11a
288
(K11a
288
)
A knot diagram
1
Linearized knot diagam
8 6 1 7 2 11 10 3 4 5 9
Solving Sequence
2,5
6
3,11
7 4 10 8 1 9
c
5
c
2
c
6
c
4
c
10
c
7
c
1
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h8.06723 × 10
36
u
30
− 2.15815 × 10
37
u
29
+ ··· + 3.48049 × 10
38
b + 2.48334 × 10
38
,
2.80307 × 10
38
u
30
− 9.56905 × 10
38
u
29
+ ··· + 4.87269 × 10
39
a + 9.46071 × 10
39
, u
31
− 4u
30
+ ··· + 50u − 28i
I
u
2
= h−2.07446 × 10
51
au
49
− 3.96254 × 10
51
u
49
+ ··· + 1.37652 × 10
52
a + 2.97634 × 10
52
,
1.89907 × 10
50
au
49
+ 3.15834 × 10
50
u
49
+ ··· − 1.33112 × 10
51
a − 2.21453 × 10
51
, u
50
+ u
49
+ ··· + 53u
2
− 5i
I
u
3
= h−120u
11
a − 53u
11
+ ··· + 159a − 21, 2244u
11
a − 88u
11
+ ··· − 4869a + 704,
u
12
− 2u
10
− u
8
+ 8u
6
− 2u
5
− 10u
4
+ 5u
3
+ 6u
2
− u − 1i
I
u
4
= h−u
3
+ u
2
+ b − 1, −2u
4
+ 2u
3
+ u
2
+ a − 2u − 2, u
5
− u
4
− u
3
+ 2u
2
+ u − 1i
* 4 irreducible components of dim
C
= 0, with total 160 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
=
h8.07×10
36
u
30
−2.16×10
37
u
29
+· · ·+3.48×10
38
b+2.48×10
38
, 2.80×10
38
u
30
−
9.57 × 10
38
u
29
+ · · · + 4.87 × 10
39
a + 9.46 × 10
39
, u
31
− 4u
30
+ · · · + 50u − 28i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
3
=
u
−u
3
+ u
a
11
=
−0.0575261u
30
+ 0.196381u
29
+ ··· − 0.668017u − 1.94158
−0.0231784u
30
+ 0.0620070u
29
+ ··· − 1.21996u − 0.713504
a
7
=
0.176167u
30
− 0.581968u
29
+ ··· − 3.39968u + 7.23962
0.0343023u
30
− 0.100932u
29
+ ··· + 0.798398u + 0.793988
a
4
=
−0.208417u
30
+ 0.691487u
29
+ ··· + 2.50241u − 7.53909
−0.0519901u
30
+ 0.176388u
29
+ ··· + 1.60836u − 1.85459
a
10
=
−0.0807046u
30
+ 0.258388u
29
+ ··· − 1.88798u − 2.65508
−0.0231784u
30
+ 0.0620070u
29
+ ··· − 1.21996u − 0.713504
a
8
=
0.0592055u
30
− 0.204794u
29
+ ··· − 3.84139u + 4.10481
0.00850606u
30
− 0.0427335u
29
+ ··· − 0.991100u + 0.713957
a
1
=
0.151056u
30
− 0.489997u
29
+ ··· − 0.795159u + 7.14890
0.0373762u
30
− 0.128110u
29
+ ··· − 0.0869666u + 1.73434
a
9
=
0.0899122u
30
− 0.296684u
29
+ ··· − 4.28680u + 4.75380
0.0118652u
30
− 0.0465465u
29
+ ··· − 0.749425u + 0.496701
a
9
=
0.0899122u
30
− 0.296684u
29
+ ··· − 4.28680u + 4.75380
0.0118652u
30
− 0.0465465u
29
+ ··· − 0.749425u + 0.496701
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.171373u
30
+ 0.572368u
29
+ ··· − 0.551385u − 4.18306
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
31
− 7u
30
+ ··· + 96u − 12
c
2
, c
5
u
31
− 4u
30
+ ··· + 50u − 28
c
3
, c
4
u
31
− 2u
30
+ ··· − 9u + 3
c
7
, c
11
u
31
− 4u
30
+ ··· − 3u − 1
c
8
, c
10
3(3u
31
− 6u
30
+ ··· + 5u − 1)
c
9
3(3u
31
+ 9u
30
+ ··· + 832u + 128)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
31
+ 5y
30
+ ··· − 1776y −144
c
2
, c
5
y
31
− 12y
30
+ ··· − 7860y −784
c
3
, c
4
y
31
− 6y
30
+ ··· + 51y −9
c
7
, c
11
y
31
+ 2y
30
+ ··· + 3y −1
c
8
, c
10
9(9y
31
+ 120y
30
+ ··· + 9y −1)
c
9
9(9y
31
+ 57y
30
+ ··· + 331776y −16384)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.902043 + 0.474320I
a = −1.36116 + 0.92502I
b = −0.249318 − 0.764075I
3.74146 − 4.83276I 8.35445 + 8.23935I
u = −0.902043 − 0.474320I
a = −1.36116 − 0.92502I
b = −0.249318 + 0.764075I
3.74146 + 4.83276I 8.35445 − 8.23935I
u = 1.005070 + 0.357655I
a = 0.56639 + 1.94456I
b = 0.045950 − 1.405710I
4.44624 + 0.88533I 2.97033 − 0.43256I
u = 1.005070 − 0.357655I
a = 0.56639 − 1.94456I
b = 0.045950 + 1.405710I
4.44624 − 0.88533I 2.97033 + 0.43256I
u = 0.396207 + 1.023040I
a = −0.134995 + 0.574699I
b = −0.276299 + 0.112521I
−2.52139 + 3.24553I −8.21889 − 3.28316I
u = 0.396207 − 1.023040I
a = −0.134995 − 0.574699I
b = −0.276299 − 0.112521I
−2.52139 − 3.24553I −8.21889 + 3.28316I
u = −0.304429 + 1.124820I
a = 0.038514 + 0.323938I
b = −0.820173 + 1.047500I
−3.41746 + 4.90251I −7.14123 − 8.81153I
u = −0.304429 − 1.124820I
a = 0.038514 − 0.323938I
b = −0.820173 − 1.047500I
−3.41746 − 4.90251I −7.14123 + 8.81153I
u = −1.073900 + 0.514023I
a = −0.42433 + 1.48714I
b = −0.668135 − 0.446989I
0.39997 − 5.14043I −3.97875 + 8.74276I
u = −1.073900 − 0.514023I
a = −0.42433 − 1.48714I
b = −0.668135 + 0.446989I
0.39997 + 5.14043I −3.97875 − 8.74276I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.360300 + 1.182790I
a = 0.1307640 − 0.0393439I
b = 1.02402 + 0.99307I
0.34389 − 13.57870I −0.70654 + 8.53646I
u = 0.360300 − 1.182790I
a = 0.1307640 + 0.0393439I
b = 1.02402 − 0.99307I
0.34389 + 13.57870I −0.70654 − 8.53646I
u = 1.161460 + 0.451121I
a = −0.090591 + 1.372090I
b = 0.330471 − 0.343611I
0.48261 + 1.92668I −1.89690 + 0.93654I
u = 1.161460 − 0.451121I
a = −0.090591 − 1.372090I
b = 0.330471 + 0.343611I
0.48261 − 1.92668I −1.89690 − 0.93654I
u = −0.417016 + 0.598371I
a = 0.699354 + 0.161448I
b = 0.733122 − 0.200454I
−1.51628 + 0.70429I −5.99175 − 2.53077I
u = −0.417016 − 0.598371I
a = 0.699354 − 0.161448I
b = 0.733122 + 0.200454I
−1.51628 − 0.70429I −5.99175 + 2.53077I
u = 0.723629
a = −2.83794
b = −0.817850
−2.61872 −6.04380
u = 1.294070 + 0.080005I
a = 0.001044 − 1.343360I
b = −0.37710 + 1.64204I
3.31474 − 0.89260I −5.46909 + 7.98486I
u = 1.294070 − 0.080005I
a = 0.001044 + 1.343360I
b = −0.37710 − 1.64204I
3.31474 + 0.89260I −5.46909 − 7.98486I
u = 0.378286 + 1.348700I
a = 0.203259 + 0.019001I
b = 0.178022 − 0.791454I
−0.69495 + 3.65306I 9.41146 − 5.59206I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.378286 − 1.348700I
a = 0.203259 − 0.019001I
b = 0.178022 + 0.791454I
−0.69495 − 3.65306I 9.41146 + 5.59206I
u = −1.261620 + 0.633674I
a = 0.30551 − 1.50157I
b = 1.27831 + 1.31389I
−0.34268 − 11.10620I −2.89392 + 11.18360I
u = −1.261620 − 0.633674I
a = 0.30551 + 1.50157I
b = 1.27831 − 1.31389I
−0.34268 + 11.10620I −2.89392 − 11.18360I
u = 1.27757 + 0.69297I
a = −0.37637 − 1.58211I
b = −1.22288 + 1.11044I
3.2833 + 20.2067I 1.01289 − 10.64976I
u = 1.27757 − 0.69297I
a = −0.37637 + 1.58211I
b = −1.22288 − 1.11044I
3.2833 − 20.2067I 1.01289 + 10.64976I
u = 1.31560 + 0.78153I
a = 0.197901 + 0.676665I
b = 0.297387 − 0.693752I
2.20531 + 3.28606I 18.4949 − 4.2675I
u = 1.31560 − 0.78153I
a = 0.197901 − 0.676665I
b = 0.297387 + 0.693752I
2.20531 − 3.28606I 18.4949 + 4.2675I
u = −1.56081 + 0.05643I
a = 0.404127 − 0.969867I
b = −0.581198 + 1.166820I
7.70413 + 8.70305I 5.79340 − 7.62622I
u = −1.56081 − 0.05643I
a = 0.404127 + 0.969867I
b = −0.581198 − 1.166820I
7.70413 − 8.70305I 5.79340 + 7.62622I
u = −0.030538 + 0.374368I
a = 0.723845 − 0.624919I
b = −0.283244 − 0.791915I
1.97471 + 1.86806I 2.78153 − 1.05232I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.030538 − 0.374368I
a = 0.723845 + 0.624919I
b = −0.283244 + 0.791915I
1.97471 − 1.86806I 2.78153 + 1.05232I
8
II. I
u
2
= h−2.07 × 10
51
au
49
− 3.96 × 10
51
u
49
+ · · · + 1.38 × 10
52
a + 2.98 ×
10
52
, 1.90 × 10
50
au
49
+ 3.16 × 10
50
u
49
+ · · · − 1.33 × 10
51
a − 2.21 ×
10
51
, u
50
+ u
49
+ · · · + 53u
2
− 5i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
3
=
u
−u
3
+ u
a
11
=
a
13.2641au
49
+ 25.3365u
49
+ ··· − 88.0147a − 190.307
a
7
=
−35.2693au
49
− 22.3441u
49
+ ··· + 248.355a + 171.960
−3.01576au
49
− 12.9869u
49
+ ··· + 19.9864a + 88.0792
a
4
=
25.0318au
49
+ 72.5925u
49
+ ··· − 171.285a − 505.558
4.95115au
49
+ 24.1394u
49
+ ··· − 34.9056a − 159.189
a
10
=
13.2641au
49
+ 25.3365u
49
+ ··· − 87.0147a − 190.307
13.2641au
49
+ 25.3365u
49
+ ··· − 88.0147a − 190.307
a
8
=
−17.6029au
49
− 49.6710u
49
+ ··· + 122.842a + 342.370
9.42507au
49
− 1.32561u
49
+ ··· − 66.3205a − 7.56378
a
1
=
−29.2084au
49
− 21.6686u
49
+ ··· + 212.663a + 171.932
−10.7220au
49
− 24.2489u
49
+ ··· + 70.8898a + 188.013
a
9
=
−27.0280au
49
− 59.6701u
49
+ ··· + 189.163a + 418.745
4.95115au
49
− 7.04917u
49
+ ··· − 34.9056a + 35.9109
a
9
=
−27.0280au
49
− 59.6701u
49
+ ··· + 189.163a + 418.745
4.95115au
49
− 7.04917u
49
+ ··· − 34.9056a + 35.9109
(ii) Obstruction class = −1
(iii) Cusp Shapes = −44.8391u
49
− 13.6966u
48
+ ··· − 563.847u + 387.015
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
100
+ 5u
99
+ ··· − 169334u + 14149
c
2
, c
5
(u
50
+ u
49
+ ··· + 53u
2
− 5)
2
c
3
, c
4
u
100
− 6u
99
+ ··· + 6u − 1
c
7
, c
11
u
100
− 2u
99
+ ··· + 37u − 1
c
8
, c
10
u
100
− 10u
98
+ ··· + 18u − 1
c
9
(u
50
− 2u
49
+ ··· + 21u + 49)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
100
− 3y
99
+ ··· + 8842579308y + 200194201
c
2
, c
5
(y
50
− 27y
49
+ ··· − 530y + 25)
2
c
3
, c
4
y
100
+ 12y
99
+ ··· + 44y + 1
c
7
, c
11
y
100
− 16y
99
+ ··· − 3373y + 1
c
8
, c
10
y
100
− 20y
99
+ ··· + 154y + 1
c
9
(y
50
− 28y
49
+ ··· − 46305y + 2401)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.548941 + 0.850283I
a = 0.759893 + 0.706027I
b = 0.731453 − 0.812003I
0.54701 + 3.37624I −1.0000 − 9.25407I
u = 0.548941 + 0.850283I
a = 0.246103 + 0.095666I
b = −0.567136 + 0.180162I
0.54701 + 3.37624I −1.0000 − 9.25407I
u = 0.548941 − 0.850283I
a = 0.759893 − 0.706027I
b = 0.731453 + 0.812003I
0.54701 − 3.37624I −1.0000 + 9.25407I
u = 0.548941 − 0.850283I
a = 0.246103 − 0.095666I
b = −0.567136 − 0.180162I
0.54701 − 3.37624I −1.0000 + 9.25407I
u = 0.812718 + 0.561361I
a = 0.447024 + 0.766749I
b = −0.0033739 + 0.1015400I
1.85560 − 0.04601I 3.11402 − 1.05223I
u = 0.812718 + 0.561361I
a = −0.063750 − 0.197431I
b = −1.025610 − 0.625983I
1.85560 − 0.04601I 3.11402 − 1.05223I
u = 0.812718 − 0.561361I
a = 0.447024 − 0.766749I
b = −0.0033739 − 0.1015400I
1.85560 + 0.04601I 3.11402 + 1.05223I
u = 0.812718 − 0.561361I
a = −0.063750 + 0.197431I
b = −1.025610 + 0.625983I
1.85560 + 0.04601I 3.11402 + 1.05223I
u = −1.016920 + 0.224360I
a = −0.19678 − 1.95023I
b = −0.096238 + 1.097620I
5.85957 − 0.63163I 13.37806 + 1.18653I
u = −1.016920 + 0.224360I
a = −1.34222 + 1.62787I
b = 0.52165 − 1.66824I
5.85957 − 0.63163I 13.37806 + 1.18653I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.016920 − 0.224360I
a = −0.19678 + 1.95023I
b = −0.096238 − 1.097620I
5.85957 + 0.63163I 13.37806 − 1.18653I
u = −1.016920 − 0.224360I
a = −1.34222 − 1.62787I
b = 0.52165 + 1.66824I
5.85957 + 0.63163I 13.37806 − 1.18653I
u = 0.836854 + 0.310102I
a = −0.412900 − 0.092303I
b = 1.40884 + 0.61468I
−2.83417 + 1.43022I −1.90225 − 5.13073I
u = 0.836854 + 0.310102I
a = 0.22663 − 2.88245I
b = −0.99852 + 1.16218I
−2.83417 + 1.43022I −1.90225 − 5.13073I
u = 0.836854 − 0.310102I
a = −0.412900 + 0.092303I
b = 1.40884 − 0.61468I
−2.83417 − 1.43022I −1.90225 + 5.13073I
u = 0.836854 − 0.310102I
a = 0.22663 + 2.88245I
b = −0.99852 − 1.16218I
−2.83417 − 1.43022I −1.90225 + 5.13073I
u = 0.891678
a = −1.52379 + 1.36189I
b = 1.77787 − 0.55907I
2.18885 3.18030
u = 0.891678
a = −1.52379 − 1.36189I
b = 1.77787 + 0.55907I
2.18885 3.18030
u = 0.135481 + 0.857453I
a = 1.63578 + 0.50962I
b = 1.066030 + 0.871487I
0.34967 + 6.29766I −1.51708 − 11.49060I
u = 0.135481 + 0.857453I
a = −0.075738 + 0.233544I
b = −0.806693 + 0.715605I
0.34967 + 6.29766I −1.51708 − 11.49060I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.135481 − 0.857453I
a = 1.63578 − 0.50962I
b = 1.066030 − 0.871487I
0.34967 − 6.29766I −1.51708 + 11.49060I
u = 0.135481 − 0.857453I
a = −0.075738 − 0.233544I
b = −0.806693 − 0.715605I
0.34967 − 6.29766I −1.51708 + 11.49060I
u = −0.701301 + 0.482229I
a = 0.185491 + 0.422356I
b = −1.197340 − 0.259748I
−1.26220 − 7.42402I −2.60909 + 11.71667I
u = −0.701301 + 0.482229I
a = −0.83741 + 2.98748I
b = −0.717876 − 1.016820I
−1.26220 − 7.42402I −2.60909 + 11.71667I
u = −0.701301 − 0.482229I
a = 0.185491 − 0.422356I
b = −1.197340 + 0.259748I
−1.26220 + 7.42402I −2.60909 − 11.71667I
u = −0.701301 − 0.482229I
a = −0.83741 − 2.98748I
b = −0.717876 + 1.016820I
−1.26220 + 7.42402I −2.60909 − 11.71667I
u = −0.868601 + 0.770886I
a = −0.293051 − 0.527261I
b = 0.745628 + 0.041107I
−0.74310 + 2.60526I 0
u = −0.868601 + 0.770886I
a = 0.099270 + 0.385470I
b = 1.063480 − 0.764874I
−0.74310 + 2.60526I 0
u = −0.868601 − 0.770886I
a = −0.293051 + 0.527261I
b = 0.745628 − 0.041107I
−0.74310 − 2.60526I 0
u = −0.868601 − 0.770886I
a = 0.099270 − 0.385470I
b = 1.063480 + 0.764874I
−0.74310 − 2.60526I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.108720 + 0.368281I
a = −1.105340 + 0.719590I
b = 0.597907 − 1.241130I
4.78147 + 2.43283I 0
u = −1.108720 + 0.368281I
a = 1.02939 − 1.34421I
b = 0.103182 + 0.382370I
4.78147 + 2.43283I 0
u = −1.108720 − 0.368281I
a = −1.105340 − 0.719590I
b = 0.597907 + 1.241130I
4.78147 − 2.43283I 0
u = −1.108720 − 0.368281I
a = 1.02939 + 1.34421I
b = 0.103182 − 0.382370I
4.78147 − 2.43283I 0
u = 1.110180 + 0.404435I
a = 1.320230 − 0.191330I
b = 0.779604 − 0.058867I
1.44032 + 9.60257I 0
u = 1.110180 + 0.404435I
a = −0.11883 + 2.12414I
b = 1.102120 − 0.793778I
1.44032 + 9.60257I 0
u = 1.110180 − 0.404435I
a = 1.320230 + 0.191330I
b = 0.779604 + 0.058867I
1.44032 − 9.60257I 0
u = 1.110180 − 0.404435I
a = −0.11883 − 2.12414I
b = 1.102120 + 0.793778I
1.44032 − 9.60257I 0
u = −1.067760 + 0.532641I
a = −0.837760 + 0.937378I
b = −0.867740 − 0.348502I
0.09660 − 5.64563I 0
u = −1.067760 + 0.532641I
a = −0.26251 + 1.80511I
b = −0.976959 − 0.654250I
0.09660 − 5.64563I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.067760 − 0.532641I
a = −0.837760 − 0.937378I
b = −0.867740 + 0.348502I
0.09660 + 5.64563I 0
u = −1.067760 − 0.532641I
a = −0.26251 − 1.80511I
b = −0.976959 + 0.654250I
0.09660 + 5.64563I 0
u = −1.174890 + 0.341252I
a = 0.00517 + 1.59762I
b = −1.50003 − 0.68731I
5.24587 − 6.28986I 0
u = −1.174890 + 0.341252I
a = −0.27694 − 1.79529I
b = 0.605227 + 0.942427I
5.24587 − 6.28986I 0
u = −1.174890 − 0.341252I
a = 0.00517 − 1.59762I
b = −1.50003 + 0.68731I
5.24587 + 6.28986I 0
u = −1.174890 − 0.341252I
a = −0.27694 + 1.79529I
b = 0.605227 − 0.942427I
5.24587 + 6.28986I 0
u = 1.122590 + 0.526509I
a = 0.27807 + 1.97868I
b = 1.34270 − 1.10887I
3.61514 + 10.02170I 0
u = 1.122590 + 0.526509I
a = −0.41461 − 1.97138I
b = −0.256101 + 0.787916I
3.61514 + 10.02170I 0
u = 1.122590 − 0.526509I
a = 0.27807 − 1.97868I
b = 1.34270 + 1.10887I
3.61514 − 10.02170I 0
u = 1.122590 − 0.526509I
a = −0.41461 + 1.97138I
b = −0.256101 − 0.787916I
3.61514 − 10.02170I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.310212 + 0.659807I
a = 1.40414 − 0.49455I
b = 0.595491 − 0.521674I
−1.97473 + 1.08010I −6.48617 − 1.37548I
u = −0.310212 + 0.659807I
a = 0.393146 + 0.047451I
b = 1.003050 − 0.403828I
−1.97473 + 1.08010I −6.48617 − 1.37548I
u = −0.310212 − 0.659807I
a = 1.40414 + 0.49455I
b = 0.595491 + 0.521674I
−1.97473 − 1.08010I −6.48617 + 1.37548I
u = −0.310212 − 0.659807I
a = 0.393146 − 0.047451I
b = 1.003050 + 0.403828I
−1.97473 − 1.08010I −6.48617 + 1.37548I
u = 0.299438 + 0.660743I
a = −0.08785 − 1.45420I
b = 0.410545 + 0.622691I
1.22345 − 5.39271I 3.60568 + 7.27334I
u = 0.299438 + 0.660743I
a = −0.206854 − 0.481835I
b = −1.113500 − 0.825660I
1.22345 − 5.39271I 3.60568 + 7.27334I
u = 0.299438 − 0.660743I
a = −0.08785 + 1.45420I
b = 0.410545 − 0.622691I
1.22345 + 5.39271I 3.60568 − 7.27334I
u = 0.299438 − 0.660743I
a = −0.206854 + 0.481835I
b = −1.113500 + 0.825660I
1.22345 + 5.39271I 3.60568 − 7.27334I
u = −0.714215 + 0.033943I
a = −1.22507 + 1.07240I
b = −0.861797 − 0.597056I
2.52892 − 4.60236I 5.46658 + 4.68357I
u = −0.714215 + 0.033943I
a = −1.24729 + 2.67337I
b = 0.940472 − 0.274274I
2.52892 − 4.60236I 5.46658 + 4.68357I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.714215 − 0.033943I
a = −1.22507 − 1.07240I
b = −0.861797 + 0.597056I
2.52892 + 4.60236I 5.46658 − 4.68357I
u = −0.714215 − 0.033943I
a = −1.24729 − 2.67337I
b = 0.940472 + 0.274274I
2.52892 + 4.60236I 5.46658 − 4.68357I
u = −1.29400
a = 0.958908
b = −0.502636
−1.60735 0
u = −1.29400
a = 0.943682
b = 1.09271
−1.60735 0
u = −0.661065 + 0.201573I
a = 0.644813 + 0.337066I
b = 1.072810 + 0.133987I
−2.96398 − 1.00000I −4.93204 + 6.02487I
u = −0.661065 + 0.201573I
a = 1.46502 + 2.77666I
b = −0.313863 + 0.081467I
−2.96398 − 1.00000I −4.93204 + 6.02487I
u = −0.661065 − 0.201573I
a = 0.644813 − 0.337066I
b = 1.072810 − 0.133987I
−2.96398 + 1.00000I −4.93204 − 6.02487I
u = −0.661065 − 0.201573I
a = 1.46502 − 2.77666I
b = −0.313863 − 0.081467I
−2.96398 + 1.00000I −4.93204 − 6.02487I
u = 1.067610 + 0.768264I
a = −0.585773 − 0.416162I
b = −0.473430 + 0.422720I
2.32102 + 5.65331I 0
u = 1.067610 + 0.768264I
a = 0.77026 + 1.52994I
b = 1.46082 − 1.09833I
2.32102 + 5.65331I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.067610 − 0.768264I
a = −0.585773 + 0.416162I
b = −0.473430 − 0.422720I
2.32102 − 5.65331I 0
u = 1.067610 − 0.768264I
a = 0.77026 − 1.52994I
b = 1.46082 + 1.09833I
2.32102 − 5.65331I 0
u = −1.232480 + 0.465944I
a = 1.083150 − 0.803208I
b = −1.07848 + 1.74540I
4.22116 − 10.84980I 0
u = −1.232480 + 0.465944I
a = 0.01539 − 1.74787I
b = 1.09006 + 1.21638I
4.22116 − 10.84980I 0
u = −1.232480 − 0.465944I
a = 1.083150 + 0.803208I
b = −1.07848 − 1.74540I
4.22116 + 10.84980I 0
u = −1.232480 − 0.465944I
a = 0.01539 + 1.74787I
b = 1.09006 − 1.21638I
4.22116 + 10.84980I 0
u = 0.595267
a = 0.834754 + 0.433598I
b = −0.717567 + 0.382010I
2.22273 4.86780
u = 0.595267
a = 0.834754 − 0.433598I
b = −0.717567 − 0.382010I
2.22273 4.86780
u = 1.308860 + 0.523454I
a = 0.791106 + 0.745051I
b = −0.77725 − 1.53501I
3.40486 + 2.98616I 0
u = 1.308860 + 0.523454I
a = −0.114612 − 0.646383I
b = −0.449568 + 0.414428I
3.40486 + 2.98616I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.308860 − 0.523454I
a = 0.791106 − 0.745051I
b = −0.77725 + 1.53501I
3.40486 − 2.98616I 0
u = 1.308860 − 0.523454I
a = −0.114612 + 0.646383I
b = −0.449568 − 0.414428I
3.40486 − 2.98616I 0
u = 1.38998 + 0.36438I
a = −0.264780 − 0.693877I
b = −0.142215 + 0.989906I
4.42644 − 0.76806I 0
u = 1.38998 + 0.36438I
a = 0.159794 − 1.264000I
b = −1.91800 + 1.10468I
4.42644 − 0.76806I 0
u = 1.38998 − 0.36438I
a = −0.264780 + 0.693877I
b = −0.142215 − 0.989906I
4.42644 + 0.76806I 0
u = 1.38998 − 0.36438I
a = 0.159794 + 1.264000I
b = −1.91800 − 1.10468I
4.42644 + 0.76806I 0
u = 1.45898
a = 0.477828 + 1.118070I
b = −0.592114 − 0.977099I
7.96610 0
u = 1.45898
a = 0.477828 − 1.118070I
b = −0.592114 + 0.977099I
7.96610 0
u = 0.468862 + 0.251297I
a = −0.818944 − 0.404936I
b = −1.187340 − 0.500194I
−0.77161 − 6.39968I −10.97216 − 0.34215I
u = 0.468862 + 0.251297I
a = 0.10642 − 5.48970I
b = −0.148091 − 0.259941I
−0.77161 − 6.39968I −10.97216 − 0.34215I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.468862 − 0.251297I
a = −0.818944 + 0.404936I
b = −1.187340 + 0.500194I
−0.77161 + 6.39968I −10.97216 + 0.34215I
u = 0.468862 − 0.251297I
a = 0.10642 + 5.48970I
b = −0.148091 + 0.259941I
−0.77161 + 6.39968I −10.97216 + 0.34215I
u = −1.33427 + 0.71530I
a = 0.050006 − 0.850151I
b = 0.619525 + 0.529012I
2.25912 − 11.62680I 0
u = −1.33427 + 0.71530I
a = −0.37021 + 1.47381I
b = −1.17795 − 1.04701I
2.25912 − 11.62680I 0
u = −1.33427 − 0.71530I
a = 0.050006 + 0.850151I
b = 0.619525 − 0.529012I
2.25912 + 11.62680I 0
u = −1.33427 − 0.71530I
a = −0.37021 − 1.47381I
b = −1.17795 + 1.04701I
2.25912 + 11.62680I 0
u = −0.23704 + 1.49901I
a = 0.247480 + 0.118820I
b = 0.913855 − 1.070400I
−1.17810 + 4.31731I 0
u = −0.23704 + 1.49901I
a = 0.0553566 − 0.1028220I
b = −0.282573 + 0.046634I
−1.17810 + 4.31731I 0
u = −0.23704 − 1.49901I
a = 0.247480 − 0.118820I
b = 0.913855 + 1.070400I
−1.17810 − 4.31731I 0
u = −0.23704 − 1.49901I
a = 0.0553566 + 0.1028220I
b = −0.282573 − 0.046634I
−1.17810 − 4.31731I 0
21
III. I
u
3
= h−120u
11
a − 53u
11
+ · · · + 159a − 21, 2244u
11
a − 88u
11
+ · · · −
4869a + 704, u
12
− 2u
10
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
3
=
u
−u
3
+ u
a
11
=
a
1.34831au
11
+ 0.595506u
11
+ ··· − 1.78652a + 0.235955
a
7
=
−1.78652au
11
+ 2.13483u
11
+ ··· + 4.29213a − 4.07865
−1.98876au
11
− 0.0449438u
11
+ ··· + 1.91011a − 0.640449
a
4
=
5.40449au
11
+ 3.10112u
11
+ ··· − 5.23596a + 1.19101
−1.39326au
11
− 5.07865u
11
+ ··· + 1.14607a + 7.62921
a
10
=
1.34831au
11
+ 0.595506u
11
+ ··· − 0.786517a + 0.235955
1.34831au
11
+ 0.595506u
11
+ ··· − 1.78652a + 0.235955
a
8
=
1.78652au
11
+ 4.29213u
11
+ ··· − 2.29213a − 6.33708
−1.16854au
11
+ 3.20225u
11
+ ··· + 1.34831a − 6.61798
a
1
=
−3.25843au
11
+ 4.31461u
11
+ ··· + 4.06742a − 8.51685
1.92135au
11
+ 8.61798u
11
+ ··· − 1.37079a − 11.9438
a
9
=
2.95506au
11
+ 5.02247u
11
+ ··· − 3.64045a − 6.17978
−1.39326au
11
+ 2.56180u
11
+ ··· + 1.14607a − 5.49438
a
9
=
2.95506au
11
+ 5.02247u
11
+ ··· − 3.64045a − 6.17978
−1.39326au
11
+ 2.56180u
11
+ ··· + 1.14607a − 5.49438
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1173
89
u
11
−
803
89
u
10
−
2101
89
u
9
+
1453
89
u
8
−
1655
89
u
7
+
1286
89
u
6
+
9112
89
u
5
−
8558
89
u
4
−
7879
89
u
3
+
11400
89
u
2
+
540
89
u −
2264
89
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
24
− 5u
22
+ ··· + 36u + 12
c
2
(u
12
− 2u
10
− u
8
+ 8u
6
+ 2u
5
− 10u
4
− 5u
3
+ 6u
2
+ u − 1)
2
c
3
u
24
+ 5u
23
+ ··· − 11u
2
− 3
c
4
u
24
− 5u
23
+ ··· − 11u
2
− 3
c
5
(u
12
− 2u
10
− u
8
+ 8u
6
− 2u
5
− 10u
4
+ 5u
3
+ 6u
2
− u − 1)
2
c
6
u
24
− 5u
22
+ ··· − 36u + 12
c
7
u
24
+ 3u
23
+ ··· − u + 1
c
8
3(3u
24
+ 3u
23
+ ··· + 2u − 1)
c
9
3(3u
24
− 16u
22
+ ··· + 343u
2
− 137)
c
10
3(3u
24
− 3u
23
+ ··· − 2u − 1)
c
11
u
24
− 3u
23
+ ··· + u + 1
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
24
− 10y
23
+ ··· + 192y + 144
c
2
, c
5
(y
12
− 4y
11
+ ··· − 13y + 1)
2
c
3
, c
4
y
24
− 9y
23
+ ··· + 66y + 9
c
7
, c
11
y
24
− 3y
23
+ ··· − 5y + 1
c
8
, c
10
9(9y
24
− 33y
23
+ ··· + 24y + 1)
c
9
9(3y
12
− 16y
11
+ ··· + 343y −137)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.810098 + 0.637530I
a = −0.712016 − 0.109438I
b = −0.705304 + 0.445585I
1.58921 + 5.87392I 1.28588 − 11.41546I
u = 0.810098 + 0.637530I
a = −1.10082 − 1.95581I
b = −1.212280 + 0.421660I
1.58921 + 5.87392I 1.28588 − 11.41546I
u = 0.810098 − 0.637530I
a = −0.712016 + 0.109438I
b = −0.705304 − 0.445585I
1.58921 − 5.87392I 1.28588 + 11.41546I
u = 0.810098 − 0.637530I
a = −1.10082 + 1.95581I
b = −1.212280 − 0.421660I
1.58921 − 5.87392I 1.28588 + 11.41546I
u = −1.17015
a = −1.17384
b = −1.00855
−1.34549 9.58470
u = −1.17015
a = −1.28421
b = 0.407100
−1.34549 9.58470
u = −1.186540 + 0.501873I
a = −0.028919 + 1.234360I
b = 0.045887 − 0.767620I
2.83828 − 9.79828I 0.33528 + 7.97194I
u = −1.186540 + 0.501873I
a = 0.14133 − 1.83780I
b = 1.22084 + 1.04970I
2.83828 − 9.79828I 0.33528 + 7.97194I
u = −1.186540 − 0.501873I
a = −0.028919 − 1.234360I
b = 0.045887 + 0.767620I
2.83828 + 9.79828I 0.33528 − 7.97194I
u = −1.186540 − 0.501873I
a = 0.14133 + 1.83780I
b = 1.22084 − 1.04970I
2.83828 + 9.79828I 0.33528 − 7.97194I
25
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.286400 + 0.289867I
a = −0.357329 − 0.892157I
b = −0.110722 + 1.183840I
4.17779 − 0.93929I 0.56283 + 7.92150I
u = 1.286400 + 0.289867I
a = −0.01095 + 1.46966I
b = 1.29407 − 1.25340I
4.17779 − 0.93929I 0.56283 + 7.92150I
u = 1.286400 − 0.289867I
a = −0.357329 + 0.892157I
b = −0.110722 − 1.183840I
4.17779 + 0.93929I 0.56283 − 7.92150I
u = 1.286400 − 0.289867I
a = −0.01095 − 1.46966I
b = 1.29407 + 1.25340I
4.17779 + 0.93929I 0.56283 − 7.92150I
u = −0.04829 + 1.42979I
a = −0.260226 − 0.088772I
b = −0.791245 + 1.038880I
−1.01122 + 4.32869I 14.3327 − 16.3128I
u = −0.04829 + 1.42979I
a = −0.189652 − 0.006595I
b = 0.054727 − 0.250321I
−1.01122 + 4.32869I 14.3327 − 16.3128I
u = −0.04829 − 1.42979I
a = −0.260226 + 0.088772I
b = −0.791245 − 1.038880I
−1.01122 − 4.32869I 14.3327 + 16.3128I
u = −0.04829 − 1.42979I
a = −0.189652 + 0.006595I
b = 0.054727 + 0.250321I
−1.01122 − 4.32869I 14.3327 + 16.3128I
u = −0.520258 + 0.093250I
a = −0.041004 + 0.846052I
b = −1.230390 + 0.458040I
−0.47186 + 6.58662I 8.10608 − 10.95891I
u = −0.520258 + 0.093250I
a = 1.49677 + 5.60060I
b = 0.306332 − 0.620019I
−0.47186 + 6.58662I 8.10608 − 10.95891I
26
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.520258 − 0.093250I
a = −0.041004 − 0.846052I
b = −1.230390 − 0.458040I
−0.47186 − 6.58662I 8.10608 + 10.95891I
u = −0.520258 − 0.093250I
a = 1.49677 − 5.60060I
b = 0.306332 + 0.620019I
−0.47186 − 6.58662I 8.10608 + 10.95891I
u = 0.487341
a = 0.79184 + 2.17616I
b = 0.928806 − 0.477456I
−3.02932 −4.83040
u = 0.487341
a = 0.79184 − 2.17616I
b = 0.928806 + 0.477456I
−3.02932 −4.83040
27
IV.
I
u
4
= h−u
3
+u
2
+b−1, −2u
4
+2u
3
+u
2
+a−2u−2, u
5
−u
4
−u
3
+2u
2
+u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
3
=
u
−u
3
+ u
a
11
=
2u
4
− 2u
3
− u
2
+ 2u + 2
u
3
− u
2
+ 1
a
7
=
2u
4
− 4u
2
+ 3u + 5
u
4
− u
3
− u
2
+ u + 1
a
4
=
−3u
4
+ u
3
+ 4u
2
− 3u − 5
−u
4
+ u
2
− u − 1
a
10
=
2u
4
− u
3
− 2u
2
+ 2u + 3
u
3
− u
2
+ 1
a
8
=
u
4
− 2u
2
+ u + 3
u
3
− 2u
2
+ 1
a
1
=
3u
4
− 2u
3
− 3u
2
+ 4u + 4
u
4
− u
3
+ u + 1
a
9
=
2u
4
− u
3
− 2u
2
+ 2u + 3
u
3
− u
2
+ 1
a
9
=
2u
4
− u
3
− 2u
2
+ 2u + 3
u
3
− u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −11u
4
+ 9u
3
+ 3u
2
− 18u − 5
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
+ u
4
− 2u
3
− u
2
+ u + 1
c
2
u
5
+ u
4
− u
3
− 2u
2
+ u + 1
c
3
u
5
+ u
3
+ 2u
2
+ 1
c
4
u
5
+ u
3
− 2u
2
− 1
c
5
u
5
− u
4
− u
3
+ 2u
2
+ u − 1
c
6
u
5
− u
4
− 2u
3
+ u
2
+ u − 1
c
7
u
5
+ 4u
4
+ 4u
3
− u
2
− 2u − 1
c
8
u
5
+ 2u
3
− u
2
− 1
c
9
u
5
c
10
u
5
+ 2u
3
+ u
2
+ 1
c
11
u
5
− 4u
4
+ 4u
3
+ u
2
− 2u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
5
− 5y
4
+ 8y
3
− 7y
2
+ 3y −1
c
2
, c
5
y
5
− 3y
4
+ 7y
3
− 8y
2
+ 5y −1
c
3
, c
4
y
5
+ 2y
4
+ y
3
− 4y
2
− 4y −1
c
7
, c
11
y
5
− 8y
4
+ 20y
3
− 9y
2
+ 2y −1
c
8
, c
10
y
5
+ 4y
4
+ 4y
3
− y
2
− 2y −1
c
9
y
5
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.904429 + 0.339760I
a = 0.57355 − 2.02208I
b = −0.12916 + 1.40912I
4.86920 − 1.42206I 8.27331 + 8.69048I
u = −0.904429 − 0.339760I
a = 0.57355 + 2.02208I
b = −0.12916 − 1.40912I
4.86920 + 1.42206I 8.27331 − 8.69048I
u = 1.116850 + 0.784420I
a = −0.402467 − 0.658928I
b = −0.300574 + 0.700535I
1.84330 + 3.45949I 0.15254 − 11.15264I
u = 1.116850 − 0.784420I
a = −0.402467 + 0.658928I
b = −0.300574 − 0.700535I
1.84330 − 3.45949I 0.15254 + 11.15264I
u = 0.575152
a = 2.65784
b = 0.859460
−3.55538 −13.8520
31
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
+ u
4
− 2u
3
− u
2
+ u + 1)(u
24
− 5u
22
+ ··· + 36u + 12)
· (u
31
− 7u
30
+ ··· + 96u − 12)(u
100
+ 5u
99
+ ··· − 169334u + 14149)
c
2
(u
5
+ u
4
− u
3
− 2u
2
+ u + 1)
· (u
12
− 2u
10
− u
8
+ 8u
6
+ 2u
5
− 10u
4
− 5u
3
+ 6u
2
+ u − 1)
2
· (u
31
− 4u
30
+ ··· + 50u − 28)(u
50
+ u
49
+ ··· + 53u
2
− 5)
2
c
3
(u
5
+ u
3
+ 2u
2
+ 1)(u
24
+ 5u
23
+ ··· − 11u
2
− 3)(u
31
− 2u
30
+ ··· − 9u + 3)
· (u
100
− 6u
99
+ ··· + 6u − 1)
c
4
(u
5
+ u
3
− 2u
2
− 1)(u
24
− 5u
23
+ ··· − 11u
2
− 3)(u
31
− 2u
30
+ ··· − 9u + 3)
· (u
100
− 6u
99
+ ··· + 6u − 1)
c
5
(u
5
− u
4
− u
3
+ 2u
2
+ u − 1)
· (u
12
− 2u
10
− u
8
+ 8u
6
− 2u
5
− 10u
4
+ 5u
3
+ 6u
2
− u − 1)
2
· (u
31
− 4u
30
+ ··· + 50u − 28)(u
50
+ u
49
+ ··· + 53u
2
− 5)
2
c
6
(u
5
− u
4
− 2u
3
+ u
2
+ u − 1)(u
24
− 5u
22
+ ··· − 36u + 12)
· (u
31
− 7u
30
+ ··· + 96u − 12)(u
100
+ 5u
99
+ ··· − 169334u + 14149)
c
7
(u
5
+ 4u
4
+ 4u
3
− u
2
− 2u − 1)(u
24
+ 3u
23
+ ··· − u + 1)
· (u
31
− 4u
30
+ ··· − 3u − 1)(u
100
− 2u
99
+ ··· + 37u − 1)
c
8
9(u
5
+ 2u
3
− u
2
− 1)(3u
24
+ 3u
23
+ ··· + 2u − 1)
· (3u
31
− 6u
30
+ ··· + 5u − 1)(u
100
− 10u
98
+ ··· + 18u − 1)
c
9
9u
5
(3u
24
− 16u
22
+ ··· + 343u
2
− 137)
· (3u
31
+ 9u
30
+ ··· + 832u + 128)(u
50
− 2u
49
+ ··· + 21u + 49)
2
c
10
9(u
5
+ 2u
3
+ u
2
+ 1)(3u
24
− 3u
23
+ ··· − 2u − 1)
· (3u
31
− 6u
30
+ ··· + 5u − 1)(u
100
− 10u
98
+ ··· + 18u − 1)
c
11
(u
5
− 4u
4
+ 4u
3
+ u
2
− 2u + 1)(u
24
− 3u
23
+ ··· + u + 1)
· (u
31
− 4u
30
+ ··· − 3u − 1)(u
100
− 2u
99
+ ··· + 37u − 1)
32
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
5
− 5y
4
+ 8y
3
− 7y
2
+ 3y −1)(y
24
− 10y
23
+ ··· + 192y + 144)
· (y
31
+ 5y
30
+ ··· − 1776y −144)
· (y
100
− 3y
99
+ ··· + 8842579308y + 200194201)
c
2
, c
5
(y
5
− 3y
4
+ 7y
3
− 8y
2
+ 5y −1)(y
12
− 4y
11
+ ··· − 13y + 1)
2
· (y
31
− 12y
30
+ ··· − 7860y −784)(y
50
− 27y
49
+ ··· − 530y + 25)
2
c
3
, c
4
(y
5
+ 2y
4
+ y
3
− 4y
2
− 4y −1)(y
24
− 9y
23
+ ··· + 66y + 9)
· (y
31
− 6y
30
+ ··· + 51y −9)(y
100
+ 12y
99
+ ··· + 44y + 1)
c
7
, c
11
(y
5
− 8y
4
+ 20y
3
− 9y
2
+ 2y −1)(y
24
− 3y
23
+ ··· − 5y + 1)
· (y
31
+ 2y
30
+ ··· + 3y −1)(y
100
− 16y
99
+ ··· − 3373y + 1)
c
8
, c
10
81(y
5
+ 4y
4
+ ··· − 2y −1)(9y
24
− 33y
23
+ ··· + 24y + 1)
· (9y
31
+ 120y
30
+ ··· + 9y −1)(y
100
− 20y
99
+ ··· + 154y + 1)
c
9
81y
5
(3y
12
− 16y
11
+ ··· + 343y −137)
2
· (9y
31
+ 57y
30
+ ··· + 331776y −16384)
· (y
50
− 28y
49
+ ··· − 46305y + 2401)
2
33
