12a
1248
(K12a
1248
)
A knot diagram
1
Linearized knot diagam
5 6 11 12 9 10 4 1 2 3 7 8
Solving Sequence
1,5 2,8
9 6 3 10 12 4 7 11
c
1
c
8
c
5
c
2
c
9
c
12
c
4
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.72425 × 10
22
u
24
+ 4.51173 × 10
21
u
23
+ ··· + 3.02574 × 10
23
b − 2.60307 × 10
23
,
2.27744 × 10
23
u
24
+ 2.18092 × 10
23
u
23
+ ··· + 3.02574 × 10
23
a + 5.33603 × 10
22
, u
25
+ u
24
+ ··· − 8u
2
+ 1i
I
u
2
= h2.52174 × 10
1084
u
129
− 1.28872 × 10
1085
u
128
+ ··· + 1.26976 × 10
1088
b + 1.02148 × 10
1088
,
1.23921 × 10
1087
u
129
− 6.11247 × 10
1087
u
128
+ ··· + 4.57115 × 10
1089
a + 1.36201 × 10
1091
,
u
130
− 5u
129
+ ··· + 9180u − 648i
I
u
3
= h−62191u
12
− 91437u
11
+ ··· + 210306b − 639878,
361221u
12
+ 540029u
11
+ ··· + 1682448a + 4563524,
u
13
+ u
12
− 5u
9
− u
8
− 5u
7
+ 2u
6
+ 5u
5
− 9u
4
+ 17u
3
− 19u
2
+ 20u − 8i
I
u
4
= h−83920313227156u
15
− 336492773056065u
14
+ ··· + 290510825873015b + 1338972540679108,
− 194022337467459u
15
− 528242471041940u
14
+ ··· + 2033575781111105a + 5329335757021752,
u
16
+ 4u
15
+ ··· − 42u − 7i
I
v
1
= ha, b − 1, v + 1i
* 5 irreducible components of dim
C
= 0, with total 185 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−1.72×10
22
u
24
+4.51×10
21
u
23
+· · ·+3.03×10
23
b−2.60×10
23
, 2.28×
10
23
u
24
+2.18×10
23
u
23
+· · ·+3.03×10
23
a+5.34×10
22
, u
25
+u
24
+· · ·−8u
2
+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
−0.752689u
24
− 0.720788u
23
+ ··· + 6.22359u − 0.176354
0.0569861u
24
− 0.0149111u
23
+ ··· − 0.307069u + 0.860306
a
9
=
−0.695703u
24
− 0.735699u
23
+ ··· + 5.91652u + 0.683952
0.0569861u
24
− 0.0149111u
23
+ ··· − 0.307069u + 0.860306
a
6
=
−0.303537u
24
− 0.138816u
23
+ ··· + 4.13713u + 0.575651
0.0375026u
24
+ 0.0458581u
23
+ ··· + 0.987489u + 0.530982
a
3
=
0.715592u
24
+ 0.997987u
23
+ ··· − 5.00417u − 0.594017
0.0903954u
24
+ 0.191020u
23
+ ··· − 1.29124u − 0.585932
a
10
=
−0.759457u
24
− 0.728490u
23
+ ··· + 6.91929u − 0.136358
0.00953838u
24
− 0.0601964u
23
+ ··· − 0.243315u + 0.789343
a
12
=
−0.613557u
24
− 0.500686u
23
+ ··· + 7.58303u + 0.141631
0.0825759u
24
+ 0.00720653u
23
+ ··· − 1.09086u + 0.845857
a
4
=
−0.330598u
24
− 0.137579u
23
+ ··· + 7.06546u − 0.560275
0.152520u
24
+ 0.119684u
23
+ ··· − 0.426542u + 0.792379
a
7
=
−0.334504u
24
− 0.115567u
23
+ ··· + 4.27349u − 0.183806
0.107237u
24
+ 0.0840051u
23
+ ··· + 0.198146u + 0.540520
a
11
=
−1.05608u
24
− 1.47895u
23
+ ··· + 4.46227u + 1.24510
−0.113686u
24
− 0.246884u
23
+ ··· − 0.542231u + 0.697244
(ii) Obstruction class = −1
(iii) Cusp Shapes =
13367505793709478061311
75643582712572142866763
u
24
+
13196896166892663371479
75643582712572142866763
u
23
+ ··· −
584894792961948670185449
75643582712572142866763
u +
589205170842196062242390
75643582712572142866763
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
25
+ u
24
+ ··· − 8u
2
+ 1
c
2
, c
5
u
25
+ u
24
+ ··· − 2u + 1
c
3
, c
8
, c
10
c
12
u
25
− 9u
23
+ ··· − 6u + 1
c
4
, c
11
u
25
− 4u
24
+ ··· + u − 1
c
7
u
25
− 18u
24
+ ··· − 32u − 64
c
9
u
25
− 17u
24
+ ··· + 2688u − 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
25
+ 7y
24
+ ··· + 16y −1
c
2
, c
5
y
25
− 25y
24
+ ··· + 22y −1
c
3
, c
8
, c
10
c
12
y
25
− 18y
24
+ ··· + 20y −1
c
4
, c
11
y
25
− 20y
24
+ ··· + 7y −1
c
7
y
25
− 4y
24
+ ··· + 289792y −4096
c
9
y
25
+ y
24
+ ··· + 16384y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.337196 + 0.923094I
a = 1.49102 + 0.25772I
b = −1.054540 − 0.467075I
3.76069 + 4.58301I 3.19626 − 6.75184I
u = 0.337196 − 0.923094I
a = 1.49102 − 0.25772I
b = −1.054540 + 0.467075I
3.76069 − 4.58301I 3.19626 + 6.75184I
u = −0.896842 + 0.531128I
a = −0.778602 − 0.201190I
b = 0.232084 − 0.768385I
−2.63343 + 2.48396I −2.77279 − 2.07312I
u = −0.896842 − 0.531128I
a = −0.778602 + 0.201190I
b = 0.232084 + 0.768385I
−2.63343 − 2.48396I −2.77279 + 2.07312I
u = 0.987903 + 0.651180I
a = −0.0585945 + 0.0362518I
b = −0.271842 + 1.020150I
−3.54126 − 8.91433I −1.59126 + 8.97639I
u = 0.987903 − 0.651180I
a = −0.0585945 − 0.0362518I
b = −0.271842 − 1.020150I
−3.54126 + 8.91433I −1.59126 − 8.97639I
u = −0.300007 + 1.177200I
a = 1.45372 − 0.60162I
b = −0.887855 − 0.197563I
3.17777 + 3.62494I 10.69614 − 2.84346I
u = −0.300007 − 1.177200I
a = 1.45372 + 0.60162I
b = −0.887855 + 0.197563I
3.17777 − 3.62494I 10.69614 + 2.84346I
u = −0.128397 + 1.241710I
a = −1.023080 + 0.123269I
b = 1.060870 + 0.527352I
4.31719 + 3.20535I 7.46974 − 2.07775I
u = −0.128397 − 1.241710I
a = −1.023080 − 0.123269I
b = 1.060870 − 0.527352I
4.31719 − 3.20535I 7.46974 + 2.07775I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.363593 + 0.550618I
a = 0.411640 − 0.252068I
b = 0.079915 + 0.737309I
−0.26775 + 1.80895I 3.29877 − 4.11187I
u = −0.363593 − 0.550618I
a = 0.411640 + 0.252068I
b = 0.079915 − 0.737309I
−0.26775 − 1.80895I 3.29877 + 4.11187I
u = 0.656386
a = −4.21036
b = −1.09928
3.95763 −6.81600
u = 0.098619 + 0.544760I
a = 1.12774 − 1.17488I
b = 0.262728 + 0.108252I
1.20157 + 1.19915I 6.22122 − 0.54689I
u = 0.098619 − 0.544760I
a = 1.12774 + 1.17488I
b = 0.262728 − 0.108252I
1.20157 − 1.19915I 6.22122 + 0.54689I
u = 0.66908 + 1.30724I
a = −1.305070 − 0.147844I
b = 1.46709 − 0.46586I
9.8117 − 11.6056I 9.31205 + 7.19740I
u = 0.66908 − 1.30724I
a = −1.305070 + 0.147844I
b = 1.46709 + 0.46586I
9.8117 + 11.6056I 9.31205 − 7.19740I
u = −1.10412 + 1.05088I
a = −0.741334 + 0.642514I
b = 1.249090 − 0.135400I
9.09783 − 3.12361I 9.72869 + 2.49477I
u = −1.10412 − 1.05088I
a = −0.741334 − 0.642514I
b = 1.249090 + 0.135400I
9.09783 + 3.12361I 9.72869 − 2.49477I
u = 1.16476 + 1.20913I
a = 1.016250 + 0.347766I
b = −1.193450 + 0.518130I
3.23815 − 12.29240I 2.87610 + 9.11066I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16476 − 1.20913I
a = 1.016250 − 0.347766I
b = −1.193450 − 0.518130I
3.23815 + 12.29240I 2.87610 − 9.11066I
u = 0.285172
a = 1.97738
b = 0.883013
1.68210 5.46770
u = −0.284977
a = −3.36690
b = 1.32340
1.77900 11.4600
u = −1.29288 + 1.12827I
a = 1.206260 − 0.419944I
b = −1.49765 − 0.50299I
7.6066 + 20.1752I 6.00932 − 10.06045I
u = −1.29288 − 1.12827I
a = 1.206260 + 0.419944I
b = −1.49765 + 0.50299I
7.6066 − 20.1752I 6.00932 + 10.06045I
7
II. I
u
2
= h2.52 × 10
1084
u
129
− 1.29 × 10
1085
u
128
+ · · · + 1.27 × 10
1088
b + 1.02 ×
10
1088
, 1.24 × 10
1087
u
129
− 6.11 × 10
1087
u
128
+ · · · + 4.57 × 10
1089
a + 1.36 ×
10
1091
, u
130
− 5u
129
+ · · · + 9180u − 648i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
−0.00271095u
129
+ 0.0133719u
128
+ ··· − 172.633u − 29.7958
−0.000198599u
129
+ 0.00101493u
128
+ ··· − 13.8817u − 0.804469
a
9
=
−0.00290955u
129
+ 0.0143868u
128
+ ··· − 186.515u − 30.6003
−0.000198599u
129
+ 0.00101493u
128
+ ··· − 13.8817u − 0.804469
a
6
=
0.00614959u
129
− 0.0303924u
128
+ ··· + 302.775u + 65.5568
0.000189288u
129
− 0.000965574u
128
+ ··· + 19.6693u + 1.84031
a
3
=
−0.0127234u
129
+ 0.0628511u
128
+ ··· − 650.343u − 155.072
−0.000436527u
129
+ 0.00215475u
128
+ ··· − 8.88201u − 6.05167
a
10
=
−0.00274753u
129
+ 0.0135520u
128
+ ··· − 173.041u − 29.9001
−0.000205267u
129
+ 0.00104599u
128
+ ··· − 13.5496u − 0.820500
a
12
=
0.00305254u
129
− 0.0150819u
128
+ ··· + 119.477u + 43.5717
−0.000212562u
129
+ 0.00107127u
128
+ ··· − 13.8280u + 2.16857
a
4
=
0.00914264u
129
− 0.0452008u
128
+ ··· + 501.331u + 98.6427
0.000501352u
129
− 0.00251547u
128
+ ··· + 37.8374u + 2.65284
a
7
=
0.00807061u
129
− 0.0399844u
128
+ ··· + 459.988u + 84.9912
0.000523481u
129
− 0.00260365u
128
+ ··· + 46.0324u + 1.61693
a
11
=
−0.00925651u
129
+ 0.0457718u
128
+ ··· − 550.967u − 103.686
−0.000560374u
129
+ 0.00279981u
128
+ ··· − 41.2275u − 2.74647
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.000852393u
129
+ 0.00437408u
128
+ ··· − 95.4233u + 4.25325
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
130
− 5u
129
+ ··· + 9180u − 648
c
2
, c
5
36(36u
130
− 144u
129
+ ··· + 650230u + 245213)
c
3
, c
8
, c
10
c
12
u
130
+ 2u
129
+ ··· − 52u + 1
c
4
, c
11
36(36u
130
− 72u
129
+ ··· + 3230u − 271)
c
7
(u
65
+ 10u
64
+ ··· + 1045u + 93)
2
c
9
(u
65
+ 6u
64
+ ··· + 13u − 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
130
− 5y
129
+ ··· − 188070336y + 419904
c
2
, c
5
1296
· (1296y
130
− 54648y
129
+ ··· − 4148969485924y + 60129415369)
c
3
, c
8
, c
10
c
12
y
130
− 102y
129
+ ··· − 32y + 1
c
4
, c
11
1296(1296y
130
+ 7560y
129
+ ··· − 4029712y + 73441)
c
7
(y
65
− 24y
64
+ ··· + 342631y −8649)
2
c
9
(y
65
− 8y
64
+ ··· + 151y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395435 + 0.921802I
a = −1.261370 + 0.120698I
b = 1.44528 + 0.52940I
4.81300 + 2.73620I 0
u = −0.395435 − 0.921802I
a = −1.261370 − 0.120698I
b = 1.44528 − 0.52940I
4.81300 − 2.73620I 0
u = −0.990847
a = 1.22238
b = −1.39688
−1.93226 0
u = 0.978863 + 0.081886I
a = −0.554763 + 0.216918I
b = −0.149553 + 0.817552I
−4.30041 + 2.40764I 0
u = 0.978863 − 0.081886I
a = −0.554763 − 0.216918I
b = −0.149553 − 0.817552I
−4.30041 − 2.40764I 0
u = 0.839840 + 0.580136I
a = −0.778737 − 0.865825I
b = 1.242750 − 0.644513I
1.97368 − 3.05261I 0
u = 0.839840 − 0.580136I
a = −0.778737 + 0.865825I
b = 1.242750 + 0.644513I
1.97368 + 3.05261I 0
u = 0.741311 + 0.594975I
a = 0.517367 − 0.026334I
b = −0.274983 − 1.131760I
0.26259 − 6.61421I 0
u = 0.741311 − 0.594975I
a = 0.517367 + 0.026334I
b = −0.274983 + 1.131760I
0.26259 + 6.61421I 0
u = 0.415423 + 0.964153I
a = −1.241100 − 0.408258I
b = 0.934964 − 0.699699I
3.82596 − 2.49917I 0
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.415423 − 0.964153I
a = −1.241100 + 0.408258I
b = 0.934964 + 0.699699I
3.82596 + 2.49917I 0
u = −0.988795 + 0.360926I
a = 0.442714 + 0.054513I
b = −0.165324 + 0.664435I
−2.42741 + 1.37850I 0
u = −0.988795 − 0.360926I
a = 0.442714 − 0.054513I
b = −0.165324 − 0.664435I
−2.42741 − 1.37850I 0
u = −0.932699 + 0.022023I
a = 0.513466 + 0.388134I
b = 0.327149 + 1.104600I
1.04342 − 6.26787I 0
u = −0.932699 − 0.022023I
a = 0.513466 − 0.388134I
b = 0.327149 − 1.104600I
1.04342 + 6.26787I 0
u = 0.228185 + 0.881951I
a = 0.703616 − 0.244061I
b = 0.053350 + 0.370991I
1.33240 + 1.86332I 0
u = 0.228185 − 0.881951I
a = 0.703616 + 0.244061I
b = 0.053350 − 0.370991I
1.33240 − 1.86332I 0
u = −0.646723 + 0.633614I
a = 0.409333 − 0.377970I
b = −0.279659 − 1.091440I
3.60085 + 5.03367I 0
u = −0.646723 − 0.633614I
a = 0.409333 + 0.377970I
b = −0.279659 + 1.091440I
3.60085 − 5.03367I 0
u = −0.726213 + 0.822663I
a = −1.06337 + 1.56707I
b = 1.154510 + 0.007583I
3.53868 + 1.05383I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.726213 − 0.822663I
a = −1.06337 − 1.56707I
b = 1.154510 − 0.007583I
3.53868 − 1.05383I 0
u = 0.183987 + 1.093660I
a = 0.428679 + 0.986543I
b = 0.0321920 − 0.0330241I
5.00433 − 9.83054I 0
u = 0.183987 − 1.093660I
a = 0.428679 − 0.986543I
b = 0.0321920 + 0.0330241I
5.00433 + 9.83054I 0
u = 0.552425 + 0.982700I
a = −0.841882 + 0.696450I
b = 0.450844 + 0.138293I
4.81300 + 2.73620I 0
u = 0.552425 − 0.982700I
a = −0.841882 − 0.696450I
b = 0.450844 − 0.138293I
4.81300 − 2.73620I 0
u = 0.220147 + 0.841369I
a = 1.272580 − 0.078974I
b = −1.58520 + 0.71407I
6.97133 − 2.42746I 0
u = 0.220147 − 0.841369I
a = 1.272580 + 0.078974I
b = −1.58520 − 0.71407I
6.97133 + 2.42746I 0
u = −0.949879 + 0.620413I
a = −0.0266755 + 0.0042224I
b = 0.349558 + 1.213370I
1.8860 + 14.1381I 0
u = −0.949879 − 0.620413I
a = −0.0266755 − 0.0042224I
b = 0.349558 − 1.213370I
1.8860 − 14.1381I 0
u = 0.705590 + 0.478780I
a = −0.044272 − 0.204131I
b = 0.201060 − 1.194120I
0.01829 − 3.97089I 0
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.705590 − 0.478780I
a = −0.044272 + 0.204131I
b = 0.201060 + 1.194120I
0.01829 + 3.97089I 0
u = 1.007200 + 0.561186I
a = −0.184306 + 0.012742I
b = 0.147273 − 0.971997I
−1.10302 − 6.81905I 0
u = 1.007200 − 0.561186I
a = −0.184306 − 0.012742I
b = 0.147273 + 0.971997I
−1.10302 + 6.81905I 0
u = −1.17072
a = 0.439190
b = −1.98790
9.43830 0
u = 1.174650 + 0.019186I
a = 0.0705133 − 0.0380614I
b = 0.716210 − 0.533561I
0.408364 + 1.264650I 0
u = 1.174650 − 0.019186I
a = 0.0705133 + 0.0380614I
b = 0.716210 + 0.533561I
0.408364 − 1.264650I 0
u = −0.479231 + 1.079250I
a = 1.16561 − 0.86245I
b = −1.373530 − 0.039474I
10.67500 + 3.52037I 0
u = −0.479231 − 1.079250I
a = 1.16561 + 0.86245I
b = −1.373530 + 0.039474I
10.67500 − 3.52037I 0
u = 0.734468 + 0.962562I
a = 1.226530 + 0.357884I
b = −1.54208 + 0.37003I
10.67500 − 3.52037I 0
u = 0.734468 − 0.962562I
a = 1.226530 − 0.357884I
b = −1.54208 − 0.37003I
10.67500 + 3.52037I 0
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.071130 + 0.581541I
a = 0.752545 − 0.598403I
b = −1.62230 − 0.64145I
8.22437 + 2.08895I 0
u = −1.071130 − 0.581541I
a = 0.752545 + 0.598403I
b = −1.62230 + 0.64145I
8.22437 − 2.08895I 0
u = −1.158480 + 0.447040I
a = 0.0908065 + 0.0033433I
b = −0.239755 − 0.733270I
−4.30041 + 2.40764I 0
u = −1.158480 − 0.447040I
a = 0.0908065 − 0.0033433I
b = −0.239755 + 0.733270I
−4.30041 − 2.40764I 0
u = −0.986130 + 0.762269I
a = 0.213638 + 0.122108I
b = 0.107496 + 0.655105I
−1.45790 + 2.77446I 0
u = −0.986130 − 0.762269I
a = 0.213638 − 0.122108I
b = 0.107496 − 0.655105I
−1.45790 − 2.77446I 0
u = −0.247362 + 1.232510I
a = −0.236034 + 0.541909I
b = −0.0161701 + 0.1172470I
0.01829 + 3.97089I 0
u = −0.247362 − 1.232510I
a = −0.236034 − 0.541909I
b = −0.0161701 − 0.1172470I
0.01829 − 3.97089I 0
u = −0.605209 + 0.418175I
a = 0.0031809 + 0.0768070I
b = −0.23895 − 1.48287I
3.90089 + 3.93483I 3.86544 − 9.05050I
u = −0.605209 − 0.418175I
a = 0.0031809 − 0.0768070I
b = −0.23895 + 1.48287I
3.90089 − 3.93483I 3.86544 + 9.05050I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.529655 + 0.497978I
a = −1.172890 − 0.019938I
b = −0.491462 + 0.543275I
3.53868 − 1.05383I 6.02195 + 1.63666I
u = −0.529655 − 0.497978I
a = −1.172890 + 0.019938I
b = −0.491462 − 0.543275I
3.53868 + 1.05383I 6.02195 − 1.63666I
u = −1.30114
a = 0.584999
b = 0.339378
−1.93226 0
u = 0.696178
a = 2.89025
b = 0.491834
3.02115 0.480760
u = −0.553482 + 0.412590I
a = 1.39325 − 1.94666I
b = −0.915449 − 0.569375I
4.26240 + 3.31423I 2.00000 − 8.31671I
u = −0.553482 − 0.412590I
a = 1.39325 + 1.94666I
b = −0.915449 + 0.569375I
4.26240 − 3.31423I 2.00000 + 8.31671I
u = −0.651942 + 0.192979I
a = 1.65481 − 0.63600I
b = −0.838881 − 0.324697I
−2.42741 + 1.37850I −2.95884 − 2.12327I
u = −0.651942 − 0.192979I
a = 1.65481 + 0.63600I
b = −0.838881 + 0.324697I
−2.42741 − 1.37850I −2.95884 + 2.12327I
u = 1.043850 + 0.833718I
a = 0.649155 + 0.942828I
b = −1.282090 + 0.127797I
9.67425 − 2.89595I 0
u = 1.043850 − 0.833718I
a = 0.649155 − 0.942828I
b = −1.282090 − 0.127797I
9.67425 + 2.89595I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.008555 + 0.648913I
a = −0.90272 − 1.93060I
b = 0.0675688 + 0.0417527I
5.37573 − 1.95373I 14.5397 + 0.9508I
u = 0.008555 − 0.648913I
a = −0.90272 + 1.93060I
b = 0.0675688 − 0.0417527I
5.37573 + 1.95373I 14.5397 − 0.9508I
u = 0.626976 + 0.068727I
a = −0.875048 + 0.085529I
b = 1.194100 + 0.665103I
2.02193 − 1.25646I −0.93519 + 5.01233I
u = 0.626976 − 0.068727I
a = −0.875048 − 0.085529I
b = 1.194100 − 0.665103I
2.02193 + 1.25646I −0.93519 − 5.01233I
u = 0.543979 + 0.252969I
a = −2.24165 − 1.29499I
b = 0.771752 − 0.399908I
0.60871 − 5.11474I 1.19356 + 9.18370I
u = 0.543979 − 0.252969I
a = −2.24165 + 1.29499I
b = 0.771752 + 0.399908I
0.60871 + 5.11474I 1.19356 − 9.18370I
u = −0.325810 + 0.494423I
a = −2.80544 − 0.43447I
b = 1.267010 + 0.184181I
2.02193 + 1.25646I −0.93519 − 5.01233I
u = −0.325810 − 0.494423I
a = −2.80544 + 0.43447I
b = 1.267010 − 0.184181I
2.02193 − 1.25646I −0.93519 + 5.01233I
u = 1.02335 + 0.99167I
a = 0.0678799 − 0.0807649I
b = −0.316582 + 0.031792I
1.97368 + 3.05261I 0
u = 1.02335 − 0.99167I
a = 0.0678799 + 0.0807649I
b = −0.316582 − 0.031792I
1.97368 − 3.05261I 0
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.89545 + 1.11500I
a = −1.045140 + 0.425759I
b = 1.400170 − 0.062307I
9.67425 − 2.89595I 0
u = −0.89545 − 1.11500I
a = −1.045140 − 0.425759I
b = 1.400170 + 0.062307I
9.67425 + 2.89595I 0
u = −0.494900 + 0.228488I
a = −2.42653 + 2.17634I
b = 1.155690 + 0.506806I
3.73798 + 11.84600I 2.61069 − 8.43405I
u = −0.494900 − 0.228488I
a = −2.42653 − 2.17634I
b = 1.155690 − 0.506806I
3.73798 − 11.84600I 2.61069 + 8.43405I
u = −1.03879 + 1.02846I
a = −1.203930 + 0.439913I
b = 1.48560 + 0.57575I
9.1733 + 10.8002I 0
u = −1.03879 − 1.02846I
a = −1.203930 − 0.439913I
b = 1.48560 − 0.57575I
9.1733 − 10.8002I 0
u = 0.424948 + 0.301997I
a = 3.12746 + 1.35746I
b = −1.187740 + 0.395406I
−1.10302 − 6.81905I −0.59050 + 7.48441I
u = 0.424948 − 0.301997I
a = 3.12746 − 1.35746I
b = −1.187740 − 0.395406I
−1.10302 + 6.81905I −0.59050 − 7.48441I
u = −1.11919 + 0.97423I
a = −1.108120 + 0.698566I
b = 1.43620 + 0.46001I
8.92180 + 10.48110I 0
u = −1.11919 − 0.97423I
a = −1.108120 − 0.698566I
b = 1.43620 − 0.46001I
8.92180 − 10.48110I 0
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.99301 + 1.10850I
a = −1.06349 − 1.04176I
b = 1.267980 − 0.097225I
8.92180 − 10.48110I 0
u = 0.99301 − 1.10850I
a = −1.06349 + 1.04176I
b = 1.267980 + 0.097225I
8.92180 + 10.48110I 0
u = 1.09956 + 1.01990I
a = 1.170100 + 0.530839I
b = −1.41877 + 0.50726I
5.00433 − 9.83054I 0
u = 1.09956 − 1.01990I
a = 1.170100 − 0.530839I
b = −1.41877 − 0.50726I
5.00433 + 9.83054I 0
u = 1.09692 + 1.06321I
a = 1.42170 + 0.50153I
b = −1.39155 + 0.43631I
3.73798 − 11.84600I 0
u = 1.09692 − 1.06321I
a = 1.42170 − 0.50153I
b = −1.39155 − 0.43631I
3.73798 + 11.84600I 0
u = 1.04639 + 1.16420I
a = 0.930949 + 0.477625I
b = −1.221710 − 0.070295I
5.37573 + 1.95373I 0
u = 1.04639 − 1.16420I
a = 0.930949 − 0.477625I
b = −1.221710 + 0.070295I
5.37573 − 1.95373I 0
u = 1.41612 + 0.67388I
a = −0.861511 − 0.274193I
b = 1.275750 − 0.264402I
0.408364 − 1.264650I 0
u = 1.41612 − 0.67388I
a = −0.861511 + 0.274193I
b = 1.275750 + 0.264402I
0.408364 + 1.264650I 0
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.202263 + 0.369821I
a = −0.778526 − 0.515950I
b = −0.383227 + 1.248350I
4.12050 − 5.84327I 9.59365 + 9.05617I
u = 0.202263 − 0.369821I
a = −0.778526 + 0.515950I
b = −0.383227 − 1.248350I
4.12050 + 5.84327I 9.59365 − 9.05617I
u = 1.59856
a = −0.636266
b = 0.379724
−3.78199 0
u = −0.367235 + 0.137446I
a = −0.602199 − 0.938495I
b = 0.65764 − 1.51103I
3.21129 + 6.10217I −2.76133 + 4.44067I
u = −0.367235 − 0.137446I
a = −0.602199 + 0.938495I
b = 0.65764 + 1.51103I
3.21129 − 6.10217I −2.76133 − 4.44067I
u = −1.62552
a = 0.150830
b = −0.873054
−3.78199 0
u = −1.19058 + 1.14745I
a = 1.117110 − 0.333973I
b = −1.167110 − 0.327843I
0.60871 + 5.11474I 0
u = −1.19058 − 1.14745I
a = 1.117110 + 0.333973I
b = −1.167110 + 0.327843I
0.60871 − 5.11474I 0
u = 0.236601 + 0.221790I
a = 0.79592 − 1.65074I
b = −0.923576 − 0.864168I
−1.45790 − 2.77446I −7.91959 + 5.52851I
u = 0.236601 − 0.221790I
a = 0.79592 + 1.65074I
b = −0.923576 + 0.864168I
−1.45790 + 2.77446I −7.91959 − 5.52851I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.93361 + 1.40206I
a = 1.222940 − 0.708515I
b = −1.211980 − 0.102192I
3.60085 + 5.03367I 0
u = −0.93361 − 1.40206I
a = 1.222940 + 0.708515I
b = −1.211980 + 0.102192I
3.60085 − 5.03367I 0
u = 0.83679 + 1.47250I
a = 1.39278 + 0.45394I
b = −1.166170 − 0.047270I
4.26240 + 3.31423I 0
u = 0.83679 − 1.47250I
a = 1.39278 − 0.45394I
b = −1.166170 + 0.047270I
4.26240 − 3.31423I 0
u = −0.60415 + 1.60748I
a = 1.306870 − 0.156086I
b = −1.323450 − 0.346010I
4.12050 + 5.84327I 0
u = −0.60415 − 1.60748I
a = 1.306870 + 0.156086I
b = −1.323450 + 0.346010I
4.12050 − 5.84327I 0
u = −1.30085 + 1.12847I
a = −1.39248 + 0.32285I
b = 1.42980 + 0.31722I
1.04342 + 6.26787I 0
u = −1.30085 − 1.12847I
a = −1.39248 − 0.32285I
b = 1.42980 − 0.31722I
1.04342 − 6.26787I 0
u = 0.171181 + 0.209100I
a = −4.45011 − 3.25264I
b = 0.962455 − 0.356074I
1.33240 − 1.86332I −1.30939 + 1.76611I
u = 0.171181 − 0.209100I
a = −4.45011 + 3.25264I
b = 0.962455 + 0.356074I
1.33240 + 1.86332I −1.30939 − 1.76611I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33486 + 1.21673I
a = −1.215660 − 0.370999I
b = 1.45229 − 0.43974I
1.8860 − 14.1381I 0
u = 1.33486 − 1.21673I
a = −1.215660 + 0.370999I
b = 1.45229 + 0.43974I
1.8860 + 14.1381I 0
u = −0.79277 + 1.64687I
a = 1.093700 − 0.496679I
b = −1.281860 + 0.120090I
9.1733 − 10.8002I 0
u = −0.79277 − 1.64687I
a = 1.093700 + 0.496679I
b = −1.281860 − 0.120090I
9.1733 + 10.8002I 0
u = 1.37358 + 1.28477I
a = −1.334020 − 0.101062I
b = 1.51526 − 0.13875I
8.22437 + 2.08895I 0
u = 1.37358 − 1.28477I
a = −1.334020 + 0.101062I
b = 1.51526 + 0.13875I
8.22437 − 2.08895I 0
u = −0.109564
a = 4.35338
b = 2.04522
8.49952 19.0480
u = −1.43063 + 1.30267I
a = −0.903001 + 0.292880I
b = 1.168580 + 0.356294I
0.26259 + 6.61421I 0
u = −1.43063 − 1.30267I
a = −0.903001 − 0.292880I
b = 1.168580 − 0.356294I
0.26259 − 6.61421I 0
u = 1.93794
a = 1.18254
b = −1.66058
9.43830 0
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.0538130
a = −36.0083
b = −1.25525
3.02115 0.480760
u = 0.55030 + 1.87311I
a = −1.225970 − 0.434713I
b = 1.256340 + 0.029273I
3.90089 + 3.93483I 0
u = 0.55030 − 1.87311I
a = −1.225970 + 0.434713I
b = 1.256340 − 0.029273I
3.90089 − 3.93483I 0
u = 0.95249 + 1.72683I
a = 0.950965 + 0.221920I
b = −1.080530 + 0.132232I
3.82596 + 2.49917I 0
u = 0.95249 − 1.72683I
a = 0.950965 − 0.221920I
b = −1.080530 − 0.132232I
3.82596 − 2.49917I 0
u = −1.29611 + 1.65030I
a = 1.274860 − 0.287073I
b = −1.364360 − 0.263713I
3.21129 + 6.10217I 0
u = −1.29611 − 1.65030I
a = 1.274860 + 0.287073I
b = −1.364360 + 0.263713I
3.21129 − 6.10217I 0
u = 1.78883 + 1.32664I
a = −0.764735 − 0.443939I
b = 1.163260 − 0.008096I
6.97133 + 2.42746I 0
u = 1.78883 − 1.32664I
a = −0.764735 + 0.443939I
b = 1.163260 + 0.008096I
6.97133 − 2.42746I 0
u = 2.23095
a = 0.686994
b = −1.35466
8.49952 0
23
III.
I
u
3
= h−6.22 × 10
4
u
12
− 9.14 × 10
4
u
11
+ · · · + 2.10 × 10
5
b − 6.40 × 10
5
, 3.61 ×
10
5
u
12
+5.40×10
5
u
11
+· · · +1.68×10
6
a+4.56×10
6
, u
13
+u
12
+· · · +20u −8i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
−0.214700u
12
− 0.320978u
11
+ ··· + 2.52230u − 2.71243
0.295717u
12
+ 0.434781u
11
+ ··· − 3.50969u + 3.04260
a
9
=
0.0810171u
12
+ 0.113803u
11
+ ··· − 0.987395u + 0.330174
0.295717u
12
+ 0.434781u
11
+ ··· − 3.50969u + 3.04260
a
6
=
−0.0401816u
12
− 0.0999921u
11
+ ··· + 0.303440u − 0.370825
−0.132419u
12
− 0.235559u
11
+ ··· + 2.16492u − 1.12662
a
3
=
0.156866u
12
+ 0.309533u
11
+ ··· − 1.77645u + 2.00139
0.196011u
12
+ 0.327469u
11
+ ··· − 2.23122u + 1.54279
a
10
=
−0.232735u
12
− 0.326651u
11
+ ··· + 2.51472u − 2.45015
0.302859u
12
+ 0.370940u
11
+ ··· − 3.48569u + 2.02900
a
12
=
−0.221462u
12
− 0.397123u
11
+ ··· + 2.68759u − 2.70748
0.0806349u
12
+ 0.123877u
11
+ ··· − 1.26739u + 2.05585
a
4
=
0.132396u
12
+ 0.210242u
11
+ ··· − 1.38827u + 2.22269
−0.278801u
12
− 0.479684u
11
+ ··· + 4.24353u − 3.83105
a
7
=
−0.134097u
12
− 0.204801u
11
+ ··· + 2.50800u − 2.23271
−0.0643372u
12
− 0.190330u
11
+ ··· − 1.86325u + 1.29625
a
11
=
−0.176298u
12
− 0.311015u
11
+ ··· + 1.45490u − 1.17633
0.0357646u
12
− 0.0455004u
11
+ ··· + 0.00546347u + 0.422087
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1033283
420612
u
12
−
1432969
420612
u
11
+ ··· +
5204925
140204
u −
6077497
210306
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
13
+ u
12
− 5u
9
− u
8
− 5u
7
+ 2u
6
+ 5u
5
− 9u
4
+ 17u
3
− 19u
2
+ 20u − 8
c
2
, c
5
4(4u
13
− 4u
12
+ ··· + 5u − 1)
c
3
, c
12
u
13
+ u
12
+ ··· − 5u + 1
c
4
, c
11
4(4u
13
+ 4u
12
+ ··· − 2u + 1)
c
7
u
13
+ 5u
12
+ ··· + 6u − 4
c
8
, c
10
u
13
− u
12
+ ··· − 5u − 1
c
9
u
13
− 3u
12
+ ··· − 2u − 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
13
− y
12
+ ··· + 96y −64
c
2
, c
5
16(16y
13
− 104y
12
+ ··· + 27y −1)
c
3
, c
8
, c
10
c
12
y
13
− 13y
12
+ ··· + 31y −1
c
4
, c
11
16(16y
13
− 72y
12
+ ··· + 12y −1)
c
7
y
13
− 3y
12
+ ··· + 60y −16
c
9
y
13
− y
12
+ ··· + 46y −1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.959414
a = 0.174476
b = −1.57470
11.7766 13.4920
u = 0.543205 + 0.733999I
a = 0.195393 − 0.204204I
b = −0.203670 − 0.781207I
−0.60005 − 3.16973I 1.33144 + 7.21605I
u = 0.543205 − 0.733999I
a = 0.195393 + 0.204204I
b = −0.203670 + 0.781207I
−0.60005 + 3.16973I 1.33144 − 7.21605I
u = −0.239973 + 1.160450I
a = 1.223010 + 0.028017I
b = −1.098240 + 0.611717I
4.72534 − 4.38147I 10.79713 + 5.92666I
u = −0.239973 − 1.160450I
a = 1.223010 − 0.028017I
b = −1.098240 − 0.611717I
4.72534 + 4.38147I 10.79713 − 5.92666I
u = 0.139616 + 1.276470I
a = −1.308880 − 0.210044I
b = 0.843036 − 0.339731I
2.57788 − 3.86066I −2.11736 + 7.14801I
u = 0.139616 − 1.276470I
a = −1.308880 + 0.210044I
b = 0.843036 + 0.339731I
2.57788 + 3.86066I −2.11736 − 7.14801I
u = −0.777627 + 1.138280I
a = −1.44155 + 0.61815I
b = 1.241310 + 0.478776I
5.98521 + 12.71410I 7.13610 − 10.54617I
u = −0.777627 − 1.138280I
a = −1.44155 − 0.61815I
b = 1.241310 − 0.478776I
5.98521 − 12.71410I 7.13610 + 10.54617I
u = 1.39357
a = −0.663516
b = 0.189578
−4.85110 −9.33550
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.605970
a = −1.85205
b = 1.46884
1.44757 −12.6450
u = −1.52754
a = 0.961958
b = −1.81382
8.67340 1.97370
u = −1.76185
a = 0.293178
b = −0.834772
−2.94480 9.22010
28
IV. I
u
4
= h−8.39 × 10
13
u
15
− 3.36 × 10
14
u
14
+ · · · + 2.91 × 10
14
b + 1.34 ×
10
15
, −1.94 × 10
14
u
15
− 5.28 × 10
14
u
14
+ · · · + 2.03 × 10
15
a + 5.33 ×
10
15
, u
16
+ 4u
15
+ · · · − 42u − 7i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
8
=
0.0954094u
15
+ 0.259760u
14
+ ··· − 9.79084u − 2.62067
0.288872u
15
+ 1.15828u
14
+ ··· − 21.0505u − 4.60903
a
9
=
0.384281u
15
+ 1.41804u
14
+ ··· − 30.8414u − 7.22970
0.288872u
15
+ 1.15828u
14
+ ··· − 21.0505u − 4.60903
a
6
=
0.220335u
15
+ 0.721107u
14
+ ··· − 15.7537u − 2.12004
0.333648u
15
+ 0.913267u
14
+ ··· − 4.76971u + 0.00714541
a
3
=
0.278621u
15
+ 1.10853u
14
+ ··· − 18.0158u − 3.99088
0.604472u
15
+ 2.16321u
14
+ ··· − 38.2260u − 9.05521
a
10
=
0.114129u
15
+ 0.389435u
14
+ ··· − 12.1024u − 3.45426
0.386081u
15
+ 1.35864u
14
+ ··· − 20.7574u − 4.24500
a
12
=
0.470250u
15
+ 1.39373u
14
+ ··· − 8.22302u − 0.458057
−0.469229u
15
− 1.05599u
14
+ ··· − 6.85269u − 4.35453
a
4
=
0.188380u
15
+ 0.543078u
14
+ ··· − 2.04815u − 0.280245
−0.249348u
15
− 0.670300u
14
+ ··· + 8.58201u + 3.24932
a
7
=
−0.196763u
15
− 0.747398u
14
+ ··· + 13.4515u + 3.19746
1.47598u
15
+ 5.17144u
14
+ ··· − 79.0543u − 17.0748
a
11
=
0.0567623u
15
− 0.00757436u
14
+ ··· + 8.14800u + 2.44631
−0.544486u
15
− 1.86232u
14
+ ··· + 33.0844u + 8.48296
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
16076929699768976
2033575781111105
u
15
+
11800360206848280
406715156222221
u
14
+ ···−
156144298567052528
290510825873015
u −
33451639400575064
290510825873015
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
16
+ 4u
15
+ ··· − 42u − 7
c
2
, c
5
7(7u
16
+ 28u
15
+ ··· − 6u − 1)
c
3
, c
12
u
16
− u
15
+ ··· − 4u + 1
c
4
, c
11
7(7u
16
− 7u
15
+ ··· + 8u − 1)
c
7
(u
8
− u
6
+ 2u
5
+ 3u
4
+ 2u
3
− u
2
+ 1)
2
c
8
, c
10
u
16
+ u
15
+ ··· + 4u + 1
c
9
(u
8
+ u
7
+ u
6
− u
5
− 2u
4
+ u
3
− 3u
2
+ 2u − 1)
2
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
16
+ 18y
14
+ ··· − 98y + 49
c
2
, c
5
49(49y
16
− 196y
15
+ ··· − 60y + 1)
c
3
, c
8
, c
10
c
12
y
16
− 11y
15
+ ··· + 54y + 1
c
4
, c
11
49(49y
16
+ 147y
15
+ ··· − 56y + 1)
c
7
(y
8
− 2y
7
+ 7y
6
− 12y
5
+ 5y
4
− 12y
3
+ 7y
2
− 2y + 1)
2
c
9
(y
8
+ y
7
− y
6
− 13y
5
− 6y
4
+ 13y
3
+ 9y
2
+ 2y + 1)
2
31
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.770750 + 0.649988I
a = −0.990425 − 0.985675I
b = 1.144790 − 0.525264I
1.66720 − 2.99663I −4.79553 + 4.48232I
u = 0.770750 − 0.649988I
a = −0.990425 + 0.985675I
b = 1.144790 + 0.525264I
1.66720 + 2.99663I −4.79553 − 4.48232I
u = −0.875289
a = −1.32085
b = 1.89545
7.98708 1.68040
u = −0.800860 + 0.871134I
a = −0.486214 + 0.113518I
b = 0.043738 + 0.164083I
1.66720 − 2.99663I −4.79553 + 4.48232I
u = −0.800860 − 0.871134I
a = −0.486214 − 0.113518I
b = 0.043738 − 0.164083I
1.66720 + 2.99663I −4.79553 − 4.48232I
u = −1.20480
a = 1.13631
b = −1.24493
−1.40735 6.31960
u = 1.33376
a = 0.300544
b = 0.709448
−1.40735 6.31960
u = −0.254592 + 0.533302I
a = 1.78589 − 1.39113I
b = −0.791069 − 0.709265I
4.91254 + 2.99663I 12.79553 − 4.48232I
u = −0.254592 − 0.533302I
a = 1.78589 + 1.39113I
b = −0.791069 + 0.709265I
4.91254 − 2.99663I 12.79553 + 4.48232I
u = −0.461018 + 0.289514I
a = 0.1083480 + 0.0094698I
b = 0.32272 − 1.68261I
3.28987 + 6.39156I 4.0000 − 20.9743I
32
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.461018 − 0.289514I
a = 0.1083480 − 0.0094698I
b = 0.32272 + 1.68261I
3.28987 − 6.39156I 4.0000 + 20.9743I
u = −1.83588
a = 0.619937
b = −1.49537
7.98708 1.68040
u = −1.09318 + 1.69730I
a = −1.104940 + 0.378816I
b = 1.189440 − 0.019296I
4.91254 − 2.99663I 12.79553 + 4.48232I
u = −1.09318 − 1.69730I
a = −1.104940 − 0.378816I
b = 1.189440 + 0.019296I
4.91254 + 2.99663I 12.79553 − 4.48232I
u = 1.13000 + 1.79940I
a = 1.319370 + 0.268466I
b = −1.341910 + 0.247920I
3.28987 − 6.39156I 4.0000 + 20.9743I
u = 1.13000 − 1.79940I
a = 1.319370 − 0.268466I
b = −1.341910 − 0.247920I
3.28987 + 6.39156I 4.0000 − 20.9743I
33
V. I
v
1
= ha, b − 1, v + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
−1
0
a
2
=
1
0
a
8
=
0
1
a
9
=
1
1
a
6
=
0
1
a
3
=
1
−1
a
10
=
0
1
a
12
=
1
1
a
4
=
0
1
a
7
=
0
1
a
11
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
u
c
2
, c
3
, c
4
c
5
, c
8
, c
9
c
10
, c
11
, c
12
u − 1
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
y
c
2
, c
3
, c
4
c
5
, c
8
, c
9
c
10
, c
11
, c
12
y −1
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
1.64493 6.00000
37
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u(u
13
+ u
12
+ ··· + 20u − 8)
· (u
16
+ 4u
15
+ ··· − 42u − 7)(u
25
+ u
24
+ ··· − 8u
2
+ 1)
· (u
130
− 5u
129
+ ··· + 9180u − 648)
c
2
, c
5
1008(u − 1)(4u
13
− 4u
12
+ ··· + 5u − 1)(7u
16
+ 28u
15
+ ··· − 6u − 1)
· (u
25
+ u
24
+ ··· − 2u + 1)
· (36u
130
− 144u
129
+ ··· + 650230u + 245213)
c
3
, c
12
(u − 1)(u
13
+ u
12
+ ··· − 5u + 1)(u
16
− u
15
+ ··· − 4u + 1)
· (u
25
− 9u
23
+ ··· − 6u + 1)(u
130
+ 2u
129
+ ··· − 52u + 1)
c
4
, c
11
1008(u − 1)(4u
13
+ 4u
12
+ ··· − 2u + 1)(7u
16
− 7u
15
+ ··· + 8u − 1)
· (u
25
− 4u
24
+ ··· + u − 1)(36u
130
− 72u
129
+ ··· + 3230u − 271)
c
7
u(u
8
− u
6
+ ··· − u
2
+ 1)
2
(u
13
+ 5u
12
+ ··· + 6u − 4)
· (u
25
− 18u
24
+ ··· − 32u − 64)(u
65
+ 10u
64
+ ··· + 1045u + 93)
2
c
8
, c
10
(u − 1)(u
13
− u
12
+ ··· − 5u − 1)(u
16
+ u
15
+ ··· + 4u + 1)
· (u
25
− 9u
23
+ ··· − 6u + 1)(u
130
+ 2u
129
+ ··· − 52u + 1)
c
9
(u − 1)(u
8
+ u
7
+ u
6
− u
5
− 2u
4
+ u
3
− 3u
2
+ 2u − 1)
2
· (u
13
− 3u
12
+ ··· − 2u − 1)(u
25
− 17u
24
+ ··· + 2688u − 256)
· (u
65
+ 6u
64
+ ··· + 13u − 1)
2
38
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y(y
13
− y
12
+ ··· + 96y −64)(y
16
+ 18y
14
+ ··· − 98y + 49)
· (y
25
+ 7y
24
+ ··· + 16y −1)
· (y
130
− 5y
129
+ ··· − 188070336y + 419904)
c
2
, c
5
1016064(y −1)(16y
13
− 104y
12
+ ··· + 27y −1)
· (49y
16
− 196y
15
+ ··· − 60y + 1)(y
25
− 25y
24
+ ··· + 22y −1)
· (1296y
130
− 54648y
129
+ ··· − 4148969485924y + 60129415369)
c
3
, c
8
, c
10
c
12
(y −1)(y
13
− 13y
12
+ ··· + 31y −1)(y
16
− 11y
15
+ ··· + 54y + 1)
· (y
25
− 18y
24
+ ··· + 20y −1)(y
130
− 102y
129
+ ··· − 32y + 1)
c
4
, c
11
1016064(y −1)(16y
13
− 72y
12
+ ··· + 12y −1)
· (49y
16
+ 147y
15
+ ··· − 56y + 1)(y
25
− 20y
24
+ ··· + 7y −1)
· (1296y
130
+ 7560y
129
+ ··· − 4029712y + 73441)
c
7
y(y
8
− 2y
7
+ 7y
6
− 12y
5
+ 5y
4
− 12y
3
+ 7y
2
− 2y + 1)
2
· (y
13
− 3y
12
+ ··· + 60y −16)(y
25
− 4y
24
+ ··· + 289792y −4096)
· (y
65
− 24y
64
+ ··· + 342631y −8649)
2
c
9
(y −1)(y
8
+ y
7
− y
6
− 13y
5
− 6y
4
+ 13y
3
+ 9y
2
+ 2y + 1)
2
· (y
13
− y
12
+ ··· + 46y −1)(y
25
+ y
24
+ ··· + 16384y −65536)
· (y
65
− 8y
64
+ ··· + 151y −1)
2
39
