12a
1062
(K12a
1062
)
A knot diagram
1
Linearized knot diagam
4 7 9 12 11 2 10 1 3 6 5 8
Solving Sequence
8,12
1
5,9
4 2 3 11 6 10 7
c
12
c
8
c
4
c
1
c
3
c
11
c
5
c
10
c
7
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.35709 × 10
18
u
28
− 2.00758 × 10
18
u
27
+ ··· + 1.77495 × 10
19
b + 4.28788 × 10
19
,
3.14140 × 10
19
u
28
− 3.48706 × 10
19
u
27
+ ··· + 1.77495 × 10
20
a − 6.60203 × 10
19
, u
29
− u
28
+ ··· + 6u + 5i
I
u
2
= h−6.62139 × 10
45
u
45
+ 4.84395 × 10
44
u
44
+ ··· + 2.87295 × 10
46
b + 1.78408 × 10
46
,
− 4.22323 × 10
46
u
45
+ 3.37044 × 10
46
u
44
+ ··· + 2.87295 × 10
46
a + 3.87573 × 10
46
, u
46
− u
45
+ ··· + 72u
3
+ 1i
I
u
3
= h3b + 2a − 1, 4a
2
+ 6au − 4a − 3u + 10, u
2
+ 1i
I
u
4
= hb, a + 1, u + 1i
* 4 irreducible components of dim
C
= 0, with total 80 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h−4.36×10
18
u
28
−2.01×10
18
u
27
+· · ·+1.77×10
19
b+4.29×10
19
, 3.14×
10
19
u
28
−3.49×10
19
u
27
+· · ·+1.77×10
20
a−6.60×10
19
, u
29
−u
28
+· · ·+6u+5i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
−0.176986u
28
+ 0.196460u
27
+ ··· + 4.44222u + 0.371956
0.245478u
28
+ 0.113107u
27
+ ··· − 3.74868u − 2.41578
a
9
=
−u
−u
3
+ u
a
4
=
0.0684919u
28
+ 0.309567u
27
+ ··· + 0.693541u − 2.04382
0.245478u
28
+ 0.113107u
27
+ ··· − 3.74868u − 2.41578
a
2
=
0.118296u
28
− 0.0893359u
27
+ ··· − 3.39351u + 0.162132
−0.00685004u
28
− 0.0793457u
27
+ ··· − 1.42658u − 0.209524
a
3
=
−0.0781184u
28
+ 0.100703u
27
+ ··· + 4.05485u − 0.0974079
0.305018u
28
+ 0.173348u
27
+ ··· − 4.24410u − 2.58483
a
11
=
−0.0910595u
28
+ 0.0224573u
27
+ ··· + 0.754174u + 1.13264
−0.122205u
28
+ 0.0768161u
27
+ ··· + 3.17685u + 0.779482
a
6
=
0.0419048u
28
− 0.0487548u
27
+ ··· − 1.40336u − 1.17515
−0.645066u
28
+ 0.272635u
27
+ ··· + 6.97049u + 2.35170
a
10
=
0.105097u
28
+ 0.0315333u
27
+ ··· − 2.30681u − 0.507286
−0.0726470u
28
+ 0.0802996u
27
+ ··· − 2.46182u − 1.60634
a
7
=
0.0129449u
28
− 0.0531223u
27
+ ··· − 0.855717u − 0.583669
−0.558870u
28
+ 0.260702u
27
+ ··· + 7.13891u + 2.31745
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1827767228747590945
8874731342588739424
u
28
−
438792885780626433
4437365671294369712
u
27
+ ··· −
78225383157899978113
8874731342588739424
u −
108059866682014660965
8874731342588739424
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
16(16u
29
− 48u
28
+ ··· + 4u − 1)
c
2
, c
6
, c
8
c
12
u
29
− u
28
+ ··· + 6u + 5
c
3
, c
9
u
29
− 3u
28
+ ··· − 172u + 58
c
4
, c
5
, c
10
c
11
u
29
+ 3u
28
+ ··· + 68u + 10
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
256(256y
29
− 640y
28
+ ··· + 62y −1)
c
2
, c
6
, c
8
c
12
y
29
− 11y
28
+ ··· + 66y −25
c
3
, c
9
y
29
+ 23y
28
+ ··· + 9980y −3364
c
4
, c
5
, c
10
c
11
y
29
+ 33y
28
+ ··· − 1196y −100
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.471326 + 0.930518I
a = −0.32444 − 2.22299I
b = 0.03883 + 1.63705I
11.23150 + 0.31670I 0.72463 − 1.97935I
u = −0.471326 − 0.930518I
a = −0.32444 + 2.22299I
b = 0.03883 − 1.63705I
11.23150 − 0.31670I 0.72463 + 1.97935I
u = 0.989283 + 0.366561I
a = −1.123300 + 0.601376I
b = −0.27077 − 1.51322I
3.87255 − 3.92564I −7.17073 + 6.57073I
u = 0.989283 − 0.366561I
a = −1.123300 − 0.601376I
b = −0.27077 + 1.51322I
3.87255 + 3.92564I −7.17073 − 6.57073I
u = −0.894844 + 0.224932I
a = 0.609672 + 0.117489I
b = 0.818306 + 0.515060I
−2.30220 + 2.09205I −7.00937 − 7.58620I
u = −0.894844 − 0.224932I
a = 0.609672 − 0.117489I
b = 0.818306 − 0.515060I
−2.30220 − 2.09205I −7.00937 + 7.58620I
u = 1.078710 + 0.415737I
a = 0.868252 − 0.609559I
b = 0.689515 + 0.698878I
−1.53035 − 7.20402I −9.10388 + 9.44165I
u = 1.078710 − 0.415737I
a = 0.868252 + 0.609559I
b = 0.689515 − 0.698878I
−1.53035 + 7.20402I −9.10388 − 9.44165I
u = −1.141380 + 0.286143I
a = −0.164359 + 0.494218I
b = −0.566117 − 1.168670I
−5.67885 + 3.21607I −12.14399 − 5.43569I
u = −1.141380 − 0.286143I
a = −0.164359 − 0.494218I
b = −0.566117 + 1.168670I
−5.67885 − 3.21607I −12.14399 + 5.43569I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.422423 + 0.698933I
a = −0.308566 + 0.892792I
b = 0.101826 − 0.815142I
2.73932 − 0.92739I 0.75660 + 2.98272I
u = 0.422423 − 0.698933I
a = −0.308566 − 0.892792I
b = 0.101826 + 0.815142I
2.73932 + 0.92739I 0.75660 − 2.98272I
u = 0.746623 + 0.193942I
a = 0.902000 − 0.966773I
b = 0.06012 + 1.74114I
6.12616 − 1.21646I −4.32561 + 4.57305I
u = 0.746623 − 0.193942I
a = 0.902000 + 0.966773I
b = 0.06012 − 1.74114I
6.12616 + 1.21646I −4.32561 − 4.57305I
u = −0.746883
a = −0.860796
b = −0.796318
−1.46174 −3.54150
u = −0.236709 + 1.286190I
a = 0.060143 + 0.822295I
b = −0.237684 − 0.540453I
0.525909 − 0.884260I −11.9177 + 8.2327I
u = −0.236709 − 1.286190I
a = 0.060143 − 0.822295I
b = −0.237684 + 0.540453I
0.525909 + 0.884260I −11.9177 − 8.2327I
u = −1.186580 + 0.554420I
a = 1.39175 + 1.13943I
b = 0.20443 − 1.61493I
6.24626 + 10.51930I −6.12287 − 7.23991I
u = −1.186580 − 0.554420I
a = 1.39175 − 1.13943I
b = 0.20443 + 1.61493I
6.24626 − 10.51930I −6.12287 + 7.23991I
u = 1.278090 + 0.410634I
a = −0.327813 + 0.182357I
b = −0.845051 + 0.136443I
−9.57615 − 8.03561I −14.4420 + 5.3510I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.278090 − 0.410634I
a = −0.327813 − 0.182357I
b = −0.845051 − 0.136443I
−9.57615 + 8.03561I −14.4420 − 5.3510I
u = −1.32626 + 0.52915I
a = −0.750008 − 0.859966I
b = −0.629916 + 0.818379I
−7.5127 + 12.8935I −11.3843 − 8.7195I
u = −1.32626 − 0.52915I
a = −0.750008 + 0.859966I
b = −0.629916 − 0.818379I
−7.5127 − 12.8935I −11.3843 + 8.7195I
u = 1.34660 + 0.62954I
a = −1.33868 + 1.46318I
b = −0.19137 − 1.64914I
0.8405 − 16.0516I −8.77423 + 7.86114I
u = 1.34660 − 0.62954I
a = −1.33868 − 1.46318I
b = −0.19137 + 1.64914I
0.8405 + 16.0516I −8.77423 − 7.86114I
u = 0.46363 + 1.46562I
a = 0.07882 − 2.15458I
b = −0.06154 + 1.57781I
7.86481 + 1.93517I −8.22751 − 3.59914I
u = 0.46363 − 1.46562I
a = 0.07882 + 2.15458I
b = −0.06154 − 1.57781I
7.86481 − 1.93517I −8.22751 + 3.59914I
u = −0.194808 + 0.345152I
a = −0.943074 + 0.687123I
b = −0.212425 + 0.288508I
−0.601308 + 0.869978I −10.08823 − 7.77060I
u = −0.194808 − 0.345152I
a = −0.943074 − 0.687123I
b = −0.212425 − 0.288508I
−0.601308 − 0.869978I −10.08823 + 7.77060I
7
II. I
u
2
= h−6.62 × 10
45
u
45
+ 4.84 × 10
44
u
44
+ · · · + 2.87 × 10
46
b + 1.78 ×
10
46
, −4.22 × 10
46
u
45
+ 3.37 × 10
46
u
44
+ · · · + 2.87 × 10
46
a + 3.88 ×
10
46
, u
46
− u
45
+ · · · + 72u
3
+ 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
1.47000u
45
− 1.17316u
44
+ ··· + 20.0764u − 1.34904
0.230474u
45
− 0.0168606u
44
+ ··· − 1.54825u − 0.620995
a
9
=
−u
−u
3
+ u
a
4
=
1.70047u
45
− 1.19003u
44
+ ··· + 18.5281u − 1.97004
0.230474u
45
− 0.0168606u
44
+ ··· − 1.54825u − 0.620995
a
2
=
0.185550u
45
− 0.0904179u
44
+ ··· + 13.6824u + 6.31036
0.00565620u
45
− 0.104925u
44
+ ··· + 1.19083u + 0.432576
a
3
=
1.51125u
45
− 1.22829u
44
+ ··· + 20.2705u − 1.45837
0.0893100u
45
+ 0.110629u
44
+ ··· − 3.10135u − 0.905173
a
11
=
−0.456685u
45
− 0.420359u
44
+ ··· − 9.08457u − 4.32491
−0.583337u
45
+ 0.373887u
44
+ ··· − 0.150803u + 0.653918
a
6
=
0.151527u
45
+ 0.286238u
44
+ ··· + 8.26354u + 0.627866
−0.825790u
45
+ 0.358853u
44
+ ··· + 3.50116u + 2.03572
a
10
=
0.521385u
45
− 0.153313u
44
+ ··· + 0.495270u − 4.38356
1.05862u
45
− 0.639836u
44
+ ··· + 5.19161u − 1.11148
a
7
=
0.840952u
45
− 0.757829u
44
+ ··· + 18.1621u + 2.90992
−1.32879u
45
+ 0.828964u
44
+ ··· − 2.95845u + 2.16499
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.26393u
45
+ 0.703208u
44
+ ··· + 0.508567u − 4.58033
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
25(25u
46
+ 105u
45
+ ··· + 114436u − 17519)
c
2
, c
6
, c
8
c
12
u
46
− u
45
+ ··· + 72u
3
+ 1
c
3
, c
9
(u
23
+ u
22
+ ··· + 2u + 1)
2
c
4
, c
5
, c
10
c
11
(u
23
− u
22
+ ··· − 2u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
625(625y
46
− 13125y
45
+ ··· − 2.98321 × 10
9
y + 3.06915 × 10
8
)
c
2
, c
6
, c
8
c
12
y
46
− 29y
45
+ ··· − 364y
2
+ 1
c
3
, c
9
(y
23
+ 19y
22
+ ··· − 4y −1)
2
c
4
, c
5
, c
10
c
11
(y
23
+ 27y
22
+ ··· − 4y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.960668 + 0.217642I
a = 1.60344 − 1.21245I
b = 0.228067 + 0.467269I
−3.14970 − 0.92592I −9.05751 + 7.44214I
u = 0.960668 − 0.217642I
a = 1.60344 + 1.21245I
b = 0.228067 − 0.467269I
−3.14970 + 0.92592I −9.05751 − 7.44214I
u = 0.944170 + 0.194325I
a = 1.66541 − 0.85193I
b = 0.09185 + 1.62814I
5.85259 − 0.83337I −5.37353 − 0.43888I
u = 0.944170 − 0.194325I
a = 1.66541 + 0.85193I
b = 0.09185 − 1.62814I
5.85259 + 0.83337I −5.37353 + 0.43888I
u = −0.260832 + 0.901044I
a = 0.10902 + 2.08680I
b = −0.11785 − 1.62483I
9.09029 − 5.22748I −2.33369 + 3.33432I
u = −0.260832 − 0.901044I
a = 0.10902 − 2.08680I
b = −0.11785 + 1.62483I
9.09029 + 5.22748I −2.33369 − 3.33432I
u = −1.060680 + 0.129047I
a = 0.965371 − 0.700301I
b = 0.324148 + 0.802707I
−2.47271 + 0.74531I −6.91991 + 0.73522I
u = −1.060680 − 0.129047I
a = 0.965371 + 0.700301I
b = 0.324148 − 0.802707I
−2.47271 − 0.74531I −6.91991 − 0.73522I
u = −0.978562 + 0.439060I
a = 2.30652 + 1.97958I
b = 0.03322 − 1.55779I
3.82738 + 1.68405I −5.64484 − 3.83025I
u = −0.978562 − 0.439060I
a = 2.30652 − 1.97958I
b = 0.03322 + 1.55779I
3.82738 − 1.68405I −5.64484 + 3.83025I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.032046 + 1.078310I
a = −0.130214 − 0.963704I
b = 0.473302 + 0.738923I
−3.45327 − 7.25342I −8.90266 + 7.25802I
u = −0.032046 − 1.078310I
a = −0.130214 + 0.963704I
b = 0.473302 − 0.738923I
−3.45327 + 7.25342I −8.90266 − 7.25802I
u = 1.013490 + 0.406902I
a = −0.920257 + 0.717264I
b = −0.413689 − 0.761868I
0.92198 − 3.22031I −3.77921 + 4.90443I
u = 1.013490 − 0.406902I
a = −0.920257 − 0.717264I
b = −0.413689 + 0.761868I
0.92198 + 3.22031I −3.77921 − 4.90443I
u = −0.882714
a = −0.656431
b = −0.546774
−1.28214 −7.98830
u = −1.116100 + 0.137828I
a = 0.095732 + 0.799884I
b = 0.228067 + 0.467269I
−3.14970 − 0.92592I −9.05751 + 7.44214I
u = −1.116100 − 0.137828I
a = 0.095732 − 0.799884I
b = 0.228067 − 0.467269I
−3.14970 + 0.92592I −9.05751 − 7.44214I
u = −0.151468 + 0.832504I
a = −0.148349 − 0.609597I
b = 0.581337 + 0.108709I
−5.29586 + 3.66457I −12.82434 − 2.67133I
u = −0.151468 − 0.832504I
a = −0.148349 + 0.609597I
b = 0.581337 − 0.108709I
−5.29586 − 3.66457I −12.82434 + 2.67133I
u = 0.174340 + 1.236240I
a = 0.13883 + 2.25785I
b = 0.13674 − 1.61894I
4.58136 + 9.54664I −8.00000 − 5.57899I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.174340 − 1.236240I
a = 0.13883 − 2.25785I
b = 0.13674 + 1.61894I
4.58136 − 9.54664I −8.00000 + 5.57899I
u = −1.125600 + 0.590859I
a = −1.39957 − 1.39854I
b = −0.11785 + 1.62483I
9.09029 + 5.22748I 0
u = −1.125600 − 0.590859I
a = −1.39957 + 1.39854I
b = −0.11785 − 1.62483I
9.09029 − 5.22748I 0
u = 1.263600 + 0.196622I
a = −0.723405 − 0.104554I
b = 0.03322 − 1.55779I
3.82738 + 1.68405I −8.00000 − 3.83025I
u = 1.263600 − 0.196622I
a = −0.723405 + 0.104554I
b = 0.03322 + 1.55779I
3.82738 − 1.68405I −8.00000 + 3.83025I
u = 0.223468 + 0.627017I
a = 0.304838 − 0.560630I
b = −0.413689 + 0.761868I
0.92198 + 3.22031I −3.77921 − 4.90443I
u = 0.223468 − 0.627017I
a = 0.304838 + 0.560630I
b = −0.413689 − 0.761868I
0.92198 − 3.22031I −3.77921 + 4.90443I
u = 1.303950 + 0.339252I
a = 0.418446 + 0.083716I
b = 0.581337 − 0.108709I
−5.29586 − 3.66457I 0
u = 1.303950 − 0.339252I
a = 0.418446 − 0.083716I
b = 0.581337 + 0.108709I
−5.29586 + 3.66457I 0
u = −1.250840 + 0.612691I
a = −0.441738 − 0.907872I
b = −0.477903 + 0.451361I
−8.25826 + 1.68040I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.250840 − 0.612691I
a = −0.441738 + 0.907872I
b = −0.477903 − 0.451361I
−8.25826 − 1.68040I 0
u = 1.09538 + 0.90096I
a = −0.88861 + 2.13172I
b = −0.08584 − 1.50808I
−1.82520 − 3.53591I 0
u = 1.09538 − 0.90096I
a = −0.88861 − 2.13172I
b = −0.08584 + 1.50808I
−1.82520 + 3.53591I 0
u = −1.35206 + 0.55810I
a = 0.633793 + 0.759928I
b = 0.473302 − 0.738923I
−3.45327 + 7.25342I 0
u = −1.35206 − 0.55810I
a = 0.633793 − 0.759928I
b = 0.473302 + 0.738923I
−3.45327 − 7.25342I 0
u = 1.42000 + 0.41703I
a = −0.051313 − 0.188624I
b = −0.477903 + 0.451361I
−8.25826 + 1.68040I 0
u = 1.42000 − 0.41703I
a = −0.051313 + 0.188624I
b = −0.477903 − 0.451361I
−8.25826 − 1.68040I 0
u = 1.37422 + 0.72873I
a = 1.09577 − 1.56402I
b = 0.13674 + 1.61894I
4.58136 − 9.54664I 0
u = 1.37422 − 0.72873I
a = 1.09577 + 1.56402I
b = 0.13674 − 1.61894I
4.58136 + 9.54664I 0
u = 0.165356 + 0.313036I
a = −2.30752 + 0.60796I
b = 0.09185 − 1.62814I
5.85259 + 0.83337I −5.37353 + 0.43888I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.165356 − 0.313036I
a = −2.30752 − 0.60796I
b = 0.09185 + 1.62814I
5.85259 − 0.83337I −5.37353 − 0.43888I
u = −1.63171 + 0.23232I
a = 0.114074 + 1.088240I
b = −0.08584 − 1.50808I
−1.82520 − 3.53591I 0
u = −1.63171 − 0.23232I
a = 0.114074 − 1.088240I
b = −0.08584 + 1.50808I
−1.82520 + 3.53591I 0
u = 0.064261 + 0.284784I
a = 2.76905 + 3.46178I
b = 0.324148 − 0.802707I
−2.47271 − 0.74531I −6.91991 − 0.73522I
u = 0.064261 − 0.284784I
a = 2.76905 − 3.46178I
b = 0.324148 + 0.802707I
−2.47271 + 0.74531I −6.91991 + 0.73522I
u = −0.203324
a = −2.56222
b = −0.546774
−1.28214 −7.98830
15
III. I
u
3
= h3b + 2a − 1, 4a
2
+ 6au − 4a − 3u + 10, u
2
+ 1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
−1
a
5
=
a
−
2
3
a +
1
3
a
9
=
−u
2u
a
4
=
1
3
a +
1
3
−
2
3
a +
1
3
a
2
=
1
6
au −
1
12
u +
3
2
−
1
3
au −
1
3
a +
1
6
u −
4
3
a
3
=
1
3
a +
4
3
−
2
3
a −
5
3
a
11
=
−au +
1
3
a +
1
2
u −
2
3
2
3
au −
1
3
u + 1
a
6
=
−
1
3
au −
1
3
a +
5
3
u +
1
6
2
3
a − u −
1
3
a
10
=
1
3
au +
1
3
u
−
2
3
au +
1
3
u
a
7
=
−
1
3
au −
1
6
a +
1
6
u +
1
12
1
3
au +
1
3
a +
1
3
u −
1
6
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
16(16u
4
− 32u
3
+ 36u
2
− 20u + 5)
c
2
, c
3
, c
6
c
8
, c
9
, c
12
(u
2
+ 1)
2
c
4
, c
5
, c
10
c
11
u
4
+ 3u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
256(256y
4
+ 128y
3
+ 176y
2
− 40y + 25)
c
2
, c
3
, c
6
c
8
, c
9
, c
12
(y + 1)
4
c
4
, c
5
, c
10
c
11
(y
2
+ 3y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.500000 + 0.927051I
b = − 0.618034I
0.986960 −4.00000
u = 1.000000I
a = 0.50000 − 2.42705I
b = 1.61803I
8.88264 −4.00000
u = − 1.000000I
a = 0.500000 − 0.927051I
b = 0.618034I
0.986960 −4.00000
u = − 1.000000I
a = 0.50000 + 2.42705I
b = − 1.61803I
8.88264 −4.00000
19
IV. I
u
4
= hb, a + 1, u + 1i
(i) Arc colorings
a
8
=
0
−1
a
12
=
1
0
a
1
=
1
1
a
5
=
−1
0
a
9
=
1
0
a
4
=
−1
0
a
2
=
0
1
a
3
=
−1
0
a
11
=
1
0
a
6
=
−1
0
a
10
=
1
0
a
7
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u − 1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
u
c
6
, c
12
u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
, c
8
, c
12
y −1
c
3
, c
4
, c
5
c
9
, c
10
, c
11
y
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−3.28987 −12.0000
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
6400(u − 1)(16u
4
− 32u
3
+ 36u
2
− 20u + 5)
· (16u
29
− 48u
28
+ ··· + 4u − 1)
· (25u
46
+ 105u
45
+ ··· + 114436u − 17519)
c
2
, c
8
(u − 1)(u
2
+ 1)
2
(u
29
− u
28
+ ··· + 6u + 5)(u
46
− u
45
+ ··· + 72u
3
+ 1)
c
3
, c
9
u(u
2
+ 1)
2
(u
23
+ u
22
+ ··· + 2u + 1)
2
(u
29
− 3u
28
+ ··· − 172u + 58)
c
4
, c
5
, c
10
c
11
u(u
4
+ 3u
2
+ 1)(u
23
− u
22
+ ··· − 2u + 1)
2
(u
29
+ 3u
28
+ ··· + 68u + 10)
c
6
, c
12
(u + 1)(u
2
+ 1)
2
(u
29
− u
28
+ ··· + 6u + 5)(u
46
− u
45
+ ··· + 72u
3
+ 1)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
40960000(y −1)(256y
4
+ 128y
3
+ 176y
2
− 40y + 25)
· (256y
29
− 640y
28
+ ··· + 62y −1)
· (625y
46
− 13125y
45
+ ··· − 2983210840y + 306915361)
c
2
, c
6
, c
8
c
12
(y −1)(y + 1)
4
(y
29
− 11y
28
+ ··· + 66y −25)
· (y
46
− 29y
45
+ ··· − 364y
2
+ 1)
c
3
, c
9
y(y + 1)
4
(y
23
+ 19y
22
+ ··· − 4y −1)
2
· (y
29
+ 23y
28
+ ··· + 9980y −3364)
c
4
, c
5
, c
10
c
11
y(y
2
+ 3y + 1)
2
(y
23
+ 27y
22
+ ··· − 4y −1)
2
· (y
29
+ 33y
28
+ ··· − 1196y −100)
25
