12a
0971
(K12a
0971
)
A knot diagram
1
Linearized knot diagam
4 6 10 1 9 3 11 12 2 8 7 5
Solving Sequence
7,11
8 12
3,9
6 2 5 10 4 1
c
7
c
11
c
8
c
6
c
2
c
5
c
10
c
3
c
1
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3.15928 × 10
85
u
86
− 7.95197 × 10
85
u
85
+ ··· + 1.03342 × 10
86
b − 3.69881 × 10
86
,
1.34443 × 10
86
u
86
− 4.14253 × 10
86
u
85
+ ··· + 9.30081 × 10
86
a − 2.18852 × 10
87
, u
87
− 3u
86
+ ··· − 13u + 9i
I
u
2
= h45u
2
a + 18au + 15u
2
+ 7b + 75a + 6u + 25, 3u
2
a + 3a
2
+ 3au − 3u
2
+ 3a − 6u − 2, u
3
+ u
2
+ 2u + 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
=
h3.16×10
85
u
86
−7.95×10
85
u
85
+· · ·+1.03×10
86
b−3.70×10
86
, 1.34×10
86
u
86
−
4.14 × 10
86
u
85
+ · · · + 9.30 × 10
86
a − 2.19 × 10
87
, u
87
− 3u
86
+ · · · − 13u + 9i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
12
=
u
u
a
3
=
−0.144550u
86
+ 0.445394u
85
+ ··· − 6.95630u + 2.35304
−0.305710u
86
+ 0.769478u
85
+ ··· − 0.412694u + 3.57918
a
9
=
−u
4
− u
2
+ 1
−u
4
− 2u
2
a
6
=
0.196170u
86
+ 0.344284u
85
+ ··· − 9.70216u + 7.17387
−0.674955u
86
+ 2.27956u
85
+ ··· − 11.0701u + 6.12964
a
2
=
−0.223344u
86
+ 0.899644u
85
+ ··· − 1.51984u − 0.0494108
−0.504613u
86
+ 1.23884u
85
+ ··· − 1.07566u + 2.53142
a
5
=
0.00372110u
86
+ 0.0603299u
85
+ ··· − 1.93409u + 3.70671
−0.148462u
86
+ 0.292758u
85
+ ··· − 6.49964u − 1.68499
a
10
=
−u
u
3
+ u
a
4
=
0.0688365u
86
+ 0.324718u
85
+ ··· − 7.35333u + 2.58991
−0.632808u
86
+ 1.81422u
85
+ ··· − 4.84845u + 8.01765
a
1
=
0.0565534u
86
− 0.521293u
85
+ ··· + 5.25049u − 5.64642
0.0666287u
86
− 0.601748u
85
+ ··· + 2.76442u − 1.49161
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.04216u
86
+ 4.97559u
85
+ ··· − 2.37897u + 25.2364
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
87
− 4u
86
+ ··· − 4u + 1
c
2
, c
6
u
87
− 4u
86
+ ··· + 4u − 1
c
3
27(27u
87
+ 27u
86
+ ··· − 601649u + 71363)
c
5
27(27u
87
− 162u
86
+ ··· − 5.84990 × 10
7
u + 8628139)
c
7
, c
10
, c
11
u
87
+ 3u
86
+ ··· − 13u − 9
c
8
u
87
− 3u
86
+ ··· + 408781u − 71217
c
9
u
87
− 3u
86
+ ··· − 9504u + 5184
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
87
+ 86y
86
+ ··· − 18y −1
c
2
, c
6
y
87
− 54y
86
+ ··· − 18y −1
c
3
729(729y
87
+ 24381y
86
+ ··· − 3.17475 × 10
11
y −5.09268 × 10
9
)
c
5
729
· (729y
87
− 46332y
86
+ ··· + 2022353001484271y −74444782603321)
c
7
, c
10
, c
11
y
87
+ 73y
86
+ ··· + 997y −81
c
8
y
87
− 51y
86
+ ··· + 33659194645y −5071861089
c
9
y
87
+ 35y
86
+ ··· − 405347328y −26873856
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.475527 + 0.805833I
a = 0.089835 − 0.551135I
b = 1.177780 − 0.150566I
2.70092 − 3.44890I 0
u = −0.475527 − 0.805833I
a = 0.089835 + 0.551135I
b = 1.177780 + 0.150566I
2.70092 + 3.44890I 0
u = 0.888902 + 0.205924I
a = 0.900561 − 0.992055I
b = −1.37273 − 0.49704I
13.2047 + 12.4115I 0
u = 0.888902 − 0.205924I
a = 0.900561 + 0.992055I
b = −1.37273 + 0.49704I
13.2047 − 12.4115I 0
u = 0.391672 + 1.023860I
a = 0.362478 + 0.178317I
b = 1.359590 − 0.374736I
3.54190 − 4.23526I 0
u = 0.391672 − 1.023860I
a = 0.362478 − 0.178317I
b = 1.359590 + 0.374736I
3.54190 + 4.23526I 0
u = −1.065520 + 0.285270I
a = 0.418557 + 0.401893I
b = −1.193590 + 0.046738I
11.06060 − 1.56959I 0
u = −1.065520 − 0.285270I
a = 0.418557 − 0.401893I
b = −1.193590 − 0.046738I
11.06060 + 1.56959I 0
u = 0.338354 + 1.064750I
a = 0.956882 − 1.019130I
b = 0.207604 − 0.939172I
5.89914 − 2.67054I 0
u = 0.338354 − 1.064750I
a = 0.956882 + 1.019130I
b = 0.207604 + 0.939172I
5.89914 + 2.67054I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.845496 + 0.226103I
a = −0.748389 − 0.724804I
b = 1.153110 − 0.049488I
4.62127 − 1.17888I 15.3214 + 4.9222I
u = −0.845496 − 0.226103I
a = −0.748389 + 0.724804I
b = 1.153110 + 0.049488I
4.62127 + 1.17888I 15.3214 − 4.9222I
u = 0.819931 + 0.174938I
a = −1.046840 + 0.926330I
b = 1.39190 + 0.49516I
6.16197 + 8.62937I 7.26098 − 7.48664I
u = 0.819931 − 0.174938I
a = −1.046840 − 0.926330I
b = 1.39190 − 0.49516I
6.16197 − 8.62937I 7.26098 + 7.48664I
u = 0.532196 + 1.037870I
a = −0.348925 − 0.031244I
b = −1.348470 + 0.419542I
10.66350 − 7.41245I 0
u = 0.532196 − 1.037870I
a = −0.348925 + 0.031244I
b = −1.348470 − 0.419542I
10.66350 + 7.41245I 0
u = −0.765759 + 0.895014I
a = −0.010074 + 0.631456I
b = −1.198210 + 0.136520I
9.18914 − 4.57999I 0
u = −0.765759 − 0.895014I
a = −0.010074 − 0.631456I
b = −1.198210 − 0.136520I
9.18914 + 4.57999I 0
u = 0.802888 + 0.153108I
a = −0.262672 + 0.297332I
b = 0.066528 + 1.077300I
8.68088 + 6.86862I 7.73382 − 5.25997I
u = 0.802888 − 0.153108I
a = −0.262672 − 0.297332I
b = 0.066528 − 1.077300I
8.68088 − 6.86862I 7.73382 + 5.25997I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.800674 + 0.019599I
a = −0.936657 − 0.466941I
b = 1.38632 − 0.56584I
12.75210 + 0.90095I 12.11282 − 0.46988I
u = 0.800674 − 0.019599I
a = −0.936657 + 0.466941I
b = 1.38632 + 0.56584I
12.75210 − 0.90095I 12.11282 + 0.46988I
u = 0.305617 + 1.178510I
a = −0.611784 − 0.323868I
b = −1.46949 + 0.37280I
2.59890 + 0.60226I 0
u = 0.305617 − 1.178510I
a = −0.611784 + 0.323868I
b = −1.46949 − 0.37280I
2.59890 − 0.60226I 0
u = 0.769265 + 0.092137I
a = 1.145640 − 0.694778I
b = −1.42038 − 0.52171I
5.88995 + 3.31153I 8.97619 − 2.85612I
u = 0.769265 − 0.092137I
a = 1.145640 + 0.694778I
b = −1.42038 + 0.52171I
5.88995 − 3.31153I 8.97619 + 2.85612I
u = −0.305917 + 0.699060I
a = 0.961569 − 0.906753I
b = 0.192565 − 0.474320I
5.14665 − 2.63882I 2.93112 + 4.29984I
u = −0.305917 − 0.699060I
a = 0.961569 + 0.906753I
b = 0.192565 + 0.474320I
5.14665 + 2.63882I 2.93112 − 4.29984I
u = −0.216484 + 1.229130I
a = 1.61808 + 2.33237I
b = 0.825856 + 0.217856I
4.04804 − 2.25597I 0
u = −0.216484 − 1.229130I
a = 1.61808 − 2.33237I
b = 0.825856 − 0.217856I
4.04804 + 2.25597I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.135515 + 1.243750I
a = −1.23739 + 0.76717I
b = 1.212330 − 0.016055I
3.39034 − 1.96317I 0
u = −0.135515 − 1.243750I
a = −1.23739 − 0.76717I
b = 1.212330 + 0.016055I
3.39034 + 1.96317I 0
u = −0.723811 + 0.167188I
a = 0.971888 − 0.512753I
b = 0.279767 − 0.169511I
7.07270 − 0.88904I 5.36870 + 1.21419I
u = −0.723811 − 0.167188I
a = 0.971888 + 0.512753I
b = 0.279767 + 0.169511I
7.07270 + 0.88904I 5.36870 − 1.21419I
u = 0.257760 + 1.249610I
a = −1.18240 + 1.27452I
b = −0.330391 + 1.218780I
−2.18501 + 0.51193I 0
u = 0.257760 − 1.249610I
a = −1.18240 − 1.27452I
b = −0.330391 − 1.218780I
−2.18501 − 0.51193I 0
u = 0.129759 + 1.281340I
a = 0.11451 − 2.07191I
b = −0.762915 − 0.936611I
−3.43050 + 4.05346I 0
u = 0.129759 − 1.281340I
a = 0.11451 + 2.07191I
b = −0.762915 + 0.936611I
−3.43050 − 4.05346I 0
u = 0.349523 + 1.243660I
a = 0.04825 + 2.17506I
b = 1.29439 + 0.65520I
8.97149 + 3.24317I 0
u = 0.349523 − 1.243660I
a = 0.04825 − 2.17506I
b = 1.29439 − 0.65520I
8.97149 − 3.24317I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.162052 + 1.282820I
a = −0.999751 − 0.932121I
b = −0.507012 − 0.172579I
−2.33280 − 2.04828I 0
u = −0.162052 − 1.282820I
a = −0.999751 + 0.932121I
b = −0.507012 + 0.172579I
−2.33280 + 2.04828I 0
u = 0.699346 + 0.071790I
a = 0.214536 − 0.019613I
b = −0.090287 − 1.176220I
1.41523 + 2.90127I 9.26737 − 6.98869I
u = 0.699346 − 0.071790I
a = 0.214536 + 0.019613I
b = −0.090287 + 1.176220I
1.41523 − 2.90127I 9.26737 + 6.98869I
u = −0.260689 + 1.294790I
a = 1.05542 + 2.01164I
b = −1.091180 + 0.113305I
−0.90408 − 3.29830I 0
u = −0.260689 − 1.294790I
a = 1.05542 − 2.01164I
b = −1.091180 − 0.113305I
−0.90408 + 3.29830I 0
u = 0.003905 + 1.322550I
a = −1.25108 + 0.82381I
b = −0.829014 + 0.579445I
−2.87276 − 1.53737I 0
u = 0.003905 − 1.322550I
a = −1.25108 − 0.82381I
b = −0.829014 − 0.579445I
−2.87276 + 1.53737I 0
u = 0.351469 + 1.275860I
a = 0.804976 + 0.104885I
b = 1.46360 − 0.48078I
8.72609 + 5.04964I 0
u = 0.351469 − 1.275860I
a = 0.804976 − 0.104885I
b = 1.46360 + 0.48078I
8.72609 − 5.04964I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.652792
a = 3.59295
b = −1.08207
3.16347 −17.1830
u = 0.296966 + 1.318480I
a = 0.95642 − 1.47053I
b = 0.080443 − 1.241100I
−2.95953 + 6.52773I 0
u = 0.296966 − 1.318480I
a = 0.95642 + 1.47053I
b = 0.080443 + 1.241100I
−2.95953 − 6.52773I 0
u = 0.038704 + 1.351680I
a = −0.05490 + 1.69619I
b = 0.485783 + 0.766327I
−6.18107 − 0.41670I 0
u = 0.038704 − 1.351680I
a = −0.05490 − 1.69619I
b = 0.485783 − 0.766327I
−6.18107 + 0.41670I 0
u = −0.232682 + 1.343270I
a = −0.157176 + 0.632391I
b = 0.030830 + 0.298245I
−3.33629 − 3.42016I 0
u = −0.232682 − 1.343270I
a = −0.157176 − 0.632391I
b = 0.030830 − 0.298245I
−3.33629 + 3.42016I 0
u = 0.329123 + 1.325740I
a = −0.14606 − 2.13239I
b = −1.38903 − 0.63090I
1.43892 + 7.28022I 0
u = 0.329123 − 1.325740I
a = −0.14606 + 2.13239I
b = −1.38903 + 0.63090I
1.43892 − 7.28022I 0
u = −0.317690 + 1.355920I
a = 0.441890 − 0.785584I
b = 0.085383 − 0.416658I
2.27643 − 4.70266I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.317690 − 1.355920I
a = 0.441890 + 0.785584I
b = 0.085383 + 0.416658I
2.27643 + 4.70266I 0
u = 0.344313 + 1.360690I
a = −0.80926 + 1.41488I
b = −0.029807 + 1.138480I
3.90795 + 11.01110I 0
u = 0.344313 − 1.360690I
a = −0.80926 − 1.41488I
b = −0.029807 − 1.138480I
3.90795 − 11.01110I 0
u = −0.574564 + 0.097485I
a = −0.526522 + 0.500182I
b = −0.133040 + 0.144638I
1.248450 − 0.464743I 7.84413 − 0.22520I
u = −0.574564 − 0.097485I
a = −0.526522 − 0.500182I
b = −0.133040 − 0.144638I
1.248450 + 0.464743I 7.84413 + 0.22520I
u = 0.34983 + 1.37354I
a = 0.15121 + 2.06930I
b = 1.38648 + 0.57465I
1.27287 + 12.84900I 0
u = 0.34983 − 1.37354I
a = 0.15121 − 2.06930I
b = 1.38648 − 0.57465I
1.27287 − 12.84900I 0
u = −0.36460 + 1.37318I
a = 0.064420 − 1.281370I
b = 1.127220 − 0.195815I
−0.38189 − 5.55156I 0
u = −0.36460 − 1.37318I
a = 0.064420 + 1.281370I
b = 1.127220 + 0.195815I
−0.38189 + 5.55156I 0
u = −0.05481 + 1.43158I
a = 0.086649 − 1.361050I
b = −0.281530 − 0.644862I
−1.53485 − 3.56929I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05481 − 1.43158I
a = 0.086649 + 1.361050I
b = −0.281530 + 0.644862I
−1.53485 + 3.56929I 0
u = 0.37889 + 1.40071I
a = −0.13618 − 2.03758I
b = −1.36671 − 0.55316I
8.1224 + 16.9671I 0
u = 0.37889 − 1.40071I
a = −0.13618 + 2.03758I
b = −1.36671 + 0.55316I
8.1224 − 16.9671I 0
u = −0.07319 + 1.45408I
a = 1.06461 − 0.98320I
b = 1.010330 − 0.418689I
−4.52259 − 4.88007I 0
u = −0.07319 − 1.45408I
a = 1.06461 + 0.98320I
b = 1.010330 + 0.418689I
−4.52259 + 4.88007I 0
u = −0.48195 + 1.42073I
a = −0.157662 + 0.989615I
b = −1.168280 + 0.209592I
5.78078 − 7.09356I 0
u = −0.48195 − 1.42073I
a = −0.157662 − 0.989615I
b = −1.168280 − 0.209592I
5.78078 + 7.09356I 0
u = −0.13146 + 1.54608I
a = −0.835423 + 0.998254I
b = −1.094330 + 0.369463I
0.89140 − 7.47263I 0
u = −0.13146 − 1.54608I
a = −0.835423 − 0.998254I
b = −1.094330 − 0.369463I
0.89140 + 7.47263I 0
u = −0.235402 + 0.326790I
a = −1.67438 + 0.65469I
b = −1.079050 + 0.173980I
1.97105 − 0.98027I 2.19878 − 2.27327I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.235402 − 0.326790I
a = −1.67438 − 0.65469I
b = −1.079050 − 0.173980I
1.97105 + 0.98027I 2.19878 + 2.27327I
u = 0.086471 + 0.387614I
a = −1.28701 + 0.84711I
b = 0.070886 + 0.548596I
−0.894236 − 0.922911I −4.05439 + 3.52210I
u = 0.086471 − 0.387614I
a = −1.28701 − 0.84711I
b = 0.070886 − 0.548596I
−0.894236 + 0.922911I −4.05439 − 3.52210I
u = −0.387761 + 0.079628I
a = 3.05711 + 4.85214I
b = 1.003890 + 0.128798I
7.29634 − 0.17116I 10.73887 − 3.23742I
u = −0.387761 − 0.079628I
a = 3.05711 − 4.85214I
b = 1.003890 − 0.128798I
7.29634 + 0.17116I 10.73887 + 3.23742I
u = 0.371714 + 0.057427I
a = 1.249700 + 0.334115I
b = −0.596116 − 0.746232I
0.65359 + 2.22706I −4.78903 − 5.61529I
u = 0.371714 − 0.057427I
a = 1.249700 − 0.334115I
b = −0.596116 + 0.746232I
0.65359 − 2.22706I −4.78903 + 5.61529I
13
II. I
u
2
= h45u
2
a + 18au + 15u
2
+ 7b + 75a + 6u + 25, 3u
2
a + 3a
2
+ 3au −
3u
2
+ 3a − 6u − 2, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
8
=
1
−u
2
a
12
=
u
u
a
3
=
a
−6.42857au
2
− 2.14286u
2
+ ··· − 10.7143a − 3.57143
a
9
=
−u
−u
2
− u − 1
a
6
=
15
7
u
2
a +
12
7
u
2
+ ··· +
32
7
a +
20
7
−6.42857au
2
− 2.14286u
2
+ ··· − 10.7143a − 4.57143
a
2
=
30
7
u
2
a +
3
7
u
2
+ ··· +
57
7
a +
12
7
−6.42857au
2
− 2.14286u
2
+ ··· − 10.7143a − 2.57143
a
5
=
3u
2
a + au + 2u
2
+ 6a + u + 3
−7.71429au
2
− 2.57143u
2
+ ··· − 12.8571a − 5.28571
a
10
=
−u
−u
2
− u − 1
a
4
=
12
7
u
2
a +
4
7
u
2
+ ··· +
27
7
a +
9
7
−9u
2
a − 4au − 3u
2
− 15a − u − 5
a
1
=
39
7
u
2
a +
13
7
u
2
+ ··· +
72
7
a +
24
7
−5.14286au
2
− 1.71429u
2
+ ··· − 8.57143a − 2.85714
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
36
7
u
2
a −
13
7
au +
16
7
u
2
−
81
7
a +
64
21
u +
43
7
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
12
(u
2
− u + 1)
3
c
2
, c
4
(u
2
+ u + 1)
3
c
3
27(27u
6
+ 9u
4
+ 6u
2
+ 1)
c
5
27(27u
6
− 27u
5
+ 9u
4
− 3u
2
+ 1)
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
8
(u
3
− u
2
+ 1)
2
c
9
u
6
c
10
, c
11
(u
3
− u
2
+ 2u − 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
12
(y
2
+ y + 1)
3
c
3
729(27y
3
+ 9y
2
+ 6y + 1)
2
c
5
729(729y
6
− 243y
5
− 81y
4
+ 27y
2
− 6y + 1)
c
7
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
8
(y
3
− y
2
+ 2y −1)
2
c
9
y
6
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 1.08379 + 0.96480I
b = 0.500000 + 0.866025I
−3.02413 − 0.79824I −1.60261 + 0.67112I
u = −0.215080 + 1.307140I
a = −0.20635 − 1.70967I
b = 0.500000 − 0.866025I
−3.02413 − 4.85801I 3.02248 + 7.08665I
u = −0.215080 − 1.307140I
a = 1.08379 − 0.96480I
b = 0.500000 − 0.866025I
−3.02413 + 0.79824I −1.60261 − 0.67112I
u = −0.215080 − 1.307140I
a = −0.20635 + 1.70967I
b = 0.500000 + 0.866025I
−3.02413 + 4.85801I 3.02248 − 7.08665I
u = −0.569840
a = −0.377439 + 0.076393I
b = 0.500000 − 0.866025I
1.11345 − 2.02988I 9.74680 − 0.93071I
u = −0.569840
a = −0.377439 − 0.076393I
b = 0.500000 + 0.866025I
1.11345 + 2.02988I 9.74680 + 0.93071I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
12
((u
2
− u + 1)
3
)(u
87
− 4u
86
+ ··· − 4u + 1)
c
2
((u
2
+ u + 1)
3
)(u
87
− 4u
86
+ ··· + 4u − 1)
c
3
729(27u
6
+ 9u
4
+ 6u
2
+ 1)(27u
87
+ 27u
86
+ ··· − 601649u + 71363)
c
4
((u
2
+ u + 1)
3
)(u
87
− 4u
86
+ ··· − 4u + 1)
c
5
729(27u
6
− 27u
5
+ 9u
4
− 3u
2
+ 1)
· (27u
87
− 162u
86
+ ··· − 58498985u + 8628139)
c
6
((u
2
− u + 1)
3
)(u
87
− 4u
86
+ ··· + 4u − 1)
c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
87
+ 3u
86
+ ··· − 13u − 9)
c
8
((u
3
− u
2
+ 1)
2
)(u
87
− 3u
86
+ ··· + 408781u − 71217)
c
9
u
6
(u
87
− 3u
86
+ ··· − 9504u + 5184)
c
10
, c
11
((u
3
− u
2
+ 2u − 1)
2
)(u
87
+ 3u
86
+ ··· − 13u − 9)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
((y
2
+ y + 1)
3
)(y
87
+ 86y
86
+ ··· − 18y −1)
c
2
, c
6
((y
2
+ y + 1)
3
)(y
87
− 54y
86
+ ··· − 18y −1)
c
3
531441(27y
3
+ 9y
2
+ 6y + 1)
2
· (729y
87
+ 24381y
86
+ ··· − 317474738263y −5092677769)
c
5
531441(729y
6
− 243y
5
− 81y
4
+ 27y
2
− 6y + 1)
· (729y
87
− 46332y
86
+ ··· + 2022353001484271y −74444782603321)
c
7
, c
10
, c
11
((y
3
+ 3y
2
+ 2y −1)
2
)(y
87
+ 73y
86
+ ··· + 997y −81)
c
8
(y
3
− y
2
+ 2y −1)
2
· (y
87
− 51y
86
+ ··· + 33659194645y −5071861089)
c
9
y
6
(y
87
+ 35y
86
+ ··· − 4.05347 × 10
8
y −2.68739 × 10
7
)
19
