12a
0063
(K12a
0063
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 11 10 4 6 12 8 1 9
Solving Sequence
3,7
4
8,10
11 6 9 5 2 1 12
c
3
c
7
c
10
c
6
c
8
c
5
c
2
c
1
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.30388 × 10
564
u
137
+ 5.80260 × 10
564
u
136
+ ··· + 2.13528 × 10
566
b − 8.99538 × 10
567
,
1.61908 × 10
565
u
137
+ 2.38731 × 10
565
u
136
+ ··· + 1.70823 × 10
566
a − 2.06670 × 10
568
,
u
138
+ u
137
+ ··· − 4096u + 512i
I
v
1
= ha, −117084v
8
− 101146v
7
+ ··· + 178147b − 213819,
v
9
+ v
8
+ 12v
7
+ 7v
6
+ 37v
5
− v
4
+ 10v
2
+ 5v + 1i
* 2 irreducible components of dim
C
= 0, with total 147 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
= h4.30 × 10
564
u
137
+ 5.80 × 10
564
u
136
+ · · · + 2.14 × 10
566
b − 9.00 ×
10
567
, 1.62 × 10
565
u
137
+ 2.39 × 10
565
u
136
+ · · · + 1.71 × 10
566
a − 2.07 ×
10
568
, u
138
+ u
137
+ · · · − 4096u + 512i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
−u
2
a
8
=
u
−u
3
+ u
a
10
=
−0.0947815u
137
− 0.139754u
136
+ ··· − 690.527u + 120.985
−0.0201560u
137
− 0.0271749u
136
+ ··· − 205.406u + 42.1274
a
11
=
−0.109900u
137
− 0.159663u
136
+ ··· − 771.989u + 134.827
−0.0307500u
137
− 0.0424307u
136
+ ··· − 274.982u + 53.5163
a
6
=
−0.0831024u
137
− 0.108477u
136
+ ··· − 560.659u + 98.6070
−0.00173320u
137
+ 0.00661599u
136
+ ··· − 97.7944u + 16.3916
a
9
=
0.0725287u
137
+ 0.102880u
136
+ ··· + 471.818u − 81.4870
0.0438673u
137
+ 0.0591812u
136
+ ··· + 293.028u − 50.0935
a
5
=
−0.0330916u
137
− 0.0487965u
136
+ ··· − 201.962u + 34.3636
0.0474245u
137
+ 0.0709201u
136
+ ··· + 317.724u − 51.4355
a
2
=
−0.0330916u
137
− 0.0487965u
136
+ ··· − 201.962u + 34.3636
−0.0405873u
137
− 0.0610350u
136
+ ··· − 270.340u + 43.3946
a
1
=
−0.0736789u
137
− 0.109832u
136
+ ··· − 472.302u + 77.7582
−0.0405873u
137
− 0.0610350u
136
+ ··· − 270.340u + 43.3946
a
12
=
−0.0908434u
137
− 0.134176u
136
+ ··· − 634.531u + 110.010
−0.0349893u
137
− 0.0500330u
136
+ ··· − 305.131u + 55.1204
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.544581u
137
+ 0.814468u
136
+ ··· + 3277.04u − 506.995
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
138
+ 70u
137
+ ··· − 82u + 1
c
2
, c
4
u
138
− 10u
137
+ ··· + 14u − 1
c
3
, c
7
u
138
− u
137
+ ··· + 4096u + 512
c
5
u
138
+ 6u
137
+ ··· − 67104u − 2117
c
6
u
138
+ 2u
137
+ ··· − 2626u − 97
c
8
u
138
− 10u
137
+ ··· + 2u − 1
c
9
, c
12
u
138
− 2u
137
+ ··· + 14u + 1
c
10
u
138
− 14u
137
+ ··· − 2u + 1
c
11
u
138
− 54u
137
+ ··· + 14u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
138
+ 6y
137
+ ··· − 5018y + 1
c
2
, c
4
y
138
− 70y
137
+ ··· + 82y + 1
c
3
, c
7
y
138
− 57y
137
+ ··· − 8912896y + 262144
c
5
y
138
− 118y
137
+ ··· − 1356064422y + 4481689
c
6
y
138
− 166y
137
+ ··· + 9748742y + 9409
c
8
y
138
− 14y
137
+ ··· − 10y + 1
c
9
, c
12
y
138
+ 54y
137
+ ··· − 14y + 1
c
10
y
138
− 10y
137
+ ··· − 14y + 1
c
11
y
138
+ 62y
137
+ ··· + 2378y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.891237 + 0.451061I
a = −0.373810 + 0.420098I
b = 0.10213 + 2.17730I
−1.21505 + 3.56819I 0
u = 0.891237 − 0.451061I
a = −0.373810 − 0.420098I
b = 0.10213 − 2.17730I
−1.21505 − 3.56819I 0
u = 1.002230 + 0.056995I
a = −0.978568 − 0.559753I
b = 1.40585 − 0.25622I
2.60318 − 4.38929I 0
u = 1.002230 − 0.056995I
a = −0.978568 + 0.559753I
b = 1.40585 + 0.25622I
2.60318 + 4.38929I 0
u = −0.535602 + 0.829305I
a = −0.579407 − 0.422359I
b = −0.03823 − 2.72025I
−2.92258 + 5.51420I 0
u = −0.535602 − 0.829305I
a = −0.579407 + 0.422359I
b = −0.03823 + 2.72025I
−2.92258 − 5.51420I 0
u = −0.607911 + 0.752609I
a = −0.586692 − 0.433371I
b = 1.38290 − 0.95935I
−4.92549 + 2.89963I 0
u = −0.607911 − 0.752609I
a = −0.586692 + 0.433371I
b = 1.38290 + 0.95935I
−4.92549 − 2.89963I 0
u = −0.856902 + 0.439878I
a = 0.776533 − 0.191475I
b = 0.248146 − 0.070340I
1.42734 − 1.67105I 0
u = −0.856902 − 0.439878I
a = 0.776533 + 0.191475I
b = 0.248146 + 0.070340I
1.42734 + 1.67105I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.399102 + 0.957238I
a = 1.047610 − 0.663365I
b = 0.23151 − 1.43448I
−2.80156 − 2.93042I 0
u = 0.399102 − 0.957238I
a = 1.047610 + 0.663365I
b = 0.23151 + 1.43448I
−2.80156 + 2.93042I 0
u = −0.901914 + 0.317542I
a = 2.35366 + 0.86813I
b = −0.25586 + 1.95557I
1.38659 + 0.85768I 0
u = −0.901914 − 0.317542I
a = 2.35366 − 0.86813I
b = −0.25586 − 1.95557I
1.38659 − 0.85768I 0
u = −0.643323 + 0.685004I
a = 0.437804 + 0.707830I
b = −0.04627 + 2.82885I
−5.01384 − 0.52036I 0
u = −0.643323 − 0.685004I
a = 0.437804 − 0.707830I
b = −0.04627 − 2.82885I
−5.01384 + 0.52036I 0
u = −1.042910 + 0.202388I
a = −2.42701 − 0.42060I
b = 0.837030 − 0.935034I
2.43266 + 1.40735I 0
u = −1.042910 − 0.202388I
a = −2.42701 + 0.42060I
b = 0.837030 + 0.935034I
2.43266 − 1.40735I 0
u = −0.447071 + 0.969480I
a = 1.042050 + 0.194188I
b = 0.357165 + 0.646159I
1.61097 + 5.54766I 0
u = −0.447071 − 0.969480I
a = 1.042050 − 0.194188I
b = 0.357165 − 0.646159I
1.61097 − 5.54766I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.983568 + 0.420621I
a = 1.125930 − 0.299292I
b = −0.980929 + 0.486896I
1.52583 + 0.05279I 0
u = −0.983568 − 0.420621I
a = 1.125930 + 0.299292I
b = −0.980929 − 0.486896I
1.52583 − 0.05279I 0
u = −1.007240 + 0.365828I
a = −2.94257 − 0.96802I
b = 0.78500 − 2.45396I
1.86133 − 3.37943I 0
u = −1.007240 − 0.365828I
a = −2.94257 + 0.96802I
b = 0.78500 + 2.45396I
1.86133 + 3.37943I 0
u = 0.562307 + 0.712073I
a = −0.467713 − 0.587197I
b = −0.682448 − 0.564071I
−2.24121 − 1.11087I 0
u = 0.562307 − 0.712073I
a = −0.467713 + 0.587197I
b = −0.682448 + 0.564071I
−2.24121 + 1.11087I 0
u = 0.049286 + 0.900920I
a = −0.852074 + 0.482128I
b = −0.437779 + 0.125177I
2.85912 − 1.44732I 0
u = 0.049286 − 0.900920I
a = −0.852074 − 0.482128I
b = −0.437779 − 0.125177I
2.85912 + 1.44732I 0
u = 1.013460 + 0.467152I
a = −0.566480 + 0.532942I
b = 1.96084 + 1.00994I
1.14019 + 6.08874I 0
u = 1.013460 − 0.467152I
a = −0.566480 − 0.532942I
b = 1.96084 − 1.00994I
1.14019 − 6.08874I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.821216 + 0.326395I
a = −0.333026 − 1.123350I
b = −0.26649 − 1.98988I
0.77318 − 3.15109I 0
u = −0.821216 − 0.326395I
a = −0.333026 + 1.123350I
b = −0.26649 + 1.98988I
0.77318 + 3.15109I 0
u = −0.974643 + 0.546694I
a = 0.543194 + 1.122300I
b = −0.58768 + 2.16848I
−5.66343 − 4.80751I 0
u = −0.974643 − 0.546694I
a = 0.543194 − 1.122300I
b = −0.58768 − 2.16848I
−5.66343 + 4.80751I 0
u = −0.973914 + 0.548572I
a = −0.246797 − 0.250807I
b = 0.45663 − 2.06237I
−2.29363 − 1.26582I 0
u = −0.973914 − 0.548572I
a = −0.246797 + 0.250807I
b = 0.45663 + 2.06237I
−2.29363 + 1.26582I 0
u = 0.775567 + 0.394484I
a = 0.947364 − 0.353639I
b = −1.45919 − 0.64014I
−1.60499 + 0.17048I 0
u = 0.775567 − 0.394484I
a = 0.947364 + 0.353639I
b = −1.45919 + 0.64014I
−1.60499 − 0.17048I 0
u = 0.356173 + 1.076340I
a = −1.099720 + 0.625012I
b = −0.75303 + 1.56834I
−1.18583 − 8.42374I 0
u = 0.356173 − 1.076340I
a = −1.099720 − 0.625012I
b = −0.75303 − 1.56834I
−1.18583 + 8.42374I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.475349 + 0.722868I
a = −2.17869 + 3.34103I
b = −0.32690 + 6.15634I
−2.03184 − 3.14136I 0
u = 0.475349 − 0.722868I
a = −2.17869 − 3.34103I
b = −0.32690 − 6.15634I
−2.03184 + 3.14136I 0
u = −0.660289 + 0.557121I
a = 0.250347 + 0.609511I
b = −1.90816 + 1.14402I
−3.27436 − 3.20135I 0
u = −0.660289 − 0.557121I
a = 0.250347 − 0.609511I
b = −1.90816 − 1.14402I
−3.27436 + 3.20135I 0
u = −0.669186 + 0.519624I
a = −1.62569 − 0.41067I
b = 0.650552 − 1.124740I
−6.65019 + 0.44704I 0
u = −0.669186 − 0.519624I
a = −1.62569 + 0.41067I
b = 0.650552 + 1.124740I
−6.65019 − 0.44704I 0
u = −0.995065 + 0.606465I
a = −0.768661 − 0.241952I
b = 1.72710 − 0.93380I
−3.92952 − 4.48424I 0
u = −0.995065 − 0.606465I
a = −0.768661 + 0.241952I
b = 1.72710 + 0.93380I
−3.92952 + 4.48424I 0
u = −1.052960 + 0.511029I
a = −0.545641 − 1.202060I
b = 0.75942 − 1.88503I
−3.97612 − 10.54010I 0
u = −1.052960 − 0.511029I
a = −0.545641 + 1.202060I
b = 0.75942 + 1.88503I
−3.97612 + 10.54010I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.028400 + 0.569460I
a = −1.98039 + 1.42157I
b = 1.49925 + 3.09584I
−0.64257 + 3.65096I 0
u = 1.028400 − 0.569460I
a = −1.98039 − 1.42157I
b = 1.49925 − 3.09584I
−0.64257 − 3.65096I 0
u = 0.807402 + 0.162485I
a = 0.0245056 + 0.0303575I
b = −0.18345 − 1.83374I
−0.41806 − 2.81299I 0
u = 0.807402 − 0.162485I
a = 0.0245056 − 0.0303575I
b = −0.18345 + 1.83374I
−0.41806 + 2.81299I 0
u = 0.513302 + 0.642122I
a = 2.04970 − 3.19938I
b = −0.02901 − 5.33581I
−2.14770 + 1.10222I 0
u = 0.513302 − 0.642122I
a = 2.04970 + 3.19938I
b = −0.02901 + 5.33581I
−2.14770 − 1.10222I 0
u = 0.142187 + 0.803358I
a = 0.605123 − 0.786228I
b = 0.251832 − 1.062410I
−1.18089 − 1.44155I 0
u = 0.142187 − 0.803358I
a = 0.605123 + 0.786228I
b = 0.251832 + 1.062410I
−1.18089 + 1.44155I 0
u = 1.084210 + 0.480895I
a = 1.90886 − 0.45684I
b = −0.97873 − 1.92428I
0.93099 + 3.37995I 0
u = 1.084210 − 0.480895I
a = 1.90886 + 0.45684I
b = −0.97873 + 1.92428I
0.93099 − 3.37995I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024840 + 0.606612I
a = −0.889765 − 0.556474I
b = −0.617516 + 0.472971I
−0.87217 + 6.18814I 0
u = 1.024840 − 0.606612I
a = −0.889765 + 0.556474I
b = −0.617516 − 0.472971I
−0.87217 − 6.18814I 0
u = −0.037414 + 1.194540I
a = 0.374263 − 0.556403I
b = 0.670339 − 0.895196I
−1.56126 − 1.16042I 0
u = −0.037414 − 1.194540I
a = 0.374263 + 0.556403I
b = 0.670339 + 0.895196I
−1.56126 + 1.16042I 0
u = −1.030340 + 0.632780I
a = 0.269726 + 0.515058I
b = −0.48587 + 2.22483I
−3.62101 − 8.17819I 0
u = −1.030340 − 0.632780I
a = 0.269726 − 0.515058I
b = −0.48587 − 2.22483I
−3.62101 + 8.17819I 0
u = −0.607381 + 1.045900I
a = −1.099300 − 0.476232I
b = −0.10491 − 1.87040I
−5.02344 + 7.63080I 0
u = −0.607381 − 1.045900I
a = −1.099300 + 0.476232I
b = −0.10491 + 1.87040I
−5.02344 − 7.63080I 0
u = −1.223500 + 0.025026I
a = 0.450072 − 0.653824I
b = 0.002928 − 0.389535I
3.62495 + 0.18798I 0
u = −1.223500 − 0.025026I
a = 0.450072 + 0.653824I
b = 0.002928 + 0.389535I
3.62495 − 0.18798I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.577195 + 0.506526I
a = −0.81310 + 1.21650I
b = 0.849600 + 0.335553I
−5.67444 + 7.70604I 0
u = 0.577195 − 0.506526I
a = −0.81310 − 1.21650I
b = 0.849600 − 0.335553I
−5.67444 − 7.70604I 0
u = 1.077150 + 0.598666I
a = 2.44174 − 1.26239I
b = −1.57702 − 3.62597I
−0.24222 + 8.22199I 0
u = 1.077150 − 0.598666I
a = 2.44174 + 1.26239I
b = −1.57702 + 3.62597I
−0.24222 − 8.22199I 0
u = 1.161370 + 0.485891I
a = 0.137744 − 0.952818I
b = −0.572229 − 1.280570I
6.18648 + 6.09287I 0
u = 1.161370 − 0.485891I
a = 0.137744 + 0.952818I
b = −0.572229 + 1.280570I
6.18648 − 6.09287I 0
u = −0.595154 + 1.111130I
a = 1.199830 + 0.475752I
b = 0.51573 + 2.11134I
−3.21354 + 13.45620I 0
u = −0.595154 − 1.111130I
a = 1.199830 − 0.475752I
b = 0.51573 − 2.11134I
−3.21354 − 13.45620I 0
u = −1.083240 + 0.646473I
a = 0.527041 + 0.430977I
b = −2.05730 + 1.17894I
−1.23497 − 11.03660I 0
u = −1.083240 − 0.646473I
a = 0.527041 − 0.430977I
b = −2.05730 − 1.17894I
−1.23497 + 11.03660I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.008480 + 0.760858I
a = −0.029650 − 0.162775I
b = 0.147420 − 0.664583I
1.12610 − 1.66732I 0
u = −1.008480 − 0.760858I
a = −0.029650 + 0.162775I
b = 0.147420 + 0.664583I
1.12610 + 1.66732I 0
u = −0.580352 + 0.452643I
a = 1.93255 + 0.42636I
b = −0.452440 + 1.034950I
−5.55713 + 6.45135I 0
u = −0.580352 − 0.452643I
a = 1.93255 − 0.42636I
b = −0.452440 − 1.034950I
−5.55713 − 6.45135I 0
u = −0.332883 + 1.227780I
a = −0.326056 + 0.491187I
b = −0.992922 + 0.434685I
−0.88815 − 5.59474I 0
u = −0.332883 − 1.227780I
a = −0.326056 − 0.491187I
b = −0.992922 − 0.434685I
−0.88815 + 5.59474I 0
u = 0.261401 + 0.675701I
a = −1.73076 + 2.21373I
b = −1.50116 + 4.28247I
−1.47744 + 0.92019I −13.1865 − 12.0789I
u = 0.261401 − 0.675701I
a = −1.73076 − 2.21373I
b = −1.50116 − 4.28247I
−1.47744 − 0.92019I −13.1865 + 12.0789I
u = 1.276750 + 0.042565I
a = 0.219940 + 0.720567I
b = 0.470091 + 0.482821I
8.11672 − 2.73587I 0
u = 1.276750 − 0.042565I
a = 0.219940 − 0.720567I
b = 0.470091 − 0.482821I
8.11672 + 2.73587I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.273680 + 0.189034I
a = −0.471650 + 0.790103I
b = 0.390567 + 0.632829I
3.28436 + 5.64107I 0
u = 1.273680 − 0.189034I
a = −0.471650 − 0.790103I
b = 0.390567 − 0.632829I
3.28436 − 5.64107I 0
u = 1.243040 + 0.380663I
a = −0.503377 + 0.008937I
b = −0.183318 + 0.558386I
−3.90120 + 1.41992I 0
u = 1.243040 − 0.380663I
a = −0.503377 − 0.008937I
b = −0.183318 − 0.558386I
−3.90120 − 1.41992I 0
u = −1.288680 + 0.281651I
a = −0.181190 + 0.598182I
b = −0.798486 + 0.333450I
7.47653 − 2.85325I 0
u = −1.288680 − 0.281651I
a = −0.181190 − 0.598182I
b = −0.798486 − 0.333450I
7.47653 + 2.85325I 0
u = 1.155250 + 0.638410I
a = −0.424700 + 1.053580I
b = 1.23511 + 1.85442I
−0.45961 + 8.68715I 0
u = 1.155250 − 0.638410I
a = −0.424700 − 1.053580I
b = 1.23511 − 1.85442I
−0.45961 − 8.68715I 0
u = 0.565089 + 0.368280I
a = 1.28485 − 1.27911I
b = −0.841611 − 0.331242I
−6.08890 + 1.96052I −7.64143 − 8.71242I
u = 0.565089 − 0.368280I
a = 1.28485 + 1.27911I
b = −0.841611 + 0.331242I
−6.08890 − 1.96052I −7.64143 + 8.71242I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.164010 + 0.662985I
a = −0.069682 − 0.970476I
b = 1.02056 − 1.46687I
3.85974 − 11.48810I 0
u = −1.164010 − 0.662985I
a = −0.069682 + 0.970476I
b = 1.02056 + 1.46687I
3.85974 + 11.48810I 0
u = 1.193220 + 0.620973I
a = 0.380214 + 0.025299I
b = 0.390431 − 0.692818I
−3.80516 − 3.12708I 0
u = 1.193220 − 0.620973I
a = 0.380214 − 0.025299I
b = 0.390431 + 0.692818I
−3.80516 + 3.12708I 0
u = 1.226050 + 0.580758I
a = −0.343290 + 0.987150I
b = 1.31512 + 0.92232I
2.14280 + 6.67345I 0
u = 1.226050 − 0.580758I
a = −0.343290 − 0.987150I
b = 1.31512 − 0.92232I
2.14280 − 6.67345I 0
u = −0.614984 + 0.187284I
a = 1.36581 + 0.68642I
b = 0.059042 − 0.133323I
1.56307 − 1.66544I 2.89954 + 4.03891I
u = −0.614984 − 0.187284I
a = 1.36581 − 0.68642I
b = 0.059042 + 0.133323I
1.56307 + 1.66544I 2.89954 − 4.03891I
u = 1.106790 + 0.792448I
a = 0.108065 − 0.388800I
b = −0.414665 − 0.969826I
−2.00335 + 6.93606I 0
u = 1.106790 − 0.792448I
a = 0.108065 + 0.388800I
b = −0.414665 + 0.969826I
−2.00335 − 6.93606I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.315550 + 0.359668I
a = 0.292144 + 0.773241I
b = −0.761965 + 0.326538I
3.97771 − 0.99477I 0
u = −1.315550 − 0.359668I
a = 0.292144 − 0.773241I
b = −0.761965 − 0.326538I
3.97771 + 0.99477I 0
u = 0.791951 + 1.123120I
a = −0.104546 + 0.242020I
b = 0.575981 + 0.363399I
−3.20951 − 0.12052I 0
u = 0.791951 − 1.123120I
a = −0.104546 − 0.242020I
b = 0.575981 − 0.363399I
−3.20951 + 0.12052I 0
u = −1.152770 + 0.759561I
a = 0.372065 + 1.084360I
b = −1.56331 + 2.11237I
−3.2577 − 14.1817I 0
u = −1.152770 − 0.759561I
a = 0.372065 − 1.084360I
b = −1.56331 − 2.11237I
−3.2577 + 14.1817I 0
u = 1.215480 + 0.657197I
a = 0.417569 − 1.169900I
b = −1.58752 − 1.68899I
1.5306 + 14.5699I 0
u = 1.215480 − 0.657197I
a = 0.417569 + 1.169900I
b = −1.58752 + 1.68899I
1.5306 − 14.5699I 0
u = 0.621808 + 1.262870I
a = 0.219946 − 0.373470I
b = −0.401665 − 0.922248I
−2.87405 − 4.60153I 0
u = 0.621808 − 1.262870I
a = 0.219946 + 0.373470I
b = −0.401665 + 0.922248I
−2.87405 + 4.60153I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.012925 + 0.583466I
a = 1.60330 − 1.20767I
b = 1.62413 − 2.79398I
−0.84910 − 2.82406I −8.14201 + 2.02804I
u = 0.012925 − 0.583466I
a = 1.60330 + 1.20767I
b = 1.62413 + 2.79398I
−0.84910 + 2.82406I −8.14201 − 2.02804I
u = −1.18737 + 0.77838I
a = −0.374933 − 1.205190I
b = 1.90542 − 2.04885I
−1.2856 − 20.2575I 0
u = −1.18737 − 0.77838I
a = −0.374933 + 1.205190I
b = 1.90542 + 2.04885I
−1.2856 + 20.2575I 0
u = 1.42457 + 0.18628I
a = 0.418549 − 0.903274I
b = −0.559011 − 0.080432I
5.52769 + 10.52010I 0
u = 1.42457 − 0.18628I
a = 0.418549 + 0.903274I
b = −0.559011 + 0.080432I
5.52769 − 10.52010I 0
u = 1.20482 + 0.82034I
a = −0.323181 + 0.487383I
b = 0.69993 + 1.36228I
−0.93423 + 11.87520I 0
u = 1.20482 − 0.82034I
a = −0.323181 − 0.487383I
b = 0.69993 − 1.36228I
−0.93423 − 11.87520I 0
u = −1.45789 + 0.02040I
a = −0.347702 + 0.766327I
b = 0.052133 − 0.281976I
5.82999 + 4.34658I 0
u = −1.45789 − 0.02040I
a = −0.347702 − 0.766327I
b = 0.052133 + 0.281976I
5.82999 − 4.34658I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.535544
a = −1.29494
b = −1.79576
−2.39938 2.13270
u = −1.26077 + 0.75154I
a = 0.258980 + 0.372530I
b = −0.606270 + 0.959787I
2.07530 − 6.01010I 0
u = −1.26077 − 0.75154I
a = 0.258980 − 0.372530I
b = −0.606270 − 0.959787I
2.07530 + 6.01010I 0
u = 0.484619
a = 1.77599
b = −0.902756
−1.42472 −7.17280
u = 0.371240 + 0.165548I
a = 0.05628 − 3.22965I
b = −0.83219 − 3.92999I
−2.14622 − 2.23521I 21.1047 − 13.0442I
u = 0.371240 − 0.165548I
a = 0.05628 + 3.22965I
b = −0.83219 + 3.92999I
−2.14622 + 2.23521I 21.1047 + 13.0442I
u = 0.219549 + 0.280103I
a = 1.65192 + 0.93172I
b = 0.61488 − 1.35760I
−0.60788 − 2.56876I −3.16211 + 2.09222I
u = 0.219549 − 0.280103I
a = 1.65192 − 0.93172I
b = 0.61488 + 1.35760I
−0.60788 + 2.56876I −3.16211 − 2.09222I
18
II. I
v
1
= ha, −1.17 × 10
5
v
8
− 1.01 × 10
5
v
7
+ · · · + 1.78 × 10
5
b − 2.14 ×
10
5
, v
9
+ v
8
+ · · · + 5v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
8
=
v
0
a
10
=
0
0.657233v
8
+ 0.567767v
7
+ ··· + 9.16478v + 1.20024
a
11
=
0.0241374v
8
− 0.0627123v
7
+ ··· + 0.209905v − 0.0894654
0.657233v
8
+ 0.567767v
7
+ ··· + 9.16478v + 1.20024
a
6
=
v
0.275340v
8
− 0.0465346v
7
+ ··· + 1.55676v − 0.961481
a
9
=
0.177685v
8
+ 0.143932v
7
+ ··· + 2.33403v + 0.321875
−1
a
5
=
0.177685v
8
+ 0.143932v
7
+ ··· + 2.33403v + 0.321875
1
a
2
=
−0.177685v
8
− 0.143932v
7
+ ··· − 2.33403v + 0.678125
−1
a
1
=
−0.177685v
8
− 0.143932v
7
+ ··· − 2.33403v − 0.321875
−1
a
12
=
−0.0347129v
8
− 0.0223692v
7
+ ··· − 0.0767568v + 0.422617
0.355369v
8
+ 0.287863v
7
+ ··· + 4.66807v − 0.356251
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1357499
178147
v
8
−
1060272
178147
v
7
−
16069905
178147
v
6
−
6006453
178147
v
5
−
49016470
178147
v
4
+
11956914
178147
v
3
−
2891346
178147
v
2
−
13052302
178147
v −
5029411
178147
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
7
u
9
c
4
(u + 1)
9
c
5
, c
11
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
8
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
9
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
10
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
12
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
9
c
3
, c
7
y
9
c
5
, c
11
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1
c
6
, c
10
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1
c
8
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1
c
9
, c
12
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.508863 + 0.531649I
a = 0
b = −0.225230 + 1.238240I
0.13850 + 2.09337I −3.38047 − 2.85927I
v = 0.508863 − 0.531649I
a = 0
b = −0.225230 − 1.238240I
0.13850 − 2.09337I −3.38047 + 2.85927I
v = −0.465349
a = 0
b = −1.77487
−2.84338 −17.4870
v = −0.234017 + 0.220643I
a = 0
b = −1.25758 + 1.97504I
−2.26187 + 2.45442I −6.9022 − 12.4598I
v = −0.234017 − 0.220643I
a = 0
b = −1.25758 − 1.97504I
−2.26187 − 2.45442I −6.9022 + 12.4598I
v = −0.65490 + 2.25183I
a = 0
b = −0.300113 − 0.434032I
−6.01628 + 1.33617I −6.48878 + 2.15019I
v = −0.65490 − 2.25183I
a = 0
b = −0.300113 + 0.434032I
−6.01628 − 1.33617I −6.48878 − 2.15019I
v = 0.11273 + 2.63847I
a = 0
b = 0.170352 + 0.451655I
−5.24306 + 7.08493I −2.48514 − 6.49599I
v = 0.11273 − 2.63847I
a = 0
b = 0.170352 − 0.451655I
−5.24306 − 7.08493I −2.48514 + 6.49599I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
138
+ 70u
137
+ ··· − 82u + 1)
c
2
((u − 1)
9
)(u
138
− 10u
137
+ ··· + 14u − 1)
c
3
, c
7
u
9
(u
138
− u
137
+ ··· + 4096u + 512)
c
4
((u + 1)
9
)(u
138
− 10u
137
+ ··· + 14u − 1)
c
5
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
138
+ 6u
137
+ ··· − 67104u − 2117)
c
6
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
138
+ 2u
137
+ ··· − 2626u − 97)
c
8
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
138
− 10u
137
+ ··· + 2u − 1)
c
9
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
138
− 2u
137
+ ··· + 14u + 1)
c
10
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
138
− 14u
137
+ ··· − 2u + 1)
c
11
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
138
− 54u
137
+ ··· + 14u + 1)
c
12
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
138
− 2u
137
+ ··· + 14u + 1)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
9
)(y
138
+ 6y
137
+ ··· − 5018y + 1)
c
2
, c
4
((y − 1)
9
)(y
138
− 70y
137
+ ··· + 82y + 1)
c
3
, c
7
y
9
(y
138
− 57y
137
+ ··· − 8912896y + 262144)
c
5
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
138
− 118y
137
+ ··· − 1356064422y + 4481689)
c
6
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
138
− 166y
137
+ ··· + 9748742y + 9409)
c
8
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
138
− 14y
137
+ ··· − 10y + 1)
c
9
, c
12
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
138
+ 54y
137
+ ··· − 14y + 1)
c
10
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
138
− 10y
137
+ ··· − 14y + 1)
c
11
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
138
+ 62y
137
+ ··· + 2378y + 1)
24
