12n
0252
(K12n
0252
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 9 11 3 6 5 7 10
Solving Sequence
3,8 9,11
7 12 6 5 2 4 10 1
c
8
c
7
c
11
c
6
c
5
c
2
c
4
c
10
c
12
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h1.74295 × 10
297
u
66
+ 2.18772 × 10
297
u
65
+ ··· + 1.47028 × 10
301
b − 2.20085 × 10
301
,
6.14451 × 10
299
u
66
+ 6.93121 × 10
299
u
65
+ ··· + 1.44088 × 10
303
a − 3.76767 × 10
303
,
u
67
+ u
66
+ ··· + 43008u − 25088i
I
u
2
= h94430u
13
− 176465u
12
+ ··· + 3057583b − 933114,
14500551u
13
− 6850118u
12
+ ··· + 3057583a + 662027,
u
14
+ 3u
12
+ 3u
11
− 5u
10
− 4u
9
− 11u
8
− 8u
7
+ 12u
6
− 8u
5
+ 20u
4
+ 6u
2
+ u + 1i
I
v
1
= ha, 82026v
8
− 2033115v
7
+ ··· + 764761b − 1552510,
7v
9
− 3v
8
+ 2v
7
+ 14v
6
− 23v
5
− 33v
4
− v
3
+ 8v
2
+ v −1i
* 3 irreducible components of dim
C
= 0, with total 90 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
= h1.74 × 10
297
u
66
+ 2.19 × 10
297
u
65
+ · · · + 1.47 × 10
301
b − 2.20 ×
10
301
, 6.14 × 10
299
u
66
+ 6.93 × 10
299
u
65
+ · · · + 1.44 × 10
303
a − 3.77 ×
10
303
, u
67
+ u
66
+ · · · + 43008u − 25088i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
−0.000426443u
66
− 0.000481041u
65
+ ··· + 23.8714u + 2.61485
−0.000118545u
66
− 0.000148796u
65
+ ··· + 1.19020u + 1.49689
a
7
=
−0.000247541u
66
− 0.000147912u
65
+ ··· + 24.8866u − 6.57361
−0.0000205091u
66
+ 0.0000421361u
65
+ ··· + 10.5559u − 4.84697
a
12
=
0.000153563u
66
+ 0.000170524u
65
+ ··· − 8.86925u − 0.350734
0.0000954123u
66
+ 0.0000873267u
65
+ ··· − 8.78651u + 0.999057
a
6
=
−0.000167486u
66
− 0.0000324937u
65
+ ··· + 24.9473u − 8.92109
7.23133 × 10
−6
u
66
+ 0.0000863901u
65
+ ··· + 10.0683u − 5.73416
a
5
=
−0.0000140055u
66
− 0.0000216075u
65
+ ··· + 1.31456u + 0.105113
−7.78737 × 10
−6
u
66
− 0.0000120618u
65
+ ··· + 0.998848u − 0.412656
a
2
=
6.21813 × 10
−6
u
66
+ 9.54570 × 10
−6
u
65
+ ··· − 0.315708u − 0.517768
−7.78737 × 10
−6
u
66
− 0.0000120618u
65
+ ··· + 0.998848u − 0.412656
a
4
=
u
u
a
10
=
−0.000359878u
66
− 0.000389095u
65
+ ··· + 22.6042u + 1.99943
−0.0000816759u
66
− 0.0000928007u
65
+ ··· + 1.70659u + 1.44097
a
1
=
−6.21813 × 10
−6
u
66
− 9.54570 × 10
−6
u
65
+ ··· + 0.315708u + 0.517768
4.29248 × 10
−6
u
66
+ 5.85448 × 10
−6
u
65
+ ··· − 0.985959u + 0.496138
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000336583u
66
+ 0.000559671u
65
+ ··· − 0.882700u − 3.59196
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
67
+ 78u
66
+ ··· + 171200u + 2401
c
2
, c
4
u
67
− 16u
66
+ ··· + 120u − 49
c
3
, c
8
u
67
+ u
66
+ ··· + 43008u − 25088
c
5
u
67
+ 4u
66
+ ··· − 2u − 1
c
6
, c
9
u
67
− 3u
66
+ ··· + 781u − 209
c
7
, c
11
u
67
− 2u
66
+ ··· + 3200u − 773
c
10
u
67
+ u
66
+ ··· + 566773u − 256243
c
12
u
67
+ 12u
66
+ ··· − 77902u − 10969
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
67
− 162y
66
+ ··· + 5062883876y −5764801
c
2
, c
4
y
67
− 78y
66
+ ··· + 171200y −2401
c
3
, c
8
y
67
+ 63y
66
+ ··· − 2491940864y −629407744
c
5
y
67
− 10y
66
+ ··· − 44y −1
c
6
, c
9
y
67
+ 33y
66
+ ··· − 240251y −43681
c
7
, c
11
y
67
+ 62y
66
+ ··· − 18480042y −597529
c
10
y
67
+ 43y
66
+ ··· + 161121782381y −65660475049
c
12
y
67
+ 16y
66
+ ··· − 1081596550y −120318961
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.972237 + 0.280854I
a = 0.153697 + 0.835171I
b = 0.437985 + 0.887119I
3.39425 − 2.09087I 8.43522 + 3.94985I
u = −0.972237 − 0.280854I
a = 0.153697 − 0.835171I
b = 0.437985 − 0.887119I
3.39425 + 2.09087I 8.43522 − 3.94985I
u = −0.111044 + 1.030770I
a = −0.447368 − 0.244256I
b = −1.094900 + 0.275542I
0.89656 − 5.19617I 2.00000 + 8.56770I
u = −0.111044 − 1.030770I
a = −0.447368 + 0.244256I
b = −1.094900 − 0.275542I
0.89656 + 5.19617I 2.00000 − 8.56770I
u = 0.502448 + 0.771343I
a = 0.544773 + 0.292063I
b = 0.060296 − 0.570771I
0.42745 + 2.04731I 1.79133 − 2.30943I
u = 0.502448 − 0.771343I
a = 0.544773 − 0.292063I
b = 0.060296 + 0.570771I
0.42745 − 2.04731I 1.79133 + 2.30943I
u = −0.163401 + 0.813880I
a = 0.496846 + 0.323676I
b = 0.477457 + 0.309386I
−1.58473 + 1.12240I −2.95098 − 3.87144I
u = −0.163401 − 0.813880I
a = 0.496846 − 0.323676I
b = 0.477457 − 0.309386I
−1.58473 − 1.12240I −2.95098 + 3.87144I
u = −0.687972 + 0.429990I
a = 1.266640 − 0.347433I
b = −0.201497 + 0.581210I
−2.34582 + 0.79184I −1.70277 + 1.36728I
u = −0.687972 − 0.429990I
a = 1.266640 + 0.347433I
b = −0.201497 − 0.581210I
−2.34582 − 0.79184I −1.70277 − 1.36728I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.423056 + 1.121960I
a = 0.352233 − 0.211840I
b = −0.121837 + 0.470824I
−4.49098 − 4.90499I 0
u = −0.423056 − 1.121960I
a = 0.352233 + 0.211840I
b = −0.121837 − 0.470824I
−4.49098 + 4.90499I 0
u = −0.683441 + 0.994440I
a = 1.027540 + 0.560982I
b = 0.204096 + 1.284980I
−2.72054 + 1.47592I 0
u = −0.683441 − 0.994440I
a = 1.027540 − 0.560982I
b = 0.204096 − 1.284980I
−2.72054 − 1.47592I 0
u = 0.412259 + 0.668041I
a = −1.50421 + 0.97445I
b = −0.172196 − 0.202734I
0.01538 + 1.90218I 1.03416 − 1.99152I
u = 0.412259 − 0.668041I
a = −1.50421 − 0.97445I
b = −0.172196 + 0.202734I
0.01538 − 1.90218I 1.03416 + 1.99152I
u = −0.734728 + 0.191087I
a = 0.112393 − 1.136120I
b = 0.561939 − 0.465578I
3.56178 + 1.95197I 9.44446 − 1.83557I
u = −0.734728 − 0.191087I
a = 0.112393 + 1.136120I
b = 0.561939 + 0.465578I
3.56178 − 1.95197I 9.44446 + 1.83557I
u = 0.705362 + 0.112303I
a = −3.77447 − 2.00026I
b = 0.813283 + 0.575619I
−0.78374 + 3.24647I 3.36554 − 8.05825I
u = 0.705362 − 0.112303I
a = −3.77447 + 2.00026I
b = 0.813283 − 0.575619I
−0.78374 − 3.24647I 3.36554 + 8.05825I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.489130 + 0.496557I
a = 0.706509 + 0.025107I
b = −0.474253 − 0.853751I
0.85096 + 2.02536I 5.69785 − 3.31418I
u = 0.489130 − 0.496557I
a = 0.706509 − 0.025107I
b = −0.474253 + 0.853751I
0.85096 − 2.02536I 5.69785 + 3.31418I
u = 0.058657 + 0.664653I
a = 3.17421 − 5.05999I
b = 0.191481 − 0.813702I
0.17719 − 3.22158I −2.38086 + 5.47011I
u = 0.058657 − 0.664653I
a = 3.17421 + 5.05999I
b = 0.191481 + 0.813702I
0.17719 + 3.22158I −2.38086 − 5.47011I
u = 0.028062 + 0.629541I
a = 0.49260 + 4.74733I
b = −0.14410 + 1.55613I
−3.79798 − 0.21805I −3.18632 − 4.76372I
u = 0.028062 − 0.629541I
a = 0.49260 − 4.74733I
b = −0.14410 − 1.55613I
−3.79798 + 0.21805I −3.18632 + 4.76372I
u = 0.580709 + 0.074213I
a = −0.089310 − 0.454917I
b = 0.661587 − 1.030950I
2.35238 − 6.89299I 11.67033 + 2.73841I
u = 0.580709 − 0.074213I
a = −0.089310 + 0.454917I
b = 0.661587 + 1.030950I
2.35238 + 6.89299I 11.67033 − 2.73841I
u = −0.568924 + 0.015800I
a = 0.637282 + 0.021987I
b = −0.145375 + 1.079460I
−2.33563 − 2.09946I 2.27732 + 3.69468I
u = −0.568924 − 0.015800I
a = 0.637282 − 0.021987I
b = −0.145375 − 1.079460I
−2.33563 + 2.09946I 2.27732 − 3.69468I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.22902 + 1.42563I
a = 0.400700 + 0.341672I
b = −0.973416 + 0.760612I
−4.88346 − 3.38279I 0
u = −0.22902 − 1.42563I
a = 0.400700 − 0.341672I
b = −0.973416 − 0.760612I
−4.88346 + 3.38279I 0
u = −0.06118 + 1.47148I
a = −0.29720 − 1.59844I
b = 0.29319 − 1.42982I
−7.03108 − 4.31642I 0
u = −0.06118 − 1.47148I
a = −0.29720 + 1.59844I
b = 0.29319 + 1.42982I
−7.03108 + 4.31642I 0
u = −0.116938 + 0.471533I
a = 1.48070 + 0.04601I
b = −0.579484 − 0.806307I
0.98108 + 2.41958I 3.63595 + 0.97039I
u = −0.116938 − 0.471533I
a = 1.48070 − 0.04601I
b = −0.579484 + 0.806307I
0.98108 − 2.41958I 3.63595 − 0.97039I
u = 1.50349 + 0.34050I
a = 0.228982 + 0.612751I
b = −0.015855 + 0.949567I
2.74618 + 3.31023I 0
u = 1.50349 − 0.34050I
a = 0.228982 − 0.612751I
b = −0.015855 − 0.949567I
2.74618 − 3.31023I 0
u = 1.55291 + 0.23943I
a = 0.441195 − 0.352617I
b = −0.16237 − 1.50460I
−8.96576 + 1.05371I 0
u = 1.55291 − 0.23943I
a = 0.441195 + 0.352617I
b = −0.16237 + 1.50460I
−8.96576 − 1.05371I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.52715 + 1.48204I
a = 0.33123 + 1.39860I
b = 0.00718 + 1.48631I
−6.16260 − 2.01828I 0
u = −0.52715 − 1.48204I
a = 0.33123 − 1.39860I
b = 0.00718 − 1.48631I
−6.16260 + 2.01828I 0
u = 0.413083
a = 0.972725
b = −0.464092
0.931638 11.2120
u = 0.14745 + 1.66191I
a = 0.18463 + 1.55098I
b = −0.037097 + 1.367450I
−8.02419 + 4.33010I 0
u = 0.14745 − 1.66191I
a = 0.18463 − 1.55098I
b = −0.037097 − 1.367450I
−8.02419 − 4.33010I 0
u = 0.45724 + 1.63971I
a = −0.105350 − 0.203867I
b = −1.68138 − 0.13047I
−6.70242 + 8.43737I 0
u = 0.45724 − 1.63971I
a = −0.105350 + 0.203867I
b = −1.68138 + 0.13047I
−6.70242 − 8.43737I 0
u = 0.05684 + 1.70857I
a = 0.180435 − 1.130630I
b = −0.67565 − 1.87495I
−12.22050 + 0.78224I 0
u = 0.05684 − 1.70857I
a = 0.180435 + 1.130630I
b = −0.67565 + 1.87495I
−12.22050 − 0.78224I 0
u = −0.13255 + 1.73913I
a = −0.171385 − 0.159888I
b = 1.169480 − 0.041809I
−10.39740 − 2.64649I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13255 − 1.73913I
a = −0.171385 + 0.159888I
b = 1.169480 + 0.041809I
−10.39740 + 2.64649I 0
u = 0.41326 + 1.75472I
a = 0.181612 − 1.340600I
b = −0.39611 − 1.52166I
−5.00803 + 10.48120I 0
u = 0.41326 − 1.75472I
a = 0.181612 + 1.340600I
b = −0.39611 + 1.52166I
−5.00803 − 10.48120I 0
u = 0.65145 + 1.69788I
a = −0.683854 + 1.063280I
b = 0.60126 + 1.43364I
−14.9522 + 8.9665I 0
u = 0.65145 − 1.69788I
a = −0.683854 − 1.063280I
b = 0.60126 − 1.43364I
−14.9522 − 8.9665I 0
u = 0.92464 + 1.58340I
a = 0.504493 − 1.126250I
b = −0.26248 − 1.61175I
−12.8012 + 7.6595I 0
u = 0.92464 − 1.58340I
a = 0.504493 + 1.126250I
b = −0.26248 + 1.61175I
−12.8012 − 7.6595I 0
u = −0.91168 + 1.66821I
a = 0.578974 + 1.151070I
b = −0.65416 + 1.61603I
−12.2648 − 16.4135I 0
u = −0.91168 − 1.66821I
a = 0.578974 − 1.151070I
b = −0.65416 − 1.61603I
−12.2648 + 16.4135I 0
u = 0.07685 + 1.90361I
a = −0.199072 + 1.200950I
b = −0.07346 + 1.43637I
−5.56017 − 2.92233I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07685 − 1.90361I
a = −0.199072 − 1.200950I
b = −0.07346 − 1.43637I
−5.56017 + 2.92233I 0
u = −1.91592 + 0.19283I
a = 0.054081 + 0.394492I
b = 0.22984 + 1.53586I
−7.74590 + 6.82406I 0
u = −1.91592 − 0.19283I
a = 0.054081 − 0.394492I
b = 0.22984 − 1.53586I
−7.74590 − 6.82406I 0
u = −0.29235 + 2.06576I
a = −0.133137 − 0.969631I
b = 0.94220 − 1.66248I
−13.6589 − 4.4760I 0
u = −0.29235 − 2.06576I
a = −0.133137 + 0.969631I
b = 0.94220 + 1.66248I
−13.6589 + 4.4760I 0
u = −0.73570 + 2.03169I
a = −0.449491 − 0.922084I
b = 0.44638 − 1.35702I
−14.4098 − 3.1017I 0
u = −0.73570 − 2.03169I
a = −0.449491 + 0.922084I
b = 0.44638 + 1.35702I
−14.4098 + 3.1017I 0
11
II. I
u
2
= h9.44 × 10
4
u
13
− 1.76 × 10
5
u
12
+ · · · + 3.06 × 10
6
b − 9.33 × 10
5
, 1.45 ×
10
7
u
13
− 6.85 × 10
6
u
12
+ · · · + 3.06 × 10
6
a + 6.62 × 10
5
, u
14
+ 3u
12
+ · · · + u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
11
=
−4.74249u
13
+ 2.24037u
12
+ ··· − 19.2443u − 0.216520
−0.0308839u
13
+ 0.0577139u
12
+ ··· − 1.36605u + 0.305180
a
7
=
−4.09128u
13
− 0.679940u
12
+ ··· − 7.20444u − 8.41674
−0.316204u
13
− 0.0156306u
12
+ ··· − 1.02247u − 0.0647390
a
12
=
−3.61004u
13
+ 0.407185u
12
+ ··· − 9.65877u − 7.47936
0.0490374u
13
− 0.177945u
12
+ ··· − 2.06678u − 0.528005
a
6
=
−3.45688u
13
− 0.525854u
12
+ ··· − 3.45569u − 7.80154
−0.366126u
13
+ 0.0265635u
12
+ ··· − 0.233986u + 0.0893477
a
5
=
0.671228u
13
− 0.305180u
12
+ ··· + 3.86235u + 0.615272
−0.0499215u
13
+ 0.0421941u
12
+ ··· + 0.788488u + 0.154087
a
2
=
−0.721149u
13
+ 0.347374u
12
+ ··· − 3.07386u − 0.461186
−0.0499215u
13
+ 0.0421941u
12
+ ··· + 0.788488u + 0.154087
a
4
=
u
u
a
10
=
−3.70513u
13
+ 1.90863u
12
+ ··· − 15.1479u − 0.690595
0.123441u
13
− 0.00225636u
12
+ ··· − 1.44893u − 0.180650
a
1
=
−0.721149u
13
+ 0.347374u
12
+ ··· − 3.07386u − 0.461186
−0.0528928u
13
+ 0.242971u
12
+ ··· + 0.414713u + 0.501461
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1775462
3057583
u
13
−
19500832
3057583
u
12
+ ··· +
38299827
3057583
u −
57496355
3057583
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
14
− 14u
13
+ ··· − 5u + 1
c
2
u
14
+ 6u
13
+ ··· − 3u + 1
c
3
u
14
+ 3u
12
+ ··· − u + 1
c
4
u
14
− 6u
13
+ ··· + 3u + 1
c
5
u
14
− 6u
13
+ ··· − 3u + 1
c
6
u
14
− 3u
13
+ ··· + 7u
2
+ 1
c
7
u
14
+ 7u
12
+ ··· + 3u + 1
c
8
u
14
+ 3u
12
+ ··· + u + 1
c
9
u
14
+ 3u
13
+ ··· + 7u
2
+ 1
c
10
u
14
+ 3u
13
+ ··· + 6u + 1
c
11
u
14
+ 7u
12
+ ··· − 3u + 1
c
12
u
14
+ 2u
12
+ ··· − 5u + 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
− 22y
13
+ ··· + 143y + 1
c
2
, c
4
y
14
− 14y
13
+ ··· − 5y + 1
c
3
, c
8
y
14
+ 6y
13
+ ··· + 11y + 1
c
5
y
14
− 10y
13
+ ··· − 5y + 1
c
6
, c
9
y
14
+ 9y
13
+ ··· + 14y + 1
c
7
, c
11
y
14
+ 14y
13
+ ··· + 9y + 1
c
10
y
14
− 5y
13
+ ··· − 10y + 1
c
12
y
14
+ 4y
13
+ ··· + 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.139126 + 0.855284I
a = 1.28622 − 2.46844I
b = 0.10927 − 1.56543I
−3.95141 − 0.77135I −5.32487 + 5.66602I
u = 0.139126 − 0.855284I
a = 1.28622 + 2.46844I
b = 0.10927 + 1.56543I
−3.95141 + 0.77135I −5.32487 − 5.66602I
u = −0.352449 + 1.175430I
a = 0.288296 − 0.319682I
b = −0.341781 + 0.418746I
−4.21220 − 5.05550I 8.55629 + 11.07069I
u = −0.352449 − 1.175430I
a = 0.288296 + 0.319682I
b = −0.341781 − 0.418746I
−4.21220 + 5.05550I 8.55629 − 11.07069I
u = 1.229090 + 0.054546I
a = −0.142585 − 0.788390I
b = −0.262265 − 0.901818I
3.33140 + 3.93339I 7.31083 − 8.00848I
u = 1.229090 − 0.054546I
a = −0.142585 + 0.788390I
b = −0.262265 + 0.901818I
3.33140 − 3.93339I 7.31083 + 8.00848I
u = 0.196848 + 0.556043I
a = 0.05395 + 1.80422I
b = −0.381345 − 0.641179I
1.09831 + 3.21998I 6.98104 − 7.97611I
u = 0.196848 − 0.556043I
a = 0.05395 − 1.80422I
b = −0.381345 + 0.641179I
1.09831 − 3.21998I 6.98104 + 7.97611I
u = −1.40215 + 0.37579I
a = −0.112945 − 0.655306I
b = −0.283501 − 1.095790I
2.59518 − 1.77882I −1.86373 − 1.12551I
u = −1.40215 − 0.37579I
a = −0.112945 + 0.655306I
b = −0.283501 + 1.095790I
2.59518 + 1.77882I −1.86373 + 1.12551I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.229849 + 0.360057I
a = −7.66848 − 11.11940I
b = 0.420766 − 0.730987I
−0.20979 − 2.65520I −8.5897 + 20.4516I
u = −0.229849 − 0.360057I
a = −7.66848 + 11.11940I
b = 0.420766 + 0.730987I
−0.20979 + 2.65520I −8.5897 − 20.4516I
u = 0.41939 + 2.04733I
a = −0.204449 + 0.988880I
b = 0.73885 + 1.60027I
−13.45590 + 4.02567I 2.43011 + 2.33585I
u = 0.41939 − 2.04733I
a = −0.204449 − 0.988880I
b = 0.73885 − 1.60027I
−13.45590 − 4.02567I 2.43011 − 2.33585I
18
III. I
v
1
= ha, 8.20 × 10
4
v
8
− 2.03 × 10
6
v
7
+ · · · + 7.65 × 10
5
b − 1.55 ×
10
6
, 7v
9
− 3v
8
+ · · · + v − 1i
(i) Arc colorings
a
3
=
v
0
a
8
=
1
0
a
9
=
1
0
a
11
=
0
−0.107257v
8
+ 2.65850v
7
+ ··· − 0.280187v + 2.03006
a
7
=
1
2.14626v
8
+ 0.185889v
7
+ ··· − 0.429870v + 1.30771
a
12
=
−0.107257v
8
+ 2.65850v
7
+ ··· − 0.280187v + 2.03006
−1.38456v
8
+ 4.21937v
7
+ ··· − 2.55986v + 1.77273
a
6
=
2.14626v
8
+ 0.185889v
7
+ ··· − 0.429870v + 2.30771
2.14626v
8
+ 0.185889v
7
+ ··· − 0.429870v + 1.30771
a
5
=
−1.01346v
8
− 0.464403v
7
+ ··· + 1.07485v + 0.182471
7v
8
− 3v
7
+ 2v
6
+ 14v
5
− 23v
4
− 33v
3
− v
2
+ 8v + 1
a
2
=
1.01346v
8
+ 0.464403v
7
+ ··· − 0.0748548v − 0.182471
−7v
8
+ 3v
7
− 2v
6
− 14v
5
+ 23v
4
+ 33v
3
+ v
2
− 8v − 1
a
4
=
v
0
a
10
=
−5.30121v
8
+ 5.22147v
7
+ ··· − 3.83160v + 0.359036
−7.44747v
8
+ 5.03558v
7
+ ··· − 3.40173v − 1.94867
a
1
=
1.01346v
8
+ 0.464403v
7
+ ··· − 1.07485v − 0.182471
−7v
8
+ 3v
7
− 2v
6
− 14v
5
+ 23v
4
+ 33v
3
+ v
2
− 8v − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
17698695
764761
v
8
−
786460
764761
v
7
−
4755547
764761
v
6
−
34014228
764761
v
5
+
35615785
764761
v
4
+
111023508
764761
v
3
+
50152809
764761
v
2
−
10570795
764761
v −
8852191
764761
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
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
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
9
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
10
, c
12
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
9
c
3
, c
8
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
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1
c
7
, 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
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.903964 + 0.094390I
a = 0
b = −0.140343 + 0.966856I
−3.42837 − 2.09337I −6.50768 + 4.08340I
v = −0.903964 − 0.094390I
a = 0
b = −0.140343 − 0.966856I
−3.42837 + 2.09337I −6.50768 − 4.08340I
v = 1.42091
a = 0
b = −0.512358
−0.446489 2.13810
v = −0.476406 + 0.294981I
a = 0
b = 0.796005 + 0.733148I
2.72642 − 1.33617I 1.72452 − 1.86826I
v = −0.476406 − 0.294981I
a = 0
b = 0.796005 − 0.733148I
2.72642 + 1.33617I 1.72452 + 1.86826I
v = 0.352455 + 0.113243I
a = 0
b = 0.728966 − 0.986295I
1.95319 − 7.08493I −4.46574 + 10.08360I
v = 0.352455 − 0.113243I
a = 0
b = 0.728966 + 0.986295I
1.95319 + 7.08493I −4.46574 − 10.08360I
v = 0.53175 + 1.59553I
a = 0
b = −0.628449 + 0.875112I
−1.02799 − 2.45442I 0.87375 + 1.42824I
v = 0.53175 − 1.59553I
a = 0
b = −0.628449 − 0.875112I
−1.02799 + 2.45442I 0.87375 − 1.42824I
22
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
14
− 14u
13
+ ··· − 5u + 1)
· (u
67
+ 78u
66
+ ··· + 171200u + 2401)
c
2
((u − 1)
9
)(u
14
+ 6u
13
+ ··· − 3u + 1)(u
67
− 16u
66
+ ··· + 120u − 49)
c
3
u
9
(u
14
+ 3u
12
+ ··· − u + 1)(u
67
+ u
66
+ ··· + 43008u − 25088)
c
4
((u + 1)
9
)(u
14
− 6u
13
+ ··· + 3u + 1)(u
67
− 16u
66
+ ··· + 120u − 49)
c
5
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
14
− 6u
13
+ ··· − 3u + 1)(u
67
+ 4u
66
+ ··· − 2u − 1)
c
6
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
14
− 3u
13
+ ··· + 7u
2
+ 1)(u
67
− 3u
66
+ ··· + 781u − 209)
c
7
(u
9
− u
8
+ ··· + u + 1)(u
14
+ 7u
12
+ ··· + 3u + 1)
· (u
67
− 2u
66
+ ··· + 3200u − 773)
c
8
u
9
(u
14
+ 3u
12
+ ··· + u + 1)(u
67
+ u
66
+ ··· + 43008u − 25088)
c
9
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
14
+ 3u
13
+ ··· + 7u
2
+ 1)(u
67
− 3u
66
+ ··· + 781u − 209)
c
10
(u
9
+ u
8
+ ··· − u − 1)(u
14
+ 3u
13
+ ··· + 6u + 1)
· (u
67
+ u
66
+ ··· + 566773u − 256243)
c
11
(u
9
+ u
8
+ ··· + u − 1)(u
14
+ 7u
12
+ ··· − 3u + 1)
· (u
67
− 2u
66
+ ··· + 3200u − 773)
c
12
(u
9
+ u
8
+ ··· − u − 1)(u
14
+ 2u
12
+ ··· − 5u + 1)
· (u
67
+ 12u
66
+ ··· − 77902u − 10969)
23
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
14
− 22y
13
+ ··· + 143y + 1)
· (y
67
− 162y
66
+ ··· + 5062883876y − 5764801)
c
2
, c
4
((y − 1)
9
)(y
14
− 14y
13
+ ··· − 5y + 1)
· (y
67
− 78y
66
+ ··· + 171200y − 2401)
c
3
, c
8
y
9
(y
14
+ 6y
13
+ ··· + 11y + 1)
· (y
67
+ 63y
66
+ ··· − 2491940864y − 629407744)
c
5
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
14
− 10y
13
+ ··· − 5y + 1)(y
67
− 10y
66
+ ··· − 44y − 1)
c
6
, c
9
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
14
+ 9y
13
+ ··· + 14y + 1)(y
67
+ 33y
66
+ ··· − 240251y − 43681)
c
7
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
14
+ 14y
13
+ ··· + 9y + 1)
· (y
67
+ 62y
66
+ ··· − 18480042y − 597529)
c
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
14
− 5y
13
+ ··· − 10y + 1)
· (y
67
+ 43y
66
+ ··· + 161121782381y − 65660475049)
c
12
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
14
+ 4y
13
+ ··· + 5y + 1)
· (y
67
+ 16y
66
+ ··· − 1081596550y − 120318961)
24
