12a
1082
(K12a
1082
)
A knot diagram
1
Linearized knot diagam
4 7 10 12 1 9 2 11 3 6 8 5
Solving Sequence
4,12
5 1 2
6,8
7 11 9 10 3
c
4
c
12
c
1
c
5
c
7
c
11
c
8
c
10
c
3
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h7.37646 × 10
158
u
119
+ 1.70979 × 10
159
u
118
+ ··· + 9.35321 × 10
158
b + 5.75418 × 10
158
,
1.29225 × 10
159
u
119
+ 3.14232 × 10
159
u
118
+ ··· + 9.35321 × 10
158
a − 2.96601 × 10
159
, u
120
+ 3u
119
+ ··· + 8u − 1i
I
u
2
= h−2u
27
+ 2u
26
+ ··· + b + 2, −6u
27
+ 6u
26
+ ··· + a − 8u, u
28
− 2u
27
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 148 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
= h7.38 × 10
158
u
119
+ 1.71 × 10
159
u
118
+ · · · + 9.35 × 10
158
b + 5.75 ×
10
158
, 1.29 × 10
159
u
119
+ 3.14 × 10
159
u
118
+ · · · + 9.35 × 10
158
a − 2.97 ×
10
159
, u
120
+ 3u
119
+ · · · + 8u − 1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
1
=
−u
−u
3
+ u
a
2
=
u
3
− 2u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
−1.38161u
119
− 3.35961u
118
+ ··· + 51.8433u + 3.17111
−0.788655u
119
− 1.82803u
118
+ ··· + 23.3617u − 0.615209
a
7
=
−2.07596u
119
− 4.65251u
118
+ ··· + 49.1162u + 3.92968
−2.17737u
119
− 4.16193u
118
+ ··· + 13.1942u + 0.316698
a
11
=
−0.0726298u
119
− 0.187189u
118
+ ··· − 39.6037u + 6.85858
2.27088u
119
+ 3.37252u
118
+ ··· + 13.7032u + 0.133101
a
9
=
2.01690u
119
+ 3.70837u
118
+ ··· + 3.84406u + 4.68181
−0.381437u
119
− 0.853970u
118
+ ··· + 10.7822u + 0.480982
a
10
=
1.73603u
119
+ 3.47491u
118
+ ··· − 35.1363u + 8.10741
−0.0452228u
119
− 0.441756u
118
+ ··· + 3.24667u + 1.38489
a
3
=
2.44612u
119
+ 3.70156u
118
+ ··· + 72.8518u − 14.1062
0.640744u
119
+ 2.05119u
118
+ ··· − 4.49843u − 1.93172
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2.90682u
119
+ 8.84972u
118
+ ··· − 6.43341u − 13.9528
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
120
− 9u
119
+ ··· − 3718u + 2197
c
2
, c
7
u
120
+ u
119
+ ··· + 505942u − 143161
c
3
, c
9
u
120
+ u
119
+ ··· − 497u − 991
c
4
, c
5
, c
12
u
120
+ 3u
119
+ ··· + 8u − 1
c
6
u
120
− 6u
119
+ ··· − 111403235u + 12357323
c
8
, c
11
u
120
+ 6u
119
+ ··· + 64698u + 4996
c
10
u
120
+ 2u
119
+ ··· + 86310u + 45641
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
120
− 3y
119
+ ··· + 654218266y + 4826809
c
2
, c
7
y
120
+ 103y
119
+ ··· + 401123665620y + 20495071921
c
3
, c
9
y
120
− 85y
119
+ ··· − 45176967y + 982081
c
4
, c
5
, c
12
y
120
− 111y
119
+ ··· + 160y + 1
c
6
y
120
− 54y
119
+ ··· − 7346690606945771y + 152703431726329
c
8
, c
11
y
120
+ 82y
119
+ ··· + 638456276y + 24960016
c
10
y
120
− 32y
119
+ ··· − 57169443552y + 2083100881
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758063 + 0.612639I
a = −1.22294 − 0.75012I
b = 0.470196 − 0.508802I
−9.18918 + 8.98662I 0
u = 0.758063 − 0.612639I
a = −1.22294 + 0.75012I
b = 0.470196 + 0.508802I
−9.18918 − 8.98662I 0
u = −0.995734 + 0.272083I
a = 0.138623 + 1.054390I
b = 0.907901 − 0.711733I
−4.04811 + 3.42712I 0
u = −0.995734 − 0.272083I
a = 0.138623 − 1.054390I
b = 0.907901 + 0.711733I
−4.04811 − 3.42712I 0
u = 0.614537 + 0.723379I
a = −0.382409 − 0.933491I
b = 0.520893 + 0.967316I
−2.87584 − 4.39613I 0
u = 0.614537 − 0.723379I
a = −0.382409 + 0.933491I
b = 0.520893 − 0.967316I
−2.87584 + 4.39613I 0
u = −0.160696 + 0.922940I
a = −1.051960 + 0.231090I
b = 1.049000 − 0.295188I
−1.37343 + 2.15773I 0
u = −0.160696 − 0.922940I
a = −1.051960 − 0.231090I
b = 1.049000 + 0.295188I
−1.37343 − 2.15773I 0
u = −1.058680 + 0.145296I
a = 0.460538 + 0.227295I
b = 0.840560 − 0.207999I
−1.56282 + 0.11358I 0
u = −1.058680 − 0.145296I
a = 0.460538 − 0.227295I
b = 0.840560 + 0.207999I
−1.56282 − 0.11358I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.771663 + 0.446424I
a = −1.14604 + 1.04772I
b = 0.541922 + 0.544394I
−4.96355 − 3.50876I 0
u = −0.771663 − 0.446424I
a = −1.14604 − 1.04772I
b = 0.541922 − 0.544394I
−4.96355 + 3.50876I 0
u = 0.357261 + 0.813565I
a = 1.15745 + 1.19649I
b = −1.19712 − 1.22505I
−7.9239 − 13.8663I 0
u = 0.357261 − 0.813565I
a = 1.15745 − 1.19649I
b = −1.19712 + 1.22505I
−7.9239 + 13.8663I 0
u = −0.404133 + 0.783971I
a = −0.866155 + 0.697337I
b = 0.748223 − 0.769256I
−1.51097 + 2.78695I 0
u = −0.404133 − 0.783971I
a = −0.866155 − 0.697337I
b = 0.748223 + 0.769256I
−1.51097 − 2.78695I 0
u = 1.094700 + 0.234164I
a = −0.577419 − 0.264483I
b = −0.549890 + 0.527872I
−4.54668 − 4.46609I 0
u = 1.094700 − 0.234164I
a = −0.577419 + 0.264483I
b = −0.549890 − 0.527872I
−4.54668 + 4.46609I 0
u = −1.033800 + 0.437885I
a = 0.257491 − 0.940473I
b = −0.686255 − 0.343745I
−4.07515 + 2.66051I 0
u = −1.033800 − 0.437885I
a = 0.257491 + 0.940473I
b = −0.686255 + 0.343745I
−4.07515 − 2.66051I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.131310 + 0.055315I
a = −0.151277 + 0.933019I
b = 0.13358 + 1.85091I
−9.53618 + 0.93120I 0
u = 1.131310 − 0.055315I
a = −0.151277 − 0.933019I
b = 0.13358 − 1.85091I
−9.53618 − 0.93120I 0
u = −0.440237 + 0.713965I
a = 0.992326 − 0.668774I
b = −0.325618 + 0.204381I
−1.69555 + 1.98381I 0
u = −0.440237 − 0.713965I
a = 0.992326 + 0.668774I
b = −0.325618 − 0.204381I
−1.69555 − 1.98381I 0
u = 0.347045 + 0.743011I
a = 0.869436 − 0.335291I
b = −0.018759 + 0.573045I
−2.03680 − 0.36310I 0
u = 0.347045 − 0.743011I
a = 0.869436 + 0.335291I
b = −0.018759 − 0.573045I
−2.03680 + 0.36310I 0
u = −0.296638 + 0.762588I
a = 1.32323 − 1.27789I
b = −1.33073 + 1.15712I
−3.39639 + 7.81505I 0
u = −0.296638 − 0.762588I
a = 1.32323 + 1.27789I
b = −1.33073 − 1.15712I
−3.39639 − 7.81505I 0
u = 1.193810 + 0.072843I
a = 0.616469 + 0.767214I
b = 0.758914 + 0.153228I
−2.23354 + 1.52529I 0
u = 1.193810 − 0.072843I
a = 0.616469 − 0.767214I
b = 0.758914 − 0.153228I
−2.23354 − 1.52529I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.045115 + 0.792707I
a = 0.995941 + 0.391751I
b = −0.248171 − 0.528968I
−1.174710 + 0.610806I −5.85025 + 1.21411I
u = −0.045115 − 0.792707I
a = 0.995941 − 0.391751I
b = −0.248171 + 0.528968I
−1.174710 − 0.610806I −5.85025 − 1.21411I
u = −1.213260 + 0.074521I
a = −0.738681 − 0.552826I
b = −0.95568 + 1.47398I
−2.10913 + 0.80254I 0
u = −1.213260 − 0.074521I
a = −0.738681 + 0.552826I
b = −0.95568 − 1.47398I
−2.10913 − 0.80254I 0
u = −0.714265 + 0.257828I
a = 0.95188 − 1.20880I
b = 0.284028 + 0.353544I
−4.34819 − 3.50064I −10.15879 + 2.61062I
u = −0.714265 − 0.257828I
a = 0.95188 + 1.20880I
b = 0.284028 − 0.353544I
−4.34819 + 3.50064I −10.15879 − 2.61062I
u = −0.267217 + 0.705736I
a = −1.37518 + 1.03742I
b = 0.584151 − 1.234020I
−2.73124 + 7.20564I −7.22129 − 8.23166I
u = −0.267217 − 0.705736I
a = −1.37518 − 1.03742I
b = 0.584151 + 1.234020I
−2.73124 − 7.20564I −7.22129 + 8.23166I
u = 0.293364 + 0.692080I
a = −0.65992 + 1.40520I
b = −0.22122 − 1.46251I
−3.72611 − 7.81436I −5.94311 + 7.27559I
u = 0.293364 − 0.692080I
a = −0.65992 − 1.40520I
b = −0.22122 + 1.46251I
−3.72611 + 7.81436I −5.94311 − 7.27559I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.164096 + 0.720950I
a = 0.242278 + 0.831725I
b = −0.196291 − 0.953290I
0.96231 + 3.37259I −0.66181 − 5.02684I
u = −0.164096 − 0.720950I
a = 0.242278 − 0.831725I
b = −0.196291 + 0.953290I
0.96231 − 3.37259I −0.66181 + 5.02684I
u = 1.255140 + 0.207604I
a = 0.600745 − 0.538593I
b = 1.30795 + 0.56083I
−0.95909 − 4.01812I 0
u = 1.255140 − 0.207604I
a = 0.600745 + 0.538593I
b = 1.30795 − 0.56083I
−0.95909 + 4.01812I 0
u = −0.719676
a = 0.701794
b = 0.424952
−1.50335 −6.04810
u = −1.273630 + 0.227101I
a = −0.623129 + 0.007221I
b = −0.024009 + 1.071650I
−1.12960 + 2.12830I 0
u = −1.273630 − 0.227101I
a = −0.623129 − 0.007221I
b = −0.024009 − 1.071650I
−1.12960 − 2.12830I 0
u = 0.297171 + 0.631786I
a = 1.29874 + 1.61569I
b = −1.50993 − 1.26578I
−8.12476 − 1.41435I −10.19810 + 3.32175I
u = 0.297171 − 0.631786I
a = 1.29874 − 1.61569I
b = −1.50993 + 1.26578I
−8.12476 + 1.41435I −10.19810 − 3.32175I
u = 0.593856 + 0.322694I
a = −1.144100 + 0.499841I
b = −0.117888 − 1.239260I
−5.01452 + 4.11784I −8.48824 − 1.68058I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.593856 − 0.322694I
a = −1.144100 − 0.499841I
b = −0.117888 + 1.239260I
−5.01452 − 4.11784I −8.48824 + 1.68058I
u = 0.235947 + 0.623765I
a = −1.57054 − 0.72572I
b = 1.60485 + 1.23476I
−7.32776 − 3.51777I −11.20872 + 5.37878I
u = 0.235947 − 0.623765I
a = −1.57054 + 0.72572I
b = 1.60485 − 1.23476I
−7.32776 + 3.51777I −11.20872 − 5.37878I
u = 1.338000 + 0.055970I
a = −0.097785 − 1.142750I
b = −0.57344 + 1.56737I
−11.78960 − 1.92476I 0
u = 1.338000 − 0.055970I
a = −0.097785 + 1.142750I
b = −0.57344 − 1.56737I
−11.78960 + 1.92476I 0
u = 0.012576 + 0.632373I
a = 0.577328 − 1.252450I
b = −0.562925 + 0.991272I
2.83723 + 0.97754I 3.54382 − 2.20940I
u = 0.012576 − 0.632373I
a = 0.577328 + 1.252450I
b = −0.562925 − 0.991272I
2.83723 − 0.97754I 3.54382 + 2.20940I
u = 1.352470 + 0.213334I
a = −0.414971 − 0.200004I
b = −0.860846 − 0.278696I
−5.08107 − 3.53397I 0
u = 1.352470 − 0.213334I
a = −0.414971 + 0.200004I
b = −0.860846 + 0.278696I
−5.08107 + 3.53397I 0
u = 0.230584 + 0.580687I
a = −1.42586 − 1.37552I
b = 0.552732 + 1.125940I
0.27877 − 3.72484I −0.25287 + 3.53714I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.230584 − 0.580687I
a = −1.42586 + 1.37552I
b = 0.552732 − 1.125940I
0.27877 + 3.72484I −0.25287 − 3.53714I
u = 1.351520 + 0.300209I
a = −0.439642 + 0.118954I
b = −0.352361 − 1.056070I
−3.81291 − 7.07815I 0
u = 1.351520 − 0.300209I
a = −0.439642 − 0.118954I
b = −0.352361 + 1.056070I
−3.81291 + 7.07815I 0
u = −1.377860 + 0.198340I
a = −0.092721 + 0.816913I
b = 1.33537 − 1.57047I
−5.39823 + 1.12081I 0
u = −1.377860 − 0.198340I
a = −0.092721 − 0.816913I
b = 1.33537 + 1.57047I
−5.39823 − 1.12081I 0
u = 1.39625
a = −0.427157
b = 0.0766782
−7.75893 0
u = 1.308430 + 0.495916I
a = 0.136018 + 0.735283I
b = −1.094890 − 0.176787I
−5.94181 − 7.24846I 0
u = 1.308430 − 0.495916I
a = 0.136018 − 0.735283I
b = −1.094890 + 0.176787I
−5.94181 + 7.24846I 0
u = −1.397780 + 0.124154I
a = −0.214087 + 0.312942I
b = −1.87470 + 0.94938I
−10.21350 + 4.66937I 0
u = −1.397780 − 0.124154I
a = −0.214087 − 0.312942I
b = −1.87470 − 0.94938I
−10.21350 − 4.66937I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.399710 + 0.129687I
a = −0.122996 − 0.787009I
b = 1.25500 + 2.69944I
−10.24600 + 2.33584I 0
u = 1.399710 − 0.129687I
a = −0.122996 + 0.787009I
b = 1.25500 − 2.69944I
−10.24600 − 2.33584I 0
u = −1.394160 + 0.180221I
a = −0.223833 + 1.000450I
b = −0.36504 − 1.80456I
−13.52120 + 1.36381I 0
u = −1.394160 − 0.180221I
a = −0.223833 − 1.000450I
b = −0.36504 + 1.80456I
−13.52120 − 1.36381I 0
u = −1.390760 + 0.230878I
a = −0.152323 − 0.959451I
b = −1.59968 + 1.94546I
−4.90359 + 6.72120I 0
u = −1.390760 − 0.230878I
a = −0.152323 + 0.959451I
b = −1.59968 − 1.94546I
−4.90359 − 6.72120I 0
u = 1.393660 + 0.218126I
a = 1.111440 + 0.019269I
b = 0.60142 + 1.46469I
−4.60265 − 4.02663I 0
u = 1.393660 − 0.218126I
a = 1.111440 − 0.019269I
b = 0.60142 − 1.46469I
−4.60265 + 4.02663I 0
u = −0.229473 + 0.539634I
a = −1.28148 − 1.86660I
b = −0.06183 + 1.62357I
0.606565 + 1.201870I −10.56206 − 6.88957I
u = −0.229473 − 0.539634I
a = −1.28148 + 1.86660I
b = −0.06183 − 1.62357I
0.606565 − 1.201870I −10.56206 + 6.88957I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.39466 + 0.24727I
a = 0.001851 − 0.833863I
b = −3.08790 + 0.93606I
−12.5379 + 6.7134I 0
u = −1.39466 − 0.24727I
a = 0.001851 + 0.833863I
b = −3.08790 − 0.93606I
−12.5379 − 6.7134I 0
u = 1.42192 + 0.10390I
a = −0.303312 + 0.815867I
b = −1.49389 − 1.92620I
−10.51730 − 3.96053I 0
u = 1.42192 − 0.10390I
a = −0.303312 − 0.815867I
b = −1.49389 + 1.92620I
−10.51730 + 3.96053I 0
u = −1.42260 + 0.14062I
a = 0.781669 − 0.266456I
b = 0.619383 − 1.235640I
−11.07080 − 2.43540I 0
u = −1.42260 − 0.14062I
a = 0.781669 + 0.266456I
b = 0.619383 + 1.235640I
−11.07080 + 2.43540I 0
u = −1.42046 + 0.17926I
a = 0.506393 − 1.120470I
b = −0.607801 + 0.428830I
−14.5928 + 4.1561I 0
u = −1.42046 − 0.17926I
a = 0.506393 + 1.120470I
b = −0.607801 − 0.428830I
−14.5928 − 4.1561I 0
u = 1.40901 + 0.27697I
a = −0.052276 + 0.948632I
b = −1.78482 − 2.12821I
−8.08136 − 10.77760I 0
u = 1.40901 − 0.27697I
a = −0.052276 − 0.948632I
b = −1.78482 + 2.12821I
−8.08136 + 10.77760I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.379883 + 0.415061I
a = −2.44465 − 1.26285I
b = 0.624684 − 0.580136I
−8.88592 − 1.83926I −12.72836 + 5.81559I
u = 0.379883 − 0.415061I
a = −2.44465 + 1.26285I
b = 0.624684 + 0.580136I
−8.88592 + 1.83926I −12.72836 − 5.81559I
u = −1.41699 + 0.24634I
a = 0.380244 + 1.024980I
b = 2.34865 − 1.24482I
−13.6123 + 4.6362I 0
u = −1.41699 − 0.24634I
a = 0.380244 − 1.024980I
b = 2.34865 + 1.24482I
−13.6123 − 4.6362I 0
u = −1.41909 + 0.26969I
a = 0.898900 + 0.166070I
b = 0.74340 − 1.28203I
−9.2019 + 11.3180I 0
u = −1.41909 − 0.26969I
a = 0.898900 − 0.166070I
b = 0.74340 + 1.28203I
−9.2019 − 11.3180I 0
u = 1.45048 + 0.06075I
a = 0.179933 + 1.069800I
b = −0.490788 − 0.997127I
−12.12480 + 2.31290I 0
u = 1.45048 − 0.06075I
a = 0.179933 − 1.069800I
b = −0.490788 + 0.997127I
−12.12480 − 2.31290I 0
u = −1.43022 + 0.28124I
a = −0.505724 + 0.128919I
b = −0.431087 + 0.172604I
−7.68688 + 4.06026I 0
u = −1.43022 − 0.28124I
a = −0.505724 − 0.128919I
b = −0.431087 − 0.172604I
−7.68688 − 4.06026I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42692 + 0.29959I
a = 0.230261 − 1.084960I
b = 2.16361 + 1.32117I
−8.9036 − 11.6654I 0
u = 1.42692 − 0.29959I
a = 0.230261 + 1.084960I
b = 2.16361 − 1.32117I
−8.9036 + 11.6654I 0
u = 1.44405 + 0.30923I
a = −0.046586 + 0.780044I
b = −1.76079 − 1.09227I
−7.34225 − 6.78476I 0
u = 1.44405 − 0.30923I
a = −0.046586 − 0.780044I
b = −1.76079 + 1.09227I
−7.34225 + 6.78476I 0
u = 1.45362 + 0.27555I
a = −0.120895 − 0.821422I
b = 0.84776 + 1.13648I
−7.69994 − 5.61368I 0
u = 1.45362 − 0.27555I
a = −0.120895 + 0.821422I
b = 0.84776 − 1.13648I
−7.69994 + 5.61368I 0
u = −1.46032 + 0.31665I
a = 0.187544 + 1.022960I
b = 2.08623 − 1.47677I
−13.7489 + 17.9654I 0
u = −1.46032 − 0.31665I
a = 0.187544 − 1.022960I
b = 2.08623 + 1.47677I
−13.7489 − 17.9654I 0
u = 0.244134 + 0.391602I
a = 2.58490 + 1.59798I
b = 0.316070 + 0.051031I
−8.25063 + 0.91007I −11.62517 + 4.79001I
u = 0.244134 − 0.391602I
a = 2.58490 − 1.59798I
b = 0.316070 − 0.051031I
−8.25063 − 0.91007I −11.62517 − 4.79001I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.217230 + 0.369963I
a = 1.89119 + 0.57807I
b = −0.340274 − 0.448029I
−0.368588 + 1.265160I −2.25179 − 3.62102I
u = 0.217230 − 0.369963I
a = 1.89119 − 0.57807I
b = −0.340274 + 0.448029I
−0.368588 − 1.265160I −2.25179 + 3.62102I
u = −1.54616 + 0.29161I
a = −0.138716 − 0.722300I
b = −1.26539 + 1.37382I
−9.88404 + 8.26349I 0
u = −1.54616 − 0.29161I
a = −0.138716 + 0.722300I
b = −1.26539 − 1.37382I
−9.88404 − 8.26349I 0
u = −1.57236 + 0.09089I
a = 0.245716 − 0.867731I
b = −0.184668 + 0.823457I
−17.1654 − 6.6641I 0
u = −1.57236 − 0.09089I
a = 0.245716 + 0.867731I
b = −0.184668 − 0.823457I
−17.1654 + 6.6641I 0
u = −0.163051 + 0.387369I
a = 0.788549 − 0.241422I
b = 0.143746 − 0.498230I
−0.376531 + 1.022460I −6.80239 − 5.91412I
u = −0.163051 − 0.387369I
a = 0.788549 + 0.241422I
b = 0.143746 + 0.498230I
−0.376531 − 1.022460I −6.80239 + 5.91412I
u = 0.0304396 + 0.1031070I
a = 5.54320 + 4.04883I
b = 0.53363 + 1.75865I
−5.11882 − 3.47087I −9.75395 − 3.64216I
u = 0.0304396 − 0.1031070I
a = 5.54320 − 4.04883I
b = 0.53363 − 1.75865I
−5.11882 + 3.47087I −9.75395 + 3.64216I
16
II. I
u
2
=
h−2u
27
+2u
26
+· · ·+b+2, −6u
27
+6u
26
+· · ·+a−8u, u
28
−2u
27
+· · ·−2u+1i
(i) Arc colorings
a
4
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
1
=
−u
−u
3
+ u
a
2
=
u
3
− 2u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
6u
27
− 6u
26
+ ··· − 51u
2
+ 8u
2u
27
− 2u
26
+ ··· + 5u − 2
a
7
=
6u
27
− 6u
26
+ ··· + 8u + 1
−u
26
− u
25
+ ··· + 3u − 1
a
11
=
−8u
27
+ 7u
26
+ ··· − 34u + 8
13u
27
− 8u
26
+ ··· + 12u − 7
a
9
=
u
27
− 3u
26
+ ··· + 5u − 6
−2u
27
+ u
26
+ ··· − 5u + 1
a
10
=
2u
27
− 26u
25
+ ··· − 29u + 2
7u
27
− 4u
26
+ ··· + 9u − 4
a
3
=
−4u
27
− 2u
26
+ ··· + 29u − 3
−4u
27
+ 3u
26
+ ··· − 6u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 8u
27
+ 4u
26
− 114u
25
− 47u
24
+ 692u
23
+ 279u
22
− 2304u
21
− 1118u
20
+ 4432u
19
+
3178u
18
− 4420u
17
− 6104u
16
+ 429u
15
+ 7139u
14
+ 4379u
13
− 3848u
12
− 5287u
11
−
685u
10
+ 2779u
9
+ 1565u
8
− 493u
7
− 162u
6
− 239u
5
− 111u
4
+ 114u
3
− 93u
2
+ 36u − 12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
28
− 6u
27
+ ··· + 4u + 1
c
2
u
28
+ 15u
26
+ ··· − 4u + 1
c
3
u
28
− 9u
26
+ ··· + u + 1
c
4
, c
5
u
28
− 2u
27
+ ··· − 2u + 1
c
6
u
28
− 11u
27
+ ··· − 11u + 1
c
7
u
28
+ 15u
26
+ ··· + 4u + 1
c
8
u
28
+ 5u
27
+ ··· + 5u + 1
c
9
u
28
− 9u
26
+ ··· − u + 1
c
10
u
28
− u
27
+ ··· + 2u + 1
c
11
u
28
− 5u
27
+ ··· − 5u + 1
c
12
u
28
+ 2u
27
+ ··· + 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
28
+ 4y
27
+ ··· + 12y + 1
c
2
, c
7
y
28
+ 30y
27
+ ··· + 18y + 1
c
3
, c
9
y
28
− 18y
27
+ ··· + 3y + 1
c
4
, c
5
, c
12
y
28
− 28y
27
+ ··· + 22y + 1
c
6
y
28
− 7y
27
+ ··· − 25y + 1
c
8
, c
11
y
28
+ 17y
27
+ ··· + 13y + 1
c
10
y
28
− 5y
27
+ ··· + 18y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.226786 + 0.922069I
a = 0.810932 − 0.039377I
b = −0.311597 − 0.150544I
−0.42346 + 1.45389I 1.12327 − 2.39365I
u = −0.226786 − 0.922069I
a = 0.810932 + 0.039377I
b = −0.311597 + 0.150544I
−0.42346 − 1.45389I 1.12327 + 2.39365I
u = −0.542882 + 0.743757I
a = −0.679455 + 0.910762I
b = 0.599496 − 0.758661I
−1.60070 + 3.70313I −4.84453 − 8.48426I
u = −0.542882 − 0.743757I
a = −0.679455 − 0.910762I
b = 0.599496 + 0.758661I
−1.60070 − 3.70313I −4.84453 + 8.48426I
u = −1.130710 + 0.071807I
a = 0.451300 + 0.743375I
b = 0.653196 − 0.236536I
−1.93774 + 2.26114I −5.63577 − 5.37479I
u = −1.130710 − 0.071807I
a = 0.451300 − 0.743375I
b = 0.653196 + 0.236536I
−1.93774 − 2.26114I −5.63577 + 5.37479I
u = −1.221060 + 0.187532I
a = 0.525667 + 0.282363I
b = 0.039023 − 1.251230I
−2.10303 + 1.88451I −8.95900 − 3.19260I
u = −1.221060 − 0.187532I
a = 0.525667 − 0.282363I
b = 0.039023 + 1.251230I
−2.10303 − 1.88451I −8.95900 + 3.19260I
u = 1.266800 + 0.101729I
a = 0.330851 + 0.460950I
b = 0.06333 + 2.42389I
−8.34689 + 2.37883I −8.66446 − 2.75796I
u = 1.266800 − 0.101729I
a = 0.330851 − 0.460950I
b = 0.06333 − 2.42389I
−8.34689 − 2.37883I −8.66446 + 2.75796I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.351230 + 0.112969I
a = −0.034822 − 1.114500I
b = 0.36679 + 2.30790I
−12.33140 + 0.03616I −13.73712 − 0.26284I
u = 1.351230 − 0.112969I
a = −0.034822 + 1.114500I
b = 0.36679 − 2.30790I
−12.33140 − 0.03616I −13.73712 + 0.26284I
u = 1.311410 + 0.397683I
a = −0.121084 − 0.454282I
b = −0.019863 + 0.349320I
−5.09637 − 6.22551I −8.74107 + 5.08707I
u = 1.311410 − 0.397683I
a = −0.121084 + 0.454282I
b = −0.019863 − 0.349320I
−5.09637 + 6.22551I −8.74107 − 5.08707I
u = 1.368250 + 0.222269I
a = −0.841608 − 0.004405I
b = −0.807875 − 0.941225I
−3.69262 − 3.64639I −5.80285 + 2.19695I
u = 1.368250 − 0.222269I
a = −0.841608 + 0.004405I
b = −0.807875 + 0.941225I
−3.69262 + 3.64639I −5.80285 − 2.19695I
u = −1.386730 + 0.137225I
a = −0.288267 + 0.986443I
b = −0.594616 − 0.605073I
−12.83980 + 3.15598I −13.8528 − 3.9585I
u = −1.386730 − 0.137225I
a = −0.288267 − 0.986443I
b = −0.594616 + 0.605073I
−12.83980 − 3.15598I −13.8528 + 3.9585I
u = −0.142885 + 0.564127I
a = 0.73374 + 1.54388I
b = 0.265172 − 1.254550I
1.160140 + 0.762431I 0.073804 + 0.154677I
u = −0.142885 − 0.564127I
a = 0.73374 − 1.54388I
b = 0.265172 + 1.254550I
1.160140 − 0.762431I 0.073804 − 0.154677I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43774 + 0.21260I
a = −0.186840 − 0.656465I
b = −2.30607 + 1.46989I
−10.76430 + 6.37236I −12.79242 − 5.59516I
u = −1.43774 − 0.21260I
a = −0.186840 + 0.656465I
b = −2.30607 − 1.46989I
−10.76430 − 6.37236I −12.79242 + 5.59516I
u = 1.47355 + 0.31709I
a = −0.023202 + 0.820560I
b = −1.49094 − 1.21794I
−7.94110 − 7.71551I −12.2861 + 7.7929I
u = 1.47355 − 0.31709I
a = −0.023202 − 0.820560I
b = −1.49094 + 1.21794I
−7.94110 + 7.71551I −12.2861 − 7.7929I
u = 0.263446 + 0.383109I
a = −0.92761 − 1.51891I
b = 0.96295 + 1.84197I
−5.06773 − 3.92340I −7.7415 + 12.8296I
u = 0.263446 − 0.383109I
a = −0.92761 + 1.51891I
b = 0.96295 − 1.84197I
−5.06773 + 3.92340I −7.7415 − 12.8296I
u = 0.054116 + 0.297330I
a = 4.75040 + 0.35248I
b = 0.081015 + 0.817773I
−7.97185 − 1.50215I −4.63946 + 5.05675I
u = 0.054116 − 0.297330I
a = 4.75040 − 0.35248I
b = 0.081015 − 0.817773I
−7.97185 + 1.50215I −4.63946 − 5.05675I
22
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
28
− 6u
27
+ ··· + 4u + 1)(u
120
− 9u
119
+ ··· − 3718u + 2197)
c
2
(u
28
+ 15u
26
+ ··· − 4u + 1)(u
120
+ u
119
+ ··· + 505942u − 143161)
c
3
(u
28
− 9u
26
+ ··· + u + 1)(u
120
+ u
119
+ ··· − 497u − 991)
c
4
, c
5
(u
28
− 2u
27
+ ··· − 2u + 1)(u
120
+ 3u
119
+ ··· + 8u − 1)
c
6
(u
28
− 11u
27
+ ··· − 11u + 1)
· (u
120
− 6u
119
+ ··· − 111403235u + 12357323)
c
7
(u
28
+ 15u
26
+ ··· + 4u + 1)(u
120
+ u
119
+ ··· + 505942u − 143161)
c
8
(u
28
+ 5u
27
+ ··· + 5u + 1)(u
120
+ 6u
119
+ ··· + 64698u + 4996)
c
9
(u
28
− 9u
26
+ ··· − u + 1)(u
120
+ u
119
+ ··· − 497u − 991)
c
10
(u
28
− u
27
+ ··· + 2u + 1)(u
120
+ 2u
119
+ ··· + 86310u + 45641)
c
11
(u
28
− 5u
27
+ ··· − 5u + 1)(u
120
+ 6u
119
+ ··· + 64698u + 4996)
c
12
(u
28
+ 2u
27
+ ··· + 2u + 1)(u
120
+ 3u
119
+ ··· + 8u − 1)
23
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 4y
27
+ ··· + 12y + 1)
· (y
120
− 3y
119
+ ··· + 654218266y + 4826809)
c
2
, c
7
(y
28
+ 30y
27
+ ··· + 18y + 1)
· (y
120
+ 103y
119
+ ··· + 401123665620y + 20495071921)
c
3
, c
9
(y
28
− 18y
27
+ ··· + 3y + 1)
· (y
120
− 85y
119
+ ··· − 45176967y + 982081)
c
4
, c
5
, c
12
(y
28
− 28y
27
+ ··· + 22y + 1)(y
120
− 111y
119
+ ··· + 160y + 1)
c
6
(y
28
− 7y
27
+ ··· − 25y + 1)
· (y
120
− 54y
119
+ ··· − 7346690606945771y + 152703431726329)
c
8
, c
11
(y
28
+ 17y
27
+ ··· + 13y + 1)
· (y
120
+ 82y
119
+ ··· + 638456276y + 24960016)
c
10
(y
28
− 5y
27
+ ··· + 18y + 1)
· (y
120
− 32y
119
+ ··· − 57169443552y + 2083100881)
24
