12a
0213
(K12a
0213
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 8 2 1 11 12 4 5 10
Solving Sequence
2,7
6 3
4,10
11 1 8 5 12 9
c
6
c
2
c
3
c
10
c
1
c
7
c
5
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.64097 × 10
40
u
124
+ 4.69661 × 10
39
u
123
+ ··· + 3.19533 × 10
40
b − 5.54363 × 10
39
,
9.07447 × 10
40
u
124
+ 6.60265 × 10
40
u
123
+ ··· + 3.19533 × 10
40
a − 5.09071 × 10
40
, u
125
+ 2u
124
+ ··· + u − 1i
I
u
2
= hb − 1, a + 2u − 1, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 127 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−2.64 × 10
40
u
124
+ 4.70 × 10
39
u
123
+ · · · + 3.20 × 10
40
b − 5.54 ×
10
39
, 9.07 × 10
40
u
124
+ 6.60 × 10
40
u
123
+ · · · + 3.20 × 10
40
a − 5.09 ×
10
40
, u
125
+ 2u
124
+ · · · + u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
−2.83992u
124
− 2.06634u
123
+ ··· + 4.13510u + 1.59317
0.826508u
124
− 0.146984u
123
+ ··· + 1.45976u + 0.173492
a
11
=
−1.24000u
124
− 0.706679u
123
+ ··· + 2.85485u + 1.83334
0.266675u
124
+ 0.333348u
123
+ ··· + 1.70001u − 0.0666735
a
1
=
u
3
u
5
+ u
3
+ u
a
8
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
5
=
u
16
+ 3u
14
+ 5u
12
+ 4u
10
+ 3u
8
+ 2u
6
+ 2u
4
+ 1
u
18
+ 4u
16
+ 9u
14
+ 12u
12
+ 11u
10
+ 6u
8
+ 2u
6
+ u
2
a
12
=
−2.64004u
124
− 1.56683u
123
+ ··· + 5.84349u + 1.44341
0.726745u
124
− 0.346510u
123
+ ··· + 2.01012u + 0.273255
a
9
=
−0.599959u
124
− 1.83317u
123
+ ··· − 3.19932u + 0.516585
0.833251u
124
+ 1.66650u
123
+ ··· + 0.949878u − 0.833252
(ii) Obstruction class = −1
(iii) Cusp Shapes = 10.6193u
124
+ 2.39865u
123
+ ··· − 23.1870u + 3.66068
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
125
+ 60u
124
+ ··· + u − 1
c
2
, c
6
u
125
− 2u
124
+ ··· + u + 1
c
3
u
125
+ 2u
124
+ ··· − 16983u + 4113
c
4
u
125
+ 4u
124
+ ··· − u − 1
c
5
u
125
+ 12u
124
+ ··· + 5527915u + 76501
c
7
u
125
− 5u
124
+ ··· − 1824u + 576
c
8
u
125
+ 21u
124
+ ··· − 4u + 4
c
9
, c
12
u
125
− 3u
124
+ ··· + 4u + 1
c
10
u
125
+ 40u
123
+ ··· + 797687u + 83807
c
11
u
125
+ 2u
124
+ ··· − 94633u + 20921
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
125
+ 12y
124
+ ··· + 93y −1
c
2
, c
6
y
125
+ 60y
124
+ ··· + y −1
c
3
y
125
− 36y
124
+ ··· + 355661613y −16916769
c
4
y
125
− 20y
124
+ ··· + y −1
c
5
y
125
+ 72y
124
+ ··· + 18972461202289y −5852403001
c
7
y
125
+ 7y
124
+ ··· − 23886720y −331776
c
8
y
125
+ 15y
124
+ ··· − 312y −16
c
9
, c
12
y
125
− 91y
124
+ ··· − 80y −1
c
10
y
125
+ 80y
124
+ ··· − 960105157739y −7023613249
c
11
y
125
+ 152y
124
+ ··· − 25666758211y −437688241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.679728 + 0.699024I
a = 0.120952 + 0.299129I
b = 1.057920 − 0.438992I
−1.66051 − 3.41079I 0
u = −0.679728 − 0.699024I
a = 0.120952 − 0.299129I
b = 1.057920 + 0.438992I
−1.66051 + 3.41079I 0
u = 0.417169 + 0.960639I
a = 0.06438 − 2.91642I
b = 1.48058 + 1.21311I
−3.43724 + 0.22308I 0
u = 0.417169 − 0.960639I
a = 0.06438 + 2.91642I
b = 1.48058 − 1.21311I
−3.43724 − 0.22308I 0
u = 0.042794 + 1.048360I
a = −0.93427 + 1.89066I
b = 0.499129 − 0.925280I
−3.55440 − 4.88679I 0
u = 0.042794 − 1.048360I
a = −0.93427 − 1.89066I
b = 0.499129 + 0.925280I
−3.55440 + 4.88679I 0
u = 0.527401 + 0.911523I
a = 0.83347 − 1.82848I
b = 0.323242 + 1.049860I
0.87667 − 1.63345I 0
u = 0.527401 − 0.911523I
a = 0.83347 + 1.82848I
b = 0.323242 − 1.049860I
0.87667 + 1.63345I 0
u = 0.654295 + 0.680316I
a = −0.249155 + 0.077471I
b = −1.84244 − 0.49259I
−2.79139 + 11.94370I 0
u = 0.654295 − 0.680316I
a = −0.249155 − 0.077471I
b = −1.84244 + 0.49259I
−2.79139 − 11.94370I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.588695 + 0.882150I
a = 0.62229 + 2.26840I
b = −1.382160 + 0.020555I
−3.39116 − 7.10514I 0
u = 0.588695 − 0.882150I
a = 0.62229 − 2.26840I
b = −1.382160 − 0.020555I
−3.39116 + 7.10514I 0
u = −0.302084 + 0.884500I
a = 1.315450 + 0.128898I
b = −0.350582 − 0.042146I
−0.17063 − 1.54245I 0
u = −0.302084 − 0.884500I
a = 1.315450 − 0.128898I
b = −0.350582 + 0.042146I
−0.17063 + 1.54245I 0
u = −0.632357 + 0.885540I
a = −0.657986 + 0.942609I
b = 0.893003 + 0.248469I
−2.20410 − 1.63394I 0
u = −0.632357 − 0.885540I
a = −0.657986 − 0.942609I
b = 0.893003 − 0.248469I
−2.20410 + 1.63394I 0
u = −0.481245 + 0.989878I
a = −2.15411 − 5.32330I
b = −1.79483 + 1.92968I
−1.99408 − 2.49462I 0
u = −0.481245 − 0.989878I
a = −2.15411 + 5.32330I
b = −1.79483 − 1.92968I
−1.99408 + 2.49462I 0
u = 0.614840 + 0.651355I
a = −0.202010 + 0.487116I
b = 1.083140 − 0.651367I
1.63436 + 6.18286I 0
u = 0.614840 − 0.651355I
a = −0.202010 − 0.487116I
b = 1.083140 + 0.651367I
1.63436 − 6.18286I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.523488 + 0.974857I
a = 0.535106 − 0.492195I
b = −0.180160 − 0.006470I
0.13723 − 2.50988I 0
u = −0.523488 − 0.974857I
a = 0.535106 + 0.492195I
b = −0.180160 + 0.006470I
0.13723 + 2.50988I 0
u = −0.714997 + 0.510109I
a = 0.136421 + 0.179960I
b = 1.06493 − 0.99596I
1.69136 − 3.90937I 0
u = −0.714997 − 0.510109I
a = 0.136421 − 0.179960I
b = 1.06493 + 0.99596I
1.69136 + 3.90937I 0
u = 0.560497 + 0.671639I
a = −0.212247 − 0.432133I
b = 1.86870 + 0.04556I
−2.79087 + 3.80135I 0
u = 0.560497 − 0.671639I
a = −0.212247 + 0.432133I
b = 1.86870 − 0.04556I
−2.79087 − 3.80135I 0
u = 0.455975 + 1.040590I
a = −0.820468 − 0.637657I
b = 1.48309 − 0.44923I
−4.48448 + 3.27623I 0
u = 0.455975 − 1.040590I
a = −0.820468 + 0.637657I
b = 1.48309 + 0.44923I
−4.48448 − 3.27623I 0
u = 0.730308 + 0.453581I
a = 0.061004 + 0.200975I
b = 0.70357 − 1.47380I
1.41787 − 6.41870I 0. + 6.69453I
u = 0.730308 − 0.453581I
a = 0.061004 − 0.200975I
b = 0.70357 + 1.47380I
1.41787 + 6.41870I 0. − 6.69453I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.799477 + 0.308689I
a = 0.020614 + 0.223738I
b = 1.24228 − 1.00231I
−3.69917 − 5.73455I −6.85671 + 7.09378I
u = 0.799477 − 0.308689I
a = 0.020614 − 0.223738I
b = 1.24228 + 1.00231I
−3.69917 + 5.73455I −6.85671 − 7.09378I
u = −0.506487 + 1.025740I
a = 3.00969 + 3.23214I
b = 0.07486 − 2.30546I
−1.62403 − 3.30259I 0
u = −0.506487 − 1.025740I
a = 3.00969 − 3.23214I
b = 0.07486 + 2.30546I
−1.62403 + 3.30259I 0
u = −0.597525 + 0.607423I
a = 0.216601 + 0.430183I
b = −0.316208 + 0.286686I
1.21505 − 1.94918I 0. + 2.49347I
u = −0.597525 − 0.607423I
a = 0.216601 − 0.430183I
b = −0.316208 − 0.286686I
1.21505 + 1.94918I 0. − 2.49347I
u = 0.262991 + 1.120360I
a = 0.663394 − 1.183930I
b = −0.044368 + 1.250050I
−4.46336 − 0.92541I 0
u = 0.262991 − 1.120360I
a = 0.663394 + 1.183930I
b = −0.044368 − 1.250050I
−4.46336 + 0.92541I 0
u = −0.785970 + 0.311936I
a = −0.141515 + 0.120432I
b = −2.20613 − 1.49290I
−4.6627 + 14.1117I −2.00000 − 7.82782I
u = −0.785970 − 0.311936I
a = −0.141515 − 0.120432I
b = −2.20613 + 1.49290I
−4.6627 − 14.1117I −2.00000 + 7.82782I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.308513 + 1.114810I
a = −1.68383 − 0.24557I
b = 1.46021 − 0.59103I
−4.94453 + 0.88598I 0
u = 0.308513 − 1.114810I
a = −1.68383 + 0.24557I
b = 1.46021 + 0.59103I
−4.94453 − 0.88598I 0
u = 0.285561 + 1.125560I
a = 4.55270 + 1.54514I
b = −3.76181 − 0.48262I
−6.48680 − 0.11053I 0
u = 0.285561 − 1.125560I
a = 4.55270 − 1.54514I
b = −3.76181 + 0.48262I
−6.48680 + 0.11053I 0
u = −0.256396 + 1.138060I
a = −2.30114 + 0.08256I
b = 1.43263 + 0.94921I
−4.43460 + 5.17173I 0
u = −0.256396 − 1.138060I
a = −2.30114 − 0.08256I
b = 1.43263 − 0.94921I
−4.43460 − 5.17173I 0
u = 0.458197 + 0.695142I
a = 0.27253 − 1.95867I
b = 0.965335 + 0.595467I
−3.15790 + 0.22084I −8.49031 − 0.86101I
u = 0.458197 − 0.695142I
a = 0.27253 + 1.95867I
b = 0.965335 − 0.595467I
−3.15790 − 0.22084I −8.49031 + 0.86101I
u = −0.278408 + 1.139920I
a = −2.84647 − 1.31941I
b = 1.15327 + 1.56068I
−8.80406 + 2.32103I 0
u = −0.278408 − 1.139920I
a = −2.84647 + 1.31941I
b = 1.15327 − 1.56068I
−8.80406 − 2.32103I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.507293 + 1.059410I
a = −2.35206 + 1.55375I
b = 0.37284 − 2.22618I
−2.52029 + 6.06447I 0
u = 0.507293 − 1.059410I
a = −2.35206 − 1.55375I
b = 0.37284 + 2.22618I
−2.52029 − 6.06447I 0
u = −0.297301 + 1.138330I
a = −0.456658 − 0.640099I
b = −0.259830 − 0.236853I
−9.01723 − 1.79866I 0
u = −0.297301 − 1.138330I
a = −0.456658 + 0.640099I
b = −0.259830 + 0.236853I
−9.01723 + 1.79866I 0
u = −0.322370 + 1.131930I
a = 1.349850 − 0.187015I
b = −0.795345 − 0.943236I
−5.16933 − 4.76940I 0
u = −0.322370 − 1.131930I
a = 1.349850 + 0.187015I
b = −0.795345 + 0.943236I
−5.16933 + 4.76940I 0
u = −0.757754 + 0.311437I
a = 0.054965 + 0.391931I
b = 1.99098 + 0.29231I
0.00638 + 8.05941I −1.16635 − 7.77341I
u = −0.757754 − 0.311437I
a = 0.054965 − 0.391931I
b = 1.99098 − 0.29231I
0.00638 − 8.05941I −1.16635 + 7.77341I
u = 0.556429 + 1.041740I
a = −0.34386 + 2.59385I
b = −1.61019 − 1.15977I
2.38931 + 6.68336I 0
u = 0.556429 − 1.041740I
a = −0.34386 − 2.59385I
b = −1.61019 + 1.15977I
2.38931 − 6.68336I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.538815 + 0.616206I
a = −2.15717 − 0.62315I
b = −2.66750 − 1.24723I
−0.88644 − 1.62714I 17.6831 − 19.5128I
u = −0.538815 − 0.616206I
a = −2.15717 + 0.62315I
b = −2.66750 + 1.24723I
−0.88644 + 1.62714I 17.6831 + 19.5128I
u = −0.242591 + 1.161340I
a = 2.94505 + 1.49559I
b = −1.60809 − 1.71649I
−9.2942 + 11.1311I 0
u = −0.242591 − 1.161340I
a = 2.94505 − 1.49559I
b = −1.60809 + 1.71649I
−9.2942 − 11.1311I 0
u = 0.653640 + 0.479882I
a = −0.174699 + 0.330105I
b = −1.61922 + 0.67646I
4.03606 − 1.95840I 5.40020 + 2.12576I
u = 0.653640 − 0.479882I
a = −0.174699 − 0.330105I
b = −1.61922 − 0.67646I
4.03606 + 1.95840I 5.40020 − 2.12576I
u = −0.596610 + 1.032710I
a = −1.54569 + 0.73226I
b = 1.158340 + 0.743651I
0.152957 − 1.109810I 0
u = −0.596610 − 1.032710I
a = −1.54569 − 0.73226I
b = 1.158340 − 0.743651I
0.152957 + 1.109810I 0
u = 0.738104 + 0.319751I
a = −0.062585 + 0.404238I
b = −0.547597 + 0.963150I
−0.13708 − 3.70904I −0.37034 + 1.40434I
u = 0.738104 − 0.319751I
a = −0.062585 − 0.404238I
b = −0.547597 − 0.963150I
−0.13708 + 3.70904I −0.37034 − 1.40434I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.238691 + 1.173180I
a = −1.74345 + 1.16783I
b = 0.869383 − 1.084780I
−8.40775 − 2.68887I 0
u = 0.238691 − 1.173180I
a = −1.74345 − 1.16783I
b = 0.869383 + 1.084780I
−8.40775 + 2.68887I 0
u = −0.676930 + 0.423743I
a = 0.021492 + 0.350755I
b = −1.51090 − 0.16761I
3.78834 − 0.01819I 5.34389 + 0.31518I
u = −0.676930 − 0.423743I
a = 0.021492 − 0.350755I
b = −1.51090 + 0.16761I
3.78834 + 0.01819I 5.34389 − 0.31518I
u = −0.743871 + 0.288769I
a = −0.243464 − 0.168390I
b = 1.94501 + 1.38998I
−4.51308 + 5.31615I −7.83628 − 6.20055I
u = −0.743871 − 0.288769I
a = −0.243464 + 0.168390I
b = 1.94501 − 1.38998I
−4.51308 − 5.31615I −7.83628 + 6.20055I
u = −0.558215 + 1.072220I
a = 0.55939 − 2.37919I
b = −1.44362 + 0.58926I
1.89272 − 4.76849I 0
u = −0.558215 − 1.072220I
a = 0.55939 + 2.37919I
b = −1.44362 − 0.58926I
1.89272 + 4.76849I 0
u = −0.340644 + 1.163610I
a = 0.237640 − 0.493467I
b = 0.034493 + 1.011380I
−10.4687 − 10.1396I 0
u = −0.340644 − 1.163610I
a = 0.237640 + 0.493467I
b = 0.034493 − 1.011380I
−10.4687 + 10.1396I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.587202 + 1.067570I
a = 1.61895 − 1.96051I
b = 0.47226 + 1.69869I
−0.39121 + 11.44140I 0
u = 0.587202 − 1.067570I
a = 1.61895 + 1.96051I
b = 0.47226 − 1.69869I
−0.39121 − 11.44140I 0
u = 0.723221 + 0.295010I
a = −0.64670 − 1.32341I
b = −3.66740 − 0.92458I
−2.31097 − 3.02394I 15.4166 − 6.5863I
u = 0.723221 − 0.295010I
a = −0.64670 + 1.32341I
b = −3.66740 + 0.92458I
−2.31097 + 3.02394I 15.4166 + 6.5863I
u = 0.350810 + 1.173570I
a = −0.563732 − 0.198462I
b = 0.020877 + 0.351961I
−9.79515 + 1.43995I 0
u = 0.350810 − 1.173570I
a = −0.563732 + 0.198462I
b = 0.020877 − 0.351961I
−9.79515 − 1.43995I 0
u = −0.724995 + 0.268071I
a = −0.558292 − 0.965632I
b = −0.079967 + 0.440838I
−4.88103 + 1.27243I −8.99250 + 0.12894I
u = −0.724995 − 0.268071I
a = −0.558292 + 0.965632I
b = −0.079967 − 0.440838I
−4.88103 − 1.27243I −8.99250 − 0.12894I
u = 0.753049 + 0.147045I
a = −0.752425 + 0.367568I
b = 0.173370 + 0.028941I
−5.85796 − 2.23562I −10.68167 + 2.74645I
u = 0.753049 − 0.147045I
a = −0.752425 − 0.367568I
b = 0.173370 − 0.028941I
−5.85796 + 2.23562I −10.68167 − 2.74645I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.536312 + 1.117790I
a = −1.40779 − 1.95839I
b = 2.14740 − 0.18715I
−3.39435 + 6.72398I 0
u = 0.536312 − 1.117790I
a = −1.40779 + 1.95839I
b = 2.14740 + 0.18715I
−3.39435 − 6.72398I 0
u = −0.739162 + 0.175015I
a = 0.771899 + 0.922373I
b = 0.067243 + 0.437011I
−6.51335 − 6.60957I −5.62101 + 4.12467I
u = −0.739162 − 0.175015I
a = 0.771899 − 0.922373I
b = 0.067243 − 0.437011I
−6.51335 + 6.60957I −5.62101 − 4.12467I
u = −0.524578 + 1.125060I
a = 1.08312 − 1.35457I
b = −1.69848 + 0.30164I
−3.80007 − 3.00363I 0
u = −0.524578 − 1.125060I
a = 1.08312 + 1.35457I
b = −1.69848 − 0.30164I
−3.80007 + 3.00363I 0
u = 0.546770 + 1.125950I
a = 3.64704 + 4.31957I
b = −3.93131 + 0.93753I
−4.71854 + 7.85425I 0
u = 0.546770 − 1.125950I
a = 3.64704 − 4.31957I
b = −3.93131 − 0.93753I
−4.71854 − 7.85425I 0
u = −0.539702 + 1.131940I
a = 0.464154 + 0.756708I
b = −0.478007 − 0.590823I
−7.37528 − 6.06661I 0
u = −0.539702 − 1.131940I
a = 0.464154 − 0.756708I
b = −0.478007 + 0.590823I
−7.37528 + 6.06661I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.557323 + 1.123800I
a = −0.75957 + 1.33123I
b = −0.73436 − 1.21005I
−2.48314 + 8.62396I 0
u = 0.557323 − 1.123800I
a = −0.75957 − 1.33123I
b = −0.73436 + 1.21005I
−2.48314 − 8.62396I 0
u = −0.508559 + 1.151200I
a = 0.612855 + 0.045245I
b = 0.467583 − 0.421339I
−9.32943 + 1.96630I 0
u = −0.508559 − 1.151200I
a = 0.612855 − 0.045245I
b = 0.467583 + 0.421339I
−9.32943 − 1.96630I 0
u = −0.549823 + 1.133070I
a = −0.00851 + 3.64990I
b = 2.09455 − 1.85308I
−6.97130 − 10.20430I 0
u = −0.549823 − 1.133070I
a = −0.00851 − 3.64990I
b = 2.09455 + 1.85308I
−6.97130 + 10.20430I 0
u = 0.681358 + 0.286026I
a = 0.643069 − 0.107415I
b = 1.57186 + 0.33127I
−1.01732 − 2.03022I −3.09406 + 4.57319I
u = 0.681358 − 0.286026I
a = 0.643069 + 0.107415I
b = 1.57186 − 0.33127I
−1.01732 + 2.03022I −3.09406 − 4.57319I
u = 0.499047 + 1.158250I
a = −0.487226 − 0.417308I
b = −0.0464337 + 0.1279410I
−8.78961 + 6.84987I 0
u = 0.499047 − 1.158250I
a = −0.487226 + 0.417308I
b = −0.0464337 − 0.1279410I
−8.78961 − 6.84987I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.560115 + 1.131450I
a = −1.19225 + 2.47759I
b = 2.39723 − 0.55290I
−2.39559 − 13.02930I 0
u = −0.560115 − 1.131450I
a = −1.19225 − 2.47759I
b = 2.39723 + 0.55290I
−2.39559 + 13.02930I 0
u = −0.530131 + 0.510836I
a = 0.772832 − 0.714498I
b = 0.53127 + 1.62919I
−0.099793 − 0.946670I −4.33653 + 4.47517I
u = −0.530131 − 0.510836I
a = 0.772832 + 0.714498I
b = 0.53127 − 1.62919I
−0.099793 + 0.946670I −4.33653 − 4.47517I
u = −0.568330 + 1.140120I
a = −0.11986 − 3.80079I
b = −2.38820 + 1.80200I
−7.1053 − 19.1835I 0
u = −0.568330 − 1.140120I
a = −0.11986 + 3.80079I
b = −2.38820 − 1.80200I
−7.1053 + 19.1835I 0
u = −0.683738 + 0.235270I
a = 0.016220 − 0.779945I
b = −1.108470 − 0.100376I
−1.28643 − 1.61583I −3.37728 + 3.87828I
u = −0.683738 − 0.235270I
a = 0.016220 + 0.779945I
b = −1.108470 + 0.100376I
−1.28643 + 1.61583I −3.37728 − 3.87828I
u = 0.570742 + 1.145300I
a = 0.19435 − 2.38956I
b = 1.34157 + 1.20026I
−6.17469 + 10.84830I 0
u = 0.570742 − 1.145300I
a = 0.19435 + 2.38956I
b = 1.34157 − 1.20026I
−6.17469 − 10.84830I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.122967 + 0.694323I
a = 1.248320 − 0.464863I
b = −0.377367 + 0.449759I
−0.15596 − 1.46517I −2.11111 + 4.06907I
u = −0.122967 − 0.694323I
a = 1.248320 + 0.464863I
b = −0.377367 − 0.449759I
−0.15596 + 1.46517I −2.11111 − 4.06907I
u = 0.529500 + 0.371661I
a = 0.750806 − 0.075379I
b = 0.14713 + 1.53695I
−0.59609 − 1.80402I −2.50103 + 5.03505I
u = 0.529500 − 0.371661I
a = 0.750806 + 0.075379I
b = 0.14713 − 1.53695I
−0.59609 + 1.80402I −2.50103 − 5.03505I
u = 0.299372
a = 3.72513
b = 0.723367
−2.39057 −2.96710
17
II. I
u
2
= hb − 1, a + 2u − 1, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u − 1
a
3
=
u
u − 1
a
4
=
1
u − 1
a
10
=
−2u + 1
1
a
11
=
−u + 1
0
a
1
=
−1
0
a
8
=
1
0
a
5
=
−u + 2
u − 1
a
12
=
−2u
1
a
9
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u − 1
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
10
c
11
u
2
− u + 1
c
2
u
2
+ u + 1
c
7
, c
8
u
2
c
9
(u − 1)
2
c
12
(u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
10
, c
11
y
2
+ y + 1
c
7
, c
8
y
2
c
9
, c
12
(y −1)
2
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = − 1.73205I
b = 1.00000
−1.64493 + 2.02988I −3.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 1.73205I
b = 1.00000
−1.64493 − 2.02988I −3.00000 + 3.46410I
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
125
+ 60u
124
+ ··· + u − 1)
c
2
(u
2
+ u + 1)(u
125
− 2u
124
+ ··· + u + 1)
c
3
(u
2
− u + 1)(u
125
+ 2u
124
+ ··· − 16983u + 4113)
c
4
(u
2
− u + 1)(u
125
+ 4u
124
+ ··· − u − 1)
c
5
(u
2
− u + 1)(u
125
+ 12u
124
+ ··· + 5527915u + 76501)
c
6
(u
2
− u + 1)(u
125
− 2u
124
+ ··· + u + 1)
c
7
u
2
(u
125
− 5u
124
+ ··· − 1824u + 576)
c
8
u
2
(u
125
+ 21u
124
+ ··· − 4u + 4)
c
9
((u − 1)
2
)(u
125
− 3u
124
+ ··· + 4u + 1)
c
10
(u
2
− u + 1)(u
125
+ 40u
123
+ ··· + 797687u + 83807)
c
11
(u
2
− u + 1)(u
125
+ 2u
124
+ ··· − 94633u + 20921)
c
12
((u + 1)
2
)(u
125
− 3u
124
+ ··· + 4u + 1)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
2
+ y + 1)(y
125
+ 12y
124
+ ··· + 93y −1)
c
2
, c
6
(y
2
+ y + 1)(y
125
+ 60y
124
+ ··· + y −1)
c
3
(y
2
+ y + 1)(y
125
− 36y
124
+ ··· + 3.55662 × 10
8
y −1.69168 × 10
7
)
c
4
(y
2
+ y + 1)(y
125
− 20y
124
+ ··· + y −1)
c
5
(y
2
+ y + 1)(y
125
+ 72y
124
+ ··· + 1.89725 × 10
13
y −5.85240 × 10
9
)
c
7
y
2
(y
125
+ 7y
124
+ ··· − 2.38867 × 10
7
y −331776)
c
8
y
2
(y
125
+ 15y
124
+ ··· − 312y −16)
c
9
, c
12
((y −1)
2
)(y
125
− 91y
124
+ ··· − 80y −1)
c
10
(y
2
+ y + 1)(y
125
+ 80y
124
+ ··· − 9.60105 × 10
11
y −7.02361 × 10
9
)
c
11
(y
2
+ y + 1)(y
125
+ 152y
124
+ ··· − 2.56668 × 10
10
y −4.37688 × 10
8
)
23
