12a
0816
(K12a
0816
)
A knot diagram
1
Linearized knot diagam
4 5 7 2 10 3 11 12 1 6 9 8
Solving Sequence
5,10 3,6
7 11 8 2 4 1 9 12
c
5
c
6
c
10
c
7
c
2
c
4
c
1
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.88375 × 10
234
u
85
− 1.46902 × 10
234
u
84
+ ··· + 2.70951 × 10
236
b + 2.78190 × 10
236
,
1.64525 × 10
236
u
85
+ 2.08852 × 10
236
u
84
+ ··· + 5.41901 × 10
236
a + 7.89723 × 10
237
,
u
86
+ 2u
85
+ ··· + 352u + 64i
I
u
2
= hb + 1, u
5
− 4u
3
+ u
2
+ a + 4u − 3, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
I
v
1
= ha, 8v
5
+ 21v
4
+ 63v
3
+ 21v
2
+ 503b − v −817, v
6
+ 3v
5
+ v
4
− 18v
3
− 7v
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 98 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
= h3.88 × 10
234
u
85
− 1.47 × 10
234
u
84
+ · · · + 2.71 × 10
236
b + 2.78 ×
10
236
, 1.65 × 10
236
u
85
+ 2.09 × 10
236
u
84
+ · · · + 5.42 × 10
236
a + 7.90 ×
10
237
, u
86
+ 2u
85
+ · · · + 352u + 64i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−0.303607u
85
− 0.385406u
84
+ ··· − 98.1776u − 14.5732
−0.0143338u
85
+ 0.00542171u
84
+ ··· − 2.27870u − 1.02672
a
6
=
1
−u
2
a
7
=
−0.400196u
85
− 0.562734u
84
+ ··· − 159.471u − 37.7347
0.0373459u
85
+ 0.124701u
84
+ ··· + 33.4026u + 11.9056
a
11
=
u
−u
3
+ u
a
8
=
−0.364855u
85
− 0.475874u
84
+ ··· − 132.797u − 29.2352
0.103811u
85
+ 0.242890u
84
+ ··· + 68.0341u + 21.4406
a
2
=
−0.317940u
85
− 0.379984u
84
+ ··· − 100.456u − 15.5999
−0.0143338u
85
+ 0.00542171u
84
+ ··· − 2.27870u − 1.02672
a
4
=
−0.000379134u
85
− 0.00662213u
84
+ ··· + 10.0057u + 7.46172
0.0314098u
85
− 0.0261001u
84
+ ··· − 6.20145u − 6.59007
a
1
=
−0.313635u
85
− 0.494466u
84
+ ··· − 134.831u − 34.4302
0.0865603u
85
+ 0.0682676u
84
+ ··· + 24.6403u + 3.30443
a
9
=
−0.428449u
85
− 0.506093u
84
+ ··· − 128.967u − 23.4151
−0.112532u
85
− 0.102360u
84
+ ··· − 14.4207u − 1.77881
a
12
=
−0.518000u
85
− 0.878705u
84
+ ··· − 263.329u − 71.7071
−0.388762u
85
− 0.550043u
84
+ ··· − 149.561u − 34.9025
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.25246u
85
− 1.96111u
84
+ ··· − 563.188u − 165.262
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
86
− 10u
85
+ ··· + 18u + 1
c
3
, c
6
u
86
+ 4u
85
+ ··· − 1152u
2
+ 64
c
5
, c
10
u
86
+ 2u
85
+ ··· + 352u + 64
c
7
, c
9
u
86
− 4u
85
+ ··· − 13134u + 977
c
8
, c
11
, c
12
u
86
+ 4u
85
+ ··· − 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
86
− 82y
85
+ ··· − 478y + 1
c
3
, c
6
y
86
− 48y
85
+ ··· − 147456y + 4096
c
5
, c
10
y
86
− 42y
85
+ ··· − 107520y + 4096
c
7
, c
9
y
86
− 56y
85
+ ··· − 14579676y + 954529
c
8
, c
11
, c
12
y
86
+ 72y
85
+ ··· − 20y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.552054 + 0.828557I
a = 0.192966 − 0.000278I
b = 1.55396 + 0.16056I
−13.69310 − 2.82580I 0
u = 0.552054 − 0.828557I
a = 0.192966 + 0.000278I
b = 1.55396 − 0.16056I
−13.69310 + 2.82580I 0
u = 0.712992 + 0.675491I
a = 0.581320 + 0.515681I
b = −0.631213 − 0.658080I
−6.37937 + 0.07950I 0
u = 0.712992 − 0.675491I
a = 0.581320 − 0.515681I
b = −0.631213 + 0.658080I
−6.37937 − 0.07950I 0
u = 0.293714 + 0.923956I
a = 0.598122 + 0.230114I
b = −0.220725 − 0.596939I
1.77443 − 1.89708I 0
u = 0.293714 − 0.923956I
a = 0.598122 − 0.230114I
b = −0.220725 + 0.596939I
1.77443 + 1.89708I 0
u = −0.399332 + 0.964359I
a = 0.562555 − 0.274132I
b = −0.274017 + 0.680285I
−2.56815 + 5.72788I 0
u = −0.399332 − 0.964359I
a = 0.562555 + 0.274132I
b = −0.274017 − 0.680285I
−2.56815 − 5.72788I 0
u = −0.814919 + 0.658478I
a = −0.82638 + 1.33174I
b = −1.383480 − 0.068743I
−8.14347 − 2.53737I 0
u = −0.814919 − 0.658478I
a = −0.82638 − 1.33174I
b = −1.383480 + 0.068743I
−8.14347 + 2.53737I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.983266 + 0.394126I
a = 0.04078 + 1.47966I
b = −0.260699 − 0.690733I
0.29357 − 3.54409I 0
u = −0.983266 − 0.394126I
a = 0.04078 − 1.47966I
b = −0.260699 + 0.690733I
0.29357 + 3.54409I 0
u = −0.225473 + 0.906689I
a = 0.191216 − 0.000872I
b = 1.48450 − 0.07065I
−8.06829 + 1.47587I −6.04730 + 0.I
u = −0.225473 − 0.906689I
a = 0.191216 + 0.000872I
b = 1.48450 + 0.07065I
−8.06829 − 1.47587I −6.04730 + 0.I
u = −1.049590 + 0.241828I
a = 0.357510 − 0.885888I
b = −1.048150 + 0.593109I
−0.89394 + 2.01684I 0
u = −1.049590 − 0.241828I
a = 0.357510 + 0.885888I
b = −1.048150 − 0.593109I
−0.89394 − 2.01684I 0
u = −0.130183 + 0.912720I
a = 0.615451 − 0.146529I
b = −0.106806 + 0.503836I
−1.74508 − 1.81197I 0
u = −0.130183 − 0.912720I
a = 0.615451 + 0.146529I
b = −0.106806 − 0.503836I
−1.74508 + 1.81197I 0
u = 0.909805 + 0.583851I
a = −0.30401 − 1.55635I
b = −0.426541 + 0.738548I
−5.77290 + 4.80475I 0
u = 0.909805 − 0.583851I
a = −0.30401 + 1.55635I
b = −0.426541 − 0.738548I
−5.77290 − 4.80475I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.048040 + 0.370428I
a = 0.390246 + 0.782737I
b = −0.981638 − 0.659900I
2.46498 + 1.91776I 0
u = 1.048040 − 0.370428I
a = 0.390246 − 0.782737I
b = −0.981638 + 0.659900I
2.46498 − 1.91776I 0
u = 0.771535 + 0.431699I
a = −0.47760 − 1.71983I
b = −1.262540 + 0.145425I
−2.36374 + 1.81286I 0. − 3.83527I
u = 0.771535 − 0.431699I
a = −0.47760 + 1.71983I
b = −1.262540 − 0.145425I
−2.36374 − 1.81286I 0. + 3.83527I
u = 0.852981 + 0.159244I
a = 0.58828 − 1.49094I
b = −0.159548 + 0.473962I
1.120900 + 0.300961I 6.91660 − 0.58498I
u = 0.852981 − 0.159244I
a = 0.58828 + 1.49094I
b = −0.159548 − 0.473962I
1.120900 − 0.300961I 6.91660 + 0.58498I
u = 1.059140 + 0.410939I
a = −0.287658 − 1.211040I
b = −1.376810 + 0.289151I
−1.68586 + 0.96431I 0
u = 1.059140 − 0.410939I
a = −0.287658 + 1.211040I
b = −1.376810 − 0.289151I
−1.68586 − 0.96431I 0
u = −1.060240 + 0.459416I
a = 0.391196 − 0.717519I
b = −0.943184 + 0.714225I
−1.95224 − 5.90463I 0
u = −1.060240 − 0.459416I
a = 0.391196 + 0.717519I
b = −0.943184 − 0.714225I
−1.95224 + 5.90463I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438702 + 0.719830I
a = −1.86531 − 1.41789I
b = −1.244600 − 0.118813I
−5.13889 − 4.02609I −2.76635 + 0.76522I
u = 0.438702 − 0.719830I
a = −1.86531 + 1.41789I
b = −1.244600 + 0.118813I
−5.13889 + 4.02609I −2.76635 − 0.76522I
u = −1.081380 + 0.516007I
a = −0.405516 + 1.145080I
b = −1.43564 − 0.25261I
1.40001 − 4.97319I 0
u = −1.081380 − 0.516007I
a = −0.405516 − 1.145080I
b = −1.43564 + 0.25261I
1.40001 + 4.97319I 0
u = −1.136010 + 0.403070I
a = −1.18436 − 1.39457I
b = 1.41697 + 0.15814I
−9.55306 + 0.49039I 0
u = −1.136010 − 0.403070I
a = −1.18436 + 1.39457I
b = 1.41697 − 0.15814I
−9.55306 − 0.49039I 0
u = −0.562219 + 0.524976I
a = 0.716658 − 0.329576I
b = 0.182504 + 0.015855I
−3.19093 − 1.95911I 3.32674 + 3.69322I
u = −0.562219 − 0.524976I
a = 0.716658 + 0.329576I
b = 0.182504 − 0.015855I
−3.19093 + 1.95911I 3.32674 − 3.69322I
u = 1.092220 + 0.579762I
a = −0.466720 − 1.099830I
b = −1.46979 + 0.22913I
−3.18556 + 9.02341I 0
u = 1.092220 − 0.579762I
a = −0.466720 + 1.099830I
b = −1.46979 − 0.22913I
−3.18556 − 9.02341I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.187690 + 0.506855I
a = −0.111325 + 1.217970I
b = −0.237680 − 0.887129I
1.53780 − 3.15145I 0
u = −1.187690 − 0.506855I
a = −0.111325 − 1.217970I
b = −0.237680 + 0.887129I
1.53780 + 3.15145I 0
u = 1.291170 + 0.123828I
a = 0.278328 + 0.884185I
b = 0.269267 − 0.656632I
3.52569 − 2.53556I 0
u = 1.291170 − 0.123828I
a = 0.278328 − 0.884185I
b = 0.269267 + 0.656632I
3.52569 + 2.53556I 0
u = −0.657648 + 0.222079I
a = 0.190415 + 0.000646I
b = 1.68329 − 0.04881I
−11.53680 − 3.32788I 1.60100 + 7.68257I
u = −0.657648 − 0.222079I
a = 0.190415 − 0.000646I
b = 1.68329 + 0.04881I
−11.53680 + 3.32788I 1.60100 − 7.68257I
u = 1.127830 + 0.663427I
a = −0.35766 + 1.65601I
b = 1.47079 − 0.27396I
−11.8702 + 8.4794I 0
u = 1.127830 − 0.663427I
a = −0.35766 − 1.65601I
b = 1.47079 + 0.27396I
−11.8702 − 8.4794I 0
u = −1.294930 + 0.226061I
a = 0.289669 − 0.819710I
b = 0.347991 + 0.605697I
7.12157 − 1.76447I 0
u = −1.294930 − 0.226061I
a = 0.289669 + 0.819710I
b = 0.347991 − 0.605697I
7.12157 + 1.76447I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.231000 + 0.473921I
a = −0.82743 + 1.23132I
b = 1.381250 − 0.202296I
−3.88741 + 2.87017I 0
u = 1.231000 − 0.473921I
a = −0.82743 − 1.23132I
b = 1.381250 + 0.202296I
−3.88741 − 2.87017I 0
u = −0.432450 + 1.250560I
a = 0.193237 − 0.006450I
b = 1.367100 − 0.183599I
−6.49234 + 0.65249I 0
u = −0.432450 − 1.250560I
a = 0.193237 + 0.006450I
b = 1.367100 + 0.183599I
−6.49234 − 0.65249I 0
u = −0.353875 + 0.574365I
a = −2.39311 + 2.12630I
b = −1.150500 + 0.085662I
−0.680663 + 0.581964I 4.76633 + 3.68087I
u = −0.353875 − 0.574365I
a = −2.39311 − 2.12630I
b = −1.150500 − 0.085662I
−0.680663 − 0.581964I 4.76633 − 3.68087I
u = 1.189690 + 0.590585I
a = −0.192525 − 1.202200I
b = −0.293585 + 0.928049I
4.52893 + 7.39783I 0
u = 1.189690 − 0.590585I
a = −0.192525 + 1.202200I
b = −0.293585 − 0.928049I
4.52893 − 7.39783I 0
u = 1.294060 + 0.316520I
a = 0.291115 + 0.764351I
b = 0.414957 − 0.554533I
2.91745 + 6.05254I 0
u = 1.294060 − 0.316520I
a = 0.291115 − 0.764351I
b = 0.414957 + 0.554533I
2.91745 − 6.05254I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.537174 + 1.231980I
a = 0.196295 + 0.005454I
b = 1.389820 + 0.235157I
−3.37770 − 4.95391I 0
u = 0.537174 − 1.231980I
a = 0.196295 − 0.005454I
b = 1.389820 − 0.235157I
−3.37770 + 4.95391I 0
u = −1.181470 + 0.644258I
a = −0.244491 + 1.194170I
b = −0.333360 − 0.947743I
−0.12892 − 11.58520I 0
u = −1.181470 − 0.644258I
a = −0.244491 − 1.194170I
b = −0.333360 + 0.947743I
−0.12892 + 11.58520I 0
u = −0.602863 + 1.211500I
a = 0.197803 − 0.003918I
b = 1.41379 − 0.26593I
−7.97081 + 9.17889I 0
u = −0.602863 − 1.211500I
a = 0.197803 + 0.003918I
b = 1.41379 + 0.26593I
−7.97081 − 9.17889I 0
u = −1.232100 + 0.594842I
a = −0.51016 − 1.34439I
b = 1.40089 + 0.26628I
−4.99770 − 7.01531I 0
u = −1.232100 − 0.594842I
a = −0.51016 + 1.34439I
b = 1.40089 − 0.26628I
−4.99770 + 7.01531I 0
u = −0.560073 + 0.243224I
a = 1.11682 + 2.93594I
b = −0.400437 − 0.305942I
−3.84146 + 2.44487I 2.67833 + 5.70811I
u = −0.560073 − 0.243224I
a = 1.11682 − 2.93594I
b = −0.400437 + 0.305942I
−3.84146 − 2.44487I 2.67833 − 5.70811I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.447171 + 0.368366I
a = 0.977140 − 0.529183I
b = −0.649137 + 0.321962I
−1.244520 + 0.136004I −5.67462 + 0.66860I
u = −0.447171 − 0.368366I
a = 0.977140 + 0.529183I
b = −0.649137 − 0.321962I
−1.244520 − 0.136004I −5.67462 − 0.66860I
u = 0.559835
a = 0.190472
b = 1.67112
−7.43832 13.1970
u = −1.26876 + 0.73301I
a = −0.171599 − 1.310850I
b = 1.42110 + 0.35592I
−3.74537 − 7.60591I 0
u = −1.26876 − 0.73301I
a = −0.171599 + 1.310850I
b = 1.42110 − 0.35592I
−3.74537 + 7.60591I 0
u = −1.22662 + 0.81031I
a = −0.010802 − 1.395770I
b = 1.47568 + 0.37982I
−5.9049 − 16.3706I 0
u = −1.22662 − 0.81031I
a = −0.010802 + 1.395770I
b = 1.47568 − 0.37982I
−5.9049 + 16.3706I 0
u = 1.24904 + 0.78295I
a = −0.069120 + 1.354280I
b = 1.45236 − 0.37556I
−1.03547 + 12.08560I 0
u = 1.24904 − 0.78295I
a = −0.069120 − 1.354280I
b = 1.45236 + 0.37556I
−1.03547 − 12.08560I 0
u = 0.099100 + 0.510038I
a = −5.06181 − 1.25504I
b = −1.001060 − 0.128912I
−4.35085 + 2.48127I −12.9227 − 14.9608I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.099100 − 0.510038I
a = −5.06181 + 1.25504I
b = −1.001060 + 0.128912I
−4.35085 − 2.48127I −12.9227 + 14.9608I
u = 0.446361
a = 1.34862
b = −0.0485703
0.791292 12.9620
u = −0.390544
a = 2.53371
b = −0.859860
−1.16619 −12.5130
u = 1.68218 + 0.12717I
a = −0.651799 + 0.146716I
b = 1.190290 − 0.040584I
1.47173 + 4.79342I 0
u = 1.68218 − 0.12717I
a = −0.651799 − 0.146716I
b = 1.190290 + 0.040584I
1.47173 − 4.79342I 0
u = −1.70399
a = −0.648277
b = 1.18657
5.42800 0
13
II. I
u
2
= hb + 1, u
5
− 4u
3
+ u
2
+ a + 4u − 3, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−u
5
+ 4u
3
− u
2
− 4u + 3
−1
a
6
=
1
−u
2
a
7
=
1
−u
2
a
11
=
u
−u
3
+ u
a
8
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 4u
3
− u
2
− 4u + 2
−1
a
4
=
−u
5
+ 4u
3
− u
2
− 4u + 3
−1
a
1
=
−1
0
a
9
=
−u
u
a
12
=
−u
5
+ 2u
3
+ u
u
5
− 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
5
− 3u
4
+ 27u
3
+ 5u
2
− 24u + 14
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
u
6
c
4
(u + 1)
6
c
5
, c
7
, c
9
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
8
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
10
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
11
, c
12
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
7
, c
9
c
10
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
c
8
, c
11
, c
12
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493180 + 0.575288I
a = −0.26610 − 1.72116I
b = −1.00000
−4.60518 + 1.97241I −6.63014 − 2.86834I
u = 0.493180 − 0.575288I
a = −0.26610 + 1.72116I
b = −1.00000
−4.60518 − 1.97241I −6.63014 + 2.86834I
u = −0.483672
a = 4.27462
b = −1.00000
−0.906083 23.7440
u = −1.52087 + 0.16310I
a = 0.417699 + 0.090629I
b = −1.00000
2.05064 − 4.59213I 5.72906 + 1.01197I
u = −1.52087 − 0.16310I
a = 0.417699 − 0.090629I
b = −1.00000
2.05064 + 4.59213I 5.72906 − 1.01197I
u = 1.53904
a = 0.422181
b = −1.00000
6.01515 10.0580
17
III.
I
v
1
= ha, 8v
5
+21 v
4
+63 v
3
+21 v
2
+503 b−v−817, v
6
+3 v
5
+v
4
−18v
3
−7v
2
+1 i
(i) Arc colorings
a
5
=
1
0
a
10
=
v
0
a
3
=
0
−0.0159046v
5
− 0.0417495v
4
+ ··· + 0.00198807v + 1.62425
a
6
=
1
0
a
7
=
1
−0.0159046v
5
− 0.0417495v
4
+ ··· + 0.00198807v + 2.62425
a
11
=
v
0
a
8
=
−0.127237v
5
− 0.333996v
4
+ ··· + 0.0159046v + 0.994036
−0.0159046v
5
− 0.0417495v
4
+ ··· + 0.00198807v + 2.62425
a
2
=
−0.0159046v
5
− 0.0417495v
4
+ ··· + 0.00198807v + 1.62425
−0.0159046v
5
− 0.0417495v
4
+ ··· + 0.00198807v + 1.62425
a
4
=
0.0159046v
5
+ 0.0417495v
4
+ ··· − 0.00198807v −1.62425
0.0159046v
5
+ 0.0417495v
4
+ ··· − 0.00198807v −2.62425
a
1
=
−1
0.0159046v
5
+ 0.0417495v
4
+ ··· − 0.00198807v −2.62425
a
9
=
0.00596421v
5
− 0.109344v
4
+ ··· + 3.62425v + 0.0159046
0.0178926v
5
− 0.328032v
4
+ ··· + 6.87276v + 0.0477137
a
12
=
−0.524851v
5
− 1.37773v
4
+ ··· + 1.06561v −1.39960
−1.00199v
5
− 2.63022v
4
+ ··· + 0.125249v −2.67197
(ii) Obstruction class = 1
(iii) Cusp Shapes =
12
503
v
5
+
283
503
v
4
+
849
503
v
3
−
220
503
v
2
−
3774
503
v −
4495
503
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u
2
+ u − 1)
3
c
4
, c
6
(u
2
− u − 1)
3
c
5
, c
10
u
6
c
7
, c
9
(u
3
− u
2
+ 1)
2
c
8
(u
3
+ u
2
+ 2u + 1)
2
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
(y
2
− 3y + 1)
3
c
5
, c
10
y
6
c
7
, c
9
(y
3
− y
2
+ 2y −1)
2
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.335152 + 0.284512I
a = 0
b = 1.61803
−11.90680 − 2.82812I −6.38118 − 1.93520I
v = −0.335152 − 0.284512I
a = 0
b = 1.61803
−11.90680 + 2.82812I −6.38118 + 1.93520I
v = 0.288338
a = 0
b = 1.61803
−7.76919 −11.0920
v = 1.97630
a = 0
b = −0.618034
0.126494 −3.14230
v = −2.29716 + 1.95007I
a = 0
b = −0.618034
−4.01109 − 2.82812I −7.00182 + 11.83005I
v = −2.29716 − 1.95007I
a = 0
b = −0.618034
−4.01109 + 2.82812I −7.00182 − 11.83005I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
6
)(u
2
+ u − 1)
3
(u
86
− 10u
85
+ ··· + 18u + 1)
c
3
u
6
(u
2
+ u − 1)
3
(u
86
+ 4u
85
+ ··· − 1152u
2
+ 64)
c
4
((u + 1)
6
)(u
2
− u − 1)
3
(u
86
− 10u
85
+ ··· + 18u + 1)
c
5
u
6
(u
6
+ u
5
+ ··· − u − 1)(u
86
+ 2u
85
+ ··· + 352u + 64)
c
6
u
6
(u
2
− u − 1)
3
(u
86
+ 4u
85
+ ··· − 1152u
2
+ 64)
c
7
, c
9
(u
3
− u
2
+ 1)
2
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
86
− 4u
85
+ ··· − 13134u + 977)
c
8
(u
3
+ u
2
+ 2u + 1)
2
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
86
+ 4u
85
+ ··· − 8u + 1)
c
10
u
6
(u
6
− u
5
+ ··· + u − 1)(u
86
+ 2u
85
+ ··· + 352u + 64)
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
86
+ 4u
85
+ ··· − 8u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
6
)(y
2
− 3y + 1)
3
(y
86
− 82y
85
+ ··· − 478y + 1)
c
3
, c
6
y
6
(y
2
− 3y + 1)
3
(y
86
− 48y
85
+ ··· − 147456y + 4096)
c
5
, c
10
y
6
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
86
− 42y
85
+ ··· − 107520y + 4096)
c
7
, c
9
(y
3
− y
2
+ 2y −1)
2
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
86
− 56y
85
+ ··· − 14579676y + 954529)
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
86
+ 72y
85
+ ··· − 20y + 1)
23
