12a
0830
(K12a
0830
)
A knot diagram
1
Linearized knot diagam
4 5 8 2 10 12 3 11 1 7 9 6
Solving Sequence
3,8 4,11
9 12 7 6 1 10 5 2
c
3
c
8
c
11
c
7
c
6
c
12
c
9
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.45248 × 10
403
u
112
+ 2.57534 × 10
403
u
111
+ ··· + 7.60655 × 10
404
b − 1.41148 × 10
405
,
− 3.58295 × 10
402
u
112
+ 6.66928 × 10
402
u
111
+ ··· + 8.94888 × 10
403
a − 1.02347 × 10
405
,
u
113
− 2u
112
+ ··· + 896u − 256i
I
u
2
= h−22u
2
+ 17b + 15u − 40, −u
2
+ a + u − 2, u
3
− u
2
+ 2u − 1i
I
v
1
= ha, 72v
7
− 466v
6
− 1954v
5
+ 4124v
4
+ 13122v
3
− 3530v
2
+ 887b − 5049v + 2666,
v
8
+ 3v
7
− 7v
6
− 28v
5
− 13v
4
+ 8v
3
− 2v + 1i
* 3 irreducible components of dim
C
= 0, with total 124 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−1.45 × 10
403
u
112
+ 2.58 × 10
403
u
111
+ · · · + 7.61 × 10
404
b − 1.41 ×
10
405
, −3.58 × 10
402
u
112
+ 6.67 × 10
402
u
111
+ · · · + 8.95 × 10
403
a − 1.02 ×
10
405
, u
113
− 2u
112
+ · · · + 896u − 256i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
0.0400380u
112
− 0.0745263u
111
+ ··· + 1.44165u + 11.4369
0.0190951u
112
− 0.0338568u
111
+ ··· + 5.71448u + 1.85561
a
9
=
−0.00768519u
112
+ 0.0258094u
111
+ ··· − 28.2706u + 7.32413
0.0215710u
112
− 0.0343632u
111
+ ··· − 2.70707u + 4.95920
a
12
=
0.0166558u
112
− 0.0116771u
111
+ ··· − 31.1306u + 11.0180
−0.00139532u
112
+ 0.00197886u
111
+ ··· + 4.41793u − 1.91206
a
7
=
u
u
a
6
=
−0.0623893u
112
+ 0.0719018u
111
+ ··· + 82.4207u − 33.2834
−0.0116805u
112
+ 0.0134724u
111
+ ··· + 15.8056u − 5.85623
a
1
=
0.0408769u
112
− 0.0373320u
111
+ ··· − 84.9975u + 34.3053
0.0107707u
112
− 0.0171522u
111
+ ··· − 3.86228u + 2.98419
a
10
=
0.0397259u
112
− 0.0772883u
111
+ ··· + 5.71328u + 11.7482
0.0187830u
112
− 0.0366188u
111
+ ··· + 9.98611u + 2.16697
a
5
=
−0.0428338u
112
+ 0.0321310u
111
+ ··· + 110.473u − 42.6931
−0.00195693u
112
− 0.00520094u
111
+ ··· + 25.4752u − 8.38781
a
2
=
0.0428338u
112
− 0.0321310u
111
+ ··· − 110.473u + 42.6931
0.00867147u
112
− 0.0107891u
111
+ ··· − 11.5282u + 5.31757
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.146247u
112
− 0.233542u
111
+ ··· − 65.9092u + 69.0820
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
113
− 10u
112
+ ··· + u − 1
c
3
, c
7
u
113
− 2u
112
+ ··· + 896u − 256
c
5
u
113
+ 2u
112
+ ··· − 41820u − 2312
c
6
, c
12
u
113
+ 3u
112
+ ··· + 3u + 1
c
8
, c
11
u
113
+ 5u
112
+ ··· − 1158u + 289
c
9
17(17u
113
+ 219u
112
+ ··· + 16199u + 2539)
c
10
17(17u
113
+ 212u
112
+ ··· − 115224u − 34421)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
113
− 100y
112
+ ··· − 13y −1
c
3
, c
7
y
113
− 48y
112
+ ··· + 1425408y −65536
c
5
y
113
+ 18y
112
+ ··· + 117380240y −5345344
c
6
, c
12
y
113
+ 61y
112
+ ··· + 19y −1
c
8
, c
11
y
113
− 69y
112
+ ··· + 10227136y −83521
c
9
289(289y
113
+ 6473y
112
+ ··· − 3.80828 × 10
8
y −6446521)
c
10
289(289y
113
− 1016y
112
+ ··· − 6.58097 × 10
9
y −1.18481 × 10
9
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.838996 + 0.519691I
a = −1.00735 − 0.99352I
b = −0.72221 − 1.67273I
2.81518 + 2.25501I 0
u = −0.838996 − 0.519691I
a = −1.00735 + 0.99352I
b = −0.72221 + 1.67273I
2.81518 − 2.25501I 0
u = −0.408038 + 0.896770I
a = 1.006650 + 0.985618I
b = −0.287546 + 0.217220I
2.05403 − 8.53878I 0
u = −0.408038 − 0.896770I
a = 1.006650 − 0.985618I
b = −0.287546 − 0.217220I
2.05403 + 8.53878I 0
u = 0.991916 + 0.215082I
a = −0.462328 − 0.945148I
b = −0.14976 − 2.01843I
−5.58135 − 3.04071I 0
u = 0.991916 − 0.215082I
a = −0.462328 + 0.945148I
b = −0.14976 + 2.01843I
−5.58135 + 3.04071I 0
u = 0.866741 + 0.411780I
a = −0.140138 + 0.673956I
b = 0.45614 + 1.69373I
−4.97488 + 1.61721I 0
u = 0.866741 − 0.411780I
a = −0.140138 − 0.673956I
b = 0.45614 − 1.69373I
−4.97488 − 1.61721I 0
u = 0.882043 + 0.367780I
a = 0.916925 − 0.363319I
b = 5.05394 − 4.27372I
−0.45862 − 1.47435I 0
u = 0.882043 − 0.367780I
a = 0.916925 + 0.363319I
b = 5.05394 + 4.27372I
−0.45862 + 1.47435I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950581 + 0.000527I
a = 0.174135 − 0.403894I
b = −0.251243 − 0.903353I
−1.61934 − 0.33597I 0
u = −0.950581 − 0.000527I
a = 0.174135 + 0.403894I
b = −0.251243 + 0.903353I
−1.61934 + 0.33597I 0
u = −0.264647 + 1.026570I
a = −0.547724 + 0.190022I
b = 0.072210 + 0.674929I
−3.04736 − 1.94290I 0
u = −0.264647 − 1.026570I
a = −0.547724 − 0.190022I
b = 0.072210 − 0.674929I
−3.04736 + 1.94290I 0
u = −0.770530 + 0.533723I
a = −1.34205 − 0.86042I
b = −0.491734 − 0.873041I
3.01974 + 2.02401I 0
u = −0.770530 − 0.533723I
a = −1.34205 + 0.86042I
b = −0.491734 + 0.873041I
3.01974 − 2.02401I 0
u = 0.916425 + 0.542126I
a = 0.543187 − 1.265160I
b = 1.04849 − 2.00825I
1.51696 − 5.57365I 0
u = 0.916425 − 0.542126I
a = 0.543187 + 1.265160I
b = 1.04849 + 2.00825I
1.51696 + 5.57365I 0
u = −0.412108 + 0.839424I
a = −1.25948 − 0.65985I
b = −0.650987 + 0.011237I
−1.33451 − 3.90121I 0
u = −0.412108 − 0.839424I
a = −1.25948 + 0.65985I
b = −0.650987 − 0.011237I
−1.33451 + 3.90121I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.421431 + 0.994250I
a = −0.613154 + 0.932683I
b = 0.151544 + 0.326452I
5.67260 + 2.25032I 0
u = 0.421431 − 0.994250I
a = −0.613154 − 0.932683I
b = 0.151544 − 0.326452I
5.67260 − 2.25032I 0
u = 1.059570 + 0.262581I
a = 0.712742 + 0.963156I
b = 0.482469 + 1.082270I
−6.01723 + 1.75193I 0
u = 1.059570 − 0.262581I
a = 0.712742 − 0.963156I
b = 0.482469 − 1.082270I
−6.01723 − 1.75193I 0
u = −0.178317 + 0.889819I
a = −0.102170 + 1.311780I
b = 0.091301 + 0.336535I
1.40611 + 4.98571I 0
u = −0.178317 − 0.889819I
a = −0.102170 − 1.311780I
b = 0.091301 − 0.336535I
1.40611 − 4.98571I 0
u = 1.026740 + 0.452876I
a = −0.206733 − 0.619596I
b = 0.322496 − 1.288060I
−0.43516 − 3.99400I 0
u = 1.026740 − 0.452876I
a = −0.206733 + 0.619596I
b = 0.322496 + 1.288060I
−0.43516 + 3.99400I 0
u = −0.147482 + 0.860639I
a = −0.078885 − 0.997481I
b = 2.01220 + 1.74431I
−2.76031 + 0.24285I 0
u = −0.147482 − 0.860639I
a = −0.078885 + 0.997481I
b = 2.01220 − 1.74431I
−2.76031 − 0.24285I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663375 + 0.552902I
a = 1.62689 − 0.44683I
b = 0.440564 + 0.189870I
2.27246 + 1.15394I 0
u = 0.663375 − 0.552902I
a = 1.62689 + 0.44683I
b = 0.440564 − 0.189870I
2.27246 − 1.15394I 0
u = −1.049270 + 0.438478I
a = −1.48445 − 0.07161I
b = −0.283300 + 0.241625I
−2.25009 + 1.62166I 0
u = −1.049270 − 0.438478I
a = −1.48445 + 0.07161I
b = −0.283300 − 0.241625I
−2.25009 − 1.62166I 0
u = 0.372291 + 1.075220I
a = 0.893472 + 0.533881I
b = −0.100674 + 0.838595I
−6.75012 + 5.58489I 0
u = 0.372291 − 1.075220I
a = 0.893472 − 0.533881I
b = −0.100674 − 0.838595I
−6.75012 − 5.58489I 0
u = 0.585401 + 0.984534I
a = −0.589549 + 0.283157I
b = 0.310277 + 0.798211I
−5.62759 + 0.96807I 0
u = 0.585401 − 0.984534I
a = −0.589549 − 0.283157I
b = 0.310277 − 0.798211I
−5.62759 − 0.96807I 0
u = −1.092830 + 0.345580I
a = −0.898356 + 0.425627I
b = −0.256094 + 1.082330I
−3.59891 + 1.83803I 0
u = −1.092830 − 0.345580I
a = −0.898356 − 0.425627I
b = −0.256094 − 1.082330I
−3.59891 − 1.83803I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.077910 + 0.497831I
a = 1.29175 − 0.59886I
b = 0.269810 − 0.726531I
−1.75667 − 5.14933I 0
u = 1.077910 − 0.497831I
a = 1.29175 + 0.59886I
b = 0.269810 + 0.726531I
−1.75667 + 5.14933I 0
u = −1.071000 + 0.514282I
a = 0.588970 − 0.871405I
b = 0.29900 − 1.80560I
−3.93453 + 7.72346I 0
u = −1.071000 − 0.514282I
a = 0.588970 + 0.871405I
b = 0.29900 + 1.80560I
−3.93453 − 7.72346I 0
u = 1.152530 + 0.421776I
a = −0.792525 + 0.804291I
b = −1.29757 + 1.95478I
−2.42982 − 8.85973I 0
u = 1.152530 − 0.421776I
a = −0.792525 − 0.804291I
b = −1.29757 − 1.95478I
−2.42982 + 8.85973I 0
u = 1.179560 + 0.366055I
a = 0.424815 − 0.004211I
b = 0.93785 + 1.68595I
−6.91302 − 4.04376I 0
u = 1.179560 − 0.366055I
a = 0.424815 + 0.004211I
b = 0.93785 − 1.68595I
−6.91302 + 4.04376I 0
u = −0.760448 + 0.076801I
a = −0.979441 − 0.447379I
b = −2.82256 + 0.44048I
−1.24671 + 2.00627I −2.16610 − 1.88869I
u = −0.760448 − 0.076801I
a = −0.979441 + 0.447379I
b = −2.82256 − 0.44048I
−1.24671 − 2.00627I −2.16610 + 1.88869I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.352613 + 0.677464I
a = 0.98942 − 1.25670I
b = 0.48534 − 1.56031I
0.082157 + 0.857061I 4.36317 + 3.16404I
u = 0.352613 − 0.677464I
a = 0.98942 + 1.25670I
b = 0.48534 + 1.56031I
0.082157 − 0.857061I 4.36317 − 3.16404I
u = 1.117590 + 0.540514I
a = 0.869855 − 0.865186I
b = 0.48115 − 1.63610I
−2.18494 − 5.60549I 0
u = 1.117590 − 0.540514I
a = 0.869855 + 0.865186I
b = 0.48115 + 1.63610I
−2.18494 + 5.60549I 0
u = 1.243700 + 0.167299I
a = −0.804444 − 0.252706I
b = −1.132900 − 0.688108I
−3.48666 + 5.58470I 0
u = 1.243700 − 0.167299I
a = −0.804444 + 0.252706I
b = −1.132900 + 0.688108I
−3.48666 − 5.58470I 0
u = −1.025570 + 0.733588I
a = 0.377118 + 0.557696I
b = −0.047638 + 1.359340I
−2.30731 + 2.91239I 0
u = −1.025570 − 0.733588I
a = 0.377118 − 0.557696I
b = −0.047638 − 1.359340I
−2.30731 − 2.91239I 0
u = −0.538375 + 0.490828I
a = 0.305851 − 0.417522I
b = −0.655309 + 0.569308I
−1.71164 + 2.03068I 0.92011 − 3.46679I
u = −0.538375 − 0.490828I
a = 0.305851 + 0.417522I
b = −0.655309 − 0.569308I
−1.71164 − 2.03068I 0.92011 + 3.46679I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.174490 + 0.500259I
a = 0.691504 + 0.602228I
b = 0.98748 + 1.40959I
1.01629 + 2.81685I 0
u = −1.174490 − 0.500259I
a = 0.691504 − 0.602228I
b = 0.98748 − 1.40959I
1.01629 − 2.81685I 0
u = −0.628169 + 0.354556I
a = −0.91755 − 1.42631I
b = −2.09261 − 2.20942I
−0.69818 + 1.82820I −0.75026 − 6.85666I
u = −0.628169 − 0.354556I
a = −0.91755 + 1.42631I
b = −2.09261 + 2.20942I
−0.69818 − 1.82820I −0.75026 + 6.85666I
u = −0.393726 + 0.603689I
a = −1.172020 + 0.730642I
b = −0.069889 + 0.668919I
−1.96447 − 3.28364I 2.37619 + 3.75916I
u = −0.393726 − 0.603689I
a = −1.172020 − 0.730642I
b = −0.069889 − 0.668919I
−1.96447 + 3.28364I 2.37619 − 3.75916I
u = −1.136990 + 0.588943I
a = −0.473097 − 1.163410I
b = −0.77465 − 1.90044I
−3.58758 + 9.21705I 0
u = −1.136990 − 0.588943I
a = −0.473097 + 1.163410I
b = −0.77465 + 1.90044I
−3.58758 − 9.21705I 0
u = −1.188380 + 0.493141I
a = −0.665288 − 0.342230I
b = −1.18550 − 5.40864I
−5.96934 + 4.58071I 0
u = −1.188380 − 0.493141I
a = −0.665288 + 0.342230I
b = −1.18550 + 5.40864I
−5.96934 − 4.58071I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428007 + 0.568291I
a = 1.14591 − 1.49846I
b = 1.44499 − 2.08811I
0.221092 + 0.868785I 3.26350 + 0.49101I
u = 0.428007 − 0.568291I
a = 1.14591 + 1.49846I
b = 1.44499 + 2.08811I
0.221092 − 0.868785I 3.26350 − 0.49101I
u = 0.532178 + 1.192600I
a = −0.840676 + 0.705816I
b = 0.384689 + 0.273579I
−3.41637 + 11.84470I 0
u = 0.532178 − 1.192600I
a = −0.840676 − 0.705816I
b = 0.384689 − 0.273579I
−3.41637 − 11.84470I 0
u = −1.253190 + 0.373770I
a = 0.622945 − 0.059145I
b = 0.673230 − 0.199297I
−2.38708 − 0.06669I 0
u = −1.253190 − 0.373770I
a = 0.622945 + 0.059145I
b = 0.673230 + 0.199297I
−2.38708 + 0.06669I 0
u = 0.280215 + 1.284960I
a = 0.169447 + 0.698452I
b = −0.149528 + 0.537782I
−5.00665 − 2.66992I 0
u = 0.280215 − 1.284960I
a = 0.169447 − 0.698452I
b = −0.149528 − 0.537782I
−5.00665 + 2.66992I 0
u = −1.164980 + 0.632243I
a = 0.656464 + 0.897532I
b = 1.06785 + 2.19969I
−0.2735 + 14.1974I 0
u = −1.164980 − 0.632243I
a = 0.656464 − 0.897532I
b = 1.06785 − 2.19969I
−0.2735 − 14.1974I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.585287 + 1.198570I
a = 0.668125 + 0.647488I
b = −0.242657 + 0.388280I
0.12401 − 5.89051I 0
u = −0.585287 − 1.198570I
a = 0.668125 − 0.647488I
b = −0.242657 − 0.388280I
0.12401 + 5.89051I 0
u = 1.170540 + 0.666864I
a = −0.638274 + 0.732254I
b = −0.91202 + 1.72998I
3.36185 − 8.25297I 0
u = 1.170540 − 0.666864I
a = −0.638274 − 0.732254I
b = −0.91202 − 1.72998I
3.36185 + 8.25297I 0
u = 0.640997 + 0.067594I
a = −2.23021 − 0.24695I
b = 0.221114 − 0.075686I
0.26523 + 6.30460I −7.61159 − 2.58041I
u = 0.640997 − 0.067594I
a = −2.23021 + 0.24695I
b = 0.221114 + 0.075686I
0.26523 − 6.30460I −7.61159 + 2.58041I
u = −0.270401 + 1.329930I
a = 0.171409 + 0.708922I
b = −0.022723 + 0.428452I
4.65181 + 2.75031I 0
u = −0.270401 − 1.329930I
a = 0.171409 − 0.708922I
b = −0.022723 − 0.428452I
4.65181 − 2.75031I 0
u = 0.482922 + 0.420367I
a = 0.970792 − 0.026578I
b = 0.261684 + 0.632534I
1.156200 + 0.168786I 8.35325 − 0.17221I
u = 0.482922 − 0.420367I
a = 0.970792 + 0.026578I
b = 0.261684 − 0.632534I
1.156200 − 0.168786I 8.35325 + 0.17221I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.237220 + 0.608323I
a = 0.276300 − 0.630774I
b = −0.250998 − 1.370000I
−6.08574 + 7.79317I 0
u = −1.237220 − 0.608323I
a = 0.276300 + 0.630774I
b = −0.250998 + 1.370000I
−6.08574 − 7.79317I 0
u = −1.379630 + 0.084770I
a = 0.402989 + 0.769939I
b = −0.02163 + 1.80379I
−13.43700 − 1.72652I 0
u = −1.379630 − 0.084770I
a = 0.402989 − 0.769939I
b = −0.02163 − 1.80379I
−13.43700 + 1.72652I 0
u = −0.609244
a = 2.37723
b = −0.188207
4.44175 −5.34930
u = 1.235000 + 0.654046I
a = −0.597436 − 0.798836I
b = −0.23923 − 1.68266I
−9.5150 − 11.7864I 0
u = 1.235000 − 0.654046I
a = −0.597436 + 0.798836I
b = −0.23923 + 1.68266I
−9.5150 + 11.7864I 0
u = 1.164930 + 0.796752I
a = −0.423703 + 0.632145I
b = −0.12702 + 1.53085I
−7.26453 − 7.54102I 0
u = 1.164930 − 0.796752I
a = −0.423703 − 0.632145I
b = −0.12702 − 1.53085I
−7.26453 + 7.54102I 0
u = 1.42862 + 0.18571I
a = −0.404911 + 0.514718I
b = −0.224979 + 1.250580I
−8.98195 − 2.48583I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42862 − 0.18571I
a = −0.404911 − 0.514718I
b = −0.224979 − 1.250580I
−8.98195 + 2.48583I 0
u = 1.33882 + 0.58562I
a = −0.417414 − 0.152829I
b = −0.077466 − 0.395061I
−8.77346 − 3.93861I 0
u = 1.33882 − 0.58562I
a = −0.417414 + 0.152829I
b = −0.077466 + 0.395061I
−8.77346 + 3.93861I 0
u = 1.24766 + 0.76806I
a = −0.556399 + 0.887270I
b = −0.87508 + 2.22966I
−5.7644 − 18.8401I 0
u = 1.24766 − 0.76806I
a = −0.556399 − 0.887270I
b = −0.87508 − 2.22966I
−5.7644 + 18.8401I 0
u = −1.23715 + 0.78781I
a = 0.561204 + 0.768188I
b = 0.75706 + 1.84911I
−2.05065 + 12.98760I 0
u = −1.23715 − 0.78781I
a = 0.561204 − 0.768188I
b = 0.75706 − 1.84911I
−2.05065 − 12.98760I 0
u = −1.51232 + 0.11748I
a = 0.647377 + 0.511295I
b = 0.83008 + 1.38338I
−12.0123 + 7.8686I 0
u = −1.51232 − 0.11748I
a = 0.647377 − 0.511295I
b = 0.83008 − 1.38338I
−12.0123 − 7.8686I 0
u = −0.459816
a = −0.203477
b = −0.818968
−1.22815 −10.8100
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.438051
a = 1.77546
b = 0.974038
1.05923 11.4410
u = 0.125896 + 0.299594I
a = 0.71491 − 3.49069I
b = 0.271476 + 0.589526I
0.958085 − 1.026070I 4.35276 − 0.71517I
u = 0.125896 − 0.299594I
a = 0.71491 + 3.49069I
b = 0.271476 − 0.589526I
0.958085 + 1.026070I 4.35276 + 0.71517I
16
II. I
u
2
= h−22u
2
+ 17b + 15u − 40, −u
2
+ a + u − 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
11
=
u
2
− u + 2
22
17
u
2
−
15
17
u +
40
17
a
9
=
u
2
− u + 2
22
17
u
2
+
2
17
u +
40
17
a
12
=
0
−u
a
7
=
u
u
a
6
=
u
u
2
− u + 1
a
1
=
−u
2
+ 2u − 1
u
2
− 2u
a
10
=
14
17
u
2
−
8
17
u +
27
17
19
17
u
2
−
6
17
u +
33
17
a
5
=
u
u
2
− u + 1
a
2
=
u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4979
289
u
2
+
13237
289
u −
8501
289
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
3
+ u
2
− 1
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
u
3
c
6
u
3
− 3u
2
+ 2u + 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
(u + 1)
3
c
9
17(17u
3
+ 23u
2
+ 8u + 1)
c
10
17(17u
3
− 10u
2
− u + 1)
c
11
(u − 1)
3
c
12
u
3
+ 3u
2
+ 2u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
3
− y
2
+ 2y −1
c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
5
y
3
c
6
, c
12
y
3
− 5y
2
+ 10y −1
c
8
, c
11
(y −1)
3
c
9
289(289y
3
− 257y
2
+ 18y −1)
c
10
289(289y
3
− 134y
2
+ 21y −1)
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.122561 − 0.744862I
b = 0.011877 − 0.425704I
4.66906 − 2.82812I 9.0758 + 50.1835I
u = 0.215080 − 1.307140I
a = 0.122561 + 0.744862I
b = 0.011877 + 0.425704I
4.66906 + 2.82812I 9.0758 − 50.1835I
u = 0.569840
a = 1.75488
b = 2.27036
0.531480 −8.90930
20
III. I
v
1
=
ha, 72v
7
−466v
6
+· · ·+887b +2666, v
8
+3v
7
−7v
6
−28v
5
−13v
4
+8v
3
−2v +1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
11
=
0
−0.0811725v
7
+ 0.525366v
6
+ ··· + 5.69222v −3.00564
a
9
=
v
0.590755v
7
+ 2.06539v
6
+ ··· + 5.07328v −2.23675
a
12
=
−0.671928v
7
− 1.54002v
6
+ ··· + 1.61894v −0.768884
−1.56483v
7
− 3.76099v
6
+ ··· + 2.23337v −1.83089
a
7
=
v
0
a
6
=
0.311161v
7
+ 0.652762v
6
+ ··· − 0.320180v + 0.188275
1.06201v
7
+ 2.29312v
6
+ ··· − 4.22322v + 0.490417
a
1
=
−0.768884v
7
− 1.63472v
6
+ ··· + 3.16798v −1.08117
−1
a
10
=
0.671928v
7
+ 1.54002v
6
+ ··· − 1.61894v + 0.768884
−0.0811725v
7
+ 0.525366v
6
+ ··· + 5.69222v −3.00564
a
5
=
0.768884v
7
+ 1.63472v
6
+ ··· − 3.16798v + 1.08117
1
a
2
=
−0.768884v
7
− 1.63472v
6
+ ··· + 3.16798v −0.0811725
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
430
887
v
7
−
2241
887
v
6
−
11719
887
v
5
+
16745
887
v
4
+
76150
887
v
3
+
12082
887
v
2
−
15740
887
v +
7594
887
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
7
u
8
c
4
(u + 1)
8
c
5
, c
9
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
6
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
8
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
10
, c
11
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
12
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
7
y
8
c
5
, c
9
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
6
, c
12
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
8
, c
10
, c
11
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.809031 + 0.055172I
a = 0
b = 0.195703 − 0.910609I
−3.80435 − 2.57849I −1.56478 + 3.68514I
v = −0.809031 − 0.055172I
a = 0
b = 0.195703 + 0.910609I
−3.80435 + 2.57849I −1.56478 − 3.68514I
v = 0.217262 + 0.361920I
a = 0
b = −0.89335 + 2.72444I
−0.604279 − 1.131230I −3.30729 − 4.28492I
v = 0.217262 − 0.361920I
a = 0
b = −0.89335 − 2.72444I
−0.604279 + 1.131230I −3.30729 + 4.28492I
v = 0.412194
a = 0
b = −1.12481
−0.799899 9.95010
v = −2.59435 + 0.51399I
a = 0
b = −0.471534 − 0.216354I
0.73474 + 6.44354I 8.02705 − 7.90662I
v = −2.59435 − 0.51399I
a = 0
b = −0.471534 + 0.216354I
0.73474 − 6.44354I 8.02705 + 7.90662I
v = 2.96004
a = 0
b = 0.463171
4.85780 14.7400
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
8
)(u
3
+ u
2
− 1)(u
113
− 10u
112
+ ··· + u − 1)
c
3
u
8
(u
3
− u
2
+ 2u − 1)(u
113
− 2u
112
+ ··· + 896u − 256)
c
4
((u + 1)
8
)(u
3
− u
2
+ 1)(u
113
− 10u
112
+ ··· + u − 1)
c
5
u
3
(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (u
113
+ 2u
112
+ ··· − 41820u − 2312)
c
6
(u
3
− 3u
2
+ 2u + 1)(u
8
+ 3u
7
+ ··· + 4u + 1)
· (u
113
+ 3u
112
+ ··· + 3u + 1)
c
7
u
8
(u
3
+ u
2
+ 2u + 1)(u
113
− 2u
112
+ ··· + 896u − 256)
c
8
(u + 1)
3
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
· (u
113
+ 5u
112
+ ··· − 1158u + 289)
c
9
289(17u
3
+ 23u
2
+ 8u + 1)(u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1)
· (17u
113
+ 219u
112
+ ··· + 16199u + 2539)
c
10
289(17u
3
− 10u
2
− u + 1)(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (17u
113
+ 212u
112
+ ··· − 115224u − 34421)
c
11
(u − 1)
3
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
· (u
113
+ 5u
112
+ ··· − 1158u + 289)
c
12
(u
3
+ 3u
2
+ 2u − 1)(u
8
− 3u
7
+ ··· − 4u + 1)
· (u
113
+ 3u
112
+ ··· + 3u + 1)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
8
)(y
3
− y
2
+ 2y −1)(y
113
− 100y
112
+ ··· − 13y −1)
c
3
, c
7
y
8
(y
3
+ 3y
2
+ 2y −1)(y
113
− 48y
112
+ ··· + 1425408y −65536)
c
5
y
3
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
113
+ 18y
112
+ ··· + 117380240y −5345344)
c
6
, c
12
(y
3
− 5y
2
+ 10y −1)
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
113
+ 61y
112
+ ··· + 19y −1)
c
8
, c
11
(y −1)
3
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
113
− 69y
112
+ ··· + 10227136y −83521)
c
9
83521(289y
3
− 257y
2
+ 18y −1)
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (289y
113
+ 6473y
112
+ ··· − 380827737y −6446521)
c
10
83521(289y
3
− 134y
2
+ 21y −1)
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (289y
113
− 1016y
112
+ ··· − 6580973566y −1184805241)
26
