − 6u − 1
c
7
u
27
− 3u
26
+ ··· + 10u
2
− 1
c
8
u
27
− 7u
26
+ ··· − 4u − 1
c
9
u
27
− 8u
26
+ ··· − 22u + 1
c
10
u
27
+ 2u
26
+ ··· − u − 1
c
11
u
27
+ 3u
26
+ ··· − 10u
2
+ 1
c
12
u
27
+ 8u
26
+ ··· − 22u − 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 10y
26
+ ··· − 13y − 1
c
2
, c
6
y
27
− 9y
26
+ ··· + 10y − 1
c
3
y
27
− 11y
26
+ ··· + 18y
2
− 1
c
4
y
27
− 7y
26
+ ··· + 2y − 1
c
5
, c
8
y
27
+ 3y
26
+ ··· + 8y − 1
c
7
, c
11
y
27
− 15y
26
+ ··· + 20y − 1
c
9
, c
12
y
27
− 24y
26
+ ··· + 430y − 1
c
10
y
27
+ 44y
25
+ ··· − 9y − 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.960256
a = 0.596635
b = 0.427535
3.28166 12.2340
u = −0.278336 + 0.913907I
a = −0.200376 − 0.846741I
b = −0.096284 − 0.605686I
−0.54501 − 2.72751I 2.90113 + 2.79754I
u = −0.278336 − 0.913907I
a = −0.200376 + 0.846741I
b = −0.096284 + 0.605686I
−0.54501 + 2.72751I 2.90113 − 2.79754I
u = 0.695603 + 0.648427I
a = 0.117632 + 0.622535I
b = 1.063860 + 0.717771I
0.79452 + 3.91333I 8.14679 − 5.26781I
u = 0.695603 − 0.648427I
a = 0.117632 − 0.622535I
b = 1.063860 − 0.717771I
0.79452 − 3.91333I 8.14679 + 5.26781I
u = 0.405951 + 0.857531I
a = 0.098439 + 0.640247I
b = 0.924519 − 0.346398I
−0.96829 + 1.35478I 2.43967 − 3.85610I
u = 0.405951 − 0.857531I
a = 0.098439 − 0.640247I
b = 0.924519 + 0.346398I
−0.96829 − 1.35478I 2.43967 + 3.85610I
u = 1.098730 + 0.102102I
a = −0.77707 + 2.70179I
b = 1.40859 − 2.49731I
2.96797 − 0.72446I 15.7942 − 4.3726I
u = 1.098730 − 0.102102I
a = −0.77707 − 2.70179I
b = 1.40859 + 2.49731I
2.96797 + 0.72446I 15.7942 + 4.3726I
u = −1.036180 + 0.551940I
a = 1.003830 − 0.889238I
b = −0.077454 + 0.352280I
10.96250 − 2.28403I 16.8451 − 1.4331I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.036180 − 0.551940I
a = 1.003830 + 0.889238I
b = −0.077454 − 0.352280I
10.96250 + 2.28403I 16.8451 + 1.4331I
u = 0.868601 + 0.841612I
a = −0.500141 − 0.453132I
b = −0.810921 + 0.059869I
−4.18369 + 3.09248I 20.0854 − 10.5481I
u = 0.868601 − 0.841612I
a = −0.500141 + 0.453132I
b = −0.810921 − 0.059869I
−4.18369 − 3.09248I 20.0854 + 10.5481I
u = −0.772117
a = 5.45860
b = 1.00432
2.77882 29.0040
u = −0.140075 + 1.374080I
a = −0.0289815 + 0.0163804I
b = 0.154620 + 0.821354I
0.50090 − 5.20648I 12.2118 + 8.9652I
u = −0.140075 − 1.374080I
a = −0.0289815 − 0.0163804I
b = 0.154620 − 0.821354I
0.50090 + 5.20648I 12.2118 − 8.9652I
u = 1.39028 + 0.39921I
a = −0.054614 + 1.367760I
b = 0.603701 − 1.150370I
6.14002 + 10.90440I 10.7101 − 9.9802I
u = 1.39028 − 0.39921I
a = −0.054614 − 1.367760I
b = 0.603701 + 1.150370I
6.14002 − 10.90440I 10.7101 + 9.9802I
u = −0.539556
a = −2.46548
b = −0.715187
0.364084 −4.03030
u = 0.204560 + 0.461308I
a = −2.05712 + 1.01061I
b = −0.853553 + 0.597527I
−3.26798 + 4.11102I 3.08862 − 6.45303I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.204560 − 0.461308I
a = −2.05712 − 1.01061I
b = −0.853553 − 0.597527I
−3.26798 − 4.11102I 3.08862 + 6.45303I
u = −1.43797 + 0.47003I
a = −0.199679 + 0.958315I
b = −0.374729 − 0.918491I
5.42247 − 1.39630I 12.16981 − 0.96989I
u = −1.43797 − 0.47003I
a = −0.199679 − 0.958315I
b = −0.374729 + 0.918491I
5.42247 + 1.39630I 12.16981 + 0.96989I
u = 0.424568 + 0.114039I
a = 3.26974 + 0.73237I
b = 0.844344 − 0.580851I
1.05272 + 9.29224I 7.38135 − 8.07216I
u = 0.424568 − 0.114039I
a = 3.26974 − 0.73237I
b = 0.844344 + 0.580851I
1.05272 − 9.29224I 7.38135 + 8.07216I
u = 1.44024 + 0.98702I
a = −0.466529 − 1.033330I
b = −2.14503 + 1.07891I
7.52044 + 4.56871I 0. + 23.7225I
u = 1.44024 − 0.98702I
a = −0.466529 + 1.033330I
b = −2.14503 − 1.07891I
7.52044 − 4.56871I 0. − 23.7225I
25
III. I
u
3
= h−3a
3
− 2a
2
+ 23b + 10a − 17, a
4
+ a
3
+ 2a
2
+ 2a + 7, u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
−1
a
3
=
1
−1
a
11
=
a
0.130435a
3
+ 0.0869565a
2
− 0.434783a + 0.739130
a
4
=
−0.0434783a
3
+ 0.304348a
2
+ 0.478261a + 0.0869565
0.173913a
3
− 0.217391a
2
+ 0.0869565a − 0.347826
a
7
=
−1
0
a
12
=
0.130435a
3
+ 0.0869565a
2
+ 0.565217a + 0.739130
0.130435a
3
+ 0.0869565a
2
− 0.434783a + 0.739130
a
8
=
0.173913a
3
− 0.217391a
2
+ 0.0869565a − 0.347826
0.217391a
3
+ 0.478261a
2
− 0.391304a + 1.56522
a
1
=
0.130435a
3
+ 0.0869565a
2
+ 0.565217a + 0.739130
0.130435a
3
+ 0.0869565a
2
− 0.434783a + 0.739130
a
5
=
−0.130435a
3
− 0.0869565a
2
+ 0.434783a − 0.739130
0.478261a
3
− 0.347826a
2
+ 0.739130a + 0.0434783
a
10
=
0.130435a
3
+ 0.0869565a
2
+ 0.565217a + 0.739130
0.130435a
3
+ 0.0869565a
2
− 0.434783a + 0.739130
a
9
=
0.130435a
3
+ 0.0869565a
2
+ 0.565217a + 0.739130
0.130435a
3
+ 0.0869565a
2
− 0.434783a + 0.739130
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
u
4
− u
3
+ 2u
2
− 2u + 1
c
2
, c
6
(u − 1)
4
c
3
(u
2
− u + 1)
2
c
7
, c
11
u
4
+ 3u
3
+ 2u
2
+ 1
c
9
, c
12
u
4
c
10
u
4
− 3u
3
+ 2u
2
+ 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
4
+ 3y
3
+ 2y
2
+ 1
c
2
, c
6
(y − 1)
4
c
3
(y
2
+ y + 1)
2
c
7
, c
10
, c
11
y
4
− 5y
3
+ 6y
2
+ 4y + 1
c
9
, c
12
y
4
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.69244 + 1.41390I
b = −0.192440 − 0.547877I
1.64493 6.00000
u = −1.00000
a = 0.69244 − 1.41390I
b = −0.192440 + 0.547877I
1.64493 6.00000
u = −1.00000
a = −1.19244 + 1.18417I
b = 1.69244 − 0.31815I
1.64493 6.00000
u = −1.00000
a = −1.19244 − 1.18417I
b = 1.69244 + 0.31815I
1.64493 6.00000
29
IV. I
u
4
= hb + 1, a + 1, u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
−1
a
3
=
1
−1
a
11
=
−1
−1
a
4
=
3
1
a
7
=
−1
0
a
12
=
−2
−1
a
8
=
1
1
a
1
=
−2
−1
a
5
=
1
0
a
10
=
−2
−1
a
9
=
−2
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
8
, c
10
u + 1
c
2
, c
6
, c
7
c
11
u − 1
c
3
u + 2
c
9
, c
12
u
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
10
, c
11
y − 1
c
3
y − 4
c
9
, c
12
y
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = −1.00000
1.64493 6.00000
33
V. I
u
5
= hb
5
+ 2b
4
a + b
3
a
2
− 3b
3
− 4b
2
a − a
2
b + 3b + a − 1, u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
−1
a
3
=
1
−1
a
11
=
a
b
a
4
=
ba + a
2
+ 1
b
2
+ ba − 1
a
7
=
−1
0
a
12
=
b + a
b
a
8
=
b
2
+ ba − 1
b
2
a
1
=
−b
3
a − 2b
2
a
2
− a
3
b − b
2
+ a
2
+ 2
−b
4
− 2b
3
a − b
2
a
2
+ 2b
2
+ 2ba − 1
a
5
=
b
4
+ 2b
3
a + b
2
a
2
− 2b
2
− 2ba + 1
b
4
+ b
3
a − b
2
− 1
a
10
=
b + a
b
a
9
=
b
3
a + 2b
2
a
2
+ a
3
b + b
2
− a
2
+ b + a − 2
b
4
+ 2b
3
a + b
2
a
2
− 2b
2
− 2ba + b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
34
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
3.28987 12.0000
35
VI. I
v
1
= ha, b
4
+ b
3
+ 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
1
0
a
3
=
1
0
a
11
=
0
b
a
4
=
1
b
2
a
7
=
1
0
a
12
=
b
b
a
8
=
−b
2
+ 1
−b
2
a
1
=
−b
2
+ 1
b
3
+ 1
a
5
=
−b
3
− b
2
−b
3
− 1
a
10
=
b
b
a
9
=
b
2
+ b − 1
−b
3
+ b − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
+ u
3
+ 2u
2
+ 1
c
2
, c
6
u
4
c
3
, c
7
, c
10
c
11
u
4
+ u
3
+ 1
c
4
u
4
− u
2
− 2u + 3
c
5
, c
8
u
4
− u
3
+ 2u
2
+ 1
c
9
, c
12
(u − 1)
4
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
8
y
4
+ 3y
3
+ 6y
2
+ 4y + 1
c
2
, c
6
y
4
c
3
, c
7
, c
10
c
11
y
4
− y
3
+ 2y
2
+ 1
c
4
y
4
− 2y
3
+ 7y
2
− 10y + 9
c
9
, c
12
(y − 1)
4
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.518913 + 0.666610I
1.64493 6.00000
v = 1.00000
a = 0
b = 0.518913 − 0.666610I
1.64493 6.00000
v = 1.00000
a = 0
b = −1.018910 + 0.602565I
1.64493 6.00000
v = 1.00000
a = 0
b = −1.018910 − 0.602565I
1.64493 6.00000
39
VII. I
v
2
= ha, b − 1, v − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
1
0
a
3
=
1
0
a
11
=
0
1
a
4
=
1
1
a
7
=
1
0
a
12
=
1
1
a
8
=
0
−1
a
1
=
0
−1
a
5
=
1
1
a
10
=
1
1
a
9
=
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u + 1
c
2
, c
4
, c
6
u
c
3
, c
5
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u − 1
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y − 1
c
2
, c
4
, c
6
y
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
1.64493 6.00000
43
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(u + 1)
2
(u
4
− u
3
+ 2u
2
− 2u + 1)(u
4
+ u
3
+ 2u
2
+ 1)
· (u
27
− 8u
26
+ ··· + u + 1)(16u
123
− 216u
122
+ ··· − 705357u + 15123)
c
2
u
5
(u − 1)
5
(u
27
− 5u
26
+ ··· − 6u + 1)
· (u
123
+ 9u
122
+ ··· − 2948798u − 321516)
c
3
48(u − 1)(u + 2)(u
2
− u + 1)
2
(u
4
+ u
3
+ 1)(u
27
− 5u
26
+ ··· + 4u + 1)
· (48u
123
+ 1409u
121
+ ··· − 1264337384u + 86498272)
c
4
48u(u + 1)(u
4
− u
2
− 2u + 3)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
27
+ 3u
26
+ ··· − 4u + 1)(48u
123
− 96u
122
+ ··· − 1112u − 192)
c
5
16(u − 1)(u + 1)(u
4
− u
3
+ 2u
2
+ 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
27
+ 7u
26
+ ··· − 4u + 1)(16u
123
+ 88u
122
+ ··· − 21054u − 1797)
c
6
u
5
(u − 1)
5
(u
27
+ 5u
26
+ ··· − 6u − 1)
· (u
123
+ 9u
122
+ ··· − 2948798u − 321516)
c
7
16(u − 1)
2
(u
4
+ u
3
+ 1)(u
4
+ 3u
3
+ 2u
2
+ 1)(u
27
− 3u
26
+ ··· + 10u
2
− 1)
· (16u
123
− 8u
122
+ ··· + 1543440u + 242409)
c
8
16(u − 1)(u + 1)(u
4
− u
3
+ 2u
2
+ 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
27
− 7u
26
+ ··· − 4u − 1)(16u
123
+ 88u
122
+ ··· − 21054u − 1797)
c
9
u
5
(u − 1)
5
(u
27
− 8u
26
+ ··· − 22u + 1)
· (u
123
+ 12u
122
+ ··· + 413544u + 22932)
c
10
16(u − 1)(u + 1)(u
4
− 3u
3
+ 2u
2
+ 1)(u
4
+ u
3
+ 1)(u
27
+ 2u
26
+ ··· − u − 1)
· (16u
123
+ 72u
122
+ ··· − 3849u − 357)
c
11
16(u − 1)
2
(u
4
+ u
3
+ 1)(u
4
+ 3u
3
+ 2u
2
+ 1)(u
27
+ 3u
26
+ ··· − 10u
2
+ 1)
· (16u
123
− 8u
122
+ ··· + 1543440u + 242409)
c
12
u
5
(u − 1)
5
(u
27
+ 8u
26
+ ··· − 22u − 1)
· (u
123
+ 12u
122
+ ··· + 413544u + 22932)
44
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
256(y − 1)
2
(y
4
+ 3y
3
+ 2y
2
+ 1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· (y
27
− 10y
26
+ ··· − 13y − 1)
· (256y
123
+ 5088y
122
+ ··· + 300704648685y − 228705129)
c
2
, c
6
y
5
(y − 1)
5
(y
27
− 9y
26
+ ··· + 10y − 1)
· (y
123
− 73y
122
+ ··· − 2074541056628y − 103372538256)
c
3
2304(y − 4)(y − 1)(y
2
+ y + 1)
2
(y
4
− y
3
+ 2y
2
+ 1)
· (y
27
− 11y
26
+ ··· + 18y
2
− 1)
· (2304y
123
+ 1.35 × 10
5
y
122
+ ··· − 6.89 × 10
16
y − 7.48 × 10
15
)
c
4
2304y(y − 1)(y
4
− 2y
3
+ 7y
2
− 10y + 9)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
27
− 7y
26
+ ··· + 2y − 1)
· (2304y
123
− 96y
122
+ ··· + 10981312y − 36864)
c
5
, c
8
256(y − 1)
2
(y
4
+ 3y
3
+ 2y
2
+ 1)(y
4
+ 3y
3
+ 6y
2
+ 4y + 1)
· (y
27
+ 3y
26
+ ··· + 8y − 1)
· (256y
123
+ 14560y
122
+ ··· + 52225746y − 3229209)
c
7
, c
11
256(y − 1)
2
(y
4
− 5y
3
+ 6y
2
+ 4y + 1)(y
4
− y
3
+ 2y
2
+ 1)
· (y
27
− 15y
26
+ ··· + 20y − 1)
· (256y
123
− 25888y
122
+ ··· + 2905429891470y − 58762123281)
c
9
, c
12
y
5
(y − 1)
5
(y
27
− 24y
26
+ ··· + 430y − 1)
· (y
123
− 88y
122
+ ··· + 39388547160y − 525876624)
c
10
256(y − 1)
2
(y
4
− 5y
3
+ 6y
2
+ 4y + 1)(y
4
− y
3
+ 2y
2
+ 1)
· (y
27
+ 44y
25
+ ··· − 9y − 1)
· (256y
123
− 544y
122
+ ··· + 13415361y − 127449)
45
