12a
0825
(K12a
0825
)
A knot diagram
1
Linearized knot diagam
4 5 8 2 10 11 3 12 1 7 6 9
Solving Sequence
1,4
2 5
3,9
10 6 12 8 7 11
c
1
c
4
c
2
c
9
c
5
c
12
c
8
c
7
c
11
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.79485 × 10
78
u
79
+ 3.24042 × 10
79
u
78
+ ··· + 3.97586 × 10
76
b + 2.32513 × 10
79
,
− 1.11614 × 10
78
u
79
− 9.33264 × 10
78
u
78
+ ··· + 5.96379 × 10
76
a − 5.21526 × 10
78
,
u
80
+ 10u
79
+ ··· − 61u + 9i
I
u
2
= h−9a
5
+ 15a
4
+ 29a
3
− 11a
2
+ 13b − 9a − 5, 3a
6
+ 2a
5
− 4a
4
− 3a
3
+ 1, u − 1i
I
u
3
= hb + 1, a
2
− 2au − 4a + 9u + 15, u
2
+ u − 1i
I
u
4
= hb − 1, a + u + 2, u
2
+ u − 1i
* 4 irreducible components of dim
C
= 0, with total 92 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
= h3.79 × 10
78
u
79
+ 3.24 × 10
79
u
78
+ · · · + 3.98 × 10
76
b + 2.33 ×
10
79
, −1.12 × 10
78
u
79
− 9.33 × 10
78
u
78
+ · · · + 5.96 × 10
76
a − 5.22 ×
10
78
, u
80
+ 10u
79
+ · · · − 61u + 9i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
3
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
18.7153u
79
+ 156.488u
78
+ ··· − 649.568u + 87.4487
−95.4474u
79
− 815.023u
78
+ ··· + 4365.64u − 584.812
a
10
=
−76.7321u
79
− 658.535u
78
+ ··· + 3716.07u − 497.363
−95.4474u
79
− 815.023u
78
+ ··· + 4365.64u − 584.812
a
6
=
−78.4351u
79
− 659.518u
78
+ ··· + 3232.63u − 436.354
−123.641u
79
− 1086.82u
78
+ ··· + 6687.09u − 885.806
a
12
=
−91.7460u
79
− 788.305u
78
+ ··· + 4317.85u − 579.520
87.9807u
79
+ 760.193u
78
+ ··· − 4426.42u + 588.470
a
8
=
−60.2340u
79
− 518.813u
78
+ ··· + 2900.90u − 389.646
89.0583u
79
+ 756.154u
78
+ ··· − 3964.33u + 532.844
a
7
=
8.30253u
79
+ 82.9747u
78
+ ··· − 735.274u + 93.4145
32.0105u
79
+ 287.801u
78
+ ··· − 1979.29u + 259.874
a
11
=
−28.5574u
79
− 246.679u
78
+ ··· + 1502.25u − 199.834
26.6383u
79
+ 236.438u
78
+ ··· − 1600.04u + 209.994
(ii) Obstruction class = −1
(iii) Cusp Shapes = −352.037u
79
− 3003.98u
78
+ ··· + 16150.8u − 2151.32
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
80
− 10u
79
+ ··· + 61u + 9
c
3
, c
7
u
80
− 2u
79
+ ··· − 2112u + 576
c
5
u
80
+ 2u
79
+ ··· + 17620u + 3460
c
6
, c
10
, c
11
u
80
− 2u
79
+ ··· − 20u + 4
c
8
, c
9
, c
12
u
80
− 4u
79
+ ··· − 61u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
80
− 78y
79
+ ··· + 1139y + 81
c
3
, c
7
y
80
− 48y
79
+ ··· − 8331264y + 331776
c
5
y
80
+ 2y
79
+ ··· − 459714960y + 11971600
c
6
, c
10
, c
11
y
80
+ 74y
79
+ ··· − 528y + 16
c
8
, c
9
, c
12
y
80
− 72y
79
+ ··· − 12613y + 361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.746557 + 0.636954I
a = −0.682165 + 0.006700I
b = −0.145904 − 0.656703I
−6.94608 + 1.67535I 0
u = 0.746557 − 0.636954I
a = −0.682165 − 0.006700I
b = −0.145904 + 0.656703I
−6.94608 − 1.67535I 0
u = 0.378618 + 0.955753I
a = −2.00786 − 0.70595I
b = 1.39851 − 0.33871I
−0.68593 − 10.88960I 0
u = 0.378618 − 0.955753I
a = −2.00786 + 0.70595I
b = 1.39851 + 0.33871I
−0.68593 + 10.88960I 0
u = 1.020620 + 0.245504I
a = −0.88354 + 1.17817I
b = −0.505450 + 0.207652I
−5.18915 − 0.90638I 0
u = 1.020620 − 0.245504I
a = −0.88354 − 1.17817I
b = −0.505450 − 0.207652I
−5.18915 + 0.90638I 0
u = 0.295108 + 0.901425I
a = 2.22025 + 0.54370I
b = −1.40020 + 0.27744I
4.80028 − 7.04030I 0
u = 0.295108 − 0.901425I
a = 2.22025 − 0.54370I
b = −1.40020 − 0.27744I
4.80028 + 7.04030I 0
u = 0.394187 + 0.827178I
a = 0.425833 − 0.162336I
b = −0.220058 + 0.822245I
−5.82377 − 6.70367I 0
u = 0.394187 − 0.827178I
a = 0.425833 + 0.162336I
b = −0.220058 − 0.822245I
−5.82377 + 6.70367I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.889457
a = 0.660649
b = 0.159297
−1.24461 0
u = 0.965727 + 0.632385I
a = 1.269500 + 0.586728I
b = −1.324860 − 0.170371I
2.78356 + 1.72362I 0
u = 0.965727 − 0.632385I
a = 1.269500 − 0.586728I
b = −1.324860 + 0.170371I
2.78356 − 1.72362I 0
u = 0.894797 + 0.767292I
a = −1.196750 − 0.393590I
b = 1.349070 + 0.268437I
−2.22008 + 5.05652I 0
u = 0.894797 − 0.767292I
a = −1.196750 + 0.393590I
b = 1.349070 − 0.268437I
−2.22008 − 5.05652I 0
u = 0.209904 + 0.762735I
a = −2.71834 − 0.30206I
b = 1.363030 − 0.189174I
3.27350 − 2.77001I 0
u = 0.209904 − 0.762735I
a = −2.71834 + 0.30206I
b = 1.363030 + 0.189174I
3.27350 + 2.77001I 0
u = −1.21097
a = 1.37295
b = −1.62302
5.30599 0
u = 0.349449 + 0.692603I
a = −0.468714 + 0.268886I
b = 0.262657 − 0.693020I
−0.48810 − 3.50449I 0
u = 0.349449 − 0.692603I
a = −0.468714 − 0.268886I
b = 0.262657 + 0.693020I
−0.48810 + 3.50449I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.221830 + 0.092628I
a = −1.38120 + 0.34319I
b = 1.59533 + 0.11935I
1.44193 + 5.11024I 0
u = −1.221830 − 0.092628I
a = −1.38120 − 0.34319I
b = 1.59533 − 0.11935I
1.44193 − 5.11024I 0
u = 1.216580 + 0.220859I
a = −0.81510 − 1.66598I
b = 1.233510 − 0.136855I
0.291229 − 1.088620I 0
u = 1.216580 − 0.220859I
a = −0.81510 + 1.66598I
b = 1.233510 + 0.136855I
0.291229 + 1.088620I 0
u = 1.254590 + 0.048642I
a = −0.47602 − 1.82196I
b = −1.064870 − 0.295239I
−5.76832 − 0.40080I 0
u = 1.254590 − 0.048642I
a = −0.47602 + 1.82196I
b = −1.064870 + 0.295239I
−5.76832 + 0.40080I 0
u = 1.170810 + 0.453578I
a = −1.07767 − 1.03396I
b = 1.338150 − 0.008543I
0.41626 − 1.41355I 0
u = 1.170810 − 0.453578I
a = −1.07767 + 1.03396I
b = 1.338150 + 0.008543I
0.41626 + 1.41355I 0
u = 0.337779 + 0.642636I
a = 1.45515 − 0.29598I
b = −0.988367 − 0.439985I
−3.47331 − 2.16270I 0. + 3.40294I
u = 0.337779 − 0.642636I
a = 1.45515 + 0.29598I
b = −0.988367 + 0.439985I
−3.47331 + 2.16270I 0. − 3.40294I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.543823 + 0.447215I
a = 0.780717 − 0.230857I
b = −0.061345 + 0.440180I
−1.39076 − 0.43253I −3.80282 + 0.I
u = 0.543823 − 0.447215I
a = 0.780717 + 0.230857I
b = −0.061345 − 0.440180I
−1.39076 + 0.43253I −3.80282 + 0.I
u = −0.121092 + 0.686429I
a = −2.34739 + 0.92267I
b = 1.43204 − 0.01520I
4.30728 − 2.43252I 5.74380 + 3.14176I
u = −0.121092 − 0.686429I
a = −2.34739 − 0.92267I
b = 1.43204 + 0.01520I
4.30728 + 2.43252I 5.74380 − 3.14176I
u = 1.302040 + 0.087314I
a = 0.048944 − 0.999851I
b = 0.124215 − 0.610162I
−2.91730 − 1.56339I 0
u = 1.302040 − 0.087314I
a = 0.048944 + 0.999851I
b = 0.124215 + 0.610162I
−2.91730 + 1.56339I 0
u = −0.475431 + 0.460281I
a = −1.20403 + 1.49499I
b = 1.44724 + 0.20682I
2.82742 + 5.64096I 5.82262 − 5.01289I
u = −0.475431 − 0.460281I
a = −1.20403 − 1.49499I
b = 1.44724 − 0.20682I
2.82742 − 5.64096I 5.82262 + 5.01289I
u = −0.318513 + 0.576883I
a = 1.76623 − 1.41274I
b = −1.44334 − 0.10431I
7.27651 + 1.62512I 9.82751 − 1.87978I
u = −0.318513 − 0.576883I
a = 1.76623 + 1.41274I
b = −1.44334 + 0.10431I
7.27651 − 1.62512I 9.82751 + 1.87978I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.373692 + 0.515975I
a = 4.02553 + 1.61667I
b = −1.198300 + 0.170105I
−3.93512 − 1.27756I 0.88119 + 5.42303I
u = 0.373692 − 0.515975I
a = 4.02553 − 1.61667I
b = −1.198300 − 0.170105I
−3.93512 + 1.27756I 0.88119 − 5.42303I
u = −1.376180 + 0.013009I
a = 0.395368 + 0.296056I
b = −0.732152 + 0.701776I
−6.68900 − 2.29161I 0
u = −1.376180 − 0.013009I
a = 0.395368 − 0.296056I
b = −0.732152 − 0.701776I
−6.68900 + 2.29161I 0
u = −1.401050 + 0.149791I
a = −0.323166 − 0.222828I
b = 0.964398 − 0.630793I
−4.19551 + 1.65648I 0
u = −1.401050 − 0.149791I
a = −0.323166 + 0.222828I
b = 0.964398 + 0.630793I
−4.19551 − 1.65648I 0
u = 1.41049 + 0.12797I
a = −0.011462 + 1.039060I
b = −0.164145 + 0.760348I
−8.46336 − 4.32726I 0
u = 1.41049 − 0.12797I
a = −0.011462 − 1.039060I
b = −0.164145 − 0.760348I
−8.46336 + 4.32726I 0
u = 1.41617 + 0.24127I
a = 0.440388 + 1.239090I
b = −1.343240 + 0.243725I
1.72668 − 4.68633I 0
u = 1.41617 − 0.24127I
a = 0.440388 − 1.239090I
b = −1.343240 − 0.243725I
1.72668 + 4.68633I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40554 + 0.30181I
a = −1.30853 + 1.14511I
b = 1.44388 + 0.31534I
−1.90678 + 6.61995I 0
u = −1.40554 − 0.30181I
a = −1.30853 − 1.14511I
b = 1.44388 − 0.31534I
−1.90678 − 6.61995I 0
u = −1.43862 + 0.20633I
a = 1.65824 − 1.25728I
b = −1.381350 − 0.249172I
−9.75541 + 4.00421I 0
u = −1.43862 − 0.20633I
a = 1.65824 + 1.25728I
b = −1.381350 + 0.249172I
−9.75541 − 4.00421I 0
u = −1.44562 + 0.16491I
a = 0.516143 − 0.423681I
b = −0.361996 − 0.777644I
−7.64528 + 2.63547I 0
u = −1.44562 − 0.16491I
a = 0.516143 + 0.423681I
b = −0.361996 + 0.777644I
−7.64528 − 2.63547I 0
u = −1.44086 + 0.24255I
a = 0.283292 + 0.184820I
b = −1.094060 + 0.603150I
−9.21105 + 5.40604I 0
u = −1.44086 − 0.24255I
a = 0.283292 − 0.184820I
b = −1.094060 − 0.603150I
−9.21105 − 5.40604I 0
u = −1.44395 + 0.26166I
a = −0.502067 + 0.493869I
b = 0.283566 + 0.907546I
−6.25190 + 6.98041I 0
u = −1.44395 − 0.26166I
a = −0.502067 − 0.493869I
b = 0.283566 − 0.907546I
−6.25190 − 6.98041I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44875 + 0.35939I
a = 1.15299 − 1.21391I
b = −1.44040 − 0.37041I
−0.76681 + 11.57640I 0
u = −1.44875 − 0.35939I
a = 1.15299 + 1.21391I
b = −1.44040 + 0.37041I
−0.76681 − 11.57640I 0
u = 1.49789 + 0.19735I
a = −0.298770 − 1.148940I
b = 1.362850 − 0.314078I
−3.63647 − 8.21163I 0
u = 1.49789 − 0.19735I
a = −0.298770 + 1.148940I
b = 1.362850 + 0.314078I
−3.63647 + 8.21163I 0
u = −1.48258 + 0.31230I
a = 0.508668 − 0.528000I
b = −0.213612 − 0.951544I
−11.8708 + 10.8394I 0
u = −1.48258 − 0.31230I
a = 0.508668 + 0.528000I
b = −0.213612 + 0.951544I
−11.8708 − 10.8394I 0
u = −1.49832 + 0.37550I
a = −1.06626 + 1.28662I
b = 1.42044 + 0.40581I
−6.6953 + 15.7029I 0
u = −1.49832 − 0.37550I
a = −1.06626 − 1.28662I
b = 1.42044 − 0.40581I
−6.6953 − 15.7029I 0
u = −1.56399 + 0.13173I
a = −0.671086 + 0.423767I
b = 0.158661 + 0.592290I
−14.7127 + 0.8961I 0
u = −1.56399 − 0.13173I
a = −0.671086 − 0.423767I
b = 0.158661 − 0.592290I
−14.7127 − 0.8961I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.020300 + 0.417964I
a = 0.043518 − 0.905516I
b = −0.637712 + 0.460503I
−2.34211 − 1.37568I 2.73341 + 4.48844I
u = 0.020300 − 0.417964I
a = 0.043518 + 0.905516I
b = −0.637712 − 0.460503I
−2.34211 + 1.37568I 2.73341 − 4.48844I
u = −0.238555 + 0.323098I
a = 0.85980 − 1.27105I
b = −0.391274 − 0.643481I
−3.11465 + 2.59899I 2.11541 − 3.74111I
u = −0.238555 − 0.323098I
a = 0.85980 + 1.27105I
b = −0.391274 + 0.643481I
−3.11465 − 2.59899I 2.11541 + 3.74111I
u = −1.66199
a = 0.346470
b = −1.11053
−6.96046 0
u = 0.083424 + 0.288430I
a = −1.74789 + 1.17095I
b = 0.582839 + 0.289556I
0.971492 + 0.107577I 9.76074 + 0.21750I
u = 0.083424 − 0.288430I
a = −1.74789 − 1.17095I
b = 0.582839 − 0.289556I
0.971492 − 0.107577I 9.76074 − 0.21750I
u = −1.70283 + 0.10707I
a = −0.308303 − 0.048165I
b = 1.225460 − 0.185717I
−11.48760 − 1.83021I 0
u = −1.70283 − 0.10707I
a = −0.308303 + 0.048165I
b = 1.225460 + 0.185717I
−11.48760 + 1.83021I 0
u = 0.265818
a = −3.31078
b = 0.827813
0.961682 15.0430
12
II.
I
u
2
= h−9a
5
+15a
4
+29a
3
−11a
2
+13b−9a−5, 3a
6
+2a
5
−4a
4
−3a
3
+1, u−1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
3
=
0
1
a
9
=
a
0.692308a
5
− 1.15385a
4
+ ··· + 0.692308a + 0.384615
a
10
=
0.692308a
5
− 1.15385a
4
+ ··· + 1.69231a + 0.384615
0.692308a
5
− 1.15385a
4
+ ··· + 0.692308a + 0.384615
a
6
=
−0.461538a
5
− 1.23077a
4
+ ··· − 0.461538a − 0.923077
1.15385a
5
+ 0.0769231a
4
+ ··· − 0.846154a + 0.307692
a
12
=
−1.61538a
5
− 1.30769a
4
+ ··· + 0.384615a + 0.769231
1.15385a
5
+ 0.0769231a
4
+ ··· − 0.846154a + 0.307692
a
8
=
0
−0.923077a
5
+ 0.538462a
4
+ ··· + 1.07692a − 0.846154
a
7
=
0
−0.923077a
5
+ 0.538462a
4
+ ··· + 1.07692a − 0.846154
a
11
=
0.692308a
5
− 1.15385a
4
+ ··· + 1.69231a + 0.384615
−1.15385a
5
− 0.0769231a
4
+ ··· − 0.153846a − 0.307692
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
24
13
a
5
−
103
13
a
4
−
44
13
a
3
+
144
13
a
2
+
132
13
a +
56
13
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
7
u
6
c
4
(u + 1)
6
c
5
, c
8
, c
9
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
6
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
10
, c
11
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
12
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
8
, c
9
c
12
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
c
6
, c
10
, c
11
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.071740 + 0.286519I
b = 1.52087 + 0.16310I
2.05064 + 4.59213I 3.29989 + 0.22957I
u = 1.00000
a = −1.071740 − 0.286519I
b = 1.52087 − 0.16310I
2.05064 − 4.59213I 3.29989 − 0.22957I
u = 1.00000
a = 1.12449
b = −1.53904
6.01515 8.93190
u = 1.00000
a = 0.631376
b = 0.483672
−0.906083 12.8380
u = 1.00000
a = −0.139525 + 0.601675I
b = −0.493180 + 0.575288I
−4.60518 − 1.97241I −1.96265 + 3.88708I
u = 1.00000
a = −0.139525 − 0.601675I
b = −0.493180 − 0.575288I
−4.60518 + 1.97241I −1.96265 − 3.88708I
16
III. I
u
3
= hb + 1, a
2
− 2au − 4a + 9u + 15, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
5
=
−u
−u + 1
a
3
=
u
u
a
9
=
a
−1
a
10
=
a − 1
−1
a
6
=
au − 4u − 5
au − a − u + 2
a
12
=
−a + 1
1
a
8
=
1
0
a
7
=
u
u − 1
a
11
=
2au − u − 1
3au − 2a − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
(u
2
+ u − 1)
2
c
3
, c
4
(u
2
− u − 1)
2
c
5
, c
6
, c
10
c
11
(u
2
+ 2)
2
c
8
, c
9
(u − 1)
4
c
12
(u + 1)
4
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
(y
2
− 3y + 1)
2
c
5
, c
6
, c
10
c
11
(y + 2)
4
c
8
, c
9
, c
12
(y −1)
4
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 2.61803 + 3.70246I
b = −1.00000
−4.27683 −4.00000
u = 0.618034
a = 2.61803 − 3.70246I
b = −1.00000
−4.27683 −4.00000
u = −1.61803
a = 0.381966 + 0.540182I
b = −1.00000
−12.1725 −4.00000
u = −1.61803
a = 0.381966 − 0.540182I
b = −1.00000
−12.1725 −4.00000
20
IV. I
u
4
= hb − 1, a + u + 2, u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
−u + 1
a
5
=
−u
−u + 1
a
3
=
u
u
a
9
=
−u − 2
1
a
10
=
−u − 1
1
a
6
=
−u
−u + 1
a
12
=
−u − 1
1
a
8
=
−1
0
a
7
=
−u
−u + 1
a
11
=
−u − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
u
2
+ u − 1
c
4
, c
7
u
2
− u − 1
c
5
, c
6
, c
10
c
11
u
2
c
8
, c
9
(u + 1)
2
c
12
(u − 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
2
− 3y + 1
c
5
, c
6
, c
10
c
11
y
2
c
8
, c
9
, c
12
(y −1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −2.61803
b = 1.00000
0.657974 −14.0000
u = −1.61803
a = −0.381966
b = 1.00000
−7.23771 −14.0000
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
6
)(u
2
+ u − 1)
3
(u
80
− 10u
79
+ ··· + 61u + 9)
c
3
u
6
(u
2
− u − 1)
2
(u
2
+ u − 1)(u
80
− 2u
79
+ ··· − 2112u + 576)
c
4
((u + 1)
6
)(u
2
− u − 1)
3
(u
80
− 10u
79
+ ··· + 61u + 9)
c
5
u
2
(u
2
+ 2)
2
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
80
+ 2u
79
+ ··· + 17620u + 3460)
c
6
u
2
(u
2
+ 2)
2
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
80
− 2u
79
+ ··· − 20u + 4)
c
7
u
6
(u
2
− u − 1)(u
2
+ u − 1)
2
(u
80
− 2u
79
+ ··· − 2112u + 576)
c
8
, c
9
(u − 1)
4
(u + 1)
2
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
80
− 4u
79
+ ··· − 61u + 19)
c
10
, c
11
u
2
(u
2
+ 2)
2
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
80
− 2u
79
+ ··· − 20u + 4)
c
12
(u − 1)
2
(u + 1)
4
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
80
− 4u
79
+ ··· − 61u + 19)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
6
)(y
2
− 3y + 1)
3
(y
80
− 78y
79
+ ··· + 1139y + 81)
c
3
, c
7
y
6
(y
2
− 3y + 1)
3
(y
80
− 48y
79
+ ··· − 8331264y + 331776)
c
5
y
2
(y + 2)
4
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
80
+ 2y
79
+ ··· − 459714960y + 11971600)
c
6
, c
10
, c
11
y
2
(y + 2)
4
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
80
+ 74y
79
+ ··· − 528y + 16)
c
8
, c
9
, c
12
(y −1)
6
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
80
− 72y
79
+ ··· − 12613y + 361)
26
