12a
0996
(K12a
0996
)
A knot diagram
1
Linearized knot diagam
4 6 12 8 3 11 10 1 5 7 2 9
Solving Sequence
6,11 3,7
2 12 5 10 8 4 1 9
c
6
c
2
c
11
c
5
c
10
c
7
c
4
c
1
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.90960 × 10
415
u
130
+ 7.68931 × 10
415
u
129
+ ··· + 1.61094 × 10
416
b + 3.02271 × 10
416
,
− 4.21404 × 10
415
u
130
+ 1.31941 × 10
416
u
129
+ ··· + 1.61094 × 10
416
a − 5.54652 × 10
416
,
u
131
− 4u
130
+ ··· + 22u + 1i
I
u
2
= h216373794u
34
− 554380012u
33
+ ··· + 116673229b + 126625703,
− 108358842u
34
− 18053119u
33
+ ··· + 116673229a + 275607483, u
35
− 3u
34
+ ··· + 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 166 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−1.91 × 10
415
u
130
+ 7.69 × 10
415
u
129
+ · · · + 1.61 × 10
416
b + 3.02 ×
10
416
, −4.21 × 10
415
u
130
+ 1.32 × 10
416
u
129
+ · · · + 1.61 × 10
416
a − 5.55 ×
10
416
, u
131
− 4u
130
+ · · · + 22u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
0.261588u
130
− 0.819027u
129
+ ··· − 50.5335u + 3.44302
0.118539u
130
− 0.477317u
129
+ ··· − 16.7988u − 1.87636
a
7
=
1
u
2
a
2
=
0.380127u
130
− 1.29634u
129
+ ··· − 67.3324u + 1.56667
0.118539u
130
− 0.477317u
129
+ ··· − 16.7988u − 1.87636
a
12
=
−0.356584u
130
+ 1.38531u
129
+ ··· − 13.6280u − 1.11146
0.218279u
130
− 0.790506u
129
+ ··· + 3.24429u − 0.106255
a
5
=
−0.184006u
130
+ 0.867658u
129
+ ··· − 5.65580u + 8.01711
0.290261u
130
− 1.07440u
129
+ ··· − 25.4372u − 2.43521
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
−0.0950145u
130
+ 0.502462u
129
+ ··· − 27.1849u + 5.79044
0.244805u
130
− 0.918752u
129
+ ··· − 25.5390u − 2.43105
a
1
=
0.509084u
130
− 1.80526u
129
+ ··· − 73.2691u − 7.71707
0.0838838u
130
− 0.379270u
129
+ ··· + 5.47489u + 0.460265
a
9
=
0.104653u
130
− 0.445112u
129
+ ··· + 92.8686u + 1.67990
0.175747u
130
− 0.633494u
129
+ ··· − 14.5893u + 0.0235265
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.288423u
130
− 0.981446u
129
+ ··· + 236.582u − 18.0453
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
131
− 12u
130
+ ··· − 72231u + 15709
c
2
, c
5
u
131
+ 6u
130
+ ··· + 24241u + 4453
c
3
u
131
+ 4u
130
+ ··· + 3336u + 641
c
4
u
131
+ 4u
130
+ ··· + 3298723u + 1083625
c
6
, c
7
, c
10
u
131
− 4u
130
+ ··· + 22u + 1
c
8
, c
12
u
131
+ 39u
129
+ ··· + 1108u + 389
c
9
u
131
− 2u
130
+ ··· + 4095541u + 816793
c
11
u
131
− 12u
130
+ ··· + 66370956u + 16737857
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
131
+ 32y
130
+ ··· + 12500700957y −246772681
c
2
, c
5
y
131
+ 92y
130
+ ··· − 429065067y −19829209
c
3
y
131
+ 4y
130
+ ··· + 4354808y −410881
c
4
y
131
+ 46y
130
+ ··· − 65696003393271y −1174243140625
c
6
, c
7
, c
10
y
131
+ 146y
130
+ ··· + 98y −1
c
8
, c
12
y
131
+ 78y
130
+ ··· − 4517088y −151321
c
9
y
131
+ 54y
130
+ ··· − 25212920648153y −667150804849
c
11
y
131
+ 62y
130
+ ··· − 5065648166473460y −280155856952449
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.525467 + 0.747489I
a = −0.516254 − 1.030700I
b = −0.381455 + 1.127400I
1.78479 + 3.41105I 0
u = −0.525467 − 0.747489I
a = −0.516254 + 1.030700I
b = −0.381455 − 1.127400I
1.78479 − 3.41105I 0
u = −0.564328 + 0.700697I
a = 1.37318 + 0.52817I
b = −0.225742 − 1.186250I
4.94780 − 1.67332I 0
u = −0.564328 − 0.700697I
a = 1.37318 − 0.52817I
b = −0.225742 + 1.186250I
4.94780 + 1.67332I 0
u = 0.880006 + 0.680875I
a = 0.869328 − 0.763444I
b = 0.234608 + 1.273540I
8.58616 − 2.59198I 0
u = 0.880006 − 0.680875I
a = 0.869328 + 0.763444I
b = 0.234608 − 1.273540I
8.58616 + 2.59198I 0
u = −0.170306 + 1.106490I
a = 0.874756 − 0.777817I
b = −0.547282 + 0.359701I
2.40346 + 1.11626I 0
u = −0.170306 − 1.106490I
a = 0.874756 + 0.777817I
b = −0.547282 − 0.359701I
2.40346 − 1.11626I 0
u = 0.844783 + 0.761981I
a = 0.759295 − 0.891229I
b = 0.460353 + 1.318470I
6.7866 − 14.3742I 0
u = 0.844783 − 0.761981I
a = 0.759295 + 0.891229I
b = 0.460353 − 1.318470I
6.7866 + 14.3742I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966463 + 0.629546I
a = −0.416587 + 0.605589I
b = −0.025810 − 1.320300I
8.31238 − 3.64670I 0
u = 0.966463 − 0.629546I
a = −0.416587 − 0.605589I
b = −0.025810 + 1.320300I
8.31238 + 3.64670I 0
u = 0.391545 + 0.745653I
a = 1.304230 − 0.411516I
b = −0.117901 + 0.935919I
3.53396 + 0.81367I 0
u = 0.391545 − 0.745653I
a = 1.304230 + 0.411516I
b = −0.117901 − 0.935919I
3.53396 − 0.81367I 0
u = 0.200353 + 0.815950I
a = 0.786898 + 0.633118I
b = 0.579221 − 1.006720I
5.44989 + 4.65781I 0
u = 0.200353 − 0.815950I
a = 0.786898 − 0.633118I
b = 0.579221 + 1.006720I
5.44989 − 4.65781I 0
u = −0.881524 + 0.774037I
a = 0.764216 + 0.836249I
b = 0.400954 − 1.240760I
2.91954 + 8.18653I 0
u = −0.881524 − 0.774037I
a = 0.764216 − 0.836249I
b = 0.400954 + 1.240760I
2.91954 − 8.18653I 0
u = 0.095734 + 1.183430I
a = 0.86236 + 1.27840I
b = −0.645368 − 0.667007I
2.96898 − 2.27833I 0
u = 0.095734 − 1.183430I
a = 0.86236 − 1.27840I
b = −0.645368 + 0.667007I
2.96898 + 2.27833I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.122440 + 0.412795I
a = −0.255003 + 0.355815I
b = 0.241394 − 1.207940I
5.60097 + 8.07537I 0
u = 1.122440 − 0.412795I
a = −0.255003 − 0.355815I
b = 0.241394 + 1.207940I
5.60097 − 8.07537I 0
u = −0.679368 + 0.423728I
a = −0.659617 − 0.405408I
b = −0.42833 + 1.38542I
4.07208 + 6.03852I 0
u = −0.679368 − 0.423728I
a = −0.659617 + 0.405408I
b = −0.42833 − 1.38542I
4.07208 − 6.03852I 0
u = 0.480287 + 0.635559I
a = 0.715445 − 0.177488I
b = 0.548545 + 0.327841I
3.95909 + 0.15415I 0
u = 0.480287 − 0.635559I
a = 0.715445 + 0.177488I
b = 0.548545 − 0.327841I
3.95909 − 0.15415I 0
u = 0.552318 + 0.563107I
a = 0.378960 + 0.091192I
b = 0.990789 − 0.041172I
2.72811 − 9.22751I 0
u = 0.552318 − 0.563107I
a = 0.378960 − 0.091192I
b = 0.990789 + 0.041172I
2.72811 + 9.22751I 0
u = −0.771525 + 0.142867I
a = 0.767470 − 0.017350I
b = 0.064087 − 0.934850I
−0.153105 + 0.774075I 0
u = −0.771525 − 0.142867I
a = 0.767470 + 0.017350I
b = 0.064087 + 0.934850I
−0.153105 − 0.774075I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547165 + 0.555129I
a = 0.537964 − 0.148403I
b = 0.781115 + 0.115429I
−0.59426 + 3.82728I 0
u = −0.547165 − 0.555129I
a = 0.537964 + 0.148403I
b = 0.781115 − 0.115429I
−0.59426 − 3.82728I 0
u = 0.407106 + 0.651459I
a = −0.94331 + 1.50803I
b = −0.49937 − 1.32345I
3.28754 − 6.16924I 0
u = 0.407106 − 0.651459I
a = −0.94331 − 1.50803I
b = −0.49937 + 1.32345I
3.28754 + 6.16924I 0
u = −0.449681 + 0.611284I
a = 0.39328 + 1.49025I
b = −0.049580 − 0.368450I
−0.777409 − 0.169873I 0
u = −0.449681 − 0.611284I
a = 0.39328 − 1.49025I
b = −0.049580 + 0.368450I
−0.777409 + 0.169873I 0
u = −0.254376 + 0.710473I
a = 0.028031 − 1.346890I
b = −0.652609 + 0.702636I
0.72715 + 3.59571I 0
u = −0.254376 − 0.710473I
a = 0.028031 + 1.346890I
b = −0.652609 − 0.702636I
0.72715 − 3.59571I 0
u = −0.202197 + 1.229300I
a = 0.522552 − 0.034197I
b = 0.326317 + 0.678215I
2.93516 + 1.86963I 0
u = −0.202197 − 1.229300I
a = 0.522552 + 0.034197I
b = 0.326317 − 0.678215I
2.93516 − 1.86963I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232849 + 0.708648I
a = 1.252010 − 0.593464I
b = 0.113498 + 1.099530I
3.55823 + 1.07562I 0
u = 0.232849 − 0.708648I
a = 1.252010 + 0.593464I
b = 0.113498 − 1.099530I
3.55823 − 1.07562I 0
u = −0.154782 + 1.255220I
a = 0.301144 − 0.147595I
b = 0.151261 + 0.356983I
2.87541 + 2.07039I 0
u = −0.154782 − 1.255220I
a = 0.301144 + 0.147595I
b = 0.151261 − 0.356983I
2.87541 − 2.07039I 0
u = 0.559761 + 0.456833I
a = 0.13149 − 1.64623I
b = 0.413078 + 0.161006I
2.36838 + 5.38591I 0
u = 0.559761 − 0.456833I
a = 0.13149 + 1.64623I
b = 0.413078 − 0.161006I
2.36838 − 5.38591I 0
u = 0.654306 + 0.281817I
a = 0.163571 − 0.924402I
b = 0.323027 − 0.483952I
2.76516 − 4.00070I 0
u = 0.654306 − 0.281817I
a = 0.163571 + 0.924402I
b = 0.323027 + 0.483952I
2.76516 + 4.00070I 0
u = −0.335606 + 1.263310I
a = 1.21402 + 1.01275I
b = 0.318585 − 1.047330I
4.21785 + 4.80654I 0
u = −0.335606 − 1.263310I
a = 1.21402 − 1.01275I
b = 0.318585 + 1.047330I
4.21785 − 4.80654I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.486105 + 0.386932I
a = −1.316180 + 0.151129I
b = −0.413118 − 1.231790I
2.35694 − 3.94596I −12.00000 + 0.I
u = 0.486105 − 0.386932I
a = −1.316180 − 0.151129I
b = −0.413118 + 1.231790I
2.35694 + 3.94596I −12.00000 + 0.I
u = 0.215248 + 1.395720I
a = −0.447921 − 0.320010I
b = 0.114724 − 0.585468I
8.07310 − 7.11989I 0
u = 0.215248 − 1.395720I
a = −0.447921 + 0.320010I
b = 0.114724 + 0.585468I
8.07310 + 7.11989I 0
u = −1.30548 + 0.54994I
a = −0.179299 − 0.558383I
b = 0.117233 + 1.157250I
1.78788 − 1.32616I 0
u = −1.30548 − 0.54994I
a = −0.179299 + 0.558383I
b = 0.117233 − 1.157250I
1.78788 + 1.32616I 0
u = −0.049316 + 0.564767I
a = 1.27988 + 0.93417I
b = 0.23935 − 1.43460I
7.79657 − 4.44788I −1.03852 + 3.60025I
u = −0.049316 − 0.564767I
a = 1.27988 − 0.93417I
b = 0.23935 + 1.43460I
7.79657 + 4.44788I −1.03852 − 3.60025I
u = −0.01958 + 1.46746I
a = 0.876230 − 0.142939I
b = −1.59124 + 0.17580I
4.31106 + 1.41186I 0
u = −0.01958 − 1.46746I
a = 0.876230 + 0.142939I
b = −1.59124 − 0.17580I
4.31106 − 1.41186I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07702 + 1.46951I
a = 0.54741 − 2.08870I
b = −0.081825 + 1.282690I
7.80979 + 2.38491I 0
u = 0.07702 − 1.46951I
a = 0.54741 + 2.08870I
b = −0.081825 − 1.282690I
7.80979 − 2.38491I 0
u = 0.09417 + 1.47358I
a = −0.327220 + 0.975715I
b = −0.819353 − 0.984384I
7.47427 − 5.33931I 0
u = 0.09417 − 1.47358I
a = −0.327220 − 0.975715I
b = −0.819353 + 0.984384I
7.47427 + 5.33931I 0
u = −0.10879 + 1.48397I
a = 0.34271 + 2.41275I
b = 0.027694 − 1.134690I
4.90605 + 2.62766I 0
u = −0.10879 − 1.48397I
a = 0.34271 − 2.41275I
b = 0.027694 + 1.134690I
4.90605 − 2.62766I 0
u = −0.195535 + 0.462414I
a = −3.15314 − 2.03501I
b = −0.151584 + 1.319220I
7.40603 + 5.36191I 1.35055 − 6.94425I
u = −0.195535 − 0.462414I
a = −3.15314 + 2.03501I
b = −0.151584 − 1.319220I
7.40603 − 5.36191I 1.35055 + 6.94425I
u = −0.07278 + 1.49703I
a = 0.1331470 − 0.0366763I
b = −0.944038 + 0.310529I
5.50497 + 0.88667I 0
u = −0.07278 − 1.49703I
a = 0.1331470 + 0.0366763I
b = −0.944038 − 0.310529I
5.50497 − 0.88667I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08477 + 1.50677I
a = −0.10017 − 2.91395I
b = 0.080506 + 1.145760I
9.92277 − 7.96764I 0
u = 0.08477 − 1.50677I
a = −0.10017 + 2.91395I
b = 0.080506 − 1.145760I
9.92277 + 7.96764I 0
u = 0.14044 + 1.51388I
a = −0.40585 + 1.86069I
b = −0.61460 − 1.46923I
8.75421 − 6.14519I 0
u = 0.14044 − 1.51388I
a = −0.40585 − 1.86069I
b = −0.61460 + 1.46923I
8.75421 + 6.14519I 0
u = −0.00720 + 1.52348I
a = 1.067230 + 0.234317I
b = −1.52493 − 0.14494I
5.01790 − 1.06490I 0
u = −0.00720 − 1.52348I
a = 1.067230 − 0.234317I
b = −1.52493 + 0.14494I
5.01790 + 1.06490I 0
u = −0.19909 + 1.51292I
a = −0.33633 − 1.96696I
b = −0.56930 + 1.64569I
10.46230 + 9.15030I 0
u = −0.19909 − 1.51292I
a = −0.33633 + 1.96696I
b = −0.56930 − 1.64569I
10.46230 − 9.15030I 0
u = 0.424862 + 0.187704I
a = −0.79025 − 1.39071I
b = −0.419498 − 0.958810I
1.82455 − 3.76967I −11.75678 + 7.09571I
u = 0.424862 − 0.187704I
a = −0.79025 + 1.39071I
b = −0.419498 + 0.958810I
1.82455 + 3.76967I −11.75678 − 7.09571I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.06958 + 1.53861I
a = −0.94463 − 2.22813I
b = −0.33669 + 1.37547I
14.2564 + 6.3702I 0
u = −0.06958 − 1.53861I
a = −0.94463 + 2.22813I
b = −0.33669 − 1.37547I
14.2564 − 6.3702I 0
u = −0.446360 + 0.102208I
a = 2.83776 + 0.86119I
b = 0.108364 − 0.708821I
−0.719730 + 0.828371I −13.9889 − 7.7855I
u = −0.446360 − 0.102208I
a = 2.83776 − 0.86119I
b = 0.108364 + 0.708821I
−0.719730 − 0.828371I −13.9889 + 7.7855I
u = −0.16340 + 1.55068I
a = −0.429415 + 0.142778I
b = 1.183210 + 0.024159I
6.44424 + 6.40666I 0
u = −0.16340 − 1.55068I
a = −0.429415 − 0.142778I
b = 1.183210 − 0.024159I
6.44424 − 6.40666I 0
u = 0.13859 + 1.55371I
a = −0.119292 − 0.402432I
b = 0.917518 + 0.228641I
11.22590 − 2.06972I 0
u = 0.13859 − 1.55371I
a = −0.119292 + 0.402432I
b = 0.917518 − 0.228641I
11.22590 + 2.06972I 0
u = 0.00146 + 1.56096I
a = 0.04824 + 1.96992I
b = 0.54559 − 1.68239I
15.0869 − 4.3684I 0
u = 0.00146 − 1.56096I
a = 0.04824 − 1.96992I
b = 0.54559 + 1.68239I
15.0869 + 4.3684I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11268 + 1.55807I
a = −0.123134 − 0.718412I
b = −0.467042 + 0.185434I
9.27779 + 3.03828I 0
u = 0.11268 − 1.55807I
a = −0.123134 + 0.718412I
b = −0.467042 − 0.185434I
9.27779 − 3.03828I 0
u = 0.16375 + 1.55556I
a = −0.636134 − 0.231500I
b = 1.371360 + 0.046679I
9.8171 − 11.8228I 0
u = 0.16375 − 1.55556I
a = −0.636134 + 0.231500I
b = 1.371360 − 0.046679I
9.8171 + 11.8228I 0
u = −0.179859 + 0.392484I
a = 0.33913 + 1.63340I
b = −0.421805 − 0.084508I
−0.693141 − 0.239546I −13.64098 + 0.46101I
u = −0.179859 − 0.392484I
a = 0.33913 − 1.63340I
b = −0.421805 + 0.084508I
−0.693141 + 0.239546I −13.64098 − 0.46101I
u = 0.298681 + 0.305306I
a = 2.10049 − 4.70701I
b = 0.255646 + 0.924205I
3.68947 − 6.65430I −6.6298 + 13.2899I
u = 0.298681 − 0.305306I
a = 2.10049 + 4.70701I
b = 0.255646 − 0.924205I
3.68947 + 6.65430I −6.6298 − 13.2899I
u = 0.02719 + 1.57899I
a = 0.21494 − 1.76058I
b = 0.47957 + 1.43896I
11.30710 + 0.37254I 0
u = 0.02719 − 1.57899I
a = 0.21494 + 1.76058I
b = 0.47957 − 1.43896I
11.30710 − 0.37254I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.398552 + 0.086514I
a = 0.138522 − 0.636070I
b = −0.916128 − 0.213738I
−0.89681 − 1.14101I −16.6958 + 4.1360I
u = −0.398552 − 0.086514I
a = 0.138522 + 0.636070I
b = −0.916128 + 0.213738I
−0.89681 + 1.14101I −16.6958 − 4.1360I
u = 0.11971 + 1.59075I
a = −0.23225 + 2.23406I
b = −0.52769 − 1.55163I
10.91940 − 8.12628I 0
u = 0.11971 − 1.59075I
a = −0.23225 − 2.23406I
b = −0.52769 + 1.55163I
10.91940 + 8.12628I 0
u = −0.12383 + 1.60412I
a = 0.92637 + 1.54070I
b = 0.092457 − 1.155070I
12.81460 + 0.70744I 0
u = −0.12383 − 1.60412I
a = 0.92637 − 1.54070I
b = 0.092457 + 1.155070I
12.81460 − 0.70744I 0
u = 0.294346 + 0.248668I
a = 1.90504 − 0.04589I
b = −0.419725 + 1.092290I
2.04540 + 3.46709I −11.53743 − 3.43649I
u = 0.294346 − 0.248668I
a = 1.90504 + 0.04589I
b = −0.419725 − 1.092290I
2.04540 − 3.46709I −11.53743 + 3.43649I
u = 0.09145 + 1.61279I
a = 0.620412 − 1.262540I
b = 0.301152 + 0.975293I
11.63010 − 0.87027I 0
u = 0.09145 − 1.61279I
a = 0.620412 + 1.262540I
b = 0.301152 − 0.975293I
11.63010 + 0.87027I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15234 + 1.61468I
a = −0.15422 − 1.93329I
b = −0.51779 + 1.45393I
9.77845 + 5.95718I 0
u = −0.15234 − 1.61468I
a = −0.15422 + 1.93329I
b = −0.51779 − 1.45393I
9.77845 − 5.95718I 0
u = 0.00633 + 1.62262I
a = −0.03722 + 1.52155I
b = 0.75800 − 1.32709I
13.9268 + 4.1788I 0
u = 0.00633 − 1.62262I
a = −0.03722 − 1.52155I
b = 0.75800 + 1.32709I
13.9268 − 4.1788I 0
u = 0.28371 + 1.60451I
a = 0.71771 − 1.71135I
b = 0.43010 + 1.36925I
16.0935 − 6.8733I 0
u = 0.28371 − 1.60451I
a = 0.71771 + 1.71135I
b = 0.43010 − 1.36925I
16.0935 + 6.8733I 0
u = 0.270101 + 0.251756I
a = −0.125875 + 1.155490I
b = −0.959335 − 0.083260I
−1.07413 − 0.92579I −15.2282 + 7.1977I
u = 0.270101 − 0.251756I
a = −0.125875 − 1.155490I
b = −0.959335 + 0.083260I
−1.07413 + 0.92579I −15.2282 − 7.1977I
u = 0.30549 + 1.62589I
a = −0.51328 + 1.68940I
b = −0.19698 − 1.51663I
15.7871 − 8.3497I 0
u = 0.30549 − 1.62589I
a = −0.51328 − 1.68940I
b = −0.19698 + 1.51663I
15.7871 + 8.3497I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27141 + 1.63294I
a = 0.49033 − 1.83101I
b = 0.58276 + 1.47182I
14.6938 − 18.5735I 0
u = 0.27141 − 1.63294I
a = 0.49033 + 1.83101I
b = 0.58276 − 1.47182I
14.6938 + 18.5735I 0
u = −0.28144 + 1.63293I
a = 0.53157 + 1.73016I
b = 0.55641 − 1.39824I
10.8234 + 12.5374I 0
u = −0.28144 − 1.63293I
a = 0.53157 − 1.73016I
b = 0.55641 + 1.39824I
10.8234 − 12.5374I 0
u = −0.330231
a = 0.862570
b = −0.276272
−0.666297 −15.1140
u = −0.23702 + 1.75688I
a = −0.25300 − 1.51117I
b = −0.270666 + 1.273020I
10.39850 + 4.90574I 0
u = −0.23702 − 1.75688I
a = −0.25300 + 1.51117I
b = −0.270666 − 1.273020I
10.39850 − 4.90574I 0
u = 0.45924 + 1.79309I
a = −0.417393 + 1.264210I
b = −0.061216 − 1.224550I
12.50850 + 1.60896I 0
u = 0.45924 − 1.79309I
a = −0.417393 − 1.264210I
b = −0.061216 + 1.224550I
12.50850 − 1.60896I 0
u = −0.0431067 + 0.0361683I
a = 5.78437 − 2.79900I
b = −1.172340 − 0.229616I
−1.05060 − 1.12049I −28.1733 + 9.5439I
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0431067 − 0.0361683I
a = 5.78437 + 2.79900I
b = −1.172340 + 0.229616I
−1.05060 + 1.12049I −28.1733 − 9.5439I
18
II.
I
u
2
= h2.16 × 10
8
u
34
− 5.54 × 10
8
u
33
+ · · · + 1.17 × 10
8
b + 1.27 × 10
8
, −1.08 ×
10
8
u
34
−1.81×10
7
u
33
+· · · +1.17×10
8
a+2.76×10
8
, u
35
−3u
34
+· · · +2u −1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
0.928738u
34
+ 0.154732u
33
+ ··· + 2.69354u − 2.36222
−1.85453u
34
+ 4.75156u
33
+ ··· + 1.08009u − 1.08530
a
7
=
1
u
2
a
2
=
−0.925790u
34
+ 4.90629u
33
+ ··· + 3.77363u − 3.44752
−1.85453u
34
+ 4.75156u
33
+ ··· + 1.08009u − 1.08530
a
12
=
−0.0519270u
34
+ 6.58517u
33
+ ··· + 3.83234u − 4.04395
0.167589u
34
+ 1.63749u
33
+ ··· + 0.645476u − 1.19399
a
5
=
−0.343407u
34
+ 2.46362u
33
+ ··· + 2.85450u − 0.908133
−0.850583u
34
+ 1.28594u
33
+ ··· − 0.248907u − 0.834372
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
0.660538u
34
− 1.00200u
33
+ ··· + 1.52551u − 1.65720
−1.35302u
34
− 0.0611587u
33
+ ··· − 4.07804u + 1.70703
a
1
=
−0.925790u
34
+ 4.90629u
33
+ ··· + 1.77363u − 2.44752
0.0766093u
34
+ 0.190531u
33
+ ··· − 2.48948u + 0.359106
a
9
=
0.350461u
34
− 4.07651u
33
+ ··· − 3.34045u + 2.61944
1.46993u
34
− 6.05091u
33
+ ··· − 4.38886u + 0.665278
(ii) Obstruction class = 1
(iii) Cusp Shapes =
219364424
116673229
u
34
+
511779779
116673229
u
33
+ ··· +
5220911812
116673229
u −
82727589
116673229
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
− 3u
34
+ ··· + u − 1
c
2
u
35
− 13u
34
+ ··· + 55u − 5
c
3
u
35
− 3u
34
+ ··· + 4u + 1
c
4
u
35
+ 3u
34
+ ··· − u − 1
c
5
u
35
+ 13u
34
+ ··· + 55u + 5
c
6
, c
7
u
35
− 3u
34
+ ··· + 2u − 1
c
8
u
35
+ 3u
34
+ ··· − 26u
2
− 5
c
9
u
35
+ u
34
+ ··· + 17u + 5
c
10
u
35
+ 3u
34
+ ··· + 2u + 1
c
11
u
35
+ u
34
+ ··· + 36u − 5
c
12
u
35
− 3u
34
+ ··· + 26u
2
+ 5
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
− 9y
34
+ ··· + 25y −1
c
2
, c
5
y
35
+ 19y
34
+ ··· − 315y −25
c
3
y
35
− 9y
34
+ ··· + 12y −1
c
4
y
35
+ y
34
+ ··· − 19y −1
c
6
, c
7
, c
10
y
35
+ 41y
34
+ ··· − 18y −1
c
8
, c
12
y
35
+ 17y
34
+ ··· − 260y −25
c
9
y
35
+ 21y
34
+ ··· + 239y −25
c
11
y
35
+ 5y
34
+ ··· − 144y −25
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.122145 + 1.004060I
a = 1.10104 − 1.31634I
b = −0.478762 + 1.079080I
3.87342 + 2.99839I −4.47816 − 6.39745I
u = 0.122145 − 1.004060I
a = 1.10104 + 1.31634I
b = −0.478762 − 1.079080I
3.87342 − 2.99839I −4.47816 + 6.39745I
u = 1.022900 + 0.445739I
a = 0.224069 − 0.270475I
b = −0.107188 + 1.109310I
1.33723 + 0.96225I −10.20506 + 1.20335I
u = 1.022900 − 0.445739I
a = 0.224069 + 0.270475I
b = −0.107188 − 1.109310I
1.33723 − 0.96225I −10.20506 − 1.20335I
u = 0.051151 + 1.158520I
a = 0.902479 + 0.773211I
b = −0.776451 − 0.477602I
1.98933 − 1.53831I −15.6685 + 4.6367I
u = 0.051151 − 1.158520I
a = 0.902479 − 0.773211I
b = −0.776451 + 0.477602I
1.98933 + 1.53831I −15.6685 − 4.6367I
u = 0.240903 + 1.211540I
a = −1.32604 + 0.91222I
b = −0.376764 − 1.035040I
4.03059 − 5.14210I −12.0000 + 12.7056I
u = 0.240903 − 1.211540I
a = −1.32604 − 0.91222I
b = −0.376764 + 1.035040I
4.03059 + 5.14210I −12.0000 − 12.7056I
u = 0.131244 + 1.256450I
a = −0.655224 + 0.387240I
b = −0.281083 + 0.598820I
2.56530 − 1.95141I −19.9036 + 4.0958I
u = 0.131244 − 1.256450I
a = −0.655224 − 0.387240I
b = −0.281083 − 0.598820I
2.56530 + 1.95141I −19.9036 − 4.0958I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.488132 + 0.522037I
a = −0.74810 + 2.18187I
b = −0.064447 − 0.734888I
−0.161826 − 0.010723I −3.32308 + 1.40241I
u = 0.488132 − 0.522037I
a = −0.74810 − 2.18187I
b = −0.064447 + 0.734888I
−0.161826 + 0.010723I −3.32308 − 1.40241I
u = 0.418014 + 0.569996I
a = −1.002590 + 0.800897I
b = −0.493707 − 1.282760I
2.93762 − 4.85759I −6.91178 + 6.85657I
u = 0.418014 − 0.569996I
a = −1.002590 − 0.800897I
b = −0.493707 + 1.282760I
2.93762 + 4.85759I −6.91178 − 6.85657I
u = 0.123340 + 1.320410I
a = 0.245699 + 0.170225I
b = −0.660906 + 0.143798I
2.21573 − 2.00607I −12.00000 + 0.I
u = 0.123340 − 1.320410I
a = 0.245699 − 0.170225I
b = −0.660906 − 0.143798I
2.21573 + 2.00607I −12.00000 + 0.I
u = −0.142168 + 1.376570I
a = 0.031076 − 0.659163I
b = 0.246715 − 0.603133I
7.81251 + 7.81096I 0
u = −0.142168 − 1.376570I
a = 0.031076 + 0.659163I
b = 0.246715 + 0.603133I
7.81251 − 7.81096I 0
u = −0.527923 + 0.200119I
a = −1.57895 − 0.13839I
b = −0.095477 + 1.328750I
6.40361 + 5.10941I −7.24097 − 5.59956I
u = −0.527923 − 0.200119I
a = −1.57895 + 0.13839I
b = −0.095477 − 1.328750I
6.40361 − 5.10941I −7.24097 + 5.59956I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01292 + 1.52144I
a = 1.027380 − 0.222140I
b = −1.60803 + 0.21423I
5.47553 + 0.82226I 0
u = 0.01292 − 1.52144I
a = 1.027380 + 0.222140I
b = −1.60803 − 0.21423I
5.47553 − 0.82226I 0
u = −0.13874 + 1.53102I
a = −0.53702 − 2.29118I
b = −0.27753 + 1.51654I
12.6081 + 7.3569I 0
u = −0.13874 − 1.53102I
a = −0.53702 + 2.29118I
b = −0.27753 − 1.51654I
12.6081 − 7.3569I 0
u = 0.452585
a = −0.885508
b = −0.583264
−1.90141 −21.3700
u = −0.409627 + 0.190953I
a = −2.95073 − 1.76263I
b = 0.220485 + 0.768433I
3.57544 − 5.92199I −6.82039 + 2.97842I
u = −0.409627 − 0.190953I
a = −2.95073 + 1.76263I
b = 0.220485 − 0.768433I
3.57544 + 5.92199I −6.82039 − 2.97842I
u = 0.13268 + 1.58332I
a = −0.19383 + 2.00083I
b = −0.60242 − 1.54121I
10.31210 − 6.95058I 0
u = 0.13268 − 1.58332I
a = −0.19383 − 2.00083I
b = −0.60242 + 1.54121I
10.31210 + 6.95058I 0
u = −0.27950 + 1.61581I
a = 0.457954 + 1.185000I
b = 0.191754 − 1.165930I
11.39260 − 1.40260I 0
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.27950 − 1.61581I
a = 0.457954 − 1.185000I
b = 0.191754 + 1.165930I
11.39260 + 1.40260I 0
u = 0.056565 + 0.286434I
a = −0.272945 − 0.201557I
b = −1.278180 + 0.247560I
−0.883230 + 1.048200I 12.6366 + 7.8894I
u = 0.056565 − 0.286434I
a = −0.272945 + 0.201557I
b = −1.278180 − 0.247560I
−0.883230 − 1.048200I 12.6366 − 7.8894I
u = −0.02833 + 1.72895I
a = 0.21848 − 1.60370I
b = 0.233629 + 1.080700I
11.00330 − 3.51278I 0
u = −0.02833 − 1.72895I
a = 0.21848 + 1.60370I
b = 0.233629 − 1.080700I
11.00330 + 3.51278I 0
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
35
− 3u
34
+ ··· + u − 1)(u
131
− 12u
130
+ ··· − 72231u + 15709)
c
2
(u
35
− 13u
34
+ ··· + 55u − 5)(u
131
+ 6u
130
+ ··· + 24241u + 4453)
c
3
(u
35
− 3u
34
+ ··· + 4u + 1)(u
131
+ 4u
130
+ ··· + 3336u + 641)
c
4
(u
35
+ 3u
34
+ ··· − u − 1)(u
131
+ 4u
130
+ ··· + 3298723u + 1083625)
c
5
(u
35
+ 13u
34
+ ··· + 55u + 5)(u
131
+ 6u
130
+ ··· + 24241u + 4453)
c
6
, c
7
(u
35
− 3u
34
+ ··· + 2u − 1)(u
131
− 4u
130
+ ··· + 22u + 1)
c
8
(u
35
+ 3u
34
+ ··· − 26u
2
− 5)(u
131
+ 39u
129
+ ··· + 1108u + 389)
c
9
(u
35
+ u
34
+ ··· + 17u + 5)(u
131
− 2u
130
+ ··· + 4095541u + 816793)
c
10
(u
35
+ 3u
34
+ ··· + 2u + 1)(u
131
− 4u
130
+ ··· + 22u + 1)
c
11
(u
35
+ u
34
+ ··· + 36u − 5)
· (u
131
− 12u
130
+ ··· + 66370956u + 16737857)
c
12
(u
35
− 3u
34
+ ··· + 26u
2
+ 5)(u
131
+ 39u
129
+ ··· + 1108u + 389)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
35
− 9y
34
+ ··· + 25y −1)
· (y
131
+ 32y
130
+ ··· + 12500700957y −246772681)
c
2
, c
5
(y
35
+ 19y
34
+ ··· − 315y −25)
· (y
131
+ 92y
130
+ ··· − 429065067y −19829209)
c
3
(y
35
− 9y
34
+ ··· + 12y −1)(y
131
+ 4y
130
+ ··· + 4354808y −410881)
c
4
(y
35
+ y
34
+ ··· − 19y −1)
· (y
131
+ 46y
130
+ ··· − 65696003393271y −1174243140625)
c
6
, c
7
, c
10
(y
35
+ 41y
34
+ ··· − 18y −1)(y
131
+ 146y
130
+ ··· + 98y −1)
c
8
, c
12
(y
35
+ 17y
34
+ ··· − 260y −25)
· (y
131
+ 78y
130
+ ··· − 4517088y −151321)
c
9
(y
35
+ 21y
34
+ ··· + 239y −25)
· (y
131
+ 54y
130
+ ··· − 25212920648153y −667150804849)
c
11
(y
35
+ 5y
34
+ ··· − 144y −25)
· (y
131
+ 62y
130
+ ··· − 5065648166473460y −280155856952449)
27
