12n
0378
(K12n
0378
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 2 11 1 4 1 5 7 10
Solving Sequence
2,6 3,11
7 1 8 5 10 4 9 12
c
2
c
6
c
1
c
7
c
5
c
10
c
4
c
8
c
12
c
3
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.40269 × 10
62
u
72
− 1.72408 × 10
63
u
71
+ ··· + 1.82435 × 10
64
b − 1.38356 × 10
64
,
2.34275 × 10
62
u
72
+ 1.14118 × 10
62
u
71
+ ··· + 4.44964 × 10
62
a + 4.68732 × 10
63
, u
73
− u
72
+ ··· + 6u − 1i
I
u
2
= hu
19
− u
18
+ ··· + b − 2, u
19
+ u
18
+ ··· + a − 6, u
20
− 4u
18
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 93 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
= h2.40 × 10
62
u
72
− 1.72 × 10
63
u
71
+ · · · + 1.82 × 10
64
b − 1.38 × 10
64
, 2.34 ×
10
62
u
72
+1.14×10
62
u
71
+· · ·+4.45×10
62
a+4.69×10
63
, u
73
−u
72
+· · ·+6u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
11
=
−0.526502u
72
− 0.256466u
71
+ ··· + 31.1936u − 10.5341
−0.0131701u
72
+ 0.0945035u
71
+ ··· − 9.10210u + 0.758385
a
7
=
0.429075u
72
− 0.253130u
71
+ ··· + 5.78589u − 1.70210
0.0237826u
72
+ 0.0747905u
71
+ ··· − 4.64228u + 2.61862
a
1
=
−u
2
+ 1
−u
4
a
8
=
0.354692u
72
− 0.179230u
71
+ ··· + 1.83197u + 0.794479
−0.134146u
72
+ 0.126424u
71
+ ··· − 4.09974u + 2.52946
a
5
=
u
u
a
10
=
−0.273639u
72
− 0.495448u
71
+ ··· + 35.8660u − 11.3984
0.239693u
72
− 0.144479u
71
+ ··· − 4.42963u − 0.105916
a
4
=
−0.141530u
72
+ 0.130114u
71
+ ··· − 13.1139u + 4.72440
0.122092u
72
− 0.537187u
71
+ ··· + 8.50726u − 3.27538
a
9
=
0.0361754u
72
+ 0.773102u
71
+ ··· − 31.3454u + 11.5188
−0.219504u
72
+ 0.183374u
71
+ ··· + 4.64947u + 0.0703768
a
12
=
−3.01500u
72
+ 3.21861u
71
+ ··· − 11.8184u − 9.35261
0.189418u
72
− 0.0254143u
71
+ ··· − 9.37084u + 1.71468
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.91581u
72
+ 6.79732u
71
+ ··· − 94.4807u + 6.97585
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
73
+ 25u
72
+ ··· + 84u + 1
c
2
, c
5
u
73
+ u
72
+ ··· + 6u + 1
c
3
, c
8
u
73
+ u
72
+ ··· − 72u − 29
c
4
, c
10
u
73
− u
72
+ ··· − 602u − 2285
c
6
, c
11
u
73
− u
72
+ ··· + 6589u + 2209
c
7
u
73
− 3u
72
+ ··· + 30630u − 13801
c
9
, c
12
u
73
− 9u
72
+ ··· + 42u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
73
+ 55y
72
+ ··· + 1088y −1
c
2
, c
5
y
73
− 25y
72
+ ··· + 84y −1
c
3
, c
8
y
73
− 29y
72
+ ··· + 20264y −841
c
4
, c
10
y
73
− 37y
72
+ ··· + 153119224y −5221225
c
6
, c
11
y
73
− 45y
72
+ ··· + 119152695y −4879681
c
7
y
73
+ 11y
72
+ ··· − 1310013602y −190467601
c
9
, c
12
y
73
− 53y
72
+ ··· + 502y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.996222 + 0.079970I
a = −0.640369 + 0.961224I
b = 0.02392 + 1.95649I
−5.68162 + 3.39874I 0
u = −0.996222 − 0.079970I
a = −0.640369 − 0.961224I
b = 0.02392 − 1.95649I
−5.68162 − 3.39874I 0
u = −0.758602 + 0.638058I
a = −0.372335 + 1.210930I
b = 0.34583 + 1.63890I
−0.54896 + 3.17316I 0
u = −0.758602 − 0.638058I
a = −0.372335 − 1.210930I
b = 0.34583 − 1.63890I
−0.54896 − 3.17316I 0
u = −0.618315 + 0.821119I
a = −0.94140 − 1.06158I
b = 0.088422 − 0.498715I
7.38525 − 1.46732I 0
u = −0.618315 − 0.821119I
a = −0.94140 + 1.06158I
b = 0.088422 + 0.498715I
7.38525 + 1.46732I 0
u = −0.969221
a = −0.747368
b = −2.30513
4.41153 −5.41240
u = 0.751264 + 0.736846I
a = 1.058580 − 0.390102I
b = −0.228660 + 0.735522I
9.38761 − 0.55526I 0
u = 0.751264 − 0.736846I
a = 1.058580 + 0.390102I
b = −0.228660 − 0.735522I
9.38761 + 0.55526I 0
u = 0.733170 + 0.756165I
a = −0.851966 − 1.016840I
b = −0.109081 − 1.382330I
−0.08676 + 2.96078I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.733170 − 0.756165I
a = −0.851966 + 1.016840I
b = −0.109081 + 1.382330I
−0.08676 − 2.96078I 0
u = −0.861502 + 0.388627I
a = 0.165858 + 1.013930I
b = 0.55739 + 1.55978I
−0.44770 + 3.61771I 3.83289 − 9.05008I
u = −0.861502 − 0.388627I
a = 0.165858 − 1.013930I
b = 0.55739 − 1.55978I
−0.44770 − 3.61771I 3.83289 + 9.05008I
u = 0.943914 + 0.043003I
a = −0.918576 + 0.881953I
b = 0.02090 + 1.95760I
−4.65821 − 2.86626I −1.66244 + 2.85840I
u = 0.943914 − 0.043003I
a = −0.918576 − 0.881953I
b = 0.02090 − 1.95760I
−4.65821 + 2.86626I −1.66244 − 2.85840I
u = −0.631153 + 0.853761I
a = 1.204560 + 0.578291I
b = −0.010140 − 0.154408I
2.19037 − 3.39728I 0
u = −0.631153 − 0.853761I
a = 1.204560 − 0.578291I
b = −0.010140 + 0.154408I
2.19037 + 3.39728I 0
u = 0.892873 + 0.267184I
a = 0.173653 − 0.505706I
b = −0.190432 − 0.912777I
−1.50577 − 0.99916I −2.39776 + 0.I
u = 0.892873 − 0.267184I
a = 0.173653 + 0.505706I
b = −0.190432 + 0.912777I
−1.50577 + 0.99916I −2.39776 + 0.I
u = −0.767998 + 0.745094I
a = 0.746725 + 0.494096I
b = −0.01556 + 1.80761I
0.46877 − 1.97857I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.767998 − 0.745094I
a = 0.746725 − 0.494096I
b = −0.01556 − 1.80761I
0.46877 + 1.97857I 0
u = 0.143541 + 0.896389I
a = −0.216547 − 1.280260I
b = 0.0239252 − 0.0949787I
0.81734 − 5.65289I 7.40959 + 5.97302I
u = 0.143541 − 0.896389I
a = −0.216547 + 1.280260I
b = 0.0239252 + 0.0949787I
0.81734 + 5.65289I 7.40959 − 5.97302I
u = 0.824608 + 0.727987I
a = −1.29265 + 0.82770I
b = −0.231633 + 0.608811I
6.55692 − 1.93707I 0
u = 0.824608 − 0.727987I
a = −1.29265 − 0.82770I
b = −0.231633 − 0.608811I
6.55692 + 1.93707I 0
u = 0.946156 + 0.586430I
a = 0.432541 − 0.667921I
b = −0.43463 − 1.49029I
−2.76173 − 2.00615I 0
u = 0.946156 − 0.586430I
a = 0.432541 + 0.667921I
b = −0.43463 + 1.49029I
−2.76173 + 2.00615I 0
u = −0.343909 + 0.787868I
a = 0.127670 + 1.043220I
b = 0.084955 − 0.115660I
0.479750 − 0.044976I 6.90143 − 1.13729I
u = −0.343909 − 0.787868I
a = 0.127670 − 1.043220I
b = 0.084955 + 0.115660I
0.479750 + 0.044976I 6.90143 + 1.13729I
u = −0.937251 + 0.657162I
a = 1.099920 − 0.537869I
b = 0.49874 − 1.35415I
−1.09504 + 1.90890I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.937251 − 0.657162I
a = 1.099920 + 0.537869I
b = 0.49874 + 1.35415I
−1.09504 − 1.90890I 0
u = 0.683384 + 0.923655I
a = 1.180580 − 0.657252I
b = −0.0799028 − 0.0563581I
4.09129 + 9.93504I 0
u = 0.683384 − 0.923655I
a = 1.180580 + 0.657252I
b = −0.0799028 + 0.0563581I
4.09129 − 9.93504I 0
u = 0.908958 + 0.710659I
a = −0.890867 + 1.087230I
b = −1.09856 + 2.00903I
6.29427 − 3.55581I 0
u = 0.908958 − 0.710659I
a = −0.890867 − 1.087230I
b = −1.09856 − 2.00903I
6.29427 + 3.55581I 0
u = 1.158780 + 0.119477I
a = −0.690279 + 0.608358I
b = −1.51845 + 1.26660I
−4.61256 − 2.51615I 0
u = 1.158780 − 0.119477I
a = −0.690279 − 0.608358I
b = −1.51845 − 1.26660I
−4.61256 + 2.51615I 0
u = −0.809794
a = 1.59121
b = 2.15213
2.28647 3.88350
u = −0.956447 + 0.710795I
a = 0.599846 + 0.745235I
b = −0.60555 + 1.54716I
−0.11113 + 7.52904I 0
u = −0.956447 − 0.710795I
a = 0.599846 − 0.745235I
b = −0.60555 − 1.54716I
−0.11113 − 7.52904I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964639 + 0.701087I
a = 0.340557 − 0.829485I
b = 1.41277 − 1.84680I
8.73288 − 4.94035I 0
u = 0.964639 − 0.701087I
a = 0.340557 + 0.829485I
b = 1.41277 + 1.84680I
8.73288 + 4.94035I 0
u = 0.853639 + 0.855312I
a = −1.151840 + 0.283826I
b = −0.300491 + 0.019376I
7.09864 + 0.53230I 0
u = 0.853639 − 0.855312I
a = −1.151840 − 0.283826I
b = −0.300491 − 0.019376I
7.09864 − 0.53230I 0
u = 0.978323 + 0.710764I
a = 0.911240 + 0.831323I
b = 0.43175 + 1.60287I
−0.83249 − 8.54524I 0
u = 0.978323 − 0.710764I
a = 0.911240 − 0.831323I
b = 0.43175 − 1.60287I
−0.83249 + 8.54524I 0
u = −1.189080 + 0.229032I
a = −0.808750 − 0.686874I
b = −1.52953 − 1.44010I
−3.81596 + 9.32233I 0
u = −1.189080 − 0.229032I
a = −0.808750 + 0.686874I
b = −1.52953 + 1.44010I
−3.81596 − 9.32233I 0
u = 1.22912
a = 1.00223
b = 1.54563
0.994441 0
u = 0.557309 + 0.526306I
a = 0.544371 − 0.023747I
b = −0.148793 − 1.306520I
−1.71887 − 2.44461I 5.05962 + 1.77262I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.557309 − 0.526306I
a = 0.544371 + 0.023747I
b = −0.148793 + 1.306520I
−1.71887 + 2.44461I 5.05962 − 1.77262I
u = −0.846572 + 0.914565I
a = −0.655447 − 0.508702I
b = 0.167328 − 0.162277I
7.36439 + 2.36950I 0
u = −0.846572 − 0.914565I
a = −0.655447 + 0.508702I
b = 0.167328 + 0.162277I
7.36439 − 2.36950I 0
u = −1.106920 + 0.577507I
a = 0.548477 + 0.039525I
b = 1.248990 + 0.006219I
−1.75051 + 5.10682I 0
u = −1.106920 − 0.577507I
a = 0.548477 − 0.039525I
b = 1.248990 − 0.006219I
−1.75051 − 5.10682I 0
u = 0.948038 + 0.819646I
a = −0.268358 + 1.134470I
b = −0.50120 + 1.94706I
6.80244 − 6.76181I 0
u = 0.948038 − 0.819646I
a = −0.268358 − 1.134470I
b = −0.50120 − 1.94706I
6.80244 + 6.76181I 0
u = 1.183950 + 0.434407I
a = 0.750592 − 0.018384I
b = 1.351730 + 0.004092I
−2.58515 + 0.91174I 0
u = 1.183950 − 0.434407I
a = 0.750592 + 0.018384I
b = 1.351730 − 0.004092I
−2.58515 − 0.91174I 0
u = −1.047120 + 0.715765I
a = −0.832244 − 0.806720I
b = −1.12523 − 1.67057I
6.11341 + 7.23773I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.047120 − 0.715765I
a = −0.832244 + 0.806720I
b = −1.12523 + 1.67057I
6.11341 − 7.23773I 0
u = −1.051990 + 0.719300I
a = 0.446861 + 1.074860I
b = 1.06139 + 2.17386I
0.91326 + 9.25948I 0
u = −1.051990 − 0.719300I
a = 0.446861 − 1.074860I
b = 1.06139 − 2.17386I
0.91326 − 9.25948I 0
u = −0.977624 + 0.850736I
a = −0.417028 − 0.618249I
b = −0.65490 − 1.45884I
6.94563 + 4.12886I 0
u = −0.977624 − 0.850736I
a = −0.417028 + 0.618249I
b = −0.65490 + 1.45884I
6.94563 − 4.12886I 0
u = 1.062780 + 0.766541I
a = 0.558144 − 1.091810I
b = 1.05492 − 2.27168I
2.9062 − 16.1647I 0
u = 1.062780 − 0.766541I
a = 0.558144 + 1.091810I
b = 1.05492 + 2.27168I
2.9062 + 16.1647I 0
u = −0.624370
a = 2.54662
b = 0.805344
3.04322 −5.86610
u = −0.362561 + 0.439077I
a = 0.900518 + 0.463831I
b = 0.193003 − 0.160197I
1.059400 − 0.337570I 9.21872 + 1.59251I
u = −0.362561 − 0.439077I
a = 0.900518 − 0.463831I
b = 0.193003 + 0.160197I
1.059400 + 0.337570I 9.21872 − 1.59251I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.318447
a = −3.97650
b = 0.921377
6.81257 17.0470
u = 0.164283 + 0.047310I
a = −0.05014 + 4.02701I
b = −1.34290 − 0.64628I
−2.12942 − 2.53807I −0.97059 + 1.61971I
u = 0.164283 − 0.047310I
a = −0.05014 − 4.02701I
b = −1.34290 + 0.64628I
−2.12942 + 2.53807I −0.97059 − 1.61971I
12
II.
I
u
2
= hu
19
− u
18
+ · · · + b − 2, u
19
+ u
18
+ · · · + a − 6, u
20
− 4u
18
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
11
=
−u
19
− u
18
+ ··· + u + 6
−u
19
+ u
18
+ ··· + 4u + 2
a
7
=
−5u
19
− u
18
+ ··· + 12u + 6
−2u
19
− u
18
+ ··· + 2u + 5
a
1
=
−u
2
+ 1
−u
4
a
8
=
−6u
19
− 2u
18
+ ··· + 13u + 9
−2u
19
− u
18
+ ··· + u + 5
a
5
=
u
u
a
10
=
−u
19
− 2u
18
+ ··· − u + 8
−u
19
+ 4u
17
+ ··· + 2u + 4
a
4
=
4u
19
− 15u
17
+ ··· − 14u − 1
u
15
− 3u
13
+ ··· − 3u − 1
a
9
=
−2u
19
− 3u
18
+ ··· − 43u
2
+ 11
−u
19
+ 4u
17
+ ··· + 2u + 4
a
12
=
4u
19
+ 3u
18
+ ··· − 4u − 8
3u
19
+ 2u
18
+ ··· − 3u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −20u
19
− 8u
18
+ 71u
17
+ 50u
16
− 199u
15
− 141u
14
+ 362u
13
+ 309u
12
− 520u
11
−
465u
10
+ 557u
9
+ 555u
8
− 458u
7
− 481u
6
+ 268u
5
+ 302u
4
− 86u
3
− 110u
2
+ 29u + 24
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
u
20
− 8u
19
+ ··· − 13u + 1
c
2
u
20
− 4u
18
+ ··· − u + 1
c
3
u
20
− 8u
18
+ ··· + u + 1
c
4
u
20
− 6u
18
+ ··· − u + 1
c
5
u
20
− 4u
18
+ ··· + u + 1
c
6
u
20
+ 4u
19
+ ··· + 4u + 1
c
7
u
20
− 2u
18
+ ··· − 343u + 37
c
8
u
20
− 8u
18
+ ··· − u + 1
c
9
u
20
− 4u
19
+ ··· + 11u − 1
c
10
u
20
− 6u
18
+ ··· + u + 1
c
11
u
20
− 4u
19
+ ··· − 4u + 1
c
12
u
20
+ 4u
19
+ ··· − 11u − 1
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
+ 16y
19
+ ··· − 13y + 1
c
2
, c
5
y
20
− 8y
19
+ ··· − 13y + 1
c
3
, c
8
y
20
− 16y
19
+ ··· − 21y + 1
c
4
, c
10
y
20
− 12y
19
+ ··· + 3y + 1
c
6
, c
11
y
20
− 16y
19
+ ··· + 4y + 1
c
7
y
20
− 4y
19
+ ··· − 48311y + 1369
c
9
, c
12
y
20
− 8y
19
+ ··· − 139y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.942703
a = 1.01394
b = 2.46434
4.96957 9.67670
u = 1.021990 + 0.401552I
a = 0.490770 + 0.256167I
b = 0.324519 − 0.338569I
−3.43274 − 0.00501I −0.269919 + 0.886126I
u = 1.021990 − 0.401552I
a = 0.490770 − 0.256167I
b = 0.324519 + 0.338569I
−3.43274 + 0.00501I −0.269919 − 0.886126I
u = −0.676743 + 0.574335I
a = −0.665466 + 0.475040I
b = −1.05039 + 1.39641I
−1.31380 − 1.46689I 1.93443 − 1.03956I
u = −0.676743 − 0.574335I
a = −0.665466 − 0.475040I
b = −1.05039 − 1.39641I
−1.31380 + 1.46689I 1.93443 + 1.03956I
u = 0.811874 + 0.794873I
a = −0.956293 + 0.516230I
b = 0.278281 − 0.253589I
10.29410 − 1.34128I 11.37265 + 3.04262I
u = 0.811874 − 0.794873I
a = −0.956293 − 0.516230I
b = 0.278281 + 0.253589I
10.29410 + 1.34128I 11.37265 − 3.04262I
u = 1.14495
a = 1.07374
b = 1.53754
0.705306 −7.89590
u = −1.011460 + 0.552332I
a = 0.125011 − 0.483876I
b = −0.386024 − 0.055826I
−2.42227 + 5.99613I 1.25444 − 6.99994I
u = −1.011460 − 0.552332I
a = 0.125011 + 0.483876I
b = −0.386024 + 0.055826I
−2.42227 − 5.99613I 1.25444 + 6.99994I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.808558 + 0.852100I
a = −1.110280 − 0.654219I
b = −0.324330 − 0.410095I
7.38412 + 0.35956I 10.74792 − 1.94607I
u = −0.808558 − 0.852100I
a = −1.110280 + 0.654219I
b = −0.324330 + 0.410095I
7.38412 − 0.35956I 10.74792 + 1.94607I
u = 0.958262 + 0.756351I
a = −0.497932 + 0.796929I
b = −1.25854 + 1.82161I
9.83772 − 4.51280I 11.07027 + 3.02713I
u = 0.958262 − 0.756351I
a = −0.497932 − 0.796929I
b = −1.25854 − 1.82161I
9.83772 + 4.51280I 11.07027 − 3.02713I
u = 0.632431 + 0.395728I
a = 0.029010 − 1.115310I
b = −0.61602 − 2.06351I
−2.02985 − 3.37926I −0.02656 + 9.44485I
u = 0.632431 − 0.395728I
a = 0.029010 + 1.115310I
b = −0.61602 + 2.06351I
−2.02985 + 3.37926I −0.02656 − 9.44485I
u = −0.981912 + 0.806314I
a = −0.565494 − 0.975827I
b = −0.72422 − 1.69291I
6.85419 + 5.82262I 8.97131 − 3.20438I
u = −0.981912 − 0.806314I
a = −0.565494 + 0.975827I
b = −0.72422 + 1.69291I
6.85419 − 5.82262I 8.97131 + 3.20438I
u = −0.603876
a = 2.10690
b = −0.708769
6.39267 −2.87160
u = 0.509858
a = 3.10678
b = 1.22034
3.38690 18.9820
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 8u
19
+ ··· − 13u + 1)(u
73
+ 25u
72
+ ··· + 84u + 1)
c
2
(u
20
− 4u
18
+ ··· − u + 1)(u
73
+ u
72
+ ··· + 6u + 1)
c
3
(u
20
− 8u
18
+ ··· + u + 1)(u
73
+ u
72
+ ··· − 72u − 29)
c
4
(u
20
− 6u
18
+ ··· − u + 1)(u
73
− u
72
+ ··· − 602u − 2285)
c
5
(u
20
− 4u
18
+ ··· + u + 1)(u
73
+ u
72
+ ··· + 6u + 1)
c
6
(u
20
+ 4u
19
+ ··· + 4u + 1)(u
73
− u
72
+ ··· + 6589u + 2209)
c
7
(u
20
− 2u
18
+ ··· − 343u + 37)(u
73
− 3u
72
+ ··· + 30630u − 13801)
c
8
(u
20
− 8u
18
+ ··· − u + 1)(u
73
+ u
72
+ ··· − 72u − 29)
c
9
(u
20
− 4u
19
+ ··· + 11u − 1)(u
73
− 9u
72
+ ··· + 42u − 1)
c
10
(u
20
− 6u
18
+ ··· + u + 1)(u
73
− u
72
+ ··· − 602u − 2285)
c
11
(u
20
− 4u
19
+ ··· − 4u + 1)(u
73
− u
72
+ ··· + 6589u + 2209)
c
12
(u
20
+ 4u
19
+ ··· − 11u − 1)(u
73
− 9u
72
+ ··· + 42u − 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
20
+ 16y
19
+ ··· − 13y + 1)(y
73
+ 55y
72
+ ··· + 1088y −1)
c
2
, c
5
(y
20
− 8y
19
+ ··· − 13y + 1)(y
73
− 25y
72
+ ··· + 84y −1)
c
3
, c
8
(y
20
− 16y
19
+ ··· − 21y + 1)(y
73
− 29y
72
+ ··· + 20264y −841)
c
4
, c
10
(y
20
− 12y
19
+ ··· + 3y + 1)
· (y
73
− 37y
72
+ ··· + 153119224y −5221225)
c
6
, c
11
(y
20
− 16y
19
+ ··· + 4y + 1)
· (y
73
− 45y
72
+ ··· + 119152695y −4879681)
c
7
(y
20
− 4y
19
+ ··· − 48311y + 1369)
· (y
73
+ 11y
72
+ ··· − 1310013602y −190467601)
c
9
, c
12
(y
20
− 8y
19
+ ··· − 139y + 1)(y
73
− 53y
72
+ ··· + 502y −1)
21
