12a
0930
(K12a
0930
)
A knot diagram
1
Linearized knot diagam
4 6 9 12 2 10 11 1 3 7 5 8
Solving Sequence
8,12
1
5,9
4 2 3 11 7 10 6
c
12
c
8
c
4
c
1
c
3
c
11
c
7
c
10
c
6
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h9.59690 × 10
335
u
96
− 1.05215 × 10
336
u
95
+ ··· + 3.44266 × 10
336
b − 5.12396 × 10
337
,
8.78993 × 10
338
u
96
− 1.24791 × 10
339
u
95
+ ··· + 3.52873 × 10
339
a + 1.10173 × 10
340
,
u
97
− 2u
96
+ ··· + 1714u + 41i
I
u
2
= h509208711230210u
22
+ 109407337183821u
21
+ ··· + 56843194846091b + 2350612385286411,
− 7.80907 × 10
15
u
22
− 1.63603 × 10
15
u
21
+ ··· + 2.84216 × 10
14
a − 3.68176 × 10
16
, u
23
− 7u
21
+ ··· + 8u − 1i
I
u
3
= hb + 1, a + 1, u + 1i
* 3 irreducible components of dim
C
= 0, with total 121 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
= h9.60 × 10
335
u
96
− 1.05 × 10
336
u
95
+ · · · + 3.44 × 10
336
b − 5.12 ×
10
337
, 8.79 × 10
338
u
96
− 1.25 × 10
339
u
95
+ · · · + 3.53 × 10
339
a + 1.10 ×
10
340
, u
97
− 2u
96
+ · · · + 1714u + 41i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
−0.249096u
96
+ 0.353643u
95
+ ··· + 791.383u − 3.12216
−0.278764u
96
+ 0.305620u
95
+ ··· + 673.123u + 14.8837
a
9
=
−u
−u
3
+ u
a
4
=
−0.527860u
96
+ 0.659263u
95
+ ··· + 1464.51u + 11.7615
−0.278764u
96
+ 0.305620u
95
+ ··· + 673.123u + 14.8837
a
2
=
−0.0762388u
96
− 0.0826739u
95
+ ··· − 282.307u + 8.80990
0.140133u
96
− 0.171057u
95
+ ··· − 376.086u − 8.22131
a
3
=
−0.340979u
96
+ 0.446598u
95
+ ··· + 974.929u + 0.494949
−0.323338u
96
+ 0.384426u
95
+ ··· + 878.917u + 19.5453
a
11
=
0.0726071u
96
− 0.0690112u
95
+ ··· − 167.910u − 16.7409
0.199514u
96
− 0.0750754u
95
+ ··· − 320.938u − 8.18508
a
7
=
−0.0146069u
96
− 0.0282631u
95
+ ··· − 99.5227u − 6.12905
−0.699903u
96
+ 0.763490u
95
+ ··· + 1488.36u + 34.3576
a
10
=
−0.366501u
96
+ 0.396659u
95
+ ··· + 785.732u + 6.52821
−0.343656u
96
+ 0.391918u
95
+ ··· + 332.980u + 7.46440
a
6
=
0.204866u
96
− 0.0714659u
95
+ ··· − 29.8300u − 8.45377
−0.0464229u
96
+ 0.0479177u
95
+ ··· + 147.679u + 3.12461
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.92098u
96
+ 3.83799u
95
+ ··· − 1343.96u − 38.2137
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
97
− 13u
96
+ ··· + 83802u − 29149
c
2
, c
5
u
97
− u
96
+ ··· − 22184u − 2161
c
3
, c
9
u
97
− 14u
96
+ ··· + 1812u − 149
c
4
, c
11
u
97
− 3u
96
+ ··· − 356u − 59
c
6
, c
7
, c
10
u
97
+ 4u
96
+ ··· + 4242u + 242
c
8
, c
12
u
97
− 2u
96
+ ··· + 1714u + 41
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
97
− 37y
96
+ ··· + 128682539484y −849664201
c
2
, c
5
y
97
− 79y
96
+ ··· + 423448954y −4669921
c
3
, c
9
y
97
− 3452y
95
+ ··· − 696744y −22201
c
4
, c
11
y
97
− 47y
96
+ ··· − 64542y −3481
c
6
, c
7
, c
10
y
97
− 110y
96
+ ··· + 17376496y −58564
c
8
, c
12
y
97
− 68y
96
+ ··· + 2983388y −1681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00099
a = 0.104557
b = 8.97759
−3.28781 −2205.50
u = −0.236628 + 0.987183I
a = 0.733045 + 1.115450I
b = −0.640466 − 1.082220I
−5.18696 − 5.17546I 0
u = −0.236628 − 0.987183I
a = 0.733045 − 1.115450I
b = −0.640466 + 1.082220I
−5.18696 + 5.17546I 0
u = 1.006690 + 0.203483I
a = 1.35334 − 1.08695I
b = 0.454354 + 0.669034I
−3.28245 − 0.83839I 0
u = 1.006690 − 0.203483I
a = 1.35334 + 1.08695I
b = 0.454354 − 0.669034I
−3.28245 + 0.83839I 0
u = 0.059389 + 1.035400I
a = 0.00927 − 1.53980I
b = 0.430082 + 1.145650I
−2.87174 − 6.62403I 0
u = 0.059389 − 1.035400I
a = 0.00927 + 1.53980I
b = 0.430082 − 1.145650I
−2.87174 + 6.62403I 0
u = −1.041690 + 0.037723I
a = 0.863323 − 0.623359I
b = 0.534994 + 1.031760I
−2.20470 + 0.29278I 0
u = −1.041690 − 0.037723I
a = 0.863323 + 0.623359I
b = 0.534994 − 1.031760I
−2.20470 − 0.29278I 0
u = −0.987860 + 0.352019I
a = −0.934926 − 0.230856I
b = −0.173771 + 0.697387I
−0.897884 − 0.166548I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.987860 − 0.352019I
a = −0.934926 + 0.230856I
b = −0.173771 − 0.697387I
−0.897884 + 0.166548I 0
u = 0.937667
a = −0.678354
b = −3.75942
−8.62239 0
u = 0.543866 + 0.923125I
a = −0.82668 + 1.28337I
b = 0.571458 − 0.472121I
−12.51620 − 5.63081I 0
u = 0.543866 − 0.923125I
a = −0.82668 − 1.28337I
b = 0.571458 + 0.472121I
−12.51620 + 5.63081I 0
u = −0.403795 + 0.996611I
a = −0.79352 − 1.17354I
b = 0.418677 + 0.887734I
−1.17057 − 1.72797I 0
u = −0.403795 − 0.996611I
a = −0.79352 + 1.17354I
b = 0.418677 − 0.887734I
−1.17057 + 1.72797I 0
u = −1.089510 + 0.121285I
a = −1.83583 + 0.43767I
b = −0.415865 − 0.714017I
−7.90895 + 0.71724I 0
u = −1.089510 − 0.121285I
a = −1.83583 − 0.43767I
b = −0.415865 + 0.714017I
−7.90895 − 0.71724I 0
u = 1.115620 + 0.034953I
a = 0.492249 − 1.264290I
b = 0.55813 + 1.63026I
−7.70818 − 2.22028I 0
u = 1.115620 − 0.034953I
a = 0.492249 + 1.264290I
b = 0.55813 − 1.63026I
−7.70818 + 2.22028I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.359991 + 0.802181I
a = −0.296638 + 1.381910I
b = 0.062718 − 1.088860I
3.34481 − 0.89059I 0
u = 0.359991 − 0.802181I
a = −0.296638 − 1.381910I
b = 0.062718 + 1.088860I
3.34481 + 0.89059I 0
u = 1.160300 + 0.029718I
a = −1.14308 + 1.74240I
b = −0.492514 − 1.084760I
−14.1423 − 5.8216I 0
u = 1.160300 − 0.029718I
a = −1.14308 − 1.74240I
b = −0.492514 + 1.084760I
−14.1423 + 5.8216I 0
u = 1.108780 + 0.425877I
a = −0.872737 + 0.916234I
b = −0.490789 − 1.054630I
0.97153 − 3.65106I 0
u = 1.108780 − 0.425877I
a = −0.872737 − 0.916234I
b = −0.490789 + 1.054630I
0.97153 + 3.65106I 0
u = 1.18971
a = 0.0975768
b = −1.62408
−7.17810 0
u = −0.790199
a = −0.687237
b = −0.309181
−1.20435 −8.00000
u = 0.260780 + 0.729992I
a = −0.81245 − 1.69234I
b = 0.106403 + 0.939014I
0.031297 − 0.283167I −10.47064 + 0.I
u = 0.260780 − 0.729992I
a = −0.81245 + 1.69234I
b = 0.106403 − 0.939014I
0.031297 + 0.283167I −10.47064 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.157150 + 0.429543I
a = 0.58879 + 1.77745I
b = 0.524055 − 1.081700I
−9.59278 + 3.62722I 0
u = −1.157150 − 0.429543I
a = 0.58879 − 1.77745I
b = 0.524055 + 1.081700I
−9.59278 − 3.62722I 0
u = −0.160568 + 0.737142I
a = −0.164412 − 0.618806I
b = 0.730298 + 0.089390I
−5.97152 + 2.38544I −14.0737 − 2.8213I
u = −0.160568 − 0.737142I
a = −0.164412 + 0.618806I
b = 0.730298 − 0.089390I
−5.97152 − 2.38544I −14.0737 + 2.8213I
u = 1.228540 + 0.266915I
a = 0.391803 + 0.241594I
b = 0.562530 − 0.408648I
−4.71575 − 3.09828I 0
u = 1.228540 − 0.266915I
a = 0.391803 − 0.241594I
b = 0.562530 + 0.408648I
−4.71575 + 3.09828I 0
u = −1.267880 + 0.177238I
a = 0.678839 + 0.142037I
b = 0.526237 − 0.977461I
−2.23986 + 3.29378I 0
u = −1.267880 − 0.177238I
a = 0.678839 − 0.142037I
b = 0.526237 + 0.977461I
−2.23986 − 3.29378I 0
u = 1.217560 + 0.402996I
a = 0.814080 − 0.788075I
b = 0.736447 + 1.145140I
−1.56639 − 7.72027I 0
u = 1.217560 − 0.402996I
a = 0.814080 + 0.788075I
b = 0.736447 − 1.145140I
−1.56639 + 7.72027I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.240650 + 0.368915I
a = 0.191262 − 0.405765I
b = −0.519677 + 1.078090I
−6.89673 + 1.47760I 0
u = 1.240650 − 0.368915I
a = 0.191262 + 0.405765I
b = −0.519677 − 1.078090I
−6.89673 − 1.47760I 0
u = 1.259380 + 0.349247I
a = −0.356452 + 0.242013I
b = −0.997759 + 0.233167I
−10.25980 − 6.27168I 0
u = 1.259380 − 0.349247I
a = −0.356452 − 0.242013I
b = −0.997759 − 0.233167I
−10.25980 + 6.27168I 0
u = 0.069586 + 0.678813I
a = 0.359342 − 1.324650I
b = −0.334946 + 1.148020I
1.89522 + 3.59670I −3.22502 − 6.27042I
u = 0.069586 − 0.678813I
a = 0.359342 + 1.324650I
b = −0.334946 − 1.148020I
1.89522 − 3.59670I −3.22502 + 6.27042I
u = −1.207750 + 0.537510I
a = 0.652393 + 1.198970I
b = 0.96200 − 1.24131I
−8.23196 + 10.60790I 0
u = −1.207750 − 0.537510I
a = 0.652393 − 1.198970I
b = 0.96200 + 1.24131I
−8.23196 − 10.60790I 0
u = −0.251619 + 1.300430I
a = 0.087461 + 1.259290I
b = −0.219236 − 0.872762I
1.21797 − 1.00031I 0
u = −0.251619 − 1.300430I
a = 0.087461 − 1.259290I
b = −0.219236 + 0.872762I
1.21797 + 1.00031I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.225120 + 0.503889I
a = −0.58912 − 1.29789I
b = −0.71519 + 1.24236I
−4.07967 + 7.14680I 0
u = −1.225120 − 0.503889I
a = −0.58912 + 1.29789I
b = −0.71519 − 1.24236I
−4.07967 − 7.14680I 0
u = 0.608427 + 0.287937I
a = −0.794839 − 0.362171I
b = 0.77786 − 1.38261I
−8.53694 − 1.57343I −10.60265 + 1.06566I
u = 0.608427 − 0.287937I
a = −0.794839 + 0.362171I
b = 0.77786 + 1.38261I
−8.53694 + 1.57343I −10.60265 − 1.06566I
u = −0.015635 + 1.347280I
a = −0.399900 + 1.334910I
b = 0.584733 − 1.067800I
−10.7431 + 10.3794I 0
u = −0.015635 − 1.347280I
a = −0.399900 − 1.334910I
b = 0.584733 + 1.067800I
−10.7431 − 10.3794I 0
u = 0.618891 + 0.184854I
a = −1.80641 + 2.28001I
b = 0.333765 + 0.342067I
−12.12580 − 5.94770I −17.3706 + 1.5513I
u = 0.618891 − 0.184854I
a = −1.80641 − 2.28001I
b = 0.333765 − 0.342067I
−12.12580 + 5.94770I −17.3706 − 1.5513I
u = −1.171010 + 0.697628I
a = −0.456614 − 1.290590I
b = −0.473878 + 0.657609I
−8.20157 + 2.65755I 0
u = −1.171010 − 0.697628I
a = −0.456614 + 1.290590I
b = −0.473878 − 0.657609I
−8.20157 − 2.65755I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.314220 + 0.407705I
a = 0.928702 − 0.304670I
b = 0.347914 + 0.703563I
−3.57329 − 3.99154I 0
u = 1.314220 − 0.407705I
a = 0.928702 + 0.304670I
b = 0.347914 − 0.703563I
−3.57329 + 3.99154I 0
u = −0.587686 + 0.184049I
a = 0.17715 − 1.94184I
b = −0.143820 + 1.355940I
1.24512 + 2.95965I −17.1971 − 8.3280I
u = −0.587686 − 0.184049I
a = 0.17715 + 1.94184I
b = −0.143820 − 1.355940I
1.24512 − 2.95965I −17.1971 + 8.3280I
u = 1.380920 + 0.295378I
a = −1.091370 + 0.168749I
b = −0.484273 − 0.978684I
−6.97072 − 4.52407I 0
u = 1.380920 − 0.295378I
a = −1.091370 − 0.168749I
b = −0.484273 + 0.978684I
−6.97072 + 4.52407I 0
u = −1.37522 + 0.33577I
a = 0.1227200 + 0.0495155I
b = −1.37069 − 0.43293I
−18.2002 + 9.6383I 0
u = −1.37522 − 0.33577I
a = 0.1227200 − 0.0495155I
b = −1.37069 + 0.43293I
−18.2002 − 9.6383I 0
u = −0.194872 + 0.521399I
a = 1.36940 + 1.36276I
b = 0.294275 − 1.219930I
−2.02000 + 1.29634I −8.59011 − 0.82038I
u = −0.194872 − 0.521399I
a = 1.36940 − 1.36276I
b = 0.294275 + 1.219930I
−2.02000 − 1.29634I −8.59011 + 0.82038I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38278 + 0.47931I
a = −0.922359 − 0.965064I
b = −0.628563 + 1.191530I
−7.44264 + 12.01200I 0
u = −1.38278 − 0.47931I
a = −0.922359 + 0.965064I
b = −0.628563 − 1.191530I
−7.44264 − 12.01200I 0
u = 0.511444 + 0.007065I
a = 1.07473 − 1.61079I
b = −0.455182 − 0.805255I
−5.90476 − 1.88902I −15.6602 + 3.6803I
u = 0.511444 − 0.007065I
a = 1.07473 + 1.61079I
b = −0.455182 + 0.805255I
−5.90476 + 1.88902I −15.6602 − 3.6803I
u = −1.38284 + 0.56555I
a = 0.667751 + 1.008680I
b = 0.533437 − 1.065920I
−2.81814 + 7.51527I 0
u = −1.38284 − 0.56555I
a = 0.667751 − 1.008680I
b = 0.533437 + 1.065920I
−2.81814 − 7.51527I 0
u = −1.47880 + 0.28152I
a = −0.075108 − 0.161487I
b = 1.069950 + 0.176091I
−13.04180 + 3.71273I 0
u = −1.47880 − 0.28152I
a = −0.075108 + 0.161487I
b = 1.069950 − 0.176091I
−13.04180 − 3.71273I 0
u = 1.44289 + 0.58865I
a = −0.589386 + 1.237170I
b = −0.78686 − 1.29449I
−15.4099 − 17.0449I 0
u = 1.44289 − 0.58865I
a = −0.589386 − 1.237170I
b = −0.78686 + 1.29449I
−15.4099 + 17.0449I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.355355 + 0.262107I
a = 3.66678 + 1.73790I
b = −0.569014 − 0.278034I
−7.32083 − 0.05422I −11.26067 − 1.17952I
u = −0.355355 − 0.262107I
a = 3.66678 − 1.73790I
b = −0.569014 + 0.278034I
−7.32083 + 0.05422I −11.26067 + 1.17952I
u = −1.56131 + 0.04903I
a = −0.088615 + 0.389218I
b = −0.401182 + 0.578109I
−15.8959 − 1.9312I 0
u = −1.56131 − 0.04903I
a = −0.088615 − 0.389218I
b = −0.401182 − 0.578109I
−15.8959 + 1.9312I 0
u = 1.33761 + 0.83433I
a = −0.26867 + 1.53959I
b = −0.547204 − 1.071990I
−14.6163 − 1.3587I 0
u = 1.33761 − 0.83433I
a = −0.26867 − 1.53959I
b = −0.547204 + 1.071990I
−14.6163 + 1.3587I 0
u = 1.56303 + 0.21448I
a = −0.176215 + 0.008120I
b = 0.463840 − 0.557066I
−11.32950 + 0.56232I 0
u = 1.56303 − 0.21448I
a = −0.176215 − 0.008120I
b = 0.463840 + 0.557066I
−11.32950 − 0.56232I 0
u = 0.36061 + 1.53955I
a = 0.465321 − 1.193640I
b = −0.470435 + 0.865629I
−5.70209 + 1.92973I 0
u = 0.36061 − 1.53955I
a = 0.465321 + 1.193640I
b = −0.470435 − 0.865629I
−5.70209 − 1.92973I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.49444 + 0.67390I
a = 0.418462 − 1.297480I
b = 0.645589 + 1.257170I
−9.81336 − 9.75749I 0
u = 1.49444 − 0.67390I
a = 0.418462 + 1.297480I
b = 0.645589 − 1.257170I
−9.81336 + 9.75749I 0
u = −0.166447 + 0.307482I
a = −0.978555 + 0.680012I
b = −0.195678 + 0.283655I
−0.483968 + 0.821988I −9.69774 − 8.32847I
u = −0.166447 − 0.307482I
a = −0.978555 − 0.680012I
b = −0.195678 − 0.283655I
−0.483968 − 0.821988I −9.69774 + 8.32847I
u = −1.71826 + 0.47540I
a = 0.209793 + 0.367422I
b = −0.518592 − 0.551800I
−16.2830 − 3.0557I 0
u = −1.71826 − 0.47540I
a = 0.209793 − 0.367422I
b = −0.518592 + 0.551800I
−16.2830 + 3.0557I 0
u = −0.0238705
a = −21.0915
b = −0.653218
−1.50308 −5.69350
14
II.
I
u
2
= h5.09×10
14
u
22
+1.09×10
14
u
21
+· · ·+5.68×10
13
b+2.35×10
15
, −7.81×
10
15
u
22
−1.64×10
15
u
21
+· · ·+2.84×10
14
a−3.68×10
16
, u
23
−7u
21
+· · ·+8u−1i
(i) Arc colorings
a
8
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
5
=
27.4758u
22
+ 5.75630u
21
+ ··· − 426.335u + 129.541
−8.95813u
22
− 1.92472u
21
+ ··· + 137.570u − 41.3526
a
9
=
−u
−u
3
+ u
a
4
=
18.5177u
22
+ 3.83157u
21
+ ··· − 288.765u + 88.1883
−8.95813u
22
− 1.92472u
21
+ ··· + 137.570u − 41.3526
a
2
=
−1.38244u
22
− 0.469686u
21
+ ··· + 25.9438u − 2.00907
−3.87936u
22
− 0.748487u
21
+ ··· + 57.0007u − 19.4066
a
3
=
18.2475u
22
+ 3.81754u
21
+ ··· − 283.192u + 86.3862
−8.62905u
22
− 1.89474u
21
+ ··· + 131.840u − 39.5645
a
11
=
−3.74239u
22
− 0.693224u
21
+ ··· + 49.6503u − 20.1633
3.58600u
22
+ 0.596297u
21
+ ··· − 56.3817u + 19.3097
a
7
=
5.78765u
22
+ 1.12595u
21
+ ··· − 83.2384u + 29.7697
−3.57259u
22
− 0.0187181u
21
+ ··· + 61.7765u − 21.1490
a
10
=
3.91862u
22
+ 0.984338u
21
+ ··· − 61.3344u + 17.2421
−0.381329u
22
+ 0.252476u
21
+ ··· + 10.4275u − 3.02976
a
6
=
2.78803u
22
+ 0.329082u
21
+ ··· − 35.3880u + 16.5738
−4.13662u
22
− 0.829994u
21
+ ··· + 61.2207u − 20.5325
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
7318270583903694
284215974230455
u
22
+
1309447333672492
284215974230455
u
21
+ ··· −
108327404387464633
284215974230455
u +
32848607482929543
284215974230455
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
− 3u
22
+ ··· + 16u − 1
c
2
u
23
+ 7u
22
+ ··· − 4u − 1
c
3
u
23
+ 2u
22
+ ··· + u
2
+ 1
c
4
u
23
− 7u
22
+ ··· − 4u − 1
c
5
u
23
− 7u
22
+ ··· − 4u + 1
c
6
, c
7
u
23
+ 3u
22
+ ··· + 7u + 1
c
8
u
23
− 7u
21
+ ··· + 8u + 1
c
9
u
23
− 2u
22
+ ··· − u
2
− 1
c
10
u
23
− 3u
22
+ ··· + 7u − 1
c
11
u
23
+ 7u
22
+ ··· − 4u + 1
c
12
u
23
− 7u
21
+ ··· + 8u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 7y
22
+ ··· + 22y −1
c
2
, c
5
y
23
− 13y
22
+ ··· + 4y −1
c
3
, c
9
y
23
+ 2y
22
+ ··· − 2y −1
c
4
, c
11
y
23
− 5y
22
+ ··· − 4y −1
c
6
, c
7
, c
10
y
23
− 29y
22
+ ··· + 97y −1
c
8
, c
12
y
23
− 14y
22
+ ··· + 50y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00790
a = −0.459350
b = −2.40493
−3.26795 0.122800
u = 0.287415 + 0.988576I
a = 1.12270 − 1.04490I
b = −0.304008 + 0.988745I
−4.47405 + 1.16683I −9.37780 − 0.15334I
u = 0.287415 − 0.988576I
a = 1.12270 + 1.04490I
b = −0.304008 − 0.988745I
−4.47405 − 1.16683I −9.37780 + 0.15334I
u = −0.752270 + 0.566346I
a = 0.55645 + 2.73540I
b = 0.406570 − 0.830074I
−11.57440 + 6.83134I −12.8239 − 7.5040I
u = −0.752270 − 0.566346I
a = 0.55645 − 2.73540I
b = 0.406570 + 0.830074I
−11.57440 − 6.83134I −12.8239 + 7.5040I
u = 0.053846 + 1.076160I
a = 0.308144 + 1.360130I
b = 0.053171 − 0.922904I
1.61758 + 0.26087I −5.81412 + 0.75603I
u = 0.053846 − 1.076160I
a = 0.308144 − 1.360130I
b = 0.053171 + 0.922904I
1.61758 − 0.26087I −5.81412 − 0.75603I
u = 0.916877
a = −1.01735
b = −2.54439
−8.74085 −32.3250
u = 1.13830
a = 0.0789085
b = −2.31821
−7.53236 −35.2440
u = −0.340767 + 1.096140I
a = −0.572338 − 1.271450I
b = 0.473344 + 0.851645I
−1.76317 − 1.95999I −16.2140 + 4.2831I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.340767 − 1.096140I
a = −0.572338 + 1.271450I
b = 0.473344 − 0.851645I
−1.76317 + 1.95999I −16.2140 − 4.2831I
u = 1.128870 + 0.502364I
a = 1.37474 − 1.15927I
b = 0.174430 + 0.715540I
−7.18576 − 2.12735I −11.11765 + 1.98047I
u = 1.128870 − 0.502364I
a = 1.37474 + 1.15927I
b = 0.174430 − 0.715540I
−7.18576 + 2.12735I −11.11765 − 1.98047I
u = −1.315210 + 0.510566I
a = −0.636833 − 1.187270I
b = −0.741762 + 1.162050I
−5.31790 + 7.73609I −15.4979 − 6.2643I
u = −1.315210 − 0.510566I
a = −0.636833 + 1.187270I
b = −0.741762 − 1.162050I
−5.31790 − 7.73609I −15.4979 + 6.2643I
u = 1.38928 + 0.34223I
a = −0.722896 + 0.271037I
b = −0.480891 − 0.867643I
−3.56509 − 4.84918I −13.3314 + 8.1284I
u = 1.38928 − 0.34223I
a = −0.722896 − 0.271037I
b = −0.480891 + 0.867643I
−3.56509 + 4.84918I −13.3314 − 8.1284I
u = −0.554871
a = −0.624890
b = 0.507385
−2.30602 −17.6770
u = 1.49949
a = −0.379057
b = 0.322041
−11.0674 −9.68470
u = −1.65976 + 0.26119I
a = 0.481768 − 0.023592I
b = −0.081123 − 0.573767I
−15.3549 − 2.6562I −10.86536 + 3.03468I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.65976 − 0.26119I
a = 0.481768 + 0.023592I
b = −0.081123 + 0.573767I
−15.3549 + 2.6562I −10.86536 − 3.03468I
u = 0.212651 + 0.005563I
a = 0.28914 − 4.01886I
b = 0.219322 + 1.288240I
1.56755 − 2.67049I −3.55373 − 3.77681I
u = 0.212651 − 0.005563I
a = 0.28914 + 4.01886I
b = 0.219322 − 1.288240I
1.56755 + 2.67049I −3.55373 + 3.77681I
20
III. I
u
3
= hb + 1, a + 1, u + 1i
(i) Arc colorings
a
8
=
0
−1
a
12
=
1
0
a
1
=
1
1
a
5
=
−1
−1
a
9
=
1
0
a
4
=
−2
−1
a
2
=
−1
0
a
3
=
−1
−1
a
11
=
0
−1
a
7
=
0
−1
a
10
=
0
−1
a
6
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
8
u − 1
c
5
, c
9
, c
11
c
12
u + 1
c
6
, c
7
, c
10
u
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
c
9
, c
11
, c
12
y −1
c
6
, c
7
, c
10
y
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −1.00000
b = −1.00000
−3.28987 −12.0000
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
23
− 3u
22
+ ··· + 16u − 1)
· (u
97
− 13u
96
+ ··· + 83802u − 29149)
c
2
(u − 1)(u
23
+ 7u
22
+ ··· − 4u − 1)(u
97
− u
96
+ ··· − 22184u − 2161)
c
3
(u − 1)(u
23
+ 2u
22
+ ··· + u
2
+ 1)(u
97
− 14u
96
+ ··· + 1812u − 149)
c
4
(u − 1)(u
23
− 7u
22
+ ··· − 4u − 1)(u
97
− 3u
96
+ ··· − 356u − 59)
c
5
(u + 1)(u
23
− 7u
22
+ ··· − 4u + 1)(u
97
− u
96
+ ··· − 22184u − 2161)
c
6
, c
7
u(u
23
+ 3u
22
+ ··· + 7u + 1)(u
97
+ 4u
96
+ ··· + 4242u + 242)
c
8
(u − 1)(u
23
− 7u
21
+ ··· + 8u + 1)(u
97
− 2u
96
+ ··· + 1714u + 41)
c
9
(u + 1)(u
23
− 2u
22
+ ··· − u
2
− 1)(u
97
− 14u
96
+ ··· + 1812u − 149)
c
10
u(u
23
− 3u
22
+ ··· + 7u − 1)(u
97
+ 4u
96
+ ··· + 4242u + 242)
c
11
(u + 1)(u
23
+ 7u
22
+ ··· − 4u + 1)(u
97
− 3u
96
+ ··· − 356u − 59)
c
12
(u + 1)(u
23
− 7u
21
+ ··· + 8u − 1)(u
97
− 2u
96
+ ··· + 1714u + 41)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
23
− 7y
22
+ ··· + 22y −1)
· (y
97
− 37y
96
+ ··· + 128682539484y −849664201)
c
2
, c
5
(y −1)(y
23
− 13y
22
+ ··· + 4y −1)
· (y
97
− 79y
96
+ ··· + 423448954y −4669921)
c
3
, c
9
(y −1)(y
23
+ 2y
22
+ ··· − 2y −1)
· (y
97
− 3452y
95
+ ··· − 696744y −22201)
c
4
, c
11
(y −1)(y
23
− 5y
22
+ ··· − 4y −1)(y
97
− 47y
96
+ ··· − 64542y −3481)
c
6
, c
7
, c
10
y(y
23
− 29y
22
+ ··· + 97y −1)
· (y
97
− 110y
96
+ ··· + 17376496y −58564)
c
8
, c
12
(y −1)(y
23
− 14y
22
+ ··· + 50y −1)
· (y
97
− 68y
96
+ ··· + 2983388y −1681)
26
