11a
350
(K11a
350
)
A knot diagram
1
Linearized knot diagam
6 5 1 11 9 10 4 3 2 7 8
Solving Sequence
2,9 6,10
7 1 5 3 4 8 11
c
9
c
6
c
1
c
5
c
2
c
3
c
8
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.21880 × 10
22
u
23
− 1.45306 × 10
23
u
22
+ ··· + 1.84096 × 10
22
b − 1.77351 × 10
21
,
1.69641 × 10
22
u
23
+ 1.16788 × 10
23
u
22
+ ··· + 1.84096 × 10
22
a + 9.02386 × 10
22
, u
24
+ 5u
23
+ ··· + 5u + 1i
I
u
2
= h−6.31384 × 10
394
u
89
+ 6.92476 × 10
394
u
88
+ ··· + 7.51178 × 10
396
b − 8.98383 × 10
397
,
− 1.55103 × 10
397
u
89
− 2.32083 × 10
398
u
88
+ ··· + 5.23571 × 10
399
a + 6.11690 × 10
401
,
u
90
+ 13u
88
+ ··· − 2331u − 697i
I
u
3
= h596388417531502u
19
− 535727113968989u
18
+ ··· + 1506447924749558b − 1004384011943253,
1534485576412749u
19
+ 1924336217084222u
18
+ ··· + 1506447924749558a + 5029781266974281,
u
20
+ 12u
18
+ ··· + 2u + 1i
I
u
4
= hu
3
+ u
2
+ b − u − 1, −u
3
− u
2
+ a + 2u + 1, u
4
+ u
3
− u
2
− u − 1i
I
u
5
= hb + u, a − u − 1, u
2
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 140 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−3.22×10
22
u
23
−1.45×10
23
u
22
+· · ·+1.84×10
22
b−1.77×10
21
, 1.70×
10
22
u
23
+1.17×10
23
u
22
+· · ·+1.84×10
22
a+9.02×10
22
, u
24
+5u
23
+· · ·+5u+1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
6
=
−0.921482u
23
− 6.34386u
22
+ ··· − 16.1753u − 4.90172
1.74844u
23
+ 7.89293u
22
+ ··· + 5.65599u + 0.0963361
a
10
=
1
u
2
a
7
=
−0.803405u
23
− 6.36897u
22
+ ··· − 20.1230u − 6.54183
1.95379u
23
+ 9.10729u
22
+ ··· + 8.61541u + 0.711836
a
1
=
5.52017u
23
+ 30.5886u
22
+ ··· + 53.7538u + 10.3116
−4.04248u
23
− 19.7310u
22
+ ··· − 22.7797u − 4.62275
a
5
=
0.826954u
23
+ 1.54907u
22
+ ··· − 10.5193u − 4.80538
1.74844u
23
+ 7.89293u
22
+ ··· + 5.65599u + 0.0963361
a
3
=
0.624051u
23
+ 5.42049u
22
+ ··· + 12.4325u + 0.988234
−0.853640u
23
− 5.43714u
22
+ ··· − 16.5416u − 4.70063
a
4
=
−9.64576u
23
− 47.9185u
22
+ ··· − 65.9753u − 12.2608
1.74443u
23
+ 8.33782u
22
+ ··· + 5.56945u + 0.493106
a
8
=
−0.493106u
23
− 0.721096u
22
+ ··· + 15.8450u + 3.10392
1.56945u
23
+ 6.25870u
22
+ ··· + 0.386352u − 1.03260
a
11
=
2.20692u
23
+ 13.4346u
22
+ ··· + 38.8975u + 9.36897
−1.36287u
23
− 5.75236u
22
+ ··· + 2.19259u + 1.11471
a
11
=
2.20692u
23
+ 13.4346u
22
+ ··· + 38.8975u + 9.36897
−1.36287u
23
− 5.75236u
22
+ ··· + 2.19259u + 1.11471
(ii) Obstruction class = −1
(iii) Cusp Shapes =
504150061088705768350224
18409584491066375925047
u
23
+
2533975755434351329384291
18409584491066375925047
u
22
+ ··· +
2937396997691488250591708
18409584491066375925047
u +
478043081351450205457199
18409584491066375925047
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
24
+ 5u
23
+ ··· + 8u + 1
c
2
, c
3
u
24
+ 3u
23
+ ··· + 3u + 1
c
5
, c
11
u
24
+ u
23
+ ··· + 7u + 1
c
6
, c
10
u
24
− 2u
23
+ ··· − 106u + 36
c
7
, c
9
u
24
− 5u
23
+ ··· − 5u + 1
c
8
u
24
− u
23
+ ··· + 320u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
24
− 7y
23
+ ··· − 6y + 1
c
2
, c
3
y
24
+ 3y
23
+ ··· + 27y + 1
c
5
, c
11
y
24
+ 7y
23
+ ··· − 29y + 1
c
6
, c
10
y
24
− 12y
23
+ ··· + 9860y + 1296
c
7
, c
9
y
24
− 21y
23
+ ··· − 5y + 1
c
8
y
24
− 23y
23
+ ··· + 30720y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.948562 + 0.118544I
a = 0.386832 − 0.880975I
b = 0.589066 − 0.233963I
−2.99609 + 1.94907I −10.80827 − 2.58369I
u = 0.948562 − 0.118544I
a = 0.386832 + 0.880975I
b = 0.589066 + 0.233963I
−2.99609 − 1.94907I −10.80827 + 2.58369I
u = −0.397178 + 0.844071I
a = −0.65338 + 1.54955I
b = 0.017160 − 0.636778I
5.31187 + 3.98651I 5.66668 − 8.11376I
u = −0.397178 − 0.844071I
a = −0.65338 − 1.54955I
b = 0.017160 + 0.636778I
5.31187 − 3.98651I 5.66668 + 8.11376I
u = −0.897247 + 0.630246I
a = −0.175373 − 0.678747I
b = −0.458367 + 1.128800I
1.59590 + 4.68195I 5.09129 − 10.67393I
u = −0.897247 − 0.630246I
a = −0.175373 + 0.678747I
b = −0.458367 − 1.128800I
1.59590 − 4.68195I 5.09129 + 10.67393I
u = 0.669369 + 0.399651I
a = 0.199150 + 0.717971I
b = −1.22208 − 1.31312I
−0.94261 − 4.71787I −11.6555 + 14.8007I
u = 0.669369 − 0.399651I
a = 0.199150 − 0.717971I
b = −1.22208 + 1.31312I
−0.94261 + 4.71787I −11.6555 − 14.8007I
u = −0.275157 + 0.682551I
a = −0.34003 − 1.57031I
b = 1.02362 + 1.39590I
5.80334 + 2.74033I 15.5158 − 11.8363I
u = −0.275157 − 0.682551I
a = −0.34003 + 1.57031I
b = 1.02362 − 1.39590I
5.80334 − 2.74033I 15.5158 + 11.8363I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.284422 + 0.660333I
a = −0.05560 − 2.91538I
b = 0.124798 + 1.311920I
5.07438 + 1.59386I 2.13582 − 1.10254I
u = −0.284422 − 0.660333I
a = −0.05560 + 2.91538I
b = 0.124798 − 1.311920I
5.07438 − 1.59386I 2.13582 + 1.10254I
u = −0.913544 + 0.934068I
a = −0.137387 + 0.975627I
b = 1.23496 − 1.04677I
−2.20266 + 13.23270I −2.28061 − 10.36959I
u = −0.913544 − 0.934068I
a = −0.137387 − 0.975627I
b = 1.23496 + 1.04677I
−2.20266 − 13.23270I −2.28061 + 10.36959I
u = 0.219244 + 0.655965I
a = 0.641636 + 0.616523I
b = −0.138317 − 0.535445I
0.112664 − 1.342820I 0.96375 + 5.78549I
u = 0.219244 − 0.655965I
a = 0.641636 − 0.616523I
b = −0.138317 + 0.535445I
0.112664 + 1.342820I 0.96375 − 5.78549I
u = 0.95916 + 1.28491I
a = 0.109942 + 1.076420I
b = −1.19384 − 1.00053I
3.9513 − 19.3243I 0.92200 + 10.02171I
u = 0.95916 − 1.28491I
a = 0.109942 − 1.076420I
b = −1.19384 + 1.00053I
3.9513 + 19.3243I 0.92200 − 10.02171I
u = −0.315740 + 0.142853I
a = −1.62304 + 1.34024I
b = −0.873029 + 0.698246I
0.03065 + 2.94504I −0.62404 − 2.53282I
u = −0.315740 − 0.142853I
a = −1.62304 − 1.34024I
b = −0.873029 − 0.698246I
0.03065 − 2.94504I −0.62404 + 2.53282I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.99393 + 1.39275I
a = −0.078356 − 0.752209I
b = 0.690199 + 0.960956I
7.26188 − 10.39510I 4.97109 + 9.26898I
u = 0.99393 − 1.39275I
a = −0.078356 + 0.752209I
b = 0.690199 − 0.960956I
7.26188 + 10.39510I 4.97109 − 9.26898I
u = −1.80800
a = −0.491944
b = −0.412432
0.0704593 10.7550
u = −4.60596
a = −0.0568603
b = −0.175899
−0.0136435 0
7
II. I
u
2
= h−6.31 × 10
394
u
89
+ 6.92 × 10
394
u
88
+ · · · + 7.51 × 10
396
b − 8.98 ×
10
397
, −1.55 × 10
397
u
89
− 2.32 × 10
398
u
88
+ · · · + 5.24 × 10
399
a + 6.12 ×
10
401
, u
90
+ 13u
88
+ · · · − 2331u − 697i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
6
=
0.00296240u
89
+ 0.0443270u
88
+ ··· − 438.837u − 116.830
0.00840525u
89
− 0.00921854u
88
+ ··· + 35.0495u + 11.9597
a
10
=
1
u
2
a
7
=
0.00615108u
89
+ 0.0463311u
88
+ ··· − 509.179u − 135.767
0.00721730u
89
− 0.00830298u
88
+ ··· + 41.9437u + 13.3565
a
1
=
−0.0981362u
89
+ 0.00893073u
88
+ ··· − 111.972u − 57.6678
−0.00924215u
89
− 0.00377916u
88
+ ··· + 55.6357u + 10.3743
a
5
=
0.0113676u
89
+ 0.0351084u
88
+ ··· − 403.788u − 104.871
0.00840525u
89
− 0.00921854u
88
+ ··· + 35.0495u + 11.9597
a
3
=
−0.0987547u
89
+ 0.00556089u
88
+ ··· − 75.5358u − 48.4670
0.00862368u
89
+ 0.000409326u
88
+ ··· − 17.1997u − 1.17357
a
4
=
0.0318351u
89
+ 0.0633408u
88
+ ··· − 419.152u − 85.0975
0.00355555u
89
+ 0.00998720u
88
+ ··· − 106.546u − 27.9283
a
8
=
0.00442432u
89
− 0.0678970u
88
+ ··· + 531.689u + 122.167
−0.0153682u
89
+ 0.0121057u
88
+ ··· − 37.2591u − 23.9882
a
11
=
0.00232107u
89
− 0.0476243u
88
+ ··· + 401.540u + 95.0377
−0.0139733u
89
+ 0.0135534u
88
+ ··· − 50.8930u − 27.4980
a
11
=
0.00232107u
89
− 0.0476243u
88
+ ··· + 401.540u + 95.0377
−0.0139733u
89
+ 0.0135534u
88
+ ··· − 50.8930u − 27.4980
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0316762u
89
− 0.0348001u
88
+ ··· + 220.805u + 45.4124
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
90
− 4u
89
+ ··· − 679u − 263
c
2
, c
3
u
90
− u
89
+ ··· − 675u + 103
c
5
, c
11
u
90
− 8u
88
+ ··· − 22u − 1
c
6
, c
10
(u
45
− 20u
43
+ ··· + 189u + 108)
2
c
7
, c
9
u
90
+ 13u
88
+ ··· + 2331u − 697
c
8
(u
45
− 2u
44
+ ··· − 45u − 9)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
90
− 20y
89
+ ··· − 4190907y + 69169
c
2
, c
3
y
90
− 7y
89
+ ··· + 296069y + 10609
c
5
, c
11
y
90
− 16y
89
+ ··· − 90y + 1
c
6
, c
10
(y
45
− 40y
44
+ ··· − 36207y −11664)
2
c
7
, c
9
y
90
+ 26y
89
+ ··· + 21978055y + 485809
c
8
(y
45
+ 20y
44
+ ··· + 2871y −81)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650238 + 0.770616I
a = 0.756665 + 0.325666I
b = −0.157441 + 0.051744I
0.40566 − 1.48274I 0
u = 0.650238 − 0.770616I
a = 0.756665 − 0.325666I
b = −0.157441 − 0.051744I
0.40566 + 1.48274I 0
u = 0.408621 + 0.900284I
a = 0.240008 + 0.792608I
b = −0.439265 − 0.984349I
0.40566 − 1.48274I 0
u = 0.408621 − 0.900284I
a = 0.240008 − 0.792608I
b = −0.439265 + 0.984349I
0.40566 + 1.48274I 0
u = 0.167555 + 0.950964I
a = 0.199750 + 0.931839I
b = 0.748689 − 1.189060I
2.94180 − 3.09675I 0
u = 0.167555 − 0.950964I
a = 0.199750 − 0.931839I
b = 0.748689 + 1.189060I
2.94180 + 3.09675I 0
u = −0.943877 + 0.072123I
a = 0.147334 + 0.330453I
b = −1.035640 + 0.455649I
0.30613 + 2.93570I 0
u = −0.943877 − 0.072123I
a = 0.147334 − 0.330453I
b = −1.035640 − 0.455649I
0.30613 − 2.93570I 0
u = 0.332333 + 0.878248I
a = 0.071797 − 1.263730I
b = −0.82943 + 1.43522I
5.23865 − 10.99060I 0
u = 0.332333 − 0.878248I
a = 0.071797 + 1.263730I
b = −0.82943 − 1.43522I
5.23865 + 10.99060I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.479257 + 0.791392I
a = −0.235215 − 0.687665I
b = 1.111250 + 0.451162I
4.85797 0
u = −0.479257 − 0.791392I
a = −0.235215 + 0.687665I
b = 1.111250 − 0.451162I
4.85797 0
u = −0.220217 + 0.884440I
a = 0.15511 + 1.68010I
b = −0.58091 − 1.47300I
6.04090 + 0.51555I 0
u = −0.220217 − 0.884440I
a = 0.15511 − 1.68010I
b = −0.58091 + 1.47300I
6.04090 − 0.51555I 0
u = 0.822790 + 0.362700I
a = −1.40778 + 1.95155I
b = −0.554046 − 0.042311I
2.29876 − 9.05121I 0
u = 0.822790 − 0.362700I
a = −1.40778 − 1.95155I
b = −0.554046 + 0.042311I
2.29876 + 9.05121I 0
u = −0.314482 + 1.066300I
a = 1.03414 − 1.04256I
b = −0.308181 + 0.222493I
3.71252 + 2.09738I 0
u = −0.314482 − 1.066300I
a = 1.03414 + 1.04256I
b = −0.308181 − 0.222493I
3.71252 − 2.09738I 0
u = 0.080321 + 1.117670I
a = −0.201246 − 0.404214I
b = −1.095680 + 0.447288I
6.00576 + 5.14134I 0
u = 0.080321 − 1.117670I
a = −0.201246 + 0.404214I
b = −1.095680 − 0.447288I
6.00576 − 5.14134I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.805949 + 0.810035I
a = −0.097220 − 0.859841I
b = −1.21296 + 1.00009I
−1.98063 + 6.23670I 0
u = −0.805949 − 0.810035I
a = −0.097220 + 0.859841I
b = −1.21296 − 1.00009I
−1.98063 − 6.23670I 0
u = 0.495841 + 1.030740I
a = −0.330084 − 0.914528I
b = 1.37807 + 0.85563I
0.29490 − 6.42715I 0
u = 0.495841 − 1.030740I
a = −0.330084 + 0.914528I
b = 1.37807 − 0.85563I
0.29490 + 6.42715I 0
u = 0.844655 + 0.809311I
a = 0.278227 + 0.876838I
b = −1.09471 − 1.01763I
−0.06231 − 4.05987I 0
u = 0.844655 − 0.809311I
a = 0.278227 − 0.876838I
b = −1.09471 + 1.01763I
−0.06231 + 4.05987I 0
u = −0.202911 + 0.802221I
a = −1.83281 + 0.37418I
b = −0.152437 + 0.165462I
5.61745 + 4.44792I 7.47292 − 6.68943I
u = −0.202911 − 0.802221I
a = −1.83281 − 0.37418I
b = −0.152437 − 0.165462I
5.61745 − 4.44792I 7.47292 + 6.68943I
u = 0.512233 + 0.648024I
a = −1.50983 + 1.35329I
b = −0.486815 − 0.769300I
0.29490 − 6.42715I 2.19076 + 11.02163I
u = 0.512233 − 0.648024I
a = −1.50983 − 1.35329I
b = −0.486815 + 0.769300I
0.29490 + 6.42715I 2.19076 − 11.02163I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.543413 + 0.608268I
a = −0.392565 + 0.981854I
b = 1.43853 − 0.71161I
−2.54435 − 3.08820I −4.24618 + 0.I
u = −0.543413 − 0.608268I
a = −0.392565 − 0.981854I
b = 1.43853 + 0.71161I
−2.54435 + 3.08820I −4.24618 + 0.I
u = 1.20673
a = 1.28610
b = 0.717017
−1.80906 0
u = −0.278683 + 0.741266I
a = −0.13737 + 2.72634I
b = 0.069665 − 1.049730I
6.04090 − 0.51555I 9.73034 + 2.24226I
u = −0.278683 − 0.741266I
a = −0.13737 − 2.72634I
b = 0.069665 + 1.049730I
6.04090 + 0.51555I 9.73034 − 2.24226I
u = 0.771121 + 0.933795I
a = 0.555560 + 0.322667I
b = −0.982231 + 0.006479I
−2.49917 − 2.89475I 0
u = 0.771121 − 0.933795I
a = 0.555560 − 0.322667I
b = −0.982231 − 0.006479I
−2.49917 + 2.89475I 0
u = 0.808260 + 0.907026I
a = 0.152451 + 1.230970I
b = −1.070580 − 0.882803I
−2.54435 − 3.08820I 0
u = 0.808260 − 0.907026I
a = 0.152451 − 1.230970I
b = −1.070580 + 0.882803I
−2.54435 + 3.08820I 0
u = 0.879902 + 0.854615I
a = 0.47163 − 1.38129I
b = 0.927006 + 0.876019I
−0.07742 − 6.14163I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.879902 − 0.854615I
a = 0.47163 + 1.38129I
b = 0.927006 − 0.876019I
−0.07742 + 6.14163I 0
u = −0.507872 + 0.568783I
a = −0.138139 − 1.370140I
b = −1.14598 + 0.87377I
−2.49917 + 2.89475I −6.29512 − 4.04782I
u = −0.507872 − 0.568783I
a = −0.138139 + 1.370140I
b = −1.14598 − 0.87377I
−2.49917 − 2.89475I −6.29512 + 4.04782I
u = 0.019987 + 0.705680I
a = 0.371096 + 0.660404I
b = 1.47903 − 0.84955I
5.20109 − 3.69707I 17.8159 + 11.7922I
u = 0.019987 − 0.705680I
a = 0.371096 − 0.660404I
b = 1.47903 + 0.84955I
5.20109 + 3.69707I 17.8159 − 11.7922I
u = −0.698365 + 0.048277I
a = −0.773970 − 1.130590I
b = −0.867504 − 0.055181I
−3.31934 − 1.40971I −9.63872 + 4.90184I
u = −0.698365 − 0.048277I
a = −0.773970 + 1.130590I
b = −0.867504 + 0.055181I
−3.31934 + 1.40971I −9.63872 − 4.90184I
u = 1.043390 + 0.776682I
a = −0.022328 − 0.666893I
b = 0.654441 + 0.081485I
−3.31934 − 1.40971I 0
u = 1.043390 − 0.776682I
a = −0.022328 + 0.666893I
b = 0.654441 − 0.081485I
−3.31934 + 1.40971I 0
u = −0.619879 + 1.143890I
a = −0.277737 + 1.211450I
b = 0.596383 − 0.931606I
5.61745 + 4.44792I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.619879 − 1.143890I
a = −0.277737 − 1.211450I
b = 0.596383 + 0.931606I
5.61745 − 4.44792I 0
u = 0.937741 + 0.997672I
a = −0.028921 − 0.696492I
b = 1.119420 + 0.654833I
−2.70611 − 5.73656I 0
u = 0.937741 − 0.997672I
a = −0.028921 + 0.696492I
b = 1.119420 − 0.654833I
−2.70611 + 5.73656I 0
u = −0.535466 + 0.312111I
a = 0.05537 + 2.59522I
b = 0.690775 − 0.155367I
−2.70611 + 5.73656I −9.46948 − 10.34279I
u = −0.535466 − 0.312111I
a = 0.05537 − 2.59522I
b = 0.690775 + 0.155367I
−2.70611 − 5.73656I −9.46948 + 10.34279I
u = 0.002400 + 0.566715I
a = 0.77472 − 1.75994I
b = 1.22053 + 0.73355I
3.71252 − 2.09738I 4.75808 + 1.45431I
u = 0.002400 − 0.566715I
a = 0.77472 + 1.75994I
b = 1.22053 − 0.73355I
3.71252 + 2.09738I 4.75808 − 1.45431I
u = 0.115651 + 0.545467I
a = 1.73050 + 4.15726I
b = 0.262196 − 0.749851I
3.90289 + 8.93089I 8.55811 − 8.07031I
u = 0.115651 − 0.545467I
a = 1.73050 − 4.15726I
b = 0.262196 + 0.749851I
3.90289 − 8.93089I 8.55811 + 8.07031I
u = −0.71086 + 1.28822I
a = 0.329302 − 1.195740I
b = −1.29161 + 0.99015I
3.90289 + 8.93089I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.71086 − 1.28822I
a = 0.329302 + 1.195740I
b = −1.29161 − 0.99015I
3.90289 − 8.93089I 0
u = 0.207589 + 0.469922I
a = 0.440453 − 1.118780I
b = 0.22781 + 1.73405I
−0.06231 + 4.05987I 8.44249 + 0.74405I
u = 0.207589 − 0.469922I
a = 0.440453 + 1.118780I
b = 0.22781 − 1.73405I
−0.06231 − 4.05987I 8.44249 − 0.74405I
u = 0.87421 + 1.20478I
a = −0.175207 + 0.280416I
b = 0.516903 − 0.721613I
0.581066 − 0.443460I 0
u = 0.87421 − 1.20478I
a = −0.175207 − 0.280416I
b = 0.516903 + 0.721613I
0.581066 + 0.443460I 0
u = −0.96765 + 1.13256I
a = 0.185823 + 1.017500I
b = 0.747500 − 0.778618I
6.00576 + 5.14134I 0
u = −0.96765 − 1.13256I
a = 0.185823 − 1.017500I
b = 0.747500 + 0.778618I
6.00576 − 5.14134I 0
u = −1.01755 + 1.10772I
a = −0.530821 + 0.238018I
b = 0.547374 + 0.283554I
−1.98063 − 6.23670I 0
u = −1.01755 − 1.10772I
a = −0.530821 − 0.238018I
b = 0.547374 − 0.283554I
−1.98063 + 6.23670I 0
u = −0.89064 + 1.22962I
a = −0.162880 + 1.145870I
b = 1.10718 − 1.02496I
5.23865 + 10.99060I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.89064 − 1.22962I
a = −0.162880 − 1.145870I
b = 1.10718 + 1.02496I
5.23865 − 10.99060I 0
u = −0.23191 + 1.52682I
a = −0.908745 + 0.223836I
b = 1.057010 − 0.093518I
−0.07742 + 6.14163I 0
u = −0.23191 − 1.52682I
a = −0.908745 − 0.223836I
b = 1.057010 + 0.093518I
−0.07742 − 6.14163I 0
u = −1.53129 + 0.40027I
a = −0.317759 + 0.118389I
b = 0.671617 + 0.211972I
2.94180 − 3.09675I 0
u = −1.53129 − 0.40027I
a = −0.317759 − 0.118389I
b = 0.671617 − 0.211972I
2.94180 + 3.09675I 0
u = −0.072897 + 0.360777I
a = −3.76410 − 0.79251I
b = −0.782879 + 0.479956I
0.30613 + 2.93570I −3.28195 − 5.62494I
u = −0.072897 − 0.360777I
a = −3.76410 + 0.79251I
b = −0.782879 − 0.479956I
0.30613 − 2.93570I −3.28195 + 5.62494I
u = 1.01061 + 1.30844I
a = −0.020694 − 0.902939I
b = 1.12727 + 0.93260I
1.78184 − 10.59480I 0
u = 1.01061 − 1.30844I
a = −0.020694 + 0.902939I
b = 1.12727 − 0.93260I
1.78184 + 10.59480I 0
u = −0.91660 + 1.45408I
a = 0.243376 − 0.843960I
b = −1.181200 + 0.693134I
2.29876 + 9.05121I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.91660 − 1.45408I
a = 0.243376 + 0.843960I
b = −1.181200 − 0.693134I
2.29876 − 9.05121I 0
u = −1.12939 + 1.35997I
a = 0.067763 − 0.640668I
b = −0.324632 + 0.690984I
5.20109 + 3.69707I 0
u = −1.12939 − 1.35997I
a = 0.067763 + 0.640668I
b = −0.324632 − 0.690984I
5.20109 − 3.69707I 0
u = 1.03662 + 1.44950I
a = −0.031756 + 0.678698I
b = −0.749926 − 0.792086I
7.04800 0
u = 1.03662 − 1.44950I
a = −0.031756 − 0.678698I
b = −0.749926 + 0.792086I
7.04800 0
u = 0.16533 + 1.80552I
a = 0.453269 + 0.136736I
b = −0.559676 − 0.331227I
0.581066 − 0.443460I 0
u = 0.16533 − 1.80552I
a = 0.453269 − 0.136736I
b = −0.559676 + 0.331227I
0.581066 + 0.443460I 0
u = −1.86135
a = 0.0776973
b = −0.886595
−1.80906 0
u = 1.75907 + 0.63951I
a = 0.258182 + 0.057089I
b = −0.710115 + 0.370499I
1.78184 + 10.59480I 0
u = 1.75907 − 0.63951I
a = 0.258182 − 0.057089I
b = −0.710115 − 0.370499I
1.78184 − 10.59480I 0
19
III. I
u
3
=
h5.96×10
14
u
19
−5.36×10
14
u
18
+· · ·+1.51×10
15
b−1.00×10
15
, 1.53×10
15
u
19
+
1.92 × 10
15
u
18
+ · · · + 1.51 × 10
15
a + 5.03 × 10
15
, u
20
+ 12u
18
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
6
=
−1.01861u
19
− 1.27740u
18
+ ··· − 5.07547u − 3.33884
−0.395890u
19
+ 0.355623u
18
+ ··· + 1.23689u + 0.666723
a
10
=
1
u
2
a
7
=
−1.92033u
19
− 1.39243u
18
+ ··· − 7.41199u − 3.94951
0.119275u
19
+ 0.322928u
18
+ ··· + 2.36868u + 0.781758
a
1
=
−0.994920u
19
+ 0.133507u
18
+ ··· − 3.85818u − 0.674866
1.19786u
19
− 0.0805278u
18
+ ··· + 2.43384u + 0.215007
a
5
=
−1.41450u
19
− 0.921777u
18
+ ··· − 3.83858u − 2.67211
−0.395890u
19
+ 0.355623u
18
+ ··· + 1.23689u + 0.666723
a
3
=
0.582346u
19
− 0.487299u
18
+ ··· − 4.07779u − 1.99593
0.379409u
19
− 0.540279u
18
+ ··· − 0.653451u − 1.53607
a
4
=
1.45889u
19
− 0.856046u
18
+ ··· − 1.97045u − 2.21037
−0.484579u
19
+ 0.200367u
18
+ ··· − 0.958662u − 0.230371
a
8
=
2.21910u
19
− 0.232443u
18
+ ··· + 3.29375u − 0.788977
0.178004u
19
− 0.943332u
18
+ ··· − 2.46348u − 1.43324
a
11
=
1.23993u
19
+ 0.574971u
18
+ ··· + 6.71591u + 2.81437
1.32381u
19
− 0.320403u
18
+ ··· + 1.10373u + 1.23049
a
11
=
1.23993u
19
+ 0.574971u
18
+ ··· + 6.71591u + 2.81437
1.32381u
19
− 0.320403u
18
+ ··· + 1.10373u + 1.23049
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
235193652872256
107603423196397
u
19
−
104114497130576
107603423196397
u
18
+ ··· −
543023431340064
107603423196397
u −
204719139518847
107603423196397
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− u
19
+ ··· + 5u + 1
c
2
u
20
− 3u
19
+ ··· + 2u + 1
c
3
u
20
+ 3u
19
+ ··· − 2u + 1
c
4
u
20
+ u
19
+ ··· − 5u + 1
c
5
u
20
+ u
18
+ ··· − u + 1
c
6
(u
10
− 3u
8
+ 2u
7
− 8u
5
+ 9u
4
+ 9u
3
− 5u
2
− 4u − 2)
2
c
7
u
20
+ 12u
18
+ ··· − 2u + 1
c
8
u
20
+ 13u
18
+ ··· + 366u
2
+ 113
c
9
u
20
+ 12u
18
+ ··· + 2u + 1
c
10
(u
10
− 3u
8
− 2u
7
+ 8u
5
+ 9u
4
− 9u
3
− 5u
2
+ 4u − 2)
2
c
11
u
20
+ u
18
+ ··· + u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
20
− 13y
19
+ ··· + 11y + 1
c
2
, c
3
y
20
− 5y
19
+ ··· − 6y + 1
c
5
, c
11
y
20
+ 2y
19
+ ··· + 19y + 1
c
6
, c
10
(y
10
− 6y
9
+ ··· + 4y + 4)
2
c
7
, c
9
y
20
+ 24y
19
+ ··· + 4y
2
+ 1
c
8
(y
10
+ 13y
9
+ ··· + 366y + 113)
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758707 + 0.684264I
a = 0.246862 + 0.784018I
b = −1.17763 − 1.06321I
−0.28461 − 4.56548I 2.10704 + 11.49589I
u = 0.758707 − 0.684264I
a = 0.246862 − 0.784018I
b = −1.17763 + 1.06321I
−0.28461 + 4.56548I 2.10704 − 11.49589I
u = 0.778657 + 0.810317I
a = −0.307274 + 1.000250I
b = −0.998713 − 0.817006I
−2.05119 − 4.76907I −4.19559 + 4.84396I
u = 0.778657 − 0.810317I
a = −0.307274 − 1.000250I
b = −0.998713 + 0.817006I
−2.05119 + 4.76907I −4.19559 − 4.84396I
u = 0.769326 + 0.148206I
a = 2.31458 − 0.52403I
b = 0.135374 + 0.516023I
3.05353 − 9.22667I 1.88985 + 9.76468I
u = 0.769326 − 0.148206I
a = 2.31458 + 0.52403I
b = 0.135374 − 0.516023I
3.05353 + 9.22667I 1.88985 − 9.76468I
u = −0.247229 + 0.712054I
a = 0.21326 + 2.75893I
b = −0.237383 − 1.305290I
5.18058 1.49359 + 0.I
u = −0.247229 − 0.712054I
a = 0.21326 − 2.75893I
b = −0.237383 + 1.305290I
5.18058 1.49359 + 0.I
u = −0.083868 + 0.715519I
a = −1.48133 − 0.32850I
b = 0.956611 − 0.035277I
−2.05119 − 4.76907I −4.19559 + 4.84396I
u = −0.083868 − 0.715519I
a = −1.48133 + 0.32850I
b = 0.956611 + 0.035277I
−2.05119 + 4.76907I −4.19559 − 4.84396I
23
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.021497 + 0.702286I
a = 0.864949 − 0.348697I
b = 1.123760 + 0.563516I
4.88933 + 3.47667I −0.85068 + 1.18559I
u = 0.021497 − 0.702286I
a = 0.864949 + 0.348697I
b = 1.123760 − 0.563516I
4.88933 − 3.47667I −0.85068 − 1.18559I
u = −0.95246 + 1.17976I
a = 0.041992 − 0.822669I
b = −0.329737 + 0.669923I
4.88933 + 3.47667I −0.85068 + 1.18559I
u = −0.95246 − 1.17976I
a = 0.041992 + 0.822669I
b = −0.329737 − 0.669923I
4.88933 − 3.47667I −0.85068 − 1.18559I
u = −0.82142 + 1.38988I
a = −0.282590 + 0.950801I
b = 1.22306 − 0.83679I
3.05353 + 9.22667I 1.88985 − 9.76468I
u = −0.82142 − 1.38988I
a = −0.282590 − 0.950801I
b = 1.22306 + 0.83679I
3.05353 − 9.22667I 1.88985 + 9.76468I
u = −0.344777 + 0.171189I
a = −1.223240 − 0.528177I
b = −0.56200 + 1.50084I
−0.28461 + 4.56548I 2.10704 − 11.49589I
u = −0.344777 − 0.171189I
a = −1.223240 + 0.528177I
b = −0.56200 − 1.50084I
−0.28461 − 4.56548I 2.10704 + 11.49589I
u = 0.12157 + 3.08967I
a = 0.1128000 − 0.0220229I
b = −0.133334 + 0.294644I
0.0546371 0
u = 0.12157 − 3.08967I
a = 0.1128000 + 0.0220229I
b = −0.133334 − 0.294644I
0.0546371 0
24
IV. I
u
4
= hu
3
+ u
2
+ b − u − 1, −u
3
− u
2
+ a + 2u + 1, u
4
+ u
3
− u
2
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
6
=
u
3
+ u
2
− 2u − 1
−u
3
− u
2
+ u + 1
a
10
=
1
u
2
a
7
=
u
3
− 2u
−u
2
a
1
=
−2u
3
− u
2
+ 3u + 1
u
3
+ u
2
− u − 1
a
5
=
−u
−u
3
− u
2
+ u + 1
a
3
=
−u
3
0
a
4
=
−u
3
+ u − 1
−u
a
8
=
1
0
a
11
=
−u
3
+ 2u
u
3
+ u
2
− u − 1
a
11
=
−u
3
+ 2u
u
3
+ u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
− 3u
2
− 8u − 4
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
4
+ u
3
− 2u
2
− 2u + 1
c
2
u
4
− 3u
3
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ u
2
− u + 1
c
4
, c
10
u
4
− u
3
− 2u
2
+ 2u + 1
c
5
u
4
+ u
3
+ u
2
− u − 1
c
7
u
4
− u
3
− u
2
+ u − 1
c
8
u
4
c
9
u
4
+ u
3
− u
2
− u − 1
c
11
u
4
− u
3
+ u
2
+ u − 1
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
4
− 5y
3
+ 10y
2
− 8y + 1
c
2
, c
3
y
4
− 7y
3
+ 9y
2
+ y + 1
c
5
, c
11
y
4
+ y
3
+ y
2
− 3y + 1
c
7
, c
9
y
4
− 3y
3
+ y
2
+ y + 1
c
8
y
4
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.17872
a = −0.330349
b = −0.848375
−3.68806 −12.6850
u = −0.332924 + 0.670769I
a = −0.26077 − 1.86693I
b = 0.593691 + 1.196160I
5.36351 + 2.52742I 0.91810 − 4.26254I
u = −0.332924 − 0.670769I
a = −0.26077 + 1.86693I
b = 0.593691 − 1.196160I
5.36351 − 2.52742I 0.91810 + 4.26254I
u = −1.51288
a = 0.851884
b = 0.660993
−0.459232 −9.15140
28
V. I
u
5
= hb + u, a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
6
=
u + 1
−u
a
10
=
1
−u − 1
a
7
=
u + 1
−u
a
1
=
u + 1
0
a
5
=
1
−u
a
3
=
−u
−1
a
4
=
0
−1
a
8
=
u + 1
1
a
11
=
1
−u − 1
a
11
=
1
−u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
8
(u − 1)
2
c
2
, c
3
, c
5
c
7
, c
9
, c
11
u
2
− u + 1
c
6
, c
10
u
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
8
(y −1)
2
c
2
, c
3
, c
5
c
7
, c
9
, c
11
y
2
+ y + 1
c
6
, c
10
y
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 − 0.866025I
3.28987 6.00000
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 0.500000 + 0.866025I
3.28987 6.00000
32
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
4
+ u
3
− 2u
2
− 2u + 1)(u
20
− u
19
+ ··· + 5u + 1)
· (u
24
+ 5u
23
+ ··· + 8u + 1)(u
90
− 4u
89
+ ··· − 679u − 263)
c
2
(u
2
− u + 1)(u
4
− 3u
3
+ u
2
+ u + 1)(u
20
− 3u
19
+ ··· + 2u + 1)
· (u
24
+ 3u
23
+ ··· + 3u + 1)(u
90
− u
89
+ ··· − 675u + 103)
c
3
(u
2
− u + 1)(u
4
+ 3u
3
+ u
2
− u + 1)(u
20
+ 3u
19
+ ··· − 2u + 1)
· (u
24
+ 3u
23
+ ··· + 3u + 1)(u
90
− u
89
+ ··· − 675u + 103)
c
4
((u − 1)
2
)(u
4
− u
3
− 2u
2
+ 2u + 1)(u
20
+ u
19
+ ··· − 5u + 1)
· (u
24
+ 5u
23
+ ··· + 8u + 1)(u
90
− 4u
89
+ ··· − 679u − 263)
c
5
(u
2
− u + 1)(u
4
+ u
3
+ u
2
− u − 1)(u
20
+ u
18
+ ··· − u + 1)
· (u
24
+ u
23
+ ··· + 7u + 1)(u
90
− 8u
88
+ ··· − 22u − 1)
c
6
u
2
(u
4
+ u
3
− 2u
2
− 2u + 1)
· (u
10
− 3u
8
+ 2u
7
− 8u
5
+ 9u
4
+ 9u
3
− 5u
2
− 4u − 2)
2
· (u
24
− 2u
23
+ ··· − 106u + 36)(u
45
− 20u
43
+ ··· + 189u + 108)
2
c
7
(u
2
− u + 1)(u
4
− u
3
− u
2
+ u − 1)(u
20
+ 12u
18
+ ··· − 2u + 1)
· (u
24
− 5u
23
+ ··· − 5u + 1)(u
90
+ 13u
88
+ ··· + 2331u − 697)
c
8
u
4
(u − 1)
2
(u
20
+ 13u
18
+ ··· + 366u
2
+ 113)
· (u
24
− u
23
+ ··· + 320u + 64)(u
45
− 2u
44
+ ··· − 45u − 9)
2
c
9
(u
2
− u + 1)(u
4
+ u
3
− u
2
− u − 1)(u
20
+ 12u
18
+ ··· + 2u + 1)
· (u
24
− 5u
23
+ ··· − 5u + 1)(u
90
+ 13u
88
+ ··· + 2331u − 697)
c
10
u
2
(u
4
− u
3
− 2u
2
+ 2u + 1)
· (u
10
− 3u
8
− 2u
7
+ 8u
5
+ 9u
4
− 9u
3
− 5u
2
+ 4u − 2)
2
· (u
24
− 2u
23
+ ··· − 106u + 36)(u
45
− 20u
43
+ ··· + 189u + 108)
2
c
11
(u
2
− u + 1)(u
4
− u
3
+ u
2
+ u − 1)(u
20
+ u
18
+ ··· + u + 1)
· (u
24
+ u
23
+ ··· + 7u + 1)(u
90
− 8u
88
+ ··· − 22u − 1)
33
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
2
)(y
4
− 5y
3
+ ··· − 8y + 1)(y
20
− 13y
19
+ ··· + 11y + 1)
· (y
24
− 7y
23
+ ··· − 6y + 1)(y
90
− 20y
89
+ ··· − 4190907y + 69169)
c
2
, c
3
(y
2
+ y + 1)(y
4
− 7y
3
+ 9y
2
+ y + 1)(y
20
− 5y
19
+ ··· − 6y + 1)
· (y
24
+ 3y
23
+ ··· + 27y + 1)(y
90
− 7y
89
+ ··· + 296069y + 10609)
c
5
, c
11
(y
2
+ y + 1)(y
4
+ y
3
+ y
2
− 3y + 1)(y
20
+ 2y
19
+ ··· + 19y + 1)
· (y
24
+ 7y
23
+ ··· − 29y + 1)(y
90
− 16y
89
+ ··· − 90y + 1)
c
6
, c
10
y
2
(y
4
− 5y
3
+ ··· − 8y + 1)(y
10
− 6y
9
+ ··· + 4y + 4)
2
· (y
24
− 12y
23
+ ··· + 9860y + 1296)
· (y
45
− 40y
44
+ ··· − 36207y −11664)
2
c
7
, c
9
(y
2
+ y + 1)(y
4
− 3y
3
+ y
2
+ y + 1)(y
20
+ 24y
19
+ ··· + 4y
2
+ 1)
· (y
24
− 21y
23
+ ··· − 5y + 1)
· (y
90
+ 26y
89
+ ··· + 21978055y + 485809)
c
8
y
4
(y −1)
2
(y
10
+ 13y
9
+ ··· + 366y + 113)
2
· (y
24
− 23y
23
+ ··· + 30720y + 4096)
· (y
45
+ 20y
44
+ ··· + 2871y −81)
2
34
