12a
0075
(K12a
0075
)
A knot diagram
1
Linearized knot diagam
3 5 7 11 2 10 12 1 4 6 9 8
Solving Sequence
1,8 4,9
10 12 7 3 6 11 5 2
c
8
c
9
c
12
c
7
c
3
c
6
c
11
c
4
c
2
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.19584 × 10
116
u
105
+ 1.86181 × 10
116
u
104
+ ··· + 6.02649 × 10
115
b − 1.28219 × 10
116
,
2.36470 × 10
115
u
105
− 1.16324 × 10
116
u
104
+ ··· + 6.02649 × 10
115
a − 3.33384 × 10
115
, u
106
− 3u
105
+ ··· − 3u − 1i
I
u
2
= hau + b − a, 5a
2
+ 3au + 4a + 3u + 5, u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 110 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−1.20 × 10
116
u
105
+ 1.86 × 10
116
u
104
+ · · · + 6.03 × 10
115
b − 1.28 ×
10
116
, 2.36 × 10
115
u
105
− 1.16 × 10
116
u
104
+ · · · + 6.03 × 10
115
a − 3.33 ×
10
115
, u
106
− 3u
105
+ · · · − 3u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−0.392385u
105
+ 1.93021u
104
+ ··· + 0.146583u + 0.553198
1.98431u
105
− 3.08938u
104
+ ··· + 7.46686u + 2.12758
a
9
=
1
u
2
a
10
=
0.967277u
105
− 1.56952u
104
+ ··· + 2.76033u + 0.392588
3.35293u
105
− 5.77616u
104
+ ··· + 9.79544u + 2.36212
a
12
=
u
u
a
7
=
−u
2
+ 1
−u
2
a
3
=
−1.75036u
105
+ 3.98608u
104
+ ··· + 1.82800u + 1.18803
1.69583u
105
− 3.62423u
104
+ ··· + 10.3896u + 2.74535
a
6
=
1.02981u
105
− 1.60166u
104
+ ··· + 2.72454u + 1.74180
0.684407u
105
− 1.13507u
104
+ ··· + 2.19871u + 0.520494
a
11
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
5
=
−2.02491u
105
+ 4.32790u
104
+ ··· − 0.782197u + 0.473046
0.486353u
105
− 1.64209u
104
+ ··· + 7.18736u + 2.04536
a
2
=
0.306755u
105
− 0.586484u
104
+ ··· + 12.5619u − 0.133826
3.87650u
105
− 6.46536u
104
+ ··· + 14.8476u + 3.23868
(ii) Obstruction class = −1
(iii) Cusp Shapes = −8.72998u
105
+ 16.9191u
104
+ ··· − 32.7341u − 9.48349
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
106
+ 39u
105
+ ··· − 6871u + 625
c
2
, c
5
u
106
+ 3u
105
+ ··· + 89u + 25
c
3
25(25u
106
− 220u
105
+ ··· − 1.88460 × 10
7
u + 6882857)
c
4
25(25u
106
+ 135u
105
+ ··· − 2.32523 × 10
8
u − 3.13965 × 10
7
)
c
6
, c
10
u
106
+ 3u
105
+ ··· + u − 1
c
7
, c
8
, c
12
u
106
+ 3u
105
+ ··· + 3u − 1
c
9
u
106
+ u
105
+ ··· − 19600u − 2000
c
11
u
106
− 9u
105
+ ··· − 363165u + 47311
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
106
+ 59y
105
+ ··· − 405121891y + 390625
c
2
, c
5
y
106
+ 39y
105
+ ··· − 6871y + 625
c
3
625
· (625y
106
+ 15400y
105
+ ··· + 710061743809250y + 47373720482449)
c
4
625(625y
106
+ 44975y
105
+ ··· + 2.18081 × 10
16
y + 9.85742 × 10
14
)
c
6
, c
10
y
106
+ 67y
105
+ ··· − 19y + 1
c
7
, c
8
, c
12
y
106
− 93y
105
+ ··· − 19y + 1
c
9
y
106
+ 25y
105
+ ··· + 144720000y + 4000000
c
11
y
106
+ 23y
105
+ ··· − 76748887567y + 2238330721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.920780 + 0.466753I
a = 0.756321 + 0.442832I
b = 1.67086 + 0.83902I
4.62802 − 9.62359I 0
u = −0.920780 − 0.466753I
a = 0.756321 − 0.442832I
b = 1.67086 − 0.83902I
4.62802 + 9.62359I 0
u = −0.816204 + 0.487065I
a = 0.215861 + 0.609548I
b = 0.208363 + 1.133060I
5.34115 + 2.64856I 0
u = −0.816204 − 0.487065I
a = 0.215861 − 0.609548I
b = 0.208363 − 1.133060I
5.34115 − 2.64856I 0
u = −0.977481 + 0.406392I
a = −0.818336 − 0.402034I
b = −1.75031 − 0.94474I
5.97827 − 3.64428I 0
u = −0.977481 − 0.406392I
a = −0.818336 + 0.402034I
b = −1.75031 + 0.94474I
5.97827 + 3.64428I 0
u = −0.938198 + 0.491834I
a = −0.214075 − 0.753717I
b = −0.421332 − 1.338260I
4.64585 + 8.16774I 0
u = −0.938198 − 0.491834I
a = −0.214075 + 0.753717I
b = −0.421332 + 1.338260I
4.64585 − 8.16774I 0
u = 0.924351 + 0.524938I
a = −0.498824 + 0.328883I
b = −1.017210 + 0.528817I
0.18493 + 3.46058I 0
u = 0.924351 − 0.524938I
a = −0.498824 − 0.328883I
b = −1.017210 − 0.528817I
0.18493 − 3.46058I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.227735 + 0.861289I
a = −0.698764 − 1.084020I
b = −0.0737764 + 0.0351104I
6.87458 − 3.38819I 0
u = −0.227735 − 0.861289I
a = −0.698764 + 1.084020I
b = −0.0737764 − 0.0351104I
6.87458 + 3.38819I 0
u = 0.247091 + 0.846456I
a = 0.10106 + 1.53739I
b = −0.0499682 − 0.0331869I
2.29410 − 8.26425I 0
u = 0.247091 − 0.846456I
a = 0.10106 − 1.53739I
b = −0.0499682 + 0.0331869I
2.29410 + 8.26425I 0
u = −0.298736 + 0.824933I
a = 0.743857 + 0.952433I
b = 0.0751467 + 0.0605634I
7.03208 + 1.99143I 0
u = −0.298736 − 0.824933I
a = 0.743857 − 0.952433I
b = 0.0751467 − 0.0605634I
7.03208 − 1.99143I 0
u = 1.033590 + 0.457122I
a = 0.473569 − 0.383473I
b = 1.066440 − 0.713288I
0.83815 − 1.62864I 0
u = 1.033590 − 0.457122I
a = 0.473569 + 0.383473I
b = 1.066440 + 0.713288I
0.83815 + 1.62864I 0
u = −0.240768 + 0.824283I
a = −0.11553 + 2.24441I
b = −0.0145449 − 0.0728026I
6.7575 + 14.2182I 0
u = −0.240768 − 0.824283I
a = −0.11553 − 2.24441I
b = −0.0145449 + 0.0728026I
6.7575 − 14.2182I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.176145 + 0.826629I
a = −0.19465 − 1.56583I
b = −0.0147810 + 0.0663483I
3.47417 − 2.93643I 0
u = 0.176145 − 0.826629I
a = −0.19465 + 1.56583I
b = −0.0147810 − 0.0663483I
3.47417 + 2.93643I 0
u = −0.201809 + 0.810263I
a = 0.25899 − 2.31993I
b = 0.0826196 + 0.0079760I
8.38154 + 8.04428I 0
u = −0.201809 − 0.810263I
a = 0.25899 + 2.31993I
b = 0.0826196 − 0.0079760I
8.38154 − 8.04428I 0
u = −1.229020 + 0.096341I
a = 1.38458 + 0.97450I
b = 2.16417 + 2.69342I
−1.87389 − 3.46118I 0
u = −1.229020 − 0.096341I
a = 1.38458 − 0.97450I
b = 2.16417 − 2.69342I
−1.87389 + 3.46118I 0
u = 1.213650 + 0.223425I
a = −0.56429 + 1.79185I
b = 0.25920 + 2.81657I
1.71141 + 1.82395I 0
u = 1.213650 − 0.223425I
a = −0.56429 − 1.79185I
b = 0.25920 − 2.81657I
1.71141 − 1.82395I 0
u = −1.255290 + 0.208643I
a = 1.39629 + 1.06735I
b = 1.84758 + 1.17794I
−2.11051 − 0.26400I 0
u = −1.255290 − 0.208643I
a = 1.39629 − 1.06735I
b = 1.84758 − 1.17794I
−2.11051 + 0.26400I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.247200 + 0.267682I
a = −1.48534 + 0.10267I
b = −3.21531 − 0.89282I
3.36411 + 1.60041I 0
u = −1.247200 − 0.267682I
a = −1.48534 − 0.10267I
b = −3.21531 + 0.89282I
3.36411 − 1.60041I 0
u = 1.264040 + 0.253171I
a = 0.462400 − 0.833389I
b = 1.51601 − 1.67220I
−1.28635 − 2.01710I 0
u = 1.264040 − 0.253171I
a = 0.462400 + 0.833389I
b = 1.51601 + 1.67220I
−1.28635 + 2.01710I 0
u = 1.268280 + 0.250780I
a = 0.098698 − 1.002360I
b = 1.28889 − 2.03570I
−1.34820 − 1.94886I 0
u = 1.268280 − 0.250780I
a = 0.098698 + 1.002360I
b = 1.28889 + 2.03570I
−1.34820 + 1.94886I 0
u = −0.024764 + 0.706428I
a = 1.67877 − 2.77309I
b = 0.552628 − 0.369872I
7.11485 + 1.92573I 4.79150 − 3.14409I
u = −0.024764 − 0.706428I
a = 1.67877 + 2.77309I
b = 0.552628 + 0.369872I
7.11485 − 1.92573I 4.79150 + 3.14409I
u = 0.537218 + 0.456113I
a = −0.641691 − 0.044249I
b = −0.736942 + 0.156147I
−2.77183 − 1.23439I −14.2698 + 2.5822I
u = 0.537218 − 0.456113I
a = −0.641691 + 0.044249I
b = −0.736942 − 0.156147I
−2.77183 + 1.23439I −14.2698 − 2.5822I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.195119 + 0.675153I
a = −0.05646 + 2.99264I
b = 0.068082 + 0.310570I
0.61895 + 6.15524I −6.03024 − 8.70363I
u = −0.195119 − 0.675153I
a = −0.05646 − 2.99264I
b = 0.068082 − 0.310570I
0.61895 − 6.15524I −6.03024 + 8.70363I
u = −1.281160 + 0.235497I
a = −1.58663 − 2.87932I
b = −3.86609 − 3.92554I
−1.37188 + 4.62252I 0
u = −1.281160 − 0.235497I
a = −1.58663 + 2.87932I
b = −3.86609 + 3.92554I
−1.37188 − 4.62252I 0
u = 0.087086 + 0.690259I
a = −2.39632 + 1.47958I
b = −0.867733 + 0.153468I
5.07026 − 5.13999I 0.90064 + 7.96283I
u = 0.087086 − 0.690259I
a = −2.39632 − 1.47958I
b = −0.867733 − 0.153468I
5.07026 + 5.13999I 0.90064 − 7.96283I
u = −1.280280 + 0.255973I
a = −1.01304 − 1.56925I
b = −1.94256 − 2.34069I
−1.39796 + 4.72699I 0
u = −1.280280 − 0.255973I
a = −1.01304 + 1.56925I
b = −1.94256 + 2.34069I
−1.39796 − 4.72699I 0
u = 1.299580 + 0.126286I
a = −0.399923 + 0.915096I
b = −1.08930 + 2.40719I
−4.66876 + 0.64884I 0
u = 1.299580 − 0.126286I
a = −0.399923 − 0.915096I
b = −1.08930 − 2.40719I
−4.66876 − 0.64884I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.281020 + 0.281013I
a = 1.12025 − 1.86438I
b = 1.19218 − 3.55348I
3.05890 − 5.49746I 0
u = 1.281020 − 0.281013I
a = 1.12025 + 1.86438I
b = 1.19218 + 3.55348I
3.05890 + 5.49746I 0
u = 0.266672 + 0.630663I
a = 0.03752 + 1.81979I
b = 0.118614 + 0.177319I
−1.85345 − 2.28906I −11.72961 + 3.90510I
u = 0.266672 − 0.630663I
a = 0.03752 − 1.81979I
b = 0.118614 − 0.177319I
−1.85345 + 2.28906I −11.72961 − 3.90510I
u = 0.005642 + 0.679539I
a = −0.41275 − 2.03681I
b = −0.256213 + 0.339588I
2.58364 − 1.36274I −4.32616 + 4.41390I
u = 0.005642 − 0.679539I
a = −0.41275 + 2.03681I
b = −0.256213 − 0.339588I
2.58364 + 1.36274I −4.32616 − 4.41390I
u = 0.000823 + 0.666898I
a = −0.15641 − 2.28476I
b = −0.417983 + 0.545250I
2.56510 − 1.37327I −5.21577 + 4.42829I
u = 0.000823 − 0.666898I
a = −0.15641 + 2.28476I
b = −0.417983 − 0.545250I
2.56510 + 1.37327I −5.21577 − 4.42829I
u = −1.322160 + 0.193322I
a = −3.61754 + 2.44355I
b = −4.72764 + 6.36461I
−1.48967 + 0.94902I 0
u = −1.322160 − 0.193322I
a = −3.61754 − 2.44355I
b = −4.72764 − 6.36461I
−1.48967 − 0.94902I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.323800 + 0.259025I
a = −0.158106 + 0.512436I
b = −1.28919 + 1.62239I
−2.97042 − 6.53501I 0
u = 1.323800 − 0.259025I
a = −0.158106 − 0.512436I
b = −1.28919 − 1.62239I
−2.97042 + 6.53501I 0
u = −1.319530 + 0.282088I
a = 1.044800 − 0.788163I
b = 2.89802 − 0.54779I
0.65423 + 8.67007I 0
u = −1.319530 − 0.282088I
a = 1.044800 + 0.788163I
b = 2.89802 + 0.54779I
0.65423 − 8.67007I 0
u = −0.080355 + 0.638344I
a = 0.19992 + 1.73379I
b = 0.768705 − 0.119150I
1.45803 + 3.26115I −7.40974 − 2.73081I
u = −0.080355 − 0.638344I
a = 0.19992 − 1.73379I
b = 0.768705 + 0.119150I
1.45803 − 3.26115I −7.40974 + 2.73081I
u = 1.373020 + 0.179579I
a = −1.165500 − 0.355208I
b = −1.54451 − 0.77366I
−1.81444 − 3.41016I 0
u = 1.373020 − 0.179579I
a = −1.165500 + 0.355208I
b = −1.54451 + 0.77366I
−1.81444 + 3.41016I 0
u = −1.39188
a = 0.642376
b = 0.308644
−6.33392 0
u = 1.369870 + 0.279288I
a = −1.35602 + 1.41036I
b = −2.49059 + 3.14102I
−4.33462 − 9.64645I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.369870 − 0.279288I
a = −1.35602 − 1.41036I
b = −2.49059 − 3.14102I
−4.33462 + 9.64645I 0
u = 1.404170 + 0.077311I
a = 0.146052 − 0.488550I
b = −0.685818 − 0.143496I
−7.04492 + 1.96557I 0
u = 1.404170 − 0.077311I
a = 0.146052 + 0.488550I
b = −0.685818 + 0.143496I
−7.04492 − 1.96557I 0
u = −1.39021 + 0.26231I
a = 0.93525 + 1.13077I
b = 1.62632 + 2.28679I
−7.09179 + 5.58629I 0
u = −1.39021 − 0.26231I
a = 0.93525 − 1.13077I
b = 1.62632 − 2.28679I
−7.09179 − 5.58629I 0
u = −1.37311 + 0.34471I
a = −0.769327 − 1.093390I
b = −1.58734 − 2.10730I
−1.41878 + 7.14733I 0
u = −1.37311 − 0.34471I
a = −0.769327 + 1.093390I
b = −1.58734 + 2.10730I
−1.41878 − 7.14733I 0
u = −0.532398 + 0.225330I
a = 1.150140 + 0.477582I
b = 1.007550 + 0.815024I
−1.07296 − 3.04928I −11.29523 + 2.98969I
u = −0.532398 − 0.225330I
a = 1.150140 − 0.477582I
b = 1.007550 − 0.815024I
−1.07296 + 3.04928I −11.29523 − 2.98969I
u = 1.38546 + 0.33854I
a = 1.21145 − 1.40603I
b = 2.35484 − 2.72340I
3.35713 − 12.19010I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38546 − 0.33854I
a = 1.21145 + 1.40603I
b = 2.35484 + 2.72340I
3.35713 + 12.19010I 0
u = 1.39852 + 0.37613I
a = 0.725149 − 0.316400I
b = 1.55261 − 0.68190I
1.73619 − 1.07513I 0
u = 1.39852 − 0.37613I
a = 0.725149 + 0.316400I
b = 1.55261 + 0.68190I
1.73619 + 1.07513I 0
u = 1.40763 + 0.34067I
a = −1.21520 + 1.37151I
b = −2.48837 + 2.66444I
1.5237 − 18.4250I 0
u = 1.40763 − 0.34067I
a = −1.21520 − 1.37151I
b = −2.48837 − 2.66444I
1.5237 + 18.4250I 0
u = 1.45256 + 0.06034I
a = −0.559577 − 0.364250I
b = −0.347311 − 0.174242I
−1.99478 − 3.94780I 0
u = 1.45256 − 0.06034I
a = −0.559577 + 0.364250I
b = −0.347311 + 0.174242I
−1.99478 + 3.94780I 0
u = −1.41155 + 0.35078I
a = 0.797419 + 1.028650I
b = 1.67070 + 2.07683I
−2.96797 + 12.58110I 0
u = −1.41155 − 0.35078I
a = 0.797419 − 1.028650I
b = 1.67070 − 2.07683I
−2.96797 − 12.58110I 0
u = −1.46566 + 0.09901I
a = −0.313535 − 0.288969I
b = 0.158697 − 0.309296I
−9.31891 + 3.12487I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.46566 − 0.09901I
a = −0.313535 + 0.288969I
b = 0.158697 + 0.309296I
−9.31891 − 3.12487I 0
u = 1.44204 + 0.34403I
a = −0.748462 + 0.232440I
b = −1.50858 + 0.58148I
1.47688 − 6.23987I 0
u = 1.44204 − 0.34403I
a = −0.748462 − 0.232440I
b = −1.50858 − 0.58148I
1.47688 + 6.23987I 0
u = 1.50724 + 0.01696I
a = 0.439244 + 0.262390I
b = 0.169307 − 0.194292I
−3.58319 − 9.03555I 0
u = 1.50724 − 0.01696I
a = 0.439244 − 0.262390I
b = 0.169307 + 0.194292I
−3.58319 + 9.03555I 0
u = −0.243074 + 0.382168I
a = 1.45223 − 0.64890I
b = −0.581368 + 0.506050I
3.17428 + 1.16632I −5.18255 − 5.32989I
u = −0.243074 − 0.382168I
a = 1.45223 + 0.64890I
b = −0.581368 − 0.506050I
3.17428 − 1.16632I −5.18255 + 5.32989I
u = 0.130352 + 0.432714I
a = 3.17054 − 1.05121I
b = −1.001500 + 0.836246I
3.00363 + 1.49026I −10.08071 − 1.95304I
u = 0.130352 − 0.432714I
a = 3.17054 + 1.05121I
b = −1.001500 − 0.836246I
3.00363 − 1.49026I −10.08071 + 1.95304I
u = 0.398116
a = −0.179777
b = 0.395924
−0.655557 −14.9730
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.63360 + 0.01594I
a = −0.0217600 − 0.0644053I
b = 0.064850 + 0.130093I
−8.81403 − 2.11872I 0
u = −1.63360 − 0.01594I
a = −0.0217600 + 0.0644053I
b = 0.064850 − 0.130093I
−8.81403 + 2.11872I 0
u = 0.302956 + 0.142061I
a = −3.33583 − 1.44267I
b = 0.698699 − 0.891430I
2.18318 − 3.32244I −9.60296 + 3.16320I
u = 0.302956 − 0.142061I
a = −3.33583 + 1.44267I
b = 0.698699 + 0.891430I
2.18318 + 3.32244I −9.60296 − 3.16320I
u = −0.199739 + 0.122555I
a = 0.08224 + 3.53502I
b = 0.252902 + 0.540317I
−0.31670 − 1.81249I −1.61690 + 1.68681I
u = −0.199739 − 0.122555I
a = 0.08224 − 3.53502I
b = 0.252902 − 0.540317I
−0.31670 + 1.81249I −1.61690 − 1.68681I
15
II. I
u
2
= hau + b − a, 5a
2
+ 3au + 4a + 3u + 5, u
2
+ u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
a
−au + a
a
9
=
1
−u + 1
a
10
=
1
−u + 1
a
12
=
u
u
a
7
=
u
u − 1
a
3
=
−au + 2a
−3au + 2a
a
6
=
0
−u
a
11
=
1
−2u + 2
a
5
=
−au + 2a
−7au + 5a
a
2
=
−au + 2a + u + 1
−3au + 2a +
8
5
u −
1
5
(ii) Obstruction class = 1
(iii) Cusp Shapes =
387
5
au −
259
5
a −
3
5
u − 15
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
− u + 1)
2
c
2
(u
2
+ u + 1)
2
c
3
25(25u
4
− 25u
3
+ 20u
2
− 5u + 1)
c
4
25(25u
4
+ 5u
2
+ 1)
c
6
, c
7
, c
8
(u
2
+ u − 1)
2
c
9
u
4
c
10
, c
12
(u
2
− u − 1)
2
c
11
(u
2
+ 3u + 1)
2
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
2
c
3
625(625y
4
+ 375y
3
+ 200y
2
+ 15y + 1)
c
4
625(25y
2
+ 5y + 1)
2
c
6
, c
7
, c
8
c
10
, c
12
(y
2
− 3y + 1)
2
c
9
y
4
c
11
(y
2
− 7y + 1)
2
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = −0.585410 + 1.013960I
b = −0.223607 + 0.387298I
−0.98696 + 2.02988I −13.05016 − 4.01951I
u = 0.618034
a = −0.585410 − 1.013960I
b = −0.223607 − 0.387298I
−0.98696 − 2.02988I −13.05016 + 4.01951I
u = −1.61803
a = 0.085410 + 0.147935I
b = 0.223607 + 0.387298I
−8.88264 − 2.02988I −29.1498 − 26.1898I
u = −1.61803
a = 0.085410 − 0.147935I
b = 0.223607 − 0.387298I
−8.88264 + 2.02988I −29.1498 + 26.1898I
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
106
+ 39u
105
+ ··· − 6871u + 625)
c
2
((u
2
+ u + 1)
2
)(u
106
+ 3u
105
+ ··· + 89u + 25)
c
3
625(25u
4
− 25u
3
+ 20u
2
− 5u + 1)
· (25u
106
− 220u
105
+ ··· − 18846012u + 6882857)
c
4
625(25u
4
+ 5u
2
+ 1)
· (25u
106
+ 135u
105
+ ··· − 232522967u − 31396523)
c
5
((u
2
− u + 1)
2
)(u
106
+ 3u
105
+ ··· + 89u + 25)
c
6
((u
2
+ u − 1)
2
)(u
106
+ 3u
105
+ ··· + u − 1)
c
7
, c
8
((u
2
+ u − 1)
2
)(u
106
+ 3u
105
+ ··· + 3u − 1)
c
9
u
4
(u
106
+ u
105
+ ··· − 19600u − 2000)
c
10
((u
2
− u − 1)
2
)(u
106
+ 3u
105
+ ··· + u − 1)
c
11
((u
2
+ 3u + 1)
2
)(u
106
− 9u
105
+ ··· − 363165u + 47311)
c
12
((u
2
− u − 1)
2
)(u
106
+ 3u
105
+ ··· + 3u − 1)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
2
)(y
106
+ 59y
105
+ ··· − 4.05122 × 10
8
y + 390625)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
106
+ 39y
105
+ ··· − 6871y + 625)
c
3
390625(625y
4
+ 375y
3
+ 200y
2
+ 15y + 1)
· (625y
106
+ 15400y
105
+ ··· + 710061743809250y + 47373720482449)
c
4
390625(25y
2
+ 5y + 1)
2
· (625y
106
+ 4.50 × 10
4
y
105
+ ··· + 2.18 × 10
16
y + 9.86 × 10
14
)
c
6
, c
10
((y
2
− 3y + 1)
2
)(y
106
+ 67y
105
+ ··· − 19y + 1)
c
7
, c
8
, c
12
((y
2
− 3y + 1)
2
)(y
106
− 93y
105
+ ··· − 19y + 1)
c
9
y
4
(y
106
+ 25y
105
+ ··· + 1.44720 × 10
8
y + 4000000)
c
11
((y
2
− 7y + 1)
2
)(y
106
+ 23y
105
+ ··· − 7.67489 × 10
10
y + 2.23833 × 10
9
)
21
