12n
0325
(K12n
0325
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 9 10 12 5 4 9 8
Solving Sequence
7,10 5,8
4 11 3 9 12 6 2 1
c
7
c
4
c
10
c
3
c
9
c
11
c
6
c
2
c
1
c
5
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.71883 × 10
322
u
80
+ 5.13115 × 10
321
u
79
+ ··· + 1.73962 × 10
324
b + 1.35587 × 10
324
,
1.38428 × 10
323
u
80
− 6.17270 × 10
322
u
79
+ ··· + 3.47923 × 10
324
a + 5.96157 × 10
323
,
u
81
− 5u
79
+ ··· − 56u + 16i
I
u
2
= h−6.30190 × 10
15
u
20
− 5.04731 × 10
15
u
19
+ ··· + 9.71732 × 10
16
b − 1.02982 × 10
17
,
− 1.87469 × 10
17
u
20
− 1.88197 × 10
17
u
19
+ ··· + 2.04064 × 10
18
a − 8.68955 × 10
18
,
u
21
+ u
20
+ ··· + 82u + 21i
I
v
1
= ha, 2v
3
− 7v
2
+ 5b + 6v + 6, v
4
− 4v
3
+ 6v
2
− v + 1i
* 3 irreducible components of dim
C
= 0, with total 106 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−5.72 × 10
322
u
80
+ 5.13 × 10
321
u
79
+ · · · + 1.74 × 10
324
b + 1.36 ×
10
324
, 1.38 × 10
323
u
80
− 6.17 × 10
322
u
79
+ · · · + 3.48 × 10
324
a + 5.96 ×
10
323
, u
81
− 5u
79
+ · · · − 56u + 16i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
5
=
−0.0397870u
80
+ 0.0177415u
79
+ ··· − 7.69291u − 0.171347
0.0328741u
80
− 0.00294959u
79
+ ··· + 2.89987u − 0.779406
a
8
=
1
−u
2
a
4
=
−0.0726610u
80
+ 0.0206911u
79
+ ··· − 10.5928u + 0.608059
0.0328741u
80
− 0.00294959u
79
+ ··· + 2.89987u − 0.779406
a
11
=
0.0404471u
80
− 0.0384726u
79
+ ··· + 16.7195u − 4.06914
−0.0462175u
80
− 0.0248072u
79
+ ··· − 4.11812u + 1.57122
a
3
=
0.00600531u
80
+ 0.0734423u
79
+ ··· − 5.37163u − 0.502405
0.00663013u
80
− 0.0144926u
79
+ ··· + 1.20447u + 0.0646126
a
9
=
−0.0146977u
80
− 0.0555582u
79
+ ··· + 8.39910u − 1.39945
−0.00892733u
80
+ 0.00772163u
79
+ ··· − 2.20233u + 1.09846
a
12
=
0.0411094u
80
+ 0.0343150u
79
+ ··· + 15.7625u − 0.848914
−0.0733906u
80
− 0.0529926u
79
+ ··· − 5.05653u + 1.28512
a
6
=
−0.157363u
80
− 0.0629909u
79
+ ··· − 10.8730u + 2.42951
0.0162201u
80
+ 0.00434497u
79
+ ··· + 1.09822u − 0.123036
a
2
=
−0.0932583u
80
− 0.0524637u
79
+ ··· − 11.7756u + 1.50276
0.0585649u
80
+ 0.0311349u
79
+ ··· + 3.73976u − 1.21412
a
1
=
0.0209487u
80
+ 0.00504618u
79
+ ··· − 11.9699u + 0.112838
0.0518225u
80
+ 0.0456388u
79
+ ··· + 3.84524u − 0.655337
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.263378u
80
− 0.100086u
79
+ ··· − 25.2033u + 11.4620
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
81
+ 24u
80
+ ··· + 53u + 1
c
2
, c
5
u
81
+ 2u
80
+ ··· + 11u − 1
c
3
u
81
− u
80
+ ··· + 2043071u − 89033
c
4
u
81
+ 5u
80
+ ··· − 6u + 1
c
6
u
81
+ u
80
+ ··· − 13206u − 919
c
7
u
81
− 5u
79
+ ··· − 56u − 16
c
8
, c
11
, c
12
u
81
− 5u
80
+ ··· − 12u − 1
c
9
u
81
+ 2u
80
+ ··· − 7u − 11
c
10
u
81
+ 6u
80
+ ··· + 26845u − 6217
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
81
+ 76y
80
+ ··· + 2869y −1
c
2
, c
5
y
81
− 24y
80
+ ··· + 53y −1
c
3
y
81
+ 77y
80
+ ··· + 1032689479609y −7926875089
c
4
y
81
− 9y
80
+ ··· − 158y −1
c
6
y
81
+ 43y
80
+ ··· + 71336262y −844561
c
7
y
81
− 10y
80
+ ··· − 448y −256
c
8
, c
11
, c
12
y
81
+ 17y
80
+ ··· − 62y −1
c
9
y
81
+ 14y
80
+ ··· − 4549y −121
c
10
y
81
− 34y
80
+ ··· + 684980879y −38651089
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.864704 + 0.515104I
a = 0.067355 − 0.956329I
b = −0.77225 − 1.40002I
6.65165 − 2.03331I 0
u = −0.864704 − 0.515104I
a = 0.067355 + 0.956329I
b = −0.77225 + 1.40002I
6.65165 + 2.03331I 0
u = 0.966443 + 0.409894I
a = −0.339969 + 0.966882I
b = 1.22854 + 0.97887I
2.72616 + 4.53398I 0
u = 0.966443 − 0.409894I
a = −0.339969 − 0.966882I
b = 1.22854 − 0.97887I
2.72616 − 4.53398I 0
u = −0.994830 + 0.338608I
a = 0.006971 + 0.922467I
b = 0.84421 + 1.40177I
6.82770 + 4.65491I 0
u = −0.994830 − 0.338608I
a = 0.006971 − 0.922467I
b = 0.84421 − 1.40177I
6.82770 − 4.65491I 0
u = 0.995164 + 0.394044I
a = −0.430835 − 0.371591I
b = −0.703603 + 0.320798I
−1.65632 − 4.60349I 0
u = 0.995164 − 0.394044I
a = −0.430835 + 0.371591I
b = −0.703603 − 0.320798I
−1.65632 + 4.60349I 0
u = −0.767333 + 0.520690I
a = 2.03065 + 0.14534I
b = −0.606396 + 0.400040I
6.34137 − 2.12224I 0
u = −0.767333 − 0.520690I
a = 2.03065 − 0.14534I
b = −0.606396 − 0.400040I
6.34137 + 2.12224I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.631355 + 0.614749I
a = −2.17032 − 0.52418I
b = 0.583634 − 0.494454I
5.37211 − 8.58308I 0. + 10.97236I
u = −0.631355 − 0.614749I
a = −2.17032 + 0.52418I
b = 0.583634 + 0.494454I
5.37211 + 8.58308I 0. − 10.97236I
u = 0.812049 + 0.295790I
a = −0.080919 − 0.949851I
b = 1.33248 − 1.24004I
7.79780 + 1.80326I 6.94176 − 3.29971I
u = 0.812049 − 0.295790I
a = −0.080919 + 0.949851I
b = 1.33248 + 1.24004I
7.79780 − 1.80326I 6.94176 + 3.29971I
u = −0.693024 + 0.899959I
a = 0.453119 − 0.585375I
b = 0.696516 − 0.250989I
0.88281 − 2.11179I 0
u = −0.693024 − 0.899959I
a = 0.453119 + 0.585375I
b = 0.696516 + 0.250989I
0.88281 + 2.11179I 0
u = 0.709599 + 0.423129I
a = 0.081228 + 1.049090I
b = −1.28895 + 1.30848I
6.61316 + 8.67249I 3.85291 − 8.97147I
u = 0.709599 − 0.423129I
a = 0.081228 − 1.049090I
b = −1.28895 − 1.30848I
6.61316 − 8.67249I 3.85291 + 8.97147I
u = 0.938083 + 0.715903I
a = 0.165581 − 1.167330I
b = −1.14860 − 1.03079I
−1.74227 + 9.69257I 0
u = 0.938083 − 0.715903I
a = 0.165581 + 1.167330I
b = −1.14860 + 1.03079I
−1.74227 − 9.69257I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.799263 + 0.166597I
a = 2.07141 + 1.21207I
b = −0.806764 − 0.009351I
7.11949 − 6.20902I 7.94528 + 4.20823I
u = 0.799263 − 0.166597I
a = 2.07141 − 1.21207I
b = −0.806764 + 0.009351I
7.11949 + 6.20902I 7.94528 − 4.20823I
u = 0.607583 + 1.032170I
a = 0.396665 + 1.147560I
b = 0.370178 + 0.457483I
−3.53662 + 1.62898I 0
u = 0.607583 − 1.032170I
a = 0.396665 − 1.147560I
b = 0.370178 − 0.457483I
−3.53662 − 1.62898I 0
u = −1.196840 + 0.151285I
a = 0.484675 + 0.322392I
b = −0.566636 − 0.008546I
2.37854 + 0.00858I 0
u = −1.196840 − 0.151285I
a = 0.484675 − 0.322392I
b = −0.566636 + 0.008546I
2.37854 − 0.00858I 0
u = −0.437058 + 0.660943I
a = −0.62890 + 1.51723I
b = −0.97286 + 1.03700I
−2.04253 − 6.44979I −3.14648 + 2.17088I
u = −0.437058 − 0.660943I
a = −0.62890 − 1.51723I
b = −0.97286 − 1.03700I
−2.04253 + 6.44979I −3.14648 − 2.17088I
u = 0.706225 + 0.292864I
a = −2.28510 − 0.86473I
b = 0.834574 + 0.090973I
7.40515 + 0.63413I 7.99415 − 1.89608I
u = 0.706225 − 0.292864I
a = −2.28510 + 0.86473I
b = 0.834574 − 0.090973I
7.40515 − 0.63413I 7.99415 + 1.89608I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.001240 + 0.736005I
a = 0.256315 − 0.742703I
b = 1.03551 − 1.10338I
−0.38191 − 5.09344I 0
u = −1.001240 − 0.736005I
a = 0.256315 + 0.742703I
b = 1.03551 + 1.10338I
−0.38191 + 5.09344I 0
u = 1.151460 + 0.487803I
a = −0.132708 + 0.482310I
b = 0.68966 + 1.39312I
0.57158 + 4.71464I 0
u = 1.151460 − 0.487803I
a = −0.132708 − 0.482310I
b = 0.68966 − 1.39312I
0.57158 − 4.71464I 0
u = −0.425288 + 0.605867I
a = −0.402409 + 0.735878I
b = −1.41930 + 1.05173I
−2.12406 − 2.49621I −6.63409 + 8.73341I
u = −0.425288 − 0.605867I
a = −0.402409 − 0.735878I
b = −1.41930 − 1.05173I
−2.12406 + 2.49621I −6.63409 − 8.73341I
u = 0.926610 + 0.858585I
a = 0.194288 − 1.235310I
b = −0.596939 − 0.501927I
−2.98305 + 5.70394I 0
u = 0.926610 − 0.858585I
a = 0.194288 + 1.235310I
b = −0.596939 + 0.501927I
−2.98305 − 5.70394I 0
u = 0.630721 + 0.297315I
a = 0.044076 − 0.323841I
b = −1.32512 − 0.80646I
−1.74333 − 0.96559I 2.53517 + 1.89595I
u = 0.630721 − 0.297315I
a = 0.044076 + 0.323841I
b = −1.32512 + 0.80646I
−1.74333 + 0.96559I 2.53517 − 1.89595I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.30677
a = 0.440104
b = −0.578903
2.39168 0
u = −0.809127 + 1.085380I
a = 0.348245 − 0.753818I
b = 1.033020 − 0.878591I
0.01437 − 3.34341I 0
u = −0.809127 − 1.085380I
a = 0.348245 + 0.753818I
b = 1.033020 + 0.878591I
0.01437 + 3.34341I 0
u = −1.343510 + 0.229960I
a = 0.136679 − 0.733260I
b = 0.0305346 + 0.0832964I
3.06582 − 2.90294I 0
u = −1.343510 − 0.229960I
a = 0.136679 + 0.733260I
b = 0.0305346 − 0.0832964I
3.06582 + 2.90294I 0
u = −0.742009 + 1.145830I
a = −0.219888 + 0.773292I
b = −1.113060 + 0.863158I
−0.56917 − 7.09177I 0
u = −0.742009 − 1.145830I
a = −0.219888 − 0.773292I
b = −1.113060 − 0.863158I
−0.56917 + 7.09177I 0
u = 0.329952 + 0.525230I
a = 0.736440 − 0.506654I
b = −0.702528 − 0.710743I
−1.71749 − 0.71942I −4.34292 + 2.51779I
u = 0.329952 − 0.525230I
a = 0.736440 + 0.506654I
b = −0.702528 + 0.710743I
−1.71749 + 0.71942I −4.34292 − 2.51779I
u = 0.529505 + 0.274692I
a = 1.46484 − 0.92641I
b = −0.980346 − 0.517594I
−2.36369 − 0.32690I −5.66562 − 9.76585I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.529505 − 0.274692I
a = 1.46484 + 0.92641I
b = −0.980346 + 0.517594I
−2.36369 + 0.32690I −5.66562 + 9.76585I
u = −0.244534 + 0.536517I
a = −0.53817 + 1.53698I
b = −0.451773 + 1.306960I
−3.40204 + 1.03279I −10.82794 − 0.78219I
u = −0.244534 − 0.536517I
a = −0.53817 − 1.53698I
b = −0.451773 − 1.306960I
−3.40204 − 1.03279I −10.82794 + 0.78219I
u = 0.96412 + 1.05607I
a = 0.231870 − 0.803520I
b = −0.645655 − 0.795469I
−5.04671 + 3.28136I 0
u = 0.96412 − 1.05607I
a = 0.231870 + 0.803520I
b = −0.645655 + 0.795469I
−5.04671 − 3.28136I 0
u = −0.386461 + 0.412162I
a = 0.76468 − 1.82667I
b = 0.797237 − 0.778612I
0.25040 − 1.87331I 0.34554 + 1.40917I
u = −0.386461 − 0.412162I
a = 0.76468 + 1.82667I
b = 0.797237 + 0.778612I
0.25040 + 1.87331I 0.34554 − 1.40917I
u = −0.524498 + 0.044281I
a = −1.62507 − 3.02956I
b = 0.330303 + 0.197370I
−1.24173 + 1.81398I 10.77561 − 2.15505I
u = −0.524498 − 0.044281I
a = −1.62507 + 3.02956I
b = 0.330303 − 0.197370I
−1.24173 − 1.81398I 10.77561 + 2.15505I
u = −1.27771 + 0.86343I
a = −0.047743 − 1.024450I
b = 1.120830 − 0.833024I
8.49340 − 2.81545I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.27771 − 0.86343I
a = −0.047743 + 1.024450I
b = 1.120830 + 0.833024I
8.49340 + 2.81545I 0
u = 1.29919 + 0.91454I
a = −0.029009 + 0.970536I
b = 1.16686 + 1.06335I
8.08845 + 10.56960I 0
u = 1.29919 − 0.91454I
a = −0.029009 − 0.970536I
b = 1.16686 − 1.06335I
8.08845 − 10.56960I 0
u = −0.110881 + 0.394837I
a = 1.95199 − 1.20586I
b = 0.744067 − 0.566714I
0.24040 − 1.80693I 2.04275 + 2.63185I
u = −0.110881 − 0.394837I
a = 1.95199 + 1.20586I
b = 0.744067 + 0.566714I
0.24040 + 1.80693I 2.04275 − 2.63185I
u = 1.08582 + 1.16909I
a = 0.014716 + 0.711655I
b = 0.351527 + 0.836307I
−4.65186 + 4.67041I 0
u = 1.08582 − 1.16909I
a = 0.014716 − 0.711655I
b = 0.351527 − 0.836307I
−4.65186 − 4.67041I 0
u = −1.29087 + 0.98632I
a = 0.033830 + 0.966217I
b = −1.121530 + 0.843319I
8.31128 − 9.42962I 0
u = −1.29087 − 0.98632I
a = 0.033830 − 0.966217I
b = −1.121530 − 0.843319I
8.31128 + 9.42962I 0
u = 1.28305 + 1.03050I
a = −0.017196 − 0.966057I
b = −1.16141 − 1.06158I
6.9973 + 17.3859I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28305 − 1.03050I
a = −0.017196 + 0.966057I
b = −1.16141 + 1.06158I
6.9973 − 17.3859I 0
u = 0.137169 + 0.220166I
a = −3.82003 − 1.10596I
b = 0.891385 + 0.431882I
0.27565 + 2.32917I 3.22220 − 5.32820I
u = 0.137169 − 0.220166I
a = −3.82003 + 1.10596I
b = 0.891385 − 0.431882I
0.27565 − 2.32917I 3.22220 + 5.32820I
u = −1.17162 + 1.66414I
a = 0.358589 − 0.091080I
b = 0.791006 + 0.130196I
6.40830 − 5.94458I 0
u = −1.17162 − 1.66414I
a = 0.358589 + 0.091080I
b = 0.791006 − 0.130196I
6.40830 + 5.94458I 0
u = 0.90423 + 1.87894I
a = 0.385525 − 0.088992I
b = 0.503904 − 0.470029I
5.85315 − 1.73778I 0
u = 0.90423 − 1.87894I
a = 0.385525 + 0.088992I
b = 0.503904 + 0.470029I
5.85315 + 1.73778I 0
u = −1.44010 + 1.58883I
a = −0.276887 + 0.100013I
b = −0.715602 − 0.117841I
6.92752 + 0.05311I 0
u = −1.44010 − 1.58883I
a = −0.276887 − 0.100013I
b = −0.715602 + 0.117841I
6.92752 − 0.05311I 0
u = 1.23014 + 1.82253I
a = −0.354642 + 0.037461I
b = −0.487203 + 0.423434I
5.57490 − 8.01859I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.23014 − 1.82253I
a = −0.354642 − 0.037461I
b = −0.487203 − 0.423434I
5.57490 + 8.01859I 0
13
II. I
u
2
= h−6.30 × 10
15
u
20
− 5.05 × 10
15
u
19
+ · · · + 9.72 × 10
16
b − 1.03 ×
10
17
, −1.87 × 10
17
u
20
− 1.88 × 10
17
u
19
+ · · · + 2.04 × 10
18
a − 8.69 ×
10
18
, u
21
+ u
20
+ · · · + 82u + 21i
(i) Arc colorings
a
7
=
1
0
a
10
=
0
u
a
5
=
0.0918677u
20
+ 0.0922247u
19
+ ··· + 10.1330u + 4.25825
0.0648523u
20
+ 0.0519414u
19
+ ··· + 5.88126u + 1.05978
a
8
=
1
−u
2
a
4
=
0.0270155u
20
+ 0.0402833u
19
+ ··· + 4.25169u + 3.19848
0.0648523u
20
+ 0.0519414u
19
+ ··· + 5.88126u + 1.05978
a
11
=
0.0296731u
20
− 0.00117994u
19
+ ··· + 0.685337u − 1.65814
−0.0772922u
20
− 0.0464391u
19
+ ··· − 6.97105u − 2.24662
a
3
=
0.0848197u
20
+ 0.0837459u
19
+ ··· + 8.47766u + 3.97963
0.0928914u
20
+ 0.0432223u
19
+ ··· + 5.91914u + 0.758605
a
9
=
−0.105108u
20
− 0.0586467u
19
+ ··· − 9.56290u − 3.55257
−0.0574885u
20
− 0.0110277u
19
+ ··· − 1.27718u + 0.352191
a
12
=
0.0605212u
20
− 0.0278204u
19
+ ··· + 2.53288u − 1.40578
−0.103104u
20
− 0.0661692u
19
+ ··· − 9.85278u − 3.47866
a
6
=
0.114510u
20
+ 0.0669967u
19
+ ··· + 8.10574u + 3.53448
0.0512777u
20
− 0.0647731u
19
+ ··· − 2.39869u − 1.32518
a
2
=
0.0680487u
20
+ 0.00948640u
19
+ ··· + 3.03949u + 0.327223
0.0863649u
20
− 0.0650135u
19
+ ··· − 0.705523u − 1.34773
a
1
=
0.0140821u
20
− 0.0536105u
19
+ ··· − 1.34684u − 3.02927
−0.120235u
20
− 0.0659225u
19
+ ··· − 9.13478u − 3.04503
(ii) Obstruction class = 1
(iii) Cusp Shapes =
−
49669659860913382
97173200599743577
u
20
−
4115535744999369
97173200599743577
u
19
+···−
2760913852914928753
97173200599743577
u−
1471524814101360942
97173200599743577
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 9u
20
+ ··· + 13u − 1
c
2
u
21
+ 3u
20
+ ··· − u − 1
c
3
u
21
− 2u
20
+ ··· + 8u − 1
c
4
u
21
+ u
19
+ ··· + 3u + 1
c
5
u
21
− 3u
20
+ ··· − u + 1
c
6
u
21
− 2u
20
+ ··· − 6u
2
+ 1
c
7
u
21
+ u
20
+ ··· + 82u + 21
c
8
u
21
+ 6u
20
+ ··· + 2u + 1
c
9
u
21
− 2u
19
+ ··· − 4u
2
+ 1
c
10
u
21
− 4u
19
+ ··· − 2u
2
+ 1
c
11
, c
12
u
21
− 6u
20
+ ··· + 2u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 11y
20
+ ··· + 21y −1
c
2
, c
5
y
21
− 9y
20
+ ··· + 13y −1
c
3
y
21
− 4y
20
+ ··· − 4y −1
c
4
y
21
+ 2y
20
+ ··· − 3y −1
c
6
y
21
+ 16y
20
+ ··· + 12y −1
c
7
y
21
+ 5y
20
+ ··· + 298y −441
c
8
, c
11
, c
12
y
21
+ 14y
20
+ ··· − 20y −1
c
9
y
21
− 4y
20
+ ··· + 8y −1
c
10
y
21
− 8y
20
+ ··· + 4y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584118 + 0.821988I
a = −0.382237 + 1.100510I
b = −1.22637 + 1.09977I
−2.16179 − 7.28514I −6.01063 + 11.10127I
u = −0.584118 − 0.821988I
a = −0.382237 − 1.100510I
b = −1.22637 − 1.09977I
−2.16179 + 7.28514I −6.01063 − 11.10127I
u = 0.727439 + 0.797873I
a = 0.283614 − 1.203610I
b = −0.374054 − 0.982956I
−5.18388 + 1.17171I −6.94253 − 1.04333I
u = 0.727439 − 0.797873I
a = 0.283614 + 1.203610I
b = −0.374054 + 0.982956I
−5.18388 − 1.17171I −6.94253 + 1.04333I
u = 0.122260 + 1.092720I
a = −0.210355 + 0.690329I
b = −0.293874 − 0.452780I
5.65023 − 7.00946I 1.49178 + 4.70625I
u = 0.122260 − 1.092720I
a = −0.210355 − 0.690329I
b = −0.293874 + 0.452780I
5.65023 + 7.00946I 1.49178 − 4.70625I
u = −0.344958 + 1.110080I
a = −0.109099 − 0.644647I
b = 0.367821 + 0.381862I
6.21689 − 0.62415I 2.36082 + 0.43899I
u = −0.344958 − 1.110080I
a = −0.109099 + 0.644647I
b = 0.367821 − 0.381862I
6.21689 + 0.62415I 2.36082 − 0.43899I
u = −1.070690 + 0.572936I
a = 0.014454 − 0.590067I
b = 0.95444 − 1.25069I
0.99387 − 4.70161I 7.91100 + 7.75482I
u = −1.070690 − 0.572936I
a = 0.014454 + 0.590067I
b = 0.95444 + 1.25069I
0.99387 + 4.70161I 7.91100 − 7.75482I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759478 + 0.986319I
a = 0.424982 − 0.756838I
b = 1.14473 − 0.94309I
−0.53568 − 3.72174I −6.08462 + 6.31570I
u = −0.759478 − 0.986319I
a = 0.424982 + 0.756838I
b = 1.14473 + 0.94309I
−0.53568 + 3.72174I −6.08462 − 6.31570I
u = 0.662872 + 1.195780I
a = −0.233661 − 1.009940I
b = −0.721695 − 0.842178I
−4.56507 + 7.07946I −5.78585 − 8.27673I
u = 0.662872 − 1.195780I
a = −0.233661 + 1.009940I
b = −0.721695 + 0.842178I
−4.56507 − 7.07946I −5.78585 + 8.27673I
u = −1.38885
a = −0.500577
b = 0.535085
2.18490 −23.2560
u = −0.561025 + 0.223517I
a = 0.964733 + 0.909802I
b = −1.10297 + 0.90533I
−2.35040 + 0.78782I −7.11653 − 4.34389I
u = −0.561025 − 0.223517I
a = 0.964733 − 0.909802I
b = −1.10297 − 0.90533I
−2.35040 − 0.78782I −7.11653 + 4.34389I
u = 1.13171 + 0.85422I
a = −0.265450 + 0.761191I
b = 0.350518 + 0.725496I
−3.86356 + 4.83551I −2.00041 − 6.96581I
u = 1.13171 − 0.85422I
a = −0.265450 − 0.761191I
b = 0.350518 − 0.725496I
−3.86356 − 4.83551I −2.00041 + 6.96581I
u = 0.87040 + 1.31729I
a = 0.144259 + 0.786102I
b = 0.633912 + 0.675830I
−3.51772 + 2.78459I −2.19526 − 4.30048I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.87040 − 1.31729I
a = 0.144259 − 0.786102I
b = 0.633912 − 0.675830I
−3.51772 − 2.78459I −2.19526 + 4.30048I
19
III. I
v
1
= ha, 2v
3
− 7v
2
+ 5b + 6v + 6, v
4
− 4v
3
+ 6v
2
− v + 1i
(i) Arc colorings
a
7
=
1
0
a
10
=
v
0
a
5
=
0
−
2
5
v
3
+
7
5
v
2
−
6
5
v −
6
5
a
8
=
1
0
a
4
=
2
5
v
3
−
7
5
v
2
+
6
5
v +
6
5
−
2
5
v
3
+
7
5
v
2
−
6
5
v −
6
5
a
11
=
2
5
v
3
−
7
5
v
2
+
16
5
v −
4
5
−
2
5
v
3
+
7
5
v
2
−
11
5
v +
4
5
a
3
=
0
−
2
5
v
3
+
7
5
v
2
−
6
5
v −
6
5
a
9
=
v
−
2
5
v
3
+
7
5
v
2
−
11
5
v +
4
5
a
12
=
1
5
v
3
−
6
5
v
2
+
13
5
v −
2
5
−
2
5
v
3
+
7
5
v
2
−
11
5
v −
1
5
a
6
=
1
5
v
3
−
1
5
v
2
−
2
5
v +
3
5
2
5
v
3
−
7
5
v
2
+
11
5
v +
1
5
a
2
=
−
1
5
v
3
+
1
5
v
2
+
2
5
v −
3
5
−
4
5
v
3
+
14
5
v
2
−
17
5
v −
7
5
a
1
=
−
1
5
v
3
+
1
5
v
2
+
2
5
v −
3
5
−
2
5
v
3
+
7
5
v
2
−
11
5
v −
1
5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
3
5
v
3
+
8
5
v
2
−
34
5
v +
11
5
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
4
u
4
− 2u
3
+ u + 1
c
5
(u + 1)
4
c
6
, c
11
, c
12
(u
2
− u + 1)
2
c
7
u
4
c
8
(u
2
+ u + 1)
2
c
9
, c
10
u
4
− u
3
+ 3u
2
− u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
4
c
3
, c
4
y
4
− 4y
3
+ 6y
2
− y + 1
c
6
, c
8
, c
11
c
12
(y
2
+ y + 1)
2
c
7
y
4
c
9
, c
10
y
4
+ 5y
3
+ 9y
2
+ 5y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.026439 + 0.421254I
a = 0
b = −1.47356 − 0.44477I
−1.64493 + 2.02988I 1.74584 − 2.78456I
v = 0.026439 − 0.421254I
a = 0
b = −1.47356 + 0.44477I
−1.64493 − 2.02988I 1.74584 + 2.78456I
v = 1.97356 + 1.31080I
a = 0
b = 0.473561 + 0.444772I
−1.64493 + 2.02988I −6.24584 − 8.47377I
v = 1.97356 − 1.31080I
a = 0
b = 0.473561 − 0.444772I
−1.64493 − 2.02988I −6.24584 + 8.47377I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
21
− 9u
20
+ ··· + 13u − 1)(u
81
+ 24u
80
+ ··· + 53u + 1)
c
2
((u − 1)
4
)(u
21
+ 3u
20
+ ··· − u − 1)(u
81
+ 2u
80
+ ··· + 11u − 1)
c
3
(u
4
− 2u
3
+ u + 1)(u
21
− 2u
20
+ ··· + 8u − 1)
· (u
81
− u
80
+ ··· + 2043071u − 89033)
c
4
(u
4
− 2u
3
+ u + 1)(u
21
+ u
19
+ ··· + 3u + 1)(u
81
+ 5u
80
+ ··· − 6u + 1)
c
5
((u + 1)
4
)(u
21
− 3u
20
+ ··· − u + 1)(u
81
+ 2u
80
+ ··· + 11u − 1)
c
6
((u
2
− u + 1)
2
)(u
21
− 2u
20
+ ··· − 6u
2
+ 1)
· (u
81
+ u
80
+ ··· − 13206u − 919)
c
7
u
4
(u
21
+ u
20
+ ··· + 82u + 21)(u
81
− 5u
79
+ ··· − 56u − 16)
c
8
((u
2
+ u + 1)
2
)(u
21
+ 6u
20
+ ··· + 2u + 1)(u
81
− 5u
80
+ ··· − 12u − 1)
c
9
(u
4
− u
3
+ 3u
2
− u + 1)(u
21
− 2u
19
+ ··· − 4u
2
+ 1)
· (u
81
+ 2u
80
+ ··· − 7u − 11)
c
10
(u
4
− u
3
+ 3u
2
− u + 1)(u
21
− 4u
19
+ ··· − 2u
2
+ 1)
· (u
81
+ 6u
80
+ ··· + 26845u − 6217)
c
11
, c
12
((u
2
− u + 1)
2
)(u
21
− 6u
20
+ ··· + 2u − 1)(u
81
− 5u
80
+ ··· − 12u − 1)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
4
)(y
21
+ 11y
20
+ ··· + 21y − 1)(y
81
+ 76y
80
+ ··· + 2869y − 1)
c
2
, c
5
((y − 1)
4
)(y
21
− 9y
20
+ ··· + 13y − 1)(y
81
− 24y
80
+ ··· + 53y − 1)
c
3
(y
4
− 4y
3
+ 6y
2
− y + 1)(y
21
− 4y
20
+ ··· − 4y − 1)
· (y
81
+ 77y
80
+ ··· + 1032689479609y − 7926875089)
c
4
(y
4
− 4y
3
+ 6y
2
− y + 1)(y
21
+ 2y
20
+ ··· − 3y − 1)
· (y
81
− 9y
80
+ ··· − 158y − 1)
c
6
((y
2
+ y + 1)
2
)(y
21
+ 16y
20
+ ··· + 12y − 1)
· (y
81
+ 43y
80
+ ··· + 71336262y − 844561)
c
7
y
4
(y
21
+ 5y
20
+ ··· + 298y − 441)(y
81
− 10y
80
+ ··· − 448y − 256)
c
8
, c
11
, c
12
((y
2
+ y + 1)
2
)(y
21
+ 14y
20
+ ··· − 20y − 1)
· (y
81
+ 17y
80
+ ··· − 62y − 1)
c
9
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
21
− 4y
20
+ ··· + 8y − 1)
· (y
81
+ 14y
80
+ ··· − 4549y − 121)
c
10
(y
4
+ 5y
3
+ 9y
2
+ 5y + 1)(y
21
− 8y
20
+ ··· + 4y − 1)
· (y
81
− 34y
80
+ ··· + 684980879y − 38651089)
25
