12a
0664
(K12a
0664
)
A knot diagram
1
Linearized knot diagam
3 7 10 1 11 2 5 12 4 6 8 9
Solving Sequence
2,6
7
3,10
4 11 1 5 8 9 12
c
6
c
2
c
3
c
10
c
1
c
5
c
7
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1185u
34
+ 14000u
33
+ ··· + 32b + 15808, 3556u
34
− 45981u
33
+ ··· + 32a + 144096,
u
35
− 14u
34
+ ··· + 608u − 64i
I
u
2
= h1.49681 × 10
45
a
11
u
5
− 5.70342 × 10
45
a
10
u
5
+ ··· − 1.15780 × 10
47
a + 2.97901 × 10
46
,
− a
11
u
5
− 4a
10
u
5
+ ··· − 55a − 18, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
I
u
3
= h−2u
22
+ 11u
20
+ ··· + b − 8, 9u
22
+ 8u
21
+ ··· + a + 17, u
23
+ u
22
+ ··· + 3u + 1i
* 3 irreducible components of dim
C
= 0, with total 130 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−1185u
34
+ 14000u
33
+ · · · + 32b + 15808, 3556u
34
− 45981u
33
+
· · · + 32a + 144096, u
35
− 14u
34
+ · · · + 608u − 64i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−111.125u
34
+ 1436.91u
33
+ ··· + 41697.5u − 4503
1185
32
u
34
−
875
2
u
33
+ ··· + 2084u − 494
a
4
=
1045
64
u
34
−
1759
8
u
33
+ ··· −
37185
4
u + 1064
−
541
32
u
34
+
847
4
u
33
+ ··· +
9217
2
u − 487
a
11
=
−74.0938u
34
+ 999.406u
33
+ ··· + 43781.5u − 4997
1185
32
u
34
−
875
2
u
33
+ ··· + 2084u − 494
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
37
64
u
34
+
65
8
u
33
+ ··· +
18751
4
u − 576
541
32
u
34
−
847
4
u
33
+ ··· −
9215
2
u + 487
a
8
=
211
8
u
34
−
11137
32
u
33
+ ··· − 13901u +
3187
2
279
32
u
34
−
2045
16
u
33
+ ··· −
17517
2
u + 1046
a
9
=
865
64
u
34
−
1229
8
u
33
+ ··· − 2691u +
667
2
56.2188u
34
− 774.938u
33
+ ··· − 36723u + 4223
a
12
=
12.7813u
34
− 135.594u
33
+ ··· + 2973.50u − 394.500
1685
32
u
34
−
5693
8
u
33
+ ··· −
58715
2
u + 3332
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
459
2
u
34
+ 3017u
33
+ ··· + 110596u − 12350
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 12u
34
+ ··· + 13312u + 4096
c
2
, c
6
u
35
− 14u
34
+ ··· + 608u − 64
c
3
, c
5
, c
9
c
10
u
35
+ 14u
33
+ ··· − 4u − 1
c
4
, c
7
u
35
− 2u
34
+ ··· + 9u − 1
c
8
, c
11
, c
12
u
35
+ 16u
34
+ ··· + 160u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 8y
34
+ ··· − 158334976y −16777216
c
2
, c
6
y
35
− 12y
34
+ ··· + 13312y −4096
c
3
, c
5
, c
9
c
10
y
35
+ 28y
34
+ ··· + 6y −1
c
4
, c
7
y
35
− 12y
34
+ ··· + 135y −1
c
8
, c
11
, c
12
y
35
− 34y
34
+ ··· + 54272y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.998696
a = 0.406523
b = 0.811456
−7.46368 −11.8760
u = 0.735848 + 0.635706I
a = −1.072540 − 0.169141I
b = 0.692633 − 0.220382I
2.59000 − 1.09744I 0
u = 0.735848 − 0.635706I
a = −1.072540 + 0.169141I
b = 0.692633 + 0.220382I
2.59000 + 1.09744I 0
u = 0.388780 + 0.979792I
a = −0.611938 − 1.089240I
b = 0.49548 + 1.43787I
−11.7814 + 11.4404I 0
u = 0.388780 − 0.979792I
a = −0.611938 + 1.089240I
b = 0.49548 − 1.43787I
−11.7814 − 11.4404I 0
u = 0.331775 + 1.023800I
a = 0.554343 + 0.837484I
b = −0.415463 − 1.254440I
−3.76301 + 7.52599I 0
u = 0.331775 − 1.023800I
a = 0.554343 − 0.837484I
b = −0.415463 + 1.254440I
−3.76301 − 7.52599I 0
u = 0.897454 + 0.638918I
a = 0.670730 + 0.645138I
b = −0.663183 + 0.017922I
2.11864 − 3.86118I 0
u = 0.897454 − 0.638918I
a = 0.670730 − 0.645138I
b = −0.663183 − 0.017922I
2.11864 + 3.86118I 0
u = 0.978827 + 0.600935I
a = −0.829355 − 1.080510I
b = 0.938507 − 0.064693I
−3.98603 − 5.50029I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.978827 − 0.600935I
a = −0.829355 + 1.080510I
b = 0.938507 + 0.064693I
−3.98603 + 5.50029I 0
u = −0.838763
a = −0.220144
b = −0.339524
−1.49579 −4.76650
u = 0.557853 + 0.610862I
a = 1.42477 + 0.11204I
b = −0.890998 + 0.031259I
−2.81360 + 0.71268I −3.56704 + 0.25723I
u = 0.557853 − 0.610862I
a = 1.42477 − 0.11204I
b = −0.890998 − 0.031259I
−2.81360 − 0.71268I −3.56704 − 0.25723I
u = 0.875442 + 0.817929I
a = 0.419001 − 0.418160I
b = −0.069182 + 0.582688I
1.43497 − 3.03675I 0
u = 0.875442 − 0.817929I
a = 0.419001 + 0.418160I
b = −0.069182 − 0.582688I
1.43497 + 3.03675I 0
u = 0.657165 + 1.106850I
a = −0.261979 + 0.777037I
b = 0.109636 − 1.218180I
−9.91255 − 5.35177I 0
u = 0.657165 − 1.106850I
a = −0.261979 − 0.777037I
b = 0.109636 + 1.218180I
−9.91255 + 5.35177I 0
u = 0.347142 + 1.298210I
a = −0.190435 − 0.549260I
b = 0.146118 + 1.125760I
−2.07712 + 1.05602I 0
u = 0.347142 − 1.298210I
a = −0.190435 + 0.549260I
b = 0.146118 − 1.125760I
−2.07712 − 1.05602I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650933
a = 2.00998
b = −0.456707
−2.54150 4.22040
u = 1.184660 + 0.653764I
a = 1.76258 + 0.22362I
b = −0.56794 + 1.53123I
−14.2397 − 17.3604I 0
u = 1.184660 − 0.653764I
a = 1.76258 − 0.22362I
b = −0.56794 − 1.53123I
−14.2397 + 17.3604I 0
u = −1.351080 + 0.086351I
a = −0.133127 + 0.458938I
b = −0.27517 + 1.49696I
−18.1528 − 7.9861I 0
u = −1.351080 − 0.086351I
a = −0.133127 − 0.458938I
b = −0.27517 − 1.49696I
−18.1528 + 7.9861I 0
u = 1.209310 + 0.645834I
a = −1.55266 − 0.28086I
b = 0.51192 − 1.37648I
−6.4732 − 13.5026I 0
u = 1.209310 − 0.645834I
a = −1.55266 + 0.28086I
b = 0.51192 + 1.37648I
−6.4732 + 13.5026I 0
u = −0.298877 + 0.500011I
a = −0.622450 + 0.276097I
b = 0.134554 + 0.535427I
−0.168508 + 1.117130I −2.41743 − 5.24581I
u = −0.298877 − 0.500011I
a = −0.622450 − 0.276097I
b = 0.134554 − 0.535427I
−0.168508 − 1.117130I −2.41743 + 5.24581I
u = 1.27152 + 0.65655I
a = 1.227090 + 0.241685I
b = −0.350162 + 1.222410I
−5.27078 − 7.68372I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.27152 − 0.65655I
a = 1.227090 − 0.241685I
b = −0.350162 − 1.222410I
−5.27078 + 7.68372I 0
u = −1.44729 + 0.08376I
a = 0.070621 − 0.374099I
b = 0.127609 − 1.345440I
−10.28340 − 3.40903I 0
u = −1.44729 − 0.08376I
a = 0.070621 + 0.374099I
b = 0.127609 + 1.345440I
−10.28340 + 3.40903I 0
u = 1.25473 + 0.80657I
a = −0.952835 + 0.203116I
b = 0.068034 − 1.227290I
−11.81200 − 1.77127I 0
u = 1.25473 − 0.80657I
a = −0.952835 − 0.203116I
b = 0.068034 + 1.227290I
−11.81200 + 1.77127I 0
8
II. I
u
2
= h1.50 × 10
45
a
11
u
5
− 5.70 × 10
45
a
10
u
5
+ · · · − 1.16 × 10
47
a + 2.98 ×
10
46
, −a
11
u
5
− 4a
10
u
5
+ · · · − 55a − 18, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
a
−0.00794015a
11
u
5
+ 0.0302550a
10
u
5
+ ··· + 0.614182a − 0.158028
a
4
=
0.00490869a
11
u
5
+ 0.0130821a
10
u
5
+ ··· + 0.785397a + 0.523477
−0.00830184a
11
u
5
+ 0.0195054a
10
u
5
+ ··· − 0.000748132a − 0.539669
a
11
=
−0.00794015a
11
u
5
+ 0.0302550a
10
u
5
+ ··· + 1.61418a − 0.158028
−0.00794015a
11
u
5
+ 0.0302550a
10
u
5
+ ··· + 0.614182a − 0.158028
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
0.0247380a
11
u
5
+ 0.0248517a
10
u
5
+ ··· + 0.0454023a + 0.368349
0.00587845a
11
u
5
+ 0.0341246a
10
u
5
+ ··· + 1.25016a − 1.03661
a
8
=
0.00249911a
11
u
5
− 0.00445033a
10
u
5
+ ··· + 0.152457a + 0.669472
0.0198608a
11
u
5
− 0.00986522a
10
u
5
+ ··· − 1.05246a + 0.630579
a
9
=
−0.0209774a
11
u
5
+ 0.0278972a
10
u
5
+ ··· + 0.449873a − 1.39397
0.0146417a
11
u
5
+ 0.0451106a
10
u
5
+ ··· + 0.588854a − 0.425328
a
12
=
0.0432844a
11
u
5
+ 0.0323424a
10
u
5
+ ··· − 1.19997a + 0.605993
−0.0459402a
11
u
5
+ 0.0636298a
10
u
5
+ ··· + 1.26067a + 0.107121
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0983999a
11
u
5
− 0.0411031a
10
u
5
+ ··· − 4.19581a − 8.39076
9
(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)
12
c
2
, c
6
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
12
c
3
, c
5
, c
9
c
10
u
72
+ u
71
+ ··· − 23968u + 5312
c
4
, c
7
u
72
− 7u
71
+ ··· − 872320u + 141376
c
8
, c
11
, c
12
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
12
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
12
c
2
, c
6
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
12
c
3
, c
5
, c
9
c
10
y
72
+ 63y
71
+ ··· + 1187419136y + 28217344
c
4
, c
7
y
72
− 33y
71
+ ··· − 667358056448y + 19987173376
c
8
, c
11
, c
12
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
12
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.045030 − 1.035750I
b = −0.10013 − 1.43609I
−7.56426 − 0.92430I −19.1335 + 0.7942I
u = 1.002190 + 0.295542I
a = −0.721644 − 0.877823I
b = 0.848818 + 0.662123I
−3.86516 + 1.04811I −10.29244 − 2.89055I
u = 1.002190 + 0.295542I
a = −1.168660 + 0.122739I
b = −0.37920 − 2.05278I
−14.4855 − 0.9243I −17.9862 + 0.7942I
u = 1.002190 + 0.295542I
a = 0.741656 + 0.239875I
b = 0.27706 + 1.71064I
−7.56426 − 0.92430I −19.1335 + 0.7942I
u = 1.002190 + 0.295542I
a = 0.373622 + 1.169080I
b = −1.22553 − 0.89354I
−10.52100 + 3.66782I −14.2979 − 2.4106I
u = 1.002190 + 0.295542I
a = 1.141790 + 0.545399I
b = −0.374590 − 0.529377I
−3.86516 − 2.89672I −10.29244 + 4.47900I
u = 1.002190 + 0.295542I
a = −1.53781 − 0.18013I
b = −0.039851 + 0.586857I
−10.52100 − 5.51643I −14.2979 + 3.9990I
u = 1.002190 + 0.295542I
a = −0.30369 + 1.55938I
b = 0.00525 + 1.47250I
−14.4855 − 0.9243I −17.9862 + 0.7942I
u = 1.002190 + 0.295542I
a = 1.47028 + 1.26859I
b = −0.386282 + 1.150280I
−3.86516 − 2.89672I −10.29244 + 4.47900I
u = 1.002190 + 0.295542I
a = −1.61023 − 1.18452I
b = 0.71298 − 1.40512I
−10.52100 − 5.51643I −14.2979 + 3.9990I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −1.42223 − 1.47106I
b = 0.030964 − 1.098510I
−3.86516 + 1.04811I −10.29244 − 2.89055I
u = 1.002190 + 0.295542I
a = 1.39583 + 1.77056I
b = 0.202269 + 1.168480I
−10.52100 + 3.66782I −14.2979 − 2.4106I
u = 1.002190 − 0.295542I
a = −0.045030 + 1.035750I
b = −0.10013 + 1.43609I
−7.56426 + 0.92430I −19.1335 − 0.7942I
u = 1.002190 − 0.295542I
a = −0.721644 + 0.877823I
b = 0.848818 − 0.662123I
−3.86516 − 1.04811I −10.29244 + 2.89055I
u = 1.002190 − 0.295542I
a = −1.168660 − 0.122739I
b = −0.37920 + 2.05278I
−14.4855 + 0.9243I −17.9862 − 0.7942I
u = 1.002190 − 0.295542I
a = 0.741656 − 0.239875I
b = 0.27706 − 1.71064I
−7.56426 + 0.92430I −19.1335 − 0.7942I
u = 1.002190 − 0.295542I
a = 0.373622 − 1.169080I
b = −1.22553 + 0.89354I
−10.52100 − 3.66782I −14.2979 + 2.4106I
u = 1.002190 − 0.295542I
a = 1.141790 − 0.545399I
b = −0.374590 + 0.529377I
−3.86516 + 2.89672I −10.29244 − 4.47900I
u = 1.002190 − 0.295542I
a = −1.53781 + 0.18013I
b = −0.039851 − 0.586857I
−10.52100 + 5.51643I −14.2979 − 3.9990I
u = 1.002190 − 0.295542I
a = −0.30369 − 1.55938I
b = 0.00525 − 1.47250I
−14.4855 + 0.9243I −17.9862 − 0.7942I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 − 0.295542I
a = 1.47028 − 1.26859I
b = −0.386282 − 1.150280I
−3.86516 + 2.89672I −10.29244 − 4.47900I
u = 1.002190 − 0.295542I
a = −1.61023 + 1.18452I
b = 0.71298 + 1.40512I
−10.52100 + 5.51643I −14.2979 − 3.9990I
u = 1.002190 − 0.295542I
a = −1.42223 + 1.47106I
b = 0.030964 + 1.098510I
−3.86516 − 1.04811I −10.29244 + 2.89055I
u = 1.002190 − 0.295542I
a = 1.39583 − 1.77056I
b = 0.202269 − 1.168480I
−10.52100 − 3.66782I −14.2979 + 2.4106I
u = −0.428243 + 0.664531I
a = −0.906890 + 0.398788I
b = 0.372111 + 0.435873I
−0.083952 + 1.048110I −2.85901 − 2.89055I
u = −0.428243 + 0.664531I
a = 0.916379 − 0.467414I
b = −0.441756 + 1.285690I
−6.73977 − 5.51643I −6.86442 + 3.99904I
u = −0.428243 + 0.664531I
a = 0.080865 − 0.896345I
b = 0.423579 − 0.174074I
−6.73977 + 3.66782I −6.86442 − 2.41059I
u = −0.428243 + 0.664531I
a = 1.036340 + 0.768690I
b = −0.391103 − 1.225920I
−6.73977 + 3.66782I −6.86442 − 2.41059I
u = −0.428243 + 0.664531I
a = −0.542048 + 0.338506I
b = 0.370059 − 1.107460I
−0.08395 − 2.89672I −2.85901 + 4.47900I
u = −0.428243 + 0.664531I
a = −0.68548 + 1.41030I
b = 0.065036 − 1.074080I
−3.78305 − 0.92430I −11.70006 + 0.79423I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 + 0.664531I
a = 1.43827 − 0.87053I
b = −0.874028 − 0.088656I
−0.08395 − 2.89672I −2.85901 + 4.47900I
u = −0.428243 + 0.664531I
a = 0.79454 − 1.49935I
b = 0.170377 + 1.190830I
−10.70430 − 0.92430I −10.55278 + 0.79423I
u = −0.428243 + 0.664531I
a = 0.54295 − 1.72628I
b = −0.479092 + 1.196190I
−3.78305 − 0.92430I −11.70006 + 0.79423I
u = −0.428243 + 0.664531I
a = −0.0851151 − 0.0791252I
b = −0.146420 + 0.842310I
−0.083952 + 1.048110I −2.85901 − 2.89055I
u = −0.428243 + 0.664531I
a = −1.75154 + 1.22038I
b = 1.228680 − 0.127334I
−6.73977 − 5.51643I −6.86442 + 3.99904I
u = −0.428243 + 0.664531I
a = −0.49331 + 2.16719I
b = 0.70475 − 1.44890I
−10.70430 − 0.92430I −10.55278 + 0.79423I
u = −0.428243 − 0.664531I
a = −0.906890 − 0.398788I
b = 0.372111 − 0.435873I
−0.083952 − 1.048110I −2.85901 + 2.89055I
u = −0.428243 − 0.664531I
a = 0.916379 + 0.467414I
b = −0.441756 − 1.285690I
−6.73977 + 5.51643I −6.86442 − 3.99904I
u = −0.428243 − 0.664531I
a = 0.080865 + 0.896345I
b = 0.423579 + 0.174074I
−6.73977 − 3.66782I −6.86442 + 2.41059I
u = −0.428243 − 0.664531I
a = 1.036340 − 0.768690I
b = −0.391103 + 1.225920I
−6.73977 − 3.66782I −6.86442 + 2.41059I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.428243 − 0.664531I
a = −0.542048 − 0.338506I
b = 0.370059 + 1.107460I
−0.08395 + 2.89672I −2.85901 − 4.47900I
u = −0.428243 − 0.664531I
a = −0.68548 − 1.41030I
b = 0.065036 + 1.074080I
−3.78305 + 0.92430I −11.70006 − 0.79423I
u = −0.428243 − 0.664531I
a = 1.43827 + 0.87053I
b = −0.874028 + 0.088656I
−0.08395 + 2.89672I −2.85901 − 4.47900I
u = −0.428243 − 0.664531I
a = 0.79454 + 1.49935I
b = 0.170377 − 1.190830I
−10.70430 + 0.92430I −10.55278 − 0.79423I
u = −0.428243 − 0.664531I
a = 0.54295 + 1.72628I
b = −0.479092 − 1.196190I
−3.78305 + 0.92430I −11.70006 − 0.79423I
u = −0.428243 − 0.664531I
a = −0.0851151 + 0.0791252I
b = −0.146420 − 0.842310I
−0.083952 − 1.048110I −2.85901 + 2.89055I
u = −0.428243 − 0.664531I
a = −1.75154 − 1.22038I
b = 1.228680 + 0.127334I
−6.73977 + 5.51643I −6.86442 − 3.99904I
u = −0.428243 − 0.664531I
a = −0.49331 − 2.16719I
b = 0.70475 + 1.44890I
−10.70430 + 0.92430I −10.55278 − 0.79423I
u = −1.073950 + 0.558752I
a = 0.999012 + 0.168429I
b = 0.192395 − 1.365660I
−8.63038 + 1.10090I −10.58114 − 2.30575I
u = −1.073950 + 0.558752I
a = −1.021630 + 0.646962I
b = 1.181040 + 0.045156I
−1.97456 + 7.66543I −6.57572 − 9.19535I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 + 0.558752I
a = −0.505352 − 0.550072I
b = 0.081749 − 0.233521I
−8.63038 + 1.10090I −10.58114 − 2.30575I
u = −1.073950 + 0.558752I
a = 0.694450 − 0.231550I
b = −0.723174 + 0.173853I
−1.97456 + 3.72061I −6.57572 − 1.82579I
u = −1.073950 + 0.558752I
a = −1.212640 + 0.488384I
b = 0.182527 + 1.229450I
−1.97456 + 3.72061I −6.57572 − 1.82579I
u = −1.073950 + 0.558752I
a = 1.29217 − 0.93526I
b = −1.55698 − 0.23708I
−8.63038 + 10.28510I −10.58114 − 8.71539I
u = −1.073950 + 0.558752I
a = 1.58392 − 0.78228I
b = −0.342193 − 1.293310I
−1.97456 + 7.66543I −6.57572 − 9.19535I
u = −1.073950 + 0.558752I
a = −1.93207 + 0.16164I
b = 0.72494 + 1.35910I
−5.67365 + 5.69302I −15.4168 − 5.5106I
u = −1.073950 + 0.558752I
a = 1.99770 + 0.01917I
b = −0.281236 − 1.128250I
−5.67365 + 5.69302I −15.4168 − 5.5106I
u = −1.073950 + 0.558752I
a = −1.91569 + 0.95908I
b = 0.40477 + 1.37943I
−8.63038 + 10.28510I −10.58114 − 8.71539I
u = −1.073950 + 0.558752I
a = 2.13763 − 0.17492I
b = −0.97229 − 1.66325I
−12.59490 + 5.69302I −14.2695 − 5.5106I
u = −1.073950 + 0.558752I
a = −2.27632 − 0.20723I
b = 0.034497 + 1.175340I
−12.59490 + 5.69302I −14.2695 − 5.5106I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = 0.999012 − 0.168429I
b = 0.192395 + 1.365660I
−8.63038 − 1.10090I −10.58114 + 2.30575I
u = −1.073950 − 0.558752I
a = −1.021630 − 0.646962I
b = 1.181040 − 0.045156I
−1.97456 − 7.66543I −6.57572 + 9.19535I
u = −1.073950 − 0.558752I
a = −0.505352 + 0.550072I
b = 0.081749 + 0.233521I
−8.63038 − 1.10090I −10.58114 + 2.30575I
u = −1.073950 − 0.558752I
a = 0.694450 + 0.231550I
b = −0.723174 − 0.173853I
−1.97456 − 3.72061I −6.57572 + 1.82579I
u = −1.073950 − 0.558752I
a = −1.212640 − 0.488384I
b = 0.182527 − 1.229450I
−1.97456 − 3.72061I −6.57572 + 1.82579I
u = −1.073950 − 0.558752I
a = 1.29217 + 0.93526I
b = −1.55698 + 0.23708I
−8.63038 − 10.28510I −10.58114 + 8.71539I
u = −1.073950 − 0.558752I
a = 1.58392 + 0.78228I
b = −0.342193 + 1.293310I
−1.97456 − 7.66543I −6.57572 + 9.19535I
u = −1.073950 − 0.558752I
a = −1.93207 − 0.16164I
b = 0.72494 − 1.35910I
−5.67365 − 5.69302I −15.4168 + 5.5106I
u = −1.073950 − 0.558752I
a = 1.99770 − 0.01917I
b = −0.281236 + 1.128250I
−5.67365 − 5.69302I −15.4168 + 5.5106I
u = −1.073950 − 0.558752I
a = −1.91569 − 0.95908I
b = 0.40477 − 1.37943I
−8.63038 − 10.28510I −10.58114 + 8.71539I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.073950 − 0.558752I
a = 2.13763 + 0.17492I
b = −0.97229 + 1.66325I
−12.59490 − 5.69302I −14.2695 + 5.5106I
u = −1.073950 − 0.558752I
a = −2.27632 + 0.20723I
b = 0.034497 − 1.175340I
−12.59490 − 5.69302I −14.2695 + 5.5106I
19
III.
I
u
3
= h−2u
22
+11u
20
+· · ·+b−8, 9u
22
+8u
21
+· · ·+a+17, u
23
+u
22
+· · ·+3u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
10
=
−9u
22
− 8u
21
+ ··· − 22u − 17
2u
22
− 11u
20
+ ··· + 16u + 8
a
4
=
3u
22
+ 2u
21
+ ··· + 2u + 5
−u
22
+ 4u
20
+ ··· − 3u − 2
a
11
=
−7u
22
− 8u
21
+ ··· − 6u − 9
2u
22
− 11u
20
+ ··· + 16u + 8
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
2u
22
+ 2u
21
+ ··· − u + 4
−u
22
+ 4u
20
+ ··· − 4u − 2
a
8
=
−6u
22
− 5u
21
+ ··· − u − 4
−u
22
− 3u
21
+ ··· + 6u + 2
a
9
=
3u
22
+ 3u
21
+ ··· − 9u − 7
3u
21
+ 3u
20
+ ··· − 13u − 3
a
12
=
−7u
22
+ 2u
21
+ ··· − 30u − 12
5u
22
+ 4u
21
+ ··· − 15u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −10u
22
− u
21
+ 36u
20
+ 8u
19
− 87u
18
− 17u
17
+ 117u
16
+ 43u
15
− 108u
14
− 85u
13
+
12u
12
+ 164u
11
+ 57u
10
−222u
9
−83u
8
+ 240u
7
+ 28u
6
−163u
5
−u
4
+ 77u
3
−7u
2
−18u −7
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 9u
22
+ ··· + 11u − 1
c
2
u
23
− u
22
+ ··· + 3u − 1
c
3
, c
10
u
23
+ 13u
21
+ ··· + 4u + 1
c
4
, c
7
u
23
+ 2u
22
+ ··· + 11u + 3
c
5
, c
9
u
23
+ 13u
21
+ ··· + 4u − 1
c
6
u
23
+ u
22
+ ··· + 3u + 1
c
8
u
23
+ 3u
22
+ ··· − 3u − 1
c
11
, c
12
u
23
− 3u
22
+ ··· − 3u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 7y
22
+ ··· − 9y −1
c
2
, c
6
y
23
− 9y
22
+ ··· + 11y −1
c
3
, c
5
, c
9
c
10
y
23
+ 26y
22
+ ··· − 16y −1
c
4
, c
7
y
23
− 6y
22
+ ··· + 121y −9
c
8
, c
11
, c
12
y
23
− 27y
22
+ ··· + 9y −1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956576 + 0.287626I
a = 0.398737 + 0.689027I
b = 0.13596 + 1.56669I
−7.00840 − 1.12592I −3.10503 + 6.73164I
u = 0.956576 − 0.287626I
a = 0.398737 − 0.689027I
b = 0.13596 − 1.56669I
−7.00840 + 1.12592I −3.10503 − 6.73164I
u = 0.897512 + 0.352142I
a = −0.549378 − 0.779464I
b = −0.10030 − 1.77152I
−13.44170 − 1.47646I −9.68435 + 4.96102I
u = 0.897512 − 0.352142I
a = −0.549378 + 0.779464I
b = −0.10030 + 1.77152I
−13.44170 + 1.47646I −9.68435 − 4.96102I
u = 0.559518 + 0.687683I
a = −0.531744 − 0.404398I
b = 0.376776 − 0.936496I
−7.70856 − 5.26009I −9.20604 + 6.12251I
u = 0.559518 − 0.687683I
a = −0.531744 + 0.404398I
b = 0.376776 + 0.936496I
−7.70856 + 5.26009I −9.20604 − 6.12251I
u = −0.217566 + 1.097960I
a = 0.371257 − 0.594299I
b = −0.142171 + 1.047860I
−1.77403 − 0.61945I −6.40574 − 3.09121I
u = −0.217566 − 1.097960I
a = 0.371257 + 0.594299I
b = −0.142171 − 1.047860I
−1.77403 + 0.61945I −6.40574 + 3.09121I
u = −1.031950 + 0.486269I
a = 2.32947 − 0.53696I
b = −0.751813 − 1.095870I
−9.86216 + 7.58052I −11.58301 − 7.49782I
u = −1.031950 − 0.486269I
a = 2.32947 + 0.53696I
b = −0.751813 + 1.095870I
−9.86216 − 7.58052I −11.58301 + 7.49782I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.878382 + 0.763757I
a = 0.1069300 + 0.0577565I
b = −0.007554 + 0.286744I
1.76332 − 2.88443I 3.57102 − 2.01988I
u = 0.878382 − 0.763757I
a = 0.1069300 − 0.0577565I
b = −0.007554 − 0.286744I
1.76332 + 2.88443I 3.57102 + 2.01988I
u = −0.822424
a = −1.57474
b = 0.229980
−2.89205 −19.3640
u = −0.662280 + 0.421621I
a = −0.85366 + 2.50451I
b = 0.685404 − 0.888568I
−8.53739 − 3.73593I −8.68609 + 1.54144I
u = −0.662280 − 0.421621I
a = −0.85366 − 2.50451I
b = 0.685404 + 0.888568I
−8.53739 + 3.73593I −8.68609 − 1.54144I
u = 1.153480 + 0.425129I
a = −0.346734 − 0.333839I
b = −0.329283 − 1.256390I
−10.02580 + 0.64452I −14.1605 − 0.5003I
u = 1.153480 − 0.425129I
a = −0.346734 + 0.333839I
b = −0.329283 + 1.256390I
−10.02580 − 0.64452I −14.1605 + 0.5003I
u = −1.108380 + 0.545841I
a = −1.74217 + 0.24886I
b = 0.475079 + 1.112810I
−4.61610 + 5.65139I −6.42575 − 4.91795I
u = −1.108380 − 0.545841I
a = −1.74217 − 0.24886I
b = 0.475079 − 1.112810I
−4.61610 − 5.65139I −6.42575 + 4.91795I
u = −0.992546 + 0.763032I
a = 1.172960 + 0.738243I
b = −0.136689 − 1.316940I
−10.87890 + 3.03878I −12.25845 − 3.57862I
24
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992546 − 0.763032I
a = 1.172960 − 0.738243I
b = −0.136689 + 1.316940I
−10.87890 − 3.03878I −12.25845 + 3.57862I
u = −0.521544 + 0.258479I
a = 0.93170 − 2.30337I
b = −0.320395 + 0.718289I
−2.13122 − 1.63396I −4.87426 + 4.06305I
u = −0.521544 − 0.258479I
a = 0.93170 + 2.30337I
b = −0.320395 − 0.718289I
−2.13122 + 1.63396I −4.87426 − 4.06305I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
12
)(u
23
− 9u
22
+ ··· + 11u − 1)
· (u
35
+ 12u
34
+ ··· + 13312u + 4096)
c
2
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
12
)(u
23
− u
22
+ ··· + 3u − 1)
· (u
35
− 14u
34
+ ··· + 608u − 64)
c
3
, c
10
(u
23
+ 13u
21
+ ··· + 4u + 1)(u
35
+ 14u
33
+ ··· − 4u − 1)
· (u
72
+ u
71
+ ··· − 23968u + 5312)
c
4
, c
7
(u
23
+ 2u
22
+ ··· + 11u + 3)(u
35
− 2u
34
+ ··· + 9u − 1)
· (u
72
− 7u
71
+ ··· − 872320u + 141376)
c
5
, c
9
(u
23
+ 13u
21
+ ··· + 4u − 1)(u
35
+ 14u
33
+ ··· − 4u − 1)
· (u
72
+ u
71
+ ··· − 23968u + 5312)
c
6
((u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
12
)(u
23
+ u
22
+ ··· + 3u + 1)
· (u
35
− 14u
34
+ ··· + 608u − 64)
c
8
((u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
12
)(u
23
+ 3u
22
+ ··· − 3u − 1)
· (u
35
+ 16u
34
+ ··· + 160u − 64)
c
11
, c
12
((u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
12
)(u
23
− 3u
22
+ ··· − 3u + 1)
· (u
35
+ 16u
34
+ ··· + 160u − 64)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
12
)(y
23
+ 7y
22
+ ··· − 9y −1)
· (y
35
+ 8y
34
+ ··· − 158334976y −16777216)
c
2
, c
6
((y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
12
)(y
23
− 9y
22
+ ··· + 11y −1)
· (y
35
− 12y
34
+ ··· + 13312y −4096)
c
3
, c
5
, c
9
c
10
(y
23
+ 26y
22
+ ··· − 16y −1)(y
35
+ 28y
34
+ ··· + 6y −1)
· (y
72
+ 63y
71
+ ··· + 1187419136y + 28217344)
c
4
, c
7
(y
23
− 6y
22
+ ··· + 121y −9)(y
35
− 12y
34
+ ··· + 135y −1)
· (y
72
− 33y
71
+ ··· − 667358056448y + 19987173376)
c
8
, c
11
, c
12
((y
6
− 7y
5
+ ··· − 5y + 1)
12
)(y
23
− 27y
22
+ ··· + 9y −1)
· (y
35
− 34y
34
+ ··· + 54272y −4096)
27
