12n
0786
(K12n
0786
)
A knot diagram
1
Linearized knot diagam
4 10 7 1 3 9 11 4 6 5 8 5
Solving Sequence
6,9 3,7
4 10 2 1 5 11 8 12
c
6
c
3
c
9
c
2
c
1
c
5
c
10
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.92258 × 10
217
u
92
− 1.17339 × 10
215
u
91
+ ··· + 5.50269 × 10
214
b + 4.31038 × 10
217
,
− 1.20339 × 10
218
u
92
− 2.33162 × 10
218
u
91
+ ··· + 5.50269 × 10
214
a + 5.33906 × 10
217
,
u
93
+ 2u
92
+ ··· + 3u − 1i
I
u
2
= h−10608396395u
23
+ 16008040214u
22
+ ··· + 27133411469b + 6807317624,
− 39241331316u
23
− 4066209209u
22
+ ··· + 27133411469a − 90858330224,
u
24
− u
23
+ ··· − 6u + 1i
* 2 irreducible components of dim
C
= 0, with total 117 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
= h1.92 × 10
217
u
92
− 1.17 × 10
215
u
91
+ · · · + 5.50 × 10
214
b + 4.31 ×
10
217
, −1.20 × 10
218
u
92
− 2.33 × 10
218
u
91
+ · · · + 5.50 × 10
214
a + 5.34 ×
10
217
, u
93
+ 2u
92
+ · · · + 3u − 1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
2186.92u
92
+ 4237.23u
91
+ ··· + 494.015u − 970.264
−349.390u
92
+ 2.13239u
91
+ ··· + 3262.94u − 783.323
a
7
=
1
u
2
a
4
=
970.001u
92
+ 1817.60u
91
+ ··· − 172.176u − 323.551
555.549u
92
+ 1430.31u
91
+ ··· + 2003.40u − 769.116
a
10
=
−u
u
a
2
=
594.533u
92
+ 1273.52u
91
+ ··· + 638.636u − 405.961
1243.00u
92
+ 2965.84u
91
+ ··· + 3118.32u − 1347.63
a
1
=
−268.181u
92
− 747.988u
91
+ ··· − 1064.88u + 427.216
727.736u
92
+ 835.981u
91
+ ··· − 2598.74u + 446.237
a
5
=
1040.25u
92
+ 2073.37u
91
+ ··· + 381.277u − 545.222
−952.405u
92
− 1172.41u
91
+ ··· + 3191.51u − 513.832
a
11
=
1807.51u
92
+ 4783.68u
91
+ ··· + 6936.30u − 2674.48
−1482.28u
92
− 2741.56u
91
+ ··· + 115.240u + 560.669
a
8
=
−1.82342u
92
− 1725.47u
91
+ ··· − 8721.80u + 2453.86
−157.679u
92
+ 622.832u
91
+ ··· + 4658.44u − 1262.27
a
12
=
−1467.45u
92
− 3084.65u
91
+ ··· − 1415.77u + 1033.53
2134.10u
92
+ 3027.40u
91
+ ··· − 4950.71u + 536.369
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3053.46u
92
− 12740.4u
91
+ ··· − 33773.0u + 10600.2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
93
+ 7u
92
+ ··· + 36u + 31
c
2
u
93
− 6u
92
+ ··· + 2531u + 103
c
3
u
93
+ 4u
91
+ ··· − 30u + 1
c
5
u
93
− 3u
92
+ ··· − 22u + 3
c
6
, c
9
u
93
− 2u
92
+ ··· + 3u + 1
c
7
, c
11
u
93
− 6u
92
+ ··· − 33u + 1
c
8
u
93
− u
92
+ ··· + 3067u + 1049
c
10
u
93
+ 5u
92
+ ··· + 48499913u + 3071059
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
93
+ 33y
92
+ ··· − 32556y −961
c
2
y
93
− 12y
92
+ ··· + 3176499y −10609
c
3
y
93
+ 8y
92
+ ··· + 98y −1
c
5
y
93
+ 7y
92
+ ··· + 316y −9
c
6
, c
9
y
93
+ 60y
92
+ ··· − 39y −1
c
7
, c
11
y
93
− 32y
92
+ ··· + 605y −1
c
8
y
93
− 17y
92
+ ··· − 40616125y −1100401
c
10
y
93
+ 39y
92
+ ··· − 302038266937865y −9431403381481
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.983543 + 0.189886I
a = 0.0479434 − 0.0594414I
b = −0.964325 − 0.836927I
−4.33888 − 5.44307I 0
u = −0.983543 − 0.189886I
a = 0.0479434 + 0.0594414I
b = −0.964325 + 0.836927I
−4.33888 + 5.44307I 0
u = 0.437652 + 0.894742I
a = 1.34164 − 0.44860I
b = 0.733399 + 0.285615I
−1.34298 − 2.68991I 0
u = 0.437652 − 0.894742I
a = 1.34164 + 0.44860I
b = 0.733399 − 0.285615I
−1.34298 + 2.68991I 0
u = 0.064066 + 1.007850I
a = −0.102771 − 0.633812I
b = −1.31555 + 0.52627I
1.95221 + 1.75855I 0
u = 0.064066 − 1.007850I
a = −0.102771 + 0.633812I
b = −1.31555 − 0.52627I
1.95221 − 1.75855I 0
u = −0.219350 + 0.986150I
a = −1.009910 − 0.952944I
b = −0.985870 + 0.226108I
−1.26066 + 2.02670I 0
u = −0.219350 − 0.986150I
a = −1.009910 + 0.952944I
b = −0.985870 − 0.226108I
−1.26066 − 2.02670I 0
u = 0.994198 + 0.203360I
a = 0.0270530 − 0.0851912I
b = −0.992506 + 0.553763I
−4.63796 − 0.81156I 0
u = 0.994198 − 0.203360I
a = 0.0270530 + 0.0851912I
b = −0.992506 − 0.553763I
−4.63796 + 0.81156I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.129951 + 1.033800I
a = 0.44287 + 1.44228I
b = −0.178263 − 0.786894I
1.80464 − 1.94003I 0
u = 0.129951 − 1.033800I
a = 0.44287 − 1.44228I
b = −0.178263 + 0.786894I
1.80464 + 1.94003I 0
u = −0.896564 + 0.237335I
a = 0.400721 − 0.177834I
b = 0.015477 − 0.837443I
2.48866 − 1.82083I 0
u = −0.896564 − 0.237335I
a = 0.400721 + 0.177834I
b = 0.015477 + 0.837443I
2.48866 + 1.82083I 0
u = 0.533598 + 0.752649I
a = 1.248080 − 0.398267I
b = −1.08447 + 1.01720I
−1.27960 + 2.87283I 0
u = 0.533598 − 0.752649I
a = 1.248080 + 0.398267I
b = −1.08447 − 1.01720I
−1.27960 − 2.87283I 0
u = −0.247343 + 1.049060I
a = −1.48412 − 0.92449I
b = 1.88874 + 1.28303I
0.45762 + 8.33356I 0
u = −0.247343 − 1.049060I
a = −1.48412 + 0.92449I
b = 1.88874 − 1.28303I
0.45762 − 8.33356I 0
u = −0.248085 + 0.882956I
a = −0.279883 + 0.572239I
b = 1.30860 − 0.54284I
4.79849 + 3.61847I 0
u = −0.248085 − 0.882956I
a = −0.279883 − 0.572239I
b = 1.30860 + 0.54284I
4.79849 − 3.61847I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.469993 + 0.983361I
a = 0.404945 + 0.623698I
b = 0.319679 + 0.191630I
2.52644 − 3.77461I 0
u = 0.469993 − 0.983361I
a = 0.404945 − 0.623698I
b = 0.319679 − 0.191630I
2.52644 + 3.77461I 0
u = −1.095110 + 0.053192I
a = 0.157178 + 0.352529I
b = 0.325305 − 0.401567I
3.87659 + 1.11388I 0
u = −1.095110 − 0.053192I
a = 0.157178 − 0.352529I
b = 0.325305 + 0.401567I
3.87659 − 1.11388I 0
u = 0.293799 + 1.073150I
a = −0.94094 + 1.25573I
b = 1.10199 − 1.45553I
−0.03086 − 2.86701I 0
u = 0.293799 − 1.073150I
a = −0.94094 − 1.25573I
b = 1.10199 + 1.45553I
−0.03086 + 2.86701I 0
u = 0.866888 + 0.084480I
a = 0.333690 − 0.521948I
b = −0.625888 − 0.525833I
0.019814 − 0.829463I 0
u = 0.866888 − 0.084480I
a = 0.333690 + 0.521948I
b = −0.625888 + 0.525833I
0.019814 + 0.829463I 0
u = −0.199400 + 0.840884I
a = 0.02352 + 3.32350I
b = 0.297727 − 0.018628I
−1.18673 + 7.11436I 0
u = −0.199400 − 0.840884I
a = 0.02352 − 3.32350I
b = 0.297727 + 0.018628I
−1.18673 − 7.11436I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.240921 + 1.118480I
a = −1.39128 + 1.27508I
b = −0.686143 − 0.525780I
1.51137 − 8.12842I 0
u = 0.240921 − 1.118480I
a = −1.39128 − 1.27508I
b = −0.686143 + 0.525780I
1.51137 + 8.12842I 0
u = −0.206885 + 0.829098I
a = 0.14083 − 1.66722I
b = −1.160490 + 0.298349I
−1.04687 + 1.12801I 0
u = −0.206885 − 0.829098I
a = 0.14083 + 1.66722I
b = −1.160490 − 0.298349I
−1.04687 − 1.12801I 0
u = −0.110650 + 0.841201I
a = 1.38963 + 0.78734I
b = −0.313850 − 0.597088I
1.47187 − 2.09814I 0
u = −0.110650 − 0.841201I
a = 1.38963 − 0.78734I
b = −0.313850 + 0.597088I
1.47187 + 2.09814I 0
u = −0.316582 + 0.784266I
a = 1.59660 − 0.20975I
b = −1.70364 − 0.59032I
−2.46533 + 1.52282I 0
u = −0.316582 − 0.784266I
a = 1.59660 + 0.20975I
b = −1.70364 + 0.59032I
−2.46533 − 1.52282I 0
u = −1.158880 + 0.071269I
a = −0.0491220 − 0.0120891I
b = 0.890799 + 0.840671I
−2.77300 − 11.97580I 0
u = −1.158880 − 0.071269I
a = −0.0491220 + 0.0120891I
b = 0.890799 − 0.840671I
−2.77300 + 11.97580I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851154 + 0.804226I
a = 0.432837 − 0.202079I
b = 0.573597 + 0.344631I
−0.61886 − 2.66614I 0
u = 0.851154 − 0.804226I
a = 0.432837 + 0.202079I
b = 0.573597 − 0.344631I
−0.61886 + 2.66614I 0
u = 1.174050 + 0.069769I
a = 0.0448578 + 0.0571294I
b = 0.864348 − 0.618909I
−4.68532 + 4.84438I 0
u = 1.174050 − 0.069769I
a = 0.0448578 − 0.0571294I
b = 0.864348 + 0.618909I
−4.68532 − 4.84438I 0
u = −0.190726 + 0.792018I
a = 0.27059 − 3.01873I
b = −0.96508 + 1.74473I
−2.64820 + 1.13387I 0
u = −0.190726 − 0.792018I
a = 0.27059 + 3.01873I
b = −0.96508 − 1.74473I
−2.64820 − 1.13387I 0
u = −0.330836 + 1.169320I
a = −0.01297 + 2.06258I
b = 0.99237 − 1.17801I
7.41773 + 6.08000I 0
u = −0.330836 − 1.169320I
a = −0.01297 − 2.06258I
b = 0.99237 + 1.17801I
7.41773 − 6.08000I 0
u = −0.354045 + 0.700122I
a = 1.54843 + 0.11322I
b = 0.929290 + 0.092186I
−1.32893 − 4.36708I 0
u = −0.354045 − 0.700122I
a = 1.54843 − 0.11322I
b = 0.929290 − 0.092186I
−1.32893 + 4.36708I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.194450 + 1.202250I
a = −0.49531 − 1.99273I
b = 0.75329 + 1.54194I
7.71205 − 3.80682I 0
u = 0.194450 − 1.202250I
a = −0.49531 + 1.99273I
b = 0.75329 − 1.54194I
7.71205 + 3.80682I 0
u = 0.218625 + 0.681653I
a = −0.85841 + 2.99840I
b = −0.21627 − 1.78802I
−1.61951 − 6.44837I 0
u = 0.218625 − 0.681653I
a = −0.85841 − 2.99840I
b = −0.21627 + 1.78802I
−1.61951 + 6.44837I 0
u = 0.017631 + 0.715431I
a = 0.47465 − 3.25113I
b = −0.163044 − 0.119086I
−2.55281 − 0.24180I 0
u = 0.017631 − 0.715431I
a = 0.47465 + 3.25113I
b = −0.163044 + 0.119086I
−2.55281 + 0.24180I 0
u = 0.744749 + 1.048260I
a = 0.300159 − 0.475233I
b = 0.497058 + 0.330795I
−0.55657 − 2.66778I 0
u = 0.744749 − 1.048260I
a = 0.300159 + 0.475233I
b = 0.497058 − 0.330795I
−0.55657 + 2.66778I 0
u = −0.386984 + 1.279280I
a = 0.239840 + 1.359720I
b = 0.84999 − 1.23688I
7.03023 + 2.41777I 0
u = −0.386984 − 1.279280I
a = 0.239840 − 1.359720I
b = 0.84999 + 1.23688I
7.03023 − 2.41777I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.542422 + 1.234570I
a = −0.00076 + 1.62500I
b = −1.006110 − 0.985167I
−1.41567 − 4.64756I 0
u = 0.542422 − 1.234570I
a = −0.00076 − 1.62500I
b = −1.006110 + 0.985167I
−1.41567 + 4.64756I 0
u = −1.042740 + 0.858031I
a = −0.378206 + 0.158138I
b = 0.219796 + 0.290474I
4.21931 + 0.74875I 0
u = −1.042740 − 0.858031I
a = −0.378206 − 0.158138I
b = 0.219796 − 0.290474I
4.21931 − 0.74875I 0
u = −0.549245 + 1.245670I
a = −0.11891 − 1.71903I
b = −1.12234 + 1.21886I
−1.04941 + 10.92380I 0
u = −0.549245 − 1.245670I
a = −0.11891 + 1.71903I
b = −1.12234 − 1.21886I
−1.04941 − 10.92380I 0
u = −0.573542 + 1.256320I
a = −0.480956 − 1.200230I
b = −0.48885 + 1.38965I
5.62490 + 7.35420I 0
u = −0.573542 − 1.256320I
a = −0.480956 + 1.200230I
b = −0.48885 − 1.38965I
5.62490 − 7.35420I 0
u = 0.300896 + 1.369670I
a = −0.362195 − 1.263370I
b = 1.20392 + 1.17959I
5.85732 − 6.29692I 0
u = 0.300896 − 1.369670I
a = −0.362195 + 1.263370I
b = 1.20392 − 1.17959I
5.85732 + 6.29692I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.51677 + 1.32088I
a = 0.295741 + 1.321040I
b = 0.637987 − 0.784814I
8.07240 + 6.60899I 0
u = −0.51677 − 1.32088I
a = 0.295741 − 1.321040I
b = 0.637987 + 0.784814I
8.07240 − 6.60899I 0
u = 0.50730 + 1.33527I
a = 0.085286 + 1.266530I
b = −0.92354 − 1.27262I
4.29131 − 5.92882I 0
u = 0.50730 − 1.33527I
a = 0.085286 − 1.266530I
b = −0.92354 + 1.27262I
4.29131 + 5.92882I 0
u = 0.58234 + 1.33991I
a = 0.04137 − 1.44155I
b = 1.08115 + 1.00548I
−0.71546 − 10.95490I 0
u = 0.58234 − 1.33991I
a = 0.04137 + 1.44155I
b = 1.08115 − 1.00548I
−0.71546 + 10.95490I 0
u = −0.58040 + 1.34422I
a = 0.06000 + 1.56952I
b = 1.13715 − 1.22968I
1.2137 + 18.0601I 0
u = −0.58040 − 1.34422I
a = 0.06000 − 1.56952I
b = 1.13715 + 1.22968I
1.2137 − 18.0601I 0
u = −0.42863 + 1.40115I
a = −0.073508 − 1.146130I
b = −0.217875 + 0.867252I
8.64430 + 4.57082I 0
u = −0.42863 − 1.40115I
a = −0.073508 + 1.146130I
b = −0.217875 − 0.867252I
8.64430 − 4.57082I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.05957 + 1.49368I
a = 0.248648 + 0.698068I
b = −0.230719 − 0.751570I
1.62426 − 1.33087I 0
u = 0.05957 − 1.49368I
a = 0.248648 − 0.698068I
b = −0.230719 + 0.751570I
1.62426 + 1.33087I 0
u = 0.331631
a = 1.03808
b = −0.534199
−0.883861 −11.2400
u = −0.328613 + 0.028247I
a = 0.971809 + 0.099963I
b = 0.908758 + 0.836136I
4.16715 − 3.11772I −9.62079 + 8.90431I
u = −0.328613 − 0.028247I
a = 0.971809 − 0.099963I
b = 0.908758 − 0.836136I
4.16715 + 3.11772I −9.62079 − 8.90431I
u = 0.68737 + 1.56791I
a = 0.136384 + 0.408190I
b = −0.607705 − 0.351428I
1.41423 − 6.57009I 0
u = 0.68737 − 1.56791I
a = 0.136384 − 0.408190I
b = −0.607705 + 0.351428I
1.41423 + 6.57009I 0
u = −0.34577 + 1.67716I
a = −0.224012 − 0.427916I
b = 0.006078 + 0.650800I
2.70253 − 5.70337I 0
u = −0.34577 − 1.67716I
a = −0.224012 + 0.427916I
b = 0.006078 − 0.650800I
2.70253 + 5.70337I 0
u = 0.223333 + 0.094354I
a = 5.03386 − 1.53563I
b = 0.003370 − 0.785282I
−2.75918 − 0.40290I −8.55360 − 0.38930I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.223333 − 0.094354I
a = 5.03386 + 1.53563I
b = 0.003370 + 0.785282I
−2.75918 + 0.40290I −8.55360 + 0.38930I
u = 0.009908 + 0.190677I
a = −2.99495 + 7.59395I
b = 0.179764 − 1.127260I
−1.61885 − 6.30244I −7.04303 + 4.01413I
u = 0.009908 − 0.190677I
a = −2.99495 − 7.59395I
b = 0.179764 + 1.127260I
−1.61885 + 6.30244I −7.04303 − 4.01413I
14
II.
I
u
2
= h−1.06×10
10
u
23
+1.60×10
10
u
22
+· · ·+2.71×10
10
b+6.81×10
9
, −3.92×
10
10
u
23
−4.07×10
9
u
22
+· · ·+2.71×10
10
a−9.09×10
10
, u
24
−u
23
+· · ·−6u+1i
(i) Arc colorings
a
6
=
1
0
a
9
=
0
u
a
3
=
1.44624u
23
+ 0.149860u
22
+ ··· − 20.0547u + 3.34858
0.390972u
23
− 0.589975u
22
+ ··· + 6.46503u − 0.250883
a
7
=
1
u
2
a
4
=
−0.786802u
23
+ 1.25865u
22
+ ··· − 18.3894u + 2.00336
1.24315u
23
− 0.895775u
22
+ ··· + 1.95260u + 0.873361
a
10
=
−u
u
a
2
=
0.439634u
23
+ 0.588286u
22
+ ··· − 13.5094u + 1.95148
1.39757u
23
− 1.02840u
22
+ ··· − 0.0803203u + 1.14621
a
1
=
−1.98981u
23
+ 3.36144u
22
+ ··· − 53.5864u + 8.96160
2.40291u
23
− 2.10814u
22
+ ··· + 22.8164u − 2.25096
a
5
=
1.74314u
23
− 3.07315u
22
+ ··· + 11.6793u + 1.14875
−0.966229u
23
+ 0.911538u
22
+ ··· + 9.68180u − 2.72345
a
11
=
1.11810u
23
+ 2.62405u
22
+ ··· − 13.6089u + 3.30447
0.986047u
23
− 2.57096u
22
+ ··· + 12.7495u − 3.07575
a
8
=
−1.84203u
23
+ 1.09916u
22
+ ··· + 17.4728u − 2.40686
0.179665u
23
+ 1.04101u
22
+ ··· − 11.8044u + 1.15597
a
12
=
−2.97483u
23
+ 7.63647u
22
+ ··· − 54.3438u + 8.73461
2.81647u
23
− 3.99876u
22
+ ··· + 17.6180u − 2.53227
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
62579771269
27133411469
u
23
+
75568649014
27133411469
u
22
+ ··· +
848802615232
27133411469
u −
208436702424
27133411469
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
12
u
24
− 8u
23
+ ··· − 5u + 1
c
2
u
24
+ u
23
+ ··· − 6u + 1
c
3
u
24
− u
23
+ ··· − u + 1
c
4
u
24
+ 8u
23
+ ··· + 5u + 1
c
5
u
24
+ 2u
23
+ ··· + u + 1
c
6
u
24
− u
23
+ ··· − 6u + 1
c
7
u
24
− u
23
+ ··· − 2u + 1
c
8
u
24
− 2u
22
+ ··· − 4u + 7
c
9
u
24
+ u
23
+ ··· + 6u + 1
c
10
u
24
− 4u
23
+ ··· − 22u + 7
c
11
u
24
+ u
23
+ ··· + 2u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
24
+ 14y
23
+ ··· + 23y + 1
c
2
y
24
− 7y
23
+ ··· − 4y + 1
c
3
y
24
+ 9y
23
+ ··· + 5y + 1
c
5
y
24
+ 4y
23
+ ··· − y + 1
c
6
, c
9
y
24
+ 17y
23
+ ··· + 18y + 1
c
7
, c
11
y
24
− 15y
23
+ ··· − 14y + 1
c
8
y
24
− 4y
23
+ ··· + 152y + 49
c
10
y
24
− 8y
23
+ ··· − 260y + 49
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.778175 + 0.797715I
a = −0.568555 + 0.005801I
b = −0.588229 − 0.259324I
−0.67529 − 2.31026I −3.79173 − 6.69902I
u = 0.778175 − 0.797715I
a = −0.568555 − 0.005801I
b = −0.588229 + 0.259324I
−0.67529 + 2.31026I −3.79173 + 6.69902I
u = 0.311253 + 0.823685I
a = 0.193306 + 1.036400I
b = −1.093120 + 0.024292I
−1.28774 − 1.51144I −6.85991 + 9.11770I
u = 0.311253 − 0.823685I
a = 0.193306 − 1.036400I
b = −1.093120 − 0.024292I
−1.28774 + 1.51144I −6.85991 − 9.11770I
u = −0.096179 + 0.856749I
a = −0.68359 − 3.09050I
b = 0.377131 + 1.015570I
−0.59789 + 6.68274I −0.01321 − 5.04238I
u = −0.096179 − 0.856749I
a = −0.68359 + 3.09050I
b = 0.377131 − 1.015570I
−0.59789 − 6.68274I −0.01321 + 5.04238I
u = 0.114071 + 0.851132I
a = −0.16885 + 2.84807I
b = −0.725864 − 0.963828I
−1.95456 − 0.82184I −3.32595 − 0.64273I
u = 0.114071 − 0.851132I
a = −0.16885 − 2.84807I
b = −0.725864 + 0.963828I
−1.95456 + 0.82184I −3.32595 + 0.64273I
u = 0.269973 + 1.207950I
a = −0.33468 − 1.94681I
b = 1.11156 + 1.48063I
7.42060 − 4.68753I 2.01822 + 5.91782I
u = 0.269973 − 1.207950I
a = −0.33468 + 1.94681I
b = 1.11156 − 1.48063I
7.42060 + 4.68753I 2.01822 − 5.91782I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.349525 + 1.330510I
a = 0.05903 + 1.58367I
b = 0.535095 − 1.183460I
10.21350 + 5.46975I 5.02737 − 4.59089I
u = −0.349525 − 1.330510I
a = 0.05903 − 1.58367I
b = 0.535095 + 1.183460I
10.21350 − 5.46975I 5.02737 + 4.59089I
u = −1.333910 + 0.453959I
a = −0.0544505 + 0.0877177I
b = 0.111907 − 0.436796I
4.42237 + 1.08521I 13.6808 − 7.4874I
u = −1.333910 − 0.453959I
a = −0.0544505 − 0.0877177I
b = 0.111907 + 0.436796I
4.42237 − 1.08521I 13.6808 + 7.4874I
u = 0.51933 + 1.33414I
a = 0.058252 + 1.154100I
b = −0.90059 − 1.21225I
4.06468 − 6.55923I −3.90378 + 10.72811I
u = 0.51933 − 1.33414I
a = 0.058252 − 1.154100I
b = −0.90059 + 1.21225I
4.06468 + 6.55923I −3.90378 − 10.72811I
u = −0.57136 + 1.36818I
a = −0.289135 − 1.059480I
b = −0.466295 + 0.855907I
8.29180 + 5.63108I 1.53548 − 4.54639I
u = −0.57136 − 1.36818I
a = −0.289135 + 1.059480I
b = −0.466295 − 0.855907I
8.29180 − 5.63108I 1.53548 + 4.54639I
u = 0.30186 + 1.45264I
a = 0.037002 − 0.190838I
b = 0.510216 − 0.055521I
1.89854 − 6.18052I 0.42008 + 6.34301I
u = 0.30186 − 1.45264I
a = 0.037002 + 0.190838I
b = 0.510216 + 0.055521I
1.89854 + 6.18052I 0.42008 − 6.34301I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.477150 + 0.154808I
a = 1.45462 + 1.26189I
b = −0.896648 + 0.507741I
−0.03348 + 1.98965I −4.72004 − 3.46066I
u = 0.477150 − 0.154808I
a = 1.45462 − 1.26189I
b = −0.896648 − 0.507741I
−0.03348 − 1.98965I −4.72004 + 3.46066I
u = 0.079160 + 0.354427I
a = −1.202950 − 0.019294I
b = 1.024830 − 0.782735I
4.42600 + 2.75033I 0.43266 + 5.26979I
u = 0.079160 − 0.354427I
a = −1.202950 + 0.019294I
b = 1.024830 + 0.782735I
4.42600 − 2.75033I 0.43266 − 5.26979I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
(u
24
− 8u
23
+ ··· − 5u + 1)(u
93
+ 7u
92
+ ··· + 36u + 31)
c
2
(u
24
+ u
23
+ ··· − 6u + 1)(u
93
− 6u
92
+ ··· + 2531u + 103)
c
3
(u
24
− u
23
+ ··· − u + 1)(u
93
+ 4u
91
+ ··· − 30u + 1)
c
4
(u
24
+ 8u
23
+ ··· + 5u + 1)(u
93
+ 7u
92
+ ··· + 36u + 31)
c
5
(u
24
+ 2u
23
+ ··· + u + 1)(u
93
− 3u
92
+ ··· − 22u + 3)
c
6
(u
24
− u
23
+ ··· − 6u + 1)(u
93
− 2u
92
+ ··· + 3u + 1)
c
7
(u
24
− u
23
+ ··· − 2u + 1)(u
93
− 6u
92
+ ··· − 33u + 1)
c
8
(u
24
− 2u
22
+ ··· − 4u + 7)(u
93
− u
92
+ ··· + 3067u + 1049)
c
9
(u
24
+ u
23
+ ··· + 6u + 1)(u
93
− 2u
92
+ ··· + 3u + 1)
c
10
(u
24
− 4u
23
+ ··· − 22u + 7)
· (u
93
+ 5u
92
+ ··· + 48499913u + 3071059)
c
11
(u
24
+ u
23
+ ··· + 2u + 1)(u
93
− 6u
92
+ ··· − 33u + 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
(y
24
+ 14y
23
+ ··· + 23y + 1)(y
93
+ 33y
92
+ ··· − 32556y −961)
c
2
(y
24
− 7y
23
+ ··· − 4y + 1)(y
93
− 12y
92
+ ··· + 3176499y −10609)
c
3
(y
24
+ 9y
23
+ ··· + 5y + 1)(y
93
+ 8y
92
+ ··· + 98y −1)
c
5
(y
24
+ 4y
23
+ ··· − y + 1)(y
93
+ 7y
92
+ ··· + 316y −9)
c
6
, c
9
(y
24
+ 17y
23
+ ··· + 18y + 1)(y
93
+ 60y
92
+ ··· − 39y −1)
c
7
, c
11
(y
24
− 15y
23
+ ··· − 14y + 1)(y
93
− 32y
92
+ ··· + 605y −1)
c
8
(y
24
− 4y
23
+ ··· + 152y + 49)
· (y
93
− 17y
92
+ ··· − 40616125y −1100401)
c
10
(y
24
− 8y
23
+ ··· − 260y + 49)
· (y
93
+ 39y
92
+ ··· − 302038266937865y −9431403381481)
22
