12a
0200
(K12a
0200
)
A knot diagram
1
Linearized knot diagam
3 5 11 7 2 10 12 1 4 6 9 8
Solving Sequence
1,8 4,9
10 12 7 5 6 11 3 2
c
8
c
9
c
12
c
7
c
4
c
6
c
11
c
3
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.88128 × 10
122
u
110
− 1.62216 × 10
123
u
109
+ ··· + 3.02078 × 10
122
b − 7.89614 × 10
122
,
2.57960 × 10
122
u
110
+ 4.87705 × 10
121
u
109
+ ··· + 3.02078 × 10
122
a + 1.07426 × 10
123
,
u
111
+ 3u
110
+ ··· + 8u
2
+ 1i
I
u
2
= hau + b + a, 5a
2
+ 3au − 4a − 3u + 5, u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 115 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−9.88 × 10
122
u
110
− 1.62 × 10
123
u
109
+ · · · + 3.02 × 10
122
b − 7.90 ×
10
122
, 2.58 × 10
122
u
110
+ 4.88 × 10
121
u
109
+ · · · + 3.02 × 10
122
a + 1.07 ×
10
123
, u
111
+ 3u
110
+ · · · + 8u
2
+ 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−0.853953u
110
− 0.161450u
109
+ ··· + 0.783670u − 3.55623
3.27110u
110
+ 5.37000u
109
+ ··· − 0.138489u + 2.61394
a
9
=
1
−u
2
a
10
=
−0.971252u
110
− 2.05773u
109
+ ··· + 0.169491u − 2.13738
2.96877u
110
+ 5.17690u
109
+ ··· − 1.37894u + 2.55675
a
12
=
−u
u
a
7
=
−u
2
+ 1
u
2
a
5
=
0.852901u
110
+ 2.69009u
109
+ ··· − 2.19989u − 2.77029
0.859350u
110
+ 1.76075u
109
+ ··· + 0.566412u + 1.25696
a
6
=
−1.70072u
110
− 2.81982u
109
+ ··· − 2.03552u − 0.407690
2.53069u
110
+ 3.23016u
109
+ ··· + 0.436662u + 1.31110
a
11
=
u
3
− 2u
−u
5
+ u
3
+ u
a
3
=
0.828171u
110
+ 2.49944u
109
+ ··· − 1.14740u − 2.51520
0.699867u
110
+ 1.64618u
109
+ ··· + 1.35387u + 1.06035
a
2
=
−0.551106u
110
− 1.46836u
109
+ ··· − 6.95085u − 2.33008
0.793459u
110
+ 1.82666u
109
+ ··· + 2.35156u + 0.541040
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.75758u
110
+ 2.71823u
109
+ ··· + 4.75842u + 0.341861
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
111
+ 49u
110
+ ··· + 3796u − 625
c
2
, c
5
u
111
+ 3u
110
+ ··· + 314u + 25
c
3
25(25u
111
− 35u
110
+ ··· + 277470u − 25993)
c
4
25(25u
111
+ 70u
110
+ ··· − 687u − 509)
c
6
, c
10
u
111
− 3u
110
+ ··· + 2u − 1
c
7
, c
8
, c
12
u
111
− 3u
110
+ ··· − 8u
2
− 1
c
9
u
111
− u
110
+ ··· − 5600u − 2000
c
11
u
111
+ 9u
110
+ ··· + 89858u + 4589
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
111
+ 29y
110
+ ··· + 12462116y −390625
c
2
, c
5
y
111
+ 49y
110
+ ··· + 3796y −625
c
3
625(625y
111
− 10275y
110
+ ··· + 4.35687 × 10
10
y −6.75636 × 10
8
)
c
4
625(625y
111
− 23850y
110
+ ··· − 6.75091 × 10
7
y −259081)
c
6
, c
10
y
111
+ 61y
110
+ ··· − 16y −1
c
7
, c
8
, c
12
y
111
− 99y
110
+ ··· − 16y −1
c
9
y
111
− 25y
110
+ ··· − 12720000y −4000000
c
11
y
111
+ 9y
110
+ ··· + 2636458452y −21058921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.848451 + 0.533037I
a = −0.292158 + 0.517168I
b = 0.443974 − 0.962375I
0.42545 + 3.75946I 0
u = −0.848451 − 0.533037I
a = −0.292158 − 0.517168I
b = 0.443974 + 0.962375I
0.42545 − 3.75946I 0
u = 0.865725 + 0.468426I
a = 0.488857 + 0.754210I
b = −0.81665 − 1.59668I
−3.34824 − 9.97292I 0
u = 0.865725 − 0.468426I
a = 0.488857 − 0.754210I
b = −0.81665 + 1.59668I
−3.34824 + 9.97292I 0
u = 0.982269 + 0.291203I
a = −0.888257 + 0.097247I
b = 1.83582 + 0.03095I
−1.48534 + 4.18722I 0
u = 0.982269 − 0.291203I
a = −0.888257 − 0.097247I
b = 1.83582 − 0.03095I
−1.48534 − 4.18722I 0
u = −1.04175
a = 0.523490
b = −1.28841
1.68448 0
u = 1.030970 + 0.293300I
a = 0.423550 + 0.949718I
b = −1.22150 − 1.85782I
−6.34532 − 1.55715I 0
u = 1.030970 − 0.293300I
a = 0.423550 − 0.949718I
b = −1.22150 + 1.85782I
−6.34532 + 1.55715I 0
u = 0.998551 + 0.450677I
a = 0.840429 + 0.185787I
b = −1.53447 − 0.47057I
−3.85932 + 8.71416I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998551 − 0.450677I
a = 0.840429 − 0.185787I
b = −1.53447 + 0.47057I
−3.85932 − 8.71416I 0
u = 0.807023 + 0.379878I
a = −0.522999 − 0.820927I
b = 0.90293 + 1.46137I
−1.05540 − 4.59060I 0
u = 0.807023 − 0.379878I
a = −0.522999 + 0.820927I
b = 0.90293 − 1.46137I
−1.05540 + 4.59060I 0
u = 0.173431 + 0.853663I
a = −1.187460 − 0.697715I
b = −0.0829174 + 0.0476338I
−6.42513 − 4.06910I −4.22635 + 4.84629I
u = 0.173431 − 0.853663I
a = −1.187460 + 0.697715I
b = −0.0829174 − 0.0476338I
−6.42513 + 4.06910I −4.22635 − 4.84629I
u = −0.282130 + 0.822678I
a = 1.56370 + 0.05524I
b = −0.0108961 + 0.0640512I
−1.36655 − 8.48240I 0. + 8.35925I
u = −0.282130 − 0.822678I
a = 1.56370 − 0.05524I
b = −0.0108961 − 0.0640512I
−1.36655 + 8.48240I 0. − 8.35925I
u = 0.263131 + 0.807594I
a = −2.28540 + 0.02260I
b = −0.0613055 + 0.0463861I
−5.2649 + 14.5040I 0. − 9.52744I
u = 0.263131 − 0.807594I
a = −2.28540 − 0.02260I
b = −0.0613055 − 0.0463861I
−5.2649 − 14.5040I 0. + 9.52744I
u = 0.333797 + 0.766731I
a = −0.847130 − 0.808429I
b = 0.145580 + 0.030472I
−6.77766 + 2.81025I −4.73274 − 4.72373I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.333797 − 0.766731I
a = −0.847130 + 0.808429I
b = 0.145580 − 0.030472I
−6.77766 − 2.81025I −4.73274 + 4.72373I
u = −0.678779 + 0.451474I
a = 0.128920 − 0.525934I
b = −0.306024 + 0.773797I
1.90849 − 0.65389I 7.58705 + 0.13678I
u = −0.678779 − 0.451474I
a = 0.128920 + 0.525934I
b = −0.306024 − 0.773797I
1.90849 + 0.65389I 7.58705 − 0.13678I
u = −1.120030 + 0.396848I
a = −0.447323 + 0.480647I
b = 0.88903 − 1.14435I
−1.02530 − 2.41413I 0
u = −1.120030 − 0.396848I
a = −0.447323 − 0.480647I
b = 0.88903 + 1.14435I
−1.02530 + 2.41413I 0
u = 0.255740 + 0.765219I
a = 2.44844 + 0.00182I
b = −0.0317545 − 0.0768044I
−2.89319 + 8.75711I 1.89232 − 6.34972I
u = 0.255740 − 0.765219I
a = 2.44844 − 0.00182I
b = −0.0317545 + 0.0768044I
−2.89319 − 8.75711I 1.89232 + 6.34972I
u = 0.668294 + 0.440594I
a = 0.381426 + 0.246199I
b = −0.946254 + 0.056017I
−5.52371 + 1.47662I −2.33166 − 2.56671I
u = 0.668294 − 0.440594I
a = 0.381426 − 0.246199I
b = −0.946254 − 0.056017I
−5.52371 − 1.47662I −2.33166 + 2.56671I
u = −0.279123 + 0.745093I
a = −1.66286 − 0.04574I
b = 0.0789298 − 0.0009419I
0.44879 − 3.45366I 5.32609 + 3.91559I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.279123 − 0.745093I
a = −1.66286 + 0.04574I
b = 0.0789298 + 0.0009419I
0.44879 + 3.45366I 5.32609 − 3.91559I
u = −0.095794 + 0.780536I
a = 1.64142 + 0.32093I
b = 0.1096960 − 0.0870152I
−4.17950 − 1.81846I −2.32506 + 3.35231I
u = −0.095794 − 0.780536I
a = 1.64142 − 0.32093I
b = 0.1096960 + 0.0870152I
−4.17950 + 1.81846I −2.32506 − 3.35231I
u = −1.218480 + 0.084617I
a = 1.246560 − 0.353208I
b = −1.66716 − 0.71596I
−0.44945 + 3.45531I 0
u = −1.218480 − 0.084617I
a = 1.246560 + 0.353208I
b = −1.66716 + 0.71596I
−0.44945 − 3.45531I 0
u = 0.164141 + 0.752127I
a = −2.62610 + 0.40767I
b = 0.162415 − 0.114911I
−8.97208 + 5.45730I −4.50761 − 5.50179I
u = 0.164141 − 0.752127I
a = −2.62610 − 0.40767I
b = 0.162415 + 0.114911I
−8.97208 − 5.45730I −4.50761 + 5.50179I
u = −1.241840 + 0.229749I
a = −1.170840 − 0.281032I
b = 2.24935 − 0.85873I
0.69363 − 1.61227I 0
u = −1.241840 − 0.229749I
a = −1.170840 + 0.281032I
b = 2.24935 + 0.85873I
0.69363 + 1.61227I 0
u = 0.171856 + 0.716149I
a = 1.23312 + 1.09879I
b = 0.074081 + 0.131507I
−3.97774 − 0.39890I −0.933790 − 0.131410I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.171856 − 0.716149I
a = 1.23312 − 1.09879I
b = 0.074081 − 0.131507I
−3.97774 + 0.39890I −0.933790 + 0.131410I
u = 1.263210 + 0.154487I
a = −0.77119 − 1.26137I
b = 0.90529 + 1.34726I
2.59030 − 0.80985I 0
u = 1.263210 − 0.154487I
a = −0.77119 + 1.26137I
b = 0.90529 − 1.34726I
2.59030 + 0.80985I 0
u = 1.306580 + 0.239131I
a = −2.36258 − 3.57462I
b = 1.74438 + 6.98773I
1.22033 + 4.76626I 0
u = 1.306580 − 0.239131I
a = −2.36258 + 3.57462I
b = 1.74438 − 6.98773I
1.22033 − 4.76626I 0
u = 1.332280 + 0.137029I
a = −1.26201 − 1.42638I
b = 3.20296 + 2.01883I
3.35257 − 2.44507I 0
u = 1.332280 − 0.137029I
a = −1.26201 + 1.42638I
b = 3.20296 − 2.01883I
3.35257 + 2.44507I 0
u = −0.172982 + 0.634595I
a = −0.36462 + 2.26997I
b = −0.012364 − 0.922385I
−3.15676 − 6.04076I −0.86742 + 10.32607I
u = −0.172982 − 0.634595I
a = −0.36462 − 2.26997I
b = −0.012364 + 0.922385I
−3.15676 + 6.04076I −0.86742 − 10.32607I
u = 1.329140 + 0.212562I
a = −0.98741 + 4.66926I
b = 4.54408 − 7.18236I
1.33372 + 0.95736I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.329140 − 0.212562I
a = −0.98741 − 4.66926I
b = 4.54408 + 7.18236I
1.33372 − 0.95736I 0
u = −0.038787 + 0.648227I
a = 2.76975 − 0.72668I
b = 0.949523 − 0.658677I
−2.97959 − 1.57809I 1.46253 + 6.32927I
u = −0.038787 − 0.648227I
a = 2.76975 + 0.72668I
b = 0.949523 + 0.658677I
−2.97959 + 1.57809I 1.46253 − 6.32927I
u = −1.341130 + 0.168721I
a = 0.836570 − 0.686707I
b = −2.39583 + 1.76770I
4.84645 − 0.43250I 0
u = −1.341130 − 0.168721I
a = 0.836570 + 0.686707I
b = −2.39583 − 1.76770I
4.84645 + 0.43250I 0
u = 1.323060 + 0.311518I
a = −1.23701 − 0.76718I
b = 2.21363 + 1.52328I
0.26439 + 5.73172I 0
u = 1.323060 − 0.311518I
a = −1.23701 + 0.76718I
b = 2.21363 − 1.52328I
0.26439 − 5.73172I 0
u = −1.349550 + 0.237179I
a = −0.353866 + 0.270005I
b = 1.45795 − 1.42502I
3.91673 − 6.31648I 0
u = −1.349550 − 0.237179I
a = −0.353866 − 0.270005I
b = 1.45795 + 1.42502I
3.91673 + 6.31648I 0
u = −1.359260 + 0.175859I
a = −0.295928 − 0.553147I
b = −0.46549 + 2.00688I
5.30135 − 0.37795I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.359260 − 0.175859I
a = −0.295928 + 0.553147I
b = −0.46549 − 2.00688I
5.30135 + 0.37795I 0
u = 1.364380 + 0.192376I
a = 1.090040 + 0.421563I
b = −1.79311 + 0.21609I
5.58685 + 3.51795I 0
u = 1.364380 − 0.192376I
a = 1.090040 − 0.421563I
b = −1.79311 − 0.21609I
5.58685 − 3.51795I 0
u = 1.363420 + 0.202853I
a = 1.25561 + 1.01262I
b = −2.57959 − 1.33084I
5.45029 + 3.78361I 0
u = 1.363420 − 0.202853I
a = 1.25561 − 1.01262I
b = −2.57959 + 1.33084I
5.45029 − 3.78361I 0
u = −1.365570 + 0.220575I
a = −1.02539 + 1.41423I
b = 2.90504 − 2.85866I
4.69045 − 6.87284I 0
u = −1.365570 − 0.220575I
a = −1.02539 − 1.41423I
b = 2.90504 + 2.85866I
4.69045 + 6.87284I 0
u = 1.360430 + 0.255439I
a = −1.067560 + 0.487762I
b = 1.34716 − 2.01980I
1.69884 + 9.29683I 0
u = 1.360430 − 0.255439I
a = −1.067560 − 0.487762I
b = 1.34716 + 2.01980I
1.69884 − 9.29683I 0
u = −1.367820 + 0.261256I
a = −0.296953 + 1.116880I
b = 0.34366 − 2.05651I
0.88982 − 3.11273I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.367820 − 0.261256I
a = −0.296953 − 1.116880I
b = 0.34366 + 2.05651I
0.88982 + 3.11273I 0
u = −1.358660 + 0.307497I
a = 1.47353 − 1.27627I
b = −3.02324 + 2.26120I
−4.16450 − 9.28584I 0
u = −1.358660 − 0.307497I
a = 1.47353 + 1.27627I
b = −3.02324 − 2.26120I
−4.16450 + 9.28584I 0
u = 0.131862 + 0.582545I
a = 1.70355 + 0.37972I
b = −0.055155 − 0.802252I
−0.78892 + 3.29378I 3.12146 − 3.00778I
u = 0.131862 − 0.582545I
a = 1.70355 − 0.37972I
b = −0.055155 + 0.802252I
−0.78892 − 3.29378I 3.12146 + 3.00778I
u = −1.355040 + 0.381279I
a = 0.383877 − 0.711688I
b = −0.76178 + 1.57252I
−1.62567 − 0.37101I 0
u = −1.355040 − 0.381279I
a = 0.383877 + 0.711688I
b = −0.76178 − 1.57252I
−1.62567 + 0.37101I 0
u = −1.40693 + 0.17203I
a = 0.268174 + 0.963385I
b = −0.422266 − 1.260740I
0.77219 − 3.38057I 0
u = −1.40693 − 0.17203I
a = 0.268174 − 0.963385I
b = −0.422266 + 1.260740I
0.77219 + 3.38057I 0
u = 0.199034 + 0.525414I
a = 3.35173 + 0.80061I
b = −0.535804 − 0.402837I
−0.26097 + 4.06974I 4.06125 − 10.23179I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.199034 − 0.525414I
a = 3.35173 − 0.80061I
b = −0.535804 + 0.402837I
−0.26097 − 4.06974I 4.06125 + 10.23179I
u = −1.40718 + 0.30970I
a = −1.37279 + 1.25640I
b = 2.84341 − 2.55407I
2.39755 − 12.65390I 0
u = −1.40718 − 0.30970I
a = −1.37279 − 1.25640I
b = 2.84341 + 2.55407I
2.39755 + 12.65390I 0
u = −0.116165 + 0.546238I
a = −1.84090 + 2.69502I
b = −0.97453 + 1.07717I
−3.19745 + 1.83468I 5.65877 − 0.22358I
u = −0.116165 − 0.546238I
a = −1.84090 − 2.69502I
b = −0.97453 − 1.07717I
−3.19745 − 1.83468I 5.65877 + 0.22358I
u = 1.41464 + 0.30140I
a = 1.061040 + 0.878788I
b = −2.18989 − 1.69422I
5.84224 + 7.26151I 0
u = 1.41464 − 0.30140I
a = 1.061040 − 0.878788I
b = −2.18989 + 1.69422I
5.84224 − 7.26151I 0
u = −1.41616 + 0.32878I
a = 1.36309 − 1.23228I
b = −2.71714 + 2.56206I
0.0783 − 18.6139I 0
u = −1.41616 − 0.32878I
a = 1.36309 + 1.23228I
b = −2.71714 − 2.56206I
0.0783 + 18.6139I 0
u = 1.42537 + 0.33368I
a = −1.021320 − 0.833669I
b = 2.11056 + 1.70902I
4.06837 + 12.66270I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42537 − 0.33368I
a = −1.021320 + 0.833669I
b = 2.11056 − 1.70902I
4.06837 − 12.66270I 0
u = −1.46504 + 0.04615I
a = −0.339493 + 0.294163I
b = −0.118355 + 0.261619I
6.11070 + 3.64220I 0
u = −1.46504 − 0.04615I
a = −0.339493 − 0.294163I
b = −0.118355 − 0.261619I
6.11070 − 3.64220I 0
u = −1.45238 + 0.31120I
a = 0.178801 − 0.780640I
b = −0.49079 + 1.48727I
−1.04831 − 6.74954I 0
u = −1.45238 − 0.31120I
a = 0.178801 + 0.780640I
b = −0.49079 − 1.48727I
−1.04831 + 6.74954I 0
u = −1.50530 + 0.01500I
a = 0.265699 − 0.377681I
b = 0.244666 + 0.006083I
4.56452 + 9.01884I 0
u = −1.50530 − 0.01500I
a = 0.265699 + 0.377681I
b = 0.244666 − 0.006083I
4.56452 − 9.01884I 0
u = −0.221727 + 0.438815I
a = −2.12355 − 0.19578I
b = 0.325288 + 0.377375I
0.488487 − 1.269530I 6.63867 + 4.16913I
u = −0.221727 − 0.438815I
a = −2.12355 + 0.19578I
b = 0.325288 − 0.377375I
0.488487 + 1.269530I 6.63867 − 4.16913I
u = −0.243843 + 0.413937I
a = −1.14024 − 1.03218I
b = 0.158306 + 0.677699I
0.577620 − 1.139480I 7.59571 + 6.13511I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.243843 − 0.413937I
a = −1.14024 + 1.03218I
b = 0.158306 − 0.677699I
0.577620 + 1.139480I 7.59571 − 6.13511I
u = 1.51849 + 0.06536I
a = 0.149500 + 0.221635I
b = −0.095618 + 0.188264I
9.19692 + 2.36753I 0
u = 1.51849 − 0.06536I
a = 0.149500 − 0.221635I
b = −0.095618 − 0.188264I
9.19692 − 2.36753I 0
u = 0.261953 + 0.330905I
a = −1.54230 − 1.70626I
b = 0.557405 + 0.825682I
0.32554 − 1.70816I 6.47908 + 1.51201I
u = 0.261953 − 0.330905I
a = −1.54230 + 1.70626I
b = 0.557405 − 0.825682I
0.32554 + 1.70816I 6.47908 − 1.51201I
u = 1.61557 + 0.02903I
a = −0.0648338 − 0.0540396I
b = −0.089057 − 0.127793I
8.92369 − 2.15451I 0
u = 1.61557 − 0.02903I
a = −0.0648338 + 0.0540396I
b = −0.089057 + 0.127793I
8.92369 + 2.15451I 0
u = −0.362095 + 0.074063I
a = 2.75243 − 1.84793I
b = −0.834069 − 0.516392I
−1.43243 + 3.58403I 4.77704 − 2.61924I
u = −0.362095 − 0.074063I
a = 2.75243 + 1.84793I
b = −0.834069 + 0.516392I
−1.43243 − 3.58403I 4.77704 + 2.61924I
u = 0.166795 + 0.275988I
a = −2.86108 − 0.37335I
b = 0.432096 + 0.470414I
0.19884 − 1.52275I 0.827561 + 0.763000I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.166795 − 0.275988I
a = −2.86108 + 0.37335I
b = 0.432096 − 0.470414I
0.19884 + 1.52275I 0.827561 − 0.763000I
16
II. I
u
2
= hau + b + a, 5a
2
+ 3au − 4a − 3u + 5, u
2
− u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
a
−au − a
a
9
=
1
−u − 1
a
10
=
1
−u − 1
a
12
=
−u
u
a
7
=
−u
u + 1
a
5
=
au + 2a
−3au − 2a
a
6
=
0
−u
a
11
=
1
−2u − 2
a
3
=
au + 2a
−7au − 5a
a
2
=
au + 2a + u − 1
−7au − 5a −
3
5
u −
1
5
(ii) Obstruction class = 1
(iii) Cusp Shapes =
387
5
au +
259
5
a +
3
5
u + 5
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
25(25u
4
+ 5u
2
+ 1)
c
4
25(25u
4
− 25u
3
+ 20u
2
− 5u + 1)
c
6
, c
7
, c
8
(u
2
− u − 1)
2
c
9
u
4
c
10
, c
12
(u
2
+ u − 1)
2
c
11
(u
2
− 3u + 1)
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
2
c
3
625(25y
2
+ 5y + 1)
2
c
4
625(625y
4
+ 375y
3
+ 200y
2
+ 15y + 1)
c
6
, c
7
, c
8
c
10
, c
12
(y
2
− 3y + 1)
2
c
9
y
4
c
11
(y
2
− 7y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 0.585410 + 1.013960I
b = −0.223607 − 0.387298I
0.98696 − 2.02988I 6.94984 + 4.01951I
u = −0.618034
a = 0.585410 − 1.013960I
b = −0.223607 + 0.387298I
0.98696 + 2.02988I 6.94984 − 4.01951I
u = 1.61803
a = −0.085410 + 0.147935I
b = 0.223607 − 0.387298I
8.88264 + 2.02988I −9.1498 + 26.1898I
u = 1.61803
a = −0.085410 − 0.147935I
b = 0.223607 + 0.387298I
8.88264 − 2.02988I −9.1498 − 26.1898I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
111
+ 49u
110
+ ··· + 3796u − 625)
c
2
((u
2
+ u + 1)
2
)(u
111
+ 3u
110
+ ··· + 314u + 25)
c
3
625(25u
4
+ 5u
2
+ 1)(25u
111
− 35u
110
+ ··· + 277470u − 25993)
c
4
625(25u
4
− 25u
3
+ ··· − 5u + 1)(25u
111
+ 70u
110
+ ··· − 687u − 509)
c
5
((u
2
− u + 1)
2
)(u
111
+ 3u
110
+ ··· + 314u + 25)
c
6
((u
2
− u − 1)
2
)(u
111
− 3u
110
+ ··· + 2u − 1)
c
7
, c
8
((u
2
− u − 1)
2
)(u
111
− 3u
110
+ ··· − 8u
2
− 1)
c
9
u
4
(u
111
− u
110
+ ··· − 5600u − 2000)
c
10
((u
2
+ u − 1)
2
)(u
111
− 3u
110
+ ··· + 2u − 1)
c
11
((u
2
− 3u + 1)
2
)(u
111
+ 9u
110
+ ··· + 89858u + 4589)
c
12
((u
2
+ u − 1)
2
)(u
111
− 3u
110
+ ··· − 8u
2
− 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
111
+ 29y
110
+ ··· + 1.24621 × 10
7
y −390625)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
111
+ 49y
110
+ ··· + 3796y −625)
c
3
390625(25y
2
+ 5y + 1)
2
· (625y
111
− 10275y
110
+ ··· + 43568737248y −675636049)
c
4
390625(625y
4
+ 375y
3
+ 200y
2
+ 15y + 1)
· (625y
111
− 23850y
110
+ ··· − 67509053y −259081)
c
6
, c
10
((y
2
− 3y + 1)
2
)(y
111
+ 61y
110
+ ··· − 16y −1)
c
7
, c
8
, c
12
((y
2
− 3y + 1)
2
)(y
111
− 99y
110
+ ··· − 16y −1)
c
9
y
4
(y
111
− 25y
110
+ ··· − 1.27200 × 10
7
y −4000000)
c
11
((y
2
− 7y + 1)
2
)(y
111
+ 9y
110
+ ··· + 2.63646 × 10
9
y −2.10589 × 10
7
)
22
