12a
0359
(K12a
0359
)
A knot diagram
1
Linearized knot diagam
3 6 9 8 2 1 12 11 7 5 4 10
Solving Sequence
8,11 5,9
4 12 3 7 10 1 2 6
c
8
c
4
c
11
c
3
c
7
c
10
c
12
c
1
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.19368 × 10
103
u
61
+ 2.38805 × 10
105
u
60
+ ··· + 6.33524 × 10
104
b − 9.63557 × 10
103
,
− 5.27642 × 10
103
u
61
+ 2.16564 × 10
105
u
60
+ ··· + 2.11175 × 10
104
a + 6.20998 × 10
104
,
u
62
− 42u
61
+ ··· + u + 1i
I
u
2
= h−583832u
30
a
3
− 50272u
30
a
2
+ ··· − 1355616a − 8946449, 24u
30
a
3
+ 144u
30
a
2
+ ··· + 838a + 793,
u
31
+ 15u
30
+ ··· + 3u + 2i
I
u
3
= h−4.46583 × 10
21
u
31
− 8.87689 × 10
22
u
30
+ ··· + 1.43348 × 10
22
b − 3.51023 × 10
23
,
4.78754 × 10
22
u
31
+ 8.67713 × 10
23
u
30
+ ··· + 7.16738 × 10
22
a + 7.19257 × 10
23
,
u
32
+ 19u
31
+ ··· + 90u + 25i
I
v
1
= ha, b
2
− bv + 2b −v + 3, v
2
− 3v + 1i
I
v
2
= ha, b
2
− b + 1, v −1i
* 5 irreducible components of dim
C
= 0, with total 224 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−6.19 × 10
103
u
61
+ 2.39 × 10
105
u
60
+ · · · + 6.34 × 10
104
b − 9.64 ×
10
103
, −5.28 × 10
103
u
61
+ 2.17 × 10
105
u
60
+ · · · + 2.11 × 10
104
a + 6.21 ×
10
104
, u
62
− 42u
61
+ · · · + u + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
5
=
0.249860u
61
− 10.2552u
60
+ ··· − 30.5916u − 2.94069
0.0977655u
61
− 3.76946u
60
+ ··· + 3.24488u + 0.152095
a
9
=
1
−u
2
a
4
=
0.152095u
61
− 6.48575u
60
+ ··· − 33.8365u − 3.09278
0.0977655u
61
− 3.76946u
60
+ ··· + 3.24488u + 0.152095
a
12
=
1.48851u
61
− 61.9811u
60
+ ··· + 9.74232u + 4.15415
−0.536530u
61
+ 22.1350u
60
+ ··· − 1.66564u + 1.48851
a
3
=
−0.0868270u
61
+ 3.37589u
60
+ ··· − 30.6459u − 2.84292
0.0990411u
61
− 4.06016u
60
+ ··· + 2.83287u − 0.0209841
a
7
=
0.368383u
61
− 15.6825u
60
+ ··· − 33.3998u − 3.23851
0.609772u
61
− 24.7449u
60
+ ··· + 2.58185u − 0.168147
a
10
=
0.814764u
61
− 34.3056u
60
+ ··· + 2.38599u + 6.59465
−0.137220u
61
+ 5.54053u
60
+ ··· − 3.69068u + 0.951984
a
1
=
0.435369u
61
− 17.8972u
60
+ ··· + 35.4392u + 0.0678684
−0.552957u
61
+ 22.6502u
60
+ ··· + 0.563674u + 0.541616
a
2
=
0.102413u
61
− 4.15773u
60
+ ··· + 39.1917u + 0.298157
−0.224608u
61
+ 9.09838u
60
+ ··· − 0.175732u + 0.131771
a
6
=
0.0118368u
61
− 0.600731u
60
+ ··· − 38.9999u − 0.409916
0.232933u
61
− 9.64908u
60
+ ··· + 0.103997u − 0.205997
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.49621u
61
+ 103.028u
60
+ ··· − 7.16311u + 4.09666
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
+ 32u
61
+ ··· + 25u + 1
c
2
, c
5
u
62
+ 10u
61
+ ··· + 9u + 1
c
3
, c
10
u
62
+ u
61
+ ··· + 157u
2
+ 9
c
4
, c
11
u
62
+ u
61
+ ··· − u + 1
c
6
u
62
+ 30u
61
+ ··· + 37547u + 2393
c
7
u
62
+ 51u
61
+ ··· + 30064771072u + 1073741824
c
8
u
62
+ 42u
61
+ ··· − u + 1
c
9
, c
12
u
62
− 3u
61
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
+ 56y
60
+ ··· + 127y + 1
c
2
, c
5
y
62
− 32y
61
+ ··· − 25y + 1
c
3
, c
10
y
62
+ 21y
61
+ ··· + 2826y + 81
c
4
, c
11
y
62
+ 9y
61
+ ··· + 17y + 1
c
6
y
62
+ 26y
61
+ ··· − 77618039y + 5726449
c
7
y
62
+ 19y
61
+ ··· − 1.15 × 10
18
y + 1.15 × 10
18
c
8
y
62
− 8y
61
+ ··· − 51y + 1
c
9
, c
12
y
62
+ 21y
61
+ ··· + y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.920164 + 0.258178I
a = −0.171522 − 0.193932I
b = −0.669614 + 0.624449I
−2.59019 − 4.63724I 0
u = 0.920164 − 0.258178I
a = −0.171522 + 0.193932I
b = −0.669614 − 0.624449I
−2.59019 + 4.63724I 0
u = 0.499373 + 0.963398I
a = 0.438750 − 0.923022I
b = −0.501971 − 0.889599I
−3.88281 − 0.46065I 0
u = 0.499373 − 0.963398I
a = 0.438750 + 0.923022I
b = −0.501971 + 0.889599I
−3.88281 + 0.46065I 0
u = 0.979389 + 0.514465I
a = −0.220792 + 0.721446I
b = 1.19645 + 1.09383I
1.85971 + 4.94822I 0
u = 0.979389 − 0.514465I
a = −0.220792 − 0.721446I
b = 1.19645 − 1.09383I
1.85971 − 4.94822I 0
u = 0.438857 + 1.057020I
a = −0.410593 + 1.007440I
b = 0.493823 + 0.915752I
−6.71452 − 5.10423I 0
u = 0.438857 − 1.057020I
a = −0.410593 − 1.007440I
b = 0.493823 − 0.915752I
−6.71452 + 5.10423I 0
u = 0.888552 + 0.744591I
a = 0.185048 − 0.989964I
b = −1.15174 − 1.03840I
−2.92298 + 9.42642I 0
u = 0.888552 − 0.744591I
a = 0.185048 + 0.989964I
b = −1.15174 + 1.03840I
−2.92298 − 9.42642I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629220 + 1.055740I
a = −0.319267 + 0.898480I
b = 0.532879 + 0.901613I
−7.79004 + 3.14172I 0
u = 0.629220 − 1.055740I
a = −0.319267 − 0.898480I
b = 0.532879 − 0.901613I
−7.79004 − 3.14172I 0
u = 1.234050 + 0.374671I
a = 0.014869 − 0.420306I
b = −0.774223 − 0.952918I
−0.34790 − 1.71219I 0
u = 1.234050 − 0.374671I
a = 0.014869 + 0.420306I
b = −0.774223 + 0.952918I
−0.34790 + 1.71219I 0
u = 0.541110 + 0.364429I
a = 0.919250 − 0.771221I
b = −1.127670 − 0.716169I
−2.36554 − 0.52359I 0
u = 0.541110 − 0.364429I
a = 0.919250 + 0.771221I
b = −1.127670 + 0.716169I
−2.36554 + 0.52359I 0
u = −0.226942 + 0.567500I
a = −1.15526 + 1.37476I
b = 0.047302 + 0.810504I
−3.30081 + 1.51078I 0
u = −0.226942 − 0.567500I
a = −1.15526 − 1.37476I
b = 0.047302 − 0.810504I
−3.30081 − 1.51078I 0
u = 1.34172 + 0.51463I
a = −0.055225 + 0.493349I
b = 0.560633 + 1.009600I
1.18701 + 3.96993I 0
u = 1.34172 − 0.51463I
a = −0.055225 − 0.493349I
b = 0.560633 − 1.009600I
1.18701 − 3.96993I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.317222 + 0.464851I
a = −1.54500 + 1.62152I
b = −0.115660 + 0.894922I
−2.78728 − 5.95527I −4.95646 + 7.62237I
u = −0.317222 − 0.464851I
a = −1.54500 − 1.62152I
b = −0.115660 − 0.894922I
−2.78728 + 5.95527I −4.95646 − 7.62237I
u = 0.249047 + 0.492818I
a = 1.049160 − 0.849645I
b = −0.446366 − 0.699671I
−1.63065 − 0.67826I −5.63896 + 2.73445I
u = 0.249047 − 0.492818I
a = 1.049160 + 0.849645I
b = −0.446366 + 0.699671I
−1.63065 + 0.67826I −5.63896 − 2.73445I
u = −0.203334 + 0.491918I
a = 1.53789 − 0.98833I
b = 0.155182 − 0.732250I
−0.19950 − 1.86693I −1.22584 + 4.41138I
u = −0.203334 − 0.491918I
a = 1.53789 + 0.98833I
b = 0.155182 + 0.732250I
−0.19950 + 1.86693I −1.22584 − 4.41138I
u = 1.19510 + 0.85598I
a = 0.111753 + 0.918781I
b = 1.16040 + 1.02724I
5.91226 + 7.99963I 0
u = 1.19510 − 0.85598I
a = 0.111753 − 0.918781I
b = 1.16040 − 1.02724I
5.91226 − 7.99963I 0
u = 1.20252 + 0.93906I
a = −0.152053 − 0.972240I
b = −1.17474 − 1.03088I
6.0483 + 13.4168I 0
u = 1.20252 − 0.93906I
a = −0.152053 + 0.972240I
b = −1.17474 + 1.03088I
6.0483 − 13.4168I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.10244 + 1.06100I
a = 0.146064 + 1.095100I
b = 1.18184 + 1.05744I
−1.67279 + 12.65800I 0
u = 1.10244 − 1.06100I
a = 0.146064 − 1.095100I
b = 1.18184 − 1.05744I
−1.67279 − 12.65800I 0
u = −1.48802 + 0.48856I
a = 0.139890 − 0.500048I
b = 0.047752 − 0.317158I
2.20261 − 2.33406I 0
u = −1.48802 − 0.48856I
a = 0.139890 + 0.500048I
b = 0.047752 + 0.317158I
2.20261 + 2.33406I 0
u = 1.21760 + 1.00691I
a = 0.063374 − 0.672036I
b = −0.561277 − 0.869964I
−5.76493 + 4.37566I 0
u = 1.21760 − 1.00691I
a = 0.063374 + 0.672036I
b = −0.561277 + 0.869964I
−5.76493 − 4.37566I 0
u = 1.16698 + 1.07593I
a = −0.191200 − 1.072920I
b = −1.19188 − 1.05052I
3.2276 + 16.0824I 0
u = 1.16698 − 1.07593I
a = −0.191200 + 1.072920I
b = −1.19188 + 1.05052I
3.2276 − 16.0824I 0
u = 1.16841 + 1.11208I
a = 0.208737 + 1.092990I
b = 1.19732 + 1.05500I
0.5718 + 21.3392I 0
u = 1.16841 − 1.11208I
a = 0.208737 − 1.092990I
b = 1.19732 − 1.05500I
0.5718 − 21.3392I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.326655 + 0.081761I
a = −1.01998 − 4.35874I
b = −0.455772 − 1.038460I
−2.34446 − 1.67897I −3.97540 + 0.64256I
u = −0.326655 − 0.081761I
a = −1.01998 + 4.35874I
b = −0.455772 + 1.038460I
−2.34446 + 1.67897I −3.97540 − 0.64256I
u = −0.238513 + 0.230540I
a = 0.43580 − 4.41695I
b = −0.545904 − 1.033350I
−2.44610 + 5.55793I −3.92344 − 7.42769I
u = −0.238513 − 0.230540I
a = 0.43580 + 4.41695I
b = −0.545904 + 1.033350I
−2.44610 − 5.55793I −3.92344 + 7.42769I
u = 1.30406 + 1.14133I
a = 0.495631 + 0.091161I
b = 0.678233 − 0.294448I
−1.69191 − 4.30137I 0
u = 1.30406 − 1.14133I
a = 0.495631 − 0.091161I
b = 0.678233 + 0.294448I
−1.69191 + 4.30137I 0
u = 1.43507 + 1.00279I
a = 0.006386 + 0.624885I
b = 0.533141 + 0.847055I
−0.63962 + 7.41146I 0
u = 1.43507 − 1.00279I
a = 0.006386 − 0.624885I
b = 0.533141 − 0.847055I
−0.63962 − 7.41146I 0
u = 1.44646 + 1.10837I
a = −0.032947 − 0.651358I
b = −0.548879 − 0.829457I
−3.10035 + 12.75660I 0
u = 1.44646 − 1.10837I
a = −0.032947 + 0.651358I
b = −0.548879 + 0.829457I
−3.10035 − 12.75660I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.059087 + 0.137841I
a = −6.27225 + 2.11029I
b = 0.575488 + 0.870652I
−0.00632 + 2.04316I 0.51473 − 3.73697I
u = 0.059087 − 0.137841I
a = −6.27225 − 2.11029I
b = 0.575488 − 0.870652I
−0.00632 − 2.04316I 0.51473 + 3.73697I
u = −0.1162010 + 0.0391791I
a = 6.30651 − 6.74361I
b = 0.451685 − 0.907545I
0.00633 − 2.03596I 0.03927 + 3.79777I
u = −0.1162010 − 0.0391791I
a = 6.30651 + 6.74361I
b = 0.451685 + 0.907545I
0.00633 + 2.03596I 0.03927 − 3.79777I
u = 1.42808 + 1.37693I
a = −0.496587 − 0.104373I
b = −0.667948 + 0.203001I
2.88874 − 7.13321I 0
u = 1.42808 − 1.37693I
a = −0.496587 + 0.104373I
b = −0.667948 − 0.203001I
2.88874 + 7.13321I 0
u = 1.53493 + 1.32200I
a = 0.507691 + 0.106764I
b = 0.710619 − 0.195157I
0.49623 − 12.18690I 0
u = 1.53493 − 1.32200I
a = 0.507691 − 0.106764I
b = 0.710619 + 0.195157I
0.49623 + 12.18690I 0
u = 1.11399 + 1.72823I
a = −0.462115 − 0.079137I
b = −0.525267 + 0.184090I
4.48939 − 4.83470I 0
u = 1.11399 − 1.72823I
a = −0.462115 + 0.079137I
b = −0.525267 − 0.184090I
4.48939 + 4.83470I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.82068 + 1.97978I
a = 0.437989 + 0.036032I
b = 0.436166 − 0.185034I
3.56951 + 0.16849I 0
u = 0.82068 − 1.97978I
a = 0.437989 − 0.036032I
b = 0.436166 + 0.185034I
3.56951 − 0.16849I 0
11
II. I
u
2
= h−5.84 × 10
5
a
3
u
30
− 5.03 × 10
4
a
2
u
30
+ · · · − 1.36 × 10
6
a − 8.95 ×
10
6
, 24u
30
a
3
+ 144u
30
a
2
+ · · · + 838a + 793, u
31
+ 15u
30
+ · · · + 3u + 2i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
5
=
a
0.495299a
3
u
30
+ 0.0426487a
2
u
30
+ ··· + 1.15005a + 7.58980
a
9
=
1
−u
2
a
4
=
−0.495299a
3
u
30
− 0.0426487a
2
u
30
+ ··· − 0.150049a − 7.58980
0.495299a
3
u
30
+ 0.0426487a
2
u
30
+ ··· + 1.15005a + 7.58980
a
12
=
−0.121390a
3
u
30
− 0.530815a
2
u
30
+ ··· + 0.594693a − 2.19483
0.0787413a
3
u
30
− 0.0221048a
2
u
30
+ ··· + 1.82404a − 0.212522
a
3
=
−0.898170a
3
u
30
+ 0.878610a
2
u
30
+ ··· + 0.903562a − 1.36728
1.92968a
3
u
30
− 1.83328a
2
u
30
+ ··· + 3.91158a + 5.36658
a
7
=
0.0407111a
3
u
30
− 0.535162a
2
u
30
+ ··· − 3.84252a − 2.55769
0.0787413a
3
u
30
− 0.0221048a
2
u
30
+ ··· + 1.82404a + 0.787478
a
10
=
a
2
u
0.0426487a
3
u
30
+ 0.552920a
2
u
30
+ ··· − 2.41874a + 2.40735
a
1
=
0.00461847a
3
u
30
− 0.960137a
2
u
30
+ ··· − 2.08530a − 1.93781
−2.09453a
3
u
30
+ 1.81444a
2
u
30
+ ··· − 4.99193a + 4.06092
a
2
=
0.953931a
3
u
30
− 0.775684a
2
u
30
+ ··· − 1.46886a − 2.39151
−3.38652a
3
u
30
+ 1.47922a
2
u
30
+ ··· − 3.39276a + 4.99159
a
6
=
−1.13256a
3
u
30
+ 0.301378a
2
u
30
+ ··· − 0.658493a + 0.715757
0.609317a
3
u
30
− 0.0145222a
2
u
30
+ ··· − 2.67703a − 5.87958
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
185632
589373
u
30
a
3
+
52112
589373
u
30
a
2
+ ··· −
4300168
589373
a +
19950327
589373
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
31
+ 16u
30
+ ··· + 2u + 1)
4
c
2
, c
5
(u
31
− 2u
30
+ ··· − 2u + 1)
4
c
3
, c
10
u
124
+ 2u
123
+ ··· + 445543889u + 54599377
c
4
, c
11
u
124
+ 2u
123
+ ··· − u + 1
c
6
(u
31
− 9u
30
+ ··· + 73u − 8)
4
c
7
(u
2
− u + 1)
62
c
8
(u
31
− 15u
30
+ ··· + 3u − 2)
4
c
9
, c
12
u
124
− 3u
123
+ ··· + 54u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
31
+ 28y
29
+ ··· − 14y −1)
4
c
2
, c
5
(y
31
− 16y
30
+ ··· + 2y −1)
4
c
3
, c
10
y
124
+ 42y
123
+ ··· − 6608919476226557y + 2981091968788129
c
4
, c
11
y
124
− 42y
123
+ ··· + 283y + 1
c
6
(y
31
+ 13y
30
+ ··· + 833y −64)
4
c
7
(y
2
+ y + 1)
62
c
8
(y
31
− 3y
30
+ ··· + 69y −4)
4
c
9
, c
12
y
124
− 31y
123
+ ··· − 498y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.409801 + 0.900274I
a = −0.506789 + 0.851719I
b = −1.53214 + 0.83196I
−0.60079 − 6.55319I −2.41907 + 9.71050I
u = −0.409801 + 0.900274I
a = 0.534702 − 0.939505I
b = 0.603624 − 0.987957I
−0.60079 − 2.49343I −2.41907 + 2.78230I
u = −0.409801 + 0.900274I
a = 1.177230 + 0.223519I
b = 0.0153756 + 0.0819040I
−0.60079 − 2.49343I −2.41907 + 2.78230I
u = −0.409801 + 0.900274I
a = −0.96924 − 1.97631I
b = 0.437980 − 0.915004I
−0.60079 − 6.55319I −2.41907 + 9.71050I
u = −0.409801 − 0.900274I
a = −0.506789 − 0.851719I
b = −1.53214 − 0.83196I
−0.60079 + 6.55319I −2.41907 − 9.71050I
u = −0.409801 − 0.900274I
a = 0.534702 + 0.939505I
b = 0.603624 + 0.987957I
−0.60079 + 2.49343I −2.41907 − 2.78230I
u = −0.409801 − 0.900274I
a = 1.177230 − 0.223519I
b = 0.0153756 − 0.0819040I
−0.60079 + 2.49343I −2.41907 − 2.78230I
u = −0.409801 − 0.900274I
a = −0.96924 + 1.97631I
b = 0.437980 + 0.915004I
−0.60079 + 6.55319I −2.41907 − 9.71050I
u = −1.020150 + 0.219444I
a = 0.137660 + 1.011220I
b = −0.599567 − 0.078037I
3.66483 + 1.12535I 9.65108 − 2.67079I
u = −1.020150 + 0.219444I
a = 0.542247 − 0.929539I
b = 1.23471 − 1.06885I
3.66483 − 2.93441I 9.65108 + 4.25741I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.020150 + 0.219444I
a = 0.445103 + 0.755471I
b = 0.991109 + 0.949417I
3.66483 + 1.12535I 9.65108 − 2.67079I
u = −1.020150 + 0.219444I
a = 0.696367 − 0.458492I
b = −0.675842 + 0.294074I
3.66483 − 2.93441I 9.65108 + 4.25741I
u = −1.020150 − 0.219444I
a = 0.137660 − 1.011220I
b = −0.599567 + 0.078037I
3.66483 − 1.12535I 9.65108 + 2.67079I
u = −1.020150 − 0.219444I
a = 0.542247 + 0.929539I
b = 1.23471 + 1.06885I
3.66483 + 2.93441I 9.65108 − 4.25741I
u = −1.020150 − 0.219444I
a = 0.445103 − 0.755471I
b = 0.991109 − 0.949417I
3.66483 − 1.12535I 9.65108 + 2.67079I
u = −1.020150 − 0.219444I
a = 0.696367 + 0.458492I
b = −0.675842 − 0.294074I
3.66483 + 2.93441I 9.65108 − 4.25741I
u = −0.350417 + 0.991768I
a = 0.504244 − 0.840575I
b = 1.53201 − 0.78532I
−3.44393 − 11.22350I −5.49289 + 12.45420I
u = −0.350417 + 0.991768I
a = −0.612387 + 0.973879I
b = −0.753682 + 1.014450I
−3.44393 − 7.16369I −5.49289 + 5.52600I
u = −0.350417 + 0.991768I
a = −1.138770 − 0.508651I
b = 0.009280 − 0.154348I
−3.44393 − 7.16369I −5.49289 + 5.52600I
u = −0.350417 + 0.991768I
a = 0.77423 + 2.12451I
b = −0.414943 + 0.999946I
−3.44393 − 11.22350I −5.49289 + 12.45420I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.350417 − 0.991768I
a = 0.504244 + 0.840575I
b = 1.53201 + 0.78532I
−3.44393 + 11.22350I −5.49289 − 12.45420I
u = −0.350417 − 0.991768I
a = −0.612387 − 0.973879I
b = −0.753682 − 1.014450I
−3.44393 + 7.16369I −5.49289 − 5.52600I
u = −0.350417 − 0.991768I
a = −1.138770 + 0.508651I
b = 0.009280 + 0.154348I
−3.44393 + 7.16369I −5.49289 − 5.52600I
u = −0.350417 − 0.991768I
a = 0.77423 − 2.12451I
b = −0.414943 − 0.999946I
−3.44393 + 11.22350I −5.49289 − 12.45420I
u = −0.270659 + 0.813098I
a = 0.525534 − 0.836875I
b = 1.61610 − 0.82213I
−4.53268 − 2.91050I −8.63801 + 6.37131I
u = −0.270659 + 0.813098I
a = −0.491451 + 1.068510I
b = −0.599508 + 1.236640I
−4.53268 + 1.14926I −8.63801 − 0.55689I
u = −0.270659 + 0.813098I
a = −1.69758 − 0.34137I
b = −0.107453 − 0.133364I
−4.53268 + 1.14926I −8.63801 − 0.55689I
u = −0.270659 + 0.813098I
a = 1.19871 + 2.36906I
b = −0.307156 + 0.882745I
−4.53268 − 2.91050I −8.63801 + 6.37131I
u = −0.270659 − 0.813098I
a = 0.525534 + 0.836875I
b = 1.61610 + 0.82213I
−4.53268 + 2.91050I −8.63801 − 6.37131I
u = −0.270659 − 0.813098I
a = −0.491451 − 1.068510I
b = −0.599508 − 1.236640I
−4.53268 − 1.14926I −8.63801 + 0.55689I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.270659 − 0.813098I
a = −1.69758 + 0.34137I
b = −0.107453 + 0.133364I
−4.53268 − 1.14926I −8.63801 + 0.55689I
u = −0.270659 − 0.813098I
a = 1.19871 − 2.36906I
b = −0.307156 − 0.882745I
−4.53268 + 2.91050I −8.63801 − 6.37131I
u = −1.143470 + 0.448145I
a = 0.115197 − 0.867097I
b = 0.636723 − 0.038100I
2.09249 − 3.38872I 5.67347 + 2.42300I
u = −1.143470 + 0.448145I
a = −0.568570 + 0.991737I
b = −1.28760 + 1.03758I
2.09249 − 7.44849I 5.67347 + 9.35121I
u = −1.143470 + 0.448145I
a = −0.473847 − 0.553922I
b = −0.967860 − 0.714214I
2.09249 − 3.38872I 5.67347 + 2.42300I
u = −1.143470 + 0.448145I
a = −0.482744 + 0.029373I
b = 0.801645 − 0.374650I
2.09249 − 7.44849I 5.67347 + 9.35121I
u = −1.143470 − 0.448145I
a = 0.115197 + 0.867097I
b = 0.636723 + 0.038100I
2.09249 + 3.38872I 5.67347 − 2.42300I
u = −1.143470 − 0.448145I
a = −0.568570 − 0.991737I
b = −1.28760 − 1.03758I
2.09249 + 7.44849I 5.67347 − 9.35121I
u = −1.143470 − 0.448145I
a = −0.473847 + 0.553922I
b = −0.967860 + 0.714214I
2.09249 + 3.38872I 5.67347 − 2.42300I
u = −1.143470 − 0.448145I
a = −0.482744 − 0.029373I
b = 0.801645 + 0.374650I
2.09249 + 7.44849I 5.67347 − 9.35121I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.822348 + 0.989602I
a = −0.395184 + 0.875113I
b = −1.32730 + 0.83675I
1.52153 − 6.66542I 0. + 12.11217I
u = −0.822348 + 0.989602I
a = 0.547490 − 0.651940I
b = 0.726923 − 0.378010I
1.52153 − 2.60565I 0
u = −0.822348 + 0.989602I
a = −0.354968 − 1.268640I
b = 0.804487 − 0.890882I
1.52153 − 6.66542I 0. + 12.11217I
u = −0.822348 + 0.989602I
a = 0.168388 + 0.199051I
b = −0.418639 − 0.047698I
1.52153 − 2.60565I 0. + 5.18397I
u = −0.822348 − 0.989602I
a = −0.395184 − 0.875113I
b = −1.32730 − 0.83675I
1.52153 + 6.66542I 0. − 12.11217I
u = −0.822348 − 0.989602I
a = 0.547490 + 0.651940I
b = 0.726923 + 0.378010I
1.52153 + 2.60565I 0
u = −0.822348 − 0.989602I
a = −0.354968 + 1.268640I
b = 0.804487 + 0.890882I
1.52153 + 6.66542I 0. − 12.11217I
u = −0.822348 − 0.989602I
a = 0.168388 − 0.199051I
b = −0.418639 + 0.047698I
1.52153 + 2.60565I 0. − 5.18397I
u = 0.622733 + 0.295826I
a = 0.639824 + 0.808155I
b = −1.184250 + 0.044416I
−0.17715 + 8.26022I 4.35716 − 7.98513I
u = 0.622733 + 0.295826I
a = 0.43247 − 1.52881I
b = 1.32230 − 1.56744I
−0.17715 + 12.32000I 4.3572 − 14.9133I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.622733 + 0.295826I
a = 0.61394 − 1.81047I
b = −0.909978 − 1.015220I
−0.17715 + 8.26022I 4.35716 − 7.98513I
u = 0.622733 + 0.295826I
a = −0.19132 + 3.11576I
b = 0.565553 + 0.239182I
−0.17715 + 12.32000I 4.3572 − 14.9133I
u = 0.622733 − 0.295826I
a = 0.639824 − 0.808155I
b = −1.184250 − 0.044416I
−0.17715 − 8.26022I 4.35716 + 7.98513I
u = 0.622733 − 0.295826I
a = 0.43247 + 1.52881I
b = 1.32230 + 1.56744I
−0.17715 − 12.32000I 4.3572 + 14.9133I
u = 0.622733 − 0.295826I
a = 0.61394 + 1.81047I
b = −0.909978 + 1.015220I
−0.17715 − 8.26022I 4.35716 + 7.98513I
u = 0.622733 − 0.295826I
a = −0.19132 − 3.11576I
b = 0.565553 − 0.239182I
−0.17715 − 12.32000I 4.3572 + 14.9133I
u = 0.601541 + 0.243060I
a = −0.914035 − 0.774581I
b = 1.107250 + 0.029166I
2.50780 + 3.03742I 8.75638 − 4.58888I
u = 0.601541 + 0.243060I
a = −0.40227 + 1.50045I
b = −1.35153 + 1.54479I
2.50780 + 7.09718I 8.7564 − 11.5171I
u = 0.601541 + 0.243060I
a = −0.57866 + 1.57246I
b = 1.020520 + 0.974779I
2.50780 + 3.03742I 8.75638 − 4.58888I
u = 0.601541 + 0.243060I
a = 0.45763 − 3.19210I
b = −0.581798 − 0.204056I
2.50780 + 7.09718I 8.7564 − 11.5171I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.601541 − 0.243060I
a = −0.914035 + 0.774581I
b = 1.107250 − 0.029166I
2.50780 − 3.03742I 8.75638 + 4.58888I
u = 0.601541 − 0.243060I
a = −0.40227 − 1.50045I
b = −1.35153 − 1.54479I
2.50780 − 7.09718I 8.7564 + 11.5171I
u = 0.601541 − 0.243060I
a = −0.57866 − 1.57246I
b = 1.020520 − 0.974779I
2.50780 − 3.03742I 8.75638 + 4.58888I
u = 0.601541 − 0.243060I
a = 0.45763 + 3.19210I
b = −0.581798 + 0.204056I
2.50780 − 7.09718I 8.7564 + 11.5171I
u = 0.631386 + 0.046109I
a = 0.02710 + 1.44042I
b = 1.29317 + 1.23847I
5.43979 + 0.59934I 12.53544 − 0.73085I
u = 0.631386 + 0.046109I
a = −0.18713 + 1.46019I
b = −1.34033 + 1.35511I
5.43979 + 4.65911I 12.5354 − 7.6590I
u = 0.631386 + 0.046109I
a = −1.37107 − 1.87145I
b = 0.808687 − 0.069132I
5.43979 + 0.59934I 12.53544 − 0.73085I
u = 0.631386 + 0.046109I
a = 1.23240 − 2.40859I
b = −0.723271 − 0.119520I
5.43979 + 4.65911I 12.5354 − 7.6590I
u = 0.631386 − 0.046109I
a = 0.02710 − 1.44042I
b = 1.29317 − 1.23847I
5.43979 − 0.59934I 12.53544 + 0.73085I
u = 0.631386 − 0.046109I
a = −0.18713 − 1.46019I
b = −1.34033 − 1.35511I
5.43979 − 4.65911I 12.5354 + 7.6590I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.631386 − 0.046109I
a = −1.37107 + 1.87145I
b = 0.808687 + 0.069132I
5.43979 − 0.59934I 12.53544 + 0.73085I
u = 0.631386 − 0.046109I
a = 1.23240 + 2.40859I
b = −0.723271 + 0.119520I
5.43979 − 4.65911I 12.5354 + 7.6590I
u = 0.489498 + 0.248123I
a = 0.637086 − 0.158363I
b = −1.325820 − 0.366582I
−2.33026 − 0.43819I 4.64802 − 6.67686I
u = 0.489498 + 0.248123I
a = 0.45350 − 1.43470I
b = 1.42531 − 1.61209I
−2.33026 + 3.62158I 4.6480 − 13.6051I
u = 0.489498 + 0.248123I
a = 1.54770 − 1.08544I
b = −0.909174 − 0.588965I
−2.33026 − 0.43819I 4.64802 − 6.67686I
u = 0.489498 + 0.248123I
a = −0.46872 + 3.94868I
b = 0.519715 + 0.154299I
−2.33026 + 3.62158I 4.6480 − 13.6051I
u = 0.489498 − 0.248123I
a = 0.637086 + 0.158363I
b = −1.325820 + 0.366582I
−2.33026 + 0.43819I 4.64802 + 6.67686I
u = 0.489498 − 0.248123I
a = 0.45350 + 1.43470I
b = 1.42531 + 1.61209I
−2.33026 − 3.62158I 4.6480 + 13.6051I
u = 0.489498 − 0.248123I
a = 1.54770 + 1.08544I
b = −0.909174 + 0.588965I
−2.33026 + 0.43819I 4.64802 + 6.67686I
u = 0.489498 − 0.248123I
a = −0.46872 − 3.94868I
b = 0.519715 − 0.154299I
−2.33026 − 3.62158I 4.6480 + 13.6051I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.24063 + 0.87066I
a = 0.208118 − 0.717998I
b = 0.666559 − 0.178120I
2.08710 + 2.52400I 0
u = −1.24063 + 0.87066I
a = −0.484779 + 1.176110I
b = −1.23957 + 1.06053I
2.08710 − 1.53576I 0
u = −1.24063 + 0.87066I
a = −0.611314 − 0.114212I
b = −1.038810 − 0.270646I
2.08710 + 2.52400I 0
u = −1.24063 + 0.87066I
a = −0.034338 − 0.410827I
b = 1.037050 − 0.513771I
2.08710 − 1.53576I 0
u = −1.24063 − 0.87066I
a = 0.208118 + 0.717998I
b = 0.666559 + 0.178120I
2.08710 − 2.52400I 0
u = −1.24063 − 0.87066I
a = −0.484779 − 1.176110I
b = −1.23957 − 1.06053I
2.08710 + 1.53576I 0
u = −1.24063 − 0.87066I
a = −0.611314 + 0.114212I
b = −1.038810 + 0.270646I
2.08710 − 2.52400I 0
u = −1.24063 − 0.87066I
a = −0.034338 + 0.410827I
b = 1.037050 + 0.513771I
2.08710 + 1.53576I 0
u = −1.16890 + 0.97715I
a = 0.384905 − 1.213680I
b = 1.18207 − 1.05155I
3.75655 − 5.67101I 0
u = −1.16890 + 0.97715I
a = −0.193226 + 0.671460I
b = −0.645853 + 0.189384I
3.75655 − 1.61124I 0
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.16890 + 0.97715I
a = 0.595165 − 0.055307I
b = 1.000140 + 0.121212I
3.75655 − 1.61124I 0
u = −1.16890 + 0.97715I
a = −0.052270 + 0.557513I
b = −1.090220 + 0.589435I
3.75655 − 5.67101I 0
u = −1.16890 − 0.97715I
a = 0.384905 + 1.213680I
b = 1.18207 + 1.05155I
3.75655 + 5.67101I 0
u = −1.16890 − 0.97715I
a = −0.193226 − 0.671460I
b = −0.645853 − 0.189384I
3.75655 + 1.61124I 0
u = −1.16890 − 0.97715I
a = 0.595165 + 0.055307I
b = 1.000140 − 0.121212I
3.75655 + 1.61124I 0
u = −1.16890 − 0.97715I
a = −0.052270 − 0.557513I
b = −1.090220 − 0.589435I
3.75655 + 5.67101I 0
u = −0.96606 + 1.18137I
a = −0.712451 + 0.453230I
b = −1.012460 + 0.269165I
0.230355 + 0.167426I 0
u = −0.96606 + 1.18137I
a = 0.338391 − 0.724664I
b = 1.28205 − 0.69278I
0.23036 − 3.89234I 0
u = −0.96606 + 1.18137I
a = −0.049246 − 0.578533I
b = 0.507273 − 0.176602I
0.230355 + 0.167426I 0
u = −0.96606 + 1.18137I
a = −0.06606 + 1.44697I
b = −0.94929 + 1.08400I
0.23036 − 3.89234I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.96606 − 1.18137I
a = −0.712451 − 0.453230I
b = −1.012460 − 0.269165I
0.230355 − 0.167426I 0
u = −0.96606 − 1.18137I
a = 0.338391 + 0.724664I
b = 1.28205 + 0.69278I
0.23036 + 3.89234I 0
u = −0.96606 − 1.18137I
a = −0.049246 + 0.578533I
b = 0.507273 + 0.176602I
0.230355 − 0.167426I 0
u = −0.96606 − 1.18137I
a = −0.06606 − 1.44697I
b = −0.94929 − 1.08400I
0.23036 + 3.89234I 0
u = −0.466333
a = −0.443642 + 1.147910I
b = −1.16747 + 1.69050I
−1.30280 − 2.02988I 15.0429 + 3.4641I
u = −0.466333
a = −0.443642 − 1.147910I
b = −1.16747 − 1.69050I
−1.30280 + 2.02988I 15.0429 − 3.4641I
u = −0.466333
a = −2.16598 + 3.37208I
b = 0.337546 − 0.253027I
−1.30280 − 2.02988I 15.0429 + 3.4641I
u = −0.466333
a = −2.16598 − 3.37208I
b = 0.337546 + 0.253027I
−1.30280 + 2.02988I 15.0429 − 3.4641I
u = −1.10803 + 1.11733I
a = 0.687315 − 0.255580I
b = 1.043690 − 0.074878I
3.31713 − 2.53416I 0
u = −1.10803 + 1.11733I
a = −0.225497 + 0.637652I
b = −1.197980 + 0.634447I
3.31713 − 6.59393I 0
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10803 + 1.11733I
a = −0.095962 + 0.635413I
b = −0.596781 + 0.197969I
3.31713 − 2.53416I 0
u = −1.10803 + 1.11733I
a = 0.258765 − 1.339700I
b = 1.08112 − 1.08303I
3.31713 − 6.59393I 0
u = −1.10803 − 1.11733I
a = 0.687315 + 0.255580I
b = 1.043690 + 0.074878I
3.31713 + 2.53416I 0
u = −1.10803 − 1.11733I
a = −0.225497 − 0.637652I
b = −1.197980 − 0.634447I
3.31713 + 6.59393I 0
u = −1.10803 − 1.11733I
a = −0.095962 − 0.635413I
b = −0.596781 − 0.197969I
3.31713 + 2.53416I 0
u = −1.10803 − 1.11733I
a = 0.258765 + 1.339700I
b = 1.08112 + 1.08303I
3.31713 + 6.59393I 0
u = −1.11153 + 1.19848I
a = −0.778587 + 0.297189I
b = −1.119500 + 0.134690I
1.10056 − 6.88524I 0
u = −1.11153 + 1.19848I
a = 0.297759 − 0.616591I
b = 1.245540 − 0.616665I
1.10056 − 10.94500I 0
u = −1.11153 + 1.19848I
a = 0.047541 − 0.674074I
b = 0.573682 − 0.227950I
1.10056 − 6.88524I 0
u = −1.11153 + 1.19848I
a = −0.25863 + 1.43814I
b = −1.05340 + 1.13598I
1.10056 − 10.94500I 0
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.11153 − 1.19848I
a = −0.778587 − 0.297189I
b = −1.119500 − 0.134690I
1.10056 + 6.88524I 0
u = −1.11153 − 1.19848I
a = 0.297759 + 0.616591I
b = 1.245540 + 0.616665I
1.10056 + 10.94500I 0
u = −1.11153 − 1.19848I
a = 0.047541 + 0.674074I
b = 0.573682 + 0.227950I
1.10056 + 6.88524I 0
u = −1.11153 − 1.19848I
a = −0.25863 − 1.43814I
b = −1.05340 − 1.13598I
1.10056 + 10.94500I 0
27
III. I
u
3
= h−4.47 × 10
21
u
31
− 8.88 × 10
22
u
30
+ · · · + 1.43 × 10
22
b − 3.51 ×
10
23
, 4.79 × 10
22
u
31
+ 8.68 × 10
23
u
30
+ · · · + 7.17 × 10
22
a + 7.19 ×
10
23
, u
32
+ 19u
31
+ · · · + 90u + 25i
(i) Arc colorings
a
8
=
1
0
a
11
=
0
u
a
5
=
−0.667963u
31
− 12.1064u
30
+ ··· − 39.4438u − 10.0351
0.311539u
31
+ 6.19257u
30
+ ··· + 53.6324u + 24.4875
a
9
=
1
−u
2
a
4
=
−0.979501u
31
− 18.2990u
30
+ ··· − 93.0762u − 34.5227
0.311539u
31
+ 6.19257u
30
+ ··· + 53.6324u + 24.4875
a
12
=
1.70114u
31
+ 30.9669u
30
+ ··· + 127.404u + 48.3701
−1.35473u
31
− 24.8075u
30
+ ··· − 103.732u − 42.5285
a
3
=
−0.394630u
31
− 7.39431u
30
+ ··· − 42.9948u − 17.8236
0.648401u
31
+ 11.7901u
30
+ ··· + 49.5454u + 19.2906
a
7
=
−2.04037u
31
− 38.4678u
30
+ ··· − 204.978u − 101.979
−0.633106u
31
− 10.5498u
30
+ ··· + 1.25683u + 17.1410
a
10
=
−0.0759806u
31
− 1.35741u
30
+ ··· − 2.66347u − 2.81860
−0.422391u
31
− 7.51682u
30
+ ··· − 24.3353u − 8.66027
a
1
=
1.71932u
31
+ 31.3533u
30
+ ··· + 125.165u + 50.2261
−0.781724u
31
− 14.5169u
30
+ ··· − 70.5173u − 30.8133
a
2
=
0.0999657u
31
+ 1.71787u
30
+ ··· + 5.19448u + 0.992100
0.262654u
31
+ 4.74927u
30
+ ··· + 19.1426u + 7.68738
a
6
=
−0.488973u
31
− 8.79151u
30
+ ··· − 33.6906u − 11.0311
0.310704u
31
+ 5.69483u
30
+ ··· + 24.6780u + 9.97506
(ii) Obstruction class = 1
(iii) Cusp Shapes =
167719621315372726751064
14334761307521948282105
u
31
+
3065892602606718019423271
14334761307521948282105
u
30
+ ··· +
14165838622959990791344032
14334761307521948282105
u +
907755503948170820806660
2866952261504389656421
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
32
− 17u
31
+ ··· − 8u + 1
c
2
u
32
+ 3u
31
+ ··· + 4u + 1
c
3
, c
10
u
32
+ 6u
30
+ ··· − u + 1
c
4
, c
11
u
32
− 2u
31
+ ··· + 2u + 1
c
5
u
32
− 3u
31
+ ··· − 4u + 1
c
6
u
32
− 9u
31
+ ··· − 170u + 25
c
7
u
32
+ 3u
31
+ ··· + 11u + 1
c
8
u
32
+ 19u
31
+ ··· + 90u + 25
c
9
, c
12
u
32
− 8u
31
+ ··· − 3u
2
+ 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
32
− y
31
+ ··· + 16y + 1
c
2
, c
5
y
32
− 17y
31
+ ··· − 8y + 1
c
3
, c
10
y
32
+ 12y
31
+ ··· + 27y + 1
c
4
, c
11
y
32
− 16y
31
+ ··· − 22y + 1
c
6
y
32
+ 13y
31
+ ··· − 6050y + 625
c
7
y
32
+ 19y
31
+ ··· + 13y + 1
c
8
y
32
− 5y
31
+ ··· − 11950y + 625
c
9
, c
12
y
32
− 12y
31
+ ··· − 6y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.382303 + 0.934070I
a = −1.010960 + 0.075541I
b = −0.534216 − 0.301258I
4.12302 − 4.19312I 4.47577 + 4.00568I
u = 0.382303 − 0.934070I
a = −1.010960 − 0.075541I
b = −0.534216 + 0.301258I
4.12302 + 4.19312I 4.47577 − 4.00568I
u = −0.675417 + 0.768967I
a = 0.226037 + 1.137460I
b = −1.13478 + 0.85700I
−1.79090 − 9.17694I 0. + 10.35277I
u = −0.675417 − 0.768967I
a = 0.226037 − 1.137460I
b = −1.13478 − 0.85700I
−1.79090 + 9.17694I 0. − 10.35277I
u = −0.944337 + 0.611040I
a = −0.177695 − 0.791351I
b = 1.13301 − 0.96276I
1.90055 − 4.71902I 5.77628 + 0.I
u = −0.944337 − 0.611040I
a = −0.177695 + 0.791351I
b = 1.13301 + 0.96276I
1.90055 + 4.71902I 5.77628 + 0.I
u = −1.088410 + 0.317668I
a = 0.140152 − 0.243786I
b = 0.966370 − 0.032542I
3.70712 − 0.85429I 9.75163 + 0.I
u = −1.088410 − 0.317668I
a = 0.140152 + 0.243786I
b = 0.966370 + 0.032542I
3.70712 + 0.85429I 9.75163 + 0.I
u = 0.659216 + 0.195884I
a = 1.61688 + 1.10693I
b = 0.578112 + 0.562424I
−0.75786 − 11.40500I −1.06255 + 7.05435I
u = 0.659216 − 0.195884I
a = 1.61688 − 1.10693I
b = 0.578112 − 0.562424I
−0.75786 + 11.40500I −1.06255 − 7.05435I
31
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.579244 + 0.299588I
a = −1.75160 − 0.79694I
b = −0.588585 − 0.512936I
1.84734 − 6.29478I 2.01774 + 3.71090I
u = 0.579244 − 0.299588I
a = −1.75160 + 0.79694I
b = −0.588585 + 0.512936I
1.84734 + 6.29478I 2.01774 − 3.71090I
u = −0.934573 + 1.046980I
a = 0.133797 − 1.040530I
b = 1.115820 − 0.851370I
2.29932 − 6.02300I 0
u = −0.934573 − 1.046980I
a = 0.133797 + 1.040530I
b = 1.115820 + 0.851370I
2.29932 + 6.02300I 0
u = −0.551583 + 0.223512I
a = 1.076320 + 0.516590I
b = −1.30623 + 0.55213I
−2.57938 + 0.49550I −36.4479 − 6.8831I
u = −0.551583 − 0.223512I
a = 1.076320 − 0.516590I
b = −1.30623 − 0.55213I
−2.57938 − 0.49550I −36.4479 + 6.8831I
u = −1.320300 + 0.486945I
a = −0.294768 + 0.282605I
b = −0.977789 + 0.126535I
2.04449 − 5.23982I 0
u = −1.320300 − 0.486945I
a = −0.294768 − 0.282605I
b = −0.977789 − 0.126535I
2.04449 + 5.23982I 0
u = 0.11829 + 1.49282I
a = 0.614440 − 0.151421I
b = 0.481912 + 0.160898I
3.50639 + 0.63489I 0
u = 0.11829 − 1.49282I
a = 0.614440 + 0.151421I
b = 0.481912 − 0.160898I
3.50639 − 0.63489I 0
32
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.12326 + 1.01606I
a = 0.194610 − 0.898929I
b = 1.089400 − 0.815943I
2.94511 − 5.61763I 0
u = −1.12326 − 1.01606I
a = 0.194610 + 0.898929I
b = 1.089400 + 0.815943I
2.94511 + 5.61763I 0
u = −1.01659 + 1.15746I
a = −0.241094 + 1.028020I
b = −1.132070 + 0.832498I
0.42325 − 2.83616I 0
u = −1.01659 − 1.15746I
a = −0.241094 − 1.028020I
b = −1.132070 − 0.832498I
0.42325 + 2.83616I 0
u = 0.383280 + 0.156976I
a = 2.69050 + 1.07564I
b = 0.683093 + 0.525840I
−2.78183 − 3.00079I −3.82465 + 1.75831I
u = 0.383280 − 0.156976I
a = 2.69050 − 1.07564I
b = 0.683093 − 0.525840I
−2.78183 + 3.00079I −3.82465 − 1.75831I
u = −1.15033 + 1.12465I
a = −0.275362 + 0.930475I
b = −1.120340 + 0.798580I
0.93635 − 9.74729I 0
u = −1.15033 − 1.12465I
a = −0.275362 − 0.930475I
b = −1.120340 − 0.798580I
0.93635 + 9.74729I 0
u = −1.39951 + 0.85040I
a = −0.302639 + 0.408785I
b = −0.833387 + 0.302247I
1.53098 + 0.83665I 0
u = −1.39951 − 0.85040I
a = −0.302639 − 0.408785I
b = −0.833387 − 0.302247I
1.53098 − 0.83665I 0
33
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41802 + 1.24729I
a = 0.261385 − 0.353992I
b = 0.579675 − 0.251102I
2.38528 − 2.94082I 0
u = −1.41802 − 1.24729I
a = 0.261385 + 0.353992I
b = 0.579675 + 0.251102I
2.38528 + 2.94082I 0
34
IV. I
v
1
= ha, b
2
− bv + 2b − v + 3, v
2
− 3v + 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
v
0
a
5
=
0
b
a
9
=
1
0
a
4
=
−b
b
a
12
=
bv − b + v − 1
−bv + b + 1
a
3
=
0
b
a
7
=
bv − v + 1
bv − b
a
10
=
v
−bv + b + 1
a
1
=
−bv + v − 1
−bv + b
a
2
=
−bv + v − 1
−bv + 2b
a
6
=
bv − v + 1
bv − b
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4bv + 4b − 9
35
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
4
, c
10
c
11
u
4
− u
3
+ 2u
2
+ u + 1
c
5
(u + 1)
4
c
6
, c
8
u
4
c
7
, c
9
, c
12
(u
2
− u + 1)
2
36
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
4
c
3
, c
4
, c
10
c
11
y
4
+ 3y
3
+ 8y
2
+ 3y + 1
c
6
, c
8
y
4
c
7
, c
9
, c
12
(y
2
+ y + 1)
2
37
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = −0.80902 + 1.40126I
−1.64493 − 2.02988I −11.00000 + 3.46410I
v = 0.381966
a = 0
b = −0.80902 − 1.40126I
−1.64493 + 2.02988I −11.00000 − 3.46410I
v = 2.61803
a = 0
b = 0.309017 + 0.535233I
−1.64493 + 2.02988I −11.00000 − 3.46410I
v = 2.61803
a = 0
b = 0.309017 − 0.535233I
−1.64493 − 2.02988I −11.00000 + 3.46410I
38
V. I
v
2
= ha, b
2
− b + 1, v − 1i
(i) Arc colorings
a
8
=
1
0
a
11
=
1
0
a
5
=
0
b
a
9
=
1
0
a
4
=
−b
b
a
12
=
b
−b + 1
a
3
=
0
b
a
7
=
0
b
a
10
=
1
−b + 1
a
1
=
0
−b
a
2
=
0
−b
a
6
=
0
b
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4b + 2
39
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
u
2
c
3
, c
4
, c
9
c
10
, c
11
, c
12
u
2
− u + 1
c
7
u
2
+ u + 1
40
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
y
2
c
3
, c
4
, c
7
c
9
, c
10
, c
11
c
12
y
2
+ y + 1
41
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.500000 + 0.866025I
2.02988I 0. − 3.46410I
v = 1.00000
a = 0
b = 0.500000 − 0.866025I
− 2.02988I 0. + 3.46410I
42
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
4
(u
31
+ 16u
30
+ ··· + 2u + 1)
4
(u
32
− 17u
31
+ ··· − 8u + 1)
· (u
62
+ 32u
61
+ ··· + 25u + 1)
c
2
u
2
(u − 1)
4
(u
31
− 2u
30
+ ··· − 2u + 1)
4
(u
32
+ 3u
31
+ ··· + 4u + 1)
· (u
62
+ 10u
61
+ ··· + 9u + 1)
c
3
, c
10
(u
2
− u + 1)(u
4
− u
3
+ 2u
2
+ u + 1)(u
32
+ 6u
30
+ ··· − u + 1)
· (u
62
+ u
61
+ ··· + 157u
2
+ 9)
· (u
124
+ 2u
123
+ ··· + 445543889u + 54599377)
c
4
, c
11
(u
2
− u + 1)(u
4
− u
3
+ 2u
2
+ u + 1)(u
32
− 2u
31
+ ··· + 2u + 1)
· (u
62
+ u
61
+ ··· − u + 1)(u
124
+ 2u
123
+ ··· − u + 1)
c
5
u
2
(u + 1)
4
(u
31
− 2u
30
+ ··· − 2u + 1)
4
(u
32
− 3u
31
+ ··· − 4u + 1)
· (u
62
+ 10u
61
+ ··· + 9u + 1)
c
6
u
6
(u
31
− 9u
30
+ ··· + 73u − 8)
4
(u
32
− 9u
31
+ ··· − 170u + 25)
· (u
62
+ 30u
61
+ ··· + 37547u + 2393)
c
7
((u
2
− u + 1)
64
)(u
2
+ u + 1)(u
32
+ 3u
31
+ ··· + 11u + 1)
· (u
62
+ 51u
61
+ ··· + 30064771072u + 1073741824)
c
8
u
6
(u
31
− 15u
30
+ ··· + 3u − 2)
4
(u
32
+ 19u
31
+ ··· + 90u + 25)
· (u
62
+ 42u
61
+ ··· − u + 1)
c
9
, c
12
((u
2
− u + 1)
3
)(u
32
− 8u
31
+ ··· − 3u
2
+ 1)(u
62
− 3u
61
+ ··· − 3u + 1)
· (u
124
− 3u
123
+ ··· + 54u + 1)
43
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y − 1)
4
(y
31
+ 28y
29
+ ··· − 14y − 1)
4
(y
32
− y
31
+ ··· + 16y + 1)
· (y
62
+ 56y
60
+ ··· + 127y + 1)
c
2
, c
5
y
2
(y − 1)
4
(y
31
− 16y
30
+ ··· + 2y − 1)
4
(y
32
− 17y
31
+ ··· − 8y + 1)
· (y
62
− 32y
61
+ ··· − 25y + 1)
c
3
, c
10
(y
2
+ y + 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
32
+ 12y
31
+ ··· + 27y + 1)
· (y
62
+ 21y
61
+ ··· + 2826y + 81)
· (y
124
+ 42y
123
+ ··· − 6608919476226557y + 2981091968788129)
c
4
, c
11
(y
2
+ y + 1)(y
4
+ 3y
3
+ ··· + 3y + 1)(y
32
− 16y
31
+ ··· − 22y + 1)
· (y
62
+ 9y
61
+ ··· + 17y + 1)(y
124
− 42y
123
+ ··· + 283y + 1)
c
6
y
6
(y
31
+ 13y
30
+ ··· + 833y − 64)
4
· (y
32
+ 13y
31
+ ··· − 6050y + 625)
· (y
62
+ 26y
61
+ ··· − 77618039y + 5726449)
c
7
((y
2
+ y + 1)
65
)(y
32
+ 19y
31
+ ··· + 13y + 1)
· (y
62
+ 19y
61
+ ··· − 1.15 × 10
18
y + 1.15 × 10
18
)
c
8
y
6
(y
31
− 3y
30
+ ··· + 69y − 4)
4
(y
32
− 5y
31
+ ··· − 11950y + 625)
· (y
62
− 8y
61
+ ··· − 51y + 1)
c
9
, c
12
((y
2
+ y + 1)
3
)(y
32
− 12y
31
+ ··· − 6y + 1)(y
62
+ 21y
61
+ ··· + y + 1)
· (y
124
− 31y
123
+ ··· − 498y + 1)
44
