12n
0527
(K12n
0527
)
A knot diagram
1
Linearized knot diagam
3 6 10 1 8 2 10 12 6 1 9 5
Solving Sequence
2,6 3,10
4 7 8 1 11 5 9 12
c
2
c
3
c
6
c
7
c
1
c
10
c
5
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h378975u
30
+ 3018590u
29
+ ··· + 228821b − 6857553,
12363803u
30
+ 93404174u
29
+ ··· + 2288210a − 220745786, u
31
+ 8u
30
+ ··· − 62u − 10i
I
u
2
= h3u
18
− 6u
17
+ ··· + 2b + 2, −2u
18
a + 10u
18
+ ··· − 3a + 21, u
19
− 3u
18
+ ··· + 6u − 1i
I
u
3
= hu
14
− 4u
13
+ 12u
12
− 24u
11
+ 40u
10
− 52u
9
+ 57u
8
− 49u
7
+ 34u
6
− 18u
5
+ 6u
4
− 2u
3
+ b − u − 1,
u
14
− 3u
13
+ 7u
12
− 8u
11
+ 4u
10
+ 12u
9
− 34u
8
+ 58u
7
− 68u
6
+ 62u
5
− 44u
4
+ 24u
3
− 11u
2
+ 2a + 5u − 4,
u
15
− 5u
14
+ ··· + 4u − 2i
I
u
4
= ha
3
u − a
3
+ a
2
u − a
2
+ 3au + 3b + u − 1, a
4
− 3a
2
u − a
2
+ 2au + 2a − 2u − 2, u
2
+ u + 1i
* 4 irreducible components of dim
C
= 0, with total 92 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
= h3.79 × 10
5
u
30
+ 3 .02 × 10
6
u
29
+ · · · + 2.29 × 10
5
b − 6.86 × 10
6
, 1.24 ×
10
7
u
30
+9.34×10
7
u
29
+· · ·+2.29×10
6
a−2.21×10
8
, u
31
+8u
30
+· · ·−62u−10i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
−5.40326u
30
− 40.8198u
29
+ ··· + 422.621u + 96.4709
−1.65621u
30
− 13.1919u
29
+ ··· + 143.370u + 29.9691
a
4
=
−7.59786u
30
− 57.1445u
29
+ ··· + 582.083u + 133.417
−2.53663u
30
− 19.5572u
29
+ ··· + 189.049u + 39.5947
a
7
=
u
u
a
8
=
−5.06123u
30
− 37.5873u
29
+ ··· + 394.034u + 92.8223
−1.48595u
30
− 10.9890u
29
+ ··· + 92.6272u + 21.5867
a
1
=
u
2
+ 1
−u
4
a
11
=
−2.01783u
30
− 15.2733u
29
+ ··· + 183.285u + 43.3542
−0.349286u
30
− 3.00908u
29
+ ··· + 131.287u + 29.6924
a
5
=
−4.17727u
30
− 31.3609u
29
+ ··· + 302.304u + 68.6386
−2.36578u
30
− 18.6263u
29
+ ··· + 194.064u + 41.2391
a
9
=
−5.40326u
30
− 40.8198u
29
+ ··· + 422.621u + 96.4709
−0.906058u
30
− 7.88315u
29
+ ··· + 48.2085u + 5.90550
a
12
=
2.85487u
30
+ 20.6866u
29
+ ··· − 172.102u − 39.1897
−0.816394u
30
− 6.48291u
29
+ ··· + 188.974u + 41.4018
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1324375
228821
u
30
−
9572041
228821
u
29
+ ··· +
117530906
228821
u +
30556088
228821
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 20u
30
+ ··· + 684u − 100
c
2
, c
6
u
31
− 8u
30
+ ··· − 62u + 10
c
3
, c
9
u
31
+ u
30
+ ··· + u + 1
c
4
, c
5
, c
12
u
31
− u
30
+ ··· + 4u + 1
c
7
, c
10
u
31
− 3u
30
+ ··· + 5u + 1
c
8
, c
11
u
31
− 11u
30
+ ··· − 122u + 10
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 12y
30
+ ··· + 1252656y −10000
c
2
, c
6
y
31
+ 20y
30
+ ··· + 684y −100
c
3
, c
9
y
31
− 29y
30
+ ··· + 23y −1
c
4
, c
5
, c
12
y
31
+ 25y
30
+ ··· − 6y −1
c
7
, c
10
y
31
− 29y
30
+ ··· − 105y −1
c
8
, c
11
y
31
+ 11y
30
+ ··· − 756y −100
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.443501 + 0.881894I
a = −1.036980 − 0.315517I
b = −1.093880 − 0.219923I
1.62568 − 2.07908I −8.15071 + 3.76851I
u = −0.443501 − 0.881894I
a = −1.036980 + 0.315517I
b = −1.093880 + 0.219923I
1.62568 + 2.07908I −8.15071 − 3.76851I
u = −0.123465 + 0.920678I
a = −0.63652 + 1.53942I
b = 0.45891 + 1.91281I
2.16097 − 0.39271I −5.96156 − 1.22021I
u = −0.123465 − 0.920678I
a = −0.63652 − 1.53942I
b = 0.45891 − 1.91281I
2.16097 + 0.39271I −5.96156 + 1.22021I
u = 0.068946 + 1.101890I
a = 0.291434 − 0.967985I
b = −0.88132 − 1.46936I
0.870446 + 0.149756I −6.74421 + 0.11134I
u = 0.068946 − 1.101890I
a = 0.291434 + 0.967985I
b = −0.88132 + 1.46936I
0.870446 − 0.149756I −6.74421 − 0.11134I
u = −1.104440 + 0.109617I
a = −1.138250 − 0.420860I
b = 0.173388 − 0.107344I
−4.10069 − 3.26217I −7.80399 + 3.14222I
u = −1.104440 − 0.109617I
a = −1.138250 + 0.420860I
b = 0.173388 + 0.107344I
−4.10069 + 3.26217I −7.80399 − 3.14222I
u = −1.120450 + 0.048451I
a = 1.313720 − 0.318482I
b = −0.155061 + 0.121217I
−1.92223 + 10.09630I −6.60164 − 5.79982I
u = −1.120450 − 0.048451I
a = 1.313720 + 0.318482I
b = −0.155061 − 0.121217I
−1.92223 − 10.09630I −6.60164 + 5.79982I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805043 + 0.864131I
a = 0.256473 + 0.055333I
b = −0.056375 − 0.617551I
6.77889 + 0.72800I 1.42894 − 3.61029I
u = 0.805043 − 0.864131I
a = 0.256473 − 0.055333I
b = −0.056375 + 0.617551I
6.77889 − 0.72800I 1.42894 + 3.61029I
u = 0.106357 + 1.194790I
a = −0.585604 + 0.611175I
b = 0.11850 + 1.64905I
−4.49263 + 1.56261I −18.4490 − 2.4112I
u = 0.106357 − 1.194790I
a = −0.585604 − 0.611175I
b = 0.11850 − 1.64905I
−4.49263 − 1.56261I −18.4490 + 2.4112I
u = −0.255201 + 0.720413I
a = 0.353004 − 0.498369I
b = 0.074523 − 0.477887I
−0.379147 − 1.186170I −4.44708 + 5.86244I
u = −0.255201 − 0.720413I
a = 0.353004 + 0.498369I
b = 0.074523 + 0.477887I
−0.379147 + 1.186170I −4.44708 − 5.86244I
u = −0.287076 + 1.208000I
a = 0.591625 − 1.023160I
b = 0.45808 − 2.00681I
−0.11428 − 4.16519I −8.00000 + 3.45619I
u = −0.287076 − 1.208000I
a = 0.591625 + 1.023160I
b = 0.45808 + 2.00681I
−0.11428 + 4.16519I −8.00000 − 3.45619I
u = 0.839144 + 0.959645I
a = −0.126368 + 0.182032I
b = 0.546509 + 0.211498I
6.52389 + 5.44822I −3.50283 + 0.I
u = 0.839144 − 0.959645I
a = −0.126368 − 0.182032I
b = 0.546509 − 0.211498I
6.52389 − 5.44822I −3.50283 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.55841 + 1.36375I
a = −0.031464 − 1.250450I
b = 0.13295 − 2.63897I
−6.0602 − 16.0464I 0
u = −0.55841 − 1.36375I
a = −0.031464 + 1.250450I
b = 0.13295 + 2.63897I
−6.0602 + 16.0464I 0
u = −0.523642 + 0.015251I
a = 1.36675 + 1.50756I
b = 0.340155 + 0.377383I
3.48762 − 1.00607I −1.97801 + 2.70347I
u = −0.523642 − 0.015251I
a = 1.36675 − 1.50756I
b = 0.340155 − 0.377383I
3.48762 + 1.00607I −1.97801 − 2.70347I
u = −0.47698 + 1.40113I
a = −0.090020 + 1.114860I
b = −0.12726 + 2.47258I
−8.91065 − 8.81717I 0
u = −0.47698 − 1.40113I
a = −0.090020 − 1.114860I
b = −0.12726 − 2.47258I
−8.91065 + 8.81717I 0
u = −0.59892 + 1.37175I
a = 0.349486 + 0.852345I
b = 0.51025 + 1.90344I
−8.00712 − 2.87739I 0
u = −0.59892 − 1.37175I
a = 0.349486 − 0.852345I
b = 0.51025 − 1.90344I
−8.00712 + 2.87739I 0
u = −0.48869 + 1.42613I
a = −0.291444 − 0.902646I
b = −0.69470 − 2.05198I
−6.65609 + 4.30866I 0
u = −0.48869 − 1.42613I
a = −0.291444 + 0.902646I
b = −0.69470 + 2.05198I
−6.65609 − 4.30866I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.322569
a = 1.42830
b = −0.609341
−1.08738 −6.65470
8
II. I
u
2
=
h3u
18
−6u
17
+· · ·+2b+2, −2u
18
a+10u
18
+· · ·−3a+21, u
19
−3u
18
+· · ·+6u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
a
−
3
2
u
18
+ 3u
17
+ ··· +
9
2
u − 1
a
4
=
−
3
2
u
18
+ 4u
17
+ ··· +
39
2
u − 4
−
3
2
u
18
a −
1
2
u
18
+ ··· −
3
2
a + 3
a
7
=
u
u
a
8
=
−
3
2
u
18
a + u
18
+ ··· −
5
2
a + 4
−
1
2
u
18
a − 2u
18
+ ··· −
3
2
a + 1
a
1
=
u
2
+ 1
−u
4
a
11
=
u
18
−
5
2
u
17
+ ··· + a +
5
2
−
5
2
u
18
+
13
2
u
17
+ ··· + 8u −
3
2
a
5
=
1
2
u
18
a −
3
2
u
18
+ ··· + a − 5
−u
18
a −
1
2
u
18
+ ··· −
5
2
a + 3
a
9
=
a
−
3
2
u
18
+ 3u
17
+ ··· +
9
2
u − 1
a
12
=
1
2
u
18
a + u
18
+ ··· +
3
2
a +
5
2
u
18
a −
3
2
u
18
+ ··· +
1
2
a +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −8u
18
+ 25u
17
− 84u
16
+ 166u
15
− 312u
14
+ 471u
13
− 637u
12
+ 808u
11
− 877u
10
+
947u
9
− 869u
8
+ 754u
7
− 616u
6
+ 432u
5
− 334u
4
+ 206u
3
− 115u
2
+ 43u − 11
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
19
+ 13u
18
+ ··· + 2u − 1)
2
c
2
, c
6
(u
19
+ 3u
18
+ ··· + 6u + 1)
2
c
3
, c
9
u
38
+ u
37
+ ··· + 5696u + 908
c
4
, c
5
, c
12
u
38
− 3u
37
+ ··· + 10u
2
+ 4
c
7
, c
10
u
38
− 5u
37
+ ··· − 28450u + 4625
c
8
, c
11
(u
19
+ 5u
18
+ ··· + 20u + 7)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
19
− 11y
18
+ ··· + 38y −1)
2
c
2
, c
6
(y
19
+ 13y
18
+ ··· + 2y −1)
2
c
3
, c
9
y
38
− 35y
37
+ ··· − 10830384y + 824464
c
4
, c
5
, c
12
y
38
+ 5y
37
+ ··· + 80y + 16
c
7
, c
10
y
38
− 37y
37
+ ··· + 236310000y + 21390625
c
8
, c
11
(y
19
+ 11y
18
+ ··· − 300y −49)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.041110 + 0.058191I
a = −1.346300 − 0.087992I
b = −0.070727 + 0.324415I
−4.78729 − 1.81592I −6.58607 + 3.74202I
u = 1.041110 + 0.058191I
a = 1.44689 − 0.14447I
b = −0.184376 + 0.150737I
−4.78729 − 1.81592I −6.58607 + 3.74202I
u = 1.041110 − 0.058191I
a = −1.346300 + 0.087992I
b = −0.070727 − 0.324415I
−4.78729 + 1.81592I −6.58607 − 3.74202I
u = 1.041110 − 0.058191I
a = 1.44689 + 0.14447I
b = −0.184376 − 0.150737I
−4.78729 + 1.81592I −6.58607 − 3.74202I
u = 0.228070 + 1.071510I
a = −0.328351 − 0.989425I
b = −0.07397 − 3.02445I
0.90159 + 7.11721I −6.24817 − 10.02307I
u = 0.228070 + 1.071510I
a = 1.72904 + 1.08620I
b = 1.44083 + 0.92301I
0.90159 + 7.11721I −6.24817 − 10.02307I
u = 0.228070 − 1.071510I
a = −0.328351 + 0.989425I
b = −0.07397 + 3.02445I
0.90159 − 7.11721I −6.24817 + 10.02307I
u = 0.228070 − 1.071510I
a = 1.72904 − 1.08620I
b = 1.44083 − 0.92301I
0.90159 − 7.11721I −6.24817 + 10.02307I
u = −0.624126 + 0.935674I
a = −0.798110 − 0.979366I
b = 0.076909 − 1.392880I
2.36034 − 1.09097I −8.98199 − 1.95962I
u = −0.624126 + 0.935674I
a = −0.346295 − 0.494801I
b = −1.004870 − 0.509384I
2.36034 − 1.09097I −8.98199 − 1.95962I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.624126 − 0.935674I
a = −0.798110 + 0.979366I
b = 0.076909 + 1.392880I
2.36034 + 1.09097I −8.98199 + 1.95962I
u = −0.624126 − 0.935674I
a = −0.346295 + 0.494801I
b = −1.004870 + 0.509384I
2.36034 + 1.09097I −8.98199 + 1.95962I
u = −0.616732 + 0.611232I
a = 0.432266 + 0.956807I
b = 0.430328 − 0.206177I
3.24466 − 3.79929I −3.99786 + 7.09998I
u = −0.616732 + 0.611232I
a = 1.37057 + 0.50609I
b = 0.46061 + 1.35578I
3.24466 − 3.79929I −3.99786 + 7.09998I
u = −0.616732 − 0.611232I
a = 0.432266 − 0.956807I
b = 0.430328 + 0.206177I
3.24466 + 3.79929I −3.99786 − 7.09998I
u = −0.616732 − 0.611232I
a = 1.37057 − 0.50609I
b = 0.46061 − 1.35578I
3.24466 + 3.79929I −3.99786 − 7.09998I
u = 0.081532 + 1.192440I
a = −0.965035 + 0.213609I
b = −0.296783 + 0.704590I
−4.55800 + 1.47269I −15.5511 − 4.2071I
u = 0.081532 + 1.192440I
a = −0.237799 + 0.845382I
b = 0.16123 + 2.37600I
−4.55800 + 1.47269I −15.5511 − 4.2071I
u = 0.081532 − 1.192440I
a = −0.965035 − 0.213609I
b = −0.296783 − 0.704590I
−4.55800 − 1.47269I −15.5511 + 4.2071I
u = 0.081532 − 1.192440I
a = −0.237799 − 0.845382I
b = 0.16123 − 2.37600I
−4.55800 − 1.47269I −15.5511 + 4.2071I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.116911 + 1.229070I
a = 0.18036 − 1.53816I
b = 0.50210 − 2.49405I
−2.01094 − 5.15095I −12.30071 + 5.73853I
u = −0.116911 + 1.229070I
a = 0.180096 − 0.187932I
b = −1.54583 − 0.63107I
−2.01094 − 5.15095I −12.30071 + 5.73853I
u = −0.116911 − 1.229070I
a = 0.18036 + 1.53816I
b = 0.50210 + 2.49405I
−2.01094 + 5.15095I −12.30071 − 5.73853I
u = −0.116911 − 1.229070I
a = 0.180096 + 0.187932I
b = −1.54583 + 0.63107I
−2.01094 + 5.15095I −12.30071 − 5.73853I
u = 0.54636 + 1.32865I
a = −0.262991 + 1.071060I
b = −0.65067 + 2.41212I
−8.72835 + 7.47965I −8.40298 − 6.61968I
u = 0.54636 + 1.32865I
a = 0.186121 − 1.293220I
b = −0.03780 − 2.40287I
−8.72835 + 7.47965I −8.40298 − 6.61968I
u = 0.54636 − 1.32865I
a = −0.262991 − 1.071060I
b = −0.65067 − 2.41212I
−8.72835 − 7.47965I −8.40298 + 6.61968I
u = 0.54636 − 1.32865I
a = 0.186121 + 1.293220I
b = −0.03780 + 2.40287I
−8.72835 − 7.47965I −8.40298 + 6.61968I
u = 0.47814 + 1.36384I
a = 0.059304 − 0.997948I
b = 0.53165 − 2.02906I
−9.27627 + 3.56613I −9.74898 + 0.43427I
u = 0.47814 + 1.36384I
a = −0.186195 + 1.207920I
b = −0.11776 + 2.60978I
−9.27627 + 3.56613I −9.74898 + 0.43427I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.47814 − 1.36384I
a = 0.059304 + 0.997948I
b = 0.53165 + 2.02906I
−9.27627 − 3.56613I −9.74898 − 0.43427I
u = 0.47814 − 1.36384I
a = −0.186195 − 1.207920I
b = −0.11776 − 2.60978I
−9.27627 − 3.56613I −9.74898 − 0.43427I
u = 0.308272 + 0.388000I
a = −2.35893 + 0.54355I
b = 0.114594 − 0.630026I
2.82450 − 4.64371I −0.81427 + 2.09655I
u = 0.308272 + 0.388000I
a = 1.78966 + 1.71963I
b = 1.44880 + 0.41504I
2.82450 − 4.64371I −0.81427 + 2.09655I
u = 0.308272 − 0.388000I
a = −2.35893 − 0.54355I
b = 0.114594 + 0.630026I
2.82450 + 4.64371I −0.81427 − 2.09655I
u = 0.308272 − 0.388000I
a = 1.78966 − 1.71963I
b = 1.44880 − 0.41504I
2.82450 + 4.64371I −0.81427 − 2.09655I
u = 0.348561
a = 1.45571 + 0.80946I
b = −0.684266 + 0.183801I
−1.06383 −4.73570
u = 0.348561
a = 1.45571 − 0.80946I
b = −0.684266 − 0.183801I
−1.06383 −4.73570
15
III.
I
u
3
= hu
14
−4u
13
+· · ·+b−1, u
14
−3u
13
+· · ·+2a−4, u
15
−5u
14
+· · ·+4u−2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
10
=
−
1
2
u
14
+
3
2
u
13
+ ··· −
5
2
u + 2
−u
14
+ 4u
13
+ ··· + u + 1
a
4
=
−
3
2
u
14
+
15
2
u
13
+ ··· +
11
2
u + 1
−u
14
+ 6u
13
+ ··· + 9u − 3
a
7
=
u
u
a
8
=
1
2
u
14
−
3
2
u
13
+ ··· +
9
2
u − 3
u
14
− 4u
13
+ ··· − u − 1
a
1
=
u
2
+ 1
−u
4
a
11
=
−
1
2
u
14
+
3
2
u
13
+ ··· −
3
2
u + 1
−u
14
+ 3u
13
+ ··· + u + 1
a
5
=
−
3
2
u
14
+
13
2
u
13
+ ··· +
5
2
u + 2
−u
14
+ 5u
13
+ ··· + 7u − 1
a
9
=
−
1
2
u
14
+
3
2
u
13
+ ··· −
5
2
u + 2
−u
14
+ 3u
13
+ ··· − 2u + 3
a
12
=
1
2
u
14
−
7
2
u
13
+ ··· −
17
2
u + 2
−u
14
+ 3u
13
+ ··· − 6u + 3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
14
+ 25u
13
− 82u
12
+ 189u
11
− 343u
10
+ 505u
9
− 614u
8
+
627u
7
− 530u
6
+ 382u
5
− 230u
4
+ 128u
3
− 69u
2
+ 30u − 22
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 9u
14
+ ··· − 36u + 4
c
2
u
15
− 5u
14
+ ··· + 4u − 2
c
3
, c
9
u
15
− u
14
+ ··· + 2u + 1
c
4
u
15
+ u
14
+ ··· + u + 1
c
5
, c
12
u
15
− u
14
+ ··· + u − 1
c
6
u
15
+ 5u
14
+ ··· + 4u + 2
c
7
, c
10
u
15
− 3u
14
+ ··· − 2u − 1
c
8
u
15
− 8u
14
+ ··· − 13u
2
+ 2
c
11
u
15
+ 8u
14
+ ··· + 13u
2
− 2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
15
+ y
14
+ ··· + 8y −16
c
2
, c
6
y
15
+ 9y
14
+ ··· − 36y −4
c
3
, c
9
y
15
− 7y
14
+ ··· + 10y −1
c
4
, c
5
, c
12
y
15
+ 7y
14
+ ··· − 3y −1
c
7
, c
10
y
15
− 15y
14
+ ··· + 2y −1
c
8
, c
11
y
15
+ 4y
14
+ ··· + 52y −4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.04105
a = −1.34448
b = 0.0574551
−5.05234 −7.86790
u = 0.142498 + 1.177400I
a = 0.797818 + 0.992560I
b = 0.36789 + 2.16887I
−0.25982 + 6.07751I −9.42891 − 6.08368I
u = 0.142498 − 1.177400I
a = 0.797818 − 0.992560I
b = 0.36789 − 2.16887I
−0.25982 − 6.07751I −9.42891 + 6.08368I
u = −0.148124 + 1.190680I
a = −0.655334 − 0.497245I
b = −0.05017 − 1.63184I
−4.01281 − 1.46048I −1.86959 − 1.16010I
u = −0.148124 − 1.190680I
a = −0.655334 + 0.497245I
b = −0.05017 + 1.63184I
−4.01281 + 1.46048I −1.86959 + 1.16010I
u = 0.887881 + 0.860290I
a = 0.167268 − 0.597728I
b = −0.258465 − 0.613512I
6.43693 + 6.13733I −4.68757 − 9.65401I
u = 0.887881 − 0.860290I
a = 0.167268 + 0.597728I
b = −0.258465 + 0.613512I
6.43693 − 6.13733I −4.68757 + 9.65401I
u = 0.875773 + 0.967963I
a = −0.497404 + 0.294113I
b = −0.306201 + 0.669414I
6.12254 + 0.37048I −8.78610 + 1.49023I
u = 0.875773 − 0.967963I
a = −0.497404 − 0.294113I
b = −0.306201 − 0.669414I
6.12254 − 0.37048I −8.78610 − 1.49023I
u = 0.033850 + 0.679992I
a = 1.52172 − 0.70551I
b = 1.200660 + 0.615415I
1.81263 − 5.19090I −8.70220 + 5.73716I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.033850 − 0.679992I
a = 1.52172 + 0.70551I
b = 1.200660 − 0.615415I
1.81263 + 5.19090I −8.70220 − 5.73716I
u = −0.336015 + 0.511815I
a = 0.171836 + 0.846334I
b = −0.756395 − 0.011183I
−1.61892 − 0.67704I −12.66646 + 4.31369I
u = −0.336015 − 0.511815I
a = 0.171836 − 0.846334I
b = −0.756395 + 0.011183I
−1.61892 + 0.67704I −12.66646 − 4.31369I
u = 0.52361 + 1.34992I
a = 0.166332 − 1.108050I
b = 0.27395 − 2.30620I
−9.24424 + 5.57231I −9.92521 − 3.30109I
u = 0.52361 − 1.34992I
a = 0.166332 + 1.108050I
b = 0.27395 + 2.30620I
−9.24424 − 5.57231I −9.92521 + 3.30109I
20
IV. I
u
4
=
ha
3
u−a
3
+a
2
u−a
2
+3au+3b+u−1, a
4
−3a
2
u−a
2
+2au+2a−2u−2, u
2
+u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u + 1
a
10
=
a
−
1
3
a
3
u −
1
3
a
2
u + ··· +
1
3
a
2
+
1
3
a
4
=
−
1
3
a
3
u −
1
3
a
2
u + ··· − a +
7
3
−a
3
u + a
2
− au − 2a + 3
a
7
=
u
u
a
8
=
2
3
a
3
u −
1
3
a
2
u + ··· + a −
2
3
2
3
a
3
u −
1
3
a
2
u + ··· + a +
1
3
a
1
=
−u
−u
a
11
=
1
3
a
3
u +
1
3
a
2
u + ··· + a +
2
3
a
3
+ a
2
− 2au + 1
a
5
=
−
2
3
a
3
u +
1
3
a
2
u + ··· − 2a +
11
3
−
4
3
a
3
u +
2
3
a
2
u + ··· − 3a +
13
3
a
9
=
a
−
1
3
a
3
u −
1
3
a
2
u + ··· + a +
1
3
a
12
=
a
3
u + a
3
− au + 2a + u
a
3
u + a
3
− a
2
u − au + 2a + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
3
, c
9
u
8
− 5u
6
+ 2u
5
+ 11u
4
− 2u
3
− 6u
2
+ 4u + 4
c
4
u
8
+ 2u
7
+ 7u
6
+ 8u
5
+ 15u
4
+ 10u
3
+ 10u
2
+ 4u + 4
c
5
, c
12
u
8
− 2u
7
+ 7u
6
− 8u
5
+ 15u
4
− 10u
3
+ 10u
2
− 4u + 4
c
7
, c
8
, c
10
c
11
(u
2
+ 1)
4
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
(y
2
+ y + 1)
4
c
3
, c
9
y
8
− 10y
7
+ 47y
6
− 126y
5
+ 197y
4
− 192y
3
+ 140y
2
− 64y + 16
c
4
, c
5
, c
12
y
8
+ 10y
7
+ 47y
6
+ 126y
5
+ 197y
4
+ 192y
3
+ 140y
2
+ 64y + 16
c
7
, c
8
, c
10
c
11
(y + 1)
8
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.178142 − 0.892797I
b = −0.687884 − 0.392797I
3.28987 − 2.02988I −2.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 0.603323 + 0.513523I
b = 1.46935 + 0.01352I
3.28987 − 2.02988I −2.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 0.68788 + 1.39280I
b = −0.17814 + 1.89280I
3.28987 − 2.02988I −2.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −1.46935 − 1.01352I
b = −0.60332 − 1.51352I
3.28987 − 2.02988I −2.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 0.178142 + 0.892797I
b = −0.687884 + 0.392797I
3.28987 + 2.02988I −2.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 0.603323 − 0.513523I
b = 1.46935 − 0.01352I
3.28987 + 2.02988I −2.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 0.68788 − 1.39280I
b = −0.17814 − 1.89280I
3.28987 + 2.02988I −2.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −1.46935 + 1.01352I
b = −0.60332 + 1.51352I
3.28987 + 2.02988I −2.00000 − 3.46410I
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
15
− 9u
14
+ ··· − 36u + 4)
· ((u
19
+ 13u
18
+ ··· + 2u − 1)
2
)(u
31
+ 20u
30
+ ··· + 684u − 100)
c
2
((u
2
+ u + 1)
4
)(u
15
− 5u
14
+ ··· + 4u − 2)(u
19
+ 3u
18
+ ··· + 6u + 1)
2
· (u
31
− 8u
30
+ ··· − 62u + 10)
c
3
, c
9
(u
8
− 5u
6
+ ··· + 4u + 4)(u
15
− u
14
+ ··· + 2u + 1)
· (u
31
+ u
30
+ ··· + u + 1)(u
38
+ u
37
+ ··· + 5696u + 908)
c
4
(u
8
+ 2u
7
+ 7u
6
+ 8u
5
+ 15u
4
+ 10u
3
+ 10u
2
+ 4u + 4)
· (u
15
+ u
14
+ ··· + u + 1)(u
31
− u
30
+ ··· + 4u + 1)
· (u
38
− 3u
37
+ ··· + 10u
2
+ 4)
c
5
, c
12
(u
8
− 2u
7
+ 7u
6
− 8u
5
+ 15u
4
− 10u
3
+ 10u
2
− 4u + 4)
· (u
15
− u
14
+ ··· + u − 1)(u
31
− u
30
+ ··· + 4u + 1)
· (u
38
− 3u
37
+ ··· + 10u
2
+ 4)
c
6
((u
2
− u + 1)
4
)(u
15
+ 5u
14
+ ··· + 4u + 2)(u
19
+ 3u
18
+ ··· + 6u + 1)
2
· (u
31
− 8u
30
+ ··· − 62u + 10)
c
7
, c
10
((u
2
+ 1)
4
)(u
15
− 3u
14
+ ··· − 2u − 1)(u
31
− 3u
30
+ ··· + 5u + 1)
· (u
38
− 5u
37
+ ··· − 28450u + 4625)
c
8
((u
2
+ 1)
4
)(u
15
− 8u
14
+ ··· − 13u
2
+ 2)(u
19
+ 5u
18
+ ··· + 20u + 7)
2
· (u
31
− 11u
30
+ ··· − 122u + 10)
c
11
((u
2
+ 1)
4
)(u
15
+ 8u
14
+ ··· + 13u
2
− 2)(u
19
+ 5u
18
+ ··· + 20u + 7)
2
· (u
31
− 11u
30
+ ··· − 122u + 10)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
15
+ y
14
+ ··· + 8y −16)
· (y
19
− 11y
18
+ ··· + 38y −1)
2
· (y
31
− 12y
30
+ ··· + 1252656y −10000)
c
2
, c
6
((y
2
+ y + 1)
4
)(y
15
+ 9y
14
+ ··· − 36y −4)
· ((y
19
+ 13y
18
+ ··· + 2y −1)
2
)(y
31
+ 20y
30
+ ··· + 684y −100)
c
3
, c
9
(y
8
− 10y
7
+ 47y
6
− 126y
5
+ 197y
4
− 192y
3
+ 140y
2
− 64y + 16)
· (y
15
− 7y
14
+ ··· + 10y −1)(y
31
− 29y
30
+ ··· + 23y −1)
· (y
38
− 35y
37
+ ··· − 10830384y + 824464)
c
4
, c
5
, c
12
(y
8
+ 10y
7
+ 47y
6
+ 126y
5
+ 197y
4
+ 192y
3
+ 140y
2
+ 64y + 16)
· (y
15
+ 7y
14
+ ··· − 3y −1)(y
31
+ 25y
30
+ ··· − 6y −1)
· (y
38
+ 5y
37
+ ··· + 80y + 16)
c
7
, c
10
((y + 1)
8
)(y
15
− 15y
14
+ ··· + 2y −1)(y
31
− 29y
30
+ ··· − 105y −1)
· (y
38
− 37y
37
+ ··· + 236310000y + 21390625)
c
8
, c
11
((y + 1)
8
)(y
15
+ 4y
14
+ ··· + 52y −4)
· ((y
19
+ 11y
18
+ ··· − 300y −49)
2
)(y
31
+ 11y
30
+ ··· − 756y −100)
26
