11a
249
(K11a
249
)
A knot diagram
1
Linearized knot diagam
9 8 1 2 3 11 10 5 4 7 6
Solving Sequence
6,11
7
1,4
3 5 10 8 2 9
c
6
c
11
c
3
c
5
c
10
c
7
c
2
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−2221u
30
+ 10362u
29
+ ··· + 1483b + 12391, 16251u
30
− 71483u
29
+ ··· + 5932a − 87087,
u
31
− 5u
30
+ ··· − 29u + 4i
I
u
2
= h−u
17
a + u
18
+ ··· + b − a, −u
18
− 2u
17
+ ··· + a + 3, u
19
+ 3u
18
+ ··· + 2u + 1i
I
u
3
= h−u
8
− 3u
7
− 8u
6
− 14u
5
− 18u
4
− 18u
3
− 12u
2
+ b − 5u − 1,
u
10
+ 2u
9
+ 8u
8
+ 11u
7
+ 20u
6
+ 18u
5
+ 16u
4
+ 7u
3
− u
2
+ a − 2u − 3,
u
11
+ 2u
10
+ 9u
9
+ 14u
8
+ 29u
7
+ 34u
6
+ 40u
5
+ 33u
4
+ 21u
3
+ 11u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 80 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−2221u
30
+ 10362u
29
+ · · · + 1483b + 12391, 16251u
30
− 71483u
29
+
· · · + 5932a − 87087, u
31
− 5u
30
+ · · · − 29u + 4i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
1
=
u
u
a
4
=
−2.73955u
30
+ 12.0504u
29
+ ··· − 82.3793u + 14.6809
1.49764u
30
− 6.98719u
29
+ ··· + 54.4889u − 8.35536
a
3
=
−2.08884u
30
+ 8.94656u
29
+ ··· − 37.0260u + 6.08749
2.14835u
30
− 10.0910u
29
+ ··· + 99.8422u − 16.9488
a
5
=
3.62053u
30
− 14.7615u
29
+ ··· + 60.7468u − 11.9584
−4.83884u
30
+ 22.6966u
29
+ ··· − 198.526u + 33.8375
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−0.160991u
30
+ 0.195381u
29
+ ··· + 25.2053u − 4.91925
1.19285u
30
− 5.61834u
29
+ ··· + 51.1949u − 8.53338
a
9
=
2.95499u
30
− 13.1485u
29
+ ··· + 127.609u − 25.1701
−0.175320u
30
+ 1.38031u
29
+ ··· − 36.5408u + 8.03034
a
9
=
2.95499u
30
− 13.1485u
29
+ ··· + 127.609u − 25.1701
−0.175320u
30
+ 1.38031u
29
+ ··· − 36.5408u + 8.03034
(ii) Obstruction class = −1
(iii) Cusp Shapes =
23165
1483
u
30
−
107745
1483
u
29
+ ··· +
898798
1483
u −
164430
1483
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
31
− u
30
+ ··· + u − 1
c
2
, c
9
u
31
− u
29
+ ··· − u − 2
c
3
, c
5
u
31
+ 4u
30
+ ··· + 18u − 1
c
4
u
31
+ 18u
30
+ ··· + 9u + 2
c
6
, c
7
, c
10
c
11
u
31
+ 5u
30
+ ··· − 29u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
31
+ 13y
30
+ ··· − 33y −1
c
2
, c
9
y
31
− 2y
30
+ ··· + 77y −4
c
3
, c
5
y
31
− 26y
30
+ ··· + 92y −1
c
4
y
31
+ 36y
29
+ ··· − 43y −4
c
6
, c
7
, c
10
c
11
y
31
+ 37y
30
+ ··· − 39y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.569679 + 0.825244I
a = 0.183588 − 0.105883I
b = 0.10987 + 1.44314I
−2.69978 + 12.95640I −0.23261 − 9.43614I
u = 0.569679 − 0.825244I
a = 0.183588 + 0.105883I
b = 0.10987 − 1.44314I
−2.69978 − 12.95640I −0.23261 + 9.43614I
u = 0.446669 + 1.022060I
a = −0.229670 + 0.139677I
b = −0.763451 + 0.817856I
−3.95736 − 4.34211I −3.34603 + 4.21375I
u = 0.446669 − 1.022060I
a = −0.229670 − 0.139677I
b = −0.763451 − 0.817856I
−3.95736 + 4.34211I −3.34603 − 4.21375I
u = 0.400265 + 0.750186I
a = 0.330472 + 0.332431I
b = 0.07889 − 1.54454I
−3.65186 + 4.72376I −6.73915 − 9.01491I
u = 0.400265 − 0.750186I
a = 0.330472 − 0.332431I
b = 0.07889 + 1.54454I
−3.65186 − 4.72376I −6.73915 + 9.01491I
u = 0.430131 + 0.658488I
a = −0.183362 + 0.477511I
b = 0.737519 − 0.745039I
−3.38752 + 1.12904I −5.86333 − 1.96216I
u = 0.430131 − 0.658488I
a = −0.183362 − 0.477511I
b = 0.737519 + 0.745039I
−3.38752 − 1.12904I −5.86333 + 1.96216I
u = 0.767504 + 0.098303I
a = 1.176040 + 0.588359I
b = −0.313167 − 0.039847I
−0.50248 − 8.50614I 2.27465 + 6.40928I
u = 0.767504 − 0.098303I
a = 1.176040 − 0.588359I
b = −0.313167 + 0.039847I
−0.50248 + 8.50614I 2.27465 − 6.40928I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.293124 + 1.250360I
a = −0.339823 + 0.206438I
b = −0.252419 + 0.385898I
−2.27354 − 3.50893I −5.54486 + 0.I
u = −0.293124 − 1.250360I
a = −0.339823 − 0.206438I
b = −0.252419 − 0.385898I
−2.27354 + 3.50893I −5.54486 + 0.I
u = −0.679912
a = −0.416450
b = −0.222046
1.65420 10.7790
u = −0.030145 + 0.632324I
a = 1.47612 + 0.64299I
b = 0.885670 − 1.002800I
−2.68102 − 0.05226I −6.06626 − 0.22401I
u = −0.030145 − 0.632324I
a = 1.47612 − 0.64299I
b = 0.885670 + 1.002800I
−2.68102 + 0.05226I −6.06626 + 0.22401I
u = −0.365675 + 0.452743I
a = −0.797328 + 0.396666I
b = −0.210849 + 0.445374I
0.46001 − 1.35442I 4.73574 + 4.98058I
u = −0.365675 − 0.452743I
a = −0.797328 − 0.396666I
b = −0.210849 − 0.445374I
0.46001 + 1.35442I 4.73574 − 4.98058I
u = 0.479267 + 0.029288I
a = −1.56796 − 0.81793I
b = 0.522074 + 0.276654I
−1.59180 − 1.67665I −1.00415 + 4.26501I
u = 0.479267 − 0.029288I
a = −1.56796 + 0.81793I
b = 0.522074 − 0.276654I
−1.59180 + 1.67665I −1.00415 − 4.26501I
u = −0.05713 + 1.54134I
a = 0.344476 + 1.160950I
b = 0.86736 + 1.36084I
−6.26363 − 2.63858I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05713 − 1.54134I
a = 0.344476 − 1.160950I
b = 0.86736 − 1.36084I
−6.26363 + 2.63858I 0
u = 0.14024 + 1.60199I
a = 1.00070 − 1.54731I
b = 0.97785 − 2.44893I
−11.09130 + 3.32383I 0
u = 0.14024 − 1.60199I
a = 1.00070 + 1.54731I
b = 0.97785 + 2.44893I
−11.09130 − 3.32383I 0
u = −0.01344 + 1.61665I
a = 0.56616 − 1.95531I
b = 0.12593 − 2.72063I
−10.59830 − 0.24605I 0
u = −0.01344 − 1.61665I
a = 0.56616 + 1.95531I
b = 0.12593 + 2.72063I
−10.59830 + 0.24605I 0
u = 0.11301 + 1.62464I
a = 0.20677 − 2.57593I
b = −0.41813 − 3.60494I
−11.79760 + 6.65579I 0
u = 0.11301 − 1.62464I
a = 0.20677 + 2.57593I
b = −0.41813 + 3.60494I
−11.79760 − 6.65579I 0
u = 0.16828 + 1.65275I
a = −0.20161 + 2.35706I
b = 0.26751 + 3.34164I
−11.1484 + 15.7970I 0
u = 0.16828 − 1.65275I
a = −0.20161 − 2.35706I
b = 0.26751 − 3.34164I
−11.1484 − 15.7970I 0
u = 0.08442 + 1.69812I
a = −0.63135 + 1.40530I
b = −0.50364 + 2.03004I
−13.53410 − 2.42013I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08442 − 1.69812I
a = −0.63135 − 1.40530I
b = −0.50364 − 2.03004I
−13.53410 + 2.42013I 0
8
II.
I
u
2
= h−u
17
a+u
18
+· · ·+b−a, −u
18
−2u
17
+· · ·+a+3, u
19
+3u
18
+· · ·+2u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
1
=
u
u
a
4
=
a
u
17
a − u
18
+ ··· + 2au + a
a
3
=
−u
18
a − 3u
17
a + ··· − 2au + u
−u
18
a − u
18
+ ··· − 2u
2
+ u
a
5
=
−u
15
a + u
16
+ ··· − a + 2
−u
18
− 3u
17
+ ··· − a − 2u
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
u
16
+ 2u
15
+ ··· + a + 1
−u
17
a − u
18
+ ··· − a + u
a
9
=
−u
16
− 4u
15
+ ··· − a − 1
−u
17
a + u
18
+ ··· − a + u
a
9
=
−u
16
− 4u
15
+ ··· − a − 1
−u
17
a + u
18
+ ··· − a + u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
18
+ 4u
17
+ 40u
16
+ 28u
15
+ 136u
14
+ 32u
13
+ 120u
12
−204u
11
−
308u
10
− 696u
9
− 780u
8
− 788u
7
− 596u
6
− 324u
5
− 172u
4
− 64u
3
− 36u
2
− 8u + 2
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
38
− 3u
37
+ ··· + u + 2
c
2
, c
9
u
38
− u
37
+ ··· − 20u + 1
c
3
, c
5
u
38
− u
37
+ ··· − 35u − 44
c
4
(u
19
− 9u
18
+ ··· − 5u
2
+ 1)
2
c
6
, c
7
, c
10
c
11
(u
19
− 3u
18
+ ··· + 2u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
38
− 9y
37
+ ··· + 59y + 4
c
2
, c
9
y
38
− 5y
37
+ ··· − 114y + 1
c
3
, c
5
y
38
+ 3y
37
+ ··· − 35633y + 1936
c
4
(y
19
− y
18
+ ··· + 10y −1)
2
c
6
, c
7
, c
10
c
11
(y
19
+ 23y
18
+ ··· − 10y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.564635 + 0.868645I
a = −0.327665 + 0.243134I
b = −0.152716 + 1.213210I
−1.04093 − 4.49011I 7.2217 + 12.2703I
u = −0.564635 + 0.868645I
a = −0.116530 + 0.236355I
b = 0.004197 − 0.674024I
−1.04093 − 4.49011I 7.2217 + 12.2703I
u = −0.564635 − 0.868645I
a = −0.327665 − 0.243134I
b = −0.152716 − 1.213210I
−1.04093 + 4.49011I 7.2217 − 12.2703I
u = −0.564635 − 0.868645I
a = −0.116530 − 0.236355I
b = 0.004197 + 0.674024I
−1.04093 + 4.49011I 7.2217 − 12.2703I
u = −0.283323 + 0.902263I
a = 0.785053 + 0.660864I
b = 0.80712 + 1.47925I
−3.51553 − 4.24269I −6.97656 + 8.05146I
u = −0.283323 + 0.902263I
a = −0.111366 + 0.437497I
b = 0.380631 − 1.057340I
−3.51553 − 4.24269I −6.97656 + 8.05146I
u = −0.283323 − 0.902263I
a = 0.785053 − 0.660864I
b = 0.80712 − 1.47925I
−3.51553 + 4.24269I −6.97656 − 8.05146I
u = −0.283323 − 0.902263I
a = −0.111366 − 0.437497I
b = 0.380631 + 1.057340I
−3.51553 + 4.24269I −6.97656 − 8.05146I
u = −0.787816
a = −0.876396
b = −0.116835
1.57116 17.6350
u = −0.787816
a = 0.131048
b = −0.319043
1.57116 17.6350
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.520505 + 0.346350I
a = −0.254122 + 1.011080I
b = −0.565052 + 0.068015I
0.28629 − 1.78365I 6.84779 + 6.86635I
u = −0.520505 + 0.346350I
a = −1.295150 − 0.060725I
b = 0.006015 + 0.732557I
0.28629 − 1.78365I 6.84779 + 6.86635I
u = −0.520505 − 0.346350I
a = −0.254122 − 1.011080I
b = −0.565052 − 0.068015I
0.28629 + 1.78365I 6.84779 − 6.86635I
u = −0.520505 − 0.346350I
a = −1.295150 + 0.060725I
b = 0.006015 − 0.732557I
0.28629 + 1.78365I 6.84779 − 6.86635I
u = 0.230003 + 0.578230I
a = −0.113241 − 0.764438I
b = −0.79066 − 1.82471I
0.35999 + 4.82230I 1.96421 − 11.27699I
u = 0.230003 + 0.578230I
a = 2.28059 + 0.47953I
b = −0.456332 − 0.059209I
0.35999 + 4.82230I 1.96421 − 11.27699I
u = 0.230003 − 0.578230I
a = −0.113241 + 0.764438I
b = −0.79066 + 1.82471I
0.35999 − 4.82230I 1.96421 + 11.27699I
u = 0.230003 − 0.578230I
a = 2.28059 − 0.47953I
b = −0.456332 + 0.059209I
0.35999 − 4.82230I 1.96421 + 11.27699I
u = −0.00390 + 1.54662I
a = −0.313255 + 0.396871I
b = 0.461659 + 0.256813I
−5.53623 − 2.54405I 2.47148 + 1.82962I
u = −0.00390 + 1.54662I
a = 0.73015 + 2.45662I
b = 1.10904 + 3.35675I
−5.53623 − 2.54405I 2.47148 + 1.82962I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00390 − 1.54662I
a = −0.313255 − 0.396871I
b = 0.461659 − 0.256813I
−5.53623 + 2.54405I 2.47148 − 1.82962I
u = −0.00390 − 1.54662I
a = 0.73015 − 2.45662I
b = 1.10904 − 3.35675I
−5.53623 + 2.54405I 2.47148 − 1.82962I
u = 0.237639 + 0.357936I
a = −0.09055 − 1.49214I
b = 0.871743 + 1.056000I
0.95751 − 2.93464I 5.91453 − 1.99663I
u = 0.237639 + 0.357936I
a = −2.88646 − 0.04775I
b = −0.399928 + 0.571323I
0.95751 − 2.93464I 5.91453 − 1.99663I
u = 0.237639 − 0.357936I
a = −0.09055 + 1.49214I
b = 0.871743 − 1.056000I
0.95751 + 2.93464I 5.91453 + 1.99663I
u = 0.237639 − 0.357936I
a = −2.88646 + 0.04775I
b = −0.399928 − 0.571323I
0.95751 + 2.93464I 5.91453 + 1.99663I
u = 0.04934 + 1.59573I
a = −1.43137 + 0.03838I
b = −2.85551 + 0.16099I
−7.20594 + 5.75076I −0.89404 − 7.30960I
u = 0.04934 + 1.59573I
a = −0.68115 − 2.96609I
b = −0.90158 − 3.44171I
−7.20594 + 5.75076I −0.89404 − 7.30960I
u = 0.04934 − 1.59573I
a = −1.43137 − 0.03838I
b = −2.85551 − 0.16099I
−7.20594 − 5.75076I −0.89404 + 7.30960I
u = 0.04934 − 1.59573I
a = −0.68115 + 2.96609I
b = −0.90158 + 3.44171I
−7.20594 − 5.75076I −0.89404 + 7.30960I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08513 + 1.66537I
a = 1.08196 + 1.76398I
b = 0.79877 + 2.26784I
−12.42410 − 5.72328I −8.36068 + 4.92699I
u = −0.08513 + 1.66537I
a = 0.40246 − 2.24376I
b = 0.92121 − 3.30609I
−12.42410 − 5.72328I −8.36068 + 4.92699I
u = −0.08513 − 1.66537I
a = 1.08196 − 1.76398I
b = 0.79877 − 2.26784I
−12.42410 + 5.72328I −8.36068 − 4.92699I
u = −0.08513 − 1.66537I
a = 0.40246 + 2.24376I
b = 0.92121 + 3.30609I
−12.42410 + 5.72328I −8.36068 − 4.92699I
u = −0.16558 + 1.66250I
a = −0.020599 − 1.400860I
b = 0.46750 − 2.07648I
−9.67769 − 7.32811I −0.00586 + 9.90539I
u = −0.16558 + 1.66250I
a = 0.23390 + 2.13484I
b = 0.01183 + 2.90292I
−9.67769 − 7.32811I −0.00586 + 9.90539I
u = −0.16558 − 1.66250I
a = −0.020599 + 1.400860I
b = 0.46750 + 2.07648I
−9.67769 + 7.32811I −0.00586 − 9.90539I
u = −0.16558 − 1.66250I
a = 0.23390 − 2.13484I
b = 0.01183 − 2.90292I
−9.67769 + 7.32811I −0.00586 − 9.90539I
15
III.
I
u
3
= h−u
8
− 3u
7
+ · · · + b − 1, u
10
+ 2u
9
+ · · · + a − 3, u
11
+ 2u
10
+ · · · + 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
1
=
u
u
a
4
=
−u
10
− 2u
9
− 8u
8
− 11u
7
− 20u
6
− 18u
5
− 16u
4
− 7u
3
+ u
2
+ 2u + 3
u
8
+ 3u
7
+ 8u
6
+ 14u
5
+ 18u
4
+ 18u
3
+ 12u
2
+ 5u + 1
a
3
=
−u
10
− 2u
9
− 9u
8
− 13u
7
− 26u
6
− 26u
5
− 26u
4
− 15u
3
− 3u
2
+ u + 3
u
7
+ 2u
6
+ 6u
5
+ 8u
4
+ 10u
3
+ 8u
2
+ 4u + 1
a
5
=
−u
10
− 2u
9
+ ··· − 14u − 1
−u
8
− u
7
− 5u
6
− 4u
5
− 7u
4
− 4u
3
− 2u
2
− u + 1
a
10
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−u
10
− 2u
9
− 8u
8
− 11u
7
− 20u
6
− 17u
5
− 15u
4
− 4u
3
+ 3u
2
+ 4u + 3
u
8
+ 2u
7
+ 7u
6
+ 10u
5
+ 15u
4
+ 14u
3
+ 10u
2
+ 5u + 1
a
9
=
u
10
+ 2u
9
+ 9u
8
+ 14u
7
+ 29u
6
+ 34u
5
+ 39u
4
+ 31u
3
+ 17u
2
+ 6u − 1
−u
4
− u
3
− 3u
2
− 2u − 1
a
9
=
u
10
+ 2u
9
+ 9u
8
+ 14u
7
+ 29u
6
+ 34u
5
+ 39u
4
+ 31u
3
+ 17u
2
+ 6u − 1
−u
4
− u
3
− 3u
2
− 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −u
10
+ u
9
− 7u
8
− 3u
7
− 28u
6
− 37u
5
− 61u
4
− 66u
3
− 51u
2
− 24u − 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
11
+ u
10
− 2u
9
− 3u
8
+ 2u
7
+ 3u
6
− 2u
5
− 3u
4
+ u
3
+ 2u
2
− 1
c
2
, c
9
u
11
− 2u
9
− u
8
+ 3u
7
+ 2u
6
− 3u
5
− 2u
4
+ 3u
3
+ 2u
2
− u − 1
c
3
, c
5
u
11
+ 4u
10
+ ··· + 5u + 1
c
4
u
11
− 7u
10
+ ··· + 7u − 1
c
6
, c
7
u
11
+ 2u
10
+ ··· + 2u + 1
c
10
, c
11
u
11
− 2u
10
+ ··· + 2u − 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
11
− 5y
10
+ ··· + 4y −1
c
2
, c
9
y
11
− 4y
10
+ ··· + 5y −1
c
3
, c
5
y
11
+ 4y
10
+ ··· − 3y −1
c
4
y
11
+ y
10
+ ··· + 3y −1
c
6
, c
7
, c
10
c
11
y
11
+ 14y
10
+ ··· − 18y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.385850 + 0.932877I
a = −0.157522 − 0.148811I
b = 0.102818 − 1.019510I
−1.97960 − 4.20350I −1.84188 + 8.05769I
u = −0.385850 − 0.932877I
a = −0.157522 + 0.148811I
b = 0.102818 + 1.019510I
−1.97960 + 4.20350I −1.84188 − 8.05769I
u = −0.126428 + 1.175880I
a = 0.006705 − 0.532724I
b = 0.471057 − 0.785734I
−1.93683 − 3.97193I 3.41224 + 7.38669I
u = −0.126428 − 1.175880I
a = 0.006705 + 0.532724I
b = 0.471057 + 0.785734I
−1.93683 + 3.97193I 3.41224 − 7.38669I
u = −0.813298
a = 0.659674
b = −0.118101
1.17683 −7.25190
u = 0.01335 + 1.54786I
a = −0.79783 + 1.65779I
b = −1.64028 + 1.88855I
−6.19976 + 3.82276I −1.00855 − 7.16549I
u = 0.01335 − 1.54786I
a = −0.79783 − 1.65779I
b = −1.64028 − 1.88855I
−6.19976 − 3.82276I −1.00855 + 7.16549I
u = 0.015546 + 0.362124I
a = 2.69116 + 1.00089I
b = −0.296234 + 1.130380I
0.53546 + 3.67768I −0.32060 − 6.20780I
u = 0.015546 − 0.362124I
a = 2.69116 − 1.00089I
b = −0.296234 − 1.130380I
0.53546 − 3.67768I −0.32060 + 6.20780I
u = −0.10997 + 1.65171I
a = −0.07235 − 2.01756I
b = 0.42168 − 2.77387I
−10.74690 − 6.11277I −2.11524 + 4.58856I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10997 − 1.65171I
a = −0.07235 + 2.01756I
b = 0.42168 + 2.77387I
−10.74690 + 6.11277I −2.11524 − 4.58856I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
11
+ u
10
− 2u
9
− 3u
8
+ 2u
7
+ 3u
6
− 2u
5
− 3u
4
+ u
3
+ 2u
2
− 1)
· (u
31
− u
30
+ ··· + u − 1)(u
38
− 3u
37
+ ··· + u + 2)
c
2
, c
9
(u
11
− 2u
9
− u
8
+ 3u
7
+ 2u
6
− 3u
5
− 2u
4
+ 3u
3
+ 2u
2
− u − 1)
· (u
31
− u
29
+ ··· − u − 2)(u
38
− u
37
+ ··· − 20u + 1)
c
3
, c
5
(u
11
+ 4u
10
+ ··· + 5u + 1)(u
31
+ 4u
30
+ ··· + 18u − 1)
· (u
38
− u
37
+ ··· − 35u − 44)
c
4
(u
11
− 7u
10
+ ··· + 7u − 1)(u
19
− 9u
18
+ ··· − 5u
2
+ 1)
2
· (u
31
+ 18u
30
+ ··· + 9u + 2)
c
6
, c
7
(u
11
+ 2u
10
+ ··· + 2u + 1)(u
19
− 3u
18
+ ··· + 2u − 1)
2
· (u
31
+ 5u
30
+ ··· − 29u − 4)
c
10
, c
11
(u
11
− 2u
10
+ ··· + 2u − 1)(u
19
− 3u
18
+ ··· + 2u − 1)
2
· (u
31
+ 5u
30
+ ··· − 29u − 4)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
11
− 5y
10
+ ··· + 4y −1)(y
31
+ 13y
30
+ ··· − 33y −1)
· (y
38
− 9y
37
+ ··· + 59y + 4)
c
2
, c
9
(y
11
− 4y
10
+ ··· + 5y −1)(y
31
− 2y
30
+ ··· + 77y −4)
· (y
38
− 5y
37
+ ··· − 114y + 1)
c
3
, c
5
(y
11
+ 4y
10
+ ··· − 3y −1)(y
31
− 26y
30
+ ··· + 92y −1)
· (y
38
+ 3y
37
+ ··· − 35633y + 1936)
c
4
(y
11
+ y
10
+ ··· + 3y −1)(y
19
− y
18
+ ··· + 10y −1)
2
· (y
31
+ 36y
29
+ ··· − 43y −4)
c
6
, c
7
, c
10
c
11
(y
11
+ 14y
10
+ ··· − 18y −1)(y
19
+ 23y
18
+ ··· − 10y −1)
2
· (y
31
+ 37y
30
+ ··· − 39y −16)
22
