12a
0609
(K12a
0609
)
A knot diagram
1
Linearized knot diagam
3 7 9 12 10 2 1 11 6 4 8 5
Solving Sequence
2,6
7
3,9
4 10 11 1 5 8 12
c
6
c
2
c
3
c
9
c
10
c
1
c
5
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.11550 × 10
270
u
147
+ 2.34975 × 10
270
u
146
+ ··· + 7.83329 × 10
269
b + 1.17176 × 10
272
,
2.42818 × 10
272
u
147
− 8.26249 × 10
271
u
146
+ ··· + 8.61662 × 10
270
a − 3.99086 × 10
273
,
u
148
− u
147
+ ··· − 28u + 11i
I
u
2
= hu
36
− 6u
35
+ ··· + b + 5, −28u
36
+ 22u
35
+ ··· + a − 30, u
37
− 10u
35
+ ··· − 7u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 185 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−7.12 × 10
270
u
147
+ 2.35 × 10
270
u
146
+ · · · + 7.83 × 10
269
b + 1.17 ×
10
272
, 2.43 × 10
272
u
147
− 8.26 × 10
271
u
146
+ · · · + 8.62 × 10
270
a − 3.99 ×
10
273
, u
148
− u
147
+ · · · − 28u + 11i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−28.1802u
147
+ 9.58902u
146
+ ··· − 500.278u + 463.158
9.08367u
147
− 2.99969u
146
+ ··· + 149.153u − 149.588
a
4
=
28.9466u
147
− 7.64764u
146
+ ··· + 511.326u − 413.056
1.87191u
147
+ 0.474465u
146
+ ··· + 37.3094u − 3.29970
a
10
=
−19.0965u
147
+ 6.58932u
146
+ ··· − 351.125u + 313.570
9.08367u
147
− 2.99969u
146
+ ··· + 149.153u − 149.588
a
11
=
−1.63584u
147
+ 2.74753u
146
+ ··· − 9.74895u + 59.5619
9.74060u
147
− 3.27722u
146
+ ··· + 170.925u − 160.730
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
19.2042u
147
− 3.52906u
146
+ ··· + 360.206u − 255.473
−15.6776u
147
+ 5.49972u
146
+ ··· − 272.591u + 266.188
a
8
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
12
=
−4.32037u
147
+ 0.0334826u
146
+ ··· − 91.4009u + 53.4061
−10.0898u
147
+ 3.69835u
146
+ ··· − 173.459u + 173.267
(ii) Obstruction class = −1
(iii) Cusp Shapes = 170.660u
147
− 53.4676u
146
+ ··· + 2947.57u − 2741.52
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
148
+ 77u
147
+ ··· + 2082u + 121
c
2
, c
6
u
148
− u
147
+ ··· − 28u + 11
c
3
u
148
− u
147
+ ··· − 437764162u + 31663951
c
4
, c
12
u
148
− 41u
146
+ ··· − 1867u − 457
c
5
, c
9
u
148
− 2u
147
+ ··· − 20681u − 4913
c
7
u
148
− 3u
147
+ ··· − 52130042u + 4546267
c
8
, c
11
u
148
+ 6u
147
+ ··· + 147861u + 10043
c
10
u
148
+ u
147
+ ··· − 171710u − 36269
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
148
− 5y
147
+ ··· − 428602y + 14641
c
2
, c
6
y
148
− 77y
147
+ ··· − 2082y + 121
c
3
y
148
+ 59y
147
+ ··· − 106286132462952552y + 1002605792930401
c
4
, c
12
y
148
− 82y
147
+ ··· − 21312345y + 208849
c
5
, c
9
y
148
+ 98y
147
+ ··· + 311191787y + 24137569
c
7
y
148
+ 87y
147
+ ··· + 203578457803668y + 20668543635289
c
8
, c
11
y
148
+ 90y
147
+ ··· + 2708328479y + 100861849
c
10
y
148
+ 23y
147
+ ··· − 9866857228y + 1315440361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.801882 + 0.564876I
a = −1.98309 − 1.20150I
b = 0.201767 + 1.107530I
−4.17373 + 5.78306I 0
u = −0.801882 − 0.564876I
a = −1.98309 + 1.20150I
b = 0.201767 − 1.107530I
−4.17373 − 5.78306I 0
u = 0.753591 + 0.626874I
a = 0.185539 − 1.185390I
b = 0.497327 + 0.904516I
2.94244 + 1.46559I 0
u = 0.753591 − 0.626874I
a = 0.185539 + 1.185390I
b = 0.497327 − 0.904516I
2.94244 − 1.46559I 0
u = 0.819922 + 0.622130I
a = 1.49093 − 0.46144I
b = −0.591941 + 1.046700I
2.73613 − 6.32545I 0
u = 0.819922 − 0.622130I
a = 1.49093 + 0.46144I
b = −0.591941 − 1.046700I
2.73613 + 6.32545I 0
u = 0.949221 + 0.199178I
a = −1.89330 − 0.09556I
b = 0.727956 − 0.713865I
−3.20129 − 5.06040I 0
u = 0.949221 − 0.199178I
a = −1.89330 + 0.09556I
b = 0.727956 + 0.713865I
−3.20129 + 5.06040I 0
u = −0.965652 + 0.381043I
a = −0.082316 + 0.291581I
b = 0.278548 − 0.430341I
−1.50408 + 1.47661I 0
u = −0.965652 − 0.381043I
a = −0.082316 − 0.291581I
b = 0.278548 + 0.430341I
−1.50408 − 1.47661I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.032450 + 0.117025I
a = −0.356571 − 0.269265I
b = 0.461349 + 0.517094I
−3.46852 − 0.71657I 0
u = −1.032450 − 0.117025I
a = −0.356571 + 0.269265I
b = 0.461349 − 0.517094I
−3.46852 + 0.71657I 0
u = −0.722106 + 0.626635I
a = −1.101530 + 0.062706I
b = 0.826797 − 0.355727I
1.99222 + 6.26430I 0
u = −0.722106 − 0.626635I
a = −1.101530 − 0.062706I
b = 0.826797 + 0.355727I
1.99222 − 6.26430I 0
u = −0.918255 + 0.497223I
a = −1.42108 + 1.16642I
b = 0.861920 + 0.742199I
3.60069 + 3.57734I 0
u = −0.918255 − 0.497223I
a = −1.42108 − 1.16642I
b = 0.861920 − 0.742199I
3.60069 − 3.57734I 0
u = 0.950293 + 0.434823I
a = −1.34910 − 0.73463I
b = 0.557261 − 0.168149I
−0.39596 − 3.88277I 0
u = 0.950293 − 0.434823I
a = −1.34910 + 0.73463I
b = 0.557261 + 0.168149I
−0.39596 + 3.88277I 0
u = −0.448329 + 0.840026I
a = 0.421644 − 0.849882I
b = −0.194488 + 1.268240I
−2.82616 − 2.12943I 0
u = −0.448329 − 0.840026I
a = 0.421644 + 0.849882I
b = −0.194488 − 1.268240I
−2.82616 + 2.12943I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.333726 + 1.007330I
a = −0.120235 + 0.741241I
b = 0.095350 − 1.282620I
−3.75918 − 2.82637I 0
u = −0.333726 − 1.007330I
a = −0.120235 − 0.741241I
b = 0.095350 + 1.282620I
−3.75918 + 2.82637I 0
u = −0.859504 + 0.623047I
a = 1.11434 − 0.94865I
b = −0.602274 − 0.505888I
1.60311 − 1.40810I 0
u = −0.859504 − 0.623047I
a = 1.11434 + 0.94865I
b = −0.602274 + 0.505888I
1.60311 + 1.40810I 0
u = 0.115334 + 1.057600I
a = −0.279424 − 0.411326I
b = 0.031526 + 1.026900I
−4.73792 + 0.18945I 0
u = 0.115334 − 1.057600I
a = −0.279424 + 0.411326I
b = 0.031526 − 1.026900I
−4.73792 − 0.18945I 0
u = 0.247947 + 0.901431I
a = −1.116440 − 0.780764I
b = 0.57458 + 1.36111I
−4.3204 + 13.9557I 0
u = 0.247947 − 0.901431I
a = −1.116440 + 0.780764I
b = 0.57458 − 1.36111I
−4.3204 − 13.9557I 0
u = −0.724944 + 0.522800I
a = 1.18389 + 0.92493I
b = −0.176138 − 0.961064I
−1.19364 + 2.08514I 0
u = −0.724944 − 0.522800I
a = 1.18389 − 0.92493I
b = −0.176138 + 0.961064I
−1.19364 − 2.08514I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.759102 + 0.461625I
a = −0.32697 − 1.90410I
b = 0.047807 + 1.073240I
−4.01726 − 1.52458I 0
u = −0.759102 − 0.461625I
a = −0.32697 + 1.90410I
b = 0.047807 − 1.073240I
−4.01726 + 1.52458I 0
u = −0.996847 + 0.518156I
a = −0.515323 + 0.715296I
b = 0.575549 − 0.924658I
−1.260890 + 0.226294I 0
u = −0.996847 − 0.518156I
a = −0.515323 − 0.715296I
b = 0.575549 + 0.924658I
−1.260890 − 0.226294I 0
u = −1.115870 + 0.152069I
a = −0.241236 − 0.379829I
b = −0.051143 − 1.079750I
−2.92928 + 2.44675I 0
u = −1.115870 − 0.152069I
a = −0.241236 + 0.379829I
b = −0.051143 + 1.079750I
−2.92928 − 2.44675I 0
u = 1.083390 + 0.374604I
a = 0.677527 + 0.958052I
b = 0.18251 + 1.54932I
−6.85236 + 0.13574I 0
u = 1.083390 − 0.374604I
a = 0.677527 − 0.958052I
b = 0.18251 − 1.54932I
−6.85236 − 0.13574I 0
u = 0.204334 + 0.826121I
a = 1.124900 + 0.715403I
b = −0.61938 − 1.35395I
−0.51756 + 7.81284I 0
u = 0.204334 − 0.826121I
a = 1.124900 − 0.715403I
b = −0.61938 + 1.35395I
−0.51756 − 7.81284I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.113590 + 0.291888I
a = 0.293297 + 1.021440I
b = 0.159837 + 1.392530I
−7.03383 + 0.08971I 0
u = 1.113590 − 0.291888I
a = 0.293297 − 1.021440I
b = 0.159837 − 1.392530I
−7.03383 − 0.08971I 0
u = 0.432270 + 0.720324I
a = 0.611532 − 1.000840I
b = −0.286130 + 0.372349I
1.19324 + 2.46533I 0
u = 0.432270 − 0.720324I
a = 0.611532 + 1.000840I
b = −0.286130 − 0.372349I
1.19324 − 2.46533I 0
u = −0.210776 + 0.813138I
a = −1.45325 + 0.79425I
b = 0.439344 − 1.255070I
−7.18334 − 7.02861I 0
u = −0.210776 − 0.813138I
a = −1.45325 − 0.79425I
b = 0.439344 + 1.255070I
−7.18334 + 7.02861I 0
u = 0.781945 + 0.857312I
a = −0.101971 + 0.902087I
b = −0.312973 − 1.056760I
−0.06242 + 4.94279I 0
u = 0.781945 − 0.857312I
a = −0.101971 − 0.902087I
b = −0.312973 + 1.056760I
−0.06242 − 4.94279I 0
u = 0.026933 + 0.836326I
a = −1.049010 − 0.576149I
b = 0.625028 + 1.186720I
−6.07873 + 2.17643I 0
u = 0.026933 − 0.836326I
a = −1.049010 + 0.576149I
b = 0.625028 − 1.186720I
−6.07873 − 2.17643I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.089850 + 0.408220I
a = 0.637757 − 0.676371I
b = −0.700513 + 0.898650I
−1.29393 + 0.96563I 0
u = −1.089850 − 0.408220I
a = 0.637757 + 0.676371I
b = −0.700513 − 0.898650I
−1.29393 − 0.96563I 0
u = 1.100130 + 0.385626I
a = 1.40067 + 2.02165I
b = 0.032025 + 1.022240I
−3.99476 + 2.05581I 0
u = 1.100130 − 0.385626I
a = 1.40067 − 2.02165I
b = 0.032025 − 1.022240I
−3.99476 − 2.05581I 0
u = 0.875901 + 0.772682I
a = −1.274370 + 0.495646I
b = 0.439542 − 1.121260I
−0.39615 − 10.89840I 0
u = 0.875901 − 0.772682I
a = −1.274370 − 0.495646I
b = 0.439542 + 1.121260I
−0.39615 + 10.89840I 0
u = 0.492360 + 0.668072I
a = 1.000830 + 0.736488I
b = −0.436862 − 0.283519I
1.53421 − 0.23768I 0
u = 0.492360 − 0.668072I
a = 1.000830 − 0.736488I
b = −0.436862 + 0.283519I
1.53421 + 0.23768I 0
u = 1.047440 + 0.555613I
a = −1.087820 − 0.185331I
b = 0.478821 − 0.312236I
−0.11027 − 4.51657I 0
u = 1.047440 − 0.555613I
a = −1.087820 + 0.185331I
b = 0.478821 + 0.312236I
−0.11027 + 4.51657I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.433187 + 0.680149I
a = 0.528844 + 1.295920I
b = 0.022821 − 0.691902I
1.67106 − 0.48268I 0
u = 0.433187 − 0.680149I
a = 0.528844 − 1.295920I
b = 0.022821 + 0.691902I
1.67106 + 0.48268I 0
u = −0.240264 + 0.766217I
a = −1.68880 + 0.13667I
b = 1.163530 + 0.077343I
−0.25443 − 7.84410I 0
u = −0.240264 − 0.766217I
a = −1.68880 − 0.13667I
b = 1.163530 − 0.077343I
−0.25443 + 7.84410I 0
u = 1.129290 + 0.397204I
a = −0.59756 − 1.42716I
b = 1.333640 − 0.128607I
−0.28445 − 2.28003I 0
u = 1.129290 − 0.397204I
a = −0.59756 + 1.42716I
b = 1.333640 + 0.128607I
−0.28445 + 2.28003I 0
u = −0.630802 + 0.496059I
a = 1.212270 − 0.453506I
b = −1.040690 + 0.562959I
4.44277 + 0.54060I 0
u = −0.630802 − 0.496059I
a = 1.212270 + 0.453506I
b = −1.040690 − 0.562959I
4.44277 − 0.54060I 0
u = 1.158480 + 0.321521I
a = 0.330875 + 0.959728I
b = −1.147530 − 0.154773I
−4.43528 + 4.50982I 0
u = 1.158480 − 0.321521I
a = 0.330875 − 0.959728I
b = −1.147530 + 0.154773I
−4.43528 − 4.50982I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.059780 + 0.571412I
a = −1.35632 + 0.45880I
b = 0.170067 − 0.674015I
−0.13946 − 4.36646I 0
u = 1.059780 − 0.571412I
a = −1.35632 − 0.45880I
b = 0.170067 + 0.674015I
−0.13946 + 4.36646I 0
u = 1.106090 + 0.508945I
a = 1.49832 + 0.02977I
b = −0.719961 + 0.618121I
−0.54021 − 6.34086I 0
u = 1.106090 − 0.508945I
a = 1.49832 − 0.02977I
b = −0.719961 − 0.618121I
−0.54021 + 6.34086I 0
u = −1.136940 + 0.443245I
a = 0.62455 − 1.53720I
b = −0.152187 − 1.152130I
−2.37651 + 5.08383I 0
u = −1.136940 − 0.443245I
a = 0.62455 + 1.53720I
b = −0.152187 + 1.152130I
−2.37651 − 5.08383I 0
u = 1.077500 + 0.580475I
a = 0.184332 − 1.015030I
b = 0.221785 + 0.414699I
−0.70142 − 7.44159I 0
u = 1.077500 − 0.580475I
a = 0.184332 + 1.015030I
b = 0.221785 − 0.414699I
−0.70142 + 7.44159I 0
u = −1.117770 + 0.510399I
a = −1.58452 + 1.63949I
b = 0.230218 + 1.150580I
−3.07745 + 9.56188I 0
u = −1.117770 − 0.510399I
a = −1.58452 − 1.63949I
b = 0.230218 − 1.150580I
−3.07745 − 9.56188I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.142330 + 0.454417I
a = −1.69292 − 1.04413I
b = 0.056090 − 0.996161I
−2.28746 − 2.85100I 0
u = 1.142330 − 0.454417I
a = −1.69292 + 1.04413I
b = 0.056090 + 0.996161I
−2.28746 + 2.85100I 0
u = 1.145310 + 0.447419I
a = −0.768700 − 0.149089I
b = −0.45578 − 1.63998I
−8.58012 − 5.99056I 0
u = 1.145310 − 0.447419I
a = −0.768700 + 0.149089I
b = −0.45578 + 1.63998I
−8.58012 + 5.99056I 0
u = −1.151020 + 0.451397I
a = 2.00793 − 0.77488I
b = −0.59356 − 1.46220I
−8.54612 + 2.06131I 0
u = −1.151020 − 0.451397I
a = 2.00793 + 0.77488I
b = −0.59356 + 1.46220I
−8.54612 − 2.06131I 0
u = 0.761864
a = 1.98239
b = 0.218074
1.42241 5.79160
u = −1.138650 + 0.496957I
a = −0.330158 + 1.160040I
b = 1.41673 − 0.30344I
0.43905 + 5.57916I 0
u = −1.138650 − 0.496957I
a = −0.330158 − 1.160040I
b = 1.41673 + 0.30344I
0.43905 − 5.57916I 0
u = −1.172170 + 0.413704I
a = 0.444061 − 0.438419I
b = −0.896065 + 0.153269I
−6.88361 + 1.34143I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.172170 − 0.413704I
a = 0.444061 + 0.438419I
b = −0.896065 − 0.153269I
−6.88361 − 1.34143I 0
u = −0.524665 + 0.541827I
a = 2.43851 + 0.12852I
b = −0.494509 − 0.942321I
0.11534 + 4.09815I 6.00000 − 7.12333I
u = −0.524665 − 0.541827I
a = 2.43851 − 0.12852I
b = −0.494509 + 0.942321I
0.11534 − 4.09815I 6.00000 + 7.12333I
u = −1.136170 + 0.518437I
a = −2.10631 + 0.65979I
b = 0.42174 + 1.36917I
−5.67172 + 7.75931I 0
u = −1.136170 − 0.518437I
a = −2.10631 − 0.65979I
b = 0.42174 − 1.36917I
−5.67172 − 7.75931I 0
u = 0.740640 + 0.107202I
a = −3.37308 − 0.25178I
b = 0.015655 + 0.554283I
−1.91615 − 4.38338I 1.49561 + 1.53528I
u = 0.740640 − 0.107202I
a = −3.37308 + 0.25178I
b = 0.015655 − 0.554283I
−1.91615 + 4.38338I 1.49561 − 1.53528I
u = −0.242014 + 0.707472I
a = 1.15107 − 0.82698I
b = −0.323365 + 1.289570I
−3.08762 − 3.10115I 4.48962 + 2.18486I
u = −0.242014 − 0.707472I
a = 1.15107 + 0.82698I
b = −0.323365 − 1.289570I
−3.08762 + 3.10115I 4.48962 − 2.18486I
u = 1.213900 + 0.322446I
a = 0.048458 − 0.542706I
b = −0.406134 − 1.353640I
−11.57340 + 3.34011I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.213900 − 0.322446I
a = 0.048458 + 0.542706I
b = −0.406134 + 1.353640I
−11.57340 − 3.34011I 0
u = 1.169180 + 0.470625I
a = 0.745459 + 0.975429I
b = −0.838286 − 0.086501I
−6.48682 − 7.03755I 0
u = 1.169180 − 0.470625I
a = 0.745459 − 0.975429I
b = −0.838286 + 0.086501I
−6.48682 + 7.03755I 0
u = −1.219920 + 0.328287I
a = 0.493037 − 0.520521I
b = 0.50711 − 1.40110I
−4.92688 − 4.04995I 0
u = −1.219920 − 0.328287I
a = 0.493037 + 0.520521I
b = 0.50711 + 1.40110I
−4.92688 + 4.04995I 0
u = −1.122330 + 0.591886I
a = −1.82644 + 0.36240I
b = 0.262115 + 1.337110I
−4.92956 + 7.44417I 0
u = −1.122330 − 0.591886I
a = −1.82644 − 0.36240I
b = 0.262115 − 1.337110I
−4.92956 − 7.44417I 0
u = 0.067798 + 0.726970I
a = −1.44135 + 0.31358I
b = 0.751232 + 0.054484I
−3.33724 + 2.64401I 4.17021 − 2.51461I
u = 0.067798 − 0.726970I
a = −1.44135 − 0.31358I
b = 0.751232 − 0.054484I
−3.33724 − 2.64401I 4.17021 + 2.51461I
u = −1.157500 + 0.536981I
a = 0.716087 − 1.064760I
b = −1.290310 + 0.071616I
−2.94521 + 12.72790I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.157500 − 0.536981I
a = 0.716087 + 1.064760I
b = −1.290310 − 0.071616I
−2.94521 − 12.72790I 0
u = 1.276300 + 0.174637I
a = −0.332097 − 0.725962I
b = 0.044430 − 1.387700I
−9.62155 − 0.77584I 0
u = 1.276300 − 0.174637I
a = −0.332097 + 0.725962I
b = 0.044430 + 1.387700I
−9.62155 + 0.77584I 0
u = −1.178100 + 0.541918I
a = 2.15590 − 0.59533I
b = −0.508755 − 1.264260I
−10.0408 + 12.0354I 0
u = −1.178100 − 0.541918I
a = 2.15590 + 0.59533I
b = −0.508755 + 1.264260I
−10.0408 − 12.0354I 0
u = 1.185720 + 0.541795I
a = −1.87506 − 0.85931I
b = 0.66336 − 1.41754I
−3.42992 − 12.85340I 0
u = 1.185720 − 0.541795I
a = −1.87506 + 0.85931I
b = 0.66336 + 1.41754I
−3.42992 + 12.85340I 0
u = 0.695320
a = 2.47142
b = −1.15814
2.41384 −14.1360
u = 1.221690 + 0.472820I
a = 1.47822 + 0.95527I
b = −0.697374 + 1.219010I
−9.63551 − 6.85706I 0
u = 1.221690 − 0.472820I
a = 1.47822 − 0.95527I
b = −0.697374 − 1.219010I
−9.63551 + 6.85706I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.281430 + 0.273869I
a = −0.178770 + 0.518702I
b = −0.47965 + 1.39577I
−9.34194 − 10.08950I 0
u = −1.281430 − 0.273869I
a = −0.178770 − 0.518702I
b = −0.47965 − 1.39577I
−9.34194 + 10.08950I 0
u = −1.236250 + 0.440992I
a = −0.473911 + 0.065980I
b = −0.579215 + 1.255340I
−9.87580 + 2.35380I 0
u = −1.236250 − 0.440992I
a = −0.473911 − 0.065980I
b = −0.579215 − 1.255340I
−9.87580 − 2.35380I 0
u = −0.266229 + 0.615904I
a = 1.08528 + 0.97445I
b = −0.274587 + 1.028270I
−0.65463 − 5.10691I 5.77736 + 7.52073I
u = −0.266229 − 0.615904I
a = 1.08528 − 0.97445I
b = −0.274587 − 1.028270I
−0.65463 + 5.10691I 5.77736 − 7.52073I
u = −0.186098 + 0.644196I
a = 1.70791 − 0.01558I
b = −1.285140 − 0.301029I
3.12787 − 1.15295I 5.18234 + 6.54015I
u = −0.186098 − 0.644196I
a = 1.70791 + 0.01558I
b = −1.285140 + 0.301029I
3.12787 + 1.15295I 5.18234 − 6.54015I
u = 1.200520 + 0.578049I
a = 1.92727 + 0.67817I
b = −0.61315 + 1.40679I
−7.1990 − 19.3509I 0
u = 1.200520 − 0.578049I
a = 1.92727 − 0.67817I
b = −0.61315 − 1.40679I
−7.1990 + 19.3509I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.341069 + 0.567524I
a = −0.99655 − 2.03848I
b = 0.500952 + 0.659786I
1.70324 + 1.95713I 7.50961 − 4.73400I
u = 0.341069 − 0.567524I
a = −0.99655 + 2.03848I
b = 0.500952 − 0.659786I
1.70324 − 1.95713I 7.50961 + 4.73400I
u = 0.624597 + 0.171495I
a = −0.267183 + 0.747969I
b = 0.08389 + 1.57642I
−5.02082 − 2.85082I 9.55604 + 4.35953I
u = 0.624597 − 0.171495I
a = −0.267183 − 0.747969I
b = 0.08389 − 1.57642I
−5.02082 + 2.85082I 9.55604 − 4.35953I
u = −0.025547 + 0.628573I
a = −1.39066 + 1.08240I
b = 0.41101 − 1.46586I
−5.47477 + 2.01722I 2.82900 − 3.32773I
u = −0.025547 − 0.628573I
a = −1.39066 − 1.08240I
b = 0.41101 + 1.46586I
−5.47477 − 2.01722I 2.82900 + 3.32773I
u = −1.225420 + 0.615330I
a = 1.268670 − 0.239357I
b = −0.184236 − 1.351230I
−6.59084 + 8.69863I 0
u = −1.225420 − 0.615330I
a = 1.268670 + 0.239357I
b = −0.184236 + 1.351230I
−6.59084 − 8.69863I 0
u = 0.045061 + 0.611973I
a = 0.913009 − 0.474315I
b = 0.157742 − 0.944384I
0.697494 − 1.209320I 7.98851 + 0.16732I
u = 0.045061 − 0.611973I
a = 0.913009 + 0.474315I
b = 0.157742 + 0.944384I
0.697494 + 1.209320I 7.98851 − 0.16732I
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.289200 + 0.524690I
a = 1.063760 + 0.527459I
b = −0.168309 + 0.988972I
−8.51204 − 5.76595I 0
u = 1.289200 − 0.524690I
a = 1.063760 − 0.527459I
b = −0.168309 − 0.988972I
−8.51204 + 5.76595I 0
u = −1.358170 + 0.336939I
a = −0.236890 + 0.470264I
b = 0.013099 + 1.172730I
−9.80541 + 4.71923I 0
u = −1.358170 − 0.336939I
a = −0.236890 − 0.470264I
b = 0.013099 − 1.172730I
−9.80541 − 4.71923I 0
u = 0.450936 + 0.386173I
a = 1.47823 + 0.11520I
b = −0.417145 − 0.041194I
0.954703 + 0.201112I 11.22068 − 1.70554I
u = 0.450936 − 0.386173I
a = 1.47823 − 0.11520I
b = −0.417145 + 0.041194I
0.954703 − 0.201112I 11.22068 + 1.70554I
u = −0.575019 + 0.118532I
a = −2.87421 + 2.06512I
b = 0.465783 + 0.998533I
0.87032 + 1.96199I 2.59548 + 2.16054I
u = −0.575019 − 0.118532I
a = −2.87421 − 2.06512I
b = 0.465783 − 0.998533I
0.87032 − 1.96199I 2.59548 − 2.16054I
19
II. I
u
2
=
hu
36
−6u
35
+· · ·+b+5, −28u
36
+22u
35
+· · ·+a−30, u
37
−10u
35
+· · ·−7u
2
+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
28u
36
− 22u
35
+ ··· − 35u + 30
−u
36
+ 6u
35
+ ··· + 29u
2
− 5
a
4
=
3u
36
− 13u
35
+ ··· + 16u − 1
3u
36
− 32u
34
+ ··· − 6u + 1
a
10
=
27u
36
− 16u
35
+ ··· − 35u + 25
−u
36
+ 6u
35
+ ··· + 29u
2
− 5
a
11
=
16u
36
− 13u
35
+ ··· − 23u + 21
−6u
36
+ 4u
35
+ ··· + 9u − 3
a
1
=
u
3
u
5
− u
3
+ u
a
5
=
−3u
35
+ 2u
34
+ ··· + 5u − 3
4u
36
− 39u
34
+ ··· − 12u + 1
a
8
=
u
6
− u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
12
=
9u
36
− 12u
35
+ ··· − 9u + 15
−4u
36
+ 39u
34
+ ··· + 12u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 54u
36
− 28u
35
− 503u
34
+ 247u
33
+ 2362u
32
− 1104u
31
−
7080u
30
+ 3035u
29
+ 14902u
28
− 5343u
27
− 22895u
26
+ 5159u
25
+ 26146u
24
+ 844u
23
−
22107u
22
− 12287u
21
+ 13248u
20
+ 23328u
19
− 3721u
18
− 27732u
17
− 4134u
16
+
24779u
15
+ 9469u
14
− 18838u
13
− 10793u
12
+ 13395u
11
+ 8109u
10
− 8963u
9
− 3831u
8
+
5044u
7
+ 921u
6
− 2125u
5
+ 104u
4
+ 577u
3
− 129u
2
− 95u + 33
20
(iv) u-Polynomials at the component
21
Crossings u-Polynomials at each crossing
c
1
u
37
− 20u
36
+ ··· + 14u − 1
c
2
u
37
− 10u
35
+ ··· + 7u
2
− 1
c
3
u
37
+ 4u
35
+ ··· − 16u
2
− 1
c
4
u
37
+ 3u
36
+ ··· − 3u − 1
c
5
u
37
− u
36
+ ··· − u + 1
c
6
u
37
− 10u
35
+ ··· − 7u
2
+ 1
c
7
u
37
+ 10u
35
+ ··· − 12u
2
+ 1
c
8
u
37
+ 7u
36
+ ··· + 7u + 1
c
9
u
37
+ u
36
+ ··· − u − 1
c
10
u
37
+ 16u
32
+ ··· − 2u + 1
c
11
u
37
− 7u
36
+ ··· + 7u − 1
c
12
u
37
− 3u
36
+ ··· − 3u + 1
22
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
37
+ 40y
35
+ ··· − 6y −1
c
2
, c
6
y
37
− 20y
36
+ ··· + 14y −1
c
3
y
37
+ 8y
36
+ ··· − 32y −1
c
4
, c
12
y
37
− 29y
36
+ ··· + 33y −1
c
5
, c
9
y
37
+ 23y
36
+ ··· − 19y −1
c
7
y
37
+ 20y
36
+ ··· + 24y −1
c
8
, c
11
y
37
+ 19y
36
+ ··· − 23y −1
c
10
y
37
+ 32y
34
+ ··· + 32y −1
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.126418 + 1.004850I
a = −0.372929 + 0.514247I
b = 0.245798 − 1.115710I
−4.68516 − 1.15715I 2.36493 + 4.35446I
u = −0.126418 − 1.004850I
a = −0.372929 − 0.514247I
b = 0.245798 + 1.115710I
−4.68516 + 1.15715I 2.36493 − 4.35446I
u = −0.973839 + 0.375194I
a = 0.23798 − 2.10843I
b = −0.277307 + 0.547700I
−2.50360 − 2.25726I 5.71927 + 2.73156I
u = −0.973839 − 0.375194I
a = 0.23798 + 2.10843I
b = −0.277307 − 0.547700I
−2.50360 + 2.25726I 5.71927 − 2.73156I
u = −0.419626 + 0.825034I
a = 0.324957 − 0.704938I
b = −0.089863 + 1.285830I
−2.59777 − 3.05067I 6.56037 + 6.23767I
u = −0.419626 − 0.825034I
a = 0.324957 + 0.704938I
b = −0.089863 − 1.285830I
−2.59777 + 3.05067I 6.56037 − 6.23767I
u = 0.607146 + 0.672527I
a = 0.973930 − 0.732680I
b = 0.151249 + 0.674640I
0.29387 + 3.25792I 4.24381 − 2.66674I
u = 0.607146 − 0.672527I
a = 0.973930 + 0.732680I
b = 0.151249 − 0.674640I
0.29387 − 3.25792I 4.24381 + 2.66674I
u = −1.008990 + 0.437769I
a = −0.938678 + 0.534023I
b = 0.550313 − 0.894606I
−0.122562 + 0.887703I 9.01578 − 1.72530I
u = −1.008990 − 0.437769I
a = −0.938678 − 0.534023I
b = 0.550313 + 0.894606I
−0.122562 − 0.887703I 9.01578 + 1.72530I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.063200 + 0.309105I
a = 0.77558 + 1.47407I
b = 0.02746 + 1.48117I
−6.91036 + 0.94699I −0.69599 − 5.57403I
u = 1.063200 − 0.309105I
a = 0.77558 − 1.47407I
b = 0.02746 − 1.48117I
−6.91036 − 0.94699I −0.69599 + 5.57403I
u = 1.024330 + 0.515292I
a = −1.61272 + 0.68895I
b = 0.462091 − 0.745535I
0.44457 − 5.19303I 7.91069 + 6.14189I
u = 1.024330 − 0.515292I
a = −1.61272 − 0.68895I
b = 0.462091 + 0.745535I
0.44457 + 5.19303I 7.91069 − 6.14189I
u = −0.799770 + 0.277679I
a = −3.42907 + 0.12036I
b = 0.354210 + 0.616794I
−1.75281 + 5.10225I 5.06745 − 11.38448I
u = −0.799770 − 0.277679I
a = −3.42907 − 0.12036I
b = 0.354210 − 0.616794I
−1.75281 − 5.10225I 5.06745 + 11.38448I
u = −1.090920 + 0.380355I
a = −0.55650 + 1.43830I
b = 0.979401 + 0.049172I
0.30294 + 2.47989I 10.49434 − 3.78883I
u = −1.090920 − 0.380355I
a = −0.55650 − 1.43830I
b = 0.979401 − 0.049172I
0.30294 − 2.47989I 10.49434 + 3.78883I
u = 1.029470 + 0.571073I
a = 0.036763 − 0.759707I
b = −0.145780 + 0.586296I
−1.04342 − 8.09231I 1.81725 + 10.87045I
u = 1.029470 − 0.571073I
a = 0.036763 + 0.759707I
b = −0.145780 − 0.586296I
−1.04342 + 8.09231I 1.81725 − 10.87045I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.806409 + 0.119495I
a = −0.765517 + 0.039792I
b = 0.09917 + 1.48310I
−5.57876 − 2.83725I −5.78371 + 3.99884I
u = 0.806409 − 0.119495I
a = −0.765517 − 0.039792I
b = 0.09917 − 1.48310I
−5.57876 + 2.83725I −5.78371 − 3.99884I
u = 0.607415 + 0.528386I
a = −0.31139 + 2.19278I
b = −0.364937 − 0.804048I
1.79098 + 0.92962I 6.07777 + 2.44142I
u = 0.607415 − 0.528386I
a = −0.31139 − 2.19278I
b = −0.364937 + 0.804048I
1.79098 − 0.92962I 6.07777 − 2.44142I
u = 1.090170 + 0.513154I
a = −0.486072 − 0.685584I
b = 0.963016 − 0.021020I
1.26383 − 4.72050I 8.61420 + 3.67188I
u = 1.090170 − 0.513154I
a = −0.486072 + 0.685584I
b = 0.963016 + 0.021020I
1.26383 + 4.72050I 8.61420 − 3.67188I
u = −0.672478 + 0.357461I
a = 2.29325 − 1.47377I
b = −0.462834 − 0.970386I
1.09063 + 2.57531I 7.13637 − 8.16815I
u = −0.672478 − 0.357461I
a = 2.29325 + 1.47377I
b = −0.462834 + 0.970386I
1.09063 − 2.57531I 7.13637 + 8.16815I
u = −1.130450 + 0.577358I
a = −1.72706 + 0.50896I
b = 0.175407 + 1.359510I
−4.82564 + 8.27734I 2.48773 − 10.16248I
u = −1.130450 − 0.577358I
a = −1.72706 − 0.50896I
b = 0.175407 − 1.359510I
−4.82564 − 8.27734I 2.48773 + 10.16248I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.267710 + 0.371975I
a = −0.527106 − 0.303539I
b = −0.282539 − 1.281220I
−9.34166 − 3.35760I 0
u = 1.267710 − 0.371975I
a = −0.527106 + 0.303539I
b = −0.282539 + 1.281220I
−9.34166 + 3.35760I 0
u = −0.650707
a = 2.93152
b = −1.02903
2.62307 25.6050
u = −1.274220 + 0.504060I
a = 1.088210 − 0.736370I
b = −0.378178 − 1.065620I
−8.39704 + 6.52609I 0. − 8.92918I
u = −1.274220 − 0.504060I
a = 1.088210 + 0.736370I
b = −0.378178 + 1.065620I
−8.39704 − 6.52609I 0. + 8.92918I
u = 0.326224 + 0.537184I
a = 1.030610 + 0.450541I
b = −0.992163 − 0.003273I
3.42694 + 0.38757I 10.76689 + 1.86191I
u = 0.326224 − 0.537184I
a = 1.030610 − 0.450541I
b = −0.992163 + 0.003273I
3.42694 − 0.38757I 10.76689 − 1.86191I
28
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
37
− 20u
36
+ ··· + 14u − 1)(u
148
+ 77u
147
+ ··· + 2082u + 121)
c
2
(u
37
− 10u
35
+ ··· + 7u
2
− 1)(u
148
− u
147
+ ··· − 28u + 11)
c
3
(u
37
+ 4u
35
+ ··· − 16u
2
− 1)
· (u
148
− u
147
+ ··· − 437764162u + 31663951)
c
4
(u
37
+ 3u
36
+ ··· − 3u − 1)(u
148
− 41u
146
+ ··· − 1867u − 457)
c
5
(u
37
− u
36
+ ··· − u + 1)(u
148
− 2u
147
+ ··· − 20681u − 4913)
c
6
(u
37
− 10u
35
+ ··· − 7u
2
+ 1)(u
148
− u
147
+ ··· − 28u + 11)
c
7
(u
37
+ 10u
35
+ ··· − 12u
2
+ 1)
· (u
148
− 3u
147
+ ··· − 52130042u + 4546267)
c
8
(u
37
+ 7u
36
+ ··· + 7u + 1)(u
148
+ 6u
147
+ ··· + 147861u + 10043)
c
9
(u
37
+ u
36
+ ··· − u − 1)(u
148
− 2u
147
+ ··· − 20681u − 4913)
c
10
(u
37
+ 16u
32
+ ··· − 2u + 1)(u
148
+ u
147
+ ··· − 171710u − 36269)
c
11
(u
37
− 7u
36
+ ··· + 7u − 1)(u
148
+ 6u
147
+ ··· + 147861u + 10043)
c
12
(u
37
− 3u
36
+ ··· − 3u + 1)(u
148
− 41u
146
+ ··· − 1867u − 457)
29
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
37
+ 40y
35
+ ··· − 6y −1)(y
148
− 5y
147
+ ··· − 428602y + 14641)
c
2
, c
6
(y
37
− 20y
36
+ ··· + 14y −1)(y
148
− 77y
147
+ ··· − 2082y + 121)
c
3
(y
37
+ 8y
36
+ ··· − 32y −1)
· (y
148
+ 59y
147
+ ··· − 106286132462952552y + 1002605792930401)
c
4
, c
12
(y
37
− 29y
36
+ ··· + 33y −1)
· (y
148
− 82y
147
+ ··· − 21312345y + 208849)
c
5
, c
9
(y
37
+ 23y
36
+ ··· − 19y −1)
· (y
148
+ 98y
147
+ ··· + 311191787y + 24137569)
c
7
(y
37
+ 20y
36
+ ··· + 24y −1)
· (y
148
+ 87y
147
+ ··· + 203578457803668y + 20668543635289)
c
8
, c
11
(y
37
+ 19y
36
+ ··· − 23y −1)
· (y
148
+ 90y
147
+ ··· + 2708328479y + 100861849)
c
10
(y
37
+ 32y
34
+ ··· + 32y −1)
· (y
148
+ 23y
147
+ ··· − 9866857228y + 1315440361)
30
