12a
0398
(K12a
0398
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 2 1 10 5 12 8 4 7
Solving Sequence
3,6
2 1
7,10
8 11 5 4 12 9
c
2
c
1
c
6
c
7
c
10
c
5
c
4
c
12
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.97226 × 10
50
u
97
+ 4.65765 × 10
50
u
96
+ ··· + 9.94685 × 10
49
b + 3.19075 × 10
50
,
7.33977 × 10
49
u
97
− 8.07721 × 10
49
u
96
+ ··· + 2.98406 × 10
50
a + 7.44119 × 10
50
, u
98
− 2u
97
+ ··· − 5u + 1i
I
u
2
= h5u
5
− 3u
4
− 7u
3
+ 8u
2
+ 17b + 11u + 1, 4u
5
− 16u
4
− 26u
3
+ 20u
2
+ 17a + 19u − 6,
u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 104 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−4.97×10
50
u
97
+4.66×10
50
u
96
+· · ·+9.95×10
49
b+3.19×10
50
, 7.34×
10
49
u
97
−8.08×10
49
u
96
+· · ·+2.98×10
50
a+7.44×10
50
, u
98
−2u
97
+· · ·−5u+1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
10
=
−0.245966u
97
+ 0.270679u
96
+ ··· − 0.544659u − 2.49365
4.99882u
97
− 4.68254u
96
+ ··· + 17.2389u − 3.20780
a
8
=
0.293712u
97
− 0.601992u
96
+ ··· + 4.46853u − 2.86203
4.85358u
97
− 4.20830u
96
+ ··· + 16.6402u − 2.74961
a
11
=
−0.979346u
97
+ 1.70885u
96
+ ··· − 8.77351u + 0.791545
0.216714u
97
− 0.560914u
96
+ ··· + 0.966260u − 0.417735
a
5
=
u
−u
3
+ u
a
4
=
2.87151u
97
− 2.46999u
96
+ ··· + 7.08329u − 1.86426
−0.626345u
97
+ 0.422548u
96
+ ··· − 3.41997u + 1.08263
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
9
=
−5.41930u
97
+ 6.52843u
96
+ ··· − 21.8687u + 3.43085
1.32970u
97
− 1.22300u
96
+ ··· + 6.06795u − 0.752344
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.95346u
97
+ 1.64120u
96
+ ··· − 1.69682u − 8.13481
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
98
+ 54u
97
+ ··· + 15u + 1
c
2
, c
5
u
98
+ 2u
97
+ ··· + 5u + 1
c
3
u
98
− u
97
+ ··· + 56576u − 18496
c
4
, c
11
u
98
− 2u
97
+ ··· + u + 1
c
6
, c
12
u
98
+ 6u
97
+ ··· − 585u − 117
c
7
, c
10
u
98
− 7u
97
+ ··· − 1854u − 289
c
8
17(17u
98
+ 153u
97
+ ··· − 1.14403 × 10
7
u − 3023343)
c
9
17(17u
98
− 17u
97
+ ··· − 1.64298 × 10
7
u + 5717884)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
98
− 18y
97
+ ··· − 63y + 1
c
2
, c
5
y
98
− 54y
97
+ ··· − 15y + 1
c
3
y
98
− 39y
97
+ ··· − 8090890240y + 342102016
c
4
, c
11
y
98
+ 66y
97
+ ··· − 15y + 1
c
6
, c
12
y
98
+ 90y
97
+ ··· − 361179y + 13689
c
7
, c
10
y
98
− 85y
97
+ ··· − 453680y + 83521
c
8
289
· (289y
98
− 16167y
97
+ ··· + 80567110376298y + 9140602895649)
c
9
289
· (289y
98
− 19669y
97
+ ··· + 565449262390916y + 32694197437456)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.880926 + 0.484109I
a = 0.126645 − 0.916864I
b = 0.660952 − 0.142781I
1.31774 + 3.33830I 0
u = −0.880926 − 0.484109I
a = 0.126645 + 0.916864I
b = 0.660952 + 0.142781I
1.31774 − 3.33830I 0
u = 0.974373 + 0.252627I
a = −1.27667 + 1.42712I
b = −0.022307 + 0.871202I
−7.11570 − 0.67586I 0
u = 0.974373 − 0.252627I
a = −1.27667 − 1.42712I
b = −0.022307 − 0.871202I
−7.11570 + 0.67586I 0
u = 0.910945 + 0.373274I
a = −0.256402 + 0.534880I
b = −0.98712 + 1.06488I
−2.23448 − 2.92840I 0
u = 0.910945 − 0.373274I
a = −0.256402 − 0.534880I
b = −0.98712 − 1.06488I
−2.23448 + 2.92840I 0
u = 0.896075 + 0.389212I
a = 0.023671 − 0.586188I
b = 0.303646 + 0.530745I
−2.08514 − 1.28187I 0
u = 0.896075 − 0.389212I
a = 0.023671 + 0.586188I
b = 0.303646 − 0.530745I
−2.08514 + 1.28187I 0
u = 0.928346 + 0.477510I
a = −0.559370 − 0.935941I
b = −1.231390 + 0.023809I
−1.86670 − 6.95902I 0
u = 0.928346 − 0.477510I
a = −0.559370 + 0.935941I
b = −1.231390 − 0.023809I
−1.86670 + 6.95902I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.974953 + 0.377265I
a = 1.247520 + 0.361901I
b = 1.09051 + 1.21557I
−6.26927 + 4.49763I 0
u = −0.974953 − 0.377265I
a = 1.247520 − 0.361901I
b = 1.09051 − 1.21557I
−6.26927 − 4.49763I 0
u = −0.941732 + 0.075068I
a = 0.495249 + 1.108090I
b = −0.774952 + 0.155770I
−4.44083 − 2.39547I −13.30877 + 3.50221I
u = −0.941732 − 0.075068I
a = 0.495249 − 1.108090I
b = −0.774952 − 0.155770I
−4.44083 + 2.39547I −13.30877 − 3.50221I
u = −0.885013 + 0.279903I
a = 1.29645 + 1.65611I
b = 0.652790 − 0.030084I
−2.90514 + 1.19408I −2.29836 − 6.69725I
u = −0.885013 − 0.279903I
a = 1.29645 − 1.65611I
b = 0.652790 + 0.030084I
−2.90514 − 1.19408I −2.29836 + 6.69725I
u = −0.524530 + 0.732654I
a = −2.08618 − 0.70829I
b = −0.761115 − 0.376453I
−0.232117 − 1.390560I −11.31130 + 4.29351I
u = −0.524530 − 0.732654I
a = −2.08618 + 0.70829I
b = −0.761115 + 0.376453I
−0.232117 + 1.390560I −11.31130 − 4.29351I
u = 0.132548 + 0.884447I
a = 0.03160 + 2.92347I
b = −0.19165 + 2.64383I
−10.92230 + 0.52550I −11.49902 + 0.I
u = 0.132548 − 0.884447I
a = 0.03160 − 2.92347I
b = −0.19165 − 2.64383I
−10.92230 − 0.52550I −11.49902 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.114489 + 0.882090I
a = 0.04997 + 3.38096I
b = 0.12413 + 3.03122I
−6.80651 − 6.89016I −7.34704 + 4.74828I
u = −0.114489 − 0.882090I
a = 0.04997 − 3.38096I
b = 0.12413 − 3.03122I
−6.80651 + 6.89016I −7.34704 − 4.74828I
u = 0.570229 + 0.676931I
a = 1.98999 − 0.86975I
b = 0.551409 − 0.736236I
−5.07076 − 5.29668I −8.08754 + 5.87006I
u = 0.570229 − 0.676931I
a = 1.98999 + 0.86975I
b = 0.551409 + 0.736236I
−5.07076 + 5.29668I −8.08754 − 5.87006I
u = 0.940783 + 0.607358I
a = −0.10800 − 1.77166I
b = −0.456724 − 1.138880I
−6.12867 + 0.37150I 0
u = 0.940783 − 0.607358I
a = −0.10800 + 1.77166I
b = −0.456724 + 1.138880I
−6.12867 − 0.37150I 0
u = 0.115348 + 0.872168I
a = −0.27789 + 3.51102I
b = −0.26189 + 3.22218I
−11.5464 + 12.6491I −9.04777 − 6.24200I
u = 0.115348 − 0.872168I
a = −0.27789 − 3.51102I
b = −0.26189 − 3.22218I
−11.5464 − 12.6491I −9.04777 + 6.24200I
u = 1.063950 + 0.366915I
a = −0.304479 − 0.401019I
b = 0.338645 + 0.700284I
−2.32999 − 1.10892I 0
u = 1.063950 − 0.366915I
a = −0.304479 + 0.401019I
b = 0.338645 − 0.700284I
−2.32999 + 1.10892I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.971094 + 0.573545I
a = −0.24373 − 1.46327I
b = 0.025972 − 0.871201I
−6.69265 − 12.33470I 0
u = 0.971094 − 0.573545I
a = −0.24373 + 1.46327I
b = 0.025972 + 0.871201I
−6.69265 + 12.33470I 0
u = −0.767801 + 0.352606I
a = 1.39070 − 2.44592I
b = −2.58577 + 0.72091I
−3.63016 + 1.65900I 3.9072 + 23.8478I
u = −0.767801 − 0.352606I
a = 1.39070 + 2.44592I
b = −2.58577 − 0.72091I
−3.63016 − 1.65900I 3.9072 − 23.8478I
u = 0.505693 + 0.675692I
a = 1.75333 − 0.84172I
b = 0.329537 − 0.231538I
−5.35571 + 7.53889I −6.81727 − 4.67967I
u = 0.505693 − 0.675692I
a = 1.75333 + 0.84172I
b = 0.329537 + 0.231538I
−5.35571 − 7.53889I −6.81727 + 4.67967I
u = −0.993504 + 0.600088I
a = 0.47368 − 1.64849I
b = 0.411373 − 0.745032I
−1.61839 + 6.44486I 0
u = −0.993504 − 0.600088I
a = 0.47368 + 1.64849I
b = 0.411373 + 0.745032I
−1.61839 − 6.44486I 0
u = −1.166400 + 0.018886I
a = −0.966641 − 0.179200I
b = −1.63225 + 0.12018I
−10.79030 − 6.22673I 0
u = −1.166400 − 0.018886I
a = −0.966641 + 0.179200I
b = −1.63225 − 0.12018I
−10.79030 + 6.22673I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.021273 + 0.831652I
a = −0.24180 − 2.58464I
b = 0.05445 − 2.72408I
−9.90385 − 2.44635I −13.17692 + 2.77402I
u = −0.021273 − 0.831652I
a = −0.24180 + 2.58464I
b = 0.05445 + 2.72408I
−9.90385 + 2.44635I −13.17692 − 2.77402I
u = 0.070842 + 0.823509I
a = −0.007588 − 0.526508I
b = −0.548057 − 0.671649I
−5.66868 + 6.21673I −8.53340 − 6.01973I
u = 0.070842 − 0.823509I
a = −0.007588 + 0.526508I
b = −0.548057 + 0.671649I
−5.66868 − 6.21673I −8.53340 + 6.01973I
u = 1.19235
a = 0.890389
b = 1.79996
−6.07258 0
u = 0.017029 + 0.804914I
a = 1.57818 − 3.43781I
b = 1.11105 − 3.17459I
−5.21434 + 1.19168I −4.90066 − 0.65015I
u = 0.017029 − 0.804914I
a = 1.57818 + 3.43781I
b = 1.11105 + 3.17459I
−5.21434 − 1.19168I −4.90066 + 0.65015I
u = −0.074672 + 0.797417I
a = −0.635672 + 0.075350I
b = −0.136067 − 0.093287I
−1.97377 − 2.83777I −2.36877 + 3.16295I
u = −0.074672 − 0.797417I
a = −0.635672 − 0.075350I
b = −0.136067 + 0.093287I
−1.97377 + 2.83777I −2.36877 − 3.16295I
u = −1.089280 + 0.516766I
a = 0.907969 − 0.774653I
b = 0.321369 + 0.406554I
−1.16942 + 6.00915I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.089280 − 0.516766I
a = 0.907969 + 0.774653I
b = 0.321369 − 0.406554I
−1.16942 − 6.00915I 0
u = −0.621107 + 0.492354I
a = −0.987856 − 0.165809I
b = −0.583250 − 0.432942I
2.05741 + 0.72072I 3.28663 − 2.76170I
u = −0.621107 − 0.492354I
a = −0.987856 + 0.165809I
b = −0.583250 + 0.432942I
2.05741 − 0.72072I 3.28663 + 2.76170I
u = 0.043406 + 0.778257I
a = 2.60159 + 1.38272I
b = 1.97585 + 0.82291I
−4.92565 + 0.14811I −9.73034 + 0.94835I
u = 0.043406 − 0.778257I
a = 2.60159 − 1.38272I
b = 1.97585 − 0.82291I
−4.92565 − 0.14811I −9.73034 − 0.94835I
u = 0.720329 + 0.089531I
a = −0.844602 + 0.270082I
b = 0.691179 − 0.042911I
−1.241080 − 0.011716I −6.07029 − 0.34761I
u = 0.720329 − 0.089531I
a = −0.844602 − 0.270082I
b = 0.691179 + 0.042911I
−1.241080 + 0.011716I −6.07029 + 0.34761I
u = −1.204210 + 0.438433I
a = 0.48976 + 2.42963I
b = −2.48928 + 1.79555I
−8.55039 + 4.15005I 0
u = −1.204210 − 0.438433I
a = 0.48976 − 2.42963I
b = −2.48928 − 1.79555I
−8.55039 − 4.15005I 0
u = 1.211950 + 0.422374I
a = 0.343218 + 0.371608I
b = 0.395207 + 0.227767I
−5.76089 − 1.40580I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.211950 − 0.422374I
a = 0.343218 − 0.371608I
b = 0.395207 − 0.227767I
−5.76089 + 1.40580I 0
u = 1.202140 + 0.472702I
a = −1.03696 − 1.68121I
b = −2.65062 + 0.27479I
−8.30327 − 4.69734I 0
u = 1.202140 − 0.472702I
a = −1.03696 + 1.68121I
b = −2.65062 − 0.27479I
−8.30327 + 4.69734I 0
u = −1.226570 + 0.422161I
a = −0.874333 − 0.195336I
b = 0.272608 − 0.498710I
−9.54621 − 1.87551I 0
u = −1.226570 − 0.422161I
a = −0.874333 + 0.195336I
b = 0.272608 + 0.498710I
−9.54621 + 1.87551I 0
u = −1.216800 + 0.449987I
a = −3.15860 + 0.95930I
b = −2.08390 − 3.33580I
−8.84908 + 3.27349I 0
u = −1.216800 − 0.449987I
a = −3.15860 − 0.95930I
b = −2.08390 + 3.33580I
−8.84908 − 3.27349I 0
u = −1.205800 + 0.487033I
a = 0.145777 − 0.154877I
b = 0.320462 − 0.390176I
−5.29805 + 7.52326I 0
u = −1.205800 − 0.487033I
a = 0.145777 + 0.154877I
b = 0.320462 + 0.390176I
−5.29805 − 7.52326I 0
u = 1.215240 + 0.464812I
a = 2.67705 − 1.24290I
b = −0.72754 − 4.01998I
−8.74284 − 5.75681I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.215240 − 0.464812I
a = 2.67705 + 1.24290I
b = −0.72754 + 4.01998I
−8.74284 + 5.75681I 0
u = 0.509463 + 0.476070I
a = 1.187850 + 0.624464I
b = 0.938899 − 0.329526I
−0.71896 + 2.95853I −2.51194 − 3.48321I
u = 0.509463 − 0.476070I
a = 1.187850 − 0.624464I
b = 0.938899 + 0.329526I
−0.71896 − 2.95853I −2.51194 + 3.48321I
u = 1.230060 + 0.448820I
a = 2.45870 + 0.09273I
b = 0.43578 − 2.81491I
−13.63800 − 2.09364I 0
u = 1.230060 − 0.448820I
a = 2.45870 − 0.09273I
b = 0.43578 + 2.81491I
−13.63800 + 2.09364I 0
u = 1.216000 + 0.489553I
a = 0.397355 + 0.396274I
b = 0.489408 − 0.959846I
−9.0634 − 10.9794I 0
u = 1.216000 − 0.489553I
a = 0.397355 − 0.396274I
b = 0.489408 + 0.959846I
−9.0634 + 10.9794I 0
u = −1.226390 + 0.469297I
a = −2.23969 − 0.06822I
b = −0.28701 − 3.14192I
−13.4906 + 7.1116I 0
u = −1.226390 − 0.469297I
a = −2.23969 + 0.06822I
b = −0.28701 + 3.14192I
−13.4906 − 7.1116I 0
u = −1.258840 + 0.392050I
a = 2.22949 − 0.20545I
b = 1.01592 + 3.37798I
−15.7926 − 8.2946I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.258840 − 0.392050I
a = 2.22949 + 0.20545I
b = 1.01592 − 3.37798I
−15.7926 + 8.2946I 0
u = −1.266160 + 0.381195I
a = 1.63607 − 0.12093I
b = 0.76801 + 2.93133I
−15.2825 + 3.8099I 0
u = −1.266160 − 0.381195I
a = 1.63607 + 0.12093I
b = 0.76801 − 2.93133I
−15.2825 − 3.8099I 0
u = 1.265500 + 0.392209I
a = −2.03627 − 0.02018I
b = −0.83587 + 3.28161I
−11.08980 + 2.49328I 0
u = 1.265500 − 0.392209I
a = −2.03627 + 0.02018I
b = −0.83587 − 3.28161I
−11.08980 − 2.49328I 0
u = −0.292512 + 0.607926I
a = −0.789378 + 0.092871I
b = −0.349256 + 0.518535I
1.06426 − 1.58419I 2.58444 + 3.77537I
u = −0.292512 − 0.607926I
a = −0.789378 − 0.092871I
b = −0.349256 − 0.518535I
1.06426 + 1.58419I 2.58444 − 3.77537I
u = 1.226290 + 0.517984I
a = −2.98532 + 0.98795I
b = −0.07289 + 3.70423I
−14.8832 − 17.6862I 0
u = 1.226290 − 0.517984I
a = −2.98532 − 0.98795I
b = −0.07289 − 3.70423I
−14.8832 + 17.6862I 0
u = −1.230600 + 0.519575I
a = 2.87770 + 0.84381I
b = 0.27887 + 3.44692I
−10.1682 + 11.9615I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.230600 − 0.519575I
a = 2.87770 − 0.84381I
b = 0.27887 − 3.44692I
−10.1682 − 11.9615I 0
u = 1.228630 + 0.527975I
a = −2.60513 + 0.78675I
b = −0.19145 + 2.92791I
−14.2246 − 5.6480I 0
u = 1.228630 − 0.527975I
a = −2.60513 − 0.78675I
b = −0.19145 − 2.92791I
−14.2246 + 5.6480I 0
u = 0.453345 + 0.432137I
a = 0.233685 − 0.550097I
b = 0.375198 + 0.493373I
−0.82753 − 2.22876I −1.82904 + 3.38087I
u = 0.453345 − 0.432137I
a = 0.233685 + 0.550097I
b = 0.375198 − 0.493373I
−0.82753 + 2.22876I −1.82904 − 3.38087I
u = −0.198026 + 0.372100I
a = 0.04825 + 3.22431I
b = −0.742638 + 0.704810I
−4.39769 − 1.30288I −6.82606 + 0.92724I
u = −0.198026 − 0.372100I
a = 0.04825 − 3.22431I
b = −0.742638 − 0.704810I
−4.39769 + 1.30288I −6.82606 − 0.92724I
u = 0.331591
a = −2.22812
b = 0.539631
−1.19004 −8.11080
14
II. I
u
2
= h5u
5
− 3u
4
− 7u
3
+ 8u
2
+ 17b + 11u + 1, 4u
5
− 16u
4
− 26u
3
+
20u
2
+ 17a + 19u − 6, u
6
+ u
5
− u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
10
=
−0.235294u
5
+ 0.941176u
4
+ ··· − 1.11765u + 0.352941
−0.294118u
5
+ 0.176471u
4
+ ··· − 0.647059u − 0.0588235
a
8
=
0.764706u
5
+ 0.941176u
4
+ ··· − 0.117647u + 0.352941
0.705882u
5
+ 0.176471u
4
+ ··· + 0.352941u − 0.0588235
a
11
=
−u
5
+ 2u
3
− u
−u
5
+ u
3
− u
a
5
=
u
−u
3
+ u
a
4
=
1
0
a
12
=
−2u
5
+ 3u
3
− 2u
−u
5
+ u
3
− u
a
9
=
0.294118u
5
+ 0.823529u
4
+ ··· − 0.352941u + 0.0588235
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1033
289
u
5
+
511
289
u
4
+
2269
289
u
3
−
337
289
u
2
−
2548
289
u −
2964
289
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
2
, c
4
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
c
3
u
6
c
5
, c
11
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
7
(u − 1)
6
c
8
17(17u
6
− 28u
5
+ 4u
4
+ 15u
3
− 6u
2
− 2u + 1)
c
9
17(17u
6
− 58u
5
+ 89u
4
− 74u
3
+ 35u
2
− 9u + 1)
c
10
(u + 1)
6
c
12
u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
12
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
2
, c
4
, c
5
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
3
y
6
c
7
, c
10
(y −1)
6
c
8
289(289y
6
− 648y
5
+ 652y
4
− 351y
3
+ 104y
2
− 16y + 1)
c
9
289(289y
6
− 338y
5
+ 527y
4
− 256y
3
+ 71y
2
− 11y + 1)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.002190 + 0.295542I
a = −0.286953 + 1.027550I
b = −0.796035 − 0.285065I
−3.53554 − 0.92430I −14.06145 + 1.00389I
u = 1.002190 − 0.295542I
a = −0.286953 − 1.027550I
b = −0.796035 + 0.285065I
−3.53554 + 0.92430I −14.06145 − 1.00389I
u = −0.428243 + 0.664531I
a = 1.66082 + 0.38372I
b = 0.520699 + 0.006734I
0.245672 − 0.924305I −2.49217 − 3.04801I
u = −0.428243 − 0.664531I
a = 1.66082 − 0.38372I
b = 0.520699 − 0.006734I
0.245672 + 0.924305I −2.49217 + 3.04801I
u = −1.073950 + 0.558752I
a = −0.93269 + 1.16339I
b = −0.548194 + 0.053856I
−1.64493 + 5.69302I −11.73704 + 0.42566I
u = −1.073950 − 0.558752I
a = −0.93269 − 1.16339I
b = −0.548194 − 0.053856I
−1.64493 − 5.69302I −11.73704 − 0.42566I
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
98
+ 54u
97
+ ··· + 15u + 1)
c
2
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
98
+ 2u
97
+ ··· + 5u + 1)
c
3
u
6
(u
98
− u
97
+ ··· + 56576u − 18496)
c
4
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)(u
98
− 2u
97
+ ··· + u + 1)
c
5
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
98
+ 2u
97
+ ··· + 5u + 1)
c
6
(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)(u
98
+ 6u
97
+ ··· − 585u − 117)
c
7
((u − 1)
6
)(u
98
− 7u
97
+ ··· − 1854u − 289)
c
8
289(17u
6
− 28u
5
+ 4u
4
+ 15u
3
− 6u
2
− 2u + 1)
· (17u
98
+ 153u
97
+ ··· − 11440320u − 3023343)
c
9
289(17u
6
− 58u
5
+ 89u
4
− 74u
3
+ 35u
2
− 9u + 1)
· (17u
98
− 17u
97
+ ··· − 16429842u + 5717884)
c
10
((u + 1)
6
)(u
98
− 7u
97
+ ··· − 1854u − 289)
c
11
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)(u
98
− 2u
97
+ ··· + u + 1)
c
12
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)(u
98
+ 6u
97
+ ··· − 585u − 117)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
98
− 18y
97
+ ··· − 63y + 1)
c
2
, c
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
98
− 54y
97
+ ··· − 15y + 1)
c
3
y
6
(y
98
− 39y
97
+ ··· − 8.09089 × 10
9
y + 3.42102 × 10
8
)
c
4
, c
11
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)(y
98
+ 66y
97
+ ··· − 15y + 1)
c
6
, c
12
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)(y
98
+ 90y
97
+ ··· − 361179y + 13689)
c
7
, c
10
((y −1)
6
)(y
98
− 85y
97
+ ··· − 453680y + 83521)
c
8
83521(289y
6
− 648y
5
+ 652y
4
− 351y
3
+ 104y
2
− 16y + 1)
· (289y
98
− 16167y
97
+ ··· + 80567110376298y + 9140602895649)
c
9
83521(289y
6
− 338y
5
+ 527y
4
− 256y
3
+ 71y
2
− 11y + 1)
· (289y
98
− 19669y
97
+ ··· + 565449262390916y + 32694197437456)
20
