11a
318
(K11a
318
)
A knot diagram
1
Linearized knot diagam
6 8 1 9 11 2 10 3 5 7 4
Solving Sequence
4,9
5
1,10
3 8 2 7 11 6
c
4
c
9
c
3
c
8
c
2
c
7
c
11
c
5
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h970383u
17
+ 408499u
16
+ ··· + 1982053b + 372351,
− 1777862u
17
− 876895u
16
+ ··· + 1982053a − 4101509, u
18
+ u
17
+ ··· + u
2
− 1i
I
u
2
= h7.25333 × 10
100
u
59
+ 1.20321 × 10
99
u
58
+ ··· + 5.25066 × 10
101
b − 1.15506 × 10
102
,
− 3.92526 × 10
102
u
59
+ 3.63473 × 10
101
u
58
+ ··· + 8.92612 × 10
102
a + 1.52814 × 10
104
,
u
60
− u
59
+ ··· − 109u + 17i
I
u
3
= h−509u
19
− 338u
18
+ ··· + 367b − 1165, 610u
19
− 321u
18
+ ··· + 367a − 671, u
20
− 8u
18
+ ··· + u − 1i
I
u
4
= hu
3
+ b + 1, u
2
+ a + u, u
4
+ u − 1i
I
u
5
= h638u
11
− 606u
10
+ ··· + 697b − 1440, 936u
11
+ 352u
10
+ ··· + 697a − 1503,
u
12
− 2u
10
+ u
9
− 5u
7
+ 6u
6
+ u
5
− 9u
4
+ 5u
3
+ 6u
2
− 2u − 1i
I
u
6
= hb + 1, a + 1, u − 1i
* 6 irreducible components of dim
C
= 0, with total 115 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
= h9.70 × 10
5
u
17
+ 4.08 × 10
5
u
16
+ · · · + 1.98 × 10
6
b + 3.72 × 10
5
, −1.78 ×
10
6
u
17
− 8.77 × 10
5
u
16
+ · · · + 1.98 × 10
6
a − 4.10 × 10
6
, u
18
+ u
17
+ · · · + u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
1
=
0.896980u
17
+ 0.442418u
16
+ ··· − 1.43884u + 2.06932
−0.489585u
17
− 0.206099u
16
+ ··· + 1.33228u − 0.187861
a
10
=
−u
−u
3
+ u
a
3
=
0.0859684u
17
+ 0.537916u
16
+ ··· − 8.56326u + 0.601597
0.459466u
17
− 0.352058u
16
+ ··· + 1.86468u + 0.0670699
a
8
=
0.799368u
17
+ 0.226871u
16
+ ··· − 7.13272u − 2.24851
0.229761u
17
+ 0.320704u
16
+ ··· + 2.30647u + 0.343733
a
2
=
0.139285u
17
+ 0.903251u
16
+ ··· − 3.05848u + 3.34917
0.00845336u
17
− 0.364603u
16
+ ··· + 1.75892u − 0.515882
a
7
=
0.515882u
17
+ 0.507429u
16
+ ··· − 6.94486u − 1.75892
0.0450356u
17
+ 0.277375u
16
+ ··· + 1.83513u + 0.418192
a
11
=
0.407395u
17
+ 0.236319u
16
+ ··· − 0.106565u + 1.88146
−0.489585u
17
− 0.206099u
16
+ ··· + 1.33228u − 0.187861
a
6
=
−1.27985u
17
− 0.522154u
16
+ ··· + 3.59568u + 1.61964
0.328021u
17
− 0.170017u
16
+ ··· − 1.31924u − 0.426645
a
6
=
−1.27985u
17
− 0.522154u
16
+ ··· + 3.59568u + 1.61964
0.328021u
17
− 0.170017u
16
+ ··· − 1.31924u − 0.426645
(ii) Obstruction class = −1
(iii) Cusp Shapes =
763801
1982053
u
17
+
1992896
1982053
u
16
+ ··· +
433836
1982053
u −
27209831
1982053
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
u
18
+ u
17
+ ··· + u
2
− 1
c
2
, c
8
u
18
+ u
17
+ ··· + 50u + 4
c
3
, c
7
, c
10
c
11
u
18
− 2u
17
+ ··· + 3u + 1
c
5
u
18
+ 6u
17
+ ··· − 416u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
18
− 11y
17
+ ··· − 2y + 1
c
2
, c
8
y
18
− 13y
17
+ ··· − 1100y + 16
c
3
, c
7
, c
10
c
11
y
18
+ 8y
17
+ ··· − 9y + 1
c
5
y
18
+ 56y
16
+ ··· − 37888y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.969317
a = −1.04231
b = −1.08420
−4.93604 −18.1160
u = 0.503027 + 0.934053I
a = 0.117406 + 1.399640I
b = 0.129111 − 1.119030I
5.93090 − 0.43570I −2.98328 + 1.68118I
u = 0.503027 − 0.934053I
a = 0.117406 − 1.399640I
b = 0.129111 + 1.119030I
5.93090 + 0.43570I −2.98328 − 1.68118I
u = −1.155400 + 0.382844I
a = −0.0504197 − 0.0044892I
b = 1.25719 + 0.67749I
−8.49225 + 3.12657I −16.5106 − 4.5687I
u = −1.155400 − 0.382844I
a = −0.0504197 + 0.0044892I
b = 1.25719 − 0.67749I
−8.49225 − 3.12657I −16.5106 + 4.5687I
u = −1.219630 + 0.122646I
a = 1.35114 + 1.57540I
b = 0.417269 − 0.993577I
−4.77876 + 5.57099I −14.6445 − 6.8943I
u = −1.219630 − 0.122646I
a = 1.35114 − 1.57540I
b = 0.417269 + 0.993577I
−4.77876 − 5.57099I −14.6445 + 6.8943I
u = 1.306390 + 0.030156I
a = −0.314125 − 0.649221I
b = 0.308458 − 0.604810I
−7.41832 + 1.14356I −14.7481 − 6.1062I
u = 1.306390 − 0.030156I
a = −0.314125 + 0.649221I
b = 0.308458 + 0.604810I
−7.41832 − 1.14356I −14.7481 + 6.1062I
u = −1.244330 + 0.432653I
a = −1.32213 − 0.57859I
b = −0.507053 + 1.110690I
0.46162 + 9.59091I −11.3598 − 8.6982I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.244330 − 0.432653I
a = −1.32213 + 0.57859I
b = −0.507053 − 1.110690I
0.46162 − 9.59091I −11.3598 + 8.6982I
u = −0.52847 + 1.35181I
a = 0.436864 + 1.177610I
b = −0.402613 − 0.935090I
2.78527 − 3.16569I −11.24611 + 7.60453I
u = −0.52847 − 1.35181I
a = 0.436864 − 1.177610I
b = −0.402613 + 0.935090I
2.78527 + 3.16569I −11.24611 − 7.60453I
u = 1.37244 + 0.65413I
a = 0.72292 − 1.23621I
b = 0.73238 + 1.24612I
−3.9350 − 17.2773I −12.8790 + 9.3490I
u = 1.37244 − 0.65413I
a = 0.72292 + 1.23621I
b = 0.73238 − 1.24612I
−3.9350 + 17.2773I −12.8790 − 9.3490I
u = −0.333926
a = 0.701030
b = −0.239136
−0.538352 −18.5400
u = 0.148267 + 0.251923I
a = 3.22899 − 2.73957I
b = −0.273082 + 0.887649I
1.73441 + 2.46344I −11.30045 − 4.80762I
u = 0.148267 − 0.251923I
a = 3.22899 + 2.73957I
b = −0.273082 − 0.887649I
1.73441 − 2.46344I −11.30045 + 4.80762I
6
II. I
u
2
= h7.25 × 10
100
u
59
+ 1.20 × 10
99
u
58
+ · · · + 5.25 × 10
101
b − 1.16 ×
10
102
, −3.93 × 10
102
u
59
+ 3.63 × 10
101
u
58
+ · · · + 8.93 × 10
102
a + 1.53 ×
10
104
, u
60
− u
59
+ · · · − 109u + 17i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
1
=
0.439749u
59
− 0.0407201u
58
+ ··· + 31.2675u − 17.1199
−0.138141u
59
− 0.00229154u
58
+ ··· − 8.07888u + 2.19983
a
10
=
−u
−u
3
+ u
a
3
=
−0.106939u
59
+ 0.0813048u
58
+ ··· + 0.961685u + 8.85949
−0.0242627u
59
+ 0.0260886u
58
+ ··· − 2.48933u − 0.0619791
a
8
=
−0.0488347u
59
− 0.0246562u
58
+ ··· + 10.6648u + 7.45876
−0.144743u
59
− 0.00850452u
58
+ ··· − 13.1254u + 2.03107
a
2
=
−0.254240u
59
− 0.0726928u
58
+ ··· − 28.4567u + 3.38184
−0.312091u
59
+ 0.0424687u
58
+ ··· − 33.3786u + 6.15466
a
7
=
−0.141036u
59
− 0.0530891u
58
+ ··· + 1.08963u + 9.25438
−0.159476u
59
+ 0.00805005u
58
+ ··· − 15.1320u + 2.28623
a
11
=
0.301608u
59
− 0.0430116u
58
+ ··· + 23.1886u − 14.9200
−0.138141u
59
− 0.00229154u
58
+ ··· − 8.07888u + 2.19983
a
6
=
−0.451448u
59
+ 0.0218306u
58
+ ··· − 41.4070u − 0.151128
0.0195413u
59
+ 0.0319909u
58
+ ··· + 2.12465u + 0.466720
a
6
=
−0.451448u
59
+ 0.0218306u
58
+ ··· − 41.4070u − 0.151128
0.0195413u
59
+ 0.0319909u
58
+ ··· + 2.12465u + 0.466720
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.457112u
59
+ 0.104838u
58
+ ··· + 36.7319u − 21.5900
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
u
60
− u
59
+ ··· − 109u + 17
c
2
, c
8
(u
30
+ 6u
29
+ ··· + 170u + 36)
2
c
3
, c
7
, c
10
c
11
u
60
− 2u
59
+ ··· + 2u − 1
c
5
(u
30
− 2u
29
+ ··· + 2u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
60
− 41y
59
+ ··· − 18409y + 289
c
2
, c
8
(y
30
− 22y
29
+ ··· − 460y + 1296)
2
c
3
, c
7
, c
10
c
11
y
60
+ 32y
59
+ ··· + 20y + 1
c
5
(y
30
− 2y
29
+ ··· − 84y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.173863 + 0.983906I
a = −0.595302 − 1.227680I
b = 0.568581 + 1.096680I
−3.15719 − 4.84917I −13.58414 + 3.73183I
u = −0.173863 − 0.983906I
a = −0.595302 + 1.227680I
b = 0.568581 − 1.096680I
−3.15719 + 4.84917I −13.58414 − 3.73183I
u = −0.884656 + 0.446724I
a = −0.96473 − 1.07896I
b = −0.529022 − 0.052524I
−2.06368 + 5.36613I −15.7641 − 4.3359I
u = −0.884656 − 0.446724I
a = −0.96473 + 1.07896I
b = −0.529022 + 0.052524I
−2.06368 − 5.36613I −15.7641 + 4.3359I
u = −0.952526 + 0.271233I
a = −0.835395 + 0.173435I
b = −0.615493 + 0.932690I
1.57409 + 1.75671I −11.26354 − 2.48942I
u = −0.952526 − 0.271233I
a = −0.835395 − 0.173435I
b = −0.615493 − 0.932690I
1.57409 − 1.75671I −11.26354 + 2.48942I
u = 0.903459 + 0.213520I
a = −0.143616 + 1.243570I
b = −0.06489 − 1.61687I
1.72325 − 5.82388I −14.0227 + 8.3964I
u = 0.903459 − 0.213520I
a = −0.143616 − 1.243570I
b = −0.06489 + 1.61687I
1.72325 + 5.82388I −14.0227 − 8.3964I
u = 0.918123 + 0.113673I
a = 1.29720 − 2.26960I
b = 0.430781 + 1.048900I
−5.82415 − 2.23290I −14.1085 − 2.1221I
u = 0.918123 − 0.113673I
a = 1.29720 + 2.26960I
b = 0.430781 − 1.048900I
−5.82415 + 2.23290I −14.1085 + 2.1221I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.058310 + 0.321731I
a = 0.993888 + 0.573737I
b = 0.319807 − 0.896497I
−0.48113 + 1.41291I −11.00000 + 0.I
u = −1.058310 − 0.321731I
a = 0.993888 − 0.573737I
b = 0.319807 + 0.896497I
−0.48113 − 1.41291I −11.00000 + 0.I
u = −0.868439 + 0.693479I
a = 0.592584 + 0.822702I
b = −0.315851 − 1.166500I
1.57409 + 1.75671I −11.00000 + 0.I
u = −0.868439 − 0.693479I
a = 0.592584 − 0.822702I
b = −0.315851 + 1.166500I
1.57409 − 1.75671I −11.00000 + 0.I
u = −0.172475 + 0.855408I
a = −0.33105 − 1.48907I
b = 0.616890 + 0.324785I
−2.27554 + 5.83321I −13.60048 − 3.60394I
u = −0.172475 − 0.855408I
a = −0.33105 + 1.48907I
b = 0.616890 − 0.324785I
−2.27554 − 5.83321I −13.60048 + 3.60394I
u = −0.723442 + 0.483773I
a = −1.08899 − 1.57094I
b = −0.601195 + 1.083620I
1.99201 + 3.02567I −9.17011 − 1.57690I
u = −0.723442 − 0.483773I
a = −1.08899 + 1.57094I
b = −0.601195 − 1.083620I
1.99201 − 3.02567I −9.17011 + 1.57690I
u = 0.913487 + 0.729355I
a = 0.84143 − 1.18997I
b = 0.839696 + 0.905250I
1.72325 − 5.82388I 0
u = 0.913487 − 0.729355I
a = 0.84143 + 1.18997I
b = 0.839696 − 0.905250I
1.72325 + 5.82388I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.681546 + 0.443831I
a = 1.314210 − 0.385156I
b = 0.168505 + 1.140690I
1.99201 + 3.02567I −9.17011 − 1.57690I
u = 0.681546 − 0.443831I
a = 1.314210 + 0.385156I
b = 0.168505 − 1.140690I
1.99201 − 3.02567I −9.17011 + 1.57690I
u = 0.639831 + 0.484680I
a = 0.649950 − 0.261552I
b = 0.343005 − 0.289428I
2.17471 − 2.01374I −7.73585 + 3.91188I
u = 0.639831 − 0.484680I
a = 0.649950 + 0.261552I
b = 0.343005 + 0.289428I
2.17471 + 2.01374I −7.73585 − 3.91188I
u = 1.036460 + 0.711450I
a = 0.32156 − 1.74527I
b = 0.521860 + 1.024170I
−6.56195 − 4.20028I 0
u = 1.036460 − 0.711450I
a = 0.32156 + 1.74527I
b = 0.521860 − 1.024170I
−6.56195 + 4.20028I 0
u = 1.26027
a = −0.136432
b = −1.08341
−5.55198 0
u = −0.673649 + 0.289156I
a = −2.03586 − 1.79948I
b = −0.100294 − 0.250395I
−2.10401 + 5.43294I −16.4599 − 1.4390I
u = −0.673649 − 0.289156I
a = −2.03586 + 1.79948I
b = −0.100294 + 0.250395I
−2.10401 − 5.43294I −16.4599 + 1.4390I
u = −0.205467 + 0.686465I
a = −0.31789 + 1.74264I
b = −0.325811 − 1.261230I
3.74729 − 5.28000I −5.18091 + 3.40493I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.205467 − 0.686465I
a = −0.31789 − 1.74264I
b = −0.325811 + 1.261230I
3.74729 + 5.28000I −5.18091 − 3.40493I
u = 1.260710 + 0.276157I
a = −0.837013 + 0.676075I
b = −0.599749 − 1.161530I
−2.06368 − 5.36613I 0
u = 1.260710 − 0.276157I
a = −0.837013 − 0.676075I
b = −0.599749 + 1.161530I
−2.06368 + 5.36613I 0
u = 0.185453 + 1.290280I
a = −0.326081 + 1.289900I
b = 0.552043 − 1.093600I
−0.13405 + 10.50230I 0
u = 0.185453 − 1.290280I
a = −0.326081 − 1.289900I
b = 0.552043 + 1.093600I
−0.13405 − 10.50230I 0
u = 1.157510 + 0.625695I
a = 1.029550 − 0.832056I
b = 0.403736 + 0.982366I
3.74729 − 5.28000I 0
u = 1.157510 − 0.625695I
a = 1.029550 + 0.832056I
b = 0.403736 − 0.982366I
3.74729 + 5.28000I 0
u = 1.292280 + 0.285538I
a = −0.858396 + 0.914234I
b = −0.583662 − 1.209510I
−2.10401 − 5.43294I 0
u = 1.292280 − 0.285538I
a = −0.858396 − 0.914234I
b = −0.583662 + 1.209510I
−2.10401 + 5.43294I 0
u = −0.335964 + 0.575378I
a = 0.270786 − 0.040171I
b = −0.749034 − 0.108799I
−0.48113 − 1.41291I −11.50731 + 0.65666I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.335964 − 0.575378I
a = 0.270786 + 0.040171I
b = −0.749034 + 0.108799I
−0.48113 + 1.41291I −11.50731 − 0.65666I
u = −1.290140 + 0.372995I
a = 0.0208764 + 0.0986315I
b = −0.980371 − 0.207899I
−3.15719 + 4.84917I 0
u = −1.290140 − 0.372995I
a = 0.0208764 − 0.0986315I
b = −0.980371 + 0.207899I
−3.15719 − 4.84917I 0
u = −0.099098 + 0.640186I
a = 0.09004 − 1.81958I
b = −0.212959 + 1.109000I
2.17471 + 2.01374I −7.73585 − 3.91188I
u = −0.099098 − 0.640186I
a = 0.09004 + 1.81958I
b = −0.212959 − 1.109000I
2.17471 − 2.01374I −7.73585 + 3.91188I
u = 1.291760 + 0.455145I
a = −0.0309170 − 0.0318134I
b = 1.187980 − 0.445839I
−6.51599 − 10.49730I 0
u = 1.291760 − 0.455145I
a = −0.0309170 + 0.0318134I
b = 1.187980 + 0.445839I
−6.51599 + 10.49730I 0
u = 1.306830 + 0.465197I
a = −0.630886 + 1.147070I
b = −0.620144 − 1.216600I
−2.27554 − 5.83321I 0
u = 1.306830 − 0.465197I
a = −0.630886 − 1.147070I
b = −0.620144 + 1.216600I
−2.27554 + 5.83321I 0
u = −1.269270 + 0.579030I
a = 0.723396 + 1.171420I
b = 0.81690 − 1.22821I
−6.51599 + 10.49730I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.269270 − 0.579030I
a = 0.723396 − 1.171420I
b = 0.81690 + 1.22821I
−6.51599 − 10.49730I 0
u = 1.40424 + 0.40913I
a = −0.380784 + 0.192994I
b = 0.481225 − 0.576338I
−7.98335 0
u = 1.40424 − 0.40913I
a = −0.380784 − 0.192994I
b = 0.481225 + 0.576338I
−7.98335 0
u = −1.50639 + 0.03128I
a = 0.313720 + 0.382658I
b = 0.350132 + 0.706526I
−5.82415 + 2.23290I 0
u = −1.50639 − 0.03128I
a = 0.313720 − 0.382658I
b = 0.350132 − 0.706526I
−5.82415 − 2.23290I 0
u = −1.33093 + 0.72650I
a = −0.54342 − 1.31576I
b = −0.605352 + 1.216900I
−0.13405 + 10.50230I 0
u = −1.33093 − 0.72650I
a = −0.54342 + 1.31576I
b = −0.605352 − 1.216900I
−0.13405 − 10.50230I 0
u = −1.64506 + 0.30278I
a = −0.056451 − 0.315590I
b = 0.504888 + 0.670086I
−6.56195 − 4.20028I 0
u = −1.64506 − 0.30278I
a = −0.056451 + 0.315590I
b = 0.504888 − 0.670086I
−6.56195 + 4.20028I 0
u = 0.135724
a = −10.1813
b = 0.678987
−5.55198 −15.3380
15
III. I
u
3
= h−509u
19
− 338u
18
+ · · · + 367b − 1165, 610u
19
− 321u
18
+ · · · +
367a − 671, u
20
− 8u
18
+ · · · + u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
1
=
−1.66213u
19
+ 0.874659u
18
+ ··· − 4.53951u + 1.82834
1.38692u
19
+ 0.920981u
18
+ ··· + 1.83379u + 3.17439
a
10
=
−u
−u
3
+ u
a
3
=
−0.250681u
19
− 0.681199u
18
+ ··· + 1.98093u − 1.32425
0.752044u
19
− 0.956403u
18
+ ··· + 5.05722u + 0.972752
a
8
=
−0.594005u
19
− 0.00544959u
18
+ ··· + 0.367847u − 1.74659
−0.681199u
19
− 1.19891u
18
+ ··· + 1.92643u − 1.25068
a
2
=
0.594005u
19
− 0.994550u
18
+ ··· + 2.63215u − 0.253406
1.34060u
19
+ 0.599455u
18
+ ··· + 4.53678u + 4.12534
a
7
=
−0.673025u
19
− 1.02452u
18
+ ··· + 1.15531u − 3.35967
−0.675749u
19
− 0.749319u
18
+ ··· + 2.07902u − 0.656676
a
11
=
−0.275204u
19
+ 1.79564u
18
+ ··· − 2.70572u + 5.00272
1.38692u
19
+ 0.920981u
18
+ ··· + 1.83379u + 3.17439
a
6
=
1.65668u
19
− 1.32425u
18
+ ··· + 3.38692u − 2.42234
−1.35422u
19
− 0.223433u
18
+ ··· − 2.91826u − 2.61035
a
6
=
1.65668u
19
− 1.32425u
18
+ ··· + 3.38692u − 2.42234
−1.35422u
19
− 0.223433u
18
+ ··· − 2.91826u − 2.61035
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1598
367
u
19
−
3955
367
u
18
+ ··· +
8778
367
u −
10786
367
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
20
− 8u
18
+ ··· + u − 1
c
2
(u
10
− 5u
8
+ 8u
6
+ 4u
5
− 6u
4
− 3u
3
+ 3u
2
− 1)
2
c
3
, c
10
u
20
+ 3u
19
+ ··· − 8u
2
− 1
c
5
u
20
+ 8u
14
− 52u
12
− 138u
10
+ 104u
8
+ 527u
6
+ 296u
4
− 356u
2
− 319
c
6
, c
9
u
20
− 8u
18
+ ··· − u − 1
c
7
, c
11
u
20
− 3u
19
+ ··· − 8u
2
− 1
c
8
(u
10
− 5u
8
+ 8u
6
− 4u
5
− 6u
4
+ 3u
3
+ 3u
2
− 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
20
− 16y
19
+ ··· − 13y + 1
c
2
, c
8
(y
10
− 10y
9
+ ··· − 6y + 1)
2
c
3
, c
7
, c
10
c
11
y
20
+ 13y
19
+ ··· + 16y + 1
c
5
(y
10
+ 8y
7
− 52y
6
− 138y
5
+ 104y
4
+ 527y
3
+ 296y
2
− 356y −319)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.006880 + 0.379394I
a = 0.71131 + 2.12605I
b = 0.406554 − 1.044110I
−5.60500 + 3.07077I −11.10306 − 5.53745I
u = −1.006880 − 0.379394I
a = 0.71131 − 2.12605I
b = 0.406554 + 1.044110I
−5.60500 − 3.07077I −11.10306 + 5.53745I
u = −0.307724 + 0.858449I
a = 0.579281 + 0.822097I
b = −0.301268 − 1.054370I
3.58542 −5.93598 + 0.I
u = −0.307724 − 0.858449I
a = 0.579281 − 0.822097I
b = −0.301268 + 1.054370I
3.58542 −5.93598 + 0.I
u = −1.005260 + 0.622930I
a = −0.917585 − 0.950908I
b = −0.723749 + 0.881883I
2.31904 + 5.08447I −9.51292 − 2.92589I
u = −1.005260 − 0.622930I
a = −0.917585 + 0.950908I
b = −0.723749 − 0.881883I
2.31904 − 5.08447I −9.51292 + 2.92589I
u = −0.543411 + 0.587321I
a = 0.318117 + 0.503113I
b = −0.424021 − 1.175640I
3.51176 −5.53076 + 0.I
u = −0.543411 − 0.587321I
a = 0.318117 − 0.503113I
b = −0.424021 + 1.175640I
3.51176 −5.53076 + 0.I
u = 0.641197 + 0.460705I
a = 1.60910 − 2.98924I
b = 0.265764 + 0.633820I
−1.76138 − 5.90098I −8.4456 + 11.9708I
u = 0.641197 − 0.460705I
a = 1.60910 + 2.98924I
b = 0.265764 − 0.633820I
−1.76138 + 5.90098I −8.4456 − 11.9708I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.22178
a = −0.206592
b = −1.34573
−6.32941 −27.2570
u = −0.721984
a = 2.63740
b = 0.842412
−6.32941 −27.2570
u = 1.322280 + 0.225447I
a = −0.769082 + 0.973657I
b = −0.528515 − 1.268130I
−1.76138 − 5.90098I −8.4456 + 11.9708I
u = 1.322280 − 0.225447I
a = −0.769082 − 0.973657I
b = −0.528515 + 1.268130I
−1.76138 + 5.90098I −8.4456 − 11.9708I
u = −1.361800 + 0.242619I
a = −0.490712 + 0.349688I
b = 0.255308 + 0.676358I
−7.12244 −10.15337 + 0.I
u = −1.361800 − 0.242619I
a = −0.490712 − 0.349688I
b = 0.255308 − 0.676358I
−7.12244 −10.15337 + 0.I
u = 0.502690 + 0.120984I
a = 0.432595 + 0.041333I
b = −0.14840 − 1.42580I
2.31904 − 5.08447I −9.51292 + 2.92589I
u = 0.502690 − 0.120984I
a = 0.432595 − 0.041333I
b = −0.14840 + 1.42580I
2.31904 + 5.08447I −9.51292 − 2.92589I
u = 1.50902 + 0.12166I
a = −0.688432 − 0.075728I
b = −0.050017 − 0.545597I
−5.60500 + 3.07077I −11.10306 − 5.53745I
u = 1.50902 − 0.12166I
a = −0.688432 + 0.075728I
b = −0.050017 + 0.545597I
−5.60500 − 3.07077I −11.10306 + 5.53745I
20
IV. I
u
4
= hu
3
+ b + 1, u
2
+ a + u, u
4
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
1
=
−u
2
− u
−u
3
− 1
a
10
=
−u
−u
3
+ u
a
3
=
−u
−u
3
− u
2
− 1
a
8
=
u
3
u + 1
a
2
=
−u
2
−1
a
7
=
u
3
+ 1
u
2
+ u
a
11
=
−u
3
− u
2
− u − 1
−u
3
− 1
a
6
=
1
u
2
a
6
=
1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
3
− 2u
2
+ 3u − 6
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
4
+ u − 1
c
2
u
4
− 2u
2
+ u + 1
c
3
, c
10
u
4
+ u
3
− 1
c
5
u
4
c
6
, c
9
u
4
− u − 1
c
7
, c
11
u
4
− u
3
− 1
c
8
u
4
− 2u
2
− u + 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
4
− 2y
2
− y + 1
c
2
, c
8
y
4
− 4y
3
+ 6y
2
− 5y + 1
c
3
, c
7
, c
10
c
11
y
4
− y
3
− 2y
2
+ 1
c
5
y
4
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.248126 + 1.033980I
a = 0.75943 − 1.54710I
b = −0.219447 + 0.914474I
3.04135 + 1.96274I −6.36273 − 1.58218I
u = 0.248126 − 1.033980I
a = 0.75943 + 1.54710I
b = −0.219447 − 0.914474I
3.04135 − 1.96274I −6.36273 + 1.58218I
u = −1.22074
a = −0.269472
b = 0.819173
−8.36260 −19.9190
u = 0.724492
a = −1.24938
b = −1.38028
−4.29983 −3.35520
24
V. I
u
5
= h638u
11
− 606u
10
+ · · · + 697b − 1440, 936u
11
+ 352u
10
+ · · · +
697a − 1503, u
12
− 2u
10
+ · · · − 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
1
=
−1.34290u
11
− 0.505022u
10
+ ··· − 9.29412u + 2.15638
−0.915352u
11
+ 0.869440u
10
+ ··· + 0.352941u + 2.06600
a
10
=
−u
−u
3
+ u
a
3
=
u
11
− 2u
9
+ u
8
− 5u
6
+ 6u
5
+ u
4
− 9u
3
+ 5u
2
+ 6u − 2
0.348637u
11
+ 0.208034u
10
+ ··· + 1.47059u − 1.05022
a
8
=
u
11
− 2u
9
+ u
8
− 5u
6
+ 6u
5
+ u
4
− 9u
3
+ 5u
2
+ 6u − 2
0.348637u
11
+ 0.208034u
10
+ ··· + 2.47059u − 1.05022
a
2
=
0
−u
a
7
=
0.984218u
11
+ 0.566714u
10
+ ··· + 7.76471u − 1.79197
0.286944u
11
+ 0.150646u
10
+ ··· + 1.82353u − 0.691535
a
11
=
−2.25825u
11
+ 0.364419u
10
+ ··· − 8.94118u + 4.22238
−0.915352u
11
+ 0.869440u
10
+ ··· + 0.352941u + 2.06600
a
6
=
−0.984218u
11
− 0.566714u
10
+ ··· − 7.76471u + 1.79197
−0.364419u
11
+ 0.358680u
10
+ ··· + 0.294118u + 1.25825
a
6
=
−0.984218u
11
− 0.566714u
10
+ ··· − 7.76471u + 1.79197
−0.364419u
11
+ 0.358680u
10
+ ··· + 0.294118u + 1.25825
(ii) Obstruction class = −1
(iii) Cusp Shapes = −14
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
9
u
12
− 2u
10
+ u
9
− 5u
7
+ 6u
6
+ u
5
− 9u
4
+ 5u
3
+ 6u
2
− 2u − 1
c
2
, c
8
(u − 1)
12
c
3
, c
7
, c
10
c
11
u
12
+ 2u
10
+ u
9
+ 5u
7
− 4u
6
+ u
5
− u
4
− 3u
3
− 4u + 1
c
5
(u
6
+ 2u
3
− 5u
2
+ 1)
2
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
y
12
− 4y
11
+ ··· − 16y + 1
c
2
, c
8
(y −1)
12
c
3
, c
7
, c
10
c
11
y
12
+ 4y
11
+ ··· − 16y + 1
c
5
(y
6
− 10y
4
− 2y
3
+ 25y
2
− 10y + 1)
2
27
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.721680 + 0.842764I
a = −0.291320 + 0.594026I
b = 0.653624 − 1.017120I
2.30291 −14.0000
u = 0.721680 − 0.842764I
a = −0.291320 − 0.594026I
b = 0.653624 + 1.017120I
2.30291 −14.0000
u = 1.13635
a = −0.0899500
b = −1.33394
−5.59278 −14.0000
u = −0.849985 + 0.107756I
a = −0.39789 + 1.38066I
b = −0.31772 − 1.47138I
2.30291 −14.0000
u = −0.849985 − 0.107756I
a = −0.39789 − 1.38066I
b = −0.31772 + 1.47138I
2.30291 −14.0000
u = 1.32540
a = −0.253927
b = −0.966860
−5.59278 −14.0000
u = 0.128305 + 1.331900I
a = 0.380195 − 1.282920I
b = −0.335906 + 0.823161I
2.30291 −14.0000
u = 0.128305 − 1.331900I
a = 0.380195 + 1.282920I
b = −0.335906 − 0.823161I
2.30291 −14.0000
u = 0.580134
a = −3.02808
b = 0.239009
−5.59278 −14.0000
u = −1.36109 + 0.59989I
a = 0.47553 + 1.40936I
b = 0.519889 − 0.970639I
−5.59278 −14.0000
28
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36109 − 0.59989I
a = 0.47553 − 1.40936I
b = 0.519889 + 0.970639I
−5.59278 −14.0000
u = −0.319710
a = 4.03893
b = 1.02201
−5.59278 −14.0000
29
VI. I
u
6
= hb + 1, a + 1, u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
1
a
5
=
1
1
a
1
=
−1
−1
a
10
=
−1
0
a
3
=
0
−1
a
8
=
0
1
a
2
=
0
−1
a
7
=
1
1
a
11
=
−2
−1
a
6
=
−1
0
a
6
=
−1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
u − 1
c
2
, c
8
u
c
3
, c
7
, c
10
c
11
u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y −1
c
2
, c
8
y
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.00000
−4.93480 −18.0000
33
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u − 1)(u
4
+ u − 1)
· (u
12
− 2u
10
+ u
9
− 5u
7
+ 6u
6
+ u
5
− 9u
4
+ 5u
3
+ 6u
2
− 2u − 1)
· (u
18
+ u
17
+ ··· + u
2
− 1)(u
20
− 8u
18
+ ··· + u − 1)
· (u
60
− u
59
+ ··· − 109u + 17)
c
2
u(u − 1)
12
(u
4
− 2u
2
+ u + 1)
· (u
10
− 5u
8
+ 8u
6
+ 4u
5
− 6u
4
− 3u
3
+ 3u
2
− 1)
2
· (u
18
+ u
17
+ ··· + 50u + 4)(u
30
+ 6u
29
+ ··· + 170u + 36)
2
c
3
, c
10
(u + 1)(u
4
+ u
3
− 1)(u
12
+ 2u
10
+ ··· − 4u + 1)
· (u
18
− 2u
17
+ ··· + 3u + 1)(u
20
+ 3u
19
+ ··· − 8u
2
− 1)
· (u
60
− 2u
59
+ ··· + 2u − 1)
c
5
u
4
(u − 1)(u
6
+ 2u
3
− 5u
2
+ 1)
2
(u
18
+ 6u
17
+ ··· − 416u − 64)
· (u
20
+ 8u
14
− 52u
12
− 138u
10
+ 104u
8
+ 527u
6
+ 296u
4
− 356u
2
− 319)
· (u
30
− 2u
29
+ ··· + 2u − 1)
2
c
6
, c
9
(u − 1)(u
4
− u − 1)
· (u
12
− 2u
10
+ u
9
− 5u
7
+ 6u
6
+ u
5
− 9u
4
+ 5u
3
+ 6u
2
− 2u − 1)
· (u
18
+ u
17
+ ··· + u
2
− 1)(u
20
− 8u
18
+ ··· − u − 1)
· (u
60
− u
59
+ ··· − 109u + 17)
c
7
, c
11
(u + 1)(u
4
− u
3
− 1)(u
12
+ 2u
10
+ ··· − 4u + 1)
· (u
18
− 2u
17
+ ··· + 3u + 1)(u
20
− 3u
19
+ ··· − 8u
2
− 1)
· (u
60
− 2u
59
+ ··· + 2u − 1)
c
8
u(u − 1)
12
(u
4
− 2u
2
− u + 1)
· (u
10
− 5u
8
+ 8u
6
− 4u
5
− 6u
4
+ 3u
3
+ 3u
2
− 1)
2
· (u
18
+ u
17
+ ··· + 50u + 4)(u
30
+ 6u
29
+ ··· + 170u + 36)
2
34
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
9
(y −1)(y
4
− 2y
2
− y + 1)(y
12
− 4y
11
+ ··· − 16y + 1)
· (y
18
− 11y
17
+ ··· − 2y + 1)(y
20
− 16y
19
+ ··· − 13y + 1)
· (y
60
− 41y
59
+ ··· − 18409y + 289)
c
2
, c
8
y(y −1)
12
(y
4
− 4y
3
+ ··· − 5y + 1)(y
10
− 10y
9
+ ··· − 6y + 1)
2
· (y
18
− 13y
17
+ ··· − 1100y + 16)(y
30
− 22y
29
+ ··· − 460y + 1296)
2
c
3
, c
7
, c
10
c
11
(y −1)(y
4
− y
3
− 2y
2
+ 1)(y
12
+ 4y
11
+ ··· − 16y + 1)
· (y
18
+ 8y
17
+ ··· − 9y + 1)(y
20
+ 13y
19
+ ··· + 16y + 1)
· (y
60
+ 32y
59
+ ··· + 20y + 1)
c
5
y
4
(y −1)(y
6
− 10y
4
− 2y
3
+ 25y
2
− 10y + 1)
2
· (y
10
+ 8y
7
− 52y
6
− 138y
5
+ 104y
4
+ 527y
3
+ 296y
2
− 356y −319)
2
· (y
18
+ 56y
16
+ ··· − 37888y + 4096)(y
30
− 2y
29
+ ··· − 84y + 1)
2
35
