12n
0499
(K12n
0499
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 2 12 11 3 6 8 4 9
Solving Sequence
3,7 4,11
8 9 12 6 2 1 5 10
c
3
c
7
c
8
c
11
c
6
c
2
c
1
c
5
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h253607u
17
− 119815u
16
+ ··· + 2792b + 534547,
− 1130011u
17
+ 534547u
16
+ ··· + 2792a − 2385431,
u
18
− u
16
+ u
15
+ 9u
14
+ u
13
− 6u
12
+ 3u
11
+ 21u
10
+ 4u
9
− 7u
8
+ 5u
7
+ 16u
6
− 9u
4
− 9u
3
− u
2
+ 3u + 1i
I
u
2
= hu
11
+ u
10
− 3u
9
+ 2u
8
+ 7u
7
− 6u
5
+ 6u
4
+ 8u
3
− 8u
2
+ 4b + u + 3,
− 9u
11
+ 3u
10
− u
9
− 10u
8
− 39u
7
+ 4u
6
− 22u
5
− 30u
4
− 36u
3
+ 12u
2
+ 4a − 17u − 7,
u
12
+ u
9
+ 5u
8
+ u
7
+ 2u
6
+ 4u
5
+ 6u
4
+ u
2
+ 2u + 1i
I
u
3
= h4.82591 × 10
21
u
23
− 1.43753 × 10
22
u
22
+ ··· + 2.64783 × 10
21
b + 1.78802 × 10
22
,
9.78596 × 10
19
u
23
− 3.52311 × 10
20
u
22
+ ··· + 1.93272 × 10
19
a + 1.09980 × 10
20
, u
24
− 3u
23
+ ··· + 8u + 1i
I
u
4
= h5u
7
− 18u
6
+ 14u
5
− 17u
4
+ 44u
3
− 53u
2
+ 11b + 21,
− 7u
7
+ 23u
6
− 24u
5
+ 26u
4
− 66u
3
+ 83u
2
+ 11a − 22u − 14,
u
8
− 2u
7
+ u
6
− 2u
5
+ 6u
4
− 4u
3
− 2u
2
+ 2u + 1i
* 4 irreducible components of dim
C
= 0, with total 62 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
= h253607u
17
− 119815u
16
+ · · · + 2792b + 534547, −1.13 × 10
6
u
17
+
5.35 × 10
5
u
16
+ · · · + 2792a − 2.39 × 10
6
, u
18
− u
16
+ · · · + 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
11
=
404.732u
17
− 191.457u
16
+ ··· + 757.847u + 854.381
−90.8335u
17
+ 42.9137u
16
+ ··· − 168.638u − 191.457
a
8
=
−123.317u
17
+ 57.5845u
16
+ ··· − 226.145u − 262.067
−63.4466u
17
+ 30.0842u
16
+ ··· − 119.201u − 133.872
a
9
=
−186.763u
17
+ 87.6687u
16
+ ··· − 345.346u − 395.939
−63.4466u
17
+ 30.0842u
16
+ ··· − 119.201u − 133.872
a
12
=
404.732u
17
− 191.457u
16
+ ··· + 758.847u + 854.381
−90.8335u
17
+ 42.9137u
16
+ ··· − 168.638u − 191.457
a
6
=
−304.984u
17
+ 143.412u
16
+ ··· − 565.421u − 644.981
−22.6307u
17
+ 10.9817u
16
+ ··· − 43.3861u − 48.0448
a
2
=
94.9466u
17
− 43.5842u
16
+ ··· + 171.201u + 201.372
28.6734u
17
− 13.9162u
16
+ ··· + 55.9921u + 60.8231
a
1
=
123.620u
17
− 57.5004u
16
+ ··· + 227.193u + 262.195
28.6734u
17
− 13.9162u
16
+ ··· + 55.9921u + 60.8231
a
5
=
−335.524u
17
+ 158.659u
16
+ ··· − 631.124u − 712.169
2.32450u
17
− 0.887536u
16
+ ··· + 5.26934u + 6.20702
a
10
=
−406.592u
17
+ 193.199u
16
+ ··· − 766.342u − 859.336
27.5838u
17
− 13.1547u
16
+ ··· + 53.8030u + 59.3266
(ii) Obstruction class = −1
(iii) Cusp Shapes =
2045515
2792
u
17
−
964335
2792
u
16
+ ··· +
1913265
1396
u +
4343639
2792
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 38u
17
+ ··· + 21004u + 2704
c
2
, c
5
u
18
+ 12u
17
+ ··· − 42u + 52
c
3
, c
11
u
18
− u
16
+ ··· + 3u + 1
c
4
, c
8
u
18
− u
17
+ ··· − 6u
2
+ 1
c
6
u
18
− 13u
17
+ ··· − 184u + 32
c
7
, c
10
u
18
− 11u
17
+ ··· − 34u + 4
c
9
, c
12
u
18
+ u
17
+ ··· + 27u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 146y
17
+ ··· − 126806384y + 7311616
c
2
, c
5
y
18
− 38y
17
+ ··· − 21004y + 2704
c
3
, c
11
y
18
− 2y
17
+ ··· − 11y + 1
c
4
, c
8
y
18
+ 29y
17
+ ··· − 12y + 1
c
6
y
18
+ 3y
17
+ ··· + 8896y + 1024
c
7
, c
10
y
18
+ 7y
17
+ ··· + 212y + 16
c
9
, c
12
y
18
+ 41y
17
+ ··· − 53y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.891966 + 0.505299I
a = −0.23675 − 1.79433I
b = 0.85339 + 1.26132I
−12.21600 − 5.30943I 1.96728 + 5.12021I
u = −0.891966 − 0.505299I
a = −0.23675 + 1.79433I
b = 0.85339 − 1.26132I
−12.21600 + 5.30943I 1.96728 − 5.12021I
u = 0.578165 + 0.938615I
a = 1.09411 − 1.04806I
b = 0.038828 − 0.821875I
−18.0039 + 5.4690I −2.64879 − 4.54026I
u = 0.578165 − 0.938615I
a = 1.09411 + 1.04806I
b = 0.038828 + 0.821875I
−18.0039 − 5.4690I −2.64879 + 4.54026I
u = −0.854287 + 0.898221I
a = 0.539073 − 0.616267I
b = 0.13299 + 1.67807I
−0.401628 − 0.023944I 0.798667 − 0.224914I
u = −0.854287 − 0.898221I
a = 0.539073 + 0.616267I
b = 0.13299 − 1.67807I
−0.401628 + 0.023944I 0.798667 + 0.224914I
u = −0.241248 + 0.688870I
a = −0.525924 + 0.059772I
b = −0.480079 + 0.538950I
−1.87297 + 1.40233I −2.30233 − 2.52603I
u = −0.241248 − 0.688870I
a = −0.525924 − 0.059772I
b = −0.480079 − 0.538950I
−1.87297 − 1.40233I −2.30233 + 2.52603I
u = 1.069570 + 0.765142I
a = −0.272123 − 0.684036I
b = 0.10197 + 1.59259I
2.96611 + 2.61050I 7.54398 − 1.84581I
u = 1.069570 − 0.765142I
a = −0.272123 + 0.684036I
b = 0.10197 − 1.59259I
2.96611 − 2.61050I 7.54398 + 1.84581I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.678153 + 0.019544I
a = 0.966784 + 0.264491I
b = 0.240917 − 0.127619I
1.208600 + 0.022955I 9.69868 + 0.48984I
u = 0.678153 − 0.019544I
a = 0.966784 − 0.264491I
b = 0.240917 + 0.127619I
1.208600 − 0.022955I 9.69868 − 0.48984I
u = −1.043070 + 0.939013I
a = −0.010456 − 0.755078I
b = 0.438217 + 1.074260I
−0.86599 − 7.63655I 0.42339 + 4.89613I
u = −1.043070 − 0.939013I
a = −0.010456 + 0.755078I
b = 0.438217 − 1.074260I
−0.86599 + 7.63655I 0.42339 − 4.89613I
u = −0.473262 + 0.000907I
a = −0.32200 + 3.04257I
b = −0.403752 − 0.680833I
1.20753 − 2.46681I 11.74185 + 5.49254I
u = −0.473262 − 0.000907I
a = −0.32200 − 3.04257I
b = −0.403752 + 0.680833I
1.20753 + 2.46681I 11.74185 − 5.49254I
u = 1.17795 + 1.15587I
a = −0.232707 − 0.959348I
b = −1.42248 + 1.83898I
−14.7900 + 13.6947I −0.22273 − 6.15238I
u = 1.17795 − 1.15587I
a = −0.232707 + 0.959348I
b = −1.42248 − 1.83898I
−14.7900 − 13.6947I −0.22273 + 6.15238I
6
II.
I
u
2
= hu
11
+u
10
+· · ·+4b+3, −9u
11
+3u
10
+· · ·+4a−7, u
12
+u
9
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
11
=
9
4
u
11
−
3
4
u
10
+ ··· +
17
4
u +
7
4
−
1
4
u
11
−
1
4
u
10
+ ··· −
1
4
u −
3
4
a
8
=
1
2
u
11
− u
10
+ ··· +
5
2
u − 4
−
5
4
u
11
+
5
4
u
10
+ ··· −
5
4
u −
1
4
a
9
=
−
3
4
u
11
+
1
4
u
10
+ ··· +
5
4
u −
17
4
−
5
4
u
11
+
5
4
u
10
+ ··· −
5
4
u −
1
4
a
12
=
9
4
u
11
−
3
4
u
10
+ ··· +
13
4
u +
7
4
−
1
4
u
11
−
1
4
u
10
+ ··· −
1
4
u −
3
4
a
6
=
u
11
−
1
2
u
10
+ ··· + u −
5
2
1
4
u
11
+
3
4
u
10
+ ··· +
1
4
u +
1
4
a
2
=
−
3
4
u
11
+
7
4
u
10
+ ··· −
15
4
u −
7
4
1
4
u
11
+
5
4
u
10
+ ··· +
9
4
u +
7
4
a
1
=
−
1
2
u
11
+ 3u
10
+ ··· + 5u
2
−
3
2
u
1
4
u
11
+
5
4
u
10
+ ··· +
9
4
u +
7
4
a
5
=
3
4
u
11
−
7
4
u
10
+ ··· +
3
4
u −
13
4
1
2
u
11
− 2u
10
+ ··· −
5
2
u − 2
a
10
=
−
5
2
u
11
+
3
2
u
10
+ ··· −
9
2
u −
17
2
3
4
u
11
+
1
4
u
10
+ ··· +
7
4
u +
7
4
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
43
4
u
11
−
23
4
u
10
−
5
4
u
9
+ 13u
8
+
183
4
u
7
− 17u
6
+
25
2
u
5
+
69
2
u
4
+ 36u
3
− 30u
2
+
35
4
u +
63
4
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− 11u
11
+ ··· + 38u + 9
c
2
u
12
+ 7u
11
+ ··· + 8u + 3
c
3
, c
11
u
12
+ u
9
+ 5u
8
+ u
7
+ 2u
6
+ 4u
5
+ 6u
4
+ u
2
+ 2u + 1
c
4
, c
8
u
12
+ u
11
+ ··· + 3u + 1
c
5
u
12
− 7u
11
+ ··· − 8u + 3
c
6
u
12
− 6u
11
+ ··· − 2u + 1
c
7
u
12
− 6u
11
+ ··· − 26u + 7
c
9
, c
12
u
12
− u
11
+ ··· − 3u + 1
c
10
u
12
+ 6u
11
+ ··· + 26u + 7
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
− 31y
11
+ ··· − 814y + 81
c
2
, c
5
y
12
− 11y
11
+ ··· + 38y + 9
c
3
, c
11
y
12
+ 10y
10
+ ··· − 2y + 1
c
4
, c
8
y
12
+ 15y
11
+ ··· + 9y + 1
c
6
y
12
+ 2y
11
+ ··· + 8y + 1
c
7
, c
10
y
12
+ 6y
11
+ ··· + 94y + 49
c
9
, c
12
y
12
+ 15y
11
+ ··· − y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.524174 + 0.935405I
a = 0.211373 + 0.651851I
b = 0.241922 − 0.751427I
−2.32559 + 0.11843I −3.60485 − 1.52557I
u = 0.524174 − 0.935405I
a = 0.211373 − 0.651851I
b = 0.241922 + 0.751427I
−2.32559 − 0.11843I −3.60485 + 1.52557I
u = −0.832813 + 0.793470I
a = −0.792558 + 0.118594I
b = 0.72679 − 1.84852I
−14.9054 + 3.0198I −0.549763 − 0.305805I
u = −0.832813 − 0.793470I
a = −0.792558 − 0.118594I
b = 0.72679 + 1.84852I
−14.9054 − 3.0198I −0.549763 + 0.305805I
u = 0.541589 + 0.596557I
a = −1.48280 + 0.71503I
b = −0.172321 + 0.406331I
−2.07362 + 3.61491I −0.01596 − 8.87319I
u = 0.541589 − 0.596557I
a = −1.48280 − 0.71503I
b = −0.172321 − 0.406331I
−2.07362 − 3.61491I −0.01596 + 8.87319I
u = −0.909125 + 0.811540I
a = −0.238321 + 1.090800I
b = −0.66042 − 1.34636I
1.42905 − 4.46443I 1.98459 + 3.93924I
u = −0.909125 − 0.811540I
a = −0.238321 − 1.090800I
b = −0.66042 + 1.34636I
1.42905 + 4.46443I 1.98459 − 3.93924I
u = −0.461441 + 0.292331I
a = −0.46843 + 2.98345I
b = −0.283743 − 0.799009I
0.90472 − 3.05984I 8.0892 + 13.7973I
u = −0.461441 − 0.292331I
a = −0.46843 − 2.98345I
b = −0.283743 + 0.799009I
0.90472 + 3.05984I 8.0892 − 13.7973I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13762 + 0.99536I
a = 0.270741 + 0.824638I
b = 0.64778 − 1.85872I
0.52151 + 9.30484I 3.09676 − 8.25985I
u = 1.13762 − 0.99536I
a = 0.270741 − 0.824638I
b = 0.64778 + 1.85872I
0.52151 − 9.30484I 3.09676 + 8.25985I
11
III.
I
u
3
= h4.83 × 10
21
u
23
− 1.44 × 10
22
u
22
+ · · · + 2.65 × 10
21
b + 1.79 × 10
22
, 9.79 ×
10
19
u
23
−3.52×10
20
u
22
+· · ·+1.93×10
19
a+1.10×10
20
, u
24
−3u
23
+· · ·+8u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
11
=
−5.06331u
23
+ 18.2287u
22
+ ··· − 48.2690u − 5.69044
−1.82259u
23
+ 5.42911u
22
+ ··· − 40.5303u − 6.75278
a
8
=
−10.1391u
23
+ 35.9200u
22
+ ··· − 106.991u − 14.7972
2.64920u
23
− 9.10533u
22
+ ··· + 27.2338u + 2.94973
a
9
=
−7.48988u
23
+ 26.8147u
22
+ ··· − 79.7574u − 11.8475
2.64920u
23
− 9.10533u
22
+ ··· + 27.2338u + 2.94973
a
12
=
−8.40607u
23
+ 28.7312u
22
+ ··· − 108.046u − 15.4820
−2.07131u
23
+ 6.35594u
22
+ ··· − 40.0796u − 6.27861
a
6
=
−9.40607u
23
+ 31.7312u
22
+ ··· − 138.046u − 23.4820
1.75146u
23
− 7.12240u
22
+ ··· − 3.70802u − 2.61876
a
2
=
−9.79160u
23
+ 32.7176u
22
+ ··· − 131.227u − 18.5553
−3.85941u
23
+ 13.5659u
22
+ ··· − 36.8737u − 5.64255
a
1
=
−13.6510u
23
+ 46.2835u
22
+ ··· − 168.100u − 24.1978
−3.85941u
23
+ 13.5659u
22
+ ··· − 36.8737u − 5.64255
a
5
=
−8.19967u
23
+ 25.0149u
22
+ ··· − 158.975u − 28.9010
−0.108090u
23
+ 1.78381u
22
+ ··· + 33.1497u + 6.11529
a
10
=
−7.41410u
23
+ 26.8547u
22
+ ··· − 78.1869u − 10.1474
−1.90049u
23
+ 4.94162u
22
+ ··· − 48.4935u − 8.37022
(ii) Obstruction class = −1
(iii) Cusp Shapes =
25674569131799378400018
2647827155991442828823
u
23
−
93630207416059654480934
2647827155991442828823
u
22
+ ··· +
253445417873904870605806
2647827155991442828823
u +
33919201463985866967416
2647827155991442828823
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 9u
5
+ 22u
4
+ 7u
3
+ 4u
2
− 4u + 1)
4
c
2
, c
5
(u
6
− 3u
5
+ 3u
3
+ 2u
2
+ 1)
4
c
3
, c
11
u
24
− 3u
23
+ ··· + 8u + 1
c
4
, c
8
u
24
+ u
23
+ ··· − 350u + 139
c
6
(u
2
+ u + 1)
12
c
7
, c
10
(u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u + 1)
4
c
9
, c
12
u
24
− u
23
+ ··· + 3722u + 2473
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− 37y
5
+ 366y
4
+ 201y
3
+ 116y
2
− 8y + 1)
4
c
2
, c
5
(y
6
− 9y
5
+ 22y
4
− 7y
3
+ 4y
2
+ 4y + 1)
4
c
3
, c
11
y
24
+ y
23
+ ··· − 4y + 1
c
4
, c
8
y
24
+ 49y
23
+ ··· + 13164y + 19321
c
6
(y
2
+ y + 1)
12
c
7
, c
10
(y
6
+ 3y
5
+ 6y
4
+ 5y
3
+ 4y
2
+ 1)
4
c
9
, c
12
y
24
+ 51y
23
+ ··· + 67849690y + 6115729
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373872 + 0.942544I
a = 0.158900 + 0.657788I
b = −0.552066 − 0.133903I
−2.03447 + 2.26308I −3.01274 − 4.61865I
u = 0.373872 − 0.942544I
a = 0.158900 − 0.657788I
b = −0.552066 + 0.133903I
−2.03447 − 2.26308I −3.01274 + 4.61865I
u = 0.382758 + 1.064110I
a = −0.497044 + 0.348026I
b = −0.579720 + 0.556799I
−2.03447 + 1.79668I −3.01274 − 2.30956I
u = 0.382758 − 1.064110I
a = −0.497044 − 0.348026I
b = −0.579720 − 0.556799I
−2.03447 − 1.79668I −3.01274 + 2.30956I
u = −0.769320 + 0.956480I
a = −0.492536 + 0.961676I
b = −0.27677 − 1.50069I
0.61992 − 6.50680I 0.39807 + 6.46471I
u = −0.769320 − 0.956480I
a = −0.492536 − 0.961676I
b = −0.27677 + 1.50069I
0.61992 + 6.50680I 0.39807 − 6.46471I
u = −1.134620 + 0.514340I
a = 0.278708 + 0.475094I
b = −0.465702 − 1.103180I
−2.03447 − 2.26308I −3.01274 + 4.61865I
u = −1.134620 − 0.514340I
a = 0.278708 − 0.475094I
b = −0.465702 + 1.103180I
−2.03447 + 2.26308I −3.01274 − 4.61865I
u = −0.335084 + 1.275540I
a = −0.790298 − 0.263948I
b = 0.550295 − 0.611586I
−15.0348 + 0.3480I −1.38532 + 0.49466I
u = −0.335084 − 1.275540I
a = −0.790298 + 0.263948I
b = 0.550295 + 0.611586I
−15.0348 − 0.3480I −1.38532 − 0.49466I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.151187 + 0.595299I
a = 1.69413 + 1.33889I
b = 0.274756 − 0.063861I
0.61992 + 2.44703I 0.398066 + 0.463490I
u = 0.151187 − 0.595299I
a = 1.69413 − 1.33889I
b = 0.274756 + 0.063861I
0.61992 − 2.44703I 0.398066 − 0.463490I
u = −0.527891 + 0.202784I
a = 0.12502 + 2.34194I
b = −0.379910 − 1.124860I
0.61992 − 2.44703I 0.398066 − 0.463490I
u = −0.527891 − 0.202784I
a = 0.12502 − 2.34194I
b = −0.379910 + 1.124860I
0.61992 + 2.44703I 0.398066 + 0.463490I
u = −0.385179 + 0.402316I
a = 0.44579 − 1.92187I
b = 1.89981 + 1.60725I
−15.0348 − 4.4077I −1.38532 + 6.43354I
u = −0.385179 − 0.402316I
a = 0.44579 + 1.92187I
b = 1.89981 − 1.60725I
−15.0348 + 4.4077I −1.38532 − 6.43354I
u = −0.373222 + 0.191183I
a = 1.62002 − 0.23037I
b = 0.249186 − 0.809251I
−2.03447 − 1.79668I −3.01274 + 2.30956I
u = −0.373222 − 0.191183I
a = 1.62002 + 0.23037I
b = 0.249186 + 0.809251I
−2.03447 + 1.79668I −3.01274 − 2.30956I
u = 1.52174 + 0.46379I
a = 0.193145 − 0.663179I
b = −1.67691 + 2.39599I
−15.0348 + 0.3480I −1.38532 + 0.49466I
u = 1.52174 − 0.46379I
a = 0.193145 + 0.663179I
b = −1.67691 − 2.39599I
−15.0348 − 0.3480I −1.38532 − 0.49466I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.29760 + 1.08646I
a = 0.214287 + 0.753794I
b = 1.24819 − 1.94012I
0.61992 + 6.50680I 0.39807 − 6.46471I
u = 1.29760 − 1.08646I
a = 0.214287 − 0.753794I
b = 1.24819 + 1.94012I
0.61992 − 6.50680I 0.39807 + 6.46471I
u = 1.29815 + 1.49503I
a = 0.549874 + 0.075134I
b = 0.20884 − 1.69072I
−15.0348 − 4.4077I 0. + 6.43354I
u = 1.29815 − 1.49503I
a = 0.549874 − 0.075134I
b = 0.20884 + 1.69072I
−15.0348 + 4.4077I 0. − 6.43354I
17
IV. I
u
4
=
h5u
7
−18u
6
+· · ·+11b+21, −7u
7
+23u
6
+· · ·+11a−14, u
8
−2u
7
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
11
=
7
11
u
7
−
23
11
u
6
+ ··· + 2u +
14
11
−0.454545u
7
+ 1.63636u
6
+ ··· + 4.81818u
2
− 1.90909
a
8
=
−u
7
+ 2u
6
− u
5
+ 2u
4
− 6u
3
+ 4u
2
+ 2u − 2
2
11
u
7
+
6
11
u
6
+ ··· − 2u −
7
11
a
9
=
−0.818182u
7
+ 2.54545u
6
+ ··· + 7.27273u
2
− 2.63636
2
11
u
7
+
6
11
u
6
+ ··· − 2u −
7
11
a
12
=
1
11
u
7
−
8
11
u
6
+ ··· + 3u +
2
11
−0.818182u
7
+ 1.54545u
6
+ ··· + 4.27273u
2
− 1.63636
a
6
=
−1.09091u
7
+ 2.72727u
6
+ ··· − u − 2.18182
1
a
2
=
12
11
u
7
−
30
11
u
6
+ ··· + u +
35
11
−1
a
1
=
12
11
u
7
−
30
11
u
6
+ ··· + u +
24
11
−1
a
5
=
1
0
a
10
=
0
1
11
u
7
+
3
11
u
6
+ ··· − u −
9
11
(ii) Obstruction class = 1
(iii) Cusp Shapes =
24
11
u
7
−
60
11
u
6
+
32
11
u
5
−
64
11
u
4
+ 16u
3
−
140
11
u
2
+
48
11
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
11
u
8
− 2u
7
+ u
6
− 2u
5
+ 6u
4
− 4u
3
− 2u
2
+ 2u + 1
c
4
, c
8
u
8
+ u
6
− 2u
5
+ 2u
4
+ 2u
3
+ 6u
2
+ 2u + 1
c
5
(u + 1)
8
c
6
(u
2
+ u + 1)
4
c
7
, c
10
(u
2
+ 1)
4
c
9
, c
12
(u
4
− u
2
+ 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
8
c
3
, c
11
y
8
− 2y
7
+ 5y
6
− 12y
5
+ 26y
4
− 30y
3
+ 32y
2
− 8y + 1
c
4
, c
8
y
8
+ 2y
7
+ 5y
6
+ 12y
5
+ 26y
4
+ 30y
3
+ 32y
2
+ 8y + 1
c
6
(y
2
+ y + 1)
4
c
7
, c
10
(y + 1)
8
c
9
, c
12
(y
2
− y + 1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.916440 + 0.695963I
a = −0.525562 − 0.692057I
b = −0.279522 + 0.746378I
− 2.02988I 2.00000 + 3.46410I
u = 0.916440 − 0.695963I
a = −0.525562 + 0.692057I
b = −0.279522 − 0.746378I
2.02988I 2.00000 − 3.46410I
u = 1.266520 + 0.378347I
a = −0.216544 − 0.724880I
b = 0.38817 + 2.51089I
2.02988I 2.00000 − 3.46410I
u = 1.266520 − 0.378347I
a = −0.216544 + 0.724880I
b = 0.38817 − 2.51089I
− 2.02988I 2.00000 + 3.46410I
u = −0.76652 + 1.24437I
a = 0.582569 − 0.358854I
b = −0.022144 + 1.144860I
− 2.02988I 2.00000 + 3.46410I
u = −0.76652 − 1.24437I
a = 0.582569 + 0.358854I
b = −0.022144 − 1.144860I
2.02988I 2.00000 − 3.46410I
u = −0.416440 + 0.170063I
a = −0.84046 + 2.05808I
b = −1.08650 − 1.11240I
− 2.02988I 2.00000 + 3.46410I
u = −0.416440 − 0.170063I
a = −0.84046 − 2.05808I
b = −1.08650 + 1.11240I
2.02988I 2.00000 − 3.46410I
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
(u
6
+ 9u
5
+ 22u
4
+ 7u
3
+ 4u
2
− 4u + 1)
4
· (u
12
− 11u
11
+ ··· + 38u + 9)(u
18
+ 38u
17
+ ··· + 21004u + 2704)
c
2
((u − 1)
8
)(u
6
− 3u
5
+ ··· + 2u
2
+ 1)
4
(u
12
+ 7u
11
+ ··· + 8u + 3)
· (u
18
+ 12u
17
+ ··· − 42u + 52)
c
3
, c
11
(u
8
− 2u
7
+ u
6
− 2u
5
+ 6u
4
− 4u
3
− 2u
2
+ 2u + 1)
· (u
12
+ u
9
+ 5u
8
+ u
7
+ 2u
6
+ 4u
5
+ 6u
4
+ u
2
+ 2u + 1)
· (u
18
− u
16
+ ··· + 3u + 1)(u
24
− 3u
23
+ ··· + 8u + 1)
c
4
, c
8
(u
8
+ u
6
+ ··· + 2u + 1)(u
12
+ u
11
+ ··· + 3u + 1)
· (u
18
− u
17
+ ··· − 6u
2
+ 1)(u
24
+ u
23
+ ··· − 350u + 139)
c
5
((u + 1)
8
)(u
6
− 3u
5
+ ··· + 2u
2
+ 1)
4
(u
12
− 7u
11
+ ··· − 8u + 3)
· (u
18
+ 12u
17
+ ··· − 42u + 52)
c
6
((u
2
+ u + 1)
16
)(u
12
− 6u
11
+ ··· − 2u + 1)
· (u
18
− 13u
17
+ ··· − 184u + 32)
c
7
(u
2
+ 1)
4
(u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u + 1)
4
· (u
12
− 6u
11
+ ··· − 26u + 7)(u
18
− 11u
17
+ ··· − 34u + 4)
c
9
, c
12
((u
4
− u
2
+ 1)
2
)(u
12
− u
11
+ ··· − 3u + 1)(u
18
+ u
17
+ ··· + 27u + 2)
· (u
24
− u
23
+ ··· + 3722u + 2473)
c
10
(u
2
+ 1)
4
(u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ 2u + 1)
4
· (u
12
+ 6u
11
+ ··· + 26u + 7)(u
18
− 11u
17
+ ··· − 34u + 4)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)
8
(y
6
− 37y
5
+ 366y
4
+ 201y
3
+ 116y
2
− 8y + 1)
4
· (y
12
− 31y
11
+ ··· − 814y + 81)
· (y
18
− 146y
17
+ ··· − 126806384y + 7311616)
c
2
, c
5
(y −1)
8
(y
6
− 9y
5
+ 22y
4
− 7y
3
+ 4y
2
+ 4y + 1)
4
· (y
12
− 11y
11
+ ··· + 38y + 9)(y
18
− 38y
17
+ ··· − 21004y + 2704)
c
3
, c
11
(y
8
− 2y
7
+ 5y
6
− 12y
5
+ 26y
4
− 30y
3
+ 32y
2
− 8y + 1)
· (y
12
+ 10y
10
+ ··· − 2y + 1)(y
18
− 2y
17
+ ··· − 11y + 1)
· (y
24
+ y
23
+ ··· − 4y + 1)
c
4
, c
8
(y
8
+ 2y
7
+ 5y
6
+ 12y
5
+ 26y
4
+ 30y
3
+ 32y
2
+ 8y + 1)
· (y
12
+ 15y
11
+ ··· + 9y + 1)(y
18
+ 29y
17
+ ··· − 12y + 1)
· (y
24
+ 49y
23
+ ··· + 13164y + 19321)
c
6
((y
2
+ y + 1)
16
)(y
12
+ 2y
11
+ ··· + 8y + 1)
· (y
18
+ 3y
17
+ ··· + 8896y + 1024)
c
7
, c
10
(y + 1)
8
(y
6
+ 3y
5
+ 6y
4
+ 5y
3
+ 4y
2
+ 1)
4
· (y
12
+ 6y
11
+ ··· + 94y + 49)(y
18
+ 7y
17
+ ··· + 212y + 16)
c
9
, c
12
((y
2
− y + 1)
4
)(y
12
+ 15y
11
+ ··· − y + 1)(y
18
+ 41y
17
+ ··· − 53y + 4)
· (y
24
+ 51y
23
+ ··· + 67849690y + 6115729)
23
