12a
0030
(K12a
0030
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 11 4 8 1 7
Solving Sequence
4,9 2,5
3 6 10
1,11
8 7 12
c
4
c
2
c
5
c
9
c
1
c
8
c
7
c
12
c
3
, c
6
, c
10
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.97380 × 10
162
u
76
− 7.99163 × 10
162
u
75
+ ··· + 1.45795 × 10
166
d − 5.67098 × 10
165
,
4.24191 × 10
162
u
76
− 1.61625 × 10
163
u
75
+ ··· + 1.45795 × 10
166
c + 2.78196 × 10
165
,
6.76436 × 10
182
u
76
− 1.29212 × 10
183
u
75
+ ··· + 1.08760 × 10
185
b − 1.19824 × 10
185
,
1.65541 × 10
183
u
76
− 4.27644 × 10
183
u
75
+ ··· + 2.17520 × 10
185
a + 1.69038 × 10
186
,
u
77
− 2u
76
+ ··· − 2560u
2
− 512i
I
u
2
= h−c
2
u + d − c, u
3
c + c
3
+ u
2
c − u
3
+ cu − u + 1, −u
2
+ b + u − 1, u
3
− u
2
+ a + u − 1, u
4
+ u
2
− u + 1i
I
u
3
= h−c
2
u + d − c, −2u
5
c − u
4
c − u
5
− 3u
3
c − u
4
+ c
3
− 2u
2
c − 2u
3
− 2cu − 2u
2
− 2c − 2u − 2,
− 2u
5
− u
4
− 3u
3
− 2u
2
+ b − 3u − 2, −u
4
− u
2
+ a − u − 1, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
I
v
1
= ha, d, c − v, b − v, v
2
− v + 1i
I
v
2
= ha, d + v + 1, av + c + 1, b + v, v
2
+ v + 1i
I
v
3
= hc, d − 1, b, a − 1, v − 1i
I
v
4
= ha, db + da − cb − d + b − 1, a
2
d − cba − da + cb + ba + d − c − a + 1, dv − 1, cv + ba − bv − b − a,
b
2
− b + 1i
* 6 irreducible components of dim
C
= 0, with total 112 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
= h2.97×10
162
u
76
−7.99×10
162
u
75
+· · ·+1.46×10
166
d−5.67×10
165
, 4.24×
10
162
u
76
−1.62×10
163
u
75
+· · · + 1.46×10
166
c+2.78×10
165
, 6.76×10
182
u
76
−
1.29 × 10
183
u
75
+ · · · + 1.09 × 10
185
b − 1.20 × 10
185
, 1.66 × 10
183
u
76
− 4.28 ×
10
183
u
75
+ · · · + 2.18 × 10
185
a + 1.69 × 10
186
, u
77
− 2u
76
+ · · · − 2560u
2
− 512i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−0.00761038u
76
+ 0.0196600u
75
+ ··· + 4.69111u − 7.77114
−0.00621954u
76
+ 0.0118805u
75
+ ··· + 6.90325u + 1.10173
a
5
=
1
−u
2
a
3
=
−0.00903125u
76
+ 0.0210962u
75
+ ··· + 7.69784u − 4.39652
−0.00575546u
76
+ 0.0105565u
75
+ ··· + 7.63073u + 1.82138
a
6
=
−0.0108390u
76
+ 0.0188168u
75
+ ··· + 14.5481u − 0.522142
0.00170046u
76
− 0.00573767u
75
+ ··· − 1.46268u + 2.50020
a
10
=
u
u
a
1
=
−0.0125394u
76
+ 0.0245545u
75
+ ··· + 16.0108u − 3.02234
−0.00622485u
76
+ 0.0135037u
75
+ ··· + 7.88286u − 2.23172
a
11
=
−0.000290951u
76
+ 0.00110858u
75
+ ··· + 1.36870u − 0.190813
−0.000203972u
76
+ 0.000548142u
75
+ ··· + 0.515526u + 0.388970
a
8
=
0.0000869789u
76
− 0.000560439u
75
+ ··· − 0.853173u + 0.579783
−0.000203972u
76
+ 0.000548142u
75
+ ··· + 0.515526u + 0.388970
a
7
=
−0.000208604u
76
− 0.0000329385u
75
+ ··· − 1.00214u + 0.849444
−0.000499554u
76
+ 0.00107564u
75
+ ··· + 0.366559u + 0.658630
a
12
=
−0.0150036u
76
+ 0.0284788u
75
+ ··· + 20.0911u − 2.34221
−0.00485367u
76
+ 0.0102965u
75
+ ··· + 6.71768u − 1.05079
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0221138u
76
− 0.0478032u
75
+ ··· − 21.6023u − 0.388088
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 36u
76
+ ··· + 216u − 16
c
2
, c
5
u
77
+ 2u
76
+ ··· + 27u
2
− 4
c
3
u
77
− 2u
76
+ ··· + 351912u − 66564
c
4
, c
9
u
77
− 2u
76
+ ··· − 2560u
2
− 512
c
6
, c
12
u
77
+ 8u
76
+ ··· − 72u − 16
c
7
, c
8
, c
10
u
77
− 8u
76
+ ··· − 72u − 16
c
11
u
77
− 34u
76
+ ··· + 1568u − 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
+ 12y
76
+ ··· + 84256y − 256
c
2
, c
5
y
77
+ 36y
76
+ ··· + 216y − 16
c
3
y
77
− 12y
76
+ ··· + 120020616504y − 4430766096
c
4
, c
9
y
77
+ 30y
76
+ ··· − 2621440y − 262144
c
6
, c
12
y
77
− 34y
76
+ ··· + 1568y − 256
c
7
, c
8
, c
10
y
77
− 74y
76
+ ··· + 7712y − 256
c
11
y
77
+ 26y
76
+ ··· + 3416576y − 65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.508886 + 0.845592I
a = −2.01821 + 2.48278I
b = 0.67033 + 1.82257I
c = 0.464983 + 0.518986I
d = 0.029827 + 0.719662I
2.40889 + 4.27390I 3.74115 − 6.44221I
u = 0.508886 − 0.845592I
a = −2.01821 − 2.48278I
b = 0.67033 − 1.82257I
c = 0.464983 − 0.518986I
d = 0.029827 − 0.719662I
2.40889 − 4.27390I 3.74115 + 6.44221I
u = −0.848496 + 0.585068I
a = 0.774643 + 0.166861I
b = 0.208609 + 0.303408I
c = −0.508850 + 0.474076I
d = −0.255576 + 0.903445I
3.78378 + 2.11500I 7.65464 − 1.99007I
u = −0.848496 − 0.585068I
a = 0.774643 − 0.166861I
b = 0.208609 − 0.303408I
c = −0.508850 − 0.474076I
d = −0.255576 − 0.903445I
3.78378 − 2.11500I 7.65464 + 1.99007I
u = −0.990280 + 0.319237I
a = 0.787830 + 0.083627I
b = −0.082157 + 0.217726I
c = 1.249660 + 0.250247I
d = −0.434460 + 0.109424I
−2.98745 + 0.86657I 0
u = −0.990280 − 0.319237I
a = 0.787830 − 0.083627I
b = −0.082157 − 0.217726I
c = 1.249660 − 0.250247I
d = −0.434460 − 0.109424I
−2.98745 − 0.86657I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617221 + 0.733532I
a = 0.462356 − 0.972183I
b = 0.323373 − 0.206230I
c = −0.468418 + 0.489504I
d = −0.119564 + 0.757735I
4.09446 + 0.35704I 8.04104 + 0.70386I
u = −0.617221 − 0.733532I
a = 0.462356 + 0.972183I
b = 0.323373 + 0.206230I
c = −0.468418 − 0.489504I
d = −0.119564 − 0.757735I
4.09446 − 0.35704I 8.04104 − 0.70386I
u = 0.517431 + 0.792256I
a = 0.648790 + 0.421877I
b = 1.21086 − 1.35430I
c = 0.457643 + 0.510225I
d = 0.061325 + 0.711547I
2.57405 − 0.08416I 4.54592 − 2.74373I
u = 0.517431 − 0.792256I
a = 0.648790 − 0.421877I
b = 1.21086 + 1.35430I
c = 0.457643 − 0.510225I
d = 0.061325 − 0.711547I
2.57405 + 0.08416I 4.54592 + 2.74373I
u = −0.082487 + 0.936352I
a = 0.533253 − 0.084017I
b = −0.1191060 − 0.0483275I
c = 0.588786 + 0.717292I
d = −0.188271 + 0.490462I
−1.72016 + 1.41215I −1.65188 − 3.77223I
u = −0.082487 − 0.936352I
a = 0.533253 + 0.084017I
b = −0.1191060 + 0.0483275I
c = 0.588786 − 0.717292I
d = −0.188271 − 0.490462I
−1.72016 − 1.41215I −1.65188 + 3.77223I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.582500 + 0.889546I
a = 0.720191 + 0.253876I
b = 0.783297 + 0.240221I
c = −0.478527 + 0.513127I
d = −0.021694 + 0.768666I
3.62010 − 5.07823I 6.10660 + 7.37918I
u = −0.582500 − 0.889546I
a = 0.720191 − 0.253876I
b = 0.783297 − 0.240221I
c = −0.478527 − 0.513127I
d = −0.021694 − 0.768666I
3.62010 + 5.07823I 6.10660 − 7.37918I
u = 0.228301 + 1.040040I
a = 0.647193 + 0.370147I
b = 1.55007 − 0.83492I
c = 0.171170 − 1.253130I
d = 0.26552 − 2.95382I
−3.92825 − 1.69884I −4.65730 + 2.32962I
u = 0.228301 − 1.040040I
a = 0.647193 − 0.370147I
b = 1.55007 + 0.83492I
c = 0.171170 + 1.253130I
d = 0.26552 + 2.95382I
−3.92825 + 1.69884I −4.65730 − 2.32962I
u = 0.782003 + 0.468875I
a = −0.09272 + 1.85079I
b = 0.738345 − 0.001201I
c = −1.262590 + 0.477339I
d = 0.371007 + 0.175352I
0.65497 − 3.51390I 3.54011 + 4.44478I
u = 0.782003 − 0.468875I
a = −0.09272 − 1.85079I
b = 0.738345 + 0.001201I
c = −1.262590 − 0.477339I
d = 0.371007 − 0.175352I
0.65497 + 3.51390I 3.54011 − 4.44478I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.374962 + 1.039940I
a = 0.686555 + 0.288879I
b = 1.169710 + 0.084807I
c = −0.259210 − 1.195820I
d = −0.39291 − 2.84551I
−3.38837 − 3.78470I 0
u = −0.374962 − 1.039940I
a = 0.686555 − 0.288879I
b = 1.169710 − 0.084807I
c = −0.259210 + 1.195820I
d = −0.39291 + 2.84551I
−3.38837 + 3.78470I 0
u = 0.965284 + 0.548957I
a = 0.625184 + 0.492951I
b = 0.68045 − 2.05306I
c = 0.522160 + 0.485983I
d = 0.278757 + 0.995907I
1.81197 − 6.85619I 0
u = 0.965284 − 0.548957I
a = 0.625184 − 0.492951I
b = 0.68045 + 2.05306I
c = 0.522160 − 0.485983I
d = 0.278757 − 0.995907I
1.81197 + 6.85619I 0
u = 0.288832 + 1.092220I
a = −0.83997 + 2.42037I
b = 0.11827 + 2.10829I
c = −0.707441 + 0.634880I
d = 0.301812 + 0.481810I
−4.40655 + 2.61636I 0
u = 0.288832 − 1.092220I
a = −0.83997 − 2.42037I
b = 0.11827 − 2.10829I
c = −0.707441 − 0.634880I
d = 0.301812 − 0.481810I
−4.40655 − 2.61636I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.815552 + 0.276755I
a = 0.799645 − 0.625291I
b = −0.468019 + 0.989394I
c = 0.581077 + 0.429556I
d = 0.567805 + 0.879067I
−0.065597 − 0.205341I 1.21551 + 1.86968I
u = 0.815552 − 0.276755I
a = 0.799645 + 0.625291I
b = −0.468019 − 0.989394I
c = 0.581077 − 0.429556I
d = 0.567805 − 0.879067I
−0.065597 + 0.205341I 1.21551 − 1.86968I
u = −0.008067 + 1.164640I
a = −0.09279 − 2.27307I
b = −0.47312 − 1.95892I
c = −0.589470 + 0.601192I
d = 0.236103 + 0.590654I
−4.97078 − 4.99360I 0
u = −0.008067 − 1.164640I
a = −0.09279 + 2.27307I
b = −0.47312 + 1.95892I
c = −0.589470 − 0.601192I
d = 0.236103 − 0.590654I
−4.97078 + 4.99360I 0
u = 1.177360 + 0.140655I
a = 0.654058 − 0.644673I
b = −0.76712 + 1.79650I
c = −1.186110 + 0.084828I
d = 0.490100 + 0.044776I
−6.72367 + 2.38646I 0
u = 1.177360 − 0.140655I
a = 0.654058 + 0.644673I
b = −0.76712 − 1.79650I
c = −1.186110 − 0.084828I
d = 0.490100 − 0.044776I
−6.72367 − 2.38646I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.516220 + 1.088150I
a = 0.619518 − 0.395918I
b = 1.72011 + 1.31893I
c = −0.298515 − 1.111320I
d = −0.42895 − 2.70075I
−2.28765 − 3.11487I 0
u = −0.516220 − 1.088150I
a = 0.619518 + 0.395918I
b = 1.72011 − 1.31893I
c = −0.298515 + 1.111320I
d = −0.42895 + 2.70075I
−2.28765 + 3.11487I 0
u = 1.143240 + 0.423905I
a = 0.611807 + 0.526230I
b = 0.33407 − 2.31050I
c = −1.127630 + 0.240108I
d = 0.489699 + 0.135615I
−5.54743 − 5.38085I 0
u = 1.143240 − 0.423905I
a = 0.611807 − 0.526230I
b = 0.33407 + 2.31050I
c = −1.127630 − 0.240108I
d = 0.489699 − 0.135615I
−5.54743 + 5.38085I 0
u = 1.079500 + 0.575143I
a = 0.737296 − 0.124322I
b = 0.002970 − 0.490365I
c = −1.087450 + 0.321582I
d = 0.479725 + 0.187227I
−1.00971 − 5.65602I 0
u = 1.079500 − 0.575143I
a = 0.737296 + 0.124322I
b = 0.002970 + 0.490365I
c = −1.087450 − 0.321582I
d = 0.479725 − 0.187227I
−1.00971 + 5.65602I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.163010 + 0.411297I
a = 0.671551 + 0.736386I
b = −1.25901 − 1.37221I
c = 1.123810 + 0.227703I
d = −0.495195 + 0.130609I
−5.58247 + 2.79509I 0
u = −1.163010 − 0.411297I
a = 0.671551 − 0.736386I
b = −1.25901 + 1.37221I
c = 1.123810 − 0.227703I
d = −0.495195 − 0.130609I
−5.58247 − 2.79509I 0
u = 0.530613 + 1.137340I
a = 0.59455 − 1.53864I
b = −1.44703 − 1.12686I
c = 0.507572 + 0.524795I
d = −0.107774 + 0.787252I
−2.68982 + 5.10175I 0
u = 0.530613 − 1.137340I
a = 0.59455 + 1.53864I
b = −1.44703 + 1.12686I
c = 0.507572 − 0.524795I
d = −0.107774 − 0.787252I
−2.68982 − 5.10175I 0
u = 0.601554 + 1.104580I
a = 0.680392 − 0.250043I
b = 1.056620 − 0.465664I
c = 0.317906 − 1.068470I
d = 0.44234 − 2.62651I
−1.29562 + 8.75795I 0
u = 0.601554 − 1.104580I
a = 0.680392 + 0.250043I
b = 1.056620 + 0.465664I
c = 0.317906 + 1.068470I
d = 0.44234 + 2.62651I
−1.29562 − 8.75795I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666542 + 1.084300I
a = 0.118135 − 0.542591I
b = 0.071442 − 0.585941I
c = −0.500654 + 0.512356I
d = 0.063520 + 0.841456I
2.21245 − 7.79054I 0
u = −0.666542 − 1.084300I
a = 0.118135 + 0.542591I
b = 0.071442 + 0.585941I
c = −0.500654 − 0.512356I
d = 0.063520 − 0.841456I
2.21245 + 7.79054I 0
u = −0.620529 + 0.325559I
a = −5.14562 − 0.27928I
b = 0.95424 − 1.08066I
c = 1.53525 + 0.58015I
d = −0.298411 + 0.132539I
−0.115678 − 1.341920I 2.41782 + 1.83708I
u = −0.620529 − 0.325559I
a = −5.14562 + 0.27928I
b = 0.95424 + 1.08066I
c = 1.53525 − 0.58015I
d = −0.298411 − 0.132539I
−0.115678 + 1.341920I 2.41782 − 1.83708I
u = −1.161000 + 0.625559I
a = 0.593536 − 0.499633I
b = 0.72499 + 2.47316I
c = 1.043590 + 0.300928I
d = −0.508606 + 0.196354I
−3.39852 + 10.69180I 0
u = −1.161000 − 0.625559I
a = 0.593536 + 0.499633I
b = 0.72499 − 2.47316I
c = 1.043590 − 0.300928I
d = −0.508606 − 0.196354I
−3.39852 − 10.69180I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.423653 + 0.527399I
a = 1.64700 − 0.10554I
b = −0.013996 + 0.147207I
c = 1.19260 + 0.97739I
d = −0.234755 + 0.236030I
−1.92120 + 0.81846I −4.58107 + 0.87681I
u = −0.423653 − 0.527399I
a = 1.64700 + 0.10554I
b = −0.013996 − 0.147207I
c = 1.19260 − 0.97739I
d = −0.234755 − 0.236030I
−1.92120 − 0.81846I −4.58107 − 0.87681I
u = −0.662834 + 0.003253I
a = 0.744320 − 0.519698I
b = 0.094140 + 1.188930I
c = −0.875349 + 0.262723I
d = −1.33599 + 0.56986I
−0.58945 + 2.77011I 1.22579 − 6.61866I
u = −0.662834 − 0.003253I
a = 0.744320 + 0.519698I
b = 0.094140 − 1.188930I
c = −0.875349 − 0.262723I
d = −1.33599 − 0.56986I
−0.58945 − 2.77011I 1.22579 + 6.61866I
u = 0.703559 + 1.143570I
a = −1.41542 + 1.63566I
b = 0.89414 + 2.47672I
c = 0.504693 + 0.509367I
d = −0.086608 + 0.865680I
−0.07596 + 12.98220I 0
u = 0.703559 − 1.143570I
a = −1.41542 − 1.63566I
b = 0.89414 − 2.47672I
c = 0.504693 − 0.509367I
d = −0.086608 − 0.865680I
−0.07596 − 12.98220I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.624723 + 1.201920I
a = 0.091608 − 0.434620I
b = −0.088537 − 0.634115I
c = −0.285261 − 1.033440I
d = −0.37754 − 2.58761I
−5.70918 − 6.67323I 0
u = −0.624723 − 1.201920I
a = 0.091608 + 0.434620I
b = −0.088537 + 0.634115I
c = −0.285261 + 1.033440I
d = −0.37754 + 2.58761I
−5.70918 + 6.67323I 0
u = 0.127875 + 0.624992I
a = 2.72583 − 3.94484I
b = 0.006337 − 0.990934I
c = 0.253619 + 0.626692I
d = 0.012949 + 0.462081I
0.93270 − 1.56780I −1.99036 − 0.81001I
u = 0.127875 − 0.624992I
a = 2.72583 + 3.94484I
b = 0.006337 + 0.990934I
c = 0.253619 − 0.626692I
d = 0.012949 − 0.462081I
0.93270 + 1.56780I −1.99036 + 0.81001I
u = −0.115044 + 1.357830I
a = 0.180939 − 0.072623I
b = −0.487158 − 0.132207I
c = −0.052504 − 1.096260I
d = −0.07087 − 2.73758I
−9.14335 − 2.92995I 0
u = −0.115044 − 1.357830I
a = 0.180939 + 0.072623I
b = −0.487158 + 0.132207I
c = −0.052504 + 1.096260I
d = −0.07087 + 2.73758I
−9.14335 + 2.92995I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.518606 + 1.307430I
a = 0.38567 − 1.50647I
b = −1.70593 − 1.48615I
c = 0.220862 − 1.037960I
d = 0.28688 − 2.62053I
−10.68990 + 3.50430I 0
u = 0.518606 − 1.307430I
a = 0.38567 + 1.50647I
b = −1.70593 + 1.48615I
c = 0.220862 + 1.037960I
d = 0.28688 + 2.62053I
−10.68990 − 3.50430I 0
u = 0.758435 + 1.184640I
a = 0.005474 + 0.499286I
b = 0.039612 + 0.773723I
c = 0.320071 − 0.988013I
d = 0.40665 − 2.50274I
−2.97939 + 12.30500I 0
u = 0.758435 − 1.184640I
a = 0.005474 − 0.499286I
b = 0.039612 − 0.773723I
c = 0.320071 + 0.988013I
d = 0.40665 + 2.50274I
−2.97939 − 12.30500I 0
u = 0.69467 + 1.24791I
a = −1.24041 + 1.58034I
b = 0.82378 + 2.69229I
c = 0.285505 − 0.998245I
d = 0.36121 − 2.53602I
−8.2281 + 11.9338I 0
u = 0.69467 − 1.24791I
a = −1.24041 − 1.58034I
b = 0.82378 − 2.69229I
c = 0.285505 + 0.998245I
d = 0.36121 + 2.53602I
−8.2281 − 11.9338I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.043030 + 0.567805I
a = 0.727863 − 0.383427I
b = 0.792925 + 0.668517I
c = 0.091032 + 0.642073I
d = 0.007274 + 0.417726I
0.91327 + 2.30980I −2.35018 − 5.72620I
u = 0.043030 − 0.567805I
a = 0.727863 + 0.383427I
b = 0.792925 − 0.668517I
c = 0.091032 − 0.642073I
d = 0.007274 − 0.417726I
0.91327 − 2.30980I −2.35018 + 5.72620I
u = −0.68480 + 1.26233I
a = 0.46647 + 1.35220I
b = −1.97021 + 1.11081I
c = −0.278588 − 0.998411I
d = −0.35134 − 2.53971I
−8.38263 − 9.37788I 0
u = −0.68480 − 1.26233I
a = 0.46647 − 1.35220I
b = −1.97021 − 1.11081I
c = −0.278588 + 0.998411I
d = −0.35134 + 2.53971I
−8.38263 + 9.37788I 0
u = −0.80648 + 1.20827I
a = −1.35815 − 1.43415I
b = 1.08361 − 2.65894I
c = −0.319340 − 0.967077I
d = −0.39362 − 2.47200I
−5.3240 − 17.7550I 0
u = −0.80648 − 1.20827I
a = −1.35815 + 1.43415I
b = 1.08361 + 2.65894I
c = −0.319340 + 0.967077I
d = −0.39362 + 2.47200I
−5.3240 + 17.7550I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00564 + 1.45291I
a = −0.21439 − 1.77515I
b = −0.81882 − 2.53575I
c = −0.002269 − 1.059790I
d = −0.00292 − 2.69163I
−13.06970 − 1.34685I 0
u = −0.00564 − 1.45291I
a = −0.21439 + 1.77515I
b = −0.81882 + 2.53575I
c = −0.002269 + 1.059790I
d = −0.00292 + 2.69163I
−13.06970 + 1.34685I 0
u = 0.22004 + 1.44810I
a = −0.50248 + 1.78125I
b = −0.35055 + 2.76095I
c = 0.087028 − 1.048760I
d = 0.11101 − 2.67072I
−12.6554 + 7.5654I 0
u = 0.22004 − 1.44810I
a = −0.50248 − 1.78125I
b = −0.35055 − 2.76095I
c = 0.087028 + 1.048760I
d = 0.11101 + 2.67072I
−12.6554 − 7.5654I 0
u = 0.499413
a = 0.957005
b = −0.00308149
c = 0.538321
d = 0.683046
1.20722 9.11790
17
II. I
u
2
= h−c
2
u + d − c, u
3
c − u
3
+ · · · + c
3
+ 1, −u
2
+ b + u − 1, u
3
− u
2
+
a + u − 1, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
−u
3
+ u
2
− u + 1
u
2
− u + 1
a
5
=
1
−u
2
a
3
=
−u
3
+ u
2
+ 1
−u
3
+ u
2
− u + 1
a
6
=
−u
3
−u
3
− u
a
10
=
u
u
a
1
=
u
u
a
11
=
c
c
2
u + c
a
8
=
c
2
u
c
2
u + c
a
7
=
c
2
u + u
2
c
c
2
u + u
2
c + c
a
12
=
u
3
c
2
+ c
u
3
c
2
+ c
2
u + c
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
+ 2
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
c
2
, c
4
, c
5
c
9
(u
4
+ u
2
− u + 1)
3
c
3
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
c
6
, c
7
, c
8
c
10
, c
12
u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1
c
11
u
12
− 8u
11
+ ··· + 5u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
c
2
, c
4
, c
5
c
9
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
c
3
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
c
6
, c
7
, c
8
c
10
, c
12
y
12
− 8y
11
+ ··· + 5y + 1
c
11
y
12
− 8y
11
+ ··· − 31y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = 0.808493 − 0.270093I
b = 0.409261 + 0.055548I
c = 0.443738 + 0.456353I
d = 0.200332 + 0.671410I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.547424 + 0.585652I
a = 0.808493 − 0.270093I
b = 0.409261 + 0.055548I
c = −1.160590 + 0.760536I
d = 0.294006 + 0.244250I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.547424 + 0.585652I
a = 0.808493 − 0.270093I
b = 0.409261 + 0.055548I
c = 0.716849 − 1.216890I
d = 1.20928 − 2.73824I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.547424 − 0.585652I
a = 0.808493 + 0.270093I
b = 0.409261 − 0.055548I
c = 0.443738 − 0.456353I
d = 0.200332 − 0.671410I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = 0.547424 − 0.585652I
a = 0.808493 + 0.270093I
b = 0.409261 − 0.055548I
c = −1.160590 − 0.760536I
d = 0.294006 − 0.244250I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = 0.547424 − 0.585652I
a = 0.808493 + 0.270093I
b = 0.409261 − 0.055548I
c = 0.716849 + 1.216890I
d = 1.20928 + 2.73824I
0.98010 − 1.39709I 3.77019 + 3.86736I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 1.120870I
a = −1.30849 − 1.94753I
b = 0.59074 − 2.34806I
c = 0.800094 + 0.563476I
d = −0.387185 + 0.431526I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = −0.547424 + 1.120870I
a = −1.30849 − 1.94753I
b = 0.59074 − 2.34806I
c = −0.294837 − 1.086830I
d = −0.41415 − 2.66421I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = −0.547424 + 1.120870I
a = −1.30849 − 1.94753I
b = 0.59074 − 2.34806I
c = −0.505257 + 0.523356I
d = 0.097717 + 0.791998I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = −0.547424 − 1.120870I
a = −1.30849 + 1.94753I
b = 0.59074 + 2.34806I
c = 0.800094 − 0.563476I
d = −0.387185 − 0.431526I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.547424 − 1.120870I
a = −1.30849 + 1.94753I
b = 0.59074 + 2.34806I
c = −0.294837 + 1.086830I
d = −0.41415 + 2.66421I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.547424 − 1.120870I
a = −1.30849 + 1.94753I
b = 0.59074 + 2.34806I
c = −0.505257 − 0.523356I
d = 0.097717 − 0.791998I
−2.62503 + 7.64338I −1.77019 − 6.51087I
22
III. I
u
3
= h−c
2
u + d − c, −2u
5
c − u
5
+ · · · − 2c − 2, −2u
5
− u
4
+ · · · + b −
2, −u
4
− u
2
+ a − u − 1, u
6
+ u
5
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
2
=
u
4
+ u
2
+ u + 1
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ 3u + 2
a
5
=
1
−u
2
a
3
=
u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2u + 2
u
5
+ 2u
3
+ u
2
+ 2u + 1
a
6
=
−u
3
−u
3
− u
a
10
=
u
u
a
1
=
u
u
a
11
=
c
c
2
u + c
a
8
=
c
2
u
c
2
u + c
a
7
=
c
2
u + u
2
c
c
2
u + u
2
c + c
a
12
=
u
3
c
2
+ c
u
3
c
2
+ c
2
u + c
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u − 2
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
c
2
, c
4
, c
5
c
9
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
c
3
(u
3
+ u
2
− 1)
6
c
6
, c
7
, c
8
c
10
, c
12
u
18
− 6u
16
+ ··· + 2u
3
+ 1
c
11
u
18
− 12u
17
+ ··· + 8u
2
+ 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
c
2
, c
4
, c
5
c
9
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
c
3
(y
3
− y
2
+ 2y − 1)
6
c
6
, c
7
, c
8
c
10
, c
12
y
18
− 12y
17
+ ··· + 8y
2
+ 1
c
11
y
18
− 12y
17
+ ··· + 16y + 1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = 0.315305 + 0.494282I
b = 0.017526 + 0.363437I
c = −0.824384 + 0.621328I
d = 0.347814 + 0.404255I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.498832 + 1.001300I
a = 0.315305 + 0.494282I
b = 0.017526 + 0.363437I
c = 0.334645 − 1.151790I
d = 0.50063 − 2.75254I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.498832 + 1.001300I
a = 0.315305 + 0.494282I
b = 0.017526 + 0.363437I
c = 0.489739 + 0.530460I
d = −0.051234 + 0.748043I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.498832 − 1.001300I
a = 0.315305 − 0.494282I
b = 0.017526 − 0.363437I
c = −0.824384 − 0.621328I
d = 0.347814 − 0.404255I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.498832 − 1.001300I
a = 0.315305 − 0.494282I
b = 0.017526 − 0.363437I
c = 0.334645 + 1.151790I
d = 0.50063 + 2.75254I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.498832 − 1.001300I
a = 0.315305 − 0.494282I
b = 0.017526 − 0.363437I
c = 0.489739 − 0.530460I
d = −0.051234 − 0.748043I
−0.26574 − 2.82812I 1.50976 + 2.97945I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.284920 + 1.115140I
a = 0.50000 + 1.95694I
b = −0.94728 + 1.47725I
c = 0.702880 + 0.625158I
d = −0.306538 + 0.489866I
−4.40332 −5.01951 + 0.I
u = −0.284920 + 1.115140I
a = 0.50000 + 1.95694I
b = −0.94728 + 1.47725I
c = −0.182034 − 1.189200I
d = −0.27134 − 2.85264I
−4.40332 −5.01951 + 0.I
u = −0.284920 + 1.115140I
a = 0.50000 + 1.95694I
b = −0.94728 + 1.47725I
c = −0.520845 + 0.564046I
d = 0.147721 + 0.679189I
−4.40332 −5.01951 + 0.I
u = −0.284920 − 1.115140I
a = 0.50000 − 1.95694I
b = −0.94728 − 1.47725I
c = 0.702880 − 0.625158I
d = −0.306538 − 0.489866I
−4.40332 −5.01951 + 0.I
u = −0.284920 − 1.115140I
a = 0.50000 − 1.95694I
b = −0.94728 − 1.47725I
c = −0.182034 + 1.189200I
d = −0.27134 + 2.85264I
−4.40332 −5.01951 + 0.I
u = −0.284920 − 1.115140I
a = 0.50000 − 1.95694I
b = −0.94728 − 1.47725I
c = −0.520845 − 0.564046I
d = 0.147721 − 0.679189I
−4.40332 −5.01951 + 0.I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.713912 + 0.305839I
a = 0.684695 − 0.494282I
b = 0.42975 + 1.50598I
c = −0.923278 − 0.830773I
d = −1.50829 − 1.87634I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.713912 + 0.305839I
a = 0.684695 − 0.494282I
b = 0.42975 + 1.50598I
c = −0.549584 + 0.390865I
d = −0.524751 + 0.743232I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.713912 + 0.305839I
a = 0.684695 − 0.494282I
b = 0.42975 + 1.50598I
c = 1.47286 + 0.43991I
d = −0.334008 + 0.119065I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.713912 − 0.305839I
a = 0.684695 + 0.494282I
b = 0.42975 − 1.50598I
c = −0.923278 + 0.830773I
d = −1.50829 + 1.87634I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.713912 − 0.305839I
a = 0.684695 + 0.494282I
b = 0.42975 − 1.50598I
c = −0.549584 − 0.390865I
d = −0.524751 − 0.743232I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.713912 − 0.305839I
a = 0.684695 + 0.494282I
b = 0.42975 − 1.50598I
c = 1.47286 − 0.43991I
d = −0.334008 − 0.119065I
−0.26574 − 2.82812I 1.50976 + 2.97945I
28
IV. I
v
1
= ha, d, c − v, b − v, v
2
− v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
2
=
0
v
a
5
=
1
0
a
3
=
v
v
a
6
=
1
−v + 1
a
10
=
v
0
a
1
=
−1
v − 1
a
11
=
v
0
a
8
=
v
0
a
7
=
v
0
a
12
=
v − 1
v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 11
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
, c
10
u
2
c
6
, c
11
(u + 1)
2
c
12
(u − 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(y − 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 0.500000 + 0.866025I
c = 0.500000 + 0.866025I
d = 0
1.64493 + 2.02988I 9.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
c = 0.500000 − 0.866025I
d = 0
1.64493 − 2.02988I 9.00000 + 3.46410I
32
V. I
v
2
= ha, d + v + 1, av + c + 1, b + v, v
2
+ v + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
2
=
0
−v
a
5
=
1
0
a
3
=
−v
−v
a
6
=
1
v + 1
a
10
=
v
0
a
1
=
−1
−v − 1
a
11
=
−1
−v − 1
a
8
=
v + 1
v + 1
a
7
=
1
v + 1
a
12
=
−1
−v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 1
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
6
, c
9
c
11
, c
12
u
2
c
7
, c
8
(u − 1)
2
c
10
(u + 1)
2
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
6
, c
9
c
11
, c
12
y
2
c
7
, c
8
, c
10
(y − 1)
2
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 0.500000 − 0.866025I
c = −1.00000
d = −0.500000 − 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
c = −1.00000
d = −0.500000 + 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
36
VI. I
v
3
= hc, d − 1, b, a − 1, v − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
1
0
a
2
=
1
0
a
5
=
1
0
a
3
=
1
0
a
6
=
1
0
a
10
=
1
0
a
1
=
1
0
a
11
=
0
1
a
8
=
1
−1
a
7
=
0
−1
a
12
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
u
c
6
, c
7
, c
8
u − 1
c
10
, c
11
, c
12
u + 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
y
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y − 1
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 1.00000
b = 0
c = 0
d = 1.00000
0 0
40
VII. I
v
4
=
ha, db+da+· · ·+b−1, a
2
d−da+· · ·−a+1, dv−1, cv+ba−bv−b−a, b
2
−b+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
2
=
0
b
a
5
=
1
0
a
3
=
b
b
a
6
=
1
−b + 1
a
10
=
v
0
a
1
=
−1
b − 1
a
11
=
c
−cb + c − 1
a
8
=
−c + v
cb − c + 1
a
7
=
−c
cb − c + 1
a
12
=
c − 1
−cb + c + b − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = c
2
b − 2cb − v
2
+ 2c − 4b + 3
(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.
41
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
− 2.02988I 3.99982 − 3.44351I
42
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
· (u
77
+ 36u
76
+ ··· + 216u − 16)
c
2
u(u
2
+ u + 1)
2
(u
4
+ u
2
− u + 1)
3
· ((u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
)(u
77
+ 2u
76
+ ··· + 27u
2
− 4)
c
3
u(u
2
− u + 1)
2
(u
3
+ u
2
− 1)
6
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
· (u
77
− 2u
76
+ ··· + 351912u − 66564)
c
4
, c
9
u
5
(u
4
+ u
2
− u + 1)
3
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
· (u
77
− 2u
76
+ ··· − 2560u
2
− 512)
c
5
u(u
2
− u + 1)
2
(u
4
+ u
2
− u + 1)
3
· ((u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
)(u
77
+ 2u
76
+ ··· + 27u
2
− 4)
c
6
u
2
(u − 1)(u + 1)
2
· (u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1)
· (u
18
− 6u
16
+ ··· + 2u
3
+ 1)(u
77
+ 8u
76
+ ··· − 72u − 16)
c
7
, c
8
u
2
(u − 1)
3
· (u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1)
· (u
18
− 6u
16
+ ··· + 2u
3
+ 1)(u
77
− 8u
76
+ ··· − 72u − 16)
c
10
u
2
(u + 1)
3
· (u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1)
· (u
18
− 6u
16
+ ··· + 2u
3
+ 1)(u
77
− 8u
76
+ ··· − 72u − 16)
c
11
u
2
(u + 1)
3
(u
12
− 8u
11
+ ··· + 5u + 1)(u
18
− 12u
17
+ ··· + 8u
2
+ 1)
· (u
77
− 34u
76
+ ··· + 1568u − 256)
c
12
u
2
(u − 1)
2
(u + 1)
· (u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1)
· (u
18
− 6u
16
+ ··· + 2u
3
+ 1)(u
77
+ 8u
76
+ ··· − 72u − 16)
43
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
· ((y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
)(y
77
+ 12y
76
+ ··· + 84256y − 256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
77
+ 36y
76
+ ··· + 216y − 16)
c
3
y(y
2
+ y + 1)
2
(y
3
− y
2
+ 2y − 1)
6
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
· (y
77
− 12y
76
+ ··· + 120020616504y − 4430766096)
c
4
, c
9
y
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
77
+ 30y
76
+ ··· − 2621440y − 262144)
c
6
, c
12
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· + 5y + 1)(y
18
− 12y
17
+ ··· + 8y
2
+ 1)
· (y
77
− 34y
76
+ ··· + 1568y − 256)
c
7
, c
8
, c
10
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· + 5y + 1)(y
18
− 12y
17
+ ··· + 8y
2
+ 1)
· (y
77
− 74y
76
+ ··· + 7712y − 256)
c
11
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· − 31y + 1)(y
18
− 12y
17
+ ··· + 16y + 1)
· (y
77
+ 26y
76
+ ··· + 3416576y − 65536)
44
