12a
0919
(K12a
0919
)
A knot diagram
1
Linearized knot diagam
4 6 9 10 3 12 11 2 1 8 7 5
Solving Sequence
6,12 3,7
2 5 1 11 8 9 10 4
c
6
c
2
c
5
c
12
c
11
c
7
c
8
c
10
c
4
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.07123 × 10
220
u
119
− 3.52410 × 10
220
u
118
+ ··· + 4.05368 × 10
221
b + 2.42001 × 10
222
,
2.71699 × 10
222
u
119
+ 7.36929 × 10
222
u
118
+ ··· + 8.51272 × 10
222
a − 2.15694 × 10
224
,
u
120
+ 3u
119
+ ··· − 113u + 21i
I
u
2
= h−u
23
− 5u
22
+ ··· + b − 2, u
25
+ 4u
24
+ ··· + a + 1, u
26
+ 4u
25
+ ··· + 4u + 1i
* 2 irreducible components of dim
C
= 0, with total 146 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−1.07 × 10
220
u
119
− 3.52 × 10
220
u
118
+ · · · + 4.05 × 10
221
b + 2.42 ×
10
222
, 2.72 × 10
222
u
119
+ 7.37 × 10
222
u
118
+ · · · + 8.51 × 10
222
a − 2.16 ×
10
224
, u
120
+ 3u
119
+ · · · − 113u + 21i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
−0.319169u
119
− 0.865680u
118
+ ··· − 155.503u + 25.3378
0.0264262u
119
+ 0.0869360u
118
+ ··· + 27.3115u − 5.96992
a
7
=
1
−u
2
a
2
=
−0.292742u
119
− 0.778744u
118
+ ··· − 128.191u + 19.3679
0.0264262u
119
+ 0.0869360u
118
+ ··· + 27.3115u − 5.96992
a
5
=
0.320534u
119
+ 1.07174u
118
+ ··· + 84.2977u − 8.85376
−0.142529u
119
− 0.544385u
118
+ ··· − 1.27315u + 0.0747437
a
1
=
0.129398u
119
+ 0.456206u
118
+ ··· + 5.28891u + 12.2308
0.109214u
119
+ 0.363655u
118
+ ··· + 20.1200u − 4.71432
a
11
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−0.420935u
119
− 1.00889u
118
+ ··· − 259.731u + 36.0750
0.0214302u
119
− 0.0238555u
118
+ ··· + 32.0363u − 4.61416
a
10
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
4
=
0.372713u
119
+ 1.18328u
118
+ ··· + 111.600u − 12.7517
−0.130679u
119
− 0.522369u
118
+ ··· − 4.64557u + 0.380200
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.52939u
119
− 5.38696u
118
+ ··· − 149.423u + 4.34876
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
120
− 7u
119
+ ··· − 7u + 3
c
2
, c
5
u
120
+ 7u
119
+ ··· − 6493u + 976
c
3
u
120
+ u
119
+ ··· + 24u + 8
c
4
u
120
− u
119
+ ··· + 45u + 1
c
6
, c
7
, c
10
c
11
u
120
− 3u
119
+ ··· + 113u + 21
c
8
u
120
− u
119
+ ··· + 4850u + 311
c
9
u
120
− 5u
119
+ ··· + 3u + 8
c
12
u
120
− u
119
+ ··· + 18390924u + 2188589
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
120
− y
119
+ ··· + 197y + 9
c
2
, c
5
y
120
+ 59y
119
+ ··· + 31208823y + 952576
c
3
y
120
+ 3y
119
+ ··· − 608y + 64
c
4
y
120
+ 13y
119
+ ··· − 627y + 1
c
6
, c
7
, c
10
c
11
y
120
+ 143y
119
+ ··· + 20117y + 441
c
8
y
120
− 3y
119
+ ··· + 32084922y + 96721
c
9
y
120
+ 3y
119
+ ··· + 1655y + 64
c
12
y
120
+ 17y
119
+ ··· + 186020618302756y + 4789921810921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.625548 + 0.784825I
a = 0.85024 + 1.72968I
b = 0.652725 − 1.237620I
0.4170 + 15.1844I 0
u = 0.625548 − 0.784825I
a = 0.85024 − 1.72968I
b = 0.652725 + 1.237620I
0.4170 − 15.1844I 0
u = −0.664268 + 0.771195I
a = −0.50275 + 1.58998I
b = −0.418010 − 1.154920I
1.59391 − 5.90280I 0
u = −0.664268 − 0.771195I
a = −0.50275 − 1.58998I
b = −0.418010 + 1.154920I
1.59391 + 5.90280I 0
u = −0.228753 + 1.013440I
a = 0.151377 − 0.335120I
b = 0.262213 − 0.633885I
−2.62048 − 2.67963I 0
u = −0.228753 − 1.013440I
a = 0.151377 + 0.335120I
b = 0.262213 + 0.633885I
−2.62048 + 2.67963I 0
u = −0.431239 + 0.853725I
a = −0.696038 + 1.146360I
b = −0.616958 − 1.221130I
−0.42618 − 6.32755I 0
u = −0.431239 − 0.853725I
a = −0.696038 − 1.146360I
b = −0.616958 + 1.221130I
−0.42618 + 6.32755I 0
u = −0.652326 + 0.821283I
a = 0.93055 − 1.45122I
b = 0.494571 + 1.042560I
1.26439 − 6.29930I 0
u = −0.652326 − 0.821283I
a = 0.93055 + 1.45122I
b = 0.494571 − 1.042560I
1.26439 + 6.29930I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.401279 + 0.815199I
a = 0.55078 + 1.66023I
b = 0.491027 − 0.653456I
−2.93538 − 2.24091I 0
u = 0.401279 − 0.815199I
a = 0.55078 − 1.66023I
b = 0.491027 + 0.653456I
−2.93538 + 2.24091I 0
u = −0.866118 + 0.211506I
a = 0.59392 − 1.51844I
b = −0.244074 + 0.985090I
3.30511 + 0.85887I 0
u = −0.866118 − 0.211506I
a = 0.59392 + 1.51844I
b = −0.244074 − 0.985090I
3.30511 − 0.85887I 0
u = 0.457164 + 0.761542I
a = −0.326621 + 0.243830I
b = 1.090030 + 0.316443I
−2.47067 + 9.00999I 0
u = 0.457164 − 0.761542I
a = −0.326621 − 0.243830I
b = 1.090030 − 0.316443I
−2.47067 − 9.00999I 0
u = −0.844345 + 0.159455I
a = −0.10365 + 1.62246I
b = 0.356203 − 0.943024I
3.28222 + 1.32962I 0
u = −0.844345 − 0.159455I
a = −0.10365 − 1.62246I
b = 0.356203 + 0.943024I
3.28222 − 1.32962I 0
u = −0.368404 + 0.775760I
a = 0.317373 + 0.103287I
b = 0.492165 − 0.323146I
−0.64502 − 2.23837I 0
u = −0.368404 − 0.775760I
a = 0.317373 − 0.103287I
b = 0.492165 + 0.323146I
−0.64502 + 2.23837I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.220280 + 0.812481I
a = 0.013441 − 0.326864I
b = −0.568421 − 0.326412I
−2.07608 − 2.53437I 0
u = −0.220280 − 0.812481I
a = 0.013441 + 0.326864I
b = −0.568421 + 0.326412I
−2.07608 + 2.53437I 0
u = 0.473153 + 0.689077I
a = −1.12745 − 1.96340I
b = −0.65606 + 1.28422I
−0.36949 + 6.90839I 0
u = 0.473153 − 0.689077I
a = −1.12745 + 1.96340I
b = −0.65606 − 1.28422I
−0.36949 − 6.90839I 0
u = −0.525177 + 0.645334I
a = 1.53665 − 0.82627I
b = −0.131909 + 0.837987I
1.16644 − 1.03471I 0
u = −0.525177 − 0.645334I
a = 1.53665 + 0.82627I
b = −0.131909 − 0.837987I
1.16644 + 1.03471I 0
u = −0.291740 + 0.776099I
a = 1.71919 − 2.20972I
b = 0.354690 + 0.973182I
−1.59714 − 5.68334I 0
u = −0.291740 − 0.776099I
a = 1.71919 + 2.20972I
b = 0.354690 − 0.973182I
−1.59714 + 5.68334I 0
u = 0.804988 + 0.181309I
a = −0.64328 − 1.70639I
b = 0.551787 + 1.154660I
2.24078 − 10.44410I 0
u = 0.804988 − 0.181309I
a = −0.64328 + 1.70639I
b = 0.551787 − 1.154660I
2.24078 + 10.44410I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.435464 + 1.163840I
a = −0.477768 − 0.452708I
b = 0.457612 + 0.986002I
−1.90871 − 6.12448I 0
u = 0.435464 − 1.163840I
a = −0.477768 + 0.452708I
b = 0.457612 − 0.986002I
−1.90871 + 6.12448I 0
u = 0.312213 + 0.670675I
a = −2.45180 − 0.62358I
b = −0.276880 + 1.179290I
2.99061 + 5.74701I 0
u = 0.312213 − 0.670675I
a = −2.45180 + 0.62358I
b = −0.276880 − 1.179290I
2.99061 − 5.74701I 0
u = −0.611234 + 0.404963I
a = −0.280714 + 1.021810I
b = 0.409342 − 0.968824I
2.06942 − 0.09531I 0
u = −0.611234 − 0.404963I
a = −0.280714 − 1.021810I
b = 0.409342 + 0.968824I
2.06942 + 0.09531I 0
u = 0.265178 + 0.675762I
a = 0.907659 + 0.058818I
b = −0.635826 − 0.742426I
−1.70927 − 1.35572I 0
u = 0.265178 − 0.675762I
a = 0.907659 − 0.058818I
b = −0.635826 + 0.742426I
−1.70927 + 1.35572I 0
u = 0.477406 + 0.539745I
a = −0.40824 − 2.03755I
b = −0.695213 + 0.661441I
−1.98346 + 3.79368I 0
u = 0.477406 − 0.539745I
a = −0.40824 + 2.03755I
b = −0.695213 − 0.661441I
−1.98346 − 3.79368I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.317025 + 1.246230I
a = −0.026753 + 0.968420I
b = 0.177012 − 0.806896I
−0.96778 − 2.86869I 0
u = −0.317025 − 1.246230I
a = −0.026753 − 0.968420I
b = 0.177012 + 0.806896I
−0.96778 + 2.86869I 0
u = −0.562362 + 0.425162I
a = 1.14356 − 1.65586I
b = 0.569282 + 0.913694I
2.01019 − 3.90867I 0
u = −0.562362 − 0.425162I
a = 1.14356 + 1.65586I
b = 0.569282 − 0.913694I
2.01019 + 3.90867I 0
u = 0.225130 + 0.643055I
a = 0.068835 − 0.831530I
b = −1.200640 − 0.266059I
−3.67039 + 0.48350I −14.9920 + 0.I
u = 0.225130 − 0.643055I
a = 0.068835 + 0.831530I
b = −1.200640 + 0.266059I
−3.67039 − 0.48350I −14.9920 + 0.I
u = −0.093216 + 0.673095I
a = −0.270909 − 0.289084I
b = −1.231520 + 0.269233I
−3.57756 − 0.12160I −10.28202 + 0.I
u = −0.093216 − 0.673095I
a = −0.270909 + 0.289084I
b = −1.231520 − 0.269233I
−3.57756 + 0.12160I −10.28202 + 0.I
u = −0.446966 + 1.257260I
a = 0.495105 − 0.621086I
b = −0.021715 + 0.799405I
−1.20679 − 3.78688I 0
u = −0.446966 − 1.257260I
a = 0.495105 + 0.621086I
b = −0.021715 − 0.799405I
−1.20679 + 3.78688I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629530 + 0.150393I
a = 0.62880 + 1.85854I
b = −0.317621 − 1.094780I
2.56408 − 2.85612I 9.46770 + 7.32949I
u = −0.629530 − 0.150393I
a = 0.62880 − 1.85854I
b = −0.317621 + 1.094780I
2.56408 + 2.85612I 9.46770 − 7.32949I
u = 0.382668 + 0.514882I
a = 1.84856 + 1.00624I
b = 0.293177 − 1.243380I
3.98923 − 1.87579I 5.54063 − 1.04613I
u = 0.382668 − 0.514882I
a = 1.84856 − 1.00624I
b = 0.293177 + 1.243380I
3.98923 + 1.87579I 5.54063 + 1.04613I
u = 0.578497 + 0.051054I
a = −0.65461 + 1.47641I
b = 0.759679 − 0.238852I
−0.40672 − 5.50449I 1.76198 + 4.14204I
u = 0.578497 − 0.051054I
a = −0.65461 − 1.47641I
b = 0.759679 + 0.238852I
−0.40672 + 5.50449I 1.76198 − 4.14204I
u = 0.532532 + 0.187598I
a = 1.18895 + 2.11769I
b = −0.497715 − 1.161640I
1.08707 − 3.42611I 1.72053 + 6.26758I
u = 0.532532 − 0.187598I
a = 1.18895 − 2.11769I
b = −0.497715 + 1.161640I
1.08707 + 3.42611I 1.72053 − 6.26758I
u = −0.04540 + 1.44920I
a = 0.367775 + 0.643599I
b = 0.026768 − 1.176870I
−3.45810 − 2.30008I 0
u = −0.04540 − 1.44920I
a = 0.367775 − 0.643599I
b = 0.026768 + 1.176870I
−3.45810 + 2.30008I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.309791 + 0.416406I
a = −0.69493 − 1.64086I
b = 0.07779 + 1.49925I
4.33831 + 4.48628I 5.04775 − 11.15203I
u = 0.309791 − 0.416406I
a = −0.69493 + 1.64086I
b = 0.07779 − 1.49925I
4.33831 − 4.48628I 5.04775 + 11.15203I
u = −0.08145 + 1.50429I
a = 1.222310 − 0.288322I
b = 0.833892 + 0.788272I
−4.18143 − 5.88825I 0
u = −0.08145 − 1.50429I
a = 1.222310 + 0.288322I
b = 0.833892 − 0.788272I
−4.18143 + 5.88825I 0
u = −0.460138 + 0.159934I
a = 0.446442 − 0.151823I
b = 0.220319 − 0.177672I
1.128220 − 0.578541I 6.90581 + 1.85948I
u = −0.460138 − 0.159934I
a = 0.446442 + 0.151823I
b = 0.220319 + 0.177672I
1.128220 + 0.578541I 6.90581 − 1.85948I
u = 0.01350 + 1.51921I
a = 0.224356 + 1.386720I
b = −0.16079 − 1.44445I
−2.02769 − 2.99413I 0
u = 0.01350 − 1.51921I
a = 0.224356 − 1.386720I
b = −0.16079 + 1.44445I
−2.02769 + 2.99413I 0
u = −0.006027 + 0.464389I
a = −2.34329 − 1.60530I
b = −0.559969 + 0.976244I
−0.49653 + 2.02090I −3.31654 − 3.14040I
u = −0.006027 − 0.464389I
a = −2.34329 + 1.60530I
b = −0.559969 − 0.976244I
−0.49653 − 2.02090I −3.31654 + 3.14040I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07646 + 1.53961I
a = 0.986531 + 0.194432I
b = 0.577422 − 1.081640I
−2.90076 − 0.32481I 0
u = 0.07646 − 1.53961I
a = 0.986531 − 0.194432I
b = 0.577422 + 1.081640I
−2.90076 + 0.32481I 0
u = −0.00038 + 1.54891I
a = −1.94500 + 0.43752I
b = −0.280651 − 0.692596I
−6.48074 + 4.22012I 0
u = −0.00038 − 1.54891I
a = −1.94500 − 0.43752I
b = −0.280651 + 0.692596I
−6.48074 − 4.22012I 0
u = 0.05314 + 1.55048I
a = −0.184731 − 0.761283I
b = 0.02432 + 1.74883I
−2.45328 + 5.55828I 0
u = 0.05314 − 1.55048I
a = −0.184731 + 0.761283I
b = 0.02432 − 1.74883I
−2.45328 − 5.55828I 0
u = 0.15491 + 1.55643I
a = −0.82924 − 1.18408I
b = −0.752148 + 0.870766I
−9.03254 + 6.14039I 0
u = 0.15491 − 1.55643I
a = −0.82924 + 1.18408I
b = −0.752148 − 0.870766I
−9.03254 − 6.14039I 0
u = −0.00212 + 1.57413I
a = −0.946756 − 0.825288I
b = −0.664242 + 1.178100I
−7.67853 + 1.98811I 0
u = −0.00212 − 1.57413I
a = −0.946756 + 0.825288I
b = −0.664242 − 1.178100I
−7.67853 − 1.98811I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.13611 + 1.57594I
a = 1.128580 − 0.382016I
b = 0.107935 + 0.661267I
−6.26155 − 3.40298I 0
u = −0.13611 − 1.57594I
a = 1.128580 + 0.382016I
b = 0.107935 − 0.661267I
−6.26155 + 3.40298I 0
u = 0.07007 + 1.59231I
a = −0.403565 − 0.426318I
b = −1.39653 − 0.42118I
−11.35050 + 1.61971I 0
u = 0.07007 − 1.59231I
a = −0.403565 + 0.426318I
b = −1.39653 + 0.42118I
−11.35050 − 1.61971I 0
u = 0.09082 + 1.60361I
a = 0.0310267 − 0.1013430I
b = −0.913355 − 0.697544I
−9.53778 + 0.07962I 0
u = 0.09082 − 1.60361I
a = 0.0310267 + 0.1013430I
b = −0.913355 + 0.697544I
−9.53778 − 0.07962I 0
u = 0.13636 + 1.60275I
a = −1.09748 − 0.97396I
b = −0.76988 + 1.36218I
−8.15606 + 9.17141I 0
u = 0.13636 − 1.60275I
a = −1.09748 + 0.97396I
b = −0.76988 − 1.36218I
−8.15606 − 9.17141I 0
u = 0.08683 + 1.61189I
a = −1.45265 − 0.10339I
b = −0.411620 + 1.085140I
−4.89872 + 7.21900I 0
u = 0.08683 − 1.61189I
a = −1.45265 + 0.10339I
b = −0.411620 − 1.085140I
−4.89872 − 7.21900I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04284 + 1.61451I
a = −0.390124 − 0.085366I
b = −1.44437 + 0.50696I
−11.56430 − 0.73640I 0
u = −0.04284 − 1.61451I
a = −0.390124 + 0.085366I
b = −1.44437 − 0.50696I
−11.56430 + 0.73640I 0
u = 0.242549 + 0.287615I
a = 0.26718 + 3.42266I
b = −0.187422 − 1.358580I
4.20331 − 3.56534I 11.53644 − 5.14411I
u = 0.242549 − 0.287615I
a = 0.26718 − 3.42266I
b = −0.187422 + 1.358580I
4.20331 + 3.56534I 11.53644 + 5.14411I
u = 0.302146 + 0.218430I
a = 1.70032 + 0.53203I
b = −0.647516 − 0.347712I
−1.39515 − 0.93354I −2.59819 + 1.05734I
u = 0.302146 − 0.218430I
a = 1.70032 − 0.53203I
b = −0.647516 + 0.347712I
−1.39515 + 0.93354I −2.59819 − 1.05734I
u = 0.13215 + 1.62639I
a = 0.235834 + 0.252213I
b = 1.274680 + 0.408764I
−10.6279 + 11.2400I 0
u = 0.13215 − 1.62639I
a = 0.235834 − 0.252213I
b = 1.274680 − 0.408764I
−10.6279 − 11.2400I 0
u = −0.09471 + 1.63132I
a = 1.09576 − 1.32590I
b = 0.415498 + 1.133850I
−9.90493 − 7.22703I 0
u = −0.09471 − 1.63132I
a = 1.09576 + 1.32590I
b = 0.415498 − 1.133850I
−9.90493 + 7.22703I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11983 + 1.63478I
a = 0.420350 − 0.053792I
b = 0.814231 − 0.470879I
−8.96610 − 4.18743I 0
u = −0.11983 − 1.63478I
a = 0.420350 + 0.053792I
b = 0.814231 + 0.470879I
−8.96610 + 4.18743I 0
u = −0.19786 + 1.62793I
a = −0.686177 + 0.983980I
b = −0.563755 − 1.295860I
−6.46228 − 9.15504I 0
u = −0.19786 − 1.62793I
a = −0.686177 − 0.983980I
b = −0.563755 + 1.295860I
−6.46228 + 9.15504I 0
u = 0.10538 + 1.63975I
a = 0.684829 + 1.032230I
b = 0.566553 − 0.984332I
−11.38700 − 0.34719I 0
u = 0.10538 − 1.63975I
a = 0.684829 − 1.032230I
b = 0.566553 + 0.984332I
−11.38700 + 0.34719I 0
u = −0.08032 + 1.64238I
a = −0.263674 − 0.067179I
b = −0.957818 − 0.135285I
−10.59110 − 3.79827I 0
u = −0.08032 − 1.64238I
a = −0.263674 + 0.067179I
b = −0.957818 + 0.135285I
−10.59110 + 3.79827I 0
u = 0.19073 + 1.63818I
a = 1.005040 + 0.964618I
b = 0.74549 − 1.29153I
−7.7737 + 18.3011I 0
u = 0.19073 − 1.63818I
a = 1.005040 − 0.964618I
b = 0.74549 + 1.29153I
−7.7737 − 18.3011I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.12817 + 1.64887I
a = −0.721083 + 0.623451I
b = −0.83820 − 1.26724I
−9.00210 − 8.51228I 0
u = −0.12817 − 1.64887I
a = −0.721083 − 0.623451I
b = −0.83820 + 1.26724I
−9.00210 + 8.51228I 0
u = −0.050019 + 0.338335I
a = −6.94756 + 1.11891I
b = 0.062101 − 0.634357I
0.21944 + 4.30614I 1.88171 + 4.03006I
u = −0.050019 − 0.338335I
a = −6.94756 − 1.11891I
b = 0.062101 + 0.634357I
0.21944 − 4.30614I 1.88171 − 4.03006I
u = −0.19822 + 1.64976I
a = 1.012780 − 0.835118I
b = 0.624628 + 1.094730I
−7.08366 − 9.56953I 0
u = −0.19822 − 1.64976I
a = 1.012780 + 0.835118I
b = 0.624628 − 1.094730I
−7.08366 + 9.56953I 0
u = −0.05801 + 1.70542I
a = 0.188637 − 0.386957I
b = 0.300986 − 0.464446I
−12.20180 − 3.83656I 0
u = −0.05801 − 1.70542I
a = 0.188637 + 0.386957I
b = 0.300986 + 0.464446I
−12.20180 + 3.83656I 0
u = 0.01854 + 1.73599I
a = 0.152199 − 0.115967I
b = 0.476701 + 0.602644I
−12.59170 − 4.70299I 0
u = 0.01854 − 1.73599I
a = 0.152199 + 0.115967I
b = 0.476701 − 0.602644I
−12.59170 + 4.70299I 0
16
II.
I
u
2
= h−u
23
−5u
22
+· · ·+b−2, u
25
+4u
24
+· · ·+a+1, u
26
+4u
25
+· · ·+4u+1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
−u
25
− 4u
24
+ ··· − 30u − 1
u
23
+ 5u
22
+ ··· + 15u + 2
a
7
=
1
−u
2
a
2
=
−u
25
− 4u
24
+ ··· − 15u + 1
u
23
+ 5u
22
+ ··· + 15u + 2
a
5
=
−2u
25
− 8u
24
+ ··· − 44u − 8
−2u
23
− 6u
22
+ ··· + 6u + 4
a
1
=
−u
22
− 4u
21
+ ··· − 36u − 10
−u
24
− 5u
23
+ ··· + u + 3
a
11
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
u
25
+ 5u
24
+ ··· + 50u + 9
−u
24
− 4u
23
+ ··· − 12u − 4
a
10
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
4
=
−2u
25
− 8u
24
+ ··· − 45u − 7
−u
23
− 2u
22
+ ··· + 8u + 4
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −2u
25
−7u
24
−50u
23
−147u
22
−551u
21
−1347u
20
−3480u
19
−7052u
18
−13852u
17
−
23223u
16
− 36165u
15
− 49939u
14
− 62589u
13
− 70498u
12
− 70952u
11
− 64028u
10
−
50884u
9
−35704u
8
−21740u
7
−11365u
6
−5190u
5
−1995u
4
−763u
3
−263u
2
−68u − 16
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 4u
25
+ ··· + 3u
2
+ 1
c
2
u
26
− 8u
25
+ ··· − 4u + 1
c
3
u
26
+ 5u
24
+ ··· + 6u
2
+ 1
c
4
u
26
+ 6u
24
+ ··· + 5u
2
+ 1
c
5
u
26
+ 8u
25
+ ··· + 4u + 1
c
6
, c
7
u
26
+ 4u
25
+ ··· + 4u + 1
c
8
u
26
− 4u
24
+ ··· − 25u + 19
c
9
u
26
− 2u
25
+ ··· + 2u
2
+ 1
c
10
, c
11
u
26
− 4u
25
+ ··· − 4u + 1
c
12
u
26
− 4u
24
+ ··· + 37u + 19
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
− 6y
25
+ ··· + 6y + 1
c
2
, c
5
y
26
+ 14y
25
+ ··· + 26y + 1
c
3
y
26
+ 10y
25
+ ··· + 12y + 1
c
4
y
26
+ 12y
25
+ ··· + 10y + 1
c
6
, c
7
, c
10
c
11
y
26
+ 34y
25
+ ··· + 42y + 1
c
8
y
26
− 8y
25
+ ··· + 287y + 361
c
9
y
26
− 6y
25
+ ··· + 4y + 1
c
12
y
26
− 8y
25
+ ··· − 1407y + 361
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.075660 + 1.010990I
a = −1.326460 − 0.463849I
b = 0.060453 + 0.631462I
−1.96200 − 3.72629I 0.36372 + 5.75292I
u = 0.075660 − 1.010990I
a = −1.326460 + 0.463849I
b = 0.060453 − 0.631462I
−1.96200 + 3.72629I 0.36372 − 5.75292I
u = −0.523509 + 0.804009I
a = −0.91178 + 1.45977I
b = −0.471030 − 1.130290I
0.61532 − 5.73624I 0.67749 + 7.26439I
u = −0.523509 − 0.804009I
a = −0.91178 − 1.45977I
b = −0.471030 + 1.130290I
0.61532 + 5.73624I 0.67749 − 7.26439I
u = −0.820777 + 0.137567I
a = 0.33177 − 1.57517I
b = −0.314875 + 0.937706I
2.80165 + 1.27529I 0.76483 − 4.01128I
u = −0.820777 − 0.137567I
a = 0.33177 + 1.57517I
b = −0.314875 − 0.937706I
2.80165 − 1.27529I 0.76483 + 4.01128I
u = −0.087067 + 1.263330I
a = −0.500286 + 0.695318I
b = −0.105564 − 1.230040I
0.68127 − 4.36817I 4.61666 + 4.88375I
u = −0.087067 − 1.263330I
a = −0.500286 − 0.695318I
b = −0.105564 + 1.230040I
0.68127 + 4.36817I 4.61666 − 4.88375I
u = −0.400450 + 1.230050I
a = 0.124823 − 0.619651I
b = −0.188953 + 0.761286I
−1.45270 − 3.11273I −3.51640 + 3.25261I
u = −0.400450 − 1.230050I
a = 0.124823 + 0.619651I
b = −0.188953 − 0.761286I
−1.45270 + 3.11273I −3.51640 − 3.25261I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.178821 + 0.592010I
a = −0.219820 + 0.544018I
b = −1.287000 + 0.158714I
−3.22698 − 0.61881I 3.93730 + 11.39562I
u = −0.178821 − 0.592010I
a = −0.219820 − 0.544018I
b = −1.287000 − 0.158714I
−3.22698 + 0.61881I 3.93730 − 11.39562I
u = −0.00514 + 1.52348I
a = 0.550174 − 0.979342I
b = −0.05694 + 1.50728I
−2.47705 + 3.70060I 0. − 7.20844I
u = −0.00514 − 1.52348I
a = 0.550174 + 0.979342I
b = −0.05694 − 1.50728I
−2.47705 − 3.70060I 0. + 7.20844I
u = 0.06342 + 1.54650I
a = 1.89982 + 0.52199I
b = 0.364208 − 0.669495I
−6.51875 + 5.57148I −1.60003 − 7.19671I
u = 0.06342 − 1.54650I
a = 1.89982 − 0.52199I
b = 0.364208 + 0.669495I
−6.51875 − 5.57148I −1.60003 + 7.19671I
u = 0.167142 + 0.367743I
a = 5.28595 + 2.93649I
b = 0.246063 − 0.655184I
0.19972 + 4.69306I 0.8121 − 15.8385I
u = 0.167142 − 0.367743I
a = 5.28595 − 2.93649I
b = 0.246063 + 0.655184I
0.19972 − 4.69306I 0.8121 + 15.8385I
u = −0.05944 + 1.59597I
a = −0.399128 + 0.226443I
b = −1.39917 + 0.35339I
−10.86180 − 1.53524I 0. + 2.31456I
u = −0.05944 − 1.59597I
a = −0.399128 − 0.226443I
b = −1.39917 − 0.35339I
−10.86180 + 1.53524I 0. − 2.31456I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14829 + 1.62552I
a = −0.947483 + 0.859182I
b = −0.657237 − 1.233060I
−7.59986 − 8.25625I 0. + 4.95434I
u = −0.14829 − 1.62552I
a = −0.947483 − 0.859182I
b = −0.657237 + 1.233060I
−7.59986 + 8.25625I 0. − 4.95434I
u = −0.042037 + 0.282733I
a = 2.42524 − 2.28986I
b = −0.104076 + 1.401760I
3.89349 + 3.83221I −3.62557 − 6.49552I
u = −0.042037 − 0.282733I
a = 2.42524 + 2.28986I
b = −0.104076 − 1.401760I
3.89349 − 3.83221I −3.62557 + 6.49552I
u = −0.04070 + 1.71759I
a = −0.312820 + 0.164008I
b = −0.085877 + 0.446316I
−11.92580 − 4.08431I 5.51713 + 7.53332I
u = −0.04070 − 1.71759I
a = −0.312820 − 0.164008I
b = −0.085877 − 0.446316I
−11.92580 + 4.08431I 5.51713 − 7.53332I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
26
− 4u
25
+ ··· + 3u
2
+ 1)(u
120
− 7u
119
+ ··· − 7u + 3)
c
2
(u
26
− 8u
25
+ ··· − 4u + 1)(u
120
+ 7u
119
+ ··· − 6493u + 976)
c
3
(u
26
+ 5u
24
+ ··· + 6u
2
+ 1)(u
120
+ u
119
+ ··· + 24u + 8)
c
4
(u
26
+ 6u
24
+ ··· + 5u
2
+ 1)(u
120
− u
119
+ ··· + 45u + 1)
c
5
(u
26
+ 8u
25
+ ··· + 4u + 1)(u
120
+ 7u
119
+ ··· − 6493u + 976)
c
6
, c
7
(u
26
+ 4u
25
+ ··· + 4u + 1)(u
120
− 3u
119
+ ··· + 113u + 21)
c
8
(u
26
− 4u
24
+ ··· − 25u + 19)(u
120
− u
119
+ ··· + 4850u + 311)
c
9
(u
26
− 2u
25
+ ··· + 2u
2
+ 1)(u
120
− 5u
119
+ ··· + 3u + 8)
c
10
, c
11
(u
26
− 4u
25
+ ··· − 4u + 1)(u
120
− 3u
119
+ ··· + 113u + 21)
c
12
(u
26
− 4u
24
+ ··· + 37u + 19)
· (u
120
− u
119
+ ··· + 18390924u + 2188589)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
26
− 6y
25
+ ··· + 6y + 1)(y
120
− y
119
+ ··· + 197y + 9)
c
2
, c
5
(y
26
+ 14y
25
+ ··· + 26y + 1)
· (y
120
+ 59y
119
+ ··· + 31208823y + 952576)
c
3
(y
26
+ 10y
25
+ ··· + 12y + 1)(y
120
+ 3y
119
+ ··· − 608y + 64)
c
4
(y
26
+ 12y
25
+ ··· + 10y + 1)(y
120
+ 13y
119
+ ··· − 627y + 1)
c
6
, c
7
, c
10
c
11
(y
26
+ 34y
25
+ ··· + 42y + 1)(y
120
+ 143y
119
+ ··· + 20117y + 441)
c
8
(y
26
− 8y
25
+ ··· + 287y + 361)
· (y
120
− 3y
119
+ ··· + 32084922y + 96721)
c
9
(y
26
− 6y
25
+ ··· + 4y + 1)(y
120
+ 3y
119
+ ··· + 1655y + 64)
c
12
(y
26
− 8y
25
+ ··· − 1407y + 361)
· (y
120
+ 17y
119
+ ··· + 186020618302756y + 4789921810921)
24
