12a
0590
(K12a
0590
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 8 2 5 6 12 1 4 10
Solving Sequence
5,8
6
9,11
4 12 10 3 7 2 1
c
5
c
8
c
4
c
11
c
9
c
3
c
7
c
2
c
1
c
6
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h1.68464 × 10
28
u
87
+ 9.72953 × 10
28
u
86
+ ··· + 7.00197 × 10
26
b + 1.37834 × 10
28
,
− 1.24196 × 10
28
u
87
− 9.51690 × 10
28
u
86
+ ··· + 1.40039 × 10
27
a − 3.17252 × 10
28
, u
88
+ 7u
87
+ ··· − 5u + 1i
I
u
2
= hb, u
7
+ 2u
6
− 2u
5
− 4u
4
+ 2u
3
+ u
2
+ a − u + 3, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
I
u
3
= ha
4
− a
3
+ a
2
+ b − 2a + 1, a
5
− a
4
+ a
3
− 2a
2
+ a − 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 101 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
= h1.68×10
28
u
87
+9.73×10
28
u
86
+· · ·+7.00×10
26
b+1.38×10
28
, −1.24×
10
28
u
87
−9.52×10
28
u
86
+· · ·+1.40×10
27
a−3.17×10
28
, u
88
+7u
87
+· · ·−5u+1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
6
=
1
u
2
a
9
=
−u
−u
3
+ u
a
11
=
8.86862u
87
+ 67.9587u
86
+ ··· − 105.878u + 22.6545
−24.0595u
87
− 138.954u
86
+ ··· + 110.889u − 19.6850
a
4
=
25.3526u
87
+ 133.819u
86
+ ··· − 76.7949u + 11.9623
89.2486u
87
+ 498.120u
86
+ ··· − 348.549u + 61.5438
a
12
=
−17.3831u
87
− 77.2993u
86
+ ··· − 14.1162u + 6.54485
−73.5892u
87
− 406.913u
86
+ ··· + 271.995u − 48.9600
a
10
=
24.9048u
87
+ 121.952u
86
+ ··· − 30.6185u − 0.170725
107.854u
87
+ 601.429u
86
+ ··· − 418.226u + 74.6075
a
3
=
110.590u
87
+ 613.566u
86
+ ··· − 427.222u + 73.2837
162.309u
87
+ 914.917u
86
+ ··· − 667.930u + 117.137
a
7
=
u
u
a
2
=
177.819u
87
+ 1015.19u
86
+ ··· − 782.351u + 133.966
229.538u
87
+ 1316.54u
86
+ ··· − 1023.06u + 177.819
a
1
=
17.8946u
87
+ 106.795u
86
+ ··· − 102.627u + 15.4769
61.3214u
87
+ 344.013u
86
+ ··· − 248.957u + 43.8200
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
3994510142988588901229060665
700197468586696191749097992
u
87
−
42648575021416709506457400371
700197468586696191749097992
u
86
+ ··· +
107123801345113766348171177997
700197468586696191749097992
u −
4216109697287061694606989229
175049367146674047937274498
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
88
+ 36u
87
+ ··· + 16896u + 1024
c
2
, c
6
u
88
− 2u
87
+ ··· + 64u − 32
c
3
u
88
− 3u
87
+ ··· + 49703u − 30649
c
4
, c
11
u
88
− 2u
87
+ ··· − 1664u − 256
c
5
, c
7
, c
8
u
88
− 7u
87
+ ··· + 5u + 1
c
9
, c
10
, c
12
u
88
− 10u
87
+ ··· − 13u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
88
+ 24y
87
+ ··· − 10092544y + 1048576
c
2
, c
6
y
88
− 36y
87
+ ··· − 16896y + 1024
c
3
y
88
− 37y
87
+ ··· − 880685877y + 939361201
c
4
, c
11
y
88
+ 54y
87
+ ··· − 49152y + 65536
c
5
, c
7
, c
8
y
88
− 77y
87
+ ··· − 7y + 1
c
9
, c
10
, c
12
y
88
− 86y
87
+ ··· − 85y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.888121 + 0.465628I
a = −0.674944 − 0.581430I
b = 1.115510 − 0.134578I
−5.34037 + 0.66509I 0
u = 0.888121 − 0.465628I
a = −0.674944 + 0.581430I
b = 1.115510 + 0.134578I
−5.34037 − 0.66509I 0
u = 0.766339 + 0.598583I
a = −1.036980 − 0.856681I
b = 0.42193 − 1.40540I
−10.41430 − 4.71583I 0
u = 0.766339 − 0.598583I
a = −1.036980 + 0.856681I
b = 0.42193 + 1.40540I
−10.41430 + 4.71583I 0
u = 0.952850 + 0.465179I
a = −0.065021 − 0.913422I
b = −0.351118 − 1.102560I
−2.96134 + 2.94865I 0
u = 0.952850 − 0.465179I
a = −0.065021 + 0.913422I
b = −0.351118 + 1.102560I
−2.96134 − 2.94865I 0
u = 0.800920 + 0.458340I
a = 0.73265 + 1.28159I
b = −0.112227 + 1.047930I
−3.55064 − 1.70767I 0
u = 0.800920 − 0.458340I
a = 0.73265 − 1.28159I
b = −0.112227 − 1.047930I
−3.55064 + 1.70767I 0
u = 0.238802 + 0.874394I
a = −1.51165 − 0.29886I
b = 0.64367 − 1.34705I
−6.87264 − 11.71080I 0
u = 0.238802 − 0.874394I
a = −1.51165 + 0.29886I
b = 0.64367 + 1.34705I
−6.87264 + 11.71080I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.106230 + 0.101887I
a = −0.38448 + 2.75149I
b = 0.253569 + 0.477806I
−3.31594 − 0.58556I 0
u = 1.106230 − 0.101887I
a = −0.38448 − 2.75149I
b = 0.253569 − 0.477806I
−3.31594 + 0.58556I 0
u = 1.074860 + 0.294544I
a = 0.609880 + 0.504609I
b = −0.493783 + 0.368228I
−0.723913 − 0.558805I 0
u = 1.074860 − 0.294544I
a = 0.609880 − 0.504609I
b = −0.493783 − 0.368228I
−0.723913 + 0.558805I 0
u = 0.998684 + 0.532410I
a = 0.123794 + 0.448994I
b = 0.58280 + 1.35034I
−9.19064 + 6.74935I 0
u = 0.998684 − 0.532410I
a = 0.123794 − 0.448994I
b = 0.58280 − 1.35034I
−9.19064 − 6.74935I 0
u = 0.394607 + 0.770272I
a = 0.455783 + 0.010772I
b = 0.31689 + 1.42777I
−9.29942 − 0.08924I 0
u = 0.394607 − 0.770272I
a = 0.455783 − 0.010772I
b = 0.31689 − 1.42777I
−9.29942 + 0.08924I 0
u = 0.236702 + 0.827946I
a = 1.33516 + 0.60966I
b = −0.428462 + 1.161060I
−0.75062 − 7.56823I 0
u = 0.236702 − 0.827946I
a = 1.33516 − 0.60966I
b = −0.428462 − 1.161060I
−0.75062 + 7.56823I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.257930 + 0.804225I
a = −0.992899 − 0.708956I
b = 1.176510 + 0.257378I
−3.37075 − 5.18603I 0
u = 0.257930 − 0.804225I
a = −0.992899 + 0.708956I
b = 1.176510 − 0.257378I
−3.37075 + 5.18603I 0
u = 0.044598 + 0.812501I
a = 0.012409 − 0.949891I
b = −0.068037 + 0.976812I
−0.94317 − 2.91824I −8.00000 + 0.I
u = 0.044598 − 0.812501I
a = 0.012409 + 0.949891I
b = −0.068037 − 0.976812I
−0.94317 + 2.91824I −8.00000 + 0.I
u = 0.265848 + 0.760527I
a = −0.709338 − 0.763779I
b = 0.074648 − 1.085590I
−1.85509 − 2.57254I 0
u = 0.265848 − 0.760527I
a = −0.709338 + 0.763779I
b = 0.074648 + 1.085590I
−1.85509 + 2.57254I 0
u = 0.164802 + 0.765395I
a = 0.640282 + 0.424932I
b = −0.640037 − 0.265485I
1.98407 − 3.37950I −3.18324 + 4.49505I
u = 0.164802 − 0.765395I
a = 0.640282 − 0.424932I
b = −0.640037 + 0.265485I
1.98407 + 3.37950I −3.18324 − 4.49505I
u = −1.210690 + 0.142812I
a = 0.167563 + 0.494552I
b = −0.564547 + 1.141500I
−8.03151 − 3.54347I 0
u = −1.210690 − 0.142812I
a = 0.167563 − 0.494552I
b = −0.564547 − 1.141500I
−8.03151 + 3.54347I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.239120 + 0.245897I
a = 0.512434 − 0.571361I
b = 0.566252 + 0.257444I
−1.10788 − 1.71772I 0
u = 1.239120 − 0.245897I
a = 0.512434 + 0.571361I
b = 0.566252 − 0.257444I
−1.10788 + 1.71772I 0
u = 1.215600 + 0.383630I
a = −0.934428 − 0.097206I
b = 0.033207 − 1.038470I
−4.54745 − 1.38520I 0
u = 1.215600 − 0.383630I
a = −0.934428 + 0.097206I
b = 0.033207 + 1.038470I
−4.54745 + 1.38520I 0
u = −1.276630 + 0.183299I
a = −0.215638 − 0.758974I
b = 0.582952 − 0.942243I
−2.95506 + 0.13185I 0
u = −1.276630 − 0.183299I
a = −0.215638 + 0.758974I
b = 0.582952 + 0.942243I
−2.95506 − 0.13185I 0
u = 0.051522 + 0.675391I
a = −0.742113 + 0.645879I
b = 0.611315 − 0.427751I
2.51572 − 1.61584I −1.91976 + 3.16837I
u = 0.051522 − 0.675391I
a = −0.742113 − 0.645879I
b = 0.611315 + 0.427751I
2.51572 + 1.61584I −1.91976 − 3.16837I
u = 1.314380 + 0.174281I
a = 1.09840 + 2.65275I
b = 0.010805 + 1.079500I
−4.65633 − 0.63571I 0
u = 1.314380 − 0.174281I
a = 1.09840 − 2.65275I
b = 0.010805 − 1.079500I
−4.65633 + 0.63571I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.320720 + 0.187553I
a = 0.655900 − 0.911111I
b = −0.908877 − 0.545626I
−6.01527 + 1.89183I 0
u = −1.320720 − 0.187553I
a = 0.655900 + 0.911111I
b = −0.908877 + 0.545626I
−6.01527 − 1.89183I 0
u = −1.307460 + 0.264842I
a = −0.436161 + 0.563621I
b = 0.704898 + 0.536481I
−1.74045 + 5.01419I 0
u = −1.307460 − 0.264842I
a = −0.436161 − 0.563621I
b = 0.704898 − 0.536481I
−1.74045 − 5.01419I 0
u = −1.292640 + 0.344864I
a = 0.615494 − 0.130607I
b = −0.165716 − 0.926745I
−5.11018 + 7.07530I 0
u = −1.292640 − 0.344864I
a = 0.615494 + 0.130607I
b = −0.165716 + 0.926745I
−5.11018 − 7.07530I 0
u = −0.174131 + 0.636836I
a = 2.02360 − 0.48082I
b = −0.580461 − 1.285720I
−5.14037 + 6.25877I −9.44624 − 3.66252I
u = −0.174131 − 0.636836I
a = 2.02360 + 0.48082I
b = −0.580461 + 1.285720I
−5.14037 − 6.25877I −9.44624 + 3.66252I
u = 1.330870 + 0.207803I
a = −0.933904 + 0.972883I
b = −1.166170 − 0.198096I
−6.30741 − 3.16964I 0
u = 1.330870 − 0.207803I
a = −0.933904 − 0.972883I
b = −1.166170 + 0.198096I
−6.30741 + 3.16964I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.332230 + 0.235913I
a = −1.36376 − 2.55428I
b = 0.386394 − 1.149300I
−3.80107 − 5.54437I 0
u = 1.332230 − 0.235913I
a = −1.36376 + 2.55428I
b = 0.386394 + 1.149300I
−3.80107 + 5.54437I 0
u = −1.339550 + 0.224805I
a = 0.091229 + 1.306420I
b = −0.487922 + 0.888767I
−5.42509 + 4.45293I 0
u = −1.339550 − 0.224805I
a = 0.091229 − 1.306420I
b = −0.487922 − 0.888767I
−5.42509 − 4.45293I 0
u = 1.380100 + 0.123580I
a = −1.09435 − 2.36932I
b = −0.37266 − 1.42969I
−11.86110 + 2.15849I 0
u = 1.380100 − 0.123580I
a = −1.09435 + 2.36932I
b = −0.37266 + 1.42969I
−11.86110 − 2.15849I 0
u = 1.365220 + 0.261535I
a = 1.33626 + 2.41346I
b = −0.61664 + 1.35909I
−10.02730 − 9.55714I 0
u = 1.365220 − 0.261535I
a = 1.33626 − 2.41346I
b = −0.61664 − 1.35909I
−10.02730 + 9.55714I 0
u = −1.363890 + 0.319129I
a = −0.234330 − 0.481461I
b = −0.705464 + 0.206220I
−2.84821 + 7.30244I 0
u = −1.363890 − 0.319129I
a = −0.234330 + 0.481461I
b = −0.705464 − 0.206220I
−2.84821 − 7.30244I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40144
a = −0.385644
b = −0.577672
−7.10454 0
u = −0.087677 + 0.585925I
a = −1.96671 + 0.65542I
b = 0.433173 + 1.031780I
0.69910 + 2.52777I −5.84354 − 3.35799I
u = −0.087677 − 0.585925I
a = −1.96671 − 0.65542I
b = 0.433173 − 1.031780I
0.69910 − 2.52777I −5.84354 + 3.35799I
u = 0.563116
a = 0.509143
b = −0.313068
−0.958674 −9.85690
u = −1.40715 + 0.30877I
a = −0.99962 + 1.99298I
b = 0.120608 + 1.188840I
−7.16857 + 6.45126I 0
u = −1.40715 − 0.30877I
a = −0.99962 − 1.99298I
b = 0.120608 − 1.188840I
−7.16857 − 6.45126I 0
u = 0.124503 + 0.544345I
a = 1.27598 − 0.81112I
b = −0.260698 − 0.771913I
−0.80366 − 1.58561I −10.67225 + 2.90476I
u = 0.124503 − 0.544345I
a = 1.27598 + 0.81112I
b = −0.260698 + 0.771913I
−0.80366 + 1.58561I −10.67225 − 2.90476I
u = −1.40680 + 0.34051I
a = 1.26967 − 1.96871I
b = −0.455387 − 1.216770I
−5.97118 + 11.78330I 0
u = −1.40680 − 0.34051I
a = 1.26967 + 1.96871I
b = −0.455387 + 1.216770I
−5.97118 − 11.78330I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.41173 + 0.32636I
a = 0.451797 + 0.801134I
b = 1.251800 − 0.295347I
−8.68021 + 9.27069I 0
u = −1.41173 − 0.32636I
a = 0.451797 − 0.801134I
b = 1.251800 + 0.295347I
−8.68021 − 9.27069I 0
u = −1.41652 + 0.36230I
a = −1.32614 + 1.85531I
b = 0.68460 + 1.36460I
−12.1310 + 16.1617I 0
u = −1.41652 − 0.36230I
a = −1.32614 − 1.85531I
b = 0.68460 − 1.36460I
−12.1310 − 16.1617I 0
u = −1.45238 + 0.27357I
a = 0.98226 − 1.57277I
b = 0.26475 − 1.52039I
−15.2401 + 3.8156I 0
u = −1.45238 − 0.27357I
a = 0.98226 + 1.57277I
b = 0.26475 + 1.52039I
−15.2401 − 3.8156I 0
u = −1.47888 + 0.02352I
a = 0.11238 − 2.43472I
b = −0.196285 − 1.246890I
−11.09960 + 2.70583I 0
u = −1.47888 − 0.02352I
a = 0.11238 + 2.43472I
b = −0.196285 + 1.246890I
−11.09960 − 2.70583I 0
u = −1.48451
a = 0.899695
b = 1.29707
−13.2474 0
u = −0.051131 + 0.501827I
a = 1.30705 − 1.31645I
b = −0.963746 + 0.258016I
−1.87492 + 0.52113I −7.46007 + 0.33584I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.051131 − 0.501827I
a = 1.30705 + 1.31645I
b = −0.963746 − 0.258016I
−1.87492 − 0.52113I −7.46007 − 0.33584I
u = −1.51084 + 0.06009I
a = −0.09053 + 2.25061I
b = 0.52441 + 1.48832I
−18.1852 + 6.5334I 0
u = −1.51084 − 0.06009I
a = −0.09053 − 2.25061I
b = 0.52441 − 1.48832I
−18.1852 − 6.5334I 0
u = −0.346736 + 0.293540I
a = −1.47471 + 0.88660I
b = −0.407022 + 1.274040I
−6.45539 − 3.75624I −8.92208 + 2.37124I
u = −0.346736 − 0.293540I
a = −1.47471 − 0.88660I
b = −0.407022 − 1.274040I
−6.45539 + 3.75624I −8.92208 − 2.37124I
u = −0.109910 + 0.191162I
a = 2.62502 − 1.00223I
b = 0.221171 − 0.788369I
−0.464107 − 1.212900I −5.34512 + 5.07325I
u = −0.109910 − 0.191162I
a = 2.62502 + 1.00223I
b = 0.221171 + 0.788369I
−0.464107 + 1.212900I −5.34512 − 5.07325I
u = 0.164075
a = 6.48224
b = −0.479550
−2.12876 −0.110400
13
II. I
u
2
=
hb, u
7
+2u
6
−2u
5
−4u
4
+2u
3
+u
2
+a−u+3, u
8
+u
7
−3u
6
−2u
5
+3u
4
+2u−1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
u
a
6
=
1
u
2
a
9
=
−u
−u
3
+ u
a
11
=
−u
7
− 2u
6
+ 2u
5
+ 4u
4
− 2u
3
− u
2
+ u − 3
0
a
4
=
1
0
a
12
=
−u
7
− 2u
6
+ 2u
5
+ 4u
4
− 2u
3
− u
2
+ u − 3
0
a
10
=
−u
7
− 2u
6
+ 2u
5
+ 4u
4
− 2u
3
− u
2
− 3
−u
3
+ u
a
3
=
−u
4
+ u
2
+ 1
−u
6
+ 2u
4
− u
2
a
7
=
u
u
a
2
=
u
7
− 2u
5
+ 2u
u
7
− u
6
− 2u
5
+ 3u
4
− 2u
2
+ 2u − 1
a
1
=
u
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
7
− 10u
6
+ 7u
5
+ 25u
4
− 9u
3
− 12u
2
+ 8u − 25
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
c
2
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
4
, c
11
u
8
c
5
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
6
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1
c
7
, c
8
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
c
9
, c
10
(u − 1)
8
c
12
(u + 1)
8
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
c
2
, c
6
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
4
, c
11
y
8
c
5
, c
7
, c
8
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
9
, c
10
, c
12
(y −1)
8
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = 0.281371 − 1.128550I
b = 0
−2.68559 − 1.13123I −9.56807 + 0.79885I
u = 1.180120 − 0.268597I
a = 0.281371 + 1.128550I
b = 0
−2.68559 + 1.13123I −9.56807 − 0.79885I
u = 0.108090 + 0.747508I
a = −0.208670 + 0.825203I
b = 0
0.51448 − 2.57849I −6.42531 + 3.25625I
u = 0.108090 − 0.747508I
a = −0.208670 − 0.825203I
b = 0
0.51448 + 2.57849I −6.42531 − 3.25625I
u = −1.37100
a = −0.829189
b = 0
−8.14766 −20.0060
u = −1.334530 + 0.318930I
a = −0.284386 − 0.605794I
b = 0
−4.02461 + 6.44354I −11.71592 − 3.92092I
u = −1.334530 − 0.318930I
a = −0.284386 + 0.605794I
b = 0
−4.02461 − 6.44354I −11.71592 + 3.92092I
u = 0.463640
a = −2.74744
b = 0
−2.48997 −23.5750
17
III. I
u
3
= ha
4
− a
3
+ a
2
+ b − 2a + 1, a
5
− a
4
+ a
3
− 2a
2
+ a − 1, u − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
0
1
a
6
=
1
1
a
9
=
−1
0
a
11
=
a
−a
4
+ a
3
− a
2
+ 2a − 1
a
4
=
0
a
4
− a − 1
a
12
=
a
−a
3
+ 1
a
10
=
a
4
− a − 1
a
3
− a
2
− 2
a
3
=
a
4
− a − 1
a
4
− a − 1
a
7
=
1
1
a
2
=
a
4
− a − 1
a
4
− a − 1
a
1
=
a
4
− a − 1
a
4
− a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5a
4
+ 5a
3
+ 7a − 14
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
5
c
3
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
4
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
5
(u − 1)
5
c
7
, c
8
(u + 1)
5
c
9
, c
10
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
11
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
12
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
5
c
3
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
4
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
5
, c
7
, c
8
(y −1)
5
c
9
, c
10
, c
12
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.428550 + 1.039280I
b = 0.339110 + 0.822375I
−1.97403 + 1.53058I −10.50099 − 3.45976I
u = 1.00000
a = −0.428550 − 1.039280I
b = 0.339110 − 0.822375I
−1.97403 − 1.53058I −10.50099 + 3.45976I
u = 1.00000
a = 0.276511 + 0.728237I
b = −0.455697 + 1.200150I
−7.51750 − 4.40083I −14.3774 + 5.8297I
u = 1.00000
a = 0.276511 − 0.728237I
b = −0.455697 − 1.200150I
−7.51750 + 4.40083I −14.3774 − 5.8297I
u = 1.00000
a = 1.30408
b = −0.766826
−4.04602 −8.24330
21
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
5
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
88
+ 36u
87
+ ··· + 16896u + 1024)
c
2
u
5
(u
8
− u
7
+ ··· + 2u − 1)(u
88
− 2u
87
+ ··· + 64u − 32)
c
3
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
· (u
88
− 3u
87
+ ··· + 49703u − 30649)
c
4
u
8
(u
5
+ u
4
+ ··· + u + 1)(u
88
− 2u
87
+ ··· − 1664u − 256)
c
5
((u − 1)
5
)(u
8
+ u
7
+ ··· + 2u − 1)(u
88
− 7u
87
+ ··· + 5u + 1)
c
6
u
5
(u
8
+ u
7
+ ··· − 2u − 1)(u
88
− 2u
87
+ ··· + 64u − 32)
c
7
, c
8
((u + 1)
5
)(u
8
− u
7
+ ··· − 2u − 1)(u
88
− 7u
87
+ ··· + 5u + 1)
c
9
, c
10
((u − 1)
8
)(u
5
+ u
4
+ ··· + u − 1)(u
88
− 10u
87
+ ··· − 13u + 1)
c
11
u
8
(u
5
− u
4
+ ··· + u − 1)(u
88
− 2u
87
+ ··· − 1664u − 256)
c
12
((u + 1)
8
)(u
5
− u
4
+ ··· + u + 1)(u
88
− 10u
87
+ ··· − 13u + 1)
22
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
5
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
88
+ 24y
87
+ ··· − 10092544y + 1048576)
c
2
, c
6
y
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
88
− 36y
87
+ ··· − 16896y + 1024)
c
3
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
88
− 37y
87
+ ··· − 880685877y + 939361201)
c
4
, c
11
y
8
(y
5
+ 3y
4
+ ··· − y −1)(y
88
+ 54y
87
+ ··· − 49152y + 65536)
c
5
, c
7
, c
8
(y −1)
5
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
88
− 77y
87
+ ··· − 7y + 1)
c
9
, c
10
, c
12
((y −1)
8
)(y
5
− 5y
4
+ ··· − y −1)(y
88
− 86y
87
+ ··· − 85y + 1)
23
