12a
0553
(K12a
0553
)
A knot diagram
1
Linearized knot diagam
3 7 8 12 10 2 6 11 5 1 4 9
Solving Sequence
4,11
12
5,9
1 8 3 2 10 6 7
c
11
c
4
c
12
c
8
c
3
c
1
c
10
c
5
c
7
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.25623 × 10
23
u
41
+ 9.66993 × 10
22
u
40
+ ··· + 3.04045 × 10
23
b + 5.01776 × 10
23
,
− 4.05453 × 10
23
u
41
− 3.26106 × 10
23
u
40
+ ··· + 3.04045 × 10
23
a − 8.85169 × 10
23
, u
42
+ u
41
+ ··· + 5u + 1i
I
u
2
= h−1.69030 × 10
239
u
79
+ 4.53403 × 10
239
u
78
+ ··· + 5.27838 × 10
239
b + 3.07543 × 10
239
,
4.23498 × 10
239
u
79
− 1.43076 × 10
239
u
78
+ ··· + 5.27838 × 10
239
a + 5.44531 × 10
240
, u
80
− u
79
+ ··· + 16u + 1i
I
u
3
= hu
2
+ b − 1, u
19
+ u
18
+ ··· + a + 2, u
20
+ u
19
+ ··· + 6u − 1i
* 3 irreducible components of dim
C
= 0, with total 142 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
= h2.26×10
23
u
41
+9.67×10
22
u
40
+· · ·+3.04×10
23
b+5.02×10
23
, −4.05×
10
23
u
41
−3.26×10
23
u
40
+· · ·+3.04×10
23
a−8.85×10
23
, u
42
+u
41
+· · ·+5u+1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
1.33353u
41
+ 1.07256u
40
+ ··· + 5.15836u + 2.91131
−0.742070u
41
− 0.318043u
40
+ ··· − 5.18702u − 1.65034
a
1
=
−0.356219u
41
− 0.656913u
40
+ ··· + 1.83103u + 1.56167
0.742070u
41
+ 0.318043u
40
+ ··· + 5.18702u + 1.65034
a
8
=
2.07560u
41
+ 1.39060u
40
+ ··· + 10.3454u + 4.56165
−0.742070u
41
− 0.318043u
40
+ ··· − 5.18702u − 1.65034
a
3
=
−0.137641u
41
− 0.218884u
40
+ ··· + 0.646429u − 0.235243
−0.424027u
41
− 0.699003u
40
+ ··· − 1.06001u − 0.742070
a
2
=
0.682566u
41
+ 0.629255u
40
+ ··· + 0.728245u + 1.43319
1.27131u
41
+ 1.19520u
40
+ ··· + 4.41786u + 1.76416
a
10
=
1.33353u
41
+ 1.07256u
40
+ ··· + 5.15836u + 2.91131
−0.742070u
41
− 0.318043u
40
+ ··· − 5.18702u − 1.65034
a
6
=
0.260974u
41
− 0.330487u
40
+ ··· + 2.75635u + 1.33353
−0.424027u
41
− 0.699003u
40
+ ··· − 1.06001u − 0.742070
a
7
=
1.01423u
41
− 0.256599u
40
+ ··· + 12.9428u + 5.13247
−1.27131u
41
− 1.19520u
40
+ ··· − 4.41786u − 1.76416
(ii) Obstruction class = −1
(iii) Cusp Shapes =
758348575428048311643999
304044864012407159949563
u
41
−
189703780989871384844127
304044864012407159949563
u
40
+ ··· −
773024156845572154682826
304044864012407159949563
u −
2397936412798830570628702
304044864012407159949563
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
42
+ 14u
41
+ ··· + 92u + 16
c
2
, c
6
u
42
− 6u
41
+ ··· + 26u − 4
c
3
u
42
+ 6u
41
+ ··· − 97086u − 58612
c
4
, c
5
, c
9
c
11
u
42
+ u
41
+ ··· + 5u + 1
c
8
, c
10
u
42
− 3u
41
+ ··· − 4u − 1
c
12
u
42
− 44u
41
+ ··· + 18874368u − 1048576
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
42
+ 26y
41
+ ··· + 10512y + 256
c
2
, c
6
y
42
− 14y
41
+ ··· − 92y + 16
c
3
y
42
− 22y
41
+ ··· − 37177652828y + 3435366544
c
4
, c
5
, c
9
c
11
y
42
− 33y
41
+ ··· − 5y + 1
c
8
, c
10
y
42
+ 5y
41
+ ··· − 102y + 1
c
12
y
42
+ 4y
41
+ ··· − 24739011624960y + 1099511627776
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.129110 + 0.837718I
a = 0.208797 + 0.545010I
b = 0.766049 − 0.963564I
1.83605 − 7.68678I −3.96818 + 6.98985I
u = −0.129110 − 0.837718I
a = 0.208797 − 0.545010I
b = 0.766049 + 0.963564I
1.83605 + 7.68678I −3.96818 − 6.98985I
u = −1.183880 + 0.049134I
a = −1.11857 + 1.10941I
b = 0.682568 + 0.572973I
−3.35379 + 2.88258I −9.71297 − 5.70027I
u = −1.183880 − 0.049134I
a = −1.11857 − 1.10941I
b = 0.682568 − 0.572973I
−3.35379 − 2.88258I −9.71297 + 5.70027I
u = −1.186440 + 0.119570I
a = −0.77152 − 2.13314I
b = 0.091296 − 0.620171I
−5.41447 + 1.52315I −20.8164 − 2.3413I
u = −1.186440 − 0.119570I
a = −0.77152 + 2.13314I
b = 0.091296 + 0.620171I
−5.41447 − 1.52315I −20.8164 + 2.3413I
u = 0.154286 + 0.788847I
a = 0.196401 − 0.509540I
b = 0.810088 + 0.862295I
2.84163 + 2.23994I −1.58112 − 1.75265I
u = 0.154286 − 0.788847I
a = 0.196401 + 0.509540I
b = 0.810088 − 0.862295I
2.84163 − 2.23994I −1.58112 + 1.75265I
u = −1.130060 + 0.426134I
a = 0.34478 − 1.74706I
b = −0.649711 − 0.498795I
0.35921 + 3.98317I −5.18876 − 5.91925I
u = −1.130060 − 0.426134I
a = 0.34478 + 1.74706I
b = −0.649711 + 0.498795I
0.35921 − 3.98317I −5.18876 + 5.91925I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.213330 + 0.075694I
a = −0.94606 − 1.09355I
b = 0.759589 − 0.683845I
−4.83918 − 8.81290I −11.6564 + 8.5892I
u = 1.213330 − 0.075694I
a = −0.94606 + 1.09355I
b = 0.759589 + 0.683845I
−4.83918 + 8.81290I −11.6564 − 8.5892I
u = 0.005260 + 0.776538I
a = 0.315859 + 0.529708I
b = 0.489355 − 0.846533I
−2.63776 − 2.01463I −9.50411 + 3.62154I
u = 0.005260 − 0.776538I
a = 0.315859 − 0.529708I
b = 0.489355 + 0.846533I
−2.63776 + 2.01463I −9.50411 − 3.62154I
u = 0.215406 + 0.717843I
a = 0.498976 + 0.594478I
b = 0.083209 − 0.718916I
1.03284 + 3.43933I −5.25606 − 1.29339I
u = 0.215406 − 0.717843I
a = 0.498976 − 0.594478I
b = 0.083209 + 0.718916I
1.03284 − 3.43933I −5.25606 + 1.29339I
u = 1.250870 + 0.029270I
a = −0.86186 + 1.52627I
b = 0.402311 + 0.797420I
−10.43820 + 1.64027I −19.3366 − 4.1061I
u = 1.250870 − 0.029270I
a = −0.86186 − 1.52627I
b = 0.402311 − 0.797420I
−10.43820 − 1.64027I −19.3366 + 4.1061I
u = 1.183600 + 0.466397I
a = 0.26597 + 1.64501I
b = −0.767402 + 0.595298I
−0.04073 − 10.00640I −6.00000 + 9.99752I
u = 1.183600 − 0.466397I
a = 0.26597 − 1.64501I
b = −0.767402 − 0.595298I
−0.04073 + 10.00640I −6.00000 − 9.99752I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.275990 + 0.184603I
a = −0.37506 + 1.80775I
b = −0.074450 + 0.897247I
−8.35329 − 6.18961I −17.4347 + 7.3045I
u = 1.275990 − 0.184603I
a = −0.37506 − 1.80775I
b = −0.074450 − 0.897247I
−8.35329 + 6.18961I −17.4347 − 7.3045I
u = −0.540941 + 0.438454I
a = −0.141478 + 0.341563I
b = 1.289300 − 0.240168I
4.31778 + 3.64803I −4.57023 − 8.96524I
u = −0.540941 − 0.438454I
a = −0.141478 − 0.341563I
b = 1.289300 + 0.240168I
4.31778 − 3.64803I −4.57023 + 8.96524I
u = 0.468364 + 0.499939I
a = −0.071909 − 0.357763I
b = 1.241650 + 0.335026I
4.66986 + 1.75891I −1.95443 + 2.74065I
u = 0.468364 − 0.499939I
a = −0.071909 + 0.357763I
b = 1.241650 − 0.335026I
4.66986 − 1.75891I −1.95443 − 2.74065I
u = −0.267732 + 0.602998I
a = 0.630356 − 0.557804I
b = 0.005521 + 0.517110I
1.74525 + 1.74697I −3.78653 − 4.83256I
u = −0.267732 − 0.602998I
a = 0.630356 + 0.557804I
b = 0.005521 − 0.517110I
1.74525 − 1.74697I −3.78653 + 4.83256I
u = 0.088989 + 0.553108I
a = 0.258260 − 0.292992I
b = 0.693618 + 0.405730I
1.27279 + 1.01412I 1.95077 − 3.41118I
u = 0.088989 − 0.553108I
a = 0.258260 + 0.292992I
b = 0.693618 − 0.405730I
1.27279 − 1.01412I 1.95077 + 3.41118I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42369 + 0.44997I
a = 0.01185 + 1.47417I
b = −0.87902 + 1.23053I
−7.37891 − 9.51051I 0
u = 1.42369 − 0.44997I
a = 0.01185 − 1.47417I
b = −0.87902 − 1.23053I
−7.37891 + 9.51051I 0
u = −1.44107 + 0.39945I
a = −0.03941 − 1.48174I
b = −0.74204 − 1.31355I
−9.51277 + 4.75387I 0
u = −1.44107 − 0.39945I
a = −0.03941 + 1.48174I
b = −0.74204 + 1.31355I
−9.51277 − 4.75387I 0
u = −0.467313
a = −0.190127
b = 1.14861
0.327792 −22.7930
u = −1.47914 + 0.46825I
a = 0.00076 − 1.42482I
b = −0.97294 − 1.38112I
−12.2925 + 11.8405I 0
u = −1.47914 − 0.46825I
a = 0.00076 + 1.42482I
b = −0.97294 + 1.38112I
−12.2925 − 11.8405I 0
u = 1.46466 + 0.51916I
a = 0.039566 + 1.412300I
b = −1.11314 + 1.29694I
−5.76180 − 12.68780I 0
u = 1.46466 − 0.51916I
a = 0.039566 − 1.412300I
b = −1.11314 − 1.29694I
−5.76180 + 12.68780I 0
u = −1.48417 + 0.52390I
a = 0.033655 − 1.398890I
b = −1.14418 − 1.35093I
−7.0633 + 18.4553I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48417 − 0.52390I
a = 0.033655 + 1.398890I
b = −1.14418 + 1.35093I
−7.0633 − 18.4553I 0
u = −0.336499
a = 1.23139
b = −0.0919546
−0.740467 −14.2860
9
II. I
u
2
= h−1.69 × 10
239
u
79
+ 4.53 × 10
239
u
78
+ · · · + 5.28 × 10
239
b + 3.08 ×
10
239
, 4.23 × 10
239
u
79
− 1.43 × 10
239
u
78
+ · · · + 5.28 × 10
239
a + 5.45 ×
10
240
, u
80
− u
79
+ · · · + 16u + 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−0.802325u
79
+ 0.271060u
78
+ ··· − 1089.56u − 10.3162
0.320231u
79
− 0.858981u
78
+ ··· − 20.8795u − 0.582647
a
1
=
−0.516068u
79
+ 0.487109u
78
+ ··· − 516.254u + 26.4919
−0.202847u
79
+ 0.477995u
78
+ ··· − 29.2026u − 0.0849526
a
8
=
−1.12256u
79
+ 1.13004u
78
+ ··· − 1068.68u − 9.73360
0.320231u
79
− 0.858981u
78
+ ··· − 20.8795u − 0.582647
a
3
=
−1.80579u
79
+ 1.76789u
78
+ ··· − 1294.87u − 2.86959
−0.636707u
79
+ 1.41921u
78
+ ··· − 39.0595u − 1.05782
a
2
=
0.876128u
79
− 0.791821u
78
+ ··· + 867.674u + 19.7324
0.852252u
79
− 1.81244u
78
+ ··· + 21.8245u + 1.25344
a
10
=
−1.03160u
79
+ 0.833907u
78
+ ··· − 1094.09u − 10.5337
0.161944u
79
− 0.475631u
78
+ ··· − 21.4547u − 0.698779
a
6
=
1.94294u
79
− 2.11379u
78
+ ··· + 1397.76u + 4.71417
−0.448779u
79
+ 0.963456u
78
+ ··· + 30.0345u + 0.437105
a
7
=
0.731095u
79
− 0.879762u
78
+ ··· + 444.056u − 14.4550
−0.724590u
79
+ 1.48433u
78
+ ··· + 9.28280u − 0.670444
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.89162u
79
+ 4.42072u
78
+ ··· − 12.3040u − 15.1389
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
20
+ 7u
19
+ ··· + 6u + 1)
4
c
2
, c
6
(u
20
+ u
19
+ ··· + 3u
2
− 1)
4
c
3
(u
20
− u
19
+ ··· + 4u − 1)
4
c
4
, c
5
, c
9
c
11
u
80
− u
79
+ ··· + 16u + 1
c
8
, c
10
u
80
+ 23u
79
+ ··· + 798776u + 37537
c
12
(u
2
+ u + 1)
40
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
20
+ 13y
19
+ ··· − 6y + 1)
4
c
2
, c
6
(y
20
− 7y
19
+ ··· − 6y + 1)
4
c
3
(y
20
− 11y
19
+ ··· − 6y + 1)
4
c
4
, c
5
, c
9
c
11
y
80
− 69y
79
+ ··· + 1440y + 1
c
8
, c
10
y
80
+ 27y
79
+ ··· + 9352736088y + 1409026369
c
12
(y
2
+ y + 1)
40
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.207784 + 0.987527I
a = 0.445184 − 0.154793I
b = −0.851402 − 0.539056I
3.03993 + 4.87637I 0
u = 0.207784 − 0.987527I
a = 0.445184 + 0.154793I
b = −0.851402 + 0.539056I
3.03993 − 4.87637I 0
u = −0.951078 + 0.228099I
a = 0.55710 + 1.83713I
b = 0.772031 + 0.458447I
3.03993 − 0.81660I 0
u = −0.951078 − 0.228099I
a = 0.55710 − 1.83713I
b = 0.772031 − 0.458447I
3.03993 + 0.81660I 0
u = 0.996696 + 0.266242I
a = 0.44755 − 1.84281I
b = 0.890900 − 0.596478I
3.03993 − 4.87637I 0
u = 0.996696 − 0.266242I
a = 0.44755 + 1.84281I
b = 0.890900 + 0.596478I
3.03993 + 4.87637I 0
u = −0.275813 + 0.910568I
a = 0.560339 + 0.160187I
b = −0.841509 + 0.463941I
3.03993 + 0.81660I 0
u = −0.275813 − 0.910568I
a = 0.560339 − 0.160187I
b = −0.841509 − 0.463941I
3.03993 − 0.81660I 0
u = −0.240644 + 1.064020I
a = 0.010895 − 0.165200I
b = −0.596302 − 0.694141I
−2.17062 + 4.19124I 0
u = −0.240644 − 1.064020I
a = 0.010895 + 0.165200I
b = −0.596302 + 0.694141I
−2.17062 − 4.19124I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.899552 + 0.699001I
a = −0.555723 + 0.260013I
b = −0.351175 − 0.083803I
−3.26827 + 4.38821I 0
u = −0.899552 − 0.699001I
a = −0.555723 − 0.260013I
b = −0.351175 + 0.083803I
−3.26827 − 4.38821I 0
u = 0.518571 + 1.015560I
a = −0.211103 + 0.058336I
b = −0.400489 + 0.599197I
−3.66592 + 0.10467I 0
u = 0.518571 − 1.015560I
a = −0.211103 − 0.058336I
b = −0.400489 − 0.599197I
−3.66592 − 0.10467I 0
u = −1.140030 + 0.123562I
a = 0.558917 − 1.144130I
b = −0.104456 − 0.760969I
−2.17062 + 0.13148I 0
u = −1.140030 − 0.123562I
a = 0.558917 + 1.144130I
b = −0.104456 + 0.760969I
−2.17062 − 0.13148I 0
u = 0.788041 + 0.320938I
a = −1.165290 − 0.395640I
b = −0.903502 + 0.071649I
−3.26827 + 0.32844I 0
u = 0.788041 − 0.320938I
a = −1.165290 + 0.395640I
b = −0.903502 − 0.071649I
−3.26827 − 0.32844I 0
u = 1.180310 + 0.012052I
a = −0.91234 − 1.30364I
b = −1.73380 − 0.97589I
−5.25931 − 1.21416I 0
u = 1.180310 − 0.012052I
a = −0.91234 + 1.30364I
b = −1.73380 + 0.97589I
−5.25931 + 1.21416I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.111090 + 0.442655I
a = 0.654258 − 0.784229I
b = −0.591917 − 0.592017I
−0.50419 + 2.40320I 0
u = −1.111090 − 0.442655I
a = 0.654258 + 0.784229I
b = −0.591917 + 0.592017I
−0.50419 − 2.40320I 0
u = −1.198430 + 0.027915I
a = −0.92147 − 1.37061I
b = −1.91445 − 1.03978I
−6.41764 + 4.04252I 0
u = −1.198430 − 0.027915I
a = −0.92147 + 1.37061I
b = −1.91445 + 1.03978I
−6.41764 − 4.04252I 0
u = 1.224920 + 0.184610I
a = −0.680597 − 1.092490I
b = −1.00390 − 1.04377I
−5.61498 − 2.02988I 0
u = 1.224920 − 0.184610I
a = −0.680597 + 1.092490I
b = −1.00390 + 1.04377I
−5.61498 + 2.02988I 0
u = 1.214950 + 0.272262I
a = 0.12453 − 1.65766I
b = 0.77124 − 1.37558I
−2.17062 − 4.19124I 0
u = 1.214950 − 0.272262I
a = 0.12453 + 1.65766I
b = 0.77124 + 1.37558I
−2.17062 + 4.19124I 0
u = −1.269020 + 0.005894I
a = −0.80674 + 1.39166I
b = −1.77834 + 1.38715I
−10.49270 + 2.02988I 0
u = −1.269020 − 0.005894I
a = −0.80674 − 1.39166I
b = −1.77834 − 1.38715I
−10.49270 − 2.02988I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.176100 + 0.483198I
a = 0.592616 + 0.752617I
b = −0.674058 + 0.672840I
−1.65238 − 8.02785I 0
u = 1.176100 − 0.483198I
a = 0.592616 − 0.752617I
b = −0.674058 − 0.672840I
−1.65238 + 8.02785I 0
u = 1.221650 + 0.370872I
a = 0.05476 − 1.79734I
b = 1.20285 − 1.51952I
−0.50419 − 6.46297I 0
u = 1.221650 − 0.370872I
a = 0.05476 + 1.79734I
b = 1.20285 + 1.51952I
−0.50419 + 6.46297I 0
u = 0.340631 + 1.244900I
a = −0.0068353 + 0.0139151I
b = −0.502001 + 0.840278I
−6.59138 − 5.99841I 0
u = 0.340631 − 1.244900I
a = −0.0068353 − 0.0139151I
b = −0.502001 − 0.840278I
−6.59138 + 5.99841I 0
u = −1.239340 + 0.384198I
a = 0.02492 + 1.80581I
b = 1.25428 + 1.61735I
−1.65238 + 12.08760I 0
u = −1.239340 − 0.384198I
a = 0.02492 − 1.80581I
b = 1.25428 − 1.61735I
−1.65238 − 12.08760I 0
u = 1.262130 + 0.312419I
a = 0.500943 + 0.892680I
b = −0.454901 + 0.863903I
−6.59138 − 1.93864I 0
u = 1.262130 − 0.312419I
a = 0.500943 − 0.892680I
b = −0.454901 − 0.863903I
−6.59138 + 1.93864I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.268080 + 0.331222I
a = 0.00849 + 1.71936I
b = 0.95703 + 1.70298I
−6.59138 + 5.99841I 0
u = −1.268080 − 0.331222I
a = 0.00849 − 1.71936I
b = 0.95703 − 1.70298I
−6.59138 − 5.99841I 0
u = 1.314510 + 0.067425I
a = −0.68640 − 1.37199I
b = −1.43973 − 1.62011I
−5.25931 − 2.84561I 0
u = 1.314510 − 0.067425I
a = −0.68640 + 1.37199I
b = −1.43973 + 1.62011I
−5.25931 + 2.84561I 0
u = −0.198524 + 1.302860I
a = 0.0821657 − 0.0079703I
b = −0.640357 − 0.895315I
−0.50419 + 6.46297I 0
u = −0.198524 − 1.302860I
a = 0.0821657 + 0.0079703I
b = −0.640357 + 0.895315I
−0.50419 − 6.46297I 0
u = −1.329160 + 0.038165I
a = −0.70698 + 1.42142I
b = −1.60376 + 1.71482I
−6.41764 + 8.10228I 0
u = −1.329160 − 0.038165I
a = −0.70698 − 1.42142I
b = −1.60376 − 1.71482I
−6.41764 − 8.10228I 0
u = −1.307500 + 0.242820I
a = −0.02283 + 1.54565I
b = 0.44377 + 1.69971I
−3.66592 − 0.10467I 0
u = −1.307500 − 0.242820I
a = −0.02283 − 1.54565I
b = 0.44377 − 1.69971I
−3.66592 + 0.10467I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227721 + 1.347240I
a = 0.0715746 − 0.0185276I
b = −0.614831 + 0.942610I
−1.65238 − 12.08760I 0
u = 0.227721 − 1.347240I
a = 0.0715746 + 0.0185276I
b = −0.614831 − 0.942610I
−1.65238 + 12.08760I 0
u = 1.366970 + 0.076347I
a = 0.287797 + 1.039200I
b = −0.180804 + 1.129850I
−3.66592 + 4.16444I 0
u = 1.366970 − 0.076347I
a = 0.287797 − 1.039200I
b = −0.180804 − 1.129850I
−3.66592 − 4.16444I 0
u = 1.373280 + 0.192811I
a = −0.212459 − 1.275000I
b = −0.21758 − 1.60360I
−3.26827 − 4.38821I 0
u = 1.373280 − 0.192811I
a = −0.212459 + 1.275000I
b = −0.21758 + 1.60360I
−3.26827 + 4.38821I 0
u = −1.46328 + 0.16377I
a = −0.056126 + 1.023110I
b = −0.128306 + 1.324110I
−3.26827 − 0.32844I 0
u = −1.46328 − 0.16377I
a = −0.056126 − 1.023110I
b = −0.128306 − 1.324110I
−3.26827 + 0.32844I 0
u = −1.40433 + 0.49536I
a = −0.316968 + 0.709311I
b = −0.060476 + 0.799784I
−5.61498 + 2.02988I 0
u = −1.40433 − 0.49536I
a = −0.316968 − 0.709311I
b = −0.060476 − 0.799784I
−5.61498 − 2.02988I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.303297 + 0.220517I
a = −2.32870 − 1.44235I
b = −0.793911 − 0.617070I
−3.66592 + 4.16444I −10.50898 − 5.63372I
u = −0.303297 − 0.220517I
a = −2.32870 + 1.44235I
b = −0.793911 + 0.617070I
−3.66592 − 4.16444I −10.50898 + 5.63372I
u = −0.032805 + 0.324330I
a = 1.22905 + 2.57528I
b = −0.573161 + 0.571751I
−2.17062 + 0.13148I −6.73748 + 0.14555I
u = −0.032805 − 0.324330I
a = 1.22905 − 2.57528I
b = −0.573161 − 0.571751I
−2.17062 − 0.13148I −6.73748 − 0.14555I
u = −1.52542 + 0.74509I
a = −0.213173 + 0.561878I
b = 0.399545 + 0.614052I
−5.25931 + 2.84561I 0
u = −1.52542 − 0.74509I
a = −0.213173 − 0.561878I
b = 0.399545 − 0.614052I
−5.25931 − 2.84561I 0
u = −1.66173 + 0.53354I
a = −0.146022 + 0.665856I
b = 0.319052 + 1.042020I
−5.25931 + 1.21416I 0
u = −1.66173 − 0.53354I
a = −0.146022 − 0.665856I
b = 0.319052 − 1.042020I
−5.25931 − 1.21416I 0
u = 1.58307 + 0.78427I
a = −0.183740 − 0.551400I
b = 0.521737 − 0.632944I
−6.41764 − 8.10228I 0
u = 1.58307 − 0.78427I
a = −0.183740 + 0.551400I
b = 0.521737 + 0.632944I
−6.41764 + 8.10228I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65518 + 0.67475I
a = −0.158684 − 0.601069I
b = 0.480098 − 0.861473I
−10.49270 − 2.02988I 0
u = 1.65518 − 0.67475I
a = −0.158684 + 0.601069I
b = 0.480098 + 0.861473I
−10.49270 + 2.02988I 0
u = −0.207602 + 0.022600I
a = 5.55991 + 3.54909I
b = −0.229911 − 0.767050I
−0.50419 − 2.40320I −6.68370 − 0.93682I
u = −0.207602 − 0.022600I
a = 5.55991 − 3.54909I
b = −0.229911 + 0.767050I
−0.50419 + 2.40320I −6.68370 + 0.93682I
u = 1.71763 + 0.56503I
a = −0.124770 − 0.644248I
b = 0.422238 − 1.071160I
−6.41764 + 4.04252I 0
u = 1.71763 − 0.56503I
a = −0.124770 + 0.644248I
b = 0.422238 + 1.071160I
−6.41764 − 4.04252I 0
u = 0.163725 + 0.088628I
a = 4.81994 − 6.15580I
b = −0.230010 + 0.889248I
−1.65238 + 8.02785I −8.70834 − 3.80202I
u = 0.163725 − 0.088628I
a = 4.81994 + 6.15580I
b = −0.230010 − 0.889248I
−1.65238 − 8.02785I −8.70834 + 3.80202I
u = −0.0071370 + 0.0339368I
a = 1.8260 − 36.6033I
b = −0.519741 − 0.826618I
−6.59138 − 1.93864I −13.89349 + 0.33377I
u = −0.0071370 − 0.0339368I
a = 1.8260 + 36.6033I
b = −0.519741 + 0.826618I
−6.59138 + 1.93864I −13.89349 − 0.33377I
20
III. I
u
3
= hu
2
+ b − 1, u
19
+ u
18
+ · · · + a + 2, u
20
+ u
19
+ · · · + 6u − 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
−u
19
− u
18
+ ··· − u − 2
−u
2
+ 1
a
1
=
−u
17
− u
16
+ ··· + u + 3
u
2
− 1
a
8
=
−u
19
− u
18
+ ··· − u − 3
−u
2
+ 1
a
3
=
−u
16
− u
15
+ ··· + 3u + 1
−u
5
+ 3u
3
− 2u
a
2
=
u
19
+ u
18
+ ··· + 2u + 3
u
12
− 7u
10
+ 20u
8
− 29u
6
+ 21u
4
− 5u
2
− 1
a
10
=
−u
19
− u
18
+ ··· − u − 2
u
4
− 2u
2
+ 1
a
6
=
−u
18
− u
17
+ ··· + 3u − 1
u
5
− 3u
3
+ 2u
a
7
=
−u
19
− u
18
+ ··· − u − 3
−u
12
+ 7u
10
− 20u
8
+ 29u
6
− 21u
4
+ 5u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
19
+ 2u
18
− 34u
17
− 22u
16
+ 176u
15
+ 110u
14
− 539u
13
− 322u
12
+ 1064u
11
+
596u
10
− 1384u
9
− 700u
8
+ 1157u
7
+ 488u
6
− 562u
5
− 157u
4
+ 106u
3
− 8u
2
+ 21u
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 7u
19
+ ··· − 4u + 1
c
2
u
20
− u
19
+ ··· − 2u
2
+ 1
c
3
u
20
+ u
19
+ ··· + 2u + 1
c
4
, c
9
u
20
− u
19
+ ··· − 6u − 1
c
5
, c
11
u
20
+ u
19
+ ··· + 6u − 1
c
6
u
20
+ u
19
+ ··· − 2u
2
+ 1
c
7
u
20
+ 7u
19
+ ··· + 4u + 1
c
8
, c
10
u
20
− 3u
19
+ ··· + 3u − 1
c
12
u
20
+ 3u
19
+ ··· − 3u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
20
+ 13y
19
+ ··· + 8y + 1
c
2
, c
6
y
20
− 7y
19
+ ··· − 4y + 1
c
3
y
20
− 11y
19
+ ··· − 10y + 1
c
4
, c
5
, c
9
c
11
y
20
− 23y
19
+ ··· − 24y + 1
c
8
, c
10
y
20
+ 3y
19
+ ··· + 3y + 1
c
12
y
20
+ 3y
19
+ ··· + 3y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.939258 + 0.398954I
a = −1.43385 − 1.17399I
b = 0.276960 − 0.749442I
−1.05097 − 3.58416I −10.08066 + 5.25033I
u = 0.939258 − 0.398954I
a = −1.43385 + 1.17399I
b = 0.276960 + 0.749442I
−1.05097 + 3.58416I −10.08066 − 5.25033I
u = −0.947941 + 0.465885I
a = −1.36124 + 1.00192I
b = 0.318455 + 0.883263I
−2.14551 + 9.38795I −10.8753 − 9.3467I
u = −0.947941 − 0.465885I
a = −1.36124 − 1.00192I
b = 0.318455 − 0.883263I
−2.14551 − 9.38795I −10.8753 + 9.3467I
u = −1.126380 + 0.446389I
a = −0.931640 + 0.989707I
b = −0.069458 + 1.005600I
−7.49729 + 3.61397I −16.6966 − 4.7869I
u = −1.126380 − 0.446389I
a = −0.931640 − 0.989707I
b = −0.069458 − 1.005600I
−7.49729 − 3.61397I −16.6966 + 4.7869I
u = 1.237350 + 0.209212I
a = −0.036037 − 1.024230I
b = −0.487275 − 0.517740I
−4.63892 − 1.50200I −7.43539 + 0.19830I
u = 1.237350 − 0.209212I
a = −0.036037 + 1.024230I
b = −0.487275 + 0.517740I
−4.63892 + 1.50200I −7.43539 − 0.19830I
u = −1.272310 + 0.476641I
a = −0.758938 + 0.746667I
b = −0.391574 + 1.212870I
−4.50767 − 1.76829I −12.48170 + 2.85072I
u = −1.272310 − 0.476641I
a = −0.758938 − 0.746667I
b = −0.391574 − 1.212870I
−4.50767 + 1.76829I −12.48170 − 2.85072I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.346880 + 0.241262I
a = −0.239350 − 0.653997I
b = −0.755888 − 0.649902I
−4.64130 − 1.40542I −9.24155 − 0.59867I
u = 1.346880 − 0.241262I
a = −0.239350 + 0.653997I
b = −0.755888 + 0.649902I
−4.64130 + 1.40542I −9.24155 + 0.59867I
u = 1.306860 + 0.436137I
a = −0.669741 − 0.727268I
b = −0.517656 − 1.139940I
−3.84788 − 3.18017I −10.94771 + 2.51139I
u = 1.306860 − 0.436137I
a = −0.669741 + 0.727268I
b = −0.517656 + 1.139940I
−3.84788 + 3.18017I −10.94771 − 2.51139I
u = −1.39060
a = 0.0709202
b = −0.933776
−9.78835 −16.3090
u = −1.42403 + 0.16860I
a = −0.187077 + 0.390574I
b = −0.999423 + 0.480180I
−5.88975 + 6.42130I −11.88741 − 5.06498I
u = −1.42403 − 0.16860I
a = −0.187077 − 0.390574I
b = −0.999423 − 0.480180I
−5.88975 − 6.42130I −11.88741 + 5.06498I
u = 0.047592 + 0.332418I
a = −1.90160 − 0.02574I
b = 1.108240 − 0.031641I
4.25390 − 2.70046I −4.09941 + 2.64710I
u = 0.047592 − 0.332418I
a = −1.90160 + 0.02574I
b = 1.108240 + 0.031641I
4.25390 + 2.70046I −4.09941 − 2.64710I
u = 0.176012
a = −2.03197
b = 0.969020
0.631930 3.80050
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 7u
19
+ ··· − 4u + 1)(u
20
+ 7u
19
+ ··· + 6u + 1)
4
· (u
42
+ 14u
41
+ ··· + 92u + 16)
c
2
(u
20
− u
19
+ ··· − 2u
2
+ 1)(u
20
+ u
19
+ ··· + 3u
2
− 1)
4
· (u
42
− 6u
41
+ ··· + 26u − 4)
c
3
((u
20
− u
19
+ ··· + 4u − 1)
4
)(u
20
+ u
19
+ ··· + 2u + 1)
· (u
42
+ 6u
41
+ ··· − 97086u − 58612)
c
4
, c
9
(u
20
− u
19
+ ··· − 6u − 1)(u
42
+ u
41
+ ··· + 5u + 1)
· (u
80
− u
79
+ ··· + 16u + 1)
c
5
, c
11
(u
20
+ u
19
+ ··· + 6u − 1)(u
42
+ u
41
+ ··· + 5u + 1)
· (u
80
− u
79
+ ··· + 16u + 1)
c
6
((u
20
+ u
19
+ ··· + 3u
2
− 1)
4
)(u
20
+ u
19
+ ··· − 2u
2
+ 1)
· (u
42
− 6u
41
+ ··· + 26u − 4)
c
7
(u
20
+ 7u
19
+ ··· + 4u + 1)(u
20
+ 7u
19
+ ··· + 6u + 1)
4
· (u
42
+ 14u
41
+ ··· + 92u + 16)
c
8
, c
10
(u
20
− 3u
19
+ ··· + 3u − 1)(u
42
− 3u
41
+ ··· − 4u − 1)
· (u
80
+ 23u
79
+ ··· + 798776u + 37537)
c
12
((u
2
+ u + 1)
40
)(u
20
+ 3u
19
+ ··· − 3u − 1)
· (u
42
− 44u
41
+ ··· + 18874368u − 1048576)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y
20
+ 13y
19
+ ··· − 6y + 1)
4
)(y
20
+ 13y
19
+ ··· + 8y + 1)
· (y
42
+ 26y
41
+ ··· + 10512y + 256)
c
2
, c
6
((y
20
− 7y
19
+ ··· − 6y + 1)
4
)(y
20
− 7y
19
+ ··· − 4y + 1)
· (y
42
− 14y
41
+ ··· − 92y + 16)
c
3
((y
20
− 11y
19
+ ··· − 6y + 1)
4
)(y
20
− 11y
19
+ ··· − 10y + 1)
· (y
42
− 22y
41
+ ··· − 37177652828y + 3435366544)
c
4
, c
5
, c
9
c
11
(y
20
− 23y
19
+ ··· − 24y + 1)(y
42
− 33y
41
+ ··· − 5y + 1)
· (y
80
− 69y
79
+ ··· + 1440y + 1)
c
8
, c
10
(y
20
+ 3y
19
+ ··· + 3y + 1)(y
42
+ 5y
41
+ ··· − 102y + 1)
· (y
80
+ 27y
79
+ ··· + 9352736088y + 1409026369)
c
12
((y
2
+ y + 1)
40
)(y
20
+ 3y
19
+ ··· + 3y + 1)
· (y
42
+ 4y
41
+ ··· − 24739011624960y + 1099511627776)
27
