12n
0612
(K12n
0612
)
A knot diagram
1
Linearized knot diagam
3 7 11 1 10 8 2 1 4 6 4 10
Solving Sequence
1,4 5,10
6 9 8 12 11 3 2 7
c
4
c
5
c
9
c
8
c
12
c
11
c
3
c
1
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u,
65065875226664520u
27
+ 9394396496362895u
26
+ ··· + 76364734116743a + 26735659168418070,
u
28
+ 23u
26
+ ··· − 3u + 1i
I
u
2
= hb + u, 5u
16
+ u
15
+ ··· + a − 5,
u
17
+ 3u
15
− u
14
− 4u
13
− 5u
11
+ 5u
10
+ 11u
9
− 6u
8
− 2u
7
− 2u
6
− 7u
5
+ 8u
4
+ 5u
3
− 5u
2
− u + 1i
I
u
3
= h1.90741 × 10
76
u
35
+ 2.50394 × 10
76
u
34
+ ··· + 5.34816 × 10
78
b − 7.63438 × 10
78
,
4.20379 × 10
66
u
35
+ 2.74371 × 10
66
u
34
+ ··· + 1.04184 × 10
69
a − 1.38242 × 10
70
,
u
36
+ u
35
+ ··· − 2560u + 121i
* 3 irreducible components of dim
C
= 0, with total 81 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
= hb − u, 6.51 × 10
16
u
27
+ 9.39 × 10
15
u
26
+ · · · + 7.64 × 10
13
a + 2.67 ×
10
16
, u
28
+ 23u
26
+ · · · − 3u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
10
=
−852.041u
27
− 123.020u
26
+ ··· − 1960.13u − 350.105
u
a
6
=
−104.065u
27
+ 370.478u
26
+ ··· − 4216.19u + 1309.36
−42.7858u
27
+ 67.8173u
26
+ ··· − 845.364u + 240.781
a
9
=
−852.041u
27
− 123.020u
26
+ ··· − 1959.13u − 350.105
u
a
8
=
−852.041u
27
− 123.020u
26
+ ··· − 1959.13u − 350.105
240.781u
27
+ 42.7858u
26
+ ··· + 483.981u + 123.020
a
12
=
−456.322u
27
+ 18.9555u
26
+ ··· − 1801.95u + 59.0018
−240.781u
27
− 42.7858u
26
+ ··· − 481.981u − 123.020
a
11
=
−697.103u
27
− 23.8304u
26
+ ··· − 2283.93u − 64.0183
−240.781u
27
− 42.7858u
26
+ ··· − 481.981u − 123.020
a
3
=
−186.897u
27
+ 111.670u
26
+ ··· − 1633.52u + 381.526
80.2342u
27
− 172.964u
26
+ ··· + 2060.86u − 611.260
a
2
=
643.875u
27
+ 247.704u
26
+ ··· − 217.453u + 810.960
−403.888u
27
+ 1.74743u
26
+ ··· − 1518.50u + 43.0095
a
7
=
20.8672u
27
− 274.777u
26
+ ··· + 2601.82u − 917.955
−35.7010u
27
+ 222.640u
26
+ ··· − 2384.15u + 774.366
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−
57088194451595465
76364734116743
u
27
+
88581311353921087
76364734116743
u
26
+···−
1111026347572146836
76364734116743
u+
313608959053702506
76364734116743
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
28
+ 9u
27
+ ··· + 84u + 16
c
2
, c
7
u
28
+ 5u
27
+ ··· + 2u + 4
c
3
, c
5
, c
10
c
11
u
28
+ u
27
+ ··· + 4u + 1
c
4
, c
9
u
28
+ 23u
26
+ ··· + 3u + 1
c
8
u
28
− 25u
27
+ ··· − 98862u + 9028
c
12
u
28
+ 21u
27
+ ··· + 3584u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
28
+ 21y
27
+ ··· + 2064y + 256
c
2
, c
7
y
28
+ 9y
27
+ ··· + 84y + 16
c
3
, c
5
, c
10
c
11
y
28
− 11y
27
+ ··· − 6y + 1
c
4
, c
9
y
28
+ 46y
27
+ ··· + 49y + 1
c
8
y
28
− 3y
27
+ ··· + 785869044y + 81504784
c
12
y
28
− 17y
27
+ ··· + 4456448y + 262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.062917 + 0.794694I
a = −1.44001 − 0.70376I
b = −0.062917 + 0.794694I
−1.93668 − 4.60321I −5.64825 + 3.26019I
u = −0.062917 − 0.794694I
a = −1.44001 + 0.70376I
b = −0.062917 − 0.794694I
−1.93668 + 4.60321I −5.64825 − 3.26019I
u = 0.193820 + 0.693750I
a = 1.312680 − 0.250146I
b = 0.193820 + 0.693750I
−0.409488 − 0.484105I −3.68035 + 2.98454I
u = 0.193820 − 0.693750I
a = 1.312680 + 0.250146I
b = 0.193820 − 0.693750I
−0.409488 + 0.484105I −3.68035 − 2.98454I
u = −0.015958 + 0.620215I
a = −2.15814 − 0.25579I
b = −0.015958 + 0.620215I
−5.53121 + 1.96442I −8.05770 − 3.63784I
u = −0.015958 − 0.620215I
a = −2.15814 + 0.25579I
b = −0.015958 − 0.620215I
−5.53121 − 1.96442I −8.05770 + 3.63784I
u = 0.007916 + 0.540155I
a = −2.68846 + 0.36830I
b = 0.007916 + 0.540155I
−0.95872 + 8.32918I −2.85757 − 9.28705I
u = 0.007916 − 0.540155I
a = −2.68846 − 0.36830I
b = 0.007916 − 0.540155I
−0.95872 − 8.32918I −2.85757 + 9.28705I
u = 0.018995 + 0.532352I
a = 2.36847 + 0.52484I
b = 0.018995 + 0.532352I
0.30181 − 2.82865I −1.29087 + 4.58370I
u = 0.018995 − 0.532352I
a = 2.36847 − 0.52484I
b = 0.018995 − 0.532352I
0.30181 + 2.82865I −1.29087 − 4.58370I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.25002 + 1.56539I
a = 0.238631 − 0.969260I
b = −0.25002 + 1.56539I
0.93824 + 1.99231I 0
u = −0.25002 − 1.56539I
a = 0.238631 + 0.969260I
b = −0.25002 − 1.56539I
0.93824 − 1.99231I 0
u = 0.005308 + 0.404634I
a = 0.23723 + 2.20308I
b = 0.005308 + 0.404634I
3.88624 − 2.72415I 0.13151 + 3.72503I
u = 0.005308 − 0.404634I
a = 0.23723 − 2.20308I
b = 0.005308 − 0.404634I
3.88624 + 2.72415I 0.13151 − 3.72503I
u = 0.182846 + 0.331511I
a = 0.690101 + 0.486506I
b = 0.182846 + 0.331511I
−0.224067 − 0.893165I −4.75660 + 7.55885I
u = 0.182846 − 0.331511I
a = 0.690101 − 0.486506I
b = 0.182846 − 0.331511I
−0.224067 + 0.893165I −4.75660 − 7.55885I
u = −0.50624 + 1.65356I
a = 0.039303 − 0.997212I
b = −0.50624 + 1.65356I
−0.51665 + 9.12206I 0
u = −0.50624 − 1.65356I
a = 0.039303 + 0.997212I
b = −0.50624 − 1.65356I
−0.51665 − 9.12206I 0
u = 0.35393 + 1.72346I
a = −0.116049 − 0.916399I
b = 0.35393 + 1.72346I
3.78322 − 6.15036I 0
u = 0.35393 − 1.72346I
a = −0.116049 + 0.916399I
b = 0.35393 − 1.72346I
3.78322 + 6.15036I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.62895 + 1.78797I
a = −0.052590 − 0.928175I
b = −0.62895 + 1.78797I
5.5259 + 15.3858I 0
u = −0.62895 − 1.78797I
a = −0.052590 + 0.928175I
b = −0.62895 − 1.78797I
5.5259 − 15.3858I 0
u = 0.57825 + 1.81066I
a = 0.026177 − 0.911601I
b = 0.57825 + 1.81066I
6.63527 − 9.39925I 0
u = 0.57825 − 1.81066I
a = 0.026177 + 0.911601I
b = 0.57825 − 1.81066I
6.63527 + 9.39925I 0
u = 0.16208 + 1.89611I
a = 0.245895 − 0.654376I
b = 0.16208 + 1.89611I
9.28183 − 2.22011I 0
u = 0.16208 − 1.89611I
a = 0.245895 + 0.654376I
b = 0.16208 − 1.89611I
9.28183 + 2.22011I 0
u = −0.03905 + 1.92499I
a = −0.203229 − 0.694596I
b = −0.03905 + 1.92499I
9.65564 − 4.10797I 0
u = −0.03905 − 1.92499I
a = −0.203229 + 0.694596I
b = −0.03905 − 1.92499I
9.65564 + 4.10797I 0
7
II. I
u
2
= hb + u, 5u
16
+ u
15
+ · · · + a − 5, u
17
+ 3u
15
+ · · · − u + 1i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
10
=
−5u
16
− u
15
+ ··· + 12u + 5
−u
a
6
=
5u
16
+ 5u
15
+ ··· + u − 16
u
2
+ 1
a
9
=
−5u
16
− u
15
+ ··· + 11u + 5
−u
a
8
=
−5u
16
− u
15
+ ··· + 11u + 5
−u
16
− 3u
14
+ ··· + 3u + 1
a
12
=
12u
16
+ 4u
15
+ ··· − 17u − 11
−u
16
− 3u
14
+ ··· + 5u + 1
a
11
=
11u
16
+ 4u
15
+ ··· − 12u − 10
−u
16
− 3u
14
+ ··· + 5u + 1
a
3
=
−10u
16
− 11u
15
+ ··· − 5u + 23
u
16
+ u
15
+ ··· + 13u
2
− 6
a
2
=
−16u
16
− 10u
15
+ ··· + 13u + 29
−23u
16
− 10u
15
+ ··· + 22u + 18
a
7
=
9u
16
+ 13u
15
+ ··· + 12u − 21
u
16
+ 2u
15
+ ··· + 3u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes = 45u
16
+ 45u
15
+ 162u
14
+ 117u
13
− 128u
12
− 110u
11
− 304u
10
−
68u
9
+ 533u
8
+ 181u
7
− 36u
6
− 69u
5
− 426u
4
+ u
3
+ 315u
2
− u − 77
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
17
− 6u
16
+ ··· − 18u
2
+ 1
c
2
u
17
+ 3u
15
+ ··· + 2u − 1
c
3
, c
10
u
17
− u
16
+ ··· + 3u
2
+ 1
c
4
, c
9
u
17
+ 3u
15
+ ··· − u + 1
c
5
, c
11
u
17
+ u
16
+ ··· − 3u
2
− 1
c
7
u
17
+ 3u
15
+ ··· + 2u + 1
c
8
u
17
− u
15
+ ··· + 2u + 1
c
12
u
17
− 6u
16
+ ··· + 2u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
17
+ 14y
16
+ ··· + 36y − 1
c
2
, c
7
y
17
+ 6y
16
+ ··· + 18y
2
− 1
c
3
, c
5
, c
10
c
11
y
17
− 11y
16
+ ··· − 6y − 1
c
4
, c
9
y
17
+ 6y
16
+ ··· + 11y − 1
c
8
y
17
− 2y
16
+ ··· − 2y − 1
c
12
y
17
− 14y
16
+ ··· + 8y − 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.944344 + 0.346033I
a = 0.447652 − 0.512355I
b = 0.944344 − 0.346033I
−1.03956 − 1.63645I −7.74530 + 1.55839I
u = −0.944344 − 0.346033I
a = 0.447652 + 0.512355I
b = 0.944344 + 0.346033I
−1.03956 + 1.63645I −7.74530 − 1.55839I
u = 0.864585 + 0.379164I
a = −0.583910 − 0.698557I
b = −0.864585 − 0.379164I
−2.10829 + 7.37198I −8.93029 − 5.91248I
u = 0.864585 − 0.379164I
a = −0.583910 + 0.698557I
b = −0.864585 + 0.379164I
−2.10829 − 7.37198I −8.93029 + 5.91248I
u = −0.037669 + 1.084830I
a = 0.11324 + 1.69832I
b = 0.037669 − 1.084830I
5.48501 − 2.53801I 5.54821 + 3.82197I
u = −0.037669 − 1.084830I
a = 0.11324 − 1.69832I
b = 0.037669 + 1.084830I
5.48501 + 2.53801I 5.54821 − 3.82197I
u = −0.878247
a = −0.337583
b = 0.878247
−3.63803 −10.5770
u = 0.791817 + 0.212409I
a = 0.104106 − 0.968399I
b = −0.791817 − 0.212409I
−7.18587 + 1.52748I −14.7986 − 1.1989I
u = 0.791817 − 0.212409I
a = 0.104106 + 0.968399I
b = −0.791817 + 0.212409I
−7.18587 − 1.52748I −14.7986 + 1.1989I
u = −0.714015 + 0.074924I
a = −1.185250 − 0.688415I
b = 0.714015 − 0.074924I
−3.09442 − 0.79036I −5.12753 − 0.89506I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.714015 − 0.074924I
a = −1.185250 + 0.688415I
b = 0.714015 + 0.074924I
−3.09442 + 0.79036I −5.12753 + 0.89506I
u = 0.704468 + 0.121688I
a = 1.00603 − 1.10552I
b = −0.704468 − 0.121688I
−3.93940 − 4.16488I −8.44169 + 5.58918I
u = 0.704468 − 0.121688I
a = 1.00603 + 1.10552I
b = −0.704468 + 0.121688I
−3.93940 + 4.16488I −8.44169 − 5.58918I
u = −0.145937 + 1.315070I
a = 0.223886 + 1.159350I
b = 0.145937 − 1.315070I
2.99124 + 0.77564I −5.07814 + 0.88442I
u = −0.145937 − 1.315070I
a = 0.223886 − 1.159350I
b = 0.145937 + 1.315070I
2.99124 − 0.77564I −5.07814 − 0.88442I
u = −0.07978 + 1.85790I
a = 0.043035 + 0.691466I
b = 0.07978 − 1.85790I
9.06537 + 3.10101I −4.13830 − 3.69699I
u = −0.07978 − 1.85790I
a = 0.043035 − 0.691466I
b = 0.07978 + 1.85790I
9.06537 − 3.10101I −4.13830 + 3.69699I
12
III. I
u
3
=
h1.91×10
76
u
35
+2.50×10
76
u
34
+· · ·+5.35×10
78
b−7.63×10
78
, 4.20×10
66
u
35
+
2.74 × 10
66
u
34
+ · · · + 1.04 × 10
69
a − 1.38 × 10
70
, u
36
+ u
35
+ · · · − 2560u + 121i
(i) Arc colorings
a
1
=
0
u
a
4
=
1
0
a
5
=
1
u
2
a
10
=
−0.00403497u
35
− 0.00263353u
34
+ ··· − 21.5564u + 13.2691
−0.00356648u
35
− 0.00468188u
34
+ ··· − 4.09637u + 1.42748
a
6
=
−0.00793734u
35
− 0.00974330u
34
+ ··· − 11.1664u + 16.8486
0.00140145u
35
+ 0.000977635u
34
+ ··· + 2.93952u + 1.48823
a
9
=
−0.00760145u
35
− 0.00731541u
34
+ ··· − 25.6527u + 14.6965
−0.00356648u
35
− 0.00468188u
34
+ ··· − 4.09637u + 1.42748
a
8
=
−0.00760145u
35
− 0.00731541u
34
+ ··· − 25.6527u + 14.6965
−0.00295648u
35
− 0.00407097u
34
+ ··· − 2.44432u + 1.39287
a
12
=
0.00422949u
35
+ 0.00563094u
34
+ ··· + 7.10480u − 7.88797
0.00138215u
35
+ 0.000407795u
34
+ ··· + 8.54688u − 1.12999
a
11
=
0.00561164u
35
+ 0.00603873u
34
+ ··· + 15.6517u − 9.01796
0.00138215u
35
+ 0.000407795u
34
+ ··· + 8.54688u − 1.12999
a
3
=
0.00402228u
35
+ 0.00505346u
34
+ ··· + 1.24783u − 5.21219
−0.00145650u
35
− 0.0000469624u
34
+ ··· − 9.38769u − 0.107969
a
2
=
−0.00308517u
35
− 0.00518618u
34
+ ··· + 5.15203u − 1.65668
0.00104331u
35
+ 0.000744287u
34
+ ··· + 5.57828u − 0.357559
a
7
=
−0.00764445u
35
− 0.00742781u
34
+ ··· − 19.3477u + 13.7010
0.00208970u
35
+ 0.00142347u
34
+ ··· + 4.84956u + 1.05281
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0117322u
35
− 0.0177224u
34
+ ··· + 5.37839u + 0.170272
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
4
c
2
, c
7
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
4
c
3
, c
5
, c
10
c
11
u
36
+ u
35
+ ··· − 356u − 31
c
4
, c
9
u
36
− u
35
+ ··· + 2560u + 121
c
8
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
4
c
12
(u
2
− u − 1)
18
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
4
c
2
, c
7
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
4
c
3
, c
5
, c
10
c
11
y
36
− 13y
35
+ ··· − 49856y + 961
c
4
, c
9
y
36
+ 23y
35
+ ··· − 5714344y + 14641
c
8
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
4
c
12
(y
2
− 3y + 1)
18
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.780953 + 0.638783I
a = 0.474153 − 0.387835I
b = −1.009880 + 0.558025I
−3.33090 + 2.45442I −5.67208 − 2.91298I
u = 0.780953 − 0.638783I
a = 0.474153 + 0.387835I
b = −1.009880 − 0.558025I
−3.33090 − 2.45442I −5.67208 + 2.91298I
u = 0.132026 + 0.843379I
a = −0.29315 + 1.87262I
b = −0.044584 − 1.300520I
4.56478 + 2.45442I −5.67208 − 2.91298I
u = 0.132026 − 0.843379I
a = −0.29315 − 1.87262I
b = −0.044584 + 1.300520I
4.56478 − 2.45442I −5.67208 + 2.91298I
u = −1.009880 + 0.558025I
a = −0.468838 − 0.259064I
b = 0.780953 + 0.638783I
−3.33090 + 2.45442I −5.67208 − 2.91298I
u = −1.009880 − 0.558025I
a = −0.468838 + 0.259064I
b = 0.780953 − 0.638783I
−3.33090 − 2.45442I −5.67208 + 2.91298I
u = −0.358853 + 0.748546I
a = −0.321847 − 0.671353I
b = −1.53825 + 0.06109I
−0.34972 − 7.08493I −2.42320 + 5.91335I
u = −0.358853 − 0.748546I
a = −0.321847 + 0.671353I
b = −1.53825 − 0.06109I
−0.34972 + 7.08493I −2.42320 − 5.91335I
u = 0.417017 + 0.614890I
a = 0.466909 − 0.688456I
b = 1.48241 + 0.01866I
0.423507 + 1.336170I −0.715907 − 0.701750I
u = 0.417017 − 0.614890I
a = 0.466909 + 0.688456I
b = 1.48241 − 0.01866I
0.423507 − 1.336170I −0.715907 + 0.701750I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28654
a = 0.480385
b = 0.0498474
−2.74940 0.652350
u = −0.044584 + 1.300520I
a = 0.042601 + 1.242690I
b = 0.132026 − 0.843379I
4.56478 − 2.45442I −5.67208 + 2.91298I
u = −0.044584 − 1.300520I
a = 0.042601 − 1.242690I
b = 0.132026 + 0.843379I
4.56478 + 2.45442I −5.67208 − 2.91298I
u = 0.491968 + 1.251860I
a = −0.439989 + 1.119590I
b = −0.01428 − 1.56727I
2.16441 − 2.09337I −8.51499 + 4.16283I
u = 0.491968 − 1.251860I
a = −0.439989 − 1.119590I
b = −0.01428 + 1.56727I
2.16441 + 2.09337I −8.51499 − 4.16283I
u = −1.357600 + 0.226779I
a = −0.442882 − 0.073981I
b = 0.106990 + 0.598986I
−5.73128 − 2.09337I −8.51499 + 4.16283I
u = −1.357600 − 0.226779I
a = −0.442882 + 0.073981I
b = 0.106990 − 0.598986I
−5.73128 + 2.09337I −8.51499 − 4.16283I
u = 0.106990 + 0.598986I
a = 0.178600 − 0.999899I
b = −1.357600 + 0.226779I
−5.73128 − 2.09337I −8.51499 + 4.16283I
u = 0.106990 − 0.598986I
a = 0.178600 + 0.999899I
b = −1.357600 − 0.226779I
−5.73128 + 2.09337I −8.51499 − 4.16283I
u = 1.48241 + 0.01866I
a = 0.416845 − 0.005247I
b = 0.417017 + 0.614890I
0.423507 + 1.336170I −0.715907 − 0.701750I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48241 − 0.01866I
a = 0.416845 + 0.005247I
b = 0.417017 − 0.614890I
0.423507 − 1.336170I −0.715907 + 0.701750I
u = −0.25523 + 1.49501I
a = 0.179535 + 1.051640I
b = −0.25523 − 1.49501I
5.14629 − 60.652349 + 0.10I
u = −0.25523 − 1.49501I
a = 0.179535 − 1.051640I
b = −0.25523 + 1.49501I
5.14629 − 60.652349 + 0.10I
u = −1.53825 + 0.06109I
a = −0.401145 − 0.015931I
b = −0.358853 + 0.748546I
−0.34972 − 7.08493I −2.42320 + 5.91335I
u = −1.53825 − 0.06109I
a = −0.401145 + 0.015931I
b = −0.358853 − 0.748546I
−0.34972 + 7.08493I −2.42320 − 5.91335I
u = −0.01428 + 1.56727I
a = 0.009404 + 1.032300I
b = 0.491968 − 1.251860I
2.16441 + 2.09337I −8.51499 − 4.16283I
u = −0.01428 − 1.56727I
a = 0.009404 − 1.032300I
b = 0.491968 + 1.251860I
2.16441 − 2.09337I −8.51499 + 4.16283I
u = 0.68303 + 1.50001I
a = −0.406822 + 0.893434I
b = 0.04160 − 1.80927I
7.54597 − 7.08493I −2.42320 + 5.91335I
u = 0.68303 − 1.50001I
a = −0.406822 − 0.893434I
b = 0.04160 + 1.80927I
7.54597 + 7.08493I −2.42320 − 5.91335I
u = −0.61176 + 1.54868I
a = 0.357003 + 0.903756I
b = −0.11375 − 1.79068I
8.31919 + 1.33617I 0
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.61176 − 1.54868I
a = 0.357003 − 0.903756I
b = −0.11375 + 1.79068I
8.31919 − 1.33617I 0
u = −0.11375 + 1.79068I
a = 0.057170 + 0.899955I
b = −0.61176 − 1.54868I
8.31919 − 1.33617I 0
u = −0.11375 − 1.79068I
a = 0.057170 − 0.899955I
b = −0.61176 + 1.54868I
8.31919 + 1.33617I 0
u = 0.04160 + 1.80927I
a = −0.020553 + 0.893830I
b = 0.68303 − 1.50001I
7.54597 + 7.08493I −4.00000 − 5.91335I
u = 0.04160 − 1.80927I
a = −0.020553 − 0.893830I
b = 0.68303 + 1.50001I
7.54597 − 7.08493I −4.00000 + 5.91335I
u = 0.0498474
a = 12.3985
b = 1.28654
−2.74940 0.652350
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
4
· (u
17
− 6u
16
+ ··· − 18u
2
+ 1)(u
28
+ 9u
27
+ ··· + 84u + 16)
c
2
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
4
· (u
17
+ 3u
15
+ ··· + 2u − 1)(u
28
+ 5u
27
+ ··· + 2u + 4)
c
3
, c
10
(u
17
− u
16
+ ··· + 3u
2
+ 1)(u
28
+ u
27
+ ··· + 4u + 1)
· (u
36
+ u
35
+ ··· − 356u − 31)
c
4
, c
9
(u
17
+ 3u
15
+ ··· − u + 1)(u
28
+ 23u
26
+ ··· + 3u + 1)
· (u
36
− u
35
+ ··· + 2560u + 121)
c
5
, c
11
(u
17
+ u
16
+ ··· − 3u
2
− 1)(u
28
+ u
27
+ ··· + 4u + 1)
· (u
36
+ u
35
+ ··· − 356u − 31)
c
7
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
4
· (u
17
+ 3u
15
+ ··· + 2u + 1)(u
28
+ 5u
27
+ ··· + 2u + 4)
c
8
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
4
· (u
17
− u
15
+ ··· + 2u + 1)(u
28
− 25u
27
+ ··· − 98862u + 9028)
c
12
((u
2
− u − 1)
18
)(u
17
− 6u
16
+ ··· + 2u + 1)
· (u
28
+ 21u
27
+ ··· + 3584u + 512)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
4
· (y
17
+ 14y
16
+ ··· + 36y − 1)(y
28
+ 21y
27
+ ··· + 2064y + 256)
c
2
, c
7
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
4
· (y
17
+ 6y
16
+ ··· + 18y
2
− 1)(y
28
+ 9y
27
+ ··· + 84y + 16)
c
3
, c
5
, c
10
c
11
(y
17
− 11y
16
+ ··· − 6y − 1)(y
28
− 11y
27
+ ··· − 6y + 1)
· (y
36
− 13y
35
+ ··· − 49856y + 961)
c
4
, c
9
(y
17
+ 6y
16
+ ··· + 11y − 1)(y
28
+ 46y
27
+ ··· + 49y + 1)
· (y
36
+ 23y
35
+ ··· − 5714344y + 14641)
c
8
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
4
· (y
17
− 2y
16
+ ··· − 2y − 1)
· (y
28
− 3y
27
+ ··· + 785869044y + 81504784)
c
12
((y
2
− 3y + 1)
18
)(y
17
− 14y
16
+ ··· + 8y − 1)
· (y
28
− 17y
27
+ ··· + 4456448y + 262144)
21
