12n
0027
(K12n
0027
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 11 10 5 12 1 9 7
Solving Sequence
5,8 9,12
10 4 7 1 11 6 3 2
c
8
c
9
c
4
c
7
c
12
c
11
c
6
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.63893 × 10
317
u
76
+ 6.90082 × 10
317
u
75
+ ··· + 1.25294 × 10
321
b + 1.60645 × 10
321
,
− 1.19015 × 10
318
u
76
− 3.51549 × 10
318
u
75
+ ··· + 2.50588 × 10
321
a − 2.87281 × 10
322
,
u
77
+ 2u
76
+ ··· + 20480u + 4096i
I
u
2
= h2u
3
+ 2u
2
+ b + 5u + 1, −u
3
− 3u
2
+ a − 3u − 6, u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
v
1
= ha, 309980v
11
+ 790238v
10
+ ··· + 707733b + 1249018,
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
= h4.64 × 10
317
u
76
+ 6.90 × 10
317
u
75
+ · · · + 1.25 × 10
321
b + 1.61 ×
10
321
, −1.19 × 10
318
u
76
− 3.52 × 10
318
u
75
+ · · · + 2.51 × 10
321
a − 2.87 ×
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
12
=
0.000474943u
76
+ 0.00140290u
75
+ ··· + 19.8888u + 11.4642
−0.000370243u
76
− 0.000550769u
75
+ ··· − 12.5316u − 1.28214
a
10
=
0.000502182u
76
+ 0.00148228u
75
+ ··· + 18.5669u + 11.5558
−0.000400721u
76
− 0.000628200u
75
+ ··· − 14.2062u − 2.01128
a
4
=
u
u
3
+ u
a
7
=
0.00403445u
76
+ 0.00701135u
75
+ ··· + 135.801u + 30.0505
0.000251477u
76
+ 0.000675536u
75
+ ··· + 18.8283u + 6.76857
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
11
=
0.000443453u
76
+ 0.00138924u
75
+ ··· + 18.5802u + 12.0376
−0.000400972u
76
− 0.000579591u
75
+ ··· − 13.4129u − 1.48420
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
− u
76
+ ··· + 7631854u − 2351327
c
7
u
77
− 7u
76
+ ··· − 18228u − 7979
c
9
, c
11
u
77
− 7u
76
+ ··· − 65u + 1
c
10
u
77
+ 13u
76
+ ··· − 200u − 16
c
12
u
77
+ 4u
76
+ ··· − 3u − 1
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
− 9y
76
+ ··· − 135685107448604y −5528738660929
c
7
y
77
− 77y
76
+ ··· + 2964755496y −63664441
c
9
, c
11
y
77
− 63y
76
+ ··· − 2399y −1
c
10
y
77
+ 21y
76
+ ··· + 15168y −256
c
12
y
77
+ 2y
76
+ ··· − 29y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.021202 + 0.991505I
a = 0.85015 + 1.14174I
b = −0.435122 − 0.281974I
−1.29984 − 4.81871I −3.73970 + 8.31831I
u = −0.021202 − 0.991505I
a = 0.85015 − 1.14174I
b = −0.435122 + 0.281974I
−1.29984 + 4.81871I −3.73970 − 8.31831I
u = 0.350174 + 0.870277I
a = 0.183615 + 1.203250I
b = 0.621978 − 0.404845I
−4.26262 − 2.29968I −11.37943 + 4.09375I
u = 0.350174 − 0.870277I
a = 0.183615 − 1.203250I
b = 0.621978 + 0.404845I
−4.26262 + 2.29968I −11.37943 − 4.09375I
u = 0.552031 + 0.673417I
a = 0.538939 − 0.192540I
b = 1.155460 − 0.244632I
−3.26120 + 0.96418I −9.85344 − 3.05224I
u = 0.552031 − 0.673417I
a = 0.538939 + 0.192540I
b = 1.155460 + 0.244632I
−3.26120 − 0.96418I −9.85344 + 3.05224I
u = 0.801656 + 0.115028I
a = 0.100644 − 1.215600I
b = 0.407413 − 0.043467I
0.77686 − 3.97780I −2.71090 + 8.29234I
u = 0.801656 − 0.115028I
a = 0.100644 + 1.215600I
b = 0.407413 + 0.043467I
0.77686 + 3.97780I −2.71090 − 8.29234I
u = −0.742333 + 0.323629I
a = 0.674206 − 0.258407I
b = −0.517206 − 1.155410I
0.963117 − 0.556760I −4.97972 − 0.27994I
u = −0.742333 − 0.323629I
a = 0.674206 + 0.258407I
b = −0.517206 + 1.155410I
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 = 2.07113 − 0.25770I
b = −0.849623 + 0.308056I
−1.18097 + 1.51108I −2.56147 − 1.04285I
u = −0.000355 − 0.774042I
a = 2.07113 + 0.25770I
b = −0.849623 − 0.308056I
−1.18097 − 1.51108I −2.56147 + 1.04285I
u = −1.241430 + 0.227325I
a = 0.236549 − 0.474818I
b = 0.342053 − 1.260670I
−2.68140 + 1.19053I 0
u = −1.241430 − 0.227325I
a = 0.236549 + 0.474818I
b = 0.342053 + 1.260670I
−2.68140 − 1.19053I 0
u = 0.116220 + 0.707665I
a = 1.044990 − 0.550262I
b = −0.426152 − 0.182747I
1.17719 + 1.40870I 3.29231 − 3.00363I
u = 0.116220 − 0.707665I
a = 1.044990 + 0.550262I
b = −0.426152 + 0.182747I
1.17719 − 1.40870I 3.29231 + 3.00363I
u = −0.715312 + 0.028489I
a = 0.85434 + 1.29507I
b = 0.556271 + 0.176958I
0.648909 − 0.975553I −3.60474 − 0.46426I
u = −0.715312 − 0.028489I
a = 0.85434 − 1.29507I
b = 0.556271 − 0.176958I
0.648909 + 0.975553I −3.60474 + 0.46426I
u = −0.378806 + 0.592823I
a = −0.74970 + 4.36413I
b = 3.08806 − 0.53632I
−1.97793 + 1.35936I −28.8056 − 39.0048I
u = −0.378806 − 0.592823I
a = −0.74970 − 4.36413I
b = 3.08806 + 0.53632I
−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 = 0.709325 − 0.442191I
b = −0.056823 − 0.605176I
1.65009 + 1.91270I −1.87415 + 0.42405I
u = 0.556381 − 0.425890I
a = 0.709325 + 0.442191I
b = −0.056823 + 0.605176I
1.65009 − 1.91270I −1.87415 − 0.42405I
u = −1.33114
a = −3.12813
b = −4.38293
−4.62840 0
u = 0.615724 + 0.225295I
a = 0.442606 + 0.279319I
b = −1.027400 + 0.849451I
−0.50082 + 7.43088I −9.83588 − 3.06441I
u = 0.615724 − 0.225295I
a = 0.442606 − 0.279319I
b = −1.027400 − 0.849451I
−0.50082 − 7.43088I −9.83588 + 3.06441I
u = −0.377234 + 0.508733I
a = 0.910926 + 0.090831I
b = −0.080814 − 0.346857I
−0.22325 + 1.43278I −1.54695 − 5.02383I
u = −0.377234 − 0.508733I
a = 0.910926 − 0.090831I
b = −0.080814 + 0.346857I
−0.22325 − 1.43278I −1.54695 + 5.02383I
u = −0.481913 + 0.382313I
a = 0.472417 + 0.298979I
b = −0.844793 + 0.392938I
−0.04977 + 4.23277I −3.74018 − 11.43224I
u = −0.481913 − 0.382313I
a = 0.472417 − 0.298979I
b = −0.844793 − 0.392938I
−0.04977 − 4.23277I −3.74018 + 11.43224I
u = 1.38453 + 0.33788I
a = −0.331549 − 0.202544I
b = −0.197769 + 0.616102I
−2.94680 − 5.49032I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38453 − 0.33788I
a = −0.331549 + 0.202544I
b = −0.197769 − 0.616102I
−2.94680 + 5.49032I 0
u = −0.13459 + 1.43811I
a = 0.510736 + 0.169564I
b = −2.29528 − 0.29972I
−3.00179 + 4.56266I 0
u = −0.13459 − 1.43811I
a = 0.510736 − 0.169564I
b = −2.29528 + 0.29972I
−3.00179 − 4.56266I 0
u = 1.45101 + 0.03574I
a = 0.081914 − 0.620709I
b = 0.71394 − 1.81215I
−6.59261 − 2.90185I 0
u = 1.45101 − 0.03574I
a = 0.081914 + 0.620709I
b = 0.71394 + 1.81215I
−6.59261 + 2.90185I 0
u = 1.46452 + 0.10406I
a = −1.48734 + 0.15258I
b = −1.59100 + 0.52581I
−7.24514 − 2.22253I 0
u = 1.46452 − 0.10406I
a = −1.48734 − 0.15258I
b = −1.59100 − 0.52581I
−7.24514 + 2.22253I 0
u = 1.47132 + 0.00598I
a = 1.74208 − 0.11100I
b = 2.41570 + 0.08447I
−3.93524 + 7.62228I 0
u = 1.47132 − 0.00598I
a = 1.74208 + 0.11100I
b = 2.41570 − 0.08447I
−3.93524 − 7.62228I 0
u = 1.41409 + 0.41604I
a = 0.106381 + 0.389440I
b = −0.08739 + 1.42927I
−5.83012 − 5.98154I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41409 − 0.41604I
a = 0.106381 − 0.389440I
b = −0.08739 − 1.42927I
−5.83012 + 5.98154I 0
u = −0.13878 + 1.48672I
a = 0.755838 + 0.008269I
b = −2.60237 − 0.35998I
5.24362 + 3.10833I 0
u = −0.13878 − 1.48672I
a = 0.755838 − 0.008269I
b = −2.60237 + 0.35998I
5.24362 − 3.10833I 0
u = 0.424249 + 0.248865I
a = −1.60490 + 7.51402I
b = −0.626376 + 0.383358I
−2.15277 + 2.70026I −9.88811 + 8.45872I
u = 0.424249 − 0.248865I
a = −1.60490 − 7.51402I
b = −0.626376 − 0.383358I
−2.15277 − 2.70026I −9.88811 − 8.45872I
u = −0.345743 + 0.345351I
a = 5.23140 − 9.13487I
b = −1.17665 − 1.19040I
−1.72233 + 1.49478I −0.6746 − 41.0959I
u = −0.345743 − 0.345351I
a = 5.23140 + 9.13487I
b = −1.17665 + 1.19040I
−1.72233 − 1.49478I −0.6746 + 41.0959I
u = −1.50984 + 0.22948I
a = 1.55997 + 0.33556I
b = 2.38243 − 0.51571I
−3.74678 − 1.39146I 0
u = −1.50984 − 0.22948I
a = 1.55997 − 0.33556I
b = 2.38243 + 0.51571I
−3.74678 + 1.39146I 0
u = 1.52087 + 0.23706I
a = −2.41757 + 0.56218I
b = −4.64875 − 0.40405I
−8.26886 − 4.60408I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52087 − 0.23706I
a = −2.41757 − 0.56218I
b = −4.64875 + 0.40405I
−8.26886 + 4.60408I 0
u = −1.56389 + 0.08723I
a = −0.166301 + 0.131482I
b = 0.044542 − 0.990744I
−7.30971 + 1.30866I 0
u = −1.56389 − 0.08723I
a = −0.166301 − 0.131482I
b = 0.044542 + 0.990744I
−7.30971 − 1.30866I 0
u = −1.50572 + 0.51745I
a = −0.379639 + 0.074193I
b = −0.510768 − 0.673818I
−6.14031 + 10.62530I 0
u = −1.50572 − 0.51745I
a = −0.379639 − 0.074193I
b = −0.510768 + 0.673818I
−6.14031 − 10.62530I 0
u = −0.16466 + 1.59990I
a = 0.464159 − 0.164254I
b = −2.70309 − 0.17160I
−6.96276 − 9.17383I 0
u = −0.16466 − 1.59990I
a = 0.464159 + 0.164254I
b = −2.70309 + 0.17160I
−6.96276 + 9.17383I 0
u = −1.64354 + 0.14674I
a = −1.243040 − 0.088377I
b = −1.59369 + 0.94791I
−11.25600 + 2.45702I 0
u = −1.64354 − 0.14674I
a = −1.243040 + 0.088377I
b = −1.59369 − 0.94791I
−11.25600 − 2.45702I 0
u = −1.61779 + 0.33663I
a = −1.260540 − 0.374517I
b = −1.91931 − 0.36768I
−10.89770 + 7.17611I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.61779 − 0.33663I
a = −1.260540 + 0.374517I
b = −1.91931 + 0.36768I
−10.89770 − 7.17611I 0
u = −0.230559 + 0.235592I
a = 2.01640 − 0.20890I
b = 0.988240 − 0.430122I
−1.89908 + 0.79590I −4.83770 + 0.82015I
u = −0.230559 − 0.235592I
a = 2.01640 + 0.20890I
b = 0.988240 + 0.430122I
−1.89908 − 0.79590I −4.83770 − 0.82015I
u = 1.55975 + 0.62424I
a = 1.44242 − 0.64185I
b = 2.71325 + 0.97362I
−8.2935 − 11.7637I 0
u = 1.55975 − 0.62424I
a = 1.44242 + 0.64185I
b = 2.71325 − 0.97362I
−8.2935 + 11.7637I 0
u = 0.33491 + 1.65140I
a = 0.521990 − 0.114366I
b = −2.61863 + 0.78521I
−6.64004 + 0.42401I 0
u = 0.33491 − 1.65140I
a = 0.521990 + 0.114366I
b = −2.61863 − 0.78521I
−6.64004 − 0.42401I 0
u = −1.55571 + 0.78921I
a = 1.30436 + 0.75861I
b = 2.70847 − 1.25612I
−11.3053 + 17.4741I 0
u = −1.55571 − 0.78921I
a = 1.30436 − 0.75861I
b = 2.70847 + 1.25612I
−11.3053 − 17.4741I 0
u = −1.62516 + 0.70906I
a = 1.218970 + 0.523530I
b = 2.46724 − 1.50899I
−7.62809 + 3.43602I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62516 − 0.70906I
a = 1.218970 − 0.523530I
b = 2.46724 + 1.50899I
−7.62809 − 3.43602I 0
u = 1.60150 + 0.85618I
a = 1.146330 − 0.596908I
b = 2.37731 + 1.76533I
−10.63730 − 9.31613I 0
u = 1.60150 − 0.85618I
a = 1.146330 + 0.596908I
b = 2.37731 − 1.76533I
−10.63730 + 9.31613I 0
u = −1.79507 + 0.49521I
a = 1.331820 + 0.400074I
b = 3.11758 − 0.72547I
−13.6570 + 7.5061I 0
u = −1.79507 − 0.49521I
a = 1.331820 − 0.400074I
b = 3.11758 + 0.72547I
−13.6570 − 7.5061I 0
u = 1.83627 + 0.59317I
a = 1.180040 − 0.374782I
b = 2.90054 + 1.35306I
−13.24420 + 0.87431I 0
u = 1.83627 − 0.59317I
a = 1.180040 + 0.374782I
b = 2.90054 − 1.35306I
−13.24420 − 0.87431I 0
12
II.
I
u
2
= h2u
3
+ 2u
2
+ b + 5u + 1 , −u
3
− 3u
2
+ a − 3u − 6, 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
12
=
u
3
+ 3u
2
+ 3u + 6
−2u
3
− 2u
2
− 5u − 1
a
10
=
u
3
+ 3u
2
+ 3u + 7
−2u
3
− u
2
− 5u − 1
a
4
=
u
u
3
+ u
a
7
=
11u
3
+ 4u
2
+ 27u + 5
3u
3
+ 4u
2
+ 8u + 8
a
1
=
−u
2
− 1
−u
2
a
11
=
u
3
+ 3u
2
+ 3u + 7
−2u
3
− u
2
− 5u − 1
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 − 1)
4
c
10
u
4
c
11
(u + 1)
4
c
12
u
4
+ 5u
3
+ 7u
2
+ 2u + 1
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
, c
11
(y −1)
4
c
10
y
4
c
12
y
4
− 11y
3
+ 31y
2
+ 10y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = 4.75515 + 0.42612I
b = 0.69151 − 1.94753I
−1.85594 + 1.41510I −24.8178 − 33.5385I
u = −0.395123 − 0.506844I
a = 4.75515 − 0.42612I
b = 0.69151 + 1.94753I
−1.85594 − 1.41510I −24.8178 + 33.5385I
u = −0.10488 + 1.55249I
a = −0.755148 − 0.010081I
b = 2.80849 + 0.27009I
5.14581 + 3.16396I −31.6822 − 20.2078I
u = −0.10488 − 1.55249I
a = −0.755148 + 0.010081I
b = 2.80849 − 0.27009I
5.14581 − 3.16396I −31.6822 + 20.2078I
16
III. I
v
1
= ha, 3.10 × 10
5
v
11
+ 7.90 × 10
5
v
10
+ · · · + 7.08 × 10
5
b + 1.25 ×
10
6
, v
12
+ 3v
11
+ · · · + v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
12
=
0
−0.437990v
11
− 1.11658v
10
+ ··· + 0.432058v − 1.76482
a
10
=
1
1.00827v
11
+ 2.68986v
10
+ ··· − 1.09637v + 2.28028
a
4
=
v
0
a
7
=
−1.00827v
11
− 2.68986v
10
+ ··· + 1.09637v − 1.28028
−1.62222v
11
− 4.40786v
10
+ ··· + 1.83221v − 1.73501
a
1
=
1.24751v
11
+ 3.51726v
10
+ ··· − 1.51765v + 2.58875
1.86146v
11
+ 5.23525v
10
+ ··· − 2.25349v + 3.04348
a
11
=
−0.437990v
11
− 1.11658v
10
+ ··· + 0.432058v − 1.76482
−0.437990v
11
− 1.11658v
10
+ ··· + 0.432058v − 1.76482
a
6
=
−1.24751v
11
− 3.51726v
10
+ ··· + 1.51765v − 2.58875
−1.86146v
11
− 5.23525v
10
+ ··· + 2.25349v − 3.04348
a
3
=
1.05885v
11
+ 2.76249v
10
+ ··· + 0.419689v + 2.48147
0.861460v
11
+ 2.23525v
10
+ ··· + 1.74651v + 2.04348
a
2
=
0.667414v
11
+ 1.61644v
10
+ ··· + 0.932022v + 2.13235
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
10
, c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
7
, c
12
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
2
c
9
(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
, c
10
c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
7
, c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 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 = −0.428243 + 0.664531I
1.89061 + 1.10558I 3.79900 − 2.81207I
v = 0.834826 − 0.083652I
a = 0
b = −0.428243 − 0.664531I
1.89061 − 1.10558I 3.79900 + 2.81207I
v = −0.489858 + 0.681154I
a = 0
b = −0.428243 + 0.664531I
1.89061 − 2.95419I 1.04064 + 4.93773I
v = −0.489858 − 0.681154I
a = 0
b = −0.428243 − 0.664531I
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 = 1.002190 − 0.295542I
−1.89061 + 2.95419I 0.48408 − 6.69677I
v = −2.51133 − 0.49706I
a = 0
b = 1.002190 + 0.295542I
−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 = 1.002190 + 0.295542I
−1.89061 + 1.10558I −11.02954 + 1.23660I
v = 0.82520 − 2.42341I
a = 0
b = 1.002190 − 0.295542I
−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
− u
5
− u
4
+ 2u
3
− u + 1)
2
· (u
77
− u
76
+ ··· + 7631854u − 2351327)
c
7
(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
8
u
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
77
+ 2u
76
+ ··· + 20480u + 4096)
c
9
((u − 1)
4
)(u
6
+ u
5
+ ··· + u + 1)
2
(u
77
− 7u
76
+ ··· − 65u + 1)
c
10
u
4
(u
6
− u
5
+ ··· − u + 1)
2
(u
77
+ 13u
76
+ ··· − 200u − 16)
c
11
((u + 1)
4
)(u
6
− u
5
+ ··· − u + 1)
2
(u
77
− 7u
76
+ ··· − 65u + 1)
c
12
(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)
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
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
77
− 9y
76
+ ··· − 135685107448604y − 5528738660929)
c
7
(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
9
, c
11
(y − 1)
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
77
− 63y
76
+ ··· − 2399y − 1)
c
10
y
4
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· (y
77
+ 21y
76
+ ··· + 15168y − 256)
c
12
(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)
23
