12a
0734
(K12a
0734
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 1 11 2 7 12 6 4 5
Solving Sequence
2,7
8 3 9 4
1,11
6 5 10 12
c
7
c
2
c
8
c
3
c
1
c
6
c
5
c
10
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.97114 × 10
105
u
133
− 5.11035 × 10
105
u
132
+ ··· + 2.97121 × 10
105
b − 1.45203 × 10
106
,
− 3.46940 × 10
104
u
133
+ 3.75417 × 10
105
u
132
+ ··· + 2.97121 × 10
105
a + 2.11161 × 10
106
,
u
134
+ u
133
+ ··· + 10u − 1i
I
u
2
= hu
22
− 3u
20
+ ··· + b + 1, −2u
22
+ 8u
20
+ ··· + a + 1, u
23
− 4u
21
+ ··· + 5u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 157 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−2.97 × 10
105
u
133
− 5.11 × 10
105
u
132
+ · · · + 2.97 × 10
105
b − 1.45 ×
10
106
, −3.47 × 10
104
u
133
+ 3.75 × 10
105
u
132
+ · · · + 2.97 × 10
105
a + 2.11 ×
10
106
, u
134
+ u
133
+ · · · + 10u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
4
=
u
7
− 2u
5
+ 2u
3
− 2u
−u
7
+ u
5
− 2u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
0.116768u
133
− 1.26352u
132
+ ··· + 60.7927u − 7.10691
0.999978u
133
+ 1.71996u
132
+ ··· − 29.3278u + 4.88700
a
6
=
3.52824u
133
+ 4.00376u
132
+ ··· − 89.9457u + 14.1154
−0.297130u
133
− 0.372411u
132
+ ··· − 19.6107u + 4.78497
a
5
=
3.80149u
133
+ 4.73934u
132
+ ··· − 86.7946u + 13.8273
−0.918708u
133
− 0.673553u
132
+ ··· − 22.2627u + 4.69214
a
10
=
−2.62310u
133
− 2.19393u
132
+ ··· + 63.9528u − 13.2154
−0.420115u
133
− 2.13033u
132
+ ··· + 16.6696u − 3.45228
a
12
=
0.830120u
133
− 0.920307u
132
+ ··· + 57.8837u − 6.78105
0.724769u
133
+ 2.05722u
132
+ ··· − 24.2254u + 4.43038
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10.8383u
133
+ 15.1679u
132
+ ··· − 191.542u + 28.8434
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
134
+ 45u
133
+ ··· + 42u + 1
c
2
, c
7
u
134
+ u
133
+ ··· + 10u − 1
c
3
u
134
− u
133
+ ··· + 2211594u − 322117
c
4
u
134
+ u
133
+ ··· − 4u + 5
c
5
, c
12
u
134
− 44u
132
+ ··· − 4575u + 919
c
6
, c
10
u
134
− 42u
132
+ ··· + 3u − 1
c
9
u
134
− 17u
133
+ ··· − 107441u + 19231
c
11
u
134
− 3u
133
+ ··· − 326u + 31
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
134
+ 91y
133
+ ··· − 342y + 1
c
2
, c
7
y
134
− 45y
133
+ ··· − 42y + 1
c
3
y
134
− 41y
133
+ ··· − 7998700268362y + 103759361689
c
4
y
134
+ 7y
133
+ ··· − 596y + 25
c
5
, c
12
y
134
− 88y
133
+ ··· + 5233305y + 844561
c
6
, c
10
y
134
− 84y
133
+ ··· − 51y + 1
c
9
y
134
− 37y
133
+ ··· − 30165676559y + 369831361
c
11
y
134
− y
133
+ ··· − 42416y + 961
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.684442 + 0.733546I
a = 2.93257 − 0.13650I
b = −1.117790 − 0.303819I
0.13126 + 3.76020I 0
u = 0.684442 − 0.733546I
a = 2.93257 + 0.13650I
b = −1.117790 + 0.303819I
0.13126 − 3.76020I 0
u = −0.993324 + 0.055528I
a = −0.87671 − 1.16073I
b = −1.072980 − 0.443967I
−1.111230 + 0.840477I 0
u = −0.993324 − 0.055528I
a = −0.87671 + 1.16073I
b = −1.072980 + 0.443967I
−1.111230 − 0.840477I 0
u = 0.983126 + 0.123044I
a = 0.04349 + 2.03867I
b = −1.020900 + 0.901256I
−2.25368 − 4.95612I 0
u = 0.983126 − 0.123044I
a = 0.04349 − 2.03867I
b = −1.020900 − 0.901256I
−2.25368 + 4.95612I 0
u = 0.980207 + 0.122170I
a = 0.67712 + 1.35533I
b = −0.144821 + 0.342733I
−3.65962 − 2.88425I 0
u = 0.980207 − 0.122170I
a = 0.67712 − 1.35533I
b = −0.144821 − 0.342733I
−3.65962 + 2.88425I 0
u = 0.699391 + 0.738009I
a = −1.60398 + 0.14202I
b = 1.37660 + 0.48386I
4.30951 + 0.70051I 0
u = 0.699391 − 0.738009I
a = −1.60398 − 0.14202I
b = 1.37660 − 0.48386I
4.30951 − 0.70051I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.646937 + 0.785603I
a = 0.352650 − 0.862831I
b = −0.185620 + 1.306980I
−2.19258 + 6.44742I 0
u = 0.646937 − 0.785603I
a = 0.352650 + 0.862831I
b = −0.185620 − 1.306980I
−2.19258 − 6.44742I 0
u = −0.725623 + 0.715193I
a = −2.72667 + 0.35767I
b = 1.76527 + 0.20617I
4.76768 + 0.25459I 0
u = −0.725623 − 0.715193I
a = −2.72667 − 0.35767I
b = 1.76527 − 0.20617I
4.76768 − 0.25459I 0
u = −1.018770 + 0.034217I
a = −0.53054 + 1.67932I
b = 1.091790 + 0.459188I
−5.23217 + 3.65374I 0
u = −1.018770 − 0.034217I
a = −0.53054 − 1.67932I
b = 1.091790 − 0.459188I
−5.23217 − 3.65374I 0
u = 0.979326
a = −0.706647
b = −1.80602
−0.121193 0
u = −0.745718 + 0.708422I
a = 2.26590 + 1.43565I
b = −0.848685 + 0.042631I
0.97082 + 3.42476I 0
u = −0.745718 − 0.708422I
a = 2.26590 − 1.43565I
b = −0.848685 − 0.042631I
0.97082 − 3.42476I 0
u = −0.704844 + 0.757071I
a = −0.158069 − 0.265759I
b = −0.104520 − 0.614928I
2.02384 − 2.44865I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704844 − 0.757071I
a = −0.158069 + 0.265759I
b = −0.104520 + 0.614928I
2.02384 + 2.44865I 0
u = 0.657855 + 0.808376I
a = 1.56797 − 0.48147I
b = −1.186820 − 0.463114I
5.16293 + 6.70891I 0
u = 0.657855 − 0.808376I
a = 1.56797 + 0.48147I
b = −1.186820 + 0.463114I
5.16293 − 6.70891I 0
u = 0.706317 + 0.642030I
a = 1.54370 + 1.33246I
b = −0.951225 + 0.587828I
−0.74094 − 3.24037I 0
u = 0.706317 − 0.642030I
a = 1.54370 − 1.33246I
b = −0.951225 − 0.587828I
−0.74094 + 3.24037I 0
u = 0.763866 + 0.719672I
a = −0.737072 + 0.150277I
b = 0.396256 − 0.628401I
3.00510 − 1.42234I 0
u = 0.763866 − 0.719672I
a = −0.737072 − 0.150277I
b = 0.396256 + 0.628401I
3.00510 + 1.42234I 0
u = 0.971285 + 0.405356I
a = 0.376939 + 0.546656I
b = −0.649772 − 0.556802I
−4.07179 − 3.37298I 0
u = 0.971285 − 0.405356I
a = 0.376939 − 0.546656I
b = −0.649772 + 0.556802I
−4.07179 + 3.37298I 0
u = 0.943457 + 0.049332I
a = 0.77885 + 1.84113I
b = 0.350763 + 0.127891I
−3.55400 − 2.88849I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.943457 − 0.049332I
a = 0.77885 − 1.84113I
b = 0.350763 − 0.127891I
−3.55400 + 2.88849I 0
u = 0.899780 + 0.555811I
a = −0.071715 + 1.275470I
b = −0.898793 + 0.052125I
1.67472 − 4.16197I 0
u = 0.899780 − 0.555811I
a = −0.071715 − 1.275470I
b = −0.898793 − 0.052125I
1.67472 + 4.16197I 0
u = −0.362484 + 0.867831I
a = −1.004240 + 0.319388I
b = 0.779929 − 0.214276I
−1.70180 − 2.29247I 0
u = −0.362484 − 0.867831I
a = −1.004240 − 0.319388I
b = 0.779929 + 0.214276I
−1.70180 + 2.29247I 0
u = −0.712312 + 0.789223I
a = −1.77504 + 0.40262I
b = 1.20788 − 0.89236I
3.80981 − 4.48373I 0
u = −0.712312 − 0.789223I
a = −1.77504 − 0.40262I
b = 1.20788 + 0.89236I
3.80981 + 4.48373I 0
u = −0.652606 + 0.845014I
a = 1.89303 − 0.10955I
b = −1.35075 + 0.66313I
1.50915 − 13.23120I 0
u = −0.652606 − 0.845014I
a = 1.89303 + 0.10955I
b = −1.35075 − 0.66313I
1.50915 + 13.23120I 0
u = −0.573471 + 0.732554I
a = −0.171084 − 0.109456I
b = −0.410102 + 0.448250I
−2.02732 − 1.13246I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.573471 − 0.732554I
a = −0.171084 + 0.109456I
b = −0.410102 − 0.448250I
−2.02732 + 1.13246I 0
u = −0.900602 + 0.582021I
a = −0.355599 + 0.775540I
b = −0.060900 + 0.569504I
−1.24223 + 2.25110I 0
u = −0.900602 − 0.582021I
a = −0.355599 − 0.775540I
b = −0.060900 − 0.569504I
−1.24223 − 2.25110I 0
u = −1.073760 + 0.080613I
a = 0.397190 − 1.192100I
b = 0.340595 − 1.245100I
−8.23494 + 5.99826I 0
u = −1.073760 − 0.080613I
a = 0.397190 + 1.192100I
b = 0.340595 + 1.245100I
−8.23494 − 5.99826I 0
u = −0.551055 + 0.738693I
a = −0.213930 + 0.122406I
b = −0.404330 − 0.120701I
−2.09099 − 1.28486I 0
u = −0.551055 − 0.738693I
a = −0.213930 − 0.122406I
b = −0.404330 + 0.120701I
−2.09099 + 1.28486I 0
u = −0.824025 + 0.696263I
a = −0.340201 − 0.106572I
b = 0.446065 + 1.023540I
0.73766 + 5.74889I 0
u = −0.824025 − 0.696263I
a = −0.340201 + 0.106572I
b = 0.446065 − 1.023540I
0.73766 − 5.74889I 0
u = −1.074080 + 0.106049I
a = 0.36031 + 1.67688I
b = 1.095130 + 0.436256I
−1.13493 + 6.37304I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.074080 − 0.106049I
a = 0.36031 − 1.67688I
b = 1.095130 − 0.436256I
−1.13493 − 6.37304I 0
u = 0.768552 + 0.778416I
a = −2.02934 + 0.23062I
b = 1.307780 − 0.520205I
4.70969 − 2.13025I 0
u = 0.768552 − 0.778416I
a = −2.02934 − 0.23062I
b = 1.307780 + 0.520205I
4.70969 + 2.13025I 0
u = 0.658952 + 0.880946I
a = −1.84008 − 0.19747I
b = 1.183440 + 0.314188I
1.81144 + 3.77799I 0
u = 0.658952 − 0.880946I
a = −1.84008 + 0.19747I
b = 1.183440 − 0.314188I
1.81144 − 3.77799I 0
u = −0.725737 + 0.835925I
a = −1.48018 − 0.35781I
b = 0.742267 − 0.113059I
2.82780 − 2.03901I 0
u = −0.725737 − 0.835925I
a = −1.48018 + 0.35781I
b = 0.742267 + 0.113059I
2.82780 + 2.03901I 0
u = 1.111060 + 0.006629I
a = 0.577799 − 0.214621I
b = 0.190841 − 0.191786I
−7.58998 + 0.01142I 0
u = 1.111060 − 0.006629I
a = 0.577799 + 0.214621I
b = 0.190841 + 0.191786I
−7.58998 − 0.01142I 0
u = 0.972411 + 0.552013I
a = 0.250380 − 0.201692I
b = 1.002960 + 0.302049I
1.44464 + 0.17219I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972411 − 0.552013I
a = 0.250380 + 0.201692I
b = 1.002960 − 0.302049I
1.44464 − 0.17219I 0
u = 1.113290 + 0.136976I
a = −0.07874 − 1.46746I
b = 1.27329 − 0.69395I
−5.23705 − 12.72340I 0
u = 1.113290 − 0.136976I
a = −0.07874 + 1.46746I
b = 1.27329 + 0.69395I
−5.23705 + 12.72340I 0
u = −0.901543 + 0.671542I
a = −1.079850 − 0.497635I
b = −0.604635 + 1.011430I
0.496744 − 0.478918I 0
u = −0.901543 − 0.671542I
a = −1.079850 + 0.497635I
b = −0.604635 − 1.011430I
0.496744 + 0.478918I 0
u = −1.113520 + 0.183490I
a = 0.502829 − 0.878263I
b = −1.036420 − 0.443824I
−5.39188 + 3.36105I 0
u = −1.113520 − 0.183490I
a = 0.502829 + 0.878263I
b = −1.036420 + 0.443824I
−5.39188 − 3.36105I 0
u = −0.830902 + 0.225120I
a = −0.905119 − 0.340070I
b = −0.955906 + 0.451896I
−1.213400 − 0.444872I 0
u = −0.830902 − 0.225120I
a = −0.905119 + 0.340070I
b = −0.955906 − 0.451896I
−1.213400 + 0.444872I 0
u = −0.845718 + 0.772491I
a = 2.40039 − 0.91885I
b = −1.329910 − 0.217967I
8.31013 + 4.43310I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.845718 − 0.772491I
a = 2.40039 + 0.91885I
b = −1.329910 + 0.217967I
8.31013 − 4.43310I 0
u = 0.997474 + 0.579143I
a = −1.65813 − 0.69858I
b = 0.480525 − 1.066170I
−5.26789 − 0.25431I 0
u = 0.997474 − 0.579143I
a = −1.65813 + 0.69858I
b = 0.480525 + 1.066170I
−5.26789 + 0.25431I 0
u = −1.045270 + 0.493316I
a = 0.191609 + 0.650376I
b = 1.152950 − 0.636975I
−3.06521 − 5.76942I 0
u = −1.045270 − 0.493316I
a = 0.191609 − 0.650376I
b = 1.152950 + 0.636975I
−3.06521 + 5.76942I 0
u = 1.16417
a = 0.0449136
b = −0.427411
−7.51483 0
u = 0.946649 + 0.685219I
a = −0.289792 + 0.644511I
b = −0.528125 − 0.626255I
2.44261 − 3.96455I 0
u = 0.946649 − 0.685219I
a = −0.289792 − 0.644511I
b = −0.528125 + 0.626255I
2.44261 + 3.96455I 0
u = 0.972681 + 0.650597I
a = −0.467017 − 0.152712I
b = 1.025890 + 0.594212I
−1.56056 − 1.84691I 0
u = 0.972681 − 0.650597I
a = −0.467017 + 0.152712I
b = 1.025890 − 0.594212I
−1.56056 + 1.84691I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.895049 + 0.759031I
a = −2.05925 + 0.91387I
b = 1.340920 − 0.172860I
8.15901 + 1.33731I 0
u = −0.895049 − 0.759031I
a = −2.05925 − 0.91387I
b = 1.340920 + 0.172860I
8.15901 − 1.33731I 0
u = −0.957084 + 0.680461I
a = −1.62682 + 2.51238I
b = 0.800593 + 0.132838I
0.32272 + 1.91916I 0
u = −0.957084 − 0.680461I
a = −1.62682 − 2.51238I
b = 0.800593 − 0.132838I
0.32272 − 1.91916I 0
u = −0.970553 + 0.682636I
a = 1.68283 − 2.13343I
b = −1.82651 + 0.17662I
4.02087 + 5.11946I 0
u = −0.970553 − 0.682636I
a = 1.68283 + 2.13343I
b = −1.82651 − 0.17662I
4.02087 − 5.11946I 0
u = 0.956768 + 0.730351I
a = 0.97582 + 1.79918I
b = −1.322770 − 0.451203I
4.13347 − 3.57074I 0
u = 0.956768 − 0.730351I
a = 0.97582 − 1.79918I
b = −1.322770 + 0.451203I
4.13347 + 3.57074I 0
u = 0.986046 + 0.690716I
a = 1.64970 + 1.99316I
b = −1.32902 + 0.55856I
3.44626 − 6.16415I 0
u = 0.986046 − 0.690716I
a = 1.64970 − 1.99316I
b = −1.32902 − 0.55856I
3.44626 + 6.16415I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.993031 + 0.684647I
a = −2.62363 − 1.84119I
b = 1.162630 − 0.338533I
−0.79602 − 9.19285I 0
u = 0.993031 − 0.684647I
a = −2.62363 + 1.84119I
b = 1.162630 + 0.338533I
−0.79602 + 9.19285I 0
u = 0.887286 + 0.818837I
a = 2.11398 + 0.37298I
b = −1.231790 + 0.362617I
5.72201 − 9.47851I 0
u = 0.887286 − 0.818837I
a = 2.11398 − 0.37298I
b = −1.231790 − 0.362617I
5.72201 + 9.47851I 0
u = 0.883503 + 0.825249I
a = −1.64011 − 1.09626I
b = 1.192810 + 0.316023I
5.73822 + 3.36674I 0
u = 0.883503 − 0.825249I
a = −1.64011 + 1.09626I
b = 1.192810 − 0.316023I
5.73822 − 3.36674I 0
u = −0.986523 + 0.699527I
a = 0.874910 − 0.352664I
b = 0.191200 − 0.609874I
1.17309 + 7.98971I 0
u = −0.986523 − 0.699527I
a = 0.874910 + 0.352664I
b = 0.191200 + 0.609874I
1.17309 − 7.98971I 0
u = −1.029730 + 0.661865I
a = −0.344960 + 0.498301I
b = 0.313366 + 0.544307I
−3.34183 + 6.47157I 0
u = −1.029730 − 0.661865I
a = −0.344960 − 0.498301I
b = 0.313366 − 0.544307I
−3.34183 − 6.47157I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.993726 + 0.717846I
a = 2.42241 − 1.46955I
b = −1.19776 − 0.94141I
2.95398 + 10.17470I 0
u = −0.993726 − 0.717846I
a = 2.42241 + 1.46955I
b = −1.19776 + 0.94141I
2.95398 − 10.17470I 0
u = −1.038350 + 0.651686I
a = 0.492741 + 0.507756I
b = 0.369761 − 0.074424I
−3.50265 + 6.59407I 0
u = −1.038350 − 0.651686I
a = 0.492741 − 0.507756I
b = 0.369761 + 0.074424I
−3.50265 − 6.59407I 0
u = −0.246431 + 0.732903I
a = 1.79748 − 0.04135I
b = −1.242930 − 0.611221I
−0.69453 + 10.16310I 0. − 7.37612I
u = −0.246431 − 0.732903I
a = 1.79748 + 0.04135I
b = −1.242930 + 0.611221I
−0.69453 − 10.16310I 0. + 7.37612I
u = −1.085870 + 0.570975I
a = 0.701874 − 0.646899I
b = −0.751925 − 0.406373I
−3.96455 + 7.44216I 0
u = −1.085870 − 0.570975I
a = 0.701874 + 0.646899I
b = −0.751925 + 0.406373I
−3.96455 − 7.44216I 0
u = 1.021430 + 0.696683I
a = 1.38338 − 0.54250I
b = 0.222377 + 1.356410I
−3.31482 − 12.05230I 0
u = 1.021430 − 0.696683I
a = 1.38338 + 0.54250I
b = 0.222377 − 1.356410I
−3.31482 + 12.05230I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.087738 + 0.756044I
a = −1.72621 + 0.35110I
b = 0.880270 − 0.294838I
−1.249260 − 0.296309I −7.28753 + 0.I
u = 0.087738 − 0.756044I
a = −1.72621 − 0.35110I
b = 0.880270 + 0.294838I
−1.249260 + 0.296309I −7.28753 + 0.I
u = −0.759386
a = −0.600655
b = −0.487135
−1.25667 −7.25320
u = 1.024920 + 0.708478I
a = −1.58312 − 2.05437I
b = 1.173760 − 0.493077I
4.05312 − 12.41580I 0
u = 1.024920 − 0.708478I
a = −1.58312 + 2.05437I
b = 1.173760 + 0.493077I
4.05312 + 12.41580I 0
u = −1.003160 + 0.741475I
a = 1.39301 − 1.26119I
b = −0.697623 − 0.201205I
1.96950 + 7.93716I 0
u = −1.003160 − 0.741475I
a = 1.39301 + 1.26119I
b = −0.697623 + 0.201205I
1.96950 − 7.93716I 0
u = −1.040440 + 0.721467I
a = −2.09702 + 1.74380I
b = 1.36061 + 0.68998I
0.3269 + 19.0807I 0
u = −1.040440 − 0.721467I
a = −2.09702 − 1.74380I
b = 1.36061 − 0.68998I
0.3269 − 19.0807I 0
u = 1.049730 + 0.734629I
a = 1.78403 + 1.33198I
b = −1.219340 + 0.362480I
0.60294 − 9.76672I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.049730 − 0.734629I
a = 1.78403 − 1.33198I
b = −1.219340 − 0.362480I
0.60294 + 9.76672I 0
u = 0.367673 + 0.596899I
a = 0.507487 + 0.683187I
b = −0.281515 − 1.040940I
−3.72418 − 4.25497I −6.08937 + 5.23557I
u = 0.367673 − 0.596899I
a = 0.507487 − 0.683187I
b = −0.281515 + 1.040940I
−3.72418 + 4.25497I −6.08937 − 5.23557I
u = 0.269050 + 0.617565I
a = 1.48508 + 0.88631I
b = −1.139340 + 0.333732I
3.17608 − 4.32551I 1.35411 + 6.19967I
u = 0.269050 − 0.617565I
a = 1.48508 − 0.88631I
b = −1.139340 − 0.333732I
3.17608 + 4.32551I 1.35411 − 6.19967I
u = 0.387092 + 0.432373I
a = −0.995704 − 0.403192I
b = 1.184950 − 0.049242I
2.70285 + 0.26610I 2.78339 + 0.22411I
u = 0.387092 − 0.432373I
a = −0.995704 + 0.403192I
b = 1.184950 + 0.049242I
2.70285 − 0.26610I 2.78339 − 0.22411I
u = −0.084896 + 0.525243I
a = −1.84860 − 0.20121I
b = 1.096610 + 0.698947I
1.03926 + 2.94824I 1.60490 − 6.40134I
u = −0.084896 − 0.525243I
a = −1.84860 + 0.20121I
b = 1.096610 − 0.698947I
1.03926 − 2.94824I 1.60490 + 6.40134I
u = −0.180376 + 0.434875I
a = −0.664695 + 0.300319I
b = 0.084546 + 0.491566I
−0.217472 + 1.237780I −2.82425 − 4.88586I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.180376 − 0.434875I
a = −0.664695 − 0.300319I
b = 0.084546 − 0.491566I
−0.217472 − 1.237780I −2.82425 + 4.88586I
u = 0.207137 + 0.168766I
a = 6.13205 + 2.14952I
b = −0.845796 + 0.370223I
−1.45340 − 3.00117I −6.83039 + 9.00039I
u = 0.207137 − 0.168766I
a = 6.13205 − 2.14952I
b = −0.845796 − 0.370223I
−1.45340 + 3.00117I −6.83039 − 9.00039I
u = 0.192711
a = 1.44974
b = 1.44990
2.70140 9.56400
18
II.
I
u
2
= hu
22
−3u
20
+· · ·+b+1, −2u
22
+8u
20
+· · ·+a+1, u
23
−4u
21
+· · ·+5u
2
−1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
4
=
u
7
− 2u
5
+ 2u
3
− 2u
−u
7
+ u
5
− 2u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
2u
22
− 8u
20
+ ··· + 4u − 1
−u
22
+ 3u
20
+ ··· − 2u − 1
a
6
=
−u
22
− 2u
21
+ ··· + 16u
3
− 5u
−u
20
+ 4u
18
+ ··· + 3u + 1
a
5
=
−u
22
− u
21
+ ··· − 5u + 1
−u
20
+ 4u
18
+ ··· + 4u + 1
a
10
=
2u
22
− 7u
20
+ ··· − 6u
3
+ 3u
2
u
22
+ u
21
+ ··· + 4u + 2
a
12
=
2u
22
− 8u
20
+ ··· + 4u − 3
−u
22
+ 3u
20
+ ··· − 5u
2
− 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −3u
22
+ 2u
21
+ 13u
20
− 9u
19
− 39u
18
+ 21u
17
+ 80u
16
− 36u
15
− 127u
14
+ 33u
13
+
164u
12
−14u
11
−163u
10
−26u
9
+139u
8
+60u
7
−79u
6
−61u
5
+31u
4
+49u
3
+u
2
−16u−13
19
(iv) u-Polynomials at the component
20
Crossings u-Polynomials at each crossing
c
1
u
23
− 8u
22
+ ··· + 10u − 1
c
2
u
23
− 4u
21
+ ··· − 5u
2
+ 1
c
3
u
23
− 4u
21
+ ··· − 2u + 1
c
4
u
23
+ 2u
20
+ ··· − 2u
2
− 1
c
5
u
23
− u
22
+ ··· − u + 1
c
6
u
23
− u
22
+ ··· − u + 1
c
7
u
23
− 4u
21
+ ··· + 5u
2
− 1
c
8
u
23
+ 8u
22
+ ··· + 10u + 1
c
9
u
23
− 6u
21
+ ··· + 11u − 1
c
10
u
23
+ u
22
+ ··· − u − 1
c
11
u
23
+ 2u
21
+ ··· − 2u
3
− 1
c
12
u
23
+ u
22
+ ··· − u − 1
21
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
23
+ 16y
22
+ ··· + 6y −1
c
2
, c
7
y
23
− 8y
22
+ ··· + 10y −1
c
3
y
23
− 8y
22
+ ··· + 14y −1
c
4
y
23
− 2y
21
+ ··· − 4y −1
c
5
, c
12
y
23
− 19y
22
+ ··· + 23y −1
c
6
, c
10
y
23
− 23y
22
+ ··· + 19y −1
c
9
y
23
− 12y
22
+ ··· + 11y −1
c
11
y
23
+ 4y
22
+ ··· + 2y
2
− 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789676 + 0.635091I
a = −0.01623 + 1.61769I
b = −0.624578 + 0.481706I
−0.09644 − 4.34636I −6.43553 + 7.86992I
u = 0.789676 − 0.635091I
a = −0.01623 − 1.61769I
b = −0.624578 − 0.481706I
−0.09644 + 4.34636I −6.43553 − 7.86992I
u = −0.963368 + 0.127646I
a = −0.89384 + 1.89023I
b = 0.826105 + 0.507900I
−3.41508 + 4.12503I −9.63250 − 7.62808I
u = −0.963368 − 0.127646I
a = −0.89384 − 1.89023I
b = 0.826105 − 0.507900I
−3.41508 − 4.12503I −9.63250 + 7.62808I
u = −0.781718 + 0.735321I
a = 2.26319 − 0.09688I
b = −1.60010 − 0.15916I
5.45220 + 1.13330I 3.45932 − 2.91783I
u = −0.781718 − 0.735321I
a = 2.26319 + 0.09688I
b = −1.60010 + 0.15916I
5.45220 − 1.13330I 3.45932 + 2.91783I
u = 0.718410 + 0.821305I
a = 1.93152 + 0.20986I
b = −1.046350 − 0.451258I
2.91868 + 3.41376I −1.19815 − 3.77673I
u = 0.718410 − 0.821305I
a = 1.93152 − 0.20986I
b = −1.046350 + 0.451258I
2.91868 − 3.41376I −1.19815 + 3.77673I
u = 0.905730
a = 1.44985
b = 1.64031
0.733078 0.0906350
u = 0.924227 + 0.639459I
a = 0.355446 + 0.708297I
b = 0.654499 + 0.532828I
−0.525275 − 0.642283I −6.84803 − 1.22318I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.924227 − 0.639459I
a = 0.355446 − 0.708297I
b = 0.654499 − 0.532828I
−0.525275 + 0.642283I −6.84803 + 1.22318I
u = 1.14910
a = 0.515546
b = 0.647002
−7.06832 0.599370
u = −0.387412 + 0.742711I
a = 0.738338 − 0.661111I
b = −0.734604 + 0.163087I
−1.46442 − 1.89698I −0.596084 − 0.928142I
u = −0.387412 − 0.742711I
a = 0.738338 + 0.661111I
b = −0.734604 − 0.163087I
−1.46442 + 1.89698I −0.596084 + 0.928142I
u = −0.943028 + 0.704990I
a = −1.47417 + 2.15490I
b = 1.64624 − 0.14078I
4.95360 + 4.36576I 3.36870 − 3.50878I
u = −0.943028 − 0.704990I
a = −1.47417 − 2.15490I
b = 1.64624 + 0.14078I
4.95360 − 4.36576I 3.36870 + 3.50878I
u = −1.045620 + 0.628888I
a = −0.011755 + 0.403755I
b = 0.613329 + 0.151958I
−3.15294 + 6.97577I −0.33481 − 9.58642I
u = −1.045620 − 0.628888I
a = −0.011755 − 0.403755I
b = 0.613329 − 0.151958I
−3.15294 − 6.97577I −0.33481 + 9.58642I
u = 1.000320 + 0.731290I
a = −2.14868 − 1.33130I
b = 1.033420 − 0.518597I
2.05059 − 9.23426I −3.39793 + 8.73183I
u = 1.000320 − 0.731290I
a = −2.14868 + 1.33130I
b = 1.033420 + 0.518597I
2.05059 + 9.23426I −3.39793 − 8.73183I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.585531 + 0.422605I
a = −0.43217 − 1.92851I
b = −0.680777 + 0.308139I
−1.44350 − 2.11057I −5.68122 + 1.44020I
u = −0.585531 − 0.422605I
a = −0.43217 + 1.92851I
b = −0.680777 − 0.308139I
−1.44350 + 2.11057I −5.68122 − 1.44020I
u = 0.493256
a = 1.41129
b = −1.46168
2.36013 −15.0980
26
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 8u
22
+ ··· + 10u − 1)(u
134
+ 45u
133
+ ··· + 42u + 1)
c
2
(u
23
− 4u
21
+ ··· − 5u
2
+ 1)(u
134
+ u
133
+ ··· + 10u − 1)
c
3
(u
23
− 4u
21
+ ··· − 2u + 1)(u
134
− u
133
+ ··· + 2211594u − 322117)
c
4
(u
23
+ 2u
20
+ ··· − 2u
2
− 1)(u
134
+ u
133
+ ··· − 4u + 5)
c
5
(u
23
− u
22
+ ··· − u + 1)(u
134
− 44u
132
+ ··· − 4575u + 919)
c
6
(u
23
− u
22
+ ··· − u + 1)(u
134
− 42u
132
+ ··· + 3u − 1)
c
7
(u
23
− 4u
21
+ ··· + 5u
2
− 1)(u
134
+ u
133
+ ··· + 10u − 1)
c
8
(u
23
+ 8u
22
+ ··· + 10u + 1)(u
134
+ 45u
133
+ ··· + 42u + 1)
c
9
(u
23
− 6u
21
+ ··· + 11u − 1)(u
134
− 17u
133
+ ··· − 107441u + 19231)
c
10
(u
23
+ u
22
+ ··· − u − 1)(u
134
− 42u
132
+ ··· + 3u − 1)
c
11
(u
23
+ 2u
21
+ ··· − 2u
3
− 1)(u
134
− 3u
133
+ ··· − 326u + 31)
c
12
(u
23
+ u
22
+ ··· − u − 1)(u
134
− 44u
132
+ ··· − 4575u + 919)
27
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
23
+ 16y
22
+ ··· + 6y −1)(y
134
+ 91y
133
+ ··· − 342y + 1)
c
2
, c
7
(y
23
− 8y
22
+ ··· + 10y −1)(y
134
− 45y
133
+ ··· − 42y + 1)
c
3
(y
23
− 8y
22
+ ··· + 14y −1)
· (y
134
− 41y
133
+ ··· − 7998700268362y + 103759361689)
c
4
(y
23
− 2y
21
+ ··· − 4y −1)(y
134
+ 7y
133
+ ··· − 596y + 25)
c
5
, c
12
(y
23
− 19y
22
+ ··· + 23y −1)
· (y
134
− 88y
133
+ ··· + 5233305y + 844561)
c
6
, c
10
(y
23
− 23y
22
+ ··· + 19y −1)(y
134
− 84y
133
+ ··· − 51y + 1)
c
9
(y
23
− 12y
22
+ ··· + 11y −1)
· (y
134
− 37y
133
+ ··· − 30165676559y + 369831361)
c
11
(y
23
+ 4y
22
+ ··· + 2y
2
− 1)(y
134
− y
133
+ ··· − 42416y + 961)
28
