12n
0416
(K12n
0416
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 12 3 7 6 4 10 9
Solving Sequence
3,7
8 4
9,12
6 10 2 1 5 11
c
7
c
3
c
8
c
6
c
9
c
2
c
1
c
5
c
11
c
4
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h261u
16
− 101u
15
+ ··· + 817b + 94, 113u
16
+ 166u
15
+ ··· + 817a − 745,
u
17
− 6u
15
+ 15u
13
− u
12
− 15u
11
+ 5u
10
− 5u
9
− 10u
8
+ 24u
7
+ 11u
6
− 18u
5
− 7u
4
+ 4u
3
+ 3u
2
+ u − 1i
I
u
2
= h−1.51873 × 10
37
u
39
− 1.89646 × 10
37
u
38
+ ··· + 1.21750 × 10
38
b − 1.24577 × 10
38
,
2.13718 × 10
37
u
39
+ 1.36142 × 10
37
u
38
+ ··· + 3.65251 × 10
38
a + 1.26689 × 10
39
, u
40
+ u
39
+ ··· − 24u − 9i
I
u
3
= h−u
8
+ 2u
6
− 2u
4
− u
3
+ u
2
+ b + 1, u
8
− u
7
− 3u
6
+ 2u
5
+ 4u
4
− 2u
3
− 4u
2
+ a + u + 1,
u
9
− 3u
7
+ 5u
5
+ u
4
− 5u
3
− u
2
+ 2u + 1i
I
u
4
= hu
6
− 2u
4
− u
3
+ u
2
+ b − 1, −2u
9
+ 2u
8
+ 5u
7
− 4u
6
− 8u
5
+ 7u
4
+ 8u
3
− 5u
2
+ a − 6u + 5,
u
10
− 3u
8
− u
7
+ 4u
6
+ u
5
− 4u
4
− u
3
+ 3u
2
− 1i
* 4 irreducible components of dim
C
= 0, with total 76 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
= h261u
16
− 101u
15
+ · · · + 817b + 94, 113u
16
+ 166u
15
+ · · · + 817a −
745, u
17
− 6u
15
+ · · · + u − 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
12
=
−0.138311u
16
− 0.203182u
15
+ ··· − 0.357405u + 0.911873
−0.319461u
16
+ 0.123623u
15
+ ··· + 0.422277u − 0.115055
a
6
=
−0.00979192u
16
+ 0.206854u
15
+ ··· + 2.23133u + 0.728274
−0.567931u
16
− 0.00244798u
15
+ ··· − 1.58262u + 0.239902
a
10
=
0.297430u
16
+ 0.0917993u
15
+ ··· − 0.151775u + 1.00367
0.138311u
16
+ 0.203182u
15
+ ··· + 0.357405u + 0.0881273
a
2
=
−0.134639u
16
+ 0.0942472u
15
+ ··· + 0.430845u + 0.763770
−0.564259u
16
+ 0.294982u
15
+ ··· + 0.205630u + 0.0917993
a
1
=
−0.134639u
16
+ 0.0942472u
15
+ ··· + 0.430845u + 0.763770
−0.198286u
16
− 0.0611995u
15
+ ··· + 0.434517u − 0.00244798
a
5
=
0.0917993u
16
+ 0.435741u
15
+ ··· + 1.70624u + 0.297430
0.203182u
16
+ 0.457772u
15
+ ··· − 1.05018u + 0.138311
a
11
=
0.297430u
16
+ 0.0917993u
15
+ ··· − 0.151775u + 1.00367
0.138311u
16
+ 0.203182u
15
+ ··· + 0.357405u + 0.0881273
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
33
817
u
16
−
1856
817
u
15
+ ··· −
7084
817
u −
8473
817
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
17
+ 14u
16
+ ··· + 3584u + 1024
c
2
, c
5
u
17
+ 10u
16
+ ··· + 160u + 32
c
3
, c
4
, c
7
c
10
u
17
− 6u
15
+ ··· + u + 1
c
6
u
17
− 6u
16
+ ··· − 12u + 8
c
8
, c
11
u
17
+ 12u
16
+ ··· + 7u + 1
c
9
, c
12
u
17
+ 2u
16
+ ··· + 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
17
− 22y
16
+ ··· − 4587520y −1048576
c
2
, c
5
y
17
− 14y
16
+ ··· + 3584y −1024
c
3
, c
4
, c
7
c
10
y
17
− 12y
16
+ ··· + 7y −1
c
6
y
17
− 6y
16
+ ··· + 720y −64
c
8
, c
11
y
17
− 12y
16
+ ··· + 19y −1
c
9
, c
12
y
17
+ 24y
16
+ ··· + 34y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.872688 + 0.309245I
a = −1.10902 + 0.97065I
b = 1.22842 + 0.81409I
−1.17696 + 5.14107I −6.11359 − 6.50734I
u = −0.872688 − 0.309245I
a = −1.10902 − 0.97065I
b = 1.22842 − 0.81409I
−1.17696 − 5.14107I −6.11359 + 6.50734I
u = 0.112694 + 1.077070I
a = 1.37425 + 0.41818I
b = −0.905176 − 0.807152I
−5.24123 + 3.03176I −5.90001 − 2.22137I
u = 0.112694 − 1.077070I
a = 1.37425 − 0.41818I
b = −0.905176 + 0.807152I
−5.24123 − 3.03176I −5.90001 + 2.22137I
u = 0.770678 + 0.254682I
a = −0.350181 − 0.951046I
b = 1.009160 − 0.082155I
−0.500652 − 0.396435I −8.19182 + 2.68087I
u = 0.770678 − 0.254682I
a = −0.350181 + 0.951046I
b = 1.009160 + 0.082155I
−0.500652 + 0.396435I −8.19182 − 2.68087I
u = −1.220540 + 0.157617I
a = −0.501451 + 0.512731I
b = −0.500714 + 0.816049I
−6.48988 + 1.76820I −13.17903 − 1.70263I
u = −1.220540 − 0.157617I
a = −0.501451 − 0.512731I
b = −0.500714 − 0.816049I
−6.48988 − 1.76820I −13.17903 + 1.70263I
u = 1.251960 + 0.260556I
a = 0.82098 + 1.51753I
b = −1.079480 + 0.641251I
−4.75266 − 7.21790I −11.92961 + 6.92939I
u = 1.251960 − 0.260556I
a = 0.82098 − 1.51753I
b = −1.079480 − 0.641251I
−4.75266 + 7.21790I −11.92961 − 6.92939I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.329090 + 0.472313I
a = −0.038538 + 0.181070I
b = −0.79169 − 1.20549I
−14.4213 − 7.4571I −11.51687 + 4.18112I
u = 1.329090 − 0.472313I
a = −0.038538 − 0.181070I
b = −0.79169 + 1.20549I
−14.4213 + 7.4571I −11.51687 − 4.18112I
u = −0.246489 + 0.489685I
a = 1.73580 − 0.42019I
b = −0.968967 + 0.317789I
1.66217 − 1.14629I 1.43775 + 2.20534I
u = −0.246489 − 0.489685I
a = 1.73580 + 0.42019I
b = −0.968967 − 0.317789I
1.66217 + 1.14629I 1.43775 − 2.20534I
u = −1.35873 + 0.57627I
a = 1.29756 − 0.84527I
b = −1.17071 − 0.90048I
−13.0830 + 14.9833I −9.98102 − 7.51290I
u = −1.35873 − 0.57627I
a = 1.29756 + 0.84527I
b = −1.17071 + 0.90048I
−13.0830 − 14.9833I −9.98102 + 7.51290I
u = 0.468027
a = 0.541197
b = 0.358302
−0.819496 −12.2520
6
II.
I
u
2
= h−1.52×10
37
u
39
−1.90×10
37
u
38
+· · ·+1.22×10
38
b−1.25×10
38
, 2.14×
10
37
u
39
+1.36×10
37
u
38
+· · ·+3.65×10
38
a+1.27×10
39
, u
40
+u
39
+· · ·−24u−9i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
12
=
−0.0585128u
39
− 0.0372737u
38
+ ··· + 1.70400u − 3.46855
0.124742u
39
+ 0.155767u
38
+ ··· + 2.43424u + 1.02322
a
6
=
−0.201855u
39
+ 0.202202u
38
+ ··· + 6.51731u + 1.59348
0.147685u
39
+ 0.0264282u
38
+ ··· + 2.61080u + 0.354275
a
10
=
0.0813577u
39
− 0.202188u
38
+ ··· + 7.28317u + 1.97309
0.0286342u
39
+ 0.0928329u
38
+ ··· − 3.22599u + 0.539866
a
2
=
−0.200240u
39
− 0.0544321u
38
+ ··· + 5.36707u − 1.24072
0.118463u
39
+ 0.127401u
38
+ ··· + 1.05224u + 0.660498
a
1
=
−0.200240u
39
− 0.0544321u
38
+ ··· + 5.36707u − 1.24072
0.420625u
39
+ 0.140972u
38
+ ··· − 0.644987u − 0.651772
a
5
=
0.835765u
39
+ 0.0374218u
38
+ ··· − 22.3043u − 11.6309
0.114623u
39
+ 0.0818378u
38
+ ··· + 5.71886u − 0.0603670
a
11
=
0.175078u
39
− 0.284313u
38
+ ··· + 4.95360u + 0.359674
−0.0140809u
39
+ 0.0620252u
38
+ ··· − 4.27325u + 0.570666
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.893186u
39
+ 0.382084u
38
+ ··· − 32.1739u − 19.4647
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
20
+ 30u
19
+ ··· + 881u + 25)
2
c
2
, c
5
(u
20
− 4u
19
+ ··· − 9u − 5)
2
c
3
, c
4
, c
7
c
10
u
40
− u
39
+ ··· + 24u − 9
c
6
(u
20
+ 2u
19
+ ··· + 2u − 1)
2
c
8
, c
11
u
40
+ 27u
39
+ ··· − 702u + 81
c
9
, c
12
u
40
+ 8u
39
+ ··· − 241750u − 136681
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
20
− 82y
19
+ ··· − 403661y + 625)
2
c
2
, c
5
(y
20
− 30y
19
+ ··· − 881y + 25)
2
c
3
, c
4
, c
7
c
10
y
40
− 27y
39
+ ··· + 702y + 81
c
6
(y
20
− 6y
19
+ ··· − 26y + 1)
2
c
8
, c
11
y
40
− 19y
39
+ ··· − 578178y + 6561
c
9
, c
12
y
40
− 2y
39
+ ··· + 22299598078y + 18681695761
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.985793 + 0.106099I
a = 1.47285 + 0.70515I
b = −1.313450 + 0.406280I
−0.81957 − 1.24696I −7.62468 + 0.13280I
u = 0.985793 − 0.106099I
a = 1.47285 − 0.70515I
b = −1.313450 − 0.406280I
−0.81957 + 1.24696I −7.62468 − 0.13280I
u = −0.061557 + 0.981252I
a = −1.42687 + 0.39525I
b = 0.740083 − 0.981052I
−10.10780 + 2.32175I −8.97701 − 0.73874I
u = −0.061557 − 0.981252I
a = −1.42687 − 0.39525I
b = 0.740083 + 0.981052I
−10.10780 − 2.32175I −8.97701 + 0.73874I
u = 0.836619 + 0.625265I
a = −1.68057 + 0.31357I
b = 0.745821 − 0.208249I
1.03980 − 5.20042I −4.45133 + 5.57600I
u = 0.836619 − 0.625265I
a = −1.68057 − 0.31357I
b = 0.745821 + 0.208249I
1.03980 + 5.20042I −4.45133 − 5.57600I
u = 1.092520 + 0.041392I
a = 0.114066 − 0.561701I
b = 0.687385 − 0.749134I
−1.84004 − 0.63402I −8.04331 − 0.15211I
u = 1.092520 − 0.041392I
a = 0.114066 + 0.561701I
b = 0.687385 + 0.749134I
−1.84004 + 0.63402I −8.04331 + 0.15211I
u = −0.671937 + 0.604612I
a = 0.525601 − 0.779399I
b = −1.313450 + 0.406280I
−0.81957 − 1.24696I −7.62468 + 0.13280I
u = −0.671937 − 0.604612I
a = 0.525601 + 0.779399I
b = −1.313450 − 0.406280I
−0.81957 + 1.24696I −7.62468 − 0.13280I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.10100
a = −3.54571
b = 0.847094
−8.45151 −8.71120
u = 0.850304 + 0.713148I
a = 1.013260 + 0.848398I
b = −0.493869
1.03533 −6.45138 + 0.I
u = 0.850304 − 0.713148I
a = 1.013260 − 0.848398I
b = −0.493869
1.03533 −6.45138 + 0.I
u = −0.562871 + 0.677759I
a = 1.350220 + 0.203953I
b = −0.846857
2.60911 − 60.518982 + 0.10I
u = −0.562871 − 0.677759I
a = 1.350220 − 0.203953I
b = −0.846857
2.60911 − 60.518982 + 0.10I
u = −0.069227 + 1.125560I
a = −1.36033 + 0.39893I
b = 1.077500 − 0.827760I
−9.04644 − 8.94980I −7.77982 + 5.10458I
u = −0.069227 − 1.125560I
a = −1.36033 − 0.39893I
b = 1.077500 + 0.827760I
−9.04644 + 8.94980I −7.77982 − 5.10458I
u = −1.093460 + 0.370616I
a = −0.98200 + 1.09858I
b = 1.011700 + 0.632363I
−0.78834 + 4.67433I −5.30649 − 6.82521I
u = −1.093460 − 0.370616I
a = −0.98200 − 1.09858I
b = 1.011700 − 0.632363I
−0.78834 − 4.67433I −5.30649 + 6.82521I
u = −1.157600 + 0.120447I
a = −0.042441 − 0.362661I
b = −0.656124 − 1.053570I
−3.80624 + 5.08920I −12.34652 − 4.90346I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.157600 − 0.120447I
a = −0.042441 + 0.362661I
b = −0.656124 + 1.053570I
−3.80624 − 5.08920I −12.34652 + 4.90346I
u = 1.043330 + 0.515865I
a = 0.976781 + 0.822046I
b = −0.656124 + 1.053570I
−3.80624 − 5.08920I −12.34652 + 4.90346I
u = 1.043330 − 0.515865I
a = 0.976781 − 0.822046I
b = −0.656124 − 1.053570I
−3.80624 + 5.08920I −12.34652 − 4.90346I
u = −0.746386
a = −4.63725
b = −0.254182
−7.16640 −21.4380
u = −1.096590 + 0.652317I
a = −0.831505 + 0.847751I
b = 0.745821 + 0.208249I
1.03980 + 5.20042I −4.45133 − 5.57600I
u = −1.096590 − 0.652317I
a = −0.831505 − 0.847751I
b = 0.745821 − 0.208249I
1.03980 − 5.20042I −4.45133 + 5.57600I
u = 0.331219 + 0.637366I
a = −0.382754 − 0.453408I
b = 0.687385 + 0.749134I
−1.84004 + 0.63402I −8.04331 + 0.15211I
u = 0.331219 − 0.637366I
a = −0.382754 + 0.453408I
b = 0.687385 − 0.749134I
−1.84004 − 0.63402I −8.04331 − 0.15211I
u = −1.300800 + 0.543331I
a = 1.58939 − 0.86240I
b = −0.919010 − 0.840072I
−13.8803 + 3.1384I −10.93015 + 0.I
u = −1.300800 − 0.543331I
a = 1.58939 + 0.86240I
b = −0.919010 + 0.840072I
−13.8803 − 3.1384I −10.93015 + 0.I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33349 + 0.57768I
a = −1.40702 − 0.79123I
b = 1.077500 − 0.827760I
−9.04644 − 8.94980I 0
u = 1.33349 − 0.57768I
a = −1.40702 + 0.79123I
b = 1.077500 + 0.827760I
−9.04644 + 8.94980I 0
u = −1.39353 + 0.44049I
a = −0.061607 + 0.191617I
b = 0.740083 − 0.981052I
−10.10780 + 2.32175I 0
u = −1.39353 − 0.44049I
a = −0.061607 − 0.191617I
b = 0.740083 + 0.981052I
−10.10780 − 2.32175I 0
u = −1.47294
a = −0.409227
b = −0.254182
−7.16640 −21.4380
u = 1.47987
a = 0.579170
b = 0.847094
−8.45151 −8.71120
u = 1.44287 + 0.49042I
a = 0.097964 + 0.290556I
b = −0.919010 − 0.840072I
−13.8803 + 3.1384I 0
u = 1.44287 − 0.49042I
a = 0.097964 − 0.290556I
b = −0.919010 + 0.840072I
−13.8803 − 3.1384I 0
u = −0.088339 + 0.296040I
a = −3.29187 + 1.03172I
b = 1.011700 + 0.632363I
−0.78834 + 4.67433I −5.30649 − 6.82521I
u = −0.088339 − 0.296040I
a = −3.29187 − 1.03172I
b = 1.011700 − 0.632363I
−0.78834 − 4.67433I −5.30649 + 6.82521I
13
III. I
u
3
= h−u
8
+ 2u
6
− 2u
4
− u
3
+ u
2
+ b + 1, u
8
− u
7
+ · · · + a + 1, u
9
−
3u
7
+ 5u
5
+ u
4
− 5u
3
− u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
12
=
−u
8
+ u
7
+ 3u
6
− 2u
5
− 4u
4
+ 2u
3
+ 4u
2
− u − 1
u
8
− 2u
6
+ 2u
4
+ u
3
− u
2
− 1
a
6
=
u
8
− 3u
6
+ 5u
4
− 5u
2
+ 2
−u
8
+ 2u
6
− u
5
− 3u
4
+ u
3
+ 2u
2
− 2u
a
10
=
u
6
− u
5
− 2u
4
+ u
3
+ 2u
2
− u − 1
u
8
− u
7
− 3u
6
+ 2u
5
+ 4u
4
− 2u
3
− 3u
2
+ u
a
2
=
−u
8
+ u
7
+ 3u
6
− 2u
5
− 5u
4
+ 2u
3
+ 5u
2
− u − 2
u
8
− 2u
6
+ 2u
4
+ u
3
− u
2
+ u − 1
a
1
=
−u
8
+ u
7
+ 3u
6
− 2u
5
− 5u
4
+ 2u
3
+ 5u
2
− u − 2
u
8
− u
7
− 2u
6
+ 2u
5
+ 3u
4
− 2u
3
− 2u
2
+ 2u
a
5
=
u
7
− u
6
− 2u
5
+ u
4
+ 3u
3
− u
2
− 2u
−u
8
+ 2u
6
− 3u
4
+ 2u
2
− u − 1
a
11
=
u
6
− u
5
− 2u
4
+ u
3
+ 3u
2
− u − 1
u
8
− u
7
− 3u
6
+ 2u
5
+ 5u
4
− 2u
3
− 4u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
8
+ 6u
7
− 3u
6
− 10u
5
+ 4u
4
+ 15u
3
+ 3u
2
− 11u − 7
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 9u
8
+ 28u
7
− 51u
6
+ 59u
5
− 48u
4
+ 29u
3
− 14u
2
+ 5u − 1
c
2
u
9
− u
8
− 4u
7
+ u
6
+ 5u
5
− 2u
4
− 3u
3
+ 2u
2
+ u − 1
c
3
, c
10
u
9
− 3u
7
+ 5u
5
− u
4
− 5u
3
+ u
2
+ 2u − 1
c
4
, c
7
u
9
− 3u
7
+ 5u
5
+ u
4
− 5u
3
− u
2
+ 2u + 1
c
5
u
9
+ u
8
− 4u
7
− u
6
+ 5u
5
+ 2u
4
− 3u
3
− 2u
2
+ u + 1
c
6
u
9
+ u
8
− 2u
7
− 3u
6
+ 2u
5
+ 5u
4
− u
3
− 4u
2
+ u + 1
c
8
, c
11
u
9
+ 6u
8
+ 19u
7
+ 40u
6
+ 59u
5
+ 63u
4
+ 47u
3
+ 23u
2
+ 6u + 1
c
9
, c
12
u
9
+ 4u
8
+ 3u
7
− u
6
− 6u
5
− 3u
4
− u
3
+ 2u
2
+ u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− 25y
8
− 16y
7
− 103y
6
− 33y
5
− 48y
4
− 15y
3
− 2y
2
− 3y −1
c
2
, c
5
y
9
− 9y
8
+ 28y
7
− 51y
6
+ 59y
5
− 48y
4
+ 29y
3
− 14y
2
+ 5y −1
c
3
, c
4
, c
7
c
10
y
9
− 6y
8
+ 19y
7
− 40y
6
+ 59y
5
− 63y
4
+ 47y
3
− 23y
2
+ 6y −1
c
6
y
9
− 5y
8
+ 14y
7
− 29y
6
+ 48y
5
− 59y
4
+ 51y
3
− 28y
2
+ 9y −1
c
8
, c
11
y
9
+ 2y
8
− y
7
− 20y
6
− 37y
5
− 47y
4
− 61y
3
− 91y
2
− 10y −1
c
9
, c
12
y
9
− 10y
8
+ 5y
7
− 15y
6
+ 10y
5
+ 5y
4
+ 3y
3
− 3y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.022180 + 0.325067I
a = 0.587091 + 1.128900I
b = −0.846738 + 0.986047I
−2.29340 − 6.07855I −8.47383 + 8.86704I
u = 1.022180 − 0.325067I
a = 0.587091 − 1.128900I
b = −0.846738 − 0.986047I
−2.29340 + 6.07855I −8.47383 − 8.86704I
u = −0.915990 + 0.694675I
a = −1.58210 + 0.48658I
b = 0.993839 + 0.427672I
1.17777 + 6.95533I −4.27023 − 9.54243I
u = −0.915990 − 0.694675I
a = −1.58210 − 0.48658I
b = 0.993839 − 0.427672I
1.17777 − 6.95533I −4.27023 + 9.54243I
u = 1.047510 + 0.647735I
a = −0.881374 − 0.604152I
b = 0.781614 + 0.355685I
0.33154 − 3.66672I −8.46619 + 1.40357I
u = 1.047510 − 0.647735I
a = −0.881374 + 0.604152I
b = 0.781614 − 0.355685I
0.33154 + 3.66672I −8.46619 − 1.40357I
u = −1.31380
a = −1.61123
b = −0.443802
−9.54268 −17.4150
u = −0.496798 + 0.288456I
a = 0.182003 − 0.761275I
b = −1.206810 + 0.297957I
0.620620 − 0.259550I −1.58232 − 1.92541I
u = −0.496798 − 0.288456I
a = 0.182003 + 0.761275I
b = −1.206810 − 0.297957I
0.620620 + 0.259550I −1.58232 + 1.92541I
17
IV. I
u
4
= hu
6
− 2u
4
− u
3
+ u
2
+ b − 1, −2u
9
+ 2u
8
+ · · · + a + 5, u
10
− 3u
8
−
u
7
+ 4u
6
+ u
5
− 4u
4
− u
3
+ 3u
2
− 1i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
4
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
12
=
2u
9
− 2u
8
− 5u
7
+ 4u
6
+ 8u
5
− 7u
4
− 8u
3
+ 5u
2
+ 6u − 5
−u
6
+ 2u
4
+ u
3
− u
2
+ 1
a
6
=
2u
9
− 5u
7
− 2u
6
+ 5u
5
+ u
4
− 4u
3
− u
2
+ 3u − 1
−u
9
− u
8
+ 2u
7
+ 3u
6
− 2u
4
+ u
3
+ 2u
2
a
10
=
−2u
9
+ u
8
+ 5u
7
− 6u
5
+ u
4
+ 5u
3
− 2u
2
− 4u + 3
u
9
+ u
8
− 2u
7
− 4u
6
+ u
5
+ 3u
4
− u
3
− 2u
2
+ u + 1
a
2
=
2u
9
− u
8
− 5u
7
+ u
6
+ 7u
5
− 3u
4
− 7u
3
+ 2u
2
+ 5u − 3
−u
6
+ 2u
4
+ u
3
− u
2
+ u + 1
a
1
=
2u
9
− u
8
− 5u
7
+ u
6
+ 7u
5
− 3u
4
− 7u
3
+ 2u
2
+ 5u − 3
−u
9
+ 2u
7
− 2u
5
+ 2u
4
+ 3u
3
− u
2
− u + 2
a
5
=
−2u
9
+ 2u
8
+ 5u
7
− 3u
6
− 8u
5
+ 4u
4
+ 7u
3
− 3u
2
− 5u + 4
−2u
9
− u
8
+ 5u
7
+ 4u
6
− 4u
5
− 3u
4
+ 4u
3
+ 3u
2
− 2u − 1
a
11
=
−2u
9
+ u
8
+ 5u
7
− 6u
5
+ u
4
+ 5u
3
− 2u
2
− 4u + 2
u
9
+ u
8
− 2u
7
− 4u
6
+ u
5
+ 3u
4
− u
3
− 3u
2
+ u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
9
+ 4u
8
+ 15u
7
− 2u
6
− 24u
5
+ u
4
+ 19u
3
− 2u
2
− 14u − 1
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
5
− 5u
4
+ 8u
3
− 7u
2
+ 3u − 1)
2
c
2
(u
5
+ u
4
− 2u
3
− u
2
+ u + 1)
2
c
3
, c
10
u
10
− 3u
8
+ u
7
+ 4u
6
− u
5
− 4u
4
+ u
3
+ 3u
2
− 1
c
4
, c
7
u
10
− 3u
8
− u
7
+ 4u
6
+ u
5
− 4u
4
− u
3
+ 3u
2
− 1
c
5
(u
5
− u
4
− 2u
3
+ u
2
+ u − 1)
2
c
6
(u
5
− u
4
− u
3
+ 2u
2
+ u − 1)
2
c
8
, c
11
u
10
+ 6u
9
+ ··· + 6u + 1
c
9
, c
12
u
10
+ u
9
− 6u
8
+ 4u
7
+ 5u
6
− 11u
5
+ 5u
4
+ 4u
3
− 7u
2
+ 4u − 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 9y
4
− 11y
2
− 5y − 1)
2
c
2
, c
5
(y
5
− 5y
4
+ 8y
3
− 7y
2
+ 3y − 1)
2
c
3
, c
4
, c
7
c
10
y
10
− 6y
9
+ ··· − 6y + 1
c
6
(y
5
− 3y
4
+ 7y
3
− 8y
2
+ 5y − 1)
2
c
8
, c
11
y
10
− 2y
9
+ ··· − 2y + 1
c
9
, c
12
y
10
− 13y
9
+ 38y
8
− 44y
7
+ 31y
6
− 29y
5
+ 23y
4
− 8y
3
+ 7y
2
− 2y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.650832 + 0.640961I
a = 2.13970 + 0.29477I
b = −0.904429 + 0.339760I
1.57933 − 1.42206I −3.99937 + 3.89082I
u = 0.650832 − 0.640961I
a = 2.13970 − 0.29477I
b = −0.904429 − 0.339760I
1.57933 + 1.42206I −3.99937 − 3.89082I
u = −0.779988 + 0.768157I
a = 0.896252 − 0.611916I
b = −0.904429 + 0.339760I
1.57933 − 1.42206I −3.99937 + 3.89082I
u = −0.779988 − 0.768157I
a = 0.896252 + 0.611916I
b = −0.904429 − 0.339760I
1.57933 + 1.42206I −3.99937 − 3.89082I
u = 0.799959 + 0.294870I
a = −0.603978 − 0.208555I
b = 1.116850 + 0.784420I
−1.44657 + 3.45949I −8.68875 − 2.10393I
u = 0.799959 − 0.294870I
a = −0.603978 + 0.208555I
b = 1.116850 − 0.784420I
−1.44657 − 3.45949I −8.68875 + 2.10393I
u = −1.100530 + 0.405664I
a = −0.894237 + 0.771397I
b = 1.116850 + 0.784420I
−1.44657 + 3.45949I −8.68875 − 2.10393I
u = −1.100530 − 0.405664I
a = −0.894237 − 0.771397I
b = 1.116850 − 0.784420I
−1.44657 − 3.45949I −8.68875 + 2.10393I
u = −0.658694
a = −6.32803
b = 0.575152
−6.84525 4.37620
u = 1.51815
a = 0.252548
b = 0.575152
−6.84525 4.37620
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− 5u
4
+ 8u
3
− 7u
2
+ 3u − 1)
2
· (u
9
− 9u
8
+ 28u
7
− 51u
6
+ 59u
5
− 48u
4
+ 29u
3
− 14u
2
+ 5u − 1)
· (u
17
+ 14u
16
+ ··· + 3584u + 1024)(u
20
+ 30u
19
+ ··· + 881u + 25)
2
c
2
(u
5
+ u
4
− 2u
3
− u
2
+ u + 1)
2
· (u
9
− u
8
− 4u
7
+ u
6
+ 5u
5
− 2u
4
− 3u
3
+ 2u
2
+ u − 1)
· (u
17
+ 10u
16
+ ··· + 160u + 32)(u
20
− 4u
19
+ ··· − 9u − 5)
2
c
3
, c
10
(u
9
− 3u
7
+ 5u
5
− u
4
− 5u
3
+ u
2
+ 2u − 1)
· (u
10
− 3u
8
+ ··· + 3u
2
− 1)(u
17
− 6u
15
+ ··· + u + 1)
· (u
40
− u
39
+ ··· + 24u − 9)
c
4
, c
7
(u
9
− 3u
7
+ 5u
5
+ u
4
− 5u
3
− u
2
+ 2u + 1)
· (u
10
− 3u
8
+ ··· + 3u
2
− 1)(u
17
− 6u
15
+ ··· + u + 1)
· (u
40
− u
39
+ ··· + 24u − 9)
c
5
(u
5
− u
4
− 2u
3
+ u
2
+ u − 1)
2
· (u
9
+ u
8
− 4u
7
− u
6
+ 5u
5
+ 2u
4
− 3u
3
− 2u
2
+ u + 1)
· (u
17
+ 10u
16
+ ··· + 160u + 32)(u
20
− 4u
19
+ ··· − 9u − 5)
2
c
6
(u
5
− u
4
− u
3
+ 2u
2
+ u − 1)
2
· (u
9
+ u
8
− 2u
7
− 3u
6
+ 2u
5
+ 5u
4
− u
3
− 4u
2
+ u + 1)
· (u
17
− 6u
16
+ ··· − 12u + 8)(u
20
+ 2u
19
+ ··· + 2u − 1)
2
c
8
, c
11
(u
9
+ 6u
8
+ 19u
7
+ 40u
6
+ 59u
5
+ 63u
4
+ 47u
3
+ 23u
2
+ 6u + 1)
· (u
10
+ 6u
9
+ ··· + 6u + 1)(u
17
+ 12u
16
+ ··· + 7u + 1)
· (u
40
+ 27u
39
+ ··· − 702u + 81)
c
9
, c
12
(u
9
+ 4u
8
+ 3u
7
− u
6
− 6u
5
− 3u
4
− u
3
+ 2u
2
+ u + 1)
· (u
10
+ u
9
− 6u
8
+ 4u
7
+ 5u
6
− 11u
5
+ 5u
4
+ 4u
3
− 7u
2
+ 4u − 1)
· (u
17
+ 2u
16
+ ··· + 12u + 1)(u
40
+ 8u
39
+ ··· − 241750u − 136681)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
5
− 9y
4
− 11y
2
− 5y − 1)
2
· (y
9
− 25y
8
− 16y
7
− 103y
6
− 33y
5
− 48y
4
− 15y
3
− 2y
2
− 3y − 1)
· (y
17
− 22y
16
+ ··· − 4587520y − 1048576)
· (y
20
− 82y
19
+ ··· − 403661y + 625)
2
c
2
, c
5
(y
5
− 5y
4
+ 8y
3
− 7y
2
+ 3y − 1)
2
· (y
9
− 9y
8
+ 28y
7
− 51y
6
+ 59y
5
− 48y
4
+ 29y
3
− 14y
2
+ 5y − 1)
· (y
17
− 14y
16
+ ··· + 3584y − 1024)(y
20
− 30y
19
+ ··· − 881y + 25)
2
c
3
, c
4
, c
7
c
10
(y
9
− 6y
8
+ 19y
7
− 40y
6
+ 59y
5
− 63y
4
+ 47y
3
− 23y
2
+ 6y − 1)
· (y
10
− 6y
9
+ ··· − 6y + 1)(y
17
− 12y
16
+ ··· + 7y − 1)
· (y
40
− 27y
39
+ ··· + 702y + 81)
c
6
(y
5
− 3y
4
+ 7y
3
− 8y
2
+ 5y − 1)
2
· (y
9
− 5y
8
+ 14y
7
− 29y
6
+ 48y
5
− 59y
4
+ 51y
3
− 28y
2
+ 9y − 1)
· (y
17
− 6y
16
+ ··· + 720y − 64)(y
20
− 6y
19
+ ··· − 26y + 1)
2
c
8
, c
11
(y
9
+ 2y
8
− y
7
− 20y
6
− 37y
5
− 47y
4
− 61y
3
− 91y
2
− 10y − 1)
· (y
10
− 2y
9
+ ··· − 2y + 1)(y
17
− 12y
16
+ ··· + 19y − 1)
· (y
40
− 19y
39
+ ··· − 578178y + 6561)
c
9
, c
12
(y
9
− 10y
8
+ 5y
7
− 15y
6
+ 10y
5
+ 5y
4
+ 3y
3
− 3y − 1)
· (y
10
− 13y
9
+ 38y
8
− 44y
7
+ 31y
6
− 29y
5
+ 23y
4
− 8y
3
+ 7y
2
− 2y + 1)
· (y
17
+ 24y
16
+ ··· + 34y − 1)
· (y
40
− 2y
39
+ ··· + 22299598078y + 18681695761)
23
