11n
184
(K11n
184
)
A knot diagram
1
Linearized knot diagam
5 7 1 10 3 9 3 11 4 7 6
Solving Sequence
4,9
10
1,5
3 6 7 2 11 8
c
9
c
4
c
3
c
5
c
6
c
2
c
11
c
8
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h9.79327 × 10
23
u
27
− 1.97941 × 10
24
u
26
+ ··· + 2.45772 × 10
24
b − 1.05681 × 10
25
,
5.11012 × 10
24
u
27
− 1.51176 × 10
25
u
26
+ ··· + 2.45772 × 10
25
a − 1.24464 × 10
26
, u
28
− 3u
27
+ ··· − 40u + 10i
I
u
2
= h2554960u
17
a − 4096933u
17
+ ··· − 42906164a + 49128383,
− 103879132u
17
a − 263156948u
17
+ ··· + 1344416472a + 157961924, u
18
− 8u
16
+ ··· − 3u − 7i
I
u
3
= h−17u
17
− 10u
16
+ ··· + 4b − 38, u
17
− 11u
16
+ ··· + 4a − 58,
u
18
− 6u
16
+ 19u
14
− 40u
12
+ 66u
10
− 82u
8
+ 76u
6
− 46u
4
+ 15u
2
− 2i
I
u
4
= hb + u + 1, 2a − u − 2, u
2
− 2i
I
v
1
= ha, b − 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 85 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
=
h9.79×10
23
u
27
−1.98×10
24
u
26
+· · ·+2.46×10
24
b−1.06×10
25
, 5.11×10
24
u
27
−
1.51 × 10
25
u
26
+ · · · + 2.46 × 10
25
a − 1.24 × 10
26
, u
28
− 3u
27
+ · · · − 40u + 10i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
1
=
−0.207921u
27
+ 0.615107u
26
+ ··· − 17.2289u + 5.06419
−0.398469u
27
+ 0.805384u
26
+ ··· − 15.8021u + 4.29997
a
5
=
u
−u
3
+ u
a
3
=
−0.598386u
27
+ 1.36198u
26
+ ··· − 25.7006u + 6.72775
−0.0606363u
27
+ 0.102546u
26
+ ··· − 2.30306u − 0.524423
a
6
=
0.429997u
27
− 0.891523u
26
+ ··· + 10.5673u − 1.39779
−0.00865581u
27
+ 0.0715894u
26
+ ··· − 3.25265u + 2.07921
a
7
=
0.438653u
27
− 0.963112u
26
+ ··· + 13.8200u − 3.47700
−0.00865581u
27
+ 0.0715894u
26
+ ··· − 3.25265u + 2.07921
a
2
=
0.0771778u
27
+ 0.0489359u
26
+ ··· − 7.53802u + 2.27914
−0.431569u
27
+ 0.843759u
26
+ ··· − 14.8252u + 4.40618
a
11
=
0.498943u
27
− 1.06015u
26
+ ··· + 13.2218u − 3.30666
−0.0479065u
27
+ 0.0970119u
26
+ ··· − 3.79894u + 1.67983
a
8
=
−0.175255u
27
+ 0.212502u
26
+ ··· + 2.68490u − 0.0259453
−0.0725597u
27
+ 0.0693962u
26
+ ··· + 2.45288u − 0.486297
a
8
=
−0.175255u
27
+ 0.212502u
26
+ ··· + 2.68490u − 0.0259453
−0.0725597u
27
+ 0.0693962u
26
+ ··· + 2.45288u − 0.486297
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
4877780988340105932664134
2457723581593567328996461
u
27
+
9987788121812337009415536
2457723581593567328996461
u
26
+
··· −
189867457763355278132012850
2457723581593567328996461
u +
43001401194012443714550992
2457723581593567328996461
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
28
+ u
27
+ ··· + 303u + 49
c
2
, c
7
u
28
+ 3u
27
+ ··· − 120u + 26
c
3
, c
6
u
28
− u
27
+ ··· − u + 1
c
4
, c
9
u
28
+ 3u
27
+ ··· + 40u + 10
c
5
, c
8
u
28
− u
27
+ ··· + 21u + 5
c
11
u
28
+ 3u
27
+ ··· + 56u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
28
+ 29y
27
+ ··· − 8019y + 2401
c
2
, c
7
y
28
+ 23y
27
+ ··· − 1816y + 676
c
3
, c
6
y
28
+ y
27
+ ··· + 17y + 1
c
4
, c
9
y
28
− 17y
27
+ ··· + 560y + 100
c
5
, c
8
y
28
+ 19y
27
+ ··· + 379y + 25
c
11
y
28
− y
27
+ ··· + 640y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.892804 + 0.444060I
a = 0.309008 + 0.559978I
b = −0.873429 + 0.799710I
1.26054 − 1.72230I −0.40850 + 1.70276I
u = −0.892804 − 0.444060I
a = 0.309008 − 0.559978I
b = −0.873429 − 0.799710I
1.26054 + 1.72230I −0.40850 − 1.70276I
u = 0.218854 + 1.012420I
a = 0.590636 − 0.144749I
b = 0.764812 − 0.117020I
−1.38872 − 0.92374I −4.94776 + 7.36786I
u = 0.218854 − 1.012420I
a = 0.590636 + 0.144749I
b = 0.764812 + 0.117020I
−1.38872 + 0.92374I −4.94776 − 7.36786I
u = 0.802643 + 0.305370I
a = 0.75217 − 1.24109I
b = −1.08256 − 1.21911I
−1.15395 + 4.47162I −7.14862 − 4.64379I
u = 0.802643 − 0.305370I
a = 0.75217 + 1.24109I
b = −1.08256 + 1.21911I
−1.15395 − 4.47162I −7.14862 + 4.64379I
u = 0.584905 + 0.590380I
a = 0.965167 − 0.178536I
b = 0.259310 − 0.627636I
−1.36729 − 0.61050I −5.48708 + 0.91172I
u = 0.584905 − 0.590380I
a = 0.965167 + 0.178536I
b = 0.259310 + 0.627636I
−1.36729 + 0.61050I −5.48708 − 0.91172I
u = 1.216130 + 0.158248I
a = −0.911081 − 0.448221I
b = 0.709894 − 0.706039I
8.36654 + 1.60580I −0.541797 − 0.240729I
u = 1.216130 − 0.158248I
a = −0.911081 + 0.448221I
b = 0.709894 + 0.706039I
8.36654 − 1.60580I −0.541797 + 0.240729I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.099020 + 0.606761I
a = −0.148240 − 0.260078I
b = −0.80758 − 1.16185I
7.22801 + 2.43402I 1.57040 − 0.59342I
u = 1.099020 − 0.606761I
a = −0.148240 + 0.260078I
b = −0.80758 + 1.16185I
7.22801 − 2.43402I 1.57040 + 0.59342I
u = 1.243000 + 0.278668I
a = 0.112693 − 0.881381I
b = −0.184859 − 0.444395I
2.92454 + 5.00287I −4.13660 − 6.40651I
u = 1.243000 − 0.278668I
a = 0.112693 + 0.881381I
b = −0.184859 + 0.444395I
2.92454 − 5.00287I −4.13660 + 6.40651I
u = −1.193670 + 0.454674I
a = 0.069212 + 0.789810I
b = −0.54519 + 1.66827I
7.75458 − 5.65256I 3.62489 + 8.19789I
u = −1.193670 − 0.454674I
a = 0.069212 − 0.789810I
b = −0.54519 − 1.66827I
7.75458 + 5.65256I 3.62489 − 8.19789I
u = −0.097920 + 0.715313I
a = 1.130000 + 0.601158I
b = −0.248100 + 0.524577I
4.52132 + 1.28199I −1.48628 − 3.62447I
u = −0.097920 − 0.715313I
a = 1.130000 − 0.601158I
b = −0.248100 − 0.524577I
4.52132 − 1.28199I −1.48628 + 3.62447I
u = −1.299880 + 0.322120I
a = −0.777664 − 0.901721I
b = 1.34969 − 1.28546I
2.44490 − 7.44961I −1.45384 + 5.70278I
u = −1.299880 − 0.322120I
a = −0.777664 + 0.901721I
b = 1.34969 + 1.28546I
2.44490 + 7.44961I −1.45384 − 5.70278I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.062707 + 1.338020I
a = −0.743793 + 0.649763I
b = −0.98144 + 1.57064I
3.71060 − 9.58638I −3.92148 + 6.82839I
u = 0.062707 − 1.338020I
a = −0.743793 − 0.649763I
b = −0.98144 − 1.57064I
3.71060 + 9.58638I −3.92148 − 6.82839I
u = 0.014763 + 0.486702I
a = −1.33238 − 2.05009I
b = −0.722499 − 1.177000I
−1.69684 + 4.08256I −6.58477 − 6.33725I
u = 0.014763 − 0.486702I
a = −1.33238 + 2.05009I
b = −0.722499 + 1.177000I
−1.69684 − 4.08256I −6.58477 + 6.33725I
u = 1.42770 + 0.62293I
a = −0.427337 + 0.931681I
b = 1.73290 + 1.45902I
8.0703 + 16.3840I −2.82061 − 8.06423I
u = 1.42770 − 0.62293I
a = −0.427337 − 0.931681I
b = 1.73290 − 1.45902I
8.0703 − 16.3840I −2.82061 + 8.06423I
u = −1.68545 + 0.44537I
a = 0.411613 − 0.574335I
b = 0.129044 + 0.831625I
9.49594 + 2.56707I 1.74205 − 3.34695I
u = −1.68545 − 0.44537I
a = 0.411613 + 0.574335I
b = 0.129044 − 0.831625I
9.49594 − 2.56707I 1.74205 + 3.34695I
7
II.
I
u
2
= h2.55 × 10
6
au
17
− 4.10 × 10
6
u
17
+ · · · − 4.29 × 10
7
a + 4.91 × 10
7
, −1.04 ×
10
8
au
17
−2.63×10
8
u
17
+· · ·+1.34×10
9
a+1.58×10
8
, u
18
−8u
16
+· · ·−3u−7i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
1
=
a
−1.25704au
17
+ 2.01569u
17
+ ··· + 21.1098a − 24.1712
a
5
=
u
−u
3
+ u
a
3
=
−0.958254au
17
+ 0.294954u
17
+ ··· + 7.30122a + 18.4962
0.820958au
17
− 1.34758u
17
+ ··· + 6.26047a − 0.681278
a
6
=
3.01569au
17
− 1.25321u
17
+ ··· − 24.1712a − 11.1950
−0.958254u
17
+ 0.246005u
16
+ ··· − 10.3700u + 7.30122
a
7
=
3.01569au
17
− 0.294954u
17
+ ··· − 24.1712a − 18.4962
−0.958254u
17
+ 0.246005u
16
+ ··· − 10.3700u + 7.30122
a
2
=
0.480313au
17
− 0.514339u
17
+ ··· − 9.60037a + 8.79929
−1.07679au
17
+ 1.51484u
17
+ ··· + 17.6039a − 18.7341
a
11
=
−4.15349au
17
− 2.19598u
17
+ ··· + 53.3616a + 29.1783
0.235482au
17
+ 1.25704u
17
+ ··· + 9.43306a − 20.1098
a
8
=
−5.87811au
17
− 0.514339u
17
+ ··· + 42.2240a + 8.79929
0.776728au
17
− 1.50135u
17
+ ··· − 10.5095a + 15.3719
a
8
=
−5.87811au
17
− 0.514339u
17
+ ··· + 42.2240a + 8.79929
0.776728au
17
− 1.50135u
17
+ ··· − 10.5095a + 15.3719
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
33551679
2032519
u
17
+
7438389
2032519
u
16
+ ··· −
495469247
2032519
u +
122235417
2032519
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
36
− u
35
+ ··· − 2025u + 675
c
2
, c
7
(u
18
+ 8u
16
+ ··· + 9u + 1)
2
c
3
, c
6
u
36
− 4u
35
+ ··· − 8u + 1
c
4
, c
9
(u
18
− 8u
16
+ ··· + 3u − 7)
2
c
5
, c
8
u
36
− 7u
35
+ ··· + 512u + 139
c
11
(u
18
− 3u
16
+ ··· + 10u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
36
− 9y
35
+ ··· − 2634525y + 455625
c
2
, c
7
(y
18
+ 16y
17
+ ··· + 23y + 1)
2
c
3
, c
6
y
36
− 16y
35
+ ··· − 18y + 1
c
4
, c
9
(y
18
− 16y
17
+ ··· − 569y + 49)
2
c
5
, c
8
y
36
− 3y
35
+ ··· − 372232y + 19321
c
11
(y
18
− 6y
17
+ ··· − 36y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.517954 + 0.930078I
a = 0.921155 + 0.564888I
b = −0.41746 + 2.45748I
3.10062 − 3.22877I −6.92519 + 4.57894I
u = −0.517954 + 0.930078I
a = 0.043469 + 0.902428I
b = −0.328101 + 0.755834I
3.10062 − 3.22877I −6.92519 + 4.57894I
u = −0.517954 − 0.930078I
a = 0.921155 − 0.564888I
b = −0.41746 − 2.45748I
3.10062 + 3.22877I −6.92519 − 4.57894I
u = −0.517954 − 0.930078I
a = 0.043469 − 0.902428I
b = −0.328101 − 0.755834I
3.10062 + 3.22877I −6.92519 − 4.57894I
u = 0.695159 + 0.848524I
a = 1.232100 − 0.246670I
b = 0.286506 − 1.257930I
−2.09116 − 0.97054I −2.23750 − 5.32372I
u = 0.695159 + 0.848524I
a = −0.206081 + 0.167522I
b = 0.137967 + 0.763918I
−2.09116 − 0.97054I −2.23750 − 5.32372I
u = 0.695159 − 0.848524I
a = 1.232100 + 0.246670I
b = 0.286506 + 1.257930I
−2.09116 + 0.97054I −2.23750 + 5.32372I
u = 0.695159 − 0.848524I
a = −0.206081 − 0.167522I
b = 0.137967 − 0.763918I
−2.09116 + 0.97054I −2.23750 + 5.32372I
u = 0.853350
a = 0.662436
b = 0.522342
−1.86607 −5.91390
u = 0.853350
a = 1.47423
b = −1.01367
−1.86607 −5.91390
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.153560 + 0.127277I
a = −0.756499 − 0.199759I
b = 2.70169 − 0.18542I
4.01524 − 4.53987I −4.29652 + 4.59405I
u = −1.153560 + 0.127277I
a = 0.85825 + 1.17347I
b = −0.440550 + 0.874036I
4.01524 − 4.53987I −4.29652 + 4.59405I
u = −1.153560 − 0.127277I
a = −0.756499 + 0.199759I
b = 2.70169 + 0.18542I
4.01524 + 4.53987I −4.29652 − 4.59405I
u = −1.153560 − 0.127277I
a = 0.85825 − 1.17347I
b = −0.440550 − 0.874036I
4.01524 + 4.53987I −4.29652 − 4.59405I
u = 0.992764 + 0.622226I
a = 0.155219 − 1.305160I
b = −0.94913 − 1.56570I
−0.99172 + 6.40330I 3.42158 − 6.30629I
u = 0.992764 + 0.622226I
a = −0.369663 + 0.558559I
b = 1.28369 + 1.07925I
−0.99172 + 6.40330I 3.42158 − 6.30629I
u = 0.992764 − 0.622226I
a = 0.155219 + 1.305160I
b = −0.94913 + 1.56570I
−0.99172 − 6.40330I 3.42158 + 6.30629I
u = 0.992764 − 0.622226I
a = −0.369663 − 0.558559I
b = 1.28369 − 1.07925I
−0.99172 − 6.40330I 3.42158 + 6.30629I
u = 0.714803
a = −1.30451
b = 2.14300
−5.42967 −25.4730
u = 0.714803
a = 2.89989
b = 0.656496
−5.42967 −25.4730
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32619
a = −0.398205 + 0.835176I
b = 0.030287 + 0.283651I
4.77670 −0.191180
u = −1.32619
a = −0.398205 − 0.835176I
b = 0.030287 − 0.283651I
4.77670 −0.191180
u = 1.35768
a = 1.73775
b = −2.10984
−3.16853 23.1980
u = 1.35768
a = −0.254521
b = −0.614155
−3.16853 23.1980
u = −0.629486 + 0.021587I
a = −0.146702 + 0.386290I
b = −2.51181 − 1.51793I
2.02553 + 3.59036I −0.89678 + 6.78897I
u = −0.629486 + 0.021587I
a = 1.89696 − 1.18998I
b = −0.340362 + 0.042357I
2.02553 + 3.59036I −0.89678 + 6.78897I
u = −0.629486 − 0.021587I
a = −0.146702 − 0.386290I
b = −2.51181 + 1.51793I
2.02553 − 3.59036I −0.89678 − 6.78897I
u = −0.629486 − 0.021587I
a = 1.89696 + 1.18998I
b = −0.340362 − 0.042357I
2.02553 − 3.59036I −0.89678 − 6.78897I
u = 1.42125 + 0.38509I
a = −0.410607 + 0.740708I
b = 0.781068 + 1.120410I
8.94298 + 7.76278I −0.81388 − 5.96589I
u = 1.42125 + 0.38509I
a = −0.900245 − 0.743462I
b = 0.280432 + 0.787705I
8.94298 + 7.76278I −0.81388 − 5.96589I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42125 − 0.38509I
a = −0.410607 − 0.740708I
b = 0.781068 − 1.120410I
8.94298 − 7.76278I −0.81388 + 5.96589I
u = 1.42125 − 0.38509I
a = −0.900245 + 0.743462I
b = 0.280432 − 0.787705I
8.94298 − 7.76278I −0.81388 + 5.96589I
u = −1.60799 + 0.59422I
a = 0.560748 + 0.927961I
b = −2.70137 + 0.93413I
5.93656 − 5.69637I −3.56158 + 12.64720I
u = −1.60799 + 0.59422I
a = −0.158968 − 0.337648I
b = 0.395079 − 0.493552I
5.93656 − 5.69637I −3.56158 + 12.64720I
u = −1.60799 − 0.59422I
a = 0.560748 − 0.927961I
b = −2.70137 − 0.93413I
5.93656 + 5.69637I −3.56158 − 12.64720I
u = −1.60799 − 0.59422I
a = −0.158968 + 0.337648I
b = 0.395079 + 0.493552I
5.93656 + 5.69637I −3.56158 − 12.64720I
14
III. I
u
3
= h−17u
17
− 10u
16
+ · · · + 4b − 38, u
17
− 11u
16
+ · · · + 4a − 58, u
18
−
6u
16
+ · · · + 15u
2
− 2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
1
=
−
1
4
u
17
+
11
4
u
16
+ ··· − 6u +
29
2
17
4
u
17
+
5
2
u
16
+ ··· +
23
2
u +
19
2
a
5
=
u
−u
3
+ u
a
3
=
37
4
u
17
−
1
2
u
16
+ ··· +
81
2
u −
17
2
1
4
u
17
+
3
2
u
16
+ ··· − 3u +
5
2
a
6
=
−
19
4
u
17
+
17
4
u
16
+ ··· − 12u +
23
2
11
4
u
17
−
1
2
u
16
+ ··· +
29
2
u +
1
2
a
7
=
−
15
2
u
17
+
19
4
u
16
+ ··· −
53
2
u + 11
11
4
u
17
−
1
2
u
16
+ ··· +
29
2
u +
1
2
a
2
=
−3u
17
+
9
4
u
16
+ ··· − 16u +
25
2
3u
17
+ 2u
16
+ ··· + 7u +
17
2
a
11
=
15u
17
−
39
4
u
16
+ ··· + 53u − 43
11
4
u
17
+
3
2
u
16
+ ··· + 10u + 9
a
8
=
−
55
4
u
17
+
7
2
u
16
+ ··· −
83
2
u +
15
2
−2u
17
−
11
4
u
16
+ ··· −
5
2
u − 10
a
8
=
−
55
4
u
17
+
7
2
u
16
+ ··· −
83
2
u +
15
2
−2u
17
−
11
4
u
16
+ ··· −
5
2
u − 10
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
73
2
u
16
− 202u
14
+
1201
2
u
12
−
2375
2
u
10
+ 1878u
8
−
4323
2
u
6
+ 1829u
4
−
1781
2
u
2
+ 163
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 6u
16
+ ··· + 13u − 1
c
2
, c
7
u
18
+ 4u
16
− 2u
14
− 22u
12
− 13u
10
+ 16u
8
− 3u
6
− 11u
4
+ 9u
2
− 2
c
3
u
18
+ 5u
17
+ ··· − 8u − 1
c
4
, c
9
u
18
− 6u
16
+ 19u
14
− 40u
12
+ 66u
10
− 82u
8
+ 76u
6
− 46u
4
+ 15u
2
− 2
c
5
u
18
− u
15
+ ··· + 2u
2
− 1
c
6
u
18
− 5u
17
+ ··· + 8u − 1
c
8
u
18
+ u
15
+ ··· + 2u
2
− 1
c
10
u
18
− 6u
16
+ ··· − 13u − 1
c
11
u
18
− 2u
16
+ 21u
14
+ 27u
10
− 174u
8
+ 205u
6
+ 30u
4
− 53u
2
− 32
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
18
− 12y
17
+ ··· − 71y + 1
c
2
, c
7
(y
9
+ 4y
8
− 2y
7
− 22y
6
− 13y
5
+ 16y
4
− 3y
3
− 11y
2
+ 9y −2)
2
c
3
, c
6
y
18
− 7y
17
+ ··· − 8y
2
+ 1
c
4
, c
9
(y
9
− 6y
8
+ 19y
7
− 40y
6
+ 66y
5
− 82y
4
+ 76y
3
− 46y
2
+ 15y −2)
2
c
5
, c
8
y
18
− 8y
16
+ ··· − 4y + 1
c
11
(y
9
− 2y
8
+ 21y
7
+ 27y
5
− 174y
4
+ 205y
3
+ 30y
2
− 53y −32)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.996123 + 0.550603I
a = −0.558599 − 0.636333I
b = 1.31998 − 1.20112I
−1.46928 − 6.40624I −13.4313 + 7.0584I
u = −0.996123 − 0.550603I
a = −0.558599 + 0.636333I
b = 1.31998 + 1.20112I
−1.46928 + 6.40624I −13.4313 − 7.0584I
u = 0.996123 + 0.550603I
a = 0.272835 − 1.383160I
b = −0.93113 − 1.54199I
−1.46928 + 6.40624I −13.4313 − 7.0584I
u = 0.996123 − 0.550603I
a = 0.272835 + 1.383160I
b = −0.93113 + 1.54199I
−1.46928 − 6.40624I −13.4313 + 7.0584I
u = −0.845186
a = 1.11324
b = −2.33451
−5.14686 3.50430
u = 0.845186
a = 2.51611
b = 0.520639
−5.14686 3.50430
u = 0.822250 + 0.912603I
a = 1.281290 − 0.101081I
b = 0.49501 − 1.66189I
−2.29959 − 1.27814I −15.7772 + 13.4535I
u = 0.822250 − 0.912603I
a = 1.281290 + 0.101081I
b = 0.49501 + 1.66189I
−2.29959 + 1.27814I −15.7772 − 13.4535I
u = −0.822250 + 0.912603I
a = −0.387008 − 0.146816I
b = −0.072626 − 0.629482I
−2.29959 + 1.27814I −15.7772 − 13.4535I
u = −0.822250 − 0.912603I
a = −0.387008 + 0.146816I
b = −0.072626 + 0.629482I
−2.29959 − 1.27814I −15.7772 + 13.4535I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.631814 + 0.103081I
a = 0.630751 − 0.645179I
b = −2.91697 − 1.31128I
1.92430 + 3.93083I −7.6382 − 13.9939I
u = 0.631814 − 0.103081I
a = 0.630751 + 0.645179I
b = −2.91697 + 1.31128I
1.92430 − 3.93083I −7.6382 + 13.9939I
u = −0.631814 + 0.103081I
a = 1.55956 + 1.65719I
b = −0.435165 + 0.428160I
1.92430 − 3.93083I −7.6382 + 13.9939I
u = −0.631814 − 0.103081I
a = 1.55956 − 1.65719I
b = −0.435165 − 0.428160I
1.92430 + 3.93083I −7.6382 − 13.9939I
u = 1.38034 + 0.42829I
a = −0.049850 − 0.309510I
b = 0.420847 − 0.609955I
6.06294 + 4.89735I −1.40550 − 2.57464I
u = 1.38034 − 0.42829I
a = −0.049850 + 0.309510I
b = 0.420847 + 0.609955I
6.06294 − 4.89735I −1.40550 + 2.57464I
u = −1.38034 + 0.42829I
a = 0.436348 + 0.936920I
b = −1.47300 + 1.00585I
6.06294 − 4.89735I −1.40550 + 2.57464I
u = −1.38034 − 0.42829I
a = 0.436348 − 0.936920I
b = −1.47300 − 1.00585I
6.06294 + 4.89735I −1.40550 − 2.57464I
19
IV. I
u
4
= hb + u + 1, 2a − u − 2, u
2
− 2i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−2
a
1
=
1
2
u + 1
−u − 1
a
5
=
u
−u
a
3
=
3
2
u + 2
−u − 3
a
6
=
1
2
u − 1
u − 1
a
7
=
−
1
2
u
u − 1
a
2
=
3
2
u + 1
−2u − 1
a
11
=
1
2
u + 1
−u − 1
a
8
=
3
2
u + 3
−2u − 3
a
8
=
3
2
u + 3
−2u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −44
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
4
, c
7
c
9
u
2
− 2
c
3
, c
8
u
2
+ 2u − 1
c
5
, c
6
u
2
− 2u − 1
c
10
(u + 1)
2
c
11
u
2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y −1)
2
c
2
, c
4
, c
7
c
9
(y −2)
2
c
3
, c
5
, c
6
c
8
y
2
− 6y + 1
c
11
y
2
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = 1.70711
b = −2.41421
−3.28987 −44.0000
u = −1.41421
a = 0.292893
b = 0.414214
−3.28987 −44.0000
23
V. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
4
=
−1
0
a
9
=
1
0
a
10
=
1
0
a
1
=
0
1
a
5
=
−1
0
a
3
=
−1
1
a
6
=
0
−1
a
7
=
1
−1
a
2
=
−1
1
a
11
=
0
1
a
8
=
1
−1
a
8
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u − 1
c
2
, c
4
, c
7
c
9
, c
11
u
c
3
, c
5
, c
10
u + 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
8
, c
10
y −1
c
2
, c
4
, c
7
c
9
, c
11
y
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
−3.28987 −12.0000
27
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
18
− 6u
16
+ ··· + 13u − 1)(u
28
+ u
27
+ ··· + 303u + 49)
· (u
36
− u
35
+ ··· − 2025u + 675)
c
2
, c
7
u(u
2
− 2)(u
18
+ 4u
16
+ ··· + 9u
2
− 2)
· ((u
18
+ 8u
16
+ ··· + 9u + 1)
2
)(u
28
+ 3u
27
+ ··· − 120u + 26)
c
3
(u + 1)(u
2
+ 2u − 1)(u
18
+ 5u
17
+ ··· − 8u − 1)(u
28
− u
27
+ ··· − u + 1)
· (u
36
− 4u
35
+ ··· − 8u + 1)
c
4
, c
9
u(u
2
− 2)(u
18
− 8u
16
+ ··· + 3u − 7)
2
· (u
18
− 6u
16
+ 19u
14
− 40u
12
+ 66u
10
− 82u
8
+ 76u
6
− 46u
4
+ 15u
2
− 2)
· (u
28
+ 3u
27
+ ··· + 40u + 10)
c
5
(u + 1)(u
2
− 2u − 1)(u
18
− u
15
+ ··· + 2u
2
− 1)(u
28
− u
27
+ ··· + 21u + 5)
· (u
36
− 7u
35
+ ··· + 512u + 139)
c
6
(u − 1)(u
2
− 2u − 1)(u
18
− 5u
17
+ ··· + 8u − 1)(u
28
− u
27
+ ··· − u + 1)
· (u
36
− 4u
35
+ ··· − 8u + 1)
c
8
(u − 1)(u
2
+ 2u − 1)(u
18
+ u
15
+ ··· + 2u
2
− 1)(u
28
− u
27
+ ··· + 21u + 5)
· (u
36
− 7u
35
+ ··· + 512u + 139)
c
10
((u + 1)
3
)(u
18
− 6u
16
+ ··· − 13u − 1)(u
28
+ u
27
+ ··· + 303u + 49)
· (u
36
− u
35
+ ··· − 2025u + 675)
c
11
u
3
(u
18
− 3u
16
+ ··· + 10u + 1)
2
· (u
18
− 2u
16
+ 21u
14
+ 27u
10
− 174u
8
+ 205u
6
+ 30u
4
− 53u
2
− 32)
· (u
28
+ 3u
27
+ ··· + 56u + 8)
28
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
((y −1)
3
)(y
18
− 12y
17
+ ··· − 71y + 1)
· (y
28
+ 29y
27
+ ··· − 8019y + 2401)
· (y
36
− 9y
35
+ ··· − 2634525y + 455625)
c
2
, c
7
y(y −2)
2
· (y
9
+ 4y
8
− 2y
7
− 22y
6
− 13y
5
+ 16y
4
− 3y
3
− 11y
2
+ 9y −2)
2
· ((y
18
+ 16y
17
+ ··· + 23y + 1)
2
)(y
28
+ 23y
27
+ ··· − 1816y + 676)
c
3
, c
6
(y −1)(y
2
− 6y + 1)(y
18
− 7y
17
+ ··· − 8y
2
+ 1)(y
28
+ y
27
+ ··· + 17y + 1)
· (y
36
− 16y
35
+ ··· − 18y + 1)
c
4
, c
9
y(y −2)
2
· (y
9
− 6y
8
+ 19y
7
− 40y
6
+ 66y
5
− 82y
4
+ 76y
3
− 46y
2
+ 15y −2)
2
· ((y
18
− 16y
17
+ ··· − 569y + 49)
2
)(y
28
− 17y
27
+ ··· + 560y + 100)
c
5
, c
8
(y −1)(y
2
− 6y + 1)(y
18
− 8y
16
+ ··· − 4y + 1)
· (y
28
+ 19y
27
+ ··· + 379y + 25)(y
36
− 3y
35
+ ··· − 372232y + 19321)
c
11
y
3
(y
9
− 2y
8
+ 21y
7
+ 27y
5
− 174y
4
+ 205y
3
+ 30y
2
− 53y −32)
2
· ((y
18
− 6y
17
+ ··· − 36y + 1)
2
)(y
28
− y
27
+ ··· + 640y + 64)
29
