12a
0074
(K12a
0074
)
A knot diagram
1
Linearized knot diagam
3 5 7 11 2 10 12 4 6 9 1 8
Solving Sequence
6,9
10 7
2,11
5 3 1 4 8 12
c
9
c
6
c
10
c
5
c
2
c
1
c
4
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h21u
30
− 29u
29
+ ··· + 128b − 34, −55u
30
+ 76u
29
+ ··· + 64a − 39, u
31
− 2u
30
+ ··· + 3u
2
+ 1i
I
u
2
= h2.72739 × 10
139
u
99
+ 1.28011 × 10
140
u
98
+ ··· + 1.15126 × 10
139
b + 3.66899 × 10
139
,
− 1.38967 × 10
138
u
99
− 9.46861 × 10
138
u
98
+ ··· + 1.15126 × 10
139
a − 5.17903 × 10
138
,
u
100
+ 5u
99
+ ··· + 2u + 1i
I
u
3
= h−au + 2b + a + 2u, a
2
+ au + a + u + 2, u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 135 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
= h21u
30
− 29u
29
+ · · · + 128b − 34, −55u
30
+ 76u
29
+ · · · + 64a −
39, u
31
− 2u
30
+ · · · + 3u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
7
=
u
−u
3
+ u
a
2
=
0.859375u
30
− 1.18750u
29
+ ··· + 0.750000u + 0.609375
−0.164063u
30
+ 0.226563u
29
+ ··· + 1.42969u + 0.265625
a
11
=
−u
2
+ 1
−u
2
a
5
=
3
64
u
30
+
3
16
u
29
+ ··· −
9
8
u +
59
64
−0.335938u
30
+ 0.460938u
29
+ ··· + 1.25781u + 0.296875
a
3
=
−0.0781250u
30
+ 0.187500u
29
+ ··· + 0.375000u + 1.29688
−0.914063u
30
+ 1.53906u
29
+ ··· + 1.74219u + 0.453125
a
1
=
−
1
2
u
30
+
1
2
u
29
+ ··· +
1
2
u + 1
−
1
2
u
30
+ u
29
+ ··· − 4u
2
−
1
2
a
4
=
0.0625000u
30
+ 0.320313u
29
+ ··· + 0.179688u + 0.867188
−0.750000u
30
+ 1.31250u
29
+ ··· + 1.68750u + 0.437500
a
8
=
1
2
u
30
−
3
2
u
29
+ ··· −
1
2
u
2
−
5
2
u
1
2
u
30
− u
29
+ ··· − u −
1
2
a
12
=
−
1
2
u
29
+
3
2
u
28
+ ··· +
1
2
u +
3
2
−
1
2
u
30
+
1
2
u
29
+ ··· −
3
2
u
2
+
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
159
128
u
30
−
693
256
u
29
+ ··· +
1725
256
u +
827
256
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 13u
30
+ ··· + 6432u − 256
c
2
, c
5
u
31
− u
30
+ ··· + 88u + 16
c
3
, c
4
16(16u
31
+ 8u
30
+ ··· − 4u
2
− 1)
c
6
, c
7
, c
9
c
12
u
31
+ 2u
30
+ ··· − 3u
2
− 1
c
8
u
31
− 5u
30
+ ··· + 6144u − 1024
c
10
, c
11
u
31
− 18u
30
+ ··· − 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 9y
30
+ ··· + 52675072y −65536
c
2
, c
5
y
31
+ 13y
30
+ ··· + 6432y −256
c
3
, c
4
256(256y
31
+ 192y
30
+ ··· − 8y −1)
c
6
, c
7
, c
9
c
12
y
31
− 18y
30
+ ··· − 6y −1
c
8
y
31
− 5y
30
+ ··· − 7995392y −1048576
c
10
, c
11
y
31
− 6y
30
+ ··· + 122y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.936680 + 0.338613I
a = 0.582188 + 1.079190I
b = 0.048866 + 0.688489I
3.50074 − 0.90322I 13.05413 + 1.36085I
u = −0.936680 − 0.338613I
a = 0.582188 − 1.079190I
b = 0.048866 − 0.688489I
3.50074 + 0.90322I 13.05413 − 1.36085I
u = 0.610112 + 0.779812I
a = 1.106790 + 0.630784I
b = 2.03656 − 0.74980I
−7.60447 + 0.14654I −4.01564 − 1.65888I
u = 0.610112 − 0.779812I
a = 1.106790 − 0.630784I
b = 2.03656 + 0.74980I
−7.60447 − 0.14654I −4.01564 + 1.65888I
u = 0.449445 + 0.919135I
a = −0.743911 − 1.014000I
b = −1.45563 + 0.84618I
−4.77494 − 8.27043I −1.01784 + 4.50252I
u = 0.449445 − 0.919135I
a = −0.743911 + 1.014000I
b = −1.45563 − 0.84618I
−4.77494 + 8.27043I −1.01784 − 4.50252I
u = 0.990236 + 0.401727I
a = −0.892639 + 0.404991I
b = −0.264917 + 0.891534I
4.39913 + 4.26165I 14.5933 − 6.3356I
u = 0.990236 − 0.401727I
a = −0.892639 − 0.404991I
b = −0.264917 − 0.891534I
4.39913 − 4.26165I 14.5933 + 6.3356I
u = 0.434243 + 0.819908I
a = 0.738201 − 0.621086I
b = 0.265245 − 0.383053I
−2.40209 − 2.98251I 1.29241 + 0.67097I
u = 0.434243 − 0.819908I
a = 0.738201 + 0.621086I
b = 0.265245 + 0.383053I
−2.40209 + 2.98251I 1.29241 − 0.67097I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.002380 + 0.466614I
a = 1.155680 − 0.270045I
b = 1.46383 + 0.71776I
3.57794 − 7.81275I 11.7195 + 11.3359I
u = −1.002380 − 0.466614I
a = 1.155680 + 0.270045I
b = 1.46383 − 0.71776I
3.57794 + 7.81275I 11.7195 − 11.3359I
u = 1.005510 + 0.542400I
a = −1.054370 − 0.734239I
b = −2.41506 + 1.08769I
0.66388 + 10.41550I 6.1852 − 13.0772I
u = 1.005510 − 0.542400I
a = −1.054370 + 0.734239I
b = −2.41506 − 1.08769I
0.66388 − 10.41550I 6.1852 + 13.0772I
u = 0.766410 + 0.276505I
a = −0.25730 + 1.48498I
b = 0.363756 − 0.337678I
1.16092 − 1.09032I 8.12696 + 0.09273I
u = 0.766410 − 0.276505I
a = −0.25730 − 1.48498I
b = 0.363756 + 0.337678I
1.16092 + 1.09032I 8.12696 − 0.09273I
u = −1.021490 + 0.642260I
a = 0.582856 − 0.986168I
b = 2.02101 + 0.91098I
−5.08603 − 10.58260I 0.75987 + 9.57565I
u = −1.021490 − 0.642260I
a = 0.582856 + 0.986168I
b = 2.02101 − 0.91098I
−5.08603 + 10.58260I 0.75987 − 9.57565I
u = −0.579199 + 0.524845I
a = −0.61005 + 1.48157I
b = −1.56698 − 0.68703I
−1.92067 + 1.62049I −0.67303 − 1.57224I
u = −0.579199 − 0.524845I
a = −0.61005 − 1.48157I
b = −1.56698 + 0.68703I
−1.92067 − 1.62049I −0.67303 + 1.57224I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.114480 + 0.634528I
a = −0.496941 − 0.671776I
b = −0.149359 − 0.970560I
1.63726 − 13.87830I 6.56033 + 8.55323I
u = −1.114480 − 0.634528I
a = −0.496941 + 0.671776I
b = −0.149359 + 0.970560I
1.63726 + 13.87830I 6.56033 − 8.55323I
u = 1.303030 + 0.092850I
a = 0.555582 + 0.574307I
b = 1.230900 − 0.232581I
8.75635 + 2.55545I 15.7194 − 2.3286I
u = 1.303030 − 0.092850I
a = 0.555582 − 0.574307I
b = 1.230900 + 0.232581I
8.75635 − 2.55545I 15.7194 + 2.3286I
u = −0.693108
a = −0.270559
b = −0.646343
1.19574 7.87080
u = −1.134090 + 0.668227I
a = −0.893764 + 0.503768I
b = −2.88013 − 0.89189I
−0.6287 − 19.8896I 4.17991 + 11.79937I
u = −1.134090 − 0.668227I
a = −0.893764 − 0.503768I
b = −2.88013 + 0.89189I
−0.6287 + 19.8896I 4.17991 − 11.79937I
u = 1.60823 + 0.02683I
a = 0.310056 − 0.550818I
b = 1.162700 + 0.700629I
8.90816 − 2.08408I 29.0927 + 62.0574I
u = 1.60823 − 0.02683I
a = 0.310056 + 0.550818I
b = 1.162700 − 0.700629I
8.90816 + 2.08408I 29.0927 − 62.0574I
u = −0.032351 + 0.347236I
a = 2.05290 + 0.96045I
b = 0.212373 + 0.529053I
−0.093331 − 1.383200I −0.26260 + 4.88905I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.032351 − 0.347236I
a = 2.05290 − 0.96045I
b = 0.212373 − 0.529053I
−0.093331 + 1.383200I −0.26260 − 4.88905I
8
II. I
u
2
= h2.73 × 10
139
u
99
+ 1.28 × 10
140
u
98
+ · · · + 1.15 × 10
139
b + 3.67 ×
10
139
, −1.39 × 10
138
u
99
− 9.47 × 10
138
u
98
+ · · · + 1.15 × 10
139
a − 5.18 ×
10
138
, u
100
+ 5u
99
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
7
=
u
−u
3
+ u
a
2
=
0.120709u
99
+ 0.822455u
98
+ ··· + 2.52213u + 0.449857
−2.36904u
99
− 11.1192u
98
+ ··· − 0.977338u − 3.18693
a
11
=
−u
2
+ 1
−u
2
a
5
=
−0.488022u
99
− 2.16943u
98
+ ··· + 3.31259u − 0.818863
−2.16817u
99
− 9.37783u
98
+ ··· − 0.240999u − 1.66392
a
3
=
−0.373898u
99
− 1.57574u
98
+ ··· + 5.49285u − 0.603726
−2.25516u
99
− 9.47053u
98
+ ··· − 0.392895u − 1.57015
a
1
=
0.0996443u
99
− 0.000163284u
98
+ ··· − 0.496826u − 0.698151
−0.844919u
99
− 4.49402u
98
+ ··· − 2.62234u − 2.17334
a
4
=
0.308833u
99
+ 2.43088u
98
+ ··· + 6.45605u + 0.901556
0.332759u
99
+ 1.55082u
98
+ ··· + 2.43896u + 0.528091
a
8
=
2.17334u
99
+ 10.0218u
98
+ ··· + 3.43426u + 1.72433
0.498385u
99
+ 1.78125u
98
+ ··· + 0.897440u + 0.0996443
a
12
=
−0.904282u
99
− 4.89024u
98
+ ··· − 4.39589u − 0.802382
−1.62929u
99
− 7.37061u
98
+ ··· − 4.26428u − 1.54217
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.53328u
99
− 25.3817u
98
+ ··· − 11.0157u − 1.28022
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
50
+ 22u
49
+ ··· − 26u + 1)
2
c
2
, c
5
(u
50
+ 2u
49
+ ··· + 10u + 1)
2
c
3
, c
4
u
100
+ 7u
99
+ ··· + 1086100u + 143123
c
6
, c
7
, c
9
c
12
u
100
− 5u
99
+ ··· − 2u + 1
c
8
(u
50
+ 2u
49
+ ··· + 4u + 1)
2
c
10
, c
11
u
100
− 41u
99
+ ··· + 30u
2
+ 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
50
+ 14y
49
+ ··· − 1050y + 1)
2
c
2
, c
5
(y
50
+ 22y
49
+ ··· − 26y + 1)
2
c
3
, c
4
y
100
− 33y
99
+ ··· + 855156748636y + 20484193129
c
6
, c
7
, c
9
c
12
y
100
− 41y
99
+ ··· + 30y
2
+ 1
c
8
(y
50
− 10y
49
+ ··· + 10y + 1)
2
c
10
, c
11
y
100
+ 35y
99
+ ··· + 60y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805392 + 0.565666I
a = 0.137398 + 0.910966I
b = 3.71411 − 1.57836I
−0.21807 + 2.45541I 0
u = 0.805392 − 0.565666I
a = 0.137398 − 0.910966I
b = 3.71411 + 1.57836I
−0.21807 − 2.45541I 0
u = 0.870372 + 0.532948I
a = −0.844290 − 0.471246I
b = −4.88150 + 8.11072I
−0.03678 + 1.97726I 0
u = 0.870372 − 0.532948I
a = −0.844290 + 0.471246I
b = −4.88150 − 8.11072I
−0.03678 − 1.97726I 0
u = 0.897882 + 0.487726I
a = −0.014174 + 0.965644I
b = −1.09023 + 8.22715I
−0.03678 − 1.97726I 0
u = 0.897882 − 0.487726I
a = −0.014174 − 0.965644I
b = −1.09023 − 8.22715I
−0.03678 + 1.97726I 0
u = −0.464448 + 0.914988I
a = 0.718491 − 1.066280I
b = 1.50650 + 0.81554I
−2.6715 + 14.0778I 0
u = −0.464448 − 0.914988I
a = 0.718491 + 1.066280I
b = 1.50650 − 0.81554I
−2.6715 − 14.0778I 0
u = 0.345540 + 0.905171I
a = −0.888803 − 0.791753I
b = −1.21930 + 0.92283I
−5.90869 − 3.57059I 0
u = 0.345540 − 0.905171I
a = −0.888803 + 0.791753I
b = −1.21930 − 0.92283I
−5.90869 + 3.57059I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.599800 + 0.750932I
a = −0.150280 − 0.616290I
b = 0.303124 + 0.349454I
−1.29692 − 5.01538I 0
u = −0.599800 − 0.750932I
a = −0.150280 + 0.616290I
b = 0.303124 − 0.349454I
−1.29692 + 5.01538I 0
u = −0.592726 + 0.753085I
a = −1.139510 + 0.755454I
b = −2.06616 − 0.74386I
−6.37316 + 5.28105I 0
u = −0.592726 − 0.753085I
a = −1.139510 − 0.755454I
b = −2.06616 + 0.74386I
−6.37316 − 5.28105I 0
u = 0.995575 + 0.307242I
a = −0.329780 − 0.755301I
b = 0.892626 − 0.159113I
−0.59812 + 5.40527I 0
u = 0.995575 − 0.307242I
a = −0.329780 + 0.755301I
b = 0.892626 + 0.159113I
−0.59812 − 5.40527I 0
u = −0.963434 + 0.399072I
a = 0.512485 + 0.510292I
b = −0.011941 + 0.888950I
2.04137 − 1.36627I 0
u = −0.963434 − 0.399072I
a = 0.512485 − 0.510292I
b = −0.011941 − 0.888950I
2.04137 + 1.36627I 0
u = 0.975907 + 0.372400I
a = −0.772650 + 0.760018I
b = −0.069798 + 0.950611I
4.18629 − 1.80724I 0
u = 0.975907 − 0.372400I
a = −0.772650 − 0.760018I
b = −0.069798 − 0.950611I
4.18629 + 1.80724I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.941662 + 0.467528I
a = 0.001522 + 0.862430I
b = −0.70376 + 3.30787I
−0.21807 − 2.45541I 0
u = −0.941662 − 0.467528I
a = 0.001522 − 0.862430I
b = −0.70376 − 3.30787I
−0.21807 + 2.45541I 0
u = −0.438799 + 0.840334I
a = −0.815677 − 0.656198I
b = −0.308347 − 0.529533I
−0.38497 + 8.39332I 0
u = −0.438799 − 0.840334I
a = −0.815677 + 0.656198I
b = −0.308347 + 0.529533I
−0.38497 − 8.39332I 0
u = −0.895331 + 0.277953I
a = 0.49067 + 1.34070I
b = −0.213926 + 0.271473I
2.41061 + 4.79603I 0
u = −0.895331 − 0.277953I
a = 0.49067 − 1.34070I
b = −0.213926 − 0.271473I
2.41061 − 4.79603I 0
u = −0.452534 + 0.971496I
a = 0.638057 − 0.904792I
b = 1.35669 + 0.76688I
1.58339 + 5.46834I 0
u = −0.452534 − 0.971496I
a = 0.638057 + 0.904792I
b = 1.35669 − 0.76688I
1.58339 − 5.46834I 0
u = −0.362849 + 0.852585I
a = −0.821536 − 0.441844I
b = −0.638247 − 0.245214I
3.03278 + 0.55194I 0
u = −0.362849 − 0.852585I
a = −0.821536 + 0.441844I
b = −0.638247 + 0.245214I
3.03278 − 0.55194I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972507 + 0.459567I
a = −0.932367 − 0.289538I
b = −1.320190 − 0.016880I
1.69220 + 4.35370I 0
u = 0.972507 − 0.459567I
a = −0.932367 + 0.289538I
b = −1.320190 + 0.016880I
1.69220 − 4.35370I 0
u = 0.845214 + 0.350717I
a = −0.269449 + 1.229150I
b = −0.360530 − 0.128486I
0.96274 − 1.04006I 0
u = 0.845214 − 0.350717I
a = −0.269449 − 1.229150I
b = −0.360530 + 0.128486I
0.96274 + 1.04006I 0
u = −0.996807 + 0.435728I
a = 1.040630 − 0.000544I
b = 0.811839 + 0.685261I
4.18629 − 1.80724I 0
u = −0.996807 − 0.435728I
a = 1.040630 + 0.000544I
b = 0.811839 − 0.685261I
4.18629 + 1.80724I 0
u = −0.940675 + 0.571103I
a = 0.797850 − 0.614339I
b = 2.78678 + 1.76470I
−0.74785 − 5.64906I 0
u = −0.940675 − 0.571103I
a = 0.797850 + 0.614339I
b = 2.78678 − 1.76470I
−0.74785 + 5.64906I 0
u = 0.640859 + 0.895863I
a = 1.012390 + 0.267051I
b = 1.88350 − 0.68017I
−5.90869 + 3.57059I 0
u = 0.640859 − 0.895863I
a = 1.012390 − 0.267051I
b = 1.88350 + 0.68017I
−5.90869 − 3.57059I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.704941 + 0.555049I
a = −0.390234 + 1.107560I
b = −1.92721 − 1.30059I
−1.47932 + 1.10651I 0
u = −0.704941 − 0.555049I
a = −0.390234 − 1.107560I
b = −1.92721 + 1.30059I
−1.47932 − 1.10651I 0
u = −0.958259 + 0.559233I
a = −0.136771 − 0.079819I
b = −1.065870 + 0.002940I
−0.223424 0
u = −0.958259 − 0.559233I
a = −0.136771 + 0.079819I
b = −1.065870 − 0.002940I
−0.223424 0
u = −0.287367 + 0.842417I
a = 1.009560 − 0.693922I
b = 1.04412 + 0.95613I
−4.78948 − 2.42792I 0
u = −0.287367 − 0.842417I
a = 1.009560 + 0.693922I
b = 1.04412 − 0.95613I
−4.78948 + 2.42792I 0
u = −0.900705 + 0.652680I
a = 0.520199 − 0.570395I
b = 1.27971 + 1.85358I
−0.59812 − 5.40527I 0
u = −0.900705 − 0.652680I
a = 0.520199 + 0.570395I
b = 1.27971 − 1.85358I
−0.59812 + 5.40527I 0
u = 0.508428 + 0.727312I
a = 0.383289 − 0.548299I
b = −0.0213567 + 0.1030520I
−3.00190 0
u = 0.508428 − 0.727312I
a = 0.383289 + 0.548299I
b = −0.0213567 − 0.1030520I
−3.00190 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.992128 + 0.505162I
a = −1.083540 − 0.520726I
b = −2.20138 + 0.72198I
2.41061 + 4.79603I 0
u = 0.992128 − 0.505162I
a = −1.083540 + 0.520726I
b = −2.20138 − 0.72198I
2.41061 − 4.79603I 0
u = −0.597441 + 0.939870I
a = −1.052590 + 0.123829I
b = −1.76623 − 0.67472I
−3.40724 − 9.26124I 0
u = −0.597441 − 0.939870I
a = −1.052590 − 0.123829I
b = −1.76623 + 0.67472I
−3.40724 + 9.26124I 0
u = −0.985911 + 0.554260I
a = 0.941721 − 0.708633I
b = 2.53950 + 1.14071I
−0.73924 − 6.06918I 0
u = −0.985911 − 0.554260I
a = 0.941721 + 0.708633I
b = 2.53950 − 1.14071I
−0.73924 + 6.06918I 0
u = −0.804423 + 0.810841I
a = −0.683704 + 0.364209I
b = −2.01847 − 0.56368I
−0.915526 − 0.076578I 0
u = −0.804423 − 0.810841I
a = −0.683704 − 0.364209I
b = −2.01847 + 0.56368I
−0.915526 + 0.076578I 0
u = −1.196350 + 0.125224I
a = −0.604684 + 0.388170I
b = −1.214590 − 0.044805I
3.03278 + 0.55194I 0
u = −1.196350 − 0.125224I
a = −0.604684 − 0.388170I
b = −1.214590 + 0.044805I
3.03278 − 0.55194I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.205060 + 0.085428I
a = 0.703335 + 0.405377I
b = 1.157630 − 0.080797I
5.29694 − 5.97751I 0
u = 1.205060 − 0.085428I
a = 0.703335 − 0.405377I
b = 1.157630 + 0.080797I
5.29694 + 5.97751I 0
u = 1.017910 + 0.659027I
a = −0.511569 − 0.951740I
b = −1.86748 + 0.89291I
−6.37316 + 5.28105I 0
u = 1.017910 − 0.659027I
a = −0.511569 + 0.951740I
b = −1.86748 − 0.89291I
−6.37316 − 5.28105I 0
u = −1.174210 + 0.323836I
a = −0.016603 − 0.726219I
b = −0.723369 + 0.106438I
−0.915526 + 0.076578I 0
u = −1.174210 − 0.323836I
a = −0.016603 + 0.726219I
b = −0.723369 − 0.106438I
−0.915526 − 0.076578I 0
u = 1.073530 + 0.580651I
a = 0.298381 − 0.400600I
b = 0.662813 − 0.460597I
−1.29692 + 5.01538I 0
u = 1.073530 − 0.580651I
a = 0.298381 + 0.400600I
b = 0.662813 + 0.460597I
−1.29692 − 5.01538I 0
u = 1.009330 + 0.740780I
a = −0.306559 − 0.815188I
b = −1.29785 + 0.84084I
−4.78948 + 2.42792I 0
u = 1.009330 − 0.740780I
a = −0.306559 + 0.815188I
b = −1.29785 − 0.84084I
−4.78948 − 2.42792I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.111390 + 0.627622I
a = 0.467225 − 0.621515I
b = 0.250207 − 0.878108I
−0.38497 + 8.39332I 0
u = 1.111390 − 0.627622I
a = 0.467225 + 0.621515I
b = 0.250207 + 0.878108I
−0.38497 − 8.39332I 0
u = 1.279170 + 0.025724I
a = 0.491611 − 0.840663I
b = 1.073100 + 0.269183I
3.73617 − 11.46140I 0
u = 1.279170 − 0.025724I
a = 0.491611 + 0.840663I
b = 1.073100 − 0.269183I
3.73617 + 11.46140I 0
u = −1.132260 + 0.619924I
a = −0.348291 − 0.675201I
b = −0.074295 − 0.616385I
5.29694 − 5.97751I 0
u = −1.132260 − 0.619924I
a = −0.348291 + 0.675201I
b = −0.074295 + 0.616385I
5.29694 + 5.97751I 0
u = 0.502314 + 0.490863I
a = 0.66915 + 1.77608I
b = 1.45721 − 0.37222I
−0.73924 − 6.06918I 2.41006 + 7.32858I
u = 0.502314 − 0.490863I
a = 0.66915 − 1.77608I
b = 1.45721 + 0.37222I
−0.73924 + 6.06918I 2.41006 − 7.32858I
u = −1.302470 + 0.047049I
a = −0.424085 − 0.805603I
b = −1.056750 + 0.299631I
1.58339 + 5.46834I 0
u = −1.302470 − 0.047049I
a = −0.424085 + 0.805603I
b = −1.056750 − 0.299631I
1.58339 − 5.46834I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.140050 + 0.665009I
a = 0.860159 + 0.509302I
b = 2.85078 − 0.81091I
−2.6715 + 14.0778I 0
u = 1.140050 − 0.665009I
a = 0.860159 − 0.509302I
b = 2.85078 + 0.81091I
−2.6715 − 14.0778I 0
u = −1.073870 + 0.793669I
a = 0.175427 − 0.796181I
b = 1.033190 + 0.651248I
−1.98760 + 2.97707I 0
u = −1.073870 − 0.793669I
a = 0.175427 + 0.796181I
b = 1.033190 − 0.651248I
−1.98760 − 2.97707I 0
u = −1.152470 + 0.680824I
a = −0.822217 + 0.436383I
b = −2.64936 − 0.82205I
3.73617 − 11.46140I 0
u = −1.152470 − 0.680824I
a = −0.822217 − 0.436383I
b = −2.64936 + 0.82205I
3.73617 + 11.46140I 0
u = 1.179930 + 0.642534I
a = 0.713472 + 0.512611I
b = 2.64710 − 0.49670I
−3.40724 + 9.26124I 0
u = 1.179930 − 0.642534I
a = 0.713472 − 0.512611I
b = 2.64710 + 0.49670I
−3.40724 − 9.26124I 0
u = −1.220660 + 0.604182I
a = −0.615660 + 0.509771I
b = −2.45269 − 0.31426I
−1.98760 − 2.97707I 0
u = −1.220660 − 0.604182I
a = −0.615660 − 0.509771I
b = −2.45269 + 0.31426I
−1.98760 + 2.97707I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.552531 + 0.276448I
a = −1.32704 − 1.20661I
b = 0.818403 + 0.846569I
−0.74785 + 5.64906I 4.57569 − 5.94359I
u = 0.552531 − 0.276448I
a = −1.32704 + 1.20661I
b = 0.818403 − 0.846569I
−0.74785 − 5.64906I 4.57569 + 5.94359I
u = −0.387777 + 0.346074I
a = 1.76529 − 0.99655I
b = −0.308640 + 0.934645I
−1.47932 − 1.10651I 1.22803 + 1.09399I
u = −0.387777 − 0.346074I
a = 1.76529 + 0.99655I
b = −0.308640 − 0.934645I
−1.47932 + 1.10651I 1.22803 − 1.09399I
u = −0.034900 + 0.411538I
a = −0.55000 + 1.74123I
b = −0.202925 + 0.724869I
2.04137 − 1.36627I 7.53684 + 1.88972I
u = −0.034900 − 0.411538I
a = −0.55000 − 1.74123I
b = −0.202925 − 0.724869I
2.04137 + 1.36627I 7.53684 − 1.88972I
u = −0.125790 + 0.375790I
a = −1.07942 + 2.42011I
b = −0.547317 + 0.575101I
1.69220 + 4.35370I 5.21676 − 6.57113I
u = −0.125790 − 0.375790I
a = −1.07942 − 2.42011I
b = −0.547317 − 0.575101I
1.69220 − 4.35370I 5.21676 + 6.57113I
u = 0.267856 + 0.279357I
a = 0.58318 + 2.91753I
b = 0.710804 + 0.143443I
0.96274 − 1.04006I 3.85927 − 1.45378I
u = 0.267856 − 0.279357I
a = 0.58318 − 2.91753I
b = 0.710804 − 0.143443I
0.96274 + 1.04006I 3.85927 + 1.45378I
21
III. I
u
3
= h−au + 2b + a + 2u, a
2
+ au + a + u + 2, u
2
+ u − 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u − 1
a
7
=
u
−u + 1
a
2
=
a
1
2
au −
1
2
a − u
a
11
=
u
u − 1
a
5
=
a + u + 1
−
1
2
au +
1
2
a +
1
2
u
a
3
=
a + u + 1
1
2
au −
1
2
a −
1
2
u
a
1
=
0
−u
a
4
=
1
2
au + a + u +
3
2
0
a
8
=
1
0
a
12
=
u
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
187
4
au + 34a + 32u − 10
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
16(16u
4
− 8u
3
+ 8u
2
+ 2u + 1)
c
4
16(16u
4
+ 8u
3
+ 8u
2
− 2u + 1)
c
6
, c
7
(u
2
− u − 1)
2
c
8
u
4
c
9
, c
12
(u
2
+ u − 1)
2
c
10
(u
2
− 3u + 1)
2
c
11
(u
2
+ 3u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
2
c
3
, c
4
256(256y
4
+ 192y
3
+ 128y
2
+ 12y + 1)
c
6
, c
7
, c
9
c
12
(y
2
− 3y + 1)
2
c
8
y
4
c
10
, c
11
(y
2
− 7y + 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.80902 + 1.40126I
b = −0.463525 − 0.267617I
0.98696 − 2.02988I 5.64551 + 7.15610I
u = 0.618034
a = −0.80902 − 1.40126I
b = −0.463525 + 0.267617I
0.98696 + 2.02988I 5.64551 − 7.15610I
u = −1.61803
a = 0.309017 + 0.535233I
b = 1.213530 − 0.700629I
8.88264 + 2.02988I −27.8955 + 58.6846I
u = −1.61803
a = 0.309017 − 0.535233I
b = 1.213530 + 0.700629I
8.88264 − 2.02988I −27.8955 − 58.6846I
25
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
31
+ 13u
30
+ ··· + 6432u − 256)
· (u
50
+ 22u
49
+ ··· − 26u + 1)
2
c
2
((u
2
+ u + 1)
2
)(u
31
− u
30
+ ··· + 88u + 16)
· (u
50
+ 2u
49
+ ··· + 10u + 1)
2
c
3
256(16u
4
− 8u
3
+ ··· + 2u + 1)(16u
31
+ 8u
30
+ ··· − 4u
2
− 1)
· (u
100
+ 7u
99
+ ··· + 1086100u + 143123)
c
4
256(16u
4
+ 8u
3
+ ··· − 2u + 1)(16u
31
+ 8u
30
+ ··· − 4u
2
− 1)
· (u
100
+ 7u
99
+ ··· + 1086100u + 143123)
c
5
((u
2
− u + 1)
2
)(u
31
− u
30
+ ··· + 88u + 16)
· (u
50
+ 2u
49
+ ··· + 10u + 1)
2
c
6
, c
7
((u
2
− u − 1)
2
)(u
31
+ 2u
30
+ ··· − 3u
2
− 1)(u
100
− 5u
99
+ ··· − 2u + 1)
c
8
u
4
(u
31
− 5u
30
+ ··· + 6144u − 1024)(u
50
+ 2u
49
+ ··· + 4u + 1)
2
c
9
, c
12
((u
2
+ u − 1)
2
)(u
31
+ 2u
30
+ ··· − 3u
2
− 1)(u
100
− 5u
99
+ ··· − 2u + 1)
c
10
((u
2
− 3u + 1)
2
)(u
31
− 18u
30
+ ··· − 6u − 1)
· (u
100
− 41u
99
+ ··· + 30u
2
+ 1)
c
11
((u
2
+ 3u + 1)
2
)(u
31
− 18u
30
+ ··· − 6u − 1)
· (u
100
− 41u
99
+ ··· + 30u
2
+ 1)
26
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
31
+ 9y
30
+ ··· + 52675072y −65536)
· (y
50
+ 14y
49
+ ··· − 1050y + 1)
2
c
2
, c
5
((y
2
+ y + 1)
2
)(y
31
+ 13y
30
+ ··· + 6432y −256)
· (y
50
+ 22y
49
+ ··· − 26y + 1)
2
c
3
, c
4
65536(256y
4
+ 192y
3
+ 128y
2
+ 12y + 1)
· (256y
31
+ 192y
30
+ ··· − 8y −1)
· (y
100
− 33y
99
+ ··· + 855156748636y + 20484193129)
c
6
, c
7
, c
9
c
12
((y
2
− 3y + 1)
2
)(y
31
− 18y
30
+ ··· − 6y −1)
· (y
100
− 41y
99
+ ··· + 30y
2
+ 1)
c
8
y
4
(y
31
− 5y
30
+ ··· − 7995392y −1048576)
· (y
50
− 10y
49
+ ··· + 10y + 1)
2
c
10
, c
11
((y
2
− 7y + 1)
2
)(y
31
− 6y
30
+ ··· + 122y −1)
· (y
100
+ 35y
99
+ ··· + 60y + 1)
27
