12a
0853
(K12a
0853
)
A knot diagram
1
Linearized knot diagam
4 5 9 10 3 11 1 12 2 7 6 8
Solving Sequence
6,11
7
3,12
5 2 10 4 1 9 8
c
6
c
11
c
5
c
2
c
10
c
4
c
1
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.02805 × 10
16
u
42
− 1.52246 × 10
16
u
41
+ ··· + 1.26321 × 10
17
b − 8.98707 × 10
16
,
− 7.21225 × 10
16
u
42
+ 3.40792 × 10
16
u
41
+ ··· + 1.68428 × 10
17
a − 9.26394 × 10
16
, u
43
− u
42
+ ··· − u − 1i
I
u
2
= h2.49774 × 10
62
u
57
− 1.12667 × 10
62
u
56
+ ··· + 3.57909 × 10
63
b − 1.55315 × 10
63
,
3.07126 × 10
63
u
57
− 3.20268 × 10
64
u
56
+ ··· + 6.08445 × 10
64
a − 8.19267 × 10
64
, u
58
− u
57
+ ··· − 120u + 17i
I
u
3
= h−12a
5
u + 60a
4
u + 50a
4
− 58a
3
u − 200a
3
− 66a
2
u + 345a
2
+ 132au + 13b − 290a − 56u + 125,
a
6
+ 5a
5
u − 6a
5
− 25a
4
u + 6a
4
+ 48a
3
u + 16a
3
− 44a
2
u − 41a
2
+ 20au + 34a − 4u − 11, u
2
+ 1i
I
u
4
= hb − 1, 4a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 114 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
= h1.03×10
16
u
42
−1.52×10
16
u
41
+· · ·+1.26×10
17
b−8.99×10
16
, −7.21×
10
16
u
42
+3.41×10
16
u
41
+· · ·+1.68×10
17
a−9.26×10
16
, u
43
−u
42
+· · ·−u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
3
=
0.428209u
42
− 0.202336u
41
+ ··· + 4.44451u + 0.550022
−0.0813834u
42
+ 0.120523u
41
+ ··· − 0.596660u + 0.711445
a
12
=
−u
u
a
5
=
0.240572u
42
+ 0.0861176u
41
+ ··· + 4.10112u + 1.07740
−0.0655795u
42
− 0.0289657u
41
+ ··· − 0.723711u + 1.05998
a
2
=
0.471566u
42
− 0.505695u
41
+ ··· + 0.182364u − 0.696209
−0.163705u
42
+ 0.294773u
41
+ ··· + 1.16777u − 0.341990
a
10
=
u
u
3
+ u
a
4
=
0.223904u
42
+ 0.101431u
41
+ ··· + 3.27806u + 0.658768
−0.217357u
42
+ 0.0632153u
41
+ ··· − 1.56479u + 0.639998
a
1
=
0.0156250u
41
− 0.0156250u
40
+ ··· + 1.98438u − 0.0156250
−0.0156250u
41
+ 0.0156250u
40
+ ··· − 0.984375u + 0.0156250
a
9
=
−
1
64
u
42
+
1
64
u
41
+ ··· +
1
64
u + 1
0.0156250u
42
− 0.0156250u
41
+ ··· + 2.98438u
2
− 0.0156250u
a
8
=
−
1
64
u
42
+
1
64
u
41
+ ··· +
1
64
u + 1
0.0156250u
42
− 0.0156250u
41
+ ··· + 1.98438u
2
− 0.0156250u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
639766218816298439
673713571663806464
u
42
−
2392691369763753
5263387278623488
u
41
+ ···+
3318446060721997959
336856785831903232
u +
4707724893365783111
673713571663806464
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
43
− 7u
42
+ ··· + 108u − 32
c
2
, c
5
u
43
+ 2u
42
+ ··· + 209u + 16
c
3
2(2u
43
− 5u
42
+ ··· − 12267u + 4806)
c
4
2(2u
43
+ 7u
42
+ ··· − 383u + 38)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
43
+ u
42
+ ··· − u + 1
c
9
u
43
+ 11u
42
+ ··· + 12u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
43
− 3y
42
+ ··· + 2640y −1024
c
2
, c
5
y
43
− 28y
42
+ ··· + 22305y −256
c
3
4(4y
43
+ 131y
42
+ ··· + 5.60152 × 10
8
y −2.30976 × 10
7
)
c
4
4(4y
43
+ 163y
42
+ ··· + 133997y −1444)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
43
+ 49y
42
+ ··· − 7y −1
c
9
y
43
− 11y
42
+ ··· + 56y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.045580 + 0.265073I
a = 0.422924 + 0.253246I
b = −1.010750 − 0.070949I
−0.099165 + 0.197199I −0.4146 − 26.5252I
u = 1.045580 − 0.265073I
a = 0.422924 − 0.253246I
b = −1.010750 + 0.070949I
−0.099165 − 0.197199I −0.4146 + 26.5252I
u = −0.736113 + 0.398028I
a = 0.84742 − 1.18772I
b = −1.281540 − 0.503412I
1.40701 + 9.37887I −3.20335 − 8.94600I
u = −0.736113 − 0.398028I
a = 0.84742 + 1.18772I
b = −1.281540 + 0.503412I
1.40701 − 9.37887I −3.20335 + 8.94600I
u = 0.473228 + 0.484138I
a = 1.232460 + 0.508002I
b = −0.614304 + 0.159820I
−0.90207 − 1.36883I −10.28742 + 6.03530I
u = 0.473228 − 0.484138I
a = 1.232460 − 0.508002I
b = −0.614304 − 0.159820I
−0.90207 + 1.36883I −10.28742 − 6.03530I
u = −0.064164 + 1.323640I
a = 0.760278 − 0.102506I
b = −0.972506 − 0.725155I
5.23305 + 6.33277I 0
u = −0.064164 − 1.323640I
a = 0.760278 + 0.102506I
b = −0.972506 + 0.725155I
5.23305 − 6.33277I 0
u = −0.628592 + 0.239030I
a = −0.366369 + 0.658186I
b = −0.086228 + 0.994383I
−2.33595 + 4.06686I −8.11663 − 7.68950I
u = −0.628592 − 0.239030I
a = −0.366369 − 0.658186I
b = −0.086228 − 0.994383I
−2.33595 − 4.06686I −8.11663 + 7.68950I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.077159 + 0.648817I
a = 1.42212 − 0.36145I
b = −1.117220 + 0.496513I
2.05786 − 5.42765I −4.51173 + 4.01745I
u = −0.077159 − 0.648817I
a = 1.42212 + 0.36145I
b = −1.117220 − 0.496513I
2.05786 + 5.42765I −4.51173 − 4.01745I
u = 0.052827 + 1.379270I
a = 0.807394 + 0.046202I
b = −0.669512 + 1.007180I
4.20635 + 0.15997I 0
u = 0.052827 − 1.379270I
a = 0.807394 − 0.046202I
b = −0.669512 − 1.007180I
4.20635 − 0.15997I 0
u = 0.581376
a = 0.597794
b = −0.108975
−1.12494 −9.33260
u = −0.28872 + 1.45678I
a = 0.0615459 + 0.1163560I
b = 0.004483 + 0.567870I
8.92969 + 6.54162I 0
u = −0.28872 − 1.45678I
a = 0.0615459 − 0.1163560I
b = 0.004483 − 0.567870I
8.92969 − 6.54162I 0
u = −0.440206 + 0.256952I
a = −0.48389 + 1.95063I
b = 1.178700 + 0.550685I
2.08265 + 2.42825I −0.56440 − 9.11743I
u = −0.440206 − 0.256952I
a = −0.48389 − 1.95063I
b = 1.178700 − 0.550685I
2.08265 − 2.42825I −0.56440 + 9.11743I
u = −0.18031 + 1.48239I
a = −0.162135 − 0.690521I
b = 0.679167 − 0.418338I
10.59230 + 3.84643I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18031 − 1.48239I
a = −0.162135 + 0.690521I
b = 0.679167 + 0.418338I
10.59230 − 3.84643I 0
u = −0.23828 + 1.49528I
a = −2.57330 + 1.37141I
b = 1.155900 + 0.144649I
11.69970 + 5.56941I 0
u = −0.23828 − 1.49528I
a = −2.57330 − 1.37141I
b = 1.155900 − 0.144649I
11.69970 − 5.56941I 0
u = 0.31669 + 1.48794I
a = −0.638218 + 0.398587I
b = 0.004964 − 1.358370I
8.9461 − 11.3255I 0
u = 0.31669 − 1.48794I
a = −0.638218 − 0.398587I
b = 0.004964 + 1.358370I
8.9461 + 11.3255I 0
u = 0.14365 + 1.51608I
a = −0.092566 − 0.461995I
b = 0.669674 + 1.208150I
11.60390 − 0.05307I 0
u = 0.14365 − 1.51608I
a = −0.092566 + 0.461995I
b = 0.669674 − 1.208150I
11.60390 + 0.05307I 0
u = 0.26648 + 1.52137I
a = −1.73238 − 0.59952I
b = 1.49175 − 0.86241I
14.0100 − 8.2907I 0
u = 0.26648 − 1.52137I
a = −1.73238 + 0.59952I
b = 1.49175 + 0.86241I
14.0100 + 8.2907I 0
u = 0.446586 + 0.089144I
a = 0.02052 − 5.32611I
b = 0.954076 − 0.043831I
0.777033 − 0.264079I 11.3014 − 20.2599I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.446586 − 0.089144I
a = 0.02052 + 5.32611I
b = 0.954076 + 0.043831I
0.777033 + 0.264079I 11.3014 + 20.2599I
u = 0.21380 + 1.53373I
a = −1.63578 − 0.65528I
b = 1.77518 + 0.39030I
14.8100 − 3.8243I 0
u = 0.21380 − 1.53373I
a = −1.63578 + 0.65528I
b = 1.77518 − 0.39030I
14.8100 + 3.8243I 0
u = 0.38589 + 1.50890I
a = 1.79076 + 0.95620I
b = −1.43641 + 0.60380I
13.5242 − 18.0612I 0
u = 0.38589 − 1.50890I
a = 1.79076 − 0.95620I
b = −1.43641 − 0.60380I
13.5242 + 18.0612I 0
u = 0.101852 + 0.424949I
a = 1.026490 + 0.504047I
b = −0.182737 − 0.500492I
−0.434486 − 1.281080I −5.70053 + 4.09830I
u = 0.101852 − 0.424949I
a = 1.026490 − 0.504047I
b = −0.182737 + 0.500492I
−0.434486 + 1.281080I −5.70053 − 4.09830I
u = −0.40091 + 1.53270I
a = 1.54564 − 0.75824I
b = −1.237910 − 0.318743I
12.6650 + 9.9628I 0
u = −0.40091 − 1.53270I
a = 1.54564 + 0.75824I
b = −1.237910 + 0.318743I
12.6650 − 9.9628I 0
u = −0.203608 + 0.274430I
a = −0.439369 + 1.267360I
b = 1.224480 − 0.262463I
2.63309 − 0.39699I 2.68829 − 3.78144I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.203608 − 0.274430I
a = −0.439369 − 1.267360I
b = 1.224480 + 0.262463I
2.63309 + 0.39699I 2.68829 + 3.78144I
u = 0.02078 + 1.67786I
a = 1.76255 + 0.12189I
b = −1.47476 − 0.22968I
18.9757 + 4.3403I 0
u = 0.02078 − 1.67786I
a = 1.76255 − 0.12189I
b = −1.47476 + 0.22968I
18.9757 − 4.3403I 0
9
II. I
u
2
=
h2.50×10
62
u
57
−1.13×10
62
u
56
+· · ·+3.58×10
63
b−1.55×10
63
, 3.07×10
63
u
57
−
3.20 × 10
64
u
56
+ · · · + 6.08 × 10
64
a − 8.19 × 10
64
, u
58
− u
57
+ · · · − 120u + 17i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
3
=
−0.0504773u
57
+ 0.526372u
56
+ ··· − 34.1344u + 1.34649
−0.0697872u
57
+ 0.0314792u
56
+ ··· − 0.190553u + 0.433951
a
12
=
−u
u
a
5
=
−0.265733u
57
+ 0.711612u
56
+ ··· − 33.4303u + 4.89579
0.0169308u
57
− 0.0789094u
56
+ ··· + 15.7229u − 3.20838
a
2
=
0.327014u
57
− 0.175535u
56
+ ··· + 11.9688u − 7.35130
−0.0763146u
57
− 0.00228602u
56
+ ··· − 0.511135u + 0.235990
a
10
=
u
u
3
+ u
a
4
=
−0.247321u
57
+ 0.615412u
56
+ ··· − 27.6376u + 4.15193
−0.0154154u
57
− 0.0157421u
56
+ ··· + 11.8680u − 2.62983
a
1
=
0.0588235u
57
− 0.0588235u
56
+ ··· + 13.1765u − 7.05882
−0.0641037u
57
+ 0.204261u
56
+ ··· − 17.3206u + 3.46570
a
9
=
0.344021u
57
− 0.282487u
56
+ ··· + 19.4211u − 6.05337
−0.140157u
57
+ 0.142726u
56
+ ··· + 4.22674u − 2.08976
a
8
=
0.203865u
57
− 0.139761u
56
+ ··· + 23.6478u − 7.14313
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.471425u
57
+ 0.710651u
56
+ ··· + 3.35966u − 9.60008
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
29
− 5u
28
+ ··· + u − 1)
2
c
2
, c
5
(u
29
+ u
28
+ ··· + 5u − 1)
2
c
3
(u
29
+ u
28
+ ··· − u + 19)
2
c
4
(u
29
− u
28
+ ··· + 21u + 11)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
58
+ u
57
+ ··· + 120u + 17
c
9
(u
29
− 3u
28
+ ··· + u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
29
+ 3y
28
+ ··· − 5y −1)
2
c
2
, c
5
(y
29
− 21y
28
+ ··· − 5y −1)
2
c
3
(y
29
+ 15y
28
+ ··· + 1103y −361)
2
c
4
(y
29
+ 31y
28
+ ··· − 1869y −121)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
58
+ 47y
57
+ ··· − 6784y + 289
c
9
(y
29
− 5y
28
+ ··· + 3y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.114956 + 0.991781I
a = 1.017780 − 0.070177I
b = −0.328130 − 0.742907I
−0.330423 − 0.986104I −7.43918 + 1.15236I
u = −0.114956 − 0.991781I
a = 1.017780 + 0.070177I
b = −0.328130 + 0.742907I
−0.330423 + 0.986104I −7.43918 − 1.15236I
u = 0.575655 + 0.782439I
a = 1.078930 + 0.547115I
b = 0.253652 + 0.975036I
4.20559 + 2.15286I 1.11617 − 3.69479I
u = 0.575655 − 0.782439I
a = 1.078930 − 0.547115I
b = 0.253652 − 0.975036I
4.20559 − 2.15286I 1.11617 + 3.69479I
u = −0.136025 + 1.027380I
a = 1.46072 + 4.08074I
b = 1.16056
5.59886 −1.48744 + 0.I
u = −0.136025 − 1.027380I
a = 1.46072 − 4.08074I
b = 1.16056
5.59886 −1.48744 + 0.I
u = 0.435379 + 0.848772I
a = 1.108170 + 0.488561I
b = −1.093360 + 0.383928I
2.02393 − 5.18635I −2.50672 + 7.03100I
u = 0.435379 − 0.848772I
a = 1.108170 − 0.488561I
b = −1.093360 − 0.383928I
2.02393 + 5.18635I −2.50672 − 7.03100I
u = 0.986825 + 0.374884I
a = 0.523680 + 1.034500I
b = −1.39544 + 0.53455I
7.4851 − 13.0999I 1.01719 + 8.12211I
u = 0.986825 − 0.374884I
a = 0.523680 − 1.034500I
b = −1.39544 − 0.53455I
7.4851 + 13.0999I 1.01719 − 8.12211I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.703908 + 0.609023I
a = 0.167707 − 0.211198I
b = 1.53445 + 0.45405I
7.77622 − 0.55125I 6.94303 + 0.19758I
u = 0.703908 − 0.609023I
a = 0.167707 + 0.211198I
b = 1.53445 − 0.45405I
7.77622 + 0.55125I 6.94303 − 0.19758I
u = 0.779580 + 0.501957I
a = −0.238984 − 1.367610I
b = 1.43653 − 0.66551I
7.40612 − 4.48763I 5.60010 + 6.67821I
u = 0.779580 − 0.501957I
a = −0.238984 + 1.367610I
b = 1.43653 + 0.66551I
7.40612 + 4.48763I 5.60010 − 6.67821I
u = 0.839019 + 0.382301I
a = −0.229288 − 0.881419I
b = 0.059577 − 1.184960I
2.90482 − 7.12556I −1.34557 + 8.10425I
u = 0.839019 − 0.382301I
a = −0.229288 + 0.881419I
b = 0.059577 + 1.184960I
2.90482 + 7.12556I −1.34557 − 8.10425I
u = −1.067450 + 0.395502I
a = 0.530432 − 0.554638I
b = −1.164370 − 0.162769I
6.46417 + 4.69569I 0
u = −1.067450 − 0.395502I
a = 0.530432 + 0.554638I
b = −1.164370 + 0.162769I
6.46417 − 4.69569I 0
u = −0.675231 + 0.482611I
a = −2.49228 + 1.77640I
b = 1.079220 + 0.058684I
5.28092 + 2.23064I −19.0558 + 8.8774I
u = −0.675231 − 0.482611I
a = −2.49228 − 1.77640I
b = 1.079220 − 0.058684I
5.28092 − 2.23064I −19.0558 − 8.8774I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.004114 + 1.175970I
a = 0.630619 + 0.805872I
b = 0.620218 − 0.307429I
3.99674 − 1.36069I 0
u = −0.004114 − 1.175970I
a = 0.630619 − 0.805872I
b = 0.620218 + 0.307429I
3.99674 + 1.36069I 0
u = −0.727738 + 0.348972I
a = 0.533803 + 0.610441I
b = 0.046849 + 0.301708I
3.13199 + 2.80514I −2.17791 − 1.85203I
u = −0.727738 − 0.348972I
a = 0.533803 − 0.610441I
b = 0.046849 − 0.301708I
3.13199 − 2.80514I −2.17791 + 1.85203I
u = 0.774616 + 0.950835I
a = 0.571035 + 0.357762I
b = −1.37838 − 0.43416I
9.18116 + 7.10658I 0
u = 0.774616 − 0.950835I
a = 0.571035 − 0.357762I
b = −1.37838 + 0.43416I
9.18116 − 7.10658I 0
u = −0.473827 + 0.581130I
a = 1.56751 − 0.75659I
b = 0.460562 − 0.048919I
4.07927 + 1.37762I 1.11267 − 4.75149I
u = −0.473827 − 0.581130I
a = 1.56751 + 0.75659I
b = 0.460562 + 0.048919I
4.07927 − 1.37762I 1.11267 + 4.75149I
u = 0.026089 + 1.270130I
a = 0.433342 + 0.790191I
b = 0.460562 + 0.048919I
4.07927 − 1.37762I 0
u = 0.026089 − 1.270130I
a = 0.433342 − 0.790191I
b = 0.460562 − 0.048919I
4.07927 + 1.37762I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.546601 + 0.418251I
a = 0.453277 − 0.847452I
b = −1.093360 + 0.383928I
2.02393 − 5.18635I −2.50672 + 7.03100I
u = −0.546601 − 0.418251I
a = 0.453277 + 0.847452I
b = −1.093360 − 0.383928I
2.02393 + 5.18635I −2.50672 − 7.03100I
u = −0.805465 + 1.064120I
a = 0.819276 − 0.467320I
b = −1.211660 − 0.045159I
8.43950 + 1.80223I 0
u = −0.805465 − 1.064120I
a = 0.819276 + 0.467320I
b = −1.211660 + 0.045159I
8.43950 − 1.80223I 0
u = 0.198901 + 1.329080I
a = 0.333173 − 0.169396I
b = 0.046849 − 0.301708I
3.13199 − 2.80514I 0
u = 0.198901 − 1.329080I
a = 0.333173 + 0.169396I
b = 0.046849 + 0.301708I
3.13199 + 2.80514I 0
u = 0.065480 + 1.347360I
a = −0.267717 + 0.891512I
b = 0.253652 − 0.975036I
4.20559 − 2.15286I 0
u = 0.065480 − 1.347360I
a = −0.267717 − 0.891512I
b = 0.253652 + 0.975036I
4.20559 + 2.15286I 0
u = 0.116012 + 1.344200I
a = −4.36296 − 1.77186I
b = 1.079220 − 0.058684I
5.28092 − 2.23064I 0
u = 0.116012 − 1.344200I
a = −4.36296 + 1.77186I
b = 1.079220 + 0.058684I
5.28092 + 2.23064I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.191636 + 0.606717I
a = 2.91401 + 0.73543I
b = 0.620218 + 0.307429I
3.99674 + 1.36069I 0.42210 − 4.47976I
u = −0.191636 − 0.606717I
a = 2.91401 − 0.73543I
b = 0.620218 − 0.307429I
3.99674 − 1.36069I 0.42210 + 4.47976I
u = −0.056090 + 1.391240I
a = −2.41142 + 0.55032I
b = 1.53445 − 0.45405I
7.77622 + 0.55125I 0
u = −0.056090 − 1.391240I
a = −2.41142 − 0.55032I
b = 1.53445 + 0.45405I
7.77622 − 0.55125I 0
u = −0.135451 + 1.404900I
a = −2.35836 + 0.45643I
b = 1.43653 + 0.66551I
7.40612 + 4.48763I 0
u = −0.135451 − 1.404900I
a = −2.35836 − 0.45643I
b = 1.43653 − 0.66551I
7.40612 − 4.48763I 0
u = −0.22028 + 1.39864I
a = −0.645746 − 0.645559I
b = 0.059577 + 1.184960I
2.90482 + 7.12556I 0
u = −0.22028 − 1.39864I
a = −0.645746 + 0.645559I
b = 0.059577 − 1.184960I
2.90482 − 7.12556I 0
u = −0.27878 + 1.48013I
a = 2.11580 − 0.80950I
b = −1.39544 − 0.53455I
7.4851 + 13.0999I 0
u = −0.27878 − 1.48013I
a = 2.11580 + 0.80950I
b = −1.39544 + 0.53455I
7.4851 − 13.0999I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.14926 + 1.50492I
a = 2.26623 + 0.33910I
b = −1.37838 + 0.43416I
9.18116 − 7.10658I 0
u = 0.14926 − 1.50492I
a = 2.26623 − 0.33910I
b = −1.37838 − 0.43416I
9.18116 + 7.10658I 0
u = 0.29727 + 1.53685I
a = 1.66201 + 0.62219I
b = −1.164370 + 0.162769I
6.46417 − 4.69569I 0
u = 0.29727 − 1.53685I
a = 1.66201 − 0.62219I
b = −1.164370 − 0.162769I
6.46417 + 4.69569I 0
u = −0.22879 + 1.54997I
a = 1.67995 − 0.58369I
b = −1.211660 + 0.045159I
8.43950 − 1.80223I 0
u = −0.22879 − 1.54997I
a = 1.67995 + 0.58369I
b = −1.211660 − 0.045159I
8.43950 + 1.80223I 0
u = 0.214429 + 0.048924I
a = −2.33130 + 1.05547I
b = −0.328130 − 0.742907I
−0.330423 − 0.986104I −7.43918 + 1.15236I
u = 0.214429 − 0.048924I
a = −2.33130 − 1.05547I
b = −0.328130 + 0.742907I
−0.330423 + 0.986104I −7.43918 − 1.15236I
18
III.
I
u
3
= h−12a
5
u+60a
4
u+· · ·−290a+125, 5a
5
u−25a
4
u+· · ·+34a−11, u
2
+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−1
a
3
=
a
0.923077a
5
u − 4.61538a
4
u + ··· + 22.3077a − 9.61538
a
12
=
−u
u
a
5
=
0.923077a
5
u − 1.07692a
4
u + ··· + 8.84615a − 2.69231
−0.615385a
5
u + 3.07692a
4
u + ··· − 17.5385a + 8.07692
a
2
=
−0.307692a
5
u + 5.23077a
4
u + ··· − 17.0769a + 7.15385
1.15385a
5
u − 5.76923a
4
u + ··· + 21.3846a − 7.76923
a
10
=
u
0
a
4
=
1.53846a
5
u − 4.15385a
4
u + ··· + 26.3846a − 10.7692
−0.615385a
5
u + 3.07692a
4
u + ··· − 17.5385a + 8.07692
a
1
=
−2.30769a
5
u + 11.5385a
4
u + ··· − 42.7692a + 13.5385
2.30769a
5
u − 11.5385a
4
u + ··· + 42.7692a − 13.5385
a
9
=
−10.6154a
4
u + 42.4615a
3
u + ··· + 40.3846a − 16.7692
10.6154a
4
u − 42.4615a
3
u + ··· − 40.3846a + 15.7692
a
8
=
−10.6154a
4
u + 42.4615a
3
u + ··· + 40.3846a − 15.7692
10.6154a
4
u − 42.4615a
3
u + ··· − 40.3846a + 14.7692
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
20
13
a
5
u +
100
13
a
4
u +
92
13
a
4
−
36
13
a
3
u −
368
13
a
3
−
292
13
a
2
u +
484
13
a
2
+
324
13
au −
232
13
a −
76
13
u +
48
13
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
6
+ u
5
− u
4
− 2u
3
+ u + 1)
2
c
2
(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
2
c
3
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
c
4
, c
9
u
12
− u
10
+ 5u
8
+ 6u
4
− 3u
2
+ 1
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(u
2
+ 1)
6
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
c
3
(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
c
4
, c
9
(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(y + 1)
12
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.901719 − 0.655968I
b = −0.428243 − 0.664531I
1.39926 − 0.92430I −1.71672 + 0.79423I
u = 1.000000I
a = 0.618748 + 0.415113I
b = −1.073950 + 0.558752I
3.28987 − 5.69302I 2.00000 + 5.51057I
u = 1.000000I
a = 1.098280 − 0.655968I
b = −0.428243 + 0.664531I
1.39926 + 0.92430I −1.71672 − 0.79423I
u = 1.000000I
a = 1.38125 + 0.41511I
b = −1.073950 − 0.558752I
3.28987 + 5.69302I 2.00000 − 5.51057I
u = 1.000000I
a = −0.43225 − 2.25915I
b = 1.002190 + 0.295542I
5.18047 + 0.92430I 5.71672 − 0.79423I
u = 1.000000I
a = 2.43225 − 2.25915I
b = 1.002190 − 0.295542I
5.18047 − 0.92430I 5.71672 + 0.79423I
u = − 1.000000I
a = 0.901719 + 0.655968I
b = −0.428243 + 0.664531I
1.39926 + 0.92430I −1.71672 − 0.79423I
u = − 1.000000I
a = 0.618748 − 0.415113I
b = −1.073950 − 0.558752I
3.28987 + 5.69302I 2.00000 − 5.51057I
u = − 1.000000I
a = 1.098280 + 0.655968I
b = −0.428243 − 0.664531I
1.39926 − 0.92430I −1.71672 + 0.79423I
u = − 1.000000I
a = 1.38125 − 0.41511I
b = −1.073950 + 0.558752I
3.28987 − 5.69302I 2.00000 + 5.51057I
22
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = − 1.000000I
a = −0.43225 + 2.25915I
b = 1.002190 − 0.295542I
5.18047 − 0.92430I 5.71672 + 0.79423I
u = − 1.000000I
a = 2.43225 + 2.25915I
b = 1.002190 + 0.295542I
5.18047 + 0.92430I 5.71672 − 0.79423I
23
IV. I
u
4
= hb − 1, 4a + 1, u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
1
a
7
=
1
1
a
3
=
−0.25
1
a
12
=
−1
1
a
5
=
0.75
1
a
2
=
−1
0
a
10
=
1
2
a
4
=
0.25
0
a
1
=
−1
0
a
9
=
−1
2
a
8
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 14.0625
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
c
2
, c
10
, c
11
c
12
u + 1
c
3
, c
4
2(2u − 1)
c
5
, c
6
, c
7
c
8
u − 1
c
9
u − 2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
c
2
, c
5
, c
6
c
7
, c
8
, c
10
c
11
, c
12
y −1
c
3
, c
4
4(4y −1)
c
9
y −4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.250000
b = 1.00000
0 14.0620
27
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
6
+ u
5
+ ··· + u + 1)
2
(u
29
− 5u
28
+ ··· + u − 1)
2
· (u
43
− 7u
42
+ ··· + 108u − 32)
c
2
(u + 1)(u
6
− u
5
+ ··· − u + 1)
2
(u
29
+ u
28
+ ··· + 5u − 1)
2
· (u
43
+ 2u
42
+ ··· + 209u + 16)
c
3
4(2u − 1)(u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1)
· ((u
29
+ u
28
+ ··· − u + 19)
2
)(2u
43
− 5u
42
+ ··· − 12267u + 4806)
c
4
4(2u − 1)(u
12
− u
10
+ ··· − 3u
2
+ 1)(u
29
− u
28
+ ··· + 21u + 11)
2
· (2u
43
+ 7u
42
+ ··· − 383u + 38)
c
5
(u − 1)(u
6
+ u
5
+ ··· + u + 1)
2
(u
29
+ u
28
+ ··· + 5u − 1)
2
· (u
43
+ 2u
42
+ ··· + 209u + 16)
c
6
, c
7
, c
8
(u − 1)(u
2
+ 1)
6
(u
43
+ u
42
+ ··· − u + 1)(u
58
+ u
57
+ ··· + 120u + 17)
c
9
(u − 2)(u
12
− u
10
+ ··· − 3u
2
+ 1)(u
29
− 3u
28
+ ··· + u − 1)
2
· (u
43
+ 11u
42
+ ··· + 12u + 4)
c
10
, c
11
, c
12
(u + 1)(u
2
+ 1)
6
(u
43
+ u
42
+ ··· − u + 1)(u
58
+ u
57
+ ··· + 120u + 17)
28
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
6
− 3y
5
+ ··· − y + 1)
2
(y
29
+ 3y
28
+ ··· − 5y −1)
2
· (y
43
− 3y
42
+ ··· + 2640y −1024)
c
2
, c
5
(y −1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
2
· ((y
29
− 21y
28
+ ··· − 5y −1)
2
)(y
43
− 28y
42
+ ··· + 22305y −256)
c
3
16(4y −1)(y
6
+ 3y
5
+ 5y
4
+ 4y
3
+ 2y
2
+ y + 1)
2
· (y
29
+ 15y
28
+ ··· + 1103y −361)
2
· (4y
43
+ 131y
42
+ ··· + 560152341y −23097636)
c
4
16(4y −1)(y
6
− y
5
+ 5y
4
+ 6y
2
− 3y + 1)
2
· (y
29
+ 31y
28
+ ··· − 1869y −121)
2
· (4y
43
+ 163y
42
+ ··· + 133997y −1444)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(y −1)(y + 1)
12
(y
43
+ 49y
42
+ ··· − 7y −1)
· (y
58
+ 47y
57
+ ··· − 6784y + 289)
c
9
(y −4)(y
6
− y
5
+ ··· − 3y + 1)
2
(y
29
− 5y
28
+ ··· + 3y −1)
2
· (y
43
− 11y
42
+ ··· + 56y −16)
29
