12n
0702
(K12n
0702
)
A knot diagram
1
Linearized knot diagam
4 11 12 8 3 4 1 5 1 5 6 10
Solving Sequence
5,8 1,9
10 11 4 2 3 7 6 12
c
8
c
9
c
10
c
4
c
1
c
2
c
7
c
6
c
12
c
3
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.28030 × 10
278
u
84
− 7.08515 × 10
277
u
83
+ ··· + 2.04829 × 10
277
b − 1.44299 × 10
278
,
− 1.59722 × 10
279
u
84
+ 5.41005 × 10
278
u
83
+ ··· + 2.04829 × 10
277
a + 4.64496 × 10
279
,
u
85
− 9u
83
+ ··· − 8u − 1i
I
u
2
= h−244772546u
18
− 1629957344u
17
+ ··· + 13743083b + 724816940,
26173603u
18
+ 166772668u
17
+ ··· + 13743083a − 60671008, u
19
+ 7u
18
+ ··· − 8u − 1i
I
u
3
= h56a
5
+ 39a
4
+ 47a
3
+ 373a
2
+ 53b − 362a − 172, a
6
+ a
5
+ a
4
+ 7a
3
− 5a
2
− 5a − 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 110 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
= h1.28 × 10
278
u
84
− 7.09 × 10
277
u
83
+ · · · + 2.05 × 10
277
b − 1.44 ×
10
278
, −1.60 × 10
279
u
84
+ 5.41 × 10
278
u
83
+ · · · + 2.05 × 10
277
a + 4.64 ×
10
279
, u
85
− 9u
83
+ · · · − 8u − 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
1
=
77.9781u
84
− 26.4125u
83
+ ··· − 1164.55u − 226.772
−6.25059u
84
+ 3.45906u
83
+ ··· + 67.2481u + 7.04483
a
9
=
1
−u
2
a
10
=
−27.5383u
84
+ 8.40815u
83
+ ··· + 427.301u + 76.0121
−4.62638u
84
+ 2.16890u
83
+ ··· + 59.0320u + 6.99337
a
11
=
−27.5383u
84
+ 8.40815u
83
+ ··· + 427.301u + 76.0121
−6.59492u
84
+ 2.34603u
83
+ ··· + 98.7589u + 15.4015
a
4
=
−u
u
a
2
=
70.9381u
84
− 24.3526u
83
+ ··· − 1052.65u − 203.819
0.789353u
84
+ 1.39912u
83
+ ··· − 44.6522u − 15.9087
a
3
=
12.5845u
84
− 4.95452u
83
+ ··· − 182.933u − 36.7101
8.12889u
84
− 1.77404u
83
+ ··· − 140.641u − 31.6057
a
7
=
33.8620u
84
− 15.4917u
83
+ ··· − 431.959u − 76.6409
−11.6733u
84
+ 5.27102u
83
+ ··· + 149.104u + 22.4851
a
6
=
29.0802u
84
− 13.3001u
83
+ ··· − 372.382u − 66.4202
−6.89151u
84
+ 3.07940u
83
+ ··· + 89.5269u + 12.2644
a
12
=
−0.635360u
84
+ 0.516056u
83
+ ··· + 4.16244u − 1.48004
−13.1197u
84
+ 3.93049u
83
+ ··· + 208.557u + 41.6369
(ii) Obstruction class = −1
(iii) Cusp Shapes = 16.6730u
84
− 5.72160u
83
+ ··· − 248.259u − 50.7302
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
85
+ 7u
84
+ ··· − 276406u − 10363
c
2
u
85
− u
84
+ ··· + 1536u − 64
c
3
u
85
+ 2u
84
+ ··· + 4329u − 551
c
4
, c
8
u
85
− 9u
83
+ ··· − 8u − 1
c
5
u
85
− 11u
83
+ ··· − 9u − 1
c
6
u
85
− 2u
84
+ ··· − 2540737042u − 524132531
c
7
u
85
+ u
84
+ ··· − 35062u − 10369
c
9
, c
12
u
85
+ 4u
84
+ ··· + 92u − 29
c
10
u
85
− 26u
83
+ ··· − 8412115u − 901067
c
11
u
85
− 4u
84
+ ··· − 78u − 43
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
85
− 105y
84
+ ··· + 28067617904y −107391769
c
2
y
85
+ 43y
84
+ ··· + 264192y −4096
c
3
y
85
− 10y
84
+ ··· + 13669939y −303601
c
4
, c
8
y
85
− 18y
84
+ ··· + 28y −1
c
5
y
85
− 22y
84
+ ··· + 81y −1
c
6
y
85
+ 48y
84
+ ··· − 2812247482606914286y −274714910052465961
c
7
y
85
+ 69y
84
+ ··· + 9340452618y −107516161
c
9
, c
12
y
85
+ 30y
84
+ ··· − 642y −841
c
10
y
85
− 52y
84
+ ··· + 30213827398679y −811921738489
c
11
y
85
+ 14y
84
+ ··· − 59104y −1849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.953246 + 0.245682I
a = 1.007570 − 0.384540I
b = −0.577244 + 0.241074I
0.871396 − 0.259267I 0
u = 0.953246 − 0.245682I
a = 1.007570 + 0.384540I
b = −0.577244 − 0.241074I
0.871396 + 0.259267I 0
u = −0.673486 + 0.784306I
a = −1.90573 − 0.56779I
b = 0.526659 − 1.072070I
0.07658 − 7.34708I 0
u = −0.673486 − 0.784306I
a = −1.90573 + 0.56779I
b = 0.526659 + 1.072070I
0.07658 + 7.34708I 0
u = −0.900856 + 0.557667I
a = 1.49030 − 0.10055I
b = −1.56321 + 0.60214I
0.25278 − 10.31380I 0
u = −0.900856 − 0.557667I
a = 1.49030 + 0.10055I
b = −1.56321 − 0.60214I
0.25278 + 10.31380I 0
u = 0.919304 + 0.040533I
a = 1.81355 + 0.10649I
b = −2.22407 − 0.17184I
0.592523 − 0.002741I 0
u = 0.919304 − 0.040533I
a = 1.81355 − 0.10649I
b = −2.22407 + 0.17184I
0.592523 + 0.002741I 0
u = −0.748567 + 0.471981I
a = −1.44360 + 0.65462I
b = 0.660672 − 0.096154I
0.76529 − 4.87151I 0
u = −0.748567 − 0.471981I
a = −1.44360 − 0.65462I
b = 0.660672 + 0.096154I
0.76529 + 4.87151I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.125640 + 0.071155I
a = 0.47625 + 1.55494I
b = −0.071839 − 0.716689I
4.27813 − 3.12428I 0
u = 1.125640 − 0.071155I
a = 0.47625 − 1.55494I
b = −0.071839 + 0.716689I
4.27813 + 3.12428I 0
u = 0.909487 + 0.669545I
a = 1.210390 − 0.046758I
b = −0.919489 − 0.617999I
2.82901 + 2.24291I 0
u = 0.909487 − 0.669545I
a = 1.210390 + 0.046758I
b = −0.919489 + 0.617999I
2.82901 − 2.24291I 0
u = 0.540941 + 0.640172I
a = −0.416849 + 0.792144I
b = 0.705707 − 0.447204I
1.89366 + 2.60688I 5.20495 − 4.85763I
u = 0.540941 − 0.640172I
a = −0.416849 − 0.792144I
b = 0.705707 + 0.447204I
1.89366 − 2.60688I 5.20495 + 4.85763I
u = −0.514416 + 0.658480I
a = −1.069110 + 0.163561I
b = 0.743351 + 0.124486I
−1.88421 − 3.29048I −5.94463 + 7.93366I
u = −0.514416 − 0.658480I
a = −1.069110 − 0.163561I
b = 0.743351 − 0.124486I
−1.88421 + 3.29048I −5.94463 − 7.93366I
u = −0.110753 + 0.800469I
a = 1.66054 + 0.49068I
b = 0.327175 + 0.029384I
−2.81942 + 2.04516I −6.43659 − 2.51371I
u = −0.110753 − 0.800469I
a = 1.66054 − 0.49068I
b = 0.327175 − 0.029384I
−2.81942 − 2.04516I −6.43659 + 2.51371I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.446712 + 0.616825I
a = −1.39986 + 0.44963I
b = 0.903744 − 0.202836I
−1.11341 + 3.76827I −7.97957 − 5.72070I
u = 0.446712 − 0.616825I
a = −1.39986 − 0.44963I
b = 0.903744 + 0.202836I
−1.11341 − 3.76827I −7.97957 + 5.72070I
u = 0.022513 + 0.738228I
a = 1.98080 − 1.09389I
b = 0.520976 + 0.287420I
−1.68094 + 6.59296I −4.00324 − 6.24155I
u = 0.022513 − 0.738228I
a = 1.98080 + 1.09389I
b = 0.520976 − 0.287420I
−1.68094 − 6.59296I −4.00324 + 6.24155I
u = −0.987717 + 0.803260I
a = 1.045390 − 0.151570I
b = −0.259808 + 1.320130I
−2.86081 − 2.98975I 0
u = −0.987717 − 0.803260I
a = 1.045390 + 0.151570I
b = −0.259808 − 1.320130I
−2.86081 + 2.98975I 0
u = −0.074158 + 1.272450I
a = 0.230434 + 0.820563I
b = 0.235221 + 0.844978I
−3.68207 + 0.90101I 0
u = −0.074158 − 1.272450I
a = 0.230434 − 0.820563I
b = 0.235221 − 0.844978I
−3.68207 − 0.90101I 0
u = −0.778773 + 1.013300I
a = −0.811119 + 0.504897I
b = 0.24015 − 1.57375I
−7.82081 − 0.90724I 0
u = −0.778773 − 1.013300I
a = −0.811119 − 0.504897I
b = 0.24015 + 1.57375I
−7.82081 + 0.90724I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.717565
a = 1.09859
b = −0.748487
1.23485 8.37230
u = −1.275380 + 0.256516I
a = −0.200937 + 0.717636I
b = −0.163799 + 0.011266I
6.70429 − 4.67725I 0
u = −1.275380 − 0.256516I
a = −0.200937 − 0.717636I
b = −0.163799 − 0.011266I
6.70429 + 4.67725I 0
u = −0.861322 + 0.988040I
a = 0.626308 − 0.287592I
b = −0.30284 + 1.82816I
−6.97709 − 2.44068I 0
u = −0.861322 − 0.988040I
a = 0.626308 + 0.287592I
b = −0.30284 − 1.82816I
−6.97709 + 2.44068I 0
u = 0.671632 + 0.108498I
a = −3.18695 − 0.42608I
b = 1.76184 + 0.45532I
−0.629345 + 0.042189I −9.3237 − 22.9586I
u = 0.671632 − 0.108498I
a = −3.18695 + 0.42608I
b = 1.76184 − 0.45532I
−0.629345 − 0.042189I −9.3237 + 22.9586I
u = 1.320680 + 0.030383I
a = 0.374873 + 0.695666I
b = −0.439824 − 0.683093I
2.63381 − 0.38628I 0
u = 1.320680 − 0.030383I
a = 0.374873 − 0.695666I
b = −0.439824 + 0.683093I
2.63381 + 0.38628I 0
u = 1.328070 + 0.070537I
a = 0.209036 − 0.094466I
b = −0.680596 − 0.890239I
3.43139 − 3.10183I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.328070 − 0.070537I
a = 0.209036 + 0.094466I
b = −0.680596 + 0.890239I
3.43139 + 3.10183I 0
u = −0.818817 + 1.054500I
a = −0.397386 + 0.496106I
b = 0.01047 − 1.52855I
−6.06632 + 1.74224I 0
u = −0.818817 − 1.054500I
a = −0.397386 − 0.496106I
b = 0.01047 + 1.52855I
−6.06632 − 1.74224I 0
u = 0.853790 + 1.031930I
a = 0.702437 + 0.384444I
b = −0.38963 − 1.74425I
−8.60891 + 10.06010I 0
u = 0.853790 − 1.031930I
a = 0.702437 − 0.384444I
b = −0.38963 + 1.74425I
−8.60891 − 10.06010I 0
u = 0.569474 + 1.212630I
a = −0.588783 − 0.156268I
b = 0.21959 + 1.40637I
−6.53669 − 0.30535I 0
u = 0.569474 − 1.212630I
a = −0.588783 + 0.156268I
b = 0.21959 − 1.40637I
−6.53669 + 0.30535I 0
u = −0.643333 + 0.126775I
a = 0.700532 + 0.525270I
b = −0.86233 − 1.30596I
1.11800 + 3.76540I 6.47146 − 0.17501I
u = −0.643333 − 0.126775I
a = 0.700532 − 0.525270I
b = −0.86233 + 1.30596I
1.11800 − 3.76540I 6.47146 + 0.17501I
u = −1.072820 + 0.880544I
a = 1.222270 − 0.647004I
b = 0.06919 + 1.47723I
−6.28594 − 4.46244I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.072820 − 0.880544I
a = 1.222270 + 0.647004I
b = 0.06919 − 1.47723I
−6.28594 + 4.46244I 0
u = −1.111240 + 0.836819I
a = −1.085760 + 0.719028I
b = 0.34024 − 1.57099I
−6.73268 − 5.90485I 0
u = −1.111240 − 0.836819I
a = −1.085760 − 0.719028I
b = 0.34024 + 1.57099I
−6.73268 + 5.90485I 0
u = −0.597072 + 0.076683I
a = 0.939533 + 0.529541I
b = −0.223355 + 1.043000I
0.72842 − 3.14108I 2.29680 + 4.43516I
u = −0.597072 − 0.076683I
a = 0.939533 − 0.529541I
b = −0.223355 − 1.043000I
0.72842 + 3.14108I 2.29680 − 4.43516I
u = −1.10536 + 0.91023I
a = −1.277440 + 0.468808I
b = 0.45655 − 1.40048I
−5.15199 − 8.90397I 0
u = −1.10536 − 0.91023I
a = −1.277440 − 0.468808I
b = 0.45655 + 1.40048I
−5.15199 + 8.90397I 0
u = −0.83913 + 1.17729I
a = 0.532658 − 0.417502I
b = 0.35403 + 1.48319I
−7.44292 + 1.34945I 0
u = −0.83913 − 1.17729I
a = 0.532658 + 0.417502I
b = 0.35403 − 1.48319I
−7.44292 − 1.34945I 0
u = 1.12975 + 0.91492I
a = 1.007260 + 0.695928I
b = 0.02880 − 1.41413I
−7.74485 − 2.88977I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12975 − 0.91492I
a = 1.007260 − 0.695928I
b = 0.02880 + 1.41413I
−7.74485 + 2.88977I 0
u = 0.82642 + 1.24387I
a = 0.435680 + 0.402752I
b = 0.26320 − 1.49705I
−7.78575 − 9.87450I 0
u = 0.82642 − 1.24387I
a = 0.435680 − 0.402752I
b = 0.26320 + 1.49705I
−7.78575 + 9.87450I 0
u = −1.16879 + 0.95091I
a = 1.168270 − 0.342096I
b = −0.62166 + 1.72667I
−6.33003 − 9.02103I 0
u = −1.16879 − 0.95091I
a = 1.168270 + 0.342096I
b = −0.62166 − 1.72667I
−6.33003 + 9.02103I 0
u = 1.18792 + 0.96818I
a = 1.189930 + 0.382393I
b = −0.56609 − 1.65671I
−6.5605 + 17.7584I 0
u = 1.18792 − 0.96818I
a = 1.189930 − 0.382393I
b = −0.56609 + 1.65671I
−6.5605 − 17.7584I 0
u = 0.91255 + 1.27572I
a = −0.413886 − 0.234512I
b = 0.090108 + 1.345540I
−6.23718 + 1.43490I 0
u = 0.91255 − 1.27572I
a = −0.413886 + 0.234512I
b = 0.090108 − 1.345540I
−6.23718 − 1.43490I 0
u = −0.267578 + 0.313151I
a = 0.055433 + 1.389690I
b = 0.473363 − 0.261089I
−1.67196 + 0.33811I −4.53587 + 0.25356I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.267578 − 0.313151I
a = 0.055433 − 1.389690I
b = 0.473363 + 0.261089I
−1.67196 − 0.33811I −4.53587 − 0.25356I
u = 1.12120 + 1.13735I
a = −0.935373 − 0.230456I
b = 0.317137 + 1.296190I
−5.58721 + 7.04673I 0
u = 1.12120 − 1.13735I
a = −0.935373 + 0.230456I
b = 0.317137 − 1.296190I
−5.58721 − 7.04673I 0
u = 0.252248 + 0.310284I
a = −0.838985 − 0.037082I
b = 0.08832 − 1.69651I
1.02683 + 4.68860I −4.5379 − 18.7431I
u = 0.252248 − 0.310284I
a = −0.838985 + 0.037082I
b = 0.08832 + 1.69651I
1.02683 − 4.68860I −4.5379 + 18.7431I
u = −0.390454 + 0.064131I
a = −4.96384 − 2.92768I
b = 0.693941 + 0.917998I
−1.33214 + 7.02424I 1.83651 − 1.94021I
u = −0.390454 − 0.064131I
a = −4.96384 + 2.92768I
b = 0.693941 − 0.917998I
−1.33214 − 7.02424I 1.83651 + 1.94021I
u = 1.31679 + 0.93534I
a = −0.877200 − 0.537108I
b = 0.24804 + 1.41028I
−4.27143 + 8.08431I 0
u = 1.31679 − 0.93534I
a = −0.877200 + 0.537108I
b = 0.24804 − 1.41028I
−4.27143 − 8.08431I 0
u = −1.64898 + 0.16129I
a = 0.084326 − 0.476991I
b = −0.207238 + 0.939937I
3.05653 − 5.84434I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.64898 − 0.16129I
a = 0.084326 + 0.476991I
b = −0.207238 − 0.939937I
3.05653 + 5.84434I 0
u = −0.312911 + 0.076595I
a = 1.31072 − 3.31226I
b = 0.225604 − 0.993144I
3.12290 + 2.74721I 1.20418 − 2.40059I
u = −0.312911 − 0.076595I
a = 1.31072 + 3.31226I
b = 0.225604 + 0.993144I
3.12290 − 2.74721I 1.20418 + 2.40059I
u = 0.134773 + 0.261504I
a = −2.21098 + 3.95237I
b = 0.443171 + 1.057770I
−2.30070 − 0.22946I −0.69908 + 2.57896I
u = 0.134773 − 0.261504I
a = −2.21098 − 3.95237I
b = 0.443171 − 1.057770I
−2.30070 + 0.22946I −0.69908 − 2.57896I
13
II.
I
u
2
= h−2.45 × 10
8
u
18
− 1.63 × 10
9
u
17
+ · · · + 1.37 × 10
7
b + 7.25 × 10
8
, 2.62 ×
10
7
u
18
+1.67×10
8
u
17
+· · · +1.37×10
7
a−6.07×10
7
, u
19
+7u
18
+· · · − 8u −1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
1
=
−1.90449u
18
− 12.1350u
17
+ ··· + 17.7714u + 4.41466
17.8106u
18
+ 118.602u
17
+ ··· − 265.643u − 52.7405
a
9
=
1
−u
2
a
10
=
25.9870u
18
+ 172.460u
17
+ ··· − 380.519u − 74.9910
−8.44948u
18
− 55.4779u
17
+ ··· + 109.905u + 17.9870
a
11
=
25.9870u
18
+ 172.460u
17
+ ··· − 380.519u − 74.9910
−4.78098u
18
− 31.1791u
17
+ ··· + 60.2962u + 8.53752
a
4
=
−u
u
a
2
=
−3.40312u
18
− 22.0099u
17
+ ··· + 40.8714u + 9.29041
19.3092u
18
+ 128.477u
17
+ ··· − 288.743u − 57.6162
a
3
=
−16.8106u
18
− 111.602u
17
+ ··· + 242.643u + 44.7405
−8.63245u
18
− 58.8669u
17
+ ··· + 148.361u + 33.4431
a
7
=
27.5490u
18
+ 183.900u
17
+ ··· − 410.543u − 79.6704
−10.7384u
18
− 71.2982u
17
+ ··· + 153.899u + 26.9299
a
6
=
26.3475u
18
+ 175.604u
17
+ ··· − 386.776u − 74.5982
−9.53695u
18
− 63.0019u
17
+ ··· + 130.132u + 21.8577
a
12
=
11.6431u
18
+ 78.9152u
17
+ ··· − 194.709u − 42.5675
−33.5319u
18
− 224.275u
17
+ ··· + 512.982u + 103.649
(ii) Obstruction class = 1
(iii) Cusp Shapes =
815245557
13743083
u
18
+
5459581744
13743083
u
17
+ ··· −
11845745429
13743083
u −
2113120363
13743083
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
19
− 8u
18
+ ··· + 36u − 5
c
2
u
19
+ 11u
17
+ ··· + 868u − 161
c
3
u
19
+ u
18
+ ··· + u + 1
c
4
u
19
− 7u
18
+ ··· − 8u + 1
c
5
u
19
+ 4u
18
+ ··· + u + 1
c
6
u
19
+ 3u
18
+ ··· + 14u + 7
c
7
u
19
+ u
18
+ ··· − 8u + 1
c
8
u
19
+ 7u
18
+ ··· − 8u − 1
c
9
u
19
− 5u
18
+ ··· + 22u
3
+ 1
c
10
u
19
− u
18
+ ··· + 43u − 1
c
11
u
19
− u
18
+ ··· + 2u − 1
c
12
u
19
+ 5u
18
+ ··· + 22u
3
− 1
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
19
− 24y
18
+ ··· − 634y −25
c
2
y
19
+ 22y
18
+ ··· + 278152y −25921
c
3
y
19
+ 11y
18
+ ··· − 19y −1
c
4
, c
8
y
19
− 9y
18
+ ··· + 20y −1
c
5
y
19
− 10y
18
+ ··· − y −1
c
6
y
19
+ 3y
18
+ ··· − 1442y −49
c
7
y
19
+ 13y
18
+ ··· + 12y −1
c
9
, c
12
y
19
+ 15y
18
+ ··· + 110y
2
− 1
c
10
y
19
− 3y
18
+ ··· + 1749y −1
c
11
y
19
+ 7y
18
+ ··· + 2y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.101971 + 1.194250I
a = −0.121869 − 0.998593I
b = −0.240972 − 0.876588I
−3.83821 + 0.57575I −7.03661 + 7.04903I
u = 0.101971 − 1.194250I
a = −0.121869 + 0.998593I
b = −0.240972 + 0.876588I
−3.83821 − 0.57575I −7.03661 − 7.04903I
u = 0.748450
a = 3.67791
b = −2.32349
−0.535625 78.4150
u = 0.427813 + 0.579261I
a = −1.282800 − 0.006750I
b = 0.444930 − 0.593169I
−0.32639 + 4.17404I −1.48783 − 8.92780I
u = 0.427813 − 0.579261I
a = −1.282800 + 0.006750I
b = 0.444930 + 0.593169I
−0.32639 − 4.17404I −1.48783 + 8.92780I
u = 1.292210 + 0.144984I
a = 0.145680 + 0.546566I
b = 0.293800 − 0.044567I
2.98574 − 1.37365I 0.97264 + 5.34570I
u = 1.292210 − 0.144984I
a = 0.145680 − 0.546566I
b = 0.293800 + 0.044567I
2.98574 + 1.37365I 0.97264 − 5.34570I
u = −0.494798 + 0.440934I
a = 4.05470 + 0.26170I
b = −0.648835 + 0.905706I
−1.45608 − 7.65096I −1.70341 + 13.93377I
u = −0.494798 − 0.440934I
a = 4.05470 − 0.26170I
b = −0.648835 − 0.905706I
−1.45608 + 7.65096I −1.70341 − 13.93377I
u = −0.729582 + 1.154870I
a = −0.586985 + 0.267393I
b = 0.12758 − 1.45789I
−6.26150 − 0.33531I −3.59873 + 1.11567I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.729582 − 1.154870I
a = −0.586985 − 0.267393I
b = 0.12758 + 1.45789I
−6.26150 + 0.33531I −3.59873 − 1.11567I
u = −1.390760 + 0.152571I
a = −0.353819 + 1.029490I
b = 0.260600 − 0.902349I
5.65950 − 5.58071I 3.63137 + 6.94784I
u = −1.390760 − 0.152571I
a = −0.353819 − 1.029490I
b = 0.260600 + 0.902349I
5.65950 + 5.58071I 3.63137 − 6.94784I
u = −1.16440 + 0.99040I
a = −1.032030 + 0.398941I
b = 0.36202 − 1.39801I
−4.92843 − 7.38688I −1.21254 + 5.93258I
u = −1.16440 − 0.99040I
a = −1.032030 − 0.398941I
b = 0.36202 + 1.39801I
−4.92843 + 7.38688I −1.21254 − 5.93258I
u = −1.58190 + 0.09635I
a = −0.150962 − 0.015584I
b = 0.335732 − 0.789452I
3.86364 − 5.68341I 6.69198 + 5.45345I
u = −1.58190 − 0.09635I
a = −0.150962 + 0.015584I
b = 0.335732 + 0.789452I
3.86364 + 5.68341I 6.69198 − 5.45345I
u = −0.334791 + 0.023571I
a = 1.48913 + 0.07516I
b = −0.27311 − 1.70449I
1.27966 + 4.46859I 12.53545 − 5.10070I
u = −0.334791 − 0.023571I
a = 1.48913 − 0.07516I
b = −0.27311 + 1.70449I
1.27966 − 4.46859I 12.53545 + 5.10070I
20
III.
I
u
3
= h56a
5
+ 53b + · · · − 362a − 172, a
6
+ a
5
+ a
4
+ 7a
3
− 5a
2
− 5a − 1, u − 1i
(i) Arc colorings
a
5
=
0
1
a
8
=
1
0
a
1
=
a
−1.05660a
5
− 0.735849a
4
+ ··· + 6.83019a + 3.24528
a
9
=
1
−1
a
10
=
0.320755a
5
+ 0.169811a
4
+ ··· − 2.03774a − 0.0566038
−0.716981a
5
− 0.320755a
4
+ ··· + 5.84906a − 0.226415
a
11
=
0.320755a
5
+ 0.169811a
4
+ ··· − 2.03774a − 0.0566038
−0.396226a
5
− 0.150943a
4
+ ··· + 3.81132a − 0.283019
a
4
=
−1
1
a
2
=
1.05660a
5
+ 0.735849a
4
+ ··· − 6.83019a − 3.24528
−2.11321a
5
− 1.47170a
4
+ ··· + 14.6604a + 6.49057
a
3
=
1.05660a
5
+ 0.735849a
4
+ ··· − 6.83019a − 3.24528
−2.11321a
5
− 1.47170a
4
+ ··· + 14.6604a + 6.49057
a
7
=
0.320755a
5
+ 0.169811a
4
+ ··· − 2.03774a − 0.0566038
−1.03774a
5
− 0.490566a
4
+ ··· + 7.88679a + 1.83019
a
6
=
1.03774a
5
+ 0.490566a
4
+ ··· − 7.88679a − 1.83019
−1.75472a
5
− 0.811321a
4
+ ··· + 13.7358a + 3.60377
a
12
=
−0.811321a
5
− 0.547170a
4
+ ··· + 6.56604a + 2.84906
1.47170a
5
+ 1.13208a
4
+ ··· − 10.5849a − 5.37736
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
128
53
a
5
−
233
53
a
4
−
62
53
a
3
−
1428
53
a
2
+
623
53
a +
749
53
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
(u
3
− u
2
+ 2u − 1)
2
c
2
u
6
c
3
(u
3
− u
2
+ 1)
2
c
4
(u + 1)
6
c
5
, c
7
u
6
− 3u
5
+ 2u
4
− 3u
3
− 2u
2
− 2u − 1
c
6
u
6
− 6u
5
+ 12u
4
− 10u
3
+ 9u
2
− 14u + 7
c
8
(u − 1)
6
c
10
, c
11
u
6
− 3u
4
− 2u
3
+ 6u
2
− 2u − 1
c
12
(u
3
+ u
2
+ 2u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
9
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
y
6
c
3
(y
3
− y
2
+ 2y −1)
2
c
4
, c
8
(y −1)
6
c
5
, c
7
y
6
− 5y
5
− 18y
4
− 31y
3
− 12y
2
+ 1
c
6
y
6
− 12y
5
+ 42y
4
− 38y
3
− 31y
2
− 70y + 49
c
10
, c
11
y
6
− 6y
5
+ 21y
4
− 42y
3
+ 34y
2
− 16y + 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.04327
b = −0.473427
0.531480 −12.4510
u = 1.00000
a = −0.312008 + 0.108803I
b = 0.527087 + 1.198340I
4.66906 − 2.82812I 8.17024 + 3.11418I
u = 1.00000
a = −0.312008 − 0.108803I
b = 0.527087 − 1.198340I
4.66906 + 2.82812I 8.17024 − 3.11418I
u = 1.00000
a = 0.40453 + 1.94320I
b = −0.189446 − 0.636059I
4.66906 − 2.82812I 11.35919 − 0.65976I
u = 1.00000
a = 0.40453 − 1.94320I
b = −0.189446 + 0.636059I
4.66906 + 2.82812I 11.35919 + 0.65976I
u = 1.00000
a = −2.22830
b = 2.79815
0.531480 −108.610
24
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
2
)(u
19
− 8u
18
+ ··· + 36u − 5)
· (u
85
+ 7u
84
+ ··· − 276406u − 10363)
c
2
u
6
(u
19
+ 11u
17
+ ··· + 868u − 161)(u
85
− u
84
+ ··· + 1536u − 64)
c
3
((u
3
− u
2
+ 1)
2
)(u
19
+ u
18
+ ··· + u + 1)(u
85
+ 2u
84
+ ··· + 4329u − 551)
c
4
((u + 1)
6
)(u
19
− 7u
18
+ ··· − 8u + 1)(u
85
− 9u
83
+ ··· − 8u − 1)
c
5
(u
6
− 3u
5
+ ··· − 2u − 1)(u
19
+ 4u
18
+ ··· + u + 1)
· (u
85
− 11u
83
+ ··· − 9u − 1)
c
6
(u
6
− 6u
5
+ ··· − 14u + 7)(u
19
+ 3u
18
+ ··· + 14u + 7)
· (u
85
− 2u
84
+ ··· − 2540737042u − 524132531)
c
7
(u
6
− 3u
5
+ ··· − 2u − 1)(u
19
+ u
18
+ ··· − 8u + 1)
· (u
85
+ u
84
+ ··· − 35062u − 10369)
c
8
((u − 1)
6
)(u
19
+ 7u
18
+ ··· − 8u − 1)(u
85
− 9u
83
+ ··· − 8u − 1)
c
9
((u
3
− u
2
+ 2u − 1)
2
)(u
19
− 5u
18
+ ··· + 22u
3
+ 1)
· (u
85
+ 4u
84
+ ··· + 92u − 29)
c
10
(u
6
− 3u
4
− 2u
3
+ 6u
2
− 2u − 1)(u
19
− u
18
+ ··· + 43u − 1)
· (u
85
− 26u
83
+ ··· − 8412115u − 901067)
c
11
(u
6
− 3u
4
− 2u
3
+ 6u
2
− 2u − 1)(u
19
− u
18
+ ··· + 2u − 1)
· (u
85
− 4u
84
+ ··· − 78u − 43)
c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
19
+ 5u
18
+ ··· + 22u
3
− 1)
· (u
85
+ 4u
84
+ ··· + 92u − 29)
25
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
3
+ 3y
2
+ 2y −1)
2
)(y
19
− 24y
18
+ ··· − 634y −25)
· (y
85
− 105y
84
+ ··· + 28067617904y −107391769)
c
2
y
6
(y
19
+ 22y
18
+ ··· + 278152y −25921)
· (y
85
+ 43y
84
+ ··· + 264192y −4096)
c
3
((y
3
− y
2
+ 2y −1)
2
)(y
19
+ 11y
18
+ ··· − 19y −1)
· (y
85
− 10y
84
+ ··· + 13669939y −303601)
c
4
, c
8
((y −1)
6
)(y
19
− 9y
18
+ ··· + 20y −1)(y
85
− 18y
84
+ ··· + 28y −1)
c
5
(y
6
− 5y
5
− 18y
4
− 31y
3
− 12y
2
+ 1)(y
19
− 10y
18
+ ··· − y −1)
· (y
85
− 22y
84
+ ··· + 81y −1)
c
6
(y
6
− 12y
5
+ 42y
4
− 38y
3
− 31y
2
− 70y + 49)
· (y
19
+ 3y
18
+ ··· − 1442y −49)
· (y
85
+ 48y
84
+ ··· − 2812247482606914286y −274714910052465961)
c
7
(y
6
− 5y
5
− 18y
4
− 31y
3
− 12y
2
+ 1)(y
19
+ 13y
18
+ ··· + 12y −1)
· (y
85
+ 69y
84
+ ··· + 9340452618y −107516161)
c
9
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
19
+ 15y
18
+ ··· + 110y
2
− 1)
· (y
85
+ 30y
84
+ ··· − 642y −841)
c
10
(y
6
− 6y
5
+ 21y
4
− 42y
3
+ 34y
2
− 16y + 1)
· (y
19
− 3y
18
+ ··· + 1749y −1)
· (y
85
− 52y
84
+ ··· + 30213827398679y −811921738489)
c
11
(y
6
− 6y
5
+ ··· − 16y + 1)(y
19
+ 7y
18
+ ··· + 2y −1)
· (y
85
+ 14y
84
+ ··· − 59104y −1849)
26
