12a
0315
(K12a
0315
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 9 5 1 7 12 4 10
Solving Sequence
5,11
4
8,12
3 7 10 1 2 9 6
c
4
c
11
c
3
c
7
c
10
c
12
c
1
c
9
c
6
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.85167 × 10
121
u
114
− 3.72449 × 10
121
u
113
+ ··· + 7.44095 × 10
121
b + 3.07946 × 10
121
,
− 5.89851 × 10
121
u
114
− 8.95585 × 10
121
u
113
+ ··· + 7.44095 × 10
121
a − 1.95302 × 10
122
,
u
115
+ 2u
114
+ ··· + 2u − 1i
I
u
2
= h3u
4
+ 4u
3
+ 5u
2
+ 5b + u, −u
4
− u
3
+ u
2
+ 5a + 3u + 4, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 120 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.85 × 10
121
u
114
− 3.72 × 10
121
u
113
+ · · · + 7.44 × 10
121
b + 3.08 ×
10
121
, −5.90 × 10
121
u
114
− 8.96 × 10
121
u
113
+ · · · + 7.44 × 10
121
a − 1.95 ×
10
122
, u
115
+ 2u
114
+ · · · + 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
8
=
0.792709u
114
+ 1.20359u
113
+ ··· − 4.75680u + 2.62469
0.248849u
114
+ 0.500539u
113
+ ··· + 3.03902u − 0.413853
a
12
=
u
u
3
+ u
a
3
=
1.62371u
114
+ 2.67004u
113
+ ··· − 3.94611u + 0.349188
−0.816496u
114
− 1.64935u
113
+ ··· + 1.57453u − 0.0503323
a
7
=
1.04156u
114
+ 1.70413u
113
+ ··· − 1.71778u + 2.21083
0.248849u
114
+ 0.500539u
113
+ ··· + 3.03902u − 0.413853
a
10
=
u
3
u
5
+ u
3
+ u
a
1
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
2
=
−0.495778u
114
+ 0.152549u
113
+ ··· + 2.54880u − 1.59091
0.430896u
114
+ 0.364813u
113
+ ··· − 0.748946u + 0.656296
a
9
=
1.35088u
114
+ 2.29904u
113
+ ··· − 4.32285u + 2.45638
0.219430u
114
+ 0.633152u
113
+ ··· + 4.57775u − 0.762711
a
6
=
−0.580563u
114
− 1.39437u
113
+ ··· + 4.59835u − 0.240154
−0.143312u
114
− 0.582118u
113
+ ··· − 1.63332u + 0.499825
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.26127u
114
− 13.4625u
113
+ ··· − 1.05644u − 6.56776
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
115
+ 52u
114
+ ··· + 8u + 1
c
2
, c
5
u
115
+ 2u
114
+ ··· + 4u + 1
c
3
u
115
+ u
114
+ ··· − 4000u + 20000
c
4
, c
11
u
115
− 2u
114
+ ··· + 2u + 1
c
6
, c
9
u
115
− 6u
114
+ ··· − 6050u + 625
c
7
25(25u
115
+ 1297u
113
+ ··· − 6356084u + 531211)
c
8
25(25u
115
+ 25u
114
+ ··· + 165472u + 46912)
c
10
, c
12
u
115
+ 36u
114
+ ··· + 8u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
115
+ 24y
114
+ ··· − 4y −1
c
2
, c
5
y
115
− 52y
114
+ ··· + 8y −1
c
3
y
115
+ 33y
114
+ ··· + 2280000000y −400000000
c
4
, c
11
y
115
+ 36y
114
+ ··· + 8y −1
c
6
, c
9
y
115
− 64y
114
+ ··· − 9508750y −390625
c
7
625
· (625y
115
+ 64850y
114
+ ··· + 4263135428918y −282185126521)
c
8
625(625y
115
− 37225y
114
+ ··· − 4.94556 × 10
10
y −2.20074 × 10
9
)
c
10
, c
12
y
115
+ 88y
114
+ ··· + 180y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.231824 + 0.953832I
a = −2.46206 + 0.91607I
b = 0.596166 − 0.796359I
−0.78095 + 7.32794I 0
u = 0.231824 − 0.953832I
a = −2.46206 − 0.91607I
b = 0.596166 + 0.796359I
−0.78095 − 7.32794I 0
u = −0.262847 + 0.932497I
a = 1.91342 + 0.84423I
b = −0.370130 − 0.643087I
0.61191 − 2.36422I 0
u = −0.262847 − 0.932497I
a = 1.91342 − 0.84423I
b = −0.370130 + 0.643087I
0.61191 + 2.36422I 0
u = 0.719284 + 0.761224I
a = −0.455850 − 1.230130I
b = −0.384714 − 0.124611I
−0.13012 − 4.17483I 0
u = 0.719284 − 0.761224I
a = −0.455850 + 1.230130I
b = −0.384714 + 0.124611I
−0.13012 + 4.17483I 0
u = 0.679610 + 0.799058I
a = −1.17140 − 1.41956I
b = 0.495600 − 0.123968I
−1.60723 + 1.91504I 0
u = 0.679610 − 0.799058I
a = −1.17140 + 1.41956I
b = 0.495600 + 0.123968I
−1.60723 − 1.91504I 0
u = −0.082837 + 0.941587I
a = 2.46261 − 1.38632I
b = −0.990156 − 0.172748I
−5.35130 − 4.97918I 0
u = −0.082837 − 0.941587I
a = 2.46261 + 1.38632I
b = −0.990156 + 0.172748I
−5.35130 + 4.97918I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.814912 + 0.678676I
a = −0.199202 + 0.199306I
b = 0.110561 + 1.268530I
4.77410 − 2.66895I 0
u = −0.814912 − 0.678676I
a = −0.199202 − 0.199306I
b = 0.110561 − 1.268530I
4.77410 + 2.66895I 0
u = −0.031070 + 0.935882I
a = 1.05114 − 1.63997I
b = −0.443506 − 0.129637I
−6.14284 + 1.16940I 0
u = −0.031070 − 0.935882I
a = 1.05114 + 1.63997I
b = −0.443506 + 0.129637I
−6.14284 − 1.16940I 0
u = −0.646217 + 0.859121I
a = 1.74516 − 1.15528I
b = −1.208750 + 0.062952I
−2.57690 + 0.59772I 0
u = −0.646217 − 0.859121I
a = 1.74516 + 1.15528I
b = −1.208750 − 0.062952I
−2.57690 − 0.59772I 0
u = −0.732062 + 0.787501I
a = 0.687215 − 0.808553I
b = 0.329674 − 0.594451I
1.59979 − 0.04409I 0
u = −0.732062 − 0.787501I
a = 0.687215 + 0.808553I
b = 0.329674 + 0.594451I
1.59979 + 0.04409I 0
u = −0.099706 + 1.078560I
a = −0.48505 − 1.37837I
b = 0.203969 + 0.981425I
−0.66867 − 2.87209I 0
u = −0.099706 − 1.078560I
a = −0.48505 + 1.37837I
b = 0.203969 − 0.981425I
−0.66867 + 2.87209I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.156085 + 0.900887I
a = −2.53802 − 0.37596I
b = 0.966548 − 0.328199I
−3.59301 + 1.68133I 0
u = 0.156085 − 0.900887I
a = −2.53802 + 0.37596I
b = 0.966548 + 0.328199I
−3.59301 − 1.68133I 0
u = 0.846369 + 0.687021I
a = 0.202537 + 0.074386I
b = 0.247444 + 1.370760I
5.98557 − 3.08518I 0
u = 0.846369 − 0.687021I
a = 0.202537 − 0.074386I
b = 0.247444 − 1.370760I
5.98557 + 3.08518I 0
u = 0.120992 + 0.896882I
a = −0.30902 − 1.97202I
b = 0.286071 + 1.066620I
−1.07660 − 2.43604I 0
u = 0.120992 − 0.896882I
a = −0.30902 + 1.97202I
b = 0.286071 − 1.066620I
−1.07660 + 2.43604I 0
u = 0.078739 + 0.893461I
a = −2.18286 − 0.57596I
b = 0.992060 − 0.472687I
−3.51720 + 1.23198I 0
u = 0.078739 − 0.893461I
a = −2.18286 + 0.57596I
b = 0.992060 + 0.472687I
−3.51720 − 1.23198I 0
u = 0.683059 + 0.873025I
a = −1.12060 − 1.09313I
b = 1.48924 + 0.10894I
−0.36733 + 2.63401I 0
u = 0.683059 − 0.873025I
a = −1.12060 + 1.09313I
b = 1.48924 − 0.10894I
−0.36733 − 2.63401I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.870156 + 0.172696I
a = −0.0912549 − 0.0114818I
b = −0.438004 + 0.516951I
−4.21088 + 0.70500I 0
u = 0.870156 − 0.172696I
a = −0.0912549 + 0.0114818I
b = −0.438004 − 0.516951I
−4.21088 − 0.70500I 0
u = −0.659858 + 0.899578I
a = 1.52640 − 0.24867I
b = −1.090120 + 0.070208I
−2.72537 − 5.66569I 0
u = −0.659858 − 0.899578I
a = 1.52640 + 0.24867I
b = −1.090120 − 0.070208I
−2.72537 + 5.66569I 0
u = −0.749840 + 0.829632I
a = 1.350280 + 0.409157I
b = 1.01467 − 1.70820I
2.33638 − 0.47130I 0
u = −0.749840 − 0.829632I
a = 1.350280 − 0.409157I
b = 1.01467 + 1.70820I
2.33638 + 0.47130I 0
u = −0.822875 + 0.764427I
a = −0.391586 + 0.012215I
b = 0.88291 − 1.12333I
5.95773 + 6.05581I 0
u = −0.822875 − 0.764427I
a = −0.391586 − 0.012215I
b = 0.88291 + 1.12333I
5.95773 − 6.05581I 0
u = −0.791646 + 0.800114I
a = 0.0681291 − 0.0048683I
b = 0.807966 − 0.785235I
2.31006 + 0.02277I 0
u = −0.791646 − 0.800114I
a = 0.0681291 + 0.0048683I
b = 0.807966 + 0.785235I
2.31006 − 0.02277I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877305 + 0.708965I
a = 0.125553 − 0.108050I
b = 0.94576 + 1.42038I
4.88341 − 7.17921I 0
u = 0.877305 − 0.708965I
a = 0.125553 + 0.108050I
b = 0.94576 − 1.42038I
4.88341 + 7.17921I 0
u = −0.889873 + 0.693456I
a = −0.0644567 − 0.0226712I
b = −0.802417 + 1.025230I
−1.07673 + 4.48539I 0
u = −0.889873 − 0.693456I
a = −0.0644567 + 0.0226712I
b = −0.802417 − 1.025230I
−1.07673 − 4.48539I 0
u = 0.747735 + 0.848567I
a = −3.17279 + 1.04812I
b = −1.29640 − 4.15597I
1.68826 + 4.75505I 0
u = 0.747735 − 0.848567I
a = −3.17279 − 1.04812I
b = −1.29640 + 4.15597I
1.68826 − 4.75505I 0
u = 0.241160 + 1.108160I
a = 2.16055 − 0.75457I
b = −1.16119 + 0.96512I
−4.80644 + 12.94150I 0
u = 0.241160 − 1.108160I
a = 2.16055 + 0.75457I
b = −1.16119 − 0.96512I
−4.80644 − 12.94150I 0
u = −0.227858 + 1.111020I
a = −1.84536 − 0.85683I
b = 0.979988 + 0.954915I
−2.58436 − 7.22243I 0
u = −0.227858 − 1.111020I
a = −1.84536 + 0.85683I
b = 0.979988 − 0.954915I
−2.58436 + 7.22243I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.829120 + 0.774149I
a = 0.315506 + 0.088053I
b = −0.732646 − 1.094480I
7.49710 − 0.85393I 0
u = 0.829120 − 0.774149I
a = 0.315506 − 0.088053I
b = −0.732646 + 1.094480I
7.49710 + 0.85393I 0
u = −0.881740 + 0.714170I
a = −0.090486 − 0.148849I
b = −1.14088 + 1.41196I
2.75920 + 12.82710I 0
u = −0.881740 − 0.714170I
a = −0.090486 + 0.148849I
b = −1.14088 − 1.41196I
2.75920 − 12.82710I 0
u = 0.688094 + 0.929601I
a = −0.419814 + 0.892789I
b = 0.265970 + 0.325650I
−2.01818 + 3.37967I 0
u = 0.688094 − 0.929601I
a = −0.419814 − 0.892789I
b = 0.265970 − 0.325650I
−2.01818 − 3.37967I 0
u = 0.351802 + 1.104650I
a = 0.31481 + 1.42375I
b = −0.747838 − 0.529760I
−4.15815 − 5.61157I 0
u = 0.351802 − 1.104650I
a = 0.31481 − 1.42375I
b = −0.747838 + 0.529760I
−4.15815 + 5.61157I 0
u = 0.739725 + 0.897296I
a = 4.36688 + 0.96638I
b = −2.03502 + 5.62532I
1.53888 + 0.89181I 0
u = 0.739725 − 0.897296I
a = 4.36688 − 0.96638I
b = −2.03502 − 5.62532I
1.53888 − 0.89181I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395665 + 1.097030I
a = 0.017649 + 1.133270I
b = 0.550820 − 0.485400I
−1.63066 − 0.10437I 0
u = −0.395665 − 1.097030I
a = 0.017649 − 1.133270I
b = 0.550820 + 0.485400I
−1.63066 + 0.10437I 0
u = 0.852961 + 0.805684I
a = 0.189912 + 0.218450I
b = −0.369955 − 0.833667I
6.76805 + 1.81713I 0
u = 0.852961 − 0.805684I
a = 0.189912 − 0.218450I
b = −0.369955 + 0.833667I
6.76805 − 1.81713I 0
u = −0.736891 + 0.914102I
a = −1.71511 + 1.24495I
b = 1.53035 + 2.03390I
2.07779 − 5.17426I 0
u = −0.736891 − 0.914102I
a = −1.71511 − 1.24495I
b = 1.53035 − 2.03390I
2.07779 + 5.17426I 0
u = 0.235020 + 1.153700I
a = 1.379800 − 0.258658I
b = −0.858017 + 0.551376I
−8.71701 + 4.21406I 0
u = 0.235020 − 1.153700I
a = 1.379800 + 0.258658I
b = −0.858017 − 0.551376I
−8.71701 − 4.21406I 0
u = −0.715019 + 0.938235I
a = −0.652037 + 1.198240I
b = 0.477053 + 0.760624I
1.14158 − 5.48296I 0
u = −0.715019 − 0.938235I
a = −0.652037 − 1.198240I
b = 0.477053 − 0.760624I
1.14158 + 5.48296I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.704427 + 0.950630I
a = 0.35943 + 1.69590I
b = −0.511142 + 0.319310I
−0.70091 + 9.63596I 0
u = 0.704427 − 0.950630I
a = 0.35943 − 1.69590I
b = −0.511142 − 0.319310I
−0.70091 − 9.63596I 0
u = −0.882104 + 0.813983I
a = −0.166014 + 0.228393I
b = 0.096019 − 0.688738I
4.46500 − 6.90957I 0
u = −0.882104 − 0.813983I
a = −0.166014 − 0.228393I
b = 0.096019 + 0.688738I
4.46500 + 6.90957I 0
u = 0.789723 + 0.079260I
a = −0.117294 − 0.153795I
b = −0.786616 + 0.935066I
−0.82292 + 9.58153I −6.99384 − 7.63586I
u = 0.789723 − 0.079260I
a = −0.117294 + 0.153795I
b = −0.786616 − 0.935066I
−0.82292 − 9.58153I −6.99384 + 7.63586I
u = −0.750613 + 0.952129I
a = −1.28098 + 1.07814I
b = 0.964262 + 0.758591I
1.83796 − 5.83738I 0
u = −0.750613 − 0.952129I
a = −1.28098 − 1.07814I
b = 0.964262 − 0.758591I
1.83796 + 5.83738I 0
u = −0.776511 + 0.107568I
a = 0.162160 − 0.106138I
b = 0.575735 + 0.918049I
1.48739 − 3.97707I −3.55800 + 4.34858I
u = −0.776511 − 0.107568I
a = 0.162160 + 0.106138I
b = 0.575735 − 0.918049I
1.48739 + 3.97707I −3.55800 − 4.34858I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.260461 + 0.725031I
a = 0.809211 − 0.131467I
b = −0.149474 + 0.142541I
−0.379020 − 1.191680I −4.70355 + 5.46552I
u = −0.260461 − 0.725031I
a = 0.809211 + 0.131467I
b = −0.149474 − 0.142541I
−0.379020 + 1.191680I −4.70355 − 5.46552I
u = −0.756696 + 0.980095I
a = −2.02487 + 0.82655I
b = 0.96401 + 1.03744I
5.29392 − 11.97440I 0
u = −0.756696 − 0.980095I
a = −2.02487 − 0.82655I
b = 0.96401 − 1.03744I
5.29392 + 11.97440I 0
u = 0.763871 + 0.976961I
a = 1.83341 + 0.62378I
b = −0.834882 + 0.993362I
6.87081 + 6.81407I 0
u = 0.763871 − 0.976961I
a = 1.83341 − 0.62378I
b = −0.834882 − 0.993362I
6.87081 − 6.81407I 0
u = 0.790765 + 0.965591I
a = 1.195680 + 0.246185I
b = −0.538179 + 0.686419I
6.26803 + 4.29794I 0
u = 0.790765 − 0.965591I
a = 1.195680 − 0.246185I
b = −0.538179 − 0.686419I
6.26803 − 4.29794I 0
u = −0.715269 + 1.030230I
a = 1.304450 + 0.320256I
b = −0.028786 − 1.211300I
3.69675 − 3.09351I 0
u = −0.715269 − 1.030230I
a = 1.304450 − 0.320256I
b = −0.028786 + 1.211300I
3.69675 + 3.09351I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.111077 + 0.731043I
a = −3.99761 − 4.11972I
b = 2.36476 + 1.68976I
−2.72278 + 1.85710I −20.2284 − 21.3976I
u = 0.111077 − 0.731043I
a = −3.99761 + 4.11972I
b = 2.36476 − 1.68976I
−2.72278 − 1.85710I −20.2284 + 21.3976I
u = 0.737371 + 1.031700I
a = −1.57828 + 0.00884I
b = 0.39482 − 1.36019I
4.92945 + 9.00434I 0
u = 0.737371 − 1.031700I
a = −1.57828 − 0.00884I
b = 0.39482 + 1.36019I
4.92945 − 9.00434I 0
u = −0.821203 + 0.971075I
a = −0.820042 − 0.054088I
b = 0.246900 + 0.462452I
3.97657 + 0.61648I 0
u = −0.821203 − 0.971075I
a = −0.820042 + 0.054088I
b = 0.246900 − 0.462452I
3.97657 − 0.61648I 0
u = 0.759832 + 1.030770I
a = −1.94134 − 0.64692I
b = 1.08828 − 1.43389I
3.88825 + 13.25810I 0
u = 0.759832 − 1.030770I
a = −1.94134 + 0.64692I
b = 1.08828 + 1.43389I
3.88825 − 13.25810I 0
u = −0.763765 + 1.030340I
a = 2.01617 − 0.83875I
b = −1.27696 − 1.42115I
1.7792 − 18.9323I 0
u = −0.763765 − 1.030340I
a = 2.01617 + 0.83875I
b = −1.27696 + 1.42115I
1.7792 + 18.9323I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759147 + 1.041600I
a = 1.49398 − 0.67166I
b = −0.94279 − 1.05428I
−2.15269 − 10.59310I 0
u = −0.759147 − 1.041600I
a = 1.49398 + 0.67166I
b = −0.94279 + 1.05428I
−2.15269 + 10.59310I 0
u = 0.486003 + 1.213410I
a = −0.014042 + 0.470500I
b = −0.338466 − 0.261282I
−7.46853 + 4.22982I 0
u = 0.486003 − 1.213410I
a = −0.014042 − 0.470500I
b = −0.338466 + 0.261282I
−7.46853 − 4.22982I 0
u = −0.620002 + 0.111838I
a = 0.361537 + 0.088056I
b = −0.140728 + 1.022380I
3.19465 − 0.64518I −0.51351 + 2.30029I
u = −0.620002 − 0.111838I
a = 0.361537 − 0.088056I
b = −0.140728 − 1.022380I
3.19465 + 0.64518I −0.51351 − 2.30029I
u = 0.581899 + 0.059252I
a = −0.463506 + 0.204086I
b = 0.438345 + 1.073690I
2.00809 − 4.57133I −2.79082 + 4.02623I
u = 0.581899 − 0.059252I
a = −0.463506 − 0.204086I
b = 0.438345 − 1.073690I
2.00809 + 4.57133I −2.79082 − 4.02623I
u = −0.183812 + 0.359179I
a = 0.00512 − 4.27303I
b = −0.723848 + 1.134910I
−2.84559 + 1.64555I −3.82019 − 3.15286I
u = −0.183812 − 0.359179I
a = 0.00512 + 4.27303I
b = −0.723848 − 1.134910I
−2.84559 − 1.64555I −3.82019 + 3.15286I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.352590 + 0.195531I
a = −0.18774 − 2.41620I
b = −1.207430 + 0.351597I
−2.18450 − 3.74259I −7.40219 + 5.01666I
u = −0.352590 − 0.195531I
a = −0.18774 + 2.41620I
b = −1.207430 − 0.351597I
−2.18450 + 3.74259I −7.40219 − 5.01666I
u = 0.355795 + 0.057281I
a = 0.596264 − 1.005330I
b = 0.877622 − 0.070652I
−1.042440 − 0.056562I −6.41884 − 0.08360I
u = 0.355795 − 0.057281I
a = 0.596264 + 1.005330I
b = 0.877622 + 0.070652I
−1.042440 + 0.056562I −6.41884 + 0.08360I
u = 0.306574
a = 1.28740
b = 0.730989
−1.07499 −8.21820
16
II. I
u
2
=
h3u
4
+4u
3
+5u
2
+5b+u, −u
4
−u
3
+u
2
+5a+3u+4, u
5
+u
4
+2u
3
+u
2
+u+1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
8
=
1
5
u
4
+
1
5
u
3
+ ··· −
3
5
u −
4
5
−
3
5
u
4
−
4
5
u
3
− u
2
−
1
5
u
a
12
=
u
u
3
+ u
a
3
=
1
u
2
a
7
=
−
2
5
u
4
−
3
5
u
3
+ ··· −
4
5
u −
4
5
−
3
5
u
4
−
4
5
u
3
− u
2
−
1
5
u
a
10
=
u
3
−u
4
− u
3
− u
2
− 1
a
1
=
−u
4
− 2u
3
− u
2
− 1
u
4
+ 2u
3
+ 2u
a
2
=
−u
3
u
3
+ u
a
9
=
−
2
5
u
4
+
2
5
u
3
+ ··· −
4
5
u −
4
5
−
8
5
u
4
−
9
5
u
3
− 2u
2
−
1
5
u − 1
a
6
=
−u
3
u
4
+ u
3
+ u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
4
−
61
25
u
3
+
27
25
u
2
+
2
5
u −
277
25
17
(iv) u-Polynomials at the component
18
Crossings u-Polynomials at each crossing
c
1
u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1
c
2
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
3
u
5
c
4
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
5
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
6
(u − 1)
5
c
7
25(25u
5
+ 25u
4
− 17u
3
− 10u
2
+ 7u − 1)
c
8
25(25u
5
− 3u
3
− 2u
2
− 2u − 1)
c
9
(u + 1)
5
c
10
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
11
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
12
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
19
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1
c
2
, c
5
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
3
y
5
c
4
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
6
, c
9
(y −1)
5
c
7
625(625y
5
− 1475y
4
+ 1139y
3
− 288y
2
+ 29y −1)
c
8
625(625y
5
− 150y
4
− 91y
3
+ 8y
2
− 1)
c
10
, c
12
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = −1.020220 − 0.784696I
b = 1.010320 − 0.128572I
−1.97403 + 1.53058I −9.93512 − 3.41297I
u = 0.339110 − 0.822375I
a = −1.020220 + 0.784696I
b = 1.010320 + 0.128572I
−1.97403 − 1.53058I −9.93512 + 3.41297I
u = −0.766826
a = −0.478537
b = −0.281390
−4.04602 −6.88530
u = −0.455697 + 1.200150I
a = 0.159483 − 0.158187I
b = −0.369623 + 0.020554I
−7.51750 − 4.40083I −14.5822 + 23.2659I
u = −0.455697 − 1.200150I
a = 0.159483 + 0.158187I
b = −0.369623 − 0.020554I
−7.51750 + 4.40083I −14.5822 − 23.2659I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− 5u
4
+ 8u
3
− 3u
2
− u − 1)(u
115
+ 52u
114
+ ··· + 8u + 1)
c
2
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
115
+ 2u
114
+ ··· + 4u + 1)
c
3
u
5
(u
115
+ u
114
+ ··· − 4000u + 20000)
c
4
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
115
− 2u
114
+ ··· + 2u + 1)
c
5
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
115
+ 2u
114
+ ··· + 4u + 1)
c
6
((u − 1)
5
)(u
115
− 6u
114
+ ··· − 6050u + 625)
c
7
625(25u
5
+ 25u
4
− 17u
3
− 10u
2
+ 7u − 1)
· (25u
115
+ 1297u
113
+ ··· − 6356084u + 531211)
c
8
625(25u
5
− 3u
3
− 2u
2
− 2u − 1)
· (25u
115
+ 25u
114
+ ··· + 165472u + 46912)
c
9
((u + 1)
5
)(u
115
− 6u
114
+ ··· − 6050u + 625)
c
10
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
115
+ 36u
114
+ ··· + 8u − 1)
c
11
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
115
− 2u
114
+ ··· + 2u + 1)
c
12
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
115
+ 36u
114
+ ··· + 8u − 1)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 9y
4
+ 32y
3
− 35y
2
− 5y −1)(y
115
+ 24y
114
+ ··· − 4y −1)
c
2
, c
5
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
115
− 52y
114
+ ··· + 8y −1)
c
3
y
5
(y
115
+ 33y
114
+ ··· + 2.28000 × 10
9
y −4.00000 × 10
8
)
c
4
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
115
+ 36y
114
+ ··· + 8y −1)
c
6
, c
9
((y −1)
5
)(y
115
− 64y
114
+ ··· − 9508750y −390625)
c
7
390625(625y
5
− 1475y
4
+ 1139y
3
− 288y
2
+ 29y −1)
· (625y
115
+ 64850y
114
+ ··· + 4263135428918y −282185126521)
c
8
390625(625y
5
− 150y
4
− 91y
3
+ 8y
2
− 1)
· (625y
115
− 37225y
114
+ ··· − 49455619072y −2200735744)
c
10
, c
12
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
115
+ 88y
114
+ ··· + 180y −1)
24
