12n
0664
(K12n
0664
)
A knot diagram
1
Linearized knot diagam
3 8 6 9 10 11 9 2 12 3 4 5
Solving Sequence
4,9 5,12
10 6 1 3 2 8 11 7
c
4
c
9
c
5
c
12
c
3
c
1
c
8
c
11
c
6
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
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).
1
I
u
1
= h74009148936u
22
− 76652535715u
21
+ ··· + 605037775238b − 84815080599,
2192438106671u
22
− 2107623026072u
21
+ ··· + 605037775238a − 2052230519656,
u
23
− u
22
+ ··· − u + 1i
I
u
2
= h−1.45654 × 10
19
u
19
+ 6.73104 × 10
18
u
18
+ ··· + 1.62289 × 10
20
b − 2.33528 × 10
19
,
3.70637 × 10
20
u
19
+ 2.33528 × 10
19
u
18
+ ··· + 1.62289 × 10
20
a + 1.58962 × 10
21
, u
20
− u
18
+ ··· + 3u + 1i
I
u
3
= h1.59937 × 10
20
u
19
+ 2.00847 × 10
20
u
18
+ ··· + 2.29962 × 10
21
b + 5.16126 × 10
21
,
191496437465195u
19
+ 59872033526663u
18
+ ··· + 4748609612427635a + 5069797018706783,
u
20
+ u
19
+ ··· − 30u + 25i
I
u
4
= h−4.98032 × 10
100
u
39
+ 3.96797 × 10
100
u
38
+ ··· + 8.14259 × 10
103
b + 9.25727 × 10
103
,
− 6.53696 × 10
86
u
39
+ 5.50591 × 10
86
u
38
+ ··· + 6.14311 × 10
89
a + 9.18988 × 10
89
,
u
40
− u
39
+ ··· − 2058u + 661i
I
u
5
= h−9.70252 × 10
33
u
33
− 1.36400 × 10
34
u
32
+ ··· + 2.93977 × 10
34
b + 1.13426 × 10
34
,
3.22079 × 10
34
u
33
+ 2.08653 × 10
34
u
32
+ ··· + 2.93977 × 10
34
a − 8.32299 × 10
34
, u
34
+ u
33
+ ··· − u + 1i
I
u
6
= hb − u, a, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
I
u
7
= h2405u
9
− 2260u
8
+ ··· + 7829b − 605, −u
9
+ u
8
+ 2u
7
+ 2u
6
+ 2u
5
− 12u
4
− 9u
3
− 9u
2
+ a − 6u,
u
10
− u
9
− 2u
8
− 2u
7
− 2u
6
+ 12u
5
+ 9u
4
+ 9u
3
+ 6u
2
− 1i
I
u
8
= hb + u − 1, a + u, u
2
− u + 1i
* 8 irreducible components of dim
C
= 0, with total 154 representations.
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I.
I
u
1
= h7.40 × 10
10
u
22
− 7.67 × 10
10
u
21
+ · · · + 6.05 × 10
11
b − 8.48 × 10
10
, 2.19 ×
10
12
u
22
−2.11×10
12
u
21
+· · ·+6.05×10
11
a−2.05×10
12
, u
23
−u
22
+· · ·−u+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−3.62364u
22
+ 3.48346u
21
+ ··· + 36.4991u + 3.39190
−0.122322u
22
+ 0.126690u
21
+ ··· + 4.48346u + 0.140181
a
10
=
−8.75272u
22
+ 8.03309u
21
+ ··· + 60.0017u + 7.21619
−0.877678u
22
+ 0.873310u
21
+ ··· + 12.5165u + 0.859819
a
6
=
2.39190u
22
+ 0.231734u
21
+ ··· + 7.02051u − 22.8910
0.140181u
22
− 0.0178599u
21
+ ··· + 0.231734u − 3.62364
a
1
=
−3.62364u
22
+ 3.48346u
21
+ ··· + 35.4991u + 3.39190
−0.122322u
22
+ 0.126690u
21
+ ··· + 4.48346u + 0.140181
a
3
=
−3.96447u
22
− 1.28694u
21
+ ··· − 19.1702u + 31.9505
−0.719637u
22
− 0.0357199u
21
+ ··· − 1.53653u + 8.75272
a
2
=
−2.70321u
22
+ 3.47564u
21
+ ··· + 3.10966u − 15.1028
−5.51731u
22
+ 4.69612u
21
+ ··· + 18.0155u + 1.76587
a
8
=
2.24735u
22
+ 0.226332u
21
+ ··· + 6.77092u − 19.3897
0.317416u
22
− 0.0214925u
21
+ ··· + 0.475926u − 5.97500
a
11
=
−3.50132u
22
+ 3.35677u
21
+ ··· + 32.0157u + 3.25172
−0.122322u
22
+ 0.126690u
21
+ ··· + 4.48346u + 0.140181
a
7
=
2.24735u
22
+ 0.226332u
21
+ ··· + 6.77092u − 19.3897
0.144550u
22
+ 0.00540143u
21
+ ··· + 0.249594u − 3.50132
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
7925175549593
302518887619
u
22
−
5141352911335
302518887619
u
21
+ ··· −
24756789749065
302518887619
u −
8458236233113
302518887619
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
23
+ 10u
22
+ ··· + 208u − 64
c
2
, c
8
u
23
+ 6u
22
+ ··· − 28u − 8
c
3
, c
9
u
23
+ 11u
22
+ ··· − 187u − 49
c
4
, c
6
, c
10
c
12
u
23
+ u
22
+ ··· − u − 1
c
5
, c
11
u
23
− 2u
22
+ ··· − u − 4
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
23
+ 6y
22
+ ··· + 153856y −4096
c
2
, c
8
y
23
+ 10y
22
+ ··· + 208y −64
c
3
, c
9
y
23
− 11y
22
+ ··· + 9979y −2401
c
4
, c
6
, c
10
c
12
y
23
− 19y
22
+ ··· + 35y −1
c
5
, c
11
y
23
− 4y
22
+ ··· + 81y −16
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.070790 + 0.187276I
a = −0.742987 − 0.362569I
b = 0.390360 − 0.513715I
−2.83605 − 0.34568I −1.92962 − 0.43168I
u = 1.070790 − 0.187276I
a = −0.742987 + 0.362569I
b = 0.390360 + 0.513715I
−2.83605 + 0.34568I −1.92962 + 0.43168I
u = −1.072600 + 0.407037I
a = 0.766205 − 0.399094I
b = −0.666528 − 0.655018I
−5.89444 + 5.46645I −3.61005 − 3.53353I
u = −1.072600 − 0.407037I
a = 0.766205 + 0.399094I
b = −0.666528 + 0.655018I
−5.89444 − 5.46645I −3.61005 + 3.53353I
u = 1.110920 + 0.398545I
a = −0.834089 + 0.961871I
b = −0.637726 + 0.694268I
2.55401 − 3.06813I −1.63871 + 4.65576I
u = 1.110920 − 0.398545I
a = −0.834089 − 0.961871I
b = −0.637726 − 0.694268I
2.55401 + 3.06813I −1.63871 − 4.65576I
u = −1.135800 + 0.574185I
a = 0.605932 + 1.053290I
b = 0.819929 + 0.795383I
2.70586 + 9.35880I 0.02921 − 9.42828I
u = −1.135800 − 0.574185I
a = 0.605932 − 1.053290I
b = 0.819929 − 0.795383I
2.70586 − 9.35880I 0.02921 + 9.42828I
u = −1.338780 + 0.103629I
a = 0.734386 − 0.447547I
b = −0.154582 − 0.897495I
−7.50009 − 3.86771I −5.29636 + 4.05215I
u = −1.338780 − 0.103629I
a = 0.734386 + 0.447547I
b = −0.154582 + 0.897495I
−7.50009 + 3.86771I −5.29636 − 4.05215I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.559367 + 0.131643I
a = 0.475373 − 0.977519I
b = 0.843832 − 0.087265I
−0.89508 − 1.63405I −5.04879 + 5.49945I
u = 0.559367 − 0.131643I
a = 0.475373 + 0.977519I
b = 0.843832 + 0.087265I
−0.89508 + 1.63405I −5.04879 − 5.49945I
u = −0.497228
a = −1.49813
b = −0.867620
1.46426 7.43570
u = 0.407932 + 0.126673I
a = 1.76152 − 2.42535I
b = 0.923455 − 0.055957I
3.57163 − 6.00249I 1.32822 + 3.13711I
u = 0.407932 − 0.126673I
a = 1.76152 + 2.42535I
b = 0.923455 + 0.055957I
3.57163 + 6.00249I 1.32822 − 3.13711I
u = −0.410517 + 0.091700I
a = −2.27314 − 1.89786I
b = −0.917370 − 0.041035I
4.23594 + 0.53344I 5.35636 + 2.56439I
u = −0.410517 − 0.091700I
a = −2.27314 + 1.89786I
b = −0.917370 + 0.041035I
4.23594 − 0.53344I 5.35636 − 2.56439I
u = −1.35567 + 1.04234I
a = 0.196756 + 0.866889I
b = 1.24211 + 1.13763I
−1.33962 + 13.52040I 1.78577 − 7.19541I
u = −1.35567 − 1.04234I
a = 0.196756 − 0.866889I
b = 1.24211 − 1.13763I
−1.33962 − 13.52040I 1.78577 + 7.19541I
u = 1.51219 + 0.87780I
a = −0.303869 + 0.790076I
b = −1.04602 + 1.26900I
−6.64500 − 9.40579I −3.02964 + 5.28602I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51219 − 0.87780I
a = −0.303869 − 0.790076I
b = −1.04602 − 1.26900I
−6.64500 + 9.40579I −3.02964 − 5.28602I
u = 1.40078 + 1.17174I
a = −0.137018 + 0.817530I
b = −1.36365 + 1.20364I
−4.3162 − 19.1491I 0. + 10.19089I
u = 1.40078 − 1.17174I
a = −0.137018 − 0.817530I
b = −1.36365 − 1.20364I
−4.3162 + 19.1491I 0. − 10.19089I
8
II.
I
u
2
= h−1.46×10
19
u
19
+6 .73×10
18
u
18
+· · ·+1.62×10
20
b−2.34×10
19
, 3.71×
10
20
u
19
+2.34×10
19
u
18
+· · ·+1.62×10
20
a+1.59×10
21
, u
20
−u
18
+· · ·+3u+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−2.28382u
19
− 0.143897u
18
+ ··· − 130.160u − 9.79501
0.0897498u
19
− 0.0414758u
18
+ ··· + 3.71551u + 0.143897
a
10
=
−5.68826u
19
− 0.375364u
18
+ ··· − 327.025u − 30.6573
0.223394u
19
+ 0.00551549u
18
+ ··· + 10.5299u + 0.519260
a
6
=
1.67369u
19
− 0.373713u
18
+ ··· + 65.0408u − 18.4882
−0.0359603u
19
+ 0.0154898u
18
+ ··· − 0.276275u + 0.686856
a
1
=
−2.28382u
19
− 0.143897u
18
+ ··· − 131.160u − 9.79501
0.0897498u
19
− 0.0414758u
18
+ ··· + 3.71551u + 0.143897
a
3
=
1.26236u
19
− 0.224579u
18
+ ··· + 51.1721u − 12.1131
−0.0559355u
19
+ 0.0231324u
18
+ ··· − 0.437705u + 0.447973
a
2
=
0.511165u
19
+ 0.148405u
18
+ ··· + 37.0146u + 8.25478
−0.0237462u
19
− 0.0172919u
18
+ ··· − 2.38333u − 0.251387
a
8
=
−0.560736u
19
+ 0.223549u
18
+ ··· − 16.6614u + 9.88233
−0.0109358u
19
+ 0.0198959u
18
+ ··· − 0.260832u − 0.446943
a
11
=
−2.37357u
19
− 0.102421u
18
+ ··· − 133.875u − 9.93890
0.0897498u
19
− 0.0414758u
18
+ ··· + 3.71551u + 0.143897
a
7
=
−0.560736u
19
+ 0.223549u
18
+ ··· − 16.6614u + 9.88233
0.00551549u
19
+ 0.0153350u
18
+ ··· − 0.150922u − 0.223394
(ii) Obstruction class = −1
(iii) Cusp Shapes =
943546448183724777466
162288606395093077853
u
19
−
173986704864028047691
162288606395093077853
u
18
+ ··· +
39708143008151636185168
162288606395093077853
u −
7084578997836399174558
162288606395093077853
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 15u
5
+ 8u
4
+ 7u
3
+ 21u
2
+ 4u + 16)
2
c
2
, c
8
(u
10
+ 4u
9
+ ··· + 10u + 4)
2
c
3
, c
9
u
20
+ 8u
19
+ ··· + 830u + 83
c
4
, c
6
, c
10
c
12
u
20
− u
18
+ ··· − 3u + 1
c
5
, c
11
(u
10
+ u
9
+ 4u
8
+ 2u
7
+ 8u
6
+ 3u
5
+ 10u
4
+ u
3
+ 6u
2
+ 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
10
+ 4y
9
+ ··· + 656y + 256)
2
c
2
, c
8
(y
10
+ 4y
9
+ 10y
8
+ 16y
7
+ 19y
6
+ 15y
5
+ 8y
4
+ 7y
3
+ 21y
2
+ 4y + 16)
2
c
3
, c
9
y
20
− 8y
19
+ ··· − 10292y + 6889
c
4
, c
6
, c
10
c
12
y
20
− 2y
19
+ ··· + 93y + 1
c
5
, c
11
(y
10
+ 7y
9
+ ··· + 12y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.878101 + 0.583301I
a = −1.39847 − 0.54079I
b = 0.829594 − 1.082270I
−5.26999 − 11.14310I −1.80160 + 8.96902I
u = 0.878101 − 0.583301I
a = −1.39847 + 0.54079I
b = 0.829594 + 1.082270I
−5.26999 + 11.14310I −1.80160 − 8.96902I
u = −0.830244 + 0.380260I
a = 1.42287 − 0.95520I
b = −0.658323 − 1.038470I
−2.57106 + 5.52159I −0.74616 − 5.88586I
u = −0.830244 − 0.380260I
a = 1.42287 + 0.95520I
b = −0.658323 + 1.038470I
−2.57106 − 5.52159I −0.74616 + 5.88586I
u = 0.754171 + 0.835150I
a = 0.078514 + 0.699849I
b = −0.137529 + 0.843982I
−0.34279 − 2.30596I −2.18955 + 2.56038I
u = 0.754171 − 0.835150I
a = 0.078514 − 0.699849I
b = −0.137529 − 0.843982I
−0.34279 + 2.30596I −2.18955 − 2.56038I
u = 1.138220 + 0.189654I
a = −0.822855 − 0.891283I
b = 0.486573 − 1.288230I
−7.88918 − 1.90048I −5.69479 + 2.00128I
u = 1.138220 − 0.189654I
a = −0.822855 + 0.891283I
b = 0.486573 + 1.288230I
−7.88918 + 1.90048I −5.69479 − 2.00128I
u = −0.566090 + 0.319060I
a = −0.53792 + 1.51199I
b = −0.137529 + 0.843982I
−0.34279 − 2.30596I −2.18955 + 2.56038I
u = −0.566090 − 0.319060I
a = −0.53792 − 1.51199I
b = −0.137529 − 0.843982I
−0.34279 + 2.30596I −2.18955 − 2.56038I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39481 + 0.86900I
a = 0.167709 + 0.693744I
b = 0.486573 + 1.288230I
−7.88918 + 1.90048I −5.69479 − 2.00128I
u = −1.39481 − 0.86900I
a = 0.167709 − 0.693744I
b = 0.486573 − 1.288230I
−7.88918 − 1.90048I −5.69479 + 2.00128I
u = 1.26570 + 1.06716I
a = −0.128939 + 0.690121I
b = −0.658323 + 1.038470I
−2.57106 − 5.52159I −0.74616 + 5.88586I
u = 1.26570 − 1.06716I
a = −0.128939 − 0.690121I
b = −0.658323 − 1.038470I
−2.57106 + 5.52159I −0.74616 − 5.88586I
u = −1.32423 + 1.16531I
a = 0.114487 + 0.683193I
b = 0.829594 + 1.082270I
−5.26999 + 11.14310I −1.80160 − 8.96902I
u = −1.32423 − 1.16531I
a = 0.114487 − 0.683193I
b = 0.829594 − 1.082270I
−5.26999 − 11.14310I −1.80160 + 8.96902I
u = 0.09778 + 1.83437I
a = −0.007047 + 0.395117I
b = −0.020315 + 0.506084I
7.84835 − 3.21983I −57.0679 + 32.9943I
u = 0.09778 − 1.83437I
a = −0.007047 − 0.395117I
b = −0.020315 − 0.506084I
7.84835 + 3.21983I −57.0679 − 32.9943I
u = −0.0185866 + 0.1384080I
a = −4.8884 − 18.2085I
b = −0.020315 + 0.506084I
7.84835 − 3.21983I −57.0679 + 32.9943I
u = −0.0185866 − 0.1384080I
a = −4.8884 + 18.2085I
b = −0.020315 − 0.506084I
7.84835 + 3.21983I −57.0679 − 32.9943I
13
III. I
u
3
=
h1.60×10
20
u
19
+2.01×10
20
u
18
+· · ·+2.30×10
21
b+5.16×10
21
, 1.91×10
14
u
19
+
5.99 × 10
13
u
18
+ · · · + 4.75 × 10
15
a + 5.07 × 10
15
, u
20
+ u
19
+ · · · − 30u + 25i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−0.0403268u
19
− 0.0126083u
18
+ ··· + 3.57021u − 1.06764
−0.0695491u
19
− 0.0873389u
18
+ ··· + 2.47363u − 2.24439
a
10
=
−0.000326844u
19
+ 0.0273917u
18
+ ··· + 2.21021u − 2.26764
0.00605246u
19
− 0.00966335u
18
+ ··· − 1.36550u − 0.249654
a
6
=
0.0343387u
19
+ 0.0363335u
18
+ ··· − 1.40311u − 0.235985
−0.0277185u
19
+ 0.00805344u
18
+ ··· + 2.27744u − 1.00817
a
1
=
−0.00654973u
19
+ 0.0303949u
18
+ ··· + 2.93631u + 0.483791
0.00444824u
19
+ 0.0442556u
18
+ ··· + 1.90598u − 2.47505
a
3
=
−0.00998617u
19
− 0.0160386u
18
+ ··· − 0.204310u + 1.66509
0.0277185u
19
− 0.00805344u
18
+ ··· − 2.27744u + 0.00817109
a
2
=
−0.139853u
19
− 0.252295u
18
+ ··· + 0.487132u + 3.71138
0.101351u
19
+ 0.234359u
18
+ ··· + 2.23784u − 3.13571
a
8
=
0.0798470u
19
+ 0.163485u
18
+ ··· + 0.650315u − 0.966541
0.0398807u
19
+ 0.0318047u
18
+ ··· − 1.54045u − 1.36040
a
11
=
0.0292222u
19
+ 0.0747306u
18
+ ··· + 1.09658u + 1.17675
−0.0695491u
19
− 0.0873389u
18
+ ··· + 2.47363u − 2.24439
a
7
=
0.0798470u
19
+ 0.163485u
18
+ ··· + 0.650315u − 0.966541
−0.0455083u
19
− 0.127152u
18
+ ··· − 2.05342u + 0.730556
(ii) Obstruction class = −1
(iii) Cusp Shapes =
63016511487834469996
459924684567833616871
u
19
+
1614067057579186795936
2299623422839168084355
u
18
+ ··· +
42480961559948402726608
2299623422839168084355
u −
8760960183302624060910
459924684567833616871
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
4
c
2
, c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
4
c
3
, c
9
(u
2
− u + 1)
10
c
4
, c
6
, c
10
c
12
u
20
− u
19
+ ··· + 30u + 25
c
5
, c
11
u
20
− 3u
19
+ ··· − 12u + 133
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
4
c
2
, c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
4
c
3
, c
9
(y
2
+ y + 1)
10
c
4
, c
6
, c
10
c
12
y
20
− 5y
19
+ ··· − 2600y + 625
c
5
, c
11
y
20
+ 15y
19
+ ··· + 154136y + 17689
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.008430 + 0.054549I
a = 0.448057 − 0.883026I
b = −0.97656 − 2.23888I
−5.87256 − 8.46060I −6.74431 + 10.42679I
u = 1.008430 − 0.054549I
a = 0.448057 + 0.883026I
b = −0.97656 + 2.23888I
−5.87256 + 8.46060I −6.74431 − 10.42679I
u = −0.706377 + 0.754086I
a = 0.280878 − 0.926161I
b = −0.62115 − 1.53213I
−0.32910 + 5.59035I −2.51511 − 11.35885I
u = −0.706377 − 0.754086I
a = 0.280878 + 0.926161I
b = −0.62115 + 1.53213I
−0.32910 − 5.59035I −2.51511 + 11.35885I
u = 0.627334 + 0.835733I
a = −0.375549 − 0.880179I
b = 1.04129 − 0.96771I
−0.32910 − 2.52919I −2.51511 + 2.49755I
u = 0.627334 − 0.835733I
a = −0.375549 + 0.880179I
b = 1.04129 + 0.96771I
−0.32910 + 2.52919I −2.51511 − 2.49755I
u = 0.003860 + 0.842294I
a = 1.030870 − 0.588893I
b = −0.100183 − 0.411243I
−0.32910 + 2.52919I −2.51511 − 2.49755I
u = 0.003860 − 0.842294I
a = 1.030870 + 0.588893I
b = −0.100183 + 0.411243I
−0.32910 − 2.52919I −2.51511 + 2.49755I
u = 0.754650 + 0.249290I
a = 0.939166 + 0.837342I
b = −1.49241 + 1.64802I
−5.87256 − 0.34107I −6.74431 − 3.42962I
u = 0.754650 − 0.249290I
a = 0.939166 − 0.837342I
b = −1.49241 − 1.64802I
−5.87256 + 0.34107I −6.74431 + 3.42962I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.750939 + 0.035102I
a = −0.610590 − 1.181800I
b = 0.95394 − 1.72247I
−2.40108 + 4.05977I −3.48114 − 6.92820I
u = −0.750939 − 0.035102I
a = −0.610590 + 1.181800I
b = 0.95394 + 1.72247I
−2.40108 − 4.05977I −3.48114 + 6.92820I
u = 0.385099 + 1.297440I
a = −0.508322 − 0.536253I
b = 0.609785 − 0.438873I
−0.32910 − 5.59035I −2.51511 + 11.35885I
u = 0.385099 − 1.297440I
a = −0.508322 + 0.536253I
b = 0.609785 + 0.438873I
−0.32910 + 5.59035I −2.51511 − 11.35885I
u = 1.35981 + 1.08969I
a = −0.086876 − 0.567255I
b = 0.872666 − 0.667883I
−2.40108 − 4.05977I −3.48114 + 6.92820I
u = 1.35981 − 1.08969I
a = −0.086876 + 0.567255I
b = 0.872666 + 0.667883I
−2.40108 + 4.05977I −3.48114 − 6.92820I
u = −1.65384 + 0.86983I
a = −0.021086 − 0.534734I
b = −0.825567 − 0.748066I
−5.87256 − 0.34107I −6.74431 − 3.42962I
u = −1.65384 − 0.86983I
a = −0.021086 + 0.534734I
b = −0.825567 + 0.748066I
−5.87256 + 0.34107I −6.74431 + 3.42962I
u = −1.52802 + 1.39283I
a = 0.103448 − 0.472469I
b = −0.961811 − 0.681432I
−5.87256 + 8.46060I −6.74431 − 10.42679I
u = −1.52802 − 1.39283I
a = 0.103448 + 0.472469I
b = −0.961811 + 0.681432I
−5.87256 − 8.46060I −6.74431 + 10.42679I
18
IV. I
u
4
= h−4.98 × 10
100
u
39
+ 3.97 × 10
100
u
38
+ · · · + 8.14 × 10
103
b + 9.26 ×
10
103
, −6.54 × 10
86
u
39
+ 5.51 × 10
86
u
38
+ · · · + 6.14 × 10
89
a + 9.19 ×
10
89
, u
40
− u
39
+ · · · − 2058u + 661i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
0.00106411u
39
− 0.000896274u
38
+ ··· + 4.19960u − 1.49596
0.000611639u
39
− 0.000487310u
38
+ ··· − 0.146617u − 1.13690
a
10
=
−0.000607927u
39
+ 0.000578380u
38
+ ··· − 3.29473u + 0.728004
−0.000592683u
39
+ 0.000499413u
38
+ ··· + 0.927163u + 0.598919
a
6
=
0.000104535u
39
− 0.0000685482u
38
+ ··· + 3.44772u + 0.445244
0.000455393u
39
− 0.000513387u
38
+ ··· + 3.63636u − 1.62677
a
1
=
0.000436418u
39
− 0.000518640u
38
+ ··· + 3.98825u − 0.470010
0.000594930u
39
− 0.000123584u
38
+ ··· − 0.246336u − 0.971606
a
3
=
0.000646542u
39
− 0.000900890u
38
+ ··· − 2.25160u − 1.27770
−0.000833117u
39
+ 0.00105792u
38
+ ··· − 8.30405u + 1.36832
a
2
=
0.000367044u
39
− 0.000242957u
38
+ ··· + 8.59321u − 0.673734
0.00187542u
39
− 0.00168201u
38
+ ··· + 3.68685u − 2.46681
a
8
=
−0.000773486u
39
+ 0.000867048u
38
+ ··· + 0.846502u + 2.07023
0.000445917u
39
− 0.000427270u
38
+ ··· + 11.5103u − 1.29118
a
11
=
0.000452474u
39
− 0.000408964u
38
+ ··· + 4.34621u − 0.359069
0.000611639u
39
− 0.000487310u
38
+ ··· − 0.146617u − 1.13690
a
7
=
−0.000773486u
39
+ 0.000867048u
38
+ ··· + 0.846502u + 2.07023
0.000462623u
39
− 0.000503228u
38
+ ··· + 10.8065u − 1.22934
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.00369208u
39
− 0.00356863u
38
+ ··· + 25.2411u + 6.36746
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
8
c
2
, c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
8
c
3
, c
9
(u
4
− u
3
+ 2u + 1)
10
c
4
, c
6
, c
10
c
12
u
40
+ u
39
+ ··· + 2058u + 661
c
5
, c
11
(u
20
+ u
19
+ ··· + 8u + 7)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
8
c
2
, c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
8
c
3
, c
9
(y
4
− y
3
+ 6y
2
− 4y + 1)
10
c
4
, c
6
, c
10
c
12
y
40
+ 25y
39
+ ··· + 1110804y + 436921
c
5
, c
11
(y
20
− 5y
19
+ ··· + 832y + 49)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637978 + 0.724823I
a = −0.05148 − 1.59323I
b = 0.413445 − 0.299501I
0.88879 − 4.05977I 8.51886 + 6.92820I
u = 0.637978 − 0.724823I
a = −0.05148 + 1.59323I
b = 0.413445 + 0.299501I
0.88879 + 4.05977I 8.51886 − 6.92820I
u = −0.242959 + 1.021930I
a = −0.036919 + 0.617393I
b = 1.31470 + 1.71034I
−2.58269 + 8.46060I 5.25569 − 10.42679I
u = −0.242959 − 1.021930I
a = −0.036919 − 0.617393I
b = 1.31470 − 1.71034I
−2.58269 − 8.46060I 5.25569 + 10.42679I
u = 0.404610 + 0.987240I
a = −0.058258 + 0.606127I
b = −1.02231 + 1.35409I
0.88879 − 4.05977I 8.51886 + 6.92820I
u = 0.404610 − 0.987240I
a = −0.058258 − 0.606127I
b = −1.02231 − 1.35409I
0.88879 + 4.05977I 8.51886 − 6.92820I
u = −0.288907 + 1.065080I
a = 0.655403 − 1.231190I
b = −1.138120 − 0.440255I
2.96077 + 2.52919I 9.48489 − 2.49755I
u = −0.288907 − 1.065080I
a = 0.655403 + 1.231190I
b = −1.138120 + 0.440255I
2.96077 − 2.52919I 9.48489 + 2.49755I
u = −1.066130 + 0.440454I
a = −0.550136 − 1.215670I
b = −1.02231 − 1.35409I
0.88879 + 4.05977I 8.51886 − 6.92820I
u = −1.066130 − 0.440454I
a = −0.550136 + 1.215670I
b = −1.02231 + 1.35409I
0.88879 − 4.05977I 8.51886 + 6.92820I
22
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.164110 + 0.023151I
a = 0.981408 + 0.885684I
b = 0.56524 + 1.63789I
−2.58269 − 0.34107I 5.25569 − 3.42962I
u = 1.164110 − 0.023151I
a = 0.981408 − 0.885684I
b = 0.56524 − 1.63789I
−2.58269 + 0.34107I 5.25569 + 3.42962I
u = −0.716452 + 0.385226I
a = −0.60133 − 1.79412I
b = −0.045656 − 0.299605I
−2.58269 − 0.34107I 5.25569 − 3.42962I
u = −0.716452 − 0.385226I
a = −0.60133 + 1.79412I
b = −0.045656 + 0.299605I
−2.58269 + 0.34107I 5.25569 + 3.42962I
u = −0.407885 + 1.125790I
a = 0.029534 + 0.541768I
b = 0.56524 + 1.63789I
−2.58269 − 0.34107I 5.25569 − 3.42962I
u = −0.407885 − 1.125790I
a = 0.029534 − 0.541768I
b = 0.56524 − 1.63789I
−2.58269 + 0.34107I 5.25569 + 3.42962I
u = −0.896389 + 0.812519I
a = −0.102151 − 1.268150I
b = −0.415504 − 0.591215I
−2.58269 + 8.46060I 5.25569 − 10.42679I
u = −0.896389 − 0.812519I
a = −0.102151 + 1.268150I
b = −0.415504 + 0.591215I
−2.58269 − 8.46060I 5.25569 + 10.42679I
u = 0.434194 + 1.213710I
a = −0.476526 − 1.094890I
b = 1.094530 − 0.430480I
2.96077 − 5.59035I 9.4849 + 11.3589I
u = 0.434194 − 1.213710I
a = −0.476526 + 1.094890I
b = 1.094530 + 0.430480I
2.96077 + 5.59035I 9.4849 − 11.3589I
23
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.308359 + 1.330800I
a = −0.566081 − 0.974243I
b = 1.45940 + 0.10309I
2.96077 − 2.52919I 9.48489 + 2.49755I
u = 0.308359 − 1.330800I
a = −0.566081 + 0.974243I
b = 1.45940 − 0.10309I
2.96077 + 2.52919I 9.48489 − 2.49755I
u = 1.42917 + 0.39610I
a = −0.370340 + 0.233998I
b = −1.138120 + 0.440255I
2.96077 − 2.52919I 9.48489 + 2.49755I
u = 1.42917 − 0.39610I
a = −0.370340 − 0.233998I
b = −1.138120 − 0.440255I
2.96077 + 2.52919I 9.48489 − 2.49755I
u = −0.67158 + 1.33468I
a = 0.292487 − 0.987795I
b = −1.72572 − 0.42392I
2.96077 + 5.59035I 9.4849 − 11.3589I
u = −0.67158 − 1.33468I
a = 0.292487 + 0.987795I
b = −1.72572 + 0.42392I
2.96077 − 5.59035I 9.4849 + 11.3589I
u = −0.174867 + 0.418319I
a = 0.91109 + 1.10596I
b = 1.45940 + 0.10309I
2.96077 − 2.52919I 9.48489 + 2.49755I
u = −0.174867 − 0.418319I
a = 0.91109 − 1.10596I
b = 1.45940 − 0.10309I
2.96077 + 2.52919I 9.48489 − 2.49755I
u = 1.44641 + 0.55826I
a = 0.430390 − 0.894647I
b = 1.31470 − 1.71034I
−2.58269 − 8.46060I 5.25569 + 10.42679I
u = 1.44641 − 0.55826I
a = 0.430390 + 0.894647I
b = 1.31470 + 1.71034I
−2.58269 + 8.46060I 5.25569 − 10.42679I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56112 + 0.48621I
a = 0.397321 + 0.003491I
b = 1.094530 − 0.430480I
2.96077 − 5.59035I 9.4849 + 11.3589I
u = −1.56112 − 0.48621I
a = 0.397321 − 0.003491I
b = 1.094530 + 0.430480I
2.96077 + 5.59035I 9.4849 − 11.3589I
u = 0.214838 + 0.164995I
a = −1.39887 + 1.94815I
b = −1.72572 + 0.42392I
2.96077 − 5.59035I 9.4849 + 11.3589I
u = 0.214838 − 0.164995I
a = −1.39887 − 1.94815I
b = −1.72572 − 0.42392I
2.96077 + 5.59035I 9.4849 − 11.3589I
u = −0.58533 + 1.89216I
a = 0.183352 + 0.271987I
b = 0.413445 − 0.299501I
0.88879 − 4.05977I 0
u = −0.58533 − 1.89216I
a = 0.183352 − 0.271987I
b = 0.413445 + 0.299501I
0.88879 + 4.05977I 0
u = 0.10021 + 2.26152I
a = −0.095010 + 0.270810I
b = −0.045656 − 0.299605I
−2.58269 − 0.34107I 0
u = 0.10021 − 2.26152I
a = −0.095010 − 0.270810I
b = −0.045656 + 0.299605I
−2.58269 + 0.34107I 0
u = 0.97174 + 2.30033I
a = −0.166174 + 0.200183I
b = −0.415504 − 0.591215I
−2.58269 + 8.46060I 0
u = 0.97174 − 2.30033I
a = −0.166174 − 0.200183I
b = −0.415504 + 0.591215I
−2.58269 − 8.46060I 0
25
V.
I
u
5
= h−9.70×10
33
u
33
−1.36×10
34
u
32
+· · ·+2.94×10
34
b+1.13×10
34
, 3.22×
10
34
u
33
+2.09×10
34
u
32
+· · ·+2.94×10
34
a−8.32×10
34
, u
34
+u
33
+· · ·−u+1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
−1.09559u
33
− 0.709759u
32
+ ··· − 22.4459u + 2.83117
0.330043u
33
+ 0.463983u
32
+ ··· + 0.481423u − 0.385832
a
10
=
−5.37913u
33
− 5.58520u
32
+ ··· − 48.2379u + 12.8517
−0.215334u
33
− 0.545172u
32
+ ··· + 4.69165u + 0.591897
a
6
=
2.37063u
33
+ 3.63782u
32
+ ··· + 15.1197u + 5.19638
0.931915u
33
+ 1.27442u
32
+ ··· − 1.53579u − 1.81257
a
1
=
−1.09559u
33
− 0.709759u
32
+ ··· − 21.4459u + 2.83117
0.330043u
33
+ 0.463983u
32
+ ··· + 0.481423u − 0.385832
a
3
=
−2.47525u
33
− 3.46325u
32
+ ··· − 9.88125u − 2.82033
−2.29891u
33
− 3.08203u
32
+ ··· + 4.31129u + 2.74504
a
2
=
−0.963759u
33
− 1.57897u
32
+ ··· + 7.48952u − 1.92757
−1.04463u
33
− 1.21170u
32
+ ··· + 1.88300u + 0.541427
a
8
=
1.17761u
33
+ 1.37985u
32
+ ··· − 8.32905u − 5.14271
2.23540u
33
+ 3.07140u
32
+ ··· − 3.79942u − 1.95927
a
11
=
−1.42563u
33
− 1.17374u
32
+ ··· − 22.9273u + 3.21700
0.330043u
33
+ 0.463983u
32
+ ··· + 0.481423u − 0.385832
a
7
=
1.17761u
33
+ 1.37985u
32
+ ··· − 8.32905u − 5.14271
1.71683u
33
+ 2.33963u
32
+ ··· − 2.82405u − 1.75703
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12.7757u
33
+ 19.8241u
32
+ ··· + 79.8197u + 31.8684
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
17
− 9u
16
+ ··· + 10u − 3)
2
c
2
, c
8
u
34
+ 9u
32
+ ··· + 10u
2
+ 3
c
3
, c
9
u
34
+ 19u
33
+ ··· + 8u + 1
c
4
, c
6
, c
10
c
12
u
34
+ u
33
+ ··· − u + 1
c
5
, c
11
(u
17
− u
16
+ ··· + 4u − 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
17
+ 7y
16
+ ··· + 82y −9)
2
c
2
, c
8
(y
17
+ 9y
16
+ ··· + 10y + 3)
2
c
3
, c
9
y
34
− 19y
33
+ ··· − 8y + 1
c
4
, c
6
, c
10
c
12
y
34
+ 19y
33
+ ··· + 13y + 1
c
5
, c
11
(y
17
− 5y
16
+ ··· + 6y −1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.976266 + 0.149592I
a = −0.81504 − 1.28743I
b = −0.158338 − 1.109770I
−3.36856 − 0.53554I −6.70592 − 0.22374I
u = −0.976266 − 0.149592I
a = −0.81504 + 1.28743I
b = −0.158338 + 1.109770I
−3.36856 + 0.53554I −6.70592 + 0.22374I
u = −0.384602 + 0.904554I
a = 0.58831 − 1.62135I
b = −1.137850 − 0.227099I
4.40354 + 7.01611I 7.72183 − 10.06852I
u = −0.384602 − 0.904554I
a = 0.58831 + 1.62135I
b = −1.137850 + 0.227099I
4.40354 − 7.01611I 7.72183 + 10.06852I
u = 0.247554 + 0.999868I
a = 0.453217 − 0.826367I
b = −0.263790
1.88654 2.67113 + 0.I
u = 0.247554 − 0.999868I
a = 0.453217 + 0.826367I
b = −0.263790
1.88654 2.67113 + 0.I
u = −0.918571 + 0.264502I
a = 0.518445 + 0.077778I
b = 1.35754 − 0.45624I
2.48881 − 5.22305I −3.94000 + 1.19179I
u = −0.918571 − 0.264502I
a = 0.518445 − 0.077778I
b = 1.35754 + 0.45624I
2.48881 + 5.22305I −3.94000 − 1.19179I
u = 0.518657 + 0.908593I
a = −0.26755 − 1.55368I
b = 1.094580 − 0.296082I
4.71928 − 1.93696I 8.82934 + 2.56871I
u = 0.518657 − 0.908593I
a = −0.26755 + 1.55368I
b = 1.094580 + 0.296082I
4.71928 + 1.93696I 8.82934 − 2.56871I
29
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.768987 + 0.557589I
a = −0.016994 − 1.408560I
b = 0.434167 − 0.967172I
−0.19288 − 3.94620I −0.68696 + 6.09510I
u = 0.768987 − 0.557589I
a = −0.016994 + 1.408560I
b = 0.434167 + 0.967172I
−0.19288 + 3.94620I −0.68696 − 6.09510I
u = 0.921631 + 0.026383I
a = −0.501515 + 0.342023I
b = −1.363900 + 0.239505I
2.27186 − 2.61623I −4.64736 + 4.07054I
u = 0.921631 − 0.026383I
a = −0.501515 − 0.342023I
b = −1.363900 − 0.239505I
2.27186 + 2.61623I −4.64736 − 4.07054I
u = 0.310664 + 1.220730I
a = −0.335927 − 0.364757I
b = 0.434167 − 0.967172I
−0.19288 − 3.94620I −0.68696 + 6.09510I
u = 0.310664 − 1.220730I
a = −0.335927 + 0.364757I
b = 0.434167 + 0.967172I
−0.19288 + 3.94620I −0.68696 − 6.09510I
u = −0.296892 + 1.237950I
a = 0.633863 − 1.013850I
b = −1.363900 − 0.239505I
2.27186 + 2.61623I −4.64736 − 4.07054I
u = −0.296892 − 1.237950I
a = 0.633863 + 1.013850I
b = −1.363900 + 0.239505I
2.27186 − 2.61623I −4.64736 + 4.07054I
u = −1.172420 + 0.680700I
a = −0.216690 − 0.982712I
b = −0.593567 − 1.230290I
−3.54020 + 8.11632I −4.12081 − 7.01955I
u = −1.172420 − 0.680700I
a = −0.216690 + 0.982712I
b = −0.593567 + 1.230290I
−3.54020 − 8.11632I −4.12081 + 7.01955I
30
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.077311 + 1.390950I
a = 0.273548 − 0.052796I
b = −0.593567 − 1.230290I
−3.54020 + 8.11632I −4.12081 − 7.01955I
u = 0.077311 − 1.390950I
a = 0.273548 + 0.052796I
b = −0.593567 + 1.230290I
−3.54020 − 8.11632I −4.12081 + 7.01955I
u = 0.555507 + 1.291860I
a = −0.358785 − 0.992839I
b = 1.35754 − 0.45624I
2.48881 − 5.22305I −3.94000 + 0.I
u = 0.555507 − 1.291860I
a = −0.358785 + 0.992839I
b = 1.35754 + 0.45624I
2.48881 + 5.22305I −3.94000 + 0.I
u = 0.589578 + 0.016869I
a = −1.53334 + 0.79026I
b = −1.137850 + 0.227099I
4.40354 − 7.01611I 7.72183 + 10.06852I
u = 0.589578 − 0.016869I
a = −1.53334 − 0.79026I
b = −1.137850 − 0.227099I
4.40354 + 7.01611I 7.72183 − 10.06852I
u = −0.552805 + 0.090382I
a = 1.84558 − 0.07153I
b = 1.094580 − 0.296082I
4.71928 − 1.93696I 8.82934 + 2.56871I
u = −0.552805 − 0.090382I
a = 1.84558 + 0.07153I
b = 1.094580 + 0.296082I
4.71928 + 1.93696I 8.82934 − 2.56871I
u = −0.35523 + 1.54438I
a = 0.108337 − 0.245021I
b = −0.158338 − 1.109770I
−3.36856 − 0.53554I 0
u = −0.35523 − 1.54438I
a = 0.108337 + 0.245021I
b = −0.158338 + 1.109770I
−3.36856 + 0.53554I 0
31
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 0.059071 + 0.276114I
a = 3.10812 − 8.72000I
b = −0.000733 + 0.459650I
7.90175 + 3.19247I 61.7143 + 27.7022I
u = 0.059071 − 0.276114I
a = 3.10812 + 8.72000I
b = −0.000733 − 0.459650I
7.90175 − 3.19247I 61.7143 − 27.7022I
u = 0.10782 + 1.81029I
a = 0.016417 − 0.411643I
b = −0.000733 − 0.459650I
7.90175 − 3.19247I 0
u = 0.10782 − 1.81029I
a = 0.016417 + 0.411643I
b = −0.000733 + 0.459650I
7.90175 + 3.19247I 0
32
VI. I
u
6
= hb − u, a, u
5
+ u
4
− 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
0
u
a
10
=
0
u
a
6
=
1
0
a
1
=
−u
−u
3
+ u
a
3
=
1
0
a
2
=
u
3
− 2u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
−u
u
a
7
=
−u
2
+ 1
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 8u − 6
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
2
, c
8
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
3
, c
9
u
5
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
8
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
, c
9
y
5
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
35
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.21774
a = 0
b = 1.21774
−2.40108 −3.48110
u = 0.309916 + 0.549911I
a = 0
b = 0.309916 + 0.549911I
−0.32910 − 1.53058I −2.51511 + 4.43065I
u = 0.309916 − 0.549911I
a = 0
b = 0.309916 − 0.549911I
−0.32910 + 1.53058I −2.51511 − 4.43065I
u = −1.41878 + 0.21917I
a = 0
b = −1.41878 + 0.21917I
−5.87256 + 4.40083I −6.74431 − 3.49859I
u = −1.41878 − 0.21917I
a = 0
b = −1.41878 − 0.21917I
−5.87256 − 4.40083I −6.74431 + 3.49859I
36
VII. I
u
7
= h2405u
9
− 2260u
8
+ · · · + 7829b − 605, −u
9
+ u
8
+ · · · + a −
6u, u
10
− u
9
+ · · · + 6u
2
− 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
12
=
u
9
− u
8
− 2u
7
− 2u
6
− 2u
5
+ 12u
4
+ 9u
3
+ 9u
2
+ 6u
−0.307191u
9
+ 0.288670u
8
+ ··· − 3.06310u + 0.0772768
a
10
=
u
9
− u
8
− 2u
7
− 2u
6
− 2u
5
+ 12u
4
+ 9u
3
+ 9u
2
+ 6u
−0.307191u
9
+ 0.288670u
8
+ ··· − 2.06310u + 0.0772768
a
6
=
−0.0772768u
9
+ 0.384468u
8
+ ··· + 1.63278u + 4.06310
−1
a
1
=
1.30719u
9
− 1.28867u
8
+ ··· + 10.0631u − 0.0772768
−0.364287u
9
+ 0.514881u
8
+ ··· − 2.75591u + 0.0957977
a
3
=
0.0772768u
9
− 0.384468u
8
+ ··· − 1.63278u − 3.06310
1
a
2
=
1.17129u
9
− 1.67863u
8
+ ··· + 4.07843u − 0.0555627
−0.478477u
9
+ 0.967301u
8
+ ··· − 1.14153u + 0.132839
a
8
=
−0.0370418u
9
+ 0.151233u
8
+ ··· + 0.154554u − 1.61438
−0.301188u
9
+ 0.374505u
8
+ ··· − 0.191595u + 0.728573
a
11
=
1.30719u
9
− 1.28867u
8
+ ··· + 9.06310u − 0.0772768
−0.307191u
9
+ 0.288670u
8
+ ··· − 3.06310u + 0.0772768
a
7
=
−0.0370418u
9
+ 0.151233u
8
+ ··· + 0.154554u − 1.61438
0.0370418u
9
− 0.151233u
8
+ ··· − 0.154554u + 0.614382
(ii) Obstruction class = −1
(iii) Cusp Shapes =
13196
7829
u
9
−
23208
7829
u
8
−
12296
7829
u
7
−
7276
7829
u
6
−
18432
7829
u
5
+
163556
7829
u
4
−
7056
7829
u
3
+
77452
7829
u
2
+
45368
7829
u+
43394
7829
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
2
c
2
, c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
3
, c
9
(u − 1)
10
c
4
, c
6
, c
10
c
12
u
10
+ u
9
− 2u
8
+ 2u
7
− 2u
6
− 12u
5
+ 9u
4
− 9u
3
+ 6u
2
− 1
c
5
, c
11
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
2
, c
8
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
3
, c
9
(y −1)
10
c
4
, c
6
, c
10
c
12
y
10
− 5y
9
+ ··· − 12y + 1
c
5
, c
11
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
7
√
−1(vol +
√
−1CS) Cusp shape
u = 0.032386 + 0.862164I
a = 0.043508 − 1.158240I
b = −0.309916 − 0.549911I
2.96077 − 1.53058I 9.48489 + 4.43065I
u = 0.032386 − 0.862164I
a = 0.043508 + 1.158240I
b = −0.309916 + 0.549911I
2.96077 + 1.53058I 9.48489 − 4.43065I
u = −0.536962 + 0.202275I
a = −1.63090 − 0.61436I
b = 1.41878 − 0.21917I
−2.58269 + 4.40083I 5.25569 − 3.49859I
u = −0.536962 − 0.202275I
a = −1.63090 + 0.61436I
b = 1.41878 + 0.21917I
−2.58269 − 4.40083I 5.25569 + 3.49859I
u = −0.34230 + 1.41207I
a = −0.162142 − 0.668873I
b = −0.309916 + 0.549911I
2.96077 + 1.53058I 9.48489 − 4.43065I
u = −0.34230 − 1.41207I
a = −0.162142 + 0.668873I
b = −0.309916 − 0.549911I
2.96077 − 1.53058I 9.48489 + 4.43065I
u = −1.53277
a = −0.652412
b = −1.21774
0.888787 8.51890
u = 0.315037
a = 3.17423
b = −1.21774
0.888787 8.51890
u = 1.95575 + 0.42144I
a = 0.488625 − 0.105293I
b = 1.41878 + 0.21917I
−2.58269 − 4.40083I 5.25569 + 3.49859I
u = 1.95575 − 0.42144I
a = 0.488625 + 0.105293I
b = 1.41878 − 0.21917I
−2.58269 + 4.40083I 5.25569 − 3.49859I
40
VIII. I
u
8
= hb + u − 1, a + u, u
2
− u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u − 1
a
12
=
−u
−u + 1
a
10
=
−1
0
a
6
=
u
u − 1
a
1
=
0
−u
a
3
=
0
−u
a
2
=
0
−u
a
8
=
0
u
a
11
=
−1
−u + 1
a
7
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u − 4
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
2
c
3
, c
5
, c
9
c
11
u
2
+ u + 1
c
4
, c
6
, c
10
c
12
u
2
− u + 1
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
2
c
3
, c
4
, c
5
c
6
, c
9
, c
10
c
11
, c
12
y
2
+ y + 1
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
8
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 0.500000 − 0.866025I
− 4.05977I 0. + 6.92820I
u = 0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 0.500000 + 0.866025I
4.05977I 0. − 6.92820I
44
IX. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
2
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
15
· (u
10
+ 4u
9
+ 10u
8
+ 16u
7
+ 19u
6
+ 15u
5
+ 8u
4
+ 7u
3
+ 21u
2
+ 4u + 16)
2
· ((u
17
− 9u
16
+ ··· + 10u − 3)
2
)(u
23
+ 10u
22
+ ··· + 208u − 64)
c
2
, c
8
u
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
14
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
· ((u
10
+ 4u
9
+ ··· + 10u + 4)
2
)(u
23
+ 6u
22
+ ··· − 28u − 8)
· (u
34
+ 9u
32
+ ··· + 10u
2
+ 3)
c
3
, c
9
u
5
(u − 1)
10
(u
2
− u + 1)
10
(u
2
+ u + 1)(u
4
− u
3
+ 2u + 1)
10
· (u
20
+ 8u
19
+ ··· + 830u + 83)(u
23
+ 11u
22
+ ··· − 187u − 49)
· (u
34
+ 19u
33
+ ··· + 8u + 1)
c
4
, c
6
, c
10
c
12
(u
2
− u + 1)(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
· (u
10
+ u
9
− 2u
8
+ 2u
7
− 2u
6
− 12u
5
+ 9u
4
− 9u
3
+ 6u
2
− 1)
· (u
20
− u
18
+ ··· − 3u + 1)(u
20
− u
19
+ ··· + 30u + 25)
· (u
23
+ u
22
+ ··· − u − 1)(u
34
+ u
33
+ ··· − u + 1)
· (u
40
+ u
39
+ ··· + 2058u + 661)
c
5
, c
11
(u
2
+ u + 1)(u
5
− u
4
+ ··· + u + 1)(u
5
+ u
4
+ ··· + u − 1)
2
· (u
10
+ u
9
+ 4u
8
+ 2u
7
+ 8u
6
+ 3u
5
+ 10u
4
+ u
3
+ 6u
2
+ 1)
2
· ((u
17
− u
16
+ ··· + 4u − 1)
2
)(u
20
− 3u
19
+ ··· − 12u + 133)
· ((u
20
+ u
19
+ ··· + 8u + 7)
2
)(u
23
− 2u
22
+ ··· − u − 4)
45
X. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
2
(y
5
− y
4
+ ··· + 3y −1)
15
(y
10
+ 4y
9
+ ··· + 656y + 256)
2
· ((y
17
+ 7y
16
+ ··· + 82y −9)
2
)(y
23
+ 6y
22
+ ··· + 153856y −4096)
c
2
, c
8
y
2
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
15
· (y
10
+ 4y
9
+ 10y
8
+ 16y
7
+ 19y
6
+ 15y
5
+ 8y
4
+ 7y
3
+ 21y
2
+ 4y + 16)
2
· ((y
17
+ 9y
16
+ ··· + 10y + 3)
2
)(y
23
+ 10y
22
+ ··· + 208y −64)
c
3
, c
9
y
5
(y −1)
10
(y
2
+ y + 1)
11
(y
4
− y
3
+ 6y
2
− 4y + 1)
10
· (y
20
− 8y
19
+ ··· − 10292y + 6889)
· (y
23
− 11y
22
+ ··· + 9979y −2401)(y
34
− 19y
33
+ ··· − 8y + 1)
c
4
, c
6
, c
10
c
12
(y
2
+ y + 1)(y
5
− 5y
4
+ ··· − y −1)(y
10
− 5y
9
+ ··· − 12y + 1)
· (y
20
− 5y
19
+ ··· − 2600y + 625)(y
20
− 2y
19
+ ··· + 93y + 1)
· (y
23
− 19y
22
+ ··· + 35y −1)(y
34
+ 19y
33
+ ··· + 13y + 1)
· (y
40
+ 25y
39
+ ··· + 1110804y + 436921)
c
5
, c
11
(y
2
+ y + 1)(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
3
· ((y
10
+ 7y
9
+ ··· + 12y + 1)
2
)(y
17
− 5y
16
+ ··· + 6y −1)
2
· (y
20
− 5y
19
+ ··· + 832y + 49)
2
· (y
20
+ 15y
19
+ ··· + 154136y + 17689)(y
23
− 4y
22
+ ··· + 81y −16)
46
