12a
0586
(K12a
0586
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 12 2 11 5 4 1 6 8
Solving Sequence
3,9
4 10
5,7
2 1 11 6 8 12
c
3
c
9
c
4
c
2
c
1
c
10
c
6
c
8
c
12
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.31307 × 10
165
u
121
+ 5.38073 × 10
164
u
120
+ ··· + 4.90444 × 10
165
b − 6.70880 × 10
165
,
− 3.23704 × 10
165
u
121
− 2.41638 × 10
165
u
120
+ ··· + 4.90444 × 10
165
a + 1.05285 × 10
166
,
u
122
− u
121
+ ··· + 14u − 1i
I
u
2
= hu
20
− 8u
18
+ ··· + b − 1, 2u
20
− u
19
+ ··· + a − 7, u
21
− 10u
19
+ ··· − 7u + 1i
* 2 irreducible components of dim
C
= 0, with total 143 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
= h2.31 × 10
165
u
121
+ 5.38 × 10
164
u
120
+ · · · + 4.90 × 10
165
b − 6.71 ×
10
165
, −3.24 × 10
165
u
121
− 2.42 × 10
165
u
120
+ · · · + 4.90 × 10
165
a + 1.05 ×
10
166
, u
122
− u
121
+ · · · + 14u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
0.660022u
121
+ 0.492694u
120
+ ··· − 53.1593u − 2.14673
−0.471629u
121
− 0.109712u
120
+ ··· − 3.50950u + 1.36790
a
2
=
−0.743016u
121
− 0.880764u
120
+ ··· + 5.83100u + 8.73557
0.0920455u
121
+ 0.774925u
120
+ ··· + 13.2435u − 1.69094
a
1
=
−0.650971u
121
− 0.105839u
120
+ ··· + 19.0745u + 7.04462
0.0920455u
121
+ 0.774925u
120
+ ··· + 13.2435u − 1.69094
a
11
=
2.30111u
121
+ 0.0727856u
120
+ ··· − 140.337u + 6.38639
−0.887005u
121
+ 0.100156u
120
+ ··· + 24.1947u − 0.623252
a
6
=
−0.308103u
121
− 0.0346067u
120
+ ··· − 134.651u + 11.8650
−0.749272u
121
+ 1.31527u
120
+ ··· + 18.1101u − 0.0215096
a
8
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
12
=
−1.05192u
121
− 0.921213u
120
+ ··· + 24.4218u + 6.68467
0.194588u
121
+ 0.843786u
120
+ ··· + 12.8019u − 1.63077
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.935769u
121
− 0.911728u
120
+ ··· − 17.5892u − 7.15303
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
122
+ 46u
121
+ ··· + 56468u + 841
c
2
, c
6
u
122
− 2u
121
+ ··· + 18u + 29
c
3
, c
4
, c
9
u
122
− u
121
+ ··· + 14u − 1
c
5
, c
11
u
122
− u
121
+ ··· + 35u − 1
c
7
u
122
+ 8u
121
+ ··· − 298520u − 40207
c
8
u
122
+ 3u
121
+ ··· − 10052u + 949
c
10
u
122
− 20u
121
+ ··· − 18800u + 1457
c
12
u
122
− 2u
121
+ ··· − 1232502u − 100871
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
122
+ 70y
121
+ ··· − 130799392y + 707281
c
2
, c
6
y
122
− 46y
121
+ ··· − 56468y + 841
c
3
, c
4
, c
9
y
122
− 105y
121
+ ··· + 116y + 1
c
5
, c
11
y
122
+ 99y
121
+ ··· + 173y + 1
c
7
y
122
+ 34y
121
+ ··· + 9443298764y + 1616602849
c
8
y
122
+ 59y
121
+ ··· + 89191938y + 900601
c
10
y
122
+ 18y
121
+ ··· − 67920452y + 2122849
c
12
y
122
+ 30y
121
+ ··· + 188566629184y + 10174958641
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.234555 + 0.988031I
a = 0.92156 + 1.12342I
b = −0.872223 − 0.630867I
5.72527 − 1.28507I 0
u = −0.234555 − 0.988031I
a = 0.92156 − 1.12342I
b = −0.872223 + 0.630867I
5.72527 + 1.28507I 0
u = 0.760590 + 0.674896I
a = −0.316027 + 0.926892I
b = 0.686502 − 0.641692I
4.42128 − 1.94594I 0
u = 0.760590 − 0.674896I
a = −0.316027 − 0.926892I
b = 0.686502 + 0.641692I
4.42128 + 1.94594I 0
u = 0.322630 + 0.970146I
a = 0.10806 + 1.82890I
b = −0.828609 − 0.630177I
5.86251 − 3.65151I 0
u = 0.322630 − 0.970146I
a = 0.10806 − 1.82890I
b = −0.828609 + 0.630177I
5.86251 + 3.65151I 0
u = −0.214504 + 0.861105I
a = 0.44544 − 2.29325I
b = −1.099800 + 0.728566I
6.9239 + 14.0853I 0
u = −0.214504 − 0.861105I
a = 0.44544 + 2.29325I
b = −1.099800 − 0.728566I
6.9239 − 14.0853I 0
u = −1.001190 + 0.502220I
a = −0.467524 − 0.781643I
b = 1.068540 + 0.711550I
4.50697 − 9.26659I 0
u = −1.001190 − 0.502220I
a = −0.467524 + 0.781643I
b = 1.068540 − 0.711550I
4.50697 + 9.26659I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.030580 + 0.445182I
a = 0.13785 − 1.45127I
b = 0.610203 + 0.880621I
5.91876 + 3.36739I 0
u = 1.030580 − 0.445182I
a = 0.13785 + 1.45127I
b = 0.610203 − 0.880621I
5.91876 − 3.36739I 0
u = −1.107230 + 0.202197I
a = 0.353996 − 0.891172I
b = −0.690022 + 0.709843I
0.251889 + 0.777032I 0
u = −1.107230 − 0.202197I
a = 0.353996 + 0.891172I
b = −0.690022 − 0.709843I
0.251889 − 0.777032I 0
u = −0.915379 + 0.675967I
a = 0.02342 + 1.50127I
b = 0.959430 − 0.636264I
3.60956 + 6.96571I 0
u = −0.915379 − 0.675967I
a = 0.02342 − 1.50127I
b = 0.959430 + 0.636264I
3.60956 − 6.96571I 0
u = 0.186110 + 0.839501I
a = 1.18588 − 1.51108I
b = −0.588144 + 0.942203I
8.51107 − 7.96464I 0
u = 0.186110 − 0.839501I
a = 1.18588 + 1.51108I
b = −0.588144 − 0.942203I
8.51107 + 7.96464I 0
u = 1.137060 + 0.083755I
a = −0.340810 − 1.362340I
b = −0.970198 + 0.697036I
−0.52167 + 4.61172I 0
u = 1.137060 − 0.083755I
a = −0.340810 + 1.362340I
b = −0.970198 − 0.697036I
−0.52167 − 4.61172I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.113200 + 0.350252I
a = 0.316835 + 0.134474I
b = −0.792717 + 0.032554I
−0.01080 + 2.42638I 0
u = −1.113200 − 0.350252I
a = 0.316835 − 0.134474I
b = −0.792717 − 0.032554I
−0.01080 − 2.42638I 0
u = 1.153350 + 0.243735I
a = −0.366981 + 1.183590I
b = −0.801289 − 0.738462I
−0.16714 − 4.78859I 0
u = 1.153350 − 0.243735I
a = −0.366981 − 1.183590I
b = −0.801289 + 0.738462I
−0.16714 + 4.78859I 0
u = −0.099249 + 0.797317I
a = −0.716625 + 0.713497I
b = 0.620262 − 0.047717I
3.11143 + 1.77129I −12.00000 − 3.74305I
u = −0.099249 − 0.797317I
a = −0.716625 − 0.713497I
b = 0.620262 + 0.047717I
3.11143 − 1.77129I −12.00000 + 3.74305I
u = −0.724566 + 0.333200I
a = 0.084913 − 0.920619I
b = −1.117180 − 0.110982I
−0.93866 − 2.49661I −12.00000 + 2.74029I
u = −0.724566 − 0.333200I
a = 0.084913 + 0.920619I
b = −1.117180 + 0.110982I
−0.93866 + 2.49661I −12.00000 − 2.74029I
u = −1.218930 + 0.045329I
a = 0.380004 + 0.484744I
b = −0.786560 − 0.829293I
−0.047384 − 0.970006I 0
u = −1.218930 − 0.045329I
a = 0.380004 − 0.484744I
b = −0.786560 + 0.829293I
−0.047384 + 0.970006I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.744074 + 0.182009I
a = −0.429229 − 0.732669I
b = −0.947133 + 0.634087I
−0.40422 + 4.44938I −14.0673 − 4.9668I
u = 0.744074 − 0.182009I
a = −0.429229 + 0.732669I
b = −0.947133 − 0.634087I
−0.40422 − 4.44938I −14.0673 + 4.9668I
u = 0.189284 + 0.736058I
a = 0.04393 − 2.54745I
b = 1.023300 + 0.644874I
1.77068 − 8.04690I −9.57286 + 9.37019I
u = 0.189284 − 0.736058I
a = 0.04393 + 2.54745I
b = 1.023300 − 0.644874I
1.77068 + 8.04690I −9.57286 − 9.37019I
u = −0.221698 + 0.720542I
a = −0.770295 + 0.907435I
b = 1.281360 − 0.189413I
0.84791 + 6.25400I −11.2890 − 8.6710I
u = −0.221698 − 0.720542I
a = −0.770295 − 0.907435I
b = 1.281360 + 0.189413I
0.84791 − 6.25400I −11.2890 + 8.6710I
u = −0.140582 + 0.739623I
a = −1.39916 − 0.87483I
b = 0.574494 + 0.702034I
3.07037 + 2.84110I −7.29913 − 4.46443I
u = −0.140582 − 0.739623I
a = −1.39916 + 0.87483I
b = 0.574494 − 0.702034I
3.07037 − 2.84110I −7.29913 + 4.46443I
u = −1.243150 + 0.100960I
a = −0.738286 − 0.774980I
b = −1.204120 − 0.528067I
−1.17292 − 3.59071I 0
u = −1.243150 − 0.100960I
a = −0.738286 + 0.774980I
b = −1.204120 + 0.528067I
−1.17292 + 3.59071I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.074658 + 0.742254I
a = −0.81283 + 1.26950I
b = 0.587696 − 0.654971I
3.04979 + 1.07688I −7.24896 − 3.00156I
u = 0.074658 − 0.742254I
a = −0.81283 − 1.26950I
b = 0.587696 + 0.654971I
3.04979 − 1.07688I −7.24896 + 3.00156I
u = −0.228245 + 0.709352I
a = −0.37252 + 2.01880I
b = 1.003610 − 0.619740I
1.85617 + 3.92199I −9.76878 − 2.82515I
u = −0.228245 − 0.709352I
a = −0.37252 − 2.01880I
b = 1.003610 + 0.619740I
1.85617 − 3.92199I −9.76878 + 2.82515I
u = 1.226380 + 0.265835I
a = −1.177270 + 0.321168I
b = 0.321693 − 1.143740I
3.59136 − 1.45213I 0
u = 1.226380 − 0.265835I
a = −1.177270 − 0.321168I
b = 0.321693 + 1.143740I
3.59136 + 1.45213I 0
u = 1.249820 + 0.142486I
a = −2.82499 + 0.56538I
b = −0.755633 + 0.350064I
0.762504 − 0.559043I 0
u = 1.249820 − 0.142486I
a = −2.82499 − 0.56538I
b = −0.755633 − 0.350064I
0.762504 + 0.559043I 0
u = −0.017426 + 0.740999I
a = 2.34826 − 1.92460I
b = −0.869803 + 0.657397I
6.22351 + 4.56633I −3.73730 − 6.98496I
u = −0.017426 − 0.740999I
a = 2.34826 + 1.92460I
b = −0.869803 − 0.657397I
6.22351 − 4.56633I −3.73730 + 6.98496I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.26617
a = 1.31692
b = −0.525476
−6.18263 0
u = 0.058524 + 0.715391I
a = 0.75668 + 2.16588I
b = −0.464647 − 1.129910I
7.14471 − 2.10096I 1.17722 + 2.65730I
u = 0.058524 − 0.715391I
a = 0.75668 − 2.16588I
b = −0.464647 + 1.129910I
7.14471 + 2.10096I 1.17722 − 2.65730I
u = −1.251400 + 0.304571I
a = −1.85642 − 0.08555I
b = 0.843838 + 0.614687I
2.41412 − 0.78698I 0
u = −1.251400 − 0.304571I
a = −1.85642 + 0.08555I
b = 0.843838 − 0.614687I
2.41412 + 0.78698I 0
u = 1.260920 + 0.268599I
a = −0.645813 + 0.337662I
b = 1.12107 − 0.86570I
1.21395 + 1.35004I 0
u = 1.260920 − 0.268599I
a = −0.645813 − 0.337662I
b = 1.12107 + 0.86570I
1.21395 − 1.35004I 0
u = −1.274760 + 0.275843I
a = −0.89496 − 1.60223I
b = 0.828740 + 0.712699I
2.37321 + 2.95488I 0
u = −1.274760 − 0.275843I
a = −0.89496 + 1.60223I
b = 0.828740 − 0.712699I
2.37321 − 2.95488I 0
u = 0.024434 + 0.693745I
a = 1.18639 + 2.36959I
b = −1.17157 − 0.81956I
5.03237 − 4.82256I −4.82716 + 7.18113I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.024434 − 0.693745I
a = 1.18639 − 2.36959I
b = −1.17157 + 0.81956I
5.03237 + 4.82256I −4.82716 − 7.18113I
u = −0.001317 + 0.691952I
a = 0.85529 − 3.52300I
b = −0.835681 + 0.659362I
6.32991 + 0.54399I −3.29943 − 0.17721I
u = −0.001317 − 0.691952I
a = 0.85529 + 3.52300I
b = −0.835681 − 0.659362I
6.32991 − 0.54399I −3.29943 + 0.17721I
u = 1.280480 + 0.271970I
a = 1.44341 − 3.07056I
b = 0.866416 + 0.606863I
2.34431 − 4.02005I 0
u = 1.280480 − 0.271970I
a = 1.44341 + 3.07056I
b = 0.866416 − 0.606863I
2.34431 + 4.02005I 0
u = 1.278930 + 0.304729I
a = −0.58243 − 2.07900I
b = 0.885814 + 0.693929I
2.19424 − 8.34091I 0
u = 1.278930 − 0.304729I
a = −0.58243 + 2.07900I
b = 0.885814 − 0.693929I
2.19424 + 8.34091I 0
u = −1.291330 + 0.278909I
a = 1.05610 + 2.01348I
b = 1.22927 − 0.79308I
0.92503 + 8.33903I 0
u = −1.291330 − 0.278909I
a = 1.05610 − 2.01348I
b = 1.22927 + 0.79308I
0.92503 − 8.33903I 0
u = −0.642168 + 0.198301I
a = 0.265917 + 0.199592I
b = −0.798044 − 0.574498I
0.088768 − 0.449411I −13.05283 − 1.45306I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.642168 − 0.198301I
a = 0.265917 − 0.199592I
b = −0.798044 + 0.574498I
0.088768 + 0.449411I −13.05283 + 1.45306I
u = 1.327070 + 0.137247I
a = 0.857852 − 0.085963I
b = 1.006020 − 0.206204I
−5.49406 − 0.39217I 0
u = 1.327070 − 0.137247I
a = 0.857852 + 0.085963I
b = 1.006020 + 0.206204I
−5.49406 + 0.39217I 0
u = −1.304730 + 0.295079I
a = 0.591703 + 1.234260I
b = 0.566057 − 1.150080I
2.87894 + 5.75928I 0
u = −1.304730 − 0.295079I
a = 0.591703 − 1.234260I
b = 0.566057 + 1.150080I
2.87894 − 5.75928I 0
u = −1.307990 + 0.288818I
a = 0.545872 + 0.387828I
b = −0.375293 − 0.698799I
−1.24382 + 2.63179I 0
u = −1.307990 − 0.288818I
a = 0.545872 − 0.387828I
b = −0.375293 + 0.698799I
−1.24382 − 2.63179I 0
u = 0.293912 + 0.579535I
a = 0.55904 + 1.34017I
b = 0.431291 − 0.009036I
3.65162 − 1.53173I −11.67260 + 4.52649I
u = 0.293912 − 0.579535I
a = 0.55904 − 1.34017I
b = 0.431291 + 0.009036I
3.65162 + 1.53173I −11.67260 − 4.52649I
u = 1.356340 + 0.002377I
a = 0.509631 − 0.034649I
b = 0.453652 − 0.267196I
−5.69404 − 0.04855I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.356340 − 0.002377I
a = 0.509631 + 0.034649I
b = 0.453652 + 0.267196I
−5.69404 + 0.04855I 0
u = −1.345300 + 0.250381I
a = 1.28141 + 0.84426I
b = 1.143410 + 0.068518I
−6.80581 + 4.92030I 0
u = −1.345300 − 0.250381I
a = 1.28141 − 0.84426I
b = 1.143410 − 0.068518I
−6.80581 − 4.92030I 0
u = 1.328260 + 0.336809I
a = −0.030301 + 0.823161I
b = −0.522814 − 0.039632I
−1.36278 − 5.84823I 0
u = 1.328260 − 0.336809I
a = −0.030301 − 0.823161I
b = −0.522814 + 0.039632I
−1.36278 + 5.84823I 0
u = −1.372790 + 0.115216I
a = −1.61595 − 1.42202I
b = −1.029850 + 0.272400I
−8.54849 + 2.02896I 0
u = −1.372790 − 0.115216I
a = −1.61595 + 1.42202I
b = −1.029850 − 0.272400I
−8.54849 − 2.02896I 0
u = 1.346710 + 0.311323I
a = 0.917348 + 0.125384I
b = −0.508217 + 0.711957I
−1.61438 − 6.65221I 0
u = 1.346710 − 0.311323I
a = 0.917348 − 0.125384I
b = −0.508217 − 0.711957I
−1.61438 + 6.65221I 0
u = 0.145021 + 0.596292I
a = 0.025912 + 0.660063I
b = −1.070710 + 0.023694I
−2.09996 − 1.78711I −13.9383 + 4.1525I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.145021 − 0.596292I
a = 0.025912 − 0.660063I
b = −1.070710 − 0.023694I
−2.09996 + 1.78711I −13.9383 − 4.1525I
u = −1.371500 + 0.308022I
a = −1.38865 − 2.05729I
b = −1.050460 + 0.634451I
−3.16511 + 11.84220I 0
u = −1.371500 − 0.308022I
a = −1.38865 + 2.05729I
b = −1.050460 − 0.634451I
−3.16511 − 11.84220I 0
u = 1.381950 + 0.299040I
a = −0.710667 + 1.131330I
b = −1.360690 − 0.155764I
−4.22593 − 9.96730I 0
u = 1.381950 − 0.299040I
a = −0.710667 − 1.131330I
b = −1.360690 + 0.155764I
−4.22593 + 9.96730I 0
u = 1.39228 + 0.29608I
a = −0.89421 + 1.57092I
b = −1.099160 − 0.591306I
−3.29441 − 7.59371I 0
u = 1.39228 − 0.29608I
a = −0.89421 − 1.57092I
b = −1.099160 + 0.591306I
−3.29441 + 7.59371I 0
u = −1.38185 + 0.35584I
a = −1.005500 − 0.339688I
b = 0.563730 + 0.977366I
3.55514 + 12.26880I 0
u = −1.38185 − 0.35584I
a = −1.005500 + 0.339688I
b = 0.563730 − 0.977366I
3.55514 − 12.26880I 0
u = −1.43060 + 0.02201I
a = 1.40350 − 0.29695I
b = 0.985570 + 0.523302I
−7.03783 − 3.96216I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43060 − 0.02201I
a = 1.40350 + 0.29695I
b = 0.985570 − 0.523302I
−7.03783 + 3.96216I 0
u = −1.44252 + 0.09911I
a = −0.082026 + 0.409806I
b = −0.360433 − 0.752094I
−2.63233 + 4.20108I 0
u = −1.44252 − 0.09911I
a = −0.082026 − 0.409806I
b = −0.360433 + 0.752094I
−2.63233 − 4.20108I 0
u = 1.39976 + 0.36294I
a = 0.89232 − 1.99894I
b = 1.123360 + 0.731271I
1.8123 − 18.4914I 0
u = 1.39976 − 0.36294I
a = 0.89232 + 1.99894I
b = 1.123360 − 0.731271I
1.8123 + 18.4914I 0
u = −1.42261 + 0.28681I
a = −0.818667 + 0.275420I
b = −0.746956 − 0.211530I
−1.90761 + 4.85839I 0
u = −1.42261 − 0.28681I
a = −0.818667 − 0.275420I
b = −0.746956 + 0.211530I
−1.90761 − 4.85839I 0
u = 1.45228 + 0.03095I
a = 1.099700 − 0.475549I
b = 1.213130 + 0.103574I
−7.86483 + 1.62494I 0
u = 1.45228 − 0.03095I
a = 1.099700 + 0.475549I
b = 1.213130 − 0.103574I
−7.86483 − 1.62494I 0
u = 1.39101 + 0.43159I
a = −0.595123 + 0.422615I
b = 0.803163 − 0.619507I
0.66548 − 3.77716I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.39101 − 0.43159I
a = −0.595123 − 0.422615I
b = 0.803163 + 0.619507I
0.66548 + 3.77716I 0
u = −1.43437 + 0.41491I
a = 0.67591 + 1.70892I
b = 0.897264 − 0.617532I
0.36776 + 8.63967I 0
u = −1.43437 − 0.41491I
a = 0.67591 − 1.70892I
b = 0.897264 + 0.617532I
0.36776 − 8.63967I 0
u = 1.52152 + 0.09850I
a = −0.897523 + 0.800823I
b = −1.079230 − 0.601792I
−4.63290 − 9.25180I 0
u = 1.52152 − 0.09850I
a = −0.897523 − 0.800823I
b = −1.079230 + 0.601792I
−4.63290 + 9.25180I 0
u = 0.292100 + 0.301100I
a = 0.91369 − 3.13908I
b = 0.910526 + 0.155742I
−3.27320 − 0.42810I −16.9385 + 10.2974I
u = 0.292100 − 0.301100I
a = 0.91369 + 3.13908I
b = 0.910526 − 0.155742I
−3.27320 + 0.42810I −16.9385 − 10.2974I
u = −0.326047
a = −0.389959
b = −0.301962
−0.523873 −18.7970
u = 0.145999 + 0.108528I
a = −4.58215 + 1.75339I
b = 0.564240 + 0.697745I
3.91036 − 0.86023I −7.46457 + 3.39085I
u = 0.145999 − 0.108528I
a = −4.58215 − 1.75339I
b = 0.564240 − 0.697745I
3.91036 + 0.86023I −7.46457 − 3.39085I
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0330393 + 0.1023890I
a = −6.81838 − 1.90836I
b = 1.037250 − 0.662214I
2.54221 + 4.42210I −9.57210 − 0.19279I
u = 0.0330393 − 0.1023890I
a = −6.81838 + 1.90836I
b = 1.037250 + 0.662214I
2.54221 − 4.42210I −9.57210 + 0.19279I
17
II.
I
u
2
= hu
20
−8u
18
+· · ·+b−1, 2u
20
−u
19
+· · ·+a−7, u
21
−10u
19
+· · ·−7u+1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
−2u
20
+ u
19
+ ··· + 8u + 7
−u
20
+ 8u
18
+ ··· − u + 1
a
2
=
u
20
+ u
19
+ ··· + 7u − 7
−2u
19
+ 18u
17
+ ··· − 12u + 1
a
1
=
u
20
− u
19
+ ··· − 5u − 6
−2u
19
+ 18u
17
+ ··· − 12u + 1
a
11
=
u
20
− u
19
+ ··· − 3u − 7
−2u
20
+ 17u
18
+ ··· + 4u − 1
a
6
=
−u
20
+ 9u
18
+ ··· − 2u
2
+ 3
−2u
20
− u
19
+ ··· − 5u + 1
a
8
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
12
=
u
20
− u
19
+ ··· − 4u − 6
−2u
19
+ 18u
17
+ ··· − 11u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −6u
20
− u
19
+ 49u
18
+ 7u
17
− 161u
16
− 26u
15
+ 245u
14
+ 65u
13
− 108u
12
− 103u
11
−
144u
10
+ 76u
9
+ 146u
8
+ 14u
7
+ 28u
6
− 48u
5
− 35u
4
+ 6u
3
− 23u
2
+ 8u − 9
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
− 9u
20
+ ··· + 9u − 1
c
2
u
21
− u
20
+ ··· + u − 1
c
3
, c
4
u
21
− 10u
19
+ ··· − 7u + 1
c
5
u
21
+ 12u
19
+ ··· − 12u − 1
c
6
u
21
+ u
20
+ ··· + u + 1
c
7
u
21
− u
20
+ ··· + u − 1
c
8
u
21
+ 6u
19
+ ··· − 7u − 1
c
9
u
21
− 10u
19
+ ··· − 7u − 1
c
10
u
21
+ 3u
20
+ ··· − 3u − 1
c
11
u
21
+ 12u
19
+ ··· − 12u + 1
c
12
u
21
+ u
20
+ ··· + u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 15y
20
+ ··· − 11y −1
c
2
, c
6
y
21
− 9y
20
+ ··· + 9y −1
c
3
, c
4
, c
9
y
21
− 20y
20
+ ··· + 45y −1
c
5
, c
11
y
21
+ 24y
20
+ ··· + 108y −1
c
7
y
21
+ 3y
20
+ ··· − 3y −1
c
8
y
21
+ 12y
20
+ ··· + 43y −1
c
10
y
21
− y
20
+ ··· − 3y −1
c
12
y
21
+ 3y
20
+ ··· − 3y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.080158 + 0.819281I
a = −0.92417 + 2.10251I
b = 0.801730 − 0.694815I
5.43744 + 2.72021I −5.85258 − 2.88441I
u = −0.080158 − 0.819281I
a = −0.92417 − 2.10251I
b = 0.801730 + 0.694815I
5.43744 − 2.72021I −5.85258 + 2.88441I
u = −1.197940 + 0.191741I
a = 0.444872 − 0.624696I
b = 0.550977 − 0.566678I
1.68891 + 2.22060I −8.80097 − 2.83222I
u = −1.197940 − 0.191741I
a = 0.444872 + 0.624696I
b = 0.550977 + 0.566678I
1.68891 − 2.22060I −8.80097 + 2.83222I
u = −1.203790 + 0.258090I
a = 1.52634 + 0.84019I
b = −0.655629 − 0.718143I
2.22236 + 1.09039I −9.47843 − 0.52625I
u = −1.203790 − 0.258090I
a = 1.52634 − 0.84019I
b = −0.655629 + 0.718143I
2.22236 − 1.09039I −9.47843 + 0.52625I
u = −0.279520 + 0.716124I
a = 0.004567 + 0.470314I
b = −0.649928 − 0.490023I
4.33403 + 0.74871I −4.95333 + 0.72657I
u = −0.279520 − 0.716124I
a = 0.004567 − 0.470314I
b = −0.649928 + 0.490023I
4.33403 − 0.74871I −4.95333 − 0.72657I
u = 1.236490 + 0.151582I
a = 0.489421 + 0.175918I
b = 1.117210 − 0.719710I
−0.23287 + 3.04198I −10.09826 − 2.24720I
u = 1.236490 − 0.151582I
a = 0.489421 − 0.175918I
b = 1.117210 + 0.719710I
−0.23287 − 3.04198I −10.09826 + 2.24720I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.28646
a = 0.642931
b = −0.717013
−6.73511 −26.5190
u = 1.257160 + 0.319824I
a = −0.30625 + 1.91883I
b = −0.919180 − 0.765143I
1.41444 − 6.86561I −10.38570 + 5.84031I
u = 1.257160 − 0.319824I
a = −0.30625 − 1.91883I
b = −0.919180 + 0.765143I
1.41444 + 6.86561I −10.38570 − 5.84031I
u = 0.277781 + 0.545491I
a = 0.27455 + 1.66102I
b = −1.082610 − 0.621058I
2.75769 − 5.29661I −7.07327 + 8.30022I
u = 0.277781 − 0.545491I
a = 0.27455 − 1.66102I
b = −1.082610 + 0.621058I
2.75769 + 5.29661I −7.07327 − 8.30022I
u = −1.39075
a = −1.76615
b = −1.05019
−8.18419 −19.7740
u = 1.39046 + 0.35637I
a = 0.0576196 − 0.0650527I
b = 0.659728 − 0.374097I
−0.94531 − 4.82332I −10.09113 + 2.96370I
u = 1.39046 − 0.35637I
a = 0.0576196 + 0.0650527I
b = 0.659728 + 0.374097I
−0.94531 + 4.82332I −10.09113 − 2.96370I
u = −1.42215 + 0.28172I
a = 0.91029 + 1.24044I
b = 1.130400 − 0.517462I
−2.78320 + 8.55534I −11.4594 − 8.6819I
u = −1.42215 − 0.28172I
a = 0.91029 − 1.24044I
b = 1.130400 + 0.517462I
−2.78320 − 8.55534I −11.4594 + 8.6819I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.147630
a = 8.16872
b = 0.861806
−2.99807 −8.32060
23
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
21
− 9u
20
+ ··· + 9u − 1)(u
122
+ 46u
121
+ ··· + 56468u + 841)
c
2
(u
21
− u
20
+ ··· + u − 1)(u
122
− 2u
121
+ ··· + 18u + 29)
c
3
, c
4
(u
21
− 10u
19
+ ··· − 7u + 1)(u
122
− u
121
+ ··· + 14u − 1)
c
5
(u
21
+ 12u
19
+ ··· − 12u − 1)(u
122
− u
121
+ ··· + 35u − 1)
c
6
(u
21
+ u
20
+ ··· + u + 1)(u
122
− 2u
121
+ ··· + 18u + 29)
c
7
(u
21
− u
20
+ ··· + u − 1)(u
122
+ 8u
121
+ ··· − 298520u − 40207)
c
8
(u
21
+ 6u
19
+ ··· − 7u − 1)(u
122
+ 3u
121
+ ··· − 10052u + 949)
c
9
(u
21
− 10u
19
+ ··· − 7u − 1)(u
122
− u
121
+ ··· + 14u − 1)
c
10
(u
21
+ 3u
20
+ ··· − 3u − 1)(u
122
− 20u
121
+ ··· − 18800u + 1457)
c
11
(u
21
+ 12u
19
+ ··· − 12u + 1)(u
122
− u
121
+ ··· + 35u − 1)
c
12
(u
21
+ u
20
+ ··· + u + 1)(u
122
− 2u
121
+ ··· − 1232502u − 100871)
24
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
21
+ 15y
20
+ ··· − 11y −1)
· (y
122
+ 70y
121
+ ··· − 130799392y + 707281)
c
2
, c
6
(y
21
− 9y
20
+ ··· + 9y −1)(y
122
− 46y
121
+ ··· − 56468y + 841)
c
3
, c
4
, c
9
(y
21
− 20y
20
+ ··· + 45y −1)(y
122
− 105y
121
+ ··· + 116y + 1)
c
5
, c
11
(y
21
+ 24y
20
+ ··· + 108y −1)(y
122
+ 99y
121
+ ··· + 173y + 1)
c
7
(y
21
+ 3y
20
+ ··· − 3y −1)
· (y
122
+ 34y
121
+ ··· + 9443298764y + 1616602849)
c
8
(y
21
+ 12y
20
+ ··· + 43y −1)
· (y
122
+ 59y
121
+ ··· + 89191938y + 900601)
c
10
(y
21
− y
20
+ ··· − 3y −1)
· (y
122
+ 18y
121
+ ··· − 67920452y + 2122849)
c
12
(y
21
+ 3y
20
+ ··· − 3y −1)
· (y
122
+ 30y
121
+ ··· + 188566629184y + 10174958641)
25
