12n
0033
(K12n
0033
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 11 5 7 1 9 10
Solving Sequence
5,8 9,11
12 4 7 10 1 6 3 2
c
8
c
11
c
4
c
7
c
9
c
12
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h9.05330 × 10
317
u
76
+ 1.41320 × 10
318
u
75
+ ··· + 2.50588 × 10
321
b + 5.09891 × 10
321
,
− 5.10110 × 10
318
u
76
− 1.08271 × 10
319
u
75
+ ··· + 5.01177 × 10
321
a − 7.58939 × 10
322
,
u
77
+ 2u
76
+ ··· + 20480u + 4096i
I
u
2
= h−2u
3
− u
2
+ b − 5u − 1, 3u
3
+ 4u
2
+ a + 8u + 8, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
v
1
= ha, 164522v
11
+ 355934v
10
+ ··· + 707733b − 176501,
v
12
+ 3v
11
+ 3v
10
+ 18v
9
+ 31v
8
− 29v
7
− 31v
6
− 9v
5
+ 19v
4
+ 5v
3
− 4v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 93 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
= h9.05 × 10
317
u
76
+ 1.41 × 10
318
u
75
+ · · · + 2.51 × 10
321
b + 5.10 ×
10
321
, −5.10 × 10
318
u
76
− 1.08 × 10
319
u
75
+ · · · + 5.01 × 10
321
a − 7.59 ×
10
322
, u
77
+ 2u
76
+ · · · + 20480u + 4096i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
0.00101783u
76
+ 0.00216033u
75
+ ··· + 36.5435u + 15.1431
−0.000361282u
76
− 0.000563952u
75
+ ··· − 12.2323u − 2.03477
a
12
=
0.000855818u
76
+ 0.00185986u
75
+ ··· + 31.0338u + 13.6191
−0.000362414u
76
− 0.000562641u
75
+ ··· − 12.0509u − 2.13122
a
4
=
u
u
3
+ u
a
7
=
−0.00303743u
76
− 0.00486392u
75
+ ··· − 99.2882u − 15.0764
−0.000239922u
76
− 0.000649688u
75
+ ··· − 15.1615u − 6.17114
a
10
=
0.000822714u
76
+ 0.00175824u
75
+ ··· + 32.3423u + 13.8923
−0.000210387u
76
− 0.000333021u
75
+ ··· − 8.20005u − 1.17725
a
1
=
0.000316716u
76
+ 0.000548963u
75
+ ··· + 6.03001u + 1.86087
−8.61974 × 10
−6
u
76
− 0.0000450420u
75
+ ··· − 2.08710u − 0.369176
a
6
=
0.000325336u
76
+ 0.000594005u
75
+ ··· + 8.11710u + 2.23004
0.0000255950u
76
+ 0.0000821978u
75
+ ··· + 1.91504u + 0.601280
a
3
=
−0.0000229625u
76
− 0.000118674u
75
+ ··· − 2.05186u − 1.28107
0.0000158254u
76
+ 0.0000361796u
75
+ ··· + 2.94000u + 0.422511
a
2
=
−0.0000229625u
76
− 0.000118674u
75
+ ··· − 2.05186u − 1.28107
0.0000353440u
76
+ 0.0000721239u
75
+ ··· + 4.52395u + 0.720490
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000265127u
76
+ 0.00273732u
75
+ ··· + 71.8347u + 33.0070
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 42u
76
+ ··· − 173u − 1
c
2
, c
5
u
77
+ 8u
76
+ ··· + 3u + 1
c
3
u
77
− 8u
76
+ ··· + 2520u + 1732
c
4
, c
8
u
77
+ 2u
76
+ ··· + 20480u + 4096
c
6
u
77
− 7u
76
+ ··· − 18228u − 7979
c
7
u
77
− u
76
+ ··· + 7631854u − 2351327
c
9
u
77
+ 4u
76
+ ··· − 3u − 1
c
10
, c
12
u
77
− 7u
76
+ ··· − 65u + 1
c
11
u
77
+ 13u
76
+ ··· − 200u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
− 6y
76
+ ··· + 13671y −1
c
2
, c
5
y
77
+ 42y
76
+ ··· − 173y −1
c
3
y
77
− 54y
76
+ ··· − 552548680y −2999824
c
4
, c
8
y
77
− 60y
76
+ ··· + 234881024y −16777216
c
6
y
77
− 77y
76
+ ··· + 2964755496y −63664441
c
7
y
77
− 9y
76
+ ··· − 135685107448604y −5528738660929
c
9
y
77
+ 2y
76
+ ··· − 29y −1
c
10
, c
12
y
77
− 63y
76
+ ··· − 2399y −1
c
11
y
77
+ 21y
76
+ ··· + 15168y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.021202 + 0.991505I
a = −0.103805 + 0.681267I
b = −0.387707 + 0.512895I
−1.29984 − 4.81871I −3.73970 + 8.31831I
u = −0.021202 − 0.991505I
a = −0.103805 − 0.681267I
b = −0.387707 − 0.512895I
−1.29984 + 4.81871I −3.73970 − 8.31831I
u = 0.350174 + 0.870277I
a = 1.63705 + 0.66516I
b = −0.136420 + 1.089040I
−4.26262 − 2.29968I −11.37943 + 4.09375I
u = 0.350174 − 0.870277I
a = 1.63705 − 0.66516I
b = −0.136420 − 1.089040I
−4.26262 + 2.29968I −11.37943 − 4.09375I
u = 0.552031 + 0.673417I
a = 1.42607 + 0.68039I
b = −0.151263 − 0.305259I
−3.26120 + 0.96418I −9.85344 − 3.05224I
u = 0.552031 − 0.673417I
a = 1.42607 − 0.68039I
b = −0.151263 + 0.305259I
−3.26120 − 0.96418I −9.85344 + 3.05224I
u = 0.801656 + 0.115028I
a = 1.26895 − 2.37999I
b = 0.618575 − 0.439872I
0.77686 − 3.97780I −2.71090 + 8.29234I
u = 0.801656 − 0.115028I
a = 1.26895 + 2.37999I
b = 0.618575 + 0.439872I
0.77686 + 3.97780I −2.71090 − 8.29234I
u = −0.742333 + 0.323629I
a = 0.107625 − 0.186343I
b = −1.236430 − 0.155289I
0.963117 − 0.556760I −4.97972 − 0.27994I
u = −0.742333 − 0.323629I
a = 0.107625 + 0.186343I
b = −1.236430 + 0.155289I
0.963117 + 0.556760I −4.97972 + 0.27994I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000355 + 0.774042I
a = 1.102990 + 0.498400I
b = −0.732884 + 0.304781I
−1.18097 + 1.51108I −2.56147 − 1.04285I
u = −0.000355 − 0.774042I
a = 1.102990 − 0.498400I
b = −0.732884 − 0.304781I
−1.18097 − 1.51108I −2.56147 + 1.04285I
u = −1.241430 + 0.227325I
a = 0.549344 − 1.064480I
b = 0.517613 − 1.212150I
−2.68140 + 1.19053I 0
u = −1.241430 − 0.227325I
a = 0.549344 + 1.064480I
b = 0.517613 + 1.212150I
−2.68140 − 1.19053I 0
u = 0.116220 + 0.707665I
a = 0.233959 − 0.456579I
b = −0.702410 − 0.390271I
1.17719 + 1.40870I 3.29231 − 3.00363I
u = 0.116220 − 0.707665I
a = 0.233959 + 0.456579I
b = −0.702410 + 0.390271I
1.17719 − 1.40870I 3.29231 + 3.00363I
u = −0.715312 + 0.028489I
a = 2.04561 + 1.88867I
b = 0.654008 + 0.310120I
0.648909 − 0.975553I −3.60474 − 0.46426I
u = −0.715312 − 0.028489I
a = 2.04561 − 1.88867I
b = 0.654008 − 0.310120I
0.648909 + 0.975553I −3.60474 + 0.46426I
u = −0.378806 + 0.592823I
a = −1.58189 + 5.75660I
b = 2.79582 − 0.75309I
−1.97793 + 1.35936I −28.8056 − 39.0048I
u = −0.378806 − 0.592823I
a = −1.58189 − 5.75660I
b = 2.79582 + 0.75309I
−1.97793 − 1.35936I −28.8056 + 39.0048I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.556381 + 0.425890I
a = 0.086610 − 0.285749I
b = −1.045290 − 0.515035I
1.65009 + 1.91270I −1.87415 + 0.42405I
u = 0.556381 − 0.425890I
a = 0.086610 + 0.285749I
b = −1.045290 + 0.515035I
1.65009 − 1.91270I −1.87415 − 0.42405I
u = −1.33114
a = −1.70526
b = −3.65459
−4.62840 0
u = 0.615724 + 0.225295I
a = 0.124878 − 0.091560I
b = 1.267570 + 0.584855I
−0.50082 + 7.43088I −9.83588 − 3.06441I
u = 0.615724 − 0.225295I
a = 0.124878 + 0.091560I
b = 1.267570 − 0.584855I
−0.50082 − 7.43088I −9.83588 + 3.06441I
u = −0.377234 + 0.508733I
a = 0.828760 − 0.255710I
b = −0.080733 − 0.346910I
−0.22325 + 1.43278I −1.54695 − 5.02383I
u = −0.377234 − 0.508733I
a = 0.828760 + 0.255710I
b = −0.080733 + 0.346910I
−0.22325 − 1.43278I −1.54695 + 5.02383I
u = −0.481913 + 0.382313I
a = 0.130464 − 0.111167I
b = 1.007620 + 0.380876I
−0.04977 + 4.23277I −3.74018 − 11.43224I
u = −0.481913 − 0.382313I
a = 0.130464 + 0.111167I
b = 1.007620 − 0.380876I
−0.04977 − 4.23277I −3.74018 + 11.43224I
u = 1.38453 + 0.33788I
a = 0.05988 − 1.46102I
b = 0.413828 − 1.035170I
−2.94680 − 5.49032I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38453 − 0.33788I
a = 0.05988 + 1.46102I
b = 0.413828 + 1.035170I
−2.94680 + 5.49032I 0
u = −0.13459 + 1.43811I
a = 0.0790412 − 0.0963284I
b = 0.312084 + 1.155850I
−3.00179 + 4.56266I 0
u = −0.13459 − 1.43811I
a = 0.0790412 + 0.0963284I
b = 0.312084 − 1.155850I
−3.00179 − 4.56266I 0
u = 1.45101 + 0.03574I
a = 0.326600 − 1.171110I
b = 0.97849 − 1.54914I
−6.59261 − 2.90185I 0
u = 1.45101 − 0.03574I
a = 0.326600 + 1.171110I
b = 0.97849 + 1.54914I
−6.59261 + 2.90185I 0
u = 1.46452 + 0.10406I
a = −0.560170 − 0.996722I
b = 0.677729 − 0.936305I
−7.24514 − 2.22253I 0
u = 1.46452 − 0.10406I
a = −0.560170 + 0.996722I
b = 0.677729 + 0.936305I
−7.24514 + 2.22253I 0
u = 1.47132 + 0.00598I
a = −0.486518 − 1.083090I
b = −0.427573 − 1.276420I
−3.93524 + 7.62228I 0
u = 1.47132 − 0.00598I
a = −0.486518 + 1.083090I
b = −0.427573 + 1.276420I
−3.93524 − 7.62228I 0
u = 1.41409 + 0.41604I
a = 0.465625 + 0.947491I
b = 0.22019 + 1.50917I
−5.83012 − 5.98154I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41409 − 0.41604I
a = 0.465625 − 0.947491I
b = 0.22019 − 1.50917I
−5.83012 + 5.98154I 0
u = −0.13878 + 1.48672I
a = 0.0825775 − 0.0176285I
b = −0.507722 + 0.084479I
5.24362 + 3.10833I 0
u = −0.13878 − 1.48672I
a = 0.0825775 + 0.0176285I
b = −0.507722 − 0.084479I
5.24362 − 3.10833I 0
u = 0.424249 + 0.248865I
a = 3.45186 + 6.12062I
b = −0.239118 + 1.076500I
−2.15277 + 2.70026I −9.88811 + 8.45872I
u = 0.424249 − 0.248865I
a = 3.45186 − 6.12062I
b = −0.239118 − 1.076500I
−2.15277 − 2.70026I −9.88811 − 8.45872I
u = −0.345743 + 0.345351I
a = 7.58843 − 5.09506I
b = −0.97044 − 1.56022I
−1.72233 + 1.49478I −0.6746 − 41.0959I
u = −0.345743 − 0.345351I
a = 7.58843 + 5.09506I
b = −0.97044 + 1.56022I
−1.72233 − 1.49478I −0.6746 + 41.0959I
u = −1.50984 + 0.22948I
a = −0.494387 + 0.821666I
b = −0.149288 + 1.166430I
−3.74678 − 1.39146I 0
u = −1.50984 − 0.22948I
a = −0.494387 − 0.821666I
b = −0.149288 − 1.166430I
−3.74678 + 1.39146I 0
u = 1.52087 + 0.23706I
a = −1.228330 + 0.361231I
b = −3.79275 − 0.22832I
−8.26886 − 4.60408I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52087 − 0.23706I
a = −1.228330 − 0.361231I
b = −3.79275 + 0.22832I
−8.26886 + 4.60408I 0
u = −1.56389 + 0.08723I
a = 0.259742 + 1.214440I
b = 0.104963 + 1.054650I
−7.30971 + 1.30866I 0
u = −1.56389 − 0.08723I
a = 0.259742 − 1.214440I
b = 0.104963 − 1.054650I
−7.30971 − 1.30866I 0
u = −1.50572 + 0.51745I
a = −0.130706 + 1.317800I
b = 0.499801 + 1.227290I
−6.14031 + 10.62530I 0
u = −1.50572 − 0.51745I
a = −0.130706 − 1.317800I
b = 0.499801 − 1.227290I
−6.14031 − 10.62530I 0
u = −0.16466 + 1.59990I
a = 0.0829607 + 0.0868689I
b = 0.54188 − 1.50526I
−6.96276 − 9.17383I 0
u = −0.16466 − 1.59990I
a = 0.0829607 − 0.0868689I
b = 0.54188 + 1.50526I
−6.96276 + 9.17383I 0
u = −1.64354 + 0.14674I
a = −0.270112 − 0.961040I
b = 0.712679 − 1.188220I
−11.25600 + 2.45702I 0
u = −1.64354 − 0.14674I
a = −0.270112 + 0.961040I
b = 0.712679 + 1.188220I
−11.25600 − 2.45702I 0
u = −1.61779 + 0.33663I
a = −0.587986 + 0.737457I
b = 0.885746 + 0.815817I
−10.89770 + 7.17611I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61779 − 0.33663I
a = −0.587986 − 0.737457I
b = 0.885746 − 0.815817I
−10.89770 − 7.17611I 0
u = −0.230559 + 0.235592I
a = 3.02477 + 1.23710I
b = 0.540667 − 0.856079I
−1.89908 + 0.79590I −4.83770 + 0.82015I
u = −0.230559 − 0.235592I
a = 3.02477 − 1.23710I
b = 0.540667 + 0.856079I
−1.89908 − 0.79590I −4.83770 − 0.82015I
u = 1.55975 + 0.62424I
a = 0.180055 + 1.270440I
b = −1.03678 + 1.64077I
−8.2935 − 11.7637I 0
u = 1.55975 − 0.62424I
a = 0.180055 − 1.270440I
b = −1.03678 − 1.64077I
−8.2935 + 11.7637I 0
u = 0.33491 + 1.65140I
a = 0.0714856 + 0.0919876I
b = −0.096733 − 1.280030I
−6.64004 + 0.42401I 0
u = 0.33491 − 1.65140I
a = 0.0714856 − 0.0919876I
b = −0.096733 + 1.280030I
−6.64004 − 0.42401I 0
u = −1.55571 + 0.78921I
a = 0.332435 − 1.219240I
b = −1.20704 − 1.68387I
−11.3053 + 17.4741I 0
u = −1.55571 − 0.78921I
a = 0.332435 + 1.219240I
b = −1.20704 + 1.68387I
−11.3053 − 17.4741I 0
u = −1.62516 + 0.70906I
a = −0.256645 + 0.724429I
b = 0.741895 + 1.089960I
−7.62809 + 3.43602I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62516 − 0.70906I
a = −0.256645 − 0.724429I
b = 0.741895 − 1.089960I
−7.62809 − 3.43602I 0
u = 1.60150 + 0.85618I
a = −0.277862 − 0.757459I
b = 0.97993 − 1.06878I
−10.63730 − 9.31613I 0
u = 1.60150 − 0.85618I
a = −0.277862 + 0.757459I
b = 0.97993 + 1.06878I
−10.63730 + 9.31613I 0
u = −1.79507 + 0.49521I
a = 0.054400 − 1.080970I
b = −0.82388 − 1.84808I
−13.6570 + 7.5061I 0
u = −1.79507 − 0.49521I
a = 0.054400 + 1.080970I
b = −0.82388 + 1.84808I
−13.6570 − 7.5061I 0
u = 1.83627 + 0.59317I
a = −0.271123 − 0.724908I
b = 0.58068 − 1.45335I
−13.24420 + 0.87431I 0
u = 1.83627 − 0.59317I
a = −0.271123 + 0.724908I
b = 0.58068 + 1.45335I
−13.24420 − 0.87431I 0
12
II.
I
u
2
= h−2u
3
− u
2
+ b − 5u − 1, 3u
3
+ 4u
2
+ a + 8u + 8 , u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
−3u
3
− 4u
2
− 8u − 8
2u
3
+ u
2
+ 5u + 1
a
12
=
−3u
3
− 4u
2
− 8u − 8
2u
3
+ u
2
+ 5u + 1
a
4
=
u
u
3
+ u
a
7
=
−8u
3
− 19u + 5
−3u
3
− 4u
2
− 8u − 8
a
10
=
−3u
3
− 3u
2
− 8u − 7
2u
3
+ 2u
2
+ 5u + 1
a
1
=
−u
2
− 1
−u
2
a
6
=
1
0
a
3
=
u
3
+ 2u
u
3
+ u
a
2
=
u
3
+ 2u
u
3
+ u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −23u
3
− 11u
2
− 70u − 48
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
2
u
4
− u
3
+ u
2
+ 1
c
3
u
4
+ u
3
+ 5u
2
− u + 2
c
5
u
4
+ u
3
+ u
2
+ 1
c
6
, c
7
u
4
+ 2u
3
+ 7u
2
+ 5u + 1
c
8
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
9
u
4
− 5u
3
+ 7u
2
− 2u + 1
c
10
(u − 1)
4
c
11
u
4
c
12
(u + 1)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
2
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
3
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
6
, c
7
y
4
+ 10y
3
+ 31y
2
− 11y + 1
c
9
y
4
− 11y
3
+ 31y
2
+ 10y + 1
c
10
, c
12
(y −1)
4
c
11
y
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −5.16441 − 2.77418I
b = −0.59074 + 2.34806I
−1.85594 + 1.41510I −24.8178 − 33.5385I
u = −0.395123 − 0.506844I
a = −5.16441 + 2.77418I
b = −0.59074 − 2.34806I
−1.85594 − 1.41510I −24.8178 + 33.5385I
u = −0.10488 + 1.55249I
a = 0.164409 − 0.045467I
b = −0.409261 + 0.055548I
5.14581 + 3.16396I −31.6822 − 20.2078I
u = −0.10488 − 1.55249I
a = 0.164409 + 0.045467I
b = −0.409261 − 0.055548I
5.14581 − 3.16396I −31.6822 + 20.2078I
16
III. I
v
1
= ha, 1.65 × 10
5
v
11
+ 3.56 × 10
5
v
10
+ · · · + 7.08 × 10
5
b − 1.77 ×
10
5
, v
12
+ 3v
11
+ · · · + v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
11
=
0
−0.232463v
11
− 0.502921v
10
+ ··· + 0.152902v + 0.249389
a
12
=
−0.232463v
11
− 0.502921v
10
+ ··· + 0.152902v + 0.249389
−0.232463v
11
− 0.502921v
10
+ ··· + 0.152902v + 0.249389
a
4
=
v
0
a
7
=
1
−1.04198v
11
− 2.90360v
10
+ ··· + 1.23849v − 0.574544
a
10
=
1.04198v
11
+ 2.90360v
10
+ ··· − 1.23849v + 1.57454
1.86146v
11
+ 5.23525v
10
+ ··· − 2.25349v + 3.04348
a
1
=
0.819476v
11
+ 2.33165v
10
+ ··· − 1.01499v + 1.46894
1.86146v
11
+ 5.23525v
10
+ ··· − 2.25349v + 3.04348
a
6
=
−0.819476v
11
− 2.33165v
10
+ ··· + 1.01499v − 1.46894
−1.86146v
11
− 5.23525v
10
+ ··· + 2.25349v − 3.04348
a
3
=
0.529427v
11
+ 1.38124v
10
+ ··· + 1.20984v + 1.24074
0.861460v
11
+ 2.23525v
10
+ ··· + 1.74651v + 2.04348
a
2
=
0.137987v
11
+ 0.235197v
10
+ ··· + 1.72218v + 0.891609
0.861460v
11
+ 2.23525v
10
+ ··· + 1.74651v + 2.04348
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1558019
235911
v
11
+
3765626
235911
v
10
+ ··· −
4340683
235911
v +
3615109
235911
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
6
c
2
(u
2
+ u + 1)
6
c
4
, c
8
u
12
c
6
, c
9
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
7
, c
12
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
10
, c
11
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
6
c
4
, c
8
y
12
c
6
, c
9
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
c
7
, c
10
, c
11
c
12
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.834826 + 0.083652I
a = 0
b = −1.002190 + 0.295542I
1.89061 + 1.10558I 3.79900 − 2.81207I
v = 0.834826 − 0.083652I
a = 0
b = −1.002190 − 0.295542I
1.89061 − 1.10558I 3.79900 + 2.81207I
v = −0.489858 + 0.681154I
a = 0
b = −1.002190 + 0.295542I
1.89061 − 2.95419I 1.04064 + 4.93773I
v = −0.489858 − 0.681154I
a = 0
b = −1.002190 − 0.295542I
1.89061 + 2.95419I 1.04064 − 4.93773I
v = −0.458424 + 0.081263I
a = 0
b = 1.073950 − 0.558752I
− 7.72290I 2.53591 + 10.48596I
v = −0.458424 − 0.081263I
a = 0
b = 1.073950 + 0.558752I
7.72290I 2.53591 − 10.48596I
v = 0.299588 + 0.356375I
a = 0
b = 1.073950 − 0.558752I
− 3.66314I −2.83009 − 2.28483I
v = 0.299588 − 0.356375I
a = 0
b = 1.073950 + 0.558752I
3.66314I −2.83009 + 2.28483I
v = −2.51133 + 0.49706I
a = 0
b = 0.428243 − 0.664531I
−1.89061 + 2.95419I 0.48408 − 6.69677I
v = −2.51133 − 0.49706I
a = 0
b = 0.428243 + 0.664531I
−1.89061 − 2.95419I 0.48408 + 6.69677I
20
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.82520 + 2.42341I
a = 0
b = 0.428243 + 0.664531I
−1.89061 + 1.10558I −11.02954 + 1.23660I
v = 0.82520 − 2.42341I
a = 0
b = 0.428243 − 0.664531I
−1.89061 − 1.10558I −11.02954 − 1.23660I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
6
)(u
4
− u
3
+ 3u
2
− 2u + 1)(u
77
+ 42u
76
+ ··· − 173u − 1)
c
2
((u
2
+ u + 1)
6
)(u
4
− u
3
+ u
2
+ 1)(u
77
+ 8u
76
+ ··· + 3u + 1)
c
3
((u
2
− u + 1)
6
)(u
4
+ u
3
+ 5u
2
− u + 2)(u
77
− 8u
76
+ ··· + 2520u + 1732)
c
4
u
12
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
77
+ 2u
76
+ ··· + 20480u + 4096)
c
5
((u
2
− u + 1)
6
)(u
4
+ u
3
+ u
2
+ 1)(u
77
+ 8u
76
+ ··· + 3u + 1)
c
6
(u
4
+ 2u
3
+ 7u
2
+ 5u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
77
− 7u
76
+ ··· − 18228u − 7979)
c
7
(u
4
+ 2u
3
+ 7u
2
+ 5u + 1)(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
77
− u
76
+ ··· + 7631854u − 2351327)
c
8
u
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
77
+ 2u
76
+ ··· + 20480u + 4096)
c
9
(u
4
− 5u
3
+ 7u
2
− 2u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
· (u
77
+ 4u
76
+ ··· − 3u − 1)
c
10
((u − 1)
4
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
77
− 7u
76
+ ··· − 65u + 1)
c
11
u
4
(u
6
+ u
5
+ ··· + u + 1)
2
(u
77
+ 13u
76
+ ··· − 200u − 16)
c
12
((u + 1)
4
)(u
6
− u
5
+ ··· − u + 1)
2
(u
77
− 7u
76
+ ··· − 65u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
6
)(y
4
+ 5y
3
+ ··· + 2y + 1)(y
77
− 6y
76
+ ··· + 13671y − 1)
c
2
, c
5
((y
2
+ y + 1)
6
)(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
77
+ 42y
76
+ ··· − 173y − 1)
c
3
(y
2
+ y + 1)
6
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
· (y
77
− 54y
76
+ ··· − 552548680y − 2999824)
c
4
, c
8
y
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
· (y
77
− 60y
76
+ ··· + 234881024y − 16777216)
c
6
(y
4
+ 10y
3
+ 31y
2
− 11y + 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
77
− 77y
76
+ ··· + 2964755496y − 63664441)
c
7
(y
4
+ 10y
3
+ 31y
2
− 11y + 1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
77
− 9y
76
+ ··· − 135685107448604y − 5528738660929)
c
9
(y
4
− 11y
3
+ 31y
2
+ 10y + 1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
2
· (y
77
+ 2y
76
+ ··· − 29y − 1)
c
10
, c
12
(y − 1)
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
77
− 63y
76
+ ··· − 2399y − 1)
c
11
y
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
77
+ 21y
76
+ ··· + 15168y − 256)
23
