12n
0766
(K12n
0766
)
A knot diagram
1
Linearized knot diagam
4 6 10 8 12 2 11 1 4 5 7 10
Solving Sequence
7,11
8
5,12
6 4 10 1 3 2 9
c
7
c
11
c
5
c
4
c
10
c
12
c
3
c
2
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h4.30257 × 10
223
u
73
− 1.59534 × 10
224
u
72
+ ··· + 3.52832 × 10
224
b − 2.38648 × 10
226
,
− 1.18385 × 10
227
u
73
+ 4.85389 × 10
227
u
72
+ ··· + 1.03768 × 10
228
a + 1.60594 × 10
229
,
2u
74
− 7u
73
+ ··· − 16845u − 2941i
I
u
2
= h−3.25053 × 10
21
u
25
− 6.44125 × 10
21
u
24
+ ··· + 2.54323 × 10
21
b − 7.68603 × 10
21
,
4.00630 × 10
22
u
25
+ 4.85877 × 10
22
u
24
+ ··· + 1.27162 × 10
22
a − 9.79215 × 10
22
, 2u
26
+ 3u
25
+ ··· + 3u + 5i
* 2 irreducible components of dim
C
= 0, with total 100 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
223
u
73
− 1.60 × 10
224
u
72
+ · · · + 3.53 × 10
224
b − 2.39 ×
10
226
, −1.18 × 10
227
u
73
+ 4.85 × 10
227
u
72
+ · · · + 1.04 × 10
228
a + 1.61 ×
10
229
, 2u
74
− 7u
73
+ · · · − 16845u − 2941i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
5
=
0.114087u
73
− 0.467764u
72
+ ··· − 245.040u − 15.4763
−0.121944u
73
+ 0.452153u
72
+ ··· + 532.776u + 67.6377
a
12
=
−u
u
a
6
=
0.0868585u
73
− 0.413586u
72
+ ··· + 129.619u + 47.9189
−0.0947156u
73
+ 0.397975u
72
+ ··· + 158.117u + 4.24257
a
4
=
0.0617274u
73
− 0.381249u
72
+ ··· + 696.582u + 152.833
−0.0171680u
73
+ 0.135545u
72
+ ··· − 359.031u − 74.6220
a
10
=
−0.312963u
73
+ 0.836273u
72
+ ··· + 3468.82u + 582.248
0.351363u
73
− 0.929137u
72
+ ··· − 4120.61u − 695.633
a
1
=
0.286378u
73
− 1.50591u
72
+ ··· + 2610.83u + 594.370
−0.182080u
73
+ 1.24961u
72
+ ··· − 3728.07u − 779.031
a
3
=
0.665053u
73
− 3.07468u
72
+ ··· + 1842.56u + 551.877
−0.448541u
73
+ 2.43442u
72
+ ··· − 3955.59u − 895.987
a
2
=
0.275851u
73
− 1.31333u
72
+ ··· + 1415.83u + 352.827
−0.132560u
73
+ 0.746912u
72
+ ··· − 1432.05u − 319.676
a
9
=
−0.530006u
73
+ 1.62015u
72
+ ··· + 4466.85u + 715.631
0.503235u
73
− 1.26199u
72
+ ··· − 6391.55u − 1090.11
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.310330u
73
− 0.873656u
72
+ ··· − 3442.04u − 587.923
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
2(2u
74
− 3u
73
+ ··· + 5635u + 1357)
c
2
, c
6
u
74
− 2u
73
+ ··· − 215u + 91
c
3
, c
9
2(2u
74
+ 5u
73
+ ··· + 1357162u − 1267391)
c
4
u
74
+ 2u
73
+ ··· − 15076u + 11221
c
5
u
74
+ u
73
+ ··· + 15239u − 3254
c
7
, c
11
2(2u
74
+ 7u
73
+ ··· + 16845u − 2941)
c
8
u
74
+ u
73
+ ··· − 327620u − 108299
c
10
u
74
+ u
73
+ ··· − 2955u − 682
c
12
4(4u
74
− 55u
73
+ ··· − 5042508u + 189693)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
4(4y
74
− 365y
73
+ ··· − 4.76298 × 10
8
y + 1841449)
c
2
, c
6
y
74
+ 44y
73
+ ··· + 374559y + 8281
c
3
, c
9
4(4y
74
− 385y
73
+ ··· − 1.71162 × 10
13
y + 1.60628 × 10
12
)
c
4
y
74
+ 42y
73
+ ··· + 674142038y + 125910841
c
5
y
74
− 23y
73
+ ··· − 131821697y + 10588516
c
7
, c
11
4(4y
74
+ 223y
73
+ ··· + 5.75137 × 10
7
y + 8649481)
c
8
y
74
− 73y
73
+ ··· − 102167052718y + 11728673401
c
10
y
74
+ 27y
73
+ ··· + 11416983y + 465124
c
12
16(16y
74
− 1361y
73
+ ··· − 3.95388 × 10
12
y + 3.59834 × 10
10
)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.282540 + 0.965432I
a = 1.97958 − 0.61451I
b = −2.36679 + 0.10892I
5.94493 + 1.20153I 0
u = −0.282540 − 0.965432I
a = 1.97958 + 0.61451I
b = −2.36679 − 0.10892I
5.94493 − 1.20153I 0
u = −0.273716 + 0.955237I
a = 0.964437 + 0.589339I
b = −1.65206 − 1.31053I
−4.12089 + 2.31752I 0
u = −0.273716 − 0.955237I
a = 0.964437 − 0.589339I
b = −1.65206 + 1.31053I
−4.12089 − 2.31752I 0
u = 0.850496 + 0.543632I
a = 0.560041 − 0.577085I
b = 0.286399 + 0.141759I
−3.21620 − 2.62127I 0
u = 0.850496 − 0.543632I
a = 0.560041 + 0.577085I
b = 0.286399 − 0.141759I
−3.21620 + 2.62127I 0
u = 0.129802 + 0.975847I
a = −0.906793 − 0.098111I
b = 1.82693 − 1.49863I
1.63235 − 1.32777I 0
u = 0.129802 − 0.975847I
a = −0.906793 + 0.098111I
b = 1.82693 + 1.49863I
1.63235 + 1.32777I 0
u = 0.227538 + 0.989919I
a = −0.949692 + 0.421748I
b = 1.44010 + 0.70533I
−0.40348 − 4.84228I 0
u = 0.227538 − 0.989919I
a = −0.949692 − 0.421748I
b = 1.44010 − 0.70533I
−0.40348 + 4.84228I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.451986 + 0.911224I
a = −0.986328 + 0.186176I
b = 1.36894 − 0.72134I
−1.94739 − 2.05739I 0
u = 0.451986 − 0.911224I
a = −0.986328 − 0.186176I
b = 1.36894 + 0.72134I
−1.94739 + 2.05739I 0
u = −0.882267 + 0.418072I
a = 0.794732 + 0.966645I
b = 0.102572 + 0.568615I
−11.22430 − 3.31101I 0
u = −0.882267 − 0.418072I
a = 0.794732 − 0.966645I
b = 0.102572 − 0.568615I
−11.22430 + 3.31101I 0
u = −0.326030 + 1.001260I
a = 1.78729 − 0.35964I
b = −2.07467 + 0.41391I
8.32262 + 1.34742I 0
u = −0.326030 − 1.001260I
a = 1.78729 + 0.35964I
b = −2.07467 − 0.41391I
8.32262 − 1.34742I 0
u = 0.112227 + 0.923316I
a = −0.552088 − 1.134390I
b = 0.487672 − 0.685782I
1.41563 + 0.22117I −8.00000 + 0.I
u = 0.112227 − 0.923316I
a = −0.552088 + 1.134390I
b = 0.487672 + 0.685782I
1.41563 − 0.22117I −8.00000 + 0.I
u = 0.819659 + 0.410089I
a = −0.311016 + 1.351220I
b = −0.577110 − 0.608864I
−3.45418 + 3.81432I −8.00000 − 3.44974I
u = 0.819659 − 0.410089I
a = −0.311016 − 1.351220I
b = −0.577110 + 0.608864I
−3.45418 − 3.81432I −8.00000 + 3.44974I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.884708 + 0.626615I
a = −1.022130 − 0.689132I
b = 1.252530 − 0.402107I
−8.51884 − 2.65252I 0
u = 0.884708 − 0.626615I
a = −1.022130 + 0.689132I
b = 1.252530 + 0.402107I
−8.51884 + 2.65252I 0
u = −0.843390 + 0.327145I
a = 0.313849 + 1.164510I
b = 0.515054 − 0.008704I
−1.78911 − 2.87710I −11.42016 + 4.01103I
u = −0.843390 − 0.327145I
a = 0.313849 − 1.164510I
b = 0.515054 + 0.008704I
−1.78911 + 2.87710I −11.42016 − 4.01103I
u = 0.932065 + 0.593886I
a = −0.359516 − 0.399971I
b = −0.016925 + 0.207404I
−1.16017 + 1.30316I 0
u = 0.932065 − 0.593886I
a = −0.359516 + 0.399971I
b = −0.016925 − 0.207404I
−1.16017 − 1.30316I 0
u = −0.248102 + 1.112950I
a = 0.348133 + 0.638683I
b = −0.168692 + 0.673985I
2.02889 + 4.36880I 0
u = −0.248102 − 1.112950I
a = 0.348133 − 0.638683I
b = −0.168692 − 0.673985I
2.02889 − 4.36880I 0
u = −0.296484 + 1.119460I
a = −0.42766 + 1.64773I
b = 1.195140 − 0.619228I
−6.67297 + 7.19206I 0
u = −0.296484 − 1.119460I
a = −0.42766 − 1.64773I
b = 1.195140 + 0.619228I
−6.67297 − 7.19206I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.139612 + 1.164800I
a = −0.503559 + 0.439878I
b = 1.40916 + 0.71610I
2.38650 + 3.81134I 0
u = −0.139612 − 1.164800I
a = −0.503559 − 0.439878I
b = 1.40916 − 0.71610I
2.38650 − 3.81134I 0
u = −0.085205 + 0.815728I
a = 0.10305 − 2.33544I
b = −0.104807 + 0.812551I
−5.12415 − 0.44406I −5.45474 − 1.65343I
u = −0.085205 − 0.815728I
a = 0.10305 + 2.33544I
b = −0.104807 − 0.812551I
−5.12415 + 0.44406I −5.45474 + 1.65343I
u = −0.480089 + 1.115540I
a = −0.721167 − 0.211751I
b = 2.27508 + 1.18426I
−9.01588 + 8.24429I 0
u = −0.480089 − 1.115540I
a = −0.721167 + 0.211751I
b = 2.27508 − 1.18426I
−9.01588 − 8.24429I 0
u = −0.037495 + 1.218510I
a = 0.588125 − 0.286537I
b = −1.72908 − 0.14105I
3.51297 − 0.84853I 0
u = −0.037495 − 1.218510I
a = 0.588125 + 0.286537I
b = −1.72908 + 0.14105I
3.51297 + 0.84853I 0
u = −0.041616 + 1.282970I
a = 0.608968 − 0.136991I
b = −2.12837 + 0.42808I
3.82386 − 0.95845I 0
u = −0.041616 − 1.282970I
a = 0.608968 + 0.136991I
b = −2.12837 − 0.42808I
3.82386 + 0.95845I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564418 + 0.431263I
a = −1.186740 + 0.350705I
b = 0.143898 − 0.524191I
2.33020 + 1.82399I −2.62562 − 4.08720I
u = −0.564418 − 0.431263I
a = −1.186740 − 0.350705I
b = 0.143898 + 0.524191I
2.33020 − 1.82399I −2.62562 + 4.08720I
u = 0.565832 + 1.189960I
a = 1.385630 − 0.142564I
b = −2.04227 + 0.69658I
−0.95117 − 9.06853I 0
u = 0.565832 − 1.189960I
a = 1.385630 + 0.142564I
b = −2.04227 − 0.69658I
−0.95117 + 9.06853I 0
u = −0.540516 + 1.218140I
a = −1.192520 − 0.017762I
b = 2.16082 + 0.66660I
1.05457 + 8.06406I 0
u = −0.540516 − 1.218140I
a = −1.192520 + 0.017762I
b = 2.16082 − 0.66660I
1.05457 − 8.06406I 0
u = 0.862645 + 1.082460I
a = −0.462609 − 0.839310I
b = 1.310950 + 0.310610I
−7.35921 − 3.79262I 0
u = 0.862645 − 1.082460I
a = −0.462609 + 0.839310I
b = 1.310950 − 0.310610I
−7.35921 + 3.79262I 0
u = −1.380710 + 0.230252I
a = 0.269437 − 0.278275I
b = 0.202962 + 0.463666I
−0.389474 − 0.354384I 0
u = −1.380710 − 0.230252I
a = 0.269437 + 0.278275I
b = 0.202962 − 0.463666I
−0.389474 + 0.354384I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.210951 + 1.392990I
a = 0.695783 − 0.339602I
b = −2.28329 − 0.58609I
−2.01031 − 5.75879I 0
u = 0.210951 − 1.392990I
a = 0.695783 + 0.339602I
b = −2.28329 + 0.58609I
−2.01031 + 5.75879I 0
u = 1.413210 + 0.032389I
a = 0.466955 − 0.622175I
b = 0.322562 − 0.042703I
−9.23639 + 9.54301I 0
u = 1.413210 − 0.032389I
a = 0.466955 + 0.622175I
b = 0.322562 + 0.042703I
−9.23639 − 9.54301I 0
u = −0.314553 + 0.484519I
a = −2.08380 + 0.18127I
b = 1.38082 + 1.62692I
−8.72504 − 4.53070I −9.46563 − 0.03654I
u = −0.314553 − 0.484519I
a = −2.08380 − 0.18127I
b = 1.38082 − 1.62692I
−8.72504 + 4.53070I −9.46563 + 0.03654I
u = 0.40349 + 1.40042I
a = 0.850562 − 0.225517I
b = −1.73948 + 0.45576I
4.66305 − 3.47646I 0
u = 0.40349 − 1.40042I
a = 0.850562 + 0.225517I
b = −1.73948 − 0.45576I
4.66305 + 3.47646I 0
u = −0.22989 + 1.46784I
a = 1.023780 + 0.634462I
b = −1.97633 − 0.61949I
8.50502 + 4.79512I 0
u = −0.22989 − 1.46784I
a = 1.023780 − 0.634462I
b = −1.97633 + 0.61949I
8.50502 − 4.79512I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.68098 + 1.32491I
a = −1.015860 − 0.099869I
b = 1.48438 + 0.51385I
3.51452 + 6.72221I 0
u = −0.68098 − 1.32491I
a = −1.015860 + 0.099869I
b = 1.48438 − 0.51385I
3.51452 − 6.72221I 0
u = 0.480013
a = −0.978637
b = 0.105834
−0.717809 −13.7110
u = −0.460554
a = −2.63177
b = 0.222685
−6.45678 −18.2290
u = 0.55731 + 1.44922I
a = −0.782460 + 0.229973I
b = 1.58134 − 0.58286I
3.10250 − 8.98573I 0
u = 0.55731 − 1.44922I
a = −0.782460 − 0.229973I
b = 1.58134 + 0.58286I
3.10250 + 8.98573I 0
u = 0.64625 + 1.43646I
a = −1.052510 + 0.238181I
b = 2.06068 − 0.85585I
−4.8082 − 16.5804I 0
u = 0.64625 − 1.43646I
a = −1.052510 − 0.238181I
b = 2.06068 + 0.85585I
−4.8082 + 16.5804I 0
u = −0.341097 + 0.196071I
a = −0.512603 + 0.829174I
b = 0.500629 + 0.652787I
−0.55991 − 1.68520I −3.94366 + 2.95348I
u = −0.341097 − 0.196071I
a = −0.512603 − 0.829174I
b = 0.500629 − 0.652787I
−0.55991 + 1.68520I −3.94366 − 2.95348I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.53573 + 1.88702I
a = −0.244801 + 0.238485I
b = 0.202955 − 0.369257I
−1.22442 + 0.74078I 0
u = 0.53573 − 1.88702I
a = −0.244801 − 0.238485I
b = 0.202955 + 0.369257I
−1.22442 − 0.74078I 0
u = 0.12508 + 2.04317I
a = 0.299929 − 0.278914I
b = −0.815962 + 0.338188I
−2.79671 + 1.13420I 0
u = 0.12508 − 2.04317I
a = 0.299929 + 0.278914I
b = −0.815962 − 0.338188I
−2.79671 − 1.13420I 0
12
II. I
u
2
= h−3.25 × 10
21
u
25
− 6.44 × 10
21
u
24
+ · · · + 2.54 × 10
21
b − 7.69 ×
10
21
, 4.01 × 10
22
u
25
+ 4.86 × 10
22
u
24
+ · · · + 1.27 × 10
22
a − 9.79 ×
10
22
, 2u
26
+ 3u
25
+ · · · + 3u + 5i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
u
2
a
5
=
−3.15056u
25
− 3.82094u
24
+ ··· − 32.1591u + 7.70055
1.27811u
25
+ 2.53270u
24
+ ··· + 10.2992u + 3.02215
a
12
=
−u
u
a
6
=
−3.17174u
25
− 2.90632u
24
+ ··· − 34.5596u + 11.5016
1.29929u
25
+ 1.61808u
24
+ ··· + 12.6997u − 0.778933
a
4
=
−3.02056u
25
− 2.73307u
24
+ ··· − 28.3790u + 12.9849
1.04423u
25
+ 1.41495u
24
+ ··· + 8.63488u + 0.789972
a
10
=
−1.28799u
25
− 1.45837u
24
+ ··· − 24.5359u + 9.00385
0.947693u
25
+ 1.79106u
24
+ ··· + 14.4576u − 1.69050
a
1
=
4.14969u
25
+ 4.29557u
24
+ ··· + 59.5932u − 13.0060
−0.880620u
25
− 0.966252u
24
+ ··· − 19.0119u + 1.59597
a
3
=
0.182558u
25
− 0.176354u
24
+ ··· + 25.0268u − 7.11541
0.533120u
25
+ 1.45644u
24
+ ··· − 6.50589u + 6.77145
a
2
=
0.743734u
25
+ 0.470887u
24
+ ··· + 12.7345u − 0.708825
−0.796874u
25
− 0.999327u
24
+ ··· − 10.5483u + 2.03149
a
9
=
−3.07289u
25
− 3.63312u
24
+ ··· − 55.1391u + 17.4838
1.26243u
25
+ 2.27407u
24
+ ··· + 19.9727u − 4.31308
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
8957706328472547967206
2543234894966602321649
u
25
−
15083092567838434344417
2543234894966602321649
u
24
+ ··· −
142260302926776775260119
2543234894966602321649
u −
54489073205343541583617
2543234894966602321649
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
2(2u
26
− 27u
25
+ ··· − 101u + 43)
c
2
u
26
− u
25
+ ··· + 3u + 1
c
3
2(2u
26
+ 7u
25
+ ··· + 2u + 1)
c
4
u
26
+ u
25
+ ··· + 60u + 31
c
5
u
26
+ 2u
25
+ ··· + u + 2
c
6
u
26
+ u
25
+ ··· − 3u + 1
c
7
2(2u
26
+ 3u
25
+ ··· + 3u + 5)
c
8
u
26
+ 4u
25
+ ··· − 2u + 1
c
9
2(2u
26
− 7u
25
+ ··· − 2u + 1)
c
10
u
26
+ 7u
24
+ ··· + u + 2
c
11
2(2u
26
− 3u
25
+ ··· − 3u + 5)
c
12
4(4u
26
− 11u
25
+ ··· − 74u + 19)
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
4(4y
26
− 113y
25
+ ··· + 3645y + 1849)
c
2
, c
6
y
26
+ 7y
25
+ ··· + 15y + 1
c
3
, c
9
4(4y
26
− 37y
25
+ ··· + 4y + 1)
c
4
y
26
+ 21y
25
+ ··· + 4646y + 961
c
5
y
26
+ 20y
24
+ ··· + 103y + 4
c
7
, c
11
4(4y
26
+ 107y
25
+ ··· + 581y + 25)
c
8
y
26
− 6y
25
+ ··· + 14y + 1
c
10
y
26
+ 14y
25
+ ··· − y + 4
c
12
16(16y
26
− 545y
25
+ ··· − 6160y + 361)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.093841 + 1.031720I
a = −1.86117 − 0.11292I
b = 2.26755 − 0.34607I
6.38440 + 0.40642I −3.29683 + 1.73011I
u = −0.093841 − 1.031720I
a = −1.86117 + 0.11292I
b = 2.26755 + 0.34607I
6.38440 − 0.40642I −3.29683 − 1.73011I
u = −0.892339 + 0.285855I
a = −0.698036 + 0.392925I
b = −0.490163 − 0.492975I
−0.34275 + 1.53093I −9.99239 − 3.21099I
u = −0.892339 − 0.285855I
a = −0.698036 − 0.392925I
b = −0.490163 + 0.492975I
−0.34275 − 1.53093I −9.99239 + 3.21099I
u = 0.857561 + 0.346086I
a = 0.170569 − 0.299589I
b = −0.159930 + 0.592271I
−1.62614 + 1.72699I −14.2649 − 3.7983I
u = 0.857561 − 0.346086I
a = 0.170569 + 0.299589I
b = −0.159930 − 0.592271I
−1.62614 − 1.72699I −14.2649 + 3.7983I
u = −0.441215 + 1.028280I
a = −1.59099 + 0.55970I
b = 2.07746 − 0.27910I
8.13583 + 1.76508I −6.93534 − 8.95904I
u = −0.441215 − 1.028280I
a = −1.59099 − 0.55970I
b = 2.07746 + 0.27910I
8.13583 − 1.76508I −6.93534 + 8.95904I
u = 0.120572 + 1.131100I
a = 0.661863 + 0.339366I
b = −1.76827 + 1.10631I
2.95392 − 3.52625I 0.774646 + 0.743499I
u = 0.120572 − 1.131100I
a = 0.661863 − 0.339366I
b = −1.76827 − 1.10631I
2.95392 + 3.52625I 0.774646 − 0.743499I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.504964 + 0.668691I
a = 0.081169 + 1.214460I
b = −1.76357 − 0.68487I
−8.64330 − 6.02727I −9.72659 + 4.66930I
u = 0.504964 − 0.668691I
a = 0.081169 − 1.214460I
b = −1.76357 + 0.68487I
−8.64330 + 6.02727I −9.72659 − 4.66930I
u = 0.255755 + 1.173940I
a = −0.827640 + 0.464151I
b = 1.64429 + 0.44080I
0.39482 − 5.40053I −4.61104 + 7.42054I
u = 0.255755 − 1.173940I
a = −0.827640 − 0.464151I
b = 1.64429 − 0.44080I
0.39482 + 5.40053I −4.61104 − 7.42054I
u = 0.017834 + 1.281180I
a = −0.518334 + 0.025264I
b = 2.18360 − 0.78912I
3.97615 + 0.02420I −1.50757 + 0.97966I
u = 0.017834 − 1.281180I
a = −0.518334 − 0.025264I
b = 2.18360 + 0.78912I
3.97615 − 0.02420I −1.50757 − 0.97966I
u = 0.012793 + 0.520722I
a = 1.35963 + 1.19227I
b = −0.422136 + 1.022280I
0.84916 + 2.58424I −7.44172 − 4.08752I
u = 0.012793 − 0.520722I
a = 1.35963 − 1.19227I
b = −0.422136 − 1.022280I
0.84916 − 2.58424I −7.44172 + 4.08752I
u = −0.23818 + 1.50712I
a = −0.960593 − 0.604711I
b = 1.96189 + 0.59778I
8.27085 + 4.64071I −15.0125 + 3.7642I
u = −0.23818 − 1.50712I
a = −0.960593 + 0.604711I
b = 1.96189 − 0.59778I
8.27085 − 4.64071I −15.0125 − 3.7642I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.61918 + 1.41182I
a = 0.921209 + 0.081616I
b = −1.63904 − 0.46965I
4.53565 + 8.09953I −3.94785 − 6.19470I
u = −0.61918 − 1.41182I
a = 0.921209 − 0.081616I
b = −1.63904 + 0.46965I
4.53565 − 8.09953I −3.94785 + 6.19470I
u = −0.091702 + 0.419701I
a = −1.08553 − 3.39215I
b = 0.372307 + 0.860688I
−5.76127 + 0.88146I −14.4603 − 4.2768I
u = −0.091702 − 0.419701I
a = −1.08553 + 3.39215I
b = 0.372307 − 0.860688I
−5.76127 − 0.88146I −14.4603 + 4.2768I
u = −0.14302 + 2.03303I
a = −0.052154 + 0.337702I
b = 0.236008 − 0.418304I
−1.033050 + 0.572499I 0
u = −0.14302 − 2.03303I
a = −0.052154 − 0.337702I
b = 0.236008 + 0.418304I
−1.033050 − 0.572499I 0
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
4(2u
26
− 27u
25
+ ··· − 101u + 43)(2u
74
− 3u
73
+ ··· + 5635u + 1357)
c
2
(u
26
− u
25
+ ··· + 3u + 1)(u
74
− 2u
73
+ ··· − 215u + 91)
c
3
4(2u
26
+ 7u
25
+ ··· + 2u + 1)
· (2u
74
+ 5u
73
+ ··· + 1357162u − 1267391)
c
4
(u
26
+ u
25
+ ··· + 60u + 31)(u
74
+ 2u
73
+ ··· − 15076u + 11221)
c
5
(u
26
+ 2u
25
+ ··· + u + 2)(u
74
+ u
73
+ ··· + 15239u − 3254)
c
6
(u
26
+ u
25
+ ··· − 3u + 1)(u
74
− 2u
73
+ ··· − 215u + 91)
c
7
4(2u
26
+ 3u
25
+ ··· + 3u + 5)(2u
74
+ 7u
73
+ ··· + 16845u − 2941)
c
8
(u
26
+ 4u
25
+ ··· − 2u + 1)(u
74
+ u
73
+ ··· − 327620u − 108299)
c
9
4(2u
26
− 7u
25
+ ··· − 2u + 1)
· (2u
74
+ 5u
73
+ ··· + 1357162u − 1267391)
c
10
(u
26
+ 7u
24
+ ··· + u + 2)(u
74
+ u
73
+ ··· − 2955u − 682)
c
11
4(2u
26
− 3u
25
+ ··· − 3u + 5)(2u
74
+ 7u
73
+ ··· + 16845u − 2941)
c
12
16(4u
26
− 11u
25
+ ··· − 74u + 19)
· (4u
74
− 55u
73
+ ··· − 5042508u + 189693)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
16(4y
26
− 113y
25
+ ··· + 3645y + 1849)
· (4y
74
− 365y
73
+ ··· − 476298283y + 1841449)
c
2
, c
6
(y
26
+ 7y
25
+ ··· + 15y + 1)(y
74
+ 44y
73
+ ··· + 374559y + 8281)
c
3
, c
9
16(4y
26
− 37y
25
+ ··· + 4y + 1)
· (4y
74
− 385y
73
+ ··· − 17116221408916y + 1606279946881)
c
4
(y
26
+ 21y
25
+ ··· + 4646y + 961)
· (y
74
+ 42y
73
+ ··· + 674142038y + 125910841)
c
5
(y
26
+ 20y
24
+ ··· + 103y + 4)
· (y
74
− 23y
73
+ ··· − 131821697y + 10588516)
c
7
, c
11
16(4y
26
+ 107y
25
+ ··· + 581y + 25)
· (4y
74
+ 223y
73
+ ··· + 57513733y + 8649481)
c
8
(y
26
− 6y
25
+ ··· + 14y + 1)
· (y
74
− 73y
73
+ ··· − 102167052718y + 11728673401)
c
10
(y
26
+ 14y
25
+ ··· − y + 4)(y
74
+ 27y
73
+ ··· + 1.14170 × 10
7
y + 465124)
c
12
256(16y
26
− 545y
25
+ ··· − 6160y + 361)
· (16y
74
− 1361y
73
+ ··· − 3953884413420y + 35983434249)
22
