12n
0665
(K12n
0665
)
A knot diagram
1
Linearized knot diagam
4 5 6 9 8 11 3 2 12 6 9 10
Solving Sequence
9,12
10
1,5
4 2 8 6 3 7 11
c
9
c
12
c
4
c
1
c
8
c
5
c
3
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.16371 × 10
21
u
21
− 5.81881 × 10
21
u
20
+ ··· + 1.46625 × 10
23
b − 4.63210 × 10
22
,
2.23290 × 10
22
u
21
− 1.79700 × 10
23
u
20
+ ··· + 1.17300 × 10
24
a − 8.46516 × 10
23
, u
22
− 7u
21
+ ··· − u − 16i
I
u
2
= h−12a
3
+ 35a
2
+ 361b + 258a + 225, 4a
4
+ 7a
3
+ 20a
2
+ 5a + 11, u + 1i
I
u
3
= h−u
8
+ 4u
7
− 6u
6
+ 2u
5
+ 5u
4
− 6u
3
+ 4u
2
+ b − 3u, u
8
− 3u
7
+ 2u
6
+ 4u
5
− 7u
4
+ u
3
+ u
2
+ a + u + 2,
u
11
− 4u
10
+ 5u
9
+ 2u
8
− 11u
7
+ 8u
6
− u
4
+ 4u
3
− 5u
2
+ u − 1i
I
u
4
= h−1309u
10
a + 39316u
10
+ ··· − 49959a − 27286, −16711u
10
a + 2773u
10
+ ··· − 53855a − 50795,
u
11
− 5u
10
+ 12u
9
− 14u
8
+ 4u
7
+ 11u
6
− 16u
5
+ 14u
4
− 8u
3
− 13u
2
+ 7u − 1i
I
u
5
= h−2a
5
− 176a
4
− 669a
3
+ 284a
2
+ 13805b + 9351a + 7409, a
6
+ 6a
5
+ 21a
4
+ 39a
3
+ 66a
2
+ 49a + 59,
u + 1i
I
u
6
= hau + b − a − 2u + 3, a
2
+ 4au − 3a − 3u + 6, u
2
− u − 1i
* 6 irreducible components of dim
C
= 0, with total 69 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
= h1.16 × 10
21
u
21
− 5.82 × 10
21
u
20
+ · · · + 1.47 × 10
23
b − 4.63 × 10
22
, 2.23 ×
10
22
u
21
−1.80×10
23
u
20
+· · ·+1.17×10
24
a−8.47×10
23
, u
22
−7u
21
+· · ·−u−16i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u
2
a
1
=
u
−u
3
+ u
a
5
=
−0.0190358u
21
+ 0.153197u
20
+ ··· + 2.30959u + 0.721667
−0.00793664u
21
+ 0.0396850u
20
+ ··· + 0.0736575u + 0.315914
a
4
=
−0.0269724u
21
+ 0.192882u
20
+ ··· + 2.38324u + 1.03758
−0.00793664u
21
+ 0.0396850u
20
+ ··· + 0.0736575u + 0.315914
a
2
=
−0.00755456u
21
+ 0.0556100u
20
+ ··· + 2.97731u + 1.14656
0.0129445u
21
− 0.0689040u
20
+ ··· + 0.462289u + 0.147994
a
8
=
0.0468616u
21
− 0.281682u
20
+ ··· + 0.728053u + 0.542790
−0.0303212u
21
+ 0.179358u
20
+ ··· − 0.268846u − 0.786470
a
6
=
−0.0501899u
21
+ 0.326221u
20
+ ··· + 0.776174u − 0.236818
0.0251088u
21
− 0.165046u
20
+ ··· + 0.287008u + 0.803039
a
3
=
−0.0503171u
21
+ 0.321861u
20
+ ··· + 0.00116367u − 0.311783
0.0264975u
21
− 0.160879u
20
+ ··· + 1.44637u + 0.689429
a
7
=
0.0529780u
21
− 0.337734u
20
+ ··· − 0.360484u + 0.467102
−0.0278969u
21
+ 0.176559u
20
+ ··· − 0.702698u − 1.03332
a
11
=
−u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1046540992390926455030041
4692001596758932331121536
u
21
−
692312832330241174483901
586500199594866541390192
u
20
+ ··· +
21996001093684558786173143
4692001596758932331121536
u +
1233054846153246715242967
293250099797433270695096
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
22
− 22u
20
+ ··· − 78u + 1
c
2
u
22
+ 17u
21
+ ··· + 72u + 4
c
4
, c
7
u
22
− 10u
20
+ ··· − 82u + 17
c
5
, c
8
u
22
+ u
21
+ ··· − u + 1
c
6
, c
10
u
22
+ 5u
21
+ ··· + 224u − 256
c
9
, c
11
, c
12
u
22
+ 7u
21
+ ··· + u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
22
− 44y
21
+ ··· − 6066y + 1
c
2
y
22
− y
21
+ ··· − 984y + 16
c
4
, c
7
y
22
− 20y
21
+ ··· − 4038y + 289
c
5
, c
8
y
22
+ 9y
21
+ ··· + 9y + 1
c
6
, c
10
y
22
+ 27y
21
+ ··· − 291840y + 65536
c
9
, c
11
, c
12
y
22
− 5y
21
+ ··· − y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073320 + 0.196864I
a = −0.633075 + 1.048060I
b = −0.468525 − 0.581818I
0.748660 − 0.578139I 4.16300 − 3.21064I
u = −1.073320 − 0.196864I
a = −0.633075 − 1.048060I
b = −0.468525 + 0.581818I
0.748660 + 0.578139I 4.16300 + 3.21064I
u = 1.196940 + 0.138834I
a = 0.69651 − 1.48448I
b = −0.525572 + 0.904919I
4.76890 + 7.93706I 14.4936 − 13.4042I
u = 1.196940 − 0.138834I
a = 0.69651 + 1.48448I
b = −0.525572 − 0.904919I
4.76890 − 7.93706I 14.4936 + 13.4042I
u = −1.281740 + 0.445541I
a = −1.340360 − 0.152402I
b = 1.042560 − 0.544528I
0.63415 − 1.82383I 3.25206 + 1.96969I
u = −1.281740 − 0.445541I
a = −1.340360 + 0.152402I
b = 1.042560 + 0.544528I
0.63415 + 1.82383I 3.25206 − 1.96969I
u = 1.41326
a = 1.00267
b = −0.555579
7.32600 23.7620
u = −0.583556
a = −0.207344
b = −0.336659
0.970302 10.0070
u = −0.37029 + 1.42559I
a = 0.958773 + 0.111950I
b = −1.88452 + 0.10002I
−3.47219 − 4.63898I 1.76510 + 3.68966I
u = −0.37029 − 1.42559I
a = 0.958773 − 0.111950I
b = −1.88452 − 0.10002I
−3.47219 + 4.63898I 1.76510 − 3.68966I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.305160 + 0.425228I
a = 0.75251 + 1.97105I
b = 0.656252 − 0.746018I
−0.88734 + 1.99220I −1.51650 − 2.98007I
u = 0.305160 − 0.425228I
a = 0.75251 − 1.97105I
b = 0.656252 + 0.746018I
−0.88734 − 1.99220I −1.51650 + 2.98007I
u = 1.01095 + 1.14167I
a = 0.424540 − 0.460153I
b = −1.387840 + 0.091887I
−9.81793 + 5.07725I −1.39233 − 9.54863I
u = 1.01095 − 1.14167I
a = 0.424540 + 0.460153I
b = −1.387840 − 0.091887I
−9.81793 − 5.07725I −1.39233 + 9.54863I
u = 1.16674 + 1.00051I
a = 0.282150 − 1.116250I
b = −1.143540 + 0.418541I
−9.23521 + 2.88093I 1.62002 + 2.72235I
u = 1.16674 − 1.00051I
a = 0.282150 + 1.116250I
b = −1.143540 − 0.418541I
−9.23521 − 2.88093I 1.62002 − 2.72235I
u = −0.238163 + 0.343586I
a = 0.92161 + 1.69413I
b = 0.423005 + 0.405652I
−1.61974 − 1.37202I −2.26771 + 5.71937I
u = −0.238163 − 0.343586I
a = 0.92161 − 1.69413I
b = 0.423005 − 0.405652I
−1.61974 + 1.37202I −2.26771 − 5.71937I
u = 1.44040 + 1.00087I
a = −0.54794 + 2.42657I
b = 1.53075 − 1.61655I
−10.9142 + 15.8777I 4.46326 − 7.01203I
u = 1.44040 − 1.00087I
a = −0.54794 − 2.42657I
b = 1.53075 + 1.61655I
−10.9142 − 15.8777I 4.46326 + 7.01203I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.92846 + 1.61543I
a = −1.69364 − 0.69437I
b = 2.20355 + 1.18551I
−13.0092 − 6.5361I 2.81617 + 3.19876I
u = 0.92846 − 1.61543I
a = −1.69364 + 0.69437I
b = 2.20355 − 1.18551I
−13.0092 + 6.5361I 2.81617 − 3.19876I
7
II.
I
u
2
= h−12a
3
+ 35a
2
+ 361b + 258a + 225, 4a
4
+ 7a
3
+ 20a
2
+ 5a + 11, u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
−1
a
10
=
1
−1
a
1
=
−1
0
a
5
=
a
0.0332410a
3
− 0.0969529a
2
− 0.714681a − 0.623269
a
4
=
0.0332410a
3
− 0.0969529a
2
+ 0.285319a − 0.623269
0.0332410a
3
− 0.0969529a
2
− 0.714681a − 0.623269
a
2
=
−0.0332410a
3
+ 0.0969529a
2
− 0.285319a − 1.37673
−0.188366a
3
− 0.783934a
2
− 0.950139a − 0.468144
a
8
=
0.443213a
3
+ 1.37396a
2
+ 1.47091a + 1.68975
−0.221607a
3
− 0.686981a
2
− 0.235457a − 0.844875
a
6
=
0.387812a
3
+ 0.202216a
2
+ 0.662050a + 0.728532
−0.387812a
3
− 0.202216a
2
− 0.662050a − 0.728532
a
3
=
0.288089a
3
+ 0.493075a
2
− 0.193906a − 0.401662
−0.221607a
3
− 0.686981a
2
− 0.235457a − 0.844875
a
7
=
0.387812a
3
+ 0.202216a
2
+ 0.662050a + 0.728532
−0.387812a
3
− 0.202216a
2
− 0.662050a − 0.728532
a
11
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
640
361
a
3
+
1623
361
a
2
+
2846
361
a +
2079
361
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
4
+ u
2
− u + 1
c
2
u
4
− 3u
3
+ 4u
2
− 3u + 2
c
5
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
6
, c
10
u
4
c
7
u
4
+ u
2
+ u + 1
c
8
u
4
− 2u
3
+ 3u
2
− u + 1
c
9
(u + 1)
4
c
11
, c
12
(u − 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
2
y
4
− y
3
+ 2y
2
+ 7y + 4
c
5
, c
8
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
6
, c
10
y
4
c
9
, c
11
, c
12
(y −1)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.017843 + 0.799588I
b = −0.547424 − 0.585652I
0.66484 − 1.39709I 2.80605 + 5.27044I
u = −1.00000
a = −0.017843 − 0.799588I
b = −0.547424 + 0.585652I
0.66484 + 1.39709I 2.80605 − 5.27044I
u = −1.00000
a = −0.85716 + 1.88797I
b = 0.547424 − 1.120870I
4.26996 + 7.64338I 1.41270 − 4.22005I
u = −1.00000
a = −0.85716 − 1.88797I
b = 0.547424 + 1.120870I
4.26996 − 7.64338I 1.41270 + 4.22005I
11
III.
I
u
3
= h−u
8
+ 4u
7
+ · · · + b − 3u, u
8
− 3u
7
+ · · · + a + 2, u
11
− 4u
10
+ · · · + u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u
2
a
1
=
u
−u
3
+ u
a
5
=
−u
8
+ 3u
7
− 2u
6
− 4u
5
+ 7u
4
− u
3
− u
2
− u − 2
u
8
− 4u
7
+ 6u
6
− 2u
5
− 5u
4
+ 6u
3
− 4u
2
+ 3u
a
4
=
−u
7
+ 4u
6
− 6u
5
+ 2u
4
+ 5u
3
− 5u
2
+ 2u − 2
u
8
− 4u
7
+ 6u
6
− 2u
5
− 5u
4
+ 6u
3
− 4u
2
+ 3u
a
2
=
−2u
10
+ 10u
9
+ ··· − 3u + 2
u
8
− 4u
7
+ 6u
6
− 2u
5
− 5u
4
+ 5u
3
− 3u
2
+ 3u − 1
a
8
=
−u
10
+ 6u
9
+ ··· − 3u + 3
u
10
− 5u
9
+ 9u
8
− 4u
7
− 8u
6
+ 10u
5
− 2u
4
+ 3u
3
− 3u
2
− 2u − 1
a
6
=
u
10
− 4u
9
+ 4u
8
+ 5u
7
− 14u
6
+ 6u
5
+ 6u
4
− 4u
3
+ 4u
2
− 4u
u
9
− 3u
8
+ 3u
7
+ 2u
6
− 6u
5
+ 3u
4
− u
2
+ u − 1
a
3
=
−u
7
+ 4u
6
− 6u
5
+ 2u
4
+ 5u
3
− 4u
2
+ 2u − 3
u
8
− 4u
7
+ 6u
6
− 2u
5
− 5u
4
+ 5u
3
− 4u
2
+ 4u
a
7
=
u
10
− 3u
9
+ u
8
+ 8u
7
− 13u
6
+ 3u
5
+ 6u
4
− 6u
3
+ 7u
2
− 4u + 1
u
6
− 3u
5
+ 3u
4
+ 2u
3
− 4u
2
+ u − 2
a
11
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −6u
10
+ 27u
9
− 43u
8
+ 8u
7
+ 58u
6
− 59u
5
+ 6u
4
+ 4u
3
− 6u
2
+ 18u + 1
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
11
− 6u
10
+ ··· + u − 1
c
2
u
11
+ 5u
10
+ ··· + 66u + 11
c
4
, c
7
u
11
− 3u
9
− 3u
8
+ 3u
7
+ 5u
6
+ u
5
− 2u
4
+ u
3
+ 4u
2
+ 3u + 1
c
5
, c
8
u
11
+ 3u
10
+ 4u
9
+ u
8
− 2u
7
+ u
6
+ 5u
5
+ 3u
4
− 3u
3
− 3u
2
+ 1
c
6
u
11
+ 2u
10
+ 5u
9
+ 3u
8
− 6u
7
− 12u
6
− 4u
5
− u
4
− 4u
3
− 5u
2
− u − 1
c
9
u
11
− 4u
10
+ 5u
9
+ 2u
8
− 11u
7
+ 8u
6
− u
4
+ 4u
3
− 5u
2
+ u − 1
c
10
u
11
− 2u
10
+ 5u
9
− 3u
8
− 6u
7
+ 12u
6
− 4u
5
+ u
4
− 4u
3
+ 5u
2
− u + 1
c
11
, c
12
u
11
+ 4u
10
+ 5u
9
− 2u
8
− 11u
7
− 8u
6
+ u
4
+ 4u
3
+ 5u
2
+ u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
11
− 6y
10
+ ··· − 11y −1
c
2
y
11
− 5y
10
+ ··· + 1056y −121
c
4
, c
7
y
11
− 6y
10
+ ··· + y −1
c
5
, c
8
y
11
− y
10
+ ··· + 6y −1
c
6
, c
10
y
11
+ 6y
10
+ ··· − 9y −1
c
9
, c
11
, c
12
y
11
− 6y
10
+ ··· − 9y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.086170 + 0.009391I
a = 4.41295 + 0.00742I
b = −0.701762 − 0.657333I
2.65196 − 3.67431I −5.84307 + 3.56499I
u = −1.086170 − 0.009391I
a = 4.41295 − 0.00742I
b = −0.701762 + 0.657333I
2.65196 + 3.67431I −5.84307 − 3.56499I
u = −0.107619 + 0.709932I
a = 0.895151 + 0.275061I
b = 0.954711 − 0.673787I
0.30466 + 2.75309I 5.01781 − 3.90984I
u = −0.107619 − 0.709932I
a = 0.895151 − 0.275061I
b = 0.954711 + 0.673787I
0.30466 − 2.75309I 5.01781 + 3.90984I
u = 1.298730 + 0.273936I
a = −0.597874 + 1.164320I
b = 0.400683 − 0.540159I
4.37786 + 7.33604I 4.82590 − 2.92832I
u = 1.298730 − 0.273936I
a = −0.597874 − 1.164320I
b = 0.400683 + 0.540159I
4.37786 − 7.33604I 4.82590 + 2.92832I
u = 1.47992
a = −1.10702
b = 0.798074
6.99554 −1.23750
u = 0.031910 + 0.483612I
a = −1.42549 − 0.63001I
b = 0.551419 + 0.729779I
0.36189 − 4.26572I 1.88771 + 6.83487I
u = 0.031910 − 0.483612I
a = −1.42549 + 0.63001I
b = 0.551419 − 0.729779I
0.36189 + 4.26572I 1.88771 − 6.83487I
u = 1.12319 + 1.19275I
a = 0.768773 − 0.735083I
b = −1.60409 + 0.22290I
−9.54921 + 4.30931I 3.23041 − 0.76635I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12319 − 1.19275I
a = 0.768773 + 0.735083I
b = −1.60409 − 0.22290I
−9.54921 − 4.30931I 3.23041 + 0.76635I
16
IV. I
u
4
= h−1309u
10
a + 39316u
10
+ · · · − 49959a − 27286, −16711u
10
a +
2773u
10
+ · · · − 53855a − 50795, u
11
− 5u
10
+ · · · + 7u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u
2
a
1
=
u
−u
3
+ u
a
5
=
a
0.00589438au
10
− 0.177038u
10
+ ··· + 0.224964a + 0.122868
a
4
=
0.00589438au
10
− 0.177038u
10
+ ··· + 1.22496a + 0.122868
0.00589438au
10
− 0.177038u
10
+ ··· + 0.224964a + 0.122868
a
2
=
−0.773073au
10
+ 0.470695u
10
+ ··· − 3.09852a − 1.05429
0.224964au
10
− 0.715602u
10
+ ··· + 0.773073a − 1.44519
a
8
=
0.119743au
10
− 1.31813u
10
+ ··· + 0.473820a − 2.23776
−0.143618au
10
+ 0.302113u
10
+ ··· − 0.296781a + 0.607909
a
6
=
1.65276u
10
− 7.83688u
9
+ ··· − 24.1541u + 5.81695
−0.426939u
10
+ 2.03454u
9
+ ··· + 5.75239u − 1.65276
a
3
=
−0.360480au
10
+ 0.470695u
10
+ ··· − 0.370306a − 1.05429
0.140546au
10
− 0.617437u
10
+ ··· + 0.591338a − 0.524865
a
7
=
−1.71387u
10
+ 8.17163u
9
+ ··· + 25.2157u − 6.14373
0.488045u
10
− 2.36929u
9
+ ··· − 6.81403u + 1.97954
a
11
=
−u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1665
1882
u
10
+
7853
1882
u
9
−
15635
1882
u
8
+
9431
1882
u
7
+
19187
1882
u
6
−
21601
941
u
5
+
38751
1882
u
4
−
9650
941
u
3
+
7699
1882
u
2
+
38133
1882
u −
2836
941
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
22
+ 4u
21
+ ··· + 3144u − 1751
c
2
(u
11
− 2u
10
+ 4u
9
− 4u
8
+ 7u
7
− 6u
6
+ 8u
5
− 3u
4
+ 7u
3
− 5u
2
+ 6u + 4)
2
c
4
, c
7
u
22
− u
21
+ ··· − 1853u − 367
c
5
, c
8
u
22
+ 3u
21
+ ··· + 43u + 17
c
6
, c
10
(u
11
− 2u
10
+ ··· + 20u + 8)
2
c
9
, c
11
, c
12
(u
11
+ 5u
10
+ ··· + 7u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
22
− 34y
21
+ ··· + 14797360y + 3066001
c
2
(y
11
+ 4y
10
+ ··· + 76y −16)
2
c
4
, c
7
y
22
− 21y
21
+ ··· − 11844515y + 134689
c
5
, c
8
y
22
− 5y
21
+ ··· + 157y + 289
c
6
, c
10
(y
11
+ 18y
10
+ ··· − 48y −64)
2
c
9
, c
11
, c
12
(y
11
− y
10
+ ··· + 23y −1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.079725 + 1.068410I
a = 0.856962 + 0.168668I
b = −2.18146 − 0.23527I
−1.62432 + 3.00088I 0.33499 − 3.49194I
u = −0.079725 + 1.068410I
a = 0.439244 + 1.098550I
b = 0.798257 − 1.114970I
−1.62432 + 3.00088I 0.33499 − 3.49194I
u = −0.079725 − 1.068410I
a = 0.856962 − 0.168668I
b = −2.18146 + 0.23527I
−1.62432 − 3.00088I 0.33499 + 3.49194I
u = −0.079725 − 1.068410I
a = 0.439244 − 1.098550I
b = 0.798257 + 1.114970I
−1.62432 − 3.00088I 0.33499 + 3.49194I
u = −0.884145 + 0.095736I
a = −1.16290 − 2.05270I
b = −0.559456 + 0.879724I
2.07033 + 3.52584I 11.0814 − 10.6105I
u = −0.884145 + 0.095736I
a = −0.69396 − 4.81962I
b = 0.969577 − 0.463172I
2.07033 + 3.52584I 11.0814 − 10.6105I
u = −0.884145 − 0.095736I
a = −1.16290 + 2.05270I
b = −0.559456 − 0.879724I
2.07033 − 3.52584I 11.0814 + 10.6105I
u = −0.884145 − 0.095736I
a = −0.69396 + 4.81962I
b = 0.969577 + 0.463172I
2.07033 − 3.52584I 11.0814 + 10.6105I
u = 1.53174
a = 0.113755
b = 0.109337
7.41447 30.3990
u = 1.53174
a = 2.58390
b = −1.70388
7.41447 30.3990
20
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.238296 + 0.095870I
a = 2.84346 − 2.84451I
b = −0.419609 + 0.270447I
0.52440 − 2.64086I 1.94796 + 2.03870I
u = 0.238296 + 0.095870I
a = −2.77344 − 3.23631I
b = 0.478533 + 1.099150I
0.52440 − 2.64086I 1.94796 + 2.03870I
u = 0.238296 − 0.095870I
a = 2.84346 + 2.84451I
b = −0.419609 − 0.270447I
0.52440 + 2.64086I 1.94796 − 2.03870I
u = 0.238296 − 0.095870I
a = −2.77344 + 3.23631I
b = 0.478533 − 1.099150I
0.52440 + 2.64086I 1.94796 − 2.03870I
u = 1.45203 + 1.04949I
a = 0.660877 − 1.207490I
b = −1.32301 + 0.63561I
−9.67193 + 7.23582I 3.59903 − 5.42641I
u = 1.45203 + 1.04949I
a = −0.68206 + 2.97589I
b = 1.68145 − 2.15398I
−9.67193 + 7.23582I 3.59903 − 5.42641I
u = 1.45203 − 1.04949I
a = 0.660877 + 1.207490I
b = −1.32301 − 0.63561I
−9.67193 − 7.23582I 3.59903 + 5.42641I
u = 1.45203 − 1.04949I
a = −0.68206 − 2.97589I
b = 1.68145 + 2.15398I
−9.67193 − 7.23582I 3.59903 + 5.42641I
u = 1.00768 + 1.54288I
a = 0.930928 − 0.584899I
b = −1.71241 + 0.28243I
−11.45500 + 2.23657I 0.837127 − 0.170303I
u = 1.00768 + 1.54288I
a = −2.26794 − 1.18182I
b = 2.56540 + 1.84699I
−11.45500 + 2.23657I 0.837127 − 0.170303I
21
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00768 − 1.54288I
a = 0.930928 + 0.584899I
b = −1.71241 − 0.28243I
−11.45500 − 2.23657I 0.837127 + 0.170303I
u = 1.00768 − 1.54288I
a = −2.26794 + 1.18182I
b = 2.56540 − 1.84699I
−11.45500 − 2.23657I 0.837127 + 0.170303I
22
V. I
u
5
= h−2a
5
+ 13805b + · · · + 9351a + 7409, a
6
+ 6a
5
+ 21a
4
+ 39a
3
+
66a
2
+ 49a + 59, u + 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
−1
a
10
=
1
−1
a
1
=
−1
0
a
5
=
a
0.000144875a
5
+ 0.0127490a
4
+ ··· − 0.677363a − 0.536690
a
4
=
0.000144875a
5
+ 0.0127490a
4
+ ··· + 0.322637a − 0.536690
0.000144875a
5
+ 0.0127490a
4
+ ··· − 0.677363a − 0.536690
a
2
=
−0.000144875a
5
− 0.0127490a
4
+ ··· − 0.322637a − 1.46331
0.0117349a
5
+ 0.0326693a
4
+ ··· − 0.866425a − 0.471858
a
8
=
−0.0231800a
5
− 0.0398406a
4
+ ··· + 1.37812a + 1.87034
0.0594712a
5
+ 0.233466a
4
+ ··· − 0.557624a − 1.81108
a
6
=
−0.0488953a
5
− 0.302789a
4
+ ··· − 0.889895a − 1.36726
0.0488953a
5
+ 0.302789a
4
+ ··· + 0.889895a + 1.36726
a
3
=
−0.0591815a
5
− 0.207968a
4
+ ··· + 0.202898a + 0.737704
0.0594712a
5
+ 0.233466a
4
+ ··· − 0.557624a − 1.81108
a
7
=
−0.0488953a
5
− 0.302789a
4
+ ··· − 0.889895a − 1.36726
0.0488953a
5
+ 0.302789a
4
+ ··· + 0.889895a + 1.36726
a
11
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
32
2761
a
5
−
5
251
a
4
+
340
2761
a
3
+
1783
2761
a
2
+
3283
2761
a +
24670
2761
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
2
(u
3
+ u
2
− 1)
2
c
5
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
6
, c
10
u
6
c
7
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
8
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
9
(u + 1)
6
c
11
, c
12
(u − 1)
6
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
7
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
2
(y
3
− y
2
+ 2y −1)
2
c
5
, c
8
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
6
, c
10
y
6
c
9
, c
11
, c
12
(y −1)
6
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.037526 + 1.309480I
b = −0.498832 − 1.001300I
1.91067 − 2.82812I 7.78492 + 1.30714I
u = −1.00000
a = 0.037526 − 1.309480I
b = −0.498832 + 1.001300I
1.91067 + 2.82812I 7.78492 − 1.30714I
u = −1.00000
a = −0.69240 + 1.75059I
b = 0.284920 − 1.115140I
6.04826 7.43016 + 0.I
u = −1.00000
a = −0.69240 − 1.75059I
b = 0.284920 + 1.115140I
6.04826 7.43016 + 0.I
u = −1.00000
a = −2.34512 + 2.04966I
b = 0.713912 − 0.305839I
1.91067 − 2.82812I 7.78492 + 1.30714I
u = −1.00000
a = −2.34512 − 2.04966I
b = 0.713912 + 0.305839I
1.91067 + 2.82812I 7.78492 − 1.30714I
26
VI. I
u
6
= hau + b − a − 2u + 3, a
2
+ 4au − 3a − 3u + 6, u
2
− u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
−u − 1
a
1
=
u
−u − 1
a
5
=
a
−au + a + 2u − 3
a
4
=
−au + 2a + 2u − 3
−au + a + 2u − 3
a
2
=
−au + 2a + 3u − 3
−au + a + u − 4
a
8
=
−2au + 2a + 3u − 8
au + 2u + 2
a
6
=
−u
u + 1
a
3
=
−au + 2a + 3u − 3
−au + a + u − 4
a
7
=
1
0
a
11
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −9u − 1
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
4
c
2
u
4
c
4
, c
5
, c
7
c
8
u
4
+ 3u
3
+ 3u
2
+ 3u + 1
c
6
, c
9
(u
2
− u − 1)
2
c
10
, c
11
, c
12
(u
2
+ u − 1)
2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
4
c
2
y
4
c
4
, c
5
, c
7
c
8
y
4
− 3y
3
− 7y
2
− 3y + 1
c
6
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 2.73607 + 0.60666I
b = 0.190983 + 0.981593I
−0.657974 4.56230
u = −0.618034
a = 2.73607 − 0.60666I
b = 0.190983 − 0.981593I
−0.657974 4.56230
u = 1.61803
a = −0.369308
b = 0.464313
7.23771 −15.5620
u = 1.61803
a = −3.10283
b = 2.15372
7.23771 −15.5620
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
(u − 1)
4
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
11
− 6u
10
+ ··· + u − 1)(u
22
− 22u
20
+ ··· − 78u + 1)
· (u
22
+ 4u
21
+ ··· + 3144u − 1751)
c
2
u
4
(u
3
+ u
2
− 1)
2
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
· (u
11
− 2u
10
+ 4u
9
− 4u
8
+ 7u
7
− 6u
6
+ 8u
5
− 3u
4
+ 7u
3
− 5u
2
+ 6u + 4)
2
· (u
11
+ 5u
10
+ ··· + 66u + 11)(u
22
+ 17u
21
+ ··· + 72u + 4)
c
4
(u
4
+ u
2
− u + 1)(u
4
+ 3u
3
+ 3u
2
+ 3u + 1)
· (u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
11
− 3u
9
− 3u
8
+ 3u
7
+ 5u
6
+ u
5
− 2u
4
+ u
3
+ 4u
2
+ 3u + 1)
· (u
22
− 10u
20
+ ··· − 82u + 17)(u
22
− u
21
+ ··· − 1853u − 367)
c
5
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
4
+ 3u
3
+ 3u
2
+ 3u + 1)
· (u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
11
+ 3u
10
+ 4u
9
+ u
8
− 2u
7
+ u
6
+ 5u
5
+ 3u
4
− 3u
3
− 3u
2
+ 1)
· (u
22
+ u
21
+ ··· − u + 1)(u
22
+ 3u
21
+ ··· + 43u + 17)
c
6
u
10
(u
2
− u − 1)
2
(u
11
− 2u
10
+ ··· + 20u + 8)
2
· (u
11
+ 2u
10
+ 5u
9
+ 3u
8
− 6u
7
− 12u
6
− 4u
5
− u
4
− 4u
3
− 5u
2
− u − 1)
· (u
22
+ 5u
21
+ ··· + 224u − 256)
c
7
(u
4
+ u
2
+ u + 1)(u
4
+ 3u
3
+ 3u
2
+ 3u + 1)
· (u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
11
− 3u
9
− 3u
8
+ 3u
7
+ 5u
6
+ u
5
− 2u
4
+ u
3
+ 4u
2
+ 3u + 1)
· (u
22
− 10u
20
+ ··· − 82u + 17)(u
22
− u
21
+ ··· − 1853u − 367)
c
8
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
4
+ 3u
3
+ 3u
2
+ 3u + 1)
· (u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
11
+ 3u
10
+ 4u
9
+ u
8
− 2u
7
+ u
6
+ 5u
5
+ 3u
4
− 3u
3
− 3u
2
+ 1)
· (u
22
+ u
21
+ ··· − u + 1)(u
22
+ 3u
21
+ ··· + 43u + 17)
c
9
(u + 1)
10
(u
2
− u − 1)
2
· (u
11
− 4u
10
+ 5u
9
+ 2u
8
− 11u
7
+ 8u
6
− u
4
+ 4u
3
− 5u
2
+ u − 1)
· ((u
11
+ 5u
10
+ ··· + 7u + 1)
2
)(u
22
+ 7u
21
+ ··· + u − 16)
c
10
u
10
(u
2
+ u − 1)
2
· (u
11
− 2u
10
+ 5u
9
− 3u
8
− 6u
7
+ 12u
6
− 4u
5
+ u
4
− 4u
3
+ 5u
2
− u + 1)
· ((u
11
− 2u
10
+ ··· + 20u + 8)
2
)(u
22
+ 5u
21
+ ··· + 224u − 256)
c
11
, c
12
(u − 1)
10
(u
2
+ u − 1)
2
· (u
11
+ 4u
10
+ 5u
9
− 2u
8
− 11u
7
− 8u
6
+ u
4
+ 4u
3
+ 5u
2
+ u + 1)
· ((u
11
+ 5u
10
+ ··· + 7u + 1)
2
)(u
22
+ 7u
21
+ ··· + u − 16)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y −1)
4
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
11
− 6y
10
+ ··· − 11y −1)(y
22
− 44y
21
+ ··· − 6066y + 1)
· (y
22
− 34y
21
+ ··· + 14797360y + 3066001)
c
2
y
4
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
11
− 5y
10
+ ··· + 1056y −121)(y
11
+ 4y
10
+ ··· + 76y −16)
2
· (y
22
− y
21
+ ··· − 984y + 16)
c
4
, c
7
(y
4
− 3y
3
− 7y
2
− 3y + 1)(y
4
+ 2y
3
+ 3y
2
+ y + 1)
· (y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)(y
11
− 6y
10
+ ··· + y −1)
· (y
22
− 21y
21
+ ··· − 11844515y + 134689)
· (y
22
− 20y
21
+ ··· − 4038y + 289)
c
5
, c
8
(y
4
− 3y
3
− 7y
2
− 3y + 1)(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
· (y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)(y
11
− y
10
+ ··· + 6y −1)
· (y
22
− 5y
21
+ ··· + 157y + 289)(y
22
+ 9y
21
+ ··· + 9y + 1)
c
6
, c
10
y
10
(y
2
− 3y + 1)
2
(y
11
+ 6y
10
+ ··· − 9y −1)
· (y
11
+ 18y
10
+ ··· − 48y −64)
2
· (y
22
+ 27y
21
+ ··· − 291840y + 65536)
c
9
, c
11
, c
12
((y −1)
10
)(y
2
− 3y + 1)
2
(y
11
− 6y
10
+ ··· − 9y −1)
· ((y
11
− y
10
+ ··· + 23y −1)
2
)(y
22
− 5y
21
+ ··· − y + 256)
32
