12a
0841
(K12a
0841
)
A knot diagram
1
Linearized knot diagam
4 5 9 2 10 11 1 12 3 7 6 8
Solving Sequence
7,10
11 6 12
3,5
2 4 9 8 1
c
10
c
6
c
11
c
5
c
2
c
4
c
9
c
8
c
12
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−3u
28
− 5u
27
+ ··· + 8b + 3, −29u
28
− 15u
27
+ ··· + 32a − 23, u
29
+ 15u
27
+ ··· + 8u
2
− 1i
I
u
2
= h4.83718 × 10
20
u
45
+ 8.97498 × 10
20
u
44
+ ··· + 9.64382 × 10
20
b + 5.08979 × 10
21
,
5.98621 × 10
21
u
45
+ 8.38005 × 10
21
u
44
+ ··· + 2.89315 × 10
21
a + 6.78007 × 10
22
, u
46
+ 2u
45
+ ··· + 36u + 9i
I
u
3
= hb, u
2
+ 2a − u + 3, u
3
+ 2u + 1i
I
u
4
= hb, u
3
+ a + u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
I
u
5
= hau + 2b − a + 2u, a
2
− au + a + 2u, u
2
+ 1i
* 5 irreducible components of dim
C
= 0, with total 86 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
= h−3u
28
− 5u
27
+ · · · + 8b + 3, −29u
28
− 15u
27
+ · · · + 32a − 23, u
29
+
15u
27
+ · · · + 8u
2
− 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
0.906250u
28
+ 0.468750u
27
+ ··· + 8.65625u + 0.718750
3
8
u
28
+
5
8
u
27
+ ··· −
1
8
u −
3
8
a
5
=
u
3
+ 2u
u
3
+ u
a
2
=
0.593750u
28
+ 0.0312500u
27
+ ··· + 7.34375u + 0.781250
1
2
u
28
+
1
2
u
27
+ ··· − u −
1
2
a
4
=
0.0312500u
28
+ 0.343750u
27
+ ··· + 8.78125u + 1.09375
−
3
8
u
28
−
3
8
u
27
+ ··· −
3
8
u +
1
8
a
9
=
−u
3
− 2u
−
1
4
u
28
−
7
2
u
26
+ ··· −
29
4
u
3
+
5
4
u
a
8
=
−u
−
1
4
u
28
−
7
2
u
26
+ ··· −
21
4
u
3
+
5
4
u
a
1
=
1
1
4
u
27
+
7
2
u
25
+ ··· +
21
4
u
2
−
1
4
(ii) Obstruction class = −1
(iii) Cusp Shapes =
153
64
u
28
−
5
64
u
27
+ ··· +
433
64
u −
445
64
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
29
− 4u
28
+ ··· + 9u − 4
c
3
, c
9
u
29
− 3u
28
+ ··· − 136u − 32
c
5
u
29
− 6u
28
+ ··· + 256u − 64
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
29
+ 15u
27
+ ··· + 8u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
29
− 30y
28
+ ··· + 449y −16
c
3
, c
9
y
29
+ 21y
28
+ ··· + 3392y −1024
c
5
y
29
− 12y
28
+ ··· + 45056y −4096
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
29
+ 30y
28
+ ··· + 16y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.850727 + 0.156624I
a = −0.33070 − 2.13581I
b = 0.52738 − 1.44214I
−11.18250 − 6.23241I −15.4958 + 4.4354I
u = 0.850727 − 0.156624I
a = −0.33070 + 2.13581I
b = 0.52738 + 1.44214I
−11.18250 + 6.23241I −15.4958 − 4.4354I
u = −0.220678 + 1.200740I
a = 0.348620 − 0.909991I
b = 0.25885 − 1.75018I
−5.29574 + 1.64756I −6.64036 − 4.87433I
u = −0.220678 − 1.200740I
a = 0.348620 + 0.909991I
b = 0.25885 + 1.75018I
−5.29574 − 1.64756I −6.64036 + 4.87433I
u = −0.776315
a = 0.835156
b = 1.22191
−6.47257 −15.0600
u = 0.762739 + 0.066975I
a = 0.24083 + 2.47525I
b = −0.215490 + 1.174450I
−4.34611 − 2.54689I −14.3374 + 3.8948I
u = 0.762739 − 0.066975I
a = 0.24083 − 2.47525I
b = −0.215490 − 1.174450I
−4.34611 + 2.54689I −14.3374 − 3.8948I
u = −0.389704 + 0.578994I
a = 0.893913 − 0.386935I
b = −0.020656 − 1.382320I
−6.72574 + 1.45946I −13.9846 − 4.7500I
u = −0.389704 − 0.578994I
a = 0.893913 + 0.386935I
b = −0.020656 + 1.382320I
−6.72574 − 1.45946I −13.9846 + 4.7500I
u = −0.295755 + 1.326220I
a = −0.65679 + 1.37777I
b = 0.152881 + 1.337510I
3.59611 + 4.94229I −5.90176 − 3.25931I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.295755 − 1.326220I
a = −0.65679 − 1.37777I
b = 0.152881 − 1.337510I
3.59611 − 4.94229I −5.90176 + 3.25931I
u = −0.031725 + 1.373280I
a = 0.498676 + 0.750755I
b = −0.833765 + 0.932700I
6.88971 + 1.52242I −3.08698 − 0.91142I
u = −0.031725 − 1.373280I
a = 0.498676 − 0.750755I
b = −0.833765 − 0.932700I
6.88971 − 1.52242I −3.08698 + 0.91142I
u = 0.334857 + 1.341710I
a = −0.052463 − 0.514744I
b = 1.363430 + 0.335492I
2.04714 − 8.02731I −6.19853 + 5.31620I
u = 0.334857 − 1.341710I
a = −0.052463 + 0.514744I
b = 1.363430 − 0.335492I
2.04714 + 8.02731I −6.19853 − 5.31620I
u = −0.35253 + 1.37355I
a = 1.02044 − 1.34914I
b = −0.486235 − 1.297300I
4.85486 + 10.72890I −4.66596 − 7.57137I
u = −0.35253 − 1.37355I
a = 1.02044 + 1.34914I
b = −0.486235 + 1.297300I
4.85486 − 10.72890I −4.66596 + 7.57137I
u = 0.24683 + 1.41814I
a = 0.066073 + 0.309790I
b = −0.764350 − 0.100103I
8.59031 − 5.90549I 1.11192 + 5.11469I
u = 0.24683 − 1.41814I
a = 0.066073 − 0.309790I
b = −0.764350 + 0.100103I
8.59031 + 5.90549I 1.11192 − 5.11469I
u = 0.07466 + 1.44080I
a = −0.513088 − 0.364599I
b = 0.808356 − 0.740580I
10.76360 − 2.89956I 0.60665 + 2.87370I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07466 − 1.44080I
a = −0.513088 + 0.364599I
b = 0.808356 + 0.740580I
10.76360 + 2.89956I 0.60665 − 2.87370I
u = −0.40528 + 1.39829I
a = −1.16438 + 1.17876I
b = 0.73766 + 1.39230I
−1.3772 + 15.4179I −7.45070 − 8.08574I
u = −0.40528 − 1.39829I
a = −1.16438 − 1.17876I
b = 0.73766 − 1.39230I
−1.3772 − 15.4179I −7.45070 + 8.08574I
u = −0.536309
a = −0.494577
b = −0.458728
−1.04228 −9.21320
u = 0.17794 + 1.53799I
a = 0.448537 − 0.057808I
b = −0.334229 + 0.884134I
7.23806 − 6.07610I −7.24625 + 5.96720I
u = 0.17794 − 1.53799I
a = 0.448537 + 0.057808I
b = −0.334229 − 0.884134I
7.23806 + 6.07610I −7.24625 − 5.96720I
u = −0.212154 + 0.255646I
a = −1.010790 + 0.763833I
b = 0.130923 + 0.622392I
−0.423563 + 0.810930I −9.27103 − 8.41081I
u = −0.212154 − 0.255646I
a = −1.010790 − 0.763833I
b = 0.130923 − 0.622392I
−0.423563 − 0.810930I −9.27103 + 8.41081I
u = 0.232774
a = 3.58165
b = −0.412704
−2.00372 −0.355130
7
II. I
u
2
=
h4.84×10
20
u
45
+8.97×10
20
u
44
+· · ·+9.64×10
20
b+5.09×10
21
, 5.99×10
21
u
45
+
8.38 × 10
21
u
44
+ · · · + 2.89 × 10
21
a + 6.78 × 10
22
, u
46
+ 2u
45
+ · · · + 36u + 9i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−2.06910u
45
− 2.89652u
44
+ ··· − 63.4881u − 23.4350
−0.501583u
45
− 0.930646u
44
+ ··· − 17.2611u − 5.27777
a
5
=
u
3
+ 2u
u
3
+ u
a
2
=
−1.14401u
45
− 1.45942u
44
+ ··· − 28.8674u − 7.34206
−0.0137503u
45
− 0.130285u
44
+ ··· + 2.36181u + 3.83874
a
4
=
−1.43328u
45
− 2.16999u
44
+ ··· − 45.8330u − 15.7079
−0.589166u
45
− 0.982067u
44
+ ··· − 18.1174u − 7.06307
a
9
=
0.318055u
45
+ 0.101865u
44
+ ··· + 12.9697u + 5.31725
−0.512383u
45
− 0.773762u
44
+ ··· − 15.6515u − 5.26019
a
8
=
−1.83572u
45
− 2.63620u
44
+ ··· − 63.5472u − 23.3857
−2.15378u
45
− 2.73806u
44
+ ··· − 74.5169u − 28.7029
a
1
=
2.15396u
45
+ 2.58331u
44
+ ··· + 66.0693u + 22.7732
1.03525u
45
+ 1.64133u
44
+ ··· + 42.7004u + 14.5215
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
354747019255657091139
321460668888655555043
u
45
−
505139044943400068515
321460668888655555043
u
44
+ ··· −
488177567341401899594
321460668888655555043
u −
3117355638652138218610
321460668888655555043
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
23
− 3u
22
+ ··· − u + 1)
2
c
3
, c
9
(u
23
+ u
22
+ ··· + 8u − 4)
2
c
5
(u
23
+ 2u
22
+ ··· + 18u + 9)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
46
+ 2u
45
+ ··· + 36u + 9
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
23
− 23y
22
+ ··· − 7y −1)
2
c
3
, c
9
(y
23
+ 15y
22
+ ··· − 40y −16)
2
c
5
(y
23
− 12y
22
+ ··· − 450y −81)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
46
+ 34y
45
+ ··· + 288y + 81
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.792003 + 0.636640I
a = −0.464182 − 0.795612I
b = 0.107498 − 1.054050I
−0.12065 − 2.74438I −10.00137 + 3.42075I
u = 0.792003 − 0.636640I
a = −0.464182 + 0.795612I
b = 0.107498 + 1.054050I
−0.12065 + 2.74438I −10.00137 − 3.42075I
u = −0.934455 + 0.180416I
a = 0.01842 − 2.02427I
b = −0.63403 − 1.38420I
−6.36348 + 10.62070I −11.02627 − 6.45650I
u = −0.934455 − 0.180416I
a = 0.01842 + 2.02427I
b = −0.63403 + 1.38420I
−6.36348 − 10.62070I −11.02627 + 6.45650I
u = −0.415847 + 1.040410I
a = −0.783548 + 1.151140I
b = −0.308169 + 0.985429I
2.62555 − 2.00215I −5.23588 + 3.62705I
u = −0.415847 − 1.040410I
a = −0.783548 − 1.151140I
b = −0.308169 − 0.985429I
2.62555 + 2.00215I −5.23588 − 3.62705I
u = −0.827301 + 0.173977I
a = −0.01971 + 2.35915I
b = 0.383777 + 1.192290I
−0.03073 + 6.47771I −8.77780 − 6.52194I
u = −0.827301 − 0.173977I
a = −0.01971 − 2.35915I
b = 0.383777 − 1.192290I
−0.03073 − 6.47771I −8.77780 + 6.52194I
u = 0.025834 + 1.168220I
a = −1.46131 + 1.12134I
b = 0.441227 + 0.551458I
1.18777 − 0.88878I −10.39291 − 0.92577I
u = 0.025834 − 1.168220I
a = −1.46131 − 1.12134I
b = 0.441227 − 0.551458I
1.18777 + 0.88878I −10.39291 + 0.92577I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.425501 + 1.089070I
a = −0.570025 − 0.705470I
b = −0.37388 − 1.47842I
−8.32991 + 1.64388I −13.30470 − 0.40272I
u = 0.425501 − 1.089070I
a = −0.570025 + 0.705470I
b = −0.37388 + 1.47842I
−8.32991 − 1.64388I −13.30470 + 0.40272I
u = 0.308254 + 1.133610I
a = −0.92194 − 1.29169I
b = 0.969482
0.502753 −6.32391 + 0.I
u = 0.308254 − 1.133610I
a = −0.92194 + 1.29169I
b = 0.969482
0.502753 −6.32391 + 0.I
u = 0.472378 + 0.647473I
a = −0.055315 + 1.183280I
b = −0.494865 + 0.507562I
4.00909 − 1.37448I −1.29822 + 4.35124I
u = 0.472378 − 0.647473I
a = −0.055315 − 1.183280I
b = −0.494865 − 0.507562I
4.00909 + 1.37448I −1.29822 − 4.35124I
u = 0.780797 + 0.120550I
a = −0.886569 − 0.462655I
b = −1.222080 − 0.199525I
−2.55344 − 3.99588I −10.60901 + 3.49800I
u = 0.780797 − 0.120550I
a = −0.886569 + 0.462655I
b = −1.222080 + 0.199525I
−2.55344 + 3.99588I −10.60901 − 3.49800I
u = 0.307733 + 1.209490I
a = 0.72001 + 1.31534I
b = 0.000983 + 1.149400I
−0.86138 − 1.33135I −11.15950 + 0.I
u = 0.307733 − 1.209490I
a = 0.72001 − 1.31534I
b = 0.000983 − 1.149400I
−0.86138 + 1.33135I −11.15950 + 0.I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.562612 + 1.118280I
a = 0.694930 − 0.643080I
b = 0.51611 − 1.32552I
−3.51902 − 5.35900I −8.00000 + 0.I
u = −0.562612 − 1.118280I
a = 0.694930 + 0.643080I
b = 0.51611 + 1.32552I
−3.51902 + 5.35900I −8.00000 + 0.I
u = 0.665930 + 0.330412I
a = 0.671534 + 0.192645I
b = 0.598699 + 0.195967I
3.01275 − 2.59653I −2.53697 + 3.78636I
u = 0.665930 − 0.330412I
a = 0.671534 − 0.192645I
b = 0.598699 − 0.195967I
3.01275 + 2.59653I −2.53697 − 3.78636I
u = −0.241954 + 1.241490I
a = 1.62697 − 0.89642I
b = −0.308169 − 0.985429I
2.62555 + 2.00215I −8.00000 + 0.I
u = −0.241954 − 1.241490I
a = 1.62697 + 0.89642I
b = −0.308169 + 0.985429I
2.62555 − 2.00215I −8.00000 + 0.I
u = −0.708329 + 0.156769I
a = 0.92255 − 2.13346I
b = −0.37388 − 1.47842I
−8.32991 + 1.64388I −13.30470 − 0.40272I
u = −0.708329 − 0.156769I
a = 0.92255 + 2.13346I
b = −0.37388 + 1.47842I
−8.32991 − 1.64388I −13.30470 + 0.40272I
u = 0.004181 + 1.278050I
a = 0.797831 + 0.327490I
b = −0.494865 − 0.507562I
4.00909 + 1.37448I 0. − 4.35124I
u = 0.004181 − 1.278050I
a = 0.797831 − 0.327490I
b = −0.494865 + 0.507562I
4.00909 − 1.37448I 0. + 4.35124I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.694715 + 0.088611I
a = −0.45479 − 2.70390I
b = 0.000983 − 1.149400I
−0.86138 + 1.33135I −11.15950 − 0.67575I
u = −0.694715 − 0.088611I
a = −0.45479 + 2.70390I
b = 0.000983 + 1.149400I
−0.86138 − 1.33135I −11.15950 + 0.67575I
u = −0.186653 + 1.293090I
a = −0.225783 + 0.453951I
b = 0.598699 − 0.195967I
3.01275 + 2.59653I 0
u = −0.186653 − 1.293090I
a = −0.225783 − 0.453951I
b = 0.598699 + 0.195967I
3.01275 − 2.59653I 0
u = −0.331769 + 1.264340I
a = 0.339428 − 0.762833I
b = −1.222080 + 0.199525I
−2.55344 + 3.99588I 0
u = −0.331769 − 1.264340I
a = 0.339428 + 0.762833I
b = −1.222080 − 0.199525I
−2.55344 − 3.99588I 0
u = 0.325464 + 1.311080I
a = −1.25782 − 1.25504I
b = 0.383777 − 1.192290I
−0.03073 − 6.47771I 0
u = 0.325464 − 1.311080I
a = −1.25782 + 1.25504I
b = 0.383777 + 1.192290I
−0.03073 + 6.47771I 0
u = −0.306328 + 1.362140I
a = −1.55159 + 0.54359I
b = 0.51611 + 1.32552I
−3.51902 + 5.35900I 0
u = −0.306328 − 1.362140I
a = −1.55159 − 0.54359I
b = 0.51611 − 1.32552I
−3.51902 − 5.35900I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.36850 + 1.37093I
a = 1.40661 + 0.98862I
b = −0.63403 + 1.38420I
−6.36348 − 10.62070I 0
u = 0.36850 − 1.37093I
a = 1.40661 − 0.98862I
b = −0.63403 − 1.38420I
−6.36348 + 10.62070I 0
u = −0.06153 + 1.44896I
a = −0.341144 − 0.682320I
b = 0.107498 + 1.054050I
−0.12065 + 2.74438I 0
u = −0.06153 − 1.44896I
a = −0.341144 + 0.682320I
b = 0.107498 − 1.054050I
−0.12065 − 2.74438I 0
u = −0.205082 + 0.466322I
a = 0.12875 − 3.30791I
b = 0.441227 − 0.551458I
1.18777 + 0.88878I −10.39291 + 0.92577I
u = −0.205082 − 0.466322I
a = 0.12875 + 3.30791I
b = 0.441227 + 0.551458I
1.18777 − 0.88878I −10.39291 − 0.92577I
15
III. I
u
3
= hb, u
2
+ 2a − u + 3, u
3
+ 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
u
−u − 1
a
12
=
u
2
+ 1
−u
a
3
=
−
1
2
u
2
+
1
2
u −
3
2
0
a
5
=
−1
−u − 1
a
2
=
−
1
2
u
2
+
1
2
u −
1
2
u + 1
a
4
=
−
1
2
u
2
+
1
2
u −
3
2
0
a
9
=
1
0
a
8
=
−u
−u
2
a
1
=
1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
25
4
u
2
+
11
4
u −
71
4
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
9
u
3
c
4
(u + 1)
3
c
5
u
3
− 3u
2
+ 5u − 2
c
6
, c
7
, c
8
u
3
+ 2u − 1
c
10
, c
11
, c
12
u
3
+ 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
9
y
3
c
5
y
3
+ y
2
+ 13y −4
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
3
+ 4y
2
+ 4y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22670 + 1.46771I
a = −0.335258 + 0.401127I
b = 0
7.79580 − 5.13794I −3.98417 − 0.12290I
u = 0.22670 − 1.46771I
a = −0.335258 − 0.401127I
b = 0
7.79580 + 5.13794I −3.98417 + 0.12290I
u = −0.453398
a = −1.82948
b = 0
−2.43213 −20.2820
19
IV. I
u
4
= hb, u
3
+ a + u − 1, u
4
− u
3
+ 2u
2
− 2u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
u
u
3
+ u
a
12
=
u
2
+ 1
u
3
+ 2u − 1
a
3
=
−u
3
− u + 1
0
a
5
=
u
3
+ 2u
u
3
+ u
a
2
=
−2u
3
− 3u + 1
−u
3
− u
a
4
=
−u
3
− u + 1
0
a
9
=
1
0
a
8
=
−2u
3
+ u
2
− 3u + 3
−u
3
+ u
2
− u + 2
a
1
=
−u
3
− 2u
−u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
3
+ 4u − 9
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
9
u
4
c
4
(u + 1)
4
c
5
(u
2
+ u + 1)
2
c
6
, c
7
, c
8
u
4
+ u
3
+ 2u
2
+ 2u + 1
c
10
, c
11
, c
12
u
4
− u
3
+ 2u
2
− 2u + 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
9
y
4
c
5
(y
2
+ y + 1)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
4
+ 3y
3
+ 2y
2
+ 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.621744 + 0.440597I
a = 0.500000 − 0.866025I
b = 0
1.64493 − 2.02988I −7.00000 + 3.46410I
u = 0.621744 − 0.440597I
a = 0.500000 + 0.866025I
b = 0
1.64493 + 2.02988I −7.00000 − 3.46410I
u = −0.121744 + 1.306620I
a = 0.500000 + 0.866025I
b = 0
1.64493 + 2.02988I −7.00000 − 3.46410I
u = −0.121744 − 1.306620I
a = 0.500000 − 0.866025I
b = 0
1.64493 − 2.02988I −7.00000 + 3.46410I
23
V. I
u
5
= hau + 2b − a + 2u, a
2
− au + a + 2u, u
2
+ 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−1
a
6
=
u
0
a
12
=
0
−1
a
3
=
a
−
1
2
au +
1
2
a − u
a
5
=
u
0
a
2
=
1
2
au +
1
2
a + u
−
1
2
au +
1
2
a − u
a
4
=
−
1
2
au +
1
2
a − 1
1
2
au −
1
2
a + 2u
a
9
=
−u
−
1
2
au −
1
2
a − 2
a
8
=
−u
−
1
2
au −
1
2
a + u − 2
a
1
=
−1
1
2
au −
1
2
a + 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u
2
+ u − 1)
2
c
3
, c
9
u
4
+ 3u
2
+ 1
c
4
(u
2
− u − 1)
2
c
5
u
4
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(u
2
+ 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
2
− 3y + 1)
2
c
3
, c
9
(y
2
+ 3y + 1)
2
c
5
y
4
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(y + 1)
4
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.618034 − 0.618034I
b = − 1.61803I
−5.59278 −8.00000
u = 1.000000I
a = −1.61803 + 1.61803I
b = 0.618034I
2.30291 −8.00000
u = − 1.000000I
a = 0.618034 + 0.618034I
b = 1.61803I
−5.59278 −8.00000
u = − 1.000000I
a = −1.61803 − 1.61803I
b = − 0.618034I
2.30291 −8.00000
27
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
7
)(u
2
+ u − 1)
2
(u
23
− 3u
22
+ ··· − u + 1)
2
· (u
29
− 4u
28
+ ··· + 9u − 4)
c
3
, c
9
u
7
(u
4
+ 3u
2
+ 1)(u
23
+ u
22
+ ··· + 8u − 4)
2
· (u
29
− 3u
28
+ ··· − 136u − 32)
c
4
((u + 1)
7
)(u
2
− u − 1)
2
(u
23
− 3u
22
+ ··· − u + 1)
2
· (u
29
− 4u
28
+ ··· + 9u − 4)
c
5
u
4
(u
2
+ u + 1)
2
(u
3
− 3u
2
+ 5u − 2)(u
23
+ 2u
22
+ ··· + 18u + 9)
2
· (u
29
− 6u
28
+ ··· + 256u − 64)
c
6
, c
7
, c
8
(u
2
+ 1)
2
(u
3
+ 2u − 1)(u
4
+ u
3
+ 2u
2
+ 2u + 1)
· (u
29
+ 15u
27
+ ··· + 8u
2
− 1)(u
46
+ 2u
45
+ ··· + 36u + 9)
c
10
, c
11
, c
12
(u
2
+ 1)
2
(u
3
+ 2u + 1)(u
4
− u
3
+ 2u
2
− 2u + 1)
· (u
29
+ 15u
27
+ ··· + 8u
2
− 1)(u
46
+ 2u
45
+ ··· + 36u + 9)
28
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
7
)(y
2
− 3y + 1)
2
(y
23
− 23y
22
+ ··· − 7y −1)
2
· (y
29
− 30y
28
+ ··· + 449y −16)
c
3
, c
9
y
7
(y
2
+ 3y + 1)
2
(y
23
+ 15y
22
+ ··· − 40y −16)
2
· (y
29
+ 21y
28
+ ··· + 3392y −1024)
c
5
y
4
(y
2
+ y + 1)
2
(y
3
+ y
2
+ 13y −4)(y
23
− 12y
22
+ ··· − 450y −81)
2
· (y
29
− 12y
28
+ ··· + 45056y −4096)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
(y + 1)
4
(y
3
+ 4y
2
+ 4y −1)(y
4
+ 3y
3
+ 2y
2
+ 1)
· (y
29
+ 30y
28
+ ··· + 16y −1)(y
46
+ 34y
45
+ ··· + 288y + 81)
29
