12n
0769
(K12n
0769
)
A knot diagram
1
Linearized knot diagam
4 6 8 11 2 12 10 2 4 7 5 8
Solving Sequence
3,8 4,6
2 9 10 1 5 7 12 11
c
3
c
2
c
8
c
9
c
1
c
5
c
7
c
12
c
11
c
4
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.83864 × 10
337
u
65
− 1.18349 × 10
338
u
64
+ ··· + 1.06451 × 10
342
b − 1.02256 × 10
342
,
− 1.56678 × 10
341
u
65
+ 4.83301 × 10
341
u
64
+ ··· + 1.39504 × 10
345
a − 4.89344 × 10
345
,
u
66
− 3u
65
+ ··· + 1022u − 2621i
I
u
2
= h−5.16198 × 10
14
u
22
+ 4.96659 × 10
15
u
21
+ ··· + 6.69596 × 10
15
b − 5.25349 × 10
15
,
− 1.04392 × 10
16
u
22
+ 4.70651 × 10
16
u
21
+ ··· + 6.69596 × 10
15
a + 1.86768 × 10
16
, u
23
− 4u
22
+ ··· − 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 89 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
= h3.84 × 10
337
u
65
− 1.18 × 10
338
u
64
+ · · · + 1.06 × 10
342
b − 1.02 ×
10
342
, −1.57 × 10
341
u
65
+ 4.83 × 10
341
u
64
+ · · · + 1.40 × 10
345
a − 4.89 ×
10
345
, u
66
− 3u
65
+ · · · + 1022u − 2621i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
6
=
0.000112311u
65
− 0.000346443u
64
+ ··· − 0.270457u + 3.50774
−0.0000360602u
65
+ 0.000111177u
64
+ ··· + 0.748848u + 0.960593
a
2
=
−0.0000377394u
65
+ 0.000109948u
64
+ ··· − 0.553697u − 3.17735
0.0000688159u
65
− 0.000214201u
64
+ ··· − 1.70637u − 0.657455
a
9
=
0.0000148168u
65
− 0.0000484765u
64
+ ··· + 10.6401u + 0.738371
0.0000284980u
65
− 0.0000667785u
64
+ ··· + 3.25127u − 0.315788
a
10
=
0.0000381472u
65
− 0.000101304u
64
+ ··· + 13.9343u + 0.412030
0.0000323377u
65
− 0.0000782973u
64
+ ··· + 3.20767u − 0.360774
a
1
=
0.0000305409u
65
− 0.000101770u
64
+ ··· − 2.35564u − 3.84338
0.0000751505u
65
− 0.000234189u
64
+ ··· − 1.89236u − 0.639428
a
5
=
0.000151268u
65
− 0.000479153u
64
+ ··· − 2.21265u + 0.437691
0.0000458801u
65
− 0.000147106u
64
+ ··· − 1.73849u + 0.898946
a
7
=
0.000249270u
65
− 0.000703271u
64
+ ··· − 2.14183u − 0.415613
0.0000538303u
65
− 0.000153736u
64
+ ··· − 0.578342u − 0.793468
a
12
=
0.0000305409u
65
− 0.000101770u
64
+ ··· − 2.35564u − 3.84338
0.0000682803u
65
− 0.000211719u
64
+ ··· − 1.80195u − 0.666025
a
11
=
−0.000148371u
65
+ 0.000457620u
64
+ ··· + 1.01930u − 2.54715
−0.0000173746u
65
+ 0.0000555578u
64
+ ··· + 0.940765u − 1.04993
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000277598u
65
+ 0.000900711u
64
+ ··· + 12.6909u + 2.52964
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
− 4u
65
+ ··· + 251u + 131
c
2
, c
5
u
66
+ 2u
65
+ ··· − 21u + 1
c
3
u
66
− 3u
65
+ ··· + 1022u − 2621
c
4
, c
11
u
66
+ 5u
65
+ ··· − 402u − 171
c
6
u
66
− 2u
65
+ ··· − 40871u − 2788
c
7
, c
10
u
66
+ 6u
65
+ ··· + 224u + 16
c
8
u
66
+ 47u
64
+ ··· + 18353u − 20690
c
9
u
66
− u
65
+ ··· + 28988118u − 18025751
c
12
u
66
− 3u
65
+ ··· + 418122130u − 132292613
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
− 94y
65
+ ··· − 1810017y + 17161
c
2
, c
5
y
66
− 48y
65
+ ··· − 193y + 1
c
3
y
66
+ 83y
65
+ ··· + 198203936y + 6869641
c
4
, c
11
y
66
− 29y
65
+ ··· − 842526y + 29241
c
6
y
66
+ 20y
65
+ ··· − 290997577y + 7772944
c
7
, c
10
y
66
+ 46y
65
+ ··· + 58848y
2
+ 256
c
8
y
66
+ 94y
65
+ ··· − 15224156589y + 428076100
c
9
y
66
+ 69y
65
+ ··· + 2987872480868112y + 324927699114001
c
12
y
66
+ 89y
65
+ ··· + 205846697467622796y + 17501335454367769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.550266 + 0.896602I
a = −0.664287 − 1.148930I
b = −1.45948 − 0.16916I
−3.94389 − 6.56961I 0
u = 0.550266 − 0.896602I
a = −0.664287 + 1.148930I
b = −1.45948 + 0.16916I
−3.94389 + 6.56961I 0
u = −0.543655 + 0.904183I
a = −0.968879 − 0.052917I
b = −1.049230 − 0.220101I
−3.67929 + 0.01280I 0
u = −0.543655 − 0.904183I
a = −0.968879 + 0.052917I
b = −1.049230 + 0.220101I
−3.67929 − 0.01280I 0
u = 0.727225 + 0.435479I
a = 1.92650 − 1.46275I
b = 0.0406553 + 0.0835342I
1.88021 + 5.73599I 12.0656 − 12.6009I
u = 0.727225 − 0.435479I
a = 1.92650 + 1.46275I
b = 0.0406553 − 0.0835342I
1.88021 − 5.73599I 12.0656 + 12.6009I
u = −0.827890 + 0.059202I
a = 0.05599 − 1.88565I
b = 0.451189 + 1.104720I
3.42513 − 3.10241I 9.91560 + 5.14976I
u = −0.827890 − 0.059202I
a = 0.05599 + 1.88565I
b = 0.451189 − 1.104720I
3.42513 + 3.10241I 9.91560 − 5.14976I
u = −0.664488 + 0.463174I
a = 0.27357 − 1.57982I
b = 1.178760 + 0.161389I
−5.21721 + 2.27069I 1.36837 + 2.87034I
u = −0.664488 − 0.463174I
a = 0.27357 + 1.57982I
b = 1.178760 − 0.161389I
−5.21721 − 2.27069I 1.36837 − 2.87034I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.977420 + 0.705417I
a = −0.661293 − 1.175570I
b = −0.332722 + 1.184590I
3.03137 + 3.75606I 0
u = 0.977420 − 0.705417I
a = −0.661293 + 1.175570I
b = −0.332722 − 1.184590I
3.03137 − 3.75606I 0
u = −0.786749 + 0.925118I
a = −0.453089 + 0.514372I
b = −1.38895 + 0.39471I
−1.16081 + 2.14752I 0
u = −0.786749 − 0.925118I
a = −0.453089 − 0.514372I
b = −1.38895 − 0.39471I
−1.16081 − 2.14752I 0
u = −0.047405 + 1.254290I
a = −0.190093 − 0.333212I
b = −0.512278 + 0.035499I
−2.79710 + 1.27551I 0
u = −0.047405 − 1.254290I
a = −0.190093 + 0.333212I
b = −0.512278 − 0.035499I
−2.79710 − 1.27551I 0
u = −0.731486
a = 3.23812
b = 0.0576281
5.84339 27.4510
u = −0.031783 + 1.279140I
a = 0.215329 + 0.518435I
b = −0.615807 − 0.121803I
−7.92413 − 3.65685I 0
u = −0.031783 − 1.279140I
a = 0.215329 − 0.518435I
b = −0.615807 + 0.121803I
−7.92413 + 3.65685I 0
u = 1.239970 + 0.427685I
a = 0.320121 + 0.726029I
b = 1.300250 − 0.297303I
−0.04669 + 2.02198I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.239970 − 0.427685I
a = 0.320121 − 0.726029I
b = 1.300250 + 0.297303I
−0.04669 − 2.02198I 0
u = −0.615400 + 0.298327I
a = −0.804927 − 0.243840I
b = −0.077417 − 0.366976I
−2.56683 − 1.80846I 4.39793 + 4.09734I
u = −0.615400 − 0.298327I
a = −0.804927 + 0.243840I
b = −0.077417 + 0.366976I
−2.56683 + 1.80846I 4.39793 − 4.09734I
u = −0.231289 + 0.589186I
a = −0.781525 − 0.000516I
b = −0.973316 + 0.353834I
−1.68768 + 1.21202I −0.72929 − 4.22771I
u = −0.231289 − 0.589186I
a = −0.781525 + 0.000516I
b = −0.973316 − 0.353834I
−1.68768 − 1.21202I −0.72929 + 4.22771I
u = 0.353427 + 0.445086I
a = −0.479282 − 0.103589I
b = 0.297714 − 0.781830I
0.61831 − 2.78529I 6.08241 + 0.51566I
u = 0.353427 − 0.445086I
a = −0.479282 + 0.103589I
b = 0.297714 + 0.781830I
0.61831 + 2.78529I 6.08241 − 0.51566I
u = 0.229774 + 0.456770I
a = −0.432205 − 0.068370I
b = 0.560078 + 0.763611I
2.23371 − 0.09039I 7.37287 − 0.87265I
u = 0.229774 − 0.456770I
a = −0.432205 + 0.068370I
b = 0.560078 − 0.763611I
2.23371 + 0.09039I 7.37287 + 0.87265I
u = −0.20016 + 1.57518I
a = −1.81945 + 0.48506I
b = −1.258840 + 0.005810I
−10.50220 + 3.38126I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20016 − 1.57518I
a = −1.81945 − 0.48506I
b = −1.258840 − 0.005810I
−10.50220 − 3.38126I 0
u = 0.377212
a = −0.878279
b = 0.221691
0.673150 14.9230
u = −0.253035 + 0.177235I
a = 2.70886 + 1.05385I
b = 1.139750 − 0.573699I
−1.86269 + 7.84926I 0.62349 − 4.16114I
u = −0.253035 − 0.177235I
a = 2.70886 − 1.05385I
b = 1.139750 + 0.573699I
−1.86269 − 7.84926I 0.62349 + 4.16114I
u = 0.03949 + 1.70848I
a = 1.64394 + 0.12321I
b = 1.60468 − 0.02089I
−12.24090 − 0.50529I 0
u = 0.03949 − 1.70848I
a = 1.64394 − 0.12321I
b = 1.60468 + 0.02089I
−12.24090 + 0.50529I 0
u = −1.51199 + 0.87275I
a = 0.624904 − 0.563500I
b = 1.359320 + 0.228726I
−3.11785 − 7.52482I 0
u = −1.51199 − 0.87275I
a = 0.624904 + 0.563500I
b = 1.359320 − 0.228726I
−3.11785 + 7.52482I 0
u = 0.189603 + 0.163078I
a = 4.45429 + 2.45755I
b = 0.939537 − 0.404470I
−4.72032 + 4.23068I 5.16490 − 8.44942I
u = 0.189603 − 0.163078I
a = 4.45429 − 2.45755I
b = 0.939537 + 0.404470I
−4.72032 − 4.23068I 5.16490 + 8.44942I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.029495 + 0.220286I
a = 2.62996 − 1.57110I
b = 1.051930 + 0.602659I
0.69632 − 5.10005I 4.21908 + 8.93882I
u = −0.029495 − 0.220286I
a = 2.62996 + 1.57110I
b = 1.051930 − 0.602659I
0.69632 + 5.10005I 4.21908 − 8.93882I
u = 0.14707 + 1.79220I
a = −0.0047642 + 0.0811756I
b = −0.384296 − 1.119010I
−9.51126 − 3.39870I 0
u = 0.14707 − 1.79220I
a = −0.0047642 − 0.0811756I
b = −0.384296 + 1.119010I
−9.51126 + 3.39870I 0
u = 0.69156 + 1.72392I
a = −0.740498 + 0.170634I
b = −0.655492 + 0.152399I
−4.48507 + 0.34747I 0
u = 0.69156 − 1.72392I
a = −0.740498 − 0.170634I
b = −0.655492 − 0.152399I
−4.48507 − 0.34747I 0
u = 0.11604 + 1.94557I
a = −0.0250709 − 0.0332917I
b = −0.08603 − 1.42479I
−7.96763 + 8.70759I 0
u = 0.11604 − 1.94557I
a = −0.0250709 + 0.0332917I
b = −0.08603 + 1.42479I
−7.96763 − 8.70759I 0
u = −0.61083 + 1.86793I
a = −1.026190 + 0.617276I
b = −1.38484 − 0.79367I
−12.39080 − 3.74278I 0
u = −0.61083 − 1.86793I
a = −1.026190 − 0.617276I
b = −1.38484 + 0.79367I
−12.39080 + 3.74278I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.20977 + 1.96700I
a = −0.0368901 − 0.0037967I
b = −0.33302 + 1.46253I
−4.04829 − 2.21767I 0
u = −0.20977 − 1.96700I
a = −0.0368901 + 0.0037967I
b = −0.33302 − 1.46253I
−4.04829 + 2.21767I 0
u = 0.40823 + 1.96292I
a = −1.43456 − 0.22542I
b = −1.213000 − 0.036513I
−5.28293 − 1.49985I 0
u = 0.40823 − 1.96292I
a = −1.43456 + 0.22542I
b = −1.213000 + 0.036513I
−5.28293 + 1.49985I 0
u = 0.32373 + 2.02205I
a = 1.154040 + 0.330512I
b = 1.70054 − 0.47367I
−13.92610 − 1.38296I 0
u = 0.32373 − 2.02205I
a = 1.154040 − 0.330512I
b = 1.70054 + 0.47367I
−13.92610 + 1.38296I 0
u = −0.39994 + 2.02628I
a = 1.205390 − 0.344773I
b = 1.54531 + 0.35640I
−10.89730 − 3.88708I 0
u = −0.39994 − 2.02628I
a = 1.205390 + 0.344773I
b = 1.54531 − 0.35640I
−10.89730 + 3.88708I 0
u = 0.56302 + 2.00209I
a = −1.076820 − 0.499150I
b = −1.48301 + 0.72273I
−7.94229 + 9.99315I 0
u = 0.56302 − 2.00209I
a = −1.076820 + 0.499150I
b = −1.48301 − 0.72273I
−7.94229 − 9.99315I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.49267 + 2.02523I
a = −1.155480 + 0.473455I
b = −1.47378 − 0.66173I
−12.4141 − 15.9549I 0
u = −0.49267 − 2.02523I
a = −1.155480 − 0.473455I
b = −1.47378 + 0.66173I
−12.4141 + 15.9549I 0
u = 0.40983 + 2.17347I
a = 1.190030 + 0.336694I
b = 1.46125 − 0.40417I
−15.3485 + 8.5623I 0
u = 0.40983 − 2.17347I
a = 1.190030 − 0.336694I
b = 1.46125 + 0.40417I
−15.3485 − 8.5623I 0
u = 2.16701 + 0.96801I
a = −1.000200 − 0.188283I
b = −1.089120 − 0.158880I
−4.90781 − 0.48946I 0
u = 2.16701 − 0.96801I
a = −1.000200 + 0.188283I
b = −1.089120 + 0.158880I
−4.90781 + 0.48946I 0
11
II.
I
u
2
= h−5.16×10
14
u
22
+4.97×10
15
u
21
+· · ·+6.70×10
15
b−5.25×10
15
, −1.04×
10
16
u
22
+4.71×10
16
u
21
+· · ·+6.70×10
15
a+1.87×10
16
, u
23
−4u
22
+· · ·−2u−1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
−u
2
a
6
=
1.55903u
22
− 7.02888u
21
+ ··· − 5.76187u − 2.78926
0.0770910u
22
− 0.741730u
21
+ ··· − 1.07988u + 0.784576
a
2
=
−0.725934u
22
+ 3.34952u
21
+ ··· + 2.91597u + 1.97536
0.407470u
22
− 2.13118u
21
+ ··· − 0.418965u − 1.02729
a
9
=
1.52368u
22
− 6.77624u
21
+ ··· − 4.93605u − 1.18246
−0.844098u
22
+ 3.83422u
21
+ ··· + 0.596351u + 1.60466
a
10
=
0.879843u
22
− 3.70740u
21
+ ··· − 4.17906u − 0.259328
−0.535247u
22
+ 2.53641u
21
+ ··· + 0.253205u + 1.11116
a
1
=
−0.705943u
22
+ 3.10076u
21
+ ··· + 2.66264u + 1.39386
0.311346u
22
− 1.61437u
21
+ ··· − 0.101348u − 0.858489
a
5
=
0.765842u
22
− 4.10351u
21
+ ··· − 3.05258u + 0.346479
−0.913552u
22
+ 4.44614u
21
+ ··· + 1.46542u + 1.24958
a
7
=
1.60544u
22
− 6.83027u
21
+ ··· + 0.708634u − 4.90601
1.09999u
22
− 5.16613u
21
+ ··· − 2.06690u − 0.748018
a
12
=
−0.705943u
22
+ 3.10076u
21
+ ··· + 2.66264u + 1.39386
0.0199903u
22
− 0.248765u
21
+ ··· − 0.253327u − 0.581507
a
11
=
−1.48194u
22
+ 6.28715u
21
+ ··· + 4.68199u + 3.57384
−1.14248u
22
+ 5.28279u
21
+ ··· + 1.81382u + 1.01860
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
1767765260313609
836994682049036
u
22
−
6469406606920041
836994682049036
u
21
+ ··· −
4410901774827063
836994682049036
u −
238227547710287
836994682049036
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
23
− 13u
22
+ ··· + 579u − 101
c
2
u
23
+ 5u
22
+ ··· + 5u + 1
c
3
u
23
− 4u
22
+ ··· − 2u − 1
c
4
u
23
+ 4u
22
+ ··· − 2u − 1
c
5
u
23
− 5u
22
+ ··· + 5u − 1
c
6
u
23
− u
22
+ ··· − 4u − 1
c
7
u
23
+ 7u
22
+ ··· + 24u + 4
c
8
u
23
+ u
22
+ ··· − 4u − 1
c
9
u
23
+ 13u
21
+ ··· − 4u + 1
c
10
u
23
− 7u
22
+ ··· + 24u − 4
c
11
u
23
− 4u
22
+ ··· − 2u + 1
c
12
u
23
+ 18u
22
+ ··· − 7u
2
+ 1
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 21y
22
+ ··· + 137079y −10201
c
2
, c
5
y
23
− 11y
22
+ ··· + 11y −1
c
3
y
23
+ 4y
22
+ ··· + 6y −1
c
4
, c
11
y
23
− 12y
22
+ ··· + 50y
2
− 1
c
6
y
23
− 7y
22
+ ··· − 24y −1
c
7
, c
10
y
23
+ 15y
22
+ ··· + 64y −16
c
8
y
23
+ 19y
22
+ ··· + 12y −1
c
9
y
23
+ 26y
22
+ ··· + 6y −1
c
12
y
23
− 166y
22
+ ··· + 14y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.874412 + 0.450439I
a = 0.49727 − 1.62551I
b = 0.197520 + 1.146350I
3.24769 − 4.37033I 10.0565 + 11.1753I
u = −0.874412 − 0.450439I
a = 0.49727 + 1.62551I
b = 0.197520 − 1.146350I
3.24769 + 4.37033I 10.0565 − 11.1753I
u = 0.862202 + 0.466629I
a = −0.52611 − 1.42655I
b = −0.627257 + 1.173710I
3.08238 + 2.29231I 4.36467 + 2.48869I
u = 0.862202 − 0.466629I
a = −0.52611 + 1.42655I
b = −0.627257 − 1.173710I
3.08238 − 2.29231I 4.36467 − 2.48869I
u = 0.822480 + 0.358939I
a = −0.155185 − 0.371353I
b = −1.155090 + 0.468700I
−0.90973 + 8.53479I 6.72404 − 8.38769I
u = 0.822480 − 0.358939I
a = −0.155185 + 0.371353I
b = −1.155090 − 0.468700I
−0.90973 − 8.53479I 6.72404 + 8.38769I
u = −0.701487 + 0.462033I
a = −2.44701 − 1.11361I
b = −0.597104 + 0.199459I
1.56421 − 5.38320I 0.163108 − 0.319571I
u = −0.701487 − 0.462033I
a = −2.44701 + 1.11361I
b = −0.597104 − 0.199459I
1.56421 + 5.38320I 0.163108 + 0.319571I
u = −0.712928 + 0.435312I
a = −0.037762 − 0.296324I
b = −1.144960 + 0.669161I
0.98056 + 4.23184I 7.06871 − 1.26450I
u = −0.712928 − 0.435312I
a = −0.037762 + 0.296324I
b = −1.144960 − 0.669161I
0.98056 − 4.23184I 7.06871 + 1.26450I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.082357 + 1.273310I
a = 0.430315 + 0.330387I
b = −0.557351 − 0.433936I
−7.43499 − 4.07830I 5.09056 + 7.35806I
u = 0.082357 − 1.273310I
a = 0.430315 − 0.330387I
b = −0.557351 + 0.433936I
−7.43499 + 4.07830I 5.09056 − 7.35806I
u = 0.720759
a = −3.39122
b = −0.506052
5.56542 −2.19910
u = 0.318509 + 0.449463I
a = 0.079165 + 0.812558I
b = 1.116300 + 0.343936I
−1.161340 − 0.595654I 5.98634 − 2.67183I
u = 0.318509 − 0.449463I
a = 0.079165 − 0.812558I
b = 1.116300 − 0.343936I
−1.161340 + 0.595654I 5.98634 + 2.67183I
u = −0.04437 + 1.45182I
a = 0.353212 + 0.027944I
b = 0.218100 + 0.647175I
−1.99194 + 0.94590I 10.18917 − 0.41452I
u = −0.04437 − 1.45182I
a = 0.353212 − 0.027944I
b = 0.218100 − 0.647175I
−1.99194 − 0.94590I 10.18917 + 0.41452I
u = −0.294434 + 0.243731I
a = 0.66187 − 2.79243I
b = 1.019620 − 0.151411I
−4.73096 + 3.15634I 4.23220 − 3.16834I
u = −0.294434 − 0.243731I
a = 0.66187 + 2.79243I
b = 1.019620 + 0.151411I
−4.73096 − 3.15634I 4.23220 + 3.16834I
u = −0.10789 + 1.73390I
a = −1.56075 + 0.22687I
b = −1.62758 − 0.14949I
−12.08590 + 1.15226I 3.47782 − 6.88892I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10789 − 1.73390I
a = −1.56075 − 0.22687I
b = −1.62758 + 0.14949I
−12.08590 − 1.15226I 3.47782 + 6.88892I
u = 2.28960 + 1.71638I
a = 0.900594 − 0.162427I
b = 0.910824 − 0.123102I
−4.72684 + 0.26589I 0
u = 2.28960 − 1.71638I
a = 0.900594 + 0.162427I
b = 0.910824 + 0.123102I
−4.72684 − 0.26589I 0
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
23
− 13u
22
+ ··· + 579u − 101)(u
66
− 4u
65
+ ··· + 251u + 131)
c
2
(u
23
+ 5u
22
+ ··· + 5u + 1)(u
66
+ 2u
65
+ ··· − 21u + 1)
c
3
(u
23
− 4u
22
+ ··· − 2u − 1)(u
66
− 3u
65
+ ··· + 1022u − 2621)
c
4
(u
23
+ 4u
22
+ ··· − 2u − 1)(u
66
+ 5u
65
+ ··· − 402u − 171)
c
5
(u
23
− 5u
22
+ ··· + 5u − 1)(u
66
+ 2u
65
+ ··· − 21u + 1)
c
6
(u
23
− u
22
+ ··· − 4u − 1)(u
66
− 2u
65
+ ··· − 40871u − 2788)
c
7
(u
23
+ 7u
22
+ ··· + 24u + 4)(u
66
+ 6u
65
+ ··· + 224u + 16)
c
8
(u
23
+ u
22
+ ··· − 4u − 1)(u
66
+ 47u
64
+ ··· + 18353u − 20690)
c
9
(u
23
+ 13u
21
+ ··· − 4u + 1)
· (u
66
− u
65
+ ··· + 28988118u − 18025751)
c
10
(u
23
− 7u
22
+ ··· + 24u − 4)(u
66
+ 6u
65
+ ··· + 224u + 16)
c
11
(u
23
− 4u
22
+ ··· − 2u + 1)(u
66
+ 5u
65
+ ··· − 402u − 171)
c
12
(u
23
+ 18u
22
+ ··· − 7u
2
+ 1)
· (u
66
− 3u
65
+ ··· + 418122130u − 132292613)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
23
− 21y
22
+ ··· + 137079y −10201)
· (y
66
− 94y
65
+ ··· − 1810017y + 17161)
c
2
, c
5
(y
23
− 11y
22
+ ··· + 11y −1)(y
66
− 48y
65
+ ··· − 193y + 1)
c
3
(y
23
+ 4y
22
+ ··· + 6y −1)
· (y
66
+ 83y
65
+ ··· + 198203936y + 6869641)
c
4
, c
11
(y
23
− 12y
22
+ ··· + 50y
2
− 1)(y
66
− 29y
65
+ ··· − 842526y + 29241)
c
6
(y
23
− 7y
22
+ ··· − 24y −1)
· (y
66
+ 20y
65
+ ··· − 290997577y + 7772944)
c
7
, c
10
(y
23
+ 15y
22
+ ··· + 64y −16)(y
66
+ 46y
65
+ ··· + 58848y
2
+ 256)
c
8
(y
23
+ 19y
22
+ ··· + 12y −1)
· (y
66
+ 94y
65
+ ··· − 15224156589y + 428076100)
c
9
(y
23
+ 26y
22
+ ··· + 6y −1)
· (y
66
+ 69y
65
+ ··· + 2987872480868112y + 324927699114001)
c
12
(y
23
− 166y
22
+ ··· + 14y −1)
· (y
66
+ 89y
65
+ ··· + 205846697467622796y + 17501335454367769)
21
