12a
0039
(K12a
0039
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 8 10 4 12 6 1 9 11
Solving Sequence
8,12 4,9
7 3 11 1 10 6 5 2
c
8
c
7
c
3
c
11
c
12
c
10
c
6
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.97511 × 10
37
u
113
+ 7.35370 × 10
38
u
112
+ ··· + 2.85889 × 10
36
b + 1.14745 × 10
38
,
− 5.68472 × 10
37
u
113
+ 5.72364 × 10
38
u
112
+ ··· + 2.85889 × 10
36
a + 1.75186 × 10
38
,
u
114
− 8u
113
+ ··· − 10u + 1i
I
u
2
= h3a
5
u + 12a
5
− 19a
4
u − 11a
4
− 32a
3
u + 15a
3
− 27a
2
u − 43a
2
− 64au + 13b − 35a − 15u − 8,
a
6
− a
5
u − a
5
− 4a
4
u + a
4
− a
3
u − 2a
3
− 7a
2
u − 4a
2
− 3au − a − u, u
2
+ u + 1i
I
u
3
= hb, −u
4
+ u
3
− u
2
+ a − 1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 135 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−8.98 × 10
37
u
113
+ 7.35 × 10
38
u
112
+ · · · + 2.86 × 10
36
b + 1.15 ×
10
38
, −5.68 × 10
37
u
113
+ 5.72 × 10
38
u
112
+ · · · + 2.86 × 10
36
a + 1.75 ×
10
38
, u
114
− 8u
113
+ · · · − 10u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
19.8844u
113
− 200.205u
112
+ ··· + 518.572u − 61.2777
31.3937u
113
− 257.222u
112
+ ··· + 385.856u − 40.1363
a
9
=
1
−u
2
a
7
=
−51.3794u
113
+ 326.932u
112
+ ··· + 7.96086u − 6.96895
69.5096u
113
− 585.675u
112
+ ··· + 960.466u − 102.166
a
3
=
64.4029u
113
− 512.039u
112
+ ··· + 716.519u − 81.1594
−8.85702u
113
+ 89.4939u
112
+ ··· − 201.213u + 22.9378
a
11
=
−u
u
3
+ u
a
1
=
−u
3
u
5
+ u
3
+ u
a
10
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
6
=
−22.3300u
113
+ 29.1895u
112
+ ··· + 766.379u − 89.5923
90.2870u
113
− 772.336u
112
+ ··· + 1308.83u − 139.642
a
5
=
−112.617u
113
+ 801.526u
112
+ ··· − 542.454u + 50.0496
90.2870u
113
− 772.336u
112
+ ··· + 1308.83u − 139.642
a
2
=
−24.7381u
113
+ 116.628u
112
+ ··· + 306.583u − 42.8522
64.8502u
113
− 546.552u
112
+ ··· + 891.089u − 94.0285
(ii) Obstruction class = −1
(iii) Cusp Shapes = −15.7662u
113
+ 115.090u
112
+ ··· − 86.6471u + 5.47371
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
114
+ 52u
113
+ ··· + 62u + 1
c
2
, c
4
u
114
− 12u
113
+ ··· + 22u − 1
c
3
, c
7
u
114
− 3u
113
+ ··· − 3072u + 512
c
5
u
114
+ 4u
113
+ ··· + 1228166u − 118529
c
6
, c
9
u
114
− 2u
113
+ ··· + 16384u − 4096
c
8
, c
11
u
114
+ 8u
113
+ ··· + 10u + 1
c
10
, c
12
u
114
+ 36u
113
+ ··· + 10u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
114
+ 32y
113
+ ··· + 6582y + 1
c
2
, c
4
y
114
− 52y
113
+ ··· − 62y + 1
c
3
, c
7
y
114
− 63y
113
+ ··· − 9437184y + 262144
c
5
y
114
− 60y
113
+ ··· − 2033070061434y + 14049123841
c
6
, c
9
y
114
− 70y
113
+ ··· − 251658240y + 16777216
c
8
, c
11
y
114
+ 36y
113
+ ··· + 10y + 1
c
10
, c
12
y
114
+ 92y
113
+ ··· + 4042y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.000620 + 0.995927I
a = 1.299800 − 0.241663I
b = 0.909069 − 0.395900I
−3.21254 − 4.24812I 0
u = 0.000620 − 0.995927I
a = 1.299800 + 0.241663I
b = 0.909069 + 0.395900I
−3.21254 + 4.24812I 0
u = −0.588448 + 0.865197I
a = −0.781789 − 0.376818I
b = 0.336616 − 0.121889I
0.46811 − 2.32542I 0
u = −0.588448 − 0.865197I
a = −0.781789 + 0.376818I
b = 0.336616 + 0.121889I
0.46811 + 2.32542I 0
u = 0.778086 + 0.701982I
a = 0.231260 − 0.133436I
b = −0.668937 − 0.129520I
3.31863 − 0.81707I 0
u = 0.778086 − 0.701982I
a = 0.231260 + 0.133436I
b = −0.668937 + 0.129520I
3.31863 + 0.81707I 0
u = −0.505823 + 0.918744I
a = 0.73874 − 2.25181I
b = −0.312072 − 0.402365I
−1.78702 − 2.46027I 0
u = −0.505823 − 0.918744I
a = 0.73874 + 2.25181I
b = −0.312072 + 0.402365I
−1.78702 + 2.46027I 0
u = 0.678178 + 0.804338I
a = 0.138606 + 0.188536I
b = 0.969106 − 0.620652I
1.08443 − 3.92816I 0
u = 0.678178 − 0.804338I
a = 0.138606 − 0.188536I
b = 0.969106 + 0.620652I
1.08443 + 3.92816I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.096539 + 1.054780I
a = −1.077720 − 0.337003I
b = −0.832093 − 0.241574I
−2.66766 − 0.82890I 0
u = −0.096539 − 1.054780I
a = −1.077720 + 0.337003I
b = −0.832093 + 0.241574I
−2.66766 + 0.82890I 0
u = −0.243867 + 1.045790I
a = 1.14280 + 1.22814I
b = −0.831060 + 0.215460I
−2.72201 − 3.15265I 0
u = −0.243867 − 1.045790I
a = 1.14280 − 1.22814I
b = −0.831060 − 0.215460I
−2.72201 + 3.15265I 0
u = −0.332538 + 1.023910I
a = 0.50463 + 1.46650I
b = −0.137018 + 0.888476I
−1.00115 − 1.37350I 0
u = −0.332538 − 1.023910I
a = 0.50463 − 1.46650I
b = −0.137018 − 0.888476I
−1.00115 + 1.37350I 0
u = −0.689886 + 0.597095I
a = −0.976474 + 0.359837I
b = 1.057270 − 0.233439I
1.74936 − 3.74948I 0
u = −0.689886 − 0.597095I
a = −0.976474 − 0.359837I
b = 1.057270 + 0.233439I
1.74936 + 3.74948I 0
u = −0.241829 + 1.089860I
a = −0.85277 − 1.16507I
b = −0.348992 − 1.012170I
−1.63970 − 5.47705I 0
u = −0.241829 − 1.089860I
a = −0.85277 + 1.16507I
b = −0.348992 + 1.012170I
−1.63970 + 5.47705I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.750758 + 0.827314I
a = 0.129507 − 0.152369I
b = −0.742772 + 0.683809I
3.89107 + 0.23526I 0
u = 0.750758 − 0.827314I
a = 0.129507 + 0.152369I
b = −0.742772 − 0.683809I
3.89107 − 0.23526I 0
u = −0.406450 + 0.778487I
a = −0.43254 + 2.00319I
b = −0.065543 + 0.578177I
−1.29179 − 1.43912I 0
u = −0.406450 − 0.778487I
a = −0.43254 − 2.00319I
b = −0.065543 − 0.578177I
−1.29179 + 1.43912I 0
u = −0.742953 + 0.844200I
a = −0.883932 + 0.716195I
b = 0.198997 − 1.006560I
1.45699 − 0.62875I 0
u = −0.742953 − 0.844200I
a = −0.883932 − 0.716195I
b = 0.198997 + 1.006560I
1.45699 + 0.62875I 0
u = 0.725849 + 0.862263I
a = −1.18363 + 1.21262I
b = 0.728078 + 0.797809I
0.27128 + 1.43083I 0
u = 0.725849 − 0.862263I
a = −1.18363 − 1.21262I
b = 0.728078 − 0.797809I
0.27128 − 1.43083I 0
u = 0.173450 + 0.850343I
a = −0.49445 + 2.33843I
b = 1.138020 + 0.614402I
−1.12370 + 7.14011I 0
u = 0.173450 − 0.850343I
a = −0.49445 − 2.33843I
b = 1.138020 − 0.614402I
−1.12370 − 7.14011I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.717891 + 0.875647I
a = −3.07883 − 0.87104I
b = 0.863296 − 0.060419I
−0.06015 − 2.74428I 0
u = −0.717891 − 0.875647I
a = −3.07883 + 0.87104I
b = 0.863296 + 0.060419I
−0.06015 + 2.74428I 0
u = −0.154972 + 0.850760I
a = −0.561945 + 1.017580I
b = −0.216470 + 0.554423I
−1.42767 − 1.72251I 0
u = −0.154972 − 0.850760I
a = −0.561945 − 1.017580I
b = −0.216470 − 0.554423I
−1.42767 + 1.72251I 0
u = −0.796337 + 0.809504I
a = −1.99032 − 0.52371I
b = 1.282890 + 0.568619I
4.87599 + 5.08003I 0
u = −0.796337 − 0.809504I
a = −1.99032 + 0.52371I
b = 1.282890 − 0.568619I
4.87599 − 5.08003I 0
u = 0.862093 + 0.740048I
a = 2.17350 + 0.06866I
b = −1.043560 + 0.201924I
4.61798 − 2.51018I 0
u = 0.862093 − 0.740048I
a = 2.17350 − 0.06866I
b = −1.043560 − 0.201924I
4.61798 + 2.51018I 0
u = 0.898219 + 0.698482I
a = 1.52519 + 0.09751I
b = −1.29527 + 0.68509I
8.8621 − 11.7414I 0
u = 0.898219 − 0.698482I
a = 1.52519 − 0.09751I
b = −1.29527 − 0.68509I
8.8621 + 11.7414I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.875646 + 0.726930I
a = 0.376919 + 0.331696I
b = −0.361892 − 1.145570I
5.87522 − 5.16417I 0
u = 0.875646 − 0.726930I
a = 0.376919 − 0.331696I
b = −0.361892 + 1.145570I
5.87522 + 5.16417I 0
u = 0.723942 + 0.887704I
a = −0.269635 − 0.247517I
b = 0.772420 − 0.738069I
0.19214 + 4.10193I 0
u = 0.723942 − 0.887704I
a = −0.269635 + 0.247517I
b = 0.772420 + 0.738069I
0.19214 − 4.10193I 0
u = 0.898278 + 0.719800I
a = −1.70037 + 0.00065I
b = 1.34759 − 0.48295I
11.08030 − 5.74617I 0
u = 0.898278 − 0.719800I
a = −1.70037 − 0.00065I
b = 1.34759 + 0.48295I
11.08030 + 5.74617I 0
u = −0.786807 + 0.841252I
a = 2.21659 + 0.68914I
b = −1.313740 − 0.317656I
6.59591 − 0.71733I 0
u = −0.786807 − 0.841252I
a = 2.21659 − 0.68914I
b = −1.313740 + 0.317656I
6.59591 + 0.71733I 0
u = 0.863492 + 0.763620I
a = −0.211292 − 0.405885I
b = −0.020762 + 1.116940I
6.62880 − 0.20671I 0
u = 0.863492 − 0.763620I
a = −0.211292 + 0.405885I
b = −0.020762 − 1.116940I
6.62880 + 0.20671I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679597 + 0.934225I
a = −0.524106 + 1.175500I
b = 0.908792 + 0.587168I
0.66698 + 9.18244I 0
u = 0.679597 − 0.934225I
a = −0.524106 − 1.175500I
b = 0.908792 − 0.587168I
0.66698 − 9.18244I 0
u = −0.252668 + 1.131290I
a = −0.14021 − 1.47612I
b = 1.263250 − 0.412499I
3.25741 − 5.78411I 0
u = −0.252668 − 1.131290I
a = −0.14021 + 1.47612I
b = 1.263250 + 0.412499I
3.25741 + 5.78411I 0
u = −0.362638 + 1.105360I
a = 0.119821 − 0.407667I
b = 1.269690 + 0.265039I
3.93592 − 1.77117I 0
u = −0.362638 − 1.105360I
a = 0.119821 + 0.407667I
b = 1.269690 − 0.265039I
3.93592 + 1.77117I 0
u = −0.735590 + 0.904142I
a = 0.725726 − 0.947975I
b = 0.269136 + 1.029520I
1.27291 − 4.99313I 0
u = −0.735590 − 0.904142I
a = 0.725726 + 0.947975I
b = 0.269136 − 1.029520I
1.27291 + 4.99313I 0
u = −0.222906 + 1.145300I
a = 0.07725 + 1.78101I
b = −1.247070 + 0.633850I
1.20391 − 11.48680I 0
u = −0.222906 − 1.145300I
a = 0.07725 − 1.78101I
b = −1.247070 − 0.633850I
1.20391 + 11.48680I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.010347 + 0.831981I
a = −1.15995 + 2.40469I
b = 0.708598 + 0.443190I
−3.84041 − 0.66669I 0
u = −0.010347 − 0.831981I
a = −1.15995 − 2.40469I
b = 0.708598 − 0.443190I
−3.84041 + 0.66669I 0
u = −0.816914 + 0.122705I
a = 1.55439 + 0.32983I
b = −1.28913 + 0.58849I
5.51494 − 8.11158I 0
u = −0.816914 − 0.122705I
a = 1.55439 − 0.32983I
b = −1.28913 − 0.58849I
5.51494 + 8.11158I 0
u = −0.566636 + 1.030070I
a = 0.24814 + 1.63336I
b = −1.020720 + 0.318129I
0.16822 − 5.53256I 0
u = −0.566636 − 1.030070I
a = 0.24814 − 1.63336I
b = −1.020720 − 0.318129I
0.16822 + 5.53256I 0
u = −0.630734 + 0.992877I
a = 0.020094 − 1.386640I
b = 0.947651 + 0.177047I
0.58805 − 1.33411I 0
u = −0.630734 − 0.992877I
a = 0.020094 + 1.386640I
b = 0.947651 − 0.177047I
0.58805 + 1.33411I 0
u = −0.408533 + 1.107270I
a = −0.390396 + 0.069212I
b = −1.247370 − 0.535713I
2.34702 + 3.84107I 0
u = −0.408533 − 1.107270I
a = −0.390396 − 0.069212I
b = −1.247370 + 0.535713I
2.34702 − 3.84107I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.739393 + 0.920177I
a = 0.949008 − 0.796004I
b = −0.652408 − 0.740624I
3.60690 + 5.42425I 0
u = 0.739393 − 0.920177I
a = 0.949008 + 0.796004I
b = −0.652408 + 0.740624I
3.60690 − 5.42425I 0
u = −0.811812 + 0.071800I
a = −1.69478 − 0.22137I
b = 1.322800 − 0.345373I
7.31771 − 2.26748I 0
u = −0.811812 − 0.071800I
a = −1.69478 + 0.22137I
b = 1.322800 + 0.345373I
7.31771 + 2.26748I 0
u = 0.891543 + 0.789415I
a = −1.96034 + 0.40220I
b = 1.43062 + 0.20234I
12.42200 − 0.63977I 0
u = 0.891543 − 0.789415I
a = −1.96034 − 0.40220I
b = 1.43062 − 0.20234I
12.42200 + 0.63977I 0
u = 0.061394 + 0.805031I
a = 1.34929 − 0.92636I
b = 0.463501 − 0.874281I
−3.25567 + 1.60314I 0
u = 0.061394 − 0.805031I
a = 1.34929 + 0.92636I
b = 0.463501 + 0.874281I
−3.25567 − 1.60314I 0
u = −0.765613 + 0.920057I
a = 2.48939 + 1.24624I
b = −1.305530 + 0.370264I
6.35197 − 5.12982I 0
u = −0.765613 − 0.920057I
a = 2.48939 − 1.24624I
b = −1.305530 − 0.370264I
6.35197 + 5.12982I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.883195 + 0.817480I
a = 1.94249 − 0.50826I
b = −1.38893 − 0.46916I
11.17360 + 5.50666I 0
u = 0.883195 − 0.817480I
a = 1.94249 + 0.50826I
b = −1.38893 + 0.46916I
11.17360 − 5.50666I 0
u = −0.655716 + 0.438810I
a = 0.730026 − 0.292071I
b = −1.042660 − 0.187766I
1.86059 + 0.80843I 7.56074 + 0.I
u = −0.655716 − 0.438810I
a = 0.730026 + 0.292071I
b = −1.042660 + 0.187766I
1.86059 − 0.80843I 7.56074 + 0.I
u = −0.759299 + 0.945159I
a = −2.46488 − 1.39050I
b = 1.276060 − 0.606390I
4.45750 − 10.93450I 0
u = −0.759299 − 0.945159I
a = −2.46488 + 1.39050I
b = 1.276060 + 0.606390I
4.45750 + 10.93450I 0
u = 0.153707 + 0.770319I
a = 0.61655 − 2.15327I
b = −1.083030 − 0.414307I
1.02118 + 1.99074I 0
u = 0.153707 − 0.770319I
a = 0.61655 + 2.15327I
b = −1.083030 + 0.414307I
1.02118 − 1.99074I 0
u = 0.713346 + 0.999659I
a = −0.237296 − 0.651586I
b = −0.661749 + 0.185958I
2.41781 + 6.46931I 0
u = 0.713346 − 0.999659I
a = −0.237296 + 0.651586I
b = −0.661749 − 0.185958I
2.41781 − 6.46931I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.744318 + 0.054975I
a = 0.097784 + 0.153327I
b = −0.228347 − 1.036310I
2.15207 − 2.22766I 7.39841 + 3.29919I
u = −0.744318 − 0.054975I
a = 0.097784 − 0.153327I
b = −0.228347 + 1.036310I
2.15207 + 2.22766I 7.39841 − 3.29919I
u = 0.777297 + 0.998087I
a = 1.063530 + 0.119091I
b = 0.029238 − 1.107390I
5.89977 + 6.30984I 0
u = 0.777297 − 0.998087I
a = 1.063530 − 0.119091I
b = 0.029238 + 1.107390I
5.89977 − 6.30984I 0
u = 0.766287 + 1.010500I
a = 2.09202 − 1.41117I
b = −1.044580 − 0.250298I
3.78052 + 8.57212I 0
u = 0.766287 − 1.010500I
a = 2.09202 + 1.41117I
b = −1.044580 + 0.250298I
3.78052 − 8.57212I 0
u = 0.818725 + 0.975456I
a = 1.20803 − 1.01064I
b = −1.39287 + 0.42869I
10.67890 + 0.78962I 0
u = 0.818725 − 0.975456I
a = 1.20803 + 1.01064I
b = −1.39287 − 0.42869I
10.67890 − 0.78962I 0
u = 0.767274 + 1.022710I
a = −1.036480 − 0.402874I
b = −0.397968 + 1.143140I
4.95866 + 11.26670I 0
u = 0.767274 − 1.022710I
a = −1.036480 + 0.402874I
b = −0.397968 − 1.143140I
4.95866 − 11.26670I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.807743 + 0.997389I
a = −1.45172 + 1.18836I
b = 1.43166 − 0.15923I
11.77180 + 6.92546I 0
u = 0.807743 − 0.997389I
a = −1.45172 − 1.18836I
b = 1.43166 + 0.15923I
11.77180 − 6.92546I 0
u = 0.774290 + 1.036290I
a = −1.80586 + 1.66123I
b = 1.33094 + 0.51022I
10.0951 + 11.9359I 0
u = 0.774290 − 1.036290I
a = −1.80586 − 1.66123I
b = 1.33094 − 0.51022I
10.0951 − 11.9359I 0
u = −0.705176
a = 2.33825
b = −0.891329
0.696942 9.32960
u = 0.764052 + 1.045550I
a = 1.82245 − 1.77530I
b = −1.28060 − 0.70154I
7.7842 + 17.8937I 0
u = 0.764052 − 1.045550I
a = 1.82245 + 1.77530I
b = −1.28060 + 0.70154I
7.7842 − 17.8937I 0
u = 0.259431 + 0.408406I
a = 0.92680 − 1.69358I
b = −1.052680 + 0.165594I
2.00261 − 0.21719I 5.54971 + 1.39301I
u = 0.259431 − 0.408406I
a = 0.92680 + 1.69358I
b = −1.052680 − 0.165594I
2.00261 + 0.21719I 5.54971 − 1.39301I
u = 0.398941 + 0.245288I
a = −1.35604 + 1.31786I
b = 1.107120 − 0.472400I
0.59513 − 5.04741I 3.03766 + 6.30161I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.398941 − 0.245288I
a = −1.35604 − 1.31786I
b = 1.107120 + 0.472400I
0.59513 + 5.04741I 3.03766 − 6.30161I
u = −0.385081
a = −0.378875
b = −0.442316
0.909019 11.6240
u = 0.108368 + 0.102060I
a = −4.77225 + 0.35493I
b = 0.330233 + 0.607236I
−1.72924 − 0.76603I −3.11872 + 1.37388I
u = 0.108368 − 0.102060I
a = −4.77225 − 0.35493I
b = 0.330233 − 0.607236I
−1.72924 + 0.76603I −3.11872 − 1.37388I
16
II.
I
u
2
= h3a
5
u − 19a
4
u + · · · − 35a − 8, −a
5
u − 4a
4
u + · · · − 4a
2
− a, u
2
+ u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
a
−0.230769a
5
u + 1.46154a
4
u + ··· + 2.69231a + 0.615385
a
9
=
1
u + 1
a
7
=
0.538462a
5
u − 0.0769231a
4
u + ··· + 0.384615a + 1.23077
0.153846a
5
u + 0.692308a
4
u + ··· + 1.53846a + 1.92308
a
3
=
−0.0769231a
5
u − 0.846154a
4
u + ··· − 2.76923a − 0.461538
0.461538a
5
u + 0.0769231a
4
u + ··· + 3.61538a + 0.769231
a
11
=
−u
u + 1
a
1
=
−1
0
a
10
=
1
u + 1
a
6
=
0.538462a
5
u − 0.0769231a
4
u + ··· + 0.384615a + 1.23077
0.153846a
5
u + 0.692308a
4
u + ··· + 1.53846a + 1.92308
a
5
=
0.384615a
5
u − 0.769231a
4
u + ··· − 1.15385a − 0.692308
0.153846a
5
u + 0.692308a
4
u + ··· + 1.53846a + 1.92308
a
2
=
0.0769231a
5
u − 0.153846a
4
u + ··· − 2.23077a − 0.538462
−0.0769231a
5
u + 0.153846a
4
u + ··· + 1.23077a + 1.53846
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
8
13
a
5
u−
32
13
a
5
+
55
13
a
4
u+
64
13
a
4
+
68
13
a
3
u−
40
13
a
3
−
32
13
a
2
u+
132
13
a
2
+
136
13
au+
76
13
a+
40
13
u+
56
13
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
2
, c
7
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
3
, c
4
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
c
6
, c
9
u
12
c
8
, c
12
(u
2
+ u + 1)
6
c
10
, c
11
(u
2
− u + 1)
6
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
2
, c
3
, c
4
c
7
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
6
, c
9
y
12
c
8
, c
10
, c
11
c
12
(y
2
+ y + 1)
6
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −0.104427 − 1.024660I
b = −0.428243 − 0.664531I
−1.89061 − 2.95419I −0.76561 + 6.31197I
u = −0.500000 + 0.866025I
a = −0.67283 − 1.28640I
b = 1.002190 − 0.295542I
1.89061 − 2.95419I 7.73749 + 4.22314I
u = −0.500000 + 0.866025I
a = −0.160939 − 0.449445I
b = 1.002190 + 0.295542I
1.89061 − 1.10558I 4.53097 + 2.95636I
u = −0.500000 + 0.866025I
a = −0.288082 + 0.269440I
b = −1.073950 − 0.558752I
3.66314I −0.57335 − 1.75283I
u = −0.500000 + 0.866025I
a = 0.67970 + 1.59070I
b = −1.073950 + 0.558752I
− 7.72290I 3.68173 + 7.68692I
u = −0.500000 + 0.866025I
a = 1.04658 + 1.76640I
b = −0.428243 + 0.664531I
−1.89061 − 1.10558I −4.61123 + 3.09109I
u = −0.500000 − 0.866025I
a = −0.104427 + 1.024660I
b = −0.428243 + 0.664531I
−1.89061 + 2.95419I −0.76561 − 6.31197I
u = −0.500000 − 0.866025I
a = −0.67283 + 1.28640I
b = 1.002190 + 0.295542I
1.89061 + 2.95419I 7.73749 − 4.22314I
u = −0.500000 − 0.866025I
a = −0.160939 + 0.449445I
b = 1.002190 − 0.295542I
1.89061 + 1.10558I 4.53097 − 2.95636I
u = −0.500000 − 0.866025I
a = −0.288082 − 0.269440I
b = −1.073950 + 0.558752I
− 3.66314I −0.57335 + 1.75283I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 − 0.866025I
a = 0.67970 − 1.59070I
b = −1.073950 − 0.558752I
7.72290I 3.68173 − 7.68692I
u = −0.500000 − 0.866025I
a = 1.04658 − 1.76640I
b = −0.428243 − 0.664531I
−1.89061 + 1.10558I −4.61123 − 3.09109I
21
III.
I
u
3
= hb, −u
4
+ u
3
− u
2
+ a − 1, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
4
=
u
4
− u
3
+ u
2
+ 1
0
a
9
=
1
−u
2
a
7
=
1
0
a
3
=
u
4
− u
3
+ u
2
+ 1
0
a
11
=
−u
u
3
+ u
a
1
=
−u
3
u
5
+ u
3
+ u
a
10
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
6
=
−u
5
− u
−u
5
− u
3
− u
a
5
=
u
3
−u
5
− u
3
− u
a
2
=
u
4
− 2u
3
+ u
2
+ 1
u
5
+ u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
8
− u
7
− 4u
3
+ 2u
2
+ 2u + 2
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
6
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
8
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
10
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
7
y
9
c
5
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
6
, c
9
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
8
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
10
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = 0.457852 + 1.072010I
b = 0
−3.42837 − 2.09337I −3.06656 + 3.71284I
u = −0.140343 − 0.966856I
a = 0.457852 − 1.072010I
b = 0
−3.42837 + 2.09337I −3.06656 − 3.71284I
u = −0.628449 + 0.875112I
a = −1.63880 − 0.65075I
b = 0
−1.02799 − 2.45442I −4.16828 + 1.00072I
u = −0.628449 − 0.875112I
a = −1.63880 + 0.65075I
b = 0
−1.02799 + 2.45442I −4.16828 − 1.00072I
u = 0.796005 + 0.733148I
a = 0.522253 + 0.392004I
b = 0
2.72642 − 1.33617I 2.51011 + 2.54413I
u = 0.796005 − 0.733148I
a = 0.522253 − 0.392004I
b = 0
2.72642 + 1.33617I 2.51011 − 2.54413I
u = 0.728966 + 0.986295I
a = 0.425734 − 0.444312I
b = 0
1.95319 + 7.08493I 1.70570 − 8.17350I
u = 0.728966 − 0.986295I
a = 0.425734 + 0.444312I
b = 0
1.95319 − 7.08493I 1.70570 + 8.17350I
u = −0.512358
a = 1.46592
b = 0
−0.446489 2.03810
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
114
+ 52u
113
+ ··· + 62u + 1)
c
2
((u − 1)
9
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
114
− 12u
113
+ ··· + 22u − 1)
c
3
u
9
(u
6
− u
5
+ ··· − u + 1)
2
(u
114
− 3u
113
+ ··· − 3072u + 512)
c
4
((u + 1)
9
)(u
6
− u
5
+ ··· − u + 1)
2
(u
114
− 12u
113
+ ··· + 22u − 1)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
2
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
114
+ 4u
113
+ ··· + 1228166u − 118529)
c
6
u
12
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
114
− 2u
113
+ ··· + 16384u − 4096)
c
7
u
9
(u
6
+ u
5
+ ··· + u + 1)
2
(u
114
− 3u
113
+ ··· − 3072u + 512)
c
8
(u
2
+ u + 1)
6
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
114
+ 8u
113
+ ··· + 10u + 1)
c
9
u
12
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
114
− 2u
113
+ ··· + 16384u − 4096)
c
10
(u
2
− u + 1)
6
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
114
+ 36u
113
+ ··· + 10u + 1)
c
11
(u
2
− u + 1)
6
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
114
+ 8u
113
+ ··· + 10u + 1)
c
12
(u
2
+ u + 1)
6
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
114
+ 36u
113
+ ··· + 10u + 1)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
114
+ 32y
113
+ ··· + 6582y + 1)
c
2
, c
4
(y −1)
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
114
− 52y
113
+ ··· − 62y + 1)
c
3
, c
7
y
9
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
114
− 63y
113
+ ··· − 9437184y + 262144)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
114
− 60y
113
+ ··· − 2033070061434y + 14049123841)
c
6
, c
9
y
12
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
114
− 70y
113
+ ··· − 251658240y + 16777216)
c
8
, c
11
(y
2
+ y + 1)
6
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
114
+ 36y
113
+ ··· + 10y + 1)
c
10
, c
12
((y
2
+ y + 1)
6
)(y
9
+ 7y
8
+ ··· + 13y −1)
· (y
114
+ 92y
113
+ ··· + 4042y + 1)
27
