12a
0524
(K12a
0524
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 12 10 2 5 4 1 6 11
Solving Sequence
2,8
7 3 4
1,10
11 6 9 5 12
c
7
c
2
c
3
c
1
c
10
c
6
c
9
c
4
c
12
c
5
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.19165 × 10
29
u
63
+ 7.17172 × 10
28
u
62
+ ··· + 8.78717 × 10
29
b + 1.18770 × 10
30
,
1.42661 × 10
31
u
63
− 8.31260 × 10
30
u
62
+ ··· + 7.02973 × 10
30
a + 1.31917 × 10
31
, u
64
− u
63
+ ··· − 2u + 1i
I
u
2
= h−u
4
− 2u
2
+ b, u
4
+ u
2
+ a − 1, u
27
+ 9u
25
+ ··· − u − 1i
I
u
3
= hb + 1, a
3
− a
2
u − 3a
2
+ 2au + a + 1, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 97 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
= h1.19 × 10
29
u
63
+ 7.17 × 10
28
u
62
+ · · · + 8.79 × 10
29
b + 1.19 × 10
30
, 1.43 ×
10
31
u
63
−8.31×10
30
u
62
+· · ·+7.03×10
30
a+1.32×10
31
, u
64
−u
63
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−2.02940u
63
+ 1.18249u
62
+ ··· − 2.99982u − 1.87655
−0.135612u
63
− 0.0816158u
62
+ ··· + 0.389219u − 1.35163
a
11
=
−2.09643u
63
+ 1.12088u
62
+ ··· − 3.17116u − 1.64675
−0.314315u
63
− 0.0337323u
62
+ ··· − 0.348072u − 1.64704
a
6
=
−1.85442u
63
+ 0.738976u
62
+ ··· − 1.32676u − 3.25750
−0.355484u
63
+ 0.0412247u
62
+ ··· − 0.0480554u − 2.11408
a
9
=
−2.16501u
63
+ 1.10088u
62
+ ··· − 2.61060u − 2.22819
−0.314049u
63
− 0.0375849u
62
+ ··· − 0.543961u − 1.53479
a
5
=
−2.41577u
63
+ 2.96723u
62
+ ··· − 13.7211u + 4.47906
−0.534793u
63
+ 0.848842u
62
+ ··· − 4.03951u + 1.61355
a
12
=
−2.57675u
63
+ 2.92049u
62
+ ··· − 15.0731u + 4.77964
−0.807524u
63
+ 1.17773u
62
+ ··· − 5.99028u + 1.80950
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.60252u
63
+ 1.80827u
62
+ ··· − 15.4271u + 3.07685
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
+ 31u
63
+ ··· + 8u + 1
c
2
, c
7
u
64
+ u
63
+ ··· + 2u + 1
c
3
u
64
+ 2u
63
+ ··· + 1984u + 128
c
4
, c
8
, c
9
u
64
+ u
63
+ ··· + 16u + 1
c
5
, c
11
u
64
+ 2u
63
+ ··· + u + 2
c
6
u
64
− 10u
63
+ ··· − 14873u + 1862
c
10
, c
12
u
64
− 20u
63
+ ··· − 19u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
+ 11y
63
+ ··· − 40y + 1
c
2
, c
7
y
64
+ 31y
63
+ ··· + 8y + 1
c
3
y
64
− 30y
63
+ ··· + 1945600y + 16384
c
4
, c
8
, c
9
y
64
+ 59y
63
+ ··· + 104y + 1
c
5
, c
11
y
64
+ 20y
63
+ ··· + 19y + 4
c
6
y
64
− 12y
63
+ ··· − 37020813y + 3467044
c
10
, c
12
y
64
+ 48y
63
+ ··· + 879y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.740864 + 0.662784I
a = −1.076250 + 0.014411I
b = 0.049744 + 0.197245I
6.16267 + 3.38539I 2.09489 − 2.71260I
u = −0.740864 − 0.662784I
a = −1.076250 − 0.014411I
b = 0.049744 − 0.197245I
6.16267 − 3.38539I 2.09489 + 2.71260I
u = −0.445418 + 0.865420I
a = −0.339938 − 0.644967I
b = 0.121992 + 1.067110I
−1.53101 − 1.39020I −5.91926 + 3.88104I
u = −0.445418 − 0.865420I
a = −0.339938 + 0.644967I
b = 0.121992 − 1.067110I
−1.53101 + 1.39020I −5.91926 − 3.88104I
u = −0.021735 + 1.036710I
a = 1.165230 + 0.128138I
b = −0.0067591 − 0.0148508I
−4.65557 − 2.80220I −13.46250 + 3.05850I
u = −0.021735 − 1.036710I
a = 1.165230 − 0.128138I
b = −0.0067591 + 0.0148508I
−4.65557 + 2.80220I −13.46250 − 3.05850I
u = 0.510043 + 0.798911I
a = −0.241579 + 1.067010I
b = −0.181458 − 1.313360I
−0.86573 + 6.45035I −3.51752 − 9.65683I
u = 0.510043 − 0.798911I
a = −0.241579 − 1.067010I
b = −0.181458 + 1.313360I
−0.86573 − 6.45035I −3.51752 + 9.65683I
u = −0.715186 + 0.790541I
a = −0.816990 + 0.099941I
b = 0.096344 − 0.304633I
9.65441 − 2.68529I 5.74999 + 0.I
u = −0.715186 − 0.790541I
a = −0.816990 − 0.099941I
b = 0.096344 + 0.304633I
9.65441 + 2.68529I 5.74999 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.636482 + 0.681496I
a = −1.048850 + 0.124326I
b = −0.239480 − 0.007765I
4.80153 + 1.37625I −0.64369 − 3.25078I
u = 0.636482 − 0.681496I
a = −1.048850 − 0.124326I
b = −0.239480 + 0.007765I
4.80153 − 1.37625I −0.64369 + 3.25078I
u = 0.897043 + 0.224964I
a = −0.162901 + 0.141407I
b = −1.21809 − 1.38009I
1.29409 − 11.08640I −1.19961 + 7.21378I
u = 0.897043 − 0.224964I
a = −0.162901 − 0.141407I
b = −1.21809 + 1.38009I
1.29409 + 11.08640I −1.19961 − 7.21378I
u = 0.631106 + 0.872776I
a = −0.402460 + 0.142378I
b = −0.248913 + 0.600652I
4.24624 + 3.53311I 0
u = 0.631106 − 0.872776I
a = −0.402460 − 0.142378I
b = −0.248913 − 0.600652I
4.24624 − 3.53311I 0
u = 0.846306 + 0.300514I
a = −0.501209 + 0.065356I
b = −0.87761 − 1.19110I
6.84859 − 5.40917I 4.32977 + 4.44506I
u = 0.846306 − 0.300514I
a = −0.501209 − 0.065356I
b = −0.87761 + 1.19110I
6.84859 + 5.40917I 4.32977 − 4.44506I
u = −0.871978 + 0.210846I
a = −0.151648 − 0.024372I
b = −1.25701 + 1.25917I
0.32985 + 5.28991I −2.86725 − 2.43047I
u = −0.871978 − 0.210846I
a = −0.151648 + 0.024372I
b = −1.25701 − 1.25917I
0.32985 − 5.28991I −2.86725 + 2.43047I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.687105 + 0.897262I
a = −0.355479 + 0.167421I
b = −0.048600 − 0.750276I
5.48639 − 8.73923I 0
u = −0.687105 − 0.897262I
a = −0.355479 − 0.167421I
b = −0.048600 + 0.750276I
5.48639 + 8.73923I 0
u = −0.373591 + 1.075490I
a = −0.795520 + 0.588147I
b = 0.914345 + 0.454271I
−1.62900 − 0.89969I 0
u = −0.373591 − 1.075490I
a = −0.795520 − 0.588147I
b = 0.914345 − 0.454271I
−1.62900 + 0.89969I 0
u = 0.731325 + 0.421281I
a = −0.938294 − 0.092021I
b = −0.543242 − 0.716970I
5.06057 + 0.57857I 2.53258 − 2.78290I
u = 0.731325 − 0.421281I
a = −0.938294 + 0.092021I
b = −0.543242 + 0.716970I
5.06057 − 0.57857I 2.53258 + 2.78290I
u = 0.434112 + 1.098840I
a = 1.43799 + 1.59048I
b = −1.29963 + 0.70752I
−3.91899 + 0.31574I 0
u = 0.434112 − 1.098840I
a = 1.43799 − 1.59048I
b = −1.29963 − 0.70752I
−3.91899 − 0.31574I 0
u = −0.176032 + 0.776472I
a = 0.607805 − 0.218610I
b = −0.208597 + 0.304278I
−0.537446 − 1.039780I −7.39933 + 6.43993I
u = −0.176032 − 0.776472I
a = 0.607805 + 0.218610I
b = −0.208597 − 0.304278I
−0.537446 + 1.039780I −7.39933 − 6.43993I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.449003 + 1.119080I
a = 1.63202 − 1.42381I
b = −1.36040 − 0.78973I
−4.40703 − 6.33923I 0
u = −0.449003 − 1.119080I
a = 1.63202 + 1.42381I
b = −1.36040 + 0.78973I
−4.40703 + 6.33923I 0
u = −0.744106 + 0.270463I
a = −0.563605 + 0.288717I
b = −0.979045 + 0.832531I
2.95946 + 3.06631I −2.59881 − 2.85106I
u = −0.744106 − 0.270463I
a = −0.563605 − 0.288717I
b = −0.979045 − 0.832531I
2.95946 − 3.06631I −2.59881 + 2.85106I
u = 0.552939 + 1.084820I
a = 1.189260 + 0.464726I
b = −1.00752 + 1.13246I
3.08597 + 4.29718I 0
u = 0.552939 − 1.084820I
a = 1.189260 − 0.464726I
b = −1.00752 − 1.13246I
3.08597 − 4.29718I 0
u = 0.446332 + 1.136180I
a = −1.55976 − 0.67921I
b = 1.45534 − 0.61315I
−4.21610 + 3.94313I 0
u = 0.446332 − 1.136180I
a = −1.55976 + 0.67921I
b = 1.45534 + 0.61315I
−4.21610 − 3.94313I 0
u = −0.503355 + 1.117530I
a = −1.83906 + 0.22387I
b = 1.52918 + 1.02332I
−0.69715 − 6.51856I 0
u = −0.503355 − 1.117530I
a = −1.83906 − 0.22387I
b = 1.52918 − 1.02332I
−0.69715 + 6.51856I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351656 + 1.195310I
a = −1.06860 + 1.58590I
b = 1.336950 − 0.118755I
−7.69997 + 3.36567I 0
u = −0.351656 − 1.195310I
a = −1.06860 − 1.58590I
b = 1.336950 + 0.118755I
−7.69997 − 3.36567I 0
u = 0.433087 + 0.616507I
a = 0.476384 + 1.128510I
b = −0.703167 − 0.846414I
2.94099 + 1.46804I 3.65440 − 4.55346I
u = 0.433087 − 0.616507I
a = 0.476384 − 1.128510I
b = −0.703167 + 0.846414I
2.94099 − 1.46804I 3.65440 + 4.55346I
u = 0.373707 + 1.194340I
a = −1.25946 − 1.48885I
b = 1.44389 + 0.01555I
−8.31434 + 2.51326I 0
u = 0.373707 − 1.194340I
a = −1.25946 + 1.48885I
b = 1.44389 − 0.01555I
−8.31434 − 2.51326I 0
u = −0.539852 + 1.141380I
a = 1.74162 − 0.49765I
b = −1.28546 − 1.23224I
0.41354 − 7.91454I 0
u = −0.539852 − 1.141380I
a = 1.74162 + 0.49765I
b = −1.28546 + 1.23224I
0.41354 + 7.91454I 0
u = 0.507249 + 1.175680I
a = −2.24365 − 0.60143I
b = 1.93649 − 0.85036I
−7.37474 + 6.05052I 0
u = 0.507249 − 1.175680I
a = −2.24365 + 0.60143I
b = 1.93649 + 0.85036I
−7.37474 − 6.05052I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.522861 + 1.172680I
a = −2.33810 + 0.47146I
b = 1.97499 + 0.97360I
−6.49800 − 11.91050I 0
u = −0.522861 − 1.172680I
a = −2.33810 − 0.47146I
b = 1.97499 − 0.97360I
−6.49800 + 11.91050I 0
u = 0.580331 + 1.159360I
a = 1.83849 + 0.06678I
b = −1.25582 + 1.48375I
4.28334 + 10.67080I 0
u = 0.580331 − 1.159360I
a = 1.83849 − 0.06678I
b = −1.25582 − 1.48375I
4.28334 − 10.67080I 0
u = −0.558133 + 1.198470I
a = 2.28120 − 0.20717I
b = −1.53555 − 1.48069I
−2.62731 − 10.51430I 0
u = −0.558133 − 1.198470I
a = 2.28120 + 0.20717I
b = −1.53555 + 1.48069I
−2.62731 + 10.51430I 0
u = 0.570313 + 1.204160I
a = 2.31459 + 0.06840I
b = −1.53389 + 1.56815I
−1.6552 + 16.4308I 0
u = 0.570313 − 1.204160I
a = 2.31459 − 0.06840I
b = −1.53389 − 1.56815I
−1.6552 − 16.4308I 0
u = 0.480253 + 0.227205I
a = 0.67734 + 1.74876I
b = −1.329360 − 0.229592I
−1.14902 − 3.02718I −2.05661 + 1.63893I
u = 0.480253 − 0.227205I
a = 0.67734 − 1.74876I
b = −1.329360 + 0.229592I
−1.14902 + 3.02718I −2.05661 − 1.63893I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.516663 + 0.054132I
a = 0.10904 − 1.70032I
b = −1.347130 − 0.074477I
−1.56361 − 2.57718I −3.22294 + 3.55315I
u = −0.516663 − 0.054132I
a = 0.10904 + 1.70032I
b = −1.347130 + 0.074477I
−1.56361 + 2.57718I −3.22294 − 3.55315I
u = 0.086910 + 0.474832I
a = −3.26761 − 0.08964I
b = −0.892529 − 0.014603I
−1.51735 + 2.93358I −0.76792 − 3.27761I
u = 0.086910 − 0.474832I
a = −3.26761 + 0.08964I
b = −0.892529 + 0.014603I
−1.51735 − 2.93358I −0.76792 + 3.27761I
11
II. I
u
2
= h−u
4
− 2u
2
+ b, u
4
+ u
2
+ a − 1, u
27
+ 9u
25
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
11
=
u
12
+ 3u
10
+ 3u
8
− 2u
4
− u
2
+ 1
u
14
+ 4u
12
+ 7u
10
+ 6u
8
+ 2u
6
+ u
2
a
6
=
u
10
+ 3u
8
+ 2u
6
− u
4
− u
2
+ 1
−u
10
− 4u
8
− 5u
6
− 2u
4
+ u
2
a
9
=
−u
2
+ 1
u
2
a
5
=
−u
u
a
12
=
u
21
+ 6u
19
+ 15u
17
+ 18u
15
+ 6u
13
− 10u
11
− 11u
9
+ 5u
5
+ 2u
3
− u
u
23
+ 7u
21
+ 22u
19
+ 39u
17
+ 40u
15
+ 20u
13
− 3u
9
+ u
7
+ u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
21
− 28u
19
− 84u
17
− 132u
15
− 100u
13
+ 4u
12
− 4u
11
+
16u
10
+ 44u
9
+ 24u
8
+ 12u
7
+ 12u
6
− 16u
5
− 4u
4
− 12u
3
− 4u
2
− 4u − 2
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
27
+ 18u
26
+ ··· + u − 1
c
2
, c
4
, c
7
c
8
, c
9
u
27
+ 9u
25
+ ··· − u + 1
c
3
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
c
5
, c
11
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
3
c
6
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
3
c
10
, c
12
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
27
− 18y
26
+ ··· + 9y −1
c
2
, c
4
, c
7
c
8
, c
9
y
27
+ 18y
26
+ ··· + y −1
c
3
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
3
c
5
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
3
c
6
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
3
c
10
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.415679 + 1.005350I
a = 1.83437 + 0.56491I
b = −1.67231 + 0.27089I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = 0.415679 − 1.005350I
a = 1.83437 − 0.56491I
b = −1.67231 − 0.27089I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = −0.302378 + 1.128850I
a = 1.24974 − 0.93235I
b = −1.43261 + 0.24968I
−1.19845 −8.65235 + 0.I
u = −0.302378 − 1.128850I
a = 1.24974 + 0.93235I
b = −1.43261 − 0.24968I
−1.19845 −8.65235 + 0.I
u = 0.426564 + 0.710315I
a = 1.58575 − 0.21502I
b = −0.908339 + 0.821007I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.426564 − 0.710315I
a = 1.58575 + 0.21502I
b = −0.908339 − 0.821007I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = −0.777660 + 0.179870I
a = 0.178219 + 0.600021I
b = 1.39418 − 0.87978I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.777660 − 0.179870I
a = 0.178219 − 0.600021I
b = 1.39418 + 0.87978I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.476346 + 1.108800I
a = 2.11333 + 1.06168I
b = −2.11585 − 0.00534I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = 0.476346 − 1.108800I
a = 2.11333 − 1.06168I
b = −2.11585 + 0.00534I
−3.59813 − 7.08493I −5.57680 + 5.91335I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.452506 + 1.125320I
a = 1.97182 − 1.14384I
b = −2.03340 + 0.12541I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = −0.452506 − 1.125320I
a = 1.97182 + 1.14384I
b = −2.03340 − 0.12541I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = 0.767882 + 0.142454I
a = 0.154353 − 0.467897I
b = 1.41500 + 0.68667I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = 0.767882 − 0.142454I
a = 0.154353 + 0.467897I
b = 1.41500 − 0.68667I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = 0.037522 + 1.261230I
a = 0.072421 + 0.206198I
b = −0.661704 − 0.111549I
−0.61694 + 2.45442I −2.32792 − 2.91298I
u = 0.037522 − 1.261230I
a = 0.072421 − 0.206198I
b = −0.661704 + 0.111549I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = 0.214742 + 1.244380I
a = 0.530910 + 1.071400I
b = −1.033270 − 0.536957I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.214742 − 1.244380I
a = 0.530910 − 1.071400I
b = −1.033270 + 0.536957I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = −0.464087 + 0.550911I
a = 1.341830 + 0.421215I
b = −0.429958 − 0.932556I
−0.61694 − 2.45442I −2.32792 + 2.91298I
u = −0.464087 − 0.550911I
a = 1.341830 − 0.421215I
b = −0.429958 + 0.932556I
−0.61694 + 2.45442I −2.32792 − 2.91298I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.315376 + 1.267770I
a = 0.87382 − 1.61174I
b = −1.38160 + 0.81209I
−4.37135 + 1.33617I −7.28409 − 0.70175I
u = −0.315376 − 1.267770I
a = 0.87382 + 1.61174I
b = −1.38160 − 0.81209I
−4.37135 − 1.33617I −7.28409 + 0.70175I
u = 0.301314 + 1.288670I
a = 0.70845 + 1.66170I
b = −1.27833 − 0.88511I
−3.59813 − 7.08493I −5.57680 + 5.91335I
u = 0.301314 − 1.288670I
a = 0.70845 − 1.66170I
b = −1.27833 + 0.88511I
−3.59813 + 7.08493I −5.57680 − 5.91335I
u = −0.630422 + 0.239022I
a = 0.634720 + 0.506481I
b = 0.705580 − 0.807851I
1.78344 + 2.09337I 0.51499 − 4.16283I
u = −0.630422 − 0.239022I
a = 0.634720 − 0.506481I
b = 0.705580 + 0.807851I
1.78344 − 2.09337I 0.51499 + 4.16283I
u = 0.604756
a = 0.500513
b = 0.865217
−1.19845 −8.65230
17
III. I
u
3
= hb + 1, a
3
− a
2
u − 3a
2
+ 2au + a + 1, u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
−1
a
3
=
u
0
a
4
=
u
0
a
1
=
−u
u
a
10
=
a
−1
a
11
=
1
a − 2
a
6
=
−a
2
+ a + 1
a − 2
a
9
=
a + 1
−1
a
5
=
−au
u
a
12
=
−au
−a
2
u + 3au − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
+ 4au + 8a − 4u − 4
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
, c
7
c
8
, c
9
(u
2
+ 1)
3
c
3
u
6
c
5
, c
11
u
6
+ u
4
+ 2u
2
+ 1
c
6
u
6
− 3u
4
+ 2u
2
+ 1
c
10
(u
3
+ u
2
+ 2u + 1)
2
c
12
(u
3
− u
2
+ 2u − 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y −1)
6
c
2
, c
4
, c
7
c
8
, c
9
(y + 1)
6
c
3
y
6
c
5
, c
11
(y
3
+ y
2
+ 2y + 1)
2
c
6
(y
3
− 3y
2
+ 2y + 1)
2
c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.000000 + 0.569840I
b = −1.00000
1.11345 −6 − 0.980489 + 0.10I
u = 1.000000I
a = −0.307141 + 0.215080I
b = −1.00000
−3.02413 + 2.82812I −7.50976 − 2.97945I
u = 1.000000I
a = 2.30714 + 0.21508I
b = −1.00000
−3.02413 − 2.82812I −7.50976 + 2.97945I
u = − 1.000000I
a = 1.000000 − 0.569840I
b = −1.00000
1.11345 −6 − 0.980489 + 0.10I
u = − 1.000000I
a = −0.307141 − 0.215080I
b = −1.00000
−3.02413 − 2.82812I −7.50976 + 2.97945I
u = − 1.000000I
a = 2.30714 − 0.21508I
b = −1.00000
−3.02413 + 2.82812I −7.50976 − 2.97945I
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
27
+ 18u
26
+ ··· + u − 1)(u
64
+ 31u
63
+ ··· + 8u + 1)
c
2
, c
7
((u
2
+ 1)
3
)(u
27
+ 9u
25
+ ··· − u + 1)(u
64
+ u
63
+ ··· + 2u + 1)
c
3
u
6
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
3
· (u
64
+ 2u
63
+ ··· + 1984u + 128)
c
4
, c
8
, c
9
((u
2
+ 1)
3
)(u
27
+ 9u
25
+ ··· − u + 1)(u
64
+ u
63
+ ··· + 16u + 1)
c
5
, c
11
(u
6
+ u
4
+ 2u
2
+ 1)(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
3
· (u
64
+ 2u
63
+ ··· + u + 2)
c
6
(u
6
− 3u
4
+ 2u
2
+ 1)
· (u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
3
· (u
64
− 10u
63
+ ··· − 14873u + 1862)
c
10
(u
3
+ u
2
+ 2u + 1)
2
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
3
· (u
64
− 20u
63
+ ··· − 19u + 4)
c
12
(u
3
− u
2
+ 2u − 1)
2
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
3
· (u
64
− 20u
63
+ ··· − 19u + 4)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
27
− 18y
26
+ ··· + 9y −1)(y
64
+ 11y
63
+ ··· − 40y + 1)
c
2
, c
7
((y + 1)
6
)(y
27
+ 18y
26
+ ··· + y −1)(y
64
+ 31y
63
+ ··· + 8y + 1)
c
3
y
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
3
· (y
64
− 30y
63
+ ··· + 1945600y + 16384)
c
4
, c
8
, c
9
((y + 1)
6
)(y
27
+ 18y
26
+ ··· + y −1)(y
64
+ 59y
63
+ ··· + 104y + 1)
c
5
, c
11
(y
3
+ y
2
+ 2y + 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
3
· (y
64
+ 20y
63
+ ··· + 19y + 4)
c
6
(y
3
− 3y
2
+ 2y + 1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
3
· (y
64
− 12y
63
+ ··· − 37020813y + 3467044)
c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
3
· (y
64
+ 48y
63
+ ··· + 879y + 16)
23
