12a
1226
(K12a
1226
)
A knot diagram
1
Linearized knot diagam
5 6 8 12 2 10 11 4 1 7 3 9
Solving Sequence
1,5
2 6
3,9
10 7 12 4 8 11
c
1
c
5
c
2
c
9
c
6
c
12
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h4.98945 × 10
144
u
84
− 1.37087 × 10
145
u
83
+ ··· + 1.92650 × 10
144
b − 2.91725 × 10
146
,
1.95093 × 10
145
u
84
− 5.15748 × 10
145
u
83
+ ··· + 1.40635 × 10
146
a − 2.25735 × 10
147
,
u
85
− 4u
84
+ ··· + 788u + 73i
I
u
2
= h−5u
18
+ 13u
17
+ ··· + b − 4, −u
17
+ 2u
16
+ ··· + a − 7u, u
19
− u
18
+ ··· + 4u + 1i
I
u
3
= hb − 1, −u
5
+ 2u
4
+ 2u
3
− 4u
2
+ a − u + 2, u
6
− u
5
− 4u
4
+ 2u
3
+ 4u
2
+ 1i
I
u
4
= hb − 1, a, u − 1i
* 4 irreducible components of dim
C
= 0, with total 111 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
= h4.99 × 10
144
u
84
− 1.37 × 10
145
u
83
+ · · · + 1.93 × 10
144
b − 2.92 ×
10
146
, 1.95 × 10
145
u
84
− 5.16 × 10
145
u
83
+ · · · + 1.41 × 10
146
a − 2.26 ×
10
147
, u
85
− 4u
84
+ · · · + 788u + 73i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
−0.138723u
84
+ 0.366728u
83
+ ··· + 130.193u + 16.0512
−2.58990u
84
+ 7.11584u
83
+ ··· + 1749.52u + 151.427
a
10
=
−2.72862u
84
+ 7.48257u
83
+ ··· + 1879.71u + 167.478
−2.58990u
84
+ 7.11584u
83
+ ··· + 1749.52u + 151.427
a
7
=
2.92578u
84
− 8.13708u
83
+ ··· − 2024.72u − 177.767
2.31664u
84
− 6.47988u
83
+ ··· − 1619.00u − 139.768
a
12
=
0.385598u
84
− 1.10673u
83
+ ··· − 283.400u − 21.1009
3.41608u
84
− 9.58363u
83
+ ··· − 2437.49u − 209.431
a
4
=
−0.561858u
84
+ 1.48323u
83
+ ··· + 383.494u + 32.0573
2.75914u
84
− 7.81915u
83
+ ··· − 1999.66u − 171.708
a
8
=
0.715497u
84
− 2.08191u
83
+ ··· − 538.570u − 40.4914
1.93432u
84
− 5.25535u
83
+ ··· − 1247.86u − 107.161
a
11
=
1.00130u
84
− 2.85966u
83
+ ··· − 737.962u − 59.9423
1.84070u
84
− 5.11536u
83
+ ··· − 1289.48u − 110.827
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.89483u
84
− 19.7102u
83
+ ··· − 4933.58u − 411.467
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
85
+ 4u
84
+ ··· + 788u − 73
c
3
, c
8
u
85
+ 2u
84
+ ··· − 13u − 1
c
4
u
85
− 2u
84
+ ··· − 10671u − 1901
c
6
, c
7
, c
10
u
85
− 3u
84
+ ··· + 10u + 1
c
9
, c
12
u
85
+ 9u
84
+ ··· − 956u − 536
c
11
u
85
+ 6u
84
+ ··· − 675913u + 208517
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
85
− 80y
84
+ ··· + 416398y −5329
c
3
, c
8
y
85
− 72y
84
+ ··· − 3y −1
c
4
y
85
+ 16y
84
+ ··· − 16272219y −3613801
c
6
, c
7
, c
10
y
85
− 93y
84
+ ··· + 246y −1
c
9
, c
12
y
85
− 63y
84
+ ··· − 14389936y −287296
c
11
y
85
+ 36y
84
+ ··· + 2472814918725y −43479339289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.624130 + 0.677501I
a = 1.27325 − 0.82874I
b = −1.172910 + 0.299627I
5.48537 − 3.36947I 0
u = −0.624130 − 0.677501I
a = 1.27325 + 0.82874I
b = −1.172910 − 0.299627I
5.48537 + 3.36947I 0
u = −0.409379 + 1.002590I
a = −1.68599 + 0.21190I
b = 1.40263 + 0.44403I
13.5552 + 11.4881I 0
u = −0.409379 − 1.002590I
a = −1.68599 − 0.21190I
b = 1.40263 − 0.44403I
13.5552 − 11.4881I 0
u = 1.12445
a = 1.58307
b = −1.67518
11.2991 0
u = 0.301457 + 0.815530I
a = 1.80925 + 0.18621I
b = −1.029340 + 0.250303I
1.17315 − 3.20365I 0
u = 0.301457 − 0.815530I
a = 1.80925 − 0.18621I
b = −1.029340 − 0.250303I
1.17315 + 3.20365I 0
u = −1.149180 + 0.081342I
a = 1.03377 + 1.54266I
b = −0.850018 − 0.005837I
6.06553 + 5.53345I 0
u = −1.149180 − 0.081342I
a = 1.03377 − 1.54266I
b = −0.850018 + 0.005837I
6.06553 − 5.53345I 0
u = 1.164800 + 0.089757I
a = 0.52166 − 1.45972I
b = −0.799484 − 0.495047I
1.60587 − 0.73292I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.164800 − 0.089757I
a = 0.52166 + 1.45972I
b = −0.799484 + 0.495047I
1.60587 + 0.73292I 0
u = −1.16926
a = 0.845667
b = −1.78576
6.73023 0
u = 0.192937 + 1.154220I
a = −1.44238 − 0.07519I
b = 1.087730 − 0.364012I
6.71901 − 5.49463I 0
u = 0.192937 − 1.154220I
a = −1.44238 + 0.07519I
b = 1.087730 + 0.364012I
6.71901 + 5.49463I 0
u = −0.360617 + 0.745031I
a = 2.20948 − 0.41944I
b = −1.300800 − 0.407023I
6.28975 + 7.97133I 7.38430 − 8.02100I
u = −0.360617 − 0.745031I
a = 2.20948 + 0.41944I
b = −1.300800 + 0.407023I
6.28975 − 7.97133I 7.38430 + 8.02100I
u = −1.198080 + 0.082837I
a = 0.214684 + 1.075630I
b = −1.12156 + 0.98848I
5.68630 − 4.05640I 0
u = −1.198080 − 0.082837I
a = 0.214684 − 1.075630I
b = −1.12156 − 0.98848I
5.68630 + 4.05640I 0
u = 1.20730
a = 0.288478
b = −2.30164
10.5815 0
u = 0.345771 + 0.669877I
a = 1.28934 + 1.71832I
b = −1.339630 − 0.095594I
12.65180 − 2.38566I 11.28357 + 3.13973I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.345771 − 0.669877I
a = 1.28934 − 1.71832I
b = −1.339630 + 0.095594I
12.65180 + 2.38566I 11.28357 − 3.13973I
u = −0.369159 + 0.631904I
a = 1.18727 − 0.96387I
b = −1.314670 − 0.246770I
8.21278 + 1.87881I 10.83009 − 0.57094I
u = −0.369159 − 0.631904I
a = 1.18727 + 0.96387I
b = −1.314670 + 0.246770I
8.21278 − 1.87881I 10.83009 + 0.57094I
u = 0.395662 + 0.581191I
a = 1.48354 + 0.44038I
b = −1.60987 + 0.54830I
12.29370 − 1.36558I 11.35480 + 4.41215I
u = 0.395662 − 0.581191I
a = 1.48354 − 0.44038I
b = −1.60987 − 0.54830I
12.29370 + 1.36558I 11.35480 − 4.41215I
u = 0.252051 + 0.653041I
a = −0.757441 + 0.041642I
b = 0.067707 + 0.675510I
3.87059 − 1.76215I 3.74742 + 3.64728I
u = 0.252051 − 0.653041I
a = −0.757441 − 0.041642I
b = 0.067707 − 0.675510I
3.87059 + 1.76215I 3.74742 − 3.64728I
u = −0.323184 + 0.612844I
a = −1.34257 − 1.28161I
b = 0.014273 + 0.180616I
8.16304 − 3.16907I 8.19689 − 1.41717I
u = −0.323184 − 0.612844I
a = −1.34257 + 1.28161I
b = 0.014273 − 0.180616I
8.16304 + 3.16907I 8.19689 + 1.41717I
u = −0.910397 + 0.940971I
a = −0.942683 + 0.660065I
b = 1.261770 − 0.234880I
12.19520 − 5.09209I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.910397 − 0.940971I
a = −0.942683 − 0.660065I
b = 1.261770 + 0.234880I
12.19520 + 5.09209I 0
u = 1.31174
a = −0.512904
b = 1.29127
1.49689 0
u = 1.310290 + 0.142010I
a = −0.460124 − 1.144650I
b = 0.950477 − 0.477408I
−2.39006 − 2.09627I 0
u = 1.310290 − 0.142010I
a = −0.460124 + 1.144650I
b = 0.950477 + 0.477408I
−2.39006 + 2.09627I 0
u = −1.315430 + 0.140434I
a = −0.389970 + 0.923304I
b = 1.30169 + 0.95849I
1.18769 + 4.19202I 0
u = −1.315430 − 0.140434I
a = −0.389970 − 0.923304I
b = 1.30169 − 0.95849I
1.18769 − 4.19202I 0
u = 1.333230 + 0.195789I
a = −1.47363 − 1.02765I
b = 1.40909 − 0.37140I
1.00589 − 5.05324I 0
u = 1.333230 − 0.195789I
a = −1.47363 + 1.02765I
b = 1.40909 + 0.37140I
1.00589 + 5.05324I 0
u = −1.353310 + 0.168736I
a = −1.135850 + 0.671511I
b = 1.275170 + 0.382326I
−2.89149 + 2.20435I 0
u = −1.353310 − 0.168736I
a = −1.135850 − 0.671511I
b = 1.275170 − 0.382326I
−2.89149 − 2.20435I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.260065 + 0.576274I
a = −0.138226 + 0.392642I
b = −0.337232 − 1.153370I
8.20231 + 6.17948I 8.20026 − 7.53712I
u = −0.260065 − 0.576274I
a = −0.138226 − 0.392642I
b = −0.337232 + 1.153370I
8.20231 − 6.17948I 8.20026 + 7.53712I
u = −0.400208 + 0.472091I
a = −0.384579 − 0.514091I
b = 0.143077 + 0.872180I
1.90136 + 3.46440I 4.11990 − 8.09520I
u = −0.400208 − 0.472091I
a = −0.384579 + 0.514091I
b = 0.143077 − 0.872180I
1.90136 − 3.46440I 4.11990 + 8.09520I
u = 0.524761 + 0.282395I
a = 0.431371 + 0.231054I
b = −0.168767 − 0.371547I
−1.053160 − 0.578747I −6.16527 + 2.76686I
u = 0.524761 − 0.282395I
a = 0.431371 − 0.231054I
b = −0.168767 + 0.371547I
−1.053160 + 0.578747I −6.16527 − 2.76686I
u = 1.347350 + 0.409713I
a = 0.949410 + 0.561746I
b = −0.935806 + 0.242242I
−1.77639 − 1.77523I 0
u = 1.347350 − 0.409713I
a = 0.949410 − 0.561746I
b = −0.935806 − 0.242242I
−1.77639 + 1.77523I 0
u = −1.387010 + 0.261595I
a = 0.036469 − 0.262545I
b = 0.347098 − 1.080660I
−1.31353 + 5.12324I 0
u = −1.387010 − 0.261595I
a = 0.036469 + 0.262545I
b = 0.347098 + 1.080660I
−1.31353 − 5.12324I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.40272 + 0.23901I
a = 0.252195 + 0.345108I
b = 0.01364 + 1.55109I
2.87646 − 9.22644I 0
u = 1.40272 − 0.23901I
a = 0.252195 − 0.345108I
b = 0.01364 − 1.55109I
2.87646 + 9.22644I 0
u = −0.375540 + 0.431749I
a = 1.146050 + 0.602010I
b = 0.047218 − 0.523660I
1.96018 − 0.39806I 4.48273 − 0.63616I
u = −0.375540 − 0.431749I
a = 1.146050 − 0.602010I
b = 0.047218 + 0.523660I
1.96018 + 0.39806I 4.48273 + 0.63616I
u = 1.38602 + 0.37040I
a = −0.400754 + 0.063344I
b = 0.711046 + 0.385814I
2.31278 − 0.56245I 0
u = 1.38602 − 0.37040I
a = −0.400754 − 0.063344I
b = 0.711046 − 0.385814I
2.31278 + 0.56245I 0
u = 1.43721 + 0.03949I
a = 0.501581 + 0.307898I
b = −0.100119 + 0.665742I
−3.84830 − 1.03714I 0
u = 1.43721 − 0.03949I
a = 0.501581 − 0.307898I
b = −0.100119 − 0.665742I
−3.84830 + 1.03714I 0
u = 1.43195 + 0.14709I
a = −0.329587 − 0.361408I
b = 0.027993 − 1.196330I
−3.98333 − 5.67696I 0
u = 1.43195 − 0.14709I
a = −0.329587 + 0.361408I
b = 0.027993 + 1.196330I
−3.98333 + 5.67696I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.42782 + 0.30450I
a = 1.029350 − 0.806960I
b = −1.203740 − 0.522812I
−4.35157 + 7.18408I 0
u = −1.42782 − 0.30450I
a = 1.029350 + 0.806960I
b = −1.203740 + 0.522812I
−4.35157 − 7.18408I 0
u = −1.45967 + 0.09531I
a = −0.022628 + 0.249071I
b = −0.182505 + 0.900172I
−7.48171 + 2.02794I 0
u = −1.45967 − 0.09531I
a = −0.022628 − 0.249071I
b = −0.182505 − 0.900172I
−7.48171 − 2.02794I 0
u = −0.058099 + 0.526758I
a = −3.74437 − 0.86928I
b = 1.226770 + 0.248698I
5.43767 + 2.43332I 12.27217 − 3.91915I
u = −0.058099 − 0.526758I
a = −3.74437 + 0.86928I
b = 1.226770 − 0.248698I
5.43767 − 2.43332I 12.27217 + 3.91915I
u = −1.44411 + 0.28089I
a = 0.124422 − 1.264770I
b = −1.062120 − 0.060649I
6.90944 + 5.91266I 0
u = −1.44411 − 0.28089I
a = 0.124422 + 1.264770I
b = −1.062120 + 0.060649I
6.90944 − 5.91266I 0
u = 1.44817 + 0.26550I
a = 0.250173 + 0.920078I
b = −1.070750 + 0.553524I
2.37812 − 5.23342I 0
u = 1.44817 − 0.26550I
a = 0.250173 − 0.920078I
b = −1.070750 − 0.553524I
2.37812 + 5.23342I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44320 + 0.29402I
a = 1.07173 + 1.00849I
b = −1.40089 + 0.55110I
0.53532 − 11.75990I 0
u = 1.44320 − 0.29402I
a = 1.07173 − 1.00849I
b = −1.40089 − 0.55110I
0.53532 + 11.75990I 0
u = −1.45461 + 0.24376I
a = 0.389692 − 0.802347I
b = −1.41742 − 1.00679I
6.34695 + 4.48091I 0
u = −1.45461 − 0.24376I
a = 0.389692 + 0.802347I
b = −1.41742 + 1.00679I
6.34695 − 4.48091I 0
u = 1.28916 + 0.74858I
a = −1.223760 − 0.579291I
b = 0.863011 − 0.274783I
2.61452 − 3.50027I 0
u = 1.28916 − 0.74858I
a = −1.223760 + 0.579291I
b = 0.863011 + 0.274783I
2.61452 + 3.50027I 0
u = −0.000669 + 0.479428I
a = −2.21076 + 0.10853I
b = 1.33078 − 0.51074I
5.30975 − 2.02687I 14.9012 + 3.2094I
u = −0.000669 − 0.479428I
a = −2.21076 − 0.10853I
b = 1.33078 + 0.51074I
5.30975 + 2.02687I 14.9012 − 3.2094I
u = −1.45774 + 0.44477I
a = −0.986710 + 0.825536I
b = 1.192490 + 0.605367I
1.39761 + 11.05220I 0
u = −1.45774 − 0.44477I
a = −0.986710 − 0.825536I
b = 1.192490 − 0.605367I
1.39761 − 11.05220I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.50394 + 0.39283I
a = −0.947921 − 0.892330I
b = 1.44979 − 0.64447I
7.4665 − 16.5073I 0
u = 1.50394 − 0.39283I
a = −0.947921 + 0.892330I
b = 1.44979 + 0.64447I
7.4665 + 16.5073I 0
u = −1.63342
a = 0.200193
b = 0.420791
−7.19573 0
u = 1.72107
a = 0.418682
b = −0.809091
−3.01365 0
u = −0.106379
a = 5.09497
b = 0.447981
0.879411 12.9870
13
II. I
u
2
=
h−5u
18
+13u
17
+· · ·+b−4, −u
17
+2u
16
+· · ·+a−7u, u
19
−u
18
+· · ·+4u+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
u
17
− 2u
16
+ ··· − 4u
2
+ 7u
5u
18
− 13u
17
+ ··· + 12u + 4
a
10
=
5u
18
− 12u
17
+ ··· + 19u + 4
5u
18
− 13u
17
+ ··· + 12u + 4
a
7
=
−2u
18
+ 4u
17
+ ··· − 8u − 2
3u
18
− 7u
17
+ ··· + 7u
2
+ 5u
a
12
=
3u
18
− 5u
17
+ ··· + 20u + 6
−2u
18
+ 5u
17
+ ··· − 9u − 1
a
4
=
2u
18
− 7u
17
+ ··· − 5u + 2
−3u
18
+ 6u
17
+ ··· − 7u − 5
a
8
=
−4u
18
+ 9u
17
+ ··· − 14u − 1
−4u
18
+ 9u
17
+ ··· − 7u − 3
a
11
=
3u
18
− 5u
17
+ ··· + 18u + 6
−u
18
+ 3u
17
+ ··· − 3u
2
− 6u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 8u
18
− 12u
17
− 84u
16
+ 122u
15
+ 366u
14
− 508u
13
− 858u
12
+ 1087u
11
+ 1167u
10
−
1187u
9
− 913u
8
+ 474u
7
+ 369u
6
+ 174u
5
− 43u
4
− 150u
3
− 15u
2
+ 7u + 10
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
19
− u
18
+ ··· + 4u + 1
c
3
u
19
+ u
18
+ ··· − u − 1
c
4
u
19
+ u
18
+ ··· + u − 1
c
5
u
19
+ u
18
+ ··· + 4u − 1
c
6
, c
7
u
19
− 2u
18
+ ··· + 2u − 1
c
8
u
19
− u
18
+ ··· − u + 1
c
9
u
19
− 3u
18
+ ··· + 7u + 1
c
10
u
19
+ 2u
18
+ ··· + 2u + 1
c
11
u
19
− u
18
+ ··· + 5u − 1
c
12
u
19
+ 3u
18
+ ··· + 7u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
y
19
− 25y
18
+ ··· + 6y −1
c
3
, c
8
y
19
− 21y
18
+ ··· + 45y −1
c
4
y
19
+ 3y
18
+ ··· + 13y −1
c
6
, c
7
, c
10
y
19
− 22y
18
+ ··· + 10y −1
c
9
, c
12
y
19
− 21y
18
+ ··· + 61y −1
c
11
y
19
+ 3y
18
+ ··· + 9y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.10278
a = 0.720093
b = −1.70355
6.99800 17.7350
u = −1.26024
a = 0.906514
b = −2.09527
9.84855 0.542410
u = 1.253900 + 0.227809I
a = −0.900344 − 0.843791I
b = 1.020270 − 0.265725I
−1.12863 − 1.33201I 5.39680 − 0.05843I
u = 1.253900 − 0.227809I
a = −0.900344 + 0.843791I
b = 1.020270 + 0.265725I
−1.12863 + 1.33201I 5.39680 + 0.05843I
u = −1.327440 + 0.099919I
a = −0.693739 + 1.130910I
b = 1.32837 + 0.65411I
0.65874 + 3.18643I 2.84941 − 0.30702I
u = −1.327440 − 0.099919I
a = −0.693739 − 1.130910I
b = 1.32837 − 0.65411I
0.65874 − 3.18643I 2.84941 + 0.30702I
u = −1.374240 + 0.196813I
a = −0.000109 − 1.119420I
b = −0.831567 − 0.883831I
4.21440 + 7.04159I 4.96365 − 5.87415I
u = −1.374240 − 0.196813I
a = −0.000109 + 1.119420I
b = −0.831567 + 0.883831I
4.21440 − 7.04159I 4.96365 + 5.87415I
u = −0.134296 + 0.586065I
a = 2.35029 + 0.60951I
b = −0.916608 + 0.500115I
8.54052 − 4.44138I 11.11085 + 4.14729I
u = −0.134296 − 0.586065I
a = 2.35029 − 0.60951I
b = −0.916608 − 0.500115I
8.54052 + 4.44138I 11.11085 − 4.14729I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35294 + 0.54742I
a = 0.862592 + 0.861954I
b = −0.811030 + 0.265564I
2.63803 − 2.91120I 5.09455 − 1.50399I
u = 1.35294 − 0.54742I
a = 0.862592 − 0.861954I
b = −0.811030 − 0.265564I
2.63803 + 2.91120I 5.09455 + 1.50399I
u = 0.539160
a = 1.08291
b = 0.394778
0.237359 −2.52210
u = −0.466068
a = −0.590861
b = −1.72859
12.7186 13.7870
u = −1.60823
a = 0.305684
b = 0.150405
−7.38733 −19.5130
u = −0.223965 + 0.281328I
a = −2.57318 + 2.47101I
b = 1.161660 − 0.354877I
4.49875 − 1.89485I 3.37367 + 0.19461I
u = −0.223965 − 0.281328I
a = −2.57318 − 2.47101I
b = 1.161660 + 0.354877I
4.49875 + 1.89485I 3.37367 − 0.19461I
u = 1.68023
a = −0.254506
b = 0.846729
−2.79077 17.2130
u = 1.91856
a = 0.739137
b = −0.766706
0.749611 −6.82050
18
III.
I
u
3
= hb − 1, −u
5
+ 2u
4
+ 2u
3
− 4u
2
+ a − u + 2, u
6
− u
5
− 4u
4
+ 2u
3
+ 4u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
6
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
u
5
− 2u
4
− 2u
3
+ 4u
2
+ u − 2
1
a
10
=
u
5
− 2u
4
− 2u
3
+ 4u
2
+ u − 1
1
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
12
=
u
5
− 2u
4
− 2u
3
+ 4u
2
+ u − 1
1
a
4
=
u
4
− 2u
3
− u
2
+ 2u + 1
−u
5
+ 2u
4
+ 2u
3
− 3u
2
− 1
a
8
=
−u
3
+ 2u
2
− 2
−u
5
+ 2u
4
+ u
3
− 4u
2
+ u
a
11
=
u
5
− 3u
4
− 2u
3
+ 6u
2
+ 2u
−u
5
+ 2u
3
+ u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
6
+ u
5
− 4u
4
− 2u
3
+ 4u
2
+ 1
c
3
, c
8
u
6
− u
5
− 4u
4
+ 2u
3
+ 4u
2
+ 1
c
4
u
6
− u
5
+ 4u
4
+ 4u
3
− 2u
2
+ 4u + 1
c
6
, c
7
, c
10
c
11
u
6
− u
5
− 2u
2
+ 2u − 1
c
9
, c
12
(u − 1)
6
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
8
y
6
− 9y
5
+ 28y
4
− 34y
3
+ 8y
2
+ 8y + 1
c
4
y
6
+ 7y
5
+ 20y
4
− 22y
3
− 20y
2
− 20y + 1
c
6
, c
7
, c
10
c
11
y
6
− y
5
− 4y
4
+ 2y
3
+ 4y
2
+ 1
c
9
, c
12
(y −1)
6
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.280890 + 0.160943I
a = −0.60066 + 1.69666I
b = 1.00000
1.64493 6.00000
u = −1.280890 − 0.160943I
a = −0.60066 − 1.69666I
b = 1.00000
1.64493 6.00000
u = 1.53631
a = −0.857960
b = 1.00000
1.64493 6.00000
u = 0.037401 + 0.445898I
a = −2.77623 + 0.79561I
b = 1.00000
1.64493 6.00000
u = 0.037401 − 0.445898I
a = −2.77623 − 0.79561I
b = 1.00000
1.64493 6.00000
u = 1.95066
a = −0.388251
b = 1.00000
1.64493 6.00000
22
IV. I
u
4
= hb − 1, a, u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
6
=
−1
0
a
3
=
0
1
a
9
=
0
1
a
10
=
1
1
a
7
=
0
1
a
12
=
1
1
a
4
=
1
2
a
8
=
−1
−1
a
11
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
10
, c
11
u + 1
c
3
, c
8
, c
9
c
12
u − 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = 1.00000
1.64493 6.00000
26
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
(u + 1)(u
6
+ u
5
+ ··· + 4u
2
+ 1)(u
19
− u
18
+ ··· + 4u + 1)
· (u
85
+ 4u
84
+ ··· + 788u − 73)
c
3
(u − 1)(u
6
− u
5
+ ··· + 4u
2
+ 1)(u
19
+ u
18
+ ··· − u − 1)
· (u
85
+ 2u
84
+ ··· − 13u − 1)
c
4
(u + 1)(u
6
− u
5
+ ··· + 4u + 1)(u
19
+ u
18
+ ··· + u − 1)
· (u
85
− 2u
84
+ ··· − 10671u − 1901)
c
5
(u + 1)(u
6
+ u
5
+ ··· + 4u
2
+ 1)(u
19
+ u
18
+ ··· + 4u − 1)
· (u
85
+ 4u
84
+ ··· + 788u − 73)
c
6
, c
7
(u + 1)(u
6
− u
5
− 2u
2
+ 2u − 1)(u
19
− 2u
18
+ ··· + 2u − 1)
· (u
85
− 3u
84
+ ··· + 10u + 1)
c
8
(u − 1)(u
6
− u
5
+ ··· + 4u
2
+ 1)(u
19
− u
18
+ ··· − u + 1)
· (u
85
+ 2u
84
+ ··· − 13u − 1)
c
9
((u − 1)
7
)(u
19
− 3u
18
+ ··· + 7u + 1)(u
85
+ 9u
84
+ ··· − 956u − 536)
c
10
(u + 1)(u
6
− u
5
− 2u
2
+ 2u − 1)(u
19
+ 2u
18
+ ··· + 2u + 1)
· (u
85
− 3u
84
+ ··· + 10u + 1)
c
11
(u + 1)(u
6
− u
5
− 2u
2
+ 2u − 1)(u
19
− u
18
+ ··· + 5u − 1)
· (u
85
+ 6u
84
+ ··· − 675913u + 208517)
c
12
((u − 1)
7
)(u
19
+ 3u
18
+ ··· + 7u − 1)(u
85
+ 9u
84
+ ··· − 956u − 536)
27
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)(y
6
− 9y
5
+ 28y
4
− 34y
3
+ 8y
2
+ 8y + 1)
· (y
19
− 25y
18
+ ··· + 6y −1)(y
85
− 80y
84
+ ··· + 416398y −5329)
c
3
, c
8
(y −1)(y
6
− 9y
5
+ 28y
4
− 34y
3
+ 8y
2
+ 8y + 1)
· (y
19
− 21y
18
+ ··· + 45y −1)(y
85
− 72y
84
+ ··· − 3y −1)
c
4
(y −1)(y
6
+ 7y
5
+ 20y
4
− 22y
3
− 20y
2
− 20y + 1)
· (y
19
+ 3y
18
+ ··· + 13y −1)
· (y
85
+ 16y
84
+ ··· − 16272219y −3613801)
c
6
, c
7
, c
10
(y −1)(y
6
− y
5
+ ··· + 4y
2
+ 1)(y
19
− 22y
18
+ ··· + 10y −1)
· (y
85
− 93y
84
+ ··· + 246y −1)
c
9
, c
12
((y −1)
7
)(y
19
− 21y
18
+ ··· + 61y −1)
· (y
85
− 63y
84
+ ··· − 14389936y −287296)
c
11
(y −1)(y
6
− y
5
+ ··· + 4y
2
+ 1)(y
19
+ 3y
18
+ ··· + 9y −1)
· (y
85
+ 36y
84
+ ··· + 2472814918725y −43479339289)
28
