12a
0686
(K12a
0686
)
A knot diagram
1
Linearized knot diagam
3 7 11 1 10 8 2 5 12 6 4 9
Solving Sequence
9,12
10
1,4
5 6 8 11 3 2 7
c
9
c
12
c
4
c
5
c
8
c
11
c
3
c
1
c
7
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3587u
44
− 59411u
43
+ ··· + 256b − 2894080, −1823u
44
− 49813u
43
+ ··· + 512a + 5447424,
u
45
+ 21u
44
+ ··· − 9728u − 512i
I
u
2
= h−7.59604 × 10
31
a
17
u
4
− 1.14352 × 10
32
a
16
u
4
+ ··· + 1.79108 × 10
32
a − 3.77085 × 10
32
,
− 6a
16
u
4
+ a
15
u
4
+ ··· − 180a + 371, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
I
u
3
= h−27u
30
+ 186u
29
+ ··· + b + 53, −29u
30
+ 147u
29
+ ··· + a − 64, u
31
− 6u
30
+ ··· + 5u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 166 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−3587u
44
− 59411u
43
+ · · · + 256b − 2894080, −1823u
44
−
49813u
43
+ · · · + 512a + 5447424, u
45
+ 21u
44
+ · · · − 9728u − 512i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
u
a
4
=
3.56055u
44
+ 97.2910u
43
+ ··· − 191511.u − 10639.5
14.0117u
44
+ 232.074u
43
+ ··· + 205133.u + 11305
a
5
=
−22.0801u
44
− 477.693u
43
+ ··· + 185231.u + 9662.50
39.6523u
44
+ 807.059u
43
+ ··· − 171609.u − 8997
a
6
=
0.439453u
44
− 28.7363u
43
+ ··· + 209228u + 11485.5
15.2461u
44
+ 383.090u
43
+ ··· − 393095.u − 21261
a
8
=
−
529
512
u
44
−
10591
512
u
43
+ ··· +
1243
2
u + 7
135
256
u
44
+
2441
256
u
43
+ ··· + 4656u + 259
a
11
=
253
512
u
44
+
5043
512
u
43
+ ··· −
8899
2
u − 247
3
256
u
44
+
77
256
u
43
+ ··· − 317u − 17
a
3
=
44.9453u
44
+ 910.176u
43
+ ··· − 198900.u − 10595.5
−56.2461u
44
− 1117.62u
43
+ ··· + 82288.5u + 3722
a
2
=
−4.48047u
44
− 89.4336u
43
+ ··· + 34007u + 1918
129
32
u
44
+
10127
128
u
43
+ ··· − 4053u − 180
a
7
=
−50.0195u
44
− 1013.30u
43
+ ··· + 228759.u + 12212
60.0117u
44
+ 1189.50u
43
+ ··· − 71845u − 3052
(ii) Obstruction class = −1
(iii) Cusp Shapes =
679
64
u
44
+
17161
64
u
43
+ ··· − 240458u − 12510
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
45
+ 15u
44
+ ··· − 1536u − 1024
c
2
, c
7
u
45
+ 11u
44
+ ··· + 128u + 32
c
3
, c
5
, c
10
c
11
u
45
+ u
44
+ ··· + 4u + 1
c
4
, c
8
u
45
− u
44
+ ··· − 5u + 1
c
9
, c
12
u
45
− 21u
44
+ ··· − 9728u + 512
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
45
+ 31y
44
+ ··· + 9830400y −1048576
c
2
, c
7
y
45
+ 15y
44
+ ··· − 1536y −1024
c
3
, c
5
, c
10
c
11
y
45
− 25y
44
+ ··· + 8y −1
c
4
, c
8
y
45
+ 29y
44
+ ··· + 71y −1
c
9
, c
12
y
45
+ 17y
44
+ ··· − 3407872y −262144
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.208020 + 1.017770I
a = 0.518836 − 0.448183I
b = −1.46031 − 0.10701I
1.31767 + 2.83862I 0
u = −0.208020 − 1.017770I
a = 0.518836 + 0.448183I
b = −1.46031 + 0.10701I
1.31767 − 2.83862I 0
u = 0.946189
a = 0.633784
b = −0.410735
−1.39480 0
u = −1.063240 + 0.314250I
a = −0.886556 − 0.815280I
b = 0.350469 − 0.222476I
−0.95255 − 6.81200I 0
u = −1.063240 − 0.314250I
a = −0.886556 + 0.815280I
b = 0.350469 + 0.222476I
−0.95255 + 6.81200I 0
u = −1.079690 + 0.283438I
a = 0.962572 + 0.810776I
b = −0.335797 + 0.200198I
−2.25231 − 12.86870I 0
u = −1.079690 − 0.283438I
a = 0.962572 − 0.810776I
b = −0.335797 − 0.200198I
−2.25231 + 12.86870I 0
u = −0.143066 + 1.150190I
a = −0.542252 + 0.522617I
b = 1.310810 − 0.279245I
3.41317 − 0.45131I 0
u = −0.143066 − 1.150190I
a = −0.542252 − 0.522617I
b = 1.310810 + 0.279245I
3.41317 + 0.45131I 0
u = −0.336154 + 1.112550I
a = 0.676007 − 0.377814I
b = −1.97704 + 0.16844I
8.08821 + 6.31292I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.336154 − 1.112550I
a = 0.676007 + 0.377814I
b = −1.97704 − 0.16844I
8.08821 − 6.31292I 0
u = −0.317978 + 1.137660I
a = −0.686649 + 0.428740I
b = 1.90789 − 0.27801I
8.41961 + 0.29227I 0
u = −0.317978 − 1.137660I
a = −0.686649 − 0.428740I
b = 1.90789 + 0.27801I
8.41961 − 0.29227I 0
u = −1.094150 + 0.527804I
a = −0.656726 − 0.627002I
b = 0.518635 − 0.238568I
−3.21307 − 2.60752I 0
u = −1.094150 − 0.527804I
a = −0.656726 + 0.627002I
b = 0.518635 + 0.238568I
−3.21307 + 2.60752I 0
u = −0.766388 + 0.963185I
a = −0.482755 − 0.428981I
b = 1.47163 − 0.30603I
5.84298 − 0.38109I 0
u = −0.766388 − 0.963185I
a = −0.482755 + 0.428981I
b = 1.47163 + 0.30603I
5.84298 + 0.38109I 0
u = −1.174520 + 0.378645I
a = 0.843485 + 0.605476I
b = −0.421155 + 0.168073I
−8.33701 − 5.85390I 0
u = −1.174520 − 0.378645I
a = 0.843485 − 0.605476I
b = −0.421155 − 0.168073I
−8.33701 + 5.85390I 0
u = −0.736297 + 1.018030I
a = 0.528992 + 0.406341I
b = −1.64434 + 0.15871I
6.06401 + 6.26641I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.736297 − 1.018030I
a = 0.528992 − 0.406341I
b = −1.64434 − 0.15871I
6.06401 − 6.26641I 0
u = 0.133405 + 1.254510I
a = 0.447547 − 0.505637I
b = −0.814640 + 0.321639I
−0.52886 − 2.12424I 0
u = 0.133405 − 1.254510I
a = 0.447547 + 0.505637I
b = −0.814640 − 0.321639I
−0.52886 + 2.12424I 0
u = −0.138187 + 1.365490I
a = −0.470658 + 0.644285I
b = 1.036310 − 0.731066I
5.34883 − 2.70325I 0
u = −0.138187 − 1.365490I
a = −0.470658 − 0.644285I
b = 1.036310 + 0.731066I
5.34883 + 2.70325I 0
u = −1.206150 + 0.670708I
a = 0.608172 + 0.509443I
b = −0.606059 + 0.130819I
−6.10066 + 2.59329I 0
u = −1.206150 − 0.670708I
a = 0.608172 − 0.509443I
b = −0.606059 − 0.130819I
−6.10066 − 2.59329I 0
u = −0.635659 + 1.245840I
a = 0.886702 + 0.620717I
b = −2.12868 − 0.87707I
1.98718 + 12.88950I 0
u = −0.635659 − 1.245840I
a = 0.886702 − 0.620717I
b = −2.12868 + 0.87707I
1.98718 − 12.88950I 0
u = −0.694335 + 1.218240I
a = 0.726779 + 0.567265I
b = −1.81930 − 0.63902I
−0.87266 + 9.07868I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.694335 − 1.218240I
a = 0.726779 − 0.567265I
b = −1.81930 + 0.63902I
−0.87266 − 9.07868I 0
u = −0.631447 + 1.256290I
a = −0.904289 − 0.657496I
b = 2.14391 + 0.96340I
0.8069 + 18.9599I 0
u = −0.631447 − 1.256290I
a = −0.904289 + 0.657496I
b = 2.14391 − 0.96340I
0.8069 − 18.9599I 0
u = −0.587391 + 0.037334I
a = −0.021046 − 1.328720I
b = 0.008378 − 0.428391I
5.05448 − 2.94618I −3.07738 + 3.17176I
u = −0.587391 − 0.037334I
a = −0.021046 + 1.328720I
b = 0.008378 + 0.428391I
5.05448 + 2.94618I −3.07738 − 3.17176I
u = −0.67285 + 1.26135I
a = −0.773811 − 0.664467I
b = 1.85557 + 0.90212I
−5.45040 + 12.36210I 0
u = −0.67285 − 1.26135I
a = −0.773811 + 0.664467I
b = 1.85557 − 0.90212I
−5.45040 − 12.36210I 0
u = −0.13532 + 1.43665I
a = 0.416738 − 0.663296I
b = −0.893009 + 0.802371I
4.09263 − 8.37531I 0
u = −0.13532 − 1.43665I
a = 0.416738 + 0.663296I
b = −0.893009 − 0.802371I
4.09263 + 8.37531I 0
u = −0.75657 + 1.23255I
a = −0.628948 − 0.591286I
b = 1.54134 + 0.61150I
−4.00755 + 4.49447I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.75657 − 1.23255I
a = −0.628948 + 0.591286I
b = 1.54134 − 0.61150I
−4.00755 − 4.49447I 0
u = 1.40518 + 0.43144I
a = −0.469825 + 0.097281I
b = 0.380597 − 0.039104I
−4.48294 − 3.96522I 0
u = 1.40518 − 0.43144I
a = −0.469825 − 0.097281I
b = 0.380597 + 0.039104I
−4.48294 + 3.96522I 0
u = −0.134253 + 0.255202I
a = 0.590793 − 1.189790I
b = −0.219829 − 0.348173I
−0.380823 − 0.987902I −6.30490 + 6.80539I
u = −0.134253 − 0.255202I
a = 0.590793 + 1.189790I
b = −0.219829 + 0.348173I
−0.380823 + 0.987902I −6.30490 − 6.80539I
9
II. I
u
2
= h−7.60 × 10
31
a
17
u
4
− 1.14 × 10
32
a
16
u
4
+ · · · + 1.79 × 10
32
a − 3.77 ×
10
32
, −6a
16
u
4
+ a
15
u
4
+ · · · − 180a + 371, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
u
a
4
=
a
4.12624a
17
u
4
+ 6.21168a
16
u
4
+ ··· − 9.72933a + 20.4836
a
5
=
−4.60935a
17
u
4
+ 9.84481a
16
u
4
+ ··· + 7.58983a − 12.3949
8.73559a
17
u
4
− 3.63312a
16
u
4
+ ··· − 16.3192a + 32.8786
a
6
=
9.19157a
17
u
4
+ 6.07892a
16
u
4
+ ··· + 9.27627a − 17.7652
−16.3897a
17
u
4
− 9.68706a
16
u
4
+ ··· − 11.3448a + 24.8604
a
8
=
−0.209327a
17
u
4
+ 8.30382a
16
u
4
+ ··· − 20.5251a − 19.9539
7.76784a
17
u
4
− 5.15782a
16
u
4
+ ··· + 15.0521a + 8.28362
a
11
=
a
2
u
4.36914a
17
u
4
+ 4.09814a
16
u
4
+ ··· − 37.3258a − 16.4733
a
3
=
−a
3
u
2
+ a
0.797957a
17
u
4
+ 3.82143a
16
u
4
+ ··· + 6.45135a − 9.14231
a
2
=
2.43152a
17
u
4
− 3.23675a
16
u
4
+ ··· − 6.46817a + 9.45064
5.23364a
17
u
4
+ 2.07480a
16
u
4
+ ··· − 22.9202a − 23.9576
a
7
=
8.03403a
17
u
4
+ 6.34108a
16
u
4
+ ··· + 13.2142a − 53.5432
−11.0746a
17
u
4
− 5.17783a
16
u
4
+ ··· − 7.91911a + 18.8410
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.46989a
17
u
4
+ 15.4911a
16
u
4
+ ··· − 9.45003a − 119.435
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
10
c
2
, c
7
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
10
c
3
, c
5
, c
10
c
11
u
90
+ u
89
+ ··· + 651136u + 56443
c
4
, c
8
u
90
− 5u
89
+ ··· + 14948u − 2189
c
9
, c
12
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
18
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
10
c
2
, c
7
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
10
c
3
, c
5
, c
10
c
11
y
90
− 65y
89
+ ··· − 225222871104y + 3185812249
c
4
, c
8
y
90
− 13y
89
+ ··· − 374991552y + 4791721
c
9
, c
12
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
18
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = −0.159381 − 0.938115I
b = 2.20160 + 1.42249I
−1.00758 − 5.55435I −9.90808 + 1.48270I
u = −0.339110 + 0.822375I
a = 0.241894 + 0.832836I
b = −2.08136 − 1.40087I
−0.234353 + 0.194409I −8.20079 − 3.72890I
u = −0.339110 + 0.822375I
a = −0.433799 − 1.204420I
b = 2.20036 + 1.00411I
−6.38914 − 0.56279I −15.9999 − 0.2678I
u = −0.339110 + 0.822375I
a = 0.826294 + 0.994064I
b = −1.83643 − 1.14645I
−3.40726 + 1.53058I −6.83254 − 4.43065I
u = −0.339110 + 0.822375I
a = −0.675713 − 1.117790I
b = 0.491959 − 1.241640I
−0.23435 + 2.86675I −8.20079 − 5.13240I
u = −0.339110 + 0.822375I
a = 0.763638 + 1.143180I
b = −0.68839 + 1.36569I
−1.00758 + 8.61551I −9.9081 − 10.3440I
u = −0.339110 + 0.822375I
a = −0.46396 − 1.45473I
b = 0.400574 − 0.166106I
−3.40726 + 1.53058I −6.83254 − 4.43065I
u = −0.339110 + 0.822375I
a = 1.40909 + 0.63481I
b = −1.91051 − 1.30463I
−0.23435 + 2.86675I −8.20079 − 5.13240I
u = −0.339110 + 0.822375I
a = 0.71153 + 1.38042I
b = −1.142030 + 0.739435I
−6.38914 + 3.62395I −15.9999 − 8.5935I
u = −0.339110 + 0.822375I
a = −0.59104 − 1.51012I
b = 2.18086 + 0.22940I
−3.98876 + 3.98500I −13.1570 − 7.3436I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.05470 − 1.65936I
b = −0.581698 + 0.216015I
−0.234353 + 0.194409I −8.20079 − 3.72890I
u = −0.339110 + 0.822375I
a = 0.66566 + 1.53082I
b = −1.99721 + 0.11079I
−3.98876 − 0.92384I −13.15696 − 1.51767I
u = −0.339110 + 0.822375I
a = −1.55709 − 0.70875I
b = 1.93149 + 1.36749I
−1.00758 + 8.61551I −9.9081 − 10.3440I
u = −0.339110 + 0.822375I
a = −1.33525 − 1.17321I
b = 1.67468 + 1.37611I
−6.38914 + 3.62395I −15.9999 − 8.5935I
u = −0.339110 + 0.822375I
a = −0.07589 + 1.81158I
b = 0.631901 − 0.429114I
−1.00758 − 5.55435I −9.90808 + 1.48270I
u = −0.339110 + 0.822375I
a = 0.37937 + 1.85940I
b = −0.045624 − 0.663020I
−6.38914 − 0.56279I −15.9999 − 0.2678I
u = −0.339110 + 0.822375I
a = −1.14028 − 1.77640I
b = 1.06771 + 1.39994I
−3.98876 − 0.92384I −13.15696 − 1.51767I
u = −0.339110 + 0.822375I
a = 0.94152 + 1.91352I
b = −0.75943 − 1.29044I
−3.98876 + 3.98500I −13.1570 − 7.3436I
u = −0.339110 − 0.822375I
a = −0.159381 + 0.938115I
b = 2.20160 − 1.42249I
−1.00758 + 5.55435I −9.90808 − 1.48270I
u = −0.339110 − 0.822375I
a = 0.241894 − 0.832836I
b = −2.08136 + 1.40087I
−0.234353 − 0.194409I −8.20079 + 3.72890I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 − 0.822375I
a = −0.433799 + 1.204420I
b = 2.20036 − 1.00411I
−6.38914 + 0.56279I −15.9999 + 0.2678I
u = −0.339110 − 0.822375I
a = 0.826294 − 0.994064I
b = −1.83643 + 1.14645I
−3.40726 − 1.53058I −6.83254 + 4.43065I
u = −0.339110 − 0.822375I
a = −0.675713 + 1.117790I
b = 0.491959 + 1.241640I
−0.23435 − 2.86675I −8.20079 + 5.13240I
u = −0.339110 − 0.822375I
a = 0.763638 − 1.143180I
b = −0.68839 − 1.36569I
−1.00758 − 8.61551I −9.9081 + 10.3440I
u = −0.339110 − 0.822375I
a = −0.46396 + 1.45473I
b = 0.400574 + 0.166106I
−3.40726 − 1.53058I −6.83254 + 4.43065I
u = −0.339110 − 0.822375I
a = 1.40909 − 0.63481I
b = −1.91051 + 1.30463I
−0.23435 − 2.86675I −8.20079 + 5.13240I
u = −0.339110 − 0.822375I
a = 0.71153 − 1.38042I
b = −1.142030 − 0.739435I
−6.38914 − 3.62395I −15.9999 + 8.5935I
u = −0.339110 − 0.822375I
a = −0.59104 + 1.51012I
b = 2.18086 − 0.22940I
−3.98876 − 3.98500I −13.1570 + 7.3436I
u = −0.339110 − 0.822375I
a = 0.05470 + 1.65936I
b = −0.581698 − 0.216015I
−0.234353 − 0.194409I −8.20079 + 3.72890I
u = −0.339110 − 0.822375I
a = 0.66566 − 1.53082I
b = −1.99721 − 0.11079I
−3.98876 + 0.92384I −13.15696 + 1.51767I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 − 0.822375I
a = −1.55709 + 0.70875I
b = 1.93149 − 1.36749I
−1.00758 − 8.61551I −9.9081 + 10.3440I
u = −0.339110 − 0.822375I
a = −1.33525 + 1.17321I
b = 1.67468 − 1.37611I
−6.38914 − 3.62395I −15.9999 + 8.5935I
u = −0.339110 − 0.822375I
a = −0.07589 − 1.81158I
b = 0.631901 + 0.429114I
−1.00758 + 5.55435I −9.90808 − 1.48270I
u = −0.339110 − 0.822375I
a = 0.37937 − 1.85940I
b = −0.045624 + 0.663020I
−6.38914 + 0.56279I −15.9999 + 0.2678I
u = −0.339110 − 0.822375I
a = −1.14028 + 1.77640I
b = 1.06771 − 1.39994I
−3.98876 + 0.92384I −13.15696 + 1.51767I
u = −0.339110 − 0.822375I
a = 0.94152 − 1.91352I
b = −0.75943 + 1.29044I
−3.98876 − 3.98500I −13.1570 + 7.3436I
u = 0.766826
a = 1.04231
b = −0.293152
−1.33528 −5.86650
u = 0.766826
a = 0.255139 + 0.891085I
b = 0.542272 − 0.127354I
−4.31716 − 2.09337I −15.0338 + 4.1628I
u = 0.766826
a = 0.255139 − 0.891085I
b = 0.542272 + 0.127354I
−4.31716 + 2.09337I −15.0338 − 4.1628I
u = 0.766826
a = 0.365127 + 1.178490I
b = −0.659727 + 0.010033I
1.83763 + 1.33617I −7.23476 − 0.70175I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.766826
a = 0.365127 − 1.178490I
b = −0.659727 − 0.010033I
1.83763 − 1.33617I −7.23476 + 0.70175I
u = 0.766826
a = 1.092700 + 0.680242I
b = 0.327016 − 0.317666I
−1.91678 + 2.45442I −12.19093 − 2.91298I
u = 0.766826
a = 1.092700 − 0.680242I
b = 0.327016 + 0.317666I
−1.91678 − 2.45442I −12.19093 + 2.91298I
u = 0.766826
a = −0.233462 + 1.297460I
b = 0.687490 − 0.032594I
1.06441 − 7.08493I −8.94206 + 5.91335I
u = 0.766826
a = −0.233462 − 1.297460I
b = 0.687490 + 0.032594I
1.06441 + 7.08493I −8.94206 − 5.91335I
u = 0.766826
a = −1.317380 + 0.494367I
b = −0.197748 − 0.358138I
−1.91678 + 2.45442I −12.19093 − 2.91298I
u = 0.766826
a = −1.317380 − 0.494367I
b = −0.197748 + 0.358138I
−1.91678 − 2.45442I −12.19093 + 2.91298I
u = 0.766826
a = −1.48255 + 0.08064I
b = 0.163914 + 0.338933I
−4.31716 + 2.09337I −15.0338 − 4.1628I
u = 0.766826
a = −1.48255 − 0.08064I
b = 0.163914 − 0.338933I
−4.31716 − 2.09337I −15.0338 + 4.1628I
u = 0.766826
a = 1.49907 + 0.55670I
b = −0.412827 + 0.367780I
1.83763 − 1.33617I −7.23476 + 0.70175I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.766826
a = 1.49907 − 0.55670I
b = −0.412827 − 0.367780I
1.83763 + 1.33617I −7.23476 − 0.70175I
u = 0.766826
a = −1.62845 + 0.50284I
b = 0.383751 + 0.424585I
1.06441 + 7.08493I −8.94206 − 5.91335I
u = 0.766826
a = −1.62845 − 0.50284I
b = 0.383751 − 0.424585I
1.06441 − 7.08493I −8.94206 + 5.91335I
u = 0.766826
a = 0.269285
b = −0.461468
−1.33528 −5.86650
u = 0.455697 + 1.200150I
a = 0.922977 − 0.396067I
b = −1.52506 + 0.89890I
1.55470 − 6.85525I −8.92776 + 6.41156I
u = 0.455697 + 1.200150I
a = −0.988853 + 0.233381I
b = 1.66740 − 0.76733I
1.55470 − 1.94642I −8.92776 + 0.58561I
u = 0.455697 + 1.200150I
a = −0.936941 − 0.257189I
b = 1.73242 − 0.16433I
−0.84567 − 6.49421I −11.77068 + 7.66142I
u = 0.455697 + 1.200150I
a = −0.758221 + 0.755620I
b = 2.22928 − 1.03996I
5.30911 − 5.73700I −3.97159 + 4.20034I
u = 0.455697 + 1.200150I
a = −0.829482 + 0.392070I
b = 1.79638 − 0.03051I
5.30911 − 3.06466I −3.97159 + 2.79684I
u = 0.455697 + 1.200150I
a = 0.733482 − 0.805208I
b = −2.25349 + 1.17599I
4.53589 − 11.48580I −5.67888 + 9.41193I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455697 + 1.200150I
a = 0.558576 − 0.707002I
b = −1.78632 + 1.25144I
−0.84567 − 6.49421I −11.77068 + 7.66142I
u = 0.455697 + 1.200150I
a = 0.913333 + 0.619535I
b = −1.78402 − 0.34445I
5.30911 − 5.73700I −3.97159 + 4.20034I
u = 0.455697 + 1.200150I
a = 0.818787 − 0.325128I
b = −1.68972 − 0.15275I
4.53589 + 2.68409I −5.67888 − 2.41476I
u = 0.455697 + 1.200150I
a = −0.694071 + 0.542414I
b = 1.71362 − 0.74170I
2.13621 − 4.40083I −2.60334 + 3.49859I
u = 0.455697 + 1.200150I
a = 0.001379 − 0.840895I
b = 0.400446 + 0.915636I
4.53589 + 2.68409I −5.67888 − 2.41476I
u = 0.455697 + 1.200150I
a = −1.007970 − 0.593699I
b = 1.91234 + 0.28273I
4.53589 − 11.48580I −5.67888 + 9.41193I
u = 0.455697 + 1.200150I
a = 0.665928 − 0.482568I
b = −1.202420 + 0.542179I
−0.84567 − 2.30746I −11.77068 − 0.66425I
u = 0.455697 + 1.200150I
a = 0.128019 + 0.800850I
b = −0.609202 − 0.809409I
5.30911 − 3.06466I −3.97159 + 2.79684I
u = 0.455697 + 1.200150I
a = 0.501872 + 0.361001I
b = −1.139350 − 0.040792I
2.13621 − 4.40083I −2.60334 + 3.49859I
u = 0.455697 + 1.200150I
a = 0.212720 − 0.560263I
b = −1.06501 + 1.41566I
1.55470 − 1.94642I −8.92776 + 0.58561I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455697 + 1.200150I
a = −0.080995 + 0.413435I
b = 0.72592 − 1.27915I
1.55470 − 6.85525I −8.92776 + 6.41156I
u = 0.455697 + 1.200150I
a = 0.072163 − 0.244100I
b = 0.181505 − 0.164757I
−0.84567 − 2.30746I −11.77068 − 0.66425I
u = 0.455697 − 1.200150I
a = 0.922977 + 0.396067I
b = −1.52506 − 0.89890I
1.55470 + 6.85525I −8.92776 − 6.41156I
u = 0.455697 − 1.200150I
a = −0.988853 − 0.233381I
b = 1.66740 + 0.76733I
1.55470 + 1.94642I −8.92776 − 0.58561I
u = 0.455697 − 1.200150I
a = −0.936941 + 0.257189I
b = 1.73242 + 0.16433I
−0.84567 + 6.49421I −11.77068 − 7.66142I
u = 0.455697 − 1.200150I
a = −0.758221 − 0.755620I
b = 2.22928 + 1.03996I
5.30911 + 5.73700I −3.97159 − 4.20034I
u = 0.455697 − 1.200150I
a = −0.829482 − 0.392070I
b = 1.79638 + 0.03051I
5.30911 + 3.06466I −3.97159 − 2.79684I
u = 0.455697 − 1.200150I
a = 0.733482 + 0.805208I
b = −2.25349 − 1.17599I
4.53589 + 11.48580I −5.67888 − 9.41193I
u = 0.455697 − 1.200150I
a = 0.558576 + 0.707002I
b = −1.78632 − 1.25144I
−0.84567 + 6.49421I −11.77068 − 7.66142I
u = 0.455697 − 1.200150I
a = 0.913333 − 0.619535I
b = −1.78402 + 0.34445I
5.30911 + 5.73700I −3.97159 − 4.20034I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455697 − 1.200150I
a = 0.818787 + 0.325128I
b = −1.68972 + 0.15275I
4.53589 − 2.68409I −5.67888 + 2.41476I
u = 0.455697 − 1.200150I
a = −0.694071 − 0.542414I
b = 1.71362 + 0.74170I
2.13621 + 4.40083I −2.60334 − 3.49859I
u = 0.455697 − 1.200150I
a = 0.001379 + 0.840895I
b = 0.400446 − 0.915636I
4.53589 − 2.68409I −5.67888 + 2.41476I
u = 0.455697 − 1.200150I
a = −1.007970 + 0.593699I
b = 1.91234 − 0.28273I
4.53589 + 11.48580I −5.67888 − 9.41193I
u = 0.455697 − 1.200150I
a = 0.665928 + 0.482568I
b = −1.202420 − 0.542179I
−0.84567 + 2.30746I −11.77068 + 0.66425I
u = 0.455697 − 1.200150I
a = 0.128019 − 0.800850I
b = −0.609202 + 0.809409I
5.30911 + 3.06466I −3.97159 − 2.79684I
u = 0.455697 − 1.200150I
a = 0.501872 − 0.361001I
b = −1.139350 + 0.040792I
2.13621 + 4.40083I −2.60334 − 3.49859I
u = 0.455697 − 1.200150I
a = 0.212720 + 0.560263I
b = −1.06501 − 1.41566I
1.55470 + 1.94642I −8.92776 − 0.58561I
u = 0.455697 − 1.200150I
a = −0.080995 − 0.413435I
b = 0.72592 + 1.27915I
1.55470 + 6.85525I −8.92776 − 6.41156I
u = 0.455697 − 1.200150I
a = 0.072163 + 0.244100I
b = 0.181505 + 0.164757I
−0.84567 + 2.30746I −11.77068 + 0.66425I
21
III. I
u
3
= h−27u
30
+ 186u
29
+ · · · + b + 53, −29u
30
+ 147u
29
+ · · · + a −
64, u
31
− 6u
30
+ · · · + 5u
2
+ 1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
10
=
1
u
2
a
1
=
−u
u
a
4
=
29u
30
− 147u
29
+ ··· + 62u + 64
27u
30
− 186u
29
+ ··· + 67u − 53
a
5
=
53u
30
− 291u
29
+ ··· + 118u + 67
3u
30
− 42u
29
+ ··· + 11u − 56
a
6
=
26u
30
− 115u
29
+ ··· + 54u + 96
13u
30
− 109u
29
+ ··· + 38u − 70
a
8
=
−u
30
+ 4u
29
+ ··· + 2u
2
+ 5u
2u
29
− 11u
28
+ ··· + 10u
2
+ 1
a
11
=
−2u
30
+ 12u
29
+ ··· − 6u − 1
u
30
− 5u
29
+ ··· + u + 2
a
3
=
39u
30
− 250u
29
+ ··· + 103u − 45
−14u
30
+ 74u
29
+ ··· − 52u − 20
a
2
=
5u
30
− 5u
29
+ ··· + 3u + 33
19u
30
− 136u
29
+ ··· + 29u − 28
a
7
=
99u
30
− 631u
29
+ ··· + 199u − 74
−66u
30
+ 379u
29
+ ··· − 125u − 38
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 49u
30
− 273u
29
+ 1084u
28
− 3026u
27
+ 6936u
26
− 13201u
25
+ 21850u
24
− 31895u
23
+
41936u
22
− 50212u
21
+ 56147u
20
− 58806u
19
+ 61042u
18
− 60923u
17
+ 63755u
16
−
63049u
15
+ 64699u
14
− 59739u
13
+ 54253u
12
− 43083u
11
+ 31547u
10
− 19891u
9
+
10451u
8
− 4037u
7
+ 951u
6
+ 852u
5
− 239u
4
+ 704u
3
+ 112u
2
+ 122u + 48
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
31
− 12u
30
+ ··· − 11u + 1
c
2
u
31
+ 6u
29
+ ··· − u − 1
c
3
, c
10
u
31
− u
30
+ ··· − 12u
2
+ 1
c
4
, c
8
u
31
+ u
30
+ ··· − 5u + 1
c
5
, c
11
u
31
+ u
30
+ ··· + 12u
2
− 1
c
7
u
31
+ 6u
29
+ ··· − u + 1
c
9
u
31
− 6u
30
+ ··· + 5u
2
+ 1
c
12
u
31
+ 6u
30
+ ··· − 5u
2
− 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
31
+ 24y
30
+ ··· − 7y − 1
c
2
, c
7
y
31
+ 12y
30
+ ··· − 11y − 1
c
3
, c
5
, c
10
c
11
y
31
− 31y
30
+ ··· + 24y − 1
c
4
, c
8
y
31
− y
30
+ ··· + 15y − 1
c
9
, c
12
y
31
+ 14y
30
+ ··· − 10y − 1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.459042 + 0.885968I
a = 0.66742 + 1.28471I
b = −1.101300 − 0.666053I
−5.12765 + 0.63375I −12.91314 − 3.32588I
u = −0.459042 − 0.885968I
a = 0.66742 − 1.28471I
b = −1.101300 + 0.666053I
−5.12765 − 0.63375I −12.91314 + 3.32588I
u = −0.910027 + 0.469262I
a = −1.083780 − 0.561867I
b = 0.838410 + 0.209768I
−6.72856 + 3.62519I −15.3022 − 5.1774I
u = −0.910027 − 0.469262I
a = −1.083780 + 0.561867I
b = 0.838410 − 0.209768I
−6.72856 − 3.62519I −15.3022 + 5.1774I
u = −0.254395 + 0.921565I
a = 0.55786 + 1.67354I
b = −1.51644 − 0.94842I
−3.08305 + 3.62047I −3.09630 − 3.18908I
u = −0.254395 − 0.921565I
a = 0.55786 − 1.67354I
b = −1.51644 + 0.94842I
−3.08305 − 3.62047I −3.09630 + 3.18908I
u = −0.223360 + 0.892887I
a = −0.63773 − 1.74218I
b = 1.66500 + 0.86994I
−3.24957 − 1.50729I −4.29080 + 4.53649I
u = −0.223360 − 0.892887I
a = −0.63773 + 1.74218I
b = 1.66500 − 0.86994I
−3.24957 + 1.50729I −4.29080 − 4.53649I
u = 0.861990 + 0.256573I
a = −0.736061 + 0.232711I
b = −0.060451 + 0.234245I
−2.22256 + 0.26900I −14.6220 − 0.6133I
u = 0.861990 − 0.256573I
a = −0.736061 − 0.232711I
b = −0.060451 − 0.234245I
−2.22256 − 0.26900I −14.6220 + 0.6133I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.624295 + 1.009080I
a = 0.389479 − 0.202152I
b = −1.56560 − 0.16523I
6.54911 − 5.82818I −2.29348 + 1.65957I
u = 0.624295 − 1.009080I
a = 0.389479 + 0.202152I
b = −1.56560 + 0.16523I
6.54911 + 5.82818I −2.29348 − 1.65957I
u = 0.666516 + 0.984333I
a = −0.376732 + 0.224711I
b = 1.38836 + 0.33452I
6.39787 + 0.56133I 0. − 1.71473I
u = 0.666516 − 0.984333I
a = −0.376732 − 0.224711I
b = 1.38836 − 0.33452I
6.39787 − 0.56133I 0. + 1.71473I
u = −0.196339 + 0.748104I
a = −0.88657 − 1.70534I
b = 1.65086 + 0.35906I
−6.16160 + 2.57607I −13.79197 − 0.41948I
u = −0.196339 − 0.748104I
a = −0.88657 + 1.70534I
b = 1.65086 − 0.35906I
−6.16160 − 2.57607I −13.79197 + 0.41948I
u = 0.465869 + 1.145850I
a = 0.547252 − 0.215334I
b = −1.45049 + 0.72438I
0.49691 − 4.90600I −10.08446 + 4.73623I
u = 0.465869 − 1.145850I
a = 0.547252 + 0.215334I
b = −1.45049 − 0.72438I
0.49691 + 4.90600I −10.08446 − 4.73623I
u = 0.333943 + 1.214950I
a = 0.675048 − 0.339836I
b = −1.18894 + 1.12319I
2.74395 − 3.01097I −3.73651 + 4.44126I
u = 0.333943 − 1.214950I
a = 0.675048 + 0.339836I
b = −1.18894 − 1.12319I
2.74395 + 3.01097I −3.73651 − 4.44126I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.010200 + 0.692049I
a = −0.84194 − 1.68217I
b = 1.79006 − 0.22353I
−0.71851 + 7.06631I −7.40121 − 5.99406I
u = −0.010200 − 0.692049I
a = −0.84194 + 1.68217I
b = 1.79006 + 0.22353I
−0.71851 − 7.06631I −7.40121 + 5.99406I
u = 0.310933 + 1.272960I
a = −0.644596 + 0.419130I
b = 1.00682 − 1.13016I
2.15172 − 8.27104I −6.85296 + 10.55351I
u = 0.310933 − 1.272960I
a = −0.644596 − 0.419130I
b = 1.00682 + 1.13016I
2.15172 + 8.27104I −6.85296 − 10.55351I
u = 0.016871 + 0.640170I
a = 0.73258 + 1.71602I
b = −1.63369 + 0.30390I
−0.065094 + 1.253440I −6.70977 − 1.20907I
u = 0.016871 − 0.640170I
a = 0.73258 − 1.71602I
b = −1.63369 − 0.30390I
−0.065094 − 1.253440I −6.70977 + 1.20907I
u = 0.55032 + 1.33102I
a = −0.464049 + 0.326781I
b = 0.953107 − 0.583162I
−0.92392 − 3.22479I 0
u = 0.55032 − 1.33102I
a = −0.464049 − 0.326781I
b = 0.953107 + 0.583162I
−0.92392 + 3.22479I 0
u = 1.39919 + 0.42826I
a = 0.478721 − 0.120013I
b = −0.250928 − 0.094841I
−4.58206 − 3.79705I −23.1475 + 0.I
u = 1.39919 − 0.42826I
a = 0.478721 + 0.120013I
b = −0.250928 + 0.094841I
−4.58206 + 3.79705I −23.1475 + 0.I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.353120
a = 3.24616
b = −1.04956
−3.85267 −9.93580
28
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
10
· (u
31
− 12u
30
+ ··· − 11u + 1)(u
45
+ 15u
44
+ ··· − 1536u − 1024)
c
2
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
10
· (u
31
+ 6u
29
+ ··· − u − 1)(u
45
+ 11u
44
+ ··· + 128u + 32)
c
3
, c
10
(u
31
− u
30
+ ··· − 12u
2
+ 1)(u
45
+ u
44
+ ··· + 4u + 1)
· (u
90
+ u
89
+ ··· + 651136u + 56443)
c
4
, c
8
(u
31
+ u
30
+ ··· − 5u + 1)(u
45
− u
44
+ ··· − 5u + 1)
· (u
90
− 5u
89
+ ··· + 14948u − 2189)
c
5
, c
11
(u
31
+ u
30
+ ··· + 12u
2
− 1)(u
45
+ u
44
+ ··· + 4u + 1)
· (u
90
+ u
89
+ ··· + 651136u + 56443)
c
7
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
10
· (u
31
+ 6u
29
+ ··· − u + 1)(u
45
+ 11u
44
+ ··· + 128u + 32)
c
9
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
18
)(u
31
− 6u
30
+ ··· + 5u
2
+ 1)
· (u
45
− 21u
44
+ ··· − 9728u + 512)
c
12
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
18
)(u
31
+ 6u
30
+ ··· − 5u
2
− 1)
· (u
45
− 21u
44
+ ··· − 9728u + 512)
29
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
10
· (y
31
+ 24y
30
+ ··· − 7y − 1)
· (y
45
+ 31y
44
+ ··· + 9830400y − 1048576)
c
2
, c
7
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
10
· (y
31
+ 12y
30
+ ··· − 11y − 1)(y
45
+ 15y
44
+ ··· − 1536y − 1024)
c
3
, c
5
, c
10
c
11
(y
31
− 31y
30
+ ··· + 24y − 1)(y
45
− 25y
44
+ ··· + 8y − 1)
· (y
90
− 65y
89
+ ··· − 225222871104y + 3185812249)
c
4
, c
8
(y
31
− y
30
+ ··· + 15y − 1)(y
45
+ 29y
44
+ ··· + 71y − 1)
· (y
90
− 13y
89
+ ··· − 374991552y + 4791721)
c
9
, c
12
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
18
)(y
31
+ 14y
30
+ ··· − 10y − 1)
· (y
45
+ 17y
44
+ ··· − 3407872y − 262144)
30
