12a
0157
(K12a
0157
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 11 12 10 4 7 8 1 6
Solving Sequence
3,9 4,5,11
6 2 1 8 10 7 12
c
3
c
5
c
2
c
1
c
8
c
10
c
7
c
12
c
4
, c
6
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.07617 × 10
162
u
76
− 1.59683 × 10
163
u
75
+ ··· + 1.45795 × 10
166
d + 6.24229 × 10
165
,
− 7.60333 × 10
161
u
76
+ 1.20057 × 10
161
u
75
+ ··· + 3.64487 × 10
165
c + 3.09611 × 10
165
,
− 3.42640 × 10
161
u
76
+ 2.87429 × 10
161
u
75
+ ··· + 2.56564 × 10
164
b + 1.17150 × 10
165
,
6.98505 × 10
162
u
76
+ 6.83866 × 10
162
u
75
+ ··· + 1.02626 × 10
165
a − 1.03017 × 10
166
,
u
77
+ 2u
76
+ ··· + 2560u
2
+ 512i
I
u
2
= hu
3
a
2
− a
2
u
2
− u
3
a + a
2
u + 2u
3
+ au + d − 4a + 4, u
3
a
2
− 2u
3
a + a
2
u + 2u
3
+ au + c − 2a + 2,
a
2
u
2
+ b + 2a − 2, 2u
3
a
2
− 2a
2
u
2
− 3u
3
a + a
3
+ 2a
2
u + 3u
2
a + u
3
− 3au − u
2
+ u, u
4
+ u
2
+ u + 1i
I
u
3
= hu
5
a
2
− 4u
5
a + 2u
3
a
2
+ 4u
4
a + 4u
5
− 5u
3
a − 4u
4
+ 2a
2
u + 8u
2
a + 6u
3
− 3au − 8u
2
+ d + 8a + 4u − 8,
− 2u
5
a + u
3
a
2
+ 2u
4
a + 2u
5
− 4u
3
a − 2u
4
+ a
2
u + 4u
2
a + 4u
3
− au − 4u
2
+ c + 4a + 2u − 4,
a
2
u
2
+ b + 2a − 2, −4u
5
a
2
+ 6u
5
a + ··· − 6a + 2, u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1i
I
v
1
= hc, d − v − 1, b, a − 1, v
2
+ v + 1i
I
v
2
= ha, d, c − v, b − 1, v
2
− v + 1i
I
v
3
= ha, d + 1, c + a, b − 1, v − 1i
I
v
4
= ha, a
2
d − c
2
v − 2ca + cv + a − v, dv + 1, c
2
v
2
+ 2cav − v
2
c + a
2
− av + v
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).
1
I. I
u
1
=
h−6.08×10
162
u
76
−1.60×10
163
u
75
+· · ·+1.46×10
166
d+6.24×10
165
, −7.60×
10
161
u
76
+1.20×10
161
u
75
+· · ·+3.64×10
165
c+3.10×10
165
, −3.43×10
161
u
76
+
2.87 × 10
161
u
75
+ · · · + 2.57 × 10
164
b + 1.17 × 10
165
, 6.99 × 10
162
u
76
+ 6.84 ×
10
162
u
75
+ · · · + 1.03 × 10
165
a − 1.03 × 10
166
, u
77
+ 2u
76
+ · · · + 2560u
2
+ 512i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
−0.00680634u
76
− 0.00666370u
75
+ ··· − 13.3533u + 10.0381
0.00133550u
76
− 0.00112030u
75
+ ··· + 4.56543u − 4.56612
a
11
=
0.000208604u
76
− 0.0000329385u
75
+ ··· − 1.00214u − 0.849444
0.000416762u
76
+ 0.00109526u
75
+ ··· + 0.259754u − 0.428156
a
6
=
−0.00584350u
76
− 0.00606296u
75
+ ··· − 10.5775u + 9.19500
−0.000891648u
76
− 0.00576153u
75
+ ··· + 4.16493u − 3.32748
a
2
=
−0.00680634u
76
− 0.00666370u
75
+ ··· − 13.3533u + 10.0381
0.000152722u
76
+ 0.00152555u
75
+ ··· − 1.08059u + 1.00825
a
1
=
−0.00665361u
76
− 0.00513815u
75
+ ··· − 14.4339u + 11.0464
0.000152722u
76
+ 0.00152555u
75
+ ··· − 1.08059u + 1.00825
a
8
=
u
u
3
+ u
a
10
=
−0.0000869789u
76
− 0.000560439u
75
+ ··· − 0.853173u − 0.579783
0.000218526u
76
+ 0.000662503u
75
+ ··· + 0.560059u − 0.191092
a
7
=
0.000290951u
76
+ 0.00110858u
75
+ ··· + 1.36870u + 0.190813
0.000499554u
76
+ 0.00107564u
75
+ ··· + 0.366559u − 0.658630
a
12
=
0.00628963u
76
+ 0.0183729u
75
+ ··· + 6.15552u + 8.93643
−0.00429774u
76
− 0.00774981u
75
+ ··· − 6.38490u − 0.700057
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0221138u
76
− 0.0478032u
75
+ ··· − 21.6023u + 0.388088
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 34u
76
+ ··· + 1568u + 256
c
2
, c
4
u
77
− 8u
76
+ ··· − 72u + 16
c
3
, c
8
u
77
+ 2u
76
+ ··· + 2560u
2
+ 512
c
5
u
77
+ 2u
76
+ ··· + 351912u + 66564
c
6
, c
12
u
77
− 2u
76
+ ··· − 27u
2
+ 4
c
7
, c
9
, c
10
u
77
+ 8u
76
+ ··· − 72u + 16
c
11
u
77
− 36u
76
+ ··· + 216u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
+ 26y
76
+ ··· + 3416576y − 65536
c
2
, c
4
y
77
− 34y
76
+ ··· + 1568y − 256
c
3
, c
8
y
77
+ 30y
76
+ ··· − 2621440y − 262144
c
5
y
77
− 12y
76
+ ··· + 120020616504y − 4430766096
c
6
, c
12
y
77
+ 36y
76
+ ··· + 216y − 16
c
7
, c
9
, c
10
y
77
− 74y
76
+ ··· + 7712y − 256
c
11
y
77
+ 12y
76
+ ··· + 84256y − 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.508886 + 0.845592I
a = 0.440978 − 0.047456I
b = 1.241720 + 0.241243I
c = 1.093870 + 0.364160I
d = 0.443416 − 0.224335I
−2.40889 + 4.27390I −3.74115 − 6.44221I
u = −0.508886 − 0.845592I
a = 0.440978 + 0.047456I
b = 1.241720 − 0.241243I
c = 1.093870 − 0.364160I
d = 0.443416 + 0.224335I
−2.40889 − 4.27390I −3.74115 + 6.44221I
u = 0.848496 + 0.585068I
a = 0.460618 + 0.092632I
b = 1.086610 − 0.419625I
c = −0.531801 + 1.113610I
d = −1.32944 + 1.48023I
−3.78378 + 2.11500I −7.65464 − 1.99007I
u = 0.848496 − 0.585068I
a = 0.460618 − 0.092632I
b = 1.086610 + 0.419625I
c = −0.531801 − 1.113610I
d = −1.32944 − 1.48023I
−3.78378 − 2.11500I −7.65464 + 1.99007I
u = 0.990280 + 0.319237I
a = 0.580990 − 0.275212I
b = 0.405766 + 0.665904I
c = 0.427768 − 0.711040I
d = 0.003575 − 0.815149I
2.98745 + 0.86657I 0
u = 0.990280 − 0.319237I
a = 0.580990 + 0.275212I
b = 0.405766 − 0.665904I
c = 0.427768 + 0.711040I
d = 0.003575 + 0.815149I
2.98745 − 0.86657I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.617221 + 0.733532I
a = 0.450662 + 0.060640I
b = 1.179500 − 0.293267I
c = −0.865693 + 0.615479I
d = −0.818586 + 0.224399I
−4.09446 + 0.35704I −8.04104 + 0.70386I
u = 0.617221 − 0.733532I
a = 0.450662 − 0.060640I
b = 1.179500 + 0.293267I
c = −0.865693 − 0.615479I
d = −0.818586 − 0.224399I
−4.09446 − 0.35704I −8.04104 − 0.70386I
u = −0.517431 + 0.792256I
a = −0.31513 − 2.57319I
b = −1.046890 + 0.382880I
c = 0.979361 + 0.392885I
d = 0.491329 − 0.041258I
−2.57405 − 0.08416I −4.54592 − 2.74373I
u = −0.517431 − 0.792256I
a = −0.31513 + 2.57319I
b = −1.046890 − 0.382880I
c = 0.979361 − 0.392885I
d = 0.491329 + 0.041258I
−2.57405 + 0.08416I −4.54592 + 2.74373I
u = 0.082487 + 0.936352I
a = 0.92003 − 1.14713I
b = −0.574527 + 0.530498I
c = 1.17847 − 0.94179I
d = −0.290045 + 0.776854I
1.72016 + 1.41215I 1.65188 − 3.77223I
u = 0.082487 − 0.936352I
a = 0.92003 + 1.14713I
b = −0.574527 − 0.530498I
c = 1.17847 + 0.94179I
d = −0.290045 − 0.776854I
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 = −0.41276 + 2.17080I
b = −1.084530 − 0.444586I
c = −1.204890 + 0.519522I
d = −0.720160 − 0.450817I
−3.62010 − 5.07823I −6.10660 + 7.37918I
u = 0.582500 − 0.889546I
a = −0.41276 − 2.17080I
b = −1.084530 + 0.444586I
c = −1.204890 − 0.519522I
d = −0.720160 + 0.450817I
−3.62010 + 5.07823I −6.10660 − 7.37918I
u = −0.228301 + 1.040040I
a = 0.723676 + 0.951160I
b = −0.493370 − 0.665886I
c = −0.513216 − 0.329220I
d = −0.312338 − 0.999680I
3.92825 − 1.69884I 4.65730 + 2.32962I
u = −0.228301 − 1.040040I
a = 0.723676 − 0.951160I
b = −0.493370 + 0.665886I
c = −0.513216 + 0.329220I
d = −0.312338 + 0.999680I
3.92825 + 1.69884I 4.65730 − 2.32962I
u = −0.782003 + 0.468875I
a = 0.479369 − 0.088840I
b = 1.016810 + 0.373767I
c = −0.789013 − 1.040910I
d = −0.598791 − 0.392671I
−0.65497 − 3.51390I −3.54011 + 4.44478I
u = −0.782003 − 0.468875I
a = 0.479369 + 0.088840I
b = 1.016810 − 0.373767I
c = −0.789013 + 1.040910I
d = −0.598791 + 0.392671I
−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 = 0.679703 − 0.804881I
b = −0.387561 + 0.725229I
c = 0.822403 − 0.322418I
d = 0.559284 − 0.573519I
3.38837 − 3.78470I 0
u = 0.374962 − 1.039940I
a = 0.679703 + 0.804881I
b = −0.387561 − 0.725229I
c = 0.822403 + 0.322418I
d = 0.559284 + 0.573519I
3.38837 + 3.78470I 0
u = −0.965284 + 0.548957I
a = 0.458449 − 0.109175I
b = 1.064210 + 0.491568I
c = 0.42927 + 1.36968I
d = 1.62931 + 2.26420I
−1.81197 − 6.85619I 0
u = −0.965284 − 0.548957I
a = 0.458449 + 0.109175I
b = 1.064210 − 0.491568I
c = 0.42927 − 1.36968I
d = 1.62931 − 2.26420I
−1.81197 + 6.85619I 0
u = −0.288832 + 1.092220I
a = 0.655250 + 0.897222I
b = −0.469158 − 0.726873I
c = −1.39360 − 1.30383I
d = 0.03743 + 1.65696I
4.40655 + 2.61636I 0
u = −0.288832 − 1.092220I
a = 0.655250 − 0.897222I
b = −0.469158 + 0.726873I
c = −1.39360 + 1.30383I
d = 0.03743 − 1.65696I
4.40655 − 2.61636I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.815552 + 0.276755I
a = 0.510621 − 0.104384I
b = 0.879842 + 0.384286I
c = −0.134802 + 0.964627I
d = −0.35977 + 2.02275I
0.065597 − 0.205341I −1.21551 + 1.86968I
u = −0.815552 − 0.276755I
a = 0.510621 + 0.104384I
b = 0.879842 − 0.384286I
c = −0.134802 − 0.964627I
d = −0.35977 − 2.02275I
0.065597 + 0.205341I −1.21551 − 1.86968I
u = 0.008067 + 1.164640I
a = 0.524425 + 1.231070I
b = −0.707115 − 0.687536I
c = −1.63638 − 0.81487I
d = 1.18786 + 0.86080I
4.97078 − 4.99360I 0
u = 0.008067 − 1.164640I
a = 0.524425 − 1.231070I
b = −0.707115 + 0.687536I
c = −1.63638 + 0.81487I
d = 1.18786 − 0.86080I
4.97078 + 4.99360I 0
u = −1.177360 + 0.140655I
a = 0.514925 + 0.236545I
b = 0.603622 − 0.736667I
c = −0.027412 − 0.316988I
d = 1.016250 − 0.656214I
6.72367 + 2.38646I 0
u = −1.177360 − 0.140655I
a = 0.514925 − 0.236545I
b = 0.603622 + 0.736667I
c = −0.027412 + 0.316988I
d = 1.016250 + 0.656214I
6.72367 − 2.38646I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.516220 + 1.088150I
a = −0.14742 + 1.74242I
b = −1.048210 − 0.569836I
c = 1.105030 − 0.234332I
d = 0.652838 + 0.110822I
2.28765 − 3.11487I 0
u = 0.516220 − 1.088150I
a = −0.14742 − 1.74242I
b = −1.048210 + 0.569836I
c = 1.105030 + 0.234332I
d = 0.652838 − 0.110822I
2.28765 + 3.11487I 0
u = −1.143240 + 0.423905I
a = 0.533939 + 0.311288I
b = 0.397778 − 0.814910I
c = −0.113421 − 0.926777I
d = −0.01193 − 1.62150I
5.54743 − 5.38085I 0
u = −1.143240 − 0.423905I
a = 0.533939 − 0.311288I
b = 0.397778 + 0.814910I
c = −0.113421 + 0.926777I
d = −0.01193 + 1.62150I
5.54743 + 5.38085I 0
u = −1.079500 + 0.575143I
a = 0.447329 − 0.120477I
b = 1.084300 + 0.561354I
c = −0.260355 − 1.216300I
d = −0.90050 − 1.58646I
1.00971 − 5.65602I 0
u = −1.079500 − 0.575143I
a = 0.447329 + 0.120477I
b = 1.084300 − 0.561354I
c = −0.260355 + 1.216300I
d = −0.90050 + 1.58646I
1.00971 + 5.65602I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.163010 + 0.411297I
a = 0.457972 + 0.144139I
b = 0.986739 − 0.625293I
c = 0.071233 − 0.902749I
d = −0.10463 − 1.67523I
5.58247 + 2.79509I 0
u = 1.163010 − 0.411297I
a = 0.457972 − 0.144139I
b = 0.986739 + 0.625293I
c = 0.071233 + 0.902749I
d = −0.10463 + 1.67523I
5.58247 − 2.79509I 0
u = −0.530613 + 1.137340I
a = −0.16592 − 1.65105I
b = −1.060260 + 0.599620I
c = 1.76242 + 0.34399I
d = −0.11353 − 1.60654I
2.68982 + 5.10175I 0
u = −0.530613 − 1.137340I
a = −0.16592 + 1.65105I
b = −1.060260 − 0.599620I
c = 1.76242 − 0.34399I
d = −0.11353 + 1.60654I
2.68982 − 5.10175I 0
u = −0.601554 + 1.104580I
a = −0.29797 − 1.68572I
b = −1.101680 + 0.575244I
c = −1.271520 − 0.218579I
d = −0.788648 + 0.590297I
1.29562 + 8.75795I 0
u = −0.601554 − 1.104580I
a = −0.29797 + 1.68572I
b = −1.101680 − 0.575244I
c = −1.271520 + 0.218579I
d = −0.788648 − 0.590297I
1.29562 − 8.75795I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.666542 + 1.084300I
a = −0.41901 + 1.68178I
b = −1.139490 − 0.559856I
c = −1.67095 + 0.67803I
d = −0.92819 − 1.72084I
−2.21245 − 7.79054I 0
u = 0.666542 − 1.084300I
a = −0.41901 − 1.68178I
b = −1.139490 + 0.559856I
c = −1.67095 − 0.67803I
d = −0.92819 + 1.72084I
−2.21245 + 7.79054I 0
u = 0.620529 + 0.325559I
a = 0.505847 + 0.065088I
b = 0.944687 − 0.250227I
c = 1.17082 − 0.90601I
d = 0.328371 − 0.105641I
0.115678 − 1.341920I −2.41782 + 1.83708I
u = 0.620529 − 0.325559I
a = 0.505847 − 0.065088I
b = 0.944687 + 0.250227I
c = 1.17082 + 0.90601I
d = 0.328371 + 0.105641I
0.115678 + 1.341920I −2.41782 − 1.83708I
u = 1.161000 + 0.625559I
a = 0.435979 + 0.124995I
b = 1.119470 − 0.607651I
c = 0.116799 − 1.332580I
d = 1.12055 − 2.13672I
3.39852 + 10.69180I 0
u = 1.161000 − 0.625559I
a = 0.435979 − 0.124995I
b = 1.119470 + 0.607651I
c = 0.116799 + 1.332580I
d = 1.12055 + 2.13672I
3.39852 − 10.69180I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.423653 + 0.527399I
a = 0.911492 − 0.383290I
b = −0.067745 + 0.392021I
c = 1.10825 − 1.37074I
d = 0.418849 + 0.237150I
1.92120 + 0.81846I 4.58107 + 0.87681I
u = 0.423653 − 0.527399I
a = 0.911492 + 0.383290I
b = −0.067745 − 0.392021I
c = 1.10825 + 1.37074I
d = 0.418849 − 0.237150I
1.92120 − 0.81846I 4.58107 − 0.87681I
u = 0.662834 + 0.003253I
a = 0.620162 + 0.068360I
b = 0.593125 − 0.175609I
c = 0.844082 + 0.426336I
d = 2.08843 + 0.88000I
0.58945 + 2.77011I −1.22579 − 6.61866I
u = 0.662834 − 0.003253I
a = 0.620162 − 0.068360I
b = 0.593125 + 0.175609I
c = 0.844082 − 0.426336I
d = 2.08843 − 0.88000I
0.58945 − 2.77011I −1.22579 + 6.61866I
u = −0.703559 + 1.143570I
a = −0.43434 − 1.56703I
b = −1.164260 + 0.592620I
c = 1.82114 + 0.75444I
d = 1.05029 − 2.27985I
0.07596 + 12.98220I 0
u = −0.703559 − 1.143570I
a = −0.43434 + 1.56703I
b = −1.164260 − 0.592620I
c = 1.82114 − 0.75444I
d = 1.05029 + 2.27985I
0.07596 − 12.98220I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.624723 + 1.201920I
a = 0.513586 − 0.684350I
b = −0.298481 + 0.934769I
c = 1.343470 − 0.036213I
d = 0.266666 + 0.986054I
5.70918 − 6.67323I 0
u = 0.624723 − 1.201920I
a = 0.513586 + 0.684350I
b = −0.298481 − 0.934769I
c = 1.343470 + 0.036213I
d = 0.266666 − 0.986054I
5.70918 + 6.67323I 0
u = −0.127875 + 0.624992I
a = 0.463873 − 0.011490I
b = 1.154440 + 0.053363I
c = 0.435762 − 0.358619I
d = −0.038269 + 0.332638I
−0.93270 − 1.56780I 1.99036 − 0.81001I
u = −0.127875 − 0.624992I
a = 0.463873 + 0.011490I
b = 1.154440 − 0.053363I
c = 0.435762 + 0.358619I
d = −0.038269 − 0.332638I
−0.93270 + 1.56780I 1.99036 + 0.81001I
u = 0.115044 + 1.357830I
a = 0.267455 + 1.195870I
b = −0.821892 − 0.796376I
c = 0.264755 + 0.381750I
d = −0.286633 − 1.330580I
9.14335 − 2.92995I 0
u = 0.115044 − 1.357830I
a = 0.267455 − 1.195870I
b = −0.821892 + 0.796376I
c = 0.264755 − 0.381750I
d = −0.286633 + 1.330580I
9.14335 + 2.92995I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.518606 + 1.307430I
a = 0.471054 + 0.753719I
b = −0.403718 − 0.954094I
c = −1.155440 + 0.212036I
d = 0.575561 + 0.435533I
10.68990 + 3.50430I 0
u = −0.518606 − 1.307430I
a = 0.471054 − 0.753719I
b = −0.403718 + 0.954094I
c = −1.155440 − 0.212036I
d = 0.575561 − 0.435533I
10.68990 − 3.50430I 0
u = −0.758435 + 1.184640I
a = −0.47779 − 1.47703I
b = −1.198260 + 0.612902I
c = −1.59692 − 0.12137I
d = −0.81262 + 1.86068I
2.97939 + 12.30500I 0
u = −0.758435 − 1.184640I
a = −0.47779 + 1.47703I
b = −1.198260 − 0.612902I
c = −1.59692 + 0.12137I
d = −0.81262 − 1.86068I
2.97939 − 12.30500I 0
u = −0.69467 + 1.24791I
a = 0.480437 + 0.659159I
b = −0.277875 − 0.990754I
c = −1.49960 + 0.03004I
d = −0.12141 + 1.59948I
8.2281 + 11.9338I 0
u = −0.69467 − 1.24791I
a = 0.480437 − 0.659159I
b = −0.277875 + 0.990754I
c = −1.49960 − 0.03004I
d = −0.12141 − 1.59948I
8.2281 − 11.9338I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.043030 + 0.567805I
a = 4.08839 − 1.11685I
b = −0.772390 + 0.062177I
c = 0.144313 − 0.425715I
d = −0.013781 + 0.345769I
−0.91327 + 2.30980I 2.35018 − 5.72620I
u = −0.043030 − 0.567805I
a = 4.08839 + 1.11685I
b = −0.772390 − 0.062177I
c = 0.144313 + 0.425715I
d = −0.013781 − 0.345769I
−0.91327 − 2.30980I 2.35018 + 5.72620I
u = 0.68480 + 1.26233I
a = −0.34737 + 1.42430I
b = −1.161620 − 0.662680I
c = 1.48561 + 0.06309I
d = −0.01550 + 1.56219I
8.38263 − 9.37788I 0
u = 0.68480 − 1.26233I
a = −0.34737 − 1.42430I
b = −1.161620 + 0.662680I
c = 1.48561 − 0.06309I
d = −0.01550 − 1.56219I
8.38263 + 9.37788I 0
u = 0.80648 + 1.20827I
a = −0.51585 + 1.41688I
b = −1.226880 − 0.623174I
c = 1.70051 − 0.09972I
d = 0.83764 + 2.32804I
5.3240 − 17.7550I 0
u = 0.80648 − 1.20827I
a = −0.51585 − 1.41688I
b = −1.226880 + 0.623174I
c = 1.70051 + 0.09972I
d = 0.83764 − 2.32804I
5.3240 + 17.7550I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00564 + 1.45291I
a = 0.279733 − 1.057890I
b = −0.766380 + 0.883500I
c = 0.013236 + 0.605297I
d = −0.02236 − 1.73200I
13.06970 − 1.34685I 0
u = 0.00564 − 1.45291I
a = 0.279733 + 1.057890I
b = −0.766380 − 0.883500I
c = 0.013236 − 0.605297I
d = −0.02236 + 1.73200I
13.06970 + 1.34685I 0
u = −0.22004 + 1.44810I
a = 0.134599 − 1.184980I
b = −0.905365 + 0.833146I
c = −0.514065 + 0.581969I
d = 0.82290 − 1.33139I
12.6554 + 7.5654I 0
u = −0.22004 − 1.44810I
a = 0.134599 + 1.184980I
b = −0.905365 − 0.833146I
c = −0.514065 − 0.581969I
d = 0.82290 + 1.33139I
12.6554 − 7.5654I 0
u = −0.499413
a = 0.544041
b = 0.838096
c = −0.278989
d = −0.886893
−1.20722 −9.11790
17
II. I
u
2
= hu
3
a
2
− u
3
a + · · · − 4a + 4, u
3
a
2
− 2u
3
a + · · · − 2a + 2, a
2
u
2
+ b +
2a − 2, 2u
3
a
2
− 3u
3
a + · · · + a
3
+ u, u
4
+ u
2
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
−a
2
u
2
− 2a + 2
a
11
=
−u
3
a
2
+ 2u
3
a − a
2
u − 2u
3
− au + 2a − 2
−u
3
a
2
+ a
2
u
2
+ u
3
a − a
2
u − 2u
3
− au + 4a − 4
a
6
=
−u
3
a
2
− a
2
u
2
− a
2
u + 2u
2
a − a
2
− 3au − 2u
2
+ 2u
−u
3
a
2
− a
2
u
2
− 3u
3
a + u
2
a + 2u
3
− a
2
− 5au − 2u
2
− 3a + 4u + 2
a
2
=
a
a
2
u
2
+ u
2
a + 2a − 2
a
1
=
a
2
u
2
+ u
2
a + 3a − 2
a
2
u
2
+ u
2
a + 2a − 2
a
8
=
u
u
3
+ u
a
10
=
2u
3
a − a
2
u − 2u
3
+ au + 2a − 2u − 2
−u
3
a
2
+ 3u
3
a − 2a
2
u − 4u
3
+ au + 4a − 2u − 4
a
7
=
2u
3
a − a
2
u − 2u
3
+ 2au + 2a − 2u − 2
−u
3
a
2
+ 4u
3
a − 2a
2
u − 4u
3
+ au + 4a − 2u − 4
a
12
=
−u
3
a
2
+ a
2
u
2
+ 2u
3
a − 2u
2
a − 2u
3
+ a
2
+ 2u
2
+ 3a − 2
−u
3
a
2
+ 2a
2
u
2
+ u
3
a − u
2
a − 2u
3
+ a
2
+ 2u
2
+ 5a − 4
(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
12
+ 8u
11
+ ··· − 5u + 1
c
2
, c
4
, c
7
c
9
, c
10
u
12
− 4u
10
+ 2u
9
+ 6u
8
− 6u
7
− u
6
+ 6u
5
− 5u
4
− u
3
+ 3u
2
− u + 1
c
3
, c
6
, c
8
c
12
(u
4
+ u
2
+ u + 1)
3
c
5
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
3
c
11
(u
4
− 2u
3
+ 3u
2
− u + 1)
3
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 8y
11
+ ··· − 31y + 1
c
2
, c
4
, c
7
c
9
, c
10
y
12
− 8y
11
+ ··· + 5y + 1
c
3
, c
6
, c
8
c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
c
5
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
c
11
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 0.585652I
a = 0.805204 + 0.420651I
b = −0.024351 − 0.509694I
c = 0.555240 + 0.479815I
d = 0.395109 + 0.559365I
−0.98010 + 1.39709I −3.77019 − 3.86736I
u = −0.547424 + 0.585652I
a = 0.468622 − 0.054836I
b = 1.105090 + 0.246330I
c = −1.24165 − 1.00900I
d = −2.55169 − 1.38604I
−0.98010 + 1.39709I −3.77019 − 3.86736I
u = −0.547424 + 0.585652I
a = −1.06407 − 3.47080I
b = −1.080740 + 0.263364I
c = −1.01721 − 1.29340I
d = −0.641886 + 0.175397I
−0.98010 + 1.39709I −3.77019 − 3.86736I
u = −0.547424 − 0.585652I
a = 0.805204 − 0.420651I
b = −0.024351 + 0.509694I
c = 0.555240 − 0.479815I
d = 0.395109 − 0.559365I
−0.98010 − 1.39709I −3.77019 + 3.86736I
u = −0.547424 − 0.585652I
a = 0.468622 + 0.054836I
b = 1.105090 − 0.246330I
c = −1.24165 + 1.00900I
d = −2.55169 + 1.38604I
−0.98010 − 1.39709I −3.77019 + 3.86736I
u = −0.547424 − 0.585652I
a = −1.06407 + 3.47080I
b = −1.080740 − 0.263364I
c = −1.01721 + 1.29340I
d = −0.641886 − 0.175397I
−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 = 0.573365 − 0.708694I
b = −0.310026 + 0.852826I
c = −1.72860 + 0.38800I
d = −0.04577 − 1.58115I
2.62503 − 7.64338I 1.77019 + 6.51087I
u = 0.547424 + 1.120870I
a = 0.415110 + 0.046138I
b = 1.379600 − 0.264482I
c = 1.170990 − 0.175799I
d = 0.561298 + 0.342574I
2.62503 − 7.64338I 1.77019 + 6.51087I
u = 0.547424 + 1.120870I
a = −0.19823 + 1.67624I
b = −1.069580 − 0.588344I
c = 1.26123 − 1.65288I
d = 1.28293 + 2.03964I
2.62503 − 7.64338I 1.77019 + 6.51087I
u = 0.547424 − 1.120870I
a = 0.573365 + 0.708694I
b = −0.310026 − 0.852826I
c = −1.72860 − 0.38800I
d = −0.04577 + 1.58115I
2.62503 + 7.64338I 1.77019 − 6.51087I
u = 0.547424 − 1.120870I
a = 0.415110 − 0.046138I
b = 1.379600 + 0.264482I
c = 1.170990 + 0.175799I
d = 0.561298 − 0.342574I
2.62503 + 7.64338I 1.77019 − 6.51087I
u = 0.547424 − 1.120870I
a = −0.19823 − 1.67624I
b = −1.069580 + 0.588344I
c = 1.26123 + 1.65288I
d = 1.28293 − 2.03964I
2.62503 + 7.64338I 1.77019 − 6.51087I
22
III. I
u
3
= hu
5
a
2
− 4u
5
a + · · · + 8a − 8, −2u
5
a + 2u
5
+ · · · + 4a − 4, a
2
u
2
+
b + 2a − 2, −4u
5
a
2
+ 6u
5
a + · · · − 6a + 2, u
6
− u
5
+ · · · − 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
5
=
a
−a
2
u
2
− 2a + 2
a
11
=
2u
5
a − 2u
5
+ ··· − 4a + 4
−u
5
a
2
+ 4u
5
a + ··· − 8a + 8
a
6
=
u
5
a
2
+ 2u
3
a
2
+ 3u
4
a − a
2
u
2
− 2u
4
+ 2a
2
u + 5u
2
a − a
2
− 4u
2
+ 3a − 2
2u
5
a
2
+ 3u
5
a + ··· − 2a
2
− a
a
2
=
a
a
2
u
2
+ u
2
a + 2a − 2
a
1
=
a
2
u
2
+ u
2
a + 3a − 2
a
2
u
2
+ u
2
a + 2a − 2
a
8
=
u
u
3
+ u
a
10
=
2u
5
a − 2u
5
+ ··· − 4a + 4
4u
5
a − 4u
5
+ ··· − 8a + 8
a
7
=
2u
5
a − 2u
5
+ ··· − 4a + 4
4u
5
a − 4u
5
+ ··· − 8a + 8
a
12
=
5u
5
a − 4u
5
+ ··· − 5a + 4
−u
5
a
2
+ 6u
5
a + ··· − 9a + 8
(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
18
+ 12u
17
+ ··· + 8u
2
+ 1
c
2
, c
4
, c
7
c
9
, c
10
u
18
− 6u
16
+ ··· − 2u
3
+ 1
c
3
, c
6
, c
8
c
12
(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
3
c
5
(u
3
− u
2
+ 1)
6
c
11
(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
3
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 12y
17
+ ··· + 16y + 1
c
2
, c
4
, c
7
c
9
, c
10
y
18
− 12y
17
+ ··· + 8y
2
+ 1
c
3
, c
6
, c
8
c
12
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
c
5
(y
3
− y
2
+ 2y − 1)
6
c
11
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.498832 + 1.001300I
a = 0.661188 + 0.699980I
b = −0.286853 − 0.754987I
c = 1.44004 + 0.30697I
d = 0.171485 − 0.832500I
0.26574 + 2.82812I −1.50976 − 2.97945I
u = −0.498832 + 1.001300I
a = 0.426451 − 0.044014I
b = 1.320220 + 0.239468I
c = −1.064340 − 0.398265I
d = −0.994564 − 0.186619I
0.26574 + 2.82812I −1.50976 − 2.97945I
u = −0.498832 + 1.001300I
a = −0.12503 − 1.93170I
b = −1.033370 + 0.515520I
c = −1.17291 − 1.50894I
d = −0.97180 + 1.42148I
0.26574 + 2.82812I −1.50976 − 2.97945I
u = −0.498832 − 1.001300I
a = 0.661188 − 0.699980I
b = −0.286853 + 0.754987I
c = 1.44004 − 0.30697I
d = 0.171485 + 0.832500I
0.26574 − 2.82812I −1.50976 + 2.97945I
u = −0.498832 − 1.001300I
a = 0.426451 + 0.044014I
b = 1.320220 − 0.239468I
c = −1.064340 + 0.398265I
d = −0.994564 + 0.186619I
0.26574 − 2.82812I −1.50976 + 2.97945I
u = −0.498832 − 1.001300I
a = −0.12503 + 1.93170I
b = −1.033370 − 0.515520I
c = −1.17291 + 1.50894I
d = −0.97180 − 1.42148I
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 = 0.633702 − 0.904691I
b = −0.480591 + 0.741524I
c = −1.63240 − 0.20951I
d = 0.919012 − 0.439251I
4.40332 5.01951 + 0.I
u = 0.284920 + 1.115140I
a = 0.419155 + 0.023943I
b = 1.377990 − 0.135834I
c = 0.633400 − 0.165486I
d = 0.184355 − 0.759840I
4.40332 5.01951 + 0.I
u = 0.284920 + 1.115140I
a = 0.27186 + 1.60496I
b = −0.897403 − 0.605690I
c = 1.42916 − 1.30860I
d = −0.10337 + 1.74578I
4.40332 5.01951 + 0.I
u = 0.284920 − 1.115140I
a = 0.633702 + 0.904691I
b = −0.480591 − 0.741524I
c = −1.63240 + 0.20951I
d = 0.919012 + 0.439251I
4.40332 5.01951 + 0.I
u = 0.284920 − 1.115140I
a = 0.419155 − 0.023943I
b = 1.377990 + 0.135834I
c = 0.633400 + 0.165486I
d = 0.184355 + 0.759840I
4.40332 5.01951 + 0.I
u = 0.284920 − 1.115140I
a = 0.27186 − 1.60496I
b = −0.897403 + 0.605690I
c = 1.42916 + 1.30860I
d = −0.10337 − 1.74578I
4.40332 5.01951 + 0.I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.713912 + 0.305839I
a = 0.699357 − 0.245678I
b = 0.272813 + 0.447127I
c = 0.033182 + 0.755013I
d = 0.26687 + 1.47455I
0.26574 + 2.82812I −1.50976 − 2.97945I
u = 0.713912 + 0.305839I
a = 0.509246 + 0.082706I
b = 0.913222 − 0.310725I
c = 1.33201 − 0.98810I
d = 3.24106 − 1.64838I
0.26574 + 2.82812I −1.50976 − 2.97945I
u = 0.713912 + 0.305839I
a = −3.49593 + 2.56326I
b = −1.186030 − 0.136403I
c = 1.001860 − 0.780958I
d = 0.286941 − 0.228535I
0.26574 + 2.82812I −1.50976 − 2.97945I
u = 0.713912 − 0.305839I
a = 0.699357 + 0.245678I
b = 0.272813 − 0.447127I
c = 0.033182 − 0.755013I
d = 0.26687 − 1.47455I
0.26574 − 2.82812I −1.50976 + 2.97945I
u = 0.713912 − 0.305839I
a = 0.509246 − 0.082706I
b = 0.913222 + 0.310725I
c = 1.33201 + 0.98810I
d = 3.24106 + 1.64838I
0.26574 − 2.82812I −1.50976 + 2.97945I
u = 0.713912 − 0.305839I
a = −3.49593 − 2.56326I
b = −1.186030 + 0.136403I
c = 1.001860 + 0.780958I
d = 0.286941 + 0.228535I
0.26574 − 2.82812I −1.50976 + 2.97945I
28
IV. I
v
1
= hc, d − v − 1, b, a − 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
1
0
a
11
=
0
v + 1
a
6
=
1
−v
a
2
=
1
0
a
1
=
1
0
a
8
=
v
0
a
10
=
v
v + 1
a
7
=
0
−v − 1
a
12
=
v + 1
v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 1
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
u
2
c
5
, c
12
u
2
− u + 1
c
6
, c
11
u
2
+ u + 1
c
7
(u + 1)
2
c
9
, c
10
(u − 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
y
2
c
5
, c
6
, c
11
c
12
y
2
+ y + 1
c
7
, c
9
, c
10
(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 = 1.00000
b = 0
c = 0
d = 0.500000 + 0.866025I
1.64493 + 2.02988I 3.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = 0.500000 − 0.866025I
1.64493 − 2.02988I 3.00000 + 3.46410I
32
V. I
v
2
= ha, d, c − v, b − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
11
=
v
0
a
6
=
v − 1
1
a
2
=
1
−1
a
1
=
0
−1
a
8
=
v
0
a
10
=
v
0
a
7
=
v
0
a
12
=
v
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 7
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
7
, c
8
c
9
, c
10
u
2
c
4
(u + 1)
2
c
5
, c
11
, c
12
u
2
+ u + 1
c
6
u
2
− u + 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
7
, c
8
c
9
, c
10
y
2
c
5
, c
6
, c
11
c
12
y
2
+ y + 1
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 = 1.00000
c = 0.500000 + 0.866025I
d = 0
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = 0.500000 − 0.866025I
d = 0
−1.64493 − 2.02988I −9.00000 + 3.46410I
36
VI. I
v
3
= ha, d + 1, c + a, b − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
1
0
a
4
=
1
0
a
5
=
0
1
a
11
=
0
−1
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
8
=
1
0
a
10
=
1
−1
a
7
=
0
1
a
12
=
0
−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
9
c
10
u − 1
c
3
, c
5
, c
6
c
8
, c
11
, c
12
u
c
4
, c
7
u + 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
7
, c
9
, c
10
y − 1
c
3
, c
5
, c
6
c
8
, c
11
, c
12
y
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
c = 0
d = −1.00000
0 0
40
VII.
I
v
4
= ha, −c
2
v + cv + · · · − 2ca + a, dv + 1, c
2
v
2
− v
2
c + · · · + a
2
− av, b − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
11
=
c
d
a
6
=
c − 1
dc + 1
a
2
=
1
−1
a
1
=
0
−1
a
8
=
v
0
a
10
=
c + v
d
a
7
=
−c
−d
a
12
=
c
d − c
(ii) Obstruction class = −1
(iii) Cusp Shapes = d
2
+ v
2
− 4c
(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 0.19616 + 2.89071I
42
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
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
2
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
3
, c
8
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
4
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
5
u(u
2
− u + 1)(u
2
+ u + 1)(u
3
− u
2
+ 1)
6
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
3
· (u
77
+ 2u
76
+ ··· + 351912u + 66564)
c
6
, c
12
u(u
2
− u + 1)(u
2
+ u + 1)(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
7
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
9
, 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(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)
43
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y − 1)
3
(y
12
− 8y
11
+ ··· − 31y + 1)(y
18
− 12y
17
+ ··· + 16y + 1)
· (y
77
+ 26y
76
+ ··· + 3416576y − 65536)
c
2
, c
4
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
3
, c
8
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
5
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
6
, c
12
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
7
, c
9
, 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(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)
44
