12a
1060
(K12a
1060
)
A knot diagram
1
Linearized knot diagam
4 7 9 11 12 10 3 1 2 6 5 8
Solving Sequence
5,12 6,8
1 9 11 4 2 3 10 7
c
5
c
12
c
8
c
11
c
4
c
1
c
3
c
10
c
6
c
2
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.57346 × 10
89
u
110
+ 1.88636 × 10
89
u
109
+ ··· + 1.74794 × 10
88
b + 1.38329 × 10
89
,
− 1.32168 × 10
89
u
110
+ 1.72858 × 10
89
u
109
+ ··· + 1.74794 × 10
88
a + 4.52966 × 10
89
,
u
111
− 2u
110
+ ··· − 17u + 1i
I
u
2
= hu
20
− u
19
+ ··· + b − u, −u
20
+ 10u
18
+ ··· + a + 1,
u
21
− 10u
19
+ 42u
17
− 92u
15
+ 99u
13
− 14u
11
− u
10
− 78u
9
+ 5u
8
+ 60u
7
− 9u
6
+ 9u
5
+ 6u
4
− 18u
3
− 1i
I
u
3
= hb, a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 133 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−2.57 × 10
89
u
110
+ 1.89 × 10
89
u
109
+ · · · + 1.75 × 10
88
b + 1.38 ×
10
89
, −1.32 × 10
89
u
110
+ 1.73 × 10
89
u
109
+ · · · + 1.75 × 10
88
a + 4.53 ×
10
89
, u
111
− 2u
110
+ · · · − 17u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
8
=
7.56139u
110
− 9.88923u
109
+ ··· + 305.838u − 25.9143
14.7228u
110
− 10.7919u
109
+ ··· + 165.490u − 7.91382
a
1
=
−0.131615u
110
+ 1.70010u
109
+ ··· − 107.174u + 6.20078
−8.70767u
110
+ 7.11868u
109
+ ··· − 150.414u + 11.0406
a
9
=
3.79909u
110
− 4.42765u
109
+ ··· + 61.8715u − 3.31532
10.8836u
110
− 8.05693u
109
+ ··· + 113.483u − 5.21542
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
3.46413u
110
− 1.77921u
109
+ ··· − 21.8214u − 0.849966
0.698222u
110
− 0.237275u
109
+ ··· − 24.5823u + 3.29697
a
3
=
0.676351u
110
+ 1.22744u
109
+ ··· − 101.879u + 5.95117
−5.00556u
110
+ 4.25267u
109
+ ··· − 104.692u + 8.32936
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
u
8
− 2u
6
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −13.5527u
110
+ 17.8532u
109
+ ··· − 506.209u + 43.1001
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
111
− 16u
110
+ ··· + 15u + 1
c
2
, c
7
u
111
− u
110
+ ··· + 2080u − 1879
c
3
u
111
− u
110
+ ··· − 49u − 5
c
4
, c
5
, c
11
u
111
− 2u
110
+ ··· − 17u + 1
c
6
, c
10
u
111
+ 3u
110
+ ··· − 42277u + 3245
c
8
, c
12
u
111
− u
110
+ ··· − 882u + 271
c
9
u
111
+ 2u
110
+ ··· − 123711u + 123383
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
111
− 4y
110
+ ··· + 567y −1
c
2
, c
7
y
111
− 85y
110
+ ··· + 140050328y −3530641
c
3
y
111
− y
110
+ ··· + 881y −25
c
4
, c
5
, c
11
y
111
− 92y
110
+ ··· + 81y −1
c
6
, c
10
y
111
+ 87y
110
+ ··· + 1070147809y −10530025
c
8
, c
12
y
111
− 63y
110
+ ··· + 624538y −73441
c
9
y
111
− 34y
110
+ ··· + 1350344005825y −15223364689
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.081166 + 0.904115I
a = −0.344352 + 0.904100I
b = −0.205252 + 0.162622I
7.50937 + 0.87155I 0
u = −0.081166 − 0.904115I
a = −0.344352 − 0.904100I
b = −0.205252 − 0.162622I
7.50937 − 0.87155I 0
u = −0.121934 + 0.870862I
a = −0.96469 − 1.31541I
b = −1.313980 + 0.103964I
6.3847 + 13.3757I 0
u = −0.121934 − 0.870862I
a = −0.96469 + 1.31541I
b = −1.313980 − 0.103964I
6.3847 − 13.3757I 0
u = 0.154867 + 0.858936I
a = −0.632403 + 0.871576I
b = −0.954252 − 0.565366I
7.30644 − 4.30172I 0
u = 0.154867 − 0.858936I
a = −0.632403 − 0.871576I
b = −0.954252 + 0.565366I
7.30644 + 4.30172I 0
u = −0.028698 + 0.855465I
a = −0.428888 − 0.916164I
b = −0.819599 − 0.897102I
7.25427 + 3.69556I 0
u = −0.028698 − 0.855465I
a = −0.428888 + 0.916164I
b = −0.819599 + 0.897102I
7.25427 − 3.69556I 0
u = 0.091469 + 0.844247I
a = −1.35317 − 0.57053I
b = −0.863472 − 0.322494I
9.30952 − 6.81701I 0
u = 0.091469 − 0.844247I
a = −1.35317 + 0.57053I
b = −0.863472 + 0.322494I
9.30952 + 6.81701I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.084410 + 0.417528I
a = 0.442236 − 0.588081I
b = 1.139120 + 0.401544I
4.45379 − 0.29837I 0
u = 1.084410 − 0.417528I
a = 0.442236 + 0.588081I
b = 1.139120 − 0.401544I
4.45379 + 0.29837I 0
u = 0.080213 + 0.812540I
a = 0.73148 − 1.41337I
b = 1.282600 + 0.337159I
1.52000 − 6.82635I 0. + 6.98056I
u = 0.080213 − 0.812540I
a = 0.73148 + 1.41337I
b = 1.282600 − 0.337159I
1.52000 + 6.82635I 0. − 6.98056I
u = −0.025621 + 0.814330I
a = 1.019490 − 0.056681I
b = 0.598997 − 0.234326I
4.98734 + 2.15996I 0
u = −0.025621 − 0.814330I
a = 1.019490 + 0.056681I
b = 0.598997 + 0.234326I
4.98734 − 2.15996I 0
u = −0.526631 + 0.615019I
a = −0.47851 − 1.41722I
b = −0.547739 − 0.056493I
0.59594 − 4.27717I 0
u = −0.526631 − 0.615019I
a = −0.47851 + 1.41722I
b = −0.547739 + 0.056493I
0.59594 + 4.27717I 0
u = −1.179560 + 0.191654I
a = −0.551352 − 0.599227I
b = −0.158132 − 0.269581I
−1.82003 + 0.41789I 0
u = −1.179560 − 0.191654I
a = −0.551352 + 0.599227I
b = −0.158132 + 0.269581I
−1.82003 − 0.41789I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.012361 + 0.800991I
a = −0.442197 − 1.094450I
b = −1.60146 + 0.33849I
6.98387 − 0.56475I 1.87354 + 0.I
u = 0.012361 − 0.800991I
a = −0.442197 + 1.094450I
b = −1.60146 − 0.33849I
6.98387 + 0.56475I 1.87354 + 0.I
u = 0.025664 + 0.796748I
a = −1.23003 + 1.38707I
b = −1.250320 + 0.348318I
2.91600 − 3.82224I 0. + 4.16476I
u = 0.025664 − 0.796748I
a = −1.23003 − 1.38707I
b = −1.250320 − 0.348318I
2.91600 + 3.82224I 0. − 4.16476I
u = −0.524571 + 0.585182I
a = 1.51013 + 0.68318I
b = 1.199700 − 0.103549I
0.56437 + 8.53514I −4.00000 − 8.97660I
u = −0.524571 − 0.585182I
a = 1.51013 − 0.68318I
b = 1.199700 + 0.103549I
0.56437 − 8.53514I −4.00000 + 8.97660I
u = 1.215450 + 0.034160I
a = −0.655743 − 0.538750I
b = −0.82287 − 1.17849I
−4.37066 − 2.85132I 0
u = 1.215450 − 0.034160I
a = −0.655743 + 0.538750I
b = −0.82287 + 1.17849I
−4.37066 + 2.85132I 0
u = −1.142310 + 0.441405I
a = 0.741922 + 0.868519I
b = 0.759050 − 0.116604I
3.25745 − 8.68324I 0
u = −1.142310 − 0.441405I
a = 0.741922 − 0.868519I
b = 0.759050 + 0.116604I
3.25745 + 8.68324I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.230730 + 0.129770I
a = 0.847427 + 0.283143I
b = 1.58411 − 1.41763I
−3.36757 − 4.77773I 0
u = 1.230730 − 0.129770I
a = 0.847427 − 0.283143I
b = 1.58411 + 1.41763I
−3.36757 + 4.77773I 0
u = 1.175080 + 0.397243I
a = −0.586512 − 0.763040I
b = −1.220310 + 0.097965I
5.98708 + 2.35229I 0
u = 1.175080 − 0.397243I
a = −0.586512 + 0.763040I
b = −1.220310 − 0.097965I
5.98708 − 2.35229I 0
u = 1.190270 + 0.350522I
a = −0.790578 + 0.647954I
b = −1.292380 − 0.473108I
−1.87331 + 2.61985I 0
u = 1.190270 − 0.350522I
a = −0.790578 − 0.647954I
b = −1.292380 + 0.473108I
−1.87331 − 2.61985I 0
u = 1.25185
a = 0.708215
b = 6.74388
−0.842109 0
u = −0.129040 + 0.730302I
a = 1.05885 + 1.38972I
b = 0.986008 + 0.154802I
1.16972 + 3.02941I 0.581656 − 0.502191I
u = −0.129040 − 0.730302I
a = 1.05885 − 1.38972I
b = 0.986008 − 0.154802I
1.16972 − 3.02941I 0.581656 + 0.502191I
u = −1.273620 + 0.076602I
a = −0.344736 − 0.467111I
b = 0.378767 + 0.209717I
−1.89161 + 0.63320I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.273620 − 0.076602I
a = −0.344736 + 0.467111I
b = 0.378767 − 0.209717I
−1.89161 − 0.63320I 0
u = −0.052261 + 0.719313I
a = 0.56144 + 1.85689I
b = 0.362230 + 0.199391I
0.82057 + 2.54626I −3.60718 − 1.85382I
u = −0.052261 − 0.719313I
a = 0.56144 − 1.85689I
b = 0.362230 − 0.199391I
0.82057 − 2.54626I −3.60718 + 1.85382I
u = −1.193200 + 0.465317I
a = −0.743332 + 0.064065I
b = −1.140780 − 0.292617I
4.08896 + 4.00061I 0
u = −1.193200 − 0.465317I
a = −0.743332 − 0.064065I
b = −1.140780 + 0.292617I
4.08896 − 4.00061I 0
u = 1.279440 + 0.124995I
a = −0.161902 − 0.194584I
b = −0.565355 − 1.026320I
−4.72872 − 2.56138I 0
u = 1.279440 − 0.124995I
a = −0.161902 + 0.194584I
b = −0.565355 + 1.026320I
−4.72872 + 2.56138I 0
u = −1.292750 + 0.034714I
a = 1.015070 − 0.528316I
b = 3.98562 − 0.36189I
−5.84342 + 3.49242I 0
u = −1.292750 − 0.034714I
a = 1.015070 + 0.528316I
b = 3.98562 + 0.36189I
−5.84342 − 3.49242I 0
u = −1.260740 + 0.296765I
a = −0.974598 − 0.581114I
b = −1.86237 − 1.41018I
−2.94268 + 1.10354I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.260740 − 0.296765I
a = −0.974598 + 0.581114I
b = −1.86237 + 1.41018I
−2.94268 − 1.10354I 0
u = 1.249570 + 0.345703I
a = 0.603798 − 0.930670I
b = −0.138375 − 0.619119I
−0.866061 − 0.293007I 0
u = 1.249570 − 0.345703I
a = 0.603798 + 0.930670I
b = −0.138375 + 0.619119I
−0.866061 + 0.293007I 0
u = −1.245970 + 0.359010I
a = 0.251361 − 0.577708I
b = 0.535194 − 0.101397I
1.21676 + 2.06299I 0
u = −1.245970 − 0.359010I
a = 0.251361 + 0.577708I
b = 0.535194 + 0.101397I
1.21676 − 2.06299I 0
u = 1.261040 + 0.349927I
a = −0.733629 − 0.044182I
b = −3.33029 + 2.29901I
3.11498 − 3.57845I 0
u = 1.261040 − 0.349927I
a = −0.733629 + 0.044182I
b = −3.33029 − 2.29901I
3.11498 + 3.57845I 0
u = −1.246320 + 0.399264I
a = 0.508156 + 0.407138I
b = −0.756437 + 0.263088I
3.48869 + 0.80412I 0
u = −1.246320 − 0.399264I
a = 0.508156 − 0.407138I
b = −0.756437 − 0.263088I
3.48869 − 0.80412I 0
u = −1.279340 + 0.353280I
a = 0.525220 + 0.477688I
b = 0.562776 − 1.283690I
2.96533 + 4.72137I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.279340 − 0.353280I
a = 0.525220 − 0.477688I
b = 0.562776 + 1.283690I
2.96533 − 4.72137I 0
u = −1.288410 + 0.349720I
a = −1.044060 + 0.445837I
b = −2.76410 − 1.24036I
−1.17957 + 7.95243I 0
u = −1.288410 − 0.349720I
a = −1.044060 − 0.445837I
b = −2.76410 + 1.24036I
−1.17957 − 7.95243I 0
u = 1.286620 + 0.362863I
a = 0.215037 + 0.603548I
b = 1.142380 + 0.534124I
0.90063 − 6.39648I 0
u = 1.286620 − 0.362863I
a = 0.215037 − 0.603548I
b = 1.142380 − 0.534124I
0.90063 + 6.39648I 0
u = 1.293240 + 0.390759I
a = −0.647394 − 0.092804I
b = −0.62304 + 1.60161I
3.13563 − 8.16662I 0
u = 1.293240 − 0.390759I
a = −0.647394 + 0.092804I
b = −0.62304 − 1.60161I
3.13563 + 8.16662I 0
u = 1.316370 + 0.314217I
a = 1.066920 − 0.099320I
b = 2.70014 − 1.07266I
−3.50013 − 6.30583I 0
u = 1.316370 − 0.314217I
a = 1.066920 + 0.099320I
b = 2.70014 + 1.07266I
−3.50013 + 6.30583I 0
u = −1.357420 + 0.123005I
a = 0.055884 − 0.790870I
b = 0.219826 − 1.339850I
−1.79691 + 5.42824I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.357420 − 0.123005I
a = 0.055884 + 0.790870I
b = 0.219826 + 1.339850I
−1.79691 − 5.42824I 0
u = −1.361100 + 0.084061I
a = −0.889472 + 0.178559I
b = −4.43462 − 0.05589I
−8.65164 + 5.28818I 0
u = −1.361100 − 0.084061I
a = −0.889472 − 0.178559I
b = −4.43462 + 0.05589I
−8.65164 − 5.28818I 0
u = −1.354580 + 0.206679I
a = 0.753347 + 0.206126I
b = 3.12215 + 1.39177I
−7.16797 + 1.58311I 0
u = −1.354580 − 0.206679I
a = 0.753347 − 0.206126I
b = 3.12215 − 1.39177I
−7.16797 − 1.58311I 0
u = −1.322880 + 0.358837I
a = 0.959315 − 0.094899I
b = 3.52906 + 1.42336I
−2.87719 + 11.04810I 0
u = −1.322880 − 0.358837I
a = 0.959315 + 0.094899I
b = 3.52906 − 1.42336I
−2.87719 − 11.04810I 0
u = 0.527747 + 0.332177I
a = 0.694115 + 0.501497I
b = 1.059300 + 0.321123I
3.19985 + 0.32140I 1.59922 + 2.05291I
u = 0.527747 − 0.332177I
a = 0.694115 − 0.501497I
b = 1.059300 − 0.321123I
3.19985 − 0.32140I 1.59922 − 2.05291I
u = 1.341820 + 0.311397I
a = 1.028620 + 0.219802I
b = 2.94137 − 1.00859I
−3.46066 − 6.81605I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.341820 − 0.311397I
a = 1.028620 − 0.219802I
b = 2.94137 + 1.00859I
−3.46066 + 6.81605I 0
u = 1.380850 + 0.001402I
a = −1.002190 + 0.099681I
b = −3.63865 + 0.11066I
−7.48663 + 0.05717I 0
u = 1.380850 − 0.001402I
a = −1.002190 − 0.099681I
b = −3.63865 − 0.11066I
−7.48663 − 0.05717I 0
u = −0.618101 + 0.029425I
a = −1.74047 + 0.02330I
b = −0.535160 − 0.050220I
−1.53250 + 0.00940I −7.61099 + 0.23089I
u = −0.618101 − 0.029425I
a = −1.74047 − 0.02330I
b = −0.535160 + 0.050220I
−1.53250 − 0.00940I −7.61099 − 0.23089I
u = −1.332360 + 0.374895I
a = −0.013321 + 0.926101I
b = −0.998412 + 0.993180I
4.84444 + 11.19960I 0
u = −1.332360 − 0.374895I
a = −0.013321 − 0.926101I
b = −0.998412 − 0.993180I
4.84444 − 11.19960I 0
u = 0.387681 + 0.471766I
a = 0.94998 + 1.12985I
b = 0.192196 − 0.091930I
3.65065 − 3.48280I 1.08914 + 6.57604I
u = 0.387681 − 0.471766I
a = 0.94998 − 1.12985I
b = 0.192196 + 0.091930I
3.65065 + 3.48280I 1.08914 − 6.57604I
u = 1.331550 + 0.416484I
a = 0.431825 − 0.390425I
b = 0.625797 − 0.534575I
3.09221 − 5.59637I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.331550 − 0.416484I
a = 0.431825 + 0.390425I
b = 0.625797 + 0.534575I
3.09221 + 5.59637I 0
u = 0.239442 + 0.553403I
a = 0.29215 − 1.63161I
b = 0.814891 + 0.000066I
−2.15238 + 1.18175I −5.85912 + 1.80919I
u = 0.239442 − 0.553403I
a = 0.29215 + 1.63161I
b = 0.814891 − 0.000066I
−2.15238 − 1.18175I −5.85912 − 1.80919I
u = 1.354290 + 0.385786I
a = −1.013040 − 0.215829I
b = −3.22338 + 1.21261I
1.7439 − 17.8882I 0
u = 1.354290 − 0.385786I
a = −1.013040 + 0.215829I
b = −3.22338 − 1.21261I
1.7439 + 17.8882I 0
u = −1.37149 + 0.37859I
a = −0.688647 + 0.081503I
b = −2.89193 − 0.66737I
2.49624 + 8.75887I 0
u = −1.37149 − 0.37859I
a = −0.688647 − 0.081503I
b = −2.89193 + 0.66737I
2.49624 − 8.75887I 0
u = 1.42545 + 0.14891I
a = 0.929723 + 0.271581I
b = 3.68084 − 0.20743I
−5.71189 − 10.93540I 0
u = 1.42545 − 0.14891I
a = 0.929723 − 0.271581I
b = 3.68084 + 0.20743I
−5.71189 + 10.93540I 0
u = 0.449955 + 0.306106I
a = −2.03754 + 0.58119I
b = −1.245410 − 0.306755I
−3.08409 − 4.01496I −8.48201 + 7.35166I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.449955 − 0.306106I
a = −2.03754 − 0.58119I
b = −1.245410 + 0.306755I
−3.08409 + 4.01496I −8.48201 − 7.35166I
u = −0.105666 + 0.512091I
a = 0.97329 + 1.87270I
b = 0.490136 + 0.627445I
0.52426 + 2.56205I 0.27637 − 5.10765I
u = −0.105666 − 0.512091I
a = 0.97329 − 1.87270I
b = 0.490136 − 0.627445I
0.52426 − 2.56205I 0.27637 + 5.10765I
u = 1.47079 + 0.14608I
a = −0.745847 + 0.294962I
b = −2.71132 + 0.77604I
−5.95978 + 1.70857I 0
u = 1.47079 − 0.14608I
a = −0.745847 − 0.294962I
b = −2.71132 − 0.77604I
−5.95978 − 1.70857I 0
u = −1.50434
a = 0.492040
b = 2.97475
−3.63276 0
u = −0.225847 + 0.327044I
a = −0.800511 + 0.558951I
b = −0.020085 + 0.267612I
−0.235196 + 0.938220I −4.68352 − 7.13050I
u = −0.225847 − 0.327044I
a = −0.800511 − 0.558951I
b = −0.020085 − 0.267612I
−0.235196 − 0.938220I −4.68352 + 7.13050I
u = 0.151934 + 0.115584I
a = 6.77942 − 0.80780I
b = 0.686578 − 0.179927I
−1.43186 − 2.95721I −9.1241 + 11.4688I
u = 0.151934 − 0.115584I
a = 6.77942 + 0.80780I
b = 0.686578 + 0.179927I
−1.43186 + 2.95721I −9.1241 − 11.4688I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119052
a = −5.01443
b = 1.98261
2.72207 12.4830
16
II.
I
u
2
= hu
20
−u
19
+· · ·+ b−u, −u
20
+10u
18
+· · ·+ a + 1 , u
21
−10u
19
+· · ·−18u
3
−1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
8
=
u
20
− 10u
18
+ ··· − 3u − 1
−u
20
+ u
19
+ ··· − 6u
2
+ u
a
1
=
u
19
+ u
18
+ ··· + 5u + 2
−u
20
+ 3u
19
+ ··· − u + 2
a
9
=
−u
19
+ 9u
17
+ ··· + 3u + 1
−2u
20
− u
19
+ ··· + u − 1
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
u
20
+ u
19
+ ··· + 6u + 2
u
20
+ 3u
19
+ ··· + 6u
2
+ 2
a
3
=
u
19
+ u
18
+ ··· + 5u + 3
3u
19
+ u
18
+ ··· − u + 2
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
u
8
− 2u
6
+ 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −12u
19
− 2u
18
+ 100u
17
+ 17u
16
− 336u
15
− 58u
14
+ 535u
13
+ 92u
12
− 271u
11
−
41u
10
− 324u
9
− 56u
8
+ 442u
7
+ 40u
6
− 28u
5
+ 46u
4
− 134u
3
− 32u
2
+ 12u − 14
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 2u
19
+ ··· − 6u + 1
c
2
u
21
+ u
20
+ ··· + u + 1
c
3
u
21
− 2u
19
+ ··· + 3u
2
+ 1
c
4
, c
5
u
21
− 10u
19
+ ··· − 18u
3
− 1
c
6
u
21
+ 6u
19
+ ··· + 3u
2
− 1
c
7
u
21
− u
20
+ ··· + u − 1
c
8
u
21
− u
20
+ ··· + u − 1
c
9
u
21
+ 3u
19
+ ··· − 2u
2
+ 1
c
10
u
21
+ 6u
19
+ ··· − 3u
2
+ 1
c
11
u
21
− 10u
19
+ ··· − 18u
3
+ 1
c
12
u
21
+ u
20
+ ··· + u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
− 4y
20
+ ··· + 10y −1
c
2
, c
7
y
21
− 21y
20
+ ··· + 15y −1
c
3
y
21
− 4y
20
+ ··· − 6y −1
c
4
, c
5
, c
11
y
21
− 20y
20
+ ··· + 12y
2
− 1
c
6
, c
10
y
21
+ 12y
20
+ ··· + 6y −1
c
8
, c
12
y
21
− 15y
20
+ ··· + 21y −1
c
9
y
21
+ 6y
20
+ ··· + 4y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.062614 + 0.857160I
a = 0.275352 + 0.744219I
b = 0.991659 + 0.241341I
7.09483 + 2.69700I 0.204052 − 0.960418I
u = −0.062614 − 0.857160I
a = 0.275352 − 0.744219I
b = 0.991659 − 0.241341I
7.09483 − 2.69700I 0.204052 + 0.960418I
u = −1.18462
a = 0.514078
b = −3.17275
−0.0653881 2.89470
u = 1.235030 + 0.104057I
a = −0.770955 − 0.434248I
b = −1.68506 − 0.31727I
−4.45553 − 3.99750I −8.33700 + 7.35069I
u = 1.235030 − 0.104057I
a = −0.770955 + 0.434248I
b = −1.68506 + 0.31727I
−4.45553 + 3.99750I −8.33700 − 7.35069I
u = 1.234780 + 0.272929I
a = 0.736844 − 0.846584I
b = 0.398323 − 0.870978I
−2.77607 + 0.23467I −9.48318 − 3.28637I
u = 1.234780 − 0.272929I
a = 0.736844 + 0.846584I
b = 0.398323 + 0.870978I
−2.77607 − 0.23467I −9.48318 + 3.28637I
u = −1.212920 + 0.392860I
a = −0.439696 − 0.262167I
b = 0.203010 + 0.888489I
3.55654 + 1.79152I −2.35096 − 2.63279I
u = −1.212920 − 0.392860I
a = −0.439696 + 0.262167I
b = 0.203010 − 0.888489I
3.55654 − 1.79152I −2.35096 + 2.63279I
u = 0.072517 + 0.710236I
a = −1.26753 + 1.64767I
b = −1.045360 + 0.236003I
0.77767 − 3.77401I −4.35410 + 8.39040I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.072517 − 0.710236I
a = −1.26753 − 1.64767I
b = −1.045360 − 0.236003I
0.77767 + 3.77401I −4.35410 − 8.39040I
u = −1.323560 + 0.298366I
a = −1.111640 + 0.313500I
b = −3.17414 − 0.98120I
−3.62134 + 7.43161I −8.6486 − 11.9040I
u = −1.323560 − 0.298366I
a = −1.111640 − 0.313500I
b = −3.17414 + 0.98120I
−3.62134 − 7.43161I −8.6486 + 11.9040I
u = 1.316400 + 0.393822I
a = 0.515998 + 0.022497I
b = 1.35440 − 1.33801I
2.78443 − 7.19164I −4.22867 + 4.01785I
u = 1.316400 − 0.393822I
a = 0.515998 − 0.022497I
b = 1.35440 + 1.33801I
2.78443 + 7.19164I −4.22867 − 4.01785I
u = −1.391350 + 0.102602I
a = 0.845334 + 0.317790I
b = 3.00093 + 0.78369I
−6.34020 − 0.86818I −9.18780 − 0.27914I
u = −1.391350 − 0.102602I
a = 0.845334 − 0.317790I
b = 3.00093 − 0.78369I
−6.34020 + 0.86818I −9.18780 + 0.27914I
u = 1.47523
a = −0.549398
b = −3.38448
−3.89149 −19.3050
u = −0.385686
a = −1.78797
b = −2.12563
2.41587 −14.8360
u = 0.179252 + 0.337282I
a = 0.12794 − 3.11208I
b = 0.297662 − 0.095157I
−1.18464 + 2.46905I −1.99075 + 0.76816I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.179252 − 0.337282I
a = 0.12794 + 3.11208I
b = 0.297662 + 0.095157I
−1.18464 − 2.46905I −1.99075 − 0.76816I
22
III. I
u
3
= hb, a + 1, u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
−1
a
6
=
1
1
a
8
=
−1
0
a
1
=
1
−1
a
9
=
0
−1
a
11
=
−1
−1
a
4
=
0
−1
a
2
=
1
0
a
3
=
0
−1
a
10
=
−1
−1
a
7
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u − 1
c
2
, c
4
, c
5
c
7
, c
8
, c
9
c
11
, c
12
u + 1
c
3
, c
6
, c
10
u
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
9
, c
11
, c
12
y −1
c
3
, c
6
, c
10
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = 0
−1.64493 −6.00000
26
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
21
− 2u
19
+ ··· − 6u + 1)(u
111
− 16u
110
+ ··· + 15u + 1)
c
2
(u + 1)(u
21
+ u
20
+ ··· + u + 1)(u
111
− u
110
+ ··· + 2080u − 1879)
c
3
u(u
21
− 2u
19
+ ··· + 3u
2
+ 1)(u
111
− u
110
+ ··· − 49u − 5)
c
4
, c
5
(u + 1)(u
21
− 10u
19
+ ··· − 18u
3
− 1)(u
111
− 2u
110
+ ··· − 17u + 1)
c
6
u(u
21
+ 6u
19
+ ··· + 3u
2
− 1)(u
111
+ 3u
110
+ ··· − 42277u + 3245)
c
7
(u + 1)(u
21
− u
20
+ ··· + u − 1)(u
111
− u
110
+ ··· + 2080u − 1879)
c
8
(u + 1)(u
21
− u
20
+ ··· + u − 1)(u
111
− u
110
+ ··· − 882u + 271)
c
9
(u + 1)(u
21
+ 3u
19
+ ··· − 2u
2
+ 1)
· (u
111
+ 2u
110
+ ··· − 123711u + 123383)
c
10
u(u
21
+ 6u
19
+ ··· − 3u
2
+ 1)(u
111
+ 3u
110
+ ··· − 42277u + 3245)
c
11
(u + 1)(u
21
− 10u
19
+ ··· − 18u
3
+ 1)(u
111
− 2u
110
+ ··· − 17u + 1)
c
12
(u + 1)(u
21
+ u
20
+ ··· + u + 1)(u
111
− u
110
+ ··· − 882u + 271)
27
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
21
− 4y
20
+ ··· + 10y −1)(y
111
− 4y
110
+ ··· + 567y −1)
c
2
, c
7
(y −1)(y
21
− 21y
20
+ ··· + 15y −1)
· (y
111
− 85y
110
+ ··· + 140050328y −3530641)
c
3
y(y
21
− 4y
20
+ ··· − 6y −1)(y
111
− y
110
+ ··· + 881y −25)
c
4
, c
5
, c
11
(y −1)(y
21
− 20y
20
+ ··· + 12y
2
− 1)(y
111
− 92y
110
+ ··· + 81y −1)
c
6
, c
10
y(y
21
+ 12y
20
+ ··· + 6y −1)
· (y
111
+ 87y
110
+ ··· + 1070147809y −10530025)
c
8
, c
12
(y −1)(y
21
− 15y
20
+ ··· + 21y −1)
· (y
111
− 63y
110
+ ··· + 624538y −73441)
c
9
(y −1)(y
21
+ 6y
20
+ ··· + 4y −1)
· (y
111
− 34y
110
+ ··· + 1350344005825y −15223364689)
28
