12a
1156
(K12a
1156
)
A knot diagram
1
Linearized knot diagam
4 9 7 10 12 3 11 6 2 1 8 5
Solving Sequence
4,10 2,5
1 9 3 12 6 7 8 11
c
4
c
1
c
9
c
2
c
12
c
5
c
6
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.39785 × 10
29
u
28
+ 7.02003 × 10
30
u
27
+ ··· + 4.21410 × 10
28
b + 1.41325 × 10
31
,
5.66571 × 10
29
u
28
− 1.06111 × 10
31
u
27
+ ··· + 5.05693 × 10
29
a − 3.29177 × 10
31
,
4u
29
− 67u
28
+ ··· − 1032u + 144i
I
u
2
= h4.09097 × 10
106
au
58
− 8.30494 × 10
109
u
58
+ ··· + 1.51366 × 10
108
a − 4.79521 × 10
111
,
3.55453 × 10
112
au
58
− 1.91263 × 10
111
u
58
+ ··· + 1.93423 × 10
114
a + 1.37454 × 10
113
,
u
59
+ 5u
58
+ ··· + 88u + 37i
I
u
3
= h−32u
6
+ 108u
5
− 177u
4
+ 170u
3
− 77u
2
+ 11b − 6u + 16,
96u
6
− 412u
5
+ 861u
4
− 1115u
3
+ 935u
2
+ 11a − 455u + 106,
4u
7
− 17u
6
+ 36u
5
− 48u
4
+ 43u
3
− 24u
2
+ 8u − 1i
I
u
4
= h−8148149u
18
a − 235125959u
18
+ ··· + 8148149a + 240741869,
7782798u
18
a + 171992551u
18
+ ··· + 92850756a − 39782144, u
19
+ 5u
18
+ ··· − 4u − 1i
* 4 irreducible components of dim
C
= 0, with total 192 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−4.40 × 10
29
u
28
+ 7.02 × 10
30
u
27
+ · · · + 4.21 × 10
28
b + 1.41 ×
10
31
, 5.67 × 10
29
u
28
− 1.06 × 10
31
u
27
+ · · · + 5.06 × 10
29
a − 3.29 ×
10
31
, 4u
29
− 67u
28
+ · · · − 1032u + 144i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
−1.12039u
28
+ 20.9833u
27
+ ··· − 489.650u + 65.0942
10.4360u
28
− 166.584u
27
+ ··· + 2133.17u − 335.363
a
5
=
1
u
2
a
1
=
9.31564u
28
− 145.601u
27
+ ··· + 1643.52u − 270.269
10.4360u
28
− 166.584u
27
+ ··· + 2133.17u − 335.363
a
9
=
−0.167275u
28
+ 1.19205u
27
+ ··· + 351.772u − 65.4652
−1.14188u
28
+ 19.5944u
27
+ ··· − 355.098u + 47.1296
a
3
=
−5.90644u
28
+ 97.0033u
27
+ ··· − 1411.96u + 203.811
9.23677u
28
− 145.692u
27
+ ··· + 1725.62u − 266.262
a
12
=
7.09885u
28
− 114.752u
27
+ ··· + 1867.48u − 310.603
2.01104u
28
− 31.9469u
27
+ ··· + 592.051u − 109.188
a
6
=
0.300652u
28
− 4.39629u
27
+ ··· + 104.297u − 23.3575
−0.314456u
28
+ 5.41479u
27
+ ··· + 45.5803u − 17.0050
a
7
=
−6.39600u
28
+ 102.252u
27
+ ··· − 1202.06u + 178.195
−3.56491u
28
+ 61.8556u
27
+ ··· − 1702.73u + 287.027
a
8
=
7.43460u
28
− 120.183u
27
+ ··· + 2485.47u − 437.881
5.17344u
28
− 80.0547u
27
+ ··· + 1078.28u − 196.079
a
11
=
10.9183u
28
− 170.654u
27
+ ··· + 2401.20u − 411.393
12.2274u
28
− 191.440u
27
+ ··· + 2406.52u − 393.058
(ii) Obstruction class = −1
(iii) Cusp Shapes = −56.3204u
28
+ 888.787u
27
+ ··· − 10030.5u + 1517.92
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
29
+ 2u
27
+ ··· + 13u + 4
c
2
, c
5
, c
9
c
12
u
29
+ 13u
27
+ ··· + 3u + 1
c
3
, c
6
, c
7
c
11
2(2u
29
+ u
28
+ ··· − 2u
2
+ 1)
c
4
4(4u
29
− 67u
28
+ ··· − 1032u + 144)
c
8
u
29
− 9u
28
+ ··· − 2794u + 324
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
29
+ 4y
28
+ ··· + 361y −16
c
2
, c
5
, c
9
c
12
y
29
+ 26y
28
+ ··· − y −1
c
3
, c
6
, c
7
c
11
4(4y
29
− 69y
28
+ ··· + 4y −1)
c
4
16(16y
29
− 113y
28
+ ··· + 197280y −20736)
c
8
y
29
− 7y
28
+ ··· + 371932y −104976
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.720097 + 0.708724I
a = 0.816159 − 0.207612I
b = −0.169307 + 1.103730I
−2.35305 + 2.75713I −6.94256 − 4.42813I
u = 0.720097 − 0.708724I
a = 0.816159 + 0.207612I
b = −0.169307 − 1.103730I
−2.35305 − 2.75713I −6.94256 + 4.42813I
u = −1.073600 + 0.143769I
a = −0.29269 + 1.43804I
b = 0.104360 − 0.757596I
−11.29210 − 3.08774I −16.1022 + 0.5651I
u = −1.073600 − 0.143769I
a = −0.29269 − 1.43804I
b = 0.104360 + 0.757596I
−11.29210 + 3.08774I −16.1022 − 0.5651I
u = 0.824430 + 0.723434I
a = −0.409830 + 0.858684I
b = −0.840941 − 1.121640I
−2.53290 − 7.99007I −6.91156 + 8.81648I
u = 0.824430 − 0.723434I
a = −0.409830 − 0.858684I
b = −0.840941 + 1.121640I
−2.53290 + 7.99007I −6.91156 − 8.81648I
u = 0.466322 + 0.746390I
a = 0.521683 − 0.597880I
b = 0.339053 + 0.681385I
2.29372 + 0.20351I 3.05461 − 1.89825I
u = 0.466322 − 0.746390I
a = 0.521683 + 0.597880I
b = 0.339053 − 0.681385I
2.29372 − 0.20351I 3.05461 + 1.89825I
u = 0.658708 + 0.957825I
a = −0.745982 − 0.471011I
b = 0.936085 − 0.375554I
−5.81070 + 3.60180I −14.0003 − 4.5219I
u = 0.658708 − 0.957825I
a = −0.745982 + 0.471011I
b = 0.936085 + 0.375554I
−5.81070 − 3.60180I −14.0003 + 4.5219I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.057443 + 0.816735I
a = 0.837762 − 0.521934I
b = −0.102754 + 0.596050I
0.31369 + 1.71075I 0.74020 − 4.40719I
u = −0.057443 − 0.816735I
a = 0.837762 + 0.521934I
b = −0.102754 − 0.596050I
0.31369 − 1.71075I 0.74020 + 4.40719I
u = 0.745889 + 0.082585I
a = −0.150710 + 0.499245I
b = −0.96323 + 1.10340I
−1.67729 + 3.70537I −2.81014 − 3.47039I
u = 0.745889 − 0.082585I
a = −0.150710 − 0.499245I
b = −0.96323 − 1.10340I
−1.67729 − 3.70537I −2.81014 + 3.47039I
u = 1.086530 + 0.685326I
a = −0.229661 − 0.935105I
b = 1.61437 + 0.77483I
−7.32559 − 9.58865I 0
u = 1.086530 − 0.685326I
a = −0.229661 + 0.935105I
b = 1.61437 − 0.77483I
−7.32559 + 9.58865I 0
u = 1.222990 + 0.529637I
a = 0.003013 + 0.787535I
b = −1.26809 − 1.31448I
−3.88276 − 6.49679I 0
u = 1.222990 − 0.529637I
a = 0.003013 − 0.787535I
b = −1.26809 + 1.31448I
−3.88276 + 6.49679I 0
u = −0.644975 + 0.131653I
a = −0.53666 + 2.56308I
b = 0.088584 − 1.040810I
−9.42418 + 4.39090I −3.18290 − 8.10704I
u = −0.644975 − 0.131653I
a = −0.53666 − 2.56308I
b = 0.088584 + 1.040810I
−9.42418 − 4.39090I −3.18290 + 8.10704I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.632833
a = 0.443093
b = −0.171728
−1.18425 −6.90200
u = 1.32674 + 0.78308I
a = 0.016779 + 0.590118I
b = −0.666236 − 0.839680I
−0.43628 − 5.75837I 0
u = 1.32674 − 0.78308I
a = 0.016779 − 0.590118I
b = −0.666236 + 0.839680I
−0.43628 + 5.75837I 0
u = 1.36364 + 0.87040I
a = −0.246329 − 0.990685I
b = 1.31604 + 1.15458I
−14.7881 − 19.4687I 0
u = 1.36364 − 0.87040I
a = −0.246329 + 0.990685I
b = 1.31604 − 1.15458I
−14.7881 + 19.4687I 0
u = 1.61175 + 0.69141I
a = 0.147204 + 0.728894I
b = −0.844171 − 1.132660I
−4.85481 − 7.14721I 0
u = 1.61175 − 0.69141I
a = 0.147204 − 0.728894I
b = −0.844171 + 1.132660I
−4.85481 + 7.14721I 0
u = 0.44033 + 1.98075I
a = −0.660627 + 0.066836I
b = 0.542107 − 0.366872I
−11.6596 + 10.7457I 0
u = 0.44033 − 1.98075I
a = −0.660627 − 0.066836I
b = 0.542107 + 0.366872I
−11.6596 − 10.7457I 0
7
II. I
u
2
= h4.09 × 10
106
au
58
− 8.30 × 10
109
u
58
+ · · · + 1.51 × 10
108
a − 4.80 ×
10
111
, 3.55 × 10
112
au
58
− 1.91 × 10
111
u
58
+ · · · + 1.93 × 10
114
a + 1.37 ×
10
113
, u
59
+ 5u
58
+ · · · + 88u + 37i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
a
−0.333333au
58
+ 676.688u
58
+ ··· − 12.3333a + 39071.5
a
5
=
1
u
2
a
1
=
−0.333333au
58
+ 676.688u
58
+ ··· − 11.3333a + 39071.5
−0.333333au
58
+ 676.688u
58
+ ··· − 12.3333a + 39071.5
a
9
=
−427.925au
58
+ 83.4254u
58
+ ··· − 23483.0a + 1263.58
−248.764au
58
+ 673.597u
58
+ ··· − 15588.5a + 28009.8
a
3
=
−359.971au
58
− 1877.03u
58
+ ··· − 13372.4a − 98725.3
−468.025au
58
− 728.793u
58
+ ··· − 21966.8a − 41528.5
a
12
=
−0.333333au
58
+ 248.764u
58
+ ··· − 11.3333a + 15588.5
−0.333333au
58
+ 488.441u
58
+ ··· − 12.3333a + 28492.8
a
6
=
−135.399au
58
+ 384.267u
58
+ ··· − 9204.26a + 20691.9
−299.329au
58
+ 543.289u
58
+ ··· − 18072.3a + 23201.5
a
7
=
−14.1655au
58
+ 2972.25u
58
+ ··· − 12657.8a + 156717.
178.414au
58
+ 913.497u
58
+ ··· + 5746.28a + 47640.1
a
8
=
−179.259au
58
− 651.148u
58
+ ··· − 5103.34a − 37252.9
392.636au
58
− 1102.18u
58
+ ··· + 24548.9a − 52252.9
a
11
=
−676.688au
58
+ 806.803u
58
+ ··· − 39071.5a + 29162.6
49.7802u
58
+ 181.256u
57
+ ··· + 3949.92u − 110.842
(ii) Obstruction class = −1
(iii) Cusp Shapes = −724.938u
58
− 3242.57u
57
+ ··· − 32438.6u − 48642.6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
118
− 11u
117
+ ··· − 3135u + 89
c
2
, c
5
u
118
− 3u
117
+ ··· − 482474u − 33653
c
3
, c
7
u
118
+ 4u
117
+ ··· + 1173178u − 289973
c
4
(u
59
+ 5u
58
+ ··· + 88u + 37)
2
c
6
, c
11
− u
118
+ 4u
117
+ ··· + 1173178u + 289973
c
8
(u
59
− u
58
+ ··· − 25551u − 10881)
2
c
9
, c
12
− u
118
− 3u
117
+ ··· − 482474u + 33653
c
10
u
118
+ 11u
117
+ ··· + 3135u + 89
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
118
− 19y
117
+ ··· − 1556387y + 7921
c
2
, c
5
, c
9
c
12
y
118
+ 105y
117
+ ··· − 4589119374y + 1132524409
c
3
, c
6
, c
7
c
11
y
118
− 90y
117
+ ··· − 3230687998032y + 84084340729
c
4
(y
59
− 29y
58
+ ··· + 56066y −1369)
2
c
8
(y
59
− 41y
58
+ ··· + 2158261713y −118396161)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.925169 + 0.382015I
a = 0.035968 + 1.143290I
b = −1.21126 − 1.25562I
−3.29612 − 3.39378I 0
u = 0.925169 + 0.382015I
a = −0.552856 − 0.144734I
b = −1.044430 − 0.552897I
−3.29612 − 3.39378I 0
u = 0.925169 − 0.382015I
a = 0.035968 − 1.143290I
b = −1.21126 + 1.25562I
−3.29612 + 3.39378I 0
u = 0.925169 − 0.382015I
a = −0.552856 + 0.144734I
b = −1.044430 + 0.552897I
−3.29612 + 3.39378I 0
u = −0.747145 + 0.669765I
a = −0.982655 + 0.906547I
b = 1.86104 − 0.60151I
−10.04250 − 1.49168I 0
u = −0.747145 + 0.669765I
a = −0.92063 − 1.15205I
b = −0.860579 + 0.360405I
−10.04250 − 1.49168I 0
u = −0.747145 − 0.669765I
a = −0.982655 − 0.906547I
b = 1.86104 + 0.60151I
−10.04250 + 1.49168I 0
u = −0.747145 − 0.669765I
a = −0.92063 + 1.15205I
b = −0.860579 − 0.360405I
−10.04250 + 1.49168I 0
u = −0.906248 + 0.369714I
a = −1.046790 + 0.147402I
b = −1.044490 + 0.604996I
−5.20943 + 4.94504I 0
u = −0.906248 + 0.369714I
a = −0.395471 + 1.285810I
b = 1.61705 − 1.45504I
−5.20943 + 4.94504I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.906248 − 0.369714I
a = −1.046790 − 0.147402I
b = −1.044490 − 0.604996I
−5.20943 − 4.94504I 0
u = −0.906248 − 0.369714I
a = −0.395471 − 1.285810I
b = 1.61705 + 1.45504I
−5.20943 − 4.94504I 0
u = −0.692262 + 0.769246I
a = 0.314146 − 1.048700I
b = −0.540795 + 0.898103I
−0.07380 + 2.38506I 0
u = −0.692262 + 0.769246I
a = 0.721905 − 0.121987I
b = 0.272743 − 0.070100I
−0.07380 + 2.38506I 0
u = −0.692262 − 0.769246I
a = 0.314146 + 1.048700I
b = −0.540795 − 0.898103I
−0.07380 − 2.38506I 0
u = −0.692262 − 0.769246I
a = 0.721905 + 0.121987I
b = 0.272743 + 0.070100I
−0.07380 − 2.38506I 0
u = −0.823608 + 0.499933I
a = 0.009280 − 1.114320I
b = −0.72575 + 1.65605I
−3.78280 + 2.08366I 0
u = −0.823608 + 0.499933I
a = 1.216570 − 0.274113I
b = 0.319259 − 0.804366I
−3.78280 + 2.08366I 0
u = −0.823608 − 0.499933I
a = 0.009280 + 1.114320I
b = −0.72575 − 1.65605I
−3.78280 − 2.08366I 0
u = −0.823608 − 0.499933I
a = 1.216570 + 0.274113I
b = 0.319259 + 0.804366I
−3.78280 − 2.08366I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.028090 + 0.174565I
a = −0.05948 + 1.49500I
b = 0.55725 − 1.55166I
−13.68870 + 1.27084I 0
u = 1.028090 + 0.174565I
a = −0.24389 − 1.58507I
b = 0.521647 + 0.028648I
−13.68870 + 1.27084I 0
u = 1.028090 − 0.174565I
a = −0.05948 − 1.49500I
b = 0.55725 + 1.55166I
−13.68870 − 1.27084I 0
u = 1.028090 − 0.174565I
a = −0.24389 + 1.58507I
b = 0.521647 − 0.028648I
−13.68870 − 1.27084I 0
u = 0.942697 + 0.483424I
a = 0.985735 − 0.088354I
b = 0.682191 + 0.581000I
−4.40219 − 0.14299I 0
u = 0.942697 + 0.483424I
a = −0.510967 − 1.076570I
b = 1.33419 + 1.27073I
−4.40219 − 0.14299I 0
u = 0.942697 − 0.483424I
a = 0.985735 + 0.088354I
b = 0.682191 − 0.581000I
−4.40219 + 0.14299I 0
u = 0.942697 − 0.483424I
a = −0.510967 + 1.076570I
b = 1.33419 − 1.27073I
−4.40219 + 0.14299I 0
u = −0.928534 + 0.003793I
a = −0.18750 + 1.50332I
b = 1.22888 − 1.06141I
−10.33520 − 4.10717I 0
u = −0.928534 + 0.003793I
a = −0.35948 + 1.54405I
b = −0.968632 − 0.406372I
−10.33520 − 4.10717I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.928534 − 0.003793I
a = −0.18750 − 1.50332I
b = 1.22888 + 1.06141I
−10.33520 + 4.10717I 0
u = −0.928534 − 0.003793I
a = −0.35948 − 1.54405I
b = −0.968632 + 0.406372I
−10.33520 + 4.10717I 0
u = −0.602517 + 0.678066I
a = −0.455795 − 1.107230I
b = −0.577694 + 0.829370I
0.62054 + 3.49413I 0
u = −0.602517 + 0.678066I
a = 0.295413 + 0.402109I
b = 0.811099 − 0.533362I
0.62054 + 3.49413I 0
u = −0.602517 − 0.678066I
a = −0.455795 + 1.107230I
b = −0.577694 − 0.829370I
0.62054 − 3.49413I 0
u = −0.602517 − 0.678066I
a = 0.295413 − 0.402109I
b = 0.811099 + 0.533362I
0.62054 − 3.49413I 0
u = 0.843807 + 0.011210I
a = −0.26781 + 1.53879I
b = 1.69725 − 1.45549I
−14.4409 − 9.2601I 0
u = 0.843807 + 0.011210I
a = 0.78291 − 1.83764I
b = 1.205240 + 0.086311I
−14.4409 − 9.2601I 0
u = 0.843807 − 0.011210I
a = −0.26781 − 1.53879I
b = 1.69725 + 1.45549I
−14.4409 + 9.2601I 0
u = 0.843807 − 0.011210I
a = 0.78291 + 1.83764I
b = 1.205240 − 0.086311I
−14.4409 + 9.2601I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.962252 + 0.649649I
a = −0.329567 + 1.313680I
b = 1.134780 − 0.386890I
−10.72170 + 6.62436I 0
u = −0.962252 + 0.649649I
a = 0.380380 + 0.097982I
b = −1.37690 − 0.36870I
−10.72170 + 6.62436I 0
u = −0.962252 − 0.649649I
a = −0.329567 − 1.313680I
b = 1.134780 + 0.386890I
−10.72170 − 6.62436I 0
u = −0.962252 − 0.649649I
a = 0.380380 − 0.097982I
b = −1.37690 + 0.36870I
−10.72170 − 6.62436I 0
u = 0.810093
a = −0.26112 + 1.67767I
b = −1.113860 − 0.750829I
−6.16998 0
u = 0.810093
a = −0.26112 − 1.67767I
b = −1.113860 + 0.750829I
−6.16998 0
u = −0.999222 + 0.769363I
a = 0.384087 − 0.908940I
b = −0.950138 + 0.948579I
−1.05556 + 3.49309I 0
u = −0.999222 + 0.769363I
a = 0.520745 + 0.338761I
b = 0.535115 − 0.475107I
−1.05556 + 3.49309I 0
u = −0.999222 − 0.769363I
a = 0.384087 + 0.908940I
b = −0.950138 − 0.948579I
−1.05556 − 3.49309I 0
u = −0.999222 − 0.769363I
a = 0.520745 − 0.338761I
b = 0.535115 + 0.475107I
−1.05556 − 3.49309I 0
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.450304 + 0.577978I
a = 0.099752 + 0.713886I
b = 0.518506 − 1.088280I
−3.01401 − 3.69735I 0. + 10.67882I
u = 0.450304 + 0.577978I
a = −1.23156 − 1.65986I
b = 0.494796 + 0.188749I
−3.01401 − 3.69735I 0. + 10.67882I
u = 0.450304 − 0.577978I
a = 0.099752 − 0.713886I
b = 0.518506 + 1.088280I
−3.01401 + 3.69735I 0. − 10.67882I
u = 0.450304 − 0.577978I
a = −1.23156 + 1.65986I
b = 0.494796 − 0.188749I
−3.01401 + 3.69735I 0. − 10.67882I
u = −0.707702
a = 0.375182 + 0.233291I
b = −0.155482 + 0.564837I
−1.10836 −4.56540
u = −0.707702
a = 0.375182 − 0.233291I
b = −0.155482 − 0.564837I
−1.10836 −4.56540
u = 0.893562 + 0.934702I
a = 0.675084 + 0.807292I
b = −1.44714 − 0.83277I
−3.84434 − 5.57990I 0
u = 0.893562 + 0.934702I
a = −0.572786 + 1.108320I
b = −0.666059 − 0.744407I
−3.84434 − 5.57990I 0
u = 0.893562 − 0.934702I
a = 0.675084 − 0.807292I
b = −1.44714 + 0.83277I
−3.84434 + 5.57990I 0
u = 0.893562 − 0.934702I
a = −0.572786 − 1.108320I
b = −0.666059 + 0.744407I
−3.84434 + 5.57990I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.696637 + 0.083139I
a = −0.38598 + 2.08102I
b = −0.75671 − 1.22228I
−9.32017 + 4.46189I −9.18240 − 6.18854I
u = −0.696637 + 0.083139I
a = 0.13988 + 2.55095I
b = 0.724644 − 0.693230I
−9.32017 + 4.46189I −9.18240 − 6.18854I
u = −0.696637 − 0.083139I
a = −0.38598 − 2.08102I
b = −0.75671 + 1.22228I
−9.32017 − 4.46189I −9.18240 + 6.18854I
u = −0.696637 − 0.083139I
a = 0.13988 − 2.55095I
b = 0.724644 + 0.693230I
−9.32017 − 4.46189I −9.18240 + 6.18854I
u = 1.035270 + 0.785518I
a = −0.427877 − 1.081950I
b = 1.20120 + 1.02676I
−5.05494 − 8.54364I 0
u = 1.035270 + 0.785518I
a = 0.369989 − 0.479615I
b = 0.843940 + 0.550322I
−5.05494 − 8.54364I 0
u = 1.035270 − 0.785518I
a = −0.427877 + 1.081950I
b = 1.20120 − 1.02676I
−5.05494 + 8.54364I 0
u = 1.035270 − 0.785518I
a = 0.369989 + 0.479615I
b = 0.843940 − 0.550322I
−5.05494 + 8.54364I 0
u = −1.018020 + 0.832767I
a = −0.641735 − 0.893634I
b = −0.793142 + 0.933931I
−8.7119 + 12.7975I 0
u = −1.018020 + 0.832767I
a = −0.510812 + 1.068150I
b = 1.42717 − 1.23594I
−8.7119 + 12.7975I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.018020 − 0.832767I
a = −0.641735 + 0.893634I
b = −0.793142 − 0.933931I
−8.7119 − 12.7975I 0
u = −1.018020 − 0.832767I
a = −0.510812 − 1.068150I
b = 1.42717 + 1.23594I
−8.7119 − 12.7975I 0
u = −0.657897 + 0.088992I
a = 0.017199 + 0.837005I
b = −0.89379 − 1.50457I
−4.50270 − 2.59075I −19.4386 + 1.2249I
u = −0.657897 + 0.088992I
a = 0.39424 + 2.06513I
b = 0.636115 + 0.361177I
−4.50270 − 2.59075I −19.4386 + 1.2249I
u = −0.657897 − 0.088992I
a = 0.017199 − 0.837005I
b = −0.89379 + 1.50457I
−4.50270 + 2.59075I −19.4386 − 1.2249I
u = −0.657897 − 0.088992I
a = 0.39424 − 2.06513I
b = 0.636115 − 0.361177I
−4.50270 + 2.59075I −19.4386 − 1.2249I
u = 0.583420 + 0.267930I
a = −0.89169 − 2.24870I
b = 1.44798 + 2.22650I
−11.83730 − 3.27693I −25.8812 + 12.8282I
u = 0.583420 + 0.267930I
a = 3.16646 + 2.07425I
b = 0.330498 + 0.136093I
−11.83730 − 3.27693I −25.8812 + 12.8282I
u = 0.583420 − 0.267930I
a = −0.89169 + 2.24870I
b = 1.44798 − 2.22650I
−11.83730 + 3.27693I −25.8812 − 12.8282I
u = 0.583420 − 0.267930I
a = 3.16646 − 2.07425I
b = 0.330498 − 0.136093I
−11.83730 + 3.27693I −25.8812 − 12.8282I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.189460 + 0.720703I
a = −0.342957 + 0.868597I
b = 1.49856 − 0.98638I
−6.57943 + 6.00487I 0
u = −1.189460 + 0.720703I
a = 0.000576 − 0.924742I
b = −1.28965 + 0.97295I
−6.57943 + 6.00487I 0
u = −1.189460 − 0.720703I
a = −0.342957 − 0.868597I
b = 1.49856 + 0.98638I
−6.57943 − 6.00487I 0
u = −1.189460 − 0.720703I
a = 0.000576 + 0.924742I
b = −1.28965 − 0.97295I
−6.57943 − 6.00487I 0
u = −0.91731 + 1.09732I
a = −0.852335 + 0.500366I
b = 0.559482 + 0.183737I
−8.08661 − 5.91230I 0
u = −0.91731 + 1.09732I
a = 0.329713 + 0.566365I
b = −0.482043 − 0.948887I
−8.08661 − 5.91230I 0
u = −0.91731 − 1.09732I
a = −0.852335 − 0.500366I
b = 0.559482 − 0.183737I
−8.08661 + 5.91230I 0
u = −0.91731 − 1.09732I
a = 0.329713 − 0.566365I
b = −0.482043 + 0.948887I
−8.08661 + 5.91230I 0
u = 0.561900
a = 0.487602
b = −1.82901
−5.64486 −23.3900
u = 0.561900
a = −2.50131
b = −0.753739
−5.64486 −23.3900
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.548044
a = 0.429754 + 0.773421I
b = −0.152143 + 0.937853I
−1.13982 −4.25130
u = −0.548044
a = 0.429754 − 0.773421I
b = −0.152143 − 0.937853I
−1.13982 −4.25130
u = 0.445877 + 0.176282I
a = −1.242670 − 0.380728I
b = −0.557235 + 0.677629I
−2.09096 + 1.40291I −8.24032 − 3.30492I
u = 0.445877 + 0.176282I
a = 0.29370 + 1.92654I
b = −0.854876 − 0.184911I
−2.09096 + 1.40291I −8.24032 − 3.30492I
u = 0.445877 − 0.176282I
a = −1.242670 + 0.380728I
b = −0.557235 − 0.677629I
−2.09096 − 1.40291I −8.24032 + 3.30492I
u = 0.445877 − 0.176282I
a = 0.29370 − 1.92654I
b = −0.854876 + 0.184911I
−2.09096 − 1.40291I −8.24032 + 3.30492I
u = 1.45834 + 0.86858I
a = 0.301924 + 0.656569I
b = −0.449909 − 0.349683I
−4.58536 − 1.70574I 0
u = 1.45834 + 0.86858I
a = 0.149226 − 0.360368I
b = −0.482370 + 0.319006I
−4.58536 − 1.70574I 0
u = 1.45834 − 0.86858I
a = 0.301924 − 0.656569I
b = −0.449909 + 0.349683I
−4.58536 + 1.70574I 0
u = 1.45834 − 0.86858I
a = 0.149226 + 0.360368I
b = −0.482370 − 0.319006I
−4.58536 + 1.70574I 0
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.45290 + 0.90357I
a = −0.241091 + 0.942961I
b = 1.12508 − 1.07027I
−10.3029 + 12.4591I 0
u = −1.45290 + 0.90357I
a = 0.280567 − 0.799779I
b = −1.16931 + 0.98371I
−10.3029 + 12.4591I 0
u = −1.45290 − 0.90357I
a = −0.241091 − 0.942961I
b = 1.12508 + 1.07027I
−10.3029 − 12.4591I 0
u = −1.45290 − 0.90357I
a = 0.280567 + 0.799779I
b = −1.16931 − 0.98371I
−10.3029 − 12.4591I 0
u = 1.44959 + 1.07777I
a = −0.303287 − 0.856609I
b = 1.025880 + 0.730032I
−16.0808 − 5.1756I 0
u = 1.44959 + 1.07777I
a = −0.486979 − 0.609835I
b = 1.183880 + 0.595302I
−16.0808 − 5.1756I 0
u = 1.44959 − 1.07777I
a = −0.303287 + 0.856609I
b = 1.025880 − 0.730032I
−16.0808 + 5.1756I 0
u = 1.44959 − 1.07777I
a = −0.486979 + 0.609835I
b = 1.183880 − 0.595302I
−16.0808 + 5.1756I 0
u = 1.60371 + 0.84957I
a = −0.347412 − 0.536087I
b = 0.406139 + 0.501138I
−4.33700 + 1.31231I 0
u = 1.60371 + 0.84957I
a = 0.203144 + 0.145405I
b = 0.1238730 − 0.0061557I
−4.33700 + 1.31231I 0
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60371 − 0.84957I
a = −0.347412 + 0.536087I
b = 0.406139 − 0.501138I
−4.33700 − 1.31231I 0
u = 1.60371 − 0.84957I
a = 0.203144 − 0.145405I
b = 0.1238730 + 0.0061557I
−4.33700 − 1.31231I 0
u = −0.40398 + 1.82642I
a = −0.567135 + 0.240518I
b = 0.466392 + 0.038981I
−3.87819 + 1.02290I 0
u = −0.40398 + 1.82642I
a = 0.436284 + 0.048963I
b = −0.469784 − 0.296912I
−3.87819 + 1.02290I 0
u = −0.40398 − 1.82642I
a = −0.567135 − 0.240518I
b = 0.466392 − 0.038981I
−3.87819 − 1.02290I 0
u = −0.40398 − 1.82642I
a = 0.436284 − 0.048963I
b = −0.469784 + 0.296912I
−3.87819 − 1.02290I 0
u = −2.43992
a = −0.047502 + 0.506009I
b = 0.033693 − 0.857425I
−6.96191 0
u = −2.43992
a = −0.047502 − 0.506009I
b = 0.033693 + 0.857425I
−6.96191 0
22
III. I
u
3
= h−32u
6
+ 108u
5
+ · · · + 11b + 16, 96u
6
− 412u
5
+ · · · + 11a +
106, 4u
7
− 17u
6
+ · · · + 8u − 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
−8.72727u
6
+ 37.4545u
5
+ ··· + 41.3636u − 9.63636
2.90909u
6
− 9.81818u
5
+ ··· + 0.545455u − 1.45455
a
5
=
1
u
2
a
1
=
−5.81818u
6
+ 27.6364u
5
+ ··· + 41.9091u − 11.0909
2.90909u
6
− 9.81818u
5
+ ··· + 0.545455u − 1.45455
a
9
=
−9.09091u
6
+ 33.1818u
5
+ ··· + 25.5455u − 6.45455
−3.63636u
6
+ 17.2727u
5
+ ··· + 16.8182u − 3.18182
a
3
=
−13.0909u
6
+ 54.1818u
5
+ ··· + 57.5455u − 14.4545
−1.45455u
6
+ 6.90909u
5
+ ··· + 10.7273u − 3.27273
a
12
=
−6.18182u
6
+ 27.3636u
5
+ ··· + 34.0909u − 8.90909
1.81818u
6
− 6.63636u
5
+ ··· + 4.09091u − 1.90909
a
6
=
−7.27273u
6
+ 30.5455u
5
+ ··· + 29.6364u − 6.36364
−3.27273u
6
+ 13.5455u
5
+ ··· + 10.6364u − 2.36364
a
7
=
7.63636u
6
− 30.2727u
5
+ ··· − 37.8182u + 11.1818
2.18182u
6
− 6.36364u
5
+ ··· − 4.09091u + 1.90909
a
8
=
−10.1818u
6
+ 40.3636u
5
+ ··· + 29.0909u − 4.90909
4u
5
− 13u
4
+ 23u
3
− 23u
2
+ 13u − 2
a
11
=
−13.8182u
6
+ 57.6364u
5
+ ··· + 55.9091u − 13.0909
−1.09091u
6
+ 7.18182u
5
+ ··· + 15.5455u − 3.45455
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
192
11
u
6
+
780
11
u
5
−
1491
11
u
4
+
1680
11
u
3
− 107u
2
+
404
11
u −
124
11
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
7
− 2u
6
+ u
5
+ 4u
4
− 3u
3
+ u
2
+ u − 4
c
2
, c
5
u
7
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 1
c
3
, c
7
2(2u
7
+ 3u
6
− 5u
5
− 8u
4
+ 4u
3
+ 5u
2
− u − 1)
c
4
4(4u
7
− 17u
6
+ 36u
5
− 48u
4
+ 43u
3
− 24u
2
+ 8u − 1)
c
6
, c
11
2(2u
7
− 3u
6
− 5u
5
+ 8u
4
+ 4u
3
− 5u
2
− u + 1)
c
8
u
7
− 4u
5
− u
4
+ 7u
3
+ 11u
2
− u − 11
c
9
, c
12
u
7
+ 2u
5
− u
4
+ 2u
3
− u
2
− 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
7
− 2y
6
+ 11y
5
− 16y
4
− 13y
3
+ 25y
2
+ 9y −16
c
2
, c
5
, c
9
c
12
y
7
+ 4y
6
+ 8y
5
+ 7y
4
+ 2y
3
− 3y
2
− 2y −1
c
3
, c
6
, c
7
c
11
4(4y
7
− 29y
6
+ 89y
5
− 138y
4
+ 112y
3
− 49y
2
+ 11y −1)
c
4
16(16y
7
− y
6
+ 8y
5
+ 40y
4
+ 87y
3
+ 16y
2
+ 16y −1)
c
8
y
7
− 8y
6
+ 30y
5
− 59y
4
+ 79y
3
− 157y
2
+ 243y −121
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376823 + 1.074160I
a = −0.885548 − 0.766128I
b = 1.061330 − 0.160261I
−12.2106 − 9.4746I −12.16424 + 5.63145I
u = 0.376823 − 1.074160I
a = −0.885548 + 0.766128I
b = 1.061330 + 0.160261I
−12.2106 + 9.4746I −12.16424 − 5.63145I
u = 1.191480 + 0.572638I
a = 0.010755 + 0.841265I
b = −1.33777 − 1.26620I
−3.79534 − 6.00484I −8.03203 − 1.33789I
u = 1.191480 − 0.572638I
a = 0.010755 − 0.841265I
b = −1.33777 + 1.26620I
−3.79534 + 6.00484I −8.03203 + 1.33789I
u = 0.436244 + 0.517635I
a = 1.085950 + 0.158069I
b = −0.180490 + 0.953697I
−1.23694 + 1.46776I −5.36065 − 3.82447I
u = 0.436244 − 0.517635I
a = 1.085950 − 0.158069I
b = −0.180490 − 0.953697I
−1.23694 − 1.46776I −5.36065 + 3.82447I
u = 0.240914
a = −3.42230
b = −1.08615
−4.99256 −6.90180
26
IV.
I
u
4
= h−8.15 × 10
6
au
18
− 2.35 × 10
8
u
18
+ · · · + 8.15 × 10
6
a + 2.41 × 10
8
, 7.78 ×
10
6
au
18
+1.72×10
8
u
18
+· · ·+9.29×10
7
a−3.98×10
7
, u
19
+5u
18
+· · ·−4u−1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
a
0.200000au
18
+ 5.77127u
18
+ ··· − 0.200000a − 5.90912
a
5
=
1
u
2
a
1
=
0.200000au
18
+ 5.77127u
18
+ ··· + 0.800000a − 5.90912
0.200000au
18
+ 5.77127u
18
+ ··· − 0.200000a − 5.90912
a
9
=
−3.98404au
18
− 15.3535u
18
+ ··· + 0.955161a + 21.1082
−1.78723au
18
− 8.37699u
18
+ ··· + 4.95396a + 23.7305
a
3
=
19.7857au
18
+ 28.0898u
18
+ ··· − 32.4552a − 88.5857
−1.93633au
18
− 8.09924u
18
+ ··· + 1.06391a + 8.30978
a
12
=
0.200000au
18
+ 1.78723u
18
+ ··· + 0.800000a − 4.95396
0.200000au
18
+ 3.44848u
18
+ ··· − 0.200000a − 1.73491
a
6
=
−0.779744au
18
+ 17.4898u
18
+ ··· + 1.78723a − 21.3721
−3.73304au
18
− 16.3394u
18
+ ··· + 3.44848a + 23.8214
a
7
=
10.7677au
18
+ 3.80821u
18
+ ··· − 25.9144a − 42.9290
−0.457859au
18
+ 8.60091u
18
+ ··· + 4.20939a − 2.79683
a
8
=
−3.68749au
18
− 28.0981u
18
+ ··· − 1.61108a + 44.5207
1.89463au
18
+ 10.4187u
18
+ ··· + 0.313779a − 7.65781
a
11
=
−5.77127au
18
− 24.5662u
18
+ ··· + 5.90912a + 50.7655
−0.835697u
18
− 4.33279u
17
+ ··· + 11.2242u + 5.92680
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
32488608
8148149
u
18
−
152731709
8148149
u
17
+ ··· +
28904977
8148149
u −
7936733
8148149
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
38
− 6u
37
+ ··· + u + 1
c
2
, c
5
u
38
+ 19u
36
+ ··· + 5u
2
+ 1
c
3
, c
7
u
38
− 5u
37
+ ··· − 12u
2
+ 1
c
4
(u
19
+ 5u
18
+ ··· − 4u − 1)
2
c
6
, c
11
u
38
+ 5u
37
+ ··· − 12u
2
+ 1
c
8
(u
19
+ 7u
18
+ ··· + u + 1)
2
c
9
, c
12
u
38
+ 19u
36
+ ··· + 5u
2
+ 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
38
+ 6y
37
+ ··· − 19y + 1
c
2
, c
5
, c
9
c
12
y
38
+ 38y
37
+ ··· + 10y + 1
c
3
, c
6
, c
7
c
11
y
38
− 21y
37
+ ··· − 24y + 1
c
4
(y
19
− 15y
18
+ ··· + 10y −1)
2
c
8
(y
19
− 3y
18
+ ··· + 25y −1)
2
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.022190 + 0.280778I
a = 0.058058 + 0.917000I
b = −1.21944 − 1.44628I
−2.80024 − 4.61458I −8.75408 + 7.60448I
u = 1.022190 + 0.280778I
a = −0.432107 − 0.143805I
b = −1.038550 − 0.867111I
−2.80024 − 4.61458I −8.75408 + 7.60448I
u = 1.022190 − 0.280778I
a = 0.058058 − 0.917000I
b = −1.21944 + 1.44628I
−2.80024 + 4.61458I −8.75408 − 7.60448I
u = 1.022190 − 0.280778I
a = −0.432107 + 0.143805I
b = −1.038550 + 0.867111I
−2.80024 + 4.61458I −8.75408 − 7.60448I
u = −0.645543 + 0.674479I
a = 0.762389 − 0.359856I
b = 0.360780 − 0.060999I
−0.81056 + 2.89349I −8.24729 − 5.80229I
u = −0.645543 + 0.674479I
a = 0.126801 − 1.263230I
b = −0.441195 + 1.029230I
−0.81056 + 2.89349I −8.24729 − 5.80229I
u = −0.645543 − 0.674479I
a = 0.762389 + 0.359856I
b = 0.360780 + 0.060999I
−0.81056 − 2.89349I −8.24729 + 5.80229I
u = −0.645543 − 0.674479I
a = 0.126801 + 1.263230I
b = −0.441195 − 1.029230I
−0.81056 − 2.89349I −8.24729 + 5.80229I
u = −0.980359 + 0.430482I
a = 0.143993 − 1.027560I
b = −0.84004 + 1.54904I
−2.48401 + 1.41073I −6.37558 − 0.35420I
u = −0.980359 + 0.430482I
a = 0.842135 − 0.198355I
b = 0.457888 − 0.810868I
−2.48401 + 1.41073I −6.37558 − 0.35420I
30
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.980359 − 0.430482I
a = 0.143993 + 1.027560I
b = −0.84004 − 1.54904I
−2.48401 − 1.41073I −6.37558 + 0.35420I
u = −0.980359 − 0.430482I
a = 0.842135 + 0.198355I
b = 0.457888 + 0.810868I
−2.48401 − 1.41073I −6.37558 + 0.35420I
u = 1.08265
a = 0.054854 + 0.583194I
b = −0.718519 − 0.303170I
−2.62092 −11.6870
u = 1.08265
a = 0.054854 − 0.583194I
b = −0.718519 + 0.303170I
−2.62092 −11.6870
u = 1.042780 + 0.722786I
a = 0.372943 + 0.813892I
b = −1.21279 − 0.91071I
−2.17064 − 4.68065I −7.60800 + 5.98175I
u = 1.042780 + 0.722786I
a = −0.388710 + 0.662587I
b = −0.805790 − 0.707990I
−2.17064 − 4.68065I −7.60800 + 5.98175I
u = 1.042780 − 0.722786I
a = 0.372943 − 0.813892I
b = −1.21279 + 0.91071I
−2.17064 + 4.68065I −7.60800 − 5.98175I
u = 1.042780 − 0.722786I
a = −0.388710 − 0.662587I
b = −0.805790 + 0.707990I
−2.17064 + 4.68065I −7.60800 − 5.98175I
u = 0.722137 + 0.071511I
a = −0.09406 − 2.16689I
b = 0.52482 + 1.76760I
−9.89636 − 4.19920I −20.3643 + 1.5662I
u = 0.722137 + 0.071511I
a = 0.62012 + 2.61024I
b = 0.339619 − 0.257537I
−9.89636 − 4.19920I −20.3643 + 1.5662I
31
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.722137 − 0.071511I
a = −0.09406 + 2.16689I
b = 0.52482 − 1.76760I
−9.89636 + 4.19920I −20.3643 − 1.5662I
u = 0.722137 − 0.071511I
a = 0.62012 − 2.61024I
b = 0.339619 + 0.257537I
−9.89636 + 4.19920I −20.3643 − 1.5662I
u = −1.102000 + 0.671129I
a = −0.275360 + 1.031890I
b = 1.48926 − 0.90734I
−6.61725 + 8.28242I −11.19023 − 5.79115I
u = −1.102000 + 0.671129I
a = 0.069748 − 0.677195I
b = −1.42131 + 0.67744I
−6.61725 + 8.28242I −11.19023 − 5.79115I
u = −1.102000 − 0.671129I
a = −0.275360 − 1.031890I
b = 1.48926 + 0.90734I
−6.61725 − 8.28242I −11.19023 + 5.79115I
u = −1.102000 − 0.671129I
a = 0.069748 + 0.677195I
b = −1.42131 − 0.67744I
−6.61725 − 8.28242I −11.19023 + 5.79115I
u = −0.452222 + 0.324558I
a = −1.47160 + 2.41353I
b = 1.31431 − 1.60761I
−11.60330 + 3.04328I −7.78934 + 3.92720I
u = −0.452222 + 0.324558I
a = −3.41177 + 1.38512I
b = −0.190438 − 0.415509I
−11.60330 + 3.04328I −7.78934 + 3.92720I
u = −0.452222 − 0.324558I
a = −1.47160 − 2.41353I
b = 1.31431 + 1.60761I
−11.60330 − 3.04328I −7.78934 − 3.92720I
u = −0.452222 − 0.324558I
a = −3.41177 − 1.38512I
b = −0.190438 + 0.415509I
−11.60330 − 3.04328I −7.78934 − 3.92720I
32
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.350920 + 0.367857I
a = −0.138762 − 0.584225I
b = −0.539677 − 1.109780I
−3.93412 − 2.87780I −7.67100 + 5.09365I
u = −0.350920 + 0.367857I
a = −1.70800 + 1.92997I
b = 0.861230 + 0.344894I
−3.93412 − 2.87780I −7.67100 + 5.09365I
u = −0.350920 − 0.367857I
a = −0.138762 + 0.584225I
b = −0.539677 + 1.109780I
−3.93412 + 2.87780I −7.67100 − 5.09365I
u = −0.350920 − 0.367857I
a = −1.70800 − 1.92997I
b = 0.861230 − 0.344894I
−3.93412 + 2.87780I −7.67100 − 5.09365I
u = −2.29739 + 1.41422I
a = −0.255506 + 0.333715I
b = 0.394878 − 0.337359I
−4.43120 − 1.09421I −21.6565 − 23.5514I
u = −2.29739 + 1.41422I
a = 0.124837 − 0.175711I
b = −0.315038 + 0.205472I
−4.43120 − 1.09421I −21.6565 − 23.5514I
u = −2.29739 − 1.41422I
a = −0.255506 − 0.333715I
b = 0.394878 + 0.337359I
−4.43120 + 1.09421I −21.6565 + 23.5514I
u = −2.29739 − 1.41422I
a = 0.124837 + 0.175711I
b = −0.315038 − 0.205472I
−4.43120 + 1.09421I −21.6565 + 23.5514I
33
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
7
− 2u
6
+ ··· + u − 4)(u
29
+ 2u
27
+ ··· + 13u + 4)
· (u
38
− 6u
37
+ ··· + u + 1)
c
2
, c
5
(u
7
+ 2u
5
+ u
4
+ 2u
3
+ u
2
+ 1)(u
29
+ 13u
27
+ ··· + 3u + 1)
· (u
38
+ 19u
36
+ ··· + 5u
2
+ 1)
c
3
, c
7
4(2u
7
+ 3u
6
+ ··· − u − 1)(2u
29
+ u
28
+ ··· − 2u
2
+ 1)
· (u
38
− 5u
37
+ ··· − 12u
2
+ 1)
c
4
16(4u
7
− 17u
6
+ 36u
5
− 48u
4
+ 43u
3
− 24u
2
+ 8u − 1)
· ((u
19
+ 5u
18
+ ··· − 4u − 1)
2
)(4u
29
− 67u
28
+ ··· − 1032u + 144)
c
6
, c
11
4(2u
7
− 3u
6
+ ··· − u + 1)(2u
29
+ u
28
+ ··· − 2u
2
+ 1)
· (u
38
+ 5u
37
+ ··· − 12u
2
+ 1)
c
8
(u
7
− 4u
5
+ ··· − u − 11)(u
19
+ 7u
18
+ ··· + u + 1)
2
· (u
29
− 9u
28
+ ··· − 2794u + 324)
c
9
, c
12
(u
7
+ 2u
5
− u
4
+ 2u
3
− u
2
− 1)(u
29
+ 13u
27
+ ··· + 3u + 1)
· (u
38
+ 19u
36
+ ··· + 5u
2
+ 1)
34
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
(y
7
− 2y
6
+ 11y
5
− 16y
4
− 13y
3
+ 25y
2
+ 9y −16)
· (y
29
+ 4y
28
+ ··· + 361y −16)(y
38
+ 6y
37
+ ··· − 19y + 1)
c
2
, c
5
, c
9
c
12
(y
7
+ 4y
6
+ ··· − 2y −1)(y
29
+ 26y
28
+ ··· − y −1)
· (y
38
+ 38y
37
+ ··· + 10y + 1)
c
3
, c
6
, c
7
c
11
16(4y
7
− 29y
6
+ 89y
5
− 138y
4
+ 112y
3
− 49y
2
+ 11y −1)
· (4y
29
− 69y
28
+ ··· + 4y −1)(y
38
− 21y
37
+ ··· − 24y + 1)
c
4
256(16y
7
− y
6
+ 8y
5
+ 40y
4
+ 87y
3
+ 16y
2
+ 16y −1)
· (y
19
− 15y
18
+ ··· + 10y −1)
2
· (16y
29
− 113y
28
+ ··· + 197280y −20736)
c
8
(y
7
− 8y
6
+ 30y
5
− 59y
4
+ 79y
3
− 157y
2
+ 243y −121)
· ((y
19
− 3y
18
+ ··· + 25y −1)
2
)(y
29
− 7y
28
+ ··· + 371932y −104976)
35
